LMFDB - Embedded newform 105.3.n.a.61.2

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			61.2
Root			$-0.336732 + 0.583237i$ of defining polynomial
Character	$\chi$	$=$	105.61
Dual form			105.3.n.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.336732 + 0.583237i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.77322 + 3.07131i) q^{4} +(1.93649 + 1.11803i) q^{5} -1.16647i q^{6} +(-6.82455 + 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.336732 + 0.583237i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.77322 + 3.07131i) q^{4} +(1.93649 + 1.11803i) q^{5} -1.16647i q^{6} +(-6.82455 + 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.30416 + 0.752955i) q^{10} +(0.0223800 + 0.0387632i) q^{11} +(-5.31967 - 3.07131i) q^{12} +23.0010i q^{13} +(1.38970 - 4.50476i) q^{14} -3.87298 q^{15} +(-5.38154 + 9.32109i) q^{16} +(-8.16292 + 4.71286i) q^{17} +(1.01020 + 1.74971i) q^{18} +(0.991050 + 0.572183i) q^{19} +7.93010i q^{20} +(8.88806 - 8.24636i) q^{21} -0.0301442 q^{22} +(22.1202 - 38.3133i) q^{23} +(7.62339 - 4.40136i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-13.4150 - 7.74518i) q^{26} +5.19615i q^{27} +(-16.8848 - 18.1987i) q^{28} +53.0004 q^{29} +(1.30416 - 2.25887i) q^{30} +(19.5690 - 11.2982i) q^{31} +(-13.7888 - 23.8829i) q^{32} +(-0.0671399 - 0.0387632i) q^{33} -6.34788i q^{34} +(-14.9569 - 4.61414i) q^{35} +10.6393 q^{36} +(-21.1418 + 36.6186i) q^{37} +(-0.667436 + 0.385344i) q^{38} +(-19.9195 - 34.5015i) q^{39} +(-9.84175 - 5.68214i) q^{40} +38.2787i q^{41} +(1.81669 + 7.96065i) q^{42} +76.5222 q^{43} +(-0.0793693 + 0.137472i) q^{44} +(5.80948 - 3.35410i) q^{45} +(14.8971 + 25.8026i) q^{46} +(-23.5070 - 13.5718i) q^{47} -18.6422i q^{48} +(44.1489 - 21.2574i) q^{49} -3.36732 q^{50} +(8.16292 - 14.1386i) q^{51} +(-70.6434 + 40.7860i) q^{52} +(-9.49388 - 16.4439i) q^{53} +(-3.03059 - 1.74971i) q^{54} +0.100086i q^{55} +(34.6841 - 7.91521i) q^{56} -1.98210 q^{57} +(-17.8469 + 30.9118i) q^{58} +(-4.21731 + 2.43486i) q^{59} +(-6.86766 - 11.8951i) q^{60} +(-33.6432 - 19.4239i) q^{61} +15.2178i q^{62} +(-6.19052 + 20.0668i) q^{63} -24.4798 q^{64} +(-25.7159 + 44.5413i) q^{65} +(0.0452163 - 0.0261056i) q^{66} +(3.50439 + 6.06978i) q^{67} +(-28.9494 - 16.7139i) q^{68} +76.6266i q^{69} +(7.72761 - 7.16970i) q^{70} -46.8735 q^{71} +(-7.62339 + 13.2041i) q^{72} +(72.3956 - 41.7976i) q^{73} +(-14.2382 - 24.6613i) q^{74} +(-7.50000 - 4.33013i) q^{75} +4.05843i q^{76} +(-0.213104 - 0.229686i) q^{77} +26.8301 q^{78} +(-10.2397 + 17.7357i) q^{79} +(-20.8426 + 12.0335i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-22.3256 - 12.8897i) q^{82} +125.683i q^{83} +(41.0877 + 12.6754i) q^{84} -21.0766 q^{85} +(-25.7674 + 44.6305i) q^{86} +(-79.5006 + 45.8997i) q^{87} +(-0.113741 - 0.197005i) q^{88} +(40.4455 + 23.3512i) q^{89} +4.51773i q^{90} +(-35.8223 - 156.972i) q^{91} +156.896 q^{92} +(-19.5690 + 33.8945i) q^{93} +(15.8311 - 9.14010i) q^{94} +(1.27944 + 2.21606i) q^{95} +(41.3663 + 23.8829i) q^{96} +3.11494i q^{97} +(-2.46826 + 32.9073i) q^{98} +0.134280 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 $

$2$	−0.336732	+	0.583237i	−0.168366	+	0.291618i	−0.937845	−	0.347053i	$-0.887182\pi$
$2$	−0.336732	+	0.583237i	−0.168366	+	0.291618i	0.769480	+	0.638671i	$0.220516\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	1.77322	+	3.07131i	0.443306	+	0.767828i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		−	1.16647i		−	0.194412i
$7$	−6.82455	+	1.55742i	−0.974935	+	0.222489i
$7$	−6.82455	+	1.55742i	−0.974935	+	0.222489i
$8$	−5.08226			−0.635282
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−1.30416	+	0.752955i	−0.130416	+	0.0752955i
$11$	0.0223800	+	0.0387632i	0.00203454	+	0.00352393i	0.867041	−	0.498237i	$-0.166019\pi$
$11$	0.0223800	+	0.0387632i	0.00203454	+	0.00352393i	−0.865006	+	0.501761i	$0.832686\pi$
$12$	−5.31967	−	3.07131i	−0.443306	−	0.255943i
$13$			23.0010i			1.76931i	0.466246	+	0.884655i	$0.345606\pi$
$13$			23.0010i			1.76931i	−0.466246	+	0.884655i	$0.654394\pi$
$14$	1.38970	−	4.50476i	0.0992641	−	0.321768i
$15$	−3.87298			−0.258199
$16$	−5.38154	+	9.32109i	−0.336346	+	0.582568i
$17$	−8.16292	+	4.71286i	−0.480172	+	0.277227i	−0.720488	−	0.693467i	$-0.756082\pi$
$17$	−8.16292	+	4.71286i	−0.480172	+	0.277227i	0.240316	+	0.970695i	$0.422749\pi$
$18$	1.01020	+	1.74971i	0.0561220	+	0.0972061i
$19$	0.991050	+	0.572183i	0.0521605	+	0.0301149i	0.525853	−	0.850575i	$-0.323746\pi$
$19$	0.991050	+	0.572183i	0.0521605	+	0.0301149i	−0.473693	+	0.880690i	$0.657079\pi$
$20$			7.93010i			0.396505i
$21$	8.88806	−	8.24636i	0.423241	−	0.392684i
$22$	−0.0301442			−0.00137019
$23$	22.1202	−	38.3133i	0.961748	−	1.66580i	0.243637	−	0.969866i	$-0.421659\pi$
$23$	22.1202	−	38.3133i	0.961748	−	1.66580i	0.718110	−	0.695929i	$-0.245007\pi$
$24$	7.62339	−	4.40136i	0.317641	−	0.183390i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−13.4150	−	7.74518i	−0.515963	−	0.297891i
$27$			5.19615i			0.192450i
$28$	−16.8848	−	18.1987i	−0.603028	−	0.649952i
$29$	53.0004			1.82760			0.913799	−	0.406166i	$-0.133134\pi$
$29$	53.0004			1.82760			0.913799	+	0.406166i	$0.133134\pi$
$30$	1.30416	−	2.25887i	0.0434719	−	0.0752955i
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	−0.149981	−	0.988689i	$-0.547921\pi$
$31$	19.5690	−	11.2982i	0.631258	−	0.364457i	0.781239	+	0.624232i	$0.214588\pi$
$32$	−13.7888	−	23.8829i	−0.430899	−	0.746340i
$33$	−0.0671399	−	0.0387632i	−0.00203454	−	0.00117464i
$34$		−	6.34788i		−	0.186702i
$35$	−14.9569	−	4.61414i	−0.427341	−	0.131833i
$36$	10.6393			0.295537
$37$	−21.1418	+	36.6186i	−0.571400	+	0.989693i	0.425023	+	0.905183i	$0.360266\pi$
$37$	−21.1418	+	36.6186i	−0.571400	+	0.989693i	−0.996423	+	0.0845106i	$0.973067\pi$
$38$	−0.667436	+	0.385344i	−0.0175641	+	0.0101406i
$39$	−19.9195	−	34.5015i	−0.510756	−	0.884655i
$40$	−9.84175	−	5.68214i	−0.246044	−	0.142053i
$41$			38.2787i			0.933628i	0.884356	+	0.466814i	$0.154598\pi$
$41$			38.2787i			0.933628i	−0.884356	+	0.466814i	$0.845402\pi$
$42$	1.81669	+	7.96065i	0.0432545	+	0.189539i
$43$	76.5222			1.77959			0.889793	−	0.456365i	$-0.150849\pi$
$43$	76.5222			1.77959			0.889793	+	0.456365i	$0.150849\pi$
$44$	−0.0793693	+	0.137472i	−0.00180385	+	0.00312436i
$45$	5.80948	−	3.35410i	0.129099	−	0.0745356i
$46$	14.8971	+	25.8026i	0.323851	+	0.560926i
$47$	−23.5070	−	13.5718i	−0.500149	−	0.288761i	0.228626	−	0.973514i	$-0.426577\pi$
$47$	−23.5070	−	13.5718i	−0.500149	−	0.288761i	−0.728775	+	0.684753i	$0.759910\pi$
$48$		−	18.6422i		−	0.388379i
$49$	44.1489	−	21.2574i	0.900998	−	0.433824i
$50$	−3.36732			−0.0673464
$51$	8.16292	−	14.1386i	0.160057	−	0.277227i
$52$	−70.6434	+	40.7860i	−1.35853	+	0.784345i
$53$	−9.49388	−	16.4439i	−0.179130	−	0.310262i	0.762453	−	0.647044i	$-0.223995\pi$
$53$	−9.49388	−	16.4439i	−0.179130	−	0.310262i	−0.941583	+	0.336782i	$0.890662\pi$
$54$	−3.03059	−	1.74971i	−0.0561220	−	0.0324020i
$55$			0.100086i			0.00181975i
$56$	34.6841	−	7.91521i	0.619359	−	0.141343i
$57$	−1.98210			−0.0347737
$58$	−17.8469	+	30.9118i	−0.307705	+	0.532961i
$59$	−4.21731	+	2.43486i	−0.0714798	+	0.0412689i	−0.535314	−	0.844653i	$-0.679807\pi$
$59$	−4.21731	+	2.43486i	−0.0714798	+	0.0412689i	0.463834	+	0.885922i	$0.346473\pi$
$60$	−6.86766	−	11.8951i	−0.114461	−	0.198252i
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	0.198210	−	0.980160i	$-0.436487\pi$
$61$	−33.6432	−	19.4239i	−0.551528	−	0.318425i	−0.749738	+	0.661735i	$0.769821\pi$
$62$			15.2178i			0.245449i
$63$	−6.19052	+	20.0668i	−0.0982623	+	0.318521i
$64$	−24.4798			−0.382497
$65$	−25.7159	+	44.5413i	−0.395630	+	0.685251i
$66$	0.0452163	−	0.0261056i	0.000685095	−	0.000395540i
$67$	3.50439	+	6.06978i	0.0523043	+	0.0905938i	0.890992	−	0.454019i	$-0.150010\pi$
$67$	3.50439	+	6.06978i	0.0523043	+	0.0905938i	−0.838688	+	0.544612i	$0.816677\pi$
$68$	−28.9494	−	16.7139i	−0.425726	−	0.245793i
$69$			76.6266i			1.11053i
$70$	7.72761	−	7.16970i	0.110394	−	0.102424i
$71$	−46.8735			−0.660190			−0.330095	−	0.943948i	$-0.607081\pi$
$71$	−46.8735			−0.660190			−0.330095	+	0.943948i	$0.607081\pi$
$72$	−7.62339	+	13.2041i	−0.105880	+	0.183390i
$73$	72.3956	−	41.7976i	0.991720	−	0.572570i	0.0859319	−	0.996301i	$-0.472613\pi$
$73$	72.3956	−	41.7976i	0.991720	−	0.572570i	0.905788	+	0.423731i	$0.139280\pi$
$74$	−14.2382	−	24.6613i	−0.192408	−	0.333261i
$75$	−7.50000	−	4.33013i	−0.100000	−	0.0577350i
$76$			4.05843i			0.0534004i
$77$	−0.213104	−	0.229686i	−0.00276758	−	0.00298294i
$78$	26.8301			0.343975
$79$	−10.2397	+	17.7357i	−0.129617	+	0.224502i	−0.923528	−	0.383531i	$-0.874708\pi$
$79$	−10.2397	+	17.7357i	−0.129617	+	0.224502i	0.793912	+	0.608033i	$0.208041\pi$
$80$	−20.8426	+	12.0335i	−0.260533	+	0.150419i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−22.3256	−	12.8897i	−0.272263	−	0.157191i
$83$			125.683i			1.51425i	0.653271	+	0.757124i	$0.273396\pi$
$83$			125.683i			1.51425i	−0.653271	+	0.757124i	$0.726604\pi$
$84$	41.0877	+	12.6754i	0.489139	+	0.150897i
$85$	−21.0766			−0.247960
$86$	−25.7674	+	44.6305i	−0.299621	+	0.518960i
$87$	−79.5006	+	45.8997i	−0.913799	+	0.527582i
$88$	−0.113741	−	0.197005i	−0.00129251	−	0.00223869i
$89$	40.4455	+	23.3512i	0.454444	+	0.262373i	0.709705	−	0.704499i	$-0.248828\pi$
$89$	40.4455	+	23.3512i	0.454444	+	0.262373i	−0.255261	+	0.966872i	$0.582162\pi$
$90$			4.51773i			0.0501970i
$91$	−35.8223	−	156.972i	−0.393651	−	1.72496i
$92$	156.896			1.70539
$93$	−19.5690	+	33.8945i	−0.210419	+	0.364457i
$94$	15.8311	−	9.14010i	0.168416	−	0.0972351i
$95$	1.27944	+	2.21606i	0.0134678	+	0.0233269i
$96$	41.3663	+	23.8829i	0.430899	+	0.248780i
$97$			3.11494i			0.0321128i	0.999871	+	0.0160564i	$0.00511112\pi$
$97$			3.11494i			0.0321128i	−0.999871	+	0.0160564i	$0.994889\pi$
$98$	−2.46826	+	32.9073i	−0.0251863	+	0.335789i
$99$	0.134280			0.00135636
$100$	−8.86612	+	15.3566i	−0.0886612	+	0.153566i
$101$	−77.4555	+	44.7189i	−0.766886	+	0.442762i	−0.831763	−	0.555132i	$-0.812668\pi$
$101$	−77.4555	+	44.7189i	−0.766886	+	0.442762i	0.0648768	+	0.997893i	$0.479335\pi$
$102$	5.49743	+	9.52183i	0.0538964	+	0.0933512i
$103$	−79.1385	−	45.6906i	−0.768335	−	0.443598i	0.0639453	−	0.997953i	$-0.479632\pi$
$103$	−79.1385	−	45.6906i	−0.768335	−	0.443598i	−0.832280	+	0.554355i	$0.812965\pi$
$104$		−	116.897i		−	1.12401i
$105$	26.4314	−	6.03186i	0.251727	−	0.0574463i
$106$	12.7876			0.120637
$107$	52.5515	−	91.0219i	0.491136	−	0.850672i	−0.508812	−	0.860877i	$-0.669915\pi$
$107$	52.5515	−	91.0219i	0.491136	−	0.850672i	0.999948	+	0.0102057i	$0.00324864\pi$
$108$	−15.9590	+	9.21394i	−0.147769	+	0.0853143i
$109$	−27.8507	−	48.2388i	−0.255511	−	0.442558i	0.709523	−	0.704682i	$-0.248910\pi$
$109$	−27.8507	−	48.2388i	−0.255511	−	0.442558i	−0.965034	+	0.262124i	$0.915577\pi$
$110$	−0.0583739	−	0.0337022i	−0.000530672	−	0.000306384i
$111$		−	73.2373i		−	0.659795i
$112$	22.2097	−	71.9936i	0.198301	−	0.642800i
$113$	−5.25425			−0.0464978			−0.0232489	−	0.999730i	$-0.507401\pi$
$113$	−5.25425			−0.0464978			−0.0232489	+	0.999730i	$0.507401\pi$
$114$	0.667436	−	1.15603i	0.00585470	−	0.0101406i
$115$	85.6711	−	49.4623i	0.744967	−	0.430107i
$116$	93.9815	+	162.781i	0.810185	+	1.40328i
$117$	59.7584	+	34.5015i	0.510756	+	0.294885i
$118$		−	3.27958i		−	0.0277931i
$119$	48.3683	−	44.8763i	0.406457	−	0.377111i
$120$	19.6835			0.164029
$121$	60.4990	−	104.787i	0.499992	−	0.866011i
$122$	22.6575	−	13.0813i	0.185717	−	0.107224i
$123$	−33.1504	−	57.4181i	−0.269515	−	0.466814i
$124$	69.4005	+	40.0684i	0.559681	+	0.323132i
$125$			11.1803i			0.0894427i
$126$	−9.61916	−	10.3677i	−0.0763425	−	0.0822832i
$127$	−5.54989			−0.0436999			−0.0218500	−	0.999761i	$-0.506956\pi$
$127$	−5.54989			−0.0436999			−0.0218500	+	0.999761i	$0.506956\pi$
$128$	63.3983	−	109.809i	0.495299	−	0.857883i
$129$	−114.783	+	66.2701i	−0.889793	+	0.513722i
$130$	−17.3187	−	29.9969i	−0.133221	−	0.230746i
$131$	−144.212	−	83.2606i	−1.10085	−	0.635577i	−0.164407	−	0.986393i	$-0.552571\pi$
$131$	−144.212	−	83.2606i	−1.10085	−	0.635577i	−0.936445	+	0.350815i	$0.885904\pi$
$132$		−	0.274943i		−	0.00208290i
$133$	−7.65460	−	2.36141i	−0.0575534	−	0.0177550i
$134$	−4.72016			−0.0352251
$135$	−5.80948	+	10.0623i	−0.0430331	+	0.0745356i
$136$	41.4861	−	23.9520i	0.305045	−	0.176118i
$137$	−36.4731	−	63.1733i	−0.266227	−	0.461119i	0.701657	−	0.712515i	$-0.252444\pi$
$137$	−36.4731	−	63.1733i	−0.266227	−	0.461119i	−0.967884	+	0.251395i	$0.919111\pi$
$138$	−44.6914	−	25.8026i	−0.323851	−	0.186975i
$139$			114.994i			0.827292i	0.910438	+	0.413646i	$0.135745\pi$
$139$			114.994i			0.827292i	−0.910438	+	0.413646i	$0.864255\pi$
$140$	−12.3505	−	54.1193i	−0.0882178	−	0.386567i
$141$	47.0140			0.333433
$142$	15.7838	−	27.3383i	0.111153	−	0.192523i
$143$	−0.891594	+	0.514762i	−0.00623492	+	0.00359973i
$144$	16.1446	+	27.9633i	0.112115	+	0.194189i
$145$	102.635	+	59.2562i	0.707826	+	0.408664i
$146$			56.2983i			0.385605i
$147$	−47.8139	+	70.1201i	−0.325265	+	0.477008i
$148$	−149.956			−1.01322
$149$	−36.3729	+	62.9997i	−0.244113	+	0.422817i	−0.961882	−	0.273465i	$-0.911830\pi$
$149$	−36.3729	+	62.9997i	−0.244113	+	0.422817i	0.717769	+	0.696282i	$0.245164\pi$
$150$	5.05098	−	2.91618i	0.0336732	−	0.0194412i
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	0.996033	−	0.0889823i	$-0.0283615\pi$
$151$	63.5643	+	110.097i	0.420956	+	0.729117i	−0.575078	+	0.818099i	$0.695028\pi$
$152$	−5.03677	−	2.90798i	−0.0331366	−	0.0191315i
$153$			28.2772i			0.184818i
$154$	0.205720	−	0.0469471i	0.00133585	−	0.000304851i
$155$	50.5270			0.325980
$156$	70.6434	−	122.358i	0.452842	−	0.784345i
$157$	130.826	−	75.5327i	0.833290	−	0.481100i	−0.0216880	−	0.999765i	$-0.506904\pi$
$157$	130.826	−	75.5327i	0.833290	−	0.481100i	0.854978	+	0.518665i	$0.173571\pi$
$158$	−6.89607	−	11.9443i	−0.0436460	−	0.0755971i
$159$	28.4816	+	16.4439i	0.179130	+	0.103421i
$160$		−	61.6653i		−	0.385408i
$161$	−91.2904	+	295.921i	−0.567021	+	1.83802i
$162$	6.06117			0.0374146
$163$	29.9639	−	51.8990i	0.183828	−	0.318399i	−0.759353	−	0.650679i	$-0.774485\pi$
$163$	29.9639	−	51.8990i	0.183828	−	0.318399i	0.943181	+	0.332280i	$0.107818\pi$
$164$	−117.566	+	67.8768i	−0.716866	+	0.413883i
$165$	−0.0866772	−	0.150129i	−0.000525316	−	0.000909875i
$166$	−73.3027	−	42.3213i	−0.441582	−	0.254948i
$167$		−	224.089i		−	1.34185i	−0.741526	−	0.670924i	$-0.765898\pi$
$167$		−	224.089i		−	1.34185i	0.741526	−	0.670924i	$-0.234102\pi$
$168$	−45.1714	+	41.9101i	−0.268877	+	0.249465i
$169$	−360.047			−2.13046
$170$	7.09715	−	12.2926i	0.0417479	−	0.0723096i
$171$	2.97315	−	1.71655i	0.0173868	−	0.0100383i
$172$	135.691	+	235.024i	0.788901	+	1.36642i
$173$	165.080	+	95.3092i	0.954221	+	0.550920i	0.894390	−	0.447288i	$-0.147610\pi$
$173$	165.080	+	95.3092i	0.954221	+	0.550920i	0.0598317	+	0.998208i	$0.480944\pi$
$174$		−	61.8235i		−	0.355307i
$175$	−23.8052	−	25.6576i	−0.136030	−	0.146615i
$176$	−0.481754			−0.00273724
$177$	4.21731	−	7.30459i	0.0238266	−	0.0412689i
$178$	−27.2386	+	15.7262i	−0.153026	+	0.0883494i
$179$	−108.931	−	188.674i	−0.608553	−	1.05404i	−0.991479	−	0.130265i	$-0.958417\pi$
$179$	−108.931	−	188.674i	−0.608553	−	1.05404i	0.382926	−	0.923779i	$-0.374916\pi$
$180$	20.6030	+	11.8951i	0.114461	+	0.0660841i
$181$			39.0804i			0.215914i	0.994156	+	0.107957i	$0.0344309\pi$
$181$			39.0804i			0.215914i	−0.994156	+	0.107957i	$0.965569\pi$
$182$	103.614	+	31.9645i	0.569308	+	0.175629i
$183$	67.2865			0.367686
$184$	−112.421	+	194.718i	−0.610981	+	1.05825i
$185$	−81.8818	+	47.2745i	−0.442604	+	0.255538i
$186$	−13.1790	−	22.8267i	−0.0708549	−	0.122724i
$187$	−0.365372	−	0.210947i	−0.00195386	−	0.00112806i
$188$		−	96.2632i		−	0.512038i
$189$	−8.09259	−	35.4614i	−0.0428179	−	0.187626i
$190$	−1.72331			−0.00907006
$191$	−94.7586	+	164.127i	−0.496118	+	0.859302i	−0.999990	−	0.00447651i	$-0.998575\pi$
$191$	−94.7586	+	164.127i	−0.496118	+	0.859302i	0.503872	+	0.863778i	$0.331908\pi$
$192$	36.7197	−	21.2001i	0.191249	−	0.110417i
$193$	136.570	+	236.547i	0.707619	+	1.22563i	0.965738	+	0.259519i	$0.0835640\pi$
$193$	136.570	+	236.547i	0.707619	+	1.22563i	−0.258119	+	0.966113i	$0.583103\pi$
$194$	−1.81675	−	1.04890i	−0.00936467	−	0.00540669i
$195$		−	89.0826i		−	0.456834i
$196$	143.574	+	97.9010i	0.732520	+	0.499495i
$197$	198.898			1.00963			0.504817	−	0.863226i	$-0.331560\pi$
$197$	198.898			1.00963			0.504817	+	0.863226i	$0.331560\pi$
$198$	−0.0452163	+	0.0783168i	−0.000228365	+	0.000395540i
$199$	33.2334	−	19.1873i	0.167002	−	0.0964185i	−0.414170	−	0.910200i	$-0.635928\pi$
$199$	33.2334	−	19.1873i	0.167002	−	0.0964185i	0.581171	+	0.813781i	$0.302595\pi$
$200$	−12.7056	−	22.0068i	−0.0635282	−	0.110034i
$201$	−10.5132	−	6.06978i	−0.0523043	−	0.0301979i
$202$		−	60.2331i		−	0.298184i
$203$	−361.704	+	82.5438i	−1.78179	+	0.406620i
$204$	57.8987			0.283817
$205$	−42.7969	+	74.1265i	−0.208766	+	0.361593i
$206$	53.2969	−	30.7710i	0.258723	−	0.149374i
$207$	−66.3606	−	114.940i	−0.320583	−	0.555265i
$208$	−214.395	−	123.781i	−1.03074	−	0.595100i
$209$			0.0512217i			0.000245080i
$210$	−5.38228	+	17.4469i	−0.0256299	+	0.0830802i
$211$	−127.283			−0.603238			−0.301619	−	0.953429i	$-0.597527\pi$
$211$	−127.283			−0.603238			−0.301619	+	0.953429i	$0.597527\pi$
$212$	33.6695	−	58.3173i	0.158819	−	0.275082i
$213$	70.3102	−	40.5936i	0.330095	−	0.190580i
$214$	35.3915	+	61.2999i	0.165381	+	0.286448i
$215$	148.185	+	85.5544i	0.689230	+	0.397927i
$216$		−	26.4082i		−	0.122260i
$217$	−115.954	+	107.582i	−0.534349	+	0.495770i
$218$	37.5129			0.172077
$219$	−72.3956	+	125.393i	−0.330573	+	0.572570i
$220$	−0.307396	+	0.177475i	−0.00139725	+	0.000806705i
$221$	−108.401	−	187.756i	−0.490501	−	0.849573i
$222$	42.7147	+	24.6613i	0.192408	+	0.111087i
$223$			293.558i			1.31641i	0.752841	+	0.658203i	$0.228683\pi$
$223$			293.558i			1.31641i	−0.752841	+	0.658203i	$0.771317\pi$
$224$	131.298	+	141.515i	0.586151	+	0.631763i
$225$	15.0000			0.0666667
$226$	1.76927	−	3.06447i	0.00782864	−	0.0135596i
$227$	186.611	−	107.740i	0.822077	−	0.474626i	−0.0290554	−	0.999578i	$-0.509250\pi$
$227$	186.611	−	107.740i	0.822077	−	0.474626i	0.851132	+	0.524952i	$0.175917\pi$
$228$	−3.51471	−	6.08765i	−0.0154154	−	0.0267002i
$229$	124.938	+	72.1332i	0.545582	+	0.314992i	0.747338	−	0.664444i	$-0.231332\pi$
$229$	124.938	+	72.1332i	0.545582	+	0.314992i	−0.201756	+	0.979436i	$0.564665\pi$
$230$			66.6221i			0.289661i
$231$	0.518570	+	0.159976i	0.00224489	+	0.000692539i
$232$	−269.361			−1.16104
$233$	143.216	−	248.058i	0.614662	−	1.06463i	−0.375781	−	0.926708i	$-0.622626\pi$
$233$	143.216	−	248.058i	0.614662	−	1.06463i	0.990444	−	0.137918i	$-0.0440410\pi$
$234$	−40.2451	+	23.2355i	−0.171988	+	0.0992971i
$235$	−30.3474	−	52.5633i	−0.129138	−	0.223673i
$236$	−14.9565	−	8.63511i	−0.0633748	−	0.0365895i
$237$		−	35.4714i		−	0.149668i
$238$	9.88632	+	43.3214i	0.0415392	+	0.182023i
$239$	−413.420			−1.72979			−0.864895	−	0.501954i	$-0.832615\pi$
$239$	−413.420			−1.72979			−0.864895	+	0.501954i	$0.832615\pi$
$240$	20.8426	−	36.1004i	0.0868442	−	0.150419i
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.136948	−	0.990578i	$-0.456271\pi$
$241$	256.252	−	147.947i	1.06329	−	0.613890i	0.926340	+	0.376689i	$0.122937\pi$
$242$	40.7439	+	70.5705i	0.168363	+	0.291613i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		−	137.772i		−	0.564639i
$245$	109.260	+	8.19523i	0.445961	+	0.0334499i
$246$	44.6511			0.181509
$247$	−13.1608	+	22.7952i	−0.0532826	+	0.0922881i
$248$	−99.4547	+	57.4202i	−0.401027	+	0.231533i
$249$	−108.844	−	188.524i	−0.437126	−	0.757124i
$250$	−6.52078	−	3.76478i	−0.0260831	−	0.0150591i
$251$		−	311.712i		−	1.24188i	−0.783858	−	0.620940i	$-0.786751\pi$
$251$		−	311.712i		−	1.24188i	0.783858	−	0.620940i	$-0.213249\pi$
$252$	−72.6087	+	16.5699i	−0.288130	+	0.0657537i
$253$	1.98020			0.00782686
$254$	1.86882	−	3.23690i	0.00735758	−	0.0127437i
$255$	31.6149	−	18.2528i	0.123980	−	0.0715798i
$256$	−6.26320	−	10.8482i	−0.0244656	−	0.0423757i
$257$	−125.335	−	72.3619i	−0.487683	−	0.281564i	0.235930	−	0.971770i	$-0.424186\pi$
$257$	−125.335	−	72.3619i	−0.487683	−	0.281564i	−0.723613	+	0.690206i	$0.757520\pi$
$258$		−	89.2610i		−	0.345973i
$259$	87.2525	−	282.832i	0.336882	−	1.09202i
$260$	−182.400			−0.701540
$261$	79.5006	−	137.699i	0.304600	−	0.527582i
$262$	97.1213	−	56.0730i	0.370692	−	0.214019i
$263$	114.833	+	198.896i	0.436626	+	0.756258i	0.997427	−	0.0716928i	$-0.0228401\pi$
$263$	114.833	+	198.896i	0.436626	+	0.756258i	−0.560801	+	0.827950i	$0.689507\pi$
$264$	0.341222	+	0.197005i	0.00129251	+	0.000746230i
$265$		−	42.4579i		−	0.160219i
$266$	3.95481	−	3.66928i	0.0148677	−	0.0137943i
$267$	−80.8910			−0.302962
$268$	−12.4281	+	21.5262i	−0.0463736	+	0.0803215i
$269$	367.508	−	212.181i	1.36620	−	0.788776i	0.375760	−	0.926717i	$-0.377382\pi$
$269$	367.508	−	212.181i	1.36620	−	0.788776i	0.990440	+	0.137941i	$0.0440485\pi$
$270$	−3.91247	−	6.77660i	−0.0144906	−	0.0250985i
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.887604	−	0.460607i	$-0.152368\pi$
$271$	252.710	+	145.902i	0.932509	+	0.538385i	0.0449051	+	0.998991i	$0.485701\pi$
$272$		−	101.450i		−	0.372977i
$273$	189.675	+	204.434i	0.694779	+	0.748844i
$274$	49.1267			0.179294
$275$	−0.111900	+	0.193816i	−0.000406908	+	0.000704786i
$276$	−235.344	+	135.876i	−0.852697	+	0.492305i
$277$	101.450	+	175.717i	0.366247	+	0.634358i	0.988975	−	0.148080i	$-0.0473092\pi$
$277$	101.450	+	175.717i	0.366247	+	0.634358i	−0.622729	+	0.782438i	$0.713976\pi$
$278$	−67.0684	−	38.7220i	−0.241253	−	0.139288i
$279$		−	67.7890i		−	0.242971i
$280$	76.0149	+	23.4503i	0.271482	+	0.0837510i
$281$	254.325			0.905071			0.452536	−	0.891746i	$-0.350520\pi$
$281$	254.325			0.905071			0.452536	+	0.891746i	$0.350520\pi$
$282$	−15.8311	+	27.4203i	−0.0561387	+	0.0972351i
$283$	384.259	−	221.852i	1.35781	−	0.783930i	0.368478	−	0.929636i	$-0.379879\pi$
$283$	384.259	−	221.852i	1.35781	−	0.783930i	0.989328	+	0.145706i	$0.0465455\pi$
$284$	−83.1172	−	143.963i	−0.292666	−	0.506912i
$285$	−3.83832	−	2.21606i	−0.0134678	−	0.00777563i
$286$		−	0.693347i		−	0.00242429i
$287$	−59.6161	−	261.235i	−0.207722	−	0.910227i
$288$	−82.7327			−0.287266
$289$	−100.078	+	173.340i	−0.346290	+	0.599792i
$290$	−69.1208	+	39.9069i	−0.238348	+	0.137610i
$291$	−2.69761	−	4.67241i	−0.00927015	−	0.0160564i
$292$	256.747	+	148.233i	0.879270	+	0.507647i
$293$		−	223.513i		−	0.762845i	−0.924401	−	0.381422i	$-0.875434\pi$
$293$		−	223.513i		−	0.762845i	0.924401	−	0.381422i	$-0.124566\pi$
$294$	−24.7962	−	51.4985i	−0.0843406	−	0.175165i
$295$	−10.8890			−0.0369120
$296$	107.448	−	186.105i	0.363000	−	0.628734i
$297$	−0.201420	+	0.116290i	−0.000678180	+	0.000391548i
$298$	−24.4958	−	42.4280i	−0.0822007	−	0.142376i
$299$	881.245	+	508.787i	2.94731	+	1.70163i
$300$		−	30.7131i		−	0.102377i
$301$	−522.229	+	119.177i	−1.73498	+	0.395937i
$302$	−85.6165			−0.283498
$303$	77.4555	−	134.157i	0.255629	−	0.442762i
$304$	−10.6667	+	6.15845i	−0.0350880	+	0.0202580i
$305$	−43.4332	−	75.2285i	−0.142404	−	0.246651i
$306$	−16.4923	−	9.52183i	−0.0538964	−	0.0311171i
$307$		−	47.3887i		−	0.154361i	−0.997017	−	0.0771803i	$-0.975408\pi$
$307$		−	47.3887i		−	0.154361i	0.997017	−	0.0771803i	$-0.0245917\pi$
$308$	0.327559	−	1.06179i	0.00106350	−	0.00344738i
$309$	158.277			0.512223
$310$	−17.0140	+	29.4692i	−0.0548840	+	0.0950619i
$311$	−313.595	+	181.054i	−1.00834	+	0.582167i	−0.910706	−	0.413055i	$-0.864462\pi$
$311$	−313.595	+	181.054i	−1.00834	+	0.582167i	−0.0976367	+	0.995222i	$0.531128\pi$
$312$	101.236	+	175.346i	0.324474	+	0.562005i
$313$	−340.880	−	196.807i	−1.08907	−	0.628777i	−0.155744	−	0.987797i	$-0.549778\pi$
$313$	−340.880	−	196.807i	−1.08907	−	0.628777i	−0.933330	+	0.359020i	$0.883111\pi$
$314$			101.737i			0.324003i
$315$	−34.4233	+	31.9380i	−0.109280	+	0.101391i
$316$	−72.6291			−0.229839
$317$	−288.788	+	500.196i	−0.911004	+	1.57791i	−0.0983557	+	0.995151i	$0.531358\pi$
$317$	−288.788	+	500.196i	−0.911004	+	1.57791i	−0.812648	+	0.582754i	$0.801975\pi$
$318$	−19.1813	+	11.0744i	−0.0603187	+	0.0348250i
$319$	1.18615	+	2.05446i	0.00371833	+	0.00644033i
$320$	−47.4049	−	27.3693i	−0.148140	−	0.0855289i
$321$			182.044i			0.567114i
$322$	−141.852	−	152.890i	−0.440533	−	0.474814i
$323$	−10.7865			−0.0333947
$324$	15.9590	−	27.6418i	0.0492562	−	0.0853143i
$325$	−99.5974	+	57.5026i	−0.306453	+	0.176931i
$326$	20.1796	+	34.9521i	0.0619006	+	0.107215i
$327$	83.5521	+	48.2388i	0.255511	+	0.147519i
$328$		−	194.542i		−	0.593117i
$329$	181.562	+	56.0109i	0.551859	+	0.170246i
$330$	0.116748			0.000353781
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	−0.693388	−	0.720565i	$-0.743883\pi$
$331$	91.7974	−	158.998i	0.277333	−	0.480356i	0.970721	+	0.240209i	$0.0772160\pi$
$332$	−386.011	+	222.863i	−1.16268	+	0.671275i
$333$	63.4254	+	109.856i	0.190467	+	0.329898i
$334$	130.697	+	75.4578i	0.391307	+	0.225921i
$335$			15.6721i			0.0467824i
$336$	29.0337	+	127.224i	0.0864099	+	0.378644i
$337$	−205.885			−0.610934			−0.305467	−	0.952203i	$-0.598813\pi$
$337$	−205.885			−0.610934			−0.305467	+	0.952203i	$0.598813\pi$
$338$	121.239	−	209.993i	0.358696	−	0.621280i
$339$	7.88138	−	4.55032i	0.0232489	−	0.0134228i
$340$	−37.3735	−	64.7327i	−0.109922	−	0.190390i
$341$	0.875907	+	0.505705i	0.00256864	+	0.00148301i
$342$			2.31207i			0.00676043i
$343$	−268.190	+	213.830i	−0.781894	+	0.623412i
$344$	−388.905			−1.13054
$345$	−85.6711	+	148.387i	−0.248322	+	0.430107i
$346$	−111.176	+	64.1872i	−0.321317	+	0.185512i
$347$	−99.7256	−	172.730i	−0.287394	−	0.497780i	0.685793	−	0.727796i	$-0.259455\pi$
$347$	−99.7256	−	172.730i	−0.287394	−	0.497780i	−0.973187	+	0.230016i	$0.926122\pi$
$348$	−281.944	−	162.781i	−0.810185	−	0.467761i
$349$		−	391.231i		−	1.12101i	−0.828152	−	0.560503i	$-0.810608\pi$
$349$		−	391.231i		−	1.12101i	0.828152	−	0.560503i	$-0.189392\pi$
$350$	22.9804	−	5.24433i	0.0656583	−	0.0149838i
$351$	−119.517			−0.340504
$352$	0.617185	−	1.06900i	0.00175337	−	0.00303692i
$353$	−81.1020	+	46.8243i	−0.229751	+	0.132647i	−0.610457	−	0.792049i	$-0.709014\pi$
$353$	−81.1020	+	46.8243i	−0.229751	+	0.132647i	0.380706	+	0.924696i	$0.375681\pi$
$354$	2.84020	+	4.91937i	0.00802317	+	0.0138965i
$355$	−90.7701	−	52.4061i	−0.255690	−	0.147623i
$356$			165.628i			0.465246i
$357$	−33.6885	+	109.203i	−0.0943656	+	0.305890i
$358$	146.722			0.409838
$359$	−73.8759	+	127.957i	−0.205782	+	0.356426i	−0.950382	−	0.311086i	$-0.899307\pi$
$359$	−73.8759	+	127.957i	−0.205782	+	0.356426i	0.744599	+	0.667512i	$0.232641\pi$
$360$	−29.5252	+	17.0464i	−0.0820146	+	0.0473511i
$361$	−179.845	−	311.501i	−0.498186	−	0.862884i
$362$	−22.7931	−	13.1596i	−0.0629644	−	0.0363525i
$363$			209.575i			0.577341i
$364$	418.588	−	388.367i	1.14997	−	1.06694i
$365$	186.925			0.512122
$366$	−22.6575	+	39.2439i	−0.0619057	+	0.107224i
$367$	−71.5485	+	41.3085i	−0.194955	+	0.112557i	−0.594300	−	0.804243i	$-0.702571\pi$
$367$	−71.5485	+	41.3085i	−0.194955	+	0.112557i	0.399345	+	0.916801i	$0.369238\pi$
$368$	238.081	+	412.369i	0.646960	+	1.12057i
$369$	99.4511	+	57.4181i	0.269515	+	0.155605i
$370$		−	63.6753i		−	0.172095i
$371$	90.4014	+	97.4361i	0.243670	+	0.262631i
$372$	−138.801			−0.373121
$373$	171.325	−	296.744i	0.459318	−	0.795561i	−0.539607	−	0.841917i	$-0.681427\pi$
$373$	171.325	−	296.744i	0.459318	−	0.795561i	0.998925	+	0.0463554i	$0.0147607\pi$
$374$	0.246064	−	0.142065i	0.000657926	−	0.000379854i
$375$	−9.68246	−	16.7705i	−0.0258199	−	0.0447214i
$376$	119.469	+	68.9752i	0.317736	+	0.183445i
$377$			1219.06i			3.23359i
$378$	23.4074	+	7.22108i	0.0619244	+	0.0191034i
$379$	355.679			0.938467			0.469233	−	0.883074i	$-0.344530\pi$
$379$	355.679			0.938467			0.469233	+	0.883074i	$0.344530\pi$
$380$	−4.53747	+	7.85912i	−0.0119407	+	0.0206819i
$381$	8.32483	−	4.80635i	0.0218500	−	0.0126151i
$382$	−63.8164	−	110.533i	−0.167059	−	0.289354i
$383$	−144.616	−	83.4939i	−0.377586	−	0.218000i	0.299181	−	0.954196i	$-0.403286\pi$
$383$	−144.616	−	83.4939i	−0.377586	−	0.218000i	−0.676768	+	0.736197i	$0.736620\pi$
$384$			219.618i			0.571922i
$385$	−0.155876	−	0.683043i	−0.000404873	−	0.00177414i
$386$	−183.950			−0.476556
$387$	114.783	−	198.810i	0.296598	−	0.513722i
$388$	−9.56695	+	5.52348i	−0.0246571	+	0.0142358i
$389$	−79.6452	−	137.950i	−0.204744	−	0.354626i	0.745307	−	0.666721i	$-0.232303\pi$
$389$	−79.6452	−	137.950i	−0.204744	−	0.354626i	−0.950051	+	0.312095i	$0.898969\pi$
$390$	51.9562	+	29.9969i	0.133221	+	0.0769152i
$391$			416.998i			1.06649i
$392$	−224.376	+	108.035i	−0.572388	+	0.275601i
$393$	288.423			0.733901
$394$	−66.9753	+	116.005i	−0.169988	+	0.294428i
$395$	−39.6582	+	22.8967i	−0.100401	+	0.0579663i
$396$	0.238108	+	0.412415i	0.000601283	+	0.00104145i
$397$	−510.352	−	294.652i	−1.28552	−	0.742196i	−0.307669	−	0.951494i	$-0.599549\pi$
$397$	−510.352	−	294.652i	−1.28552	−	0.742196i	−0.977852	+	0.209298i	$0.932882\pi$
$398$			25.8439i			0.0649344i
$399$	13.5269	−	3.08696i	0.0339021	−	0.00773675i
$400$	−53.8154			−0.134538
$401$	83.1535	−	144.026i	0.207365	−	0.359167i	−0.743518	−	0.668716i	$-0.766844\pi$
$401$	83.1535	−	144.026i	0.207365	−	0.359167i	0.950884	+	0.309548i	$0.100178\pi$
$402$	7.08024	−	4.08778i	0.0176125	−	0.0101686i
$403$	259.870	+	450.107i	0.644838	+	1.11689i
$404$	−274.692	−	158.593i	−0.679930	−	0.392558i
$405$		−	20.1246i		−	0.0496904i
$406$	73.6545	−	238.754i	0.181415	−	0.588064i
$407$	−1.89261			−0.00465014
$408$	−41.4861	+	71.8560i	−0.101682	+	0.176118i
$409$	−189.742	+	109.548i	−0.463917	+	0.267843i	−0.713690	−	0.700462i	$-0.752977\pi$
$409$	−189.742	+	109.548i	−0.463917	+	0.267843i	0.249773	+	0.968304i	$0.419644\pi$
$410$	−28.8222	−	49.9215i	−0.0702980	−	0.121760i
$411$	109.419	+	63.1733i	0.266227	+	0.153706i
$412$		−	324.079i		−	0.786599i
$413$	24.9891	−	23.1850i	0.0605063	−	0.0561379i
$414$	89.3829			0.215901
$415$	−140.517	+	243.383i	−0.338596	+	0.586466i
$416$	549.331	−	317.156i	1.32051	−	0.762395i
$417$	−99.5873	−	172.490i	−0.238819	−	0.413646i
$418$	−0.0298744	−	0.0172480i	−7.14698e−5	−	4.12631e-5i
$419$		−	554.704i		−	1.32388i	−0.749558	−	0.661938i	$-0.769734\pi$
$419$		−	554.704i		−	1.32388i	0.749558	−	0.661938i	$-0.230266\pi$
$420$	65.3944	+	70.4831i	0.155701	+	0.167817i
$421$	642.342			1.52575			0.762876	−	0.646545i	$-0.223787\pi$
$421$	642.342			1.52575			0.762876	+	0.646545i	$0.223787\pi$
$422$	42.8603	−	74.2362i	0.101565	−	0.175915i
$423$	−70.5210	+	40.7153i	−0.166716	+	0.0962537i
$424$	48.2503	+	83.5720i	0.113798	+	0.197104i
$425$	−40.8146	−	23.5643i	−0.0960344	−	0.0554455i
$426$			54.6767i			0.128349i
$427$	259.851	+	80.1629i	0.608550	+	0.187735i
$428$	372.742			0.870893
$429$	0.891594	−	1.54429i	0.00207831	−	0.00359973i
$430$	−99.7969	+	57.6178i	−0.232086	+	0.133995i
$431$	−37.6661	−	65.2395i	−0.0873923	−	0.151368i	0.819016	−	0.573771i	$-0.194520\pi$
$431$	−37.6661	−	65.2395i	−0.0873923	−	0.151368i	−0.906408	+	0.422403i	$0.861187\pi$
$432$	−48.4338	−	27.9633i	−0.112115	−	0.0647298i
$433$		−	353.064i		−	0.815391i	−0.913118	−	0.407695i	$-0.866333\pi$
$433$		−	353.064i		−	0.815391i	0.913118	−	0.407695i	$-0.133667\pi$
$434$	−23.7005	−	103.855i	−0.0546095	−	0.239297i
$435$	−205.270			−0.471884
$436$	98.7710	−	171.076i	0.226539	−	0.392377i
$437$	43.8444	−	25.3136i	0.100331	−	0.0579259i
$438$	−48.7558	−	84.4475i	−0.111315	−	0.192802i
$439$	−235.512	−	135.973i	−0.536473	−	0.309733i	0.207175	−	0.978304i	$-0.433573\pi$
$439$	−235.512	−	135.973i	−0.536473	−	0.309733i	−0.743648	+	0.668571i	$0.766906\pi$
$440$		−	0.508664i		−	0.00115605i
$441$	10.9951	−	146.588i	0.0249321	−	0.332400i
$442$	146.008			0.330335
$443$	55.1204	−	95.4714i	0.124425	−	0.215511i	−0.797083	−	0.603870i	$-0.793625\pi$
$443$	55.1204	−	95.4714i	0.124425	−	0.215511i	0.921508	+	0.388359i	$0.126958\pi$
$444$	224.935	−	129.866i	0.506610	−	0.292491i
$445$	52.2149	+	90.4389i	0.117337	+	0.203233i
$446$	−171.214	−	98.8504i	−0.383888	−	0.221638i
$447$		−	125.999i		−	0.281878i
$448$	167.064	−	38.1253i	0.372910	−	0.0851012i
$449$	59.1007			0.131627			0.0658137	−	0.997832i	$-0.479036\pi$
$449$	59.1007			0.131627			0.0658137	+	0.997832i	$0.479036\pi$
$450$	−5.05098	+	8.74855i	−0.0112244	+	0.0194412i
$451$	−1.48381	+	0.856677i	−0.00329004	+	0.00189950i
$452$	−9.31696	−	16.1375i	−0.0206127	−	0.0357023i
$453$	−190.693	−	110.097i	−0.420956	−	0.243039i
$454$			145.118i			0.319643i
$455$	106.130	−	344.025i	0.233253	−	0.756098i
$456$	10.0735			0.0220911
$457$	102.638	−	177.775i	0.224592	−	0.389004i	−0.731605	−	0.681729i	$-0.761228\pi$
$457$	102.638	−	177.775i	0.224592	−	0.389004i	0.956197	+	0.292724i	$0.0945618\pi$
$458$	−84.1414	+	48.5791i	−0.183715	+	0.106068i
$459$	−24.4888	−	42.4158i	−0.0533524	−	0.0924091i
$460$	303.828	+	175.415i	0.660496	+	0.381338i
$461$		−	466.172i		−	1.01122i	−0.862762	−	0.505610i	$-0.831268\pi$
$461$		−	466.172i		−	1.01122i	0.862762	−	0.505610i	$-0.168732\pi$
$462$	−0.267923	+	0.248580i	−0.000579920	+	0.000538051i
$463$	191.705			0.414051			0.207025	−	0.978336i	$-0.433622\pi$
$463$	191.705			0.414051			0.207025	+	0.978336i	$0.433622\pi$
$464$	−285.223	+	494.021i	−0.614706	+	1.06470i
$465$	−75.7905	+	43.7576i	−0.162990	+	0.0941024i
$466$	96.4510	+	167.058i	0.206976	+	0.358493i
$467$	−730.261	−	421.617i	−1.56373	−	0.902819i	−0.996874	−	0.0790015i	$-0.974827\pi$
$467$	−730.261	−	421.617i	−1.56373	−	0.902819i	−0.566855	−	0.823818i	$-0.691840\pi$
$468$			244.716i			0.522897i
$469$	−33.3691	−	35.9657i	−0.0711494	−	0.0766859i
$470$	40.8758			0.0869697
$471$	−130.826	+	226.598i	−0.277763	+	0.481100i
$472$	21.4334	−	12.3746i	0.0454098	−	0.0262174i
$473$	1.71256	+	2.96625i	0.00362064	+	0.00627113i
$474$	20.6882	+	11.9443i	0.0436460	+	0.0251990i
$475$			5.72183i			0.0120460i
$476$	223.597	+	68.9786i	0.469741	+	0.144913i
$477$	−56.9633			−0.119420
$478$	139.212	−	241.121i	0.291237	−	0.504438i
$479$	−246.540	+	142.340i	−0.514698	+	0.297161i	−0.734763	−	0.678324i	$-0.762707\pi$
$479$	−246.540	+	142.340i	−0.514698	+	0.297161i	0.220065	+	0.975485i	$0.429373\pi$
$480$	53.4037	+	92.4980i	0.111258	+	0.192704i
$481$	−842.267	−	486.283i	−1.75107	−	1.01098i
$482$			199.274i			0.413432i
$483$	−119.340	−	522.942i	−0.247080	−	1.08270i
$484$	429.113			0.886597
$485$	−3.48261	+	6.03205i	−0.00718063	+	0.0124372i
$486$	−9.09176	+	5.24913i	−0.0187073	+	0.0108007i
$487$	97.8228	+	169.434i	0.200868	+	0.347914i	0.948808	−	0.315852i	$-0.102290\pi$
$487$	97.8228	+	169.434i	0.200868	+	0.347914i	−0.747940	+	0.663766i	$0.768957\pi$
$488$	170.984	+	98.7174i	0.350376	+	0.202290i
$489$			103.798i			0.212266i
$490$	−41.5712	+	60.9651i	−0.0848392	+	0.124419i
$491$	745.464			1.51826			0.759128	−	0.650941i	$-0.225625\pi$
$491$	745.464			1.51826			0.759128	+	0.650941i	$0.225625\pi$
$492$	117.566	−	203.630i	0.238955	−	0.413883i
$493$	−432.638	+	249.784i	−0.877562	+	0.506660i
$494$	−8.86332	−	15.3517i	−0.0179419	−	0.0310763i
$495$	0.260032	+	0.150129i	0.000525316	+	0.000303292i
$496$			243.206i			0.490335i
$497$	319.890	−	73.0017i	0.643642	−	0.146885i
$498$	146.605			0.294388
$499$	−45.9747	+	79.6306i	−0.0921337	+	0.159580i	−0.908409	−	0.418083i	$-0.862702\pi$
$499$	−45.9747	+	79.6306i	−0.0921337	+	0.159580i	0.816275	+	0.577663i	$0.196035\pi$
$500$	−34.3383	+	19.8252i	−0.0686766	+	0.0396505i
$501$	194.066	+	336.133i	0.387358	+	0.670924i
$502$	181.802	+	104.963i	0.362155	+	0.209090i
$503$			672.220i			1.33642i	0.743972	+	0.668211i	$0.232940\pi$
$503$			672.220i			1.33642i	−0.743972	+	0.668211i	$0.767060\pi$
$504$	31.4618	−	101.985i	0.0624243	−	0.202351i
$505$	−199.989			−0.396018
$506$	−0.666795	+	1.15492i	−0.00131778	+	0.00228246i
$507$	540.071	−	311.810i	1.06523	−	0.615010i
$508$	−9.84119	−	17.0454i	−0.0193724	−	0.0335540i
$509$	282.238	+	162.950i	0.554495	+	0.320138i	0.750933	−	0.660378i	$-0.229604\pi$
$509$	282.238	+	162.950i	0.554495	+	0.320138i	−0.196438	+	0.980516i	$0.562937\pi$
$510$			24.5853i			0.0482064i
$511$	−428.970	+	398.000i	−0.839473	+	0.778865i
$512$	515.622			1.00707
$513$	−2.97315	+	5.14965i	−0.00579561	+	0.0100383i
$514$	84.4082	−	48.7331i	0.164218	−	0.0948115i
$515$	−102.167	−	176.959i	−0.198383	−	0.343610i
$516$	−407.073	−	235.024i	−0.788901	−	0.455472i
$517$		−	1.21494i		−	0.00234999i
$518$	135.577	+	146.127i	0.261733	+	0.282099i
$519$	−330.161			−0.636148
$520$	130.695	−	226.370i	0.251336	−	0.435328i
$521$	515.449	−	297.595i	0.989346	−	0.571199i	0.0842672	−	0.996443i	$-0.473145\pi$
$521$	515.449	−	297.595i	0.989346	−	0.571199i	0.905079	+	0.425244i	$0.139812\pi$
$522$	53.5407	+	92.7353i	0.102568	+	0.177654i
$523$	−43.6490	−	25.2007i	−0.0834588	−	0.0481850i	0.457690	−	0.889112i	$-0.348677\pi$
$523$	−43.6490	−	25.2007i	−0.0834588	−	0.0481850i	−0.541149	+	0.840927i	$0.682010\pi$
$524$		−	590.559i		−	1.12702i
$525$	57.9279	+	17.8705i	0.110339	+	0.0340391i
$526$	−154.671			−0.294051
$527$	−106.494	+	184.452i	−0.202075	+	0.350004i
$528$	0.722631	−	0.417211i	0.00136862	−	0.000790173i
$529$	−714.106	−	1236.87i	−1.34992	−	2.33812i
$530$	24.7630	+	14.2969i	0.0467227	+	0.0269753i
$531$			14.6092i			0.0275126i
$532$	−6.32068	−	27.6970i	−0.0118810	−	0.0520620i
$533$	−880.451			−1.65188
$534$	27.2386	−	47.1786i	0.0510085	−	0.0883494i
$535$	203.531	−	117.509i	0.380432	−	0.219642i
$536$	−17.8102	−	30.8482i	−0.0332280	−	0.0575526i
$537$	326.793	+	188.674i	0.608553	+	0.351348i
$538$			285.792i			0.531212i
$539$	1.81205	+	1.23561i	0.00336188	+	0.00229242i
$540$	−41.2060			−0.0763074
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	0.000512769		1.00000i	$0.499837\pi$
$541$	−468.381	+	811.260i	−0.865769	+	1.49956i	−0.866282	+	0.499556i	$0.833497\pi$
$542$	−170.191	+	98.2598i	−0.314006	+	0.181291i
$543$	−33.8446	−	58.6206i	−0.0623290	−	0.107957i
$544$	225.113	+	129.969i	0.413812	+	0.238914i
$545$		−	124.552i		−	0.228536i
$546$	−183.103	+	41.7857i	−0.335354	+	0.0765306i
$547$	−3.89041			−0.00711227			−0.00355613	−	0.999994i	$-0.501132\pi$
$547$	−3.89041			−0.00711227			−0.00355613	+	0.999994i	$0.501132\pi$
$548$	129.350	−	224.041i	0.236040	−	0.408834i
$549$	−100.930	+	58.2718i	−0.183843	+	0.106142i
$550$	−0.0753604	−	0.130528i	−0.000137019	−	0.000237324i
$551$	52.5260	+	30.3259i	0.0953285	+	0.0550379i
$552$		−	389.436i		−	0.705500i
$553$	42.2594	−	136.986i	0.0764185	−	0.247714i
$554$	−136.646			−0.246654
$555$	81.8818	−	141.823i	0.147535	−	0.255538i
$556$	−353.181	+	203.909i	−0.635218	+	0.366743i
$557$	−193.381	−	334.945i	−0.347183	−	0.601338i	0.638565	−	0.769568i	$-0.279528\pi$
$557$	−193.381	−	334.945i	−0.347183	−	0.601338i	−0.985748	+	0.168230i	$0.946195\pi$
$558$	39.5370	+	22.8267i	0.0708549	+	0.0409081i
$559$			1760.09i			3.14864i
$560$	123.500	−	114.584i	0.220536	−	0.204614i
$561$	0.730743			0.00130257
$562$	−85.6393	+	148.332i	−0.152383	+	0.263935i
$563$	−105.001	+	60.6226i	−0.186503	+	0.107678i	−0.590345	−	0.807151i	$-0.701008\pi$
$563$	−105.001	+	60.6226i	−0.186503	+	0.107678i	0.403841	+	0.914829i	$0.367675\pi$
$564$	83.3663	+	144.395i	0.147813	+	0.256019i
$565$	−10.1748	−	5.87443i	−0.0180085	−	0.0103972i
$566$			298.819i			0.527948i
$567$	42.8493	+	46.1837i	0.0755720	+	0.0814527i
$568$	238.223			0.419407
$569$	−204.955	+	354.993i	−0.360202	+	0.623889i	−0.987994	−	0.154493i	$-0.950626\pi$
$569$	−204.955	+	354.993i	−0.360202	+	0.623889i	0.627792	+	0.778381i	$0.283959\pi$
$570$	2.58497	−	1.49243i	0.00453503	−	0.00261830i
$571$	287.861	+	498.591i	0.504136	+	0.873188i	0.999989	+	0.00478199i	$0.00152216\pi$
$571$	287.861	+	498.591i	0.504136	+	0.873188i	−0.495853	+	0.868406i	$0.665145\pi$
$572$	−3.16199	−	1.82558i	−0.00552796	−	0.00319157i
$573$		−	328.253i		−	0.572868i
$574$	172.436	+	53.1959i	0.300412	+	0.0926758i
$575$	221.202			0.384699
$576$	−36.7197	+	63.6004i	−0.0637495	+	0.110417i
$577$	−202.254	+	116.772i	−0.350527	+	0.202377i	−0.664917	−	0.746917i	$-0.731533\pi$
$577$	−202.254	+	116.772i	−0.350527	+	0.202377i	0.314390	+	0.949294i	$0.398200\pi$
$578$	−67.3988	−	116.738i	−0.116607	−	0.201969i
$579$	−409.711	−	236.547i	−0.707619	−	0.408544i
$580$			420.298i			0.724652i
$581$	−195.741	−	857.727i	−0.336903	−	1.47629i
$582$	3.63349			0.00624311
$583$	0.424945	−	0.736027i	0.000728894	−	0.00126248i
$584$	−367.933	+	212.426i	−0.630022	+	0.363743i
$585$	77.1478	+	133.624i	0.131877	+	0.228417i
$586$	130.361	+	75.2641i	0.222459	+	0.128437i
$587$			606.882i			1.03387i	0.856024	+	0.516935i	$0.172927\pi$
$587$			606.882i			1.03387i	−0.856024	+	0.516935i	$0.827073\pi$
$588$	−300.146	−	22.5128i	−0.510452	−	0.0382872i
$589$	25.8585			0.0439024
$590$	3.66668	−	6.35088i	0.00621472	−	0.0107642i
$591$	−298.347	+	172.251i	−0.504817	+	0.291456i
$592$	−227.551	−	394.129i	−0.384376	−	0.665759i
$593$	−701.998	−	405.299i	−1.18381	−	0.683472i	−0.226915	−	0.973914i	$-0.572864\pi$
$593$	−701.998	−	405.299i	−1.18381	−	0.683472i	−0.956892	+	0.290443i	$0.906197\pi$
$594$		−	0.156634i		−	0.000263693i
$595$	143.838	−	32.8251i	0.241745	−	0.0551682i
$596$	−257.989			−0.432867
$597$	−33.2334	+	57.5619i	−0.0556673	+	0.0964185i
$598$	−593.487	+	342.650i	−0.992453	+	0.572993i
$599$	511.389	+	885.752i	0.853738	+	1.47872i	0.877811	+	0.479007i	$0.159003\pi$
$599$	511.389	+	885.752i	0.853738	+	1.47872i	−0.0240732	+	0.999710i	$0.507663\pi$
$600$	38.1169	+	22.0068i	0.0635282	+	0.0366780i
$601$			147.884i			0.246063i	0.992403	+	0.123032i	$0.0392617\pi$
$601$			147.884i			0.246063i	−0.992403	+	0.123032i	$0.960738\pi$
$602$	106.343	−	344.714i	0.176649	−	0.572614i
$603$	21.0263			0.0348696
$604$	−225.427	+	390.452i	−0.373224	+	0.646443i
$605$	234.312	−	135.280i	0.387292	−	0.223603i
$606$	52.1634	+	90.3497i	0.0860783	+	0.149092i
$607$	815.490	+	470.823i	1.34348	+	0.775656i	0.987316	−	0.158769i	$-0.0507524\pi$
$607$	815.490	+	470.823i	1.34348	+	0.775656i	0.356160	+	0.934425i	$0.384086\pi$
$608$		−	31.5588i		−	0.0519060i
$609$	471.070	−	437.060i	0.773514	−	0.717669i
$610$	58.5014			0.0959039
$611$	312.165	−	540.685i	0.510908	−	0.884919i
$612$	−86.8481	+	50.1418i	−0.141909	+	0.0819310i
$613$	−180.068	−	311.886i	−0.293748	−	0.508786i	0.680945	−	0.732335i	$-0.261569\pi$
$613$	−180.068	−	311.886i	−0.293748	−	0.508786i	−0.974693	+	0.223548i	$0.928236\pi$
$614$	27.6388	+	15.9573i	0.0450144	+	0.0259891i
$615$		−	148.253i		−	0.241062i
$616$	1.08305	+	1.16733i	0.00175819	+	0.00189501i
$617$	769.687			1.24747			0.623734	−	0.781637i	$-0.285615\pi$
$617$	769.687			1.24747			0.623734	+	0.781637i	$0.285615\pi$
$618$	−53.2969	+	92.3129i	−0.0862409	+	0.149374i
$619$	−853.542	+	492.793i	−1.37890	+	0.796111i	−0.992028	−	0.126020i	$-0.959780\pi$
$619$	−853.542	+	492.793i	−1.37890	+	0.796111i	−0.386877	+	0.922131i	$0.626446\pi$
$620$	89.5956	+	155.184i	0.144509	+	0.250297i
$621$	199.082	+	114.940i	0.320583	+	0.185088i
$622$		−	243.866i		−	0.392068i
$623$	−312.390	−	96.3709i	−0.501428	−	0.154688i
$624$	428.790			0.687163
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	229.570	−	132.542i	0.366726	−	0.211729i
$627$	−0.0443593	−	0.0768326i	−7.07485e−5	−	0.000122540i
$628$	463.969	+	267.873i	0.738804	+	0.426549i
$629$		−	398.554i		−	0.633630i
$630$	−7.03600	−	30.8315i	−0.0111683	−	0.0489388i
$631$	−89.7688			−0.142264			−0.0711322	−	0.997467i	$-0.522661\pi$
$631$	−89.7688			−0.142264			−0.0711322	+	0.997467i	$0.522661\pi$
$632$	52.0408	−	90.1373i	0.0823431	−	0.142622i
$633$	190.925	−	110.230i	0.301619	−	0.174140i
$634$	−194.488	−	336.864i	−0.306764	−	0.531331i
$635$	−10.7473	−	6.20497i	−0.0169249	−	0.00977160i
$636$			116.635i			0.183388i
$637$	488.941	+	1015.47i	0.767569	+	1.59414i
$638$	−1.59765			−0.00250416
$639$	−70.3102	+	121.781i	−0.110032	+	0.190580i
$640$	245.540	−	141.763i	0.383657	−	0.221504i
$641$	214.166	+	370.947i	0.334113	+	0.578701i	0.983314	−	0.181916i	$-0.0582300\pi$
$641$	214.166	+	370.947i	0.334113	+	0.578701i	−0.649201	+	0.760617i	$0.724897\pi$
$642$	−106.175	−	61.2999i	−0.165381	−	0.0954827i
$643$			111.498i			0.173403i	0.996234	+	0.0867015i	$0.0276326\pi$
$643$			111.498i			0.173403i	−0.996234	+	0.0867015i	$0.972367\pi$
$644$	−1070.75	+	244.353i	−1.66265	+	0.379431i
$645$	−296.369			−0.459487
$646$	3.63215	−	6.29107i	0.00562253	−	0.00973850i
$647$	−250.033	+	144.357i	−0.386450	+	0.223117i	−0.680621	−	0.732636i	$-0.738290\pi$
$647$	−250.033	+	144.357i	−0.386450	+	0.223117i	0.294171	+	0.955753i	$0.404957\pi$
$648$	22.8702	+	39.6123i	0.0352934	+	0.0611300i
$649$	−0.188766	−	0.108984i	−0.000290857	−	0.000167926i
$650$		−	77.4518i		−	0.119157i
$651$	80.7616	−	261.792i	0.124058	−	0.402138i
$652$	212.531			0.325967
$653$	−426.848	+	739.322i	−0.653672	+	1.13219i	0.328553	+	0.944485i	$0.393439\pi$
$653$	−426.848	+	739.322i	−0.653672	+	1.13219i	−0.982225	+	0.187707i	$0.939894\pi$
$654$	−56.2693	+	32.4871i	−0.0860387	+	0.0496744i
$655$	−186.176	−	322.467i	−0.284239	−	0.492316i
$656$	−356.800	−	205.998i	−0.543902	−	0.314022i
$657$		−	250.786i		−	0.381713i
$658$	−93.8052	+	87.0327i	−0.142561	+	0.132269i
$659$	−288.693			−0.438077			−0.219039	−	0.975716i	$-0.570292\pi$
$659$	−288.693			−0.438077			−0.219039	+	0.975716i	$0.570292\pi$
$660$	0.307396	−	0.532426i	0.000465752	−	0.000806705i
$661$	182.367	−	105.289i	0.275895	−	0.159288i	−0.355668	−	0.934612i	$-0.615747\pi$
$661$	182.367	−	105.289i	0.275895	−	0.159288i	0.631564	+	0.775324i	$0.282413\pi$
$662$	61.8222	+	107.079i	0.0933870	+	0.161751i
$663$	325.202	+	187.756i	0.490501	+	0.283191i
$664$		−	638.751i		−	0.961974i
$665$	−12.1829	−	13.1309i	−0.0183202	−	0.0197458i
$666$	−85.4293			−0.128272
$667$	1172.38	−	2030.62i	1.75769	−	3.04441i
$668$	688.246	−	397.359i	1.03031	−	0.594849i
$669$	−254.229	−	440.338i	−0.380013	−	0.658203i
$670$	−9.14055	−	5.27730i	−0.0136426	−	0.00787656i
$671$		−	1.73883i		−	0.00259140i
$672$	−319.502	−	98.5650i	−0.475450	−	0.146674i
$673$	760.139			1.12948			0.564739	−	0.825269i	$-0.308977\pi$
$673$	760.139			1.12948			0.564739	+	0.825269i	$0.308977\pi$
$674$	69.3279	−	120.080i	0.102860	−	0.178160i
$675$	−22.5000	+	12.9904i	−0.0333333	+	0.0192450i
$676$	−638.444	−	1105.82i	−0.944444	−	1.63583i
$677$	163.263	+	94.2600i	0.241157	+	0.139232i	0.615708	−	0.787974i	$-0.288870\pi$
$677$	163.263	+	94.2600i	0.241157	+	0.139232i	−0.374552	+	0.927206i	$0.622203\pi$
$678$			6.12894i			0.00903974i
$679$	−4.85126	−	21.2580i	−0.00714472	−	0.0313079i
$680$	107.117			0.157524
$681$	−186.611	+	323.220i	−0.274026	+	0.474626i
$682$	−0.589892	+	0.340574i	−0.000864944	+	0.000499375i
$683$	−260.243	−	450.754i	−0.381029	−	0.659962i	0.610181	−	0.792262i	$-0.291097\pi$
$683$	−260.243	−	450.754i	−0.381029	−	0.659962i	−0.991210	+	0.132301i	$0.957764\pi$
$684$	10.5441	+	6.08765i	0.0154154	+	0.00890007i
$685$		−	163.113i		−	0.238121i
$686$	−34.4057	−	228.421i	−0.0501541	−	0.332976i
$687$	−249.877			−0.363721
$688$	−411.807	+	713.270i	−0.598556	+	1.03673i
$689$	378.226	−	218.369i	0.548949	−	0.316936i
$690$	−57.6964	−	99.9331i	−0.0836180	−	0.144831i
$691$	590.615	+	340.991i	0.854724	+	0.493475i	0.862242	−	0.506496i	$-0.169060\pi$
$691$	590.615	+	340.991i	0.854724	+	0.493475i	−0.00751772	+	0.999972i	$0.502393\pi$
$692$			676.018i			0.976904i
$693$	−0.916398	+	0.209130i	−0.00132236	+	0.000301775i
$694$	134.323			0.193549
$695$	−128.567	+	222.684i	−0.184988	+	0.320409i
$696$	404.042	−	233.274i	0.580520	−	0.335164i
$697$	−180.403	−	312.466i	−0.258827	−	0.448302i
$698$	228.180	+	131.740i	0.326906	+	0.188739i
$699$			496.116i			0.709751i
$700$	36.5906	−	118.610i	0.0522723	−	0.169443i
$701$	−946.473			−1.35018			−0.675088	−	0.737737i	$-0.735894\pi$
$701$	−946.473			−1.35018			−0.675088	+	0.737737i	$0.735894\pi$
$702$	40.2451	−	69.7066i	0.0573292	−	0.0992971i
$703$	−41.9051	+	24.1939i	−0.0596090	+	0.0344153i
$704$	−0.547857	−	0.948916i	−0.000778206	−	0.00134789i
$705$	91.0422	+	52.5633i	0.129138	+	0.0745578i
$706$		−	63.0689i		−	0.0893327i
$707$	458.952	−	425.817i	0.649155	−	0.602287i
$708$	29.9129			0.0422499
$709$	504.785	−	874.313i	0.711967	−	1.23316i	−0.252150	−	0.967688i	$-0.581138\pi$
$709$	504.785	−	874.313i	0.711967	−	1.23316i	0.964118	−	0.265475i	$-0.0855289\pi$
$710$	61.1304	−	35.2936i	0.0860991	−	0.0497093i
$711$	30.7191	+	53.2071i	0.0432055	+	0.0748341i
$712$	−205.554	−	118.677i	−0.288700	−	0.166681i
$713$		−	999.671i		−	1.40206i
$714$	−52.3470	−	56.4204i	−0.0733151	−	0.0790201i
$715$	−2.30209			−0.00321970
$716$	386.318	−	669.122i	0.539550	−	0.934528i
$717$	620.129	−	358.032i	0.864895	−	0.499347i
$718$	−49.7527	−	86.1742i	−0.0692935	−	0.120020i
$719$	783.382	+	452.286i	1.08954	+	0.629049i	0.933455	−	0.358694i	$-0.116778\pi$
$719$	783.382	+	452.286i	1.08954	+	0.629049i	0.156089	+	0.987743i	$0.450111\pi$
$720$			72.2009i			0.100279i
$721$	611.244	+	188.566i	0.847773	+	0.261534i
$722$	242.238			0.335510
$723$	−256.252	+	443.842i	−0.354429	+	0.613890i
$724$	−120.028	+	69.2983i	−0.165785	+	0.0957159i
$725$	132.501	+	229.498i	0.182760	+	0.316549i
$726$	−122.232	−	70.5705i	−0.168363	−	0.0972045i
$727$		−	535.515i		−	0.736609i	−0.929705	−	0.368304i	$-0.879938\pi$
$727$		−	535.515i		−	0.736609i	0.929705	−	0.368304i	$-0.120062\pi$
$728$	182.058	+	797.770i	0.250080	+	1.09584i
$729$	−27.0000			−0.0370370
$730$	−62.9434	+	109.021i	−0.0862239	+	0.149344i
$731$	−624.644	+	360.639i	−0.854507	+	0.493350i
$732$	119.314	+	206.658i	0.162997	+	0.282319i
$733$	−652.583	−	376.769i	−0.890290	−	0.514009i	−0.0162527	−	0.999868i	$-0.505174\pi$
$733$	−652.583	−	376.769i	−0.890290	−	0.514009i	−0.874037	+	0.485859i	$0.838507\pi$
$734$		−	55.6396i		−	0.0758033i
$735$	−170.988	+	82.3294i	−0.232637	+	0.112013i
$736$	−1220.04			−1.65767
$737$	−0.156856	+	0.271683i	−0.000212831	+	0.000368634i
$738$	−66.9767	+	38.6690i	−0.0907543	+	0.0523970i
$739$	546.157	+	945.972i	0.739049	+	1.28007i	0.952924	+	0.303209i	$0.0980580\pi$
$739$	546.157	+	945.972i	0.739049	+	1.28007i	−0.213875	+	0.976861i	$0.568609\pi$
$740$	−290.389	−	167.656i	−0.392418	−	0.226563i
$741$		−	45.5903i		−	0.0615254i
$742$	−87.2693	+	19.9156i	−0.117614	+	0.0268404i
$743$	−362.303			−0.487622			−0.243811	−	0.969823i	$-0.578398\pi$
$743$	−362.303			−0.487622			−0.243811	+	0.969823i	$0.578398\pi$
$744$	99.4547	−	172.261i	0.133676	−	0.231533i
$745$	−140.872	+	81.3322i	−0.189089	+	0.109171i
$746$	115.381	+	199.847i	0.154667	+	0.267891i
$747$	326.533	+	188.524i	0.437126	+	0.252375i
$748$		−	1.49623i		−	0.00200030i
$749$	−216.881	+	703.028i	−0.289561	+	0.938622i
$750$	13.0416			0.0173888
$751$	336.270	−	582.437i	0.447763	−	0.775548i	−0.550477	−	0.834850i	$-0.685554\pi$
$751$	336.270	−	582.437i	0.447763	−	0.775548i	0.998240	+	0.0593020i	$0.0188875\pi$
$752$	253.008	−	146.074i	0.336446	−	0.194247i
$753$	269.950	+	467.568i	0.358500	+	0.620940i
$754$	−711.002	−	410.497i	−0.942974	−	0.544426i
$755$			284.268i			0.376514i
$756$	94.5630	−	87.7358i	0.125083	−	0.116053i
$757$	−368.166			−0.486349			−0.243174	−	0.969983i	$-0.578189\pi$
$757$	−368.166			−0.486349			−0.243174	+	0.969983i	$0.578189\pi$
$758$	−119.768	+	207.445i	−0.158006	+	0.273674i
$759$	−2.97029	+	1.71490i	−0.00391343	+	0.00225942i
$760$	−6.50244	−	11.2626i	−0.00855585	−	0.0148192i
$761$	565.660	+	326.584i	0.743312	+	0.429151i	0.823272	−	0.567647i	$-0.192146\pi$
$761$	565.660	+	326.584i	0.743312	+	0.429151i	−0.0799606	+	0.996798i	$0.525479\pi$
$762$			6.47380i			0.00849580i
$763$	265.197	+	285.833i	0.347571	+	0.374617i
$764$	−672.113			−0.879728
$765$	−31.6149	+	54.7585i	−0.0413266	+	0.0715798i
$766$	97.3933	−	56.2301i	0.127145	−	0.0734074i
$767$	−56.0043	−	97.0024i	−0.0730174	−	0.126470i
$768$	18.7896	+	10.8482i	0.0244656	+	0.0141252i
$769$		−	1393.19i		−	1.81170i	−0.423602	−	0.905848i	$-0.639235\pi$
$769$		−	1393.19i		−	1.81170i	0.423602	−	0.905848i	$-0.360765\pi$
$770$	0.450864	+	0.139090i	0.000585538	+	0.000180636i
$771$	250.669			0.325122
$772$	−484.340	+	838.901i	−0.627383	+	1.08666i
$773$	1129.82	−	652.302i	1.46160	−	0.843858i	0.462519	−	0.886609i	$-0.346946\pi$
$773$	1129.82	−	652.302i	1.46160	−	0.843858i	0.999086	+	0.0427514i	$0.0136124\pi$
$774$	77.3023	+	133.892i	0.0998738	+	0.172987i
$775$	97.8451	+	56.4909i	0.126252	+	0.0728914i
$776$		−	15.8309i		−	0.0204007i
$777$	114.061	+	499.811i	0.146797	+	0.643258i
$778$	107.276			0.137887
$779$	−21.9024	+	37.9362i	−0.0281161	+	0.0486985i
$780$	273.601	−	157.963i	0.350770	−	0.202517i
$781$	−1.04903	−	1.81697i	−0.00134318	−	0.00232646i
$782$	−243.208	−	140.416i	−0.311008	−	0.179561i
$783$			275.398i			0.351722i
$784$	−39.4469	+	525.913i	−0.0503149	+	0.670808i
$785$	337.793			0.430309
$786$	−97.1213	+	168.219i	−0.123564	+	0.214019i
$787$	182.275	−	105.237i	0.231607	−	0.133719i	−0.379706	−	0.925107i	$-0.623975\pi$
$787$	182.275	−	105.237i	0.231607	−	0.133719i	0.611313	+	0.791389i	$0.290642\pi$
$788$	352.691	+	610.878i	0.447577	+	0.775226i
$789$	−344.498	−	198.896i	−0.436626	−	0.252086i
$790$		−	30.8402i		−	0.0390382i
$791$	35.8579	−	8.18308i	0.0453323	−	0.0103452i
$792$	−0.682444			−0.000861672
$793$	446.770	−	773.829i	0.563393	−	0.975825i
$794$	343.703	−	198.437i	0.432876	−	0.249921i
$795$	36.7696	+	63.6869i	0.0462511	+	0.0801093i
$796$	117.860	+	68.0467i	0.148066	+	0.0854858i
$797$			254.794i			0.319691i	0.987142	+	0.159845i	$0.0510996\pi$
$797$			254.794i			0.319691i	−0.987142	+	0.159845i	$0.948900\pi$
$798$	−2.75452	+	8.92888i	−0.00345178	+	0.0111891i
$799$	255.848			0.320210
$800$	68.9439	−	119.414i	0.0861799	−	0.149268i
$801$	121.336	−	70.0536i	0.151481	−	0.0874577i
$802$	56.0009	+	96.9964i	0.0698265	+	0.120943i
$803$	3.24042	+	1.87086i	0.00403539	+	0.00232983i
$804$		−	43.0523i		−	0.0535477i
$805$	−507.633	+	470.983i	−0.630600	+	0.585073i
$806$	−350.025			−0.434275
$807$	−367.508	+	636.542i	−0.455400	+	0.788776i
$808$	393.649	−	227.273i	0.487189	−	0.281279i
$809$	114.683	+	198.637i	0.141759	+	0.245533i	0.928159	−	0.372184i	$-0.121391\pi$
$809$	114.683	+	198.637i	0.141759	+	0.245533i	−0.786400	+	0.617717i	$0.788058\pi$
$810$	11.7374	+	6.77660i	0.0144906	+	0.00836617i
$811$		−	1108.59i		−	1.36694i	−0.729978	−	0.683470i	$-0.760470\pi$
$811$		−	1108.59i		−	1.36694i	0.729978	−	0.683470i	$-0.239530\pi$
$812$	−894.899	−	964.536i	−1.10209	−	1.18785i
$813$	−505.420			−0.621673
$814$	0.637302	−	1.10384i	0.000782926	−	0.00135607i
$815$	116.050	−	67.0013i	0.142392	−	0.0822102i
$816$	87.8581	+	152.175i	0.107669	+	0.186489i
$817$	75.8373	+	43.7847i	0.0928241	+	0.0535920i
$818$		−	147.553i		−	0.180382i
$819$	−461.558	−	142.388i	−0.563562	−	0.173856i
$820$	−303.554			−0.370188
$821$	−433.762	+	751.297i	−0.528333	+	0.915100i	0.471121	+	0.882069i	$0.343850\pi$
$821$	−433.762	+	751.297i	−0.528333	+	0.915100i	−0.999454	+	0.0330318i	$0.989484\pi$
$822$	−73.6900	+	42.5449i	−0.0896472	+	0.0517578i
$823$	−492.440	−	852.931i	−0.598348	−	1.03637i	−0.993065	−	0.117566i	$-0.962491\pi$
$823$	−492.440	−	852.931i	−0.598348	−	1.03637i	0.394718	−	0.918802i	$-0.370842\pi$
$824$	402.202	+	232.212i	0.488110	+	0.281810i
$825$		−	0.387632i		−	0.000469857i
$826$	5.10769	+	22.3817i	0.00618364	+	0.0270964i
$827$	−767.641			−0.928224			−0.464112	−	0.885777i	$-0.653626\pi$
$827$	−767.641			−0.928224			−0.464112	+	0.885777i	$0.653626\pi$
$828$	235.344	−	407.628i	0.284232	−	0.492305i
$829$	−153.578	+	88.6684i	−0.185257	+	0.106958i	−0.589760	−	0.807578i	$-0.700778\pi$
$829$	−153.578	+	88.6684i	−0.185257	+	0.106958i	0.404503	+	0.914537i	$0.367444\pi$
$830$	−94.6333	−	163.910i	−0.114016	−	0.197482i
$831$	−304.351	−	175.717i	−0.366247	−	0.211453i
$832$		−	563.061i		−	0.676756i
$833$	−260.201	+	381.590i	−0.312366	+	0.458091i
$834$	134.137			0.160836
$835$	250.539	−	433.946i	0.300046	−	0.519696i
$836$	−0.157318	+	0.0908275i	−0.000188179	+	0.000108645i
$837$	58.7070	+	101.684i	0.0701398	+	0.121486i
$838$	323.524	+	186.787i	0.386067	+	0.222896i
$839$		−	15.9176i		−	0.0189721i	−0.999955	−	0.00948606i	$-0.996980\pi$
$839$		−	15.9176i		−	0.0189721i	0.999955	−	0.00948606i	$-0.00301955\pi$
$840$	−134.331	+	30.6555i	−0.159918	+	0.0364946i
$841$	1968.04			2.34012
$842$	−216.297	+	374.637i	−0.256885	+	0.444937i
$843$	−381.488	+	220.252i	−0.452536	+	0.261272i
$844$	−225.701	−	390.926i	−0.267419	−	0.463183i
$845$	−697.229	−	402.545i	−0.825123	−	0.476385i
$846$		−	54.8406i		−	0.0648234i
$847$	−249.680	+	809.348i	−0.294782	+	0.955547i
$848$	204.367			0.240998
$849$	−384.259	+	665.556i	−0.452602	+	0.783930i
$850$	27.4871	−	15.8697i	0.0323378	−	0.0186702i
$851$	935.321	+	1620.02i	1.09908	+	1.90367i
$852$	249.351	+	143.963i	0.292666	+	0.168971i
$853$			694.629i			0.814336i	0.913353	+	0.407168i	$0.133484\pi$
$853$			694.629i			0.814336i	−0.913353	+	0.407168i	$0.866516\pi$
$854$	−134.254	+	124.561i	−0.157206	+	0.145856i
$855$	7.67664			0.00897853
$856$	−267.080	+	462.597i	−0.312010	+	0.540417i
$857$	−1301.17	+	751.232i	−1.51829	+	0.876583i	−0.518518	+	0.855067i	$0.673516\pi$
$857$	−1301.17	+	751.232i	−1.51829	+	0.876583i	−0.999769	+	0.0215161i	$0.993151\pi$
$858$	0.600456	+	1.04002i	0.000699832	+	0.00121214i
$859$	−254.436	−	146.898i	−0.296200	−	0.171011i	0.344535	−	0.938774i	$-0.388037\pi$
$859$	−254.436	−	146.898i	−0.296200	−	0.171011i	−0.640734	+	0.767763i	$0.721370\pi$
$860$			606.828i			0.705614i
$861$	315.660	+	340.224i	0.366621	+	0.395149i
$862$	50.7334			0.0588555
$863$	129.059	−	223.537i	0.149547	−	0.259023i	−0.781513	−	0.623889i	$-0.785552\pi$
$863$	129.059	−	223.537i	0.149547	−	0.259023i	0.931060	+	0.364866i	$0.118885\pi$
$864$	124.099	−	71.6486i	0.143633	−	0.0829266i
$865$	213.118	+	369.131i	0.246379	+	0.426741i
$866$	205.920	+	118.888i	0.237783	+	0.137284i
$867$		−	346.680i		−	0.399861i
$868$	−536.030	−	165.363i	−0.617546	−	0.190510i
$869$	−0.916657			−0.00105484
$870$	69.1208	−	119.721i	0.0794492	−	0.137610i
$871$	−139.611	+	80.6046i	−0.160288	+	0.0925426i
$872$	141.544	+	245.162i	0.162322	+	0.281149i
$873$	8.09284	+	4.67241i	0.00927015	+	0.00535213i
$874$			34.0956i			0.0390109i
$875$	−17.4125	−	76.3008i	−0.0199000	−	0.0872009i
$876$	−513.494			−0.586180
$877$	−668.747	+	1158.30i	−0.762539	+	1.32076i	0.178999	+	0.983849i	$0.442714\pi$
$877$	−668.747	+	1158.30i	−0.762539	+	1.32076i	−0.941538	+	0.336907i	$0.890619\pi$
$878$	158.609	−	91.5727i	0.180648	−	0.104297i
$879$	193.568	+	335.270i	0.220214	+	0.381422i
$880$	−0.932913	−	0.538618i	−0.00106013	−	0.000612065i
$881$		−	606.188i		−	0.688069i	−0.938957	−	0.344034i	$-0.888206\pi$
$881$		−	606.188i		−	0.688069i	0.938957	−	0.344034i	$-0.111794\pi$
$882$	81.7932	+	55.7736i	0.0927361	+	0.0632354i
$883$	−862.650			−0.976953			−0.488477	−	0.872577i	$-0.662447\pi$
$883$	−862.650			−0.976953			−0.488477	+	0.872577i	$0.662447\pi$
$884$	384.437	−	665.865i	0.434884	−	0.753241i
$885$	16.3336	−	9.43018i	0.0184560	−	0.0106556i
$886$	37.1216	+	64.2965i	0.0418980	+	0.0725694i
$887$	−799.662	−	461.685i	−0.901536	−	0.520502i	−0.0238378	−	0.999716i	$-0.507589\pi$
$887$	−799.662	−	461.685i	−0.901536	−	0.520502i	−0.877698	+	0.479214i	$0.840922\pi$
$888$			372.211i			0.419156i
$889$	37.8755	−	8.64351i	0.0426046	−	0.00972273i
$890$	−70.3297			−0.0790221
$891$	0.201420	−	0.348869i	0.000226060	−	0.000391548i
$892$	−901.610	+	520.545i	−1.01077	+	0.583570i
$893$	−15.5311	−	26.9006i	−0.0173920	−	0.0301239i
$894$	73.4874	+	42.4280i	0.0822007	+	0.0474586i
$895$		−	487.154i		−	0.544306i
$896$	−261.646	+	848.134i	−0.292015	+	0.946579i
$897$	−1762.49			−1.96487
$898$	−19.9011	+	34.4697i	−0.0221616	+	0.0383850i
$899$	1037.16	−	598.807i	1.15369	−	0.666082i
$900$	26.5984	+	46.0697i	0.0295537	+	0.0511886i
$901$	154.996	+	89.4867i	0.172026	+	0.0993193i
$902$		−	1.15388i		−	0.00127925i
$903$	680.133	−	631.029i	0.753193	−	0.698814i
$904$	26.7035			0.0295392
$905$	−43.6932	+	75.6789i	−0.0482798	+	0.0836231i
$906$	128.425	−	74.1461i	0.141749	−	0.0818389i
$907$	47.3567	+	82.0242i	0.0522125	+	0.0904346i	0.890950	−	0.454101i	$-0.150039\pi$
$907$	47.3567	+	82.0242i	0.0522125	+	0.0904346i	−0.838738	+	0.544535i	$0.816706\pi$
$908$	661.807	+	382.095i	0.728863	+	0.420809i
$909$			268.314i			0.295174i
$910$	164.910	+	177.743i	0.181220	+	0.195322i
$911$	−556.948			−0.611359			−0.305679	−	0.952134i	$-0.598884\pi$
$911$	−556.948			−0.611359			−0.305679	+	0.952134i	$0.598884\pi$
$912$	10.6667	−	18.4753i	0.0116960	−	0.0202580i
$913$	−4.87186	+	2.81277i	−0.00533610	+	0.00308080i
$914$	69.1233	+	119.725i	0.0756272	+	0.130990i
$915$	130.300	+	75.2285i	0.142404	+	0.0822170i
$916$			511.633i			0.558551i
$917$	1113.85	+	343.618i	1.21467	+	0.374720i
$918$	32.9846			0.0359309
$919$	478.581	−	828.926i	0.520762	−	0.901987i	−0.478946	−	0.877844i	$-0.658981\pi$
$919$	478.581	−	828.926i	0.520762	−	0.901987i	0.999709	−	0.0241428i	$-0.00768562\pi$
$920$	−435.403	+	251.380i	−0.473264	+	0.273239i
$921$	41.0398	+	71.0831i	0.0445601	+	0.0771803i
$922$	271.889	+	156.975i	0.294890	+	0.170255i
$923$		−	1078.14i		−	1.16808i
$924$	0.428202	+	1.87636i	0.000463422	+	0.00203070i
$925$	−211.418			−0.228560
$926$	−64.5533	+	111.810i	−0.0697120	+	0.120745i
$927$	−237.416	+	137.072i	−0.256112	+	0.147866i
$928$	−730.811	−	1265.80i	−0.787511	−	1.36401i
$929$	−990.414	−	571.816i	−1.06611	−	0.615517i	−0.138992	−	0.990294i	$-0.544386\pi$
$929$	−990.414	−	571.816i	−1.06611	−	0.615517i	−0.927115	+	0.374776i	$0.877720\pi$
$930$		−	58.9383i		−	0.0633746i
$931$	55.9169	+	4.19412i	0.0600611	+	0.00450497i
$932$	1015.82			1.08993
$933$	313.595	−	543.162i	0.336114	−	0.582167i
$934$	491.804	−	283.943i	0.526557	−	0.304008i
$935$	−0.471693	−	0.816996i	−0.000504484	−	0.000873792i
$936$	−303.708	−	175.346i	−0.324474	−	0.187335i
$937$		−	578.660i		−	0.617567i	−0.951132	−	0.308783i	$-0.900078\pi$
$937$		−	578.660i		−	0.617567i	0.951132	−	0.308783i	$-0.0999218\pi$
$938$	32.2129	−	7.35127i	0.0343422	−	0.00783717i
$939$	681.760			0.726049
$940$	107.625	−	186.413i	0.114495	−	0.198312i
$941$	−1086.18	+	627.108i	−1.15428	+	0.666427i	−0.949928	−	0.312470i	$-0.898844\pi$
$941$	−1086.18	+	627.108i	−1.15428	+	0.666427i	−0.204357	+	0.978896i	$0.565510\pi$
$942$	−88.1069	−	152.606i	−0.0935317	−	0.162002i
$943$	1466.59	+	846.733i	1.55523	+	0.897915i
$944$		−	52.4132i		−	0.0555225i
$945$	23.9758	−	77.7185i	0.0253712	−	0.0822418i
$946$	−2.30670			−0.00243837
$947$	878.012	−	1520.76i	0.927151	−	1.60587i	0.139086	−	0.990280i	$-0.455583\pi$
$947$	878.012	−	1520.76i	0.927151	−	1.60587i	0.788065	−	0.615592i	$-0.211083\pi$
$948$	108.944	−	62.8987i	0.114920	−	0.0663488i
$949$	961.388	+	1665.17i	1.01305	+	1.75466i
$950$	−3.33718	−	1.92672i	−0.00351282	−	0.00202813i
$951$		−	1000.39i		−	1.05194i
$952$	−245.820	+	228.073i	−0.258215	+	0.239572i
$953$	−1048.32			−1.10002			−0.550011	−	0.835157i	$-0.685376\pi$
$953$	−1048.32			−1.10002			−0.550011	+	0.835157i	$0.685376\pi$
$954$	19.1813	−	33.2231i	0.0201062	−	0.0348250i
$955$	−366.998	+	211.887i	−0.384292	+	0.221871i
$956$	−733.085	−	1269.74i	−0.766826	−	1.32818i
$957$	−3.55844	−	2.05446i	−0.00371833	−	0.00214678i
$958$		−	191.722i		−	0.200127i
$959$	347.300	+	374.325i	0.362148	+	0.390329i
$960$	94.8099			0.0987603
$961$	−225.203	+	390.062i	−0.234342	+	0.405892i
$962$	567.236	−	327.494i	0.589642	−	0.340430i
$963$	−157.655	−	273.066i	−0.163712	−	0.283557i
$964$	908.785	+	524.688i	0.942723	+	0.544282i
$965$			610.762i			0.632914i
$966$	345.184	+	106.488i	0.357334	+	0.110236i
$967$	−1770.86			−1.83130			−0.915648	−	0.401982i	$-0.868321\pi$
$967$	−1770.86			−1.83130			−0.915648	+	0.401982i	$0.868321\pi$
$968$	−307.471	+	532.556i	−0.317636	+	0.550161i
$969$	16.1797	−	9.34137i	0.0166973	−	0.00964022i
$970$	−2.34541	−	4.06237i	−0.00241795	−	0.00418801i
$971$	834.000	+	481.510i	0.858908	+	0.495891i	0.863646	−	0.504098i	$-0.168175\pi$
$971$	834.000	+	481.510i	0.858908	+	0.495891i	−0.00473848	+	0.999989i	$0.501508\pi$
$972$			55.2836i			0.0568762i
$973$	−179.093	−	784.779i	−0.184063	−	0.806556i
$974$	−131.760			−0.135277
$975$	99.5974	−	172.508i	0.102151	−	0.176931i
$976$	362.105	−	209.061i	0.371009	−	0.214202i
$977$	269.150	+	466.182i	0.275487	+	0.477157i	0.970258	−	0.242074i	$-0.0778277\pi$
$977$	269.150	+	466.182i	0.275487	+	0.477157i	−0.694771	+	0.719231i	$0.744494\pi$
$978$	−60.5388	−	34.9521i	−0.0619006	−	0.0357383i
$979$			2.09040i			0.00213524i
$980$	168.573	+	350.105i	0.172013	+	0.357250i
$981$	−167.104			−0.170341
$982$	−251.021	+	434.782i	−0.255623	+	0.442751i
$983$	−586.233	+	338.462i	−0.596371	+	0.344315i	−0.767613	−	0.640914i	$-0.778556\pi$
$983$	−586.233	+	338.462i	−0.596371	+	0.344315i	0.171241	+	0.985229i	$0.445222\pi$
$984$	168.479	+	291.814i	0.171218	+	0.296559i
$985$	385.164	+	222.375i	0.391030	+	0.225761i
$986$		−	336.440i		−	0.341217i
$987$	−320.849	+	73.2206i	−0.325075	+	0.0741850i
$988$	−93.3481			−0.0944819
$989$	1692.69	−	2931.82i	1.71151	−	2.96443i
$990$	−0.175122	+	0.101107i	−0.000176891	+	0.000102128i
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	−0.994204	−	0.107514i	$-0.965711\pi$
$991$	−584.900	−	1013.08i	−0.590212	−	1.02228i	0.403992	−	0.914763i	$-0.367622\pi$
$992$	−539.666	−	311.576i	−0.544018	−	0.314089i
$993$			317.995i			0.320237i
$994$	−65.1400	+	211.154i	−0.0655332	+	0.212428i
$995$	85.8082			0.0862394
$996$	386.011	−	668.590i	0.387561	−	0.671275i
$997$	523.016	−	301.963i	0.524590	−	0.302872i	−0.214221	−	0.976785i	$-0.568721\pi$
$997$	523.016	−	301.963i	0.524590	−	0.302872i	0.738810	+	0.673913i	$0.235388\pi$
$998$	−30.9623	−	53.6283i	−0.0310244	−	0.0537358i
$999$	−190.276	−	109.856i	−0.190467	−	0.109966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.n.a.61.2	yes	8
3.2	odd	2		315.3.w.a.271.3		8
5.2	odd	4		525.3.s.h.124.4		16
5.3	odd	4		525.3.s.h.124.5		16
5.4	even	2		525.3.o.l.376.3		8
7.2	even	3		735.3.h.a.391.5		8
7.3	odd	6	inner	105.3.n.a.31.2	✓	8
7.5	odd	6		735.3.h.a.391.6		8
21.17	even	6		315.3.w.a.136.3		8
35.3	even	12		525.3.s.h.199.4		16
35.17	even	12		525.3.s.h.199.5		16
35.24	odd	6		525.3.o.l.451.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.n.a.31.2	✓	8	7.3	odd	6	inner
105.3.n.a.61.2	yes	8	1.1	even	1	trivial
315.3.w.a.136.3		8	21.17	even	6
315.3.w.a.271.3		8	3.2	odd	2
525.3.o.l.376.3		8	5.4	even	2
525.3.o.l.451.3		8	35.24	odd	6
525.3.s.h.124.4		16	5.2	odd	4
525.3.s.h.124.5		16	5.3	odd	4
525.3.s.h.199.4		16	35.3	even	12
525.3.s.h.199.5		16	35.17	even	12
735.3.h.a.391.5		8	7.2	even	3
735.3.h.a.391.6		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)

\(f(q)\)	\(=\)	\(q+(-0.336732 + 0.583237i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.77322 + 3.07131i) q^{4} +(1.93649 + 1.11803i) q^{5} -1.16647i q^{6} +(-6.82455 + 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.336732 + 0.583237i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.77322 + 3.07131i) q^{4} +(1.93649 + 1.11803i) q^{5} -1.16647i q^{6} +(-6.82455 + 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.30416 + 0.752955i) q^{10} +(0.0223800 + 0.0387632i) q^{11} +(-5.31967 - 3.07131i) q^{12} +23.0010i q^{13} +(1.38970 - 4.50476i) q^{14} -3.87298 q^{15} +(-5.38154 + 9.32109i) q^{16} +(-8.16292 + 4.71286i) q^{17} +(1.01020 + 1.74971i) q^{18} +(0.991050 + 0.572183i) q^{19} +7.93010i q^{20} +(8.88806 - 8.24636i) q^{21} -0.0301442 q^{22} +(22.1202 - 38.3133i) q^{23} +(7.62339 - 4.40136i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-13.4150 - 7.74518i) q^{26} +5.19615i q^{27} +(-16.8848 - 18.1987i) q^{28} +53.0004 q^{29} +(1.30416 - 2.25887i) q^{30} +(19.5690 - 11.2982i) q^{31} +(-13.7888 - 23.8829i) q^{32} +(-0.0671399 - 0.0387632i) q^{33} -6.34788i q^{34} +(-14.9569 - 4.61414i) q^{35} +10.6393 q^{36} +(-21.1418 + 36.6186i) q^{37} +(-0.667436 + 0.385344i) q^{38} +(-19.9195 - 34.5015i) q^{39} +(-9.84175 - 5.68214i) q^{40} +38.2787i q^{41} +(1.81669 + 7.96065i) q^{42} +76.5222 q^{43} +(-0.0793693 + 0.137472i) q^{44} +(5.80948 - 3.35410i) q^{45} +(14.8971 + 25.8026i) q^{46} +(-23.5070 - 13.5718i) q^{47} -18.6422i q^{48} +(44.1489 - 21.2574i) q^{49} -3.36732 q^{50} +(8.16292 - 14.1386i) q^{51} +(-70.6434 + 40.7860i) q^{52} +(-9.49388 - 16.4439i) q^{53} +(-3.03059 - 1.74971i) q^{54} +0.100086i q^{55} +(34.6841 - 7.91521i) q^{56} -1.98210 q^{57} +(-17.8469 + 30.9118i) q^{58} +(-4.21731 + 2.43486i) q^{59} +(-6.86766 - 11.8951i) q^{60} +(-33.6432 - 19.4239i) q^{61} +15.2178i q^{62} +(-6.19052 + 20.0668i) q^{63} -24.4798 q^{64} +(-25.7159 + 44.5413i) q^{65} +(0.0452163 - 0.0261056i) q^{66} +(3.50439 + 6.06978i) q^{67} +(-28.9494 - 16.7139i) q^{68} +76.6266i q^{69} +(7.72761 - 7.16970i) q^{70} -46.8735 q^{71} +(-7.62339 + 13.2041i) q^{72} +(72.3956 - 41.7976i) q^{73} +(-14.2382 - 24.6613i) q^{74} +(-7.50000 - 4.33013i) q^{75} +4.05843i q^{76} +(-0.213104 - 0.229686i) q^{77} +26.8301 q^{78} +(-10.2397 + 17.7357i) q^{79} +(-20.8426 + 12.0335i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-22.3256 - 12.8897i) q^{82} +125.683i q^{83} +(41.0877 + 12.6754i) q^{84} -21.0766 q^{85} +(-25.7674 + 44.6305i) q^{86} +(-79.5006 + 45.8997i) q^{87} +(-0.113741 - 0.197005i) q^{88} +(40.4455 + 23.3512i) q^{89} +4.51773i q^{90} +(-35.8223 - 156.972i) q^{91} +156.896 q^{92} +(-19.5690 + 33.8945i) q^{93} +(15.8311 - 9.14010i) q^{94} +(1.27944 + 2.21606i) q^{95} +(41.3663 + 23.8829i) q^{96} +3.11494i q^{97} +(-2.46826 + 32.9073i) q^{98} +0.134280 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

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