LMFDB - Embedded newform 78.2.g.a.47.5

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			47.5
Root			$-0.949550 - 1.44857i$ of defining polynomial
Character	$\chi$	$=$	78.47
Dual form			78.2.g.a.5.5

$q$-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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

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

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	−0.809831	−	0.586663i	$-0.800441\pi$
$5$	−0.499019	+	0.499019i	−0.223168	+	0.223168i	0.586663	+	0.809831i	$0.300441\pi$
$6$	1.44857	+	0.949550i	0.591376	+	0.387652i
$7$	1.39812	−	1.39812i	0.528440	−	0.528440i	−0.391667	−	0.920107i	$-0.628102\pi$
$7$	1.39812	−	1.39812i	0.528440	−	0.528440i	0.920107	+	0.391667i	$0.128102\pi$
$8$	−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	−0.999740	−	0.0228223i	$-0.992735\pi$
$11$	−3.39145	−	3.39145i	−1.02256	−	1.02256i	−0.0228223	−	0.999740i	$-0.507265\pi$
$12$	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	0.483838	−	0.875157i	$-0.339242\pi$
$19$	−1.70572	−	1.70572i	−0.391319	−	0.391319i	−0.875157	+	0.483838i	$0.839242\pi$
$20$	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	$0.0295387\pi$
$29$			0.998038i			0.185331i	−0.995697	+	0.0926655i	$0.970461\pi$
$30$	−1.19671	+	0.249020i	−0.218488	+	0.0454646i
$31$	6.50196	+	6.50196i	1.16779	+	1.16779i	0.982727	+	0.185059i	$0.0592476\pi$
$31$	6.50196	+	6.50196i	1.16779	+	1.16779i	0.185059	+	0.982727i	$0.440752\pi$
$32$	−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	−0.284121	−	0.958788i	$-0.591702\pi$
$37$	4.10384	−	4.10384i	0.674667	−	0.674667i	0.958788	+	0.284121i	$0.0917018\pi$
$38$	−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	−0.167428	−	0.985884i	$-0.553546\pi$
$41$	5.24068	−	5.24068i	0.818457	−	0.818457i	0.985884	+	0.167428i	$0.0535461\pi$
$42$	3.35286	−	0.697689i	0.517358	−	0.107656i
$43$		−	8.88676i		−	1.35522i	−0.735422	−	0.677609i	$-0.763016\pi$
$43$		−	8.88676i		−	1.35522i	0.735422	−	0.677609i	$-0.236984\pi$
$44$	−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	0.680956	−	0.732325i	$-0.261565\pi$
$47$	−0.352168	−	0.352168i	−0.0513689	−	0.0513689i	−0.732325	+	0.680956i	$0.761565\pi$
$48$	−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	$0.436356\pi$
$53$			14.2702i			1.96016i	−0.198613	+	0.980078i	$0.563644\pi$
$54$	−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	0.769083	−	0.639149i	$-0.220713\pi$
$59$	0.998038	+	0.998038i	0.129934	+	0.129934i	−0.639149	+	0.769083i	$0.720713\pi$
$60$	−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	0.258017	−	0.966140i	$-0.416931\pi$
$67$	−5.79624	−	5.79624i	−0.708123	−	0.708123i	−0.966140	+	0.258017i	$0.916931\pi$
$68$		−	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	−0.989730	−	0.142952i	$-0.954341\pi$
$71$	−7.13508	+	7.13508i	−0.846778	+	0.846778i	0.142952	+	0.989730i	$0.454341\pi$
$72$	2.79144	+	1.09904i	0.328974	+	0.129523i
$73$	−1.70572	+	1.70572i	−0.199639	+	0.199639i	−0.799845	−	0.600206i	$-0.795085\pi$
$73$	−1.70572	+	1.70572i	−0.199639	+	0.199639i	0.600206	+	0.799845i	$0.295085\pi$
$74$		−	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	0.00725871	−	0.999974i	$-0.497689\pi$
$83$	9.17632	−	9.17632i	1.00723	−	1.00723i	0.999974	−	0.00725871i	$-0.00231054\pi$
$84$	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	0.828805	−	0.559537i	$-0.189021\pi$
$89$	2.54027	+	2.54027i	0.269268	+	0.269268i	−0.559537	+	0.828805i	$0.689021\pi$
$90$	−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	0.501053	−	0.865416i	$-0.332946\pi$
$97$	−3.58856	−	3.58856i	−0.364363	−	0.364363i	−0.865416	+	0.501053i	$0.832946\pi$
$98$	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	$-0.794598\pi$
$103$		−	12.2077i		−	1.20286i	0.798926	−	0.601429i	$-0.205402\pi$
$104$	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	$0.106329\pi$
$107$			6.78291i			0.655728i	−0.944725	+	0.327864i	$0.893671\pi$
$108$	−4.24264	+	3.00000i	−0.408248	+	0.288675i
$109$	3.30760	+	3.30760i	0.316811	+	0.316811i	0.847541	−	0.530730i	$-0.178082\pi$
$109$	3.30760	+	3.30760i	0.316811	+	0.316811i	−0.530730	+	0.847541i	$0.678082\pi$
$110$	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	$-0.785397\pi$
$113$		−	13.2721i		−	1.24854i	0.781211	−	0.624268i	$-0.214603\pi$
$114$	−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	$-0.827601\pi$
$127$		−	11.6191i		−	1.03103i	0.856881	−	0.515515i	$-0.172399\pi$
$128$	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	$0.100237\pi$
$131$			7.08990i			0.619448i	−0.950827	+	0.309724i	$0.899763\pi$
$132$	−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	−0.916142	−	0.400854i	$-0.868714\pi$
$137$	−15.4150	−	15.4150i	−1.31700	−	1.31700i	−0.400854	−	0.916142i	$-0.631286\pi$
$138$	−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	−0.595356	−	0.803462i	$-0.702989\pi$
$149$	2.54027	−	2.54027i	0.208107	−	0.208107i	0.803462	+	0.595356i	$0.202989\pi$
$150$	−4.27484	+	6.52140i	−0.349039	+	0.532470i
$151$	−4.01332	+	4.01332i	−0.326599	+	0.326599i	−0.851292	−	0.524693i	$-0.824180\pi$
$151$	−4.01332	+	4.01332i	−0.326599	+	0.326599i	0.524693	+	0.851292i	$0.324180\pi$
$152$			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	−0.994908	−	0.100788i	$-0.967864\pi$
$163$	−11.4154	+	11.4154i	−0.894120	+	0.894120i	0.100788	+	0.994908i	$0.467864\pi$
$164$	−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	0.338764	−	0.940871i	$-0.389991\pi$
$167$	−7.78095	−	7.78095i	−0.602108	−	0.602108i	−0.940871	+	0.338764i	$0.889991\pi$
$168$	−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	$-0.925896\pi$
$181$		−	6.20768i		−	0.461413i	0.973023	−	0.230707i	$-0.0741038\pi$
$182$	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	$0.115084\pi$
$191$			9.77702i			0.707441i	−0.935351	+	0.353720i	$0.884916\pi$
$192$	−1.69573	+	0.352860i	−0.122379	+	0.0254655i
$193$	3.79624	−	3.79624i	0.273259	−	0.273259i	−0.557152	−	0.830411i	$-0.688106\pi$
$193$	3.79624	−	3.79624i	0.273259	−	0.273259i	0.830411	+	0.557152i	$0.188106\pi$
$194$	−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	−0.917213	−	0.398397i	$-0.869567\pi$
$197$	−7.28193	+	7.28193i	−0.518816	+	0.518816i	0.398397	+	0.917213i	$0.369567\pi$
$198$	13.1944	−	5.73970i	0.937682	−	0.407903i
$199$			18.1544i			1.28693i	0.765475	+	0.643466i	$0.222504\pi$
$199$			18.1544i			1.28693i	−0.765475	+	0.643466i	$0.777496\pi$
$200$	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	0.883409	−	0.468604i	$-0.155243\pi$
$223$	6.19436	+	6.19436i	0.414805	+	0.414805i	−0.468604	+	0.883409i	$0.655243\pi$
$224$			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	−0.995470	−	0.0950753i	$-0.969691\pi$
$227$	−13.5658	+	13.5658i	−0.900395	+	0.900395i	0.0950753	+	0.995470i	$0.469691\pi$
$228$	−3.49431	−	2.29055i	−0.231417	−	0.151696i
$229$	3.30760	−	3.30760i	0.218572	−	0.218572i	−0.589324	−	0.807897i	$-0.700606\pi$
$229$	3.30760	−	3.30760i	0.218572	−	0.218572i	0.807897	+	0.589324i	$0.200606\pi$
$230$		−	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	−0.853503	−	0.521088i	$-0.825526\pi$
$239$	−5.13900	+	5.13900i	−0.332414	+	0.332414i	0.521088	+	0.853503i	$0.325526\pi$
$240$	1.02228	+	0.670116i	0.0659881	+	0.0432558i
$241$	−5.06388	+	5.06388i	−0.326193	+	0.326193i	−0.851137	−	0.524944i	$-0.824086\pi$
$241$	−5.06388	+	5.06388i	−0.326193	+	0.326193i	0.524944	+	0.851137i	$0.324086\pi$
$242$	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	$-0.960722\pi$
$263$		−	3.99215i		−	0.246167i	0.992396	−	0.123083i	$-0.0392783\pi$
$264$	−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	$0.103525\pi$
$269$			10.4814i			0.639060i	−0.947576	+	0.319530i	$0.896475\pi$
$270$	2.99411	−	2.11716i	0.182216	−	0.128846i
$271$	−3.37148	+	3.37148i	−0.204803	+	0.204803i	−0.802054	−	0.597251i	$-0.796260\pi$
$271$	−3.37148	+	3.37148i	−0.204803	+	0.204803i	0.597251	+	0.802054i	$0.296260\pi$
$272$	−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	$0.305080\pi$
$277$			27.2382i			1.63659i	−0.574801	+	0.818294i	$0.694920\pi$
$278$	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	0.636915	−	0.770934i	$-0.280210\pi$
$281$	−2.24656	−	2.24656i	−0.134019	−	0.134019i	−0.770934	+	0.636915i	$0.780210\pi$
$282$	−0.175738	−	0.844540i	−0.0104651	−	0.0502916i
$283$			3.00392i			0.178564i	0.996006	+	0.0892822i	$0.0284573\pi$
$283$			3.00392i			0.178564i	−0.996006	+	0.0892822i	$0.971543\pi$
$284$	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	0.881130	−	0.472874i	$-0.156783\pi$
$293$	6.98822	+	6.98822i	0.408256	+	0.408256i	−0.472874	+	0.881130i	$0.656783\pi$
$294$	−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	−0.913595	−	0.406625i	$-0.866706\pi$
$307$	−8.88284	+	8.88284i	−0.506971	+	0.506971i	0.406625	+	0.913595i	$0.366706\pi$
$308$			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	−0.722224	−	0.691659i	$-0.756880\pi$
$317$	−0.544191	+	0.544191i	−0.0305648	+	0.0305648i	0.691659	+	0.722224i	$0.256880\pi$
$318$	−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	0.353296	−	0.935512i	$-0.385061\pi$
$331$	−10.5925	−	10.5925i	−0.582215	−	0.582215i	−0.935512	+	0.353296i	$0.885061\pi$
$332$	−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	$0.122059\pi$
$337$			13.7363i			0.748263i	−0.927376	+	0.374131i	$0.877941\pi$
$338$	−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	$-0.773216\pi$
$347$		−	24.3542i		−	1.30740i	0.756754	−	0.653700i	$-0.226784\pi$
$348$	0.352168	+	1.69240i	0.0188782	+	0.0907222i
$349$	6.48472	−	6.48472i	0.347119	−	0.347119i	−0.511916	−	0.859035i	$-0.671064\pi$
$349$	6.48472	−	6.48472i	0.347119	−	0.347119i	0.859035	+	0.511916i	$0.171064\pi$
$350$	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	−0.898472	−	0.439030i	$-0.855322\pi$
$353$	−8.63213	+	8.63213i	−0.459442	+	0.459442i	0.439030	+	0.898472i	$0.355322\pi$
$354$	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	0.292855	−	0.956157i	$-0.405395\pi$
$359$	−12.5678	−	12.5678i	−0.663302	−	0.663302i	−0.956157	+	0.292855i	$0.905395\pi$
$360$	−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	0.648977	−	0.760808i	$-0.275197\pi$
$379$	−2.17712	−	2.17712i	−0.111831	−	0.111831i	−0.760808	+	0.648977i	$0.775197\pi$
$380$		−	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	−0.593351	−	0.804944i	$-0.702195\pi$
$383$	4.14096	−	4.14096i	0.211593	−	0.211593i	0.804944	+	0.593351i	$0.202195\pi$
$384$	−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	−0.125286	−	0.992121i	$-0.539985\pi$
$397$	17.2716	−	17.2716i	0.866835	−	0.866835i	0.992121	+	0.125286i	$0.0399848\pi$
$398$	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	0.993346	+	0.115166i	$0.0367401\pi$
$401$	22.1979	+	22.1979i	1.10851	+	1.10851i	0.115166	+	0.993346i	$0.463260\pi$
$402$	−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	0.777965	−	0.628307i	$-0.216252\pi$
$409$	3.02664	+	3.02664i	0.149658	+	0.149658i	−0.628307	+	0.777965i	$0.716252\pi$
$410$	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	$0.315063\pi$
$419$			34.2215i			1.67183i	−0.548858	+	0.835916i	$0.684937\pi$
$420$	0.492373	+	2.36618i	0.0240253	+	0.115458i
$421$	2.87344	+	2.87344i	0.140043	+	0.140043i	0.773653	−	0.633610i	$-0.218428\pi$
$421$	2.87344	+	2.87344i	0.140043	+	0.140043i	−0.633610	+	0.773653i	$0.718428\pi$
$422$	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	−0.852410	−	0.522873i	$-0.824860\pi$
$431$	−6.84137	+	6.84137i	−0.329537	+	0.329537i	0.522873	+	0.852410i	$0.324860\pi$
$432$	3.00000	+	4.24264i	0.144338	+	0.204124i
$433$		−	29.2833i		−	1.40727i	−0.710563	−	0.703633i	$-0.751560\pi$
$433$		−	29.2833i		−	1.40727i	0.710563	−	0.703633i	$-0.248440\pi$
$434$	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	$0.141327\pi$
$439$			18.0000i			0.859093i	−0.903045	+	0.429547i	$0.858673\pi$
$440$	−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	$-0.781845\pi$
$443$		−	26.6439i		−	1.26589i	0.774196	−	0.632946i	$-0.218155\pi$
$444$	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	−0.965320	−	0.261070i	$-0.915925\pi$
$449$	−25.9867	−	25.9867i	−1.22639	−	1.22639i	−0.261070	−	0.965320i	$-0.584075\pi$
$450$	−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	0.110237	−	0.993905i	$-0.464839\pi$
$457$	−18.8907	−	18.8907i	−0.883669	−	0.883669i	−0.993905	+	0.110237i	$0.964839\pi$
$458$		−	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	0.171773	−	0.985137i	$-0.445051\pi$
$461$	24.8399	−	24.8399i	1.15691	−	1.15691i	0.985137	−	0.171773i	$-0.0549495\pi$
$462$	−13.7372	−	9.00489i	−0.639115	−	0.418945i
$463$	−14.0944	+	14.0944i	−0.655024	+	0.655024i	−0.954198	−	0.299174i	$-0.903289\pi$
$463$	−14.0944	+	14.0944i	−0.655024	+	0.655024i	0.299174	+	0.954198i	$0.403289\pi$
$464$		−	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	0.970972	+	0.239193i	$0.0768830\pi$
$479$	26.4858	+	26.4858i	1.21017	+	1.21017i	0.239193	+	0.970972i	$0.423117\pi$
$480$	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	0.785534	−	0.618819i	$-0.212388\pi$
$487$	3.67908	+	3.67908i	0.166715	+	0.166715i	−0.618819	+	0.785534i	$0.712388\pi$
$488$	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	0.431825	−	0.901957i	$-0.357870\pi$
$499$	−10.5020	−	10.5020i	−0.470132	−	0.470132i	−0.901957	+	0.431825i	$0.857870\pi$
$500$	−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	$-0.990191\pi$
$503$		−	1.38208i		−	0.0616241i	0.999525	−	0.0308120i	$-0.00980933\pi$
$504$	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	−0.850593	−	0.525825i	$-0.823757\pi$
$509$	−7.32710	+	7.32710i	−0.324768	+	0.324768i	0.525825	+	0.850593i	$0.323757\pi$
$510$	−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	$-0.985354\pi$
$521$		−	2.09971i		−	0.0919901i	0.998942	−	0.0459950i	$-0.0146458\pi$
$522$	−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	−0.00877191	−	0.999962i	$-0.502792\pi$
$541$	23.0545	−	23.0545i	0.991190	−	0.991190i	0.999962	+	0.00877191i	$0.00279222\pi$
$542$			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	0.343285	−	0.939231i	$-0.388460\pi$
$557$	−14.0648	−	14.0648i	−0.595946	−	0.595946i	−0.939231	+	0.343285i	$0.888460\pi$
$558$	−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	$-0.964308\pi$
$571$		−	5.34756i		−	0.223788i	0.993720	−	0.111894i	$-0.0356918\pi$
$572$	−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	0.994147	+	0.108035i	$0.0344558\pi$
$577$	26.4753	+	26.4753i	1.10218	+	1.10218i	0.108035	+	0.994147i	$0.465544\pi$
$578$	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	−0.982975	−	0.183738i	$-0.941180\pi$
$587$	−19.3640	+	19.3640i	−0.799237	+	0.799237i	0.183738	+	0.982975i	$0.441180\pi$
$588$	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	0.639668	−	0.768652i	$-0.279072\pi$
$593$	−3.14097	−	3.14097i	−0.128984	−	0.128984i	−0.768652	+	0.639668i	$0.779072\pi$
$594$	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	$-0.709462\pi$
$599$		−	38.7280i		−	1.58238i	0.611570	−	0.791191i	$-0.290538\pi$
$600$	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	0.477278	−	0.878752i	$-0.341623\pi$
$613$	−9.94004	−	9.94004i	−0.401474	−	0.401474i	−0.878752	+	0.477278i	$0.841623\pi$
$614$			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	−0.662370	−	0.749177i	$-0.730449\pi$
$617$	2.15622	−	2.15622i	0.0868062	−	0.0868062i	0.749177	+	0.662370i	$0.230449\pi$
$618$	11.5918	−	17.6837i	0.466291	−	0.711342i
$619$	0.683001	−	0.683001i	0.0274521	−	0.0274521i	−0.693247	−	0.720700i	$-0.743821\pi$
$619$	0.683001	−	0.683001i	0.0274521	−	0.0274521i	0.720700	+	0.693247i	$0.243821\pi$
$620$			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	−0.847977	−	0.530033i	$-0.822180\pi$
$631$	−7.98668	+	7.98668i	−0.317945	+	0.317945i	0.530033	+	0.847977i	$0.322180\pi$
$632$	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	0.919975	−	0.391976i	$-0.128208\pi$
$643$	13.3887	+	13.3887i	0.528000	+	0.528000i	−0.391976	+	0.919975i	$0.628208\pi$
$644$	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	$-0.798645\pi$
$653$		−	30.2161i		−	1.18245i	0.806508	−	0.591223i	$-0.201355\pi$
$654$	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	$0.0317156\pi$
$659$			5.10712i			0.198945i	−0.995040	+	0.0994726i	$0.968284\pi$
$660$	5.73970	−	1.19436i	0.223417	−	0.0464904i
$661$	−30.2488	+	30.2488i	−1.17654	+	1.17654i	−0.195925	+	0.980619i	$0.562771\pi$
$661$	−30.2488	+	30.2488i	−1.17654	+	1.17654i	−0.980619	+	0.195925i	$0.937229\pi$
$662$	−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	$0.288636\pi$
$673$			40.8601i			1.57504i	−0.616288	+	0.787521i	$0.711364\pi$
$674$	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	$-0.834599\pi$
$677$		−	25.8399i		−	0.993108i	0.868006	−	0.496554i	$-0.165401\pi$
$678$	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	0.665793	−	0.746136i	$-0.268093\pi$
$683$	−2.09971	−	2.09971i	−0.0803433	−	0.0803433i	−0.746136	+	0.665793i	$0.768093\pi$
$684$	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	0.997837	−	0.0657384i	$-0.0209403\pi$
$691$	24.5020	+	24.5020i	0.932098	+	0.932098i	−0.0657384	+	0.997837i	$0.520940\pi$
$692$		−	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	−0.999804	−	0.0198066i	$-0.993695\pi$
$709$	−26.0944	+	26.0944i	−0.979997	+	0.979997i	0.0198066	+	0.999804i	$0.493695\pi$
$710$	−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	$-0.932289\pi$
$727$		−	11.3848i		−	0.422239i	0.977460	−	0.211119i	$-0.0677109\pi$
$728$	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	0.999960	+	0.00895888i	$0.00285174\pi$
$733$	27.3154	+	27.3154i	1.00892	+	1.00892i	0.00895888	+	0.999960i	$0.497148\pi$
$734$	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	−0.747584	−	0.664167i	$-0.768786\pi$
$739$	−2.26764	+	2.26764i	−0.0834166	+	0.0834166i	0.664167	+	0.747584i	$0.268786\pi$
$740$	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	−0.718855	−	0.695160i	$-0.755333\pi$
$743$	−0.645871	+	0.645871i	−0.0236947	+	0.0236947i	0.695160	+	0.718855i	$0.255333\pi$
$744$	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	$-0.838726\pi$
$751$		−	26.5964i		−	0.970516i	0.874371	−	0.485258i	$-0.161274\pi$
$752$	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	0.831997	−	0.554780i	$-0.187197\pi$
$761$	7.64739	+	7.64739i	0.277218	+	0.277218i	−0.554780	+	0.831997i	$0.687197\pi$
$762$	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	0.809211	−	0.587518i	$-0.199895\pi$
$769$	6.14772	+	6.14772i	0.221692	+	0.221692i	−0.587518	+	0.809211i	$0.699895\pi$
$770$		−	6.69256i		−	0.241183i
$771$	6.43934	+	30.9453i	0.231907	+	1.11447i
$772$	−3.79624	−	3.79624i	−0.136630	−	0.136630i

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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