LMFDB - Embedded newform 399.2.bq.b.100.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(4,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 12, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [90] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.1
Character	$\chi$	$=$	399.100
Dual form			399.2.bq.b.4.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.486024 + 2.75638i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-5.48202 - 1.99529i) q^{4} +(3.19171 - 1.16169i) q^{5} +(-0.486024 - 2.75638i) q^{6} +(2.40200 + 1.10923i) q^{7} +(5.36527 - 9.29292i) q^{8} +(0.766044 - 0.642788i) q^{9} +(1.65080 + 9.36217i) q^{10} +3.52983 q^{11} +5.83384 q^{12} +(-0.169019 - 0.958552i) q^{13} +(-4.22489 + 6.08171i) q^{14} +(-2.60191 + 2.18326i) q^{15} +(14.0692 + 11.8055i) q^{16} +(-1.78344 - 1.49648i) q^{17} +(1.39945 + 2.42392i) q^{18} +(2.46604 - 3.59425i) q^{19} -19.8149 q^{20} +(-2.63652 - 0.220802i) q^{21} +(-1.71558 + 9.72955i) q^{22} +(0.270598 + 1.53464i) q^{23} +(-1.86334 + 10.5675i) q^{24} +(5.00728 - 4.20160i) q^{25} +2.72428 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-10.9546 - 10.8735i) q^{28} +(-4.62561 - 1.68358i) q^{29} +(-4.75330 - 8.23296i) q^{30} +(1.30522 - 2.26071i) q^{31} +(-22.9381 + 19.2474i) q^{32} +(-3.31696 + 1.20727i) q^{33} +(4.99166 - 4.18850i) q^{34} +(8.95507 + 0.749963i) q^{35} +(-5.48202 + 1.99529i) q^{36} +(-2.89283 + 5.01052i) q^{37} +(8.70857 + 8.54423i) q^{38} +(0.486669 + 0.842936i) q^{39} +(6.32892 - 35.8931i) q^{40} +(-0.257477 + 1.46022i) q^{41} +(1.89003 - 7.15994i) q^{42} +(5.57137 + 4.67493i) q^{43} +(-19.3506 - 7.04304i) q^{44} +(1.69827 - 2.94150i) q^{45} -4.36156 q^{46} +(0.474997 - 0.398569i) q^{47} +(-17.2584 - 6.28156i) q^{48} +(4.53922 + 5.32874i) q^{49} +(9.14756 + 15.8440i) q^{50} +(2.18771 + 0.796261i) q^{51} +(-0.986028 + 5.59204i) q^{52} +(-5.94756 - 2.16474i) q^{53} +(-2.14408 - 1.79910i) q^{54} +(11.2662 - 4.10056i) q^{55} +(23.1954 - 16.3703i) q^{56} +(-1.08801 + 4.22093i) q^{57} +(6.88875 - 11.9317i) q^{58} +(-4.71422 - 3.95570i) q^{59} +(18.6199 - 6.77710i) q^{60} +(1.26980 + 7.20141i) q^{61} +(5.59701 + 4.69645i) q^{62} +(2.55304 - 0.694258i) q^{63} +(-23.5386 - 40.7700i) q^{64} +(-1.65300 - 2.86307i) q^{65} +(-1.71558 - 9.72955i) q^{66} +(1.45453 + 8.24904i) q^{67} +(6.79092 + 11.7622i) q^{68} +(-0.779156 - 1.34954i) q^{69} +(-6.41956 + 24.3191i) q^{70} +(-7.41290 - 6.22016i) q^{71} +(-1.86334 - 10.5675i) q^{72} +(-8.47953 + 3.08630i) q^{73} +(-12.4049 - 10.4090i) q^{74} +(-3.26827 + 5.66081i) q^{75} +(-20.6905 + 14.7833i) q^{76} +(8.47866 + 3.91539i) q^{77} +(-2.55998 + 0.931758i) q^{78} +(0.591627 + 0.496434i) q^{79} +(58.6191 + 21.3356i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-3.89979 - 1.41941i) q^{82} +(5.63263 + 9.75600i) q^{83} +(14.0129 + 6.47107i) q^{84} +(-7.43066 - 2.70454i) q^{85} +(-15.5937 + 13.0847i) q^{86} +4.92247 q^{87} +(18.9385 - 32.8024i) q^{88} +(0.267953 + 0.0975269i) q^{89} +(7.28248 + 6.11072i) q^{90} +(0.657271 - 2.48992i) q^{91} +(1.57863 - 8.95283i) q^{92} +(-0.453299 + 2.57079i) q^{93} +(0.867749 + 1.50298i) q^{94} +(3.69549 - 14.3366i) q^{95} +(14.9718 - 25.9319i) q^{96} +(13.0550 - 4.75162i) q^{97} +(-16.8942 + 9.92192i) q^{98} +(2.70401 - 2.26893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 6 q^{7} - 6 q^{10} + 18 q^{11} + 108 q^{12} - 9 q^{13} - 3 q^{14} - 12 q^{17} - 30 q^{19} - 60 q^{20} - 9 q^{21} + 18 q^{23} + 9 q^{24} + 6 q^{25} + 12 q^{26} - 45 q^{27} - 45 q^{28} - 18 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) $ 90 * q + 6 * q^7 - 6 * q^10 + 18 * q^11 + 108 * q^12 - 9 * q^13 - 3 * q^14 - 12 * q^17 - 30 * q^19 - 60 * q^20 - 9 * q^21 + 18 * q^23 + 9 * q^24 + 6 * q^25 + 12 * q^26 - 45 * q^27 - 45 * q^28 - 18 * q^29 - 12 * q^30 - 18 * q^31 - 21 * q^32 - 12 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 + 39 * q^38 - 12 * q^39 + 18 * q^40 + 27 * q^41 - 3 * q^42 - 39 * q^43 - 78 * q^44 + 3 * q^45 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 9 * q^50 + 6 * q^51 - 48 * q^52 + 27 * q^53 - 42 * q^55 + 39 * q^56 - 6 * q^57 - 18 * q^58 - 60 * q^59 - 18 * q^60 - 12 * q^61 + 93 * q^62 - 12 * q^63 - 108 * q^64 - 33 * q^65 - 42 * q^67 + 18 * q^68 - 12 * q^69 + 6 * q^70 - 18 * q^71 + 9 * q^72 + 51 * q^73 + 114 * q^74 - 72 * q^75 + 24 * q^76 - 39 * q^77 + 9 * q^78 + 87 * q^79 + 42 * q^80 + 12 * q^82 + 24 * q^83 + 3 * q^84 + 36 * q^85 - 69 * q^86 - 36 * q^88 - 48 * q^89 + 3 * q^90 + 6 * q^91 - 18 * q^92 - 21 * q^93 - 54 * q^94 + 36 * q^95 + 21 * q^97 - 75 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.486024	+	2.75638i	−0.343671	+	1.94905i	−0.0299082	+	0.999553i	$0.509521\pi$
$2$	−0.486024	+	2.75638i	−0.343671	+	1.94905i	−0.313763	+	0.949501i	$0.601590\pi$
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	−5.48202	−	1.99529i	−2.74101	−	0.997646i
$5$	3.19171	−	1.16169i	1.42738	−	0.519523i	0.491198	−	0.871048i	$-0.336559\pi$
$5$	3.19171	−	1.16169i	1.42738	−	0.519523i	0.936178	+	0.351525i	$0.114337\pi$
$6$	−0.486024	−	2.75638i	−0.198418	−	1.12529i
$7$	2.40200	+	1.10923i	0.907871	+	0.419249i
$7$	2.40200	+	1.10923i	0.907871	+	0.419249i
$8$	5.36527	−	9.29292i	1.89691	−	3.28554i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	1.65080	+	9.36217i	0.522030	+	2.96058i
$11$	3.52983			1.06428			0.532142	−	0.846655i	$-0.321387\pi$
$11$	3.52983			1.06428			0.532142	+	0.846655i	$0.321387\pi$
$12$	5.83384			1.68409
$13$	−0.169019	−	0.958552i	−0.0468773	−	0.265854i	0.952357	−	0.304986i	$-0.0986519\pi$
$13$	−0.169019	−	0.958552i	−0.0468773	−	0.265854i	−0.999234	+	0.0391319i	$0.987541\pi$
$14$	−4.22489	+	6.08171i	−1.12915	+	1.62541i
$15$	−2.60191	+	2.18326i	−0.671809	+	0.563715i
$16$	14.0692	+	11.8055i	3.51730	+	2.95137i
$17$	−1.78344	−	1.49648i	−0.432547	−	0.362950i	0.400365	−	0.916356i	$-0.368883\pi$
$17$	−1.78344	−	1.49648i	−0.432547	−	0.362950i	−0.832912	+	0.553406i	$0.813328\pi$
$18$	1.39945	+	2.42392i	0.329854	+	0.571323i
$19$	2.46604	−	3.59425i	0.565748	−	0.824578i
$19$	2.46604	−	3.59425i	0.565748	−	0.824578i
$20$	−19.8149			−4.43075
$21$	−2.63652	−	0.220802i	−0.575336	−	0.0481828i
$22$	−1.71558	+	9.72955i	−0.365763	+	2.07435i
$23$	0.270598	+	1.53464i	0.0564236	+	0.319994i	0.999936	−	0.0113442i	$-0.00361104\pi$
$23$	0.270598	+	1.53464i	0.0564236	+	0.319994i	−0.943512	+	0.331338i	$0.892500\pi$
$24$	−1.86334	+	10.5675i	−0.380353	+	2.15709i
$25$	5.00728	−	4.20160i	1.00146	−	0.840321i
$26$	2.72428			0.534275
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−10.9546	−	10.8735i	−2.07022	−	2.05490i
$29$	−4.62561	−	1.68358i	−0.858954	−	0.312634i	−0.125268	−	0.992123i	$-0.539979\pi$
$29$	−4.62561	−	1.68358i	−0.858954	−	0.312634i	−0.733686	+	0.679489i	$0.762201\pi$
$30$	−4.75330	−	8.23296i	−0.867830	−	1.50313i
$31$	1.30522	−	2.26071i	0.234425	−	0.406036i	−0.724681	−	0.689085i	$-0.758013\pi$
$31$	1.30522	−	2.26071i	0.234425	−	0.406036i	0.959105	+	0.283049i	$0.0913460\pi$
$32$	−22.9381	+	19.2474i	−4.05493	+	3.40249i
$33$	−3.31696	+	1.20727i	−0.577408	+	0.210159i
$34$	4.99166	−	4.18850i	0.856063	−	0.718322i
$35$	8.95507	+	0.749963i	1.51368	+	0.126767i
$36$	−5.48202	+	1.99529i	−0.913670	+	0.332549i
$37$	−2.89283	+	5.01052i	−0.475578	+	0.823725i	−0.999609	−	0.0279744i	$-0.991094\pi$
$37$	−2.89283	+	5.01052i	−0.475578	+	0.823725i	0.524031	+	0.851699i	$0.324428\pi$
$38$	8.70857	+	8.54423i	1.41272	+	1.38606i
$39$	0.486669	+	0.842936i	0.0779295	+	0.134978i
$40$	6.32892	−	35.8931i	1.00069	−	5.67520i
$41$	−0.257477	+	1.46022i	−0.0402111	+	0.228048i	−0.998290	−	0.0584561i	$-0.981382\pi$
$41$	−0.257477	+	1.46022i	−0.0402111	+	0.228048i	0.958079	+	0.286505i	$0.0924933\pi$
$42$	1.89003	−	7.15994i	0.291637	−	1.10480i
$43$	5.57137	+	4.67493i	0.849626	+	0.712921i	0.959707	−	0.281002i	$-0.0906667\pi$
$43$	5.57137	+	4.67493i	0.849626	+	0.712921i	−0.110081	+	0.993923i	$0.535111\pi$
$44$	−19.3506	−	7.04304i	−2.91721	−	1.06178i
$45$	1.69827	−	2.94150i	0.253164	−	0.438492i
$46$	−4.36156			−0.643077
$47$	0.474997	−	0.398569i	0.0692854	−	0.0581373i	−0.607487	−	0.794329i	$-0.707822\pi$
$47$	0.474997	−	0.398569i	0.0692854	−	0.0581373i	0.676773	+	0.736192i	$0.263378\pi$
$48$	−17.2584	−	6.28156i	−2.49104	−	0.906664i
$49$	4.53922	+	5.32874i	0.648460	+	0.761249i
$50$	9.14756	+	15.8440i	1.29366	+	2.24068i
$51$	2.18771	+	0.796261i	0.306341	+	0.111499i
$52$	−0.986028	+	5.59204i	−0.136737	+	0.775476i
$53$	−5.94756	−	2.16474i	−0.816961	−	0.297349i	−0.100465	−	0.994941i	$-0.532033\pi$
$53$	−5.94756	−	2.16474i	−0.816961	−	0.297349i	−0.716496	+	0.697591i	$0.754255\pi$
$54$	−2.14408	−	1.79910i	−0.291773	−	0.244826i
$55$	11.2662	−	4.10056i	1.51913	−	0.552919i
$56$	23.1954	−	16.3703i	3.09961	−	2.18757i
$57$	−1.08801	+	4.22093i	−0.144111	+	0.559076i
$58$	6.88875	−	11.9317i	0.904537	−	1.56670i
$59$	−4.71422	−	3.95570i	−0.613739	−	0.514988i	0.282089	−	0.959388i	$-0.408973\pi$
$59$	−4.71422	−	3.95570i	−0.613739	−	0.514988i	−0.895829	+	0.444400i	$0.853417\pi$
$60$	18.6199	−	6.77710i	2.40382	−	0.874920i
$61$	1.26980	+	7.20141i	0.162582	+	0.922046i	0.951523	+	0.307577i	$0.0995183\pi$
$61$	1.26980	+	7.20141i	0.162582	+	0.922046i	−0.788942	+	0.614468i	$0.789371\pi$
$62$	5.59701	+	4.69645i	0.710820	+	0.596449i
$63$	2.55304	−	0.694258i	0.321653	−	0.0874683i
$64$	−23.5386	−	40.7700i	−2.94232	−	5.09625i
$65$	−1.65300	−	2.86307i	−0.205029	−	0.355120i
$66$	−1.71558	−	9.72955i	−0.211174	−	1.19762i
$67$	1.45453	+	8.24904i	0.177699	+	1.00778i	0.934982	+	0.354694i	$0.115415\pi$
$67$	1.45453	+	8.24904i	0.177699	+	1.00778i	−0.757284	+	0.653086i	$0.773474\pi$
$68$	6.79092	+	11.7622i	0.823520	+	1.42638i
$69$	−0.779156	−	1.34954i	−0.0937993	−	0.162465i
$70$	−6.41956	+	24.3191i	−0.767284	+	2.90668i
$71$	−7.41290	−	6.22016i	−0.879750	−	0.738198i	0.0863779	−	0.996262i	$-0.472471\pi$
$71$	−7.41290	−	6.22016i	−0.879750	−	0.738198i	−0.966128	+	0.258065i	$0.916915\pi$
$72$	−1.86334	−	10.5675i	−0.219597	−	1.24539i
$73$	−8.47953	+	3.08630i	−0.992454	+	0.361224i	−0.786670	−	0.617374i	$-0.788197\pi$
$73$	−8.47953	+	3.08630i	−0.992454	+	0.361224i	−0.205784	+	0.978597i	$0.565974\pi$
$74$	−12.4049	−	10.4090i	−1.44204	−	1.21002i
$75$	−3.26827	+	5.66081i	−0.377387	+	0.653654i
$76$	−20.6905	+	14.7833i	−2.37336	+	1.69576i
$77$	8.47866	+	3.91539i	0.966233	+	0.446200i
$78$	−2.55998	+	0.931758i	−0.289861	+	0.105501i
$79$	0.591627	+	0.496434i	0.0665633	+	0.0558532i	0.675462	−	0.737395i	$-0.263944\pi$
$79$	0.591627	+	0.496434i	0.0665633	+	0.0558532i	−0.608899	+	0.793248i	$0.708389\pi$
$80$	58.6191	+	21.3356i	6.55381	+	2.38539i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−3.89979	−	1.41941i	−0.430659	−	0.156747i
$83$	5.63263	+	9.75600i	0.618261	+	1.07086i	0.989803	+	0.142444i	$0.0454960\pi$
$83$	5.63263	+	9.75600i	0.618261	+	1.07086i	−0.371541	+	0.928416i	$0.621171\pi$
$84$	14.0129	+	6.47107i	1.52893	+	0.706051i
$85$	−7.43066	−	2.70454i	−0.805968	−	0.293348i
$86$	−15.5937	+	13.0847i	−1.68151	+	1.41096i
$87$	4.92247			0.527744
$88$	18.9385	−	32.8024i	2.01885	−	3.49675i
$89$	0.267953	+	0.0975269i	0.0284030	+	0.0103378i	0.356183	−	0.934416i	$-0.384078\pi$
$89$	0.267953	+	0.0975269i	0.0284030	+	0.0103378i	−0.327780	+	0.944754i	$0.606300\pi$
$90$	7.28248	+	6.11072i	0.767640	+	0.644127i
$91$	0.657271	−	2.48992i	0.0689007	−	0.261015i
$92$	1.57863	−	8.95283i	0.164583	−	0.933397i
$93$	−0.453299	+	2.57079i	−0.0470049	+	0.266578i
$94$	0.867749	+	1.50298i	0.0895014	+	0.155021i
$95$	3.69549	−	14.3366i	0.379149	−	1.47090i
$96$	14.9718	−	25.9319i	1.52805	−	2.64667i
$97$	13.0550	−	4.75162i	1.32553	−	0.482454i	0.420304	−	0.907383i	$-0.361923\pi$
$97$	13.0550	−	4.75162i	1.32553	−	0.482454i	0.905226	+	0.424930i	$0.139701\pi$
$98$	−16.8942	+	9.92192i	−1.70657	+	1.00227i
$99$	2.70401	−	2.26893i	0.271763	−	0.228036i
$100$	−35.8334	+	13.0423i	−3.58334	+	1.30423i
$101$	−0.959690	+	0.805276i	−0.0954928	+	0.0801279i	−0.689284	−	0.724491i	$-0.742075\pi$
$101$	−0.959690	+	0.805276i	−0.0954928	+	0.0801279i	0.593791	+	0.804619i	$0.297630\pi$
$102$	−3.25808	+	5.64315i	−0.322598	+	0.558755i
$103$	−1.30688	−	2.26358i	−0.128771	−	0.223037i	0.794430	−	0.607356i	$-0.207770\pi$
$103$	−1.30688	−	2.26358i	−0.128771	−	0.223037i	−0.923201	+	0.384318i	$0.874436\pi$
$104$	−9.81458	−	3.57221i	−0.962399	−	0.350284i
$105$	−8.67152	+	2.35808i	−0.846253	+	0.230125i
$106$	8.85749	−	15.3416i	0.860316	−	1.49011i
$107$	13.6966			1.32410			0.662050	−	0.749460i	$-0.269687\pi$
$107$	13.6966			1.32410			0.662050	+	0.749460i	$0.269687\pi$
$108$	4.46898	−	3.74992i	0.430028	−	0.360836i
$109$	−0.641087	+	3.63579i	−0.0614050	+	0.348245i	0.938590	+	0.345035i	$0.112133\pi$
$109$	−0.641087	+	3.63579i	−0.0614050	+	0.348245i	−0.999995	+	0.00321016i	$0.998978\pi$
$110$	5.82706	+	33.0469i	0.555588	+	3.15090i
$111$	1.00467	−	5.69776i	0.0953589	−	0.540807i
$112$	20.6993	+	43.9627i	1.95590	+	4.15409i
$113$	−10.8340			−1.01918			−0.509590	−	0.860417i	$-0.670203\pi$
$113$	−10.8340			−1.01918			−0.509590	+	0.860417i	$0.670203\pi$
$114$	−11.1057	−	5.05045i	−1.04014	−	0.473018i
$115$	2.64644	+	4.58377i	0.246782	+	0.427438i
$116$	21.9984	+	18.4589i	2.04250	+	1.71386i
$117$	−0.745621	−	0.625650i	−0.0689327	−	0.0578414i
$118$	13.1946	−	11.0716i	1.21466	−	1.01922i
$119$	−2.62388	−	5.57279i	−0.240530	−	0.510857i
$120$	6.32892	+	35.8931i	0.577749	+	3.27658i
$121$	1.45970			0.132700
$122$	−20.4670			−1.85299
$123$	−0.257477	−	1.46022i	−0.0232159	−	0.131664i
$124$	−11.6660	+	9.78896i	−1.04764	+	0.879075i
$125$	2.60946	−	4.51972i	0.233397	−	0.404256i
$126$	0.672800	+	7.37457i	0.0599378	+	0.656979i
$127$	2.00432	+	11.3670i	0.177854	+	1.00866i	0.934798	+	0.355181i	$0.115581\pi$
$127$	2.00432	+	11.3670i	0.177854	+	1.00866i	−0.756943	+	0.653481i	$0.773308\pi$
$128$	67.5423	−	24.5834i	5.96995	−	2.17288i
$129$	−6.83430	−	2.48748i	−0.601726	−	0.219010i
$130$	8.69511	−	3.16476i	0.762612	−	0.277568i
$131$	3.50569	−	19.8818i	0.306294	−	1.73708i	−0.311057	−	0.950391i	$-0.600683\pi$
$131$	3.50569	−	19.8818i	0.306294	−	1.73708i	0.617351	−	0.786688i	$-0.288206\pi$
$132$	20.5925			1.79234
$133$	9.91028	−	5.89800i	0.859330	−	0.511421i
$134$	−23.4444			−2.02529
$135$	−0.589804	+	3.34495i	−0.0507623	+	0.287887i
$136$	−23.4753	+	8.54431i	−2.01299	+	0.732669i
$137$	−20.1365	−	7.32910i	−1.72038	−	0.626167i	−0.722508	−	0.691363i	$-0.757011\pi$
$137$	−20.1365	−	7.32910i	−1.72038	−	0.626167i	−0.997873	+	0.0651956i	$0.979233\pi$
$138$	4.09852	−	1.49174i	0.348889	−	0.126985i
$139$	−0.256888	−	1.45689i	−0.0217890	−	0.123572i	0.971973	−	0.235092i	$-0.0755391\pi$
$139$	−0.256888	−	1.45689i	−0.0217890	−	0.123572i	−0.993762	+	0.111520i	$0.964428\pi$
$140$	−47.5955	−	21.9793i	−4.02255	−	1.85759i
$141$	−0.310032	+	0.536991i	−0.0261094	+	0.0452228i
$142$	20.7480	−	17.4096i	1.74113	−	1.46098i
$143$	−0.596607	−	3.38352i	−0.0498908	−	0.282945i
$144$	18.3660			1.53050
$145$	−16.7194			−1.38847
$146$	−4.38575	−	24.8728i	−0.362967	−	2.05849i
$147$	−6.08801	−	3.45487i	−0.502131	−	0.284953i
$148$	25.8560	−	21.6957i	2.12535	−	1.78338i
$149$	−9.95746	−	8.35530i	−0.815747	−	0.684493i	0.136225	−	0.990678i	$-0.456503\pi$
$149$	−9.95746	−	8.35530i	−0.815747	−	0.684493i	−0.951972	+	0.306185i	$0.900947\pi$
$150$	−14.0149	−	11.7599i	−1.14431	−	0.960190i
$151$	−2.21010	−	3.82800i	−0.179855	−	0.311518i	0.761976	−	0.647606i	$-0.224230\pi$
$151$	−2.21010	−	3.82800i	−0.179855	−	0.311518i	−0.941831	+	0.336087i	$0.890896\pi$
$152$	−20.1701	−	42.2009i	−1.63601	−	3.42294i
$153$	−2.32811			−0.188217
$154$	−14.9131	+	21.4674i	−1.20173	+	1.72989i
$155$	1.53965	−	8.73179i	0.123668	−	0.701355i
$156$	−0.986028	−	5.59204i	−0.0789454	−	0.447722i
$157$	2.15327	−	12.2118i	0.171850	−	0.974607i	−0.769868	−	0.638203i	$-0.779678\pi$
$157$	2.15327	−	12.2118i	0.171850	−	0.974607i	0.941718	−	0.336404i	$-0.109211\pi$
$158$	−1.65591	+	1.38947i	−0.131737	+	0.110540i
$159$	6.32926			0.501943
$160$	−50.8525	+	88.0791i	−4.02024	+	6.96326i
$161$	−1.05229	+	3.98635i	−0.0829319	+	0.314169i
$162$	2.63011	+	0.957280i	0.206641	+	0.0752110i
$163$	−5.15975	−	8.93695i	−0.404143	−	0.699996i	0.590078	−	0.807346i	$-0.299097\pi$
$163$	−5.15975	−	8.93695i	−0.404143	−	0.699996i	−0.994221	+	0.107350i	$0.965764\pi$
$164$	4.32506	−	7.49123i	0.337731	−	0.584967i
$165$	−9.18429	+	7.70653i	−0.714996	+	0.599953i
$166$	−29.6288	+	10.7840i	−2.29964	+	0.837002i
$167$	10.8842	−	9.13293i	0.842245	−	0.706727i	−0.115823	−	0.993270i	$-0.536950\pi$
$167$	10.8842	−	9.13293i	0.842245	−	0.706727i	0.958067	+	0.286543i	$0.0925060\pi$
$168$	−16.1975	+	23.3163i	−1.24967	+	1.79889i
$169$	11.3258	−	4.12224i	0.871212	−	0.317095i
$170$	11.0662	−	19.1672i	0.848740	−	1.47006i
$171$	−0.421245	−	4.33850i	−0.0322134	−	0.331773i
$172$	−21.2145	−	36.7446i	−1.61759	−	2.80175i
$173$	−1.37828	+	7.81661i	−0.104789	+	0.594286i	0.886516	+	0.462698i	$0.153119\pi$
$173$	−1.37828	+	7.81661i	−0.104789	+	0.594286i	−0.991305	+	0.131588i	$0.957992\pi$
$174$	−2.39244	+	13.5682i	−0.181370	+	1.02860i
$175$	16.6880	−	4.53804i	1.26150	−	0.343044i
$176$	49.6619	+	41.6713i	3.74341	+	3.14109i
$177$	5.78285	+	2.10478i	0.434666	+	0.158205i
$178$	−0.399053	+	0.691179i	−0.0299103	+	0.0518061i
$179$	−10.2401			−0.765383			−0.382691	−	0.923876i	$-0.625003\pi$
$179$	−10.2401			−0.765383			−0.382691	+	0.923876i	$0.625003\pi$
$180$	−15.1791	+	12.7368i	−1.13138	+	0.949344i
$181$	0.246085	+	0.0895674i	0.0182913	+	0.00665750i	0.351150	−	0.936319i	$-0.385791\pi$
$181$	0.246085	+	0.0895674i	0.0182913	+	0.00665750i	−0.332858	+	0.942977i	$0.608013\pi$
$182$	6.54372	+	3.02185i	0.485053	+	0.223994i
$183$	−3.65625	−	6.33281i	−0.270278	−	0.468135i
$184$	15.7131	+	5.71910i	1.15838	+	0.421618i
$185$	−3.41240	+	19.3527i	−0.250885	+	1.42284i
$186$	−6.86574	−	2.49893i	−0.503421	−	0.183230i
$187$	−6.29523	−	5.28232i	−0.460353	−	0.386282i
$188$	−3.39920	+	1.23721i	−0.247912	+	0.0902327i
$189$	−2.16162	+	1.52558i	−0.157235	+	0.110970i
$190$	37.7210	+	17.1541i	2.73657	+	1.24449i
$191$	−4.79971	+	8.31334i	−0.347295	+	0.601532i	−0.985768	−	0.168112i	$-0.946233\pi$
$191$	−4.79971	+	8.31334i	−0.347295	+	0.601532i	0.638473	+	0.769644i	$0.279566\pi$
$192$	36.0632	+	30.2606i	2.60264	+	2.18387i
$193$	−1.85832	+	0.676373i	−0.133765	+	0.0486864i	−0.408035	−	0.912966i	$-0.633786\pi$
$193$	−1.85832	+	0.676373i	−0.133765	+	0.0486864i	0.274270	+	0.961653i	$0.411564\pi$
$194$	6.75223	+	38.2938i	0.484782	+	2.74934i
$195$	2.53254	+	2.12505i	0.181359	+	0.152178i
$196$	−14.2517	−	38.2693i	−1.01798	−	2.73352i
$197$	−1.24140	−	2.15017i	−0.0884462	−	0.153193i	0.818408	−	0.574637i	$-0.194857\pi$
$197$	−1.24140	−	2.15017i	−0.0884462	−	0.153193i	−0.906855	+	0.421444i	$0.861523\pi$
$198$	4.93982	+	8.55602i	0.351058	+	0.608050i
$199$	−0.0118456	−	0.0671800i	−0.000839716	−	0.00476226i	0.984385	−	0.176029i	$-0.0563252\pi$
$199$	−0.0118456	−	0.0671800i	−0.000839716	−	0.00476226i	−0.985225	+	0.171267i	$0.945214\pi$
$200$	−12.1798	−	69.0750i	−0.861241	−	4.88434i
$201$	−4.18815	−	7.25408i	−0.295409	−	0.511663i
$202$	−1.75321	−	3.03665i	−0.123356	−	0.213658i
$203$	−9.24324	−	9.17483i	−0.648748	−	0.643947i
$204$	−10.4043	−	8.73024i	−0.728446	−	0.611239i
$205$	0.874532	+	4.95972i	0.0610799	+	0.346402i
$206$	6.87447	−	2.50210i	0.478967	−	0.174330i
$207$	1.19374	+	1.00166i	0.0829704	+	0.0696204i
$208$	8.93819	−	15.4814i	0.619752	−	1.07344i
$209$	8.70470	−	12.6871i	0.602117	−	0.877585i
$210$	−2.28520	−	25.0481i	−0.157694	−	1.72848i
$211$	−25.5574	+	9.30213i	−1.75944	+	0.640385i	−0.999949	−	0.0101297i	$-0.996776\pi$
$211$	−25.5574	+	9.30213i	−1.75944	+	0.640385i	−0.759494	+	0.650514i	$0.774553\pi$
$212$	28.2854	+	23.7342i	1.94265	+	1.63007i
$213$	9.09327	+	3.30968i	0.623061	+	0.226776i
$214$	−6.65687	+	37.7530i	−0.455055	+	2.58074i
$215$	23.2130	+	8.44885i	1.58311	+	0.576207i
$216$	5.36527	+	9.29292i	0.365061	+	0.632303i
$217$	5.64279	−	3.98244i	0.383058	−	0.270346i
$218$	−9.71002	−	3.53416i	−0.657645	−	0.239363i
$219$	6.91258	−	5.80034i	0.467109	−	0.391951i
$220$	−69.9433			−4.71558
$221$	−1.13302	+	1.96245i	−0.0762152	+	0.132009i
$222$	15.2169	+	5.53849i	1.02129	+	0.371719i
$223$	18.6977	+	15.6893i	1.25209	+	1.05063i	0.996478	+	0.0838520i	$0.0267223\pi$
$223$	18.6977	+	15.6893i	1.25209	+	1.05063i	0.255615	+	0.966779i	$0.417722\pi$
$224$	−76.4472	+	20.7886i	−5.10785	+	1.38900i
$225$	1.13506	−	6.43723i	0.0756705	−	0.429149i
$226$	5.26560	−	29.8627i	0.350263	−	1.98644i
$227$	9.22493	+	15.9780i	0.612280	+	1.06050i	0.990855	+	0.134930i	$0.0430809\pi$
$227$	9.22493	+	15.9780i	0.612280	+	1.06050i	−0.378575	+	0.925571i	$0.623586\pi$
$228$	14.3865	−	20.9683i	0.952768	−	1.38866i
$229$	−12.3004	+	21.3050i	−0.812836	+	1.40787i	0.0980347	+	0.995183i	$0.468744\pi$
$229$	−12.3004	+	21.3050i	−0.812836	+	1.40787i	−0.910871	+	0.412691i	$0.864589\pi$
$230$	−13.9208	+	5.06677i	−0.917912	+	0.334093i
$231$	−9.30647	−	0.779392i	−0.612321	−	0.0512802i
$232$	−40.4631	+	33.9525i	−2.65653	+	2.22909i
$233$	−14.7458	+	5.36701i	−0.966026	+	0.351605i	−0.776392	−	0.630250i	$-0.782952\pi$
$233$	−14.7458	+	5.36701i	−0.966026	+	0.351605i	−0.189634	+	0.981855i	$0.560730\pi$
$234$	2.08692	−	1.75113i	0.136426	−	0.114475i
$235$	1.05304	−	1.82392i	0.0686926	−	0.118979i
$236$	17.9507	+	31.0915i	1.16849	+	2.02388i
$237$	−0.725739	−	0.264147i	−0.0471418	−	0.0171582i
$238$	16.6360	−	4.52389i	1.07835	−	0.293240i
$239$	4.40350	−	7.62709i	0.284839	−	0.493356i	−0.687731	−	0.725966i	$-0.741393\pi$
$239$	4.40350	−	7.62709i	0.284839	−	0.493356i	0.972570	+	0.232610i	$0.0747265\pi$
$240$	−62.3811			−4.02668
$241$	−4.80752	+	4.03399i	−0.309680	+	0.259852i	−0.784360	−	0.620306i	$-0.787008\pi$
$241$	−4.80752	+	4.03399i	−0.309680	+	0.259852i	0.474680	+	0.880158i	$0.342564\pi$
$242$	−0.709449	+	4.02349i	−0.0456051	+	0.258639i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	7.40783	−	42.0119i	0.474238	−	2.68953i
$245$	20.6782	+	11.7346i	1.32108	+	0.749699i
$246$	4.15007			0.264599
$247$	−3.86208	−	1.75633i	−0.245738	−	0.111753i
$248$	−14.0057	−	24.2587i	−0.889365	−	1.54043i
$249$	−8.62969	−	7.24117i	−0.546884	−	0.458890i
$250$	11.1898	+	9.38935i	0.707704	+	0.593835i
$251$	−16.3448	+	13.7149i	−1.03168	+	0.865678i	−0.991049	−	0.133496i	$-0.957380\pi$
$251$	−16.3448	+	13.7149i	−1.03168	+	0.865678i	−0.0406259	+	0.999174i	$0.512935\pi$
$252$	−15.3811	−	1.28812i	−0.968915	−	0.0811440i
$253$	0.955165	+	5.41701i	0.0600507	+	0.340564i
$254$	−32.3060			−2.02706
$255$	7.90754			0.495189
$256$	18.5842	+	105.396i	1.16151	+	6.58727i
$257$	4.96473	−	4.16590i	0.309691	−	0.259862i	−0.474673	−	0.880162i	$-0.657434\pi$
$257$	4.96473	−	4.16590i	0.309691	−	0.259862i	0.784364	+	0.620300i	$0.212989\pi$
$258$	10.1781	−	17.6289i	0.633659	−	1.09753i
$259$	−12.5064	+	8.82647i	−0.777109	+	0.548450i
$260$	3.34909	+	18.9936i	0.207702	+	1.17793i
$261$	−4.62561	+	1.68358i	−0.286318	+	0.104211i
$262$	53.0979	+	19.3260i	3.28040	+	1.19397i
$263$	−27.7809	+	10.1114i	−1.71304	+	0.623496i	−0.997201	−	0.0747683i	$-0.976178\pi$
$263$	−27.7809	+	10.1114i	−1.71304	+	0.623496i	−0.715840	+	0.698264i	$0.753956\pi$
$264$	−6.57727	+	37.3016i	−0.404803	+	2.29575i
$265$	−21.4976			−1.32059
$266$	11.4405	+	30.1831i	0.701461	+	1.85064i
$267$	−0.285150			−0.0174509
$268$	8.48549	−	48.1236i	0.518334	−	2.93962i
$269$	7.01846	−	2.55451i	0.427923	−	0.155751i	−0.119075	−	0.992885i	$-0.537993\pi$
$269$	7.01846	−	2.55451i	0.427923	−	0.155751i	0.546998	+	0.837134i	$0.315771\pi$
$270$	−8.93328	−	3.25145i	−0.543662	−	0.197877i
$271$	16.2637	−	5.91952i	0.987952	−	0.359585i	0.203025	−	0.979174i	$-0.434923\pi$
$271$	16.2637	−	5.91952i	0.987952	−	0.359585i	0.784927	+	0.619589i	$0.212701\pi$
$272$	−7.42488	−	42.1086i	−0.450200	−	2.55321i
$273$	0.233971	+	2.56456i	0.0141606	+	0.155214i
$274$	29.9886	−	51.9418i	1.81168	−	3.13792i
$275$	17.6748	−	14.8309i	1.06583	−	0.894340i
$276$	1.57863	+	8.95283i	0.0950221	+	0.538897i
$277$	−4.63447			−0.278458			−0.139229	−	0.990260i	$-0.544462\pi$
$277$	−4.63447			−0.278458			−0.139229	+	0.990260i	$0.544462\pi$
$278$	4.14059			0.248336
$279$	−0.453299	−	2.57079i	−0.0271383	−	0.153909i
$280$	55.0157	−	79.1950i	3.28782	−	4.73281i
$281$	7.79269	−	6.53884i	0.464873	−	0.390075i	−0.380047	−	0.924967i	$-0.624092\pi$
$281$	7.79269	−	6.53884i	0.464873	−	0.390075i	0.844920	+	0.534892i	$0.179648\pi$
$282$	−1.32947	−	1.11556i	−0.0791687	−	0.0664304i
$283$	−20.4185	−	17.1331i	−1.21375	−	1.01846i	−0.999128	−	0.0417617i	$-0.986703\pi$
$283$	−20.4185	−	17.1331i	−1.21375	−	1.01846i	−0.214624	−	0.976697i	$-0.568853\pi$
$284$	28.2266	+	48.8900i	1.67494	+	2.90109i
$285$	1.43078	+	14.7359i	0.0847520	+	0.872880i
$286$	9.61624			0.568620
$287$	−2.23818	+	3.22186i	−0.132116	+	0.190180i
$288$	−5.19966	+	29.4887i	−0.306393	+	1.73764i
$289$	−2.01083	−	11.4040i	−0.118284	−	0.670822i
$290$	8.12603	−	46.0850i	0.477177	−	2.70621i
$291$	−10.6425	+	8.93012i	−0.623874	+	0.523493i
$292$	52.6430			3.08070
$293$	10.5030	−	18.1917i	0.613592	−	1.06277i	−0.377038	−	0.926198i	$-0.623057\pi$
$293$	10.5030	−	18.1917i	0.613592	−	1.06277i	0.990630	−	0.136575i	$-0.0436093\pi$
$294$	12.4819	−	15.1017i	0.727957	−	0.880750i
$295$	−19.6417	−	7.14900i	−1.14359	−	0.416231i
$296$	31.0416	+	53.7656i	1.80426	+	3.12506i
$297$	−1.76492	+	3.05692i	−0.102411	+	0.177381i
$298$	27.8700	−	23.3857i	1.61446	−	1.35470i
$299$	1.42529	−	0.518764i	0.0824268	−	0.0300009i
$300$	29.2117	−	24.5115i	1.68654	−	1.41517i
$301$	8.19686	+	17.4091i	0.472459	+	1.00345i
$302$	11.6256	−	4.23137i	0.668977	−	0.243488i
$303$	0.626393	−	1.08495i	0.0359854	−	0.0623285i
$304$	77.1270	−	21.4555i	4.42354	−	1.23056i
$305$	12.4186	+	21.5097i	0.711089	+	1.23164i
$306$	1.13152	−	6.41716i	0.0646846	−	0.366844i
$307$	−1.64037	+	9.30299i	−0.0936207	+	0.530950i	0.901541	+	0.432695i	$0.142437\pi$
$307$	−1.64037	+	9.30299i	−0.0936207	+	0.530950i	−0.995161	+	0.0982549i	$0.968674\pi$
$308$	−38.6678	−	38.3816i	−2.20330	−	2.18700i
$309$	2.00226	+	1.68009i	0.113904	+	0.0955772i
$310$	23.3198	+	8.48772i	1.32448	+	0.482070i
$311$	−5.89653	+	10.2131i	−0.334362	+	0.579131i	−0.983362	−	0.181657i	$-0.941854\pi$
$311$	−5.89653	+	10.2131i	−0.334362	+	0.579131i	0.649000	+	0.760788i	$0.275187\pi$
$312$	10.4445			0.591301
$313$	−9.18996	+	7.71129i	−0.519447	+	0.435868i	−0.864439	−	0.502738i	$-0.832326\pi$
$313$	−9.18996	+	7.71129i	−0.519447	+	0.435868i	0.344992	+	0.938606i	$0.387882\pi$
$314$	32.6138	+	11.8704i	1.84050	+	0.669888i
$315$	7.34205	−	5.18170i	0.413678	−	0.291956i
$316$	−2.25278	−	3.90193i	−0.126729	−	0.219501i
$317$	−4.97769	−	1.81173i	−0.279575	−	0.101757i	0.198427	−	0.980116i	$-0.436417\pi$
$317$	−4.97769	−	1.81173i	−0.279575	−	0.101757i	−0.478002	+	0.878359i	$0.658639\pi$
$318$	−3.07617	+	17.4459i	−0.172503	+	0.978315i
$319$	−16.3276	−	5.94277i	−0.914171	−	0.332731i
$320$	−122.490	−	102.782i	−6.84742	−	5.74567i
$321$	−12.8706	+	4.68451i	−0.718366	+	0.261464i
$322$	−10.4765	−	4.83797i	−0.583831	−	0.269609i
$323$	−9.77676	+	2.71974i	−0.543993	+	0.151330i
$324$	−2.91692	+	5.05226i	−0.162051	+	0.280681i
$325$	−4.87378	−	4.08958i	−0.270349	−	0.226849i
$326$	27.1414	−	9.87866i	1.50322	−	0.547128i
$327$	−0.641087	−	3.63579i	−0.0354522	−	0.201059i
$328$	12.1883	+	10.2272i	0.672987	+	0.564703i
$329$	1.58305	−	0.430484i	0.0872762	−	0.0237334i
$330$	−16.7783	−	29.0609i	−0.923617	−	1.59975i
$331$	9.69912	+	16.7994i	0.533112	+	0.923377i	0.999252	+	0.0386659i	$0.0123108\pi$
$331$	9.69912	+	16.7994i	0.533112	+	0.923377i	−0.466140	+	0.884711i	$0.654356\pi$
$332$	−11.4121	−	64.7213i	−0.626321	−	3.55204i
$333$	1.00467	+	5.69776i	0.0550555	+	0.312235i
$334$	19.8838	+	34.4398i	1.08799	+	1.88446i
$335$	14.2252	+	24.6388i	0.777208	+	1.34616i
$336$	−34.4871	−	34.2319i	−1.88143	−	1.86750i
$337$	13.8558	+	11.6264i	0.754772	+	0.633329i	0.936760	−	0.349972i	$-0.113809\pi$
$337$	13.8558	+	11.6264i	0.754772	+	0.633329i	−0.181988	+	0.983301i	$0.558253\pi$
$338$	5.85786	+	33.2216i	0.318625	+	1.80701i
$339$	10.1807	−	3.70546i	0.552938	−	0.201253i
$340$	35.3387	+	29.6527i	1.91651	+	1.60814i
$341$	4.60721	−	7.97992i	0.249494	−	0.432137i
$342$	12.1633	+	0.947502i	0.657715	+	0.0512350i
$343$	4.99242	+	17.8347i	0.269566	+	0.962982i
$344$	73.3357	−	26.6920i	3.95400	−	1.43914i
$345$	−4.05458	−	3.40220i	−0.218291	−	0.183168i
$346$	−20.8757	−	7.59812i	−1.12228	−	0.408478i
$347$	0.901804	−	5.11438i	0.0484114	−	0.274554i	−0.950987	−	0.309230i	$-0.899929\pi$
$347$	0.901804	−	5.11438i	0.0484114	−	0.274554i	0.999399	+	0.0346756i	$0.0110398\pi$
$348$	−26.9851	−	9.82176i	−1.44655	−	0.526502i
$349$	−8.93008	−	15.4673i	−0.478016	−	0.827948i	0.521666	−	0.853150i	$-0.325311\pi$
$349$	−8.93008	−	15.4673i	−0.478016	−	0.827948i	−0.999682	+	0.0252016i	$0.991977\pi$
$350$	4.39778	+	48.2041i	0.235071	+	2.57662i
$351$	0.914639	+	0.332901i	0.0488198	+	0.0177690i
$352$	−80.9678	+	67.9400i	−4.31560	+	3.62122i
$353$	16.3147			0.868343			0.434172	−	0.900830i	$-0.357041\pi$
$353$	16.3147			0.868343			0.434172	+	0.900830i	$0.357041\pi$
$354$	−8.61219	+	14.9167i	−0.457733	+	0.792816i
$355$	−30.8857	−	11.2415i	−1.63924	−	0.596636i
$356$	−1.27433	−	1.06929i	−0.0675393	−	0.0566722i
$357$	4.37164	+	4.33929i	0.231372	+	0.229660i
$358$	4.97695	−	28.2257i	0.263040	−	1.49177i
$359$	2.09188	−	11.8637i	0.110405	−	0.626140i	−0.878517	−	0.477710i	$-0.841467\pi$
$359$	2.09188	−	11.8637i	0.110405	−	0.626140i	0.988923	−	0.148430i	$-0.0474220\pi$
$360$	−18.2234	−	31.5639i	−0.960458	−	1.66356i
$361$	−6.83730	−	17.7271i	−0.359858	−	0.933007i
$362$	−0.366485	+	0.634770i	−0.0192620	+	0.0333628i
$363$	−1.37167	+	0.499247i	−0.0719940	+	0.0262037i
$364$	−8.57129	+	12.3384i	−0.449258	+	0.646706i
$365$	−23.4789	+	19.7011i	−1.22894	+	1.03120i
$366$	19.2327	−	7.00011i	1.00531	−	0.365902i
$367$	18.2867	−	15.3444i	0.954557	−	0.800969i	−0.0255018	−	0.999675i	$-0.508118\pi$
$367$	18.2867	−	15.3444i	0.954557	−	0.800969i	0.980059	+	0.198706i	$0.0636739\pi$
$368$	−14.3100	+	24.7856i	−0.745960	+	1.29204i
$369$	0.741374	+	1.28410i	0.0385944	+	0.0668475i
$370$	−51.6849	−	18.8118i	−2.68697	−	0.977976i
$371$	−11.8849	−	11.7969i	−0.617032	−	0.612465i
$372$	7.61446	−	13.1886i	0.394791	−	0.683799i
$373$	−20.7172			−1.07270			−0.536348	−	0.843997i	$-0.680197\pi$
$373$	−20.7172			−1.07270			−0.536348	+	0.843997i	$0.680197\pi$
$374$	17.6197	−	14.7847i	0.911094	−	0.764499i
$375$	−0.906256	+	5.13963i	−0.0467988	+	0.265409i
$376$	−1.15539	−	6.55254i	−0.0595847	−	0.337921i
$377$	−0.831989	+	4.71844i	−0.0428496	+	0.243012i
$378$	−3.15448	−	6.69972i	−0.162249	−	0.344596i
$379$	−1.23951			−0.0636694			−0.0318347	−	0.999493i	$-0.510135\pi$
$379$	−1.23951			−0.0636694			−0.0318347	+	0.999493i	$0.510135\pi$
$380$	−48.8644	+	71.2198i	−2.50669	+	3.65350i
$381$	−5.77120	−	9.99601i	−0.295667	−	0.512111i
$382$	−20.5819	−	17.2703i	−1.05306	−	0.883625i
$383$	5.29254	+	4.44097i	0.270436	+	0.226923i	0.767913	−	0.640555i	$-0.221295\pi$
$383$	5.29254	+	4.44097i	0.270436	+	0.226923i	−0.497476	+	0.867477i	$0.665740\pi$
$384$	−55.0610	+	46.2016i	−2.80982	+	2.35772i
$385$	31.6099	+	2.64724i	1.61099	+	0.134916i
$386$	−0.961152	−	5.45097i	−0.0489214	−	0.277447i
$387$	7.27291			0.369703
$388$	−81.0484			−4.11461
$389$	−1.20131	−	6.81295i	−0.0609087	−	0.345430i	−0.999998	−	0.00175836i	$-0.999440\pi$
$389$	−1.20131	−	6.81295i	−0.0609087	−	0.345430i	0.939090	−	0.343672i	$-0.111671\pi$
$390$	−7.08832	+	5.94780i	−0.358931	+	0.301179i
$391$	1.81396	−	3.14187i	0.0917360	−	0.158891i
$392$	73.8737	−	13.5925i	3.73119	−	0.686525i
$393$	3.50569	+	19.8818i	0.176839	+	1.00290i
$394$	6.53003	−	2.37674i	0.328978	−	0.119738i
$395$	2.46501	+	0.897189i	0.124028	+	0.0451425i
$396$	−19.3506	+	7.04304i	−0.972404	+	0.353926i
$397$	−4.15270	+	23.5511i	−0.208418	+	1.18200i	0.683551	+	0.729902i	$0.260434\pi$
$397$	−4.15270	+	23.5511i	−0.208418	+	1.18200i	−0.891970	+	0.452095i	$0.850677\pi$
$398$	0.190931			0.00957050
$399$	−7.29538	+	8.93182i	−0.365226	+	0.447150i
$400$	120.050			6.00251
$401$	5.13123	−	29.1007i	0.256241	−	1.45322i	−0.536624	−	0.843821i	$-0.680301\pi$
$401$	5.13123	−	29.1007i	0.256241	−	1.45322i	0.792866	−	0.609396i	$-0.208588\pi$
$402$	22.0305	−	8.01846i	1.09878	−	0.399924i
$403$	−2.38761	−	0.869021i	−0.118936	−	0.0432890i
$404$	6.86780	−	2.49968i	0.341686	−	0.124363i
$405$	−0.589804	−	3.34495i	−0.0293076	−	0.166212i
$406$	29.7817	−	21.0187i	1.47804	−	1.04314i
$407$	−10.2112	+	17.6863i	−0.506150	+	0.876677i
$408$	19.1372	−	16.0581i	0.947435	−	0.794992i
$409$	−1.87597	−	10.6391i	−0.0927606	−	0.526071i	−0.995411	−	0.0956960i	$-0.969492\pi$
$409$	−1.87597	−	10.6391i	−0.0927606	−	0.526071i	0.902650	−	0.430375i	$-0.141619\pi$
$410$	−14.0959			−0.696147
$411$	21.4289			1.05701
$412$	2.64783	+	15.0166i	0.130449	+	0.739815i
$413$	−6.93579	−	14.7308i	−0.341288	−	0.724853i
$414$	−3.34115	+	2.80356i	−0.164208	+	0.137787i
$415$	29.3112	+	24.5950i	1.43883	+	1.20732i
$416$	22.3266	+	18.7342i	1.09465	+	0.918521i
$417$	0.739681	+	1.28116i	0.0362223	+	0.0627389i
$418$	30.7398	+	30.1597i	1.50353	+	1.47516i
$419$	11.1160			0.543054			0.271527	−	0.962431i	$-0.412471\pi$
$419$	11.1160			0.543054			0.271527	+	0.962431i	$0.412471\pi$
$420$	52.2425	+	4.37517i	2.54917	+	0.213486i
$421$	−2.50081	+	14.1828i	−0.121882	+	0.691227i	0.861229	+	0.508217i	$0.169695\pi$
$421$	−2.50081	+	14.1828i	−0.121882	+	0.691227i	−0.983111	+	0.183010i	$0.941416\pi$
$422$	−13.2187	−	74.9669i	−0.643475	−	3.64933i
$423$	0.107673	−	0.610644i	0.00523524	−	0.0296905i
$424$	−52.0270	+	43.6559i	−2.52666	+	2.12012i
$425$	−15.2178			−0.738171
$426$	−13.5423	+	23.4559i	−0.656126	+	1.13644i
$427$	−4.93794	+	18.7063i	−0.238964	+	0.905261i
$428$	−75.0850	−	27.3287i	−3.62937	−	1.32098i
$429$	1.71786	+	2.97542i	0.0829391	+	0.143655i
$430$	−34.5703	+	59.8775i	−1.66713	+	2.88755i
$431$	−17.8327	+	14.9635i	−0.858973	+	0.720764i	−0.961747	−	0.273941i	$-0.911673\pi$
$431$	−17.8327	+	14.9635i	−0.858973	+	0.720764i	0.102773	+	0.994705i	$0.467228\pi$
$432$	−17.2584	+	6.28156i	−0.830347	+	0.302221i
$433$	16.1254	−	13.5308i	0.774939	−	0.650251i	−0.167030	−	0.985952i	$-0.553418\pi$
$433$	16.1254	−	13.5308i	0.774939	−	0.650251i	0.941969	+	0.335701i	$0.108973\pi$
$434$	8.23458	+	17.4892i	0.395273	+	0.839510i
$435$	15.7111	−	5.71837i	0.753290	−	0.274175i
$436$	10.7689	−	18.6523i	0.515737	−	0.893283i
$437$	6.18318	+	2.81188i	0.295781	+	0.134510i
$438$	12.6283	+	21.8728i	0.603401	+	1.04512i
$439$	3.70518	−	21.0131i	0.176839	−	1.00290i	−0.759161	−	0.650903i	$-0.774391\pi$
$439$	3.70518	−	21.0131i	0.176839	−	1.00290i	0.936000	−	0.352000i	$-0.114498\pi$
$440$	22.3400	−	126.697i	1.06502	−	6.04002i
$441$	6.90249	+	1.16430i	0.328690	+	0.0554427i
$442$	−4.85858	−	4.07683i	−0.231099	−	0.193915i
$443$	8.98760	+	3.27122i	0.427014	+	0.155420i	0.546582	−	0.837406i	$-0.315929\pi$
$443$	8.98760	+	3.27122i	0.427014	+	0.155420i	−0.119568	+	0.992826i	$0.538151\pi$
$444$	−16.8763	+	29.2306i	−0.800914	+	1.38722i
$445$	0.968524			0.0459124
$446$	−52.3331	+	43.9127i	−2.47804	+	2.07933i
$447$	12.2146	+	4.44576i	0.577733	+	0.210277i
$448$	−11.3164	−	124.039i	−0.534650	−	5.86030i
$449$	15.7752	+	27.3235i	0.744478	+	1.28947i	0.950438	+	0.310913i	$0.100635\pi$
$449$	15.7752	+	27.3235i	0.744478	+	1.28947i	−0.205960	+	0.978560i	$0.566032\pi$
$450$	17.1918	+	6.25730i	0.810428	+	0.294972i
$451$	−0.908849	+	5.15434i	−0.0427960	+	0.242708i
$452$	59.3924	+	21.6171i	2.79358	+	1.01678i
$453$	3.38607	+	2.84125i	0.159091	+	0.133493i
$454$	−48.5251	+	17.6617i	−2.27740	+	0.828904i
$455$	−0.794695	−	8.71066i	−0.0372559	−	0.408362i
$456$	33.3873	+	32.7572i	1.56350	+	1.53400i
$457$	−9.93573	+	17.2092i	−0.464774	+	0.805012i	−0.999191	−	0.0402088i	$-0.987198\pi$
$457$	−9.93573	+	17.2092i	−0.464774	+	0.805012i	0.534417	+	0.845221i	$0.320531\pi$
$458$	−52.7463	−	44.2594i	−2.46467	−	2.06811i
$459$	2.18771	−	0.796261i	0.102114	−	0.0371663i
$460$	−5.36188	−	30.4087i	−0.249999	−	1.41781i
$461$	−23.1820	−	19.4520i	−1.07969	−	0.905971i	−0.0837990	−	0.996483i	$-0.526705\pi$
$461$	−23.1820	−	19.4520i	−1.07969	−	0.905971i	−0.995895	+	0.0905115i	$0.971150\pi$
$462$	6.67147	−	25.2734i	0.310385	−	1.17582i
$463$	18.4153	+	31.8962i	0.855831	+	1.48234i	0.875871	+	0.482544i	$0.160287\pi$
$463$	18.4153	+	31.8962i	0.855831	+	1.48234i	−0.0200400	+	0.999799i	$0.506379\pi$
$464$	−45.2031	−	78.2941i	−2.09850	−	3.63471i
$465$	1.53965	+	8.73179i	0.0713996	+	0.404927i
$466$	−7.62674	−	43.2534i	−0.353302	−	2.00367i
$467$	−9.42770	−	16.3293i	−0.436262	−	0.755628i	0.561136	−	0.827724i	$-0.310365\pi$
$467$	−9.42770	−	16.3293i	−0.436262	−	0.755628i	−0.997398	+	0.0720958i	$0.977031\pi$
$468$	2.83915	+	4.91756i	0.131240	+	0.227314i
$469$	−5.65629	+	21.4276i	−0.261183	+	0.989435i
$470$	4.51560	+	3.78904i	0.208289	+	0.174775i
$471$	2.15327	+	12.2118i	0.0992174	+	0.562690i
$472$	−62.0531	+	22.5855i	−2.85623	+	1.03958i
$473$	19.6660	+	16.5017i	0.904243	+	0.758750i
$474$	1.08082	−	1.87203i	0.0496435	−	0.0859851i
$475$	−2.75348	−	28.3587i	−0.126339	−	1.30119i
$476$	3.26480	+	35.7855i	0.149642	+	1.64023i
$477$	−5.94756	+	2.16474i	−0.272320	+	0.0991165i
$478$	18.8830	+	15.8447i	0.863686	+	0.724719i
$479$	−15.0257	−	5.46890i	−0.686541	−	0.249881i	−0.0248877	−	0.999690i	$-0.507923\pi$
$479$	−15.0257	−	5.46890i	−0.686541	−	0.249881i	−0.661654	+	0.749810i	$0.730145\pi$
$480$	17.6609	−	100.160i	0.806105	−	4.57165i
$481$	5.29179	+	1.92605i	0.241285	+	0.0878204i
$482$	−8.78263	−	15.2120i	−0.400038	−	0.692886i
$483$	−0.374587	−	4.10585i	−0.0170443	−	0.186823i
$484$	−8.00210	−	2.91253i	−0.363732	−	0.132388i
$485$	36.1478	−	30.3316i	1.64139	−	1.37729i
$486$	−2.79890			−0.126961
$487$	12.0995	−	20.9569i	0.548280	−	0.949648i	−0.450113	−	0.892972i	$-0.648616\pi$
$487$	12.0995	−	20.9569i	0.548280	−	0.949648i	0.998393	−	0.0566764i	$-0.0180503\pi$
$488$	73.7350	+	26.8373i	3.33783	+	1.21487i
$489$	7.90520	+	6.63325i	0.357485	+	0.299966i
$490$	−42.3952	+	51.2937i	−1.91522	+	2.31721i
$491$	−2.17324	+	12.3250i	−0.0980769	+	0.556222i	0.895684	+	0.444691i	$0.146686\pi$
$491$	−2.17324	+	12.3250i	−0.0980769	+	0.556222i	−0.993761	+	0.111531i	$0.964425\pi$
$492$	−1.50208	+	8.51871i	−0.0677189	+	0.384053i
$493$	5.73003	+	9.92470i	0.258068	+	0.446986i
$494$	6.71818	−	9.79174i	0.302265	−	0.440551i
$495$	5.99462	−	10.3830i	0.269438	−	0.466680i
$496$	45.0522	−	16.3976i	2.02290	−	0.736276i
$497$	−10.9062	−	23.1634i	−0.489211	−	1.03902i
$498$	24.1536	−	20.2673i	1.08235	−	0.908200i
$499$	−20.6784	+	7.52633i	−0.925693	+	0.336925i	−0.760501	−	0.649337i	$-0.775047\pi$
$499$	−20.6784	+	7.52633i	−0.925693	+	0.336925i	−0.165192	+	0.986261i	$0.552824\pi$
$500$	−23.3233	+	19.5705i	−1.04305	+	0.875221i
$501$	−7.10416	+	12.3048i	−0.317390	+	0.549736i
$502$	−29.8596	−	51.7183i	−1.33270	−	2.30830i
$503$	26.7252	+	9.72716i	1.19162	+	0.433713i	0.860291	−	0.509804i	$-0.170282\pi$
$503$	26.7252	+	9.72716i	1.19162	+	0.433713i	0.331325	+	0.943517i	$0.392504\pi$
$504$	7.24606	−	27.4501i	0.322765	−	1.22272i
$505$	−2.12758	+	3.68507i	−0.0946759	+	0.163983i
$506$	−15.3956			−0.684416
$507$	−9.23284	+	7.74727i	−0.410045	+	0.344068i
$508$	11.6929	−	66.3135i	0.518787	−	2.94219i
$509$	−0.612342	−	3.47277i	−0.0271416	−	0.153928i	0.968225	−	0.250081i	$-0.0804572\pi$
$509$	−0.612342	−	3.47277i	−0.0271416	−	0.153928i	−0.995367	+	0.0961533i	$0.969346\pi$
$510$	−3.84325	+	21.7962i	−0.170182	+	0.965151i
$511$	−23.7913	−	1.99245i	−1.05246	−	0.0881409i
$512$	−155.791			−6.88503
$513$	1.87969	+	3.93278i	0.0829905	+	0.173636i
$514$	9.06983	+	15.7094i	0.400053	+	0.692912i
$515$	−6.80076	−	5.70652i	−0.299677	−	0.251459i
$516$	32.5025	+	27.2728i	1.43084	+	1.20062i
$517$	1.67666	−	1.40688i	0.0737393	−	0.0618746i
$518$	−18.2507	−	38.7622i	−0.801890	−	1.70311i
$519$	−1.37828	−	7.81661i	−0.0604998	−	0.343111i
$520$	−35.4751			−1.55569
$521$	5.42389			0.237625			0.118813	−	0.992917i	$-0.462091\pi$
$521$	5.42389			0.237625			0.118813	+	0.992917i	$0.462091\pi$
$522$	−2.39244	−	13.5682i	−0.104714	−	0.593864i
$523$	1.49539	−	1.25478i	0.0653889	−	0.0548678i	−0.609507	−	0.792780i	$-0.708633\pi$
$523$	1.49539	−	1.25478i	0.0653889	−	0.0548678i	0.674896	+	0.737913i	$0.264188\pi$
$524$	−58.8882	+	101.997i	−2.57254	+	4.45578i
$525$	−14.1295	+	9.97201i	−0.616663	+	0.435214i
$526$	−14.3687	−	81.4890i	−0.626505	−	3.55309i
$527$	−5.71089	+	2.07859i	−0.248770	+	0.0905450i
$528$	−60.9193	−	22.1728i	−2.65117	−	0.964948i
$529$	19.3310	−	7.03592i	0.840480	−	0.305910i
$530$	10.4484	−	59.2557i	0.453848	−	2.57390i
$531$	−6.15398			−0.267060
$532$	−66.0966	+	12.5590i	−2.86565	+	0.544503i
$533$	1.44322			0.0625127
$534$	0.138589	−	0.785980i	0.00599735	−	0.0340127i
$535$	43.7156	−	15.9112i	1.88999	−	0.687900i
$536$	84.4616	+	30.7415i	3.64819	+	1.32783i
$537$	9.62257	−	3.50233i	0.415244	−	0.151137i
$538$	3.63006	+	20.5871i	0.156503	+	0.887573i
$539$	16.0227	+	18.8095i	0.690146	+	0.810184i
$540$	9.90746	−	17.1602i	0.426349	−	0.738459i
$541$	18.5767	−	15.5877i	0.798676	−	0.670169i	−0.149200	−	0.988807i	$-0.547670\pi$
$541$	18.5767	−	15.5877i	0.798676	−	0.670169i	0.947877	+	0.318638i	$0.103225\pi$
$542$	8.41186	+	47.7060i	0.361320	+	2.04915i
$543$	−0.261878			−0.0112382
$544$	69.7121			2.98888
$545$	2.17748	+	12.3491i	0.0932731	+	0.528978i
$546$	−7.18262	−	0.601525i	−0.307388	−	0.0257429i
$547$	−4.07802	+	3.42186i	−0.174363	+	0.146308i	−0.725793	−	0.687913i	$-0.758527\pi$
$547$	−4.07802	+	3.42186i	−0.174363	+	0.146308i	0.551430	+	0.834221i	$0.314083\pi$
$548$	95.7652	+	80.3565i	4.09089	+	3.43266i
$549$	5.60170	+	4.70038i	0.239075	+	0.200608i
$550$	32.2893	+	55.9267i	1.37682	+	2.38472i
$551$	−17.4582	+	12.4738i	−0.743743	+	0.531403i
$552$	−16.7215			−0.711715
$553$	0.870431	+	1.84869i	0.0370145	+	0.0786142i
$554$	2.25246	−	12.7743i	0.0956979	−	0.542730i
$555$	−3.41240	−	19.3527i	−0.144848	−	0.821476i
$556$	−1.49865	+	8.49925i	−0.0635568	+	0.360448i
$557$	31.3536	−	26.3088i	1.32850	−	1.11474i	0.344070	−	0.938944i	$-0.388194\pi$
$557$	31.3536	−	26.3088i	1.32850	−	1.11474i	0.984427	−	0.175796i	$-0.0562501\pi$
$558$	7.30637			0.309303
$559$	3.53950	−	6.13060i	0.149705	−	0.259297i
$560$	117.137	+	116.270i	4.94994	+	4.91331i
$561$	7.72224	+	2.81067i	0.326033	+	0.118666i
$562$	14.2361	+	24.6576i	0.600513	+	1.04012i
$563$	5.01217	−	8.68133i	0.211238	−	0.365874i	−0.740864	−	0.671655i	$-0.765584\pi$
$563$	5.01217	−	8.68133i	0.211238	−	0.365874i	0.952102	+	0.305780i	$0.0989173\pi$
$564$	2.77106	−	2.32519i	0.116682	−	0.0979082i
$565$	−34.5791	+	12.5858i	−1.45475	+	0.529487i
$566$	57.1492	−	47.9539i	2.40216	−	2.01565i
$567$	1.50948	−	2.17289i	0.0633922	−	0.0912530i
$568$	−97.5758	+	35.5147i	−4.09419	+	1.49016i
$569$	−8.65233	+	14.9863i	−0.362725	+	0.628258i	−0.988408	−	0.151819i	$-0.951487\pi$
$569$	−8.65233	+	14.9863i	−0.362725	+	0.628258i	0.625684	+	0.780077i	$0.284820\pi$
$570$	−41.3131	−	3.21824i	−1.73042	−	0.134797i
$571$	12.5893	+	21.8053i	0.526846	+	0.912523i	0.999511	+	0.0312812i	$0.00995875\pi$
$571$	12.5893	+	21.8053i	0.526846	+	0.912523i	−0.472665	+	0.881242i	$0.656708\pi$
$572$	−3.48051	+	19.7390i	−0.145527	+	0.825327i
$573$	1.66692	−	9.45358i	0.0696366	−	0.394929i
$574$	−7.79285	−	7.73517i	−0.325267	−	0.322860i
$575$	7.80290	+	6.54741i	0.325403	+	0.273046i
$576$	−44.2380	−	16.1013i	−1.84325	−	0.670889i
$577$	−11.6704	+	20.2137i	−0.485844	+	0.841506i	−0.999868	−	0.0162696i	$-0.994821\pi$
$577$	−11.6704	+	20.2137i	−0.485844	+	0.841506i	0.514024	+	0.857776i	$0.328154\pi$
$578$	32.4110			1.34812
$579$	1.51492	−	1.27117i	0.0629578	−	0.0528278i
$580$	91.6561	+	33.3601i	3.80581	+	1.38520i
$581$	2.70794	+	29.6818i	0.112344	+	1.23141i
$582$	−19.4423	−	33.6750i	−0.805908	−	1.39587i
$583$	−20.9939	−	7.64115i	−0.869478	−	0.316464i
$584$	−16.8143	+	95.3585i	−0.695779	+	3.94596i
$585$	−3.10662	−	1.13072i	−0.128443	−	0.0467493i
$586$	45.0386	+	37.7919i	1.86053	+	1.56117i
$587$	−30.6093	+	11.1409i	−1.26338	+	0.459833i	−0.884902	−	0.465777i	$-0.845775\pi$
$587$	−30.6093	+	11.1409i	−1.26338	+	0.459833i	−0.378478	+	0.925610i	$0.623553\pi$
$588$	26.4811	+	31.0870i	1.09206	+	1.28201i
$589$	−4.90684	−	10.2663i	−0.202183	−	0.423015i
$590$	29.2517	−	50.6654i	1.20427	−	2.08586i
$591$	1.90194	+	1.59591i	0.0782352	+	0.0656472i
$592$	−99.8513	+	36.3429i	−4.10386	+	1.49368i
$593$	−3.09231	−	17.5374i	−0.126986	−	0.720174i	−0.980108	−	0.198463i	$-0.936405\pi$
$593$	−3.09231	−	17.5374i	−0.126986	−	0.720174i	0.853122	−	0.521711i	$-0.174706\pi$
$594$	−7.56825	−	6.35051i	−0.310529	−	0.260565i
$595$	−14.8485	−	14.7386i	−0.608729	−	0.604224i
$596$	37.9157	+	65.6720i	1.55309	+	2.69003i
$597$	0.0341082	+	0.0590771i	0.00139595	+	0.00241786i
$598$	0.737184	+	4.18078i	0.0301457	+	0.170965i
$599$	−0.0338152	−	0.191775i	−0.00138165	−	0.00783573i	0.984109	−	0.177565i	$-0.0568219\pi$
$599$	−0.0338152	−	0.191775i	−0.00138165	−	0.00783573i	−0.985491	+	0.169729i	$0.945711\pi$
$600$	35.0703	+	60.7435i	1.43174	+	2.47984i
$601$	−18.8868	−	32.7129i	−0.770409	−	1.33439i	−0.937339	−	0.348419i	$-0.886719\pi$
$601$	−18.8868	−	32.7129i	−0.770409	−	1.33439i	0.166930	−	0.985969i	$-0.446615\pi$
$602$	−51.9700	+	14.1324i	−2.11814	+	0.575994i
$603$	6.41661	+	5.38418i	0.261305	+	0.219261i
$604$	4.47782	+	25.3950i	0.182200	+	1.03331i
$605$	4.65894	−	1.69572i	0.189413	−	0.0689406i
$606$	2.68608	+	2.25389i	0.109114	+	0.0915579i
$607$	21.9369	−	37.9958i	0.890392	−	1.54220i	0.0509855	−	0.998699i	$-0.483764\pi$
$607$	21.9369	−	37.9958i	0.890392	−	1.54220i	0.839406	−	0.543504i	$-0.182903\pi$
$608$	12.6136	+	129.910i	0.511549	+	5.26856i
$609$	11.8238	+	5.46015i	0.479124	+	0.221256i
$610$	−65.3246	+	23.7762i	−2.64492	+	0.962671i
$611$	−0.462333	−	0.387943i	−0.0187040	−	0.0156945i
$612$	12.7628	+	4.64526i	0.515904	+	0.187774i
$613$	3.49020	−	19.7939i	0.140968	−	0.799467i	−0.829549	−	0.558434i	$-0.811402\pi$
$613$	3.49020	−	19.7939i	0.140968	−	0.799467i	0.970517	−	0.241034i	$-0.0774864\pi$
$614$	−24.8453	−	9.04295i	−1.00267	−	0.364944i
$615$	−2.51811	−	4.36150i	−0.101540	−	0.175873i
$616$	81.8757	−	57.7844i	3.29887	−	2.32820i
$617$	−1.57629	−	0.573722i	−0.0634590	−	0.0230972i	0.310096	−	0.950705i	$-0.399639\pi$
$617$	−1.57629	−	0.573722i	−0.0634590	−	0.0230972i	−0.373555	+	0.927608i	$0.621861\pi$
$618$	−5.60412	+	4.70241i	−0.225431	+	0.189159i
$619$	24.6061			0.989004			0.494502	−	0.869176i	$-0.335350\pi$
$619$	24.6061			0.989004			0.494502	+	0.869176i	$0.335350\pi$
$620$	−25.8629	+	44.7958i	−1.03868	+	1.79904i
$621$	−1.46433	−	0.532974i	−0.0587617	−	0.0213875i
$622$	−25.2853	−	21.2169i	−1.01385	−	0.850719i
$623$	0.535444	+	0.531481i	0.0214521	+	0.0212933i
$624$	−3.10420	+	17.6048i	−0.124267	+	0.704756i
$625$	−2.59715	+	14.7292i	−0.103886	+	0.589166i
$626$	−16.7887	−	29.0789i	−0.671011	−	1.16223i
$627$	−3.84050	+	14.8992i	−0.153375	+	0.595015i
$628$	−36.1703	+	62.6489i	−1.44335	+	2.49996i
$629$	12.6573	−	4.60689i	0.504681	−	0.183689i
$630$	10.7143	+	22.7559i	0.426869	+	0.906617i
$631$	−13.1803	+	11.0596i	−0.524698	+	0.440274i	−0.866266	−	0.499583i	$-0.833487\pi$
$631$	−13.1803	+	11.0596i	−0.524698	+	0.440274i	0.341568	+	0.939857i	$0.389042\pi$
$632$	7.78757	−	2.83444i	0.309773	−	0.112748i
$633$	20.8346	−	17.4823i	0.828100	−	0.694858i
$634$	7.41309	−	12.8398i	0.294411	−	0.509935i
$635$	19.6021	+	33.9519i	0.777887	+	1.34734i
$636$	−34.6972	−	12.6287i	−1.37583	−	0.500762i
$637$	4.34066	−	5.25173i	0.171983	−	0.208081i
$638$	24.3161	−	42.1168i	0.962685	−	1.66742i
$639$	−9.67686			−0.382811
$640$	187.017	−	156.926i	7.39250	−	6.20305i
$641$	2.19870	−	12.4695i	0.0868435	−	0.492514i	−0.910100	−	0.414389i	$-0.863995\pi$
$641$	2.19870	−	12.4695i	0.0868435	−	0.492514i	0.996944	−	0.0781253i	$-0.0248934\pi$
$642$	−6.65687	−	37.7530i	−0.262726	−	1.48999i
$643$	7.57028	−	42.9332i	0.298543	−	1.69312i	−0.353900	−	0.935283i	$-0.615145\pi$
$643$	7.57028	−	42.9332i	0.298543	−	1.69312i	0.652443	−	0.757838i	$-0.273744\pi$
$644$	13.7226	−	19.7537i	0.540746	−	0.778403i
$645$	−24.7028			−0.972671
$646$	−2.74490	−	28.2703i	−0.107997	−	1.11228i
$647$	3.76532	+	6.52172i	0.148030	+	0.256395i	0.930499	−	0.366294i	$-0.119373\pi$
$647$	3.76532	+	6.52172i	0.148030	+	0.256395i	−0.782469	+	0.622689i	$0.786040\pi$
$648$	−8.22007	−	6.89746i	−0.322915	−	0.270958i
$649$	−16.6404	−	13.9630i	−0.653193	−	0.548094i
$650$	13.6412	−	11.4463i	0.535053	−	0.448962i
$651$	−3.94041	+	5.67222i	−0.154437	+	0.222312i
$652$	10.4540	+	59.2878i	0.409411	+	2.32189i
$653$	−9.39654			−0.367715			−0.183858	−	0.982953i	$-0.558858\pi$
$653$	−9.39654			−0.367715			−0.183858	+	0.982953i	$0.558858\pi$
$654$	10.3332			0.404060
$655$	−11.9073	−	67.5294i	−0.465255	−	2.63859i
$656$	−20.8611	+	17.5045i	−0.814489	+	0.683437i
$657$	−4.51186	+	7.81478i	−0.176025	+	0.304884i
$658$	0.417179	+	4.57270i	0.0162633	+	0.178263i
$659$	−7.03336	−	39.8882i	−0.273981	−	1.55382i	−0.742180	−	0.670200i	$-0.766208\pi$
$659$	−7.03336	−	39.8882i	−0.273981	−	1.55382i	0.468199	−	0.883623i	$-0.344903\pi$
$660$	65.7252	−	23.9220i	2.55835	−	0.931164i
$661$	−12.1356	−	4.41699i	−0.472019	−	0.171801i	0.0950477	−	0.995473i	$-0.469700\pi$
$661$	−12.1356	−	4.41699i	−0.472019	−	0.171801i	−0.567067	+	0.823672i	$0.691922\pi$
$662$	−51.0194	+	18.5695i	−1.98293	+	0.721726i
$663$	0.393494	−	2.23162i	0.0152820	−	0.0866688i
$664$	120.882			4.69115
$665$	24.7791	−	30.3373i	0.960893	−	1.17643i
$666$	−16.1935			−0.627484
$667$	1.33201	−	7.55420i	0.0515756	−	0.292500i
$668$	−77.8903	+	28.3497i	−3.01366	+	1.09688i
$669$	−22.9362	−	8.34808i	−0.886763	−	0.322756i
$670$	−74.8278	+	27.2351i	−2.89085	+	1.05218i
$671$	4.48219	+	25.4197i	0.173033	+	0.981318i
$672$	64.7268	−	45.6814i	2.49689	−	1.76220i
$673$	−17.6144	+	30.5091i	−0.678986	+	1.17604i	0.296300	+	0.955095i	$0.404247\pi$
$673$	−17.6144	+	30.5091i	−0.678986	+	1.17604i	−0.975287	+	0.220944i	$0.929086\pi$
$674$	−38.7809	+	32.5411i	−1.49379	+	1.25344i
$675$	1.13506	+	6.43723i	0.0436884	+	0.247769i
$676$	−70.3130			−2.70435
$677$	−49.4344			−1.89992			−0.949960	−	0.312372i	$-0.898876\pi$
$677$	−49.4344			−1.89992			−0.949960	+	0.312372i	$0.898876\pi$
$678$	5.26560	+	29.8627i	0.202224	+	1.14687i
$679$	36.6287	+	3.06755i	1.40568	+	0.117722i
$680$	−65.0006	+	54.5420i	−2.49266	+	2.09159i
$681$	−14.1334	−	11.8593i	−0.541594	−	0.454451i
$682$	19.7565	+	16.5777i	0.756515	+	0.634791i
$683$	24.1381	+	41.8084i	0.923618	+	1.59975i	0.793768	+	0.608220i	$0.208116\pi$
$683$	24.1381	+	41.8084i	0.923618	+	1.59975i	0.129850	+	0.991534i	$0.458550\pi$
$684$	−6.34729	+	24.6242i	−0.242695	+	0.941531i
$685$	−72.7841			−2.78094
$686$	−51.5856	+	5.09293i	−1.96955	+	0.194449i
$687$	4.27190	−	24.2272i	0.162983	−	0.924323i
$688$	23.1950	+	131.545i	0.884300	+	5.01511i
$689$	−1.06976	+	6.06693i	−0.0407547	+	0.231132i
$690$	11.3484	−	9.52241i	0.432025	−	0.362512i
$691$	−18.0653			−0.687236			−0.343618	−	0.939109i	$-0.611653\pi$
$691$	−18.0653			−0.687236			−0.343618	+	0.939109i	$0.611653\pi$
$692$	23.1522	−	40.1007i	0.880114	−	1.52440i
$693$	9.01179	−	2.45061i	0.342330	−	0.0930911i
$694$	13.6589	+	4.97142i	0.518484	+	0.188713i
$695$	−2.51236	−	4.35154i	−0.0952993	−	0.165063i
$696$	26.4104	−	45.7441i	1.00108	−	1.73393i
$697$	2.64439	−	2.21891i	0.100163	−	0.0840471i
$698$	46.9741	−	17.0972i	1.77800	−	0.647137i
$699$	12.0208	−	10.0867i	0.454670	−	0.381514i
$700$	−100.539	−	8.41985i	−3.80001	−	0.318240i
$701$	−14.1217	+	5.13988i	−0.533370	+	0.194131i	−0.594642	−	0.803990i	$-0.702706\pi$
$701$	−14.1217	+	5.13988i	−0.533370	+	0.194131i	0.0612726	+	0.998121i	$0.480484\pi$
$702$	−1.36214	+	2.35929i	−0.0514106	+	0.0890458i
$703$	10.8753	+	22.7537i	0.410168	+	0.858172i
$704$	−83.0872	−	143.911i	−3.13146	−	5.42386i
$705$	−0.365716	+	2.07408i	−0.0137737	+	0.0781144i
$706$	−7.92933	+	44.9695i	−0.298424	+	1.69245i
$707$	−3.19841	+	0.869757i	−0.120289	+	0.0327106i
$708$	−27.5020	−	23.0769i	−1.03359	−	0.867285i
$709$	−39.4528	−	14.3597i	−1.48168	−	0.539288i	−0.530437	−	0.847724i	$-0.677972\pi$
$709$	−39.4528	−	14.3597i	−1.48168	−	0.539288i	−0.951245	+	0.308436i	$0.900195\pi$
$710$	45.9970	−	79.6691i	1.72624	−	2.98993i
$711$	0.772315			0.0289641
$712$	2.34395	−	1.96681i	0.0878433	−	0.0737092i
$713$	3.82256	+	1.39130i	0.143156	+	0.0521045i
$714$	−14.0855	+	9.94091i	−0.527135	+	0.372029i
$715$	−5.83479	−	10.1062i	−0.218209	−	0.377949i
$716$	56.1366	+	20.4320i	2.09792	+	0.763581i
$717$	−1.52932	+	8.67321i	−0.0571135	+	0.323907i
$718$	31.6840	+	11.5321i	1.18244	+	0.430372i
$719$	11.9449	+	10.0230i	0.445471	+	0.373795i	0.837752	−	0.546051i	$-0.183869\pi$
$719$	11.9449	+	10.0230i	0.445471	+	0.373795i	−0.392281	+	0.919845i	$0.628314\pi$
$720$	58.6191	−	21.3356i	2.18460	−	0.795131i
$721$	−0.628296	−	6.88676i	−0.0233990	−	0.256476i
$722$	52.1858	−	10.2304i	1.94215	−	0.380735i
$723$	3.13789	−	5.43498i	0.116699	−	0.202129i
$724$	−1.17033	−	0.982021i	−0.0434949	−	0.0364965i
$725$	−30.2355	+	11.0048i	−1.12292	+	0.408708i
$726$	−0.709449	−	4.02349i	−0.0263301	−	0.149326i
$727$	19.1030	+	16.0293i	0.708492	+	0.594495i	0.924176	−	0.381968i	$-0.124754\pi$
$727$	19.1030	+	16.0293i	0.708492	+	0.594495i	−0.215684	+	0.976463i	$0.569198\pi$
$728$	−19.6122	−	19.4671i	−0.726877	−	0.721498i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−42.8925	−	74.2920i	−1.58752	−	2.74967i
$731$	−2.94023	−	16.6749i	−0.108749	−	0.616743i
$732$	7.40783	+	42.0119i	0.273801	+	1.55280i
$733$	−18.3010	−	31.6982i	−0.675962	−	1.17080i	−0.976187	−	0.216932i	$-0.930395\pi$
$733$	−18.3010	−	31.6982i	−0.675962	−	1.17080i	0.300225	−	0.953868i	$-0.402938\pi$
$734$	33.4071	+	57.8628i	1.23308	+	2.13575i
$735$	−23.4446	−	3.95459i	−0.864769	−	0.145867i
$736$	−35.7448	−	29.9934i	−1.31757	−	1.10557i
$737$	5.13424	+	29.1177i	0.189122	+	1.07256i
$738$	−3.89979	+	1.41941i	−0.143553	+	0.0522491i
$739$	−2.24660	−	1.88513i	−0.0826427	−	0.0693455i	0.600530	−	0.799602i	$-0.294956\pi$
$739$	−2.24660	−	1.88513i	−0.0826427	−	0.0693455i	−0.683173	+	0.730256i	$0.739401\pi$
$740$	57.3211	−	99.2831i	2.10717	−	3.64972i
$741$	4.22987	+	0.329501i	0.155388	+	0.0121045i
$742$	38.2931	−	27.0256i	1.40578	−	0.992142i
$743$	34.2020	−	12.4485i	1.25475	−	0.456692i	0.372746	−	0.927933i	$-0.378416\pi$
$743$	34.2020	−	12.4485i	1.25475	−	0.456692i	0.882004	+	0.471241i	$0.156194\pi$
$744$	21.4580	+	18.0054i	0.786690	+	0.660111i
$745$	−41.4876	−	15.1003i	−1.51999	−	0.553230i
$746$	10.0691	−	57.1045i	0.368654	−	2.09074i
$747$	10.5859	+	3.85295i	0.387317	+	0.140972i
$748$	23.9708	+	41.5186i	0.876459	+	1.51807i
$749$	32.8992	+	15.1927i	1.20211	+	0.555128i
$750$	−13.7263	−	4.99597i	−0.501214	−	0.182427i
$751$	−28.4975	+	23.9122i	−1.03989	+	0.872570i	−0.991994	−	0.126282i	$-0.959695\pi$
$751$	−28.4975	+	23.9122i	−1.03989	+	0.872570i	−0.0478942	+	0.998852i	$0.515251\pi$
$752$	11.3881			0.415282
$753$	10.6683	−	18.4781i	0.388775	−	0.673378i
$754$	−12.6014	−	4.58655i	−0.458918	−	0.167032i
$755$	−11.5009	−	9.65043i	−0.418562	−	0.351215i
$756$	14.8940	−	4.05019i	0.541691	−	0.147304i
$757$	−3.37168	+	19.1217i	−0.122546	+	0.694991i	0.860190	+	0.509974i	$0.170345\pi$
$757$	−3.37168	+	19.1217i	−0.122546	+	0.694991i	−0.982735	+	0.185017i	$0.940766\pi$
$758$	0.602432	−	3.41656i	0.0218813	−	0.124095i
$759$	−2.75029	−	4.76364i	−0.0998291	−	0.172909i
$760$	−113.401	−	111.262i	−4.11350	−	4.03588i
$761$	11.9354	−	20.6728i	0.432660	−	0.749388i	−0.564442	−	0.825473i	$-0.690909\pi$
$761$	11.9354	−	20.6728i	0.432660	−	0.749388i	0.997101	+	0.0760844i	$0.0242419\pi$
$762$	30.3577	−	11.0493i	1.09974	−	0.400274i
$763$	−5.57281	+	8.02205i	−0.201749	+	0.290418i
$764$	42.8996	−	35.9971i	1.55205	−	1.30233i
$765$	−7.43066	+	2.70454i	−0.268656	+	0.0977828i
$766$	−14.8133	+	12.4298i	−0.535226	+	0.449108i
$767$	−2.99495	+	5.18741i	−0.108142	+	0.187307i
$768$	−53.5111	−	92.6840i	−1.93092	−	3.34444i
$769$	49.5801	+	18.0457i	1.78790	+	0.650743i	0.999360	+	0.0357626i	$0.0113860\pi$
$769$	49.5801	+	18.0457i	1.78790	+	0.650743i	0.788542	+	0.614981i	$0.210836\pi$
$770$	−22.6600	+	85.8422i	−0.816608	+	3.09354i
$771$	−3.24050	+	5.61271i	−0.116704	+	0.202137i
$772$	11.5369			0.415222
$773$	−0.623531	+	0.523205i	−0.0224269	+	0.0188184i	−0.653932	−	0.756553i	$-0.726882\pi$
$773$	−0.623531	+	0.523205i	−0.0224269	+	0.0188184i	0.631505	+	0.775372i	$0.282437\pi$
$774$	−3.53481	+	20.0469i	−0.127056	+	0.720570i
$775$	−2.96300	−	16.8040i	−0.106434	−	0.603619i
$776$	25.8870	−	146.812i	0.929289	−	5.27026i
$777$	8.73333	−	12.5716i	0.313306	−	0.451004i
$778$	19.3629			0.694195
$779$	4.61346	+	4.52640i	0.165294	+	0.162175i
$780$	−9.64332	−	16.7027i	−0.345286	−	0.598053i
$781$	−26.1663	−	21.9561i	−0.936303	−	0.785652i
$782$	7.77856	+	6.52699i	0.278161	+	0.233405i
$783$	3.77083	−	3.16410i	0.134759	−	0.113076i
$784$	0.954992	+	128.559i	0.0341069	+	4.59138i
$785$	−7.31368	−	41.4779i	−0.261036	−	1.48041i
$786$	−56.5056			−2.01549
$787$	23.7500			0.846595			0.423297	−	0.905991i	$-0.360873\pi$
$787$	23.7500			0.846595			0.423297	+	0.905991i	$0.360873\pi$
$788$	2.51517	+	14.2642i	0.0895992	+	0.508142i
$789$	22.6472	−	19.0032i	0.806260	−	0.676533i
$790$	−3.67104	+	6.35843i	−0.130610	+	0.226223i
$791$	−26.0234	−	12.0174i	−0.925285	−	0.427291i
$792$	−6.57727	−	37.3016i	−0.233713	−	1.32545i
$793$	6.68830	−	2.43434i	0.237509	−	0.0864460i
$794$	−62.8975	−	22.8928i	−2.23215	−	0.812436i
$795$	20.2012	−	7.35263i	0.716462	−	0.260771i
$796$	−0.0691056	+	0.391918i	−0.00244938	+	0.0138911i
$797$	−16.1649			−0.572592			−0.286296	−	0.958141i	$-0.592424\pi$
$797$	−16.1649			−0.572592			−0.286296	+	0.958141i	$0.592424\pi$
$798$	−21.0737	−	24.4499i	−0.746003	−	0.865518i
$799$	−1.44358			−0.0510701
$800$	−33.9877	+	192.754i	−1.20165	+	6.81488i
$801$	0.267953	−	0.0975269i	0.00946765	−	0.00344594i
$802$	77.7185	+	28.2872i	2.74434	+	0.998857i
$803$	−29.9313	+	10.8941i	−1.05625	+	0.384445i
$804$	8.48549	+	48.1236i	0.299260	+	1.69719i
$805$	1.27230	+	13.9457i	0.0448428	+	0.491522i
$806$	3.55579	−	6.15881i	0.125247	−	0.216935i
$807$	−5.72150	+	4.80091i	−0.201406	+	0.169000i
$808$	2.33437	+	13.2389i	0.0821228	+	0.465741i
$809$	14.1202			0.496439			0.248220	−	0.968704i	$-0.420155\pi$
$809$	14.1202			0.496439			0.248220	+	0.968704i	$0.420155\pi$
$810$	9.50660			0.334028
$811$	2.43617	+	13.8162i	0.0855457	+	0.485154i	0.997238	+	0.0742789i	$0.0236655\pi$
$811$	2.43617	+	13.8162i	0.0855457	+	0.485154i	−0.911692	+	0.410875i	$0.865223\pi$
$812$	32.3651	+	68.7396i	1.13579	+	2.41229i
$813$	−13.2583	+	11.1251i	−0.464990	+	0.390173i
$814$	−43.7872	−	36.7419i	−1.53474	−	1.28780i
$815$	−26.8504	−	22.5301i	−0.940528	−	0.789197i
$816$	21.3791	+	37.0297i	0.748418	+	1.29630i
$817$	30.5421	−	8.49634i	1.06853	−	0.297249i
$818$	30.2372			1.05722
$819$	−1.09699	−	2.32988i	−0.0383320	−	0.0814125i
$820$	5.10188	−	28.9342i	0.178165	−	1.01043i
$821$	1.93004	+	10.9458i	0.0673588	+	0.382011i	0.999787	+	0.0206547i	$0.00657505\pi$
$821$	1.93004	+	10.9458i	0.0673588	+	0.382011i	−0.932428	+	0.361356i	$0.882314\pi$
$822$	−10.4149	+	59.0660i	−0.363263	+	2.06016i
$823$	7.76000	−	6.51142i	0.270497	−	0.226974i	−0.497442	−	0.867497i	$-0.665727\pi$
$823$	7.76000	−	6.51142i	0.270497	−	0.226974i	0.767938	+	0.640524i	$0.221283\pi$
$824$	−28.0471			−0.977066
$825$	−11.5364	+	19.9817i	−0.401647	+	0.695673i
$826$	43.9745	−	11.9582i	1.53007	−	0.416078i
$827$	25.7098	+	9.35760i	0.894017	+	0.325396i	0.747853	−	0.663865i	$-0.231085\pi$
$827$	25.7098	+	9.35760i	0.894017	+	0.325396i	0.146164	+	0.989260i	$0.453307\pi$
$828$	−4.54547	−	7.87299i	−0.157966	−	0.273605i
$829$	−5.24941	+	9.09224i	−0.182319	+	0.315787i	−0.942670	−	0.333726i	$-0.891694\pi$
$829$	−5.24941	+	9.09224i	−0.182319	+	0.315787i	0.760351	+	0.649513i	$0.225027\pi$
$830$	−82.0390	+	68.8389i	−2.84762	+	2.38943i
$831$	4.35497	−	1.58508i	0.151072	−	0.0549858i
$832$	−35.1017	+	29.4538i	−1.21693	+	1.02113i
$833$	−0.121057	−	16.2963i	−0.00419436	−	0.564634i
$834$	−3.89088	+	1.41616i	−0.134730	+	0.0490377i
$835$	24.1296	−	41.7937i	0.835040	−	1.44633i
$836$	−73.0338	+	52.1825i	−2.52593	+	1.80477i
$837$	1.30522	+	2.26071i	0.0451151	+	0.0781416i
$838$	−5.40266	+	30.6400i	−0.186632	+	1.05844i
$839$	−6.39319	+	36.2576i	−0.220717	+	1.25175i	0.649987	+	0.759945i	$0.274774\pi$
$839$	−6.39319	+	36.2576i	−0.220717	+	1.25175i	−0.870705	+	0.491806i	$0.836337\pi$
$840$	−24.6116	+	93.2355i	−0.849181	+	3.21693i
$841$	−3.65349	−	3.06564i	−0.125982	−	0.105712i
$842$	−37.8777	−	13.7864i	−1.30535	−	0.475109i
$843$	−5.08632	+	8.80976i	−0.175182	+	0.303424i
$844$	158.667			5.46153
$845$	31.3598	−	26.3140i	1.07881	−	0.905228i
$846$	1.63083	+	0.593575i	0.0560692	+	0.0204075i
$847$	3.50620	+	1.61914i	0.120475	+	0.0556344i
$848$	−58.1218	−	100.670i	−1.99591	−	3.45702i
$849$	25.0469	+	9.11634i	0.859609	+	0.312872i
$850$	7.39621	−	41.9460i	0.253688	−	1.43874i
$851$	−8.47213	−	3.08360i	−0.290421	−	0.105704i
$852$	−43.2457	−	36.2875i	−1.48157	−	1.24319i
$853$	−53.4075	+	19.4387i	−1.82864	+	0.665570i	−0.835375	+	0.549680i	$0.814750\pi$
$853$	−53.4075	+	19.4387i	−1.82864	+	0.665570i	−0.993262	+	0.115889i	$0.963028\pi$
$854$	−49.1617	−	22.7025i	−1.68228	−	0.776865i
$855$	−6.38447	−	13.3579i	−0.218344	−	0.456830i
$856$	73.4860	−	127.281i	2.51170	−	4.35039i
$857$	21.0761	+	17.6849i	0.719944	+	0.604105i	0.927370	−	0.374146i	$-0.122064\pi$
$857$	21.0761	+	17.6849i	0.719944	+	0.604105i	−0.207426	+	0.978251i	$0.566509\pi$
$858$	−9.03631	+	3.28895i	−0.308495	+	0.112283i
$859$	−0.167142	−	0.947909i	−0.00570281	−	0.0323423i	0.981824	−	0.189796i	$-0.0607826\pi$
$859$	−0.167142	−	0.947909i	−0.00570281	−	0.0323423i	−0.987526	+	0.157454i	$0.949672\pi$
$860$	−110.396	−	92.6335i	−3.76448	−	3.15878i
$861$	1.00126	−	3.79306i	0.0341229	−	0.129267i
$862$	−32.5778	−	56.4264i	−1.10960	−	1.92189i
$863$	−1.01228	−	1.75333i	−0.0344586	−	0.0596840i	0.848282	−	0.529545i	$-0.177637\pi$
$863$	−1.01228	−	1.75333i	−0.0344586	−	0.0596840i	−0.882740	+	0.469861i	$0.844304\pi$
$864$	−5.19966	−	29.4887i	−0.176896	−	1.00323i
$865$	4.68139	+	26.5495i	0.159172	+	0.902710i
$866$	29.4588	+	51.0241i	1.00105	+	1.73387i
$867$	5.78995	+	10.0285i	0.196637	+	0.340585i
$868$	−38.8800	+	10.5728i	−1.31967	+	0.358864i
$869$	2.08834	+	1.75233i	0.0708422	+	0.0594437i
$870$	8.12603	+	46.0850i	0.275498	+	1.56243i
$871$	7.66129	−	2.78848i	0.259593	−	0.0944840i
$872$	30.3475	+	25.4646i	1.02770	+	0.862339i
$873$	6.94640	−	12.0315i	0.235100	−	0.407205i
$874$	−10.7558	+	15.6765i	−0.363819	+	0.530267i
$875$	11.2813	−	7.96188i	0.381378	−	0.269161i
$876$	−49.4683	+	18.0050i	−1.67138	+	0.608332i
$877$	10.5619	+	8.86249i	0.356650	+	0.299265i	0.803454	−	0.595367i	$-0.202993\pi$
$877$	10.5619	+	8.86249i	0.356650	+	0.299265i	−0.446804	+	0.894632i	$0.647438\pi$
$878$	56.1194	+	20.4258i	1.89394	+	0.689337i
$879$	−3.64765	+	20.6869i	−0.123032	+	0.697751i
$880$	206.915	+	75.3111i	6.97512	+	2.53873i
$881$	1.24190	+	2.15103i	0.0418406	+	0.0724701i	0.886187	−	0.463327i	$-0.153344\pi$
$881$	1.24190	+	2.15103i	0.0418406	+	0.0724701i	−0.844347	+	0.535797i	$0.820011\pi$
$882$	−6.56402	+	18.4600i	−0.221022	+	0.621581i
$883$	0.193144	+	0.0702988i	0.00649982	+	0.00236574i	0.345268	−	0.938504i	$-0.387788\pi$
$883$	0.193144	+	0.0702988i	0.00649982	+	0.00236574i	−0.338768	+	0.940870i	$0.610010\pi$
$884$	10.1269	−	8.49748i	0.340605	−	0.285801i
$885$	20.9023			0.702623
$886$	−13.3849	+	23.1833i	−0.449675	+	0.778860i
$887$	−46.4304	−	16.8993i	−1.55898	−	0.567423i	−0.588479	−	0.808513i	$-0.700273\pi$
$887$	−46.4304	−	16.8993i	−1.55898	−	0.567423i	−0.970503	+	0.241090i	$0.922495\pi$
$888$	−47.5585	−	39.9063i	−1.59596	−	1.33917i
$889$	−7.79428	+	29.5269i	−0.261412	+	0.990300i
$890$	−0.470726	+	2.66962i	−0.0157788	+	0.0894858i
$891$	0.612949	−	3.47620i	0.0205345	−	0.116457i
$892$	−71.1967	−	123.316i	−2.38384	−	4.12893i
$893$	−0.261199	−	2.69015i	−0.00874069	−	0.0900223i
$894$	−18.1908	+	31.5074i	−0.608392	+	1.05377i
$895$	−32.6835	+	11.8958i	−1.09249	+	0.397634i
$896$	189.505	+	15.8705i	6.33092	+	0.530198i
$897$	−1.16191	+	0.974958i	−0.0387950	+	0.0325529i
$898$	−82.9809	+	30.2026i	−2.76911	+	1.00787i
$899$	−9.84354	+	8.25971i	−0.328300	+	0.275477i
$900$	−19.0666	+	33.0243i	−0.635552	+	1.10081i
$901$	7.36762	+	12.7611i	0.245451	+	0.425133i
$902$	−13.7656	−	5.01026i	−0.458344	−	0.166824i
$903$	−13.6568	−	13.5557i	−0.454470	−	0.451107i
$904$	−58.1276	+	100.680i	−1.93329	+	3.34856i
$905$	0.889480			0.0295673
$906$	−9.47726	+	7.95237i	−0.314861	+	0.264200i
$907$	0.613364	−	3.47856i	0.0203664	−	0.115504i	−0.972930	−	0.231101i	$-0.925767\pi$
$907$	0.613364	−	3.47856i	0.0203664	−	0.115504i	0.993296	+	0.115598i	$0.0368783\pi$
$908$	−18.6904	−	105.998i	−0.620262	−	3.51768i
$909$	−0.217544	+	1.23375i	−0.00721548	+	0.0409210i
$910$	24.3961	+	2.04311i	0.808723	+	0.0677284i
$911$	−43.0280			−1.42558			−0.712790	−	0.701377i	$-0.752569\pi$
$911$	−43.0280			−1.42558			−0.712790	+	0.701377i	$0.752569\pi$
$912$	−65.1375	+	46.5406i	−2.15692	+	1.54111i
$913$	19.8822	+	34.4370i	0.658006	+	1.13970i
$914$	−42.6060	−	35.7507i	−1.40928	−	1.18253i
$915$	−19.0264	−	15.9651i	−0.628995	−	0.527789i
$916$	109.941	−	92.2514i	3.63255	−	3.04807i
$917$	30.4741	−	43.8674i	1.00634	−	1.44863i
$918$	1.13152	+	6.41716i	0.0373457	+	0.211798i
$919$	20.0470			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$919$	20.0470			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$920$	56.7955			1.87249
$921$	−1.64037	−	9.30299i	−0.0540520	−	0.306544i
$922$	64.8842	−	54.4443i	2.13685	−	1.79303i
$923$	−4.70943	+	8.15697i	−0.155013	+	0.268490i
$924$	49.4632	+	22.8418i	1.62722	+	0.751439i
$925$	6.56705	+	37.2436i	0.215923	+	1.22456i
$926$	−96.8684	+	35.2572i	−3.18329	+	1.15862i
$927$	−2.45613	−	0.893959i	−0.0806699	−	0.0293615i
$928$	138.507	−	50.4126i	4.54673	−	1.65487i
$929$	−1.97256	+	11.1869i	−0.0647175	+	0.367031i	0.935199	+	0.354122i	$0.115220\pi$
$929$	−1.97256	+	11.1869i	−0.0647175	+	0.367031i	−0.999917	+	0.0129090i	$0.995891\pi$
$930$	−24.8164			−0.813763
$931$	30.3467	−	3.17423i	0.994574	−	0.104031i
$932$	91.5453			2.99866
$933$	2.04784	−	11.6139i	0.0670434	−	0.380222i
$934$	49.5917	−	18.0499i	1.62269	−	0.590611i
$935$	−26.2290	−	9.54656i	−0.857779	−	0.312206i
$936$	−9.81458	+	3.57221i	−0.320800	+	0.116761i
$937$	−3.93790	−	22.3329i	−0.128646	−	0.729586i	−0.979076	−	0.203497i	$-0.934769\pi$
$937$	−3.93790	−	22.3329i	−0.128646	−	0.729586i	0.850430	−	0.526088i	$-0.176342\pi$
$938$	−56.3135	−	26.0052i	−1.83870	−	0.849100i
$939$	5.99832	−	10.3894i	0.195748	−	0.339045i
$940$	−9.41202	+	7.89762i	−0.306986	+	0.257592i
$941$	−0.897592	−	5.09050i	−0.0292607	−	0.165945i	0.966676	−	0.256003i	$-0.0824059\pi$
$941$	−0.897592	−	5.09050i	−0.0292607	−	0.165945i	−0.995937	+	0.0900580i	$0.971295\pi$
$942$	−34.7069			−1.13081
$943$	−2.31058			−0.0752430
$944$	−19.6265	−	111.307i	−0.638787	−	3.62274i
$945$	−5.12702	+	7.38034i	−0.166782	+	0.240082i
$946$	−55.0431	+	46.1867i	−1.78961	+	1.50166i
$947$	21.5290	+	18.0650i	0.699599	+	0.587033i	0.921659	−	0.388000i	$-0.126834\pi$
$947$	21.5290	+	18.0650i	0.699599	+	0.587033i	−0.222061	+	0.975033i	$0.571278\pi$
$948$	3.45146	+	2.89612i	0.112098	+	0.0940616i
$949$	4.39157	+	7.60643i	0.142556	+	0.246915i
$950$	79.5057	+	6.19338i	2.57951	+	0.200940i
$951$	5.29714			0.171772
$952$	−65.8653	−	5.51604i	−2.13471	−	0.178776i
$953$	9.25392	−	52.4816i	0.299764	−	1.70005i	−0.347418	−	0.937710i	$-0.612941\pi$
$953$	9.25392	−	52.4816i	0.299764	−	1.70005i	0.647182	−	0.762336i	$-0.275947\pi$
$954$	−3.07617	−	17.4459i	−0.0995948	−	0.564830i
$955$	−5.66178	+	32.1095i	−0.183211	+	1.03904i
$956$	−39.3584	+	33.0256i	−1.27294	+	1.06812i
$957$	17.3755			0.561670
$958$	22.3772	−	38.7585i	0.722975	−	1.25223i
$959$	−40.2383	−	39.9405i	−1.29936	−	1.28975i
$960$	150.257	+	54.6889i	4.84951	+	1.76508i
$961$	12.0928	+	20.9453i	0.390090	+	0.675656i
$962$	−7.88086	+	13.6501i	−0.254089	+	0.440096i
$963$	10.4922	−	8.80400i	0.338106	−	0.283705i
$964$	34.4039	−	12.5220i	1.10807	−	0.403306i
$965$	−5.14548	+	4.31757i	−0.165639	+	0.138988i
$966$	11.4993	+	0.963038i	0.369985	+	0.0309853i
$967$	53.1689	−	19.3519i	1.70980	−	0.622315i	0.712916	−	0.701249i	$-0.247374\pi$
$967$	53.1689	−	19.3519i	1.70980	−	0.622315i	0.996880	+	0.0789345i	$0.0251518\pi$
$968$	7.83169	−	13.5649i	0.251720	−	0.435992i
$969$	8.25694	−	5.89957i	0.265251	−	0.189521i
$970$	66.0366	+	114.379i	2.12031	+	3.67248i
$971$	−1.11984	+	6.35095i	−0.0359375	+	0.203812i	−0.997490	−	0.0708102i	$-0.977442\pi$
$971$	−1.11984	+	6.35095i	−0.0359375	+	0.203812i	0.961552	+	0.274622i	$0.0885526\pi$
$972$	1.01304	−	5.74521i	0.0324932	−	0.184278i
$973$	0.998975	−	3.78439i	0.0320257	−	0.121322i
$974$	51.8845	+	43.5363i	1.66249	+	1.39499i
$975$	5.97857	+	2.17602i	0.191468	+	0.0696885i
$976$	−67.1508	+	116.309i	−2.14945	+	3.72295i
$977$	24.0240			0.768595			0.384298	−	0.923209i	$-0.374444\pi$
$977$	24.0240			0.768595			0.384298	+	0.923209i	$0.374444\pi$
$978$	−22.1259	+	18.5658i	−0.707507	+	0.593669i
$979$	0.945828	+	0.344253i	0.0302288	+	0.0110024i
$980$	−89.9443	−	105.589i	−2.87317	−	3.37290i
$981$	1.84594	+	3.19726i	0.0589362	+	0.102081i
$982$	−32.9163	−	11.9805i	−1.05040	−	0.382314i
$983$	−6.71948	+	38.1080i	−0.214318	+	1.21546i	0.667768	+	0.744369i	$0.267250\pi$
$983$	−6.71948	+	38.1080i	−0.214318	+	1.21546i	−0.882086	+	0.471088i	$0.843861\pi$
$984$	−14.9512	−	5.44178i	−0.476626	−	0.173478i
$985$	−6.46002	−	5.42060i	−0.205833	−	0.172715i
$986$	−30.1412	+	10.9705i	−0.959890	+	0.349372i
$987$	−1.34034	+	0.945957i	−0.0426636	+	0.0301101i
$988$	17.6676	+	17.3342i	0.562082	+	0.551475i
$989$	−5.66673	+	9.81506i	−0.180191	+	0.312101i
$990$	25.7059	+	21.5698i	0.816987	+	0.685534i
$991$	53.5159	−	19.4782i	1.69999	−	0.618746i	0.704165	−	0.710036i	$-0.251321\pi$
$991$	53.5159	−	19.4782i	1.69999	−	0.618746i	0.995824	+	0.0912906i	$0.0290992\pi$
$992$	13.5734	+	76.9786i	0.430956	+	2.44407i
$993$	−14.8599	−	12.4689i	−0.471565	−	0.395690i
$994$	69.1479	−	18.8037i	2.19324	−	0.596416i
$995$	−0.115850	−	0.200658i	−0.00367269	−	0.00636129i
$996$	32.8599	+	56.9150i	1.04121	+	1.80342i
$997$	0.462097	+	2.62068i	0.0146348	+	0.0829979i	0.991250	−	0.131995i	$-0.0421383\pi$
$997$	0.462097	+	2.62068i	0.0146348	+	0.0829979i	−0.976616	+	0.214993i	$0.931027\pi$
$998$	−10.6952	−	60.6555i	−0.338551	−	1.92002i
$999$	−2.89283	−	5.01052i	−0.0915250	−	0.158526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.bq.b.100.1	yes	90
7.4	even	3		399.2.bp.b.214.1	✓	90
19.4	even	9		399.2.bp.b.289.1	yes	90
133.4	even	9	inner	399.2.bq.b.4.1	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.bp.b.214.1	✓	90	7.4	even	3
399.2.bp.b.289.1	yes	90	19.4	even	9
399.2.bq.b.4.1	yes	90	133.4	even	9	inner
399.2.bq.b.100.1	yes	90	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.486024 + 2.75638i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-5.48202 - 1.99529i) q^{4} +(3.19171 - 1.16169i) q^{5} +(-0.486024 - 2.75638i) q^{6} +(2.40200 + 1.10923i) q^{7} +(5.36527 - 9.29292i) q^{8} +(0.766044 - 0.642788i) q^{9} +(1.65080 + 9.36217i) q^{10} +3.52983 q^{11} +5.83384 q^{12} +(-0.169019 - 0.958552i) q^{13} +(-4.22489 + 6.08171i) q^{14} +(-2.60191 + 2.18326i) q^{15} +(14.0692 + 11.8055i) q^{16} +(-1.78344 - 1.49648i) q^{17} +(1.39945 + 2.42392i) q^{18} +(2.46604 - 3.59425i) q^{19} -19.8149 q^{20} +(-2.63652 - 0.220802i) q^{21} +(-1.71558 + 9.72955i) q^{22} +(0.270598 + 1.53464i) q^{23} +(-1.86334 + 10.5675i) q^{24} +(5.00728 - 4.20160i) q^{25} +2.72428 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-10.9546 - 10.8735i) q^{28} +(-4.62561 - 1.68358i) q^{29} +(-4.75330 - 8.23296i) q^{30} +(1.30522 - 2.26071i) q^{31} +(-22.9381 + 19.2474i) q^{32} +(-3.31696 + 1.20727i) q^{33} +(4.99166 - 4.18850i) q^{34} +(8.95507 + 0.749963i) q^{35} +(-5.48202 + 1.99529i) q^{36} +(-2.89283 + 5.01052i) q^{37} +(8.70857 + 8.54423i) q^{38} +(0.486669 + 0.842936i) q^{39} +(6.32892 - 35.8931i) q^{40} +(-0.257477 + 1.46022i) q^{41} +(1.89003 - 7.15994i) q^{42} +(5.57137 + 4.67493i) q^{43} +(-19.3506 - 7.04304i) q^{44} +(1.69827 - 2.94150i) q^{45} -4.36156 q^{46} +(0.474997 - 0.398569i) q^{47} +(-17.2584 - 6.28156i) q^{48} +(4.53922 + 5.32874i) q^{49} +(9.14756 + 15.8440i) q^{50} +(2.18771 + 0.796261i) q^{51} +(-0.986028 + 5.59204i) q^{52} +(-5.94756 - 2.16474i) q^{53} +(-2.14408 - 1.79910i) q^{54} +(11.2662 - 4.10056i) q^{55} +(23.1954 - 16.3703i) q^{56} +(-1.08801 + 4.22093i) q^{57} +(6.88875 - 11.9317i) q^{58} +(-4.71422 - 3.95570i) q^{59} +(18.6199 - 6.77710i) q^{60} +(1.26980 + 7.20141i) q^{61} +(5.59701 + 4.69645i) q^{62} +(2.55304 - 0.694258i) q^{63} +(-23.5386 - 40.7700i) q^{64} +(-1.65300 - 2.86307i) q^{65} +(-1.71558 - 9.72955i) q^{66} +(1.45453 + 8.24904i) q^{67} +(6.79092 + 11.7622i) q^{68} +(-0.779156 - 1.34954i) q^{69} +(-6.41956 + 24.3191i) q^{70} +(-7.41290 - 6.22016i) q^{71} +(-1.86334 - 10.5675i) q^{72} +(-8.47953 + 3.08630i) q^{73} +(-12.4049 - 10.4090i) q^{74} +(-3.26827 + 5.66081i) q^{75} +(-20.6905 + 14.7833i) q^{76} +(8.47866 + 3.91539i) q^{77} +(-2.55998 + 0.931758i) q^{78} +(0.591627 + 0.496434i) q^{79} +(58.6191 + 21.3356i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-3.89979 - 1.41941i) q^{82} +(5.63263 + 9.75600i) q^{83} +(14.0129 + 6.47107i) q^{84} +(-7.43066 - 2.70454i) q^{85} +(-15.5937 + 13.0847i) q^{86} +4.92247 q^{87} +(18.9385 - 32.8024i) q^{88} +(0.267953 + 0.0975269i) q^{89} +(7.28248 + 6.11072i) q^{90} +(0.657271 - 2.48992i) q^{91} +(1.57863 - 8.95283i) q^{92} +(-0.453299 + 2.57079i) q^{93} +(0.867749 + 1.50298i) q^{94} +(3.69549 - 14.3366i) q^{95} +(14.9718 - 25.9319i) q^{96} +(13.0550 - 4.75162i) q^{97} +(-16.8942 + 9.92192i) q^{98} +(2.70401 - 2.26893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 6 q^{7} - 6 q^{10} + 18 q^{11} + 108 q^{12} - 9 q^{13} - 3 q^{14} - 12 q^{17} - 30 q^{19} - 60 q^{20} - 9 q^{21} + 18 q^{23} + 9 q^{24} + 6 q^{25} + 12 q^{26} - 45 q^{27} - 45 q^{28} - 18 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) \) 90 * q + 6 * q^7 - 6 * q^10 + 18 * q^11 + 108 * q^12 - 9 * q^13 - 3 * q^14 - 12 * q^17 - 30 * q^19 - 60 * q^20 - 9 * q^21 + 18 * q^23 + 9 * q^24 + 6 * q^25 + 12 * q^26 - 45 * q^27 - 45 * q^28 - 18 * q^29 - 12 * q^30 - 18 * q^31 - 21 * q^32 - 12 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 + 39 * q^38 - 12 * q^39 + 18 * q^40 + 27 * q^41 - 3 * q^42 - 39 * q^43 - 78 * q^44 + 3 * q^45 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 9 * q^50 + 6 * q^51 - 48 * q^52 + 27 * q^53 - 42 * q^55 + 39 * q^56 - 6 * q^57 - 18 * q^58 - 60 * q^59 - 18 * q^60 - 12 * q^61 + 93 * q^62 - 12 * q^63 - 108 * q^64 - 33 * q^65 - 42 * q^67 + 18 * q^68 - 12 * q^69 + 6 * q^70 - 18 * q^71 + 9 * q^72 + 51 * q^73 + 114 * q^74 - 72 * q^75 + 24 * q^76 - 39 * q^77 + 9 * q^78 + 87 * q^79 + 42 * q^80 + 12 * q^82 + 24 * q^83 + 3 * q^84 + 36 * q^85 - 69 * q^86 - 36 * q^88 - 48 * q^89 + 3 * q^90 + 6 * q^91 - 18 * q^92 - 21 * q^93 - 54 * q^94 + 36 * q^95 + 21 * q^97 - 75 * q^98 + 6 * q^99

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