LMFDB - Embedded newform 150.3.k.a.37.3

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			37.3
Character	$\chi$	$=$	150.37
Dual form			150.3.k.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(1.54327 + 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-3.00822 + 3.99382i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(4.19292 + 4.19292i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})$	\(q+(0.221232 + 1.39680i) q^{2} +(1.54327 + 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-3.00822 + 3.99382i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(4.19292 + 4.19292i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +(-6.24409 - 3.31834i) q^{10} +(-11.1250 - 8.08275i) q^{11} +(-3.42145 - 0.541905i) q^{12} +(-3.35414 + 21.1772i) q^{13} +(-4.92907 + 6.78429i) q^{14} +(-7.78298 + 3.79806i) q^{15} +(3.23607 - 2.35114i) q^{16} +(5.28415 - 2.69241i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(14.5420 + 4.72499i) q^{19} +(3.25367 - 9.45588i) q^{20} +(3.17376 + 9.76784i) q^{21} +(8.82881 - 17.3275i) q^{22} +(0.809542 - 0.128219i) q^{23} -4.89898i q^{24} +(-6.90117 - 24.0286i) q^{25} -30.3224 q^{26} +(0.812857 + 5.13218i) q^{27} +(-10.5668 - 5.38404i) q^{28} +(19.8685 - 6.45568i) q^{29} +(-7.02698 - 10.0310i) q^{30} +(-5.92541 + 18.2365i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-10.8130 - 21.2218i) q^{33} +(4.92978 + 6.78527i) q^{34} +(-29.3590 + 4.13252i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(67.7814 + 10.7355i) q^{37} +(-3.38272 + 21.3577i) q^{38} +(-21.8287 + 30.0446i) q^{39} +(13.9278 + 2.45279i) q^{40} +(-15.9869 + 11.6152i) q^{41} +(-12.9416 + 6.59407i) q^{42} +(51.6054 - 51.6054i) q^{43} +(26.1563 + 8.49871i) q^{44} +(-14.9978 - 0.258591i) q^{45} +(0.358193 + 1.10240i) q^{46} +(18.7247 - 36.7493i) q^{47} +(6.84291 - 1.08381i) q^{48} -13.8389i q^{49} +(32.0365 - 14.9555i) q^{50} +10.2720 q^{51} +(-6.70828 - 42.3544i) q^{52} +(-28.2875 - 14.4132i) q^{53} +(-6.98881 + 2.27080i) q^{54} +(65.7474 - 20.1163i) q^{55} +(5.18273 - 15.9508i) q^{56} +(18.7268 + 18.7268i) q^{57} +(13.4129 + 26.3242i) q^{58} +(50.3574 + 69.3111i) q^{59} +(12.4568 - 12.0345i) q^{60} +(24.0145 + 17.4475i) q^{61} +(-26.7837 - 4.24212i) q^{62} +(-2.78282 + 17.5700i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-74.4879 - 77.1016i) q^{65} +(27.2505 - 19.7986i) q^{66} +(70.2007 - 35.7691i) q^{67} +(-8.38705 + 8.38705i) q^{68} +(1.35016 + 0.438695i) q^{69} +(-12.2674 - 40.0945i) q^{70} +(13.1111 + 40.3518i) q^{71} +(3.85224 - 7.56044i) q^{72} +(-140.743 + 22.2915i) q^{73} +97.0522i q^{74} +(8.24416 - 42.5092i) q^{75} -30.5808 q^{76} +(-12.7557 - 80.5364i) q^{77} +(-46.7956 - 23.8436i) q^{78} +(-13.9674 + 4.53827i) q^{79} +(-0.344789 + 19.9970i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-19.7609 - 19.7609i) q^{82} +(-7.45144 - 14.6243i) q^{83} +(-12.0737 - 16.6180i) q^{84} +(-5.14292 + 29.2033i) q^{85} +(83.4992 + 60.6657i) q^{86} +(35.7388 + 5.66047i) q^{87} +(-6.08440 + 38.4154i) q^{88} +(-11.4146 + 15.7108i) q^{89} +(-2.95678 - 21.0061i) q^{90} +(-102.858 + 74.7307i) q^{91} +(-1.46060 + 0.744211i) q^{92} +(-23.4845 + 23.4845i) q^{93} +(55.4739 + 18.0246i) q^{94} +(-62.6165 + 43.8644i) q^{95} +(3.02774 + 9.31841i) q^{96} +(-28.0614 + 55.0736i) q^{97} +(19.3302 - 3.06160i) q^{98} -41.2536i 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
$5$	−3.00822	+	3.99382i	−0.601645	+	0.798764i
$5$	−3.00822	+	3.99382i	−0.601645	+	0.798764i
$6$	−0.756934	+	2.32960i	−0.126156	+	0.388267i
$7$	4.19292	+	4.19292i	0.598988	+	0.598988i	0.940043	−	0.341055i	$-0.110784\pi$
$7$	4.19292	+	4.19292i	0.598988	+	0.598988i	−0.341055	+	0.940043i	$0.610784\pi$
$8$	−1.28408	−	2.52015i	−0.160510	−	0.315018i
$9$	1.76336	+	2.42705i	0.195928	+	0.269672i
$10$	−6.24409	−	3.31834i	−0.624409	−	0.331834i
$11$	−11.1250	−	8.08275i	−1.01136	−	0.734796i	−0.0468658	−	0.998901i	$-0.514923\pi$
$11$	−11.1250	−	8.08275i	−1.01136	−	0.734796i	−0.964494	+	0.264105i	$0.914923\pi$
$12$	−3.42145	−	0.541905i	−0.285121	−	0.0451587i
$13$	−3.35414	+	21.1772i	−0.258011	+	1.62902i	0.429658	+	0.902992i	$0.358634\pi$
$13$	−3.35414	+	21.1772i	−0.258011	+	1.62902i	−0.687669	+	0.726024i	$0.741366\pi$
$14$	−4.92907	+	6.78429i	−0.352077	+	0.484592i
$15$	−7.78298	+	3.79806i	−0.518865	+	0.253204i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	5.28415	−	2.69241i	0.310832	−	0.158377i	−0.291615	−	0.956536i	$-0.594192\pi$
$17$	5.28415	−	2.69241i	0.310832	−	0.158377i	0.602447	+	0.798159i	$0.294192\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	14.5420	+	4.72499i	0.765370	+	0.248684i	0.665582	−	0.746325i	$-0.268183\pi$
$19$	14.5420	+	4.72499i	0.765370	+	0.248684i	0.0997883	+	0.995009i	$0.468183\pi$
$20$	3.25367	−	9.45588i	0.162683	−	0.472794i
$21$	3.17376	+	9.76784i	0.151132	+	0.465135i
$22$	8.82881	−	17.3275i	0.401310	−	0.787615i
$23$	0.809542	−	0.128219i	0.0351975	−	0.00557473i	−0.138811	−	0.990319i	$-0.544328\pi$
$23$	0.809542	−	0.128219i	0.0351975	−	0.00557473i	0.174008	+	0.984744i	$0.444328\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−6.90117	−	24.0286i	−0.276047	−	0.961144i
$26$	−30.3224			−1.16625
$27$	0.812857	+	5.13218i	0.0301058	+	0.190081i
$28$	−10.5668	−	5.38404i	−0.377385	−	0.192287i
$29$	19.8685	−	6.45568i	0.685122	−	0.222610i	0.0542854	−	0.998525i	$-0.482712\pi$
$29$	19.8685	−	6.45568i	0.685122	−	0.222610i	0.630836	+	0.775916i	$0.282712\pi$
$30$	−7.02698	−	10.0310i	−0.234233	−	0.334368i
$31$	−5.92541	+	18.2365i	−0.191142	+	0.588275i	0.808858	+	0.588004i	$0.200086\pi$
$31$	−5.92541	+	18.2365i	−0.191142	+	0.588275i	−1.00000		0.000270739i	$0.999914\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−10.8130	−	21.2218i	−0.327668	−	0.643085i
$34$	4.92978	+	6.78527i	0.144994	+	0.199567i
$35$	−29.3590	+	4.13252i	−0.838829	+	0.118072i
$36$	−4.85410	−	3.52671i	−0.134836	−	0.0979642i
$37$	67.7814	+	10.7355i	1.83193	+	0.290149i	0.974489	−	0.224434i	$-0.0720534\pi$
$37$	67.7814	+	10.7355i	1.83193	+	0.290149i	0.857440	+	0.514583i	$0.172053\pi$
$38$	−3.38272	+	21.3577i	−0.0890190	+	0.562044i
$39$	−21.8287	+	30.0446i	−0.559710	+	0.770375i
$40$	13.9278	+	2.45279i	0.348195	+	0.0613197i
$41$	−15.9869	+	11.6152i	−0.389925	+	0.283297i	−0.765425	−	0.643526i	$-0.777471\pi$
$41$	−15.9869	+	11.6152i	−0.389925	+	0.283297i	0.375500	+	0.926822i	$0.377471\pi$
$42$	−12.9416	+	6.59407i	−0.308133	+	0.157002i
$43$	51.6054	−	51.6054i	1.20012	−	1.20012i	0.225996	−	0.974128i	$-0.427436\pi$
$43$	51.6054	−	51.6054i	1.20012	−	1.20012i	0.974128	−	0.225996i	$-0.0725637\pi$
$44$	26.1563	+	8.49871i	0.594462	+	0.193153i
$45$	−14.9978	−	0.258591i	−0.333284	−	0.00574648i
$46$	0.358193	+	1.10240i	0.00778680	+	0.0239653i
$47$	18.7247	−	36.7493i	0.398397	−	0.781899i	−0.601458	−	0.798904i	$-0.705413\pi$
$47$	18.7247	−	36.7493i	0.398397	−	0.781899i	0.999855	+	0.0170055i	$0.00541327\pi$
$48$	6.84291	−	1.08381i	0.142561	−	0.0225794i
$49$		−	13.8389i		−	0.282426i
$50$	32.0365	−	14.9555i	0.640729	−	0.299109i
$51$	10.2720			0.201412
$52$	−6.70828	−	42.3544i	−0.129005	−	0.814508i
$53$	−28.2875	−	14.4132i	−0.533726	−	0.271947i	0.166287	−	0.986077i	$-0.446822\pi$
$53$	−28.2875	−	14.4132i	−0.533726	−	0.271947i	−0.700013	+	0.714130i	$0.746822\pi$
$54$	−6.98881	+	2.27080i	−0.129422	+	0.0420519i
$55$	65.7474	−	20.1163i	1.19541	−	0.365751i
$56$	5.18273	−	15.9508i	0.0925488	−	0.284836i
$57$	18.7268	+	18.7268i	0.328541	+	0.328541i
$58$	13.4129	+	26.3242i	0.231256	+	0.453866i
$59$	50.3574	+	69.3111i	0.853516	+	1.17476i	0.983077	+	0.183192i	$0.0586431\pi$
$59$	50.3574	+	69.3111i	0.853516	+	1.17476i	−0.129561	+	0.991571i	$0.541357\pi$
$60$	12.4568	−	12.0345i	0.207613	−	0.200575i
$61$	24.0145	+	17.4475i	0.393680	+	0.286025i	0.766962	−	0.641693i	$-0.221768\pi$
$61$	24.0145	+	17.4475i	0.393680	+	0.286025i	−0.373282	+	0.927718i	$0.621768\pi$
$62$	−26.7837	−	4.24212i	−0.431995	−	0.0684213i
$63$	−2.78282	+	17.5700i	−0.0441717	+	0.278889i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	−74.4879	−	77.1016i	−1.14597	−	1.18618i
$66$	27.2505	−	19.7986i	0.412886	−	0.299979i
$67$	70.2007	−	35.7691i	1.04777	−	0.533867i	0.156661	−	0.987652i	$-0.449927\pi$
$67$	70.2007	−	35.7691i	1.04777	−	0.533867i	0.891111	+	0.453786i	$0.149927\pi$
$68$	−8.38705	+	8.38705i	−0.123339	+	0.123339i
$69$	1.35016	+	0.438695i	0.0195676	+	0.00635790i
$70$	−12.2674	−	40.0945i	−0.175249	−	0.572778i
$71$	13.1111	+	40.3518i	0.184663	+	0.568335i	0.999942	−	0.0107334i	$-0.00341661\pi$
$71$	13.1111	+	40.3518i	0.184663	+	0.568335i	−0.815279	+	0.579068i	$0.803417\pi$
$72$	3.85224	−	7.56044i	0.0535033	−	0.105006i
$73$	−140.743	+	22.2915i	−1.92798	+	0.305363i	−0.998053	−	0.0623709i	$-0.980134\pi$
$73$	−140.743	+	22.2915i	−1.92798	+	0.305363i	−0.929931	+	0.367734i	$0.880134\pi$
$74$			97.0522i			1.31152i
$75$	8.24416	−	42.5092i	0.109922	−	0.566790i
$76$	−30.5808			−0.402379
$77$	−12.7557	−	80.5364i	−0.165659	−	1.04593i
$78$	−46.7956	−	23.8436i	−0.599944	−	0.305687i
$79$	−13.9674	+	4.53827i	−0.176802	+	0.0574465i	−0.396080	−	0.918216i	$-0.629630\pi$
$79$	−13.9674	+	4.53827i	−0.176802	+	0.0574465i	0.219278	+	0.975662i	$0.429630\pi$
$80$	−0.344789	+	19.9970i	−0.00430986	+	0.249963i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−19.7609	−	19.7609i	−0.240987	−	0.240987i
$83$	−7.45144	−	14.6243i	−0.0897764	−	0.176196i	0.841752	−	0.539864i	$-0.181524\pi$
$83$	−7.45144	−	14.6243i	−0.0897764	−	0.176196i	−0.931529	+	0.363668i	$0.881524\pi$
$84$	−12.0737	−	16.6180i	−0.143735	−	0.197834i
$85$	−5.14292	+	29.2033i	−0.0605049	+	0.343568i
$86$	83.4992	+	60.6657i	0.970921	+	0.705415i
$87$	35.7388	+	5.66047i	0.410791	+	0.0650629i
$88$	−6.08440	+	38.4154i	−0.0691410	+	0.436539i
$89$	−11.4146	+	15.7108i	−0.128254	+	0.176526i	−0.868315	−	0.496014i	$-0.834797\pi$
$89$	−11.4146	+	15.7108i	−0.128254	+	0.176526i	0.740061	+	0.672540i	$0.234797\pi$
$90$	−2.95678	−	21.0061i	−0.0328531	−	0.233401i
$91$	−102.858	+	74.7307i	−1.13031	+	0.821216i
$92$	−1.46060	+	0.744211i	−0.0158761	+	0.00808925i
$93$	−23.4845	+	23.4845i	−0.252522	+	0.252522i
$94$	55.4739	+	18.0246i	0.590148	+	0.191751i
$95$	−62.6165	+	43.8644i	−0.659121	+	0.461731i
$96$	3.02774	+	9.31841i	0.0315389	+	0.0970668i
$97$	−28.0614	+	55.0736i	−0.289293	+	0.567769i	−0.989219	−	0.146446i	$-0.953216\pi$
$97$	−28.0614	+	55.0736i	−0.289293	+	0.567769i	0.699926	+	0.714216i	$0.253216\pi$
$98$	19.3302	−	3.06160i	0.197246	−	0.0312408i
$99$		−	41.2536i		−	0.416703i
$100$	27.9773	+	41.4400i	0.279773	+	0.414400i
$101$	−134.598			−1.33265			−0.666327	−	0.745660i	$-0.732134\pi$
$101$	−134.598			−1.33265			−0.666327	+	0.745660i	$0.732134\pi$
$102$	2.27249	+	14.3479i	0.0222793	+	0.140666i
$103$	−81.4074	−	41.4791i	−0.790363	−	0.402710i	0.0117137	−	0.999931i	$-0.496271\pi$
$103$	−81.4074	−	41.4791i	−0.790363	−	0.402710i	−0.802076	+	0.597221i	$0.796271\pi$
$104$	57.6767	−	18.7403i	0.554583	−	0.180195i
$105$	−48.5584	−	16.7084i	−0.462461	−	0.159128i
$106$	13.8743	−	42.7007i	0.130890	−	0.402837i
$107$	59.7592	+	59.7592i	0.558497	+	0.558497i	0.928879	−	0.370382i	$-0.120773\pi$
$107$	59.7592	+	59.7592i	0.558497	+	0.558497i	−0.370382	+	0.928879i	$0.620773\pi$
$108$	−4.71801	−	9.25961i	−0.0436853	−	0.0857371i
$109$	−113.862	−	156.717i	−1.04460	−	1.43777i	−0.893395	−	0.449271i	$-0.851684\pi$
$109$	−113.862	−	156.717i	−1.04460	−	1.43777i	−0.151208	−	0.988502i	$-0.548316\pi$
$110$	42.6439	+	87.3858i	0.387672	+	0.794416i
$111$	96.1632	+	69.8666i	0.866335	+	0.629429i
$112$	23.4267	+	3.71043i	0.209167	+	0.0331288i
$113$	28.5817	−	180.458i	0.252935	−	1.59697i	−0.454866	−	0.890560i	$-0.650313\pi$
$113$	28.5817	−	180.458i	0.252935	−	1.59697i	0.707801	−	0.706411i	$-0.249687\pi$
$114$	−22.0147	+	30.3007i	−0.193112	+	0.265795i
$115$	−1.92320	+	3.61888i	−0.0167235	+	0.0314685i
$116$	−33.8024	+	24.5589i	−0.291400	+	0.211714i
$117$	−57.3127	+	29.2023i	−0.489852	+	0.249592i
$118$	−85.6732	+	85.6732i	−0.726044	+	0.726044i
$119$	33.4451	+	10.8670i	0.281051	+	0.0913190i
$120$	19.5656	+	14.7372i	0.163047	+	0.122810i
$121$	21.0427	+	64.7627i	0.173906	+	0.535229i
$122$	−19.0580	+	37.4034i	−0.156213	+	0.306585i
$123$	−33.8055	+	5.35427i	−0.274842	+	0.0435306i
$124$		−	38.3500i		−	0.309274i
$125$	116.726	+	44.7214i	0.933809	+	0.357771i
$126$	−25.1575			−0.199663
$127$	0.759645	+	4.79621i	0.00598146	+	0.0377655i	0.990499	−	0.137523i	$-0.0439141\pi$
$127$	0.759645	+	4.79621i	0.00598146	+	0.0377655i	−0.984517	+	0.175289i	$0.943914\pi$
$128$	−10.0806	−	5.13632i	−0.0787546	−	0.0401275i
$129$	120.220	−	39.0618i	0.931938	−	0.302805i
$130$	91.2166	−	121.102i	0.701666	−	0.931555i
$131$	−36.3190	+	111.778i	−0.277244	+	0.853270i	0.711373	+	0.702815i	$0.248074\pi$
$131$	−36.3190	+	111.778i	−0.277244	+	0.853270i	−0.988617	+	0.150455i	$0.951926\pi$
$132$	33.6834	+	33.6834i	0.255177	+	0.255177i
$133$	41.1621	+	80.7851i	0.309489	+	0.607407i
$134$	65.4929	+	90.1433i	0.488753	+	0.672711i
$135$	−22.9422	−	12.1923i	−0.169943	−	0.0903136i
$136$	−13.5705	−	9.85957i	−0.0997833	−	0.0724968i
$137$	−255.337	−	40.4415i	−1.86378	−	0.295193i	−0.880052	−	0.474878i	$-0.842492\pi$
$137$	−255.337	−	40.4415i	−1.86378	−	0.295193i	−0.983724	+	0.179685i	$0.942492\pi$
$138$	−0.314071	+	1.98297i	−0.00227588	+	0.0143693i
$139$	−57.8735	+	79.6560i	−0.416356	+	0.573065i	−0.964754	−	0.263153i	$-0.915238\pi$
$139$	−57.8735	+	79.6560i	−0.416356	+	0.573065i	0.548398	+	0.836217i	$0.315238\pi$
$140$	53.2901	−	26.0054i	0.380644	−	0.185753i
$141$	57.7944	−	41.9901i	0.409889	−	0.297802i
$142$	−53.4628	+	27.2407i	−0.376499	+	0.191836i
$143$	208.485	−	208.485i	1.45794	−	1.45794i
$144$	11.4127	+	3.70820i	0.0792547	+	0.0257514i
$145$	−33.9862	+	98.7714i	−0.234388	+	0.681182i
$146$	−62.2736	−	191.658i	−0.426531	−	1.31273i
$147$	10.8820	−	21.3571i	0.0740271	−	0.145286i
$148$	−135.563	+	21.4710i	−0.915965	+	0.145075i
$149$		−	49.9826i		−	0.335454i	−0.985833	−	0.167727i	$-0.946357\pi$
$149$		−	49.9826i		−	0.335454i	0.985833	−	0.167727i	$-0.0536427\pi$
$150$	61.2008	+	2.11108i	0.408006	+	0.0140738i
$151$	69.8475			0.462566			0.231283	−	0.972886i	$-0.425708\pi$
$151$	69.8475			0.462566			0.231283	+	0.972886i	$0.425708\pi$
$152$	−6.76544	−	42.7153i	−0.0445095	−	0.281022i
$153$	15.8524	+	8.07723i	0.103611	+	0.0527923i
$154$	109.671	−	35.6344i	0.712152	−	0.231392i
$155$	−55.0084	−	78.5246i	−0.354893	−	0.506610i
$156$	22.9521	−	70.6392i	0.147129	−	0.452815i
$157$	156.823	+	156.823i	0.998873	+	0.998873i	0.999999	−	0.00112611i	$-0.000358453\pi$
$157$	156.823	+	156.823i	0.998873	+	0.998873i	−0.00112611	+	0.999999i	$0.500358\pi$
$158$	−9.42910	−	18.5056i	−0.0596778	−	0.117124i
$159$	−32.3216	−	44.4869i	−0.203280	−	0.279792i
$160$	−28.0082	+	3.94238i	−0.175051	+	0.0246398i
$161$	3.93196	+	2.85673i	0.0244221	+	0.0177437i
$162$	−12.5712	−	1.99109i	−0.0776001	−	0.0122907i
$163$	−33.7265	+	212.941i	−0.206911	+	1.30639i	0.637400	+	0.770533i	$0.280010\pi$
$163$	−33.7265	+	212.941i	−0.206911	+	1.30639i	−0.844311	+	0.535853i	$0.819990\pi$
$164$	23.2303	−	31.9738i	0.141648	−	0.194962i
$165$	117.284	+	20.6546i	0.710813	+	0.125179i
$166$	18.7787	−	13.6435i	0.113125	−	0.0821901i
$167$	244.858	−	124.761i	1.46621	−	0.747073i	0.475080	−	0.879943i	$-0.342419\pi$
$167$	244.858	−	124.761i	1.46621	−	0.747073i	0.991134	+	0.132869i	$0.0424191\pi$
$168$	20.5410	−	20.5410i	0.122268	−	0.122268i
$169$	−276.495	−	89.8387i	−1.63607	−	0.531590i
$170$	−41.9290	−	0.722940i	−0.246641	−	0.00425259i
$171$	14.1750	+	43.6261i	0.0828946	+	0.255123i
$172$	−66.2654	+	130.053i	−0.385264	+	0.756123i
$173$	57.4394	−	9.09750i	0.332019	−	0.0525867i	0.0118007	−	0.999930i	$-0.496244\pi$
$173$	57.4394	−	9.09750i	0.332019	−	0.0525867i	0.320219	+	0.947344i	$0.396244\pi$
$174$			51.1723i			0.294094i
$175$	71.8139	−	129.686i	0.410365	−	0.741063i
$176$	−55.0048			−0.312527
$177$	23.2134	+	146.563i	0.131149	+	0.828042i
$178$	−24.4702	−	12.4682i	−0.137473	−	0.0700460i
$179$	298.328	−	96.9326i	1.66664	−	0.541523i	0.684390	−	0.729116i	$-0.260069\pi$
$179$	298.328	−	96.9326i	1.66664	−	0.541523i	0.982247	+	0.187593i	$0.0600687\pi$
$180$	28.6873	−	8.77726i	0.159374	−	0.0487626i
$181$	3.19961	−	9.84739i	0.0176774	−	0.0544055i	−0.941829	−	0.336093i	$-0.890894\pi$
$181$	3.19961	−	9.84739i	0.0176774	−	0.0544055i	0.959506	+	0.281688i	$0.0908943\pi$
$182$	−127.139	−	127.139i	−0.698568	−	0.698568i
$183$	23.3412	+	45.8096i	0.127547	+	0.250326i
$184$	−1.36265	−	1.87552i	−0.00740569	−	0.0101931i
$185$	−246.777	+	238.412i	−1.33393	+	1.28871i
$186$	−37.9987	−	27.6077i	−0.204294	−	0.148428i
$187$	−80.5480	−	12.7576i	−0.430738	−	0.0682222i
$188$	−12.9042	+	81.4737i	−0.0686392	+	0.433371i
$189$	−18.1106	+	24.9271i	−0.0958231	+	0.131889i
$190$	−75.1226	−	77.7586i	−0.395382	−	0.409256i
$191$	108.229	−	78.6328i	0.566643	−	0.411690i	−0.267241	−	0.963630i	$-0.586112\pi$
$191$	108.229	−	78.6328i	0.566643	−	0.411690i	0.833884	+	0.551939i	$0.186112\pi$
$192$	−12.3461	+	6.29068i	−0.0643029	+	0.0327639i
$193$	234.128	−	234.128i	1.21310	−	1.21310i	0.243095	−	0.970003i	$-0.421837\pi$
$193$	234.128	−	234.128i	1.21310	−	1.21310i	0.970003	−	0.243095i	$-0.0781626\pi$
$194$	−83.1350	−	27.0122i	−0.428531	−	0.139238i
$195$	−54.3272	−	177.561i	−0.278601	−	0.910569i
$196$	8.55289	+	26.3231i	0.0436372	+	0.134301i
$197$	52.5918	−	103.217i	0.266964	−	0.523946i	−0.718142	−	0.695897i	$-0.755007\pi$
$197$	52.5918	−	103.217i	0.266964	−	0.523946i	0.985105	+	0.171951i	$0.0550071\pi$
$198$	57.6231	−	9.12661i	0.291026	−	0.0460940i
$199$		−	171.043i		−	0.859512i	−0.902945	−	0.429756i	$-0.858600\pi$
$199$		−	171.043i		−	0.859512i	0.902945	−	0.429756i	$-0.141400\pi$
$200$	−51.6940	+	48.2466i	−0.258470	+	0.241233i
$201$	136.465			0.678931
$202$	−29.7773	−	188.007i	−0.147413	−	0.930727i
$203$	110.375	+	56.2390i	0.543720	+	0.277039i
$204$	−19.5385	+	6.34844i	−0.0957770	+	0.0311198i
$205$	1.70333	−	98.7899i	0.00830895	−	0.481902i
$206$	39.9282	−	122.886i	0.193826	−	0.596536i
$207$	1.73870	+	1.73870i	0.00839954	+	0.00839954i
$208$	38.9364	+	76.4169i	0.187194	+	0.367389i
$209$	−123.589	−	170.105i	−0.591333	−	0.813900i
$210$	12.5957	−	71.5229i	0.0599795	−	0.340585i
$211$	−247.342	−	179.705i	−1.17224	−	0.851681i	−0.180964	−	0.983490i	$-0.557922\pi$
$211$	−247.342	−	179.705i	−1.17224	−	0.851681i	−0.991275	+	0.131809i	$0.957922\pi$
$212$	62.7138	+	9.93290i	0.295820	+	0.0468533i
$213$	−11.4961	+	72.5833i	−0.0539721	+	0.340767i
$214$	−70.2512	+	96.6924i	−0.328276	+	0.451834i
$215$	50.8619	+	361.343i	0.236567	+	1.68066i
$216$	11.8901	−	8.63864i	0.0550466	−	0.0399937i
$217$	−101.309	+	51.6195i	−0.466862	+	0.237878i
$218$	193.713	−	193.713i	0.888593	−	0.888593i
$219$	−234.733	−	76.2692i	−1.07184	−	0.348261i
$220$	−112.626	+	78.8976i	−0.511938	+	0.358626i
$221$	39.2939	+	120.934i	0.177801	+	0.547214i
$222$	−76.3155	+	149.778i	−0.343764	+	0.674674i
$223$	318.260	−	50.4074i	1.42717	−	0.226042i	0.605429	−	0.795899i	$-0.293001\pi$
$223$	318.260	−	50.4074i	1.42717	−	0.226042i	0.821744	+	0.569857i	$0.193001\pi$
$224$			33.5434i			0.149747i
$225$	46.1494	−	59.1205i	0.205109	−	0.262758i
$226$	258.387			1.14331
$227$	7.43515	+	46.9437i	0.0327540	+	0.206800i	0.998638	−	0.0521746i	$-0.0166152\pi$
$227$	7.43515	+	46.9437i	0.0327540	+	0.206800i	−0.965884	+	0.258975i	$0.916615\pi$
$228$	−47.1944	−	24.0467i	−0.206993	−	0.105468i
$229$	−18.3676	+	5.96799i	−0.0802079	+	0.0260611i	−0.348846	−	0.937180i	$-0.613426\pi$
$229$	−18.3676	+	5.96799i	−0.0802079	+	0.0260611i	0.268638	+	0.963241i	$0.413426\pi$
$230$	−5.48033	−	1.88572i	−0.0238275	−	0.00819879i
$231$	43.6431	−	134.319i	0.188931	−	0.581470i
$232$	−41.7820	−	41.7820i	−0.180095	−	0.180095i
$233$	166.634	+	327.037i	0.715165	+	1.40359i	0.906560	+	0.422078i	$0.138699\pi$
$233$	166.634	+	327.037i	0.715165	+	1.40359i	−0.191394	+	0.981513i	$0.561301\pi$
$234$	−53.4692	−	73.5940i	−0.228501	−	0.314504i
$235$	90.4418	+	185.333i	0.384859	+	0.788651i
$236$	−138.622	−	100.715i	−0.587382	−	0.426758i
$237$	−25.1240	−	3.97925i	−0.106008	−	0.0167901i
$238$	−7.77988	+	49.1203i	−0.0326886	+	0.206388i
$239$	−250.542	+	344.842i	−1.04829	+	1.44285i	−0.158014	+	0.987437i	$0.550509\pi$
$239$	−250.542	+	344.842i	−1.04829	+	1.44285i	−0.890279	+	0.455415i	$0.849491\pi$
$240$	−16.2565	+	30.5897i	−0.0677352	+	0.127457i
$241$	148.035	−	107.553i	0.614252	−	0.446280i	−0.236657	−	0.971593i	$-0.576052\pi$
$241$	148.035	−	107.553i	0.614252	−	0.446280i	0.850909	+	0.525313i	$0.176052\pi$
$242$	−85.8054	+	43.7200i	−0.354568	+	0.180661i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$	−56.4614	−	18.3454i	−0.231399	−	0.0751861i
$245$	55.2699	+	41.6304i	0.225591	+	0.169920i
$246$	−14.9577	−	46.0351i	−0.0608037	−	0.187134i
$247$	−148.838	+	292.111i	−0.602584	+	1.18264i
$248$	53.5674	−	8.48424i	0.215998	−	0.0342107i
$249$		−	28.4285i		−	0.114171i
$250$	−36.6434	+	172.937i	−0.146574	+	0.691749i
$251$	−160.530			−0.639562			−0.319781	−	0.947492i	$-0.603609\pi$
$251$	−160.530			−0.639562			−0.319781	+	0.947492i	$0.603609\pi$
$252$	−5.56564	−	35.1401i	−0.0220859	−	0.139445i
$253$	−10.0425	−	5.11690i	−0.0396936	−	0.0202249i
$254$	−6.53130	+	2.12215i	−0.0257138	+	0.00835492i
$255$	−30.9005	+	41.0245i	−0.121178	+	0.160880i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−184.669	−	184.669i	−0.718556	−	0.718556i	0.249754	−	0.968309i	$-0.419650\pi$
$257$	−184.669	−	184.669i	−0.718556	−	0.718556i	−0.968309	+	0.249754i	$0.919650\pi$
$258$	81.1581	+	159.282i	0.314566	+	0.617371i
$259$	239.189	+	329.215i	0.923509	+	1.27110i
$260$	189.336	+	100.620i	0.728215	+	0.387000i
$261$	50.7035	+	36.8383i	0.194266	+	0.141143i
$262$	−164.167	−	26.0015i	−0.626592	−	0.0992425i
$263$	−31.9423	+	201.676i	−0.121454	+	0.766828i	0.849505	+	0.527581i	$0.176901\pi$
$263$	−31.9423	+	201.676i	−0.121454	+	0.766828i	−0.970959	+	0.239248i	$0.923099\pi$
$264$	−39.5972	+	54.5009i	−0.149990	+	0.206443i
$265$	142.659	−	69.6170i	0.538335	−	0.262706i
$266$	−103.734	+	75.3675i	−0.389979	+	0.283336i
$267$	−29.9698	+	15.2704i	−0.112246	+	0.0571923i
$268$	−111.423	+	111.423i	−0.415758	+	0.415758i
$269$	107.825	+	35.0345i	0.400837	+	0.130240i	0.502496	−	0.864580i	$-0.332415\pi$
$269$	107.825	+	35.0345i	0.400837	+	0.130240i	−0.101659	+	0.994819i	$0.532415\pi$
$270$	11.9547	−	34.7431i	0.0442768	−	0.128678i
$271$	−78.0535	−	240.224i	−0.288020	−	0.886435i	−0.985477	−	0.169808i	$-0.945685\pi$
$271$	−78.0535	−	240.224i	−0.288020	−	0.886435i	0.697457	−	0.716627i	$-0.254315\pi$
$272$	10.7696	−	21.1366i	0.0395942	−	0.0777081i
$273$	−217.501	+	34.4487i	−0.796706	+	0.126186i
$274$		−	365.603i		−	1.33432i
$275$	−117.442	+	323.098i	−0.427062	+	1.17490i
$276$	−2.83929			−0.0102873
$277$	8.02990	+	50.6988i	0.0289888	+	0.183028i	0.997934	−	0.0642474i	$-0.0204647\pi$
$277$	8.02990	+	50.6988i	0.0289888	+	0.183028i	−0.968945	+	0.247276i	$0.920465\pi$
$278$	−124.067	−	63.2154i	−0.446285	−	0.227393i
$279$	−54.7096	+	17.7762i	−0.196092	+	0.0637140i
$280$	48.1138	+	68.6825i	0.171835	+	0.245295i
$281$	−24.6244	+	75.7862i	−0.0876314	+	0.269702i	−0.985263	−	0.171044i	$-0.945286\pi$
$281$	−24.6244	+	75.7862i	−0.0876314	+	0.269702i	0.897632	+	0.440746i	$0.145286\pi$
$282$	71.4378	+	71.4378i	0.253326	+	0.253326i
$283$	−112.664	−	221.115i	−0.398105	−	0.781324i	0.601745	−	0.798689i	$-0.294473\pi$
$283$	−112.664	−	221.115i	−0.398105	−	0.781324i	−0.999849	+	0.0173642i	$0.994473\pi$
$284$	−49.8775	−	68.6505i	−0.175625	−	0.241727i
$285$	−131.126	+	18.4571i	−0.460092	+	0.0647616i
$286$	337.335	+	245.089i	1.17949	+	0.856953i
$287$	−115.733	−	18.3304i	−0.403252	−	0.0638688i
$288$	−2.65478	+	16.7616i	−0.00921799	+	0.0582001i
$289$	−149.197	+	205.352i	−0.516252	+	0.710560i
$290$	−145.483	−	25.6206i	−0.501665	−	0.0883470i
$291$	−86.6126	+	62.9277i	−0.297638	+	0.216246i
$292$	253.932	−	129.385i	0.869630	−	0.443099i
$293$	159.725	−	159.725i	0.545137	−	0.545137i	−0.379893	−	0.925030i	$-0.624039\pi$
$293$	159.725	−	159.725i	0.545137	−	0.545137i	0.925030	+	0.379893i	$0.124039\pi$
$294$	32.2391	+	10.4751i	0.109657	+	0.0356296i
$295$	−428.302	−	7.38478i	−1.45187	−	0.0250332i
$296$	−59.9816	−	184.604i	−0.202640	−	0.623663i
$297$	32.4391	−	63.6654i	0.109223	−	0.214362i
$298$	69.8159	−	11.0577i	0.234281	−	0.0371065i
$299$			17.5739i			0.0587756i
$300$	10.5908	+	85.9525i	0.0353027	+	0.286508i
$301$	432.754			1.43772
$302$	15.4525	+	97.5632i	0.0511672	+	0.323057i
$303$	−207.721	−	105.839i	−0.685547	−	0.349304i
$304$	58.1681	−	18.9000i	0.191343	−	0.0621710i
$305$	−141.923	+	43.4233i	−0.465322	+	0.142372i
$306$	−7.77522	+	23.9297i	−0.0254092	+	0.0782016i
$307$	60.8095	+	60.8095i	0.198077	+	0.198077i	0.799175	−	0.601098i	$-0.205270\pi$
$307$	60.8095	+	60.8095i	0.198077	+	0.198077i	−0.601098	+	0.799175i	$0.705270\pi$
$308$	74.0370	+	145.306i	0.240380	+	0.471772i
$309$	−93.0169	−	128.027i	−0.301026	−	0.414326i
$310$	97.5137	−	94.2080i	0.314560	−	0.303897i
$311$	−307.189	−	223.186i	−0.987747	−	0.717640i	−0.0283207	−	0.999599i	$-0.509016\pi$
$311$	−307.189	−	223.186i	−0.987747	−	0.717640i	−0.959427	+	0.281958i	$0.909016\pi$
$312$	103.747	+	16.4319i	0.332521	+	0.0526662i
$313$	−1.83130	+	11.5623i	−0.00585079	+	0.0369404i	−0.990441	−	0.137937i	$-0.955953\pi$
$313$	−1.83130	+	11.5623i	−0.00585079	+	0.0369404i	0.984590	+	0.174877i	$0.0559529\pi$
$314$	−184.357	+	253.745i	−0.587123	+	0.808105i
$315$	−61.8002	−	63.9687i	−0.196191	−	0.203075i
$316$	23.7627	−	17.2646i	0.0751985	−	0.0546349i
$317$	−121.465	+	61.8894i	−0.383170	+	0.195235i	−0.634956	−	0.772548i	$-0.718982\pi$
$317$	−121.465	+	61.8894i	−0.383170	+	0.195235i	0.251787	+	0.967783i	$0.418982\pi$
$318$	54.9888	−	54.9888i	0.172921	−	0.172921i
$319$	−273.216	−	88.7733i	−0.856477	−	0.278286i
$320$	−11.7030	−	38.2497i	−0.0365719	−	0.119530i
$321$	45.2338	+	139.215i	0.140915	+	0.433692i
$322$	−3.12042	+	6.12417i	−0.00969074	+	0.0190191i
$323$	89.5639	−	14.1855i	0.277288	−	0.0439180i
$324$		−	18.0000i		−	0.0555556i
$325$	532.006	−	65.5522i	1.63694	−	0.201699i
$326$	−304.898			−0.935269
$327$	−52.4871	−	331.390i	−0.160511	−	1.01343i
$328$	49.8004	+	25.3746i	0.151830	+	0.0773615i
$329$	232.598	−	75.5756i	0.706984	−	0.229713i
$330$	−2.90342	+	168.392i	−0.00879823	+	0.510279i
$331$	157.908	−	485.990i	0.477062	−	1.46825i	−0.366094	−	0.930578i	$-0.619305\pi$
$331$	157.908	−	485.990i	0.477062	−	1.46825i	0.843156	−	0.537668i	$-0.180695\pi$
$332$	23.2118	+	23.2118i	0.0699150	+	0.0699150i
$333$	93.4671	+	183.439i	0.280682	+	0.550869i
$334$	228.437	+	314.417i	0.683943	+	0.941367i
$335$	−68.3244	+	387.970i	−0.203954	+	1.15812i
$336$	33.2361	+	24.1474i	0.0989169	+	0.0718673i
$337$	98.2193	+	15.5564i	0.291452	+	0.0461615i	0.300448	−	0.953798i	$-0.402864\pi$
$337$	98.2193	+	15.5564i	0.291452	+	0.0461615i	−0.00899642	+	0.999960i	$0.502864\pi$
$338$	64.3174	−	406.084i	0.190288	−	1.20143i
$339$	186.009	−	256.020i	0.548700	−	0.755221i
$340$	−8.26623	−	58.7265i	−0.0243124	−	0.172725i
$341$	213.321	−	154.987i	0.625575	−	0.454507i
$342$	−57.8011	+	29.4511i	−0.169009	+	0.0861144i
$343$	263.478	−	263.478i	0.768158	−	0.768158i
$344$	−196.318	−	63.7877i	−0.570693	−	0.185429i
$345$	−5.81366	+	4.07262i	−0.0168512	+	0.0118047i
$346$	25.4148	+	78.2188i	0.0734532	+	0.226066i
$347$	126.633	−	248.531i	0.364936	−	0.716227i	−0.633404	−	0.773821i	$-0.718343\pi$
$347$	126.633	−	248.531i	0.364936	−	0.716227i	0.998340	+	0.0575940i	$0.0183429\pi$
$348$	−71.4776	+	11.3209i	−0.205395	+	0.0325314i
$349$		−	396.777i		−	1.13690i	−0.822718	−	0.568449i	$-0.807544\pi$
$349$		−	396.777i		−	1.13690i	0.822718	−	0.568449i	$-0.192456\pi$
$350$	197.033	+	71.6192i	0.562952	+	0.204626i
$351$	−111.412			−0.317412
$352$	−12.1688	−	76.8308i	−0.0345705	−	0.218269i
$353$	−497.366	−	253.421i	−1.40897	−	0.717905i	−0.426527	−	0.904475i	$-0.640263\pi$
$353$	−497.366	−	253.421i	−1.40897	−	0.717905i	−0.982442	+	0.186569i	$0.940263\pi$
$354$	−199.584	+	64.8489i	−0.563798	+	0.183189i
$355$	−200.599	−	69.0239i	−0.565067	−	0.194433i
$356$	12.0020	−	36.9384i	0.0337135	−	0.103760i
$357$	43.0696	+	43.0696i	0.120643	+	0.120643i
$358$	201.395	+	395.261i	0.562557	+	1.10408i
$359$	75.4495	+	103.847i	0.210166	+	0.289268i	0.901066	−	0.433682i	$-0.142786\pi$
$359$	75.4495	+	103.847i	0.210166	+	0.289268i	−0.690901	+	0.722950i	$0.742786\pi$
$360$	18.6066	+	38.1286i	0.0516851	+	0.105913i
$361$	−102.910	−	74.7685i	−0.285069	−	0.207115i
$362$	14.4627	+	2.29067i	0.0399522	+	0.00632781i
$363$	−18.4507	+	116.493i	−0.0508282	+	0.320917i
$364$	149.461	−	205.716i	0.410608	−	0.565154i
$365$	334.358	−	629.159i	0.916049	−	1.72372i
$366$	−58.8232	+	42.7375i	−0.160719	+	0.116769i
$367$	131.678	−	67.0935i	0.358797	−	0.182816i	−0.265295	−	0.964167i	$-0.585469\pi$
$367$	131.678	−	67.0935i	0.358797	−	0.182816i	0.624092	+	0.781351i	$0.285469\pi$
$368$	2.31827	−	2.31827i	0.00629965	−	0.00629965i
$369$	−56.3812	−	18.3194i	−0.152795	−	0.0496460i
$370$	−387.609	−	291.955i	−1.04759	−	0.789067i
$371$	−58.1738	−	179.040i	−0.156803	−	0.482589i
$372$	30.1560	−	59.1844i	0.0810644	−	0.159098i
$373$	−279.760	+	44.3097i	−0.750027	+	0.118793i	−0.519733	−	0.854328i	$-0.673969\pi$
$373$	−279.760	+	44.3097i	−0.750027	+	0.118793i	−0.230294	+	0.973121i	$0.573969\pi$
$374$		−	115.332i		−	0.308374i
$375$	144.974	+	160.803i	0.386597	+	0.428808i
$376$	−116.657			−0.310259
$377$	70.0714	+	442.413i	0.185866	+	1.17351i
$378$	−38.8248	−	19.7822i	−0.102711	−	0.0523339i
$379$	−380.023	+	123.477i	−1.00270	+	0.325797i	−0.763944	−	0.645282i	$-0.776740\pi$
$379$	−380.023	+	123.477i	−1.00270	+	0.325797i	−0.238756	+	0.971080i	$0.576740\pi$
$380$	91.9939	−	122.134i	0.242089	−	0.321406i
$381$	−2.59909	+	7.99918i	−0.00682176	+	0.0209952i
$382$	133.778	+	133.778i	0.350205	+	0.350205i
$383$	185.839	+	364.730i	0.485221	+	0.952299i	0.995720	+	0.0924208i	$0.0294605\pi$
$383$	185.839	+	364.730i	0.485221	+	0.952299i	−0.510500	+	0.859878i	$0.670539\pi$
$384$	−11.5182	−	15.8534i	−0.0299953	−	0.0412850i
$385$	360.020	+	191.327i	0.935116	+	0.496955i
$386$	378.827	+	275.234i	0.981416	+	0.713041i
$387$	216.247	+	34.2502i	0.558779	+	0.0885019i
$388$	19.3386	−	122.099i	0.0498418	−	0.314689i
$389$	97.2912	−	133.910i	0.250106	−	0.344241i	−0.665442	−	0.746449i	$-0.731757\pi$
$389$	97.2912	−	133.910i	0.250106	−	0.344241i	0.915548	+	0.402208i	$0.131757\pi$
$390$	235.999	−	115.166i	0.605125	−	0.295299i
$391$	3.93252	−	2.85715i	0.0100576	−	0.00730728i
$392$	−34.8760	+	17.7702i	−0.0889693	+	0.0453321i
$393$	−143.945	+	143.945i	−0.366273	+	0.366273i
$394$	155.809	+	50.6255i	0.395455	+	0.128491i
$395$	23.8919	−	69.4353i	0.0604859	−	0.175786i
$396$	25.4961	+	78.4690i	0.0643842	+	0.198154i
$397$	−176.988	+	347.358i	−0.445813	+	0.874958i	0.553305	+	0.832979i	$0.313366\pi$
$397$	−176.988	+	347.358i	−0.445813	+	0.874958i	−0.999118	+	0.0419791i	$0.986634\pi$
$398$	238.913	−	37.8401i	0.600284	−	0.0950756i
$399$			157.040i			0.393584i
$400$	−78.8273	−	61.5326i	−0.197068	−	0.153831i
$401$	270.754			0.675197			0.337598	−	0.941290i	$-0.390385\pi$
$401$	270.754			0.675197			0.337598	+	0.941290i	$0.390385\pi$
$402$	30.1904	+	190.615i	0.0751005	+	0.474166i
$403$	−366.324	−	186.651i	−0.908993	−	0.463155i
$404$	256.021	−	83.1861i	0.633714	−	0.205906i
$405$	−25.8188	−	36.8563i	−0.0637501	−	0.0910033i
$406$	−54.1363	+	166.614i	−0.133341	+	0.410380i
$407$	−667.293	−	667.293i	−1.63954	−	1.63954i
$408$	−13.1901	−	25.8869i	−0.0323286	−	0.0634484i
$409$	177.082	+	243.733i	0.432964	+	0.595924i	0.968630	−	0.248506i	$-0.0799395\pi$
$409$	177.082	+	243.733i	0.432964	+	0.595924i	−0.535666	+	0.844430i	$0.679940\pi$
$410$	138.367	−	19.4762i	0.337480	−	0.0475030i
$411$	−362.254	−	263.193i	−0.881395	−	0.640371i
$412$	180.481	+	28.5855i	0.438062	+	0.0693822i
$413$	−79.4710	+	501.760i	−0.192424	+	1.21492i
$414$	−2.04397	+	2.81328i	−0.00493713	+	0.00679537i
$415$	80.8223	+	14.2334i	0.194753	+	0.0342974i
$416$	−98.1254	+	71.2923i	−0.235878	+	0.171376i
$417$	−151.951	+	77.4227i	−0.364390	+	0.185666i
$418$	210.261	−	210.261i	0.503018	−	0.503018i
$419$	613.003	+	199.177i	1.46301	+	0.475362i	0.928989	−	0.370106i	$-0.120679\pi$
$419$	613.003	+	199.177i	1.46301	+	0.475362i	0.534025	+	0.845468i	$0.320679\pi$
$420$	102.690	+	1.77058i	0.244500	+	0.00421566i
$421$	17.1372	+	52.7428i	0.0407059	+	0.125280i	0.969344	−	0.245706i	$-0.0790198\pi$
$421$	17.1372	+	52.7428i	0.0407059	+	0.125280i	−0.928638	+	0.370986i	$0.879020\pi$
$422$	196.292	−	385.245i	0.465147	−	0.912902i
$423$	122.211	−	19.3563i	0.288914	−	0.0457595i
$424$			89.7963i			0.211784i
$425$	−101.162	−	108.390i	−0.238027	−	0.255035i
$426$	−103.928			−0.243962
$427$	27.5346	+	173.847i	0.0644839	+	0.407135i
$428$	−150.602	−	76.7356i	−0.351874	−	0.179289i
$429$	485.687	−	157.809i	1.13214	−	0.367854i
$430$	−493.472	+	150.985i	−1.14761	+	0.351127i
$431$	−212.188	+	653.048i	−0.492316	+	1.51519i	0.328781	+	0.944406i	$0.393362\pi$
$431$	−212.188	+	653.048i	−0.492316	+	1.51519i	−0.821098	+	0.570788i	$0.806638\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−84.1013	−	165.058i	−0.194229	−	0.381196i	0.773267	−	0.634080i	$-0.218621\pi$
$433$	−84.1013	−	165.058i	−0.194229	−	0.381196i	−0.967497	+	0.252884i	$0.918621\pi$
$434$	−94.5150	−	130.089i	−0.217777	−	0.299744i
$435$	−130.117	+	125.706i	−0.299120	+	0.288980i
$436$	313.435	+	227.724i	0.718887	+	0.522302i
$437$	12.3782	+	1.96052i	0.0283255	+	0.00448631i
$438$	54.6027	−	344.748i	0.124664	−	0.787096i
$439$	164.938	−	227.018i	0.375714	−	0.517126i	−0.578729	−	0.815520i	$-0.696451\pi$
$439$	164.938	−	227.018i	0.375714	−	0.517126i	0.954443	+	0.298394i	$0.0964510\pi$
$440$	−135.121	−	139.862i	−0.307093	−	0.317869i
$441$	33.5876	−	24.4028i	0.0761624	−	0.0553352i
$442$	−160.228	+	81.6403i	−0.362507	+	0.184707i
$443$	190.359	−	190.359i	0.429704	−	0.429704i	−0.458824	−	0.888527i	$-0.651729\pi$
$443$	190.359	−	190.359i	0.429704	−	0.429704i	0.888527	+	0.458824i	$0.151729\pi$
$444$	−226.093	−	73.4621i	−0.509219	−	0.165455i
$445$	−28.4086	−	92.8495i	−0.0638395	−	0.208651i
$446$	140.818	+	433.394i	0.315736	+	0.971736i
$447$	39.3031	−	77.1366i	0.0879263	−	0.172565i
$448$	−46.8534	+	7.42085i	−0.104584	+	0.0165644i
$449$		−	316.138i		−	0.704093i	−0.935982	−	0.352047i	$-0.885486\pi$
$449$		−	316.138i		−	0.704093i	0.935982	−	0.352047i	$-0.114514\pi$
$450$	92.7893	+	51.3823i	0.206199	+	0.114183i
$451$	271.736			0.602519
$452$	57.1634	+	360.916i	0.126468	+	0.798486i
$453$	107.794	+	54.9235i	0.237955	+	0.121244i
$454$	−63.9262	+	20.7709i	−0.140807	+	0.0457508i
$455$	10.9591	−	635.603i	0.0240858	−	1.39693i
$456$	23.1476	−	71.2411i	0.0507624	−	0.156231i
$457$	182.252	+	182.252i	0.398801	+	0.398801i	0.877810	−	0.479009i	$-0.159004\pi$
$457$	182.252	+	182.252i	0.398801	+	0.398801i	−0.479009	+	0.877810i	$0.659004\pi$
$458$	−12.3996	−	24.3356i	−0.0270734	−	0.0531345i
$459$	18.1132	+	24.9307i	0.0394623	+	0.0543152i
$460$	1.42156	−	8.07211i	0.00309035	−	0.0175481i
$461$	−48.1235	−	34.9638i	−0.104389	−	0.0758434i	0.534366	−	0.845253i	$-0.320550\pi$
$461$	−48.1235	−	34.9638i	−0.104389	−	0.0758434i	−0.638755	+	0.769410i	$0.720550\pi$
$462$	197.273	+	31.2450i	0.426998	+	0.0676298i
$463$	14.7800	−	93.3175i	0.0319223	−	0.201550i	−0.966573	−	0.256393i	$-0.917466\pi$
$463$	14.7800	−	93.3175i	0.0319223	−	0.201550i	0.998495	+	0.0548432i	$0.0174659\pi$
$464$	49.1177	−	67.6047i	0.105857	−	0.145700i
$465$	−23.1462	−	164.440i	−0.0497767	−	0.353633i
$466$	−419.941	+	305.105i	−0.901161	+	0.654732i
$467$	338.148	−	172.295i	0.724086	−	0.368940i	−0.0527797	−	0.998606i	$-0.516808\pi$
$467$	338.148	−	172.295i	0.724086	−	0.368940i	0.776866	+	0.629666i	$0.216808\pi$
$468$	90.9672	−	90.9672i	0.194374	−	0.194374i
$469$	444.323	+	144.369i	0.947383	+	0.307824i
$470$	−238.865	+	167.331i	−0.508223	+	0.356023i
$471$	118.705	+	365.336i	0.252027	+	0.775659i
$472$	110.011	−	215.909i	0.233074	−	0.457434i
$473$	−991.221	+	156.994i	−2.09560	+	0.331911i
$474$		−	35.9736i		−	0.0758937i
$475$	13.1779	−	382.033i	0.0277430	−	0.804279i
$476$	−70.3324			−0.147757
$477$	−14.8993	−	94.0708i	−0.0312355	−	0.197213i
$478$	−537.103	−	273.668i	−1.12365	−	0.572527i
$479$	−60.3797	+	19.6185i	−0.126054	+	0.0409573i	−0.371364	−	0.928487i	$-0.621110\pi$
$479$	−60.3797	+	19.6185i	−0.126054	+	0.0409573i	0.245311	+	0.969444i	$0.421110\pi$
$480$	−46.3242	−	15.9397i	−0.0965087	−	0.0332076i
$481$	−454.697	+	1399.41i	−0.945315	+	2.90938i
$482$	182.981	+	182.981i	0.379628	+	0.379628i
$483$	3.82172	+	7.50054i	0.00791246	+	0.0155291i
$484$	−80.0511	−	110.181i	−0.165395	−	0.227647i
$485$	−135.539	−	277.746i	−0.279462	−	0.572672i
$486$	−17.8351	−	12.9580i	−0.0366978	−	0.0266625i
$487$	−690.508	−	109.366i	−1.41788	−	0.224570i	−0.600019	−	0.799985i	$-0.704840\pi$
$487$	−690.508	−	109.366i	−1.41788	−	0.224570i	−0.817861	+	0.575415i	$0.804840\pi$
$488$	13.1339	−	82.9240i	0.0269137	−	0.169926i
$489$	−219.492	+	302.105i	−0.448859	+	0.617801i
$490$	−45.9220	+	86.4111i	−0.0937183	+	0.176349i
$491$	−287.798	+	209.097i	−0.586147	+	0.425860i	−0.840935	−	0.541136i	$-0.817994\pi$
$491$	−287.798	+	209.097i	−0.586147	+	0.425860i	0.254788	+	0.966997i	$0.417994\pi$
$492$	60.9928	−	31.0774i	0.123969	−	0.0631654i
$493$	87.6070	−	87.6070i	0.177702	−	0.177702i
$494$	−440.949	−	143.273i	−0.892610	−	0.290027i
$495$	164.759	+	124.100i	0.332847	+	0.250707i
$496$	23.7016	+	72.9461i	0.0477855	+	0.147069i
$497$	−114.218	+	224.165i	−0.229815	+	0.451037i
$498$	39.7090	−	6.28929i	0.0797370	−	0.0126291i
$499$			574.580i			1.15146i	0.817639	+	0.575731i	$0.195283\pi$
$499$			574.580i			1.15146i	−0.817639	+	0.575731i	$0.804717\pi$
$500$	−249.666	−	12.9244i	−0.499331	−	0.0258489i
$501$	475.985			0.950070
$502$	−35.5143	−	224.229i	−0.0707457	−	0.446671i
$503$	−27.0911	−	13.8036i	−0.0538590	−	0.0274425i	0.426854	−	0.904321i	$-0.359622\pi$
$503$	−27.0911	−	13.8036i	−0.0538590	−	0.0274425i	−0.480713	+	0.876878i	$0.659622\pi$
$504$	47.8524	−	15.5482i	0.0949453	−	0.0308496i
$505$	404.901	−	537.560i	0.801784	−	1.06448i
$506$	4.92558	−	15.1594i	0.00973435	−	0.0299593i
$507$	−356.063	−	356.063i	−0.702294	−	0.702294i
$508$	−4.40915	−	8.65345i	−0.00867944	−	0.0170344i
$509$	375.013	+	516.161i	0.736763	+	1.01407i	0.998798	+	0.0490095i	$0.0156065\pi$
$509$	375.013	+	516.161i	0.736763	+	1.01407i	−0.262035	+	0.965058i	$0.584394\pi$
$510$	−64.1393	−	34.0859i	−0.125763	−	0.0668352i
$511$	−683.590	−	496.657i	−1.33775	−	0.971931i
$512$	22.3488	+	3.53971i	0.0436501	+	0.00691349i
$513$	−12.4289	+	78.4731i	−0.0242279	+	0.152969i
$514$	217.091	−	298.800i	0.422357	−	0.581324i
$515$	410.552	−	200.348i	0.797188	−	0.389025i
$516$	−204.530	+	148.600i	−0.396377	+	0.287985i
$517$	−505.346	+	257.487i	−0.977459	+	0.498040i
$518$	−406.932	+	406.932i	−0.785583	+	0.785583i
$519$	95.7980	+	31.1267i	0.184582	+	0.0599743i
$520$	−98.6590	+	286.725i	−0.189729	+	0.551394i
$521$	−82.9098	−	255.170i	−0.159136	−	0.489770i	0.839421	−	0.543482i	$-0.182895\pi$
$521$	−82.9098	−	255.170i	−0.159136	−	0.489770i	−0.998556	+	0.0537126i	$0.982895\pi$
$522$	−40.2386	+	78.9726i	−0.0770854	+	0.151289i
$523$	−541.641	+	85.7876i	−1.03564	+	0.164030i	−0.651033	−	0.759049i	$-0.725664\pi$
$523$	−541.641	+	85.7876i	−1.03564	+	0.164030i	−0.384610	+	0.923079i	$0.625664\pi$
$524$		−	235.061i		−	0.448591i
$525$	212.805	−	143.671i	0.405343	−	0.273658i
$526$	−288.768			−0.548988
$527$	17.7894	+	112.318i	0.0337561	+	0.213127i
$528$	−84.8872	−	43.2522i	−0.160771	−	0.0819170i
$529$	−502.470	+	163.262i	−0.949849	+	0.308625i
$530$	128.802	+	183.865i	0.243022	+	0.346914i
$531$	−79.4234	+	244.440i	−0.149573	+	0.460339i
$532$	−128.223	−	128.223i	−0.241020	−	0.241020i
$533$	−192.355	−	377.517i	−0.360890	−	0.708287i
$534$	−27.9599	−	38.4835i	−0.0523594	−	0.0720665i
$535$	−418.437	+	58.8983i	−0.782124	+	0.110090i
$536$	−180.287	−	130.986i	−0.336356	−	0.244377i
$537$	536.622	+	84.9925i	0.999295	+	0.158273i
$538$	−25.0819	+	158.361i	−0.0466207	+	0.294351i
$539$	−111.856	+	153.957i	−0.207525	+	0.285634i
$540$	51.1740	+	9.01212i	0.0947667	+	0.0166891i
$541$	225.815	−	164.064i	0.417404	−	0.303262i	−0.359189	−	0.933265i	$-0.616947\pi$
$541$	225.815	−	164.064i	0.417404	−	0.303262i	0.776592	+	0.630003i	$0.216947\pi$
$542$	318.277	−	162.170i	0.587228	−	0.299207i
$543$	12.6812	−	12.6812i	0.0233540	−	0.0233540i
$544$	31.9062	+	10.3670i	0.0586512	+	0.0190569i
$545$	968.422	+	16.6975i	1.77692	+	0.0306377i
$546$	−96.2361	−	296.184i	−0.176257	−	0.542462i
$547$	306.313	−	601.174i	0.559988	−	1.09904i	−0.421377	−	0.906885i	$-0.638453\pi$
$547$	306.313	−	601.174i	0.559988	−	1.09904i	0.981365	−	0.192152i	$-0.0615468\pi$
$548$	510.675	−	80.8829i	0.931888	−	0.147597i
$549$			89.0505i			0.162205i
$550$	−477.285	−	92.5639i	−0.867792	−	0.168298i
$551$	319.432			0.579731
$552$	−0.628142	−	3.96593i	−0.00113794	−	0.00718466i
$553$	−77.5927	−	39.5354i	−0.140312	−	0.0714927i
$554$	−69.0398	+	22.4324i	−0.124620	+	0.0404917i
$555$	−568.315	+	173.884i	−1.02399	+	0.313304i
$556$	60.8518	−	187.282i	0.109446	−	0.336839i
$557$	601.175	+	601.175i	1.07931	+	1.07931i	0.996571	+	0.0827372i	$0.0263662\pi$
$557$	601.175	+	601.175i	1.07931	+	1.07931i	0.0827372	+	0.996571i	$0.473634\pi$
$558$	−36.9334	−	72.4858i	−0.0661888	−	0.129903i
$559$	919.766	+	1265.95i	1.64538	+	2.26467i
$560$	−85.2916	+	82.4002i	−0.152306	+	0.147143i
$561$	−114.276	−	83.0260i	−0.203700	−	0.147996i
$562$	−111.306	−	17.6291i	−0.198053	−	0.0313686i
$563$	−125.339	+	791.360i	−0.222627	+	1.40561i	0.582654	+	0.812720i	$0.302014\pi$
$563$	−125.339	+	791.360i	−0.222627	+	1.40561i	−0.805281	+	0.592893i	$0.797986\pi$
$564$	−83.9802	+	115.589i	−0.148901	+	0.204945i
$565$	634.735	+	657.008i	1.12343	+	1.16285i
$566$	283.929	−	206.286i	0.501641	−	0.364464i
$567$	−47.5505	+	24.2282i	−0.0838633	+	0.0427305i
$568$	84.8567	−	84.8567i	0.149396	−	0.149396i
$569$	−1037.82	−	337.207i	−1.82393	−	0.592631i	−0.999650	−	0.0264520i	$-0.991579\pi$
$569$	−1037.82	−	337.207i	−1.82393	−	0.592631i	−0.824282	−	0.566179i	$-0.808421\pi$
$570$	−54.7901	−	179.074i	−0.0961230	−	0.314165i
$571$	−40.5620	−	124.837i	−0.0710368	−	0.218629i	0.909235	−	0.416283i	$-0.136668\pi$
$571$	−40.5620	−	124.837i	−0.0710368	−	0.218629i	−0.980272	+	0.197655i	$0.936668\pi$
$572$	−267.711	+	525.412i	−0.468026	+	0.918553i
$573$	228.858	−	36.2475i	0.399403	−	0.0632592i
$574$		−	165.712i		−	0.288696i
$575$	−8.66771	−	18.5673i	−0.0150743	−	0.0322910i
$576$	−24.0000			−0.0416667
$577$	−131.824	−	832.307i	−0.228465	−	1.44247i	−0.789026	−	0.614359i	$-0.789415\pi$
$577$	−131.824	−	832.307i	−0.228465	−	1.44247i	0.560561	−	0.828113i	$-0.310585\pi$
$578$	−319.843	−	162.968i	−0.553361	−	0.281952i
$579$	545.425	−	177.219i	0.942012	−	0.306078i
$580$	3.60149	−	208.879i	0.00620947	−	0.360136i
$581$	30.0751	−	92.5617i	0.0517644	−	0.159315i
$582$	−107.059	−	107.059i	−0.183950	−	0.183950i
$583$	198.199	+	388.987i	0.339964	+	0.667216i
$584$	236.903	+	326.069i	0.405655	+	0.558337i
$585$	55.7809	−	316.744i	0.0953519	−	0.541442i
$586$	258.441	+	187.768i	0.441025	+	0.320424i
$587$	594.126	+	94.1003i	1.01214	+	0.160307i	0.640409	−	0.768034i	$-0.278765\pi$
$587$	594.126	+	94.1003i	1.01214	+	0.160307i	0.371730	+	0.928341i	$0.378765\pi$
$588$	−7.49935	+	47.3490i	−0.0127540	+	0.0805255i
$589$	−172.335	+	237.199i	−0.292589	+	0.402714i
$590$	−84.4390	−	599.887i	−0.143117	−	1.01676i
$591$	162.327	−	117.937i	0.274664	−	0.199555i
$592$	244.586	−	124.623i	0.413152	−	0.210511i
$593$	57.6453	−	57.6453i	0.0972096	−	0.0972096i	−0.656830	−	0.754039i	$-0.728103\pi$
$593$	57.6453	−	57.6453i	0.0972096	−	0.0972096i	0.754039	+	0.656830i	$0.228103\pi$
$594$	96.1045	+	31.2263i	0.161792	+	0.0525695i
$595$	−144.011	+	100.883i	−0.242035	+	0.169552i
$596$	30.8910	+	95.0726i	0.0518305	+	0.159518i
$597$	134.497	−	263.965i	0.225288	−	0.442152i
$598$	−24.5473	+	3.88791i	−0.0410489	+	0.00650151i
$599$			448.062i			0.748016i	0.927425	+	0.374008i	$0.122017\pi$
$599$			448.062i			0.748016i	−0.927425	+	0.374008i	$0.877983\pi$
$600$	−117.716	+	33.8087i	−0.196193	+	0.0563478i
$601$	−1086.19			−1.80731			−0.903653	−	0.428266i	$-0.859125\pi$
$601$	−1086.19			−1.80731			−0.903653	+	0.428266i	$0.859125\pi$
$602$	95.7389	+	604.472i	0.159035	+	1.00411i
$603$	210.602	+	107.307i	0.349257	+	0.177956i
$604$	−132.858	+	43.1682i	−0.219963	+	0.0714705i
$605$	−321.952	−	110.780i	−0.532151	−	0.183108i
$606$	101.882	−	313.560i	0.168122	−	0.517426i
$607$	544.057	+	544.057i	0.896304	+	0.896304i	0.995107	−	0.0988030i	$-0.0315014\pi$
$607$	544.057	+	544.057i	0.896304	+	0.896304i	−0.0988030	+	0.995107i	$0.531501\pi$
$608$	39.2682	+	77.0681i	0.0645858	+	0.126757i
$609$	126.116	+	173.584i	0.207087	+	0.285031i
$610$	−92.0517	−	188.632i	−0.150904	−	0.309233i
$611$	715.441	+	519.798i	1.17093	+	0.850734i
$612$	−35.1452	−	5.56644i	−0.0574267	−	0.00909550i
$613$	−47.3523	+	298.971i	−0.0772469	+	0.487718i	0.918487	+	0.395450i	$0.129411\pi$
$613$	−47.3523	+	298.971i	−0.0772469	+	0.487718i	−0.995734	+	0.0922674i	$0.970589\pi$
$614$	−71.4859	+	98.3918i	−0.116426	+	0.160247i
$615$	80.3106	−	151.120i	0.130586	−	0.245723i
$616$	−186.584	+	135.561i	−0.302896	+	0.220067i
$617$	537.535	−	273.888i	0.871208	−	0.443902i	0.0395671	−	0.999217i	$-0.487402\pi$
$617$	537.535	−	273.888i	0.871208	−	0.443902i	0.831640	+	0.555314i	$0.187402\pi$
$618$	158.250	−	158.250i	0.256068	−	0.256068i
$619$	−149.194	−	48.4759i	−0.241024	−	0.0783133i	0.186014	−	0.982547i	$-0.440443\pi$
$619$	−149.194	−	48.4759i	−0.241024	−	0.0783133i	−0.427038	+	0.904234i	$0.640443\pi$
$620$	153.163	+	115.366i	0.247037	+	0.186073i
$621$	1.31608	+	4.05049i	0.00211930	+	0.00652253i
$622$	243.787	−	478.459i	0.391940	−	0.769226i
$623$	−113.735	+	18.0138i	−0.182560	+	0.0289146i
$624$			148.549i			0.238059i
$625$	−529.748	+	331.651i	−0.847596	+	0.530642i
$626$	−16.5555			−0.0264464
$627$	−56.9708	−	359.700i	−0.0908626	−	0.573684i
$628$	−395.217	−	201.373i	−0.629327	−	0.320658i
$629$	387.071	−	125.767i	0.615376	−	0.199948i
$630$	75.6794	−	100.475i	0.120126	−	0.159483i
$631$	55.6778	−	171.359i	0.0882374	−	0.271567i	−0.897195	−	0.441635i	$-0.854399\pi$
$631$	55.6778	−	171.359i	0.0882374	−	0.271567i	0.985432	+	0.170068i	$0.0543987\pi$
$632$	29.3723	+	29.3723i	0.0464752	+	0.0464752i
$633$	−240.408	−	471.827i	−0.379791	−	0.745382i
$634$	−113.319	−	155.970i	−0.178737	−	0.246010i
$635$	−21.4404	−	11.3942i	−0.0337644	−	0.0179436i
$636$	88.9737	+	64.6432i	0.139896	+	0.101640i
$637$	293.068	+	46.4175i	0.460076	+	0.0728689i
$638$	63.5547	−	401.268i	0.0996155	−	0.628947i
$639$	−74.8163	+	102.976i	−0.117083	+	0.161151i
$640$	50.8382	−	24.8088i	0.0794347	−	0.0387638i
$641$	692.295	−	502.982i	1.08002	−	0.784683i	0.102336	−	0.994750i	$-0.467368\pi$
$641$	692.295	−	502.982i	1.08002	−	0.784683i	0.977687	+	0.210067i	$0.0673682\pi$
$642$	−184.449	+	93.9815i	−0.287304	+	0.146389i
$643$	238.032	−	238.032i	0.370189	−	0.370189i	−0.497357	−	0.867546i	$-0.665696\pi$
$643$	238.032	−	238.032i	0.370189	−	0.370189i	0.867546	+	0.497357i	$0.165696\pi$
$644$	−9.24458	−	3.00375i	−0.0143549	−	0.00466420i
$645$	−205.643	+	597.644i	−0.318826	+	0.926579i
$646$	39.6288	+	121.965i	0.0613448	+	0.188800i
$647$	377.202	−	740.301i	0.583002	−	1.14421i	−0.391573	−	0.920147i	$-0.628069\pi$
$647$	377.202	−	740.301i	0.583002	−	1.14421i	0.974576	−	0.224059i	$-0.0719309\pi$
$648$	25.1424	−	3.98217i	0.0388001	−	0.00614533i
$649$		−	1178.11i		−	1.81527i
$650$	209.260	+	728.605i	0.321939	+	1.12093i
$651$	−196.937			−0.302515
$652$	−67.4530	−	425.882i	−0.103456	−	0.653193i
$653$	−830.057	−	422.935i	−1.27114	−	0.647680i	−0.317397	−	0.948293i	$-0.602809\pi$
$653$	−830.057	−	422.935i	−1.27114	−	0.647680i	−0.953746	+	0.300613i	$0.902809\pi$
$654$	451.275	−	146.628i	0.690023	−	0.224202i
$655$	−337.167	−	481.306i	−0.514758	−	0.734818i
$656$	−24.4258	+	75.1750i	−0.0372345	+	0.114596i
$657$	−302.282	−	302.282i	−0.460095	−	0.460095i
$658$	157.022	+	308.173i	0.238635	+	0.468348i
$659$	−498.484	−	686.105i	−0.756425	−	1.04113i	−0.997503	−	0.0706241i	$-0.977501\pi$
$659$	−498.484	−	686.105i	−0.756425	−	1.04113i	0.241078	−	0.970506i	$-0.422499\pi$
$660$	−235.853	+	33.1982i	−0.357353	+	0.0503003i
$661$	−167.565	−	121.743i	−0.253503	−	0.184180i	0.453775	−	0.891116i	$-0.350077\pi$
$661$	−167.565	−	121.743i	−0.253503	−	0.184180i	−0.707278	+	0.706936i	$0.750077\pi$
$662$	713.765	+	113.049i	1.07820	+	0.170769i
$663$	−34.4537	+	217.532i	−0.0519664	+	0.328103i
$664$	−27.2871	+	37.5575i	−0.0410950	+	0.0565625i
$665$	−446.466	−	78.6259i	−0.671377	−	0.118234i
$666$	−235.551	+	171.138i	−0.353680	+	0.256963i
$667$	15.2567	−	7.77366i	0.0228736	−	0.0116547i
$668$	−388.640	+	388.640i	−0.581797	+	0.581797i
$669$	530.797	+	172.466i	0.793419	+	0.257797i
$670$	−557.033	−	9.60437i	−0.831393	−	0.0143349i
$671$	−126.136	−	388.206i	−0.187982	−	0.578548i
$672$	−26.3763	+	51.7664i	−0.0392504	+	0.0770333i
$673$	134.184	−	21.2527i	0.199383	−	0.0315791i	−0.0559443	−	0.998434i	$-0.517817\pi$
$673$	134.184	−	21.2527i	0.199383	−	0.0315791i	0.255327	+	0.966855i	$0.417817\pi$
$674$			140.635i			0.208657i
$675$	117.709	−	54.9499i	0.174384	−	0.0814072i
$676$	581.449			0.860131
$677$	−2.35732	−	14.8836i	−0.00348201	−	0.0219846i	0.985886	−	0.167417i	$-0.0535426\pi$
$677$	−2.35732	−	14.8836i	−0.00348201	−	0.0219846i	−0.989368	+	0.145432i	$0.953543\pi$
$678$	398.761	+	203.179i	0.588142	+	0.299674i
$679$	−348.578	+	113.260i	−0.513370	+	0.166804i
$680$	80.2005	−	24.5384i	0.117942	−	0.0360859i
$681$	−25.4390	+	78.2933i	−0.0373554	+	0.114968i
$682$	263.680	+	263.680i	0.386627	+	0.386627i
$683$	33.7948	+	66.3260i	0.0494799	+	0.0971098i	0.914423	−	0.404761i	$-0.132645\pi$
$683$	33.7948	+	66.3260i	0.0494799	+	0.0971098i	−0.864943	+	0.501871i	$0.832645\pi$
$684$	−53.9248	−	74.2212i	−0.0788375	−	0.108510i
$685$	929.628	−	898.114i	1.35712	−	1.31112i
$686$	426.317	+	309.737i	0.621453	+	0.451512i
$687$	−33.0390	−	5.23286i	−0.0480917	−	0.00761697i
$688$	45.6670	−	288.330i	0.0663764	−	0.419084i
$689$	400.111	−	550.706i	0.580713	−	0.799283i
$690$	−6.97481	−	7.21955i	−0.0101084	−	0.0104631i
$691$	414.218	−	300.947i	0.599448	−	0.435524i	−0.246235	−	0.969210i	$-0.579194\pi$
$691$	414.218	−	300.947i	0.599448	−	0.435524i	0.845683	+	0.533686i	$0.179194\pi$
$692$	−103.634	+	52.8039i	−0.149760	+	0.0763063i
$693$	172.973	−	172.973i	0.249600	−	0.249600i
$694$	375.164	+	121.898i	0.540582	+	0.175646i
$695$	−144.035	−	470.759i	−0.207245	−	0.677351i
$696$	−31.6262	−	97.3355i	−0.0454400	−	0.139850i
$697$	−53.2044	+	104.420i	−0.0763335	+	0.149813i
$698$	554.220	−	87.7798i	0.794011	−	0.125759i
$699$			635.735i			0.909492i
$700$	−56.4478	+	291.061i	−0.0806398	+	0.415801i
$701$	−63.3053			−0.0903072			−0.0451536	−	0.998980i	$-0.514378\pi$
$701$	−63.3053			−0.0903072			−0.0451536	+	0.998980i	$0.514378\pi$
$702$	−24.6478	−	155.620i	−0.0351108	−	0.221681i
$703$	934.954	+	476.383i	1.32995	+	0.677643i
$704$	104.625	−	33.9948i	0.148616	−	0.0482881i
$705$	−6.15774	+	357.136i	−0.00873438	+	0.506576i
$706$	243.945	−	750.787i	0.345532	−	1.06344i
$707$	−564.358	−	564.358i	−0.798244	−	0.798244i
$708$	−134.736	−	264.433i	−0.190304	−	0.373494i
$709$	445.898	+	613.725i	0.628910	+	0.865621i	0.997964	−	0.0637873i	$-0.0203179\pi$
$709$	445.898	+	613.725i	0.628910	+	0.865621i	−0.369053	+	0.929408i	$0.620318\pi$
$710$	52.0339	−	295.467i	0.0732872	−	0.416151i
$711$	−35.6441	−	25.8969i	−0.0501323	−	0.0364233i
$712$	54.2509	+	8.59249i	0.0761950	+	0.0120681i
$713$	−2.45860	+	15.5230i	−0.00344825	+	0.0217714i
$714$	−50.6314	+	69.6882i	−0.0709123	+	0.0976025i
$715$	205.481	+	1459.82i	0.287387	+	2.04171i
$716$	−507.546	+	368.754i	−0.708863	+	0.515019i
$717$	−657.815	+	335.173i	−0.917454	+	0.467466i
$718$	−128.362	+	128.362i	−0.178778	+	0.178778i
$719$	−1055.82	−	343.055i	−1.46845	−	0.477128i	−0.537810	−	0.843066i	$-0.680748\pi$
$719$	−1055.82	−	343.055i	−1.46845	−	0.477128i	−0.930639	+	0.365938i	$0.880748\pi$
$720$	−49.1418	+	34.4251i	−0.0682525	+	0.0478126i
$721$	−167.416	−	515.253i	−0.232200	−	0.714637i
$722$	81.6698	−	160.286i	0.113116	−	0.222003i
$723$	313.030	−	49.5791i	0.432960	−	0.0685742i
$724$			20.7083i			0.0286026i
$725$	−292.237	−	432.861i	−0.403086	−	0.597050i
$726$	−166.799			−0.229751
$727$	−36.3791	−	229.688i	−0.0500400	−	0.315940i	−0.999994	−	0.00354933i	$-0.998870\pi$
$727$	−36.3791	−	229.688i	−0.0500400	−	0.315940i	0.949954	−	0.312391i	$-0.101130\pi$
$728$	320.410	+	163.257i	0.440124	+	0.224254i
$729$	−25.6785	+	8.34346i	−0.0352243	+	0.0114451i
$730$	952.782	+	327.842i	1.30518	+	0.449099i
$731$	133.748	−	411.633i	0.182965	−	0.563110i
$732$	−72.7095	−	72.7095i	−0.0993299	−	0.0993299i
$733$	301.710	+	592.139i	0.411609	+	0.807829i	1.00000		0.000748183i	$-0.000238154\pi$
$733$	301.710	+	592.139i	0.411609	+	0.807829i	−0.588390	+	0.808577i	$0.700238\pi$
$734$	122.848	+	169.086i	0.167368	+	0.230362i
$735$	52.5609	+	107.708i	0.0715114	+	0.146541i
$736$	3.75104	+	2.72529i	0.00509653	+	0.00370284i
$737$	−1070.09	−	169.486i	−1.45196	−	0.229967i
$738$	13.1152	−	82.8062i	0.0177713	−	0.112204i
$739$	373.601	−	514.217i	0.505549	−	0.695828i	−0.477612	−	0.878571i	$-0.658497\pi$
$739$	373.601	−	514.217i	0.505549	−	0.695828i	0.983161	+	0.182743i	$0.0584975\pi$
$740$	322.052	−	606.003i	0.435205	−	0.818923i
$741$	−459.394	+	333.770i	−0.619966	+	0.450431i
$742$	237.214	−	120.867i	0.319696	−	0.162893i
$743$	−152.345	+	152.345i	−0.205040	+	0.205040i	−0.802155	−	0.597115i	$-0.796313\pi$
$743$	−152.345	+	152.345i	−0.205040	+	0.205040i	0.597115	+	0.802155i	$0.296313\pi$
$744$	89.3404	+	29.0284i	0.120081	+	0.0390167i
$745$	199.622	+	150.359i	0.267948	+	0.201824i
$746$	−123.784	−	380.967i	−0.165930	−	0.510680i
$747$	22.3543	−	43.8728i	0.0299255	−	0.0587321i
$748$	161.096	−	25.5151i	0.215369	−	0.0341111i
$749$			501.131i			0.669067i
$750$	−192.537	+	238.074i	−0.256716	+	0.317433i
$751$	−536.133			−0.713892			−0.356946	−	0.934125i	$-0.616182\pi$
$751$	−536.133			−0.713892			−0.356946	+	0.934125i	$0.616182\pi$
$752$	−25.8083	−	162.947i	−0.0343196	−	0.216685i
$753$	−247.741	−	126.230i	−0.329005	−	0.167636i
$754$	−602.462	+	195.752i	−0.799021	+	0.259618i
$755$	−210.117	+	278.958i	−0.278301	+	0.369481i
$756$	19.0426	−	58.6070i	0.0251886	−	0.0775225i
$757$	−222.395	−	222.395i	−0.293784	−	0.293784i	0.544789	−	0.838573i	$-0.316610\pi$
$757$	−222.395	−	222.395i	−0.293784	−	0.293784i	−0.838573	+	0.544789i	$0.816610\pi$
$758$	−256.546	−	503.501i	−0.338452	−	0.664249i
$759$	−11.4747	−	15.7935i	−0.0151181	−	0.0208083i
$760$	190.949	+	101.477i	0.251249	+	0.133523i
$761$	804.184	+	584.274i	1.05675	+	0.767771i	0.973484	−	0.228756i	$-0.0734659\pi$
$761$	804.184	+	584.274i	1.05675	+	0.767771i	0.0832629	+	0.996528i	$0.473466\pi$
$762$	−11.7483	−	1.86074i	−0.0154177	−	0.00244192i
$763$	179.690	−	1134.52i	0.235504	−	1.48691i
$764$	−157.266	+	216.458i	−0.205845	+	0.283322i
$765$	−79.9467	+	39.0137i	−0.104505	+	0.0509983i
$766$	−468.343	+	340.271i	−0.611414	+	0.444218i
$767$	−1636.72	+	833.951i	−2.13392	+	1.08729i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$	−469.681	−	152.608i	−0.610768	−	0.198451i	−0.0127309	−	0.999919i	$-0.504052\pi$
$769$	−469.681	−	152.608i	−0.610768	−	0.198451i	−0.598037	+	0.801468i	$0.704052\pi$
$770$	−187.599	+	545.204i	−0.243635	+	0.708057i
$771$	−139.782	−	430.205i	−0.181300	−	0.557983i
$772$	−300.639	+	590.036i	−0.389428	+	0.764296i
$773$	−1072.84	+	169.920i	−1.38789	+	0.219820i	−0.805260	−	0.592921i	$-0.797974\pi$
$773$	−1072.84	+	169.920i	−1.38789	+	0.219820i	−0.582625	+	0.812741i	$0.697974\pi$
$774$			309.632i			0.400041i
$775$	479.090	+	16.5259i	0.618181	+	0.0213237i
$776$	174.827			0.225292
$777$	110.259	+	696.150i	0.141904	+	0.895945i
$778$	208.570	+	106.271i	0.268084	+	0.136596i
$779$	−287.364	+	93.3702i	−0.368888	+	0.119859i
$780$	213.075	+	304.165i	0.273173	+	0.389955i
$781$	180.293	−	554.885i	0.230849	−	0.710480i
$782$	4.86087	+	4.86087i	0.00621594	+	0.00621594i
$783$	49.2820	+	96.7213i	0.0629399	+	0.123527i
$784$	−32.5371	−	44.7835i	−0.0415014	−	0.0571218i
$785$	−1098.08	+	154.564i	−1.39883	+	0.196897i
$786$	−232.908	−	169.218i	−0.296321	−	0.215290i
$787$	264.055	+	41.8222i	0.335521	+	0.0531413i	0.321922	−	0.946766i	$-0.395671\pi$
$787$	264.055	+	41.8222i	0.335521	+	0.0531413i	0.0135992	+	0.999908i	$0.495671\pi$
$788$	−36.2438	+	228.834i	−0.0459947	+	0.290399i
$789$	−207.880	+	286.123i	−0.263473	+	0.362640i
$790$	102.273	+	18.0110i	0.129460	+	0.0227988i
$791$	876.486	−	636.804i	1.10807	−	0.805062i
$792$	−103.965	+	52.9729i	−0.131269	+	0.0668850i
$793$	−450.038	+	450.038i	−0.567513	+	0.567513i
$794$	−524.346	−	170.370i	−0.660385	−	0.214572i
$795$	274.903	+	4.73988i	0.345790	+	0.00596211i
$796$	105.710	+	325.343i	0.132802	+	0.408722i
$797$	−502.982	+	987.158i	−0.631094	+	1.23859i	0.325051	+	0.945697i	$0.394619\pi$
$797$	−502.982	+	987.158i	−0.631094	+	1.23859i	−0.956145	+	0.292895i	$0.905381\pi$
$798$	−219.354	+	34.7423i	−0.274880	+	0.0435367i
$799$		−	244.603i		−	0.306136i
$800$	68.5097	−	123.719i	0.0856372	−	0.154649i
$801$	−58.2590			−0.0727328
$802$	59.8994	+	378.190i	0.0746875	+	0.471558i
$803$	1745.93	+	889.598i	2.17426	+	1.10784i
$804$	−259.572	+	84.3400i	−0.322851	+	0.104901i
$805$	−23.2375	+	7.10982i	−0.0288664	+	0.00883208i
$806$	179.673	−	552.975i	0.222919	−	0.686074i
$807$	138.854	+	138.854i	0.172062	+	0.172062i
$808$	172.834	+	339.207i	0.213904	+	0.419810i
$809$	−656.398	−	903.454i	−0.811370	−	1.11675i	−0.991111	−	0.133040i	$-0.957526\pi$
$809$	−656.398	−	903.454i	−0.811370	−	1.11675i	0.179741	−	0.983714i	$-0.442474\pi$
$810$	45.7691	−	44.2175i	0.0565050	−	0.0545896i
$811$	−656.209	−	476.763i	−0.809135	−	0.587871i	0.104445	−	0.994531i	$-0.466694\pi$
$811$	−656.209	−	476.763i	−0.809135	−	0.587871i	−0.913580	+	0.406660i	$0.866694\pi$
$812$	−244.704	−	38.7573i	−0.301359	−	0.0477306i
$813$	68.4389	−	432.106i	0.0841807	−	0.531496i
$814$	784.449	−	1079.70i	0.963697	−	1.32642i
$815$	−748.990	−	775.272i	−0.919006	−	0.951253i
$816$	33.2409	−	24.1509i	0.0407364	−	0.0295967i
$817$	994.282	−	506.612i	1.21699	−	0.620088i
$818$	−301.270	+	301.270i	−0.368301	+	0.368301i
$819$	−362.750	−	117.865i	−0.442919	−	0.143913i
$820$	57.8156	+	188.962i	0.0705068	+	0.230442i
$821$	305.491	+	940.204i	0.372096	+	1.14519i	0.945417	+	0.325863i	$0.105655\pi$
$821$	305.491	+	940.204i	0.372096	+	1.14519i	−0.573321	+	0.819331i	$0.694345\pi$
$822$	287.486	−	564.223i	0.349740	−	0.686403i
$823$	1296.01	−	205.268i	1.57474	−	0.249415i	0.692926	−	0.721009i	$-0.256321\pi$
$823$	1296.01	−	205.268i	1.57474	−	0.249415i	0.881816	+	0.471595i	$0.156321\pi$
$824$			258.421i			0.313618i
$825$	−435.307	+	406.278i	−0.527645	+	0.492458i
$826$	−718.441			−0.869784
$827$	193.172	+	1219.64i	0.233582	+	1.47478i	0.773895	+	0.633314i	$0.218306\pi$
$827$	193.172	+	1219.64i	0.233582	+	1.47478i	−0.540314	+	0.841464i	$0.681694\pi$
$828$	−4.38179	−	2.23263i	−0.00529202	−	0.00269642i
$829$	−995.061	+	323.315i	−1.20031	+	0.390006i	−0.839877	−	0.542777i	$-0.817373\pi$
$829$	−995.061	+	323.315i	−1.20031	+	0.390006i	−0.360438	+	0.932783i	$0.617373\pi$
$830$	−2.00079	+	116.042i	−0.00241059	+	0.139809i
$831$	−27.4739	+	84.5561i	−0.0330613	+	0.101752i
$832$	−121.290	−	121.290i	−0.145781	−	0.145781i
$833$	−37.2599	−	73.1266i	−0.0447297	−	0.0877871i
$834$	−141.760	−	195.117i	−0.169977	−	0.233953i
$835$	−238.313	+	1353.23i	−0.285405	+	1.62063i
$836$	340.210	+	247.177i	0.406950	+	0.295666i
$837$	−98.4096	−	15.5866i	−0.117574	−	0.0186219i
$838$	−142.595	+	900.308i	−0.170161	+	1.07435i
$839$	449.367	−	618.501i	0.535599	−	0.737188i	−0.452372	−	0.891829i	$-0.649422\pi$
$839$	449.367	−	618.501i	0.535599	−	0.737188i	0.987971	+	0.154641i	$0.0494221\pi$
$840$	20.2451	+	143.829i	0.0241013	+	0.171225i
$841$	−327.301	+	237.798i	−0.389180	+	0.282756i
$842$	−69.8800	+	35.6056i	−0.0829929	+	0.0422870i
$843$	−97.5954	+	97.5954i	−0.115772	+	0.115772i
$844$	581.537	+	188.953i	0.689025	+	0.223878i
$845$	1190.56	−	834.017i	1.40895	−	0.987002i
$846$	54.0737	+	166.422i	0.0639169	+	0.196716i
$847$	−183.315	+	359.775i	−0.216428	+	0.424764i
$848$	−125.428	+	19.8658i	−0.147910	+	0.0234266i
$849$		−	429.831i		−	0.506279i
$850$	129.019	−	165.282i	0.151787	−	0.194450i
$851$	56.2484			0.0660968
$852$	−22.9921	−	145.167i	−0.0269861	−	0.170383i
$853$	904.746	+	460.991i	1.06066	+	0.540435i	0.895147	−	0.445772i	$-0.147071\pi$
$853$	904.746	+	460.991i	1.06066	+	0.540435i	0.165517	+	0.986207i	$0.447071\pi$
$854$	−236.738	+	76.9209i	−0.277211	+	0.0900713i
$855$	−216.876	−	74.6248i	−0.253656	−	0.0872805i
$856$	73.8665	−	227.338i	0.0862926	−	0.265581i
$857$	721.748	+	721.748i	0.842180	+	0.842180i	0.989142	−	0.146962i	$-0.0469495\pi$
$857$	721.748	+	721.748i	0.842180	+	0.842180i	−0.146962	+	0.989142i	$0.546949\pi$
$858$	327.878	+	643.496i	0.382142	+	0.749995i
$859$	−318.119	−	437.853i	−0.370336	−	0.509724i	0.582656	−	0.812719i	$-0.302013\pi$
$859$	−318.119	−	437.853i	−0.370336	−	0.509724i	−0.952992	+	0.302995i	$0.902013\pi$
$860$	−320.067	−	655.881i	−0.372171	−	0.762652i
$861$	−164.194	−	119.294i	−0.190701	−	0.138553i
$862$	−959.122	−	151.910i	−1.11267	−	0.176230i
$863$	106.575	−	672.890i	0.123494	−	0.779711i	−0.845745	−	0.533588i	$-0.820843\pi$
$863$	106.575	−	672.890i	0.123494	−	0.779711i	0.969239	−	0.246123i	$-0.0791567\pi$
$864$	−17.2773	+	23.7801i	−0.0199969	+	0.0275233i
$865$	−136.457	+	256.770i	−0.157753	+	0.296844i
$866$	211.948	−	153.989i	0.244743	−	0.177816i
$867$	−391.726	+	199.594i	−0.451818	+	0.230213i
$868$	160.799	−	160.799i	0.185252	−	0.185252i
$869$	192.068	+	62.4067i	0.221022	+	0.0718144i
$870$	−204.373	−	153.938i	−0.234911	−	0.176940i
$871$	522.026	+	1606.63i	0.599341	+	1.84458i
$872$	−248.743	+	488.186i	−0.285256	+	0.559846i
$873$	−183.149	+	29.0079i	−0.209792	+	0.0332278i
$874$			17.7237i			0.0202788i
$875$	301.910	+	676.937i	0.345040	+	0.773642i
$876$	493.625			0.563499
$877$	−184.910	−	1167.48i	−0.210844	−	1.33122i	−0.835144	−	0.550031i	$-0.814616\pi$
$877$	−184.910	−	1167.48i	−0.210844	−	1.33122i	0.624300	−	0.781184i	$-0.285384\pi$
$878$	353.589	+	180.163i	0.402721	+	0.205197i
$879$	372.096	−	120.901i	0.423318	−	0.137544i
$880$	165.467	−	219.679i	0.188030	−	0.249635i
$881$	−180.657	+	556.006i	−0.205059	+	0.631107i	0.794652	+	0.607066i	$0.207653\pi$
$881$	−180.657	+	556.006i	−0.205059	+	0.631107i	−0.999711	+	0.0240417i	$0.992347\pi$
$882$	41.5166	+	41.5166i	0.0470710	+	0.0470710i
$883$	−750.597	−	1473.13i	−0.850053	−	1.66832i	−0.738183	−	0.674601i	$-0.764316\pi$
$883$	−750.597	−	1473.13i	−0.850053	−	1.66832i	−0.111870	−	0.993723i	$-0.535684\pi$
$884$	−149.483	−	205.746i	−0.169098	−	0.232744i
$885$	−655.178	−	348.186i	−0.740315	−	0.393430i
$886$	308.007	+	223.780i	0.347638	+	0.252573i
$887$	1489.44	+	235.903i	1.67918	+	0.265957i	0.921984	−	0.387227i	$-0.126567\pi$
$887$	1489.44	+	235.903i	1.67918	+	0.265957i	0.757199	+	0.653184i	$0.226567\pi$
$888$	52.5931	−	332.060i	0.0592264	−	0.373941i
$889$	−16.9250	+	23.2953i	−0.0190382	+	0.0262039i
$890$	123.408	−	60.2224i	0.138660	−	0.0676657i
$891$	100.125	−	72.7448i	0.112373	−	0.0816440i
$892$	−574.212	+	292.576i	−0.643736	+	0.328000i
$893$	445.935	−	445.935i	0.499367	−	0.499367i
$894$	116.440	+	37.8336i	0.130246	+	0.0423194i
$895$	−510.306	+	1483.06i	−0.570174	+	1.65705i
$896$	−20.7309	−	63.8032i	−0.0231372	−	0.0712090i
$897$	−13.8190	+	27.1213i	−0.0154058	+	0.0302355i
$898$	441.582	−	69.9398i	0.491740	−	0.0778839i
$899$			400.585i			0.445590i
$900$	−51.2430	+	140.976i	−0.0569366	+	0.156640i
$901$	−188.282			−0.208969
$902$	60.1167	+	379.562i	0.0666482	+	0.420800i
$903$	667.856	+	340.290i	0.739597	+	0.376843i
$904$	−491.481	+	159.692i	−0.543674	+	0.176650i
$905$	29.7035	+	42.4018i	0.0328216	+	0.0468528i
$906$	−52.8700	+	162.717i	−0.0583554	+	0.179599i
$907$	−125.237	−	125.237i	−0.138079	−	0.138079i	0.634689	−	0.772768i	$-0.281128\pi$
$907$	−125.237	−	125.237i	−0.138079	−	0.138079i	−0.772768	+	0.634689i	$0.781128\pi$
$908$	−43.1553	−	84.6970i	−0.0475279	−	0.0932787i
$909$	−237.344	−	326.676i	−0.261105	−	0.359380i
$910$	890.236	−	125.308i	0.978281	−	0.137701i
$911$	−994.444	−	722.506i	−1.09160	−	0.793091i	−0.111928	−	0.993716i	$-0.535702\pi$
$911$	−994.444	−	722.506i	−1.09160	−	0.793091i	−0.979668	+	0.200626i	$0.935702\pi$
$912$	104.631	+	16.5719i	0.114727	+	0.0181709i
$913$	−35.3075	+	222.923i	−0.0386719	+	0.244165i
$914$	−214.250	+	294.890i	−0.234409	+	0.322637i
$915$	−253.171	−	44.5852i	−0.276689	−	0.0487270i
$916$	31.2488	−	22.7036i	0.0341144	−	0.0247856i
$917$	−620.960	+	316.395i	−0.677165	+	0.345033i
$918$	−30.8160	+	30.8160i	−0.0335686	+	0.0335686i
$919$	1475.64	+	479.464i	1.60570	+	0.521723i	0.968508	−	0.248982i	$-0.0800960\pi$
$919$	1475.64	+	479.464i	1.60570	+	0.521723i	0.637192	+	0.770705i	$0.280096\pi$
$920$	11.5896	+	0.199829i	0.0125974	+	0.000217205i
$921$	46.0288	+	141.662i	0.0499770	+	0.153813i
$922$	38.1911	−	74.9542i	0.0414220	−	0.0812952i
$923$	−898.514	+	142.311i	−0.973471	+	0.154183i
$924$			282.464i			0.305697i
$925$	−209.811	−	1702.78i	−0.226823	−	1.84084i
$926$	133.616			0.144294
$927$	−42.8782	−	270.722i	−0.0462548	−	0.292041i
$928$	105.297	+	53.6514i	0.113466	+	0.0578140i
$929$	−1162.48	+	377.712i	−1.25132	+	0.406579i	−0.858395	−	0.512990i	$-0.828538\pi$
$929$	−1162.48	+	377.712i	−1.25132	+	0.406579i	−0.392928	+	0.919569i	$0.628538\pi$
$930$	224.569	−	68.7099i	0.241472	−	0.0738816i
$931$	65.3885	−	201.245i	0.0702347	−	0.216160i
$932$	−519.076	−	519.076i	−0.556948	−	0.556948i
$933$	−298.577	−	585.990i	−0.320018	−	0.628071i
$934$	315.471	+	434.209i	0.337764	+	0.464892i
$935$	293.258	−	283.317i	0.313645	−	0.303012i
$936$	147.188	+	106.938i	0.157252	+	0.114250i
$937$	−598.257	−	94.7546i	−0.638482	−	0.101126i	−0.171203	−	0.985236i	$-0.554765\pi$
$937$	−598.257	−	94.7546i	−0.638482	−	0.101126i	−0.467278	+	0.884110i	$0.654765\pi$
$938$	−103.357	+	652.570i	−0.110189	+	0.695704i
$939$	−11.9181	+	16.4038i	−0.0126923	+	0.0174694i
$940$	−286.573	−	296.628i	−0.304864	−	0.315562i
$941$	355.393	−	258.208i	0.377676	−	0.274398i	−0.382711	−	0.923868i	$-0.625009\pi$
$941$	355.393	−	258.208i	0.377676	−	0.274398i	0.760387	+	0.649470i	$0.225009\pi$
$942$	−484.040	+	246.631i	−0.513843	+	0.261816i
$943$	−11.4528	+	11.4528i	−0.0121451	+	0.0121451i
$944$	325.920	+	105.898i	0.345254	+	0.112180i
$945$	−45.0735	−	147.316i	−0.0476968	−	0.155890i
$946$	−438.579	−	1349.81i	−0.463614	−	1.42686i
$947$	−115.363	+	226.413i	−0.121820	+	0.239084i	−0.943861	−	0.330344i	$-0.892835\pi$
$947$	−115.363	+	226.413i	−0.121820	+	0.239084i	0.822041	+	0.569428i	$0.192835\pi$
$948$	50.2480	−	7.95850i	0.0530042	−	0.00839505i
$949$		−	3055.31i		−	3.21950i
$950$	536.540	−	66.1108i	0.564778	−	0.0695903i
$951$	−236.118			−0.248284
$952$	−15.5598	−	98.2405i	−0.0163443	−	0.103194i
$953$	534.472	+	272.327i	0.560831	+	0.285758i	0.711337	−	0.702851i	$-0.248090\pi$
$953$	534.472	+	272.327i	0.560831	+	0.285758i	−0.150505	+	0.988609i	$0.548090\pi$
$954$	128.102	−	41.6229i	0.134279	−	0.0436298i
$955$	−11.5313	+	668.792i	−0.0120747	+	0.700305i
$956$	263.436	−	810.771i	0.275560	−	0.848087i
$957$	−351.840	−	351.840i	−0.367649	−	0.367649i
$958$	−40.7611	−	79.9982i	−0.0425481	−	0.0835054i
$959$	−901.041	−	1240.18i	−0.939563	−	1.29320i
$960$	12.0162	−	68.2320i	0.0125168	−	0.0710750i
$961$	480.005	+	348.744i	0.499485	+	0.362897i
$962$	−2055.30	−	325.527i	−2.13648	−	0.338385i
$963$	−39.6619	+	250.415i	−0.0411858	+	0.260037i
$964$	−215.107	+	296.069i	−0.223140	+	0.307126i
$965$	230.755	+	1639.37i	0.239124	+	1.69883i
$966$	−9.63129	+	6.99754i	−0.00997028	+	0.00724383i
$967$	492.235	−	250.806i	0.509033	−	0.259365i	−0.180558	−	0.983564i	$-0.557790\pi$
$967$	492.235	−	250.806i	0.509033	−	0.259365i	0.689591	+	0.724199i	$0.257790\pi$
$968$	136.191	−	136.191i	0.140693	−	0.140693i
$969$	149.376	+	48.5351i	0.154154	+	0.0500878i
$970$	357.971	−	250.767i	0.369042	−	0.258523i
$971$	−228.190	−	702.296i	−0.235005	−	0.723271i	−0.997121	−	0.0758301i	$-0.975839\pi$
$971$	−228.190	−	702.296i	−0.235005	−	0.723271i	0.762116	−	0.647441i	$-0.224161\pi$
$972$	14.1540	−	27.7788i	0.0145618	−	0.0285790i
$973$	−576.650	+	91.3324i	−0.592651	+	0.0938668i
$974$		−	988.698i		−	1.01509i
$975$	872.574	+	317.170i	0.894948	+	0.325303i
$976$	118.734			0.121654
$977$	257.066	+	1623.05i	0.263118	+	1.66126i	0.665957	+	0.745990i	$0.268024\pi$
$977$	257.066	+	1623.05i	0.263118	+	1.66126i	−0.402839	+	0.915271i	$0.631976\pi$
$978$	−470.539	−	239.752i	−0.481124	−	0.245145i
$979$	253.974	−	82.5210i	0.259422	−	0.0842912i
$980$	−130.859	−	45.0271i	−0.133529	−	0.0459460i
$981$	179.582	−	552.697i	0.183060	−	0.563401i
$982$	−355.738	−	355.738i	−0.362259	−	0.362259i
$983$	−24.5756	−	48.2324i	−0.0250006	−	0.0490665i	0.878168	−	0.478352i	$-0.158766\pi$
$983$	−24.5756	−	48.2324i	−0.0250006	−	0.0490665i	−0.903169	+	0.429285i	$0.858766\pi$
$984$	56.9025	+	78.3196i	0.0578277	+	0.0795930i
$985$	254.023	+	520.543i	0.257891	+	0.528470i
$986$	141.751	+	102.988i	0.143764	+	0.104450i
$987$	418.388	+	66.2662i	0.423899	+	0.0671390i
$988$	102.572	−	647.616i	0.103818	−	0.655482i
$989$	35.1599	−	48.3935i	0.0355510	−	0.0489317i
$990$	−136.893	+	257.591i	−0.138276	+	0.260193i
$991$	541.278	−	393.262i	0.546194	−	0.396833i	−0.280186	−	0.959946i	$-0.590396\pi$
$991$	541.278	−	393.262i	0.546194	−	0.396833i	0.826380	+	0.563113i	$0.190396\pi$
$992$	−96.6477	+	49.2445i	−0.0974271	+	0.0496416i
$993$	625.844	−	625.844i	0.630256	−	0.630256i
$994$	−338.383	−	109.947i	−0.340426	−	0.110611i
$995$	683.114	+	514.535i	0.686547	+	0.517121i
$996$	17.5698	+	54.0743i	0.0176404	+	0.0542914i
$997$	−759.467	+	1490.54i	−0.761752	+	1.49502i	0.104016	+	0.994576i	$0.466831\pi$
$997$	−759.467	+	1490.54i	−0.761752	+	1.49502i	−0.865767	+	0.500446i	$0.833169\pi$
$998$	−802.574	+	127.115i	−0.804183	+	0.127370i
$999$			356.593i			0.356950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.k.a.37.3	✓	32
25.23	odd	20	inner	150.3.k.a.73.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.k.a.37.3	✓	32	1.1	even	1	trivial
150.3.k.a.73.3	yes	32	25.23	odd	20	inner

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(1.54327 + 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-3.00822 + 3.99382i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(4.19292 + 4.19292i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +O(q^{10})\)	\(q+(0.221232 + 1.39680i) q^{2} +(1.54327 + 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-3.00822 + 3.99382i) q^{5} +(-0.756934 + 2.32960i) q^{6} +(4.19292 + 4.19292i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +(-6.24409 - 3.31834i) q^{10} +(-11.1250 - 8.08275i) q^{11} +(-3.42145 - 0.541905i) q^{12} +(-3.35414 + 21.1772i) q^{13} +(-4.92907 + 6.78429i) q^{14} +(-7.78298 + 3.79806i) q^{15} +(3.23607 - 2.35114i) q^{16} +(5.28415 - 2.69241i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(14.5420 + 4.72499i) q^{19} +(3.25367 - 9.45588i) q^{20} +(3.17376 + 9.76784i) q^{21} +(8.82881 - 17.3275i) q^{22} +(0.809542 - 0.128219i) q^{23} -4.89898i q^{24} +(-6.90117 - 24.0286i) q^{25} -30.3224 q^{26} +(0.812857 + 5.13218i) q^{27} +(-10.5668 - 5.38404i) q^{28} +(19.8685 - 6.45568i) q^{29} +(-7.02698 - 10.0310i) q^{30} +(-5.92541 + 18.2365i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-10.8130 - 21.2218i) q^{33} +(4.92978 + 6.78527i) q^{34} +(-29.3590 + 4.13252i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(67.7814 + 10.7355i) q^{37} +(-3.38272 + 21.3577i) q^{38} +(-21.8287 + 30.0446i) q^{39} +(13.9278 + 2.45279i) q^{40} +(-15.9869 + 11.6152i) q^{41} +(-12.9416 + 6.59407i) q^{42} +(51.6054 - 51.6054i) q^{43} +(26.1563 + 8.49871i) q^{44} +(-14.9978 - 0.258591i) q^{45} +(0.358193 + 1.10240i) q^{46} +(18.7247 - 36.7493i) q^{47} +(6.84291 - 1.08381i) q^{48} -13.8389i q^{49} +(32.0365 - 14.9555i) q^{50} +10.2720 q^{51} +(-6.70828 - 42.3544i) q^{52} +(-28.2875 - 14.4132i) q^{53} +(-6.98881 + 2.27080i) q^{54} +(65.7474 - 20.1163i) q^{55} +(5.18273 - 15.9508i) q^{56} +(18.7268 + 18.7268i) q^{57} +(13.4129 + 26.3242i) q^{58} +(50.3574 + 69.3111i) q^{59} +(12.4568 - 12.0345i) q^{60} +(24.0145 + 17.4475i) q^{61} +(-26.7837 - 4.24212i) q^{62} +(-2.78282 + 17.5700i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-74.4879 - 77.1016i) q^{65} +(27.2505 - 19.7986i) q^{66} +(70.2007 - 35.7691i) q^{67} +(-8.38705 + 8.38705i) q^{68} +(1.35016 + 0.438695i) q^{69} +(-12.2674 - 40.0945i) q^{70} +(13.1111 + 40.3518i) q^{71} +(3.85224 - 7.56044i) q^{72} +(-140.743 + 22.2915i) q^{73} +97.0522i q^{74} +(8.24416 - 42.5092i) q^{75} -30.5808 q^{76} +(-12.7557 - 80.5364i) q^{77} +(-46.7956 - 23.8436i) q^{78} +(-13.9674 + 4.53827i) q^{79} +(-0.344789 + 19.9970i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-19.7609 - 19.7609i) q^{82} +(-7.45144 - 14.6243i) q^{83} +(-12.0737 - 16.6180i) q^{84} +(-5.14292 + 29.2033i) q^{85} +(83.4992 + 60.6657i) q^{86} +(35.7388 + 5.66047i) q^{87} +(-6.08440 + 38.4154i) q^{88} +(-11.4146 + 15.7108i) q^{89} +(-2.95678 - 21.0061i) q^{90} +(-102.858 + 74.7307i) q^{91} +(-1.46060 + 0.744211i) q^{92} +(-23.4845 + 23.4845i) q^{93} +(55.4739 + 18.0246i) q^{94} +(-62.6165 + 43.8644i) q^{95} +(3.02774 + 9.31841i) q^{96} +(-28.0614 + 55.0736i) q^{97} +(19.3302 - 3.06160i) q^{98} -41.2536i 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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