LMFDB - Embedded newform 114.2.i.b.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [114,2,Mod(25,114)] 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("114.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(114, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$0.910294583043$
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			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.25
Dual form			114.2.i.b.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0812519 - 0.460802i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(2.20574 - 3.82045i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.358441 - 0.300767i) q^{10} +(2.76604 + 4.79093i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-5.62449 + 2.04715i) q^{13} +(-0.766044 - 4.34445i) q^{14} +(-0.0812519 + 0.460802i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.33022 + 2.79439i) q^{17} +1.00000 q^{18} +(4.34002 + 0.405223i) q^{19} -0.467911 q^{20} +(-3.37939 + 2.83564i) q^{21} +(5.19846 + 1.89209i) q^{22} +(-0.549163 + 3.11446i) q^{23} +(0.173648 + 0.984808i) q^{24} +(4.49273 - 1.63522i) q^{25} +(-2.99273 + 5.18355i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-3.37939 - 2.83564i) q^{28} +(-1.15657 - 0.970481i) q^{29} +(0.233956 + 0.405223i) q^{30} +(1.09240 - 1.89209i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.960637 - 5.44804i) q^{33} +(-0.754900 + 4.28125i) q^{34} +(-1.93969 - 0.705990i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.75877 q^{37} +(3.58512 - 2.47929i) q^{38} +5.98545 q^{39} +(-0.358441 + 0.300767i) q^{40} +(1.84002 + 0.669713i) q^{41} +(-0.766044 + 4.34445i) q^{42} +(0.624485 + 3.54163i) q^{43} +(5.19846 - 1.89209i) q^{44} +(0.233956 - 0.405223i) q^{45} +(1.58125 + 2.73881i) q^{46} +(-7.08512 - 5.94512i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-6.23055 - 10.7916i) q^{49} +(2.39053 - 4.14052i) q^{50} +(4.08512 - 1.48686i) q^{51} +(1.03936 + 5.89452i) q^{52} +(-0.464508 + 2.63435i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(1.98293 - 1.66387i) q^{55} -4.41147 q^{56} +(-3.93969 - 1.86516i) q^{57} -1.50980 q^{58} +(1.01707 - 0.853427i) q^{59} +(0.439693 + 0.160035i) q^{60} +(-1.15270 + 6.53731i) q^{61} +(-0.379385 - 2.15160i) q^{62} +(4.14543 - 1.50881i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.40033 + 2.42544i) q^{65} +(-4.23783 - 3.55596i) q^{66} +(-1.90760 - 1.60067i) q^{67} +(2.17365 + 3.76487i) q^{68} +(1.58125 - 2.73881i) q^{69} +(-1.93969 + 0.705990i) q^{70} +(-1.31908 - 7.48086i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-2.97431 - 1.08256i) q^{73} +(-2.11334 + 1.77330i) q^{74} -4.78106 q^{75} +(1.15270 - 4.20372i) q^{76} +24.4047 q^{77} +(4.58512 - 3.84737i) q^{78} +(-1.18732 - 0.432149i) q^{79} +(-0.0812519 + 0.460802i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.84002 - 0.669713i) q^{82} +(8.96838 - 15.5337i) q^{83} +(2.20574 + 3.82045i) q^{84} +(1.55825 + 1.30753i) q^{85} +(2.75490 + 2.31164i) q^{86} +(0.754900 + 1.30753i) q^{87} +(2.76604 - 4.79093i) q^{88} +(-11.7280 + 4.26865i) q^{89} +(-0.0812519 - 0.460802i) q^{90} +(-4.58512 + 26.0035i) q^{91} +(2.97178 + 1.08164i) q^{92} +(-1.67365 + 1.40436i) q^{93} -9.24897 q^{94} +(-0.165907 - 2.03282i) q^{95} +1.00000 q^{96} +(-6.36618 + 5.34186i) q^{97} +(-11.7096 - 4.26195i) q^{98} +(-0.960637 + 5.44804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.0812519	−	0.460802i	−0.0363370	−	0.206077i	0.961234	−	0.275734i	$-0.0889208\pi$
$5$	−0.0812519	−	0.460802i	−0.0363370	−	0.206077i	−0.997571	+	0.0696565i	$0.977810\pi$
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	2.20574	−	3.82045i	0.833690	−	1.44399i	−0.0614021	−	0.998113i	$-0.519557\pi$
$7$	2.20574	−	3.82045i	0.833690	−	1.44399i	0.895092	−	0.445881i	$-0.147109\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	−0.358441	−	0.300767i	−0.113349	−	0.0951110i
$11$	2.76604	+	4.79093i	0.833994	+	1.44452i	0.894847	+	0.446373i	$0.147284\pi$
$11$	2.76604	+	4.79093i	0.833994	+	1.44452i	−0.0608533	+	0.998147i	$0.519382\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−5.62449	+	2.04715i	−1.55995	+	0.567776i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−5.62449	+	2.04715i	−1.55995	+	0.567776i	−0.589226	+	0.807968i	$0.700567\pi$
$14$	−0.766044	−	4.34445i	−0.204734	−	1.16110i
$15$	−0.0812519	+	0.460802i	−0.0209792	+	0.118979i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.33022	+	2.79439i	−0.807698	+	0.677739i	−0.950057	−	0.312076i	$-0.898976\pi$
$17$	−3.33022	+	2.79439i	−0.807698	+	0.677739i	0.142360	+	0.989815i	$0.454531\pi$
$18$	1.00000			0.235702
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$	−0.467911			−0.104628
$21$	−3.37939	+	2.83564i	−0.737442	+	0.618788i
$22$	5.19846	+	1.89209i	1.10832	+	0.403394i
$23$	−0.549163	+	3.11446i	−0.114508	+	0.649409i	0.872484	+	0.488643i	$0.162508\pi$
$23$	−0.549163	+	3.11446i	−0.114508	+	0.649409i	−0.986992	+	0.160767i	$0.948603\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	4.49273	−	1.63522i	0.898545	−	0.327044i
$26$	−2.99273	+	5.18355i	−0.586922	+	1.01658i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−3.37939	−	2.83564i	−0.638644	−	0.535886i
$29$	−1.15657	−	0.970481i	−0.214770	−	0.180214i	0.529055	−	0.848587i	$-0.322546\pi$
$29$	−1.15657	−	0.970481i	−0.214770	−	0.180214i	−0.743826	+	0.668374i	$0.766991\pi$
$30$	0.233956	+	0.405223i	0.0427142	+	0.0739832i
$31$	1.09240	−	1.89209i	0.196200	−	0.339829i	−0.751093	−	0.660196i	$-0.770473\pi$
$31$	1.09240	−	1.89209i	0.196200	−	0.339829i	0.947293	+	0.320368i	$0.103806\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.960637	−	5.44804i	−0.167225	−	0.948383i
$34$	−0.754900	+	4.28125i	−0.129464	+	0.734229i
$35$	−1.93969	−	0.705990i	−0.327868	−	0.119334i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−2.75877			−0.453539			−0.226770	−	0.973948i	$-0.572816\pi$
$37$	−2.75877			−0.453539			−0.226770	+	0.973948i	$0.572816\pi$
$38$	3.58512	−	2.47929i	0.581584	−	0.402195i
$39$	5.98545			0.958439
$40$	−0.358441	+	0.300767i	−0.0566745	+	0.0475555i
$41$	1.84002	+	0.669713i	0.287363	+	0.104592i	0.481680	−	0.876347i	$-0.340027\pi$
$41$	1.84002	+	0.669713i	0.287363	+	0.104592i	−0.194317	+	0.980939i	$0.562249\pi$
$42$	−0.766044	+	4.34445i	−0.118203	+	0.670364i
$43$	0.624485	+	3.54163i	0.0952331	+	0.540094i	0.994676	+	0.103055i	$0.0328617\pi$
$43$	0.624485	+	3.54163i	0.0952331	+	0.540094i	−0.899443	+	0.437039i	$0.856027\pi$
$44$	5.19846	−	1.89209i	0.783698	−	0.285243i
$45$	0.233956	−	0.405223i	0.0348760	−	0.0604071i
$46$	1.58125	+	2.73881i	0.233143	+	0.403815i
$47$	−7.08512	−	5.94512i	−1.03347	−	0.867185i	−0.0422114	−	0.999109i	$-0.513440\pi$
$47$	−7.08512	−	5.94512i	−1.03347	−	0.867185i	−0.991260	+	0.131923i	$0.957885\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	−6.23055	−	10.7916i	−0.890079	−	1.54166i
$50$	2.39053	−	4.14052i	0.338072	−	0.585558i
$51$	4.08512	−	1.48686i	0.572032	−	0.208202i
$52$	1.03936	+	5.89452i	0.144134	+	0.817423i
$53$	−0.464508	+	2.63435i	−0.0638050	+	0.361856i	0.936143	+	0.351621i	$0.114369\pi$
$53$	−0.464508	+	2.63435i	−0.0638050	+	0.361856i	−0.999948	+	0.0102357i	$0.996742\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	1.98293	−	1.66387i	0.267378	−	0.224357i
$56$	−4.41147			−0.589508
$57$	−3.93969	−	1.86516i	−0.521825	−	0.247046i
$58$	−1.50980			−0.198246
$59$	1.01707	−	0.853427i	0.132412	−	0.111107i	−0.574177	−	0.818731i	$-0.694678\pi$
$59$	1.01707	−	0.853427i	0.132412	−	0.111107i	0.706588	+	0.707625i	$0.250233\pi$
$60$	0.439693	+	0.160035i	0.0567641	+	0.0206604i
$61$	−1.15270	+	6.53731i	−0.147589	+	0.837016i	0.817664	+	0.575696i	$0.195269\pi$
$61$	−1.15270	+	6.53731i	−0.147589	+	0.837016i	−0.965252	+	0.261320i	$0.915842\pi$
$62$	−0.379385	−	2.15160i	−0.0481820	−	0.273254i
$63$	4.14543	−	1.50881i	0.522275	−	0.190093i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.40033	+	2.42544i	0.173690	+	0.300839i
$66$	−4.23783	−	3.55596i	−0.521640	−	0.437708i
$67$	−1.90760	−	1.60067i	−0.233051	−	0.195553i	0.518782	−	0.854907i	$-0.326386\pi$
$67$	−1.90760	−	1.60067i	−0.233051	−	0.195553i	−0.751833	+	0.659354i	$0.770830\pi$
$68$	2.17365	+	3.76487i	0.263594	+	0.456557i
$69$	1.58125	−	2.73881i	0.190360	−	0.329714i
$70$	−1.93969	+	0.705990i	−0.231838	+	0.0843820i
$71$	−1.31908	−	7.48086i	−0.156546	−	0.887815i	−0.957359	−	0.288901i	$-0.906710\pi$
$71$	−1.31908	−	7.48086i	−0.156546	−	0.887815i	0.800813	−	0.598914i	$-0.204401\pi$
$72$	0.173648	−	0.984808i	0.0204646	−	0.116061i
$73$	−2.97431	−	1.08256i	−0.348116	−	0.126704i	0.162043	−	0.986784i	$-0.448192\pi$
$73$	−2.97431	−	1.08256i	−0.348116	−	0.126704i	−0.510160	+	0.860080i	$0.670414\pi$
$74$	−2.11334	+	1.77330i	−0.245671	+	0.206142i
$75$	−4.78106			−0.552069
$76$	1.15270	−	4.20372i	0.132224	−	0.482200i
$77$	24.4047			2.78117
$78$	4.58512	−	3.84737i	0.519163	−	0.435629i
$79$	−1.18732	−	0.432149i	−0.133584	−	0.0486205i	0.274363	−	0.961626i	$-0.411533\pi$
$79$	−1.18732	−	0.432149i	−0.133584	−	0.0486205i	−0.407947	+	0.913006i	$0.633755\pi$
$80$	−0.0812519	+	0.460802i	−0.00908424	+	0.0515193i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	1.84002	−	0.669713i	0.203196	−	0.0739575i
$83$	8.96838	−	15.5337i	0.984407	−	1.70504i	0.339867	−	0.940474i	$-0.389618\pi$
$83$	8.96838	−	15.5337i	0.984407	−	1.70504i	0.644541	−	0.764570i	$-0.277049\pi$
$84$	2.20574	+	3.82045i	0.240666	+	0.416845i
$85$	1.55825	+	1.30753i	0.169016	+	0.141821i
$86$	2.75490	+	2.31164i	0.297069	+	0.249270i
$87$	0.754900	+	1.30753i	0.0809338	+	0.140181i
$88$	2.76604	−	4.79093i	0.294861	−	0.510715i
$89$	−11.7280	+	4.26865i	−1.24317	+	0.452476i	−0.878088	−	0.478500i	$-0.841181\pi$
$89$	−11.7280	+	4.26865i	−1.24317	+	0.452476i	−0.365081	+	0.930976i	$0.618959\pi$
$90$	−0.0812519	−	0.460802i	−0.00856470	−	0.0485728i
$91$	−4.58512	+	26.0035i	−0.480651	+	2.72591i
$92$	2.97178	+	1.08164i	0.309830	+	0.112769i
$93$	−1.67365	+	1.40436i	−0.173549	+	0.145625i
$94$	−9.24897			−0.953958
$95$	−0.165907	−	2.03282i	−0.0170217	−	0.208563i
$96$	1.00000			0.102062
$97$	−6.36618	+	5.34186i	−0.646388	+	0.542384i	−0.905972	−	0.423337i	$-0.860859\pi$
$97$	−6.36618	+	5.34186i	−0.646388	+	0.542384i	0.259585	+	0.965720i	$0.416414\pi$
$98$	−11.7096	−	4.26195i	−1.18285	−	0.430522i
$99$	−0.960637	+	5.44804i	−0.0965477	+	0.547549i
$100$	−0.830222	−	4.70842i	−0.0830222	−	0.470842i
$101$	−1.16637	+	0.424525i	−0.116059	+	0.0422419i	−0.399397	−	0.916778i	$-0.630780\pi$
$101$	−1.16637	+	0.424525i	−0.116059	+	0.0422419i	0.283338	+	0.959020i	$0.408558\pi$
$102$	2.17365	−	3.76487i	0.215223	−	0.372778i
$103$	−1.69207	−	2.93075i	−0.166724	−	0.288775i	0.770542	−	0.637389i	$-0.219986\pi$
$103$	−1.69207	−	2.93075i	−0.166724	−	0.288775i	−0.937266	+	0.348614i	$0.886652\pi$
$104$	4.58512	+	3.84737i	0.449608	+	0.377266i
$105$	1.58125	+	1.32683i	0.154314	+	0.129485i
$106$	1.33750	+	2.31661i	0.129909	+	0.225009i
$107$	−7.90807	+	13.6972i	−0.764502	+	1.32416i	0.176007	+	0.984389i	$0.443682\pi$
$107$	−7.90807	+	13.6972i	−0.764502	+	1.32416i	−0.940509	+	0.339768i	$0.889652\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	−1.00980	−	5.72686i	−0.0967213	−	0.548534i	−0.994206	−	0.107489i	$-0.965719\pi$
$109$	−1.00980	−	5.72686i	−0.0967213	−	0.548534i	0.897485	−	0.441045i	$-0.145392\pi$
$110$	0.449493	−	2.54920i	0.0428575	−	0.243057i
$111$	2.59240	+	0.943555i	0.246059	+	0.0895583i
$112$	−3.37939	+	2.83564i	−0.319322	+	0.267943i
$113$	12.1361			1.14167			0.570834	−	0.821066i	$-0.306620\pi$
$113$	12.1361			1.14167			0.570834	+	0.821066i	$0.306620\pi$
$114$	−4.21688	+	1.10359i	−0.394947	+	0.103361i
$115$	1.47977			0.137989
$116$	−1.15657	+	0.970481i	−0.107385	+	0.0901069i
$117$	−5.62449	−	2.04715i	−0.519984	−	0.189259i
$118$	0.230552	−	1.30753i	0.0212240	−	0.120367i
$119$	3.33022	+	18.8866i	0.305281	+	1.73133i
$120$	0.439693	−	0.160035i	0.0401383	−	0.0146091i
$121$	−9.80200	+	16.9776i	−0.891091	+	1.54342i
$122$	3.31908	+	5.74881i	0.300495	+	0.520473i
$123$	−1.50000	−	1.25865i	−0.135250	−	0.113489i
$124$	−1.67365	−	1.40436i	−0.150298	−	0.126115i
$125$	−2.28833	−	3.96351i	−0.204675	−	0.354507i
$126$	2.20574	−	3.82045i	0.196503	−	0.340353i
$127$	−0.426022	+	0.155059i	−0.0378033	+	0.0137593i	−0.360853	−	0.932623i	$-0.617514\pi$
$127$	−0.426022	+	0.155059i	−0.0378033	+	0.0137593i	0.323049	+	0.946382i	$0.395292\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.624485	−	3.54163i	0.0549829	−	0.311823i
$130$	2.63176	+	0.957882i	0.230821	+	0.0840118i
$131$	−8.27972	+	6.94751i	−0.723402	+	0.607006i	−0.928324	−	0.371772i	$-0.878750\pi$
$131$	−8.27972	+	6.94751i	−0.723402	+	0.607006i	0.204922	+	0.978778i	$0.434306\pi$
$132$	−5.53209			−0.481507
$133$	11.1211	−	15.6870i	0.964320	−	1.36024i
$134$	−2.49020			−0.215120
$135$	−0.358441	+	0.300767i	−0.0308497	+	0.0258859i
$136$	4.08512	+	1.48686i	0.350296	+	0.127497i
$137$	1.90508	−	10.8042i	0.162762	−	0.923068i	−0.788580	−	0.614932i	$-0.789184\pi$
$137$	1.90508	−	10.8042i	0.162762	−	0.923068i	0.951342	−	0.308136i	$-0.0997053\pi$
$138$	−0.549163	−	3.11446i	−0.0467479	−	0.265120i
$139$	12.6493	−	4.60397i	1.07290	−	0.390504i	0.255639	−	0.966772i	$-0.417714\pi$
$139$	12.6493	−	4.60397i	1.07290	−	0.390504i	0.817260	+	0.576269i	$0.195492\pi$
$140$	−1.03209	+	1.78763i	−0.0872274	+	0.151082i
$141$	4.62449	+	8.00984i	0.389452	+	0.674550i
$142$	−5.81908	−	4.88279i	−0.488326	−	0.409754i
$143$	−25.3653	−	21.2840i	−2.12115	−	1.77986i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.353226	+	0.611806i	−0.0293338	+	0.0508077i
$146$	−2.97431	+	1.08256i	−0.246155	+	0.0895933i
$147$	2.16385	+	12.2718i	0.178471	+	1.01216i
$148$	−0.479055	+	2.71686i	−0.0393781	+	0.223324i
$149$	−7.69594	−	2.80109i	−0.630476	−	0.229474i	0.00696263	−	0.999976i	$-0.497784\pi$
$149$	−7.69594	−	2.80109i	−0.630476	−	0.229474i	−0.637438	+	0.770501i	$0.720006\pi$
$150$	−3.66250	+	3.07321i	−0.299042	+	0.250926i
$151$	21.1411			1.72044			0.860221	−	0.509921i	$-0.170325\pi$
$151$	21.1411			1.72044			0.860221	+	0.509921i	$0.170325\pi$
$152$	−1.81908	−	3.96118i	−0.147547	−	0.321294i
$153$	−4.34730			−0.351458
$154$	18.6951	−	15.6870i	1.50649	−	1.26410i
$155$	−0.960637	−	0.349643i	−0.0771602	−	0.0280840i
$156$	1.03936	−	5.89452i	0.0832156	−	0.471939i
$157$	3.41013	+	19.3398i	0.272158	+	1.54348i	0.747847	+	0.663871i	$0.231088\pi$
$157$	3.41013	+	19.3398i	0.272158	+	1.54348i	−0.475689	+	0.879614i	$0.657801\pi$
$158$	−1.18732	+	0.432149i	−0.0944580	+	0.0343799i
$159$	1.33750	−	2.31661i	0.106070	−	0.183719i
$160$	0.233956	+	0.405223i	0.0184958	+	0.0320357i
$161$	10.6873	+	8.96773i	0.842279	+	0.706756i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	−2.27584	−	3.94188i	−0.178258	−	0.308752i	0.763026	−	0.646368i	$-0.223713\pi$
$163$	−2.27584	−	3.94188i	−0.178258	−	0.308752i	−0.941284	+	0.337616i	$0.890379\pi$
$164$	0.979055	−	1.69577i	0.0764514	−	0.132418i
$165$	−2.43242	+	0.885328i	−0.189364	+	0.0689227i
$166$	−3.11468	−	17.6643i	−0.241746	−	1.37101i
$167$	3.32383	−	18.8504i	0.257205	−	1.45868i	−0.533142	−	0.846026i	$-0.678989\pi$
$167$	3.32383	−	18.8504i	0.257205	−	1.45868i	0.790348	−	0.612658i	$-0.209900\pi$
$168$	4.14543	+	1.50881i	0.319827	+	0.116407i
$169$	17.4855	−	14.6720i	1.34503	−	1.12862i
$170$	2.03415			0.156012
$171$	3.06418	+	3.10013i	0.234324	+	0.237073i
$172$	3.59627			0.274213
$173$	4.25284	−	3.56856i	0.323337	−	0.271312i	−0.466641	−	0.884447i	$-0.654536\pi$
$173$	4.25284	−	3.56856i	0.323337	−	0.271312i	0.789979	+	0.613134i	$0.210092\pi$
$174$	1.41875	+	0.516382i	0.107555	+	0.0391468i
$175$	3.66250	−	20.7711i	0.276859	−	1.57015i
$176$	−0.960637	−	5.44804i	−0.0724107	−	0.410662i
$177$	−1.24763	+	0.454099i	−0.0937773	+	0.0341322i
$178$	−6.24035	+	10.8086i	−0.467734	+	0.810139i
$179$	4.17499	+	7.23130i	0.312054	+	0.540493i	0.978807	−	0.204786i	$-0.0656498\pi$
$179$	4.17499	+	7.23130i	0.312054	+	0.540493i	−0.666753	+	0.745279i	$0.732316\pi$
$180$	−0.358441	−	0.300767i	−0.0267166	−	0.0224179i
$181$	−9.64337	−	8.09175i	−0.716786	−	0.601455i	0.209708	−	0.977764i	$-0.432749\pi$
$181$	−9.64337	−	8.09175i	−0.716786	−	0.601455i	−0.926494	+	0.376309i	$0.877193\pi$
$182$	13.2023	+	22.8671i	0.978622	+	1.69502i
$183$	3.31908	−	5.74881i	0.245353	−	0.424964i
$184$	2.97178	−	1.08164i	0.219083	−	0.0797396i
$185$	0.224155	+	1.27125i	0.0164802	+	0.0934640i
$186$	−0.379385	+	2.15160i	−0.0278179	+	0.157763i
$187$	−22.5993	−	8.22546i	−1.65262	−	0.601505i
$188$	−7.08512	+	5.94512i	−0.516736	+	0.433593i
$189$	−4.41147			−0.320888
$190$	−1.43376	−	1.45059i	−0.104016	−	0.105237i
$191$	−6.71688			−0.486016			−0.243008	−	0.970024i	$-0.578134\pi$
$191$	−6.71688			−0.486016			−0.243008	+	0.970024i	$0.578134\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	11.7763	+	4.28623i	0.847677	+	0.308529i	0.729093	−	0.684415i	$-0.239942\pi$
$193$	11.7763	+	4.28623i	0.847677	+	0.308529i	0.118584	+	0.992944i	$0.462164\pi$
$194$	−1.44310	+	8.18421i	−0.103608	+	0.587592i
$195$	−0.486329	−	2.75811i	−0.0348268	−	0.197512i
$196$	−11.7096	+	4.26195i	−0.836401	+	0.304425i
$197$	2.03596	−	3.52638i	0.145056	−	0.251245i	−0.784338	−	0.620334i	$-0.786997\pi$
$197$	2.03596	−	3.52638i	0.145056	−	0.251245i	0.929394	+	0.369089i	$0.120330\pi$
$198$	2.76604	+	4.79093i	0.196574	+	0.340477i
$199$	−5.48158	−	4.59959i	−0.388579	−	0.326057i	0.427480	−	0.904025i	$-0.359401\pi$
$199$	−5.48158	−	4.59959i	−0.388579	−	0.326057i	−0.816059	+	0.577968i	$0.803846\pi$
$200$	−3.66250	−	3.07321i	−0.258978	−	0.217308i
$201$	1.24510	+	2.15658i	0.0878226	+	0.152113i
$202$	−0.620615	+	1.07494i	−0.0436663	+	0.0756323i
$203$	−6.25877	+	2.27801i	−0.439280	+	0.159885i
$204$	−0.754900	−	4.28125i	−0.0528536	−	0.299748i
$205$	0.159100	−	0.902302i	0.0111120	−	0.0630195i
$206$	−3.18004	−	1.15744i	−0.221564	−	0.0806428i
$207$	−2.42262	+	2.03282i	−0.168384	+	0.141291i
$208$	5.98545			0.415016
$209$	10.0633	+	21.9136i	0.696093	+	1.51580i
$210$	2.06418			0.142442
$211$	−2.03209	+	1.70513i	−0.139895	+	0.117386i	−0.710050	−	0.704151i	$-0.751328\pi$
$211$	−2.03209	+	1.70513i	−0.139895	+	0.117386i	0.570155	+	0.821537i	$0.306883\pi$
$212$	2.51367	+	0.914901i	0.172640	+	0.0628357i
$213$	−1.31908	+	7.48086i	−0.0903817	+	0.512580i
$214$	2.74644	+	15.5759i	0.187743	+	1.06474i
$215$	1.58125	−	0.575529i	0.107840	−	0.0392507i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−4.81908	−	8.34689i	−0.327140	−	0.566624i
$218$	−4.45471	−	3.73794i	−0.301711	−	0.253165i
$219$	2.42468	+	2.03455i	0.163845	+	0.137482i
$220$	−1.29426	−	2.24173i	−0.0872592	−	0.151137i
$221$	13.0103	−	22.5344i	0.875165	−	1.51583i
$222$	2.59240	−	0.943555i	0.173990	−	0.0633273i
$223$	2.42246	+	13.7384i	0.162220	+	0.919993i	0.951885	+	0.306456i	$0.0991431\pi$
$223$	2.42246	+	13.7384i	0.162220	+	0.919993i	−0.789665	+	0.613538i	$0.789746\pi$
$224$	−0.766044	+	4.34445i	−0.0511835	+	0.290276i
$225$	4.49273	+	1.63522i	0.299515	+	0.109015i
$226$	9.29679	−	7.80093i	0.618413	−	0.518910i
$227$	−23.6117			−1.56717			−0.783583	−	0.621287i	$-0.786610\pi$
$227$	−23.6117			−1.56717			−0.783583	+	0.621287i	$0.786610\pi$
$228$	−2.52094	+	3.55596i	−0.166954	+	0.235499i
$229$	8.61081			0.569019			0.284509	−	0.958673i	$-0.408169\pi$
$229$	8.61081			0.569019			0.284509	+	0.958673i	$0.408169\pi$
$230$	1.13357	−	0.951178i	0.0747454	−	0.0627188i
$231$	−22.9329	−	8.34689i	−1.50887	−	0.549185i
$232$	−0.262174	+	1.48686i	−0.0172126	+	0.0976173i
$233$	−2.68139	−	15.2069i	−0.175664	−	0.996238i	−0.937375	−	0.348322i	$-0.886752\pi$
$233$	−2.68139	−	15.2069i	−0.175664	−	0.996238i	0.761711	−	0.647916i	$-0.224359\pi$
$234$	−5.62449	+	2.04715i	−0.367684	+	0.133826i
$235$	−2.16385	+	3.74789i	−0.141154	+	0.244486i
$236$	−0.663848	−	1.14982i	−0.0432128	−	0.0748468i
$237$	0.967911	+	0.812174i	0.0628726	+	0.0527564i
$238$	14.6912	+	12.3274i	0.952288	+	0.799065i
$239$	−3.87939	−	6.71929i	−0.250937	−	0.434635i	0.712847	−	0.701319i	$-0.247405\pi$
$239$	−3.87939	−	6.71929i	−0.250937	−	0.434635i	−0.963784	+	0.266684i	$0.914072\pi$
$240$	0.233956	−	0.405223i	0.0151018	−	0.0261570i
$241$	12.4846	−	4.54401i	0.804202	−	0.292706i	0.0929755	−	0.995668i	$-0.470362\pi$
$241$	12.4846	−	4.54401i	0.804202	−	0.292706i	0.711227	+	0.702963i	$0.248140\pi$
$242$	3.40420	+	19.3062i	0.218830	+	1.24105i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	6.23783	+	2.27038i	0.399336	+	0.145346i
$245$	−4.46657	+	3.74789i	−0.285358	+	0.239444i
$246$	−1.95811			−0.124845
$247$	−25.2399	+	6.60549i	−1.60598	+	0.420297i
$248$	−2.18479			−0.138734
$249$	−13.7404	+	11.5295i	−0.870759	+	0.730654i
$250$	−4.30066	−	1.56531i	−0.271998	−	0.0989990i
$251$	−3.06506	+	17.3828i	−0.193465	+	1.09719i	0.721124	+	0.692806i	$0.243626\pi$
$251$	−3.06506	+	17.3828i	−0.193465	+	1.09719i	−0.914588	+	0.404386i	$0.867485\pi$
$252$	−0.766044	−	4.34445i	−0.0482563	−	0.273675i
$253$	−16.4402	+	5.98373i	−1.03358	+	0.376194i
$254$	−0.226682	+	0.392624i	−0.0142233	+	0.0246354i
$255$	−1.01707	−	1.76162i	−0.0636917	−	0.110317i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.05303	+	5.07910i	0.377578	+	0.316825i	0.811751	−	0.584004i	$-0.198515\pi$
$257$	6.05303	+	5.07910i	0.377578	+	0.316825i	−0.434173	+	0.900830i	$0.642959\pi$
$258$	−1.79813	−	3.11446i	−0.111947	−	0.193898i
$259$	−6.08512	+	10.5397i	−0.378111	+	0.654908i
$260$	2.63176	−	0.957882i	0.163215	−	0.0594053i
$261$	−0.262174	−	1.48686i	−0.0162282	−	0.0920345i
$262$	−1.87686	+	10.6442i	−0.115953	+	0.657601i
$263$	23.8405	+	8.67723i	1.47007	+	0.535061i	0.948119	−	0.317916i	$-0.102983\pi$
$263$	23.8405	+	8.67723i	1.47007	+	0.535061i	0.521949	+	0.852977i	$0.325205\pi$
$264$	−4.23783	+	3.55596i	−0.260820	+	0.218854i
$265$	1.25166			0.0768888
$266$	−1.56418	−	19.1654i	−0.0959059	−	1.17511i
$267$	12.4807			0.763807
$268$	−1.90760	+	1.60067i	−0.116525	+	0.0977765i
$269$	−18.9538	−	6.89863i	−1.15564	−	0.420617i	−0.308099	−	0.951354i	$-0.599693\pi$
$269$	−18.9538	−	6.89863i	−1.15564	−	0.420617i	−0.847536	+	0.530737i	$0.821915\pi$
$270$	−0.0812519	+	0.460802i	−0.00494483	+	0.0280435i
$271$	3.56165	+	20.1991i	0.216355	+	1.22701i	0.878540	+	0.477669i	$0.158518\pi$
$271$	3.56165	+	20.1991i	0.216355	+	1.22701i	−0.662185	+	0.749341i	$0.730371\pi$
$272$	4.08512	−	1.48686i	0.247697	−	0.0901543i
$273$	13.2023	−	22.8671i	0.799042	−	1.38398i
$274$	−5.48545	−	9.50108i	−0.331388	−	0.573981i
$275$	20.2613	+	17.0012i	1.22180	+	1.02521i
$276$	−2.42262	−	2.03282i	−0.145824	−	0.122361i
$277$	−4.56758	−	7.91128i	−0.274439	−	0.475343i	0.695554	−	0.718474i	$-0.255159\pi$
$277$	−4.56758	−	7.91128i	−0.274439	−	0.475343i	−0.969994	+	0.243131i	$0.921826\pi$
$278$	6.73055	−	11.6577i	0.403672	−	0.699180i
$279$	2.05303	−	0.747243i	0.122912	−	0.0447363i
$280$	0.358441	+	2.03282i	0.0214209	+	0.121484i
$281$	−0.595800	+	3.37895i	−0.0355424	+	0.201571i	−0.997408	−	0.0719508i	$-0.977078\pi$
$281$	−0.595800	+	3.37895i	−0.0355424	+	0.201571i	0.961866	+	0.273522i	$0.0881886\pi$
$282$	8.69119	+	3.16333i	0.517553	+	0.188374i
$283$	8.61200	−	7.22632i	0.511930	−	0.429560i	−0.349878	−	0.936795i	$-0.613777\pi$
$283$	8.61200	−	7.22632i	0.511930	−	0.429560i	0.861808	+	0.507235i	$0.169332\pi$
$284$	−7.59627			−0.450755
$285$	−0.539363	+	1.96697i	−0.0319491	+	0.116513i
$286$	−33.1121			−1.95796
$287$	6.61721	−	5.55250i	0.390602	−	0.327754i
$288$	−0.939693	−	0.342020i	−0.0553719	−	0.0201537i
$289$	0.329755	−	1.87014i	0.0193974	−	0.110008i
$290$	0.122674	+	0.695720i	0.00720367	+	0.0408541i
$291$	7.80928	−	2.84234i	0.457788	−	0.166621i
$292$	−1.58260	+	2.74114i	−0.0926144	+	0.160413i
$293$	7.26604	+	12.5852i	0.424487	+	0.735233i	0.996372	−	0.0851007i	$-0.0271212\pi$
$293$	7.26604	+	12.5852i	0.424487	+	0.735233i	−0.571886	+	0.820333i	$0.693788\pi$
$294$	9.54576	+	8.00984i	0.556720	+	0.467144i
$295$	−0.475900	−	0.399328i	−0.0277080	−	0.0232498i
$296$	1.37939	+	2.38917i	0.0801751	+	0.138867i
$297$	2.76604	−	4.79093i	0.160502	−	0.277998i
$298$	−7.69594	+	2.80109i	−0.445814	+	0.162263i
$299$	−3.28699	−	18.6414i	−0.190091	−	1.07806i
$300$	−0.830222	+	4.70842i	−0.0479329	+	0.271841i
$301$	14.9081	+	5.42609i	0.859287	+	0.312755i
$302$	16.1951	−	13.5893i	0.931921	−	0.781975i
$303$	1.24123			0.0713068
$304$	−3.93969	−	1.86516i	−0.225957	−	0.106974i
$305$	3.10607			0.177853
$306$	−3.33022	+	2.79439i	−0.190376	+	0.159745i
$307$	24.1532	+	8.79104i	1.37849	+	0.501731i	0.921721	−	0.387853i	$-0.126783\pi$
$307$	24.1532	+	8.79104i	1.37849	+	0.501731i	0.456773	+	0.889583i	$0.349005\pi$
$308$	4.23783	−	24.0339i	0.241473	−	1.36946i
$309$	0.587649	+	3.33272i	0.0334302	+	0.189592i
$310$	−0.960637	+	0.349643i	−0.0545605	+	0.0198584i
$311$	−2.91875	+	5.05542i	−0.165507	+	0.286667i	−0.936835	−	0.349771i	$-0.886259\pi$
$311$	−2.91875	+	5.05542i	−0.165507	+	0.286667i	0.771328	+	0.636438i	$0.219593\pi$
$312$	−2.99273	−	5.18355i	−0.169430	−	0.293461i
$313$	−12.6480	−	10.6129i	−0.714905	−	0.599876i	0.211066	−	0.977472i	$-0.432307\pi$
$313$	−12.6480	−	10.6129i	−0.714905	−	0.599876i	−0.925971	+	0.377596i	$0.876751\pi$
$314$	15.0437	+	12.6232i	0.848965	+	0.712366i
$315$	−1.03209	−	1.78763i	−0.0581516	−	0.100722i
$316$	−0.631759	+	1.09424i	−0.0355392	+	0.0615557i
$317$	25.3243	−	9.21729i	1.42235	−	0.517695i	0.487624	−	0.873054i	$-0.337864\pi$
$317$	25.3243	−	9.21729i	1.42235	−	0.517695i	0.934730	+	0.355359i	$0.115641\pi$
$318$	−0.464508	−	2.63435i	−0.0260483	−	0.147727i
$319$	1.45037	−	8.22546i	0.0812051	−	0.460537i
$320$	0.439693	+	0.160035i	0.0245796	+	0.00894623i
$321$	12.1159	−	10.1664i	0.676242	−	0.567434i
$322$	13.9513			0.777476
$323$	−15.5856	+	10.7782i	−0.867205	+	0.599716i
$324$	1.00000			0.0555556
$325$	−21.9217	+	18.3945i	−1.21600	+	1.02034i
$326$	−4.27719	−	1.55677i	−0.236892	−	0.0862215i
$327$	−1.00980	+	5.72686i	−0.0558421	+	0.316696i
$328$	−0.340022	−	1.92836i	−0.0187746	−	0.106476i
$329$	−38.3410	+	13.9550i	−2.11381	+	0.769362i
$330$	−1.29426	+	2.24173i	−0.0712468	+	0.123403i
$331$	−14.2442	−	24.6717i	−0.782933	−	1.35608i	−0.930226	−	0.366987i	$-0.880389\pi$
$331$	−14.2442	−	24.6717i	−0.782933	−	1.35608i	0.147293	−	0.989093i	$-0.452944\pi$
$332$	−13.7404	−	11.5295i	−0.754100	−	0.632765i
$333$	−2.11334	−	1.77330i	−0.115810	−	0.0971764i
$334$	−9.57057	−	16.5767i	−0.523679	−	0.907038i
$335$	−0.582596	+	1.00909i	−0.0318306	+	0.0551323i
$336$	4.14543	−	1.50881i	0.226152	−	0.0823125i
$337$	2.89780	+	16.4343i	0.157853	+	0.895231i	0.956131	+	0.292941i	$0.0946339\pi$
$337$	2.89780	+	16.4343i	0.157853	+	0.895231i	−0.798277	+	0.602290i	$0.794255\pi$
$338$	3.96363	−	22.4789i	0.215593	−	1.22269i
$339$	−11.4042	−	4.15079i	−0.619391	−	0.225440i
$340$	1.55825	−	1.30753i	0.0845079	−	0.0709105i
$341$	12.0865			0.654519
$342$	4.34002	+	0.405223i	0.234682	+	0.0219119i
$343$	−24.0915			−1.30082
$344$	2.75490	−	2.31164i	0.148534	−	0.124635i
$345$	−1.39053	−	0.506111i	−0.0748636	−	0.0272481i
$346$	0.964041	−	5.46735i	0.0518272	−	0.293926i
$347$	−3.25237	−	18.4451i	−0.174597	−	0.990186i	−0.938608	−	0.344984i	$-0.887884\pi$
$347$	−3.25237	−	18.4451i	−0.174597	−	0.990186i	0.764012	−	0.645202i	$-0.223227\pi$
$348$	1.41875	−	0.516382i	0.0760529	−	0.0276810i
$349$	0.820422	−	1.42101i	0.0439162	−	0.0760651i	−0.843232	−	0.537550i	$-0.819350\pi$
$349$	0.820422	−	1.42101i	0.0439162	−	0.0760651i	0.887148	+	0.461485i	$0.152683\pi$
$350$	−10.5458	−	18.2658i	−0.563695	−	0.976348i
$351$	4.58512	+	3.84737i	0.244736	+	0.205358i
$352$	−4.23783	−	3.55596i	−0.225877	−	0.189533i
$353$	5.95336	+	10.3115i	0.316866	+	0.548827i	0.979832	−	0.199822i	$-0.0640363\pi$
$353$	5.95336	+	10.3115i	0.316866	+	0.548827i	−0.662967	+	0.748649i	$0.730703\pi$
$354$	−0.663848	+	1.14982i	−0.0352831	+	0.0611122i
$355$	−3.34002	+	1.21567i	−0.177270	+	0.0645210i
$356$	2.16725	+	12.2911i	0.114864	+	0.651427i
$357$	3.33022	−	18.8866i	0.176254	−	0.999586i
$358$	7.84642	+	2.85586i	0.414696	+	0.150937i
$359$	1.75877	−	1.47578i	0.0928244	−	0.0778889i	−0.595195	−	0.803582i	$-0.702925\pi$
$359$	1.75877	−	1.47578i	0.0928244	−	0.0778889i	0.688019	+	0.725693i	$0.258481\pi$
$360$	−0.467911			−0.0246611
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$	−12.5885			−0.661638
$363$	15.0175	−	12.6012i	0.788216	−	0.661392i
$364$	24.8123	+	9.03093i	1.30052	+	0.473349i
$365$	−0.257178	+	1.45853i	−0.0134613	+	0.0763429i
$366$	−1.15270	−	6.53731i	−0.0602528	−	0.341711i
$367$	20.1989	−	7.35181i	1.05438	−	0.383761i	0.244063	−	0.969759i	$-0.421520\pi$
$367$	20.1989	−	7.35181i	1.05438	−	0.383761i	0.810312	+	0.585998i	$0.199297\pi$
$368$	1.58125	−	2.73881i	0.0824285	−	0.142770i
$369$	0.979055	+	1.69577i	0.0509676	+	0.0882785i
$370$	0.988856	+	0.829748i	0.0514082	+	0.0431366i
$371$	9.03983	+	7.58532i	0.469325	+	0.393810i
$372$	1.09240	+	1.89209i	0.0566381	+	0.0981001i
$373$	−13.9907	+	24.2325i	−0.724409	+	1.25471i	0.234807	+	0.972042i	$0.424554\pi$
$373$	−13.9907	+	24.2325i	−0.724409	+	1.25471i	−0.959217	+	0.282672i	$0.908779\pi$
$374$	−22.5993	+	8.22546i	−1.16858	+	0.425328i
$375$	0.794730	+	4.50714i	0.0410397	+	0.232748i
$376$	−1.60607	+	9.10846i	−0.0828266	+	0.469733i
$377$	8.49185	+	3.09078i	0.437352	+	0.159183i
$378$	−3.37939	+	2.83564i	−0.173817	+	0.145850i
$379$	8.88981			0.456639			0.228320	−	0.973586i	$-0.426677\pi$
$379$	8.88981			0.456639			0.228320	+	0.973586i	$0.426677\pi$
$380$	−2.03074	−	0.189608i	−0.104175	−	0.00972670i
$381$	0.453363			0.0232265
$382$	−5.14543	+	4.31753i	−0.263263	+	0.220904i
$383$	23.5069	+	8.55580i	1.20114	+	0.437181i	0.863624	−	0.504137i	$-0.168189\pi$
$383$	23.5069	+	8.55580i	1.20114	+	0.437181i	0.337521	+	0.941318i	$0.390412\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	−1.98293	−	11.2457i	−0.101059	−	0.573136i
$386$	11.7763	−	4.28623i	0.599398	−	0.218163i
$387$	−1.79813	+	3.11446i	−0.0914043	+	0.158317i
$388$	4.15523	+	7.19707i	0.210950	+	0.365376i
$389$	−17.8739	−	14.9980i	−0.906244	−	0.760429i	0.0651569	−	0.997875i	$-0.479245\pi$
$389$	−17.8739	−	14.9980i	−0.906244	−	0.760429i	−0.971401	+	0.237446i	$0.923690\pi$
$390$	−2.14543	−	1.80023i	−0.108638	−	0.0911582i
$391$	−6.87417	−	11.9064i	−0.347642	−	0.602133i
$392$	−6.23055	+	10.7916i	−0.314690	+	0.545060i
$393$	10.1566	−	3.69669i	0.512331	−	0.186473i
$394$	−0.707081	−	4.01006i	−0.0356222	−	0.202024i
$395$	−0.102663	+	0.582232i	−0.00516555	+	0.0292953i
$396$	5.19846	+	1.89209i	0.261233	+	0.0950809i
$397$	2.90239	−	2.43539i	0.145667	−	0.122229i	−0.567042	−	0.823689i	$-0.691912\pi$
$397$	2.90239	−	2.43539i	0.145667	−	0.122229i	0.712709	+	0.701460i	$0.247468\pi$
$398$	−7.15570			−0.358683
$399$	−15.8157	+	10.9373i	−0.791774	+	0.547552i
$400$	−4.78106			−0.239053
$401$	−16.7456	+	14.0512i	−0.836234	+	0.701683i	−0.956713	−	0.291032i	$-0.906001\pi$
$401$	−16.7456	+	14.0512i	−0.836234	+	0.701683i	0.120479	+	0.992716i	$0.461557\pi$
$402$	2.34002	+	0.851698i	0.116710	+	0.0424789i
$403$	−2.27079	+	12.8783i	−0.113116	+	0.641514i
$404$	0.215537	+	1.22237i	0.0107234	+	0.0608153i
$405$	0.439693	−	0.160035i	0.0218485	−	0.00795220i
$406$	−3.33022	+	5.76811i	−0.165276	+	0.286267i
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$	−3.33022	−	2.79439i	−0.164871	−	0.138343i
$409$	−6.06418	−	5.08845i	−0.299854	−	0.251608i	0.480429	−	0.877033i	$-0.340481\pi$
$409$	−6.06418	−	5.08845i	−0.299854	−	0.251608i	−0.780284	+	0.625426i	$0.784925\pi$
$410$	−0.458111	−	0.793471i	−0.0226245	−	0.0391868i
$411$	−5.48545	+	9.50108i	−0.270577	+	0.468654i
$412$	−3.18004	+	1.15744i	−0.156670	+	0.0570231i
$413$	−1.01707	−	5.76811i	−0.0500469	−	0.283830i
$414$	−0.549163	+	3.11446i	−0.0269899	+	0.153067i
$415$	−7.88666	−	2.87051i	−0.387141	−	0.140908i
$416$	4.58512	−	3.84737i	0.224804	−	0.188633i
$417$	−13.4611			−0.659193
$418$	21.7947	+	10.3182i	1.06602	+	0.504681i
$419$	6.22937			0.304325			0.152162	−	0.988356i	$-0.451376\pi$
$419$	6.22937			0.304325			0.152162	+	0.988356i	$0.451376\pi$
$420$	1.58125	−	1.32683i	0.0771572	−	0.0647426i
$421$	3.35591	+	1.22145i	0.163557	+	0.0595300i	0.422501	−	0.906362i	$-0.361152\pi$
$421$	3.35591	+	1.22145i	0.163557	+	0.0595300i	−0.258944	+	0.965892i	$0.583374\pi$
$422$	−0.460637	+	2.61240i	−0.0224235	+	0.127170i
$423$	−1.60607	−	9.10846i	−0.0780896	−	0.442868i
$424$	2.51367	−	0.914901i	0.122075	−	0.0444315i
$425$	−10.3923	+	18.0001i	−0.504103	+	0.873131i
$426$	3.79813	+	6.57856i	0.184020	+	0.318732i
$427$	22.4329	+	18.8234i	1.08560	+	0.910929i
$428$	12.1159	+	10.1664i	0.585643	+	0.491412i
$429$	16.5560	+	28.6759i	0.799332	+	1.38448i
$430$	0.841367	−	1.45729i	0.0405743	−	0.0702767i
$431$	24.2520	−	8.82699i	1.16818	−	0.425181i	0.316164	−	0.948704i	$-0.397605\pi$
$431$	24.2520	−	8.82699i	1.16818	−	0.425181i	0.852011	+	0.523523i	$0.175383\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	4.53209	−	25.7028i	0.217798	−	1.23520i	−0.658186	−	0.752856i	$-0.728676\pi$
$433$	4.53209	−	25.7028i	0.217798	−	1.23520i	0.875984	−	0.482340i	$-0.160213\pi$
$434$	−9.05690	−	3.29644i	−0.434745	−	0.158234i
$435$	0.541174	−	0.454099i	0.0259473	−	0.0217724i
$436$	−5.81521			−0.278498
$437$	−3.64543	+	13.2943i	−0.174385	+	0.635952i
$438$	3.16519			0.151239
$439$	17.3366	−	14.5472i	0.827432	−	0.694298i	−0.127268	−	0.991868i	$-0.540621\pi$
$439$	17.3366	−	14.5472i	0.827432	−	0.694298i	0.954700	+	0.297571i	$0.0961764\pi$
$440$	−2.43242	−	0.885328i	−0.115961	−	0.0422064i
$441$	2.16385	−	12.2718i	0.103040	−	0.584371i
$442$	−4.51842	−	25.6252i	−0.214919	−	1.21887i
$443$	−13.5432	+	4.92933i	−0.643458	+	0.234200i	−0.643079	−	0.765800i	$-0.722343\pi$
$443$	−13.5432	+	4.92933i	−0.643458	+	0.234200i	−0.000379869		1.00000i	$0.500121\pi$
$444$	1.37939	−	2.38917i	0.0654627	−	0.113385i
$445$	2.91993	+	5.05747i	0.138418	+	0.239747i
$446$	10.6866	+	8.96713i	0.506025	+	0.424606i
$447$	6.27379	+	5.26433i	0.296740	+	0.248994i
$448$	2.20574	+	3.82045i	0.104211	+	0.180499i
$449$	−18.1361	+	31.4126i	−0.855895	+	1.48245i	0.0199166	+	0.999802i	$0.493660\pi$
$449$	−18.1361	+	31.4126i	−0.855895	+	1.48245i	−0.875812	+	0.482653i	$0.839673\pi$
$450$	4.49273	−	1.63522i	0.211789	−	0.0770849i
$451$	1.88103	+	10.6679i	0.0885744	+	0.502331i
$452$	2.10741	−	11.9517i	0.0991243	−	0.562162i
$453$	−19.8662	−	7.23070i	−0.933395	−	0.339728i
$454$	−18.0876	+	15.1773i	−0.848895	+	0.712308i
$455$	12.3550			0.579213
$456$	0.354570	+	4.34445i	0.0166043	+	0.203448i
$457$	−40.4543			−1.89237			−0.946186	−	0.323623i	$-0.895099\pi$
$457$	−40.4543			−1.89237			−0.946186	+	0.323623i	$0.895099\pi$
$458$	6.59627	−	5.53492i	0.308223	−	0.258630i
$459$	4.08512	+	1.48686i	0.190677	+	0.0694008i
$460$	0.256959	−	1.45729i	0.0119808	−	0.0679465i
$461$	−6.81996	−	38.6779i	−0.317637	−	1.80141i	−0.557037	−	0.830488i	$-0.688062\pi$
$461$	−6.81996	−	38.6779i	−0.317637	−	1.80141i	0.239400	−	0.970921i	$-0.423049\pi$
$462$	−22.9329	+	8.34689i	−1.06693	+	0.388332i
$463$	−10.4167	+	18.0422i	−0.484105	+	0.838494i	−0.999833	−	0.0182582i	$-0.994188\pi$
$463$	−10.4167	+	18.0422i	−0.484105	+	0.838494i	0.515729	+	0.856752i	$0.327521\pi$
$464$	0.754900	+	1.30753i	0.0350454	+	0.0607003i
$465$	0.783119	+	0.657115i	0.0363163	+	0.0304730i
$466$	−11.8289	−	9.92561i	−0.547962	−	0.459795i
$467$	5.96198	+	10.3265i	0.275888	+	0.477851i	0.970359	−	0.241669i	$-0.0776949\pi$
$467$	5.96198	+	10.3265i	0.275888	+	0.477851i	−0.694471	+	0.719521i	$0.744362\pi$
$468$	−2.99273	+	5.18355i	−0.138339	+	0.239610i
$469$	−10.3229	+	3.75725i	−0.476669	+	0.173493i
$470$	0.751497	+	4.26195i	0.0346639	+	0.196589i
$471$	3.41013	−	19.3398i	0.157130	−	0.891131i
$472$	−1.24763	−	0.454099i	−0.0574266	−	0.0209016i
$473$	−15.2404	+	12.7882i	−0.700752	+	0.588001i
$474$	1.26352			0.0580353
$475$	20.1612	−	5.27633i	0.925057	−	0.242095i
$476$	19.1780			0.879022
$477$	−2.04916	+	1.71945i	−0.0938247	+	0.0787283i
$478$	−7.29086	−	2.65366i	−0.333476	−	0.121375i
$479$	−1.28564	+	7.29125i	−0.0587426	+	0.333146i	−0.999990	−	0.00457323i	$-0.998544\pi$
$479$	−1.28564	+	7.29125i	−0.0587426	+	0.333146i	0.941247	+	0.337719i	$0.109655\pi$
$480$	−0.0812519	−	0.460802i	−0.00370863	−	0.0210327i
$481$	15.5167	−	5.64760i	0.707499	−	0.257509i
$482$	6.64290	−	11.5058i	0.302576	−	0.524077i
$483$	−6.97565	−	12.0822i	−0.317403	−	0.549758i
$484$	15.0175	+	12.6012i	0.682615	+	0.572782i
$485$	2.97881	+	2.49952i	0.135261	+	0.113497i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	11.2934	−	19.5607i	0.511752	−	0.886381i	−0.488155	−	0.872757i	$-0.662330\pi$
$487$	11.2934	−	19.5607i	0.511752	−	0.886381i	0.999907	−	0.0136238i	$-0.00433672\pi$
$488$	6.23783	−	2.27038i	0.282373	−	0.102775i
$489$	0.790393	+	4.48254i	0.0357428	+	0.202707i
$490$	−1.01249	+	5.74211i	−0.0457396	+	0.259402i
$491$	−15.0680	−	5.48432i	−0.680011	−	0.247504i	−0.0211590	−	0.999776i	$-0.506736\pi$
$491$	−15.0680	−	5.48432i	−0.680011	−	0.247504i	−0.658852	+	0.752272i	$0.728958\pi$
$492$	−1.50000	+	1.25865i	−0.0676252	+	0.0567443i
$493$	6.56355			0.295607
$494$	−15.0890	+	21.2840i	−0.678886	+	0.957613i
$495$	2.58853			0.116346
$496$	−1.67365	+	1.40436i	−0.0751490	+	0.0630575i
$497$	−31.4898	−	11.4613i	−1.41251	−	0.514112i
$498$	−3.11468	+	17.6643i	−0.139572	+	0.791554i
$499$	−6.09879	−	34.5880i	−0.273019	−	1.54837i	−0.745183	−	0.666860i	$-0.767638\pi$
$499$	−6.09879	−	34.5880i	−0.273019	−	1.54837i	0.472164	−	0.881511i	$-0.343473\pi$
$500$	−4.30066	+	1.56531i	−0.192331	+	0.0700029i
$501$	−9.57057	+	16.5767i	−0.427582	+	0.740593i
$502$	8.82547	+	15.2862i	0.393900	+	0.682255i
$503$	30.7395	+	25.7935i	1.37061	+	1.15007i	0.972545	+	0.232715i	$0.0747611\pi$
$503$	30.7395	+	25.7935i	1.37061	+	1.15007i	0.398061	+	0.917359i	$0.369683\pi$
$504$	−3.37939	−	2.83564i	−0.150530	−	0.126309i
$505$	0.290393	+	0.502975i	0.0129223	+	0.0223821i
$506$	−8.74763	+	15.1513i	−0.388879	+	0.673559i
$507$	−21.4491	+	7.80683i	−0.952587	+	0.346713i
$508$	0.0787257	+	0.446476i	0.00349289	+	0.0198092i
$509$	0.745100	−	4.22567i	0.0330260	−	0.187300i	−0.963832	−	0.266511i	$-0.914129\pi$
$509$	0.745100	−	4.22567i	0.0330260	−	0.187300i	0.996858	+	0.0792114i	$0.0252402\pi$
$510$	−1.91147	−	0.695720i	−0.0846415	−	0.0308070i
$511$	−10.6964	+	8.97535i	−0.473181	+	0.397046i
$512$	1.00000			0.0441942
$513$	−1.81908	−	3.96118i	−0.0803142	−	0.174890i
$514$	7.90167			0.348528
$515$	−1.21301	+	1.01784i	−0.0534517	+	0.0448513i
$516$	−3.37939	−	1.23000i	−0.148769	−	0.0541475i
$517$	8.88490	−	50.3888i	0.390758	−	2.21610i
$518$	2.11334	+	11.9854i	0.0928549	+	0.526606i
$519$	−5.21688	+	1.89879i	−0.228996	+	0.0833476i
$520$	1.40033	−	2.42544i	0.0614085	−	0.106363i
$521$	−4.38532	−	7.59559i	−0.192124	−	0.332769i	0.753830	−	0.657070i	$-0.228204\pi$
$521$	−4.38532	−	7.59559i	−0.192124	−	0.332769i	−0.945954	+	0.324301i	$0.894871\pi$
$522$	−1.15657	−	0.970481i	−0.0506219	−	0.0424768i
$523$	22.9800	+	19.2825i	1.00484	+	0.843165i	0.987648	−	0.156687i	$-0.0500815\pi$
$523$	22.9800	+	19.2825i	1.00484	+	0.843165i	0.0171965	+	0.999852i	$0.494526\pi$
$524$	5.40420	+	9.36035i	0.236084	+	0.408909i
$525$	−10.5458	+	18.2658i	−0.460255	+	0.797184i
$526$	23.8405	−	8.67723i	1.03949	−	0.378345i
$527$	1.64930	+	9.35365i	0.0718446	+	0.407451i
$528$	−0.960637	+	5.44804i	−0.0418064	+	0.237096i
$529$	12.2147	+	4.44577i	0.531072	+	0.193294i
$530$	0.958826	−	0.804551i	0.0416487	−	0.0349474i
$531$	1.32770			0.0576171
$532$	−13.5175	−	13.6761i	−0.586060	−	0.592936i
$533$	−11.7202			−0.507657
$534$	9.56077	−	8.02244i	0.413735	−	0.347165i
$535$	6.95424	+	2.53114i	0.300658	+	0.109431i
$536$	−0.432419	+	2.45237i	−0.0186776	+	0.105926i
$537$	−1.44996	−	8.22313i	−0.0625704	−	0.354854i
$538$	−18.9538	+	6.89863i	−0.817158	+	0.297421i
$539$	34.4680	−	59.7003i	1.48464	−	2.57147i
$540$	0.233956	+	0.405223i	0.0100678	+	0.0174380i
$541$	3.83544	+	3.21831i	0.164898	+	0.138366i	0.721503	−	0.692411i	$-0.243452\pi$
$541$	3.83544	+	3.21831i	0.164898	+	0.138366i	−0.556605	+	0.830778i	$0.687896\pi$
$542$	15.7121	+	13.1840i	0.674894	+	0.566303i
$543$	6.29426	+	10.9020i	0.270113	+	0.467849i
$544$	2.17365	−	3.76487i	0.0931944	−	0.161417i
$545$	−2.55690	+	0.930637i	−0.109526	+	0.0398641i
$546$	−4.58512	−	26.0035i	−0.196225	−	1.11285i
$547$	2.35803	−	13.3731i	0.100822	−	0.571790i	−0.891985	−	0.452065i	$-0.850687\pi$
$547$	2.35803	−	13.3731i	0.100822	−	0.571790i	0.992807	−	0.119725i	$-0.0382014\pi$
$548$	−10.3093	−	3.75227i	−0.440391	−	0.160289i
$549$	−5.08512	+	4.26692i	−0.217028	+	0.182108i
$550$	26.4492			1.12780
$551$	−4.62630	−	4.68058i	−0.197087	−	0.199399i
$552$	−3.16250			−0.134605
$553$	−4.26991	+	3.58288i	−0.181575	+	0.152360i
$554$	−8.58424	−	3.12441i	−0.364710	−	0.132743i
$555$	0.224155	−	1.27125i	0.00951487	−	0.0539615i
$556$	−2.33750	−	13.2566i	−0.0991319	−	0.562205i
$557$	22.2961	−	8.11511i	0.944715	−	0.343848i	0.176689	−	0.984267i	$-0.443461\pi$
$557$	22.2961	−	8.11511i	0.944715	−	0.343848i	0.768026	+	0.640419i	$0.221239\pi$
$558$	1.09240	−	1.89209i	0.0462448	−	0.0800984i
$559$	−10.7626	−	18.6414i	−0.455211	−	0.788449i
$560$	1.58125	+	1.32683i	0.0668201	+	0.0560687i
$561$	18.4231	+	15.4588i	0.777823	+	0.652671i
$562$	1.71554	+	2.97140i	0.0723656	+	0.125341i
$563$	7.37211	−	12.7689i	0.310697	−	0.538144i	−0.667816	−	0.744326i	$-0.732771\pi$
$563$	7.37211	−	12.7689i	0.310697	−	0.538144i	0.978514	+	0.206183i	$0.0661041\pi$
$564$	8.69119	−	3.16333i	0.365965	−	0.133200i
$565$	−0.986081	−	5.59234i	−0.0414847	−	0.235272i
$566$	1.95218	−	11.0714i	0.0820563	−	0.465364i
$567$	4.14543	+	1.50881i	0.174092	+	0.0633642i
$568$	−5.81908	+	4.88279i	−0.244163	+	0.204877i
$569$	23.9668			1.00474			0.502370	−	0.864653i	$-0.332462\pi$
$569$	23.9668			1.00474			0.502370	+	0.864653i	$0.332462\pi$
$570$	0.851167	+	1.85348i	0.0356515	+	0.0776338i
$571$	−41.0847			−1.71934			−0.859671	−	0.510848i	$-0.829331\pi$
$571$	−41.0847			−1.71934			−0.859671	+	0.510848i	$0.829331\pi$
$572$	−25.3653	+	21.2840i	−1.06058	+	0.889929i
$573$	6.31180	+	2.29731i	0.263679	+	0.0959714i
$574$	1.50000	−	8.50692i	0.0626088	−	0.355072i
$575$	2.62558	+	14.8904i	0.109494	+	0.620973i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	3.72756	−	6.45632i	0.155180	−	0.268780i	−0.777944	−	0.628333i	$-0.783737\pi$
$577$	3.72756	−	6.45632i	0.155180	−	0.268780i	0.933125	+	0.359553i	$0.117071\pi$
$578$	−0.949493	−	1.64457i	−0.0394937	−	0.0684051i
$579$	−9.60014	−	8.05547i	−0.398968	−	0.334774i
$580$	0.541174	+	0.454099i	0.0224710	+	0.0188554i
$581$	−39.5638	−	68.5265i	−1.64138	−	2.84296i
$582$	4.15523	−	7.19707i	0.172240	−	0.298328i
$583$	−13.9058	+	5.06132i	−0.575921	+	0.209618i
$584$	0.549630	+	3.11711i	0.0227438	+	0.128987i
$585$	−0.486329	+	2.75811i	−0.0201072	+	0.114034i
$586$	13.6557	+	4.97027i	0.564112	+	0.205320i
$587$	4.53462	−	3.80499i	0.187164	−	0.157049i	−0.544391	−	0.838831i	$-0.683239\pi$
$587$	4.53462	−	3.80499i	0.187164	−	0.157049i	0.731555	+	0.681782i	$0.238795\pi$
$588$	12.4611			0.513887
$589$	5.50774	−	7.76903i	0.226943	−	0.320117i
$590$	−0.621244			−0.0255762
$591$	−3.11927	+	2.61738i	−0.128310	+	0.107665i
$592$	2.59240	+	0.943555i	0.106547	+	0.0387799i
$593$	−0.870767	+	4.93837i	−0.0357581	+	0.202794i	−0.997453	−	0.0713281i	$-0.977276\pi$
$593$	−0.870767	+	4.93837i	−0.0357581	+	0.202794i	0.961695	+	0.274122i	$0.0883874\pi$
$594$	−0.960637	−	5.44804i	−0.0394154	−	0.223536i
$595$	8.43242	−	3.06915i	0.345695	−	0.125823i
$596$	−4.09492	+	7.09261i	−0.167735	+	0.290525i
$597$	3.57785	+	6.19702i	0.146432	+	0.253627i
$598$	−14.5005	−	12.1673i	−0.592968	−	0.497559i
$599$	3.68164	+	3.08926i	0.150428	+	0.126224i	0.714896	−	0.699231i	$-0.246474\pi$
$599$	3.68164	+	3.08926i	0.150428	+	0.126224i	−0.564468	+	0.825455i	$0.690919\pi$
$600$	2.39053	+	4.14052i	0.0975930	+	0.169036i
$601$	−4.42468	+	7.66377i	−0.180486	+	0.312612i	−0.942046	−	0.335483i	$-0.891101\pi$
$601$	−4.42468	+	7.66377i	−0.180486	+	0.312612i	0.761560	+	0.648095i	$0.224434\pi$
$602$	14.9081	−	5.42609i	0.607608	−	0.221151i
$603$	−0.432419	−	2.45237i	−0.0176094	−	0.0998681i
$604$	3.67112	−	20.8200i	0.149376	−	0.847152i
$605$	8.61974	+	3.13733i	0.350442	+	0.127551i
$606$	0.950837	−	0.797847i	0.0386251	−	0.0324103i
$607$	0.715948			0.0290594			0.0145297	−	0.999894i	$-0.495375\pi$
$607$	0.715948			0.0290594			0.0145297	+	0.999894i	$0.495375\pi$
$608$	−4.21688	+	1.10359i	−0.171017	+	0.0447565i
$609$	6.66044			0.269895
$610$	2.37939	−	1.99654i	0.0963385	−	0.0808376i
$611$	52.0207	+	18.9340i	2.10453	+	0.765987i
$612$	−0.754900	+	4.28125i	−0.0305150	+	0.173059i
$613$	4.23870	+	24.0389i	0.171200	+	0.970921i	0.942440	+	0.334377i	$0.108526\pi$
$613$	4.23870	+	24.0389i	0.171200	+	0.970921i	−0.771240	+	0.636545i	$0.780363\pi$
$614$	24.1532	−	8.79104i	0.974743	−	0.354777i
$615$	−0.458111	+	0.793471i	−0.0184728	+	0.0319959i
$616$	−12.2023	−	21.1351i	−0.491646	−	0.851556i
$617$	−33.2918	−	27.9351i	−1.34028	−	1.12463i	−0.981555	−	0.191182i	$-0.938768\pi$
$617$	−33.2918	−	27.9351i	−1.34028	−	1.12463i	−0.358722	−	0.933444i	$-0.616788\pi$
$618$	2.59240	+	2.17528i	0.104281	+	0.0875025i
$619$	−11.8648	−	20.5505i	−0.476888	−	0.825994i	0.522761	−	0.852479i	$-0.324902\pi$
$619$	−11.8648	−	20.5505i	−0.476888	−	0.825994i	−0.999649	+	0.0264848i	$0.991569\pi$
$620$	−0.511144	+	0.885328i	−0.0205281	+	0.0355556i
$621$	2.97178	−	1.08164i	0.119253	−	0.0434047i
$622$	1.01367	+	5.74881i	0.0406445	+	0.230506i
$623$	−9.56077	+	54.2218i	−0.383044	+	2.17235i
$624$	−5.62449	−	2.04715i	−0.225160	−	0.0819514i
$625$	16.6721	−	13.9895i	0.666882	−	0.559581i
$626$	−16.5107			−0.659902
$627$	−1.96151	−	24.0339i	−0.0783353	−	0.959822i
$628$	19.6382			0.783648
$629$	9.18732	−	7.70908i	0.366322	−	0.307381i
$630$	−1.93969	−	0.705990i	−0.0772792	−	0.0281273i
$631$	−4.48293	+	25.4239i	−0.178462	+	1.01211i	0.755609	+	0.655023i	$0.227341\pi$
$631$	−4.48293	+	25.4239i	−0.178462	+	1.01211i	−0.934071	+	0.357087i	$0.883770\pi$
$632$	0.219408	+	1.24432i	0.00872757	+	0.0494965i
$633$	2.49273	−	0.907278i	0.0990770	−	0.0360611i
$634$	13.4748	−	23.3390i	0.535152	−	0.926910i
$635$	0.106067	+	0.183713i	0.00420913	+	0.00729043i
$636$	−2.04916	−	1.71945i	−0.0812546	−	0.0681807i
$637$	57.1357	+	47.9425i	2.26380	+	1.89955i
$638$	−4.17617	−	7.23335i	−0.165336	−	0.286371i
$639$	3.79813	−	6.57856i	0.150252	−	0.260244i
$640$	0.439693	−	0.160035i	0.0173804	−	0.00632594i
$641$	−1.87645	−	10.6419i	−0.0741153	−	0.420329i	−0.999179	−	0.0405163i	$-0.987100\pi$
$641$	−1.87645	−	10.6419i	−0.0741153	−	0.420329i	0.925064	−	0.379812i	$-0.124011\pi$
$642$	2.74644	−	15.5759i	0.108394	−	0.614730i
$643$	−13.5360	−	4.92669i	−0.533806	−	0.194290i	0.0610309	−	0.998136i	$-0.480561\pi$
$643$	−13.5360	−	4.92669i	−0.533806	−	0.194290i	−0.594837	+	0.803846i	$0.702783\pi$
$644$	10.6873	−	8.96773i	0.421139	−	0.353378i
$645$	−1.68273			−0.0662576
$646$	−5.01114	+	18.2748i	−0.197161	+	0.719013i
$647$	−24.9463			−0.980738			−0.490369	−	0.871515i	$-0.663138\pi$
$647$	−24.9463			−0.980738			−0.490369	+	0.871515i	$0.663138\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	6.90198	+	2.51211i	0.270926	+	0.0986091i
$650$	−4.96926	+	28.1820i	−0.194910	+	1.10539i
$651$	1.67365	+	9.49173i	0.0655954	+	0.372010i
$652$	−4.27719	+	1.55677i	−0.167508	+	0.0609678i
$653$	−17.8071	+	30.8427i	−0.696844	+	1.20697i	0.272711	+	0.962096i	$0.412080\pi$
$653$	−17.8071	+	30.8427i	−0.696844	+	1.20697i	−0.969555	+	0.244873i	$0.921254\pi$
$654$	2.90760	+	5.03612i	0.113696	+	0.196928i
$655$	3.87417	+	3.25082i	0.151376	+	0.127020i
$656$	−1.50000	−	1.25865i	−0.0585652	−	0.0491420i
$657$	−1.58260	−	2.74114i	−0.0617430	−	0.106942i
$658$	−20.4008	+	35.3352i	−0.795306	+	1.37751i
$659$	46.0163	−	16.7485i	1.79254	−	0.652431i	0.793501	−	0.608569i	$-0.208256\pi$
$659$	46.0163	−	16.7485i	1.79254	−	0.652431i	0.999038	−	0.0438619i	$-0.0139662\pi$
$660$	0.449493	+	2.54920i	0.0174965	+	0.0992275i
$661$	−5.90966	+	33.5154i	−0.229859	+	1.30360i	0.623315	+	0.781971i	$0.285785\pi$
$661$	−5.90966	+	33.5154i	−0.229859	+	1.30360i	−0.853174	+	0.521626i	$0.825326\pi$
$662$	−26.7704	−	9.74362i	−1.04046	−	0.378697i
$663$	−19.9329	+	16.7257i	−0.774129	+	0.649571i
$664$	−17.9368			−0.696081
$665$	−8.13223	−	3.85002i	−0.315354	−	0.149297i
$666$	−2.75877			−0.106900
$667$	3.65767	−	3.06915i	0.141626	−	0.118838i
$668$	−17.9868	−	6.54666i	−0.695930	−	0.253298i
$669$	2.42246	−	13.7384i	0.0936576	−	0.531158i
$670$	0.202333	+	1.14749i	0.00781682	+	0.0443314i
$671$	−34.5082	+	12.5600i	−1.33217	+	0.484872i
$672$	2.20574	−	3.82045i	0.0850882	−	0.147377i
$673$	14.1493	+	24.5073i	0.545415	+	0.944687i	0.998581	+	0.0532607i	$0.0169614\pi$
$673$	14.1493	+	24.5073i	0.545415	+	0.944687i	−0.453165	+	0.891427i	$0.649705\pi$
$674$	12.7836	+	10.7267i	0.492405	+	0.413177i
$675$	−3.66250	−	3.07321i	−0.140970	−	0.118288i
$676$	−11.4128	−	19.7676i	−0.438955	−	0.760292i
$677$	−12.5025	+	21.6550i	−0.480511	+	0.832270i	−0.999750	−	0.0223595i	$-0.992882\pi$
$677$	−12.5025	+	21.6550i	−0.480511	+	0.832270i	0.519239	+	0.854629i	$0.326215\pi$
$678$	−11.4042	+	4.15079i	−0.437976	+	0.159410i
$679$	6.36618	+	36.1044i	0.244312	+	1.38556i
$680$	0.353226	−	2.00324i	0.0135456	−	0.0768209i
$681$	22.1878	+	8.07569i	0.850238	+	0.309461i
$682$	9.25877	−	7.76903i	0.354537	−	0.297492i
$683$	−40.1284			−1.53547			−0.767734	−	0.640768i	$-0.778616\pi$
$683$	−40.1284			−1.53547			−0.767734	+	0.640768i	$0.778616\pi$
$684$	3.58512	−	2.47929i	0.137081	−	0.0947982i
$685$	−5.13341			−0.196137
$686$	−18.4552	+	15.4857i	−0.704622	+	0.591248i
$687$	−8.09152	−	2.94507i	−0.308711	−	0.112362i
$688$	0.624485	−	3.54163i	0.0238083	−	0.135023i
$689$	−2.78029	−	15.7678i	−0.105921	−	0.600705i
$690$	−1.39053	+	0.506111i	−0.0529366	+	0.0192673i
$691$	−1.44087	+	2.49567i	−0.0548135	+	0.0949397i	−0.892130	−	0.451778i	$-0.850790\pi$
$691$	−1.44087	+	2.49567i	−0.0548135	+	0.0949397i	0.837317	+	0.546718i	$0.184123\pi$
$692$	−2.77584	−	4.80790i	−0.105522	−	0.182769i
$693$	18.6951	+	15.6870i	0.710167	+	0.595901i
$694$	−14.3478	−	12.0392i	−0.544634	−	0.457002i
$695$	−3.14930	−	5.45475i	−0.119460	−	0.206910i
$696$	0.754900	−	1.30753i	0.0286144	−	0.0495616i
$697$	−7.99912	+	2.91144i	−0.302988	+	0.110279i
$698$	−0.284930	−	1.61592i	−0.0107847	−	0.0611633i
$699$	−2.68139	+	15.2069i	−0.101419	+	0.575178i
$700$	−19.8195	−	7.21372i	−0.749108	−	0.272653i
$701$	11.8491	−	9.94258i	0.447535	−	0.375526i	−0.390985	−	0.920397i	$-0.627866\pi$
$701$	11.8491	−	9.94258i	0.447535	−	0.375526i	0.838520	+	0.544871i	$0.183421\pi$
$702$	5.98545			0.225906
$703$	−11.9731	−	1.11792i	−0.451575	−	0.0421630i
$704$	−5.53209			−0.208498
$705$	3.31521	−	2.78179i	0.124858	−	0.104768i
$706$	11.1887	+	4.07234i	0.421091	+	0.153265i
$707$	−0.950837	+	5.39246i	−0.0357599	+	0.202804i
$708$	0.230552	+	1.30753i	0.00866467	+	0.0491398i
$709$	−43.8353	+	15.9548i	−1.64627	+	0.599193i	−0.988119	−	0.153692i	$-0.950884\pi$
$709$	−43.8353	+	15.9548i	−1.64627	+	0.599193i	−0.658152	+	0.752885i	$0.728661\pi$
$710$	−1.77719	+	3.07818i	−0.0666967	+	0.115522i
$711$	−0.631759	−	1.09424i	−0.0236928	−	0.0410372i
$712$	9.56077	+	8.02244i	0.358305	+	0.300654i
$713$	5.29292	+	4.44129i	0.198221	+	0.166327i
$714$	−9.58899	−	16.6086i	−0.358859	−	0.621562i
$715$	−7.74675	+	13.4178i	−0.289712	+	0.501796i
$716$	7.84642	−	2.85586i	0.293234	−	0.106729i
$717$	1.34730	+	7.64090i	0.0503157	+	0.285355i
$718$	0.398681	−	2.26103i	0.0148786	−	0.0843810i
$719$	10.8020	+	3.93161i	0.402847	+	0.146624i	0.535494	−	0.844539i	$-0.320125\pi$
$719$	10.8020	+	3.93161i	0.402847	+	0.146624i	−0.132647	+	0.991163i	$0.542348\pi$
$720$	−0.358441	+	0.300767i	−0.0133583	+	0.0112089i
$721$	−14.9290			−0.555986
$722$	16.5642	−	9.30742i	0.616455	−	0.346386i
$723$	−13.2858			−0.494104
$724$	−9.64337	+	8.09175i	−0.358393	+	0.300727i
$725$	−6.78312	−	2.46885i	−0.251919	−	0.0916909i
$726$	3.40420	−	19.3062i	0.126342	−	0.716519i
$727$	3.02687	+	17.1663i	0.112261	+	0.636661i	0.988070	+	0.154004i	$0.0492170\pi$
$727$	3.02687	+	17.1663i	0.112261	+	0.636661i	−0.875810	+	0.482657i	$0.839672\pi$
$728$	24.8123	−	9.03093i	0.919604	−	0.334708i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.740514	+	1.28261i	0.0274077	+	0.0474715i
$731$	−11.9764	−	10.0494i	−0.442962	−	0.371689i
$732$	−5.08512	−	4.26692i	−0.187952	−	0.157710i
$733$	21.9393	+	38.0000i	0.810346	+	1.40356i	0.912622	+	0.408804i	$0.134054\pi$
$733$	21.9393	+	38.0000i	0.810346	+	1.40356i	−0.102276	+	0.994756i	$0.532613\pi$
$734$	10.7476	−	18.6154i	0.396702	−	0.687108i
$735$	5.47906	−	1.99421i	0.202098	−	0.0735577i
$736$	−0.549163	−	3.11446i	−0.0202424	−	0.114800i
$737$	2.39218	−	13.5667i	0.0881170	−	0.499736i
$738$	1.84002	+	0.669713i	0.0677322	+	0.0246525i
$739$	−13.6040	+	11.4151i	−0.500432	+	0.419912i	−0.857747	−	0.514072i	$-0.828136\pi$
$739$	−13.6040	+	11.4151i	−0.500432	+	0.419912i	0.357316	+	0.933984i	$0.383692\pi$
$740$	1.29086			0.0474529
$741$	25.9770	+	2.42544i	0.954289	+	0.0891008i
$742$	11.8007			0.433216
$743$	7.98751	−	6.70232i	0.293033	−	0.245884i	−0.484404	−	0.874844i	$-0.660964\pi$
$743$	7.98751	−	6.70232i	0.293033	−	0.245884i	0.777438	+	0.628960i	$0.216519\pi$
$744$	2.05303	+	0.747243i	0.0752679	+	0.0273953i
$745$	−0.665441	+	3.77390i	−0.0243799	+	0.138265i
$746$	4.85891	+	27.5562i	0.177897	+	1.00891i
$747$	16.8550	−	6.13473i	0.616694	−	0.224458i
$748$	−12.0248	+	20.8276i	−0.439671	+	0.761532i
$749$	34.8862	+	60.4248i	1.27472	+	2.20787i
$750$	3.50593	+	2.94182i	0.128018	+	0.107420i
$751$	−26.0915	−	21.8934i	−0.952093	−	0.798901i	0.0275557	−	0.999620i	$-0.491228\pi$
$751$	−26.0915	−	21.8934i	−0.952093	−	0.798901i	−0.979649	+	0.200719i	$0.935672\pi$
$752$	4.62449	+	8.00984i	0.168638	+	0.292089i
$753$	8.82547	−	15.2862i	0.321618	−	0.557059i
$754$	8.49185	−	3.09078i	0.309255	−	0.112560i
$755$	−1.71776	−	9.74189i	−0.0625156	−	0.354544i
$756$	−0.766044	+	4.34445i	−0.0278608	+	0.158006i
$757$	−40.6664	−	14.8014i	−1.47805	−	0.537965i	−0.527774	−	0.849385i	$-0.676973\pi$
$757$	−40.6664	−	14.8014i	−1.47805	−	0.537965i	−0.950272	+	0.311420i	$0.899195\pi$
$758$	6.80999	−	5.71426i	0.247350	−	0.207551i
$759$	17.4953			0.635037
$760$	−1.67752	+	1.16009i	−0.0608500	+	0.0420809i
$761$	14.1679			0.513585			0.256793	−	0.966467i	$-0.417334\pi$
$761$	14.1679			0.513585			0.256793	+	0.966467i	$0.417334\pi$
$762$	0.347296	−	0.291416i	0.0125812	−	0.0105569i
$763$	−24.1065	−	8.77406i	−0.872715	−	0.317642i
$764$	−1.16637	+	6.61484i	−0.0421979	+	0.239316i
$765$	0.353226	+	2.00324i	0.0127709	+	0.0724275i
$766$	23.5069	−	8.55580i	0.849338	−	0.309134i
$767$	−3.97343	+	6.88218i	−0.143472	+	0.248501i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−13.9722	−	11.7241i	−0.503852	−	0.422782i	0.355107	−	0.934825i	$-0.384444\pi$
$769$	−13.9722	−	11.7241i	−0.503852	−	0.422782i	−0.858960	+	0.512043i	$0.828889\pi$
$770$	−8.74763	−	7.34013i	−0.315243	−	0.264520i
$771$	−3.95084	−	6.84305i	−0.142286	−	0.246446i
$772$	6.26604	−	10.8531i	0.225520	−	0.390612i
$773$	26.5437	−	9.66112i	0.954711	−	0.347486i	0.182752	−	0.983159i	$-0.441499\pi$
$773$	26.5437	−	9.66112i	0.954711	−	0.347486i	0.771959	+	0.635673i	$0.219277\pi$
$774$	0.624485	+	3.54163i	0.0224467	+	0.127301i
$775$	1.81386	−	10.2869i	0.0651559	−	0.369517i
$776$	7.80928	+	2.84234i	0.280337	+	0.102034i
$777$	9.32295	−	7.82288i	0.334459	−	0.280644i
$778$	−23.3327			−0.836520
$779$	7.71436	+	3.65219i	0.276395	+	0.130853i
$780$	−2.80066			−0.100280
$781$	32.1917	−	27.0120i	1.15191	−	0.966566i
$782$	−12.9192	−	4.70221i	−0.461990	−	0.168151i
$783$	−0.262174	+	1.48686i	−0.00936934	+	0.0531361i
$784$	2.16385	+	12.2718i	0.0772803	+	0.438278i
$785$	8.63475	−	3.14279i	0.308188	−	0.112171i
$786$	5.40420	−	9.36035i	0.192761	−	0.333873i
$787$	−9.07057	−	15.7107i	−0.323331	−	0.560026i	0.657842	−	0.753156i	$-0.271469\pi$
$787$	−9.07057	−	15.7107i	−0.323331	−	0.560026i	−0.981173	+	0.193130i	$0.938136\pi$
$788$	−3.11927	−	2.61738i	−0.111119	−	0.0932403i
$789$	−19.4349	−	16.3079i	−0.691902	−	0.580575i
$790$	0.295607	+	0.512007i	0.0105172	+	0.0182164i
$791$	26.7690	−	46.3653i	0.951797	−	1.64856i
$792$	5.19846	−	1.89209i	0.184719	−	0.0672323i
$793$	−6.89945	−	39.1287i	−0.245007	−	1.38950i
$794$	0.657918	−	3.73124i	0.0233486	−	0.132417i
$795$	−1.17617	−	0.428092i	−0.0417146	−	0.0151829i
$796$	−5.48158	+	4.59959i	−0.194290	+	0.163028i
$797$	−32.8111			−1.16223			−0.581114	−	0.813822i	$-0.697383\pi$
$797$	−32.8111			−1.16223			−0.581114	+	0.813822i	$0.697383\pi$
$798$	−5.08512	+	18.5446i	−0.180011	+	0.656472i
$799$	40.2080			1.42246
$800$	−3.66250	+	3.07321i	−0.129489	+	0.108654i
$801$	−11.7280	−	4.26865i	−0.414389	−	0.150825i
$802$	−3.79591	+	21.5277i	−0.134038	+	0.760169i
$803$	−3.04060	−	17.2441i	−0.107300	−	0.608531i
$804$	2.34002	−	0.851698i	0.0825262	−	0.0300371i
$805$	3.26399	−	5.65339i	0.115040	−	0.199256i
$806$	6.53849	+	11.3250i	0.230308	+	0.398906i
$807$	15.4513	+	12.9652i	0.543912	+	0.456396i
$808$	0.950837	+	0.797847i	0.0334503	+	0.0280682i
$809$	4.67112	+	8.09062i	0.164228	+	0.284451i	0.936381	−	0.350986i	$-0.114153\pi$
$809$	4.67112	+	8.09062i	0.164228	+	0.284451i	−0.772153	+	0.635437i	$0.780820\pi$
$810$	0.233956	−	0.405223i	0.00822036	−	0.0142381i
$811$	14.1027	−	5.13295i	0.495211	−	0.180242i	−0.0823275	−	0.996605i	$-0.526235\pi$
$811$	14.1027	−	5.13295i	0.495211	−	0.180242i	0.577539	+	0.816363i	$0.304013\pi$
$812$	1.15657	+	6.55926i	0.0405878	+	0.230185i
$813$	3.56165	−	20.1991i	0.124913	−	0.708414i
$814$	−14.3414	−	5.21983i	−0.502665	−	0.182955i
$815$	−1.63151	+	1.36900i	−0.0571493	+	0.0479540i
$816$	−4.34730			−0.152186
$817$	1.27513	+	15.6238i	0.0446111	+	0.546608i
$818$	−7.91622			−0.276784
$819$	−20.2271	+	16.9726i	−0.706794	+	0.593070i
$820$	−0.860967	−	0.313366i	−0.0300663	−	0.0109432i
$821$	6.34760	−	35.9990i	0.221533	−	1.25637i	−0.647671	−	0.761920i	$-0.724257\pi$
$821$	6.34760	−	35.9990i	0.221533	−	1.25637i	0.869203	−	0.494455i	$-0.164632\pi$
$822$	1.90508	+	10.8042i	0.0664472	+	0.376841i
$823$	−21.4595	+	7.81060i	−0.748030	+	0.272261i	−0.687776	−	0.725923i	$-0.741413\pi$
$823$	−21.4595	+	7.81060i	−0.748030	+	0.272261i	−0.0602532	+	0.998183i	$0.519191\pi$
$824$	−1.69207	+	2.93075i	−0.0589459	+	0.102097i
$825$	−13.2246	−	22.9057i	−0.460422	−	0.797475i
$826$	−4.48680	−	3.76487i	−0.156116	−	0.130997i
$827$	1.86303	+	1.56326i	0.0647838	+	0.0543600i	0.674605	−	0.738179i	$-0.264314\pi$
$827$	1.86303	+	1.56326i	0.0647838	+	0.0543600i	−0.609821	+	0.792539i	$0.708759\pi$
$828$	1.58125	+	2.73881i	0.0549523	+	0.0951802i
$829$	11.6702	−	20.2135i	0.405324	−	0.702042i	−0.589035	−	0.808108i	$-0.700492\pi$
$829$	11.6702	−	20.2135i	0.405324	−	0.702042i	0.994359	+	0.106065i	$0.0338253\pi$
$830$	−7.88666	+	2.87051i	−0.273750	+	0.0996368i
$831$	1.58630	+	8.99638i	0.0550283	+	0.312081i
$832$	1.03936	−	5.89452i	0.0360334	−	0.204356i
$833$	50.9051	+	18.5280i	1.76376	+	0.641956i
$834$	−10.3118	+	8.65263i	−0.357069	+	0.299616i
$835$	−8.95636			−0.309947
$836$	23.3282	−	6.10516i	0.806821	−	0.211151i
$837$	−2.18479			−0.0755175
$838$	4.77197	−	4.00416i	0.164845	−	0.138321i
$839$	1.37851	+	0.501736i	0.0475914	+	0.0173218i	0.365706	−	0.930730i	$-0.380828\pi$
$839$	1.37851	+	0.501736i	0.0475914	+	0.0173218i	−0.318115	+	0.948052i	$0.603050\pi$
$840$	0.358441	−	2.03282i	0.0123674	−	0.0701389i
$841$	−4.63997	−	26.3146i	−0.159999	−	0.907399i
$842$	3.35591	−	1.22145i	0.115652	−	0.0420940i
$843$	1.71554	−	2.97140i	0.0590862	−	0.102340i
$844$	1.32635	+	2.29731i	0.0456549	+	0.0790766i
$845$	−8.18164	−	6.86521i	−0.281457	−	0.236170i
$846$	−7.08512	−	5.94512i	−0.243592	−	0.204398i
$847$	43.2413	+	74.8961i	1.48579	+	2.57346i
$848$	1.33750	−	2.31661i	0.0459298	−	0.0795528i
$849$	−10.5642	+	3.84505i	−0.362562	+	0.131962i
$850$	3.60922	+	20.4689i	0.123795	+	0.702078i
$851$	1.51501	−	8.59208i	0.0519340	−	0.294533i
$852$	7.13816	+	2.59808i	0.244549	+	0.0890086i
$853$	−7.15207	+	6.00130i	−0.244882	+	0.205481i	−0.756965	−	0.653456i	$-0.773319\pi$
$853$	−7.15207	+	6.00130i	−0.244882	+	0.205481i	0.512083	+	0.858936i	$0.328874\pi$
$854$	29.2841			1.00208
$855$	1.17958	−	1.66387i	0.0403407	−	0.0569032i
$856$	15.8161			0.540585
$857$	26.6930	−	22.3981i	0.911816	−	0.765104i	−0.0606480	−	0.998159i	$-0.519317\pi$
$857$	26.6930	−	22.3981i	0.911816	−	0.765104i	0.972464	+	0.233055i	$0.0748723\pi$
$858$	31.1152	+	11.3250i	1.06225	+	0.386629i
$859$	−4.00758	+	22.7281i	−0.136737	+	0.775473i	0.836898	+	0.547359i	$0.184367\pi$
$859$	−4.00758	+	22.7281i	−0.136737	+	0.775473i	−0.973635	+	0.228114i	$0.926744\pi$
$860$	−0.292204	−	1.65717i	−0.00996406	−	0.0565090i
$861$	−8.11721	+	2.95442i	−0.276634	+	0.100686i
$862$	12.9042	−	22.3507i	0.439519	−	0.761269i
$863$	−21.5788	−	37.3755i	−0.734550	−	1.27228i	−0.954920	−	0.296862i	$-0.904060\pi$
$863$	−21.5788	−	37.3755i	−0.734550	−	1.27228i	0.220370	−	0.975416i	$-0.429273\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	−1.98995	−	1.66977i	−0.0676604	−	0.0567738i
$866$	−13.0496	−	22.6026i	−0.443444	−	0.768068i
$867$	−0.949493	+	1.64457i	−0.0322465	+	0.0558525i
$868$	−9.05690	+	3.29644i	−0.307411	+	0.111889i
$869$	−1.21378	−	6.88370i	−0.0411748	−	0.233514i
$870$	0.122674	−	0.695720i	0.00415904	−	0.0235871i
$871$	14.0061	+	5.09780i	0.474578	+	0.172732i
$872$	−4.45471	+	3.73794i	−0.150855	+	0.126583i
$873$	−8.31046			−0.281266
$874$	5.75284	+	12.5273i	0.194593	+	0.423741i
$875$	−20.1898			−0.682541
$876$	2.42468	−	2.03455i	0.0819223	−	0.0687409i
$877$	−42.1374	−	15.3368i	−1.42288	−	0.517886i	−0.487998	−	0.872845i	$-0.662273\pi$
$877$	−42.1374	−	15.3368i	−1.42288	−	0.517886i	−0.934882	+	0.354959i	$0.884495\pi$
$878$	3.92989	−	22.2875i	0.132627	−	0.752168i
$879$	−2.52347	−	14.3113i	−0.0851146	−	0.482709i
$880$	−2.43242	+	0.885328i	−0.0819968	+	0.0298444i
$881$	2.29932	−	3.98253i	0.0774659	−	0.134175i	−0.824690	−	0.565585i	$-0.808650\pi$
$881$	2.29932	−	3.98253i	0.0774659	−	0.134175i	0.902156	+	0.431410i	$0.141984\pi$
$882$	−6.23055	−	10.7916i	−0.209794	−	0.363373i
$883$	−5.53524	−	4.64462i	−0.186276	−	0.156304i	0.544881	−	0.838513i	$-0.316575\pi$
$883$	−5.53524	−	4.64462i	−0.186276	−	0.156304i	−0.731157	+	0.682209i	$0.761019\pi$
$884$	−19.9329	−	16.7257i	−0.670415	−	0.562545i
$885$	0.310622	+	0.538013i	0.0104414	+	0.0180851i
$886$	−7.20620	+	12.4815i	−0.242097	+	0.419325i
$887$	−43.5676	+	15.8573i	−1.46286	+	0.532437i	−0.946151	−	0.323725i	$-0.895065\pi$
$887$	−43.5676	+	15.8573i	−1.46286	+	0.532437i	−0.516707	+	0.856162i	$0.672842\pi$
$888$	−0.479055	−	2.71686i	−0.0160760	−	0.0911718i
$889$	−0.347296	+	1.96962i	−0.0116479	+	0.0660588i
$890$	5.48767	+	1.99735i	0.183947	+	0.0669513i
$891$	−4.23783	+	3.55596i	−0.141973	+	0.119129i
$892$	13.9504			0.467093
$893$	−28.3405	−	28.6730i	−0.948378	−	0.959506i
$894$	8.18984			0.273909
$895$	2.99297	−	2.51140i	0.100044	−	0.0839470i
$896$	4.14543	+	1.50881i	0.138489	+	0.0504059i
$897$	−3.28699	+	18.6414i	−0.109749	+	0.622420i
$898$	6.29860	+	35.7211i	0.210187	+	1.19203i
$899$	−3.09967	+	1.12819i	−0.103380	+	0.0376272i
$900$	2.39053	−	4.14052i	0.0796843	−	0.138017i
$901$	−5.81449	−	10.0710i	−0.193709	−	0.335514i
$902$	8.29813	+	6.96296i	0.276298	+	0.231841i
$903$	−12.1532	−	10.1977i	−0.404432	−	0.339359i
$904$	−6.06805	−	10.5102i	−0.201820	−	0.349563i
$905$	−2.94516	+	5.10116i	−0.0979003	+	0.169568i
$906$	−19.8662	+	7.23070i	−0.660010	+	0.240224i
$907$	−9.44222	−	53.5495i	−0.313524	−	1.77808i	−0.580381	−	0.814345i	$-0.697096\pi$
$907$	−9.44222	−	53.5495i	−0.313524	−	1.77808i	0.266857	−	0.963736i	$-0.414015\pi$
$908$	−4.10014	+	23.2530i	−0.136068	+	0.771679i
$909$	−1.16637	−	0.424525i	−0.0386862	−	0.0140806i
$910$	9.46451	−	7.94166i	0.313745	−	0.263264i
$911$	−16.8993			−0.559899			−0.279950	−	0.960015i	$-0.590318\pi$
$911$	−16.8993			−0.559899			−0.279950	+	0.960015i	$0.590318\pi$
$912$	3.06418	+	3.10013i	0.101465	+	0.102656i
$913$	99.2277			3.28396
$914$	−30.9898	+	26.0035i	−1.02505	+	0.860120i
$915$	−2.91875	−	1.06234i	−0.0964908	−	0.0351198i
$916$	1.49525	−	8.48000i	0.0494045	−	0.280187i
$917$	8.27972	+	46.9566i	0.273420	+	1.55064i
$918$	4.08512	−	1.48686i	0.134829	−	0.0490738i
$919$	3.85100	−	6.67014i	0.127033	−	0.220027i	−0.795493	−	0.605963i	$-0.792788\pi$
$919$	3.85100	−	6.67014i	0.127033	−	0.220027i	0.922526	+	0.385936i	$0.126121\pi$
$920$	−0.739885	−	1.28152i	−0.0243933	−	0.0422504i
$921$	−19.6898	−	16.5217i	−0.648802	−	0.544410i
$922$	−30.0861	−	25.2452i	−0.990831	−	0.831406i
$923$	22.7335	+	39.3757i	0.748284	+	1.29607i
$924$	−12.2023	+	21.1351i	−0.401427	+	0.695292i
$925$	−12.3944	+	4.51119i	−0.407525	+	0.148327i
$926$	3.61768	+	20.5169i	0.118884	+	0.674226i
$927$	0.587649	−	3.33272i	0.0193009	−	0.109461i
$928$	1.41875	+	0.516382i	0.0465727	+	0.0169511i
$929$	−13.9010	+	11.6644i	−0.456078	+	0.382695i	−0.841686	−	0.539968i	$-0.818436\pi$
$929$	−13.9010	+	11.6644i	−0.456078	+	0.382695i	0.385607	+	0.922663i	$0.373992\pi$
$930$	1.02229			0.0335222
$931$	−22.6677	−	49.3607i	−0.742904	−	1.61773i
$932$	−15.4415			−0.505803
$933$	4.47178	−	3.75227i	0.146400	−	0.122844i
$934$	11.2049	+	4.07824i	0.366634	+	0.133444i
$935$	−1.95408	+	11.0821i	−0.0639052	+	0.362424i
$936$	1.03936	+	5.89452i	0.0339726	+	0.192668i
$937$	9.71436	−	3.53574i	0.317354	−	0.115507i	−0.178432	−	0.983952i	$-0.557102\pi$
$937$	9.71436	−	3.53574i	0.317354	−	0.115507i	0.495786	+	0.868445i	$0.334880\pi$
$938$	−5.49273	+	9.51368i	−0.179344	+	0.310633i
$939$	8.25537	+	14.2987i	0.269404	+	0.466621i
$940$	3.31521	+	2.78179i	0.108130	+	0.0907320i
$941$	34.5808	+	29.0168i	1.12730	+	0.945920i	0.998950	−	0.0458088i	$-0.0145865\pi$
$941$	34.5808	+	29.0168i	1.12730	+	0.945920i	0.128353	+	0.991729i	$0.459031\pi$
$942$	−9.81908	−	17.0071i	−0.319923	−	0.554123i
$943$	−3.09627	+	5.36289i	−0.100828	+	0.174640i
$944$	−1.24763	+	0.454099i	−0.0406068	+	0.0147797i
$945$	0.358441	+	2.03282i	0.0116601	+	0.0661276i
$946$	−3.45471	+	19.5926i	−0.112322	+	0.637011i
$947$	18.9561	+	6.89944i	0.615989	+	0.224202i	0.631122	−	0.775684i	$-0.282595\pi$
$947$	18.9561	+	6.89944i	0.615989	+	0.224202i	−0.0151327	+	0.999885i	$0.504817\pi$
$948$	0.967911	−	0.812174i	0.0314363	−	0.0263782i
$949$	18.9451			0.614984
$950$	12.0528	−	17.0012i	0.391044	−	0.551593i
$951$	−26.9495			−0.873899
$952$	14.6912	−	12.3274i	0.476144	−	0.399532i
$953$	42.0232	+	15.2952i	1.36127	+	0.495460i	0.916445	−	0.400160i	$-0.131045\pi$
$953$	42.0232	+	15.2952i	1.36127	+	0.495460i	0.444820	+	0.895620i	$0.353268\pi$
$954$	−0.464508	+	2.63435i	−0.0150390	+	0.0852903i
$955$	0.545759	+	3.09516i	0.0176604	+	0.100157i
$956$	−7.29086	+	2.65366i	−0.235803	+	0.0858254i
$957$	−4.17617	+	7.23335i	−0.134997	+	0.233821i
$958$	3.70187	+	6.41182i	0.119602	+	0.207157i
$959$	−37.0749	−	31.1095i	−1.19721	−	1.00458i
$960$	−0.358441	−	0.300767i	−0.0115686	−	0.00970723i
$961$	13.1133	+	22.7130i	0.423011	+	0.732677i
$962$	8.25624	−	14.3002i	0.266192	−	0.461058i
$963$	−14.8623	+	5.40944i	−0.478931	+	0.174317i
$964$	−2.30706	−	13.0840i	−0.0743053	−	0.421406i
$965$	1.01826	−	5.77482i	0.0327788	−	0.185898i
$966$	−13.1099	−	4.77163i	−0.421805	−	0.153525i
$967$	−8.96270	+	7.52060i	−0.288221	+	0.241846i	−0.775421	−	0.631444i	$-0.782463\pi$
$967$	−8.96270	+	7.52060i	−0.288221	+	0.241846i	0.487201	+	0.873290i	$0.338018\pi$
$968$	19.6040			0.630097
$969$	18.3320	−	4.79763i	0.588910	−	0.154122i
$970$	3.88856			0.124854
$971$	27.9786	−	23.4769i	0.897877	−	0.753409i	−0.0718969	−	0.997412i	$-0.522905\pi$
$971$	27.9786	−	23.4769i	0.897877	−	0.753409i	0.969774	+	0.244003i	$0.0784608\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	10.3118	−	58.4811i	0.330581	−	1.87482i
$974$	−3.92215	−	22.2436i	−0.125674	−	0.712732i
$975$	26.8910	−	9.78752i	0.861201	−	0.313452i
$976$	3.31908	−	5.74881i	0.106241	−	0.184015i
$977$	25.0219	+	43.3392i	0.800521	+	1.38654i	0.919274	+	0.393619i	$0.128777\pi$
$977$	25.0219	+	43.3392i	0.800521	+	1.38654i	−0.118753	+	0.992924i	$0.537890\pi$
$978$	3.48680	+	2.92577i	0.111495	+	0.0935558i
$979$	−52.8911	−	44.3809i	−1.69041	−	1.41842i
$980$	2.91534	+	5.04952i	0.0931273	+	0.161301i
$981$	2.90760	−	5.03612i	0.0928326	−	0.160791i
$982$	−15.0680	+	5.48432i	−0.480841	+	0.175012i
$983$	1.71317	+	9.71589i	0.0546417	+	0.309889i	0.999863	−	0.0165411i	$-0.00526544\pi$
$983$	1.71317	+	9.71589i	0.0546417	+	0.309889i	−0.945221	+	0.326430i	$0.894154\pi$
$984$	−0.340022	+	1.92836i	−0.0108395	+	0.0614740i
$985$	−1.79039	−	0.651650i	−0.0570466	−	0.0207633i
$986$	5.02797	−	4.21897i	0.160123	−	0.134359i
$987$	40.8016			1.29873
$988$	2.12226	+	26.0035i	0.0675182	+	0.827282i
$989$	−11.3732			−0.361647
$990$	1.98293	−	1.66387i	0.0630215	−	0.0528813i
$991$	−32.1596	−	11.7051i	−1.02158	−	0.371826i	−0.223712	−	0.974655i	$-0.571818\pi$
$991$	−32.1596	−	11.7051i	−1.02158	−	0.371826i	−0.797870	+	0.602830i	$0.794040\pi$
$992$	−0.379385	+	2.15160i	−0.0120455	+	0.0683134i
$993$	4.94697	+	28.0556i	0.156987	+	0.890319i
$994$	−31.4898	+	11.4613i	−0.998795	+	0.363532i
$995$	−1.67412	+	2.89965i	−0.0530730	+	0.0919252i
$996$	8.96838	+	15.5337i	0.284174	+	0.492204i
$997$	30.4818	+	25.5773i	0.965368	+	0.810040i	0.981818	−	0.189825i	$-0.0607919\pi$
$997$	30.4818	+	25.5773i	0.965368	+	0.810040i	−0.0164497	+	0.999865i	$0.505236\pi$
$998$	−26.9047	−	22.5757i	−0.851652	−	0.714621i
$999$	1.37939	+	2.38917i	0.0436418	+	0.0755898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.b.25.1	✓	6
3.2	odd	2		342.2.u.d.253.1		6
4.3	odd	2		912.2.bo.c.481.1		6
19.4	even	9		2166.2.a.t.1.3		3
19.15	odd	18		2166.2.a.n.1.3		3
19.16	even	9	inner	114.2.i.b.73.1	yes	6
57.23	odd	18		6498.2.a.bo.1.1		3
57.35	odd	18		342.2.u.d.73.1		6
57.53	even	18		6498.2.a.bt.1.1		3
76.35	odd	18		912.2.bo.c.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.25.1	✓	6	1.1	even	1	trivial
114.2.i.b.73.1	yes	6	19.16	even	9	inner
342.2.u.d.73.1		6	57.35	odd	18
342.2.u.d.253.1		6	3.2	odd	2
912.2.bo.c.481.1		6	4.3	odd	2
912.2.bo.c.529.1		6	76.35	odd	18
2166.2.a.n.1.3		3	19.15	odd	18
2166.2.a.t.1.3		3	19.4	even	9
6498.2.a.bo.1.1		3	57.23	odd	18
6498.2.a.bt.1.1		3	57.53	even	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.0812519 - 0.460802i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(2.20574 - 3.82045i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.358441 - 0.300767i) q^{10} +(2.76604 + 4.79093i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-5.62449 + 2.04715i) q^{13} +(-0.766044 - 4.34445i) q^{14} +(-0.0812519 + 0.460802i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-3.33022 + 2.79439i) q^{17} +1.00000 q^{18} +(4.34002 + 0.405223i) q^{19} -0.467911 q^{20} +(-3.37939 + 2.83564i) q^{21} +(5.19846 + 1.89209i) q^{22} +(-0.549163 + 3.11446i) q^{23} +(0.173648 + 0.984808i) q^{24} +(4.49273 - 1.63522i) q^{25} +(-2.99273 + 5.18355i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-3.37939 - 2.83564i) q^{28} +(-1.15657 - 0.970481i) q^{29} +(0.233956 + 0.405223i) q^{30} +(1.09240 - 1.89209i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.960637 - 5.44804i) q^{33} +(-0.754900 + 4.28125i) q^{34} +(-1.93969 - 0.705990i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.75877 q^{37} +(3.58512 - 2.47929i) q^{38} +5.98545 q^{39} +(-0.358441 + 0.300767i) q^{40} +(1.84002 + 0.669713i) q^{41} +(-0.766044 + 4.34445i) q^{42} +(0.624485 + 3.54163i) q^{43} +(5.19846 - 1.89209i) q^{44} +(0.233956 - 0.405223i) q^{45} +(1.58125 + 2.73881i) q^{46} +(-7.08512 - 5.94512i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-6.23055 - 10.7916i) q^{49} +(2.39053 - 4.14052i) q^{50} +(4.08512 - 1.48686i) q^{51} +(1.03936 + 5.89452i) q^{52} +(-0.464508 + 2.63435i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(1.98293 - 1.66387i) q^{55} -4.41147 q^{56} +(-3.93969 - 1.86516i) q^{57} -1.50980 q^{58} +(1.01707 - 0.853427i) q^{59} +(0.439693 + 0.160035i) q^{60} +(-1.15270 + 6.53731i) q^{61} +(-0.379385 - 2.15160i) q^{62} +(4.14543 - 1.50881i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.40033 + 2.42544i) q^{65} +(-4.23783 - 3.55596i) q^{66} +(-1.90760 - 1.60067i) q^{67} +(2.17365 + 3.76487i) q^{68} +(1.58125 - 2.73881i) q^{69} +(-1.93969 + 0.705990i) q^{70} +(-1.31908 - 7.48086i) q^{71} +(0.173648 - 0.984808i) q^{72} +(-2.97431 - 1.08256i) q^{73} +(-2.11334 + 1.77330i) q^{74} -4.78106 q^{75} +(1.15270 - 4.20372i) q^{76} +24.4047 q^{77} +(4.58512 - 3.84737i) q^{78} +(-1.18732 - 0.432149i) q^{79} +(-0.0812519 + 0.460802i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.84002 - 0.669713i) q^{82} +(8.96838 - 15.5337i) q^{83} +(2.20574 + 3.82045i) q^{84} +(1.55825 + 1.30753i) q^{85} +(2.75490 + 2.31164i) q^{86} +(0.754900 + 1.30753i) q^{87} +(2.76604 - 4.79093i) q^{88} +(-11.7280 + 4.26865i) q^{89} +(-0.0812519 - 0.460802i) q^{90} +(-4.58512 + 26.0035i) q^{91} +(2.97178 + 1.08164i) q^{92} +(-1.67365 + 1.40436i) q^{93} -9.24897 q^{94} +(-0.165907 - 2.03282i) q^{95} +1.00000 q^{96} +(-6.36618 + 5.34186i) q^{97} +(-11.7096 - 4.26195i) q^{98} +(-0.960637 + 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7} - 3 q^{8} + 6 q^{10} + 12 q^{11} - 3 q^{12} - 21 q^{13} - 3 q^{15} + 3 q^{17} + 6 q^{18} + 6 q^{19} - 12 q^{20} - 9 q^{21} + 3 q^{22} - 15 q^{23} + 9 q^{25} - 3 q^{27} - 9 q^{28}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 - 3 * q^8 + 6 * q^10 + 12 * q^11 - 3 * q^12 - 21 * q^13 - 3 * q^15 + 3 * q^17 + 6 * q^18 + 6 * q^19 - 12 * q^20 - 9 * q^21 + 3 * q^22 - 15 * q^23 + 9 * q^25 - 3 * q^27 - 9 * q^28 + 15 * q^29 + 6 * q^30 + 3 * q^31 + 3 * q^33 - 6 * q^34 - 6 * q^35 + 6 * q^37 + 6 * q^40 - 9 * q^41 - 9 * q^43 + 3 * q^44 + 6 * q^45 + 12 * q^46 - 21 * q^47 - 3 * q^50 + 3 * q^51 + 15 * q^52 + 30 * q^53 - 9 * q^55 - 6 * q^56 - 18 * q^57 - 12 * q^58 + 27 * q^59 - 3 * q^60 - 9 * q^61 + 9 * q^62 + 9 * q^63 - 3 * q^64 - 6 * q^65 - 6 * q^66 - 15 * q^67 + 12 * q^68 + 12 * q^69 - 6 * q^70 + 9 * q^71 + 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 42 * q^77 + 6 * q^78 + 15 * q^79 - 3 * q^80 - 9 * q^82 - 3 * q^83 + 3 * q^84 - 36 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 48 * q^89 - 3 * q^90 - 6 * q^91 + 3 * q^92 - 9 * q^93 - 30 * q^94 - 48 * q^95 + 6 * q^96 + 18 * q^97 - 36 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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