LMFDB - Embedded newform 273.2.ba.c.38.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(38,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("273.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.ba (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.17
Character	$\chi$	$=$	273.38
Dual form			273.2.ba.c.194.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.100354 + 0.173818i) q^{2} +(-1.73110 + 0.0572655i) q^{3} +(0.979858 - 1.69716i) q^{4} +(-2.67317 + 1.54335i) q^{5} +(-0.183677 - 0.295150i) q^{6} +(2.55853 + 0.673741i) q^{7} +0.794745 q^{8} +(2.99344 - 0.198265i) q^{9} +O(q^{10})$	\(q+(0.100354 + 0.173818i) q^{2} +(-1.73110 + 0.0572655i) q^{3} +(0.979858 - 1.69716i) q^{4} +(-2.67317 + 1.54335i) q^{5} +(-0.183677 - 0.295150i) q^{6} +(2.55853 + 0.673741i) q^{7} +0.794745 q^{8} +(2.99344 - 0.198265i) q^{9} +(-0.536525 - 0.309763i) q^{10} +(1.43801 - 2.49070i) q^{11} +(-1.59905 + 2.99408i) q^{12} +(2.85209 - 2.20581i) q^{13} +(0.139650 + 0.512330i) q^{14} +(4.53915 - 2.82479i) q^{15} +(-1.87996 - 3.25619i) q^{16} +(3.04653 - 5.27675i) q^{17} +(0.334865 + 0.500417i) q^{18} +(0.575023 + 0.995969i) q^{19} +6.04908i q^{20} +(-4.46766 - 1.01980i) q^{21} +0.577238 q^{22} +(3.18579 - 1.83931i) q^{23} +(-1.37579 + 0.0455115i) q^{24} +(2.26389 - 3.92117i) q^{25} +(0.669627 + 0.274383i) q^{26} +(-5.17060 + 0.514638i) q^{27} +(3.65045 - 3.68207i) q^{28} +7.77891i q^{29} +(0.946519 + 0.505507i) q^{30} +(-3.80568 + 6.59163i) q^{31} +(1.17207 - 2.03008i) q^{32} +(-2.34671 + 4.39401i) q^{33} +1.22292 q^{34} +(-7.87920 + 2.14769i) q^{35} +(2.59666 - 5.27463i) q^{36} +(-1.11374 + 0.643021i) q^{37} +(-0.115411 + 0.199898i) q^{38} +(-4.81094 + 3.98181i) q^{39} +(-2.12449 + 1.22657i) q^{40} -1.74625i q^{41} +(-0.271087 - 0.878900i) q^{42} +0.749286 q^{43} +(-2.81809 - 4.88107i) q^{44} +(-7.69598 + 5.14994i) q^{45} +(0.639411 + 0.369164i) q^{46} +(8.80645 - 5.08440i) q^{47} +(3.44087 + 5.52914i) q^{48} +(6.09215 + 3.44757i) q^{49} +0.908758 q^{50} +(-4.97169 + 9.30906i) q^{51} +(-0.948977 - 7.00184i) q^{52} +(2.60900 + 1.50631i) q^{53} +(-0.608343 - 0.847097i) q^{54} +8.87743i q^{55} +(2.03338 + 0.535452i) q^{56} +(-1.05246 - 1.69120i) q^{57} +(-1.35211 + 0.780643i) q^{58} +(-10.3004 - 5.94692i) q^{59} +(-0.346403 - 10.4716i) q^{60} +(4.12566 - 2.38195i) q^{61} -1.52766 q^{62} +(7.79239 + 1.50954i) q^{63} -7.04936 q^{64} +(-4.21977 + 10.2983i) q^{65} +(-0.999259 + 0.0330558i) q^{66} +(-11.8291 - 6.82951i) q^{67} +(-5.97034 - 10.3409i) q^{68} +(-5.40960 + 3.36648i) q^{69} +(-1.16402 - 1.15402i) q^{70} -10.2745 q^{71} +(2.37902 - 0.157570i) q^{72} +(0.359690 - 0.623001i) q^{73} +(-0.223537 - 0.129059i) q^{74} +(-3.69448 + 6.91759i) q^{75} +2.25376 q^{76} +(5.35728 - 5.40369i) q^{77} +(-1.17491 - 0.436638i) q^{78} +(1.54719 + 2.67981i) q^{79} +(10.0509 + 5.80289i) q^{80} +(8.92138 - 1.18699i) q^{81} +(0.303530 - 0.175243i) q^{82} +8.31078i q^{83} +(-6.10844 + 6.58310i) q^{84} +18.8075i q^{85} +(0.0751937 + 0.130239i) q^{86} +(-0.445463 - 13.4661i) q^{87} +(1.14285 - 1.97947i) q^{88} +(-6.51669 + 3.76241i) q^{89} +(-1.66747 - 0.820883i) q^{90} +(8.78330 - 3.72206i) q^{91} -7.20907i q^{92} +(6.21055 - 11.6287i) q^{93} +(1.76752 + 1.02048i) q^{94} +(-3.07427 - 1.77493i) q^{95} +(-1.91272 + 3.58140i) q^{96} +10.9793 q^{97} +(0.0121201 + 1.40490i) q^{98} +(3.81077 - 7.74088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9}+O(q^{10}) $ 64 * q - 12 * q^3 - 40 * q^4 - 12 * q^9	$ 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9} - 12 q^{10} - 6 q^{12} - 32 q^{16} - 24 q^{22} + 28 q^{25} - 22 q^{30} + 44 q^{36} + 6 q^{39} - 108 q^{40} + 24 q^{42} + 20 q^{49} + 28 q^{51} + 36 q^{52} + 48 q^{61} + 32 q^{64} + 90 q^{66} - 60 q^{75} - 68 q^{78} + 16 q^{79} + 60 q^{81} + 120 q^{82} + 60 q^{87} + 12 q^{88} - 32 q^{91} + 168 q^{94}+O(q^{100}) $ 64 * q - 12 * q^3 - 40 * q^4 - 12 * q^9 - 12 * q^10 - 6 * q^12 - 32 * q^16 - 24 * q^22 + 28 * q^25 - 22 * q^30 + 44 * q^36 + 6 * q^39 - 108 * q^40 + 24 * q^42 + 20 * q^49 + 28 * q^51 + 36 * q^52 + 48 * q^61 + 32 * q^64 + 90 * q^66 - 60 * q^75 - 68 * q^78 + 16 * q^79 + 60 * q^81 + 120 * q^82 + 60 * q^87 + 12 * q^88 - 32 * q^91 + 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.100354	+	0.173818i	0.0709608	+	0.122908i	0.899323	−	0.437286i	$-0.144060\pi$
$2$	0.100354	+	0.173818i	0.0709608	+	0.122908i	−0.828362	+	0.560193i	$0.810727\pi$
$3$	−1.73110	+	0.0572655i	−0.999453	+	0.0330623i
$3$	−1.73110	+	0.0572655i	−0.999453	+	0.0330623i
$4$	0.979858	−	1.69716i	0.489929	−	0.848582i
$5$	−2.67317	+	1.54335i	−1.19548	+	0.690209i	−0.959544	−	0.281560i	$-0.909148\pi$
$5$	−2.67317	+	1.54335i	−1.19548	+	0.690209i	−0.235934	+	0.971769i	$0.575815\pi$
$6$	−0.183677	−	0.295150i	−0.0749856	−	0.120494i
$7$	2.55853	+	0.673741i	0.967033	+	0.254650i
$7$	2.55853	+	0.673741i	0.967033	+	0.254650i
$8$	0.794745			0.280985
$9$	2.99344	−	0.198265i	0.997814	−	0.0660884i
$10$	−0.536525	−	0.309763i	−0.169664	−	0.0979556i
$11$	1.43801	−	2.49070i	0.433576	−	0.750975i	−0.563602	−	0.826046i	$-0.690585\pi$
$11$	1.43801	−	2.49070i	0.433576	−	0.750975i	0.997178	+	0.0750709i	$0.0239183\pi$
$12$	−1.59905	+	2.99408i	−0.461605	+	0.864316i
$13$	2.85209	−	2.20581i	0.791027	−	0.611781i
$13$	2.85209	−	2.20581i	0.791027	−	0.611781i
$14$	0.139650	+	0.512330i	0.0373230	+	0.136926i
$15$	4.53915	−	2.82479i	1.17200	−	0.729357i
$16$	−1.87996	−	3.25619i	−0.469990	−	0.814047i
$17$	3.04653	−	5.27675i	0.738892	−	1.27980i	−0.214102	−	0.976811i	$-0.568682\pi$
$17$	3.04653	−	5.27675i	0.738892	−	1.27980i	0.952994	−	0.302988i	$-0.0979842\pi$
$18$	0.334865	+	0.500417i	0.0789285	+	0.117949i
$19$	0.575023	+	0.995969i	0.131919	+	0.228491i	0.924416	−	0.381385i	$-0.124553\pi$
$19$	0.575023	+	0.995969i	0.131919	+	0.228491i	−0.792497	+	0.609876i	$0.791219\pi$
$20$			6.04908i			1.35261i
$21$	−4.46766	−	1.01980i	−0.974924	−	0.222539i
$22$	0.577238			0.123068
$23$	3.18579	−	1.83931i	0.664282	−	0.383524i	−0.129624	−	0.991563i	$-0.541377\pi$
$23$	3.18579	−	1.83931i	0.664282	−	0.383524i	0.793907	+	0.608040i	$0.208044\pi$
$24$	−1.37579	+	0.0455115i	−0.280831	+	0.00928999i
$25$	2.26389	−	3.92117i	0.452777	−	0.784234i
$26$	0.669627	+	0.274383i	0.131325	+	0.0538109i
$27$	−5.17060	+	0.514638i	−0.995083	+	0.0990422i
$28$	3.65045	−	3.68207i	0.689869	−	0.695847i
$29$			7.77891i			1.44451i	0.691629	+	0.722253i	$0.256894\pi$
$29$			7.77891i			1.44451i	−0.691629	+	0.722253i	$0.743106\pi$
$30$	0.946519	+	0.505507i	0.172810	+	0.0922926i
$31$	−3.80568	+	6.59163i	−0.683520	+	1.18389i	0.290379	+	0.956912i	$0.406219\pi$
$31$	−3.80568	+	6.59163i	−0.683520	+	1.18389i	−0.973899	+	0.226980i	$0.927115\pi$
$32$	1.17207	−	2.03008i	0.207194	−	0.358871i
$33$	−2.34671	+	4.39401i	−0.408510	+	0.764900i
$34$	1.22292			0.209730
$35$	−7.87920	+	2.14769i	−1.33183	+	0.363027i
$36$	2.59666	−	5.27463i	0.432777	−	0.879106i
$37$	−1.11374	+	0.643021i	−0.183098	+	0.105712i	−0.588748	−	0.808317i	$-0.700379\pi$
$37$	−1.11374	+	0.643021i	−0.183098	+	0.105712i	0.405649	+	0.914029i	$0.367045\pi$
$38$	−0.115411	+	0.199898i	−0.0187222	+	0.0324278i
$39$	−4.81094	+	3.98181i	−0.770368	+	0.637600i
$40$	−2.12449	+	1.22657i	−0.335911	+	0.193938i
$41$		−	1.74625i		−	0.272719i	−0.990659	−	0.136359i	$-0.956460\pi$
$41$		−	1.74625i		−	0.272719i	0.990659	−	0.136359i	$-0.0435402\pi$
$42$	−0.271087	−	0.878900i	−0.0418297	−	0.135617i
$43$	0.749286			0.114265			0.0571325	−	0.998367i	$-0.481804\pi$
$43$	0.749286			0.114265			0.0571325	+	0.998367i	$0.481804\pi$
$44$	−2.81809	−	4.88107i	−0.424843	−	0.735849i
$45$	−7.69598	+	5.14994i	−1.14725	+	0.767707i
$46$	0.639411	+	0.369164i	0.0942760	+	0.0544303i
$47$	8.80645	−	5.08440i	1.28455	−	0.741636i	0.306875	−	0.951750i	$-0.400717\pi$
$47$	8.80645	−	5.08440i	1.28455	−	0.741636i	0.977677	+	0.210113i	$0.0673833\pi$
$48$	3.44087	+	5.52914i	0.496647	+	0.798063i
$49$	6.09215	+	3.44757i	0.870307	+	0.492510i
$50$	0.908758			0.128518
$51$	−4.97169	+	9.30906i	−0.696175	+	1.30353i
$52$	−0.948977	−	7.00184i	−0.131599	−	0.970981i
$53$	2.60900	+	1.50631i	0.358373	+	0.206907i	0.668367	−	0.743832i	$-0.266994\pi$
$53$	2.60900	+	1.50631i	0.358373	+	0.206907i	−0.309994	+	0.950739i	$0.600327\pi$
$54$	−0.608343	−	0.847097i	−0.0827850	−	0.115275i
$55$			8.87743i			1.19703i
$56$	2.03338	+	0.535452i	0.271722	+	0.0715528i
$57$	−1.05246	−	1.69120i	−0.139402	−	0.224004i
$58$	−1.35211	+	0.780643i	−0.177541	+	0.102503i
$59$	−10.3004	−	5.94692i	−1.34099	−	0.774224i	−0.354041	−	0.935230i	$-0.615193\pi$
$59$	−10.3004	−	5.94692i	−1.34099	−	0.774224i	−0.986953	+	0.161006i	$0.948526\pi$
$60$	−0.346403	−	10.4716i	−0.0447205	−	1.35187i
$61$	4.12566	−	2.38195i	0.528237	−	0.304978i	−0.212061	−	0.977256i	$-0.568018\pi$
$61$	4.12566	−	2.38195i	0.528237	−	0.304978i	0.740298	+	0.672279i	$0.234684\pi$
$62$	−1.52766			−0.194013
$63$	7.79239	+	1.50954i	0.981748	+	0.190184i
$64$	−7.04936			−0.881170
$65$	−4.21977	+	10.2983i	−0.523398	+	1.27734i
$66$	−0.999259	+	0.0330558i	−0.123000	+	0.00406889i
$67$	−11.8291	−	6.82951i	−1.44515	−	0.834358i	−0.446963	−	0.894552i	$-0.647495\pi$
$67$	−11.8291	−	6.82951i	−1.44515	−	0.834358i	−0.998187	+	0.0601944i	$0.980828\pi$
$68$	−5.97034	−	10.3409i	−0.724010	−	1.25402i
$69$	−5.40960	+	3.36648i	−0.651239	+	0.405277i
$70$	−1.16402	−	1.15402i	−0.139126	−	0.137931i
$71$	−10.2745			−1.21935			−0.609677	−	0.792650i	$-0.708701\pi$
$71$	−10.2745			−1.21935			−0.609677	+	0.792650i	$0.708701\pi$
$72$	2.37902	−	0.157570i	0.280370	−	0.0185698i
$73$	0.359690	−	0.623001i	0.0420985	−	0.0729167i	−0.844208	−	0.536015i	$-0.819929\pi$
$73$	0.359690	−	0.623001i	0.0420985	−	0.0729167i	0.886307	+	0.463098i	$0.153262\pi$
$74$	−0.223537	−	0.129059i	−0.0259856	−	0.0150028i
$75$	−3.69448	+	6.91759i	−0.426601	+	0.798775i
$76$	2.25376			0.258524
$77$	5.35728	−	5.40369i	0.610518	−	0.615808i
$78$	−1.17491	−	0.436638i	−0.133032	−	0.0494395i
$79$	1.54719	+	2.67981i	0.174072	+	0.301502i	0.939840	−	0.341615i	$-0.110974\pi$
$79$	1.54719	+	2.67981i	0.174072	+	0.301502i	−0.765768	+	0.643117i	$0.777641\pi$
$80$	10.0509	+	5.80289i	1.12373	+	0.648783i
$81$	8.92138	−	1.18699i	0.991265	−	0.131888i
$82$	0.303530	−	0.175243i	0.0335192	−	0.0193523i
$83$			8.31078i			0.912227i	0.889922	+	0.456113i	$0.150759\pi$
$83$			8.31078i			0.912227i	−0.889922	+	0.456113i	$0.849241\pi$
$84$	−6.10844	+	6.58310i	−0.666486	+	0.718275i
$85$			18.8075i			2.03996i
$86$	0.0751937	+	0.130239i	0.00810834	+	0.0140441i
$87$	−0.445463	−	13.4661i	−0.0477587	−	1.44372i
$88$	1.14285	−	1.97947i	0.121828	−	0.211013i
$89$	−6.51669	+	3.76241i	−0.690767	+	0.398815i	−0.803899	−	0.594765i	$-0.797245\pi$
$89$	−6.51669	+	3.76241i	−0.690767	+	0.398815i	0.113132	+	0.993580i	$0.463912\pi$
$90$	−1.66747	−	0.820883i	−0.175767	−	0.0865286i
$91$	8.78330	−	3.72206i	0.920740	−	0.390178i
$92$		−	7.20907i		−	0.751597i
$93$	6.21055	−	11.6287i	0.644004	−	1.20584i
$94$	1.76752	+	1.02048i	0.182306	+	0.105254i
$95$	−3.07427	−	1.77493i	−0.315413	−	0.182104i
$96$	−1.91272	+	3.58140i	−0.195216	+	0.365525i
$97$	10.9793			1.11478			0.557391	−	0.830250i	$-0.311802\pi$
$97$	10.9793			1.11478			0.557391	+	0.830250i	$0.311802\pi$
$98$	0.0121201	+	1.40490i	0.00122431	+	0.141916i
$99$	3.81077	−	7.74088i	0.382997	−	0.777988i
$100$	−4.43658	−	7.68438i	−0.443658	−	0.768438i
$101$	−3.24985	+	5.62890i	−0.323372	+	0.560097i	−0.981182	−	0.193087i	$-0.938150\pi$
$101$	−3.24985	+	5.62890i	−0.323372	+	0.560097i	0.657809	+	0.753184i	$0.271483\pi$
$102$	−2.11701	+	0.0700313i	−0.209615	+	0.00693414i
$103$	5.03135	−	2.90485i	0.495754	−	0.286223i	−0.231205	−	0.972905i	$-0.574267\pi$
$103$	5.03135	−	2.90485i	0.495754	−	0.286223i	0.726958	+	0.686682i	$0.240933\pi$
$104$	2.26668	−	1.75306i	0.222267	−	0.171901i
$105$	13.5167	−	4.16909i	1.31910	−	0.406861i
$106$			0.604653i			0.0587291i
$107$	2.45377	−	1.41668i	0.237215	−	0.136956i	−0.376681	−	0.926343i	$-0.622935\pi$
$107$	2.45377	−	1.41668i	0.237215	−	0.136956i	0.613896	+	0.789387i	$0.289601\pi$
$108$	−4.19303	+	9.27964i	−0.403475	+	0.892934i
$109$	−0.177371	−	0.102405i	−0.0169890	−	0.00980863i	0.491481	−	0.870888i	$-0.336456\pi$
$109$	−0.177371	−	0.102405i	−0.0169890	−	0.00980863i	−0.508470	+	0.861079i	$0.669789\pi$
$110$	−1.54305	+	0.890883i	−0.147125	+	0.0849424i
$111$	1.89118	−	1.17691i	0.179503	−	0.111708i
$112$	−2.61611	−	9.59766i	−0.247199	−	0.906894i
$113$			10.1913i			0.958717i	0.877619	+	0.479359i	$0.159131\pi$
$113$			10.1913i			0.958717i	−0.877619	+	0.479359i	$0.840869\pi$
$114$	0.188342	−	0.352654i	0.0176398	−	0.0330291i
$115$	−5.67743	+	9.83360i	−0.529423	+	0.916987i
$116$	13.2021	+	7.62223i	1.22578	+	0.707706i
$117$	8.10022	−	7.16843i	0.748866	−	0.662721i
$118$		−	2.38719i		−	0.219758i
$119$	11.3498	−	11.4481i	1.04043	−	1.04945i
$120$	3.60747	−	2.24499i	0.329315	−	0.204938i
$121$	1.36426	+	2.36298i	0.124024	+	0.214816i
$122$	0.828052	+	0.478076i	0.0749683	+	0.0432830i
$123$	0.100000	+	3.02294i	0.00901669	+	0.272570i
$124$	7.45805	+	12.9177i	0.669753	+	1.16005i
$125$		−	1.45762i		−	0.130374i
$126$	0.519611	+	1.50594i	0.0462906	+	0.134160i
$127$	−17.1871			−1.52510			−0.762552	−	0.646927i	$-0.776054\pi$
$127$	−17.1871			−1.52510			−0.762552	+	0.646927i	$0.776054\pi$
$128$	−3.05156	−	5.28546i	−0.269723	−	0.467173i
$129$	−1.29709	+	0.0429082i	−0.114203	+	0.00377786i
$130$	−2.21349	+	0.300000i	−0.194136	+	0.0263118i
$131$	−0.660084	−	1.14330i	−0.0576718	−	0.0998905i	0.835748	−	0.549113i	$-0.185034\pi$
$131$	−0.660084	−	1.14330i	−0.0576718	−	0.0998905i	−0.893420	+	0.449223i	$0.851701\pi$
$132$	5.15792	+	8.28826i	0.448939	+	0.721401i
$133$	0.800188	+	2.93563i	0.0693851	+	0.254552i
$134$		−	2.74147i		−	0.236827i
$135$	13.0276	−	9.35579i	1.12124	−	0.805218i
$136$	2.42122	−	4.19367i	0.207618	−	0.359604i
$137$	−1.32870	+	2.30138i	−0.113519	+	0.196620i	−0.917187	−	0.398458i	$-0.869546\pi$
$137$	−1.32870	+	2.30138i	−0.113519	+	0.196620i	0.803668	+	0.595078i	$0.202879\pi$
$138$	−1.12803	−	0.602445i	−0.0960241	−	0.0512836i
$139$			2.47162i			0.209640i	0.994491	+	0.104820i	$0.0334266\pi$
$139$			2.47162i			0.209640i	−0.994491	+	0.104820i	$0.966573\pi$
$140$	−4.07551	+	15.4767i	−0.344444	+	1.30802i
$141$	−14.9537	+	9.30594i	−1.25933	+	0.783701i
$142$	−1.03108	−	1.78588i	−0.0865264	−	0.149868i
$143$	−1.39269	−	10.2757i	−0.116462	−	0.859295i
$144$	−6.27314	−	9.37448i	−0.522762	−	0.781206i
$145$	−12.0056	−	20.7943i	−0.997012	−	1.72688i
$146$	0.144385			0.0119494
$147$	−10.7436	−	5.61924i	−0.886114	−	0.463467i
$148$			2.52028i			0.207165i
$149$	10.8991	+	18.8778i	0.892891	+	1.54653i	0.836393	+	0.548130i	$0.184660\pi$
$149$	10.8991	+	18.8778i	0.892891	+	1.54653i	0.0564976	+	0.998403i	$0.482007\pi$
$150$	−1.57316	+	0.0520405i	−0.128448	+	0.00424909i
$151$	5.59209	+	3.22860i	0.455078	+	0.262739i	0.709972	−	0.704230i	$-0.248707\pi$
$151$	5.59209	+	3.22860i	0.455078	+	0.262739i	−0.254894	+	0.966969i	$0.582041\pi$
$152$	0.456997	+	0.791541i	0.0370673	+	0.0642025i
$153$	8.07342	−	16.3997i	0.652697	−	1.32583i
$154$	1.47688	+	0.388909i	0.119010	+	0.0313392i
$155$		−	23.4941i		−	1.88709i
$156$	2.04374	+	12.0666i	0.163630	+	0.966099i
$157$	−5.20259	−	3.00372i	−0.415212	−	0.239723i	0.277815	−	0.960635i	$-0.410390\pi$
$157$	−5.20259	−	3.00372i	−0.415212	−	0.239723i	−0.693027	+	0.720912i	$0.743723\pi$
$158$	−0.310532	+	0.537858i	−0.0247046	+	0.0427897i
$159$	−4.60270	−	2.45816i	−0.365018	−	0.194945i
$160$			7.23566i			0.572029i
$161$	9.39015	−	2.55954i	0.740047	−	0.201720i
$162$	1.10161	+	1.43158i	0.0865510	+	0.112475i
$163$	−15.2034	+	8.77771i	−1.19083	+	0.687523i	−0.958494	−	0.285113i	$-0.907969\pi$
$163$	−15.2034	+	8.77771i	−1.19083	+	0.687523i	−0.232331	+	0.972637i	$0.574635\pi$
$164$	−2.96368	−	1.71108i	−0.231424	−	0.133613i
$165$	−0.508370	−	15.3677i	−0.0395766	−	1.19638i
$166$	−1.44456	+	0.834018i	−0.112120	+	0.0647324i
$167$			3.51044i			0.271646i	0.990733	+	0.135823i	$0.0433679\pi$
$167$			3.51044i			0.271646i	−0.990733	+	0.135823i	$0.956632\pi$
$168$	−3.55065	−	0.810481i	−0.273939	−	0.0625300i
$169$	3.26882	−	12.5823i	0.251447	−	0.967871i
$170$	−3.26908	+	1.88740i	−0.250727	+	0.144757i
$171$	1.91876	+	2.86737i	0.146732	+	0.219273i
$172$	0.734194	−	1.27166i	0.0559818	−	0.0969633i
$173$	11.9212	+	20.6481i	0.906353	+	1.56985i	0.819090	+	0.573664i	$0.194479\pi$
$173$	11.9212	+	20.6481i	0.906353	+	1.56985i	0.0872626	+	0.996185i	$0.472188\pi$
$174$	2.29594	−	1.42880i	0.174055	−	0.108317i
$175$	8.43407	−	8.50715i	0.637556	−	0.643080i
$176$	−10.8136			−0.815106
$177$	18.1716	+	9.70489i	1.36586	+	0.729464i
$178$	−1.30795	−	0.755144i	−0.0980348	−	0.0566004i
$179$	−5.67351	−	3.27560i	−0.424058	−	0.244830i	0.272754	−	0.962084i	$-0.412065\pi$
$179$	−5.67351	−	3.27560i	−0.424058	−	0.244830i	−0.696812	+	0.717254i	$0.745399\pi$
$180$	1.19932	+	18.1076i	0.0893921	+	1.34966i
$181$			9.75028i			0.724733i	0.932036	+	0.362366i	$0.118031\pi$
$181$			9.75028i			0.724733i	−0.932036	+	0.362366i	$0.881969\pi$
$182$	1.52840	+	1.15317i	0.113292	+	0.0854787i
$183$	−7.00555	+	4.35967i	−0.517865	+	0.322276i
$184$	2.53189	−	1.46179i	0.186653	−	0.107764i
$185$	1.98482	−	3.43781i	0.145927	−	0.252753i
$186$	2.64453	−	0.0874821i	0.193907	−	0.00641450i
$187$	−8.76187	−	15.1760i	−0.640732	−	1.10978i
$188$		−	19.9280i		−	1.45340i
$189$	−13.5759	−	2.16693i	−0.987500	−	0.157621i
$190$		−	0.712483i		−	0.0516890i
$191$	4.72711	−	2.72920i	0.342042	−	0.197478i	−0.319133	−	0.947710i	$-0.603392\pi$
$191$	4.72711	−	2.72920i	0.342042	−	0.197478i	0.661175	+	0.750232i	$0.270058\pi$
$192$	12.2032	−	0.403685i	0.880688	−	0.0291335i
$193$	10.6464	+	6.14669i	0.766343	+	0.442449i	0.831569	−	0.555422i	$-0.187443\pi$
$193$	10.6464	+	6.14669i	0.766343	+	0.442449i	−0.0652253	+	0.997871i	$0.520777\pi$
$194$	1.10182	+	1.90840i	0.0791058	+	0.137015i
$195$	6.71512	−	18.0690i	0.480880	−	1.29395i
$196$	11.8205	−	6.96124i	0.844324	−	0.497231i
$197$	6.43866			0.458736			0.229368	−	0.973340i	$-0.426334\pi$
$197$	6.43866			0.458736			0.229368	+	0.973340i	$0.426334\pi$
$198$	1.72793	−	0.114446i	0.122799	−	0.00813334i
$199$	−18.4283	−	10.6396i	−1.30635	−	0.754219i	−0.324861	−	0.945762i	$-0.605318\pi$
$199$	−18.4283	−	10.6396i	−1.30635	−	0.754219i	−0.981484	+	0.191543i	$0.938651\pi$
$200$	1.79921	−	3.11633i	0.127224	−	0.220358i
$201$	20.8684	+	11.1452i	1.47195	+	0.786122i
$202$	−1.30454			−0.0917870
$203$	−5.24097	+	19.9026i	−0.367844	+	1.39689i
$204$	10.9275	+	17.5593i	0.765075	+	1.22940i
$205$	2.69509	+	4.66802i	0.188233	+	0.326029i
$206$	1.00983	+	0.583025i	0.0703582	+	0.0406213i
$207$	9.17179	−	6.13751i	0.637484	−	0.426586i
$208$	−12.5443	−	5.14010i	−0.869794	−	0.356402i
$209$	3.30755			0.228788
$210$	2.08112	+	1.93106i	0.143611	+	0.133256i
$211$	5.77010			0.397230			0.198615	−	0.980078i	$-0.436356\pi$
$211$	5.77010			0.397230			0.198615	+	0.980078i	$0.436356\pi$
$212$	5.11289	−	2.95193i	0.351155	−	0.202739i
$213$	17.7862	−	0.588372i	1.21869	−	0.0403146i
$214$	0.492490	+	0.284339i	0.0336659	+	0.0194370i
$215$	−2.00297	+	1.15641i	−0.136601	+	0.0788668i
$216$	−4.10931	+	0.409006i	−0.279603	+	0.0278294i
$217$	−14.1780	+	14.3008i	−0.962465	+	0.970804i
$218$		−	0.0411069i		−	0.00278411i
$219$	−0.586984	+	1.09908i	−0.0396647	+	0.0742687i
$220$	15.0665	+	8.69862i	1.01578	+	0.586461i
$221$	−2.95052	−	21.7698i	−0.198473	−	1.46440i
$222$	0.394356	+	0.210614i	0.0264675	+	0.0141355i
$223$	−13.0347			−0.872866			−0.436433	−	0.899737i	$-0.643758\pi$
$223$	−13.0347			−0.872866			−0.436433	+	0.899737i	$0.643758\pi$
$224$	4.36652	−	4.40435i	0.291750	−	0.294278i
$225$	5.99938	−	12.1866i	0.399959	−	0.812442i
$226$	−1.77143	+	1.02274i	−0.117834	+	0.0680314i
$227$	−5.06762	−	2.92579i	−0.336349	−	0.194191i	0.322307	−	0.946635i	$-0.395542\pi$
$227$	−5.06762	−	2.92579i	−0.336349	−	0.194191i	−0.658657	+	0.752444i	$0.728875\pi$
$228$	−3.90150	+	0.129063i	−0.258383	+	0.00854740i
$229$	4.58675	+	7.94449i	0.303101	+	0.524987i	0.976837	−	0.213986i	$-0.0686447\pi$
$229$	4.58675	+	7.94449i	0.303101	+	0.524987i	−0.673736	+	0.738972i	$0.735311\pi$
$230$	−2.27901			−0.150273
$231$	−8.96456	+	9.66114i	−0.589824	+	0.635656i
$232$			6.18225i			0.405884i
$233$	−0.469079	+	0.270823i	−0.0307304	+	0.0177422i	−0.515286	−	0.857018i	$-0.672314\pi$
$233$	−0.469079	+	0.270823i	−0.0307304	+	0.0177422i	0.484556	+	0.874760i	$0.338981\pi$
$234$	2.05889	+	0.688585i	0.134594	+	0.0450142i
$235$	−15.6941	+	27.1829i	−1.02377	+	1.77322i
$236$	−20.1858	+	11.6543i	−1.31398	+	0.758629i
$237$	−2.83180	−	4.55043i	−0.183945	−	0.295582i
$238$	3.12889	+	0.823934i	0.202816	+	0.0534077i
$239$	18.0765			1.16927			0.584636	−	0.811296i	$-0.301237\pi$
$239$	18.0765			1.16927			0.584636	+	0.811296i	$0.301237\pi$
$240$	−17.7315	−	9.46984i	−1.14456	−	0.611276i
$241$	−13.6826	+	23.6989i	−0.881371	+	1.52658i	−0.0315541	+	0.999502i	$0.510046\pi$
$241$	−13.6826	+	23.6989i	−0.881371	+	1.52658i	−0.849817	+	0.527078i	$0.823288\pi$
$242$	−0.273818	+	0.474267i	−0.0176017	+	0.0304870i
$243$	−15.3759	+	2.56569i	−0.986362	+	0.164589i
$244$		−	9.33590i		−	0.597670i
$245$	−21.6062	+	0.186397i	−1.38037	+	0.0119084i
$246$	−0.515406	+	0.320745i	−0.0328611	+	0.0204500i
$247$	3.83693	+	1.57220i	0.244138	+	0.100037i
$248$	−3.02454	+	5.23866i	−0.192059	+	0.332655i
$249$	−0.475921	−	14.3868i	−0.0301603	−	0.911728i
$250$	0.253361	−	0.146278i	0.0160239	−	0.00925142i
$251$	−24.4617			−1.54401			−0.772006	−	0.635616i	$-0.780746\pi$
$251$	−24.4617			−1.54401			−0.772006	+	0.635616i	$0.780746\pi$
$252$	10.1974	−	11.7458i	0.642374	−	0.739918i
$253$		−	10.5798i		−	0.665146i
$254$	−1.72479	−	2.98742i	−0.108223	−	0.187447i
$255$	−1.07702	−	32.5578i	−0.0674457	−	2.03885i
$256$	−6.43689	+	11.1490i	−0.402305	+	0.696813i
$257$	−7.54477	−	13.0679i	−0.470630	−	0.815154i	0.528806	−	0.848743i	$-0.322640\pi$
$257$	−7.54477	−	13.0679i	−0.470630	−	0.815154i	−0.999436	+	0.0335883i	$0.989307\pi$
$258$	−0.137626	−	0.221152i	−0.00856824	−	0.0137683i
$259$	−3.28278	+	0.894812i	−0.203982	+	0.0556009i
$260$	13.3431	+	17.2525i	0.827504	+	1.06995i
$261$	1.54229	+	23.2857i	0.0954651	+	1.44135i
$262$	0.132484	−	0.229469i	0.00818488	−	0.0141766i
$263$	3.65930	+	2.11270i	0.225642	+	0.130275i	0.608560	−	0.793508i	$-0.291747\pi$
$263$	3.65930	+	2.11270i	0.225642	+	0.130275i	−0.382918	+	0.923782i	$0.625081\pi$
$264$	−1.86504	+	3.49212i	−0.114785	+	0.214925i
$265$	−9.29905			−0.571236
$266$	−0.429963	+	0.433689i	−0.0263627	+	0.0265912i
$267$	11.0656	−	6.88630i	0.677204	−	0.421435i
$268$	−23.1816	+	13.3839i	−1.41604	+	0.817552i
$269$	1.13772	−	1.97059i	0.0693682	−	0.120149i	−0.829255	−	0.558870i	$-0.811235\pi$
$269$	1.13772	−	1.97059i	0.0693682	−	0.120149i	0.898623	+	0.438721i	$0.144568\pi$
$270$	2.93357	+	1.32554i	0.178532	+	0.0806701i
$271$	−5.29182	−	9.16571i	−0.321455	−	0.556777i	0.659333	−	0.751851i	$-0.270839\pi$
$271$	−5.29182	−	9.16571i	−0.321455	−	0.556777i	−0.980789	+	0.195074i	$0.937505\pi$
$272$	−22.9094			−1.38909
$273$	−14.9917	+	6.94625i	−0.907336	+	0.420406i
$274$	−0.533362			−0.0322216
$275$	−6.51098	−	11.2773i	−0.392627	−	0.680049i
$276$	0.412831	+	12.4796i	0.0248495	+	0.751187i
$277$	−3.70889	+	6.42398i	−0.222845	+	0.385980i	−0.955671	−	0.294437i	$-0.904868\pi$
$277$	−3.70889	+	6.42398i	−0.222845	+	0.385980i	0.732825	+	0.680417i	$0.238201\pi$
$278$	−0.429611	+	0.248036i	−0.0257663	+	0.0148762i
$279$	−10.0852	+	20.4862i	−0.603784	+	1.22648i
$280$	−6.26196	+	1.70687i	−0.374223	+	0.102005i
$281$	−4.87501			−0.290819			−0.145409	−	0.989372i	$-0.546450\pi$
$281$	−4.87501			−0.290819			−0.145409	+	0.989372i	$0.546450\pi$
$282$	−3.11820	−	1.66534i	−0.185686	−	0.0991693i
$283$	16.4736	+	9.51104i	0.979254	+	0.565373i	0.902045	−	0.431642i	$-0.142066\pi$
$283$	16.4736	+	9.51104i	0.979254	+	0.565373i	0.0772091	+	0.997015i	$0.475399\pi$
$284$	−10.0675	+	17.4375i	−0.597397	+	1.03472i
$285$	5.42352	+	2.89654i	0.321261	+	0.171576i
$286$	1.64633	−	1.27328i	0.0973498	−	0.0752904i
$287$	1.17652	−	4.46784i	0.0694479	−	0.263728i
$288$	3.10602	−	6.30930i	0.183024	−	0.371779i
$289$	−10.0627	−	17.4291i	−0.591924	−	1.02524i
$290$	2.40962	−	4.17358i	0.141498	−	0.245081i
$291$	−19.0064	+	0.628737i	−1.11417	+	0.0368572i
$292$	−0.704890	−	1.22090i	−0.0412505	−	0.0714480i
$293$		−	22.5772i		−	1.31898i	−0.751715	−	0.659488i	$-0.770773\pi$
$293$		−	22.5772i		−	1.31898i	0.751715	−	0.659488i	$-0.229227\pi$
$294$	−0.101433	−	2.43133i	−0.00591572	−	0.141798i
$295$	36.7129			2.13751
$296$	−0.885143	+	0.511037i	−0.0514479	+	0.0297034i
$297$	−6.15356	+	13.6185i	−0.357066	+	0.790225i
$298$	−2.18754	+	3.78892i	−0.126721	+	0.219486i
$299$	5.02897	−	12.2731i	0.290833	−	0.709773i
$300$	8.12023	+	13.0484i	0.468821	+	0.753349i
$301$	1.91707	+	0.504825i	0.110498	+	0.0290976i
$302$			1.29601i			0.0745768i
$303$	5.30349	−	9.93032i	0.304677	−	0.570482i
$304$	2.16204	−	3.74477i	0.124002	−	0.214777i
$305$	−7.35240	+	12.7347i	−0.420997	+	0.729188i
$306$	3.66075	−	0.242463i	0.209271	−	0.0138607i
$307$	7.94961			0.453708			0.226854	−	0.973929i	$-0.427156\pi$
$307$	7.94961			0.453708			0.226854	+	0.973929i	$0.427156\pi$
$308$	−3.92158	−	14.3870i	−0.223453	−	0.819777i
$309$	−8.54344	+	5.31672i	−0.486019	+	0.302458i
$310$	4.08368	−	2.35772i	0.231938	−	0.133909i
$311$	−16.8929	+	29.2593i	−0.957906	+	1.65914i	−0.230334	+	0.973112i	$0.573982\pi$
$311$	−16.8929	+	29.2593i	−0.957906	+	1.65914i	−0.727573	+	0.686031i	$0.759352\pi$
$312$	−3.82347	+	3.16452i	−0.216462	+	0.179156i
$313$	22.3596	−	12.9093i	1.26384	−	0.729677i	0.290023	−	0.957020i	$-0.406337\pi$
$313$	22.3596	−	12.9093i	1.26384	−	0.729677i	0.973815	+	0.227342i	$0.0730037\pi$
$314$		−	1.20574i		−	0.0680437i
$315$	−23.1601	+	7.99117i	−1.30492	+	0.450251i
$316$	6.06410			0.341132
$317$	−10.7752	−	18.6633i	−0.605198	−	1.04823i	−0.992020	−	0.126079i	$-0.959761\pi$
$317$	−10.7752	−	18.6633i	−0.605198	−	1.04823i	0.386822	−	0.922154i	$-0.373573\pi$
$318$	−0.0346258	−	1.04672i	−0.00194172	−	0.0586970i
$319$	19.3750	+	11.1861i	1.08479	+	0.626303i
$320$	18.8441	−	10.8797i	1.05342	−	0.608191i
$321$	−4.16660	+	2.59294i	−0.232557	+	0.144724i
$322$	1.38723	+	1.37532i	0.0773074	+	0.0766433i
$323$	7.00730			0.389897
$324$	6.72717	−	16.3041i	0.373732	−	0.905785i
$325$	−2.19254	−	16.1772i	−0.121620	−	0.897351i
$326$	−3.05144	−	1.76175i	−0.169004	−	0.0975744i
$327$	0.312912	+	0.167117i	0.0173041	+	0.00924157i
$328$		−	1.38782i		−	0.0766298i
$329$	25.9571	−	7.07533i	1.43106	−	0.390076i
$330$	2.62017	−	1.63058i	0.144236	−	0.0897602i
$331$	−0.264399	+	0.152651i	−0.0145327	+	0.00839046i	−0.507249	−	0.861800i	$-0.669337\pi$
$331$	−0.264399	+	0.152651i	−0.0145327	+	0.00839046i	0.492716	+	0.870190i	$0.336004\pi$
$332$	14.1048	+	8.14339i	0.774099	+	0.446926i
$333$	−3.20644	+	2.14566i	−0.175712	+	0.117582i
$334$	−0.610177	+	0.352286i	−0.0333874	+	0.0192762i
$335$	42.1614			2.30353
$336$	5.07837	+	16.4647i	0.277048	+	0.898225i
$337$	−30.5565			−1.66452			−0.832259	−	0.554386i	$-0.812953\pi$
$337$	−30.5565			−1.66452			−0.832259	+	0.554386i	$0.812953\pi$
$338$	2.51507	−	0.694505i	0.136802	−	0.0377761i
$339$	−0.583610	−	17.6422i	−0.0316974	−	0.958193i
$340$	31.9194	+	18.4287i	1.73107	+	0.999436i
$341$	10.9452	+	18.9576i	0.592716	+	1.02661i
$342$	−0.305844	+	0.621266i	−0.0165382	+	0.0335942i
$343$	13.2642	+	12.9252i	0.716197	+	0.697898i
$344$	0.595491			0.0321067
$345$	9.26509	−	17.3481i	0.498816	−	0.933990i
$346$	−2.39268	+	4.14424i	−0.128631	+	0.222796i
$347$	16.0598	+	9.27214i	0.862136	+	0.497754i	0.864727	−	0.502242i	$-0.167491\pi$
$347$	16.0598	+	9.27214i	0.862136	+	0.497754i	−0.00259099	+	0.999997i	$0.500825\pi$
$348$	−23.2907	−	12.4388i	−1.24851	−	0.666792i
$349$	2.24282			0.120055			0.0600276	−	0.998197i	$-0.480881\pi$
$349$	2.24282			0.120055			0.0600276	+	0.998197i	$0.480881\pi$
$350$	2.32509	+	0.612268i	0.124281	+	0.0327271i
$351$	−13.6118	+	12.8732i	−0.726546	+	0.687118i
$352$	−3.37088	−	5.83854i	−0.179669	−	0.311195i
$353$	13.7678	+	7.94883i	0.732785	+	0.423074i	0.819440	−	0.573165i	$-0.194284\pi$
$353$	13.7678	+	7.94883i	0.732785	+	0.423074i	−0.0866551	+	0.996238i	$0.527618\pi$
$354$	0.136703	+	4.13247i	0.00726570	+	0.219638i
$355$	27.4654	−	15.8571i	1.45771	−	0.841610i
$356$			14.7465i			0.781564i
$357$	−18.9921	+	20.4679i	−1.00517	+	1.08327i
$358$		−	1.31488i		−	0.0694933i
$359$	3.35083	+	5.80381i	0.176850	+	0.306313i	0.940800	−	0.338962i	$-0.110076\pi$
$359$	3.35083	+	5.80381i	0.176850	+	0.306313i	−0.763950	+	0.645275i	$0.776743\pi$
$360$	−6.11634	+	4.09289i	−0.322359	+	0.215714i
$361$	8.83870	−	15.3091i	0.465195	−	0.805741i
$362$	−1.69477	+	0.978477i	−0.0890752	+	0.0514276i
$363$	−2.49700	−	4.01243i	−0.131059	−	0.210598i
$364$	2.28944	−	18.5538i	0.119999	−	0.972483i
$365$			2.22051i			0.116227i
$366$	−1.46082	−	0.780180i	−0.0763583	−	0.0407807i
$367$	−7.53635	−	4.35111i	−0.393394	−	0.227126i	0.290236	−	0.956955i	$-0.406266\pi$
$367$	−7.53635	−	4.35111i	−0.393394	−	0.227126i	−0.683630	+	0.729829i	$0.739600\pi$
$368$	−11.9783	−	6.91568i	−0.624412	−	0.360505i
$369$	−0.346221	−	5.22730i	−0.0180235	−	0.272122i
$370$	0.796736			0.0414203
$371$	5.66034	+	5.61171i	0.293870	+	0.291346i
$372$	−13.6504	−	21.9348i	−0.707740	−	1.13727i
$373$	−5.39338	−	9.34160i	−0.279258	−	0.483690i	0.691942	−	0.721953i	$-0.256755\pi$
$373$	−5.39338	−	9.34160i	−0.279258	−	0.483690i	−0.971201	+	0.238263i	$0.923422\pi$
$374$	1.75857	−	3.04594i	0.0909337	−	0.157502i
$375$	0.0834715	+	2.52330i	0.00431045	+	0.130302i
$376$	6.99888	−	4.04080i	0.360940	−	0.208389i
$377$	17.1588	+	22.1861i	0.883722	+	1.14264i
$378$	−0.985739	−	2.57719i	−0.0507009	−	0.132556i
$379$		−	16.7046i		−	0.858056i	−0.903291	−	0.429028i	$-0.858856\pi$
$379$		−	16.7046i		−	0.858056i	0.903291	−	0.429028i	$-0.141144\pi$
$380$	−6.02469	+	3.47836i	−0.309060	+	0.178436i
$381$	29.7526	−	0.984225i	1.52427	−	0.0504234i
$382$	0.948767	+	0.547771i	0.0485431	+	0.0280264i
$383$	10.0555	−	5.80553i	0.513811	−	0.296649i	−0.220588	−	0.975367i	$-0.570798\pi$
$383$	10.0555	−	5.80553i	0.513811	−	0.296649i	0.734399	+	0.678718i	$0.237464\pi$
$384$	5.58525	+	8.97494i	0.285021	+	0.458000i
$385$	−5.98109	+	22.7132i	−0.304824	+	1.15757i
$386$			2.46737i			0.125586i
$387$	2.24294	−	0.148557i	0.114015	−	0.00755159i
$388$	10.7582	−	18.6337i	0.546164	−	0.945984i
$389$	−6.23894	−	3.60205i	−0.316327	−	0.182631i	0.333427	−	0.942776i	$-0.391795\pi$
$389$	−6.23894	−	3.60205i	−0.316327	−	0.182631i	−0.649754	+	0.760144i	$0.725128\pi$
$390$	3.81461	−	0.646089i	0.193160	−	0.0327160i
$391$		−	22.4141i		−	1.13353i
$392$	4.84170	+	2.73994i	0.244543	+	0.138388i
$393$	1.20815	+	1.94137i	0.0609429	+	0.0979291i
$394$	0.646144	+	1.11915i	0.0325523	+	0.0563822i
$395$	−8.27179	−	4.77572i	−0.416199	−	0.240293i
$396$	−9.40353	−	14.0525i	−0.472545	−	0.706163i
$397$	−11.5091	−	19.9344i	−0.577626	−	1.00048i	−0.995751	−	0.0920879i	$-0.970646\pi$
$397$	−11.5091	−	19.9344i	−0.577626	−	1.00048i	0.418125	−	0.908390i	$-0.362687\pi$
$398$		−	4.27088i		−	0.214080i
$399$	−1.55332	−	5.03606i	−0.0777632	−	0.252118i
$400$	−17.0241			−0.851204
$401$	−8.00447	−	13.8641i	−0.399724	−	0.692343i	0.593968	−	0.804489i	$-0.297561\pi$
$401$	−8.00447	−	13.8641i	−0.399724	−	0.692343i	−0.993692	+	0.112146i	$0.964227\pi$
$402$	0.156992	+	4.74577i	0.00783003	+	0.236697i
$403$	3.68574	+	27.1945i	0.183600	+	1.35466i
$404$	6.36878	+	11.0311i	0.316859	+	0.548816i
$405$	−22.0164	+	16.9419i	−1.09400	+	0.841849i
$406$	−3.98537	+	1.08632i	−0.197791	+	0.0539133i
$407$			3.69868i			0.183337i
$408$	−3.95122	+	7.39833i	−0.195615	+	0.366272i
$409$	13.8383	−	23.9686i	0.684259	−	1.18517i	−0.289409	−	0.957205i	$-0.593459\pi$
$409$	13.8383	−	23.9686i	0.684259	−	1.18517i	0.973669	−	0.227967i	$-0.0732078\pi$
$410$	−0.540924	+	0.936908i	−0.0267143	+	0.0462706i
$411$	2.16834	−	4.06002i	0.106956	−	0.200266i
$412$		−	11.3854i		−	0.560917i
$413$	−22.3471	−	22.1552i	−1.09963	−	1.09018i
$414$	1.98723	+	0.978299i	0.0976671	+	0.0480807i
$415$	−12.8265	−	22.2161i	−0.629627	−	1.09055i
$416$	−1.13513	−	8.37532i	−0.0556543	−	0.410634i
$417$	−0.141538	−	4.27862i	−0.00693116	−	0.209525i
$418$	0.331925	+	0.574911i	0.0162350	+	0.0281198i
$419$	−19.3674			−0.946158			−0.473079	−	0.881020i	$-0.656858\pi$
$419$	−19.3674			−0.946158			−0.473079	+	0.881020i	$0.656858\pi$
$420$	6.16885	−	27.0252i	0.301009	−	1.31870i
$421$			13.6844i			0.666936i	0.942761	+	0.333468i	$0.108219\pi$
$421$			13.6844i			0.666936i	−0.942761	+	0.333468i	$0.891781\pi$
$422$	0.579051	+	1.00295i	0.0281878	+	0.0488227i
$423$	25.3535	−	16.9659i	1.23273	−	0.824909i
$424$	2.07349	+	1.19713i	0.100697	+	0.0581377i
$425$	−13.7940	−	23.8919i	−0.669108	−	1.15893i
$426$	1.88718	+	3.03251i	0.0914341	+	0.146925i
$427$	12.1604	−	3.31467i	0.588485	−	0.160408i
$428$		−	5.55260i		−	0.268395i
$429$	2.99933	+	17.7085i	0.144809	+	0.854975i
$430$	−0.402011	−	0.232101i	−0.0193867	−	0.0111929i
$431$	−6.80704	+	11.7901i	−0.327884	+	0.567911i	−0.982092	−	0.188403i	$-0.939669\pi$
$431$	−6.80704	+	11.7901i	−0.327884	+	0.567911i	0.654208	+	0.756315i	$0.273002\pi$
$432$	11.3963	+	15.8690i	0.548304	+	0.763496i
$433$			20.1902i			0.970279i	0.874437	+	0.485140i	$0.161231\pi$
$433$			20.1902i			0.970279i	−0.874437	+	0.485140i	$0.838769\pi$
$434$	−3.90855	−	1.02925i	−0.187617	−	0.0494054i
$435$	21.9738	+	35.3096i	1.05356	+	1.69297i
$436$	−0.347597	+	0.200685i	−0.0166469	+	0.00961107i
$437$	3.66380	+	2.11530i	0.175263	+	0.101188i
$438$	−0.249945	+	0.00826827i	−0.0119428	+	0.000395073i
$439$	8.46944	−	4.88983i	0.404224	−	0.233379i	−0.284081	−	0.958800i	$-0.591688\pi$
$439$	8.46944	−	4.88983i	0.404224	−	0.233379i	0.688305	+	0.725421i	$0.258355\pi$
$440$			7.05529i			0.336348i
$441$	18.9200	+	9.11225i	0.900953	+	0.433917i
$442$	3.48789	−	2.69754i	0.165902	−	0.128309i
$443$	−5.48775	+	3.16835i	−0.260731	+	0.150533i	−0.624668	−	0.780890i	$-0.714766\pi$
$443$	−5.48775	+	3.16835i	−0.260731	+	0.150533i	0.363937	+	0.931424i	$0.381432\pi$
$444$	−0.144325	−	4.36286i	−0.00684936	−	0.207052i
$445$	11.6135	−	20.1151i	0.550531	−	0.953548i
$446$	−1.30808	−	2.26566i	−0.0619393	−	0.107282i
$447$	−19.9486	−	32.0553i	−0.943535	−	1.51617i
$448$	−18.0360	−	4.74944i	−0.852120	−	0.224390i
$449$	−9.84999			−0.464850			−0.232425	−	0.972614i	$-0.574666\pi$
$449$	−9.84999			−0.464850			−0.232425	+	0.972614i	$0.574666\pi$
$450$	2.72032	−	0.180175i	0.128237	−	0.00849354i
$451$	−4.34939	−	2.51112i	−0.204805	−	0.118244i
$452$	17.2963	+	9.98603i	0.813550	+	0.469703i
$453$	−9.86538	−	5.26880i	−0.463516	−	0.247550i
$454$		−	1.17446i		−	0.0551199i
$455$	−17.7348	+	23.5054i	−0.831419	+	1.10195i
$456$	−0.836437	−	1.34407i	−0.0391697	−	0.0629418i
$457$	10.0375	−	5.79518i	0.469536	−	0.271087i	−0.246509	−	0.969140i	$-0.579284\pi$
$457$	10.0375	−	5.79518i	0.469536	−	0.271087i	0.716046	+	0.698054i	$0.245950\pi$
$458$	−0.920596	+	1.59452i	−0.0430166	+	0.0745070i
$459$	−13.0368	+	28.8518i	−0.608505	+	1.34669i
$460$	11.1262	+	19.2711i	0.518759	+	0.898518i
$461$		−	2.92419i		−	0.136193i	−0.997679	−	0.0680966i	$-0.978307\pi$
$461$		−	2.92419i		−	0.136193i	0.997679	−	0.0680966i	$-0.0216926\pi$
$462$	−2.57891	−	0.588668i	−0.119982	−	0.0273873i
$463$			33.6311i			1.56297i	0.623925	+	0.781484i	$0.285537\pi$
$463$			33.6311i			1.56297i	−0.623925	+	0.781484i	$0.714463\pi$
$464$	25.3296	−	14.6240i	1.17590	−	0.678904i
$465$	1.34540	+	40.6706i	0.0623914	+	1.88606i
$466$	−0.0941477	−	0.0543562i	−0.00436131	−	0.00251800i
$467$	10.9091	+	18.8951i	0.504812	+	0.874361i	0.999985	+	0.00556578i	$0.00177165\pi$
$467$	10.9091	+	18.8951i	0.504812	+	0.874361i	−0.495172	+	0.868795i	$0.664895\pi$
$468$	−4.22893	−	20.7715i	−0.195482	−	0.960161i
$469$	−25.6637	−	25.4432i	−1.18504	−	1.17486i
$470$	−6.29984			−0.290590
$471$	9.17824	+	4.90182i	0.422911	+	0.225864i
$472$	−8.18617	−	4.72629i	−0.376799	−	0.217545i
$473$	1.07748	−	1.86625i	0.0495425	−	0.0858102i
$474$	0.506763	−	0.948871i	0.0232764	−	0.0435831i
$475$	5.20715			0.238920
$476$	−8.30818	−	30.4800i	−0.380805	−	1.39705i
$477$	8.10853	+	3.99176i	0.371264	+	0.182770i
$478$	1.81405	+	3.14202i	0.0829725	+	0.143713i
$479$	14.2302	+	8.21582i	0.650195	+	0.375391i	0.788531	−	0.614995i	$-0.210842\pi$
$479$	14.2302	+	8.21582i	0.650195	+	0.375391i	−0.138336	+	0.990385i	$0.544175\pi$
$480$	−0.414354	−	12.5257i	−0.0189126	−	0.571717i
$481$	−1.75812	+	4.29066i	−0.0801633	+	0.195637i
$482$	−5.49239			−0.250171
$483$	−16.1087	+	4.96857i	−0.732973	+	0.226078i
$484$	5.34714			0.243052
$485$	−29.3496	+	16.9450i	−1.33270	+	0.769433i
$486$	−1.98899	−	2.41512i	−0.0902224	−	0.109552i
$487$	8.12368	+	4.69021i	0.368119	+	0.212534i	0.672636	−	0.739973i	$-0.265162\pi$
$487$	8.12368	+	4.69021i	0.368119	+	0.212534i	−0.304517	+	0.952507i	$0.598495\pi$
$488$	3.27885	−	1.89304i	0.148427	−	0.0856941i
$489$	25.8161	−	16.0658i	1.16744	−	0.726519i
$490$	−2.20066	−	3.73683i	−0.0994156	−	0.168813i
$491$		−	8.97782i		−	0.405163i	−0.979265	−	0.202582i	$-0.935067\pi$
$491$		−	8.97782i		−	0.405163i	0.979265	−	0.202582i	$-0.0649332\pi$
$492$	5.22842	+	2.79234i	0.235715	+	0.125888i
$493$	41.0473	+	23.6987i	1.84868	+	1.06734i
$494$	0.111774	+	0.824704i	0.00502896	+	0.0371052i
$495$	1.76008	+	26.5741i	0.0791099	+	1.19442i
$496$	28.6181			1.28499
$497$	−26.2875	−	6.92233i	−1.17916	−	0.310509i
$498$	2.45293	−	1.52650i	0.109918	−	0.0684039i
$499$	−11.6425	+	6.72178i	−0.521188	+	0.300908i	−0.737421	−	0.675434i	$-0.763956\pi$
$499$	−11.6425	+	6.72178i	−0.521188	+	0.300908i	0.216232	+	0.976342i	$0.430623\pi$
$500$	−2.47382	−	1.42826i	−0.110633	−	0.0638739i
$501$	−0.201027	−	6.07694i	−0.00898123	−	0.271498i
$502$	−2.45483	−	4.25189i	−0.109564	−	0.189771i
$503$	30.8630			1.37611			0.688056	−	0.725658i	$-0.258465\pi$
$503$	30.8630			1.37611			0.688056	+	0.725658i	$0.258465\pi$
$504$	6.19296	+	1.19970i	0.275856	+	0.0534388i
$505$		−	20.0627i		−	0.892778i
$506$	1.83896	−	1.06172i	0.0817516	−	0.0471993i
$507$	−4.93813	+	21.9685i	−0.219310	+	0.975655i
$508$	−16.8409	+	29.1692i	−0.747193	+	1.29418i
$509$	6.54695	−	3.77988i	0.290189	−	0.167540i	−0.347838	−	0.937555i	$-0.613084\pi$
$509$	6.54695	−	3.77988i	0.290189	−	0.167540i	0.638027	+	0.770014i	$0.279751\pi$
$510$	5.55104	−	3.45450i	0.245804	−	0.152968i
$511$	1.34002	−	1.35163i	0.0592789	−	0.0597925i
$512$	−14.7901			−0.653637
$513$	−3.48578	−	4.85383i	−0.153901	−	0.214302i
$514$	1.51429	−	2.62283i	0.0667925	−	0.115688i
$515$	−8.96643	+	15.5303i	−0.395108	+	0.684347i
$516$	−1.19814	+	2.24342i	−0.0527453	+	0.0987611i
$517$		−	29.2457i		−	1.28622i
$518$	−0.484973	−	0.480808i	−0.0213085	−	0.0211255i
$519$	−21.8193	−	35.0614i	−0.957760	−	1.53903i
$520$	−3.35364	+	8.18451i	−0.147067	+	0.358914i
$521$	10.5893	−	18.3411i	0.463924	−	0.803539i	−0.535229	−	0.844707i	$-0.679774\pi$
$521$	10.5893	−	18.3411i	0.463924	−	0.803539i	0.999152	+	0.0411678i	$0.0131078\pi$
$522$	−3.89270	+	2.60488i	−0.170379	+	0.114013i
$523$	−4.36472	+	2.51997i	−0.190856	+	0.110191i	−0.592383	−	0.805656i	$-0.701813\pi$
$523$	−4.36472	+	2.51997i	−0.190856	+	0.110191i	0.401527	+	0.915847i	$0.368480\pi$
$524$	−2.58716			−0.113020
$525$	−14.1131	+	15.2097i	−0.615946	+	0.663808i
$526$			0.848069i			0.0369776i
$527$	23.1882	+	40.1632i	1.01010	+	1.74954i
$528$	18.7195	−	0.619246i	0.814660	−	0.0269492i
$529$	−4.73385	+	8.19926i	−0.205819	+	0.356490i
$530$	−0.933195	−	1.61634i	−0.0405354	−	0.0702094i
$531$	−32.0126	−	15.7596i	−1.38923	−	0.683907i
$532$	5.76632	+	1.51845i	0.250002	+	0.0658333i
$533$	−3.85190	−	4.98046i	−0.166844	−	0.215728i
$534$	2.30744	+	1.23233i	0.0998526	+	0.0533282i
$535$	−4.37289	+	7.57407i	−0.189057	+	0.327456i
$536$	−9.40109	−	5.42772i	−0.406065	−	0.234442i
$537$	10.0090	+	5.34551i	0.431921	+	0.230676i
$538$	0.456699			0.0196897
$539$	17.3474	−	10.2161i	0.747207	−	0.440038i
$540$	−3.11309	−	31.2774i	−0.133966	−	1.34596i
$541$	−16.4608	+	9.50363i	−0.707704	+	0.408593i	−0.810210	−	0.586139i	$-0.800647\pi$
$541$	−16.4608	+	9.50363i	−0.707704	+	0.408593i	0.102507	+	0.994732i	$0.467314\pi$
$542$	1.06211	−	1.83963i	0.0456215	−	0.0790187i
$543$	−0.558355	−	16.8787i	−0.0239613	−	0.724336i
$544$	−7.14148	−	12.3694i	−0.306188	−	0.530334i
$545$	0.632190			0.0270800
$546$	−2.71185	−	1.90873i	−0.116056	−	0.0816863i
$547$	30.0863			1.28640			0.643198	−	0.765700i	$-0.277607\pi$
$547$	30.0863			1.28640			0.643198	+	0.765700i	$0.277607\pi$
$548$	2.60388	+	4.51006i	0.111232	+	0.192660i
$549$	11.8777	−	7.94821i	0.506927	−	0.339221i
$550$	1.30680	−	2.26345i	0.0557222	−	0.0965137i
$551$	−7.74755	+	4.47305i	−0.330057	+	0.190558i
$552$	−4.29925	+	2.67549i	−0.182988	+	0.113877i
$553$	2.15303	+	7.89878i	0.0915561	+	0.335890i
$554$	−1.48880			−0.0632532
$555$	−3.23906	+	6.06486i	−0.137490	+	0.257439i
$556$	4.19474	+	2.42183i	0.177896	+	0.102709i
$557$	18.3818	−	31.8382i	0.778861	−	1.34903i	−0.153738	−	0.988112i	$-0.549131\pi$
$557$	18.3818	−	31.8382i	0.778861	−	1.34903i	0.932599	−	0.360915i	$-0.117536\pi$
$558$	−4.57295	+	0.302881i	−0.193588	+	0.0128220i
$559$	2.13703	−	1.65278i	0.0903867	−	0.0699052i
$560$	21.8059	+	21.6186i	0.921467	+	0.913552i
$561$	16.0368	+	25.7695i	0.677073	+	1.08799i
$562$	−0.489225	−	0.847363i	−0.0206367	−	0.0357438i
$563$	−12.5611	+	21.7565i	−0.529389	+	0.916928i	0.470024	+	0.882654i	$0.344245\pi$
$563$	−12.5611	+	21.7565i	−0.529389	+	0.916928i	−0.999412	+	0.0342743i	$0.989088\pi$
$564$	1.14119	+	34.4974i	0.0480526	+	1.45260i
$565$	−15.7288	−	27.2431i	−0.661715	−	1.14612i
$566$			3.81787i			0.160477i
$567$	23.6253	+	2.97375i	0.992171	+	0.124886i
$568$	−8.16558			−0.342620
$569$	−5.89275	+	3.40218i	−0.247037	+	0.142627i	−0.618407	−	0.785858i	$-0.712222\pi$
$569$	−5.89275	+	3.40218i	−0.247037	+	0.142627i	0.371370	+	0.928485i	$0.378888\pi$
$570$	0.0408007	+	1.23338i	0.00170895	+	0.0516607i
$571$	11.9657	−	20.7252i	0.500750	−	0.867324i	−0.499250	−	0.866458i	$-0.666391\pi$
$571$	11.9657	−	20.7252i	0.500750	−	0.867324i	1.00000		0.000865904i	$-0.000275626\pi$
$572$	−18.8041	−	7.70509i	−0.786241	−	0.322166i
$573$	−8.02683	+	4.99523i	−0.335326	+	0.208679i
$574$	0.894658	−	0.243864i	0.0373423	−	0.0101787i
$575$		−	16.6560i		−	0.694603i
$576$	−21.1018	+	1.39764i	−0.879243	+	0.0582351i
$577$	−3.85323	+	6.67400i	−0.160412	+	0.277842i	−0.935017	−	0.354604i	$-0.884616\pi$
$577$	−3.85323	+	6.67400i	−0.160412	+	0.277842i	0.774604	+	0.632446i	$0.217949\pi$
$578$	2.01966	−	3.49816i	0.0840068	−	0.145504i
$579$	−18.7820	−	10.0309i	−0.780553	−	0.416870i
$580$	−47.0552			−1.95386
$581$	−5.59931	+	21.2634i	−0.232299	+	0.882153i
$582$	−2.01665	−	3.24055i	−0.0835926	−	0.134325i
$583$	7.50352	−	4.33216i	0.310764	−	0.179420i
$584$	0.285861	−	0.495127i	0.0118290	−	0.0204885i
$585$	−10.5898	+	31.6639i	−0.437836	+	1.30914i
$586$	3.92433	−	2.26571i	0.162112	−	0.0935957i
$587$		−	38.7983i		−	1.60138i	−0.599081	−	0.800688i	$-0.704467\pi$
$587$		−	38.7983i		−	1.60138i	0.599081	−	0.800688i	$-0.295533\pi$
$588$	−20.0639	+	12.7275i	−0.827423	+	0.524875i
$589$	−8.75341			−0.360678
$590$	3.68427	+	6.38135i	0.151679	+	0.262716i
$591$	−11.1460	+	0.368713i	−0.458485	+	0.0151668i
$592$	4.18759	+	2.41771i	0.172109	+	0.0993672i
$593$	−27.9375	+	16.1297i	−1.14726	+	0.662368i	−0.948217	−	0.317623i	$-0.897115\pi$
$593$	−27.9375	+	16.1297i	−1.14726	+	0.662368i	−0.199039	+	0.979992i	$0.563782\pi$
$594$	−2.98467	+	0.297069i	−0.122462	+	0.0121889i
$595$	−12.6714	+	48.1196i	−0.519477	+	1.97271i
$596$	42.7184			1.74981
$597$	32.5105	+	17.3629i	1.33057	+	0.710616i
$598$	2.63796	−	0.357530i	0.107874	−	0.0146205i
$599$	−31.6610	−	18.2795i	−1.29363	−	0.746879i	−0.314336	−	0.949312i	$-0.601782\pi$
$599$	−31.6610	−	18.2795i	−1.29363	−	0.746879i	−0.979296	+	0.202433i	$0.935115\pi$
$600$	−2.93617	+	5.49772i	−0.119868	+	0.224444i
$601$			32.3904i			1.32123i	0.750723	+	0.660617i	$0.229705\pi$
$601$			32.3904i			1.32123i	−0.750723	+	0.660617i	$0.770295\pi$
$602$	0.104638	+	0.383882i	0.00426471	+	0.0156459i
$603$	−36.7637	−	18.0985i	−1.49713	−	0.737026i
$604$	10.9589	−	6.32713i	0.445912	−	0.257447i
$605$	−7.29382	−	4.21109i	−0.296536	−	0.171205i
$606$	2.25829	−	0.0747051i	0.0917368	−	0.00303469i
$607$	−1.18286	+	0.682927i	−0.0480110	+	0.0277192i	−0.523813	−	0.851833i	$-0.675491\pi$
$607$	−1.18286	+	0.682927i	−0.0480110	+	0.0277192i	0.475802	+	0.879552i	$0.342158\pi$
$608$	2.69586			0.109332
$609$	7.93293	−	34.7535i	0.321459	−	1.40828i
$610$	−2.95136			−0.119497
$611$	13.9015	−	33.9265i	0.562396	−	1.37252i
$612$	−19.9221	−	29.7713i	−0.805303	−	1.20343i
$613$	−13.2794	−	7.66688i	−0.536351	−	0.309662i	0.207248	−	0.978288i	$-0.433549\pi$
$613$	−13.2794	−	7.66688i	−0.536351	−	0.309662i	−0.743599	+	0.668626i	$0.766883\pi$
$614$	0.797773	+	1.38178i	0.0321955	+	0.0557642i
$615$	−4.93279	−	7.92650i	−0.198909	−	0.319627i
$616$	4.25767	−	4.29456i	0.171546	−	0.173033i
$617$	−37.4008			−1.50570			−0.752849	−	0.658193i	$-0.771321\pi$
$617$	−37.4008			−1.50570			−0.752849	+	0.658193i	$0.771321\pi$
$618$	−1.78151	−	0.951449i	−0.0716627	−	0.0382729i
$619$	−16.2940	+	28.2220i	−0.654911	+	1.13434i	0.327005	+	0.945022i	$0.393960\pi$
$619$	−16.2940	+	28.2220i	−0.654911	+	1.13434i	−0.981916	+	0.189316i	$0.939373\pi$
$620$	−39.8733	−	23.0208i	−1.60135	−	0.924539i
$621$	−15.5259	+	11.1499i	−0.623031	+	0.447430i
$622$	−6.78105			−0.271895
$623$	−19.2080	+	5.23568i	−0.769553	+	0.209763i
$624$	22.0099	+	8.17969i	0.881102	+	0.327450i
$625$	13.5691	+	23.5023i	0.542763	+	0.940092i
$626$	4.48774	+	2.59100i	0.179366	+	0.103557i
$627$	−5.72571	+	0.189409i	−0.228663	+	0.00756425i
$628$	−10.1956	+	5.88644i	−0.406849	+	0.234894i
$629$			7.83593i			0.312439i
$630$	−3.71321	−	3.22370i	−0.147938	−	0.128435i
$631$		−	13.7056i		−	0.545613i	−0.962069	−	0.272806i	$-0.912048\pi$
$631$		−	13.7056i		−	0.545613i	0.962069	−	0.272806i	$-0.0879518\pi$
$632$	1.22962	+	2.12976i	0.0489117	+	0.0847175i
$633$	−9.98865	+	0.330428i	−0.397013	+	0.0131333i
$634$	2.16267	−	3.74586i	0.0858907	−	0.148767i
$635$	45.9439	−	26.5257i	1.82323	−	1.05264i
$636$	−8.68191	+	5.40289i	−0.344260	+	0.214239i
$637$	24.9800	−	3.60532i	0.989745	−	0.142848i
$638$			4.49028i			0.177772i
$639$	−30.7560	+	2.03707i	−1.21669	+	0.0805851i
$640$	16.3147	+	9.41929i	0.644895	+	0.372330i
$641$	22.4987	+	12.9897i	0.888647	+	0.513061i	0.873500	−	0.486825i	$-0.161845\pi$
$641$	22.4987	+	12.9897i	0.888647	+	0.513061i	0.0151474	+	0.999885i	$0.495178\pi$
$642$	−0.868834	−	0.464018i	−0.0342901	−	0.0183133i
$643$	−23.1671			−0.913620			−0.456810	−	0.889564i	$-0.651008\pi$
$643$	−23.1671			−0.913620			−0.456810	+	0.889564i	$0.651008\pi$
$644$	4.85705	−	18.4446i	0.191394	−	0.726820i
$645$	3.40112	−	2.11657i	0.133919	−	0.0833400i
$646$	0.703209	+	1.21799i	0.0276674	+	0.0479213i
$647$	−9.68267	+	16.7709i	−0.380665	+	0.659331i	−0.991157	−	0.132691i	$-0.957638\pi$
$647$	−9.68267	+	16.7709i	−0.380665	+	0.659331i	0.610492	+	0.792022i	$0.290972\pi$
$648$	7.09022	−	0.943354i	0.278530	−	0.0370585i
$649$	−29.6241	+	17.1035i	−1.16285	+	0.671369i
$650$	2.59186	−	2.00455i	0.101661	−	0.0786248i
$651$	23.7246	−	25.5681i	0.929842	−	1.00209i
$652$			34.4036i			1.34735i
$653$	25.1076	−	14.4959i	0.982536	−	0.567268i	0.0795013	−	0.996835i	$-0.474667\pi$
$653$	25.1076	−	14.4959i	0.982536	−	0.567268i	0.903035	+	0.429567i	$0.141334\pi$
$654$	0.00235401	+	0.0711604i	9.20491e−5	+	0.00278259i
$655$	3.52903	+	2.03749i	0.137891	+	0.0796112i
$656$	−5.68612	+	3.28288i	−0.222006	+	0.128175i
$657$	0.953190	−	1.93623i	0.0371875	−	0.0755395i
$658$	3.83471	+	3.80177i	0.149493	+	0.148209i
$659$			47.5717i			1.85313i	0.376134	+	0.926565i	$0.377253\pi$
$659$			47.5717i			1.85313i	−0.376134	+	0.926565i	$0.622747\pi$
$660$	−26.5797	−	14.1954i	−1.03461	−	0.552556i
$661$	21.5219	−	37.2770i	0.837104	−	1.44991i	−0.0552015	−	0.998475i	$-0.517580\pi$
$661$	21.5219	−	37.2770i	0.837104	−	1.44991i	0.892306	−	0.451432i	$-0.149087\pi$
$662$	−0.0530669	−	0.0306382i	−0.00206250	−	0.00119079i
$663$	6.35431	+	37.5168i	0.246781	+	1.45703i
$664$			6.60495i			0.256322i
$665$	−6.66976	−	6.61247i	−0.258642	−	0.256421i
$666$	−0.694733	−	0.342011i	−0.0269203	−	0.0132527i
$667$	14.3079	+	24.7819i	0.554002	+	0.959560i
$668$	5.95779	+	3.43973i	0.230514	+	0.133087i
$669$	22.5644	−	0.746437i	0.872389	−	0.0288589i
$670$	4.23106	+	7.32841i	0.163460	+	0.283121i
$671$		−	13.7011i		−	0.528924i
$672$	−7.30668	+	7.87444i	−0.281861	+	0.303763i
$673$	−19.5943			−0.755306			−0.377653	−	0.925947i	$-0.623269\pi$
$673$	−19.5943			−0.755306			−0.377653	+	0.925947i	$0.623269\pi$
$674$	−3.06646	−	5.31126i	−0.118116	−	0.204582i
$675$	−9.68768	+	21.4399i	−0.372879	+	0.825222i
$676$	−18.1513	−	17.8766i	−0.698127	−	0.687562i
$677$	4.21773	+	7.30533i	0.162101	+	0.280766i	0.935622	−	0.353004i	$-0.114840\pi$
$677$	4.21773	+	7.30533i	0.162101	+	0.280766i	−0.773521	+	0.633770i	$0.781506\pi$
$678$	3.00796	−	1.87190i	0.115520	−	0.0718900i
$679$	28.0909	+	7.39723i	1.07803	+	0.283879i
$680$			14.9472i			0.573198i
$681$	8.94011	+	4.77465i	0.342586	+	0.182965i
$682$	−2.19678	+	3.80494i	−0.0841192	+	0.145699i
$683$	6.55471	−	11.3531i	0.250809	−	0.434414i	−0.712940	−	0.701225i	$-0.752637\pi$
$683$	6.55471	−	11.3531i	0.250809	−	0.434414i	0.963749	+	0.266811i	$0.0859701\pi$
$684$	6.74651	−	0.446843i	0.257959	−	0.0170855i
$685$		−	8.20265i		−	0.313407i
$686$	−0.915530	+	3.60264i	−0.0349551	+	0.137550i
$687$	−8.39509	−	13.4901i	−0.320293	−	0.514678i
$688$	−1.40863	−	2.43982i	−0.0537034	−	0.0930171i
$689$	10.7637	−	1.45883i	0.410065	−	0.0555771i
$690$	3.94520	−	0.130508i	0.150191	−	0.00496837i
$691$	12.1116	+	20.9779i	0.460747	+	0.798037i	0.998998	−	0.0447471i	$-0.0142482\pi$
$691$	12.1116	+	20.9779i	0.460747	+	0.798037i	−0.538251	+	0.842784i	$0.680915\pi$
$692$	46.7244			1.77620
$693$	14.9653	−	17.2378i	0.568486	−	0.654810i
$694$			3.72198i			0.141284i
$695$	−3.81458	−	6.60704i	−0.144695	−	0.250619i
$696$	−0.354030	−	10.7021i	−0.0134195	−	0.405662i
$697$	−9.21453	−	5.32001i	−0.349025	−	0.201510i
$698$	0.225075	+	0.389841i	0.00851922	+	0.0147557i
$699$	0.796516	−	0.495685i	0.0301270	−	0.0187485i
$700$	−6.17383	−	22.6498i	−0.233349	−	0.856082i
$701$		−	18.0323i		−	0.681069i	−0.940232	−	0.340535i	$-0.889392\pi$
$701$		−	18.0323i		−	0.681069i	0.940232	−	0.340535i	$-0.110608\pi$
$702$	−3.60358	−	1.07411i	−0.136008	−	0.0405396i
$703$	−1.28086	−	0.739503i	−0.0483085	−	0.0278909i
$704$	−10.1370	+	17.5579i	−0.382054	+	0.661737i
$705$	25.6114	−	47.9552i	0.964582	−	1.80610i
$706$			3.19078i			0.120087i
$707$	−12.1073	+	12.2122i	−0.455340	+	0.459286i
$708$	34.2764	−	21.3307i	1.28818	−	0.801658i
$709$	−14.3556	+	8.28819i	−0.539135	+	0.311270i	−0.744728	−	0.667368i	$-0.767421\pi$
$709$	−14.3556	+	8.28819i	−0.539135	+	0.311270i	0.205593	+	0.978637i	$0.434088\pi$
$710$	5.51251	+	3.18265i	0.206881	+	0.119443i
$711$	5.16273	+	7.71510i	0.193618	+	0.289339i
$712$	−5.17910	+	2.99016i	−0.194095	+	0.112061i
$713$			27.9994i			1.04858i
$714$	−5.46361	−	1.24714i	−0.204470	−	0.0466730i
$715$	19.5819	+	25.3192i	0.732322	+	0.946885i
$716$	−11.1185	+	6.41925i	−0.415517	+	0.239899i
$717$	−31.2923	+	1.03516i	−1.16863	+	0.0386588i
$718$	−0.672537	+	1.16487i	−0.0250988	+	0.0434725i
$719$	−19.2899	−	33.4110i	−0.719390	−	1.24602i	−0.961242	−	0.275707i	$-0.911088\pi$
$719$	−19.2899	−	33.4110i	−0.719390	−	1.24602i	0.241852	−	0.970313i	$-0.422245\pi$
$720$	31.2373	+	15.3779i	1.16415	+	0.573100i
$721$	14.8300	−	4.04232i	0.552297	−	0.150544i
$722$	3.54799			0.132042
$723$	22.3288	−	41.8088i	0.830417	−	1.55489i
$724$	16.5478	+	9.55389i	0.614995	+	0.355068i
$725$	30.5024	+	17.6106i	1.13283	+	0.654040i
$726$	0.446849	−	0.836686i	0.0165841	−	0.0310523i
$727$		−	17.4282i		−	0.646376i	−0.946335	−	0.323188i	$-0.895245\pi$
$727$		−	17.4282i		−	0.646376i	0.946335	−	0.323188i	$-0.104755\pi$
$728$	6.98048	−	2.95809i	0.258714	−	0.109634i
$729$	26.4703	−	5.32198i	0.980381	−	0.197110i
$730$	−0.385965	+	0.222837i	−0.0142852	+	0.00824757i
$731$	2.28272	−	3.95379i	0.0844296	−	0.146236i
$732$	0.534625	+	16.1614i	0.0197603	+	0.597343i
$733$	5.30069	+	9.18106i	0.195785	+	0.339110i	0.947158	−	0.320768i	$-0.103941\pi$
$733$	5.30069	+	9.18106i	0.195785	+	0.339110i	−0.751372	+	0.659878i	$0.770608\pi$
$734$		−	1.74660i		−	0.0644682i
$735$	37.3918	−	1.55996i	1.37922	−	0.0575400i
$736$		−	8.62320i		−	0.317855i
$737$	−34.0206	+	19.6418i	−1.25316	+	0.723515i
$738$	0.873853	−	0.584759i	0.0321670	−	0.0215253i
$739$	−31.8268	−	18.3752i	−1.17077	−	0.675944i	−0.216908	−	0.976192i	$-0.569597\pi$
$739$	−31.8268	−	18.3752i	−1.17077	−	0.675944i	−0.953861	+	0.300248i	$0.902931\pi$
$740$	−3.88968	−	6.73713i	−0.142988	−	0.247662i
$741$	−6.73216	−	2.50192i	−0.247312	−	0.0919103i
$742$	−0.407380	+	1.54702i	−0.0149554	+	0.0567930i
$743$	−46.0146			−1.68811			−0.844055	−	0.536256i	$-0.819838\pi$
$743$	−46.0146			−1.68811			−0.844055	+	0.536256i	$0.819838\pi$
$744$	4.93581	−	9.24187i	0.180955	−	0.338824i
$745$	−58.2704	−	33.6424i	−2.13486	−	1.23256i
$746$	1.08249	−	1.87493i	0.0396328	−	0.0686461i
$747$	1.64774	+	24.8778i	0.0602876	+	0.910232i
$748$	−34.3416			−1.25565
$749$	7.23252	−	1.97142i	0.264270	−	0.0720342i
$750$	−0.430217	+	0.267731i	−0.0157093	+	0.00977615i
$751$	−13.9161	−	24.1035i	−0.507807	−	0.879547i	−0.999959	−	0.00903830i	$-0.997123\pi$
$751$	−13.9161	−	24.1035i	−0.507807	−	0.879547i	0.492152	−	0.870509i	$-0.336210\pi$
$752$	−33.1115	−	19.1170i	−1.20745	−	0.697124i
$753$	42.3458	−	1.40081i	1.54317	−	0.0510485i
$754$	−2.13440	+	5.20896i	−0.0777301	+	0.189699i
$755$	−19.9315			−0.725381
$756$	−16.9801	+	20.9172i	−0.617559	+	0.760751i
$757$	−29.1874			−1.06083			−0.530416	−	0.847737i	$-0.677964\pi$
$757$	−29.1874			−1.06083			−0.530416	+	0.847737i	$0.677964\pi$
$758$	2.90355	−	1.67637i	0.105462	−	0.0608883i
$759$	0.605857	+	18.3147i	0.0219912	+	0.664782i
$760$	−2.44326	−	1.41062i	−0.0886263	−	0.0511684i
$761$	−8.44881	+	4.87792i	−0.306269	+	0.176825i	−0.645256	−	0.763967i	$-0.723249\pi$
$761$	−8.44881	+	4.87792i	−0.306269	+	0.176825i	0.338987	+	0.940791i	$0.389916\pi$
$762$	3.15686	+	5.07276i	0.114361	+	0.183767i
$763$	−0.384814	−	0.381508i	−0.0139312	−	0.0138115i
$764$		−	10.6969i		−	0.387001i
$765$	3.72887	+	56.2992i	0.134818	+	2.03550i
$766$	2.01821	+	1.16521i	0.0729209	+	0.0421009i
$767$	−42.4954	+	5.75950i	−1.53442	+	0.207964i
$768$	10.5045	−	19.6687i	0.379047	−	0.709734i
$769$	−2.45786			−0.0886326			−0.0443163	−	0.999018i	$-0.514111\pi$
$769$	−2.45786			−0.0886326			−0.0443163	+	0.999018i	$0.514111\pi$
$770$	−4.54818	+	1.23973i	−0.163905	+	0.0446768i
$771$	13.8091	+	22.1899i	0.497323	+	0.799149i
$772$	20.8639	−	12.0458i	0.750908	−	0.433537i
$773$	32.9432	+	19.0198i	1.18489	+	0.684094i	0.957140	−	0.289627i	$-0.0935313\pi$
$773$	32.9432	+	19.0198i	1.18489	+	0.684094i	0.227745	+	0.973721i	$0.426865\pi$
$774$	0.250910	+	0.374955i	0.00901876	+	0.0134775i
$775$	17.2313	+	29.8454i	0.618965	+	1.07208i
$776$	8.72577			0.313237
$777$	5.63159	−	1.73700i	0.202032	−	0.0623146i
$778$		−	1.44592i		−	0.0518387i
$779$	1.73921	−	1.00413i	0.0623137	−	0.0359769i
$780$	−24.0863	−	29.1018i	−0.862427	−	1.04201i
$781$	−14.7748	+	25.5906i	−0.528683	+	0.915705i
$782$	3.89597	−	2.24934i	0.139320	−	0.0804363i
$783$	−4.00332	−	40.2216i	−0.143067	−	1.43740i
$784$	−0.227050	−	26.3185i	−0.00810892	−	0.939945i
$785$	18.5432			0.661836
$786$	−0.216203	+	0.404821i	−0.00771169	+	0.0144395i
$787$	16.0907	−	27.8700i	0.573573	−	0.993458i	−0.422622	−	0.906306i	$-0.638890\pi$
$787$	16.0907	−	27.8700i	0.573573	−	0.993458i	0.996195	−	0.0871518i	$-0.0277765\pi$
$788$	6.30898	−	10.9275i	0.224748	−	0.389275i
$789$	−6.45562	−	3.44775i	−0.229826	−	0.122743i
$790$		−	1.91705i		−	0.0682054i
$791$	−6.86630	+	26.0747i	−0.244138	+	0.927111i
$792$	3.02859	−	6.15203i	0.107616	−	0.218603i
$793$	6.51262	−	15.8940i	0.231270	−	0.564411i
$794$	2.30997	−	4.00098i	0.0819776	−	0.141989i
$795$	16.0976	−	0.532515i	0.570924	−	0.0188864i
$796$	−36.1142	+	20.8505i	−1.28003	+	0.739028i
$797$	14.0876			0.499010			0.249505	−	0.968374i	$-0.419732\pi$
$797$	14.0876			0.499010			0.249505	+	0.968374i	$0.419732\pi$
$798$	0.719476	−	0.775382i	0.0254692	−	0.0274482i
$799$		−	61.9592i		−	2.19196i
$800$	−5.30686	−	9.19174i	−0.187626	−	0.324977i
$801$	−18.7614	+	12.5546i	−0.662900	+	0.443594i
$802$	1.60656	−	2.78264i	0.0567295	−	0.0982584i
$803$	−1.03447	−	1.79176i	−0.0365058	−	0.0632298i
$804$	39.3633	−	24.4964i	1.38824	−	0.863923i
$805$	−21.1512	+	21.3344i	−0.745481	+	0.751940i
$806$	−4.35701	+	3.36972i	−0.153469	+	0.118693i
$807$	−1.85667	+	3.47645i	−0.0653578	+	0.122377i
$808$	−2.58280	+	4.47354i	−0.0908626	+	0.157379i
$809$	25.5782	+	14.7676i	0.899281	+	0.519200i	0.876967	−	0.480551i	$-0.159563\pi$
$809$	25.5782	+	14.7676i	0.899281	+	0.519200i	0.0223142	+	0.999751i	$0.492897\pi$
$810$	−5.15423	−	2.12666i	−0.181101	−	0.0747233i
$811$	33.8613			1.18903			0.594515	−	0.804085i	$-0.297344\pi$
$811$	33.8613			1.18903			0.594515	+	0.804085i	$0.297344\pi$
$812$	28.6425	+	28.3965i	1.00516	+	0.996521i
$813$	9.68557	+	15.5638i	0.339688	+	0.545845i
$814$	−0.642896	+	0.371176i	−0.0225335	+	0.0130097i
$815$	27.0942	−	46.9286i	0.949070	−	1.64384i
$816$	39.6586	−	1.31192i	1.38833	−	0.0459264i
$817$	0.430857	+	0.746265i	0.0150738	+	0.0261085i
$818$	5.55490			0.194222
$819$	25.5543	−	12.8832i	0.892940	−	0.450175i
$820$	10.5632			0.368883
$821$	27.4556	+	47.5546i	0.958208	+	1.65967i	0.726849	+	0.686797i	$0.240984\pi$
$821$	27.4556	+	47.5546i	0.958208	+	1.65967i	0.231359	+	0.972868i	$0.425683\pi$
$822$	0.923305	−	0.0305432i	0.0322040	−	0.00106532i
$823$	14.7841	−	25.6069i	0.515343	−	0.892600i	−0.484499	−	0.874792i	$-0.660998\pi$
$823$	14.7841	−	25.6069i	0.515343	−	0.892600i	0.999841	−	0.0178078i	$-0.00566871\pi$
$824$	3.99864	−	2.30862i	0.139299	−	0.0804244i
$825$	11.9170	+	19.1494i	0.414896	+	0.666697i
$826$	1.60834	−	6.10768i	0.0559615	−	0.212513i
$827$	18.6801			0.649571			0.324785	−	0.945788i	$-0.394708\pi$
$827$	18.6801			0.649571			0.324785	+	0.945788i	$0.394708\pi$
$828$	−1.42931	−	21.5799i	−0.0496718	−	0.749954i
$829$	22.7270	+	13.1215i	0.789343	+	0.455727i	0.839731	−	0.543002i	$-0.182713\pi$
$829$	22.7270	+	13.1215i	0.789343	+	0.455727i	−0.0503883	+	0.998730i	$0.516046\pi$
$830$	2.57437	−	4.45894i	0.0893577	−	0.154772i
$831$	6.05260	−	11.3330i	0.209962	−	0.393136i
$832$	−20.1054	+	15.5495i	−0.697029	+	0.539083i
$833$	36.7519	−	21.6436i	1.27338	−	0.749905i
$834$	0.729497	−	0.453978i	0.0252604	−	0.0157200i
$835$	−5.41786	−	9.38400i	−0.187493	−	0.324747i
$836$	3.24093	−	5.61346i	0.112090	−	0.194145i
$837$	16.2854	−	36.0413i	0.562904	−	1.24577i
$838$	−1.94359	−	3.36640i	−0.0671402	−	0.116290i
$839$		−	0.275788i		−	0.00952126i	−0.999989	−	0.00476063i	$-0.998485\pi$
$839$		−	0.275788i		−	0.00952126i	0.999989	−	0.00476063i	$-0.00151536\pi$
$840$	10.7424	−	3.31336i	0.370646	−	0.114322i
$841$	−31.5114			−1.08660
$842$	−2.37859	+	1.37328i	−0.0819716	+	0.0473263i
$843$	8.43914	−	0.279170i	0.290660	−	0.00961512i
$844$	5.65388	−	9.79281i	0.194615	−	0.337082i
$845$	10.6809	+	38.6796i	0.367434	+	1.33062i
$846$	5.49329	+	2.70430i	0.188863	+	0.0929759i
$847$	1.89848	+	6.96490i	0.0652324	+	0.239317i
$848$		−	11.3272i		−	0.388977i
$849$	−29.0622	−	15.5212i	−0.997411	−	0.532687i
$850$	2.76856	−	4.79529i	0.0949609	−	0.164477i
$851$	−2.36543	+	4.09705i	−0.0810861	+	0.140445i
$852$	16.4294	−	30.7626i	0.562860	−	1.05391i
$853$	33.9231			1.16151			0.580753	−	0.814080i	$-0.302758\pi$
$853$	33.9231			1.16151			0.580753	+	0.814080i	$0.302758\pi$
$854$	1.79650	+	1.78106i	0.0614748	+	0.0609467i
$855$	−9.55454	−	4.70363i	−0.326759	−	0.160861i
$856$	1.95012	−	1.12590i	0.0666537	−	0.0384825i
$857$	0.981057	−	1.69924i	0.0335123	−	0.0580449i	−0.848783	−	0.528742i	$-0.822664\pi$
$857$	0.981057	−	1.69924i	0.0335123	−	0.0580449i	0.882295	+	0.470697i	$0.155997\pi$
$858$	−2.77706	+	2.29845i	−0.0948073	+	0.0784679i
$859$	−13.8230	+	7.98073i	−0.471636	+	0.272299i	−0.716924	−	0.697151i	$-0.754451\pi$
$859$	−13.8230	+	7.98073i	−0.471636	+	0.272299i	0.245289	+	0.969450i	$0.421117\pi$
$860$			4.53249i			0.154557i
$861$	−1.78083	+	7.80166i	−0.0606905	+	0.265880i
$862$	−2.73245			−0.0930676
$863$	−0.934427	−	1.61848i	−0.0318083	−	0.0550936i	0.849683	−	0.527294i	$-0.176793\pi$
$863$	−0.934427	−	1.61848i	−0.0318083	−	0.0550936i	−0.881491	+	0.472200i	$0.843460\pi$
$864$	−5.01554	+	11.0999i	−0.170632	+	0.377627i
$865$	−63.7348	−	36.7973i	−2.16705	−	1.25115i
$866$	−3.50942	+	2.02616i	−0.119255	+	0.0688518i
$867$	18.4177	+	29.5954i	0.625497	+	1.00511i
$868$	10.3784	+	38.0752i	0.352267	+	1.29236i
$869$	8.89948			0.301894
$870$	−3.93229	+	7.36289i	−0.133317	+	0.249625i
$871$	−48.8021	+	6.61427i	−1.65360	+	0.224116i
$872$	−0.140965	−	0.0813859i	−0.00477366	−	0.00275608i
$873$	32.8660	−	2.17682i	1.11234	−	0.0736741i
$874$			0.849112i			0.0287216i
$875$	0.982060	−	3.72937i	0.0331997	−	0.126076i
$876$	1.29015	+	2.07315i	0.0435902	+	0.0700451i
$877$	41.1524	−	23.7593i	1.38962	−	0.802295i	0.396345	−	0.918102i	$-0.370279\pi$
$877$	41.1524	−	23.7593i	1.38962	−	0.802295i	0.993272	+	0.115806i	$0.0369452\pi$
$878$	1.69988	+	0.981426i	0.0573682	+	0.0331215i
$879$	1.29290	+	39.0836i	0.0436083	+	1.31826i
$880$	28.9066	−	16.6892i	0.974440	−	0.562593i
$881$	−46.4127			−1.56369			−0.781843	−	0.623476i	$-0.785720\pi$
$881$	−46.4127			−1.56369			−0.781843	+	0.623476i	$0.785720\pi$
$882$	0.314823	+	4.20308i	0.0106007	+	0.141525i
$883$	23.9618			0.806380			0.403190	−	0.915116i	$-0.367901\pi$
$883$	23.9618			0.806380			0.403190	+	0.915116i	$0.367901\pi$
$884$	−39.8380	−	16.3238i	−1.33990	−	0.549029i
$885$	−63.5538	+	2.10238i	−2.13634	+	0.0706707i
$886$	−1.10143	−	0.635913i	−0.0370034	−	0.0213639i
$887$	−4.07445	−	7.05716i	−0.136807	−	0.236956i	0.789479	−	0.613777i	$-0.210351\pi$
$887$	−4.07445	−	7.05716i	−0.136807	−	0.236956i	−0.926286	+	0.376821i	$0.877017\pi$
$888$	1.50301	−	0.935347i	0.0504377	−	0.0313882i
$889$	−43.9736	−	11.5796i	−1.47483	−	0.388368i
$890$	4.66182			0.156265
$891$	9.87258	−	23.9274i	0.330744	−	0.801599i
$892$	−12.7721	+	22.1220i	−0.427642	+	0.740698i
$893$	10.1278	+	5.84730i	0.338914	+	0.195672i
$894$	3.56988	−	6.68429i	0.119395	−	0.223556i
$895$	20.2217			0.675935
$896$	−4.24648	−	15.5790i	−0.141865	−	0.520457i
$897$	−8.00284	+	21.5340i	−0.267207	+	0.719000i
$898$	−0.988484	−	1.71210i	−0.0329861	−	0.0571336i
$899$	−51.2757	−	29.6040i	−1.71014	−	0.987349i
$900$	−14.8042	−	22.1231i	−0.493473	−	0.737437i
$901$	15.8968	−	9.17801i	0.529599	−	0.305764i
$902$		−	1.00800i		−	0.0335628i
$903$	−3.34756	−	0.764122i	−0.111400	−	0.0254284i
$904$			8.09949i			0.269385i
$905$	−15.0481	−	26.0641i	−0.500217	−	0.866401i
$906$	−0.0742165	−	2.24352i	−0.00246568	−	0.0745360i
$907$	16.3494	−	28.3180i	0.542873	−	0.940284i	−0.455864	−	0.890049i	$-0.650670\pi$
$907$	16.3494	−	28.3180i	0.542873	−	0.940284i	0.998737	−	0.0502345i	$-0.0159969\pi$
$908$	−9.93109	+	5.73372i	−0.329575	+	0.190280i
$909$	−8.61222	+	17.4941i	−0.285649	+	0.580244i
$910$	−5.86541	−	0.723762i	−0.194437	−	0.0239925i
$911$			35.6411i			1.18084i	0.807095	+	0.590422i	$0.201039\pi$
$911$			35.6411i			1.18084i	−0.807095	+	0.590422i	$0.798961\pi$
$912$	−3.52827	+	6.60639i	−0.116833	+	0.218759i
$913$	20.6997	+	11.9510i	0.685060	+	0.395519i
$914$	2.01461	+	1.16314i	0.0666374	+	0.0384731i
$915$	11.9985	−	22.4662i	0.396658	−	0.742709i
$916$	17.9775			0.593992
$917$	−0.918557	−	3.36989i	−0.0303334	−	0.111284i
$918$	−6.32325	+	0.629363i	−0.208698	+	0.0207721i
$919$	15.0224	+	26.0195i	0.495542	+	0.858304i	0.999987	−	0.00513976i	$-0.00163604\pi$
$919$	15.0224	+	26.0195i	0.495542	+	0.858304i	−0.504445	+	0.863444i	$0.668303\pi$
$920$	−4.51211	+	7.81520i	−0.148760	+	0.257659i
$921$	−13.7616	+	0.455238i	−0.453460	+	0.0150006i
$922$	0.508277	−	0.293454i	0.0167392	−	0.00966439i
$923$	−29.3037	+	22.6635i	−0.964542	+	0.745978i
$924$	7.61255	+	24.6809i	0.250434	+	0.811941i
$925$			5.82291i			0.191456i
$926$	−5.84568	+	3.37501i	−0.192101	+	0.110910i
$927$	14.4851	−	9.69304i	0.475754	−	0.318361i
$928$	15.7918	+	9.11740i	0.518391	+	0.299293i
$929$	10.3260	−	5.96173i	0.338786	−	0.195598i	−0.320949	−	0.947096i	$-0.604002\pi$
$929$	10.3260	−	5.96173i	0.338786	−	0.195598i	0.659735	+	0.751498i	$0.270669\pi$
$930$	−6.93427	+	4.31531i	−0.227384	+	0.141504i
$931$	0.0694476	+	8.05002i	0.00227605	+	0.263829i
$932$			1.06147i			0.0347697i
$933$	27.5677	−	51.6183i	0.902528	−	1.68991i
$934$	−2.18954	+	3.79239i	−0.0716438	+	0.124091i
$935$	46.8439	+	27.0454i	1.53196	+	0.884478i
$936$	6.43761	−	5.69707i	0.210420	−	0.186215i
$937$			22.6386i			0.739572i	0.929117	+	0.369786i	$0.120569\pi$
$937$			22.6386i			0.739572i	−0.929117	+	0.369786i	$0.879431\pi$
$938$	1.84704	−	7.01413i	0.0603080	−	0.229019i
$939$	−37.9675	+	23.6278i	−1.23902	+	0.771064i
$940$	30.7559	+	53.2708i	1.00315	+	1.73750i
$941$	−25.3798	−	14.6530i	−0.827359	−	0.477676i	0.0255888	−	0.999673i	$-0.491854\pi$
$941$	−25.3798	−	14.6530i	−0.827359	−	0.477676i	−0.852947	+	0.521997i	$0.825187\pi$
$942$	0.0690472	+	2.08726i	0.00224968	+	0.0680065i
$943$	−3.21191	−	5.56318i	−0.104594	−	0.181162i
$944$			44.7199i			1.45551i
$945$	39.6350	−	15.1598i	1.28933	−	0.493149i
$946$	0.432516			0.0140623
$947$	−4.86174	−	8.42079i	−0.157985	−	0.273639i	0.776157	−	0.630540i	$-0.217167\pi$
$947$	−4.86174	−	8.42079i	−0.157985	−	0.273639i	−0.934142	+	0.356901i	$0.883833\pi$
$948$	−10.4976	+	0.347264i	−0.340946	+	0.0112786i
$949$	−0.348354	−	2.57026i	−0.0113080	−	0.0834342i
$950$	0.522557	+	0.905095i	0.0169540	+	0.0293652i
$951$	19.7218	+	31.6910i	0.639524	+	1.02765i
$952$	9.02020	−	9.09835i	0.292346	−	0.294879i
$953$		−	30.8355i		−	0.998859i	−0.866354	−	0.499430i	$-0.833543\pi$
$953$		−	30.8355i		−	0.998859i	0.866354	−	0.499430i	$-0.166457\pi$
$954$	0.119882	+	1.80999i	0.00388131	+	0.0586007i
$955$	−8.42424	+	14.5912i	−0.272602	+	0.472161i
$956$	17.7124	−	30.6788i	0.572861	−	0.992224i
$957$	−34.1806	−	18.2548i	−1.10490	−	0.590095i
$958$			3.29795i			0.106552i
$959$	−4.95007	+	4.99296i	−0.159846	+	0.161231i
$960$	−31.9981	+	19.9129i	−1.03273	+	0.642687i
$961$	−13.4664	−	23.3245i	−0.434400	−	0.752402i
$962$	−0.922227	+	0.124992i	−0.0297338	+	0.00402989i
$963$	7.06433	−	4.72726i	0.227645	−	0.152334i
$964$	26.8139	+	46.4431i	0.863619	+	1.49583i
$965$	−37.9461			−1.22153
$966$	−2.48020	−	2.30137i	−0.0797991	−	0.0740455i
$967$		−	24.5542i		−	0.789611i	−0.918765	−	0.394806i	$-0.870812\pi$
$967$		−	24.5542i		−	0.789611i	0.918765	−	0.394806i	$-0.129188\pi$
$968$	1.08424	+	1.87796i	0.0348489	+	0.0603600i
$969$	−12.1304	+	0.401277i	−0.389684	+	0.0128909i
$970$	−5.89069	−	3.40099i	−0.189139	−	0.109199i
$971$	−1.18422	−	2.05113i	−0.0380035	−	0.0658240i	0.846398	−	0.532551i	$-0.178766\pi$
$971$	−1.18422	−	2.05113i	−0.0380035	−	0.0658240i	−0.884402	+	0.466727i	$0.845433\pi$
$972$	−10.7118	+	28.6094i	−0.343580	+	0.917646i
$973$	−1.66523	+	6.32370i	−0.0533848	+	0.202729i
$974$			1.88272i			0.0603263i
$975$	4.72191	+	27.8789i	0.151222	+	0.892839i
$976$	−15.5122	−	8.95596i	−0.496532	−	0.286673i
$977$	9.87151	−	17.0980i	0.315818	−	0.547012i	−0.663793	−	0.747916i	$-0.731055\pi$
$977$	9.87151	−	17.0980i	0.315818	−	0.547012i	0.979611	+	0.200904i	$0.0643879\pi$
$978$	5.38325	+	2.87503i	0.172138	+	0.0919334i
$979$			21.6415i			0.691666i
$980$	−20.8546	+	36.8518i	−0.666177	+	1.17719i
$981$	−0.551253	−	0.271377i	−0.0176001	−	0.00866441i
$982$	1.56051	−	0.900958i	0.0497977	−	0.0287507i
$983$	3.21719	+	1.85745i	0.102613	+	0.0592434i	0.550428	−	0.834883i	$-0.314465\pi$
$983$	3.21719	+	1.85745i	0.102613	+	0.0592434i	−0.447816	+	0.894126i	$0.647798\pi$
$984$	0.0794745	+	2.40247i	0.00253355	+	0.0765879i
$985$	−17.2116	+	9.93714i	−0.548408	+	0.316624i
$986$			9.51301i			0.302956i
$987$	−44.5293	+	13.7346i	−1.41738	+	0.437177i
$988$	6.42793	−	4.97137i	0.204500	−	0.158160i
$989$	2.38706	−	1.37817i	0.0759042	−	0.0438233i
$990$	−4.44241	+	2.97274i	−0.141189	+	0.0944799i
$991$	16.7156	−	28.9523i	0.530988	−	0.919699i	−0.468358	−	0.883539i	$-0.655154\pi$
$991$	16.7156	−	28.9523i	0.530988	−	0.919699i	0.999346	−	0.0361598i	$-0.0115125\pi$
$992$	8.92102	+	15.4517i	0.283243	+	0.490591i
$993$	0.448961	−	0.279396i	0.0142473	−	0.00886636i
$994$	−1.43483	−	5.26392i	−0.0455100	−	0.166961i
$995$	65.6825			2.08228
$996$	−24.8831	−	13.2893i	−0.788452	−	0.421089i
$997$	−27.1132	−	15.6538i	−0.858685	−	0.495762i	0.00488676	−	0.999988i	$-0.498444\pi$
$997$	−27.1132	−	15.6538i	−0.858685	−	0.495762i	−0.863572	+	0.504226i	$0.831778\pi$
$998$	−2.33673	−	1.34911i	−0.0739679	−	0.0427054i
$999$	5.42781	−	3.89798i	0.171728	−	0.123327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.ba.c.38.17	yes	64
3.2	odd	2	inner	273.2.ba.c.38.16	yes	64
7.5	odd	6	inner	273.2.ba.c.194.18	yes	64
13.12	even	2	inner	273.2.ba.c.38.15	✓	64
21.5	even	6	inner	273.2.ba.c.194.15	yes	64
39.38	odd	2	inner	273.2.ba.c.38.18	yes	64
91.12	odd	6	inner	273.2.ba.c.194.16	yes	64
273.194	even	6	inner	273.2.ba.c.194.17	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.ba.c.38.15	✓	64	13.12	even	2	inner
273.2.ba.c.38.16	yes	64	3.2	odd	2	inner
273.2.ba.c.38.17	yes	64	1.1	even	1	trivial
273.2.ba.c.38.18	yes	64	39.38	odd	2	inner
273.2.ba.c.194.15	yes	64	21.5	even	6	inner
273.2.ba.c.194.16	yes	64	91.12	odd	6	inner
273.2.ba.c.194.17	yes	64	273.194	even	6	inner
273.2.ba.c.194.18	yes	64	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.100354 + 0.173818i) q^{2} +(-1.73110 + 0.0572655i) q^{3} +(0.979858 - 1.69716i) q^{4} +(-2.67317 + 1.54335i) q^{5} +(-0.183677 - 0.295150i) q^{6} +(2.55853 + 0.673741i) q^{7} +0.794745 q^{8} +(2.99344 - 0.198265i) q^{9} +O(q^{10})\)	\(q+(0.100354 + 0.173818i) q^{2} +(-1.73110 + 0.0572655i) q^{3} +(0.979858 - 1.69716i) q^{4} +(-2.67317 + 1.54335i) q^{5} +(-0.183677 - 0.295150i) q^{6} +(2.55853 + 0.673741i) q^{7} +0.794745 q^{8} +(2.99344 - 0.198265i) q^{9} +(-0.536525 - 0.309763i) q^{10} +(1.43801 - 2.49070i) q^{11} +(-1.59905 + 2.99408i) q^{12} +(2.85209 - 2.20581i) q^{13} +(0.139650 + 0.512330i) q^{14} +(4.53915 - 2.82479i) q^{15} +(-1.87996 - 3.25619i) q^{16} +(3.04653 - 5.27675i) q^{17} +(0.334865 + 0.500417i) q^{18} +(0.575023 + 0.995969i) q^{19} +6.04908i q^{20} +(-4.46766 - 1.01980i) q^{21} +0.577238 q^{22} +(3.18579 - 1.83931i) q^{23} +(-1.37579 + 0.0455115i) q^{24} +(2.26389 - 3.92117i) q^{25} +(0.669627 + 0.274383i) q^{26} +(-5.17060 + 0.514638i) q^{27} +(3.65045 - 3.68207i) q^{28} +7.77891i q^{29} +(0.946519 + 0.505507i) q^{30} +(-3.80568 + 6.59163i) q^{31} +(1.17207 - 2.03008i) q^{32} +(-2.34671 + 4.39401i) q^{33} +1.22292 q^{34} +(-7.87920 + 2.14769i) q^{35} +(2.59666 - 5.27463i) q^{36} +(-1.11374 + 0.643021i) q^{37} +(-0.115411 + 0.199898i) q^{38} +(-4.81094 + 3.98181i) q^{39} +(-2.12449 + 1.22657i) q^{40} -1.74625i q^{41} +(-0.271087 - 0.878900i) q^{42} +0.749286 q^{43} +(-2.81809 - 4.88107i) q^{44} +(-7.69598 + 5.14994i) q^{45} +(0.639411 + 0.369164i) q^{46} +(8.80645 - 5.08440i) q^{47} +(3.44087 + 5.52914i) q^{48} +(6.09215 + 3.44757i) q^{49} +0.908758 q^{50} +(-4.97169 + 9.30906i) q^{51} +(-0.948977 - 7.00184i) q^{52} +(2.60900 + 1.50631i) q^{53} +(-0.608343 - 0.847097i) q^{54} +8.87743i q^{55} +(2.03338 + 0.535452i) q^{56} +(-1.05246 - 1.69120i) q^{57} +(-1.35211 + 0.780643i) q^{58} +(-10.3004 - 5.94692i) q^{59} +(-0.346403 - 10.4716i) q^{60} +(4.12566 - 2.38195i) q^{61} -1.52766 q^{62} +(7.79239 + 1.50954i) q^{63} -7.04936 q^{64} +(-4.21977 + 10.2983i) q^{65} +(-0.999259 + 0.0330558i) q^{66} +(-11.8291 - 6.82951i) q^{67} +(-5.97034 - 10.3409i) q^{68} +(-5.40960 + 3.36648i) q^{69} +(-1.16402 - 1.15402i) q^{70} -10.2745 q^{71} +(2.37902 - 0.157570i) q^{72} +(0.359690 - 0.623001i) q^{73} +(-0.223537 - 0.129059i) q^{74} +(-3.69448 + 6.91759i) q^{75} +2.25376 q^{76} +(5.35728 - 5.40369i) q^{77} +(-1.17491 - 0.436638i) q^{78} +(1.54719 + 2.67981i) q^{79} +(10.0509 + 5.80289i) q^{80} +(8.92138 - 1.18699i) q^{81} +(0.303530 - 0.175243i) q^{82} +8.31078i q^{83} +(-6.10844 + 6.58310i) q^{84} +18.8075i q^{85} +(0.0751937 + 0.130239i) q^{86} +(-0.445463 - 13.4661i) q^{87} +(1.14285 - 1.97947i) q^{88} +(-6.51669 + 3.76241i) q^{89} +(-1.66747 - 0.820883i) q^{90} +(8.78330 - 3.72206i) q^{91} -7.20907i q^{92} +(6.21055 - 11.6287i) q^{93} +(1.76752 + 1.02048i) q^{94} +(-3.07427 - 1.77493i) q^{95} +(-1.91272 + 3.58140i) q^{96} +10.9793 q^{97} +(0.0121201 + 1.40490i) q^{98} +(3.81077 - 7.74088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9}+O(q^{10}) \) 64 * q - 12 * q^3 - 40 * q^4 - 12 * q^9	\( 64 q - 12 q^{3} - 40 q^{4} - 12 q^{9} - 12 q^{10} - 6 q^{12} - 32 q^{16} - 24 q^{22} + 28 q^{25} - 22 q^{30} + 44 q^{36} + 6 q^{39} - 108 q^{40} + 24 q^{42} + 20 q^{49} + 28 q^{51} + 36 q^{52} + 48 q^{61} + 32 q^{64} + 90 q^{66} - 60 q^{75} - 68 q^{78} + 16 q^{79} + 60 q^{81} + 120 q^{82} + 60 q^{87} + 12 q^{88} - 32 q^{91} + 168 q^{94}+O(q^{100}) \) 64 * q - 12 * q^3 - 40 * q^4 - 12 * q^9 - 12 * q^10 - 6 * q^12 - 32 * q^16 - 24 * q^22 + 28 * q^25 - 22 * q^30 + 44 * q^36 + 6 * q^39 - 108 * q^40 + 24 * q^42 + 20 * q^49 + 28 * q^51 + 36 * q^52 + 48 * q^61 + 32 * q^64 + 90 * q^66 - 60 * q^75 - 68 * q^78 + 16 * q^79 + 60 * q^81 + 120 * q^82 + 60 * q^87 + 12 * q^88 - 32 * q^91 + 168 * q^94

Introduction

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