LMFDB - Embedded newform 273.2.cg.b.262.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.3
Character	$\chi$	$=$	273.262
Dual form			273.2.cg.b.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.449968 - 1.67930i) q^{2} +1.00000i q^{3} +(-0.885540 + 0.511267i) q^{4} +(-0.524353 + 1.95691i) q^{5} +(1.67930 - 0.449968i) q^{6} +(-0.616155 + 2.57300i) q^{7} +(-1.20163 - 1.20163i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.449968 - 1.67930i) q^{2} +1.00000i q^{3} +(-0.885540 + 0.511267i) q^{4} +(-0.524353 + 1.95691i) q^{5} +(1.67930 - 0.449968i) q^{6} +(-0.616155 + 2.57300i) q^{7} +(-1.20163 - 1.20163i) q^{8} -1.00000 q^{9} +3.52219 q^{10} +(2.56310 + 2.56310i) q^{11} +(-0.511267 - 0.885540i) q^{12} +(1.78841 + 3.13075i) q^{13} +(4.59811 - 0.123058i) q^{14} +(-1.95691 - 0.524353i) q^{15} +(-2.49975 + 4.32969i) q^{16} +(-0.752896 - 1.30405i) q^{17} +(0.449968 + 1.67930i) q^{18} +(2.92473 + 2.92473i) q^{19} +(-0.536169 - 2.00101i) q^{20} +(-2.57300 - 0.616155i) q^{21} +(3.15091 - 5.45753i) q^{22} +(-3.21414 - 1.85568i) q^{23} +(1.20163 - 1.20163i) q^{24} +(0.775564 + 0.447772i) q^{25} +(4.45275 - 4.41202i) q^{26} -1.00000i q^{27} +(-0.769862 - 2.59352i) q^{28} +(-1.84505 - 3.19572i) q^{29} +3.52219i q^{30} +(7.05794 - 1.89117i) q^{31} +(5.11274 + 1.36995i) q^{32} +(-2.56310 + 2.56310i) q^{33} +(-1.85112 + 1.85112i) q^{34} +(-4.71206 - 2.55493i) q^{35} +(0.885540 - 0.511267i) q^{36} +(-2.52920 + 0.677697i) q^{37} +(3.59548 - 6.22755i) q^{38} +(-3.13075 + 1.78841i) q^{39} +(2.98158 - 1.72141i) q^{40} +(1.33248 - 4.97288i) q^{41} +(0.123058 + 4.59811i) q^{42} +(-4.51217 - 2.60510i) q^{43} +(-3.58015 - 0.959299i) q^{44} +(0.524353 - 1.95691i) q^{45} +(-1.67000 + 6.23251i) q^{46} +(0.255554 + 0.0684756i) q^{47} +(-4.32969 - 2.49975i) q^{48} +(-6.24071 - 3.17074i) q^{49} +(0.402966 - 1.50389i) q^{50} +(1.30405 - 0.752896i) q^{51} +(-3.18436 - 1.85805i) q^{52} +(-2.63938 + 4.57154i) q^{53} +(-1.67930 + 0.449968i) q^{54} +(-6.35973 + 3.67179i) q^{55} +(3.83220 - 2.35142i) q^{56} +(-2.92473 + 2.92473i) q^{57} +(-4.53637 + 4.53637i) q^{58} +(1.24693 + 0.334114i) q^{59} +(2.00101 - 0.536169i) q^{60} +10.6182i q^{61} +(-6.35170 - 11.0015i) q^{62} +(0.616155 - 2.57300i) q^{63} +0.796700i q^{64} +(-7.06436 + 1.85815i) q^{65} +(5.45753 + 3.15091i) q^{66} +(9.48626 - 9.48626i) q^{67} +(1.33344 + 0.769862i) q^{68} +(1.85568 - 3.21414i) q^{69} +(-2.17022 + 9.06262i) q^{70} +(3.11400 + 11.6216i) q^{71} +(1.20163 + 1.20163i) q^{72} +(-0.744113 - 2.77707i) q^{73} +(2.27612 + 3.94235i) q^{74} +(-0.447772 + 0.775564i) q^{75} +(-4.08528 - 1.09465i) q^{76} +(-8.17413 + 5.01560i) q^{77} +(4.41202 + 4.45275i) q^{78} +(-8.09801 - 14.0262i) q^{79} +(-7.16207 - 7.16207i) q^{80} +1.00000 q^{81} -8.95055 q^{82} +(10.3721 + 10.3721i) q^{83} +(2.59352 - 0.769862i) q^{84} +(2.94671 - 0.789567i) q^{85} +(-2.34443 + 8.74952i) q^{86} +(3.19572 - 1.84505i) q^{87} -6.15981i q^{88} +(-2.60486 - 9.72147i) q^{89} -3.52219 q^{90} +(-9.15737 + 2.67257i) q^{91} +3.79500 q^{92} +(1.89117 + 7.05794i) q^{93} -0.459965i q^{94} +(-7.25704 + 4.18985i) q^{95} +(-1.36995 + 5.11274i) q^{96} +(0.645956 - 0.173083i) q^{97} +(-2.51652 + 11.9068i) q^{98} +(-2.56310 - 2.56310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.449968	−	1.67930i	−0.318176	−	1.18745i	−0.920997	−	0.389571i	$-0.872623\pi$
$2$	−0.449968	−	1.67930i	−0.318176	−	1.18745i	0.602821	−	0.797876i	$-0.294043\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.885540	+	0.511267i	−0.442770	+	0.255633i
$5$	−0.524353	+	1.95691i	−0.234498	+	0.875158i	0.743877	+	0.668317i	$0.232985\pi$
$5$	−0.524353	+	1.95691i	−0.234498	+	0.875158i	−0.978375	+	0.206841i	$0.933682\pi$
$6$	1.67930	−	0.449968i	0.685573	−	0.183699i
$7$	−0.616155	+	2.57300i	−0.232885	+	0.972504i
$7$	−0.616155	+	2.57300i	−0.232885	+	0.972504i
$8$	−1.20163	−	1.20163i	−0.424842	−	0.424842i
$9$	−1.00000			−0.333333
$10$	3.52219			1.11382
$11$	2.56310	+	2.56310i	0.772803	+	0.772803i	0.978596	−	0.205793i	$-0.0659772\pi$
$11$	2.56310	+	2.56310i	0.772803	+	0.772803i	−0.205793	+	0.978596i	$0.565977\pi$
$12$	−0.511267	−	0.885540i	−0.147590	−	0.255633i
$13$	1.78841	+	3.13075i	0.496016	+	0.868313i
$13$	1.78841	+	3.13075i	0.496016	+	0.868313i
$14$	4.59811	−	0.123058i	1.22890	−	0.0328887i
$15$	−1.95691	−	0.524353i	−0.505273	−	0.135387i
$16$	−2.49975	+	4.32969i	−0.624937	+	1.08242i
$17$	−0.752896	−	1.30405i	−0.182604	−	0.316280i	0.760162	−	0.649733i	$-0.225119\pi$
$17$	−0.752896	−	1.30405i	−0.182604	−	0.316280i	−0.942767	+	0.333453i	$0.891786\pi$
$18$	0.449968	+	1.67930i	0.106059	+	0.395816i
$19$	2.92473	+	2.92473i	0.670979	+	0.670979i	0.957942	−	0.286963i	$-0.0926455\pi$
$19$	2.92473	+	2.92473i	0.670979	+	0.670979i	−0.286963	+	0.957942i	$0.592646\pi$
$20$	−0.536169	−	2.00101i	−0.119891	−	0.447439i
$21$	−2.57300	−	0.616155i	−0.561476	−	0.134456i
$22$	3.15091	−	5.45753i	0.671776	−	1.16355i
$23$	−3.21414	−	1.85568i	−0.670194	−	0.386937i	0.125956	−	0.992036i	$-0.459800\pi$
$23$	−3.21414	−	1.85568i	−0.670194	−	0.386937i	−0.796150	+	0.605099i	$0.793133\pi$
$24$	1.20163	−	1.20163i	0.245283	−	0.245283i
$25$	0.775564	+	0.447772i	0.155113	+	0.0895544i
$26$	4.45275	−	4.41202i	0.873256	−	0.865269i
$27$		−	1.00000i		−	0.192450i
$28$	−0.769862	−	2.59352i	−0.145490	−	0.490129i
$29$	−1.84505	−	3.19572i	−0.342617	−	0.593430i	0.642301	−	0.766452i	$-0.277980\pi$
$29$	−1.84505	−	3.19572i	−0.342617	−	0.593430i	−0.984918	+	0.173023i	$0.944647\pi$
$30$			3.52219i			0.643062i
$31$	7.05794	−	1.89117i	1.26764	−	0.339664i	0.438516	−	0.898723i	$-0.355504\pi$
$31$	7.05794	−	1.89117i	1.26764	−	0.339664i	0.829128	+	0.559059i	$0.188838\pi$
$32$	5.11274	+	1.36995i	0.903814	+	0.242176i
$33$	−2.56310	+	2.56310i	−0.446178	+	0.446178i
$34$	−1.85112	+	1.85112i	−0.317465	+	0.317465i
$35$	−4.71206	−	2.55493i	−0.796484	−	0.431861i
$36$	0.885540	−	0.511267i	0.147590	−	0.0852111i
$37$	−2.52920	+	0.677697i	−0.415798	+	0.111413i	−0.460652	−	0.887581i	$-0.652384\pi$
$37$	−2.52920	+	0.677697i	−0.415798	+	0.111413i	0.0448541	+	0.998994i	$0.485718\pi$
$38$	3.59548	−	6.22755i	0.583263	−	1.01024i
$39$	−3.13075	+	1.78841i	−0.501321	+	0.286375i
$40$	2.98158	−	1.72141i	0.471428	−	0.272179i
$41$	1.33248	−	4.97288i	0.208098	−	0.776634i	−0.780384	−	0.625300i	$-0.784977\pi$
$41$	1.33248	−	4.97288i	0.208098	−	0.776634i	0.988483	−	0.151334i	$-0.0483568\pi$
$42$	0.123058	+	4.59811i	0.0189883	+	0.709503i
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	0.114800	−	0.993389i	$-0.463377\pi$
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	−0.802900	+	0.596114i	$0.796711\pi$
$44$	−3.58015	−	0.959299i	−0.539728	−	0.144620i
$45$	0.524353	−	1.95691i	0.0781660	−	0.291719i
$46$	−1.67000	+	6.23251i	−0.246228	+	0.918934i
$47$	0.255554	+	0.0684756i	0.0372764	+	0.00998819i	0.277409	−	0.960752i	$-0.410524\pi$
$47$	0.255554	+	0.0684756i	0.0372764	+	0.00998819i	−0.240133	+	0.970740i	$0.577191\pi$
$48$	−4.32969	−	2.49975i	−0.624937	−	0.360807i
$49$	−6.24071	−	3.17074i	−0.891529	−	0.452963i
$50$	0.402966	−	1.50389i	0.0569881	−	0.212682i
$51$	1.30405	−	0.752896i	0.182604	−	0.105427i
$52$	−3.18436	−	1.85805i	−0.441591	−	0.257665i
$53$	−2.63938	+	4.57154i	−0.362547	+	0.627949i	−0.988379	−	0.152008i	$-0.951426\pi$
$53$	−2.63938	+	4.57154i	−0.362547	+	0.627949i	0.625832	+	0.779958i	$0.284759\pi$
$54$	−1.67930	+	0.449968i	−0.228524	+	0.0612329i
$55$	−6.35973	+	3.67179i	−0.857546	+	0.495104i
$56$	3.83220	−	2.35142i	0.512100	−	0.314221i
$57$	−2.92473	+	2.92473i	−0.387390	+	0.387390i
$58$	−4.53637	+	4.53637i	−0.595654	+	0.595654i
$59$	1.24693	+	0.334114i	0.162337	+	0.0434980i	0.339072	−	0.940760i	$-0.389887\pi$
$59$	1.24693	+	0.334114i	0.162337	+	0.0434980i	−0.176735	+	0.984258i	$0.556554\pi$
$60$	2.00101	−	0.536169i	0.258329	−	0.0692191i
$61$			10.6182i			1.35952i	0.733433	+	0.679762i	$0.237917\pi$
$61$			10.6182i			1.35952i	−0.733433	+	0.679762i	$0.762083\pi$
$62$	−6.35170	−	11.0015i	−0.806667	−	1.39719i
$63$	0.616155	−	2.57300i	0.0776283	−	0.324168i
$64$			0.796700i			0.0995875i
$65$	−7.06436	+	1.85815i	−0.876226	+	0.230475i
$66$	5.45753	+	3.15091i	0.671776	+	0.387850i
$67$	9.48626	−	9.48626i	1.15893	−	1.15893i	0.174225	−	0.984706i	$-0.444258\pi$
$67$	9.48626	−	9.48626i	1.15893	−	1.15893i	0.984706	−	0.174225i	$-0.0557421\pi$
$68$	1.33344	+	0.769862i	0.161703	+	0.0933595i
$69$	1.85568	−	3.21414i	0.223398	−	0.386937i
$70$	−2.17022	+	9.06262i	−0.259391	+	1.08319i
$71$	3.11400	+	11.6216i	0.369564	+	1.37923i	0.861127	+	0.508390i	$0.169759\pi$
$71$	3.11400	+	11.6216i	0.369564	+	1.37923i	−0.491562	+	0.870842i	$0.663574\pi$
$72$	1.20163	+	1.20163i	0.141614	+	0.141614i
$73$	−0.744113	−	2.77707i	−0.0870919	−	0.325031i	0.908610	−	0.417645i	$-0.137144\pi$
$73$	−0.744113	−	2.77707i	−0.0870919	−	0.325031i	−0.995702	+	0.0926138i	$0.970478\pi$
$74$	2.27612	+	3.94235i	0.264593	+	0.458289i
$75$	−0.447772	+	0.775564i	−0.0517043	+	0.0895544i
$76$	−4.08528	−	1.09465i	−0.468614	−	0.125565i
$77$	−8.17413	+	5.01560i	−0.931528	+	0.571580i
$78$	4.41202	+	4.45275i	0.499563	+	0.504175i
$79$	−8.09801	−	14.0262i	−0.911098	−	1.57807i	−0.812516	−	0.582939i	$-0.801903\pi$
$79$	−8.09801	−	14.0262i	−0.911098	−	1.57807i	−0.0985815	−	0.995129i	$-0.531431\pi$
$80$	−7.16207	−	7.16207i	−0.800744	−	0.800744i
$81$	1.00000			0.111111
$82$	−8.95055			−0.988423
$83$	10.3721	+	10.3721i	1.13849	+	1.13849i	0.988722	+	0.149764i	$0.0478513\pi$
$83$	10.3721	+	10.3721i	1.13849	+	1.13849i	0.149764	+	0.988722i	$0.452149\pi$
$84$	2.59352	−	0.769862i	0.282976	−	0.0839988i
$85$	2.94671	−	0.789567i	0.319615	−	0.0856406i
$86$	−2.34443	+	8.74952i	−0.252806	+	0.943485i
$87$	3.19572	−	1.84505i	0.342617	−	0.197810i
$88$		−	6.15981i		−	0.656638i
$89$	−2.60486	−	9.72147i	−0.276115	−	1.03047i	−0.955091	−	0.296313i	$-0.904243\pi$
$89$	−2.60486	−	9.72147i	−0.276115	−	1.03047i	0.678976	−	0.734160i	$-0.262424\pi$
$90$	−3.52219			−0.371272
$91$	−9.15737	+	2.67257i	−0.959953	+	0.280161i
$92$	3.79500			0.395656
$93$	1.89117	+	7.05794i	0.196105	+	0.731875i
$94$		−	0.459965i		−	0.0474418i
$95$	−7.25704	+	4.18985i	−0.744556	+	0.429870i
$96$	−1.36995	+	5.11274i	−0.139820	+	0.521817i
$97$	0.645956	−	0.173083i	0.0655869	−	0.0175739i	−0.225876	−	0.974156i	$-0.572525\pi$
$97$	0.645956	−	0.173083i	0.0655869	−	0.0175739i	0.291463	+	0.956582i	$0.405858\pi$
$98$	−2.51652	+	11.9068i	−0.254207	+	1.20277i
$99$	−2.56310	−	2.56310i	−0.257601	−	0.257601i
$100$	−0.915724			−0.0915724
$101$	7.25219			0.721619			0.360810	−	0.932639i	$-0.382500\pi$
$101$	7.25219			0.721619			0.360810	+	0.932639i	$0.382500\pi$
$102$	−1.85112	−	1.85112i	−0.183289	−	0.183289i
$103$	−7.23449	−	12.5305i	−0.712835	−	1.23467i	−0.963789	−	0.266667i	$-0.914077\pi$
$103$	−7.23449	−	12.5305i	−0.712835	−	1.23467i	0.250954	−	0.967999i	$-0.419256\pi$
$104$	1.61300	−	5.91103i	0.158167	−	0.579624i
$105$	2.55493	−	4.71206i	0.249335	−	0.459850i
$106$	8.86465	+	2.37527i	0.861010	+	0.230707i
$107$	2.94039	−	5.09290i	0.284258	−	0.492350i	−0.688171	−	0.725549i	$-0.741586\pi$
$107$	2.94039	−	5.09290i	0.284258	−	0.492350i	0.972429	+	0.233199i	$0.0749194\pi$
$108$	0.511267	+	0.885540i	0.0491967	+	0.0852111i
$109$	−0.133153	−	0.496935i	−0.0127538	−	0.0475977i	0.959256	−	0.282539i	$-0.0911768\pi$
$109$	−0.133153	−	0.496935i	−0.0127538	−	0.0475977i	−0.972009	+	0.234942i	$0.924510\pi$
$110$	9.02773	+	9.02773i	0.860760	+	0.860760i
$111$	−0.677697	−	2.52920i	−0.0643241	−	0.240061i
$112$	−9.60007	−	9.09962i	−0.907122	−	0.859833i
$113$	3.88416	−	6.72757i	0.365391	−	0.632876i	−0.623448	−	0.781865i	$-0.714269\pi$
$113$	3.88416	−	6.72757i	0.365391	−	0.632876i	0.988839	+	0.148989i	$0.0476018\pi$
$114$	6.22755	+	3.59548i	0.583263	+	0.336747i
$115$	5.31675	−	5.31675i	0.495790	−	0.495790i
$116$	3.26773	+	1.88662i	0.303401	+	0.175169i
$117$	−1.78841	−	3.13075i	−0.165339	−	0.289438i
$118$		−	2.24432i		−	0.206606i
$119$	3.81924	−	1.13371i	0.350109	−	0.103927i
$120$	1.72141	+	2.98158i	0.157143	+	0.272179i
$121$			2.13894i			0.194449i
$122$	17.8312	−	4.77786i	1.61436	−	0.432567i
$123$	4.97288	+	1.33248i	0.448390	+	0.120146i
$124$	−5.28320	+	5.28320i	−0.474445	+	0.474445i
$125$	−8.44572	+	8.44572i	−0.755408	+	0.755408i
$126$	−4.59811	+	0.123058i	−0.409632	+	0.0109629i
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.464201	−	0.885730i	$-0.346341\pi$
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.999165	+	0.0408546i	$0.0130081\pi$
$128$	11.5634	−	3.09840i	1.02207	−	0.273862i
$129$	2.60510	−	4.51217i	0.229366	−	0.397274i
$130$	6.29914	+	11.0271i	0.552471	+	0.967141i
$131$	15.7198	−	9.07584i	1.37345	−	0.792960i	0.382087	−	0.924127i	$-0.375206\pi$
$131$	15.7198	−	9.07584i	1.37345	−	0.792960i	0.991360	+	0.131167i	$0.0418723\pi$
$132$	0.959299	−	3.58015i	0.0834963	−	0.311612i
$133$	−9.32743	+	5.72326i	−0.808791	+	0.496269i
$134$	−20.1988	−	11.6618i	−1.74491	−	1.00743i
$135$	1.95691	+	0.524353i	0.168424	+	0.0451291i
$136$	−0.662291	+	2.47170i	−0.0567910	+	0.211947i
$137$	−5.21037	+	19.4454i	−0.445152	+	1.66133i	0.270384	+	0.962753i	$0.412849\pi$
$137$	−5.21037	+	19.4454i	−0.445152	+	1.66133i	−0.715536	+	0.698576i	$0.753817\pi$
$138$	−6.23251	−	1.67000i	−0.530547	−	0.142160i
$139$	17.7595	+	10.2535i	1.50634	+	0.869687i	0.999973	+	0.00736980i	$0.00234590\pi$
$139$	17.7595	+	10.2535i	1.50634	+	0.869687i	0.506369	+	0.862317i	$0.330987\pi$
$140$	5.47897	−	0.146633i	0.463058	−	0.0123927i
$141$	−0.0684756	+	0.255554i	−0.00576669	+	0.0215216i
$142$	18.1150	−	10.4587i	1.52018	−	0.877676i
$143$	−3.44054	+	12.6083i	−0.287712	+	1.05436i
$144$	2.49975	−	4.32969i	0.208312	−	0.360807i
$145$	7.22120	−	1.93491i	0.599688	−	0.160686i
$146$	−4.32872	+	2.49919i	−0.358247	+	0.206834i
$147$	3.17074	−	6.24071i	0.261518	−	0.514725i
$148$	1.89322	−	1.89322i	0.155622	−	0.155622i
$149$	8.91258	−	8.91258i	0.730147	−	0.730147i	−0.240502	−	0.970649i	$-0.577312\pi$
$149$	8.91258	−	8.91258i	0.730147	−	0.730147i	0.970649	+	0.240502i	$0.0773120\pi$
$150$	1.50389	+	0.402966i	0.122792	+	0.0329021i
$151$	20.3890	−	5.46323i	1.65924	−	0.444591i	0.697059	−	0.717014i	$-0.254491\pi$
$151$	20.3890	−	5.46323i	1.65924	−	0.444591i	0.962178	+	0.272422i	$0.0878248\pi$
$152$		−	7.02891i		−	0.570120i
$153$	0.752896	+	1.30405i	0.0608681	+	0.105427i
$154$	12.1008	+	11.4700i	0.975111	+	0.924278i
$155$			14.8034i			1.18904i
$156$	1.85805	−	3.18436i	0.148763	−	0.254953i
$157$	−3.20707	−	1.85160i	−0.255952	−	0.147774i	0.366535	−	0.930404i	$-0.380544\pi$
$157$	−3.20707	−	1.85160i	−0.255952	−	0.147774i	−0.622487	+	0.782630i	$0.713877\pi$
$158$	−19.9104	+	19.9104i	−1.58398	+	1.58398i
$159$	−4.57154	−	2.63938i	−0.362547	−	0.209316i
$160$	−5.36177	+	9.28685i	−0.423885	+	0.734190i
$161$	6.75509	−	7.12660i	0.532375	−	0.561655i
$162$	−0.449968	−	1.67930i	−0.0353528	−	0.131939i
$163$	−6.98158	−	6.98158i	−0.546839	−	0.546839i	0.378686	−	0.925525i	$-0.376376\pi$
$163$	−6.98158	−	6.98158i	−0.546839	−	0.546839i	−0.925525	+	0.378686i	$0.876376\pi$
$164$	1.36251	+	5.08494i	0.106394	+	0.397067i
$165$	−3.67179	−	6.35973i	−0.285849	−	0.495104i
$166$	12.7508	−	22.0850i	0.989653	−	1.71413i
$167$	−20.4714	−	5.48528i	−1.58412	−	0.424464i	−0.643922	−	0.765091i	$-0.722694\pi$
$167$	−20.4714	−	5.48528i	−1.58412	−	0.424464i	−0.940199	+	0.340627i	$0.889361\pi$
$168$	2.35142	+	3.83220i	0.181416	+	0.295661i
$169$	−6.60316	+	11.1981i	−0.507936	+	0.861395i
$170$	−2.65185	−	4.59313i	−0.203387	−	0.352277i
$171$	−2.92473	−	2.92473i	−0.223660	−	0.223660i
$172$	5.32761			0.406226
$173$	−13.3105			−1.01198			−0.505990	−	0.862539i	$-0.668873\pi$
$173$	−13.3105			−1.01198			−0.505990	+	0.862539i	$0.668873\pi$
$174$	−4.53637	−	4.53637i	−0.343901	−	0.343901i
$175$	−1.62999	+	1.71963i	−0.123215	+	0.129992i
$176$	−17.5045	+	4.69032i	−1.31945	+	0.353546i
$177$	−0.334114	+	1.24693i	−0.0251136	+	0.0937251i
$178$	−15.1532	+	8.74870i	−1.13578	+	0.655743i
$179$		−	4.66735i		−	0.348854i	−0.984670	−	0.174427i	$-0.944193\pi$
$179$		−	4.66735i		−	0.348854i	0.984670	−	0.174427i	$-0.0558074\pi$
$180$	0.536169	+	2.00101i	0.0399637	+	0.149146i
$181$	−1.72036			−0.127874			−0.0639368	−	0.997954i	$-0.520366\pi$
$181$	−1.72036			−0.127874			−0.0639368	+	0.997954i	$0.520366\pi$
$182$	8.60858	+	14.1754i	0.638110	+	1.05075i
$183$	−10.6182			−0.784922
$184$	1.63237	+	6.09207i	0.120340	+	0.449113i
$185$		−	5.30478i		−	0.390015i
$186$	11.0015	−	6.35170i	0.806667	−	0.465729i
$187$	1.41267	−	5.27217i	0.103305	−	0.385539i
$188$	−0.261313	+	0.0700186i	−0.0190582	+	0.00510663i
$189$	2.57300	+	0.616155i	0.187159	+	0.0448187i
$190$	10.3015	+	10.3015i	0.747347	+	0.747347i
$191$	9.71661			0.703069			0.351535	−	0.936175i	$-0.385660\pi$
$191$	9.71661			0.703069			0.351535	+	0.936175i	$0.385660\pi$
$192$	−0.796700			−0.0574969
$193$	−5.21877	−	5.21877i	−0.375655	−	0.375655i	0.493877	−	0.869532i	$-0.335579\pi$
$193$	−5.21877	−	5.21877i	−0.375655	−	0.375655i	−0.869532	+	0.493877i	$0.835579\pi$
$194$	−0.581319	−	1.00687i	−0.0417363	−	0.0722894i
$195$	−1.85815	−	7.06436i	−0.133065	−	0.505889i
$196$	7.14749	−	0.382848i	0.510535	−	0.0273463i
$197$	0.502809	+	0.134727i	0.0358236	+	0.00959892i	0.276686	−	0.960960i	$-0.410764\pi$
$197$	0.502809	+	0.134727i	0.0358236	+	0.00959892i	−0.240863	+	0.970559i	$0.577430\pi$
$198$	−3.15091	+	5.45753i	−0.223925	+	0.387850i
$199$	7.84176	+	13.5823i	0.555887	+	0.962825i	0.997834	+	0.0657837i	$0.0209547\pi$
$199$	7.84176	+	13.5823i	0.555887	+	0.962825i	−0.441947	+	0.897041i	$0.645712\pi$
$200$	−0.393886	−	1.47000i	−0.0278520	−	0.103945i
$201$	9.48626	+	9.48626i	0.669109	+	0.669109i
$202$	−3.26325	−	12.1786i	−0.229602	−	0.856885i
$203$	9.35943	−	2.77826i	0.656903	−	0.194996i
$204$	−0.769862	+	1.33344i	−0.0539011	+	0.0933595i
$205$	9.03281	+	5.21509i	0.630879	+	0.364238i
$206$	−17.7872	+	17.7872i	−1.23929	+	1.23929i
$207$	3.21414	+	1.85568i	0.223398	+	0.128979i
$208$	−18.0257	−	0.0828099i	−1.24986	−	0.00574183i
$209$			14.9927i			1.03707i
$210$	−9.06262	−	2.17022i	−0.625380	−	0.149759i
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	0.763081	−	0.646302i	$-0.223686\pi$
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	−0.941255	+	0.337697i	$0.890352\pi$
$212$		−	5.39771i		−	0.370716i
$213$	−11.6216	+	3.11400i	−0.796300	+	0.213368i
$214$	−9.87562	−	2.64616i	−0.675083	−	0.180888i
$215$	7.46393	−	7.46393i	0.509036	−	0.509036i
$216$	−1.20163	+	1.20163i	−0.0817609	+	0.0817609i
$217$	0.517201	+	19.3254i	0.0351099	+	1.31189i
$218$	−0.774590	+	0.447210i	−0.0524618	+	0.0302889i
$219$	2.77707	−	0.744113i	0.187657	−	0.0502825i
$220$	3.75453	−	6.50304i	0.253130	−	0.438435i
$221$	2.73618	−	4.68932i	0.184055	−	0.315437i
$222$	−3.94235	+	2.27612i	−0.264593	+	0.152763i
$223$	−3.25346	+	12.1421i	−0.217868	+	0.813093i	0.767270	+	0.641325i	$0.221615\pi$
$223$	−3.25346	+	12.1421i	−0.217868	+	0.813093i	−0.985137	+	0.171769i	$0.945052\pi$
$224$	−6.67514	+	12.3110i	−0.446002	+	0.822563i
$225$	−0.775564	−	0.447772i	−0.0517043	−	0.0298515i
$226$	−13.0454	−	3.49550i	−0.867766	−	0.232517i
$227$	−1.70352	+	6.35762i	−0.113067	+	0.421970i	−0.999135	−	0.0415843i	$-0.986759\pi$
$227$	−1.70352	+	6.35762i	−0.113067	+	0.421970i	0.886068	+	0.463554i	$0.153426\pi$
$228$	1.09465	−	4.08528i	0.0724949	−	0.270555i
$229$	−8.83413	−	2.36710i	−0.583776	−	0.156422i	−0.0451689	−	0.998979i	$-0.514383\pi$
$229$	−8.83413	−	2.36710i	−0.583776	−	0.156422i	−0.538607	+	0.842557i	$0.681049\pi$
$230$	−11.3208	−	6.53608i	−0.746472	−	0.430976i
$231$	−5.01560	−	8.17413i	−0.330002	−	0.537818i
$232$	−1.62301	+	6.05716i	−0.106556	+	0.397672i
$233$	−6.66005	+	3.84518i	−0.436315	+	0.251906i	−0.702033	−	0.712144i	$-0.747724\pi$
$233$	−6.66005	+	3.84518i	−0.436315	+	0.251906i	0.265719	+	0.964051i	$0.414391\pi$
$234$	−4.45275	+	4.41202i	−0.291085	+	0.288423i
$235$	−0.268002	+	0.464192i	−0.0174825	+	0.0302806i
$236$	−1.27503	+	0.341643i	−0.0829974	+	0.0222391i
$237$	14.0262	−	8.09801i	0.911098	−	0.526023i
$238$	−3.62237	−	5.90353i	−0.234804	−	0.382669i
$239$	−14.4981	+	14.4981i	−0.937806	+	0.937806i	−0.998176	−	0.0603699i	$-0.980772\pi$
$239$	−14.4981	+	14.4981i	−0.937806	+	0.937806i	0.0603699	+	0.998176i	$0.480772\pi$
$240$	7.16207	−	7.16207i	0.462310	−	0.462310i
$241$	9.63068	+	2.58053i	0.620366	+	0.166227i	0.555294	−	0.831654i	$-0.312606\pi$
$241$	9.63068	+	2.58053i	0.620366	+	0.166227i	0.0650721	+	0.997881i	$0.479272\pi$
$242$	3.59194	−	0.962456i	0.230898	−	0.0618690i
$243$			1.00000i			0.0641500i
$244$	−5.42875	−	9.40286i	−0.347540	−	0.601957i
$245$	9.47720	−	10.5499i	0.605476	−	0.674010i
$246$		−	8.95055i		−	0.570666i
$247$	−3.92597	+	14.3872i	−0.249804	+	0.915437i
$248$	−10.7536	−	6.20857i	−0.682852	−	0.394245i
$249$	−10.3721	+	10.3721i	−0.657305	+	0.657305i
$250$	17.9832	+	10.3826i	1.13736	+	0.656655i
$251$	3.38103	−	5.85611i	0.213409	−	0.369635i	−0.739371	−	0.673299i	$-0.764877\pi$
$251$	3.38103	−	5.85611i	0.213409	−	0.369635i	0.952779	+	0.303664i	$0.0982101\pi$
$252$	0.769862	+	2.59352i	0.0484967	+	0.163376i
$253$	−3.48185	−	12.9944i	−0.218902	−	0.816954i
$254$	−23.4096	−	23.4096i	−1.46885	−	1.46885i
$255$	0.789567	+	2.94671i	0.0494446	+	0.184530i
$256$	−9.60961	−	16.6443i	−0.600601	−	1.04027i
$257$	−9.65309	+	16.7196i	−0.602143	+	1.04294i	0.390353	+	0.920665i	$0.372353\pi$
$257$	−9.65309	+	16.7196i	−0.602143	+	1.04294i	−0.992496	+	0.122277i	$0.960980\pi$
$258$	−8.74952	−	2.34443i	−0.544721	−	0.145958i
$259$	−0.185338	−	6.92521i	−0.0115163	−	0.430311i
$260$	5.30577	−	5.25724i	0.329050	−	0.326040i
$261$	1.84505	+	3.19572i	0.114206	+	0.197810i
$262$	−22.3145	−	22.3145i	−1.37860	−	1.37860i
$263$	28.1759			1.73740			0.868701	−	0.495336i	$-0.164955\pi$
$263$	28.1759			1.73740			0.868701	+	0.495336i	$0.164955\pi$
$264$	6.15981			0.379110
$265$	−7.56214	−	7.56214i	−0.464539	−	0.464539i
$266$	13.8081	+	13.0883i	0.846631	+	0.802496i
$267$	9.72147	−	2.60486i	0.594944	−	0.159415i
$268$	−3.55045	+	13.2505i	−0.216879	+	0.809402i
$269$	15.1416	−	8.74198i	0.923197	−	0.533008i	0.0385436	−	0.999257i	$-0.487728\pi$
$269$	15.1416	−	8.74198i	0.923197	−	0.533008i	0.884654	+	0.466249i	$0.154395\pi$
$270$		−	3.52219i		−	0.214354i
$271$	−2.13748	−	7.97719i	−0.129843	−	0.484580i	0.870123	−	0.492834i	$-0.164039\pi$
$271$	−2.13748	−	7.97719i	−0.129843	−	0.484580i	−0.999966	+	0.00825451i	$0.997372\pi$
$272$	7.52820			0.456464
$273$	−2.67257	−	9.15737i	−0.161751	−	0.554229i
$274$	34.9992			2.11438
$275$	0.840163	+	3.13553i	0.0506637	+	0.189080i
$276$			3.79500i			0.228432i
$277$	−17.8724	+	10.3186i	−1.07385	+	0.619987i	−0.929231	−	0.369501i	$-0.879529\pi$
$277$	−17.8724	+	10.3186i	−1.07385	+	0.619987i	−0.144618	+	0.989488i	$0.546195\pi$
$278$	9.22746	−	34.4373i	0.553426	−	2.06541i
$279$	−7.05794	+	1.89117i	−0.422548	+	0.113221i
$280$	2.59209	+	8.73226i	0.154907	+	0.521853i
$281$	3.70317	+	3.70317i	0.220913	+	0.220913i	0.808883	−	0.587970i	$-0.200073\pi$
$281$	3.70317	+	3.70317i	0.220913	+	0.220913i	−0.587970	+	0.808883i	$0.700073\pi$
$282$	0.459965			0.0273905
$283$	0.843947			0.0501674			0.0250837	−	0.999685i	$-0.492015\pi$
$283$	0.843947			0.0501674			0.0250837	+	0.999685i	$0.492015\pi$
$284$	−8.69933	−	8.69933i	−0.516210	−	0.516210i
$285$	−4.18985	−	7.25704i	−0.248185	−	0.429870i
$286$	22.7213	+	0.104381i	1.34354	+	0.00617219i
$287$	11.9742	+	6.49254i	0.706817	+	0.383243i
$288$	−5.11274	−	1.36995i	−0.301271	−	0.0807254i
$289$	7.36629	−	12.7588i	0.433311	−	0.750517i
$290$	−6.49862	−	11.2559i	−0.381612	−	0.660971i
$291$	0.173083	+	0.645956i	0.0101463	+	0.0378666i
$292$	2.07877	+	2.07877i	0.121651	+	0.121651i
$293$	4.34707	+	16.2235i	0.253959	+	0.947787i	0.968667	+	0.248364i	$0.0798929\pi$
$293$	4.34707	+	16.2235i	0.253959	+	0.947787i	−0.714708	+	0.699423i	$0.753440\pi$
$294$	−11.9068	−	2.51652i	−0.694417	−	0.146766i
$295$	−1.30767	+	2.26494i	−0.0761352	+	0.131870i
$296$	3.85352	+	2.22483i	0.223981	+	0.129316i
$297$	2.56310	−	2.56310i	0.148726	−	0.148726i
$298$	−18.9773	−	10.9566i	−1.09933	−	0.634696i
$299$	0.0614738	−	13.3814i	0.00355512	−	0.773865i
$300$		−	0.915724i		−	0.0528694i
$301$	9.48314	−	10.0047i	0.546599	−	0.576660i
$302$	−18.3488	−	31.7811i	−1.05586	−	1.82880i
$303$			7.25219i			0.416627i
$304$	−19.9743	+	5.35208i	−1.14560	+	0.306963i
$305$	−20.7789	−	5.56770i	−1.18980	−	0.318806i
$306$	1.85112	−	1.85112i	0.105822	−	0.105822i
$307$	19.8317	−	19.8317i	1.13185	−	1.13185i	0.141986	−	0.989869i	$-0.454651\pi$
$307$	19.8317	−	19.8317i	1.13185	−	1.13185i	0.989869	−	0.141986i	$-0.0453488\pi$
$308$	4.67421	−	8.62067i	0.266338	−	0.491208i
$309$	12.5305	−	7.23449i	0.712835	−	0.411555i
$310$	24.8594	−	6.66107i	1.41192	−	0.378323i
$311$	−11.9512	+	20.7001i	−0.677690	+	1.17379i	0.297985	+	0.954571i	$0.403686\pi$
$311$	−11.9512	+	20.7001i	−0.677690	+	1.17379i	−0.975675	+	0.219223i	$0.929648\pi$
$312$	5.91103	+	1.61300i	0.334646	+	0.0913180i
$313$	−21.1920	+	12.2352i	−1.19784	+	0.691576i	−0.960074	−	0.279746i	$-0.909750\pi$
$313$	−21.1920	+	12.2352i	−1.19784	+	0.691576i	−0.237770	+	0.971321i	$0.576417\pi$
$314$	−1.66632	+	6.21881i	−0.0940361	+	0.350948i
$315$	4.71206	+	2.55493i	0.265495	+	0.143954i
$316$	14.3422	+	8.28049i	0.806814	+	0.465814i
$317$	−24.0424	−	6.44215i	−1.35036	−	0.361827i	−0.490091	−	0.871671i	$-0.663037\pi$
$317$	−24.0424	−	6.44215i	−1.35036	−	0.361827i	−0.860267	+	0.509844i	$0.829703\pi$
$318$	−2.37527	+	8.86465i	−0.133199	+	0.497105i
$319$	3.46190	−	12.9200i	0.193829	−	0.723380i
$320$	−1.55907	−	0.417752i	−0.0871548	−	0.0233531i
$321$	5.09290	+	2.94039i	0.284258	+	0.164117i
$322$	−15.0073	−	8.13710i	−0.836324	−	0.453463i
$323$	1.61199	−	6.01603i	0.0896935	−	0.334741i
$324$	−0.885540	+	0.511267i	−0.0491967	+	0.0284037i
$325$	−0.0148335	+	3.22890i	−0.000822814	+	0.179107i
$326$	−8.58270	+	14.8657i	−0.475352	+	0.823334i
$327$	0.496935	−	0.133153i	0.0274806	−	0.00736339i
$328$	−7.57674	+	4.37443i	−0.418355	+	0.241538i
$329$	−0.333649	+	0.615351i	−0.0183947	+	0.0339254i
$330$	−9.02773	+	9.02773i	−0.496960	+	0.496960i
$331$	3.49185	−	3.49185i	0.191930	−	0.191930i	−0.604600	−	0.796529i	$-0.706667\pi$
$331$	3.49185	−	3.49185i	0.191930	−	0.191930i	0.796529	+	0.604600i	$0.206667\pi$
$332$	−14.4878	−	3.88200i	−0.795122	−	0.213052i
$333$	2.52920	−	0.677697i	0.138599	−	0.0371376i
$334$			36.8458i			2.01611i
$335$	13.5896	+	23.5379i	0.742481	+	1.28602i
$336$	9.09962	−	9.60007i	0.496425	−	0.523727i
$337$			4.37276i			0.238200i	0.992882	+	0.119100i	$0.0380009\pi$
$337$			4.37276i			0.238200i	−0.992882	+	0.119100i	$0.961999\pi$
$338$	21.7763	+	6.04992i	1.18447	+	0.329072i
$339$	6.72757	+	3.88416i	0.365391	+	0.210959i
$340$	−2.20575	+	2.20575i	−0.119623	+	0.119623i
$341$	22.9375	+	13.2429i	1.24213	+	0.717146i
$342$	−3.59548	+	6.22755i	−0.194421	+	0.336747i
$343$	12.0036	−	14.1037i	0.648132	−	0.761528i
$344$	2.29160	+	8.55236i	0.123555	+	0.461112i
$345$	5.31675	+	5.31675i	0.286244	+	0.286244i
$346$	5.98931	+	22.3524i	0.321987	+	1.20167i
$347$	−13.6420	−	23.6286i	−0.732338	−	1.26845i	−0.955881	−	0.293753i	$-0.905096\pi$
$347$	−13.6420	−	23.6286i	−0.732338	−	1.26845i	0.223543	−	0.974694i	$-0.428238\pi$
$348$	−1.88662	+	3.26773i	−0.101134	+	0.175169i
$349$	4.48654	+	1.20217i	0.240159	+	0.0643505i	0.376891	−	0.926258i	$-0.376993\pi$
$349$	4.48654	+	1.20217i	0.240159	+	0.0643505i	−0.136732	+	0.990608i	$0.543660\pi$
$350$	3.62123	+	1.96346i	0.193563	+	0.104952i
$351$	3.13075	−	1.78841i	0.167107	−	0.0954584i
$352$	9.59313	+	16.6158i	0.511315	+	0.885624i
$353$	−2.96642	−	2.96642i	−0.157886	−	0.157886i	0.623743	−	0.781629i	$-0.285611\pi$
$353$	−2.96642	−	2.96642i	−0.157886	−	0.157886i	−0.781629	+	0.623743i	$0.785611\pi$
$354$	2.24432			0.119284
$355$	−24.3753			−1.29371
$356$	7.27697	+	7.27697i	0.385679	+	0.385679i
$357$	1.13371	+	3.81924i	0.0600021	+	0.202136i
$358$	−7.83790	+	2.10016i	−0.414246	+	0.110997i
$359$	−1.84503	+	6.88575i	−0.0973770	+	0.363416i	−0.997369	−	0.0724902i	$-0.976905\pi$
$359$	−1.84503	+	6.88575i	−0.0973770	+	0.363416i	0.899992	+	0.435906i	$0.143572\pi$
$360$	−2.98158	+	1.72141i	−0.157143	+	0.0907264i
$361$		−	1.89190i		−	0.0995738i
$362$	0.774109	+	2.88901i	0.0406862	+	0.151843i
$363$	−2.13894			−0.112265
$364$	6.74282	−	7.04852i	0.353420	−	0.369443i
$365$	5.82466			0.304877
$366$	4.77786	+	17.8312i	0.249743	+	0.932053i
$367$			3.11291i			0.162492i	0.996694	+	0.0812462i	$0.0258900\pi$
$367$			3.11291i			0.162492i	−0.996694	+	0.0812462i	$0.974110\pi$
$368$	16.0691	−	9.27747i	0.837657	−	0.483622i
$369$	−1.33248	+	4.97288i	−0.0693661	+	0.258878i
$370$	−8.90833	+	2.38698i	−0.463122	+	0.124093i
$371$	−10.1363	−	9.60792i	−0.526252	−	0.498818i
$372$	−5.28320	−	5.28320i	−0.273921	−	0.273921i
$373$	12.2136			0.632395			0.316197	−	0.948693i	$-0.397594\pi$
$373$	12.2136			0.632395			0.316197	+	0.948693i	$0.397594\pi$
$374$	−9.48923			−0.490676
$375$	−8.44572	−	8.44572i	−0.436135	−	0.436135i
$376$	−0.224800	−	0.389366i	−0.0115932	−	0.0200800i
$377$	6.70528	−	11.4916i	0.345339	−	0.591849i
$378$	−0.123058	−	4.59811i	−0.00632944	−	0.236501i
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.440760	−	0.897625i	$-0.645291\pi$
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.830522	+	0.556986i	$0.811958\pi$
$380$	4.28426	−	7.42056i	0.219778	−	0.380667i
$381$	9.52126	+	16.4913i	0.487789	+	0.844875i
$382$	−4.37217	−	16.3171i	−0.223699	−	0.834858i
$383$	25.5467	+	25.5467i	1.30538	+	1.30538i	0.924714	+	0.380664i	$0.124304\pi$
$383$	25.5467	+	25.5467i	1.30538	+	1.30538i	0.380664	+	0.924714i	$0.375696\pi$
$384$	3.09840	+	11.5634i	0.158115	+	0.590092i
$385$	−5.52896	−	18.6260i	−0.281782	−	0.949269i
$386$	−6.41562	+	11.1122i	−0.326547	+	0.565595i
$387$	4.51217	+	2.60510i	0.229366	+	0.132425i
$388$	−0.483528	+	0.483528i	−0.0245474	+	0.0245474i
$389$	−10.5275	−	6.07805i	−0.533765	−	0.308170i	0.208783	−	0.977962i	$-0.433050\pi$
$389$	−10.5275	−	6.07805i	−0.533765	−	0.308170i	−0.742548	+	0.669792i	$0.766383\pi$
$390$	−11.0271	+	6.29914i	−0.558379	+	0.318969i
$391$			5.58855i			0.282625i
$392$	3.68898	+	11.3091i	0.186321	+	0.571197i
$393$	9.07584	+	15.7198i	0.457816	+	0.792960i
$394$		−	0.904992i		−	0.0455928i
$395$	31.6942	−	8.49244i	1.59471	−	0.427301i
$396$	3.58015	+	0.959299i	0.179909	+	0.0482066i
$397$	−10.5534	+	10.5534i	−0.529660	+	0.529660i	−0.920471	−	0.390811i	$-0.872195\pi$
$397$	−10.5534	+	10.5534i	−0.529660	+	0.529660i	0.390811	+	0.920471i	$0.372195\pi$
$398$	19.2803	−	19.2803i	0.966434	−	0.966434i
$399$	−5.72326	−	9.32743i	−0.286521	−	0.466956i
$400$	−3.87743	+	2.23863i	−0.193871	+	0.111932i
$401$	−4.31771	+	1.15693i	−0.215616	+	0.0577741i	−0.365010	−	0.931004i	$-0.618934\pi$
$401$	−4.31771	+	1.15693i	−0.215616	+	0.0577741i	0.149394	+	0.988778i	$0.452268\pi$
$402$	11.6618	−	20.1988i	0.581638	−	1.00743i
$403$	18.5433	+	18.7144i	0.923707	+	0.932233i
$404$	−6.42210	+	3.70780i	−0.319512	+	0.184470i
$405$	−0.524353	+	1.95691i	−0.0260553	+	0.0972398i
$406$	−8.87699	−	14.4672i	−0.440558	−	0.717995i
$407$	−8.21959	−	4.74558i	−0.407430	−	0.235230i
$408$	−2.47170	−	0.662291i	−0.122368	−	0.0327883i
$409$	−0.143340	+	0.534951i	−0.00708769	+	0.0264516i	−0.969379	−	0.245569i	$-0.921025\pi$
$409$	−0.143340	+	0.534951i	−0.00708769	+	0.0264516i	0.962291	+	0.272021i	$0.0876919\pi$
$410$	4.69325	−	17.5155i	0.231783	−	0.865027i
$411$	−19.4454	−	5.21037i	−0.959169	−	0.257008i
$412$	12.8129	+	7.39751i	0.631244	+	0.364449i
$413$	−1.62798	+	3.00249i	−0.0801077	+	0.147743i
$414$	1.67000	−	6.23251i	0.0820758	−	0.306311i
$415$	−25.7359	+	14.8587i	−1.26333	+	0.729383i
$416$	4.85471	+	18.4567i	0.238022	+	0.904917i
$417$	−10.2535	+	17.7595i	−0.502114	+	0.869687i
$418$	25.1774	−	6.74626i	1.23147	−	0.329970i
$419$	20.1383	−	11.6268i	0.983819	−	0.568008i	0.0803983	−	0.996763i	$-0.474381\pi$
$419$	20.1383	−	11.6268i	0.983819	−	0.568008i	0.903421	+	0.428754i	$0.141047\pi$
$420$	0.146633	+	5.47897i	0.00715494	+	0.267346i
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	−0.997617	−	0.0690021i	$-0.978018\pi$
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	0.0690021	+	0.997617i	$0.478018\pi$
$422$	−6.36334	+	6.36334i	−0.309763	+	0.309763i
$423$	−0.255554	−	0.0684756i	−0.0124255	−	0.00332940i
$424$	8.66489	−	2.32175i	0.420804	−	0.112754i
$425$		−	1.34850i		−	0.0654121i
$426$	10.4587	+	18.1150i	0.506727	+	0.877676i
$427$	−27.3207	−	6.54247i	−1.32214	−	0.316612i
$428$			6.01330i			0.290664i
$429$	−12.6083	−	3.44054i	−0.608734	−	0.166111i
$430$	−15.8927	−	9.17568i	−0.766416	−	0.442490i
$431$	−14.4777	+	14.4777i	−0.697365	+	0.697365i	−0.963842	−	0.266476i	$-0.914141\pi$
$431$	−14.4777	+	14.4777i	−0.697365	+	0.697365i	0.266476	+	0.963842i	$0.414141\pi$
$432$	4.32969	+	2.49975i	0.208312	+	0.120269i
$433$	13.7982	−	23.8993i	0.663101	−	1.14852i	−0.316695	−	0.948527i	$-0.602573\pi$
$433$	13.7982	−	23.8993i	0.663101	−	1.14852i	0.979796	−	0.199997i	$-0.0640934\pi$
$434$	32.2205	−	9.56434i	1.54663	−	0.459103i
$435$	1.93491	+	7.22120i	0.0927720	+	0.346230i
$436$	0.371979	+	0.371979i	0.0178146	+	0.0178146i
$437$	−3.97311	−	14.8279i	−0.190060	−	0.709313i
$438$	−2.49919	−	4.32872i	−0.119416	−	0.206834i
$439$	−9.02753	+	15.6361i	−0.430860	+	0.746272i	−0.996948	−	0.0780733i	$-0.975123\pi$
$439$	−9.02753	+	15.6361i	−0.430860	+	0.746272i	0.566087	+	0.824345i	$0.308456\pi$
$440$	12.0542	+	3.22992i	0.574662	+	0.153980i
$441$	6.24071	+	3.17074i	0.297176	+	0.150988i
$442$	−9.10598	−	2.48483i	−0.433127	−	0.118191i
$443$	−19.5401	−	33.8445i	−0.928380	−	1.60800i	−0.786033	−	0.618185i	$-0.787868\pi$
$443$	−19.5401	−	33.8445i	−0.928380	−	1.60800i	−0.142348	−	0.989817i	$-0.545465\pi$
$444$	1.89322	+	1.89322i	0.0898484	+	0.0898484i
$445$	20.3899			0.966576
$446$	21.8542			1.03483
$447$	8.91258	+	8.91258i	0.421551	+	0.421551i
$448$	−2.04991	−	0.490891i	−0.0968493	−	0.0231924i
$449$	21.8252	−	5.84805i	1.03000	−	0.275987i	0.296034	−	0.955177i	$-0.404336\pi$
$449$	21.8252	−	5.84805i	1.03000	−	0.275987i	0.733962	+	0.679191i	$0.237669\pi$
$450$	−0.402966	+	1.50389i	−0.0189960	+	0.0708941i
$451$	16.1613	−	9.33071i	0.761004	−	0.439366i
$452$			7.94338i			0.373625i
$453$	5.46323	+	20.3890i	0.256685	+	0.957961i
$454$	11.4429			0.537042
$455$	−0.428283	−	19.3215i	−0.0200782	−	0.905808i
$456$	7.02891			0.329159
$457$	5.08518	+	18.9781i	0.237875	+	0.887760i	0.976832	+	0.214008i	$0.0686519\pi$
$457$	5.08518	+	18.9781i	0.237875	+	0.887760i	−0.738957	+	0.673752i	$0.764681\pi$
$458$			15.9003i			0.742973i
$459$	−1.30405	+	0.752896i	−0.0608681	+	0.0351422i
$460$	−1.98992	+	7.42648i	−0.0927804	+	0.346261i
$461$	−14.3331	+	3.84054i	−0.667559	+	0.178872i	−0.576655	−	0.816988i	$-0.695642\pi$
$461$	−14.3331	+	3.84054i	−0.667559	+	0.178872i	−0.0909042	+	0.995860i	$0.528976\pi$
$462$	−11.4700	+	12.1008i	−0.533632	+	0.562981i
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.999972	−	0.00741751i	$-0.997639\pi$
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.00741751	−	0.999972i	$-0.502361\pi$
$464$	18.4486			0.856455
$465$	−14.8034			−0.686492
$466$	9.45404	+	9.45404i	0.437950	+	0.437950i
$467$	10.6105	+	18.3780i	0.490996	+	0.850431i	0.999946	−	0.0103654i	$-0.00329948\pi$
$467$	10.6105	+	18.3780i	0.490996	+	0.850431i	−0.508950	+	0.860796i	$0.669966\pi$
$468$	3.18436	+	1.85805i	0.147197	+	0.0858883i
$469$	18.5632	+	30.2532i	0.857168	+	1.39696i
$470$	0.900112	+	0.241184i	0.0415191	+	0.0111250i
$471$	1.85160	−	3.20707i	0.0853173	−	0.147774i
$472$	−1.09687	−	1.89984i	−0.0504877	−	0.0874472i
$473$	−4.88800	−	18.2423i	−0.224750	−	0.838780i
$474$	−19.9104	−	19.9104i	−0.914513	−	0.914513i
$475$	0.958703	+	3.57793i	0.0439883	+	0.164167i
$476$	−2.80246	+	2.95659i	−0.128451	+	0.135515i
$477$	2.63938	−	4.57154i	0.120849	−	0.209316i
$478$	30.8705	+	17.8231i	1.41198	+	0.815208i
$479$	7.56345	−	7.56345i	0.345583	−	0.345583i	−0.512878	−	0.858461i	$-0.671421\pi$
$479$	7.56345	−	7.56345i	0.345583	−	0.345583i	0.858461	+	0.512878i	$0.171421\pi$
$480$	−9.28685	−	5.36177i	−0.423885	−	0.244730i
$481$	−6.64495	−	6.70628i	−0.302984	−	0.305780i
$482$		−	17.3340i		−	0.789542i
$483$	7.12660	+	6.75509i	0.324272	+	0.307367i
$484$	−1.09357	−	1.89412i	−0.0497078	−	0.0860964i
$485$			1.35484i			0.0615199i
$486$	1.67930	−	0.449968i	0.0761748	−	0.0204110i
$487$	−30.8488	−	8.26590i	−1.39789	−	0.374564i	−0.520304	−	0.853981i	$-0.674181\pi$
$487$	−30.8488	−	8.26590i	−1.39789	−	0.374564i	−0.877587	+	0.479417i	$0.840848\pi$
$488$	12.7592	−	12.7592i	0.577583	−	0.577583i
$489$	6.98158	−	6.98158i	0.315718	−	0.315718i
$490$	−21.9810	−	11.1680i	−0.992999	−	0.504517i
$491$	7.33827	−	4.23675i	0.331171	−	0.191202i	−0.325190	−	0.945649i	$-0.605428\pi$
$491$	7.33827	−	4.23675i	0.331171	−	0.191202i	0.656361	+	0.754447i	$0.272095\pi$
$492$	−5.08494	+	1.36251i	−0.229247	+	0.0614265i
$493$	−2.77826	+	4.81209i	−0.125127	+	0.216725i
$494$	25.9271	+	0.119109i	1.16651	+	0.00535895i
$495$	6.35973	−	3.67179i	0.285849	−	0.165035i
$496$	−9.45489	+	35.2861i	−0.424537	+	1.58439i
$497$	−31.8212	+	0.851625i	−1.42738	+	0.0382006i
$498$	22.0850	+	12.7508i	0.989653	+	0.571377i
$499$	−24.4581	−	6.55352i	−1.09489	−	0.293376i	−0.334210	−	0.942499i	$-0.608469\pi$
$499$	−24.4581	−	6.55352i	−1.09489	−	0.293376i	−0.760684	+	0.649123i	$0.775136\pi$
$500$	3.16101	−	11.7970i	0.141365	−	0.527580i
$501$	5.48528	−	20.4714i	0.245064	−	0.914593i
$502$	−11.3555	−	3.04271i	−0.506823	−	0.135803i
$503$	5.83735	+	3.37020i	0.260275	+	0.150270i	0.624460	−	0.781057i	$-0.285319\pi$
$503$	5.83735	+	3.37020i	0.260275	+	0.150270i	−0.364185	+	0.931327i	$0.618652\pi$
$504$	−3.83220	+	2.35142i	−0.170700	+	0.104740i
$505$	−3.80271	+	14.1919i	−0.169218	+	0.631531i
$506$	−20.2549	+	11.6942i	−0.900440	+	0.519869i
$507$	−11.1981	−	6.60316i	−0.497327	−	0.293257i
$508$	−9.73581	+	16.8629i	−0.431957	+	0.748171i
$509$	−2.97301	+	0.796615i	−0.131776	+	0.0353094i	−0.324104	−	0.946021i	$-0.605063\pi$
$509$	−2.97301	+	0.796615i	−0.131776	+	0.0353094i	0.192328	+	0.981331i	$0.438396\pi$
$510$	4.59313	−	2.65185i	0.203387	−	0.117426i
$511$	7.60390	−	0.203502i	0.336377	−	0.00900239i
$512$	−6.69691	+	6.69691i	−0.295964	+	0.295964i
$513$	2.92473	−	2.92473i	0.129130	−	0.129130i
$514$	32.4210	+	8.68717i	1.43003	+	0.383175i
$515$	28.3145	−	7.58685i	1.24769	−	0.334317i
$516$			5.32761i			0.234535i
$517$	0.479501	+	0.830521i	0.0210884	+	0.0365263i
$518$	−11.5461	+	3.42736i	−0.507308	+	0.150590i
$519$		−	13.3105i		−	0.584267i
$520$	10.7216	+	6.25596i	0.470173	+	0.274342i
$521$	−22.0369	−	12.7230i	−0.965453	−	0.557405i	−0.0676060	−	0.997712i	$-0.521536\pi$
$521$	−22.0369	−	12.7230i	−0.965453	−	0.557405i	−0.897847	+	0.440308i	$0.854869\pi$
$522$	4.53637	−	4.53637i	0.198551	−	0.198551i
$523$	12.9246	+	7.46200i	0.565151	+	0.326290i	0.755211	−	0.655482i	$-0.227535\pi$
$523$	12.9246	+	7.46200i	0.565151	+	0.326290i	−0.190059	+	0.981773i	$0.560868\pi$
$524$	−9.28035	+	16.0740i	−0.405414	+	0.702198i
$525$	−1.71963	−	1.62999i	−0.0750509	−	0.0711385i
$526$	−12.6783	−	47.3160i	−0.552799	−	2.06307i
$527$	−7.78009	−	7.78009i	−0.338906	−	0.338906i
$528$	−4.69032	−	17.5045i	−0.204120	−	0.761786i
$529$	−4.61288	−	7.98975i	−0.200560	−	0.347380i
$530$	−9.29641	+	16.1019i	−0.403810	+	0.699420i
$531$	−1.24693	−	0.334114i	−0.0541122	−	0.0144993i
$532$	5.33370	−	9.83698i	0.231245	−	0.426487i
$533$	17.9519	−	4.72190i	0.777581	−	0.204528i
$534$	−8.74870	−	15.1532i	−0.378593	−	0.655743i
$535$	8.42457	+	8.42457i	0.364226	+	0.364226i
$536$	−22.7980			−0.984725
$537$	4.66735			0.201411
$538$	−21.4937	−	21.4937i	−0.926658	−	0.926658i
$539$	−7.86862	−	24.1225i	−0.338926	−	1.03903i
$540$	−2.00101	+	0.536169i	−0.0861097	+	0.0230730i
$541$	2.99446	−	11.1755i	0.128742	−	0.480471i	−0.871204	−	0.490922i	$-0.836660\pi$
$541$	2.99446	−	11.1755i	0.128742	−	0.480471i	0.999945	+	0.0104509i	$0.00332668\pi$
$542$	−12.4343	+	7.17896i	−0.534100	+	0.308363i
$543$		−	1.72036i		−	0.0738278i
$544$	−2.06287	−	7.69873i	−0.0884447	−	0.330080i
$545$	1.04228			0.0446463
$546$	−14.1754	+	8.60858i	−0.606653	+	0.368413i
$547$	−1.37820			−0.0589275			−0.0294637	−	0.999566i	$-0.509380\pi$
$547$	−1.37820			−0.0589275			−0.0294637	+	0.999566i	$0.509380\pi$
$548$	−5.32778	−	19.8835i	−0.227591	−	0.849382i
$549$		−	10.6182i		−	0.453175i
$550$	4.88746	−	2.82178i	0.208402	−	0.120321i
$551$	3.95034	−	14.7429i	0.168290	−	0.628068i
$552$	−6.09207	+	1.63237i	−0.259296	+	0.0694781i
$553$	41.0790	−	12.1939i	1.74686	−	0.518539i
$554$	25.3701	+	25.3701i	1.07787	+	1.07787i
$555$	5.30478			0.225175
$556$	−20.9690			−0.889284
$557$	20.8703	+	20.8703i	0.884303	+	0.884303i	0.993969	−	0.109666i	$-0.0349781\pi$
$557$	20.8703	+	20.8703i	0.884303	+	0.884303i	−0.109666	+	0.993969i	$0.534978\pi$
$558$	6.35170	+	11.0015i	0.268889	+	0.465729i
$559$	0.0863000	−	18.7855i	0.00365010	−	0.794540i
$560$	22.8410	−	14.0151i	0.965208	−	0.592246i
$561$	5.27217	+	1.41267i	0.222591	+	0.0596431i
$562$	4.55244	−	7.88506i	0.192033	−	0.332611i
$563$	−17.4133	−	30.1607i	−0.733882	−	1.27112i	−0.955212	−	0.295922i	$-0.904373\pi$
$563$	−17.4133	−	30.1607i	−0.733882	−	1.27112i	0.221330	−	0.975199i	$-0.428960\pi$
$564$	−0.0700186	−	0.261313i	−0.00294832	−	0.0110033i
$565$	11.1286	+	11.1286i	0.468183	+	0.468183i
$566$	−0.379749	−	1.41724i	−0.0159620	−	0.0595712i
$567$	−0.616155	+	2.57300i	−0.0258761	+	0.108056i
$568$	10.2230	−	17.7068i	0.428949	−	0.742962i
$569$	−33.8192	−	19.5255i	−1.41777	−	0.818553i	−0.421672	−	0.906749i	$-0.638556\pi$
$569$	−33.8192	−	19.5255i	−1.41777	−	0.818553i	−0.996103	+	0.0881961i	$0.971890\pi$
$570$	−10.3015	+	10.3015i	−0.431481	+	0.431481i
$571$	−10.3165	−	5.95625i	−0.431733	−	0.249261i	0.268351	−	0.963321i	$-0.413521\pi$
$571$	−10.3165	−	5.95625i	−0.431733	−	0.249261i	−0.700085	+	0.714060i	$0.746854\pi$
$572$	−3.39947	−	12.9242i	−0.142139	−	0.540387i
$573$			9.71661i			0.405917i
$574$	5.51493	−	23.0298i	0.230189	−	0.961246i
$575$	−1.66185	−	2.87840i	−0.0693038	−	0.120038i
$576$		−	0.796700i		−	0.0331958i
$577$	24.4431	−	6.54951i	1.01758	−	0.272660i	0.288787	−	0.957393i	$-0.406748\pi$
$577$	24.4431	−	6.54951i	1.01758	−	0.272660i	0.728793	+	0.684734i	$0.240082\pi$
$578$	−24.7405	−	6.62920i	−1.02907	−	0.275738i
$579$	5.21877	−	5.21877i	0.216885	−	0.216885i
$580$	−5.40540	+	5.40540i	−0.224447	+	0.224447i
$581$	−33.0783	+	20.2966i	−1.37232	+	0.842046i
$582$	1.00687	−	0.581319i	0.0417363	−	0.0240965i
$583$	−18.4823	+	4.95232i	−0.765459	+	0.205104i
$584$	−2.44287	+	4.23117i	−0.101087	+	0.175087i
$585$	7.06436	−	1.85815i	0.292075	−	0.0768250i
$586$	25.2881	−	14.6001i	1.04464	−	0.603125i
$587$	0.718902	−	2.68298i	0.0296723	−	0.110738i	−0.949501	−	0.313763i	$-0.898410\pi$
$587$	0.718902	−	2.68298i	0.0296723	−	0.110738i	0.979174	+	0.203024i	$0.0650770\pi$
$588$	0.382848	+	7.14749i	0.0157884	+	0.294758i
$589$	26.1737	+	15.1114i	1.07847	+	0.622655i
$590$	4.39194	+	1.17682i	0.180813	+	0.0484487i
$591$	−0.134727	+	0.502809i	−0.00554194	+	0.0206828i
$592$	3.38814	−	12.6447i	0.139252	−	0.519694i
$593$	−25.9060	−	6.94149i	−1.06383	−	0.285053i	−0.315875	−	0.948801i	$-0.602298\pi$
$593$	−25.9060	−	6.94149i	−1.06383	−	0.285053i	−0.747956	+	0.663748i	$0.768965\pi$
$594$	−5.45753	−	3.15091i	−0.223925	−	0.129283i
$595$	0.215933	+	8.06838i	0.00885238	+	0.330771i
$596$	−3.33574	+	12.4492i	−0.136637	+	0.509937i
$597$	−13.5823	+	7.84176i	−0.555887	+	0.320942i
$598$	−22.4991	+	5.91796i	−0.920055	+	0.242003i
$599$	−12.6948	+	21.9880i	−0.518695	+	0.898407i	0.481069	+	0.876683i	$0.340249\pi$
$599$	−12.6948	+	21.9880i	−0.518695	+	0.898407i	−0.999764	+	0.0217238i	$0.993085\pi$
$600$	1.47000	−	0.393886i	0.0600126	−	0.0160803i
$601$	−27.2508	+	15.7333i	−1.11158	+	0.641774i	−0.939239	−	0.343263i	$-0.888468\pi$
$601$	−27.2508	+	15.7333i	−1.11158	+	0.641774i	−0.172345	+	0.985037i	$0.555134\pi$
$602$	−21.0680	−	11.4233i	−0.858668	−	0.465578i
$603$	−9.48626	+	9.48626i	−0.386310	+	0.386310i
$604$	−15.2622	+	15.2622i	−0.621008	+	0.621008i
$605$	−4.18573	−	1.12156i	−0.170174	−	0.0455980i
$606$	12.1786	−	3.26325i	0.494723	−	0.132561i
$607$			33.5338i			1.36110i	0.732704	+	0.680548i	$0.238258\pi$
$607$			33.5338i			1.36110i	−0.732704	+	0.680548i	$0.761742\pi$
$608$	10.9466	+	18.9601i	0.443945	+	0.768935i
$609$	2.77826	+	9.35943i	0.112581	+	0.379263i
$610$			37.3995i			1.51426i
$611$	0.242657	+	0.922539i	0.00981684	+	0.0373219i
$612$	−1.33344	−	0.769862i	−0.0539011	−	0.0311198i
$613$	22.6604	−	22.6604i	0.915245	−	0.915245i	−0.0814340	−	0.996679i	$-0.525950\pi$
$613$	22.6604	−	22.6604i	0.915245	−	0.915245i	0.996679	+	0.0814340i	$0.0259500\pi$
$614$	−42.2271	−	24.3798i	−1.70415	−	0.983889i
$615$	−5.21509	+	9.03281i	−0.210293	+	0.364238i
$616$	15.8492	+	3.79540i	0.638584	+	0.152921i
$617$	1.63790	+	6.11271i	0.0659392	+	0.246088i	0.991026	−	0.133666i	$-0.0426751\pi$
$617$	1.63790	+	6.11271i	0.0659392	+	0.246088i	−0.925087	+	0.379755i	$0.876008\pi$
$618$	−17.7872	−	17.7872i	−0.715507	−	0.715507i
$619$	5.22223	+	19.4896i	0.209899	+	0.783355i	0.987900	+	0.155092i	$0.0495673\pi$
$619$	5.22223	+	19.4896i	0.209899	+	0.783355i	−0.778001	+	0.628263i	$0.783766\pi$
$620$	−7.56850	−	13.1090i	−0.303958	−	0.526471i
$621$	−1.85568	+	3.21414i	−0.0744660	+	0.128979i
$622$	40.1394	+	10.7553i	1.60944	+	0.431249i
$623$	26.6184	−	0.712383i	1.06644	−	0.0285410i
$624$	0.0828099	−	18.0257i	0.00331505	−	0.721607i
$625$	−9.86014	−	17.0783i	−0.394406	−	0.683130i
$626$	30.0824	+	30.0824i	1.20233	+	1.20233i
$627$	−14.9927			−0.598752
$628$	3.78665			0.151104
$629$	2.78798	+	2.78798i	0.111164	+	0.111164i
$630$	2.17022	−	9.06262i	0.0864636	−	0.361064i
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.927938	−	0.372735i	$-0.878420\pi$
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.617250	+	0.786767i	$0.711753\pi$
$632$	−7.12348	+	26.5852i	−0.283357	+	1.05750i
$633$	4.48276	−	2.58812i	0.178174	−	0.102869i
$634$			43.2733i			1.71860i
$635$	9.98501	+	37.2646i	0.396243	+	1.47880i
$636$	5.39771			0.214033
$637$	−1.23417	−	25.2087i	−0.0488994	−	0.998804i
$638$	−23.2543			−0.920647
$639$	−3.11400	−	11.6216i	−0.123188	−	0.459744i
$640$			24.2532i			0.958692i
$641$	−4.88340	+	2.81943i	−0.192883	+	0.111361i	−0.593331	−	0.804958i	$-0.702188\pi$
$641$	−4.88340	+	2.81943i	−0.192883	+	0.111361i	0.400449	+	0.916319i	$0.368854\pi$
$642$	2.64616	−	9.87562i	0.104436	−	0.389760i
$643$	−6.33945	+	1.69865i	−0.250003	+	0.0669882i	−0.381644	−	0.924309i	$-0.624642\pi$
$643$	−6.33945	+	1.69865i	−0.250003	+	0.0669882i	0.131641	+	0.991297i	$0.457975\pi$
$644$	−2.33831	+	9.76454i	−0.0921422	+	0.384777i
$645$	7.46393	+	7.46393i	0.293892	+	0.293892i
$646$	−10.8281			−0.426025
$647$	−35.2920			−1.38747			−0.693736	−	0.720229i	$-0.744037\pi$
$647$	−35.2920			−1.38747			−0.693736	+	0.720229i	$0.744037\pi$
$648$	−1.20163	−	1.20163i	−0.0472047	−	0.0472047i
$649$	2.33964	+	4.05238i	0.0918389	+	0.159070i
$650$	5.42897	−	1.42799i	0.212942	−	0.0560104i
$651$	−19.3254	+	0.517201i	−0.757421	+	0.0202707i
$652$	9.75192	+	2.61302i	0.381914	+	0.102334i
$653$	25.2072	−	43.6601i	0.986433	−	1.70855i	0.351044	−	0.936359i	$-0.385827\pi$
$653$	25.2072	−	43.6601i	0.986433	−	1.70855i	0.635389	−	0.772192i	$-0.280840\pi$
$654$	−0.447210	−	0.774590i	−0.0174873	−	0.0302889i
$655$	9.51789	+	35.5213i	0.371895	+	1.38793i
$656$	18.2002	+	18.2002i	0.710597	+	0.710597i
$657$	0.744113	+	2.77707i	0.0290306	+	0.108344i
$658$	1.18349	+	0.283410i	0.0461374	+	0.0110485i
$659$	3.05790	−	5.29643i	0.119119	−	0.206320i	−0.800300	−	0.599600i	$-0.795326\pi$
$659$	3.05790	−	5.29643i	0.119119	−	0.206320i	0.919419	+	0.393280i	$0.128660\pi$
$660$	6.50304	+	3.75453i	0.253130	+	0.146145i
$661$	−3.88313	+	3.88313i	−0.151036	+	0.151036i	−0.778581	−	0.627544i	$-0.784060\pi$
$661$	−3.88313	+	3.88313i	−0.151036	+	0.151036i	0.627544	+	0.778581i	$0.284060\pi$
$662$	−7.43510	−	4.29266i	−0.288974	−	0.166839i
$663$	4.68932	+	2.73618i	0.182118	+	0.106264i
$664$		−	24.9269i		−	0.967353i
$665$	−6.30905	−	21.2540i	−0.244654	−	0.824194i
$666$	−2.27612	−	3.94235i	−0.0881978	−	0.152763i
$667$			13.6953i			0.530284i
$668$	20.9326	−	5.60889i	0.809908	−	0.217014i
$669$	−12.1421	−	3.25346i	−0.469440	−	0.125786i
$670$	33.4125	−	33.4125i	1.29084	−	1.29084i
$671$	−27.2155	+	27.2155i	−1.05064	+	1.05064i
$672$	−12.3110	−	6.67514i	−0.474907	−	0.257499i
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	−0.0864726	−	0.996254i	$-0.527560\pi$
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	0.819545	+	0.573015i	$0.194226\pi$
$674$	7.34320	−	1.96760i	0.282850	−	0.0757893i
$675$	0.447772	−	0.775564i	0.0172348	−	0.0298515i
$676$	0.122132	−	13.2924i	0.00469740	−	0.511245i
$677$	6.64801	−	3.83823i	0.255504	−	0.147515i	−0.366778	−	0.930308i	$-0.619539\pi$
$677$	6.64801	−	3.83823i	0.255504	−	0.147515i	0.622282	+	0.782793i	$0.286206\pi$
$678$	3.49550	−	13.0454i	0.134244	−	0.501005i
$679$	0.0473352	+	1.76869i	0.00181656	+	0.0678762i
$680$	−4.48963	−	2.59209i	−0.172170	−	0.0994022i
$681$	−6.35762	−	1.70352i	−0.243625	−	0.0652790i
$682$	11.9178	−	44.4779i	0.456356	−	1.70315i
$683$	−4.84748	+	18.0911i	−0.185484	+	0.692235i	0.809043	+	0.587750i	$0.199986\pi$
$683$	−4.84748	+	18.0911i	−0.185484	+	0.692235i	−0.994526	+	0.104485i	$0.966681\pi$
$684$	4.08528	+	1.09465i	0.156205	+	0.0418549i
$685$	−35.3208	−	20.3925i	−1.34954	−	0.779156i
$686$	−29.0856	−	13.8114i	−1.11049	−	0.527323i
$687$	2.36710	−	8.83413i	0.0903105	−	0.337043i
$688$	22.5586	−	13.0242i	0.860037	−	0.496542i
$689$	−19.0326	−	0.0874356i	−0.725086	−	0.00333103i
$690$	6.53608	−	11.3208i	0.248824	−	0.430976i
$691$	21.9854	−	5.89097i	0.836364	−	0.224103i	0.184876	−	0.982762i	$-0.440812\pi$
$691$	21.9854	−	5.89097i	0.836364	−	0.224103i	0.651488	+	0.758659i	$0.274145\pi$
$692$	11.7870	−	6.80523i	0.448074	−	0.258696i
$693$	8.17413	−	5.01560i	0.310509	−	0.190527i
$694$	−33.5411	+	33.5411i	−1.27320	+	1.27320i
$695$	−29.3774	+	29.3774i	−1.11435	+	1.11435i
$696$	−6.05716	−	1.62301i	−0.229596	−	0.0615200i
$697$	−7.48813	+	2.00644i	−0.283633	+	0.0759993i
$698$		−	8.07521i		−	0.305651i
$699$	−3.84518	−	6.66005i	−0.145438	−	0.251906i
$700$	0.564228	−	2.35616i	0.0213258	−	0.0890546i
$701$		−	27.1008i		−	1.02358i	−0.859110	−	0.511791i	$-0.828982\pi$
$701$		−	27.1008i		−	1.02358i	0.859110	−	0.511791i	$-0.171018\pi$
$702$	−4.41202	−	4.45275i	−0.166521	−	0.168058i
$703$	−9.37931	−	5.41515i	−0.353747	−	0.204236i
$704$	−2.04202	+	2.04202i	−0.0769616	+	0.0769616i
$705$	−0.464192	−	0.268002i	−0.0174825	−	0.0100935i
$706$	−3.64672	+	6.31631i	−0.137246	+	0.237717i
$707$	−4.46847	+	18.6599i	−0.168054	+	0.701778i
$708$	−0.341643	−	1.27503i	−0.0128397	−	0.0479185i
$709$	16.7885	+	16.7885i	0.630504	+	0.630504i	0.948194	−	0.317691i	$-0.102907\pi$
$709$	16.7885	+	16.7885i	0.630504	+	0.630504i	−0.317691	+	0.948194i	$0.602907\pi$
$710$	10.9681	+	40.9336i	0.411627	+	1.53621i
$711$	8.09801	+	14.0262i	0.303699	+	0.526023i
$712$	−8.55156	+	14.8117i	−0.320483	+	0.555093i
$713$	−26.1946	−	7.01882i	−0.980996	−	0.262857i
$714$	5.90353	−	3.62237i	0.220934	−	0.135564i
$715$	−22.8693	−	13.3440i	−0.855262	−	0.499039i
$716$	2.38626	+	4.13313i	0.0891788	+	0.154462i
$717$	−14.4981	−	14.4981i	−0.541443	−	0.541443i
$718$	12.3935			0.462520
$719$	−14.2056			−0.529779			−0.264890	−	0.964279i	$-0.585336\pi$
$719$	−14.2056			−0.529779			−0.264890	+	0.964279i	$0.585336\pi$
$720$	7.16207	+	7.16207i	0.266915	+	0.266915i
$721$	36.6986	−	10.8936i	1.36673	−	0.405700i
$722$	−3.17708	+	0.851296i	−0.118239	+	0.0316819i
$723$	−2.58053	+	9.63068i	−0.0959710	+	0.358169i
$724$	1.52345	−	0.879564i	0.0566186	−	0.0326888i
$725$		−	3.30464i		−	0.122731i
$726$	0.962456	+	3.59194i	0.0357201	+	0.133309i
$727$	−30.9551			−1.14806			−0.574030	−	0.818834i	$-0.694621\pi$
$727$	−30.9551			−1.14806			−0.574030	+	0.818834i	$0.694621\pi$
$728$	14.2153	+	7.79236i	0.526852	+	0.288804i
$729$	−1.00000			−0.0370370
$730$	−2.62091	−	9.78138i	−0.0970043	−	0.362025i
$731$			7.84549i			0.290176i
$732$	9.40286	−	5.42875i	0.347540	−	0.200652i
$733$	−2.80061	+	10.4520i	−0.103443	+	0.386054i	−0.998164	−	0.0605714i	$-0.980708\pi$
$733$	−2.80061	+	10.4520i	−0.103443	+	0.386054i	0.894721	+	0.446626i	$0.147374\pi$
$734$	5.22752	−	1.40071i	0.192951	−	0.0517011i
$735$	10.5499	+	9.47720i	0.389140	+	0.349572i
$736$	−13.8908	−	13.8908i	−0.512023	−	0.512023i
$737$	48.6284			1.79125
$738$	8.95055			0.329474
$739$	−20.5838	−	20.5838i	−0.757186	−	0.757186i	0.218624	−	0.975809i	$-0.429843\pi$
$739$	−20.5838	−	20.5838i	−0.757186	−	0.757186i	−0.975809	+	0.218624i	$0.929843\pi$
$740$	2.71216	+	4.69759i	0.0997008	+	0.172687i
$741$	−14.3872	−	3.92597i	−0.528528	−	0.144224i
$742$	−11.5736	+	21.3452i	−0.424880	+	0.783608i
$743$	50.7369	+	13.5949i	1.86135	+	0.498749i	0.999958	−	0.00918346i	$-0.00292323\pi$
$743$	50.7369	+	13.5949i	1.86135	+	0.498749i	0.861397	+	0.507932i	$0.169590\pi$
$744$	6.20857	−	10.7536i	0.227617	−	0.394245i
$745$	12.7678	+	22.1145i	0.467776	+	0.810212i
$746$	−5.49572	−	20.5103i	−0.201213	−	0.750935i
$747$	−10.3721	−	10.3721i	−0.379495	−	0.379495i
$748$	1.44451	+	5.39097i	0.0528164	+	0.197113i
$749$	11.2923	+	10.7037i	0.412613	+	0.391103i
$750$	−10.3826	+	17.9832i	−0.379120	+	0.656655i
$751$	37.0993	+	21.4193i	1.35377	+	0.781600i	0.988776	−	0.149409i	$-0.0477370\pi$
$751$	37.0993	+	21.4193i	1.35377	+	0.781600i	0.364996	+	0.931009i	$0.381070\pi$
$752$	−0.935299	+	0.935299i	−0.0341068	+	0.0341068i
$753$	5.85611	+	3.38103i	0.213409	+	0.123212i
$754$	−22.3151	−	6.08933i	−0.812669	−	0.221760i
$755$			42.7643i			1.55635i
$756$	−2.59352	+	0.769862i	−0.0943254	+	0.0279996i
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	0.787184	−	0.616718i	$-0.211538\pi$
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	−0.927686	+	0.373362i	$0.878205\pi$
$758$			44.5455i			1.61796i
$759$	12.9944	−	3.48185i	0.471668	−	0.126383i
$760$	13.7550	+	3.68563i	0.498945	+	0.133692i
$761$	−14.9547	+	14.9547i	−0.542106	+	0.542106i	−0.924146	−	0.382040i	$-0.875222\pi$
$761$	−14.9547	+	14.9547i	−0.542106	+	0.542106i	0.382040	+	0.924146i	$0.375222\pi$
$762$	23.4096	−	23.4096i	0.848042	−	0.848042i
$763$	1.36066	−	0.0364151i	0.0492591	−	0.00131831i
$764$	−8.60445	+	4.96778i	−0.311298	+	0.179728i
$765$	−2.94671	+	0.789567i	−0.106538	+	0.0285469i
$766$	31.4055	−	54.3960i	1.13473	−	1.96541i
$767$	1.18400	+	4.50136i	0.0427518	+	0.162535i
$768$	16.6443	−	9.60961i	0.600601	−	0.346757i
$769$	8.37135	−	31.2423i	0.301879	−	1.12663i	−0.633720	−	0.773562i	$-0.718473\pi$
$769$	8.37135	−	31.2423i	0.301879	−	1.12663i	0.935599	−	0.353064i	$-0.114860\pi$
$770$	−28.7909	+	17.6659i	−1.03755	+	0.636635i
$771$	−16.7196	−	9.65309i	−0.602143	−	0.347648i
$772$	7.28962	+	1.95325i	0.262359	+	0.0702989i
$773$	11.5730	−	43.1908i	0.416250	−	1.55347i	−0.366068	−	0.930588i	$-0.619296\pi$
$773$	11.5730	−	43.1908i	0.416250	−	1.55347i	0.782319	−	0.622879i	$-0.214037\pi$
$774$	2.34443	−	8.74952i	0.0842686	−	0.314495i
$775$	6.32070	+	1.69363i	0.227046	+	0.0608369i
$776$	−0.984186	−	0.568220i	−0.0353302	−	0.0203979i
$777$	6.92521	−	0.185338i	0.248440	−	0.00664897i
$778$	−5.46986	+	20.4138i	−0.196104	+	0.731870i
$779$	18.4415	−	10.6472i	0.660735	−	0.381475i
$780$	5.25724	+	5.30577i	0.188239	+	0.189977i
$781$	−21.8059	+	37.7688i	−0.780275	+	1.35148i
$782$	9.38487	−	2.51467i	0.335602	−	0.0899243i
$783$	−3.19572	+	1.84505i	−0.114206	+	0.0659366i
$784$	29.3285	−	19.0943i	1.04745	−	0.681938i
$785$	5.30506	−	5.30506i	0.189346	−	0.189346i
$786$	22.3145	−	22.3145i	0.795932	−	0.795932i
$787$	−7.26984	−	1.94795i	−0.259142	−	0.0694369i	0.126909	−	0.991914i	$-0.459494\pi$
$787$	−7.26984	−	1.94795i	−0.259142	−	0.0694369i	−0.386051	+	0.922478i	$0.626161\pi$
$788$	−0.514139	+	0.137763i	−0.0183154	+	0.00490761i
$789$			28.1759i			1.00309i
$790$	−28.5228	−	49.4029i	−1.01480	−	1.75768i
$791$	14.9168	+	14.1392i	0.530381	+	0.502732i
$792$			6.15981i			0.218879i
$793$	−33.2430	+	18.9898i	−1.18049	+	0.674346i
$794$	22.4711	+	12.9737i	0.797468	+	0.460418i
$795$	7.56214	−	7.56214i	0.268202	−	0.268202i
$796$	−13.8884	−	8.01846i	−0.492261	−	0.284207i
$797$	5.44428	−	9.42978i	0.192846	−	0.334020i	−0.753346	−	0.657624i	$-0.771561\pi$
$797$	5.44428	−	9.42978i	0.192846	−	0.334020i	0.946192	+	0.323605i	$0.104895\pi$
$798$	−13.0883	+	13.8081i	−0.463321	+	0.488803i
$799$	−0.103110	−	0.384812i	−0.00364777	−	0.0136137i
$800$	3.35183	+	3.35183i	0.118505	+	0.118505i
$801$	2.60486	+	9.72147i	0.0920382	+	0.343491i
$802$	3.88566	+	6.73016i	0.137207	+	0.237650i
$803$	5.21066	−	9.02513i	0.183880	−	0.318490i
$804$	−13.2505	−	3.55045i	−0.467308	−	0.125215i
$805$	10.4041	+	16.9560i	0.366696	+	0.597620i
$806$	23.0834	−	39.5607i	0.813077	−	1.39347i
$807$	8.74198	+	15.1416i	0.307732	+	0.533008i
$808$	−8.71448	−	8.71448i	−0.306574	−	0.306574i
$809$	8.38702			0.294872			0.147436	−	0.989072i	$-0.452898\pi$
$809$	8.38702			0.294872			0.147436	+	0.989072i	$0.452898\pi$
$810$	3.52219			0.123757
$811$	24.6534	+	24.6534i	0.865699	+	0.865699i	0.991993	−	0.126294i	$-0.0403083\pi$
$811$	24.6534	+	24.6534i	0.865699	+	0.865699i	−0.126294	+	0.991993i	$0.540308\pi$
$812$	−6.86772	+	7.24543i	−0.241010	+	0.254265i
$813$	7.97719	−	2.13748i	0.279772	−	0.0749648i
$814$	−4.27072	+	15.9386i	−0.149689	+	0.558646i
$815$	17.3232	−	10.0015i	0.606804	−	0.350338i
$816$			7.52820i			0.263540i
$817$	−5.57766	−	20.8161i	−0.195138	−	0.728263i
$818$	0.962843			0.0336650
$819$	9.15737	−	2.67257i	0.319984	−	0.0933870i
$820$	−10.6652			−0.372446
$821$	−1.62451	−	6.06276i	−0.0566959	−	0.211592i	0.931767	−	0.363058i	$-0.118267\pi$
$821$	−1.62451	−	6.06276i	−0.0566959	−	0.211592i	−0.988462	+	0.151466i	$0.951601\pi$
$822$			34.9992i			1.22074i
$823$	21.8835	−	12.6344i	0.762810	−	0.440409i	−0.0674934	−	0.997720i	$-0.521500\pi$
$823$	21.8835	−	12.6344i	0.762810	−	0.440409i	0.830304	+	0.557311i	$0.188167\pi$
$824$	−6.36387	+	23.7503i	−0.221696	+	0.827380i
$825$	−3.13553	+	0.840163i	−0.109165	+	0.0292507i
$826$	5.77464	+	1.38285i	0.200925	+	0.0481154i
$827$	34.6333	+	34.6333i	1.20432	+	1.20432i	0.972840	+	0.231479i	$0.0743564\pi$
$827$	34.6333	+	34.6333i	1.20432	+	1.20432i	0.231479	+	0.972840i	$0.425644\pi$
$828$	−3.79500			−0.131885
$829$	−23.5553			−0.818111			−0.409056	−	0.912509i	$-0.634142\pi$
$829$	−23.5553			−0.818111			−0.409056	+	0.912509i	$0.634142\pi$
$830$	36.5325	+	36.5325i	1.26806	+	1.26806i
$831$	−10.3186	−	17.8724i	−0.357950	−	0.619987i
$832$	−2.49427	+	1.42483i	−0.0864732	+	0.0493970i
$833$	0.563786	+	10.5255i	0.0195340	+	0.364686i
$834$	34.4373	+	9.22746i	1.19247	+	0.319521i
$835$	21.4684	−	37.1844i	0.742946	−	1.28682i
$836$	−7.66529	−	13.2767i	−0.265110	−	0.459183i
$837$	−1.89117	−	7.05794i	−0.0653684	−	0.243958i
$838$	−28.5866	−	28.5866i	−0.987507	−	0.987507i
$839$	−1.73270	−	6.46654i	−0.0598196	−	0.223250i	0.929545	−	0.368710i	$-0.120200\pi$
$839$	−1.73270	−	6.46654i	−0.0598196	−	0.223250i	−0.989364	+	0.145460i	$0.953534\pi$
$840$	−8.73226	+	2.59209i	−0.301292	+	0.0894356i
$841$	7.69160	−	13.3222i	0.265227	−	0.459387i
$842$	40.5702	+	23.4232i	1.39814	+	0.807218i
$843$	−3.70317	+	3.70317i	−0.127544	+	0.127544i
$844$	4.58377	+	2.64644i	0.157780	+	0.0910943i
$845$	−18.4514	−	18.7936i	−0.634747	−	0.646519i
$846$			0.459965i			0.0158139i
$847$	−5.50351	−	1.31792i	−0.189103	−	0.0452843i
$848$	−13.1956	−	22.8554i	−0.453137	−	0.784857i
$849$			0.843947i			0.0289642i
$850$	−2.26455	+	0.606784i	−0.0776734	+	0.0208125i
$851$	9.38678	+	2.51518i	0.321775	+	0.0862193i
$852$	8.69933	−	8.69933i	0.298034	−	0.298034i
$853$	12.3363	−	12.3363i	0.422386	−	0.422386i	−0.463638	−	0.886025i	$-0.653456\pi$
$853$	12.3363	−	12.3363i	0.422386	−	0.422386i	0.886025	+	0.463638i	$0.153456\pi$
$854$	1.30666	+	48.8237i	0.0447130	+	1.67071i
$855$	7.25704	−	4.18985i	0.248185	−	0.143290i
$856$	−9.65308	+	2.58654i	−0.329936	+	0.0884060i
$857$	−11.7995	+	20.4373i	−0.403062	+	0.698123i	−0.994094	−	0.108525i	$-0.965387\pi$
$857$	−11.7995	+	20.4373i	−0.403062	+	0.698123i	0.591032	+	0.806648i	$0.298721\pi$
$858$	−0.104381	+	22.7213i	−0.00356351	+	0.775692i
$859$	8.42384	−	4.86350i	0.287418	−	0.165941i	−0.349359	−	0.936989i	$-0.613601\pi$
$859$	8.42384	−	4.86350i	0.287418	−	0.165941i	0.636777	+	0.771048i	$0.280267\pi$
$860$	−2.79355	+	10.4257i	−0.0952592	+	0.355512i
$861$	−6.49254	+	11.9742i	−0.221265	+	0.408081i
$862$	30.8269	+	17.7979i	1.04997	+	0.606200i
$863$	42.3300	+	11.3423i	1.44093	+	0.386096i	0.892860	−	0.450335i	$-0.148695\pi$
$863$	42.3300	+	11.3423i	1.44093	+	0.386096i	0.548072	+	0.836431i	$0.315362\pi$
$864$	1.36995	−	5.11274i	0.0466068	−	0.173939i
$865$	6.97941	−	26.0475i	0.237307	−	0.885642i
$866$	−46.3429	−	12.4175i	−1.57480	−	0.421965i
$867$	12.7588	+	7.36629i	0.433311	+	0.250172i
$868$	−10.3384	−	16.8490i	−0.350909	−	0.571891i
$869$	15.1944	−	56.7065i	0.515436	−	1.92363i
$870$	11.2559	−	6.49862i	0.381612	−	0.220324i
$871$	46.6644	+	12.7337i	1.58116	+	0.431467i
$872$	−0.437132	+	0.757135i	−0.0148032	+	0.0256398i
$873$	−0.645956	+	0.173083i	−0.0218623	+	0.00585798i
$874$	−23.1127	+	13.3441i	−0.781799	+	0.451372i
$875$	−16.5270	−	26.9348i	−0.558715	−	0.910561i
$876$	−2.07877	+	2.07877i	−0.0702350	+	0.0702350i
$877$	32.5031	−	32.5031i	1.09755	−	1.09755i	0.102856	−	0.994696i	$-0.467202\pi$
$877$	32.5031	−	32.5031i	1.09755	−	1.09755i	0.994696	−	0.102856i	$-0.0327982\pi$
$878$	30.3199	+	8.12420i	1.02325	+	0.274178i
$879$	−16.2235	+	4.34707i	−0.547205	+	0.146623i
$880$		−	36.7142i		−	1.23763i
$881$	−0.277040	−	0.479848i	−0.00933373	−	0.0161665i	0.861321	−	0.508061i	$-0.169638\pi$
$881$	−0.277040	−	0.479848i	−0.00933373	−	0.0161665i	−0.870655	+	0.491895i	$0.836304\pi$
$882$	2.51652	−	11.9068i	0.0847356	−	0.400922i
$883$			21.2142i			0.713914i	0.934121	+	0.356957i	$0.116186\pi$
$883$			21.2142i			0.713914i	−0.934121	+	0.356957i	$0.883814\pi$
$884$	−0.0255035	+	5.55149i	−0.000857774	+	0.186717i
$885$	−2.26494	−	1.30767i	−0.0761352	−	0.0439567i
$886$	−48.0428	+	48.0428i	−1.61403	+	1.61403i
$887$	−26.5374	−	15.3214i	−0.891040	−	0.514442i	−0.0167572	−	0.999860i	$-0.505334\pi$
$887$	−26.5374	−	15.3214i	−0.891040	−	0.514442i	−0.874282	+	0.485418i	$0.838668\pi$
$888$	−2.22483	+	3.85352i	−0.0746604	+	0.129316i
$889$	14.3370	+	48.2988i	0.480849	+	1.61989i
$890$	−9.17482	−	34.2409i	−0.307541	−	1.14776i
$891$	2.56310	+	2.56310i	0.0858670	+	0.0858670i
$892$	−3.32677	−	12.4157i	−0.111389	−	0.415708i
$893$	0.547155	+	0.947701i	0.0183098	+	0.0317136i
$894$	10.9566	−	18.9773i	0.366442	−	0.634696i
$895$	9.13360	+	2.44734i	0.305303	+	0.0818056i
$896$	0.847357	+	31.6617i	0.0283082	+	1.05774i
$897$	13.3814	+	0.0614738i	0.446791	+	0.00205255i
$898$	−19.6413	−	34.0198i	−0.655439	−	1.13525i
$899$	−19.0659	−	19.0659i	−0.635883	−	0.635883i
$900$	0.915724			0.0305241
$901$	7.94872			0.264810
$902$	−22.9411	−	22.9411i	−0.763857	−	0.763857i
$903$	10.0047	+	9.48314i	0.332935	+	0.315579i
$904$	−12.7514	+	3.41673i	−0.424106	+	0.113639i
$905$	0.902078	−	3.36660i	0.0299861	−	0.111910i
$906$	31.7811	−	18.3488i	1.05586	−	0.609600i
$907$			9.33990i			0.310126i	0.987905	+	0.155063i	$0.0495581\pi$
$907$			9.33990i			0.310126i	−0.987905	+	0.155063i	$0.950442\pi$
$908$	−1.74191	−	6.50088i	−0.0578072	−	0.215739i
$909$	−7.25219			−0.240540
$910$	−32.2540	+	9.41330i	−1.06921	+	0.312048i
$911$	−23.5831			−0.781342			−0.390671	−	0.920530i	$-0.627757\pi$
$911$	−23.5831			−0.781342			−0.390671	+	0.920530i	$0.627757\pi$
$912$	−5.35208	−	19.9743i	−0.177225	−	0.661414i
$913$			53.1694i			1.75965i
$914$	29.5819	−	17.0791i	0.978483	−	0.564927i
$915$	5.56770	−	20.7789i	0.184063	−	0.686931i
$916$	9.03320	−	2.42044i	0.298465	−	0.0799735i
$917$	13.6663	+	46.0393i	0.451302	+	1.52035i
$918$	1.85112	+	1.85112i	0.0610962	+	0.0610962i
$919$	1.97069			0.0650071			0.0325036	−	0.999472i	$-0.489652\pi$
$919$	1.97069			0.0650071			0.0325036	+	0.999472i	$0.489652\pi$
$920$	−12.7776			−0.421265
$921$	19.8317	+	19.8317i	0.653477	+	0.653477i
$922$	12.8989	+	22.3415i	0.424802	+	0.735779i
$923$	−30.8152	+	30.5334i	−1.01430	+	1.00502i
$924$	8.62067	+	4.67421i	0.283599	+	0.153770i
$925$	−2.26501	−	0.606908i	−0.0744731	−	0.0199550i
$926$	−26.6476	+	46.1551i	−0.875696	+	1.51675i
$927$	7.23449	+	12.5305i	0.237612	+	0.411555i
$928$	−5.05527	−	18.8665i	−0.165947	−	0.619323i
$929$	−41.7592	−	41.7592i	−1.37007	−	1.37007i	−0.860321	−	0.509753i	$-0.829737\pi$
$929$	−41.7592	−	41.7592i	−1.37007	−	1.37007i	−0.509753	−	0.860321i	$-0.670263\pi$
$930$	6.66107	+	24.8594i	0.218425	+	0.815173i
$931$	−8.97882	−	27.5259i	−0.294269	−	0.902126i
$932$	3.93183	−	6.81013i	0.128791	−	0.223073i
$933$	−20.7001	−	11.9512i	−0.677690	−	0.391265i
$934$	26.0878	−	26.0878i	0.853619	−	0.853619i
$935$	9.57643	+	5.52896i	0.313183	+	0.180816i
$936$	−1.61300	+	5.91103i	−0.0527225	+	0.193208i
$937$		−	49.8381i		−	1.62814i	−0.580767	−	0.814070i	$-0.697247\pi$
$937$		−	49.8381i		−	1.62814i	0.580767	−	0.814070i	$-0.302753\pi$
$938$	42.4515	−	44.7862i	1.38609	−	1.46232i
$939$	−12.2352	−	21.1920i	−0.399282	−	0.691576i
$940$		−	0.548081i		−	0.0178764i
$941$	−12.2019	+	3.26950i	−0.397771	+	0.106583i	−0.452159	−	0.891937i	$-0.649346\pi$
$941$	−12.2019	+	3.26950i	−0.397771	+	0.106583i	0.0543875	+	0.998520i	$0.482679\pi$
$942$	−6.21881	−	1.66632i	−0.202620	−	0.0542918i
$943$	−13.5109	+	13.5109i	−0.439974	+	0.439974i
$944$	−4.56362	+	4.56362i	−0.148533	+	0.148533i
$945$	−2.55493	+	4.71206i	−0.0831117	+	0.153283i
$946$	−28.4349	+	16.4169i	−0.924497	+	0.533759i
$947$	−30.7696	+	8.24470i	−0.999879	+	0.267917i	−0.721395	−	0.692524i	$-0.756499\pi$
$947$	−30.7696	+	8.24470i	−0.999879	+	0.267917i	−0.278484	+	0.960441i	$0.589832\pi$
$948$	−8.28049	+	14.3422i	−0.268938	+	0.465814i
$949$	7.36352	−	7.29617i	0.239030	−	0.236844i
$950$	5.57705	−	3.21991i	0.180943	−	0.104468i
$951$	6.44215	−	24.0424i	0.208901	−	0.779630i
$952$	−5.95163	−	3.22703i	−0.192893	−	0.104589i
$953$	30.8939	+	17.8366i	1.00075	+	0.577784i	0.908470	−	0.417949i	$-0.137251\pi$
$953$	30.8939	+	17.8366i	1.00075	+	0.577784i	0.0922803	+	0.995733i	$0.470584\pi$
$954$	−8.86465	−	2.37527i	−0.287003	−	0.0769024i
$955$	−5.09494	+	19.0146i	−0.164868	+	0.615297i
$956$	5.42626	−	20.2511i	0.175498	−	0.654967i
$957$	12.9200	+	3.46190i	0.417643	+	0.111907i
$958$	−16.1046	−	9.29802i	−0.520318	−	0.300405i
$959$	−46.8226	−	25.3877i	−1.51198	−	0.819810i
$960$	0.417752	−	1.55907i	0.0134829	−	0.0503189i
$961$	19.3912	−	11.1955i	0.625524	−	0.361146i
$962$	−8.27188	+	14.1765i	−0.266696	+	0.457069i
$963$	−2.94039	+	5.09290i	−0.0947527	+	0.164117i
$964$	−9.84769	+	2.63868i	−0.317173	+	0.0849862i
$965$	12.9492	−	7.47620i	0.416848	−	0.240667i
$966$	8.13710	−	15.0073i	0.261807	−	0.482852i
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	−0.223994	−	0.974591i	$-0.571910\pi$
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	0.974591	+	0.223994i	$0.0719096\pi$
$968$	2.57023	−	2.57023i	0.0826102	−	0.0826102i
$969$	6.01603	+	1.61199i	0.193263	+	0.0517846i
$970$	2.27518	−	0.609633i	0.0730517	−	0.0195741i
$971$		−	9.95673i		−	0.319527i	−0.987155	−	0.159763i	$-0.948927\pi$
$971$		−	9.95673i		−	0.319527i	0.987155	−	0.159763i	$-0.0510731\pi$
$972$	−0.511267	−	0.885540i	−0.0163989	−	0.0284037i
$973$	−37.3248	+	39.3776i	−1.19658	+	1.26239i
$974$			55.5239i			1.77910i
$975$	−3.22890	−	0.0148335i	−0.103407	−	0.000475052i
$976$	−45.9736	−	26.5429i	−1.47158	−	0.849616i
$977$	11.1637	−	11.1637i	0.357158	−	0.357158i	−0.505606	−	0.862764i	$-0.668731\pi$
$977$	11.1637	−	11.1637i	0.357158	−	0.357158i	0.862764	+	0.505606i	$0.168731\pi$
$978$	−14.8657	−	8.58270i	−0.475352	−	0.274445i
$979$	18.2406	−	31.5936i	0.582971	−	1.00974i
$980$	−2.99861	+	14.1878i	−0.0957871	+	0.453212i
$981$	0.133153	+	0.496935i	0.00425126	+	0.0158659i
$982$	−10.4168	−	10.4168i	−0.332413	−	0.332413i
$983$	−0.434633	−	1.62207i	−0.0138626	−	0.0517361i	0.958648	−	0.284594i	$-0.0918589\pi$
$983$	−0.434633	−	1.62207i	−0.0138626	−	0.0517361i	−0.972511	+	0.232858i	$0.925192\pi$
$984$	−4.37443	−	7.57674i	−0.139452	−	0.241538i
$985$	−0.527299	+	0.913309i	−0.0168011	+	0.0291004i
$986$	9.33109	+	2.50026i	0.297162	+	0.0796244i
$987$	−0.615351	−	0.333649i	−0.0195868	−	0.0106202i
$988$	−3.87910	−	14.7477i	−0.123411	−	0.469186i
$989$	9.66848	+	16.7463i	0.307440	+	0.532502i
$990$	−9.02773	−	9.02773i	−0.286920	−	0.286920i
$991$	−16.3645			−0.519837			−0.259918	−	0.965631i	$-0.583696\pi$
$991$	−16.3645			−0.519837			−0.259918	+	0.965631i	$0.583696\pi$
$992$	38.6763			1.22797
$993$	3.49185	+	3.49185i	0.110811	+	0.110811i
$994$	15.7487	+	53.0543i	0.499517	+	1.68278i
$995$	−30.6913	+	8.22370i	−0.972979	+	0.260709i
$996$	3.88200	−	14.4878i	0.123006	−	0.459064i
$997$	−16.4282	+	9.48480i	−0.520285	+	0.300387i	−0.737051	−	0.675837i	$-0.763782\pi$
$997$	−16.4282	+	9.48480i	−0.520285	+	0.300387i	0.216766	+	0.976224i	$0.430449\pi$
$998$			44.0214i			1.39347i
$999$	0.677697	+	2.52920i	0.0214414	+	0.0800203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.262.3	yes	40
3.2	odd	2		819.2.gh.d.262.8		40
7.5	odd	6		273.2.bt.b.145.3	✓	40
13.7	odd	12		273.2.bt.b.241.3	yes	40
21.5	even	6		819.2.et.d.145.8		40
39.20	even	12		819.2.et.d.514.8		40
91.33	even	12	inner	273.2.cg.b.124.3	yes	40
273.215	odd	12		819.2.gh.d.397.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.3	✓	40	7.5	odd	6
273.2.bt.b.241.3	yes	40	13.7	odd	12
273.2.cg.b.124.3	yes	40	91.33	even	12	inner
273.2.cg.b.262.3	yes	40	1.1	even	1	trivial
819.2.et.d.145.8		40	21.5	even	6
819.2.et.d.514.8		40	39.20	even	12
819.2.gh.d.262.8		40	3.2	odd	2
819.2.gh.d.397.8		40	273.215	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.449968 - 1.67930i) q^{2} +1.00000i q^{3} +(-0.885540 + 0.511267i) q^{4} +(-0.524353 + 1.95691i) q^{5} +(1.67930 - 0.449968i) q^{6} +(-0.616155 + 2.57300i) q^{7} +(-1.20163 - 1.20163i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.449968 - 1.67930i) q^{2} +1.00000i q^{3} +(-0.885540 + 0.511267i) q^{4} +(-0.524353 + 1.95691i) q^{5} +(1.67930 - 0.449968i) q^{6} +(-0.616155 + 2.57300i) q^{7} +(-1.20163 - 1.20163i) q^{8} -1.00000 q^{9} +3.52219 q^{10} +(2.56310 + 2.56310i) q^{11} +(-0.511267 - 0.885540i) q^{12} +(1.78841 + 3.13075i) q^{13} +(4.59811 - 0.123058i) q^{14} +(-1.95691 - 0.524353i) q^{15} +(-2.49975 + 4.32969i) q^{16} +(-0.752896 - 1.30405i) q^{17} +(0.449968 + 1.67930i) q^{18} +(2.92473 + 2.92473i) q^{19} +(-0.536169 - 2.00101i) q^{20} +(-2.57300 - 0.616155i) q^{21} +(3.15091 - 5.45753i) q^{22} +(-3.21414 - 1.85568i) q^{23} +(1.20163 - 1.20163i) q^{24} +(0.775564 + 0.447772i) q^{25} +(4.45275 - 4.41202i) q^{26} -1.00000i q^{27} +(-0.769862 - 2.59352i) q^{28} +(-1.84505 - 3.19572i) q^{29} +3.52219i q^{30} +(7.05794 - 1.89117i) q^{31} +(5.11274 + 1.36995i) q^{32} +(-2.56310 + 2.56310i) q^{33} +(-1.85112 + 1.85112i) q^{34} +(-4.71206 - 2.55493i) q^{35} +(0.885540 - 0.511267i) q^{36} +(-2.52920 + 0.677697i) q^{37} +(3.59548 - 6.22755i) q^{38} +(-3.13075 + 1.78841i) q^{39} +(2.98158 - 1.72141i) q^{40} +(1.33248 - 4.97288i) q^{41} +(0.123058 + 4.59811i) q^{42} +(-4.51217 - 2.60510i) q^{43} +(-3.58015 - 0.959299i) q^{44} +(0.524353 - 1.95691i) q^{45} +(-1.67000 + 6.23251i) q^{46} +(0.255554 + 0.0684756i) q^{47} +(-4.32969 - 2.49975i) q^{48} +(-6.24071 - 3.17074i) q^{49} +(0.402966 - 1.50389i) q^{50} +(1.30405 - 0.752896i) q^{51} +(-3.18436 - 1.85805i) q^{52} +(-2.63938 + 4.57154i) q^{53} +(-1.67930 + 0.449968i) q^{54} +(-6.35973 + 3.67179i) q^{55} +(3.83220 - 2.35142i) q^{56} +(-2.92473 + 2.92473i) q^{57} +(-4.53637 + 4.53637i) q^{58} +(1.24693 + 0.334114i) q^{59} +(2.00101 - 0.536169i) q^{60} +10.6182i q^{61} +(-6.35170 - 11.0015i) q^{62} +(0.616155 - 2.57300i) q^{63} +0.796700i q^{64} +(-7.06436 + 1.85815i) q^{65} +(5.45753 + 3.15091i) q^{66} +(9.48626 - 9.48626i) q^{67} +(1.33344 + 0.769862i) q^{68} +(1.85568 - 3.21414i) q^{69} +(-2.17022 + 9.06262i) q^{70} +(3.11400 + 11.6216i) q^{71} +(1.20163 + 1.20163i) q^{72} +(-0.744113 - 2.77707i) q^{73} +(2.27612 + 3.94235i) q^{74} +(-0.447772 + 0.775564i) q^{75} +(-4.08528 - 1.09465i) q^{76} +(-8.17413 + 5.01560i) q^{77} +(4.41202 + 4.45275i) q^{78} +(-8.09801 - 14.0262i) q^{79} +(-7.16207 - 7.16207i) q^{80} +1.00000 q^{81} -8.95055 q^{82} +(10.3721 + 10.3721i) q^{83} +(2.59352 - 0.769862i) q^{84} +(2.94671 - 0.789567i) q^{85} +(-2.34443 + 8.74952i) q^{86} +(3.19572 - 1.84505i) q^{87} -6.15981i q^{88} +(-2.60486 - 9.72147i) q^{89} -3.52219 q^{90} +(-9.15737 + 2.67257i) q^{91} +3.79500 q^{92} +(1.89117 + 7.05794i) q^{93} -0.459965i q^{94} +(-7.25704 + 4.18985i) q^{95} +(-1.36995 + 5.11274i) q^{96} +(0.645956 - 0.173083i) q^{97} +(-2.51652 + 11.9068i) q^{98} +(-2.56310 - 2.56310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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