LMFDB - Embedded newform 105.3.n.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(31,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("105.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.n (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.523596960000.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 $ x^8 - 2x^7 + 13x^6 - 2x^5 + 91x^4 - 50x^3 + 190x^2 + 100*x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.1
Root			$-1.26021 + 2.18275i$ of defining polynomial
Character	$\chi$	$=$	105.61
Dual form			105.3.n.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26021 + 2.18275i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.17628 - 2.03737i) q^{4} +(-1.93649 - 1.11803i) q^{5} -4.36551i q^{6} +(-6.18050 - 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.26021 + 2.18275i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.17628 - 2.03737i) q^{4} +(-1.93649 - 1.11803i) q^{5} -4.36551i q^{6} +(-6.18050 - 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 - 2.59808i) q^{9} +(4.88079 - 2.81792i) q^{10} +(4.36036 + 7.55236i) q^{11} +(3.52883 + 2.03737i) q^{12} -21.5286i q^{13} +(14.9625 - 9.34874i) q^{14} +3.87298 q^{15} +(9.93785 - 17.2129i) q^{16} +(-18.7862 + 10.8462i) q^{17} +(3.78064 + 6.54826i) q^{18} +(-2.71590 - 1.56803i) q^{19} +5.26047i q^{20} +(12.1170 - 0.422628i) q^{21} -21.9799 q^{22} +(-2.05421 + 3.55799i) q^{23} +(6.22840 - 3.59597i) q^{24} +(2.50000 + 4.33013i) q^{25} +(46.9917 + 27.1307i) q^{26} +5.19615i q^{27} +(0.574033 + 16.4579i) q^{28} -50.8583 q^{29} +(-4.88079 + 8.45377i) q^{30} +(-33.9213 + 19.5845i) q^{31} +(16.7431 + 28.9999i) q^{32} +(-13.0811 - 7.55236i) q^{33} -54.6743i q^{34} +(8.29399 + 13.2744i) q^{35} -7.05767 q^{36} +(-26.4906 + 45.8831i) q^{37} +(6.84523 - 3.95209i) q^{38} +(18.6443 + 32.2929i) q^{39} +(8.04083 + 4.64237i) q^{40} -36.8122i q^{41} +(-14.3475 + 26.9810i) q^{42} +17.6504 q^{43} +(10.2580 - 17.7674i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(-5.17748 - 8.96766i) q^{46} +(-3.49804 - 2.01959i) q^{47} +34.4257i q^{48} +(27.3971 + 40.6251i) q^{49} -12.6021 q^{50} +(18.7862 - 32.5387i) q^{51} +(-43.8618 + 25.3236i) q^{52} +(-2.22593 - 3.85542i) q^{53} +(-11.3419 - 6.54826i) q^{54} -19.5001i q^{55} +(25.6631 + 13.6467i) q^{56} +5.43180 q^{57} +(64.0923 - 111.011i) q^{58} +(81.5032 - 47.0559i) q^{59} +(-4.55570 - 7.89071i) q^{60} +(-63.3781 - 36.5913i) q^{61} -98.7226i q^{62} +(-17.8095 + 11.1276i) q^{63} -4.89677 q^{64} +(-24.0697 + 41.6900i) q^{65} +(32.9699 - 19.0352i) q^{66} +(50.2661 + 87.0635i) q^{67} +(44.1956 + 25.5164i) q^{68} -7.11598i q^{69} +(-39.4270 + 1.37517i) q^{70} -56.6975 q^{71} +(-6.22840 + 10.7879i) q^{72} +(64.8042 - 37.4147i) q^{73} +(-66.7676 - 115.645i) q^{74} +(-7.50000 - 4.33013i) q^{75} +7.37773i q^{76} +(-2.12789 - 61.0079i) q^{77} -93.9833 q^{78} +(-14.4903 + 25.0980i) q^{79} +(-38.4891 + 22.2217i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(80.3519 + 46.3912i) q^{82} -21.1116i q^{83} +(-15.1140 - 24.1897i) q^{84} +48.5058 q^{85} +(-22.2433 + 38.5266i) q^{86} +(76.2875 - 44.0446i) q^{87} +(-18.1054 - 31.3594i) q^{88} +(63.1066 + 36.4346i) q^{89} -16.9075i q^{90} +(-70.7551 + 133.057i) q^{91} +9.66528 q^{92} +(33.9213 - 58.7535i) q^{93} +(8.81655 - 5.09024i) q^{94} +(3.50621 + 6.07294i) q^{95} +(-50.2293 - 28.9999i) q^{96} -73.7985i q^{97} +(-123.201 + 8.60469i) q^{98} +26.1622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	$ 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.26021	+	2.18275i	−0.630107	+	1.09138i	0.357423	+	0.933943i	$0.383656\pi$
$2$	−1.26021	+	2.18275i	−0.630107	+	1.09138i	−0.987529	+	0.157434i	$0.949678\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−1.17628	−	2.03737i	−0.294069	−	0.509343i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$		−	4.36551i		−	0.727585i
$7$	−6.18050	−	3.28656i	−0.882928	−	0.469508i
$7$	−6.18050	−	3.28656i	−0.882928	−	0.469508i
$8$	−4.15226			−0.519033
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	4.88079	−	2.81792i	0.488079	−	0.281792i
$11$	4.36036	+	7.55236i	0.396396	+	0.686579i	0.993278	−	0.115750i	$-0.0369273\pi$
$11$	4.36036	+	7.55236i	0.396396	+	0.686579i	−0.596882	+	0.802329i	$0.703594\pi$
$12$	3.52883	+	2.03737i	0.294069	+	0.169781i
$13$		−	21.5286i		−	1.65605i	−0.560693	−	0.828024i	$-0.689465\pi$
$13$		−	21.5286i		−	1.65605i	0.560693	−	0.828024i	$-0.310535\pi$
$14$	14.9625	−	9.34874i	1.06875	−	0.667767i
$15$	3.87298			0.258199
$16$	9.93785	−	17.2129i	0.621116	−	1.07580i
$17$	−18.7862	+	10.8462i	−1.10507	+	0.638013i	−0.937548	−	0.347855i	$-0.886910\pi$
$17$	−18.7862	+	10.8462i	−1.10507	+	0.638013i	−0.167523	+	0.985868i	$0.553577\pi$
$18$	3.78064	+	6.54826i	0.210036	+	0.363792i
$19$	−2.71590	−	1.56803i	−0.142942	−	0.0825276i	0.426823	−	0.904335i	$-0.359633\pi$
$19$	−2.71590	−	1.56803i	−0.142942	−	0.0825276i	−0.569765	+	0.821807i	$0.692966\pi$
$20$			5.26047i			0.263024i
$21$	12.1170	−	0.422628i	0.576999	−	0.0201251i
$22$	−21.9799			−0.999088
$23$	−2.05421	+	3.55799i	−0.0893134	+	0.154695i	−0.907221	−	0.420654i	$-0.861801\pi$
$23$	−2.05421	+	3.55799i	−0.0893134	+	0.154695i	0.817908	+	0.575349i	$0.195134\pi$
$24$	6.22840	−	3.59597i	0.259517	−	0.149832i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	46.9917	+	27.1307i	1.80737	+	1.04349i
$27$			5.19615i			0.192450i
$28$	0.574033	+	16.4579i	0.0205012	+	0.587781i
$29$	−50.8583			−1.75373			−0.876867	−	0.480732i	$-0.840371\pi$
$29$	−50.8583			−1.75373			−0.876867	+	0.480732i	$0.840371\pi$
$30$	−4.88079	+	8.45377i	−0.162693	+	0.281792i
$31$	−33.9213	+	19.5845i	−1.09424	+	0.631758i	−0.934701	−	0.355434i	$-0.884333\pi$
$31$	−33.9213	+	19.5845i	−1.09424	+	0.631758i	−0.159536	+	0.987192i	$0.551000\pi$
$32$	16.7431	+	28.9999i	0.523222	+	0.906247i
$33$	−13.0811	−	7.55236i	−0.396396	−	0.228860i
$34$		−	54.6743i		−	1.60807i
$35$	8.29399	+	13.2744i	0.236971	+	0.379269i
$36$	−7.05767			−0.196046
$37$	−26.4906	+	45.8831i	−0.715962	+	1.24008i	0.246625	+	0.969111i	$0.420678\pi$
$37$	−26.4906	+	45.8831i	−0.715962	+	1.24008i	−0.962587	+	0.270972i	$0.912655\pi$
$38$	6.84523	−	3.95209i	0.180138	−	0.104002i
$39$	18.6443	+	32.2929i	0.478060	+	0.828024i
$40$	8.04083	+	4.64237i	0.201021	+	0.116059i
$41$		−	36.8122i		−	0.897857i	−0.893568	−	0.448929i	$-0.851806\pi$
$41$		−	36.8122i		−	0.897857i	0.893568	−	0.448929i	$-0.148194\pi$
$42$	−14.3475	+	26.9810i	−0.341607	+	0.642405i
$43$	17.6504			0.410475			0.205238	−	0.978712i	$-0.434203\pi$
$43$	17.6504			0.410475			0.205238	+	0.978712i	$0.434203\pi$
$44$	10.2580	−	17.7674i	0.233136	−	0.403804i
$45$	−5.80948	+	3.35410i	−0.129099	+	0.0745356i
$46$	−5.17748	−	8.96766i	−0.112554	−	0.194949i
$47$	−3.49804	−	2.01959i	−0.0744263	−	0.0429701i	0.462325	−	0.886711i	$-0.347015\pi$
$47$	−3.49804	−	2.01959i	−0.0744263	−	0.0429701i	−0.536751	+	0.843740i	$0.680349\pi$
$48$			34.4257i			0.717203i
$49$	27.3971	+	40.6251i	0.559124	+	0.829084i
$50$	−12.6021			−0.252043
$51$	18.7862	−	32.5387i	0.368357	−	0.638013i
$52$	−43.8618	+	25.3236i	−0.843496	+	0.486993i
$53$	−2.22593	−	3.85542i	−0.0419986	−	0.0727438i	0.844262	−	0.535931i	$-0.180039\pi$
$53$	−2.22593	−	3.85542i	−0.0419986	−	0.0727438i	−0.886261	+	0.463187i	$0.846706\pi$
$54$	−11.3419	−	6.54826i	−0.210036	−	0.121264i
$55$		−	19.5001i		−	0.354548i
$56$	25.6631	+	13.6467i	0.458269	+	0.243690i
$57$	5.43180			0.0952947
$58$	64.0923	−	111.011i	1.10504	−	1.91399i
$59$	81.5032	−	47.0559i	1.38141	−	0.797558i	0.389084	−	0.921202i	$-0.372792\pi$
$59$	81.5032	−	47.0559i	1.38141	−	0.797558i	0.992327	+	0.123644i	$0.0394582\pi$
$60$	−4.55570	−	7.89071i	−0.0759284	−	0.131512i
$61$	−63.3781	−	36.5913i	−1.03898	−	0.599858i	−0.119439	−	0.992842i	$-0.538110\pi$
$61$	−63.3781	−	36.5913i	−1.03898	−	0.599858i	−0.919546	+	0.392984i	$0.871443\pi$
$62$		−	98.7226i		−	1.59230i
$63$	−17.8095	+	11.1276i	−0.282690	+	0.176628i
$64$	−4.89677			−0.0765121
$65$	−24.0697	+	41.6900i	−0.370303	+	0.641384i
$66$	32.9699	−	19.0352i	0.499544	−	0.288412i
$67$	50.2661	+	87.0635i	0.750241	+	1.29946i	0.947706	+	0.319145i	$0.103396\pi$
$67$	50.2661	+	87.0635i	0.750241	+	1.29946i	−0.197465	+	0.980310i	$0.563271\pi$
$68$	44.1956	+	25.5164i	0.649936	+	0.375241i
$69$		−	7.11598i		−	0.103130i
$70$	−39.4270	+	1.37517i	−0.563242	+	0.0196453i
$71$	−56.6975			−0.798557			−0.399278	−	0.916830i	$-0.630739\pi$
$71$	−56.6975			−0.798557			−0.399278	+	0.916830i	$0.630739\pi$
$72$	−6.22840	+	10.7879i	−0.0865055	+	0.149832i
$73$	64.8042	−	37.4147i	0.887729	−	0.512531i	0.0145299	−	0.999894i	$-0.495375\pi$
$73$	64.8042	−	37.4147i	0.887729	−	0.512531i	0.873199	+	0.487364i	$0.162041\pi$
$74$	−66.7676	−	115.645i	−0.902266	−	1.56277i
$75$	−7.50000	−	4.33013i	−0.100000	−	0.0577350i
$76$			7.37773i			0.0970754i
$77$	−2.12789	−	61.0079i	−0.0276350	−	0.792311i
$78$	−93.9833			−1.20491
$79$	−14.4903	+	25.0980i	−0.183422	+	0.317696i	−0.943044	−	0.332669i	$-0.892051\pi$
$79$	−14.4903	+	25.0980i	−0.183422	+	0.317696i	0.759622	+	0.650365i	$0.225384\pi$
$80$	−38.4891	+	22.2217i	−0.481114	+	0.277771i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	80.3519	+	46.3912i	0.979901	+	0.565746i
$83$		−	21.1116i		−	0.254357i	−0.991880	−	0.127179i	$-0.959408\pi$
$83$		−	21.1116i		−	0.254357i	0.991880	−	0.127179i	$-0.0405921\pi$
$84$	−15.1140	−	24.1897i	−0.179928	−	0.287973i
$85$	48.5058			0.570657
$86$	−22.2433	+	38.5266i	−0.258643	+	0.447983i
$87$	76.2875	−	44.0446i	0.876867	−	0.506260i
$88$	−18.1054	−	31.3594i	−0.205743	−	0.356357i
$89$	63.1066	+	36.4346i	0.709063	+	0.409378i	0.810714	−	0.585442i	$-0.199079\pi$
$89$	63.1066	+	36.4346i	0.709063	+	0.409378i	−0.101651	+	0.994820i	$0.532412\pi$
$90$		−	16.9075i		−	0.187862i
$91$	−70.7551	+	133.057i	−0.777528	+	1.46217i
$92$	9.66528			0.105057
$93$	33.9213	−	58.7535i	0.364746	−	0.631758i
$94$	8.81655	−	5.09024i	0.0937931	−	0.0541515i
$95$	3.50621	+	6.07294i	0.0369075	+	0.0639256i
$96$	−50.2293	−	28.9999i	−0.523222	−	0.302082i
$97$		−	73.7985i		−	0.760809i	−0.924820	−	0.380405i	$-0.875785\pi$
$97$		−	73.7985i		−	0.760809i	0.924820	−	0.380405i	$-0.124215\pi$
$98$	−123.201	+	8.60469i	−1.25715	+	0.0878030i
$99$	26.1622			0.264264
$100$	5.88139	−	10.1869i	0.0588139	−	0.101869i
$101$	−92.6245	+	53.4768i	−0.917075	+	0.529473i	−0.882701	−	0.469936i	$-0.844277\pi$
$101$	−92.6245	+	53.4768i	−0.917075	+	0.529473i	−0.0343741	+	0.999409i	$0.510944\pi$
$102$	47.3493	+	82.0114i	0.464209	+	0.804033i
$103$	18.6535	+	10.7696i	0.181102	+	0.104559i	0.587810	−	0.808999i	$-0.299990\pi$
$103$	18.6535	+	10.7696i	0.181102	+	0.104559i	−0.406708	+	0.913558i	$0.633323\pi$
$104$			89.3925i			0.859543i
$105$	−23.9370	−	12.7288i	−0.227971	−	0.121227i
$106$	11.2206			0.105855
$107$	−44.8184	+	77.6277i	−0.418863	+	0.725492i	−0.995825	−	0.0912785i	$-0.970905\pi$
$107$	−44.8184	+	77.6277i	−0.418863	+	0.725492i	0.576962	+	0.816771i	$0.304238\pi$
$108$	10.5865	−	6.11212i	0.0980232	−	0.0565937i
$109$	−13.6751	−	23.6859i	−0.125459	−	0.217302i	0.796453	−	0.604700i	$-0.206707\pi$
$109$	−13.6751	−	23.6859i	−0.125459	−	0.217302i	−0.921912	+	0.387398i	$0.873374\pi$
$110$	42.5640	+	24.5743i	0.386945	+	0.223403i
$111$		−	91.7661i		−	0.826722i
$112$	−117.992	+	73.7227i	−1.05350	+	0.658238i
$113$	−92.3372			−0.817144			−0.408572	−	0.912726i	$-0.633973\pi$
$113$	−92.3372			−0.817144			−0.408572	+	0.912726i	$0.633973\pi$
$114$	−6.84523	+	11.8563i	−0.0600459	+	0.104002i
$115$	7.95591	−	4.59335i	0.0691818	−	0.0399422i
$116$	59.8235	+	103.617i	0.515720	+	0.893253i
$117$	−55.9330	−	32.2929i	−0.478060	−	0.276008i
$118$			237.202i			2.01019i
$119$	151.755	−	5.29305i	1.27525	−	0.0444794i
$120$	−16.0817			−0.134014
$121$	22.4745	−	38.9270i	0.185740	−	0.321711i
$122$	159.740	−	92.2258i	1.30934	−	0.755949i
$123$	31.8803	+	55.2182i	0.259189	+	0.448929i
$124$	79.8019	+	46.0736i	0.643563	+	0.371562i
$125$		−	11.1803i		−	0.0894427i
$126$	−1.84498	−	52.8968i	−0.0146427	−	0.419816i
$127$	191.591			1.50859			0.754297	−	0.656534i	$-0.227978\pi$
$127$	191.591			1.50859			0.754297	+	0.656534i	$0.227978\pi$
$128$	−60.8015	+	105.311i	−0.475011	+	0.822744i
$129$	−26.4757	+	15.2857i	−0.205238	+	0.118494i
$130$	−60.6660	−	105.077i	−0.466661	−	0.808281i
$131$	50.9329	+	29.4062i	0.388801	+	0.224474i	0.681641	−	0.731687i	$-0.261267\pi$
$131$	50.9329	+	29.4062i	0.388801	+	0.224474i	−0.292839	+	0.956162i	$0.594600\pi$
$132$			35.5347i			0.269202i
$133$	11.6322	+	18.6171i	0.0874601	+	0.139978i
$134$	−253.384			−1.89093
$135$	5.80948	−	10.0623i	0.0430331	−	0.0745356i
$136$	78.0054	−	45.0364i	0.573569	−	0.331150i
$137$	−82.9571	−	143.686i	−0.605526	−	1.04880i	−0.991968	−	0.126488i	$-0.959629\pi$
$137$	−82.9571	−	143.686i	−0.605526	−	1.04880i	0.386442	−	0.922314i	$-0.373704\pi$
$138$	15.5324	+	8.96766i	0.112554	+	0.0649831i
$139$			139.625i			1.00449i	0.864724	+	0.502247i	$0.167493\pi$
$139$			139.625i			1.00449i	−0.864724	+	0.502247i	$0.832507\pi$
$140$	17.2889	−	32.5123i	0.123492	−	0.232231i
$141$	6.99607			0.0496176
$142$	71.4510	−	123.757i	0.503176	−	0.871527i
$143$	162.592	−	93.8725i	1.13701	−	0.656451i
$144$	−29.8136	−	51.6386i	−0.207039	−	0.358601i
$145$	98.4867	+	56.8613i	0.679219	+	0.392147i
$146$			188.602i			1.29180i
$147$	−76.2780	−	37.2111i	−0.518898	−	0.253137i
$148$	124.641			0.842171
$149$	7.16861	−	12.4164i	0.0481115	−	0.0833315i	−0.840967	−	0.541087i	$-0.818013\pi$
$149$	7.16861	−	12.4164i	0.0481115	−	0.0833315i	0.889078	+	0.457755i	$0.151346\pi$
$150$	18.9032	−	10.9138i	0.126021	−	0.0727585i
$151$	−106.187	−	183.922i	−0.703226	−	1.21802i	−0.967328	−	0.253529i	$-0.918409\pi$
$151$	−106.187	−	183.922i	−0.703226	−	1.21802i	0.264102	−	0.964495i	$-0.414925\pi$
$152$	11.2771	+	6.51085i	0.0741917	+	0.0428346i
$153$			65.0774i			0.425342i
$154$	135.847	+	72.2384i	0.882123	+	0.469080i
$155$	87.5845			0.565062
$156$	43.8618	−	75.9709i	0.281165	−	0.486993i
$157$	−210.373	+	121.459i	−1.33996	+	0.773624i	−0.986801	−	0.161941i	$-0.948225\pi$
$157$	−210.373	+	121.459i	−1.33996	+	0.773624i	−0.353156	+	0.935565i	$0.614891\pi$
$158$	−36.5218	−	63.2577i	−0.231151	−	0.400365i
$159$	6.67778	+	3.85542i	0.0419986	+	0.0242479i
$160$		−	74.8775i		−	0.467984i
$161$	24.3896	−	15.2389i	0.151488	−	0.0946514i
$162$	22.6838			0.140024
$163$	−6.61728	+	11.4615i	−0.0405968	+	0.0703157i	−0.885610	−	0.464430i	$-0.846259\pi$
$163$	−6.61728	+	11.4615i	−0.0405968	+	0.0703157i	0.845013	+	0.534746i	$0.179593\pi$
$164$	−75.0001	+	43.3013i	−0.457318	+	0.264032i
$165$	16.8876	+	29.2502i	0.102349	+	0.177274i
$166$	46.0815	+	26.6052i	0.277600	+	0.160272i
$167$		−	212.616i		−	1.27315i	−0.771216	−	0.636574i	$-0.780351\pi$
$167$		−	212.616i		−	1.27315i	0.771216	−	0.636574i	$-0.219649\pi$
$168$	−50.3129	+	1.75486i	−0.299482	+	0.0104456i
$169$	−294.481			−1.74249
$170$	−61.1277	+	105.876i	−0.359575	+	0.622802i
$171$	−8.14770	+	4.70408i	−0.0476474	+	0.0275092i
$172$	−20.7618	−	35.9605i	−0.120708	−	0.209073i
$173$	−215.456	−	124.393i	−1.24541	−	0.719037i	−0.275219	−	0.961382i	$-0.588750\pi$
$173$	−215.456	−	124.393i	−1.24541	−	0.719037i	−0.970190	+	0.242345i	$0.922084\pi$
$174$			222.022i			1.27599i
$175$	−1.22002	−	34.9787i	−0.00697155	−	0.199878i
$176$	173.330			0.984832
$177$	−81.5032	+	141.168i	−0.460470	+	0.797558i
$178$	−159.056	+	91.8308i	−0.893571	+	0.515903i
$179$	−27.6352	−	47.8655i	−0.154386	−	0.267405i	0.778449	−	0.627708i	$-0.216007\pi$
$179$	−27.6352	−	47.8655i	−0.154386	−	0.267405i	−0.932835	+	0.360303i	$0.882673\pi$
$180$	13.6671	+	7.89071i	0.0759284	+	0.0438373i
$181$		−	46.9001i		−	0.259117i	−0.991572	−	0.129558i	$-0.958644\pi$
$181$		−	46.9001i		−	0.259117i	0.991572	−	0.129558i	$-0.0413559\pi$
$182$	−201.265	−	322.122i	−1.10585	−	1.76990i
$183$	126.756			0.692656
$184$	8.52961	−	14.7737i	0.0463566	−	0.0802920i
$185$	102.598	−	59.2348i	0.554582	−	0.320188i
$186$	85.4963	+	148.084i	0.459658	+	0.796150i
$187$	−163.829	−	94.5869i	−0.876093	−	0.505812i
$188$			9.50241i			0.0505447i
$189$	17.0775	−	32.1148i	0.0903569	−	0.169920i
$190$	−17.6743			−0.0930226
$191$	10.0561	−	17.4177i	0.0526499	−	0.0911923i	−0.838499	−	0.544903i	$-0.816567\pi$
$191$	10.0561	−	17.4177i	0.0526499	−	0.0911923i	0.891149	+	0.453710i	$0.149900\pi$
$192$	7.34516	−	4.24073i	0.0382560	−	0.0220871i
$193$	−14.3516	−	24.8578i	−0.0743609	−	0.128797i	0.826447	−	0.563014i	$-0.190358\pi$
$193$	−14.3516	−	24.8578i	−0.0743609	−	0.128797i	−0.900808	+	0.434217i	$0.857025\pi$
$194$	161.084	+	93.0019i	0.830330	+	0.479391i
$195$		−	83.3800i		−	0.427589i
$196$	50.5420	−	103.604i	0.257867	−	0.528594i
$197$	224.436			1.13927			0.569636	−	0.821897i	$-0.307084\pi$
$197$	224.436			1.13927			0.569636	+	0.821897i	$0.307084\pi$
$198$	−32.9699	+	57.1056i	−0.166515	+	0.288412i
$199$	−275.447	+	159.030i	−1.38416	+	0.799144i	−0.992649	−	0.121030i	$-0.961380\pi$
$199$	−275.447	+	159.030i	−1.38416	+	0.799144i	−0.391509	+	0.920174i	$0.628047\pi$
$200$	−10.3807	−	17.9798i	−0.0519033	−	0.0898992i
$201$	−150.798	−	87.0635i	−0.750241	−	0.433152i
$202$		−	269.569i		−	1.33450i
$203$	314.330	+	167.149i	1.54842	+	0.823393i
$204$	−88.3913			−0.433290
$205$	−41.1572	+	71.2864i	−0.200767	+	0.347739i
$206$	−47.0148	+	27.1440i	−0.228227	+	0.131767i
$207$	6.16262	+	10.6740i	0.0297711	+	0.0515651i
$208$	−370.569	−	213.948i	−1.78158	−	1.02860i
$209$		−	27.3486i		−	0.130855i
$210$	57.9495	−	36.2075i	0.275950	−	0.172417i
$211$	285.317			1.35221			0.676107	−	0.736804i	$-0.263666\pi$
$211$	285.317			1.35221			0.676107	+	0.736804i	$0.263666\pi$
$212$	−5.23662	+	9.07009i	−0.0247010	+	0.0427835i
$213$	85.0463	−	49.1015i	0.399278	−	0.230523i
$214$	−112.961	−	195.655i	−0.527857	−	0.914276i
$215$	−34.1799	−	19.7338i	−0.158976	−	0.0917851i
$216$		−	21.5758i		−	0.0998880i
$217$	274.016	−	9.55740i	1.26275	−	0.0440433i
$218$	68.9341			0.316211
$219$	−64.8042	+	112.244i	−0.295910	+	0.512531i
$220$	−39.7290	+	22.9376i	−0.180586	+	0.104262i
$221$	233.504	+	404.441i	1.05658	+	1.83005i
$222$	200.303	+	115.645i	0.902266	+	0.520923i
$223$		−	57.0977i		−	0.256044i	−0.991771	−	0.128022i	$-0.959137\pi$
$223$		−	57.0977i		−	0.256044i	0.991771	−	0.128022i	$-0.0408627\pi$
$224$	−8.17078	−	234.261i	−0.0364767	−	1.04581i
$225$	15.0000			0.0666667
$226$	116.365	−	201.549i	0.514888	−	0.891812i
$227$	−158.185	+	91.3279i	−0.696848	+	0.402325i	−0.806172	−	0.591681i	$-0.798465\pi$
$227$	−158.185	+	91.3279i	−0.696848	+	0.402325i	0.109324	+	0.994006i	$0.465131\pi$
$228$	−6.38930	−	11.0666i	−0.0280233	−	0.0485377i
$229$	−14.5347	−	8.39159i	−0.0634702	−	0.0366445i	0.467929	−	0.883766i	$-0.345000\pi$
$229$	−14.5347	−	8.39159i	−0.0634702	−	0.0366445i	−0.531399	+	0.847121i	$0.678334\pi$
$230$			23.1544i			0.100671i
$231$	56.0263	+	89.6691i	0.242538	+	0.388178i
$232$	211.177			0.910246
$233$	133.203	−	230.715i	0.571688	−	0.990193i	−0.424704	−	0.905332i	$-0.639622\pi$
$233$	133.203	−	230.715i	0.571688	−	0.990193i	0.996393	−	0.0848612i	$-0.0270447\pi$
$234$	140.975	−	81.3920i	0.602457	−	0.347829i
$235$	4.51595	+	7.82185i	0.0192168	+	0.0332845i
$236$	−191.741	−	110.702i	−0.812461	−	0.469075i
$237$		−	50.1960i		−	0.211797i
$238$	−179.690	+	337.914i	−0.755001	+	1.41981i
$239$	−39.7012			−0.166114			−0.0830568	−	0.996545i	$-0.526468\pi$
$239$	−39.7012			−0.166114			−0.0830568	+	0.996545i	$0.526468\pi$
$240$	38.4891	−	66.6651i	0.160371	−	0.277771i
$241$	72.1896	−	41.6787i	0.299542	−	0.172941i	−0.342695	−	0.939447i	$-0.611340\pi$
$241$	72.1896	−	41.6787i	0.299542	−	0.172941i	0.642237	+	0.766506i	$0.278006\pi$
$242$	56.6454	+	98.1128i	0.234072	+	0.405425i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			172.166i			0.705600i
$245$	−7.63390	−	109.301i	−0.0311588	−	0.446127i
$246$	−160.704			−0.653267
$247$	−33.7574	+	58.4695i	−0.136670	+	0.236719i
$248$	140.850	−	81.3200i	0.567945	−	0.327903i
$249$	18.2832	+	31.6675i	0.0734266	+	0.127179i
$250$	24.4039	+	14.0896i	0.0976157	+	0.0563585i
$251$			111.464i			0.444079i	0.975038	+	0.222039i	$0.0712713\pi$
$251$			111.464i			0.444079i	−0.975038	+	0.222039i	$0.928729\pi$
$252$	43.6199	+	23.1954i	0.173095	+	0.0920454i
$253$	−35.8283			−0.141614
$254$	−241.446	+	418.197i	−0.950575	+	1.64644i
$255$	−72.7587	+	42.0073i	−0.285328	+	0.164734i
$256$	−163.039	−	282.392i	−0.636872	−	1.10309i
$257$	−193.043	−	111.454i	−0.751141	−	0.433672i	0.0749649	−	0.997186i	$-0.476116\pi$
$257$	−193.043	−	111.454i	−0.751141	−	0.433672i	−0.826106	+	0.563515i	$0.809449\pi$
$258$		−	77.0531i		−	0.298656i
$259$	314.522	−	196.517i	1.21437	−	0.758754i
$260$	113.251			0.435580
$261$	−76.2875	+	132.134i	−0.292289	+	0.506260i
$262$	−128.373	+	74.1161i	−0.489973	+	0.282886i
$263$	213.250	+	369.360i	0.810837	+	1.40441i	0.912279	+	0.409569i	$0.134321\pi$
$263$	213.250	+	369.360i	0.810837	+	1.40441i	−0.101442	+	0.994841i	$0.532346\pi$
$264$	54.3161	+	31.3594i	0.205743	+	0.118786i
$265$			9.95465i			0.0375647i
$266$	−55.2957	+	1.92865i	−0.207879	+	0.00725058i
$267$	−126.213			−0.472709
$268$	118.254	−	204.822i	0.441246	−	0.764260i
$269$	−51.5210	+	29.7457i	−0.191528	+	0.110579i	−0.592698	−	0.805425i	$-0.701937\pi$
$269$	−51.5210	+	29.7457i	−0.191528	+	0.110579i	0.401170	+	0.916004i	$0.368604\pi$
$270$	14.6424	+	25.3613i	0.0542310	+	0.0939308i
$271$	−47.1819	−	27.2405i	−0.174103	−	0.100518i	0.410416	−	0.911898i	$-0.365383\pi$
$271$	−47.1819	−	27.2405i	−0.174103	−	0.100518i	−0.584519	+	0.811380i	$0.698717\pi$
$272$			431.153i			1.58512i
$273$	−9.09858	−	260.862i	−0.0333281	−	0.955538i
$274$	418.175			1.52618
$275$	−21.8018	+	37.7618i	−0.0792793	+	0.137316i
$276$	−14.4979	+	8.37037i	−0.0525287	+	0.0303274i
$277$	236.189	+	409.092i	0.852669	+	1.47687i	0.878791	+	0.477207i	$0.158351\pi$
$277$	236.189	+	409.092i	0.852669	+	1.47687i	−0.0261222	+	0.999659i	$0.508316\pi$
$278$	−304.766	−	175.957i	−1.09628	−	0.632939i
$279$			117.507i			0.421172i
$280$	−34.4389	−	55.1188i	−0.122996	−	0.196853i
$281$	−534.544			−1.90229			−0.951146	−	0.308743i	$-0.900092\pi$
$281$	−534.544			−1.90229			−0.951146	+	0.308743i	$0.900092\pi$
$282$	−8.81655	+	15.2707i	−0.0312644	+	0.0541515i
$283$	−387.352	+	223.638i	−1.36873	+	0.790239i	−0.990766	−	0.135580i	$-0.956710\pi$
$283$	−387.352	+	223.638i	−1.36873	+	0.790239i	−0.377967	+	0.925819i	$0.623377\pi$
$284$	66.6921	+	115.514i	0.234831	+	0.406740i
$285$	−10.5186	−	6.07294i	−0.0369075	−	0.0213085i
$286$			473.198i			1.65454i
$287$	−120.985	+	227.517i	−0.421552	+	0.792743i
$288$	100.459			0.348815
$289$	90.7814	−	157.238i	0.314122	−	0.544076i
$290$	−248.229	+	143.315i	−0.855961	+	0.494189i
$291$	63.9114	+	110.698i	0.219627	+	0.380405i
$292$	−152.456	−	88.0202i	−0.522108	−	0.301439i
$293$			504.200i			1.72082i	0.509604	+	0.860409i	$0.329792\pi$
$293$			504.200i			1.72082i	−0.509604	+	0.860409i	$0.670208\pi$
$294$	177.349	−	119.602i	0.603229	−	0.406810i
$295$	−210.440			−0.713357
$296$	109.996	−	190.519i	0.371608	−	0.643644i
$297$	−39.2432	+	22.6571i	−0.132132	+	0.0762865i
$298$	18.0680	+	31.2946i	0.0606308	+	0.105016i
$299$	76.5986	+	44.2242i	0.256183	+	0.147907i
$300$			20.3737i			0.0679124i
$301$	−109.088	−	58.0092i	−0.362420	−	0.192722i
$302$	535.274			1.77243
$303$	92.6245	−	160.430i	0.305692	−	0.529473i
$304$	−53.9804	+	31.1656i	−0.177567	+	0.102518i
$305$	81.8207	+	141.718i	0.268265	+	0.464648i
$306$	−142.048	−	82.0114i	−0.464209	−	0.268011i
$307$		−	398.792i		−	1.29900i	−0.760363	−	0.649499i	$-0.774979\pi$
$307$		−	398.792i		−	1.29900i	0.760363	−	0.649499i	$-0.225021\pi$
$308$	−121.793	+	76.0976i	−0.395432	+	0.247070i
$309$	−37.3070			−0.120735
$310$	−110.375	+	191.176i	−0.356049	+	0.616695i
$311$	−207.085	+	119.561i	−0.665869	+	0.384440i	−0.794510	−	0.607252i	$-0.792272\pi$
$311$	−207.085	+	119.561i	−0.665869	+	0.384440i	0.128640	+	0.991691i	$0.458939\pi$
$312$	−77.4162	−	134.089i	−0.248129	−	0.429772i
$313$	193.296	+	111.599i	0.617559	+	0.356548i	0.775918	−	0.630834i	$-0.217287\pi$
$313$	193.296	+	111.599i	0.617559	+	0.356548i	−0.158359	+	0.987382i	$0.550620\pi$
$314$		−	612.257i		−	1.94986i
$315$	46.9289	−	1.63683i	0.148981	−	0.00519628i
$316$	68.1786			0.215755
$317$	143.007	−	247.695i	0.451126	−	0.781373i	−0.547330	−	0.836917i	$-0.684356\pi$
$317$	143.007	−	247.695i	0.451126	−	0.781373i	0.998456	+	0.0555434i	$0.0176891\pi$
$318$	−16.8309	+	9.71731i	−0.0529273	+	0.0305576i
$319$	−221.761	−	384.100i	−0.695174	−	1.20408i
$320$	9.48256	+	5.47476i	0.0296330	+	0.0171086i
$321$		−	155.255i		−	0.483662i
$322$	2.52665	+	72.4407i	0.00784675	+	0.224971i
$323$	68.0286			0.210615
$324$	−10.5865	+	18.3364i	−0.0326744	+	0.0565937i
$325$	93.2216	−	53.8215i	0.286836	−	0.165605i
$326$	−16.6784	−	28.8878i	−0.0511607	−	0.0886129i
$327$	41.0252	+	23.6859i	0.125459	+	0.0724340i
$328$			152.854i			0.466018i
$329$	14.9821	+	23.9786i	0.0455383	+	0.0728833i
$330$	−85.1279			−0.257963
$331$	−269.512	+	466.809i	−0.814236	+	1.41030i	0.0956391	+	0.995416i	$0.469511\pi$
$331$	−269.512	+	466.809i	−0.814236	+	1.41030i	−0.909875	+	0.414882i	$0.863823\pi$
$332$	−43.0123	+	24.8332i	−0.129555	+	0.0747987i
$333$	79.4718	+	137.649i	0.238654	+	0.413361i
$334$	464.088	+	267.941i	1.38948	+	0.802219i
$335$		−	224.797i		−	0.671036i
$336$	113.142	−	212.768i	0.336733	−	0.633238i
$337$	68.2484			0.202518			0.101259	−	0.994860i	$-0.467713\pi$
$337$	68.2484			0.202518			0.101259	+	0.994860i	$0.467713\pi$
$338$	371.109	−	642.780i	1.09796	−	1.90172i
$339$	138.506	−	79.9664i	0.408572	−	0.235889i
$340$	−57.0563	−	98.8244i	−0.167813	−	0.290660i
$341$	−295.819	−	170.791i	−0.867503	−	0.500853i
$342$		−	23.7126i		−	0.0693350i
$343$	−35.8105	−	341.126i	−0.104404	−	0.994535i
$344$	−73.2893			−0.213050
$345$	−7.95591	+	13.7800i	−0.0230606	+	0.0399422i
$346$	543.041	−	313.525i	1.56948	−	0.906141i
$347$	−190.947	−	330.731i	−0.550281	−	0.953114i	−0.998254	−	0.0590672i	$-0.981187\pi$
$347$	−190.947	−	330.731i	−0.550281	−	0.953114i	0.447973	−	0.894047i	$-0.352146\pi$
$348$	−179.470	−	103.617i	−0.515720	−	0.297751i
$349$		−	301.869i		−	0.864953i	−0.901645	−	0.432477i	$-0.857640\pi$
$349$		−	301.869i		−	0.864953i	0.901645	−	0.432477i	$-0.142360\pi$
$350$	77.8875	+	41.4177i	0.222536	+	0.118336i
$351$	111.866			0.318706
$352$	−146.012	+	252.900i	−0.414807	+	0.718466i
$353$	110.891	−	64.0227i	0.314138	−	0.181367i	−0.334639	−	0.942346i	$-0.608614\pi$
$353$	110.891	−	64.0227i	0.314138	−	0.181367i	0.648776	+	0.760979i	$0.275281\pi$
$354$	−205.423	−	355.803i	−0.580291	−	1.00509i
$355$	109.794	+	63.3898i	0.309280	+	0.178563i
$356$		−	171.429i		−	0.481542i
$357$	−223.048	+	139.363i	−0.624786	+	0.390373i
$358$	139.305			0.389120
$359$	262.113	−	453.993i	0.730119	−	1.26460i	−0.226713	−	0.973962i	$-0.572798\pi$
$359$	262.113	−	453.993i	0.730119	−	1.26460i	0.956832	−	0.290642i	$-0.0938688\pi$
$360$	24.1225	−	13.9271i	0.0670069	−	0.0386864i
$361$	−175.583	−	304.118i	−0.486378	−	0.842432i
$362$	102.371	+	59.1041i	0.282794	+	0.163271i
$363$			77.8541i			0.214474i
$364$	354.315	−	12.3581i	0.973394	−	0.0339509i
$365$	−167.324			−0.458421
$366$	−159.740	+	276.677i	−0.436448	+	0.755949i
$367$	30.8202	−	17.7941i	0.0839789	−	0.0484852i	−0.457423	−	0.889249i	$-0.651227\pi$
$367$	30.8202	−	17.7941i	0.0839789	−	0.0484852i	0.541401	+	0.840764i	$0.317894\pi$
$368$	40.8288	+	70.7176i	0.110948	+	0.192167i
$369$	−95.6408	−	55.2182i	−0.259189	−	0.149643i
$370$			298.594i			0.807011i
$371$	1.08627	+	31.1441i	0.00292796	+	0.0839462i
$372$	−159.604			−0.429042
$373$	133.546	−	231.308i	0.358031	−	0.620128i	−0.629601	−	0.776919i	$-0.716781\pi$
$373$	133.546	−	231.308i	0.358031	−	0.620128i	0.987632	+	0.156791i	$0.0501148\pi$
$374$	412.920	−	238.399i	1.10406	−	0.637432i
$375$	9.68246	+	16.7705i	0.0258199	+	0.0447214i
$376$	14.5248	+	8.38588i	0.0386297	+	0.0223029i
$377$			1094.91i			2.90427i
$378$	48.5775	+	77.7474i	0.128512	+	0.205681i
$379$	−125.687			−0.331627			−0.165813	−	0.986157i	$-0.553025\pi$
$379$	−125.687			−0.331627			−0.165813	+	0.986157i	$0.553025\pi$
$380$	8.24856	−	14.2869i	0.0217067	−	0.0375972i
$381$	−287.387	+	165.923i	−0.754297	+	0.435493i
$382$	25.3457	+	43.9001i	0.0663501	+	0.114922i
$383$	−308.755	−	178.260i	−0.806149	−	0.465430i	0.0394677	−	0.999221i	$-0.487434\pi$
$383$	−308.755	−	178.260i	−0.806149	−	0.465430i	−0.845617	+	0.533790i	$0.820767\pi$
$384$		−	210.622i		−	0.548496i
$385$	−64.0883	+	120.520i	−0.166463	+	0.313040i
$386$	72.3446			0.187421
$387$	26.4757	−	45.8572i	0.0684126	−	0.118494i
$388$	−150.355	+	86.8076i	−0.387513	+	0.223731i
$389$	−223.316	−	386.795i	−0.574078	−	0.994332i	−0.996141	−	0.0877654i	$-0.972027\pi$
$389$	−223.316	−	386.795i	−0.574078	−	0.994332i	0.422064	−	0.906566i	$-0.361306\pi$
$390$	181.998	+	105.077i	0.466661	+	0.269427i
$391$		−	89.1216i		−	0.227933i
$392$	−113.760	−	168.686i	−0.290204	−	0.430322i
$393$	−101.866			−0.259201
$394$	−282.838	+	489.890i	−0.717863	+	1.24337i
$395$	56.1208	−	32.4014i	0.142078	−	0.0820288i
$396$	−30.7740	−	53.3021i	−0.0777120	−	0.134601i
$397$	525.089	+	303.160i	1.32264	+	0.763627i	0.984149	−	0.177342i	$-0.0567499\pi$
$397$	525.089	+	303.160i	1.32264	+	0.763627i	0.338492	+	0.940969i	$0.390083\pi$
$398$		−	801.645i		−	2.01418i
$399$	−33.5712	−	17.8519i	−0.0841384	−	0.0447417i
$400$	99.3785			0.248446
$401$	364.402	−	631.163i	0.908734	−	1.57397i	0.0929080	−	0.995675i	$-0.470384\pi$
$401$	364.402	−	631.163i	0.908734	−	1.57397i	0.815826	−	0.578298i	$-0.196283\pi$
$402$	380.076	−	219.437i	0.945464	−	0.545864i
$403$	421.627	+	730.280i	1.04622	+	1.81211i
$404$	217.904	+	125.807i	0.539367	+	0.311404i
$405$			20.1246i			0.0496904i
$406$	−760.967	+	475.461i	−1.87430	+	1.17109i
$407$	−462.034			−1.13522
$408$	−78.0054	+	135.109i	−0.191190	+	0.331150i
$409$	−459.563	+	265.329i	−1.12363	+	0.648725i	−0.942324	−	0.334702i	$-0.891364\pi$
$409$	−459.563	+	265.329i	−1.12363	+	0.648725i	−0.181301	+	0.983428i	$0.558031\pi$
$410$	−103.734	−	179.672i	−0.253009	−	0.438225i
$411$	248.871	+	143.686i	0.605526	+	0.349601i
$412$		−	50.6722i		−	0.122991i
$413$	−658.382	+	22.9637i	−1.59415	+	0.0556021i
$414$	−31.0649			−0.0750360
$415$	−23.6035	+	40.8825i	−0.0568760	+	0.0985121i
$416$	624.328	−	360.456i	1.50079	−	0.866481i
$417$	−120.919	−	209.437i	−0.289973	−	0.502247i
$418$	59.6953	+	34.4651i	0.142812	+	0.0824524i
$419$			282.637i			0.674552i	0.941406	+	0.337276i	$0.109506\pi$
$419$			282.637i			0.674552i	−0.941406	+	0.337276i	$0.890494\pi$
$420$	2.22322	+	63.7411i	0.00529338	+	0.151765i
$421$	440.590			1.04653			0.523267	−	0.852169i	$-0.324713\pi$
$421$	440.590			1.04653			0.523267	+	0.852169i	$0.324713\pi$
$422$	−359.560	+	622.777i	−0.852039	+	1.47577i
$423$	−10.4941	+	6.05878i	−0.0248088	+	0.0143234i
$424$	9.24264	+	16.0087i	0.0217987	+	0.0377564i
$425$	−93.9311	−	54.2311i	−0.221014	−	0.127603i
$426$			247.514i			0.581018i
$427$	271.448	+	434.448i	0.635710	+	1.01744i
$428$	210.875			0.492700
$429$	−162.592	+	281.617i	−0.379002	+	0.656451i
$430$	86.1480	−	49.7376i	0.200344	−	0.115669i
$431$	63.7174	+	110.362i	0.147836	+	0.256060i	0.930427	−	0.366476i	$-0.119436\pi$
$431$	63.7174	+	110.362i	0.147836	+	0.256060i	−0.782591	+	0.622536i	$0.786103\pi$
$432$	89.4407	+	51.6386i	0.207039	+	0.119534i
$433$		−	433.284i		−	1.00066i	−0.865836	−	0.500328i	$-0.833213\pi$
$433$		−	433.284i		−	1.00066i	0.865836	−	0.500328i	$-0.166787\pi$
$434$	−324.458	+	610.155i	−0.747599	+	1.40589i
$435$	−196.973			−0.452812
$436$	−32.1714	+	55.7225i	−0.0737876	+	0.127804i
$437$	11.1580	−	6.44210i	0.0255333	−	0.0147416i
$438$	−163.334	−	282.903i	−0.372909	−	0.645898i
$439$	−54.7578	−	31.6144i	−0.124733	−	0.0720146i	0.436335	−	0.899784i	$-0.356276\pi$
$439$	−54.7578	−	31.6144i	−0.124733	−	0.0720146i	−0.561068	+	0.827770i	$0.689609\pi$
$440$			80.9697i			0.184022i
$441$	146.643	−	10.2419i	0.332523	−	0.0232244i
$442$	−1177.06			−2.66303
$443$	−219.190	+	379.648i	−0.494785	+	0.856992i	−0.999982	−	0.00601155i	$-0.998086\pi$
$443$	−219.190	+	379.648i	−0.494785	+	0.856992i	0.505197	+	0.863004i	$0.331420\pi$
$444$	−186.962	+	107.942i	−0.421085	+	0.243114i
$445$	−81.4703	−	141.111i	−0.183079	−	0.317103i
$446$	124.630	+	71.9553i	0.279440	+	0.161335i
$447$			24.8328i			0.0555544i
$448$	30.2645	+	16.0935i	0.0675547	+	0.0359231i
$449$	214.986			0.478810			0.239405	−	0.970920i	$-0.423048\pi$
$449$	214.986			0.478810			0.239405	+	0.970920i	$0.423048\pi$
$450$	−18.9032	+	32.7413i	−0.0420071	+	0.0727585i
$451$	278.019	−	160.514i	0.616450	−	0.355907i
$452$	108.614	+	188.125i	0.240297	+	0.416207i
$453$	318.561	+	183.922i	0.703226	+	0.406008i
$454$		−	460.371i		−	1.01403i
$455$	285.779	−	178.558i	0.628087	−	0.392436i
$456$	−22.5543			−0.0494611
$457$	120.600	−	208.885i	0.263894	−	0.457078i	−0.703379	−	0.710815i	$-0.748326\pi$
$457$	120.600	−	208.885i	0.263894	−	0.457078i	0.967273	+	0.253737i	$0.0816597\pi$
$458$	36.6336	−	21.1504i	0.0799860	−	0.0461799i
$459$	−56.3587	−	97.6161i	−0.122786	−	0.212671i
$460$	−18.7167	−	10.8061i	−0.0406885	−	0.0234915i
$461$		−	343.383i		−	0.744865i	−0.928059	−	0.372432i	$-0.878524\pi$
$461$		−	343.383i		−	0.744865i	0.928059	−	0.372432i	$-0.121476\pi$
$462$	−266.331	+	9.28933i	−0.576473	+	0.0201068i
$463$	74.7714			0.161493			0.0807467	−	0.996735i	$-0.474270\pi$
$463$	74.7714			0.161493			0.0807467	+	0.996735i	$0.474270\pi$
$464$	−505.422	+	875.417i	−1.08927	+	1.88667i
$465$	−131.377	+	75.8504i	−0.282531	+	0.163119i
$466$	335.730	+	581.501i	0.720450	+	1.24786i
$467$	−308.470	−	178.095i	−0.660535	−	0.381360i	0.131946	−	0.991257i	$-0.457878\pi$
$467$	−308.470	−	178.095i	−0.660535	−	0.381360i	−0.792481	+	0.609897i	$0.791211\pi$
$468$			151.942i			0.324662i
$469$	−24.5303	−	703.298i	−0.0523034	−	1.49957i
$470$	−22.7642			−0.0484345
$471$	210.373	−	364.377i	0.446652	−	0.773624i
$472$	−338.423	+	195.389i	−0.716998	+	0.413959i
$473$	76.9623	+	133.303i	0.162711	+	0.281824i
$474$	109.565	+	63.2577i	0.231151	+	0.133455i
$475$		−	15.6803i		−	0.0330111i
$476$	−189.290	−	302.955i	−0.397668	−	0.636461i
$477$	−13.3556			−0.0279991
$478$	50.0319	−	86.6579i	0.104669	−	0.181293i
$479$	323.678	−	186.876i	0.675737	−	0.390137i	−0.122510	−	0.992467i	$-0.539094\pi$
$479$	323.678	−	186.876i	0.675737	−	0.390137i	0.798247	+	0.602330i	$0.205761\pi$
$480$	64.8458	+	112.316i	0.135095	+	0.233992i
$481$	987.799	+	570.306i	2.05364	+	1.18567i
$482$			210.096i			0.435884i
$483$	−23.3871	+	43.9803i	−0.0484205	+	0.0910565i
$484$	−105.745			−0.218482
$485$	−82.5093	+	142.910i	−0.170122	+	0.294660i
$486$	−34.0258	+	19.6448i	−0.0700119	+	0.0404214i
$487$	−388.781	−	673.389i	−0.798319	−	1.38273i	−0.920710	−	0.390247i	$-0.872390\pi$
$487$	−388.781	−	673.389i	−0.798319	−	1.38273i	0.122391	−	0.992482i	$-0.460944\pi$
$488$	263.162	+	151.937i	0.539267	+	0.311346i
$489$		−	22.9229i		−	0.0468772i
$490$	248.198	+	121.080i	0.506526	+	0.247102i
$491$	458.794			0.934407			0.467203	−	0.884150i	$-0.345262\pi$
$491$	458.794			0.934407			0.467203	+	0.884150i	$0.345262\pi$
$492$	75.0001	−	129.904i	0.152439	−	0.264032i
$493$	955.435	−	551.621i	1.93800	−	1.11891i
$494$	−85.0831	−	147.368i	−0.172233	−	0.298316i
$495$	−50.6628	−	29.2502i	−0.102349	−	0.0590913i
$496$			778.511i			1.56958i
$497$	350.419	+	186.340i	0.705068	+	0.374929i
$498$	−92.1631			−0.185066
$499$	−317.772	+	550.396i	−0.636817	+	1.10300i	0.349310	+	0.937007i	$0.386416\pi$
$499$	−317.772	+	550.396i	−0.636817	+	1.10300i	−0.986127	+	0.165992i	$0.946917\pi$
$500$	−22.7785	+	13.1512i	−0.0455570	+	0.0263024i
$501$	184.131	+	318.924i	0.367526	+	0.636574i
$502$	−243.298	−	140.468i	−0.484657	−	0.279817i
$503$			10.6561i			0.0211852i	0.999944	+	0.0105926i	$0.00337179\pi$
$503$			10.6561i			0.0211852i	−0.999944	+	0.0105926i	$0.996628\pi$
$504$	73.9496	−	46.2046i	0.146725	−	0.0916757i
$505$	239.156			0.473575
$506$	45.1514	−	78.2045i	0.0892319	−	0.154554i
$507$	441.722	−	255.028i	0.871246	−	0.503014i
$508$	−225.365	−	390.343i	−0.443631	−	0.768392i
$509$	706.084	+	407.658i	1.38720	+	0.800899i	0.992999	−	0.118126i	$-0.0376885\pi$
$509$	706.084	+	407.658i	1.38720	+	0.800899i	0.394200	+	0.919025i	$0.371022\pi$
$510$		−	211.753i		−	0.415201i
$511$	−523.488	+	18.2587i	−1.02444	+	0.0357313i
$512$	335.445			0.655167
$513$	8.14770	−	14.1122i	0.0158825	−	0.0275092i
$514$	486.552	−	280.911i	0.946599	−	0.546519i
$515$	−24.0816	−	41.7105i	−0.0467604	−	0.0809913i
$516$	62.2855	+	35.9605i	0.120708	+	0.0696909i
$517$		−	35.2246i		−	0.0681327i
$518$	32.5832	+	934.179i	0.0629019	+	1.80343i
$519$	430.911			0.830273
$520$	99.9438	−	173.108i	0.192200	−	0.332900i
$521$	−383.930	+	221.662i	−0.736911	+	0.425456i	−0.820945	−	0.571007i	$-0.806553\pi$
$521$	−383.930	+	221.662i	−0.736911	+	0.425456i	0.0840344	+	0.996463i	$0.473219\pi$
$522$	−192.277	−	333.034i	−0.368347	−	0.637995i
$523$	−549.148	−	317.051i	−1.05000	−	0.606216i	−0.127348	−	0.991858i	$-0.540646\pi$
$523$	−549.148	−	317.051i	−1.05000	−	0.606216i	−0.922648	+	0.385642i	$0.873980\pi$
$524$		−	138.359i		−	0.264044i
$525$	32.1225	+	51.4115i	0.0611857	+	0.0979267i
$526$	−1074.96			−2.04366
$527$	424.836	−	735.837i	0.806140	−	1.39628i
$528$	−259.996	+	150.109i	−0.492416	+	0.284297i
$529$	256.060	+	443.510i	0.484046	+	0.838393i
$530$	−21.7286	−	12.5450i	−0.0409973	−	0.0236698i
$531$		−	282.335i		−	0.531705i
$532$	24.2474	−	45.5980i	0.0455777	−	0.0857106i
$533$	−792.515			−1.48689
$534$	159.056	−	275.492i	0.297857	−	0.515903i
$535$	173.581	−	100.217i	0.324450	−	0.187321i
$536$	−208.718	−	361.511i	−0.389400	−	0.674460i
$537$	82.9055	+	47.8655i	0.154386	+	0.0891351i
$538$		−	149.944i		−	0.278706i
$539$	−187.355	+	384.053i	−0.347597	+	0.712528i
$540$	−27.3342			−0.0506189
$541$	87.5750	−	151.684i	0.161876	−	0.280378i	−0.773665	−	0.633594i	$-0.781579\pi$
$541$	87.5750	−	151.684i	0.161876	−	0.280378i	0.935542	+	0.353217i	$0.114912\pi$
$542$	118.919	−	68.6577i	0.219407	−	0.126675i
$543$	40.6167	+	70.3501i	0.0748005	+	0.129558i
$544$	−629.079	−	363.199i	−1.15640	−	0.667646i
$545$			61.1568i			0.112214i
$546$	580.864	+	308.882i	1.06385	+	0.565718i
$547$	−773.543			−1.41416			−0.707078	−	0.707136i	$-0.749987\pi$
$547$	−773.543			−1.41416			−0.707078	+	0.707136i	$0.749987\pi$
$548$	−195.161	+	338.029i	−0.356133	+	0.616841i
$549$	−190.134	+	109.774i	−0.346328	+	0.199953i
$550$	−54.9499	−	95.1759i	−0.0999088	−	0.173047i
$551$	138.126	+	79.7471i	0.250682	+	0.144732i
$552$			29.5474i			0.0535280i
$553$	172.043	−	107.495i	0.311109	−	0.194385i
$554$	−1190.60			−2.14909
$555$	−102.598	+	177.704i	−0.184861	+	0.320188i
$556$	284.468	−	164.237i	0.511632	−	0.295391i
$557$	378.264	+	655.173i	0.679110	+	1.17625i	0.975249	+	0.221108i	$0.0709673\pi$
$557$	378.264	+	655.173i	0.679110	+	1.17625i	−0.296140	+	0.955145i	$0.595699\pi$
$558$	−256.489	−	148.084i	−0.459658	−	0.265383i
$559$		−	379.989i		−	0.679766i
$560$	310.915	−	10.8444i	0.555205	−	0.0193650i
$561$	327.659			0.584062
$562$	673.639	−	1166.78i	1.19865	−	2.07612i
$563$	−451.185	+	260.492i	−0.801394	+	0.462685i	−0.843958	−	0.536409i	$-0.819781\pi$
$563$	−451.185	+	260.492i	−0.801394	+	0.462685i	0.0425646	+	0.999094i	$0.486447\pi$
$564$	−8.22933	−	14.2536i	−0.0145910	−	0.0252724i
$565$	178.810	+	103.236i	0.316478	+	0.182719i
$566$		−	1127.32i		−	1.99174i
$567$	2.19604	+	62.9617i	0.00387308	+	0.111044i
$568$	235.423			0.414477
$569$	91.5332	−	158.540i	0.160867	−	0.278629i	−0.774313	−	0.632803i	$-0.781904\pi$
$569$	91.5332	−	158.540i	0.160867	−	0.278629i	0.935180	+	0.354173i	$0.115238\pi$
$570$	26.5115	−	15.3064i	0.0465113	−	0.0268533i
$571$	−498.800	−	863.947i	−0.873555	−	1.51304i	−0.858294	−	0.513159i	$-0.828475\pi$
$571$	−498.800	−	863.947i	−0.873555	−	1.51304i	−0.0152618	−	0.999884i	$-0.504858\pi$
$572$	−382.507	−	220.840i	−0.668718	−	0.386084i
$573$			34.8355i			0.0607949i
$574$	−344.147	−	550.802i	−0.599560	−	0.959585i
$575$	−20.5421			−0.0357254
$576$	−7.34516	+	12.7222i	−0.0127520	+	0.0220871i
$577$	279.135	−	161.158i	0.483769	−	0.279304i	−0.238217	−	0.971212i	$-0.576563\pi$
$577$	279.135	−	161.158i	0.483769	−	0.279304i	0.721986	+	0.691908i	$0.243230\pi$
$578$	228.808	+	396.307i	0.395861	+	0.685652i
$579$	43.0549	+	24.8578i	0.0743609	+	0.0429323i
$580$		−	267.539i		−	0.461274i
$581$	−69.3847	+	130.480i	−0.119423	+	0.224579i
$582$	−322.168			−0.553553
$583$	19.4117	−	33.6220i	0.0332962	−	0.0576707i
$584$	−269.084	+	155.356i	−0.460761	+	0.266020i
$585$	72.2092	+	125.070i	0.123434	+	0.213795i
$586$	−1100.54	−	635.400i	−1.87806	−	1.08430i
$587$			406.391i			0.692318i	0.938176	+	0.346159i	$0.112514\pi$
$587$			406.391i			0.692318i	−0.938176	+	0.346159i	$0.887486\pi$
$588$	13.9111	+	199.177i	0.0236583	+	0.338737i
$589$	122.836			0.208550
$590$	265.200	−	459.340i	0.449491	−	0.778542i
$591$	−336.655	+	194.368i	−0.569636	+	0.328879i
$592$	526.519	+	911.958i	0.889391	+	1.54047i
$593$	333.688	+	192.655i	0.562711	+	0.324881i	0.754233	−	0.656607i	$-0.228009\pi$
$593$	333.688	+	192.655i	0.562711	+	0.324881i	−0.191522	+	0.981488i	$0.561342\pi$
$594$		−	114.211i		−	0.192275i
$595$	−299.790	−	159.417i	−0.503849	−	0.267928i
$596$	−33.7291			−0.0565925
$597$	275.447	−	477.089i	0.461386	−	0.799144i
$598$	−193.061	+	111.464i	−0.322845	+	0.186395i
$599$	448.272	+	776.430i	0.748367	+	1.29621i	0.948605	+	0.316463i	$0.102495\pi$
$599$	448.272	+	776.430i	0.748367	+	1.29621i	−0.200238	+	0.979747i	$0.564171\pi$
$600$	31.1420	+	17.9798i	0.0519033	+	0.0299664i
$601$			599.296i			0.997166i	0.866842	+	0.498583i	$0.166146\pi$
$601$			599.296i			0.997166i	−0.866842	+	0.498583i	$0.833854\pi$
$602$	264.095	−	165.009i	0.438695	−	0.274102i
$603$	301.597			0.500161
$604$	−249.811	+	432.686i	−0.413595	+	0.716367i
$605$	−87.0435	+	50.2546i	−0.143874	+	0.0830654i
$606$	233.453	+	404.353i	0.385237	+	0.667250i
$607$	−426.925	−	246.485i	−0.703336	−	0.406071i	0.105253	−	0.994445i	$-0.466435\pi$
$607$	−426.925	−	246.485i	−0.703336	−	0.406071i	−0.808589	+	0.588374i	$0.799768\pi$
$608$		−	105.014i		−	0.172721i
$609$	−616.249	+	21.4941i	−1.01190	+	0.0352941i
$610$	−412.446			−0.676142
$611$	−43.4790	+	75.3079i	−0.0711604	+	0.123253i
$612$	132.587	−	76.5491i	0.216645	−	0.125080i
$613$	70.4822	+	122.079i	0.114979	+	0.199150i	0.917771	−	0.397109i	$-0.129987\pi$
$613$	70.4822	+	122.079i	0.114979	+	0.199150i	−0.802792	+	0.596259i	$0.796653\pi$
$614$	870.465	+	502.563i	1.41770	+	0.818507i
$615$		−	142.573i		−	0.231826i
$616$	8.83557	+	253.321i	0.0143435	+	0.411236i
$617$	61.9853			0.100462			0.0502312	−	0.998738i	$-0.484004\pi$
$617$	61.9853			0.100462			0.0502312	+	0.998738i	$0.484004\pi$
$618$	47.0148	−	81.4321i	0.0760758	−	0.131767i
$619$	−549.456	+	317.228i	−0.887651	+	0.512485i	−0.873173	−	0.487410i	$-0.837942\pi$
$619$	−549.456	+	317.228i	−0.887651	+	0.512485i	−0.0144774	+	0.999895i	$0.504608\pi$
$620$	−103.024	−	178.442i	−0.166167	−	0.287810i
$621$	−18.4879	−	10.6740i	−0.0297711	−	0.0171884i
$622$		−	602.689i		−	0.968953i
$623$	−270.286	−	432.588i	−0.433845	−	0.694362i
$624$	741.138			1.18772
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−487.188	+	281.278i	−0.778256	+	0.449326i
$627$	23.6846	+	41.0229i	0.0377745	+	0.0654273i
$628$	494.914	+	285.739i	0.788080	+	0.454998i
$629$		−	1149.29i		−	1.82717i
$630$	−55.5676	+	104.497i	−0.0882026	+	0.165868i
$631$	93.3216			0.147895			0.0739474	−	0.997262i	$-0.476440\pi$
$631$	93.3216			0.147895			0.0739474	+	0.997262i	$0.476440\pi$
$632$	60.1677	−	104.213i	0.0952020	−	0.164895i
$633$	−427.976	+	247.092i	−0.676107	+	0.390350i
$634$	360.439	+	624.298i	0.568515	+	0.984698i
$635$	−371.015	−	214.206i	−0.584276	−	0.337332i
$636$		−	18.1402i		−	0.0285223i
$637$	874.603	−	589.821i	1.37300	−	0.925935i
$638$	1117.86			1.75214
$639$	−85.0463	+	147.305i	−0.133093	+	0.230523i
$640$	235.483	−	135.956i	0.367942	−	0.212432i
$641$	−153.961	−	266.668i	−0.240188	−	0.416018i	0.720579	−	0.693372i	$-0.243876\pi$
$641$	−153.961	−	266.668i	−0.240188	−	0.416018i	−0.960768	+	0.277354i	$0.910543\pi$
$642$	338.884	+	195.655i	0.527857	+	0.304759i
$643$		−	296.519i		−	0.461150i	−0.973055	−	0.230575i	$-0.925939\pi$
$643$		−	296.519i		−	0.461150i	0.973055	−	0.230575i	$-0.0740607\pi$
$644$	−59.7362	−	31.7655i	−0.0927581	−	0.0493253i
$645$	68.3599			0.105984
$646$	−85.7306	+	148.490i	−0.132710	+	0.229860i
$647$	203.727	−	117.622i	0.314880	−	0.181796i	−0.334228	−	0.942492i	$-0.608476\pi$
$647$	203.727	−	117.622i	0.314880	−	0.181796i	0.649108	+	0.760696i	$0.275142\pi$
$648$	18.6852	+	32.3637i	0.0288352	+	0.0499440i
$649$	710.767	+	410.361i	1.09517	+	0.632298i
$650$			271.307i			0.417395i
$651$	−402.748	+	251.641i	−0.618660	+	0.386546i
$652$	31.1350			0.0477531
$653$	−148.823	+	257.769i	−0.227906	+	0.394746i	−0.957187	−	0.289469i	$-0.906521\pi$
$653$	−148.823	+	257.769i	−0.227906	+	0.394746i	0.729281	+	0.684214i	$0.239855\pi$
$654$	−103.401	+	59.6987i	−0.158106	+	0.0912823i
$655$	−65.7542	−	113.890i	−0.100388	−	0.173877i
$656$	−633.643	−	365.834i	−0.965919	−	0.557673i
$657$		−	224.488i		−	0.341687i
$658$	−71.2200	+	2.48408i	−0.108237	+	0.00377519i
$659$	−127.740			−0.193839			−0.0969197	−	0.995292i	$-0.530899\pi$
$659$	−127.740			−0.193839			−0.0969197	+	0.995292i	$0.530899\pi$
$660$	39.7290	−	68.8127i	0.0601955	−	0.104262i
$661$	−823.610	+	475.512i	−1.24601	+	0.719382i	−0.970311	−	0.241863i	$-0.922242\pi$
$661$	−823.610	+	475.512i	−1.24601	+	0.719382i	−0.275696	+	0.961245i	$0.588908\pi$
$662$	−679.286	−	1176.56i	−1.02611	−	1.77728i
$663$	−700.513	−	404.441i	−1.05658	−	0.610017i
$664$			87.6611i			0.132020i
$665$	−1.71106	−	49.0571i	−0.00257302	−	0.0737701i
$666$	−400.606			−0.601510
$667$	104.474	−	180.953i	0.156632	−	0.271295i
$668$	−433.178	+	250.095i	−0.648469	+	0.374394i
$669$	49.4481	+	85.6466i	0.0739134	+	0.128022i
$670$	490.677	+	283.292i	0.732353	+	0.422824i
$671$		−	638.206i		−	0.951126i
$672$	215.132	+	344.316i	0.320137	+	0.512374i
$673$	−1003.39			−1.49092			−0.745460	−	0.666550i	$-0.767770\pi$
$673$	−1003.39			−1.49092			−0.745460	+	0.666550i	$0.767770\pi$
$674$	−86.0076	+	148.970i	−0.127608	+	0.221023i
$675$	−22.5000	+	12.9904i	−0.0333333	+	0.0192450i
$676$	346.392	+	599.968i	0.512414	+	0.887526i
$677$	408.603	+	235.907i	0.603550	+	0.348460i	0.770437	−	0.637516i	$-0.220038\pi$
$677$	408.603	+	235.907i	0.603550	+	0.348460i	−0.166887	+	0.985976i	$0.553371\pi$
$678$			403.099i			0.594541i
$679$	−242.543	+	456.111i	−0.357206	+	0.671740i
$680$	−201.409			−0.296190
$681$	158.185	−	273.984i	0.232283	−	0.402325i
$682$	745.589	−	430.466i	1.09324	−	0.631182i
$683$	−208.614	−	361.330i	−0.305438	−	0.529034i	0.671921	−	0.740623i	$-0.265470\pi$
$683$	−208.614	−	361.330i	−0.305438	−	0.529034i	−0.977359	+	0.211589i	$0.932136\pi$
$684$	19.1679	+	11.0666i	0.0280233	+	0.0161792i
$685$			370.995i			0.541599i
$686$	789.722	+	351.726i	1.15120	+	0.512719i
$687$	29.0693			0.0423134
$688$	175.407	−	303.815i	0.254953	−	0.441591i
$689$	−83.0019	+	47.9211i	−0.120467	+	0.0695517i
$690$	−20.0523	−	34.7316i	−0.0290613	−	0.0503357i
$691$	160.907	+	92.8995i	0.232860	+	0.134442i	0.611891	−	0.790942i	$-0.290409\pi$
$691$	160.907	+	92.8995i	0.232860	+	0.134442i	−0.379030	+	0.925384i	$0.623742\pi$
$692$			585.285i			0.845787i
$693$	−161.695	−	85.9835i	−0.233326	−	0.124074i
$694$	962.538			1.38694
$695$	156.105	−	270.382i	0.224612	−	0.389039i
$696$	−316.766	+	182.885i	−0.455123	+	0.262765i
$697$	399.273	+	691.561i	0.572845	+	0.992197i
$698$	658.905	+	380.419i	0.943990	+	0.545013i
$699$			461.430i			0.660129i
$700$	−69.8296	+	43.6303i	−0.0997566	+	0.0623291i
$701$	1034.80			1.47618			0.738089	−	0.674704i	$-0.235729\pi$
$701$	1034.80			1.47618			0.738089	+	0.674704i	$0.235729\pi$
$702$	−140.975	+	244.176i	−0.200819	+	0.347829i
$703$	143.892	−	83.0759i	0.204682	−	0.118173i
$704$	−21.3517	−	36.9822i	−0.0303291	−	0.0525316i
$705$	−13.5478	−	7.82185i	−0.0192168	−	0.0110948i
$706$			322.729i			0.457123i
$707$	748.220	−	26.0971i	1.05830	−	0.0369125i
$708$	383.482			0.541641
$709$	108.321	−	187.618i	0.152780	−	0.264623i	−0.779468	−	0.626442i	$-0.784511\pi$
$709$	108.321	−	187.618i	0.152780	−	0.264623i	0.932248	+	0.361819i	$0.117844\pi$
$710$	−276.729	+	159.769i	−0.389759	+	0.225027i
$711$	43.4710	+	75.2940i	0.0611406	+	0.105899i
$712$	−262.035	−	151.286i	−0.368027	−	0.212481i
$713$		−	160.923i		−	0.225698i
$714$	−23.1069	−	662.487i	−0.0323625	−	0.927854i
$715$	−419.811			−0.587148
$716$	−65.0133	+	112.606i	−0.0908007	+	0.157271i
$717$	59.5517	−	34.3822i	0.0830568	−	0.0479529i
$718$	660.636	+	1144.26i	0.920106	+	1.59367i
$719$	0.325449	+	0.187898i	0.000452641	+	0.000261332i	0.500226	−	0.865895i	$-0.333250\pi$
$719$	0.325449	+	0.187898i	0.000452641	+	0.000261332i	−0.499774	+	0.866156i	$0.666583\pi$
$720$			133.330i			0.185181i
$721$	−79.8930	−	127.867i	−0.110809	−	0.177347i
$722$	885.086			1.22588
$723$	−72.1896	+	125.036i	−0.0998473	+	0.172941i
$724$	−95.5530	+	55.1675i	−0.131979	+	0.0761983i
$725$	−127.146	−	220.223i	−0.175373	−	0.303756i
$726$	−169.936	−	98.1128i	−0.234072	−	0.135142i
$727$			174.857i			0.240518i	0.992743	+	0.120259i	$0.0383726\pi$
$727$			174.857i			0.240518i	−0.992743	+	0.120259i	$0.961627\pi$
$728$	293.794	−	552.490i	0.403563	−	0.758915i
$729$	−27.0000			−0.0370370
$730$	210.864	−	365.227i	0.288854	−	0.500310i
$731$	−331.585	+	191.441i	−0.453605	+	0.261889i
$732$	−149.100	−	258.249i	−0.203689	−	0.352800i
$733$	−738.210	−	426.206i	−1.00711	−	0.581454i	−0.0967645	−	0.995307i	$-0.530849\pi$
$733$	−738.210	−	426.206i	−1.00711	−	0.581454i	−0.910344	+	0.413853i	$0.864183\pi$
$734$			89.6973i			0.122203i
$735$	106.108	+	157.340i	0.144365	+	0.214069i
$736$	−137.575			−0.186923
$737$	−438.357	+	759.256i	−0.594785	+	1.03020i
$738$	241.056	−	139.174i	0.326634	−	0.188582i
$739$	584.126	+	1011.74i	0.790428	+	1.36906i	0.925702	+	0.378253i	$0.123475\pi$
$739$	584.126	+	1011.74i	0.790428	+	1.36906i	−0.135275	+	0.990808i	$0.543192\pi$
$740$	−241.367	−	139.353i	−0.326171	−	0.188315i
$741$		−	116.939i		−	0.157813i
$742$	−69.3488	−	36.8771i	−0.0934619	−	0.0496996i
$743$	−558.877			−0.752190			−0.376095	−	0.926581i	$-0.622733\pi$
$743$	−558.877			−0.752190			−0.376095	+	0.926581i	$0.622733\pi$
$744$	−140.850	+	243.960i	−0.189315	+	0.327903i
$745$	−27.7639	+	16.0295i	−0.0372670	+	0.0215161i
$746$	336.592	+	582.995i	0.451196	+	0.781494i
$747$	−54.8497	−	31.6675i	−0.0734266	−	0.0423929i
$748$			445.042i			0.594976i
$749$	532.128	−	332.479i	0.710451	−	0.443898i
$750$	−48.8079			−0.0650772
$751$	−630.654	+	1092.32i	−0.839752	+	1.45449i	0.0503493	+	0.998732i	$0.483967\pi$
$751$	−630.654	+	1092.32i	−0.839752	+	1.45449i	−0.890102	+	0.455762i	$0.849367\pi$
$752$	−69.5260	+	40.1408i	−0.0924547	+	0.0533788i
$753$	−96.5304	−	167.196i	−0.128194	−	0.222039i
$754$	−2389.92	−	1379.82i	−3.16965	−	1.83000i
$755$			474.883i			0.628985i
$756$	−85.5177	+	2.98276i	−0.113119	+	0.00394546i
$757$	−1269.13			−1.67652			−0.838262	−	0.545268i	$-0.816428\pi$
$757$	−1269.13			−1.67652			−0.838262	+	0.545268i	$0.816428\pi$
$758$	158.392	−	274.343i	0.208960	−	0.361930i
$759$	53.7425	−	31.0282i	0.0708070	−	0.0408804i
$760$	−14.5587	−	25.2164i	−0.0191562	−	0.0331795i
$761$	−157.718	−	91.0585i	−0.207251	−	0.119656i	0.392782	−	0.919632i	$-0.371513\pi$
$761$	−157.718	−	91.0585i	−0.207251	−	0.119656i	−0.600033	+	0.799975i	$0.704846\pi$
$762$		−	836.394i		−	1.09763i
$763$	6.67355	+	191.335i	0.00874646	+	0.250766i
$764$	−47.3152			−0.0619309
$765$	72.7587	−	126.022i	0.0951094	−	0.164734i
$766$	778.195	−	449.291i	1.01592	−	0.586542i
$767$	−1013.05	−	1754.65i	−1.32079	−	2.28768i
$768$	489.118	+	282.392i	0.636872	+	0.367698i
$769$			810.237i			1.05362i	0.849982	+	0.526812i	$0.176613\pi$
$769$			810.237i			1.05362i	−0.849982	+	0.526812i	$0.823387\pi$
$770$	−182.301	−	291.771i	−0.236755	−	0.378923i
$771$	386.087			0.500761
$772$	−33.7630	+	58.4793i	−0.0437345	+	0.0757504i
$773$	212.492	−	122.682i	0.274893	−	0.158709i	−0.356216	−	0.934404i	$-0.615933\pi$
$773$	212.492	−	122.682i	0.274893	−	0.158709i	0.631109	+	0.775694i	$0.282600\pi$
$774$	66.7300	+	115.580i	0.0862144	+	0.149328i
$775$	−169.607	−	97.9225i	−0.218847	−	0.126352i
$776$			306.431i			0.394885i
$777$	−301.595	+	567.160i	−0.388153	+	0.729936i
$778$	1125.70			1.44692
$779$	−57.7224	+	99.9781i	−0.0740981	+	0.128342i
$780$	−169.876	+	98.0780i	−0.217790	+	0.125741i
$781$	−247.222	−	428.200i	−0.316545	−	0.548272i
$782$	194.531	+	112.312i	0.248760	+	0.143622i
$783$		−	264.268i		−	0.337506i
$784$	971.543	−	67.8553i	1.23921	−	0.0865501i
$785$	543.181			0.691950
$786$	128.373	−	222.348i	0.163324	−	0.282886i
$787$	−373.020	+	215.363i	−0.473977	+	0.273651i	−0.717903	−	0.696143i	$-0.754898\pi$
$787$	−373.020	+	215.363i	−0.473977	+	0.273651i	0.243926	+	0.969794i	$0.421565\pi$
$788$	−264.000	−	457.261i	−0.335025	−	0.580280i
$789$	−639.750	−	369.360i	−0.810837	−	0.468137i
$790$			163.331i			0.206748i
$791$	570.690	+	303.472i	0.721479	+	0.383656i
$792$	−108.632			−0.137162
$793$	−787.761	+	1364.44i	−0.993393	+	1.72061i
$794$	−1323.45	+	764.093i	−1.66681	+	0.962334i
$795$	−8.62098	−	14.9320i	−0.0108440	−	0.0187824i
$796$	648.005	+	374.126i	0.814077	+	0.470008i
$797$			1137.61i			1.42737i	0.700468	+	0.713684i	$0.252975\pi$
$797$			1137.61i			1.42737i	−0.700468	+	0.713684i	$0.747025\pi$
$798$	81.2733	−	50.7805i	0.101846	−	0.0636347i
$799$	87.6199			0.109662
$800$	−83.7155	+	145.000i	−0.104644	+	0.181249i
$801$	189.320	−	109.304i	0.236354	−	0.136459i
$802$	918.449	+	1590.80i	1.14520	+	1.98354i
$803$	565.139	+	326.283i	0.703785	+	0.406330i
$804$			409.643i			0.509507i
$805$	−64.2678	+	2.24159i	−0.0798358	+	0.00278459i
$806$	−2125.36			−2.63692
$807$	51.5210	−	89.2370i	0.0638426	−	0.110579i
$808$	384.602	−	222.050i	0.475992	−	0.274814i
$809$	−455.336	−	788.665i	−0.562838	−	0.974864i	−0.997247	−	0.0741482i	$-0.976376\pi$
$809$	−455.336	−	788.665i	−0.562838	−	0.974864i	0.434409	−	0.900716i	$-0.356957\pi$
$810$	−43.9271	−	25.3613i	−0.0542310	−	0.0313103i
$811$		−	546.361i		−	0.673688i	−0.941560	−	0.336844i	$-0.890640\pi$
$811$		−	546.361i		−	0.673688i	0.941560	−	0.336844i	$-0.109360\pi$
$812$	−29.1944	−	837.020i	−0.0359537	−	1.03081i
$813$	94.3638			0.116069
$814$	582.262	−	1008.51i	0.715309	−	1.23895i
$815$	25.6286	−	14.7967i	0.0314462	−	0.0181554i
$816$	−373.389	−	646.729i	−0.457585	−	0.792560i
$817$	−47.9368	−	27.6763i	−0.0586742	−	0.0338756i
$818$		−	1337.48i		−	1.63507i
$819$	239.561	+	383.413i	0.292504	+	0.468148i
$820$	193.649			0.236158
$821$	−322.150	+	557.980i	−0.392388	+	0.679635i	−0.992764	−	0.120082i	$-0.961684\pi$
$821$	−322.150	+	557.980i	−0.392388	+	0.679635i	0.600376	+	0.799718i	$0.295017\pi$
$822$	−627.262	+	362.150i	−0.763092	+	0.440572i
$823$	−384.661	−	666.252i	−0.467388	−	0.809540i	0.531917	−	0.846796i	$-0.321472\pi$
$823$	−384.661	−	666.252i	−0.467388	−	0.809540i	−0.999306	+	0.0372559i	$0.988138\pi$
$824$	−77.4543	−	44.7183i	−0.0939980	−	0.0542697i
$825$		−	75.5236i		−	0.0915438i
$826$	779.579	−	1466.03i	0.943800	−	1.77485i
$827$	715.404			0.865060			0.432530	−	0.901620i	$-0.357621\pi$
$827$	715.404			0.865060			0.432530	+	0.901620i	$0.357621\pi$
$828$	14.4979	−	25.1111i	0.0175096	−	0.0303274i
$829$	68.2973	−	39.4315i	0.0823852	−	0.0475651i	−0.458241	−	0.888828i	$-0.651521\pi$
$829$	68.2973	−	39.4315i	0.0823852	−	0.0475651i	0.540627	+	0.841263i	$0.318187\pi$
$830$	−59.4910	−	103.041i	−0.0716759	−	0.124146i
$831$	−708.568	−	409.092i	−0.852669	−	0.492289i
$832$			105.421i			0.126708i
$833$	−955.317	−	466.038i	−1.14684	−	0.559469i
$834$	609.533			0.730855
$835$	−237.712	+	411.729i	−0.284685	+	0.493088i
$836$	−55.7193	+	32.1696i	−0.0666499	+	0.0384803i
$837$	−101.764	−	176.261i	−0.121582	−	0.210586i
$838$	−616.928	−	356.184i	−0.736191	−	0.425040i
$839$			165.698i			0.197494i	0.995113	+	0.0987471i	$0.0314835\pi$
$839$			165.698i			0.197494i	−0.995113	+	0.0987471i	$0.968517\pi$
$840$	99.3926	+	52.8533i	0.118324	+	0.0629206i
$841$	1745.57			2.07559
$842$	−555.238	+	961.701i	−0.659428	+	1.14216i
$843$	801.816	−	462.929i	0.951146	−	0.549144i
$844$	−335.612	−	581.297i	−0.397645	−	0.688741i
$845$	570.260	+	329.240i	0.674864	+	0.389633i
$846$		−	30.5414i		−	0.0361010i
$847$	−266.840	+	166.724i	−0.315041	+	0.196841i
$848$	−88.4838			−0.104344
$849$	387.352	−	670.913i	0.456245	−	0.790239i
$850$	236.747	−	136.686i	0.278525	−	0.160807i
$851$	−108.834	−	188.507i	−0.127890	−	0.221512i
$852$	−200.076	−	115.514i	−0.234831	−	0.135580i
$853$			1066.17i			1.24991i	0.780661	+	0.624955i	$0.214883\pi$
$853$			1066.17i			1.24991i	−0.780661	+	0.624955i	$0.785117\pi$
$854$	−1290.38	+	45.0070i	−1.51098	+	0.0527014i
$855$	21.0373			0.0246050
$856$	186.098	−	322.331i	0.217404	−	0.376555i
$857$	192.821	−	111.325i	0.224995	−	0.129901i	−0.383266	−	0.923638i	$-0.625201\pi$
$857$	192.821	−	111.325i	0.224995	−	0.129901i	0.608261	+	0.793737i	$0.291867\pi$
$858$	−409.801	−	709.796i	−0.477624	−	0.827269i
$859$	1313.46	+	758.329i	1.52906	+	0.882805i	0.999401	+	0.0345956i	$0.0110143\pi$
$859$	1313.46	+	758.329i	1.52906	+	0.882805i	0.529661	+	0.848209i	$0.322319\pi$
$860$			92.8497i			0.107965i
$861$	−15.5578	−	446.052i	−0.0180695	−	0.518063i
$862$	−321.190			−0.372610
$863$	−69.0180	+	119.543i	−0.0799745	+	0.138520i	−0.903239	−	0.429139i	$-0.858817\pi$
$863$	−69.0180	+	119.543i	−0.0799745	+	0.138520i	0.823264	+	0.567658i	$0.192151\pi$
$864$	−150.688	+	86.9997i	−0.174407	+	0.100694i
$865$	278.152	+	481.774i	0.321563	+	0.556964i
$866$	945.752	+	546.030i	1.09209	+	0.630520i
$867$			314.476i			0.362717i
$868$	−341.791	−	547.031i	−0.393769	−	0.630221i
$869$	−252.732			−0.290831
$870$	248.229	−	429.945i	0.285320	−	0.494189i
$871$	1874.36	−	1082.16i	2.15196	−	1.24243i
$872$	56.7825	+	98.3502i	0.0651176	+	0.112787i
$873$	−191.734	−	110.698i	−0.219627	−	0.126802i
$874$			32.4737i			0.0371552i
$875$	−36.7448	+	69.1000i	−0.0419941	+	0.0789715i
$876$	304.911			0.348072
$877$	308.810	−	534.875i	0.352121	−	0.609892i	−0.634500	−	0.772923i	$-0.718794\pi$
$877$	308.810	−	534.875i	0.352121	−	0.609892i	0.986621	+	0.163031i	$0.0521271\pi$
$878$	138.013	−	79.6818i	0.157190	−	0.0907538i
$879$	−436.650	−	756.300i	−0.496757	−	0.860409i
$880$	−335.653	−	193.789i	−0.381424	−	0.220215i
$881$		−	425.629i		−	0.483120i	−0.970386	−	0.241560i	$-0.922341\pi$
$881$		−	425.629i		−	0.483120i	0.970386	−	0.241560i	$-0.0776591\pi$
$882$	−162.446	+	332.992i	−0.184179	+	0.377542i
$883$	295.270			0.334394			0.167197	−	0.985923i	$-0.446528\pi$
$883$	295.270			0.334394			0.167197	+	0.985923i	$0.446528\pi$
$884$	549.332	−	951.471i	0.621416	−	1.07632i
$885$	315.661	−	182.247i	0.356679	−	0.205929i
$886$	−552.452	−	956.874i	−0.623535	−	1.07999i
$887$	−1463.38	−	844.884i	−1.64981	−	0.952519i	−0.977146	−	0.212571i	$-0.931816\pi$
$887$	−1463.38	−	844.884i	−1.64981	−	0.952519i	−0.672665	−	0.739947i	$-0.734850\pi$
$888$			381.037i			0.429096i
$889$	−1184.13	−	629.676i	−1.33198	−	0.708297i
$890$	410.680			0.461438
$891$	39.2432	−	67.9713i	0.0440440	−	0.0762865i
$892$	−116.329	+	67.1628i	−0.130414	+	0.0752946i
$893$	6.33354	+	10.9700i	0.00709244	+	0.0122845i
$894$	−54.2039	−	31.2946i	−0.0606308	−	0.0350052i
$895$			123.588i			0.138087i
$896$	721.895	−	451.048i	0.805686	−	0.503402i
$897$	−153.197			−0.170788
$898$	−270.928	+	469.261i	−0.301702	+	0.522563i
$899$	1725.18	−	996.035i	1.91900	−	1.10794i
$900$	−17.6442	−	30.5606i	−0.0196046	−	0.0339562i
$901$	83.6336	+	48.2859i	0.0928230	+	0.0535914i
$902$			809.129i			0.897039i
$903$	213.870	−	7.45956i	0.236844	−	0.00826087i
$904$	383.409			0.424124
$905$	−52.4359	+	90.8216i	−0.0579402	+	0.100355i
$906$	−802.911	+	463.561i	−0.886215	+	0.511657i
$907$	−221.038	−	382.848i	−0.243702	−	0.422104i	0.718064	−	0.695977i	$-0.245028\pi$
$907$	−221.038	−	382.848i	−0.243702	−	0.422104i	−0.961766	+	0.273873i	$0.911695\pi$
$908$	372.138	+	214.854i	0.409843	+	0.236623i
$909$			320.861i			0.352982i
$910$	29.6055	+	848.808i	0.0325335	+	0.932756i
$911$	998.378			1.09591			0.547957	−	0.836507i	$-0.315406\pi$
$911$	998.378			1.09591			0.547957	+	0.836507i	$0.315406\pi$
$912$	53.9804	−	93.4968i	0.0591890	−	0.102518i
$913$	159.443	−	92.0544i	0.174636	−	0.100826i
$914$	303.963	+	526.479i	0.332563	+	0.576016i
$915$	−245.462	−	141.718i	−0.268265	−	0.154883i
$916$			39.4834i			0.0431041i
$917$	−218.146	−	349.139i	−0.237891	−	0.380740i
$918$	284.096			0.309473
$919$	−154.797	+	268.116i	−0.168441	+	0.291748i	−0.937872	−	0.346982i	$-0.887206\pi$
$919$	−154.797	+	268.116i	−0.168441	+	0.291748i	0.769431	+	0.638730i	$0.220540\pi$
$920$	−33.0350	+	19.0728i	−0.0359077	+	0.0207313i
$921$	345.364	+	598.188i	0.374988	+	0.649499i
$922$	749.520	+	432.736i	0.812928	+	0.469344i
$923$			1220.62i			1.32245i
$924$	116.787	−	219.622i	0.126393	−	0.237686i
$925$	−264.906			−0.286385
$926$	−94.2280	+	163.208i	−0.101758	+	0.176250i
$927$	55.9605	−	32.3088i	0.0603674	−	0.0348531i
$928$	−851.526	−	1474.89i	−0.917593	−	1.58932i
$929$	−443.269	−	255.921i	−0.477146	−	0.275480i	0.242080	−	0.970256i	$-0.422170\pi$
$929$	−443.269	−	255.921i	−0.477146	−	0.275480i	−0.719226	+	0.694776i	$0.755504\pi$
$930$		−	382.351i		−	0.411130i
$931$	−10.7064	−	153.293i	−0.0114999	−	0.164654i
$932$	−626.737			−0.672464
$933$	207.085	−	358.682i	0.221956	−	0.384440i
$934$	777.476	−	448.876i	0.832415	−	0.480595i
$935$	211.503	+	366.334i	0.226206	+	0.391801i
$936$	232.248	+	134.089i	0.248129	+	0.143257i
$937$			592.935i			0.632801i	0.948626	+	0.316401i	$0.102474\pi$
$937$			592.935i			0.632801i	−0.948626	+	0.316401i	$0.897526\pi$
$938$	1566.04	+	832.762i	1.66955	+	0.887807i
$939$	−386.592			−0.411706
$940$	10.6240	−	18.4013i	0.0113021	−	0.0195759i
$941$	−549.458	+	317.230i	−0.583909	+	0.337120i	−0.762685	−	0.646770i	$-0.776119\pi$
$941$	−549.458	+	317.230i	−0.583909	+	0.337120i	0.178777	+	0.983890i	$0.442786\pi$
$942$	530.230	+	918.386i	0.562877	+	0.974932i
$943$	130.977	+	75.6198i	0.138894	+	0.0801907i
$944$		−	1870.54i		−	1.98150i
$945$	−68.9758	+	43.0969i	−0.0729903	+	0.0456051i
$946$	−387.956			−0.410101
$947$	−329.805	+	571.239i	−0.348263	+	0.603209i	−0.985941	−	0.167094i	$-0.946562\pi$
$947$	−329.805	+	571.239i	−0.348263	+	0.603209i	0.637678	+	0.770303i	$0.279895\pi$
$948$	−102.268	+	59.0444i	−0.107878	+	0.0622831i
$949$	−805.487	−	1395.14i	−0.848775	−	1.47012i
$950$	34.2261	+	19.7605i	0.0360275	+	0.0208005i
$951$			495.391i			0.520916i
$952$	−630.127	+	21.9781i	−0.661898	+	0.0230863i
$953$	−615.571			−0.645930			−0.322965	−	0.946411i	$-0.604680\pi$
$953$	−615.571			−0.645930			−0.322965	+	0.946411i	$0.604680\pi$
$954$	16.8309	−	29.1519i	0.0176424	−	0.0305576i
$955$	−38.9472	+	22.4862i	−0.0407824	+	0.0235457i
$956$	46.6996	+	80.8861i	0.0488489	+	0.0846088i
$957$	665.282	+	384.100i	0.695174	+	0.401359i
$958$			942.013i			0.983312i
$959$	40.4837	+	1160.69i	0.0422145	+	1.21032i
$960$	−18.9651			−0.0197553
$961$	286.605	−	496.415i	0.298237	−	0.516561i
$962$	−2489.68	+	1437.41i	−2.58802	+	1.49419i
$963$	134.455	+	232.883i	0.139621	+	0.241831i
$964$	−169.830	−	98.0515i	−0.176172	−	0.101713i
$965$			64.1825i			0.0665104i
$966$	−66.5255	−	106.473i	−0.0688669	−	0.110220i
$967$	386.702			0.399899			0.199949	−	0.979806i	$-0.435922\pi$
$967$	386.702			0.399899			0.199949	+	0.979806i	$0.435922\pi$
$968$	−93.3202	+	161.635i	−0.0964052	+	0.166979i
$969$	−102.043	+	58.9145i	−0.105307	+	0.0607993i
$970$	−207.959	−	360.195i	−0.214390	−	0.371335i
$971$	487.138	+	281.249i	0.501687	+	0.289649i	0.729410	−	0.684077i	$-0.239795\pi$
$971$	487.138	+	281.249i	0.501687	+	0.289649i	−0.227723	+	0.973726i	$0.573128\pi$
$972$		−	36.6727i		−	0.0377291i
$973$	458.885	−	862.950i	0.471619	−	0.886896i
$974$	1959.79			2.01211
$975$	−93.2216	+	161.465i	−0.0956119	+	0.165605i
$976$	−1259.68	+	727.279i	−1.29066	+	0.745163i
$977$	−356.041	−	616.682i	−0.364423	−	0.631199i	0.624260	−	0.781216i	$-0.285400\pi$
$977$	−356.041	−	616.682i	−0.364423	−	0.631199i	−0.988683	+	0.150017i	$0.952067\pi$
$978$	50.0351	+	28.8878i	0.0511607	+	0.0295376i
$979$			635.472i			0.649103i
$980$	−213.707	+	144.122i	−0.218069	+	0.147063i
$981$	−82.0504			−0.0836396
$982$	−578.178	+	1001.43i	−0.588776	+	1.01979i
$983$	1064.18	−	614.407i	1.08259	−	0.625032i	0.150995	−	0.988535i	$-0.451752\pi$
$983$	1064.18	−	614.407i	1.08259	−	0.625032i	0.931593	+	0.363502i	$0.118419\pi$
$984$	−132.375	−	229.281i	−0.134528	−	0.233009i
$985$	−434.619	−	250.928i	−0.441238	−	0.254749i
$986$			2780.64i			2.82012i
$987$	−43.2392	−	22.9930i	−0.0438087	−	0.0232959i
$988$	158.832			0.160761
$989$	−36.2577	+	62.8001i	−0.0366609	+	0.0634986i
$990$	127.692	−	73.7230i	0.128982	−	0.0744676i
$991$	621.249	+	1076.04i	0.626892	+	1.08581i	0.988172	+	0.153351i	$0.0490064\pi$
$991$	621.249	+	1076.04i	0.626892	+	1.08581i	−0.361280	+	0.932457i	$0.617660\pi$
$992$	−1135.90	−	655.811i	−1.14506	−	0.661100i
$993$		−	933.617i		−	0.940199i
$994$	−848.337	+	530.050i	−0.853457	+	0.533250i
$995$	711.202			0.714776
$996$	43.0123	−	74.4995i	0.0431850	−	0.0747987i
$997$	−694.350	+	400.883i	−0.696439	+	0.402089i	−0.806020	−	0.591889i	$-0.798382\pi$
$997$	−694.350	+	400.883i	−0.696439	+	0.402089i	0.109581	+	0.993978i	$0.465049\pi$
$998$	−800.920	−	1387.23i	−0.802525	−	1.39001i
$999$	−238.415	−	137.649i	−0.238654	−	0.137787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.a.61.1	yes	8
3.2	odd	2		315.3.w.a.271.4		8
5.2	odd	4		525.3.s.h.124.2		16
5.3	odd	4		525.3.s.h.124.7		16
5.4	even	2		525.3.o.l.376.4		8
7.2	even	3		735.3.h.a.391.7		8
7.3	odd	6	inner	105.3.n.a.31.1	✓	8
7.5	odd	6		735.3.h.a.391.8		8
21.17	even	6		315.3.w.a.136.4		8
35.3	even	12		525.3.s.h.199.2		16
35.17	even	12		525.3.s.h.199.7		16
35.24	odd	6		525.3.o.l.451.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.1	✓	8	7.3	odd	6	inner
105.3.n.a.61.1	yes	8	1.1	even	1	trivial
315.3.w.a.136.4		8	21.17	even	6
315.3.w.a.271.4		8	3.2	odd	2
525.3.o.l.376.4		8	5.4	even	2
525.3.o.l.451.4		8	35.24	odd	6
525.3.s.h.124.2		16	5.2	odd	4
525.3.s.h.124.7		16	5.3	odd	4
525.3.s.h.199.2		16	35.3	even	12
525.3.s.h.199.7		16	35.17	even	12
735.3.h.a.391.7		8	7.2	even	3
735.3.h.a.391.8		8	7.5	odd	6

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26021 + 2.18275i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.17628 - 2.03737i) q^{4} +(-1.93649 - 1.11803i) q^{5} -4.36551i q^{6} +(-6.18050 - 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.26021 + 2.18275i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.17628 - 2.03737i) q^{4} +(-1.93649 - 1.11803i) q^{5} -4.36551i q^{6} +(-6.18050 - 3.28656i) q^{7} -4.15226 q^{8} +(1.50000 - 2.59808i) q^{9} +(4.88079 - 2.81792i) q^{10} +(4.36036 + 7.55236i) q^{11} +(3.52883 + 2.03737i) q^{12} -21.5286i q^{13} +(14.9625 - 9.34874i) q^{14} +3.87298 q^{15} +(9.93785 - 17.2129i) q^{16} +(-18.7862 + 10.8462i) q^{17} +(3.78064 + 6.54826i) q^{18} +(-2.71590 - 1.56803i) q^{19} +5.26047i q^{20} +(12.1170 - 0.422628i) q^{21} -21.9799 q^{22} +(-2.05421 + 3.55799i) q^{23} +(6.22840 - 3.59597i) q^{24} +(2.50000 + 4.33013i) q^{25} +(46.9917 + 27.1307i) q^{26} +5.19615i q^{27} +(0.574033 + 16.4579i) q^{28} -50.8583 q^{29} +(-4.88079 + 8.45377i) q^{30} +(-33.9213 + 19.5845i) q^{31} +(16.7431 + 28.9999i) q^{32} +(-13.0811 - 7.55236i) q^{33} -54.6743i q^{34} +(8.29399 + 13.2744i) q^{35} -7.05767 q^{36} +(-26.4906 + 45.8831i) q^{37} +(6.84523 - 3.95209i) q^{38} +(18.6443 + 32.2929i) q^{39} +(8.04083 + 4.64237i) q^{40} -36.8122i q^{41} +(-14.3475 + 26.9810i) q^{42} +17.6504 q^{43} +(10.2580 - 17.7674i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(-5.17748 - 8.96766i) q^{46} +(-3.49804 - 2.01959i) q^{47} +34.4257i q^{48} +(27.3971 + 40.6251i) q^{49} -12.6021 q^{50} +(18.7862 - 32.5387i) q^{51} +(-43.8618 + 25.3236i) q^{52} +(-2.22593 - 3.85542i) q^{53} +(-11.3419 - 6.54826i) q^{54} -19.5001i q^{55} +(25.6631 + 13.6467i) q^{56} +5.43180 q^{57} +(64.0923 - 111.011i) q^{58} +(81.5032 - 47.0559i) q^{59} +(-4.55570 - 7.89071i) q^{60} +(-63.3781 - 36.5913i) q^{61} -98.7226i q^{62} +(-17.8095 + 11.1276i) q^{63} -4.89677 q^{64} +(-24.0697 + 41.6900i) q^{65} +(32.9699 - 19.0352i) q^{66} +(50.2661 + 87.0635i) q^{67} +(44.1956 + 25.5164i) q^{68} -7.11598i q^{69} +(-39.4270 + 1.37517i) q^{70} -56.6975 q^{71} +(-6.22840 + 10.7879i) q^{72} +(64.8042 - 37.4147i) q^{73} +(-66.7676 - 115.645i) q^{74} +(-7.50000 - 4.33013i) q^{75} +7.37773i q^{76} +(-2.12789 - 61.0079i) q^{77} -93.9833 q^{78} +(-14.4903 + 25.0980i) q^{79} +(-38.4891 + 22.2217i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(80.3519 + 46.3912i) q^{82} -21.1116i q^{83} +(-15.1140 - 24.1897i) q^{84} +48.5058 q^{85} +(-22.2433 + 38.5266i) q^{86} +(76.2875 - 44.0446i) q^{87} +(-18.1054 - 31.3594i) q^{88} +(63.1066 + 36.4346i) q^{89} -16.9075i q^{90} +(-70.7551 + 133.057i) q^{91} +9.66528 q^{92} +(33.9213 - 58.7535i) q^{93} +(8.81655 - 5.09024i) q^{94} +(3.50621 + 6.07294i) q^{95} +(-50.2293 - 28.9999i) q^{96} -73.7985i q^{97} +(-123.201 + 8.60469i) q^{98} +26.1622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9	\( 8 q + 2 q^{2} - 12 q^{3} - 6 q^{4} - 16 q^{7} - 32 q^{8} + 12 q^{9} + 20 q^{11} + 18 q^{12} - 16 q^{14} - 2 q^{16} - 18 q^{17} - 6 q^{18} + 48 q^{21} - 16 q^{22} + 62 q^{23} + 48 q^{24} + 20 q^{25} + 120 q^{26} - 120 q^{28} - 100 q^{29} - 126 q^{31} + 36 q^{32} - 60 q^{33} - 36 q^{36} - 80 q^{37} + 114 q^{38} - 12 q^{39} + 90 q^{40} + 90 q^{42} + 352 q^{43} - 18 q^{44} - 82 q^{46} - 72 q^{47} + 38 q^{49} + 20 q^{50} + 18 q^{51} - 48 q^{52} - 76 q^{53} + 18 q^{54} + 196 q^{56} - 40 q^{58} - 54 q^{59} - 60 q^{60} - 396 q^{61} - 96 q^{63} - 4 q^{64} - 60 q^{65} + 24 q^{66} + 184 q^{67} - 312 q^{68} + 164 q^{71} - 48 q^{72} + 348 q^{73} - 140 q^{74} - 60 q^{75} + 152 q^{77} - 240 q^{78} - 206 q^{79} - 36 q^{81} + 204 q^{82} + 132 q^{84} - 60 q^{85} + 178 q^{86} + 150 q^{87} + 124 q^{88} + 282 q^{89} - 114 q^{91} - 288 q^{92} + 126 q^{93} + 30 q^{94} - 120 q^{95} - 108 q^{96} - 592 q^{98} + 120 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 12 * q^3 - 6 * q^4 - 16 * q^7 - 32 * q^8 + 12 * q^9 + 20 * q^11 + 18 * q^12 - 16 * q^14 - 2 * q^16 - 18 * q^17 - 6 * q^18 + 48 * q^21 - 16 * q^22 + 62 * q^23 + 48 * q^24 + 20 * q^25 + 120 * q^26 - 120 * q^28 - 100 * q^29 - 126 * q^31 + 36 * q^32 - 60 * q^33 - 36 * q^36 - 80 * q^37 + 114 * q^38 - 12 * q^39 + 90 * q^40 + 90 * q^42 + 352 * q^43 - 18 * q^44 - 82 * q^46 - 72 * q^47 + 38 * q^49 + 20 * q^50 + 18 * q^51 - 48 * q^52 - 76 * q^53 + 18 * q^54 + 196 * q^56 - 40 * q^58 - 54 * q^59 - 60 * q^60 - 396 * q^61 - 96 * q^63 - 4 * q^64 - 60 * q^65 + 24 * q^66 + 184 * q^67 - 312 * q^68 + 164 * q^71 - 48 * q^72 + 348 * q^73 - 140 * q^74 - 60 * q^75 + 152 * q^77 - 240 * q^78 - 206 * q^79 - 36 * q^81 + 204 * q^82 + 132 * q^84 - 60 * q^85 + 178 * q^86 + 150 * q^87 + 124 * q^88 + 282 * q^89 - 114 * q^91 - 288 * q^92 + 126 * q^93 + 30 * q^94 - 120 * q^95 - 108 * q^96 - 592 * q^98 + 120 * q^99

Introduction

L-functions

Modular forms

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