LMFDB - Embedded newform 546.2.i.i.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.i.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.70711 + 2.95680i) q^{10} +(-1.20711 - 2.09077i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(1.62132 - 2.09077i) q^{14} +3.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.207107 - 0.358719i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.91421 - 6.77962i) q^{19} -3.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} +2.41421 q^{22} +(0.707107 - 1.22474i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 2.44949i) q^{28} +3.82843 q^{29} +(-1.70711 + 2.95680i) q^{30} +(-4.24264 - 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.20711 - 2.09077i) q^{33} +0.414214 q^{34} +(-5.53553 + 7.13834i) q^{35} +1.00000 q^{36} +(0.707107 - 1.22474i) q^{37} +(3.91421 + 6.77962i) q^{38} +(0.500000 + 0.866025i) q^{39} +(1.70711 - 2.95680i) q^{40} +9.89949 q^{41} +(2.62132 + 0.358719i) q^{42} -10.4853 q^{43} +(-1.20711 + 2.09077i) q^{44} +(1.70711 + 2.95680i) q^{45} +(0.707107 + 1.22474i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(6.74264 + 1.88064i) q^{49} +6.65685 q^{50} +(0.207107 - 0.358719i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(3.74264 + 6.48244i) q^{53} +(0.500000 - 0.866025i) q^{54} -8.24264 q^{55} +(-2.62132 - 0.358719i) q^{56} +7.82843 q^{57} +(-1.91421 + 3.31552i) q^{58} +(6.03553 + 10.4539i) q^{59} +(-1.70711 - 2.95680i) q^{60} +(0.792893 - 1.37333i) q^{61} +8.48528 q^{62} +(1.62132 - 2.09077i) q^{63} +1.00000 q^{64} +(1.70711 - 2.95680i) q^{65} +(1.20711 + 2.09077i) q^{66} +(1.91421 + 3.31552i) q^{67} +(-0.207107 + 0.358719i) q^{68} +1.41421 q^{69} +(-3.41421 - 8.36308i) q^{70} -5.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.707107 + 1.22474i) q^{73} +(0.707107 + 1.22474i) q^{74} +(3.32843 - 5.76500i) q^{75} -7.82843 q^{76} +(2.41421 + 5.91359i) q^{77} -1.00000 q^{78} +(0.171573 - 0.297173i) q^{79} +(1.70711 + 2.95680i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.94975 + 8.57321i) q^{82} -3.65685 q^{83} +(-1.62132 + 2.09077i) q^{84} -1.41421 q^{85} +(5.24264 - 9.08052i) q^{86} +(1.91421 + 3.31552i) q^{87} +(-1.20711 - 2.09077i) q^{88} +(-2.70711 + 4.68885i) q^{89} -3.41421 q^{90} +(-2.62132 - 0.358719i) q^{91} -1.41421 q^{92} +(4.24264 - 7.34847i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-13.3640 - 23.1471i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.0711 q^{97} +(-5.00000 + 4.89898i) q^{98} +2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{32} + 2 q^{33} - 4 q^{34} - 8 q^{35} + 4 q^{36} + 10 q^{38} + 2 q^{39} + 4 q^{40} + 2 q^{42} - 8 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} + 2 q^{54} - 16 q^{55} - 2 q^{56} + 20 q^{57} - 2 q^{58} + 10 q^{59} - 4 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} + 2 q^{67} + 2 q^{68} - 8 q^{70} - 20 q^{71} - 2 q^{72} + 2 q^{75} - 20 q^{76} + 4 q^{77} - 4 q^{78} + 12 q^{79} + 4 q^{80} - 2 q^{81} + 8 q^{83} + 2 q^{84} + 4 q^{86} + 2 q^{87} - 2 q^{88} - 8 q^{89} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 28 q^{95} + 2 q^{96} - 32 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^17 - 2 * q^18 + 10 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^32 + 2 * q^33 - 4 * q^34 - 8 * q^35 + 4 * q^36 + 10 * q^38 + 2 * q^39 + 4 * q^40 + 2 * q^42 - 8 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 2 * q^54 - 16 * q^55 - 2 * q^56 + 20 * q^57 - 2 * q^58 + 10 * q^59 - 4 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 + 2 * q^67 + 2 * q^68 - 8 * q^70 - 20 * q^71 - 2 * q^72 + 2 * q^75 - 20 * q^76 + 4 * q^77 - 4 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^83 + 2 * q^84 + 4 * q^86 + 2 * q^87 - 2 * q^88 - 8 * q^89 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 28 * q^95 + 2 * q^96 - 32 * q^97 - 20 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.70711	−	2.95680i	0.763441	−	1.32232i	−0.177625	−	0.984098i	$-0.556842\pi$
$5$	1.70711	−	2.95680i	0.763441	−	1.32232i	0.941067	−	0.338221i	$-0.109825\pi$
$6$	−1.00000			−0.408248
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.70711	+	2.95680i	0.539835	+	0.935021i
$11$	−1.20711	−	2.09077i	−0.363956	−	0.630391i	0.624652	−	0.780903i	$-0.285241\pi$
$11$	−1.20711	−	2.09077i	−0.363956	−	0.630391i	−0.988608	+	0.150513i	$0.951908\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	1.62132	−	2.09077i	0.433316	−	0.558782i
$15$	3.41421			0.881546
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.207107	−	0.358719i	−0.0502308	−	0.0870023i	0.839817	−	0.542870i	$-0.182662\pi$
$17$	−0.207107	−	0.358719i	−0.0502308	−	0.0870023i	−0.890048	+	0.455868i	$0.849329\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.91421	−	6.77962i	0.897982	−	1.55535i	0.0679123	−	0.997691i	$-0.478366\pi$
$19$	3.91421	−	6.77962i	0.897982	−	1.55535i	0.830070	−	0.557659i	$-0.188300\pi$
$20$	−3.41421			−0.763441
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$	2.41421			0.514712
$23$	0.707107	−	1.22474i	0.147442	−	0.255377i	−0.782839	−	0.622224i	$-0.786229\pi$
$23$	0.707107	−	1.22474i	0.147442	−	0.255377i	0.930281	+	0.366847i	$0.119563\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.32843	−	5.76500i	−0.665685	−	1.15300i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	−1.00000			−0.192450
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$	3.82843			0.710921			0.355461	−	0.934691i	$-0.384324\pi$
$29$	3.82843			0.710921			0.355461	+	0.934691i	$0.384324\pi$
$30$	−1.70711	+	2.95680i	−0.311674	+	0.539835i
$31$	−4.24264	−	7.34847i	−0.762001	−	1.31982i	−0.941818	−	0.336124i	$-0.890884\pi$
$31$	−4.24264	−	7.34847i	−0.762001	−	1.31982i	0.179817	−	0.983700i	$-0.442449\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.20711	−	2.09077i	0.210130	−	0.363956i
$34$	0.414214			0.0710370
$35$	−5.53553	+	7.13834i	−0.935676	+	1.20660i
$36$	1.00000			0.166667
$37$	0.707107	−	1.22474i	0.116248	−	0.201347i	−0.802030	−	0.597284i	$-0.796247\pi$
$37$	0.707107	−	1.22474i	0.116248	−	0.201347i	0.918278	+	0.395937i	$0.129580\pi$
$38$	3.91421	+	6.77962i	0.634969	+	1.09980i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	1.70711	−	2.95680i	0.269917	−	0.467510i
$41$	9.89949			1.54604			0.773021	−	0.634381i	$-0.218745\pi$
$41$	9.89949			1.54604			0.773021	+	0.634381i	$0.218745\pi$
$42$	2.62132	+	0.358719i	0.404479	+	0.0553516i
$43$	−10.4853			−1.59899			−0.799495	−	0.600672i	$-0.794900\pi$
$43$	−10.4853			−1.59899			−0.799495	+	0.600672i	$0.794900\pi$
$44$	−1.20711	+	2.09077i	−0.181978	+	0.315195i
$45$	1.70711	+	2.95680i	0.254480	+	0.440773i
$46$	0.707107	+	1.22474i	0.104257	+	0.180579i
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	−0.900185	−	0.435507i	$-0.856569\pi$
$47$	−0.500000	+	0.866025i	−0.0729325	+	0.126323i	0.827253	+	0.561830i	$0.189902\pi$
$48$	−1.00000			−0.144338
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$	6.65685			0.941421
$51$	0.207107	−	0.358719i	0.0290008	−	0.0502308i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	3.74264	+	6.48244i	0.514091	+	0.890432i	0.999866	+	0.0163483i	$0.00520406\pi$
$53$	3.74264	+	6.48244i	0.514091	+	0.890432i	−0.485775	+	0.874084i	$0.661463\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−8.24264			−1.11144
$56$	−2.62132	−	0.358719i	−0.350289	−	0.0479359i
$57$	7.82843			1.03690
$58$	−1.91421	+	3.31552i	−0.251349	+	0.435348i
$59$	6.03553	+	10.4539i	0.785760	+	1.36098i	0.928544	+	0.371222i	$0.121061\pi$
$59$	6.03553	+	10.4539i	0.785760	+	1.36098i	−0.142785	+	0.989754i	$0.545606\pi$
$60$	−1.70711	−	2.95680i	−0.220387	−	0.381721i
$61$	0.792893	−	1.37333i	0.101520	−	0.175837i	−0.810791	−	0.585335i	$-0.800963\pi$
$61$	0.792893	−	1.37333i	0.101520	−	0.175837i	0.912311	+	0.409498i	$0.134296\pi$
$62$	8.48528			1.07763
$63$	1.62132	−	2.09077i	0.204267	−	0.263412i
$64$	1.00000			0.125000
$65$	1.70711	−	2.95680i	0.211741	−	0.366745i
$66$	1.20711	+	2.09077i	0.148585	+	0.257356i
$67$	1.91421	+	3.31552i	0.233858	+	0.405055i	0.958940	−	0.283608i	$-0.0915314\pi$
$67$	1.91421	+	3.31552i	0.233858	+	0.405055i	−0.725082	+	0.688663i	$0.758198\pi$
$68$	−0.207107	+	0.358719i	−0.0251154	+	0.0435011i
$69$	1.41421			0.170251
$70$	−3.41421	−	8.36308i	−0.408077	−	0.999579i
$71$	−5.00000			−0.593391			−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000			−0.593391			−0.296695	+	0.954972i	$0.595885\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	0.707107	+	1.22474i	0.0821995	+	0.142374i
$75$	3.32843	−	5.76500i	0.384334	−	0.665685i
$76$	−7.82843			−0.897982
$77$	2.41421	+	5.91359i	0.275125	+	0.673916i
$78$	−1.00000			−0.113228
$79$	0.171573	−	0.297173i	0.0193035	−	0.0334346i	−0.856212	−	0.516624i	$-0.827188\pi$
$79$	0.171573	−	0.297173i	0.0193035	−	0.0334346i	0.875516	+	0.483190i	$0.160522\pi$
$80$	1.70711	+	2.95680i	0.190860	+	0.330580i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.94975	+	8.57321i	−0.546608	+	0.946753i
$83$	−3.65685			−0.401392			−0.200696	−	0.979654i	$-0.564320\pi$
$83$	−3.65685			−0.401392			−0.200696	+	0.979654i	$0.564320\pi$
$84$	−1.62132	+	2.09077i	−0.176901	+	0.228122i
$85$	−1.41421			−0.153393
$86$	5.24264	−	9.08052i	0.565328	−	0.979178i
$87$	1.91421	+	3.31552i	0.205225	+	0.355461i
$88$	−1.20711	−	2.09077i	−0.128678	−	0.222877i
$89$	−2.70711	+	4.68885i	−0.286953	+	0.497017i	−0.973081	−	0.230464i	$-0.925976\pi$
$89$	−2.70711	+	4.68885i	−0.286953	+	0.497017i	0.686128	+	0.727481i	$0.259309\pi$
$90$	−3.41421			−0.359890
$91$	−2.62132	−	0.358719i	−0.274789	−	0.0376040i
$92$	−1.41421			−0.147442
$93$	4.24264	−	7.34847i	0.439941	−	0.762001i
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$	−13.3640	−	23.1471i	−1.37111	−	2.37484i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−15.0711			−1.53024			−0.765118	−	0.643891i	$-0.777319\pi$
$97$	−15.0711			−1.53024			−0.765118	+	0.643891i	$0.777319\pi$
$98$	−5.00000	+	4.89898i	−0.505076	+	0.494872i
$99$	2.41421			0.242638
$100$	−3.32843	+	5.76500i	−0.332843	+	0.576500i
$101$	4.58579	+	7.94282i	0.456303	+	0.790340i	0.998762	−	0.0497425i	$-0.0158401\pi$
$101$	4.58579	+	7.94282i	0.456303	+	0.790340i	−0.542459	+	0.840082i	$0.682507\pi$
$102$	0.207107	+	0.358719i	0.0205066	+	0.0355185i
$103$	5.58579	−	9.67487i	0.550384	−	0.953293i	−0.447863	−	0.894102i	$-0.647815\pi$
$103$	5.58579	−	9.67487i	0.550384	−	0.953293i	0.998247	−	0.0591906i	$-0.0188520\pi$
$104$	1.00000			0.0980581
$105$	−8.94975	−	1.22474i	−0.873406	−	0.119523i
$106$	−7.48528			−0.727035
$107$	−1.65685	+	2.86976i	−0.160174	+	0.277430i	−0.934931	−	0.354830i	$-0.884539\pi$
$107$	−1.65685	+	2.86976i	−0.160174	+	0.277430i	0.774757	+	0.632259i	$0.217872\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	0.823620	−	0.567142i	$-0.191951\pi$
$109$	−0.828427	−	1.43488i	−0.0793489	−	0.137436i	−0.902969	+	0.429705i	$0.858617\pi$
$110$	4.12132	−	7.13834i	0.392952	−	0.680614i
$111$	1.41421			0.134231
$112$	1.62132	−	2.09077i	0.153200	−	0.197559i
$113$	−14.8995			−1.40163			−0.700813	−	0.713345i	$-0.747179\pi$
$113$	−14.8995			−1.40163			−0.700813	+	0.713345i	$0.747179\pi$
$114$	−3.91421	+	6.77962i	−0.366600	+	0.634969i
$115$	−2.41421	−	4.18154i	−0.225127	−	0.389931i
$116$	−1.91421	−	3.31552i	−0.177730	−	0.307838i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	−12.0711			−1.11123
$119$	0.414214	+	1.01461i	0.0379709	+	0.0930093i
$120$	3.41421			0.311674
$121$	2.58579	−	4.47871i	0.235071	−	0.407156i
$122$	0.792893	+	1.37333i	0.0717852	+	0.124336i
$123$	4.94975	+	8.57321i	0.446304	+	0.773021i
$124$	−4.24264	+	7.34847i	−0.381000	+	0.659912i
$125$	−5.65685			−0.505964
$126$	1.00000	+	2.44949i	0.0890871	+	0.218218i
$127$	11.8995			1.05591			0.527955	−	0.849273i	$-0.322959\pi$
$127$	11.8995			1.05591			0.527955	+	0.849273i	$0.322959\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.24264	−	9.08052i	−0.461589	−	0.799495i
$130$	1.70711	+	2.95680i	0.149723	+	0.259328i
$131$	−10.7782	+	18.6683i	−0.941693	+	1.63106i	−0.179453	+	0.983766i	$0.557433\pi$
$131$	−10.7782	+	18.6683i	−0.941693	+	1.63106i	−0.762240	+	0.647295i	$0.775900\pi$
$132$	−2.41421			−0.210130
$133$	−12.6924	+	16.3674i	−1.10057	+	1.41924i
$134$	−3.82843			−0.330726
$135$	−1.70711	+	2.95680i	−0.146924	+	0.254480i
$136$	−0.207107	−	0.358719i	−0.0177593	−	0.0307599i
$137$	1.53553	+	2.65962i	0.131190	+	0.227227i	0.924135	−	0.382065i	$-0.124787\pi$
$137$	1.53553	+	2.65962i	0.131190	+	0.227227i	−0.792946	+	0.609292i	$0.791454\pi$
$138$	−0.707107	+	1.22474i	−0.0601929	+	0.104257i
$139$	1.07107			0.0908468			0.0454234	−	0.998968i	$-0.485536\pi$
$139$	1.07107			0.0908468			0.0454234	+	0.998968i	$0.485536\pi$
$140$	8.94975	+	1.22474i	0.756392	+	0.103510i
$141$	−1.00000			−0.0842152
$142$	2.50000	−	4.33013i	0.209795	−	0.363376i
$143$	−1.20711	−	2.09077i	−0.100943	−	0.174839i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	6.53553	−	11.3199i	0.542747	−	0.940065i
$146$	−1.41421			−0.117041
$147$	1.74264	+	6.77962i	0.143731	+	0.559173i
$148$	−1.41421			−0.116248
$149$	9.53553	−	16.5160i	0.781181	−	1.35305i	−0.150073	−	0.988675i	$-0.547951\pi$
$149$	9.53553	−	16.5160i	0.781181	−	1.35305i	0.931254	−	0.364371i	$-0.118716\pi$
$150$	3.32843	+	5.76500i	0.271765	+	0.470711i
$151$	5.03553	+	8.72180i	0.409786	+	0.709770i	0.994866	−	0.101206i	$-0.0322701\pi$
$151$	5.03553	+	8.72180i	0.409786	+	0.709770i	−0.585080	+	0.810976i	$0.698937\pi$
$152$	3.91421	−	6.77962i	0.317485	−	0.549900i
$153$	0.414214			0.0334872
$154$	−6.32843	−	0.866025i	−0.509959	−	0.0697863i
$155$	−28.9706			−2.32697
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	7.86396	+	13.6208i	0.627612	+	1.08706i	0.988029	+	0.154265i	$0.0493011\pi$
$157$	7.86396	+	13.6208i	0.627612	+	1.08706i	−0.360417	+	0.932791i	$0.617366\pi$
$158$	0.171573	+	0.297173i	0.0136496	+	0.0236418i
$159$	−3.74264	+	6.48244i	−0.296811	+	0.514091i
$160$	−3.41421			−0.269917
$161$	−2.29289	+	2.95680i	−0.180705	+	0.233028i
$162$	1.00000			0.0785674
$163$	3.67157	−	6.35935i	0.287580	−	0.498103i	−0.685652	−	0.727930i	$-0.740483\pi$
$163$	3.67157	−	6.35935i	0.287580	−	0.498103i	0.973232	+	0.229827i	$0.0738160\pi$
$164$	−4.94975	−	8.57321i	−0.386510	−	0.669456i
$165$	−4.12132	−	7.13834i	−0.320844	−	0.555719i
$166$	1.82843	−	3.16693i	0.141913	−	0.245801i
$167$	10.6569			0.824652			0.412326	−	0.911036i	$-0.364716\pi$
$167$	10.6569			0.824652			0.412326	+	0.911036i	$0.364716\pi$
$168$	−1.00000	−	2.44949i	−0.0771517	−	0.188982i
$169$	1.00000			0.0769231
$170$	0.707107	−	1.22474i	0.0542326	−	0.0939336i
$171$	3.91421	+	6.77962i	0.299327	+	0.518450i
$172$	5.24264	+	9.08052i	0.399748	+	0.692383i
$173$	5.74264	−	9.94655i	0.436605	−	0.756222i	−0.560820	−	0.827938i	$-0.689514\pi$
$173$	5.74264	−	9.94655i	0.436605	−	0.756222i	0.997425	+	0.0717158i	$0.0228474\pi$
$174$	−3.82843			−0.290232
$175$	6.65685	+	16.3059i	0.503211	+	1.23261i
$176$	2.41421			0.181978
$177$	−6.03553	+	10.4539i	−0.453659	+	0.785760i
$178$	−2.70711	−	4.68885i	−0.202906	−	0.351444i
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	0.666954	−	0.745099i	$-0.267598\pi$
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	−0.978752	+	0.205049i	$0.934265\pi$
$180$	1.70711	−	2.95680i	0.127240	−	0.220387i
$181$	−16.8995			−1.25613			−0.628065	−	0.778161i	$-0.716153\pi$
$181$	−16.8995			−1.25613			−0.628065	+	0.778161i	$0.716153\pi$
$182$	1.62132	−	2.09077i	0.120180	−	0.154978i
$183$	1.58579			0.117225
$184$	0.707107	−	1.22474i	0.0521286	−	0.0902894i
$185$	−2.41421	−	4.18154i	−0.177497	−	0.307433i
$186$	4.24264	+	7.34847i	0.311086	+	0.538816i
$187$	−0.500000	+	0.866025i	−0.0365636	+	0.0633300i
$188$	1.00000			0.0729325
$189$	2.62132	+	0.358719i	0.190673	+	0.0260930i
$190$	26.7279			1.93905
$191$	10.8284	−	18.7554i	0.783517	−	1.35709i	−0.146363	−	0.989231i	$-0.546757\pi$
$191$	10.8284	−	18.7554i	0.783517	−	1.35709i	0.929881	−	0.367861i	$-0.119910\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	8.53553	+	14.7840i	0.614401	+	1.06417i	0.990489	+	0.137590i	$0.0439357\pi$
$193$	8.53553	+	14.7840i	0.614401	+	1.06417i	−0.376088	+	0.926584i	$0.622731\pi$
$194$	7.53553	−	13.0519i	0.541020	−	0.937074i
$195$	3.41421			0.244497
$196$	−1.74264	−	6.77962i	−0.124474	−	0.484258i
$197$	15.5563			1.10834			0.554172	−	0.832402i	$-0.313035\pi$
$197$	15.5563			1.10834			0.554172	+	0.832402i	$0.313035\pi$
$198$	−1.20711	+	2.09077i	−0.0857853	+	0.148585i
$199$	11.3640	+	19.6830i	0.805570	+	1.39529i	0.915906	+	0.401394i	$0.131474\pi$
$199$	11.3640	+	19.6830i	0.805570	+	1.39529i	−0.110336	+	0.993894i	$0.535193\pi$
$200$	−3.32843	−	5.76500i	−0.235355	−	0.407647i
$201$	−1.91421	+	3.31552i	−0.135018	+	0.233858i
$202$	−9.17157			−0.645310
$203$	−10.0355	−	1.37333i	−0.704356	−	0.0963890i
$204$	−0.414214			−0.0290008
$205$	16.8995	−	29.2708i	1.18031	−	2.04436i
$206$	5.58579	+	9.67487i	0.389180	+	0.674080i
$207$	0.707107	+	1.22474i	0.0491473	+	0.0851257i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−18.8995			−1.30731
$210$	5.53553	−	7.13834i	0.381988	−	0.492592i
$211$	−27.0711			−1.86365			−0.931825	−	0.362909i	$-0.881784\pi$
$211$	−27.0711			−1.86365			−0.931825	+	0.362909i	$0.881784\pi$
$212$	3.74264	−	6.48244i	0.257046	−	0.445216i
$213$	−2.50000	−	4.33013i	−0.171297	−	0.296695i
$214$	−1.65685	−	2.86976i	−0.113260	−	0.196172i
$215$	−17.8995	+	31.0028i	−1.22074	+	2.11438i
$216$	−1.00000			−0.0680414
$217$	8.48528	+	20.7846i	0.576018	+	1.41095i
$218$	1.65685			0.112216
$219$	−0.707107	+	1.22474i	−0.0477818	+	0.0827606i
$220$	4.12132	+	7.13834i	0.277859	+	0.481267i
$221$	−0.207107	−	0.358719i	−0.0139315	−	0.0241301i
$222$	−0.707107	+	1.22474i	−0.0474579	+	0.0821995i
$223$	−22.0711			−1.47799			−0.738994	−	0.673712i	$-0.764699\pi$
$223$	−22.0711			−1.47799			−0.738994	+	0.673712i	$0.764699\pi$
$224$	1.00000	+	2.44949i	0.0668153	+	0.163663i
$225$	6.65685			0.443790
$226$	7.44975	−	12.9033i	0.495550	−	0.858317i
$227$	13.4142	+	23.2341i	0.890333	+	1.54210i	0.839477	+	0.543395i	$0.182862\pi$
$227$	13.4142	+	23.2341i	0.890333	+	1.54210i	0.0508557	+	0.998706i	$0.483805\pi$
$228$	−3.91421	−	6.77962i	−0.259225	−	0.448991i
$229$	−4.75736	+	8.23999i	−0.314375	+	0.544514i	−0.979304	−	0.202393i	$-0.935128\pi$
$229$	−4.75736	+	8.23999i	−0.314375	+	0.544514i	0.664929	+	0.746906i	$0.268462\pi$
$230$	4.82843			0.318377
$231$	−3.91421	+	5.04757i	−0.257536	+	0.332105i
$232$	3.82843			0.251349
$233$	−3.86396	+	6.69258i	−0.253137	+	0.438445i	−0.964388	−	0.264493i	$-0.914796\pi$
$233$	−3.86396	+	6.69258i	−0.253137	+	0.438445i	0.711251	+	0.702938i	$0.248129\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	1.70711	+	2.95680i	0.111359	+	0.192880i
$236$	6.03553	−	10.4539i	0.392880	−	0.680488i
$237$	0.343146			0.0222897
$238$	−1.08579	−	0.148586i	−0.0703811	−	0.00963143i
$239$	21.4853			1.38977			0.694884	−	0.719122i	$-0.255456\pi$
$239$	21.4853			1.38977			0.694884	+	0.719122i	$0.255456\pi$
$240$	−1.70711	+	2.95680i	−0.110193	+	0.190860i
$241$	−13.0711	−	22.6398i	−0.841981	−	1.45835i	−0.888217	−	0.459424i	$-0.848056\pi$
$241$	−13.0711	−	22.6398i	−0.841981	−	1.45835i	0.0462355	−	0.998931i	$-0.485278\pi$
$242$	2.58579	+	4.47871i	0.166221	+	0.287903i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.58579			−0.101520
$245$	17.0711	−	16.7262i	1.09063	−	1.06860i
$246$	−9.89949			−0.631169
$247$	3.91421	−	6.77962i	0.249055	−	0.431377i
$248$	−4.24264	−	7.34847i	−0.269408	−	0.466628i
$249$	−1.82843	−	3.16693i	−0.115872	−	0.200696i
$250$	2.82843	−	4.89898i	0.178885	−	0.309839i
$251$	19.1716			1.21010			0.605049	−	0.796188i	$-0.293153\pi$
$251$	19.1716			1.21010			0.605049	+	0.796188i	$0.293153\pi$
$252$	−2.62132	−	0.358719i	−0.165128	−	0.0225972i
$253$	−3.41421			−0.214650
$254$	−5.94975	+	10.3053i	−0.373320	+	0.646610i
$255$	−0.707107	−	1.22474i	−0.0442807	−	0.0766965i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.75736	+	8.23999i	−0.296756	+	0.513996i	−0.975392	−	0.220479i	$-0.929238\pi$
$257$	−4.75736	+	8.23999i	−0.296756	+	0.513996i	0.678636	+	0.734475i	$0.262571\pi$
$258$	10.4853			0.652785
$259$	−2.29289	+	2.95680i	−0.142473	+	0.183726i
$260$	−3.41421			−0.211741
$261$	−1.91421	+	3.31552i	−0.118487	+	0.205225i
$262$	−10.7782	−	18.6683i	−0.665878	−	1.15333i
$263$	−11.7071	−	20.2773i	−0.721891	−	1.25035i	−0.960241	−	0.279173i	$-0.909940\pi$
$263$	−11.7071	−	20.2773i	−0.721891	−	1.25035i	0.238350	−	0.971179i	$-0.423394\pi$
$264$	1.20711	−	2.09077i	0.0742923	−	0.128678i
$265$	25.5563			1.56991
$266$	−7.82843	−	19.1757i	−0.479992	−	1.17573i
$267$	−5.41421			−0.331344
$268$	1.91421	−	3.31552i	0.116929	−	0.202527i
$269$	−9.57107	−	16.5776i	−0.583558	−	1.01075i	−0.995053	−	0.0993407i	$-0.968327\pi$
$269$	−9.57107	−	16.5776i	−0.583558	−	1.01075i	0.411495	−	0.911412i	$-0.365007\pi$
$270$	−1.70711	−	2.95680i	−0.103891	−	0.179945i
$271$	8.10660	−	14.0410i	0.492441	−	0.852933i	−0.507521	−	0.861639i	$-0.669438\pi$
$271$	8.10660	−	14.0410i	0.492441	−	0.852933i	0.999962	+	0.00870652i	$0.00277141\pi$
$272$	0.414214			0.0251154
$273$	−1.00000	−	2.44949i	−0.0605228	−	0.148250i
$274$	−3.07107			−0.185530
$275$	−8.03553	+	13.9180i	−0.484561	+	0.839284i
$276$	−0.707107	−	1.22474i	−0.0425628	−	0.0737210i
$277$	−1.96447	−	3.40256i	−0.118033	−	0.204440i	0.800955	−	0.598725i	$-0.204326\pi$
$277$	−1.96447	−	3.40256i	−0.118033	−	0.204440i	−0.918988	+	0.394285i	$0.870992\pi$
$278$	−0.535534	+	0.927572i	−0.0321192	+	0.0556321i
$279$	8.48528			0.508001
$280$	−5.53553	+	7.13834i	−0.330811	+	0.426597i
$281$	23.3137			1.39078			0.695390	−	0.718633i	$-0.255232\pi$
$281$	23.3137			1.39078			0.695390	+	0.718633i	$0.255232\pi$
$282$	0.500000	−	0.866025i	0.0297746	−	0.0515711i
$283$	12.1213	+	20.9947i	0.720538	+	1.24801i	0.960785	+	0.277296i	$0.0894383\pi$
$283$	12.1213	+	20.9947i	0.720538	+	1.24801i	−0.240247	+	0.970712i	$0.577228\pi$
$284$	2.50000	+	4.33013i	0.148348	+	0.256946i
$285$	13.3640	−	23.1471i	0.791613	−	1.37111i
$286$	2.41421			0.142755
$287$	−25.9497	−	3.55114i	−1.53177	−	0.209617i
$288$	1.00000			0.0589256
$289$	8.41421	−	14.5738i	0.494954	−	0.857285i
$290$	6.53553	+	11.3199i	0.383780	+	0.664726i
$291$	−7.53553	−	13.0519i	−0.441741	−	0.765118i
$292$	0.707107	−	1.22474i	0.0413803	−	0.0716728i
$293$	9.89949			0.578335			0.289167	−	0.957279i	$-0.406622\pi$
$293$	9.89949			0.578335			0.289167	+	0.957279i	$0.406622\pi$
$294$	−6.74264	−	1.88064i	−0.393239	−	0.109681i
$295$	41.2132			2.39953
$296$	0.707107	−	1.22474i	0.0410997	−	0.0711868i
$297$	1.20711	+	2.09077i	0.0700434	+	0.121319i
$298$	9.53553	+	16.5160i	0.552379	+	0.956748i
$299$	0.707107	−	1.22474i	0.0408930	−	0.0708288i
$300$	−6.65685			−0.384334
$301$	27.4853	+	3.76127i	1.58423	+	0.216796i
$302$	−10.0711			−0.579525
$303$	−4.58579	+	7.94282i	−0.263447	+	0.456303i
$304$	3.91421	+	6.77962i	0.224496	+	0.388838i
$305$	−2.70711	−	4.68885i	−0.155008	−	0.268483i
$306$	−0.207107	+	0.358719i	−0.0118395	+	0.0205066i
$307$	34.1127			1.94691			0.973457	−	0.228869i	$-0.0735027\pi$
$307$	34.1127			1.94691			0.973457	+	0.228869i	$0.0735027\pi$
$308$	3.91421	−	5.04757i	0.223033	−	0.287612i
$309$	11.1716			0.635529
$310$	14.4853	−	25.0892i	0.822709	−	1.42497i
$311$	13.9497	+	24.1617i	0.791018	+	1.37008i	0.925337	+	0.379145i	$0.123782\pi$
$311$	13.9497	+	24.1617i	0.791018	+	1.37008i	−0.134320	+	0.990938i	$0.542885\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−10.2426	+	17.7408i	−0.578948	+	1.00277i	0.416652	+	0.909066i	$0.363203\pi$
$313$	−10.2426	+	17.7408i	−0.578948	+	1.00277i	−0.995600	+	0.0937018i	$0.970130\pi$
$314$	−15.7279			−0.887578
$315$	−3.41421	−	8.36308i	−0.192369	−	0.471206i
$316$	−0.343146			−0.0193035
$317$	4.89949	−	8.48617i	0.275183	−	0.476631i	−0.694998	−	0.719011i	$-0.744595\pi$
$317$	4.89949	−	8.48617i	0.275183	−	0.476631i	0.970181	+	0.242380i	$0.0779282\pi$
$318$	−3.74264	−	6.48244i	−0.209877	−	0.363517i
$319$	−4.62132	−	8.00436i	−0.258744	−	0.448158i
$320$	1.70711	−	2.95680i	0.0954302	−	0.165290i
$321$	−3.31371			−0.184953
$322$	−1.41421	−	3.46410i	−0.0788110	−	0.193047i
$323$	−3.24264			−0.180425
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−3.32843	−	5.76500i	−0.184628	−	0.319785i
$326$	3.67157	+	6.35935i	0.203350	+	0.352212i
$327$	0.828427	−	1.43488i	0.0458121	−	0.0793489i
$328$	9.89949			0.546608
$329$	1.62132	−	2.09077i	0.0893863	−	0.115268i
$330$	8.24264			0.453742
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	−0.780242	−	0.625477i	$-0.784904\pi$
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	0.931800	+	0.362971i	$0.118238\pi$
$332$	1.82843	+	3.16693i	0.100348	+	0.173808i
$333$	0.707107	+	1.22474i	0.0387492	+	0.0671156i
$334$	−5.32843	+	9.22911i	−0.291559	+	0.504994i
$335$	13.0711			0.714149
$336$	2.62132	+	0.358719i	0.143005	+	0.0195698i
$337$	2.31371			0.126036			0.0630179	−	0.998012i	$-0.479927\pi$
$337$	2.31371			0.126036			0.0630179	+	0.998012i	$0.479927\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	−7.44975	−	12.9033i	−0.404615	−	0.700813i
$340$	0.707107	+	1.22474i	0.0383482	+	0.0664211i
$341$	−10.2426	+	17.7408i	−0.554670	+	0.960717i
$342$	−7.82843			−0.423313
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	−10.4853			−0.565328
$345$	2.41421	−	4.18154i	0.129977	−	0.225127i
$346$	5.74264	+	9.94655i	0.308726	+	0.534730i
$347$	−8.36396	−	14.4868i	−0.449001	−	0.777692i	0.549320	−	0.835612i	$-0.314887\pi$
$347$	−8.36396	−	14.4868i	−0.449001	−	0.777692i	−0.998321	+	0.0579194i	$0.981553\pi$
$348$	1.91421	−	3.31552i	0.102613	−	0.177730i
$349$	18.7279			1.00248			0.501241	−	0.865308i	$-0.332877\pi$
$349$	18.7279			1.00248			0.501241	+	0.865308i	$0.332877\pi$
$350$	−17.4497	−	2.38794i	−0.932728	−	0.127641i
$351$	−1.00000			−0.0533761
$352$	−1.20711	+	2.09077i	−0.0643390	+	0.111438i
$353$	16.3137	+	28.2562i	0.868291	+	1.50392i	0.863742	+	0.503935i	$0.168115\pi$
$353$	16.3137	+	28.2562i	0.868291	+	1.50392i	0.00454930	+	0.999990i	$0.498552\pi$
$354$	−6.03553	−	10.4539i	−0.320785	−	0.555616i
$355$	−8.53553	+	14.7840i	−0.453019	+	0.784652i
$356$	5.41421			0.286953
$357$	−0.671573	+	0.866025i	−0.0355434	+	0.0458349i
$358$	8.34315			0.440949
$359$	−2.41421	+	4.18154i	−0.127417	+	0.220693i	−0.922675	−	0.385578i	$-0.874002\pi$
$359$	−2.41421	+	4.18154i	−0.127417	+	0.220693i	0.795258	+	0.606271i	$0.207335\pi$
$360$	1.70711	+	2.95680i	0.0899724	+	0.155837i
$361$	−21.1421	−	36.6193i	−1.11274	−	1.92733i
$362$	8.44975	−	14.6354i	0.444109	−	0.769219i
$363$	5.17157			0.271437
$364$	1.00000	+	2.44949i	0.0524142	+	0.128388i
$365$	4.82843			0.252731
$366$	−0.792893	+	1.37333i	−0.0414452	+	0.0717852i
$367$	16.3137	+	28.2562i	0.851569	+	1.47496i	0.879792	+	0.475359i	$0.157682\pi$
$367$	16.3137	+	28.2562i	0.851569	+	1.47496i	−0.0282235	+	0.999602i	$0.508985\pi$
$368$	0.707107	+	1.22474i	0.0368605	+	0.0638442i
$369$	−4.94975	+	8.57321i	−0.257674	+	0.446304i
$370$	4.82843			0.251018
$371$	−7.48528	−	18.3351i	−0.388616	−	0.951912i
$372$	−8.48528			−0.439941
$373$	4.20711	−	7.28692i	0.217836	−	0.377303i	−0.736310	−	0.676644i	$-0.763434\pi$
$373$	4.20711	−	7.28692i	0.217836	−	0.377303i	0.954146	+	0.299341i	$0.0967670\pi$
$374$	−0.500000	−	0.866025i	−0.0258544	−	0.0447811i
$375$	−2.82843	−	4.89898i	−0.146059	−	0.252982i
$376$	−0.500000	+	0.866025i	−0.0257855	+	0.0446619i
$377$	3.82843			0.197174
$378$	−1.62132	+	2.09077i	−0.0833917	+	0.107538i
$379$	−26.6274			−1.36776			−0.683879	−	0.729595i	$-0.739709\pi$
$379$	−26.6274			−1.36776			−0.683879	+	0.729595i	$0.739709\pi$
$380$	−13.3640	+	23.1471i	−0.685557	+	1.18742i
$381$	5.94975	+	10.3053i	0.304815	+	0.527955i
$382$	10.8284	+	18.7554i	0.554031	+	0.959609i
$383$	−8.41421	+	14.5738i	−0.429946	+	0.744689i	−0.996868	−	0.0790829i	$-0.974801\pi$
$383$	−8.41421	+	14.5738i	−0.429946	+	0.744689i	0.566922	+	0.823772i	$0.308134\pi$
$384$	−1.00000			−0.0510310
$385$	21.6066	+	2.95680i	1.10117	+	0.150692i
$386$	−17.0711			−0.868894
$387$	5.24264	−	9.08052i	0.266498	−	0.461589i
$388$	7.53553	+	13.0519i	0.382559	+	0.662611i
$389$	10.7426	+	18.6068i	0.544674	+	0.943402i	0.998627	+	0.0523770i	$0.0166797\pi$
$389$	10.7426	+	18.6068i	0.544674	+	0.943402i	−0.453954	+	0.891025i	$0.649987\pi$
$390$	−1.70711	+	2.95680i	−0.0864427	+	0.149723i
$391$	−0.585786			−0.0296245
$392$	6.74264	+	1.88064i	0.340555	+	0.0949865i
$393$	−21.5563			−1.08737
$394$	−7.77817	+	13.4722i	−0.391859	+	0.678719i
$395$	−0.585786	−	1.01461i	−0.0294741	−	0.0510507i
$396$	−1.20711	−	2.09077i	−0.0606594	−	0.105065i
$397$	−10.7782	+	18.6683i	−0.540941	+	0.936937i	0.457909	+	0.888999i	$0.348598\pi$
$397$	−10.7782	+	18.6683i	−0.540941	+	0.936937i	−0.998850	+	0.0479385i	$0.984735\pi$
$398$	−22.7279			−1.13925
$399$	−20.5208	−	2.80821i	−1.02733	−	0.140586i
$400$	6.65685			0.332843
$401$	−0.0502525	+	0.0870399i	−0.00250949	+	0.00434657i	−0.867277	−	0.497825i	$-0.834132\pi$
$401$	−0.0502525	+	0.0870399i	−0.00250949	+	0.00434657i	0.864768	+	0.502172i	$0.167465\pi$
$402$	−1.91421	−	3.31552i	−0.0954723	−	0.165363i
$403$	−4.24264	−	7.34847i	−0.211341	−	0.366053i
$404$	4.58579	−	7.94282i	0.228151	−	0.395170i
$405$	−3.41421			−0.169654
$406$	6.20711	−	8.00436i	0.308054	−	0.397250i
$407$	−3.41421			−0.169236
$408$	0.207107	−	0.358719i	0.0102533	−	0.0177593i
$409$	−17.7071	−	30.6696i	−0.875560	−	1.51651i	−0.856165	−	0.516703i	$-0.827159\pi$
$409$	−17.7071	−	30.6696i	−0.875560	−	1.51651i	−0.0193952	−	0.999812i	$-0.506174\pi$
$410$	16.8995	+	29.2708i	0.834607	+	1.44558i
$411$	−1.53553	+	2.65962i	−0.0757423	+	0.131190i
$412$	−11.1716			−0.550384
$413$	−12.0711	−	29.5680i	−0.593978	−	1.45494i
$414$	−1.41421			−0.0695048
$415$	−6.24264	+	10.8126i	−0.306439	+	0.530768i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	0.535534	+	0.927572i	0.0262252	+	0.0454234i
$418$	9.44975	−	16.3674i	0.462202	−	0.800558i
$419$	−23.4558			−1.14589			−0.572946	−	0.819593i	$-0.694200\pi$
$419$	−23.4558			−1.14589			−0.572946	+	0.819593i	$0.694200\pi$
$420$	3.41421	+	8.36308i	0.166597	+	0.408077i
$421$	−13.0711			−0.637045			−0.318522	−	0.947915i	$-0.603187\pi$
$421$	−13.0711			−0.637045			−0.318522	+	0.947915i	$0.603187\pi$
$422$	13.5355	−	23.4442i	0.658899	−	1.14125i
$423$	−0.500000	−	0.866025i	−0.0243108	−	0.0421076i
$424$	3.74264	+	6.48244i	0.181759	+	0.314815i
$425$	−1.37868	+	2.38794i	−0.0668758	+	0.115832i
$426$	5.00000			0.242251
$427$	−2.57107	+	3.31552i	−0.124423	+	0.160449i
$428$	3.31371			0.160174
$429$	1.20711	−	2.09077i	0.0582797	−	0.100943i
$430$	−17.8995	−	31.0028i	−0.863190	−	1.49509i
$431$	−6.75736	−	11.7041i	−0.325491	−	0.563766i	0.656121	−	0.754656i	$-0.272196\pi$
$431$	−6.75736	−	11.7041i	−0.325491	−	0.563766i	−0.981612	+	0.190890i	$0.938863\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−3.97056			−0.190813			−0.0954065	−	0.995438i	$-0.530415\pi$
$433$	−3.97056			−0.190813			−0.0954065	+	0.995438i	$0.530415\pi$
$434$	−22.2426	−	3.04384i	−1.06768	−	0.146109i
$435$	13.0711			0.626710
$436$	−0.828427	+	1.43488i	−0.0396745	+	0.0687182i
$437$	−5.53553	−	9.58783i	−0.264800	−	0.458648i
$438$	−0.707107	−	1.22474i	−0.0337869	−	0.0585206i
$439$	−9.70711	+	16.8132i	−0.463295	+	0.802450i	−0.999123	−	0.0418769i	$-0.986666\pi$
$439$	−9.70711	+	16.8132i	−0.463295	+	0.802450i	0.535828	+	0.844327i	$0.320000\pi$
$440$	−8.24264			−0.392952
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$	0.414214			0.0197021
$443$	−12.8492	+	22.2555i	−0.610486	+	1.05739i	0.380673	+	0.924710i	$0.375692\pi$
$443$	−12.8492	+	22.2555i	−0.610486	+	1.05739i	−0.991159	+	0.132683i	$0.957641\pi$
$444$	−0.707107	−	1.22474i	−0.0335578	−	0.0581238i
$445$	9.24264	+	16.0087i	0.438143	+	0.758886i
$446$	11.0355	−	19.1141i	0.522548	−	0.905079i
$447$	19.0711			0.902031
$448$	−2.62132	−	0.358719i	−0.123846	−	0.0169479i
$449$	−8.97056			−0.423347			−0.211674	−	0.977340i	$-0.567891\pi$
$449$	−8.97056			−0.423347			−0.211674	+	0.977340i	$0.567891\pi$
$450$	−3.32843	+	5.76500i	−0.156904	+	0.271765i
$451$	−11.9497	−	20.6976i	−0.562692	−	0.974610i
$452$	7.44975	+	12.9033i	0.350407	+	0.606922i
$453$	−5.03553	+	8.72180i	−0.236590	+	0.409786i
$454$	−26.8284			−1.25912
$455$	−5.53553	+	7.13834i	−0.259510	+	0.334650i
$456$	7.82843			0.366600
$457$	−5.53553	+	9.58783i	−0.258941	+	0.448500i	−0.965959	−	0.258697i	$-0.916707\pi$
$457$	−5.53553	+	9.58783i	−0.258941	+	0.448500i	0.707017	+	0.707196i	$0.250040\pi$
$458$	−4.75736	−	8.23999i	−0.222297	−	0.385029i
$459$	0.207107	+	0.358719i	0.00966692	+	0.0167436i
$460$	−2.41421	+	4.18154i	−0.112563	+	0.194965i
$461$	12.4853			0.581498			0.290749	−	0.956799i	$-0.406096\pi$
$461$	12.4853			0.581498			0.290749	+	0.956799i	$0.406096\pi$
$462$	−2.41421	−	5.91359i	−0.112319	−	0.275125i
$463$	12.9706			0.602793			0.301397	−	0.953499i	$-0.402547\pi$
$463$	12.9706			0.602793			0.301397	+	0.953499i	$0.402547\pi$
$464$	−1.91421	+	3.31552i	−0.0888651	+	0.153919i
$465$	−14.4853	−	25.0892i	−0.671739	−	1.16349i
$466$	−3.86396	−	6.69258i	−0.178995	−	0.310028i
$467$	4.29289	−	7.43551i	0.198651	−	0.344074i	−0.749440	−	0.662072i	$-0.769677\pi$
$467$	4.29289	−	7.43551i	0.198651	−	0.344074i	0.948091	+	0.317998i	$0.103011\pi$
$468$	1.00000			0.0462250
$469$	−3.82843	−	9.37769i	−0.176780	−	0.433022i
$470$	−3.41421			−0.157486
$471$	−7.86396	+	13.6208i	−0.362352	+	0.627612i
$472$	6.03553	+	10.4539i	0.277808	+	0.481178i
$473$	12.6569	+	21.9223i	0.581963	+	1.00799i
$474$	−0.171573	+	0.297173i	−0.00788060	+	0.0136496i
$475$	−52.1127			−2.39109
$476$	0.671573	−	0.866025i	0.0307815	−	0.0396942i
$477$	−7.48528			−0.342727
$478$	−10.7426	+	18.6068i	−0.491357	+	0.851055i
$479$	−15.0563	−	26.0784i	−0.687942	−	1.19155i	−0.972502	−	0.232893i	$-0.925181\pi$
$479$	−15.0563	−	26.0784i	−0.687942	−	1.19155i	0.284560	−	0.958658i	$-0.408152\pi$
$480$	−1.70711	−	2.95680i	−0.0779184	−	0.134959i
$481$	0.707107	−	1.22474i	0.0322413	−	0.0558436i
$482$	26.1421			1.19074
$483$	−3.70711	−	0.507306i	−0.168679	−	0.0230832i
$484$	−5.17157			−0.235071
$485$	−25.7279	+	44.5621i	−1.16824	+	2.02346i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	13.1066	+	22.7013i	0.593917	+	1.02869i	0.993699	+	0.112084i	$0.0357525\pi$
$487$	13.1066	+	22.7013i	0.593917	+	1.02869i	−0.399782	+	0.916610i	$0.630914\pi$
$488$	0.792893	−	1.37333i	0.0358926	−	0.0621678i
$489$	7.34315			0.332069
$490$	5.94975	+	23.1471i	0.268782	+	1.04568i
$491$	12.3431			0.557038			0.278519	−	0.960431i	$-0.410156\pi$
$491$	12.3431			0.557038			0.278519	+	0.960431i	$0.410156\pi$
$492$	4.94975	−	8.57321i	0.223152	−	0.386510i
$493$	−0.792893	−	1.37333i	−0.0357101	−	0.0618517i
$494$	3.91421	+	6.77962i	0.176109	+	0.305029i
$495$	4.12132	−	7.13834i	0.185240	−	0.320844i
$496$	8.48528			0.381000
$497$	13.1066	+	1.79360i	0.587911	+	0.0804538i
$498$	3.65685			0.163868
$499$	3.82843	−	6.63103i	0.171384	−	0.296846i	−0.767520	−	0.641025i	$-0.778509\pi$
$499$	3.82843	−	6.63103i	0.171384	−	0.296846i	0.938904	+	0.344179i	$0.111843\pi$
$500$	2.82843	+	4.89898i	0.126491	+	0.219089i
$501$	5.32843	+	9.22911i	0.238057	+	0.412326i
$502$	−9.58579	+	16.6031i	−0.427835	+	0.741031i
$503$	−2.14214			−0.0955131			−0.0477566	−	0.998859i	$-0.515207\pi$
$503$	−2.14214			−0.0955131			−0.0477566	+	0.998859i	$0.515207\pi$
$504$	1.62132	−	2.09077i	0.0722193	−	0.0931303i
$505$	31.3137			1.39344
$506$	1.70711	−	2.95680i	0.0758902	−	0.131446i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	−5.94975	−	10.3053i	−0.263977	−	0.457222i
$509$	17.3137	−	29.9882i	0.767417	−	1.32920i	−0.171543	−	0.985177i	$-0.554875\pi$
$509$	17.3137	−	29.9882i	0.767417	−	1.32920i	0.938959	−	0.344028i	$-0.111791\pi$
$510$	1.41421			0.0626224
$511$	−1.41421	−	3.46410i	−0.0625611	−	0.153243i
$512$	1.00000			0.0441942
$513$	−3.91421	+	6.77962i	−0.172817	+	0.299327i
$514$	−4.75736	−	8.23999i	−0.209838	−	0.363450i
$515$	−19.0711	−	33.0321i	−0.840372	−	1.45557i
$516$	−5.24264	+	9.08052i	−0.230794	+	0.399748i
$517$	2.41421			0.106177
$518$	−1.41421	−	3.46410i	−0.0621370	−	0.152204i
$519$	11.4853			0.504148
$520$	1.70711	−	2.95680i	0.0748616	−	0.129664i
$521$	2.31371	+	4.00746i	0.101365	+	0.175570i	0.912247	−	0.409640i	$-0.134346\pi$
$521$	2.31371	+	4.00746i	0.101365	+	0.175570i	−0.810882	+	0.585210i	$0.801012\pi$
$522$	−1.91421	−	3.31552i	−0.0837829	−	0.145116i
$523$	5.58579	−	9.67487i	0.244249	−	0.423052i	−0.717671	−	0.696382i	$-0.754792\pi$
$523$	5.58579	−	9.67487i	0.244249	−	0.423052i	0.961920	+	0.273330i	$0.0881251\pi$
$524$	21.5563			0.941693
$525$	−10.7929	+	13.9180i	−0.471040	+	0.607429i
$526$	23.4142			1.02091
$527$	−1.75736	+	3.04384i	−0.0765518	+	0.132592i
$528$	1.20711	+	2.09077i	0.0525326	+	0.0909891i
$529$	10.5000	+	18.1865i	0.456522	+	0.790719i
$530$	−12.7782	+	22.1324i	−0.555048	+	0.961372i
$531$	−12.0711			−0.523840
$532$	20.5208	+	2.80821i	0.889690	+	0.121751i
$533$	9.89949			0.428795
$534$	2.70711	−	4.68885i	0.117148	−	0.202906i
$535$	5.65685	+	9.79796i	0.244567	+	0.423603i
$536$	1.91421	+	3.31552i	0.0826814	+	0.143208i
$537$	4.17157	−	7.22538i	0.180017	−	0.311798i
$538$	19.1421			0.825276
$539$	−4.20711	−	16.3674i	−0.181213	−	0.704996i
$540$	3.41421			0.146924
$541$	−4.46447	+	7.73268i	−0.191942	+	0.332454i	−0.945894	−	0.324476i	$-0.894812\pi$
$541$	−4.46447	+	7.73268i	−0.191942	+	0.332454i	0.753952	+	0.656930i	$0.228145\pi$
$542$	8.10660	+	14.0410i	0.348208	+	0.603115i
$543$	−8.44975	−	14.6354i	−0.362613	−	0.628065i
$544$	−0.207107	+	0.358719i	−0.00887963	+	0.0153800i
$545$	−5.65685			−0.242313
$546$	2.62132	+	0.358719i	0.112182	+	0.0153518i
$547$	22.8701			0.977853			0.488927	−	0.872325i	$-0.337389\pi$
$547$	22.8701			0.977853			0.488927	+	0.872325i	$0.337389\pi$
$548$	1.53553	−	2.65962i	0.0655948	−	0.113613i
$549$	0.792893	+	1.37333i	0.0338399	+	0.0586124i
$550$	−8.03553	−	13.9180i	−0.342636	−	0.593464i
$551$	14.9853	−	25.9553i	0.638394	−	1.10573i
$552$	1.41421			0.0601929
$553$	−0.556349	+	0.717439i	−0.0236584	+	0.0305086i
$554$	3.92893			0.166924
$555$	2.41421	−	4.18154i	0.102478	−	0.177497i
$556$	−0.535534	−	0.927572i	−0.0227117	−	0.0393378i
$557$	−6.31371	−	10.9357i	−0.267520	−	0.463359i	0.700700	−	0.713456i	$-0.252871\pi$
$557$	−6.31371	−	10.9357i	−0.267520	−	0.463359i	−0.968221	+	0.250097i	$0.919538\pi$
$558$	−4.24264	+	7.34847i	−0.179605	+	0.311086i
$559$	−10.4853			−0.443480
$560$	−3.41421	−	8.36308i	−0.144277	−	0.353405i
$561$	−1.00000			−0.0422200
$562$	−11.6569	+	20.1903i	−0.491715	+	0.851675i
$563$	−20.3848	−	35.3075i	−0.859116	−	1.48803i	−0.872773	−	0.488126i	$-0.837681\pi$
$563$	−20.3848	−	35.3075i	−0.859116	−	1.48803i	0.0136575	−	0.999907i	$-0.495653\pi$
$564$	0.500000	+	0.866025i	0.0210538	+	0.0364662i
$565$	−25.4350	+	44.0548i	−1.07006	+	1.85340i
$566$	−24.2426			−1.01899
$567$	1.00000	+	2.44949i	0.0419961	+	0.102869i
$568$	−5.00000			−0.209795
$569$	0.863961	−	1.49642i	0.0362191	−	0.0627334i	−0.847348	−	0.531039i	$-0.821802\pi$
$569$	0.863961	−	1.49642i	0.0362191	−	0.0627334i	0.883567	+	0.468305i	$0.155135\pi$
$570$	13.3640	+	23.1471i	0.559755	+	0.969524i
$571$	4.34315	+	7.52255i	0.181755	+	0.314809i	0.942478	−	0.334267i	$-0.108489\pi$
$571$	4.34315	+	7.52255i	0.181755	+	0.314809i	−0.760723	+	0.649076i	$0.775156\pi$
$572$	−1.20711	+	2.09077i	−0.0504717	+	0.0874195i
$573$	21.6569			0.904728
$574$	16.0503	−	20.6976i	0.669925	−	0.863900i
$575$	−9.41421			−0.392600
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−13.8284	−	23.9515i	−0.575685	−	0.997116i	−0.995967	−	0.0897220i	$-0.971402\pi$
$577$	−13.8284	−	23.9515i	−0.575685	−	0.997116i	0.420282	−	0.907394i	$-0.361931\pi$
$578$	8.41421	+	14.5738i	0.349985	+	0.606192i
$579$	−8.53553	+	14.7840i	−0.354725	+	0.614401i
$580$	−13.0711			−0.542747
$581$	9.58579	+	1.31178i	0.397685	+	0.0544220i
$582$	15.0711			0.624716
$583$	9.03553	−	15.6500i	0.374214	−	0.648157i
$584$	0.707107	+	1.22474i	0.0292603	+	0.0506803i
$585$	1.70711	+	2.95680i	0.0705802	+	0.122248i
$586$	−4.94975	+	8.57321i	−0.204472	+	0.354156i
$587$	−4.41421			−0.182194			−0.0910970	−	0.995842i	$-0.529037\pi$
$587$	−4.41421			−0.182194			−0.0910970	+	0.995842i	$0.529037\pi$
$588$	5.00000	−	4.89898i	0.206197	−	0.202031i
$589$	−66.4264			−2.73705
$590$	−20.6066	+	35.6917i	−0.848360	+	1.46940i
$591$	7.77817	+	13.4722i	0.319951	+	0.554172i
$592$	0.707107	+	1.22474i	0.0290619	+	0.0503367i
$593$	−1.19239	+	2.06528i	−0.0489655	+	0.0848108i	−0.889469	−	0.456995i	$-0.848926\pi$
$593$	−1.19239	+	2.06528i	−0.0489655	+	0.0848108i	0.840504	+	0.541806i	$0.182259\pi$
$594$	−2.41421			−0.0990564
$595$	3.70711	+	0.507306i	0.151977	+	0.0207975i
$596$	−19.0711			−0.781181
$597$	−11.3640	+	19.6830i	−0.465096	+	0.805570i
$598$	0.707107	+	1.22474i	0.0289157	+	0.0500835i
$599$	14.7782	+	25.5965i	0.603820	+	1.04585i	0.992237	+	0.124363i	$0.0396887\pi$
$599$	14.7782	+	25.5965i	0.603820	+	1.04585i	−0.388417	+	0.921484i	$0.626978\pi$
$600$	3.32843	−	5.76500i	0.135882	−	0.235355i
$601$	40.7990			1.66423			0.832113	−	0.554606i	$-0.187131\pi$
$601$	40.7990			1.66423			0.832113	+	0.554606i	$0.187131\pi$
$602$	−17.0000	+	21.9223i	−0.692868	+	0.893487i
$603$	−3.82843			−0.155906
$604$	5.03553	−	8.72180i	0.204893	−	0.354885i
$605$	−8.82843	−	15.2913i	−0.358927	−	0.621679i
$606$	−4.58579	−	7.94282i	−0.186285	−	0.322655i
$607$	15.2635	−	26.4371i	0.619525	−	1.07305i	−0.370048	−	0.929013i	$-0.620659\pi$
$607$	15.2635	−	26.4371i	0.619525	−	1.07305i	0.989573	−	0.144035i	$-0.0460079\pi$
$608$	−7.82843			−0.317485
$609$	−3.82843	−	9.37769i	−0.155136	−	0.380003i
$610$	5.41421			0.219215
$611$	−0.500000	+	0.866025i	−0.0202278	+	0.0350356i
$612$	−0.207107	−	0.358719i	−0.00837180	−	0.0145004i
$613$	−15.8995	−	27.5387i	−0.642175	−	1.11228i	−0.984946	−	0.172860i	$-0.944699\pi$
$613$	−15.8995	−	27.5387i	−0.642175	−	1.11228i	0.342772	−	0.939419i	$-0.388634\pi$
$614$	−17.0563	+	29.5425i	−0.688338	+	1.19224i
$615$	33.7990			1.36291
$616$	2.41421	+	5.91359i	0.0972714	+	0.238265i
$617$	4.14214			0.166756			0.0833781	−	0.996518i	$-0.473429\pi$
$617$	4.14214			0.166756			0.0833781	+	0.996518i	$0.473429\pi$
$618$	−5.58579	+	9.67487i	−0.224693	+	0.389180i
$619$	−7.58579	−	13.1390i	−0.304898	−	0.528100i	0.672340	−	0.740242i	$-0.265289\pi$
$619$	−7.58579	−	13.1390i	−0.304898	−	0.528100i	−0.977239	+	0.212143i	$0.931956\pi$
$620$	14.4853	+	25.0892i	0.581743	+	1.00761i
$621$	−0.707107	+	1.22474i	−0.0283752	+	0.0491473i
$622$	−27.8995			−1.11867
$623$	8.77817	−	11.3199i	0.351690	−	0.453521i
$624$	−1.00000			−0.0400320
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	−10.2426	−	17.7408i	−0.409378	−	0.709064i
$627$	−9.44975	−	16.3674i	−0.377387	−	0.653653i
$628$	7.86396	−	13.6208i	0.313806	−	0.543528i
$629$	−0.585786			−0.0233568
$630$	8.94975	+	1.22474i	0.356566	+	0.0487950i
$631$	−12.6274			−0.502690			−0.251345	−	0.967898i	$-0.580873\pi$
$631$	−12.6274			−0.502690			−0.251345	+	0.967898i	$0.580873\pi$
$632$	0.171573	−	0.297173i	0.00682480	−	0.0118209i
$633$	−13.5355	−	23.4442i	−0.537989	−	0.931825i
$634$	4.89949	+	8.48617i	0.194584	+	0.337029i
$635$	20.3137	−	35.1844i	0.806125	−	1.39625i
$636$	7.48528			0.296811
$637$	6.74264	+	1.88064i	0.267153	+	0.0745136i
$638$	9.24264			0.365920
$639$	2.50000	−	4.33013i	0.0988985	−	0.171297i
$640$	1.70711	+	2.95680i	0.0674793	+	0.116878i
$641$	3.89949	+	6.75412i	0.154021	+	0.266772i	0.932702	−	0.360648i	$-0.117444\pi$
$641$	3.89949	+	6.75412i	0.154021	+	0.266772i	−0.778681	+	0.627420i	$0.784111\pi$
$642$	1.65685	−	2.86976i	0.0653908	−	0.113260i
$643$	−19.4853			−0.768424			−0.384212	−	0.923245i	$-0.625527\pi$
$643$	−19.4853			−0.768424			−0.384212	+	0.923245i	$0.625527\pi$
$644$	3.70711	+	0.507306i	0.146080	+	0.0199907i
$645$	−35.7990			−1.40958
$646$	1.62132	−	2.80821i	0.0637900	−	0.110488i
$647$	21.4853	+	37.2136i	0.844674	+	1.46302i	0.885904	+	0.463868i	$0.153539\pi$
$647$	21.4853	+	37.2136i	0.844674	+	1.46302i	−0.0412308	+	0.999150i	$0.513128\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	14.5711	−	25.2378i	0.571964	−	0.990671i
$650$	6.65685			0.261103
$651$	−13.7574	+	17.7408i	−0.539193	+	0.695316i
$652$	−7.34315			−0.287580
$653$	3.07107	−	5.31925i	0.120180	−	0.208158i	−0.799658	−	0.600455i	$-0.794986\pi$
$653$	3.07107	−	5.31925i	0.120180	−	0.208158i	0.919839	+	0.392297i	$0.128319\pi$
$654$	0.828427	+	1.43488i	0.0323941	+	0.0561082i
$655$	36.7990	+	63.7377i	1.43786	+	2.49044i
$656$	−4.94975	+	8.57321i	−0.193255	+	0.334728i
$657$	−1.41421			−0.0551737
$658$	1.00000	+	2.44949i	0.0389841	+	0.0954911i
$659$	13.4142			0.522544			0.261272	−	0.965265i	$-0.415858\pi$
$659$	13.4142			0.522544			0.261272	+	0.965265i	$0.415858\pi$
$660$	−4.12132	+	7.13834i	−0.160422	+	0.277859i
$661$	−15.8787	−	27.5027i	−0.617609	−	1.06973i	−0.989921	−	0.141623i	$-0.954768\pi$
$661$	−15.8787	−	27.5027i	−0.617609	−	1.06973i	0.372312	−	0.928108i	$-0.378565\pi$
$662$	2.75736	+	4.77589i	0.107168	+	0.185620i
$663$	0.207107	−	0.358719i	0.00804336	−	0.0139315i
$664$	−3.65685			−0.141913
$665$	26.7279	+	65.4698i	1.03646	+	2.53881i
$666$	−1.41421			−0.0547997
$667$	2.70711	−	4.68885i	0.104820	−	0.181553i
$668$	−5.32843	−	9.22911i	−0.206163	−	0.357085i
$669$	−11.0355	−	19.1141i	−0.426658	−	0.738994i
$670$	−6.53553	+	11.3199i	−0.252490	+	0.437325i
$671$	−3.82843			−0.147795
$672$	−1.62132	+	2.09077i	−0.0625438	+	0.0806532i
$673$	13.8579			0.534181			0.267091	−	0.963671i	$-0.413938\pi$
$673$	13.8579			0.534181			0.267091	+	0.963671i	$0.413938\pi$
$674$	−1.15685	+	2.00373i	−0.0445604	+	0.0771808i
$675$	3.32843	+	5.76500i	0.128111	+	0.221895i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	−0.973392	−	0.229147i	$-0.926406\pi$
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	0.685143	+	0.728408i	$0.259740\pi$
$678$	14.8995			0.572212
$679$	39.5061	+	5.40629i	1.51610	+	0.207474i
$680$	−1.41421			−0.0542326
$681$	−13.4142	+	23.2341i	−0.514034	+	0.890333i
$682$	−10.2426	−	17.7408i	−0.392211	−	0.679329i
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	0.698440	−	0.715668i	$-0.253878\pi$
$683$	−7.07107	−	12.2474i	−0.270567	−	0.468636i	−0.969007	+	0.247033i	$0.920544\pi$
$684$	3.91421	−	6.77962i	0.149664	−	0.259225i
$685$	10.4853			0.400622
$686$	14.8640	−	11.0482i	0.567509	−	0.421822i
$687$	−9.51472			−0.363009
$688$	5.24264	−	9.08052i	0.199874	−	0.346192i
$689$	3.74264	+	6.48244i	0.142583	+	0.246961i
$690$	2.41421	+	4.18154i	0.0919075	+	0.159189i
$691$	4.67157	−	8.09140i	0.177715	−	0.307811i	−0.763383	−	0.645947i	$-0.776463\pi$
$691$	4.67157	−	8.09140i	0.177715	−	0.307811i	0.941098	+	0.338135i	$0.109796\pi$
$692$	−11.4853			−0.436605
$693$	−6.32843	−	0.866025i	−0.240397	−	0.0328976i
$694$	16.7279			0.634983
$695$	1.82843	−	3.16693i	0.0693562	−	0.120128i
$696$	1.91421	+	3.31552i	0.0725581	+	0.125674i
$697$	−2.05025	−	3.55114i	−0.0776589	−	0.134509i
$698$	−9.36396	+	16.2189i	−0.354431	+	0.613893i
$699$	−7.72792			−0.292297
$700$	10.7929	−	13.9180i	0.407933	−	0.526049i
$701$	−34.8284			−1.31545			−0.657726	−	0.753257i	$-0.728481\pi$
$701$	−34.8284			−1.31545			−0.657726	+	0.753257i	$0.728481\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$	−5.53553	−	9.58783i	−0.208777	−	0.361612i
$704$	−1.20711	−	2.09077i	−0.0454945	−	0.0787989i
$705$	−1.70711	+	2.95680i	−0.0642934	+	0.111359i
$706$	−32.6274			−1.22795
$707$	−9.17157	−	22.4657i	−0.344932	−	0.844909i
$708$	12.0711			0.453659
$709$	−8.43503	+	14.6099i	−0.316784	+	0.548686i	−0.979815	−	0.199906i	$-0.935936\pi$
$709$	−8.43503	+	14.6099i	−0.316784	+	0.548686i	0.663031	+	0.748592i	$0.269270\pi$
$710$	−8.53553	−	14.7840i	−0.320333	−	0.554833i
$711$	0.171573	+	0.297173i	0.00643449	+	0.0111449i
$712$	−2.70711	+	4.68885i	−0.101453	+	0.175722i
$713$	−12.0000			−0.449404
$714$	−0.414214	−	1.01461i	−0.0155016	−	0.0379709i
$715$	−8.24264			−0.308257
$716$	−4.17157	+	7.22538i	−0.155899	+	0.270025i
$717$	10.7426	+	18.6068i	0.401191	+	0.694884i
$718$	−2.41421	−	4.18154i	−0.0900976	−	0.156054i
$719$	6.65685	−	11.5300i	0.248259	−	0.429997i	−0.714784	−	0.699345i	$-0.753475\pi$
$719$	6.65685	−	11.5300i	0.248259	−	0.429997i	0.963043	+	0.269348i	$0.0868083\pi$
$720$	−3.41421			−0.127240
$721$	−18.1127	+	23.3572i	−0.674552	+	0.869867i
$722$	42.2843			1.57366
$723$	13.0711	−	22.6398i	0.486118	−	0.841981i
$724$	8.44975	+	14.6354i	0.314032	+	0.543920i
$725$	−12.7426	−	22.0709i	−0.473250	−	0.819693i
$726$	−2.58579	+	4.47871i	−0.0959675	+	0.166221i
$727$	34.4264			1.27680			0.638402	−	0.769703i	$-0.279596\pi$
$727$	34.4264			1.27680			0.638402	+	0.769703i	$0.279596\pi$
$728$	−2.62132	−	0.358719i	−0.0971526	−	0.0132950i
$729$	1.00000			0.0370370
$730$	−2.41421	+	4.18154i	−0.0893541	+	0.154766i
$731$	2.17157	+	3.76127i	0.0803185	+	0.139116i
$732$	−0.792893	−	1.37333i	−0.0293062	−	0.0507598i
$733$	15.7071	−	27.2055i	0.580155	−	1.00486i	−0.415305	−	0.909682i	$-0.636325\pi$
$733$	15.7071	−	27.2055i	0.580155	−	1.00486i	0.995460	−	0.0951762i	$-0.0303415\pi$
$734$	−32.6274			−1.20430
$735$	23.0208	+	6.42090i	0.849136	+	0.236838i
$736$	−1.41421			−0.0521286
$737$	4.62132	−	8.00436i	0.170229	−	0.294844i
$738$	−4.94975	−	8.57321i	−0.182203	−	0.315584i
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	0.998146	+	0.0608653i	$0.0193860\pi$
$739$	15.0000	+	25.9808i	0.551784	+	0.955718i	−0.446362	+	0.894852i	$0.647281\pi$
$740$	−2.41421	+	4.18154i	−0.0887483	+	0.153716i
$741$	7.82843			0.287584
$742$	19.6213	+	2.68512i	0.720321	+	0.0985737i
$743$	17.8284			0.654062			0.327031	−	0.945014i	$-0.393952\pi$
$743$	17.8284			0.654062			0.327031	+	0.945014i	$0.393952\pi$
$744$	4.24264	−	7.34847i	0.155543	−	0.269408i
$745$	−32.5563	−	56.3893i	−1.19277	−	2.06594i
$746$	4.20711	+	7.28692i	0.154033	+	0.266793i
$747$	1.82843	−	3.16693i	0.0668987	−	0.115872i
$748$	1.00000			0.0365636
$749$	5.37258	−	6.92820i	0.196310	−	0.253151i
$750$	5.65685			0.206559
$751$	−1.65685	+	2.86976i	−0.0604595	+	0.104719i	−0.894671	−	0.446726i	$-0.852590\pi$
$751$	−1.65685	+	2.86976i	−0.0604595	+	0.104719i	0.834211	+	0.551445i	$0.185923\pi$
$752$	−0.500000	−	0.866025i	−0.0182331	−	0.0315807i
$753$	9.58579	+	16.6031i	0.349325	+	0.605049i
$754$	−1.91421	+	3.31552i	−0.0697115	+	0.120744i
$755$	34.3848			1.25139
$756$	−1.00000	−	2.44949i	−0.0363696	−	0.0890871i
$757$	−39.2426			−1.42630			−0.713149	−	0.701012i	$-0.752732\pi$
$757$	−39.2426			−1.42630			−0.713149	+	0.701012i	$0.752732\pi$
$758$	13.3137	−	23.0600i	0.483576	−	0.837578i
$759$	−1.70711	−	2.95680i	−0.0619641	−	0.107325i
$760$	−13.3640	−	23.1471i	−0.484762	−	0.839632i
$761$	9.55635	−	16.5521i	0.346417	−	0.600013i	−0.639193	−	0.769046i	$-0.720731\pi$
$761$	9.55635	−	16.5521i	0.346417	−	0.600013i	0.985610	+	0.169034i	$0.0540648\pi$
$762$	−11.8995			−0.431073
$763$	1.65685	+	4.05845i	0.0599822	+	0.146926i
$764$	−21.6569			−0.783517
$765$	0.707107	−	1.22474i	0.0255655	−	0.0442807i
$766$	−8.41421	−	14.5738i	−0.304018	−	0.526574i
$767$	6.03553	+	10.4539i	0.217930	+	0.377467i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−9.89949			−0.356985			−0.178492	−	0.983941i	$-0.557122\pi$
$769$	−9.89949			−0.356985			−0.178492	+	0.983941i	$0.557122\pi$
$770$	−13.3640	+	17.2335i	−0.481604	+	0.621051i
$771$	−9.51472			−0.342664
$772$	8.53553	−	14.7840i	0.307201	−	0.532087i
$773$	7.48528	+	12.9649i	0.269227	+	0.466315i	0.968662	−	0.248381i	$-0.0798985\pi$
$773$	7.48528	+	12.9649i	0.269227	+	0.466315i	−0.699436	+	0.714696i	$0.746565\pi$
$774$	5.24264	+	9.08052i	0.188443	+	0.326393i
$775$	−28.2426	+	48.9177i	−1.01451	+	1.75718i
$776$	−15.0711			−0.541020
$777$	−3.70711	−	0.507306i	−0.132992	−	0.0181995i
$778$	−21.4853			−0.770285
$779$	38.7487	−	67.1148i	1.38832	−	2.40464i
$780$	−1.70711	−	2.95680i	−0.0611242	−	0.105870i
$781$	6.03553	+	10.4539i	0.215968	+	0.374068i
$782$	0.292893	−	0.507306i	0.0104738	−	0.0181412i
$783$	−3.82843			−0.136817
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$	53.6985			1.91658
$786$	10.7782	−	18.6683i	0.384445	−	0.665878i
$787$	1.84315	+	3.19242i	0.0657011	+	0.113798i	0.897005	−	0.442021i	$-0.145738\pi$
$787$	1.84315	+	3.19242i	0.0657011	+	0.113798i	−0.831304	+	0.555818i	$0.812405\pi$
$788$	−7.77817	−	13.4722i	−0.277086	−	0.479927i
$789$	11.7071	−	20.2773i	0.416784	−	0.721891i
$790$	1.17157			0.0416827
$791$	39.0563	+	5.34474i	1.38868	+	0.190037i
$792$	2.41421			0.0857853
$793$	0.792893	−	1.37333i	0.0281565	−	0.0487684i
$794$	−10.7782	−	18.6683i	−0.382503	−	0.662515i
$795$	12.7782	+	22.1324i	0.453195	+	0.784957i
$796$	11.3640	−	19.6830i	0.402785	−	0.697644i
$797$	45.6569			1.61725			0.808624	−	0.588325i	$-0.200213\pi$
$797$	45.6569			1.61725			0.808624	+	0.588325i	$0.200213\pi$
$798$	12.6924	−	16.3674i	0.449306	−	0.579401i
$799$	0.414214			0.0146538
$800$	−3.32843	+	5.76500i	−0.117678	+	0.203824i
$801$	−2.70711	−	4.68885i	−0.0956509	−	0.165672i
$802$	−0.0502525	−	0.0870399i	−0.00177448	−	0.00307349i
$803$	1.70711	−	2.95680i	0.0602425	−	0.104343i
$804$	3.82843			0.135018
$805$	4.82843	+	11.8272i	0.170180	+	0.416853i
$806$	8.48528			0.298881
$807$	9.57107	−	16.5776i	0.336918	−	0.583558i
$808$	4.58579	+	7.94282i	0.161327	+	0.279427i
$809$	10.2071	+	17.6792i	0.358863	+	0.621569i	0.987771	−	0.155911i	$-0.0498313\pi$
$809$	10.2071	+	17.6792i	0.358863	+	0.621569i	−0.628908	+	0.777479i	$0.716498\pi$
$810$	1.70711	−	2.95680i	0.0599816	−	0.103891i
$811$	4.54416			0.159567			0.0797834	−	0.996812i	$-0.474577\pi$
$811$	4.54416			0.159567			0.0797834	+	0.996812i	$0.474577\pi$
$812$	3.82843	+	9.37769i	0.134351	+	0.329093i
$813$	16.2132			0.568622
$814$	1.70711	−	2.95680i	0.0598341	−	0.103636i
$815$	−12.5355	−	21.7122i	−0.439101	−	0.760545i
$816$	0.207107	+	0.358719i	0.00725019	+	0.0125577i
$817$	−41.0416	+	71.0862i	−1.43586	+	2.48699i
$818$	35.4142			1.23823
$819$	1.62132	−	2.09077i	0.0566535	−	0.0730574i
$820$	−33.7990			−1.18031
$821$	−14.0503	+	24.3358i	−0.490357	+	0.849324i	−0.999938	−	0.0110990i	$-0.996467\pi$
$821$	−14.0503	+	24.3358i	−0.490357	+	0.849324i	0.509581	+	0.860423i	$0.329800\pi$
$822$	−1.53553	−	2.65962i	−0.0535579	−	0.0927650i
$823$	−21.9203	−	37.9671i	−0.764094	−	1.32345i	−0.940724	−	0.339172i	$-0.889853\pi$
$823$	−21.9203	−	37.9671i	−0.764094	−	1.32345i	0.176630	−	0.984277i	$-0.443480\pi$
$824$	5.58579	−	9.67487i	0.194590	−	0.337040i
$825$	−16.0711			−0.559523
$826$	31.6421	+	4.33013i	1.10097	+	0.150664i
$827$	−24.3553			−0.846918			−0.423459	−	0.905915i	$-0.639184\pi$
$827$	−24.3553			−0.846918			−0.423459	+	0.905915i	$0.639184\pi$
$828$	0.707107	−	1.22474i	0.0245737	−	0.0425628i
$829$	−16.3492	−	28.3177i	−0.567833	−	0.983515i	−0.996780	−	0.0801855i	$-0.974449\pi$
$829$	−16.3492	−	28.3177i	−0.567833	−	0.983515i	0.428947	−	0.903330i	$-0.358885\pi$
$830$	−6.24264	−	10.8126i	−0.216685	−	0.375310i
$831$	1.96447	−	3.40256i	0.0681466	−	0.118033i
$832$	1.00000			0.0346688
$833$	−0.721825	−	2.80821i	−0.0250098	−	0.0972987i
$834$	−1.07107			−0.0370880
$835$	18.1924	−	31.5101i	0.629574	−	1.09045i
$836$	9.44975	+	16.3674i	0.326826	+	0.566080i
$837$	4.24264	+	7.34847i	0.146647	+	0.254000i
$838$	11.7279	−	20.3134i	0.405134	−	0.701713i
$839$	−26.1716			−0.903543			−0.451772	−	0.892134i	$-0.649208\pi$
$839$	−26.1716			−0.903543			−0.451772	+	0.892134i	$0.649208\pi$
$840$	−8.94975	−	1.22474i	−0.308796	−	0.0422577i
$841$	−14.3431			−0.494591
$842$	6.53553	−	11.3199i	0.225229	−	0.390109i
$843$	11.6569	+	20.1903i	0.401483	+	0.695390i
$844$	13.5355	+	23.4442i	0.465912	+	0.806984i
$845$	1.70711	−	2.95680i	0.0587263	−	0.101717i
$846$	1.00000			0.0343807
$847$	−8.38478	+	10.8126i	−0.288104	+	0.371524i
$848$	−7.48528			−0.257046
$849$	−12.1213	+	20.9947i	−0.416003	+	0.720538i
$850$	−1.37868	−	2.38794i	−0.0472883	−	0.0819058i
$851$	−1.00000	−	1.73205i	−0.0342796	−	0.0593739i
$852$	−2.50000	+	4.33013i	−0.0856486	+	0.148348i
$853$	−18.7279			−0.641232			−0.320616	−	0.947209i	$-0.603890\pi$
$853$	−18.7279			−0.641232			−0.320616	+	0.947209i	$0.603890\pi$
$854$	−1.58579	−	3.88437i	−0.0542645	−	0.132920i
$855$	26.7279			0.914076
$856$	−1.65685	+	2.86976i	−0.0566301	+	0.0980862i
$857$	5.27817	+	9.14207i	0.180299	+	0.312287i	0.941982	−	0.335662i	$-0.108960\pi$
$857$	5.27817	+	9.14207i	0.180299	+	0.312287i	−0.761683	+	0.647949i	$0.775627\pi$
$858$	1.20711	+	2.09077i	0.0412099	+	0.0713777i
$859$	−13.8995	+	24.0746i	−0.474245	+	0.821416i	−0.999565	−	0.0294886i	$-0.990612\pi$
$859$	−13.8995	+	24.0746i	−0.474245	+	0.821416i	0.525320	+	0.850904i	$0.323945\pi$
$860$	35.7990			1.22074
$861$	−9.89949	−	24.2487i	−0.337374	−	0.826394i
$862$	13.5147			0.460313
$863$	−8.34315	+	14.4508i	−0.284004	+	0.491909i	−0.972367	−	0.233457i	$-0.924996\pi$
$863$	−8.34315	+	14.4508i	−0.284004	+	0.491909i	0.688363	+	0.725366i	$0.258330\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−19.6066	−	33.9596i	−0.666644	−	1.15466i
$866$	1.98528	−	3.43861i	0.0674626	−	0.116849i
$867$	16.8284			0.571523
$868$	13.7574	−	17.7408i	0.466955	−	0.602161i
$869$	−0.828427			−0.0281025
$870$	−6.53553	+	11.3199i	−0.221575	+	0.383780i
$871$	1.91421	+	3.31552i	0.0648607	+	0.112342i
$872$	−0.828427	−	1.43488i	−0.0280541	−	0.0485911i
$873$	7.53553	−	13.0519i	0.255039	−	0.441741i
$874$	11.0711			0.374484
$875$	14.8284	+	2.02922i	0.501292	+	0.0686003i
$876$	1.41421			0.0477818
$877$	−4.02082	+	6.96426i	−0.135773	+	0.235166i	−0.925893	−	0.377787i	$-0.876685\pi$
$877$	−4.02082	+	6.96426i	−0.135773	+	0.235166i	0.790119	+	0.612953i	$0.210019\pi$
$878$	−9.70711	−	16.8132i	−0.327599	−	0.567418i
$879$	4.94975	+	8.57321i	0.166951	+	0.289167i
$880$	4.12132	−	7.13834i	0.138930	−	0.240633i
$881$	1.51472			0.0510322			0.0255161	−	0.999674i	$-0.491877\pi$
$881$	1.51472			0.0510322			0.0255161	+	0.999674i	$0.491877\pi$
$882$	−1.74264	−	6.77962i	−0.0586778	−	0.228282i
$883$	−18.2426			−0.613914			−0.306957	−	0.951723i	$-0.599311\pi$
$883$	−18.2426			−0.613914			−0.306957	+	0.951723i	$0.599311\pi$
$884$	−0.207107	+	0.358719i	−0.00696575	+	0.0120650i
$885$	20.6066	+	35.6917i	0.692683	+	1.19976i
$886$	−12.8492	−	22.2555i	−0.431679	−	0.747690i
$887$	26.4558	−	45.8229i	0.888300	−	1.53858i	0.0464167	−	0.998922i	$-0.485220\pi$
$887$	26.4558	−	45.8229i	0.888300	−	1.53858i	0.841884	−	0.539659i	$-0.181447\pi$
$888$	1.41421			0.0474579
$889$	−31.1924	−	4.26858i	−1.04616	−	0.143164i
$890$	−18.4853			−0.619628
$891$	−1.20711	+	2.09077i	−0.0404396	+	0.0700434i
$892$	11.0355	+	19.1141i	0.369497	+	0.639988i
$893$	3.91421	+	6.77962i	0.130984	+	0.226871i
$894$	−9.53553	+	16.5160i	−0.318916	+	0.552379i
$895$	−28.4853			−0.952158
$896$	1.62132	−	2.09077i	0.0541645	−	0.0698477i
$897$	1.41421			0.0472192
$898$	4.48528	−	7.76874i	0.149676	−	0.259246i
$899$	−16.2426	−	28.1331i	−0.541722	−	0.938291i
$900$	−3.32843	−	5.76500i	−0.110948	−	0.192167i
$901$	1.55025	−	2.68512i	0.0516464	−	0.0894542i
$902$	23.8995			0.795766
$903$	10.4853	+	25.6836i	0.348928	+	0.854696i
$904$	−14.8995			−0.495550
$905$	−28.8492	+	49.9684i	−0.958981	+	1.66100i
$906$	−5.03553	−	8.72180i	−0.167294	−	0.289762i
$907$	−8.80761	−	15.2552i	−0.292452	−	0.506542i	0.681937	−	0.731411i	$-0.261138\pi$
$907$	−8.80761	−	15.2552i	−0.292452	−	0.506542i	−0.974389	+	0.224869i	$0.927804\pi$
$908$	13.4142	−	23.2341i	0.445166	−	0.771051i
$909$	−9.17157			−0.304202
$910$	−3.41421	−	8.36308i	−0.113180	−	0.277233i
$911$	−15.6569			−0.518735			−0.259367	−	0.965779i	$-0.583514\pi$
$911$	−15.6569			−0.518735			−0.259367	+	0.965779i	$0.583514\pi$
$912$	−3.91421	+	6.77962i	−0.129613	+	0.224496i
$913$	4.41421	+	7.64564i	0.146089	+	0.253034i
$914$	−5.53553	−	9.58783i	−0.183099	−	0.317137i
$915$	2.70711	−	4.68885i	0.0894942	−	0.155008i
$916$	9.51472			0.314375
$917$	34.9497	−	45.0694i	1.15414	−	1.48832i
$918$	−0.414214			−0.0136711
$919$	18.8995	−	32.7349i	0.623437	−	1.07982i	−0.365404	−	0.930849i	$-0.619069\pi$
$919$	18.8995	−	32.7349i	0.623437	−	1.07982i	0.988841	−	0.148975i	$-0.0475975\pi$
$920$	−2.41421	−	4.18154i	−0.0795943	−	0.137861i
$921$	17.0563	+	29.5425i	0.562026	+	0.973457i
$922$	−6.24264	+	10.8126i	−0.205590	+	0.356093i
$923$	−5.00000			−0.164577
$924$	6.32843	+	0.866025i	0.208190	+	0.0284901i
$925$	−9.41421			−0.309537
$926$	−6.48528	+	11.2328i	−0.213120	+	0.369134i
$927$	5.58579	+	9.67487i	0.183461	+	0.317764i
$928$	−1.91421	−	3.31552i	−0.0628371	−	0.108837i
$929$	−28.6569	+	49.6351i	−0.940201	+	1.62848i	−0.175114	+	0.984548i	$0.556030\pi$
$929$	−28.6569	+	49.6351i	−0.940201	+	1.62848i	−0.765086	+	0.643928i	$0.777304\pi$
$930$	28.9706			0.949982
$931$	39.1421	−	38.3513i	1.28283	−	1.25691i
$932$	7.72792			0.253137
$933$	−13.9497	+	24.1617i	−0.456694	+	0.791018i
$934$	4.29289	+	7.43551i	0.140468	+	0.243297i
$935$	1.70711	+	2.95680i	0.0558284	+	0.0966976i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	31.3431			1.02394			0.511968	−	0.859005i	$-0.328917\pi$
$937$	31.3431			1.02394			0.511968	+	0.859005i	$0.328917\pi$
$938$	10.0355	+	1.37333i	0.327672	+	0.0448409i
$939$	−20.4853			−0.668512
$940$	1.70711	−	2.95680i	0.0556797	−	0.0964400i
$941$	−10.4853	−	18.1610i	−0.341810	−	0.592033i	0.642959	−	0.765901i	$-0.277707\pi$
$941$	−10.4853	−	18.1610i	−0.341810	−	0.592033i	−0.984769	+	0.173868i	$0.944373\pi$
$942$	−7.86396	−	13.6208i	−0.256222	−	0.443789i
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	−12.0711			−0.392880
$945$	5.53553	−	7.13834i	0.180071	−	0.232210i
$946$	−25.3137			−0.823020
$947$	−2.79289	+	4.83743i	−0.0907568	+	0.157195i	−0.907830	−	0.419339i	$-0.862262\pi$
$947$	−2.79289	+	4.83743i	−0.0907568	+	0.157195i	0.817073	+	0.576534i	$0.195595\pi$
$948$	−0.171573	−	0.297173i	−0.00557243	−	0.00965173i
$949$	0.707107	+	1.22474i	0.0229537	+	0.0397569i
$950$	26.0563	−	45.1309i	0.845380	−	1.46424i
$951$	9.79899			0.317754
$952$	0.414214	+	1.01461i	0.0134247	+	0.0328838i
$953$	−44.4142			−1.43872			−0.719359	−	0.694639i	$-0.755564\pi$
$953$	−44.4142			−1.43872			−0.719359	+	0.694639i	$0.755564\pi$
$954$	3.74264	−	6.48244i	0.121172	−	0.209877i
$955$	−36.9706	−	64.0349i	−1.19634	−	2.07212i
$956$	−10.7426	−	18.6068i	−0.347442	−	0.601787i
$957$	4.62132	−	8.00436i	0.149386	−	0.258744i
$958$	30.1127			0.972897
$959$	−3.07107	−	7.52255i	−0.0991700	−	0.242916i
$960$	3.41421			0.110193
$961$	−20.5000	+	35.5070i	−0.661290	+	1.14539i
$962$	0.707107	+	1.22474i	0.0227980	+	0.0394874i
$963$	−1.65685	−	2.86976i	−0.0533914	−	0.0924766i
$964$	−13.0711	+	22.6398i	−0.420991	+	0.729177i
$965$	58.2843			1.87624
$966$	2.29289	−	2.95680i	0.0737726	−	0.0951333i
$967$	−16.4142			−0.527846			−0.263923	−	0.964544i	$-0.585016\pi$
$967$	−16.4142			−0.527846			−0.263923	+	0.964544i	$0.585016\pi$
$968$	2.58579	−	4.47871i	0.0831103	−	0.143951i
$969$	−1.62132	−	2.80821i	−0.0520843	−	0.0902127i
$970$	−25.7279	−	44.5621i	−0.826074	−	1.43080i
$971$	−16.2635	+	28.1691i	−0.521919	+	0.903990i	0.477756	+	0.878493i	$0.341450\pi$
$971$	−16.2635	+	28.1691i	−0.521919	+	0.903990i	−0.999675	+	0.0254978i	$0.991883\pi$
$972$	−1.00000			−0.0320750
$973$	−2.80761	−	0.384213i	−0.0900079	−	0.0123173i
$974$	−26.2132			−0.839925
$975$	3.32843	−	5.76500i	0.106595	−	0.184628i
$976$	0.792893	+	1.37333i	0.0253799	+	0.0439593i
$977$	−24.4142	−	42.2867i	−0.781080	−	1.35287i	−0.931313	−	0.364219i	$-0.881336\pi$
$977$	−24.4142	−	42.2867i	−0.781080	−	1.35287i	0.150233	−	0.988651i	$-0.451998\pi$
$978$	−3.67157	+	6.35935i	−0.117404	+	0.203350i
$979$	13.0711			0.417753
$980$	−23.0208	−	6.42090i	−0.735373	−	0.205108i
$981$	1.65685			0.0528993
$982$	−6.17157	+	10.6895i	−0.196943	+	0.341115i
$983$	6.25736	+	10.8381i	0.199579	+	0.345681i	0.948392	−	0.317101i	$-0.102709\pi$
$983$	6.25736	+	10.8381i	0.199579	+	0.345681i	−0.748813	+	0.662781i	$0.769376\pi$
$984$	4.94975	+	8.57321i	0.157792	+	0.273304i
$985$	26.5563	−	45.9969i	0.846156	−	1.46558i
$986$	1.58579			0.0505017
$987$	2.62132	+	0.358719i	0.0834375	+	0.0114182i
$988$	−7.82843			−0.249055
$989$	−7.41421	+	12.8418i	−0.235758	+	0.408345i
$990$	4.12132	+	7.13834i	0.130984	+	0.226871i
$991$	11.6569	+	20.1903i	0.370292	+	0.641365i	0.989610	−	0.143775i	$-0.0459242\pi$
$991$	11.6569	+	20.1903i	0.370292	+	0.641365i	−0.619318	+	0.785140i	$0.712591\pi$
$992$	−4.24264	+	7.34847i	−0.134704	+	0.233314i
$993$	5.51472			0.175004
$994$	−8.10660	+	10.4539i	−0.257126	+	0.331576i
$995$	77.5980			2.46002
$996$	−1.82843	+	3.16693i	−0.0579359	+	0.100348i
$997$	23.2487	+	40.2680i	0.736295	+	1.27530i	0.954153	+	0.299320i	$0.0967597\pi$
$997$	23.2487	+	40.2680i	0.736295	+	1.27530i	−0.217858	+	0.975980i	$0.569907\pi$
$998$	3.82843	+	6.63103i	0.121187	+	0.209902i
$999$	−0.707107	+	1.22474i	−0.0223719	+	0.0387492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.i.79.2	✓	4
3.2	odd	2		1638.2.j.m.1171.1		4
7.2	even	3		3822.2.a.bn.1.1		2
7.4	even	3	inner	546.2.i.i.235.2	yes	4
7.5	odd	6		3822.2.a.bu.1.2		2
21.11	odd	6		1638.2.j.m.235.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.i.79.2	✓	4	1.1	even	1	trivial
546.2.i.i.235.2	yes	4	7.4	even	3	inner
1638.2.j.m.235.1		4	21.11	odd	6
1638.2.j.m.1171.1		4	3.2	odd	2
3822.2.a.bn.1.1		2	7.2	even	3
3822.2.a.bu.1.2		2	7.5	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.70711 - 2.95680i) q^{5} -1.00000 q^{6} +(-2.62132 - 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.70711 + 2.95680i) q^{10} +(-1.20711 - 2.09077i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(1.62132 - 2.09077i) q^{14} +3.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.207107 - 0.358719i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.91421 - 6.77962i) q^{19} -3.41421 q^{20} +(-1.00000 - 2.44949i) q^{21} +2.41421 q^{22} +(0.707107 - 1.22474i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.32843 - 5.76500i) q^{25} +(-0.500000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 2.44949i) q^{28} +3.82843 q^{29} +(-1.70711 + 2.95680i) q^{30} +(-4.24264 - 7.34847i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.20711 - 2.09077i) q^{33} +0.414214 q^{34} +(-5.53553 + 7.13834i) q^{35} +1.00000 q^{36} +(0.707107 - 1.22474i) q^{37} +(3.91421 + 6.77962i) q^{38} +(0.500000 + 0.866025i) q^{39} +(1.70711 - 2.95680i) q^{40} +9.89949 q^{41} +(2.62132 + 0.358719i) q^{42} -10.4853 q^{43} +(-1.20711 + 2.09077i) q^{44} +(1.70711 + 2.95680i) q^{45} +(0.707107 + 1.22474i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000 q^{48} +(6.74264 + 1.88064i) q^{49} +6.65685 q^{50} +(0.207107 - 0.358719i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(3.74264 + 6.48244i) q^{53} +(0.500000 - 0.866025i) q^{54} -8.24264 q^{55} +(-2.62132 - 0.358719i) q^{56} +7.82843 q^{57} +(-1.91421 + 3.31552i) q^{58} +(6.03553 + 10.4539i) q^{59} +(-1.70711 - 2.95680i) q^{60} +(0.792893 - 1.37333i) q^{61} +8.48528 q^{62} +(1.62132 - 2.09077i) q^{63} +1.00000 q^{64} +(1.70711 - 2.95680i) q^{65} +(1.20711 + 2.09077i) q^{66} +(1.91421 + 3.31552i) q^{67} +(-0.207107 + 0.358719i) q^{68} +1.41421 q^{69} +(-3.41421 - 8.36308i) q^{70} -5.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(0.707107 + 1.22474i) q^{73} +(0.707107 + 1.22474i) q^{74} +(3.32843 - 5.76500i) q^{75} -7.82843 q^{76} +(2.41421 + 5.91359i) q^{77} -1.00000 q^{78} +(0.171573 - 0.297173i) q^{79} +(1.70711 + 2.95680i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.94975 + 8.57321i) q^{82} -3.65685 q^{83} +(-1.62132 + 2.09077i) q^{84} -1.41421 q^{85} +(5.24264 - 9.08052i) q^{86} +(1.91421 + 3.31552i) q^{87} +(-1.20711 - 2.09077i) q^{88} +(-2.70711 + 4.68885i) q^{89} -3.41421 q^{90} +(-2.62132 - 0.358719i) q^{91} -1.41421 q^{92} +(4.24264 - 7.34847i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-13.3640 - 23.1471i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.0711 q^{97} +(-5.00000 + 4.89898i) q^{98} +2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 2 q^{24} - 2 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{32} + 2 q^{33} - 4 q^{34} - 8 q^{35} + 4 q^{36} + 10 q^{38} + 2 q^{39} + 4 q^{40} + 2 q^{42} - 8 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} - 2 q^{51} - 2 q^{52} - 2 q^{53} + 2 q^{54} - 16 q^{55} - 2 q^{56} + 20 q^{57} - 2 q^{58} + 10 q^{59} - 4 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} + 2 q^{67} + 2 q^{68} - 8 q^{70} - 20 q^{71} - 2 q^{72} + 2 q^{75} - 20 q^{76} + 4 q^{77} - 4 q^{78} + 12 q^{79} + 4 q^{80} - 2 q^{81} + 8 q^{83} + 2 q^{84} + 4 q^{86} + 2 q^{87} - 2 q^{88} - 8 q^{89} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 28 q^{95} + 2 q^{96} - 32 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^17 - 2 * q^18 + 10 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 2 * q^24 - 2 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^32 + 2 * q^33 - 4 * q^34 - 8 * q^35 + 4 * q^36 + 10 * q^38 + 2 * q^39 + 4 * q^40 + 2 * q^42 - 8 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 2 * q^54 - 16 * q^55 - 2 * q^56 + 20 * q^57 - 2 * q^58 + 10 * q^59 - 4 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 + 2 * q^67 + 2 * q^68 - 8 * q^70 - 20 * q^71 - 2 * q^72 + 2 * q^75 - 20 * q^76 + 4 * q^77 - 4 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 + 8 * q^83 + 2 * q^84 + 4 * q^86 + 2 * q^87 - 2 * q^88 - 8 * q^89 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 28 * q^95 + 2 * q^96 - 32 * q^97 - 20 * q^98 + 4 * q^99

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