LMFDB - Embedded newform 150.3.k.a.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("150.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.2
Character	$\chi$	$=$	150.67
Dual form			150.3.k.a.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-2.43941 + 4.36455i) q^{5} +(1.98168 + 1.43977i) q^{6} +(4.46938 + 4.46938i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(3.93346 + 5.87604i) q^{10} +(4.11407 + 12.6618i) q^{11} +(3.08654 - 1.57267i) q^{12} +(3.12732 + 6.13772i) q^{13} +(8.50127 - 2.76223i) q^{14} +(-6.80559 - 5.35574i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(1.26467 + 7.98483i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(6.62068 - 9.11259i) q^{19} +(9.92968 - 1.18379i) q^{20} +(-8.85688 + 6.43490i) q^{21} +(18.5962 + 2.94535i) q^{22} +(0.409422 + 0.208611i) q^{23} -4.89898i q^{24} +(-13.0986 - 21.2938i) q^{25} +9.74184 q^{26} +(2.35900 - 4.62981i) q^{27} +(1.97754 - 12.4857i) q^{28} +(-2.55597 - 3.51799i) q^{29} +(-11.1181 + 5.13694i) q^{30} +(-22.7575 - 16.5343i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-22.7756 + 3.60730i) q^{33} +(10.8734 + 3.53300i) q^{34} +(-30.4095 + 8.60421i) q^{35} +(1.85410 + 5.70634i) q^{36} +(54.4644 - 27.7510i) q^{37} +(-7.23179 - 14.1932i) q^{38} +(-11.3473 + 3.68697i) q^{39} +(4.88358 - 13.2722i) q^{40} +(-19.2764 + 59.3265i) q^{41} +(2.42198 + 15.2918i) q^{42} +(23.6476 - 23.6476i) q^{43} +(15.6509 - 21.5416i) q^{44} +(11.0062 - 10.1913i) q^{45} +(0.525730 - 0.381966i) q^{46} +(-9.41029 - 1.49044i) q^{47} +(-6.17307 - 3.14534i) q^{48} -9.04920i q^{49} +(-35.2416 + 2.83372i) q^{50} -14.0025 q^{51} +(6.25465 - 12.2754i) q^{52} +(6.51666 - 41.1446i) q^{53} +(-4.31932 - 5.94504i) q^{54} +(-65.2990 - 12.9312i) q^{55} +(-14.4632 - 10.5082i) q^{56} +(13.7953 + 13.7953i) q^{57} +(-6.07395 + 0.962020i) q^{58} +(-76.9714 - 25.0095i) q^{59} +(-0.665323 + 17.3077i) q^{60} +(29.1718 + 89.7817i) q^{61} +(-35.4456 + 18.0605i) q^{62} +(-8.60856 - 16.8953i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-34.4172 - 1.32302i) q^{65} +(-10.0774 + 31.0150i) q^{66} +(-13.6532 - 86.2026i) q^{67} +(11.4330 - 11.4330i) q^{68} +(-0.467810 + 0.643886i) q^{69} +(-8.68216 + 43.8424i) q^{70} +(26.9523 - 19.5820i) q^{71} +(8.38081 + 1.32739i) q^{72} +(104.261 + 53.1237i) q^{73} -86.4464i q^{74} +(39.9770 - 16.6385i) q^{75} -22.5276 q^{76} +(-38.2031 + 74.9779i) q^{77} +(-2.63958 + 16.6656i) q^{78} +(15.5360 + 21.3834i) q^{79} +(-13.5885 - 14.6749i) q^{80} +(7.28115 + 5.29007i) q^{81} +(62.3796 + 62.3796i) q^{82} +(152.851 - 24.2092i) q^{83} +(20.8238 + 6.76606i) q^{84} +(-37.9352 - 13.9585i) q^{85} +(-14.6150 - 44.9804i) q^{86} +(6.71086 - 3.41935i) q^{87} +(-17.0955 - 33.5518i) q^{88} +(-52.8670 + 17.1775i) q^{89} +(-5.77543 - 20.4119i) q^{90} +(-13.4546 + 41.4090i) q^{91} +(-0.143765 - 0.907696i) q^{92} +(34.4519 - 34.4519i) q^{93} +(-7.91984 + 10.9007i) q^{94} +(23.6218 + 51.1256i) q^{95} +(-7.92672 + 5.75910i) q^{96} +(72.4360 + 11.4727i) q^{97} +(-11.4027 - 5.80995i) q^{98} -39.9403i 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$2$	0.642040	−	1.26007i	0.321020	−	0.630037i
$3$	−0.270952	+	1.71073i	−0.0903175	+	0.570242i
$3$	−0.270952	+	1.71073i	−0.0903175	+	0.570242i
$4$	−1.17557	−	1.61803i	−0.293893	−	0.404508i
$5$	−2.43941	+	4.36455i	−0.487881	+	0.872910i
$5$	−2.43941	+	4.36455i	−0.487881	+	0.872910i
$6$	1.98168	+	1.43977i	0.330280	+	0.239962i
$7$	4.46938	+	4.46938i	0.638484	+	0.638484i	0.950181	−	0.311698i	$-0.100898\pi$
$7$	4.46938	+	4.46938i	0.638484	+	0.638484i	−0.311698	+	0.950181i	$0.600898\pi$
$8$	−2.79360	+	0.442463i	−0.349201	+	0.0553079i
$9$	−2.85317	−	0.927051i	−0.317019	−	0.103006i
$10$	3.93346	+	5.87604i	0.393346	+	0.587604i
$11$	4.11407	+	12.6618i	0.374007	+	1.15107i	0.944146	+	0.329526i	$0.106889\pi$
$11$	4.11407	+	12.6618i	0.374007	+	1.15107i	−0.570140	+	0.821548i	$0.693111\pi$
$12$	3.08654	−	1.57267i	0.257211	−	0.131056i
$13$	3.12732	+	6.13772i	0.240563	+	0.472132i	0.979447	−	0.201701i	$-0.0646468\pi$
$13$	3.12732	+	6.13772i	0.240563	+	0.472132i	−0.738884	+	0.673833i	$0.764647\pi$
$14$	8.50127	−	2.76223i	0.607234	−	0.197302i
$15$	−6.80559	−	5.35574i	−0.453706	−	0.357049i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	1.26467	+	7.98483i	0.0743925	+	0.469696i	0.996558	+	0.0829000i	$0.0264182\pi$
$17$	1.26467	+	7.98483i	0.0743925	+	0.469696i	−0.922165	+	0.386796i	$0.873582\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$	6.62068	−	9.11259i	0.348457	−	0.479610i	−0.598431	−	0.801175i	$-0.704209\pi$
$19$	6.62068	−	9.11259i	0.348457	−	0.479610i	0.946888	+	0.321565i	$0.104209\pi$
$20$	9.92968	−	1.18379i	0.496484	−	0.0591897i
$21$	−8.85688	+	6.43490i	−0.421756	+	0.306424i
$22$	18.5962	+	2.94535i	0.845282	+	0.133880i
$23$	0.409422	+	0.208611i	0.0178010	+	0.00907004i	0.462868	−	0.886427i	$-0.346820\pi$
$23$	0.409422	+	0.208611i	0.0178010	+	0.00907004i	−0.445067	+	0.895497i	$0.646820\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−13.0986	−	21.2938i	−0.523944	−	0.851753i
$26$	9.74184			0.374686
$27$	2.35900	−	4.62981i	0.0873705	−	0.171474i
$28$	1.97754	−	12.4857i	0.0706264	−	0.445918i
$29$	−2.55597	−	3.51799i	−0.0881368	−	0.121310i	0.762672	−	0.646786i	$-0.223887\pi$
$29$	−2.55597	−	3.51799i	−0.0881368	−	0.121310i	−0.850808	+	0.525476i	$0.823887\pi$
$30$	−11.1181	+	5.13694i	−0.370603	+	0.171231i
$31$	−22.7575	−	16.5343i	−0.734113	−	0.533364i	0.156749	−	0.987638i	$-0.449899\pi$
$31$	−22.7575	−	16.5343i	−0.734113	−	0.533364i	−0.890862	+	0.454274i	$0.849899\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−22.7756	+	3.60730i	−0.690170	+	0.109312i
$34$	10.8734	+	3.53300i	0.319807	+	0.103912i
$35$	−30.4095	+	8.60421i	−0.868843	+	0.245835i
$36$	1.85410	+	5.70634i	0.0515028	+	0.158509i
$37$	54.4644	−	27.7510i	1.47201	−	0.750027i	0.480130	−	0.877198i	$-0.340590\pi$
$37$	54.4644	−	27.7510i	1.47201	−	0.750027i	0.991881	+	0.127171i	$0.0405896\pi$
$38$	−7.23179	−	14.1932i	−0.190310	−	0.373505i
$39$	−11.3473	+	3.68697i	−0.290957	+	0.0945376i
$40$	4.88358	−	13.2722i	0.122090	−	0.331804i
$41$	−19.2764	+	59.3265i	−0.470155	+	1.44699i	0.382226	+	0.924069i	$0.375157\pi$
$41$	−19.2764	+	59.3265i	−0.470155	+	1.44699i	−0.852382	+	0.522920i	$0.824843\pi$
$42$	2.42198	+	15.2918i	0.0576662	+	0.364090i
$43$	23.6476	−	23.6476i	0.549944	−	0.549944i	−0.376480	−	0.926425i	$-0.622866\pi$
$43$	23.6476	−	23.6476i	0.549944	−	0.549944i	0.926425	+	0.376480i	$0.122866\pi$
$44$	15.6509	−	21.5416i	0.355701	−	0.489581i
$45$	11.0062	−	10.1913i	0.244582	−	0.226474i
$46$	0.525730	−	0.381966i	0.0114289	−	0.00830360i
$47$	−9.41029	−	1.49044i	−0.200219	−	0.0317116i	0.0555194	−	0.998458i	$-0.482319\pi$
$47$	−9.41029	−	1.49044i	−0.200219	−	0.0317116i	−0.255738	+	0.966746i	$0.582319\pi$
$48$	−6.17307	−	3.14534i	−0.128606	−	0.0655279i
$49$		−	9.04920i		−	0.184678i
$50$	−35.2416	+	2.83372i	−0.704832	+	0.0566744i
$51$	−14.0025			−0.274559
$52$	6.25465	−	12.2754i	0.120282	−	0.236066i
$53$	6.51666	−	41.1446i	0.122956	−	0.776313i	−0.846742	−	0.532004i	$-0.821439\pi$
$53$	6.51666	−	41.1446i	0.122956	−	0.776313i	0.969698	−	0.244308i	$-0.0785609\pi$
$54$	−4.31932	−	5.94504i	−0.0799874	−	0.110093i
$55$	−65.2990	−	12.9312i	−1.18725	−	0.235113i
$56$	−14.4632	−	10.5082i	−0.258272	−	0.187646i
$57$	13.7953	+	13.7953i	0.242022	+	0.242022i
$58$	−6.07395	+	0.962020i	−0.104723	+	0.0165866i
$59$	−76.9714	−	25.0095i	−1.30460	−	0.423890i	−0.427421	−	0.904053i	$-0.640578\pi$
$59$	−76.9714	−	25.0095i	−1.30460	−	0.423890i	−0.877180	+	0.480163i	$0.840578\pi$
$60$	−0.665323	+	17.3077i	−0.0110887	+	0.288462i
$61$	29.1718	+	89.7817i	0.478227	+	1.47183i	0.841556	+	0.540170i	$0.181640\pi$
$61$	29.1718	+	89.7817i	0.478227	+	1.47183i	−0.363329	+	0.931661i	$0.618360\pi$
$62$	−35.4456	+	18.0605i	−0.571704	+	0.291298i
$63$	−8.60856	−	16.8953i	−0.136644	−	0.268179i
$64$	7.60845	−	2.47214i	0.118882	−	0.0386271i
$65$	−34.4172	−	1.32302i	−0.529495	−	0.0203542i
$66$	−10.0774	+	31.0150i	−0.152688	+	0.469924i
$67$	−13.6532	−	86.2026i	−0.203778	−	1.28661i	−0.851349	−	0.524600i	$-0.824215\pi$
$67$	−13.6532	−	86.2026i	−0.203778	−	1.28661i	0.647570	−	0.762006i	$-0.275785\pi$
$68$	11.4330	−	11.4330i	0.168133	−	0.168133i
$69$	−0.467810	+	0.643886i	−0.00677986	+	0.00933168i
$70$	−8.68216	+	43.8424i	−0.124031	+	0.626321i
$71$	26.9523	−	19.5820i	0.379610	−	0.275803i	−0.381575	−	0.924338i	$-0.624618\pi$
$71$	26.9523	−	19.5820i	0.379610	−	0.275803i	0.761185	+	0.648535i	$0.224618\pi$
$72$	8.38081	+	1.32739i	0.116400	+	0.0184360i
$73$	104.261	+	53.1237i	1.42823	+	0.727721i	0.985618	−	0.168990i	$-0.0540506\pi$
$73$	104.261	+	53.1237i	1.42823	+	0.727721i	0.442616	+	0.896711i	$0.354051\pi$
$74$		−	86.4464i		−	1.16819i
$75$	39.9770	−	16.6385i	0.533027	−	0.221847i
$76$	−22.5276			−0.296415
$77$	−38.2031	+	74.9779i	−0.496145	+	0.973739i
$78$	−2.63958	+	16.6656i	−0.0338407	+	0.213662i
$79$	15.5360	+	21.3834i	0.196658	+	0.270676i	0.895945	−	0.444164i	$-0.146499\pi$
$79$	15.5360	+	21.3834i	0.196658	+	0.270676i	−0.699288	+	0.714840i	$0.746499\pi$
$80$	−13.5885	−	14.6749i	−0.169856	−	0.183437i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	62.3796	+	62.3796i	0.760727	+	0.760727i
$83$	152.851	−	24.2092i	1.84158	−	0.291677i	0.864196	−	0.503155i	$-0.167828\pi$
$83$	152.851	−	24.2092i	1.84158	−	0.291677i	0.977383	+	0.211478i	$0.0678277\pi$
$84$	20.8238	+	6.76606i	0.247902	+	0.0805483i
$85$	−37.9352	−	13.9585i	−0.446297	−	0.164218i
$86$	−14.6150	−	44.9804i	−0.169942	−	0.523028i
$87$	6.71086	−	3.41935i	0.0771363	−	0.0393029i
$88$	−17.0955	−	33.5518i	−0.194267	−	0.381270i
$89$	−52.8670	+	17.1775i	−0.594011	+	0.193006i	−0.590568	−	0.806988i	$-0.701096\pi$
$89$	−52.8670	+	17.1775i	−0.594011	+	0.193006i	−0.00344353	+	0.999994i	$0.501096\pi$
$90$	−5.77543	−	20.4119i	−0.0641715	−	0.226799i
$91$	−13.4546	+	41.4090i	−0.147853	+	0.455044i
$92$	−0.143765	−	0.907696i	−0.00156266	−	0.00986626i
$93$	34.4519	−	34.4519i	0.370450	−	0.370450i
$94$	−7.91984	+	10.9007i	−0.0842537	+	0.115965i
$95$	23.6218	+	51.1256i	0.248651	+	0.538164i
$96$	−7.92672	+	5.75910i	−0.0825700	+	0.0599906i
$97$	72.4360	+	11.4727i	0.746763	+	0.118276i	0.518207	−	0.855255i	$-0.326600\pi$
$97$	72.4360	+	11.4727i	0.746763	+	0.118276i	0.228556	+	0.973531i	$0.426600\pi$
$98$	−11.4027	−	5.80995i	−0.116354	−	0.0592852i
$99$		−	39.9403i		−	0.403437i
$100$	−19.0558	+	46.2264i	−0.190558	+	0.462264i
$101$	190.230			1.88347			0.941733	−	0.336361i	$-0.109196\pi$
$101$	190.230			1.88347			0.941733	+	0.336361i	$0.109196\pi$
$102$	−8.99017	+	17.6442i	−0.0881390	+	0.172982i
$103$	25.7613	−	162.650i	0.250110	−	1.57913i	−0.468338	−	0.883549i	$-0.655147\pi$
$103$	25.7613	−	162.650i	0.250110	−	1.57913i	0.718448	−	0.695581i	$-0.244853\pi$
$104$	−11.4522	−	15.7626i	−0.110118	−	0.151564i
$105$	−6.47992	−	54.3537i	−0.0617135	−	0.517654i
$106$	−47.6612	−	34.6279i	−0.449634	−	0.326678i
$107$	32.0521	+	32.0521i	0.299553	+	0.299553i	0.840839	−	0.541286i	$-0.182062\pi$
$107$	32.0521	+	32.0521i	0.299553	+	0.299553i	−0.541286	+	0.840839i	$0.682062\pi$
$108$	−10.2644	+	1.62571i	−0.0950404	+	0.0150529i
$109$	−3.48677	−	1.13292i	−0.0319887	−	0.0103938i	0.292979	−	0.956119i	$-0.405353\pi$
$109$	−3.48677	−	1.13292i	−0.0319887	−	0.0103938i	−0.324968	+	0.945725i	$0.605353\pi$
$110$	−58.2188	+	73.9792i	−0.529262	+	0.672538i
$111$	32.7171	+	100.693i	0.294749	+	0.907143i
$112$	−22.5270	+	11.4781i	−0.201134	+	0.102483i
$113$	67.7341	+	132.936i	0.599417	+	1.17642i	0.968962	+	0.247209i	$0.0795133\pi$
$113$	67.7341	+	132.936i	0.599417	+	1.17642i	−0.369546	+	0.929213i	$0.620487\pi$
$114$	26.2401	−	8.52594i	0.230177	−	0.0747889i
$115$	−1.90924	+	1.27806i	−0.0166021	+	0.0111135i
$116$	−2.68750	+	8.27128i	−0.0231681	+	0.0713042i
$117$	−3.23281	−	20.4111i	−0.0276308	−	0.174454i
$118$	−80.9325	+	80.9325i	−0.685869	+	0.685869i
$119$	−30.0350	+	41.3396i	−0.252395	+	0.347391i
$120$	21.3818	+	11.9506i	0.178182	+	0.0995883i
$121$	−45.5049	+	33.0612i	−0.376073	+	0.273233i
$122$	131.861	+	20.8847i	1.08083	+	0.171186i
$123$	−96.2685	−	49.0513i	−0.782671	−	0.398791i
$124$			56.2596i			0.453707i
$125$	124.891	−	5.22522i	0.999126	−	0.0418018i
$126$	−26.8163			−0.212828
$127$	−48.9575	+	96.0844i	−0.385492	+	0.756570i	−0.999463	−	0.0327578i	$-0.989571\pi$
$127$	−48.9575	+	96.0844i	−0.385492	+	0.756570i	0.613971	+	0.789328i	$0.289571\pi$
$128$	1.76985	−	11.1744i	0.0138270	−	0.0873001i
$129$	34.0472	+	46.8620i	0.263932	+	0.363271i
$130$	−23.7643	+	42.5188i	−0.182802	+	0.327067i
$131$	−46.8592	−	34.0452i	−0.357704	−	0.259887i	0.394390	−	0.918943i	$-0.370956\pi$
$131$	−46.8592	−	34.0452i	−0.357704	−	0.259887i	−0.752094	+	0.659056i	$0.770956\pi$
$132$	32.6111	+	32.6111i	0.247054	+	0.247054i
$133$	70.3181	−	11.1373i	0.528707	−	0.0837390i
$134$	−117.387	−	38.1415i	−0.876026	−	0.284638i
$135$	14.4525	+	21.5900i	0.107055	+	0.159926i
$136$	−7.06599	−	21.7469i	−0.0519558	−	0.159904i
$137$	−217.605	+	110.875i	−1.58836	+	0.809309i	−0.588358	+	0.808601i	$0.700225\pi$
$137$	−217.605	+	110.875i	−1.58836	+	0.809309i	−1.00000		0.000707950i	$0.999775\pi$
$138$	0.510991	+	1.00288i	0.00370283	+	0.00726721i
$139$	−215.498	+	70.0197i	−1.55035	+	0.503739i	−0.954209	−	0.299142i	$-0.903299\pi$
$139$	−215.498	+	70.0197i	−1.55035	+	0.503739i	−0.596140	+	0.802881i	$0.703299\pi$
$140$	49.6704	+	39.0887i	0.354789	+	0.279205i
$141$	5.09948	−	15.6946i	0.0361665	−	0.111309i
$142$	−7.37031	−	46.5343i	−0.0519036	−	0.327706i
$143$	−64.8486	+	64.8486i	−0.453487	+	0.453487i
$144$	7.05342	−	9.70820i	0.0489821	−	0.0674181i
$145$	21.5895	−	2.57385i	0.148893	−	0.0177507i
$146$	133.879	−	97.2691i	0.916982	−	0.666227i
$147$	15.4807	+	2.45190i	0.105311	+	0.0166796i
$148$	−108.929	−	55.5020i	−0.736005	−	0.375013i
$149$		−	248.314i		−	1.66653i	−0.552871	−	0.833267i	$-0.686468\pi$
$149$		−	248.314i		−	1.66653i	0.552871	−	0.833267i	$-0.313532\pi$
$150$	4.70107	−	61.0565i	0.0313405	−	0.407044i
$151$	−191.158			−1.26595			−0.632975	−	0.774172i	$-0.718166\pi$
$151$	−191.158			−1.26595			−0.632975	+	0.774172i	$0.718166\pi$
$152$	−14.4636	+	28.3864i	−0.0951552	+	0.186753i
$153$	3.79402	−	23.9545i	0.0247975	−	0.156565i
$154$	69.9497	+	96.2775i	0.454219	+	0.625179i
$155$	127.680	−	58.9924i	0.823739	−	0.380596i
$156$	19.3052	+	14.0260i	0.123751	+	0.0899106i
$157$	16.3094	+	16.3094i	0.103882	+	0.103882i	0.757137	−	0.653256i	$-0.226597\pi$
$157$	16.3094	+	16.3094i	0.103882	+	0.103882i	−0.653256	+	0.757137i	$0.726597\pi$
$158$	36.9194	−	5.84746i	0.233667	−	0.0370092i
$159$	68.6214	+	22.2964i	0.431581	+	0.140229i
$160$	−27.2158	+	7.70058i	−0.170099	+	0.0481286i
$161$	0.897502	+	2.76223i	0.00557455	+	0.0171567i
$162$	11.3407	−	5.77836i	0.0700041	−	0.0356689i
$163$	20.0640	+	39.3779i	0.123092	+	0.241582i	0.944327	−	0.329008i	$-0.106714\pi$
$163$	20.0640	+	39.3779i	0.123092	+	0.241582i	−0.821235	+	0.570590i	$0.806714\pi$
$164$	118.653	−	38.5527i	0.723494	−	0.235078i
$165$	39.8147	−	108.205i	0.241301	−	0.655788i
$166$	67.6310	−	208.147i	0.407416	−	1.25390i
$167$	−41.1904	−	260.066i	−0.246649	−	1.55728i	−0.730982	−	0.682396i	$-0.760938\pi$
$167$	−41.1904	−	260.066i	−0.246649	−	1.55728i	0.484333	−	0.874884i	$-0.339062\pi$
$168$	21.8954	−	21.8954i	0.130330	−	0.130330i
$169$	71.4443	−	98.3346i	0.422747	−	0.581862i
$170$	−41.9447	+	38.8393i	−0.246733	+	0.228466i
$171$	−27.3378	+	19.8621i	−0.159870	+	0.116152i
$172$	−66.0620	−	10.4632i	−0.384082	−	0.0608326i
$173$	125.189	+	63.7868i	0.723634	+	0.368710i	0.776691	−	0.629882i	$-0.216897\pi$
$173$	125.189	+	63.7868i	0.723634	+	0.368710i	−0.0530572	+	0.998591i	$0.516897\pi$
$174$		−	10.6515i		−	0.0612157i
$175$	36.6276	−	153.713i	0.209301	−	0.878360i
$176$	−53.2537			−0.302578
$177$	63.6401	−	124.901i	0.359548	−	0.705653i
$178$	−12.2978	+	77.6450i	−0.0690885	+	0.436208i
$179$	−67.7817	−	93.2935i	−0.378669	−	0.521193i	0.576562	−	0.817053i	$-0.304394\pi$
$179$	−67.7817	−	93.2935i	−0.378669	−	0.521193i	−0.955231	+	0.295860i	$0.904394\pi$
$180$	−29.4285	−	5.82776i	−0.163492	−	0.0323764i
$181$	−156.525	−	113.722i	−0.864777	−	0.628297i	0.0644032	−	0.997924i	$-0.479486\pi$
$181$	−156.525	−	113.722i	−0.864777	−	0.628297i	−0.929180	+	0.369627i	$0.879486\pi$
$182$	43.5400	+	43.5400i	0.239231	+	0.239231i
$183$	−161.496	+	25.5785i	−0.882492	+	0.139773i
$184$	−1.23607	−	0.401622i	−0.00671775	−	0.00218273i
$185$	−11.7402	+	305.408i	−0.0634603	+	1.65086i
$186$	−21.2924	−	65.5313i	−0.114475	−	0.352319i
$187$	−95.8995	+	48.8632i	−0.512831	+	0.261301i
$188$	8.65087	+	16.9783i	0.0460153	+	0.0903100i
$189$	31.2357	−	10.1491i	0.165268	−	0.0536989i
$190$	79.5882	+	3.05943i	0.418885	+	0.0161023i
$191$	100.783	−	310.179i	0.527661	−	1.62397i	−0.231332	−	0.972875i	$-0.574308\pi$
$191$	100.783	−	310.179i	0.527661	−	1.62397i	0.758993	−	0.651098i	$-0.225692\pi$
$192$	2.16762	+	13.6858i	0.0112897	+	0.0712803i
$193$	−160.639	+	160.639i	−0.832326	+	0.832326i	−0.987835	−	0.155508i	$-0.950298\pi$
$193$	−160.639	+	160.639i	−0.832326	+	0.832326i	0.155508	+	0.987835i	$0.450298\pi$
$194$	60.9632	−	83.9087i	0.314244	−	0.432519i
$195$	11.5888	−	58.5199i	0.0594295	−	0.300102i
$196$	−14.6419	+	10.6380i	−0.0747037	+	0.0542754i
$197$	−303.089	−	48.0045i	−1.53852	−	0.243678i	−0.671143	−	0.741328i	$-0.734197\pi$
$197$	−303.089	−	48.0045i	−1.53852	−	0.243678i	−0.867378	+	0.497650i	$0.834197\pi$
$198$	−50.3277	−	25.6432i	−0.254180	−	0.129511i
$199$			294.270i			1.47875i	0.673297	+	0.739373i	$0.264878\pi$
$199$			294.270i			1.47875i	−0.673297	+	0.739373i	$0.735122\pi$
$200$	46.0140	+	53.6909i	0.230070	+	0.268454i
$201$	151.168			0.752082
$202$	122.135	−	239.704i	0.604630	−	1.18665i
$203$	4.29964	−	27.1468i	0.0211805	−	0.133728i
$204$	16.4610	+	22.6566i	0.0806910	+	0.111062i
$205$	−211.911	−	228.854i	−1.03371	−	1.11636i
$206$	−188.412	−	136.889i	−0.914620	−	0.664510i
$207$	−0.974758	−	0.974758i	−0.00470897	−	0.00470897i
$208$	−27.2149	+	4.31041i	−0.130841	+	0.0207231i
$209$	142.620	+	46.3400i	0.682392	+	0.221723i
$210$	−72.6500	−	26.7320i	−0.345952	−	0.127295i
$211$	104.896	+	322.836i	0.497136	+	1.53003i	0.813601	+	0.581424i	$0.197504\pi$
$211$	104.896	+	322.836i	0.497136	+	1.53003i	−0.316464	+	0.948604i	$0.602496\pi$
$212$	−74.2341	+	37.8242i	−0.350161	+	0.178416i
$213$	26.1966	+	51.4138i	0.122989	+	0.241379i
$214$	60.9668	−	19.8093i	0.284892	−	0.0925669i
$215$	45.5250	+	160.897i	0.211744	+	0.748359i
$216$	−4.54160	+	13.9776i	−0.0210259	+	0.0647112i
$217$	−27.8139	−	175.610i	−0.128175	−	0.809263i
$218$	−3.66620	+	3.66620i	−0.0168174	+	0.0168174i
$219$	−119.130	+	163.968i	−0.543972	+	0.748713i
$220$	55.8404	+	120.858i	0.253820	+	0.549353i
$221$	−45.0536	+	32.7333i	−0.203862	+	0.148115i
$222$	147.886	+	23.4229i	0.666154	+	0.105508i
$223$	−206.767	−	105.353i	−0.927204	−	0.472434i	−0.0759052	−	0.997115i	$-0.524185\pi$
$223$	−206.767	−	105.353i	−0.927204	−	0.472434i	−0.851299	+	0.524681i	$0.824185\pi$
$224$			35.7551i			0.159621i
$225$	17.6321	+	72.8979i	0.0783647	+	0.323991i
$226$	210.997			0.933613
$227$	51.5088	−	101.092i	0.226911	−	0.445338i	−0.749279	−	0.662254i	$-0.769600\pi$
$227$	51.5088	−	101.092i	0.226911	−	0.445338i	0.976190	+	0.216916i	$0.0695998\pi$
$228$	6.10390	−	38.5385i	0.0267715	−	0.169028i
$229$	66.8989	+	92.0785i	0.292135	+	0.402089i	0.929706	−	0.368302i	$-0.120061\pi$
$229$	66.8989	+	92.0785i	0.292135	+	0.402089i	−0.637571	+	0.770391i	$0.720061\pi$
$230$	0.384638	+	3.22635i	0.00167234	+	0.0140276i
$231$	−117.915	−	85.6706i	−0.510456	−	0.370868i
$232$	8.69694	+	8.69694i	0.0374868	+	0.0374868i
$233$	−84.7393	+	13.4214i	−0.363688	+	0.0576025i	−0.335604	−	0.942003i	$-0.608941\pi$
$233$	−84.7393	+	13.4214i	−0.363688	+	0.0576025i	−0.0280838	+	0.999606i	$0.508941\pi$
$234$	−27.7951	−	9.03118i	−0.118783	−	0.0385948i
$235$	29.4606	−	37.4359i	0.125364	−	0.159302i
$236$	50.0191	+	153.943i	0.211945	+	0.652300i
$237$	−40.7907	+	20.7839i	−0.172113	+	0.0876958i
$238$	32.8073	+	64.3879i	0.137846	+	0.270537i
$239$	−121.771	+	39.5659i	−0.509504	+	0.165548i	−0.552477	−	0.833528i	$-0.686317\pi$
$239$	−121.771	+	39.5659i	−0.509504	+	0.165548i	0.0429728	+	0.999076i	$0.486317\pi$
$240$	28.7866	−	19.2699i	0.119944	−	0.0802914i
$241$	−14.7642	+	45.4395i	−0.0612621	+	0.188545i	−0.977004	−	0.213222i	$-0.931604\pi$
$241$	−14.7642	+	45.4395i	−0.0612621	+	0.188545i	0.915742	+	0.401768i	$0.131604\pi$
$242$	12.4437	+	78.5661i	0.0514200	+	0.324653i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$	110.976	−	152.746i	0.454821	−	0.626007i
$245$	39.4957	+	22.0747i	0.161207	+	0.0901007i
$246$	−123.616	+	89.8126i	−0.502506	+	0.365092i
$247$	76.6355	+	12.1379i	0.310265	+	0.0491412i
$248$	70.8913	+	36.1209i	0.285852	+	0.145649i
$249$			268.046i			1.07649i
$250$	73.6006	−	160.726i	0.294403	−	0.642905i
$251$	245.752			0.979092			0.489546	−	0.871977i	$-0.337162\pi$
$251$	245.752			0.979092			0.489546	+	0.871977i	$0.337162\pi$
$252$	−17.2171	+	33.7905i	−0.0683219	+	0.134089i
$253$	−0.957001	+	6.04227i	−0.00378261	+	0.0238825i
$254$	89.6408	+	123.380i	0.352917	+	0.485748i
$255$	34.1578	−	61.1147i	0.133952	−	0.239666i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−82.2310	−	82.2310i	−0.319965	−	0.319965i	0.528789	−	0.848754i	$-0.322646\pi$
$257$	−82.2310	−	82.2310i	−0.319965	−	0.319965i	−0.848754	+	0.528789i	$0.822646\pi$
$258$	80.9092	−	12.8148i	0.313601	−	0.0496696i
$259$	367.452	+	119.392i	1.41873	+	0.460975i
$260$	38.3191	+	57.2435i	0.147381	+	0.220167i
$261$	4.03125	+	12.4069i	0.0154454	+	0.0475361i
$262$	−72.9850	+	37.1877i	−0.278569	+	0.141938i
$263$	−33.6616	−	66.0647i	−0.127991	−	0.251196i	0.818114	−	0.575056i	$-0.195020\pi$
$263$	−33.6616	−	66.0647i	−0.127991	−	0.251196i	−0.946105	+	0.323859i	$0.895020\pi$
$264$	62.0300	−	20.1548i	0.234962	−	0.0763438i
$265$	163.681	+	128.811i	0.617663	+	0.486078i
$266$	31.1132	−	95.7565i	0.116967	−	0.359987i
$267$	−15.0616	−	95.0953i	−0.0564105	−	0.356162i
$268$	−123.428	+	123.428i	−0.460554	+	0.460554i
$269$	−186.916	+	257.268i	−0.694855	+	0.956386i	0.305137	+	0.952309i	$0.401298\pi$
$269$	−186.916	+	257.268i	−0.694855	+	0.956386i	−0.999992	+	0.00407713i	$0.998702\pi$
$270$	36.4840	−	4.34954i	0.135126	−	0.0161094i
$271$	80.1417	−	58.2263i	0.295726	−	0.214857i	−0.430022	−	0.902819i	$-0.641494\pi$
$271$	80.1417	−	58.2263i	0.295726	−	0.214857i	0.725747	+	0.687961i	$0.241494\pi$
$272$	−31.9393	−	5.05869i	−0.117424	−	0.0185981i
$273$	−67.1940	−	34.2370i	−0.246132	−	0.125410i
$274$			345.385i			1.26053i
$275$	215.730	−	253.456i	0.784472	−	0.921659i
$276$	1.59177			0.00576729
$277$	15.2334	−	29.8973i	0.0549943	−	0.107932i	−0.861874	−	0.507123i	$-0.830709\pi$
$277$	15.2334	−	29.8973i	0.0549943	−	0.107932i	0.916868	+	0.399191i	$0.130709\pi$
$278$	−50.1285	+	316.499i	−0.180319	+	1.13849i
$279$	49.6029	+	68.2725i	0.177788	+	0.244704i
$280$	81.1451	−	37.4919i	0.289804	−	0.133899i
$281$	−49.9955	−	36.3238i	−0.177920	−	0.129266i	0.495261	−	0.868744i	$-0.335072\pi$
$281$	−49.9955	−	36.3238i	−0.177920	−	0.129266i	−0.673181	+	0.739478i	$0.735072\pi$
$282$	−16.5023	−	16.5023i	−0.0585187	−	0.0585187i
$283$	−16.9304	+	2.68151i	−0.0598247	+	0.00947530i	−0.186275	−	0.982498i	$-0.559642\pi$
$283$	−16.9304	+	2.68151i	−0.0598247	+	0.00947530i	0.126450	+	0.991973i	$0.459642\pi$
$284$	−63.3686	−	20.5897i	−0.223129	−	0.0724990i
$285$	−93.8623	+	26.5579i	−0.329342	+	0.0931855i
$286$	40.0786	+	123.349i	0.140135	+	0.431292i
$287$	−351.307	+	179.000i	−1.22406	+	0.623692i
$288$	−7.70447	−	15.1209i	−0.0267516	−	0.0525031i
$289$	212.697	−	69.1095i	0.735977	−	0.239133i
$290$	10.6181	−	28.8568i	0.0366140	−	0.0995063i
$291$	−39.2534	+	120.810i	−0.134891	+	0.415153i
$292$	−36.6103	−	231.148i	−0.125378	−	0.791604i
$293$	−57.3285	+	57.3285i	−0.195660	+	0.195660i	−0.798137	−	0.602476i	$-0.794181\pi$
$293$	−57.3285	+	57.3285i	−0.195660	+	0.195660i	0.602476	+	0.798137i	$0.294181\pi$
$294$	13.0288	−	17.9326i	0.0443157	−	0.0609953i
$295$	296.920	−	274.937i	1.00651	−	0.931991i
$296$	−139.873	+	101.624i	−0.472544	+	0.343324i
$297$	68.3269	+	10.8219i	0.230057	+	0.0364374i
$298$	−312.893	−	159.427i	−1.04998	−	0.534990i
$299$			3.16531i			0.0105863i
$300$	−73.9174	−	45.1244i	−0.246391	−	0.150415i
$301$	211.380			0.702261
$302$	−122.731	+	240.874i	−0.406395	+	0.797595i
$303$	−51.5433	+	325.432i	−0.170110	+	1.07403i
$304$	26.4827	+	36.4504i	0.0871143	+	0.119903i
$305$	−463.019	−	91.6920i	−1.51809	−	0.300630i
$306$	−27.7485	−	20.1605i	−0.0906814	−	0.0658839i
$307$	424.372	+	424.372i	1.38232	+	1.38232i	0.840486	+	0.541833i	$0.182269\pi$
$307$	424.372	+	424.372i	1.38232	+	1.38232i	0.541833	+	0.840486i	$0.317731\pi$
$308$	166.227	−	26.3278i	0.539699	−	0.0854799i
$309$	271.270	+	88.1410i	0.877897	+	0.285246i
$310$	7.64054	−	198.761i	0.0246469	−	0.641165i
$311$	−79.9847	−	246.168i	−0.257185	−	0.791536i	−0.993391	−	0.114778i	$-0.963384\pi$
$311$	−79.9847	−	246.168i	−0.257185	−	0.791536i	0.736206	−	0.676758i	$-0.236616\pi$
$312$	30.0686	−	15.3207i	0.0963736	−	0.0491048i
$313$	144.446	+	283.492i	0.461489	+	0.905724i	0.998083	+	0.0618833i	$0.0197107\pi$
$313$	144.446	+	283.492i	0.461489	+	0.905724i	−0.536594	+	0.843841i	$0.680289\pi$
$314$	31.0224	−	10.0798i	0.0987974	−	0.0321012i
$315$	94.7400	+	3.64188i	0.300762	+	0.0115615i
$316$	16.3355	−	50.2755i	0.0516946	−	0.159100i
$317$	−83.0522	−	524.371i	−0.261994	−	1.65417i	−0.670869	−	0.741576i	$-0.734079\pi$
$317$	−83.0522	−	524.371i	−0.261994	−	1.65417i	0.408875	−	0.912590i	$-0.365921\pi$
$318$	72.1528	−	72.1528i	0.226896	−	0.226896i
$319$	34.0287	−	46.8364i	0.106673	−	0.146823i
$320$	−7.77034	+	39.2380i	−0.0242823	+	0.122619i
$321$	−63.5171	+	46.1478i	−0.197872	+	0.143763i
$322$	4.05684	+	0.642541i	0.0125989	+	0.00199547i
$323$	81.1355	+	41.3406i	0.251193	+	0.127989i
$324$		−	18.0000i		−	0.0555556i
$325$	89.7319	−	146.988i	0.276098	−	0.452271i
$326$	62.5009			0.191720
$327$	2.88286	−	5.65794i	0.00881609	−	0.0173026i
$328$	27.6007	−	174.264i	0.0841485	−	0.531293i
$329$	−35.3968	−	48.7196i	−0.107589	−	0.148084i
$330$	−110.784	−	119.641i	−0.335708	−	0.362550i
$331$	−153.071	−	111.212i	−0.462449	−	0.335989i	0.332042	−	0.943265i	$-0.392262\pi$
$331$	−153.071	−	111.212i	−0.462449	−	0.335989i	−0.794491	+	0.607276i	$0.792262\pi$
$332$	−218.859	−	218.859i	−0.659212	−	0.659212i
$333$	−181.123	+	28.6870i	−0.543912	+	0.0861472i
$334$	−354.148	−	115.070i	−1.06032	−	0.344520i
$335$	409.541	+	150.693i	1.22251	+	0.449831i
$336$	−13.5321	−	41.6476i	−0.0402742	−	0.123951i
$337$	−178.580	+	90.9910i	−0.529911	+	0.270003i	−0.698409	−	0.715699i	$-0.746108\pi$
$337$	−178.580	+	90.9910i	−0.529911	+	0.270003i	0.168498	+	0.985702i	$0.446108\pi$
$338$	−78.0388	−	153.160i	−0.230884	−	0.453135i
$339$	−245.769	+	79.8552i	−0.724983	+	0.235561i
$340$	22.0102	+	77.7897i	0.0647359	+	0.228793i
$341$	115.728	−	356.175i	0.339379	−	1.04450i
$342$	7.47572	+	47.1998i	0.0218588	+	0.138011i
$343$	259.444	−	259.444i	0.756397	−	0.756397i
$344$	−55.5988	+	76.5252i	−0.161625	+	0.222457i
$345$	−1.66909	−	3.61248i	−0.00483795	−	0.0104710i
$346$	160.752	−	116.793i	0.464602	−	0.337553i
$347$	272.609	+	43.1770i	0.785615	+	0.124429i	0.536339	−	0.844003i	$-0.319807\pi$
$347$	272.609	+	43.1770i	0.785615	+	0.124429i	0.249277	+	0.968432i	$0.419807\pi$
$348$	−13.4217	−	6.83871i	−0.0385682	−	0.0196515i
$349$		−	570.145i		−	1.63365i	−0.576883	−	0.816827i	$-0.695731\pi$
$349$		−	570.145i		−	1.63365i	0.576883	−	0.816827i	$-0.304269\pi$
$350$	−170.173	−	144.843i	−0.486209	−	0.413838i
$351$	35.7938			0.101977
$352$	−34.1910	+	67.1035i	−0.0971334	+	0.190635i
$353$	−47.9348	+	302.649i	−0.135793	+	0.857362i	0.821913	+	0.569613i	$0.192907\pi$
$353$	−47.9348	+	302.649i	−0.135793	+	0.857362i	−0.957706	+	0.287749i	$0.907093\pi$
$354$	−116.525	−	160.382i	−0.329165	−	0.453057i
$355$	19.7190	+	165.403i	0.0555464	+	0.465924i
$356$	89.9427	+	65.3472i	0.252648	+	0.183560i
$357$	−62.5827	−	62.5827i	−0.175302	−	0.175302i
$358$	−161.075	+	25.5118i	−0.449931	+	0.0712621i
$359$	56.3971	+	18.3245i	0.157095	+	0.0510432i	0.386509	−	0.922286i	$-0.373681\pi$
$359$	56.3971	+	18.3245i	0.157095	+	0.0510432i	−0.229414	+	0.973329i	$0.573681\pi$
$360$	−26.2377	+	33.3404i	−0.0728824	+	0.0926123i
$361$	72.3493	+	222.668i	0.200414	+	0.616810i
$362$	−243.793	+	124.219i	−0.673461	+	0.343146i
$363$	−44.2291	−	86.8044i	−0.121843	−	0.239131i
$364$	82.8181	−	26.9092i	0.227522	−	0.0739264i
$365$	−486.196	+	325.462i	−1.33204	+	0.891678i
$366$	−71.4561	+	219.919i	−0.195235	+	0.600872i
$367$	−27.1947	−	171.701i	−0.0741000	−	0.467849i	−0.996637	−	0.0819408i	$-0.973888\pi$
$367$	−27.1947	−	171.701i	−0.0741000	−	0.467849i	0.922537	−	0.385908i	$-0.126112\pi$
$368$	−1.29968	+	1.29968i	−0.00353173	+	0.00353173i
$369$	109.997	−	151.399i	0.298096	−	0.410294i
$370$	377.300	+	210.878i	1.01973	+	0.569940i
$371$	213.016	−	154.765i	0.574168	−	0.417158i
$372$	−96.2449	−	15.2437i	−0.258723	−	0.0409777i
$373$	−147.365	−	75.0864i	−0.395081	−	0.201304i	0.245152	−	0.969485i	$-0.421162\pi$
$373$	−147.365	−	75.0864i	−0.395081	−	0.201304i	−0.640233	+	0.768181i	$0.721162\pi$
$374$			152.213i			0.406985i
$375$	−24.9005	+	215.070i	−0.0664014	+	0.573519i
$376$	26.9481			0.0716704
$377$	13.5991	−	26.6897i	0.0360718	−	0.0707949i
$378$	7.26594	−	45.8754i	0.0192221	−	0.121363i
$379$	−286.581	−	394.445i	−0.756151	−	1.04075i	−0.997524	−	0.0703207i	$-0.977598\pi$
$379$	−286.581	−	394.445i	−0.756151	−	1.04075i	0.241373	−	0.970432i	$-0.422402\pi$
$380$	54.9539	−	98.3227i	0.144615	−	0.258744i
$381$	−151.109	−	109.787i	−0.396612	−	0.288155i
$382$	−326.141	−	326.141i	−0.853773	−	0.853773i
$383$	220.039	−	34.8507i	0.574514	−	0.0909940i	0.137585	−	0.990490i	$-0.456066\pi$
$383$	220.039	−	34.8507i	0.574514	−	0.0909940i	0.436929	+	0.899496i	$0.356066\pi$
$384$	18.6368	+	6.05547i	0.0485334	+	0.0157695i
$385$	−234.052	−	349.641i	−0.607927	−	0.908159i
$386$	99.2803	+	305.553i	0.257203	+	0.791589i
$387$	−89.3931	+	45.5481i	−0.230990	+	0.117695i
$388$	−66.5903	−	130.691i	−0.171625	−	0.336832i
$389$	189.774	−	61.6612i	0.487850	−	0.158512i	−0.0547555	−	0.998500i	$-0.517438\pi$
$389$	189.774	−	61.6612i	0.487850	−	0.158512i	0.542605	+	0.839988i	$0.317438\pi$
$390$	−66.2990	−	52.1748i	−0.169997	−	0.133781i
$391$	−1.14794	+	3.53299i	−0.00293590	+	0.00903578i
$392$	4.00394	+	25.2799i	0.0102141	+	0.0644895i
$393$	70.9387	−	70.9387i	0.180506	−	0.180506i
$394$	−255.084	+	351.093i	−0.647422	+	0.891100i
$395$	−131.228	+	15.6447i	−0.332222	+	0.0396067i
$396$	−64.6247	+	46.9526i	−0.163194	+	0.118567i
$397$	326.973	+	51.7874i	0.823609	+	0.130447i	0.553993	−	0.832521i	$-0.313103\pi$
$397$	326.973	+	51.7874i	0.823609	+	0.130447i	0.269616	+	0.962968i	$0.413103\pi$
$398$	370.802	+	188.933i	0.931664	+	0.474706i
$399$			123.313i			0.309054i
$400$	97.1973	−	23.5094i	0.242993	−	0.0587735i
$401$	177.978			0.443835			0.221917	−	0.975065i	$-0.428769\pi$
$401$	177.978			0.443835			0.221917	+	0.975065i	$0.428769\pi$
$402$	97.0561	−	190.483i	0.241433	−	0.473839i
$403$	30.3128	−	191.387i	0.0752178	−	0.474906i
$404$	−223.629	−	307.799i	−0.553537	−	0.761878i
$405$	−40.8505	+	18.8743i	−0.100865	+	0.0466033i
$406$	−31.4465	−	22.8472i	−0.0774544	−	0.0562739i
$407$	575.448	+	575.448i	1.41388	+	1.41388i
$408$	39.1175	−	6.19561i	0.0958763	−	0.0151853i
$409$	−305.692	−	99.3253i	−0.747413	−	0.242849i	−0.0895452	−	0.995983i	$-0.528541\pi$
$409$	−305.692	−	99.3253i	−0.747413	−	0.242849i	−0.657868	+	0.753134i	$0.728541\pi$
$410$	−424.428	+	120.090i	−1.03519	+	0.292902i
$411$	−130.717	−	402.305i	−0.318045	−	0.978843i
$412$	−293.458	+	149.524i	−0.712277	+	0.362923i
$413$	−232.238	−	455.792i	−0.562319	−	1.10361i
$414$	−1.85410	+	0.602433i	−0.00447850	+	0.00145515i
$415$	−267.203	+	726.182i	−0.643863	+	1.74984i
$416$	−12.0416	+	37.0602i	−0.0289461	+	0.0890869i
$417$	−61.3947	−	387.631i	−0.147229	−	0.929570i
$418$	149.959	−	149.959i	0.358755	−	0.358755i
$419$	−88.5237	+	121.842i	−0.211274	+	0.290793i	−0.901481	−	0.432818i	$-0.857519\pi$
$419$	−88.5237	+	121.842i	−0.211274	+	0.290793i	0.690208	+	0.723611i	$0.257519\pi$
$420$	−80.3285	+	74.3813i	−0.191258	+	0.177098i
$421$	−155.898	+	113.266i	−0.370304	+	0.269041i	−0.757337	−	0.653025i	$-0.773500\pi$
$421$	−155.898	+	113.266i	−0.370304	+	0.269041i	0.387033	+	0.922066i	$0.373500\pi$
$422$	474.144	+	75.0971i	1.12356	+	0.177955i
$423$	25.4674	+	12.9763i	0.0602067	+	0.0306768i
$424$			117.825i			0.277889i
$425$	153.462	−	131.520i	0.361087	−	0.309458i
$426$	81.6044			0.191560
$427$	−270.889	+	531.649i	−0.634400	+	1.24508i
$428$	14.1819	−	89.5410i	0.0331353	−	0.209208i
$429$	−93.3673	−	128.509i	−0.217639	−	0.299555i
$430$	231.971	+	45.9375i	0.539468	+	0.106831i
$431$	−291.340	−	211.671i	−0.675963	−	0.491116i	0.196053	−	0.980593i	$-0.437188\pi$
$431$	−291.340	−	211.671i	−0.675963	−	0.491116i	−0.872016	+	0.489477i	$0.837188\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−48.2272	+	7.63844i	−0.111379	+	0.0176407i	−0.211875	−	0.977297i	$-0.567957\pi$
$433$	−48.2272	+	7.63844i	−0.111379	+	0.0176407i	0.100496	+	0.994937i	$0.467957\pi$
$434$	−239.139	−	77.7011i	−0.551012	−	0.179035i
$435$	−1.44657	+	37.6311i	−0.00332545	+	0.0865082i
$436$	2.26584	+	6.97353i	0.00519688	+	0.0159943i
$437$	4.61164	−	2.34975i	0.0105530	−	0.00537700i
$438$	130.126	+	255.386i	0.297091	+	0.583074i
$439$	112.018	−	36.3969i	0.255167	−	0.0829087i	−0.178640	−	0.983914i	$-0.557170\pi$
$439$	112.018	−	36.3969i	0.255167	−	0.0829087i	0.433807	+	0.901006i	$0.357170\pi$
$440$	188.141	+	7.23230i	0.427594	+	0.0164371i
$441$	−8.38907	+	25.8189i	−0.0190228	+	0.0585463i
$442$	12.3202	+	77.7869i	0.0278738	+	0.175989i
$443$	67.5353	−	67.5353i	0.152450	−	0.152450i	−0.626761	−	0.779211i	$-0.715620\pi$
$443$	67.5353	−	67.5353i	0.152450	−	0.152450i	0.779211	+	0.626761i	$0.215620\pi$
$444$	124.463	−	171.309i	0.280323	−	0.385831i
$445$	53.9919	−	272.644i	0.121330	−	0.612682i
$446$	−265.505	+	192.900i	−0.595302	+	0.432512i
$447$	424.797	+	67.2812i	0.950328	+	0.150517i
$448$	45.0540	+	22.9562i	0.100567	+	0.0512415i
$449$		−	232.122i		−	0.516975i	−0.966015	−	0.258488i	$-0.916776\pi$
$449$		−	232.122i		−	0.516975i	0.966015	−	0.258488i	$-0.0832242\pi$
$450$	103.177	+	24.5857i	0.229283	+	0.0546348i
$451$	−830.486			−1.84143
$452$	135.468	−	265.871i	0.299708	−	0.588211i
$453$	51.7949	−	327.020i	0.114337	−	0.721898i
$454$	−94.3124	−	129.810i	−0.207737	−	0.285925i
$455$	−147.911	−	159.737i	−0.325078	−	0.351070i
$456$	−44.6424	−	32.4346i	−0.0979000	−	0.0711285i
$457$	360.686	+	360.686i	0.789247	+	0.789247i	0.981371	−	0.192124i	$-0.0615375\pi$
$457$	360.686	+	360.686i	0.789247	+	0.789247i	−0.192124	+	0.981371i	$0.561538\pi$
$458$	158.977	−	25.1795i	0.347112	−	0.0549772i
$459$	39.9516	+	12.9811i	0.0870405	+	0.0282812i
$460$	4.31239	+	1.58677i	0.00937475	+	0.00344950i
$461$	−99.9616	−	307.650i	−0.216836	−	0.667354i	−0.999018	−	0.0443034i	$-0.985893\pi$
$461$	−99.9616	−	307.650i	−0.216836	−	0.667354i	0.782182	−	0.623050i	$-0.214107\pi$
$462$	−183.658	+	93.5782i	−0.397527	+	0.202550i
$463$	111.727	+	219.278i	0.241312	+	0.473602i	0.979619	−	0.200863i	$-0.0643746\pi$
$463$	111.727	+	219.278i	0.241312	+	0.473602i	−0.738307	+	0.674464i	$0.764375\pi$
$464$	16.5426	−	5.37501i	0.0356521	−	0.0115841i
$465$	66.3248	+	234.409i	0.142634	+	0.504105i
$466$	−37.4941	+	115.395i	−0.0804594	+	0.247628i
$467$	54.1305	+	341.767i	0.115911	+	0.731834i	0.975361	+	0.220614i	$0.0708063\pi$
$467$	54.1305	+	341.767i	0.115911	+	0.731834i	−0.859450	+	0.511220i	$0.829194\pi$
$468$	−29.2255	+	29.2255i	−0.0624477	+	0.0624477i
$469$	324.251	−	446.294i	0.691368	−	0.951586i
$470$	−28.2571	−	61.1579i	−0.0601214	−	0.130123i
$471$	−32.3201	+	23.4819i	−0.0686201	+	0.0498554i
$472$	226.093	+	35.8097i	0.479012	+	0.0758680i
$473$	396.709	+	202.134i	0.838709	+	0.427344i
$474$			64.7434i			0.136589i
$475$	−280.764	−	21.6175i	−0.591081	−	0.0455105i
$476$	102.197			0.214700
$477$	−56.7363	+	111.351i	−0.118944	+	0.233441i
$478$	−28.3261	+	178.844i	−0.0592596	+	0.374150i
$479$	273.543	+	376.499i	0.571070	+	0.786011i	0.992681	−	0.120766i	$-0.0385352\pi$
$479$	273.543	+	376.499i	0.571070	+	0.786011i	−0.421611	+	0.906777i	$0.638535\pi$
$480$	−5.79939	−	48.6453i	−0.0120821	−	0.101344i
$481$	340.656	+	247.501i	0.708224	+	0.514555i
$482$	47.7779	+	47.7779i	0.0991242	+	0.0991242i
$483$	−4.96860	+	0.786948i	−0.0102869	+	0.00162929i
$484$	106.988	+	34.7626i	0.221050	+	0.0718236i
$485$	−226.774	+	288.164i	−0.467575	+	0.594152i
$486$	6.81241	+	20.9664i	0.0140173	+	0.0431408i
$487$	−187.998	+	95.7900i	−0.386034	+	0.196694i	−0.636227	−	0.771502i	$-0.719506\pi$
$487$	−187.998	+	95.7900i	−0.386034	+	0.196694i	0.250193	+	0.968196i	$0.419506\pi$
$488$	−121.220	−	237.907i	−0.248401	−	0.487514i
$489$	−72.8011	+	23.6545i	−0.148878	+	0.0483733i
$490$	53.1735	−	35.5947i	0.108517	−	0.0726422i
$491$	−131.594	+	405.005i	−0.268013	+	0.824858i	0.722971	+	0.690878i	$0.242776\pi$
$491$	−131.594	+	405.005i	−0.268013	+	0.824858i	−0.990984	+	0.133980i	$0.957224\pi$
$492$	33.8038	+	213.429i	0.0687070	+	0.433799i
$493$	24.8581	−	24.8581i	0.0504220	−	0.0504220i
$494$	64.4977	−	88.7734i	0.130562	−	0.179703i
$495$	174.321	+	97.4305i	0.352164	+	0.196829i
$496$	91.0300	−	66.1372i	0.183528	−	0.133341i
$497$	207.980	+	32.9407i	0.418470	+	0.0662791i
$498$	337.757	+	172.096i	0.678228	+	0.345574i
$499$		−	357.072i		−	0.715575i	−0.933803	−	0.357788i	$-0.883531\pi$
$499$		−	357.072i		−	0.715575i	0.933803	−	0.357788i	$-0.116469\pi$
$500$	−155.272	−	195.935i	−0.310545	−	0.391870i
$501$	456.062			0.910303
$502$	157.783	−	309.666i	0.314308	−	0.616864i
$503$	48.8913	−	308.687i	0.0971994	−	0.613693i	−0.890215	−	0.455540i	$-0.849446\pi$
$503$	48.8913	−	308.687i	0.0971994	−	0.613693i	0.987415	−	0.158153i	$-0.0505538\pi$
$504$	31.5245	+	43.3897i	0.0625485	+	0.0860907i
$505$	−464.048	+	830.269i	−0.918908	+	1.64410i
$506$	6.99927	+	5.08527i	0.0138325	+	0.0100499i
$507$	148.866	+	148.866i	0.293621	+	0.293621i
$508$	213.021	−	33.7392i	0.419332	−	0.0664157i
$509$	−92.5225	−	30.0624i	−0.181773	−	0.0590617i	0.216716	−	0.976235i	$-0.430465\pi$
$509$	−92.5225	−	30.0624i	−0.181773	−	0.0590617i	−0.398489	+	0.917173i	$0.630465\pi$
$510$	−55.0784	−	82.2795i	−0.107997	−	0.161332i
$511$	228.553	+	703.413i	0.447265	+	1.37654i
$512$	−20.1612	+	10.2726i	−0.0393773	+	0.0200637i
$513$	−26.5713	−	52.1491i	−0.0517959	−	0.101655i
$514$	−156.413	+	50.8216i	−0.304305	+	0.0988746i
$515$	647.054	+	509.207i	1.25641	+	0.988751i
$516$	35.7993	−	110.179i	0.0693786	−	0.213525i
$517$	−19.8429	−	125.283i	−0.0383808	−	0.242327i
$518$	386.362	−	386.362i	0.745873	−	0.745873i
$519$	−143.042	+	196.880i	−0.275611	+	0.379346i
$520$	96.7334	−	11.5323i	0.186026	−	0.0221776i
$521$	−740.991	+	538.362i	−1.42225	+	1.03332i	−0.430853	+	0.902422i	$0.641787\pi$
$521$	−740.991	+	538.362i	−1.42225	+	1.03332i	−0.991395	+	0.130902i	$0.958213\pi$
$522$	18.2219	+	2.88606i	0.0349078	+	0.00552885i
$523$	−287.644	−	146.562i	−0.549988	−	0.280233i	0.156833	−	0.987625i	$-0.449872\pi$
$523$	−287.644	−	146.562i	−0.549988	−	0.280233i	−0.706821	+	0.707392i	$0.749872\pi$
$524$			115.842i			0.221073i
$525$	253.036	+	104.309i	0.481974	+	0.198683i
$526$	−104.858			−0.199351
$527$	103.243	−	202.625i	0.195907	−	0.384488i
$528$	14.4292	−	91.1025i	0.0273281	−	0.172543i
$529$	−310.814	−	427.799i	−0.587551	−	0.808694i
$530$	267.400	−	123.548i	0.504529	−	0.233110i
$531$	196.427	+	142.713i	0.369920	+	0.268762i
$532$	−100.684	−	100.684i	−0.189256	−	0.189256i
$533$	−424.413	+	67.2204i	−0.796272	+	0.126117i
$534$	−129.497	−	42.0762i	−0.242504	−	0.0787943i
$535$	−218.081	+	61.7050i	−0.407629	+	0.115336i
$536$	76.2830	+	234.775i	0.142319	+	0.438013i
$537$	177.965	−	90.6779i	0.331407	−	0.168860i
$538$	204.169	+	400.704i	0.379496	+	0.744803i
$539$	114.579	−	37.2291i	0.212578	−	0.0690707i
$540$	17.9434	−	48.7651i	0.0332286	−	0.0903057i
$541$	308.267	−	948.749i	0.569810	−	1.75369i	−0.0833988	−	0.996516i	$-0.526578\pi$
$541$	308.267	−	948.749i	0.569810	−	1.75369i	0.653209	−	0.757178i	$-0.273422\pi$
$542$	−21.9153	−	138.368i	−0.0404342	−	0.255292i
$543$	236.958	−	236.958i	0.436386	−	0.436386i
$544$	−26.8806	+	36.9980i	−0.0494129	+	0.0680110i
$545$	13.4503	−	12.4545i	0.0246795	−	0.0228523i
$546$	−86.2824	+	62.6878i	−0.158026	+	0.114813i
$547$	306.761	+	48.5862i	0.560807	+	0.0888231i	0.430401	−	0.902638i	$-0.358372\pi$
$547$	306.761	+	48.5862i	0.560807	+	0.0888231i	0.130406	+	0.991461i	$0.458372\pi$
$548$	435.210	+	221.751i	0.794179	+	0.404654i
$549$		−	283.206i		−	0.515858i
$550$	−180.867	−	434.564i	−0.328848	−	0.790117i
$551$	−48.9802			−0.0888933
$552$	1.02198	−	2.00575i	0.00185142	−	0.00363361i
$553$	−26.1345	+	165.007i	−0.0472596	+	0.298385i
$554$	−27.8923	−	38.3905i	−0.0503471	−	0.0692969i
$555$	−519.289	−	102.835i	−0.935656	−	0.185289i
$556$	366.628	+	266.371i	0.659402	+	0.479084i
$557$	−231.263	−	231.263i	−0.415193	−	0.415193i	0.468350	−	0.883543i	$-0.344849\pi$
$557$	−231.263	−	231.263i	−0.415193	−	0.415193i	−0.883543	+	0.468350i	$0.844849\pi$
$558$	117.875	−	18.6696i	0.211246	−	0.0334581i
$559$	219.096	+	71.1886i	0.391943	+	0.127350i
$560$	4.85584	−	126.320i	0.00867115	−	0.225571i
$561$	−57.6074	−	177.297i	−0.102687	−	0.316038i
$562$	−77.8698	+	39.6766i	−0.138558	+	0.0705990i
$563$	−463.291	−	909.261i	−0.822898	−	1.61503i	−0.788031	−	0.615636i	$-0.788899\pi$
$563$	−463.291	−	909.261i	−0.822898	−	1.61503i	−0.0348670	−	0.999392i	$-0.511101\pi$
$564$	−31.3892	+	10.1990i	−0.0556546	+	0.0180833i
$565$	−745.435	−	28.6551i	−1.31935	−	0.0507170i
$566$	−7.49108	+	23.0552i	−0.0132351	+	0.0407335i
$567$	8.89893	+	56.1856i	0.0156948	+	0.0990928i
$568$	−66.6297	+	66.6297i	−0.117306	+	0.117306i
$569$	2.54931	−	3.50882i	0.00448033	−	0.00616665i	−0.806771	−	0.590864i	$-0.798787\pi$
$569$	2.54931	−	3.50882i	0.00448033	−	0.00616665i	0.811251	+	0.584698i	$0.198787\pi$
$570$	−26.7985	+	135.325i	−0.0470149	+	0.237412i
$571$	−568.551	+	413.077i	−0.995712	+	0.723427i	−0.961164	−	0.275976i	$-0.910999\pi$
$571$	−568.551	+	413.077i	−0.995712	+	0.723427i	−0.0345472	+	0.999403i	$0.510999\pi$
$572$	181.161	+	28.6931i	0.316716	+	0.0501628i
$573$	503.324	+	256.456i	0.878401	+	0.447568i
$574$			557.597i			0.971423i
$575$	−0.920731	−	11.4507i	−0.00160127	−	0.0199142i
$576$	−24.0000			−0.0416667
$577$	−212.740	+	417.525i	−0.368699	+	0.723613i	−0.998591	−	0.0530700i	$-0.983099\pi$
$577$	−212.740	+	417.525i	−0.368699	+	0.723613i	0.629891	+	0.776683i	$0.283099\pi$
$578$	49.4770	−	312.385i	0.0856003	−	0.540459i
$579$	−231.284	−	318.335i	−0.399454	−	0.549801i
$580$	−29.5445	−	31.9068i	−0.0509388	−	0.0550117i
$581$	791.350	+	574.950i	1.36205	+	0.989586i
$582$	127.027	+	127.027i	0.218259	+	0.218259i
$583$	547.775	−	86.7590i	0.939580	−	0.148815i
$584$	−314.769	−	102.275i	−0.538989	−	0.175128i
$585$	96.9716	+	35.6813i	0.165763	+	0.0609937i
$586$	35.4310	+	109.045i	0.0604624	+	0.186084i
$587$	559.377	−	285.017i	0.952942	−	0.485548i	0.0928461	−	0.995680i	$-0.470404\pi$
$587$	559.377	−	285.017i	0.952942	−	0.485548i	0.860096	+	0.510132i	$0.170404\pi$
$588$	−14.2314	−	27.9307i	−0.0242031	−	0.0475012i
$589$	−301.341	+	97.9115i	−0.511614	+	0.166233i
$590$	−155.807	−	550.661i	−0.264079	−	0.933324i
$591$	164.245	−	505.495i	0.277911	−	0.855321i
$592$	38.2494	+	241.497i	0.0646104	+	0.407934i
$593$	−790.827	+	790.827i	−1.33360	+	1.33360i	−0.431481	+	0.902122i	$0.642009\pi$
$593$	−790.827	+	790.827i	−1.33360	+	1.33360i	−0.902122	+	0.431481i	$0.857991\pi$
$594$	57.5049	−	79.1488i	0.0968097	−	0.133247i
$595$	−107.161	−	231.933i	−0.180103	−	0.389804i
$596$	−401.780	+	291.910i	−0.674127	+	0.489782i
$597$	−503.416	−	79.7333i	−0.843243	−	0.133557i
$598$	3.98853	+	2.03226i	0.00666978	+	0.00339842i
$599$		−	446.487i		−	0.745387i	−0.927955	−	0.372693i	$-0.878434\pi$
$599$		−	446.487i		−	0.745387i	0.927955	−	0.372693i	$-0.121566\pi$
$600$	−104.318	+	64.1698i	−0.173863	+	0.106950i
$601$	139.951			0.232863			0.116432	−	0.993199i	$-0.462854\pi$
$601$	139.951			0.232863			0.116432	+	0.993199i	$0.462854\pi$
$602$	135.715	−	266.355i	0.225440	−	0.442450i
$603$	−40.9595	+	258.608i	−0.0679261	+	0.428869i
$604$	224.720	+	309.301i	0.372053	+	0.512088i
$605$	−33.2925	−	279.258i	−0.0550290	−	0.461584i
$606$	376.975	+	273.888i	0.622071	+	0.451961i
$607$	174.526	+	174.526i	0.287522	+	0.287522i	0.836100	−	0.548578i	$-0.184830\pi$
$607$	174.526	+	174.526i	0.287522	+	0.287522i	−0.548578	+	0.836100i	$0.684830\pi$
$608$	62.9331	−	9.96762i	0.103508	−	0.0163941i
$609$	45.2758	+	14.7110i	0.0743445	+	0.0241560i
$610$	−412.815	+	524.568i	−0.676746	+	0.859947i
$611$	−20.2811	−	62.4188i	−0.0331933	−	0.102158i
$612$	−43.2193	+	22.0213i	−0.0706198	+	0.0359826i
$613$	167.121	+	327.993i	0.272627	+	0.535061i	0.986208	−	0.165512i	$-0.0529277\pi$
$613$	167.121	+	327.993i	0.272627	+	0.535061i	−0.713580	+	0.700573i	$0.752928\pi$
$614$	807.203	−	262.276i	1.31466	−	0.427160i
$615$	448.925	−	300.513i	0.729959	−	0.488639i
$616$	73.5495	−	226.362i	0.119399	−	0.367471i
$617$	54.1928	+	342.160i	0.0878327	+	0.554554i	0.991886	+	0.127133i	$0.0405776\pi$
$617$	54.1928	+	342.160i	0.0878327	+	0.554554i	−0.904053	+	0.427421i	$0.859422\pi$
$618$	285.230	−	285.230i	0.461538	−	0.461538i
$619$	−314.620	+	433.038i	−0.508272	+	0.699576i	−0.983627	−	0.180218i	$-0.942320\pi$
$619$	−314.620	+	433.038i	−0.508272	+	0.699576i	0.475355	+	0.879794i	$0.342320\pi$
$620$	−245.548	−	137.240i	−0.396045	−	0.221355i
$621$	1.93166	−	1.40343i	0.00311056	−	0.00225995i
$622$	−361.543	−	57.2627i	−0.581258	−	0.0920622i
$623$	−313.056	−	159.510i	−0.502497	−	0.256035i
$624$		−	47.7251i		−	0.0764825i
$625$	−281.853	+	557.838i	−0.450966	+	0.892541i
$626$	449.960			0.718787
$627$	−117.918	+	231.428i	−0.188067	+	0.369103i
$628$	7.21633	−	45.5621i	0.0114910	−	0.0725512i
$629$	290.467	+	399.793i	0.461791	+	0.635601i
$630$	65.4159	−	117.041i	0.103835	−	0.185780i
$631$	−689.110	−	500.668i	−1.09209	−	0.793451i	−0.112341	−	0.993670i	$-0.535835\pi$
$631$	−689.110	−	500.668i	−1.09209	−	0.793451i	−0.979751	+	0.200219i	$0.935835\pi$
$632$	−52.8628	−	52.8628i	−0.0836436	−	0.0836436i
$633$	−580.706	+	91.9748i	−0.917387	+	0.145300i
$634$	−714.068	−	232.015i	−1.12629	−	0.365954i
$635$	−299.938	−	448.066i	−0.472344	−	0.705616i
$636$	−44.5929	−	137.243i	−0.0701146	−	0.215791i
$637$	55.5415	−	28.2998i	0.0871922	−	0.0444267i
$638$	−37.1696	−	72.9495i	−0.0582596	−	0.114341i
$639$	−95.0530	+	30.8846i	−0.148753	+	0.0483327i
$640$	44.4539	+	34.9836i	0.0694592	+	0.0546618i
$641$	−155.882	+	479.756i	−0.243186	+	0.748449i	0.752744	+	0.658314i	$0.228730\pi$
$641$	−155.882	+	479.756i	−0.243186	+	0.748449i	−0.995930	+	0.0901356i	$0.971270\pi$
$642$	17.3692	+	109.665i	0.0270549	+	0.170818i
$643$	420.254	−	420.254i	0.653584	−	0.653584i	−0.300270	−	0.953854i	$-0.597077\pi$
$643$	420.254	−	420.254i	0.653584	−	0.653584i	0.953854	+	0.300270i	$0.0970769\pi$
$644$	3.41430	−	4.69938i	0.00530171	−	0.00729718i
$645$	−287.586	+	34.2854i	−0.445870	+	0.0531557i
$646$	104.184	−	75.6944i	0.161276	−	0.117174i
$647$	−283.344	−	44.8773i	−0.437935	−	0.0693621i	−0.0664259	−	0.997791i	$-0.521160\pi$
$647$	−283.344	−	44.8773i	−0.437935	−	0.0693621i	−0.371509	+	0.928429i	$0.621160\pi$
$648$	−22.6813	−	11.5567i	−0.0350020	−	0.0178344i
$649$		−	1077.49i		−	1.66023i
$650$	−127.604	−	207.441i	−0.196315	−	0.319140i
$651$	307.957			0.473053
$652$	40.1280	−	78.7557i	0.0615461	−	0.120791i
$653$	24.7424	−	156.218i	0.0378904	−	0.239231i	−0.961473	−	0.274898i	$-0.911356\pi$
$653$	24.7424	−	156.218i	0.0378904	−	0.239231i	0.999364	+	0.0356677i	$0.0113558\pi$
$654$	−5.27850	−	7.26524i	−0.00807111	−	0.0111089i
$655$	262.901	−	121.469i	0.401375	−	0.185449i
$656$	−201.865	−	146.663i	−0.307721	−	0.223572i
$657$	−248.226	−	248.226i	−0.377817	−	0.377817i
$658$	−84.1164	+	13.3227i	−0.127836	+	0.0202473i
$659$	260.255	+	84.5620i	0.394924	+	0.128319i	0.499745	−	0.866172i	$-0.333427\pi$
$659$	260.255	+	84.5620i	0.394924	+	0.128319i	−0.104821	+	0.994491i	$0.533427\pi$
$660$	−221.884	+	62.7810i	−0.336188	+	0.0951228i
$661$	324.542	+	998.839i	0.490987	+	1.51110i	0.823119	+	0.567870i	$0.192232\pi$
$661$	324.542	+	998.839i	0.490987	+	1.51110i	−0.332131	+	0.943233i	$0.607768\pi$
$662$	−238.413	+	121.478i	−0.360141	+	0.183501i
$663$	−43.7904	−	85.9435i	−0.0660489	−	0.129628i
$664$	−416.294	+	135.262i	−0.626948	+	0.203708i
$665$	−122.925	+	334.075i	−0.184850	+	0.502368i
$666$	−80.1402	+	246.646i	−0.120331	+	0.370340i
$667$	−0.312579	−	1.97355i	−0.000468634	−	0.00295884i
$668$	−372.373	+	372.373i	−0.557445	+	0.557445i
$669$	236.254	−	325.175i	0.353145	−	0.486062i
$670$	452.826	−	419.301i	0.675860	−	0.625822i
$671$	−1016.78	+	738.737i	−1.51533	+	1.10095i
$672$	−61.1672	−	9.68793i	−0.0910225	−	0.0144166i
$673$	−454.012	−	231.331i	−0.674609	−	0.343731i	0.0828972	−	0.996558i	$-0.473583\pi$
$673$	−454.012	−	231.331i	−0.674609	−	0.343731i	−0.757507	+	0.652827i	$0.773583\pi$
$674$			283.444i			0.420539i
$675$	−129.486	+	10.4118i	−0.191831	+	0.0154248i
$676$	−243.097			−0.359610
$677$	197.659	−	387.928i	0.291963	−	0.573010i	−0.697705	−	0.716385i	$-0.745795\pi$
$677$	197.659	−	387.928i	0.291963	−	0.573010i	0.989668	+	0.143375i	$0.0457954\pi$
$678$	−57.1700	+	360.957i	−0.0843216	+	0.532386i
$679$	272.468	+	375.020i	0.401279	+	0.552313i
$680$	112.152	+	22.2096i	0.164930	+	0.0326612i
$681$	158.984	+	115.509i	0.233457	+	0.169616i
$682$	−374.504	−	374.504i	−0.549126	−	0.549126i
$683$	−701.555	+	111.115i	−1.02717	+	0.162687i	−0.647206	−	0.762315i	$-0.724063\pi$
$683$	−701.555	+	111.115i	−1.02717	+	0.162687i	−0.379961	+	0.925003i	$0.624063\pi$
$684$	64.2750	+	20.8842i	0.0939692	+	0.0305325i
$685$	46.9062	−	1220.22i	0.0684762	−	1.78134i
$686$	−160.345	−	493.492i	−0.233740	−	0.719376i
$687$	−175.647	+	89.4969i	−0.255673	+	0.130272i
$688$	60.7308	+	119.191i	0.0882715	+	0.173243i
$689$	272.913	−	88.6750i	0.396101	−	0.128701i
$690$	−5.62361	−	0.216176i	−0.00815016	−	0.000313299i
$691$	337.257	−	1037.97i	0.488071	−	1.50213i	−0.339413	−	0.940637i	$-0.610228\pi$
$691$	337.257	−	1037.97i	0.488071	−	1.50213i	0.827484	−	0.561490i	$-0.189772\pi$
$692$	−43.9589	−	277.545i	−0.0635244	−	0.401077i
$693$	178.508	−	178.508i	0.257588	−	0.257588i
$694$	229.432	−	315.786i	0.330593	−	0.455022i
$695$	220.084	−	1111.36i	0.316667	−	1.59908i
$696$	−17.2345	+	12.5216i	−0.0247623	+	0.0179909i
$697$	−498.091	−	78.8898i	−0.714621	−	0.113185i
$698$	−718.425	−	366.056i	−1.02926	−	0.524435i
$699$		−	148.602i		−	0.212593i
$700$	−291.771	+	121.436i	−0.416816	+	0.173480i
$701$	308.289			0.439785			0.219892	−	0.975524i	$-0.429429\pi$
$701$	308.289			0.439785			0.219892	+	0.975524i	$0.429429\pi$
$702$	22.9810	−	45.1028i	0.0327365	−	0.0642490i
$703$	107.708	−	680.042i	0.153212	−	0.967343i
$704$	62.6035	+	86.1663i	0.0889254	+	0.122395i
$705$	56.0601	+	60.5424i	0.0795179	+	0.0858757i
$706$	350.583	+	254.714i	0.496577	+	0.360784i
$707$	850.212	+	850.212i	1.20256	+	1.20256i
$708$	−276.907	+	43.8577i	−0.391111	+	0.0619460i
$709$	605.178	+	196.634i	0.853566	+	0.277340i	0.702939	−	0.711250i	$-0.251871\pi$
$709$	605.178	+	196.634i	0.853566	+	0.277340i	0.150627	+	0.988591i	$0.451871\pi$
$710$	221.080	+	81.3479i	0.311381	+	0.114575i
$711$	−24.5032	−	75.4132i	−0.0344631	−	0.106066i
$712$	140.089	−	71.3789i	0.196754	−	0.100251i
$713$	−5.86819	−	11.5170i	−0.00823028	−	0.0161528i
$714$	−119.039	+	38.6782i	−0.166722	+	0.0541712i
$715$	−124.843	−	441.227i	−0.174605	−	0.617101i
$716$	−71.2699	+	219.346i	−0.0995390	+	0.306350i
$717$	−34.6922	−	219.038i	−0.0483852	−	0.305492i
$718$	59.2994	−	59.2994i	0.0825897	−	0.0825897i
$719$	−242.820	+	334.214i	−0.337720	+	0.464831i	−0.943774	−	0.330592i	$-0.892751\pi$
$719$	−242.820	+	334.214i	−0.337720	+	0.464831i	0.606054	+	0.795423i	$0.292751\pi$
$720$	25.1658	+	54.4673i	0.0349525	+	0.0756490i
$721$	842.084	−	611.810i	1.16794	−	0.848558i
$722$	327.029	+	51.7964i	0.452949	+	0.0717401i
$723$	−73.7341	−	37.5694i	−0.101984	−	0.0519632i
$724$			386.950i			0.534462i
$725$	−41.4318	+	100.507i	−0.0571473	+	0.138630i
$726$	−137.777			−0.189775
$727$	415.131	−	814.740i	0.571019	−	1.12069i	−0.407244	−	0.913319i	$-0.633510\pi$
$727$	415.131	−	814.740i	0.571019	−	1.12069i	0.978263	−	0.207368i	$-0.0664897\pi$
$728$	19.2649	−	121.634i	0.0264627	−	0.167079i
$729$	−15.8702	−	21.8435i	−0.0217698	−	0.0299636i
$730$	97.9496	+	821.602i	0.134178	+	1.12548i
$731$	218.729	+	158.916i	0.299218	+	0.217395i
$732$	231.237	+	231.237i	0.315897	+	0.315897i
$733$	1046.19	−	165.701i	1.42728	−	0.226059i	0.605490	−	0.795853i	$-0.292977\pi$
$733$	1046.19	−	165.701i	1.42728	−	0.226059i	0.821787	+	0.569794i	$0.192977\pi$
$734$	−233.815	−	75.9712i	−0.318550	−	0.103503i
$735$	−48.4652	+	61.5852i	−0.0659390	+	0.0837893i
$736$	0.803245	+	2.47213i	0.00109136	+	0.00335888i
$737$	1035.31	−	527.517i	1.40476	−	0.715763i
$738$	−120.151	−	235.809i	−0.162806	−	0.319524i
$739$	94.7944	−	30.8006i	0.128274	−	0.0416787i	−0.244177	−	0.969731i	$-0.578518\pi$
$739$	94.7944	−	30.8006i	0.128274	−	0.0416787i	0.372450	+	0.928052i	$0.378518\pi$
$740$	507.963	−	340.033i	0.686436	−	0.459504i
$741$	−41.5292	+	127.814i	−0.0560448	+	0.172488i
$742$	−58.2509	−	367.782i	−0.0785053	−	0.495663i
$743$	−46.6959	+	46.6959i	−0.0628477	+	0.0628477i	−0.737832	−	0.674984i	$-0.764150\pi$
$743$	−46.6959	+	46.6959i	−0.0628477	+	0.0628477i	0.674984	+	0.737832i	$0.264150\pi$
$744$	−81.0012	+	111.489i	−0.108873	+	0.149850i
$745$	1083.78	+	605.738i	1.45473	+	0.813070i
$746$	−189.229	+	137.483i	−0.253658	+	0.184293i
$747$	−458.553	−	72.6277i	−0.613860	−	0.0972258i
$748$	191.799	+	97.7264i	0.256416	+	0.130650i
$749$			286.507i			0.382519i
$750$	255.016	+	169.460i	0.340022	+	0.225946i
$751$	−1263.32			−1.68218			−0.841089	−	0.540897i	$-0.818085\pi$
$751$	−1263.32			−1.68218			−0.841089	+	0.540897i	$0.818085\pi$
$752$	17.3017	−	33.9566i	0.0230076	−	0.0451550i
$753$	−66.5871	+	420.415i	−0.0884291	+	0.558320i
$754$	−24.8998	−	34.2717i	−0.0330236	−	0.0454531i
$755$	466.313	−	834.321i	0.617633	−	1.10506i
$756$	−53.1413	−	38.6094i	−0.0702927	−	0.0510707i
$757$	−75.2273	−	75.2273i	−0.0993756	−	0.0993756i	0.655671	−	0.755047i	$-0.272386\pi$
$757$	−75.2273	−	75.2273i	−0.0993756	−	0.0993756i	−0.755047	+	0.655671i	$0.772386\pi$
$758$	−681.027	+	107.864i	−0.898452	+	0.142301i
$759$	−10.0774	−	3.27433i	−0.0132772	−	0.00431401i
$760$	−88.6112	−	132.373i	−0.116594	−	0.174175i
$761$	−22.3294	−	68.7229i	−0.0293422	−	0.0903061i	0.935313	−	0.353822i	$-0.115118\pi$
$761$	−22.3294	−	68.7229i	−0.0293422	−	0.0903061i	−0.964655	+	0.263515i	$0.915118\pi$
$762$	−235.358	+	119.921i	−0.308869	+	0.157376i
$763$	−10.5202	−	20.6471i	−0.0137880	−	0.0270605i
$764$	−620.358	+	201.566i	−0.811987	+	0.263830i
$765$	95.2954	+	74.9939i	0.124569	+	0.0980313i
$766$	97.3591	−	299.641i	0.127101	−	0.391176i
$767$	−87.2131	−	550.642i	−0.113707	−	0.717916i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$	−645.482	+	888.430i	−0.839379	+	1.15531i	0.146725	+	0.989177i	$0.453127\pi$
$769$	−645.482	+	888.430i	−0.839379	+	1.15531i	−0.986104	+	0.166129i	$0.946873\pi$
$770$	−590.844	+	70.4391i	−0.767330	+	0.0914793i
$771$	162.955	−	118.394i	0.211356	−	0.153559i
$772$	448.762	+	71.0769i	0.581298	+	0.0920685i
$773$	47.9713	+	24.4426i	0.0620586	+	0.0316205i	0.484744	−	0.874656i	$-0.338913\pi$
$773$	47.9713	+	24.4426i	0.0620586	+	0.0316205i	−0.422686	+	0.906276i	$0.638913\pi$
$774$			141.886i			0.183315i
$775$	−53.9869	+	701.170i	−0.0696605	+	0.904736i
$776$	−207.434			−0.267312
$777$	−303.810	+	596.260i	−0.391004	+	0.767388i
$778$	44.1445	−	278.718i	0.0567410	−	0.358249i
$779$	412.996	+	568.440i	0.530161	+	0.729705i
$780$	−108.311	+	50.0433i	−0.138860	+	0.0641581i
$781$	358.827	+	260.703i	0.459446	+	0.333807i
$782$	3.71481	+	3.71481i	0.00475039	+	0.00475039i
$783$	−22.3171	+	3.53469i	−0.0285021	+	0.00451429i
$784$	34.4252	+	11.1854i	0.0439097	+	0.0142671i
$785$	−110.969	+	31.3980i	−0.141361	+	0.0399975i
$786$	−43.8425	−	134.933i	−0.0557793	−	0.171671i
$787$	−73.5938	+	37.4979i	−0.0935119	+	0.0476467i	−0.500121	−	0.865956i	$-0.666711\pi$
$787$	−73.5938	+	37.4979i	−0.0935119	+	0.0476467i	0.406609	+	0.913602i	$0.366711\pi$
$788$	278.629	+	546.841i	0.353590	+	0.693960i
$789$	122.139	−	39.6855i	0.154803	−	0.0502984i
$790$	−64.5399	+	175.401i	−0.0816961	+	0.222027i
$791$	−291.411	+	896.870i	−0.368408	+	1.13384i
$792$	17.6721	+	111.577i	0.0223133	+	0.140880i
$793$	−459.825	+	459.825i	−0.579855	+	0.579855i
$794$	275.186	−	378.760i	0.346581	−	0.477028i
$795$	−264.709	+	245.111i	−0.332968	+	0.308316i
$796$	476.139	−	345.935i	0.598165	−	0.434592i
$797$	−66.1574	−	10.4783i	−0.0830081	−	0.0131472i	0.114792	−	0.993390i	$-0.463380\pi$
$797$	−66.1574	−	10.4783i	−0.0830081	−	0.0131472i	−0.197800	+	0.980242i	$0.563380\pi$
$798$	155.383	+	79.1716i	0.194716	+	0.0992125i
$799$		−	77.0245i		−	0.0964011i
$800$	32.7809	−	137.570i	0.0409761	−	0.171962i
$801$	166.763			0.208193
$802$	114.269	−	224.265i	0.142480	−	0.279632i
$803$	−243.704	+	1538.69i	−0.303492	+	1.91617i
$804$	−177.709	−	244.596i	−0.221031	−	0.304223i
$805$	−14.2453	−	2.82100i	−0.0176960	−	0.00350435i
$806$	−221.700	−	161.074i	−0.275062	−	0.199844i
$807$	−389.469	−	389.469i	−0.482614	−	0.482614i
$808$	−531.428	+	84.1699i	−0.657708	+	0.104171i
$809$	1403.20	+	455.928i	1.73449	+	0.563569i	0.994086	−	0.108595i	$-0.0346351\pi$
$809$	1403.20	+	455.928i	1.73449	+	0.563569i	0.740402	+	0.672164i	$0.234635\pi$
$810$	−2.44455	+	63.5926i	−0.00301797	+	0.0785094i
$811$	−295.507	−	909.476i	−0.364373	−	1.12143i	−0.950373	−	0.311114i	$-0.899298\pi$
$811$	−295.507	−	909.476i	−0.364373	−	1.12143i	0.585999	−	0.810312i	$-0.300702\pi$
$812$	−48.9790	+	24.9561i	−0.0603190	+	0.0307341i
$813$	77.8948	+	152.877i	0.0958115	+	0.188041i
$814$	1094.57	−	355.647i	1.34468	−	0.436912i
$815$	−220.811	−	8.48815i	−0.270934	−	0.0104149i
$816$	17.3081	−	53.2688i	0.0212109	−	0.0652804i
$817$	−58.9276	−	372.054i	−0.0721268	−	0.455391i
$818$	−321.423	+	321.423i	−0.392938	+	0.392938i
$819$	76.7766	−	105.674i	0.0937443	−	0.129028i
$820$	−121.178	+	611.913i	−0.147778	+	0.746236i
$821$	650.424	−	472.561i	0.792234	−	0.575592i	−0.116392	−	0.993203i	$-0.537133\pi$
$821$	650.424	−	472.561i	0.792234	−	0.575592i	0.908626	+	0.417612i	$0.137133\pi$
$822$	−590.859	−	93.5828i	−0.718806	−	0.113848i
$823$	1408.24	+	717.532i	1.71110	+	0.871850i	0.982345	+	0.187076i	$0.0599011\pi$
$823$	1408.24	+	717.532i	1.71110	+	0.871850i	0.728756	+	0.684774i	$0.240099\pi$
$824$			465.779i			0.565266i
$825$	375.142	+	437.729i	0.454717	+	0.530581i
$826$	−723.437			−0.875832
$827$	−372.254	+	730.590i	−0.450126	+	0.883422i	0.548748	+	0.835988i	$0.315105\pi$
$827$	−372.254	+	730.590i	−0.450126	+	0.883422i	−0.998874	+	0.0474345i	$0.984895\pi$
$828$	−0.431295	+	2.72309i	−0.000520887	+	0.00328875i
$829$	473.578	+	651.824i	0.571264	+	0.786278i	0.992704	−	0.120579i	$-0.0384750\pi$
$829$	473.578	+	651.824i	0.571264	+	0.786278i	−0.421440	+	0.906857i	$0.638475\pi$
$830$	743.488	+	802.933i	0.895768	+	0.967390i
$831$	47.0185	+	34.1610i	0.0565807	+	0.0411083i
$832$	38.9674	+	38.9674i	0.0468358	+	0.0468358i
$833$	72.2564	−	11.4443i	0.0867423	−	0.0137386i
$834$	−527.861	−	171.512i	−0.632927	−	0.205650i
$835$	1235.55	+	454.629i	1.47970	+	0.544465i
$836$	−92.6800	−	285.240i	−0.110861	−	0.341196i
$837$	−130.236	+	66.3584i	−0.155598	+	0.0792812i
$838$	96.6947	+	189.774i	0.115387	+	0.226461i
$839$	−1102.02	+	358.068i	−1.31349	+	0.426779i	−0.880255	−	0.474501i	$-0.842629\pi$
$839$	−1102.02	+	358.068i	−1.31349	+	0.426779i	−0.433236	+	0.901280i	$0.642629\pi$
$840$	42.1519	+	148.975i	0.0501808	+	0.177352i
$841$	254.040	−	781.855i	0.302069	−	0.929673i
$842$	42.6314	+	269.164i	0.0506311	+	0.319672i
$843$	75.6865	−	75.6865i	0.0897824	−	0.0897824i
$844$	399.047	−	549.241i	0.472805	−	0.650760i
$845$	254.905	+	551.700i	0.301662	+	0.652900i
$846$	32.7022	−	23.7595i	0.0386551	−	0.0280846i
$847$	−351.142	−	55.6155i	−0.414572	−	0.0656617i
$848$	148.468	+	75.6483i	0.175080	+	0.0892079i
$849$		−	29.6898i		−	0.0349704i
$850$	−67.1959	−	277.814i	−0.0790540	−	0.326840i
$851$	28.0881			0.0330060
$852$	52.3933	−	102.828i	0.0614944	−	0.120690i
$853$	−48.3227	+	305.098i	−0.0566503	+	0.357676i	0.943037	+	0.332687i	$0.107955\pi$
$853$	−48.3227	+	305.098i	−0.0566503	+	0.357676i	−0.999688	+	0.0249892i	$0.992045\pi$
$854$	495.996	+	682.679i	0.580791	+	0.799390i
$855$	−20.0010	−	167.769i	−0.0233930	−	0.196221i
$856$	−103.723	−	75.3591i	−0.121172	−	0.0880363i
$857$	−378.129	−	378.129i	−0.441224	−	0.441224i	0.451199	−	0.892423i	$-0.350996\pi$
$857$	−378.129	−	378.129i	−0.441224	−	0.441224i	−0.892423	+	0.451199i	$0.850996\pi$
$858$	−221.876	+	35.1418i	−0.258597	+	0.0409578i
$859$	679.916	+	220.918i	0.791520	+	0.257181i	0.676751	−	0.736212i	$-0.263387\pi$
$859$	679.916	+	220.918i	0.791520	+	0.257181i	0.114769	+	0.993392i	$0.463387\pi$
$860$	206.819	−	262.807i	0.240488	−	0.305590i
$861$	−211.032	−	649.490i	−0.245101	−	0.754344i
$862$	−453.773	+	231.209i	−0.526419	+	0.268224i
$863$	−360.184	−	706.901i	−0.417363	−	0.819120i	−0.999980	−	0.00637355i	$-0.997971\pi$
$863$	−360.184	−	706.901i	−0.417363	−	0.819120i	0.582617	−	0.812747i	$-0.302029\pi$
$864$	27.9552	−	9.08321i	0.0323556	−	0.0105130i
$865$	−583.787	+	390.790i	−0.674898	+	0.451781i
$866$	−21.3388	+	65.6740i	−0.0246406	+	0.0758360i
$867$	60.5966	+	382.592i	0.0698923	+	0.441283i
$868$	−251.446	+	251.446i	−0.289684	+	0.289684i
$869$	−206.837	+	284.687i	−0.238017	+	0.327603i
$870$	46.4892	+	25.9834i	0.0534358	+	0.0298660i
$871$	486.389	−	353.383i	0.558426	−	0.405721i
$872$	10.2419	+	1.62216i	0.0117453	+	0.00186028i
$873$	−196.036	−	99.8855i	−0.224555	−	0.114416i
$874$		−	7.31964i		−	0.00837487i
$875$	581.538	+	534.831i	0.664615	+	0.611236i
$876$	405.351			0.462730
$877$	−261.361	+	512.950i	−0.298017	+	0.584892i	−0.990655	−	0.136394i	$-0.956449\pi$
$877$	−261.361	+	512.950i	−0.298017	+	0.584892i	0.692637	+	0.721286i	$0.256449\pi$
$878$	26.0573	−	164.519i	0.0296780	−	0.187380i
$879$	−82.5401	−	113.607i	−0.0939023	−	0.129245i
$880$	129.907	−	232.428i	0.147622	−	0.264123i
$881$	−373.233	−	271.169i	−0.423647	−	0.307797i	0.355457	−	0.934693i	$-0.384325\pi$
$881$	−373.233	−	271.169i	−0.423647	−	0.307797i	−0.779103	+	0.626895i	$0.784325\pi$
$882$	27.1476	+	27.1476i	0.0307796	+	0.0307796i
$883$	−589.727	+	93.4036i	−0.667868	+	0.105780i	−0.481156	−	0.876635i	$-0.659783\pi$
$883$	−589.727	+	93.4036i	−0.667868	+	0.105780i	−0.186712	+	0.982415i	$0.559783\pi$
$884$	105.927	+	34.4179i	0.119827	+	0.0389343i
$885$	389.891	+	582.444i	0.440555	+	0.658128i
$886$	−41.7391	−	128.460i	−0.0471096	−	0.144989i
$887$	132.811	−	67.6704i	0.149730	−	0.0762914i	−0.377520	−	0.926001i	$-0.623223\pi$
$887$	132.811	−	67.6704i	0.149730	−	0.0762914i	0.527250	+	0.849710i	$0.323223\pi$
$888$	−135.952	−	266.820i	−0.153099	−	0.300473i
$889$	−648.248	+	210.629i	−0.729188	+	0.236928i
$890$	−308.886	−	243.082i	−0.347063	−	0.273126i
$891$	−37.0267	+	113.956i	−0.0415563	+	0.127897i
$892$	72.6042	+	458.405i	0.0813949	+	0.513907i
$893$	−75.8843	+	75.8843i	−0.0849769	+	0.0849769i
$894$	357.515	−	492.078i	0.399905	−	0.550422i
$895$	572.531	−	68.2559i	0.639700	−	0.0762636i
$896$	57.8529	−	42.0326i	0.0645680	−	0.0469114i
$897$	−5.41498	−	0.857649i	−0.00603677	−	0.000956130i
$898$	−292.491	−	149.031i	−0.325714	−	0.165959i
$899$			122.322i			0.136064i
$900$	97.2236	−	114.226i	0.108026	−	0.126918i
$901$	336.774			0.373778
$902$	−533.205	+	1046.47i	−0.591136	+	1.16017i
$903$	−57.2740	+	361.614i	−0.0634264	+	0.400459i
$904$	−248.041	−	341.400i	−0.274382	−	0.377654i
$905$	878.172	−	405.746i	0.970356	−	0.448338i
$906$	−378.815	−	275.225i	−0.418118	−	0.303780i
$907$	−1033.74	−	1033.74i	−1.13974	−	1.13974i	−0.988497	−	0.151242i	$-0.951673\pi$
$907$	−1033.74	−	1033.74i	−1.13974	−	1.13974i	−0.151242	−	0.988497i	$-0.548327\pi$
$908$	−224.122	+	35.4975i	−0.246831	+	0.0390941i
$909$	−542.759	−	176.353i	−0.597094	−	0.194008i
$910$	−296.244	+	83.8208i	−0.325543	+	0.0921108i
$911$	−482.269	−	1484.27i	−0.529385	−	1.62928i	−0.755479	−	0.655173i	$-0.772596\pi$
$911$	−482.269	−	1484.27i	−0.529385	−	1.62928i	0.226094	−	0.974105i	$-0.427404\pi$
$912$	−69.5322	+	35.4284i	−0.0762414	+	0.0388469i
$913$	935.373	+	1835.77i	1.02450	+	2.01070i
$914$	686.065	−	222.916i	0.750618	−	0.243891i
$915$	282.316	−	767.254i	0.308542	−	0.838529i
$916$	70.3417	−	216.489i	0.0767922	−	0.236342i
$917$	−57.2707	−	361.593i	−0.0624545	−	0.394322i
$918$	42.0076	−	42.0076i	0.0457599	−	0.0457599i
$919$	440.176	−	605.850i	0.478972	−	0.659249i	−0.499335	−	0.866409i	$-0.666422\pi$
$919$	440.176	−	605.850i	0.478972	−	0.659249i	0.978307	+	0.207160i	$0.0664222\pi$
$920$	4.76817	−	4.41515i	0.00518279	−	0.00479908i
$921$	−840.969	+	611.000i	−0.913104	+	0.663409i
$922$	−451.841	−	71.5646i	−0.490066	−	0.0776189i
$923$	204.477	+	104.186i	0.221535	+	0.112878i
$924$			291.503i			0.315479i
$925$	−1304.33	−	796.256i	−1.41009	−	0.860817i
$926$	348.039			0.375852
$927$	−224.287	+	440.187i	−0.241949	+	0.474851i
$928$	3.84808	−	24.2958i	0.00414664	−	0.0261808i
$929$	−0.844797	−	1.16276i	−0.000909361	−	0.00125163i	0.808562	−	0.588411i	$-0.200246\pi$
$929$	−0.844797	−	1.16276i	−0.000909361	−	0.00125163i	−0.809471	+	0.587159i	$0.800246\pi$
$930$	337.956	+	66.9257i	0.363393	+	0.0719631i
$931$	−82.4617	−	59.9119i	−0.0885732	−	0.0643522i
$932$	121.333	+	121.333i	0.130186	+	0.130186i
$933$	442.797	−	70.1322i	0.474595	−	0.0751685i
$934$	465.405	+	151.219i	0.498292	+	0.161905i
$935$	20.6718	−	537.755i	0.0221088	−	0.575139i
$936$	18.0624	+	55.5902i	0.0192974	+	0.0593913i
$937$	1288.20	−	656.372i	1.37482	−	0.700504i	0.398564	−	0.917140i	$-0.369509\pi$
$937$	1288.20	−	656.372i	1.37482	−	0.700504i	0.976252	+	0.216636i	$0.0695086\pi$
$938$	−354.181	−	695.119i	−0.377591	−	0.741065i
$939$	−524.115	+	170.295i	−0.558162	+	0.181358i
$940$	−95.2056	−	3.65978i	−0.101283	−	0.00389338i
$941$	−187.589	+	577.340i	−0.199351	+	0.613539i	0.800547	+	0.599270i	$0.204542\pi$
$941$	−187.589	+	577.340i	−0.199351	+	0.613539i	−0.999898	+	0.0142695i	$0.995458\pi$
$942$	8.83817	+	55.8020i	0.00938234	+	0.0592378i
$943$	−20.2683	+	20.2683i	−0.0214935	+	0.0214935i
$944$	190.284	−	261.903i	0.201572	−	0.277440i
$945$	−31.9003	+	161.087i	−0.0337569	+	0.170463i
$946$	509.406	−	370.105i	0.538485	−	0.391232i
$947$	−1670.19	−	264.532i	−1.76366	−	0.279336i	−0.811371	−	0.584532i	$-0.801278\pi$
$947$	−1670.19	−	264.532i	−1.76366	−	0.279336i	−0.952290	+	0.305195i	$0.901278\pi$
$948$	81.5814	+	41.5678i	0.0860564	+	0.0438479i
$949$			806.060i			0.849378i
$950$	−207.501	+	339.903i	−0.218422	+	0.357793i
$951$	919.558			0.966938
$952$	65.6146	−	128.776i	0.0689229	−	0.135269i
$953$	47.5675	−	300.330i	0.0499135	−	0.315141i	−0.950082	−	0.312002i	$-0.899001\pi$
$953$	47.5675	−	300.330i	0.0499135	−	0.315141i	0.999995	−	0.00313971i	$-0.000999402\pi$
$954$	103.884	+	142.984i	0.108893	+	0.149878i
$955$	1107.94	+	1196.53i	1.16015	+	1.25291i
$956$	207.170	+	150.518i	0.216705	+	0.157445i
$957$	70.9042	+	70.9042i	0.0740901	+	0.0740901i
$958$	650.042	−	102.956i	0.678540	−	0.107470i
$959$	−1468.10	−	477.016i	−1.53087	−	0.497410i
$960$	−65.0201	−	23.9246i	−0.0677293	−	0.0249214i
$961$	−52.4442	−	161.407i	−0.0545725	−	0.167957i
$962$	530.583	−	270.346i	0.551542	−	0.281025i
$963$	−61.7362	−	121.164i	−0.0641082	−	0.125819i
$964$	90.8789	−	29.5283i	0.0942727	−	0.0306311i
$965$	−309.253	−	1092.98i	−0.320470	−	1.13262i
$966$	−2.19842	+	6.76605i	−0.00227580	+	0.00700419i
$967$	11.8946	+	75.0996i	0.0123005	+	0.0776625i	0.993075	−	0.117482i	$-0.0374823\pi$
$967$	11.8946	+	75.0996i	0.0123005	+	0.0776625i	−0.980774	+	0.195145i	$0.937482\pi$
$968$	112.494	−	112.494i	0.116213	−	0.116213i
$969$	−92.7063	+	127.599i	−0.0956721	+	0.131681i
$970$	217.510	+	470.765i	0.224237	+	0.485324i
$971$	1550.55	−	1126.54i	1.59686	−	1.16018i	0.703642	−	0.710554i	$-0.251556\pi$
$971$	1550.55	−	1126.54i	1.59686	−	1.16018i	0.893215	−	0.449630i	$-0.148444\pi$
$972$	30.7931	+	4.87714i	0.0316801	+	0.00501764i
$973$	−1276.09	−	650.200i	−1.31150	−	0.668243i
$974$			298.393i			0.306358i
$975$	227.143	+	193.334i	0.232968	+	0.198291i
$976$	−377.608			−0.386894
$977$	308.784	−	606.023i	0.316054	−	0.620290i	−0.677259	−	0.735744i	$-0.736832\pi$
$977$	308.784	−	606.023i	0.316054	−	0.620290i	0.993313	+	0.115454i	$0.0368324\pi$
$978$	−16.9348	+	106.922i	−0.0173157	+	0.109327i
$979$	−434.997	−	598.722i	−0.444328	−	0.611565i
$980$	−10.7124	−	89.8557i	−0.0109310	−	0.0916895i
$981$	8.89806	+	6.46482i	0.00907040	+	0.00659003i
$982$	425.848	+	425.848i	0.433654	+	0.433654i
$983$	−936.062	+	148.258i	−0.952250	+	0.150822i	−0.613183	−	0.789941i	$-0.710111\pi$
$983$	−936.062	+	148.258i	−0.952250	+	0.150822i	−0.339067	+	0.940762i	$0.610111\pi$
$984$	290.640	+	94.4345i	0.295365	+	0.0959700i
$985$	948.875	−	1205.74i	0.963325	−	1.22411i
$986$	−15.3631	−	47.2829i	−0.0155813	−	0.0479542i
$987$	92.9367	−	47.3536i	0.0941608	−	0.0479773i
$988$	−70.4510	−	138.268i	−0.0713067	−	0.139947i
$989$	14.6150	−	4.74870i	0.0147776	−	0.00480152i
$990$	234.691	−	157.103i	0.237061	−	0.158690i
$991$	−227.689	+	700.755i	−0.229757	+	0.707120i	0.768017	+	0.640430i	$0.221244\pi$
$991$	−227.689	+	700.755i	−0.229757	+	0.707120i	−0.997774	+	0.0666897i	$0.978756\pi$
$992$	−24.8928	−	157.167i	−0.0250936	−	0.158435i
$993$	231.729	−	231.729i	0.233362	−	0.233362i
$994$	175.039	−	240.920i	0.176095	−	0.242375i
$995$	−1284.36	−	717.845i	−1.29081	−	0.721452i
$996$	433.707	−	315.107i	0.435449	−	0.316372i
$997$	−1020.04	−	161.559i	−1.02311	−	0.162045i	−0.377738	−	0.925912i	$-0.623298\pi$
$997$	−1020.04	−	161.559i	−1.02311	−	0.162045i	−0.645373	+	0.763867i	$0.723298\pi$
$998$	−449.937	−	229.254i	−0.450839	−	0.229714i
$999$		−	317.624i		−	0.317942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.k.a.67.2	✓	32
25.3	odd	20	inner	150.3.k.a.103.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.3.k.a.67.2	✓	32	1.1	even	1	trivial
150.3.k.a.103.2	yes	32	25.3	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.642040 - 1.26007i) q^{2} +(-0.270952 + 1.71073i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-2.43941 + 4.36455i) q^{5} +(1.98168 + 1.43977i) q^{6} +(4.46938 + 4.46938i) q^{7} +(-2.79360 + 0.442463i) q^{8} +(-2.85317 - 0.927051i) q^{9} +(3.93346 + 5.87604i) q^{10} +(4.11407 + 12.6618i) q^{11} +(3.08654 - 1.57267i) q^{12} +(3.12732 + 6.13772i) q^{13} +(8.50127 - 2.76223i) q^{14} +(-6.80559 - 5.35574i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(1.26467 + 7.98483i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(6.62068 - 9.11259i) q^{19} +(9.92968 - 1.18379i) q^{20} +(-8.85688 + 6.43490i) q^{21} +(18.5962 + 2.94535i) q^{22} +(0.409422 + 0.208611i) q^{23} -4.89898i q^{24} +(-13.0986 - 21.2938i) q^{25} +9.74184 q^{26} +(2.35900 - 4.62981i) q^{27} +(1.97754 - 12.4857i) q^{28} +(-2.55597 - 3.51799i) q^{29} +(-11.1181 + 5.13694i) q^{30} +(-22.7575 - 16.5343i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-22.7756 + 3.60730i) q^{33} +(10.8734 + 3.53300i) q^{34} +(-30.4095 + 8.60421i) q^{35} +(1.85410 + 5.70634i) q^{36} +(54.4644 - 27.7510i) q^{37} +(-7.23179 - 14.1932i) q^{38} +(-11.3473 + 3.68697i) q^{39} +(4.88358 - 13.2722i) q^{40} +(-19.2764 + 59.3265i) q^{41} +(2.42198 + 15.2918i) q^{42} +(23.6476 - 23.6476i) q^{43} +(15.6509 - 21.5416i) q^{44} +(11.0062 - 10.1913i) q^{45} +(0.525730 - 0.381966i) q^{46} +(-9.41029 - 1.49044i) q^{47} +(-6.17307 - 3.14534i) q^{48} -9.04920i q^{49} +(-35.2416 + 2.83372i) q^{50} -14.0025 q^{51} +(6.25465 - 12.2754i) q^{52} +(6.51666 - 41.1446i) q^{53} +(-4.31932 - 5.94504i) q^{54} +(-65.2990 - 12.9312i) q^{55} +(-14.4632 - 10.5082i) q^{56} +(13.7953 + 13.7953i) q^{57} +(-6.07395 + 0.962020i) q^{58} +(-76.9714 - 25.0095i) q^{59} +(-0.665323 + 17.3077i) q^{60} +(29.1718 + 89.7817i) q^{61} +(-35.4456 + 18.0605i) q^{62} +(-8.60856 - 16.8953i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-34.4172 - 1.32302i) q^{65} +(-10.0774 + 31.0150i) q^{66} +(-13.6532 - 86.2026i) q^{67} +(11.4330 - 11.4330i) q^{68} +(-0.467810 + 0.643886i) q^{69} +(-8.68216 + 43.8424i) q^{70} +(26.9523 - 19.5820i) q^{71} +(8.38081 + 1.32739i) q^{72} +(104.261 + 53.1237i) q^{73} -86.4464i q^{74} +(39.9770 - 16.6385i) q^{75} -22.5276 q^{76} +(-38.2031 + 74.9779i) q^{77} +(-2.63958 + 16.6656i) q^{78} +(15.5360 + 21.3834i) q^{79} +(-13.5885 - 14.6749i) q^{80} +(7.28115 + 5.29007i) q^{81} +(62.3796 + 62.3796i) q^{82} +(152.851 - 24.2092i) q^{83} +(20.8238 + 6.76606i) q^{84} +(-37.9352 - 13.9585i) q^{85} +(-14.6150 - 44.9804i) q^{86} +(6.71086 - 3.41935i) q^{87} +(-17.0955 - 33.5518i) q^{88} +(-52.8670 + 17.1775i) q^{89} +(-5.77543 - 20.4119i) q^{90} +(-13.4546 + 41.4090i) q^{91} +(-0.143765 - 0.907696i) q^{92} +(34.4519 - 34.4519i) q^{93} +(-7.91984 + 10.9007i) q^{94} +(23.6218 + 51.1256i) q^{95} +(-7.92672 + 5.75910i) q^{96} +(72.4360 + 11.4727i) q^{97} +(-11.4027 - 5.80995i) q^{98} -39.9403i 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

Introduction

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