LMFDB - Embedded newform 45.3.k.a.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$45 = 3^{2} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	45.k (of order $12$ , degree $4$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			22.6
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.194442 - 0.725667i) q^{2} +(-1.34163 - 2.68329i) q^{3} +(2.97532 + 1.71780i) q^{4} +(-1.25521 - 4.83988i) q^{5} +(-2.20804 + 0.451834i) q^{6} +(0.481578 - 1.79727i) q^{7} +(3.94998 - 3.94998i) q^{8} +(-5.40005 + 7.19996i) q^{9} +(-3.75621 - 0.0302083i) q^{10} +(5.82294 + 10.0856i) q^{11} +(0.617573 - 10.2883i) q^{12} +(5.30726 + 19.8070i) q^{13} +(-1.21058 - 0.698930i) q^{14} +(-11.3028 + 9.86143i) q^{15} +(4.77288 + 8.26686i) q^{16} +(-10.0254 - 10.0254i) q^{17} +(4.17477 + 5.31861i) q^{18} -10.8032i q^{19} +(4.57929 - 16.5564i) q^{20} +(-5.46870 + 1.11907i) q^{21} +(8.45102 - 2.26444i) q^{22} +(0.360576 + 1.34569i) q^{23} +(-15.8983 - 5.29951i) q^{24} +(-21.8489 + 12.1502i) q^{25} +15.4052 q^{26} +(26.5644 + 4.83020i) q^{27} +(4.52021 - 4.52021i) q^{28} +(-20.7968 + 12.0070i) q^{29} +(4.95838 + 10.1195i) q^{30} +(21.6233 - 37.4526i) q^{31} +(28.5101 - 7.63926i) q^{32} +(19.2504 - 29.1558i) q^{33} +(-9.22442 + 5.32572i) q^{34} +(-9.30307 - 0.0748176i) q^{35} +(-28.4350 + 12.1460i) q^{36} +(-32.5443 - 32.5443i) q^{37} +(-7.83949 - 2.10058i) q^{38} +(46.0274 - 40.8145i) q^{39} +(-24.0755 - 14.1593i) q^{40} +(-20.5409 + 35.5778i) q^{41} +(-0.251275 + 4.18605i) q^{42} +(-8.01349 - 2.14721i) q^{43} +40.0106i q^{44} +(41.6252 + 17.0981i) q^{45} +1.04663 q^{46} +(-4.62418 + 17.2577i) q^{47} +(15.7789 - 23.8981i) q^{48} +(39.4370 + 22.7689i) q^{49} +(4.56864 + 18.2175i) q^{50} +(-13.4506 + 40.3513i) q^{51} +(-18.2336 + 68.0488i) q^{52} +(-51.3281 + 51.3281i) q^{53} +(8.67035 - 18.3377i) q^{54} +(41.5042 - 40.8419i) q^{55} +(-5.19697 - 9.00141i) q^{56} +(-28.9880 + 14.4938i) q^{57} +(4.66933 + 17.4262i) q^{58} +(-24.3449 - 14.0555i) q^{59} +(-50.5692 + 9.92501i) q^{60} +(-41.1002 - 71.1876i) q^{61} +(-22.9736 - 22.9736i) q^{62} +(10.3398 + 13.1727i) q^{63} +16.0088i q^{64} +(89.2016 - 50.5485i) q^{65} +(-17.4143 - 19.6385i) q^{66} +(-32.3105 + 8.65757i) q^{67} +(-12.6071 - 47.0502i) q^{68} +(3.12710 - 2.77294i) q^{69} +(-1.86320 + 6.73638i) q^{70} +99.6917 q^{71} +(7.10958 + 49.7697i) q^{72} +(-22.3583 + 22.3583i) q^{73} +(-29.9443 + 17.2883i) q^{74} +(61.9155 + 42.3258i) q^{75} +(18.5577 - 32.1428i) q^{76} +(20.9308 - 5.60840i) q^{77} +(-20.6681 - 41.3366i) q^{78} +(52.9926 - 30.5953i) q^{79} +(34.0196 - 33.4768i) q^{80} +(-22.6788 - 77.7603i) q^{81} +(21.8237 + 21.8237i) q^{82} +(-49.9199 - 13.3760i) q^{83} +(-18.1935 - 6.06456i) q^{84} +(-35.9376 + 61.1056i) q^{85} +(-3.11631 + 5.39761i) q^{86} +(60.1198 + 39.6947i) q^{87} +(62.8384 + 16.8375i) q^{88} -113.914i q^{89} +(20.5012 - 26.8814i) q^{90} +38.1544 q^{91} +(-1.23879 + 4.62324i) q^{92} +(-129.506 - 7.77386i) q^{93} +(11.6242 + 6.71123i) q^{94} +(-52.2860 + 13.5603i) q^{95} +(-58.7483 - 66.2517i) q^{96} +(7.92297 - 29.5689i) q^{97} +(24.1909 - 24.1909i) q^{98} +(-104.060 - 12.5380i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100})$ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.194442	−	0.725667i	0.0972209	−	0.362833i	−0.900126	−	0.435630i	$-0.856526\pi$
$2$	0.194442	−	0.725667i	0.0972209	−	0.362833i	0.997347	+	0.0727965i	$0.0231924\pi$
$3$	−1.34163	−	2.68329i	−0.447210	−	0.894429i
$3$	−1.34163	−	2.68329i	−0.447210	−	0.894429i
$4$	2.97532	+	1.71780i	0.743829	+	0.429450i
$5$	−1.25521	−	4.83988i	−0.251043	−	0.967976i
$5$	−1.25521	−	4.83988i	−0.251043	−	0.967976i
$6$	−2.20804	+	0.451834i	−0.368007	+	0.0753056i
$7$	0.481578	−	1.79727i	0.0687969	−	0.256753i	−0.922958	−	0.384900i	$-0.874236\pi$
$7$	0.481578	−	1.79727i	0.0687969	−	0.256753i	0.991755	+	0.128146i	$0.0409027\pi$
$8$	3.94998	−	3.94998i	0.493747	−	0.493747i
$9$	−5.40005	+	7.19996i	−0.600006	+	0.799996i
$10$	−3.75621	−	0.0302083i	−0.375621	−	0.00302083i
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	0.999414	+	0.0342381i	$0.0109005\pi$
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	−0.470056	+	0.882637i	$0.655766\pi$
$12$	0.617573	−	10.2883i	0.0514644	−	0.857357i
$13$	5.30726	+	19.8070i	0.408251	+	1.52361i	0.797980	+	0.602684i	$0.205902\pi$
$13$	5.30726	+	19.8070i	0.408251	+	1.52361i	−0.389729	+	0.920930i	$0.627431\pi$
$14$	−1.21058	−	0.698930i	−0.0864702	−	0.0499236i
$15$	−11.3028	+	9.86143i	−0.753517	+	0.657429i
$16$	4.77288	+	8.26686i	0.298305	+	0.516679i
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	0.347830	−	0.937558i	$-0.386919\pi$
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	−0.937558	+	0.347830i	$0.886919\pi$
$18$	4.17477	+	5.31861i	0.231932	+	0.295478i
$19$		−	10.8032i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$19$		−	10.8032i		−	0.568587i	0.958737	−	0.284294i	$-0.0917590\pi$
$20$	4.57929	−	16.5564i	0.228964	−	0.827819i
$21$	−5.46870	+	1.11907i	−0.260414	+	0.0532889i
$22$	8.45102	−	2.26444i	0.384137	−	0.102929i
$23$	0.360576	+	1.34569i	0.0156772	+	0.0585081i	0.973321	−	0.229446i	$-0.0736915\pi$
$23$	0.360576	+	1.34569i	0.0156772	+	0.0585081i	−0.957644	+	0.287954i	$0.907025\pi$
$24$	−15.8983	−	5.29951i	−0.662430	−	0.220813i
$25$	−21.8489	+	12.1502i	−0.873955	+	0.486007i
$26$	15.4052			0.592508
$27$	26.5644	+	4.83020i	0.983868	+	0.178896i
$28$	4.52021	−	4.52021i	0.161436	−	0.161436i
$29$	−20.7968	+	12.0070i	−0.717130	+	0.414035i	−0.813695	−	0.581292i	$-0.802548\pi$
$29$	−20.7968	+	12.0070i	−0.717130	+	0.414035i	0.0965656	+	0.995327i	$0.469214\pi$
$30$	4.95838	+	10.1195i	0.165279	+	0.337317i
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	−0.271798	−	0.962354i	$-0.587618\pi$
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	0.969322	−	0.245793i	$-0.0790484\pi$
$32$	28.5101	−	7.63926i	0.890941	−	0.238727i
$33$	19.2504	−	29.1558i	0.583345	−	0.883509i
$34$	−9.22442	+	5.32572i	−0.271307	+	0.156639i
$35$	−9.30307	−	0.0748176i	−0.265802	−	0.00213765i
$36$	−28.4350	+	12.1460i	−0.789860	+	0.337388i
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	0.113915	−	0.993491i	$-0.463661\pi$
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	−0.993491	+	0.113915i	$0.963661\pi$
$38$	−7.83949	−	2.10058i	−0.206302	−	0.0552785i
$39$	46.0274	−	40.8145i	1.18019	−	1.04653i
$40$	−24.0755	−	14.1593i	−0.601887	−	0.353984i
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	0.499002	+	0.866601i	$0.333700\pi$
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	−0.999999	+	0.00115173i	$0.999633\pi$
$42$	−0.251275	+	4.18605i	−0.00598274	+	0.0996678i
$43$	−8.01349	−	2.14721i	−0.186360	−	0.0499351i	0.164432	−	0.986388i	$-0.447421\pi$
$43$	−8.01349	−	2.14721i	−0.186360	−	0.0499351i	−0.350792	+	0.936453i	$0.614088\pi$
$44$			40.0106i			0.909331i
$45$	41.6252	+	17.0981i	0.925004	+	0.379958i
$46$	1.04663			0.0227528
$47$	−4.62418	+	17.2577i	−0.0983868	+	0.367185i	−0.997511	−	0.0705087i	$-0.977538\pi$
$47$	−4.62418	+	17.2577i	−0.0983868	+	0.367185i	0.899124	+	0.437693i	$0.144204\pi$
$48$	15.7789	−	23.8981i	0.328728	−	0.497876i
$49$	39.4370	+	22.7689i	0.804836	+	0.464672i
$50$	4.56864	+	18.2175i	0.0913727	+	0.364350i
$51$	−13.4506	+	40.3513i	−0.263737	+	0.791202i
$52$	−18.2336	+	68.0488i	−0.350647	+	1.30863i
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	−0.999517	−	0.0310621i	$-0.990111\pi$
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	0.0310621	+	0.999517i	$0.490111\pi$
$54$	8.67035	−	18.3377i	0.160562	−	0.339588i
$55$	41.5042	−	40.8419i	0.754621	−	0.742580i
$56$	−5.19697	−	9.00141i	−0.0928030	−	0.160739i
$57$	−28.9880	+	14.4938i	−0.508561	+	0.254278i
$58$	4.66933	+	17.4262i	0.0805057	+	0.300451i
$59$	−24.3449	−	14.0555i	−0.412625	−	0.238229i	0.279292	−	0.960206i	$-0.409900\pi$
$59$	−24.3449	−	14.0555i	−0.412625	−	0.238229i	−0.691917	+	0.721977i	$0.743234\pi$
$60$	−50.5692	+	9.92501i	−0.842821	+	0.165417i
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	−0.976826	−	0.214036i	$-0.931339\pi$
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	0.303052	−	0.952974i	$-0.401994\pi$
$62$	−22.9736	−	22.9736i	−0.370542	−	0.370542i
$63$	10.3398	+	13.1727i	0.164123	+	0.209091i
$64$			16.0088i			0.250137i
$65$	89.2016	−	50.5485i	1.37233	−	0.777669i
$66$	−17.4143	−	19.6385i	−0.263853	−	0.297552i
$67$	−32.3105	+	8.65757i	−0.482246	+	0.129217i	−0.491748	−	0.870737i	$-0.663642\pi$
$67$	−32.3105	+	8.65757i	−0.482246	+	0.129217i	0.00950210	+	0.999955i	$0.496975\pi$
$68$	−12.6071	−	47.0502i	−0.185398	−	0.691915i
$69$	3.12710	−	2.77294i	0.0453203	−	0.0401876i
$70$	−1.86320	+	6.73638i	−0.0266171	+	0.0962340i
$71$	99.6917			1.40411			0.702054	−	0.712123i	$-0.252266\pi$
$71$	99.6917			1.40411			0.702054	+	0.712123i	$0.252266\pi$
$72$	7.10958	+	49.7697i	0.0987442	+	0.691246i
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	−0.843464	−	0.537186i	$-0.819487\pi$
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	0.537186	+	0.843464i	$0.319487\pi$
$74$	−29.9443	+	17.2883i	−0.404653	+	0.233626i
$75$	61.9155	+	42.3258i	0.825540	+	0.564344i
$76$	18.5577	−	32.1428i	0.244180	−	0.422932i
$77$	20.9308	−	5.60840i	0.271829	−	0.0728363i
$78$	−20.6681	−	41.3366i	−0.264976	−	0.529956i
$79$	52.9926	−	30.5953i	0.670793	−	0.387282i	−0.125584	−	0.992083i	$-0.540081\pi$
$79$	52.9926	−	30.5953i	0.670793	−	0.387282i	0.796377	+	0.604801i	$0.206747\pi$
$80$	34.0196	−	33.4768i	0.425246	−	0.418460i
$81$	−22.6788	−	77.7603i	−0.279986	−	0.960004i
$82$	21.8237	+	21.8237i	0.266142	+	0.266142i
$83$	−49.9199	−	13.3760i	−0.601444	−	0.161157i	−0.0547660	−	0.998499i	$-0.517441\pi$
$83$	−49.9199	−	13.3760i	−0.601444	−	0.161157i	−0.546678	+	0.837343i	$0.684108\pi$
$84$	−18.1935	−	6.06456i	−0.216589	−	0.0721971i
$85$	−35.9376	+	61.1056i	−0.422795	+	0.718889i
$86$	−3.11631	+	5.39761i	−0.0362362	+	0.0627630i
$87$	60.1198	+	39.6947i	0.691033	+	0.456261i
$88$	62.8384	+	16.8375i	0.714073	+	0.191335i
$89$		−	113.914i		−	1.27993i	−0.768402	−	0.639967i	$-0.778948\pi$
$89$		−	113.914i		−	1.27993i	0.768402	−	0.639967i	$-0.221052\pi$
$90$	20.5012	−	26.8814i	0.227791	−	0.298682i
$91$	38.1544			0.419279
$92$	−1.23879	+	4.62324i	−0.0134651	+	0.0502526i
$93$	−129.506	−	7.77386i	−1.39254	−	0.0835899i
$94$	11.6242	+	6.71123i	0.123662	+	0.0713960i
$95$	−52.2860	+	13.5603i	−0.550379	+	0.142740i
$96$	−58.7483	−	66.2517i	−0.611962	−	0.690122i
$97$	7.92297	−	29.5689i	0.0816801	−	0.304834i	−0.912985	−	0.407994i	$-0.866229\pi$
$97$	7.92297	−	29.5689i	0.0816801	−	0.304834i	0.994665	+	0.103160i	$0.0328952\pi$
$98$	24.1909	−	24.1909i	0.246845	−	0.246845i
$99$	−104.060	−	12.5380i	−1.05111	−	0.126646i
$100$	−85.8789	−	1.38141i	−0.858789	−	0.0138141i
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	0.975208	−	0.221291i	$-0.0710270\pi$
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	−0.679247	+	0.733909i	$0.737694\pi$
$102$	26.6662	+	17.6066i	0.261433	+	0.172614i
$103$	13.1011	+	48.8939i	0.127195	+	0.474698i	0.999908	−	0.0135348i	$-0.00430840\pi$
$103$	13.1011	+	48.8939i	0.127195	+	0.474698i	−0.872713	+	0.488233i	$0.837642\pi$
$104$	99.2006	+	57.2735i	0.953852	+	0.550707i
$105$	12.2805	+	25.0632i	0.116957	+	0.238697i
$106$	27.2668	+	47.2274i	0.257234	+	0.445542i
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	0.634374	−	0.773027i	$-0.281258\pi$
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	−0.773027	+	0.634374i	$0.781258\pi$
$108$	70.7403	+	60.0038i	0.655003	+	0.555591i
$109$			115.290i			1.05770i	0.848714	+	0.528852i	$0.177377\pi$
$109$			115.290i			1.05770i	−0.848714	+	0.528852i	$0.822623\pi$
$110$	−21.5675	−	38.0596i	−0.196068	−	0.345996i
$111$	−43.6633	+	130.988i	−0.393363	+	1.18007i
$112$	17.1563	−	4.59703i	0.153182	−	0.0410449i
$113$	−27.1198	−	101.212i	−0.239998	−	0.895686i	−0.975832	−	0.218523i	$-0.929876\pi$
$113$	−27.1198	−	101.212i	−0.239998	−	0.895686i	0.735833	−	0.677163i	$-0.236791\pi$
$114$	4.88123	+	23.8538i	0.0428178	+	0.209244i
$115$	6.06036	−	3.43427i	0.0526988	−	0.0298632i
$116$	−82.5026			−0.711229
$117$	−171.269	−	68.7466i	−1.46384	−	0.587578i
$118$	−14.9333	+	14.9333i	−0.126553	+	0.126553i
$119$	−22.8463	+	13.1903i	−0.191986	+	0.110843i
$120$	−5.69319	+	83.5980i	−0.0474432	+	0.696650i
$121$	−7.31319	+	12.6668i	−0.0604396	+	0.104684i
$122$	−59.6501	+	15.9832i	−0.488935	+	0.131010i
$123$	123.024	+	7.38473i	1.00019	+	0.0600385i
$124$	128.672	−	74.2889i	1.03768	−	0.599104i
$125$	86.2304	+	90.4949i	0.689843	+	0.723959i
$126$	11.5695	−	4.94189i	0.0918213	−	0.0392213i
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	0.892549	−	0.450950i	$-0.148915\pi$
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	−0.450950	+	0.892549i	$0.648915\pi$
$128$	125.657	+	33.6698i	0.981699	+	0.263045i
$129$	4.98957	+	24.3832i	0.0386788	+	0.189017i
$130$	−19.3368	−	74.5594i	−0.148745	−	0.573534i
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	−0.874735	−	0.484602i	$-0.838964\pi$
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	0.857045	+	0.515241i	$0.172298\pi$
$132$	107.360	−	53.6794i	0.813332	−	0.406662i
$133$	−19.4162	−	5.20256i	−0.145987	−	0.0391170i
$134$			25.1300i			0.187538i
$135$	−9.96643	−	134.632i	−0.0738254	−	0.997271i
$136$	−79.1999			−0.582352
$137$	−0.615617	+	2.29751i	−0.00449355	+	0.0167702i	−0.968136	−	0.250424i	$-0.919430\pi$
$137$	−0.615617	+	2.29751i	−0.00449355	+	0.0167702i	0.963643	+	0.267194i	$0.0860966\pi$
$138$	−1.40419	−	2.80841i	−0.0101753	−	0.0203508i
$139$	−221.925	−	128.128i	−1.59658	−	0.921786i	−0.992140	−	0.125136i	$-0.960063\pi$
$139$	−221.925	−	128.128i	−1.59658	−	0.921786i	−0.604441	−	0.796650i	$-0.706603\pi$
$140$	−27.5511	−	16.2034i	−0.196793	−	0.115739i
$141$	52.5112	−	10.7454i	0.372420	−	0.0762087i
$142$	19.3842	−	72.3429i	0.136509	−	0.509457i
$143$	−168.862	+	168.862i	−1.18085	+	1.18085i
$144$	−85.2949	−	10.2770i	−0.592325	−	0.0713680i
$145$	84.2169	+	85.5825i	0.580806	+	0.590224i
$146$	11.8773	+	20.5721i	0.0813513	+	0.140905i
$147$	8.18575	−	136.368i	0.0556854	−	0.927675i
$148$	−40.9250	−	152.734i	−0.276520	−	1.03199i
$149$	81.5954	+	47.1091i	0.547620	+	0.316168i	0.748161	−	0.663517i	$-0.230937\pi$
$149$	81.5954	+	47.1091i	0.547620	+	0.316168i	−0.200542	+	0.979685i	$0.564270\pi$
$150$	42.7534	−	36.7001i	0.285022	−	0.244667i
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	0.908785	−	0.417265i	$-0.137011\pi$
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	−0.815755	+	0.578398i	$0.803678\pi$
$152$	−42.6722	−	42.6722i	−0.280738	−	0.280738i
$153$	126.320	−	18.0447i	0.825619	−	0.117939i
$154$		−	16.2793i		−	0.105710i
$155$	−208.408	−	57.6430i	−1.34457	−	0.371890i
$156$	207.057	−	42.3704i	1.32729	−	0.271605i
$157$	−37.2690	+	9.98621i	−0.237382	+	0.0636064i	−0.375549	−	0.926803i	$-0.622546\pi$
$157$	−37.2690	+	9.98621i	−0.237382	+	0.0636064i	0.138166	+	0.990409i	$0.455879\pi$
$158$	−11.8980	−	44.4040i	−0.0753039	−	0.281038i
$159$	206.591	+	68.8647i	1.29932	+	0.433111i
$160$	−72.7594	−	128.397i	−0.454746	−	0.802479i
$161$	2.59221			0.0161007
$162$	−60.8378	+	1.33742i	−0.375542	+	0.00825566i
$163$	140.797	−	140.797i	0.863787	−	0.863787i	−0.127989	−	0.991776i	$-0.540852\pi$
$163$	140.797	−	140.797i	0.863787	−	0.863787i	0.991776	+	0.127989i	$0.0408522\pi$
$164$	−122.231	+	70.5703i	−0.745313	+	0.430306i
$165$	−165.274	−	56.5728i	−1.00166	−	0.342866i
$166$	−19.4130	+	33.6243i	−0.116946	+	0.202556i
$167$	273.273	−	73.2232i	1.63636	−	0.438462i	0.680614	−	0.732642i	$-0.261713\pi$
$167$	273.273	−	73.2232i	1.63636	−	0.438462i	0.955750	+	0.294180i	$0.0950466\pi$
$168$	−17.1810	+	26.0215i	−0.102268	+	0.154890i
$169$	−217.791	+	125.742i	−1.28870	+	0.744033i
$170$	37.3545	+	37.9602i	0.219732	+	0.223295i
$171$	77.7823	+	58.3376i	0.454867	+	0.341156i
$172$	−20.1542	−	20.1542i	−0.117176	−	0.117176i
$173$	299.418	+	80.2289i	1.73074	+	0.463751i	0.980354	−	0.197248i	$-0.0632003\pi$
$173$	299.418	+	80.2289i	1.73074	+	0.463751i	0.750387	+	0.660998i	$0.229867\pi$
$174$	40.4949	−	35.9087i	0.232729	−	0.206372i
$175$	11.3152	+	45.1197i	0.0646585	+	0.257827i
$176$	−55.5843	+	96.2748i	−0.315820	+	0.547016i
$177$	−5.05315	+	84.1816i	−0.0285489	+	0.475602i
$178$	−82.6637	−	22.1497i	−0.464403	−	0.124436i
$179$		−	151.884i		−	0.848512i	−0.905542	−	0.424256i	$-0.860536\pi$
$179$		−	151.884i		−	0.848512i	0.905542	−	0.424256i	$-0.139464\pi$
$180$	94.4769	+	122.376i	0.524872	+	0.679867i
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	7.41881	−	27.6874i	0.0407627	−	0.152128i
$183$	−135.876	+	205.791i	−0.742489	+	1.12454i
$184$	6.73969	+	3.89116i	0.0366288	+	0.0211476i
$185$	−116.660	+	198.361i	−0.630597	+	1.07222i
$186$	−30.8227	+	92.4669i	−0.165713	+	0.497134i
$187$	42.7350	−	159.489i	0.228529	−	0.852883i
$188$	−43.4036	+	43.4036i	−0.230870	+	0.230870i
$189$	21.4741	−	45.4174i	0.113619	−	0.240304i
$190$	−0.326345	+	40.5789i	−0.00171761	+	0.213573i
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.742617	−	0.669717i	$-0.766416\pi$
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.208683	−	0.977983i	$-0.566918\pi$
$192$	42.9562	−	21.4779i	0.223730	−	0.111864i
$193$	−3.09769	−	11.5607i	−0.0160502	−	0.0599001i	0.957436	−	0.288645i	$-0.0932046\pi$
$193$	−3.09769	−	11.5607i	−0.0160502	−	0.0599001i	−0.973486	+	0.228745i	$0.926538\pi$
$194$	−19.9166	−	11.4989i	−0.102663	−	0.0592725i
$195$	−255.312	−	171.536i	−1.30929	−	0.879672i
$196$	78.2250	+	135.490i	0.399107	+	0.691274i
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	0.812759	−	0.582600i	$-0.197964\pi$
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	−0.582600	+	0.812759i	$0.697964\pi$
$198$	−29.3321	+	73.0751i	−0.148142	+	0.369066i
$199$		−	17.0082i		−	0.0854685i	−0.999086	−	0.0427343i	$-0.986393\pi$
$199$		−	17.0082i		−	0.0854685i	0.999086	−	0.0427343i	$-0.0136069\pi$
$200$	−38.3097	+	134.295i	−0.191548	+	0.671477i
$201$	66.5795	+	75.0831i	0.331241	+	0.373548i
$202$	43.3833	−	11.6245i	0.214769	−	0.0575471i
$203$	11.5646	+	43.1598i	0.0569686	+	0.212610i
$204$	−109.335	+	96.9524i	−0.535957	+	0.475257i
$205$	197.976	+	54.7576i	0.965735	+	0.267110i
$206$	38.0281			0.184602
$207$	−11.6360	−	4.67065i	−0.0562126	−	0.0225635i
$208$	−138.411	+	138.411i	−0.665436	+	0.665436i
$209$	108.957	−	62.9061i	0.521323	−	0.300986i
$210$	20.5754	−	4.03824i	0.0979780	−	0.0192297i
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	0.260842	+	0.965382i	$0.416000\pi$
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	−0.966466	+	0.256795i	$0.917333\pi$
$212$	−240.889	+	64.5460i	−1.13627	+	0.304462i
$213$	−133.749	−	267.501i	−0.627932	−	1.25588i
$214$	−13.6506	+	7.88119i	−0.0637879	+	0.0368280i
$215$	−0.333589	+	41.4795i	−0.00155157	+	0.192928i
$216$	124.008	−	85.8497i	0.574111	−	0.397452i
$217$	−56.8993	−	56.8993i	−0.262209	−	0.262209i
$218$	83.6620	+	22.4172i	0.383771	+	0.102831i
$219$	89.9903	+	29.9971i	0.410915	+	0.136973i
$220$	193.646	−	50.2218i	0.880211	−	0.228281i
$221$	145.365	−	251.779i	0.657760	−	1.13927i
$222$	86.5638	+	57.1545i	0.389927	+	0.257453i
$223$	30.8773	+	8.27356i	0.138463	+	0.0371012i	0.327385	−	0.944891i	$-0.393833\pi$
$223$	30.8773	+	8.27356i	0.138463	+	0.0371012i	−0.188922	+	0.981992i	$0.560499\pi$
$224$		−	54.9194i		−	0.245176i
$225$	30.5044	−	222.923i	0.135575	−	0.990767i
$226$	−78.7197			−0.348317
$227$	−101.241	+	377.838i	−0.445997	+	1.66449i	0.267292	+	0.963616i	$0.413871\pi$
$227$	−101.241	+	377.838i	−0.445997	+	1.66449i	−0.713289	+	0.700870i	$0.752795\pi$
$228$	−111.146	−	6.67174i	−0.487482	−	0.0292620i
$229$	217.228	+	125.417i	0.948594	+	0.547671i	0.892644	−	0.450762i	$-0.148848\pi$
$229$	217.228	+	125.417i	0.948594	+	0.547671i	0.0559502	+	0.998434i	$0.482181\pi$
$230$	−1.31374	−	5.06557i	−0.00571193	−	0.0220242i
$231$	−43.1304	−	48.6390i	−0.186712	−	0.210558i
$232$	−34.7193	+	129.574i	−0.149652	+	0.558509i
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.0264709	−	0.999650i	$-0.491573\pi$
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.999650	−	0.0264709i	$-0.00842693\pi$
$234$	−83.1890	+	110.917i	−0.355508	+	0.474004i
$235$	89.3294	+	0.718409i	0.380125	+	0.00305706i
$236$	−48.2891	−	83.6392i	−0.204615	−	0.354404i
$237$	−153.193	−	101.147i	−0.646382	−	0.426780i
$238$	5.12950	+	19.1436i	0.0215525	+	0.0804352i
$239$	−33.8483	−	19.5423i	−0.141625	−	0.0817672i	0.427513	−	0.904009i	$-0.359390\pi$
$239$	−33.8483	−	19.5423i	−0.141625	−	0.0817672i	−0.569138	+	0.822242i	$0.692723\pi$
$240$	−135.470	−	46.3709i	−0.564457	−	0.193212i
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	0.766036	−	0.642798i	$-0.222227\pi$
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	−0.939697	+	0.342007i	$0.888893\pi$
$242$	7.76989	+	7.76989i	0.0321070	+	0.0321070i
$243$	−178.227	+	165.179i	−0.733443	+	0.679751i
$244$		−	282.408i		−	1.15741i
$245$	60.6971	−	219.450i	0.247743	−	0.895715i
$246$	29.2798	−	87.8384i	0.119024	−	0.357067i
$247$	213.978	−	57.3352i	0.866307	−	0.232126i
$248$	−62.5254	−	233.348i	−0.252119	−	0.940920i
$249$	31.0824	+	151.895i	0.124829	+	0.610020i
$250$	82.4359	−	44.9785i	0.329744	−	0.179914i
$251$	−116.674			−0.464837			−0.232418	−	0.972616i	$-0.574664\pi$
$251$	−116.674			−0.464837			−0.232418	+	0.972616i	$0.574664\pi$
$252$	8.13594	+	56.9546i	0.0322855	+	0.226011i
$253$	−11.4725	+	11.4725i	−0.0453458	+	0.0453458i
$254$	51.6025	−	29.7927i	0.203159	−	0.117294i
$255$	212.179	+	14.4498i	0.832073	+	0.0566658i
$256$	16.8485	−	29.1825i	0.0658146	−	0.113994i
$257$	4.62189	−	1.23843i	0.0179840	−	0.00481880i	−0.249816	−	0.968293i	$-0.580370\pi$
$257$	4.62189	−	1.23843i	0.0179840	−	0.00481880i	0.267800	+	0.963475i	$0.413703\pi$
$258$	18.6643	+	1.12036i	0.0723422	+	0.00434247i
$259$	−74.1637	+	42.8184i	−0.286346	+	0.165322i
$260$	352.235	+	2.83276i	1.35475	+	0.0108952i
$261$	25.8536	−	214.574i	0.0990559	−	0.822124i
$262$	2.46203	+	2.46203i	0.00939706	+	0.00939706i
$263$	94.4750	+	25.3145i	0.359221	+	0.0962529i	0.433916	−	0.900954i	$-0.357132\pi$
$263$	94.4750	+	25.3145i	0.359221	+	0.0962529i	−0.0746949	+	0.997206i	$0.523798\pi$
$264$	−39.1261	−	191.203i	−0.148205	−	0.724255i
$265$	312.850	+	183.994i	1.18057	+	0.694318i
$266$	−7.55065	+	13.0781i	−0.0283859	+	0.0491658i
$267$	−305.664	+	152.831i	−1.14481	+	0.572400i
$268$	−111.006	−	29.7440i	−0.414201	−	0.110985i
$269$		−	212.871i		−	0.791340i	−0.918393	−	0.395670i	$-0.870512\pi$
$269$		−	212.871i		−	0.791340i	0.918393	−	0.395670i	$-0.129488\pi$
$270$	−99.6356	−	18.9457i	−0.369021	−	0.0701693i
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	35.0285	−	130.728i	0.128781	−	0.480618i
$273$	−51.1891	−	102.379i	−0.187506	−	0.375016i
$274$	1.54753	+	0.893465i	0.00564791	+	0.00326082i
$275$	−249.767	−	149.610i	−0.908242	−	0.544036i
$276$	14.0675	−	2.87864i	0.0509691	−	0.0104299i
$277$	−84.7048	+	316.123i	−0.305794	+	1.14124i	0.626467	+	0.779448i	$0.284501\pi$
$277$	−84.7048	+	316.123i	−0.305794	+	1.14124i	−0.932260	+	0.361789i	$0.882166\pi$
$278$	−136.130	+	136.130i	−0.489676	+	0.489676i
$279$	152.890	+	357.932i	0.547994	+	1.28291i
$280$	−37.0424	+	36.4514i	−0.132294	+	0.130184i
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	0.836862	−	0.547413i	$-0.184387\pi$
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	−0.892505	+	0.451037i	$0.851054\pi$
$282$	2.41278	−	40.1950i	0.00855596	−	0.142535i
$283$	−52.4715	−	195.826i	−0.185412	−	0.691966i	−0.994542	−	0.104337i	$-0.966728\pi$
$283$	−52.4715	−	195.826i	−0.185412	−	0.691966i	0.809130	−	0.587629i	$-0.199939\pi$
$284$	296.614	+	171.250i	1.04442	+	0.602995i
$285$	106.535	+	122.105i	0.373805	+	0.428440i
$286$	89.7036	+	155.371i	0.313649	+	0.543256i
$287$	54.0511	+	54.0511i	0.188331	+	0.188331i
$288$	−98.9537	+	246.524i	−0.343589	+	0.855986i
$289$		−	87.9840i		−	0.304443i
$290$	78.4796	−	44.4726i	0.270619	−	0.153354i
$291$	−89.9715	+	18.4110i	−0.309181	+	0.0632679i
$292$	−104.930	+	28.1159i	−0.359350	+	0.0962875i
$293$	10.0935	+	37.6696i	0.0344490	+	0.128565i	0.981009	−	0.193963i	$-0.0621341\pi$
$293$	10.0935	+	37.6696i	0.0344490	+	0.128565i	−0.946560	+	0.322528i	$0.895467\pi$
$294$	−97.3662	−	32.4558i	−0.331178	−	0.110394i
$295$	−37.4690	+	135.469i	−0.127014	+	0.459217i
$296$	−257.098			−0.868576
$297$	105.967	+	296.045i	0.356793	+	0.996784i
$298$	50.0510	−	50.0510i	0.167957	−	0.167957i
$299$	−24.7403	+	14.2838i	−0.0827435	+	0.0477720i
$300$	111.511	+	232.291i	0.371704	+	0.774303i
$301$	−7.71824	+	13.3684i	−0.0256420	+	0.0444132i
$302$	20.3876	−	5.46285i	0.0675087	−	0.0180889i
$303$	98.8217	−	149.671i	0.326144	−	0.493964i
$304$	89.3082	−	51.5621i	0.293777	−	0.169612i
$305$	−292.950	+	288.276i	−0.960492	+	0.945166i
$306$	11.4674	−	95.1747i	0.0374751	−	0.311028i
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	0.659276	−	0.751901i	$-0.270863\pi$
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	−0.751901	+	0.659276i	$0.770863\pi$
$308$	71.9100	+	19.2682i	0.233474	+	0.0625591i
$309$	113.619	−	100.751i	0.367701	−	0.326057i
$310$	−82.3528	+	140.026i	−0.265654	+	0.451698i
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	0.276007	+	0.961156i	$0.410989\pi$
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	−0.970389	+	0.241548i	$0.922345\pi$
$312$	20.5906	−	343.024i	0.0659956	−	1.09943i
$313$	−200.386	−	53.6933i	−0.640211	−	0.171544i	−0.0759119	−	0.997115i	$-0.524187\pi$
$313$	−200.386	−	53.6933i	−0.640211	−	0.171544i	−0.564299	+	0.825571i	$0.690853\pi$
$314$			28.9866i			0.0923141i
$315$	50.7758	−	66.5777i	0.161193	−	0.211358i
$316$	210.226			0.665274
$317$	−91.9060	+	342.998i	−0.289924	+	1.08201i	0.655241	+	0.755420i	$0.272567\pi$
$317$	−91.9060	+	342.998i	−0.289924	+	1.08201i	−0.945165	+	0.326593i	$0.894100\pi$
$318$	90.1428	−	136.526i	0.283468	−	0.429328i
$319$	−242.196	−	139.832i	−0.759237	−	0.438345i
$320$	77.4806	−	20.0944i	0.242127	−	0.0627951i
$321$	−19.9046	+	59.7132i	−0.0620082	+	0.186022i
$322$	0.504034	−	1.88108i	0.00156532	−	0.00584187i
$323$	−108.306	+	108.306i	−0.335311	+	0.335311i
$324$	66.1000	−	270.319i	0.204012	−	0.834319i
$325$	−356.616	−	368.276i	−1.09728	−	1.13316i
$326$	−74.7950	−	129.549i	−0.229432	−	0.397389i
$327$	309.356	−	154.676i	0.946042	−	0.473016i
$328$	59.3957	+	221.668i	0.181084	+	0.675816i
$329$	28.7899	+	16.6218i	0.0875072	+	0.0505223i
$330$	−73.1891	+	108.934i	−0.221785	+	0.330102i
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	−0.996926	−	0.0783519i	$-0.975034\pi$
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	0.430608	−	0.902539i	$-0.358299\pi$
$332$	−125.550	−	125.550i	−0.378163	−	0.378163i
$333$	410.059	−	58.5767i	1.23141	−	0.175906i
$334$		−	212.543i		−	0.636355i
$335$	82.4582	+	145.512i	0.246144	+	0.434364i
$336$	−35.3526	−	39.8678i	−0.105216	−	0.118654i
$337$	143.584	−	38.4732i	0.426065	−	0.114164i	−0.0394135	−	0.999223i	$-0.512549\pi$
$337$	143.584	−	38.4732i	0.426065	−	0.114164i	0.465478	+	0.885059i	$0.345882\pi$
$338$	48.8988	+	182.493i	0.144671	+	0.539920i
$339$	−235.197	+	208.560i	−0.693797	+	0.615221i
$340$	−211.893	+	120.075i	−0.623214	+	0.353161i
$341$	503.643			1.47696
$342$	57.4578	−	45.1007i	0.168005	−	0.131873i
$343$	124.383	−	124.383i	0.362633	−	0.362633i
$344$	−40.1345	+	23.1717i	−0.116670	+	0.0673595i
$345$	−17.3459	−	11.6542i	−0.0502779	−	0.0337802i
$346$	116.439	−	201.678i	0.336528	−	0.582884i
$347$	233.258	−	62.5014i	0.672214	−	0.180119i	0.0934622	−	0.995623i	$-0.470207\pi$
$347$	233.258	−	62.5014i	0.672214	−	0.180119i	0.578752	+	0.815504i	$0.303540\pi$
$348$	110.688	+	221.378i	0.318069	+	0.636144i
$349$	−331.191	+	191.213i	−0.948971	+	0.547889i	−0.892761	−	0.450530i	$-0.851235\pi$
$349$	−331.191	+	191.213i	−0.948971	+	0.547889i	−0.0562101	+	0.998419i	$0.517902\pi$
$350$	34.9420	+	0.562061i	0.0998343	+	0.00160589i
$351$	45.3127	+	551.796i	0.129096	+	1.57207i
$352$	243.059	+	243.059i	0.690509	+	0.690509i
$353$	−503.013	−	134.782i	−1.42497	−	0.381819i	−0.537724	−	0.843121i	$-0.680716\pi$
$353$	−503.013	−	134.782i	−1.42497	−	0.381819i	−0.887243	+	0.461302i	$0.847382\pi$
$354$	60.1052	+	20.0353i	0.169789	+	0.0565969i
$355$	−125.134	−	482.496i	−0.352491	−	1.35914i
$356$	195.682	−	338.931i	0.549668	−	0.952052i
$357$	66.0448	+	43.6067i	0.184999	+	0.122148i
$358$	−110.217	−	29.5325i	−0.307868	−	0.0824931i
$359$			326.956i			0.910741i	0.890302	+	0.455370i	$0.150493\pi$
$359$			326.956i			0.910741i	−0.890302	+	0.455370i	$0.849507\pi$
$360$	231.956	−	96.8812i	0.644321	−	0.269114i
$361$	244.292			0.676709
$362$	9.35222	−	34.9030i	0.0258349	−	0.0964170i
$363$	43.8003	+	2.62919i	0.120662	+	0.00724296i
$364$	113.521	+	65.5417i	0.311872	+	0.180060i
$365$	136.276	+	80.1471i	0.373359	+	0.219581i
$366$	122.916	+	138.615i	0.335836	+	0.378729i
$367$	135.325	−	505.039i	0.368733	−	1.37613i	−0.493557	−	0.869713i	$-0.664304\pi$
$367$	135.325	−	505.039i	0.368733	−	1.37613i	0.862290	−	0.506415i	$-0.169030\pi$
$368$	−9.40362	+	9.40362i	−0.0255533	+	0.0255533i
$369$	−145.237	−	340.016i	−0.393597	−	0.921452i
$370$	121.260	+	123.226i	0.327730	+	0.333044i
$371$	67.5322	+	116.969i	0.182028	+	0.315281i
$372$	−371.969	−	245.596i	−0.999916	−	0.660204i
$373$	6.28693	+	23.4631i	0.0168550	+	0.0629039i	0.973841	−	0.227230i	$-0.0729669\pi$
$373$	6.28693	+	23.4631i	0.0168550	+	0.0629039i	−0.956986	+	0.290134i	$0.906300\pi$
$374$	−107.426	−	62.0227i	−0.287237	−	0.165836i
$375$	127.134	−	352.791i	0.339025	−	0.940777i
$376$	49.9020	+	86.4328i	0.132718	+	0.229874i
$377$	−348.197	−	348.197i	−0.923598	−	0.923598i
$378$	−28.7825	−	24.4141i	−0.0761441	−	0.0645874i
$379$			364.939i			0.962900i	0.876474	+	0.481450i	$0.159890\pi$
$379$			364.939i			0.962900i	−0.876474	+	0.481450i	$0.840110\pi$
$380$	−178.861	−	49.4708i	−0.470687	−	0.130186i
$381$	75.2442	−	225.730i	0.197491	−	0.592466i
$382$	−263.705	+	70.6595i	−0.690327	+	0.184972i
$383$	−0.870084	−	3.24720i	−0.00227176	−	0.00847832i	0.964781	−	0.263056i	$-0.0847303\pi$
$383$	−0.870084	−	3.24720i	−0.00227176	−	0.00847832i	−0.967052	+	0.254577i	$0.918064\pi$
$384$	−78.2401	−	382.347i	−0.203750	−	0.995696i
$385$	−53.4166	−	94.2630i	−0.138744	−	0.244839i
$386$	−8.99155			−0.0232942
$387$	58.7331	−	46.1018i	0.151765	−	0.119126i
$388$	74.3668	−	74.3668i	0.191667	−	0.191667i
$389$	−131.808	+	76.0995i	−0.338838	+	0.195628i	−0.659758	−	0.751478i	$-0.729341\pi$
$389$	−131.808	+	76.0995i	−0.338838	+	0.195628i	0.320920	+	0.947106i	$0.396008\pi$
$390$	−174.121	+	151.917i	−0.446465	+	0.389532i
$391$	9.87610	−	17.1059i	0.0252586	−	0.0437491i
$392$	245.712	−	65.8383i	0.626816	−	0.167955i
$393$	13.8789	+	0.833107i	0.0353153	+	0.00211986i
$394$	41.7190	−	24.0865i	0.105886	−	0.0611332i
$395$	−214.595	−	218.074i	−0.543278	−	0.552087i
$396$	−288.074	−	216.059i	−0.727461	−	0.545604i
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	0.268420	−	0.963302i	$-0.413498\pi$
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	−0.963302	+	0.268420i	$0.913498\pi$
$398$	−12.3423	−	3.30711i	−0.0310108	−	0.00830933i
$399$	12.0894	+	59.0792i	0.0302994	+	0.148068i
$400$	−204.726	−	122.630i	−0.511814	−	0.306576i
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	0.0469080	+	0.998899i	$0.485063\pi$
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	−0.888526	+	0.458826i	$0.848270\pi$
$402$	67.4311	−	33.7152i	0.167739	−	0.0838688i
$403$	856.582	+	229.521i	2.12551	+	0.569530i
$404$			205.394i			0.508401i
$405$	−347.884	+	207.369i	−0.858973	+	0.512021i
$406$	33.5683			0.0826805
$407$	138.726	−	517.733i	0.340850	−	1.27207i
$408$	106.257	+	212.516i	0.260434	+	0.520873i
$409$	375.213	+	216.629i	0.917390	+	0.529655i	0.882802	−	0.469746i	$-0.155655\pi$
$409$	375.213	+	216.629i	0.917390	+	0.529655i	0.0345887	+	0.999402i	$0.488988\pi$
$410$	78.2305	−	133.017i	0.190806	−	0.324432i
$411$	6.99082	−	1.43054i	0.0170093	−	0.00348063i
$412$	−45.0101	+	167.980i	−0.109248	+	0.407718i
$413$	−36.9856	+	36.9856i	−0.0895534	+	0.0895534i
$414$	−5.65186	+	7.53570i	−0.0136518	+	0.0182022i
$415$	−2.07808	+	258.396i	−0.00500743	+	0.622641i
$416$	302.621	+	524.155i	0.727455	+	1.25999i
$417$	−46.0639	+	767.388i	−0.110465	+	1.84026i
$418$	−24.4631	−	91.2977i	−0.0585243	−	0.218416i
$419$	−432.869	−	249.917i	−1.03310	−	0.596461i	−0.115229	−	0.993339i	$-0.536760\pi$
$419$	−432.869	−	249.917i	−1.03310	−	0.596461i	−0.917871	+	0.396878i	$0.870093\pi$
$420$	−6.51507	+	95.6664i	−0.0155121	+	0.227777i
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	0.883338	−	0.468737i	$-0.155291\pi$
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	−0.847607	+	0.530624i	$0.821958\pi$
$422$	158.185	+	158.185i	0.374845	+	0.374845i
$423$	−99.2837	−	126.486i	−0.234713	−	0.299022i
$424$			405.490i			0.956344i
$425$	340.853	+	97.2331i	0.802007	+	0.228784i
$426$	−220.123	+	45.0441i	−0.516721	+	0.105737i
$427$	−147.737	+	39.5859i	−0.345987	+	0.0927071i
$428$	−18.6564	−	69.6265i	−0.0435896	−	0.162679i
$429$	679.655	+	226.554i	1.58428	+	0.528099i
$430$	30.0354	+	8.30743i	0.0698499	+	0.0193196i
$431$	515.749			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$431$	515.749			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$432$	86.8581	+	242.659i	0.201060	+	0.561710i
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	−0.965740	−	0.259511i	$-0.916439\pi$
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	0.259511	+	0.965740i	$0.416439\pi$
$434$	−52.3535	+	30.2263i	−0.120630	+	0.0696458i
$435$	116.654	−	340.798i	0.268171	−	0.783444i
$436$	−198.045	+	343.024i	−0.454231	+	0.786752i
$437$	14.5377	−	3.89535i	0.0332669	−	0.00891385i
$438$	39.2658	−	59.4703i	0.0896480	−	0.135777i
$439$	437.591	−	252.643i	0.996790	−	0.575497i	0.0894929	−	0.995987i	$-0.471475\pi$
$439$	437.591	−	252.643i	0.996790	−	0.575497i	0.907297	+	0.420491i	$0.138142\pi$
$440$	2.61586	−	325.265i	0.00594514	−	0.739239i
$441$	−376.897	+	160.991i	−0.854642	+	0.365059i
$442$	−154.443	−	154.443i	−0.349418	−	0.349418i
$443$	195.215	+	52.3076i	0.440665	+	0.118076i	0.472328	−	0.881423i	$-0.343414\pi$
$443$	195.215	+	52.3076i	0.440665	+	0.118076i	−0.0316632	+	0.999499i	$0.510080\pi$
$444$	−354.923	+	314.726i	−0.799377	+	0.708843i
$445$	−551.331	+	142.987i	−1.23895	+	0.321318i
$446$	12.0077	−	20.7979i	0.0269231	−	0.0466321i
$447$	16.9364	−	282.147i	0.0378890	−	0.631201i
$448$	28.7722	+	7.70948i	0.0642236	+	0.0172087i
$449$		−	145.089i		−	0.323138i	−0.986861	−	0.161569i	$-0.948345\pi$
$449$		−	145.089i		−	0.323138i	0.986861	−	0.161569i	$-0.0516554\pi$
$450$	−155.836	−	65.4815i	−0.346303	−	0.145514i
$451$	−478.433			−1.06083
$452$	93.1728	−	347.726i	0.206135	−	0.769305i
$453$	46.4405	−	70.3367i	0.102518	−	0.155269i
$454$	254.499	+	146.935i	0.560570	+	0.323645i
$455$	−47.8919	−	184.663i	−0.105257	−	0.405852i
$456$	−57.2514	+	171.752i	−0.125551	+	0.376649i
$457$	76.7746	−	286.527i	0.167997	−	0.626973i	−0.829642	−	0.558296i	$-0.811455\pi$
$457$	76.7746	−	286.527i	0.167997	−	0.626973i	0.997639	−	0.0686775i	$-0.0218780\pi$
$458$	133.249	−	133.249i	0.290936	−	0.290936i
$459$	−217.894	−	314.743i	−0.474714	−	0.685714i
$460$	23.9309	+	0.192458i	0.0520236	+	0.000418387i
$461$	143.044	+	247.759i	0.310291	+	0.537439i	0.978425	−	0.206601i	$-0.0662403\pi$
$461$	143.044	+	247.759i	0.310291	+	0.537439i	−0.668135	+	0.744040i	$0.732907\pi$
$462$	−43.6821	+	21.8408i	−0.0945499	+	0.0472745i
$463$	64.7653	+	241.707i	0.139882	+	0.522046i	0.999930	+	0.0118333i	$0.00376674\pi$
$463$	64.7653	+	241.707i	0.139882	+	0.522046i	−0.860048	+	0.510213i	$0.829567\pi$
$464$	−198.521	−	114.616i	−0.427846	−	0.247017i
$465$	124.934	+	636.553i	0.268675	+	1.36893i
$466$	−127.008	−	219.985i	−0.272550	−	0.472071i
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	0.626601	−	0.779340i	$-0.284446\pi$
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	−0.779340	+	0.626601i	$0.784446\pi$
$468$	−391.486	−	498.749i	−0.836509	−	1.06570i
$469$			62.2401i			0.132708i
$470$	17.8907	−	64.6837i	0.0380653	−	0.137625i
$471$	76.7972	+	86.6057i	0.163051	+	0.183876i
$472$	−151.681	+	40.6427i	−0.321357	+	0.0861074i
$473$	−25.0061	−	93.3241i	−0.0528670	−	0.197302i
$474$	−103.186	+	91.4995i	−0.217692	+	0.193037i
$475$	131.260	+	236.037i	0.276337	+	0.496920i
$476$	−90.6334			−0.190406
$477$	−92.3858	−	646.735i	−0.193681	−	1.35584i
$478$	−20.7628	+	20.7628i	−0.0434367	+	0.0434367i
$479$	169.803	−	98.0357i	0.354494	−	0.204667i	−0.312169	−	0.950027i	$-0.601055\pi$
$479$	169.803	−	98.0357i	0.354494	−	0.204667i	0.666663	+	0.745359i	$0.267722\pi$
$480$	−246.909	+	367.495i	−0.514393	+	0.765615i
$481$	471.883	−	817.325i	0.981046	−	1.69922i
$482$	−60.7419	+	16.2758i	−0.126021	+	0.0337671i
$483$	−3.47779	−	6.95565i	−0.00720040	−	0.0144009i
$484$	−43.5181	+	25.1252i	−0.0899135	+	0.0519116i
$485$	−153.055	−	1.23091i	−0.315577	−	0.00253795i
$486$	85.2105	+	161.451i	0.175330	+	0.332204i
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.879391	+	0.476100i	$0.157950\pi$
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.476100	+	0.879391i	$0.342050\pi$
$488$	−443.534	−	118.845i	−0.908882	−	0.243534i
$489$	−566.697	−	188.901i	−1.15889	−	0.386301i
$490$	−147.446	−	86.7162i	−0.300909	−	0.176972i
$491$	393.999	−	682.426i	0.802442	−	1.38987i	−0.115562	−	0.993300i	$-0.536867\pi$
$491$	393.999	−	682.426i	0.802442	−	1.38987i	0.918004	−	0.396570i	$-0.129800\pi$
$492$	353.349	+	233.302i	0.718190	+	0.474192i
$493$	328.870	+	88.1204i	0.667079	+	0.178743i
$494$		−	166.425i		−	0.336892i
$495$	69.9355	+	519.377i	0.141284	+	1.04925i
$496$	412.820			0.832299
$497$	48.0093	−	179.173i	0.0965983	−	0.360510i
$498$	116.269	+	6.97925i	0.233472	+	0.0140146i
$499$	−144.756	−	83.5751i	−0.290093	−	0.167485i	0.347891	−	0.937535i	$-0.386898\pi$
$499$	−144.756	−	83.5751i	−0.290093	−	0.167485i	−0.637984	+	0.770050i	$0.720231\pi$
$500$	101.111	+	417.378i	0.202221	+	0.834755i
$501$	−563.110	−	635.031i	−1.12397	−	1.26753i
$502$	−22.6863	+	84.6664i	−0.0451918	+	0.168658i
$503$	249.990	−	249.990i	0.496998	−	0.496998i	−0.413504	−	0.910502i	$-0.635695\pi$
$503$	249.990	−	249.990i	0.496998	−	0.496998i	0.910502	+	0.413504i	$0.135695\pi$
$504$	92.8737	+	11.1901i	0.184273	+	0.0222027i
$505$	213.061	−	209.662i	0.421904	−	0.415172i
$506$	6.09446	+	10.5559i	0.0120444	+	0.0208615i
$507$	629.596	+	415.696i	1.24181	+	0.819914i
$508$	70.5254	+	263.204i	0.138830	+	0.518119i
$509$	−95.6645	−	55.2319i	−0.187946	−	0.108511i	0.403075	−	0.915167i	$-0.367941\pi$
$509$	−95.6645	−	55.2319i	−0.187946	−	0.108511i	−0.591021	+	0.806656i	$0.701275\pi$
$510$	51.7421	−	151.161i	0.101455	−	0.296395i
$511$	29.4167	+	50.9513i	0.0575670	+	0.0997089i
$512$	350.050	+	350.050i	0.683691	+	0.683691i
$513$	52.1814	−	286.980i	0.101718	−	0.559415i
$514$		−	3.59475i		−	0.00699368i
$515$	220.196	−	124.780i	0.427565	−	0.242291i
$516$	−27.0400	+	81.1190i	−0.0524031	+	0.157207i
$517$	−200.981	+	53.8526i	−0.388744	+	0.104164i
$518$	16.6514	+	62.1438i	0.0321455	+	0.119969i
$519$	−186.432	−	911.062i	−0.359213	−	1.75542i
$520$	152.679	−	552.010i	0.293613	−	1.06156i
$521$	−415.088			−0.796715			−0.398357	−	0.917230i	$-0.630420\pi$
$521$	−415.088			−0.796715			−0.398357	+	0.917230i	$0.630420\pi$
$522$	−150.682	−	60.4833i	−0.288664	−	0.115868i
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	−0.971673	−	0.236329i	$-0.924056\pi$
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	0.236329	+	0.971673i	$0.424056\pi$
$524$	−13.7895	+	7.96136i	−0.0263158	+	0.0151934i
$525$	105.888	−	90.8960i	0.201692	−	0.173135i
$526$	36.7398	−	63.6352i	0.0698475	−	0.120979i
$527$	−592.257	+	158.695i	−1.12383	+	0.301129i
$528$	332.907	+	19.9833i	0.630505	+	0.0378472i
$529$	456.447	−	263.530i	0.862848	−	0.498166i
$530$	194.350	−	191.248i	0.366697	−	0.360846i
$531$	232.663	−	99.3815i	0.438160	−	0.187159i
$532$	−48.8325	−	48.8325i	−0.0917904	−	0.0917904i
$533$	−813.705	−	218.032i	−1.52665	−	0.409065i
$534$	51.4702	+	251.527i	0.0963862	+	0.471024i
$535$	−53.1817	+	90.4261i	−0.0994050	+	0.169021i
$536$	−93.4285	+	161.823i	−0.174307	+	0.301908i
$537$	−407.547	+	203.772i	−0.758933	+	0.379463i
$538$	−154.473	−	41.3909i	−0.287125	−	0.0769348i
$539$			530.329i			0.983912i
$540$	201.617	−	417.692i	0.373365	−	0.773504i
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	−35.0467	+	130.796i	−0.0646618	+	0.241321i
$543$	−64.5295	−	129.060i	−0.118839	−	0.237680i
$544$	−362.411	−	209.238i	−0.666196	−	0.384628i
$545$	557.989	−	144.713i	1.02383	−	0.265529i
$546$	−84.2465	+	17.2394i	−0.154298	+	0.0315741i
$547$	−144.553	+	539.479i	−0.264265	+	0.986251i	0.698433	+	0.715675i	$0.253881\pi$
$547$	−144.553	+	539.479i	−0.264265	+	0.986251i	−0.962699	+	0.270576i	$0.912786\pi$
$548$	−5.77833	+	5.77833i	−0.0105444	+	0.0105444i
$549$	734.491	+	88.4973i	1.33787	+	0.161197i
$550$	−157.132	+	152.157i	−0.285694	+	0.276649i
$551$	129.714	+	224.671i	0.235415	+	0.407751i
$552$	1.39893	−	23.3050i	0.00253429	−	0.0422193i
$553$	−29.4681	−	109.976i	−0.0532876	−	0.198872i
$554$	212.930	+	122.935i	0.384349	+	0.221904i
$555$	688.774	+	46.9068i	1.24103	+	0.0845168i
$556$	−440.197	−	762.444i	−0.791722	−	1.37130i
$557$	302.419	+	302.419i	0.542943	+	0.542943i	0.924391	−	0.381447i	$-0.124574\pi$
$557$	302.419	+	302.419i	0.542943	+	0.542943i	−0.381447	+	0.924391i	$0.624574\pi$
$558$	289.468	−	41.3504i	0.518760	−	0.0741046i
$559$		−	170.119i		−	0.304327i
$560$	−43.7839	−	77.2643i	−0.0781856	−	0.137972i
$561$	−485.290	+	99.3053i	−0.865044	+	0.177015i
$562$	−22.6924	+	6.08041i	−0.0403780	+	0.0108192i
$563$	234.221	+	874.123i	0.416022	+	1.55262i	0.782779	+	0.622300i	$0.213802\pi$
$563$	234.221	+	874.123i	0.416022	+	1.55262i	−0.366756	+	0.930317i	$0.619532\pi$
$564$	174.696	+	58.2327i	0.309745	+	0.103250i
$565$	−455.815	+	258.300i	−0.806752	+	0.457168i
$566$	−152.307			−0.269094
$567$	−150.678	+	3.31241i	−0.265747	+	0.00584199i
$568$	393.780	−	393.780i	0.693274	−	0.693274i
$569$	−194.081	+	112.053i	−0.341092	+	0.196929i	−0.660755	−	0.750602i	$-0.729764\pi$
$569$	−194.081	+	112.053i	−0.341092	+	0.196929i	0.319663	+	0.947531i	$0.396430\pi$
$570$	109.323	−	53.5662i	0.191794	−	0.0939758i
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	−0.889747	−	0.456454i	$-0.849119\pi$
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	0.840174	+	0.542317i	$0.182453\pi$
$572$	−792.488	+	212.347i	−1.38547	+	0.371235i
$573$	−600.687	+	909.774i	−1.04832	+	1.58774i
$574$	49.7329	−	28.7133i	0.0866426	−	0.0500232i
$575$	−24.2285	−	25.0207i	−0.0421365	−	0.0435142i
$576$	−115.263	−	86.4483i	−0.200109	−	0.150084i
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	0.199135	−	0.979972i	$-0.436187\pi$
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	−0.979972	+	0.199135i	$0.936187\pi$
$578$	−63.8471	−	17.1078i	−0.110462	−	0.0295982i
$579$	−26.8648	+	23.8222i	−0.0463986	+	0.0411437i
$580$	103.558	+	399.303i	0.178549	+	0.688453i
$581$	−48.0806	+	83.2781i	−0.0827550	+	0.143336i
$582$	−4.13400	+	68.8692i	−0.00710309	+	0.118332i
$583$	−816.557	−	218.796i	−1.40061	−	0.375293i
$584$			176.630i			0.302448i
$585$	−117.746	+	915.213i	−0.201276	+	1.56447i
$586$	29.2982			0.0499969
$587$	−89.8623	+	335.371i	−0.153087	+	0.571330i	0.846174	+	0.532906i	$0.178900\pi$
$587$	−89.8623	+	335.371i	−0.153087	+	0.571330i	−0.999262	+	0.0384234i	$0.987766\pi$
$588$	258.609	−	391.677i	0.439810	−	0.666118i
$589$	−404.606	−	233.599i	−0.686937	−	0.396603i
$590$	91.0197	+	53.5308i	0.154271	+	0.0907302i
$591$	60.8326	−	182.495i	0.102932	−	0.308791i
$592$	113.709	−	424.369i	0.192077	−	0.716840i
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	−0.877297	−	0.479948i	$-0.840656\pi$
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	0.479948	+	0.877297i	$0.340656\pi$
$594$	235.434	−	19.3335i	0.396354	−	0.0325480i
$595$	92.5167	+	94.0168i	0.155490	+	0.158011i
$596$	161.848	+	280.329i	0.271557	+	0.470351i
$597$	−45.6380	+	22.8188i	−0.0764455	+	0.0382224i
$598$	5.55474	+	20.7306i	0.00928887	+	0.0346665i
$599$	513.829	+	296.659i	0.857811	+	0.495258i	0.863279	−	0.504727i	$-0.168407\pi$
$599$	513.829	+	296.659i	0.857811	+	0.495258i	−0.00546746	+	0.999985i	$0.501740\pi$
$600$	411.750	−	77.3790i	0.686251	−	0.128965i
$601$	269.249	+	466.354i	0.448002	+	0.775963i	0.998256	−	0.0590349i	$-0.0188023\pi$
$601$	269.249	+	466.354i	0.448002	+	0.775963i	−0.550254	+	0.834998i	$0.685469\pi$
$602$	8.20024	+	8.20024i	0.0136217	+	0.0136217i
$603$	112.144	−	279.386i	0.185977	−	0.463326i
$604$			96.5233i			0.159807i
$605$	70.4855	+	19.4954i	0.116505	+	0.0322238i
$606$	−89.3962	−	100.814i	−0.147519	−	0.166360i
$607$	−395.280	+	105.915i	−0.651203	+	0.174489i	−0.569273	−	0.822149i	$-0.692775\pi$
$607$	−395.280	+	105.915i	−0.651203	+	0.174489i	−0.0819303	+	0.996638i	$0.526108\pi$
$608$	−82.5281	−	307.999i	−0.135737	−	0.506577i
$609$	100.295	−	88.9357i	0.164687	−	0.146036i
$610$	152.230	+	268.637i	0.249558	+	0.440388i
$611$	−366.364			−0.599614
$612$	406.839	+	163.303i	0.664769	+	0.266836i
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	−0.715621	−	0.698488i	$-0.753856\pi$
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	0.698488	+	0.715621i	$0.253856\pi$
$614$	−26.1641	+	15.1059i	−0.0426126	+	0.0246024i
$615$	−118.680	−	604.690i	−0.192976	−	0.983236i
$616$	60.5232	−	104.829i	0.0982520	−	0.170177i
$617$	421.900	−	113.048i	0.683793	−	0.183222i	0.0998331	−	0.995004i	$-0.468169\pi$
$617$	421.900	−	113.048i	0.683793	−	0.183222i	0.583960	+	0.811782i	$0.301502\pi$
$618$	−51.0196	−	102.040i	−0.0825560	−	0.165114i
$619$	8.91186	−	5.14527i	0.0143972	−	0.00831222i	−0.492784	−	0.870152i	$-0.664021\pi$
$619$	8.91186	−	5.14527i	0.0143972	−	0.00831222i	0.507181	+	0.861839i	$0.330687\pi$
$620$	−521.060	−	529.509i	−0.840420	−	0.854047i
$621$	3.07855	+	37.4890i	0.00495740	+	0.0603688i
$622$	229.439	+	229.439i	0.368873	+	0.368873i
$623$	−204.735	−	54.8585i	−0.328627	−	0.0880554i
$624$	557.091	+	185.699i	0.892775	+	0.297595i
$625$	329.747	−	530.935i	0.527595	−	0.849496i
$626$	−77.9268	+	134.973i	−0.124484	+	0.215612i
$627$	−314.975	−	207.965i	−0.502352	−	0.331682i
$628$	−128.042	−	34.3086i	−0.203888	−	0.0546316i
$629$			652.537i			1.03742i
$630$	−38.4403	−	49.7918i	−0.0610164	−	0.0790346i
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	88.4689	−	330.170i	0.139982	−	0.522421i
$633$	891.715	+	53.5268i	1.40871	+	0.0845606i
$634$	231.032	+	133.386i	0.364403	+	0.210388i
$635$	201.039	−	341.832i	0.316597	−	0.538317i
$636$	496.379	+	559.777i	0.780471	+	0.880153i
$637$	−241.682	+	901.968i	−0.379406	+	1.41596i
$638$	−148.565	+	148.565i	−0.232860	+	0.232860i
$639$	−538.341	+	717.776i	−0.842474	+	1.12328i
$640$	5.23092	−	650.430i	0.00817331	−	1.01630i
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	0.527089	−	0.849810i	$-0.323283\pi$
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	−0.999502	+	0.0315680i	$0.989950\pi$
$642$	39.4616	+	26.0549i	0.0614666	+	0.0405839i
$643$	−120.761	−	450.687i	−0.187809	−	0.700912i	−0.994012	−	0.109273i	$-0.965148\pi$
$643$	−120.761	−	450.687i	−0.187809	−	0.700912i	0.806203	−	0.591639i	$-0.201519\pi$
$644$	7.71265	+	4.45290i	0.0119762	+	0.00691444i
$645$	111.749	−	54.7551i	0.173254	−	0.0848916i
$646$	57.5346	+	99.6529i	0.0890629	+	0.154261i
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	0.610811	−	0.791776i	$-0.290843\pi$
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	−0.791776	+	0.610811i	$0.790843\pi$
$648$	−396.732	−	217.571i	−0.612241	−	0.335757i
$649$		−	327.378i		−	0.504434i
$650$	−336.587	+	187.176i	−0.517826	+	0.287963i
$651$	−76.3392	+	229.015i	−0.117265	+	0.351789i
$652$	660.778	−	177.055i	1.01346	−	0.271557i
$653$	−86.4506	−	322.638i	−0.132390	−	0.494086i	0.867605	−	0.497254i	$-0.165658\pi$
$653$	−86.4506	−	322.638i	−0.132390	−	0.494086i	−0.999995	+	0.00316798i	$0.998992\pi$
$654$	−52.0918	−	254.565i	−0.0796511	−	0.389242i
$655$	22.3346	+	6.17746i	0.0340986	+	0.00943124i
$656$	−392.156			−0.597799
$657$	−40.2428	−	281.715i	−0.0612524	−	0.428790i
$658$	17.6599	−	17.6599i	0.0268387	−	0.0268387i
$659$	1062.27	−	613.303i	1.61195	−	0.930657i	0.623027	−	0.782200i	$-0.285903\pi$
$659$	1062.27	−	613.303i	1.61195	−	0.930657i	0.988919	−	0.148457i	$-0.0474308\pi$
$660$	−394.561	−	452.230i	−0.597820	−	0.685196i
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	−0.799257	−	0.600989i	$-0.794773\pi$
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	0.920101	+	0.391682i	$0.128107\pi$
$662$	−272.054	+	72.8967i	−0.410958	+	0.110116i
$663$	−870.622	−	52.2607i	−1.31316	−	0.0788246i
$664$	−250.017	+	144.347i	−0.376532	+	0.217391i
$665$	−0.808266	+	100.503i	−0.00121544	+	0.151132i
$666$	37.2254	−	308.956i	0.0558940	−	0.463897i
$667$	−23.6565	−	23.6565i	−0.0354670	−	0.0354670i
$668$	938.856	+	251.566i	1.40547	+	0.376595i
$669$	−19.2257	−	93.9528i	−0.0287379	−	0.140438i
$670$	121.626	−	31.5436i	0.181532	−	0.0470800i
$671$	478.648	−	829.042i	0.713335	−	1.23553i
$672$	−147.364	+	73.6815i	−0.219292	+	0.109645i
$673$	−45.9717	−	12.3181i	−0.0683086	−	0.0183032i	0.224503	−	0.974473i	$-0.427924\pi$
$673$	−45.9717	−	12.3181i	−0.0683086	−	0.0183032i	−0.292811	+	0.956170i	$0.594591\pi$
$674$		−	111.675i		−	0.165690i
$675$	−639.091	+	217.228i	−0.946801	+	0.321819i
$676$	−863.996			−1.27810
$677$	37.9504	−	141.633i	0.0560567	−	0.209206i	−0.932217	−	0.361900i	$-0.882128\pi$
$677$	37.9504	−	141.633i	0.0560567	−	0.209206i	0.988274	+	0.152694i	$0.0487948\pi$
$678$	105.613	+	211.228i	0.155771	+	0.311545i
$679$	−49.3279	−	28.4795i	−0.0726479	−	0.0419433i
$680$	99.4128	+	383.318i	0.146195	+	0.563703i
$681$	1149.68	−	235.260i	1.68822	−	0.345462i
$682$	97.9293	−	365.477i	0.143591	−	0.535890i
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.358860	−	0.933391i	$-0.383165\pi$
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.933391	−	0.358860i	$-0.116835\pi$
$684$	131.215	+	307.187i	0.191834	+	0.449104i
$685$	11.8924	+	0.0956418i	0.0173612	+	0.000139623i
$686$	−66.0754	−	114.446i	−0.0963198	−	0.166831i
$687$	45.0890	−	751.148i	0.0656318	−	1.09337i
$688$	−20.4967	−	76.4948i	−0.0297917	−	0.111184i
$689$	−1289.07	−	744.243i	−1.87092	−	1.08018i
$690$	−11.8298	+	10.3213i	−0.0171446	+	0.0149584i
$691$	253.832	+	439.650i	0.367340	+	0.636252i	0.989149	−	0.146917i	$-0.0469351\pi$
$691$	253.832	+	439.650i	0.367340	+	0.636252i	−0.621808	+	0.783169i	$0.713602\pi$
$692$	753.047	+	753.047i	1.08822	+	1.08822i
$693$	−72.6473	+	180.987i	−0.104830	+	0.261164i
$694$		−	181.421i		−	0.261413i
$695$	−341.563	+	1234.92i	−0.491457	+	1.77686i
$696$	394.265	−	80.6788i	0.566473	−	0.115918i
$697$	562.611	−	150.751i	0.807189	−	0.216286i
$698$	74.3597	+	277.514i	0.106532	+	0.397585i
$699$	−962.302	−	320.771i	−1.37668	−	0.458900i
$700$	−43.8402	+	153.683i	−0.0626288	+	0.219547i
$701$	194.042			0.276807			0.138403	−	0.990376i	$-0.455803\pi$
$701$	194.042			0.276807			0.138403	+	0.990376i	$0.455803\pi$
$702$	409.231	+	74.4103i	0.582950	+	0.105998i
$703$	−351.581	+	351.581i	−0.500115	+	0.500115i
$704$	−161.459	+	93.2182i	−0.229345	+	0.132412i
$705$	−117.919	−	240.660i	−0.167262	−	0.341362i
$706$	−195.614	+	338.813i	−0.277073	+	0.479905i
$707$	107.448	−	28.7907i	0.151978	−	0.0407223i
$708$	−159.642	+	241.787i	−0.225483	+	0.341506i
$709$	−414.499	+	239.311i	−0.584625	+	0.337534i	−0.762969	−	0.646435i	$-0.776259\pi$
$709$	−414.499	+	239.311i	−0.584625	+	0.337534i	0.178344	+	0.983968i	$0.442926\pi$
$710$	−374.463	−	3.01152i	−0.527412	−	0.00424158i
$711$	−65.8781	+	546.761i	−0.0926555	+	0.769003i
$712$	−449.958	−	449.958i	−0.631963	−	0.631963i
$713$	58.1962	+	15.5936i	0.0816216	+	0.0218705i
$714$	44.4858	−	39.4475i	0.0623050	−	0.0552486i
$715$	1029.23	+	605.313i	1.43948	+	0.846592i
$716$	260.906	−	451.902i	0.364393	−	0.631148i
$717$	−7.02575	+	117.043i	−0.00979881	+	0.163240i
$718$	237.261	+	63.5739i	0.330447	+	0.0885430i
$719$		−	443.536i		−	0.616879i	−0.951244	−	0.308439i	$-0.900193\pi$
$719$		−	443.536i		−	0.616879i	0.951244	−	0.308439i	$-0.0998067\pi$
$720$	57.3239	+	425.717i	0.0796165	+	0.591273i
$721$	94.1849			0.130631
$722$	47.5005	−	177.274i	0.0657902	−	0.245532i
$723$	−138.363	+	209.558i	−0.191373	+	0.289845i
$724$	143.106	+	82.6224i	0.197660	+	0.114119i
$725$	308.499	−	515.024i	0.425515	−	0.710378i
$726$	10.4245	−	31.2732i	0.0143588	−	0.0430760i
$727$	75.0285	−	280.010i	0.103203	−	0.385158i	−0.894932	−	0.446202i	$-0.852776\pi$
$727$	75.0285	−	280.010i	0.103203	−	0.385158i	0.998135	+	0.0610438i	$0.0194429\pi$
$728$	150.709	−	150.709i	0.207018	−	0.207018i
$729$	682.338	+	256.623i	0.935992	+	0.352021i
$730$	84.6578	−	83.3070i	0.115970	−	0.114119i
$731$	58.8116	+	101.865i	0.0804536	+	0.139350i
$732$	−757.781	+	378.887i	−1.03522	+	0.517605i
$733$	264.583	+	987.435i	0.360958	+	1.34712i	0.872818	+	0.488046i	$0.162290\pi$
$733$	264.583	+	987.435i	0.360958	+	1.34712i	−0.511859	+	0.859069i	$0.671043\pi$
$734$	−340.177	−	196.401i	−0.463457	−	0.267577i
$735$	−670.281	+	131.553i	−0.911946	+	0.178984i
$736$	20.5601	+	35.6111i	0.0279349	+	0.0483847i
$737$	−275.459	−	275.459i	−0.373757	−	0.373757i
$738$	−274.978	+	39.2805i	−0.372599	+	0.0532256i
$739$			153.917i			0.208277i	0.994563	+	0.104138i	$0.0332085\pi$
$739$			153.917i			0.208277i	−0.994563	+	0.104138i	$0.966791\pi$
$740$	−687.846	+	389.786i	−0.929521	+	0.526738i
$741$	−440.926	−	497.241i	−0.595042	−	0.671041i
$742$	98.0117	−	26.2622i	0.132091	−	0.0353938i
$743$	337.889	+	1261.02i	0.454763	+	1.69720i	0.688784	+	0.724966i	$0.258145\pi$
$743$	337.889	+	1261.02i	0.454763	+	1.69720i	−0.234021	+	0.972231i	$0.575189\pi$
$744$	−542.254	+	480.841i	−0.728836	+	0.646291i
$745$	125.583	−	454.044i	0.168568	−	0.609455i
$746$	18.2489			0.0244623
$747$	365.877	−	287.190i	0.489795	−	0.384458i
$748$	401.121	−	401.121i	0.536258	−	0.536258i
$749$	−33.8088	+	19.5195i	−0.0451385	+	0.0260607i
$750$	−231.289	−	160.855i	−0.308385	−	0.214473i
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.276783	+	0.960933i	$0.589268\pi$
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.693801	+	0.720167i	$0.744065\pi$
$752$	−164.737	+	44.1413i	−0.219066	+	0.0586985i
$753$	156.533	+	313.070i	0.207880	+	0.415763i
$754$	−320.379	+	184.971i	−0.424905	+	0.245319i
$755$	100.127	−	98.5289i	0.132618	−	0.130502i
$756$	141.910	−	98.2432i	0.187712	−	0.129951i
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	0.216434	−	0.976297i	$-0.430557\pi$
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	−0.976297	+	0.216434i	$0.930557\pi$
$758$	264.824	+	70.9594i	0.349372	+	0.0936140i
$759$	46.1758	+	15.3921i	0.0608376	+	0.0202795i
$760$	−152.966	+	260.091i	−0.201271	+	0.342225i
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	0.313187	+	0.949691i	$0.398603\pi$
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	−0.979051	+	0.203618i	$0.934730\pi$
$762$	−149.174	−	98.4935i	−0.195766	−	0.129257i
$763$	207.207	+	55.5211i	0.271569	+	0.0727668i
$764$		−	1248.49i		−	1.63414i
$765$	−245.893	−	588.723i	−0.321428	−	0.769572i
$766$	−2.52556			−0.00329708
$767$	149.193	−	556.794i	0.194515	−	0.725938i
$768$	−100.910	−	6.05728i	−0.131393	−	0.00788709i
$769$	486.081	+	280.639i	0.632095	+	0.364940i	0.781563	−	0.623827i	$-0.214423\pi$
$769$	486.081	+	280.639i	0.632095	+	0.364940i	−0.149468	+	0.988767i	$0.547756\pi$
$770$	−78.7899	+	20.4340i	−0.102325	+	0.0265377i
$771$	−9.52393	−	10.7403i	−0.0123527	−	0.0139304i
$772$	10.6424	−	39.7180i	0.0137855	−	0.0514482i
$773$	445.834	−	445.834i	0.576758	−	0.576758i	−0.357251	−	0.934008i	$-0.616286\pi$
$773$	445.834	−	445.834i	0.576758	−	0.576758i	0.934008	+	0.357251i	$0.116286\pi$
$774$	−22.0343	−	51.5847i	−0.0284681	−	0.0666469i
$775$	−17.3888	+	1081.02i	−0.0224372	+	1.39487i
$776$	−85.5009	−	148.092i	−0.110182	−	0.190840i
$777$	214.394	+	141.556i	0.275926	+	0.182183i
$778$	29.5938	+	110.446i	0.0380383	+	0.141961i
$779$	384.353	+	221.906i	0.493393	+	0.284860i
$780$	−464.969	−	948.949i	−0.596114	−	1.21660i
$781$	580.499	+	1005.45i	0.743276	+	1.28739i
$782$	−10.4929	−	10.4929i	−0.0134180	−	0.0134180i
$783$	−610.451	+	218.507i	−0.779630	+	0.279064i
$784$			434.693i			0.554456i
$785$	95.1127	+	167.843i	0.121163	+	0.213813i
$786$	3.30320	−	9.90946i	0.00420254	−	0.0126075i
$787$	1353.23	−	362.598i	1.71948	−	0.460734i	0.741766	−	0.670659i	$-0.233989\pi$
$787$	1353.23	−	362.598i	1.71948	−	0.460734i	0.977717	+	0.209925i	$0.0673220\pi$
$788$	57.0176	+	212.793i	0.0723573	+	0.270041i
$789$	−58.8245	−	287.466i	−0.0745558	−	0.364343i
$790$	−199.975	+	113.321i	−0.253133	+	0.143445i
$791$	−194.967			−0.246482
$792$	−460.560	+	361.511i	−0.581515	+	0.456453i
$793$	1191.88	−	1191.88i	1.50300	−	1.50300i
$794$	−253.828	+	146.548i	−0.319683	+	0.184569i
$795$	73.9804	−	1086.32i	0.0930571	−	1.36644i
$796$	29.2167	−	50.6049i	0.0367045	−	0.0635740i
$797$	458.403	−	122.829i	0.575160	−	0.154114i	0.0404981	−	0.999180i	$-0.487106\pi$
$797$	458.403	−	122.829i	0.575160	−	0.154114i	0.534662	+	0.845066i	$0.320439\pi$
$798$	45.2225	+	2.71456i	0.0566698	+	0.00340171i
$799$	219.374	−	126.655i	0.274560	−	0.158517i
$800$	−530.095	+	513.312i	−0.662619	+	0.641640i
$801$	820.177	+	615.142i	1.02394	+	0.767968i
$802$	358.565	+	358.565i	0.447088	+	0.447088i
$803$	−355.688	−	95.3064i	−0.442949	−	0.118688i
$804$	69.1175	+	337.766i	0.0859670	+	0.420107i
$805$	−3.25378	−	12.5460i	−0.00404196	−	0.0155851i
$806$	333.111	−	576.965i	0.413289	−	0.715837i
$807$	−571.193	+	285.594i	−0.707798	+	0.353895i
$808$	322.581	+	86.4352i	0.399234	+	0.106974i
$809$			806.321i			0.996689i	0.866979	+	0.498344i	$0.166059\pi$
$809$			806.321i			0.996689i	−0.866979	+	0.498344i	$0.833941\pi$
$810$	82.8374	+	292.769i	0.102268	+	0.361443i
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	−39.7315	+	148.280i	−0.0489304	+	0.182611i
$813$	241.819	+	483.642i	0.297440	+	0.594886i
$814$	−348.727	−	201.338i	−0.428412	−	0.247344i
$815$	−858.172	−	504.711i	−1.05297	−	0.619277i
$816$	−397.776	+	81.3974i	−0.487471	+	0.0997517i
$817$	−23.1966	+	86.5709i	−0.0283924	+	0.105962i
$818$	230.158	−	230.158i	0.281366	−	0.281366i
$819$	−206.036	+	274.710i	−0.251570	+	0.335422i
$820$	494.978	+	503.004i	0.603632	+	0.613419i
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	0.663502	−	0.748174i	$-0.269069\pi$
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	−0.979689	+	0.200523i	$0.935736\pi$
$822$	0.321213	−	5.35116i	0.000390770	−	0.00650993i
$823$	−333.724	−	1245.48i	−0.405497	−	1.51334i	−0.803136	−	0.595795i	$-0.796837\pi$
$823$	−333.724	−	1245.48i	−0.405497	−	1.51334i	0.397639	−	0.917542i	$-0.369830\pi$
$824$	244.879	+	141.381i	0.297183	+	0.171579i
$825$	−66.3516	+	870.917i	−0.0804262	+	1.05566i
$826$	19.6477	+	34.0307i	0.0237865	+	0.0411994i
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	0.438876	−	0.898548i	$-0.355377\pi$
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	−0.898548	+	0.438876i	$0.855377\pi$
$828$	−26.5976	−	33.8850i	−0.0321227	−	0.0409239i
$829$		−	511.167i		−	0.616606i	−0.951288	−	0.308303i	$-0.900239\pi$
$829$		−	511.167i		−	0.616606i	0.951288	−	0.308303i	$-0.0997611\pi$
$830$	187.105	+	51.7510i	0.225428	+	0.0623506i
$831$	961.890	−	196.833i	1.15751	−	0.236862i
$832$	−317.086	+	84.9628i	−0.381113	+	0.102119i
$833$	−167.103	−	623.637i	−0.200604	−	0.748664i
$834$	547.911	+	182.639i	0.656968	+	0.218992i
$835$	−697.407	−	1230.70i	−0.835218	−	1.47389i
$836$	432.240			0.517034
$837$	755.313	−	890.462i	0.902405	−	1.06387i
$838$	−265.524	+	265.524i	−0.316855	+	0.316855i
$839$	889.044	−	513.290i	1.05965	−	0.611788i	0.134313	−	0.990939i	$-0.457117\pi$
$839$	889.044	−	513.290i	1.05965	−	0.611788i	0.925335	+	0.379151i	$0.123784\pi$
$840$	147.507	+	50.4912i	0.175603	+	0.0601086i
$841$	−132.163	+	228.913i	−0.157150	+	0.272192i
$842$	21.8317	−	5.84978i	0.0259284	−	0.00694749i
$843$	−51.6905	+	78.2882i	−0.0613173	+	0.0928686i
$844$	−885.970	+	511.515i	−1.04973	+	0.606061i
$845$	881.948	+	896.249i	1.04373	+	1.06065i
$846$	−111.092	+	47.4527i	−0.131314	+	0.0560906i
$847$	19.2439	+	19.2439i	0.0227200	+	0.0227200i
$848$	−669.305	−	179.340i	−0.789275	−	0.211486i
$849$	−455.061	+	403.523i	−0.535996	+	0.475292i
$850$	136.835	−	228.439i	0.160982	−	0.268752i
$851$	32.0597	−	55.5291i	0.0376730	−	0.0652516i
$852$	61.5669	−	1025.66i	0.0722616	−	1.20382i
$853$	−1345.32	−	360.478i	−1.57717	−	0.422600i	−0.639119	−	0.769108i	$-0.720701\pi$
$853$	−1345.32	−	360.478i	−1.57717	−	0.422600i	−0.938047	+	0.346508i	$0.887367\pi$
$854$			114.905i			0.134549i
$855$	184.714	−	449.683i	0.216039	−	0.525945i
$856$	−117.203			−0.136919
$857$	−85.4914	+	319.058i	−0.0997566	+	0.372297i	−0.997698	−	0.0678191i	$-0.978396\pi$
$857$	−85.4914	+	319.058i	−0.0997566	+	0.372297i	0.897941	+	0.440116i	$0.145063\pi$
$858$	296.556	−	449.151i	0.345637	−	0.523486i
$859$	−264.795	−	152.879i	−0.308259	−	0.177974i	0.337888	−	0.941186i	$-0.390287\pi$
$859$	−264.795	−	152.879i	−0.308259	−	0.177974i	−0.646147	+	0.763213i	$0.723621\pi$
$860$	−72.2461	+	122.842i	−0.0840071	+	0.142839i
$861$	72.5180	−	217.551i	0.0842253	−	0.252673i
$862$	100.283	−	374.262i	0.116338	−	0.434178i
$863$	386.017	−	386.017i	0.447297	−	0.447297i	−0.447158	−	0.894455i	$-0.647564\pi$
$863$	386.017	−	386.017i	0.447297	−	0.447297i	0.894455	+	0.447158i	$0.147564\pi$
$864$	794.254	−	65.2230i	0.919275	−	0.0754895i
$865$	12.4643	−	1549.85i	0.0144096	−	1.79174i
$866$	162.447	+	281.367i	0.187583	+	0.324904i
$867$	−236.086	+	118.042i	−0.272303	+	0.136150i
$868$	−71.5518	−	267.035i	−0.0824329	−	0.307644i
$869$	617.145	+	356.309i	0.710179	+	0.410022i
$870$	−224.623	−	150.918i	−0.258188	−	0.173468i
$871$	−342.961	−	594.025i	−0.393755	−	0.682004i
$872$	455.392	+	455.392i	0.522238	+	0.522238i
$873$	170.111	+	216.719i	0.194857	+	0.248246i
$874$		−	11.3069i		−	0.0129370i
$875$	204.171	−	111.399i	0.233338	−	0.127313i
$876$	216.221	+	243.836i	0.246827	+	0.278352i
$877$	−403.592	+	108.142i	−0.460196	+	0.123309i	−0.481466	−	0.876465i	$-0.659896\pi$
$877$	−403.592	+	108.142i	−0.460196	+	0.123309i	0.0212701	+	0.999774i	$0.493229\pi$
$878$	−98.2488	−	366.669i	−0.111901	−	0.417619i
$879$	87.5366	−	77.6226i	0.0995865	−	0.0883078i
$880$	535.729	+	148.176i	0.608783	+	0.168382i
$881$	−1495.93			−1.69799			−0.848993	−	0.528403i	$-0.822791\pi$
$881$	−1495.93			−1.69799			−0.848993	+	0.528403i	$0.822791\pi$
$882$	43.5413	+	304.805i	0.0493665	+	0.345584i
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	−0.791081	−	0.611712i	$-0.790481\pi$
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	0.611712	+	0.791081i	$0.290481\pi$
$884$	865.014	−	499.416i	0.978522	−	0.564950i
$885$	413.772	−	81.2092i	0.467538	−	0.0917618i
$886$	75.9157	−	131.490i	0.0856837	−	0.148408i
$887$	−1325.65	+	355.206i	−1.49453	+	0.400458i	−0.911264	−	0.411823i	$-0.864892\pi$
$887$	−1325.65	+	355.206i	−1.49453	+	0.400458i	−0.583266	+	0.812281i	$0.698225\pi$
$888$	344.931	+	689.869i	0.388436	+	0.776879i
$889$	127.805	−	73.7883i	0.143763	−	0.0830014i
$890$	−3.44115	+	427.885i	−0.00386647	+	0.480769i
$891$	652.204	−	681.524i	0.731991	−	0.764898i
$892$	77.6576	+	77.6576i	0.0870601	+	0.0870601i
$893$	186.437	+	49.9557i	0.208776	+	0.0559415i
$894$	−201.451	−	67.1513i	−0.225337	−	0.0751133i
$895$	−735.098	+	190.646i	−0.821339	+	0.213013i
$896$	121.028	−	209.626i	0.135076	−	0.233958i
$897$	71.5199	+	47.2217i	0.0797324	+	0.0526440i
$898$	−105.286	−	28.2113i	−0.117245	−	0.0314157i
$899$			1038.52i			1.15520i
$900$	473.697	−	610.865i	0.526330	−	0.678739i
$901$	1029.17			1.14225
$902$	−93.0274	+	347.183i	−0.103135	+	0.384903i
$903$	46.2262	+	2.77482i	0.0511918	+	0.00307288i
$904$	−506.909	−	292.664i	−0.560741	−	0.323744i
$905$	−60.3730	−	232.788i	−0.0667105	−	0.257224i
$906$	−42.0111	−	47.3767i	−0.0463698	−	0.0522922i
$907$	−143.552	+	535.743i	−0.158271	+	0.590676i	0.840532	+	0.541762i	$0.182243\pi$
$907$	−143.552	+	535.743i	−0.158271	+	0.590676i	−0.998803	+	0.0489140i	$0.984424\pi$
$908$	−950.276	+	950.276i	−1.04656	+	1.04656i
$909$	−534.193	−	64.3637i	−0.587671	−	0.0708072i
$910$	−143.316	−	1.15258i	−0.157490	−	0.00126657i
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	−0.999314	−	0.0370382i	$-0.988208\pi$
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	0.467581	−	0.883950i	$-0.345126\pi$
$912$	−258.175	−	170.462i	−0.283086	−	0.186910i
$913$	−155.775	−	581.361i	−0.170619	−	0.636759i
$914$	−192.995	−	111.426i	−0.211154	−	0.121910i
$915$	1166.56	+	399.309i	1.27493	+	0.436404i
$916$	430.882	+	746.309i	0.470395	+	0.814748i
$917$	6.09776	+	6.09776i	0.00664968	+	0.00664968i
$918$	−270.766	+	96.9190i	−0.294952	+	0.105576i
$919$		−	600.903i		−	0.653866i	−0.945048	−	0.326933i	$-0.893985\pi$
$919$		−	600.903i		−	0.653866i	0.945048	−	0.326933i	$-0.106015\pi$
$920$	10.3730	−	37.5035i	0.0112750	−	0.0407647i
$921$	−38.1512	+	114.452i	−0.0414237	+	0.124270i
$922$	207.604	−	55.6275i	0.225168	−	0.0603335i
$923$	529.090	+	1974.59i	0.573229	+	2.13932i
$924$	−44.7745	−	218.806i	−0.0484572	−	0.236803i
$925$	1106.48	+	315.638i	1.19619	+	0.341230i
$926$	187.992			0.203015
$927$	−422.780	−	169.702i	−0.456074	−	0.183066i
$928$	−501.193	+	501.193i	−0.540079	+	0.540079i
$929$	−435.996	+	251.722i	−0.469318	+	0.270961i	−0.715954	−	0.698147i	$-0.754008\pi$
$929$	−435.996	+	251.722i	−0.469318	+	0.270961i	0.246636	+	0.969108i	$0.420675\pi$
$930$	486.218	+	33.1124i	0.522815	+	0.0356047i
$931$	245.976	−	426.044i	0.264207	−	0.457619i
$932$	1122.06	−	300.655i	1.20393	−	0.322591i
$933$	1293.39	+	77.6380i	1.38627	+	0.0832133i
$934$	−65.6305	+	37.8918i	−0.0702682	+	0.0405694i
$935$	−825.550	−	6.63928i	−0.882941	−	0.00710083i
$936$	−948.056	+	404.960i	−1.01288	+	0.432650i
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.950847	+	0.309660i	$0.100215\pi$
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.309660	+	0.950847i	$0.399785\pi$
$938$	45.1656	+	12.1021i	0.0481509	+	0.0129020i
$939$	124.770	+	609.730i	0.132875	+	0.649339i
$940$	264.549	+	155.588i	0.281435	+	0.165519i
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	0.378002	+	0.925805i	$0.376611\pi$
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	−0.990771	+	0.135543i	$0.956722\pi$
$942$	77.7795	−	38.8894i	0.0825684	−	0.0412838i
$943$	−55.2832	−	14.8131i	−0.0586248	−	0.0157085i
$944$		−	268.341i		−	0.284259i
$945$	−246.770	−	46.9232i	−0.261132	−	0.0496542i
$946$	−72.5844			−0.0767277
$947$	−354.616	+	1323.45i	−0.374463	+	1.39751i	0.479665	+	0.877451i	$0.340758\pi$
$947$	−354.616	+	1323.45i	−0.374463	+	1.39751i	−0.854128	+	0.520063i	$0.825909\pi$
$948$	−282.046	−	564.098i	−0.297517	−	0.595040i
$949$	−561.512	−	324.189i	−0.591688	−	0.341611i
$950$	196.806	−	49.3557i	0.207165	−	0.0519533i
$951$	1043.67	−	213.566i	1.09744	−	0.224570i
$952$	−38.1409	+	142.344i	−0.0400640	+	0.149521i
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	−0.665306	−	0.746571i	$-0.731699\pi$
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	0.746571	+	0.665306i	$0.231699\pi$
$954$	−487.278	−	58.7110i	−0.510773	−	0.0615420i
$955$	−1295.09	+	1274.43i	−1.35612	+	1.33448i
$956$	−67.1397	−	116.289i	−0.0702298	−	0.121642i
$957$	−50.2716	+	837.486i	−0.0525304	+	0.875116i
$958$	−38.1245	−	142.282i	−0.0397959	−	0.148520i
$959$	3.83279	+	2.21286i	0.00399666	+	0.00230747i
$960$	−157.870	−	180.943i	−0.164447	−	0.188483i
$961$	−454.630	−	787.443i	−0.473080	−	0.819399i
$962$	−501.352	−	501.352i	−0.521156	−	0.521156i
$963$	186.932	−	26.7032i	0.194114	−	0.0277292i
$964$		−	287.577i		−	0.298316i
$965$	−52.0643	+	29.5036i	−0.0539526	+	0.0305737i
$966$	−5.72371	+	1.17125i	−0.00592517	+	0.00121247i
$967$	−1559.00	+	417.733i	−1.61220	+	0.431989i	−0.948698	−	0.316183i	$-0.897599\pi$
$967$	−1559.00	+	417.733i	−1.61220	+	0.431989i	−0.663505	+	0.748172i	$0.730932\pi$
$968$	21.1467	+	78.9205i	0.0218458	+	0.0815295i
$969$	435.921	+	145.309i	0.449867	+	0.149958i
$970$	−30.6535	+	110.828i	−0.0316016	+	0.114255i
$971$	158.612			0.163349			0.0816745	−	0.996659i	$-0.473973\pi$
$971$	158.612			0.163349			0.0816745	+	0.996659i	$0.473973\pi$
$972$	−814.026	+	185.304i	−0.837475	+	0.190642i
$973$	−337.156	+	337.156i	−0.346511	+	0.346511i
$974$	607.386	−	350.674i	0.623599	−	0.360035i
$975$	−509.743	+	1450.99i	−0.522814	+	1.48820i
$976$	392.332	−	679.539i	0.401980	−	0.696249i
$977$	−10.6944	+	2.86555i	−0.0109461	+	0.00293301i	−0.264288	−	0.964444i	$-0.585137\pi$
$977$	−10.6944	+	2.86555i	−0.0109461	+	0.00293301i	0.253342	+	0.967377i	$0.418470\pi$
$978$	−247.269	+	374.503i	−0.252831	+	0.382927i
$979$	1148.89	−	663.315i	1.17354	−	0.677543i
$980$	557.565	−	548.668i	0.568944	−	0.559865i
$981$	−830.082	−	622.571i	−0.846159	−	0.634629i
$982$	−418.604	−	418.604i	−0.426277	−	0.426277i
$983$	−1101.63	−	295.182i	−1.12069	−	0.300287i	−0.349525	−	0.936927i	$-0.613657\pi$
$983$	−1101.63	−	295.182i	−1.12069	−	0.300287i	−0.771161	+	0.636640i	$0.780324\pi$
$984$	515.111	−	456.772i	0.523486	−	0.464199i
$985$	162.534	−	276.360i	0.165009	−	0.280569i
$986$	127.892	−	221.516i	0.129708	−	0.224661i
$987$	5.97578	−	99.5518i	0.00605449	−	0.100863i
$988$	735.142	+	196.981i	0.744071	+	0.199373i
$989$		−	11.5579i		−	0.0116864i
$990$	390.493	+	50.2388i	0.394437	+	0.0507462i
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	330.371	−	1232.96i	0.333036	−	1.24291i
$993$	−619.706	+	938.579i	−0.624074	+	0.945195i
$994$	−120.685	−	69.6776i	−0.121414	−	0.0700982i
$995$	−82.3178	+	21.3490i	−0.0827315	+	0.0214562i
$996$	−168.445	+	505.329i	−0.169122	+	0.507359i
$997$	227.782	−	850.093i	0.228467	−	0.852651i	−0.752518	−	0.658571i	$-0.771161\pi$
$997$	227.782	−	850.093i	0.228467	−	0.852651i	0.980986	−	0.194080i	$-0.0621722\pi$
$998$	−88.7943	+	88.7943i	−0.0889723	+	0.0889723i
$999$	−707.325	−	1021.72i	−0.708033	−	1.02274i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.22.6	yes	40
3.2	odd	2		135.3.l.a.37.5		40
5.2	odd	4		225.3.o.b.193.6		40
5.3	odd	4	inner	45.3.k.a.13.5	yes	40
5.4	even	2		225.3.o.b.157.5		40
9.2	odd	6		135.3.l.a.127.6		40
9.4	even	3		405.3.g.h.82.6		20
9.5	odd	6		405.3.g.g.82.5		20
9.7	even	3	inner	45.3.k.a.7.5	✓	40
15.8	even	4		135.3.l.a.118.6		40
45.7	odd	12		225.3.o.b.43.5		40
45.13	odd	12		405.3.g.h.163.6		20
45.23	even	12		405.3.g.g.163.5		20
45.34	even	6		225.3.o.b.7.6		40
45.38	even	12		135.3.l.a.73.5		40
45.43	odd	12	inner	45.3.k.a.43.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	9.7	even	3	inner
45.3.k.a.13.5	yes	40	5.3	odd	4	inner
45.3.k.a.22.6	yes	40	1.1	even	1	trivial
45.3.k.a.43.6	yes	40	45.43	odd	12	inner
135.3.l.a.37.5		40	3.2	odd	2
135.3.l.a.73.5		40	45.38	even	12
135.3.l.a.118.6		40	15.8	even	4
135.3.l.a.127.6		40	9.2	odd	6
225.3.o.b.7.6		40	45.34	even	6
225.3.o.b.43.5		40	45.7	odd	12
225.3.o.b.157.5		40	5.4	even	2
225.3.o.b.193.6		40	5.2	odd	4
405.3.g.g.82.5		20	9.5	odd	6
405.3.g.g.163.5		20	45.23	even	12
405.3.g.h.82.6		20	9.4	even	3
405.3.g.h.163.6		20	45.13	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

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	45.3.k.a.22.6

Level	$45$
Weight	$3$
Character	45.22
Analytic conductor	$1.226$
Analytic rank	$0$
Dimension	$40$
Inner twists	$4$