LMFDB - Embedded newform 462.2.j.f.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			295.1
Root			$1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	462.295
Dual form			462.2.j.f.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.02224 - 3.14612i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.02224 - 3.14612i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.30803 q^{10} +(3.14027 + 1.06710i) q^{11} -1.00000 q^{12} +(0.682489 - 2.10049i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-2.67625 - 1.94441i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.16251 - 6.65551i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-5.44830 + 3.95842i) q^{19} +(-1.02224 + 3.14612i) q^{20} +1.00000 q^{21} +(1.98527 - 2.65682i) q^{22} -4.39698 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.80803 + 3.49324i) q^{25} +(-1.78678 - 1.29817i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(5.65303 + 4.10716i) q^{29} +(-2.67625 + 1.94441i) q^{30} +(-1.09904 + 3.38250i) q^{31} +1.00000 q^{32} +(3.16776 - 0.982504i) q^{33} -6.99802 q^{34} +(1.02224 - 3.14612i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-2.55982 - 1.85982i) q^{37} +(2.08107 + 6.40486i) q^{38} +(-0.682489 - 2.10049i) q^{39} +(2.67625 + 1.94441i) q^{40} +(8.54250 - 6.20649i) q^{41} +(0.309017 - 0.951057i) q^{42} +11.2604 q^{43} +(-1.91331 - 2.70911i) q^{44} -3.30803 q^{45} +(-1.35874 + 4.18177i) q^{46} +(-0.317511 + 0.230685i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.83650 + 5.65218i) q^{50} +(-5.66152 - 4.11333i) q^{51} +(-1.78678 + 1.29817i) q^{52} +(2.11180 - 6.49944i) q^{53} -1.00000 q^{54} +(0.147120 - 10.9705i) q^{55} -1.00000 q^{56} +(-2.08107 + 6.40486i) q^{57} +(5.65303 - 4.10716i) q^{58} +(6.19910 + 4.50391i) q^{59} +(1.02224 + 3.14612i) q^{60} +(1.30339 + 4.01142i) q^{61} +(2.87733 + 2.09050i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -7.30605 q^{65} +(0.0444738 - 3.31633i) q^{66} +2.06998 q^{67} +(-2.16251 + 6.65551i) q^{68} +(-3.55723 + 2.58448i) q^{69} +(-2.67625 - 1.94441i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(5.69750 + 4.13948i) q^{73} +(-2.55982 + 1.85982i) q^{74} +(-1.83650 + 5.65218i) q^{75} +6.73447 q^{76} +(1.91331 + 2.70911i) q^{77} -2.20858 q^{78} +(2.25019 - 6.92537i) q^{79} +(2.67625 - 1.94441i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.26294 - 10.0423i) q^{82} +(-2.02163 - 6.22192i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(-18.7285 + 13.6070i) q^{85} +(3.47964 - 10.7092i) q^{86} +6.98752 q^{87} +(-3.16776 + 0.982504i) q^{88} +3.70698 q^{89} +(-1.02224 + 3.14612i) q^{90} +(1.78678 - 1.29817i) q^{91} +(3.55723 + 2.58448i) q^{92} +(1.09904 + 3.38250i) q^{93} +(0.121278 + 0.373256i) q^{94} +(18.0231 + 13.0946i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.223719 + 0.688535i) q^{97} +1.00000 q^{98} +(1.98527 - 2.65682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.02224	−	3.14612i	−0.457158	−	1.40699i	−0.868583	−	0.495544i	$-0.834969\pi$
$5$	−1.02224	−	3.14612i	−0.457158	−	1.40699i	0.411424	−	0.911444i	$-0.365031\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.30803			−1.04609
$11$	3.14027	+	1.06710i	0.946827	+	0.321742i
$11$	3.14027	+	1.06710i	0.946827	+	0.321742i
$12$	−1.00000			−0.288675
$13$	0.682489	−	2.10049i	0.189288	−	0.582570i	−0.810707	−	0.585452i	$-0.800917\pi$
$13$	0.682489	−	2.10049i	0.189288	−	0.582570i	0.999996	+	0.00288157i	$0.000917234\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	−2.67625	−	1.94441i	−0.691005	−	0.502045i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.16251	−	6.65551i	−0.524485	−	1.61420i	−0.765332	−	0.643636i	$-0.777425\pi$
$17$	−2.16251	−	6.65551i	−0.524485	−	1.61420i	0.240846	−	0.970563i	$-0.422575\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−5.44830	+	3.95842i	−1.24993	+	0.908124i	−0.998218	−	0.0596792i	$-0.980992\pi$
$19$	−5.44830	+	3.95842i	−1.24993	+	0.908124i	−0.251708	+	0.967803i	$0.580992\pi$
$20$	−1.02224	+	3.14612i	−0.228579	+	0.703494i
$21$	1.00000			0.218218
$22$	1.98527	−	2.65682i	0.423261	−	0.566437i
$23$	−4.39698			−0.916833			−0.458416	−	0.888738i	$-0.651583\pi$
$23$	−4.39698			−0.916833			−0.458416	+	0.888738i	$0.651583\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.80803	+	3.49324i	−0.961606	+	0.698647i
$26$	−1.78678	−	1.29817i	−0.350416	−	0.254592i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	5.65303	+	4.10716i	1.04974	+	0.762681i	0.972163	−	0.234305i	$-0.0752815\pi$
$29$	5.65303	+	4.10716i	1.04974	+	0.762681i	0.0775773	+	0.996986i	$0.475282\pi$
$30$	−2.67625	+	1.94441i	−0.488614	+	0.354999i
$31$	−1.09904	+	3.38250i	−0.197394	+	0.607515i	0.802547	+	0.596589i	$0.203478\pi$
$31$	−1.09904	+	3.38250i	−0.197394	+	0.607515i	−0.999940	+	0.0109259i	$0.996522\pi$
$32$	1.00000			0.176777
$33$	3.16776	−	0.982504i	0.551436	−	0.171032i
$34$	−6.99802			−1.20015
$35$	1.02224	−	3.14612i	0.172790	−	0.531792i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−2.55982	−	1.85982i	−0.420831	−	0.305752i	0.357141	−	0.934051i	$-0.383752\pi$
$37$	−2.55982	−	1.85982i	−0.420831	−	0.305752i	−0.777972	+	0.628299i	$0.783752\pi$
$38$	2.08107	+	6.40486i	0.337593	+	1.03901i
$39$	−0.682489	−	2.10049i	−0.109286	−	0.336347i
$40$	2.67625	+	1.94441i	0.423152	+	0.307438i
$41$	8.54250	−	6.20649i	1.33411	−	0.969290i	0.334475	−	0.942405i	$-0.391441\pi$
$41$	8.54250	−	6.20649i	1.33411	−	0.969290i	0.999639	−	0.0268858i	$-0.00855905\pi$
$42$	0.309017	−	0.951057i	0.0476824	−	0.146751i
$43$	11.2604			1.71719			0.858594	−	0.512656i	$-0.171338\pi$
$43$	11.2604			1.71719			0.858594	+	0.512656i	$0.171338\pi$
$44$	−1.91331	−	2.70911i	−0.288442	−	0.408413i
$45$	−3.30803			−0.493132
$46$	−1.35874	+	4.18177i	−0.200335	+	0.616569i
$47$	−0.317511	+	0.230685i	−0.0463137	+	0.0336489i	−0.610701	−	0.791861i	$-0.709112\pi$
$47$	−0.317511	+	0.230685i	−0.0463137	+	0.0336489i	0.564388	+	0.825510i	$0.309112\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.83650	+	5.65218i	0.259721	+	0.799338i
$51$	−5.66152	−	4.11333i	−0.792771	−	0.575982i
$52$	−1.78678	+	1.29817i	−0.247782	+	0.180024i
$53$	2.11180	−	6.49944i	0.290077	−	0.892767i	−0.694753	−	0.719248i	$-0.744486\pi$
$53$	2.11180	−	6.49944i	0.290077	−	0.892767i	0.984831	−	0.173518i	$-0.0555136\pi$
$54$	−1.00000			−0.136083
$55$	0.147120	−	10.9705i	0.0198377	−	1.47926i
$56$	−1.00000			−0.133631
$57$	−2.08107	+	6.40486i	−0.275644	+	0.848344i
$58$	5.65303	−	4.10716i	0.742279	−	0.539297i
$59$	6.19910	+	4.50391i	0.807054	+	0.586359i	0.912975	−	0.408016i	$-0.133779\pi$
$59$	6.19910	+	4.50391i	0.807054	+	0.586359i	−0.105921	+	0.994375i	$0.533779\pi$
$60$	1.02224	+	3.14612i	0.131970	+	0.406163i
$61$	1.30339	+	4.01142i	0.166882	+	0.513610i	0.999170	−	0.0407335i	$-0.0129695\pi$
$61$	1.30339	+	4.01142i	0.166882	+	0.513610i	−0.832288	+	0.554343i	$0.812969\pi$
$62$	2.87733	+	2.09050i	0.365421	+	0.265494i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−7.30605			−0.906204
$66$	0.0444738	−	3.31633i	0.00547434	−	0.408212i
$67$	2.06998			0.252889			0.126444	−	0.991974i	$-0.459644\pi$
$67$	2.06998			0.252889			0.126444	+	0.991974i	$0.459644\pi$
$68$	−2.16251	+	6.65551i	−0.262243	+	0.807100i
$69$	−3.55723	+	2.58448i	−0.428240	+	0.311135i
$70$	−2.67625	−	1.94441i	−0.319873	−	0.232401i
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	0.868297	+	0.496045i	$0.165215\pi$
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	−0.410899	+	0.911681i	$0.634785\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	5.69750	+	4.13948i	0.666842	+	0.484489i	0.868967	−	0.494871i	$-0.164785\pi$
$73$	5.69750	+	4.13948i	0.666842	+	0.484489i	−0.202125	+	0.979360i	$0.564785\pi$
$74$	−2.55982	+	1.85982i	−0.297573	+	0.216199i
$75$	−1.83650	+	5.65218i	−0.212061	+	0.652657i
$76$	6.73447			0.772496
$77$	1.91331	+	2.70911i	0.218042	+	0.308731i
$78$	−2.20858			−0.250073
$79$	2.25019	−	6.92537i	0.253166	−	0.779165i	−0.741019	−	0.671484i	$-0.765657\pi$
$79$	2.25019	−	6.92537i	0.253166	−	0.779165i	0.994185	−	0.107681i	$-0.0343426\pi$
$80$	2.67625	−	1.94441i	0.299214	−	0.217392i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.26294	−	10.0423i	−0.360332	−	1.10899i
$83$	−2.02163	−	6.22192i	−0.221902	−	0.682945i	−0.998591	−	0.0530607i	$-0.983102\pi$
$83$	−2.02163	−	6.22192i	−0.221902	−	0.682945i	0.776689	−	0.629884i	$-0.216898\pi$
$84$	−0.809017	−	0.587785i	−0.0882710	−	0.0641326i
$85$	−18.7285	+	13.6070i	−2.03139	+	1.47589i
$86$	3.47964	−	10.7092i	0.375219	−	1.15481i
$87$	6.98752			0.749141
$88$	−3.16776	+	0.982504i	−0.337684	+	0.104735i
$89$	3.70698			0.392939			0.196470	−	0.980510i	$-0.437052\pi$
$89$	3.70698			0.392939			0.196470	+	0.980510i	$0.437052\pi$
$90$	−1.02224	+	3.14612i	−0.107753	+	0.331630i
$91$	1.78678	−	1.29817i	0.187305	−	0.136085i
$92$	3.55723	+	2.58448i	0.370867	+	0.269450i
$93$	1.09904	+	3.38250i	0.113965	+	0.350749i
$94$	0.121278	+	0.373256i	0.0125089	+	0.0384984i
$95$	18.0231	+	13.0946i	1.84913	+	1.34347i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−0.223719	+	0.688535i	−0.0227152	+	0.0699102i	−0.961772	−	0.273853i	$-0.911702\pi$
$97$	−0.223719	+	0.688535i	−0.0227152	+	0.0699102i	0.939056	+	0.343763i	$0.111702\pi$
$98$	1.00000			0.101015
$99$	1.98527	−	2.65682i	0.199527	−	0.267021i
$100$	5.94305			0.594305
$101$	3.79667	−	11.6849i	0.377783	−	1.16270i	−0.563800	−	0.825912i	$-0.690661\pi$
$101$	3.79667	−	11.6849i	0.377783	−	1.16270i	0.941582	−	0.336784i	$-0.109339\pi$
$102$	−5.66152	+	4.11333i	−0.560574	+	0.407281i
$103$	−6.62919	−	4.81639i	−0.653193	−	0.474573i	0.211164	−	0.977451i	$-0.432275\pi$
$103$	−6.62919	−	4.81639i	−0.653193	−	0.474573i	−0.864357	+	0.502878i	$0.832275\pi$
$104$	0.682489	+	2.10049i	0.0669236	+	0.205970i
$105$	−1.02224	−	3.14612i	−0.0997601	−	0.307030i
$106$	−5.52875	−	4.01687i	−0.537000	−	0.390153i
$107$	−2.21223	+	1.60728i	−0.213864	+	0.155382i	−0.689560	−	0.724228i	$-0.742196\pi$
$107$	−2.21223	+	1.60728i	−0.213864	+	0.155382i	0.475696	+	0.879610i	$0.342196\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−16.4852			−1.57899			−0.789496	−	0.613755i	$-0.789658\pi$
$109$	−16.4852			−1.57899			−0.789496	+	0.613755i	$0.789658\pi$
$110$	−10.3881	−	3.52999i	−0.990467	−	0.336571i
$111$	−3.16411			−0.300324
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−0.280876	+	0.204068i	−0.0264225	+	0.0191971i	−0.600918	−	0.799311i	$-0.705198\pi$
$113$	−0.280876	+	0.204068i	−0.0264225	+	0.0191971i	0.574496	+	0.818508i	$0.305198\pi$
$114$	5.44830	+	3.95842i	0.510280	+	0.370740i
$115$	4.49475	+	13.8334i	0.419138	+	1.28997i
$116$	−2.15926	−	6.64553i	−0.200483	−	0.617022i
$117$	−1.78678	−	1.29817i	−0.165188	−	0.120016i
$118$	6.19910	−	4.50391i	0.570673	−	0.414618i
$119$	2.16251	−	6.65551i	0.198237	−	0.610110i
$120$	3.30803			0.301980
$121$	8.72260	+	6.70196i	0.792964	+	0.609269i
$122$	4.21786			0.381867
$123$	3.26294	−	10.0423i	0.294210	−	0.905484i
$124$	2.87733	−	2.09050i	0.258392	−	0.187733i
$125$	2.52384	+	1.83367i	0.225739	+	0.164009i
$126$	−0.309017	−	0.951057i	−0.0275294	−	0.0847268i
$127$	2.02571	+	6.23451i	0.179753	+	0.553223i	0.999819	−	0.0190465i	$-0.00606306\pi$
$127$	2.02571	+	6.23451i	0.179753	+	0.553223i	−0.820065	+	0.572270i	$0.806063\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	9.10982	−	6.61867i	0.802075	−	0.582741i
$130$	−2.25769	+	6.94847i	−0.198013	+	0.609421i
$131$	19.8239			1.73202			0.866010	−	0.500026i	$-0.166676\pi$
$131$	19.8239			1.73202			0.866010	+	0.500026i	$0.166676\pi$
$132$	−3.14027	−	1.06710i	−0.273325	−	0.0928790i
$133$	−6.73447			−0.583952
$134$	0.639660	−	1.96867i	0.0552582	−	0.170067i
$135$	−2.67625	+	1.94441i	−0.230335	+	0.167348i
$136$	5.66152	+	4.11333i	0.485471	+	0.352715i
$137$	5.54696	+	17.0718i	0.473909	+	1.45854i	0.847423	+	0.530918i	$0.178153\pi$
$137$	5.54696	+	17.0718i	0.473909	+	1.45854i	−0.373514	+	0.927624i	$0.621847\pi$
$138$	1.35874	+	4.18177i	0.115664	+	0.355976i
$139$	−2.64187	−	1.91943i	−0.224081	−	0.162804i	0.470081	−	0.882623i	$-0.344225\pi$
$139$	−2.64187	−	1.91943i	−0.224081	−	0.162804i	−0.694162	+	0.719819i	$0.744225\pi$
$140$	−2.67625	+	1.94441i	−0.226184	+	0.164333i
$141$	−0.121278	+	0.373256i	−0.0102135	+	0.0314338i
$142$	12.4721			1.04664
$143$	4.38463	−	5.86781i	0.366661	−	0.490691i
$144$	1.00000			0.0833333
$145$	7.14290	−	21.9836i	0.593186	−	1.82564i
$146$	5.69750	−	4.13948i	0.471528	−	0.342585i
$147$	0.809017	+	0.587785i	0.0667266	+	0.0484797i
$148$	0.977763	+	3.00925i	0.0803716	+	0.247358i
$149$	−0.674984	−	2.07739i	−0.0552969	−	0.170186i	0.919594	−	0.392871i	$-0.128518\pi$
$149$	−0.674984	−	2.07739i	−0.0552969	−	0.170186i	−0.974891	+	0.222684i	$0.928518\pi$
$150$	4.80803	+	3.49324i	0.392574	+	0.285222i
$151$	5.04713	−	3.66696i	0.410730	−	0.298413i	−0.363167	−	0.931724i	$-0.618305\pi$
$151$	5.04713	−	3.66696i	0.410730	−	0.298413i	0.773897	+	0.633311i	$0.218305\pi$
$152$	2.08107	−	6.40486i	0.168797	−	0.519503i
$153$	−6.99802			−0.565757
$154$	3.16776	−	0.982504i	0.255265	−	0.0791724i
$155$	11.7652			0.945007
$156$	−0.682489	+	2.10049i	−0.0546429	+	0.168173i
$157$	−10.9411	+	7.94915i	−0.873193	+	0.634412i	−0.931442	−	0.363891i	$-0.881448\pi$
$157$	−10.9411	+	7.94915i	−0.873193	+	0.634412i	0.0582491	+	0.998302i	$0.481448\pi$
$158$	−5.89107	−	4.28011i	−0.468668	−	0.340508i
$159$	−2.11180	−	6.49944i	−0.167476	−	0.515439i
$160$	−1.02224	−	3.14612i	−0.0808149	−	0.248723i
$161$	−3.55723	−	2.58448i	−0.280349	−	0.203685i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	0.646830	+	0.762634i	$0.276094\pi$
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	−0.971562	+	0.236787i	$0.923906\pi$
$164$	−10.5591			−0.824528
$165$	−6.32928	−	8.96180i	−0.492733	−	0.697675i
$166$	−6.54212			−0.507767
$167$	1.59341	−	4.90402i	0.123302	−	0.379485i	−0.870286	−	0.492547i	$-0.836066\pi$
$167$	1.59341	−	4.90402i	0.123302	−	0.379485i	0.993588	+	0.113062i	$0.0360659\pi$
$168$	−0.809017	+	0.587785i	−0.0624170	+	0.0453486i
$169$	6.57097	+	4.77409i	0.505459	+	0.367238i
$170$	7.15364	+	22.0166i	0.548659	+	1.68860i
$171$	2.08107	+	6.40486i	0.159143	+	0.489792i
$172$	−9.10982	−	6.61867i	−0.694617	−	0.504669i
$173$	−19.5211	+	14.1829i	−1.48417	+	1.07831i	−0.507981	+	0.861369i	$0.669608\pi$
$173$	−19.5211	+	14.1829i	−1.48417	+	1.07831i	−0.976185	+	0.216941i	$0.930392\pi$
$174$	2.15926	−	6.64553i	0.163693	−	0.503796i
$175$	−5.94305			−0.449252
$176$	−0.0444738	+	3.31633i	−0.00335234	+	0.249978i
$177$	7.66251			0.575949
$178$	1.14552	−	3.52555i	0.0858604	−	0.264251i
$179$	−18.4812	+	13.4274i	−1.38135	+	1.00361i	−0.384600	+	0.923083i	$0.625661\pi$
$179$	−18.4812	+	13.4274i	−1.38135	+	1.00361i	−0.996752	+	0.0805284i	$0.974339\pi$
$180$	2.67625	+	1.94441i	0.199476	+	0.144928i
$181$	2.03697	+	6.26915i	0.151407	+	0.465982i	0.997779	−	0.0666096i	$-0.0212182\pi$
$181$	2.03697	+	6.26915i	0.151407	+	0.465982i	−0.846372	+	0.532592i	$0.821218\pi$
$182$	−0.682489	−	2.10049i	−0.0505895	−	0.155698i
$183$	3.41232	+	2.47919i	0.252246	+	0.183267i
$184$	3.55723	−	2.58448i	0.262242	−	0.190530i
$185$	−3.23447	+	9.95467i	−0.237803	+	0.731882i
$186$	3.55657			0.260781
$187$	0.311228	−	23.2077i	0.0227593	−	1.69712i
$188$	0.392465			0.0286234
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	18.0231	−	13.0946i	1.30753	−	0.949980i
$191$	−13.5379	−	9.83583i	−0.979565	−	0.711696i	−0.0219536	−	0.999759i	$-0.506989\pi$
$191$	−13.5379	−	9.83583i	−0.979565	−	0.711696i	−0.957611	+	0.288063i	$0.906989\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	6.53700	+	20.1188i	0.470543	+	1.44818i	0.851875	+	0.523745i	$0.175466\pi$
$193$	6.53700	+	20.1188i	0.470543	+	1.44818i	−0.381332	+	0.924438i	$0.624534\pi$
$194$	0.585703	+	0.425538i	0.0420510	+	0.0305519i
$195$	−5.91072	+	4.29439i	−0.423275	+	0.307528i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−18.2843			−1.30270			−0.651351	−	0.758776i	$-0.725797\pi$
$197$	−18.2843			−1.30270			−0.651351	+	0.758776i	$0.725797\pi$
$198$	−1.91331	−	2.70911i	−0.135973	−	0.192528i
$199$	3.59907			0.255131			0.127566	−	0.991830i	$-0.459284\pi$
$199$	3.59907			0.255131			0.127566	+	0.991830i	$0.459284\pi$
$200$	1.83650	−	5.65218i	0.129860	−	0.399669i
$201$	1.67465	−	1.21670i	0.118121	−	0.0858198i
$202$	−9.93981	−	7.22169i	−0.699362	−	0.508116i
$203$	2.15926	+	6.64553i	0.151551	+	0.466425i
$204$	2.16251	+	6.65551i	0.151406	+	0.465979i
$205$	−28.2588	−	20.5312i	−1.97368	−	1.43396i
$206$	−6.62919	+	4.81639i	−0.461877	+	0.335574i
$207$	−1.35874	+	4.18177i	−0.0944390	+	0.290653i
$208$	2.20858			0.153138
$209$	−21.3332	+	6.61664i	−1.47565	+	0.457683i
$210$	−3.30803			−0.228276
$211$	−1.46628	+	4.51273i	−0.100943	+	0.310669i	−0.988757	−	0.149533i	$-0.952223\pi$
$211$	−1.46628	+	4.51273i	−0.100943	+	0.310669i	0.887814	+	0.460202i	$0.152223\pi$
$212$	−5.52875	+	4.01687i	−0.379716	+	0.275880i
$213$	10.0902	+	7.33094i	0.691367	+	0.502308i
$214$	0.844997	+	2.60063i	0.0577628	+	0.177776i
$215$	−11.5107	−	35.4264i	−0.785027	−	2.41606i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−2.87733	+	2.09050i	−0.195326	+	0.141912i
$218$	−5.09420	+	15.6783i	−0.345023	+	1.06187i
$219$	7.04250			0.475888
$220$	−6.56732	+	8.78885i	−0.442769	+	0.592544i
$221$	−15.4557			−1.03966
$222$	−0.977763	+	3.00925i	−0.0656232	+	0.201967i
$223$	23.0476	−	16.7450i	1.54338	−	1.12133i	0.595208	−	0.803571i	$-0.297070\pi$
$223$	23.0476	−	16.7450i	1.54338	−	1.12133i	0.948171	−	0.317760i	$-0.102930\pi$
$224$	0.809017	+	0.587785i	0.0540547	+	0.0392731i
$225$	1.83650	+	5.65218i	0.122434	+	0.376812i
$226$	0.107285	+	0.330189i	0.00713649	+	0.0219638i
$227$	−19.5788	−	14.2248i	−1.29949	−	0.944133i	−0.299537	−	0.954085i	$-0.596832\pi$
$227$	−19.5788	−	14.2248i	−1.29949	−	0.944133i	−0.999950	+	0.00995175i	$0.996832\pi$
$228$	5.44830	−	3.95842i	0.360822	−	0.262153i
$229$	−3.92020	+	12.0651i	−0.259054	+	0.797287i	0.733950	+	0.679204i	$0.237675\pi$
$229$	−3.92020	+	12.0651i	−0.259054	+	0.797287i	−0.993004	+	0.118083i	$0.962325\pi$
$230$	14.5453			0.959090
$231$	3.14027	+	1.06710i	0.206615	+	0.0702099i
$232$	−6.98752			−0.458753
$233$	7.13178	−	21.9494i	0.467218	−	1.43795i	−0.388953	−	0.921258i	$-0.627163\pi$
$233$	7.13178	−	21.9494i	0.467218	−	1.43795i	0.856171	−	0.516692i	$-0.172837\pi$
$234$	−1.78678	+	1.29817i	−0.116805	+	0.0848641i
$235$	1.05033	+	0.763113i	0.0685163	+	0.0497800i
$236$	−2.36785	−	7.28748i	−0.154134	−	0.474374i
$237$	−2.25019	−	6.92537i	−0.146165	−	0.449851i
$238$	−5.66152	−	4.11333i	−0.366982	−	0.266628i
$239$	−10.6769	+	7.75719i	−0.690629	+	0.501771i	−0.876867	−	0.480733i	$-0.840370\pi$
$239$	−10.6769	+	7.75719i	−0.690629	+	0.501771i	0.186238	+	0.982505i	$0.440370\pi$
$240$	1.02224	−	3.14612i	0.0659851	−	0.203081i
$241$	18.1889			1.17165			0.585827	−	0.810436i	$-0.300770\pi$
$241$	18.1889			1.17165			0.585827	+	0.810436i	$0.300770\pi$
$242$	9.06937	−	6.22467i	0.583001	−	0.400137i
$243$	−1.00000			−0.0641500
$244$	1.30339	−	4.01142i	0.0834410	−	0.256805i
$245$	2.67625	−	1.94441i	0.170979	−	0.124224i
$246$	−8.54250	−	6.20649i	−0.544650	−	0.395711i
$247$	4.59620	+	14.1457i	0.292449	+	0.900066i
$248$	−1.09904	−	3.38250i	−0.0697892	−	0.214789i
$249$	−5.29268	−	3.84536i	−0.335410	−	0.243690i
$250$	2.52384	−	1.83367i	0.159621	−	0.115972i
$251$	−7.04836	+	21.6926i	−0.444888	+	1.36923i	0.437718	+	0.899112i	$0.355787\pi$
$251$	−7.04836	+	21.6926i	−0.444888	+	1.36923i	−0.882606	+	0.470113i	$0.844213\pi$
$252$	−1.00000			−0.0629941
$253$	−13.8077	−	4.69201i	−0.868082	−	0.294984i
$254$	6.55535			0.411319
$255$	−7.15364	+	22.0166i	−0.447978	+	1.37873i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.61902	+	1.17629i	0.100992	+	0.0733749i	0.637135	−	0.770752i	$-0.280119\pi$
$257$	1.61902	+	1.17629i	0.100992	+	0.0733749i	−0.536143	+	0.844127i	$0.680119\pi$
$258$	−3.47964	−	10.7092i	−0.216633	−	0.666728i
$259$	−0.977763	−	3.00925i	−0.0607552	−	0.186985i
$260$	5.91072	+	4.29439i	0.366567	+	0.266327i
$261$	5.65303	−	4.10716i	0.349913	−	0.254227i
$262$	6.12592	−	18.8536i	0.378460	−	1.16478i
$263$	19.7584			1.21836			0.609178	−	0.793034i	$-0.291500\pi$
$263$	19.7584			1.21836			0.609178	+	0.793034i	$0.291500\pi$
$264$	−1.98527	+	2.65682i	−0.122185	+	0.163516i
$265$	−22.6068			−1.38872
$266$	−2.08107	+	6.40486i	−0.127598	+	0.392707i
$267$	2.99901	−	2.17891i	0.183536	−	0.133347i
$268$	−1.67465	−	1.21670i	−0.102296	−	0.0743221i
$269$	−5.34323	−	16.4448i	−0.325782	−	1.00265i	−0.971086	−	0.238729i	$-0.923269\pi$
$269$	−5.34323	−	16.4448i	−0.325782	−	1.00265i	0.645304	−	0.763926i	$-0.276731\pi$
$270$	1.02224	+	3.14612i	0.0622114	+	0.191467i
$271$	13.7314	+	9.97647i	0.834125	+	0.606027i	0.920723	−	0.390216i	$-0.127600\pi$
$271$	13.7314	+	9.97647i	0.834125	+	0.606027i	−0.0865984	+	0.996243i	$0.527600\pi$
$272$	5.66152	−	4.11333i	0.343280	−	0.249408i
$273$	0.682489	−	2.10049i	0.0413061	−	0.127127i
$274$	17.9503			1.08442
$275$	−18.8261	+	5.83907i	−1.13526	+	0.352109i
$276$	4.39698			0.264667
$277$	6.10391	−	18.7859i	0.366749	−	1.12874i	−0.582130	−	0.813096i	$-0.697781\pi$
$277$	6.10391	−	18.7859i	0.366749	−	1.12874i	0.948879	−	0.315641i	$-0.102219\pi$
$278$	−2.64187	+	1.91943i	−0.158449	+	0.115120i
$279$	2.87733	+	2.09050i	0.172261	+	0.125155i
$280$	1.02224	+	3.14612i	0.0610903	+	0.188017i
$281$	−2.35263	−	7.24065i	−0.140346	−	0.431941i	0.856037	−	0.516914i	$-0.172919\pi$
$281$	−2.35263	−	7.24065i	−0.140346	−	0.431941i	−0.996383	+	0.0849735i	$0.972919\pi$
$282$	0.317511	+	0.230685i	0.0189075	+	0.0137371i
$283$	0.0608772	−	0.0442299i	0.00361877	−	0.00262919i	−0.585974	−	0.810330i	$-0.699288\pi$
$283$	0.0608772	−	0.0442299i	0.00361877	−	0.00262919i	0.589593	+	0.807700i	$0.299288\pi$
$284$	3.85410	−	11.8617i	0.228699	−	0.703863i
$285$	22.2778			1.31962
$286$	−4.22570	−	5.98328i	−0.249871	−	0.353799i
$287$	10.5591			0.623284
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−25.8661	+	18.7929i	−1.52154	+	1.10546i
$290$	−18.7004	−	13.5866i	−1.09812	−	0.797833i
$291$	0.223719	+	0.688535i	0.0131146	+	0.0403627i
$292$	−2.17625	−	6.69781i	−0.127355	−	0.391960i
$293$	−8.69446	−	6.31690i	−0.507936	−	0.369037i	0.304104	−	0.952639i	$-0.401643\pi$
$293$	−8.69446	−	6.31690i	−0.507936	−	0.369037i	−0.812040	+	0.583602i	$0.801643\pi$
$294$	0.809017	−	0.587785i	0.0471828	−	0.0342803i
$295$	7.83290	−	24.1072i	0.456049	−	1.40357i
$296$	3.16411			0.183910
$297$	0.0444738	−	3.31633i	0.00258063	−	0.192433i
$298$	−2.18430			−0.126533
$299$	−3.00089	+	9.23579i	−0.173546	+	0.534119i
$300$	4.80803	−	3.49324i	0.277592	−	0.201682i
$301$	9.10982	+	6.61867i	0.525081	+	0.381494i
$302$	−1.92783	−	5.93326i	−0.110934	−	0.341421i
$303$	−3.79667	−	11.6849i	−0.218113	−	0.671282i
$304$	−5.44830	−	3.95842i	−0.312481	−	0.227031i
$305$	11.2880	−	8.20125i	0.646352	−	0.469602i
$306$	−2.16251	+	6.65551i	−0.123622	+	0.380470i
$307$	−17.4877			−0.998076			−0.499038	−	0.866580i	$-0.666313\pi$
$307$	−17.4877			−0.998076			−0.499038	+	0.866580i	$0.666313\pi$
$308$	0.0444738	−	3.31633i	0.00253413	−	0.188965i
$309$	−8.19413			−0.466148
$310$	3.63566	−	11.1894i	0.206492	−	0.635516i
$311$	−20.9564	+	15.2257i	−1.18833	+	0.863372i	−0.993087	−	0.117383i	$-0.962549\pi$
$311$	−20.9564	+	15.2257i	−1.18833	+	0.863372i	−0.195243	+	0.980755i	$0.562549\pi$
$312$	1.78678	+	1.29817i	0.101157	+	0.0734945i
$313$	−0.800695	−	2.46428i	−0.0452579	−	0.139290i	0.925874	−	0.377832i	$-0.123330\pi$
$313$	−0.800695	−	2.46428i	−0.0452579	−	0.139290i	−0.971132	+	0.238543i	$0.923330\pi$
$314$	4.17912	+	12.8620i	0.235841	+	0.725845i
$315$	−2.67625	−	1.94441i	−0.150790	−	0.109555i
$316$	−5.89107	+	4.28011i	−0.331399	+	0.240775i
$317$	2.34137	−	7.20601i	0.131505	−	0.404730i	−0.863525	−	0.504306i	$-0.831749\pi$
$317$	2.34137	−	7.20601i	0.131505	−	0.404730i	0.995030	+	0.0995757i	$0.0317485\pi$
$318$	−6.83391			−0.383227
$319$	13.3693	+	18.9299i	0.748536	+	1.05987i
$320$	−3.30803			−0.184924
$321$	−0.844997	+	2.60063i	−0.0471631	+	0.145153i
$322$	−3.55723	+	2.58448i	−0.198237	+	0.144027i
$323$	38.1273	+	27.7011i	2.12146	+	1.54133i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	4.05607	+	12.4833i	0.224990	+	0.692448i
$326$	10.8541	+	7.88597i	0.601153	+	0.436763i
$327$	−13.3368	+	9.68974i	−0.737526	+	0.535844i
$328$	−3.26294	+	10.0423i	−0.180166	+	0.554494i
$329$	−0.392465			−0.0216373
$330$	−10.4790	+	3.25015i	−0.576852	+	0.178915i
$331$	5.57929			0.306666			0.153333	−	0.988175i	$-0.450999\pi$
$331$	5.57929			0.306666			0.153333	+	0.988175i	$0.450999\pi$
$332$	−2.02163	+	6.22192i	−0.110951	+	0.341472i
$333$	−2.55982	+	1.85982i	−0.140277	+	0.101917i
$334$	−4.17161	−	3.03085i	−0.228260	−	0.165841i
$335$	−2.11601	−	6.51242i	−0.115610	−	0.355811i
$336$	0.309017	+	0.951057i	0.0168583	+	0.0518844i
$337$	0.306428	+	0.222633i	0.0166922	+	0.0121276i	0.596100	−	0.802910i	$-0.296716\pi$
$337$	0.306428	+	0.222633i	0.0166922	+	0.0121276i	−0.579408	+	0.815038i	$0.696716\pi$
$338$	6.57097	−	4.77409i	0.357414	−	0.259676i
$339$	−0.107285	+	0.330189i	−0.00582692	+	0.0179334i
$340$	23.1497			1.25547
$341$	−7.06075	+	9.44919i	−0.382361	+	0.511702i
$342$	6.73447			0.364158
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−9.10982	+	6.61867i	−0.491168	+	0.356855i
$345$	11.7674	+	8.54952i	0.633536	+	0.460291i
$346$	7.45641	+	22.9485i	0.400859	+	1.23372i
$347$	−2.13041	−	6.55673i	−0.114366	−	0.351984i	0.877448	−	0.479672i	$-0.159244\pi$
$347$	−2.13041	−	6.55673i	−0.114366	−	0.351984i	−0.991814	+	0.127688i	$0.959244\pi$
$348$	−5.65303	−	4.10716i	−0.303034	−	0.220167i
$349$	−13.2691	+	9.64055i	−0.710278	+	0.516047i	−0.883263	−	0.468877i	$-0.844659\pi$
$349$	−13.2691	+	9.64055i	−0.710278	+	0.516047i	0.172986	+	0.984924i	$0.444659\pi$
$350$	−1.83650	+	5.65218i	−0.0981652	+	0.302122i
$351$	−2.20858			−0.117885
$352$	3.14027	+	1.06710i	0.167377	+	0.0568765i
$353$	−31.5354			−1.67846			−0.839229	−	0.543778i	$-0.816993\pi$
$353$	−31.5354			−1.67846			−0.839229	+	0.543778i	$0.816993\pi$
$354$	2.36785	−	7.28748i	0.125850	−	0.387325i
$355$	33.3786	−	24.2509i	1.77155	−	1.28711i
$356$	−2.99901	−	2.17891i	−0.158947	−	0.115482i
$357$	−2.16251	−	6.65551i	−0.114452	−	0.352247i
$358$	7.05921	+	21.7260i	0.373091	+	1.14825i
$359$	−5.68376	−	4.12949i	−0.299977	−	0.217946i	0.427607	−	0.903965i	$-0.359357\pi$
$359$	−5.68376	−	4.12949i	−0.299977	−	0.217946i	−0.727584	+	0.686019i	$0.759357\pi$
$360$	2.67625	−	1.94441i	0.141051	−	0.102479i
$361$	8.14354	−	25.0632i	0.428607	−	1.31912i
$362$	6.59177			0.346456
$363$	10.9960	+	0.294979i	0.577143	+	0.0154824i
$364$	−2.20858			−0.115761
$365$	7.19910	−	22.1565i	0.376818	−	1.15973i
$366$	3.41232	−	2.47919i	0.178365	−	0.129590i
$367$	17.5136	+	12.7244i	0.914201	+	0.664206i	0.942074	−	0.335406i	$-0.108873\pi$
$367$	17.5136	+	12.7244i	0.914201	+	0.664206i	−0.0278728	+	0.999611i	$0.508873\pi$
$368$	−1.35874	−	4.18177i	−0.0708292	−	0.217990i
$369$	−3.26294	−	10.0423i	−0.169862	−	0.522782i
$370$	8.46795	+	6.15232i	0.440228	+	0.319844i
$371$	5.52875	−	4.01687i	0.287039	−	0.208546i
$372$	1.09904	−	3.38250i	0.0569826	−	0.175375i
$373$	1.74770			0.0904925			0.0452462	−	0.998976i	$-0.485593\pi$
$373$	1.74770			0.0904925			0.0452462	+	0.998976i	$0.485593\pi$
$374$	−21.9757	−	7.46758i	−1.13634	−	0.386139i
$375$	3.11963			0.161097
$376$	0.121278	−	0.373256i	0.00625445	−	0.0192492i
$377$	12.4852	−	9.07101i	0.643019	−	0.467181i
$378$	−0.809017	−	0.587785i	−0.0416113	−	0.0302324i
$379$	−2.86173	−	8.80751i	−0.146997	−	0.452412i	0.850265	−	0.526355i	$-0.176442\pi$
$379$	−2.86173	−	8.80751i	−0.146997	−	0.452412i	−0.997262	+	0.0739433i	$0.976442\pi$
$380$	−6.88422	−	21.1875i	−0.353153	−	1.08689i
$381$	5.30339	+	3.85314i	0.271701	+	0.197402i
$382$	−13.5379	+	9.83583i	−0.692657	+	0.503245i
$383$	1.44267	−	4.44009i	0.0737171	−	0.226878i	−0.907408	−	0.420250i	$-0.861942\pi$
$383$	1.44267	−	4.44009i	0.0737171	−	0.226878i	0.981126	+	0.193372i	$0.0619424\pi$
$384$	−1.00000			−0.0510310
$385$	6.56732	−	8.78885i	0.334702	−	0.447921i
$386$	21.1542			1.07672
$387$	3.47964	−	10.7092i	0.176880	−	0.544381i
$388$	0.585703	−	0.425538i	0.0297346	−	0.0216034i
$389$	13.2557	+	9.63084i	0.672091	+	0.488303i	0.870725	−	0.491771i	$-0.163650\pi$
$389$	13.2557	+	9.63084i	0.672091	+	0.488303i	−0.198633	+	0.980074i	$0.563650\pi$
$390$	2.25769	+	6.94847i	0.114323	+	0.351849i
$391$	9.50849	+	29.2641i	0.480865	+	1.47995i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	16.0379	−	11.6522i	0.809003	−	0.587775i
$394$	−5.65016	+	17.3894i	−0.284651	+	0.876065i
$395$	−24.0883			−1.21201
$396$	−3.16776	+	0.982504i	−0.159186	+	0.0493727i
$397$	25.5140			1.28051			0.640255	−	0.768163i	$-0.278829\pi$
$397$	25.5140			1.28051			0.640255	+	0.768163i	$0.278829\pi$
$398$	1.11217	−	3.42292i	0.0557482	−	0.171575i
$399$	−5.44830	+	3.95842i	−0.272756	+	0.198169i
$400$	−4.80803	−	3.49324i	−0.240401	−	0.174662i
$401$	−6.37535	−	19.6213i	−0.318370	−	0.979841i	−0.974345	−	0.225059i	$-0.927742\pi$
$401$	−6.37535	−	19.6213i	−0.318370	−	0.979841i	0.655975	−	0.754782i	$-0.272258\pi$
$402$	−0.639660	−	1.96867i	−0.0319033	−	0.0981883i
$403$	6.35481	+	4.61704i	0.316556	+	0.229991i
$404$	−9.93981	+	7.22169i	−0.494524	+	0.359293i
$405$	−1.02224	+	3.14612i	−0.0507954	+	0.156332i
$406$	6.98752			0.346785
$407$	−6.05391	−	8.57190i	−0.300081	−	0.424893i
$408$	6.99802			0.346454
$409$	−2.61155	+	8.03751i	−0.129133	+	0.397429i	−0.994631	−	0.103482i	$-0.967002\pi$
$409$	−2.61155	+	8.03751i	−0.129133	+	0.397429i	0.865499	+	0.500911i	$0.167002\pi$
$410$	−28.2588	+	20.5312i	−1.39560	+	1.01397i
$411$	14.5221	+	10.5509i	0.716324	+	0.520440i
$412$	2.53212	+	7.79308i	0.124749	+	0.383937i
$413$	2.36785	+	7.28748i	0.116514	+	0.358593i
$414$	3.55723	+	2.58448i	0.174828	+	0.127020i
$415$	−17.5083	+	12.7206i	−0.859451	+	0.624428i
$416$	0.682489	−	2.10049i	0.0334618	−	0.102985i
$417$	−3.26553			−0.159914
$418$	−0.299507	+	22.3337i	−0.0146494	+	1.09238i
$419$	−20.2753			−0.990512			−0.495256	−	0.868747i	$-0.664926\pi$
$419$	−20.2753			−0.990512			−0.495256	+	0.868747i	$0.664926\pi$
$420$	−1.02224	+	3.14612i	−0.0498801	+	0.153515i
$421$	−7.33153	+	5.32667i	−0.357317	+	0.259606i	−0.751932	−	0.659241i	$-0.770878\pi$
$421$	−7.33153	+	5.32667i	−0.357317	+	0.259606i	0.394615	+	0.918846i	$0.370878\pi$
$422$	3.83876	+	2.78902i	0.186868	+	0.135767i
$423$	0.121278	+	0.373256i	0.00589675	+	0.0181483i
$424$	2.11180	+	6.49944i	0.102558	+	0.315641i
$425$	33.6467	+	24.4457i	1.63210	+	1.18579i
$426$	10.0902	−	7.33094i	0.488870	−	0.355185i
$427$	−1.30339	+	4.01142i	−0.0630755	+	0.194126i
$428$	2.73447			0.132175
$429$	0.0982239	−	7.32438i	0.00474230	−	0.353624i
$430$	−37.2496			−1.79633
$431$	9.50774	−	29.2618i	0.457972	−	1.40949i	−0.409639	−	0.912248i	$-0.634345\pi$
$431$	9.50774	−	29.2618i	0.457972	−	1.40949i	0.867611	−	0.497244i	$-0.165655\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	13.4505	+	9.77237i	0.646390	+	0.469630i	0.862040	−	0.506841i	$-0.169187\pi$
$433$	13.4505	+	9.77237i	0.646390	+	0.469630i	−0.215649	+	0.976471i	$0.569187\pi$
$434$	1.09904	+	3.38250i	0.0527557	+	0.162365i
$435$	−7.14290	−	21.9836i	−0.342476	−	1.05403i
$436$	13.3368	+	9.68974i	0.638716	+	0.464054i
$437$	23.9560	−	17.4051i	1.14597	−	0.832598i
$438$	2.17625	−	6.69781i	0.103985	−	0.320034i
$439$	−14.0587			−0.670986			−0.335493	−	0.942043i	$-0.608903\pi$
$439$	−14.0587			−0.670986			−0.335493	+	0.942043i	$0.608903\pi$
$440$	6.32928	+	8.96180i	0.301736	+	0.427237i
$441$	1.00000			0.0476190
$442$	−4.77608	+	14.6992i	−0.227175	+	0.699172i
$443$	−8.35295	+	6.06877i	−0.396861	+	0.288336i	−0.768261	−	0.640137i	$-0.778878\pi$
$443$	−8.35295	+	6.06877i	−0.396861	+	0.288336i	0.371400	+	0.928473i	$0.378878\pi$
$444$	2.55982	+	1.85982i	0.121484	+	0.0882630i
$445$	−3.78941	−	11.6626i	−0.179635	−	0.552861i
$446$	−8.80339	−	27.0940i	−0.416853	−	1.28294i
$447$	−1.76713	−	1.28390i	−0.0835825	−	0.0607262i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	−9.21950	+	28.3747i	−0.435095	+	1.33909i	0.457894	+	0.889007i	$0.348604\pi$
$449$	−9.21950	+	28.3747i	−0.435095	+	1.33909i	−0.892989	+	0.450078i	$0.851396\pi$
$450$	5.94305			0.280158
$451$	33.4487	−	10.3744i	1.57504	−	0.488510i
$452$	0.347181			0.0163300
$453$	1.92783	−	5.93326i	0.0905775	−	0.278769i
$454$	−19.5788	+	14.2248i	−0.918876	+	0.667603i
$455$	−5.91072	−	4.29439i	−0.277099	−	0.201324i
$456$	−2.08107	−	6.40486i	−0.0974548	−	0.299935i
$457$	6.95076	+	21.3922i	0.325143	+	1.00069i	0.971376	+	0.237547i	$0.0763433\pi$
$457$	6.95076	+	21.3922i	0.325143	+	1.00069i	−0.646233	+	0.763140i	$0.723657\pi$
$458$	10.2632	+	7.45667i	0.479569	+	0.348427i
$459$	−5.66152	+	4.11333i	−0.264257	+	0.191994i
$460$	4.49475	−	13.8334i	0.209569	−	0.644987i
$461$	16.9679			0.790273			0.395137	−	0.918622i	$-0.370697\pi$
$461$	16.9679			0.790273			0.395137	+	0.918622i	$0.370697\pi$
$462$	1.98527	−	2.65682i	0.0923630	−	0.123607i
$463$	4.29997			0.199837			0.0999184	−	0.994996i	$-0.468142\pi$
$463$	4.29997			0.199837			0.0999184	+	0.994996i	$0.468142\pi$
$464$	−2.15926	+	6.64553i	−0.100241	+	0.308511i
$465$	9.51828	−	6.91544i	0.441400	−	0.320696i
$466$	−18.6712	−	13.5654i	−0.864928	−	0.628407i
$467$	−1.24766	−	3.83991i	−0.0577349	−	0.177690i	0.918030	−	0.396511i	$-0.129779\pi$
$467$	−1.24766	−	3.83991i	−0.0577349	−	0.177690i	−0.975765	+	0.218821i	$0.929779\pi$
$468$	0.682489	+	2.10049i	0.0315481	+	0.0970950i
$469$	1.67465	+	1.21670i	0.0773282	+	0.0561822i
$470$	1.05033	−	0.763113i	0.0484483	−	0.0351998i
$471$	−4.17912	+	12.8620i	−0.192564	+	0.592650i
$472$	−7.66251			−0.352696
$473$	35.3606	+	12.0159i	1.62588	+	0.552492i
$474$	−7.28176			−0.334463
$475$	12.3679	−	38.0644i	0.567477	−	1.74651i
$476$	−5.66152	+	4.11333i	−0.259495	+	0.188534i
$477$	−5.52875	−	4.01687i	−0.253144	−	0.183920i
$478$	4.07820	+	12.5514i	0.186532	+	0.574088i
$479$	2.73325	+	8.41206i	0.124885	+	0.384357i	0.993880	−	0.110464i	$-0.0352337\pi$
$479$	2.73325	+	8.41206i	0.124885	+	0.384357i	−0.868995	+	0.494821i	$0.835234\pi$
$480$	−2.67625	−	1.94441i	−0.122154	−	0.0887498i
$481$	−5.65357	+	4.10756i	−0.257780	+	0.187288i
$482$	5.62069	−	17.2987i	0.256016	−	0.787935i
$483$	−4.39698			−0.200069
$484$	−3.11742	−	10.5490i	−0.141701	−	0.479501i
$485$	2.39491			0.108747
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	14.8675	−	10.8018i	0.673709	−	0.489478i	−0.197556	−	0.980292i	$-0.563300\pi$
$487$	14.8675	−	10.8018i	0.673709	−	0.489478i	0.871265	+	0.490813i	$0.163300\pi$
$488$	−3.41232	−	2.47919i	−0.154468	−	0.112228i
$489$	4.14590	+	12.7598i	0.187484	+	0.577016i
$490$	−1.02224	−	3.14612i	−0.0461800	−	0.142127i
$491$	17.3344	+	12.5942i	0.782290	+	0.568367i	0.905666	−	0.423993i	$-0.139372\pi$
$491$	17.3344	+	12.5942i	0.782290	+	0.568367i	−0.123375	+	0.992360i	$0.539372\pi$
$492$	−8.54250	+	6.20649i	−0.385125	+	0.279810i
$493$	15.1106	−	46.5056i	0.680546	−	2.09451i
$494$	14.8736			0.669196
$495$	−10.3881	−	3.52999i	−0.466911	−	0.158661i
$496$	−3.55657			−0.159695
$497$	−3.85410	+	11.8617i	−0.172880	+	0.532070i
$498$	−5.29268	+	3.84536i	−0.237171	+	0.172315i
$499$	−5.77948	−	4.19904i	−0.258725	−	0.187975i	0.450860	−	0.892595i	$-0.351117\pi$
$499$	−5.77948	−	4.19904i	−0.258725	−	0.187975i	−0.709585	+	0.704620i	$0.751117\pi$
$500$	−0.964020	−	2.96695i	−0.0431123	−	0.132686i
$501$	−1.59341	−	4.90402i	−0.0711885	−	0.219096i
$502$	18.4528	+	13.4068i	0.823590	+	0.598373i
$503$	−17.0879	+	12.4151i	−0.761910	+	0.553560i	−0.899496	−	0.436930i	$-0.856066\pi$
$503$	−17.0879	+	12.4151i	−0.761910	+	0.553560i	0.137586	+	0.990490i	$0.456066\pi$
$504$	−0.309017	+	0.951057i	−0.0137647	+	0.0423634i
$505$	−40.6433			−1.80860
$506$	−8.72917	+	11.6820i	−0.388059	+	0.519328i
$507$	8.12217			0.360718
$508$	2.02571	−	6.23451i	0.0898766	−	0.276612i
$509$	−11.3250	+	8.22807i	−0.501971	+	0.364703i	−0.809769	−	0.586749i	$-0.800408\pi$
$509$	−11.3250	+	8.22807i	−0.501971	+	0.364703i	0.307799	+	0.951452i	$0.400408\pi$
$510$	18.7285	+	13.6070i	0.829310	+	0.602529i
$511$	2.17625	+	6.69781i	0.0962717	+	0.296294i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	5.44830	+	3.95842i	0.240548	+	0.174769i
$514$	1.61902	−	1.17629i	0.0714120	−	0.0518839i
$515$	−8.37634	+	25.7797i	−0.369106	+	1.13599i
$516$	−11.2604			−0.495709
$517$	−1.24323	+	0.385598i	−0.0546773	+	0.0169586i
$518$	−3.16411			−0.139023
$519$	−7.45641	+	22.9485i	−0.327300	+	1.00733i
$520$	5.91072	−	4.29439i	0.259202	−	0.188321i
$521$	23.9884	+	17.4286i	1.05095	+	0.763559i	0.972393	−	0.233350i	$-0.0749688\pi$
$521$	23.9884	+	17.4286i	1.05095	+	0.763559i	0.0785567	+	0.996910i	$0.474969\pi$
$522$	−2.15926	−	6.64553i	−0.0945084	−	0.290867i
$523$	1.96341	+	6.04275i	0.0858539	+	0.264231i	0.984762	−	0.173905i	$-0.0556387\pi$
$523$	1.96341	+	6.04275i	0.0858539	+	0.264231i	−0.898908	+	0.438136i	$0.855639\pi$
$524$	−16.0379	−	11.6522i	−0.700617	−	0.509028i
$525$	−4.80803	+	3.49324i	−0.209840	+	0.152457i
$526$	6.10568	−	18.7914i	0.266221	−	0.819342i
$527$	24.8890			1.08418
$528$	1.91331	+	2.70911i	0.0832660	+	0.117899i
$529$	−3.66661			−0.159418
$530$	−6.98588	+	21.5003i	−0.303447	+	0.933914i
$531$	6.19910	−	4.50391i	0.269018	−	0.195453i
$532$	5.44830	+	3.95842i	0.236214	+	0.171619i
$533$	−7.20648	−	22.1793i	−0.312147	−	0.960690i
$534$	−1.14552	−	3.52555i	−0.0495715	−	0.152565i
$535$	7.31812	+	5.31693i	0.316390	+	0.229871i
$536$	−1.67465	+	1.21670i	−0.0723339	+	0.0525537i
$537$	−7.05921	+	21.7260i	−0.304627	+	0.937546i
$538$	−17.2910			−0.745470
$539$	−0.0444738	+	3.31633i	−0.00191562	+	0.142844i
$540$	3.30803			0.142355
$541$	−4.04775	+	12.4577i	−0.174026	+	0.535597i	−0.999588	−	0.0287147i	$-0.990859\pi$
$541$	−4.04775	+	12.4577i	−0.174026	+	0.535597i	0.825561	+	0.564312i	$0.190859\pi$
$542$	13.7314	−	9.97647i	0.589815	−	0.428526i
$543$	5.33285	+	3.87455i	0.228855	+	0.166273i
$544$	−2.16251	−	6.65551i	−0.0927168	−	0.285353i
$545$	16.8517	+	51.8643i	0.721850	+	2.22162i
$546$	−1.78678	−	1.29817i	−0.0764671	−	0.0555566i
$547$	−22.8698	+	16.6159i	−0.977842	+	0.710444i	−0.957225	−	0.289344i	$-0.906563\pi$
$547$	−22.8698	+	16.6159i	−0.977842	+	0.710444i	−0.0206165	+	0.999787i	$0.506563\pi$
$548$	5.54696	−	17.0718i	0.236954	−	0.729271i
$549$	4.21786			0.180014
$550$	−0.264310	+	19.7091i	−0.0112702	+	0.840399i
$551$	−47.0573			−2.00471
$552$	1.35874	−	4.18177i	0.0578318	−	0.177988i
$553$	5.89107	−	4.28011i	0.250514	−	0.182009i
$554$	−15.9803	−	11.6103i	−0.678936	−	0.493276i
$555$	3.23447	+	9.95467i	0.137296	+	0.422552i
$556$	1.00910	+	3.10571i	0.0427956	+	0.131711i
$557$	−1.58735	−	1.15328i	−0.0672581	−	0.0488658i	0.553648	−	0.832751i	$-0.313235\pi$
$557$	−1.58735	−	1.15328i	−0.0672581	−	0.0488658i	−0.620906	+	0.783885i	$0.713235\pi$
$558$	2.87733	−	2.09050i	0.121807	−	0.0884980i
$559$	7.68507	−	23.6522i	0.325044	−	1.00038i
$560$	3.30803			0.139790
$561$	−13.3894	−	18.9584i	−0.565300	−	0.800423i
$562$	−7.61327			−0.321146
$563$	−4.54785	+	13.9968i	−0.191669	+	0.589896i	0.808330	+	0.588729i	$0.200371\pi$
$563$	−4.54785	+	13.9968i	−0.191669	+	0.589896i	−0.999999	+	0.00116703i	$0.999629\pi$
$564$	0.317511	−	0.230685i	0.0133696	−	0.00971359i
$565$	0.929144	+	0.675063i	0.0390894	+	0.0284001i
$566$	−0.0232530	−	0.0715654i	−0.000977397	−	0.00300812i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	−10.0902	−	7.33094i	−0.423374	−	0.307599i
$569$	19.4898	−	14.1602i	0.817055	−	0.593625i	−0.0988123	−	0.995106i	$-0.531504\pi$
$569$	19.4898	−	14.1602i	0.817055	−	0.593625i	0.915867	+	0.401481i	$0.131504\pi$
$570$	6.88422	−	21.1875i	0.288348	−	0.887445i
$571$	−8.32182			−0.348257			−0.174129	−	0.984723i	$-0.555711\pi$
$571$	−8.32182			−0.348257			−0.174129	+	0.984723i	$0.555711\pi$
$572$	−6.99625	+	2.16994i	−0.292528	+	0.0907298i
$573$	−16.7337			−0.699061
$574$	3.26294	−	10.0423i	0.136193	−	0.419158i
$575$	21.1408	−	15.3597i	0.881632	−	0.640543i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−0.668368	−	2.05703i	−0.0278245	−	0.0856351i	0.936180	−	0.351521i	$-0.114335\pi$
$577$	−0.668368	−	2.05703i	−0.0278245	−	0.0856351i	−0.964004	+	0.265886i	$0.914335\pi$
$578$	9.87999	+	30.4075i	0.410953	+	1.26478i
$579$	17.1141	+	12.4341i	0.711237	+	0.516744i
$580$	−18.7004	+	13.5866i	−0.776490	+	0.564153i
$581$	2.02163	−	6.22192i	0.0838712	−	0.258129i
$582$	0.723969			0.0300095
$583$	13.5672	−	18.1565i	0.561894	−	0.751966i
$584$	−7.04250			−0.291421
$585$	−2.25769	+	6.94847i	−0.0933441	+	0.287284i
$586$	−8.69446	+	6.31690i	−0.359165	+	0.260949i
$587$	5.85730	+	4.25558i	0.241757	+	0.175647i	0.702066	−	0.712112i	$-0.252261\pi$
$587$	5.85730	+	4.25558i	0.241757	+	0.175647i	−0.460309	+	0.887759i	$0.652261\pi$
$588$	−0.309017	−	0.951057i	−0.0127436	−	0.0392209i
$589$	−7.40146	−	22.7793i	−0.304972	−	0.938607i
$590$	−20.5068	−	14.8991i	−0.844251	−	0.613384i
$591$	−14.7923	+	10.7472i	−0.608474	+	0.442082i
$592$	0.977763	−	3.00925i	0.0401858	−	0.123679i
$593$	40.2594			1.65326			0.826628	−	0.562749i	$-0.190256\pi$
$593$	40.2594			1.65326			0.826628	+	0.562749i	$0.190256\pi$
$594$	−3.14027	−	1.06710i	−0.128847	−	0.0437836i
$595$	−23.1497			−0.949043
$596$	−0.674984	+	2.07739i	−0.0276484	+	0.0850932i
$597$	2.91171	−	2.11548i	0.119168	−	0.0865808i
$598$	7.85643	+	5.70803i	0.321273	+	0.233419i
$599$	−10.7794	−	33.1757i	−0.440436	−	1.35552i	−0.887412	−	0.460977i	$-0.847499\pi$
$599$	−10.7794	−	33.1757i	−0.440436	−	1.35552i	0.446976	−	0.894546i	$-0.352501\pi$
$600$	−1.83650	−	5.65218i	−0.0749749	−	0.230749i
$601$	5.19159	+	3.77191i	0.211770	+	0.153860i	0.688614	−	0.725128i	$-0.258219\pi$
$601$	5.19159	+	3.77191i	0.211770	+	0.153860i	−0.476844	+	0.878988i	$0.658219\pi$
$602$	9.10982	−	6.61867i	0.371288	−	0.269757i
$603$	0.639660	−	1.96867i	0.0260490	−	0.0801704i
$604$	−6.23860			−0.253845
$605$	12.1686	−	34.2934i	0.494724	−	1.39422i
$606$	−12.2863			−0.499096
$607$	−12.4967	+	38.4608i	−0.507224	+	1.56108i	0.289775	+	0.957095i	$0.406420\pi$
$607$	−12.4967	+	38.4608i	−0.507224	+	1.56108i	−0.796999	+	0.603981i	$0.793580\pi$
$608$	−5.44830	+	3.95842i	−0.220958	+	0.160535i
$609$	5.65303	+	4.10716i	0.229072	+	0.166431i
$610$	−4.31165	−	13.2699i	−0.174574	−	0.537282i
$611$	0.267853	+	0.824367i	0.0108362	+	0.0333503i
$612$	5.66152	+	4.11333i	0.228853	+	0.166272i
$613$	16.4310	−	11.9378i	0.663641	−	0.482163i	−0.204250	−	0.978919i	$-0.565475\pi$
$613$	16.4310	−	11.9378i	0.663641	−	0.482163i	0.867891	+	0.496755i	$0.165475\pi$
$614$	−5.40400	+	16.6318i	−0.218088	+	0.671204i
$615$	−34.9298			−1.40851
$616$	−3.14027	−	1.06710i	−0.126525	−	0.0429946i
$617$	8.89924			0.358270			0.179135	−	0.983824i	$-0.442670\pi$
$617$	8.89924			0.358270			0.179135	+	0.983824i	$0.442670\pi$
$618$	−2.53212	+	7.79308i	−0.101857	+	0.313484i
$619$	25.6329	−	18.6234i	1.03027	−	0.748537i	0.0619090	−	0.998082i	$-0.480281\pi$
$619$	25.6329	−	18.6234i	1.03027	−	0.748537i	0.968363	+	0.249545i	$0.0802811\pi$
$620$	−9.51828	−	6.91544i	−0.382263	−	0.277731i
$621$	1.35874	+	4.18177i	0.0545244	+	0.167809i
$622$	8.00464	+	24.6357i	0.320957	+	0.987803i
$623$	2.99901	+	2.17891i	0.120153	+	0.0872961i
$624$	1.78678	−	1.29817i	0.0715285	−	0.0519685i
$625$	−5.99351	+	18.4461i	−0.239740	+	0.737845i
$626$	−2.59110			−0.103561
$627$	−13.3697	+	17.8923i	−0.533935	+	0.714549i
$628$	13.5239			0.539663
$629$	−6.84241	+	21.0588i	−0.272825	+	0.839668i
$630$	−2.67625	+	1.94441i	−0.106624	+	0.0774672i
$631$	−28.8603	−	20.9682i	−1.14891	−	0.834733i	−0.160575	−	0.987024i	$-0.551335\pi$
$631$	−28.8603	−	20.9682i	−1.14891	−	0.834733i	−0.988336	+	0.152291i	$0.951335\pi$
$632$	2.25019	+	6.92537i	0.0895077	+	0.275476i
$633$	1.46628	+	4.51273i	0.0582792	+	0.179365i
$634$	−6.12980	−	4.45356i	−0.243445	−	0.176873i
$635$	17.5438	−	12.7463i	0.696203	−	0.505821i
$636$	−2.11180	+	6.49944i	−0.0837381	+	0.257720i
$637$	2.20858			0.0875072
$638$	22.1348	−	6.86527i	0.876324	−	0.271799i
$639$	12.4721			0.493390
$640$	−1.02224	+	3.14612i	−0.0404075	+	0.124361i
$641$	−35.9668	+	26.1314i	−1.42060	+	1.03213i	−0.428931	+	0.903337i	$0.641110\pi$
$641$	−35.9668	+	26.1314i	−1.42060	+	1.03213i	−0.991672	+	0.128791i	$0.958890\pi$
$642$	2.21223	+	1.60728i	0.0873098	+	0.0634343i
$643$	−10.5884	−	32.5877i	−0.417566	−	1.28513i	−0.909936	−	0.414749i	$-0.863869\pi$
$643$	−10.5884	−	32.5877i	−0.417566	−	1.28513i	0.492370	−	0.870386i	$-0.336131\pi$
$644$	1.35874	+	4.18177i	0.0535419	+	0.164785i
$645$	−30.1355	−	21.8947i	−1.18659	−	0.862105i
$646$	38.1273	−	27.7011i	1.50010	−	1.08989i
$647$	7.10906	−	21.8794i	0.279486	−	0.860169i	−0.708512	−	0.705699i	$-0.750633\pi$
$647$	7.10906	−	21.8794i	0.279486	−	0.860169i	0.987997	−	0.154470i	$-0.0493670\pi$
$648$	1.00000			0.0392837
$649$	14.6607	+	20.7585i	0.575484	+	0.814844i
$650$	13.1257			0.514833
$651$	−1.09904	+	3.38250i	−0.0430748	+	0.132571i
$652$	10.8541	−	7.88597i	0.425079	−	0.308838i
$653$	1.24268	+	0.902863i	0.0486300	+	0.0353318i	0.611835	−	0.790986i	$-0.290432\pi$
$653$	1.24268	+	0.902863i	0.0486300	+	0.0353318i	−0.563205	+	0.826317i	$0.690432\pi$
$654$	5.09420	+	15.6783i	0.199199	+	0.613071i
$655$	−20.2647	−	62.3683i	−0.791807	−	2.43693i
$656$	8.54250	+	6.20649i	0.333528	+	0.242323i
$657$	5.69750	−	4.13948i	0.222281	−	0.161496i
$658$	−0.121278	+	0.373256i	−0.00472792	+	0.0145510i
$659$	−12.9361			−0.503921			−0.251960	−	0.967738i	$-0.581075\pi$
$659$	−12.9361			−0.503921			−0.251960	+	0.967738i	$0.581075\pi$
$660$	−0.147120	+	10.9705i	−0.00572666	+	0.427026i
$661$	−28.9632			−1.12654			−0.563270	−	0.826273i	$-0.690457\pi$
$661$	−28.9632			−1.12654			−0.563270	+	0.826273i	$0.690457\pi$
$662$	1.72410	−	5.30622i	0.0670089	−	0.206232i
$663$	−12.5039	+	9.08463i	−0.485612	+	0.352818i
$664$	5.29268	+	3.84536i	0.205396	+	0.149229i
$665$	6.88422	+	21.1875i	0.266959	+	0.821614i
$666$	0.977763	+	3.00925i	0.0378876	+	0.116606i
$667$	−24.8562	−	18.0591i	−0.962436	−	0.699251i
$668$	−4.17161	+	3.03085i	−0.161405	+	0.117267i
$669$	8.80339	−	27.0940i	0.340359	−	1.04752i
$670$	−6.84756			−0.264544
$671$	−0.187584	+	13.9878i	−0.00724160	+	0.539993i
$672$	1.00000			0.0385758
$673$	11.9213	−	36.6900i	0.459532	−	1.41429i	−0.406199	−	0.913785i	$-0.633146\pi$
$673$	11.9213	−	36.6900i	0.459532	−	1.41429i	0.865731	−	0.500510i	$-0.166854\pi$
$674$	0.306428	−	0.222633i	0.0118032	−	0.00857550i
$675$	4.80803	+	3.49324i	0.185061	+	0.134455i
$676$	−2.50989	−	7.72464i	−0.0965341	−	0.297102i
$677$	12.3343	+	37.9610i	0.474045	+	1.45896i	0.847241	+	0.531209i	$0.178262\pi$
$677$	12.3343	+	37.9610i	0.474045	+	1.45896i	−0.373196	+	0.927753i	$0.621738\pi$
$678$	0.280876	+	0.204068i	0.0107870	+	0.00783718i
$679$	−0.585703	+	0.425538i	−0.0224772	+	0.0163307i
$680$	7.15364	−	22.0166i	0.274329	−	0.844299i
$681$	−24.2007			−0.927372
$682$	6.80482	+	9.63513i	0.260570	+	0.368948i
$683$	25.3924			0.971611			0.485806	−	0.874067i	$-0.338526\pi$
$683$	25.3924			0.971611			0.485806	+	0.874067i	$0.338526\pi$
$684$	2.08107	−	6.40486i	0.0795715	−	0.244896i
$685$	48.0396	−	34.9028i	1.83550	−	1.33357i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	3.92020	+	12.0651i	0.149565	+	0.460314i
$688$	3.47964	+	10.7092i	0.132660	+	0.408286i
$689$	−12.2107	−	8.87159i	−0.465191	−	0.337981i
$690$	11.7674	−	8.54952i	0.447978	−	0.325475i
$691$	−4.77557	+	14.6977i	−0.181671	+	0.559127i	−0.999875	−	0.0158016i	$-0.994970\pi$
$691$	−4.77557	+	14.6977i	−0.181671	+	0.559127i	0.818204	+	0.574928i	$0.194970\pi$
$692$	24.1295			0.917265
$693$	3.16776	−	0.982504i	0.120333	−	0.0373222i
$694$	−6.89415			−0.261698
$695$	−3.33815	+	10.2738i	−0.126623	+	0.389706i
$696$	−5.65303	+	4.10716i	−0.214277	+	0.155682i
$697$	−59.7806	−	43.4331i	−2.26435	−	1.64515i
$698$	5.06834	+	15.5987i	0.191839	+	0.590421i
$699$	−7.13178	−	21.9494i	−0.269749	−	0.830201i
$700$	4.80803	+	3.49324i	0.181726	+	0.132032i
$701$	5.70854	−	4.14750i	0.215608	−	0.156649i	−0.474739	−	0.880127i	$-0.657458\pi$
$701$	5.70854	−	4.14750i	0.215608	−	0.156649i	0.690348	+	0.723478i	$0.257458\pi$
$702$	−0.682489	+	2.10049i	−0.0257589	+	0.0792777i
$703$	21.3086			0.803668
$704$	1.98527	−	2.65682i	0.0748226	−	0.100133i
$705$	1.29828			0.0488962
$706$	−9.74497	+	29.9919i	−0.366757	+	1.12876i
$707$	9.93981	−	7.22169i	0.373825	−	0.271600i
$708$	−6.19910	−	4.50391i	−0.232976	−	0.169267i
$709$	1.85534	+	5.71015i	0.0696788	+	0.214449i	0.979832	−	0.199822i	$-0.0640364\pi$
$709$	1.85534	+	5.71015i	0.0696788	+	0.214449i	−0.910153	+	0.414271i	$0.864036\pi$
$710$	−12.7495	−	39.2389i	−0.478479	−	1.47261i
$711$	−5.89107	−	4.28011i	−0.220932	−	0.160517i
$712$	−2.99901	+	2.17891i	−0.112393	+	0.0816581i
$713$	4.83246	−	14.8728i	0.180977	−	0.556990i
$714$	−6.99802			−0.261894
$715$	−22.9430	−	7.79627i	−0.858019	−	0.291564i
$716$	22.8441			0.853723
$717$	−4.07820	+	12.5514i	−0.152303	+	0.468741i
$718$	−5.68376	+	4.12949i	−0.212116	+	0.154111i
$719$	−39.5580	−	28.7406i	−1.47527	−	1.07184i	−0.979045	−	0.203646i	$-0.934721\pi$
$719$	−39.5580	−	28.7406i	−1.47527	−	1.07184i	−0.496221	−	0.868197i	$-0.665279\pi$
$720$	−1.02224	−	3.14612i	−0.0380965	−	0.117249i
$721$	−2.53212	−	7.79308i	−0.0943012	−	0.290229i
$722$	−21.3201	−	15.4899i	−0.793451	−	0.576476i
$723$	14.7152	−	10.6912i	0.547263	−	0.397610i
$724$	2.03697	−	6.26915i	0.0757034	−	0.232991i
$725$	−41.5272			−1.54228
$726$	3.67851	−	10.3667i	0.136522	−	0.384745i
$727$	−30.0098			−1.11300			−0.556502	−	0.830847i	$-0.687857\pi$
$727$	−30.0098			−1.11300			−0.556502	+	0.830847i	$0.687857\pi$
$728$	−0.682489	+	2.10049i	−0.0252947	+	0.0778492i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−18.8475	−	13.6935i	−0.697577	−	0.506819i
$731$	−24.3506	−	74.9434i	−0.900640	−	2.77188i
$732$	−1.30339	−	4.01142i	−0.0481747	−	0.148266i
$733$	20.4352	+	14.8470i	0.754790	+	0.548387i	0.897308	−	0.441405i	$-0.145520\pi$
$733$	20.4352	+	14.8470i	0.754790	+	0.548387i	−0.142518	+	0.989792i	$0.545520\pi$
$734$	17.5136	−	12.7244i	0.646438	−	0.469665i
$735$	1.02224	−	3.14612i	0.0377058	−	0.116046i
$736$	−4.39698			−0.162075
$737$	6.50030	+	2.20887i	0.239442	+	0.0813649i
$738$	−10.5591			−0.388686
$739$	−1.56682	+	4.82217i	−0.0576363	+	0.177386i	−0.975730	−	0.218977i	$-0.929728\pi$
$739$	−1.56682	+	4.82217i	−0.0576363	+	0.177386i	0.918094	+	0.396363i	$0.129728\pi$
$740$	8.46795	−	6.15232i	0.311288	−	0.226164i
$741$	12.0330	+	8.74250i	0.442044	+	0.321164i
$742$	−2.11180	−	6.49944i	−0.0775265	−	0.238602i
$743$	−2.43333	−	7.48903i	−0.0892703	−	0.274746i	0.896448	−	0.443149i	$-0.146139\pi$
$743$	−2.43333	−	7.48903i	−0.0892703	−	0.274746i	−0.985718	+	0.168403i	$0.946139\pi$
$744$	−2.87733	−	2.09050i	−0.105488	−	0.0766415i
$745$	−5.84572	+	4.24717i	−0.214171	+	0.155604i
$746$	0.540069	−	1.66216i	0.0197733	−	0.0608561i
$747$	−6.54212			−0.239364
$748$	−13.8929	+	18.5925i	−0.507977	+	0.679809i
$749$	−2.73447			−0.0999153
$750$	0.964020	−	2.96695i	0.0352010	−	0.108338i
$751$	20.9194	−	15.1989i	0.763361	−	0.554615i	−0.136578	−	0.990629i	$-0.543610\pi$
$751$	20.9194	−	15.1989i	0.763361	−	0.554615i	0.899940	+	0.436015i	$0.143610\pi$
$752$	−0.317511	−	0.230685i	−0.0115784	−	0.00841222i
$753$	7.04836	+	21.6926i	0.256856	+	0.790523i
$754$	−4.76891	−	14.6772i	−0.173673	−	0.534512i
$755$	−16.6961	−	12.1304i	−0.607632	−	0.441470i
$756$	−0.809017	+	0.587785i	−0.0294237	+	0.0213775i
$757$	−3.00051	+	9.23462i	−0.109055	+	0.335638i	−0.990661	−	0.136349i	$-0.956463\pi$
$757$	−3.00051	+	9.23462i	−0.109055	+	0.335638i	0.881605	+	0.471987i	$0.156463\pi$
$758$	−9.26077			−0.336366
$759$	−13.9286	+	4.32005i	−0.505574	+	0.156808i
$760$	−22.2778			−0.808101
$761$	9.60433	−	29.5591i	0.348157	−	1.07152i	−0.611715	−	0.791078i	$-0.709520\pi$
$761$	9.60433	−	29.5591i	0.348157	−	1.07152i	0.959872	−	0.280439i	$-0.0904799\pi$
$762$	5.30339	−	3.85314i	0.192122	−	0.139584i
$763$	−13.3368	−	9.68974i	−0.482824	−	0.350792i
$764$	5.17100	+	15.9147i	0.187080	+	0.575774i
$765$	7.15364	+	22.0166i	0.258640	+	0.796013i
$766$	−3.77696	−	2.74412i	−0.136467	−	0.0991493i
$767$	13.6912	−	9.94725i	0.494361	−	0.359174i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	21.7811			0.785445			0.392723	−	0.919657i	$-0.371533\pi$
$769$	21.7811			0.785445			0.392723	+	0.919657i	$0.371533\pi$
$770$	−6.32928	−	8.96180i	−0.228091	−	0.322961i
$771$	2.00122			0.0720723
$772$	6.53700	−	20.1188i	0.235272	−	0.724092i
$773$	−40.6447	+	29.5301i	−1.46189	+	1.06212i	−0.479020	+	0.877804i	$0.659008\pi$
$773$	−40.6447	+	29.5301i	−1.46189	+	1.06212i	−0.982867	+	0.184319i	$0.940992\pi$
$774$	−9.10982	−	6.61867i	−0.327446	−	0.237903i
$775$	−6.53166	−	20.1024i	−0.234624	−	0.722099i
$776$	−0.223719	−	0.688535i	−0.00803103	−	0.0247170i
$777$	−2.55982	−	1.85982i	−0.0918329	−	0.0667205i
$778$	13.2557	−	9.63084i	0.475240	−	0.345282i
$779$	−21.9742	+	67.6296i	−0.787307	+	2.42308i
$780$	7.30605			0.261599
$781$	−0.554683	+	41.3617i	−0.0198481	+	1.48004i
$782$	30.7701			1.10034
$783$	2.15926	−	6.64553i	0.0771658	−	0.237492i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	36.1934	+	26.2960i	1.29180	+	0.938545i
$786$	−6.12592	−	18.8536i	−0.218504	−	0.672487i
$787$	2.59757	+	7.99449i	0.0925933	+	0.284973i	0.986619	−	0.163043i	$-0.0521309\pi$
$787$	2.59757	+	7.99449i	0.0925933	+	0.284973i	−0.894026	+	0.448016i	$0.852131\pi$
$788$	14.7923	+	10.7472i	0.526954	+	0.382855i
$789$	15.9849	−	11.6137i	0.569077	−	0.413459i
$790$	−7.44369	+	22.9093i	−0.264835	+	0.815077i
$791$	−0.347181			−0.0123443
$792$	−0.0444738	+	3.31633i	−0.00158031	+	0.117841i
$793$	9.31548			0.330803
$794$	7.88425	−	24.2652i	0.279802	−	0.861141i
$795$	−18.2893	+	13.2879i	−0.648654	+	0.471274i
$796$	−2.91171	−	2.11548i	−0.103203	−	0.0749812i
$797$	−0.674246	−	2.07512i	−0.0238830	−	0.0735044i	0.938405	−	0.345538i	$-0.112304\pi$
$797$	−0.674246	−	2.07512i	−0.0238830	−	0.0735044i	−0.962288	+	0.272034i	$0.912304\pi$
$798$	2.08107	+	6.40486i	0.0736689	+	0.226730i
$799$	2.22195	+	1.61434i	0.0786068	+	0.0571112i
$800$	−4.80803	+	3.49324i	−0.169989	+	0.123505i
$801$	1.14552	−	3.52555i	0.0404750	−	0.124569i
$802$	−20.6311			−0.728508
$803$	13.4745	+	19.0789i	0.475503	+	0.673279i
$804$	−2.06998			−0.0730026
$805$	−4.49475	+	13.8334i	−0.158419	+	0.487564i
$806$	6.35481	−	4.61704i	0.223839	−	0.162628i
$807$	−13.9887	−	10.1634i	−0.492427	−	0.357769i
$808$	3.79667	+	11.6849i	0.133566	+	0.411075i
$809$	−11.1151	−	34.2088i	−0.390787	−	1.20272i	−0.932194	−	0.361959i	$-0.882108\pi$
$809$	−11.1151	−	34.2088i	−0.390787	−	1.20272i	0.541407	−	0.840761i	$-0.317892\pi$
$810$	2.67625	+	1.94441i	0.0940339	+	0.0683196i
$811$	−8.57158	+	6.22762i	−0.300989	+	0.218681i	−0.728020	−	0.685556i	$-0.759559\pi$
$811$	−8.57158	+	6.22762i	−0.300989	+	0.218681i	0.427031	+	0.904237i	$0.359559\pi$
$812$	2.15926	−	6.64553i	0.0757753	−	0.233212i
$813$	16.9730			0.595268
$814$	−10.0231	+	3.10875i	−0.351310	+	0.108962i
$815$	44.3819			1.55463
$816$	2.16251	−	6.65551i	0.0757029	−	0.232990i
$817$	−61.3498	+	44.5732i	−2.14636	+	1.55942i
$818$	6.83711	+	4.96745i	0.239054	+	0.173683i
$819$	−0.682489	−	2.10049i	−0.0238481	−	0.0733969i
$820$	10.7939	+	33.2202i	0.376940	+	1.16010i
$821$	18.0419	+	13.1082i	0.629668	+	0.457481i	0.856285	−	0.516503i	$-0.172767\pi$
$821$	18.0419	+	13.1082i	0.629668	+	0.457481i	−0.226617	+	0.973984i	$0.572767\pi$
$822$	14.5221	−	10.5509i	0.506518	−	0.368007i
$823$	−11.2282	+	34.5567i	−0.391389	+	1.20457i	0.540350	+	0.841441i	$0.318292\pi$
$823$	−11.2282	+	34.5567i	−0.391389	+	1.20457i	−0.931738	+	0.363130i	$0.881708\pi$
$824$	8.19413			0.285456
$825$	−11.7985	+	15.7896i	−0.410773	+	0.549724i
$826$	7.66251			0.266613
$827$	5.88674	−	18.1175i	0.204702	−	0.630008i	−0.795024	−	0.606579i	$-0.792542\pi$
$827$	5.88674	−	18.1175i	0.204702	−	0.630008i	0.999725	−	0.0234292i	$-0.00745843\pi$
$828$	3.55723	−	2.58448i	0.123622	−	0.0898168i
$829$	−32.3586	−	23.5099i	−1.12386	−	0.816532i	−0.139070	−	0.990283i	$-0.544411\pi$
$829$	−32.3586	−	23.5099i	−1.12386	−	0.816532i	−0.984790	+	0.173750i	$0.944411\pi$
$830$	6.68759	+	20.5823i	0.232130	+	0.714422i
$831$	−6.10391	−	18.7859i	−0.211742	−	0.651676i
$832$	−1.78678	−	1.29817i	−0.0619455	−	0.0450060i
$833$	5.66152	−	4.11333i	0.196160	−	0.142519i
$834$	−1.00910	+	3.10571i	−0.0349424	+	0.107542i
$835$	−17.0575			−0.590299
$836$	21.1481	+	7.18634i	0.731421	+	0.248545i
$837$	3.55657			0.122933
$838$	−6.26540	+	19.2829i	−0.216435	+	0.666118i
$839$	−19.4643	+	14.1416i	−0.671982	+	0.488224i	−0.870688	−	0.491836i	$-0.836326\pi$
$839$	−19.4643	+	14.1416i	−0.671982	+	0.488224i	0.198706	+	0.980059i	$0.436326\pi$
$840$	2.67625	+	1.94441i	0.0923394	+	0.0670885i
$841$	6.12641	+	18.8552i	0.211256	+	0.650178i
$842$	2.80040	+	8.61873i	0.0965080	+	0.297021i
$843$	−6.15926	−	4.47497i	−0.212136	−	0.154126i
$844$	3.83876	−	2.78902i	0.132136	−	0.0960021i
$845$	8.30278	−	25.5533i	0.285624	−	0.879061i
$846$	0.392465			0.0134932
$847$	3.11742	+	10.5490i	0.107116	+	0.362468i
$848$	6.83391			0.234678
$849$	0.0232530	−	0.0715654i	0.000798042	−	0.00245612i
$850$	33.6467	−	24.4457i	1.15407	−	0.838482i
$851$	11.2555	+	8.17757i	0.385832	+	0.280323i
$852$	−3.85410	−	11.8617i	−0.132039	−	0.406375i
$853$	2.59253	+	7.97897i	0.0887664	+	0.273195i	0.985579	−	0.169216i	$-0.0541234\pi$
$853$	2.59253	+	7.97897i	0.0887664	+	0.273195i	−0.896813	+	0.442410i	$0.854123\pi$
$854$	3.41232	+	2.47919i	0.116767	+	0.0848363i
$855$	18.0231	−	13.0946i	0.616378	−	0.447825i
$856$	0.844997	−	2.60063i	0.0288814	−	0.0888878i
$857$	−15.0372			−0.513660			−0.256830	−	0.966457i	$-0.582678\pi$
$857$	−15.0372			−0.513660			−0.256830	+	0.966457i	$0.582678\pi$
$858$	−6.93554	−	2.35677i	−0.236776	−	0.0804589i
$859$	−28.0471			−0.956953			−0.478477	−	0.878100i	$-0.658811\pi$
$859$	−28.0471			−0.956953			−0.478477	+	0.878100i	$0.658811\pi$
$860$	−11.5107	+	35.4264i	−0.392513	+	1.20803i
$861$	8.54250	−	6.20649i	0.291127	−	0.211516i
$862$	−24.8916	−	18.0848i	−0.847811	−	0.615970i
$863$	7.76606	+	23.9015i	0.264360	+	0.813616i	0.991840	+	0.127487i	$0.0406912\pi$
$863$	7.76606	+	23.9015i	0.264360	+	0.813616i	−0.727480	+	0.686128i	$0.759309\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	64.5765	+	46.9176i	2.19567	+	1.59525i
$866$	13.4505	−	9.77237i	0.457067	−	0.332079i
$867$	−9.87999	+	30.4075i	−0.335542	+	1.03269i
$868$	3.55657			0.120718
$869$	14.4563	−	19.3464i	0.490395	−	0.656280i
$870$	−23.1149			−0.783669
$871$	1.41274	−	4.34797i	0.0478689	−	0.147325i
$872$	13.3368	−	9.68974i	0.451640	−	0.328136i
$873$	0.585703	+	0.425538i	0.0198231	+	0.0144023i
$874$	−9.15039	−	28.1620i	−0.309517	−	0.952594i
$875$	0.964020	+	2.96695i	0.0325898	+	0.100301i
$876$	−5.69750	−	4.13948i	−0.192501	−	0.139860i
$877$	−22.4007	+	16.2751i	−0.756419	+	0.549571i	−0.897810	−	0.440383i	$-0.854843\pi$
$877$	−22.4007	+	16.2751i	−0.756419	+	0.549571i	0.141391	+	0.989954i	$0.454843\pi$
$878$	−4.34439	+	13.3706i	−0.146616	+	0.451237i
$879$	−10.7469			−0.362485
$880$	10.4790	−	3.25015i	0.353248	−	0.109563i
$881$	33.5512			1.13037			0.565184	−	0.824965i	$-0.308805\pi$
$881$	33.5512			1.13037			0.565184	+	0.824965i	$0.308805\pi$
$882$	0.309017	−	0.951057i	0.0104051	−	0.0320237i
$883$	20.2795	−	14.7339i	0.682458	−	0.495835i	−0.191714	−	0.981451i	$-0.561405\pi$
$883$	20.2795	−	14.7339i	0.682458	−	0.495835i	0.874172	+	0.485616i	$0.161405\pi$
$884$	12.5039	+	9.08463i	0.420553	+	0.305549i
$885$	−7.83290	−	24.1072i	−0.263300	−	0.810354i
$886$	3.19054	+	9.81948i	0.107188	+	0.329892i
$887$	−5.13895	−	3.73366i	−0.172549	−	0.125364i	0.498159	−	0.867086i	$-0.334010\pi$
$887$	−5.13895	−	3.73366i	−0.172549	−	0.125364i	−0.670708	+	0.741722i	$0.734010\pi$
$888$	2.55982	−	1.85982i	0.0859018	−	0.0624113i
$889$	−2.02571	+	6.23451i	−0.0679403	+	0.209099i
$890$	−12.2628			−0.411050
$891$	−1.91331	−	2.70911i	−0.0640982	−	0.0907585i
$892$	−28.4884			−0.953861
$893$	0.816745	−	2.51368i	0.0273313	−	0.0841172i
$894$	−1.76713	+	1.28390i	−0.0591017	+	0.0429399i
$895$	61.1365	+	44.4182i	2.04357	+	1.48474i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	3.00089	+	9.23579i	0.100197	+	0.308374i
$898$	24.1370	+	17.5365i	0.805461	+	0.585202i
$899$	−20.1054	+	14.6074i	−0.670552	+	0.487185i
$900$	1.83650	−	5.65218i	0.0612168	−	0.188406i
$901$	−47.8239			−1.59324
$902$	0.469603	−	35.0174i	0.0156361	−	1.16595i
$903$	11.2604			0.374721
$904$	0.107285	−	0.330189i	0.00356824	−	0.0109819i
$905$	17.6412	−	12.8171i	0.586414	−	0.426055i
$906$	−5.04713	−	3.66696i	−0.167680	−	0.121827i
$907$	−2.08444	−	6.41524i	−0.0692126	−	0.213014i	0.910468	−	0.413580i	$-0.135722\pi$
$907$	−2.08444	−	6.41524i	−0.0692126	−	0.213014i	−0.979680	+	0.200566i	$0.935722\pi$
$908$	7.47842	+	23.0162i	0.248180	+	0.763820i
$909$	−9.93981	−	7.22169i	−0.329683	−	0.239528i
$910$	−5.91072	+	4.29439i	−0.195938	+	0.142358i
$911$	−9.09418	+	27.9890i	−0.301304	+	0.927317i	0.679727	+	0.733465i	$0.262098\pi$
$911$	−9.09418	+	27.9890i	−0.301304	+	0.927317i	−0.981031	+	0.193852i	$0.937902\pi$
$912$	−6.73447			−0.223001
$913$	0.290953	−	21.6958i	0.00962913	−	0.718026i
$914$	22.4931			0.744007
$915$	4.31165	−	13.2699i	0.142539	−	0.438689i
$916$	10.2632	−	7.45667i	0.339106	−	0.246375i
$917$	16.0379	+	11.6522i	0.529617	+	0.384789i
$918$	2.16251	+	6.65551i	0.0713734	+	0.219665i
$919$	7.45010	+	22.9290i	0.245756	+	0.756359i	0.995511	+	0.0946440i	$0.0301713\pi$
$919$	7.45010	+	22.9290i	0.245756	+	0.756359i	−0.749755	+	0.661715i	$0.769829\pi$
$920$	−11.7674	−	8.54952i	−0.387960	−	0.281869i
$921$	−14.1478	+	10.2790i	−0.466187	+	0.338705i
$922$	5.24337	−	16.1374i	0.172681	−	0.531458i
$923$	27.5457			0.906679
$924$	−1.91331	−	2.70911i	−0.0629432	−	0.0891230i
$925$	18.8044			0.618287
$926$	1.32877	−	4.08952i	0.0436659	−	0.134390i
$927$	−6.62919	+	4.81639i	−0.217731	+	0.158191i
$928$	5.65303	+	4.10716i	0.185570	+	0.134824i
$929$	0.140755	+	0.433198i	0.00461801	+	0.0142128i	0.953339	−	0.301902i	$-0.0976215\pi$
$929$	0.140755	+	0.433198i	0.00461801	+	0.0142128i	−0.948721	+	0.316115i	$0.897622\pi$
$930$	−3.63566	−	11.1894i	−0.119218	−	0.366915i
$931$	−5.44830	−	3.95842i	−0.178561	−	0.129732i
$932$	−18.6712	+	13.5654i	−0.611597	+	0.444351i
$933$	−8.00464	+	24.6357i	−0.262060	+	0.806538i
$934$	−4.03752			−0.132112
$935$	−73.3325	+	22.7446i	−2.39823	+	0.743829i
$936$	2.20858			0.0721898
$937$	4.09059	−	12.5895i	0.133634	−	0.411283i	−0.861741	−	0.507348i	$-0.830626\pi$
$937$	4.09059	−	12.5895i	0.133634	−	0.411283i	0.995375	+	0.0960655i	$0.0306258\pi$
$938$	1.67465	−	1.21670i	0.0546793	−	0.0397268i
$939$	−2.09625	−	1.52301i	−0.0684084	−	0.0497016i
$940$	−0.401192	−	1.23474i	−0.0130854	−	0.0402728i
$941$	6.77890	+	20.8633i	0.220986	+	0.680124i	0.998674	+	0.0514745i	$0.0163921\pi$
$941$	6.77890	+	20.8633i	0.220986	+	0.680124i	−0.777689	+	0.628650i	$0.783608\pi$
$942$	10.9411	+	7.94915i	0.356479	+	0.258997i
$943$	−37.5611	+	27.2898i	−1.22316	+	0.888677i
$944$	−2.36785	+	7.28748i	−0.0770668	+	0.237187i
$945$	−3.30803			−0.107610
$946$	22.3548	−	29.9168i	0.726818	−	0.972678i
$947$	30.1901			0.981046			0.490523	−	0.871428i	$-0.336806\pi$
$947$	30.1901			0.981046			0.490523	+	0.871428i	$0.336806\pi$
$948$	−2.25019	+	6.92537i	−0.0730827	+	0.224926i
$949$	12.5834	−	9.14237i	0.408474	−	0.296774i
$950$	−32.3795	−	23.5251i	−1.05053	−	0.763255i
$951$	−2.34137	−	7.20601i	−0.0759243	−	0.233671i
$952$	2.16251	+	6.65551i	0.0700873	+	0.215706i
$953$	−47.6528	−	34.6218i	−1.54363	−	1.12151i	−0.948010	−	0.318241i	$-0.896908\pi$
$953$	−47.6528	−	34.6218i	−1.54363	−	1.12151i	−0.595617	−	0.803269i	$-0.703092\pi$
$954$	−5.52875	+	4.01687i	−0.179000	+	0.130051i
$955$	−17.1058	+	52.6463i	−0.553531	+	1.70359i
$956$	13.1973			0.426832
$957$	21.9427	+	7.45637i	0.709307	+	0.241030i
$958$	8.84497			0.285768
$959$	−5.54696	+	17.0718i	−0.179121	+	0.551277i
$960$	−2.67625	+	1.94441i	−0.0863756	+	0.0627556i
$961$	14.8461	+	10.7863i	0.478906	+	0.347946i
$962$	2.15947	+	6.64616i	0.0696241	+	0.214281i
$963$	0.844997	+	2.60063i	0.0272296	+	0.0838042i
$964$	−14.7152	−	10.6912i	−0.473944	−	0.344340i
$965$	56.6139	−	41.1324i	1.82246	−	1.32410i
$966$	−1.35874	+	4.18177i	−0.0437167	+	0.134546i
$967$	31.8510			1.02426			0.512130	−	0.858908i	$-0.328857\pi$
$967$	31.8510			1.02426			0.512130	+	0.858908i	$0.328857\pi$
$968$	−10.9960	−	0.294979i	−0.353426	−	0.00948099i
$969$	47.1280			1.51397
$970$	0.740068	−	2.27769i	0.0237621	−	0.0731324i
$971$	−5.52821	+	4.01648i	−0.177409	+	0.128895i	−0.672946	−	0.739692i	$-0.734971\pi$
$971$	−5.52821	+	4.01648i	−0.177409	+	0.128895i	0.495537	+	0.868587i	$0.334971\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−1.00910	−	3.10571i	−0.0323504	−	0.0995644i
$974$	−5.67887	−	17.4778i	−0.181963	−	0.560023i
$975$	10.6189	+	7.71510i	0.340078	+	0.247081i
$976$	−3.41232	+	2.47919i	−0.109226	+	0.0793571i
$977$	−2.29466	+	7.06225i	−0.0734128	+	0.225941i	−0.981029	−	0.193859i	$-0.937900\pi$
$977$	−2.29466	+	7.06225i	−0.0734128	+	0.225941i	0.907617	+	0.419800i	$0.137900\pi$
$978$	13.4164			0.429009
$979$	11.6409	+	3.95571i	0.372046	+	0.126425i
$980$	−3.30803			−0.105671
$981$	−5.09420	+	15.6783i	−0.162645	+	0.500570i
$982$	17.3344	−	12.5942i	0.553163	−	0.401896i
$983$	−18.5716	−	13.4930i	−0.592341	−	0.430361i	0.250811	−	0.968036i	$-0.419303\pi$
$983$	−18.5716	−	13.4930i	−0.592341	−	0.430361i	−0.843152	+	0.537675i	$0.819303\pi$
$984$	3.26294	+	10.0423i	0.104019	+	0.320137i
$985$	18.6909	+	57.5246i	0.595541	+	1.83289i
$986$	−39.5600	−	28.7420i	−1.25985	−	0.915332i
$987$	−0.317511	+	0.230685i	−0.0101065	+	0.00734279i
$988$	4.59620	−	14.1457i	0.146225	−	0.450033i
$989$	−49.5115			−1.57437
$990$	−6.56732	+	8.78885i	−0.208723	+	0.279328i
$991$	47.5339			1.50996			0.754981	−	0.655746i	$-0.227646\pi$
$991$	47.5339			1.50996			0.754981	+	0.655746i	$0.227646\pi$
$992$	−1.09904	+	3.38250i	−0.0348946	+	0.107395i
$993$	4.51374	−	3.27943i	0.143239	−	0.104069i
$994$	10.0902	+	7.33094i	0.320041	+	0.232523i
$995$	−3.67910	−	11.3231i	−0.116635	−	0.358967i
$996$	2.02163	+	6.22192i	0.0640577	+	0.197149i
$997$	−36.3964	−	26.4436i	−1.15269	−	0.837476i	−0.163851	−	0.986485i	$-0.552392\pi$
$997$	−36.3964	−	26.4436i	−1.15269	−	0.837476i	−0.988836	+	0.149009i	$0.952392\pi$
$998$	−5.77948	+	4.19904i	−0.182946	+	0.132918i
$999$	−0.977763	+	3.00925i	−0.0309351	+	0.0952083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.f.295.1	✓	8
11.4	even	5		5082.2.a.cc.1.1		4
11.5	even	5	inner	462.2.j.f.379.1	yes	8
11.7	odd	10		5082.2.a.bx.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.f.295.1	✓	8	1.1	even	1	trivial
462.2.j.f.379.1	yes	8	11.5	even	5	inner
5082.2.a.bx.1.1		4	11.7	odd	10
5082.2.a.cc.1.1		4	11.4	even	5

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.02224 - 3.14612i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.02224 - 3.14612i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} -3.30803 q^{10} +(3.14027 + 1.06710i) q^{11} -1.00000 q^{12} +(0.682489 - 2.10049i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-2.67625 - 1.94441i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.16251 - 6.65551i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-5.44830 + 3.95842i) q^{19} +(-1.02224 + 3.14612i) q^{20} +1.00000 q^{21} +(1.98527 - 2.65682i) q^{22} -4.39698 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.80803 + 3.49324i) q^{25} +(-1.78678 - 1.29817i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(5.65303 + 4.10716i) q^{29} +(-2.67625 + 1.94441i) q^{30} +(-1.09904 + 3.38250i) q^{31} +1.00000 q^{32} +(3.16776 - 0.982504i) q^{33} -6.99802 q^{34} +(1.02224 - 3.14612i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-2.55982 - 1.85982i) q^{37} +(2.08107 + 6.40486i) q^{38} +(-0.682489 - 2.10049i) q^{39} +(2.67625 + 1.94441i) q^{40} +(8.54250 - 6.20649i) q^{41} +(0.309017 - 0.951057i) q^{42} +11.2604 q^{43} +(-1.91331 - 2.70911i) q^{44} -3.30803 q^{45} +(-1.35874 + 4.18177i) q^{46} +(-0.317511 + 0.230685i) q^{47} +(0.809017 + 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.83650 + 5.65218i) q^{50} +(-5.66152 - 4.11333i) q^{51} +(-1.78678 + 1.29817i) q^{52} +(2.11180 - 6.49944i) q^{53} -1.00000 q^{54} +(0.147120 - 10.9705i) q^{55} -1.00000 q^{56} +(-2.08107 + 6.40486i) q^{57} +(5.65303 - 4.10716i) q^{58} +(6.19910 + 4.50391i) q^{59} +(1.02224 + 3.14612i) q^{60} +(1.30339 + 4.01142i) q^{61} +(2.87733 + 2.09050i) q^{62} +(0.809017 - 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -7.30605 q^{65} +(0.0444738 - 3.31633i) q^{66} +2.06998 q^{67} +(-2.16251 + 6.65551i) q^{68} +(-3.55723 + 2.58448i) q^{69} +(-2.67625 - 1.94441i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(5.69750 + 4.13948i) q^{73} +(-2.55982 + 1.85982i) q^{74} +(-1.83650 + 5.65218i) q^{75} +6.73447 q^{76} +(1.91331 + 2.70911i) q^{77} -2.20858 q^{78} +(2.25019 - 6.92537i) q^{79} +(2.67625 - 1.94441i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.26294 - 10.0423i) q^{82} +(-2.02163 - 6.22192i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(-18.7285 + 13.6070i) q^{85} +(3.47964 - 10.7092i) q^{86} +6.98752 q^{87} +(-3.16776 + 0.982504i) q^{88} +3.70698 q^{89} +(-1.02224 + 3.14612i) q^{90} +(1.78678 - 1.29817i) q^{91} +(3.55723 + 2.58448i) q^{92} +(1.09904 + 3.38250i) q^{93} +(0.121278 + 0.373256i) q^{94} +(18.0231 + 13.0946i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-0.223719 + 0.688535i) q^{97} +1.00000 q^{98} +(1.98527 - 2.65682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20} + 8 q^{21} - 6 q^{22} + 4 q^{23} + 2 q^{24} - 8 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} - 10 q^{31} + 8 q^{32} + 6 q^{33} - 4 q^{34} + 6 q^{35} - 2 q^{36} - 20 q^{37} - 12 q^{38} - 8 q^{39} + 4 q^{40} + 12 q^{41} - 2 q^{42} + 48 q^{43} - 6 q^{44} + 4 q^{45} + 4 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} - 12 q^{53} - 8 q^{54} - 8 q^{55} - 8 q^{56} + 12 q^{57} + 4 q^{58} + 12 q^{59} + 6 q^{60} - 32 q^{61} + 20 q^{62} + 2 q^{63} - 2 q^{64} + 24 q^{65} - 4 q^{66} - 48 q^{67} - 4 q^{68} + 6 q^{69} - 4 q^{70} + 4 q^{71} - 2 q^{72} - 20 q^{74} - 2 q^{75} + 28 q^{76} + 6 q^{77} - 8 q^{78} + 40 q^{79} + 4 q^{80} - 2 q^{81} - 18 q^{82} - 32 q^{83} - 2 q^{84} - 42 q^{85} - 32 q^{86} + 16 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 6 q^{92} + 10 q^{93} + 54 q^{95} + 2 q^{96} + 8 q^{97} + 8 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

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