LMFDB - Embedded newform 627.2.r.c.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(100,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("627.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.r (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	627.199
Dual form			627.2.r.c.397.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.180996 + 1.02648i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.858479 - 0.312461i) q^{4} +(0.862251 + 0.313834i) q^{5} +(0.798461 + 0.669989i) q^{6} +(1.34164 - 2.32379i) q^{7} +(1.51843 + 2.63001i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.166080 + 0.941888i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.456787 - 0.791179i) q^{12} +(-0.948563 - 0.795939i) q^{13} +(2.62817 + 0.956574i) q^{14} +(0.862251 - 0.313834i) q^{15} +(-1.02514 + 0.860199i) q^{16} +(-0.102402 - 0.580753i) q^{17} +1.04232 q^{18} +(-4.19267 + 1.19228i) q^{19} +0.838286 q^{20} +(-0.465948 - 2.64252i) q^{21} +(-0.798461 + 0.669989i) q^{22} +(5.29299 - 1.92649i) q^{23} +(2.85372 + 1.03867i) q^{24} +(-3.18524 - 2.67273i) q^{25} +(0.645331 - 1.11775i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.425678 - 2.41414i) q^{28} +(-0.392951 + 2.22854i) q^{29} +(0.478209 + 0.828282i) q^{30} +(-1.12537 + 1.94920i) q^{31} +(3.58423 + 3.00752i) q^{32} +(0.939693 + 0.342020i) q^{33} +(0.577598 - 0.210228i) q^{34} +(1.88612 - 1.58264i) q^{35} +(-0.158641 - 0.899696i) q^{36} +3.34135 q^{37} +(-1.98271 - 4.08790i) q^{38} -1.23826 q^{39} +(0.483887 + 2.74426i) q^{40} +(-3.96418 + 3.32634i) q^{41} +(2.62817 - 0.956574i) q^{42} +(-1.98672 - 0.723108i) q^{43} +(0.699839 + 0.587235i) q^{44} +(0.458794 - 0.794655i) q^{45} +(2.93552 + 5.08448i) q^{46} +(-0.0965200 + 0.547392i) q^{47} +(-0.232381 + 1.31790i) q^{48} +(-0.100014 - 0.173229i) q^{49} +(2.16699 - 3.75334i) q^{50} +(-0.451745 - 0.379059i) q^{51} +(-1.06302 - 0.386908i) q^{52} +(-3.64737 + 1.32753i) q^{53} +(0.798461 - 0.669989i) q^{54} +(0.159338 + 0.903648i) q^{55} +8.14879 q^{56} +(-2.44539 + 3.60834i) q^{57} -2.35867 q^{58} +(-0.242091 - 1.37296i) q^{59} +(0.642164 - 0.538840i) q^{60} +(4.98589 - 1.81472i) q^{61} +(-2.20451 - 0.802375i) q^{62} +(-2.05552 - 1.72478i) q^{63} +(-3.77667 + 6.54138i) q^{64} +(-0.568107 - 0.983990i) q^{65} +(-0.180996 + 1.02648i) q^{66} +(-0.794626 + 4.50655i) q^{67} +(-0.269373 - 0.466567i) q^{68} +(2.81634 - 4.87805i) q^{69} +(1.96593 + 1.64961i) q^{70} +(4.00735 + 1.45856i) q^{71} +(2.85372 - 1.03867i) q^{72} +(-3.57161 + 2.99694i) q^{73} +(0.604773 + 3.42984i) q^{74} -4.15803 q^{75} +(-3.22678 + 2.33359i) q^{76} +2.68329 q^{77} +(-0.224121 - 1.27105i) q^{78} +(-4.41506 + 3.70468i) q^{79} +(-1.15389 + 0.419982i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-4.13193 - 3.46710i) q^{82} +(-4.30882 + 7.46309i) q^{83} +(-1.22569 - 2.12296i) q^{84} +(0.0939632 - 0.532892i) q^{85} +(0.382668 - 2.17022i) q^{86} +(1.13146 + 1.95974i) q^{87} +(-1.51843 + 2.63001i) q^{88} +(3.38494 + 2.84030i) q^{89} +(0.898739 + 0.327114i) q^{90} +(-3.12223 + 1.13640i) q^{91} +(3.94197 - 3.30771i) q^{92} +(0.390837 + 2.21655i) q^{93} -0.579358 q^{94} +(-3.98931 - 0.287755i) q^{95} +4.67888 q^{96} +(-1.67819 - 9.51746i) q^{97} +(0.159714 - 0.134016i) q^{98} +(0.939693 - 0.342020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{2} + 3 q^{4} + 3 q^{6} - 18 q^{7} - 12 q^{8} + 30 q^{10} + 27 q^{11} - 33 q^{12} + 9 q^{14} - 21 q^{16} - 24 q^{17} + 6 q^{18} + 3 q^{19} + 30 q^{20} - 3 q^{22} + 12 q^{23} - 39 q^{24} + 30 q^{25}+ \cdots - 54 q^{98}+O(q^{100}) $ 54 * q + 3 * q^2 + 3 * q^4 + 3 * q^6 - 18 * q^7 - 12 * q^8 + 30 * q^10 + 27 * q^11 - 33 * q^12 + 9 * q^14 - 21 * q^16 - 24 * q^17 + 6 * q^18 + 3 * q^19 + 30 * q^20 - 3 * q^22 + 12 * q^23 - 39 * q^24 + 30 * q^25 - 6 * q^26 - 27 * q^27 - 30 * q^28 + 33 * q^29 + 15 * q^30 + 15 * q^31 + 39 * q^32 + 3 * q^34 - 27 * q^35 + 3 * q^36 - 24 * q^37 + 15 * q^38 + 6 * q^39 + 84 * q^40 - 15 * q^41 + 9 * q^42 - 48 * q^43 + 6 * q^44 - 36 * q^46 + 3 * q^47 + 24 * q^48 - 21 * q^49 - 30 * q^50 + 3 * q^51 - 45 * q^52 - 21 * q^53 + 3 * q^54 + 21 * q^57 + 90 * q^58 + 45 * q^59 - 39 * q^60 - 21 * q^61 - 87 * q^62 - 9 * q^63 - 54 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 - 39 * q^69 + 15 * q^70 - 57 * q^71 - 39 * q^72 - 30 * q^73 - 105 * q^74 + 54 * q^75 - 6 * q^76 - 36 * q^77 + 51 * q^78 - 27 * q^79 - 3 * q^80 + 102 * q^82 - 63 * q^83 - 51 * q^84 + 60 * q^85 - 42 * q^86 - 27 * q^87 + 12 * q^88 + 21 * q^89 - 6 * q^90 - 72 * q^91 + 78 * q^92 - 6 * q^93 - 36 * q^94 + 63 * q^95 + 114 * q^96 + 45 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.180996	+	1.02648i	0.127984	+	0.725832i	0.979491	+	0.201489i	$0.0645781\pi$
$2$	0.180996	+	1.02648i	0.127984	+	0.725832i	−0.851507	+	0.524343i	$0.824311\pi$
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	0.858479	−	0.312461i	0.429240	−	0.156230i
$5$	0.862251	+	0.313834i	0.385610	+	0.140351i	0.527549	−	0.849525i	$-0.323111\pi$
$5$	0.862251	+	0.313834i	0.385610	+	0.140351i	−0.141938	+	0.989876i	$0.545333\pi$
$6$	0.798461	+	0.669989i	0.325970	+	0.273522i
$7$	1.34164	−	2.32379i	0.507094	−	0.878312i	−0.492873	−	0.870101i	$-0.664053\pi$
$7$	1.34164	−	2.32379i	0.507094	−	0.878312i	0.999966	−	0.00821034i	$-0.00261346\pi$
$8$	1.51843	+	2.63001i	0.536848	+	0.929847i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−0.166080	+	0.941888i	−0.0525192	+	0.297851i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.456787	−	0.791179i	0.131863	−	0.228394i
$13$	−0.948563	−	0.795939i	−0.263084	−	0.220754i	0.501698	−	0.865043i	$-0.332709\pi$
$13$	−0.948563	−	0.795939i	−0.263084	−	0.220754i	−0.764782	+	0.644289i	$0.777153\pi$
$14$	2.62817	+	0.956574i	0.702407	+	0.255655i
$15$	0.862251	−	0.313834i	0.222632	−	0.0810315i
$16$	−1.02514	+	0.860199i	−0.256286	+	0.215050i
$17$	−0.102402	−	0.580753i	−0.0248362	−	0.140853i	0.969868	−	0.243630i	$-0.0783383\pi$
$17$	−0.102402	−	0.580753i	−0.0248362	−	0.140853i	−0.994704	+	0.102777i	$0.967227\pi$
$18$	1.04232			0.245677
$19$	−4.19267	+	1.19228i	−0.961864	+	0.273528i
$19$	−4.19267	+	1.19228i	−0.961864	+	0.273528i
$20$	0.838286			0.187446
$21$	−0.465948	−	2.64252i	−0.101678	−	0.576645i
$22$	−0.798461	+	0.669989i	−0.170233	+	0.142842i
$23$	5.29299	−	1.92649i	1.10367	−	0.401701i	0.274999	−	0.961444i	$-0.411322\pi$
$23$	5.29299	−	1.92649i	1.10367	−	0.401701i	0.828666	+	0.559743i	$0.189100\pi$
$24$	2.85372	+	1.03867i	0.582514	+	0.212018i
$25$	−3.18524	−	2.67273i	−0.637047	−	0.534546i
$26$	0.645331	−	1.11775i	0.126560	−	0.219208i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.425678	−	2.41414i	0.0804456	−	0.456230i
$29$	−0.392951	+	2.22854i	−0.0729692	+	0.413829i	0.926341	+	0.376686i	$0.122937\pi$
$29$	−0.392951	+	2.22854i	−0.0729692	+	0.413829i	−0.999310	+	0.0371423i	$0.988175\pi$
$30$	0.478209	+	0.828282i	0.0873086	+	0.151223i
$31$	−1.12537	+	1.94920i	−0.202123	+	0.350087i	−0.949212	−	0.314637i	$-0.898117\pi$
$31$	−1.12537	+	1.94920i	−0.202123	+	0.350087i	0.747089	+	0.664724i	$0.231451\pi$
$32$	3.58423	+	3.00752i	0.633608	+	0.531660i
$33$	0.939693	+	0.342020i	0.163579	+	0.0595381i
$34$	0.577598	−	0.210228i	0.0990572	−	0.0360539i
$35$	1.88612	−	1.58264i	0.318812	−	0.267515i
$36$	−0.158641	−	0.899696i	−0.0264401	−	0.149949i
$37$	3.34135			0.549315			0.274657	−	0.961542i	$-0.411436\pi$
$37$	3.34135			0.549315			0.274657	+	0.961542i	$0.411436\pi$
$38$	−1.98271	−	4.08790i	−0.321639	−	0.663145i
$39$	−1.23826			−0.198281
$40$	0.483887	+	2.74426i	0.0765093	+	0.433906i
$41$	−3.96418	+	3.32634i	−0.619101	+	0.519487i	−0.897521	−	0.440972i	$-0.854634\pi$
$41$	−3.96418	+	3.32634i	−0.619101	+	0.519487i	0.278420	+	0.960459i	$0.410189\pi$
$42$	2.62817	−	0.956574i	0.405535	−	0.147603i
$43$	−1.98672	−	0.723108i	−0.302972	−	0.110273i	0.186060	−	0.982538i	$-0.440428\pi$
$43$	−1.98672	−	0.723108i	−0.302972	−	0.110273i	−0.489033	+	0.872265i	$0.662650\pi$
$44$	0.699839	+	0.587235i	0.105505	+	0.0885289i
$45$	0.458794	−	0.794655i	0.0683930	−	0.118460i
$46$	2.93552	+	5.08448i	0.432819	+	0.749665i
$47$	−0.0965200	+	0.547392i	−0.0140789	+	0.0798453i	−0.991038	−	0.133583i	$-0.957352\pi$
$47$	−0.0965200	+	0.547392i	−0.0140789	+	0.0798453i	0.976959	+	0.213428i	$0.0684629\pi$
$48$	−0.232381	+	1.31790i	−0.0335414	+	0.190223i
$49$	−0.100014	−	0.173229i	−0.0142877	−	0.0247469i
$50$	2.16699	−	3.75334i	0.306459	−	0.530803i
$51$	−0.451745	−	0.379059i	−0.0632570	−	0.0530789i
$52$	−1.06302	−	0.386908i	−0.147415	−	0.0536545i
$53$	−3.64737	+	1.32753i	−0.501004	+	0.182351i	−0.580146	−	0.814513i	$-0.697004\pi$
$53$	−3.64737	+	1.32753i	−0.501004	+	0.182351i	0.0791414	+	0.996863i	$0.474782\pi$
$54$	0.798461	−	0.669989i	0.108657	−	0.0911739i
$55$	0.159338	+	0.903648i	0.0214851	+	0.121848i
$56$	8.14879			1.08893
$57$	−2.44539	+	3.60834i	−0.323899	+	0.477936i
$58$	−2.35867			−0.309709
$59$	−0.242091	−	1.37296i	−0.0315175	−	0.178745i	0.964985	−	0.262304i	$-0.0844823\pi$
$59$	−0.242091	−	1.37296i	−0.0315175	−	0.178745i	−0.996503	+	0.0835592i	$0.973371\pi$
$60$	0.642164	−	0.538840i	0.0829030	−	0.0695639i
$61$	4.98589	−	1.81472i	0.638378	−	0.232351i	−0.00249560	−	0.999997i	$-0.500794\pi$
$61$	4.98589	−	1.81472i	0.638378	−	0.232351i	0.640874	+	0.767646i	$0.278572\pi$
$62$	−2.20451	−	0.802375i	−0.279973	−	0.101902i
$63$	−2.05552	−	1.72478i	−0.258971	−	0.217302i
$64$	−3.77667	+	6.54138i	−0.472084	+	0.817673i
$65$	−0.568107	−	0.983990i	−0.0704650	−	0.122049i
$66$	−0.180996	+	1.02648i	−0.0222791	+	0.126351i
$67$	−0.794626	+	4.50655i	−0.0970790	+	0.550562i	0.897011	+	0.442007i	$0.145733\pi$
$67$	−0.794626	+	4.50655i	−0.0970790	+	0.550562i	−0.994090	+	0.108555i	$0.965378\pi$
$68$	−0.269373	−	0.466567i	−0.0326663	−	0.0565796i
$69$	2.81634	−	4.87805i	0.339048	−	0.587248i
$70$	1.96593	+	1.64961i	0.234974	+	0.197167i
$71$	4.00735	+	1.45856i	0.475585	+	0.173099i	0.568681	−	0.822558i	$-0.307454\pi$
$71$	4.00735	+	1.45856i	0.475585	+	0.173099i	−0.0930958	+	0.995657i	$0.529676\pi$
$72$	2.85372	−	1.03867i	0.336315	−	0.122408i
$73$	−3.57161	+	2.99694i	−0.418026	+	0.350765i	−0.827411	−	0.561596i	$-0.810187\pi$
$73$	−3.57161	+	2.99694i	−0.418026	+	0.350765i	0.409386	+	0.912361i	$0.365743\pi$
$74$	0.604773	+	3.42984i	0.0703034	+	0.398710i
$75$	−4.15803			−0.480128
$76$	−3.22678	+	2.33359i	−0.370137	+	0.267682i
$77$	2.68329			0.305789
$78$	−0.224121	−	1.27105i	−0.0253767	−	0.143918i
$79$	−4.41506	+	3.70468i	−0.496733	+	0.416809i	−0.856432	−	0.516260i	$-0.827324\pi$
$79$	−4.41506	+	3.70468i	−0.496733	+	0.416809i	0.359699	+	0.933068i	$0.382879\pi$
$80$	−1.15389	+	0.419982i	−0.129009	+	0.0469554i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−4.13193	−	3.46710i	−0.456296	−	0.382877i
$83$	−4.30882	+	7.46309i	−0.472954	+	0.819181i	−0.999521	−	0.0309530i	$-0.990146\pi$
$83$	−4.30882	+	7.46309i	−0.472954	+	0.819181i	0.526567	+	0.850134i	$0.323479\pi$
$84$	−1.22569	−	2.12296i	−0.133734	−	0.231634i
$85$	0.0939632	−	0.532892i	0.0101917	−	0.0578002i
$86$	0.382668	−	2.17022i	0.0412641	−	0.234020i
$87$	1.13146	+	1.95974i	0.121305	+	0.210106i
$88$	−1.51843	+	2.63001i	−0.161866	+	0.280360i
$89$	3.38494	+	2.84030i	0.358803	+	0.301072i	0.804313	−	0.594205i	$-0.202533\pi$
$89$	3.38494	+	2.84030i	0.358803	+	0.301072i	−0.445510	+	0.895277i	$0.646978\pi$
$90$	0.898739	+	0.327114i	0.0947354	+	0.0344809i
$91$	−3.12223	+	1.13640i	−0.327299	+	0.119127i
$92$	3.94197	−	3.30771i	0.410979	−	0.344852i
$93$	0.390837	+	2.21655i	0.0405280	+	0.229845i
$94$	−0.579358			−0.0597562
$95$	−3.98931	−	0.287755i	−0.409295	−	0.0295230i
$96$	4.67888			0.477536
$97$	−1.67819	−	9.51746i	−0.170394	−	0.966352i	−0.943327	−	0.331864i	$-0.892322\pi$
$97$	−1.67819	−	9.51746i	−0.170394	−	0.966352i	0.772933	−	0.634487i	$-0.218789\pi$
$98$	0.159714	−	0.134016i	0.0161335	−	0.0135377i
$99$	0.939693	−	0.342020i	0.0944427	−	0.0343743i
$100$	−3.56958	−	1.29922i	−0.356958	−	0.129922i
$101$	−7.99155	−	6.70571i	−0.795189	−	0.667243i	0.151835	−	0.988406i	$-0.451482\pi$
$101$	−7.99155	−	6.70571i	−0.795189	−	0.667243i	−0.947024	+	0.321163i	$0.895926\pi$
$102$	0.307333	−	0.532317i	0.0304305	−	0.0527072i
$103$	0.193756	+	0.335595i	0.0190913	+	0.0330671i	0.875413	−	0.483375i	$-0.160589\pi$
$103$	0.193756	+	0.335595i	0.0190913	+	0.0330671i	−0.856322	+	0.516442i	$0.827256\pi$
$104$	0.652993	−	3.70331i	0.0640312	−	0.363139i
$105$	0.427548	−	2.42475i	0.0417244	−	0.236631i
$106$	−2.02285	−	3.50368i	−0.196476	−	0.340307i
$107$	−6.25806	+	10.8393i	−0.604990	+	1.04787i	0.387063	+	0.922053i	$0.373489\pi$
$107$	−6.25806	+	10.8393i	−0.604990	+	1.04787i	−0.992053	+	0.125820i	$0.959844\pi$
$108$	−0.699839	−	0.587235i	−0.0673420	−	0.0565067i
$109$	−17.4168	−	6.33918i	−1.66822	−	0.607184i	−0.676601	−	0.736350i	$-0.736548\pi$
$109$	−17.4168	−	6.33918i	−1.66822	−	0.607184i	−0.991623	+	0.129166i	$0.958770\pi$
$110$	−0.898739	+	0.327114i	−0.0856914	+	0.0311891i
$111$	2.55962	−	2.14778i	0.242949	−	0.203858i
$112$	0.623546	+	3.53631i	0.0589196	+	0.334149i
$113$	5.32271			0.500719			0.250359	−	0.968153i	$-0.419451\pi$
$113$	5.32271			0.500719			0.250359	+	0.968153i	$0.419451\pi$
$114$	−4.14650	−	1.85705i	−0.388355	−	0.173929i
$115$	5.16849			0.481964
$116$	0.358990	+	2.03593i	0.0333314	+	0.189032i
$117$	−0.948563	+	0.795939i	−0.0876947	+	0.0735846i
$118$	1.36551	−	0.497004i	0.125705	−	0.0457529i
$119$	−1.48694	−	0.541201i	−0.136307	−	0.0496118i
$120$	2.13466	+	1.79119i	0.194867	+	0.163512i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.76520	+	4.78947i	0.250350	+	0.433619i
$123$	−0.898606	+	5.09625i	−0.0810246	+	0.459513i
$124$	−0.357059	+	2.02498i	−0.0320649	+	0.181849i
$125$	−4.20165	−	7.27747i	−0.375807	−	0.650917i
$126$	1.39842	−	2.42213i	0.124581	−	0.215781i
$127$	3.10113	+	2.60215i	0.275180	+	0.230904i	0.769925	−	0.638135i	$-0.220294\pi$
$127$	3.10113	+	2.60215i	0.275180	+	0.230904i	−0.494744	+	0.869039i	$0.664738\pi$
$128$	1.39524	+	0.507825i	0.123323	+	0.0448858i
$129$	−1.98672	+	0.723108i	−0.174921	+	0.0636661i
$130$	0.907223	−	0.761251i	0.0795687	−	0.0667661i
$131$	0.154224	+	0.874648i	0.0134746	+	0.0764184i	0.990804	−	0.135308i	$-0.0432025\pi$
$131$	0.154224	+	0.874648i	0.0134746	+	0.0764184i	−0.977329	+	0.211727i	$0.932091\pi$
$132$	0.913575			0.0795165
$133$	−2.85445	+	11.3425i	−0.247512	+	0.983521i
$134$	−4.76971			−0.412041
$135$	−0.159338	−	0.903648i	−0.0137136	−	0.0777736i
$136$	1.37189	−	1.15115i	0.117639	−	0.0987106i
$137$	8.55806	−	3.11488i	0.731165	−	0.266122i	0.0505068	−	0.998724i	$-0.483916\pi$
$137$	8.55806	−	3.11488i	0.731165	−	0.266122i	0.680658	+	0.732602i	$0.261694\pi$
$138$	5.51698	+	2.00802i	0.469636	+	0.170934i
$139$	−13.6447	−	11.4493i	−1.15733	−	0.971116i	−0.157465	−	0.987525i	$-0.550332\pi$
$139$	−13.6447	−	11.4493i	−1.15733	−	0.971116i	−0.999865	+	0.0164087i	$0.994777\pi$
$140$	1.12468	−	1.94800i	0.0950528	−	0.164636i
$141$	0.277918	+	0.481368i	0.0234049	+	0.0405385i
$142$	−0.771865	+	4.37746i	−0.0647735	+	0.367349i
$143$	0.215022	−	1.21945i	0.0179810	−	0.101975i
$144$	0.669116	+	1.15894i	0.0557597	+	0.0965785i
$145$	−1.03821	+	1.79824i	−0.0862188	+	0.149335i
$146$	−3.72275	−	3.12376i	−0.308097	−	0.258524i
$147$	−0.187964	−	0.0684133i	−0.0155030	−	0.00564263i
$148$	2.86848	−	1.04404i	0.235788	−	0.0858197i
$149$	8.98629	−	7.54039i	0.736186	−	0.617733i	−0.195625	−	0.980679i	$-0.562673\pi$
$149$	8.98629	−	7.54039i	0.736186	−	0.617733i	0.931810	+	0.362946i	$0.118229\pi$
$150$	−0.752589	−	4.26815i	−0.0614486	−	0.348493i
$151$	10.7135			0.871856			0.435928	−	0.899981i	$-0.356420\pi$
$151$	10.7135			0.871856			0.435928	+	0.899981i	$0.356420\pi$
$152$	−9.50200	−	9.21634i	−0.770714	−	0.747544i
$153$	−0.589712			−0.0476754
$154$	0.485665	+	2.75435i	0.0391360	+	0.221952i
$155$	−1.58208	+	1.32752i	−0.127076	+	0.106629i
$156$	−1.06302	+	0.386908i	−0.0851099	+	0.0309775i
$157$	−17.4874	−	6.36489i	−1.39565	−	0.507974i	−0.468763	−	0.883324i	$-0.655300\pi$
$157$	−17.4874	−	6.36489i	−1.39565	−	0.507974i	−0.926883	+	0.375351i	$0.877522\pi$
$158$	−4.60189	−	3.86145i	−0.366107	−	0.307200i
$159$	−1.94072	+	3.36143i	−0.153909	+	0.266579i
$160$	2.14664	+	3.71809i	0.169707	+	0.293941i
$161$	2.62454	−	14.8845i	0.206843	−	1.17306i
$162$	0.180996	−	1.02648i	0.0142204	−	0.0806481i
$163$	−4.66871	−	8.08644i	−0.365681	−	0.633379i	0.623204	−	0.782059i	$-0.285831\pi$
$163$	−4.66871	−	8.08644i	−0.365681	−	0.633379i	−0.988885	+	0.148681i	$0.952497\pi$
$164$	−2.36381	+	4.09425i	−0.184583	+	0.319707i
$165$	0.702913	+	0.589814i	0.0547217	+	0.0459170i
$166$	−8.44061	−	3.07213i	−0.655119	−	0.238444i
$167$	−13.1907	+	4.80103i	−1.02073	+	0.371515i	−0.797544	−	0.603261i	$-0.793868\pi$
$167$	−13.1907	+	4.80103i	−1.02073	+	0.371515i	−0.223185	+	0.974776i	$0.571645\pi$
$168$	6.24234	−	5.23794i	0.481607	−	0.404116i
$169$	−1.99117	−	11.2925i	−0.153167	−	0.868654i
$170$	0.564011			0.0432577
$171$	0.446119	+	4.33601i	0.0341156	+	0.331583i
$172$	−1.93150			−0.147276
$173$	2.92606	+	16.5945i	0.222464	+	1.26166i	0.867474	+	0.497482i	$0.165742\pi$
$173$	2.92606	+	16.5945i	0.222464	+	1.26166i	−0.645011	+	0.764174i	$0.723147\pi$
$174$	−1.80685	+	1.51613i	−0.136977	+	0.114937i
$175$	−10.4843	+	3.81598i	−0.792541	+	0.288461i
$176$	−1.25753	−	0.457702i	−0.0947896	−	0.0345006i
$177$	−1.06798	−	0.896139i	−0.0802741	−	0.0673579i
$178$	−2.30286	+	3.98867i	−0.172607	+	0.298963i
$179$	−11.8536	−	20.5310i	−0.885978	−	1.53456i	−0.844589	−	0.535416i	$-0.820155\pi$
$179$	−11.8536	−	20.5310i	−0.885978	−	1.53456i	−0.0413892	−	0.999143i	$-0.513178\pi$
$180$	0.145567	−	0.825550i	0.0108499	−	0.0615329i
$181$	1.65658	−	9.39493i	0.123133	−	0.698320i	−0.859267	−	0.511528i	$-0.829080\pi$
$181$	1.65658	−	9.39493i	0.123133	−	0.698320i	0.982399	−	0.186792i	$-0.0598091\pi$
$182$	−1.73161	−	2.99923i	−0.128355	−	0.222318i
$183$	2.65294	−	4.59502i	0.196111	−	0.339674i
$184$	13.1038	+	10.9954i	0.966021	+	0.810588i
$185$	2.88108	+	1.04863i	0.211821	+	0.0770967i
$186$	−2.20451	+	0.802375i	−0.161642	+	0.0588330i
$187$	0.451745	−	0.379059i	0.0330349	−	0.0277196i
$188$	0.0881782	+	0.500084i	0.00643106	+	0.0364723i
$189$	−2.68329			−0.195180
$190$	−0.426676	−	4.14704i	−0.0309543	−	0.300858i
$191$	5.09561			0.368705			0.184353	−	0.982860i	$-0.440981\pi$
$191$	5.09561			0.368705			0.184353	+	0.982860i	$0.440981\pi$
$192$	1.31162	+	7.43858i	0.0946583	+	0.536834i
$193$	13.7969	−	11.5770i	0.993123	−	0.833329i	0.00710637	−	0.999975i	$-0.497738\pi$
$193$	13.7969	−	11.5770i	0.993123	−	0.833329i	0.986017	+	0.166645i	$0.0532935\pi$
$194$	9.46576	−	3.44525i	0.679602	−	0.247355i
$195$	−1.06769	−	0.388608i	−0.0764590	−	0.0278288i
$196$	−0.139987	−	0.117463i	−0.00999905	−	0.00839020i
$197$	−0.191066	+	0.330937i	−0.0136129	+	0.0235783i	−0.872752	−	0.488165i	$-0.837667\pi$
$197$	−0.191066	+	0.330937i	−0.0136129	+	0.0235783i	0.859139	+	0.511743i	$0.171000\pi$
$198$	0.521159	+	0.902673i	0.0370371	+	0.0641502i
$199$	−0.454405	+	2.57706i	−0.0322119	+	0.182683i	−0.996669	−	0.0815582i	$-0.974010\pi$
$199$	−0.454405	+	2.57706i	−0.0322119	+	0.182683i	0.964457	+	0.264241i	$0.0851215\pi$
$200$	2.19272	−	12.4356i	0.155049	−	0.879327i
$201$	2.28803	+	3.96299i	0.161385	+	0.279528i
$202$	5.43685	−	9.41689i	0.382535	−	0.662570i
$203$	4.65146	+	3.90304i	0.326468	+	0.273940i
$204$	−0.506255	−	0.184262i	−0.0354450	−	0.0129009i
$205$	−4.46203	+	1.62405i	−0.311642	+	0.113428i
$206$	−0.309413	+	0.259628i	−0.0215578	+	0.0180892i
$207$	−0.978106	−	5.54711i	−0.0679831	−	0.385551i
$208$	1.65708			0.114898
$209$	−3.12888	−	3.03482i	−0.216429	−	0.209923i
$210$	2.56634			0.177095
$211$	1.96335	+	11.1347i	0.135163	+	0.766547i	0.974746	+	0.223316i	$0.0716881\pi$
$211$	1.96335	+	11.1347i	0.135163	+	0.766547i	−0.839583	+	0.543231i	$0.817201\pi$
$212$	−2.71639	+	2.27932i	−0.186562	+	0.156544i
$213$	4.00735	−	1.45856i	0.274579	−	0.0999386i
$214$	−12.2590	−	4.46192i	−0.838009	−	0.305010i
$215$	−1.48612	−	1.24700i	−0.101352	−	0.0850448i
$216$	1.51843	−	2.63001i	0.103316	−	0.178949i
$217$	3.01969	+	5.23026i	0.204990	+	0.355054i
$218$	3.35469	−	19.0254i	0.227208	−	1.28856i
$219$	−0.809619	+	4.59158i	−0.0547090	+	0.310270i
$220$	0.419143	+	0.725977i	0.0282586	+	0.0489453i
$221$	−0.365109	+	0.632387i	−0.0245599	+	0.0425389i
$222$	2.66794	+	2.23867i	0.179060	+	0.150250i
$223$	3.73365	+	1.35894i	0.250024	+	0.0910012i	0.463992	−	0.885839i	$-0.346417\pi$
$223$	3.73365	+	1.35894i	0.250024	+	0.0910012i	−0.213968	+	0.976841i	$0.568639\pi$
$224$	11.7976	−	4.29398i	0.788262	−	0.286904i
$225$	−3.18524	+	2.67273i	−0.212349	+	0.178182i
$226$	0.963393	+	5.46367i	0.0640839	+	0.363438i
$227$	−21.7297			−1.44225			−0.721125	−	0.692805i	$-0.756375\pi$
$227$	−21.7297			−1.44225			−0.721125	+	0.692805i	$0.756375\pi$
$228$	−0.971850	+	3.86177i	−0.0643623	+	0.255752i
$229$	3.45618			0.228391			0.114195	−	0.993458i	$-0.463571\pi$
$229$	3.45618			0.228391			0.114195	+	0.993458i	$0.463571\pi$
$230$	0.935478	+	5.30536i	0.0616836	+	0.349825i
$231$	2.05552	−	1.72478i	0.135243	−	0.113482i
$232$	−6.45773	+	2.35042i	−0.423971	+	0.154313i
$233$	−3.87142	−	1.40908i	−0.253625	−	0.0923119i	0.212079	−	0.977253i	$-0.431977\pi$
$233$	−3.87142	−	1.40908i	−0.253625	−	0.0923119i	−0.465704	+	0.884941i	$0.654199\pi$
$234$	−0.988704	−	0.829621i	−0.0646336	−	0.0542340i
$235$	−0.255015	+	0.441698i	−0.0166353	+	0.0288132i
$236$	−0.636828	−	1.10302i	−0.0414540	−	0.0718004i
$237$	−1.00081	+	5.67589i	−0.0650098	+	0.368689i
$238$	0.286403	−	1.62427i	0.0185647	−	0.105286i
$239$	11.5985	+	20.0892i	0.750244	+	1.29946i	0.947704	+	0.319150i	$0.103397\pi$
$239$	11.5985	+	20.0892i	0.750244	+	1.29946i	−0.197460	+	0.980311i	$0.563269\pi$
$240$	−0.613973	+	1.06343i	−0.0396318	+	0.0686443i
$241$	15.1941	+	12.7494i	0.978739	+	0.821260i	0.983899	−	0.178727i	$-0.0571978\pi$
$241$	15.1941	+	12.7494i	0.978739	+	0.821260i	−0.00515931	+	0.999987i	$0.501642\pi$
$242$	−0.979458	−	0.356493i	−0.0629619	−	0.0229163i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	3.71326	−	3.11579i	0.237717	−	0.199468i
$245$	−0.0318718	−	0.180754i	−0.00203622	−	0.0115480i
$246$	−5.39385			−0.343900
$247$	4.92599	+	2.20615i	0.313433	+	0.140374i
$248$	−6.83521			−0.434036
$249$	1.49644	+	8.48672i	0.0948328	+	0.537824i
$250$	6.70971	−	5.63012i	0.424359	−	0.356080i
$251$	3.43638	−	1.25074i	0.216903	−	0.0789461i	−0.231283	−	0.972886i	$-0.574292\pi$
$251$	3.43638	−	1.25074i	0.216903	−	0.0789461i	0.448186	+	0.893940i	$0.352070\pi$
$252$	−2.30355	−	0.838422i	−0.145110	−	0.0528156i
$253$	4.31489	+	3.62062i	0.271275	+	0.227627i
$254$	−2.10977	+	3.65423i	−0.132379	+	0.229287i
$255$	−0.270556	−	0.468617i	−0.0169429	−	0.0293459i
$256$	−2.89199	+	16.4013i	−0.180749	+	1.02508i
$257$	−0.600568	+	3.40599i	−0.0374624	+	0.212460i	−0.997793	−	0.0664050i	$-0.978847\pi$
$257$	−0.600568	+	3.40599i	−0.0374624	+	0.212460i	0.960330	+	0.278865i	$0.0899582\pi$
$258$	−1.10185	−	1.90846i	−0.0685980	−	0.118815i
$259$	4.48290	−	7.76461i	0.278554	−	0.482470i
$260$	−0.795167	−	0.667224i	−0.0493142	−	0.0413795i
$261$	2.12644	+	0.773962i	0.131624	+	0.0479071i
$262$	−0.869897	+	0.316616i	−0.0537424	+	0.0195606i
$263$	−3.40982	+	2.86118i	−0.210258	+	0.176428i	−0.741835	−	0.670583i	$-0.766044\pi$
$263$	−3.40982	+	2.86118i	−0.210258	+	0.176428i	0.531577	+	0.847010i	$0.321600\pi$
$264$	0.527347	+	2.99073i	0.0324560	+	0.184067i
$265$	−3.56157			−0.218785
$266$	−12.1595	−	0.877085i	−0.745549	−	0.0537775i
$267$	4.41873			0.270422
$268$	0.725950	+	4.11707i	0.0443445	+	0.251490i
$269$	4.80871	−	4.03499i	0.293192	−	0.246018i	−0.484312	−	0.874896i	$-0.660930\pi$
$269$	4.80871	−	4.03499i	0.293192	−	0.246018i	0.777504	+	0.628878i	$0.216485\pi$
$270$	0.898739	−	0.327114i	0.0546955	−	0.0199075i
$271$	0.631100	+	0.229702i	0.0383366	+	0.0139534i	0.361117	−	0.932520i	$-0.382395\pi$
$271$	0.631100	+	0.229702i	0.0383366	+	0.0139534i	−0.322781	+	0.946474i	$0.604618\pi$
$272$	0.604540	+	0.507269i	0.0366556	+	0.0307577i
$273$	−1.66131	+	2.87746i	−0.100547	+	0.174152i
$274$	4.74635	+	8.22091i	0.286737	+	0.496644i
$275$	0.722035	−	4.09486i	0.0435403	−	0.246929i
$276$	0.893573	−	5.06770i	0.0537868	−	0.305040i
$277$	8.10318	+	14.0351i	0.486873	+	0.843288i	0.999886	−	0.0150924i	$-0.00480426\pi$
$277$	8.10318	+	14.0351i	0.486873	+	0.843288i	−0.513013	+	0.858381i	$0.671471\pi$
$278$	9.28284	−	16.0784i	0.556748	−	0.964315i
$279$	1.72417	+	1.44675i	0.103223	+	0.0866147i
$280$	7.02630	+	2.55737i	0.419902	+	0.152832i
$281$	−8.83461	+	3.21554i	−0.527029	+	0.191823i	−0.591811	−	0.806077i	$-0.701587\pi$
$281$	−8.83461	+	3.21554i	−0.527029	+	0.191823i	0.0647825	+	0.997899i	$0.479365\pi$
$282$	−0.443814	+	0.372404i	−0.0264287	+	0.0221763i
$283$	2.76549	+	15.6839i	0.164391	+	0.932308i	0.949690	+	0.313191i	$0.101398\pi$
$283$	2.76549	+	15.6839i	0.164391	+	0.932308i	−0.785299	+	0.619117i	$0.787491\pi$
$284$	3.89597			0.231183
$285$	−3.24095	+	2.34385i	−0.191978	+	0.138837i
$286$	1.29066			0.0763184
$287$	2.41122	+	13.6747i	0.142330	+	0.807192i
$288$	3.58423	−	3.00752i	0.211203	−	0.177220i
$289$	15.6480	−	5.69540i	0.920470	−	0.335024i
$290$	−2.03377	−	0.740232i	−0.119427	−	0.0434679i
$291$	−7.40327	−	6.21208i	−0.433987	−	0.364159i
$292$	−2.12973	+	3.68880i	−0.124633	+	0.215871i
$293$	9.50140	+	16.4569i	0.555078	+	0.961423i	0.997897	+	0.0648123i	$0.0206449\pi$
$293$	9.50140	+	16.4569i	0.555078	+	0.961423i	−0.442820	+	0.896611i	$0.646022\pi$
$294$	0.0362042	−	0.205324i	0.00211147	−	0.0119748i
$295$	0.222140	−	1.25982i	0.0129335	−	0.0733493i
$296$	5.07362	+	8.78777i	0.294898	+	0.510779i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	9.36657	+	7.85948i	0.542591	+	0.455288i
$299$	−6.55411	−	2.38550i	−0.379034	−	0.137957i
$300$	−3.56958	+	1.29922i	−0.206090	+	0.0750107i
$301$	−4.34583	+	3.64658i	−0.250489	+	0.210186i
$302$	1.93911	+	10.9973i	0.111584	+	0.632822i
$303$	−10.4322			−0.599316
$304$	3.27249	−	4.82879i	0.187690	−	0.276950i
$305$	4.86861			0.278776
$306$	−0.106736	−	0.605328i	−0.00610168	−	0.0346043i
$307$	9.71481	−	8.15169i	0.554453	−	0.465242i	−0.321992	−	0.946742i	$-0.604353\pi$
$307$	9.71481	−	8.15169i	0.554453	−	0.465242i	0.876446	+	0.481501i	$0.159908\pi$
$308$	2.30355	−	0.838422i	0.131257	−	0.0477735i
$309$	0.364142	+	0.132537i	0.0207153	+	0.00753975i
$310$	−1.64903	−	1.38370i	−0.0936584	−	0.0785888i
$311$	−7.51462	+	13.0157i	−0.426115	+	0.738053i	−0.996524	−	0.0833080i	$-0.973451\pi$
$311$	−7.51462	+	13.0157i	−0.426115	+	0.738053i	0.570409	+	0.821361i	$0.306785\pi$
$312$	−1.88022	−	3.25663i	−0.106446	−	0.184371i
$313$	2.07525	−	11.7693i	0.117300	−	0.665242i	−0.868286	−	0.496065i	$-0.834778\pi$
$313$	2.07525	−	11.7693i	0.117300	−	0.665242i	0.985586	−	0.169177i	$-0.0541110\pi$
$314$	3.36829	−	19.1025i	0.190084	−	1.07802i
$315$	−1.23108	−	2.13229i	−0.0693633	−	0.120141i
$316$	−2.63267	+	4.55992i	−0.148099	+	0.256516i
$317$	17.4901	+	14.6759i	0.982340	+	0.824281i	0.984441	−	0.175717i	$-0.0562243\pi$
$317$	17.4901	+	14.6759i	0.982340	+	0.824281i	−0.00210095	+	0.999998i	$0.500669\pi$
$318$	−3.80171	−	1.38371i	−0.213189	−	0.0775946i
$319$	−2.12644	+	0.773962i	−0.119058	+	0.0433336i
$320$	−5.30934	+	4.45507i	−0.296801	+	0.249046i
$321$	2.17340	+	12.3260i	0.121308	+	0.687969i
$322$	15.7537			0.877919
$323$	1.12176	+	2.31281i	0.0624164	+	0.128688i
$324$	−0.913575			−0.0507542
$325$	0.894068	+	5.07051i	0.0495939	+	0.281261i
$326$	7.45556	−	6.25596i	0.412925	−	0.346486i
$327$	−17.4168	+	6.33918i	−0.963149	+	0.350558i
$328$	−14.7676	−	5.37498i	−0.815407	−	0.296784i
$329$	1.14253	+	0.958697i	0.0629898	+	0.0528547i
$330$	−0.478209	+	0.828282i	−0.0263245	+	0.0455954i
$331$	9.66059	+	16.7326i	0.530994	+	0.919709i	0.999346	+	0.0361668i	$0.0115147\pi$
$331$	9.66059	+	16.7326i	0.530994	+	0.919709i	−0.468352	+	0.883542i	$0.655152\pi$
$332$	−1.36711	+	7.75325i	−0.0750298	+	0.425515i
$333$	0.580220	−	3.29059i	0.0317958	−	0.180323i
$334$	−7.31565	−	12.6711i	−0.400294	−	0.693330i
$335$	−2.09947	+	3.63639i	−0.114706	+	0.198677i
$336$	2.75076	+	2.30816i	0.150066	+	0.125920i
$337$	−13.7869	−	5.01801i	−0.751019	−	0.273348i	−0.0619843	−	0.998077i	$-0.519743\pi$
$337$	−13.7869	−	5.01801i	−0.751019	−	0.273348i	−0.689034	+	0.724729i	$0.741965\pi$
$338$	11.2312	−	4.08781i	0.610894	−	0.222347i
$339$	4.07744	−	3.42138i	0.221456	−	0.185824i
$340$	−0.0858424	−	0.486836i	−0.00465546	−	0.0264024i
$341$	−2.25074			−0.121885
$342$	−4.37009	+	1.24274i	−0.236307	+	0.0671994i
$343$	18.2463			0.985206
$344$	−1.11493	−	6.32308i	−0.0601130	−	0.340918i
$345$	3.95929	−	3.32224i	0.213161	−	0.178863i
$346$	−16.5043	+	6.00709i	−0.887279	+	0.322943i
$347$	−10.4154	−	3.79091i	−0.559130	−	0.203507i	0.0469686	−	0.998896i	$-0.485044\pi$
$347$	−10.4154	−	3.79091i	−0.559130	−	0.203507i	−0.606098	+	0.795390i	$0.707266\pi$
$348$	1.58368	+	1.32886i	0.0848939	+	0.0712345i
$349$	9.35324	−	16.2003i	0.500668	−	0.867182i	−0.499332	−	0.866411i	$-0.666421\pi$
$349$	9.35324	−	16.2003i	0.500668	−	0.867182i	1.00000		0.000771020i	$-0.000245423\pi$
$350$	−5.81467	−	10.0713i	−0.310807	−	0.538333i
$351$	−0.215022	+	1.21945i	−0.0114770	+	0.0650894i
$352$	−0.812478	+	4.60779i	−0.0433052	+	0.245596i
$353$	17.6842	+	30.6299i	0.941233	+	1.63026i	0.763124	+	0.646252i	$0.223665\pi$
$353$	17.6842	+	30.6299i	0.941233	+	1.63026i	0.178109	+	0.984011i	$0.443002\pi$
$354$	0.726571	−	1.25846i	0.0386168	−	0.0668863i
$355$	2.99760	+	2.51528i	0.159096	+	0.133497i
$356$	3.79339	+	1.38068i	0.201049	+	0.0731759i
$357$	−1.48694	+	0.541201i	−0.0786970	+	0.0286434i
$358$	18.9292	−	15.8835i	1.00044	−	0.839470i
$359$	−2.63232	−	14.9287i	−0.138929	−	0.787904i	−0.972043	−	0.234803i	$-0.924555\pi$
$359$	−2.63232	−	14.9287i	−0.138929	−	0.787904i	0.833114	−	0.553101i	$-0.186556\pi$
$360$	2.78660			0.146866
$361$	16.1569	−	9.99768i	0.850365	−	0.526194i
$362$	9.94357			0.522622
$363$	0.173648	+	0.984808i	0.00911417	+	0.0516890i
$364$	−2.32529	+	1.95115i	−0.121878	+	0.102268i
$365$	−4.02017	+	1.46322i	−0.210425	+	0.0765885i
$366$	5.19688	+	1.89151i	0.271645	+	0.0988708i
$367$	−14.1767	−	11.8957i	−0.740018	−	0.620949i	0.192825	−	0.981233i	$-0.438235\pi$
$367$	−14.1767	−	11.8957i	−0.740018	−	0.620949i	−0.932842	+	0.360285i	$0.882680\pi$
$368$	−3.76892	+	6.52796i	−0.196469	+	0.340293i
$369$	2.58743	+	4.48157i	0.134696	+	0.233301i
$370$	−0.554932	+	3.14718i	−0.0288496	+	0.163614i
$371$	−1.80855	+	10.2568i	−0.0938953	+	0.532507i
$372$	1.02811	+	1.78074i	0.0533051	+	0.0923271i
$373$	18.9564	−	32.8335i	0.981526	−	1.70005i	0.325065	−	0.945692i	$-0.394614\pi$
$373$	18.9564	−	32.8335i	0.981526	−	1.70005i	0.656461	−	0.754360i	$-0.272053\pi$
$374$	0.470862	+	0.395100i	0.0243477	+	0.0204301i
$375$	−7.89652	−	2.87410i	−0.407775	−	0.148418i
$376$	−1.58620	+	0.577331i	−0.0818022	+	0.0297736i
$377$	2.14652	−	1.80114i	0.110551	−	0.0927635i
$378$	−0.485665	−	2.75435i	−0.0249799	−	0.141668i
$379$	12.6241			0.648456			0.324228	−	0.945979i	$-0.394896\pi$
$379$	12.6241			0.648456			0.324228	+	0.945979i	$0.394896\pi$
$380$	−3.51465	+	0.999472i	−0.180298	+	0.0512718i
$381$	4.04823			0.207397
$382$	0.922287	+	5.23055i	0.0471883	+	0.267618i
$383$	−18.6753	+	15.6705i	−0.954264	+	0.800723i	−0.980010	−	0.198946i	$-0.936248\pi$
$383$	−18.6753	+	15.6705i	−0.954264	+	0.800723i	0.0257463	+	0.999669i	$0.491804\pi$
$384$	1.39524	−	0.507825i	0.0712004	−	0.0259148i
$385$	2.31367	+	0.842106i	0.117915	+	0.0429177i
$386$	14.3808	+	12.0669i	0.731961	+	0.614188i
$387$	−1.05711	+	1.83097i	−0.0537361	+	0.0930736i
$388$	−4.41452	−	7.64618i	−0.224113	−	0.388176i
$389$	5.39901	−	30.6193i	0.273741	−	1.55246i	−0.469193	−	0.883096i	$-0.655455\pi$
$389$	5.39901	−	30.6193i	0.273741	−	1.55246i	0.742934	−	0.669365i	$-0.233434\pi$
$390$	0.205651	−	1.16630i	0.0104135	−	0.0590581i
$391$	−1.66083	−	2.87664i	−0.0839918	−	0.145478i
$392$	0.303728	−	0.526073i	0.0153406	−	0.0265707i
$393$	0.680355	+	0.570886i	0.0343194	+	0.0287974i
$394$	−0.374283	−	0.136228i	−0.0188561	−	0.00686306i
$395$	−4.96954	+	1.80877i	−0.250045	+	0.0910089i
$396$	0.699839	−	0.587235i	0.0351682	−	0.0295096i
$397$	5.60092	+	31.7644i	0.281102	+	1.59421i	0.718885	+	0.695129i	$0.244653\pi$
$397$	5.60092	+	31.7644i	0.281102	+	1.59421i	−0.437783	+	0.899081i	$0.644236\pi$
$398$	−2.72755			−0.136720
$399$	5.10419	+	10.5237i	0.255529	+	0.526843i
$400$	5.56441			0.278220
$401$	2.67214	+	15.1544i	0.133440	+	0.756777i	0.975933	+	0.218070i	$0.0699760\pi$
$401$	2.67214	+	15.1544i	0.133440	+	0.756777i	−0.842493	+	0.538707i	$0.818913\pi$
$402$	−3.65381	+	3.06591i	−0.182236	+	0.152914i
$403$	2.61893	−	0.953213i	0.130458	−	0.0474829i
$404$	−8.95585	−	3.25966i	−0.445570	−	0.162174i
$405$	−0.702913	−	0.589814i	−0.0349280	−	0.0293081i
$406$	−3.16450	+	5.48108i	−0.157052	+	0.272021i
$407$	1.67068	+	2.89369i	0.0828123	+	0.143435i
$408$	0.310983	−	1.76367i	0.0153959	−	0.0873147i
$409$	3.60232	−	20.4297i	0.178123	−	1.01019i	−0.756354	−	0.654163i	$-0.773021\pi$
$409$	3.60232	−	20.4297i	0.178123	−	1.01019i	0.934477	−	0.356023i	$-0.115868\pi$
$410$	−2.47467	−	4.28625i	−0.122215	−	0.211683i
$411$	4.55365	−	7.88715i	0.224615	−	0.389045i
$412$	0.271196	+	0.227560i	0.0133608	+	0.0112111i
$413$	−3.51529	−	1.27946i	−0.172976	−	0.0629581i
$414$	5.51698	−	2.00802i	0.271145	−	0.0986886i
$415$	−6.05745	+	5.08281i	−0.297349	+	0.249505i
$416$	−1.00606	−	5.70565i	−0.0493262	−	0.279743i
$417$	−17.8119			−0.872254
$418$	2.54887	−	3.76103i	0.124669	−	0.183958i
$419$	28.3296			1.38399			0.691995	−	0.721903i	$-0.256732\pi$
$419$	28.3296			1.38399			0.691995	+	0.721903i	$0.256732\pi$
$420$	−0.390597	−	2.21519i	−0.0190592	−	0.108090i
$421$	5.78724	−	4.85607i	0.282053	−	0.236671i	−0.490775	−	0.871287i	$-0.663286\pi$
$421$	5.78724	−	4.85607i	0.282053	−	0.236671i	0.772828	+	0.634616i	$0.218842\pi$
$422$	−11.0742	+	4.03070i	−0.539086	+	0.196211i
$423$	0.522315	+	0.190107i	0.0253958	+	0.00924333i
$424$	−9.02971	−	7.57682i	−0.438521	−	0.367963i
$425$	−1.22602	+	2.12353i	−0.0594707	+	0.103006i
$426$	2.22250	+	3.84948i	0.107680	+	0.186508i
$427$	2.47226	−	14.0209i	0.119641	−	0.678519i
$428$	−1.98557	+	11.2607i	−0.0959759	+	0.544307i
$429$	−0.619131	−	1.07237i	−0.0298919	−	0.0517743i
$430$	1.01104	−	1.75118i	0.0487568	−	0.0844492i
$431$	2.11597	+	1.77551i	0.101923	+	0.0855232i	0.692325	−	0.721586i	$-0.256586\pi$
$431$	2.11597	+	1.77551i	0.101923	+	0.0855232i	−0.590402	+	0.807109i	$0.701031\pi$
$432$	1.25753	+	0.457702i	0.0605028	+	0.0220212i
$433$	34.8477	−	12.6835i	1.67467	−	0.609531i	0.682107	−	0.731252i	$-0.261064\pi$
$433$	34.8477	−	12.6835i	1.67467	−	0.609531i	0.992564	+	0.121721i	$0.0388414\pi$
$434$	−4.82222	+	4.04632i	−0.231474	+	0.194230i
$435$	0.360567	+	2.04488i	0.0172879	+	0.0980444i
$436$	−16.9327			−0.810928
$437$	−19.8948	+	14.3879i	−0.951700	+	0.688266i
$438$	−4.85971			−0.232206
$439$	−6.39912	−	36.2912i	−0.305413	−	1.73209i	−0.621552	−	0.783373i	$-0.713498\pi$
$439$	−6.39912	−	36.2912i	−0.305413	−	1.73209i	0.316139	−	0.948713i	$-0.397613\pi$
$440$	−2.13466	+	1.79119i	−0.101766	+	0.0853916i
$441$	−0.187964	+	0.0684133i	−0.00895067	+	0.00325778i
$442$	−0.715217	−	0.260318i	−0.0340194	−	0.0123820i
$443$	−15.3036	−	12.8412i	−0.727095	−	0.610105i	0.202243	−	0.979335i	$-0.435177\pi$
$443$	−15.3036	−	12.8412i	−0.727095	−	0.610105i	−0.929338	+	0.369230i	$0.879621\pi$
$444$	1.52629	−	2.64361i	0.0724344	−	0.125460i
$445$	2.02729	+	3.51136i	0.0961026	+	0.166455i
$446$	−0.719147	+	4.07849i	−0.0340526	+	0.193122i
$447$	2.03703	−	11.5526i	0.0963481	−	0.546417i
$448$	10.1339	+	17.5524i	0.478781	+	0.829273i
$449$	3.94887	−	6.83965i	0.186359	−	0.322783i	−0.757675	−	0.652632i	$-0.773665\pi$
$449$	3.94887	−	6.83965i	0.186359	−	0.322783i	0.944034	+	0.329849i	$0.106998\pi$
$450$	−3.32003	−	2.78583i	−0.156508	−	0.131325i
$451$	−4.86279	−	1.76991i	−0.228980	−	0.0833418i
$452$	4.56944	−	1.66314i	0.214928	−	0.0782276i
$453$	8.20706	−	6.88654i	0.385601	−	0.323558i
$454$	−3.93300	−	22.3051i	−0.184585	−	1.04683i
$455$	−3.04879			−0.142929
$456$	−13.2031	−	0.952359i	−0.618292	−	0.0445983i
$457$	18.3332			0.857592			0.428796	−	0.903401i	$-0.358938\pi$
$457$	18.3332			0.857592			0.428796	+	0.903401i	$0.358938\pi$
$458$	0.625556	+	3.54771i	0.0292303	+	0.165773i
$459$	−0.451745	+	0.379059i	−0.0210857	+	0.0176930i
$460$	4.43704	−	1.61495i	0.206878	−	0.0752975i
$461$	−0.242033	−	0.0880929i	−0.0112726	−	0.00410290i	0.336378	−	0.941727i	$-0.390798\pi$
$461$	−0.242033	−	0.0880929i	−0.0112726	−	0.00410290i	−0.347650	+	0.937624i	$0.613020\pi$
$462$	2.14250	+	1.79777i	0.0996781	+	0.0836399i
$463$	−4.81928	+	8.34724i	−0.223971	+	0.387929i	−0.956010	−	0.293333i	$-0.905235\pi$
$463$	−4.81928	+	8.34724i	−0.223971	+	0.387929i	0.732039	+	0.681262i	$0.238569\pi$
$464$	−1.51415	−	2.62259i	−0.0702927	−	0.121751i
$465$	−0.358628	+	2.03388i	−0.0166310	+	0.0943189i
$466$	0.745683	−	4.22898i	0.0345431	−	0.195904i
$467$	11.1450	+	19.3037i	0.515730	+	0.893270i	0.999833	+	0.0182595i	$0.00581250\pi$
$467$	11.1450	+	19.3037i	0.515730	+	0.893270i	−0.484103	+	0.875011i	$0.660854\pi$
$468$	−0.565622	+	0.979686i	−0.0261459	+	0.0452860i
$469$	9.40618	+	7.89272i	0.434337	+	0.364452i
$470$	−0.499552	−	0.181822i	−0.0230426	−	0.00838682i
$471$	−17.4874	+	6.36489i	−0.805776	+	0.293279i
$472$	3.24331	−	2.72146i	0.149285	−	0.125265i
$473$	−0.367132	−	2.08211i	−0.0168807	−	0.0957353i
$474$	−6.00735			−0.275927
$475$	16.5413	+	7.40818i	0.758966	+	0.339910i
$476$	−1.44561			−0.0662594
$477$	0.674006	+	3.82248i	0.0308606	+	0.175019i
$478$	−18.5219	+	15.5417i	−0.847172	+	0.710862i
$479$	−18.7504	+	6.82457i	−0.856725	+	0.311823i	−0.732779	−	0.680466i	$-0.761777\pi$
$479$	−18.7504	+	6.82457i	−0.856725	+	0.311823i	−0.123946	+	0.992289i	$0.539555\pi$
$480$	4.03437	+	1.46839i	0.184143	+	0.0670225i
$481$	−3.16948	−	2.65951i	−0.144516	−	0.121263i
$482$	−10.3369	+	17.9041i	−0.470834	+	0.815509i
$483$	−7.55706	−	13.0892i	−0.343858	−	0.595580i
$484$	−0.158641	+	0.899696i	−0.00721094	+	0.0408953i
$485$	1.53988	−	8.73311i	0.0699225	−	0.396550i
$486$	−0.521159	−	0.902673i	−0.0236402	−	0.0409461i
$487$	8.70178	−	15.0719i	0.394315	−	0.682974i	−0.598698	−	0.800975i	$-0.704315\pi$
$487$	8.70178	−	15.0719i	0.394315	−	0.682974i	0.993014	+	0.118001i	$0.0376485\pi$
$488$	12.3435	+	10.3574i	0.558763	+	0.468857i
$489$	−8.77430	−	3.19358i	−0.396787	−	0.144419i
$490$	0.179772	−	0.0654317i	0.00812128	−	0.00295590i
$491$	28.5811	−	23.9824i	1.28985	−	1.08231i	0.298041	−	0.954553i	$-0.403667\pi$
$491$	28.5811	−	23.9824i	1.28985	−	1.08231i	0.991806	−	0.127756i	$-0.0407776\pi$
$492$	0.820944	+	4.65581i	0.0370110	+	0.209900i
$493$	1.33447			0.0601014
$494$	−1.37299	+	5.45575i	−0.0617737	+	0.245466i
$495$	0.917588			0.0412425
$496$	−0.523031	−	2.96626i	−0.0234848	−	0.133189i
$497$	8.76581	−	7.35539i	0.393201	−	0.329934i
$498$	−8.44061	+	3.07213i	−0.378233	+	0.137666i
$499$	−33.4779	−	12.1850i	−1.49868	−	0.545474i	−0.542960	−	0.839759i	$-0.682696\pi$
$499$	−33.4779	−	12.1850i	−1.49868	−	0.545474i	−0.955718	+	0.294285i	$0.904919\pi$
$500$	−5.88096	−	4.93471i	−0.263004	−	0.220687i
$501$	−7.01864	+	12.1566i	−0.313570	+	0.543119i
$502$	1.90584	+	3.30101i	0.0850617	+	0.147331i
$503$	4.50827	−	25.5677i	0.201014	−	1.14001i	−0.702576	−	0.711608i	$-0.747967\pi$
$503$	4.50827	−	25.5677i	0.201014	−	1.14001i	0.903590	−	0.428398i	$-0.140922\pi$
$504$	1.41502	−	8.02499i	0.0630301	−	0.357462i
$505$	−4.78625	−	8.29002i	−0.212985	−	0.368901i
$506$	−2.93552	+	5.08448i	−0.130500	+	0.226033i
$507$	−8.78401	−	7.37066i	−0.390112	−	0.327342i
$508$	3.47533	+	1.26491i	0.154193	+	0.0561215i
$509$	−10.7502	+	3.91275i	−0.476494	+	0.173429i	−0.569092	−	0.822274i	$-0.692705\pi$
$509$	−10.7502	+	3.91275i	−0.476494	+	0.173429i	0.0925981	+	0.995704i	$0.470483\pi$
$510$	0.432057	−	0.362539i	0.0191318	−	0.0160535i
$511$	2.17244	+	12.3205i	0.0961031	+	0.545028i
$512$	−14.3895			−0.635932
$513$	3.12888	+	3.03482i	0.138143	+	0.133990i
$514$	−3.60489			−0.159005
$515$	0.0617451	+	0.350174i	0.00272081	+	0.0154305i
$516$	−1.47962	+	1.24155i	−0.0651365	+	0.0546560i
$517$	−0.522315	+	0.190107i	−0.0229714	+	0.00836091i
$518$	8.78163	+	3.19625i	0.385842	+	0.140435i
$519$	12.9082	+	10.8313i	0.566608	+	0.475441i
$520$	1.72527	−	2.98825i	0.0756580	−	0.131043i
$521$	−16.3687	−	28.3514i	−0.717125	−	1.24210i	−0.962134	−	0.272576i	$-0.912125\pi$
$521$	−16.3687	−	28.3514i	−0.717125	−	1.24210i	0.245010	−	0.969521i	$-0.421209\pi$
$522$	−0.409580	+	2.32284i	−0.0179268	+	0.101668i
$523$	−0.948800	+	5.38091i	−0.0414881	+	0.235291i	−0.998500	−	0.0547592i	$-0.982561\pi$
$523$	−0.948800	+	5.38091i	−0.0414881	+	0.235291i	0.957011	+	0.290050i	$0.0936720\pi$
$524$	0.405692	+	0.702678i	0.0177227	+	0.0306967i
$525$	−5.57860	+	9.66241i	−0.243470	+	0.421702i
$526$	−3.55411	−	2.98225i	−0.154967	−	0.130032i
$527$	1.24724	+	0.453960i	0.0543308	+	0.0197748i
$528$	−1.25753	+	0.457702i	−0.0547268	+	0.0199189i
$529$	6.68540	−	5.60971i	0.290669	−	0.243901i
$530$	−0.644632	−	3.65589i	−0.0280010	−	0.158802i
$531$	−1.39414			−0.0605007
$532$	1.09361	+	10.6292i	0.0474139	+	0.460835i
$533$	6.40784			0.277554
$534$	0.799774	+	4.53575i	0.0346096	+	0.196281i
$535$	−8.79775	+	7.38219i	−0.380360	+	0.319160i
$536$	−13.0588	+	4.75303i	−0.564056	+	0.205299i
$537$	−22.2774	−	8.10832i	−0.961342	−	0.349900i
$538$	5.01220	+	4.20574i	0.216091	+	0.181322i
$539$	0.100014	−	0.173229i	0.00430789	−	0.00746148i
$540$	−0.419143	−	0.725977i	−0.0180370	−	0.0312411i
$541$	3.45965	−	19.6206i	0.148742	−	0.843557i	−0.815545	−	0.578694i	$-0.803562\pi$
$541$	3.45965	−	19.6206i	0.148742	−	0.843557i	0.964286	−	0.264862i	$-0.0853265\pi$
$542$	−0.121558	+	0.689388i	−0.00522135	+	0.0296118i
$543$	−4.76993	−	8.26177i	−0.204697	−	0.354546i
$544$	1.37959	−	2.38953i	0.0591496	−	0.102450i
$545$	−13.0282	−	10.9319i	−0.558066	−	0.468273i
$546$	−3.25436	−	1.18449i	−0.139274	−	0.0506914i
$547$	−12.1586	+	4.42536i	−0.519863	+	0.189215i	−0.588606	−	0.808420i	$-0.700323\pi$
$547$	−12.1586	+	4.42536i	−0.519863	+	0.189215i	0.0687434	+	0.997634i	$0.478101\pi$
$548$	6.37364	−	5.34812i	0.272268	−	0.228460i
$549$	−0.921356	−	5.22527i	−0.0393225	−	0.223009i
$550$	4.33399			0.184802
$551$	−1.00953	−	9.81202i	−0.0430074	−	0.418006i
$552$	17.1057			0.728068
$553$	2.68547	+	15.2300i	0.114198	+	0.647647i
$554$	−12.9401	+	10.8581i	−0.549774	+	0.461315i
$555$	2.88108	−	1.04863i	0.122295	−	0.0445118i
$556$	−15.2912	−	5.56553i	−0.648490	−	0.236031i
$557$	−27.5605	−	23.1260i	−1.16777	−	0.979879i	−0.167792	−	0.985822i	$-0.553664\pi$
$557$	−27.5605	−	23.1260i	−1.16777	−	0.979879i	−0.999982	+	0.00594352i	$0.998108\pi$
$558$	−1.17299	+	2.03169i	−0.0496568	+	0.0860081i
$559$	1.30898	+	2.26722i	0.0553641	+	0.0958933i
$560$	−0.572159	+	3.24487i	−0.0241781	+	0.137121i
$561$	0.102402	−	0.580753i	0.00432343	−	0.0245194i
$562$	−4.89972	−	8.48657i	−0.206682	−	0.357984i
$563$	−3.95711	+	6.85392i	−0.166772	+	0.288858i	−0.937283	−	0.348569i	$-0.886668\pi$
$563$	−3.95711	+	6.85392i	−0.166772	+	0.288858i	0.770511	+	0.637427i	$0.220001\pi$
$564$	0.388996	+	0.326406i	0.0163797	+	0.0137442i
$565$	4.58952	+	1.67045i	0.193082	+	0.0702762i
$566$	−15.5986	+	5.67744i	−0.655660	+	0.238641i
$567$	−2.05552	+	1.72478i	−0.0863236	+	0.0724341i
$568$	2.24889	+	12.7541i	0.0943612	+	0.535149i
$569$	14.5574			0.610276			0.305138	−	0.952308i	$-0.401297\pi$
$569$	14.5574			0.610276			0.305138	+	0.952308i	$0.401297\pi$
$570$	−2.99252	−	2.90255i	−0.125343	−	0.121575i
$571$	24.1091			1.00893			0.504467	−	0.863431i	$-0.331689\pi$
$571$	24.1091			1.00893			0.504467	+	0.863431i	$0.331689\pi$
$572$	−0.196439	−	1.11406i	−0.00821351	−	0.0465811i
$573$	3.90346	−	3.27539i	0.163070	−	0.136832i
$574$	−13.6004	+	4.95015i	−0.567670	+	0.206615i
$575$	−22.0084	−	8.01042i	−0.917815	−	0.334057i
$576$	5.78619	+	4.85519i	0.241091	+	0.202300i
$577$	20.8681	−	36.1446i	0.868749	−	1.50472i	0.00547378	−	0.999985i	$-0.498258\pi$
$577$	20.8681	−	36.1446i	0.868749	−	1.50472i	0.863276	−	0.504733i	$-0.168409\pi$
$578$	8.67846	+	15.0315i	0.360976	+	0.625229i
$579$	3.12751	−	17.7370i	0.129975	−	0.737123i
$580$	−0.329405	+	1.86815i	−0.0136778	+	0.0775707i
$581$	11.5618	+	20.0256i	0.479664	+	0.830803i
$582$	5.03662	−	8.72369i	0.208775	−	0.361609i
$583$	−2.97336	−	2.49495i	−0.123144	−	0.103330i
$584$	−13.3052	−	4.84271i	−0.550574	−	0.200393i
$585$	−1.06769	+	0.388608i	−0.0441436	+	0.0160670i
$586$	−15.1730	+	12.7317i	−0.626791	+	0.525940i
$587$	−6.16316	−	34.9530i	−0.254381	−	1.44267i	−0.797657	−	0.603112i	$-0.793927\pi$
$587$	−6.16316	−	34.9530i	−0.254381	−	1.44267i	0.543276	−	0.839554i	$-0.317184\pi$
$588$	−0.182740			−0.00753606
$589$	2.39431	−	9.51411i	0.0986560	−	0.392022i
$590$	1.33339			0.0548946
$591$	0.0663567	+	0.376327i	0.00272955	+	0.0154800i
$592$	−3.42537	+	2.87423i	−0.140782	+	0.118130i
$593$	17.8905	−	6.51162i	0.734676	−	0.267400i	0.0525331	−	0.998619i	$-0.483271\pi$
$593$	17.8905	−	6.51162i	0.734676	−	0.267400i	0.682143	+	0.731219i	$0.261048\pi$
$594$	0.979458	+	0.356493i	0.0401876	+	0.0146271i
$595$	−1.11227	−	0.933302i	−0.0455985	−	0.0382616i
$596$	5.35847	−	9.28114i	0.219491	−	0.380170i
$597$	1.30841	+	2.26623i	0.0535495	+	0.0927505i
$598$	1.26240	−	7.15944i	0.0516235	−	0.292771i
$599$	−7.60733	+	43.1433i	−0.310827	+	1.76279i	0.283893	+	0.958856i	$0.408374\pi$
$599$	−7.60733	+	43.1433i	−0.310827	+	1.76279i	−0.594720	+	0.803933i	$0.702737\pi$
$600$	−6.31370	−	10.9356i	−0.257756	−	0.446446i
$601$	12.3924	−	21.4642i	0.505496	−	0.875545i	−0.494484	−	0.869187i	$-0.664643\pi$
$601$	12.3924	−	21.4642i	0.505496	−	0.875545i	0.999980	−	0.00635778i	$-0.00202376\pi$
$602$	−4.52973	−	3.80090i	−0.184618	−	0.154913i
$603$	4.30010	+	1.56511i	0.175113	+	0.0637361i
$604$	9.19736	−	3.34757i	0.374235	−	0.136211i
$605$	−0.702913	+	0.589814i	−0.0285775	+	0.0239794i
$606$	−1.88820	−	10.7085i	−0.0767028	−	0.435003i
$607$	9.04807			0.367250			0.183625	−	0.982996i	$-0.441217\pi$
$607$	9.04807			0.367250			0.183625	+	0.982996i	$0.441217\pi$
$608$	−18.6133	−	8.33614i	−0.754869	−	0.338075i
$609$	6.07205			0.246052
$610$	0.881201	+	4.99754i	0.0356788	+	0.202345i
$611$	0.527246	−	0.442412i	0.0213301	−	0.0178981i
$612$	−0.506255	+	0.184262i	−0.0204642	+	0.00744834i
$613$	0.711943	+	0.259126i	0.0287551	+	0.0104660i	0.356358	−	0.934350i	$-0.384018\pi$
$613$	0.711943	+	0.259126i	0.0287551	+	0.0104660i	−0.327603	+	0.944816i	$0.606241\pi$
$614$	10.1259	+	8.49665i	0.408649	+	0.342897i
$615$	−2.37420	+	4.11223i	−0.0957369	+	0.165821i
$616$	4.07440	+	7.05706i	0.164162	+	0.284337i
$617$	−6.63437	+	37.6254i	−0.267090	+	1.51474i	0.495928	+	0.868364i	$0.334828\pi$
$617$	−6.63437	+	37.6254i	−0.267090	+	1.51474i	−0.763017	+	0.646378i	$0.776283\pi$
$618$	−0.0701382	+	0.397774i	−0.00282137	+	0.0160008i
$619$	11.5762	+	20.0506i	0.465287	+	0.805901i	0.999214	−	0.0396291i	$-0.0126177\pi$
$619$	11.5762	+	20.0506i	0.465287	+	0.805901i	−0.533927	+	0.845531i	$0.679284\pi$
$620$	−0.943383	+	1.63399i	−0.0378872	+	0.0656225i
$621$	−4.31489	−	3.62062i	−0.173151	−	0.145291i
$622$	−14.7205	−	5.35783i	−0.590239	−	0.214829i
$623$	11.1417	−	4.05524i	0.446381	−	0.162470i
$624$	1.26940	−	1.06515i	0.0508166	−	0.0426402i
$625$	2.27121	+	12.8807i	0.0908485	+	0.515227i
$626$	12.4566			0.497867
$627$	−4.34760	−	0.313599i	−0.173627	−	0.0125239i
$628$	−17.0013			−0.678428
$629$	−0.342162	−	1.94050i	−0.0136429	−	0.0773727i
$630$	1.96593	−	1.64961i	0.0783247	−	0.0657222i
$631$	−3.49307	+	1.27137i	−0.139057	+	0.0506126i	−0.410611	−	0.911811i	$-0.634685\pi$
$631$	−3.49307	+	1.27137i	−0.139057	+	0.0506126i	0.271554	+	0.962423i	$0.412462\pi$
$632$	−16.4473	−	5.98633i	−0.654238	−	0.238123i
$633$	8.66129	+	7.26768i	0.344255	+	0.288865i
$634$	−11.8989	+	20.6095i	−0.472566	+	0.818509i
$635$	1.85731	+	3.21695i	0.0737049	+	0.127661i
$636$	−0.615755	+	3.49212i	−0.0244163	+	0.138472i
$637$	−0.0430102	+	0.243923i	−0.00170413	+	0.00966458i
$638$	−1.17934	−	2.04267i	−0.0466904	−	0.0808702i
$639$	2.13227	−	3.69319i	0.0843511	−	0.146100i
$640$	1.04367	+	0.875744i	0.0412547	+	0.0346168i
$641$	12.9764	+	4.72302i	0.512537	+	0.186548i	0.585324	−	0.810799i	$-0.300967\pi$
$641$	12.9764	+	4.72302i	0.512537	+	0.186548i	−0.0727873	+	0.997347i	$0.523189\pi$
$642$	−12.2590	+	4.46192i	−0.483825	+	0.176098i
$643$	2.84255	−	2.38518i	0.112099	−	0.0940625i	−0.585015	−	0.811022i	$-0.698911\pi$
$643$	2.84255	−	2.38518i	0.112099	−	0.0940625i	0.697114	+	0.716960i	$0.254467\pi$
$644$	−2.39771	−	13.5981i	−0.0944831	−	0.535840i
$645$	−1.93999			−0.0763870
$646$	−2.17102	+	1.57008i	−0.0854178	+	0.0617738i
$647$	−8.17317			−0.321320			−0.160660	−	0.987010i	$-0.551362\pi$
$647$	−8.17317			−0.321320			−0.160660	+	0.987010i	$0.551362\pi$
$648$	−0.527347	−	2.99073i	−0.0207161	−	0.117487i
$649$	1.06798	−	0.896139i	0.0419218	−	0.0351765i
$650$	−5.04296	+	1.83549i	−0.197801	+	0.0719938i
$651$	5.67517	+	2.06559i	0.222427	+	0.0809570i
$652$	−6.53468	−	5.48325i	−0.255918	−	0.214741i
$653$	−19.2072	+	33.2679i	−0.751637	+	1.30187i	0.195391	+	0.980725i	$0.437402\pi$
$653$	−19.2072	+	33.2679i	−0.751637	+	1.30187i	−0.947029	+	0.321149i	$0.895931\pi$
$654$	−9.65943	−	16.7306i	−0.377714	−	0.654219i
$655$	−0.141514	+	0.802567i	−0.00552942	+	0.0313589i
$656$	1.20254	−	6.81996i	0.0469514	−	0.266275i
$657$	2.33121	+	4.03777i	0.0909490	+	0.157528i
$658$	−0.777292	+	1.34631i	−0.0303020	+	0.0524846i
$659$	6.75804	+	5.67067i	0.263256	+	0.220898i	0.764855	−	0.644202i	$-0.222810\pi$
$659$	6.75804	+	5.67067i	0.263256	+	0.220898i	−0.501599	+	0.865100i	$0.667255\pi$
$660$	0.787731	+	0.286711i	0.0306624	+	0.0111602i
$661$	−35.3860	+	12.8795i	−1.37636	+	0.500953i	−0.921072	−	0.389393i	$-0.872685\pi$
$661$	−35.3860	+	12.8795i	−1.37636	+	0.500953i	−0.455285	+	0.890346i	$0.650463\pi$
$662$	−15.4272	+	12.9450i	−0.599596	+	0.503121i
$663$	0.126801	+	0.719123i	0.00492454	+	0.0279284i
$664$	−26.1706			−1.01562
$665$	−6.02091	+	8.88427i	−0.233481	+	0.344517i
$666$	3.48275			0.134954
$667$	2.21337	+	12.5526i	0.0857020	+	0.486040i
$668$	−9.82383	+	8.24317i	−0.380095	+	0.318938i
$669$	3.73365	−	1.35894i	0.144351	−	0.0525396i
$670$	−4.11269	−	1.49690i	−0.158887	−	0.0578302i
$671$	4.06454	+	3.41055i	0.156910	+	0.131663i
$672$	6.27738	−	10.8727i	0.242155	−	0.419425i
$673$	18.4914	+	32.0280i	0.712789	+	1.23459i	0.963806	+	0.266605i	$0.0859018\pi$
$673$	18.4914	+	32.0280i	0.712789	+	1.23459i	−0.251017	+	0.967983i	$0.580765\pi$
$674$	2.65552	−	15.0602i	0.102287	−	0.580098i
$675$	−0.722035	+	4.09486i	−0.0277911	+	0.157611i
$676$	−5.23785	−	9.07222i	−0.201456	−	0.348931i
$677$	−13.4036	+	23.2157i	−0.515141	+	0.892250i	0.484705	+	0.874678i	$0.338927\pi$
$677$	−13.4036	+	23.2157i	−0.515141	+	0.892250i	−0.999846	+	0.0175724i	$0.994406\pi$
$678$	4.24998	+	3.56616i	0.163220	+	0.136957i
$679$	−24.3681	−	8.86928i	−0.935164	−	0.340372i
$680$	1.54419	−	0.562038i	0.0592168	−	0.0215532i
$681$	−16.6459	+	13.9676i	−0.637873	+	0.535239i
$682$	−0.407377	−	2.31035i	−0.0155993	−	0.0884678i
$683$	26.5523			1.01600			0.507998	−	0.861359i	$-0.330386\pi$
$683$	26.5523			1.01600			0.507998	+	0.861359i	$0.330386\pi$
$684$	1.73782	+	3.58298i	0.0664471	+	0.136999i
$685$	8.35675			0.319295
$686$	3.30251	+	18.7295i	0.126090	+	0.715095i
$687$	2.64759	−	2.22159i	0.101012	−	0.0847589i
$688$	2.65870	−	0.967686i	0.101362	−	0.0368927i
$689$	4.51639	+	1.64383i	0.172061	+	0.0626250i
$690$	4.12684	+	3.46283i	0.157106	+	0.131828i
$691$	−6.54513	+	11.3365i	−0.248989	+	0.431261i	−0.963245	−	0.268623i	$-0.913432\pi$
$691$	−6.54513	+	11.3365i	−0.248989	+	0.431261i	0.714257	+	0.699884i	$0.246765\pi$
$692$	7.69709	+	13.3317i	0.292599	+	0.506797i
$693$	0.465948	−	2.64252i	0.0176999	−	0.100381i
$694$	2.00614	−	11.3774i	0.0761521	−	0.431880i
$695$	−8.17201	−	14.1543i	−0.309982	−	0.536904i
$696$	−3.43609	+	5.95148i	−0.130245	+	0.225590i
$697$	2.33772	+	1.96158i	0.0885475	+	0.0743002i
$698$	18.3222	+	6.66874i	0.693506	+	0.252416i
$699$	−3.87142	+	1.40908i	−0.146430	+	0.0532963i
$700$	−7.80824	+	6.55189i	−0.295124	+	0.247638i
$701$	−8.53073	−	48.3802i	−0.322201	−	1.82729i	−0.528653	−	0.848838i	$-0.677303\pi$
$701$	−8.53073	−	48.3802i	−0.322201	−	1.82729i	0.206452	−	0.978457i	$-0.433808\pi$
$702$	−1.29066			−0.0487129
$703$	−14.0092	+	3.98383i	−0.528366	+	0.150253i
$704$	−7.55334			−0.284677
$705$	0.0885656	+	0.502281i	0.00333557	+	0.0189170i
$706$	−28.2402	+	23.6964i	−1.06284	+	0.891825i
$707$	−26.3045	+	9.57405i	−0.989282	+	0.360069i
$708$	−1.19684	−	0.435616i	−0.0449802	−	0.0163714i
$709$	−20.0232	−	16.8015i	−0.751987	−	0.630992i	0.184040	−	0.982919i	$-0.441082\pi$
$709$	−20.0232	−	16.8015i	−0.751987	−	0.630992i	−0.936028	+	0.351926i	$0.885527\pi$
$710$	−2.03934	+	3.53224i	−0.0765350	+	0.132562i
$711$	2.88173	+	4.99130i	0.108073	+	0.187188i
$712$	−2.33020	+	13.2152i	−0.0873280	+	0.495262i
$713$	−2.20147	+	12.4851i	−0.0824455	+	0.467572i
$714$	−0.824663	−	1.42836i	−0.0308622	−	0.0534550i
$715$	0.568107	−	0.983990i	0.0212460	−	0.0367992i
$716$	−16.5912	−	13.9217i	−0.620042	−	0.520277i
$717$	21.7980	+	7.93384i	0.814063	+	0.296295i
$718$	14.8476	−	5.40407i	0.554106	−	0.201678i
$719$	−0.414399	+	0.347722i	−0.0154545	+	0.0129678i	−0.650482	−	0.759522i	$-0.725433\pi$
$719$	−0.414399	+	0.347722i	−0.0154545	+	0.0129678i	0.635028	+	0.772489i	$0.280989\pi$
$720$	0.213231	+	1.20929i	0.00794663	+	0.0450676i
$721$	1.03980			0.0387243
$722$	13.1868	+	14.7753i	0.490761	+	0.549878i
$723$	19.8345			0.737654
$724$	−1.51341	−	8.58297i	−0.0562454	−	0.318984i
$725$	7.20792	−	6.04816i	0.267695	−	0.224623i
$726$	−0.979458	+	0.356493i	−0.0363511	+	0.0132307i
$727$	−48.5107	−	17.6565i	−1.79916	−	0.654842i	−0.998442	−	0.0558041i	$-0.982228\pi$
$727$	−48.5107	−	17.6565i	−1.79916	−	0.654842i	−0.800721	−	0.599038i	$-0.795550\pi$
$728$	−7.72964	−	6.48594i	−0.286480	−	0.240385i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−2.22961	−	3.86179i	−0.0825215	−	0.142931i
$731$	−0.216502	+	1.22784i	−0.00800760	+	0.0454134i
$732$	0.841727	−	4.77367i	0.0311111	−	0.176440i
$733$	0.0514290	+	0.0890776i	0.00189957	+	0.00329016i	0.866974	−	0.498354i	$-0.166062\pi$
$733$	0.0514290	+	0.0890776i	0.00189957	+	0.00329016i	−0.865074	+	0.501644i	$0.832729\pi$
$734$	9.64475	−	16.7052i	0.355994	−	0.616600i
$735$	−0.140602	−	0.117979i	−0.00518617	−	0.00435172i
$736$	24.7653	+	9.01382i	0.912860	+	0.332254i
$737$	−4.30010	+	1.56511i	−0.158396	+	0.0576515i
$738$	−4.13193	+	3.46710i	−0.152099	+	0.127626i
$739$	0.250152	+	1.41868i	0.00920200	+	0.0521872i	0.989063	−	0.147494i	$-0.0471206\pi$
$739$	0.250152	+	1.41868i	0.00920200	+	0.0521872i	−0.979861	+	0.199681i	$0.936009\pi$
$740$	2.80101			0.102967
$741$	5.19162	−	1.47636i	0.190719	−	0.0542353i
$742$	−10.8558			−0.398528
$743$	−0.159319	−	0.903545i	−0.00584486	−	0.0331478i	0.981746	−	0.190198i	$-0.0609128\pi$
$743$	−0.159319	−	0.903545i	−0.00584486	−	0.0331478i	−0.987591	+	0.157050i	$0.949802\pi$
$744$	−5.23608	+	4.39359i	−0.191964	+	0.161077i
$745$	10.1149	−	3.68151i	0.370580	−	0.134880i
$746$	37.1340	+	13.5157i	1.35957	+	0.494844i
$747$	6.60149	+	5.53931i	0.241536	+	0.202673i
$748$	0.269373	−	0.466567i	0.00984925	−	0.0170594i
$749$	16.7922	+	29.0849i	0.613573	+	1.06274i
$750$	1.52097	−	8.62584i	0.0555379	−	0.314971i
$751$	−4.90612	+	27.8240i	−0.179027	+	1.01531i	0.754365	+	0.656455i	$0.227945\pi$
$751$	−4.90612	+	27.8240i	−0.179027	+	1.01531i	−0.933392	+	0.358858i	$0.883166\pi$
$752$	−0.371919	−	0.644183i	−0.0135625	−	0.0234909i
$753$	1.82846	−	3.16699i	0.0666329	−	0.115411i
$754$	2.23735	+	1.87736i	0.0814796	+	0.0683695i
$755$	9.23777	+	3.36227i	0.336197	+	0.122366i
$756$	−2.30355	+	0.838422i	−0.0837792	+	0.0304931i
$757$	28.0333	−	23.5227i	1.01889	−	0.854948i	0.0294004	−	0.999568i	$-0.490640\pi$
$757$	28.0333	−	23.5227i	1.01889	−	0.854948i	0.989487	+	0.144619i	$0.0461958\pi$
$758$	2.28491	+	12.9584i	0.0829918	+	0.470670i
$759$	5.63269			0.204454
$760$	−5.30071	−	10.9288i	−0.192277	−	0.396431i
$761$	18.6553			0.676254			0.338127	−	0.941101i	$-0.390207\pi$
$761$	18.6553			0.676254			0.338127	+	0.941101i	$0.390207\pi$
$762$	0.732716	+	4.15544i	0.0265435	+	0.150536i
$763$	−38.0980	+	31.9681i	−1.37924	+	1.15732i
$764$	4.37448	−	1.59218i	0.158263	−	0.0576030i
$765$	−0.508479	−	0.185071i	−0.0183841	−	0.00669127i
$766$	−19.4656	−	16.3336i	−0.703321	−	0.590156i
$767$	−0.863158	+	1.49503i	−0.0311668	+	0.0539825i
$768$	8.32714	+	14.4230i	0.300480	+	0.520446i
$769$	6.59987	−	37.4297i	0.237997	−	1.34975i	−0.598211	−	0.801339i	$-0.704122\pi$
$769$	6.59987	−	37.4297i	0.237997	−	1.34975i	0.836208	−	0.548412i	$-0.184767\pi$
$770$	−0.445641	+	2.52736i	−0.0160598	+	0.0910796i
$771$	1.72927	+	2.99518i	0.0622780	+	0.107869i
$772$	8.22701	−	14.2496i	0.296097	−	0.512854i
$773$	−23.1434	−	19.4197i	−0.832412	−	0.698476i	0.123432	−	0.992353i	$-0.460610\pi$
$773$	−23.1434	−	19.4197i	−0.832412	−	0.698476i	−0.955843	+	0.293877i	$0.905055\pi$
$774$	−2.07080	−	0.753708i	−0.0744332	−	0.0270915i
$775$	8.79427	−	3.20085i	0.315899	−	0.114978i
$776$	22.4828	−	18.8653i	0.807084	−	0.677224i
$777$	−1.55690	−	8.82959i	−0.0558533	−	0.316760i
$778$	32.4074			1.16186
$779$	12.6546	−	18.6727i	0.453396	−	0.669017i
$780$	−1.03802			−0.0371670
$781$	0.740528	+	4.19974i	0.0264982	+	0.150279i
$782$	2.65222	−	2.22547i	0.0948431	−	0.0795828i
$783$	2.12644	−	0.773962i	0.0759929	−	0.0276592i
$784$	0.251539	+	0.0915529i	0.00898355	+	0.00326974i
$785$	−13.0810	−	10.9763i	−0.466881	−	0.391760i
$786$	−0.462862	+	0.801701i	−0.0165098	+	0.0285957i
$787$	23.3409	+	40.4277i	0.832015	+	1.44109i	0.896438	+	0.443169i	$0.146146\pi$
$787$	23.3409	+	40.4277i	0.832015	+	1.44109i	−0.0644229	+	0.997923i	$0.520521\pi$
$788$	−0.0606218	+	0.343803i	−0.00215956	+	0.0122475i
$789$	−0.772943	+	4.38358i	−0.0275175	+	0.156059i
$790$	−2.75614	−	4.77377i	−0.0980589	−	0.169843i
$791$	7.14118	−	12.3689i	0.253911	−	0.439787i
$792$	2.32638	+	1.95206i	0.0826642	+	0.0693635i
$793$	−6.17384	−	2.24709i	−0.219239	−	0.0797966i
$794$	−31.5919	+	11.4985i	−1.12115	+	0.408066i
$795$	−2.72832	+	2.28933i	−0.0967636	+	0.0811943i
$796$	0.415133	+	2.35434i	0.0147140	+	0.0834472i
$797$	47.0891			1.66798			0.833991	−	0.551778i	$-0.186050\pi$
$797$	47.0891			1.66798			0.833991	+	0.551778i	$0.186050\pi$
$798$	−9.87852	+	7.14411i	−0.349696	+	0.252899i
$799$	0.327783			0.0115961
$800$	−3.37831	−	19.1594i	−0.119441	−	0.677385i
$801$	3.38494	−	2.84030i	0.119601	−	0.100357i
$802$	−15.0721	+	5.48580i	−0.532215	+	0.193710i
$803$	−4.38123	−	1.59464i	−0.154610	−	0.0562736i
$804$	3.20251	+	2.68722i	0.112944	+	0.0947711i
$805$	6.93427	−	12.0105i	0.244401	−	0.423315i
$806$	1.45247	+	2.51576i	0.0511612	+	0.0886138i
$807$	1.09005	−	6.18196i	0.0383715	−	0.217615i
$808$	5.50140	−	31.2000i	0.193539	−	1.09761i
$809$	−21.5512	−	37.3278i	−0.757701	−	1.31238i	−0.944020	−	0.329887i	$-0.892989\pi$
$809$	−21.5512	−	37.3278i	−0.757701	−	1.31238i	0.186319	−	0.982489i	$-0.440344\pi$
$810$	0.478209	−	0.828282i	0.0168026	−	0.0291029i
$811$	−23.2659	−	19.5224i	−0.816975	−	0.685523i	0.135287	−	0.990807i	$-0.456804\pi$
$811$	−23.2659	−	19.5224i	−0.816975	−	0.685523i	−0.952262	+	0.305283i	$0.901249\pi$
$812$	5.21273	+	1.89728i	0.182931	+	0.0665814i
$813$	0.631100	−	0.229702i	0.0221337	−	0.00805599i
$814$	−2.66794	+	2.23867i	−0.0935112	+	0.0784652i
$815$	−1.48780	−	8.43774i	−0.0521154	−	0.295561i
$816$	0.789171			0.0276265
$817$	9.19182	+	0.663019i	0.321581	+	0.0231961i
$818$	21.6228			0.756023
$819$	0.576965	+	3.27213i	0.0201608	+	0.114338i
$820$	−3.32311	+	2.78842i	−0.116048	+	0.0973760i
$821$	17.8909	−	6.51176i	0.624398	−	0.227262i	−0.0103935	−	0.999946i	$-0.503308\pi$
$821$	17.8909	−	6.51176i	0.624398	−	0.227262i	0.634791	+	0.772684i	$0.281086\pi$
$822$	8.92021	+	3.24669i	0.311128	+	0.113241i
$823$	−13.7345	−	11.5246i	−0.478756	−	0.401724i	0.371220	−	0.928545i	$-0.378939\pi$
$823$	−13.7345	−	11.5246i	−0.478756	−	0.401724i	−0.849976	+	0.526821i	$0.823384\pi$
$824$	−0.588411	+	1.01916i	−0.0204983	+	0.0355040i
$825$	−2.07902	−	3.60096i	−0.0723820	−	0.125369i
$826$	0.677088	−	3.83996i	0.0235589	−	0.133609i
$827$	1.99689	−	11.3249i	0.0694387	−	0.393807i	−0.930203	−	0.367045i	$-0.880369\pi$
$827$	1.99689	−	11.3249i	0.0694387	−	0.393807i	0.999642	−	0.0267614i	$-0.00851944\pi$
$828$	−2.57294	−	4.45646i	−0.0894159	−	0.154873i
$829$	6.00855	−	10.4071i	0.208685	−	0.361454i	−0.742615	−	0.669718i	$-0.766415\pi$
$829$	6.00855	−	10.4071i	0.208685	−	0.361454i	0.951301	+	0.308265i	$0.0997482\pi$
$830$	−6.31379	−	5.29790i	−0.219155	−	0.183893i
$831$	15.2290	+	5.54290i	0.528288	+	0.192281i
$832$	8.78895	−	3.19892i	0.304702	−	0.110902i
$833$	−0.0903613	+	0.0758221i	−0.00313083	+	0.00262708i
$834$	−3.22390	−	18.2836i	−0.111634	−	0.633110i
$835$	−12.8804			−0.445746
$836$	−3.63434	−	1.62767i	−0.125696	−	0.0562943i
$837$	2.25074			0.0777971
$838$	5.12755	+	29.0798i	0.177128	+	1.00454i
$839$	26.1868	−	21.9733i	0.904068	−	0.758603i	−0.0669134	−	0.997759i	$-0.521315\pi$
$839$	26.1868	−	21.9733i	0.904068	−	0.758603i	0.970981	+	0.239156i	$0.0768707\pi$
$840$	7.02630	−	2.55737i	0.242430	−	0.0882375i
$841$	22.4391	+	8.16717i	0.773763	+	0.281627i
$842$	6.03214	+	5.06157i	0.207881	+	0.174433i
$843$	−4.70080	+	8.14202i	−0.161904	+	0.280426i
$844$	5.16467	+	8.94547i	0.177775	+	0.307916i
$845$	1.82708	−	10.3619i	0.0628534	−	0.356459i
$846$	−0.100604	+	0.570556i	−0.00345885	+	0.0196161i
$847$	1.34164	+	2.32379i	0.0460994	+	0.0798465i
$848$	2.59714	−	4.49837i	0.0891860	−	0.154475i
$849$	12.1999	+	10.2369i	0.418698	+	0.351330i
$850$	−2.40167	−	0.874136i	−0.0823766	−	0.0299826i
$851$	17.6858	−	6.43709i	0.606260	−	0.220661i
$852$	2.98448	−	2.50428i	0.102247	−	0.0857952i
$853$	6.64899	+	37.7083i	0.227657	+	1.29111i	0.857540	+	0.514417i	$0.171992\pi$
$853$	6.64899	+	37.7083i	0.227657	+	1.29111i	−0.629883	+	0.776690i	$0.716897\pi$
$854$	14.8397			0.507803
$855$	−0.976120	+	3.87874i	−0.0333826	+	0.132650i
$856$	−38.0098			−1.29915
$857$	−0.688157	−	3.90273i	−0.0235070	−	0.133315i	0.970796	−	0.239907i	$-0.0771171\pi$
$857$	−0.688157	−	3.90273i	−0.0235070	−	0.133315i	−0.994303	+	0.106593i	$0.966006\pi$
$858$	0.988704	−	0.829621i	0.0337538	−	0.0283228i
$859$	−48.7262	+	17.7349i	−1.66252	+	0.605107i	−0.990756	−	0.135659i	$-0.956685\pi$
$859$	−48.7262	+	17.7349i	−1.66252	+	0.605107i	−0.671763	+	0.740766i	$0.734463\pi$
$860$	−1.66544	−	0.606171i	−0.0567911	−	0.0206703i
$861$	10.6370	+	8.92553i	0.362509	+	0.304181i
$862$	−1.43954	+	2.49336i	−0.0490310	+	0.0849243i
$863$	8.84026	+	15.3118i	0.300926	+	0.521219i	0.976346	−	0.216214i	$-0.0693709\pi$
$863$	8.84026	+	15.3118i	0.300926	+	0.521219i	−0.675420	+	0.737433i	$0.736038\pi$
$864$	0.812478	−	4.60779i	0.0276411	−	0.156760i
$865$	−2.68491	+	15.2269i	−0.0912898	+	0.517730i
$866$	19.3267	+	33.4748i	0.656748	+	1.13752i
$867$	8.32612	−	14.4213i	0.282770	−	0.489772i
$868$	4.22660	+	3.54654i	0.143460	+	0.120377i
$869$	−5.41587	−	1.97122i	−0.183721	−	0.0668689i
$870$	−2.03377	+	0.740232i	−0.0689513	+	0.0250962i
$871$	4.34069	−	3.64227i	0.147079	−	0.123414i
$872$	−9.77413	−	55.4318i	−0.330994	−	1.87716i
$873$	−9.66428			−0.327086
$874$	−18.3698	−	17.8175i	−0.621368	−	0.602688i
$875$	−22.5485			−0.762277
$876$	0.739648	+	4.19475i	0.0249904	+	0.141727i
$877$	3.56023	−	2.98739i	0.120220	−	0.100877i	−0.580695	−	0.814121i	$-0.697219\pi$
$877$	3.56023	−	2.98739i	0.120220	−	0.100877i	0.700916	+	0.713244i	$0.252775\pi$
$878$	36.0941	−	13.1372i	1.21812	−	0.443358i
$879$	17.8568	+	6.49934i	0.602295	+	0.219217i
$880$	−0.940661	−	0.789308i	−0.0317097	−	0.0266076i
$881$	18.3819	−	31.8384i	0.619303	−	1.07266i	−0.370311	−	0.928908i	$-0.620749\pi$
$881$	18.3819	−	31.8384i	0.619303	−	1.07266i	0.989613	−	0.143756i	$-0.0459179\pi$
$882$	−0.104246	−	0.180559i	−0.00351014	−	0.00607974i
$883$	−8.45031	+	47.9241i	−0.284376	+	1.61277i	0.423132	+	0.906068i	$0.360931\pi$
$883$	−8.45031	+	47.9241i	−0.284376	+	1.61277i	−0.707507	+	0.706706i	$0.750180\pi$
$884$	−0.115842	+	0.656973i	−0.00389619	+	0.0220964i
$885$	−0.639626	−	1.10786i	−0.0215008	−	0.0372404i
$886$	10.4114	−	18.0331i	0.349778	−	0.605833i
$887$	−9.78436	−	8.21005i	−0.328527	−	0.275667i	0.463573	−	0.886059i	$-0.346567\pi$
$887$	−9.78436	−	8.21005i	−0.328527	−	0.275667i	−0.792099	+	0.610392i	$0.791012\pi$
$888$	9.53529	+	3.47056i	0.319983	+	0.116464i
$889$	10.2075	−	3.71522i	0.342348	−	0.124604i
$890$	−3.23742	+	2.71652i	−0.108519	+	0.0910579i
$891$	−0.173648	−	0.984808i	−0.00581743	−	0.0329923i
$892$	3.62988			0.121537
$893$	−0.247969	−	2.41011i	−0.00829797	−	0.0806513i
$894$	12.2272			0.408938
$895$	−3.77744	−	21.4229i	−0.126266	−	0.716089i
$896$	3.05199	−	2.56092i	0.101960	−	0.0855544i
$897$	−6.55411	+	2.38550i	−0.218835	+	0.0796496i
$898$	7.73551	+	2.81550i	0.258137	+	0.0939543i
$899$	−3.90165	−	3.27387i	−0.130127	−	0.109190i
$900$	−1.89934	+	3.28975i	−0.0633112	+	0.109658i
$901$	1.14447	+	1.98227i	0.0381277	+	0.0660391i
$902$	0.936633	−	5.31191i	0.0311865	−	0.176867i
$903$	−0.985119	+	5.58689i	−0.0327827	+	0.185920i
$904$	8.08219	+	13.9988i	0.268810	+	0.465592i
$905$	4.37683	−	7.58090i	0.145491	−	0.251998i
$906$	8.55436	+	7.17796i	0.284199	+	0.238472i
$907$	42.3281	+	15.4062i	1.40548	+	0.511554i	0.929801	−	0.368064i	$-0.119979\pi$
$907$	42.3281	+	15.4062i	1.40548	+	0.511554i	0.475682	+	0.879618i	$0.342201\pi$
$908$	−18.6545	+	6.78968i	−0.619071	+	0.225324i
$909$	−7.99155	+	6.70571i	−0.265063	+	0.222414i
$910$	−0.551820	−	3.12953i	−0.0182927	−	0.103743i
$911$	13.0843			0.433502			0.216751	−	0.976227i	$-0.430454\pi$
$911$	13.0843			0.433502			0.216751	+	0.976227i	$0.430454\pi$
$912$	−0.597010	−	5.80258i	−0.0197690	−	0.192143i
$913$	−8.61764			−0.285202
$914$	3.31825	+	18.8187i	0.109758	+	0.622468i
$915$	3.72957	−	3.12948i	0.123296	−	0.103458i
$916$	2.96706	−	1.07992i	0.0980344	−	0.0356816i
$917$	2.23942	+	0.815081i	0.0739520	+	0.0269163i
$918$	−0.470862	−	0.395100i	−0.0155408	−	0.0130402i
$919$	−10.3703	+	17.9619i	−0.342084	+	0.592507i	−0.984820	−	0.173581i	$-0.944466\pi$
$919$	−10.3703	+	17.9619i	−0.342084	+	0.592507i	0.642736	+	0.766088i	$0.277799\pi$
$920$	7.84801	+	13.5932i	0.258741	+	0.448153i
$921$	2.20217	−	12.4891i	0.0725639	−	0.411530i
$922$	0.0466186	−	0.264387i	0.00153530	−	0.00870713i
$923$	−2.64030	−	4.57314i	−0.0869066	−	0.150527i
$924$	1.22569	−	2.12296i	0.0403223	−	0.0698403i
$925$	−10.6430	−	8.93053i	−0.349940	−	0.293634i
$926$	−9.44057	−	3.43608i	−0.310236	−	0.112917i
$927$	0.364142	−	0.132537i	0.0119600	−	0.00435308i
$928$	−8.11080	+	6.80577i	−0.266250	+	0.223410i
$929$	−7.19322	−	40.7948i	−0.236002	−	1.33843i	−0.840493	−	0.541822i	$-0.817735\pi$
$929$	−7.19322	−	40.7948i	−0.236002	−	1.33843i	0.604491	−	0.796612i	$-0.293376\pi$
$930$	−2.15265			−0.0705882
$931$	0.625861	+	0.607046i	0.0205118	+	0.0198951i
$932$	−3.76381			−0.123288
$933$	2.60980	+	14.8009i	0.0854410	+	0.484560i
$934$	−17.7977	+	14.9341i	−0.582359	+	0.488658i
$935$	0.508479	−	0.185071i	0.0166291	−	0.00605248i
$936$	−3.53366	−	1.28615i	−0.115501	−	0.0420390i
$937$	22.9320	+	19.2422i	0.749155	+	0.628616i	0.935279	−	0.353910i	$-0.115148\pi$
$937$	22.9320	+	19.2422i	0.749155	+	0.628616i	−0.186124	+	0.982526i	$0.559593\pi$
$938$	−6.39925	+	11.0838i	−0.208943	+	0.361900i
$939$	−5.97545	−	10.3498i	−0.195001	−	0.337752i
$940$	−0.0809113	+	0.458871i	−0.00263904	+	0.0149667i
$941$	−2.38811	+	13.5436i	−0.0778501	+	0.441510i	0.920822	+	0.389984i	$0.127519\pi$
$941$	−2.38811	+	13.5436i	−0.0778501	+	0.441510i	−0.998672	+	0.0515256i	$0.983592\pi$
$942$	−9.69860	−	16.7985i	−0.315998	−	0.547324i
$943$	−14.5742	+	25.2433i	−0.474601	+	0.822034i
$944$	1.42920	+	1.19924i	0.0465165	+	0.0390320i
$945$	−2.31367	−	0.842106i	−0.0752636	−	0.0273937i
$946$	2.07080	−	0.753708i	0.0673274	−	0.0245052i
$947$	14.6472	−	12.2904i	0.475969	−	0.399386i	−0.372997	−	0.927832i	$-0.621670\pi$
$947$	14.6472	−	12.2904i	0.475969	−	0.399386i	0.848966	+	0.528447i	$0.177225\pi$
$948$	0.914317	+	5.18535i	0.0296957	+	0.168412i
$949$	5.77328			0.187409
$950$	−4.61044	+	18.3202i	−0.149583	+	0.594385i
$951$	22.8317			0.740367
$952$	−0.834455	−	4.73243i	−0.0270448	−	0.153379i
$953$	7.25029	−	6.08372i	0.234860	−	0.197071i	−0.517760	−	0.855526i	$-0.673234\pi$
$953$	7.25029	−	6.08372i	0.234860	−	0.197071i	0.752620	+	0.658455i	$0.228790\pi$
$954$	−3.80171	+	1.38371i	−0.123085	+	0.0447993i
$955$	4.39369	+	1.59917i	0.142177	+	0.0517481i
$956$	16.2342	+	13.6221i	0.525050	+	0.440569i
$957$	−1.13146	+	1.95974i	−0.0365748	+	0.0633494i
$958$	−10.3990	−	18.0117i	−0.335978	−	0.581931i
$959$	4.24353	−	24.0662i	0.137031	−	0.777139i
$960$	−1.20353	+	6.82556i	−0.0388438	+	0.220294i
$961$	12.9671	+	22.4596i	0.418293	+	0.724504i
$962$	2.15628	−	3.73478i	0.0695211	−	0.120414i
$963$	9.58791	+	8.04521i	0.308966	+	0.259253i
$964$	17.0275	+	6.19751i	0.548420	+	0.199608i
$965$	15.5296	−	5.65233i	0.499917	−	0.181955i
$966$	12.0680	−	10.1263i	0.388283	−	0.325808i
$967$	7.15302	+	40.5668i	0.230026	+	1.30454i	0.852841	+	0.522171i	$0.174878\pi$
$967$	7.15302	+	40.5668i	0.230026	+	1.30454i	−0.622815	+	0.782369i	$0.714011\pi$
$968$	−3.03687			−0.0976087
$969$	2.34596	+	1.05066i	0.0753632	+	0.0337521i
$970$	9.24310			0.296778
$971$	−0.124727	−	0.707364i	−0.00400269	−	0.0227004i	0.982741	−	0.184987i	$-0.0592243\pi$
$971$	−0.124727	−	0.707364i	−0.00400269	−	0.0227004i	−0.986744	+	0.162286i	$0.948113\pi$
$972$	−0.699839	+	0.587235i	−0.0224473	+	0.0188356i
$973$	−44.9121	+	16.3467i	−1.43982	+	0.524051i
$974$	17.0461	+	6.20426i	0.546191	+	0.198797i
$975$	3.94416	+	3.30954i	0.126314	+	0.105990i
$976$	−3.55025	+	6.14921i	−0.113641	+	0.196831i
$977$	26.8570	+	46.5176i	0.859231	+	1.48823i	0.872664	+	0.488322i	$0.162391\pi$
$977$	26.8570	+	46.5176i	0.859231	+	1.48823i	−0.0134330	+	0.999910i	$0.504276\pi$
$978$	1.69004	−	9.58469i	0.0540415	−	0.306485i
$979$	−0.767304	+	4.35160i	−0.0245231	+	0.139078i
$980$	−0.0838399	−	0.145215i	−0.00267817	−	0.00463872i
$981$	−9.26727	+	16.0514i	−0.295881	+	0.512481i
$982$	29.7906	+	24.9972i	0.950655	+	0.797694i
$983$	−28.2285	−	10.2743i	−0.900351	−	0.327701i	−0.149957	−	0.988692i	$-0.547914\pi$
$983$	−28.2285	−	10.2743i	−0.900351	−	0.327701i	−0.750393	+	0.660992i	$0.770136\pi$
$984$	−14.7676	+	5.37498i	−0.470775	+	0.171348i
$985$	−0.268606	+	0.225387i	−0.00855851	+	0.00718144i
$986$	0.241534	+	1.36981i	0.00769200	+	0.0436235i
$987$	1.49147			0.0474740
$988$	4.91820	+	0.354757i	0.156469	+	0.0112863i
$989$	−11.9088			−0.378677
$990$	0.166080	+	0.941888i	0.00527838	+	0.0299352i
$991$	−1.86430	+	1.56433i	−0.0592215	+	0.0496927i	−0.671918	−	0.740626i	$-0.734529\pi$
$991$	−1.86430	+	1.56433i	−0.0592215	+	0.0496927i	0.612696	+	0.790318i	$0.290085\pi$
$992$	−9.89586	+	3.60180i	−0.314194	+	0.114357i
$993$	18.1560	+	6.60823i	0.576162	+	0.209706i
$994$	9.13676	+	7.66665i	0.289800	+	0.243171i
$995$	−1.20058	+	2.07946i	−0.0380609	+	0.0659234i
$996$	3.93643	+	6.81809i	0.124730	+	0.216040i
$997$	3.11053	−	17.6407i	0.0985115	−	0.558687i	−0.895103	−	0.445859i	$-0.852898\pi$
$997$	3.11053	−	17.6407i	0.0985115	−	0.558687i	0.993615	−	0.112827i	$-0.0359907\pi$
$998$	6.44826	−	36.5699i	0.204116	−	1.15760i
$999$	−1.67068	−	2.89369i	−0.0528578	−	0.0915525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.r.c.199.6	✓	54
19.17	even	9	inner	627.2.r.c.397.6	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.r.c.199.6	✓	54	1.1	even	1	trivial
627.2.r.c.397.6	yes	54	19.17	even	9	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.r (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.180996 + 1.02648i) q^{2} +(0.766044 - 0.642788i) q^{3} +(0.858479 - 0.312461i) q^{4} +(0.862251 + 0.313834i) q^{5} +(0.798461 + 0.669989i) q^{6} +(1.34164 - 2.32379i) q^{7} +(1.51843 + 2.63001i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.166080 + 0.941888i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.456787 - 0.791179i) q^{12} +(-0.948563 - 0.795939i) q^{13} +(2.62817 + 0.956574i) q^{14} +(0.862251 - 0.313834i) q^{15} +(-1.02514 + 0.860199i) q^{16} +(-0.102402 - 0.580753i) q^{17} +1.04232 q^{18} +(-4.19267 + 1.19228i) q^{19} +0.838286 q^{20} +(-0.465948 - 2.64252i) q^{21} +(-0.798461 + 0.669989i) q^{22} +(5.29299 - 1.92649i) q^{23} +(2.85372 + 1.03867i) q^{24} +(-3.18524 - 2.67273i) q^{25} +(0.645331 - 1.11775i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.425678 - 2.41414i) q^{28} +(-0.392951 + 2.22854i) q^{29} +(0.478209 + 0.828282i) q^{30} +(-1.12537 + 1.94920i) q^{31} +(3.58423 + 3.00752i) q^{32} +(0.939693 + 0.342020i) q^{33} +(0.577598 - 0.210228i) q^{34} +(1.88612 - 1.58264i) q^{35} +(-0.158641 - 0.899696i) q^{36} +3.34135 q^{37} +(-1.98271 - 4.08790i) q^{38} -1.23826 q^{39} +(0.483887 + 2.74426i) q^{40} +(-3.96418 + 3.32634i) q^{41} +(2.62817 - 0.956574i) q^{42} +(-1.98672 - 0.723108i) q^{43} +(0.699839 + 0.587235i) q^{44} +(0.458794 - 0.794655i) q^{45} +(2.93552 + 5.08448i) q^{46} +(-0.0965200 + 0.547392i) q^{47} +(-0.232381 + 1.31790i) q^{48} +(-0.100014 - 0.173229i) q^{49} +(2.16699 - 3.75334i) q^{50} +(-0.451745 - 0.379059i) q^{51} +(-1.06302 - 0.386908i) q^{52} +(-3.64737 + 1.32753i) q^{53} +(0.798461 - 0.669989i) q^{54} +(0.159338 + 0.903648i) q^{55} +8.14879 q^{56} +(-2.44539 + 3.60834i) q^{57} -2.35867 q^{58} +(-0.242091 - 1.37296i) q^{59} +(0.642164 - 0.538840i) q^{60} +(4.98589 - 1.81472i) q^{61} +(-2.20451 - 0.802375i) q^{62} +(-2.05552 - 1.72478i) q^{63} +(-3.77667 + 6.54138i) q^{64} +(-0.568107 - 0.983990i) q^{65} +(-0.180996 + 1.02648i) q^{66} +(-0.794626 + 4.50655i) q^{67} +(-0.269373 - 0.466567i) q^{68} +(2.81634 - 4.87805i) q^{69} +(1.96593 + 1.64961i) q^{70} +(4.00735 + 1.45856i) q^{71} +(2.85372 - 1.03867i) q^{72} +(-3.57161 + 2.99694i) q^{73} +(0.604773 + 3.42984i) q^{74} -4.15803 q^{75} +(-3.22678 + 2.33359i) q^{76} +2.68329 q^{77} +(-0.224121 - 1.27105i) q^{78} +(-4.41506 + 3.70468i) q^{79} +(-1.15389 + 0.419982i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-4.13193 - 3.46710i) q^{82} +(-4.30882 + 7.46309i) q^{83} +(-1.22569 - 2.12296i) q^{84} +(0.0939632 - 0.532892i) q^{85} +(0.382668 - 2.17022i) q^{86} +(1.13146 + 1.95974i) q^{87} +(-1.51843 + 2.63001i) q^{88} +(3.38494 + 2.84030i) q^{89} +(0.898739 + 0.327114i) q^{90} +(-3.12223 + 1.13640i) q^{91} +(3.94197 - 3.30771i) q^{92} +(0.390837 + 2.21655i) q^{93} -0.579358 q^{94} +(-3.98931 - 0.287755i) q^{95} +4.67888 q^{96} +(-1.67819 - 9.51746i) q^{97} +(0.159714 - 0.134016i) q^{98} +(0.939693 - 0.342020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{2} + 3 q^{4} + 3 q^{6} - 18 q^{7} - 12 q^{8} + 30 q^{10} + 27 q^{11} - 33 q^{12} + 9 q^{14} - 21 q^{16} - 24 q^{17} + 6 q^{18} + 3 q^{19} + 30 q^{20} - 3 q^{22} + 12 q^{23} - 39 q^{24} + 30 q^{25}+ \cdots - 54 q^{98}+O(q^{100}) \) 54 * q + 3 * q^2 + 3 * q^4 + 3 * q^6 - 18 * q^7 - 12 * q^8 + 30 * q^10 + 27 * q^11 - 33 * q^12 + 9 * q^14 - 21 * q^16 - 24 * q^17 + 6 * q^18 + 3 * q^19 + 30 * q^20 - 3 * q^22 + 12 * q^23 - 39 * q^24 + 30 * q^25 - 6 * q^26 - 27 * q^27 - 30 * q^28 + 33 * q^29 + 15 * q^30 + 15 * q^31 + 39 * q^32 + 3 * q^34 - 27 * q^35 + 3 * q^36 - 24 * q^37 + 15 * q^38 + 6 * q^39 + 84 * q^40 - 15 * q^41 + 9 * q^42 - 48 * q^43 + 6 * q^44 - 36 * q^46 + 3 * q^47 + 24 * q^48 - 21 * q^49 - 30 * q^50 + 3 * q^51 - 45 * q^52 - 21 * q^53 + 3 * q^54 + 21 * q^57 + 90 * q^58 + 45 * q^59 - 39 * q^60 - 21 * q^61 - 87 * q^62 - 9 * q^63 - 54 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 - 39 * q^69 + 15 * q^70 - 57 * q^71 - 39 * q^72 - 30 * q^73 - 105 * q^74 + 54 * q^75 - 6 * q^76 - 36 * q^77 + 51 * q^78 - 27 * q^79 - 3 * q^80 + 102 * q^82 - 63 * q^83 - 51 * q^84 + 60 * q^85 - 42 * q^86 - 27 * q^87 + 12 * q^88 + 21 * q^89 - 6 * q^90 - 72 * q^91 + 78 * q^92 - 6 * q^93 - 36 * q^94 + 63 * q^95 + 114 * q^96 + 45 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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