LMFDB - Embedded newform 273.2.t.d.205.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.7
Root			$0.915396i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.d.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.915396i q^{2} +(0.500000 - 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 - 1.30902i) q^{5} +(0.792756 + 0.457698i) q^{6} +(2.57477 + 0.608732i) q^{7} +2.89453i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+0.915396i q^{2} +(0.500000 - 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 - 1.30902i) q^{5} +(0.792756 + 0.457698i) q^{6} +(2.57477 + 0.608732i) q^{7} +2.89453i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.19827 - 2.07547i) q^{10} +(2.20526 + 1.27321i) q^{11} +(0.581025 - 1.00636i) q^{12} +(0.523154 - 3.56740i) q^{13} +(-0.557231 + 2.35694i) q^{14} +(-2.26729 + 1.30902i) q^{15} -0.325542 q^{16} +6.19960 q^{17} +(0.792756 - 0.457698i) q^{18} +(2.36676 - 1.36645i) q^{19} +(-2.63470 - 1.52115i) q^{20} +(1.81456 - 1.92545i) q^{21} +(-1.16549 + 2.01868i) q^{22} -7.89025 q^{23} +(2.50674 + 1.44726i) q^{24} +(0.927071 + 1.60573i) q^{25} +(3.26558 + 0.478894i) q^{26} -1.00000 q^{27} +(2.99201 + 0.707377i) q^{28} +(-1.77706 - 3.07796i) q^{29} +(-1.19827 - 2.07547i) q^{30} +(-7.91220 + 4.56811i) q^{31} +5.49106i q^{32} +(2.20526 - 1.27321i) q^{33} +5.67509i q^{34} +(-5.04091 - 4.75060i) q^{35} +(-0.581025 - 1.00636i) q^{36} +8.68684i q^{37} +(1.25084 + 2.16652i) q^{38} +(-2.82788 - 2.23676i) q^{39} +(3.78900 - 6.56274i) q^{40} +(-3.98821 + 2.30259i) q^{41} +(1.76255 + 1.66104i) q^{42} +(-2.11228 + 3.65857i) q^{43} +(2.56262 + 1.47953i) q^{44} +2.61804i q^{45} -7.22271i q^{46} +(-1.53652 - 0.887113i) q^{47} +(-0.162771 + 0.281927i) q^{48} +(6.25889 + 3.13469i) q^{49} +(-1.46988 + 0.848638i) q^{50} +(3.09980 - 5.36901i) q^{51} +(0.607931 - 4.14549i) q^{52} +(-3.42283 - 5.92852i) q^{53} -0.915396i q^{54} +(-3.33331 - 5.77345i) q^{55} +(-1.76199 + 7.45275i) q^{56} -2.73290i q^{57} +(2.81755 - 1.62671i) q^{58} +2.25835i q^{59} +(-2.63470 + 1.52115i) q^{60} +(-6.18601 - 10.7145i) q^{61} +(-4.18163 - 7.24280i) q^{62} +(-0.760208 - 2.53418i) q^{63} -5.67758 q^{64} +(-5.85594 + 7.40350i) q^{65} +(1.16549 + 2.01868i) q^{66} +(0.536530 + 0.309766i) q^{67} +7.20424 q^{68} +(-3.94513 + 6.83316i) q^{69} +(4.34868 - 4.61443i) q^{70} +(6.48057 + 3.74156i) q^{71} +(2.50674 - 1.44726i) q^{72} +(-10.8250 + 6.24982i) q^{73} -7.95190 q^{74} +1.85414 q^{75} +(2.75029 - 1.58788i) q^{76} +(4.90299 + 4.62062i) q^{77} +(2.04752 - 2.58863i) q^{78} +(0.621752 - 1.07691i) q^{79} +(0.738098 + 0.426141i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.10779 - 3.65079i) q^{82} -2.10018i q^{83} +(2.10861 - 2.23747i) q^{84} +(-14.0563 - 8.11541i) q^{85} +(-3.34904 - 1.93357i) q^{86} -3.55412 q^{87} +(-3.68533 + 6.38318i) q^{88} -11.4071i q^{89} -2.39655 q^{90} +(3.51859 - 8.86677i) q^{91} -9.16886 q^{92} +9.13622i q^{93} +(0.812060 - 1.40653i) q^{94} -7.15484 q^{95} +(4.75540 + 2.74553i) q^{96} +(-1.32935 - 0.767503i) q^{97} +(-2.86948 + 5.72937i) q^{98} -2.54641i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.915396i			0.647283i	0.946180	+	0.323641i	$0.104907\pi$
$2$			0.915396i			0.647283i	−0.946180	+	0.323641i	$0.895093\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.16205			0.581025
$5$	−2.26729	−	1.30902i	−1.01396	−	0.585412i	−0.101614	−	0.994824i	$-0.532401\pi$
$5$	−2.26729	−	1.30902i	−1.01396	−	0.585412i	−0.912350	+	0.409412i	$0.865734\pi$
$6$	0.792756	+	0.457698i	0.323641	+	0.186854i
$7$	2.57477	+	0.608732i	0.973172	+	0.230079i
$7$	2.57477	+	0.608732i	0.973172	+	0.230079i
$8$			2.89453i			1.02337i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.19827	−	2.07547i	0.378927	−	0.656321i
$11$	2.20526	+	1.27321i	0.664910	+	0.383886i	0.794145	−	0.607728i	$-0.207919\pi$
$11$	2.20526	+	1.27321i	0.664910	+	0.383886i	−0.129235	+	0.991614i	$0.541252\pi$
$12$	0.581025	−	1.00636i	0.167727	−	0.290512i
$13$	0.523154	−	3.56740i	0.145097	−	0.989417i
$13$	0.523154	−	3.56740i	0.145097	−	0.989417i
$14$	−0.557231	+	2.35694i	−0.148926	+	0.629918i
$15$	−2.26729	+	1.30902i	−0.585412	+	0.337988i
$16$	−0.325542			−0.0813854
$17$	6.19960			1.50362			0.751812	−	0.659377i	$-0.229180\pi$
$17$	6.19960			1.50362			0.751812	+	0.659377i	$0.229180\pi$
$18$	0.792756	−	0.457698i	0.186854	−	0.107880i
$19$	2.36676	−	1.36645i	0.542971	−	0.313485i	−0.203311	−	0.979114i	$-0.565170\pi$
$19$	2.36676	−	1.36645i	0.542971	−	0.313485i	0.746282	+	0.665630i	$0.231837\pi$
$20$	−2.63470	−	1.52115i	−0.589138	−	0.340139i
$21$	1.81456	−	1.92545i	0.395970	−	0.420168i
$22$	−1.16549	+	2.01868i	−0.248483	+	0.430385i
$23$	−7.89025			−1.64523			−0.822616	−	0.568598i	$-0.807486\pi$
$23$	−7.89025			−1.64523			−0.822616	+	0.568598i	$0.807486\pi$
$24$	2.50674	+	1.44726i	0.511685	+	0.295422i
$25$	0.927071	+	1.60573i	0.185414	+	0.321147i
$26$	3.26558	+	0.478894i	0.640433	+	0.0939188i
$27$	−1.00000			−0.192450
$28$	2.99201	+	0.707377i	0.565437	+	0.133682i
$29$	−1.77706	−	3.07796i	−0.329992	−	0.571562i	0.652518	−	0.757773i	$-0.273713\pi$
$29$	−1.77706	−	3.07796i	−0.329992	−	0.571562i	−0.982510	+	0.186211i	$0.940379\pi$
$30$	−1.19827	−	2.07547i	−0.218774	−	0.378927i
$31$	−7.91220	+	4.56811i	−1.42107	+	0.820457i	−0.996391	−	0.0848850i	$-0.972948\pi$
$31$	−7.91220	+	4.56811i	−1.42107	+	0.820457i	−0.424683	+	0.905342i	$0.639614\pi$
$32$			5.49106i			0.970691i
$33$	2.20526	−	1.27321i	0.383886	−	0.221637i
$34$			5.67509i			0.973270i
$35$	−5.04091	−	4.75060i	−0.852069	−	0.802998i
$36$	−0.581025	−	1.00636i	−0.0968375	−	0.167727i
$37$			8.68684i			1.42811i	0.700091	+	0.714054i	$0.253143\pi$
$37$			8.68684i			1.42811i	−0.700091	+	0.714054i	$0.746857\pi$
$38$	1.25084	+	2.16652i	0.202913	+	0.351456i
$39$	−2.82788	−	2.23676i	−0.452823	−	0.358169i
$40$	3.78900	−	6.56274i	0.599093	−	1.03766i
$41$	−3.98821	+	2.30259i	−0.622854	+	0.359605i	−0.777979	−	0.628290i	$-0.783755\pi$
$41$	−3.98821	+	2.30259i	−0.622854	+	0.359605i	0.155125	+	0.987895i	$0.450422\pi$
$42$	1.76255	+	1.66104i	0.271967	+	0.256305i
$43$	−2.11228	+	3.65857i	−0.322119	+	0.557926i	−0.980925	−	0.194386i	$-0.937728\pi$
$43$	−2.11228	+	3.65857i	−0.322119	+	0.557926i	0.658806	+	0.752313i	$0.271062\pi$
$44$	2.56262	+	1.47953i	0.386329	+	0.223047i
$45$			2.61804i			0.390275i
$46$		−	7.22271i		−	1.06493i
$47$	−1.53652	−	0.887113i	−0.224125	−	0.129399i	0.383734	−	0.923444i	$-0.374638\pi$
$47$	−1.53652	−	0.887113i	−0.224125	−	0.129399i	−0.607859	+	0.794045i	$0.707971\pi$
$48$	−0.162771	+	0.281927i	−0.0234940	+	0.0406927i
$49$	6.25889	+	3.13469i	0.894127	+	0.447813i
$50$	−1.46988	+	0.848638i	−0.207873	+	0.120015i
$51$	3.09980	−	5.36901i	0.434059	−	0.751812i
$52$	0.607931	−	4.14549i	0.0843049	−	0.574876i
$53$	−3.42283	−	5.92852i	−0.470162	−	0.814345i	0.529255	−	0.848463i	$-0.322471\pi$
$53$	−3.42283	−	5.92852i	−0.470162	−	0.814345i	−0.999418	+	0.0341173i	$0.989138\pi$
$54$		−	0.915396i		−	0.124570i
$55$	−3.33331	−	5.77345i	−0.449463	−	0.778492i
$56$	−1.76199	+	7.45275i	−0.235456	+	0.995915i
$57$		−	2.73290i		−	0.361981i
$58$	2.81755	−	1.62671i	0.369962	−	0.213598i
$59$			2.25835i			0.294012i	0.989136	+	0.147006i	$0.0469637\pi$
$59$			2.25835i			0.294012i	−0.989136	+	0.147006i	$0.953036\pi$
$60$	−2.63470	+	1.52115i	−0.340139	+	0.196379i
$61$	−6.18601	−	10.7145i	−0.792038	−	1.37185i	−0.924703	−	0.380688i	$-0.875687\pi$
$61$	−6.18601	−	10.7145i	−0.792038	−	1.37185i	0.132666	−	0.991161i	$-0.457646\pi$
$62$	−4.18163	−	7.24280i	−0.531068	−	0.919837i
$63$	−0.760208	−	2.53418i	−0.0957772	−	0.319277i
$64$	−5.67758			−0.709697
$65$	−5.85594	+	7.40350i	−0.726340	+	0.918291i
$66$	1.16549	+	2.01868i	0.143462	+	0.248483i
$67$	0.536530	+	0.309766i	0.0655476	+	0.0378439i	0.532416	−	0.846483i	$-0.321284\pi$
$67$	0.536530	+	0.309766i	0.0655476	+	0.0378439i	−0.466868	+	0.884327i	$0.654618\pi$
$68$	7.20424			0.873643
$69$	−3.94513	+	6.83316i	−0.474937	+	0.822616i
$70$	4.34868	−	4.61443i	0.519767	−	0.551530i
$71$	6.48057	+	3.74156i	0.769102	+	0.444041i	0.832554	−	0.553944i	$-0.186878\pi$
$71$	6.48057	+	3.74156i	0.769102	+	0.444041i	−0.0634524	+	0.997985i	$0.520211\pi$
$72$	2.50674	−	1.44726i	0.295422	−	0.170562i
$73$	−10.8250	+	6.24982i	−1.26697	+	0.731486i	−0.974414	−	0.224762i	$-0.927840\pi$
$73$	−10.8250	+	6.24982i	−1.26697	+	0.731486i	−0.292557	+	0.956248i	$0.594506\pi$
$74$	−7.95190			−0.924390
$75$	1.85414			0.214098
$76$	2.75029	−	1.58788i	0.315480	−	0.182142i
$77$	4.90299	+	4.62062i	0.558748	+	0.526569i
$78$	2.04752	−	2.58863i	0.231836	−	0.293105i
$79$	0.621752	−	1.07691i	0.0699526	−	0.121161i	−0.828928	−	0.559356i	$-0.811049\pi$
$79$	0.621752	−	1.07691i	0.0699526	−	0.121161i	0.898880	+	0.438194i	$0.144382\pi$
$80$	0.738098	+	0.426141i	0.0825218	+	0.0476440i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.10779	−	3.65079i	−0.232766	−	0.403163i
$83$		−	2.10018i		−	0.230524i	−0.993335	−	0.115262i	$-0.963229\pi$
$83$		−	2.10018i		−	0.230524i	0.993335	−	0.115262i	$-0.0367708\pi$
$84$	2.10861	−	2.23747i	0.230068	−	0.244128i
$85$	−14.0563	−	8.11541i	−1.52462	−	0.880240i
$86$	−3.34904	−	1.93357i	−0.361136	−	0.208502i
$87$	−3.55412			−0.381041
$88$	−3.68533	+	6.38318i	−0.392857	+	0.680449i
$89$		−	11.4071i		−	1.20915i	−0.796550	−	0.604573i	$-0.793344\pi$
$89$		−	11.4071i		−	1.20915i	0.796550	−	0.604573i	$-0.206656\pi$
$90$	−2.39655			−0.252618
$91$	3.51859	−	8.86677i	0.368848	−	0.929490i
$92$	−9.16886			−0.955920
$93$			9.13622i			0.947382i
$94$	0.812060	−	1.40653i	0.0837576	−	0.145072i
$95$	−7.15484			−0.734071
$96$	4.75540	+	2.74553i	0.485345	+	0.280214i
$97$	−1.32935	−	0.767503i	−0.134975	−	0.0779281i	0.430992	−	0.902356i	$-0.358164\pi$
$97$	−1.32935	−	0.767503i	−0.134975	−	0.0779281i	−0.565967	+	0.824428i	$0.691497\pi$
$98$	−2.86948	+	5.72937i	−0.289862	+	0.578753i
$99$		−	2.54641i		−	0.255924i
$100$	1.07730	+	1.86594i	0.107730	+	0.186594i
$101$	−0.252376	+	0.437129i	−0.0251124	+	0.0434959i	−0.878308	−	0.478094i	$-0.841328\pi$
$101$	−0.252376	+	0.437129i	−0.0251124	+	0.0434959i	0.853196	+	0.521590i	$0.174661\pi$
$102$	4.91477	+	2.83755i	0.486635	+	0.280959i
$103$	−2.66915	+	4.62310i	−0.262999	+	0.455528i	−0.967038	−	0.254634i	$-0.918045\pi$
$103$	−2.66915	+	4.62310i	−0.262999	+	0.455528i	0.704038	+	0.710162i	$0.251378\pi$
$104$	10.3259	+	1.51429i	1.01254	+	0.148488i
$105$	−6.63460	+	1.99026i	−0.647470	+	0.194229i
$106$	5.42695	−	3.13325i	0.527112	−	0.304328i
$107$	17.8113			1.72189			0.860944	−	0.508700i	$-0.169874\pi$
$107$	17.8113			1.72189			0.860944	+	0.508700i	$0.169874\pi$
$108$	−1.16205			−0.111818
$109$	16.0930	−	9.29129i	1.54143	−	0.889944i	0.542679	−	0.839940i	$-0.317410\pi$
$109$	16.0930	−	9.29129i	1.54143	−	0.889944i	0.998749	−	0.0500036i	$-0.0159233\pi$
$110$	5.28500	−	3.05130i	0.503905	−	0.290930i
$111$	7.52303	+	4.34342i	0.714054	+	0.412259i
$112$	−0.838195	−	0.198168i	−0.0792020	−	0.0187251i
$113$	−3.61615	+	6.26336i	−0.340179	+	0.589207i	−0.984466	−	0.175577i	$-0.943821\pi$
$113$	−3.61615	+	6.26336i	−0.340179	+	0.589207i	0.644287	+	0.764784i	$0.277154\pi$
$114$	2.50168			0.234304
$115$	17.8895	+	10.3285i	1.66820	+	0.963138i
$116$	−2.06503	−	3.57674i	−0.191733	−	0.332092i
$117$	−3.35103	+	1.33063i	−0.309803	+	0.123017i
$118$	−2.06729			−0.190309
$119$	15.9626	+	3.77390i	1.46328	+	0.345952i
$120$	−3.78900	−	6.56274i	−0.345887	−	0.599093i
$121$	−2.25790	−	3.91079i	−0.205263	−	0.355526i
$122$	9.80800	−	5.66265i	0.887975	−	0.512672i
$123$			4.60519i			0.415236i
$124$	−9.19437	+	5.30837i	−0.825679	+	0.476706i
$125$			8.23599i			0.736649i
$126$	2.31978	−	0.695892i	0.206663	−	0.0619950i
$127$	4.21069	+	7.29312i	0.373638	+	0.647160i	0.990122	−	0.140207i	$-0.0447769\pi$
$127$	4.21069	+	7.29312i	0.373638	+	0.647160i	−0.616484	+	0.787367i	$0.711444\pi$
$128$			5.78488i			0.511316i
$129$	2.11228	+	3.65857i	0.185975	+	0.322119i
$130$	−6.77714	−	5.36050i	−0.594394	−	0.470147i
$131$	8.26809	−	14.3207i	0.722386	−	1.25121i	−0.237655	−	0.971350i	$-0.576379\pi$
$131$	8.26809	−	14.3207i	0.722386	−	1.25121i	0.960041	−	0.279860i	$-0.0902879\pi$
$132$	2.56262	−	1.47953i	0.223047	−	0.128776i
$133$	6.92566	−	2.07757i	0.600531	−	0.180148i
$134$	−0.283559	+	0.491138i	−0.0244957	+	0.0424278i
$135$	2.26729	+	1.30902i	0.195137	+	0.112663i
$136$			17.9449i			1.53876i
$137$			1.91854i			0.163912i	0.996636	+	0.0819558i	$0.0261166\pi$
$137$			1.91854i			0.163912i	−0.996636	+	0.0819558i	$0.973883\pi$
$138$	−6.25505	−	3.61135i	−0.532465	−	0.307419i
$139$	−11.0300	+	19.1046i	−0.935556	+	1.62043i	−0.161916	+	0.986805i	$0.551767\pi$
$139$	−11.0300	+	19.1046i	−0.935556	+	1.62043i	−0.773640	+	0.633626i	$0.781566\pi$
$140$	−5.85779	−	5.52043i	−0.495073	−	0.466562i
$141$	−1.53652	+	0.887113i	−0.129399	+	0.0747084i
$142$	−3.42501	+	5.93229i	−0.287420	+	0.497826i
$143$	5.69572	−	7.20094i	0.476300	−	0.602173i
$144$	0.162771	+	0.281927i	0.0135642	+	0.0234940i
$145$			9.30483i			0.772724i
$146$	−5.72106	−	9.90917i	−0.473478	−	0.820089i
$147$	5.84417	−	3.85301i	0.482019	−	0.317791i
$148$			10.0945i			0.829766i
$149$	−12.9855	+	7.49720i	−1.06382	+	0.614195i	−0.926485	−	0.376331i	$-0.877186\pi$
$149$	−12.9855	+	7.49720i	−1.06382	+	0.614195i	−0.137331	+	0.990525i	$0.543852\pi$
$150$			1.69728i			0.138582i
$151$	7.81993	−	4.51484i	0.636377	−	0.367413i	−0.146840	−	0.989160i	$-0.546910\pi$
$151$	7.81993	−	4.51484i	0.636377	−	0.367413i	0.783218	+	0.621748i	$0.213577\pi$
$152$	3.95522	+	6.85065i	0.320811	+	0.555661i
$153$	−3.09980	−	5.36901i	−0.250604	−	0.434059i
$154$	−4.22970	+	4.48818i	−0.340839	+	0.361668i
$155$	23.9190			1.92122
$156$	−3.28613	−	2.59923i	−0.263101	−	0.208105i
$157$	0.0998014	+	0.172861i	0.00796501	+	0.0137958i	0.869980	−	0.493086i	$-0.164131\pi$
$157$	0.0998014	+	0.172861i	0.00796501	+	0.0137958i	−0.862015	+	0.506882i	$0.830798\pi$
$158$	0.985797	+	0.569150i	0.0784258	+	0.0452791i
$159$	−6.84567			−0.542897
$160$	7.18791	−	12.4498i	0.568254	−	0.984245i
$161$	−20.3156	−	4.80305i	−1.60109	−	0.378533i
$162$	−0.792756	−	0.457698i	−0.0622848	−	0.0359602i
$163$	−6.10731	+	3.52606i	−0.478362	+	0.276182i	−0.719733	−	0.694250i	$-0.755736\pi$
$163$	−6.10731	+	3.52606i	−0.478362	+	0.276182i	0.241372	+	0.970433i	$0.422403\pi$
$164$	−4.63450	+	2.67573i	−0.361894	+	0.208939i
$165$	−6.66661			−0.518995
$166$	1.92249			0.149214
$167$	−1.55981	+	0.900559i	−0.120702	+	0.0696874i	−0.559135	−	0.829076i	$-0.688867\pi$
$167$	−1.55981	+	0.900559i	−0.120702	+	0.0696874i	0.438433	+	0.898764i	$0.355534\pi$
$168$	5.57327	+	5.25230i	0.429987	+	0.405224i
$169$	−12.4526	−	3.73260i	−0.957894	−	0.287123i
$170$	7.42881	−	12.8671i	0.569764	−	0.986860i
$171$	−2.36676	−	1.36645i	−0.180990	−	0.104495i
$172$	−2.45457	+	4.25144i	−0.187159	+	0.324169i
$173$	5.96284	+	10.3279i	0.453346	+	0.785219i	0.998591	−	0.0530578i	$-0.0168968\pi$
$173$	5.96284	+	10.3279i	0.453346	+	0.785219i	−0.545245	+	0.838277i	$0.683563\pi$
$174$		−	3.25343i		−	0.246642i
$175$	1.40953	+	4.69874i	0.106551	+	0.355191i
$176$	−0.717903	−	0.414482i	−0.0541140	−	0.0312427i
$177$	1.95579	+	1.12918i	0.147006	+	0.0848741i
$178$	10.4420			0.782659
$179$	8.17000	−	14.1509i	0.610655	−	1.05768i	−0.380476	−	0.924791i	$-0.624240\pi$
$179$	8.17000	−	14.1509i	0.610655	−	1.05768i	0.991130	−	0.132894i	$-0.0424269\pi$
$180$			3.04229i			0.226759i
$181$	16.7748			1.24686			0.623429	−	0.781880i	$-0.285739\pi$
$181$	16.7748			1.24686			0.623429	+	0.781880i	$0.285739\pi$
$182$	8.11660	+	3.22090i	0.601643	+	0.238749i
$183$	−12.3720			−0.914566
$184$		−	22.8386i		−	1.68368i
$185$	11.3713	−	19.6956i	0.836031	−	1.44805i
$186$	−8.36327			−0.613224
$187$	13.6717	+	7.89337i	0.999775	+	0.577220i
$188$	−1.78552	−	1.03087i	−0.130222	−	0.0751839i
$189$	−2.57477	−	0.608732i	−0.187287	−	0.0442787i
$190$		−	6.54951i		−	0.475151i
$191$	−3.74195	−	6.48125i	−0.270758	−	0.468967i	0.698298	−	0.715807i	$-0.253941\pi$
$191$	−3.74195	−	6.48125i	−0.270758	−	0.468967i	−0.969056	+	0.246840i	$0.920608\pi$
$192$	−2.83879	+	4.91693i	−0.204872	+	0.354849i
$193$	−10.1206	−	5.84311i	−0.728494	−	0.420596i	0.0893768	−	0.995998i	$-0.471512\pi$
$193$	−10.1206	−	5.84311i	−0.728494	−	0.420596i	−0.817871	+	0.575402i	$0.804846\pi$
$194$	0.702569	−	1.21689i	0.0504416	−	0.0873673i
$195$	3.48365	+	8.77314i	0.249469	+	0.628258i
$196$	7.27314	+	3.64267i	0.519510	+	0.260190i
$197$	0.388915	−	0.224540i	0.0277091	−	0.0159978i	−0.486081	−	0.873913i	$-0.661574\pi$
$197$	0.388915	−	0.224540i	0.0277091	−	0.0159978i	0.513791	+	0.857916i	$0.328241\pi$
$198$	2.33098			0.165655
$199$	−9.82331			−0.696356			−0.348178	−	0.937428i	$-0.613200\pi$
$199$	−9.82331			−0.696356			−0.348178	+	0.937428i	$0.613200\pi$
$200$	−4.64784	+	2.68343i	−0.328652	+	0.189747i
$201$	0.536530	−	0.309766i	0.0378439	−	0.0218492i
$202$	−0.400146	−	0.231024i	−0.0281542	−	0.0162548i
$203$	−2.70187	−	9.00678i	−0.189634	−	0.632152i
$204$	3.60212	−	6.23906i	0.252199	−	0.436821i
$205$	12.0566			0.842068
$206$	−4.23197	−	2.44333i	−0.294856	−	0.170235i
$207$	3.94513	+	6.83316i	0.274205	+	0.474937i
$208$	−0.170309	+	1.16134i	−0.0118088	+	0.0805242i
$209$	6.95908			0.481369
$210$	−1.82187	−	6.07329i	−0.125721	−	0.419097i
$211$	1.80752	+	3.13072i	0.124435	+	0.215528i	0.921512	−	0.388350i	$-0.126955\pi$
$211$	1.80752	+	3.13072i	0.124435	+	0.215528i	−0.797077	+	0.603878i	$0.793621\pi$
$212$	−3.97750	−	6.88924i	−0.273176	−	0.473155i
$213$	6.48057	−	3.74156i	0.444041	−	0.256367i
$214$			16.3044i			1.11455i
$215$	9.57828	−	5.53002i	0.653233	−	0.377145i
$216$		−	2.89453i		−	0.196948i
$217$	−23.1529	+	6.94543i	−1.57172	+	0.471487i
$218$	8.50521	+	14.7315i	0.576045	+	0.997740i
$219$			12.4996i			0.844647i
$220$	−3.87347	−	6.70904i	−0.261149	−	0.452323i
$221$	3.24335	−	22.1164i	0.218171	−	1.48771i
$222$	−3.97595	+	6.88655i	−0.266848	+	0.462195i
$223$	3.07998	−	1.77823i	0.206251	−	0.119079i	−0.393317	−	0.919403i	$-0.628672\pi$
$223$	3.07998	−	1.77823i	0.206251	−	0.119079i	0.599568	+	0.800324i	$0.295339\pi$
$224$	−3.34258	+	14.1382i	−0.223336	+	0.944649i
$225$	0.927071	−	1.60573i	0.0618047	−	0.107049i
$226$	−5.73345	−	3.31021i	−0.381384	−	0.220192i
$227$		−	7.79500i		−	0.517372i	−0.965961	−	0.258686i	$-0.916711\pi$
$227$		−	7.79500i		−	0.517372i	0.965961	−	0.258686i	$-0.0832895\pi$
$228$		−	3.17576i		−	0.210320i
$229$	−14.2182	−	8.20887i	−0.939563	−	0.542457i	−0.0497400	−	0.998762i	$-0.515839\pi$
$229$	−14.2182	−	8.20887i	−0.939563	−	0.542457i	−0.889823	+	0.456305i	$0.849173\pi$
$230$	−9.45467	+	16.3760i	−0.623423	+	1.07980i
$231$	6.45307	−	1.93580i	0.424581	−	0.127366i
$232$	8.90923	−	5.14375i	0.584920	−	0.337704i
$233$	−3.78863	+	6.56210i	−0.248201	+	0.429898i	−0.963027	−	0.269405i	$-0.913173\pi$
$233$	−3.78863	+	6.56210i	−0.248201	+	0.429898i	0.714825	+	0.699303i	$0.246506\pi$
$234$	−1.21806	−	3.06752i	−0.0796268	−	0.200530i
$235$	2.32250	+	4.02269i	0.151503	+	0.262411i
$236$			2.62432i			0.170829i
$237$	−0.621752	−	1.07691i	−0.0403872	−	0.0699526i
$238$	−3.45461	+	14.6121i	−0.223929	+	0.947159i
$239$			4.68654i			0.303147i	0.988446	+	0.151574i	$0.0484341\pi$
$239$			4.68654i			0.303147i	−0.988446	+	0.151574i	$0.951566\pi$
$240$	0.738098	−	0.426141i	0.0476440	−	0.0275073i
$241$		−	10.7233i		−	0.690748i	−0.938465	−	0.345374i	$-0.887752\pi$
$241$		−	10.7233i		−	0.690748i	0.938465	−	0.345374i	$-0.112248\pi$
$242$	3.57992	−	2.06687i	0.230126	−	0.132863i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−7.18845	−	12.4508i	−0.460193	−	0.797078i
$245$	−10.0873	−	15.3003i	−0.644457	−	0.977499i
$246$	−4.21557			−0.268775
$247$	−3.63648	−	9.15802i	−0.231384	−	0.582711i
$248$	−13.2225	−	22.9021i	−0.839632	−	1.45428i
$249$	−1.81881	−	1.05009i	−0.115262	−	0.0665466i
$250$	−7.53919			−0.476820
$251$	5.93135	−	10.2734i	0.374384	−	0.648452i	−0.615851	−	0.787863i	$-0.711188\pi$
$251$	5.93135	−	10.2734i	0.374384	−	0.648452i	0.990235	+	0.139411i	$0.0445209\pi$
$252$	−0.883400	−	2.94485i	−0.0556489	−	0.185508i
$253$	−17.4000	−	10.0459i	−1.09393	−	0.631581i
$254$	−6.67610	+	3.85445i	−0.418896	+	0.241849i
$255$	−14.0563	+	8.11541i	−0.880240	+	0.508207i
$256$	−16.6506			−1.04066
$257$	9.34756			0.583085			0.291542	−	0.956558i	$-0.405832\pi$
$257$	9.34756			0.583085			0.291542	+	0.956558i	$0.405832\pi$
$258$	−3.34904	+	1.93357i	−0.208502	+	0.120379i
$259$	−5.28796	+	22.3666i	−0.328578	+	1.38979i
$260$	−6.80489	+	8.60324i	−0.422021	+	0.533550i
$261$	−1.77706	+	3.07796i	−0.109997	+	0.190521i
$262$	13.1092	+	7.56858i	0.809886	+	0.467588i
$263$	−0.471710	+	0.817026i	−0.0290869	+	0.0503800i	−0.880202	−	0.474598i	$-0.842593\pi$
$263$	−0.471710	+	0.817026i	−0.0290869	+	0.0503800i	0.851116	+	0.524978i	$0.175927\pi$
$264$	3.68533	+	6.38318i	0.226816	+	0.392857i
$265$			17.9222i			1.10095i
$266$	1.90180	+	6.33972i	0.116607	+	0.388713i
$267$	−9.87880	−	5.70353i	−0.604573	−	0.349050i
$268$	0.623475	+	0.359963i	0.0380848	+	0.0219883i
$269$	−7.58306			−0.462347			−0.231174	−	0.972913i	$-0.574257\pi$
$269$	−7.58306			−0.462347			−0.231174	+	0.972913i	$0.574257\pi$
$270$	−1.19827	+	2.07547i	−0.0729246	+	0.126309i
$271$		−	20.5902i		−	1.25077i	−0.780317	−	0.625384i	$-0.784942\pi$
$271$		−	20.5902i		−	1.25077i	0.780317	−	0.625384i	$-0.215058\pi$
$272$	−2.01823			−0.122373
$273$	−5.91955	−	7.48057i	−0.358267	−	0.452745i
$274$	−1.75622			−0.106097
$275$			4.72141i			0.284712i
$276$	−4.58443	+	7.94047i	−0.275950	+	0.477960i
$277$	20.4256			1.22726			0.613628	−	0.789595i	$-0.289710\pi$
$277$	20.4256			1.22726			0.613628	+	0.789595i	$0.289710\pi$
$278$	−17.4883	−	10.0969i	−1.04888	−	0.605569i
$279$	7.91220	+	4.56811i	0.473691	+	0.273486i
$280$	13.7508	−	14.5911i	0.821765	−	0.871983i
$281$			10.8703i			0.648466i	0.945977	+	0.324233i	$0.105106\pi$
$281$			10.8703i			0.648466i	−0.945977	+	0.324233i	$0.894894\pi$
$282$	−0.812060	−	1.40653i	−0.0483575	−	0.0837576i
$283$	−1.91077	+	3.30955i	−0.113583	+	0.196732i	−0.917213	−	0.398398i	$-0.869566\pi$
$283$	−1.91077	+	3.30955i	−0.113583	+	0.196732i	0.803629	+	0.595130i	$0.202900\pi$
$284$	7.53074	+	4.34787i	0.446867	+	0.257999i
$285$	−3.57742	+	6.19627i	−0.211908	+	0.367035i
$286$	6.59171	+	5.21384i	0.389776	+	0.308301i
$287$	−11.6704	+	3.50090i	−0.688882	+	0.206652i
$288$	4.75540	−	2.74553i	0.280214	−	0.161782i
$289$	21.4351			1.26089
$290$	−8.51760			−0.500171
$291$	−1.32935	+	0.767503i	−0.0779281	+	0.0449918i
$292$	−12.5792	+	7.26260i	−0.736141	+	0.425011i
$293$	15.6392	+	9.02929i	0.913651	+	0.527497i	0.881604	−	0.471989i	$-0.156464\pi$
$293$	15.6392	+	9.02929i	0.913651	+	0.527497i	0.0320472	+	0.999486i	$0.489797\pi$
$294$	3.52703	+	5.34973i	0.205701	+	0.312003i
$295$	2.95623	−	5.12034i	0.172118	−	0.298118i
$296$	−25.1443			−1.46148
$297$	−2.20526	−	1.27321i	−0.127962	−	0.0738789i
$298$	−6.86291	−	11.8869i	−0.397558	−	0.688590i
$299$	−4.12782	+	28.1476i	−0.238718	+	1.62782i
$300$	2.15461			0.124396
$301$	−7.66571	+	8.13416i	−0.441844	+	0.468845i
$302$	4.13287	+	7.15834i	0.237820	+	0.411916i
$303$	0.252376	+	0.437129i	0.0144986	+	0.0251124i
$304$	−0.770478	+	0.444836i	−0.0441900	+	0.0255131i
$305$			32.3905i			1.85467i
$306$	4.91477	−	2.83755i	0.280959	−	0.162212i
$307$			8.88791i			0.507260i	0.967301	+	0.253630i	$0.0816246\pi$
$307$			8.88791i			0.507260i	−0.967301	+	0.253630i	$0.918375\pi$
$308$	5.69752	+	5.36939i	0.324646	+	0.305950i
$309$	2.66915	+	4.62310i	0.151843	+	0.262999i
$310$			21.8954i			1.24357i
$311$	−8.24533	−	14.2813i	−0.467550	−	0.809820i	0.531763	−	0.846893i	$-0.321530\pi$
$311$	−8.24533	−	14.2813i	−0.467550	−	0.809820i	−0.999313	+	0.0370736i	$0.988196\pi$
$312$	6.47437	−	8.18537i	0.366539	−	0.463405i
$313$	−11.0236	+	19.0935i	−0.623092	+	1.07923i	0.365815	+	0.930688i	$0.380790\pi$
$313$	−11.0236	+	19.0935i	−0.623092	+	1.07923i	−0.988907	+	0.148539i	$0.952543\pi$
$314$	−0.158236	+	0.0913578i	−0.00892979	+	0.00515562i
$315$	−1.59369	+	6.74086i	−0.0897940	+	0.379804i
$316$	0.722507	−	1.25142i	0.0406442	−	0.0703978i
$317$	−19.7541	−	11.4050i	−1.10950	−	0.640569i	−0.170799	−	0.985306i	$-0.554635\pi$
$317$	−19.7541	−	11.4050i	−1.10950	−	0.640569i	−0.938699	+	0.344737i	$0.887968\pi$
$318$		−	6.26650i		−	0.351408i
$319$		−	9.05024i		−	0.506716i
$320$	12.8727	+	7.43207i	0.719607	+	0.415465i
$321$	8.90567	−	15.4251i	0.497066	−	0.860944i
$322$	4.39669	−	18.5968i	0.245018	−	1.03636i
$323$	14.6730	−	8.47143i	0.816425	−	0.471363i
$324$	−0.581025	+	1.00636i	−0.0322792	+	0.0559091i
$325$	6.21329	−	2.46718i	0.344651	−	0.136855i
$326$	−3.22774	−	5.59061i	−0.178768	−	0.309635i
$327$		−	18.5826i		−	1.02762i
$328$	−6.66493	−	11.5440i	−0.368009	−	0.637410i
$329$	−3.41619	−	3.21944i	−0.188340	−	0.177494i
$330$		−	6.10259i		−	0.335937i
$331$	27.7264	−	16.0079i	1.52398	−	0.879871i	0.524385	−	0.851481i	$-0.324295\pi$
$331$	27.7264	−	16.0079i	1.52398	−	0.879871i	0.999597	−	0.0283898i	$-0.00903797\pi$
$332$		−	2.44051i		−	0.133940i
$333$	7.52303	−	4.34342i	0.412259	−	0.238018i
$334$	−0.824369	−	1.42785i	−0.0451074	−	0.0781284i
$335$	−0.810980	−	1.40466i	−0.0443086	−	0.0767447i
$336$	−0.590716	+	0.626815i	−0.0322262	+	0.0341955i
$337$	4.99719			0.272214			0.136107	−	0.990694i	$-0.456541\pi$
$337$	4.99719			0.272214			0.136107	+	0.990694i	$0.456541\pi$
$338$	3.41681	−	11.3991i	0.185850	−	0.620028i
$339$	3.61615	+	6.26336i	0.196402	+	0.340179i
$340$	−16.3341	−	9.43051i	−0.885842	−	0.511441i
$341$	−23.2646			−1.25985
$342$	1.25084	−	2.16652i	0.0676378	−	0.117152i
$343$	14.2070	+	11.8811i	0.767107	+	0.641519i
$344$	−10.5898	−	6.11404i	−0.570965	−	0.329647i
$345$	17.8895	−	10.3285i	0.963138	−	0.556068i
$346$	−9.45416	+	5.45836i	−0.508259	+	0.293443i
$347$	34.3420			1.84358			0.921789	−	0.387692i	$-0.126728\pi$
$347$	34.3420			1.84358			0.921789	+	0.387692i	$0.126728\pi$
$348$	−4.13006			−0.221394
$349$	8.51580	−	4.91660i	0.455841	−	0.263180i	−0.254453	−	0.967085i	$-0.581895\pi$
$349$	8.51580	−	4.91660i	0.455841	−	0.263180i	0.710294	+	0.703905i	$0.248562\pi$
$350$	−4.30121	+	1.29028i	−0.229909	+	0.0689685i
$351$	−0.523154	+	3.56740i	−0.0279239	+	0.190413i
$352$	−6.99124	+	12.1092i	−0.372635	+	0.645422i
$353$	13.2871	+	7.67129i	0.707199	+	0.408302i	0.810023	−	0.586398i	$-0.199454\pi$
$353$	13.2871	+	7.67129i	0.707199	+	0.408302i	−0.102824	+	0.994700i	$0.532788\pi$
$354$	−1.03364	+	1.79032i	−0.0549375	+	0.0951546i
$355$	−9.79555	−	16.9664i	−0.519894	−	0.900483i
$356$		−	13.2556i		−	0.702544i
$357$	11.2496	−	11.9370i	0.595390	−	0.631775i
$358$	12.9536	+	7.47879i	0.684621	+	0.395266i
$359$	25.1701	+	14.5319i	1.32842	+	0.766966i	0.985056	−	0.172235i	$-0.0550987\pi$
$359$	25.1701	+	14.5319i	1.32842	+	0.766966i	0.343369	+	0.939201i	$0.388432\pi$
$360$	−7.57800			−0.399395
$361$	−5.76564	+	9.98638i	−0.303455	+	0.525599i
$362$			15.3555i			0.807070i
$363$	−4.51579			−0.237018
$364$	4.08878	−	10.3036i	0.214310	−	0.540056i
$365$	32.7246			1.71288
$366$		−	11.3253i		−	0.591983i
$367$	−9.15105	+	15.8501i	−0.477681	+	0.827368i	−0.999673	−	0.0255830i	$-0.991856\pi$
$367$	−9.15105	+	15.8501i	−0.477681	+	0.827368i	0.521992	+	0.852950i	$0.325189\pi$
$368$	2.56861			0.133898
$369$	3.98821	+	2.30259i	0.207618	+	0.119868i
$370$	18.0293	+	10.4092i	0.937297	+	0.541149i
$371$	−5.20413	−	17.3482i	−0.270185	−	0.900672i
$372$			10.6167i			0.550453i
$373$	−6.43274	−	11.1418i	−0.333074	−	0.576902i	0.650039	−	0.759901i	$-0.274753\pi$
$373$	−6.43274	−	11.1418i	−0.333074	−	0.576902i	−0.983113	+	0.182999i	$0.941419\pi$
$374$	−7.22556	+	12.5150i	−0.373625	+	0.647137i
$375$	7.13257	+	4.11799i	0.368325	+	0.212652i
$376$	2.56777	−	4.44752i	0.132423	−	0.229363i
$377$	−11.9100	+	4.72922i	−0.613394	+	0.243567i
$378$	0.557231	−	2.35694i	0.0286609	−	0.121228i
$379$	22.8080	−	13.1682i	1.17157	−	0.676405i	0.217519	−	0.976056i	$-0.430204\pi$
$379$	22.8080	−	13.1682i	1.17157	−	0.676405i	0.954049	+	0.299651i	$0.0968703\pi$
$380$	−8.31427			−0.426513
$381$	8.42137			0.431440
$382$	5.93291	−	3.42537i	0.303554	−	0.175257i
$383$	−12.4747	+	7.20224i	−0.637425	+	0.368017i	−0.783622	−	0.621238i	$-0.786630\pi$
$383$	−12.4747	+	7.20224i	−0.637425	+	0.368017i	0.146197	+	0.989255i	$0.453297\pi$
$384$	5.00985	+	2.89244i	0.255658	+	0.147604i
$385$	−5.06801	−	16.8944i	−0.258290	−	0.861019i
$386$	5.34876	−	9.26433i	0.272245	−	0.471542i
$387$	4.22455			0.214746
$388$	−1.54478	−	0.891877i	−0.0784241	−	0.0452782i
$389$	3.30891	+	5.73120i	0.167768	+	0.290584i	0.937635	−	0.347621i	$-0.113011\pi$
$389$	3.30891	+	5.73120i	0.167768	+	0.290584i	−0.769866	+	0.638205i	$0.779677\pi$
$390$	−8.03090	+	3.18892i	−0.406661	+	0.161477i
$391$	−48.9164			−2.47381
$392$	−9.07345	+	18.1165i	−0.458279	+	0.915023i
$393$	−8.26809	−	14.3207i	−0.417070	−	0.722386i
$394$	0.205543	+	0.356012i	0.0103551	+	0.0179356i
$395$	−2.81939	+	1.62777i	−0.141859	+	0.0819022i
$396$		−	2.95906i		−	0.148698i
$397$	−19.6031	+	11.3178i	−0.983851	+	0.568027i	−0.903431	−	0.428734i	$-0.858960\pi$
$397$	−19.6031	+	11.3178i	−0.983851	+	0.568027i	−0.0804203	+	0.996761i	$0.525626\pi$
$398$		−	8.99222i		−	0.450739i
$399$	1.66360	−	7.03658i	0.0832842	−	0.352270i
$400$	−0.301800	−	0.522734i	−0.0150900	−	0.0261367i
$401$		−	0.450563i		−	0.0225000i	−0.999937	−	0.0112500i	$-0.996419\pi$
$401$		−	0.450563i		−	0.0225000i	0.999937	−	0.0112500i	$-0.00358107\pi$
$402$	0.283559	+	0.491138i	0.0141426	+	0.0244957i
$403$	12.1570	+	30.6158i	0.605581	+	1.52508i
$404$	−0.293274	+	0.507965i	−0.0145909	+	0.0252722i
$405$	2.26729	−	1.30902i	0.112663	−	0.0650458i
$406$	8.24478	−	2.47328i	0.409181	−	0.122747i
$407$	−11.0601	+	19.1567i	−0.548231	+	0.949563i
$408$	15.5408	+	8.97246i	0.769382	+	0.444203i
$409$		−	34.4616i		−	1.70402i	−0.523529	−	0.852008i	$-0.675385\pi$
$409$		−	34.4616i		−	1.70402i	0.523529	−	0.852008i	$-0.324615\pi$
$410$			11.0365i			0.545056i
$411$	1.66150	+	0.959268i	0.0819558	+	0.0473172i
$412$	−3.10169	+	5.37228i	−0.152809	+	0.264673i
$413$	−1.37473	+	5.81474i	−0.0676461	+	0.286125i
$414$	−6.25505	+	3.61135i	−0.307419	+	0.177488i
$415$	−2.74917	+	4.76171i	−0.134952	+	0.233743i
$416$	19.5888	+	2.87267i	0.960419	+	0.140844i
$417$	11.0300	+	19.1046i	0.540143	+	0.935556i
$418$			6.37031i			0.311582i
$419$	0.195021	+	0.337787i	0.00952742	+	0.0165020i	0.870750	−	0.491726i	$-0.163634\pi$
$419$	0.195021	+	0.337787i	0.00952742	+	0.0165020i	−0.861222	+	0.508228i	$0.830301\pi$
$420$	−7.70973	+	2.31278i	−0.376196	+	0.112852i
$421$		−	24.5494i		−	1.19646i	−0.801323	−	0.598232i	$-0.795870\pi$
$421$		−	24.5494i		−	1.19646i	0.801323	−	0.598232i	$-0.204130\pi$
$422$	−2.86585	+	1.65460i	−0.139507	+	0.0805447i
$423$			1.77423i			0.0862658i
$424$	17.1603	−	9.90749i	0.833377	−	0.481150i
$425$	5.74747	+	9.95491i	0.278793	+	0.482884i
$426$	3.42501	+	5.93229i	0.165942	+	0.287420i
$427$	−9.40531	−	31.3530i	−0.455155	−	1.51728i
$428$	20.6977			1.00046
$429$	−3.38834	−	8.53311i	−0.163590	−	0.411982i
$430$	5.06216	+	8.76793i	0.244119	+	0.422827i
$431$	−0.983361	−	0.567744i	−0.0473668	−	0.0273473i	0.476130	−	0.879375i	$-0.342039\pi$
$431$	−0.983361	−	0.567744i	−0.0473668	−	0.0273473i	−0.523496	+	0.852028i	$0.675373\pi$
$432$	0.325542			0.0156626
$433$	10.1233	−	17.5341i	0.486495	−	0.842634i	−0.513385	−	0.858159i	$-0.671609\pi$
$433$	10.1233	−	17.5341i	0.486495	−	0.842634i	0.999879	+	0.0155250i	$0.00494195\pi$
$434$	−6.35782	−	21.1940i	−0.305185	−	1.01735i
$435$	8.05822	+	4.65241i	0.386362	+	0.223066i
$436$	18.7008	−	10.7969i	0.895608	−	0.517079i
$437$	−18.6743	+	10.7816i	−0.893313	+	0.515755i
$438$	−11.4421			−0.546726
$439$	27.9764			1.33524			0.667621	−	0.744501i	$-0.267313\pi$
$439$	27.9764			1.33524			0.667621	+	0.744501i	$0.267313\pi$
$440$	16.7114	−	9.64835i	0.796686	−	0.459967i
$441$	−0.414724	−	6.98770i	−0.0197487	−	0.332748i
$442$	20.2453	+	2.96895i	0.962971	+	0.141219i
$443$	10.7712	−	18.6562i	0.511755	−	0.886385i	−0.488153	−	0.872758i	$-0.662329\pi$
$443$	10.7712	−	18.6562i	0.511755	−	0.886385i	0.999907	−	0.0136266i	$-0.00433761\pi$
$444$	8.74213	+	5.04727i	0.414883	+	0.239533i
$445$	−14.9321	+	25.8631i	−0.707848	+	1.22603i
$446$	1.62778	+	2.81941i	0.0770778	+	0.133503i
$447$			14.9944i			0.709211i
$448$	−14.6185	−	3.45612i	−0.690657	−	0.163286i
$449$	−2.50177	−	1.44440i	−0.118066	−	0.0681652i	0.439804	−	0.898094i	$-0.355048\pi$
$449$	−2.50177	−	1.44440i	−0.118066	−	0.0681652i	−0.557870	+	0.829928i	$0.688381\pi$
$450$	1.46988	+	0.848638i	0.0692910	+	0.0400052i
$451$	−11.7267			−0.552189
$452$	−4.20215	+	7.27833i	−0.197652	+	0.342344i
$453$		−	9.02968i		−	0.424251i
$454$	7.13551			0.334886
$455$	−19.5844	+	15.4976i	−0.918133	+	0.726540i
$456$	7.91045			0.370441
$457$			32.6685i			1.52817i	0.645118	+	0.764083i	$0.276808\pi$
$457$			32.6685i			1.52817i	−0.645118	+	0.764083i	$0.723192\pi$
$458$	7.51437	−	13.0153i	0.351123	−	0.608163i
$459$	−6.19960			−0.289373
$460$	20.7885	+	12.0022i	0.969268	+	0.559607i
$461$	−32.7978	−	18.9358i	−1.52755	−	0.881930i	−0.999464	−	0.0327376i	$-0.989577\pi$
$461$	−32.7978	−	18.9358i	−1.52755	−	0.881930i	−0.528084	−	0.849192i	$-0.677089\pi$
$462$	1.77203	+	5.90712i	0.0824421	+	0.274824i
$463$		−	20.8936i		−	0.971006i	−0.874235	−	0.485503i	$-0.838636\pi$
$463$		−	20.8936i		−	0.971006i	0.874235	−	0.485503i	$-0.161364\pi$
$464$	0.578507	+	1.00200i	0.0268565	+	0.0465168i
$465$	11.9595	−	20.7145i	0.554609	−	0.960611i
$466$	−6.00692	−	3.46810i	−0.278265	−	0.160657i
$467$	−10.8858	+	18.8548i	−0.503735	+	0.872494i	0.496256	+	0.868176i	$0.334708\pi$
$467$	−10.8858	+	18.8548i	−0.503735	+	0.872494i	−0.999991	+	0.00431766i	$0.998626\pi$
$468$	−3.89407	+	1.54626i	−0.180003	+	0.0714759i
$469$	1.19288	+	1.12418i	0.0550820	+	0.0519098i
$470$	−3.68235	+	2.12601i	−0.169854	+	0.0980654i
$471$	0.199603			0.00919721
$472$	−6.53687			−0.300884
$473$	−9.31622	+	5.37872i	−0.428360	+	0.247314i
$474$	0.985797	−	0.569150i	0.0452791	−	0.0261419i
$475$	4.38830	+	2.53359i	0.201349	+	0.116249i
$476$	18.5493	+	4.38545i	0.850205	+	0.201007i
$477$	−3.42283	+	5.92852i	−0.156721	+	0.271448i
$478$	−4.29004			−0.196222
$479$	−9.43952	−	5.44991i	−0.431303	−	0.249013i	0.268599	−	0.963252i	$-0.413439\pi$
$479$	−9.43952	−	5.44991i	−0.431303	−	0.249013i	−0.699901	+	0.714239i	$0.746773\pi$
$480$	−7.18791	−	12.4498i	−0.328082	−	0.568254i
$481$	30.9894	+	4.54456i	1.41299	+	0.207214i
$482$	9.81606			0.447109
$483$	−14.3174	+	15.1923i	−0.651462	+	0.691273i
$484$	−2.62379	−	4.54453i	−0.119263	−	0.206570i
$485$	2.00936	+	3.48031i	0.0912401	+	0.158033i
$486$	−0.792756	+	0.457698i	−0.0359602	+	0.0207616i
$487$			6.15209i			0.278778i	0.990238	+	0.139389i	$0.0445138\pi$
$487$			6.15209i			0.278778i	−0.990238	+	0.139389i	$0.955486\pi$
$488$	31.0134	−	17.9056i	1.40391	−	0.810548i
$489$			7.05212i			0.318908i
$490$	14.0058	−	9.23392i	0.632718	−	0.417146i
$491$	5.40015	+	9.35334i	0.243705	+	0.422110i	0.961767	−	0.273869i	$-0.0883036\pi$
$491$	5.40015	+	9.35334i	0.243705	+	0.422110i	−0.718061	+	0.695980i	$0.754970\pi$
$492$			5.35146i			0.241262i
$493$	−11.0171	−	19.0821i	−0.496183	−	0.859415i
$494$	8.38322	−	3.32882i	0.377179	−	0.149771i
$495$	−3.33331	+	5.77345i	−0.149821	+	0.259497i
$496$	2.57575	−	1.48711i	0.115655	−	0.0667733i
$497$	14.4084	+	13.5786i	0.646304	+	0.609082i
$498$	0.961247	−	1.66493i	0.0430745	−	0.0746072i
$499$	−1.85936	−	1.07350i	−0.0832362	−	0.0480565i	0.457804	−	0.889053i	$-0.348636\pi$
$499$	−1.85936	−	1.07350i	−0.0832362	−	0.0480565i	−0.541040	+	0.840997i	$0.681969\pi$
$500$			9.57062i			0.428011i
$501$			1.80112i			0.0804680i
$502$	9.40424	+	5.42954i	0.419732	+	0.242332i
$503$	−3.07639	+	5.32846i	−0.137169	+	0.237584i	−0.926424	−	0.376482i	$-0.877134\pi$
$503$	−3.07639	+	5.32846i	−0.137169	+	0.237584i	0.789255	+	0.614066i	$0.210467\pi$
$504$	7.33527	−	2.20044i	0.326739	−	0.0980156i
$505$	1.14442	−	0.660732i	0.0509261	−	0.0294022i
$506$	9.19599	−	15.9279i	0.408812	−	0.708083i
$507$	−9.45883	+	8.91799i	−0.420082	+	0.396062i
$508$	4.89302	+	8.47497i	0.217093	+	0.376016i
$509$			4.58685i			0.203309i	0.994820	+	0.101654i	$0.0324136\pi$
$509$			4.58685i			0.203309i	−0.994820	+	0.101654i	$0.967586\pi$
$510$	−7.42881	−	12.8671i	−0.328953	−	0.569764i
$511$	−31.6764	+	9.50233i	−1.40128	+	0.420358i
$512$		−	3.67215i		−	0.162288i
$513$	−2.36676	+	1.36645i	−0.104495	+	0.0603302i
$514$			8.55672i			0.377421i
$515$	12.1035	−	6.98795i	0.533343	−	0.307926i
$516$	2.45457	+	4.25144i	0.108056	+	0.187159i
$517$	−2.25895	−	3.91262i	−0.0993487	−	0.172077i
$518$	−20.4743	−	4.84058i	−0.899590	−	0.212683i
$519$	11.9257			0.523479
$520$	−21.4296	−	16.9502i	−0.939752	−	0.743315i
$521$	10.7536	+	18.6258i	0.471123	+	0.816009i	0.999454	−	0.0330292i	$-0.0105154\pi$
$521$	10.7536	+	18.6258i	0.471123	+	0.816009i	−0.528331	+	0.849038i	$0.677182\pi$
$522$	−2.81755	−	1.62671i	−0.123321	−	0.0711993i
$523$	−12.0380			−0.526387			−0.263193	−	0.964743i	$-0.584776\pi$
$523$	−12.0380			−0.526387			−0.263193	+	0.964743i	$0.584776\pi$
$524$	9.60793	−	16.6414i	0.419724	−	0.726984i
$525$	4.77399	+	1.12868i	0.208354	+	0.0492594i
$526$	−0.747902	−	0.431802i	−0.0326101	−	0.0188274i
$527$	−49.0525	+	28.3205i	−2.13676	+	1.23366i
$528$	−0.717903	+	0.414482i	−0.0312427	+	0.0180380i
$529$	39.2561			1.70679
$530$	−16.4060			−0.712629
$531$	1.95579	−	1.12918i	0.0848741	−	0.0490021i
$532$	8.04796	−	2.41424i	0.348923	−	0.104671i
$533$	6.12782	+	15.4321i	0.265425	+	0.668440i
$534$	5.22099	−	9.04302i	0.225934	−	0.391330i
$535$	−40.3835	−	23.3154i	−1.74593	−	1.00801i
$536$	−0.896626	+	1.55300i	−0.0387283	+	0.0670795i
$537$	−8.17000	−	14.1509i	−0.352562	−	0.610655i
$538$		−	6.94150i		−	0.299269i
$539$	9.81135	+	14.8817i	0.422605	+	0.640998i
$540$	2.63470	+	1.52115i	0.113380	+	0.0654597i
$541$	−1.68945	−	0.975405i	−0.0726352	−	0.0419360i	0.463243	−	0.886232i	$-0.346686\pi$
$541$	−1.68945	−	0.975405i	−0.0726352	−	0.0419360i	−0.535878	+	0.844296i	$0.680019\pi$
$542$	18.8482			0.809601
$543$	8.38738	−	14.5274i	0.359937	−	0.623429i
$544$			34.0424i			1.45955i
$545$	−48.6500			−2.08393
$546$	6.84769	−	5.41873i	0.293054	−	0.231900i
$547$	4.27037			0.182588			0.0912940	−	0.995824i	$-0.470900\pi$
$547$	4.27037			0.182588			0.0912940	+	0.995824i	$0.470900\pi$
$548$			2.22943i			0.0952367i
$549$	−6.18601	+	10.7145i	−0.264013	+	0.457283i
$550$	−4.32196			−0.184289
$551$	−8.41173	−	4.85652i	−0.358352	−	0.206895i
$552$	−19.7788	−	11.4193i	−0.841840	−	0.486037i
$553$	2.25642	−	2.39431i	0.0959527	−	0.101816i
$554$			18.6975i			0.794382i
$555$	−11.3713	−	19.6956i	−0.482683	−	0.836031i
$556$	−12.8175	+	22.2005i	−0.543581	+	0.941510i
$557$	−34.6266	−	19.9917i	−1.46718	−	0.847075i	−0.467852	−	0.883807i	$-0.654972\pi$
$557$	−34.6266	−	19.9917i	−1.46718	−	0.847075i	−0.999325	+	0.0367316i	$0.988305\pi$
$558$	−4.18163	+	7.24280i	−0.177023	+	0.306612i
$559$	11.9465	+	9.44932i	0.505284	+	0.399663i
$560$	1.64103	+	1.54652i	0.0693460	+	0.0653524i
$561$	13.6717	−	7.89337i	0.577220	−	0.333258i
$562$	−9.95061			−0.419741
$563$	33.5147			1.41248			0.706239	−	0.707974i	$-0.250391\pi$
$563$	33.5147			1.41248			0.706239	+	0.707974i	$0.250391\pi$
$564$	−1.78552	+	1.03087i	−0.0751839	+	0.0434074i
$565$	16.3977	−	9.46723i	0.689858	−	0.398290i
$566$	−3.02955	−	1.74911i	−0.127342	−	0.0735207i
$567$	−1.81456	+	1.92545i	−0.0762045	+	0.0808613i
$568$	−10.8300	+	18.7582i	−0.454418	+	0.787076i
$569$	−38.8836			−1.63009			−0.815043	−	0.579401i	$-0.803287\pi$
$569$	−38.8836			−1.63009			−0.815043	+	0.579401i	$0.803287\pi$
$570$	−5.67204	−	3.27476i	−0.237576	−	0.137164i
$571$	11.3324	+	19.6282i	0.474245	+	0.821417i	0.999565	−	0.0294882i	$-0.00938774\pi$
$571$	11.3324	+	19.6282i	0.474245	+	0.821417i	−0.525320	+	0.850905i	$0.676054\pi$
$572$	6.61871	−	8.36785i	0.276742	−	0.349877i
$573$	−7.48391			−0.312645
$574$	−3.20471	−	10.6830i	−0.133762	−	0.445901i
$575$	−7.31482	−	12.6696i	−0.305049	−	0.528361i
$576$	2.83879	+	4.91693i	0.118283	+	0.204872i
$577$	20.1472	−	11.6320i	0.838740	−	0.484247i	−0.0180956	−	0.999836i	$-0.505760\pi$
$577$	20.1472	−	11.6320i	0.838740	−	0.484247i	0.856836	+	0.515589i	$0.172427\pi$
$578$			19.6216i			0.816150i
$579$	−10.1206	+	5.84311i	−0.420596	+	0.242831i
$580$			10.8127i			0.448972i
$581$	1.27844	−	5.40747i	0.0530388	−	0.224340i
$582$	−0.702569	−	1.21689i	−0.0291224	−	0.0504416i
$583$		−	17.4319i		−	0.721955i
$584$	−18.0903	−	31.3333i	−0.748581	−	1.29658i
$585$	9.33959	+	1.36964i	0.386145	+	0.0566276i
$586$	−8.26538	+	14.3161i	−0.341440	+	0.591391i
$587$	−11.6230	+	6.71057i	−0.479734	+	0.276975i	−0.720306	−	0.693657i	$-0.755998\pi$
$587$	−11.6230	+	6.71057i	−0.479734	+	0.276975i	0.240571	+	0.970631i	$0.422665\pi$
$588$	6.79121	−	4.47739i	0.280065	−	0.184645i
$589$	−12.4842	+	21.6232i	−0.514402	+	0.890970i
$590$	4.68714	+	2.70612i	0.192967	+	0.111409i
$591$		−	0.449081i		−	0.0184727i
$592$		−	2.82793i		−	0.116227i
$593$	−7.76746	−	4.48455i	−0.318972	−	0.184158i	0.331963	−	0.943293i	$-0.392289\pi$
$593$	−7.76746	−	4.48455i	−0.318972	−	0.184158i	−0.650934	+	0.759134i	$0.725623\pi$
$594$	1.16549	−	2.01868i	0.0478205	−	0.0828276i
$595$	−31.2516	−	29.4518i	−1.28119	−	1.20741i
$596$	−15.0898	+	8.71212i	−0.618104	+	0.356862i
$597$	−4.91166	+	8.50724i	−0.201021	+	0.348178i
$598$	−25.7663	−	3.77859i	−1.05366	−	0.154518i
$599$	−17.2505	−	29.8787i	−0.704836	−	1.22081i	−0.966751	−	0.255721i	$-0.917687\pi$
$599$	−17.2505	−	29.8787i	−0.704836	−	1.22081i	0.261914	−	0.965091i	$-0.415646\pi$
$600$			5.36687i			0.219101i
$601$	10.6843	+	18.5058i	0.435824	+	0.754869i	0.997362	−	0.0725818i	$-0.0231238\pi$
$601$	10.6843	+	18.5058i	0.435824	+	0.754869i	−0.561539	+	0.827450i	$0.689791\pi$
$602$	−7.44598	−	7.01716i	−0.303476	−	0.285998i
$603$		−	0.619532i		−	0.0252293i
$604$	9.08715	−	5.24647i	0.369751	−	0.213476i
$605$			11.8225i			0.480654i
$606$	−0.400146	+	0.231024i	−0.0162548	+	0.00938472i
$607$	0.563082	+	0.975286i	0.0228548	+	0.0395857i	0.877227	−	0.480077i	$-0.159391\pi$
$607$	0.563082	+	0.975286i	0.0228548	+	0.0395857i	−0.854372	+	0.519662i	$0.826058\pi$
$608$	7.50324	+	12.9960i	0.304297	+	0.527057i
$609$	−9.15104	−	2.16350i	−0.370819	−	0.0876696i
$610$	−29.6501			−1.20050
$611$	−3.96852	+	5.01729i	−0.160549	+	0.202978i
$612$	−3.60212	−	6.23906i	−0.145607	−	0.252199i
$613$	−25.0649	−	14.4712i	−1.01236	−	0.584486i	−0.100478	−	0.994939i	$-0.532037\pi$
$613$	−25.0649	−	14.4712i	−1.01236	−	0.584486i	−0.911882	+	0.410453i	$0.865371\pi$
$614$	−8.13596			−0.328341
$615$	6.02829	−	10.4413i	0.243084	−	0.421034i
$616$	−13.3745	+	14.1918i	−0.538875	+	0.571806i
$617$	−3.55424	−	2.05204i	−0.143088	−	0.0826120i	0.426747	−	0.904371i	$-0.359660\pi$
$617$	−3.55424	−	2.05204i	−0.143088	−	0.0826120i	−0.569835	+	0.821759i	$0.692993\pi$
$618$	−4.23197	+	2.44333i	−0.170235	+	0.0982852i
$619$	9.06150	−	5.23166i	0.364212	−	0.210278i	−0.306715	−	0.951802i	$-0.599230\pi$
$619$	9.06150	−	5.23166i	0.364212	−	0.210278i	0.670927	+	0.741523i	$0.265896\pi$
$620$	27.7951			1.11628
$621$	7.89025			0.316625
$622$	13.0731	−	7.54774i	0.524182	−	0.302637i
$623$	6.94384	−	29.3706i	0.278199	−	1.17671i
$624$	0.920592	+	0.728160i	0.0368532	+	0.0291497i
$625$	15.4164	−	26.7020i	0.616657	−	1.06808i
$626$	−17.4781	−	10.0910i	−0.698565	−	0.403317i
$627$	3.47954	−	6.02674i	0.138959	−	0.240685i
$628$	0.115974	+	0.200873i	0.00462787	+	0.00801571i
$629$			53.8550i			2.14734i
$630$	−6.17056	−	1.45885i	−0.245841	−	0.0581221i
$631$	24.3336	+	14.0490i	0.968704	+	0.559281i	0.898841	−	0.438275i	$-0.144410\pi$
$631$	24.3336	+	14.0490i	0.968704	+	0.559281i	0.0698630	+	0.997557i	$0.477744\pi$
$632$	3.11714	+	1.79968i	0.123993	+	0.0715874i
$633$	3.61505			0.143685
$634$	10.4401	−	18.0828i	0.414629	−	0.718159i
$635$		−	22.0475i		−	0.874928i
$636$	−7.95501			−0.315437
$637$	14.4570	−	20.6880i	0.572809	−	0.819689i
$638$	8.28456			0.327989
$639$		−	7.48311i		−	0.296027i
$640$	7.57253	−	13.1160i	0.299331	−	0.518456i
$641$	−28.6276			−1.13072			−0.565362	−	0.824843i	$-0.691263\pi$
$641$	−28.6276			−1.13072			−0.565362	+	0.824843i	$0.691263\pi$
$642$	14.1201	+	8.15222i	0.557274	+	0.321742i
$643$	−7.81711	−	4.51321i	−0.308277	−	0.177984i	0.337878	−	0.941190i	$-0.390291\pi$
$643$	−7.81711	−	4.51321i	−0.308277	−	0.177984i	−0.646155	+	0.763206i	$0.723624\pi$
$644$	−23.6077	−	5.58138i	−0.930275	−	0.219937i
$645$		−	11.0600i		−	0.435489i
$646$	7.75472	+	13.4316i	0.305105	+	0.528458i
$647$	13.1024	−	22.6940i	0.515109	−	0.892195i	−0.484737	−	0.874660i	$-0.661085\pi$
$647$	13.1024	−	22.6940i	0.515109	−	0.892195i	0.999846	−	0.0175353i	$-0.00558194\pi$
$648$	−2.50674	−	1.44726i	−0.0984739	−	0.0568539i
$649$	−2.87535	+	4.98025i	−0.112867	+	0.195492i
$650$	2.25845	+	5.68762i	0.0885837	+	0.223087i
$651$	−5.56151	+	23.5237i	−0.217973	+	0.921966i
$652$	−7.09700	+	4.09745i	−0.277940	+	0.160469i
$653$	45.4789			1.77973			0.889864	−	0.456226i	$-0.150799\pi$
$653$	45.4789			1.77973			0.889864	+	0.456226i	$0.150799\pi$
$654$	17.0104			0.665160
$655$	−37.4923	+	21.6462i	−1.46495	+	0.845787i
$656$	1.29833	−	0.749591i	0.0506912	−	0.0292666i
$657$	10.8250	+	6.24982i	0.422324	+	0.243829i
$658$	2.94707	−	3.12716i	0.114889	−	0.121910i
$659$	10.1806	−	17.6334i	0.396581	−	0.686899i	−0.596720	−	0.802449i	$-0.703530\pi$
$659$	10.1806	−	17.6334i	0.396581	−	0.686899i	0.993302	+	0.115550i	$0.0368632\pi$
$660$	−7.74693			−0.301549
$661$	34.7308	+	20.0518i	1.35087	+	0.779926i	0.988372	−	0.152057i	$-0.0485898\pi$
$661$	34.7308	+	20.0518i	1.35087	+	0.779926i	0.362501	+	0.931984i	$0.381923\pi$
$662$	14.6535	+	25.3807i	0.569526	+	0.986447i
$663$	−17.5317	−	13.8670i	−0.680875	−	0.538551i
$664$	6.07902			0.235912
$665$	−18.4221	−	4.35538i	−0.714377	−	0.168894i
$666$	3.97595	+	6.88655i	0.154065	+	0.266848i
$667$	14.0214	+	24.2858i	0.542912	+	0.940352i
$668$	−1.81258	+	1.04649i	−0.0701309	+	0.0404901i
$669$		−	3.55646i		−	0.137501i
$670$	1.28582	−	0.742368i	0.0496755	−	0.0286802i
$671$		−	31.5043i		−	1.21621i
$672$	10.5728	+	9.96387i	0.407853	+	0.384365i
$673$	10.2385	+	17.7336i	0.394666	+	0.683581i	0.993058	−	0.117622i	$-0.0375270\pi$
$673$	10.2385	+	17.7336i	0.394666	+	0.683581i	−0.598393	+	0.801203i	$0.704194\pi$
$674$			4.57441i			0.176200i
$675$	−0.927071	−	1.60573i	−0.0356830	−	0.0618047i
$676$	−14.4706	−	4.33746i	−0.556560	−	0.166825i
$677$	18.6224	−	32.2549i	0.715717	−	1.23966i	−0.246966	−	0.969024i	$-0.579433\pi$
$677$	18.6224	−	32.2549i	0.715717	−	1.23966i	0.962682	−	0.270634i	$-0.0872332\pi$
$678$	−5.73345	+	3.31021i	−0.220192	+	0.127128i
$679$	−2.95558	−	2.78537i	−0.113425	−	0.106893i
$680$	23.4903	−	40.6864i	0.900811	−	1.56025i
$681$	−6.75066	−	3.89750i	−0.258686	−	0.149352i
$682$		−	21.2963i		−	0.815478i
$683$			5.92465i			0.226700i	0.993555	+	0.113350i	$0.0361582\pi$
$683$			5.92465i			0.226700i	−0.993555	+	0.113350i	$0.963842\pi$
$684$	−2.75029	−	1.58788i	−0.105160	−	0.0607141i
$685$	2.51140	−	4.34988i	0.0959558	−	0.166200i
$686$	−10.8759	+	13.0051i	−0.415244	+	0.496535i
$687$	−14.2182	+	8.20887i	−0.542457	+	0.313188i
$688$	0.687634	−	1.19102i	0.0262158	−	0.0454071i
$689$	−22.9401	+	9.10907i	−0.873946	+	0.347028i
$690$	9.45467	+	16.3760i	0.359933	+	0.623423i
$691$			3.05713i			0.116299i	0.998308	+	0.0581493i	$0.0185199\pi$
$691$			3.05713i			0.116299i	−0.998308	+	0.0581493i	$0.981480\pi$
$692$	6.92912	+	12.0016i	0.263405	+	0.456232i
$693$	1.55008	−	6.55643i	0.0588827	−	0.249058i
$694$			31.4366i			1.19332i
$695$	50.0166	−	28.8771i	1.89724	−	1.09537i
$696$		−	10.2875i		−	0.389946i
$697$	−24.7253	+	14.2752i	−0.936538	+	0.540711i
$698$	4.50064	+	7.79534i	0.170352	+	0.295058i
$699$	3.78863	+	6.56210i	0.143299	+	0.248201i
$700$	1.63795	+	5.46016i	0.0619086	+	0.206375i
$701$	−2.81064			−0.106156			−0.0530782	−	0.998590i	$-0.516903\pi$
$701$	−2.81064			−0.106156			−0.0530782	+	0.998590i	$0.516903\pi$
$702$	−3.26558	−	0.478894i	−0.123251	−	0.0180747i
$703$	11.8701	+	20.5596i	0.447690	+	0.775422i
$704$	−12.5205	−	7.22872i	−0.471885	−	0.272443i
$705$	4.64500			0.174941
$706$	−7.02227	+	12.1629i	−0.264287	+	0.457758i
$707$	−0.915906	+	0.971877i	−0.0344462	+	0.0365512i
$708$	2.27273	+	1.31216i	0.0854143	+	0.0493139i
$709$	−33.2799	+	19.2141i	−1.24985	+	0.721602i	−0.971080	−	0.238755i	$-0.923261\pi$
$709$	−33.2799	+	19.2141i	−1.24985	+	0.721602i	−0.278772	+	0.960357i	$0.589927\pi$
$710$	15.5310	−	8.96681i	0.582867	−	0.336518i
$711$	−1.24350			−0.0466351
$712$	33.0181			1.23740
$713$	62.4293	−	36.0436i	2.33799	−	1.34984i
$714$	10.9271	+	10.2978i	0.408937	+	0.385386i
$715$	−22.3400	+	8.87081i	−0.835470	+	0.331749i
$716$	9.49395	−	16.4440i	0.354805	−	0.614541i
$717$	4.05866	+	2.34327i	0.151574	+	0.0875111i
$718$	−13.3025	+	23.0406i	−0.496444	+	0.859867i
$719$	13.2943	+	23.0263i	0.495792	+	0.858737i	0.999988	−	0.00485212i	$-0.00154448\pi$
$719$	13.2943	+	23.0263i	0.495792	+	0.858737i	−0.504196	+	0.863589i	$0.668211\pi$
$720$		−	0.852282i		−	0.0317627i
$721$	−9.68668	+	10.2786i	−0.360751	+	0.382797i
$722$	−9.14150	−	5.27785i	−0.340211	−	0.196421i
$723$	−9.28664	−	5.36164i	−0.345374	−	0.199402i
$724$	19.4931			0.724455
$725$	3.29492	−	5.70697i	0.122370	−	0.211951i
$726$		−	4.13374i		−	0.153417i
$727$	−26.5203			−0.983583			−0.491792	−	0.870713i	$-0.663658\pi$
$727$	−26.5203			−0.983583			−0.491792	+	0.870713i	$0.663658\pi$
$728$	25.6651	+	10.1847i	0.951212	+	0.377469i
$729$	1.00000			0.0370370
$730$			29.9560i			1.10872i
$731$	−13.0953	+	22.6817i	−0.484346	+	0.838912i
$732$	−14.3769			−0.531386
$733$	−22.0215	−	12.7141i	−0.813384	−	0.469607i	0.0347458	−	0.999396i	$-0.488938\pi$
$733$	−22.0215	−	12.7141i	−0.813384	−	0.469607i	−0.848130	+	0.529789i	$0.822271\pi$
$734$	−14.5091	−	8.37684i	−0.535541	−	0.309195i
$735$	−18.2941	+	1.08576i	−0.674788	+	0.0400490i
$736$		−	43.3258i		−	1.59701i
$737$	0.788791	+	1.36623i	0.0290555	+	0.0503256i
$738$	−2.10779	+	3.65079i	−0.0775887	+	0.134388i
$739$	−25.3568	−	14.6397i	−0.932763	−	0.538531i	−0.0450789	−	0.998983i	$-0.514354\pi$
$739$	−25.3568	−	14.6397i	−0.932763	−	0.538531i	−0.887684	+	0.460452i	$0.847687\pi$
$740$	13.2140	−	22.8873i	0.485755	−	0.841352i
$741$	−9.74932	−	1.42973i	−0.358150	−	0.0525223i
$742$	15.8805	−	4.76384i	0.582990	−	0.174886i
$743$	11.9142	−	6.87868i	0.437090	−	0.252354i	−0.265272	−	0.964174i	$-0.585462\pi$
$743$	11.9142	−	6.87868i	0.437090	−	0.252354i	0.702363	+	0.711819i	$0.252129\pi$
$744$	−26.4451			−0.969523
$745$	39.2560			1.43823
$746$	10.1992	−	5.88850i	0.373419	−	0.215593i
$747$	−1.81881	+	1.05009i	−0.0665466	+	0.0384207i
$748$	15.8872	+	9.17248i	0.580894	+	0.335379i
$749$	45.8601	+	10.8423i	1.67569	+	0.396170i
$750$	−3.76960	+	6.52913i	−0.137646	+	0.238410i
$751$	31.4688			1.14831			0.574156	−	0.818746i	$-0.305330\pi$
$751$	31.4688			1.14831			0.574156	+	0.818746i	$0.305330\pi$
$752$	0.500203	+	0.288792i	0.0182405	+	0.0105312i
$753$	−5.93135	−	10.2734i	−0.216151	−	0.374384i
$754$	−4.32911	−	10.9023i	−0.157657	−	0.397040i
$755$	−23.6401			−0.860351
$756$	−2.99201	−	0.707377i	−0.108818	−	0.0257270i
$757$	−20.2956	−	35.1531i	−0.737657	−	1.27766i	−0.953548	−	0.301243i	$-0.902599\pi$
$757$	−20.2956	−	35.1531i	−0.737657	−	1.27766i	0.215890	−	0.976418i	$-0.430735\pi$
$758$	12.0541	+	20.8784i	0.437825	+	0.758336i
$759$	−17.4000	+	10.0459i	−0.631581	+	0.364644i
$760$		−	20.7099i		−	0.751226i
$761$	−35.0760	+	20.2511i	−1.27150	+	0.734103i	−0.975271	−	0.221013i	$-0.929064\pi$
$761$	−35.0760	+	20.2511i	−1.27150	+	0.734103i	−0.296232	+	0.955116i	$0.595730\pi$
$762$			7.70889i			0.279264i
$763$	47.0916	−	14.1266i	1.70483	−	0.511418i
$764$	−4.34833	−	7.53154i	−0.157317	−	0.272481i
$765$			16.2308i			0.586826i
$766$	−6.59291	−	11.4193i	−0.238211	−	0.412594i
$767$	8.05644	+	1.18147i	0.290901	+	0.0426603i
$768$	−8.32531	+	14.4199i	−0.300414	+	0.520332i
$769$	25.2026	−	14.5507i	0.908828	−	0.524712i	0.0287743	−	0.999586i	$-0.490840\pi$
$769$	25.2026	−	14.5507i	0.908828	−	0.524712i	0.880054	+	0.474874i	$0.157506\pi$
$770$	15.4651	−	4.63924i	0.557323	−	0.167187i
$771$	4.67378	−	8.09523i	0.168322	−	0.291542i
$772$	−11.7606	−	6.78998i	−0.423273	−	0.244377i
$773$			10.3478i			0.372186i	0.982532	+	0.186093i	$0.0595825\pi$
$773$			10.3478i			0.372186i	−0.982532	+	0.186093i	$0.940417\pi$
$774$			3.86714i			0.139001i
$775$	−14.6704	−	8.46993i	−0.526975	−	0.304249i
$776$	2.22156	−	3.84785i	0.0797493	−	0.138130i
$777$	16.7261	+	15.7628i	0.600045	+	0.565488i
$778$	−5.24632	+	3.02897i	−0.188090	+	0.108594i
$779$	−6.29275	+	10.8994i	−0.225461	+	0.390510i
$780$	4.04818	+	10.1948i	0.144948	+	0.365033i
$781$	9.52754	+	16.5022i	0.340922	+	0.590495i
$782$		−	44.7779i		−	1.60125i
$783$	1.77706	+	3.07796i	0.0635069	+	0.109997i
$784$	−2.03753	−	1.02047i	−0.0727689	−	0.0364455i
$785$		−	0.522568i		−	0.0186513i
$786$	13.1092	−	7.56858i	0.467588	−	0.269962i
$787$			29.1016i			1.03736i	0.854968	+	0.518680i	$0.173577\pi$
$787$			29.1016i			1.03736i	−0.854968	+	0.518680i	$0.826423\pi$
$788$	0.451939	−	0.260927i	0.0160997	−	0.00929514i
$789$	0.471710	+	0.817026i	0.0167933	+	0.0290869i
$790$	−1.49006	−	2.58086i	−0.0530139	−	0.0918228i
$791$	−13.1235	+	13.9254i	−0.466617	+	0.495132i
$792$	7.37066			0.261905
$793$	−41.4590	+	16.4626i	−1.47225	+	0.584605i
$794$	−10.3603	−	17.9446i	−0.367674	−	0.636830i
$795$	15.5211	+	8.96112i	0.550477	+	0.317818i
$796$	−11.4152			−0.404600
$797$	−14.9812	+	25.9482i	−0.530661	+	0.919131i	0.468699	+	0.883358i	$0.344723\pi$
$797$	−14.9812	+	25.9482i	−0.530661	+	0.919131i	−0.999360	+	0.0357733i	$0.988611\pi$
$798$	6.44126	+	1.52285i	0.228018	+	0.0539085i
$799$	−9.52584	−	5.49975i	−0.337000	−	0.194567i
$800$	−8.81718	+	5.09060i	−0.311734	+	0.179980i
$801$	−9.87880	+	5.70353i	−0.349050	+	0.201524i
$802$	0.412443			0.0145639
$803$	−31.8292			−1.12323
$804$	0.623475	−	0.359963i	0.0219883	−	0.0126949i
$805$	39.7741	+	37.4834i	1.40185	+	1.32112i
$806$	−28.0256	+	11.1284i	−0.987159	+	0.391982i
$807$	−3.79153	+	6.56712i	−0.133468	+	0.231174i
$808$	−1.26528	−	0.730511i	−0.0445124	−	0.0256993i
$809$	8.03836	−	13.9228i	0.282614	−	0.489501i	−0.689414	−	0.724367i	$-0.742132\pi$
$809$	8.03836	−	13.9228i	0.282614	−	0.489501i	0.972028	+	0.234866i	$0.0754653\pi$
$810$	1.19827	+	2.07547i	0.0421030	+	0.0729246i
$811$		−	41.5793i		−	1.46005i	−0.683423	−	0.730023i	$-0.739509\pi$
$811$		−	41.5793i		−	1.46005i	0.683423	−	0.730023i	$-0.260491\pi$
$812$	−3.13971	−	10.4663i	−0.110182	−	0.367296i
$813$	−17.8317	−	10.2951i	−0.625384	−	0.361066i
$814$	−17.5360	−	10.1244i	−0.614636	−	0.354860i
$815$	18.4627			0.646721
$816$	−1.00911	+	1.74784i	−0.0353261	+	0.0611866i
$817$			11.5453i			0.403917i
$818$	31.5460			1.10298
$819$	−9.43814	+	1.38619i	−0.329795	+	0.0484375i
$820$	14.0103			0.489262
$821$			4.07383i			0.142178i	0.997470	+	0.0710888i	$0.0226474\pi$
$821$			4.07383i			0.142178i	−0.997470	+	0.0710888i	$0.977353\pi$
$822$	−0.878110	+	1.52093i	−0.0306276	+	0.0530486i
$823$	42.6371			1.48624			0.743118	−	0.669160i	$-0.233346\pi$
$823$	42.6371			1.48624			0.743118	+	0.669160i	$0.233346\pi$
$824$	−13.3817	−	7.72593i	−0.466174	−	0.269146i
$825$	4.08886	+	2.36070i	0.142356	+	0.0821892i
$826$	−5.32279	−	1.25842i	−0.185204	−	0.0437862i
$827$		−	21.7244i		−	0.755431i	−0.925922	−	0.377716i	$-0.876710\pi$
$827$		−	21.7244i		−	0.755431i	0.925922	−	0.377716i	$-0.123290\pi$
$828$	4.58443	+	7.94047i	0.159320	+	0.275950i
$829$	−0.461472	+	0.799293i	−0.0160276	+	0.0277606i	−0.873928	−	0.486055i	$-0.838435\pi$
$829$	−0.461472	+	0.799293i	−0.0160276	+	0.0277606i	0.857900	+	0.513816i	$0.171769\pi$
$830$	−4.35885	−	2.51658i	−0.151298	−	0.0873519i
$831$	10.2128	−	17.6891i	0.354278	−	0.613628i
$832$	−2.97025	+	20.2542i	−0.102975	+	0.702187i
$833$	38.8026	+	19.4338i	1.34443	+	0.673342i
$834$	−17.4883	+	10.0969i	−0.605569	+	0.349626i
$835$	4.71540			0.163183
$836$	8.08679			0.279688
$837$	7.91220	−	4.56811i	0.273486	−	0.157897i
$838$	−0.309209	+	0.178522i	−0.0106814	+	0.00616693i
$839$	10.4845	+	6.05325i	0.361966	+	0.208981i	0.669943	−	0.742413i	$-0.266319\pi$
$839$	10.4845	+	6.05325i	0.361966	+	0.208981i	−0.307977	+	0.951394i	$0.599652\pi$
$840$	−5.76085	−	19.2040i	−0.198768	−	0.662602i
$841$	8.18413	−	14.1753i	0.282211	−	0.488804i
$842$	22.4724			0.774451
$843$	9.41393	+	5.43514i	0.324233	+	0.187196i
$844$	2.10043	+	3.63805i	0.0722998	+	0.125227i
$845$	23.3477	+	24.7636i	0.803184	+	0.851894i
$846$	−1.62412			−0.0558384
$847$	−3.43294	−	11.4438i	−0.117957	−	0.393215i
$848$	1.11428	+	1.92998i	0.0382644	+	0.0662758i
$849$	1.91077	+	3.30955i	0.0655775	+	0.113583i
$850$	−9.11269	+	5.26121i	−0.312563	+	0.180458i
$851$		−	68.5414i		−	2.34957i
$852$	7.53074	−	4.34787i	0.257999	−	0.148956i
$853$			25.9127i			0.887233i	0.896217	+	0.443616i	$0.146305\pi$
$853$			25.9127i			0.887233i	−0.896217	+	0.443616i	$0.853695\pi$
$854$	28.7004	−	8.60959i	0.982107	−	0.294614i
$855$	3.57742	+	6.19627i	0.122345	+	0.211908i
$856$			51.5554i			1.76213i
$857$	−7.12117	−	12.3342i	−0.243255	−	0.421329i	0.718385	−	0.695646i	$-0.244882\pi$
$857$	−7.12117	−	12.3342i	−0.243255	−	0.421329i	−0.961639	+	0.274317i	$0.911548\pi$
$858$	7.81117	−	3.10167i	0.266669	−	0.105889i
$859$	−7.79426	+	13.5001i	−0.265937	+	0.460616i	−0.967809	−	0.251687i	$-0.919015\pi$
$859$	−7.79426	+	13.5001i	−0.265937	+	0.460616i	0.701872	+	0.712303i	$0.252348\pi$
$860$	11.1304	−	6.42616i	0.379545	−	0.219130i
$861$	−2.80333	+	11.8573i	−0.0955371	+	0.404096i
$862$	0.519711	−	0.900165i	0.0177014	−	0.0306597i
$863$	18.3943	+	10.6200i	0.626150	+	0.361508i	0.779260	−	0.626701i	$-0.215595\pi$
$863$	18.3943	+	10.6200i	0.626150	+	0.361508i	−0.153109	+	0.988209i	$0.548929\pi$
$864$		−	5.49106i		−	0.186810i
$865$		−	31.2219i		−	1.06158i
$866$	16.0506	+	9.26683i	0.545422	+	0.314900i
$867$	10.7175	−	18.5633i	0.363986	−	0.630443i
$868$	−26.9048	+	8.07094i	−0.913208	+	0.273945i
$869$	2.74225	−	1.58324i	0.0930244	−	0.0537077i
$870$	−4.25880	+	7.37646i	−0.144387	+	0.250085i
$871$	1.38575	−	1.75196i	0.0469542	−	0.0593629i
$872$	26.8939	+	46.5816i	0.910742	+	1.57745i
$873$			1.53501i			0.0519521i
$874$	−9.86945	−	17.0944i	−0.333839	−	0.578227i
$875$	−5.01351	+	21.2058i	−0.169488	+	0.716886i
$876$			14.5252i			0.490761i
$877$	26.0572	−	15.0441i	0.879889	−	0.508004i	0.00926688	−	0.999957i	$-0.497050\pi$
$877$	26.0572	−	15.0441i	0.879889	−	0.508004i	0.870622	+	0.491953i	$0.163717\pi$
$878$			25.6095i			0.864280i
$879$	15.6392	−	9.02929i	0.527497	−	0.304550i
$880$	1.08513	+	1.87950i	0.0365797	+	0.0633579i
$881$	22.2785	+	38.5876i	0.750583	+	1.30005i	0.947540	+	0.319636i	$0.103561\pi$
$881$	22.2785	+	38.5876i	0.750583	+	1.30005i	−0.196957	+	0.980412i	$0.563106\pi$
$882$	6.39652	−	0.379636i	0.215382	−	0.0127830i
$883$	−1.96438			−0.0661066			−0.0330533	−	0.999454i	$-0.510523\pi$
$883$	−1.96438			−0.0661066			−0.0330533	+	0.999454i	$0.510523\pi$
$884$	3.76893	−	25.7004i	0.126763	−	0.864398i
$885$	−2.95623	−	5.12034i	−0.0993726	−	0.172118i
$886$	17.0779	+	9.85991i	0.573742	+	0.331250i
$887$	4.61734			0.155035			0.0775175	−	0.996991i	$-0.475301\pi$
$887$	4.61734			0.155035			0.0775175	+	0.996991i	$0.475301\pi$
$888$	−12.5722	+	21.7756i	−0.421894	+	0.730742i
$889$	6.40199	+	21.3413i	0.214716	+	0.715764i
$890$	−23.6750	−	13.6688i	−0.793588	−	0.458178i
$891$	−2.20526	+	1.27321i	−0.0738789	+	0.0426540i
$892$	3.57909	−	2.06639i	0.119837	−	0.0691879i
$893$	−4.84878			−0.162258
$894$	−13.7258			−0.459060
$895$	−37.0475	+	21.3894i	−1.23836	+	0.714969i
$896$	−3.52144	+	14.8947i	−0.117643	+	0.497598i
$897$	22.3127	+	17.6486i	0.744998	+	0.589270i
$898$	1.32219	−	2.29011i	0.0441222	−	0.0764219i
$899$	28.1209	+	16.2356i	0.937884	+	0.541488i
$900$	1.07730	−	1.86594i	0.0359101	−	0.0621981i
$901$	−21.2202	−	36.7545i	−0.706948	−	1.22447i
$902$		−	10.7346i		−	0.357423i
$903$	3.21154	+	10.7058i	0.106873	+	0.356266i
$904$	−18.1295	−	10.4671i	−0.602977	−	0.348129i
$905$	−38.0332	−	21.9585i	−1.26427	−	0.729925i
$906$	8.26574			0.274611
$907$	10.3823	−	17.9827i	0.344740	−	0.597107i	−0.640567	−	0.767903i	$-0.721300\pi$
$907$	10.3823	−	17.9827i	0.344740	−	0.597107i	0.985306	+	0.170796i	$0.0546338\pi$
$908$		−	9.05817i		−	0.300606i
$909$	0.504753			0.0167416
$910$	−14.1865	−	17.9275i	−0.470277	−	0.594292i
$911$	−49.6547			−1.64513			−0.822567	−	0.568669i	$-0.807459\pi$
$911$	−49.6547			−1.64513			−0.822567	+	0.568669i	$0.807459\pi$
$912$			0.889672i			0.0294600i
$913$	2.67396	−	4.63143i	0.0884950	−	0.153278i
$914$	−29.9046			−0.989156
$915$	28.0510	+	16.1952i	0.927336	+	0.535398i
$916$	−16.5222	−	9.53911i	−0.545910	−	0.315181i
$917$	30.0059	−	31.8396i	0.990883	−	1.05144i
$918$		−	5.67509i		−	0.187306i
$919$	−27.5731	−	47.7580i	−0.909553	−	1.57539i	−0.814686	−	0.579902i	$-0.803091\pi$
$919$	−27.5731	−	47.7580i	−0.909553	−	1.57539i	−0.0948669	−	0.995490i	$-0.530243\pi$
$920$	−29.8961	+	51.7817i	−0.985647	+	1.70719i
$921$	7.69716	+	4.44396i	0.253630	+	0.146433i
$922$	17.3338	−	30.0230i	0.570858	−	0.988756i
$923$	16.7379	−	21.1613i	0.550936	−	0.696534i
$924$	7.49879	−	2.24950i	0.246692	−	0.0740031i
$925$	−13.9488	+	8.05332i	−0.458632	+	0.264792i
$926$	19.1259			0.628516
$927$	5.33830			0.175333
$928$	16.9012	−	9.75793i	0.554810	−	0.320320i
$929$	−3.77027	+	2.17677i	−0.123699	+	0.0714174i	−0.560573	−	0.828105i	$-0.689419\pi$
$929$	−3.77027	+	2.17677i	−0.123699	+	0.0714174i	0.436874	+	0.899523i	$0.356086\pi$
$930$	18.9620	+	10.9477i	0.621787	+	0.358989i
$931$	19.0967	−	1.13340i	0.625868	−	0.0371456i
$932$	−4.40258	+	7.62549i	−0.144211	+	0.249781i
$933$	−16.4907			−0.539880
$934$	−17.2596	−	9.96482i	−0.564750	−	0.326059i
$935$	−20.6652	−	35.7931i	−0.675823	−	1.17056i
$936$	−3.85155	−	9.69966i	−0.125892	−	0.317043i
$937$	0.712633			0.0232807			0.0116404	−	0.999932i	$-0.496295\pi$
$937$	0.712633			0.0232807			0.0116404	+	0.999932i	$0.496295\pi$
$938$	−1.02907	+	1.09196i	−0.0336003	+	0.0356536i
$939$	11.0236	+	19.0935i	0.359742	+	0.623092i
$940$	2.69886	+	4.67456i	0.0880271	+	0.152467i
$941$	−10.1930	+	5.88493i	−0.332282	+	0.191843i	−0.656854	−	0.754018i	$-0.728113\pi$
$941$	−10.1930	+	5.88493i	−0.332282	+	0.191843i	0.324572	+	0.945861i	$0.394780\pi$
$942$			0.182716i			0.00595320i
$943$	31.4680	−	18.1681i	1.02474	−	0.591633i
$944$		−	0.735188i		−	0.0239283i
$945$	5.04091	+	4.75060i	0.163981	+	0.154537i
$946$	−4.92366	−	8.52803i	−0.160082	−	0.277270i
$947$			30.7176i			0.998187i	0.866548	+	0.499093i	$0.166334\pi$
$947$			30.7176i			0.998187i	−0.866548	+	0.499093i	$0.833666\pi$
$948$	−0.722507	−	1.25142i	−0.0234659	−	0.0406442i
$949$	16.6324	+	41.8867i	0.539911	+	1.35970i
$950$	−2.31924	+	4.01704i	−0.0752460	+	0.130330i
$951$	−19.7541	+	11.4050i	−0.640569	+	0.369833i
$952$	−10.9236	+	46.2041i	−0.354037	+	1.49748i
$953$	−13.0794	+	22.6542i	−0.423684	+	0.733843i	−0.996297	−	0.0859835i	$-0.972597\pi$
$953$	−13.0794	+	22.6542i	−0.423684	+	0.733843i	0.572612	+	0.819826i	$0.305930\pi$
$954$	−5.42695	−	3.13325i	−0.175704	−	0.101443i
$955$			19.5932i			0.634020i
$956$			5.44599i			0.176136i
$957$	−7.83774	−	4.52512i	−0.253358	−	0.146276i
$958$	4.98883	−	8.64090i	0.161182	−	0.279175i
$959$	−1.16787	+	4.93979i	−0.0377126	+	0.159514i
$960$	12.8727	−	7.43207i	0.415465	−	0.239869i
$961$	26.2353	−	45.4409i	0.846300	−	1.46583i
$962$	−4.16007	+	28.3676i	−0.134126	+	0.914608i
$963$	−8.90567	−	15.4251i	−0.286981	−	0.497066i
$964$		−	12.4610i		−	0.401342i
$965$	15.2975	+	26.4961i	0.492444	+	0.852938i
$966$	−13.9070	−	13.1061i	−0.447449	−	0.421680i
$967$			2.99020i			0.0961582i	0.998844	+	0.0480791i	$0.0153100\pi$
$967$			2.99020i			0.0961582i	−0.998844	+	0.0480791i	$0.984690\pi$
$968$	11.3199	−	6.53554i	0.363835	−	0.210060i
$969$		−	16.9429i		−	0.544283i
$970$	−3.18586	+	1.83936i	−0.102292	+	0.0590582i
$971$	9.27532	+	16.0653i	0.297659	+	0.515561i	0.975600	−	0.219556i	$-0.0704608\pi$
$971$	9.27532	+	16.0653i	0.297659	+	0.515561i	−0.677941	+	0.735116i	$0.737127\pi$
$972$	0.581025	+	1.00636i	0.0186364	+	0.0322792i
$973$	−40.0294	+	42.4756i	−1.28328	+	1.36171i
$974$	−5.63160			−0.180448
$975$	0.970003	−	6.61446i	0.0310649	−	0.211832i
$976$	2.01380	+	3.48801i	0.0644603	+	0.111649i
$977$	3.31539	+	1.91414i	0.106069	+	0.0612387i	0.552096	−	0.833781i	$-0.313828\pi$
$977$	3.31539	+	1.91414i	0.106069	+	0.0612387i	−0.446027	+	0.895019i	$0.647162\pi$
$978$	−6.45548			−0.206424
$979$	14.5235	−	25.1555i	0.464174	−	0.803973i
$980$	−11.7220	−	17.7797i	−0.374446	−	0.567951i
$981$	−16.0930	−	9.29129i	−0.513809	−	0.296648i
$982$	−8.56201	+	4.94328i	−0.273225	+	0.157746i
$983$	−27.0572	+	15.6215i	−0.862992	+	0.498248i	−0.865013	−	0.501749i	$-0.832690\pi$
$983$	−27.0572	+	15.6215i	−0.862992	+	0.498248i	0.00202132	+	0.999998i	$0.499357\pi$
$984$	−13.3299			−0.424940
$985$	−1.17571			−0.0374613
$986$	17.4677	−	10.0850i	0.556284	−	0.321171i
$987$	−4.49621	+	1.34878i	−0.143116	+	0.0429322i
$988$	−4.22577	−	10.6421i	−0.134440	−	0.338570i
$989$	16.6664	−	28.8670i	0.529960	−	0.917918i
$990$	−5.28500	−	3.05130i	−0.167968	−	0.0969765i
$991$	−2.96796	+	5.14066i	−0.0942805	+	0.163299i	−0.909308	−	0.416124i	$-0.863388\pi$
$991$	−2.96796	+	5.14066i	−0.0942805	+	0.163299i	0.815028	+	0.579422i	$0.196722\pi$
$992$	−25.0838	−	43.4464i	−0.796410	−	1.37942i
$993$		−	32.0157i		−	1.01599i
$994$	−12.4298	+	13.1894i	−0.394249	+	0.418341i
$995$	22.2723	+	12.8589i	0.706079	+	0.407655i
$996$	−2.11354	−	1.22025i	−0.0669702	−	0.0386652i
$997$	−7.84640			−0.248498			−0.124249	−	0.992251i	$-0.539652\pi$
$997$	−7.84640			−0.248498			−0.124249	+	0.992251i	$0.539652\pi$
$998$	0.982678	−	1.70205i	0.0311061	−	0.0538774i
$999$		−	8.68684i		−	0.274840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.205.7	yes	20
3.2	odd	2		819.2.bm.g.478.4		20
7.4	even	3		273.2.bl.d.88.4	yes	20
13.4	even	6		273.2.bl.d.121.4	yes	20
21.11	odd	6		819.2.do.g.361.7		20
39.17	odd	6		819.2.do.g.667.7		20
91.4	even	6	inner	273.2.t.d.4.4	✓	20
273.95	odd	6		819.2.bm.g.550.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.4	✓	20	91.4	even	6	inner
273.2.t.d.205.7	yes	20	1.1	even	1	trivial
273.2.bl.d.88.4	yes	20	7.4	even	3
273.2.bl.d.121.4	yes	20	13.4	even	6
819.2.bm.g.478.4		20	3.2	odd	2
819.2.bm.g.550.7		20	273.95	odd	6
819.2.do.g.361.7		20	21.11	odd	6
819.2.do.g.667.7		20	39.17	odd	6

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.915396i q^{2} +(0.500000 - 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 - 1.30902i) q^{5} +(0.792756 + 0.457698i) q^{6} +(2.57477 + 0.608732i) q^{7} +2.89453i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+0.915396i q^{2} +(0.500000 - 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 - 1.30902i) q^{5} +(0.792756 + 0.457698i) q^{6} +(2.57477 + 0.608732i) q^{7} +2.89453i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.19827 - 2.07547i) q^{10} +(2.20526 + 1.27321i) q^{11} +(0.581025 - 1.00636i) q^{12} +(0.523154 - 3.56740i) q^{13} +(-0.557231 + 2.35694i) q^{14} +(-2.26729 + 1.30902i) q^{15} -0.325542 q^{16} +6.19960 q^{17} +(0.792756 - 0.457698i) q^{18} +(2.36676 - 1.36645i) q^{19} +(-2.63470 - 1.52115i) q^{20} +(1.81456 - 1.92545i) q^{21} +(-1.16549 + 2.01868i) q^{22} -7.89025 q^{23} +(2.50674 + 1.44726i) q^{24} +(0.927071 + 1.60573i) q^{25} +(3.26558 + 0.478894i) q^{26} -1.00000 q^{27} +(2.99201 + 0.707377i) q^{28} +(-1.77706 - 3.07796i) q^{29} +(-1.19827 - 2.07547i) q^{30} +(-7.91220 + 4.56811i) q^{31} +5.49106i q^{32} +(2.20526 - 1.27321i) q^{33} +5.67509i q^{34} +(-5.04091 - 4.75060i) q^{35} +(-0.581025 - 1.00636i) q^{36} +8.68684i q^{37} +(1.25084 + 2.16652i) q^{38} +(-2.82788 - 2.23676i) q^{39} +(3.78900 - 6.56274i) q^{40} +(-3.98821 + 2.30259i) q^{41} +(1.76255 + 1.66104i) q^{42} +(-2.11228 + 3.65857i) q^{43} +(2.56262 + 1.47953i) q^{44} +2.61804i q^{45} -7.22271i q^{46} +(-1.53652 - 0.887113i) q^{47} +(-0.162771 + 0.281927i) q^{48} +(6.25889 + 3.13469i) q^{49} +(-1.46988 + 0.848638i) q^{50} +(3.09980 - 5.36901i) q^{51} +(0.607931 - 4.14549i) q^{52} +(-3.42283 - 5.92852i) q^{53} -0.915396i q^{54} +(-3.33331 - 5.77345i) q^{55} +(-1.76199 + 7.45275i) q^{56} -2.73290i q^{57} +(2.81755 - 1.62671i) q^{58} +2.25835i q^{59} +(-2.63470 + 1.52115i) q^{60} +(-6.18601 - 10.7145i) q^{61} +(-4.18163 - 7.24280i) q^{62} +(-0.760208 - 2.53418i) q^{63} -5.67758 q^{64} +(-5.85594 + 7.40350i) q^{65} +(1.16549 + 2.01868i) q^{66} +(0.536530 + 0.309766i) q^{67} +7.20424 q^{68} +(-3.94513 + 6.83316i) q^{69} +(4.34868 - 4.61443i) q^{70} +(6.48057 + 3.74156i) q^{71} +(2.50674 - 1.44726i) q^{72} +(-10.8250 + 6.24982i) q^{73} -7.95190 q^{74} +1.85414 q^{75} +(2.75029 - 1.58788i) q^{76} +(4.90299 + 4.62062i) q^{77} +(2.04752 - 2.58863i) q^{78} +(0.621752 - 1.07691i) q^{79} +(0.738098 + 0.426141i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.10779 - 3.65079i) q^{82} -2.10018i q^{83} +(2.10861 - 2.23747i) q^{84} +(-14.0563 - 8.11541i) q^{85} +(-3.34904 - 1.93357i) q^{86} -3.55412 q^{87} +(-3.68533 + 6.38318i) q^{88} -11.4071i q^{89} -2.39655 q^{90} +(3.51859 - 8.86677i) q^{91} -9.16886 q^{92} +9.13622i q^{93} +(0.812060 - 1.40653i) q^{94} -7.15484 q^{95} +(4.75540 + 2.74553i) q^{96} +(-1.32935 - 0.767503i) q^{97} +(-2.86948 + 5.72937i) q^{98} -2.54641i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

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