LMFDB - Embedded newform 150.3.k.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(13,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("150.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.k (of order $20$, degree $8$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	150.37
Dual form			150.3.k.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(3.55879 - 3.51212i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-5.48204 - 5.48204i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})$	\(q+(0.221232 + 1.39680i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(3.55879 - 3.51212i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-5.48204 - 5.48204i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +(5.69306 + 4.19393i) q^{10} +(-11.2621 - 8.18242i) q^{11} +(3.42145 + 0.541905i) q^{12} +(1.89809 - 11.9840i) q^{13} +(6.44453 - 8.87013i) q^{14} +(-8.25387 + 2.62175i) q^{15} +(3.23607 - 2.35114i) q^{16} +(27.6774 - 14.1023i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(25.8955 + 8.41395i) q^{19} +(-4.59861 + 8.87991i) q^{20} +(4.14955 + 12.7710i) q^{21} +(8.93768 - 17.5412i) q^{22} +(-30.6030 + 4.84704i) q^{23} +4.89898i q^{24} +(0.329991 - 24.9978i) q^{25} +17.1593 q^{26} +(-0.812857 - 5.13218i) q^{27} +(13.8156 + 7.03938i) q^{28} +(-51.9065 + 16.8654i) q^{29} +(-5.48808 - 10.9490i) q^{30} +(-0.628911 + 1.93559i) q^{31} +(4.00000 + 4.00000i) q^{32} +(10.9464 + 21.4835i) q^{33} +(25.8213 + 35.5400i) q^{34} +(-38.7631 - 0.255840i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(30.9652 + 4.90440i) q^{37} +(-6.02372 + 38.0323i) q^{38} +(-12.3527 + 17.0021i) q^{39} +(-13.4208 - 4.45883i) q^{40} +(-30.7098 + 22.3120i) q^{41} +(-16.9205 + 8.62144i) q^{42} +(0.187340 - 0.187340i) q^{43} +(26.4789 + 8.60351i) q^{44} +(14.7995 + 2.44425i) q^{45} +(-13.5407 - 41.6740i) q^{46} +(26.5717 - 52.1499i) q^{47} +(-6.84291 + 1.08381i) q^{48} +11.1056i q^{49} +(34.9900 - 5.06938i) q^{50} -53.8028 q^{51} +(3.79617 + 23.9681i) q^{52} +(-5.62578 - 2.86648i) q^{53} +(6.98881 - 2.27080i) q^{54} +(-68.8173 + 10.4345i) q^{55} +(-6.77618 + 20.8549i) q^{56} +(-33.3475 - 33.3475i) q^{57} +(-35.0410 - 68.7719i) q^{58} +(5.07252 + 6.98172i) q^{59} +(14.0795 - 10.0880i) q^{60} +(87.6266 + 63.6644i) q^{61} +(-2.84277 - 0.450251i) q^{62} +(3.63841 - 22.9720i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-35.3345 - 49.3150i) q^{65} +(-27.5865 + 20.0428i) q^{66} +(7.98376 - 4.06793i) q^{67} +(-43.9298 + 43.9298i) q^{68} +(51.0401 + 16.5839i) q^{69} +(-8.21826 - 54.2009i) q^{70} +(39.4041 + 121.273i) q^{71} +(3.85224 - 7.56044i) q^{72} +(13.7512 - 2.17798i) q^{73} +44.3372i q^{74} +(-20.1659 + 38.3189i) q^{75} -54.4562 q^{76} +(16.8831 + 106.596i) q^{77} +(-26.4813 - 13.4929i) q^{78} +(40.6892 - 13.2207i) q^{79} +(3.25900 - 19.7327i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-37.9594 - 37.9594i) q^{82} +(-18.4050 - 36.1218i) q^{83} +(-15.7858 - 21.7273i) q^{84} +(48.9689 - 147.394i) q^{85} +(0.303122 + 0.220231i) q^{86} +(93.3675 + 14.7880i) q^{87} +(-6.15943 + 38.8891i) q^{88} +(79.2350 - 109.058i) q^{89} +(-0.140006 + 21.2127i) q^{90} +(-76.1025 + 55.2917i) q^{91} +(55.2148 - 28.1333i) q^{92} +(2.49260 - 2.49260i) q^{93} +(78.7215 + 25.5782i) q^{94} +(121.707 - 61.0046i) q^{95} +(-3.02774 - 9.31841i) q^{96} +(24.2763 - 47.6449i) q^{97} +(-15.5124 + 2.45692i) q^{98} -41.7623i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 + 8 * q^7 - 16 * q^8	$ 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} + 20 q^{10} + 32 q^{11} - 16 q^{13} - 60 q^{14} + 32 q^{16} + 148 q^{17} - 96 q^{18} + 180 q^{19} + 40 q^{20} - 36 q^{21} + 48 q^{22} + 48 q^{23} - 160 q^{25} - 8 q^{26} - 56 q^{28} - 200 q^{29} - 120 q^{30} + 120 q^{31} + 128 q^{32} - 156 q^{33} - 100 q^{34} - 180 q^{35} - 48 q^{36} + 444 q^{37} + 32 q^{38} - 120 q^{39} - 304 q^{41} - 24 q^{42} + 216 q^{43} + 40 q^{44} + 60 q^{45} - 16 q^{46} + 32 q^{47} + 40 q^{50} + 24 q^{51} - 32 q^{52} - 340 q^{53} + 80 q^{55} + 72 q^{56} - 24 q^{57} - 192 q^{58} - 560 q^{59} + 312 q^{61} + 40 q^{62} + 24 q^{63} - 520 q^{65} - 108 q^{66} + 688 q^{67} - 16 q^{68} + 180 q^{69} + 80 q^{70} + 212 q^{71} + 48 q^{72} - 376 q^{73} + 120 q^{75} - 64 q^{76} - 176 q^{77} - 48 q^{78} + 440 q^{79} + 80 q^{80} + 72 q^{81} - 256 q^{82} - 96 q^{83} - 240 q^{85} + 408 q^{86} + 264 q^{87} + 184 q^{88} - 560 q^{89} - 516 q^{91} + 216 q^{92} + 48 q^{93} + 80 q^{94} + 520 q^{95} - 716 q^{97} - 108 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 + 8 * q^7 - 16 * q^8 + 20 * q^10 + 32 * q^11 - 16 * q^13 - 60 * q^14 + 32 * q^16 + 148 * q^17 - 96 * q^18 + 180 * q^19 + 40 * q^20 - 36 * q^21 + 48 * q^22 + 48 * q^23 - 160 * q^25 - 8 * q^26 - 56 * q^28 - 200 * q^29 - 120 * q^30 + 120 * q^31 + 128 * q^32 - 156 * q^33 - 100 * q^34 - 180 * q^35 - 48 * q^36 + 444 * q^37 + 32 * q^38 - 120 * q^39 - 304 * q^41 - 24 * q^42 + 216 * q^43 + 40 * q^44 + 60 * q^45 - 16 * q^46 + 32 * q^47 + 40 * q^50 + 24 * q^51 - 32 * q^52 - 340 * q^53 + 80 * q^55 + 72 * q^56 - 24 * q^57 - 192 * q^58 - 560 * q^59 + 312 * q^61 + 40 * q^62 + 24 * q^63 - 520 * q^65 - 108 * q^66 + 688 * q^67 - 16 * q^68 + 180 * q^69 + 80 * q^70 + 212 * q^71 + 48 * q^72 - 376 * q^73 + 120 * q^75 - 64 * q^76 - 176 * q^77 - 48 * q^78 + 440 * q^79 + 80 * q^80 + 72 * q^81 - 256 * q^82 - 96 * q^83 - 240 * q^85 + 408 * q^86 + 264 * q^87 + 184 * q^88 - 560 * q^89 - 516 * q^91 + 216 * q^92 + 48 * q^93 + 80 * q^94 + 520 * q^95 - 716 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	0.221232	+	1.39680i	0.110616	+	0.698401i
$2$	0.221232	+	1.39680i	0.110616	+	0.698401i
$3$	−1.54327	−	0.786335i	−0.514423	−	0.262112i
$3$	−1.54327	−	0.786335i	−0.514423	−	0.262112i
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$	3.55879	−	3.51212i	0.711758	−	0.702425i
$5$	3.55879	−	3.51212i	0.711758	−	0.702425i
$6$	0.756934	−	2.32960i	0.126156	−	0.388267i
$7$	−5.48204	−	5.48204i	−0.783149	−	0.783149i	0.197212	−	0.980361i	$-0.436811\pi$
$7$	−5.48204	−	5.48204i	−0.783149	−	0.783149i	−0.980361	+	0.197212i	$0.936811\pi$
$8$	−1.28408	−	2.52015i	−0.160510	−	0.315018i
$9$	1.76336	+	2.42705i	0.195928	+	0.269672i
$10$	5.69306	+	4.19393i	0.569306	+	0.419393i
$11$	−11.2621	−	8.18242i	−1.02383	−	0.743857i	−0.0567661	−	0.998388i	$-0.518079\pi$
$11$	−11.2621	−	8.18242i	−1.02383	−	0.743857i	−0.967065	+	0.254531i	$0.918079\pi$
$12$	3.42145	+	0.541905i	0.285121	+	0.0451587i
$13$	1.89809	−	11.9840i	0.146007	−	0.921850i	−0.800539	−	0.599280i	$-0.795453\pi$
$13$	1.89809	−	11.9840i	0.146007	−	0.921850i	0.946546	−	0.322569i	$-0.104547\pi$
$14$	6.44453	−	8.87013i	0.460324	−	0.633581i
$15$	−8.25387	+	2.62175i	−0.550258	+	0.174783i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	27.6774	−	14.1023i	1.62808	−	0.829549i	0.629462	−	0.777032i	$-0.283276\pi$
$17$	27.6774	−	14.1023i	1.62808	−	0.829549i	0.998620	−	0.0525174i	$-0.0167245\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	25.8955	+	8.41395i	1.36292	+	0.442839i	0.897017	−	0.441997i	$-0.145730\pi$
$19$	25.8955	+	8.41395i	1.36292	+	0.442839i	0.465903	+	0.884836i	$0.345730\pi$
$20$	−4.59861	+	8.87991i	−0.229931	+	0.443995i
$21$	4.14955	+	12.7710i	0.197597	+	0.608142i
$22$	8.93768	−	17.5412i	0.406258	−	0.797327i
$23$	−30.6030	+	4.84704i	−1.33057	+	0.210741i	−0.780907	−	0.624648i	$-0.785243\pi$
$23$	−30.6030	+	4.84704i	−1.33057	+	0.210741i	−0.549659	+	0.835389i	$0.685243\pi$
$24$			4.89898i			0.204124i
$25$	0.329991	−	24.9978i	0.0131996	−	0.999913i
$26$	17.1593			0.659971
$27$	−0.812857	−	5.13218i	−0.0301058	−	0.190081i
$28$	13.8156	+	7.03938i	0.493413	+	0.251406i
$29$	−51.9065	+	16.8654i	−1.78988	+	0.581567i	−0.999517	−	0.0310745i	$-0.990107\pi$
$29$	−51.9065	+	16.8654i	−1.78988	+	0.581567i	−0.790361	+	0.612641i	$0.790107\pi$
$30$	−5.48808	−	10.9490i	−0.182936	−	0.364967i
$31$	−0.628911	+	1.93559i	−0.0202875	+	0.0624384i	−0.960688	−	0.277631i	$-0.910451\pi$
$31$	−0.628911	+	1.93559i	−0.0202875	+	0.0624384i	0.940400	+	0.340070i	$0.110451\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	10.9464	+	21.4835i	0.331709	+	0.651015i
$34$	25.8213	+	35.5400i	0.759450	+	1.04529i
$35$	−38.7631	−	0.255840i	−1.10752	−	0.00730973i
$36$	−4.85410	−	3.52671i	−0.134836	−	0.0979642i
$37$	30.9652	+	4.90440i	0.836896	+	0.132551i	0.560150	−	0.828392i	$-0.310744\pi$
$37$	30.9652	+	4.90440i	0.836896	+	0.132551i	0.276747	+	0.960943i	$0.410744\pi$
$38$	−6.02372	+	38.0323i	−0.158519	+	1.00085i
$39$	−12.3527	+	17.0021i	−0.316737	+	0.435950i
$40$	−13.4208	−	4.45883i	−0.335521	−	0.111471i
$41$	−30.7098	+	22.3120i	−0.749020	+	0.544195i	−0.895523	−	0.445016i	$-0.853198\pi$
$41$	−30.7098	+	22.3120i	−0.749020	+	0.544195i	0.146503	+	0.989210i	$0.453198\pi$
$42$	−16.9205	+	8.62144i	−0.402870	+	0.205272i
$43$	0.187340	−	0.187340i	0.00435674	−	0.00435674i	−0.704925	−	0.709282i	$-0.749019\pi$
$43$	0.187340	−	0.187340i	0.00435674	−	0.00435674i	0.709282	+	0.704925i	$0.249019\pi$
$44$	26.4789	+	8.60351i	0.601793	+	0.195534i
$45$	14.7995	+	2.44425i	0.328878	+	0.0543166i
$46$	−13.5407	−	41.6740i	−0.294363	−	0.905958i
$47$	26.5717	−	52.1499i	0.565355	−	1.10957i	−0.414535	−	0.910033i	$-0.636056\pi$
$47$	26.5717	−	52.1499i	0.565355	−	1.10957i	0.979890	−	0.199538i	$-0.0639442\pi$
$48$	−6.84291	+	1.08381i	−0.142561	+	0.0225794i
$49$			11.1056i			0.226645i
$50$	34.9900	−	5.06938i	0.699800	−	0.101388i
$51$	−53.8028			−1.05496
$52$	3.79617	+	23.9681i	0.0730033	+	0.460925i
$53$	−5.62578	−	2.86648i	−0.106147	−	0.0540844i	0.400111	−	0.916467i	$-0.368972\pi$
$53$	−5.62578	−	2.86648i	−0.106147	−	0.0540844i	−0.506258	+	0.862382i	$0.668972\pi$
$54$	6.98881	−	2.27080i	0.129422	−	0.0420519i
$55$	−68.8173	+	10.4345i	−1.25122	+	0.189718i
$56$	−6.77618	+	20.8549i	−0.121003	+	0.372410i
$57$	−33.3475	−	33.3475i	−0.585044	−	0.585044i
$58$	−35.0410	−	68.7719i	−0.604156	−	1.18572i
$59$	5.07252	+	6.98172i	0.0859749	+	0.118334i	0.849838	−	0.527044i	$-0.176700\pi$
$59$	5.07252	+	6.98172i	0.0859749	+	0.118334i	−0.763863	+	0.645378i	$0.776700\pi$
$60$	14.0795	−	10.0880i	0.234658	−	0.168134i
$61$	87.6266	+	63.6644i	1.43650	+	1.04368i	0.988759	+	0.149517i	$0.0477717\pi$
$61$	87.6266	+	63.6644i	1.43650	+	1.04368i	0.447742	+	0.894163i	$0.352228\pi$
$62$	−2.84277	−	0.450251i	−0.0458512	−	0.00726211i
$63$	3.63841	−	22.9720i	0.0577525	−	0.364635i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	−35.3345	−	49.3150i	−0.543608	−	0.758693i
$66$	−27.5865	+	20.0428i	−0.417977	+	0.303678i
$67$	7.98376	−	4.06793i	0.119161	−	0.0607154i	−0.393394	−	0.919370i	$-0.628699\pi$
$67$	7.98376	−	4.06793i	0.119161	−	0.0607154i	0.512555	+	0.858655i	$0.328699\pi$
$68$	−43.9298	+	43.9298i	−0.646026	+	0.646026i
$69$	51.0401	+	16.5839i	0.739711	+	0.240347i
$70$	−8.21826	−	54.2009i	−0.117404	−	0.774299i
$71$	39.4041	+	121.273i	0.554988	+	1.70808i	0.695975	+	0.718066i	$0.254972\pi$
$71$	39.4041	+	121.273i	0.554988	+	1.70808i	−0.140987	+	0.990011i	$0.545028\pi$
$72$	3.85224	−	7.56044i	0.0535033	−	0.105006i
$73$	13.7512	−	2.17798i	0.188373	−	0.0298354i	−0.0615350	−	0.998105i	$-0.519600\pi$
$73$	13.7512	−	2.17798i	0.188373	−	0.0298354i	0.249908	+	0.968270i	$0.419600\pi$
$74$			44.3372i			0.599152i
$75$	−20.1659	+	38.3189i	−0.268879	+	0.510918i
$76$	−54.4562			−0.716529
$77$	16.8831	+	106.596i	0.219262	+	1.38436i
$78$	−26.4813	−	13.4929i	−0.339504	−	0.172986i
$79$	40.6892	−	13.2207i	0.515054	−	0.167351i	−0.0399456	−	0.999202i	$-0.512718\pi$
$79$	40.6892	−	13.2207i	0.515054	−	0.167351i	0.554999	+	0.831851i	$0.312718\pi$
$80$	3.25900	−	19.7327i	0.0407374	−	0.246659i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−37.9594	−	37.9594i	−0.462920	−	0.462920i
$83$	−18.4050	−	36.1218i	−0.221746	−	0.435202i	0.753154	−	0.657845i	$-0.228532\pi$
$83$	−18.4050	−	36.1218i	−0.221746	−	0.435202i	−0.974900	+	0.222643i	$0.928532\pi$
$84$	−15.7858	−	21.7273i	−0.187926	−	0.258658i
$85$	48.9689	−	147.394i	0.576105	−	1.73404i
$86$	0.303122	+	0.220231i	0.00352467	+	0.00256082i
$87$	93.3675	+	14.7880i	1.07319	+	0.169977i
$88$	−6.15943	+	38.8891i	−0.0699935	+	0.441922i
$89$	79.2350	−	109.058i	0.890281	−	1.22537i	−0.0831852	−	0.996534i	$-0.526509\pi$
$89$	79.2350	−	109.058i	0.890281	−	1.22537i	0.973466	−	0.228832i	$-0.0734907\pi$
$90$	−0.140006	+	21.2127i	−0.00155563	+	0.235697i
$91$	−76.1025	+	55.2917i	−0.836291	+	0.607601i
$92$	55.2148	−	28.1333i	0.600160	−	0.305797i
$93$	2.49260	−	2.49260i	0.0268022	−	0.0268022i
$94$	78.7215	+	25.5782i	0.837463	+	0.272108i
$95$	121.707	−	61.0046i	1.28113	−	0.642153i
$96$	−3.02774	−	9.31841i	−0.0315389	−	0.0970668i
$97$	24.2763	−	47.6449i	0.250271	−	0.491184i	−0.731356	−	0.681996i	$-0.761112\pi$
$97$	24.2763	−	47.6449i	0.250271	−	0.491184i	0.981627	+	0.190812i	$0.0611121\pi$
$98$	−15.5124	+	2.45692i	−0.158289	+	0.0250706i
$99$		−	41.7623i		−	0.421841i
$100$	14.8218	+	47.7526i	0.148218	+	0.477526i
$101$	11.5764			0.114618			0.0573090	−	0.998356i	$-0.481748\pi$
$101$	11.5764			0.114618			0.0573090	+	0.998356i	$0.481748\pi$
$102$	−11.9029	−	75.1519i	−0.116695	−	0.736783i
$103$	−16.3182	−	8.31453i	−0.158429	−	0.0807236i	0.372978	−	0.927840i	$-0.378337\pi$
$103$	−16.3182	−	8.31453i	−0.158429	−	0.0807236i	−0.531407	+	0.847116i	$0.678337\pi$
$104$	−32.6388	+	10.6050i	−0.313835	+	0.101971i
$105$	59.6206	+	30.8756i	0.567816	+	0.294053i
$106$	2.75930	−	8.49225i	0.0260311	−	0.0801156i
$107$	20.3055	+	20.3055i	0.189771	+	0.189771i	0.795597	−	0.605826i	$-0.207157\pi$
$107$	20.3055	+	20.3055i	0.189771	+	0.189771i	−0.605826	+	0.795597i	$0.707157\pi$
$108$	4.71801	+	9.25961i	0.0436853	+	0.0857371i
$109$	63.6297	+	87.5787i	0.583758	+	0.803475i	0.994101	−	0.108457i	$-0.0345909\pi$
$109$	63.6297	+	87.5787i	0.583758	+	0.803475i	−0.410343	+	0.911931i	$0.634591\pi$
$110$	−29.7995	−	93.8157i	−0.270904	−	0.852870i
$111$	−43.9311	−	31.9178i	−0.395775	−	0.287548i
$112$	−30.6293	−	4.85121i	−0.273476	−	0.0433144i
$113$	8.27464	−	52.2440i	0.0732269	−	0.462337i	−0.923641	−	0.383258i	$-0.874802\pi$
$113$	8.27464	−	52.2440i	0.0732269	−	0.462337i	0.996868	−	0.0790789i	$-0.0251979\pi$
$114$	39.2023	−	53.9574i	0.343880	−	0.473310i
$115$	−91.8864	+	124.731i	−0.799012	+	1.08462i
$116$	88.3086	−	64.1599i	0.761281	−	0.553103i
$117$	32.4329	−	16.5254i	0.277204	−	0.141243i
$118$	−8.62988	+	8.62988i	−0.0731346	+	0.0731346i
$119$	−229.038	−	74.4190i	−1.92469	−	0.625370i
$120$	17.2058	+	17.4344i	0.143382	+	0.145287i
$121$	22.4927	+	69.2253i	0.185890	+	0.572110i
$122$	−69.5408	+	136.482i	−0.570007	+	1.11870i
$123$	64.9381	−	10.2852i	0.527952	−	0.0836194i
$124$		−	4.07040i		−	0.0328258i
$125$	−86.6210	−	90.1210i	−0.692968	−	0.720968i
$126$	32.8923			0.261050
$127$	1.24487	+	7.85977i	0.00980209	+	0.0618879i	0.992105	−	0.125414i	$-0.0400258\pi$
$127$	1.24487	+	7.85977i	0.00980209	+	0.0618879i	−0.982302	+	0.187302i	$0.940026\pi$
$128$	−10.0806	−	5.13632i	−0.0787546	−	0.0401275i
$129$	−0.436427	+	0.141804i	−0.00338315	+	0.00109925i
$130$	61.0662	−	60.2654i	0.469740	−	0.463580i
$131$	54.1410	−	166.629i	0.413290	−	1.27198i	−0.500481	−	0.865747i	$-0.666844\pi$
$131$	54.1410	−	166.629i	0.413290	−	1.27198i	0.913771	−	0.406229i	$-0.133156\pi$
$132$	−34.0988	−	34.0988i	−0.258324	−	0.258324i
$133$	−95.8345	−	188.086i	−0.720560	−	1.41418i
$134$	7.44835	+	10.2518i	0.0555847	+	0.0765058i
$135$	−20.9176	−	15.4095i	−0.154945	−	0.114144i
$136$	−71.0799	−	51.6426i	−0.522646	−	0.379725i
$137$	128.139	+	20.2952i	0.935321	+	0.148140i	0.605448	−	0.795885i	$-0.292994\pi$
$137$	128.139	+	20.2952i	0.935321	+	0.148140i	0.329873	+	0.944025i	$0.392994\pi$
$138$	−11.8728	+	74.9618i	−0.0860346	+	0.543201i
$139$	76.5154	−	105.314i	0.550470	−	0.757657i	−0.439606	−	0.898191i	$-0.644882\pi$
$139$	76.5154	−	105.314i	0.550470	−	0.757657i	0.990076	+	0.140534i	$0.0448818\pi$
$140$	73.8898	−	23.4703i	0.527785	−	0.167645i
$141$	−82.0145	+	59.5870i	−0.581663	+	0.422603i
$142$	−160.678	+	81.8693i	−1.13153	+	0.576545i
$143$	−119.435	+	119.435i	−0.835210	+	0.835210i
$144$	11.4127	+	3.70820i	0.0792547	+	0.0257514i
$145$	−125.491	+	242.322i	−0.865454	+	1.67119i
$146$	6.08442	+	18.7259i	0.0416741	+	0.128260i
$147$	8.73273	−	17.1390i	0.0594064	−	0.116592i
$148$	−61.9303	+	9.80880i	−0.418448	+	0.0662757i
$149$		−	19.1056i		−	0.128226i	−0.997943	−	0.0641129i	$-0.979578\pi$
$149$		−	19.1056i		−	0.128226i	0.997943	−	0.0641129i	$-0.0204218\pi$
$150$	−57.9852	−	19.6904i	−0.386568	−	0.131270i
$151$	29.8328			0.197568			0.0987841	−	0.995109i	$-0.468505\pi$
$151$	29.8328			0.197568			0.0987841	+	0.995109i	$0.468505\pi$
$152$	−12.0474	−	76.0646i	−0.0792595	−	0.500425i
$153$	83.0322	+	42.3070i	0.542694	+	0.276516i
$154$	−145.158	+	47.1648i	−0.942587	+	0.306265i
$155$	4.55987	+	9.09718i	0.0294185	+	0.0586915i
$156$	12.9884	−	39.9743i	0.0832591	−	0.256245i
$157$	98.3938	+	98.3938i	0.626712	+	0.626712i	0.947239	−	0.320527i	$-0.103860\pi$
$157$	98.3938	+	98.3938i	0.626712	+	0.626712i	−0.320527	+	0.947239i	$0.603860\pi$
$158$	27.4685	+	53.9100i	0.173851	+	0.341202i
$159$	6.42807	+	8.84748i	0.0404281	+	0.0556446i
$160$	28.2837	+	0.186675i	0.176773	+	0.00116672i
$161$	194.339	+	141.195i	1.20707	+	0.876990i
$162$	−12.5712	−	1.99109i	−0.0776001	−	0.0122907i
$163$	8.21896	−	51.8924i	0.0504230	−	0.318359i	−0.949565	−	0.313569i	$-0.898475\pi$
$163$	8.21896	−	51.8924i	0.0504230	−	0.318359i	0.999989	−	0.00478977i	$-0.00152464\pi$
$164$	44.6240	−	61.4196i	0.272097	−	0.374510i
$165$	114.409	+	38.0102i	0.693385	+	0.230365i
$166$	46.3832	−	33.6994i	0.279417	−	0.203008i
$167$	1.51815	−	0.773536i	0.00909072	−	0.00463195i	−0.449439	−	0.893311i	$-0.648376\pi$
$167$	1.51815	−	0.773536i	0.00909072	−	0.00463195i	0.458530	+	0.888679i	$0.348376\pi$
$168$	26.8564	−	26.8564i	0.159860	−	0.159860i
$169$	20.7140	+	6.73038i	0.122568	+	0.0398247i
$170$	216.713	+	35.7918i	1.27478	+	0.210540i
$171$	25.2418	+	77.6864i	0.147613	+	0.454306i
$172$	−0.240559	+	0.472123i	−0.00139860	+	0.00274490i
$173$	−231.444	+	36.6571i	−1.33783	+	0.211891i	−0.784010	−	0.620748i	$-0.786829\pi$
$173$	−231.444	+	36.6571i	−1.33783	+	0.211891i	−0.553816	+	0.832639i	$0.686829\pi$
$174$			133.687i			0.768319i
$175$	−138.848	+	135.230i	−0.793418	+	0.772744i
$176$	−55.6831			−0.316381
$177$	−2.33829	−	14.7634i	−0.0132107	−	0.0834089i
$178$	169.861	+	86.5486i	0.954276	+	0.486228i
$179$	−131.466	+	42.7160i	−0.734449	+	0.238637i	−0.652277	−	0.757981i	$-0.726186\pi$
$179$	−131.466	+	42.7160i	−0.734449	+	0.238637i	−0.0821728	+	0.996618i	$0.526186\pi$
$180$	−29.6610	+	4.49737i	−0.164783	+	0.0249854i
$181$	−39.8514	+	122.650i	−0.220173	+	0.677624i	0.778573	+	0.627555i	$0.215944\pi$
$181$	−39.8514	+	122.650i	−0.220173	+	0.677624i	−0.998746	+	0.0500689i	$0.984056\pi$
$182$	−94.0678	−	94.0678i	−0.516856	−	0.516856i
$183$	−85.1698	−	167.155i	−0.465409	−	0.913416i
$184$	51.5120	+	70.9001i	0.279956	+	0.385327i
$185$	127.423	−	91.2997i	0.688775	−	0.493512i
$186$	4.03311	+	2.93023i	0.0216834	+	0.0157539i
$187$	−427.098	−	67.6456i	−2.28395	−	0.361741i
$188$	−18.3120	+	115.617i	−0.0974040	+	0.614985i
$189$	−23.6787	+	32.5910i	−0.125284	+	0.172439i
$190$	112.137	+	156.505i	0.590194	+	0.823710i
$191$	61.7019	−	44.8290i	0.323046	−	0.234707i	−0.414428	−	0.910082i	$-0.636018\pi$
$191$	61.7019	−	44.8290i	0.323046	−	0.234707i	0.737474	+	0.675375i	$0.236018\pi$
$192$	12.3461	−	6.29068i	0.0643029	−	0.0327639i
$193$	−17.3648	+	17.3648i	−0.0899728	+	0.0899728i	−0.750661	−	0.660688i	$-0.770265\pi$
$193$	−17.3648	+	17.3648i	−0.0899728	+	0.0899728i	0.660688	+	0.750661i	$0.270265\pi$
$194$	71.9211	+	23.3686i	0.370728	+	0.120457i
$195$	15.7526	+	103.891i	0.0807824	+	0.532775i
$196$	−6.86365	−	21.1241i	−0.0350186	−	0.107776i
$197$	−67.9180	+	133.297i	−0.344762	+	0.676633i	−0.996659	−	0.0816744i	$-0.973973\pi$
$197$	−67.9180	+	133.297i	−0.344762	+	0.676633i	0.651897	+	0.758307i	$0.273973\pi$
$198$	58.3337	−	9.23915i	0.294615	−	0.0466624i
$199$			103.645i			0.520827i	0.965497	+	0.260413i	$0.0838589\pi$
$199$			103.645i			0.520827i	−0.965497	+	0.260413i	$0.916141\pi$
$200$	−63.4219	+	31.2676i	−0.317110	+	0.156338i
$201$	−15.5198			−0.0772131
$202$	2.56107	+	16.1700i	0.0126786	+	0.0800494i
$203$	377.011	+	192.097i	1.85720	+	0.946288i
$204$	102.339	−	33.2520i	0.501662	−	0.163000i
$205$	−30.9274	+	187.260i	−0.150865	+	0.913465i
$206$	8.00365	−	24.6327i	0.0388527	−	0.119576i
$207$	−65.7280	−	65.7280i	−0.317527	−	0.317527i
$208$	−22.0338	−	43.2438i	−0.105932	−	0.207903i
$209$	−222.792	−	306.647i	−1.06599	−	1.46721i
$210$	−29.9371	+	90.1089i	−0.142558	+	0.429090i
$211$	−144.613	−	105.068i	−0.685372	−	0.497952i	0.189764	−	0.981830i	$-0.439228\pi$
$211$	−144.613	−	105.068i	−0.685372	−	0.497952i	−0.875135	+	0.483878i	$0.839228\pi$
$212$	12.4724	+	1.97544i	0.0588323	+	0.00931812i
$213$	34.5504	−	218.142i	0.162208	−	1.02414i
$214$	−23.8706	+	32.8551i	−0.111545	+	0.153528i
$215$	0.00874291	−	1.32466i	4.06647e−5	−	0.00616122i
$216$	−11.8901	+	8.63864i	−0.0550466	+	0.0399937i
$217$	14.0587	−	7.16327i	0.0647867	−	0.0330105i
$218$	−108.253	+	108.253i	−0.496575	+	0.496575i
$219$	−22.9345	−	7.45187i	−0.104724	−	0.0340268i
$220$	124.449	−	62.3790i	0.565679	−	0.283541i
$221$	−116.469	−	358.454i	−0.527009	−	1.62197i
$222$	34.8639	−	68.4242i	0.157045	−	0.308217i
$223$	341.154	−	54.0335i	1.52984	−	0.242303i	0.665954	−	0.745993i	$-0.268025\pi$
$223$	341.154	−	54.0335i	1.52984	−	0.242303i	0.863884	+	0.503690i	$0.168025\pi$
$224$		−	43.8564i		−	0.195787i
$225$	61.2529	−	43.2791i	0.272235	−	0.192352i
$226$	74.8052			0.330997
$227$	68.2830	+	431.122i	0.300806	+	1.89921i	0.422017	+	0.906588i	$0.361322\pi$
$227$	68.2830	+	431.122i	0.300806	+	1.89921i	−0.121211	+	0.992627i	$0.538678\pi$
$228$	84.0406	+	42.8208i	0.368599	+	0.187811i
$229$	−366.890	+	119.210i	−1.60214	+	0.520567i	−0.967635	−	0.252353i	$-0.918796\pi$
$229$	−366.890	+	119.210i	−1.60214	+	0.520567i	−0.634504	+	0.772920i	$0.718796\pi$
$230$	−194.553	−	100.753i	−0.845882	−	0.438055i
$231$	57.7649	−	177.782i	0.250064	−	0.769619i
$232$	109.155	+	109.155i	0.470497	+	0.470497i
$233$	−15.3034	−	30.0346i	−0.0656799	−	0.128904i	0.855832	−	0.517253i	$-0.173045\pi$
$233$	−15.3034	−	30.0346i	−0.0656799	−	0.128904i	−0.921512	+	0.388349i	$0.873045\pi$
$234$	30.2579	+	41.6464i	0.129307	+	0.177976i
$235$	−88.5936	−	278.913i	−0.376994	−	1.18687i
$236$	−13.9634	−	10.1450i	−0.0591671	−	0.0429875i
$237$	−73.1904	−	11.5922i	−0.308820	−	0.0489123i
$238$	53.2782	−	336.385i	0.223858	−	1.41338i
$239$	28.8357	−	39.6890i	0.120652	−	0.166063i	−0.744419	−	0.667713i	$-0.767273\pi$
$239$	28.8357	−	39.6890i	0.120652	−	0.166063i	0.865071	+	0.501650i	$0.167273\pi$
$240$	−20.5460	+	27.8902i	−0.0856083	+	0.116209i
$241$	186.104	−	135.212i	0.772214	−	0.561046i	−0.130418	−	0.991459i	$-0.541632\pi$
$241$	186.104	−	135.212i	0.772214	−	0.561046i	0.902632	+	0.430413i	$0.141632\pi$
$242$	−91.7180	+	46.7326i	−0.379000	+	0.193110i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	−206.022	−	66.9407i	−0.844354	−	0.274347i
$245$	39.0043	+	39.5226i	0.159201	+	0.161317i
$246$	28.7328	+	88.4303i	0.116800	+	0.359473i
$247$	149.985	−	294.362i	0.607227	−	1.19175i
$248$	5.68554	−	0.900502i	0.0229256	−	0.00363106i
$249$			70.2180i			0.282000i
$250$	106.718	−	140.930i	0.426872	−	0.563720i
$251$	38.4802			0.153307			0.0766537	−	0.997058i	$-0.475576\pi$
$251$	38.4802			0.153307			0.0766537	+	0.997058i	$0.475576\pi$
$252$	7.27681	+	45.9440i	0.0288762	+	0.182317i
$253$	384.316	+	195.819i	1.51904	+	0.773987i
$254$	−10.7031	+	3.47766i	−0.0421383	+	0.0136916i
$255$	−191.473	+	188.962i	−0.750874	+	0.741027i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	50.8928	+	50.8928i	0.198026	+	0.198026i	0.799153	−	0.601127i	$-0.205281\pi$
$257$	50.8928	+	50.8928i	0.198026	+	0.198026i	−0.601127	+	0.799153i	$0.705281\pi$
$258$	−0.294623	−	0.578231i	−0.00114195	−	0.00224120i
$259$	−142.866	−	196.639i	−0.551607	−	0.759222i
$260$	97.6886	+	71.9648i	0.375726	+	0.276788i
$261$	−132.463	−	96.2399i	−0.507520	−	0.368735i
$262$	244.725	+	38.7607i	0.934066	+	0.147942i
$263$	29.0601	−	183.479i	0.110495	−	0.697637i	−0.868795	−	0.495172i	$-0.835105\pi$
$263$	29.0601	−	183.479i	0.110495	−	0.697637i	0.979290	−	0.202465i	$-0.0648951\pi$
$264$	40.0855	−	55.1730i	0.151839	−	0.208989i
$265$	−30.0884	+	9.55722i	−0.113541	+	0.0360650i
$266$	241.517	−	175.472i	0.907958	−	0.659670i
$267$	−208.037	+	106.000i	−0.779163	+	0.397004i
$268$	−12.6719	+	12.6719i	−0.0472832	+	0.0472832i
$269$	−78.2531	−	25.4260i	−0.290904	−	0.0945204i	0.159930	−	0.987128i	$-0.448873\pi$
$269$	−78.2531	−	25.4260i	−0.290904	−	0.0945204i	−0.450834	+	0.892608i	$0.648873\pi$
$270$	16.8964	−	32.6269i	0.0625792	−	0.120840i
$271$	−81.0758	−	249.526i	−0.299173	−	0.920759i	−0.981788	−	0.189981i	$-0.939157\pi$
$271$	−81.0758	−	249.526i	−0.299173	−	0.920759i	0.682615	−	0.730778i	$-0.260843\pi$
$272$	56.4093	−	110.710i	0.207387	−	0.407020i
$273$	160.924	−	25.4879i	0.589466	−	0.0933623i
$274$			183.475i			0.669616i
$275$	−208.259	+	278.829i	−0.757306	+	1.01392i
$276$	−107.333			−0.388889
$277$	−52.3898	−	330.776i	−0.189133	−	1.19414i	−0.881355	−	0.472454i	$-0.843368\pi$
$277$	−52.3898	−	330.776i	−0.189133	−	1.19414i	0.692222	−	0.721684i	$-0.256632\pi$
$278$	164.031	+	83.5779i	0.590039	+	0.300640i
$279$	−5.80677	+	1.88673i	−0.0208128	+	0.00676249i
$280$	49.1301	+	98.0171i	0.175465	+	0.350061i
$281$	6.44237	−	19.8276i	0.0229266	−	0.0705607i	−0.938939	−	0.344085i	$-0.888189\pi$
$281$	6.44237	−	19.8276i	0.0229266	−	0.0705607i	0.961865	+	0.273524i	$0.0881893\pi$
$282$	−101.375	−	101.375i	−0.359487	−	0.359487i
$283$	150.039	+	294.468i	0.530173	+	1.04052i	0.988426	+	0.151702i	$0.0484753\pi$
$283$	150.039	+	294.468i	0.530173	+	1.04052i	−0.458253	+	0.888822i	$0.651525\pi$
$284$	−149.902	−	206.323i	−0.527825	−	0.726489i
$285$	−235.797	−	1.55629i	−0.827359	−	0.00546066i
$286$	−193.250	−	140.404i	−0.675699	−	0.490924i
$287$	290.668	+	46.0372i	1.01278	+	0.160409i
$288$	−2.65478	+	16.7616i	−0.00921799	+	0.0582001i
$289$	397.292	−	546.826i	1.37471	−	1.89213i
$290$	−366.239	−	121.676i	−1.26289	−	0.419574i
$291$	−74.9296	+	54.4396i	−0.257490	+	0.187077i
$292$	−24.8104	+	12.6415i	−0.0849670	+	0.0432928i
$293$	−340.304	+	340.304i	−1.16145	+	1.16145i	−0.177286	+	0.984159i	$0.556732\pi$
$293$	−340.304	+	340.304i	−1.16145	+	1.16145i	−0.984159	+	0.177286i	$0.943268\pi$
$294$	25.8717	+	8.40622i	0.0879989	+	0.0285926i
$295$	42.5727	+	7.03119i	0.144314	+	0.0238345i
$296$	−27.4019	−	84.3344i	−0.0925740	−	0.284914i
$297$	−32.8391	+	64.4505i	−0.110570	+	0.217005i
$298$	26.6868	−	4.22677i	0.0895530	−	0.0141838i
$299$			375.948i			1.25735i
$300$	14.6755	−	85.3500i	0.0489183	−	0.284500i
$301$	−2.05401			−0.00682395
$302$	6.59996	+	41.6705i	0.0218542	+	0.137982i
$303$	−17.8655	−	9.10295i	−0.0589622	−	0.0300427i
$304$	103.582	−	33.6558i	0.340730	−	0.110710i
$305$	535.442	−	81.1868i	1.75555	−	0.266186i
$306$	−40.7252	+	125.339i	−0.133089	+	0.409605i
$307$	−197.706	−	197.706i	−0.643994	−	0.643994i	0.307541	−	0.951535i	$-0.400494\pi$
$307$	−197.706	−	197.706i	−0.643994	−	0.643994i	−0.951535	+	0.307541i	$0.900494\pi$
$308$	−97.9936	−	192.323i	−0.318161	−	0.624426i
$309$	18.6453	+	25.6631i	0.0603409	+	0.0830521i
$310$	−11.6982	+	8.38181i	−0.0377360	+	0.0270381i
$311$	278.817	+	202.572i	0.896518	+	0.651358i	0.937569	−	0.347799i	$-0.113071\pi$
$311$	278.817	+	202.572i	0.896518	+	0.651358i	−0.0410515	+	0.999157i	$0.513071\pi$
$312$	58.7096	+	9.29869i	0.188172	+	0.0298035i
$313$	−4.78055	+	30.1832i	−0.0152733	+	0.0964319i	−0.994147	−	0.108032i	$-0.965545\pi$
$313$	−4.78055	+	30.1832i	−0.0152733	+	0.0964319i	0.978874	+	0.204464i	$0.0655451\pi$
$314$	−115.669	+	159.205i	−0.368372	+	0.507021i
$315$	−67.7321	−	94.5311i	−0.215023	−	0.300099i
$316$	−69.2247	+	50.2947i	−0.219065	+	0.159160i
$317$	−373.174	+	190.142i	−1.17721	+	0.599817i	−0.929429	−	0.369000i	$-0.879700\pi$
$317$	−373.174	+	190.142i	−1.17721	+	0.599817i	−0.247777	+	0.968817i	$0.579700\pi$
$318$	−10.9361	+	10.9361i	−0.0343902	+	0.0343902i
$319$	722.578	+	234.780i	2.26513	+	0.735987i
$320$	5.99649	+	39.5480i	0.0187390	+	0.123587i
$321$	−15.3700	−	47.3039i	−0.0478815	−	0.147364i
$322$	−154.228	+	302.690i	−0.478969	+	0.940030i
$323$	835.375	−	132.310i	2.58630	−	0.409630i
$324$		−	18.0000i		−	0.0555556i
$325$	−298.949	−	51.4026i	−0.919842	−	0.158162i
$326$	74.3018			0.227920
$327$	−29.3315	−	185.192i	−0.0896987	−	0.566335i
$328$	95.6633	+	48.7429i	0.291656	+	0.148606i
$329$	−431.555	+	140.221i	−1.31172	+	0.426203i
$330$	−27.7819	+	168.215i	−0.0841877	+	0.509743i
$331$	47.3536	−	145.739i	0.143062	−	0.440300i	−0.853694	−	0.520774i	$-0.825643\pi$
$331$	47.3536	−	145.739i	0.143062	−	0.440300i	0.996757	+	0.0804739i	$0.0256434\pi$
$332$	57.3328	+	57.3328i	0.172689	+	0.172689i
$333$	42.6994	+	83.8022i	0.128226	+	0.251658i
$334$	1.41634	+	1.94942i	0.00424054	+	0.00583660i
$335$	14.1255	−	42.5169i	0.0421656	−	0.126916i
$336$	43.4546	+	31.5716i	0.129329	+	0.0939632i
$337$	163.674	+	25.9234i	0.485680	+	0.0769241i	0.394472	−	0.918908i	$-0.370927\pi$
$337$	163.674	+	25.9234i	0.485680	+	0.0769241i	0.0912074	+	0.995832i	$0.470927\pi$
$338$	−4.81842	+	30.4223i	−0.0142557	+	0.0900068i
$339$	−53.8513	+	74.1200i	−0.158853	+	0.218643i
$340$	−2.05015	+	310.624i	−0.00602985	+	0.913599i
$341$	22.9207	−	16.6529i	0.0672161	−	0.0488354i
$342$	−102.928	+	52.4446i	−0.300960	+	0.153347i
$343$	−207.739	+	207.739i	−0.605652	+	0.605652i
$344$	−0.712682	−	0.231564i	−0.00207175	−	0.000673153i
$345$	239.886	−	120.240i	0.695321	−	0.348523i
$346$	−102.405	−	315.172i	−0.295970	−	0.910901i
$347$	33.6766	−	66.0940i	0.0970506	−	0.190473i	−0.837377	−	0.546626i	$-0.815912\pi$
$347$	33.6766	−	66.0940i	0.0970506	−	0.190473i	0.934427	+	0.356153i	$0.115912\pi$
$348$	−186.735	+	29.5759i	−0.536595	+	0.0849883i
$349$		−	665.198i		−	1.90601i	−0.302951	−	0.953006i	$-0.597972\pi$
$349$		−	665.198i		−	1.90601i	0.302951	−	0.953006i	$-0.402028\pi$
$350$	−219.607	−	164.026i	−0.627450	−	0.468646i
$351$	−63.0471			−0.179621
$352$	−12.3189	−	77.7782i	−0.0349968	−	0.220961i
$353$	−455.232	−	231.952i	−1.28961	−	0.657089i	−0.331491	−	0.943458i	$-0.607552\pi$
$353$	−455.232	−	231.952i	−1.28961	−	0.657089i	−0.958119	+	0.286369i	$0.907552\pi$
$354$	20.1042	−	6.53225i	0.0567915	−	0.0184527i
$355$	566.158	+	293.195i	1.59481	+	0.825901i
$356$	−83.3126	+	256.410i	−0.234024	+	0.720252i
$357$	294.949	+	294.949i	0.826189	+	0.826189i
$358$	−88.7504	−	174.182i	−0.247906	−	0.486543i
$359$	17.0749	+	23.5015i	0.0475623	+	0.0654639i	0.832136	−	0.554572i	$-0.187118\pi$
$359$	17.0749	+	23.5015i	0.0475623	+	0.0654639i	−0.784573	+	0.620036i	$0.787118\pi$
$360$	−12.8439	−	40.4356i	−0.0356775	−	0.112321i
$361$	307.726	+	223.576i	0.852425	+	0.619323i
$362$	−180.134	−	28.5304i	−0.497608	−	0.0788133i
$363$	19.7220	−	124.520i	0.0543307	−	0.343030i
$364$	110.583	−	152.205i	0.303800	−	0.418145i
$365$	41.2885	−	56.0470i	0.113119	−	0.153554i
$366$	214.640	−	155.945i	0.586449	−	0.426080i
$367$	279.478	−	142.401i	0.761521	−	0.388014i	−0.0296888	−	0.999559i	$-0.509452\pi$
$367$	279.478	−	142.401i	0.761521	−	0.388014i	0.791210	+	0.611545i	$0.209452\pi$
$368$	−87.6374	+	87.6374i	−0.238145	+	0.238145i
$369$	−108.305	−	35.1903i	−0.293508	−	0.0953667i
$370$	155.718	+	157.787i	0.420859	+	0.426451i
$371$	15.1266	+	46.5549i	0.0407725	+	0.125485i
$372$	−3.20070	+	6.28172i	−0.00860402	+	0.0168863i
$373$	−483.801	+	76.6265i	−1.29705	+	0.205433i	−0.766514	−	0.642228i	$-0.778010\pi$
$373$	−483.801	+	76.6265i	−1.29705	+	0.205433i	−0.530539	+	0.847661i	$0.678010\pi$
$374$		−	611.537i		−	1.63512i
$375$	62.8143	+	207.194i	0.167505	+	0.552517i
$376$	−165.545			−0.440280
$377$	103.593	+	654.061i	0.274783	+	1.73491i
$378$	−50.7616	−	25.8643i	−0.134290	−	0.0684241i
$379$	−528.560	+	171.740i	−1.39462	+	0.453139i	−0.907446	−	0.420168i	$-0.861971\pi$
$379$	−528.560	+	171.740i	−1.39462	+	0.453139i	−0.487171	+	0.873307i	$0.661971\pi$
$380$	−193.798	+	191.257i	−0.509996	+	0.503308i
$381$	4.25925	−	13.1086i	0.0111791	−	0.0344058i
$382$	76.2677	+	76.2677i	0.199654	+	0.199654i
$383$	−106.277	−	208.580i	−0.277485	−	0.544595i	0.709636	−	0.704568i	$-0.248859\pi$
$383$	−106.277	−	208.580i	−0.277485	−	0.544595i	−0.987121	+	0.159973i	$0.948859\pi$
$384$	11.5182	+	15.8534i	0.0299953	+	0.0412850i
$385$	434.462	+	320.057i	1.12847	+	0.831317i
$386$	−28.0968	−	20.4135i	−0.0727895	−	0.0528847i
$387$	0.785029	+	0.124336i	0.00202850	+	0.000321283i
$388$	−16.7301	+	105.629i	−0.0431187	+	0.272241i
$389$	−71.2000	+	97.9985i	−0.183034	+	0.251924i	−0.890668	−	0.454655i	$-0.849763\pi$
$389$	−71.2000	+	97.9985i	−0.183034	+	0.251924i	0.707634	+	0.706579i	$0.249763\pi$
$390$	−141.630	+	44.9872i	−0.363155	+	0.115352i
$391$	−778.657	+	565.727i	−1.99145	+	1.44687i
$392$	27.9878	−	14.2605i	0.0713974	−	0.0363788i
$393$	−214.580	+	214.580i	−0.546006	+	0.546006i
$394$	−201.215	−	65.3786i	−0.510697	−	0.165936i
$395$	98.3717	−	189.955i	0.249042	−	0.480900i
$396$	25.8105	+	79.4366i	0.0651781	+	0.200598i
$397$	−220.371	+	432.502i	−0.555090	+	1.08943i	0.427566	+	0.903984i	$0.359371\pi$
$397$	−220.371	+	432.502i	−0.555090	+	1.08943i	−0.982655	+	0.185441i	$0.940629\pi$
$398$	−144.771	+	22.9295i	−0.363746	+	0.0576117i
$399$			365.625i			0.916353i
$400$	−57.7055	−	81.6705i	−0.144264	−	0.204176i
$401$	−11.6629			−0.0290846			−0.0145423	−	0.999894i	$-0.504629\pi$
$401$	−11.6629			−0.0290846			−0.0145423	+	0.999894i	$0.504629\pi$
$402$	−3.43348	−	21.6781i	−0.00854100	−	0.0539257i
$403$	22.0025	+	11.2108i	0.0545967	+	0.0278184i
$404$	−22.0197	+	7.15463i	−0.0545041	+	0.0177095i
$405$	20.1645	+	40.2293i	0.0497889	+	0.0993315i
$406$	−184.914	+	569.107i	−0.455453	+	1.40174i
$407$	−308.604	−	308.604i	−0.758241	−	0.758241i
$408$	69.0870	+	135.591i	0.169331	+	0.332331i
$409$	314.065	+	432.273i	0.767884	+	1.05690i	0.996517	+	0.0833893i	$0.0265745\pi$
$409$	314.065	+	432.273i	0.767884	+	1.05690i	−0.228633	+	0.973513i	$0.573425\pi$
$410$	−268.408	−	1.77152i	−0.654653	−	0.00432078i
$411$	−181.794	−	132.081i	−0.442321	−	0.321365i
$412$	36.1777	+	5.72998i	0.0878099	+	0.0139077i
$413$	10.4663	−	66.0819i	0.0253422	−	0.160005i
$414$	77.2679	−	106.350i	0.186638	−	0.256885i
$415$	−192.363	−	63.9094i	−0.463526	−	0.153998i
$416$	55.5285	−	40.3438i	0.133482	−	0.0969804i
$417$	−200.896	+	102.362i	−0.481765	+	0.245472i
$418$	379.036	−	379.036i	0.906785	−	0.906785i
$419$	659.020	+	214.128i	1.57284	+	0.511047i	0.960199	−	0.279316i	$-0.0901076\pi$
$419$	659.020	+	214.128i	1.57284	+	0.511047i	0.612640	+	0.790362i	$0.290108\pi$
$420$	−132.487	−	21.8812i	−0.315446	−	0.0520982i
$421$	145.679	+	448.353i	0.346030	+	1.06497i	0.961030	+	0.276444i	$0.0891559\pi$
$421$	145.679	+	448.353i	0.346030	+	1.06497i	−0.615000	+	0.788527i	$0.710844\pi$
$422$	114.766	−	225.241i	0.271957	−	0.533746i
$423$	173.426	−	27.4679i	0.409990	−	0.0649360i
$424$			17.8586i			0.0421193i
$425$	−343.394	−	696.528i	−0.807987	−	1.63889i
$426$	312.345			0.733205
$427$	−131.362	−	829.384i	−0.307638	−	1.94235i
$428$	−51.1729	−	26.0739i	−0.119563	−	0.0609204i
$429$	278.236	−	90.4044i	0.648569	−	0.210733i
$430$	1.85223	−	0.280845i	0.00430750	−	0.000653128i
$431$	8.39892	−	25.8492i	0.0194871	−	0.0599750i	−0.940840	−	0.338851i	$-0.889962\pi$
$431$	8.39892	−	25.8492i	0.0194871	−	0.0599750i	0.960327	+	0.278876i	$0.0899618\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−256.456	−	503.323i	−0.592277	−	1.16241i	−0.971486	−	0.237098i	$-0.923804\pi$
$433$	−256.456	−	503.323i	−0.592277	−	1.16241i	0.379209	−	0.925311i	$-0.376196\pi$
$434$	13.1159	+	18.0525i	0.0302210	+	0.0415956i
$435$	384.213	−	275.291i	0.883247	−	0.632852i
$436$	−175.157	−	127.259i	−0.401737	−	0.291879i
$437$	−833.262	−	131.976i	−1.90678	−	0.302004i
$438$	5.33495	−	33.6835i	0.0121802	−	0.0769030i
$439$	−57.0608	+	78.5375i	−0.129979	+	0.178901i	−0.869046	−	0.494731i	$-0.835267\pi$
$439$	−57.0608	+	78.5375i	−0.129979	+	0.178901i	0.739067	+	0.673632i	$0.235267\pi$
$440$	114.663	+	160.031i	0.260598	+	0.363707i
$441$	−26.9539	+	19.5832i	−0.0611200	+	0.0444063i
$442$	474.923	−	241.986i	1.07449	−	0.547479i
$443$	−271.214	+	271.214i	−0.612221	+	0.612221i	−0.943524	−	0.331303i	$-0.892512\pi$
$443$	−271.214	+	271.214i	−0.612221	+	0.612221i	0.331303	+	0.943524i	$0.392512\pi$
$444$	103.288	+	33.5603i	0.232631	+	0.0755864i
$445$	−101.043	−	666.396i	−0.227063	−	1.49752i
$446$	150.948	+	464.571i	0.338449	+	1.04164i
$447$	−15.0234	+	29.4851i	−0.0336095	+	0.0659623i
$448$	61.2587	−	9.70242i	0.136738	−	0.0216572i
$449$			690.437i			1.53772i	0.639416	+	0.768861i	$0.279176\pi$
$449$			690.437i			1.53772i	−0.639416	+	0.768861i	$0.720824\pi$
$450$	74.0035	+	75.9834i	0.164452	+	0.168852i
$451$	528.424			1.17167
$452$	16.5493	+	104.488i	0.0366135	+	0.231168i
$453$	−46.0400	−	23.4586i	−0.101634	−	0.0517849i
$454$	−587.085	+	190.756i	−1.29314	+	0.420167i
$455$	−76.6416	+	464.053i	−0.168443	+	1.01990i
$456$	−41.2198	+	126.861i	−0.0903942	+	0.278205i
$457$	106.711	+	106.711i	0.233503	+	0.233503i	0.814153	−	0.580650i	$-0.197202\pi$
$457$	106.711	+	106.711i	0.233503	+	0.233503i	−0.580650	+	0.814153i	$0.697202\pi$
$458$	−247.680	−	486.100i	−0.540786	−	1.06135i
$459$	−94.8735	−	130.582i	−0.206696	−	0.284493i
$460$	97.6901	−	294.042i	0.212370	−	0.639221i
$461$	−70.8181	−	51.4524i	−0.153618	−	0.111610i	0.508321	−	0.861168i	$-0.330266\pi$
$461$	−70.8181	−	51.4524i	−0.153618	−	0.111610i	−0.661939	+	0.749557i	$0.730266\pi$
$462$	261.106	+	41.3551i	0.565164	+	0.0895132i
$463$	−89.0229	+	562.069i	−0.192274	+	1.21397i	0.683027	+	0.730393i	$0.260663\pi$
$463$	−89.0229	+	562.069i	−0.192274	+	1.21397i	−0.875301	+	0.483578i	$0.839337\pi$
$464$	−128.320	+	176.617i	−0.276551	+	0.380640i
$465$	0.116327	−	17.6250i	0.000250165	−	0.0379031i
$466$	38.5668	−	28.0205i	0.0827615	−	0.0601297i
$467$	807.481	−	411.432i	1.72908	−	0.881011i	0.754713	−	0.656055i	$-0.227776\pi$
$467$	807.481	−	411.432i	1.72908	−	0.881011i	0.974369	−	0.224956i	$-0.0722239\pi$
$468$	−51.4778	+	51.4778i	−0.109995	+	0.109995i
$469$	−66.0679	−	21.4668i	−0.140870	−	0.0457713i
$470$	369.987	−	185.452i	0.787207	−	0.394579i
$471$	−74.4776	−	229.219i	−0.158127	−	0.486664i
$472$	11.0815	−	21.7486i	0.0234777	−	0.0460775i
$473$	−3.64274	+	0.576953i	−0.00770135	+	0.00121977i
$474$		−	104.797i		−	0.221091i
$475$	218.876	−	644.554i	0.460791	−	1.35696i
$476$	481.650			1.01187
$477$	−2.96316	−	18.7087i	−0.00621208	−	0.0392215i
$478$	61.8170	+	31.4974i	0.129324	+	0.0658940i
$479$	856.445	−	278.276i	1.78799	−	0.580952i	0.788563	−	0.614953i	$-0.210825\pi$
$479$	856.445	−	278.276i	1.78799	−	0.580952i	0.999422	+	0.0340018i	$0.0108252\pi$
$480$	−43.5025	−	22.5285i	−0.0906302	−	0.0469344i
$481$	117.549	−	361.779i	0.244385	−	0.752139i
$482$	230.037	+	230.037i	0.477254	+	0.477254i
$483$	−188.890	−	370.718i	−0.391077	−	0.767532i
$484$	−85.5672	−	117.773i	−0.176792	−	0.243333i
$485$	−80.9404	−	254.819i	−0.166887	−	0.525401i
$486$	17.8351	+	12.9580i	0.0366978	+	0.0266625i
$487$	209.791	+	33.2277i	0.430783	+	0.0682294i	0.368061	−	0.929802i	$-0.380022\pi$
$487$	209.791	+	33.2277i	0.430783	+	0.0682294i	0.0627223	+	0.998031i	$0.480022\pi$
$488$	47.9243	−	302.582i	0.0982055	−	0.620045i
$489$	−53.4889	+	73.6211i	−0.109384	+	0.150554i
$490$	−46.5763	+	63.2249i	−0.0950536	+	0.129031i
$491$	410.190	−	298.021i	0.835418	−	0.606967i	−0.0856691	−	0.996324i	$-0.527303\pi$
$491$	410.190	−	298.021i	0.835418	−	0.606967i	0.921087	+	0.389357i	$0.127303\pi$
$492$	−117.163	+	59.6976i	−0.238136	+	0.121337i
$493$	−1198.79	+	1198.79i	−2.43163	+	2.43163i
$494$	444.347	+	144.377i	0.899488	+	0.292261i
$495$	−146.674	−	148.623i	−0.296312	−	0.300249i
$496$	2.51565	+	7.74236i	0.00507187	+	0.0156096i
$497$	448.811	−	880.842i	0.903041	−	1.77232i
$498$	−98.0807	+	15.5345i	−0.196949	+	0.0311937i
$499$			50.5100i			0.101222i	0.998718	+	0.0506112i	$0.0161169\pi$
$499$			50.5100i			0.101222i	−0.998718	+	0.0506112i	$0.983883\pi$
$500$	220.461	+	117.886i	0.440922	+	0.235771i
$501$	−2.95117			−0.00589056
$502$	8.51304	+	53.7492i	0.0169582	+	0.107070i
$503$	−240.811	−	122.699i	−0.478749	−	0.243935i	0.197926	−	0.980217i	$-0.436580\pi$
$503$	−240.811	−	122.699i	−0.478749	−	0.243935i	−0.676675	+	0.736282i	$0.736580\pi$
$504$	−62.5648	+	20.3285i	−0.124137	+	0.0403344i
$505$	41.1981	−	40.6578i	0.0815804	−	0.0805106i
$506$	−188.497	+	580.135i	−0.372524	+	1.14651i
$507$	−26.6749	−	26.6749i	−0.0526132	−	0.0526132i
$508$	−7.22548	−	14.1808i	−0.0142234	−	0.0279150i
$509$	−488.441	−	672.282i	−0.959610	−	1.32079i	−0.947124	−	0.320867i	$-0.896026\pi$
$509$	−488.441	−	672.282i	−0.959610	−	1.32079i	−0.0124854	−	0.999922i	$-0.503974\pi$
$510$	−306.302	−	225.645i	−0.600593	−	0.442442i
$511$	−87.3247	−	63.4451i	−0.170890	−	0.124159i
$512$	22.3488	+	3.53971i	0.0436501	+	0.00691349i
$513$	22.1326	−	139.740i	0.0431434	−	0.272397i
$514$	−59.8281	+	82.3463i	−0.116397	+	0.160207i
$515$	−87.2746	+	27.7218i	−0.169465	+	0.0538287i
$516$	0.742494	−	0.539453i	0.00143894	−	0.00104545i
$517$	−725.966	+	369.898i	−1.40419	+	0.715470i
$518$	243.059	−	243.059i	0.469225	−	0.469225i
$519$	386.005	+	125.421i	0.743747	+	0.241658i
$520$	−78.9088	+	152.373i	−0.151748	+	0.293024i
$521$	32.4500	+	99.8708i	0.0622841	+	0.191691i	0.977357	−	0.211598i	$-0.0678669\pi$
$521$	32.4500	+	99.8708i	0.0622841	+	0.191691i	−0.915073	+	0.403289i	$0.867867\pi$
$522$	105.123	−	206.316i	0.201385	−	0.395241i
$523$	269.858	−	42.7413i	0.515981	−	0.0817234i	0.106987	−	0.994260i	$-0.465880\pi$
$523$	269.858	−	42.7413i	0.515981	−	0.0817234i	0.408994	+	0.912537i	$0.365880\pi$
$524$			350.408i			0.668718i
$525$	320.616	−	99.5153i	0.610698	−	0.189553i
$526$	262.712			0.499453
$527$	9.88971	+	62.4412i	0.0187661	+	0.118484i
$528$	85.9339	+	43.7855i	0.162754	+	0.0829271i
$529$	409.942	−	133.198i	0.774938	−	0.251793i
$530$	−20.0061	−	39.9131i	−0.0377473	−	0.0753078i
$531$	−8.00034	+	24.6225i	−0.0150666	+	0.0463701i
$532$	298.531	+	298.531i	0.561149	+	0.561149i
$533$	209.098	+	410.378i	0.392304	+	0.769939i
$534$	−194.085	−	267.135i	−0.363456	−	0.500254i
$535$	143.579	+	0.947635i	0.268371	+	0.00177128i
$536$	−20.5036	−	14.8967i	−0.0382529	−	0.0277924i
$537$	236.477	+	37.4543i	0.440367	+	0.0697473i
$538$	18.2030	−	114.929i	0.0338346	−	0.213623i
$539$	90.8709	−	125.073i	0.168592	−	0.232046i
$540$	49.3113	+	16.3828i	0.0913172	+	0.0303385i
$541$	76.3499	−	55.4714i	0.141127	−	0.102535i	−0.514982	−	0.857201i	$-0.672201\pi$
$541$	76.3499	−	55.4714i	0.141127	−	0.102535i	0.656109	+	0.754666i	$0.272201\pi$
$542$	330.602	−	168.450i	0.609966	−	0.310793i
$543$	157.945	−	157.945i	0.290875	−	0.290875i
$544$	167.119	+	54.3002i	0.307204	+	0.0998166i
$545$	534.032	+	88.1992i	0.979875	+	0.161833i
$546$	71.2031	+	219.141i	0.130409	+	0.401357i
$547$	−202.500	+	397.429i	−0.370202	+	0.726562i	−0.998685	−	0.0512609i	$-0.983676\pi$
$547$	−202.500	+	397.429i	−0.370202	+	0.726562i	0.628483	+	0.777823i	$0.283676\pi$
$548$	−256.278	+	40.5904i	−0.467661	+	0.0740702i
$549$			324.937i			0.591871i
$550$	−435.542	−	229.211i	−0.791895	−	0.416747i
$551$	−1486.05			−2.69700
$552$	−23.7456	−	149.924i	−0.0430173	−	0.271601i
$553$	−295.537	−	150.584i	−0.534425	−	0.272303i
$554$	450.439	−	146.356i	0.813066	−	0.264181i
$555$	−268.441	+	40.7025i	−0.483677	+	0.0733379i
$556$	−80.4530	+	247.609i	−0.144700	+	0.445340i
$557$	−186.224	−	186.224i	−0.334334	−	0.334334i	0.519896	−	0.854230i	$-0.325971\pi$
$557$	−186.224	−	186.224i	−0.334334	−	0.334334i	−0.854230	+	0.519896i	$0.825971\pi$
$558$	−3.92004	−	7.69350i	−0.00702515	−	0.0137876i
$559$	−1.88950	−	2.60067i	−0.00338014	−	0.00465237i
$560$	−126.041	+	90.3095i	−0.225074	+	0.161267i
$561$	605.934	+	440.237i	1.08010	+	0.784737i
$562$	29.1204	+	4.61223i	0.0518157	+	0.00820681i
$563$	108.733	−	686.514i	0.193132	−	1.21939i	−0.680482	−	0.732765i	$-0.738229\pi$
$563$	108.733	−	686.514i	0.193132	−	1.21939i	0.873613	−	0.486621i	$-0.161771\pi$
$564$	119.174	−	164.029i	0.211301	−	0.290831i
$565$	−154.040	−	214.987i	−0.272637	−	0.380508i
$566$	−378.120	+	274.721i	−0.668057	+	0.485372i
$567$	62.1700	−	31.6772i	0.109647	−	0.0558681i
$568$	255.029	−	255.029i	0.448995	−	0.448995i
$569$	−78.2446	−	25.4232i	−0.137513	−	0.0446805i	0.239452	−	0.970908i	$-0.423032\pi$
$569$	−78.2446	−	25.4232i	−0.137513	−	0.0446805i	−0.376965	+	0.926228i	$0.623032\pi$
$570$	−49.9920	−	329.706i	−0.0877053	−	0.578432i
$571$	54.5276	+	167.819i	0.0954950	+	0.293903i	0.987382	−	0.158354i	$-0.0506188\pi$
$571$	54.5276	+	167.819i	0.0954950	+	0.293903i	−0.891887	+	0.452258i	$0.850619\pi$
$572$	153.364	−	300.994i	0.268119	−	0.526213i
$573$	−130.473	+	20.6649i	−0.227702	+	0.0360644i
$574$			416.190i			0.725070i
$575$	111.067	+	766.608i	0.193160	+	1.33323i
$576$	−24.0000			−0.0416667
$577$	−74.1018	−	467.860i	−0.128426	−	0.810849i	−0.964857	−	0.262777i	$-0.915362\pi$
$577$	−74.1018	−	467.860i	−0.128426	−	0.810849i	0.836431	−	0.548073i	$-0.184638\pi$
$578$	851.701	+	433.963i	1.47353	+	0.750801i
$579$	40.4530	−	13.1440i	0.0698670	−	0.0227012i
$580$	88.9342	−	538.482i	0.153335	−	0.928418i
$581$	−97.1243	+	298.918i	−0.167168	+	0.514489i
$582$	−92.6181	−	92.6181i	−0.159138	−	0.159138i
$583$	39.9035	+	78.3151i	0.0684452	+	0.134331i
$584$	−23.1465	−	31.8585i	−0.0396345	−	0.0545521i
$585$	57.3827	−	172.719i	0.0980901	−	0.295246i
$586$	−550.623	−	400.051i	−0.939629	−	0.682681i
$587$	−313.927	−	49.7211i	−0.534798	−	0.0847037i	−0.116807	−	0.993155i	$-0.537266\pi$
$587$	−313.927	−	49.7211i	−0.534798	−	0.0847037i	−0.417991	+	0.908451i	$0.637266\pi$
$588$	−6.01819	+	37.9974i	−0.0102350	+	0.0646214i
$589$	−32.5719	+	44.8314i	−0.0553004	+	0.0761144i
$590$	−0.402746	+	61.0212i	−0.000682621	+	0.103426i
$591$	209.632	−	152.306i	0.354706	−	0.257709i
$592$	111.736	−	56.9325i	0.188744	−	0.0961698i
$593$	351.897	−	351.897i	0.593418	−	0.593418i	−0.345135	−	0.938553i	$-0.612167\pi$
$593$	351.897	−	351.897i	0.593418	−	0.593418i	0.938553	+	0.345135i	$0.112167\pi$
$594$	−97.2896	−	31.6113i	−0.163787	−	0.0532177i
$595$	−1076.47	+	539.569i	−1.80919	+	0.906838i
$596$	11.8079	+	36.3411i	0.0198120	+	0.0609750i
$597$	81.4993	−	159.951i	0.136515	−	0.267925i
$598$	−525.125	+	83.1716i	−0.878136	+	0.139083i
$599$			910.481i			1.52000i	0.649922	+	0.760001i	$0.274802\pi$
$599$			910.481i			1.52000i	−0.649922	+	0.760001i	$0.725198\pi$
$600$	122.464	+	1.61662i	0.204106	+	0.00269437i
$601$	−58.8854			−0.0979790			−0.0489895	−	0.998799i	$-0.515600\pi$
$601$	−58.8854			−0.0979790			−0.0489895	+	0.998799i	$0.515600\pi$
$602$	−0.454412	−	2.86904i	−0.000754837	−	0.00476585i
$603$	23.9513	+	12.2038i	0.0397202	+	0.0202385i
$604$	−56.7454	+	18.4377i	−0.0939493	+	0.0305260i
$605$	323.174	+	167.361i	0.534173	+	0.276630i
$606$	8.76259	−	26.9685i	0.0144597	−	0.0445024i
$607$	124.840	+	124.840i	0.205668	+	0.205668i	0.802423	−	0.596756i	$-0.203544\pi$
$607$	124.840	+	124.840i	0.205668	+	0.205668i	−0.596756	+	0.802423i	$0.703544\pi$
$608$	69.9261	+	137.238i	0.115010	+	0.225720i
$609$	−430.777	−	592.913i	−0.707351	−	0.973585i
$610$	231.859	+	729.945i	0.380096	+	1.19663i
$611$	−574.531	−	417.421i	−0.940312	−	0.683177i
$612$	−184.084	−	29.1560i	−0.300790	−	0.0476405i
$613$	121.977	−	770.135i	0.198984	−	1.25634i	−0.662697	−	0.748888i	$-0.730588\pi$
$613$	121.977	−	770.135i	0.198984	−	1.25634i	0.861681	−	0.507450i	$-0.169412\pi$
$614$	232.417	−	319.895i	0.378530	−	0.521002i
$615$	194.978	−	264.674i	0.317038	−	0.430364i
$616$	246.958	−	179.426i	0.400906	−	0.291275i
$617$	164.536	−	83.8350i	0.266670	−	0.135875i	−0.315543	−	0.948911i	$-0.602187\pi$
$617$	164.536	−	83.8350i	0.266670	−	0.135875i	0.582214	+	0.813036i	$0.302187\pi$
$618$	−31.7213	+	31.7213i	−0.0513290	+	0.0513290i
$619$	444.918	+	144.563i	0.718770	+	0.233542i	0.645490	−	0.763769i	$-0.276653\pi$
$619$	444.918	+	144.563i	0.718770	+	0.233542i	0.0732800	+	0.997311i	$0.476653\pi$
$620$	−14.2957	−	14.4857i	−0.0230576	−	0.0233640i
$621$	49.7518	+	153.120i	0.0801156	+	0.246570i
$622$	−221.270	+	434.268i	−0.355740	+	0.698179i
$623$	−1032.23	+	163.489i	−1.65687	+	0.262422i
$624$			84.0628i			0.134716i
$625$	−624.782	−	16.4981i	−0.999652	−	0.0263970i
$626$	−43.2176			−0.0690376
$627$	102.701	+	648.427i	0.163797	+	1.03417i
$628$	−247.967	−	126.345i	−0.394852	−	0.201187i
$629$	926.198	−	300.940i	1.47249	−	0.478442i
$630$	117.057	−	115.522i	0.185804	−	0.183368i
$631$	58.7960	−	180.956i	0.0931792	−	0.286776i	−0.893596	−	0.448873i	$-0.851826\pi$
$631$	58.7960	−	180.956i	0.0931792	−	0.286776i	0.986775	+	0.162097i	$0.0518257\pi$
$632$	−85.5664	−	85.5664i	−0.135390	−	0.135390i
$633$	140.559	+	275.862i	0.222052	+	0.435801i
$634$	−348.149	−	479.185i	−0.549130	−	0.755813i
$635$	32.0347	+	23.5992i	0.0504483	+	0.0371640i
$636$	−17.6950	−	12.8561i	−0.0278223	−	0.0202141i
$637$	133.090	+	21.0794i	0.208933	+	0.0330917i
$638$	−168.084	+	1061.24i	−0.263454	+	1.66338i
$639$	−224.853	+	309.484i	−0.351883	+	0.484326i
$640$	−53.9141	+	17.1252i	−0.0842408	+	0.0267581i
$641$	−694.832	+	504.825i	−1.08398	+	0.787558i	−0.978373	−	0.206849i	$-0.933679\pi$
$641$	−694.832	+	504.825i	−1.08398	+	0.787558i	−0.105608	+	0.994408i	$0.533679\pi$
$642$	62.6738	−	31.9339i	0.0976228	−	0.0497413i
$643$	−600.234	+	600.234i	−0.933490	+	0.933490i	−0.997922	−	0.0644322i	$-0.979476\pi$
$643$	−600.234	+	600.234i	−0.933490	+	0.933490i	0.0644322	+	0.997922i	$0.479476\pi$
$644$	−456.918	−	148.462i	−0.709500	−	0.230530i
$645$	−1.05512	+	2.03743i	−0.00163585	+	0.00315881i
$646$	369.623	+	1137.58i	0.572172	+	1.76096i
$647$	−379.917	+	745.629i	−0.587198	+	1.15244i	0.386006	+	0.922496i	$0.373854\pi$
$647$	−379.917	+	745.629i	−0.587198	+	1.15244i	−0.973204	+	0.229944i	$0.926146\pi$
$648$	25.1424	−	3.98217i	0.0388001	−	0.00614533i
$649$		−	120.135i		−	0.185107i
$650$	5.66240	−	428.944i	0.00871139	−	0.659914i
$651$	−27.3291			−0.0419802
$652$	16.4379	+	103.785i	0.0252115	+	0.159179i
$653$	406.909	+	207.330i	0.623137	+	0.317504i	0.736898	−	0.676004i	$-0.236290\pi$
$653$	406.909	+	207.330i	0.623137	+	0.317504i	−0.113761	+	0.993508i	$0.536290\pi$
$654$	252.187	−	81.9406i	0.385607	−	0.125291i
$655$	−392.545	−	783.147i	−0.599305	−	1.19564i
$656$	−46.9204	+	144.406i	−0.0715250	+	0.220131i
$657$	29.5344	+	29.5344i	0.0449534	+	0.0449534i
$658$	−291.334	−	571.776i	−0.442757	−	0.868960i
$659$	477.397	+	657.080i	0.724426	+	0.997087i	0.999365	+	0.0356250i	$0.0113422\pi$
$659$	477.397	+	657.080i	0.724426	+	0.997087i	−0.274939	+	0.961462i	$0.588658\pi$
$660$	−241.110	−	1.59135i	−0.365317	−	0.00241113i
$661$	451.645	+	328.140i	0.683276	+	0.496429i	0.874443	−	0.485128i	$-0.161227\pi$
$661$	451.645	+	328.140i	0.683276	+	0.496429i	−0.191167	+	0.981558i	$0.561227\pi$
$662$	214.045	+	33.9014i	0.323331	+	0.0512106i
$663$	−102.122	+	644.775i	−0.154031	+	0.972511i
$664$	−67.3987	+	92.7664i	−0.101504	+	0.139708i
$665$	−1001.64	−	332.775i	−1.50622	−	0.500414i
$666$	−107.609	+	78.1823i	−0.161575	+	0.117391i
$667$	1506.75	−	767.726i	2.25899	−	1.15101i
$668$	−2.40962	+	2.40962i	−0.00360722	+	0.00360722i
$669$	−568.980	−	184.873i	−0.850494	−	0.276342i
$670$	62.5126	+	10.3244i	0.0933024	+	0.0154096i
$671$	−465.933	−	1434.00i	−0.694386	−	2.13710i
$672$	−34.4858	+	67.6821i	−0.0513181	+	0.100717i
$673$	306.054	−	48.4741i	0.454760	−	0.0720269i	0.0751475	−	0.997172i	$-0.476057\pi$
$673$	306.054	−	48.4741i	0.454760	−	0.0720269i	0.379613	+	0.925145i	$0.376057\pi$
$674$			234.355i			0.347708i
$675$	−128.562	+	18.6261i	−0.190462	+	0.0275942i
$676$	−43.5599			−0.0644377
$677$	−90.7371	−	572.891i	−0.134028	−	0.846220i	−0.959486	−	0.281757i	$-0.909083\pi$
$677$	−90.7371	−	572.891i	−0.134028	−	0.846220i	0.825458	−	0.564464i	$-0.190917\pi$
$678$	−115.445	−	58.8219i	−0.170272	−	0.0867580i
$679$	−394.275	+	128.108i	−0.580670	+	0.188671i
$680$	−434.334	+	65.8562i	−0.638726	+	0.0968473i
$681$	233.627	−	719.030i	0.343065	−	1.05584i
$682$	28.3315	+	28.3315i	0.0415419	+	0.0415419i
$683$	87.5006	+	171.730i	0.128112	+	0.251434i	0.946149	−	0.323732i	$-0.104938\pi$
$683$	87.5006	+	171.730i	0.128112	+	0.251434i	−0.818037	+	0.575166i	$0.804938\pi$
$684$	−96.0257	−	132.168i	−0.140388	−	0.193228i
$685$	527.299	−	377.813i	0.769780	−	0.551552i
$686$	−336.128	−	244.211i	−0.489983	−	0.355993i
$687$	659.948	+	104.526i	0.960624	+	0.152148i
$688$	0.165782	−	1.04671i	0.000240962	−	0.00152137i
$689$	−45.0302	+	61.9787i	−0.0653558	+	0.0899546i
$690$	221.022	+	308.472i	0.320322	+	0.447061i
$691$	−480.763	+	349.295i	−0.695750	+	0.505492i	−0.878545	−	0.477659i	$-0.841485\pi$
$691$	−480.763	+	349.295i	−0.695750	+	0.505492i	0.182795	+	0.983151i	$0.441485\pi$
$692$	417.577	−	212.766i	0.603435	−	0.307466i
$693$	−228.943	+	228.943i	−0.330365	+	0.330365i
$694$	99.7705	+	32.4174i	0.143762	+	0.0467110i
$695$	−97.5747	−	643.523i	−0.140395	−	0.925932i
$696$	−82.6234	−	254.289i	−0.118712	−	0.365357i
$697$	−535.316	+	1050.62i	−0.768029	+	1.50734i
$698$	929.151	−	147.163i	1.33116	−	0.210835i
$699$			58.3851i			0.0835266i
$700$	180.528	−	343.036i	0.257897	−	0.490051i
$701$	69.5400			0.0992012			0.0496006	−	0.998769i	$-0.484205\pi$
$701$	69.5400			0.0992012			0.0496006	+	0.998769i	$0.484205\pi$
$702$	−13.9480	−	88.0644i	−0.0198690	−	0.125448i
$703$	760.592	+	387.541i	1.08192	+	0.551267i
$704$	105.916	−	34.4140i	0.150448	−	0.0488836i
$705$	−82.5955	+	500.103i	−0.117157	+	0.709365i
$706$	223.280	−	687.185i	0.316260	−	0.973350i
$707$	−63.4625	−	63.4625i	−0.0897631	−	0.0897631i
$708$	13.5720	+	26.6365i	0.0191694	+	0.0376221i
$709$	619.381	+	852.505i	0.873598	+	1.20241i	0.978153	+	0.207886i	$0.0666583\pi$
$709$	619.381	+	852.505i	0.873598	+	1.20241i	−0.104555	+	0.994519i	$0.533342\pi$
$710$	−284.283	+	855.675i	−0.400399	+	1.20518i
$711$	103.837	+	75.4420i	0.146044	+	0.106107i
$712$	−376.585	−	59.6452i	−0.528912	−	0.0837714i
$713$	9.86470	−	62.2833i	0.0138355	−	0.0873538i
$714$	−346.734	+	477.238i	−0.485621	+	0.668401i
$715$	−5.57389	+	844.515i	−0.00779565	+	1.18114i
$716$	223.664	−	162.501i	0.312380	−	0.226957i
$717$	−75.7101	+	38.5762i	−0.105593	+	0.0538023i
$718$	−29.0495	+	29.0495i	−0.0404589	+	0.0404589i
$719$	450.271	+	146.302i	0.626246	+	0.203480i	0.604911	−	0.796293i	$-0.293209\pi$
$719$	450.271	+	146.302i	0.626246	+	0.203480i	0.0213345	+	0.999772i	$0.493209\pi$
$720$	53.6390	−	26.8860i	0.0744986	−	0.0373417i
$721$	43.8764	+	135.038i	0.0608549	+	0.187292i
$722$	−244.212	+	479.294i	−0.338244	+	0.663842i
$723$	−393.530	+	62.3290i	−0.544301	+	0.0862088i
$724$		−	257.923i		−	0.356248i
$725$	404.470	+	1303.11i	0.557890	+	1.79740i
$726$	178.293			0.245583
$727$	−58.5127	−	369.435i	−0.0804852	−	0.508163i	−0.994690	−	0.102912i	$-0.967184\pi$
$727$	−58.5127	−	369.435i	−0.0804852	−	0.508163i	0.914205	−	0.405251i	$-0.132816\pi$
$728$	237.065	+	120.791i	0.325638	+	0.165921i
$729$	−25.6785	+	8.34346i	−0.0352243	+	0.0114451i
$730$	87.4209	+	45.2724i	0.119755	+	0.0620170i
$731$	2.54315	−	7.82700i	0.00347899	−	0.0107072i
$732$	265.310	+	265.310i	0.362446	+	0.362446i
$733$	513.871	+	1008.53i	0.701052	+	1.37589i	0.916762	+	0.399435i	$0.130794\pi$
$733$	513.871	+	1008.53i	0.701052	+	1.37589i	−0.215709	+	0.976458i	$0.569206\pi$
$734$	260.736	+	358.872i	0.355226	+	0.488927i
$735$	−29.1161	−	91.6644i	−0.0396138	−	0.124713i
$736$	−141.800	−	103.024i	−0.192663	−	0.139978i
$737$	−123.200	−	19.5129i	−0.167164	−	0.0264761i
$738$	25.1935	−	159.065i	0.0341375	−	0.215536i
$739$	−375.175	+	516.385i	−0.507680	+	0.698761i	−0.983526	−	0.180767i	$-0.942142\pi$
$739$	−375.175	+	516.385i	−0.507680	+	0.698761i	0.475846	+	0.879529i	$0.342142\pi$
$740$	−185.947	+	252.414i	−0.251280	+	0.341101i
$741$	−462.934	+	336.341i	−0.624742	+	0.453902i
$742$	−61.6815	+	31.4283i	−0.0831287	+	0.0423562i
$743$	740.645	−	740.645i	0.996830	−	0.996830i	−0.00316478	−	0.999995i	$-0.501007\pi$
$743$	740.645	−	740.645i	0.996830	−	0.996830i	0.999995	+	0.00316478i	$0.00100738\pi$
$744$	−9.48242	−	3.08102i	−0.0127452	−	0.00414116i
$745$	−67.1013	−	67.9930i	−0.0900689	−	0.0912657i
$746$	−214.064	−	658.822i	−0.286949	−	0.883139i
$747$	55.2149	−	108.365i	0.0739155	−	0.145067i
$748$	854.196	−	135.291i	1.14197	−	0.180871i
$749$		−	222.632i		−	0.297239i
$750$	−275.513	+	133.577i	−0.367350	+	0.178103i
$751$	365.498			0.486682			0.243341	−	0.969941i	$-0.421757\pi$
$751$	365.498			0.486682			0.243341	+	0.969941i	$0.421757\pi$
$752$	−36.6239	−	231.234i	−0.0487020	−	0.307492i
$753$	−59.3853	−	30.2583i	−0.0788649	−	0.0401837i
$754$	−890.676	+	289.398i	−1.18127	+	0.383817i
$755$	106.169	−	104.776i	0.140621	−	0.138777i
$756$	24.8973	−	76.6259i	0.0329329	−	0.101357i
$757$	662.539	+	662.539i	0.875217	+	0.875217i	0.993035	−	0.117818i	$-0.0375899\pi$
$757$	662.539	+	662.539i	0.875217	+	0.875217i	−0.117818	+	0.993035i	$0.537590\pi$
$758$	−356.820	−	700.300i	−0.470739	−	0.923878i
$759$	−439.124	−	604.402i	−0.578556	−	0.796313i
$760$	−310.022	−	228.386i	−0.407924	−	0.300508i
$761$	869.717	+	631.886i	1.14286	+	0.830337i	0.987515	−	0.157524i	$-0.0503511\pi$
$761$	869.717	+	631.886i	1.14286	+	0.830337i	0.155345	+	0.987860i	$0.450351\pi$
$762$	19.2524	+	3.04928i	0.0252656	+	0.00400169i
$763$	131.290	−	828.931i	0.172070	−	1.08641i
$764$	−89.6581	+	123.404i	−0.117353	+	0.161523i
$765$	444.081	−	141.057i	0.580499	−	0.184389i
$766$	267.833	−	194.592i	0.349652	−	0.254037i
$767$	93.2974	−	47.5374i	0.121639	−	0.0619783i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$	−213.450	−	69.3540i	−0.277568	−	0.0901873i	0.166925	−	0.985970i	$-0.446616\pi$
$769$	−213.450	−	69.3540i	−0.277568	−	0.0901873i	−0.444493	+	0.895782i	$0.646616\pi$
$770$	−350.940	+	677.664i	−0.455766	+	0.880083i
$771$	−38.5225	−	118.560i	−0.0499643	−	0.153774i
$772$	22.2977	−	43.7617i	0.0288830	−	0.0566862i
$773$	528.855	−	83.7624i	0.684159	−	0.108360i	0.195327	−	0.980738i	$-0.437423\pi$
$773$	528.855	−	83.7624i	0.684159	−	0.108360i	0.488832	+	0.872378i	$0.337423\pi$
$774$			1.12404i			0.00145225i
$775$	48.1780	+	16.3601i	0.0621652	+	0.0211099i
$776$	−151.245			−0.194903
$777$	65.8573	+	415.807i	0.0847585	+	0.535144i
$778$	−152.636	−	77.7720i	−0.196190	−	0.0999640i
$779$	−982.976	+	319.388i	−1.26184	+	0.409998i
$780$	−94.1714	−	187.877i	−0.120733	−	0.240868i
$781$	548.536	−	1688.22i	0.702351	−	2.16161i
$782$	−962.473	−	962.473i	−1.23078	−	1.23078i
$783$	128.749	+	252.684i	0.164430	+	0.322713i
$784$	26.1109	+	35.9385i	0.0333047	+	0.0458400i
$785$	695.734	+	4.59192i	0.886286	+	0.00584958i
$786$	−347.198	−	252.254i	−0.441728	−	0.320934i
$787$	−1361.44	−	215.631i	−1.72992	−	0.273992i	−0.789434	−	0.613836i	$-0.789626\pi$
$787$	−1361.44	−	215.631i	−1.72992	−	0.273992i	−0.940482	+	0.339844i	$0.889626\pi$
$788$	46.8059	−	295.521i	0.0593984	−	0.375027i
$789$	−189.123	+	260.306i	−0.239700	+	0.329918i
$790$	287.093	+	95.3816i	0.363409	+	0.120736i
$791$	−331.766	+	241.042i	−0.419426	+	0.304731i
$792$	−105.247	+	53.6261i	−0.132888	+	0.0677097i
$793$	929.280	−	929.280i	1.17185	−	1.17185i
$794$	−652.872	−	212.131i	−0.822258	−	0.267168i
$795$	53.9496	+	8.91017i	0.0678612	+	0.0112078i
$796$	−64.0558	−	197.144i	−0.0804722	−	0.247668i
$797$	41.8178	−	82.0721i	0.0524691	−	0.102976i	−0.863283	−	0.504720i	$-0.831596\pi$
$797$	41.8178	−	82.0721i	0.0524691	−	0.102976i	0.915752	+	0.401744i	$0.131596\pi$
$798$	−510.705	+	80.8878i	−0.639982	+	0.101363i
$799$		−	1818.09i		−	2.27546i
$800$	101.311	−	98.6713i	0.126639	−	0.123339i
$801$	404.408			0.504879
$802$	−2.58021	−	16.2908i	−0.00321722	−	0.0203127i
$803$	−172.690	−	87.9897i	−0.215056	−	0.109576i
$804$	29.5205	−	9.59179i	0.0367170	−	0.0119301i
$805$	1187.51	−	180.057i	1.47516	−	0.223673i
$806$	−10.7917	+	33.2133i	−0.0133891	+	0.0412076i
$807$	100.772	+	100.772i	0.124873	+	0.124873i
$808$	−14.8650	−	29.1743i	−0.0183973	−	0.0361068i
$809$	−560.717	−	771.760i	−0.693098	−	0.953968i	−0.999998	−	0.00222599i	$-0.999291\pi$
$809$	−560.717	−	771.760i	−0.693098	−	0.953968i	0.306899	−	0.951742i	$-0.400709\pi$
$810$	−51.7313	+	37.0658i	−0.0638658	+	0.0457603i
$811$	723.429	+	525.602i	0.892021	+	0.648091i	0.936404	−	0.350923i	$-0.114132\pi$
$811$	723.429	+	525.602i	0.892021	+	0.648091i	−0.0443831	+	0.999015i	$0.514132\pi$
$812$	−835.839	−	132.384i	−1.02936	−	0.163034i
$813$	−71.0890	+	448.838i	−0.0874403	+	0.552076i
$814$	362.786	−	499.332i	0.445683	−	0.613430i
$815$	−153.003	−	213.540i	−0.187734	−	0.262013i
$816$	−174.109	+	126.498i	−0.213369	+	0.155022i
$817$	6.42751	−	3.27498i	0.00786721	−	0.00400854i
$818$	−534.319	+	534.319i	−0.653201	+	0.653201i
$819$	−268.391	−	87.2057i	−0.327706	−	0.106478i
$820$	−56.9058	−	375.304i	−0.0693974	−	0.457688i
$821$	−65.0858	−	200.314i	−0.0792763	−	0.243987i	0.903562	−	0.428458i	$-0.140943\pi$
$821$	−65.0858	−	200.314i	−0.0792763	−	0.243987i	−0.982838	+	0.184471i	$0.940943\pi$
$822$	144.273	−	283.151i	0.175514	−	0.344466i
$823$	315.519	−	49.9732i	0.383376	−	0.0607208i	0.0382281	−	0.999269i	$-0.487829\pi$
$823$	315.519	−	49.9732i	0.383376	−	0.0607208i	0.345148	+	0.938548i	$0.387829\pi$
$824$			51.8007i			0.0628650i
$825$	540.653	−	266.546i	0.655336	−	0.323086i
$826$	94.6188			0.114551
$827$	−212.778	−	1343.42i	−0.257289	−	1.62446i	−0.690618	−	0.723220i	$-0.742661\pi$
$827$	−212.778	−	1343.42i	−0.257289	−	1.62446i	0.433329	−	0.901236i	$-0.357339\pi$
$828$	165.644	+	84.4000i	0.200053	+	0.101932i
$829$	437.124	−	142.030i	0.527291	−	0.171327i	−0.0332608	−	0.999447i	$-0.510589\pi$
$829$	437.124	−	142.030i	0.527291	−	0.171327i	0.560551	+	0.828120i	$0.310589\pi$
$830$	46.7118	−	282.833i	0.0562793	−	0.340762i
$831$	−179.249	+	551.673i	−0.215703	+	0.663866i
$832$	68.6370	+	68.6370i	0.0824964	+	0.0824964i
$833$	156.615	+	307.375i	0.188013	+	0.368997i
$834$	−187.424	−	257.966i	−0.224728	−	0.309312i
$835$	2.68602	−	8.08478i	0.00321680	−	0.00968237i
$836$	613.293	+	445.584i	0.733605	+	0.532995i
$837$	10.4450	+	1.65433i	0.0124791	+	0.00197650i
$838$	−153.299	+	967.892i	−0.182934	+	1.15500i
$839$	−230.282	+	316.957i	−0.274473	+	0.377779i	−0.923893	−	0.382650i	$-0.875011\pi$
$839$	−230.282	+	316.957i	−0.274473	+	0.377779i	0.649421	+	0.760429i	$0.275011\pi$
$840$	1.25336	−	189.899i	0.00149209	−	0.226071i
$841$	1729.46	−	1256.52i	2.05643	−	1.49408i
$842$	−594.031	+	302.674i	−0.705500	+	0.359470i
$843$	−25.5334	+	25.5334i	−0.0302887	+	0.0302887i
$844$	340.007	+	110.475i	0.402851	+	0.130894i
$845$	97.3546	−	48.7980i	0.115213	−	0.0577491i
$846$	76.7345	+	236.165i	0.0907028	+	0.279154i
$847$	256.190	−	502.802i	0.302468	−	0.593627i
$848$	−24.9449	+	3.95088i	−0.0294161	+	0.00465906i
$849$		−	572.424i		−	0.674234i
$850$	896.942	−	633.748i	1.05523	−	0.745586i
$851$	−971.399			−1.14148
$852$	69.1007	+	436.285i	0.0811041	+	0.512071i
$853$	−1059.33	−	539.754i	−1.24188	−	0.632772i	−0.295355	−	0.955388i	$-0.595438\pi$
$853$	−1059.33	−	539.754i	−1.24188	−	0.632772i	−0.946530	+	0.322616i	$0.895438\pi$
$854$	1129.42	−	366.972i	1.32251	−	0.429710i
$855$	362.675	+	187.817i	0.424181	+	0.219669i
$856$	25.0990	−	77.2469i	0.0293213	−	0.0902417i
$857$	−80.9800	−	80.9800i	−0.0944924	−	0.0944924i	0.658280	−	0.752773i	$-0.271284\pi$
$857$	−80.9800	−	80.9800i	−0.0944924	−	0.0944924i	−0.752773	+	0.658280i	$0.771284\pi$
$858$	187.832	+	368.641i	0.218918	+	0.429651i
$859$	373.635	+	514.265i	0.434966	+	0.598679i	0.969084	−	0.246731i	$-0.0793564\pi$
$859$	373.635	+	514.265i	0.434966	+	0.598679i	−0.534118	+	0.845410i	$0.679356\pi$
$860$	0.802056	+	2.52506i	0.000932624	+	0.00293612i
$861$	−412.378	−	299.610i	−0.478952	−	0.347979i
$862$	37.9644	+	6.01296i	0.0440422	+	0.00697560i
$863$	43.1283	−	272.302i	0.0499749	−	0.315529i	−0.950020	−	0.312190i	$-0.898937\pi$
$863$	43.1283	−	272.302i	0.0499749	−	0.315529i	0.999994	−	0.00333858i	$-0.00106271\pi$
$864$	17.2773	−	23.7801i	0.0199969	−	0.0275233i
$865$	−694.916	+	943.314i	−0.803371	+	1.09054i
$866$	646.307	−	469.569i	0.746313	−	0.542228i
$867$	−1043.12	+	531.494i	−1.20313	+	0.613027i
$868$	−22.3141	+	22.3141i	−0.0257075	+	0.0257075i
$869$	−566.426	−	184.043i	−0.651813	−	0.211787i
$870$	469.527	+	475.766i	0.539686	+	0.546857i
$871$	−33.5964	−	103.399i	−0.0385722	−	0.118713i
$872$	139.006	−	272.814i	0.159410	−	0.312860i
$873$	158.444	−	25.0951i	0.181494	−	0.0287458i
$874$		−	1193.10i		−	1.36510i
$875$	−19.1869	+	968.908i	−0.0219279	+	1.10732i
$876$	48.2295			0.0550565
$877$	181.442	+	1145.58i	0.206889	+	1.30625i	0.844362	+	0.535773i	$0.179980\pi$
$877$	181.442	+	1145.58i	0.206889	+	1.30625i	−0.637473	+	0.770472i	$0.720020\pi$
$878$	−122.325	−	62.3277i	−0.139322	−	0.0709883i
$879$	792.772	−	257.587i	0.901902	−	0.293046i
$880$	−198.164	+	195.566i	−0.225187	+	0.222234i
$881$	−43.7080	+	134.519i	−0.0496118	+	0.152689i	−0.972793	−	0.231675i	$-0.925579\pi$
$881$	−43.7080	+	134.519i	−0.0496118	+	0.152689i	0.923181	+	0.384365i	$0.125579\pi$
$882$	−33.3169	−	33.3169i	−0.0377742	−	0.0377742i
$883$	−296.413	−	581.744i	−0.335689	−	0.658826i	0.660032	−	0.751237i	$-0.270543\pi$
$883$	−296.413	−	581.744i	−0.335689	−	0.658826i	−0.995721	+	0.0924111i	$0.970543\pi$
$884$	443.074	+	609.839i	0.501215	+	0.689863i
$885$	−60.1723	−	44.3274i	−0.0679912	−	0.0500875i
$886$	−438.833	−	318.831i	−0.495297	−	0.359854i
$887$	−788.532	−	124.891i	−0.888987	−	0.140802i	−0.304796	−	0.952418i	$-0.598588\pi$
$887$	−788.532	−	124.891i	−0.888987	−	0.140802i	−0.584191	+	0.811616i	$0.698588\pi$
$888$	−24.0266	+	151.698i	−0.0270569	+	0.170831i
$889$	36.2632	−	49.9120i	0.0407910	−	0.0561440i
$890$	908.470	−	288.565i	1.02075	−	0.324230i
$891$	101.359	−	73.6418i	0.113759	−	0.0826507i
$892$	−615.519	+	313.622i	−0.690043	+	0.351595i
$893$	1126.87	−	1126.87i	1.26189	−	1.26189i
$894$	−44.5086	−	14.4617i	−0.0497859	−	0.0161764i
$895$	−317.838	+	613.744i	−0.355126	+	0.685747i
$896$	27.1047	+	83.4197i	0.0302508	+	0.0931024i
$897$	295.621	−	580.189i	0.329566	−	0.646810i
$898$	−964.405	+	152.747i	−1.07395	+	0.170097i
$899$		−	111.077i		−	0.123556i
$900$	−89.7619	+	120.178i	−0.0997355	+	0.133531i
$901$	−196.131			−0.217681
$902$	116.904	+	738.104i	0.129606	+	0.818297i
$903$	3.16989	+	1.61514i	0.00351039	+	0.00178864i
$904$	−142.288	+	46.2322i	−0.157398	+	0.0511418i
$905$	288.939	+	576.448i	0.319269	+	0.636959i
$906$	22.5815	−	69.4986i	0.0249244	−	0.0767093i
$907$	100.712	+	100.712i	0.111039	+	0.111039i	0.760443	−	0.649404i	$-0.224982\pi$
$907$	100.712	+	100.712i	0.111039	+	0.111039i	−0.649404	+	0.760443i	$0.724982\pi$
$908$	−396.330	−	777.841i	−0.436487	−	0.856653i
$909$	20.4134	+	28.0966i	0.0224569	+	0.0309093i
$910$	−665.145	−	4.39003i	−0.730929	−	0.00482421i
$911$	654.460	+	475.493i	0.718398	+	0.521947i	0.885872	−	0.463930i	$-0.153561\pi$
$911$	654.460	+	475.493i	0.718398	+	0.521947i	−0.167474	+	0.985876i	$0.553561\pi$
$912$	−186.319	−	29.5101i	−0.204298	−	0.0323576i
$913$	−88.2844	+	557.405i	−0.0966970	+	0.610521i
$914$	−125.446	+	172.662i	−0.137250	+	0.188908i
$915$	−890.171	−	295.743i	−0.972864	−	0.323217i
$916$	624.190	−	453.501i	0.681431	−	0.495088i
$917$	−1210.27	+	616.664i	−1.31982	+	0.672479i
$918$	161.408	−	161.408i	0.175826	−	0.175826i
$919$	−1740.98	−	565.678i	−1.89442	−	0.615536i	−0.974968	−	0.222345i	$-0.928629\pi$
$919$	−1740.98	−	565.678i	−1.89442	−	0.615536i	−0.919457	−	0.393191i	$-0.871371\pi$
$920$	432.330	+	71.4024i	0.469924	+	0.0776114i
$921$	149.650	+	460.577i	0.162487	+	0.500083i
$922$	56.2016	−	110.302i	0.0609562	−	0.119633i
$923$	1528.14	−	242.033i	1.65562	−	0.262225i
$924$			373.862i			0.404613i
$925$	132.818	−	772.443i	0.143587	−	0.835074i
$926$	−804.793			−0.869107
$927$	−8.59497	−	54.2665i	−0.00927182	−	0.0585399i
$928$	−275.088	−	140.164i	−0.296431	−	0.151039i
$929$	497.402	−	161.616i	0.535416	−	0.173967i	−0.0288139	−	0.999585i	$-0.509173\pi$
$929$	497.402	−	161.616i	0.535416	−	0.173967i	0.564230	+	0.825617i	$0.309173\pi$
$930$	24.6443	−	3.73672i	0.0264993	−	0.00401797i
$931$	−93.4421	+	287.585i	−0.100367	+	0.308899i
$932$	47.6712	+	47.6712i	0.0511494	+	0.0511494i
$933$	−271.000	−	531.867i	−0.290461	−	0.570061i
$934$	753.330	+	1036.87i	0.806563	+	1.11014i
$935$	−1757.53	+	1259.28i	−1.87971	+	1.34683i
$936$	−83.2928	−	60.5157i	−0.0889880	−	0.0646536i
$937$	258.518	+	40.9452i	0.275899	+	0.0436982i	0.292851	−	0.956158i	$-0.405396\pi$
$937$	258.518	+	40.9452i	0.275899	+	0.0436982i	−0.0169514	+	0.999856i	$0.505396\pi$
$938$	15.3685	−	97.0329i	0.0163843	−	0.103447i
$939$	31.1118	−	42.8217i	0.0331329	−	0.0456035i
$940$	340.893	+	475.771i	0.362652	+	0.506139i
$941$	−607.164	+	441.131i	−0.645233	+	0.468789i	−0.861644	−	0.507513i	$-0.830565\pi$
$941$	−607.164	+	441.131i	−0.645233	+	0.468789i	0.216411	+	0.976302i	$0.430565\pi$
$942$	303.696	−	154.741i	0.322395	−	0.164269i
$943$	831.666	−	831.666i	0.881936	−	0.881936i
$944$	32.8300	+	10.6671i	0.0347776	+	0.0112999i
$945$	30.1958	+	199.147i	0.0319533	+	0.210738i
$946$	−1.61178	−	4.96054i	−0.00170378	−	0.00524370i
$947$	142.677	−	280.019i	0.150662	−	0.295691i	−0.803324	−	0.595542i	$-0.796937\pi$
$947$	142.677	−	280.019i	0.150662	−	0.295691i	0.953986	+	0.299852i	$0.0969372\pi$
$948$	146.381	−	23.1844i	0.154410	−	0.0244561i
$949$		−	168.929i		−	0.178008i
$950$	948.736	+	163.130i	0.998670	+	0.171716i
$951$	725.424			0.762801
$952$	106.556	+	672.770i	0.111929	+	0.706691i
$953$	−532.513	−	271.329i	−0.558776	−	0.284711i	0.151706	−	0.988426i	$-0.451523\pi$
$953$	−532.513	−	271.329i	−0.558776	−	0.284711i	−0.710482	+	0.703715i	$0.751523\pi$
$954$	25.4768	−	8.27790i	0.0267052	−	0.00867704i
$955$	62.1390	−	376.242i	0.0650670	−	0.393970i
$956$	−30.3197	+	93.3144i	−0.0317151	+	0.0976092i
$957$	−930.516	−	930.516i	−0.972326	−	0.972326i
$958$	578.169	+	1134.72i	0.603517	+	1.18447i
$959$	−591.204	−	813.723i	−0.616480	−	0.848512i
$960$	21.8437	−	65.7484i	0.0227539	−	0.0684879i
$961$	774.114	+	562.427i	0.805530	+	0.585252i
$962$	531.339	+	84.1559i	0.552328	+	0.0874801i
$963$	−13.4767	+	85.0885i	−0.0139945	+	0.0883577i
$964$	−270.424	+	372.207i	−0.280523	+	0.386107i
$965$	−0.810392	+	122.785i	−0.000839784	+	0.127238i
$966$	476.031	−	345.857i	0.492786	−	0.358030i
$967$	−704.778	+	359.102i	−0.728829	+	0.371357i	−0.778698	−	0.627399i	$-0.784120\pi$
$967$	−704.778	+	359.102i	−0.728829	+	0.371357i	0.0498689	+	0.998756i	$0.484120\pi$
$968$	145.576	−	145.576i	0.150388	−	0.150388i
$969$	−1393.25	−	452.694i	−1.43782	−	0.467176i
$970$	338.026	−	169.432i	0.348480	−	0.174672i
$971$	514.883	+	1584.65i	0.530261	+	1.63197i	0.753673	+	0.657250i	$0.228280\pi$
$971$	514.883	+	1584.65i	0.530261	+	1.63197i	−0.223412	+	0.974724i	$0.571720\pi$
$972$	−14.1540	+	27.7788i	−0.0145618	+	0.0285790i
$973$	−996.798	+	157.877i	−1.02446	+	0.162258i
$974$			300.388i			0.308407i
$975$	420.938	+	314.402i	0.431732	+	0.322463i
$976$	433.250			0.443903
$977$	284.049	+	1793.42i	0.290736	+	1.83563i	0.510251	+	0.860026i	$0.329553\pi$
$977$	284.049	+	1793.42i	0.290736	+	1.83563i	−0.219515	+	0.975609i	$0.570447\pi$
$978$	−114.668	−	58.4261i	−0.117247	−	0.0597403i
$979$	−1784.71	+	579.888i	−1.82299	+	0.592326i
$980$	−98.6169	−	51.0704i	−0.100629	−	0.0521127i
$981$	−100.356	+	308.865i	−0.102300	+	0.314847i
$982$	507.023	+	507.023i	0.516317	+	0.516317i
$983$	737.472	+	1447.37i	0.750226	+	1.47240i	0.877011	+	0.480471i	$0.159534\pi$
$983$	737.472	+	1447.37i	0.750226	+	1.47240i	−0.126785	+	0.991930i	$0.540466\pi$
$984$	−109.306	−	150.447i	−0.111083	−	0.152893i
$985$	226.448	+	712.911i	0.229896	+	0.723768i
$986$	−1939.69	−	1409.27i	−1.96723	−	1.42928i
$987$	776.266	+	122.948i	0.786490	+	0.124568i
$988$	−103.363	+	652.606i	−0.104618	+	0.660532i
$989$	−4.82511	+	6.64120i	−0.00487878	+	0.00671507i
$990$	175.148	−	237.755i	0.176918	−	0.240157i
$991$	−949.851	+	690.107i	−0.958477	+	0.696374i	−0.952797	−	0.303609i	$-0.901808\pi$
$991$	−949.851	+	690.107i	−0.958477	+	0.696374i	−0.00568067	+	0.999984i	$0.501808\pi$
$992$	−10.2580	+	5.22672i	−0.0103407	+	0.00526887i
$993$	−187.679	+	187.679i	−0.189002	+	0.189002i
$994$	1329.65	+	432.030i	1.33768	+	0.434638i
$995$	364.012	+	368.849i	0.365842	+	0.370703i
$996$	−43.3971	−	133.563i	−0.0435714	−	0.134099i
$997$	−679.196	+	1333.00i	−0.681240	+	1.33701i	0.248443	+	0.968646i	$0.420081\pi$
$997$	−679.196	+	1333.00i	−0.681240	+	1.33701i	−0.929683	+	0.368361i	$0.879919\pi$
$998$	−70.5525	+	11.1744i	−0.0706939	+	0.0111968i
$999$		−	162.905i		−	0.163068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.k.a.37.2	✓	32
25.23	odd	20	inner	150.3.k.a.73.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.k.a.37.2	✓	32	1.1	even	1	trivial
150.3.k.a.73.2	yes	32	25.23	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(3.55879 - 3.51212i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-5.48204 - 5.48204i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})\)	\(q+(0.221232 + 1.39680i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(3.55879 - 3.51212i) q^{5} +(0.756934 - 2.32960i) q^{6} +(-5.48204 - 5.48204i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +(5.69306 + 4.19393i) q^{10} +(-11.2621 - 8.18242i) q^{11} +(3.42145 + 0.541905i) q^{12} +(1.89809 - 11.9840i) q^{13} +(6.44453 - 8.87013i) q^{14} +(-8.25387 + 2.62175i) q^{15} +(3.23607 - 2.35114i) q^{16} +(27.6774 - 14.1023i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(25.8955 + 8.41395i) q^{19} +(-4.59861 + 8.87991i) q^{20} +(4.14955 + 12.7710i) q^{21} +(8.93768 - 17.5412i) q^{22} +(-30.6030 + 4.84704i) q^{23} +4.89898i q^{24} +(0.329991 - 24.9978i) q^{25} +17.1593 q^{26} +(-0.812857 - 5.13218i) q^{27} +(13.8156 + 7.03938i) q^{28} +(-51.9065 + 16.8654i) q^{29} +(-5.48808 - 10.9490i) q^{30} +(-0.628911 + 1.93559i) q^{31} +(4.00000 + 4.00000i) q^{32} +(10.9464 + 21.4835i) q^{33} +(25.8213 + 35.5400i) q^{34} +(-38.7631 - 0.255840i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(30.9652 + 4.90440i) q^{37} +(-6.02372 + 38.0323i) q^{38} +(-12.3527 + 17.0021i) q^{39} +(-13.4208 - 4.45883i) q^{40} +(-30.7098 + 22.3120i) q^{41} +(-16.9205 + 8.62144i) q^{42} +(0.187340 - 0.187340i) q^{43} +(26.4789 + 8.60351i) q^{44} +(14.7995 + 2.44425i) q^{45} +(-13.5407 - 41.6740i) q^{46} +(26.5717 - 52.1499i) q^{47} +(-6.84291 + 1.08381i) q^{48} +11.1056i q^{49} +(34.9900 - 5.06938i) q^{50} -53.8028 q^{51} +(3.79617 + 23.9681i) q^{52} +(-5.62578 - 2.86648i) q^{53} +(6.98881 - 2.27080i) q^{54} +(-68.8173 + 10.4345i) q^{55} +(-6.77618 + 20.8549i) q^{56} +(-33.3475 - 33.3475i) q^{57} +(-35.0410 - 68.7719i) q^{58} +(5.07252 + 6.98172i) q^{59} +(14.0795 - 10.0880i) q^{60} +(87.6266 + 63.6644i) q^{61} +(-2.84277 - 0.450251i) q^{62} +(3.63841 - 22.9720i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-35.3345 - 49.3150i) q^{65} +(-27.5865 + 20.0428i) q^{66} +(7.98376 - 4.06793i) q^{67} +(-43.9298 + 43.9298i) q^{68} +(51.0401 + 16.5839i) q^{69} +(-8.21826 - 54.2009i) q^{70} +(39.4041 + 121.273i) q^{71} +(3.85224 - 7.56044i) q^{72} +(13.7512 - 2.17798i) q^{73} +44.3372i q^{74} +(-20.1659 + 38.3189i) q^{75} -54.4562 q^{76} +(16.8831 + 106.596i) q^{77} +(-26.4813 - 13.4929i) q^{78} +(40.6892 - 13.2207i) q^{79} +(3.25900 - 19.7327i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-37.9594 - 37.9594i) q^{82} +(-18.4050 - 36.1218i) q^{83} +(-15.7858 - 21.7273i) q^{84} +(48.9689 - 147.394i) q^{85} +(0.303122 + 0.220231i) q^{86} +(93.3675 + 14.7880i) q^{87} +(-6.15943 + 38.8891i) q^{88} +(79.2350 - 109.058i) q^{89} +(-0.140006 + 21.2127i) q^{90} +(-76.1025 + 55.2917i) q^{91} +(55.2148 - 28.1333i) q^{92} +(2.49260 - 2.49260i) q^{93} +(78.7215 + 25.5782i) q^{94} +(121.707 - 61.0046i) q^{95} +(-3.02774 - 9.31841i) q^{96} +(24.2763 - 47.6449i) q^{97} +(-15.5124 + 2.45692i) q^{98} -41.7623i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 + 8 * q^7 - 16 * q^8	\( 32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} + 20 q^{10} + 32 q^{11} - 16 q^{13} - 60 q^{14} + 32 q^{16} + 148 q^{17} - 96 q^{18} + 180 q^{19} + 40 q^{20} - 36 q^{21} + 48 q^{22} + 48 q^{23} - 160 q^{25} - 8 q^{26} - 56 q^{28} - 200 q^{29} - 120 q^{30} + 120 q^{31} + 128 q^{32} - 156 q^{33} - 100 q^{34} - 180 q^{35} - 48 q^{36} + 444 q^{37} + 32 q^{38} - 120 q^{39} - 304 q^{41} - 24 q^{42} + 216 q^{43} + 40 q^{44} + 60 q^{45} - 16 q^{46} + 32 q^{47} + 40 q^{50} + 24 q^{51} - 32 q^{52} - 340 q^{53} + 80 q^{55} + 72 q^{56} - 24 q^{57} - 192 q^{58} - 560 q^{59} + 312 q^{61} + 40 q^{62} + 24 q^{63} - 520 q^{65} - 108 q^{66} + 688 q^{67} - 16 q^{68} + 180 q^{69} + 80 q^{70} + 212 q^{71} + 48 q^{72} - 376 q^{73} + 120 q^{75} - 64 q^{76} - 176 q^{77} - 48 q^{78} + 440 q^{79} + 80 q^{80} + 72 q^{81} - 256 q^{82} - 96 q^{83} - 240 q^{85} + 408 q^{86} + 264 q^{87} + 184 q^{88} - 560 q^{89} - 516 q^{91} + 216 q^{92} + 48 q^{93} + 80 q^{94} + 520 q^{95} - 716 q^{97} - 108 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 + 8 * q^7 - 16 * q^8 + 20 * q^10 + 32 * q^11 - 16 * q^13 - 60 * q^14 + 32 * q^16 + 148 * q^17 - 96 * q^18 + 180 * q^19 + 40 * q^20 - 36 * q^21 + 48 * q^22 + 48 * q^23 - 160 * q^25 - 8 * q^26 - 56 * q^28 - 200 * q^29 - 120 * q^30 + 120 * q^31 + 128 * q^32 - 156 * q^33 - 100 * q^34 - 180 * q^35 - 48 * q^36 + 444 * q^37 + 32 * q^38 - 120 * q^39 - 304 * q^41 - 24 * q^42 + 216 * q^43 + 40 * q^44 + 60 * q^45 - 16 * q^46 + 32 * q^47 + 40 * q^50 + 24 * q^51 - 32 * q^52 - 340 * q^53 + 80 * q^55 + 72 * q^56 - 24 * q^57 - 192 * q^58 - 560 * q^59 + 312 * q^61 + 40 * q^62 + 24 * q^63 - 520 * q^65 - 108 * q^66 + 688 * q^67 - 16 * q^68 + 180 * q^69 + 80 * q^70 + 212 * q^71 + 48 * q^72 - 376 * q^73 + 120 * q^75 - 64 * q^76 - 176 * q^77 - 48 * q^78 + 440 * q^79 + 80 * q^80 + 72 * q^81 - 256 * q^82 - 96 * q^83 - 240 * q^85 + 408 * q^86 + 264 * q^87 + 184 * q^88 - 560 * q^89 - 516 * q^91 + 216 * q^92 + 48 * q^93 + 80 * q^94 + 520 * q^95 - 716 * q^97 - 108 * q^98

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