LMFDB - Embedded newform 46.3.d.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,3,Mod(5,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("46.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	46.d (of order $22$, degree $10$, 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:	$1.25340921606$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	46.15
Dual form			46.3.d.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.201264 + 1.39982i) q^{2} +(1.30738 + 2.86277i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(0.389792 - 0.337757i) q^{5} +(-4.27048 + 1.25393i) q^{6} +(-2.12361 + 3.30440i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-0.592439 + 0.683711i) q^{9} +(0.394348 + 0.613617i) q^{10} +(7.42324 - 1.06730i) q^{11} +(-0.895778 - 6.23027i) q^{12} +(8.61901 - 5.53910i) q^{13} +(-4.19816 - 3.63773i) q^{14} +(1.47653 + 0.674307i) q^{15} +(3.36501 + 2.16256i) q^{16} +(-7.18729 - 24.4776i) q^{17} +(-0.837835 - 0.966913i) q^{18} +(-1.85729 + 6.32534i) q^{19} +(-0.938321 + 0.428517i) q^{20} +(-12.2361 - 1.75929i) q^{21} +10.6060i q^{22} +(2.66286 - 22.8453i) q^{23} +8.90154 q^{24} +(-3.52001 + 24.4822i) q^{25} +(6.01905 + 13.1799i) q^{26} +(24.4453 + 7.17780i) q^{27} +(5.93709 - 5.14452i) q^{28} +(-42.5751 + 12.5012i) q^{29} +(-1.24108 + 1.93116i) q^{30} +(-17.1179 + 37.4830i) q^{31} +(-3.70445 + 4.27517i) q^{32} +(12.7604 + 19.8556i) q^{33} +(35.7108 - 5.13444i) q^{34} +(0.288318 + 2.00530i) q^{35} +(1.52213 - 0.978213i) q^{36} +(-37.8198 - 32.7711i) q^{37} +(-8.48053 - 3.87293i) q^{38} +(27.1255 + 17.4325i) q^{39} +(-0.410996 - 1.39972i) q^{40} +(-22.3446 - 25.7871i) q^{41} +(4.92536 - 16.7742i) q^{42} +(34.0315 - 15.5417i) q^{43} +(-14.8465 - 2.13460i) q^{44} +0.466606i q^{45} +(31.4434 + 8.32545i) q^{46} -22.6392 q^{47} +(-1.79156 + 12.4605i) q^{48} +(13.9460 + 30.5374i) q^{49} +(-33.5622 - 9.85476i) q^{50} +(60.6773 - 52.5772i) q^{51} +(-19.6609 + 5.77295i) q^{52} +(21.4358 - 33.3547i) q^{53} +(-14.9676 + 32.7744i) q^{54} +(2.53304 - 2.92328i) q^{55} +(6.00648 + 9.34626i) q^{56} +(-20.5362 + 2.95265i) q^{57} +(-8.93056 - 62.1134i) q^{58} +(22.5580 - 14.4971i) q^{59} +(-2.45349 - 2.12596i) q^{60} +(-26.8087 - 12.2431i) q^{61} +(-49.0242 - 31.5059i) q^{62} +(-1.00115 - 3.40959i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(1.48875 - 5.07023i) q^{65} +(-30.3625 + 13.8661i) q^{66} +(-66.1101 - 9.50519i) q^{67} +51.0220i q^{68} +(68.8822 - 22.2444i) q^{69} -2.86508 q^{70} +(-7.12282 + 49.5403i) q^{71} +(1.06297 + 2.32758i) q^{72} +(94.8939 + 27.8634i) q^{73} +(53.4853 - 46.3453i) q^{74} +(-74.6889 + 21.9306i) q^{75} +(7.12822 - 11.0917i) q^{76} +(-12.2373 + 26.7959i) q^{77} +(-29.8617 + 34.4623i) q^{78} +(38.8314 + 60.4228i) q^{79} +(2.04208 - 0.293607i) q^{80} +(12.5698 + 87.4247i) q^{81} +(40.5944 - 26.0884i) q^{82} +(89.4100 + 77.4742i) q^{83} +(22.4896 + 10.2707i) q^{84} +(-11.0690 - 7.11365i) q^{85} +(14.9062 + 50.7659i) q^{86} +(-91.4498 - 105.539i) q^{87} +(5.97611 - 20.3528i) q^{88} +(56.8021 - 25.9407i) q^{89} +(-0.653163 - 0.0939107i) q^{90} +40.2436i q^{91} +(-17.9825 + 42.3394i) q^{92} -129.685 q^{93} +(4.55645 - 31.6908i) q^{94} +(1.41247 + 3.09288i) q^{95} +(-17.0819 - 5.01571i) q^{96} +(51.8369 - 44.9169i) q^{97} +(-45.5537 + 13.3758i) q^{98} +(-3.66809 + 5.70766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 8 q^{4} - 8 q^{6} + 24 q^{9} + 8 q^{12} + 4 q^{13} - 154 q^{15} - 16 q^{16} - 110 q^{17} - 160 q^{18} - 66 q^{19} - 44 q^{20} - 66 q^{21} - 8 q^{23} - 16 q^{24} + 264 q^{25} + 152 q^{26}+ \cdots - 1122 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 8 * q^4 - 8 * q^6 + 24 * q^9 + 8 * q^12 + 4 * q^13 - 154 * q^15 - 16 * q^16 - 110 * q^17 - 160 * q^18 - 66 * q^19 - 44 * q^20 - 66 * q^21 - 8 * q^23 - 16 * q^24 + 264 * q^25 + 152 * q^26 + 286 * q^27 + 132 * q^28 + 70 * q^29 + 352 * q^30 + 82 * q^31 + 242 * q^33 - 276 * q^35 + 48 * q^36 - 352 * q^37 - 204 * q^39 - 108 * q^41 - 88 * q^43 - 56 * q^46 + 116 * q^47 + 16 * q^48 + 412 * q^49 - 176 * q^50 + 264 * q^51 + 8 * q^52 + 176 * q^53 - 204 * q^54 - 76 * q^55 - 264 * q^56 - 198 * q^57 - 360 * q^58 - 300 * q^59 - 176 * q^60 - 616 * q^61 - 372 * q^62 - 550 * q^63 - 32 * q^64 - 462 * q^65 - 176 * q^66 - 44 * q^67 + 106 * q^69 - 112 * q^70 + 430 * q^71 + 208 * q^72 + 368 * q^73 + 528 * q^74 + 418 * q^75 + 646 * q^77 + 604 * q^78 + 704 * q^79 + 264 * q^80 + 636 * q^81 + 664 * q^82 + 814 * q^83 + 352 * q^84 + 736 * q^85 + 396 * q^86 - 100 * q^87 - 44 * q^89 - 104 * q^92 + 140 * q^93 - 136 * q^94 - 594 * q^95 - 32 * q^96 - 990 * q^97 - 304 * q^98 - 1122 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.201264	+	1.39982i	−0.100632	+	0.699909i
$2$	−0.201264	+	1.39982i	−0.100632	+	0.699909i
$3$	1.30738	+	2.86277i	0.435794	+	0.954255i	0.992351	+	0.123446i	$0.0393947\pi$
$3$	1.30738	+	2.86277i	0.435794	+	0.954255i	−0.556557	+	0.830809i	$0.687878\pi$
$4$	−1.91899	−	0.563465i	−0.479746	−	0.140866i
$5$	0.389792	−	0.337757i	0.0779585	−	0.0675514i	−0.615010	−	0.788519i	$-0.710848\pi$
$5$	0.389792	−	0.337757i	0.0779585	−	0.0675514i	0.692968	+	0.720968i	$0.256303\pi$
$6$	−4.27048	+	1.25393i	−0.711747	+	0.208988i
$7$	−2.12361	+	3.30440i	−0.303373	+	0.472057i	−0.959150	−	0.282897i	$-0.908705\pi$
$7$	−2.12361	+	3.30440i	−0.303373	+	0.472057i	0.655777	+	0.754954i	$0.272341\pi$
$8$	1.17497	−	2.57283i	0.146871	−	0.321603i
$9$	−0.592439	+	0.683711i	−0.0658265	+	0.0759678i
$10$	0.394348	+	0.613617i	0.0394348	+	0.0613617i
$11$	7.42324	−	1.06730i	0.674840	−	0.0970274i	0.203630	−	0.979048i	$-0.434726\pi$
$11$	7.42324	−	1.06730i	0.674840	−	0.0970274i	0.471211	+	0.882021i	$0.343817\pi$
$12$	−0.895778	−	6.23027i	−0.0746482	−	0.519189i
$13$	8.61901	−	5.53910i	0.663001	−	0.426085i	−0.165395	−	0.986227i	$-0.552890\pi$
$13$	8.61901	−	5.53910i	0.663001	−	0.426085i	0.828396	+	0.560143i	$0.189254\pi$
$14$	−4.19816	−	3.63773i	−0.299869	−	0.259838i
$15$	1.47653	+	0.674307i	0.0984351	+	0.0449538i
$16$	3.36501	+	2.16256i	0.210313	+	0.135160i
$17$	−7.18729	−	24.4776i	−0.422782	−	1.43986i	−0.845683	−	0.533686i	$-0.820806\pi$
$17$	−7.18729	−	24.4776i	−0.422782	−	1.43986i	0.422901	−	0.906176i	$-0.361012\pi$
$18$	−0.837835	−	0.966913i	−0.0465464	−	0.0537174i
$19$	−1.85729	+	6.32534i	−0.0977520	+	0.332913i	−0.993820	−	0.111004i	$-0.964593\pi$
$19$	−1.85729	+	6.32534i	−0.0977520	+	0.332913i	0.896068	+	0.443917i	$0.146411\pi$
$20$	−0.938321	+	0.428517i	−0.0469160	+	0.0214258i
$21$	−12.2361	−	1.75929i	−0.582672	−	0.0837755i
$22$			10.6060i			0.482091i
$23$	2.66286	−	22.8453i	0.115776	−	0.993275i
$23$	2.66286	−	22.8453i	0.115776	−	0.993275i
$24$	8.90154			0.370898
$25$	−3.52001	+	24.4822i	−0.140801	+	0.979289i
$26$	6.01905	+	13.1799i	0.231502	+	0.506918i
$27$	24.4453	+	7.17780i	0.905383	+	0.265844i
$28$	5.93709	−	5.14452i	0.212039	−	0.183733i
$29$	−42.5751	+	12.5012i	−1.46811	+	0.431075i	−0.915483	−	0.402357i	$-0.868191\pi$
$29$	−42.5751	+	12.5012i	−1.46811	+	0.431075i	−0.552623	+	0.833431i	$0.686373\pi$
$30$	−1.24108	+	1.93116i	−0.0413693	+	0.0643719i
$31$	−17.1179	+	37.4830i	−0.552191	+	1.20913i	0.403561	+	0.914953i	$0.367772\pi$
$31$	−17.1179	+	37.4830i	−0.552191	+	1.20913i	−0.955751	+	0.294176i	$0.904955\pi$
$32$	−3.70445	+	4.27517i	−0.115764	+	0.133599i
$33$	12.7604	+	19.8556i	0.386680	+	0.601686i
$34$	35.7108	−	5.13444i	1.05032	−	0.151013i
$35$	0.288318	+	2.00530i	0.00823766	+	0.0572942i
$36$	1.52213	−	0.978213i	0.0422813	−	0.0271726i
$37$	−37.8198	−	32.7711i	−1.02216	−	0.885704i	−0.0286631	−	0.999589i	$-0.509125\pi$
$37$	−37.8198	−	32.7711i	−1.02216	−	0.885704i	−0.993494	+	0.113885i	$0.963670\pi$
$38$	−8.48053	−	3.87293i	−0.223172	−	0.101919i
$39$	27.1255	+	17.4325i	0.695525	+	0.446987i
$40$	−0.410996	−	1.39972i	−0.0102749	−	0.0349931i
$41$	−22.3446	−	25.7871i	−0.544991	−	0.628953i	0.414718	−	0.909950i	$-0.363880\pi$
$41$	−22.3446	−	25.7871i	−0.544991	−	0.628953i	−0.959709	+	0.280997i	$0.909335\pi$
$42$	4.92536	−	16.7742i	0.117271	−	0.399387i
$43$	34.0315	−	15.5417i	0.791430	−	0.361434i	0.0216684	−	0.999765i	$-0.493102\pi$
$43$	34.0315	−	15.5417i	0.791430	−	0.361434i	0.769762	+	0.638331i	$0.220375\pi$
$44$	−14.8465	−	2.13460i	−0.337420	−	0.0485137i
$45$			0.466606i			0.0103690i
$46$	31.4434	+	8.32545i	0.683552	+	0.180988i
$47$	−22.6392			−0.481685			−0.240843	−	0.970564i	$-0.577424\pi$
$47$	−22.6392			−0.481685			−0.240843	+	0.970564i	$0.577424\pi$
$48$	−1.79156	+	12.4605i	−0.0373241	+	0.259595i
$49$	13.9460	+	30.5374i	0.284612	+	0.623213i
$50$	−33.5622	−	9.85476i	−0.671245	−	0.197095i
$51$	60.6773	−	52.5772i	1.18975	−	1.03092i
$52$	−19.6609	+	5.77295i	−0.378093	+	0.111018i
$53$	21.4358	−	33.3547i	0.404449	−	0.629335i	−0.577963	−	0.816063i	$-0.696152\pi$
$53$	21.4358	−	33.3547i	0.404449	−	0.629335i	0.982412	+	0.186729i	$0.0597885\pi$
$54$	−14.9676	+	32.7744i	−0.277177	+	0.606934i
$55$	2.53304	−	2.92328i	0.0460552	−	0.0531505i
$56$	6.00648	+	9.34626i	0.107259	+	0.166898i
$57$	−20.5362	+	2.95265i	−0.360283	+	0.0518009i
$58$	−8.93056	−	62.1134i	−0.153975	−	1.07092i
$59$	22.5580	−	14.4971i	0.382339	−	0.245714i	−0.335327	−	0.942102i	$-0.608847\pi$
$59$	22.5580	−	14.4971i	0.382339	−	0.245714i	0.717666	+	0.696388i	$0.245211\pi$
$60$	−2.45349	−	2.12596i	−0.0408914	−	0.0354326i
$61$	−26.8087	−	12.2431i	−0.439488	−	0.200707i	0.183368	−	0.983044i	$-0.441300\pi$
$61$	−26.8087	−	12.2431i	−0.439488	−	0.200707i	−0.622855	+	0.782337i	$0.714027\pi$
$62$	−49.0242	−	31.5059i	−0.790713	−	0.508160i
$63$	−1.00115	−	3.40959i	−0.0158912	−	0.0541205i
$64$	−5.23889	−	6.04600i	−0.0818576	−	0.0944687i
$65$	1.48875	−	5.07023i	0.0229039	−	0.0780036i
$66$	−30.3625	+	13.8661i	−0.460038	+	0.210092i
$67$	−66.1101	−	9.50519i	−0.986717	−	0.141869i	−0.369982	−	0.929039i	$-0.620636\pi$
$67$	−66.1101	−	9.50519i	−0.986717	−	0.141869i	−0.616736	+	0.787170i	$0.711545\pi$
$68$			51.0220i			0.750324i
$69$	68.8822	−	22.2444i	0.998293	−	0.322383i
$70$	−2.86508			−0.0409297
$71$	−7.12282	+	49.5403i	−0.100321	+	0.697751i	0.876140	+	0.482057i	$0.160110\pi$
$71$	−7.12282	+	49.5403i	−0.100321	+	0.697751i	−0.976461	+	0.215694i	$0.930799\pi$
$72$	1.06297	+	2.32758i	0.0147635	+	0.0323275i
$73$	94.8939	+	27.8634i	1.29992	+	0.381690i	0.857206	−	0.514974i	$-0.172198\pi$
$73$	94.8939	+	27.8634i	1.29992	+	0.381690i	0.442711	+	0.896664i	$0.354017\pi$
$74$	53.4853	−	46.3453i	0.722774	−	0.626287i
$75$	−74.6889	+	21.9306i	−0.995852	+	0.292409i
$76$	7.12822	−	11.0917i	0.0937923	−	0.145944i
$77$	−12.2373	+	26.7959i	−0.158926	+	0.347999i
$78$	−29.8617	+	34.4623i	−0.382842	+	0.441824i
$79$	38.8314	+	60.4228i	0.491536	+	0.764845i	0.995075	−	0.0991274i	$-0.0316051\pi$
$79$	38.8314	+	60.4228i	0.491536	+	0.764845i	−0.503538	+	0.863973i	$0.667969\pi$
$80$	2.04208	−	0.293607i	0.0255260	−	0.00367008i
$81$	12.5698	+	87.4247i	0.155182	+	1.07932i
$82$	40.5944	−	26.0884i	0.495053	−	0.318151i
$83$	89.4100	+	77.4742i	1.07723	+	0.933424i	0.997986	−	0.0634310i	$-0.0202043\pi$
$83$	89.4100	+	77.4742i	1.07723	+	0.933424i	0.0792429	+	0.996855i	$0.474750\pi$
$84$	22.4896	+	10.2707i	0.267733	+	0.122270i
$85$	−11.0690	−	7.11365i	−0.130224	−	0.0836899i
$86$	14.9062	+	50.7659i	0.173328	+	0.590301i
$87$	−91.4498	−	105.539i	−1.05115	−	1.21309i
$88$	5.97611	−	20.3528i	0.0679104	−	0.231282i
$89$	56.8021	−	25.9407i	0.638226	−	0.291468i	−0.0699001	−	0.997554i	$-0.522268\pi$
$89$	56.8021	−	25.9407i	0.638226	−	0.291468i	0.708126	+	0.706086i	$0.249541\pi$
$90$	−0.653163	−	0.0939107i	−0.00725737	−	0.00104345i
$91$			40.2436i			0.442237i
$92$	−17.9825	+	42.3394i	−0.195462	+	0.460211i
$93$	−129.685			−1.39446
$94$	4.55645	−	31.6908i	0.0484728	−	0.337136i
$95$	1.41247	+	3.09288i	0.0148681	+	0.0325567i
$96$	−17.0819	−	5.01571i	−0.177937	−	0.0522470i
$97$	51.8369	−	44.9169i	0.534401	−	0.463061i	−0.345365	−	0.938469i	$-0.612245\pi$
$97$	51.8369	−	44.9169i	0.534401	−	0.463061i	0.879766	+	0.475407i	$0.157699\pi$
$98$	−45.5537	+	13.3758i	−0.464834	+	0.136487i
$99$	−3.66809	+	5.70766i	−0.0370514	+	0.0576531i
$100$	20.5497	−	44.9976i	0.205497	−	0.449976i
$101$	27.9188	−	32.2200i	0.276424	−	0.319010i	−0.600514	−	0.799615i	$-0.705037\pi$
$101$	27.9188	−	32.2200i	0.276424	−	0.319010i	0.876938	+	0.480604i	$0.159583\pi$
$102$	61.3864	+	95.5190i	0.601827	+	0.936461i
$103$	−183.069	+	26.3213i	−1.77736	+	0.255546i	−0.951352	−	0.308105i	$-0.900305\pi$
$103$	−183.069	+	26.3213i	−1.77736	+	0.255546i	−0.826012	+	0.563652i	$0.809396\pi$
$104$	−4.12407	−	28.6835i	−0.0396545	−	0.275803i
$105$	−5.36375	+	3.44707i	−0.0510833	+	0.0328293i
$106$	42.3763	+	36.7193i	0.399777	+	0.346409i
$107$	−176.230	−	80.4817i	−1.64701	−	0.752165i	−0.647065	−	0.762435i	$-0.724004\pi$
$107$	−176.230	−	80.4817i	−1.64701	−	0.752165i	−0.999947	+	0.0102695i	$0.996731\pi$
$108$	−42.8658	−	27.5482i	−0.396906	−	0.255076i
$109$	−23.7111	−	80.7527i	−0.217533	−	0.740851i	−0.993872	−	0.110535i	$-0.964744\pi$
$109$	−23.7111	−	80.7527i	−0.217533	−	0.740851i	0.776339	−	0.630316i	$-0.217075\pi$
$110$	3.58225	+	4.13414i	0.0325659	+	0.0375831i
$111$	44.3709	−	151.114i	0.399738	−	1.36138i
$112$	−14.2920	+	6.52692i	−0.127607	+	0.0582761i
$113$	145.476	+	20.9162i	1.28740	+	0.185100i	0.751809	−	0.659381i	$-0.229181\pi$
$113$	145.476	+	20.9162i	1.28740	+	0.185100i	0.535587	+	0.844480i	$0.320091\pi$
$114$		−	29.3412i		−	0.257379i
$115$	−6.67821	−	9.80434i	−0.0580714	−	0.0852551i
$116$	88.7449			0.765043
$117$	−1.31909	+	9.17449i	−0.0112743	+	0.0784144i
$118$	15.7533	+	34.4948i	0.133502	+	0.292329i
$119$	96.1470	+	28.2313i	0.807958	+	0.237238i
$120$	3.46975	−	3.00656i	0.0289146	−	0.0250547i
$121$	−62.1332	+	18.2440i	−0.513498	+	0.150777i
$122$	22.5338	−	35.0633i	0.184703	−	0.287404i
$123$	44.6094	−	97.6809i	0.362678	−	0.794154i
$124$	53.9694	−	62.2840i	0.435237	−	0.502290i
$125$	13.8681	+	21.5792i	0.110945	+	0.172634i
$126$	4.97430	−	0.715197i	0.0394786	−	0.00567617i
$127$	1.03446	+	7.19482i	0.00814535	+	0.0566522i	0.993489	−	0.113930i	$-0.0363441\pi$
$127$	1.03446	+	7.19482i	0.00814535	+	0.0566522i	−0.985343	+	0.170583i	$0.945435\pi$
$128$	9.51770	−	6.11665i	0.0743570	−	0.0477863i
$129$	88.9843	+	77.1054i	0.689801	+	0.597716i
$130$	6.79777	+	3.10444i	0.0522906	+	0.0238803i
$131$	−44.9713	−	28.9013i	−0.343292	−	0.220621i	0.357621	−	0.933867i	$-0.383588\pi$
$131$	−44.9713	−	28.9013i	−0.343292	−	0.220621i	−0.700914	+	0.713246i	$0.747224\pi$
$132$	−13.2992	−	45.2928i	−0.100751	−	0.343127i
$133$	−16.9573	−	19.5698i	−0.127499	−	0.147141i
$134$	26.6111	−	90.6291i	0.198590	−	0.676336i
$135$	11.9530	−	5.45873i	0.0885405	−	0.0404351i
$136$	−71.4216	−	10.2689i	−0.525159	−	0.0755065i
$137$			228.565i			1.66836i	0.551495	+	0.834178i	$0.314057\pi$
$137$			228.565i			1.66836i	−0.551495	+	0.834178i	$0.685943\pi$
$138$	17.2747	+	100.900i	0.125179	+	0.731157i
$139$	−84.5119			−0.607999			−0.303999	−	0.952672i	$-0.598322\pi$
$139$	−84.5119			−0.607999			−0.303999	+	0.952672i	$0.598322\pi$
$140$	0.576636	−	4.01059i	0.00411883	−	0.0286471i
$141$	−29.5981	−	64.8107i	−0.209915	−	0.459651i
$142$	−67.9139	−	19.9413i	−0.478267	−	0.140432i
$143$	58.0691	−	50.3172i	0.406078	−	0.351868i
$144$	−3.47213	+	1.01951i	−0.0241120	+	0.00707993i
$145$	−12.3731	+	19.2529i	−0.0853316	+	0.132779i
$146$	−58.1024	+	127.226i	−0.397961	+	0.871414i
$147$	−69.1888	+	79.8482i	−0.470672	+	0.543185i
$148$	54.1103	+	84.1973i	0.365610	+	0.568901i
$149$	−72.3905	+	10.4082i	−0.485842	+	0.0698536i	−0.380884	−	0.924623i	$-0.624380\pi$
$149$	−72.3905	+	10.4082i	−0.485842	+	0.0698536i	−0.104959	+	0.994477i	$0.533471\pi$
$150$	−15.6668	−	108.965i	−0.104445	−	0.726432i
$151$	21.0708	−	13.5414i	0.139542	−	0.0896781i	−0.469007	−	0.883194i	$-0.655388\pi$
$151$	21.0708	−	13.5414i	0.139542	−	0.0896781i	0.608549	+	0.793516i	$0.291752\pi$
$152$	14.0918	+	12.2106i	0.0927089	+	0.0803327i
$153$	20.9937	+	9.58748i	0.137213	+	0.0626633i
$154$	−35.0465	−	22.5230i	−0.227575	−	0.146253i
$155$	5.98771	+	20.3923i	0.0386304	+	0.131563i
$156$	−42.2308	−	48.7370i	−0.270710	−	0.312417i
$157$	−22.5141	+	76.6759i	−0.143402	+	0.488381i	−0.999600	−	0.0282652i	$-0.991002\pi$
$157$	−22.5141	+	76.6759i	−0.143402	+	0.488381i	0.856199	+	0.516647i	$0.172820\pi$
$158$	−92.3963	+	42.1960i	−0.584787	+	0.267063i
$159$	123.512	+	17.7583i	0.776802	+	0.111687i
$160$			2.91763i			0.0182352i
$161$	69.8353	+	57.3137i	0.433760	+	0.355986i
$162$	−124.909			−0.771040
$163$	−30.6274	+	213.018i	−0.187898	+	1.30686i	0.649539	+	0.760328i	$0.274962\pi$
$163$	−30.6274	+	213.018i	−0.187898	+	1.30686i	−0.837438	+	0.546533i	$0.815947\pi$
$164$	28.3489	+	62.0754i	0.172859	+	0.378509i
$165$	11.6803	+	3.42965i	0.0707897	+	0.0207857i
$166$	−126.445	+	109.565i	−0.761716	+	0.660031i
$167$	238.208	−	69.9441i	1.42639	−	0.418827i	0.524731	−	0.851268i	$-0.324166\pi$
$167$	238.208	−	69.9441i	1.42639	−	0.418827i	0.901662	+	0.432441i	$0.142348\pi$
$168$	−18.9034	+	29.4143i	−0.112520	+	0.175085i
$169$	−26.5994	+	58.2446i	−0.157393	+	0.344643i
$170$	12.1856	−	14.0629i	0.0716801	−	0.0827232i
$171$	−3.22437	−	5.01722i	−0.0188560	−	0.0293405i
$172$	−74.0632	+	10.6487i	−0.430600	+	0.0619109i
$173$	−27.6904	−	192.591i	−0.160060	−	1.11324i	−0.898515	−	0.438942i	$-0.855353\pi$
$173$	−27.6904	−	192.591i	−0.160060	−	1.11324i	0.738455	−	0.674303i	$-0.235556\pi$
$174$	166.141	−	106.772i	0.954831	−	0.613633i
$175$	−73.4240	−	63.6222i	−0.419566	−	0.363556i
$176$	27.2874	+	12.4617i	0.155042	+	0.0708054i
$177$	70.9938	+	45.6249i	0.401095	+	0.257768i
$178$	24.8800	+	84.7336i	0.139775	+	0.476031i
$179$	86.4011	+	99.7122i	0.482688	+	0.557052i	0.943897	−	0.330240i	$-0.107130\pi$
$179$	86.4011	+	99.7122i	0.482688	+	0.557052i	−0.461209	+	0.887291i	$0.652584\pi$
$180$	0.262916	−	0.895409i	0.00146064	−	0.00497450i
$181$	326.253	−	148.995i	1.80250	−	0.823176i	0.844994	−	0.534776i	$-0.179604\pi$
$181$	326.253	−	148.995i	1.80250	−	0.823176i	0.957510	−	0.288400i	$-0.0931232\pi$
$182$	−56.3337	−	8.09957i	−0.309526	−	0.0445031i
$183$		−	92.7536i		−	0.506850i
$184$	−55.6483	−	33.6937i	−0.302437	−	0.183118i
$185$	−25.8105			−0.139516
$186$	26.1008	−	181.535i	0.140327	−	0.975995i
$187$	−79.4780	−	174.033i	−0.425016	−	0.930655i
$188$	43.4443	+	12.7564i	0.231087	+	0.0678532i
$189$	−75.6307	+	65.5344i	−0.400163	+	0.346743i
$190$	−4.61375	+	1.35472i	−0.0242829	+	0.00713011i
$191$	−111.836	+	174.021i	−0.585531	+	0.911104i	0.414469	+	0.910064i	$0.363967\pi$
$191$	−111.836	+	174.021i	−0.585531	+	0.911104i	−0.999999	+	0.00104009i	$0.999669\pi$
$192$	10.4591	−	22.9021i	0.0544742	−	0.119282i
$193$	133.418	−	153.972i	0.691283	−	0.797783i	−0.296264	−	0.955106i	$-0.595741\pi$
$193$	133.418	−	153.972i	0.691283	−	0.797783i	0.987547	+	0.157323i	$0.0502863\pi$
$194$	52.4427	+	81.6024i	0.270323	+	0.420631i
$195$	16.4613	−	2.36677i	0.0844167	−	0.0121373i
$196$	−9.55536	−	66.4590i	−0.0487518	−	0.339077i
$197$	−201.567	+	129.540i	−1.02319	+	0.657561i	−0.940773	−	0.339037i	$-0.889899\pi$
$197$	−201.567	+	129.540i	−1.02319	+	0.657561i	−0.0824122	+	0.996598i	$0.526262\pi$
$198$	−7.25144	−	6.28341i	−0.0366234	−	0.0317344i
$199$	−59.7602	−	27.2916i	−0.300302	−	0.137143i	0.259565	−	0.965726i	$-0.416421\pi$
$199$	−59.7602	−	27.2916i	−0.300302	−	0.137143i	−0.559868	+	0.828582i	$0.689148\pi$
$200$	58.8526	+	37.8223i	0.294263	+	0.189111i
$201$	−59.2199	−	201.685i	−0.294627	−	1.00341i
$202$	39.4832	+	45.5660i	0.195461	+	0.225574i
$203$	49.1040	−	167.233i	0.241892	−	0.823807i
$204$	−146.064	+	66.7053i	−0.716001	+	0.326987i
$205$	−17.4195	−	2.50455i	−0.0849733	−	0.0122173i
$206$		−	261.560i		−	1.26971i
$207$	14.0420	+	15.3551i	0.0678358	+	0.0741791i
$208$	40.9818			0.197028
$209$	−7.03605	+	48.9368i	−0.0336653	+	0.234147i
$210$	−3.74575	−	8.20205i	−0.0178369	−	0.0390574i
$211$	−202.452	−	59.4452i	−0.959486	−	0.281731i	−0.235755	−	0.971813i	$-0.575756\pi$
$211$	−202.452	−	59.4452i	−0.959486	−	0.281731i	−0.723731	+	0.690082i	$0.757574\pi$
$212$	−59.9292	+	51.9289i	−0.282685	+	0.244948i
$213$	−151.135	+	44.3771i	−0.709552	+	0.208343i
$214$	148.129	−	230.492i	0.692189	−	1.07707i
$215$	8.01591	−	17.5524i	0.0372833	−	0.0816391i
$216$	47.1898	−	54.4599i	0.218471	−	0.252129i
$217$	−87.5071	−	136.164i	−0.403259	−	0.627483i
$218$	117.811	−	16.9387i	0.540419	−	0.0777006i
$219$	44.2963	+	308.087i	0.202266	+	1.40679i
$220$	−6.50803	+	4.18245i	−0.0295819	+	0.0190112i
$221$	−197.531	−	171.162i	−0.893808	−	0.774489i
$222$	202.601	+	92.5249i	0.912619	+	0.416779i
$223$	249.680	+	160.460i	1.11964	+	0.719550i	0.963373	−	0.268165i	$-0.0864173\pi$
$223$	249.680	+	160.460i	1.11964	+	0.719550i	0.156268	+	0.987715i	$0.450054\pi$
$224$	−6.26005	−	21.3198i	−0.0279467	−	0.0951776i
$225$	−14.6534	−	16.9109i	−0.0651261	−	0.0751595i
$226$	−58.5579	+	199.430i	−0.259106	+	0.882433i
$227$	124.134	−	56.6900i	0.546845	−	0.249736i	−0.122782	−	0.992434i	$-0.539181\pi$
$227$	124.134	−	56.6900i	0.546845	−	0.249736i	0.669627	+	0.742698i	$0.266454\pi$
$228$	41.0723	+	5.90531i	0.180142	+	0.0259005i
$229$		−	36.2794i		−	0.158425i	−0.996858	−	0.0792126i	$-0.974759\pi$
$229$		−	36.2794i		−	0.158425i	0.996858	−	0.0792126i	$-0.0252406\pi$
$230$	15.0684	−	7.37503i	0.0655147	−	0.0320653i
$231$	−92.7092			−0.401339
$232$	−17.8611	+	124.227i	−0.0769876	+	0.535461i
$233$	−48.8262	−	106.914i	−0.209554	−	0.458860i	0.775446	−	0.631414i	$-0.217525\pi$
$233$	−48.8262	−	106.914i	−0.209554	−	0.458860i	−0.985000	+	0.172554i	$0.944798\pi$
$234$	−12.5771	−	3.69298i	−0.0537484	−	0.0157820i
$235$	−8.82459	+	7.64655i	−0.0375514	+	0.0325385i
$236$	−51.4571	+	15.1092i	−0.218038	+	0.0640219i
$237$	−122.209	+	190.161i	−0.515649	+	0.802366i
$238$	−58.8696	+	128.906i	−0.247351	+	0.541624i
$239$	−179.110	+	206.704i	−0.749414	+	0.864870i	−0.994511	−	0.104628i	$-0.966635\pi$
$239$	−179.110	+	206.704i	−0.749414	+	0.864870i	0.245097	+	0.969499i	$0.421180\pi$
$240$	3.51030	+	5.46214i	0.0146263	+	0.0227589i
$241$	373.137	−	53.6491i	1.54829	−	0.222610i	0.685461	−	0.728109i	$-0.259601\pi$
$241$	373.137	−	53.6491i	1.54829	−	0.222610i	0.862827	+	0.505499i	$0.168692\pi$
$242$	−13.0331	−	90.6471i	−0.0538557	−	0.374575i
$243$	−40.9467	+	26.3148i	−0.168505	+	0.108292i
$244$	44.5470	+	38.6002i	0.182570	+	0.158198i
$245$	15.7503	+	7.19291i	0.0642868	+	0.0293588i
$246$	127.757	+	82.1047i	0.519339	+	0.333759i
$247$	19.0287	+	64.8059i	0.0770394	+	0.262372i
$248$	76.3242	+	88.0829i	0.307759	+	0.355173i
$249$	−104.898	+	357.248i	−0.421275	+	1.43473i
$250$	−32.9981	+	15.0697i	−0.131993	+	0.0602790i
$251$	71.2272	+	10.2409i	0.283774	+	0.0408005i	0.282732	−	0.959199i	$-0.408759\pi$
$251$	71.2272	+	10.2409i	0.283774	+	0.0408005i	0.00104182	+	0.999999i	$0.499668\pi$
$252$			7.10707i			0.0282026i
$253$	−4.61580	−	172.429i	−0.0182443	−	0.681536i
$254$	−10.2797			−0.0404711
$255$	5.89324	−	40.9884i	0.0231107	−	0.160739i
$256$	6.64664	+	14.5541i	0.0259634	+	0.0568520i
$257$	−218.622	−	64.1931i	−0.850668	−	0.249779i	−0.172795	−	0.984958i	$-0.555280\pi$
$257$	−218.622	−	64.1931i	−0.850668	−	0.249779i	−0.677873	+	0.735179i	$0.737098\pi$
$258$	−125.843	+	109.043i	−0.487763	+	0.422649i
$259$	188.603	−	55.3789i	0.728198	−	0.213818i
$260$	−5.71380	+	8.89084i	−0.0219761	+	0.0341955i
$261$	16.6759	−	36.5152i	0.0638925	−	0.139905i
$262$	49.5077	−	57.1349i	0.188961	−	0.218072i
$263$	−187.521	−	291.788i	−0.713007	−	1.10946i	−0.988945	−	0.148285i	$-0.952625\pi$
$263$	−187.521	−	291.788i	−0.713007	−	1.10946i	0.275937	−	0.961176i	$-0.411012\pi$
$264$	66.0783	−	9.50063i	0.250297	−	0.0359872i
$265$	−2.91029	−	20.2415i	−0.0109822	−	0.0763831i
$266$	30.8070	−	19.7985i	0.115816	−	0.0744304i
$267$	148.524	+	128.697i	0.556270	+	0.482011i
$268$	121.508	+	55.4911i	0.453390	+	0.207056i
$269$	−222.153	−	142.769i	−0.825847	−	0.530740i	0.0581085	−	0.998310i	$-0.481493\pi$
$269$	−222.153	−	142.769i	−0.825847	−	0.530740i	−0.883956	+	0.467570i	$0.845129\pi$
$270$	5.23554	+	17.8306i	0.0193909	+	0.0660394i
$271$	210.039	+	242.398i	0.775053	+	0.894458i	0.996742	−	0.0806590i	$-0.0257025\pi$
$271$	210.039	+	242.398i	0.775053	+	0.894458i	−0.221689	+	0.975117i	$0.571157\pi$
$272$	28.7491	−	97.9106i	0.105695	−	0.359965i
$273$	−115.208	+	52.6137i	−0.422007	+	0.192724i
$274$	−319.949	−	46.0018i	−1.16770	−	0.167890i
$275$			185.494i			0.674525i
$276$	−144.718	+	3.87401i	−0.524340	+	0.0140363i
$277$	478.892			1.72885			0.864426	−	0.502761i	$-0.167682\pi$
$277$	478.892			1.72885			0.864426	+	0.502761i	$0.167682\pi$
$278$	17.0092	−	118.301i	0.0611840	−	0.425544i
$279$	−15.4862	−	33.9101i	−0.0555061	−	0.121541i
$280$	5.49805	+	1.61437i	0.0196359	+	0.00576561i
$281$	−188.074	+	162.967i	−0.669301	+	0.579953i	−0.921810	−	0.387642i	$-0.873290\pi$
$281$	−188.074	+	162.967i	−0.669301	+	0.579953i	0.252509	+	0.967595i	$0.418744\pi$
$282$	96.6803	−	28.3879i	0.342838	−	0.100666i
$283$	63.6081	−	98.9762i	0.224764	−	0.349739i	−0.710496	−	0.703701i	$-0.751529\pi$
$283$	63.6081	−	98.9762i	0.224764	−	0.349739i	0.935260	+	0.353962i	$0.115166\pi$
$284$	41.5828	−	91.0537i	0.146418	−	0.320612i
$285$	−7.00756	+	8.08715i	−0.0245879	+	0.0283760i
$286$	58.7477	+	91.4133i	0.205412	+	0.319627i
$287$	132.662	−	19.0739i	0.462237	−	0.0664597i
$288$	−0.728316	−	5.06555i	−0.00252887	−	0.0175887i
$289$	−304.376	+	195.611i	−1.05320	+	0.676853i
$290$	−24.4603	−	21.1950i	−0.0843459	−	0.0730861i
$291$	196.357	+	89.6734i	0.674768	+	0.308156i
$292$	−166.400	−	106.939i	−0.569863	−	0.366229i
$293$	−12.7186	−	43.3157i	−0.0434083	−	0.147835i	0.934937	−	0.354813i	$-0.115455\pi$
$293$	−12.7186	−	43.3157i	−0.0434083	−	0.147835i	−0.978346	+	0.206978i	$0.933637\pi$
$294$	−97.8478	−	112.922i	−0.332816	−	0.384090i
$295$	3.89642	−	13.2700i	0.0132082	−	0.0449830i
$296$	−128.751	+	58.7988i	−0.434971	+	0.198645i
$297$	189.125	+	27.1920i	0.636783	+	0.0915556i
$298$		−	103.428i		−	0.347075i
$299$	−103.591	−	211.654i	−0.346460	−	0.707873i
$300$	155.684			0.518947
$301$	−20.9137	+	145.458i	−0.0694808	+	0.483250i
$302$	14.7147	+	32.2207i	0.0487242	+	0.106691i
$303$	128.739	+	37.8012i	0.424881	+	0.124756i
$304$	−19.9287	+	17.2684i	−0.0655551	+	0.0568038i
$305$	−14.5851	+	4.28256i	−0.0478198	+	0.0140412i
$306$	−17.6460	+	27.4577i	−0.0576666	+	0.0897311i
$307$	191.399	−	419.106i	0.623450	−	1.36516i	−0.289533	−	0.957168i	$-0.593500\pi$
$307$	191.399	−	419.106i	0.623450	−	1.36516i	0.912983	−	0.407997i	$-0.133773\pi$
$308$	38.5817	−	44.5257i	0.125265	−	0.144564i
$309$	−314.692	−	489.671i	−1.01842	−	1.58469i
$310$	−29.7506	+	4.27749i	−0.0959697	+	0.0137984i
$311$	12.0687	+	83.9398i	0.0388062	+	0.269903i	0.999982	−	0.00603451i	$-0.00192086\pi$
$311$	12.0687	+	83.9398i	0.0388062	+	0.269903i	−0.961176	+	0.275937i	$0.911012\pi$
$312$	76.7225	−	49.3065i	0.245905	−	0.158034i
$313$	−231.972	−	201.005i	−0.741124	−	0.642187i	0.200176	−	0.979760i	$-0.435849\pi$
$313$	−231.972	−	201.005i	−0.741124	−	0.642187i	−0.941299	+	0.337573i	$0.890394\pi$
$314$	−102.801	−	46.9477i	−0.327392	−	0.149515i
$315$	−1.54185	−	0.990888i	−0.00489477	−	0.00314568i
$316$	−40.4707	−	137.831i	−0.128072	−	0.436173i
$317$	229.704	+	265.092i	0.724618	+	0.836254i	0.991854	−	0.127377i	$-0.0406559\pi$
$317$	229.704	+	265.092i	0.724618	+	0.836254i	−0.267236	+	0.963631i	$0.586110\pi$
$318$	−49.7168	+	169.320i	−0.156342	+	0.532452i
$319$	−302.703	+	138.240i	−0.948911	+	0.433353i
$320$	−4.08416	−	0.587213i	−0.0127630	−	0.00183504i
$321$		−	609.727i		−	1.89946i
$322$	−94.2842	+	86.2216i	−0.292808	+	0.267769i
$323$	168.178			0.520676
$324$	25.1395	−	174.849i	0.0775912	−	0.539658i
$325$	105.271	+	230.510i	0.323909	+	0.709262i
$326$	−292.023	−	85.7457i	−0.895776	−	0.263023i
$327$	200.177	−	173.454i	0.612161	−	0.530441i
$328$	−92.5999	+	27.1898i	−0.282317	+	0.0828957i
$329$	48.0768	−	74.8090i	0.146130	−	0.227383i
$330$	−7.15171	+	15.6601i	−0.0216718	+	0.0474547i
$331$	85.2737	−	98.4111i	0.257624	−	0.297314i	−0.612173	−	0.790724i	$-0.709704\pi$
$331$	85.2737	−	98.4111i	0.257624	−	0.297314i	0.869797	+	0.493410i	$0.164250\pi$
$332$	−127.923	−	199.051i	−0.385309	−	0.599552i
$333$	44.8118	−	6.44297i	0.134570	−	0.0193483i
$334$	49.9665	+	347.525i	0.149600	+	1.04049i
$335$	−28.9797	+	18.6241i	−0.0865064	+	0.0555943i
$336$	−37.3701	−	32.3814i	−0.111221	−	0.0963731i
$337$	172.442	+	78.7518i	0.511698	+	0.233685i	0.654494	−	0.756067i	$-0.272882\pi$
$337$	172.442	+	78.7518i	0.511698	+	0.233685i	−0.142795	+	0.989752i	$0.545609\pi$
$338$	−76.1785	−	48.9569i	−0.225380	−	0.144843i
$339$	130.314	+	443.808i	0.384407	+	1.30917i
$340$	17.2331	+	19.8880i	0.0506855	+	0.0584941i
$341$	−87.0648	+	296.515i	−0.255322	+	0.869546i
$342$	7.67215	−	3.50375i	0.0224332	−	0.0102449i
$343$	−321.034	−	46.1578i	−0.935960	−	0.134571i
$344$		−	105.818i		−	0.307611i
$345$	19.3366	−	31.9362i	0.0560480	−	0.0925686i
$346$	275.166			0.795278
$347$	76.1555	−	529.673i	0.219468	−	1.52644i	−0.520539	−	0.853838i	$-0.674269\pi$
$347$	76.1555	−	529.673i	0.219468	−	1.52644i	0.740008	−	0.672598i	$-0.234822\pi$
$348$	116.024	+	254.056i	0.333401	+	0.730046i
$349$	329.903	+	96.8684i	0.945282	+	0.277560i	0.717821	−	0.696227i	$-0.245139\pi$
$349$	329.903	+	96.8684i	0.945282	+	0.277560i	0.227461	+	0.973787i	$0.426958\pi$
$350$	103.837	−	89.9754i	0.296678	−	0.257073i
$351$	250.453	−	73.5397i	0.713542	−	0.209515i
$352$	−22.9362	+	35.6894i	−0.0651595	+	0.101390i
$353$	−15.1745	+	33.2275i	−0.0429873	+	0.0941290i	−0.929907	−	0.367794i	$-0.880113\pi$
$353$	−15.1745	+	33.2275i	−0.0429873	+	0.0941290i	0.886920	+	0.461923i	$0.152840\pi$
$354$	−78.1551	+	90.1958i	−0.220777	+	0.254790i
$355$	13.9562	+	21.7162i	0.0393131	+	0.0611725i
$356$	−123.619	+	17.7737i	−0.347245	+	0.0499263i
$357$	44.8812	+	312.155i	0.125718	+	0.874385i
$358$	−156.968	+	100.878i	−0.438459	+	0.281781i
$359$	−16.7343	−	14.5003i	−0.0466135	−	0.0403909i	0.631242	−	0.775586i	$-0.282545\pi$
$359$	−16.7343	−	14.5003i	−0.0466135	−	0.0403909i	−0.677856	+	0.735195i	$0.737091\pi$
$360$	1.20050	+	0.548248i	0.00333471	+	0.00152291i
$361$	267.132	+	171.675i	0.739978	+	0.475555i
$362$	142.903	+	486.683i	0.394759	+	1.34443i
$363$	−133.460	−	154.021i	−0.367659	−	0.424301i
$364$	22.6759	−	77.2269i	0.0622963	−	0.212162i
$365$	46.4000	−	21.1902i	0.127123	−	0.0580553i
$366$	129.838	+	18.6679i	0.354749	+	0.0510053i
$367$			316.786i			0.863176i	0.902071	+	0.431588i	$0.142047\pi$
$367$			316.786i			0.863176i	−0.902071	+	0.431588i	$0.857953\pi$
$368$	58.3650	−	71.1163i	0.158601	−	0.193251i
$369$	30.8687			0.0836550
$370$	5.19472	−	36.1301i	0.0140398	−	0.0976488i
$371$	64.6962	+	141.665i	0.174383	+	0.381846i
$372$	248.863	+	73.0728i	0.668987	+	0.196432i
$373$	−315.166	+	273.093i	−0.844950	+	0.732153i	−0.965458	−	0.260559i	$-0.916093\pi$
$373$	−315.166	+	273.093i	−0.844950	+	0.732153i	0.120508	+	0.992712i	$0.461548\pi$
$374$	259.610	−	76.2284i	0.694145	−	0.203819i
$375$	−43.6453	+	67.9135i	−0.116388	+	0.181103i
$376$	−26.6004	+	58.2468i	−0.0707458	+	0.154912i
$377$	−297.710	+	343.575i	−0.789681	+	0.911341i
$378$	−76.5146	−	119.059i	−0.202419	−	0.314971i
$379$	−661.740	+	95.1439i	−1.74602	+	0.251039i	−0.940078	−	0.340960i	$-0.889248\pi$
$379$	−661.740	+	95.1439i	−1.74602	+	0.251039i	−0.805938	+	0.591999i	$0.798339\pi$
$380$	−0.967783	−	6.73108i	−0.00254680	−	0.0177134i
$381$	−19.2447	+	12.3678i	−0.0505109	+	0.0324614i
$382$	−221.089	−	191.575i	−0.578767	−	0.501505i
$383$	−395.078	−	180.426i	−1.03154	−	0.471086i	−0.173585	−	0.984819i	$-0.555535\pi$
$383$	−395.078	−	180.426i	−1.03154	−	0.471086i	−0.857950	+	0.513733i	$0.828262\pi$
$384$	29.9538	+	19.2501i	0.0780047	+	0.0501306i
$385$	4.28051	+	14.5781i	0.0111182	+	0.0378651i
$386$	188.681	+	217.750i	0.488811	+	0.564118i
$387$	−9.53557	+	32.4752i	−0.0246397	+	0.0839152i
$388$	−124.783	+	56.9867i	−0.321607	+	0.146873i
$389$	140.553	+	20.2084i	0.361318	+	0.0519497i	0.320583	−	0.947220i	$-0.396121\pi$
$389$	140.553	+	20.2084i	0.361318	+	0.0519497i	0.0407347	+	0.999170i	$0.487030\pi$
$390$			23.5191i			0.0603055i
$391$	−578.339	+	99.0154i	−1.47913	+	0.253236i
$392$	94.9537			0.242229
$393$	23.9430	−	166.527i	0.0609237	−	0.423734i
$394$	−140.764	−	308.230i	−0.357268	−	0.782309i
$395$	35.5444	+	10.4368i	0.0899858	+	0.0264222i
$396$	10.2551	−	8.88608i	0.0258967	−	0.0224396i
$397$	526.008	−	154.450i	1.32496	−	0.389043i	0.458678	−	0.888603i	$-0.348323\pi$
$397$	526.008	−	154.450i	1.32496	−	0.389043i	0.866279	+	0.499560i	$0.166505\pi$
$398$	50.2308	−	78.1606i	0.126208	−	0.196383i
$399$	33.8540	−	74.1300i	0.0848472	−	0.185790i
$400$	−64.7893	+	74.7708i	−0.161973	+	0.186927i
$401$	−137.285	−	213.619i	−0.342356	−	0.532716i	0.626795	−	0.779184i	$-0.284366\pi$
$401$	−137.285	−	213.619i	−0.342356	−	0.532716i	−0.969151	+	0.246468i	$0.920730\pi$
$402$	294.241	−	42.3054i	0.731942	−	0.105237i
$403$	60.0827	+	417.884i	0.149089	+	1.03693i
$404$	−71.7307	+	46.0985i	−0.177551	+	0.114105i
$405$	34.4279	+	29.8319i	0.0850072	+	0.0736591i
$406$	224.213	+	102.395i	0.552248	+	0.252203i
$407$	−315.722	−	202.902i	−0.775730	−	0.498532i
$408$	−63.9779	−	217.889i	−0.156809	−	0.534041i
$409$	−391.356	−	451.648i	−0.956860	−	1.10428i	−0.994474	−	0.104983i	$-0.966521\pi$
$409$	−391.356	−	451.648i	−0.956860	−	1.10428i	0.0376143	−	0.999292i	$-0.488024\pi$
$410$	7.01183	−	23.8801i	0.0171020	−	0.0582442i
$411$	−654.328	+	298.821i	−1.59204	+	0.727059i
$412$	366.137	+	52.6426i	0.888682	+	0.127773i
$413$			105.327i			0.255029i
$414$	−24.3205	+	16.5659i	−0.0587451	+	0.0400142i
$415$	61.0188			0.147033
$416$	−8.24813	+	57.3670i	−0.0198272	+	0.137902i
$417$	−110.489	−	241.938i	−0.264962	−	0.580186i
$418$	−67.0866	−	19.6984i	−0.160494	−	0.0471254i
$419$	161.014	−	139.519i	0.384281	−	0.332982i	−0.441202	−	0.897408i	$-0.645448\pi$
$419$	161.014	−	139.519i	0.384281	−	0.332982i	0.825484	+	0.564426i	$0.190902\pi$
$420$	12.2353	−	3.59260i	0.0291316	−	0.00855381i
$421$	233.721	−	363.677i	0.555156	−	0.863840i	−0.444331	−	0.895863i	$-0.646559\pi$
$421$	233.721	−	363.677i	0.555156	−	0.863840i	0.999487	+	0.0320229i	$0.0101949\pi$
$422$	123.959	−	271.431i	0.293741	−	0.643202i
$423$	13.4123	−	15.4787i	0.0317077	−	0.0365926i
$424$	−60.6296	−	94.3414i	−0.142994	−	0.222503i
$425$	624.567	−	89.7991i	1.46957	−	0.211292i
$426$	−31.7020	−	220.493i	−0.0744179	−	0.517588i
$427$	97.3876	−	62.5872i	0.228074	−	0.146574i
$428$	292.835	+	253.743i	0.684194	+	0.592857i
$429$	219.965	+	100.455i	0.512739	+	0.234160i
$430$	22.9569	+	14.7535i	0.0533881	+	0.0343104i
$431$	144.423	+	491.861i	0.335089	+	1.14121i	0.938931	+	0.344105i	$0.111818\pi$
$431$	144.423	+	491.861i	0.335089	+	1.14121i	−0.603842	+	0.797104i	$0.706364\pi$
$432$	66.7365	+	77.0180i	0.154483	+	0.178282i
$433$	−53.9146	+	183.616i	−0.124514	+	0.424056i	−0.998030	−	0.0627396i	$-0.980016\pi$
$433$	−53.9146	+	183.616i	−0.124514	+	0.424056i	0.873516	+	0.486796i	$0.161834\pi$
$434$	208.217	−	95.0893i	0.479762	−	0.219100i
$435$	−71.2929	−	10.2504i	−0.163892	−	0.0235641i
$436$			168.324i			0.386064i
$437$	139.559	+	59.2738i	0.319357	+	0.135638i
$438$	−440.182			−1.00498
$439$	106.087	−	737.854i	0.241657	−	1.68076i	−0.402151	−	0.915573i	$-0.631737\pi$
$439$	106.087	−	737.854i	0.241657	−	1.68076i	0.643808	−	0.765187i	$-0.277353\pi$
$440$	−4.54485	−	9.95183i	−0.0103292	−	0.0226178i
$441$	−29.1409	−	8.55654i	−0.0660792	−	0.0194026i
$442$	279.352	−	242.060i	0.632017	−	0.547646i
$443$	415.164	−	121.903i	0.937166	−	0.275177i	0.222732	−	0.974880i	$-0.428503\pi$
$443$	415.164	−	121.903i	0.937166	−	0.275177i	0.714434	+	0.699703i	$0.246684\pi$
$444$	−170.294	+	264.983i	−0.383546	+	0.596809i
$445$	13.3794	−	29.2968i	0.0300661	−	0.0658355i
$446$	−274.866	+	317.212i	−0.616291	+	0.711238i
$447$	−124.438	−	193.630i	−0.278385	−	0.433176i
$448$	31.1038	−	4.47205i	0.0694280	−	0.00998224i
$449$	4.73273	+	32.9168i	0.0105406	+	0.0733115i	0.994413	−	0.105561i	$-0.0336640\pi$
$449$	4.73273	+	32.9168i	0.0105406	+	0.0733115i	−0.983872	+	0.178873i	$0.942755\pi$
$450$	26.6214	−	17.1085i	0.0591586	−	0.0380189i
$451$	−193.392	−	167.575i	−0.428807	−	0.371564i
$452$	−267.380	−	122.108i	−0.591549	−	0.270151i
$453$	66.3135	+	42.6171i	0.146387	+	0.0940775i
$454$	54.3721	+	185.174i	0.119762	+	0.407873i
$455$	13.5926	+	15.6866i	0.0298737	+	0.0344761i
$456$	−16.5327	+	56.3053i	−0.0362560	+	0.123476i
$457$	263.236	−	120.216i	0.576009	−	0.263055i	−0.106039	−	0.994362i	$-0.533817\pi$
$457$	263.236	−	120.216i	0.576009	−	0.263055i	0.682048	+	0.731307i	$0.261089\pi$
$458$	50.7845	+	7.30171i	0.110883	+	0.0159426i
$459$		−	649.953i		−	1.41602i
$460$	7.29099	+	22.5773i	0.0158500	+	0.0490811i
$461$	20.1985			0.0438145			0.0219073	−	0.999760i	$-0.493026\pi$
$461$	20.1985			0.0438145			0.0219073	+	0.999760i	$0.493026\pi$
$462$	18.6590	−	129.776i	0.0403874	−	0.280901i
$463$	−16.6640	−	36.4890i	−0.0359913	−	0.0788099i	0.890782	−	0.454430i	$-0.150157\pi$
$463$	−16.6640	−	36.4890i	−0.0359913	−	0.0788099i	−0.926774	+	0.375620i	$0.877430\pi$
$464$	−170.300	−	50.0047i	−0.367026	−	0.107769i
$465$	−50.5501	+	43.8019i	−0.108710	+	0.0941977i
$466$	159.488	−	46.8298i	0.342248	−	0.100493i
$467$	−65.3042	+	101.615i	−0.139838	+	0.217592i	−0.904108	−	0.427305i	$-0.859463\pi$
$467$	−65.3042	+	101.615i	−0.139838	+	0.217592i	0.764270	+	0.644896i	$0.223100\pi$
$468$	7.70082	−	16.8624i	0.0164547	−	0.0360309i
$469$	171.801	−	198.269i	0.366313	−	0.422748i
$470$	−8.92772	−	13.8918i	−0.0189951	−	0.0295570i
$471$	−248.940	+	35.7921i	−0.528534	+	0.0759918i
$472$	−10.7937	−	75.0715i	−0.0228679	−	0.159050i
$473$	236.036	−	151.691i	0.499020	−	0.320701i
$474$	−241.594	−	209.343i	−0.509693	−	0.441651i
$475$	−148.321	−	67.7358i	−0.312254	−	0.142602i
$476$	−168.597	−	108.351i	−0.354196	−	0.227628i
$477$	10.1056	+	34.4165i	0.0211857	+	0.0721520i
$478$	−253.300	−	292.324i	−0.529916	−	0.611556i
$479$	−40.8630	+	139.167i	−0.0853089	+	0.290536i	−0.991087	−	0.133217i	$-0.957469\pi$
$479$	−40.8630	+	139.167i	−0.0853089	+	0.290536i	0.905778	+	0.423753i	$0.139287\pi$
$480$	−8.35250	+	3.81446i	−0.0174010	+	0.00794679i
$481$	−507.492	−	72.9663i	−1.05508	−	0.151697i
$482$			533.123i			1.10606i
$483$	−72.7745	+	274.853i	−0.150672	+	0.569054i
$484$	129.513			0.267588
$485$	5.03462	−	35.0166i	0.0103807	−	0.0721991i
$486$	−28.5949	−	62.6142i	−0.0588373	−	0.128836i
$487$	−142.457	−	41.8291i	−0.292519	−	0.0858914i	0.132180	−	0.991226i	$-0.457802\pi$
$487$	−142.457	−	41.8291i	−0.292519	−	0.0858914i	−0.424700	+	0.905334i	$0.639620\pi$
$488$	−62.9990	+	54.5889i	−0.129096	+	0.111863i
$489$	−649.863	+	190.817i	−1.32896	+	0.390219i
$490$	−13.2387	+	20.5999i	−0.0270178	+	0.0420405i
$491$	−43.6846	+	95.6560i	−0.0889707	+	0.194819i	−0.948887	−	0.315617i	$-0.897789\pi$
$491$	−43.6846	+	95.6560i	−0.0889707	+	0.194819i	0.859916	+	0.510436i	$0.170516\pi$
$492$	−140.645	+	162.313i	−0.285863	+	0.329903i
$493$	611.998	+	952.288i	1.24138	+	1.93162i
$494$	−94.5463	+	13.5937i	−0.191389	+	0.0275176i
$495$	0.498009	+	3.46373i	0.00100608	+	0.00699743i
$496$	−138.661	+	89.1122i	−0.279559	+	0.179662i
$497$	−148.575	−	128.741i	−0.298944	−	0.259036i
$498$	−478.971	−	218.739i	−0.961789	−	0.439234i
$499$	306.780	+	197.156i	0.614790	+	0.395102i	0.810651	−	0.585530i	$-0.199114\pi$
$499$	306.780	+	197.156i	0.614790	+	0.395102i	−0.195861	+	0.980632i	$0.562750\pi$
$500$	−14.4536	−	49.2244i	−0.0289072	−	0.0984488i
$501$	511.662	+	590.489i	1.02128	+	1.17862i
$502$	−28.6709	+	97.6441i	−0.0571133	+	0.194510i
$503$	89.5170	−	40.8810i	0.177966	−	0.0812744i	−0.324440	−	0.945906i	$-0.605176\pi$
$503$	89.5170	−	40.8810i	0.177966	−	0.0812744i	0.502406	+	0.864632i	$0.332448\pi$
$504$	−9.94861	−	1.43039i	−0.0197393	−	0.00283808i
$505$		−	21.9889i		−	0.0435424i
$506$	242.298	+	28.2423i	0.478849	+	0.0558148i
$507$	−201.516			−0.397468
$508$	2.06892	−	14.3896i	0.00407268	−	0.0283261i
$509$	314.457	+	688.564i	0.617793	+	1.35278i	0.917114	+	0.398626i	$0.130513\pi$
$509$	314.457	+	688.564i	0.617793	+	1.35278i	−0.299320	+	0.954153i	$0.596760\pi$
$510$	56.1902	+	16.4989i	0.110177	+	0.0323508i
$511$	−293.590	+	254.397i	−0.574539	+	0.497841i
$512$	−21.7108	+	6.37488i	−0.0424040	+	0.0124509i
$513$	−90.8041	+	141.294i	−0.177006	+	0.275427i
$514$	133.859	−	293.111i	0.260427	−	0.570255i
$515$	−62.4685	+	72.0925i	−0.121298	+	0.139986i
$516$	−127.313	−	198.104i	−0.246732	−	0.383922i
$517$	−168.056	+	24.1628i	−0.325061	+	0.0467367i
$518$	39.5615	+	275.156i	0.0763735	+	0.531190i
$519$	515.142	−	331.062i	0.992566	−	0.637884i
$520$	−11.2956	−	9.78768i	−0.0217223	−	0.0188225i
$521$	743.235	+	339.424i	1.42655	+	0.651486i	0.971078	−	0.238762i	$-0.0767416\pi$
$521$	743.235	+	339.424i	1.42655	+	0.651486i	0.455477	+	0.890248i	$0.349469\pi$
$522$	47.7584	+	30.6925i	0.0914912	+	0.0587978i
$523$	−39.4255	−	134.271i	−0.0753833	−	0.256732i	0.913176	−	0.407566i	$-0.133622\pi$
$523$	−39.4255	−	134.271i	−0.0753833	−	0.256732i	−0.988559	+	0.150834i	$0.951804\pi$
$524$	70.0144	+	80.8009i	0.133615	+	0.154200i
$525$	86.1425	−	293.374i	0.164081	−	0.558808i
$526$	446.192	−	203.769i	0.848274	−	0.387394i
$527$	1040.53	+	149.605i	1.97443	+	0.283881i
$528$			94.4098i			0.178806i
$529$	−514.818	−	121.668i	−0.973192	−	0.229996i
$530$	28.9202			0.0545664
$531$	−3.45237	+	24.0118i	−0.00650165	+	0.0452199i
$532$	21.5140	+	47.1090i	0.0404398	+	0.0885507i
$533$	−335.426	−	98.4898i	−0.629316	−	0.184784i
$534$	−210.045	+	182.005i	−0.393342	+	0.340833i
$535$	−95.8765	+	28.1519i	−0.179208	+	0.0526203i
$536$	−102.133	+	158.922i	−0.190546	+	0.296495i
$537$	−172.494	+	377.708i	−0.321217	+	0.703367i
$538$	244.562	−	282.240i	0.454576	−	0.524609i
$539$	136.117	+	211.802i	0.252536	+	0.392954i
$540$	−26.0134	+	3.74016i	−0.0481729	+	0.00692622i
$541$	−91.9586	−	639.586i	−0.169979	−	1.18223i	−0.878923	−	0.476964i	$-0.841737\pi$
$541$	−91.9586	−	639.586i	−0.169979	−	1.18223i	0.708944	−	0.705265i	$-0.249172\pi$
$542$	−381.587	+	245.231i	−0.704035	+	0.452456i
$543$	853.075	+	739.194i	1.57104	+	1.36131i
$544$	131.271	+	59.9494i	0.241307	+	0.110201i
$545$	−36.5172	−	23.4682i	−0.0670041	−	0.0430609i
$546$	−50.4625	−	171.860i	−0.0924222	−	0.314761i
$547$	−219.336	−	253.127i	−0.400980	−	0.462755i	0.518969	−	0.854793i	$-0.326316\pi$
$547$	−219.336	−	253.127i	−0.400980	−	0.462755i	−0.919949	+	0.392037i	$0.871770\pi$
$548$	128.788	−	438.613i	0.235015	−	0.800388i
$549$	24.2533	−	11.0761i	0.0441772	−	0.0201751i
$550$	−259.659	−	37.3333i	−0.472107	−	0.0678787i
$551$		−	292.520i		−	0.530889i
$552$	23.7035	−	203.359i	0.0429412	−	0.368403i
$553$	−282.124			−0.510170
$554$	−96.3835	+	670.362i	−0.173977	+	1.21004i
$555$	−33.7442	−	73.8895i	−0.0608004	−	0.133134i
$556$	162.177	+	47.6195i	0.291685	+	0.0856465i
$557$	−193.217	+	167.424i	−0.346889	+	0.300581i	−0.810826	−	0.585287i	$-0.800982\pi$
$557$	−193.217	+	167.424i	−0.346889	+	0.300581i	0.463937	+	0.885868i	$0.346436\pi$
$558$	50.5848	−	14.8530i	0.0906537	−	0.0266183i
$559$	207.231	−	322.458i	0.370717	−	0.576847i
$560$	−3.36638	+	7.37135i	−0.00601140	+	0.0131631i
$561$	394.306	−	455.054i	0.702864	−	0.811148i
$562$	−190.272	−	296.068i	−0.338561	−	0.526812i
$563$	−451.233	+	64.8775i	−0.801479	+	0.115235i	−0.530869	−	0.847454i	$-0.678135\pi$
$563$	−451.233	+	64.8775i	−0.801479	+	0.115235i	−0.270610	+	0.962689i	$0.587225\pi$
$564$	20.2797	+	141.048i	0.0359569	+	0.250086i
$565$	63.7699	−	40.9825i	0.112867	−	0.0725353i
$566$	125.747	+	108.960i	0.222167	+	0.192509i
$567$	−315.580	−	144.120i	−0.556578	−	0.254181i
$568$	119.090	+	76.5342i	0.209665	+	0.134743i
$569$	−314.918	−	1072.51i	−0.553459	−	1.88491i	−0.456748	−	0.889596i	$-0.650986\pi$
$569$	−314.918	−	1072.51i	−0.553459	−	1.88491i	−0.0967117	−	0.995312i	$-0.530832\pi$
$570$	−9.91018	−	11.4370i	−0.0173863	−	0.0200648i
$571$	−39.3458	+	133.999i	−0.0689068	+	0.234675i	−0.986745	−	0.162281i	$-0.948115\pi$
$571$	−39.3458	+	133.999i	−0.0689068	+	0.234675i	0.917838	+	0.396955i	$0.129933\pi$
$572$	−139.786	+	63.8380i	−0.244381	+	0.111605i
$573$	−644.394	−	92.6498i	−1.12460	−	0.161693i
$574$			189.542i			0.330212i
$575$	549.931	+	145.609i	0.956402	+	0.253232i
$576$	7.23743			0.0125650
$577$	−128.359	+	892.755i	−0.222459	+	1.54724i	0.506235	+	0.862396i	$0.331037\pi$
$577$	−128.359	+	892.755i	−0.222459	+	1.54724i	−0.728694	+	0.684840i	$0.759872\pi$
$578$	−212.560	−	465.440i	−0.367750	−	0.805260i
$579$	615.214	+	180.643i	1.06255	+	0.311992i
$580$	34.5921	−	29.9742i	0.0596416	−	0.0516797i
$581$	−445.878	+	130.922i	−0.767432	+	0.225338i
$582$	−165.046	+	256.817i	−0.283584	+	0.441266i
$583$	123.524	−	270.479i	0.211876	−	0.463943i
$584$	183.185	−	211.407i	0.313673	−	0.361999i
$585$	2.58458	+	4.02168i	0.00441808	+	0.00687466i
$586$	63.1939	−	9.08591i	0.107839	−	0.0155050i
$587$	−108.289	−	753.165i	−0.184478	−	1.28308i	−0.846013	−	0.533162i	$-0.821004\pi$
$587$	−108.289	−	753.165i	−0.184478	−	1.28308i	0.661535	−	0.749914i	$-0.269905\pi$
$588$	177.764	−	114.242i	0.302320	−	0.194289i
$589$	−205.300	−	177.893i	−0.348557	−	0.302026i
$590$	17.7914	+	8.12505i	0.0301549	+	0.0137713i
$591$	−634.367	−	407.683i	−1.07338	−	0.689819i
$592$	−56.3947	−	192.063i	−0.0952614	−	0.324430i
$593$	17.8172	+	20.5622i	0.0300459	+	0.0346748i	0.770574	−	0.637351i	$-0.219970\pi$
$593$	17.8172	+	20.5622i	0.0300459	+	0.0346748i	−0.740528	+	0.672026i	$0.765424\pi$
$594$	−76.1278	+	259.267i	−0.128161	+	0.436477i
$595$	47.0127	−	21.4700i	0.0790129	−	0.0360840i
$596$	144.781	+	20.8164i	0.242921	+	0.0349268i
$597$		−	206.760i		−	0.346331i
$598$	317.126	−	102.411i	0.530312	−	0.171256i
$599$	−128.190			−0.214007			−0.107004	−	0.994259i	$-0.534126\pi$
$599$	−128.190			−0.214007			−0.107004	+	0.994259i	$0.534126\pi$
$600$	−31.3335	+	217.930i	−0.0522226	+	0.363216i
$601$	−300.954	−	658.996i	−0.500755	−	1.09650i	−0.976223	−	0.216767i	$-0.930449\pi$
$601$	−300.954	−	658.996i	−0.500755	−	1.09650i	0.475469	−	0.879733i	$-0.342279\pi$
$602$	−199.406	−	58.5509i	−0.331239	−	0.0972606i
$603$	45.6650	−	39.5689i	0.0757296	−	0.0656201i
$604$	−48.0647	+	14.1131i	−0.0795774	+	0.0233660i
$605$	−18.0570	+	28.0973i	−0.0298463	+	0.0464418i
$606$	−78.8253	+	172.603i	−0.130075	+	0.284824i
$607$	−53.8455	+	62.1411i	−0.0887076	+	0.102374i	−0.798368	−	0.602170i	$-0.794303\pi$
$607$	−53.8455	+	62.1411i	−0.0887076	+	0.102374i	0.709660	+	0.704544i	$0.248848\pi$
$608$	−20.1616	−	31.3721i	−0.0331606	−	0.0515989i
$609$	542.946	−	78.0639i	0.891537	−	0.128184i
$610$	−3.05937	−	21.2784i	−0.00501535	−	0.0348825i
$611$	−195.128	+	125.401i	−0.319358	+	0.205239i
$612$	−34.8843	−	30.2274i	−0.0570005	−	0.0493912i
$613$	316.854	+	144.702i	0.516891	+	0.236056i	0.656741	−	0.754117i	$-0.271935\pi$
$613$	316.854	+	144.702i	0.516891	+	0.236056i	−0.139850	+	0.990173i	$0.544662\pi$
$614$	548.150	+	352.275i	0.892753	+	0.573737i
$615$	−15.6040	−	53.1424i	−0.0253724	−	0.0864104i
$616$	54.5628	+	62.9688i	0.0885760	+	0.102222i
$617$	191.517	−	652.245i	0.310400	−	1.05712i	−0.645581	−	0.763692i	$-0.723385\pi$
$617$	191.517	−	652.245i	0.310400	−	1.05712i	0.955980	−	0.293432i	$-0.0947973\pi$
$618$	748.786	−	341.959i	1.21163	−	0.553332i
$619$	−577.823	−	83.0784i	−0.933479	−	0.134214i	−0.341240	−	0.939976i	$-0.610847\pi$
$619$	−577.823	−	83.0784i	−0.933479	−	0.134214i	−0.592239	+	0.805762i	$0.701756\pi$
$620$		−	42.5064i		−	0.0685587i
$621$	229.074	−	539.348i	0.368879	−	0.868516i
$622$	−119.929			−0.192813
$623$	−34.9072	+	242.785i	−0.0560308	+	0.389703i
$624$	53.5788	+	117.321i	0.0858634	+	0.188015i
$625$	−580.608	−	170.482i	−0.928973	−	0.272771i
$626$	328.057	−	284.263i	0.524053	−	0.454095i
$627$	−149.294	+	43.8365i	−0.238108	+	0.0699147i
$628$	86.4084	−	134.454i	0.137593	−	0.214099i
$629$	−530.337	+	1161.28i	−0.843142	+	1.84622i
$630$	1.69738	−	1.95888i	0.00269426	−	0.00310934i
$631$	610.443	+	949.867i	0.967421	+	1.50534i	0.859474	+	0.511180i	$0.170791\pi$
$631$	610.443	+	949.867i	0.967421	+	1.50534i	0.107948	+	0.994157i	$0.465572\pi$
$632$	201.083	−	28.9114i	0.318170	−	0.0457459i
$633$	−94.5039	−	657.289i	−0.149295	−	1.03837i
$634$	−417.312	+	268.190i	−0.658222	+	0.423013i
$635$	2.83333	+	2.45509i	0.00446193	+	0.00386629i
$636$	−227.011	−	103.672i	−0.356935	−	0.163007i
$637$	289.351	+	185.954i	0.454240	+	0.291922i
$638$	−132.587	−	451.551i	−0.207817	−	0.707761i
$639$	−29.6514	−	34.2195i	−0.0464028	−	0.0535517i
$640$	1.64398	−	5.59889i	0.00256872	−	0.00874827i
$641$	−751.953	+	343.405i	−1.17309	+	0.535734i	−0.904064	−	0.427398i	$-0.859430\pi$
$641$	−751.953	+	343.405i	−1.17309	+	0.535734i	−0.269030	+	0.963132i	$0.586703\pi$
$642$	853.507	+	122.716i	1.32945	+	0.191146i
$643$			1029.49i			1.60107i	0.599285	+	0.800536i	$0.295452\pi$
$643$			1029.49i			1.60107i	−0.599285	+	0.800536i	$0.704548\pi$
$644$	−101.719	−	149.334i	−0.157948	−	0.231885i
$645$	60.7283			0.0941524
$646$	−33.8482	+	235.419i	−0.0523965	+	0.364426i
$647$	95.4370	+	208.978i	0.147507	+	0.322995i	0.968934	−	0.247318i	$-0.0795492\pi$
$647$	95.4370	+	208.978i	0.147507	+	0.322995i	−0.821427	+	0.570313i	$0.806822\pi$
$648$	239.698	+	70.3816i	0.369904	+	0.108614i
$649$	151.981	−	131.692i	0.234177	−	0.202915i
$650$	−343.860	+	100.966i	−0.529015	+	0.155333i
$651$	275.400	−	428.530i	0.423041	−	0.658265i
$652$	178.802	−	391.522i	0.274236	−	0.600493i
$653$	447.092	−	515.972i	0.684675	−	0.790157i	−0.301922	−	0.953332i	$-0.597628\pi$
$653$	447.092	−	515.972i	0.684675	−	0.790157i	0.986597	+	0.163176i	$0.0521738\pi$
$654$	202.516	+	315.121i	0.309658	+	0.481837i
$655$	−27.2911	+	3.92387i	−0.0416658	+	0.00599063i
$656$	−19.4238	−	135.095i	−0.0296094	−	0.205938i
$657$	−75.2693	+	48.3727i	−0.114565	+	0.0736266i
$658$	95.0430	+	82.3552i	0.144442	+	0.125160i
$659$	94.0164	+	42.9358i	0.142665	+	0.0651530i	0.485468	−	0.874254i	$-0.338649\pi$
$659$	94.0164	+	42.9358i	0.142665	+	0.0651530i	−0.342803	+	0.939407i	$0.611376\pi$
$660$	−20.4819	−	13.1629i	−0.0310331	−	0.0199438i
$661$	−51.3946	−	175.034i	−0.0777528	−	0.264802i	0.911438	−	0.411438i	$-0.134973\pi$
$661$	−51.3946	−	175.034i	−0.0777528	−	0.264802i	−0.989190	+	0.146636i	$0.953155\pi$
$662$	120.595	+	139.174i	0.182168	+	0.210233i
$663$	231.748	−	789.261i	0.349544	−	1.19044i
$664$	304.382	−	139.007i	0.458407	−	0.209347i
$665$	−13.2197	−	1.90070i	−0.0198792	−	0.00285820i
$666$			64.0252i			0.0961339i
$667$	172.222	+	1005.93i	0.258204	+	1.50814i
$668$	−496.528			−0.743306
$669$	−132.931	+	924.557i	−0.198701	+	1.38200i
$670$	−20.2378	−	44.3146i	−0.0302057	−	0.0661412i
$671$	−212.075	−	62.2708i	−0.316058	−	0.0928030i
$672$	52.8493	−	45.7942i	0.0786448	−	0.0681461i
$673$	−887.535	+	260.604i	−1.31877	+	0.387227i	−0.864050	−	0.503405i	$-0.832080\pi$
$673$	−887.535	+	260.604i	−1.31877	+	0.387227i	−0.454724	+	0.890632i	$0.650262\pi$
$674$	−144.945	+	225.538i	−0.215051	+	0.334626i
$675$	−261.776	+	573.210i	−0.387817	+	0.849201i
$676$	83.8628	−	96.7828i	0.124057	−	0.143170i
$677$	−179.583	−	279.437i	−0.265263	−	0.412757i	0.682915	−	0.730498i	$-0.260712\pi$
$677$	−179.583	−	279.437i	−0.265263	−	0.412757i	−0.948178	+	0.317741i	$0.897076\pi$
$678$	−647.479	+	93.0934i	−0.954984	+	0.137306i
$679$	38.3422	+	266.676i	0.0564687	+	0.392748i
$680$	−31.3080	+	20.1204i	−0.0460412	+	0.0295889i
$681$	324.581	+	281.251i	0.476623	+	0.412997i
$682$	−397.545	−	181.553i	−0.582910	−	0.266206i
$683$	−309.873	−	199.143i	−0.453694	−	0.291571i	0.293767	−	0.955877i	$-0.405091\pi$
$683$	−309.873	−	199.143i	−0.453694	−	0.291571i	−0.747461	+	0.664306i	$0.768727\pi$
$684$	3.36050	+	11.4448i	0.00491301	+	0.0167322i
$685$	77.1994	+	89.0928i	0.112700	+	0.130063i
$686$	129.225	−	440.100i	0.188375	−	0.641545i
$687$	103.859	−	47.4310i	0.151178	−	0.0690407i
$688$	148.126	+	21.2973i	0.215300	+	0.0309554i
$689$		−	406.220i		−	0.589579i
$690$	40.8131	+	33.4953i	0.0591494	+	0.0485439i
$691$	617.419			0.893515			0.446758	−	0.894655i	$-0.352579\pi$
$691$	617.419			0.893515			0.446758	+	0.894655i	$0.352579\pi$
$692$	−55.3809	+	385.183i	−0.0800302	+	0.556622i
$693$	−11.0708	−	24.2417i	−0.0159752	−	0.0349808i
$694$	726.119	+	213.208i	1.04628	+	0.307216i
$695$	−32.9421	+	28.5445i	−0.0473987	+	0.0410712i
$696$	−378.984	+	111.280i	−0.544517	+	0.159885i
$697$	−470.609	+	732.283i	−0.675193	+	1.05062i
$698$	−201.996	+	442.309i	−0.289392	+	0.633681i
$699$	242.237	−	279.556i	0.346547	−	0.399937i
$700$	105.051	+	163.462i	0.150072	+	0.233517i
$701$	758.057	−	108.992i	1.08139	−	0.155481i	0.421491	−	0.906833i	$-0.361507\pi$
$701$	758.057	−	108.992i	1.08139	−	0.155481i	0.659902	+	0.751352i	$0.270598\pi$
$702$	52.5352	+	365.390i	0.0748364	+	0.520499i
$703$	277.530	−	178.358i	0.394780	−	0.253710i
$704$	−45.3424	−	39.2894i	−0.0644069	−	0.0558089i
$705$	−33.4274	−	15.2658i	−0.0474147	−	0.0216536i
$706$	−43.4585	−	27.9291i	−0.0615559	−	0.0395596i
$707$	47.1793	+	160.678i	0.0667317	+	0.227267i
$708$	−110.528	−	127.556i	−0.156113	−	0.180164i
$709$	36.4867	−	124.262i	0.0514623	−	0.175264i	−0.929752	−	0.368187i	$-0.879979\pi$
$709$	36.4867	−	124.262i	0.0514623	−	0.175264i	0.981214	+	0.192923i	$0.0617967\pi$
$710$	−33.2076	+	15.1654i	−0.0467713	+	0.0213598i
$711$	−64.3169	−	9.24737i	−0.0904598	−	0.0130062i
$712$		−	176.622i		−	0.248064i
$713$	810.729	+	490.876i	1.13707	+	0.688466i
$714$	−445.994			−0.624642
$715$	5.63992	−	39.2265i	0.00788800	−	0.0548623i
$716$	−109.618	−	240.030i	−0.153098	−	0.335238i
$717$	−825.911	−	242.509i	−1.15190	−	0.338228i
$718$	23.6658	−	20.5065i	0.0329607	−	0.0285607i
$719$	−514.681	+	151.124i	−0.715830	+	0.210187i	−0.619312	−	0.785145i	$-0.712588\pi$
$719$	−514.681	+	151.124i	−0.715830	+	0.210187i	−0.0965173	+	0.995331i	$0.530770\pi$
$720$	−1.00906	+	1.57013i	−0.00140148	+	0.00218074i
$721$	301.790	−	660.828i	0.418572	−	0.916544i
$722$	−294.078	+	339.385i	−0.407311	+	0.470062i
$723$	641.418	+	998.066i	0.887162	+	1.38045i
$724$	−710.029	+	102.087i	−0.980703	+	0.141004i
$725$	−156.192	−	1086.34i	−0.215437	−	1.49840i
$726$	242.462	−	155.821i	0.333970	−	0.214630i
$727$	310.509	+	269.058i	0.427110	+	0.370093i	0.841727	−	0.539903i	$-0.181539\pi$
$727$	310.509	+	269.058i	0.427110	+	0.370093i	−0.414617	+	0.909996i	$0.636085\pi$
$728$	103.540	+	47.2850i	0.142225	+	0.0649520i
$729$	539.857	+	346.945i	0.740545	+	0.475919i
$730$	20.3238	+	69.2164i	0.0278408	+	0.0948170i
$731$	−625.018	−	721.309i	−0.855017	−	0.986742i
$732$	−52.2634	+	177.993i	−0.0713981	+	0.243160i
$733$	631.668	−	288.473i	0.861757	−	0.393551i	0.0650249	−	0.997884i	$-0.479287\pi$
$733$	631.668	−	288.473i	0.861757	−	0.393551i	0.796732	+	0.604332i	$0.206560\pi$
$734$	−443.443	−	63.7574i	−0.604145	−	0.0868630i
$735$			54.4932i			0.0741405i
$736$	87.8031	+	96.0136i	0.119298	+	0.130453i
$737$	−500.896			−0.679642
$738$	−6.21274	+	43.2106i	−0.00841835	+	0.0585509i
$739$	−22.6077	−	49.5039i	−0.0305922	−	0.0669877i	0.893719	−	0.448627i	$-0.148087\pi$
$739$	−22.6077	−	49.5039i	−0.0305922	−	0.0669877i	−0.924311	+	0.381639i	$0.875360\pi$
$740$	49.5300	+	14.5433i	0.0669325	+	0.0196532i
$741$	−160.646	+	139.201i	−0.216797	+	0.187855i
$742$	−211.326	+	62.0510i	−0.284806	+	0.0836267i
$743$	201.898	−	314.160i	0.271734	−	0.422826i	−0.678389	−	0.734703i	$-0.737321\pi$
$743$	201.898	−	314.160i	0.271734	−	0.422826i	0.950122	+	0.311877i	$0.100958\pi$
$744$	−152.376	+	333.656i	−0.204806	+	0.448463i
$745$	−24.7018	+	28.5074i	−0.0331568	+	0.0382650i
$746$	−318.850	−	496.140i	−0.427412	−	0.665066i
$747$	−105.940	+	15.2319i	−0.141820	+	0.0203907i
$748$	54.4559	+	378.749i	0.0728020	+	0.506349i
$749$	640.188	−	411.424i	0.854724	−	0.549298i
$750$	−86.2823	−	74.7641i	−0.115043	−	0.0996854i
$751$	642.096	+	293.236i	0.854988	+	0.390460i	0.794175	−	0.607689i	$-0.207903\pi$
$751$	642.096	+	293.236i	0.854988	+	0.390460i	0.0608134	+	0.998149i	$0.480631\pi$
$752$	−76.1812	−	48.9587i	−0.101305	−	0.0651047i
$753$	63.8038	+	217.296i	0.0847328	+	0.288573i
$754$	−421.025	−	485.889i	−0.558389	−	0.644415i
$755$	3.63955	−	12.3952i	0.00482059	−	0.0164174i
$756$	182.061	−	83.1443i	0.240821	−	0.109979i
$757$	−1012.87	−	145.629i	−1.33800	−	0.192376i	−0.564115	−	0.825696i	$-0.690782\pi$
$757$	−1012.87	−	145.629i	−1.33800	−	0.192376i	−0.773890	+	0.633320i	$0.781692\pi$
$758$		−	945.465i		−	1.24732i
$759$	487.588	−	238.644i	0.642408	−	0.314419i
$760$	9.61707			0.0126540
$761$	50.1193	−	348.587i	0.0658598	−	0.458065i	−0.930029	−	0.367485i	$-0.880219\pi$
$761$	50.1193	−	348.587i	0.0658598	−	0.458065i	0.995889	−	0.0905797i	$-0.0288720\pi$
$762$	−13.4394	−	29.4282i	−0.0176370	−	0.0386197i
$763$	317.193	+	93.1362i	0.415718	+	0.122066i
$764$	312.667	−	270.928i	0.409250	−	0.354617i
$765$	11.4214	−	3.35363i	0.0149299	−	0.00438383i
$766$	332.079	−	516.724i	0.433523	−	0.674575i
$767$	114.126	−	249.902i	0.148796	−	0.325817i
$768$	−32.9753	+	38.0556i	−0.0429366	+	0.0495515i
$769$	457.255	+	711.502i	0.594609	+	0.925230i	0.999939	+	0.0110597i	$0.00352049\pi$
$769$	457.255	+	711.502i	0.594609	+	0.925230i	−0.405329	+	0.914171i	$0.632843\pi$
$770$	−21.2682	+	3.05790i	−0.0276210	+	0.00397130i
$771$	−102.052	−	709.788i	−0.132363	−	0.920607i
$772$	−342.785	+	220.294i	−0.444022	+	0.285355i
$773$	−185.211	−	160.486i	−0.239600	−	0.207615i	0.526781	−	0.850001i	$-0.323399\pi$
$773$	−185.211	−	160.486i	−0.239600	−	0.207615i	−0.766381	+	0.642386i	$0.777944\pi$
$774$	−43.5402	−	19.8841i	−0.0562535	−	0.0256901i
$775$	−857.412	−	551.025i	−1.10634	−	0.711000i
$776$	−54.6567	−	186.144i	−0.0704339	−	0.239876i
$777$	405.113	+	467.526i	0.521381	+	0.601706i
$778$	−56.5763	+	192.681i	−0.0727202	+	0.247662i
$779$	204.612	−	93.4433i	0.262660	−	0.119953i
$780$	−32.9225	−	4.73354i	−0.0422084	−	0.00606865i
$781$			375.352i			0.480604i
$782$	−22.2051	−	829.498i	−0.0283953	−	1.06074i
$783$	−1130.49			−1.44380
$784$	−19.1107	+	132.918i	−0.0243759	+	0.169538i
$785$	17.1220	+	37.4920i	0.0218115	+	0.0477605i
$786$	228.289	+	67.0318i	0.290444	+	0.0852821i
$787$	967.124	−	838.018i	1.22887	−	1.06483i	0.233151	−	0.972441i	$-0.425096\pi$
$787$	967.124	−	838.018i	1.22887	−	1.06483i	0.995723	−	0.0923851i	$-0.0294491\pi$
$788$	459.796	−	135.008i	0.583498	−	0.171330i
$789$	590.160	−	918.307i	0.747985	−	1.16389i
$790$	−21.7634	+	47.6552i	−0.0275486	+	0.0603230i
$791$	−378.049	+	436.292i	−0.477939	+	0.551571i
$792$	10.3749	+	16.1437i	0.0130997	+	0.0203835i
$793$	−298.881	+	42.9726i	−0.376899	+	0.0541899i
$794$	110.336	+	767.401i	0.138962	+	0.966500i
$795$	54.1419	−	34.7949i	0.0681030	−	0.0437671i
$796$	99.3011	+	86.0449i	0.124750	+	0.108097i
$797$	−1400.74	−	639.697i	−1.75752	−	0.802631i	−0.986068	−	0.166341i	$-0.946805\pi$
$797$	−1400.74	−	639.697i	−1.75752	−	0.802631i	−0.771449	−	0.636291i	$-0.780468\pi$
$798$	96.9550	+	62.3092i	0.121498	+	0.0780817i
$799$	162.714	+	554.154i	0.203648	+	0.693560i
$800$	−91.6258	−	105.742i	−0.114532	−	0.132177i
$801$	−15.9159	+	54.2045i	−0.0198700	+	0.0676710i
$802$	326.658	−	149.180i	0.407305	−	0.186010i
$803$	734.159	+	105.556i	0.914271	+	0.131452i
$804$			420.398i			0.522883i
$805$	46.5794	−	1.24690i	0.0578626	−	0.00154894i
$806$	−597.055			−0.740763
$807$	118.276	−	822.626i	0.146562	−	1.01936i
$808$	−50.0928	−	109.688i	−0.0619961	−	0.135752i
$809$	641.985	+	188.504i	0.793554	+	0.233009i	0.653292	−	0.757106i	$-0.273387\pi$
$809$	641.985	+	188.504i	0.793554	+	0.233009i	0.140262	+	0.990114i	$0.455206\pi$
$810$	−48.6884	+	42.1887i	−0.0601091	+	0.0520849i
$811$	542.031	−	159.155i	0.668348	−	0.196245i	0.0700810	−	0.997541i	$-0.477674\pi$
$811$	542.031	−	159.155i	0.668348	−	0.196245i	0.598267	+	0.801296i	$0.295856\pi$
$812$	−188.460	+	293.249i	−0.232093	+	0.361144i
$813$	−419.328	+	918.200i	−0.515779	+	1.12940i
$814$	347.570	−	401.117i	0.426990	−	0.492773i
$815$	60.0101	+	93.3775i	0.0736320	+	0.114574i
$816$	317.881	−	45.7044i	0.389560	−	0.0560103i
$817$	35.1000	+	244.126i	0.0429621	+	0.298808i
$818$	710.992	−	456.927i	0.869183	−	0.558590i
$819$	−27.5150	−	23.8418i	−0.0335958	−	0.0291109i
$820$	32.0166	+	14.6215i	0.0390446	+	0.0178311i
$821$	−115.466	−	74.2057i	−0.140641	−	0.0903845i	0.468428	−	0.883502i	$-0.344820\pi$
$821$	−115.466	−	74.2057i	−0.140641	−	0.0903845i	−0.609069	+	0.793117i	$0.708457\pi$
$822$	−286.604	−	976.082i	−0.348666	−	1.18745i
$823$	−919.134	−	1060.74i	−1.11681	−	1.28887i	−0.953200	−	0.302341i	$-0.902232\pi$
$823$	−919.134	−	1060.74i	−1.11681	−	1.28887i	−0.163609	−	0.986525i	$-0.552314\pi$
$824$	−147.380	+	501.931i	−0.178859	+	0.609139i
$825$	−531.027	+	242.512i	−0.643669	+	0.293954i
$826$	−147.439	−	21.1985i	−0.178497	−	0.0256640i
$827$			1386.97i			1.67710i	0.544821	+	0.838552i	$0.316598\pi$
$827$			1386.97i			1.67710i	−0.544821	+	0.838552i	$0.683402\pi$
$828$	−18.2944	−	37.3784i	−0.0220947	−	0.0451430i
$829$	265.743			0.320559			0.160279	−	0.987072i	$-0.448761\pi$
$829$	265.743			0.320559			0.160279	+	0.987072i	$0.448761\pi$
$830$	−12.2809	+	85.4153i	−0.0147962	+	0.102910i
$831$	626.094	+	1370.96i	0.753423	+	1.64977i
$832$	−78.6434	−	23.0918i	−0.0945233	−	0.0277546i
$833$	647.251	−	560.846i	0.777012	−	0.673285i
$834$	360.906	−	105.972i	0.432742	−	0.127064i
$835$	69.2274	−	107.720i	0.0829071	−	0.129006i
$836$	41.0763	−	89.9445i	0.0491343	−	0.107589i
$837$	−687.499	+	793.416i	−0.821384	+	0.947928i
$838$	162.896	+	253.470i	0.194386	+	0.302471i
$839$	−234.494	+	33.7151i	−0.279492	+	0.0401849i	−0.280635	−	0.959814i	$-0.590545\pi$
$839$	−234.494	+	33.7151i	−0.279492	+	0.0401849i	0.00114335	+	0.999999i	$0.499636\pi$
$840$	2.56647	+	17.8502i	0.00305533	+	0.0212503i
$841$	948.863	−	609.797i	1.12826	−	0.725086i
$842$	462.042	+	400.362i	0.548743	+	0.475489i
$843$	−712.420	−	325.351i	−0.845100	−	0.385944i
$844$	355.007	+	228.149i	0.420624	+	0.270319i
$845$	9.30428	+	31.6875i	0.0110110	+	0.0375000i
$846$	18.9679	+	21.8901i	0.0224207	+	0.0258749i
$847$	71.6614	−	244.056i	0.0846061	−	0.288142i
$848$	144.263	−	65.8829i	0.170122	−	0.0776921i
$849$	366.506	+	52.6956i	0.431691	+	0.0620678i
$850$			892.354i			1.04983i
$851$	−849.374	+	776.741i	−0.998090	+	0.912740i
$852$	315.030			0.369754
$853$	−162.294	+	1128.78i	−0.190263	+	1.32331i	0.641049	+	0.767500i	$0.278500\pi$
$853$	−162.294	+	1128.78i	−0.190263	+	1.32331i	−0.831312	+	0.555807i	$0.812409\pi$
$854$	68.0102	+	148.922i	0.0796372	+	0.174381i
$855$	−2.95144	−	0.866621i	−0.00345198	−	0.00101359i
$856$	−414.131	+	358.847i	−0.483798	+	0.419213i
$857$	−1096.58	+	321.986i	−1.27956	+	0.375713i	−0.849741	−	0.527201i	$-0.823241\pi$
$857$	−1096.58	+	321.986i	−1.27956	+	0.375713i	−0.429821	+	0.902914i	$0.641423\pi$
$858$	−184.889	+	287.693i	−0.215489	+	0.335307i
$859$	483.368	−	1058.43i	0.562710	−	1.23216i	−0.387879	−	0.921710i	$-0.626792\pi$
$859$	483.368	−	1058.43i	0.562710	−	1.23216i	0.950589	−	0.310453i	$-0.100481\pi$
$860$	−25.2726	+	29.1661i	−0.0293867	+	0.0339141i
$861$	228.044	+	354.844i	0.264860	+	0.412130i
$862$	−717.584	+	103.173i	−0.832464	+	0.119690i
$863$	−6.72587	−	46.7795i	−0.00779359	−	0.0542056i	0.985554	−	0.169364i	$-0.0541714\pi$
$863$	−6.72587	−	46.7795i	−0.00779359	−	0.0542056i	−0.993347	+	0.115159i	$0.963262\pi$
$864$	−121.243	+	77.9181i	−0.140327	+	0.0901829i
$865$	−75.8426	−	65.7180i	−0.0876793	−	0.0759746i
$866$	−246.179	−	112.426i	−0.284271	−	0.129822i
$867$	−957.923	−	615.620i	−1.10487	−	0.710057i
$868$	91.2014	+	310.604i	0.105071	+	0.357838i
$869$	352.744	+	407.088i	0.405919	+	0.468456i
$870$	28.6973	−	97.7341i	0.0329854	−	0.112338i
$871$	−622.454	+	284.265i	−0.714643	+	0.326366i
$872$	−235.623	−	33.8774i	−0.270210	−	0.0388503i
$873$			62.0520i			0.0710790i
$874$	−111.061	+	183.427i	−0.127072	+	0.209871i
$875$	−100.757			−0.115151
$876$	88.5925	−	616.175i	0.101133	−	0.703396i
$877$	−100.725	−	220.556i	−0.114851	−	0.251490i	0.843473	−	0.537172i	$-0.180507\pi$
$877$	−100.725	−	220.556i	−0.114851	−	0.251490i	−0.958325	+	0.285682i	$0.907780\pi$
$878$	1011.51	+	297.006i	1.15206	+	0.338276i
$879$	107.375	−	93.0405i	0.122155	−	0.105848i
$880$	14.8455	−	4.35902i	0.0168699	−	0.00495344i
$881$	−641.093	+	997.559i	−0.727687	+	1.13230i	0.258394	+	0.966040i	$0.416807\pi$
$881$	−641.093	+	997.559i	−0.727687	+	1.13230i	−0.986081	+	0.166264i	$0.946830\pi$
$882$	17.8426	−	39.0699i	0.0202297	−	0.0442969i
$883$	−33.1093	+	38.2102i	−0.0374964	+	0.0432732i	−0.774188	−	0.632956i	$-0.781842\pi$
$883$	−33.1093	+	38.2102i	−0.0374964	+	0.0432732i	0.736692	+	0.676229i	$0.236387\pi$
$884$	282.616	+	439.760i	0.319702	+	0.497466i
$885$	43.0830	−	6.19440i	0.0486813	−	0.00699932i
$886$	87.0850	+	605.690i	0.0982901	+	0.683623i
$887$	−852.441	+	547.831i	−0.961038	+	0.617622i	−0.924285	−	0.381703i	$-0.875338\pi$
$887$	−852.441	+	547.831i	−0.961038	+	0.617622i	−0.0367531	+	0.999324i	$0.511701\pi$
$888$	−336.655	−	291.713i	−0.379116	−	0.328505i
$889$	−25.9714	−	11.8607i	−0.0292142	−	0.0133417i
$890$	38.3174	+	24.6251i	0.0430533	+	0.0276687i
$891$	186.617	+	635.559i	0.209447	+	0.713309i
$892$	−388.719	−	448.606i	−0.435784	−	0.502921i
$893$	42.0475	−	143.201i	0.0470857	−	0.160359i
$894$	296.091	−	135.220i	0.331198	−	0.151253i
$895$	67.3570	+	9.68448i	0.0752592	+	0.0108206i
$896$			44.4397i			0.0495979i
$897$	470.483	−	573.271i	0.524507	−	0.639098i
$898$	−47.0301			−0.0523721
$899$	260.215	−	1809.84i	0.289449	−	2.01316i
$900$	18.5909	+	40.7084i	0.0206566	+	0.0452316i
$901$	−970.511	−	284.968i	−1.07715	−	0.316279i
$902$	273.498	−	236.987i	0.303212	−	0.262735i
$903$	−443.755	+	130.298i	−0.491423	+	0.144295i
$904$	224.744	−	349.708i	0.248610	−	0.386845i
$905$	76.8470	−	168.271i	0.0849138	−	0.185935i
$906$	−73.0027	+	84.2496i	−0.0805769	+	0.0929907i
$907$	−667.307	−	1038.35i	−0.735730	−	1.14482i	−0.984351	−	0.176217i	$-0.943614\pi$
$907$	−667.307	−	1038.35i	−0.735730	−	1.14482i	0.248621	−	0.968601i	$-0.420023\pi$
$908$	−270.154	+	38.8423i	−0.297526	+	0.0427778i
$909$	5.48899	+	38.1768i	0.00603850	+	0.0419987i
$910$	−24.6941	+	15.8700i	−0.0271364	+	0.0174395i
$911$	438.589	+	380.039i	0.481436	+	0.417167i	0.861472	−	0.507805i	$-0.169543\pi$
$911$	438.589	+	380.039i	0.481436	+	0.417167i	−0.380036	+	0.924972i	$0.624088\pi$
$912$	−75.4898	−	34.4750i	−0.0827739	−	0.0378016i
$913$	746.401	+	479.683i	0.817525	+	0.525392i
$914$	115.301	+	392.678i	0.126150	+	0.429626i
$915$	−31.3282	−	36.1547i	−0.0342385	−	0.0395133i
$916$	−20.4422	+	69.6196i	−0.0223168	+	0.0760039i
$917$	191.003	−	87.2281i	0.208291	−	0.0951234i
$918$	909.817	+	130.812i	0.991086	+	0.142497i
$919$			28.6129i			0.0311348i	0.999879	+	0.0155674i	$0.00495545\pi$
$919$			28.6129i			0.0311348i	−0.999879	+	0.0155674i	$0.995045\pi$
$920$	−33.0716	+	5.66207i	−0.0359474	+	0.00615443i
$921$	1450.03			1.57441
$922$	−4.06522	+	28.2743i	−0.00440914	+	0.0306662i
$923$	213.017	+	466.443i	0.230788	+	0.505355i
$924$	177.908	+	52.2384i	0.192541	+	0.0565351i
$925$	935.435	−	810.559i	1.01128	−	0.876280i
$926$	54.4318	−	15.9826i	0.0587816	−	0.0172598i
$927$	90.4607	−	140.760i	0.0975844	−	0.151844i
$928$	104.273	−	228.325i	0.112363	−	0.246040i
$929$	−273.617	+	315.770i	−0.294528	+	0.339903i	−0.883656	−	0.468136i	$-0.844926\pi$
$929$	−273.617	+	315.770i	−0.294528	+	0.339903i	0.589128	+	0.808039i	$0.299471\pi$
$930$	−51.1409	−	79.5767i	−0.0549902	−	0.0855664i
$931$	−219.061	+	31.4963i	−0.235297	+	0.0338306i
$932$	33.4542	+	232.679i	0.0358951	+	0.249656i
$933$	−224.522	+	144.291i	−0.240645	+	0.154653i
$934$	−129.100	−	111.866i	−0.138222	−	0.119770i
$935$	−89.7606	−	40.9923i	−0.0960007	−	0.0438420i
$936$	22.0545	+	14.1736i	0.0235625	+	0.0151427i
$937$	147.708	+	503.049i	0.157640	+	0.536872i	0.999998	−	0.00204649i	$-0.000651418\pi$
$937$	147.708	+	503.049i	0.157640	+	0.536872i	−0.842358	+	0.538918i	$0.818833\pi$
$938$	242.963	+	280.395i	0.259023	+	0.298928i
$939$	272.154	−	926.870i	0.289834	−	0.987082i
$940$	21.2428	−	9.70127i	0.0225988	−	0.0103205i
$941$	14.3478	+	2.06290i	0.0152474	+	0.00219224i	0.149934	−	0.988696i	$-0.452094\pi$
$941$	14.3478	+	2.06290i	0.0152474	+	0.00219224i	−0.134687	+	0.990888i	$0.543003\pi$
$942$		−	355.674i		−	0.377573i
$943$	−648.614	+	441.803i	−0.687820	+	0.468508i
$944$	107.259			0.113622
$945$	−7.34558	+	51.0896i	−0.00777310	+	0.0540631i
$946$	164.835	+	360.938i	0.174244	+	0.381542i
$947$	295.396	+	86.7360i	0.311928	+	0.0915903i	0.433950	−	0.900937i	$-0.357120\pi$
$947$	295.396	+	86.7360i	0.311928	+	0.0915903i	−0.122022	+	0.992527i	$0.538938\pi$
$948$	341.666	−	296.055i	0.360407	−	0.312295i
$949$	972.230	−	285.473i	1.02448	−	0.300814i
$950$	124.669	−	193.989i	0.131231	−	0.204199i
$951$	−458.587	+	1004.17i	−0.482216	+	1.05591i
$952$	185.604	−	214.199i	0.194962	−	0.224999i
$953$	379.938	+	591.196i	0.398676	+	0.620352i	0.981322	−	0.192374i	$-0.0616188\pi$
$953$	379.938	+	591.196i	0.398676	+	0.620352i	−0.582646	+	0.812726i	$0.697982\pi$
$954$	−50.2108	+	7.21922i	−0.0526318	+	0.00756731i
$955$	15.1838	+	105.606i	0.0158992	+	0.110582i
$956$	460.180	−	295.740i	0.481360	−	0.309351i
$957$	−791.496	−	685.835i	−0.827059	−	0.716651i
$958$	−186.584	−	85.2099i	−0.194764	−	0.0889456i
$959$	−755.270	−	485.383i	−0.787560	−	0.506134i
$960$	−3.65850	−	12.4597i	−0.00381093	−	0.0129789i
$961$	−482.631	−	556.986i	−0.502217	−	0.579590i
$962$	204.279	−	695.711i	0.212348	−	0.723192i
$963$	159.432	−	72.8101i	0.165557	−	0.0756076i
$964$	−746.275	−	107.298i	−0.774144	−	0.111305i
$965$		−	105.080i		−	0.108891i
$966$	−370.098	−	157.189i	−0.383124	−	0.162722i
$967$	407.406			0.421310			0.210655	−	0.977561i	$-0.432440\pi$
$967$	407.406			0.421310			0.210655	+	0.977561i	$0.432440\pi$
$968$	−26.0662	+	181.294i	−0.0269279	+	0.187287i
$969$	219.873	+	481.455i	0.226907	+	0.496858i
$970$	48.0036	+	14.0951i	0.0494882	+	0.0145311i
$971$	−877.446	+	760.311i	−0.903652	+	0.783019i	−0.976767	−	0.214305i	$-0.931251\pi$
$971$	−877.446	+	760.311i	−0.903652	+	0.783019i	0.0731152	+	0.997324i	$0.476706\pi$
$972$	93.4036	−	27.4258i	0.0960942	−	0.0282158i
$973$	179.470	−	279.261i	0.184450	−	0.287010i
$974$	87.2246	−	190.995i	0.0895530	−	0.196094i
$975$	−522.268	+	602.730i	−0.535660	+	0.618184i
$976$	−63.7352	−	99.1739i	−0.0653025	−	0.101613i
$977$	1543.96	−	221.988i	1.58031	−	0.227214i	0.704438	−	0.709765i	$-0.251199\pi$
$977$	1543.96	−	221.988i	1.58031	−	0.227214i	0.875868	+	0.482552i	$0.160290\pi$
$978$	−136.316	−	948.096i	−0.139382	−	0.969423i
$979$	393.969	−	253.189i	0.402420	−	0.258620i
$980$	−26.1716	−	22.6778i	−0.0267057	−	0.0231406i
$981$	69.2589	+	31.6295i	0.0706003	+	0.0322421i
$982$	−125.109	−	80.4026i	−0.127402	−	0.0818764i
$983$	−231.859	−	789.638i	−0.235868	−	0.803294i	−0.989316	−	0.145786i	$-0.953429\pi$
$983$	−231.859	−	789.638i	−0.235868	−	0.803294i	0.753448	−	0.657508i	$-0.228389\pi$
$984$	−198.901	−	229.545i	−0.202136	−	0.233277i
$985$	−34.8166	+	118.574i	−0.0353468	+	0.120380i
$986$	−1456.20	+	665.026i	−1.47688	+	0.674469i
$987$	277.016	+	39.8288i	0.280664	+	0.0403534i
$988$		−	135.084i		−	0.136724i
$989$	−264.433	−	818.846i	−0.267375	−	0.827954i
$990$	−4.94882			−0.00499881
$991$	180.575	−	1255.92i	0.182215	−	1.26733i	−0.669297	−	0.742995i	$-0.733405\pi$
$991$	180.575	−	1255.92i	0.182215	−	1.26733i	0.851512	−	0.524336i	$-0.175686\pi$
$992$	−96.8335	−	212.036i	−0.0976144	−	0.213746i
$993$	393.213	+	115.458i	0.395985	+	0.116272i
$994$	210.117	−	182.067i	0.211385	−	0.183166i
$995$	−32.5120	+	9.54638i	−0.0326753	+	0.00959435i
$996$	402.594	−	626.448i	0.404211	−	0.628964i
$997$	214.364	−	469.393i	0.215009	−	0.470805i	−0.771140	−	0.636666i	$-0.780313\pi$
$997$	214.364	−	469.393i	0.215009	−	0.470805i	0.986149	+	0.165861i	$0.0530403\pi$
$998$	−337.726	+	389.757i	−0.338403	+	0.390538i
$999$	−689.294	−	1072.56i	−0.689984	−	1.07364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.3.d.a.15.2	✓	40
3.2	odd	2		414.3.l.a.199.4		40
4.3	odd	2		368.3.p.b.337.1		40
23.7	odd	22		1058.3.b.e.1057.33		40
23.16	even	11		1058.3.b.e.1057.28		40
23.20	odd	22	inner	46.3.d.a.43.2	yes	40
69.20	even	22		414.3.l.a.181.4		40
92.43	even	22		368.3.p.b.273.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.3.d.a.15.2	✓	40	1.1	even	1	trivial
46.3.d.a.43.2	yes	40	23.20	odd	22	inner
368.3.p.b.273.1		40	92.43	even	22
368.3.p.b.337.1		40	4.3	odd	2
414.3.l.a.181.4		40	69.20	even	22
414.3.l.a.199.4		40	3.2	odd	2
1058.3.b.e.1057.28		40	23.16	even	11
1058.3.b.e.1057.33		40	23.7	odd	22

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	46.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.201264 + 1.39982i) q^{2} +(1.30738 + 2.86277i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(0.389792 - 0.337757i) q^{5} +(-4.27048 + 1.25393i) q^{6} +(-2.12361 + 3.30440i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-0.592439 + 0.683711i) q^{9} +(0.394348 + 0.613617i) q^{10} +(7.42324 - 1.06730i) q^{11} +(-0.895778 - 6.23027i) q^{12} +(8.61901 - 5.53910i) q^{13} +(-4.19816 - 3.63773i) q^{14} +(1.47653 + 0.674307i) q^{15} +(3.36501 + 2.16256i) q^{16} +(-7.18729 - 24.4776i) q^{17} +(-0.837835 - 0.966913i) q^{18} +(-1.85729 + 6.32534i) q^{19} +(-0.938321 + 0.428517i) q^{20} +(-12.2361 - 1.75929i) q^{21} +10.6060i q^{22} +(2.66286 - 22.8453i) q^{23} +8.90154 q^{24} +(-3.52001 + 24.4822i) q^{25} +(6.01905 + 13.1799i) q^{26} +(24.4453 + 7.17780i) q^{27} +(5.93709 - 5.14452i) q^{28} +(-42.5751 + 12.5012i) q^{29} +(-1.24108 + 1.93116i) q^{30} +(-17.1179 + 37.4830i) q^{31} +(-3.70445 + 4.27517i) q^{32} +(12.7604 + 19.8556i) q^{33} +(35.7108 - 5.13444i) q^{34} +(0.288318 + 2.00530i) q^{35} +(1.52213 - 0.978213i) q^{36} +(-37.8198 - 32.7711i) q^{37} +(-8.48053 - 3.87293i) q^{38} +(27.1255 + 17.4325i) q^{39} +(-0.410996 - 1.39972i) q^{40} +(-22.3446 - 25.7871i) q^{41} +(4.92536 - 16.7742i) q^{42} +(34.0315 - 15.5417i) q^{43} +(-14.8465 - 2.13460i) q^{44} +0.466606i q^{45} +(31.4434 + 8.32545i) q^{46} -22.6392 q^{47} +(-1.79156 + 12.4605i) q^{48} +(13.9460 + 30.5374i) q^{49} +(-33.5622 - 9.85476i) q^{50} +(60.6773 - 52.5772i) q^{51} +(-19.6609 + 5.77295i) q^{52} +(21.4358 - 33.3547i) q^{53} +(-14.9676 + 32.7744i) q^{54} +(2.53304 - 2.92328i) q^{55} +(6.00648 + 9.34626i) q^{56} +(-20.5362 + 2.95265i) q^{57} +(-8.93056 - 62.1134i) q^{58} +(22.5580 - 14.4971i) q^{59} +(-2.45349 - 2.12596i) q^{60} +(-26.8087 - 12.2431i) q^{61} +(-49.0242 - 31.5059i) q^{62} +(-1.00115 - 3.40959i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(1.48875 - 5.07023i) q^{65} +(-30.3625 + 13.8661i) q^{66} +(-66.1101 - 9.50519i) q^{67} +51.0220i q^{68} +(68.8822 - 22.2444i) q^{69} -2.86508 q^{70} +(-7.12282 + 49.5403i) q^{71} +(1.06297 + 2.32758i) q^{72} +(94.8939 + 27.8634i) q^{73} +(53.4853 - 46.3453i) q^{74} +(-74.6889 + 21.9306i) q^{75} +(7.12822 - 11.0917i) q^{76} +(-12.2373 + 26.7959i) q^{77} +(-29.8617 + 34.4623i) q^{78} +(38.8314 + 60.4228i) q^{79} +(2.04208 - 0.293607i) q^{80} +(12.5698 + 87.4247i) q^{81} +(40.5944 - 26.0884i) q^{82} +(89.4100 + 77.4742i) q^{83} +(22.4896 + 10.2707i) q^{84} +(-11.0690 - 7.11365i) q^{85} +(14.9062 + 50.7659i) q^{86} +(-91.4498 - 105.539i) q^{87} +(5.97611 - 20.3528i) q^{88} +(56.8021 - 25.9407i) q^{89} +(-0.653163 - 0.0939107i) q^{90} +40.2436i q^{91} +(-17.9825 + 42.3394i) q^{92} -129.685 q^{93} +(4.55645 - 31.6908i) q^{94} +(1.41247 + 3.09288i) q^{95} +(-17.0819 - 5.01571i) q^{96} +(51.8369 - 44.9169i) q^{97} +(-45.5537 + 13.3758i) q^{98} +(-3.66809 + 5.70766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 8 q^{4} - 8 q^{6} + 24 q^{9} + 8 q^{12} + 4 q^{13} - 154 q^{15} - 16 q^{16} - 110 q^{17} - 160 q^{18} - 66 q^{19} - 44 q^{20} - 66 q^{21} - 8 q^{23} - 16 q^{24} + 264 q^{25} + 152 q^{26}+ \cdots - 1122 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 8 * q^4 - 8 * q^6 + 24 * q^9 + 8 * q^12 + 4 * q^13 - 154 * q^15 - 16 * q^16 - 110 * q^17 - 160 * q^18 - 66 * q^19 - 44 * q^20 - 66 * q^21 - 8 * q^23 - 16 * q^24 + 264 * q^25 + 152 * q^26 + 286 * q^27 + 132 * q^28 + 70 * q^29 + 352 * q^30 + 82 * q^31 + 242 * q^33 - 276 * q^35 + 48 * q^36 - 352 * q^37 - 204 * q^39 - 108 * q^41 - 88 * q^43 - 56 * q^46 + 116 * q^47 + 16 * q^48 + 412 * q^49 - 176 * q^50 + 264 * q^51 + 8 * q^52 + 176 * q^53 - 204 * q^54 - 76 * q^55 - 264 * q^56 - 198 * q^57 - 360 * q^58 - 300 * q^59 - 176 * q^60 - 616 * q^61 - 372 * q^62 - 550 * q^63 - 32 * q^64 - 462 * q^65 - 176 * q^66 - 44 * q^67 + 106 * q^69 - 112 * q^70 + 430 * q^71 + 208 * q^72 + 368 * q^73 + 528 * q^74 + 418 * q^75 + 646 * q^77 + 604 * q^78 + 704 * q^79 + 264 * q^80 + 636 * q^81 + 664 * q^82 + 814 * q^83 + 352 * q^84 + 736 * q^85 + 396 * q^86 - 100 * q^87 - 44 * q^89 - 104 * q^92 + 140 * q^93 - 136 * q^94 - 594 * q^95 - 32 * q^96 - 990 * q^97 - 304 * q^98 - 1122 * q^99

Introduction

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