LMFDB - Embedded newform 78.2.g.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(5,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("78.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.g (of order $4$, 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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.58498535041007616.52
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 $ x^12 - 12x^9 + 72x^6 - 324*x^3 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.5
Root			$-0.949550 + 1.44857i$ of defining polynomial
Character	$\chi$	$=$	78.5
Dual form			78.2.g.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} -0.705720i q^{10} +(-3.39145 + 3.39145i) q^{11} +(1.69573 + 0.352860i) q^{12} +(-2.39812 - 2.69240i) q^{13} +1.97724i q^{14} +(-1.02228 + 0.670116i) q^{15} -1.00000 q^{16} +4.38949 q^{17} +(-1.09904 - 2.79144i) q^{18} +(-1.70572 + 1.70572i) q^{19} +(0.499019 - 0.499019i) q^{20} +(2.86417 - 1.87749i) q^{21} -4.79624 q^{22} -0.998038 q^{23} +(0.949550 + 1.44857i) q^{24} -4.50196i q^{25} +(0.208088 - 3.59954i) q^{26} +(-3.00000 + 4.24264i) q^{27} +(-1.39812 + 1.39812i) q^{28} -0.998038i q^{29} +(-1.19671 - 0.249020i) q^{30} +(6.50196 - 6.50196i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.55427 + 6.94769i) q^{33} +(3.10384 + 3.10384i) q^{34} -1.39538i q^{35} +(1.19671 - 2.75098i) q^{36} +(4.10384 + 4.10384i) q^{37} -2.41225 q^{38} +(-5.41178 + 3.11652i) q^{39} +0.705720 q^{40} +(5.24068 + 5.24068i) q^{41} +(3.35286 + 0.697689i) q^{42} +8.88676i q^{43} +(-3.39145 - 3.39145i) q^{44} +(0.775612 + 1.96997i) q^{45} +(-0.705720 - 0.705720i) q^{46} +(-0.352168 + 0.352168i) q^{47} +(-0.352860 + 1.69573i) q^{48} -3.09052i q^{49} +(3.18337 - 3.18337i) q^{50} +(1.54888 - 7.44338i) q^{51} +(2.69240 - 2.39812i) q^{52} -14.2702i q^{53} +(-5.12132 + 0.878680i) q^{54} +3.38480 q^{55} -1.97724 q^{56} +(2.29055 + 3.49431i) q^{57} +(0.705720 - 0.705720i) q^{58} +(0.998038 - 0.998038i) q^{59} +(-0.670116 - 1.02228i) q^{60} -9.59248 q^{61} +9.19516 q^{62} +(-2.17306 - 5.51934i) q^{63} -1.00000i q^{64} +(-0.146852 + 2.54027i) q^{65} +(-1.69240 + 8.13311i) q^{66} +(-5.79624 + 5.79624i) q^{67} +4.38949i q^{68} +(-0.352168 + 1.69240i) q^{69} +(0.986681 - 0.986681i) q^{70} +(-7.13508 - 7.13508i) q^{71} +(2.79144 - 1.09904i) q^{72} +(-1.70572 - 1.70572i) q^{73} +5.80371i q^{74} +(-7.63409 - 1.58856i) q^{75} +(-1.70572 - 1.70572i) q^{76} -9.48332 q^{77} +(-6.03041 - 1.62299i) q^{78} -0.207679 q^{79} +(0.499019 + 0.499019i) q^{80} +(6.13578 + 6.58424i) q^{81} +7.41144i q^{82} +(9.17632 + 9.17632i) q^{83} +(1.87749 + 2.86417i) q^{84} +(-2.19044 - 2.19044i) q^{85} +(-6.28389 + 6.28389i) q^{86} +(-1.69240 - 0.352168i) q^{87} -4.79624i q^{88} +(2.54027 - 2.54027i) q^{89} +(-0.844540 + 1.94142i) q^{90} +(0.411439 - 7.11716i) q^{91} -0.998038i q^{92} +(-8.73127 - 13.3198i) q^{93} -0.498040 q^{94} +1.70237 q^{95} +(-1.44857 + 0.949550i) q^{96} +(-3.58856 + 3.58856i) q^{97} +(2.18533 - 2.18533i) q^{98} +(13.3884 - 5.27124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^7 - 12 * q^16 - 12 * q^19 - 36 * q^27 + 12 * q^28 + 12 * q^31 + 36 * q^33 + 12 * q^37 + 36 * q^42 + 36 * q^45 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 36 * q^93 - 72 * q^94 - 60 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.352860	−	1.69573i	0.203724	−	0.979028i
$3$	0.352860	−	1.69573i	0.203724	−	0.979028i
$4$			1.00000i			0.500000i
$5$	−0.499019	−	0.499019i	−0.223168	−	0.223168i	0.586663	−	0.809831i	$-0.300441\pi$
$5$	−0.499019	−	0.499019i	−0.223168	−	0.223168i	−0.809831	+	0.586663i	$0.800441\pi$
$6$	1.44857	−	0.949550i	0.591376	−	0.387652i
$7$	1.39812	+	1.39812i	0.528440	+	0.528440i	0.920107	−	0.391667i	$-0.128102\pi$
$7$	1.39812	+	1.39812i	0.528440	+	0.528440i	−0.391667	+	0.920107i	$0.628102\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.75098	−	1.19671i	−0.916993	−	0.398903i
$10$		−	0.705720i		−	0.223168i
$11$	−3.39145	+	3.39145i	−1.02256	+	1.02256i	−0.0228223	+	0.999740i	$0.507265\pi$
$11$	−3.39145	+	3.39145i	−1.02256	+	1.02256i	−0.999740	+	0.0228223i	$0.992735\pi$
$12$	1.69573	+	0.352860i	0.489514	+	0.101862i
$13$	−2.39812	−	2.69240i	−0.665119	−	0.746738i
$13$	−2.39812	−	2.69240i	−0.665119	−	0.746738i
$14$			1.97724i			0.528440i
$15$	−1.02228	+	0.670116i	−0.263953	+	0.173023i
$16$	−1.00000			−0.250000
$17$	4.38949			1.06461			0.532304	−	0.846553i	$-0.321326\pi$
$17$	4.38949			1.06461			0.532304	+	0.846553i	$0.321326\pi$
$18$	−1.09904	−	2.79144i	−0.259045	−	0.657948i
$19$	−1.70572	+	1.70572i	−0.391319	+	0.391319i	−0.875157	−	0.483838i	$-0.839242\pi$
$19$	−1.70572	+	1.70572i	−0.391319	+	0.391319i	0.483838	+	0.875157i	$0.339242\pi$
$20$	0.499019	−	0.499019i	0.111584	−	0.111584i
$21$	2.86417	−	1.87749i	0.625013	−	0.409702i
$22$	−4.79624			−1.02256
$23$	−0.998038			−0.208105			−0.104053	−	0.994572i	$-0.533181\pi$
$23$	−0.998038			−0.208105			−0.104053	+	0.994572i	$0.533181\pi$
$24$	0.949550	+	1.44857i	0.193826	+	0.295688i
$25$		−	4.50196i		−	0.900392i
$26$	0.208088	−	3.59954i	0.0408093	−	0.705928i
$27$	−3.00000	+	4.24264i	−0.577350	+	0.816497i
$28$	−1.39812	+	1.39812i	−0.264220	+	0.264220i
$29$		−	0.998038i		−	0.185331i	−0.995697	−	0.0926655i	$-0.970461\pi$
$29$		−	0.998038i		−	0.185331i	0.995697	−	0.0926655i	$-0.0295387\pi$
$30$	−1.19671	−	0.249020i	−0.218488	−	0.0454646i
$31$	6.50196	−	6.50196i	1.16779	−	1.16779i	0.185059	−	0.982727i	$-0.440752\pi$
$31$	6.50196	−	6.50196i	1.16779	−	1.16779i	0.982727	−	0.185059i	$-0.0592476\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.55427	+	6.94769i	0.792797	+	1.20944i
$34$	3.10384	+	3.10384i	0.532304	+	0.532304i
$35$		−	1.39538i		−	0.235862i
$36$	1.19671	−	2.75098i	0.199451	−	0.458497i
$37$	4.10384	+	4.10384i	0.674667	+	0.674667i	0.958788	−	0.284121i	$-0.0917018\pi$
$37$	4.10384	+	4.10384i	0.674667	+	0.674667i	−0.284121	+	0.958788i	$0.591702\pi$
$38$	−2.41225			−0.391319
$39$	−5.41178	+	3.11652i	−0.866578	+	0.499042i
$40$	0.705720			0.111584
$41$	5.24068	+	5.24068i	0.818457	+	0.818457i	0.985884	−	0.167428i	$-0.0535461\pi$
$41$	5.24068	+	5.24068i	0.818457	+	0.818457i	−0.167428	+	0.985884i	$0.553546\pi$
$42$	3.35286	+	0.697689i	0.517358	+	0.107656i
$43$			8.88676i			1.35522i	0.735422	+	0.677609i	$0.236984\pi$
$43$			8.88676i			1.35522i	−0.735422	+	0.677609i	$0.763016\pi$
$44$	−3.39145	−	3.39145i	−0.511281	−	0.511281i
$45$	0.775612	+	1.96997i	0.115621	+	0.293666i
$46$	−0.705720	−	0.705720i	−0.104053	−	0.104053i
$47$	−0.352168	+	0.352168i	−0.0513689	+	0.0513689i	−0.732325	−	0.680956i	$-0.761565\pi$
$47$	−0.352168	+	0.352168i	−0.0513689	+	0.0513689i	0.680956	+	0.732325i	$0.261565\pi$
$48$	−0.352860	+	1.69573i	−0.0509309	+	0.244757i
$49$		−	3.09052i		−	0.441503i
$50$	3.18337	−	3.18337i	0.450196	−	0.450196i
$51$	1.54888	−	7.44338i	0.216886	−	1.04228i
$52$	2.69240	−	2.39812i	0.373369	−	0.332559i
$53$		−	14.2702i		−	1.96016i	−0.198613	−	0.980078i	$-0.563644\pi$
$53$		−	14.2702i		−	1.96016i	0.198613	−	0.980078i	$-0.436356\pi$
$54$	−5.12132	+	0.878680i	−0.696923	+	0.119573i
$55$	3.38480			0.456406
$56$	−1.97724			−0.264220
$57$	2.29055	+	3.49431i	0.303391	+	0.462833i
$58$	0.705720	−	0.705720i	0.0926655	−	0.0926655i
$59$	0.998038	−	0.998038i	0.129934	−	0.129934i	−0.639149	−	0.769083i	$-0.720713\pi$
$59$	0.998038	−	0.998038i	0.129934	−	0.129934i	0.769083	+	0.639149i	$0.220713\pi$
$60$	−0.670116	−	1.02228i	−0.0865117	−	0.131976i
$61$	−9.59248			−1.22819			−0.614096	−	0.789232i	$-0.710479\pi$
$61$	−9.59248			−1.22819			−0.614096	+	0.789232i	$0.710479\pi$
$62$	9.19516			1.16779
$63$	−2.17306	−	5.51934i	−0.273780	−	0.695372i
$64$		−	1.00000i		−	0.125000i
$65$	−0.146852	+	2.54027i	−0.0182147	+	0.315081i
$66$	−1.69240	+	8.13311i	−0.208320	+	1.00112i
$67$	−5.79624	+	5.79624i	−0.708123	+	0.708123i	−0.966140	−	0.258017i	$-0.916931\pi$
$67$	−5.79624	+	5.79624i	−0.708123	+	0.708123i	0.258017	+	0.966140i	$0.416931\pi$
$68$			4.38949i			0.532304i
$69$	−0.352168	+	1.69240i	−0.0423960	+	0.203741i
$70$	0.986681	−	0.986681i	0.117931	−	0.117931i
$71$	−7.13508	−	7.13508i	−0.846778	−	0.846778i	0.142952	−	0.989730i	$-0.454341\pi$
$71$	−7.13508	−	7.13508i	−0.846778	−	0.846778i	−0.989730	+	0.142952i	$0.954341\pi$
$72$	2.79144	−	1.09904i	0.328974	−	0.129523i
$73$	−1.70572	−	1.70572i	−0.199639	−	0.199639i	0.600206	−	0.799845i	$-0.295085\pi$
$73$	−1.70572	−	1.70572i	−0.199639	−	0.199639i	−0.799845	+	0.600206i	$0.795085\pi$
$74$			5.80371i			0.674667i
$75$	−7.63409	−	1.58856i	−0.881509	−	0.183431i
$76$	−1.70572	−	1.70572i	−0.195659	−	0.195659i
$77$	−9.48332			−1.08072
$78$	−6.03041	−	1.62299i	−0.682810	−	0.183768i
$79$	−0.207679			−0.0233658			−0.0116829	−	0.999932i	$-0.503719\pi$
$79$	−0.207679			−0.0233658			−0.0116829	+	0.999932i	$0.503719\pi$
$80$	0.499019	+	0.499019i	0.0557920	+	0.0557920i
$81$	6.13578	+	6.58424i	0.681753	+	0.731582i
$82$			7.41144i			0.818457i
$83$	9.17632	+	9.17632i	1.00723	+	1.00723i	0.999974	+	0.00725871i	$0.00231054\pi$
$83$	9.17632	+	9.17632i	1.00723	+	1.00723i	0.00725871	+	0.999974i	$0.497689\pi$
$84$	1.87749	+	2.86417i	0.204851	+	0.312507i
$85$	−2.19044	−	2.19044i	−0.237587	−	0.237587i
$86$	−6.28389	+	6.28389i	−0.677609	+	0.677609i
$87$	−1.69240	−	0.352168i	−0.181444	−	0.0377563i
$88$		−	4.79624i		−	0.511281i
$89$	2.54027	−	2.54027i	0.269268	−	0.269268i	−0.559537	−	0.828805i	$-0.689021\pi$
$89$	2.54027	−	2.54027i	0.269268	−	0.269268i	0.828805	+	0.559537i	$0.189021\pi$
$90$	−0.844540	+	1.94142i	−0.0890224	+	0.204644i
$91$	0.411439	−	7.11716i	0.0431306	−	0.746081i
$92$		−	0.998038i		−	0.104053i
$93$	−8.73127	−	13.3198i	−0.905390	−	1.38120i
$94$	−0.498040			−0.0513689
$95$	1.70237			0.174660
$96$	−1.44857	+	0.949550i	−0.147844	+	0.0969131i
$97$	−3.58856	+	3.58856i	−0.364363	+	0.364363i	−0.865416	−	0.501053i	$-0.832946\pi$
$97$	−3.58856	+	3.58856i	−0.364363	+	0.364363i	0.501053	+	0.865416i	$0.332946\pi$
$98$	2.18533	−	2.18533i	0.220751	−	0.220751i
$99$	13.3884	−	5.27124i	1.34558	−	0.529780i
$100$	4.50196			0.450196
$101$	−5.08053			−0.505532			−0.252766	−	0.967527i	$-0.581340\pi$
$101$	−5.08053			−0.505532			−0.252766	+	0.967527i	$0.581340\pi$
$102$	6.35849	−	4.16804i	0.629584	−	0.412698i
$103$			12.2077i			1.20286i	0.798926	+	0.601429i	$0.205402\pi$
$103$			12.2077i			1.20286i	−0.798926	+	0.601429i	$0.794598\pi$
$104$	3.59954	+	0.208088i	0.352964	+	0.0204047i
$105$	−2.36618	−	0.492373i	−0.230915	−	0.0480506i
$106$	10.0905	−	10.0905i	0.980078	−	0.980078i
$107$		−	6.78291i		−	0.655728i	−0.944725	−	0.327864i	$-0.893671\pi$
$107$		−	6.78291i		−	0.655728i	0.944725	−	0.327864i	$-0.106329\pi$
$108$	−4.24264	−	3.00000i	−0.408248	−	0.288675i
$109$	3.30760	−	3.30760i	0.316811	−	0.316811i	−0.530730	−	0.847541i	$-0.678082\pi$
$109$	3.30760	−	3.30760i	0.316811	−	0.316811i	0.847541	+	0.530730i	$0.178082\pi$
$110$	2.39342	+	2.39342i	0.228203	+	0.228203i
$111$	8.40707	−	5.51091i	0.797964	−	0.523073i
$112$	−1.39812	−	1.39812i	−0.132110	−	0.132110i
$113$			13.2721i			1.24854i	0.781211	+	0.624268i	$0.214603\pi$
$113$			13.2721i			1.24854i	−0.781211	+	0.624268i	$0.785397\pi$
$114$	−0.851187	+	4.09052i	−0.0797209	+	0.383112i
$115$	0.498040	+	0.498040i	0.0464425	+	0.0464425i
$116$	0.998038			0.0926655
$117$	3.37516	+	10.2766i	0.312034	+	0.950071i
$118$	1.41144			0.129934
$119$	6.13704	+	6.13704i	0.562581	+	0.562581i
$120$	0.249020	−	1.19671i	0.0227323	−	0.109244i
$121$		−	12.0039i		−	1.09127i
$122$	−6.78291	−	6.78291i	−0.614096	−	0.614096i
$123$	10.7360	−	7.03754i	0.968031	−	0.634553i
$124$	6.50196	+	6.50196i	0.583893	+	0.583893i
$125$	−4.74166	+	4.74166i	−0.424107	+	0.424107i
$126$	2.36618	−	5.43935i	0.210796	−	0.484576i
$127$			11.6191i			1.03103i	0.856881	+	0.515515i	$0.172399\pi$
$127$			11.6191i			1.03103i	−0.856881	+	0.515515i	$0.827601\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	15.0695	+	3.13578i	1.32680	+	0.276090i
$130$	−1.90008	+	1.69240i	−0.166648	+	0.148433i
$131$		−	7.08990i		−	0.619448i	−0.950827	−	0.309724i	$-0.899763\pi$
$131$		−	7.08990i		−	0.619448i	0.950827	−	0.309724i	$-0.100237\pi$
$132$	−6.94769	+	4.55427i	−0.604719	+	0.396399i
$133$	−4.76960			−0.413577
$134$	−8.19712			−0.708123
$135$	3.61422	−	0.620101i	0.311062	−	0.0533698i
$136$	−3.10384	+	3.10384i	−0.266152	+	0.266152i
$137$	−15.4150	+	15.4150i	−1.31700	+	1.31700i	−0.400854	+	0.916142i	$0.631286\pi$
$137$	−15.4150	+	15.4150i	−1.31700	+	1.31700i	−0.916142	+	0.400854i	$0.868714\pi$
$138$	−1.44573	+	0.947688i	−0.123069	+	0.0806725i
$139$	10.8868			0.923403			0.461701	−	0.887035i	$-0.347239\pi$
$139$	10.8868			0.923403			0.461701	+	0.887035i	$0.347239\pi$
$140$	1.39538			0.117931
$141$	0.472914	+	0.721446i	0.0398266	+	0.0607567i
$142$		−	10.0905i		−	0.846778i
$143$	17.2643	+	0.998038i	1.44371	+	0.0834602i
$144$	2.75098	+	1.19671i	0.229248	+	0.0997257i
$145$	−0.498040	+	0.498040i	−0.0413600	+	0.0413600i
$146$		−	2.41225i		−	0.199639i
$147$	−5.24068	−	1.09052i	−0.432244	−	0.0899446i
$148$	−4.10384	+	4.10384i	−0.337334	+	0.337334i
$149$	2.54027	+	2.54027i	0.208107	+	0.208107i	0.803462	−	0.595356i	$-0.202989\pi$
$149$	2.54027	+	2.54027i	0.208107	+	0.208107i	−0.595356	+	0.803462i	$0.702989\pi$
$150$	−4.27484	−	6.52140i	−0.349039	−	0.532470i
$151$	−4.01332	−	4.01332i	−0.326599	−	0.326599i	0.524693	−	0.851292i	$-0.324180\pi$
$151$	−4.01332	−	4.01332i	−0.326599	−	0.326599i	−0.851292	+	0.524693i	$0.824180\pi$
$152$		−	2.41225i		−	0.195659i
$153$	−12.0754	−	5.25294i	−0.976239	−	0.424675i
$154$	−6.70572	−	6.70572i	−0.540362	−	0.540362i
$155$	−6.48920			−0.521225
$156$	−3.11652	−	5.41178i	−0.249521	−	0.433289i
$157$	4.76960			0.380656			0.190328	−	0.981721i	$-0.439045\pi$
$157$	4.76960			0.380656			0.190328	+	0.981721i	$0.439045\pi$
$158$	−0.146852	−	0.146852i	−0.0116829	−	0.0116829i
$159$	−24.1983	−	5.03536i	−1.91905	−	0.399330i
$160$			0.705720i			0.0557920i
$161$	−1.39538	−	1.39538i	−0.109971	−	0.109971i
$162$	−0.317107	+	8.99441i	−0.0249143	+	0.706668i
$163$	−11.4154	−	11.4154i	−0.894120	−	0.894120i	0.100788	−	0.994908i	$-0.467864\pi$
$163$	−11.4154	−	11.4154i	−0.894120	−	0.894120i	−0.994908	+	0.100788i	$0.967864\pi$
$164$	−5.24068	+	5.24068i	−0.409228	+	0.409228i
$165$	1.19436	−	5.73970i	0.0929808	−	0.446835i
$166$			12.9773i			1.00723i
$167$	−7.78095	+	7.78095i	−0.602108	+	0.602108i	−0.940871	−	0.338764i	$-0.889991\pi$
$167$	−7.78095	+	7.78095i	−0.602108	+	0.602108i	0.338764	+	0.940871i	$0.389991\pi$
$168$	−0.697689	+	3.35286i	−0.0538279	+	0.258679i
$169$	−1.49804	+	12.9134i	−0.115234	+	0.993338i
$170$		−	3.09775i		−	0.237587i
$171$	6.73365	−	2.65115i	0.514935	−	0.202739i
$172$	−8.88676			−0.677609
$173$	19.3507			1.47121			0.735603	−	0.677413i	$-0.236899\pi$
$173$	19.3507			1.47121			0.735603	+	0.677413i	$0.236899\pi$
$174$	−0.947688	−	1.44573i	−0.0718440	−	0.109600i
$175$	6.29428	−	6.29428i	0.475803	−	0.475803i
$176$	3.39145	−	3.39145i	0.255640	−	0.255640i
$177$	−1.34023	−	2.04457i	−0.100738	−	0.153679i
$178$	3.59248			0.269268
$179$	7.08990			0.529924			0.264962	−	0.964259i	$-0.414641\pi$
$179$	7.08990			0.529924			0.264962	+	0.964259i	$0.414641\pi$
$180$	−1.96997	+	0.775612i	−0.146833	+	0.0578107i
$181$			6.20768i			0.461413i	0.973023	+	0.230707i	$0.0741038\pi$
$181$			6.20768i			0.461413i	−0.973023	+	0.230707i	$0.925896\pi$
$182$	5.32352	−	4.74166i	0.394606	−	0.351475i
$183$	−3.38480	+	16.2662i	−0.250212	+	1.20243i
$184$	0.705720	−	0.705720i	0.0520263	−	0.0520263i
$185$		−	4.09579i		−	0.301128i
$186$	3.24460	−	15.5925i	0.237906	−	1.14330i
$187$	−14.8868	+	14.8868i	−1.08863	+	1.08863i
$188$	−0.352168	−	0.352168i	−0.0256845	−	0.0256845i
$189$	−10.1261	+	1.73736i	−0.736564	+	0.126374i
$190$	1.20376	+	1.20376i	0.0873299	+	0.0873299i
$191$		−	9.77702i		−	0.707441i	−0.935351	−	0.353720i	$-0.884916\pi$
$191$		−	9.77702i		−	0.707441i	0.935351	−	0.353720i	$-0.115084\pi$
$192$	−1.69573	−	0.352860i	−0.122379	−	0.0254655i
$193$	3.79624	+	3.79624i	0.273259	+	0.273259i	0.830411	−	0.557152i	$-0.188106\pi$
$193$	3.79624	+	3.79624i	0.273259	+	0.273259i	−0.557152	+	0.830411i	$0.688106\pi$
$194$	−5.07499			−0.364363
$195$	4.25578	+	1.14538i	0.304763	+	0.0820222i
$196$	3.09052			0.220751
$197$	−7.28193	−	7.28193i	−0.518816	−	0.518816i	0.398397	−	0.917213i	$-0.369567\pi$
$197$	−7.28193	−	7.28193i	−0.518816	−	0.518816i	−0.917213	+	0.398397i	$0.869567\pi$
$198$	13.1944	+	5.73970i	0.937682	+	0.407903i
$199$		−	18.1544i		−	1.28693i	−0.765475	−	0.643466i	$-0.777496\pi$
$199$		−	18.1544i		−	1.28693i	0.765475	−	0.643466i	$-0.222504\pi$
$200$	3.18337	+	3.18337i	0.225098	+	0.225098i
$201$	7.78358	+	11.8741i	0.549011	+	0.837535i
$202$	−3.59248	−	3.59248i	−0.252766	−	0.252766i
$203$	1.39538	−	1.39538i	0.0979363	−	0.0979363i
$204$	7.44338	+	1.54888i	0.521141	+	0.108443i
$205$		−	5.23040i		−	0.365307i
$206$	−8.63213	+	8.63213i	−0.601429	+	0.601429i
$207$	2.74558	+	1.19436i	0.190831	+	0.0830138i
$208$	2.39812	+	2.69240i	0.166280	+	0.186684i
$209$		−	11.5697i		−	0.800296i
$210$	−1.32498	−	2.02130i	−0.0914324	−	0.139483i
$211$	11.2943			0.777530			0.388765	−	0.921337i	$-0.372902\pi$
$211$	11.2943			0.777530			0.388765	+	0.921337i	$0.372902\pi$
$212$	14.2702			0.980078
$213$	−14.6168	+	9.58146i	−1.00153	+	0.656511i
$214$	4.79624	−	4.79624i	0.327864	−	0.327864i
$215$	4.43466	−	4.43466i	0.302442	−	0.302442i
$216$	−0.878680	−	5.12132i	−0.0597866	−	0.348462i
$217$	18.1810			1.23421
$218$	4.67765			0.316811
$219$	−3.49431	+	2.29055i	−0.236124	+	0.154781i
$220$			3.38480i			0.228203i
$221$	−10.5265	−	11.8183i	−0.708091	−	0.794983i
$222$	9.84150	+	2.04789i	0.660518	+	0.137446i
$223$	6.19436	−	6.19436i	0.414805	−	0.414805i	−0.468604	−	0.883409i	$-0.655243\pi$
$223$	6.19436	−	6.19436i	0.414805	−	0.414805i	0.883409	+	0.468604i	$0.155243\pi$
$224$		−	1.97724i		−	0.132110i
$225$	−5.38753	+	12.3848i	−0.359169	+	0.825653i
$226$	−9.38480	+	9.38480i	−0.624268	+	0.624268i
$227$	−13.5658	−	13.5658i	−0.900395	−	0.900395i	0.0950753	−	0.995470i	$-0.469691\pi$
$227$	−13.5658	−	13.5658i	−0.900395	−	0.900395i	−0.995470	+	0.0950753i	$0.969691\pi$
$228$	−3.49431	+	2.29055i	−0.231417	+	0.151696i
$229$	3.30760	+	3.30760i	0.218572	+	0.218572i	0.807897	−	0.589324i	$-0.200606\pi$
$229$	3.30760	+	3.30760i	0.218572	+	0.218572i	−0.589324	+	0.807897i	$0.700606\pi$
$230$			0.704335i			0.0464425i
$231$	−3.34628	+	16.0811i	−0.220169	+	1.05806i
$232$	0.705720	+	0.705720i	0.0463328	+	0.0463328i
$233$	10.8787			0.712687			0.356344	−	0.934355i	$-0.384023\pi$
$233$	10.8787			0.712687			0.356344	+	0.934355i	$0.384023\pi$
$234$	−4.88004	+	9.65325i	−0.319018	+	0.631052i
$235$	0.351477			0.0229278
$236$	0.998038	+	0.998038i	0.0649668	+	0.0649668i
$237$	−0.0732817	+	0.352168i	−0.00476016	+	0.0228757i
$238$			8.67908i			0.562581i
$239$	−5.13900	−	5.13900i	−0.332414	−	0.332414i	0.521088	−	0.853503i	$-0.325526\pi$
$239$	−5.13900	−	5.13900i	−0.332414	−	0.332414i	−0.853503	+	0.521088i	$0.825526\pi$
$240$	1.02228	−	0.670116i	0.0659881	−	0.0432558i
$241$	−5.06388	−	5.06388i	−0.326193	−	0.326193i	0.524944	−	0.851137i	$-0.324086\pi$
$241$	−5.06388	−	5.06388i	−0.326193	−	0.326193i	−0.851137	+	0.524944i	$0.824086\pi$
$242$	8.48805	−	8.48805i	0.545633	−	0.545633i
$243$	13.3301	−	8.08130i	0.855129	−	0.518415i
$244$		−	9.59248i		−	0.614096i
$245$	−1.54223	+	1.54223i	−0.0985294	+	0.0985294i
$246$	12.5678	+	2.61520i	0.801292	+	0.166739i
$247$	8.68300	+	0.501960i	0.552486	+	0.0319389i
$248$			9.19516i			0.583893i
$249$	18.7985	−	12.3226i	1.19131	−	0.780912i
$250$	−6.70572			−0.424107
$251$	−19.2603			−1.21570			−0.607851	−	0.794051i	$-0.707968\pi$
$251$	−19.2603			−1.21570			−0.607851	+	0.794051i	$0.707968\pi$
$252$	5.51934	−	2.17306i	0.347686	−	0.136890i
$253$	3.38480	−	3.38480i	0.212801	−	0.212801i
$254$	−8.21596	+	8.21596i	−0.515515	+	0.515515i
$255$	−4.48731	+	2.94147i	−0.281006	+	0.184202i
$256$	1.00000			0.0625000
$257$	18.2490			1.13834			0.569171	−	0.822219i	$-0.307264\pi$
$257$	18.2490			1.13834			0.569171	+	0.822219i	$0.307264\pi$
$258$	8.43843	+	12.8731i	0.525354	+	0.801444i
$259$			11.4753i			0.713042i
$260$	−2.54027	−	0.146852i	−0.157541	−	0.00910735i
$261$	−1.19436	+	2.74558i	−0.0739290	+	0.169947i
$262$	5.01332	−	5.01332i	0.309724	−	0.309724i
$263$			3.99215i			0.246167i	0.992396	+	0.123083i	$0.0392783\pi$
$263$			3.99215i			0.246167i	−0.992396	+	0.123083i	$0.960722\pi$
$264$	−8.13311	−	1.69240i	−0.500559	−	0.104160i
$265$	−7.12108	+	7.12108i	−0.437444	+	0.437444i
$266$	−3.37262	−	3.37262i	−0.206788	−	0.206788i
$267$	−3.41124	−	5.20396i	−0.208765	−	0.318477i
$268$	−5.79624	−	5.79624i	−0.354062	−	0.354062i
$269$		−	10.4814i		−	0.639060i	−0.947576	−	0.319530i	$-0.896475\pi$
$269$		−	10.4814i		−	0.639060i	0.947576	−	0.319530i	$-0.103525\pi$
$270$	2.99411	+	2.11716i	0.182216	+	0.128846i
$271$	−3.37148	−	3.37148i	−0.204803	−	0.204803i	0.597251	−	0.802054i	$-0.296260\pi$
$271$	−3.37148	−	3.37148i	−0.204803	−	0.204803i	−0.802054	+	0.597251i	$0.796260\pi$
$272$	−4.38949			−0.266152
$273$	−11.9236	−	3.20905i	−0.721648	−	0.194220i
$274$	−21.8002			−1.31700
$275$	15.2682	+	15.2682i	0.920706	+	0.920706i
$276$	−1.69240	−	0.352168i	−0.101871	−	0.0211980i
$277$		−	27.2382i		−	1.63659i	−0.574801	−	0.818294i	$-0.694920\pi$
$277$		−	27.2382i		−	1.63659i	0.574801	−	0.818294i	$-0.305080\pi$
$278$	7.69810	+	7.69810i	0.461701	+	0.461701i
$279$	−25.6677	+	10.1058i	−1.53669	+	0.605019i
$280$	0.986681	+	0.986681i	0.0589655	+	0.0589655i
$281$	−2.24656	+	2.24656i	−0.134019	+	0.134019i	−0.770934	−	0.636915i	$-0.780210\pi$
$281$	−2.24656	+	2.24656i	−0.134019	+	0.134019i	0.636915	+	0.770934i	$0.280210\pi$
$282$	−0.175738	+	0.844540i	−0.0104651	+	0.0502916i
$283$		−	3.00392i		−	0.178564i	−0.996006	−	0.0892822i	$-0.971543\pi$
$283$		−	3.00392i		−	0.178564i	0.996006	−	0.0892822i	$-0.0284573\pi$
$284$	7.13508	−	7.13508i	0.423389	−	0.423389i
$285$	0.600699	−	2.88676i	0.0355824	−	0.170997i
$286$	11.5020	+	12.9134i	0.680125	+	0.763585i
$287$			14.6542i			0.865010i
$288$	1.09904	+	2.79144i	0.0647613	+	0.164487i
$289$	2.26764			0.133391
$290$	−0.704335			−0.0413600
$291$	4.81896	+	7.35148i	0.282492	+	0.430951i
$292$	1.70572	−	1.70572i	0.0998197	−	0.0998197i
$293$	6.98822	−	6.98822i	0.408256	−	0.408256i	−0.472874	−	0.881130i	$-0.656783\pi$
$293$	6.98822	−	6.98822i	0.408256	−	0.408256i	0.881130	+	0.472874i	$0.156783\pi$
$294$	−2.93461	−	4.47683i	−0.171150	−	0.261094i
$295$	−0.996080			−0.0579940
$296$	−5.80371			−0.337334
$297$	−4.21436	−	24.5631i	−0.244542	−	1.42529i
$298$			3.59248i			0.208107i
$299$	2.39342	+	2.68712i	0.138415	+	0.155400i
$300$	1.58856	−	7.63409i	0.0917156	−	0.440755i
$301$	−12.4248	+	12.4248i	−0.716151	+	0.716151i
$302$		−	5.67569i		−	0.326599i
$303$	−1.79272	+	8.61520i	−0.102989	+	0.494930i
$304$	1.70572	−	1.70572i	0.0978297	−	0.0978297i
$305$	4.78683	+	4.78683i	0.274093	+	0.274093i
$306$	−4.82421	−	12.2530i	−0.275782	−	0.700457i
$307$	−8.88284	−	8.88284i	−0.506971	−	0.506971i	0.406625	−	0.913595i	$-0.366706\pi$
$307$	−8.88284	−	8.88284i	−0.506971	−	0.506971i	−0.913595	+	0.406625i	$0.866706\pi$
$308$		−	9.48332i		−	0.540362i
$309$	20.7009	+	4.30760i	1.17763	+	0.245051i
$310$	−4.58856	−	4.58856i	−0.260613	−	0.260613i
$311$	−13.2721			−0.752592			−0.376296	−	0.926499i	$-0.622803\pi$
$311$	−13.2721			−0.752592			−0.376296	+	0.926499i	$0.622803\pi$
$312$	1.62299	−	6.03041i	0.0918839	−	0.341405i
$313$	−0.913399			−0.0516284			−0.0258142	−	0.999667i	$-0.508218\pi$
$313$	−0.913399			−0.0516284			−0.0258142	+	0.999667i	$0.508218\pi$
$314$	3.37262	+	3.37262i	0.190328	+	0.190328i
$315$	−1.66986	+	3.83866i	−0.0940859	+	0.216284i
$316$		−	0.207679i		−	0.0116829i
$317$	−0.544191	−	0.544191i	−0.0305648	−	0.0305648i	0.691659	−	0.722224i	$-0.256880\pi$
$317$	−0.544191	−	0.544191i	−0.0305648	−	0.0305648i	−0.722224	+	0.691659i	$0.756880\pi$
$318$	−13.5502	−	20.6713i	−0.759859	−	1.15919i
$319$	3.38480	+	3.38480i	0.189512	+	0.189512i
$320$	−0.499019	+	0.499019i	−0.0278960	+	0.0278960i
$321$	−11.5020	−	2.39342i	−0.641977	−	0.133587i
$322$		−	1.97336i		−	0.109971i
$323$	−7.48724	+	7.48724i	−0.416601	+	0.416601i
$324$	−6.58424	+	6.13578i	−0.365791	+	0.340877i
$325$	−12.1211	+	10.7962i	−0.672356	+	0.598868i
$326$		−	16.1438i		−	0.894120i
$327$	−4.44167	−	6.77590i	−0.245625	−	0.374708i
$328$	−7.41144			−0.409228
$329$	−0.984745			−0.0542908
$330$	4.90312	−	3.21404i	0.269908	−	0.176927i
$331$	−10.5925	+	10.5925i	−0.582215	+	0.582215i	−0.935512	−	0.353296i	$-0.885061\pi$
$331$	−10.5925	+	10.5925i	−0.582215	+	0.582215i	0.353296	+	0.935512i	$0.385061\pi$
$332$	−9.17632	+	9.17632i	−0.503616	+	0.503616i
$333$	−6.37848	−	16.2007i	−0.349539	−	0.887792i
$334$	−11.0039			−0.602108
$335$	5.78487			0.316061
$336$	−2.86417	+	1.87749i	−0.156253	+	0.102425i
$337$		−	13.7363i		−	0.748263i	−0.927376	−	0.374131i	$-0.877941\pi$
$337$		−	13.7363i		−	0.748263i	0.927376	−	0.374131i	$-0.122059\pi$
$338$	−10.1904	+	8.07188i	−0.554286	+	0.439052i
$339$	22.5059	+	4.68320i	1.22235	+	0.254356i
$340$	2.19044	−	2.19044i	0.118793	−	0.118793i
$341$			44.1022i			2.38827i
$342$	6.63606	+	2.88676i	0.358837	+	0.156098i
$343$	14.1078	−	14.1078i	0.761747	−	0.761747i
$344$	−6.28389	−	6.28389i	−0.338805	−	0.338805i
$345$	1.02028	−	0.668802i	0.0549300	−	0.0360071i
$346$	13.6830	+	13.6830i	0.735603	+	0.735603i
$347$			24.3542i			1.30740i	0.756754	+	0.653700i	$0.226784\pi$
$347$			24.3542i			1.30740i	−0.756754	+	0.653700i	$0.773216\pi$
$348$	0.352168	−	1.69240i	0.0188782	−	0.0907222i
$349$	6.48472	+	6.48472i	0.347119	+	0.347119i	0.859035	−	0.511916i	$-0.171064\pi$
$349$	6.48472	+	6.48472i	0.347119	+	0.347119i	−0.511916	+	0.859035i	$0.671064\pi$
$350$	8.90146			0.475803
$351$	18.6172	−	2.09716i	0.993715	−	0.111938i
$352$	4.79624			0.255640
$353$	−8.63213	−	8.63213i	−0.459442	−	0.459442i	0.439030	−	0.898472i	$-0.355322\pi$
$353$	−8.63213	−	8.63213i	−0.459442	−	0.459442i	−0.898472	+	0.439030i	$0.855322\pi$
$354$	0.498040	−	2.39342i	0.0264705	−	0.127209i
$355$			7.12108i			0.377948i
$356$	2.54027	+	2.54027i	0.134634	+	0.134634i
$357$	12.5723	−	8.24123i	0.665394	−	0.436172i
$358$	5.01332	+	5.01332i	0.264962	+	0.264962i
$359$	−12.5678	+	12.5678i	−0.663302	+	0.663302i	−0.956157	−	0.292855i	$-0.905395\pi$
$359$	−12.5678	+	12.5678i	−0.663302	+	0.663302i	0.292855	+	0.956157i	$0.405395\pi$
$360$	−1.94142	−	0.844540i	−0.102322	−	0.0445112i
$361$			13.1810i			0.693739i
$362$	−4.38949	+	4.38949i	−0.230707	+	0.230707i
$363$	−20.3554	−	4.23570i	−1.06838	−	0.222317i
$364$	7.11716	+	0.411439i	0.373040	+	0.0215653i
$365$			1.70237i			0.0891063i
$366$	−13.8954	+	9.10854i	−0.726323	+	0.476111i
$367$	19.3848			1.01188			0.505939	−	0.862569i	$-0.331146\pi$
$367$	19.3848			1.01188			0.505939	+	0.862569i	$0.331146\pi$
$368$	0.998038			0.0520263
$369$	−8.14544	−	20.6886i	−0.424035	−	1.07700i
$370$	2.89616	−	2.89616i	0.150564	−	0.150564i
$371$	19.9514	−	19.9514i	1.03582	−	1.03582i
$372$	13.3198	−	8.73127i	0.690601	−	0.452695i
$373$	24.4154			1.26418			0.632090	−	0.774895i	$-0.282197\pi$
$373$	24.4154			1.26418			0.632090	+	0.774895i	$0.282197\pi$
$374$	−21.0531			−1.08863
$375$	6.36742	+	9.71370i	0.328812	+	0.501613i
$376$		−	0.498040i		−	0.0256845i
$377$	−2.68712	+	2.39342i	−0.138394	+	0.123267i
$378$	−8.38872	−	5.93172i	−0.431469	−	0.305095i
$379$	−2.17712	+	2.17712i	−0.111831	+	0.111831i	−0.760808	−	0.648977i	$-0.775197\pi$
$379$	−2.17712	+	2.17712i	−0.111831	+	0.111831i	0.648977	+	0.760808i	$0.275197\pi$
$380$			1.70237i			0.0873299i
$381$	19.7029	+	4.09992i	1.00941	+	0.210045i
$382$	6.91340	−	6.91340i	0.353720	−	0.353720i
$383$	4.14096	+	4.14096i	0.211593	+	0.211593i	0.804944	−	0.593351i	$-0.202195\pi$
$383$	4.14096	+	4.14096i	0.211593	+	0.211593i	−0.593351	+	0.804944i	$0.702195\pi$
$384$	−0.949550	−	1.44857i	−0.0484565	−	0.0739220i
$385$	4.73236	+	4.73236i	0.241183	+	0.241183i
$386$			5.36869i			0.273259i
$387$	10.6349	−	24.4473i	0.540600	−	1.24273i
$388$	−3.58856	−	3.58856i	−0.182182	−	0.182182i
$389$	6.78291			0.343907			0.171954	−	0.985105i	$-0.444992\pi$
$389$	6.78291			0.343907			0.171954	+	0.985105i	$0.444992\pi$
$390$	2.19939	+	3.81920i	0.111370	+	0.193393i
$391$	−4.38088			−0.221551
$392$	2.18533	+	2.18533i	0.110376	+	0.110376i
$393$	−12.0225	−	2.50174i	−0.606457	−	0.126196i
$394$		−	10.2982i		−	0.518816i
$395$	0.103636	+	0.103636i	0.00521449	+	0.00521449i
$396$	5.27124	+	13.3884i	0.264890	+	0.672792i
$397$	17.2716	+	17.2716i	0.866835	+	0.866835i	0.992121	−	0.125286i	$-0.0399848\pi$
$397$	17.2716	+	17.2716i	0.866835	+	0.866835i	−0.125286	+	0.992121i	$0.539985\pi$
$398$	12.8371	−	12.8371i	0.643466	−	0.643466i
$399$	−1.68300	+	8.08794i	−0.0842554	+	0.404904i
$400$			4.50196i			0.225098i
$401$	22.1979	−	22.1979i	1.10851	−	1.10851i	0.115166	−	0.993346i	$-0.463260\pi$
$401$	22.1979	−	22.1979i	1.10851	−	1.10851i	0.993346	−	0.115166i	$-0.0367401\pi$
$402$	−2.89243	+	13.9001i	−0.144262	+	0.693273i
$403$	−33.0984	−	1.91340i	−1.64875	−	0.0953132i
$404$		−	5.08053i		−	0.252766i
$405$	0.223789	−	6.34753i	0.0111202	−	0.315411i
$406$	1.97336			0.0979363
$407$	−27.8360			−1.37978
$408$	4.16804	+	6.35849i	0.206349	+	0.314792i
$409$	3.02664	−	3.02664i	0.149658	−	0.149658i	−0.628307	−	0.777965i	$-0.716252\pi$
$409$	3.02664	−	3.02664i	0.149658	−	0.149658i	0.777965	+	0.628307i	$0.216252\pi$
$410$	3.69845	−	3.69845i	0.182653	−	0.182653i
$411$	20.7004	+	31.5790i	1.02107	+	1.55768i
$412$	−12.2077			−0.601429
$413$	2.79075			0.137324
$414$	1.09688	+	2.78596i	0.0539087	+	0.136923i
$415$		−	9.15832i		−	0.449564i
$416$	−0.208088	+	3.59954i	−0.0102023	+	0.176482i
$417$	3.84150	−	18.4610i	0.188119	−	0.904038i
$418$	8.18104	−	8.18104i	0.400148	−	0.400148i
$419$		−	34.2215i		−	1.67183i	−0.548858	−	0.835916i	$-0.684937\pi$
$419$		−	34.2215i		−	1.67183i	0.548858	−	0.835916i	$-0.315063\pi$
$420$	0.492373	−	2.36618i	0.0240253	−	0.115458i
$421$	2.87344	−	2.87344i	0.140043	−	0.140043i	−0.633610	−	0.773653i	$-0.718428\pi$
$421$	2.87344	−	2.87344i	0.140043	−	0.140043i	0.773653	+	0.633610i	$0.218428\pi$
$422$	7.98626	+	7.98626i	0.388765	+	0.388765i
$423$	1.39025	−	0.547364i	0.0675962	−	0.0266138i
$424$	10.0905	+	10.0905i	0.490039	+	0.490039i
$425$		−	19.7613i		−	0.958565i
$426$	−17.1108	−	3.56054i	−0.829019	−	0.172509i
$427$	−13.4114	−	13.4114i	−0.649025	−	0.649025i
$428$	6.78291			0.327864
$429$	7.78427	−	28.9233i	0.375828	−	1.39643i
$430$	6.27156			0.302442
$431$	−6.84137	−	6.84137i	−0.329537	−	0.329537i	0.522873	−	0.852410i	$-0.324860\pi$
$431$	−6.84137	−	6.84137i	−0.329537	−	0.329537i	−0.852410	+	0.522873i	$0.824860\pi$
$432$	3.00000	−	4.24264i	0.144338	−	0.204124i
$433$			29.2833i			1.40727i	0.710563	+	0.703633i	$0.248440\pi$
$433$			29.2833i			1.40727i	−0.710563	+	0.703633i	$0.751560\pi$
$434$	12.8559	+	12.8559i	0.617105	+	0.617105i
$435$	0.668802	+	1.02028i	0.0320666	+	0.0489186i
$436$	3.30760	+	3.30760i	0.158405	+	0.158405i
$437$	1.70237	−	1.70237i	0.0814356	−	0.0814356i
$438$	−4.09052	−	0.851187i	−0.195453	−	0.0406713i
$439$		−	18.0000i		−	0.859093i	−0.903045	−	0.429547i	$-0.858673\pi$
$439$		−	18.0000i		−	0.859093i	0.903045	−	0.429547i	$-0.141327\pi$
$440$	−2.39342	+	2.39342i	−0.114102	+	0.114102i
$441$	−3.69845	+	8.50196i	−0.176117	+	0.404855i
$442$	0.913399	−	15.8002i	0.0434460	−	0.751537i
$443$			26.6439i			1.26589i	0.774196	+	0.632946i	$0.218155\pi$
$443$			26.6439i			1.26589i	−0.774196	+	0.632946i	$0.781845\pi$
$444$	5.51091	+	8.40707i	0.261536	+	0.398982i
$445$	−2.53528			−0.120184
$446$	8.76015			0.414805
$447$	5.20396	−	3.41124i	0.246139	−	0.161346i
$448$	1.39812	−	1.39812i	0.0660550	−	0.0660550i
$449$	−25.9867	+	25.9867i	−1.22639	+	1.22639i	−0.261070	+	0.965320i	$0.584075\pi$
$449$	−25.9867	+	25.9867i	−1.22639	+	1.22639i	−0.965320	+	0.261070i	$0.915925\pi$
$450$	−12.5669	+	4.94782i	−0.592411	+	0.233242i
$451$	−35.5470			−1.67384
$452$	−13.2721			−0.624268
$453$	−8.22163	+	5.38935i	−0.386286	+	0.253214i
$454$		−	19.1850i		−	0.900395i
$455$	−3.75691	+	3.34628i	−0.176127	+	0.156876i
$456$	−4.09052	−	0.851187i	−0.191556	−	0.0398605i
$457$	−18.8907	+	18.8907i	−0.883669	+	0.883669i	−0.993905	−	0.110237i	$-0.964839\pi$
$457$	−18.8907	+	18.8907i	−0.883669	+	0.883669i	0.110237	+	0.993905i	$0.464839\pi$
$458$			4.67765i			0.218572i
$459$	−13.1685	+	18.6230i	−0.614652	+	0.869249i
$460$	−0.498040	+	0.498040i	−0.0232212	+	0.0232212i
$461$	24.8399	+	24.8399i	1.15691	+	1.15691i	0.985137	+	0.171773i	$0.0549495\pi$
$461$	24.8399	+	24.8399i	1.15691	+	1.15691i	0.171773	+	0.985137i	$0.445051\pi$
$462$	−13.7372	+	9.00489i	−0.639115	+	0.418945i
$463$	−14.0944	−	14.0944i	−0.655024	−	0.655024i	0.299174	−	0.954198i	$-0.403289\pi$
$463$	−14.0944	−	14.0944i	−0.655024	−	0.655024i	−0.954198	+	0.299174i	$0.903289\pi$
$464$			0.998038i			0.0463328i
$465$	−2.28978	+	11.0039i	−0.106186	+	0.510295i
$466$	7.69240	+	7.69240i	0.356344	+	0.356344i
$467$	16.6769			0.771713			0.385857	−	0.922559i	$-0.373906\pi$
$467$	16.6769			0.771713			0.385857	+	0.922559i	$0.373906\pi$
$468$	−10.2766	+	3.37516i	−0.475035	+	0.156017i
$469$	−16.2077			−0.748401
$470$	0.248532	+	0.248532i	0.0114639	+	0.0114639i
$471$	1.68300	−	8.08794i	0.0775486	−	0.372673i
$472$			1.41144i			0.0649668i
$473$	−30.1390	−	30.1390i	−1.38579	−	1.38579i
$474$	−0.300838	+	0.197202i	−0.0138180	+	0.00905779i
$475$	7.67908	+	7.67908i	0.352340	+	0.352340i
$476$	−6.13704	+	6.13704i	−0.281291	+	0.281291i
$477$	−17.0772	+	39.2569i	−0.781911	+	1.79745i
$478$		−	7.26764i		−	0.332414i
$479$	26.4858	−	26.4858i	1.21017	−	1.21017i	0.239193	−	0.970972i	$-0.423117\pi$
$479$	26.4858	−	26.4858i	1.21017	−	1.21017i	0.970972	−	0.239193i	$-0.0768830\pi$
$480$	1.19671	+	0.249020i	0.0546220	+	0.0113662i
$481$	1.20768	−	20.8907i	0.0550654	−	0.952533i
$482$		−	7.16141i		−	0.326193i
$483$	−2.85855	+	1.87381i	−0.130069	+	0.0852611i
$484$	12.0039			0.545633
$485$	3.58152			0.162628
$486$	15.1402	+	3.71149i	0.686772	+	0.168357i
$487$	3.67908	−	3.67908i	0.166715	−	0.166715i	−0.618819	−	0.785534i	$-0.712388\pi$
$487$	3.67908	−	3.67908i	0.166715	−	0.166715i	0.785534	+	0.618819i	$0.212388\pi$
$488$	6.78291	−	6.78291i	0.307048	−	0.307048i
$489$	−23.3854	+	15.3293i	−1.05752	+	0.693215i
$490$	−2.18104			−0.0985294
$491$	−40.7107			−1.83725			−0.918625	−	0.395131i	$-0.870699\pi$
$491$	−40.7107			−1.83725			−0.918625	+	0.395131i	$0.870699\pi$
$492$	7.03754	+	10.7360i	0.317277	+	0.484016i
$493$		−	4.38088i		−	0.197305i
$494$	5.78487	+	6.49475i	0.260274	+	0.292213i
$495$	−9.31152	−	4.05062i	−0.418522	−	0.182062i
$496$	−6.50196	+	6.50196i	−0.291947	+	0.291947i
$497$		−	19.9514i		−	0.894942i
$498$	22.0059	+	4.57916i	0.986109	+	0.205197i
$499$	−10.5020	+	10.5020i	−0.470132	+	0.470132i	−0.901957	−	0.431825i	$-0.857870\pi$
$499$	−10.5020	+	10.5020i	−0.470132	+	0.470132i	0.431825	+	0.901957i	$0.357870\pi$
$500$	−4.74166	−	4.74166i	−0.212053	−	0.212053i
$501$	10.4488	+	15.9399i	0.466817	+	0.712144i
$502$	−13.6191	−	13.6191i	−0.607851	−	0.607851i
$503$			1.38208i			0.0616241i	0.999525	+	0.0308120i	$0.00980933\pi$
$503$			1.38208i			0.0616241i	−0.999525	+	0.0308120i	$0.990191\pi$
$504$	5.43935	+	2.36618i	0.242288	+	0.105398i
$505$	2.53528	+	2.53528i	0.112819	+	0.112819i
$506$	4.78683			0.212801
$507$	21.3690	+	7.09689i	0.949031	+	0.315184i
$508$	−11.6191			−0.515515
$509$	−7.32710	−	7.32710i	−0.324768	−	0.324768i	0.525825	−	0.850593i	$-0.323757\pi$
$509$	−7.32710	−	7.32710i	−0.324768	−	0.324768i	−0.850593	+	0.525825i	$0.823757\pi$
$510$	−5.25294	−	1.09307i	−0.232604	−	0.0484020i
$511$		−	4.76960i		−	0.210995i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.11960	−	12.3539i	−0.0935825	−	0.545439i
$514$	12.9040	+	12.9040i	0.569171	+	0.569171i
$515$	6.09187	−	6.09187i	0.268440	−	0.268440i
$516$	−3.13578	+	15.0695i	−0.138045	+	0.663399i
$517$		−	2.38872i		−	0.105056i
$518$	−8.11428	+	8.11428i	−0.356521	+	0.356521i
$519$	6.82808	−	32.8135i	0.299719	−	1.44035i
$520$	−1.69240	−	1.90008i	−0.0742167	−	0.0833240i
$521$			2.09971i			0.0919901i	0.998942	+	0.0459950i	$0.0146458\pi$
$521$			2.09971i			0.0919901i	−0.998942	+	0.0459950i	$0.985354\pi$
$522$	−2.78596	+	1.09688i	−0.121938	+	0.0480091i
$523$	−2.76960			−0.121106			−0.0605531	−	0.998165i	$-0.519286\pi$
$523$	−2.76960			−0.121106			−0.0605531	+	0.998165i	$0.519286\pi$
$524$	7.08990			0.309724
$525$	−8.45238	−	12.8944i	−0.368892	−	0.562757i
$526$	−2.82288	+	2.82288i	−0.123083	+	0.123083i
$527$	28.5403	−	28.5403i	1.24324	−	1.24324i
$528$	−4.55427	−	6.94769i	−0.198199	−	0.302359i
$529$	−22.0039			−0.956692
$530$	−10.0707			−0.437444
$531$	−3.93994	+	1.55122i	−0.170979	+	0.0673173i
$532$		−	4.76960i		−	0.206788i
$533$	1.54223	−	26.6778i	0.0668013	−	1.15554i
$534$	1.26764	−	6.09187i	0.0548562	−	0.263621i
$535$	−3.38480	+	3.38480i	−0.146338	+	0.146338i
$536$		−	8.19712i		−	0.354062i
$537$	2.50174	−	12.0225i	0.107958	−	0.518811i
$538$	7.41144	−	7.41144i	0.319530	−	0.319530i
$539$	10.4814	+	10.4814i	0.451464	+	0.451464i
$540$	0.620101	+	3.61422i	0.0266849	+	0.155531i
$541$	23.0545	+	23.0545i	0.991190	+	0.991190i	0.999962	−	0.00877191i	$-0.00279222\pi$
$541$	23.0545	+	23.0545i	0.991190	+	0.991190i	−0.00877191	+	0.999962i	$0.502792\pi$
$542$		−	4.76800i		−	0.204803i
$543$	10.5265	+	2.19044i	0.451737	+	0.0940008i
$544$	−3.10384	−	3.10384i	−0.133076	−	0.133076i
$545$	−3.30111			−0.141404
$546$	−6.16210	−	10.7004i	−0.263714	−	0.457934i
$547$	28.1172			1.20220			0.601101	−	0.799173i	$-0.294729\pi$
$547$	28.1172			1.20220			0.601101	+	0.799173i	$0.294729\pi$
$548$	−15.4150	−	15.4150i	−0.658498	−	0.658498i
$549$	26.3887	+	11.4794i	1.12624	+	0.489929i
$550$			21.5925i			0.920706i
$551$	1.70237	+	1.70237i	0.0725235	+	0.0725235i
$552$	−0.947688	−	1.44573i	−0.0403363	−	0.0615343i
$553$	−0.290361	−	0.290361i	−0.0123474	−	0.0123474i
$554$	19.2603	−	19.2603i	0.818294	−	0.818294i
$555$	−6.94534	−	1.44524i	−0.294813	−	0.0613470i
$556$			10.8868i			0.461701i
$557$	−14.0648	+	14.0648i	−0.595946	+	0.595946i	−0.939231	−	0.343285i	$-0.888460\pi$
$557$	−14.0648	+	14.0648i	−0.595946	+	0.595946i	0.343285	+	0.939231i	$0.388460\pi$
$558$	−25.2957	−	11.0039i	−1.07085	−	0.465833i
$559$	23.9267	−	21.3115i	1.01199	−	0.901381i
$560$			1.39538i			0.0589655i
$561$	19.9909	+	30.4968i	0.844018	+	1.28758i
$562$	−3.17712			−0.134019
$563$	28.6400			1.20703			0.603517	−	0.797350i	$-0.293766\pi$
$563$	28.6400			1.20703			0.603517	+	0.797350i	$0.293766\pi$
$564$	−0.721446	+	0.472914i	−0.0303784	+	0.0199133i
$565$	6.62304	−	6.62304i	0.278633	−	0.278633i
$566$	2.12409	−	2.12409i	0.0892822	−	0.0892822i
$567$	−0.626998	+	17.7841i	−0.0263314	+	0.746863i
$568$	10.0905			0.423389
$569$	3.48180			0.145965			0.0729823	−	0.997333i	$-0.476748\pi$
$569$	3.48180			0.145965			0.0729823	+	0.997333i	$0.476748\pi$
$570$	2.46601	−	1.61649i	0.103290	−	0.0677073i
$571$			5.34756i			0.223788i	0.993720	+	0.111894i	$0.0356918\pi$
$571$			5.34756i			0.223788i	−0.993720	+	0.111894i	$0.964308\pi$
$572$	−0.998038	+	17.2643i	−0.0417301	+	0.721855i
$573$	−16.5792	−	3.44992i	−0.692604	−	0.144122i
$574$	−10.3621	+	10.3621i	−0.432505	+	0.432505i
$575$			4.49313i			0.187376i
$576$	−1.19671	+	2.75098i	−0.0498628	+	0.114624i
$577$	26.4753	−	26.4753i	1.10218	−	1.10218i	0.108035	−	0.994147i	$-0.465544\pi$
$577$	26.4753	−	26.4753i	1.10218	−	1.10218i	0.994147	−	0.108035i	$-0.0344558\pi$
$578$	1.60347	+	1.60347i	0.0666954	+	0.0666954i
$579$	7.77693	−	5.09785i	0.323198	−	0.211859i
$580$	−0.498040	−	0.498040i	−0.0206800	−	0.0206800i
$581$			25.6592i			1.06452i
$582$	−1.79076	+	8.60580i	−0.0742294	+	0.356722i
$583$	48.3966	+	48.3966i	2.00438	+	2.00438i
$584$	2.41225			0.0998197
$585$	3.44394	−	6.81249i	0.142390	−	0.281662i
$586$	9.88284			0.408256
$587$	−19.3640	−	19.3640i	−0.799237	−	0.799237i	0.183738	−	0.982975i	$-0.441180\pi$
$587$	−19.3640	−	19.3640i	−0.799237	−	0.799237i	−0.982975	+	0.183738i	$0.941180\pi$
$588$	1.09052	−	5.24068i	0.0449723	−	0.216122i
$589$			22.1810i			0.913954i
$590$	−0.704335	−	0.704335i	−0.0289970	−	0.0289970i
$591$	−14.9177	+	9.77866i	−0.613631	+	0.402240i
$592$	−4.10384	−	4.10384i	−0.168667	−	0.168667i
$593$	−3.14097	+	3.14097i	−0.128984	+	0.128984i	−0.768652	−	0.639668i	$-0.779072\pi$
$593$	−3.14097	+	3.14097i	−0.128984	+	0.128984i	0.639668	+	0.768652i	$0.279072\pi$
$594$	14.3887	−	20.3487i	0.590376	−	0.834918i
$595$		−	6.12500i		−	0.251100i
$596$	−2.54027	+	2.54027i	−0.104053	+	0.104053i
$597$	−30.7849	−	6.40596i	−1.25994	−	0.262178i
$598$	−0.207679	+	3.59248i	−0.00849264	+	0.146907i
$599$			38.7280i			1.58238i	0.611570	+	0.791191i	$0.290538\pi$
$599$			38.7280i			1.58238i	−0.611570	+	0.791191i	$0.709462\pi$
$600$	6.52140	−	4.27484i	0.266235	−	0.174520i
$601$	16.2794			0.664051			0.332025	−	0.943270i	$-0.392268\pi$
$601$	16.2794			0.664051			0.332025	+	0.943270i	$0.392268\pi$
$602$	−17.5713			−0.716151
$603$	22.8817	−	9.00893i	0.931817	−	0.366872i
$604$	4.01332	−	4.01332i	0.163300	−	0.163300i
$605$	−5.99019	+	5.99019i	−0.243536	+	0.243536i
$606$	−7.35951	+	4.82422i	−0.298960	+	0.195971i
$607$	−29.0118			−1.17755			−0.588775	−	0.808297i	$-0.700390\pi$
$607$	−29.0118			−1.17755			−0.588775	+	0.808297i	$0.700390\pi$
$608$	2.41225			0.0978297
$609$	−1.87381	−	2.85855i	−0.0759305	−	0.115834i
$610$			6.76960i			0.274093i
$611$	1.79272	+	0.103636i	0.0725255	+	0.00419266i
$612$	5.25294	−	12.0754i	0.212338	−	0.488119i
$613$	−9.94004	+	9.94004i	−0.401474	+	0.401474i	−0.878752	−	0.477278i	$-0.841623\pi$
$613$	−9.94004	+	9.94004i	−0.401474	+	0.401474i	0.477278	+	0.878752i	$0.341623\pi$
$614$		−	12.5622i		−	0.506971i
$615$	−8.86933	−	1.84560i	−0.357646	−	0.0744217i
$616$	6.70572	−	6.70572i	0.270181	−	0.270181i
$617$	2.15622	+	2.15622i	0.0868062	+	0.0868062i	0.749177	−	0.662370i	$-0.230449\pi$
$617$	2.15622	+	2.15622i	0.0868062	+	0.0868062i	−0.662370	+	0.749177i	$0.730449\pi$
$618$	11.5918	+	17.6837i	0.466291	+	0.711342i
$619$	0.683001	+	0.683001i	0.0274521	+	0.0274521i	0.720700	−	0.693247i	$-0.243821\pi$
$619$	0.683001	+	0.683001i	0.0274521	+	0.0274521i	−0.693247	+	0.720700i	$0.743821\pi$
$620$		−	6.48920i		−	0.260613i
$621$	2.99411	−	4.23432i	0.120150	−	0.169917i
$622$	−9.38480	−	9.38480i	−0.376296	−	0.376296i
$623$	7.10320			0.284584
$624$	5.41178	−	3.11652i	0.216644	−	0.124761i
$625$	−17.7774			−0.711098
$626$	−0.645871	−	0.645871i	−0.0258142	−	0.0258142i
$627$	−19.6191	−	4.08250i	−0.783512	−	0.163039i
$628$			4.76960i			0.190328i
$629$	18.0138	+	18.0138i	0.718256	+	0.718256i
$630$	−3.89511	+	1.53357i	−0.155185	+	0.0610989i
$631$	−7.98668	−	7.98668i	−0.317945	−	0.317945i	0.530033	−	0.847977i	$-0.322180\pi$
$631$	−7.98668	−	7.98668i	−0.317945	−	0.317945i	−0.847977	+	0.530033i	$0.822180\pi$
$632$	0.146852	−	0.146852i	0.00584144	−	0.00584144i
$633$	3.98530	−	19.1520i	0.158401	−	0.761224i
$634$		−	0.769602i		−	0.0305648i
$635$	5.79816	−	5.79816i	0.230093	−	0.230093i
$636$	5.03536	−	24.1983i	0.199665	−	0.959524i
$637$	−8.32092	+	7.41144i	−0.329687	+	0.293652i
$638$			4.78683i			0.189512i
$639$	11.0898	+	28.1670i	0.438708	+	1.11427i
$640$	−0.705720			−0.0278960
$641$	−29.7417			−1.17473			−0.587363	−	0.809323i	$-0.699834\pi$
$641$	−29.7417			−1.17473			−0.587363	+	0.809323i	$0.699834\pi$
$642$	−6.44071	−	9.82551i	−0.254195	−	0.387782i
$643$	13.3887	−	13.3887i	0.528000	−	0.528000i	−0.391976	−	0.919975i	$-0.628208\pi$
$643$	13.3887	−	13.3887i	0.528000	−	0.528000i	0.919975	+	0.391976i	$0.128208\pi$
$644$	1.39538	−	1.39538i	0.0549856	−	0.0549856i
$645$	−5.95516	−	9.08479i	−0.234484	−	0.357713i
$646$	−10.5886			−0.416601
$647$	8.77898			0.345137			0.172569	−	0.984997i	$-0.444793\pi$
$647$	8.77898			0.345137			0.172569	+	0.984997i	$0.444793\pi$
$648$	−8.99441	−	0.317107i	−0.353334	−	0.0124572i
$649$			6.76960i			0.265730i
$650$	−16.2050	−	0.936802i	−0.635612	−	0.0367444i
$651$	6.41536	−	30.8301i	0.251438	−	1.20833i
$652$	11.4154	−	11.4154i	0.447060	−	0.447060i
$653$			30.2161i			1.18245i	0.806508	+	0.591223i	$0.201355\pi$
$653$			30.2161i			1.18245i	−0.806508	+	0.591223i	$0.798645\pi$
$654$	1.65056	−	7.93202i	0.0645418	−	0.310167i
$655$	−3.53800	+	3.53800i	−0.138241	+	0.138241i
$656$	−5.24068	−	5.24068i	−0.204614	−	0.204614i
$657$	2.65115	+	6.73365i	0.103431	+	0.262705i
$658$	−0.696320	−	0.696320i	−0.0271454	−	0.0271454i
$659$		−	5.10712i		−	0.198945i	−0.995040	−	0.0994726i	$-0.968284\pi$
$659$		−	5.10712i		−	0.198945i	0.995040	−	0.0994726i	$-0.0317156\pi$
$660$	5.73970	+	1.19436i	0.223417	+	0.0464904i
$661$	−30.2488	−	30.2488i	−1.17654	−	1.17654i	−0.980619	−	0.195925i	$-0.937229\pi$
$661$	−30.2488	−	30.2488i	−1.17654	−	1.17654i	−0.195925	−	0.980619i	$-0.562771\pi$
$662$	−14.9800			−0.582215
$663$	−23.7549	+	13.6799i	−0.922566	+	0.531284i
$664$	−12.9773			−0.503616
$665$	2.38012	+	2.38012i	0.0922972	+	0.0922972i
$666$	6.94534	−	15.9659i	0.269126	−	0.618665i
$667$			0.996080i			0.0385684i
$668$	−7.78095	−	7.78095i	−0.301054	−	0.301054i
$669$	−8.31820	−	12.6897i	−0.321600	−	0.490612i
$670$	4.09052	+	4.09052i	0.158031	+	0.158031i
$671$	32.5325	−	32.5325i	1.25590	−	1.25590i
$672$	−3.35286	−	0.697689i	−0.129339	−	0.0269139i
$673$		−	40.8601i		−	1.57504i	−0.616288	−	0.787521i	$-0.711364\pi$
$673$		−	40.8601i		−	1.57504i	0.616288	−	0.787521i	$-0.288636\pi$
$674$	9.71302	−	9.71302i	0.374131	−	0.374131i
$675$	19.1002	+	13.5059i	0.735167	+	0.519842i
$676$	−12.9134	−	1.49804i	−0.496669	−	0.0576169i
$677$			25.8399i			0.993108i	0.868006	+	0.496554i	$0.165401\pi$
$677$			25.8399i			0.993108i	−0.868006	+	0.496554i	$0.834599\pi$
$678$	12.6025	+	19.2256i	0.483998	+	0.738354i
$679$	−10.0345			−0.385088
$680$	3.09775			0.118793
$681$	−27.7908	+	18.2171i	−1.06494	+	0.698080i
$682$	−31.1850	+	31.1850i	−1.19413	+	1.19413i
$683$	−2.09971	+	2.09971i	−0.0803433	+	0.0803433i	−0.746136	−	0.665793i	$-0.768093\pi$
$683$	−2.09971	+	2.09971i	−0.0803433	+	0.0803433i	0.665793	+	0.746136i	$0.268093\pi$
$684$	2.65115	+	6.73365i	0.101369	+	0.257467i
$685$	15.3848			0.587823
$686$	19.9514			0.761747
$687$	6.77590	−	4.44167i	0.258517	−	0.169460i
$688$		−	8.88676i		−	0.338805i
$689$	−38.4210	+	34.2215i	−1.46372	+	1.30374i
$690$	1.19436	+	0.248532i	0.0454685	+	0.00946144i
$691$	24.5020	−	24.5020i	0.932098	−	0.932098i	−0.0657384	−	0.997837i	$-0.520940\pi$
$691$	24.5020	−	24.5020i	0.932098	−	0.932098i	0.997837	+	0.0657384i	$0.0209403\pi$
$692$			19.3507i			0.735603i
$693$	26.0884	+	11.3488i	0.991017	+	0.431104i
$694$	−17.2210	+	17.2210i	−0.653700	+	0.653700i
$695$	−5.43270	−	5.43270i	−0.206074	−	0.206074i
$696$	1.44573	−	0.947688i	0.0548002	−	0.0359220i
$697$	23.0039	+	23.0039i	0.871336	+	0.871336i
$698$			9.17078i			0.347119i
$699$	3.83866	−	18.4473i	0.145191	−	0.697741i
$700$	6.29428	+	6.29428i	0.237901	+	0.237901i
$701$	19.6710			0.742962			0.371481	−	0.928440i	$-0.378850\pi$
$701$	19.6710			0.742962			0.371481	+	0.928440i	$0.378850\pi$
$702$	14.6473	+	11.6815i	0.552827	+	0.440889i
$703$	−14.0000			−0.528020
$704$	3.39145	+	3.39145i	0.127820	+	0.127820i
$705$	0.124022	−	0.596009i	0.00467094	−	0.0224470i
$706$		−	12.2077i		−	0.459442i
$707$	−7.10320	−	7.10320i	−0.267143	−	0.267143i
$708$	2.04457	−	1.34023i	0.0768396	−	0.0503690i
$709$	−26.0944	−	26.0944i	−0.979997	−	0.979997i	0.0198066	−	0.999804i	$-0.493695\pi$
$709$	−26.0944	−	26.0944i	−0.979997	−	0.979997i	−0.999804	+	0.0198066i	$0.993695\pi$
$710$	−5.03536	+	5.03536i	−0.188974	+	0.188974i
$711$	0.571322	+	0.248532i	0.0214262	+	0.00932066i
$712$			3.59248i			0.134634i
$713$	−6.48920	+	6.48920i	−0.243023	+	0.243023i
$714$	14.7174	+	3.06250i	0.550783	+	0.114611i
$715$	−8.11716	−	9.11324i	−0.303565	−	0.340816i
$716$			7.08990i			0.264962i
$717$	−10.5277	+	6.90099i	−0.393164	+	0.257722i
$718$	−17.7735			−0.663302
$719$	−28.7437			−1.07196			−0.535979	−	0.844231i	$-0.680057\pi$
$719$	−28.7437			−1.07196			−0.535979	+	0.844231i	$0.680057\pi$
$720$	−0.775612	−	1.96997i	−0.0289053	−	0.0734165i
$721$	−17.0678	+	17.0678i	−0.635638	+	0.635638i
$722$	−9.32040	+	9.32040i	−0.346870	+	0.346870i
$723$	−10.3738	+	6.80012i	−0.385806	+	0.252899i
$724$	−6.20768			−0.230707
$725$	−4.49313			−0.166871
$726$	−11.3983	−	17.3885i	−0.423032	−	0.645348i
$727$			11.3848i			0.422239i	0.977460	+	0.211119i	$0.0677109\pi$
$727$			11.3848i			0.422239i	−0.977460	+	0.211119i	$0.932289\pi$
$728$	4.74166	+	5.32352i	0.175738	+	0.197303i
$729$	−9.00000	−	25.4558i	−0.333333	−	0.942809i
$730$	−1.20376	+	1.20376i	−0.0445532	+	0.0445532i
$731$			39.0084i			1.44278i
$732$	−16.2662	−	3.38480i	−0.601217	−	0.125106i
$733$	27.3154	−	27.3154i	1.00892	−	1.00892i	0.00895888	−	0.999960i	$-0.497148\pi$
$733$	27.3154	−	27.3154i	1.00892	−	1.00892i	0.999960	−	0.00895888i	$-0.00285174\pi$
$734$	13.7071	+	13.7071i	0.505939	+	0.505939i
$735$	2.07101	+	3.15939i	0.0763903	+	0.116536i
$736$	0.705720	+	0.705720i	0.0260132	+	0.0260132i
$737$		−	39.3154i		−	1.44820i
$738$	8.86933	−	20.3887i	0.326484	−	0.750519i
$739$	−2.26764	−	2.26764i	−0.0834166	−	0.0834166i	0.664167	−	0.747584i	$-0.268786\pi$
$739$	−2.26764	−	2.26764i	−0.0834166	−	0.0834166i	−0.747584	+	0.664167i	$0.768786\pi$
$740$	4.09579			0.150564
$741$	3.91507	−	14.5469i	0.143824	−	0.534393i
$742$	28.2155			1.03582
$743$	−0.645871	−	0.645871i	−0.0236947	−	0.0236947i	0.695160	−	0.718855i	$-0.255333\pi$
$743$	−0.645871	−	0.645871i	−0.0236947	−	0.0236947i	−0.718855	+	0.695160i	$0.755333\pi$
$744$	15.5925	+	3.24460i	0.571648	+	0.118953i
$745$		−	2.53528i		−	0.0928856i
$746$	17.2643	+	17.2643i	0.632090	+	0.632090i
$747$	−14.2625	−	36.2253i	−0.521838	−	1.32541i
$748$	−14.8868	−	14.8868i	−0.544314	−	0.544314i
$749$	9.48332	−	9.48332i	0.346513	−	0.346513i
$750$	−2.36618	+	11.3711i	−0.0864006	+	0.415213i
$751$			26.5964i			0.970516i	0.874371	+	0.485258i	$0.161274\pi$
$751$			26.5964i			0.970516i	−0.874371	+	0.485258i	$0.838726\pi$
$752$	0.352168	−	0.352168i	0.0128422	−	0.0128422i
$753$	−6.79620	+	32.6603i	−0.247667	+	1.19021i
$754$	−3.59248	−	0.207679i	−0.130830	−	0.00756324i
$755$			4.00545i			0.145773i
$756$	−1.73736	−	10.1261i	−0.0631872	−	0.368282i
$757$	−8.19984			−0.298028			−0.149014	−	0.988835i	$-0.547610\pi$
$757$	−8.19984			−0.298028			−0.149014	+	0.988835i	$0.547610\pi$
$758$	−3.07891			−0.111831
$759$	−4.54534	−	6.93406i	−0.164985	−	0.251690i
$760$	−1.20376	+	1.20376i	−0.0436650	+	0.0436650i
$761$	7.64739	−	7.64739i	0.277218	−	0.277218i	−0.554780	−	0.831997i	$-0.687197\pi$
$761$	7.64739	−	7.64739i	0.277218	−	0.277218i	0.831997	+	0.554780i	$0.187197\pi$
$762$	11.0329	+	16.8311i	0.399681	+	0.609727i
$763$	9.24884			0.334831
$764$	9.77702			0.353720
$765$	3.40454	+	8.64718i	0.123091	+	0.312639i
$766$			5.85620i			0.211593i
$767$	−5.08053	−	0.293703i	−0.183447	−	0.0106050i
$768$	0.352860	−	1.69573i	0.0127327	−	0.0611893i
$769$	6.14772	−	6.14772i	0.221692	−	0.221692i	−0.587518	−	0.809211i	$-0.699895\pi$
$769$	6.14772	−	6.14772i	0.221692	−	0.221692i	0.809211	+	0.587518i	$0.199895\pi$
$770$			6.69256i			0.241183i
$771$	6.43934	−	30.9453i	0.231907	−	1.11447i
$772$	−3.79624	+	3.79624i	−0.136630	+	0.136630i
$773$	−25.8379	−	25.8379i	−0.929326	−	0.929326i	0.0683364	−	0.997662i	$-0.478231\pi$
$773$	−25.8379	−	25.8379i	−0.929326	−	0.929326i	−0.997662	+	0.0683364i	$0.978231\pi$
$774$	24.8068	−	9.76687i	0.891663	−	0.351063i
$775$	−29.2716	−	29.2716i	−1.05147	−	1.05147i
$776$		−	5.07499i		−	0.182182i
$777$	19.4590	+	4.04918i	0.698088	+	0.145264i
$778$	4.79624	+	4.79624i	0.171954	+	0.171954i
$779$	−17.8783			−0.640555
$780$	−1.14538	+	4.25578i	−0.0410111	+	0.152381i
$781$	48.3966			1.73177
$782$	−3.09775	−	3.09775i	−0.110775	−	0.110775i
$783$	4.23432	+	2.99411i	0.151322	+	0.107001i
$784$			3.09052i			0.110376i
$785$	−2.38012	−	2.38012i	−0.0849502	−	0.0849502i
$786$	−6.73222	−	10.2702i	−0.240130	−	0.366327i
$787$	17.0905	+	17.0905i	0.609211	+	0.609211i	0.942740	−	0.333529i	$-0.108239\pi$
$787$	17.0905	+	17.0905i	0.609211	+	0.609211i	−0.333529	+	0.942740i	$0.608239\pi$
$788$	7.28193	−	7.28193i	0.259408	−	0.259408i
$789$	6.76960	+	1.40867i	0.241004	+	0.0501500i
$790$			0.146563i			0.00521449i
$791$	−18.5560	+	18.5560i	−0.659776	+	0.659776i
$792$	−5.73970	+	13.1944i	−0.203951	+	0.468841i
$793$	23.0039	+	25.8268i	0.816893	+	0.917136i
$794$			24.4257i			0.866835i
$795$	9.56266	+	14.5881i	0.339153	+	0.517388i
$796$	18.1544			0.643466
$797$	44.8969			1.59033			0.795164	−	0.606394i	$-0.207385\pi$
$797$	44.8969			1.59033			0.795164	+	0.606394i	$0.207385\pi$
$798$	−6.90910	+	4.52898i	−0.244579	+	0.160324i
$799$	−1.54584	+	1.54584i	−0.0546878	+	0.0546878i
$800$	−3.18337	+	3.18337i	−0.112549	+	0.112549i
$801$	−10.0282	+	3.94827i	−0.354328	+	0.139505i
$802$	31.3926			1.10851
$803$	11.5697			0.408287
$804$	−11.8741	+	7.78358i	−0.418767	+	0.274506i
$805$			1.39264i			0.0490841i
$806$	−22.0511	−	24.7571i	−0.776717	−	0.872030i
$807$	−17.7735	−	3.69845i	−0.625658	−	0.130192i
$808$	3.59248	−	3.59248i	0.126383	−	0.126383i
$809$		−	40.8011i		−	1.43449i	−0.696821	−	0.717245i	$-0.745403\pi$
$809$		−	40.8011i		−	1.43449i	0.696821	−	0.717245i	$-0.254597\pi$
$810$	4.64663	−	4.33014i	0.163266	−	0.152146i
$811$	−23.2794	+	23.2794i	−0.817450	+	0.817450i	−0.985738	−	0.168288i	$-0.946176\pi$
$811$	−23.2794	+	23.2794i	−0.817450	+	0.817450i	0.168288	+	0.985738i	$0.446176\pi$
$812$	1.39538	+	1.39538i	0.0489681	+	0.0489681i
$813$	−6.90677	+	4.52745i	−0.242231	+	0.158785i
$814$	−19.6830	−	19.6830i	−0.689889	−	0.689889i
$815$			11.3930i			0.399078i
$816$	−1.54888	+	7.44338i	−0.0542215	+	0.260570i
$817$	−15.1583	−	15.1583i	−0.530323	−	0.530323i
$818$	4.28031			0.149658
$819$	−9.64902	+	19.0868i	−0.337164	+	0.666946i
$820$	5.23040			0.182653
$821$	−17.7633	−	17.7633i	−0.619943	−	0.619943i	0.325574	−	0.945517i	$-0.394443\pi$
$821$	−17.7633	−	17.7633i	−0.619943	−	0.619943i	−0.945517	+	0.325574i	$0.894443\pi$
$822$	−7.69240	+	36.9671i	−0.268303	+	1.28938i
$823$			19.1238i			0.666615i	0.942818	+	0.333308i	$0.108165\pi$
$823$			19.1238i			0.666615i	−0.942818	+	0.333308i	$0.891835\pi$
$824$	−8.63213	−	8.63213i	−0.300715	−	0.300715i
$825$	31.2782	−	20.5031i	1.08897	−	0.713828i
$826$	1.97336	+	1.97336i	0.0686620	+	0.0686620i
$827$	12.8615	−	12.8615i	0.447237	−	0.447237i	−0.447198	−	0.894435i	$-0.647578\pi$
$827$	12.8615	−	12.8615i	0.447237	−	0.447237i	0.894435	+	0.447198i	$0.147578\pi$
$828$	−1.19436	+	2.74558i	−0.0415069	+	0.0954156i
$829$			39.3926i			1.36816i	0.729406	+	0.684081i	$0.239797\pi$
$829$			39.3926i			1.36816i	−0.729406	+	0.684081i	$0.760203\pi$
$830$	6.47591	−	6.47591i	0.224782	−	0.224782i
$831$	−46.1886	−	9.61128i	−1.60227	−	0.333412i
$832$	−2.69240	+	2.39812i	−0.0933422	+	0.0831399i
$833$		−	13.5658i		−	0.470028i
$834$	15.7702	−	10.3375i	0.546078	−	0.357959i
$835$	7.76568			0.268743
$836$	11.5697			0.400148
$837$	8.07960	+	47.0914i	0.279272	+	1.62772i
$838$	24.1983	−	24.1983i	0.835916	−	0.835916i
$839$	−21.9608	+	21.9608i	−0.758169	+	0.758169i	−0.975989	−	0.217820i	$-0.930106\pi$
$839$	−21.9608	+	21.9608i	−0.758169	+	0.758169i	0.217820	+	0.975989i	$0.430106\pi$
$840$	2.02130	−	1.32498i	0.0697415	−	0.0457162i
$841$	28.0039			0.965652
$842$	4.06366			0.140043
$843$	3.01684	+	4.60228i	0.103905	+	0.158511i
$844$			11.2943i			0.388765i
$845$	7.19158	−	5.69648i	0.247398	−	0.195965i
$846$	1.37010	+	0.596009i	0.0471050	+	0.0204912i
$847$	16.7829	−	16.7829i	0.576668	−	0.576668i
$848$			14.2702i			0.490039i
$849$	−5.09383	−	1.05996i	−0.174820	−	0.0363778i
$850$	13.9734	−	13.9734i	0.479282	−	0.479282i
$851$	−4.09579	−	4.09579i	−0.140402	−	0.140402i
$852$	−9.58146	−	14.6168i	−0.328255	−	0.500764i
$853$	−18.8813	−	18.8813i	−0.646483	−	0.646483i	0.305658	−	0.952141i	$-0.401123\pi$
$853$	−18.8813	−	18.8813i	−0.646483	−	0.646483i	−0.952141	+	0.305658i	$0.901123\pi$
$854$		−	18.9666i		−	0.649025i
$855$	−4.68320	−	2.03724i	−0.160162	−	0.0696723i
$856$	4.79624	+	4.79624i	0.163932	+	0.163932i
$857$	52.3802			1.78927			0.894637	−	0.446794i	$-0.147434\pi$
$857$	52.3802			1.78927			0.894637	+	0.446794i	$0.147434\pi$
$858$	25.9562	−	14.9476i	0.886129	−	0.510301i
$859$	30.9585			1.05629			0.528145	−	0.849154i	$-0.322888\pi$
$859$	30.9585			1.05629			0.528145	+	0.849154i	$0.322888\pi$
$860$	4.43466	+	4.43466i	0.151221	+	0.151221i
$861$	24.8495	+	5.17088i	0.846869	+	0.176223i
$862$		−	9.67516i		−	0.329537i
$863$	17.1155	+	17.1155i	0.582617	+	0.582617i	0.935622	−	0.353005i	$-0.114840\pi$
$863$	17.1155	+	17.1155i	0.582617	+	0.582617i	−0.353005	+	0.935622i	$0.614840\pi$
$864$	5.12132	−	0.878680i	0.174231	−	0.0298933i
$865$	−9.65636	−	9.65636i	−0.328326	−	0.328326i
$866$	−20.7064	+	20.7064i	−0.703633	+	0.703633i
$867$	0.800160	−	3.84530i	0.0271748	−	0.130593i
$868$			18.1810i			0.617105i
$869$	0.704335	−	0.704335i	0.0238929	−	0.0238929i
$870$	−0.248532	+	1.19436i	−0.00842601	+	0.0404926i
$871$	29.5059	+	1.70572i	0.999769	+	0.0577961i
$872$			4.67765i			0.158405i
$873$	14.1665	−	5.57760i	0.479464	−	0.188773i
$874$	2.40752			0.0814356
$875$	−13.2588			−0.448230
$876$	−2.29055	−	3.49431i	−0.0773907	−	0.118062i
$877$	−36.1117	+	36.1117i	−1.21940	+	1.21940i	−0.251564	+	0.967841i	$0.580945\pi$
$877$	−36.1117	+	36.1117i	−1.21940	+	1.21940i	−0.967841	+	0.251564i	$0.919055\pi$
$878$	12.7279	−	12.7279i	0.429547	−	0.429547i
$879$	−9.38426	−	14.3160i	−0.316523	−	0.482866i
$880$	−3.38480			−0.114102
$881$	9.49661			0.319949			0.159975	−	0.987121i	$-0.448859\pi$
$881$	9.49661			0.319949			0.159975	+	0.987121i	$0.448859\pi$
$882$	−8.62699	+	3.39659i	−0.290486	+	0.114369i
$883$			3.64852i			0.122783i	0.998114	+	0.0613913i	$0.0195538\pi$
$883$			3.64852i			0.122783i	−0.998114	+	0.0613913i	$0.980446\pi$
$884$	11.8183	−	10.5265i	0.397491	−	0.354045i
$885$	−0.351477	+	1.68908i	−0.0118148	+	0.0567778i
$886$	−18.8401	+	18.8401i	−0.632946	+	0.632946i
$887$		−	33.6208i		−	1.12888i	−0.825475	−	0.564439i	$-0.809093\pi$
$887$		−	33.6208i		−	1.12888i	0.825475	−	0.564439i	$-0.190907\pi$
$888$	−2.04789	+	9.84150i	−0.0687228	+	0.330259i
$889$	−16.2449	+	16.2449i	−0.544837	+	0.544837i
$890$	−1.79272	−	1.79272i	−0.0600920	−	0.0600920i
$891$	−43.1394	−	1.52092i	−1.44522	−	0.0509528i
$892$	6.19436	+	6.19436i	0.207403	+	0.207403i
$893$		−	1.20140i		−	0.0402033i
$894$	6.09187	+	1.26764i	0.203742	+	0.0423963i
$895$	−3.53800	−	3.53800i	−0.118262	−	0.118262i
$896$	1.97724			0.0660550
$897$	5.40116	−	3.11040i	0.180339	−	0.103853i
$898$	−36.7508			−1.22639
$899$	−6.48920	−	6.48920i	−0.216427	−	0.216427i
$900$	−12.3848	−	5.38753i	−0.412827	−	0.179584i
$901$		−	62.6387i		−	2.08680i
$902$	−25.1356	−	25.1356i	−0.836922	−	0.836922i
$903$	16.6848	+	25.4532i	0.555235	+	0.847029i
$904$	−9.38480	−	9.38480i	−0.312134	−	0.312134i
$905$	3.09775	−	3.09775i	0.102973	−	0.102973i
$906$	−9.62442	−	2.00272i	−0.319750	−	0.0665360i
$907$			17.8907i			0.594050i	0.954870	+	0.297025i	$0.0959945\pi$
$907$			17.8907i			0.594050i	−0.954870	+	0.297025i	$0.904005\pi$
$908$	13.5658	−	13.5658i	0.450197	−	0.450197i
$909$	13.9764	+	6.07992i	0.463570	+	0.201658i
$910$	−5.02272	−	0.290361i	−0.166502	−	0.00962537i
$911$		−	22.7554i		−	0.753921i	−0.926229	−	0.376961i	$-0.876969\pi$
$911$		−	22.7554i		−	0.753921i	0.926229	−	0.376961i	$-0.123031\pi$
$912$	−2.29055	−	3.49431i	−0.0758479	−	0.115708i
$913$	−62.2422			−2.05991
$914$	−26.7155			−0.883669
$915$	9.80624	−	6.42808i	0.324184	−	0.212506i
$916$	−3.30760	+	3.30760i	−0.109286	+	0.109286i
$917$	9.91254	−	9.91254i	0.327341	−	0.327341i
$918$	−22.4800	+	3.85696i	−0.741950	+	0.127299i
$919$	9.78136			0.322657			0.161329	−	0.986901i	$-0.448422\pi$
$919$	9.78136			0.322657			0.161329	+	0.986901i	$0.448422\pi$
$920$	−0.704335			−0.0232212
$921$	−18.1973	+	11.9285i	−0.599620	+	0.393057i
$922$			35.1289i			1.15691i
$923$	−2.09971	+	36.3212i	−0.0691129	+	1.19553i
$924$	−16.0811	−	3.34628i	−0.529030	−	0.110085i
$925$	18.4753	−	18.4753i	0.607465	−	0.607465i
$926$		−	19.9325i		−	0.655024i
$927$	14.6090	−	33.5831i	0.479823	−	1.10301i
$928$	−0.705720	+	0.705720i	−0.0231664	+	0.0231664i
$929$	23.5933	+	23.5933i	0.774072	+	0.774072i	0.978816	−	0.204744i	$-0.0656361\pi$
$929$	23.5933	+	23.5933i	0.774072	+	0.774072i	−0.204744	+	0.978816i	$0.565636\pi$
$930$	−9.40006	+	6.16183i	−0.308240	+	0.202054i
$931$	5.27156	+	5.27156i	0.172768	+	0.172768i
$932$			10.8787i			0.356344i
$933$	−4.68320	+	22.5059i	−0.153321	+	0.736809i
$934$	11.7923	+	11.7923i	0.385857	+	0.385857i
$935$	14.8576			0.485894
$936$	−9.65325	−	4.88004i	−0.315526	−	0.159509i
$937$	−32.8840			−1.07427			−0.537137	−	0.843495i	$-0.680494\pi$
$937$	−32.8840			−1.07427			−0.537137	+	0.843495i	$0.680494\pi$
$938$	−11.4606	−	11.4606i	−0.374201	−	0.374201i
$939$	−0.322302	+	1.54888i	−0.0105179	+	0.0505456i
$940$			0.351477i			0.0114639i
$941$	−10.3930	−	10.3930i	−0.338801	−	0.338801i	0.517115	−	0.855916i	$-0.327006\pi$
$941$	−10.3930	−	10.3930i	−0.338801	−	0.338801i	−0.855916	+	0.517115i	$0.827006\pi$
$942$	6.90910	−	4.52898i	0.225111	−	0.147562i
$943$	−5.23040	−	5.23040i	−0.170325	−	0.170325i
$944$	−0.998038	+	0.998038i	−0.0324834	+	0.0324834i
$945$	5.92008	+	4.18613i	0.192580	+	0.136175i
$946$		−	42.6230i		−	1.38579i
$947$	−5.88851	+	5.88851i	−0.191351	+	0.191351i	−0.796280	−	0.604929i	$-0.793202\pi$
$947$	−5.88851	+	5.88851i	−0.191351	+	0.191351i	0.604929	+	0.796280i	$0.293202\pi$
$948$	−0.352168	−	0.0732817i	−0.0114379	−	0.00238008i
$949$	−0.501960	+	8.68300i	−0.0162943	+	0.281862i
$950$			10.8599i			0.352340i
$951$	−1.11482	+	0.730776i	−0.0361506	+	0.0236970i
$952$	−8.67908			−0.281291
$953$	−35.4268			−1.14759			−0.573794	−	0.819000i	$-0.694529\pi$
$953$	−35.4268			−1.14759			−0.573794	+	0.819000i	$0.694529\pi$
$954$	−39.8342	+	15.6834i	−1.28968	+	0.507769i
$955$	−4.87892	+	4.87892i	−0.157878	+	0.157878i
$956$	5.13900	−	5.13900i	0.166207	−	0.166207i
$957$	6.93406	−	4.54534i	0.224146	−	0.146930i
$958$	37.4565			1.21017
$959$	−43.1042			−1.39191
$960$	0.670116	+	1.02228i	0.0216279	+	0.0329941i
$961$		−	53.5510i		−	1.72745i
$962$	15.6259	−	13.9180i	0.503799	−	0.448734i
$963$	−8.11716	+	18.6596i	−0.261572	+	0.601299i
$964$	5.06388	−	5.06388i	0.163097	−	0.163097i
$965$		−	3.78879i		−	0.121966i
$966$	−3.34628	−	0.696320i	−0.107665	−	0.0224037i
$967$	−32.3221	+	32.3221i	−1.03941	+	1.03941i	−0.0402185	+	0.999191i	$0.512805\pi$
$967$	−32.3221	+	32.3221i	−1.03941	+	1.03941i	−0.999191	+	0.0402185i	$0.987195\pi$
$968$	8.48805	+	8.48805i	0.272816	+	0.272816i
$969$	10.0544	+	15.3383i	0.322993	+	0.492736i
$970$	2.53252	+	2.53252i	0.0813142	+	0.0813142i
$971$		−	58.4760i		−	1.87658i	−0.345845	−	0.938292i	$-0.612408\pi$
$971$		−	58.4760i		−	1.87658i	0.345845	−	0.938292i	$-0.387592\pi$
$972$	8.08130	+	13.3301i	0.259208	+	0.427564i
$973$	15.2210	+	15.2210i	0.487963	+	0.487963i
$974$	5.20301			0.166715
$975$	14.0304	+	24.3636i	0.449333	+	0.780260i
$976$	9.59248			0.307048
$977$	34.4720	+	34.4720i	1.10286	+	1.10286i	0.994064	+	0.108793i	$0.0346987\pi$
$977$	34.4720	+	34.4720i	1.10286	+	1.10286i	0.108793	+	0.994064i	$0.465301\pi$
$978$	−27.3754	−	5.69648i	−0.875369	−	0.182153i
$979$			17.2304i			0.550686i
$980$	−1.54223	−	1.54223i	−0.0492647	−	0.0492647i
$981$	−13.0574	+	5.14091i	−0.416890	+	0.164137i
$982$	−28.7868	−	28.7868i	−0.918625	−	0.918625i
$983$	−26.6891	+	26.6891i	−0.851251	+	0.851251i	−0.990287	−	0.139037i	$-0.955599\pi$
$983$	−26.6891	+	26.6891i	−0.851251	+	0.851251i	0.139037	+	0.990287i	$0.455599\pi$
$984$	−2.61520	+	12.5678i	−0.0833695	+	0.400646i
$985$			7.26764i			0.231566i
$986$	3.09775	−	3.09775i	0.0986525	−	0.0986525i
$987$	−0.347477	+	1.66986i	−0.0110603	+	0.0531522i
$988$	−0.501960	+	8.68300i	−0.0159695	+	0.276243i
$989$		−	8.86933i		−	0.282028i
$990$	−3.72002	−	9.44846i	−0.118230	−	0.300292i
$991$	−13.3049			−0.422644			−0.211322	−	0.977417i	$-0.567777\pi$
$991$	−13.3049			−0.422644			−0.211322	+	0.977417i	$0.567777\pi$
$992$	−9.19516			−0.291947
$993$	14.2243	+	21.6996i	0.451394	+	0.688616i
$994$	14.1078	−	14.1078i	0.447471	−	0.447471i
$995$	−9.05939	+	9.05939i	−0.287202	+	0.287202i
$996$	12.3226	+	18.7985i	0.390456	+	0.595653i
$997$	15.0838			0.477710			0.238855	−	0.971055i	$-0.423228\pi$
$997$	15.0838			0.477710			0.238855	+	0.971055i	$0.423228\pi$
$998$	−14.8520			−0.470132
$999$	−29.7226	+	5.09960i	−0.940383	+	0.161344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.g.a.5.5	yes	12
3.2	odd	2	inner	78.2.g.a.5.2	✓	12
4.3	odd	2		624.2.bf.f.161.4		12
12.11	even	2		624.2.bf.f.161.3		12
13.5	odd	4		1014.2.g.b.437.5		12
13.8	odd	4	inner	78.2.g.a.47.2	yes	12
13.12	even	2		1014.2.g.b.239.2		12
39.5	even	4		1014.2.g.b.437.2		12
39.8	even	4	inner	78.2.g.a.47.5	yes	12
39.38	odd	2		1014.2.g.b.239.5		12
52.47	even	4		624.2.bf.f.593.4		12
156.47	odd	4		624.2.bf.f.593.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.g.a.5.2	✓	12	3.2	odd	2	inner
78.2.g.a.5.5	yes	12	1.1	even	1	trivial
78.2.g.a.47.2	yes	12	13.8	odd	4	inner
78.2.g.a.47.5	yes	12	39.8	even	4	inner
624.2.bf.f.161.3		12	12.11	even	2
624.2.bf.f.161.4		12	4.3	odd	2
624.2.bf.f.593.3		12	156.47	odd	4
624.2.bf.f.593.4		12	52.47	even	4
1014.2.g.b.239.2		12	13.12	even	2
1014.2.g.b.239.5		12	39.38	odd	2
1014.2.g.b.437.2		12	39.5	even	4
1014.2.g.b.437.5		12	13.5	odd	4

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} -0.705720i q^{10} +(-3.39145 + 3.39145i) q^{11} +(1.69573 + 0.352860i) q^{12} +(-2.39812 - 2.69240i) q^{13} +1.97724i q^{14} +(-1.02228 + 0.670116i) q^{15} -1.00000 q^{16} +4.38949 q^{17} +(-1.09904 - 2.79144i) q^{18} +(-1.70572 + 1.70572i) q^{19} +(0.499019 - 0.499019i) q^{20} +(2.86417 - 1.87749i) q^{21} -4.79624 q^{22} -0.998038 q^{23} +(0.949550 + 1.44857i) q^{24} -4.50196i q^{25} +(0.208088 - 3.59954i) q^{26} +(-3.00000 + 4.24264i) q^{27} +(-1.39812 + 1.39812i) q^{28} -0.998038i q^{29} +(-1.19671 - 0.249020i) q^{30} +(6.50196 - 6.50196i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.55427 + 6.94769i) q^{33} +(3.10384 + 3.10384i) q^{34} -1.39538i q^{35} +(1.19671 - 2.75098i) q^{36} +(4.10384 + 4.10384i) q^{37} -2.41225 q^{38} +(-5.41178 + 3.11652i) q^{39} +0.705720 q^{40} +(5.24068 + 5.24068i) q^{41} +(3.35286 + 0.697689i) q^{42} +8.88676i q^{43} +(-3.39145 - 3.39145i) q^{44} +(0.775612 + 1.96997i) q^{45} +(-0.705720 - 0.705720i) q^{46} +(-0.352168 + 0.352168i) q^{47} +(-0.352860 + 1.69573i) q^{48} -3.09052i q^{49} +(3.18337 - 3.18337i) q^{50} +(1.54888 - 7.44338i) q^{51} +(2.69240 - 2.39812i) q^{52} -14.2702i q^{53} +(-5.12132 + 0.878680i) q^{54} +3.38480 q^{55} -1.97724 q^{56} +(2.29055 + 3.49431i) q^{57} +(0.705720 - 0.705720i) q^{58} +(0.998038 - 0.998038i) q^{59} +(-0.670116 - 1.02228i) q^{60} -9.59248 q^{61} +9.19516 q^{62} +(-2.17306 - 5.51934i) q^{63} -1.00000i q^{64} +(-0.146852 + 2.54027i) q^{65} +(-1.69240 + 8.13311i) q^{66} +(-5.79624 + 5.79624i) q^{67} +4.38949i q^{68} +(-0.352168 + 1.69240i) q^{69} +(0.986681 - 0.986681i) q^{70} +(-7.13508 - 7.13508i) q^{71} +(2.79144 - 1.09904i) q^{72} +(-1.70572 - 1.70572i) q^{73} +5.80371i q^{74} +(-7.63409 - 1.58856i) q^{75} +(-1.70572 - 1.70572i) q^{76} -9.48332 q^{77} +(-6.03041 - 1.62299i) q^{78} -0.207679 q^{79} +(0.499019 + 0.499019i) q^{80} +(6.13578 + 6.58424i) q^{81} +7.41144i q^{82} +(9.17632 + 9.17632i) q^{83} +(1.87749 + 2.86417i) q^{84} +(-2.19044 - 2.19044i) q^{85} +(-6.28389 + 6.28389i) q^{86} +(-1.69240 - 0.352168i) q^{87} -4.79624i q^{88} +(2.54027 - 2.54027i) q^{89} +(-0.844540 + 1.94142i) q^{90} +(0.411439 - 7.11716i) q^{91} -0.998038i q^{92} +(-8.73127 - 13.3198i) q^{93} -0.498040 q^{94} +1.70237 q^{95} +(-1.44857 + 0.949550i) q^{96} +(-3.58856 + 3.58856i) q^{97} +(2.18533 - 2.18533i) q^{98} +(13.3884 - 5.27124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^7 - 12 * q^16 - 12 * q^19 - 36 * q^27 + 12 * q^28 + 12 * q^31 + 36 * q^33 + 12 * q^37 + 36 * q^42 + 36 * q^45 + 12 * q^52 - 36 * q^54 - 36 * q^57 - 36 * q^63 - 12 * q^67 - 12 * q^73 - 12 * q^76 - 36 * q^78 + 72 * q^79 - 72 * q^85 - 12 * q^91 + 36 * q^93 - 72 * q^94 - 60 * q^97 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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