LMFDB - Embedded newform 378.2.u.a.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	378.337
Dual form			378.2.u.a.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-0.592396 - 1.62760i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-0.592396 - 1.62760i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +(0.673648 - 1.16679i) q^{10} +(3.64543 - 3.05888i) q^{11} +(1.50000 - 0.866025i) q^{12} +(0.266044 - 1.50881i) q^{13} +(0.173648 - 0.984808i) q^{14} +(2.02094 + 1.16679i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.11334 + 1.92836i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.79813 + 4.84651i) q^{19} +(1.26604 + 0.460802i) q^{20} +(1.70574 + 0.300767i) q^{21} +(3.64543 + 3.05888i) q^{22} +(7.57785 - 2.75811i) q^{23} +(1.11334 + 1.32683i) q^{24} +(-0.553033 - 3.13641i) q^{25} +1.53209 q^{26} +(-4.50000 + 2.59808i) q^{27} +1.00000 q^{28} +(-1.85844 - 10.5397i) q^{29} +(-0.798133 + 2.19285i) q^{30} +(1.37939 - 0.502055i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-5.29813 + 6.31407i) q^{33} +(-2.09240 - 0.761570i) q^{34} +(0.673648 + 1.16679i) q^{35} +(-2.29813 + 1.92836i) q^{36} +(0.815207 - 1.41198i) q^{37} +(-4.28699 + 3.59721i) q^{38} +2.65366i q^{39} +(-0.233956 + 1.32683i) q^{40} +(1.75877 - 9.97448i) q^{41} +1.73205i q^{42} +(-6.70961 + 5.63003i) q^{43} +(-2.37939 + 4.12122i) q^{44} +(-3.79813 - 1.38241i) q^{45} +(4.03209 + 6.98378i) q^{46} +(8.35117 + 3.03958i) q^{47} +(-1.11334 + 1.32683i) q^{48} +(0.766044 + 0.642788i) q^{49} +(2.99273 - 1.08926i) q^{50} +(1.31908 - 3.62414i) q^{51} +(0.266044 + 1.50881i) q^{52} +1.32770 q^{53} +(-3.34002 - 3.98048i) q^{54} -6.41147 q^{55} +(0.173648 + 0.984808i) q^{56} +(-6.23055 - 7.42528i) q^{57} +(10.0569 - 3.66041i) q^{58} +(-7.16637 - 6.01330i) q^{59} +(-2.29813 - 0.405223i) q^{60} +(3.08512 + 1.12289i) q^{61} +(0.733956 + 1.27125i) q^{62} -3.00000 q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.58125 + 1.32683i) q^{65} +(-7.13816 - 4.12122i) q^{66} +(-0.470437 + 2.66798i) q^{67} +(0.386659 - 2.19285i) q^{68} +(-12.0963 + 6.98378i) q^{69} +(-1.03209 + 0.866025i) q^{70} +(-2.10220 + 3.64111i) q^{71} +(-2.29813 - 1.92836i) q^{72} +(-4.54576 - 7.87349i) q^{73} +(1.53209 + 0.557635i) q^{74} +(1.88666 + 5.18355i) q^{75} +(-4.28699 - 3.59721i) q^{76} +(-4.47178 + 1.62760i) q^{77} +(-2.61334 + 0.460802i) q^{78} +(0.556437 + 3.15571i) q^{79} -1.34730 q^{80} +(6.89440 - 5.78509i) q^{81} +10.1284 q^{82} +(-2.22668 - 12.6281i) q^{83} +(-1.70574 + 0.300767i) q^{84} +(2.81908 - 1.02606i) q^{85} +(-6.70961 - 5.63003i) q^{86} +(6.34002 + 17.4191i) q^{87} +(-4.47178 - 1.62760i) q^{88} +(-0.779715 - 1.35051i) q^{89} +(0.701867 - 3.98048i) q^{90} +(-0.766044 + 1.32683i) q^{91} +(-6.17752 + 5.18355i) q^{92} +(-2.20187 + 1.27125i) q^{93} +(-1.54323 + 8.75211i) q^{94} +(1.30928 - 7.42528i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-9.91534 + 8.31996i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(7.13816 - 12.3636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^8	$ 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.03209	−	0.866025i	−0.461564	−	0.387298i	0.382142	−	0.924104i	$-0.375187\pi$
$5$	−1.03209	−	0.866025i	−0.461564	−	0.387298i	−0.843706	+	0.536805i	$0.819631\pi$
$6$	−0.592396	−	1.62760i	−0.241845	−	0.664463i
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$7$	−0.939693	−	0.342020i	−0.355170	−	0.129271i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$	0.673648	−	1.16679i	0.213026	−	0.368972i
$11$	3.64543	−	3.05888i	1.09914	−	0.922287i	0.101772	−	0.994808i	$-0.467549\pi$
$11$	3.64543	−	3.05888i	1.09914	−	0.922287i	0.997367	+	0.0725212i	$0.0231045\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	0.266044	−	1.50881i	0.0737875	−	0.418469i	−0.925430	−	0.378918i	$-0.876296\pi$
$13$	0.266044	−	1.50881i	0.0737875	−	0.418469i	0.999218	−	0.0395511i	$-0.0125928\pi$
$14$	0.173648	−	0.984808i	0.0464094	−	0.263201i
$15$	2.02094	+	1.16679i	0.521806	+	0.301265i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.11334	+	1.92836i	−0.270025	+	0.467697i	−0.968868	−	0.247578i	$-0.920365\pi$
$17$	−1.11334	+	1.92836i	−0.270025	+	0.467697i	0.698843	+	0.715275i	$0.253699\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	2.79813	+	4.84651i	0.641936	+	1.11187i	0.985000	+	0.172554i	$0.0552018\pi$
$19$	2.79813	+	4.84651i	0.641936	+	1.11187i	−0.343064	+	0.939312i	$0.611465\pi$
$20$	1.26604	+	0.460802i	0.283096	+	0.103039i
$21$	1.70574	+	0.300767i	0.372222	+	0.0656328i
$22$	3.64543	+	3.05888i	0.777208	+	0.652155i
$23$	7.57785	−	2.75811i	1.58009	−	0.575106i	0.604867	−	0.796327i	$-0.293226\pi$
$23$	7.57785	−	2.75811i	1.58009	−	0.575106i	0.975224	+	0.221221i	$0.0710041\pi$
$24$	1.11334	+	1.32683i	0.227260	+	0.270838i
$25$	−0.553033	−	3.13641i	−0.110607	−	0.627282i
$26$	1.53209			0.300467
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$	1.00000			0.188982
$29$	−1.85844	−	10.5397i	−0.345104	−	1.95718i	−0.283038	−	0.959109i	$-0.591342\pi$
$29$	−1.85844	−	10.5397i	−0.345104	−	1.95718i	−0.0620658	−	0.998072i	$-0.519769\pi$
$30$	−0.798133	+	2.19285i	−0.145719	+	0.400358i
$31$	1.37939	−	0.502055i	0.247745	−	0.0901718i	−0.215163	−	0.976578i	$-0.569028\pi$
$31$	1.37939	−	0.502055i	0.247745	−	0.0901718i	0.462908	+	0.886406i	$0.346806\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−5.29813	+	6.31407i	−0.922287	+	1.09914i
$34$	−2.09240	−	0.761570i	−0.358843	−	0.130608i
$35$	0.673648	+	1.16679i	0.113867	+	0.197224i
$36$	−2.29813	+	1.92836i	−0.383022	+	0.321394i
$37$	0.815207	−	1.41198i	0.134019	−	0.232128i	−0.791203	−	0.611553i	$-0.790545\pi$
$37$	0.815207	−	1.41198i	0.134019	−	0.232128i	0.925222	+	0.379425i	$0.123878\pi$
$38$	−4.28699	+	3.59721i	−0.695441	+	0.583545i
$39$			2.65366i			0.424925i
$40$	−0.233956	+	1.32683i	−0.0369916	+	0.209790i
$41$	1.75877	−	9.97448i	0.274674	−	1.55775i	−0.465322	−	0.885141i	$-0.654062\pi$
$41$	1.75877	−	9.97448i	0.274674	−	1.55775i	0.739996	−	0.672611i	$-0.234827\pi$
$42$			1.73205i			0.267261i
$43$	−6.70961	+	5.63003i	−1.02321	+	0.858571i	−0.990027	−	0.140878i	$-0.955007\pi$
$43$	−6.70961	+	5.63003i	−1.02321	+	0.858571i	−0.0331786	+	0.999449i	$0.510563\pi$
$44$	−2.37939	+	4.12122i	−0.358706	+	0.621297i
$45$	−3.79813	−	1.38241i	−0.566192	−	0.206077i
$46$	4.03209	+	6.98378i	0.594499	+	1.02970i
$47$	8.35117	+	3.03958i	1.21814	+	0.443368i	0.869521	−	0.493896i	$-0.164428\pi$
$47$	8.35117	+	3.03958i	1.21814	+	0.443368i	0.348622	+	0.937264i	$0.386650\pi$
$48$	−1.11334	+	1.32683i	−0.160697	+	0.191511i
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$	2.99273	−	1.08926i	0.423235	−	0.154045i
$51$	1.31908	−	3.62414i	0.184708	−	0.507481i
$52$	0.266044	+	1.50881i	0.0368937	+	0.209235i
$53$	1.32770			0.182373			0.0911865	−	0.995834i	$-0.470934\pi$
$53$	1.32770			0.182373			0.0911865	+	0.995834i	$0.470934\pi$
$54$	−3.34002	−	3.98048i	−0.454519	−	0.541675i
$55$	−6.41147			−0.864523
$56$	0.173648	+	0.984808i	0.0232047	+	0.131600i
$57$	−6.23055	−	7.42528i	−0.825257	−	0.983503i
$58$	10.0569	−	3.66041i	1.32054	−	0.480636i
$59$	−7.16637	−	6.01330i	−0.932982	−	0.782865i	0.0433680	−	0.999059i	$-0.486191\pi$
$59$	−7.16637	−	6.01330i	−0.932982	−	0.782865i	−0.976350	+	0.216194i	$0.930636\pi$
$60$	−2.29813	−	0.405223i	−0.296688	−	0.0523141i
$61$	3.08512	+	1.12289i	0.395009	+	0.143772i	0.531885	−	0.846817i	$-0.321484\pi$
$61$	3.08512	+	1.12289i	0.395009	+	0.143772i	−0.136876	+	0.990588i	$0.543706\pi$
$62$	0.733956	+	1.27125i	0.0932124	+	0.161449i
$63$	−3.00000			−0.377964
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.58125	+	1.32683i	−0.196130	+	0.164573i
$66$	−7.13816	−	4.12122i	−0.878646	−	0.507287i
$67$	−0.470437	+	2.66798i	−0.0574731	+	0.325946i	−0.999966	−	0.00828093i	$-0.997364\pi$
$67$	−0.470437	+	2.66798i	−0.0574731	+	0.325946i	0.942493	+	0.334227i	$0.108475\pi$
$68$	0.386659	−	2.19285i	0.0468893	−	0.265923i
$69$	−12.0963	+	6.98378i	−1.45622	+	0.840749i
$70$	−1.03209	+	0.866025i	−0.123358	+	0.103510i
$71$	−2.10220	+	3.64111i	−0.249485	+	0.432120i	−0.963383	−	0.268129i	$-0.913595\pi$
$71$	−2.10220	+	3.64111i	−0.249485	+	0.432120i	0.713898	+	0.700250i	$0.246928\pi$
$72$	−2.29813	−	1.92836i	−0.270838	−	0.227260i
$73$	−4.54576	−	7.87349i	−0.532041	−	0.921522i	−0.999300	−	0.0374016i	$-0.988092\pi$
$73$	−4.54576	−	7.87349i	−0.532041	−	0.921522i	0.467259	−	0.884120i	$-0.345241\pi$
$74$	1.53209	+	0.557635i	0.178102	+	0.0648237i
$75$	1.88666	+	5.18355i	0.217853	+	0.598545i
$76$	−4.28699	−	3.59721i	−0.491751	−	0.412628i
$77$	−4.47178	+	1.62760i	−0.509607	+	0.185482i
$78$	−2.61334	+	0.460802i	−0.295903	+	0.0521756i
$79$	0.556437	+	3.15571i	0.0626041	+	0.355045i	0.999977	+	0.00671900i	$0.00213874\pi$
$79$	0.556437	+	3.15571i	0.0626041	+	0.355045i	−0.937373	+	0.348326i	$0.886750\pi$
$80$	−1.34730			−0.150632
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$	10.1284			1.11849
$83$	−2.22668	−	12.6281i	−0.244410	−	1.38612i	−0.821859	−	0.569691i	$-0.807063\pi$
$83$	−2.22668	−	12.6281i	−0.244410	−	1.38612i	0.577449	−	0.816427i	$-0.304048\pi$
$84$	−1.70574	+	0.300767i	−0.186111	+	0.0328164i
$85$	2.81908	−	1.02606i	0.305772	−	0.111292i
$86$	−6.70961	−	5.63003i	−0.723516	−	0.607102i
$87$	6.34002	+	17.4191i	0.679722	+	1.86752i
$88$	−4.47178	−	1.62760i	−0.476694	−	0.173502i
$89$	−0.779715	−	1.35051i	−0.0826496	−	0.143153i	0.821738	−	0.569866i	$-0.193005\pi$
$89$	−0.779715	−	1.35051i	−0.0826496	−	0.143153i	−0.904387	+	0.426713i	$0.859672\pi$
$90$	0.701867	−	3.98048i	0.0739832	−	0.419580i
$91$	−0.766044	+	1.32683i	−0.0803033	+	0.139089i
$92$	−6.17752	+	5.18355i	−0.644051	+	0.540423i
$93$	−2.20187	+	1.27125i	−0.228323	+	0.131822i
$94$	−1.54323	+	8.75211i	−0.159172	+	0.902711i
$95$	1.30928	−	7.42528i	0.134329	−	0.761818i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	−9.91534	+	8.31996i	−1.00675	+	0.844764i	−0.987905	−	0.155058i	$-0.950443\pi$
$97$	−9.91534	+	8.31996i	−1.00675	+	0.844764i	−0.0188454	+	0.999822i	$0.505999\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	7.13816	−	12.3636i	0.717412	−	1.24259i
$100$	1.59240	+	2.75811i	0.159240	+	0.275811i
$101$	3.72668	+	1.35640i	0.370819	+	0.134967i	0.520706	−	0.853736i	$-0.325669\pi$
$101$	3.72668	+	1.35640i	0.370819	+	0.134967i	−0.149887	+	0.988703i	$0.547891\pi$
$102$	3.79813	+	0.669713i	0.376071	+	0.0663115i
$103$	4.98680	+	4.18442i	0.491364	+	0.412303i	0.854515	−	0.519427i	$-0.173855\pi$
$103$	4.98680	+	4.18442i	0.491364	+	0.412303i	−0.363151	+	0.931730i	$0.618299\pi$
$104$	−1.43969	+	0.524005i	−0.141173	+	0.0513829i
$105$	−1.50000	−	1.78763i	−0.146385	−	0.174455i
$106$	0.230552	+	1.30753i	0.0223932	+	0.126998i
$107$	−6.92902			−0.669853			−0.334927	−	0.942244i	$-0.608712\pi$
$107$	−6.92902			−0.669853			−0.334927	+	0.942244i	$0.608712\pi$
$108$	3.34002	−	3.98048i	0.321394	−	0.383022i
$109$	8.30541			0.795514			0.397757	−	0.917491i	$-0.369789\pi$
$109$	8.30541			0.795514			0.397757	+	0.917491i	$0.369789\pi$
$110$	−1.11334	−	6.31407i	−0.106153	−	0.602023i
$111$	−0.965852	+	2.65366i	−0.0916746	+	0.251874i
$112$	−0.939693	+	0.342020i	−0.0887926	+	0.0323179i
$113$	1.74376	+	1.46318i	0.164039	+	0.137645i	0.721112	−	0.692819i	$-0.243631\pi$
$113$	1.74376	+	1.46318i	0.164039	+	0.137645i	−0.557073	+	0.830463i	$0.688076\pi$
$114$	6.23055	−	7.42528i	0.583545	−	0.695441i
$115$	−10.2096	−	3.71599i	−0.952051	−	0.346518i
$116$	5.35117	+	9.26849i	0.496843	+	0.860558i
$117$	−0.798133	−	4.52644i	−0.0737875	−	0.418469i
$118$	4.67752	−	8.10170i	0.430600	−	0.745822i
$119$	1.70574	−	1.43128i	0.156365	−	0.131206i
$120$		−	2.33359i		−	0.213026i
$121$	2.02229	−	11.4690i	0.183844	−	1.04263i
$122$	−0.570108	+	3.23324i	−0.0516151	+	0.292724i
$123$			17.5428i			1.58178i
$124$	−1.12449	+	0.943555i	−0.100982	+	0.0847337i
$125$	−5.51367	+	9.54996i	−0.493158	+	0.854174i
$126$	−0.520945	−	2.95442i	−0.0464094	−	0.263201i
$127$	10.1454	+	17.5724i	0.900261	+	1.55930i	0.827155	+	0.561974i	$0.189958\pi$
$127$	10.1454	+	17.5724i	0.900261	+	1.55930i	0.0731065	+	0.997324i	$0.476709\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	9.75150	−	11.6214i	0.858571	−	1.02321i
$130$	−1.58125	−	1.32683i	−0.138685	−	0.116371i
$131$	−1.11334	+	0.405223i	−0.0972730	+	0.0354045i	−0.390198	−	0.920731i	$-0.627594\pi$
$131$	−1.11334	+	0.405223i	−0.0972730	+	0.0354045i	0.292925	+	0.956135i	$0.405371\pi$
$132$	2.81908	−	7.74535i	0.245369	−	0.674146i
$133$	−0.971782	−	5.51125i	−0.0842641	−	0.477886i
$134$	−2.70914			−0.234034
$135$	6.89440	+	1.21567i	0.593375	+	0.104628i
$136$	2.22668			0.190936
$137$	3.57738	+	20.2883i	0.305636	+	1.73335i	0.620494	+	0.784211i	$0.286932\pi$
$137$	3.57738	+	20.2883i	0.305636	+	1.73335i	−0.314858	+	0.949139i	$0.601957\pi$
$138$	−8.97818	−	10.6998i	−0.764273	−	0.910825i
$139$	16.6694	−	6.06715i	1.41388	−	0.514609i	0.481612	−	0.876385i	$-0.340051\pi$
$139$	16.6694	−	6.06715i	1.41388	−	0.514609i	0.932265	+	0.361775i	$0.117829\pi$
$140$	−1.03209	−	0.866025i	−0.0872274	−	0.0731925i
$141$	−15.1591	−	2.67296i	−1.27663	−	0.225104i
$142$	−3.95084	−	1.43799i	−0.331547	−	0.120673i
$143$	−3.64543	−	6.31407i	−0.304846	−	0.528009i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−7.20961	+	12.4874i	−0.598725	+	1.03702i
$146$	6.96451	−	5.84392i	0.576387	−	0.483646i
$147$	−1.50000	−	0.866025i	−0.123718	−	0.0714286i
$148$	−0.283119	+	1.60565i	−0.0232722	+	0.131983i
$149$	−1.39734	+	7.92469i	−0.114474	+	0.649216i	0.872535	+	0.488552i	$0.162475\pi$
$149$	−1.39734	+	7.92469i	−0.114474	+	0.649216i	−0.987009	+	0.160664i	$0.948636\pi$
$150$	−4.77719	+	2.75811i	−0.390056	+	0.225199i
$151$	9.05169	−	7.59527i	0.736616	−	0.618094i	−0.195310	−	0.980741i	$-0.562571\pi$
$151$	9.05169	−	7.59527i	0.736616	−	0.618094i	0.931926	+	0.362647i	$0.118127\pi$
$152$	2.79813	−	4.84651i	0.226959	−	0.393104i
$153$	−1.15998	+	6.57856i	−0.0937786	+	0.531845i
$154$	−2.37939	−	4.12122i	−0.191736	−	0.332097i
$155$	−1.85844	−	0.676417i	−0.149274	−	0.0543311i
$156$	−0.907604	−	2.49362i	−0.0726665	−	0.199649i
$157$	−17.1348	−	14.3778i	−1.36750	−	1.14747i	−0.973585	−	0.228324i	$-0.926675\pi$
$157$	−17.1348	−	14.3778i	−1.36750	−	1.14747i	−0.393917	−	0.919146i	$-0.628880\pi$
$158$	−3.01114	+	1.09597i	−0.239554	+	0.0871904i
$159$	−2.26470	+	0.399328i	−0.179602	+	0.0316688i
$160$	−0.233956	−	1.32683i	−0.0184958	−	0.104895i
$161$	−8.06418			−0.635546
$162$	6.89440	+	5.78509i	0.541675	+	0.454519i
$163$	−10.4611			−0.819377			−0.409688	−	0.912226i	$-0.634363\pi$
$163$	−10.4611			−0.819377			−0.409688	+	0.912226i	$0.634363\pi$
$164$	1.75877	+	9.97448i	0.137337	+	0.778876i
$165$	10.9363	−	1.92836i	0.851389	−	0.150123i
$166$	12.0496	−	4.38571i	0.935233	−	0.340397i
$167$	17.3045	+	14.5202i	1.33906	+	1.12361i	0.981865	+	0.189581i	$0.0607128\pi$
$167$	17.3045	+	14.5202i	1.33906	+	1.12361i	0.357200	+	0.934028i	$0.383732\pi$
$168$	−0.592396	−	1.62760i	−0.0457044	−	0.125572i
$169$	10.0103	+	3.64344i	0.770021	+	0.280265i
$170$	1.50000	+	2.59808i	0.115045	+	0.199263i
$171$	12.8610	+	10.7916i	0.983503	+	0.825257i
$172$	4.37939	−	7.58532i	0.333925	−	0.578375i
$173$	5.48886	−	4.60570i	0.417310	−	0.350165i	−0.409829	−	0.912162i	$-0.634412\pi$
$173$	5.48886	−	4.60570i	0.417310	−	0.350165i	0.827139	+	0.561998i	$0.189967\pi$
$174$	−16.0535	+	9.26849i	−1.21701	+	0.702643i
$175$	−0.553033	+	3.13641i	−0.0418054	+	0.237090i
$176$	0.826352	−	4.68647i	0.0622886	−	0.353256i
$177$	14.0326	+	8.10170i	1.05475	+	0.608961i
$178$	1.19459	−	1.00238i	0.0895385	−	0.0751317i
$179$	−3.31180	+	5.73621i	−0.247536	+	0.428745i	−0.962842	−	0.270067i	$-0.912954\pi$
$179$	−3.31180	+	5.73621i	−0.247536	+	0.428745i	0.715306	+	0.698812i	$0.246287\pi$
$180$	4.04189			0.301265
$181$	1.67617	+	2.90322i	0.124589	+	0.215795i	0.921572	−	0.388207i	$-0.126905\pi$
$181$	1.67617	+	2.90322i	0.124589	+	0.215795i	−0.796983	+	0.604002i	$0.793572\pi$
$182$	−1.43969	−	0.524005i	−0.106717	−	0.0388419i
$183$	−5.60014	−	0.987455i	−0.413974	−	0.0729948i
$184$	−6.17752	−	5.18355i	−0.455413	−	0.382137i
$185$	−2.06418	+	0.751299i	−0.151761	+	0.0552366i
$186$	−1.63429	−	1.94767i	−0.119832	−	0.142810i
$187$	1.84002	+	10.4353i	0.134556	+	0.763104i
$188$	−8.88713			−0.648160
$189$	5.11721	−	0.902302i	0.372222	−	0.0656328i
$190$	7.53983			0.546997
$191$	0.708263	+	4.01676i	0.0512481	+	0.290643i	0.999651	−	0.0264259i	$-0.00841260\pi$
$191$	0.708263	+	4.01676i	0.0512481	+	0.290643i	−0.948403	+	0.317068i	$0.897301\pi$
$192$	0.592396	−	1.62760i	0.0427525	−	0.117462i
$193$	3.57145	−	1.29990i	0.257079	−	0.0935690i	−0.210266	−	0.977644i	$-0.567433\pi$
$193$	3.57145	−	1.29990i	0.257079	−	0.0935690i	0.467345	+	0.884075i	$0.345211\pi$
$194$	−9.91534	−	8.31996i	−0.711880	−	0.597338i
$195$	2.29813	−	2.73881i	0.164573	−	0.196130i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	−8.52869	−	14.7721i	−0.607644	−	1.05247i	−0.991628	−	0.129130i	$-0.958782\pi$
$197$	−8.52869	−	14.7721i	−0.607644	−	1.05247i	0.383984	−	0.923340i	$-0.374552\pi$
$198$	13.4153	+	4.88279i	0.953387	+	0.347004i
$199$	−4.47313	+	7.74768i	−0.317091	+	0.549219i	−0.979880	−	0.199588i	$-0.936040\pi$
$199$	−4.47313	+	7.74768i	−0.317091	+	0.549219i	0.662788	+	0.748807i	$0.269373\pi$
$200$	−2.43969	+	2.04715i	−0.172512	+	0.144755i
$201$		−	4.69237i		−	0.330974i
$202$	−0.688663	+	3.90560i	−0.0484542	+	0.274797i
$203$	−1.85844	+	10.5397i	−0.130437	+	0.739745i
$204$			3.85673i			0.270025i
$205$	−10.4534	+	8.77141i	−0.730095	+	0.612622i
$206$	−3.25490	+	5.63765i	−0.226780	+	0.392794i
$207$	18.5326	−	15.5507i	1.28810	−	1.08085i
$208$	−0.766044	−	1.32683i	−0.0531156	−	0.0919990i
$209$	25.0253	+	9.10846i	1.73103	+	0.630045i
$210$	1.50000	−	1.78763i	0.103510	−	0.123358i
$211$	−16.9440	−	14.2177i	−1.16648	−	0.978789i	−0.166501	−	0.986041i	$-0.553247\pi$
$211$	−16.9440	−	14.2177i	−1.16648	−	0.978789i	−0.999974	+	0.00725237i	$0.997691\pi$
$212$	−1.24763	+	0.454099i	−0.0856873	+	0.0311876i
$213$	2.49067	−	6.84305i	0.170658	−	0.468878i
$214$	−1.20321	−	6.82375i	−0.0822498	−	0.466462i
$215$	11.8007			0.804798
$216$	4.50000	+	2.59808i	0.306186	+	0.176777i
$217$	−1.46791			−0.0996483
$218$	1.44222	+	8.17923i	0.0976794	+	0.553967i
$219$	10.1220	+	12.0629i	0.683979	+	0.815134i
$220$	6.02481	−	2.19285i	0.406193	−	0.147842i
$221$	2.61334	+	2.19285i	0.175792	+	0.147507i
$222$	−2.78106	−	0.490376i	−0.186652	−	0.0329119i
$223$	−18.5719	−	6.75963i	−1.24367	−	0.452658i	−0.365410	−	0.930847i	$-0.619071\pi$
$223$	−18.5719	−	6.75963i	−1.24367	−	0.452658i	−0.878257	+	0.478189i	$0.841294\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−4.77719	−	8.27433i	−0.318479	−	0.551622i
$226$	−1.13816	+	1.97134i	−0.0757090	+	0.131132i
$227$	9.50253	−	7.97357i	0.630705	−	0.529224i	−0.270443	−	0.962736i	$-0.587170\pi$
$227$	9.50253	−	7.97357i	0.630705	−	0.529224i	0.901148	+	0.433512i	$0.142726\pi$
$228$	8.39440	+	4.84651i	0.555933	+	0.320968i
$229$	−1.08466	+	6.15139i	−0.0716761	+	0.406495i	0.927768	+	0.373157i	$0.121725\pi$
$229$	−1.08466	+	6.15139i	−0.0716761	+	0.406495i	−0.999444	+	0.0333378i	$0.989386\pi$
$230$	1.88666	−	10.6998i	0.124403	−	0.705522i
$231$	7.13816	−	4.12122i	0.469656	−	0.271156i
$232$	−8.19846	+	6.87933i	−0.538255	+	0.451650i
$233$	−10.1532	+	17.5858i	−0.665156	+	1.15208i	0.314087	+	0.949394i	$0.398302\pi$
$233$	−10.1532	+	17.5858i	−0.665156	+	1.15208i	−0.979243	+	0.202690i	$0.935032\pi$
$234$	4.31908	−	1.57202i	0.282347	−	0.102766i
$235$	−5.98680	−	10.3694i	−0.390536	−	0.676427i
$236$	8.79086	+	3.19961i	0.572236	+	0.208277i
$237$	−1.89827	−	5.21546i	−0.123306	−	0.338780i
$238$	1.70574	+	1.43128i	0.110567	+	0.0927763i
$239$	13.8204	−	5.03022i	0.893969	−	0.325378i	0.146135	−	0.989265i	$-0.453316\pi$
$239$	13.8204	−	5.03022i	0.893969	−	0.325378i	0.747833	+	0.663887i	$0.231094\pi$
$240$	2.29813	−	0.405223i	0.148344	−	0.0261570i
$241$	0.0655219	+	0.371593i	0.00422064	+	0.0239364i	0.986845	−	0.161667i	$-0.0516871\pi$
$241$	0.0655219	+	0.371593i	0.00422064	+	0.0239364i	−0.982625	+	0.185604i	$0.940576\pi$
$242$	11.6459			0.748627
$243$	−10.0201	+	11.9415i	−0.642788	+	0.766044i
$244$	−3.28312			−0.210180
$245$	−0.233956	−	1.32683i	−0.0149469	−	0.0847679i
$246$	−17.2763	+	3.04628i	−1.10150	+	0.194224i
$247$	8.05690	−	2.93247i	0.512649	−	0.186589i
$248$	−1.12449	−	0.943555i	−0.0714049	−	0.0599158i
$249$	7.59627	+	20.8706i	0.481394	+	1.32262i
$250$	−10.3623	−	3.77157i	−0.655370	−	0.238535i
$251$	−0.807934	−	1.39938i	−0.0509963	−	0.0883282i	0.839400	−	0.543514i	$-0.182906\pi$
$251$	−0.807934	−	1.39938i	−0.0509963	−	0.0883282i	−0.890397	+	0.455185i	$0.849573\pi$
$252$	2.81908	−	1.02606i	0.177585	−	0.0646357i
$253$	19.1878	−	33.2342i	1.20633	−	2.08942i
$254$	−15.5437	+	13.0427i	−0.975298	+	0.818373i
$255$	−4.50000	+	2.59808i	−0.281801	+	0.162698i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.76382	−	15.6744i	0.172403	−	0.977743i	−0.768697	−	0.639613i	$-0.779095\pi$
$257$	2.76382	−	15.6744i	0.172403	−	0.977743i	0.941099	−	0.338130i	$-0.109794\pi$
$258$	13.1382	+	7.58532i	0.817946	+	0.472241i
$259$	−1.24897	+	1.04801i	−0.0776072	+	0.0651202i
$260$	1.03209	−	1.78763i	0.0640074	−	0.110864i
$261$	−16.0535	−	27.8055i	−0.993687	−	1.72112i
$262$	−0.592396	−	1.02606i	−0.0365984	−	0.0633902i
$263$	1.40033	+	0.509678i	0.0863480	+	0.0314281i	0.384833	−	0.922986i	$-0.374259\pi$
$263$	1.40033	+	0.509678i	0.0863480	+	0.0314281i	−0.298485	+	0.954414i	$0.596481\pi$
$264$	8.11721	+	1.43128i	0.499580	+	0.0880894i
$265$	−1.37030	−	1.14982i	−0.0841769	−	0.0706328i
$266$	5.25877	−	1.91404i	0.322436	−	0.117357i
$267$	1.73618	+	2.06910i	0.106252	+	0.126627i
$268$	−0.470437	−	2.66798i	−0.0287365	−	0.162973i
$269$	7.88444			0.480723			0.240361	−	0.970683i	$-0.422734\pi$
$269$	7.88444			0.480723			0.240361	+	0.970683i	$0.422734\pi$
$270$			7.00076i			0.426053i
$271$	−3.59533			−0.218401			−0.109200	−	0.994020i	$-0.534829\pi$
$271$	−3.59533			−0.218401			−0.109200	+	0.994020i	$0.534829\pi$
$272$	0.386659	+	2.19285i	0.0234447	+	0.132961i
$273$	0.907604	−	2.49362i	0.0549307	−	0.150921i
$274$	−19.3589	+	7.04607i	−1.16951	+	0.425668i
$275$	−11.6099	−	9.74189i	−0.700106	−	0.587458i
$276$	8.97818	−	10.6998i	0.540423	−	0.644051i
$277$	3.99912	+	1.45556i	0.240284	+	0.0874562i	0.459355	−	0.888253i	$-0.348080\pi$
$277$	3.99912	+	1.45556i	0.240284	+	0.0874562i	−0.219071	+	0.975709i	$0.570303\pi$
$278$	8.86959	+	15.3626i	0.531962	+	0.921386i
$279$	3.37346	−	2.83067i	0.201963	−	0.169467i
$280$	0.673648	−	1.16679i	0.0402582	−	0.0697292i
$281$	−5.61515	+	4.71167i	−0.334972	+	0.281075i	−0.794722	−	0.606974i	$-0.792383\pi$
$281$	−5.61515	+	4.71167i	−0.334972	+	0.281075i	0.459750	+	0.888048i	$0.347939\pi$
$282$		−	15.3930i		−	0.916637i
$283$	4.90373	−	27.8105i	0.291497	−	1.65316i	−0.389613	−	0.920979i	$-0.627391\pi$
$283$	4.90373	−	27.8105i	0.291497	−	1.65316i	0.681110	−	0.732181i	$-0.261498\pi$
$284$	0.730085	−	4.14052i	0.0433226	−	0.245695i
$285$			13.0594i			0.773570i
$286$	5.58512	−	4.68647i	0.330255	−	0.277117i
$287$	−5.06418	+	8.77141i	−0.298929	+	0.517760i
$288$	2.81908	+	1.02606i	0.166116	+	0.0604612i
$289$	6.02094	+	10.4286i	0.354173	+	0.613446i
$290$	−13.5496	−	4.93166i	−0.795662	−	0.289597i
$291$	14.4106	−	17.1739i	0.844764	−	1.00675i
$292$	6.96451	+	5.84392i	0.407567	+	0.341989i
$293$	−18.5954	+	6.76817i	−1.08635	+	0.395401i	−0.822269	−	0.569099i	$-0.807292\pi$
$293$	−18.5954	+	6.76817i	−1.08635	+	0.395401i	−0.264085	+	0.964499i	$0.585070\pi$
$294$	0.592396	−	1.62760i	0.0345493	−	0.0949233i
$295$	2.18866	+	12.4125i	0.127429	+	0.722685i
$296$	−1.63041			−0.0947659
$297$	−8.45723	+	23.2361i	−0.490738	+	1.34829i
$298$	−8.04694			−0.466147
$299$	−2.14543	−	12.1673i	−0.124073	−	0.703655i
$300$	−3.54576	−	4.22567i	−0.204715	−	0.243969i
$301$	8.23055	−	2.99568i	0.474401	−	0.172668i
$302$	9.05169	+	7.59527i	0.520866	+	0.437059i
$303$	−6.76470	−	1.19280i	−0.388622	−	0.0685245i
$304$	5.25877	+	1.91404i	0.301611	+	0.109777i
$305$	−2.21167	−	3.83072i	−0.126640	−	0.219346i
$306$	−6.68004			−0.381873
$307$	−12.2849	+	21.2781i	−0.701138	+	1.21441i	0.266929	+	0.963716i	$0.413991\pi$
$307$	−12.2849	+	21.2781i	−0.701138	+	1.21441i	−0.968067	+	0.250690i	$0.919342\pi$
$308$	3.64543	−	3.05888i	0.207718	−	0.174296i
$309$	−9.76470	−	5.63765i	−0.555494	−	0.320715i
$310$	0.343426	−	1.94767i	0.0195053	−	0.110620i
$311$	−1.92468	+	10.9154i	−0.109138	+	0.618955i	0.880348	+	0.474329i	$0.157309\pi$
$311$	−1.92468	+	10.9154i	−0.109138	+	0.618955i	−0.989486	+	0.144626i	$0.953802\pi$
$312$	2.29813	−	1.32683i	0.130106	−	0.0751168i
$313$	12.6361	−	10.6029i	0.714234	−	0.599314i	−0.211549	−	0.977367i	$-0.567851\pi$
$313$	12.6361	−	10.6029i	0.714234	−	0.599314i	0.925784	+	0.378053i	$0.123406\pi$
$314$	11.1839	−	19.3711i	0.631145	−	1.09317i
$315$	3.09627	+	2.59808i	0.174455	+	0.146385i
$316$	−1.60220	−	2.77509i	−0.0901306	−	0.156111i
$317$	15.1741	+	5.52293i	0.852263	+	0.310198i	0.730963	−	0.682417i	$-0.239071\pi$
$317$	15.1741	+	5.52293i	0.852263	+	0.310198i	0.121300	+	0.992616i	$0.461294\pi$
$318$	−0.786522	−	2.16095i	−0.0441060	−	0.121180i
$319$	−39.0146	−	32.7371i	−2.18440	−	1.83293i
$320$	1.26604	−	0.460802i	0.0707740	−	0.0257596i
$321$	11.8191	−	2.08402i	0.659677	−	0.116319i
$322$	−1.40033	−	7.94166i	−0.0780373	−	0.442572i
$323$	−12.4611			−0.693354
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−4.87939			−0.270660
$326$	−1.81655	−	10.3022i	−0.100609	−	0.570585i
$327$	−14.1668	+	2.49800i	−0.783428	+	0.138140i
$328$	−9.51754	+	3.46410i	−0.525518	+	0.191273i
$329$	−6.80793	−	5.71253i	−0.375334	−	0.314942i
$330$	3.79813	+	10.4353i	0.209080	+	0.574444i
$331$	−5.42514	−	1.97459i	−0.298193	−	0.108533i	0.188591	−	0.982056i	$-0.439608\pi$
$331$	−5.42514	−	1.97459i	−0.298193	−	0.108533i	−0.486784	+	0.873522i	$0.661830\pi$
$332$	6.41147	+	11.1050i	0.351875	+	0.609466i
$333$	0.849356	−	4.81694i	0.0465444	−	0.263966i
$334$	−11.2947	+	19.5630i	−0.618020	+	1.07044i
$335$	2.79607	−	2.34618i	0.152766	−	0.128186i
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	−3.60132	+	20.4241i	−0.196176	+	1.11257i	0.714557	+	0.699577i	$0.246628\pi$
$337$	−3.60132	+	20.4241i	−0.196176	+	1.11257i	−0.910734	+	0.412994i	$0.864483\pi$
$338$	−1.84982	+	10.4909i	−0.100617	+	0.570628i
$339$	−3.41447	−	1.97134i	−0.185448	−	0.107069i
$340$	−2.29813	+	1.92836i	−0.124634	+	0.104580i
$341$	3.49273	−	6.04958i	0.189142	−	0.327603i
$342$	−8.39440	+	14.5395i	−0.453917	+	0.786208i
$343$	−0.500000	−	0.866025i	−0.0269975	−	0.0467610i
$344$	8.23055	+	2.99568i	0.443762	+	0.161516i
$345$	18.5326	+	3.26779i	0.997759	+	0.175932i
$346$	5.48886	+	4.60570i	0.295083	+	0.247604i
$347$	−2.86571	+	1.04303i	−0.153840	+	0.0559930i	−0.417792	−	0.908543i	$-0.637196\pi$
$347$	−2.86571	+	1.04303i	−0.153840	+	0.0559930i	0.263953	+	0.964536i	$0.414974\pi$
$348$	−11.9153	−	14.2002i	−0.638730	−	0.761208i
$349$	−1.09745	−	6.22394i	−0.0587451	−	0.333160i	0.941244	−	0.337726i	$-0.109658\pi$
$349$	−1.09745	−	6.22394i	−0.0587451	−	0.333160i	−0.999990	+	0.00456601i	$0.998547\pi$
$350$	−3.18479			−0.170234
$351$	2.72281	+	7.48086i	0.145333	+	0.399299i
$352$	4.75877			0.253643
$353$	−0.420092	−	2.38246i	−0.0223593	−	0.126806i	0.971585	−	0.236691i	$-0.0760628\pi$
$353$	−0.420092	−	2.38246i	−0.0223593	−	0.126806i	−0.993944	+	0.109885i	$0.964952\pi$
$354$	−5.54189	+	15.2262i	−0.294548	+	0.809264i
$355$	5.32295	−	1.93739i	0.282513	−	0.102826i
$356$	1.19459	+	1.00238i	0.0633133	+	0.0531262i
$357$	−2.47906	+	2.95442i	−0.131206	+	0.156365i
$358$	−6.22416	−	2.26541i	−0.328957	−	0.119730i
$359$	2.46064	+	4.26195i	0.129867	+	0.224937i	0.923625	−	0.383297i	$-0.125211\pi$
$359$	2.46064	+	4.26195i	0.129867	+	0.224937i	−0.793758	+	0.608234i	$0.791878\pi$
$360$	0.701867	+	3.98048i	0.0369916	+	0.209790i
$361$	−6.15910	+	10.6679i	−0.324163	+	0.561467i
$362$	−2.56805	+	2.15485i	−0.134974	+	0.113256i
$363$			20.1713i			1.05872i
$364$	0.266044	−	1.50881i	0.0139445	−	0.0790833i
$365$	−2.12701	+	12.0629i	−0.111333	+	0.631400i
$366$		−	5.68653i		−	0.297240i
$367$	−5.54782	+	4.65517i	−0.289594	+	0.242998i	−0.775997	−	0.630736i	$-0.782753\pi$
$367$	−5.54782	+	4.65517i	−0.289594	+	0.242998i	0.486403	+	0.873734i	$0.338309\pi$
$368$	4.03209	−	6.98378i	0.210187	−	0.364055i
$369$	−5.27631	−	29.9234i	−0.274674	−	1.55775i
$370$	−1.09833	−	1.90236i	−0.0570993	−	0.0988988i
$371$	−1.24763	−	0.454099i	−0.0647735	−	0.0235756i
$372$	1.63429	−	1.94767i	0.0847337	−	0.100982i
$373$	−11.1814	−	9.38230i	−0.578950	−	0.485797i	0.305652	−	0.952143i	$-0.401126\pi$
$373$	−11.1814	−	9.38230i	−0.578950	−	0.485797i	−0.884602	+	0.466346i	$0.845570\pi$
$374$	−9.95723	+	3.62414i	−0.514876	+	0.187400i
$375$	6.53256	−	17.9480i	0.337340	−	0.926833i
$376$	−1.54323	−	8.75211i	−0.0795862	−	0.451356i
$377$	−16.3969			−0.844485
$378$	1.77719	+	4.88279i	0.0914087	+	0.251143i
$379$	−5.81521			−0.298707			−0.149354	−	0.988784i	$-0.547719\pi$
$379$	−5.81521			−0.298707			−0.149354	+	0.988784i	$0.547719\pi$
$380$	1.30928	+	7.42528i	0.0671645	+	0.380909i
$381$	−22.5906	−	26.9225i	−1.15735	−	1.37928i
$382$	−3.83275	+	1.39501i	−0.196100	+	0.0713747i
$383$	−20.1466	−	16.9050i	−1.02944	−	0.863806i	−0.0386591	−	0.999252i	$-0.512309\pi$
$383$	−20.1466	−	16.9050i	−1.02944	−	0.863806i	−0.990785	+	0.135447i	$0.956753\pi$
$384$	1.70574	+	0.300767i	0.0870455	+	0.0153485i
$385$	6.02481	+	2.19285i	0.307053	+	0.111758i
$386$	1.90033	+	3.29147i	0.0967242	+	0.167531i
$387$	−13.1382	+	22.7560i	−0.667850	+	1.15675i
$388$	6.47178	−	11.2095i	0.328555	−	0.569074i
$389$	−28.5763	+	23.9783i	−1.44887	+	1.21575i	−0.515477	+	0.856904i	$0.672385\pi$
$389$	−28.5763	+	23.9783i	−1.44887	+	1.21575i	−0.933397	+	0.358846i	$0.883170\pi$
$390$	3.09627	+	1.78763i	0.156786	+	0.0905202i
$391$	−3.11809	+	17.6836i	−0.157689	+	0.894296i
$392$	0.173648	−	0.984808i	0.00877056	−	0.0497403i
$393$	1.77719	−	1.02606i	0.0896473	−	0.0517579i
$394$	13.0667	−	10.9643i	0.658291	−	0.552372i
$395$	2.15863	−	3.73886i	0.108613	−	0.188123i
$396$	−2.47906	+	14.0594i	−0.124577	+	0.706513i
$397$	14.9256	+	25.8519i	0.749095	+	1.29747i	0.948257	+	0.317504i	$0.102845\pi$
$397$	14.9256	+	25.8519i	0.749095	+	1.29747i	−0.199162	+	0.979967i	$0.563822\pi$
$398$	−8.40673	−	3.05980i	−0.421391	−	0.153374i
$399$	3.31521	+	9.10846i	0.165968	+	0.455993i
$400$	−2.43969	−	2.04715i	−0.121985	−	0.102357i
$401$	−14.9089	+	5.42641i	−0.744517	+	0.270982i	−0.686297	−	0.727322i	$-0.740765\pi$
$401$	−14.9089	+	5.42641i	−0.744517	+	0.270982i	−0.0582205	+	0.998304i	$0.518543\pi$
$402$	4.62108	−	0.814821i	0.230479	−	0.0406396i
$403$	−0.390530	−	2.21480i	−0.0194537	−	0.110327i
$404$	−3.96585			−0.197308
$405$	−12.1257			−0.602529
$406$	−10.7023			−0.531148
$407$	−1.34730	−	7.64090i	−0.0667830	−	0.378745i
$408$	−3.79813	+	0.669713i	−0.188036	+	0.0331558i
$409$	9.74257	−	3.54601i	0.481739	−	0.175339i	−0.0897236	−	0.995967i	$-0.528598\pi$
$409$	9.74257	−	3.54601i	0.481739	−	0.175339i	0.571463	+	0.820628i	$0.306376\pi$
$410$	−10.4534	−	8.77141i	−0.516255	−	0.433189i
$411$	−12.2041	−	33.5306i	−0.601986	−	1.65394i
$412$	−6.11721	−	2.22648i	−0.301373	−	0.109691i
$413$	4.67752	+	8.10170i	0.230166	+	0.398659i
$414$	18.5326	+	15.5507i	0.910825	+	0.764273i
$415$	−8.63816	+	14.9617i	−0.424030	+	0.734442i
$416$	1.17365	−	0.984808i	0.0575428	−	0.0482842i
$417$	−26.6088	+	15.3626i	−1.30304	+	0.752308i
$418$	−4.62449	+	26.2268i	−0.226191	+	1.28279i
$419$	1.87346	−	10.6249i	0.0915243	−	0.519060i	−0.904233	−	0.427040i	$-0.859556\pi$
$419$	1.87346	−	10.6249i	0.0915243	−	0.519060i	0.995757	−	0.0920203i	$-0.0293325\pi$
$420$	2.02094	+	1.16679i	0.0986120	+	0.0569337i
$421$	−2.16978	+	1.82066i	−0.105748	+	0.0887335i	−0.694129	−	0.719851i	$-0.744210\pi$
$421$	−2.16978	+	1.82066i	−0.105748	+	0.0887335i	0.588380	+	0.808584i	$0.299766\pi$
$422$	11.0594	−	19.1555i	0.538365	−	0.932475i
$423$	26.6614			1.29632
$424$	−0.663848	−	1.14982i	−0.0322393	−	0.0558401i
$425$	6.66385	+	2.42544i	0.323244	+	0.117651i
$426$	7.17159	+	1.26454i	0.347465	+	0.0612674i
$427$	−2.51501	−	2.11035i	−0.121710	−	0.102127i
$428$	6.51114	−	2.36986i	0.314728	−	0.114552i
$429$	8.11721	+	9.67372i	0.391903	+	0.467051i
$430$	2.04916	+	11.6214i	0.0988194	+	0.560433i
$431$	−19.2044			−0.925043			−0.462522	−	0.886608i	$-0.653055\pi$
$431$	−19.2044			−0.925043			−0.462522	+	0.886608i	$0.653055\pi$
$432$	−1.77719	+	4.88279i	−0.0855050	+	0.234923i
$433$	11.2986			0.542976			0.271488	−	0.962442i	$-0.412484\pi$
$433$	11.2986			0.542976			0.271488	+	0.962442i	$0.412484\pi$
$434$	−0.254900	−	1.44561i	−0.0122356	−	0.0693915i
$435$	8.54189	−	23.4686i	0.409552	−	1.12524i
$436$	−7.80453	+	2.84062i	−0.373769	+	0.136041i
$437$	34.5710	+	29.0085i	1.65376	+	1.38767i
$438$	−10.1220	+	12.0629i	−0.483646	+	0.576387i
$439$	34.4666	+	12.5448i	1.64500	+	0.598732i	0.987903	−	0.155072i	$-0.0495611\pi$
$439$	34.4666	+	12.5448i	1.64500	+	0.598732i	0.657099	+	0.753804i	$0.271783\pi$
$440$	3.20574	+	5.55250i	0.152828	+	0.264705i
$441$	2.81908	+	1.02606i	0.134242	+	0.0488600i
$442$	−1.70574	+	2.95442i	−0.0811336	+	0.140528i
$443$	−12.5307	+	10.5145i	−0.595354	+	0.499561i	−0.889948	−	0.456061i	$-0.849260\pi$
$443$	−12.5307	+	10.5145i	−0.595354	+	0.499561i	0.294595	+	0.955622i	$0.404815\pi$
$444$		−	2.82396i		−	0.134019i
$445$	−0.364837	+	2.06910i	−0.0172949	+	0.0980845i
$446$	3.43195	−	19.4636i	0.162508	−	0.921627i
$447$		−	13.9377i		−	0.659231i
$448$	0.766044	−	0.642788i	0.0361922	−	0.0303689i
$449$	14.8491	−	25.7194i	0.700773	−	1.21377i	−0.267423	−	0.963579i	$-0.586172\pi$
$449$	14.8491	−	25.7194i	0.700773	−	1.21377i	0.968196	−	0.250195i	$-0.0804946\pi$
$450$	7.31908	−	6.14144i	0.345025	−	0.289510i
$451$	−24.0993	−	41.7411i	−1.13479	−	1.96551i
$452$	−2.13903	−	0.778544i	−0.100612	−	0.0366196i
$453$	−13.1554	+	15.6780i	−0.618094	+	0.736616i
$454$	9.50253	+	7.97357i	0.445976	+	0.374218i
$455$	1.93969	−	0.705990i	0.0909342	−	0.0330973i
$456$	−3.31521	+	9.10846i	−0.155249	+	0.426543i
$457$	−5.86783	−	33.2781i	−0.274486	−	1.55668i	−0.740591	−	0.671956i	$-0.765454\pi$
$457$	−5.86783	−	33.2781i	−0.274486	−	1.55668i	0.466106	−	0.884729i	$-0.345657\pi$
$458$	−6.24628			−0.291870
$459$		−	11.5702i		−	0.540050i
$460$	10.8648			0.506576
$461$	−1.86942	−	10.6020i	−0.0870677	−	0.493785i	−0.996891	−	0.0787901i	$-0.974894\pi$
$461$	−1.86942	−	10.6020i	−0.0870677	−	0.493785i	0.909824	−	0.414995i	$-0.136217\pi$
$462$	5.29813	+	6.31407i	0.246491	+	0.293757i
$463$	31.7656	−	11.5617i	1.47627	−	0.537320i	0.526478	−	0.850189i	$-0.323512\pi$
$463$	31.7656	−	11.5617i	1.47627	−	0.537320i	0.949796	+	0.312869i	$0.101290\pi$
$464$	−8.19846	−	6.87933i	−0.380604	−	0.319365i
$465$	3.37346	+	0.594831i	0.156440	+	0.0275846i
$466$	−19.0817	−	6.94518i	−0.883944	−	0.321729i
$467$	0.798133	+	1.38241i	0.0369332	+	0.0639702i	0.883901	−	0.467674i	$-0.154908\pi$
$467$	0.798133	+	1.38241i	0.0369332	+	0.0639702i	−0.846968	+	0.531644i	$0.821574\pi$
$468$	2.29813	+	3.98048i	0.106231	+	0.183998i
$469$	1.35457	−	2.34618i	0.0625482	−	0.108337i
$470$	9.17230	−	7.69648i	0.423087	−	0.355012i
$471$	33.5517	+	19.3711i	1.54598	+	0.892574i
$472$	−1.62449	+	9.21291i	−0.0747730	+	0.424059i
$473$	−7.23783	+	41.0478i	−0.332796	+	1.88738i
$474$	4.80659	−	2.77509i	0.220774	−	0.127464i
$475$	13.6532	−	11.4564i	0.626450	−	0.525654i
$476$	−1.11334	+	1.92836i	−0.0510299	+	0.0883864i
$477$	3.74288	−	1.36230i	0.171375	−	0.0623753i
$478$	7.35369	+	12.7370i	0.336350	+	0.582575i
$479$	6.52734	+	2.37576i	0.298242	+	0.108551i	0.486807	−	0.873510i	$-0.338161\pi$
$479$	6.52734	+	2.37576i	0.298242	+	0.108551i	−0.188565	+	0.982061i	$0.560384\pi$
$480$	0.798133	+	2.19285i	0.0364296	+	0.100090i
$481$	−1.91353	−	1.60565i	−0.0872496	−	0.0732111i
$482$	−0.354570	+	0.129053i	−0.0161502	+	0.00587820i
$483$	13.7554	−	2.42544i	0.625891	−	0.110361i
$484$	2.02229	+	11.4690i	0.0919222	+	0.521317i
$485$	17.4388			0.791856
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−12.5621			−0.569244			−0.284622	−	0.958640i	$-0.591868\pi$
$487$	−12.5621			−0.569244			−0.284622	+	0.958640i	$0.591868\pi$
$488$	−0.570108	−	3.23324i	−0.0258076	−	0.146362i
$489$	17.8439	−	3.14636i	0.806929	−	0.142283i
$490$	1.26604	−	0.460802i	0.0571941	−	0.0208169i
$491$	24.6819	+	20.7105i	1.11388	+	0.934653i	0.998279	−	0.0586427i	$-0.0186773\pi$
$491$	24.6819	+	20.7105i	1.11388	+	0.934653i	0.115598	+	0.993296i	$0.463122\pi$
$492$	−6.00000	−	16.4849i	−0.270501	−	0.743195i
$493$	22.3935	+	8.15058i	1.00855	+	0.367083i
$494$	4.28699	+	7.42528i	0.192881	+	0.334079i
$495$	−18.0744	+	6.57856i	−0.812386	+	0.295684i
$496$	0.733956	−	1.27125i	0.0329556	−	0.0570807i
$497$	3.22075	−	2.70253i	0.144470	−	0.121225i
$498$	−19.2344	+	11.1050i	−0.861915	+	0.497627i
$499$	−5.18701	+	29.4170i	−0.232203	+	1.31689i	0.616223	+	0.787572i	$0.288662\pi$
$499$	−5.18701	+	29.4170i	−0.232203	+	1.31689i	−0.848426	+	0.529315i	$0.822449\pi$
$500$	1.91488	−	10.8598i	0.0856359	−	0.485666i
$501$	−33.8842	−	19.5630i	−1.51383	−	0.874012i
$502$	1.23783	−	1.03866i	0.0552469	−	0.0463576i
$503$	−8.54710	+	14.8040i	−0.381097	+	0.660079i	−0.991219	−	0.132228i	$-0.957787\pi$
$503$	−8.54710	+	14.8040i	−0.381097	+	0.660079i	0.610123	+	0.792307i	$0.291120\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−2.67159	−	4.62733i	−0.118884	−	0.205913i
$506$	36.0612	+	13.1252i	1.60312	+	0.583487i
$507$	−18.1707	−	3.20399i	−0.806990	−	0.142294i
$508$	−15.5437	−	13.0427i	−0.689640	−	0.578677i
$509$	−10.6061	+	3.86029i	−0.470106	+	0.171104i	−0.566200	−	0.824268i	$-0.691587\pi$
$509$	−10.6061	+	3.86029i	−0.470106	+	0.171104i	0.0960946	+	0.995372i	$0.469365\pi$
$510$	−3.34002	−	3.98048i	−0.147899	−	0.176259i
$511$	1.57873	+	8.95340i	0.0698387	+	0.396075i
$512$	1.00000			0.0441942
$513$	−25.1832	−	14.5395i	−1.11187	−	0.641936i
$514$	15.9162			0.702034
$515$	−1.52300	−	8.63738i	−0.0671116	−	0.380609i
$516$	−5.18866	+	14.2557i	−0.228418	+	0.627574i
$517$	39.7413	−	14.4646i	1.74782	−	0.636154i
$518$	−1.24897	−	1.04801i	−0.0548766	−	0.0460469i
$519$	−7.97730	+	9.50698i	−0.350165	+	0.417310i
$520$	1.93969	+	0.705990i	0.0850611	+	0.0309597i
$521$	−15.8696	−	27.4869i	−0.695259	−	1.20422i	−0.970093	−	0.242733i	$-0.921956\pi$
$521$	−15.8696	−	27.4869i	−0.695259	−	1.20422i	0.274834	−	0.961492i	$-0.411377\pi$
$522$	24.5954	−	20.6380i	1.07651	−	0.903300i
$523$	−10.5988	+	18.3576i	−0.463453	+	0.802724i	−0.999130	−	0.0416988i	$-0.986723\pi$
$523$	−10.5988	+	18.3576i	−0.463453	+	0.802724i	0.535677	+	0.844423i	$0.320056\pi$
$524$	0.907604	−	0.761570i	0.0396489	−	0.0332693i
$525$		−	5.51622i		−	0.240748i
$526$	−0.258770	+	1.46756i	−0.0112829	+	0.0639887i
$527$	−0.567581	+	3.21891i	−0.0247242	+	0.140218i
$528$			8.24243i			0.358706i
$529$	32.1976	−	27.0170i	1.39990	−	1.17465i
$530$	0.894400	−	1.54915i	0.0388503	−	0.0672906i
$531$	−26.3726	−	9.59883i	−1.14447	−	0.416554i
$532$	2.79813	+	4.84651i	0.121314	+	0.210123i
$533$	−14.5817	−	5.30731i	−0.631604	−	0.229885i
$534$	−1.73618	+	2.06910i	−0.0751317	+	0.0895385i
$535$	7.15136	+	6.00070i	0.309180	+	0.259433i
$536$	2.54576	−	0.926581i	0.109960	−	0.0400222i
$537$	3.92380	−	10.7806i	0.169324	−	0.465215i
$538$	1.36912	+	7.76466i	0.0590269	+	0.334758i
$539$	4.75877			0.204975
$540$	−6.89440	+	1.21567i	−0.296688	+	0.0523141i
$541$	38.7033			1.66398			0.831992	−	0.554788i	$-0.187201\pi$
$541$	38.7033			1.66398			0.831992	+	0.554788i	$0.187201\pi$
$542$	−0.624323	−	3.54071i	−0.0268170	−	0.152087i
$543$	−3.73231	−	4.44799i	−0.160169	−	0.190882i
$544$	−2.09240	+	0.761570i	−0.0897107	+	0.0326520i
$545$	−8.57192	−	7.19269i	−0.367181	−	0.308101i
$546$	2.61334	+	0.460802i	0.111841	+	0.0197205i
$547$	38.3264	+	13.9497i	1.63872	+	0.596445i	0.986814	−	0.161856i	$-0.0517481\pi$
$547$	38.3264	+	13.9497i	1.63872	+	0.596445i	0.651905	+	0.758301i	$0.273970\pi$
$548$	−10.3007	−	17.8413i	−0.440022	−	0.762141i
$549$	9.84936			0.420360
$550$	7.57785	−	13.1252i	0.323121	−	0.559661i
$551$	45.8808	−	38.4986i	1.95459	−	1.64009i
$552$	12.0963	+	6.98378i	0.514851	+	0.297250i
$553$	0.556437	−	3.15571i	0.0236621	−	0.134194i
$554$	−0.739008	+	4.19112i	−0.0313974	+	0.178064i
$555$	3.29498	−	1.90236i	0.139864	−	0.0807505i
$556$	−13.5890	+	11.4025i	−0.576302	+	0.483575i
$557$	3.53936	−	6.13036i	0.149968	−	0.259752i	−0.781248	−	0.624221i	$-0.785416\pi$
$557$	3.53936	−	6.13036i	0.149968	−	0.259752i	0.931215	+	0.364470i	$0.118750\pi$
$558$	3.37346	+	2.83067i	0.142810	+	0.119832i
$559$	6.70961	+	11.6214i	0.283786	+	0.491532i
$560$	1.26604	+	0.460802i	0.0535001	+	0.0194725i
$561$	−6.27719	−	17.2464i	−0.265023	−	0.728145i
$562$	−5.61515	−	4.71167i	−0.236861	−	0.198750i
$563$	14.1638	−	5.15522i	0.596935	−	0.217267i	−0.0258419	−	0.999666i	$-0.508227\pi$
$563$	14.1638	−	5.15522i	0.596935	−	0.217267i	0.622777	+	0.782399i	$0.286004\pi$
$564$	15.1591	−	2.67296i	0.638313	−	0.112552i
$565$	−0.532556	−	3.02027i	−0.0224048	−	0.127064i
$566$	28.2395			1.18699
$567$	−8.45723	+	3.07818i	−0.355170	+	0.129271i
$568$	4.20439			0.176412
$569$	−3.09286	−	17.5405i	−0.129660	−	0.735336i	−0.978431	−	0.206575i	$-0.933768\pi$
$569$	−3.09286	−	17.5405i	−0.129660	−	0.735336i	0.848771	−	0.528760i	$-0.177343\pi$
$570$	−12.8610	+	2.26774i	−0.538687	+	0.0949850i
$571$	−18.5719	+	6.75963i	−0.777211	+	0.282882i	−0.700009	−	0.714134i	$-0.746821\pi$
$571$	−18.5719	+	6.75963i	−0.777211	+	0.282882i	−0.0772016	+	0.997016i	$0.524598\pi$
$572$	5.58512	+	4.68647i	0.233526	+	0.195951i
$573$	−2.41622	−	6.63852i	−0.100939	−	0.277328i
$574$	−9.51754	−	3.46410i	−0.397254	−	0.144589i
$575$	−12.8414	−	22.2419i	−0.535522	−	0.927551i
$576$	−0.520945	+	2.95442i	−0.0217060	+	0.123101i
$577$	−7.05303	+	12.2162i	−0.293622	+	0.508568i	−0.974663	−	0.223677i	$-0.928194\pi$
$577$	−7.05303	+	12.2162i	−0.293622	+	0.508568i	0.681042	+	0.732245i	$0.261527\pi$
$578$	−9.22462	+	7.74038i	−0.383694	+	0.321957i
$579$	−5.70099	+	3.29147i	−0.236925	+	0.136789i
$580$	2.50387	−	14.2002i	0.103968	−	0.589629i
$581$	−2.22668	+	12.6281i	−0.0923783	+	0.523903i
$582$	19.4153	+	11.2095i	0.804792	+	0.464647i
$583$	4.84002	−	4.06126i	0.200453	−	0.168200i
$584$	−4.54576	+	7.87349i	−0.188105	+	0.325807i
$585$	−3.09627	+	5.36289i	−0.128015	+	0.221728i
$586$	−9.89440	−	17.1376i	−0.408734	−	0.707948i
$587$	−1.74035	−	0.633436i	−0.0718320	−	0.0261447i	0.305854	−	0.952078i	$-0.401058\pi$
$587$	−1.74035	−	0.633436i	−0.0718320	−	0.0261447i	−0.377686	+	0.925934i	$0.623280\pi$
$588$	1.70574	+	0.300767i	0.0703434	+	0.0124034i
$589$	6.29292	+	5.28039i	0.259295	+	0.217575i
$590$	−11.8439	+	4.31082i	−0.487605	+	0.177474i
$591$	18.9907	+	22.6322i	0.781172	+	0.930964i
$592$	−0.283119	−	1.60565i	−0.0116361	−	0.0659916i
$593$	12.1325			0.498221			0.249111	−	0.968475i	$-0.419862\pi$
$593$	12.1325			0.498221			0.249111	+	0.968475i	$0.419862\pi$
$594$	−24.3516	−	4.29385i	−0.999160	−	0.176179i
$595$	−3.00000			−0.122988
$596$	−1.39734	−	7.92469i	−0.0572371	−	0.324608i
$597$	5.29973	−	14.5609i	0.216903	−	0.595937i
$598$	11.6099	−	4.22567i	0.474766	−	0.172801i
$599$	−18.8523	−	15.8190i	−0.770286	−	0.646347i	0.170496	−	0.985358i	$-0.445463\pi$
$599$	−18.8523	−	15.8190i	−0.770286	−	0.646347i	−0.940782	+	0.339012i	$0.889907\pi$
$600$	3.54576	−	4.22567i	0.144755	−	0.172512i
$601$	6.14038	+	2.23491i	0.250471	+	0.0911641i	0.464205	−	0.885728i	$-0.346340\pi$
$601$	6.14038	+	2.23491i	0.250471	+	0.0911641i	−0.213734	+	0.976892i	$0.568562\pi$
$602$	4.37939	+	7.58532i	0.178490	+	0.309154i
$603$	1.41131	+	8.00395i	0.0574731	+	0.325946i
$604$	−5.90807	+	10.2331i	−0.240396	+	0.416378i
$605$	−12.0196	+	10.0856i	−0.488666	+	0.410040i
$606$		−	6.86906i		−	0.279036i
$607$	−2.79261	+	15.8377i	−0.113349	+	0.642832i	0.874206	+	0.485556i	$0.161383\pi$
$607$	−2.79261	+	15.8377i	−0.113349	+	0.642832i	−0.987555	+	0.157277i	$0.949728\pi$
$608$	−0.971782	+	5.51125i	−0.0394109	+	0.223511i
$609$		−	18.5370i		−	0.751157i
$610$	3.38847	−	2.84326i	0.137195	−	0.115120i
$611$	6.80793	−	11.7917i	0.275420	−	0.477041i
$612$	−1.15998	−	6.57856i	−0.0468893	−	0.265923i
$613$	21.2540	+	36.8130i	0.858442	+	1.48686i	0.873415	+	0.486977i	$0.161900\pi$
$613$	21.2540	+	36.8130i	0.858442	+	1.48686i	−0.0149729	+	0.999888i	$0.504766\pi$
$614$	−23.0881	−	8.40339i	−0.931761	−	0.339133i
$615$	15.1925	−	18.1058i	0.612622	−	0.730095i
$616$	3.64543	+	3.05888i	0.146879	+	0.123246i
$617$	14.2819	−	5.19820i	0.574969	−	0.209272i	−0.0381366	−	0.999273i	$-0.512142\pi$
$617$	14.2819	−	5.19820i	0.574969	−	0.209272i	0.613106	+	0.790001i	$0.289920\pi$
$618$	3.85638	−	10.5953i	0.155126	−	0.426206i
$619$	6.40074	+	36.3004i	0.257267	+	1.45904i	0.790185	+	0.612869i	$0.209985\pi$
$619$	6.40074	+	36.3004i	0.257267	+	1.45904i	−0.532917	+	0.846167i	$0.678904\pi$
$620$	1.97771			0.0794268
$621$	−26.9345	+	32.0993i	−1.08085	+	1.28810i
$622$	−11.0838			−0.444419
$623$	0.270792	+	1.53574i	0.0108491	+	0.0615281i
$624$	1.70574	+	2.03282i	0.0682841	+	0.0813779i
$625$	−1.00253	+	0.364890i	−0.0401010	+	0.0145956i
$626$	12.6361	+	10.6029i	0.505040	+	0.423779i
$627$	−45.4261	−	8.00984i	−1.81414	−	0.319882i
$628$	21.0189	+	7.65025i	0.838745	+	0.305278i
$629$	1.81521	+	3.14403i	0.0723771	+	0.125361i
$630$	−2.02094	+	3.50038i	−0.0805164	+	0.139458i
$631$	13.5069	−	23.3946i	0.537700	−	0.931323i	−0.461328	−	0.887230i	$-0.652627\pi$
$631$	13.5069	−	23.3946i	0.537700	−	0.931323i	0.999027	−	0.0440934i	$-0.0140399\pi$
$632$	2.45471	−	2.05974i	0.0976430	−	0.0819322i
$633$	33.1783	+	19.1555i	1.31872	+	0.761363i
$634$	−2.80406	+	15.9026i	−0.111364	+	0.631574i
$635$	4.74716	−	26.9225i	0.188385	−	1.06839i
$636$	1.99154	−	1.14982i	0.0789699	−	0.0455933i
$637$	1.17365	−	0.984808i	0.0465016	−	0.0390195i
$638$	25.4650	−	44.1066i	1.00817	−	1.74620i
$639$	−2.19026	+	12.4216i	−0.0866452	+	0.491389i
$640$	0.673648	+	1.16679i	0.0266283	+	0.0461215i
$641$	−25.1088	−	9.13884i	−0.991736	−	0.360962i	−0.205344	−	0.978690i	$-0.565831\pi$
$641$	−25.1088	−	9.13884i	−0.991736	−	0.360962i	−0.786392	+	0.617727i	$0.788054\pi$
$642$	4.10472	+	11.2776i	0.162000	+	0.445093i
$643$	32.5638	+	27.3242i	1.28419	+	1.07756i	0.992652	+	0.121004i	$0.0386113\pi$
$643$	32.5638	+	27.3242i	1.28419	+	1.07756i	0.291538	+	0.956559i	$0.405833\pi$
$644$	7.57785	−	2.75811i	0.298609	−	0.108685i
$645$	−20.1288	+	3.54925i	−0.792572	+	0.139752i
$646$	−2.16385	−	12.2718i	−0.0851355	−	0.482827i
$647$	19.6887			0.774043			0.387022	−	0.922071i	$-0.373504\pi$
$647$	19.6887			0.774043			0.387022	+	0.922071i	$0.373504\pi$
$648$	−8.45723	−	3.07818i	−0.332232	−	0.120922i
$649$	−44.5185			−1.74750
$650$	−0.847296	−	4.80526i	−0.0332337	−	0.188478i
$651$	2.50387	−	0.441500i	0.0981344	−	0.0173037i
$652$	9.83022	−	3.57791i	0.384981	−	0.140122i
$653$	−3.45652	−	2.90036i	−0.135264	−	0.113500i	0.572646	−	0.819803i	$-0.305917\pi$
$653$	−3.45652	−	2.90036i	−0.135264	−	0.113500i	−0.707910	+	0.706303i	$0.750362\pi$
$654$	−4.92009	−	13.5178i	−0.192391	−	0.528589i
$655$	1.50000	+	0.545955i	0.0586098	+	0.0213322i
$656$	−5.06418	−	8.77141i	−0.197723	−	0.342466i
$657$	−20.8935	−	17.5317i	−0.815134	−	0.683979i
$658$	4.44356	−	7.69648i	0.173228	−	0.300040i
$659$	−24.0260	+	20.1602i	−0.935920	+	0.785330i	−0.976871	−	0.213831i	$-0.931406\pi$
$659$	−24.0260	+	20.1602i	−0.935920	+	0.785330i	0.0409507	+	0.999161i	$0.486961\pi$
$660$	−9.61721	+	5.55250i	−0.374349	+	0.216131i
$661$	−7.51754	+	42.6341i	−0.292398	+	1.65827i	0.385193	+	0.922836i	$0.374135\pi$
$661$	−7.51754	+	42.6341i	−0.292398	+	1.65827i	−0.677592	+	0.735438i	$0.736976\pi$
$662$	1.00253	−	5.68561i	0.0389643	−	0.220977i
$663$	−5.11721	−	2.95442i	−0.198736	−	0.114740i
$664$	−9.82295	+	8.24243i	−0.381204	+	0.319868i
$665$	−3.76991	+	6.52968i	−0.146191	+	0.253210i
$666$	4.89124			0.189532
$667$	−43.1528	−	74.7428i	−1.67088	−	2.89405i
$668$	−21.2271	−	7.72605i	−0.821303	−	0.298930i
$669$	33.7119	+	5.94431i	1.30338	+	0.229820i
$670$	2.79607	+	2.34618i	0.108022	+	0.0906410i
$671$	14.6814	−	5.34359i	0.566769	−	0.206287i
$672$	1.11334	+	1.32683i	0.0429481	+	0.0511835i
$673$	7.77425	+	44.0900i	0.299675	+	1.69954i	0.647567	+	0.762009i	$0.275787\pi$
$673$	7.77425	+	44.0900i	0.299675	+	1.69954i	−0.347891	+	0.937535i	$0.613102\pi$
$674$	−20.7392			−0.798843
$675$	10.6373	+	12.6770i	0.409429	+	0.487939i
$676$	−10.6527			−0.409719
$677$	5.02094	+	28.4752i	0.192971	+	1.09439i	0.915279	+	0.402820i	$0.131970\pi$
$677$	5.02094	+	28.4752i	0.192971	+	1.09439i	−0.722309	+	0.691571i	$0.756919\pi$
$678$	1.34848	−	3.70491i	0.0517880	−	0.142286i
$679$	12.1630	−	4.42696i	0.466772	−	0.169891i
$680$	−2.29813	−	1.92836i	−0.0881294	−	0.0739493i
$681$	−13.8106	+	16.4589i	−0.529224	+	0.630705i
$682$	6.56418	+	2.38917i	0.251355	+	0.0914859i
$683$	−4.69594	−	8.13360i	−0.179685	−	0.311224i	0.762088	−	0.647474i	$-0.224175\pi$
$683$	−4.69594	−	8.13360i	−0.179685	−	0.311224i	−0.941773	+	0.336250i	$0.890841\pi$
$684$	−15.7763	−	5.74211i	−0.603222	−	0.219555i
$685$	13.8780	−	24.0375i	0.530253	−	0.918425i
$686$	0.766044	−	0.642788i	0.0292477	−	0.0245417i
$687$		−	10.8189i		−	0.412766i
$688$	−1.52094	+	8.62571i	−0.0579855	+	0.328852i
$689$	0.353226	−	2.00324i	0.0134568	−	0.0763176i
$690$			18.8185i			0.716406i
$691$	−11.4153	+	9.57861i	−0.434260	+	0.364388i	−0.833556	−	0.552434i	$-0.813699\pi$
$691$	−11.4153	+	9.57861i	−0.434260	+	0.364388i	0.399296	+	0.916822i	$0.369255\pi$
$692$	−3.58260	+	6.20524i	−0.136190	+	0.235888i
$693$	−10.9363	+	9.17664i	−0.415435	+	0.348592i
$694$	−1.52481	−	2.64106i	−0.0578812	−	0.100253i
$695$	−22.4586	−	8.17425i	−0.851902	−	0.310067i
$696$	11.9153	−	14.2002i	0.451650	−	0.538255i
$697$	17.2763	+	14.4965i	0.654387	+	0.549096i
$698$	5.93882	−	2.16155i	0.224787	−	0.0818159i
$699$	12.0294	−	33.0505i	0.454994	−	1.25008i
$700$	−0.553033	−	3.13641i	−0.0209027	−	0.118545i
$701$	29.4861			1.11367			0.556837	−	0.830622i	$-0.312015\pi$
$701$	29.4861			1.11367			0.556837	+	0.830622i	$0.312015\pi$
$702$	−6.89440	+	3.98048i	−0.260212	+	0.150234i
$703$	9.12424			0.344127
$704$	0.826352	+	4.68647i	0.0311443	+	0.176628i
$705$	13.3307	+	15.8869i	0.502063	+	0.598335i
$706$	2.27332	−	0.827420i	0.0855575	−	0.0311404i
$707$	−3.03802	−	2.54920i	−0.114256	−	0.0958725i
$708$	−15.9572	−	2.81369i	−0.599710	−	0.105745i
$709$	−5.88666	−	2.14257i	−0.221078	−	0.0804659i	0.229106	−	0.973401i	$-0.426420\pi$
$709$	−5.88666	−	2.14257i	−0.221078	−	0.0804659i	−0.450185	+	0.892936i	$0.648642\pi$
$710$	2.83228	+	4.90566i	0.106294	+	0.184106i
$711$	4.80659	+	8.32526i	0.180261	+	0.312222i
$712$	−0.779715	+	1.35051i	−0.0292211	+	0.0506124i
$713$	9.06805	−	7.60900i	0.339601	−	0.284959i
$714$	−3.34002	−	1.92836i	−0.124997	−	0.0721672i
$715$	−1.70574	+	9.67372i	−0.0637909	+	0.361776i
$716$	1.15018	−	6.52298i	0.0429841	−	0.243775i
$717$	−22.0611	+	12.7370i	−0.823886	+	0.475671i
$718$	−3.76991	+	3.16333i	−0.140692	+	0.118055i
$719$	−15.0484	+	26.0647i	−0.561212	+	0.972048i	0.436179	+	0.899860i	$0.356332\pi$
$719$	−15.0484	+	26.0647i	−0.561212	+	0.972048i	−0.997391	+	0.0721883i	$0.977002\pi$
$720$	−3.79813	+	1.38241i	−0.141548	+	0.0515193i
$721$	−3.25490	−	5.63765i	−0.121219	−	0.209957i
$722$	−11.5753	−	4.21307i	−0.430789	−	0.156794i
$723$	−0.223526	−	0.614134i	−0.00831304	−	0.0228399i
$724$	−2.56805	−	2.15485i	−0.0954408	−	0.0800843i
$725$	−32.0292	+	11.6577i	−1.18953	+	0.432955i
$726$	−19.8648	+	3.50271i	−0.737253	+	0.129998i
$727$	4.42824	+	25.1138i	0.164234	+	0.931420i	0.949850	+	0.312705i	$0.101235\pi$
$727$	4.42824	+	25.1138i	0.164234	+	0.931420i	−0.785616	+	0.618715i	$0.787654\pi$
$728$	1.53209			0.0567830
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−12.2490			−0.453355
$731$	−3.38666	−	19.2067i	−0.125260	−	0.710385i
$732$	5.60014	−	0.987455i	0.206987	−	0.0364974i
$733$	12.2747	−	4.46761i	0.453375	−	0.165015i	−0.105232	−	0.994448i	$-0.533558\pi$
$733$	12.2747	−	4.46761i	0.453375	−	0.165015i	0.558607	+	0.829433i	$0.311336\pi$
$734$	−5.54782	−	4.65517i	−0.204774	−	0.171826i
$735$	0.798133	+	2.19285i	0.0294396	+	0.0808846i
$736$	7.57785	+	2.75811i	0.279323	+	0.101665i
$737$	6.44609	+	11.1650i	0.237445	+	0.411266i
$738$	28.5526	−	10.3923i	1.05104	−	0.382546i
$739$	6.40554	−	11.0947i	0.235632	−	0.408126i	−0.723824	−	0.689984i	$-0.757617\pi$
$739$	6.40554	−	11.0947i	0.235632	−	0.408126i	0.959456	+	0.281858i	$0.0909507\pi$
$740$	1.68273	−	1.41198i	0.0618585	−	0.0519054i
$741$	−12.8610	+	7.42528i	−0.472459	+	0.272775i
$742$	0.230552	−	1.30753i	0.00846383	−	0.0480008i
$743$	−7.74494	+	43.9237i	−0.284134	+	1.61141i	0.424228	+	0.905556i	$0.360546\pi$
$743$	−7.74494	+	43.9237i	−0.284134	+	1.61141i	−0.708362	+	0.705850i	$0.750565\pi$
$744$	2.20187	+	1.27125i	0.0807243	+	0.0466062i
$745$	8.30516	−	6.96886i	0.304277	−	0.255319i
$746$	7.29813	−	12.6407i	0.267204	−	0.462810i
$747$	−19.2344	−	33.3150i	−0.703751	−	1.21893i
$748$	−5.29813	−	9.17664i	−0.193719	−	0.335531i
$749$	6.51114	+	2.36986i	0.237912	+	0.0865929i
$750$	18.8097	+	3.31667i	0.686835	+	0.121107i
$751$	−8.34208	−	6.99984i	−0.304407	−	0.255428i	0.477769	−	0.878486i	$-0.341446\pi$
$751$	−8.34208	−	6.99984i	−0.304407	−	0.255428i	−0.782176	+	0.623058i	$0.785890\pi$
$752$	8.35117	−	3.03958i	0.304536	−	0.110842i
$753$	1.79901	+	2.14398i	0.0655596	+	0.0781309i
$754$	−2.84730	−	16.1478i	−0.103692	−	0.588069i
$755$	−15.9198			−0.579382
$756$	−4.50000	+	2.59808i	−0.163663	+	0.0944911i
$757$	29.8658			1.08549			0.542745	−	0.839898i	$-0.317385\pi$
$757$	29.8658			1.08549			0.542745	+	0.839898i	$0.317385\pi$
$758$	−1.00980	−	5.72686i	−0.0366776	−	0.208009i
$759$	−22.7335	+	62.4599i	−0.825175	+	2.26715i
$760$	−7.08512	+	2.57877i	−0.257004	+	0.0935420i
$761$	32.1935	+	27.0135i	1.16701	+	0.979240i	0.999977	−	0.00671144i	$-0.00213633\pi$
$761$	32.1935	+	27.0135i	1.16701	+	0.979240i	0.167035	+	0.985951i	$0.446581\pi$
$762$	22.5906	−	26.9225i	0.818373	−	0.975298i
$763$	−7.80453	−	2.84062i	−0.282543	−	0.102837i
$764$	−2.03936	−	3.53228i	−0.0737816	−	0.127793i
$765$	6.89440	−	5.78509i	0.249268	−	0.209160i
$766$	13.1498	−	22.7761i	0.475120	−	0.822933i
$767$	−10.9795	+	9.21291i	−0.396448	+	0.332659i
$768$			1.73205i			0.0625000i
$769$	−5.74897	+	32.6040i	−0.207313	+	1.17573i	0.686445	+	0.727182i	$0.259170\pi$
$769$	−5.74897	+	32.6040i	−0.207313	+	1.17573i	−0.893758	+	0.448550i	$0.851941\pi$
$770$	−1.11334	+	6.31407i	−0.0401220	+	0.227543i
$771$			27.5677i			0.992827i
$772$	−2.91147	+	2.44302i	−0.104786	+	0.0879261i
$773$	14.6186	−	25.3201i	0.525793	−	0.910700i	−0.473756	−	0.880656i	$-0.657102\pi$
$773$	14.6186	−	25.3201i	0.525793	−	0.910700i	0.999549	−	0.0300437i	$-0.00956464\pi$
$774$	−24.6917	−	8.98703i	−0.887523	−	0.323032i
$775$	−2.33750	−	4.04866i	−0.0839653	−	0.145432i
$776$	12.1630	+	4.42696i	0.436625	+	0.158919i
$777$	1.81521	−	2.16328i	0.0651202	−	0.0776072i
$778$	−28.5763	−	23.9783i	−1.02451	−	0.859665i
$779$	53.2627	−	19.3860i	1.90833	−	0.694577i
$780$	−1.22281	+	3.35965i	−0.0437837	+	0.120295i
$781$	3.47431	+	19.7038i	0.124321	+	0.705057i
$782$	−17.9564			−0.642118
$783$	35.7460	+	42.6005i	1.27746	+	1.52242i
$784$	1.00000			0.0357143
$785$	5.23308	+	29.6783i	0.186777	+	1.05926i
$786$	1.31908	+	1.57202i	0.0470499	+	0.0560719i
$787$	−43.3858	+	15.7912i	−1.54654	+	0.562894i	−0.967602	−	0.252479i	$-0.918754\pi$
$787$	−43.3858	+	15.7912i	−1.54654	+	0.562894i	−0.578936	+	0.815373i	$0.696532\pi$
$788$	13.0667	+	10.9643i	0.465482	+	0.390586i
$789$	−2.54189	−	0.448204i	−0.0904936	−	0.0159565i
$790$	4.05690	+	1.47659i	0.144338	+	0.0525348i
$791$	−1.13816	−	1.97134i	−0.0404682	−	0.0700929i
$792$	−14.2763			−0.507287
$793$	2.51501	−	4.35613i	0.0893108	−	0.154691i
$794$	−22.8674	+	19.1880i	−0.811532	+	0.680957i
$795$	2.68320	+	1.54915i	0.0951633	+	0.0549426i
$796$	1.55350	−	8.81034i	0.0550624	−	0.312274i
$797$	−3.89322	+	22.0795i	−0.137905	+	0.782097i	0.834888	+	0.550420i	$0.185532\pi$
$797$	−3.89322	+	22.0795i	−0.137905	+	0.782097i	−0.972793	+	0.231677i	$0.925579\pi$
$798$	−8.39440	+	4.84651i	−0.297159	+	0.171565i
$799$	−15.1591	+	12.7200i	−0.536290	+	0.450001i
$800$	1.59240	−	2.75811i	0.0562997	−	0.0975140i
$801$	−3.58378	−	3.00715i	−0.126627	−	0.106252i
$802$	−7.93289	−	13.7402i	−0.280120	−	0.485182i
$803$	−40.6553	−	14.7973i	−1.43469	−	0.522186i
$804$	1.60488	+	4.40938i	0.0565999	+	0.155507i
$805$	8.32295	+	6.98378i	0.293345	+	0.246146i
$806$	2.11334	−	0.769193i	0.0744393	−	0.0270937i
$807$	−13.4488	+	2.37138i	−0.473419	+	0.0834766i
$808$	−0.688663	−	3.90560i	−0.0242271	−	0.137399i
$809$	40.7452			1.43252			0.716262	−	0.697832i	$-0.245852\pi$
$809$	40.7452			1.43252			0.716262	+	0.697832i	$0.245852\pi$
$810$	−2.10560	−	11.9415i	−0.0739832	−	0.419580i
$811$	−7.31820			−0.256977			−0.128488	−	0.991711i	$-0.541013\pi$
$811$	−7.31820			−0.256977			−0.128488	+	0.991711i	$0.541013\pi$
$812$	−1.85844	−	10.5397i	−0.0652185	−	0.369872i
$813$	6.13269	−	1.08136i	0.215083	−	0.0379249i
$814$	7.29086	−	2.65366i	0.255544	−	0.0930106i
$815$	10.7968	+	9.05958i	0.378195	+	0.317343i
$816$	−1.31908	−	3.62414i	−0.0461770	−	0.126870i
$817$	−46.0604	−	16.7646i	−1.61145	−	0.586519i
$818$	5.18392	+	8.97880i	0.181251	+	0.313937i
$819$	−0.798133	+	4.52644i	−0.0278890	+	0.158167i
$820$	6.82295	−	11.8177i	0.238268	−	0.412692i
$821$	3.34065	−	2.80314i	0.116590	−	0.0978302i	−0.582629	−	0.812738i	$-0.697976\pi$
$821$	3.34065	−	2.80314i	0.116590	−	0.0978302i	0.699218	+	0.714908i	$0.253531\pi$
$822$	30.9020	−	17.8413i	1.07783	−	0.622286i
$823$	7.00933	−	39.7519i	0.244330	−	1.38566i	−0.577714	−	0.816240i	$-0.696055\pi$
$823$	7.00933	−	39.7519i	0.244330	−	1.38566i	0.822044	−	0.569425i	$-0.192834\pi$
$824$	1.13041	−	6.41090i	0.0393799	−	0.223334i
$825$	22.7335	+	13.1252i	0.791480	+	0.456961i
$826$	−7.16637	+	6.01330i	−0.249350	+	0.209230i
$827$	−0.449493	+	0.778544i	−0.0156304	+	0.0270726i	−0.873735	−	0.486403i	$-0.838309\pi$
$827$	−0.449493	+	0.778544i	−0.0156304	+	0.0270726i	0.858104	+	0.513475i	$0.171642\pi$
$828$	−12.0963	+	20.9513i	−0.420374	+	0.728110i
$829$	−5.37733	−	9.31380i	−0.186762	−	0.323482i	0.757407	−	0.652943i	$-0.226466\pi$
$829$	−5.37733	−	9.31380i	−0.186762	−	0.323482i	−0.944169	+	0.329462i	$0.893133\pi$
$830$	−16.2344	−	5.90885i	−0.563505	−	0.205099i
$831$	−7.25924	−	1.28000i	−0.251820	−	0.0444027i
$832$	1.17365	+	0.984808i	0.0406889	+	0.0341421i
$833$	−2.09240	+	0.761570i	−0.0724972	+	0.0263868i
$834$	−19.7497	−	23.5368i	−0.683878	−	0.815014i
$835$	−5.28493	−	29.9723i	−0.182893	−	1.03724i
$836$	−26.6313			−0.921064
$837$	−4.90286	+	5.84300i	−0.169467	+	0.201963i
$838$	10.7888			0.372693
$839$	−2.26352	−	12.8370i	−0.0781453	−	0.443184i	−0.998626	−	0.0523969i	$-0.983314\pi$
$839$	−2.26352	−	12.8370i	−0.0781453	−	0.443184i	0.920481	−	0.390787i	$-0.127797\pi$
$840$	−0.798133	+	2.19285i	−0.0275382	+	0.0756606i
$841$	−80.3813	+	29.2564i	−2.77177	+	1.00884i
$842$	−2.16978	−	1.82066i	−0.0747755	−	0.0627441i
$843$	8.16085	−	9.72573i	0.281075	−	0.334972i
$844$	20.7849	+	7.56510i	0.715447	+	0.260401i
$845$	−7.17617	−	12.4295i	−0.246868	−	0.427588i
$846$	4.62970	+	26.2563i	0.159172	+	0.902711i
$847$	−5.82295	+	10.0856i	−0.200079	+	0.346547i
$848$	1.01707	−	0.853427i	0.0349265	−	0.0293068i
$849$			48.9122i			1.67866i
$850$	−1.23143	+	6.98378i	−0.0422377	+	0.239542i
$851$	2.28312	−	12.9482i	0.0782643	−	0.443859i
$852$			7.28222i			0.249485i
$853$	27.5692	−	23.1333i	0.943952	−	0.792070i	−0.0343163	−	0.999411i	$-0.510925\pi$
$853$	27.5692	−	23.1333i	0.943952	−	0.792070i	0.978269	+	0.207341i	$0.0664809\pi$
$854$	1.64156	−	2.84326i	0.0561730	−	0.0972945i
$855$	−3.92783	−	22.2758i	−0.134329	−	0.761818i
$856$	3.46451	+	6.00070i	0.118414	+	0.205100i
$857$	−9.00000	−	3.27573i	−0.307434	−	0.111897i	0.183696	−	0.982983i	$-0.441194\pi$
$857$	−9.00000	−	3.27573i	−0.307434	−	0.111897i	−0.491130	+	0.871086i	$0.663416\pi$
$858$	−8.11721	+	9.67372i	−0.277117	+	0.330255i
$859$	−5.50521	−	4.61942i	−0.187835	−	0.157613i	0.544021	−	0.839072i	$-0.316901\pi$
$859$	−5.50521	−	4.61942i	−0.187835	−	0.157613i	−0.731856	+	0.681459i	$0.761346\pi$
$860$	−11.0890	+	4.03606i	−0.378132	+	0.137629i
$861$	6.00000	−	16.4849i	0.204479	−	0.561803i
$862$	−3.33481	−	18.9126i	−0.113584	−	0.644167i
$863$	30.0969			1.02451			0.512255	−	0.858833i	$-0.328810\pi$
$863$	30.0969			1.02451			0.512255	+	0.858833i	$0.328810\pi$
$864$	−5.11721	−	0.902302i	−0.174091	−	0.0306970i
$865$	−9.65364			−0.328234
$866$	1.96198	+	11.1269i	0.0666708	+	0.378109i
$867$	−13.4067	−	15.9775i	−0.455316	−	0.542625i
$868$	1.37939	−	0.502055i	0.0468194	−	0.0170409i
$869$	11.6814	+	9.80185i	0.396264	+	0.332505i
$870$	24.5954	+	4.33683i	0.833862	+	0.147032i
$871$	3.90033	+	1.41960i	0.132158	+	0.0481014i
$872$	−4.15270	−	7.19269i	−0.140628	−	0.243575i
$873$	−19.4153	+	33.6284i	−0.657110	+	1.13815i
$874$	−22.5646	+	39.0831i	−0.763260	+	1.32201i
$875$	8.44743	−	7.08824i	0.285575	−	0.239626i
$876$	−13.6373	−	7.87349i	−0.460761	−	0.266020i
$877$	−0.713422	+	4.04601i	−0.0240905	+	0.136624i	−0.994481	−	0.104918i	$-0.966542\pi$
$877$	−0.713422	+	4.04601i	−0.0240905	+	0.136624i	0.970390	+	0.241542i	$0.0776532\pi$
$878$	−6.36917	+	36.1214i	−0.214949	+	1.21904i
$879$	29.6832	−	17.1376i	1.00119	−	0.578037i
$880$	−4.91147	+	4.12122i	−0.165566	+	0.138926i
$881$	−10.1848	+	17.6406i	−0.343134	+	0.594326i	−0.985013	−	0.172480i	$-0.944822\pi$
$881$	−10.1848	+	17.6406i	−0.343134	+	0.594326i	0.641879	+	0.766806i	$0.278155\pi$
$882$	−0.520945	+	2.95442i	−0.0175411	+	0.0994806i
$883$	−13.9222	−	24.1140i	−0.468520	−	0.811500i	0.530833	−	0.847476i	$-0.321879\pi$
$883$	−13.9222	−	24.1140i	−0.468520	−	0.811500i	−0.999353	+	0.0359767i	$0.988546\pi$
$884$	−3.20574	−	1.16679i	−0.107821	−	0.0392435i
$885$	−7.46657	−	20.5142i	−0.250986	−	0.689578i
$886$	−12.5307	−	10.5145i	−0.420979	−	0.353243i
$887$	−53.7144	+	19.5504i	−1.80355	+	0.656440i	−0.805602	+	0.592456i	$0.798158\pi$
$887$	−53.7144	+	19.5504i	−1.80355	+	0.656440i	−0.997951	+	0.0639833i	$0.979620\pi$
$888$	2.78106	−	0.490376i	0.0933262	−	0.0164559i
$889$	−3.52347	−	19.9826i	−0.118173	−	0.670195i
$890$	−2.10101			−0.0704262
$891$	7.43717	−	42.1783i	0.249154	−	1.41303i
$892$	19.7638			0.661742
$893$	8.63634	+	48.9791i	0.289004	+	1.63902i
$894$	13.7260	−	2.42026i	0.459065	−	0.0809455i
$895$	8.38578	−	3.05217i	0.280306	−	0.102023i
$896$	0.766044	+	0.642788i	0.0255917	+	0.0214740i
$897$	7.31908	+	20.1090i	0.244377	+	0.671420i
$898$	27.9072	+	10.1574i	0.931275	+	0.338956i
$899$	−7.85504	−	13.6053i	−0.261980	−	0.453763i
$900$	7.31908	+	6.14144i	0.243969	+	0.204715i
$901$	−1.47818	+	2.56028i	−0.0492453	+	0.0852953i
$902$	36.9222	−	30.9814i	1.22938	−	1.03157i
$903$	−13.1382	+	7.58532i	−0.437210	+	0.252424i
$904$	0.395277	−	2.24173i	0.0131467	−	0.0745588i
$905$	0.784301	−	4.44799i	0.0260710	−	0.147856i
$906$	−17.7242	−	10.2331i	−0.588847	−	0.339971i
$907$	−15.7556	+	13.2205i	−0.523157	+	0.438981i	−0.865731	−	0.500510i	$-0.833146\pi$
$907$	−15.7556	+	13.2205i	−0.523157	+	0.438981i	0.342574	+	0.939491i	$0.388701\pi$
$908$	−6.20233	+	10.7428i	−0.205832	+	0.356511i
$909$	11.8976			0.394617
$910$	1.03209	+	1.78763i	0.0342134	+	0.0592594i
$911$	−50.9322	−	18.5378i	−1.68746	−	0.614185i	−0.693156	−	0.720787i	$-0.743780\pi$
$911$	−50.9322	−	18.5378i	−1.68746	−	0.614185i	−0.994302	+	0.106603i	$0.966003\pi$
$912$	−9.54576	−	1.68317i	−0.316092	−	0.0557355i
$913$	−46.7452	−	39.2238i	−1.54704	−	1.29812i
$914$	31.7536	−	11.5574i	1.05032	−	0.382284i
$915$	4.92468	+	5.86900i	0.162805	+	0.194023i
$916$	−1.08466	−	6.15139i	−0.0358380	−	0.203248i
$917$	1.18479			0.0391253
$918$	11.3944	−	2.00914i	0.376071	−	0.0663115i
$919$	−8.26083			−0.272500			−0.136250	−	0.990675i	$-0.543505\pi$
$919$	−8.26083			−0.272500			−0.136250	+	0.990675i	$0.543505\pi$
$920$	1.88666	+	10.6998i	0.0622013	+	0.352761i
$921$	14.5551	−	39.9898i	0.479607	−	1.31771i
$922$	10.1163	−	3.68204i	0.333164	−	0.121262i
$923$	4.93448	+	4.14052i	0.162420	+	0.136287i
$924$	−5.29813	+	6.31407i	−0.174296	+	0.207718i
$925$	−4.87939	−	1.77595i	−0.160433	−	0.0583929i
$926$	16.9021	+	29.2754i	0.555439	+	0.962048i
$927$	18.3516	+	6.67945i	0.602747	+	0.219382i
$928$	5.35117	−	9.26849i	0.175661	−	0.304253i
$929$	24.0266	−	20.1607i	0.788288	−	0.661452i	−0.157033	−	0.987593i	$-0.550193\pi$
$929$	24.0266	−	20.1607i	0.788288	−	0.661452i	0.945321	+	0.326141i	$0.105748\pi$
$930$			3.42550i			0.112326i
$931$	−0.971782	+	5.51125i	−0.0318489	+	0.180624i
$932$	3.52616	−	19.9978i	0.115503	−	0.655051i
$933$		−	19.1977i		−	0.628503i
$934$	−1.22281	+	1.02606i	−0.0400116	+	0.0335737i
$935$	7.13816	−	12.3636i	0.233443	−	0.404335i
$936$	−3.52094	+	2.95442i	−0.115086	+	0.0965683i
$937$	−1.63903	−	2.83889i	−0.0535449	−	0.0927424i	0.838011	−	0.545654i	$-0.183719\pi$
$937$	−1.63903	−	2.83889i	−0.0535449	−	0.0927424i	−0.891555	+	0.452911i	$0.850385\pi$
$938$	2.54576	+	0.926581i	0.0831220	+	0.0302539i
$939$	−18.3648	+	21.8864i	−0.599314	+	0.714234i
$940$	9.17230	+	7.69648i	0.299168	+	0.251031i
$941$	22.1088	−	8.04693i	0.720725	−	0.262322i	0.0444914	−	0.999010i	$-0.485833\pi$
$941$	22.1088	−	8.04693i	0.720725	−	0.262322i	0.676233	+	0.736687i	$0.263611\pi$
$942$	−13.2506	+	36.4058i	−0.431729	+	1.18616i
$943$	−14.1830	−	80.4360i	−0.461863	−	2.61936i
$944$	−9.35504			−0.304481
$945$	−6.06283	−	3.50038i	−0.197224	−	0.113867i
$946$	−41.6810			−1.35517
$947$	−8.74840	−	49.6146i	−0.284285	−	1.61226i	−0.707829	−	0.706384i	$-0.750325\pi$
$947$	−8.74840	−	49.6146i	−0.284285	−	1.61226i	0.423545	−	0.905875i	$-0.360786\pi$
$948$	3.56758	+	4.25168i	0.115870	+	0.138088i
$949$	−13.0890	+	4.76400i	−0.424887	+	0.154646i
$950$	13.6532	+	11.4564i	0.442967	+	0.371694i
$951$	−27.5442	−	4.85678i	−0.893181	−	0.157492i
$952$	−2.09240	−	0.761570i	−0.0678150	−	0.0246826i
$953$	−7.29767	−	12.6399i	−0.236395	−	0.409447i	0.723282	−	0.690552i	$-0.242632\pi$
$953$	−7.29767	−	12.6399i	−0.236395	−	0.409447i	−0.959677	+	0.281105i	$0.909299\pi$
$954$	1.99154	+	3.44946i	0.0644786	+	0.111680i
$955$	2.74763	−	4.75903i	0.0889111	−	0.153999i
$956$	−11.2665	+	9.45373i	−0.364385	+	0.305755i
$957$	76.3949	+	44.1066i	2.46950	+	1.42576i
$958$	−1.20620	+	6.84072i	−0.0389707	+	0.221014i
$959$	3.57738	−	20.2883i	0.115520	−	0.655145i
$960$	−2.02094	+	1.16679i	−0.0652257	+	0.0376581i
$961$	−22.0967	+	18.5414i	−0.712798	+	0.598108i
$962$	1.24897	−	2.16328i	0.0402684	−	0.0697469i
$963$	−19.5334	+	7.10959i	−0.629456	+	0.229103i
$964$	−0.188663	−	0.326774i	−0.00607642	−	0.0105247i
$965$	−4.81180	−	1.75135i	−0.154897	−	0.0563781i
$966$	4.77719	+	13.1252i	0.153704	+	0.422297i
$967$	−21.5271	−	18.0634i	−0.692265	−	0.580879i	0.227297	−	0.973826i	$-0.427011\pi$
$967$	−21.5271	−	18.0634i	−0.692265	−	0.580879i	−0.919561	+	0.392947i	$0.871456\pi$
$968$	−10.9436	+	3.98313i	−0.351739	+	0.128023i
$969$	21.2554	−	3.74789i	0.682821	−	0.120400i
$970$	3.02822	+	17.1739i	0.0972302	+	0.551420i
$971$	51.4671			1.65166			0.825829	−	0.563921i	$-0.190708\pi$
$971$	51.4671			1.65166			0.825829	+	0.563921i	$0.190708\pi$
$972$	5.33157	−	14.6484i	0.171010	−	0.469846i
$973$	−17.7392			−0.568692
$974$	−2.18139	−	12.3713i	−0.0698962	−	0.396401i
$975$	8.32295	−	1.46756i	0.266548	−	0.0469995i
$976$	3.08512	−	1.12289i	0.0987524	−	0.0359429i
$977$	−28.3273	−	23.7694i	−0.906270	−	0.760451i	0.0651356	−	0.997876i	$-0.479252\pi$
$977$	−28.3273	−	23.7694i	−0.906270	−	0.760451i	−0.971406	+	0.237425i	$0.923696\pi$
$978$	6.19712	+	17.0264i	0.198162	+	0.544446i
$979$	−6.97343	−	2.53812i	−0.222872	−	0.0811187i
$980$	0.673648	+	1.16679i	0.0215189	+	0.0372718i
$981$	23.4136	−	8.52185i	0.747538	−	0.272082i
$982$	−16.1099	+	27.9032i	−0.514089	+	0.890428i
$983$	14.9579	−	12.5512i	0.477084	−	0.400321i	−0.372286	−	0.928118i	$-0.621426\pi$
$983$	14.9579	−	12.5512i	0.477084	−	0.400321i	0.849371	+	0.527797i	$0.176982\pi$
$984$	15.1925	−	8.77141i	0.484320	−	0.279622i
$985$	−3.99067	+	22.6322i	−0.127153	+	0.721122i
$986$	−4.13816	+	23.4686i	−0.131786	+	0.747394i
$987$	13.3307	+	7.69648i	0.424321	+	0.244982i
$988$	−6.56805	+	5.51125i	−0.208957	+	0.175336i
$989$	−35.3161	+	61.1694i	−1.12299	+	1.94507i
$990$	−9.61721	−	16.6575i	−0.305655	−	0.529410i
$991$	13.9368	+	24.1392i	0.442716	+	0.766806i	0.997890	−	0.0649280i	$-0.0206818\pi$
$991$	13.9368	+	24.1392i	0.442716	+	0.766806i	−0.555174	+	0.831734i	$0.687348\pi$
$992$	1.37939	+	0.502055i	0.0437955	+	0.0159403i
$993$	9.84776	+	1.73643i	0.312509	+	0.0551038i
$994$	3.22075	+	2.70253i	0.102156	+	0.0857191i
$995$	11.3264	−	4.12245i	0.359069	−	0.130691i
$996$	−14.2763	−	17.0138i	−0.452362	−	0.539104i
$997$	−9.34699	−	53.0094i	−0.296022	−	1.67883i	−0.663019	−	0.748603i	$-0.730725\pi$
$997$	−9.34699	−	53.0094i	−0.296022	−	1.67883i	0.366996	−	0.930222i	$-0.380386\pi$
$998$	−29.8708			−0.945544
$999$			8.47188i			0.268039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.a.337.1	yes	6
27.25	even	9	inner	378.2.u.a.295.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.a.295.1	✓	6	27.25	even	9	inner
378.2.u.a.337.1	yes	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-0.592396 - 1.62760i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.03209 - 0.866025i) q^{5} +(-0.592396 - 1.62760i) q^{6} +(-0.939693 - 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81908 - 1.02606i) q^{9} +(0.673648 - 1.16679i) q^{10} +(3.64543 - 3.05888i) q^{11} +(1.50000 - 0.866025i) q^{12} +(0.266044 - 1.50881i) q^{13} +(0.173648 - 0.984808i) q^{14} +(2.02094 + 1.16679i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.11334 + 1.92836i) q^{17} +(1.50000 + 2.59808i) q^{18} +(2.79813 + 4.84651i) q^{19} +(1.26604 + 0.460802i) q^{20} +(1.70574 + 0.300767i) q^{21} +(3.64543 + 3.05888i) q^{22} +(7.57785 - 2.75811i) q^{23} +(1.11334 + 1.32683i) q^{24} +(-0.553033 - 3.13641i) q^{25} +1.53209 q^{26} +(-4.50000 + 2.59808i) q^{27} +1.00000 q^{28} +(-1.85844 - 10.5397i) q^{29} +(-0.798133 + 2.19285i) q^{30} +(1.37939 - 0.502055i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-5.29813 + 6.31407i) q^{33} +(-2.09240 - 0.761570i) q^{34} +(0.673648 + 1.16679i) q^{35} +(-2.29813 + 1.92836i) q^{36} +(0.815207 - 1.41198i) q^{37} +(-4.28699 + 3.59721i) q^{38} +2.65366i q^{39} +(-0.233956 + 1.32683i) q^{40} +(1.75877 - 9.97448i) q^{41} +1.73205i q^{42} +(-6.70961 + 5.63003i) q^{43} +(-2.37939 + 4.12122i) q^{44} +(-3.79813 - 1.38241i) q^{45} +(4.03209 + 6.98378i) q^{46} +(8.35117 + 3.03958i) q^{47} +(-1.11334 + 1.32683i) q^{48} +(0.766044 + 0.642788i) q^{49} +(2.99273 - 1.08926i) q^{50} +(1.31908 - 3.62414i) q^{51} +(0.266044 + 1.50881i) q^{52} +1.32770 q^{53} +(-3.34002 - 3.98048i) q^{54} -6.41147 q^{55} +(0.173648 + 0.984808i) q^{56} +(-6.23055 - 7.42528i) q^{57} +(10.0569 - 3.66041i) q^{58} +(-7.16637 - 6.01330i) q^{59} +(-2.29813 - 0.405223i) q^{60} +(3.08512 + 1.12289i) q^{61} +(0.733956 + 1.27125i) q^{62} -3.00000 q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.58125 + 1.32683i) q^{65} +(-7.13816 - 4.12122i) q^{66} +(-0.470437 + 2.66798i) q^{67} +(0.386659 - 2.19285i) q^{68} +(-12.0963 + 6.98378i) q^{69} +(-1.03209 + 0.866025i) q^{70} +(-2.10220 + 3.64111i) q^{71} +(-2.29813 - 1.92836i) q^{72} +(-4.54576 - 7.87349i) q^{73} +(1.53209 + 0.557635i) q^{74} +(1.88666 + 5.18355i) q^{75} +(-4.28699 - 3.59721i) q^{76} +(-4.47178 + 1.62760i) q^{77} +(-2.61334 + 0.460802i) q^{78} +(0.556437 + 3.15571i) q^{79} -1.34730 q^{80} +(6.89440 - 5.78509i) q^{81} +10.1284 q^{82} +(-2.22668 - 12.6281i) q^{83} +(-1.70574 + 0.300767i) q^{84} +(2.81908 - 1.02606i) q^{85} +(-6.70961 - 5.63003i) q^{86} +(6.34002 + 17.4191i) q^{87} +(-4.47178 - 1.62760i) q^{88} +(-0.779715 - 1.35051i) q^{89} +(0.701867 - 3.98048i) q^{90} +(-0.766044 + 1.32683i) q^{91} +(-6.17752 + 5.18355i) q^{92} +(-2.20187 + 1.27125i) q^{93} +(-1.54323 + 8.75211i) q^{94} +(1.30928 - 7.42528i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-9.91534 + 8.31996i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(7.13816 - 12.3636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^8	\( 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^8 + 3 * q^10 + 6 * q^11 + 9 * q^12 - 3 * q^13 + 9 * q^15 + 9 * q^18 + 3 * q^19 + 3 * q^20 + 6 * q^22 + 6 * q^23 + 9 * q^25 - 27 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^30 - 3 * q^31 - 18 * q^33 - 9 * q^34 + 3 * q^35 + 12 * q^37 - 18 * q^38 - 6 * q^40 - 12 * q^41 - 6 * q^43 - 3 * q^44 - 9 * q^45 + 15 * q^46 + 24 * q^47 - 9 * q^51 - 3 * q^52 - 18 * q^55 + 24 * q^58 - 24 * q^59 - 3 * q^61 + 9 * q^62 - 18 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 3 * q^67 + 9 * q^68 - 45 * q^69 + 3 * q^70 - 12 * q^71 + 3 * q^73 + 18 * q^75 - 18 * q^76 - 12 * q^77 - 9 * q^78 + 33 * q^79 - 6 * q^80 + 24 * q^82 - 6 * q^86 + 18 * q^87 - 12 * q^88 + 21 * q^89 + 18 * q^90 - 12 * q^92 - 27 * q^93 + 6 * q^94 - 12 * q^95 - 9 * q^96 - 15 * q^97 - 3 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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