LMFDB - Embedded newform 150.3.k.a.37.1

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			37.1
Character	$\chi$	$=$	150.37
Dual form			150.3.k.a.73.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(-1.54327 - 0.786335i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.48914 - 4.77310i) q^{5} +(0.756934 - 2.32960i) q^{6} +(9.35986 + 9.35986i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(1.76336 + 2.42705i) q^{9} +(6.33763 - 3.13599i) q^{10} +(13.3667 + 9.71148i) q^{11} +(3.42145 + 0.541905i) q^{12} +(-1.86256 + 11.7598i) q^{13} +(-11.0032 + 15.1446i) q^{14} +(-1.45512 + 8.53713i) q^{15} +(3.23607 - 2.35114i) q^{16} +(17.3995 - 8.86551i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-16.4119 - 5.33255i) q^{19} +(5.78244 + 8.15864i) q^{20} +(-7.08479 - 21.8047i) q^{21} +(-10.6079 + 20.8191i) q^{22} +(17.1062 - 2.70936i) q^{23} +4.89898i q^{24} +(-20.5649 + 14.2156i) q^{25} -16.8381 q^{26} +(-0.812857 - 5.13218i) q^{27} +(-23.5882 - 12.0188i) q^{28} +(7.90234 - 2.56763i) q^{29} +(-12.2466 - 0.143824i) q^{30} +(-0.527352 + 1.62302i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-12.9919 - 25.4981i) q^{33} +(16.2327 + 22.3424i) q^{34} +(30.7374 - 58.6136i) q^{35} +(-4.85410 - 3.52671i) q^{36} +(26.7701 + 4.23997i) q^{37} +(3.81769 - 24.1039i) q^{38} +(12.1215 - 16.6839i) q^{39} +(-10.1167 + 9.88188i) q^{40} +(-41.3813 + 30.0653i) q^{41} +(28.8895 - 14.7200i) q^{42} +(16.8295 - 16.8295i) q^{43} +(-31.4270 - 10.2112i) q^{44} +(8.95868 - 12.0309i) q^{45} +(7.56889 + 23.2946i) q^{46} +(9.38971 - 18.4284i) q^{47} +(-6.84291 + 1.08381i) q^{48} +126.214i q^{49} +(-24.4060 - 25.5802i) q^{50} -33.8234 q^{51} +(-3.72513 - 23.5195i) q^{52} +(-29.4849 - 15.0233i) q^{53} +(6.98881 - 2.27080i) q^{54} +(26.4490 - 78.2623i) q^{55} +(11.5694 - 35.6070i) q^{56} +(21.1348 + 21.1348i) q^{57} +(5.33471 + 10.4700i) q^{58} +(-49.9720 - 68.7805i) q^{59} +(-2.50844 - 17.1379i) q^{60} +(-62.4364 - 45.3627i) q^{61} +(-2.38371 - 0.377542i) q^{62} +(-6.21209 + 39.2216i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(58.9041 - 8.62168i) q^{65} +(32.7416 - 23.7882i) q^{66} +(49.3261 - 25.1329i) q^{67} +(-27.6167 + 27.6167i) q^{68} +(-28.5300 - 9.26995i) q^{69} +(88.6717 + 29.9669i) q^{70} +(3.44376 + 10.5988i) q^{71} +(3.85224 - 7.56044i) q^{72} +(15.9934 - 2.53311i) q^{73} +38.3305i q^{74} +(42.9154 - 5.76754i) q^{75} +34.5130 q^{76} +(34.2124 + 216.008i) q^{77} +(25.9857 + 13.2404i) q^{78} +(-84.5955 + 27.4868i) q^{79} +(-16.0412 - 11.9449i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-51.1501 - 51.1501i) q^{82} +(-48.3016 - 94.7972i) q^{83} +(26.9522 + 37.0965i) q^{84} +(-68.2262 - 69.8478i) q^{85} +(27.2308 + 19.7843i) q^{86} +(-14.2144 - 2.25135i) q^{87} +(7.31045 - 46.1563i) q^{88} +(56.1054 - 77.2225i) q^{89} +(18.7867 + 9.85189i) q^{90} +(-127.503 + 92.6363i) q^{91} +(-30.8635 + 15.7257i) q^{92} +(2.09008 - 2.09008i) q^{93} +(27.8181 + 9.03864i) q^{94} +(-1.01323 + 86.2766i) q^{95} +(-3.02774 - 9.31841i) q^{96} +(-49.5492 + 97.2457i) q^{97} +(-176.296 + 27.9225i) q^{98} +49.5664i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 8 q^{2} + 8 q^{7} - 16 q^{8} + 20 q^{10} + 32 q^{11} - 16 q^{13} - 60 q^{14} + 32 q^{16} + 148 q^{17} - 96 q^{18} + 180 q^{19} + 40 q^{20} - 36 q^{21} + 48 q^{22} + 48 q^{23} - 160 q^{25} - 8 q^{26}+ \cdots - 108 q^{98}+O(q^{100})$ 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

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
$5$	−1.48914	−	4.77310i	−0.297827	−	0.954620i
$5$	−1.48914	−	4.77310i	−0.297827	−	0.954620i
$6$	0.756934	−	2.32960i	0.126156	−	0.388267i
$7$	9.35986	+	9.35986i	1.33712	+	1.33712i	0.898835	+	0.438287i	$0.144415\pi$
$7$	9.35986	+	9.35986i	1.33712	+	1.33712i	0.438287	+	0.898835i	$0.355585\pi$
$8$	−1.28408	−	2.52015i	−0.160510	−	0.315018i
$9$	1.76336	+	2.42705i	0.195928	+	0.269672i
$10$	6.33763	−	3.13599i	0.633763	−	0.313599i
$11$	13.3667	+	9.71148i	1.21515	+	0.882861i	0.995689	−	0.0927588i	$-0.0295685\pi$
$11$	13.3667	+	9.71148i	1.21515	+	0.882861i	0.219466	+	0.975620i	$0.429569\pi$
$12$	3.42145	+	0.541905i	0.285121	+	0.0451587i
$13$	−1.86256	+	11.7598i	−0.143274	+	0.904597i	0.806403	+	0.591366i	$0.201411\pi$
$13$	−1.86256	+	11.7598i	−0.143274	+	0.904597i	−0.949677	+	0.313230i	$0.898589\pi$
$14$	−11.0032	+	15.1446i	−0.785941	+	1.08175i
$15$	−1.45512	+	8.53713i	−0.0970077	+	0.569142i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	17.3995	−	8.86551i	1.02350	−	0.521500i	0.140110	−	0.990136i	$-0.455254\pi$
$17$	17.3995	−	8.86551i	1.02350	−	0.521500i	0.883392	+	0.468636i	$0.155254\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	−16.4119	−	5.33255i	−0.863785	−	0.280661i	−0.156577	−	0.987666i	$-0.550046\pi$
$19$	−16.4119	−	5.33255i	−0.863785	−	0.280661i	−0.707209	+	0.707005i	$0.750046\pi$
$20$	5.78244	+	8.15864i	0.289122	+	0.407932i
$21$	−7.08479	−	21.8047i	−0.337371	−	1.03832i
$22$	−10.6079	+	20.8191i	−0.482176	+	0.946324i
$23$	17.1062	−	2.70936i	0.743749	−	0.117798i	0.226952	−	0.973906i	$-0.427124\pi$
$23$	17.1062	−	2.70936i	0.743749	−	0.117798i	0.516798	+	0.856108i	$0.327124\pi$
$24$			4.89898i			0.204124i
$25$	−20.5649	+	14.2156i	−0.822598	+	0.568624i
$26$	−16.8381			−0.647620
$27$	−0.812857	−	5.13218i	−0.0301058	−	0.190081i
$28$	−23.5882	−	12.0188i	−0.842436	−	0.429243i
$29$	7.90234	−	2.56763i	0.272494	−	0.0885388i	−0.169582	−	0.985516i	$-0.554242\pi$
$29$	7.90234	−	2.56763i	0.272494	−	0.0885388i	0.442077	+	0.896977i	$0.354242\pi$
$30$	−12.2466	−	0.143824i	−0.408220	−	0.00479415i
$31$	−0.527352	+	1.62302i	−0.0170114	+	0.0523556i	−0.959202	−	0.282722i	$-0.908763\pi$
$31$	−0.527352	+	1.62302i	−0.0170114	+	0.0523556i	0.942190	+	0.335078i	$0.108763\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−12.9919	−	25.4981i	−0.393695	−	0.772670i
$34$	16.2327	+	22.3424i	0.477432	+	0.657129i
$35$	30.7374	−	58.6136i	0.878212	−	1.67467i
$36$	−4.85410	−	3.52671i	−0.134836	−	0.0979642i
$37$	26.7701	+	4.23997i	0.723516	+	0.114594i	0.507322	−	0.861757i	$-0.330636\pi$
$37$	26.7701	+	4.23997i	0.723516	+	0.114594i	0.216194	+	0.976350i	$0.430636\pi$
$38$	3.81769	−	24.1039i	0.100465	−	0.634314i
$39$	12.1215	−	16.6839i	0.310809	−	0.427791i
$40$	−10.1167	+	9.88188i	−0.252919	+	0.247047i
$41$	−41.3813	+	30.0653i	−1.00930	+	0.733300i	−0.964062	−	0.265676i	$-0.914405\pi$
$41$	−41.3813	+	30.0653i	−1.00930	+	0.733300i	−0.0452386	+	0.998976i	$0.514405\pi$
$42$	28.8895	−	14.7200i	0.687846	−	0.350475i
$43$	16.8295	−	16.8295i	0.391385	−	0.391385i	−0.483796	−	0.875181i	$-0.660742\pi$
$43$	16.8295	−	16.8295i	0.391385	−	0.391385i	0.875181	+	0.483796i	$0.160742\pi$
$44$	−31.4270	−	10.2112i	−0.714250	−	0.232074i
$45$	8.95868	−	12.0309i	0.199082	−	0.267353i
$46$	7.56889	+	23.2946i	0.164541	+	0.506405i
$47$	9.38971	−	18.4284i	0.199781	−	0.392093i	−0.769281	−	0.638911i	$-0.779385\pi$
$47$	9.38971	−	18.4284i	0.199781	−	0.392093i	0.969062	+	0.246819i	$0.0793852\pi$
$48$	−6.84291	+	1.08381i	−0.142561	+	0.0225794i
$49$			126.214i			2.57579i
$50$	−24.4060	−	25.5802i	−0.488120	−	0.511605i
$51$	−33.8234			−0.663204
$52$	−3.72513	−	23.5195i	−0.0716370	−	0.452298i
$53$	−29.4849	−	15.0233i	−0.556319	−	0.283459i	0.153141	−	0.988204i	$-0.451061\pi$
$53$	−29.4849	−	15.0233i	−0.556319	−	0.283459i	−0.709460	+	0.704746i	$0.751061\pi$
$54$	6.98881	−	2.27080i	0.129422	−	0.0420519i
$55$	26.4490	−	78.2623i	0.480891	−	1.42295i
$56$	11.5694	−	35.6070i	0.206597	−	0.635839i
$57$	21.1348	+	21.1348i	0.370786	+	0.370786i
$58$	5.33471	+	10.4700i	0.0919778	+	0.180517i
$59$	−49.9720	−	68.7805i	−0.846983	−	1.16577i	−0.984520	−	0.175275i	$-0.943919\pi$
$59$	−49.9720	−	68.7805i	−0.846983	−	1.16577i	0.137537	−	0.990497i	$-0.456081\pi$
$60$	−2.50844	−	17.1379i	−0.0418074	−	0.285632i
$61$	−62.4364	−	45.3627i	−1.02355	−	0.743651i	−0.0565405	−	0.998400i	$-0.518007\pi$
$61$	−62.4364	−	45.3627i	−1.02355	−	0.743651i	−0.967007	+	0.254749i	$0.918007\pi$
$62$	−2.38371	−	0.377542i	−0.0384469	−	0.00608939i
$63$	−6.21209	+	39.2216i	−0.0986046	+	0.622565i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	58.9041	−	8.62168i	0.906217	−	0.132641i
$66$	32.7416	−	23.7882i	0.496085	−	0.360427i
$67$	49.3261	−	25.1329i	0.736210	−	0.375118i	−0.0453308	−	0.998972i	$-0.514434\pi$
$67$	49.3261	−	25.1329i	0.736210	−	0.375118i	0.781541	+	0.623854i	$0.214434\pi$
$68$	−27.6167	+	27.6167i	−0.406128	+	0.406128i
$69$	−28.5300	−	9.26995i	−0.413478	−	0.134347i
$70$	88.6717	+	29.9669i	1.26674	+	0.428099i
$71$	3.44376	+	10.5988i	0.0485036	+	0.149279i	0.972375	−	0.233424i	$-0.0749932\pi$
$71$	3.44376	+	10.5988i	0.0485036	+	0.149279i	−0.923871	+	0.382703i	$0.874993\pi$
$72$	3.85224	−	7.56044i	0.0535033	−	0.105006i
$73$	15.9934	−	2.53311i	0.219088	−	0.0347001i	−0.0459253	−	0.998945i	$-0.514624\pi$
$73$	15.9934	−	2.53311i	0.219088	−	0.0347001i	0.265013	+	0.964245i	$0.414624\pi$
$74$			38.3305i			0.517980i
$75$	42.9154	−	5.76754i	0.572206	−	0.0769005i
$76$	34.5130			0.454119
$77$	34.2124	+	216.008i	0.444316	+	2.80530i
$78$	25.9857	+	13.2404i	0.333150	+	0.169749i
$79$	−84.5955	+	27.4868i	−1.07083	+	0.347934i	−0.790811	−	0.612061i	$-0.790341\pi$
$79$	−84.5955	+	27.4868i	−1.07083	+	0.347934i	−0.280019	+	0.959994i	$0.590341\pi$
$80$	−16.0412	−	11.9449i	−0.200515	−	0.149311i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−51.1501	−	51.1501i	−0.623782	−	0.623782i
$83$	−48.3016	−	94.7972i	−0.581947	−	1.14214i	−0.974914	−	0.222583i	$-0.928551\pi$
$83$	−48.3016	−	94.7972i	−0.581947	−	1.14214i	0.392967	−	0.919553i	$-0.371449\pi$
$84$	26.9522	+	37.0965i	0.320859	+	0.441624i
$85$	−68.2262	−	69.8478i	−0.802661	−	0.821738i
$86$	27.2308	+	19.7843i	0.316637	+	0.230050i
$87$	−14.2144	−	2.25135i	−0.163384	−	0.0258776i
$88$	7.31045	−	46.1563i	0.0830733	−	0.524504i
$89$	56.1054	−	77.2225i	0.630398	−	0.867669i	−0.367660	−	0.929960i	$-0.619841\pi$
$89$	56.1054	−	77.2225i	0.630398	−	0.867669i	0.998058	+	0.0622918i	$0.0198409\pi$
$90$	18.7867	+	9.85189i	0.208741	+	0.109465i
$91$	−127.503	+	92.6363i	−1.40113	+	1.01798i
$92$	−30.8635	+	15.7257i	−0.335473	+	0.170932i
$93$	2.09008	−	2.09008i	0.0224740	−	0.0224740i
$94$	27.8181	+	9.03864i	0.295937	+	0.0961557i
$95$	−1.01323	+	86.2766i	−0.0106656	+	0.908175i
$96$	−3.02774	−	9.31841i	−0.0315389	−	0.0970668i
$97$	−49.5492	+	97.2457i	−0.510816	+	1.00253i	0.481222	+	0.876599i	$0.340193\pi$
$97$	−49.5492	+	97.2457i	−0.510816	+	1.00253i	−0.992039	+	0.125935i	$0.959807\pi$
$98$	−176.296	+	27.9225i	−1.79894	+	0.284923i
$99$			49.5664i			0.500671i
$100$	30.3311	−	39.7495i	0.303311	−	0.397495i
$101$	−112.180			−1.11069			−0.555347	−	0.831619i	$-0.687414\pi$
$101$	−112.180			−1.11069			−0.555347	+	0.831619i	$0.687414\pi$
$102$	−7.48281	−	47.2446i	−0.0733609	−	0.463183i
$103$	173.466	+	88.3853i	1.68413	+	0.858109i	0.990457	+	0.137823i	$0.0440107\pi$
$103$	173.466	+	88.3853i	1.68413	+	0.858109i	0.693677	+	0.720286i	$0.255989\pi$
$104$	32.0280	−	10.4065i	0.307961	−	0.100063i
$105$	−93.5260	+	66.2867i	−0.890724	+	0.631301i
$106$	14.4616	−	44.5082i	0.136430	−	0.419889i
$107$	49.4555	+	49.4555i	0.462201	+	0.462201i	0.899376	−	0.437176i	$-0.144021\pi$
$107$	49.4555	+	49.4555i	0.462201	+	0.462201i	−0.437176	+	0.899376i	$0.644021\pi$
$108$	4.71801	+	9.25961i	0.0436853	+	0.0857371i
$109$	70.2800	+	96.7321i	0.644771	+	0.887451i	0.998859	−	0.0477614i	$-0.0152087\pi$
$109$	70.2800	+	96.7321i	0.644771	+	0.887451i	−0.354088	+	0.935212i	$0.615209\pi$
$110$	115.168	+	19.6299i	1.04698	+	0.178454i
$111$	−37.9794	−	27.5937i	−0.342157	−	0.248592i
$112$	52.2955	+	8.28279i	0.466924	+	0.0739535i
$113$	13.7637	−	86.9005i	0.121803	−	0.769031i	−0.848866	−	0.528609i	$-0.822714\pi$
$113$	13.7637	−	86.9005i	0.121803	−	0.769031i	0.970668	−	0.240423i	$-0.0772861\pi$
$114$	−24.8455	+	34.1969i	−0.217943	+	0.299972i
$115$	−38.4056	−	77.6152i	−0.333961	−	0.674914i
$116$	−13.4443	+	9.76783i	−0.115899	+	0.0842054i
$117$	−31.8259	+	16.2161i	−0.272016	+	0.138599i
$118$	85.0174	−	85.0174i	0.720487	−	0.720487i
$119$	245.837	+	79.8773i	2.06586	+	0.671238i
$120$	23.3833	−	7.29525i	0.194861	−	0.0607937i
$121$	46.9648	+	144.543i	0.388139	+	1.19457i
$122$	49.5498	−	97.2470i	0.406146	−	0.797106i
$123$	87.5039	−	13.8593i	0.711414	−	0.112677i
$124$		−	3.41309i		−	0.0275250i
$125$	98.4764	+	76.9896i	0.787811	+	0.615917i
$126$	−56.1591			−0.445707
$127$	−13.6546	−	86.2116i	−0.107516	−	0.678832i	−0.981295	−	0.192508i	$-0.938338\pi$
$127$	−13.6546	−	86.2116i	−0.107516	−	0.678832i	0.873779	−	0.486323i	$-0.161662\pi$
$128$	−10.0806	−	5.13632i	−0.0787546	−	0.0401275i
$129$	−39.2062	+	12.7389i	−0.303924	+	0.0987508i
$130$	25.0742	+	80.3700i	0.192879	+	0.618231i
$131$	−8.55490	+	26.3293i	−0.0653045	+	0.200987i	−0.978385	−	0.206794i	$-0.933697\pi$
$131$	−8.55490	+	26.3293i	−0.0653045	+	0.200987i	0.913080	+	0.407780i	$0.133697\pi$
$132$	40.4708	+	40.4708i	0.306597	+	0.306597i
$133$	−103.701	−	203.525i	−0.779708	−	1.53026i
$134$	46.0182	+	63.3386i	0.343419	+	0.472676i
$135$	−23.2859	+	11.5224i	−0.172488	+	0.0853508i
$136$	−44.6848	−	32.4654i	−0.328564	−	0.238716i
$137$	−49.8817	−	7.90049i	−0.364100	−	0.0576678i	−0.0282959	−	0.999600i	$-0.509008\pi$
$137$	−49.8817	−	7.90049i	−0.364100	−	0.0576678i	−0.335804	+	0.941932i	$0.609008\pi$
$138$	6.63655	−	41.9016i	0.0480910	−	0.303634i
$139$	124.008	−	170.682i	0.892142	−	1.22793i	−0.0807648	−	0.996733i	$-0.525736\pi$
$139$	124.008	−	170.682i	0.892142	−	1.22793i	0.972907	−	0.231196i	$-0.0742637\pi$
$140$	−22.2408	+	130.486i	−0.158863	+	0.932046i
$141$	−28.9817	+	21.0564i	−0.205544	+	0.149336i
$142$	−14.0426	+	7.15504i	−0.0988913	+	0.0503876i
$143$	−139.101	+	139.101i	−0.972734	+	0.972734i
$144$	11.4127	+	3.70820i	0.0792547	+	0.0257514i
$145$	−24.0232	−	33.8951i	−0.165677	−	0.233759i
$146$	7.07651	+	21.7792i	0.0484692	+	0.149173i
$147$	99.2463	−	194.782i	0.675145	−	1.32505i
$148$	−53.5402	+	8.47993i	−0.361758	+	0.0572969i
$149$		−	284.172i		−	1.90719i	−0.301086	−	0.953597i	$-0.597349\pi$
$149$		−	284.172i		−	1.90719i	0.301086	−	0.953597i	$-0.402651\pi$
$150$	17.5504	+	58.6684i	0.117002	+	0.391123i
$151$	60.1745			0.398507			0.199253	−	0.979948i	$-0.436148\pi$
$151$	60.1745			0.398507			0.199253	+	0.979948i	$0.436148\pi$
$152$	7.63538	+	48.2079i	0.0502327	+	0.317157i
$153$	52.1986	+	26.5965i	0.341167	+	0.173833i
$154$	−294.152	+	95.5758i	−1.91008	+	0.620622i
$155$	8.53215	+	0.100202i	0.0550461	+	0.000646463i
$156$	−12.7453	+	39.2261i	−0.0817009	+	0.251449i
$157$	−217.264	−	217.264i	−1.38384	−	1.38384i	−0.837674	−	0.546170i	$-0.816085\pi$
$157$	−217.264	−	217.264i	−1.38384	−	1.38384i	−0.546170	−	0.837674i	$-0.683915\pi$
$158$	−57.1088	−	112.082i	−0.361448	−	0.709382i
$159$	33.6898	+	46.3700i	0.211885	+	0.291635i
$160$	13.1359	−	25.0489i	0.0820991	−	0.156556i
$161$	185.471	+	134.753i	1.15199	+	0.836973i
$162$	−12.5712	−	1.99109i	−0.0776001	−	0.0122907i
$163$	14.8260	−	93.6075i	0.0909569	−	0.574279i	−0.899550	−	0.436817i	$-0.856106\pi$
$163$	14.8260	−	93.6075i	0.0909569	−	0.574279i	0.990507	−	0.137462i	$-0.0438944\pi$
$164$	60.1306	−	82.7627i	0.366650	−	0.504650i
$165$	−102.358	+	99.9820i	−0.620353	+	0.605951i
$166$	121.727	−	88.4399i	0.733296	−	0.532771i
$167$	−213.739	+	108.905i	−1.27987	+	0.652127i	−0.955831	−	0.293916i	$-0.905041\pi$
$167$	−213.739	+	108.905i	−1.27987	+	0.652127i	−0.324041	+	0.946043i	$0.605041\pi$
$168$	−45.8537	+	45.8537i	−0.272939	+	0.272939i
$169$	25.9058	+	8.41731i	0.153289	+	0.0498066i
$170$	82.4697	−	110.751i	0.485116	−	0.651477i
$171$	−15.9977	−	49.2358i	−0.0935536	−	0.287928i
$172$	−21.6105	+	42.4129i	−0.125642	+	0.246587i
$173$	97.6521	−	15.4666i	0.564463	−	0.0894021i	0.132320	−	0.991207i	$-0.457757\pi$
$173$	97.6521	−	15.4666i	0.564463	−	0.0894021i	0.432143	+	0.901805i	$0.357757\pi$
$174$		−	20.3528i		−	0.116970i
$175$	−325.541	−	59.4291i	−1.86023	−	0.339595i
$176$	66.0886			0.375503
$177$	23.0357	+	145.442i	0.130145	+	0.821704i
$178$	120.277	+	61.2841i	0.675713	+	0.344293i
$179$	−332.101	+	107.906i	−1.85531	+	0.602828i	−0.859529	+	0.511086i	$0.829243\pi$
$179$	−332.101	+	107.906i	−1.85531	+	0.602828i	−0.995783	+	0.0917412i	$0.970757\pi$
$180$	−9.60492	+	28.4209i	−0.0533607	+	0.157894i
$181$	72.4852	−	223.087i	0.400471	−	1.23252i	−0.524147	−	0.851628i	$-0.675616\pi$
$181$	72.4852	−	223.087i	0.400471	−	1.23252i	0.924618	−	0.380895i	$-0.124384\pi$
$182$	−157.602	−	157.602i	−0.865947	−	0.865947i
$183$	60.6859	+	119.103i	0.331617	+	0.650835i
$184$	−28.7938	−	39.6312i	−0.156488	−	0.215387i
$185$	−19.6265	−	134.090i	−0.106089	−	0.724812i
$186$	3.38183	+	2.45704i	0.0181819	+	0.0132099i
$187$	318.672	+	50.4726i	1.70413	+	0.269907i
$188$	−6.47095	+	40.8560i	−0.0344199	+	0.217319i
$189$	40.4282	−	55.6447i	0.213906	−	0.294416i
$190$	−120.736	+	17.6718i	−0.635450	+	0.0930097i
$191$	242.139	−	175.925i	1.26775	−	0.921071i	0.268636	−	0.963242i	$-0.413427\pi$
$191$	242.139	−	175.925i	1.26775	−	0.921071i	0.999110	+	0.0421705i	$0.0134273\pi$
$192$	12.3461	−	6.29068i	0.0643029	−	0.0327639i
$193$	−163.317	+	163.317i	−0.846204	+	0.846204i	−0.989657	−	0.143453i	$-0.954179\pi$
$193$	−163.317	+	163.317i	−0.846204	+	0.846204i	0.143453	+	0.989657i	$0.454179\pi$
$194$	−146.795	−	47.6966i	−0.756675	−	0.245859i
$195$	−97.6844	−	33.0128i	−0.500945	−	0.169296i
$196$	−78.0044	−	240.073i	−0.397982	−	1.22486i
$197$	−44.0674	+	86.4871i	−0.223692	+	0.439021i	−0.975390	−	0.220487i	$-0.929235\pi$
$197$	−44.0674	+	86.4871i	−0.223692	+	0.439021i	0.751698	+	0.659508i	$0.229235\pi$
$198$	−69.2345	+	10.9657i	−0.349669	+	0.0553822i
$199$		−	256.886i		−	1.29089i	−0.763808	−	0.645443i	$-0.776673\pi$
$199$		−	256.886i		−	1.29089i	0.763808	−	0.645443i	$-0.223327\pi$
$200$	62.2324	+	33.5728i	0.311162	+	0.167864i
$201$	−95.8862			−0.477046
$202$	−24.8178	−	156.693i	−0.122860	−	0.775710i
$203$	97.9974	+	49.9322i	0.482746	+	0.245971i
$204$	64.3360	−	20.9040i	0.315372	−	0.102471i
$205$	205.127	+	152.746i	1.00062	+	0.745102i
$206$	−85.0806	+	261.851i	−0.413012	+	1.27112i
$207$	36.7401	+	36.7401i	0.177489	+	0.177489i
$208$	21.6215	+	42.4345i	0.103949	+	0.204012i
$209$	−167.586	−	230.663i	−0.801848	−	1.10365i
$210$	−113.280	−	115.973i	−0.539430	−	0.552251i
$211$	110.774	+	80.4819i	0.524994	+	0.381431i	0.818482	−	0.574532i	$-0.194816\pi$
$211$	110.774	+	80.4819i	0.524994	+	0.381431i	−0.293488	+	0.955963i	$0.594816\pi$
$212$	65.3685	+	10.3534i	0.308342	+	0.0488366i
$213$	3.01956	−	19.0647i	0.0141763	−	0.0895058i
$214$	−58.1384	+	80.0206i	−0.271675	+	0.373928i
$215$	−105.391	−	55.2676i	−0.490189	−	0.257059i
$216$	−11.8901	+	8.63864i	−0.0550466	+	0.0399937i
$217$	−20.1272	+	10.2553i	−0.0927521	+	0.0472595i
$218$	−119.567	+	119.567i	−0.548475	+	0.548475i
$219$	−26.6740	−	8.66692i	−0.121799	−	0.0395750i
$220$	−1.94023	+	165.210i	−0.00881924	+	0.750955i
$221$	71.8485	+	221.127i	0.325106	+	1.00057i
$222$	30.1406	−	59.1543i	0.135769	−	0.266461i
$223$	201.268	−	31.8778i	0.902549	−	0.142950i	0.312123	−	0.950042i	$-0.398960\pi$
$223$	201.268	−	31.8778i	0.902549	−	0.142950i	0.590426	+	0.807092i	$0.298960\pi$
$224$			74.8788i			0.334281i
$225$	−70.7653	−	24.8450i	−0.314512	−	0.110422i
$226$	124.428			0.550566
$227$	12.3023	+	77.6734i	0.0541949	+	0.342173i	0.999855	+	0.0170170i	$0.00541694\pi$
$227$	12.3023	+	77.6734i	0.0541949	+	0.342173i	−0.945660	+	0.325156i	$0.894583\pi$
$228$	−53.2629	−	27.1388i	−0.233609	−	0.119030i
$229$	75.2866	−	24.4621i	0.328762	−	0.106821i	−0.139985	−	0.990154i	$-0.544705\pi$
$229$	75.2866	−	24.4621i	0.328762	−	0.106821i	0.468747	+	0.883332i	$0.344705\pi$
$230$	99.9165	−	70.8159i	0.434420	−	0.307895i
$231$	117.056	−	360.261i	0.506736	−	1.55957i
$232$	−16.6180	−	16.6180i	−0.0716294	−	0.0716294i
$233$	36.8592	+	72.3402i	0.158194	+	0.310473i	0.956476	−	0.291811i	$-0.0942577\pi$
$233$	36.8592	+	72.3402i	0.158194	+	0.310473i	−0.798282	+	0.602283i	$0.794258\pi$
$234$	−29.6916	−	40.8670i	−0.126887	−	0.174645i
$235$	−101.943	−	17.3757i	−0.433800	−	0.0739392i
$236$	137.561	+	99.9440i	0.582886	+	0.423491i
$237$	152.167	+	24.1010i	0.642057	+	0.101692i
$238$	−57.1858	+	361.057i	−0.240277	+	1.51705i
$239$	136.367	−	187.693i	0.570572	−	0.785324i	−0.422051	−	0.906572i	$-0.638690\pi$
$239$	136.367	−	187.693i	0.570572	−	0.785324i	0.992622	+	0.121248i	$0.0386896\pi$
$240$	15.3631	+	31.0479i	0.0640131	+	0.129366i
$241$	−341.336	+	247.995i	−1.41633	+	1.02902i	−0.423967	+	0.905678i	$0.639363\pi$
$241$	−341.336	+	247.995i	−1.41633	+	1.02902i	−0.992364	+	0.123347i	$0.960637\pi$
$242$	−191.508	+	97.5781i	−0.791354	+	0.403215i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	146.797	+	47.6972i	0.601626	+	0.195480i
$245$	602.431	−	187.950i	2.45890	−	0.767141i
$246$	38.7173	+	119.160i	0.157387	+	0.484388i
$247$	93.2778	−	183.068i	0.377643	−	0.741166i
$248$	4.76742	−	0.755085i	0.0192235	−	0.00304470i
$249$			184.279i			0.740075i
$250$	−85.7531	+	154.585i	−0.343012	+	0.618338i
$251$	−22.2969			−0.0888322			−0.0444161	−	0.999013i	$-0.514143\pi$
$251$	−22.2969			−0.0888322			−0.0444161	+	0.999013i	$0.514143\pi$
$252$	−12.4242	−	78.4432i	−0.0493023	−	0.311283i
$253$	254.966	+	129.912i	1.00777	+	0.513484i
$254$	117.400	−	38.1455i	0.462204	−	0.150179i
$255$	50.3677	+	161.442i	0.197520	+	0.633108i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−133.848	−	133.848i	−0.520810	−	0.520810i	0.397006	−	0.917816i	$-0.370049\pi$
$257$	−133.848	−	133.848i	−0.520810	−	0.520810i	−0.917816	+	0.397006i	$0.870049\pi$
$258$	−26.4673	−	51.9450i	−0.102586	−	0.201337i
$259$	210.879	+	290.250i	0.814204	+	1.12066i
$260$	−106.714	+	52.8041i	−0.410437	+	0.203093i
$261$	20.1664	+	14.6517i	0.0772659	+	0.0561369i
$262$	−38.6694	−	6.12463i	−0.147593	−	0.0233764i
$263$	−7.02668	+	44.3647i	−0.0267174	+	0.168687i	−0.997439	−	0.0715194i	$-0.977215\pi$
$263$	−7.02668	+	44.3647i	−0.0267174	+	0.168687i	0.970722	+	0.240207i	$0.0772152\pi$
$264$	−47.5763	+	65.4832i	−0.180213	+	0.248042i
$265$	−27.8007	+	163.106i	−0.104908	+	0.615494i
$266$	261.342	−	189.876i	0.982490	−	0.713821i
$267$	−147.308	+	75.0574i	−0.551717	+	0.281114i
$268$	−78.2908	+	78.2908i	−0.292130	+	0.292130i
$269$	−207.330	−	67.3656i	−0.770743	−	0.250430i	−0.102860	−	0.994696i	$-0.532799\pi$
$269$	−207.330	−	67.3656i	−0.770743	−	0.250430i	−0.667883	+	0.744266i	$0.732799\pi$
$270$	−21.2461	−	29.9767i	−0.0786891	−	0.111025i
$271$	−60.1563	−	185.142i	−0.221979	−	0.683181i	−0.998584	−	0.0531936i	$-0.983060\pi$
$271$	−60.1563	−	185.142i	−0.221979	−	0.683181i	0.776605	−	0.629988i	$-0.216940\pi$
$272$	35.4620	−	69.5981i	0.130375	−	0.255876i
$273$	269.614	−	42.7027i	0.987599	−	0.156420i
$274$		−	71.4227i		−	0.260667i
$275$	−412.940	−	9.70049i	−1.50160	−	0.0352745i
$276$	59.9964			0.217378
$277$	5.41276	+	34.1748i	0.0195407	+	0.123375i	0.995530	−	0.0944416i	$-0.0301066\pi$
$277$	5.41276	+	34.1748i	0.0195407	+	0.123375i	−0.975990	+	0.217817i	$0.930107\pi$
$278$	265.844	+	135.454i	0.956272	+	0.487245i
$279$	−4.86907	+	1.58206i	−0.0174519	+	0.00567045i
$280$	−187.184	−	2.19830i	−0.668515	−	0.00785106i
$281$	−13.6307	+	41.9511i	−0.0485080	+	0.149292i	−0.972377	−	0.233418i	$-0.925009\pi$
$281$	−13.6307	+	41.9511i	−0.0485080	+	0.149292i	0.923869	+	0.382710i	$0.125009\pi$
$282$	−35.8234	−	35.8234i	−0.127033	−	0.127033i
$283$	83.8653	+	164.595i	0.296344	+	0.581607i	0.990387	−	0.138326i	$-0.0441723\pi$
$283$	83.8653	+	164.595i	0.296344	+	0.581607i	−0.694043	+	0.719934i	$0.744172\pi$
$284$	−13.1008	−	18.0318i	−0.0461297	−	0.0634921i
$285$	69.4060	−	132.351i	0.243530	−	0.464390i
$286$	−225.070	−	163.523i	−0.786958	−	0.571758i
$287$	−668.730	−	105.916i	−2.33007	−	0.369047i
$288$	−2.65478	+	16.7616i	−0.00921799	+	0.0582001i
$289$	54.2767	−	74.7055i	0.187809	−	0.258496i
$290$	42.0301	−	41.0543i	0.144931	−	0.141567i
$291$	152.935	−	111.114i	0.525551	−	0.381835i
$292$	−28.8558	+	14.7027i	−0.0988211	+	0.0503519i
$293$	−160.459	+	160.459i	−0.547642	+	0.547642i	−0.925758	−	0.378116i	$-0.876572\pi$
$293$	−160.459	+	160.459i	−0.547642	+	0.547642i	0.378116	+	0.925758i	$0.376572\pi$
$294$	294.028	+	95.5355i	1.00010	+	0.324951i
$295$	−253.881	+	340.945i	−0.860614	+	1.15575i
$296$	−23.6896	−	72.9090i	−0.0800324	−	0.246314i
$297$	38.9758	−	76.4943i	0.131232	−	0.257557i
$298$	396.932	−	62.8678i	1.33199	−	0.210966i
$299$			206.212i			0.689671i
$300$	−78.0655	+	37.4937i	−0.260218	+	0.124979i
$301$	315.044			1.04666
$302$	13.3125	+	84.0519i	0.0440812	+	0.278318i
$303$	173.124	+	88.2111i	0.571366	+	0.291126i
$304$	−65.6477	+	21.3302i	−0.215946	+	0.0701652i
$305$	−123.544	+	365.566i	−0.405063	+	1.19858i
$306$	−25.6021	+	78.7951i	−0.0836670	+	0.257500i
$307$	407.559	+	407.559i	1.32755	+	1.32755i	0.907498	+	0.420056i	$0.137990\pi$
$307$	407.559	+	407.559i	1.32755	+	1.32755i	0.420056	+	0.907498i	$0.362010\pi$
$308$	−198.576	−	389.728i	−0.644728	−	1.26535i
$309$	−198.204	−	272.804i	−0.641437	−	0.882862i
$310$	1.74762	+	11.9399i	0.00563748	+	0.0385158i
$311$	69.3234	+	50.3664i	0.222905	+	0.161950i	0.693633	−	0.720328i	$-0.256009\pi$
$311$	69.3234	+	50.3664i	0.222905	+	0.161950i	−0.470729	+	0.882278i	$0.656009\pi$
$312$	−57.6108	−	9.12466i	−0.184650	−	0.0292457i
$313$	13.2934	−	83.9311i	0.0424709	−	0.268150i	−0.957310	−	0.289062i	$-0.906657\pi$
$313$	13.2934	−	83.9311i	0.0424709	−	0.268150i	0.999781	+	0.0209112i	$0.00665674\pi$
$314$	255.409	−	351.540i	0.813403	−	1.11955i
$315$	196.459	−	28.7554i	0.623680	−	0.0912869i
$316$	143.923	−	104.566i	0.455451	−	0.330905i
$317$	266.387	−	135.731i	0.840336	−	0.428173i	0.0198254	−	0.999803i	$-0.493689\pi$
$317$	266.387	−	135.731i	0.840336	−	0.428173i	0.820511	+	0.571631i	$0.193689\pi$
$318$	−57.3164	+	57.3164i	−0.180240	+	0.180240i
$319$	130.564	+	42.4227i	0.409290	+	0.132987i
$320$	37.8945	+	12.8066i	0.118420	+	0.0400205i
$321$	−37.4345	−	115.212i	−0.116618	−	0.358915i
$322$	−147.191	+	288.878i	−0.457114	+	0.897137i
$323$	−332.836	+	52.7160i	−1.03045	+	0.163207i
$324$		−	18.0000i		−	0.0555556i
$325$	−128.868	−	268.316i	−0.396518	−	0.825588i
$326$	134.031			0.411138
$327$	−32.3971	−	204.547i	−0.0990737	−	0.625527i
$328$	128.906	+	65.6808i	0.393006	+	0.200246i
$329$	260.373	−	84.6003i	0.791407	−	0.257144i
$330$	−162.300	−	120.855i	−0.491818	−	0.366227i
$331$	−70.2468	+	216.198i	−0.212226	+	0.653165i	0.787113	+	0.616809i	$0.211575\pi$
$331$	−70.2468	+	216.198i	−0.212226	+	0.653165i	−0.999339	+	0.0363557i	$0.988425\pi$
$332$	150.463	+	150.463i	0.453202	+	0.453202i
$333$	36.9146	+	72.4490i	0.110855	+	0.217564i
$334$	−199.405	−	274.457i	−0.597021	−	0.821728i
$335$	−193.415	−	198.012i	−0.577358	−	0.591080i
$336$	−74.1929	−	53.9043i	−0.220812	−	0.160429i
$337$	−377.403	−	59.7747i	−1.11989	−	0.177373i	−0.431078	−	0.902314i	$-0.641867\pi$
$337$	−377.403	−	59.7747i	−1.11989	−	0.177373i	−0.688811	+	0.724941i	$0.741867\pi$
$338$	−6.02613	+	38.0475i	−0.0178288	+	0.112566i
$339$	−89.5740	+	123.288i	−0.264230	+	0.363681i
$340$	172.942	+	90.6922i	0.508654	+	0.266742i
$341$	−22.8109	+	16.5731i	−0.0668941	+	0.0486014i
$342$	65.2334	−	33.2381i	0.190741	−	0.0971874i
$343$	−722.710	+	722.710i	−2.10703	+	2.10703i
$344$	−64.0234	−	20.8025i	−0.186115	−	0.0604723i
$345$	−1.76138	+	149.981i	−0.00510544	+	0.434727i
$346$	43.2075	+	132.979i	0.124877	+	0.384332i
$347$	−107.942	+	211.849i	−0.311073	+	0.610515i	−0.992621	−	0.121258i	$-0.961307\pi$
$347$	−107.942	+	211.849i	−0.311073	+	0.610515i	0.681548	+	0.731773i	$0.261307\pi$
$348$	28.4289	−	4.50269i	0.0816922	−	0.0129388i
$349$			268.339i			0.768879i	0.923150	+	0.384440i	$0.125605\pi$
$349$			268.339i			0.768879i	−0.923150	+	0.384440i	$0.874395\pi$
$350$	10.9907	−	467.864i	0.0314021	−	1.33675i
$351$	61.8672			0.176260
$352$	14.6209	+	92.3127i	0.0415366	+	0.262252i
$353$	−94.8772	−	48.3423i	−0.268774	−	0.136947i	0.314410	−	0.949287i	$-0.398193\pi$
$353$	−94.8772	−	48.3423i	−0.268774	−	0.136947i	−0.583184	+	0.812340i	$0.698193\pi$
$354$	−198.057	+	64.3526i	−0.559483	+	0.181787i
$355$	45.4609	−	32.2205i	0.128059	−	0.0907618i
$356$	−58.9927	+	181.561i	−0.165710	+	0.510003i
$357$	−316.582	−	316.582i	−0.886785	−	0.886785i
$358$	−224.195	−	440.007i	−0.626242	−	1.22907i
$359$	−210.061	−	289.124i	−0.585127	−	0.805358i	0.409119	−	0.912481i	$-0.365836\pi$
$359$	−210.061	−	289.124i	−0.585127	−	0.805358i	−0.994246	+	0.107123i	$0.965836\pi$
$360$	−41.8232	−	7.12858i	−0.116176	−	0.0198016i
$361$	−51.1403	−	37.1556i	−0.141663	−	0.102924i
$362$	327.644	+	51.8937i	0.905094	+	0.143353i
$363$	41.1797	−	259.999i	0.113443	−	0.716250i
$364$	185.273	−	255.006i	0.508991	−	0.700566i
$365$	−35.9072	−	72.5661i	−0.0983758	−	0.198811i
$366$	−152.937	+	111.115i	−0.417862	+	0.303594i
$367$	207.854	−	105.907i	0.566358	−	0.288574i	−0.147272	−	0.989096i	$-0.547049\pi$
$367$	207.854	−	105.907i	0.566358	−	0.288574i	0.713631	+	0.700522i	$0.247049\pi$
$368$	48.9869	−	48.9869i	0.133116	−	0.133116i
$369$	−145.940	−	47.4188i	−0.395501	−	0.128506i
$370$	182.955	−	57.0794i	0.494474	−	0.154269i
$371$	−135.358	−	416.590i	−0.364847	−	1.12288i
$372$	−2.68383	+	5.26732i	−0.00721461	+	0.0141595i
$373$	−621.176	+	98.3846i	−1.66535	+	0.263766i	−0.916811	−	0.399322i	$-0.869245\pi$
$373$	−621.176	+	98.3846i	−1.66535	+	0.263766i	−0.748541	+	0.663088i	$0.769245\pi$
$374$			456.287i			1.22002i
$375$	−91.4360	−	196.251i	−0.243829	−	0.523336i
$376$	−58.4993			−0.155583
$377$	15.4761	+	97.7120i	0.0410505	+	0.259183i
$378$	86.6686	+	44.1599i	0.229282	+	0.116825i
$379$	−406.752	+	132.162i	−1.07323	+	0.348712i	−0.791743	−	0.610854i	$-0.790826\pi$
$379$	−406.752	+	132.162i	−1.07323	+	0.348712i	−0.281482	+	0.959566i	$0.590826\pi$
$380$	−51.3946	−	164.734i	−0.135249	−	0.433511i
$381$	−46.7185	+	143.785i	−0.122621	+	0.377388i
$382$	299.301	+	299.301i	0.783510	+	0.783510i
$383$	43.6902	+	85.7468i	0.114074	+	0.223882i	0.940984	−	0.338452i	$-0.109903\pi$
$383$	43.6902	+	85.7468i	0.114074	+	0.223882i	−0.826910	+	0.562334i	$0.809903\pi$
$384$	11.5182	+	15.8534i	0.0299953	+	0.0412850i
$385$	980.082	−	484.965i	2.54567	−	1.25965i
$386$	−264.253	−	191.991i	−0.684594	−	0.497386i
$387$	70.5226	+	11.1697i	0.182229	+	0.0288622i
$388$	34.1470	−	215.595i	0.0880076	−	0.555658i
$389$	207.188	−	285.170i	0.532617	−	0.733084i	−0.454910	−	0.890538i	$-0.650328\pi$
$389$	207.188	−	285.170i	0.532617	−	0.733084i	0.987526	+	0.157454i	$0.0503284\pi$
$390$	24.5014	−	143.749i	0.0628241	−	0.368588i
$391$	273.621	−	198.797i	0.699797	−	0.508432i
$392$	318.077	−	162.068i	0.811422	−	0.413440i
$393$	33.9061	−	33.9061i	0.0862751	−	0.0862751i
$394$	−130.554	−	42.4197i	−0.331356	−	0.107664i
$395$	257.171	+	362.851i	0.651067	+	0.918611i
$396$	−30.6337	−	94.2810i	−0.0773580	−	0.238083i
$397$	222.141	−	435.976i	0.559549	−	1.09818i	−0.421934	−	0.906627i	$-0.638649\pi$
$397$	222.141	−	435.976i	0.559549	−	1.09818i	0.981483	−	0.191550i	$-0.0613515\pi$
$398$	358.820	−	56.8314i	0.901557	−	0.142793i
$399$			395.638i			0.991573i
$400$	−33.1267	+	94.3537i	−0.0828168	+	0.235884i
$401$	178.879			0.446082			0.223041	−	0.974809i	$-0.428402\pi$
$401$	178.879			0.446082			0.223041	+	0.974809i	$0.428402\pi$
$402$	−21.2131	−	133.934i	−0.0527688	−	0.333169i
$403$	−18.1041	−	9.22451i	−0.0449234	−	0.0228896i
$404$	213.379	−	69.3311i	0.528166	−	0.171612i
$405$	44.9969	+	0.528445i	0.111103	+	0.00130480i
$406$	−48.0652	+	147.930i	−0.118387	+	0.364358i
$407$	316.652	+	316.652i	0.778014	+	0.778014i
$408$	43.4319	+	85.2400i	0.106451	+	0.208921i
$409$	−31.0344	−	42.7151i	−0.0758786	−	0.104438i	0.769391	−	0.638779i	$-0.220560\pi$
$409$	−31.0344	−	42.7151i	−0.0758786	−	0.104438i	−0.845269	+	0.534341i	$0.820560\pi$
$410$	−167.975	+	320.314i	−0.409696	+	0.781254i
$411$	70.7685	+	51.4163i	0.172186	+	0.125100i
$412$	−384.577	−	60.9110i	−0.933439	−	0.147842i
$413$	176.045	−	1111.51i	0.426260	−	2.69130i
$414$	−43.1906	+	59.4468i	−0.104325	+	0.143591i
$415$	−380.549	+	371.714i	−0.916985	+	0.895697i
$416$	−54.4893	+	39.5888i	−0.130984	+	0.0951653i
$417$	−325.591	+	165.897i	−0.780793	+	0.397834i
$418$	285.115	−	285.115i	0.682092	−	0.682092i
$419$	−0.271832	−	0.0883236i	−0.000648764	−	0.000210796i	0.308693	−	0.951162i	$-0.400109\pi$
$419$	−0.271832	−	0.0883236i	−0.000648764	−	0.000210796i	−0.309341	+	0.950951i	$0.600109\pi$
$420$	136.930	−	183.887i	0.326023	−	0.437826i
$421$	−23.5473	−	72.4712i	−0.0559319	−	0.172141i	0.919188	−	0.393819i	$-0.128846\pi$
$421$	−23.5473	−	72.4712i	−0.0559319	−	0.172141i	−0.975120	+	0.221679i	$0.928846\pi$
$422$	−87.9106	+	172.534i	−0.208319	+	0.408849i
$423$	61.2840	−	9.70642i	0.144879	−	0.0229466i
$424$			93.5974i			0.220748i
$425$	−231.792	+	429.663i	−0.545393	+	1.01097i
$426$	27.2977			0.0640791
$427$	−159.807	−	1008.98i	−0.374256	−	2.36296i
$428$	−124.635	−	63.5047i	−0.291203	−	0.148376i
$429$	324.050	−	105.290i	0.755361	−	0.245432i
$430$	53.8822	−	159.437i	0.125307	−	0.370783i
$431$	−22.2409	+	68.4503i	−0.0516029	+	0.158817i	−0.973537	−	0.228529i	$-0.926608\pi$
$431$	−22.2409	+	68.4503i	−0.0516029	+	0.158817i	0.921934	+	0.387347i	$0.126608\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−129.129	−	253.431i	−0.298220	−	0.585291i	0.692466	−	0.721450i	$-0.256524\pi$
$433$	−129.129	−	253.431i	−0.298220	−	0.585291i	−0.990687	+	0.136159i	$0.956524\pi$
$434$	−18.7774	−	25.8449i	−0.0432660	−	0.0595505i
$435$	10.4213	+	71.1995i	0.0239571	+	0.163677i
$436$	−193.464	−	140.560i	−0.443725	−	0.322385i
$437$	−295.194	−	46.7541i	−0.675501	−	0.106989i
$438$	6.20483	−	39.1757i	0.0141663	−	0.0894423i
$439$	91.8564	−	126.429i	0.209240	−	0.287994i	−0.691479	−	0.722397i	$-0.743040\pi$
$439$	91.8564	−	126.429i	0.209240	−	0.287994i	0.900719	+	0.434403i	$0.143040\pi$
$440$	−231.195	+	33.8396i	−0.525443	+	0.0769082i
$441$	−306.327	+	222.560i	−0.694620	+	0.504671i
$442$	−292.975	+	149.278i	−0.662840	+	0.337734i
$443$	53.6158	−	53.6158i	0.121029	−	0.121029i	−0.643998	−	0.765027i	$-0.722726\pi$
$443$	53.6158	−	53.6158i	0.121029	−	0.121029i	0.765027	+	0.643998i	$0.222726\pi$
$444$	89.2950	+	29.0137i	0.201115	+	0.0653462i
$445$	−452.139	−	152.802i	−1.01604	−	0.343375i
$446$	89.0540	+	274.080i	0.199673	+	0.614529i
$447$	−223.454	+	438.554i	−0.499897	+	0.981104i
$448$	−104.591	+	16.5656i	−0.233462	+	0.0369767i
$449$			417.651i			0.930180i	0.885263	+	0.465090i	$0.153978\pi$
$449$			417.651i			0.930180i	−0.885263	+	0.465090i	$0.846022\pi$
$450$	19.0481	−	104.342i	0.0423291	−	0.231870i
$451$	−845.110			−1.87386
$452$	27.5274	+	173.801i	0.0609013	+	0.384516i
$453$	−92.8655	−	47.3173i	−0.205001	−	0.104453i
$454$	−105.773	+	34.3676i	−0.232979	+	0.0756996i
$455$	632.032	+	470.636i	1.38908	+	1.03437i
$456$	26.1241	−	80.4016i	0.0572896	−	0.176319i
$457$	123.448	+	123.448i	0.270127	+	0.270127i	0.829151	−	0.559024i	$-0.188824\pi$
$457$	123.448	+	123.448i	0.270127	+	0.270127i	−0.559024	+	0.829151i	$0.688824\pi$
$458$	50.8245	+	99.7487i	0.110971	+	0.217792i
$459$	−59.6427	−	82.0911i	−0.129941	−	0.178848i
$460$	121.021	+	123.897i	0.263088	+	0.269341i
$461$	196.302	+	142.621i	0.425817	+	0.309374i	0.779974	−	0.625812i	$-0.215232\pi$
$461$	196.302	+	142.621i	0.425817	+	0.309374i	−0.354157	+	0.935186i	$0.615232\pi$
$462$	529.110	+	83.8028i	1.14526	+	0.181391i
$463$	60.5369	−	382.215i	0.130749	−	0.825518i	−0.831932	−	0.554878i	$-0.812765\pi$
$463$	60.5369	−	382.215i	0.130749	−	0.825518i	0.962681	−	0.270640i	$-0.0872352\pi$
$464$	19.5357	−	26.8885i	0.0421027	−	0.0579494i
$465$	−13.0886	−	6.86376i	−0.0281475	−	0.0147608i
$466$	−92.8905	+	67.4889i	−0.199336	+	0.144826i
$467$	380.057	−	193.649i	0.813826	−	0.414665i	0.00303104	−	0.999995i	$-0.499035\pi$
$467$	380.057	−	193.649i	0.813826	−	0.414665i	0.810795	+	0.585330i	$0.199035\pi$
$468$	50.5143	−	50.5143i	0.107937	−	0.107937i
$469$	696.925	+	226.445i	1.48598	+	0.482824i
$470$	1.71742	−	146.238i	0.00365410	−	0.311145i
$471$	164.454	+	506.138i	0.349160	+	1.07460i
$472$	−109.169	+	214.256i	−0.231290	+	0.453933i
$473$	388.395	−	61.5158i	0.821131	−	0.130054i
$474$			217.880i			0.459662i
$475$	413.316	−	123.641i	0.870138	−	0.260298i
$476$	−516.977			−1.08609
$477$	−15.5300	−	98.0527i	−0.0325577	−	0.205561i
$478$	292.338	+	148.954i	0.611586	+	0.311618i
$479$	−469.758	+	152.633i	−0.980705	+	0.318650i	−0.755130	−	0.655576i	$-0.772426\pi$
$479$	−469.758	+	152.633i	−0.980705	+	0.318650i	−0.225575	+	0.974226i	$0.572426\pi$
$480$	−39.9690	+	28.3281i	−0.0832687	+	0.0590168i
$481$	−99.7220	+	306.913i	−0.207322	+	0.638072i
$482$	−421.914	−	421.914i	−0.875340	−	0.875340i
$483$	−180.271	−	353.802i	−0.373232	−	0.732509i
$484$	−178.665	−	245.911i	−0.369142	−	0.508081i
$485$	537.949	+	91.6910i	1.10917	+	0.189054i
$486$	17.8351	+	12.9580i	0.0366978	+	0.0266625i
$487$	578.613	+	91.6434i	1.18812	+	0.188179i	0.719034	−	0.694975i	$-0.244584\pi$
$487$	578.613	+	91.6434i	1.18812	+	0.188179i	0.469083	+	0.883154i	$0.344584\pi$
$488$	−34.1474	+	215.598i	−0.0699742	+	0.441800i
$489$	−96.4873	+	132.803i	−0.197315	+	0.271581i
$490$	395.805	+	799.896i	0.807766	+	1.63244i
$491$	−558.175	+	405.538i	−1.13681	+	0.825943i	−0.986672	−	0.162722i	$-0.947973\pi$
$491$	−558.175	+	405.538i	−1.13681	+	0.825943i	−0.150141	+	0.988665i	$0.547973\pi$
$492$	−157.877	+	80.4423i	−0.320888	+	0.163501i
$493$	114.734	−	114.734i	0.232726	−	0.232726i
$494$	276.346	+	89.7902i	0.559404	+	0.181761i
$495$	236.586	−	73.8112i	0.477951	−	0.149114i
$496$	2.10941	+	6.49209i	0.00425284	+	0.0130889i
$497$	−66.9701	+	131.436i	−0.134749	+	0.264459i
$498$	−257.401	+	40.7683i	−0.516870	+	0.0818641i
$499$			481.490i			0.964910i	0.875921	+	0.482455i	$0.160255\pi$
$499$			481.490i			0.964910i	−0.875921	+	0.482455i	$0.839745\pi$
$500$	−234.895	−	85.5811i	−0.469791	−	0.171162i
$501$	415.492			0.829326
$502$	−4.93278	−	31.1443i	−0.00982625	−	0.0620405i
$503$	94.3709	+	48.0844i	0.187616	+	0.0955952i	0.545275	−	0.838257i	$-0.316425\pi$
$503$	94.3709	+	48.0844i	0.187616	+	0.0955952i	−0.357659	+	0.933852i	$0.616425\pi$
$504$	106.821	−	34.7083i	0.211946	−	0.0688656i
$505$	167.051	+	535.446i	0.330795	+	1.06029i
$506$	−125.054	+	384.877i	−0.247143	+	0.760627i
$507$	−33.3608	−	33.3608i	−0.0658004	−	0.0658004i
$508$	79.2543	+	155.545i	0.156012	+	0.306191i
$509$	75.2148	+	103.524i	0.147770	+	0.203388i	0.876485	−	0.481429i	$-0.159882\pi$
$509$	75.2148	+	103.524i	0.147770	+	0.203388i	−0.728715	+	0.684817i	$0.759882\pi$
$510$	−214.360	+	106.070i	−0.420314	+	0.207980i
$511$	173.406	+	125.987i	0.339346	+	0.246549i
$512$	22.3488	+	3.53971i	0.0436501	+	0.00691349i
$513$	−14.0271	+	88.5635i	−0.0273432	+	0.172638i
$514$	157.348	−	216.571i	0.306125	−	0.421344i
$515$	163.557	−	959.587i	0.317587	−	1.86328i
$516$	66.7015	−	48.4615i	0.129266	−	0.0939176i
$517$	304.476	−	155.138i	0.588928	−	0.300074i
$518$	−358.768	+	358.768i	−0.692603	+	0.692603i
$519$	−162.865	−	52.9181i	−0.313806	−	0.101962i
$520$	−97.3654	−	137.376i	−0.187241	−	0.264185i
$521$	−10.3159	−	31.7492i	−0.0198003	−	0.0609389i	0.940668	−	0.339328i	$-0.110200\pi$
$521$	−10.3159	−	31.7492i	−0.0198003	−	0.0609389i	−0.960468	+	0.278389i	$0.910200\pi$
$522$	−16.0041	+	31.4099i	−0.0306593	+	0.0601722i
$523$	450.408	−	71.3376i	0.861201	−	0.136401i	0.289815	−	0.957083i	$-0.406406\pi$
$523$	450.408	−	71.3376i	0.861201	−	0.136401i	0.571386	+	0.820682i	$0.306406\pi$
$524$		−	55.3684i		−	0.105665i
$525$	455.666	+	347.699i	0.867935	+	0.662284i
$526$	−63.5233			−0.120767
$527$	5.21324	+	32.9151i	0.00989229	+	0.0624575i
$528$	−101.992	−	51.9677i	−0.193168	−	0.0984238i
$529$	−217.826	+	70.7760i	−0.411770	+	0.133792i
$530$	−233.977	−	2.74784i	−0.441467	−	0.00518460i
$531$	78.8155	−	242.569i	0.148428	−	0.456816i
$532$	323.037	+	323.037i	0.607212	+	0.607212i
$533$	−276.485	−	542.633i	−0.518734	−	1.01807i
$534$	−137.430	−	189.156i	−0.257359	−	0.354224i
$535$	162.410	−	309.702i	0.303570	−	0.578882i
$536$	−126.677	−	92.0363i	−0.236338	−	0.171710i
$537$	597.371	+	94.6143i	1.11242	+	0.176191i
$538$	48.2284	−	304.502i	0.0896439	−	0.565990i
$539$	−1225.72	+	1687.06i	−2.27407	+	3.12998i
$540$	37.1713	−	36.3083i	0.0688357	−	0.0672377i
$541$	−98.7081	+	71.7156i	−0.182455	+	0.132561i	−0.675264	−	0.737576i	$-0.735970\pi$
$541$	−98.7081	+	71.7156i	−0.182455	+	0.132561i	0.492809	+	0.870138i	$0.335970\pi$
$542$	245.298	−	124.986i	0.452580	−	0.230601i
$543$	−287.285	+	287.285i	−0.529070	+	0.529070i
$544$	105.060	+	34.1361i	0.193125	+	0.0627502i
$545$	357.056	−	479.501i	0.655148	−	0.879818i
$546$	119.295	+	367.151i	0.218488	+	0.672437i
$547$	71.3632	−	140.058i	0.130463	−	0.256048i	−0.816530	−	0.577304i	$-0.804105\pi$
$547$	71.3632	−	140.058i	0.130463	−	0.256048i	0.946992	+	0.321256i	$0.104105\pi$
$548$	99.7634	−	15.8010i	0.182050	−	0.0288339i
$549$		−	231.527i		−	0.421725i
$550$	−77.8057	−	578.941i	−0.141465	−	1.05262i
$551$	−143.385			−0.260226
$552$	13.2731	+	83.8031i	0.0240455	+	0.151817i
$553$	−1049.07	−	534.530i	−1.89706	−	0.966600i
$554$	−46.5380	+	15.1211i	−0.0840037	+	0.0272944i
$555$	−75.1508	+	222.370i	−0.135407	+	0.400667i
$556$	−130.390	+	401.298i	−0.234514	+	0.721758i
$557$	−417.767	−	417.767i	−0.750031	−	0.750031i	0.224454	−	0.974485i	$-0.427940\pi$
$557$	−417.767	−	417.767i	−0.750031	−	0.750031i	−0.974485	+	0.224454i	$0.927940\pi$
$558$	−3.28701	−	6.45112i	−0.00589070	−	0.0115612i
$559$	166.565	+	229.257i	0.297970	+	0.410121i
$560$	−38.3405	−	261.946i	−0.0684652	−	0.467760i
$561$	−452.107	−	328.475i	−0.805895	−	0.585517i
$562$	−61.6130	−	9.75854i	−0.109632	−	0.0173639i
$563$	−119.811	+	756.454i	−0.212807	+	1.34361i	0.617616	+	0.786480i	$0.288099\pi$
$563$	−119.811	+	756.454i	−0.212807	+	1.34361i	−0.830423	+	0.557133i	$0.811901\pi$
$564$	42.1129	−	57.9634i	0.0746682	−	0.102772i
$565$	−435.281	+	63.7113i	−0.770409	+	0.112763i
$566$	−211.353	+	153.557i	−0.373415	+	0.271302i
$567$	−106.147	+	54.0846i	−0.187208	+	0.0953873i
$568$	22.2885	−	22.2885i	0.0392403	−	0.0392403i
$569$	695.480	+	225.975i	1.22229	+	0.397145i	0.847914	−	0.530134i	$-0.177858\pi$
$569$	695.480	+	225.975i	1.22229	+	0.397145i	0.374372	+	0.927279i	$0.377858\pi$
$570$	200.223	+	67.6661i	0.351269	+	0.118713i
$571$	−274.251	−	844.059i	−0.480300	−	1.47821i	−0.838674	−	0.544633i	$-0.816669\pi$
$571$	−274.251	−	844.059i	−0.480300	−	1.47821i	0.358374	−	0.933578i	$-0.383331\pi$
$572$	178.617	−	350.555i	0.312267	−	0.612858i
$573$	−512.022	+	81.0963i	−0.893581	+	0.141529i
$574$		−	957.516i		−	1.66815i
$575$	−313.274	+	298.893i	−0.544824	+	0.519814i
$576$	−24.0000			−0.0416667
$577$	151.676	+	957.643i	0.262870	+	1.65969i	0.667049	+	0.745014i	$0.267557\pi$
$577$	151.676	+	957.643i	0.262870	+	1.65969i	−0.404179	+	0.914680i	$0.632443\pi$
$578$	116.357	+	59.2866i	0.201309	+	0.102572i
$579$	380.465	−	123.620i	0.657107	−	0.213507i
$580$	66.6432	+	49.6252i	0.114902	+	0.0855606i
$581$	435.192	−	1339.38i	0.749040	−	2.30531i
$582$	189.039	+	189.039i	0.324808	+	0.324808i
$583$	−248.217	−	487.154i	−0.425759	−	0.835598i
$584$	−26.9206	−	37.0531i	−0.0460970	−	0.0634470i
$585$	124.794	+	127.760i	0.213323	+	0.218393i
$586$	−259.628	−	188.631i	−0.443051	−	0.321896i
$587$	865.425	+	137.070i	1.47432	+	0.233509i	0.841275	−	0.540607i	$-0.181805\pi$
$587$	865.425	+	137.070i	1.47432	+	0.233509i	0.633043	+	0.774116i	$0.281805\pi$
$588$	−68.3959	+	431.835i	−0.116320	+	0.734412i
$589$	17.3097	−	23.8248i	0.0293883	−	0.0404495i
$590$	−532.399	−	279.194i	−0.902371	−	0.473210i
$591$	136.016	−	98.8211i	0.230145	−	0.167210i
$592$	96.5986	−	49.2195i	0.163173	−	0.0831410i
$593$	−370.077	+	370.077i	−0.624076	+	0.624076i	−0.946571	−	0.322495i	$-0.895478\pi$
$593$	−370.077	+	370.077i	−0.624076	+	0.624076i	0.322495	+	0.946571i	$0.395478\pi$
$594$	115.470	+	37.5185i	0.194394	+	0.0631625i
$595$	15.1774	−	1292.35i	0.0255083	−	2.17202i
$596$	175.628	+	540.527i	0.294678	+	0.906925i
$597$	−201.999	+	396.445i	−0.338356	+	0.664062i
$598$	−288.037	+	45.6205i	−0.481667	+	0.0762885i
$599$			597.708i			0.997843i	0.866647	+	0.498922i	$0.166270\pi$
$599$			597.708i			0.997843i	−0.866647	+	0.498922i	$0.833730\pi$
$600$	−69.6419	−	100.747i	−0.116070	−	0.167912i
$601$	672.379			1.11877			0.559383	−	0.828909i	$-0.311038\pi$
$601$	672.379			1.11877			0.559383	+	0.828909i	$0.311038\pi$
$602$	69.6978	+	440.054i	0.115777	+	0.730987i
$603$	147.978	+	75.3986i	0.245403	+	0.125039i
$604$	−114.459	+	37.1899i	−0.189501	+	0.0615727i
$605$	619.981	−	439.412i	1.02476	−	0.726301i
$606$	−84.9129	+	261.335i	−0.140120	+	0.431246i
$607$	457.570	+	457.570i	0.753822	+	0.753822i	0.975190	−	0.221368i	$-0.0710523\pi$
$607$	457.570	+	457.570i	0.753822	+	0.753822i	−0.221368	+	0.975190i	$0.571052\pi$
$608$	−44.3174	−	86.9779i	−0.0728905	−	0.143056i
$609$	−111.973	−	154.117i	−0.183864	−	0.253066i
$610$	−537.956	−	91.6922i	−0.881895	−	0.150315i
$611$	199.224	+	144.745i	0.326062	+	0.236898i
$612$	−115.725	−	18.3291i	−0.189093	−	0.0299495i
$613$	12.0102	−	75.8294i	0.0195925	−	0.123702i	−0.975954	−	0.217979i	$-0.930054\pi$
$613$	12.0102	−	75.8294i	0.0195925	−	0.123702i	0.995546	+	0.0942764i	$0.0300537\pi$
$614$	−479.115	+	659.445i	−0.780317	+	1.07401i
$615$	−196.457	−	397.026i	−0.319442	−	0.645572i
$616$	500.441	−	363.592i	0.812405	−	0.590247i
$617$	−81.3611	+	41.4556i	−0.131866	+	0.0671889i	−0.518679	−	0.854969i	$-0.673576\pi$
$617$	−81.3611	+	41.4556i	−0.131866	+	0.0671889i	0.386813	+	0.922158i	$0.373576\pi$
$618$	337.205	−	337.205i	0.545639	−	0.545639i
$619$	280.924	+	91.2779i	0.453836	+	0.147460i	0.527010	−	0.849859i	$-0.323313\pi$
$619$	280.924	+	91.2779i	0.453836	+	0.147460i	−0.0731744	+	0.997319i	$0.523313\pi$
$620$	−16.2910	+	5.08256i	−0.0262759	+	0.00819768i
$621$	−27.8099	−	85.5899i	−0.0447824	−	0.137826i
$622$	−55.0153	+	107.974i	−0.0884491	+	0.173591i
$623$	1247.93	−	197.653i	2.00310	−	0.317260i
$624$		−	82.4896i		−	0.132195i
$625$	220.834	−	584.686i	0.353335	−	0.935497i
$626$	120.176			0.191974
$627$	77.2525	+	487.753i	0.123210	+	0.777916i
$628$	547.536	+	278.984i	0.871873	+	0.444241i
$629$	503.377	−	163.557i	0.800281	−	0.260027i
$630$	83.6286	+	268.053i	0.132744	+	0.425481i
$631$	109.118	−	335.832i	0.172929	−	0.532222i	−0.826604	−	0.562785i	$-0.809730\pi$
$631$	109.118	−	335.832i	0.172929	−	0.532222i	0.999533	+	0.0305630i	$0.00973003\pi$
$632$	177.898	+	177.898i	0.281484	+	0.281484i
$633$	−107.668	−	211.310i	−0.170092	−	0.333824i
$634$	248.522	+	342.061i	0.391991	+	0.539529i
$635$	−391.163	+	193.556i	−0.616005	+	0.304812i
$636$	−92.7400	−	67.3795i	−0.145818	−	0.105943i
$637$	−1484.24	−	235.081i	−2.33005	−	0.369044i
$638$	−30.3713	+	191.757i	−0.0476039	+	0.300559i
$639$	−19.6513	+	27.0476i	−0.0307531	+	0.0423281i
$640$	−9.50478	+	55.7643i	−0.0148512	+	0.0871317i
$641$	−121.108	+	87.9903i	−0.188936	+	0.137270i	−0.678232	−	0.734847i	$-0.737254\pi$
$641$	−121.108	+	87.9903i	−0.188936	+	0.137270i	0.489296	+	0.872118i	$0.337254\pi$
$642$	152.646	−	77.7771i	0.237767	−	0.121148i
$643$	−322.059	+	322.059i	−0.500870	+	0.500870i	−0.911708	−	0.410838i	$-0.865236\pi$
$643$	−322.059	+	322.059i	−0.500870	+	0.500870i	0.410838	+	0.911708i	$0.365236\pi$
$644$	−436.069	−	141.687i	−0.677125	−	0.220011i
$645$	119.187	+	168.165i	0.184786	+	0.260721i
$646$	−147.268	−	453.243i	−0.227968	−	0.701615i
$647$	549.370	−	1078.20i	0.849103	−	1.66646i	0.108922	−	0.994050i	$-0.465260\pi$
$647$	549.370	−	1078.20i	0.849103	−	1.66646i	0.740181	−	0.672408i	$-0.234740\pi$
$648$	25.1424	−	3.98217i	0.0388001	−	0.00614533i
$649$		−	1404.67i		−	2.16436i
$650$	346.275	−	239.364i	0.532731	−	0.368252i
$651$	39.1258			0.0601010
$652$	29.6519	+	187.215i	0.0454784	+	0.287140i
$653$	314.418	+	160.204i	0.481497	+	0.245335i	0.677853	−	0.735198i	$-0.262911\pi$
$653$	314.418	+	160.204i	0.481497	+	0.245335i	−0.196355	+	0.980533i	$0.562911\pi$
$654$	278.545	−	90.5047i	0.425909	−	0.138386i
$655$	138.412	+	1.62551i	0.211315	+	0.00248169i
$656$	−63.2251	+	194.587i	−0.0963797	+	0.296626i
$657$	34.3501	+	34.3501i	0.0522832	+	0.0522832i
$658$	175.773	+	344.973i	0.267132	+	0.524276i
$659$	−422.373	−	581.347i	−0.640931	−	0.882166i	0.357734	−	0.933824i	$-0.383549\pi$
$659$	−422.373	−	581.347i	−0.640931	−	0.882166i	−0.998665	+	0.0516578i	$0.983549\pi$
$660$	132.905	−	253.438i	0.201371	−	0.383997i
$661$	630.225	+	457.886i	0.953442	+	0.692716i	0.951619	−	0.307282i	$-0.0994194\pi$
$661$	630.225	+	457.886i	0.953442	+	0.692716i	0.00182387	+	0.999998i	$0.499419\pi$
$662$	−317.526	−	50.2912i	−0.479647	−	0.0759686i
$663$	62.9982	−	397.755i	0.0950199	−	0.599932i
$664$	−176.880	+	243.454i	−0.266385	+	0.366648i
$665$	−817.020	+	798.053i	−1.22860	+	1.20008i
$666$	−93.0302	+	67.5904i	−0.139685	+	0.101487i
$667$	128.223	−	65.3327i	0.192238	−	0.0979501i
$668$	339.248	−	339.248i	0.507856	−	0.507856i
$669$	−335.678	−	109.068i	−0.501761	−	0.163032i
$670$	233.794	−	313.969i	0.348946	−	0.468610i
$671$	−394.030	−	1212.70i	−0.587228	−	1.80730i
$672$	58.8798	−	115.558i	0.0876188	−	0.171962i
$673$	−263.860	+	41.7914i	−0.392066	+	0.0620972i	−0.349355	−	0.936990i	$-0.613599\pi$
$673$	−263.860	+	41.7914i	−0.392066	+	0.0620972i	−0.0427107	+	0.999087i	$0.513599\pi$
$674$		−	540.381i		−	0.801752i
$675$	89.6733	+	93.9877i	0.132849	+	0.139241i
$676$	−54.4780			−0.0805887
$677$	44.1844	+	278.969i	0.0652650	+	0.412067i	0.998592	+	0.0530404i	$0.0168912\pi$
$677$	44.1844	+	278.969i	0.0652650	+	0.412067i	−0.933327	+	0.359026i	$0.883109\pi$
$678$	−192.026	−	97.8419i	−0.283224	−	0.144310i
$679$	−1373.98	+	446.433i	−2.02353	+	0.657486i
$680$	−88.4188	+	261.630i	−0.130028	+	0.384750i
$681$	42.0916	−	129.545i	0.0618085	−	0.190227i
$682$	−28.1958	−	28.1958i	−0.0413428	−	0.0413428i
$683$	360.074	+	706.685i	0.527194	+	1.03468i	0.989030	+	0.147712i	$0.0471909\pi$
$683$	360.074	+	706.685i	0.527194	+	1.03468i	−0.461836	+	0.886965i	$0.652809\pi$
$684$	60.8587	+	83.7649i	0.0889748	+	0.122463i
$685$	36.5709	+	249.855i	0.0533881	+	0.364752i
$686$	−1169.37	−	849.596i	−1.70462	−	1.23848i
$687$	−135.423	−	21.4489i	−0.197122	−	0.0312211i
$688$	14.8929	−	94.0302i	0.0216467	−	0.136672i
$689$	231.588	−	318.753i	0.336122	−	0.462632i
$690$	−209.883	+	30.7202i	−0.304178	+	0.0445220i
$691$	−121.653	+	88.3864i	−0.176054	+	0.127911i	−0.672323	−	0.740258i	$-0.734703\pi$
$691$	−121.653	+	88.3864i	−0.176054	+	0.127911i	0.496268	+	0.868169i	$0.334703\pi$
$692$	−176.186	+	89.7715i	−0.254605	+	0.129728i
$693$	−463.935	+	463.935i	−0.669459	+	0.669459i
$694$	−319.791	−	103.906i	−0.460794	−	0.149721i
$695$	−999.347	−	337.733i	−1.43791	−	0.485946i
$696$	12.5787	+	38.7134i	0.0180729	+	0.0556227i
$697$	−453.472	+	889.989i	−0.650605	+	1.27688i
$698$	−374.816	+	59.3651i	−0.536986	+	0.0850502i
$699$		−	140.624i		−	0.201179i
$700$	655.945	−	88.1544i	0.937064	−	0.125935i
$701$	−965.298			−1.37703			−0.688515	−	0.725222i	$-0.741737\pi$
$701$	−965.298			−1.37703			−0.688515	+	0.725222i	$0.741737\pi$
$702$	13.6870	+	86.4162i	0.0194971	+	0.123100i
$703$	−416.739	−	212.339i	−0.592801	−	0.302047i
$704$	−125.708	+	40.8450i	−0.178562	+	0.0580185i
$705$	143.662	+	106.977i	0.203776	+	0.151740i
$706$	46.5348	−	143.220i	0.0659134	−	0.202861i
$707$	−1049.99	−	1049.99i	−1.48513	−	1.48513i
$708$	−133.704	−	262.409i	−0.188848	−	0.370635i
$709$	484.225	+	666.478i	0.682968	+	0.940025i	0.999965	−	0.00840133i	$-0.00267426\pi$
$709$	484.225	+	666.478i	0.682968	+	0.940025i	−0.316996	+	0.948427i	$0.602674\pi$
$710$	55.0630	+	56.3717i	0.0775535	+	0.0793967i
$711$	−215.884	−	156.849i	−0.303634	−	0.220603i
$712$	−266.656	−	42.2341i	−0.374517	−	0.0593176i
$713$	−4.62365	+	29.1926i	−0.00648479	+	0.0409433i
$714$	372.165	−	512.241i	0.521239	−	0.717424i
$715$	871.083	+	456.802i	1.21830	+	0.638884i
$716$	565.004	−	410.499i	0.789111	−	0.573323i
$717$	−358.039	+	182.430i	−0.499358	+	0.254435i
$718$	357.376	−	357.376i	0.497739	−	0.497739i
$719$	834.750	+	271.227i	1.16099	+	0.377228i	0.825272	−	0.564736i	$-0.191022\pi$
$719$	834.750	+	271.227i	1.16099	+	0.377228i	0.335715	+	0.941963i	$0.391022\pi$
$720$	0.704593	−	59.9959i	0.000978602	−	0.0833276i
$721$	796.342	+	2450.89i	1.10450	+	3.39929i
$722$	40.5851	−	79.6528i	0.0562121	−	0.110322i
$723$	721.779	−	114.319i	0.998312	−	0.158117i
$724$			469.134i			0.647976i
$725$	−126.011	+	165.139i	−0.173808	+	0.227779i
$726$	372.277			0.512778
$727$	−167.881	−	1059.96i	−0.230922	−	1.45799i	−0.781867	−	0.623445i	$-0.785733\pi$
$727$	−167.881	−	1059.96i	−0.230922	−	1.45799i	0.550945	−	0.834542i	$-0.314267\pi$
$728$	397.181	+	202.374i	0.545578	+	0.277986i
$729$	−25.6785	+	8.34346i	−0.0352243	+	0.0114451i
$730$	93.4166	−	66.2091i	0.127968	−	0.0906974i
$731$	143.624	−	442.029i	0.196476	−	0.604690i
$732$	−189.041	−	189.041i	−0.258253	−	0.258253i
$733$	−79.9973	−	157.004i	−0.109137	−	0.214193i	0.829978	−	0.557796i	$-0.188353\pi$
$733$	−79.9973	−	157.004i	−0.109137	−	0.214193i	−0.939115	+	0.343602i	$0.888353\pi$
$734$	193.914	+	266.900i	0.264189	+	0.363625i
$735$	−1077.50	−	183.656i	−1.46599	−	0.249872i
$736$	79.2624	+	57.5875i	0.107693	+	0.0782439i
$737$	903.404	+	143.085i	1.22579	+	0.194145i
$738$	33.9481	−	214.340i	0.0460001	−	0.290433i
$739$	166.726	−	229.478i	0.225610	−	0.310525i	−0.681174	−	0.732122i	$-0.738530\pi$
$739$	166.726	−	229.478i	0.225610	−	0.310525i	0.906784	+	0.421597i	$0.138530\pi$
$740$	120.204	+	242.925i	0.162438	+	0.328277i
$741$	−287.905	+	209.175i	−0.388536	+	0.282288i
$742$	551.949	−	281.232i	0.743866	−	0.379019i
$743$	414.648	−	414.648i	0.558072	−	0.558072i	−0.370686	−	0.928758i	$-0.620877\pi$
$743$	414.648	−	414.648i	0.558072	−	0.558072i	0.928758	+	0.370686i	$0.120877\pi$
$744$	−7.95115	−	2.58349i	−0.0106870	−	0.00347243i
$745$	−1356.38	+	423.171i	−1.82064	+	0.568014i
$746$	−274.848	−	845.895i	−0.368429	−	1.13391i
$747$	144.905	−	284.392i	0.193982	−	0.380712i
$748$	−637.343	+	100.945i	−0.852063	+	0.134953i
$749$			925.792i			1.23604i
$750$	253.895	−	171.135i	0.338527	−	0.228180i
$751$	−660.553			−0.879564			−0.439782	−	0.898104i	$-0.644944\pi$
$751$	−660.553			−0.879564			−0.439782	+	0.898104i	$0.644944\pi$
$752$	−12.9419	−	81.7119i	−0.0172100	−	0.108659i
$753$	34.4101	+	17.5328i	0.0456973	+	0.0232839i
$754$	−133.060	+	43.2340i	−0.176473	+	0.0573395i
$755$	−89.6081	−	287.219i	−0.118686	−	0.380423i
$756$	−42.5088	+	130.828i	−0.0562285	+	0.173054i
$757$	229.345	+	229.345i	0.302965	+	0.302965i	0.842173	−	0.539208i	$-0.181276\pi$
$757$	229.345	+	229.345i	0.302965	+	0.302965i	−0.539208	+	0.842173i	$0.681276\pi$
$758$	−274.590	−	538.914i	−0.362257	−	0.710969i
$759$	−291.327	−	400.977i	−0.383830	−	0.528296i
$760$	218.731	−	108.232i	0.287804	−	0.142411i
$761$	290.376	+	210.971i	0.381572	+	0.277228i	0.761993	−	0.647585i	$-0.224221\pi$
$761$	290.376	+	210.971i	0.381572	+	0.277228i	−0.380421	+	0.924813i	$0.624221\pi$
$762$	−211.175	−	33.4468i	−0.277132	−	0.0438934i
$763$	−247.588	+	1563.21i	−0.324493	+	2.04877i
$764$	−351.849	+	484.279i	−0.460536	+	0.633873i
$765$	49.2170	−	288.755i	0.0643359	−	0.377457i
$766$	−110.106	+	79.9965i	−0.143741	+	0.104434i
$767$	901.918	−	459.550i	1.17590	−	0.599153i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$	−390.772	−	126.969i	−0.508155	−	0.165110i	0.0437078	−	0.999044i	$-0.486083\pi$
$769$	−390.772	−	126.969i	−0.508155	−	0.165110i	−0.551863	+	0.833935i	$0.686083\pi$
$770$	894.225	+	1261.69i	1.16133	+	1.63856i
$771$	101.314	+	311.813i	0.131406	+	0.404427i
$772$	209.712	−	411.584i	0.271648	−	0.533140i
$773$	−1216.56	+	192.684i	−1.57381	+	0.249268i	−0.881449	−	0.472280i	$-0.843431\pi$
$773$	−1216.56	+	192.684i	−1.57381	+	0.249268i	−0.692365	+	0.721548i	$0.743431\pi$
$774$			100.977i			0.130462i
$775$	−12.2273	−	40.8740i	−0.0157771	−	0.0527406i
$776$	308.699			0.397807
$777$	−97.2092	−	613.755i	−0.125108	−	0.789903i
$778$	444.162	+	226.312i	0.570903	+	0.290889i
$779$	839.472	−	272.761i	1.07763	−	0.350142i
$780$	206.210	+	2.42173i	0.264371	+	0.00310479i
$781$	−56.8983	+	175.115i	−0.0728531	+	0.224219i
$782$	338.214	+	338.214i	0.432498	+	0.432498i
$783$	−19.6010	−	38.4691i	−0.0250332	−	0.0491304i
$784$	296.746	+	408.436i	0.378503	+	0.520965i
$785$	−713.486	+	1360.56i	−0.908899	+	1.73319i
$786$	54.8612	+	39.8590i	0.0697980	+	0.0507112i
$787$	−904.418	−	143.246i	−1.14920	−	0.182015i	−0.447361	−	0.894354i	$-0.647636\pi$
$787$	−904.418	−	143.246i	−1.14920	−	0.182015i	−0.701836	+	0.712339i	$0.747636\pi$
$788$	30.3692	−	191.743i	0.0385395	−	0.243329i
$789$	45.7296	−	62.9414i	0.0579589	−	0.0797736i
$790$	−449.937	+	439.492i	−0.569541	+	0.556319i
$791$	942.203	−	684.550i	1.19115	−	0.865424i
$792$	124.915	−	63.6472i	0.157721	−	0.0803627i
$793$	649.746	−	649.746i	0.819352	−	0.819352i
$794$	658.117	+	213.835i	0.828863	+	0.269314i
$795$	171.160	−	229.856i	0.215295	−	0.289127i
$796$	158.765	+	488.627i	0.199453	+	0.613853i
$797$	−9.14721	+	17.9524i	−0.0114771	+	0.0225250i	−0.896674	−	0.442692i	$-0.854024\pi$
$797$	−9.14721	+	17.9524i	−0.0114771	+	0.0225250i	0.885197	+	0.465217i	$0.154024\pi$
$798$	−552.628	+	87.5276i	−0.692516	+	0.109684i
$799$		−	403.889i		−	0.505494i
$800$	−139.122	−	25.3974i	−0.173903	−	0.0317468i
$801$	286.357			0.357499
$802$	39.5736	+	249.858i	0.0493437	+	0.311544i
$803$	238.380	+	121.460i	0.296861	+	0.151258i
$804$	182.386	−	59.2609i	0.226849	−	0.0737076i
$805$	366.996	−	1085.94i	0.455896	−	1.34899i
$806$	8.87961	−	27.3286i	0.0110169	−	0.0339065i
$807$	266.994	+	266.994i	0.330848	+	0.330848i
$808$	144.048	+	282.710i	0.178277	+	0.349889i
$809$	−391.410	−	538.729i	−0.483819	−	0.665920i	0.495414	−	0.868657i	$-0.335016\pi$
$809$	−391.410	−	538.729i	−0.483819	−	0.665920i	−0.979233	+	0.202737i	$0.935016\pi$
$810$	9.21661	+	62.9687i	0.0113785	+	0.0777391i
$811$	888.046	+	645.204i	1.09500	+	0.795565i	0.980237	−	0.197827i	$-0.0633885\pi$
$811$	888.046	+	645.204i	1.09500	+	0.795565i	0.114765	+	0.993393i	$0.463389\pi$
$812$	−217.262	−	34.4109i	−0.267564	−	0.0423779i
$813$	−52.7463	+	333.027i	−0.0648786	+	0.409627i
$814$	−372.246	+	512.353i	−0.457305	+	0.629426i
$815$	−468.876	+	68.6285i	−0.575308	+	0.0842067i
$816$	−109.455	+	79.5236i	−0.134136	+	0.0974554i
$817$	−365.950	+	186.461i	−0.447919	+	0.228226i
$818$	52.7988	−	52.7988i	0.0645462	−	0.0645462i
$819$	−449.666	−	146.105i	−0.549043	−	0.178395i
$820$	−484.577	−	163.764i	−0.590948	−	0.199713i
$821$	−119.663	−	368.285i	−0.145753	−	0.448581i	0.851354	−	0.524591i	$-0.175782\pi$
$821$	−119.663	−	368.285i	−0.145753	−	0.448581i	−0.997107	+	0.0760103i	$0.975782\pi$
$822$	−56.1622	+	110.224i	−0.0683238	+	0.134093i
$823$	568.232	−	89.9991i	0.690440	−	0.109355i	0.198652	−	0.980070i	$-0.436344\pi$
$823$	568.232	−	89.9991i	0.690440	−	0.109355i	0.491788	+	0.870715i	$0.336344\pi$
$824$		−	550.653i		−	0.668268i
$825$	629.649	+	339.679i	0.763211	+	0.411733i
$826$	1591.50			1.92676
$827$	117.645	+	742.781i	0.142255	+	0.898163i	0.950817	+	0.309753i	$0.100246\pi$
$827$	117.645	+	742.781i	0.142255	+	0.898163i	−0.808562	+	0.588411i	$0.799754\pi$
$828$	−92.5906	−	47.1772i	−0.111824	−	0.0569773i
$829$	−261.936	+	85.1081i	−0.315966	+	0.102664i	−0.462707	−	0.886511i	$-0.653122\pi$
$829$	−261.936	+	85.1081i	−0.315966	+	0.102664i	0.146741	+	0.989175i	$0.453122\pi$
$830$	−603.401	−	449.317i	−0.726989	−	0.541345i
$831$	18.5195	−	56.9972i	0.0222858	−	0.0685887i
$832$	−67.3525	−	67.3525i	−0.0809525	−	0.0809525i
$833$	1118.95	+	2196.06i	1.34328	+	2.63633i
$834$	−303.756	−	418.084i	−0.364216	−	0.501300i
$835$	838.102	+	858.021i	1.00371	+	1.02757i
$836$	461.325	+	335.172i	0.551824	+	0.400924i
$837$	8.75830	+	1.38718i	0.0104639	+	0.00165732i
$838$	0.0632327	−	0.399236i	7.54567e−5	−	0.000476415i
$839$	327.731	−	451.083i	0.390621	−	0.537644i	−0.567738	−	0.823209i	$-0.692181\pi$
$839$	327.731	−	451.083i	0.390621	−	0.537644i	0.958359	+	0.285565i	$0.0921814\pi$
$840$	287.147	+	150.582i	0.341842	+	0.179264i
$841$	−624.529	+	453.747i	−0.742603	+	0.539533i
$842$	96.0185	−	48.9239i	0.114036	−	0.0581044i
$843$	54.0235	−	54.0235i	0.0640849	−	0.0640849i
$844$	−260.445	−	84.6237i	−0.308584	−	0.100265i
$845$	1.59937	−	136.185i	0.00189274	−	0.161166i
$846$	27.1159	+	83.4542i	0.0320519	+	0.0986456i
$847$	−913.317	+	1792.48i	−1.07830	+	2.11627i
$848$	−130.737	+	20.7067i	−0.154171	+	0.0244183i
$849$		−	319.960i		−	0.376867i
$850$	−651.434	−	228.713i	−0.766393	−	0.269074i
$851$	469.423			0.551614
$852$	6.03912	+	38.1295i	0.00708816	+	0.0447529i
$853$	702.428	+	357.905i	0.823479	+	0.419584i	0.814350	−	0.580375i	$-0.197094\pi$
$853$	702.428	+	357.905i	0.823479	+	0.419584i	0.00912957	+	0.999958i	$0.497094\pi$
$854$	1374.00	−	446.439i	1.60890	−	0.522762i
$855$	−211.184	+	149.677i	−0.246999	+	0.175061i
$856$	61.1303	−	188.140i	0.0714139	−	0.219789i
$857$	−149.707	−	149.707i	−0.174687	−	0.174687i	0.614348	−	0.789035i	$-0.289419\pi$
$857$	−149.707	−	149.707i	−0.174687	−	0.174687i	−0.789035	+	0.614348i	$0.789419\pi$
$858$	218.760	+	429.340i	0.254965	+	0.500396i
$859$	−373.194	−	513.658i	−0.434452	−	0.597972i	0.534516	−	0.845158i	$-0.320494\pi$
$859$	−373.194	−	513.658i	−0.434452	−	0.597972i	−0.968968	+	0.247187i	$0.920494\pi$
$860$	234.622	+	39.9903i	0.272816	+	0.0465003i
$861$	948.745	+	689.303i	1.10191	+	0.800585i
$862$	−100.532	−	15.9227i	−0.116626	−	0.0184718i
$863$	96.8260	−	611.335i	0.112197	−	0.708384i	−0.865897	−	0.500222i	$-0.833252\pi$
$863$	96.8260	−	611.335i	0.112197	−	0.708384i	0.978094	−	0.208162i	$-0.0667481\pi$
$864$	17.2773	−	23.7801i	0.0199969	−	0.0275233i
$865$	−219.241	−	443.071i	−0.253457	−	0.512221i
$866$	325.425	−	236.435i	0.375780	−	0.273020i
$867$	−142.507	+	72.6110i	−0.164368	+	0.0837497i
$868$	31.9461	−	31.9461i	0.0368042	−	0.0368042i
$869$	−1397.70	−	454.140i	−1.60840	−	0.522601i
$870$	−97.1461	+	30.3081i	−0.111662	+	0.0348370i
$871$	203.684	+	626.874i	0.233850	+	0.719718i
$872$	153.534	−	301.328i	0.176071	−	0.345559i
$873$	−323.393	+	51.2204i	−0.370439	+	0.0586718i
$874$		−	422.671i		−	0.483605i
$875$	201.114	+	1642.34i	0.229844	+	1.87696i
$876$	56.0935			0.0640336
$877$	−245.221	−	1548.26i	−0.279613	−	1.76541i	−0.582932	−	0.812521i	$-0.698095\pi$
$877$	−245.221	−	1548.26i	−0.279613	−	1.76541i	0.303319	−	0.952889i	$-0.401905\pi$
$878$	196.919	+	100.335i	0.224281	+	0.114277i
$879$	373.806	−	121.457i	0.425263	−	0.138176i
$880$	−98.4149	−	315.447i	−0.111835	−	0.358463i
$881$	−256.051	+	788.044i	−0.290637	+	0.894488i	0.694016	+	0.719960i	$0.255840\pi$
$881$	−256.051	+	788.044i	−0.290637	+	0.894488i	−0.984652	+	0.174528i	$0.944160\pi$
$882$	−378.641	−	378.641i	−0.429299	−	0.429299i
$883$	700.731	+	1375.26i	0.793580	+	1.55749i	0.829745	+	0.558142i	$0.188486\pi$
$883$	700.731	+	1375.26i	0.793580	+	1.55749i	−0.0361654	+	0.999346i	$0.511514\pi$
$884$	−273.328	−	376.204i	−0.309194	−	0.425570i
$885$	659.904	−	326.534i	0.745654	−	0.368965i
$886$	86.7522	+	63.0291i	0.0979144	+	0.0711390i
$887$	785.452	+	124.403i	0.885515	+	0.140252i	0.582594	−	0.812764i	$-0.302038\pi$
$887$	785.452	+	124.403i	0.885515	+	0.140252i	0.302922	+	0.953015i	$0.402038\pi$
$888$	−20.7715	+	131.146i	−0.0233913	+	0.147687i
$889$	679.124	−	934.733i	0.763918	−	1.05144i
$890$	113.407	−	665.354i	0.127423	−	0.747589i
$891$	−120.300	+	87.4033i	−0.135017	+	0.0980957i
$892$	−363.134	+	185.026i	−0.407101	+	0.207428i
$893$	−252.373	+	252.373i	−0.282613	+	0.282613i
$894$	−662.008	−	215.099i	−0.740501	−	0.240603i
$895$	1009.59	+	1424.46i	1.12803	+	1.59158i
$896$	−46.2777	−	142.428i	−0.0516492	−	0.158960i
$897$	162.151	−	318.240i	0.180771	−	0.354782i
$898$	−583.376	+	92.3977i	−0.649639	+	0.102893i
$899$			14.1797i			0.0157728i
$900$	149.959	+	3.52272i	0.166621	+	0.00391414i
$901$	−646.213			−0.717217
$902$	−186.965	−	1180.45i	−0.207279	−	1.30871i
$903$	−486.198	−	247.730i	−0.538425	−	0.274341i
$904$	−236.676	+	76.9006i	−0.261810	+	0.0850671i
$905$	−1172.75	−	13.7729i	−1.29586	−	0.0152186i
$906$	45.5482	−	140.183i	0.0502739	−	0.154727i
$907$	28.3761	+	28.3761i	0.0312857	+	0.0312857i	0.722577	−	0.691291i	$-0.242958\pi$
$907$	28.3761	+	28.3761i	0.0312857	+	0.0312857i	−0.691291	+	0.722577i	$0.742958\pi$
$908$	−71.4050	−	140.140i	−0.0786399	−	0.154340i
$909$	−197.813	−	272.267i	−0.217616	−	0.299523i
$910$	−517.560	+	986.943i	−0.568747	+	1.08455i
$911$	−232.494	−	168.917i	−0.255207	−	0.185419i	0.452824	−	0.891600i	$-0.350417\pi$
$911$	−232.494	−	168.917i	−0.255207	−	0.185419i	−0.708031	+	0.706181i	$0.750417\pi$
$912$	118.085	+	18.7028i	0.129479	+	0.0205074i
$913$	274.988	−	1736.21i	0.301192	−	1.90165i
$914$	−145.122	+	199.743i	−0.158777	+	0.218537i
$915$	478.120	−	467.020i	0.522535	−	0.510404i
$916$	−128.085	+	93.0593i	−0.139831	+	0.101593i
$917$	−326.511	+	166.365i	−0.356064	+	0.181424i
$918$	101.470	−	101.470i	0.110534	−	0.110534i
$919$	390.332	+	126.827i	0.424735	+	0.138005i	0.513582	−	0.858040i	$-0.328318\pi$
$919$	390.332	+	126.827i	0.424735	+	0.138005i	−0.0888467	+	0.996045i	$0.528318\pi$
$920$	−146.286	+	196.452i	−0.159006	+	0.213534i
$921$	−308.495	−	949.451i	−0.334957	−	1.03089i
$922$	−155.786	+	305.747i	−0.168965	+	0.331613i
$923$	−131.054	+	20.7568i	−0.141986	+	0.0224884i
$924$			757.602i			0.819916i
$925$	−610.799	+	293.358i	−0.660324	+	0.317144i
$926$	547.271			0.591006
$927$	91.3664	+	576.865i	0.0985614	+	0.622292i
$928$	41.8799	+	21.3389i	0.0451292	+	0.0229945i
$929$	107.971	−	35.0818i	0.116222	−	0.0377629i	−0.250328	−	0.968161i	$-0.580539\pi$
$929$	107.971	−	35.0818i	0.116222	−	0.0377629i	0.366551	+	0.930398i	$0.380539\pi$
$930$	6.69170	−	19.8007i	0.00719538	−	0.0212910i
$931$	673.042	−	2071.41i	0.722924	−	2.22493i
$932$	−114.819	−	114.819i	−0.123196	−	0.123196i
$933$	−67.3798	−	132.240i	−0.0722184	−	0.141737i
$934$	354.569	+	488.023i	0.379625	+	0.522508i
$935$	−233.634	−	1596.21i	−0.249876	−	1.70718i
$936$	81.7339	+	59.3832i	0.0873226	+	0.0634436i
$937$	−431.528	−	68.3473i	−0.460542	−	0.0729427i	−0.0781474	−	0.996942i	$-0.524900\pi$
$937$	−431.528	−	68.3473i	−0.460542	−	0.0729427i	−0.382395	+	0.923999i	$0.624900\pi$
$938$	−162.116	+	1023.56i	−0.172832	+	1.09122i
$939$	−86.5132	+	119.075i	−0.0921333	+	0.126811i
$940$	204.646	−	29.9536i	0.217708	−	0.0318655i
$941$	−63.2023	+	45.9191i	−0.0671650	+	0.0487982i	−0.620861	−	0.783921i	$-0.713217\pi$
$941$	−63.2023	+	45.9191i	−0.0671650	+	0.0487982i	0.553696	+	0.832719i	$0.313217\pi$
$942$	−670.592	+	341.684i	−0.711881	+	0.362722i
$943$	−626.421	+	626.421i	−0.664285	+	0.664285i
$944$	−323.425	−	105.087i	−0.342612	−	0.111321i
$945$	−325.801	−	110.105i	−0.344763	−	0.116514i
$946$	171.851	+	528.902i	0.181660	+	0.559093i
$947$	−10.4432	+	20.4960i	−0.0110277	+	0.0216431i	−0.896455	−	0.443135i	$-0.853866\pi$
$947$	−10.4432	+	20.4960i	−0.0110277	+	0.0216431i	0.885427	+	0.464779i	$0.153866\pi$
$948$	−304.335	+	48.2019i	−0.321028	+	0.0508459i
$949$			192.797i			0.203158i
$950$	264.141	+	549.967i	0.278043	+	0.578912i
$951$	−517.836			−0.544517
$952$	−114.372	−	722.114i	−0.120138	−	0.758523i
$953$	−380.724	−	193.989i	−0.399501	−	0.203556i	0.242684	−	0.970105i	$-0.421972\pi$
$953$	−380.724	−	193.989i	−0.399501	−	0.203556i	−0.642185	+	0.766549i	$0.721972\pi$
$954$	133.525	−	43.3848i	0.139963	−	0.0454767i
$955$	−1200.28	−	893.780i	−1.25684	−	0.935895i
$956$	−143.384	+	441.292i	−0.149984	+	0.461602i
$957$	−168.136	−	168.136i	−0.175691	−	0.175691i
$958$	−317.124	−	622.391i	−0.331027	−	0.649677i
$959$	−392.938	−	540.833i	−0.409737	−	0.563955i
$960$	−48.4111	−	49.5617i	−0.0504282	−	0.0516268i
$961$	775.109	+	563.150i	0.806565	+	0.586004i
$962$	−450.758	−	71.3930i	−0.468563	−	0.0742131i
$963$	−32.8234	+	207.239i	−0.0340845	+	0.215201i
$964$	495.990	−	682.671i	0.514512	−	0.708165i
$965$	1022.73	+	536.328i	1.05983	+	0.555781i
$966$	454.310	−	330.075i	0.470300	−	0.341693i
$967$	254.614	−	129.732i	0.263303	−	0.134160i	−0.317356	−	0.948306i	$-0.602795\pi$
$967$	254.614	−	129.732i	0.263303	−	0.134160i	0.580659	+	0.814147i	$0.302795\pi$
$968$	303.963	−	303.963i	0.314011	−	0.314011i
$969$	555.107	+	180.365i	0.572866	+	0.186135i
$970$	−9.06279	+	771.693i	−0.00934308	+	0.795560i
$971$	−104.206	−	320.714i	−0.107319	−	0.330293i	0.882949	−	0.469469i	$-0.155555\pi$
$971$	−104.206	−	320.714i	−0.107319	−	0.330293i	−0.990268	+	0.139176i	$0.955555\pi$
$972$	−14.1540	+	27.7788i	−0.0145618	+	0.0285790i
$973$	2758.25	−	436.865i	2.83479	−	0.448987i
$974$			828.483i			0.850598i
$975$	−12.1078	+	515.418i	−0.0124183	+	0.528633i
$976$	−308.703			−0.316294
$977$	−192.429	−	1214.95i	−0.196959	−	1.24355i	−0.865892	−	0.500230i	$-0.833249\pi$
$977$	−192.429	−	1214.95i	−0.196959	−	1.24355i	0.668933	−	0.743323i	$-0.266751\pi$
$978$	−206.846	−	105.393i	−0.211499	−	0.107764i
$979$	1499.89	−	487.343i	1.53206	−	0.497797i
$980$	−1029.73	+	729.824i	−1.05075	+	0.744718i
$981$	−110.845	+	341.146i	−0.112992	+	0.347754i
$982$	−689.942	−	689.942i	−0.702589	−	0.702589i
$983$	−723.128	−	1419.22i	−0.735633	−	1.44376i	−0.890101	−	0.455764i	$-0.849366\pi$
$983$	−723.128	−	1419.22i	−0.735633	−	1.44376i	0.154467	−	0.987998i	$-0.450634\pi$
$984$	−147.289	−	202.726i	−0.149684	−	0.206023i
$985$	478.434	+	81.5469i	0.485719	+	0.0827887i
$986$	185.643	+	134.878i	0.188279	+	0.136793i
$987$	−468.350	−	74.1793i	−0.474518	−	0.0751563i
$988$	−64.2827	+	405.865i	−0.0650634	+	0.410794i
$989$	242.293	−	333.488i	0.244988	−	0.337197i
$990$	155.440	+	314.134i	0.157010	+	0.317307i
$991$	−386.879	+	281.084i	−0.390393	+	0.283637i	−0.765616	−	0.643297i	$-0.777566\pi$
$991$	−386.879	+	281.084i	−0.390393	+	0.283637i	0.375224	+	0.926934i	$0.377566\pi$
$992$	−8.60150	+	4.38268i	−0.00867087	+	0.00441803i
$993$	278.413	−	278.413i	0.280376	−	0.280376i
$994$	−198.406	−	64.4662i	−0.199604	−	0.0648553i
$995$	−1226.14	+	382.539i	−1.23231	+	0.384461i
$996$	−113.891	−	350.519i	−0.114348	−	0.351927i
$997$	−404.003	+	792.901i	−0.405219	+	0.795287i	−0.999963	−	0.00862856i	$-0.997253\pi$
$997$	−404.003	+	792.901i	−0.405219	+	0.795287i	0.594744	+	0.803915i	$0.297253\pi$
$998$	−672.546	+	106.521i	−0.673894	+	0.106734i
$999$		−	140.835i		−	0.140976i

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a_n

instead) (See

a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.k.a.37.1	✓	32
25.23	odd	20	inner	150.3.k.a.73.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.k.a.37.1	✓	32	1.1	even	1	trivial
150.3.k.a.73.1	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 $\F_{q}$

Introduction

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	150.3.k.a.37.1

Level	$150$
Weight	$3$
Character	150.37
Analytic conductor	$4.087$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$