LMFDB - Embedded newform 280.2.bl.b.221.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(221,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("280.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bl (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			221.7
Character	$\chi$	$=$	280.221
Dual form			280.2.bl.b.261.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02369 - 0.975735i) q^{2} +(-0.992927 - 0.573266i) q^{3} +(0.0958836 + 1.99770i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.457093 + 1.55568i) q^{6} +(2.64418 + 0.0910290i) q^{7} +(1.85107 - 2.13858i) q^{8} +(-0.842731 - 1.45965i) q^{9} +O(q^{10})$	\(q+(-1.02369 - 0.975735i) q^{2} +(-0.992927 - 0.573266i) q^{3} +(0.0958836 + 1.99770i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.457093 + 1.55568i) q^{6} +(2.64418 + 0.0910290i) q^{7} +(1.85107 - 2.13858i) q^{8} +(-0.842731 - 1.45965i) q^{9} +(1.37441 + 0.333166i) q^{10} +(-1.35435 - 0.781932i) q^{11} +(1.05001 - 2.03854i) q^{12} -3.73272i q^{13} +(-2.61801 - 2.67321i) q^{14} +1.14653 q^{15} +(-3.98161 + 0.383093i) q^{16} +(1.82061 - 3.15340i) q^{17} +(-0.561539 + 2.31651i) q^{18} +(-3.59115 + 2.07335i) q^{19} +(-1.08189 - 1.68212i) q^{20} +(-2.57330 - 1.60621i) q^{21} +(0.623472 + 2.12194i) q^{22} +(-3.41892 - 5.92174i) q^{23} +(-3.06396 + 1.06230i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.64215 + 3.82115i) q^{26} +5.37204i q^{27} +(0.0716851 + 5.29102i) q^{28} -7.01871i q^{29} +(-1.17369 - 1.11871i) q^{30} +(-1.95368 + 3.38388i) q^{31} +(4.44974 + 3.49283i) q^{32} +(0.896511 + 1.55280i) q^{33} +(-4.94062 + 1.45166i) q^{34} +(-2.33545 + 1.24326i) q^{35} +(2.83515 - 1.82348i) q^{36} +(7.74580 - 4.47204i) q^{37} +(5.69927 + 1.38154i) q^{38} +(-2.13985 + 3.70632i) q^{39} +(-0.533782 + 2.77760i) q^{40} -3.61472 q^{41} +(1.06703 + 4.15511i) q^{42} -4.48787i q^{43} +(1.43221 - 2.78055i) q^{44} +(1.45965 + 0.842731i) q^{45} +(-2.27813 + 9.39798i) q^{46} +(-2.03371 - 3.52249i) q^{47} +(4.17306 + 1.90214i) q^{48} +(6.98343 + 0.481395i) q^{49} +(-1.35686 + 0.398674i) q^{50} +(-3.61547 + 2.08739i) q^{51} +(7.45686 - 0.357907i) q^{52} +(-5.16597 - 2.98258i) q^{53} +(5.24168 - 5.49930i) q^{54} +1.56386 q^{55} +(5.08925 - 5.48631i) q^{56} +4.75434 q^{57} +(-6.84840 + 7.18498i) q^{58} +(0.485737 + 0.280440i) q^{59} +(0.109934 + 2.29043i) q^{60} +(8.36260 - 4.82815i) q^{61} +(5.30173 - 1.55777i) q^{62} +(-2.09547 - 3.93631i) q^{63} +(-1.14708 - 7.91734i) q^{64} +(1.86636 + 3.23263i) q^{65} +(0.597374 - 2.46434i) q^{66} +(9.87337 + 5.70039i) q^{67} +(6.47411 + 3.33468i) q^{68} +7.83980i q^{69} +(3.60386 + 1.00606i) q^{70} +5.31558 q^{71} +(-4.68154 - 0.899670i) q^{72} +(-6.36488 + 11.0243i) q^{73} +(-12.2928 - 2.97986i) q^{74} +(-0.992927 + 0.573266i) q^{75} +(-4.48627 - 6.97525i) q^{76} +(-3.50996 - 2.19086i) q^{77} +(5.80693 - 1.70620i) q^{78} +(6.67016 + 11.5530i) q^{79} +(3.25663 - 2.32257i) q^{80} +(0.551415 - 0.955078i) q^{81} +(3.70035 + 3.52700i) q^{82} +9.30425i q^{83} +(2.96198 - 5.29469i) q^{84} +3.64123i q^{85} +(-4.37897 + 4.59419i) q^{86} +(-4.02359 + 6.96906i) q^{87} +(-4.17922 + 1.44897i) q^{88} +(4.10788 + 7.11506i) q^{89} +(-0.671951 - 2.28693i) q^{90} +(0.339786 - 9.87001i) q^{91} +(11.5020 - 7.39777i) q^{92} +(3.87973 - 2.23996i) q^{93} +(-1.35512 + 5.59029i) q^{94} +(2.07335 - 3.59115i) q^{95} +(-2.41594 - 6.01901i) q^{96} -9.13070 q^{97} +(-6.67915 - 7.30677i) q^{98} +2.63583i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9}+O(q^{10}) $ 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9	$ 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9} + 2 q^{10} - 10 q^{12} + 20 q^{14} - 22 q^{16} - 12 q^{17} + 6 q^{18} - 16 q^{20} - 28 q^{22} - 2 q^{23} - 32 q^{24} + 30 q^{25} - 4 q^{26} - 22 q^{28} - 6 q^{32} - 16 q^{34} + 20 q^{36} - 42 q^{38} + 4 q^{40} - 36 q^{41} - 62 q^{42} + 14 q^{44} + 28 q^{46} - 30 q^{47} + 124 q^{48} + 12 q^{49} + 8 q^{50} + 8 q^{52} - 40 q^{54} - 44 q^{55} + 8 q^{56} - 32 q^{57} - 14 q^{58} + 14 q^{60} - 16 q^{62} - 74 q^{63} + 4 q^{64} + 2 q^{65} + 60 q^{66} + 28 q^{68} + 10 q^{70} - 8 q^{71} - 72 q^{72} - 52 q^{74} - 12 q^{76} - 40 q^{78} + 32 q^{79} - 22 q^{81} - 16 q^{82} - 8 q^{84} - 44 q^{86} + 48 q^{87} - 16 q^{88} + 4 q^{89} - 48 q^{90} + 84 q^{92} - 56 q^{94} + 2 q^{95} - 16 q^{96} - 96 q^{97} - 80 q^{98}+O(q^{100}) $ 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9 + 2 * q^10 - 10 * q^12 + 20 * q^14 - 22 * q^16 - 12 * q^17 + 6 * q^18 - 16 * q^20 - 28 * q^22 - 2 * q^23 - 32 * q^24 + 30 * q^25 - 4 * q^26 - 22 * q^28 - 6 * q^32 - 16 * q^34 + 20 * q^36 - 42 * q^38 + 4 * q^40 - 36 * q^41 - 62 * q^42 + 14 * q^44 + 28 * q^46 - 30 * q^47 + 124 * q^48 + 12 * q^49 + 8 * q^50 + 8 * q^52 - 40 * q^54 - 44 * q^55 + 8 * q^56 - 32 * q^57 - 14 * q^58 + 14 * q^60 - 16 * q^62 - 74 * q^63 + 4 * q^64 + 2 * q^65 + 60 * q^66 + 28 * q^68 + 10 * q^70 - 8 * q^71 - 72 * q^72 - 52 * q^74 - 12 * q^76 - 40 * q^78 + 32 * q^79 - 22 * q^81 - 16 * q^82 - 8 * q^84 - 44 * q^86 + 48 * q^87 - 16 * q^88 + 4 * q^89 - 48 * q^90 + 84 * q^92 - 56 * q^94 + 2 * q^95 - 16 * q^96 - 96 * q^97 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.02369	−	0.975735i	−0.723858	−	0.689949i
$2$	−1.02369	−	0.975735i	−0.723858	−	0.689949i
$3$	−0.992927	−	0.573266i	−0.573266	−	0.330976i	0.185186	−	0.982703i	$-0.440711\pi$
$3$	−0.992927	−	0.573266i	−0.573266	−	0.330976i	−0.758453	+	0.651728i	$0.774044\pi$
$4$	0.0958836	+	1.99770i	0.0479418	+	0.998850i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	0.457093	+	1.55568i	0.186608	+	0.635104i
$7$	2.64418	+	0.0910290i	0.999408	+	0.0344057i
$7$	2.64418	+	0.0910290i	0.999408	+	0.0344057i
$8$	1.85107	−	2.13858i	0.654452	−	0.756103i
$9$	−0.842731	−	1.45965i	−0.280910	−	0.486551i
$10$	1.37441	+	0.333166i	0.434626	+	0.105356i
$11$	−1.35435	−	0.781932i	−0.408351	−	0.235761i	0.281730	−	0.959494i	$-0.409092\pi$
$11$	−1.35435	−	0.781932i	−0.408351	−	0.235761i	−0.690081	+	0.723732i	$0.742425\pi$
$12$	1.05001	−	2.03854i	0.303112	−	0.588475i
$13$		−	3.73272i		−	1.03527i	−0.855601	−	0.517636i	$-0.826812\pi$
$13$		−	3.73272i		−	1.03527i	0.855601	−	0.517636i	$-0.173188\pi$
$14$	−2.61801	−	2.67321i	−0.699692	−	0.714445i
$15$	1.14653			0.296034
$16$	−3.98161	+	0.383093i	−0.995403	+	0.0957733i
$17$	1.82061	−	3.15340i	0.441564	−	0.764811i	−0.556242	−	0.831020i	$-0.687757\pi$
$17$	1.82061	−	3.15340i	0.441564	−	0.764811i	0.997806	+	0.0662095i	$0.0210906\pi$
$18$	−0.561539	+	2.31651i	−0.132356	+	0.546008i
$19$	−3.59115	+	2.07335i	−0.823867	+	0.475660i	−0.851748	−	0.523951i	$-0.824457\pi$
$19$	−3.59115	+	2.07335i	−0.823867	+	0.475660i	0.0278809	+	0.999611i	$0.491124\pi$
$20$	−1.08189	−	1.68212i	−0.241917	−	0.376133i
$21$	−2.57330	−	1.60621i	−0.561540	−	0.350503i
$22$	0.623472	+	2.12194i	0.132925	+	0.452399i
$23$	−3.41892	−	5.92174i	−0.712893	−	1.23477i	−0.963766	−	0.266747i	$-0.914051\pi$
$23$	−3.41892	−	5.92174i	−0.712893	−	1.23477i	0.250873	−	0.968020i	$-0.419282\pi$
$24$	−3.06396	+	1.06230i	−0.625427	+	0.216841i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−3.64215	+	3.82115i	−0.714284	+	0.749390i
$27$			5.37204i			1.03385i
$28$	0.0716851	+	5.29102i	0.0135472	+	0.999908i
$29$		−	7.01871i		−	1.30334i	−0.758502	−	0.651671i	$-0.774068\pi$
$29$		−	7.01871i		−	1.30334i	0.758502	−	0.651671i	$-0.225932\pi$
$30$	−1.17369	−	1.11871i	−0.214286	−	0.204248i
$31$	−1.95368	+	3.38388i	−0.350892	+	0.607762i	−0.986406	−	0.164327i	$-0.947455\pi$
$31$	−1.95368	+	3.38388i	−0.350892	+	0.607762i	0.635514	+	0.772089i	$0.280788\pi$
$32$	4.44974	+	3.49283i	0.786610	+	0.617451i
$33$	0.896511	+	1.55280i	0.156062	+	0.270308i
$34$	−4.94062	+	1.45166i	−0.847310	+	0.248958i
$35$	−2.33545	+	1.24326i	−0.394762	+	0.210149i
$36$	2.83515	−	1.82348i	0.472524	−	0.303914i
$37$	7.74580	−	4.47204i	1.27340	−	0.735199i	0.297775	−	0.954636i	$-0.403755\pi$
$37$	7.74580	−	4.47204i	1.27340	−	0.735199i	0.975627	+	0.219437i	$0.0704222\pi$
$38$	5.69927	+	1.38154i	0.924544	+	0.224116i
$39$	−2.13985	+	3.70632i	−0.342650	+	0.593486i
$40$	−0.533782	+	2.77760i	−0.0843984	+	0.439178i
$41$	−3.61472			−0.564524			−0.282262	−	0.959337i	$-0.591085\pi$
$41$	−3.61472			−0.564524			−0.282262	+	0.959337i	$0.591085\pi$
$42$	1.06703	+	4.15511i	0.164646	+	0.641148i
$43$		−	4.48787i		−	0.684394i	−0.939628	−	0.342197i	$-0.888829\pi$
$43$		−	4.48787i		−	0.684394i	0.939628	−	0.342197i	$-0.111171\pi$
$44$	1.43221	−	2.78055i	0.215913	−	0.419184i
$45$	1.45965	+	0.842731i	0.217592	+	0.125627i
$46$	−2.27813	+	9.39798i	−0.335892	+	1.38566i
$47$	−2.03371	−	3.52249i	−0.296647	−	0.513807i	0.678720	−	0.734397i	$-0.262535\pi$
$47$	−2.03371	−	3.52249i	−0.296647	−	0.513807i	−0.975367	+	0.220590i	$0.929202\pi$
$48$	4.17306	+	1.90214i	0.602330	+	0.274550i
$49$	6.98343	+	0.481395i	0.997632	+	0.0687708i
$50$	−1.35686	+	0.398674i	−0.191888	+	0.0563811i
$51$	−3.61547	+	2.08739i	−0.506267	+	0.292294i
$52$	7.45686	−	0.357907i	1.03408	−	0.0496327i
$53$	−5.16597	−	2.98258i	−0.709601	−	0.409688i	0.101312	−	0.994855i	$-0.467696\pi$
$53$	−5.16597	−	2.98258i	−0.709601	−	0.409688i	−0.810913	+	0.585166i	$0.801029\pi$
$54$	5.24168	−	5.49930i	0.713303	−	0.748360i
$55$	1.56386			0.210871
$56$	5.08925	−	5.48631i	0.680079	−	0.733139i
$57$	4.75434			0.629727
$58$	−6.84840	+	7.18498i	−0.899239	+	0.943435i
$59$	0.485737	+	0.280440i	0.0632376	+	0.0365102i	0.531285	−	0.847193i	$-0.321709\pi$
$59$	0.485737	+	0.280440i	0.0632376	+	0.0365102i	−0.468048	+	0.883703i	$0.655043\pi$
$60$	0.109934	+	2.29043i	0.0141924	+	0.295693i
$61$	8.36260	−	4.82815i	1.07072	−	0.618181i	0.142343	−	0.989817i	$-0.454537\pi$
$61$	8.36260	−	4.82815i	1.07072	−	0.618181i	0.928378	+	0.371636i	$0.121203\pi$
$62$	5.30173	−	1.55777i	0.673321	−	0.197837i
$63$	−2.09547	−	3.93631i	−0.264004	−	0.495928i
$64$	−1.14708	−	7.91734i	−0.143385	−	0.989667i
$65$	1.86636	+	3.23263i	0.231494	+	0.400959i
$66$	0.597374	−	2.46434i	0.0735316	−	0.303340i
$67$	9.87337	+	5.70039i	1.20622	+	0.696414i	0.961932	−	0.273288i	$-0.0881111\pi$
$67$	9.87337	+	5.70039i	1.20622	+	0.696414i	0.244292	+	0.969702i	$0.421444\pi$
$68$	6.47411	+	3.33468i	0.785101	+	0.404390i
$69$			7.83980i			0.943801i
$70$	3.60386	+	1.00606i	0.430744	+	0.120248i
$71$	5.31558			0.630843			0.315422	−	0.948952i	$-0.397854\pi$
$71$	5.31558			0.630843			0.315422	+	0.948952i	$0.397854\pi$
$72$	−4.68154	−	0.899670i	−0.551725	−	0.106027i
$73$	−6.36488	+	11.0243i	−0.744952	+	1.29030i	0.205265	+	0.978706i	$0.434194\pi$
$73$	−6.36488	+	11.0243i	−0.744952	+	1.29030i	−0.950217	+	0.311589i	$0.899139\pi$
$74$	−12.2928	−	2.97986i	−1.42901	−	0.346402i
$75$	−0.992927	+	0.573266i	−0.114653	+	0.0661951i
$76$	−4.48627	−	6.97525i	−0.514611	−	0.800116i
$77$	−3.50996	−	2.19086i	−0.399997	−	0.249671i
$78$	5.80693	−	1.70620i	0.657505	−	0.193189i
$79$	6.67016	+	11.5530i	0.750451	+	1.29982i	0.947604	+	0.319447i	$0.103497\pi$
$79$	6.67016	+	11.5530i	0.750451	+	1.29982i	−0.197153	+	0.980373i	$0.563170\pi$
$80$	3.25663	−	2.32257i	0.364102	−	0.259672i
$81$	0.551415	−	0.955078i	0.0612683	−	0.106120i
$82$	3.70035	+	3.52700i	0.408635	+	0.389492i
$83$			9.30425i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$83$			9.30425i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$84$	2.96198	−	5.29469i	0.323179	−	0.577698i
$85$			3.64123i			0.394947i
$86$	−4.37897	+	4.59419i	−0.472197	+	0.495404i
$87$	−4.02359	+	6.96906i	−0.431374	+	0.747162i
$88$	−4.17922	+	1.44897i	−0.445506	+	0.154461i
$89$	4.10788	+	7.11506i	0.435435	+	0.754195i	0.997331	−	0.0730125i	$-0.0232613\pi$
$89$	4.10788	+	7.11506i	0.435435	+	0.754195i	−0.561896	+	0.827208i	$0.689928\pi$
$90$	−0.671951	−	2.28693i	−0.0708298	−	0.241064i
$91$	0.339786	−	9.87001i	0.0356193	−	1.03466i
$92$	11.5020	−	7.39777i	1.19917	−	0.771270i
$93$	3.87973	−	2.23996i	0.402309	−	0.232273i
$94$	−1.35512	+	5.59029i	−0.139770	+	0.576595i
$95$	2.07335	−	3.59115i	0.212722	−	0.368445i
$96$	−2.41594	−	6.01901i	−0.246576	−	0.614312i
$97$	−9.13070			−0.927082			−0.463541	−	0.886076i	$-0.653421\pi$
$97$	−9.13070			−0.927082			−0.463541	+	0.886076i	$0.653421\pi$
$98$	−6.67915	−	7.30677i	−0.674696	−	0.738095i
$99$			2.63583i			0.264911i
$100$	1.77800	+	0.915813i	0.177800	+	0.0915813i
$101$	13.1837	+	7.61159i	1.31182	+	0.757381i	0.982398	−	0.186801i	$-0.0598118\pi$
$101$	13.1837	+	7.61159i	1.31182	+	0.757381i	0.329425	+	0.944182i	$0.393145\pi$
$102$	5.73787	+	1.39090i	0.568133	+	0.137719i
$103$	−7.92571	−	13.7277i	−0.780943	−	1.35263i	−0.931393	−	0.364016i	$-0.881405\pi$
$103$	−7.92571	−	13.7277i	−0.780943	−	1.35263i	0.150449	−	0.988618i	$-0.451928\pi$
$104$	−7.98274	−	6.90954i	−0.782772	−	0.677536i
$105$	3.03164	+	0.104368i	0.295858	+	0.0101853i
$106$	2.37815	+	8.09385i	0.230987	+	0.786145i
$107$	−1.29502	+	0.747682i	−0.125195	+	0.0722811i	−0.561289	−	0.827620i	$-0.689695\pi$
$107$	−1.29502	+	0.747682i	−0.125195	+	0.0722811i	0.436095	+	0.899901i	$0.356361\pi$
$108$	−10.7317	+	0.515090i	−1.03266	+	0.0495646i
$109$	−7.61218	−	4.39490i	−0.729115	−	0.420955i	0.0889833	−	0.996033i	$-0.471638\pi$
$109$	−7.61218	−	4.39490i	−0.729115	−	0.420955i	−0.818098	+	0.575078i	$0.804972\pi$
$110$	−1.60091	−	1.52592i	−0.152641	−	0.145490i
$111$	−10.2547			−0.973331
$112$	−10.5630	+	0.650527i	−0.998109	+	0.0614690i
$113$	−5.11335			−0.481023			−0.240512	−	0.970646i	$-0.577315\pi$
$113$	−5.11335			−0.481023			−0.240512	+	0.970646i	$0.577315\pi$
$114$	−4.86697	−	4.63897i	−0.455833	−	0.434480i
$115$	5.92174	+	3.41892i	0.552205	+	0.318816i
$116$	14.0213	−	0.672979i	1.30184	−	0.0624845i
$117$	−5.44848	+	3.14568i	−0.503712	+	0.290819i
$118$	−0.223609	−	0.761034i	−0.0205849	−	0.0700589i
$119$	5.10109	−	8.17243i	0.467616	−	0.749166i
$120$	2.12231	−	2.45196i	0.193740	−	0.223832i
$121$	−4.27717	−	7.40827i	−0.388833	−	0.673479i
$122$	−13.2717	−	3.21715i	−1.20156	−	0.291267i
$123$	3.58915	+	2.07219i	0.323622	+	0.186844i
$124$	−6.94730	−	3.57841i	−0.623886	−	0.321351i
$125$			1.00000i			0.0894427i
$126$	−1.69568	+	6.07418i	−0.151063	+	0.541131i
$127$	3.58772			0.318359			0.159180	−	0.987250i	$-0.449115\pi$
$127$	3.58772			0.318359			0.159180	+	0.987250i	$0.449115\pi$
$128$	−6.55097	+	9.22414i	−0.579029	+	0.815307i
$129$	−2.57275	+	4.45613i	−0.226518	+	0.392340i
$130$	1.24362	−	5.13029i	0.109072	−	0.449956i
$131$	−7.15175	+	4.12906i	−0.624851	+	0.360758i	−0.778755	−	0.627328i	$-0.784149\pi$
$131$	−7.15175	+	4.12906i	−0.624851	+	0.360758i	0.153904	+	0.988086i	$0.450815\pi$
$132$	−3.01607	+	1.93985i	−0.262515	+	0.168842i
$133$	−9.68441	+	5.15543i	−0.839745	+	0.447033i
$134$	−4.54520	−	15.4692i	−0.392646	−	1.33634i
$135$	−2.68602	−	4.65232i	−0.231176	−	0.400408i
$136$	−3.37371	−	9.73069i	−0.289294	−	0.834400i
$137$	7.45311	−	12.9092i	0.636762	−	1.10290i	−0.349377	−	0.936982i	$-0.613607\pi$
$137$	7.45311	−	12.9092i	0.636762	−	1.10290i	0.986139	−	0.165922i	$-0.0530601\pi$
$138$	7.64956	−	8.02553i	0.651174	−	0.683178i
$139$			17.4883i			1.48334i	0.670767	+	0.741668i	$0.265965\pi$
$139$			17.4883i			1.48334i	−0.670767	+	0.741668i	$0.734035\pi$
$140$	−2.70759	−	4.54631i	−0.228833	−	0.384234i
$141$			4.66343i			0.392731i
$142$	−5.44151	−	5.18660i	−0.456641	−	0.435250i
$143$	−2.91874	+	5.05540i	−0.244077	+	0.422754i
$144$	3.91461	+	5.48893i	0.326218	+	0.457411i
$145$	3.50935	+	6.07838i	0.291436	+	0.504782i
$146$	17.2724	−	5.07503i	1.42948	−	0.420012i
$147$	−6.65806	−	4.48135i	−0.549148	−	0.369616i
$148$	9.67649	+	15.0450i	0.795402	+	1.23669i
$149$	−1.10446	+	0.637661i	−0.0904810	+	0.0522393i	−0.544558	−	0.838723i	$-0.683303\pi$
$149$	−1.10446	+	0.637661i	−0.0904810	+	0.0522393i	0.454077	+	0.890963i	$0.349969\pi$
$150$	1.57581	+	0.381986i	0.128664	+	0.0311890i
$151$	−3.63278	+	6.29216i	−0.295632	+	0.512049i	−0.975132	−	0.221627i	$-0.928863\pi$
$151$	−3.63278	+	6.29216i	−0.295632	+	0.512049i	0.679500	+	0.733675i	$0.262197\pi$
$152$	−2.21344	+	11.5179i	−0.179534	+	0.934226i
$153$	−6.13715			−0.496159
$154$	1.45542	+	5.66755i	0.117281	+	0.456704i
$155$		−	3.90737i		−	0.313847i
$156$	−7.60929	−	3.91939i	−0.609231	−	0.313803i
$157$	0.226539	+	0.130792i	0.0180798	+	0.0104384i	0.509013	−	0.860759i	$-0.330011\pi$
$157$	0.226539	+	0.130792i	0.0180798	+	0.0104384i	−0.490933	+	0.871197i	$0.663344\pi$
$158$	4.44454	−	18.3350i	0.353588	−	1.45866i
$159$	3.41962	+	5.92296i	0.271194	+	0.469721i
$160$	−5.60000	−	0.800011i	−0.442719	−	0.0632464i
$161$	−8.50120	−	15.9694i	−0.669988	−	1.25856i
$162$	−1.49638	+	0.439670i	−0.117567	+	0.0345437i
$163$	14.2783	−	8.24361i	1.11837	−	0.645689i	0.177383	−	0.984142i	$-0.443237\pi$
$163$	14.2783	−	8.24361i	1.11837	−	0.645689i	0.940983	+	0.338453i	$0.109904\pi$
$164$	−0.346592	−	7.22112i	−0.0270643	−	0.563875i
$165$	−1.55280	−	0.896511i	−0.120885	−	0.0697933i
$166$	9.07848	−	9.52467i	0.704627	−	0.739258i
$167$	0.594243			0.0459839			0.0229920	−	0.999736i	$-0.492681\pi$
$167$	0.594243			0.0459839			0.0229920	+	0.999736i	$0.492681\pi$
$168$	−8.19836	+	2.53001i	−0.632517	+	0.195194i
$169$	−0.933230			−0.0717869
$170$	3.55287	−	3.72749i	0.272493	−	0.285885i
$171$	6.05276	+	3.49456i	0.462866	+	0.267236i
$172$	8.96542	−	0.430313i	0.683607	−	0.0328111i
$173$	17.0330	−	9.83400i	1.29499	−	0.747665i	0.315459	−	0.948939i	$-0.397841\pi$
$173$	17.0330	−	9.83400i	1.29499	−	0.747665i	0.979535	+	0.201274i	$0.0645081\pi$
$174$	10.9189	−	3.20821i	0.827757	−	0.243213i
$175$	1.40093	−	2.24442i	0.105900	−	0.169662i
$176$	5.69203	+	2.59451i	0.429053	+	0.195568i
$177$	−0.321534	−	0.556913i	−0.0241680	−	0.0418602i
$178$	2.73721	−	11.2918i	0.205163	−	0.846358i
$179$	−13.9986	−	8.08208i	−1.04630	−	0.604083i	−0.124691	−	0.992196i	$-0.539794\pi$
$179$	−13.9986	−	8.08208i	−1.04630	−	0.604083i	−0.921612	+	0.388112i	$0.873127\pi$
$180$	−1.54357	+	2.99675i	−0.115051	+	0.223365i
$181$			2.61126i			0.194094i	0.995280	+	0.0970468i	$0.0309396\pi$
$181$			2.61126i			0.194094i	−0.995280	+	0.0970468i	$0.969060\pi$
$182$	−9.97835	+	9.77229i	−0.739645	+	0.724371i
$183$	−11.0713			−0.818411
$184$	−18.9928	−	3.64991i	−1.40017	−	0.269075i
$185$	−4.47204	+	7.74580i	−0.328791	+	0.569482i
$186$	−6.15725	−	1.49256i	−0.451471	−	0.109440i
$187$	−4.93148	+	2.84719i	−0.360626	+	0.208207i
$188$	6.84187	−	4.40049i	0.498995	−	0.320939i
$189$	−0.489011	+	14.2047i	−0.0355703	+	1.03324i
$190$	−5.62649	+	1.65319i	−0.408188	+	0.119935i
$191$	8.67766	+	15.0301i	0.627893	+	1.08754i	0.987974	+	0.154622i	$0.0494158\pi$
$191$	8.67766	+	15.0301i	0.627893	+	1.08754i	−0.360081	+	0.932921i	$0.617251\pi$
$192$	−3.39978	+	8.51891i	−0.245358	+	0.614800i
$193$	2.58885	−	4.48402i	0.186349	−	0.322767i	−0.757681	−	0.652625i	$-0.773668\pi$
$193$	2.58885	−	4.48402i	0.186349	−	0.322767i	0.944030	+	0.329859i	$0.107001\pi$
$194$	9.34700	+	8.90914i	0.671076	+	0.639639i
$195$		−	4.27969i		−	0.306475i
$196$	−0.292088	+	13.9970i	−0.0208634	+	0.999782i
$197$			23.4678i			1.67201i	0.548720	+	0.836006i	$0.315115\pi$
$197$			23.4678i			1.67201i	−0.548720	+	0.836006i	$0.684885\pi$
$198$	2.57187	−	2.69828i	0.182775	−	0.191758i
$199$	6.05111	−	10.4808i	0.428952	−	0.742966i	−0.567829	−	0.823147i	$-0.692216\pi$
$199$	6.05111	−	10.4808i	0.428952	−	0.742966i	0.996780	+	0.0801806i	$0.0255497\pi$
$200$	−0.926532	−	2.67237i	−0.0655157	−	0.188965i
$201$	−6.53569	−	11.3201i	−0.460992	−	0.798461i
$202$	−6.06909	−	20.6557i	−0.427020	−	1.45333i
$203$	0.638906	−	18.5588i	0.0448424	−	1.30257i
$204$	−4.51665	−	7.02248i	−0.316229	−	0.491672i
$205$	3.13044	−	1.80736i	0.218639	−	0.126231i
$206$	−5.28115	+	21.7863i	−0.367955	+	1.51793i
$207$	−5.76245	+	9.98086i	−0.400518	+	0.693718i
$208$	1.42998	+	14.8623i	0.0991514	+	1.03051i
$209$	6.48489			0.448569
$210$	−3.00163	−	3.06492i	−0.207132	−	0.211500i
$211$		−	20.2963i		−	1.39726i	−0.715485	−	0.698629i	$-0.753794\pi$
$211$		−	20.2963i		−	1.39726i	0.715485	−	0.698629i	$-0.246206\pi$
$212$	5.46296	−	10.6060i	0.375198	−	0.728426i
$213$	−5.27798	−	3.04724i	−0.361641	−	0.208794i
$214$	2.05524	+	0.498204i	0.140493	+	0.0340565i
$215$	2.24394	+	3.88661i	0.153035	+	0.265065i
$216$	11.4885	+	9.94402i	0.781697	+	0.676605i
$217$	−5.47393	+	8.76976i	−0.371595	+	0.595330i
$218$	3.50427	+	11.9265i	0.237339	+	0.807764i
$219$	12.6397	−	7.29754i	0.854112	−	0.493122i
$220$	0.149949	+	3.12413i	0.0101095	+	0.210629i
$221$	−11.7708	−	6.79585i	−0.791787	−	0.457138i
$222$	10.4976	+	10.0058i	0.704554	+	0.671548i
$223$	11.8778			0.795395			0.397698	−	0.917517i	$-0.369809\pi$
$223$	11.8778			0.795395			0.397698	+	0.917517i	$0.369809\pi$
$224$	11.4480	+	9.64074i	0.764900	+	0.644149i
$225$	−1.68546			−0.112364
$226$	5.23448	+	4.98927i	0.348193	+	0.331881i
$227$	−9.39496	−	5.42418i	−0.623566	−	0.360016i	0.154690	−	0.987963i	$-0.450562\pi$
$227$	−9.39496	−	5.42418i	−0.623566	−	0.360016i	−0.778256	+	0.627947i	$0.783895\pi$
$228$	0.455863	+	9.49774i	0.0301902	+	0.629003i
$229$	−7.07221	+	4.08314i	−0.467345	+	0.269822i	−0.715128	−	0.698994i	$-0.753631\pi$
$229$	−7.07221	+	4.08314i	−0.467345	+	0.269822i	0.247783	+	0.968816i	$0.420298\pi$
$230$	−2.72607	−	9.27795i	−0.179752	−	0.611770i
$231$	2.22919	+	4.18750i	0.146670	+	0.275518i
$232$	−15.0101	−	12.9921i	−0.985461	−	0.852975i
$233$	10.0314	+	17.3748i	0.657177	+	1.13826i	0.981343	+	0.192264i	$0.0615828\pi$
$233$	10.0314	+	17.3748i	0.657177	+	1.13826i	−0.324167	+	0.946000i	$0.605084\pi$
$234$	8.64691	+	2.09607i	0.565266	+	0.137024i
$235$	3.52249	+	2.03371i	0.229782	+	0.132665i
$236$	−0.513662	+	0.997246i	−0.0334365	+	0.0649152i
$237$		−	15.2951i		−	0.993524i
$238$	−13.1961	+	3.38873i	−0.855374	+	0.219659i
$239$	−3.07299			−0.198775			−0.0993876	−	0.995049i	$-0.531688\pi$
$239$	−3.07299			−0.198775			−0.0993876	+	0.995049i	$0.531688\pi$
$240$	−4.56505	+	0.439229i	−0.294673	+	0.0283521i
$241$	9.73245	−	16.8571i	0.626922	−	1.08586i	−0.361244	−	0.932471i	$-0.617648\pi$
$241$	9.73245	−	16.8571i	0.626922	−	1.08586i	0.988166	−	0.153390i	$-0.0490189\pi$
$242$	−2.85001	+	11.7571i	−0.183206	+	0.755778i
$243$	12.8619	−	7.42584i	0.825093	−	0.476368i
$244$	10.4470	+	16.2430i	0.668802	+	1.03985i
$245$	−6.28852	+	3.07481i	−0.401759	+	0.196443i
$246$	−1.65226	−	5.62334i	−0.105344	−	0.358531i
$247$	7.73926	+	13.4048i	0.492437	+	0.852926i
$248$	3.62030	+	10.4419i	0.229889	+	0.663062i
$249$	5.33381	−	9.23844i	0.338017	−	0.585462i
$250$	0.975735	−	1.02369i	0.0617109	−	0.0647439i
$251$			8.26729i			0.521827i	0.965362	+	0.260913i	$0.0840237\pi$
$251$			8.26729i			0.521827i	−0.965362	+	0.260913i	$0.915976\pi$
$252$	7.66264	−	4.56354i	0.482701	−	0.287476i
$253$			10.6934i			0.672291i
$254$	−3.67272	−	3.50067i	−0.230447	−	0.219651i
$255$	2.08739	−	3.61547i	0.130718	−	0.226410i
$256$	15.7065	−	3.05066i	0.981655	−	0.190666i
$257$	−1.75105	−	3.03291i	−0.109228	−	0.189188i	0.806230	−	0.591602i	$-0.201504\pi$
$257$	−1.75105	−	3.03291i	−0.109228	−	0.189188i	−0.915458	+	0.402414i	$0.868171\pi$
$258$	6.98169	−	2.05138i	0.434661	−	0.127713i
$259$	20.8884	−	11.1198i	1.29794	−	0.690951i
$260$	−6.27888	+	4.03839i	−0.389400	+	0.250450i
$261$	−10.2449	+	5.91489i	−0.634142	+	0.366122i
$262$	11.3500	+	2.75133i	0.701208	+	0.169977i
$263$	14.0416	−	24.3207i	0.865841	−	1.49968i	−0.000368323	−	1.00000i	$-0.500117\pi$
$263$	14.0416	−	24.3207i	0.865841	−	1.49968i	0.866210	−	0.499681i	$-0.166549\pi$
$264$	4.98030	+	0.957083i	0.306516	+	0.0589044i
$265$	5.96515			0.366436
$266$	14.9442	+	4.17185i	0.916286	+	0.255793i
$267$		−	9.41965i		−	0.576473i
$268$	−10.4410	+	20.2706i	−0.637785	+	1.23822i
$269$	16.3707	+	9.45160i	0.998136	+	0.576274i	0.907696	−	0.419628i	$-0.137839\pi$
$269$	16.3707	+	9.45160i	0.998136	+	0.576274i	0.0904399	+	0.995902i	$0.471173\pi$
$270$	−1.78978	+	7.38338i	−0.108923	+	0.449338i
$271$	4.10440	+	7.10904i	0.249325	+	0.431843i	0.963339	−	0.268288i	$-0.0864580\pi$
$271$	4.10440	+	7.10904i	0.249325	+	0.431843i	−0.714014	+	0.700132i	$0.753125\pi$
$272$	−6.04094	+	13.2531i	−0.366285	+	0.803585i
$273$	−5.99553	+	9.60541i	−0.362866	+	0.581346i
$274$	−20.2256	+	5.94273i	−1.22187	+	0.359013i
$275$	−1.35435	+	0.781932i	−0.0816701	+	0.0471523i
$276$	−15.6616	+	0.751708i	−0.942716	+	0.0452475i
$277$	−18.3971	−	10.6216i	−1.10538	−	0.638189i	−0.167748	−	0.985830i	$-0.553650\pi$
$277$	−18.3971	−	10.6216i	−1.10538	−	0.638189i	−0.937628	+	0.347641i	$0.886983\pi$
$278$	17.0639	−	17.9026i	1.02343	−	1.07373i
$279$	6.58572			0.394277
$280$	−1.66426	+	7.29591i	−0.0994587	+	0.436014i
$281$	4.03244			0.240555			0.120278	−	0.992740i	$-0.461622\pi$
$281$	4.03244			0.240555			0.120278	+	0.992740i	$0.461622\pi$
$282$	4.55027	−	4.77390i	0.270964	−	0.284282i
$283$	−11.3679	−	6.56324i	−0.675749	−	0.390144i	0.122502	−	0.992468i	$-0.460908\pi$
$283$	−11.3679	−	6.56324i	−0.675749	−	0.390144i	−0.798251	+	0.602324i	$0.794241\pi$
$284$	0.509677	+	10.6189i	0.0302438	+	0.630118i
$285$	−4.11738	+	2.37717i	−0.243892	+	0.140811i
$286$	7.92061	−	2.32725i	0.468355	−	0.137613i
$287$	−9.55798	−	0.329044i	−0.564189	−	0.0194229i
$288$	1.34839	−	9.43859i	0.0794545	−	0.556174i
$289$	1.87073	+	3.24020i	0.110043	+	0.190600i
$290$	2.33839	−	9.64658i	0.137315	−	0.566467i
$291$	9.06611	+	5.23432i	0.531465	+	0.306841i
$292$	−22.6335	−	11.6581i	−1.32453	−	0.682237i
$293$			21.9459i			1.28209i	0.767502	+	0.641046i	$0.221499\pi$
$293$			21.9459i			1.28209i	−0.767502	+	0.641046i	$0.778501\pi$
$294$	2.44318	+	11.0840i	0.142489	+	0.646433i
$295$	−0.560881			−0.0326557
$296$	4.77419	−	24.8431i	0.277494	−	1.44398i
$297$	4.20057	−	7.27559i	0.243742	−	0.422173i
$298$	1.75282	+	0.424894i	0.101538	+	0.0246135i
$299$	−22.1042	+	12.7619i	−1.27832	+	0.738038i
$300$	−1.24042	−	1.92860i	−0.0716157	−	0.111348i
$301$	0.408527	−	11.8668i	0.0235471	−	0.683989i
$302$	9.85832	−	2.89659i	0.567283	−	0.166680i
$303$	−8.72693	−	15.1155i	−0.501349	−	0.868362i
$304$	13.5043	−	9.63104i	0.774525	−	0.552378i
$305$	−4.82815	+	8.36260i	−0.276459	+	0.478841i
$306$	6.28254	+	5.98823i	0.359149	+	0.342324i
$307$		−	29.4747i		−	1.68221i	−0.540870	−	0.841106i	$-0.681905\pi$
$307$		−	29.4747i		−	1.68221i	0.540870	−	0.841106i	$-0.318095\pi$
$308$	4.04013	−	7.22192i	0.230208	−	0.411507i
$309$			18.1742i			1.03389i
$310$	−3.81255	+	3.99993i	−0.216538	+	0.227181i
$311$	−1.99107	+	3.44864i	−0.112903	+	0.195554i	−0.916940	−	0.399026i	$-0.869348\pi$
$311$	−1.99107	+	3.44864i	−0.112903	+	0.195554i	0.804036	+	0.594580i	$0.202682\pi$
$312$	3.96527	+	11.4369i	0.224489	+	0.647487i
$313$	5.73080	+	9.92604i	0.323924	+	0.561053i	0.981294	−	0.192515i	$-0.0616644\pi$
$313$	5.73080	+	9.92604i	0.323924	+	0.561053i	−0.657370	+	0.753568i	$0.728331\pi$
$314$	−0.104287	−	0.354933i	−0.00588527	−	0.0200300i
$315$	3.78288	+	2.36121i	0.213141	+	0.133039i
$316$	−22.4400	+	14.4327i	−1.26235	+	0.811904i
$317$	26.0110	−	15.0175i	1.46092	−	0.843465i	0.461870	−	0.886948i	$-0.347179\pi$
$317$	26.0110	−	15.0175i	1.46092	−	0.843465i	0.999054	+	0.0434825i	$0.0138453\pi$
$318$	2.27860	−	9.39992i	0.127778	−	0.527121i
$319$	−5.48815	+	9.50576i	−0.307278	+	0.532220i
$320$	4.95207	+	6.28308i	0.276829	+	0.351235i
$321$	1.71448			0.0956931
$322$	−6.87929	+	24.6426i	−0.383368	+	1.37328i
$323$			15.0991i			0.840137i
$324$	1.96083	+	1.00998i	0.108935	+	0.0561103i
$325$	−3.23263	−	1.86636i	−0.179314	−	0.103527i
$326$	−22.6602	−	5.49298i	−1.25503	−	0.304228i
$327$	5.03889	+	8.72762i	0.278651	+	0.482638i
$328$	−6.69109	+	7.73037i	−0.369454	+	0.426838i
$329$	−5.05685	−	9.49923i	−0.278793	−	0.523710i
$330$	0.714832	+	2.43287i	0.0393502	+	0.133925i
$331$	−2.45369	+	1.41664i	−0.134867	+	0.0778656i	−0.565916	−	0.824463i	$-0.691477\pi$
$331$	−2.45369	+	1.41664i	−0.134867	+	0.0778656i	0.431048	+	0.902329i	$0.358144\pi$
$332$	−18.5871	+	0.892125i	−1.02010	+	0.0489617i
$333$	−13.0553	−	7.53745i	−0.715423	−	0.413050i
$334$	−0.608321	−	0.579824i	−0.0332858	−	0.0317265i
$335$	−11.4008			−0.622892
$336$	10.8612	+	5.40948i	0.592527	+	0.295112i
$337$	−19.1317			−1.04217			−0.521084	−	0.853505i	$-0.674472\pi$
$337$	−19.1317			−1.04217			−0.521084	+	0.853505i	$0.674472\pi$
$338$	0.955338	+	0.910585i	0.0519635	+	0.0495293i
$339$	5.07718	+	2.93131i	0.275754	+	0.159207i
$340$	−7.27408	+	0.349134i	−0.394492	+	0.0189344i
$341$	5.29192	−	3.05529i	0.286574	−	0.165453i
$342$	−2.78638	−	9.48323i	−0.150670	−	0.512794i
$343$	18.4217	+	1.90859i	0.994676	+	0.103054i
$344$	−9.59769	−	8.30736i	−0.517473	−	0.447903i
$345$	−3.91990	−	6.78947i	−0.211040	−	0.365533i
$346$	−27.0319	−	6.55271i	−1.45324	−	0.352276i
$347$	3.48097	+	2.00974i	0.186868	+	0.107889i	0.590516	−	0.807026i	$-0.298924\pi$
$347$	3.48097	+	2.00974i	0.186868	+	0.107889i	−0.403647	+	0.914915i	$0.632258\pi$
$348$	−14.3079	−	7.36971i	−0.766984	−	0.395058i
$349$		−	22.6377i		−	1.21177i	−0.795552	−	0.605885i	$-0.792819\pi$
$349$		−	22.6377i		−	1.21177i	0.795552	−	0.605885i	$-0.207181\pi$
$350$	−3.62407	+	0.930656i	−0.193715	+	0.0497456i
$351$	20.0523			1.07031
$352$	−3.29533	−	8.20989i	−0.175641	−	0.437588i
$353$	−10.3827	+	17.9833i	−0.552614	+	0.957156i	0.445471	+	0.895297i	$0.353036\pi$
$353$	−10.3827	+	17.9833i	−0.552614	+	0.957156i	−0.998085	+	0.0618594i	$0.980297\pi$
$354$	−0.214248	+	0.883839i	−0.0113872	+	0.0469755i
$355$	−4.60343	+	2.65779i	−0.244325	+	0.141061i
$356$	−13.8199	+	8.88854i	−0.732452	+	0.471092i
$357$	−9.74999	+	5.19034i	−0.516024	+	0.274702i
$358$	6.44424	+	21.9325i	0.340589	+	1.15917i
$359$	−3.09283	−	5.35694i	−0.163233	−	0.282728i	0.772793	−	0.634658i	$-0.218859\pi$
$359$	−3.09283	−	5.35694i	−0.163233	−	0.282728i	−0.936026	+	0.351930i	$0.885526\pi$
$360$	4.50417	−	1.56164i	0.237391	−	0.0823054i
$361$	−0.902406	+	1.56301i	−0.0474951	+	0.0822638i
$362$	2.54790	−	2.67312i	0.133915	−	0.140496i
$363$			9.80782i			0.514777i
$364$	19.7499	−	0.267581i	1.03518	−	0.0140250i
$365$		−	12.7298i		−	0.666306i
$366$	11.3335	+	10.8026i	0.592414	+	0.564662i
$367$	14.6195	−	25.3216i	0.763129	−	1.32178i	−0.178100	−	0.984012i	$-0.556995\pi$
$367$	14.6195	−	25.3216i	0.763129	−	1.32178i	0.941230	−	0.337767i	$-0.109671\pi$
$368$	15.8814	+	22.2683i	0.827874	+	1.16082i
$369$	3.04623	+	5.27623i	0.158581	+	0.274670i
$370$	12.1358	−	3.56578i	0.630912	−	0.185376i
$371$	−13.3883	−	8.35674i	−0.695085	−	0.433860i
$372$	4.84677	+	7.53576i	0.251294	+	0.390711i
$373$	−13.1750	+	7.60658i	−0.682175	+	0.393854i	−0.800674	−	0.599100i	$-0.795525\pi$
$373$	−13.1750	+	7.60658i	−0.682175	+	0.393854i	0.118499	+	0.992954i	$0.462192\pi$
$374$	7.82641	+	1.89717i	0.404694	+	0.0981006i
$375$	0.573266	−	0.992927i	0.0296034	−	0.0512745i
$376$	−11.2977	−	2.17112i	−0.582633	−	0.111967i
$377$	−26.1989			−1.34931
$378$	14.3606	−	14.0640i	0.738628	−	0.723375i
$379$		−	26.2237i		−	1.34702i	−0.739177	−	0.673511i	$-0.764785\pi$
$379$		−	26.2237i		−	1.34702i	0.739177	−	0.673511i	$-0.235215\pi$
$380$	7.37285	+	3.79761i	0.378219	+	0.194813i
$381$	−3.56235	−	2.05672i	−0.182505	−	0.105369i
$382$	5.78220	−	23.8533i	0.295843	−	1.22044i
$383$	−16.0805	−	27.8522i	−0.821674	−	1.42318i	−0.904435	−	0.426612i	$-0.859707\pi$
$383$	−16.0805	−	27.8522i	−0.821674	−	1.42318i	0.0827604	−	0.996569i	$-0.473626\pi$
$384$	11.7925	−	5.40345i	0.601785	−	0.275743i
$385$	4.13514	+	0.142357i	0.210746	+	0.00725519i
$386$	−7.02539	+	2.06421i	−0.357583	+	0.105066i
$387$	−6.55074	+	3.78207i	−0.332993	+	0.192253i
$388$	−0.875484	−	18.2404i	−0.0444459	−	0.926016i
$389$	−10.8592	−	6.26958i	−0.550585	−	0.317880i	0.198773	−	0.980046i	$-0.436304\pi$
$389$	−10.8592	−	6.26958i	−0.550585	−	0.317880i	−0.749358	+	0.662165i	$0.769638\pi$
$390$	−4.17584	+	4.38108i	−0.211452	+	0.221845i
$391$	−24.8981			−1.25915
$392$	13.9563	−	14.0435i	0.704901	−	0.709306i
$393$	9.46821			0.477608
$394$	22.8984	−	24.0238i	1.15360	−	1.21030i
$395$	−11.5530	−	6.67016i	−0.581297	−	0.335612i
$396$	−5.26561	+	0.252733i	−0.264607	+	0.0127003i
$397$	−4.52501	+	2.61251i	−0.227104	+	0.131118i	−0.609235	−	0.792990i	$-0.708523\pi$
$397$	−4.52501	+	2.61251i	−0.227104	+	0.131118i	0.382132	+	0.924108i	$0.375190\pi$
$398$	−16.4210	+	4.82484i	−0.823109	+	0.241848i
$399$	12.5713	+	0.432783i	0.629355	+	0.0216662i
$400$	−1.65904	+	3.63972i	−0.0829519	+	0.181986i
$401$	18.6975	+	32.3850i	0.933708	+	1.61723i	0.776922	+	0.629597i	$0.216780\pi$
$401$	18.6975	+	32.3850i	0.933708	+	1.61723i	0.156787	+	0.987633i	$0.449887\pi$
$402$	−4.35494	+	17.9654i	−0.217205	+	0.896034i
$403$	12.6311	+	7.29256i	0.629199	+	0.363268i
$404$	−13.9416	+	27.0668i	−0.693619	+	1.34662i
$405$			1.10283i			0.0548000i
$406$	−18.7625	+	18.3750i	−0.931166	+	0.911937i
$407$	−13.9873			−0.693326
$408$	−2.22843	+	11.5959i	−0.110324	+	0.574083i
$409$	18.8605	−	32.6674i	0.932593	−	1.61530i	0.153721	−	0.988114i	$-0.450874\pi$
$409$	18.8605	−	32.6674i	0.932593	−	1.61530i	0.778872	−	0.627183i	$-0.215792\pi$
$410$	−4.96810	−	1.20430i	−0.245357	−	0.0594761i
$411$	−14.8008	+	8.54524i	−0.730069	+	0.421505i
$412$	26.6640	−	17.1495i	1.31364	−	0.844893i
$413$	1.25885	+	0.785752i	0.0619440	+	0.0386643i
$414$	15.6376	−	4.59469i	0.768548	−	0.225817i
$415$	−4.65213	−	8.05772i	−0.228364	−	0.395538i
$416$	13.0378	−	16.6096i	0.639229	−	0.814354i
$417$	10.0254	−	17.3646i	0.490948	−	0.850347i
$418$	−6.63851	−	6.32753i	−0.324700	−	0.309490i
$419$			8.43841i			0.412243i	0.978526	+	0.206122i	$0.0660843\pi$
$419$			8.43841i			0.412243i	−0.978526	+	0.206122i	$0.933916\pi$
$420$	0.0821893	+	6.06632i	0.00401043	+	0.296006i
$421$			4.85811i			0.236770i	0.992968	+	0.118385i	$0.0377717\pi$
$421$			4.85811i			0.236770i	−0.992968	+	0.118385i	$0.962228\pi$
$422$	−19.8038	+	20.7772i	−0.964036	+	1.01142i
$423$	−3.42774	+	5.93702i	−0.166662	+	0.288668i
$424$	−15.9411	+	5.52691i	−0.774167	+	0.268410i
$425$	−1.82061	−	3.15340i	−0.0883127	−	0.152962i
$426$	2.42972	+	8.26934i	0.117720	+	0.400651i
$427$	22.5518	−	12.0053i	1.09136	−	0.580976i
$428$	−1.61781	−	2.51538i	−0.0782000	−	0.121585i
$429$	5.79618	−	3.34643i	0.279842	−	0.161567i
$430$	1.49521	−	6.16817i	0.0721052	−	0.297456i
$431$	1.29667	−	2.24591i	0.0624586	−	0.108181i	−0.833105	−	0.553115i	$-0.813439\pi$
$431$	1.29667	−	2.24591i	0.0624586	−	0.108181i	0.895564	+	0.444933i	$0.146773\pi$
$432$	−2.05799	−	21.3894i	−0.0990151	−	1.02910i
$433$	35.2164			1.69239			0.846196	−	0.532872i	$-0.178887\pi$
$433$	35.2164			1.69239			0.846196	+	0.532872i	$0.178887\pi$
$434$	14.1606	−	3.63641i	0.679729	−	0.174553i
$435$		−	8.04718i		−	0.385833i
$436$	8.04980	−	15.6283i	0.385516	−	0.748458i
$437$	24.5557	+	14.1772i	1.17466	+	0.678190i
$438$	−20.0596	−	4.86258i	−0.958485	−	0.232343i
$439$	−1.91640	−	3.31931i	−0.0914650	−	0.158422i	0.816663	−	0.577115i	$-0.195822\pi$
$439$	−1.91640	−	3.31931i	−0.0914650	−	0.158422i	−0.908128	+	0.418693i	$0.862488\pi$
$440$	2.89482	−	3.34445i	0.138005	−	0.159441i
$441$	−5.18248	−	10.5991i	−0.246785	−	0.504718i
$442$	5.41866	+	18.4420i	0.257740	+	0.877196i
$443$	1.87854	−	1.08458i	0.0892523	−	0.0515298i	−0.454710	−	0.890640i	$-0.650257\pi$
$443$	1.87854	−	1.08458i	0.0892523	−	0.0515298i	0.543962	+	0.839110i	$0.316924\pi$
$444$	−0.983255	−	20.4858i	−0.0466632	−	0.972212i
$445$	−7.11506	−	4.10788i	−0.337286	−	0.194732i
$446$	−12.1592	−	11.5896i	−0.575753	−	0.548782i
$447$	1.46220			0.0691597
$448$	−2.31237	−	21.0393i	−0.109249	−	0.994014i
$449$	−21.0399			−0.992934			−0.496467	−	0.868056i	$-0.665370\pi$
$449$	−21.0399			−0.992934			−0.496467	+	0.868056i	$0.665370\pi$
$450$	1.72539	+	1.64456i	0.0813357	+	0.0775255i
$451$	4.89557	+	2.82646i	0.230524	+	0.133093i
$452$	−0.490286	−	10.2149i	−0.0230611	−	0.480470i
$453$	7.21417	−	4.16510i	0.338951	−	0.195694i
$454$	4.32497	+	14.7197i	0.202981	+	0.690829i
$455$	4.64074	+	8.71758i	0.217561	+	0.408686i
$456$	8.80061	−	10.1675i	0.412126	−	0.476139i
$457$	6.26437	+	10.8502i	0.293035	+	0.507552i	0.974526	−	0.224275i	$-0.0720014\pi$
$457$	6.26437	+	10.8502i	0.293035	+	0.507552i	−0.681491	+	0.731827i	$0.738668\pi$
$458$	11.2238	+	2.72073i	0.524455	+	0.127131i
$459$	16.9402	+	9.78040i	0.790699	+	0.456510i
$460$	−6.26217	+	12.1577i	−0.291975	+	0.566854i
$461$		−	4.27916i		−	0.199301i	−0.995023	−	0.0996503i	$-0.968228\pi$
$461$		−	4.27916i		−	0.199301i	0.995023	−	0.0996503i	$-0.0317724\pi$
$462$	1.80389	−	6.46180i	0.0839247	−	0.300630i
$463$	8.23280			0.382611			0.191305	−	0.981531i	$-0.438728\pi$
$463$	8.23280			0.382611			0.191305	+	0.981531i	$0.438728\pi$
$464$	2.68882	+	27.9458i	0.124825	+	1.29735i
$465$	−2.23996	+	3.87973i	−0.103876	+	0.179918i
$466$	6.68422	−	27.5744i	0.309640	−	1.27736i
$467$	−17.7188	+	10.2300i	−0.819930	+	0.473387i	−0.850392	−	0.526149i	$-0.823635\pi$
$467$	−17.7188	+	10.2300i	−0.819930	+	0.473387i	0.0304621	+	0.999536i	$0.490302\pi$
$468$	−6.80655	−	10.5828i	−0.314633	−	0.489191i
$469$	25.5881	+	15.9717i	1.18155	+	0.737503i
$470$	−1.62157	−	5.51890i	−0.0747977	−	0.254568i
$471$	−0.149958	−	0.259735i	−0.00690969	−	0.0119679i
$472$	1.49888	−	0.519674i	0.0689915	−	0.0239199i
$473$	−3.50921	+	6.07813i	−0.161354	+	0.279473i
$474$	−14.9240	+	15.6575i	−0.685480	+	0.719171i
$475$			4.14671i			0.190264i
$476$	16.8152	+	9.40685i	0.770723	+	0.431162i
$477$			10.0540i			0.460343i
$478$	3.14579	+	2.99842i	0.143885	+	0.137145i
$479$	−1.37130	+	2.37517i	−0.0626564	+	0.108524i	−0.895652	−	0.444756i	$-0.853291\pi$
$479$	−1.37130	+	2.37517i	−0.0626564	+	0.108524i	0.832996	+	0.553280i	$0.186624\pi$
$480$	5.10177	+	4.00464i	0.232863	+	0.182786i
$481$	−16.6929	−	28.9129i	−0.761130	−	1.31832i
$482$	−26.4111	+	7.76016i	−1.20299	+	0.353465i
$483$	−0.713649	+	20.7299i	−0.0324722	+	0.943242i
$484$	14.3894	−	9.25483i	0.654063	−	0.420674i
$485$	7.90741	−	4.56535i	0.359057	−	0.207302i
$486$	−20.4123	−	4.94807i	−0.925920	−	0.224449i
$487$	−12.1679	+	21.0755i	−0.551381	+	0.955020i	0.446794	+	0.894637i	$0.352566\pi$
$487$	−12.1679	+	21.0755i	−0.551381	+	0.955020i	−0.998175	+	0.0603832i	$0.980768\pi$
$488$	5.15436	−	26.8214i	0.233327	−	1.21415i
$489$	−18.9031			−0.854829
$490$	9.43770	+	2.98827i	0.426352	+	0.134996i
$491$			36.6203i			1.65265i	0.563191	+	0.826327i	$0.309573\pi$
$491$			36.6203i			1.65265i	−0.563191	+	0.826327i	$0.690427\pi$
$492$	−3.79548	+	7.36873i	−0.171114	+	0.332208i
$493$	−22.1328	−	12.7784i	−0.996810	−	0.575508i
$494$	5.15691	−	21.2738i	0.232021	−	0.957154i
$495$	−1.31792	−	2.28270i	−0.0592360	−	0.102600i
$496$	6.48247	−	14.2217i	0.291071	−	0.638575i
$497$	14.0554	+	0.483872i	0.630470	+	0.0217046i
$498$	−14.4744	+	4.25291i	−0.648615	+	0.190577i
$499$	−7.95426	+	4.59239i	−0.356082	+	0.205584i	−0.667361	−	0.744735i	$-0.732576\pi$
$499$	−7.95426	+	4.59239i	−0.356082	+	0.205584i	0.311279	+	0.950319i	$0.399243\pi$
$500$	−1.99770	+	0.0958836i	−0.0893399	+	0.00428804i
$501$	−0.590040	−	0.340660i	−0.0263610	−	0.0152195i
$502$	8.06668	−	8.46314i	0.360034	−	0.377729i
$503$	−4.21681			−0.188018			−0.0940092	−	0.995571i	$-0.529968\pi$
$503$	−4.21681			−0.188018			−0.0940092	+	0.995571i	$0.529968\pi$
$504$	−12.2970	−	2.80505i	−0.547751	−	0.124947i
$505$	−15.2232			−0.677422
$506$	10.4340	−	10.9468i	0.463846	−	0.486643i
$507$	0.926629	+	0.534989i	0.0411530	+	0.0237597i
$508$	0.344004	+	7.16720i	0.0152627	+	0.317993i
$509$	28.3459	−	16.3655i	1.25641	−	0.725389i	0.284036	−	0.958814i	$-0.408326\pi$
$509$	28.3459	−	16.3655i	1.25641	−	0.725389i	0.972375	+	0.233424i	$0.0749931\pi$
$510$	−5.66459	+	1.66438i	−0.250832	+	0.0737000i
$511$	−17.8334	+	28.5709i	−0.788905	+	1.26390i
$512$	−19.0552	−	12.2024i	−0.842129	−	0.539276i
$513$	−11.1381	−	19.2918i	−0.491761	−	0.851754i
$514$	−1.16678	+	4.81333i	−0.0514645	+	0.212307i
$515$	13.7277	+	7.92571i	0.604916	+	0.349249i
$516$	−9.14869	−	4.71231i	−0.402749	−	0.207448i
$517$			6.36089i			0.279751i
$518$	−32.2332	−	8.99831i	−1.41625	−	0.395363i
$519$	−22.5500			−0.989836
$520$	10.3680	+	1.99246i	0.454668	+	0.0873753i
$521$	−5.80245	+	10.0501i	−0.254210	+	0.440304i	−0.964681	−	0.263422i	$-0.915149\pi$
$521$	−5.80245	+	10.0501i	−0.254210	+	0.440304i	0.710471	+	0.703727i	$0.248482\pi$
$522$	16.2589	+	3.94128i	0.711635	+	0.172505i
$523$	−18.2848	+	10.5568i	−0.799540	+	0.461615i	−0.843310	−	0.537427i	$-0.819396\pi$
$523$	−18.2848	+	10.5568i	−0.799540	+	0.461615i	0.0437701	+	0.999042i	$0.486063\pi$
$524$	−8.93436	−	13.8911i	−0.390300	−	0.606837i
$525$	−2.67767	+	1.42544i	−0.116863	+	0.0622112i
$526$	−38.1048	+	11.1960i	−1.66145	+	0.488171i
$527$	7.11380	+	12.3215i	0.309882	+	0.536732i
$528$	−4.16443	−	5.83921i	−0.181233	−	0.254119i
$529$	−11.8780	+	20.5733i	−0.516434	+	0.894489i
$530$	−6.10647	−	5.82041i	−0.265248	−	0.252822i
$531$		−	0.945343i		−	0.0410244i
$532$	−11.2276	−	18.8522i	−0.486777	−	0.817348i
$533$			13.4927i			0.584435i
$534$	−9.19108	+	9.64280i	−0.397737	+	0.417285i
$535$	0.747682	−	1.29502i	0.0323251	−	0.0559887i
$536$	30.4671	−	10.5632i	1.31598	−	0.456261i
$537$	9.26638	+	16.0498i	0.399874	+	0.692601i
$538$	−7.53622	−	25.6489i	−0.324910	−	1.10580i
$539$	−9.08156	−	6.11254i	−0.391170	−	0.263286i
$540$	9.03640	−	5.81194i	0.388865	−	0.250106i
$541$	12.4963	−	7.21475i	0.537259	−	0.310186i	−0.206709	−	0.978403i	$-0.566275\pi$
$541$	12.4963	−	7.21475i	0.537259	−	0.310186i	0.743967	+	0.668216i	$0.232942\pi$
$542$	2.73490	−	11.2823i	0.117474	−	0.484615i
$543$	1.49695	−	2.59279i	0.0642402	−	0.111267i
$544$	19.1155	−	7.67268i	0.819571	−	0.328964i
$545$	8.78979			0.376513
$546$	15.5099	−	3.98292i	0.663762	−	0.170453i
$547$			32.2999i			1.38104i	0.723312	+	0.690521i	$0.242619\pi$
$547$			32.2999i			1.38104i	−0.723312	+	0.690521i	$0.757381\pi$
$548$	26.5033	+	13.6513i	1.13216	+	0.583155i
$549$	−14.0948	−	8.13766i	−0.601553	−	0.347307i
$550$	2.14939	+	0.521026i	0.0916502	+	0.0222166i
$551$	14.5523	+	25.2053i	0.619948	+	1.07378i
$552$	16.7661	+	14.5120i	0.713611	+	0.617673i
$553$	16.5855	+	31.1556i	0.705286	+	1.32487i
$554$	8.46911	+	28.8239i	0.359818	+	1.22461i
$555$	8.88081	−	5.12734i	0.376970	−	0.217643i
$556$	−34.9363	+	1.67684i	−1.48163	+	0.0711138i
$557$	9.42443	+	5.44120i	0.399326	+	0.230551i	0.686193	−	0.727419i	$-0.259280\pi$
$557$	9.42443	+	5.44120i	0.399326	+	0.230551i	−0.286867	+	0.957970i	$0.592614\pi$
$558$	−6.74173	−	6.42591i	−0.285400	−	0.272031i
$559$	−16.7520			−0.708533
$560$	8.82256	−	5.84487i	0.372821	−	0.246991i
$561$	6.52880			0.275646
$562$	−4.12797	−	3.93459i	−0.174128	−	0.165971i
$563$	−23.2316	−	13.4128i	−0.979095	−	0.565281i	−0.0770979	−	0.997024i	$-0.524565\pi$
$563$	−23.2316	−	13.4128i	−0.979095	−	0.565281i	−0.901997	+	0.431743i	$0.857899\pi$
$564$	−9.31613	+	0.447146i	−0.392280	+	0.0188282i
$565$	4.42829	−	2.55667i	0.186299	−	0.107560i
$566$	5.23319	+	17.8107i	0.219967	+	0.748641i
$567$	1.54498	−	2.47521i	0.0648832	−	0.103949i
$568$	9.83951	−	11.3678i	0.412857	−	0.476983i
$569$	−13.4468	−	23.2906i	−0.563721	−	0.976393i	−0.997167	−	0.0752136i	$-0.976036\pi$
$569$	−13.4468	−	23.2906i	−0.563721	−	0.976393i	0.433447	−	0.901179i	$-0.357297\pi$
$570$	6.53440	+	1.58398i	0.273696	+	0.0663457i
$571$	33.8752	+	19.5579i	1.41763	+	0.818472i	0.996091	−	0.0883365i	$-0.0281551\pi$
$571$	33.8752	+	19.5579i	1.41763	+	0.818472i	0.421544	+	0.906808i	$0.361488\pi$
$572$	−10.3790	−	5.34603i	−0.433969	−	0.223529i
$573$		−	19.8984i		−	0.831269i
$574$	9.46335	+	9.66289i	0.394992	+	0.403321i
$575$	−6.83783			−0.285157
$576$	−10.5899	+	8.34652i	−0.441245	+	0.347772i
$577$	−3.02842	+	5.24538i	−0.126075	+	0.218368i	−0.922153	−	0.386826i	$-0.873571\pi$
$577$	−3.02842	+	5.24538i	−0.126075	+	0.218368i	0.796078	+	0.605194i	$0.206905\pi$
$578$	1.24653	−	5.14230i	0.0518487	−	0.213891i
$579$	−5.14107	+	2.96820i	−0.213656	+	0.123354i
$580$	−11.8063	+	7.59346i	−0.490230	+	0.315301i
$581$	−0.846957	+	24.6022i	−0.0351377	+	1.02067i
$582$	−4.17358	−	14.2044i	−0.173000	−	0.588793i
$583$	4.66434	+	8.07888i	0.193177	+	0.334593i
$584$	11.7945	+	34.0185i	0.488061	+	1.40770i
$585$	3.14568	−	5.44848i	0.130058	−	0.225267i
$586$	21.4134	−	22.4658i	0.884578	−	0.928054i
$587$			9.94005i			0.410270i	0.978734	+	0.205135i	$0.0657633\pi$
$587$			9.94005i			0.410270i	−0.978734	+	0.205135i	$0.934237\pi$
$588$	8.31400	−	13.7305i	0.342864	−	0.566236i
$589$		−	16.2027i		−	0.667621i
$590$	0.574168	+	0.547271i	0.0236381	+	0.0225308i
$591$	13.4533	−	23.3018i	0.553395	−	0.958509i
$592$	−29.1276	+	20.7733i	−1.19714	+	0.853777i
$593$	−15.8642	−	27.4776i	−0.651466	−	1.12837i	−0.982767	−	0.184847i	$-0.940821\pi$
$593$	−15.8642	−	27.4776i	−0.651466	−	1.12837i	0.331302	−	0.943525i	$-0.392512\pi$
$594$	−11.3991	+	3.34932i	−0.467712	+	0.137424i
$595$	−0.331458	+	9.62808i	−0.0135884	+	0.394713i
$596$	−1.37976	−	2.14524i	−0.0565170	−	0.0878726i
$597$	−12.0166	+	6.93780i	−0.491807	+	0.283945i
$598$	35.0801	+	8.50364i	1.43453	+	0.347740i
$599$	−8.50437	+	14.7300i	−0.347479	+	0.601852i	−0.985801	−	0.167918i	$-0.946296\pi$
$599$	−8.50437	+	14.7300i	−0.347479	+	0.601852i	0.638322	+	0.769770i	$0.279629\pi$
$600$	−0.611999	+	3.18461i	−0.0249848	+	0.130011i
$601$	38.3759			1.56539			0.782693	−	0.622407i	$-0.213845\pi$
$601$	38.3759			1.56539			0.782693	+	0.622407i	$0.213845\pi$
$602$	−11.9970	+	11.7493i	−0.488962	+	0.478865i
$603$		−	19.2156i		−	0.782520i
$604$	−12.9182	−	6.65389i	−0.525633	−	0.270743i
$605$	7.40827	+	4.27717i	0.301189	+	0.173891i
$606$	−5.81503	+	23.9888i	−0.236220	+	0.974477i
$607$	−10.9724	−	19.0048i	−0.445357	−	0.771382i	0.552720	−	0.833367i	$-0.313590\pi$
$607$	−10.9724	−	19.0048i	−0.445357	−	0.771382i	−0.998077	+	0.0619857i	$0.980257\pi$
$608$	−23.2216	−	3.31741i	−0.941759	−	0.134539i
$609$	−11.2735	+	18.0612i	−0.456825	+	0.731878i
$610$	13.1022	−	3.84972i	0.530493	−	0.155871i
$611$	−13.1485	+	7.59127i	−0.531930	+	0.307110i
$612$	−0.588452	−	12.2602i	−0.0237868	−	0.495589i
$613$	30.9128	+	17.8475i	1.24856	+	0.720855i	0.970822	−	0.239802i	$-0.0770825\pi$
$613$	30.9128	+	17.8475i	1.24856	+	0.720855i	0.277736	+	0.960657i	$0.410416\pi$
$614$	−28.7595	+	30.1730i	−1.16064	+	1.21768i
$615$	−4.14439			−0.167118
$616$	−11.1825	+	3.45091i	−0.450556	+	0.139041i
$617$	26.2933			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$617$	26.2933			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$618$	17.7332	−	18.6047i	0.713333	−	0.748392i
$619$	2.57921	+	1.48911i	0.103667	+	0.0598522i	0.550937	−	0.834547i	$-0.314270\pi$
$619$	2.57921	+	1.48911i	0.103667	+	0.0598522i	−0.447270	+	0.894399i	$0.647604\pi$
$620$	7.80574	−	0.374652i	0.313486	−	0.0150464i
$621$	31.8118	−	18.3665i	1.27656	−	0.737024i
$622$	5.40320	−	1.58758i	0.216649	−	0.0636561i
$623$	10.2143	+	19.1875i	0.409228	+	0.768730i
$624$	7.10017	−	15.5769i	0.284234	−	0.623575i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.81862	−	15.7529i	0.152623	−	0.629614i
$627$	−6.43902	−	3.71757i	−0.257150	−	0.148465i
$628$	−0.239563	+	0.465098i	−0.00955959	+	0.0185594i
$629$		−	32.5674i		−	1.29855i
$630$	−1.56858	−	6.10823i	−0.0624939	−	0.243358i
$631$	19.2236			0.765280			0.382640	−	0.923897i	$-0.375015\pi$
$631$	19.2236			0.765280			0.382640	+	0.923897i	$0.375015\pi$
$632$	37.0541	+	7.12082i	1.47393	+	0.283251i
$633$	−11.6352	+	20.1528i	−0.462458	+	0.801001i
$634$	−41.2803	−	10.0066i	−1.63945	−	0.397414i
$635$	−3.10706	+	1.79386i	−0.123300	+	0.0711872i
$636$	−11.5044	+	7.39929i	−0.456180	+	0.293401i
$637$	1.79692	−	26.0672i	0.0711964	−	1.03282i
$638$	14.8933	−	4.37597i	0.589630	−	0.173246i
$639$	−4.47961	−	7.75891i	−0.177210	−	0.306938i
$640$	1.06123	−	11.2638i	0.0419490	−	0.445242i
$641$	−12.0208	+	20.8206i	−0.474792	+	0.822364i	−0.999583	−	0.0288669i	$-0.990810\pi$
$641$	−12.0208	+	20.8206i	−0.474792	+	0.822364i	0.524791	+	0.851231i	$0.324143\pi$
$642$	−1.75510	−	1.67288i	−0.0692683	−	0.0660233i
$643$			37.0874i			1.46259i	0.682064	+	0.731293i	$0.261083\pi$
$643$			37.0874i			1.46259i	−0.682064	+	0.731293i	$0.738917\pi$
$644$	31.0869	−	18.5140i	1.22500	−	0.729556i
$645$		−	5.14549i		−	0.202604i
$646$	14.7327	−	15.4568i	0.579651	−	0.608140i
$647$	0.361167	−	0.625560i	0.0141989	−	0.0245933i	−0.858839	−	0.512246i	$-0.828814\pi$
$647$	0.361167	−	0.625560i	0.0141989	−	0.0245933i	0.873038	+	0.487653i	$0.162147\pi$
$648$	−1.02181	−	2.94716i	−0.0401404	−	0.115776i
$649$	−0.438570	−	0.759626i	−0.0172154	−	0.0298179i
$650$	1.48814	+	5.06477i	0.0583697	+	0.198657i
$651$	10.4626	−	5.56970i	0.410062	−	0.218294i
$652$	17.8373	+	27.7334i	0.698563	+	1.08612i
$653$	18.0347	−	10.4123i	0.705751	−	0.407466i	−0.103735	−	0.994605i	$-0.533079\pi$
$653$	18.0347	−	10.4123i	0.705751	−	0.407466i	0.809486	+	0.587139i	$0.199746\pi$
$654$	3.35758	−	13.8510i	0.131292	−	0.541617i
$655$	4.12906	−	7.15175i	0.161336	−	0.279442i
$656$	14.3924	−	1.38477i	0.561929	−	0.0540663i
$657$	21.4555			0.837059
$658$	−4.09208	+	14.6584i	−0.159526	+	0.571445i
$659$		−	11.3364i		−	0.441605i	−0.975319	−	0.220803i	$-0.929132\pi$
$659$		−	11.3364i		−	0.441605i	0.975319	−	0.220803i	$-0.0708676\pi$
$660$	1.64207	−	3.18799i	0.0639175	−	0.124092i
$661$	−10.9233	−	6.30659i	−0.424869	−	0.245298i	0.272290	−	0.962215i	$-0.412219\pi$
$661$	−10.9233	−	6.30659i	−0.424869	−	0.245298i	−0.697158	+	0.716917i	$0.745552\pi$
$662$	3.89409	+	0.943953i	0.151348	+	0.0366878i
$663$	7.79167	+	13.4956i	0.302603	+	0.524124i
$664$	19.8979	+	17.2228i	0.772189	+	0.668375i
$665$	5.80923	−	9.30694i	0.225272	−	0.360908i
$666$	6.00998	+	20.4545i	0.232882	+	0.792595i
$667$	−41.5629	+	23.9964i	−1.60932	+	0.929143i
$668$	0.0569781	+	1.18712i	0.00220455	+	0.0459310i
$669$	−11.7938	−	6.80913i	−0.455973	−	0.263256i
$670$	11.6709	+	11.1241i	0.450885	+	0.429763i
$671$	−15.1011			−0.582973
$672$	−5.84029	−	16.1353i	−0.225294	−	0.622432i
$673$	7.44074			0.286820			0.143410	−	0.989663i	$-0.454193\pi$
$673$	7.44074			0.286820			0.143410	+	0.989663i	$0.454193\pi$
$674$	19.5849	+	18.6674i	0.754382	+	0.719043i
$675$	4.65232	+	2.68602i	0.179068	+	0.103385i
$676$	−0.0894814	−	1.86431i	−0.00344159	−	0.0717044i
$677$	19.3802	−	11.1892i	0.744843	−	0.430035i	−0.0789844	−	0.996876i	$-0.525168\pi$
$677$	19.3802	−	11.1892i	0.744843	−	0.430035i	0.823828	+	0.566840i	$0.191834\pi$
$678$	−2.33728	−	7.95473i	−0.0897626	−	0.305500i
$679$	−24.1432	−	0.831159i	−0.926533	−	0.0318969i
$680$	7.78707	+	6.74017i	0.298620	+	0.258474i
$681$	6.21901	+	10.7716i	0.238313	+	0.412770i
$682$	−8.39845	−	2.03584i	−0.321593	−	0.0779563i
$683$	15.0440	+	8.68565i	0.575642	+	0.332347i	0.759400	−	0.650624i	$-0.225493\pi$
$683$	15.0440	+	8.68565i	0.575642	+	0.332347i	−0.183758	+	0.982972i	$0.558826\pi$
$684$	−6.40072	+	12.4267i	−0.244738	+	0.475145i
$685$			14.9062i			0.569538i
$686$	−16.9958	−	19.9285i	−0.648902	−	0.760872i
$687$	9.36292			0.357217
$688$	1.71927	+	17.8690i	0.0655467	+	0.681248i
$689$	−11.1331	+	19.2832i	−0.424139	+	0.734630i
$690$	−2.61195	+	10.7751i	−0.0994354	+	0.410201i
$691$	29.5541	−	17.0631i	1.12429	−	0.649110i	0.181799	−	0.983336i	$-0.441808\pi$
$691$	29.5541	−	17.0631i	1.12429	−	0.649110i	0.942493	+	0.334225i	$0.108475\pi$
$692$	21.2786	+	33.0839i	0.808890	+	1.25766i
$693$	−0.239937	+	6.96963i	−0.00911447	+	0.264754i
$694$	−1.60246	−	5.45386i	−0.0608287	−	0.207026i
$695$	−8.74414	−	15.1453i	−0.331684	−	0.574494i
$696$	7.45597	+	21.5050i	0.282618	+	0.815145i
$697$	−6.58100	+	11.3986i	−0.249273	+	0.431754i
$698$	−22.0884	+	23.1740i	−0.836059	+	0.877150i
$699$		−	23.0026i		−	0.870038i
$700$	4.61800	+	2.58343i	0.174544	+	0.0976444i
$701$		−	6.36556i		−	0.240424i	−0.992748	−	0.120212i	$-0.961643\pi$
$701$		−	6.36556i		−	0.240424i	0.992748	−	0.120212i	$-0.0383574\pi$
$702$	−20.5274	−	19.5658i	−0.774756	−	0.738462i
$703$	−18.5442	+	32.1196i	−0.699409	+	1.21141i
$704$	−4.63728	+	11.6197i	−0.174774	+	0.437936i
$705$	−2.33171	−	4.03865i	−0.0878174	−	0.152104i
$706$	28.1756	−	8.27862i	1.06040	−	0.311570i
$707$	34.1671	+	21.3265i	1.28499	+	0.802067i
$708$	1.08172	−	0.695728i	0.0406534	−	0.0261470i
$709$	−7.51642	+	4.33961i	−0.282285	+	0.162977i	−0.634457	−	0.772958i	$-0.718776\pi$
$709$	−7.51642	+	4.33961i	−0.282285	+	0.162977i	0.352172	+	0.935935i	$0.385443\pi$
$710$	7.30578	+	1.77097i	0.274181	+	0.0664633i
$711$	11.2423	−	19.4722i	0.421619	−	0.730266i
$712$	22.8201	+	4.38543i	0.855221	+	0.164351i
$713$	26.7179			1.00059
$714$	15.0454	+	4.20010i	0.563059	+	0.157185i
$715$		−	5.83747i		−	0.218309i
$716$	14.8033	−	28.7399i	0.553227	−	1.07406i
$717$	3.05125	+	1.76164i	0.113951	+	0.0657897i
$718$	−2.06085	+	8.50163i	−0.0769103	+	0.317278i
$719$	−15.2096	−	26.3439i	−0.567224	−	0.982460i	−0.996839	−	0.0794482i	$-0.974684\pi$
$719$	−15.2096	−	26.3439i	−0.567224	−	0.982460i	0.429615	−	0.903012i	$-0.358649\pi$
$720$	−6.13462	−	2.79625i	−0.228624	−	0.104210i
$721$	−19.7074	−	37.0201i	−0.733943	−	1.37870i
$722$	2.44887	−	0.719532i	0.0911375	−	0.0267782i
$723$	−19.3272	+	11.1586i	−0.718787	+	0.414992i
$724$	−5.21652	+	0.250377i	−0.193870	+	0.00930519i
$725$	−6.07838	−	3.50935i	−0.225745	−	0.130334i
$726$	9.56983	−	10.0402i	0.355170	−	0.372626i
$727$	48.1335			1.78517			0.892587	−	0.450875i	$-0.148888\pi$
$727$	48.1335			1.78517			0.892587	+	0.450875i	$0.148888\pi$
$728$	−20.4789	−	18.9968i	−0.758998	−	0.704066i
$729$	−20.3364			−0.753201
$730$	−12.4209	+	13.0313i	−0.459717	+	0.482311i
$731$	−14.1520	−	8.17068i	−0.523432	−	0.302204i
$732$	−1.06155	−	22.1171i	−0.0392361	−	0.817470i
$733$	−19.2436	+	11.1103i	−0.710778	+	0.410368i	−0.811349	−	0.584562i	$-0.801266\pi$
$733$	−19.2436	+	11.1103i	−0.710778	+	0.410368i	0.100571	+	0.994930i	$0.467933\pi$
$734$	−39.6730	+	11.6568i	−1.46436	+	0.430261i
$735$	8.00673	+	0.551935i	0.295333	+	0.0203584i
$736$	5.47034	−	38.2918i	0.201639	−	1.41146i
$737$	−8.91464	−	15.4406i	−0.328375	−	0.568762i
$738$	2.02980	−	8.37354i	0.0747181	−	0.308234i
$739$	−13.8846	−	8.01629i	−0.510754	−	0.294884i	0.222390	−	0.974958i	$-0.428614\pi$
$739$	−13.8846	−	8.01629i	−0.510754	−	0.294884i	−0.733143	+	0.680074i	$0.761948\pi$
$740$	−15.9026	−	8.19110i	−0.584590	−	0.301111i
$741$		−	17.7466i		−	0.651939i
$742$	5.55150	+	21.6181i	0.203802	+	0.793626i
$743$	22.7771			0.835611			0.417806	−	0.908536i	$-0.362799\pi$
$743$	22.7771			0.835611			0.417806	+	0.908536i	$0.362799\pi$
$744$	2.39130	−	12.4434i	0.0876695	−	0.456199i
$745$	0.637661	−	1.10446i	0.0233621	−	0.0404644i
$746$	20.9091	+	5.06851i	0.765537	+	0.185571i
$747$	13.5810	−	7.84098i	0.496902	−	0.286887i
$748$	−6.16068	−	9.57862i	−0.225257	−	0.350229i
$749$	−3.49234	+	1.85912i	−0.127607	+	0.0679309i
$750$	−1.55568	+	0.457093i	−0.0568054	+	0.0166907i
$751$	−19.9744	−	34.5966i	−0.728875	−	1.26245i	−0.957359	−	0.288901i	$-0.906710\pi$
$751$	−19.9744	−	34.5966i	−0.728875	−	1.26245i	0.228484	−	0.973548i	$-0.426623\pi$
$752$	9.44688	+	13.2461i	0.344492	+	0.483035i
$753$	4.73936	−	8.20881i	0.172712	−	0.299146i
$754$	26.8196	+	25.5632i	0.976711	+	0.930956i
$755$		−	7.26556i		−	0.264421i
$756$	−28.4235	+	0.385095i	−1.03375	+	0.0140058i
$757$		−	5.02814i		−	0.182751i	−0.995817	−	0.0913754i	$-0.970874\pi$
$757$		−	5.02814i		−	0.182751i	0.995817	−	0.0913754i	$-0.0291263\pi$
$758$	−25.5874	+	26.8450i	−0.929377	+	0.975054i
$759$	6.13019	−	10.6178i	0.222512	−	0.385402i
$760$	−3.84206	−	11.0815i	−0.139366	−	0.401969i
$761$	20.8652	+	36.1396i	0.756363	+	1.31006i	0.944694	+	0.327953i	$0.106359\pi$
$761$	20.8652	+	36.1396i	0.756363	+	1.31006i	−0.188331	+	0.982106i	$0.560308\pi$
$762$	1.63992	+	5.58135i	0.0594082	+	0.202191i
$763$	−19.7280	−	12.3138i	−0.714200	−	0.445791i
$764$	−29.1937	+	18.7765i	−1.05619	+	0.679310i
$765$	5.31493	−	3.06858i	0.192162	−	0.110945i
$766$	−10.7149	+	44.2023i	−0.387146	+	1.59709i
$767$	1.04681	−	1.81312i	0.0377980	−	0.0654680i
$768$	−17.3442	−	5.97492i	−0.625856	−	0.215601i
$769$	−3.06049			−0.110364			−0.0551821	−	0.998476i	$-0.517574\pi$
$769$	−3.06049			−0.110364			−0.0551821	+	0.998476i	$0.517574\pi$
$770$	−4.09420	−	4.18053i	−0.147545	−	0.150656i
$771$			4.01528i			0.144607i
$772$	9.20595	+	4.74180i	0.331329	+	0.170661i
$773$	−22.9983	−	13.2781i	−0.827193	−	0.477580i	0.0256977	−	0.999670i	$-0.491819\pi$
$773$	−22.9983	−	13.2781i	−0.827193	−	0.477580i	−0.852891	+	0.522090i	$0.825153\pi$
$774$	10.3962	+	2.52011i	0.373684	+	0.0905836i
$775$	1.95368	+	3.38388i	0.0701784	+	0.121552i
$776$	−16.9016	+	19.5268i	−0.606731	+	0.700970i
$777$	−27.1153	−	0.933474i	−0.972755	−	0.0334882i
$778$	4.99904	+	17.0138i	0.179224	+	0.609976i
$779$	12.9810	−	7.49458i	0.465093	−	0.268521i
$780$	8.54954	−	0.410352i	0.306123	−	0.0146930i
$781$	−7.19913	−	4.15642i	−0.257605	−	0.148728i
$782$	25.4879	+	24.2939i	0.911447	+	0.868750i
$783$	37.7048			1.34746
$784$	−27.9897	+	0.758574i	−0.999633	+	0.0270919i
$785$	−0.261585			−0.00933637
$786$	−9.69252	−	9.23846i	−0.345721	−	0.329525i
$787$	−16.1231	−	9.30869i	−0.574727	−	0.331819i	0.184308	−	0.982869i	$-0.440996\pi$
$787$	−16.1231	−	9.30869i	−0.574727	−	0.331819i	−0.759035	+	0.651050i	$0.774329\pi$
$788$	−46.8817	+	2.25018i	−1.67009	+	0.0801592i
$789$	−27.8845	+	16.0991i	−0.992715	+	0.573144i
$790$	5.31844	+	18.1009i	0.189222	+	0.644001i
$791$	−13.5206	−	0.465463i	−0.480738	−	0.0165500i
$792$	5.63695	+	4.87911i	0.200300	+	0.173372i
$793$	−18.0221	−	31.2153i	−0.639985	−	1.10849i
$794$	7.18133	+	1.74080i	0.254856	+	0.0617787i
$795$	−5.92296	−	3.41962i	−0.210066	−	0.121281i
$796$	21.5178	+	11.0834i	0.762677	+	0.392839i
$797$			9.92406i			0.351528i	0.984432	+	0.175764i	$0.0562396\pi$
$797$			9.92406i			0.351528i	−0.984432	+	0.175764i	$0.943760\pi$
$798$	−12.4469	−	12.7093i	−0.440615	−	0.449906i
$799$	−14.8104			−0.523954
$800$	5.24975	−	2.10717i	0.185607	−	0.0744997i
$801$	6.92368	−	11.9922i	0.244636	−	0.423723i
$802$	12.4587	−	51.3960i	0.439933	−	1.81486i
$803$	17.2405	−	9.95380i	0.608403	−	0.351262i
$804$	21.9876	−	14.1418i	0.775443	−	0.498742i
$805$	15.3469	+	9.57930i	0.540909	+	0.337626i
$806$	−5.81471	−	19.7899i	−0.204815	−	0.697070i
$807$	−10.8366	−	18.7695i	−0.381465	−	0.660717i
$808$	40.6819	−	14.1048i	1.43118	−	0.496204i
$809$	12.1867	−	21.1080i	0.428462	−	0.742118i	−0.568275	−	0.822839i	$-0.692389\pi$
$809$	12.1867	−	21.1080i	0.428462	−	0.742118i	0.996737	+	0.0807211i	$0.0257223\pi$
$810$	1.07607	−	1.12896i	0.0378092	−	0.0396675i
$811$		−	26.3606i		−	0.925644i	−0.886451	−	0.462822i	$-0.846837\pi$
$811$		−	26.3606i		−	0.925644i	0.886451	−	0.462822i	$-0.153163\pi$
$812$	37.1361	−	0.503137i	1.30322	−	0.0176566i
$813$		−	9.41167i		−	0.330082i
$814$	14.3187	+	13.6479i	0.501870	+	0.478359i
$815$	−8.24361	+	14.2783i	−0.288761	+	0.500149i
$816$	13.5957	−	9.69626i	0.475946	−	0.339437i
$817$	9.30494	+	16.1166i	0.325539	+	0.563850i
$818$	−51.1820	+	15.0384i	−1.78954	+	0.525806i
$819$	−14.6931	+	7.82180i	−0.513420	+	0.273316i
$820$	3.91072	+	6.08038i	0.136568	+	0.212336i
$821$	−45.8332	+	26.4618i	−1.59959	+	0.923523i	−0.608024	+	0.793919i	$0.708037\pi$
$821$	−45.8332	+	26.4618i	−1.59959	+	0.923523i	−0.991566	+	0.129604i	$0.958629\pi$
$822$	23.4893	+	5.69396i	0.819284	+	0.198600i
$823$	−12.1762	+	21.0897i	−0.424434	+	0.735142i	−0.996367	−	0.0851584i	$-0.972860\pi$
$823$	−12.1762	+	21.0897i	−0.424434	+	0.735142i	0.571933	+	0.820300i	$0.306194\pi$
$824$	−44.0289	−	8.46121i	−1.53382	−	0.294760i
$825$	1.79302			0.0624250
$826$	−0.521987	−	2.03267i	−0.0181622	−	0.0707257i
$827$		−	24.8966i		−	0.865741i	−0.901456	−	0.432870i	$-0.857501\pi$
$827$		−	24.8966i		−	0.865741i	0.901456	−	0.432870i	$-0.142499\pi$
$828$	−20.4913	−	10.5547i	−0.712122	−	0.366800i
$829$	−9.70381	−	5.60250i	−0.337027	−	0.194583i	0.321929	−	0.946764i	$-0.395669\pi$
$829$	−9.70381	−	5.60250i	−0.337027	−	0.194583i	−0.658957	+	0.752181i	$0.729002\pi$
$830$	−3.09986	+	12.7878i	−0.107598	+	0.443873i
$831$	12.1780	+	21.0929i	0.422450	+	0.731705i
$832$	−29.5532	+	4.28172i	−1.02457	+	0.148442i
$833$	14.2322	−	21.1451i	0.493115	−	0.732633i
$834$	−27.2062	+	7.99377i	−0.942072	+	0.276802i
$835$	−0.514630	+	0.297122i	−0.0178095	+	0.0102823i
$836$	0.621794	+	12.9549i	0.0215052	+	0.448053i
$837$	−18.1783	−	10.4953i	−0.628334	−	0.362769i
$838$	8.23365	−	8.63832i	0.284427	−	0.298406i
$839$	0.783522			0.0270502			0.0135251	−	0.999909i	$-0.495695\pi$
$839$	0.783522			0.0270502			0.0135251	+	0.999909i	$0.495695\pi$
$840$	5.83499	−	6.29023i	0.201326	−	0.217034i
$841$	−20.2623			−0.698699
$842$	4.74023	−	4.97320i	0.163359	−	0.171388i
$843$	−4.00392	−	2.31166i	−0.137902	−	0.0796179i
$844$	40.5460	−	1.94608i	1.39565	−	0.0669870i
$845$	0.808201	−	0.466615i	0.0278029	−	0.0160520i
$846$	9.30190	−	2.73310i	0.319806	−	0.0939660i
$847$	−10.6352	−	19.9782i	−0.365431	−	0.686458i
$848$	21.7115	+	9.89641i	0.745576	+	0.339844i
$849$	7.52497	+	13.0336i	0.258256	+	0.447313i
$850$	−1.21313	+	5.00454i	−0.0416101	+	0.171654i
$851$	−52.9645	−	30.5791i	−1.81560	−	1.04824i
$852$	5.58141	−	10.8360i	0.191216	−	0.371235i
$853$		−	9.94864i		−	0.340635i	−0.985389	−	0.170317i	$-0.945521\pi$
$853$		−	9.94864i		−	0.340635i	0.985389	−	0.170317i	$-0.0544793\pi$
$854$	−34.8000	−	9.71485i	−1.19083	−	0.332435i
$855$	−6.98912			−0.239023
$856$	−0.798198	+	4.15352i	−0.0272819	+	0.141965i
$857$	23.9520	−	41.4862i	0.818186	−	1.41714i	−0.0888310	−	0.996047i	$-0.528313\pi$
$857$	23.9520	−	41.4862i	0.818186	−	1.41714i	0.907017	−	0.421093i	$-0.138354\pi$
$858$	−9.19872	−	2.22983i	−0.314039	−	0.0761252i
$859$	−9.10119	+	5.25458i	−0.310529	+	0.179284i	−0.647163	−	0.762352i	$-0.724045\pi$
$859$	−9.10119	+	5.25458i	−0.310529	+	0.179284i	0.336634	+	0.941635i	$0.390711\pi$
$860$	−7.54913	+	4.85537i	−0.257423	+	0.165567i
$861$	9.30174	+	5.80598i	0.317002	+	0.197867i
$862$	−3.51880	+	1.03390i	−0.119851	+	0.0352148i
$863$	−3.69169	−	6.39420i	−0.125667	−	0.217661i	0.796327	−	0.604867i	$-0.206774\pi$
$863$	−3.69169	−	6.39420i	−0.125667	−	0.217661i	−0.921993	+	0.387206i	$0.873440\pi$
$864$	−18.7636	+	23.9041i	−0.638351	+	0.813235i
$865$	−9.83400	+	17.0330i	−0.334366	+	0.579139i
$866$	−36.0507	−	34.3619i	−1.22505	−	1.16766i
$867$		−	4.28971i		−	0.145686i
$868$	−18.0442	−	10.0944i	−0.612460	−	0.342626i
$869$		−	20.8624i		−	0.707709i
$870$	−7.85191	+	8.23782i	−0.266205	+	0.279288i
$871$	21.2780	−	36.8546i	0.720977	−	1.24877i
$872$	−23.4895	+	8.14403i	−0.795456	+	0.275792i
$873$	7.69472	+	13.3277i	0.260427	+	0.451073i
$874$	−11.3042	−	38.4730i	−0.382371	−	1.30137i
$875$	−0.0910290	+	2.64418i	−0.00307734	+	0.0893898i
$876$	15.7902	+	24.5506i	0.533503	+	0.829489i
$877$	−47.7683	+	27.5790i	−1.61302	+	0.931278i	−0.624356	+	0.781140i	$0.714638\pi$
$877$	−47.7683	+	27.5790i	−1.61302	+	0.931278i	−0.988665	+	0.150138i	$0.952028\pi$
$878$	−1.27696	+	5.26785i	−0.0430953	+	0.177781i
$879$	12.5808	−	21.7907i	0.424341	−	0.734981i
$880$	−6.22670	+	0.599106i	−0.209902	+	0.0201958i
$881$	14.4165			0.485705			0.242852	−	0.970063i	$-0.421917\pi$
$881$	14.4165			0.485705			0.242852	+	0.970063i	$0.421917\pi$
$882$	−5.03662	+	15.9069i	−0.169592	+	0.535613i
$883$		−	17.4769i		−	0.588143i	−0.955783	−	0.294072i	$-0.904990\pi$
$883$		−	17.4769i		−	0.588143i	0.955783	−	0.294072i	$-0.0950104\pi$
$884$	12.4474	−	24.1661i	0.418653	−	0.812792i
$885$	0.556913	+	0.321534i	0.0187204	+	0.0108082i
$886$	−2.98131	−	0.722688i	−0.100159	−	0.0242792i
$887$	−15.9804	−	27.6788i	−0.536568	−	0.929363i	−0.999086	−	0.0427528i	$-0.986387\pi$
$887$	−15.9804	−	27.6788i	−0.536568	−	0.929363i	0.462518	−	0.886610i	$-0.346946\pi$
$888$	−18.9821	+	21.9305i	−0.636999	+	0.735939i
$889$	9.48661	+	0.326587i	0.318171	+	0.0109534i
$890$	3.27542	+	11.1476i	0.109792	+	0.373669i
$891$	−1.49361	+	0.862337i	−0.0500379	+	0.0288894i
$892$	1.13888	+	23.7282i	0.0381327	+	0.794480i
$893$	14.6067	+	8.43319i	0.488795	+	0.282206i
$894$	−1.49684	−	1.42672i	−0.0500618	−	0.0477166i
$895$	16.1642			0.540309
$896$	−18.1616	+	23.7940i	−0.606738	+	0.794902i
$897$	29.2638			0.977090
$898$	21.5383	+	20.5294i	0.718744	+	0.685074i
$899$	23.7505	+	13.7123i	0.792122	+	0.457332i
$900$	−0.161608	−	3.36705i	−0.00538694	−	0.112235i
$901$	−18.8105	+	10.8602i	−0.626668	+	0.361807i
$902$	−2.25368	−	7.67020i	−0.0750392	−	0.255390i
$903$	−7.20845	+	11.5486i	−0.239882	+	0.384314i
$904$	−9.46516	+	10.9353i	−0.314807	+	0.363703i
$905$	−1.30563	−	2.26142i	−0.0434006	−	0.0751721i
$906$	−11.4491	−	2.77534i	−0.380371	−	0.0922045i
$907$	34.0841	+	19.6785i	1.13174	+	0.653412i	0.944373	−	0.328877i	$-0.106670\pi$
$907$	34.0841	+	19.6785i	1.13174	+	0.653412i	0.187371	+	0.982289i	$0.440003\pi$
$908$	9.93507	−	19.2884i	0.329707	−	0.640108i
$909$		−	25.6581i		−	0.851025i
$910$	3.75536	−	13.4522i	0.124489	−	0.445937i
$911$	6.61364			0.219120			0.109560	−	0.993980i	$-0.465056\pi$
$911$	6.61364			0.219120			0.109560	+	0.993980i	$0.465056\pi$
$912$	−18.9299	+	1.82135i	−0.626833	+	0.0603111i
$913$	7.27529	−	12.6012i	0.240777	−	0.417038i
$914$	4.17415	−	17.2196i	0.138069	−	0.569575i
$915$	9.58799	−	5.53563i	0.316969	−	0.183002i
$916$	−8.83500	−	13.7367i	−0.291917	−	0.453872i
$917$	−19.2864	+	10.2670i	−0.636893	+	0.339046i
$918$	−7.79839	−	26.5412i	−0.257385	−	0.875990i
$919$	−3.64662	−	6.31613i	−0.120291	−	0.208350i	0.799591	−	0.600544i	$-0.205049\pi$
$919$	−3.64662	−	6.31613i	−0.120291	−	0.208350i	−0.919882	+	0.392194i	$0.871716\pi$
$920$	18.2732	−	6.33547i	0.602449	−	0.208874i
$921$	−16.8969	+	29.2663i	−0.556771	+	0.964356i
$922$	−4.17533	+	4.38054i	−0.137507	+	0.144265i
$923$		−	19.8416i		−	0.653094i
$924$	−8.15163	+	4.85477i	−0.268169	+	0.159710i
$925$		−	8.94408i		−	0.294079i
$926$	−8.42784	−	8.03303i	−0.276956	−	0.263982i
$927$	−13.3585	+	23.1376i	−0.438750	+	0.759938i
$928$	24.5152	−	31.2314i	0.804749	−	1.02522i
$929$	22.0313	+	38.1593i	0.722822	+	1.25197i	0.959864	+	0.280466i	$0.0904889\pi$
$929$	22.0313	+	38.1593i	0.722822	+	1.25197i	−0.237042	+	0.971499i	$0.576178\pi$
$930$	6.07861	−	1.78603i	0.199326	−	0.0585663i
$931$	−26.0767	+	12.7504i	−0.854628	+	0.417876i
$932$	−33.7479	+	21.7056i	−1.10545	+	0.710991i
$933$	3.95398	−	2.28283i	0.129447	−	0.0747365i
$934$	28.1204	+	6.81656i	0.920126	+	0.223045i
$935$	2.84719	−	4.93148i	0.0931131	−	0.161277i
$936$	−3.35822	+	17.4749i	−0.109767	+	0.571185i
$937$	−57.3638			−1.87399			−0.936996	−	0.349340i	$-0.886406\pi$
$937$	−57.3638			−1.87399			−0.936996	+	0.349340i	$0.886406\pi$
$938$	−10.6102	−	41.3172i	−0.346436	−	1.34906i
$939$		−	13.1411i		−	0.428844i
$940$	−3.72499	+	7.23187i	−0.121496	+	0.235878i
$941$	36.9316	+	21.3225i	1.20394	+	0.695092i	0.961428	−	0.275057i	$-0.0886968\pi$
$941$	36.9316	+	21.3225i	1.20394	+	0.695092i	0.242507	+	0.970150i	$0.422030\pi$
$942$	−0.0999217	+	0.412207i	−0.00325562	+	0.0134304i
$943$	12.3584	+	21.4054i	0.402445	+	0.697055i
$944$	−2.04145	−	0.930522i	−0.0664436	−	0.0302859i
$945$	−6.67883	−	12.5461i	−0.217262	−	0.408125i
$946$	9.52298	−	2.79806i	0.309619	−	0.0909729i
$947$	18.3844	−	10.6142i	0.597412	−	0.344916i	−0.170611	−	0.985338i	$-0.554574\pi$
$947$	18.3844	−	10.6142i	0.597412	−	0.344916i	0.768023	+	0.640423i	$0.221241\pi$
$948$	30.5550	−	1.46655i	0.992381	−	0.0476313i
$949$	41.1506	+	23.7583i	1.33581	+	0.771228i
$950$	4.04609	−	4.24494i	0.131272	−	0.137724i
$951$	−34.4360			−1.11667
$952$	−8.03495	−	26.0369i	−0.260414	−	0.843859i
$953$	−26.4626			−0.857207			−0.428603	−	0.903493i	$-0.640994\pi$
$953$	−26.4626			−0.857207			−0.428603	+	0.903493i	$0.640994\pi$
$954$	9.81008	−	10.2922i	0.317613	−	0.333223i
$955$	−15.0301	−	8.67766i	−0.486364	−	0.280802i
$956$	−0.294649	−	6.13891i	−0.00952964	−	0.198547i
$957$	10.8987	−	6.29235i	0.352304	−	0.203403i
$958$	3.72132	−	1.09341i	0.120230	−	0.0353264i
$959$	20.8825	−	33.4558i	0.674332	−	1.08034i
$960$	−1.31516	−	9.07749i	−0.0424466	−	0.292975i
$961$	7.86625	+	13.6247i	0.253750	+	0.439508i
$962$	−11.1230	+	45.8857i	−0.358620	+	1.47941i
$963$	2.18271	+	1.26019i	0.0703369	+	0.0406090i
$964$	34.6086	+	17.8262i	1.11467	+	0.574143i
$965$			5.17770i			0.166676i
$966$	20.9574	−	20.5246i	0.674294	−	0.660370i
$967$	14.0017			0.450263			0.225131	−	0.974328i	$-0.427719\pi$
$967$	14.0017			0.450263			0.225131	+	0.974328i	$0.427719\pi$
$968$	−23.7605	−	4.56615i	−0.763692	−	0.146762i
$969$	8.65581	−	14.9923i	0.278065	−	0.481622i
$970$	−12.5493	−	3.04204i	−0.402934	−	0.0976739i
$971$	−20.1131	+	11.6123i	−0.645460	+	0.372657i	−0.786715	−	0.617317i	$-0.788220\pi$
$971$	−20.1131	+	11.6123i	−0.645460	+	0.372657i	0.141255	+	0.989973i	$0.454886\pi$
$972$	16.0678	+	24.9823i	0.515377	+	0.801307i
$973$	−1.59194	+	46.2422i	−0.0510353	+	1.48246i
$974$	33.0202	−	9.70208i	1.05804	−	0.310875i
$975$	2.13985	+	3.70632i	0.0685299	+	0.118697i
$976$	−31.4470	+	22.4275i	−1.00659	+	0.717886i
$977$	9.22181	−	15.9726i	0.295032	−	0.511010i	−0.679960	−	0.733249i	$-0.738003\pi$
$977$	9.22181	−	15.9726i	0.295032	−	0.511010i	0.974992	+	0.222239i	$0.0713364\pi$
$978$	19.3510	+	18.4444i	0.618775	+	0.589788i
$979$		−	12.8483i		−	0.410635i
$980$	−6.74552	−	12.2678i	−0.215478	−	0.391879i
$981$			14.8149i			0.473002i
$982$	35.7317	−	37.4879i	1.14025	−	1.19629i
$983$	−13.6731	+	23.6825i	−0.436104	+	0.755355i	−0.997385	−	0.0722705i	$-0.976976\pi$
$983$	−13.6731	+	23.6825i	−0.436104	+	0.755355i	0.561281	+	0.827626i	$0.310309\pi$
$984$	11.0753	−	3.83991i	0.353068	−	0.122412i
$985$	−11.7339	−	20.3237i	−0.373873	−	0.647568i
$986$	10.1888	+	34.6768i	0.324478	+	1.10433i
$987$	−0.424507	+	12.3310i	−0.0135122	+	0.392499i
$988$	−26.0367	+	16.7460i	−0.828337	+	0.532762i
$989$	−26.5760	+	15.3437i	−0.845067	+	0.487900i
$990$	−0.878170	+	3.62271i	−0.0279101	+	0.115137i
$991$	27.2519	−	47.2016i	0.865684	−	1.49941i	−0.000683250	−	1.00000i	$-0.500217\pi$
$991$	27.2519	−	47.2016i	0.865684	−	1.49941i	0.866367	−	0.499408i	$-0.166449\pi$
$992$	−20.5127	+	8.23348i	−0.651278	+	0.261413i
$993$	3.24845			0.103086
$994$	−13.9162	−	14.2097i	−0.441396	−	0.450703i
$995$			12.1022i			0.383666i
$996$	18.9671	+	9.76955i	0.600994	+	0.309560i
$997$	4.48590	+	2.58994i	0.142070	+	0.0820241i	0.569350	−	0.822095i	$-0.307195\pi$
$997$	4.48590	+	2.58994i	0.142070	+	0.0820241i	−0.427280	+	0.904119i	$0.640528\pi$
$998$	12.6237	+	3.06006i	0.399595	+	0.0968644i
$999$	24.0240	+	41.6107i	0.760084	+	1.31650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bl.b.221.7	✓	60
4.3	odd	2		1120.2.cb.b.81.20		60
7.2	even	3	inner	280.2.bl.b.261.12	yes	60
8.3	odd	2		1120.2.cb.b.81.11		60
8.5	even	2	inner	280.2.bl.b.221.12	yes	60
28.23	odd	6		1120.2.cb.b.401.11		60
56.37	even	6	inner	280.2.bl.b.261.7	yes	60
56.51	odd	6		1120.2.cb.b.401.20		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bl.b.221.7	✓	60	1.1	even	1	trivial
280.2.bl.b.221.12	yes	60	8.5	even	2	inner
280.2.bl.b.261.7	yes	60	56.37	even	6	inner
280.2.bl.b.261.12	yes	60	7.2	even	3	inner
1120.2.cb.b.81.11		60	8.3	odd	2
1120.2.cb.b.81.20		60	4.3	odd	2
1120.2.cb.b.401.11		60	28.23	odd	6
1120.2.cb.b.401.20		60	56.51	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02369 - 0.975735i) q^{2} +(-0.992927 - 0.573266i) q^{3} +(0.0958836 + 1.99770i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.457093 + 1.55568i) q^{6} +(2.64418 + 0.0910290i) q^{7} +(1.85107 - 2.13858i) q^{8} +(-0.842731 - 1.45965i) q^{9} +O(q^{10})\)	\(q+(-1.02369 - 0.975735i) q^{2} +(-0.992927 - 0.573266i) q^{3} +(0.0958836 + 1.99770i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.457093 + 1.55568i) q^{6} +(2.64418 + 0.0910290i) q^{7} +(1.85107 - 2.13858i) q^{8} +(-0.842731 - 1.45965i) q^{9} +(1.37441 + 0.333166i) q^{10} +(-1.35435 - 0.781932i) q^{11} +(1.05001 - 2.03854i) q^{12} -3.73272i q^{13} +(-2.61801 - 2.67321i) q^{14} +1.14653 q^{15} +(-3.98161 + 0.383093i) q^{16} +(1.82061 - 3.15340i) q^{17} +(-0.561539 + 2.31651i) q^{18} +(-3.59115 + 2.07335i) q^{19} +(-1.08189 - 1.68212i) q^{20} +(-2.57330 - 1.60621i) q^{21} +(0.623472 + 2.12194i) q^{22} +(-3.41892 - 5.92174i) q^{23} +(-3.06396 + 1.06230i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-3.64215 + 3.82115i) q^{26} +5.37204i q^{27} +(0.0716851 + 5.29102i) q^{28} -7.01871i q^{29} +(-1.17369 - 1.11871i) q^{30} +(-1.95368 + 3.38388i) q^{31} +(4.44974 + 3.49283i) q^{32} +(0.896511 + 1.55280i) q^{33} +(-4.94062 + 1.45166i) q^{34} +(-2.33545 + 1.24326i) q^{35} +(2.83515 - 1.82348i) q^{36} +(7.74580 - 4.47204i) q^{37} +(5.69927 + 1.38154i) q^{38} +(-2.13985 + 3.70632i) q^{39} +(-0.533782 + 2.77760i) q^{40} -3.61472 q^{41} +(1.06703 + 4.15511i) q^{42} -4.48787i q^{43} +(1.43221 - 2.78055i) q^{44} +(1.45965 + 0.842731i) q^{45} +(-2.27813 + 9.39798i) q^{46} +(-2.03371 - 3.52249i) q^{47} +(4.17306 + 1.90214i) q^{48} +(6.98343 + 0.481395i) q^{49} +(-1.35686 + 0.398674i) q^{50} +(-3.61547 + 2.08739i) q^{51} +(7.45686 - 0.357907i) q^{52} +(-5.16597 - 2.98258i) q^{53} +(5.24168 - 5.49930i) q^{54} +1.56386 q^{55} +(5.08925 - 5.48631i) q^{56} +4.75434 q^{57} +(-6.84840 + 7.18498i) q^{58} +(0.485737 + 0.280440i) q^{59} +(0.109934 + 2.29043i) q^{60} +(8.36260 - 4.82815i) q^{61} +(5.30173 - 1.55777i) q^{62} +(-2.09547 - 3.93631i) q^{63} +(-1.14708 - 7.91734i) q^{64} +(1.86636 + 3.23263i) q^{65} +(0.597374 - 2.46434i) q^{66} +(9.87337 + 5.70039i) q^{67} +(6.47411 + 3.33468i) q^{68} +7.83980i q^{69} +(3.60386 + 1.00606i) q^{70} +5.31558 q^{71} +(-4.68154 - 0.899670i) q^{72} +(-6.36488 + 11.0243i) q^{73} +(-12.2928 - 2.97986i) q^{74} +(-0.992927 + 0.573266i) q^{75} +(-4.48627 - 6.97525i) q^{76} +(-3.50996 - 2.19086i) q^{77} +(5.80693 - 1.70620i) q^{78} +(6.67016 + 11.5530i) q^{79} +(3.25663 - 2.32257i) q^{80} +(0.551415 - 0.955078i) q^{81} +(3.70035 + 3.52700i) q^{82} +9.30425i q^{83} +(2.96198 - 5.29469i) q^{84} +3.64123i q^{85} +(-4.37897 + 4.59419i) q^{86} +(-4.02359 + 6.96906i) q^{87} +(-4.17922 + 1.44897i) q^{88} +(4.10788 + 7.11506i) q^{89} +(-0.671951 - 2.28693i) q^{90} +(0.339786 - 9.87001i) q^{91} +(11.5020 - 7.39777i) q^{92} +(3.87973 - 2.23996i) q^{93} +(-1.35512 + 5.59029i) q^{94} +(2.07335 - 3.59115i) q^{95} +(-2.41594 - 6.01901i) q^{96} -9.13070 q^{97} +(-6.67915 - 7.30677i) q^{98} +2.63583i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9}+O(q^{10}) \) 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9	\( 60 q + 4 q^{2} - 2 q^{4} + 8 q^{7} + 4 q^{8} + 38 q^{9} + 2 q^{10} - 10 q^{12} + 20 q^{14} - 22 q^{16} - 12 q^{17} + 6 q^{18} - 16 q^{20} - 28 q^{22} - 2 q^{23} - 32 q^{24} + 30 q^{25} - 4 q^{26} - 22 q^{28} - 6 q^{32} - 16 q^{34} + 20 q^{36} - 42 q^{38} + 4 q^{40} - 36 q^{41} - 62 q^{42} + 14 q^{44} + 28 q^{46} - 30 q^{47} + 124 q^{48} + 12 q^{49} + 8 q^{50} + 8 q^{52} - 40 q^{54} - 44 q^{55} + 8 q^{56} - 32 q^{57} - 14 q^{58} + 14 q^{60} - 16 q^{62} - 74 q^{63} + 4 q^{64} + 2 q^{65} + 60 q^{66} + 28 q^{68} + 10 q^{70} - 8 q^{71} - 72 q^{72} - 52 q^{74} - 12 q^{76} - 40 q^{78} + 32 q^{79} - 22 q^{81} - 16 q^{82} - 8 q^{84} - 44 q^{86} + 48 q^{87} - 16 q^{88} + 4 q^{89} - 48 q^{90} + 84 q^{92} - 56 q^{94} + 2 q^{95} - 16 q^{96} - 96 q^{97} - 80 q^{98}+O(q^{100}) \) 60 * q + 4 * q^2 - 2 * q^4 + 8 * q^7 + 4 * q^8 + 38 * q^9 + 2 * q^10 - 10 * q^12 + 20 * q^14 - 22 * q^16 - 12 * q^17 + 6 * q^18 - 16 * q^20 - 28 * q^22 - 2 * q^23 - 32 * q^24 + 30 * q^25 - 4 * q^26 - 22 * q^28 - 6 * q^32 - 16 * q^34 + 20 * q^36 - 42 * q^38 + 4 * q^40 - 36 * q^41 - 62 * q^42 + 14 * q^44 + 28 * q^46 - 30 * q^47 + 124 * q^48 + 12 * q^49 + 8 * q^50 + 8 * q^52 - 40 * q^54 - 44 * q^55 + 8 * q^56 - 32 * q^57 - 14 * q^58 + 14 * q^60 - 16 * q^62 - 74 * q^63 + 4 * q^64 + 2 * q^65 + 60 * q^66 + 28 * q^68 + 10 * q^70 - 8 * q^71 - 72 * q^72 - 52 * q^74 - 12 * q^76 - 40 * q^78 + 32 * q^79 - 22 * q^81 - 16 * q^82 - 8 * q^84 - 44 * q^86 + 48 * q^87 - 16 * q^88 + 4 * q^89 - 48 * q^90 + 84 * q^92 - 56 * q^94 + 2 * q^95 - 16 * q^96 - 96 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more