LMFDB - Embedded newform 1110.2.u.a.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.a.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} -2.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} -2.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000 q^{10} +2.82843 q^{11} +(1.00000 - 1.41421i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(-1.41421 - 1.41421i) q^{14} +(1.70711 - 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-1.00000 - 1.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(2.82843 + 2.00000i) q^{21} +(2.00000 + 2.00000i) q^{22} +(5.65685 - 5.65685i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -4.24264i q^{26} +(1.41421 - 5.00000i) q^{27} -2.00000i q^{28} +(-1.41421 - 1.41421i) q^{29} +(1.41421 + 1.00000i) q^{30} +(1.00000 - 1.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.00000 - 2.82843i) q^{33} -2.00000 q^{34} +(1.41421 - 1.41421i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-1.00000 - 6.00000i) q^{37} -1.41421i q^{38} +(1.24264 + 7.24264i) q^{39} -1.00000i q^{40} +(0.585786 + 3.41421i) q^{42} +(-5.00000 - 5.00000i) q^{43} +2.82843i q^{44} +(-2.70711 - 1.29289i) q^{45} +8.00000 q^{46} +(1.41421 + 1.00000i) q^{48} -3.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(3.00000 - 3.00000i) q^{52} -5.65685i q^{53} +(4.53553 - 2.53553i) q^{54} +(-2.00000 + 2.00000i) q^{55} +(1.41421 - 1.41421i) q^{56} +(0.414214 + 2.41421i) q^{57} -2.00000i q^{58} +(2.82843 - 2.82843i) q^{59} +(0.292893 + 1.70711i) q^{60} +(9.00000 - 9.00000i) q^{61} +1.41421 q^{62} +(-2.00000 - 5.65685i) q^{63} -1.00000i q^{64} +4.24264 q^{65} +(-0.828427 - 4.82843i) q^{66} -4.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(-13.6569 + 2.34315i) q^{69} +2.00000 q^{70} +2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -10.0000i q^{73} +(3.53553 - 4.94975i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(1.00000 - 1.00000i) q^{76} -5.65685 q^{77} +(-4.24264 + 6.00000i) q^{78} +(3.00000 + 3.00000i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +2.82843i q^{83} +(-2.00000 + 2.82843i) q^{84} -2.00000i q^{85} -7.07107i q^{86} +(0.585786 + 3.41421i) q^{87} +(-2.00000 + 2.00000i) q^{88} +(-7.07107 - 7.07107i) q^{89} +(-1.00000 - 2.82843i) q^{90} +(6.00000 + 6.00000i) q^{91} +(5.65685 + 5.65685i) q^{92} +(-2.41421 + 0.414214i) q^{93} +1.41421 q^{95} +(0.292893 + 1.70711i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-2.12132 - 2.12132i) q^{98} +(2.82843 + 8.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^6 - 8 * q^7 + 4 * q^9	$ 4 q - 4 q^{6} - 8 q^{7} + 4 q^{9} - 4 q^{10} + 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 4 q^{19} + 8 q^{22} + 4 q^{24} + 4 q^{31} - 16 q^{33} - 8 q^{34} - 4 q^{37} - 12 q^{39} + 8 q^{42} - 20 q^{43} - 8 q^{45} + 32 q^{46} - 12 q^{49} + 8 q^{51} + 12 q^{52} + 4 q^{54} - 8 q^{55} - 4 q^{57} + 4 q^{60} + 36 q^{61} - 8 q^{63} + 8 q^{66} - 32 q^{69} + 8 q^{70} - 8 q^{72} - 4 q^{75} + 4 q^{76} + 12 q^{79} - 28 q^{81} - 8 q^{84} + 8 q^{87} - 8 q^{88} - 4 q^{90} + 24 q^{91} - 4 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^6 - 8 * q^7 + 4 * q^9 - 4 * q^10 + 4 * q^12 - 12 * q^13 + 4 * q^15 - 4 * q^16 - 8 * q^18 - 4 * q^19 + 8 * q^22 + 4 * q^24 + 4 * q^31 - 16 * q^33 - 8 * q^34 - 4 * q^37 - 12 * q^39 + 8 * q^42 - 20 * q^43 - 8 * q^45 + 32 * q^46 - 12 * q^49 + 8 * q^51 + 12 * q^52 + 4 * q^54 - 8 * q^55 - 4 * q^57 + 4 * q^60 + 36 * q^61 - 8 * q^63 + 8 * q^66 - 32 * q^69 + 8 * q^70 - 8 * q^72 - 4 * q^75 + 4 * q^76 + 12 * q^79 - 28 * q^81 - 8 * q^84 + 8 * q^87 - 8 * q^88 - 4 * q^90 + 24 * q^91 - 4 * q^93 + 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.292893	−	1.70711i	−0.119573	−	0.696923i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$	−1.00000			−0.316228
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$	1.00000	−	1.41421i	0.288675	−	0.408248i
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$	−1.41421	−	1.41421i	−0.377964	−	0.377964i
$15$	1.70711	−	0.292893i	0.440773	−	0.0756247i
$16$	−1.00000			−0.250000
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	0.583033	−	0.812449i	$-0.301866\pi$
$19$	−1.00000	−	1.00000i	−0.229416	−	0.229416i	−0.812449	+	0.583033i	$0.801866\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	2.82843	+	2.00000i	0.617213	+	0.436436i
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	5.65685	−	5.65685i	1.17954	−	1.17954i	0.199673	−	0.979863i	$-0.436012\pi$
$23$	5.65685	−	5.65685i	1.17954	−	1.17954i	0.979863	−	0.199673i	$-0.0639880\pi$
$24$	1.70711	−	0.292893i	0.348462	−	0.0597866i
$25$		−	1.00000i		−	0.200000i
$26$		−	4.24264i		−	0.832050i
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$		−	2.00000i		−	0.377964i
$29$	−1.41421	−	1.41421i	−0.262613	−	0.262613i	0.563502	−	0.826115i	$-0.309454\pi$
$29$	−1.41421	−	1.41421i	−0.262613	−	0.262613i	−0.826115	+	0.563502i	$0.809454\pi$
$30$	1.41421	+	1.00000i	0.258199	+	0.182574i
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.00000	−	2.82843i	−0.696311	−	0.492366i
$34$	−2.00000			−0.342997
$35$	1.41421	−	1.41421i	0.239046	−	0.239046i
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	−1.00000	−	6.00000i	−0.164399	−	0.986394i
$37$	−1.00000	−	6.00000i	−0.164399	−	0.986394i
$38$		−	1.41421i		−	0.229416i
$39$	1.24264	+	7.24264i	0.198982	+	1.15975i
$40$		−	1.00000i		−	0.158114i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.585786	+	3.41421i	0.0903888	+	0.526825i
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$			2.82843i			0.426401i
$45$	−2.70711	−	1.29289i	−0.403552	−	0.192733i
$46$	8.00000			1.17954
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	1.41421	+	1.00000i	0.204124	+	0.144338i
$49$	−3.00000			−0.428571
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	3.41421	−	0.585786i	0.478086	−	0.0820265i
$52$	3.00000	−	3.00000i	0.416025	−	0.416025i
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	4.53553	−	2.53553i	0.617208	−	0.345042i
$55$	−2.00000	+	2.00000i	−0.269680	+	0.269680i
$56$	1.41421	−	1.41421i	0.188982	−	0.188982i
$57$	0.414214	+	2.41421i	0.0548639	+	0.319770i
$58$		−	2.00000i		−	0.262613i
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	−0.498601	−	0.866831i	$-0.666153\pi$
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	0.866831	+	0.498601i	$0.166153\pi$
$60$	0.292893	+	1.70711i	0.0378124	+	0.220387i
$61$	9.00000	−	9.00000i	1.15233	−	1.15233i	0.166248	−	0.986084i	$-0.446835\pi$
$61$	9.00000	−	9.00000i	1.15233	−	1.15233i	0.986084	−	0.166248i	$-0.0531652\pi$
$62$	1.41421			0.179605
$63$	−2.00000	−	5.65685i	−0.251976	−	0.712697i
$64$		−	1.00000i		−	0.125000i
$65$	4.24264			0.526235
$66$	−0.828427	−	4.82843i	−0.101972	−	0.594338i
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	−1.41421	−	1.41421i	−0.171499	−	0.171499i
$69$	−13.6569	+	2.34315i	−1.64409	+	0.282082i
$70$	2.00000			0.239046
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	3.53553	−	4.94975i	0.410997	−	0.575396i
$75$	−1.00000	+	1.41421i	−0.115470	+	0.163299i
$76$	1.00000	−	1.00000i	0.114708	−	0.114708i
$77$	−5.65685			−0.644658
$78$	−4.24264	+	6.00000i	−0.480384	+	0.679366i
$79$	3.00000	+	3.00000i	0.337526	+	0.337526i	0.855436	−	0.517909i	$-0.173290\pi$
$79$	3.00000	+	3.00000i	0.337526	+	0.337526i	−0.517909	+	0.855436i	$0.673290\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		0			0
$83$			2.82843i			0.310460i	0.987878	+	0.155230i	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$	−2.00000	+	2.82843i	−0.218218	+	0.308607i
$85$		−	2.00000i		−	0.216930i
$86$		−	7.07107i		−	0.762493i
$87$	0.585786	+	3.41421i	0.0628029	+	0.366042i
$88$	−2.00000	+	2.00000i	−0.213201	+	0.213201i
$89$	−7.07107	−	7.07107i	−0.749532	−	0.749532i	0.224860	−	0.974391i	$-0.427808\pi$
$89$	−7.07107	−	7.07107i	−0.749532	−	0.749532i	−0.974391	+	0.224860i	$0.927808\pi$
$90$	−1.00000	−	2.82843i	−0.105409	−	0.298142i
$91$	6.00000	+	6.00000i	0.628971	+	0.628971i
$92$	5.65685	+	5.65685i	0.589768	+	0.589768i
$93$	−2.41421	+	0.414214i	−0.250342	+	0.0429519i
$94$		0			0
$95$	1.41421			0.145095
$96$	0.292893	+	1.70711i	0.0298933	+	0.174231i
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$	−2.12132	−	2.12132i	−0.214286	−	0.214286i
$99$	2.82843	+	8.00000i	0.284268	+	0.804030i
$100$	1.00000			0.100000
$101$	−5.65685			−0.562878			−0.281439	−	0.959579i	$-0.590812\pi$
$101$	−5.65685			−0.562878			−0.281439	+	0.959579i	$0.590812\pi$
$102$	2.82843	+	2.00000i	0.280056	+	0.198030i
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	−0.962172	−	0.272442i	$-0.912169\pi$
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	0.272442	+	0.962172i	$0.412169\pi$
$104$	4.24264			0.416025
$105$	−3.41421	+	0.585786i	−0.333193	+	0.0571669i
$106$	4.00000	−	4.00000i	0.388514	−	0.388514i
$107$			11.3137i			1.09374i	0.837218	+	0.546869i	$0.184180\pi$
$107$			11.3137i			1.09374i	−0.837218	+	0.546869i	$0.815820\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	0.836031	−	0.548683i	$-0.184871\pi$
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	−0.548683	+	0.836031i	$0.684871\pi$
$110$	−2.82843			−0.269680
$111$	−4.58579	+	9.48528i	−0.435264	+	0.900303i
$112$	2.00000			0.188982
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$	−1.41421	+	2.00000i	−0.132453	+	0.187317i
$115$			8.00000i			0.746004i
$116$	1.41421	−	1.41421i	0.131306	−	0.131306i
$117$	5.48528	−	11.4853i	0.507114	−	1.06181i
$118$	4.00000			0.368230
$119$	2.82843	−	2.82843i	0.259281	−	0.259281i
$120$	−1.00000	+	1.41421i	−0.0912871	+	0.129099i
$121$	−3.00000			−0.272727
$122$	12.7279			1.15233
$123$		0			0
$124$	1.00000	+	1.00000i	0.0898027	+	0.0898027i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	2.58579	−	5.41421i	0.230360	−	0.482336i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	2.07107	+	12.0711i	0.182347	+	1.06280i
$130$	3.00000	+	3.00000i	0.263117	+	0.263117i
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	0.231478	−	0.972840i	$-0.425644\pi$
$131$	−8.48528	−	8.48528i	−0.741362	−	0.741362i	−0.972840	+	0.231478i	$0.925644\pi$
$132$	2.82843	−	4.00000i	0.246183	−	0.348155i
$133$	2.00000	+	2.00000i	0.173422	+	0.173422i
$134$	2.82843	−	2.82843i	0.244339	−	0.244339i
$135$	2.53553	+	4.53553i	0.218224	+	0.390357i
$136$		−	2.00000i		−	0.171499i
$137$			5.65685i			0.483298i	0.970364	+	0.241649i	$0.0776882\pi$
$137$			5.65685i			0.483298i	−0.970364	+	0.241649i	$0.922312\pi$
$138$	−11.3137	−	8.00000i	−0.963087	−	0.681005i
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	1.41421	+	1.41421i	0.119523	+	0.119523i
$141$		0			0
$142$	−2.00000	+	2.00000i	−0.167836	+	0.167836i
$143$	−8.48528	−	8.48528i	−0.709575	−	0.709575i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	2.00000			0.166091
$146$	7.07107	−	7.07107i	0.585206	−	0.585206i
$147$	4.24264	+	3.00000i	0.349927	+	0.247436i
$148$	6.00000	−	1.00000i	0.493197	−	0.0821995i
$149$		−	11.3137i		−	0.926855i	−0.886135	−	0.463428i	$-0.846619\pi$
$149$		−	11.3137i		−	0.926855i	0.886135	−	0.463428i	$-0.153381\pi$
$150$	−1.70711	+	0.292893i	−0.139385	+	0.0239146i
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$	1.41421			0.114708
$153$	−5.41421	−	2.58579i	−0.437713	−	0.209048i
$154$	−4.00000	−	4.00000i	−0.322329	−	0.322329i
$155$			1.41421i			0.113592i
$156$	−7.24264	+	1.24264i	−0.579875	+	0.0994909i
$157$	4.00000			0.319235			0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000			0.319235			0.159617	+	0.987179i	$0.448974\pi$
$158$			4.24264i			0.337526i
$159$	−5.65685	+	8.00000i	−0.448618	+	0.634441i
$160$	1.00000			0.0790569
$161$	−11.3137	+	11.3137i	−0.891645	+	0.891645i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	−3.00000	+	3.00000i	−0.234978	+	0.234978i	−0.814767	−	0.579789i	$-0.803135\pi$
$163$	−3.00000	+	3.00000i	−0.234978	+	0.234978i	0.579789	+	0.814767i	$0.303135\pi$
$164$		0			0
$165$	4.82843	−	0.828427i	0.375893	−	0.0644930i
$166$	−2.00000	+	2.00000i	−0.155230	+	0.155230i
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	−0.297966	−	0.954577i	$-0.596308\pi$
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	0.954577	+	0.297966i	$0.0963081\pi$
$168$	−3.41421	+	0.585786i	−0.263412	+	0.0451944i
$169$			5.00000i			0.384615i
$170$	1.41421	−	1.41421i	0.108465	−	0.108465i
$171$	1.82843	−	3.82843i	0.139823	−	0.292767i
$172$	5.00000	−	5.00000i	0.381246	−	0.381246i
$173$	−11.3137			−0.860165			−0.430083	−	0.902790i	$-0.641516\pi$
$173$	−11.3137			−0.860165			−0.430083	+	0.902790i	$0.641516\pi$
$174$	−2.00000	+	2.82843i	−0.151620	+	0.214423i
$175$			2.00000i			0.151186i
$176$	−2.82843			−0.213201
$177$	−6.82843	+	1.17157i	−0.513256	+	0.0880608i
$178$		−	10.0000i		−	0.749532i
$179$	16.9706	+	16.9706i	1.26844	+	1.26844i	0.946894	+	0.321545i	$0.104202\pi$
$179$	16.9706	+	16.9706i	1.26844	+	1.26844i	0.321545	+	0.946894i	$0.395798\pi$
$180$	1.29289	−	2.70711i	0.0963666	−	0.201776i
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$			8.48528i			0.628971i
$183$	−21.7279	+	3.72792i	−1.60617	+	0.275576i
$184$			8.00000i			0.589768i
$185$	4.94975	+	3.53553i	0.363913	+	0.259938i
$186$	−2.00000	−	1.41421i	−0.146647	−	0.103695i
$187$	−4.00000	+	4.00000i	−0.292509	+	0.292509i
$188$		0			0
$189$	−2.82843	+	10.0000i	−0.205738	+	0.727393i
$190$	1.00000	+	1.00000i	0.0725476	+	0.0725476i
$191$	−8.48528	+	8.48528i	−0.613973	+	0.613973i	−0.943979	−	0.330006i	$-0.892949\pi$
$191$	−8.48528	+	8.48528i	−0.613973	+	0.613973i	0.330006	+	0.943979i	$0.392949\pi$
$192$	−1.00000	+	1.41421i	−0.0721688	+	0.102062i
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.996534	−	0.0831899i	$-0.973489\pi$
$193$	−15.0000	−	15.0000i	−1.07972	−	1.07972i	−0.0831899	−	0.996534i	$-0.526511\pi$
$194$		−	4.24264i		−	0.304604i
$195$	−6.00000	−	4.24264i	−0.429669	−	0.303822i
$196$		−	3.00000i		−	0.214286i
$197$			19.7990i			1.41062i	0.708899	+	0.705310i	$0.249192\pi$
$197$			19.7990i			1.41062i	−0.708899	+	0.705310i	$0.750808\pi$
$198$	−3.65685	+	7.65685i	−0.259881	+	0.544149i
$199$	13.0000	−	13.0000i	0.921546	−	0.921546i	−0.0755932	−	0.997139i	$-0.524085\pi$
$199$	13.0000	−	13.0000i	0.921546	−	0.921546i	0.997139	+	0.0755932i	$0.0240850\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−4.00000	+	5.65685i	−0.282138	+	0.399004i
$202$	−4.00000	−	4.00000i	−0.281439	−	0.281439i
$203$	2.82843	+	2.82843i	0.198517	+	0.198517i
$204$	0.585786	+	3.41421i	0.0410133	+	0.239043i
$205$		0			0
$206$	−9.89949			−0.689730
$207$	21.6569	+	10.3431i	1.50526	+	0.718898i
$208$	3.00000	+	3.00000i	0.208013	+	0.208013i
$209$	−2.82843	−	2.82843i	−0.195646	−	0.195646i
$210$	−2.82843	−	2.00000i	−0.195180	−	0.138013i
$211$	28.0000			1.92760			0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000			1.92760			0.963800	+	0.266627i	$0.0859092\pi$
$212$	5.65685			0.388514
$213$	2.82843	−	4.00000i	0.193801	−	0.274075i
$214$	−8.00000	+	8.00000i	−0.546869	+	0.546869i
$215$	7.07107			0.482243
$216$	2.53553	+	4.53553i	0.172521	+	0.308604i
$217$	−2.00000	+	2.00000i	−0.135769	+	0.135769i
$218$			4.24264i			0.287348i
$219$	−10.0000	+	14.1421i	−0.675737	+	0.955637i
$220$	−2.00000	−	2.00000i	−0.134840	−	0.134840i
$221$	8.48528			0.570782
$222$	−9.94975	+	3.46447i	−0.667783	+	0.232520i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	1.41421	+	1.41421i	0.0944911	+	0.0944911i
$225$	2.82843	−	1.00000i	0.188562	−	0.0666667i
$226$			6.00000i			0.399114i
$227$	−14.1421	+	14.1421i	−0.938647	+	0.938647i	−0.998224	−	0.0595772i	$-0.981025\pi$
$227$	−14.1421	+	14.1421i	−0.938647	+	0.938647i	0.0595772	+	0.998224i	$0.481025\pi$
$228$	−2.41421	+	0.414214i	−0.159885	+	0.0274320i
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	−5.65685	+	5.65685i	−0.373002	+	0.373002i
$231$	8.00000	+	5.65685i	0.526361	+	0.372194i
$232$	2.00000			0.131306
$233$	−14.1421			−0.926482			−0.463241	−	0.886232i	$-0.653314\pi$
$233$	−14.1421			−0.926482			−0.463241	+	0.886232i	$0.653314\pi$
$234$	12.0000	−	4.24264i	0.784465	−	0.277350i
$235$		0			0
$236$	2.82843	+	2.82843i	0.184115	+	0.184115i
$237$	−1.24264	−	7.24264i	−0.0807182	−	0.470460i
$238$	4.00000			0.259281
$239$	11.3137	−	11.3137i	0.731823	−	0.731823i	−0.239158	−	0.970981i	$-0.576871\pi$
$239$	11.3137	−	11.3137i	0.731823	−	0.731823i	0.970981	+	0.239158i	$0.0768713\pi$
$240$	−1.70711	+	0.292893i	−0.110193	+	0.0189062i
$241$	5.00000	+	5.00000i	0.322078	+	0.322078i	0.849564	−	0.527486i	$-0.176865\pi$
$241$	5.00000	+	5.00000i	0.322078	+	0.322078i	−0.527486	+	0.849564i	$0.676865\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$	15.5563	−	1.00000i	0.997940	−	0.0641500i
$244$	9.00000	+	9.00000i	0.576166	+	0.576166i
$245$	2.12132	−	2.12132i	0.135526	−	0.135526i
$246$		0			0
$247$			6.00000i			0.381771i
$248$			1.41421i			0.0898027i
$249$	2.82843	−	4.00000i	0.179244	−	0.253490i
$250$			1.00000i			0.0632456i
$251$	−16.9706	−	16.9706i	−1.07117	−	1.07117i	−0.997265	−	0.0739073i	$-0.976453\pi$
$251$	−16.9706	−	16.9706i	−1.07117	−	1.07117i	−0.0739073	−	0.997265i	$-0.523547\pi$
$252$	5.65685	−	2.00000i	0.356348	−	0.125988i
$253$	16.0000	−	16.0000i	1.00591	−	1.00591i
$254$	11.3137	+	11.3137i	0.709885	+	0.709885i
$255$	−2.00000	+	2.82843i	−0.125245	+	0.177123i
$256$	1.00000			0.0625000
$257$	−12.7279	+	12.7279i	−0.793946	+	0.793946i	−0.982133	−	0.188187i	$-0.939739\pi$
$257$	−12.7279	+	12.7279i	−0.793946	+	0.793946i	0.188187	+	0.982133i	$0.439739\pi$
$258$	−7.07107	+	10.0000i	−0.440225	+	0.622573i
$259$	2.00000	+	12.0000i	0.124274	+	0.745644i
$260$			4.24264i			0.263117i
$261$	2.58579	−	5.41421i	0.160056	−	0.335131i
$262$		−	12.0000i		−	0.741362i
$263$	−16.9706			−1.04645			−0.523225	−	0.852195i	$-0.675271\pi$
$263$	−16.9706			−1.04645			−0.523225	+	0.852195i	$0.675271\pi$
$264$	4.82843	−	0.828427i	0.297169	−	0.0509862i
$265$	4.00000	+	4.00000i	0.245718	+	0.245718i
$266$			2.82843i			0.173422i
$267$	2.92893	+	17.0711i	0.179248	+	1.04473i
$268$	4.00000			0.244339
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−1.41421	+	5.00000i	−0.0860663	+	0.304290i
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	1.41421	−	1.41421i	0.0857493	−	0.0857493i
$273$	−2.48528	−	14.4853i	−0.150416	−	0.876689i
$274$	−4.00000	+	4.00000i	−0.241649	+	0.241649i
$275$		−	2.82843i		−	0.170561i
$276$	−2.34315	−	13.6569i	−0.141041	−	0.822046i
$277$	11.0000	−	11.0000i	0.660926	−	0.660926i	−0.294672	−	0.955598i	$-0.595211\pi$
$277$	11.0000	−	11.0000i	0.660926	−	0.660926i	0.955598	+	0.294672i	$0.0952105\pi$
$278$	−2.82843	+	2.82843i	−0.169638	+	0.169638i
$279$	3.82843	+	1.82843i	0.229202	+	0.109465i
$280$			2.00000i			0.119523i
$281$	−12.7279	+	12.7279i	−0.759284	+	0.759284i	−0.976192	−	0.216908i	$-0.930403\pi$
$281$	−12.7279	+	12.7279i	−0.759284	+	0.759284i	0.216908	+	0.976192i	$0.430403\pi$
$282$		0			0
$283$	−1.00000	+	1.00000i	−0.0594438	+	0.0594438i	−0.736204	−	0.676760i	$-0.763384\pi$
$283$	−1.00000	+	1.00000i	−0.0594438	+	0.0594438i	0.676760	+	0.736204i	$0.263384\pi$
$284$	−2.82843			−0.167836
$285$	−2.00000	−	1.41421i	−0.118470	−	0.0837708i
$286$		−	12.0000i		−	0.709575i
$287$		0			0
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$			13.0000i			0.764706i
$290$	1.41421	+	1.41421i	0.0830455	+	0.0830455i
$291$	1.24264	+	7.24264i	0.0728449	+	0.424571i
$292$	10.0000			0.585206
$293$		−	5.65685i		−	0.330477i	−0.986254	−	0.165238i	$-0.947161\pi$
$293$		−	5.65685i		−	0.330477i	0.986254	−	0.165238i	$-0.0528394\pi$
$294$	0.878680	+	5.12132i	0.0512456	+	0.298681i
$295$			4.00000i			0.232889i
$296$	4.94975	+	3.53553i	0.287698	+	0.205499i
$297$	4.00000	−	14.1421i	0.232104	−	0.820610i
$298$	8.00000	−	8.00000i	0.463428	−	0.463428i
$299$	−33.9411			−1.96287
$300$	−1.41421	−	1.00000i	−0.0816497	−	0.0577350i
$301$	10.0000	+	10.0000i	0.576390	+	0.576390i
$302$	−7.07107	+	7.07107i	−0.406894	+	0.406894i
$303$	8.00000	+	5.65685i	0.459588	+	0.324978i
$304$	1.00000	+	1.00000i	0.0573539	+	0.0573539i
$305$			12.7279i			0.728799i
$306$	−2.00000	−	5.65685i	−0.114332	−	0.323381i
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$		−	5.65685i		−	0.322329i
$309$	16.8995	−	2.89949i	0.961379	−	0.164947i
$310$	−1.00000	+	1.00000i	−0.0567962	+	0.0567962i
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$	−6.00000	−	4.24264i	−0.339683	−	0.240192i
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	0.405420	−	0.914130i	$-0.367125\pi$
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	−0.914130	+	0.405420i	$0.867125\pi$
$314$	2.82843	+	2.82843i	0.159617	+	0.159617i
$315$	5.41421	+	2.58579i	0.305056	+	0.145693i
$316$	−3.00000	+	3.00000i	−0.168763	+	0.168763i
$317$	−16.9706			−0.953162			−0.476581	−	0.879131i	$-0.658124\pi$
$317$	−16.9706			−0.953162			−0.476581	+	0.879131i	$0.658124\pi$
$318$	−9.65685	+	1.65685i	−0.541529	+	0.0929118i
$319$	−4.00000	−	4.00000i	−0.223957	−	0.223957i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	11.3137	−	16.0000i	0.631470	−	0.893033i
$322$	−16.0000			−0.891645
$323$	2.82843			0.157378
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−3.00000	+	3.00000i	−0.166410	+	0.166410i
$326$	−4.24264			−0.234978
$327$	−1.24264	−	7.24264i	−0.0687182	−	0.400519i
$328$		0			0
$329$		0			0
$330$	4.00000	+	2.82843i	0.220193	+	0.155700i
$331$	−23.0000	−	23.0000i	−1.26419	−	1.26419i	−0.949041	−	0.315154i	$-0.897944\pi$
$331$	−23.0000	−	23.0000i	−1.26419	−	1.26419i	−0.315154	−	0.949041i	$-0.602056\pi$
$332$	−2.82843			−0.155230
$333$	15.9706	−	8.82843i	0.875181	−	0.483795i
$334$	12.0000			0.656611
$335$	2.82843	+	2.82843i	0.154533	+	0.154533i
$336$	−2.82843	−	2.00000i	−0.154303	−	0.109109i
$337$			16.0000i			0.871576i	0.900049	+	0.435788i	$0.143530\pi$
$337$			16.0000i			0.871576i	−0.900049	+	0.435788i	$0.856470\pi$
$338$	−3.53553	+	3.53553i	−0.192308	+	0.192308i
$339$	−1.75736	−	10.2426i	−0.0954467	−	0.556304i
$340$	2.00000			0.108465
$341$	2.82843	−	2.82843i	0.153168	−	0.153168i
$342$	4.00000	−	1.41421i	0.216295	−	0.0764719i
$343$	20.0000			1.07990
$344$	7.07107			0.381246
$345$	8.00000	−	11.3137i	0.430706	−	0.609110i
$346$	−8.00000	−	8.00000i	−0.430083	−	0.430083i
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.997887	−	0.0649788i	$-0.979302\pi$
$347$	−19.7990	−	19.7990i	−1.06287	−	1.06287i	−0.0649788	−	0.997887i	$-0.520698\pi$
$348$	−3.41421	+	0.585786i	−0.183021	+	0.0314014i
$349$	−4.00000			−0.214115			−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000			−0.214115			−0.107058	+	0.994253i	$0.534143\pi$
$350$	−1.41421	+	1.41421i	−0.0755929	+	0.0755929i
$351$	−19.2426	+	10.7574i	−1.02710	+	0.574185i
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	0.281981	−	0.959420i	$-0.409008\pi$
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	−0.959420	+	0.281981i	$0.909008\pi$
$354$	−5.65685	−	4.00000i	−0.300658	−	0.212598i
$355$	−2.00000	−	2.00000i	−0.106149	−	0.106149i
$356$	7.07107	−	7.07107i	0.374766	−	0.374766i
$357$	−6.82843	+	1.17157i	−0.361399	+	0.0620062i
$358$			24.0000i			1.26844i
$359$			16.9706i			0.895672i	0.894116	+	0.447836i	$0.147805\pi$
$359$			16.9706i			0.895672i	−0.894116	+	0.447836i	$0.852195\pi$
$360$	2.82843	−	1.00000i	0.149071	−	0.0527046i
$361$		−	17.0000i		−	0.894737i
$362$	−14.1421	−	14.1421i	−0.743294	−	0.743294i
$363$	4.24264	+	3.00000i	0.222681	+	0.157459i
$364$	−6.00000	+	6.00000i	−0.314485	+	0.314485i
$365$	7.07107	+	7.07107i	0.370117	+	0.370117i
$366$	−18.0000	−	12.7279i	−0.940875	−	0.665299i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$	−5.65685	+	5.65685i	−0.294884	+	0.294884i
$369$		0			0
$370$	1.00000	+	6.00000i	0.0519875	+	0.311925i
$371$			11.3137i			0.587378i
$372$	−0.414214	−	2.41421i	−0.0214760	−	0.125171i
$373$		−	18.0000i		−	0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$373$		−	18.0000i		−	0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$374$	−5.65685			−0.292509
$375$	−0.292893	−	1.70711i	−0.0151249	−	0.0881546i
$376$		0			0
$377$			8.48528i			0.437014i
$378$	−9.07107	+	5.07107i	−0.466565	+	0.260828i
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$			1.41421i			0.0725476i
$381$	−22.6274	−	16.0000i	−1.15924	−	0.819705i
$382$	−12.0000			−0.613973
$383$	8.48528	−	8.48528i	0.433578	−	0.433578i	−0.456266	−	0.889843i	$-0.650813\pi$
$383$	8.48528	−	8.48528i	0.433578	−	0.433578i	0.889843	+	0.456266i	$0.150813\pi$
$384$	−1.70711	+	0.292893i	−0.0871154	+	0.0149466i
$385$	4.00000	−	4.00000i	0.203859	−	0.203859i
$386$		−	21.2132i		−	1.07972i
$387$	9.14214	−	19.1421i	0.464721	−	0.973049i
$388$	3.00000	−	3.00000i	0.152302	−	0.152302i
$389$	24.0416	−	24.0416i	1.21896	−	1.21896i	0.250962	−	0.967997i	$-0.419253\pi$
$389$	24.0416	−	24.0416i	1.21896	−	1.21896i	0.967997	−	0.250962i	$-0.0807470\pi$
$390$	−1.24264	−	7.24264i	−0.0629236	−	0.366745i
$391$			16.0000i			0.809155i
$392$	2.12132	−	2.12132i	0.107143	−	0.107143i
$393$	3.51472	+	20.4853i	0.177294	+	1.03335i
$394$	−14.0000	+	14.0000i	−0.705310	+	0.705310i
$395$	−4.24264			−0.213470
$396$	−8.00000	+	2.82843i	−0.402015	+	0.142134i
$397$		−	34.0000i		−	1.70641i	−0.521575	−	0.853206i	$-0.674655\pi$
$397$		−	34.0000i		−	1.70641i	0.521575	−	0.853206i	$-0.325345\pi$
$398$	18.3848			0.921546
$399$	−0.828427	−	4.82843i	−0.0414732	−	0.241724i
$400$			1.00000i			0.0500000i
$401$	21.2132	+	21.2132i	1.05934	+	1.05934i	0.998125	+	0.0612120i	$0.0194966\pi$
$401$	21.2132	+	21.2132i	1.05934	+	1.05934i	0.0612120	+	0.998125i	$0.480503\pi$
$402$	−6.82843	+	1.17157i	−0.340571	+	0.0584327i
$403$	−6.00000			−0.298881
$404$		−	5.65685i		−	0.281439i
$405$	0.949747	−	8.94975i	0.0471933	−	0.444717i
$406$			4.00000i			0.198517i
$407$	−2.82843	−	16.9706i	−0.140200	−	0.841200i
$408$	−2.00000	+	2.82843i	−0.0990148	+	0.140028i
$409$	−17.0000	+	17.0000i	−0.840596	+	0.840596i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−17.0000	+	17.0000i	−0.840596	+	0.840596i	0.148340	+	0.988936i	$0.452607\pi$
$410$		0			0
$411$	5.65685	−	8.00000i	0.279032	−	0.394611i
$412$	−7.00000	−	7.00000i	−0.344865	−	0.344865i
$413$	−5.65685	+	5.65685i	−0.278356	+	0.278356i
$414$	8.00000	+	22.6274i	0.393179	+	1.11208i
$415$	−2.00000	−	2.00000i	−0.0981761	−	0.0981761i
$416$			4.24264i			0.208013i
$417$	4.00000	−	5.65685i	0.195881	−	0.277017i
$418$		−	4.00000i		−	0.195646i
$419$			11.3137i			0.552711i	0.961056	+	0.276355i	$0.0891267\pi$
$419$			11.3137i			0.552711i	−0.961056	+	0.276355i	$0.910873\pi$
$420$	−0.585786	−	3.41421i	−0.0285835	−	0.166597i
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	−0.386276	−	0.922383i	$-0.626239\pi$
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	0.922383	+	0.386276i	$0.126239\pi$
$422$	19.7990	+	19.7990i	0.963800	+	0.963800i
$423$		0			0
$424$	4.00000	+	4.00000i	0.194257	+	0.194257i
$425$	1.41421	+	1.41421i	0.0685994	+	0.0685994i
$426$	4.82843	−	0.828427i	0.233938	−	0.0401374i
$427$	−18.0000	+	18.0000i	−0.871081	+	0.871081i
$428$	−11.3137			−0.546869
$429$	3.51472	+	20.4853i	0.169692	+	0.989039i
$430$	5.00000	+	5.00000i	0.241121	+	0.241121i
$431$	11.3137	+	11.3137i	0.544962	+	0.544962i	0.924979	−	0.380017i	$-0.124082\pi$
$431$	11.3137	+	11.3137i	0.544962	+	0.544962i	−0.380017	+	0.924979i	$0.624082\pi$
$432$	−1.41421	+	5.00000i	−0.0680414	+	0.240563i
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$	−2.82843			−0.135769
$435$	−2.82843	−	2.00000i	−0.135613	−	0.0958927i
$436$	−3.00000	+	3.00000i	−0.143674	+	0.143674i
$437$	−11.3137			−0.541208
$438$	−17.0711	+	2.92893i	−0.815687	+	0.139950i
$439$	−9.00000	+	9.00000i	−0.429547	+	0.429547i	−0.888474	−	0.458927i	$-0.848234\pi$
$439$	−9.00000	+	9.00000i	−0.429547	+	0.429547i	0.458927	+	0.888474i	$0.348234\pi$
$440$		−	2.82843i		−	0.134840i
$441$	−3.00000	−	8.48528i	−0.142857	−	0.404061i
$442$	6.00000	+	6.00000i	0.285391	+	0.285391i
$443$	31.1127			1.47821			0.739104	−	0.673591i	$-0.235249\pi$
$443$	31.1127			1.47821			0.739104	+	0.673591i	$0.235249\pi$
$444$	−9.48528	−	4.58579i	−0.450152	−	0.217632i
$445$	10.0000			0.474045
$446$	5.65685	+	5.65685i	0.267860	+	0.267860i
$447$	−11.3137	+	16.0000i	−0.535120	+	0.756774i
$448$			2.00000i			0.0944911i
$449$	24.0416	−	24.0416i	1.13459	−	1.13459i	0.145191	−	0.989404i	$-0.453620\pi$
$449$	24.0416	−	24.0416i	1.13459	−	1.13459i	0.989404	−	0.145191i	$-0.0463797\pi$
$450$	2.70711	+	1.29289i	0.127614	+	0.0609476i
$451$		0			0
$452$	−4.24264	+	4.24264i	−0.199557	+	0.199557i
$453$	10.0000	−	14.1421i	0.469841	−	0.664455i
$454$	−20.0000			−0.938647
$455$	−8.48528			−0.397796
$456$	−2.00000	−	1.41421i	−0.0936586	−	0.0662266i
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	0.580424	−	0.814314i	$-0.302887\pi$
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	−0.814314	+	0.580424i	$0.802887\pi$
$458$	4.24264	+	4.24264i	0.198246	+	0.198246i
$459$	5.07107	+	9.07107i	0.236697	+	0.423401i
$460$	−8.00000			−0.373002
$461$	−21.2132	+	21.2132i	−0.987997	+	0.987997i	−0.999929	−	0.0119314i	$-0.996202\pi$
$461$	−21.2132	+	21.2132i	−0.987997	+	0.987997i	0.0119314	+	0.999929i	$0.496202\pi$
$462$	1.65685	+	9.65685i	0.0770838	+	0.449278i
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	0.981503	−	0.191446i	$-0.0613177\pi$
$463$	17.0000	+	17.0000i	0.790057	+	0.790057i	−0.191446	+	0.981503i	$0.561318\pi$
$464$	1.41421	+	1.41421i	0.0656532	+	0.0656532i
$465$	1.41421	−	2.00000i	0.0655826	−	0.0927478i
$466$	−10.0000	−	10.0000i	−0.463241	−	0.463241i
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	−0.0805616	−	0.996750i	$-0.525671\pi$
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	0.996750	+	0.0805616i	$0.0256714\pi$
$468$	11.4853	+	5.48528i	0.530907	+	0.253557i
$469$			8.00000i			0.369406i
$470$		0			0
$471$	−5.65685	−	4.00000i	−0.260654	−	0.184310i
$472$			4.00000i			0.184115i
$473$	−14.1421	−	14.1421i	−0.650256	−	0.650256i
$474$	4.24264	−	6.00000i	0.194871	−	0.275589i
$475$	−1.00000	+	1.00000i	−0.0458831	+	0.0458831i
$476$	2.82843	+	2.82843i	0.129641	+	0.129641i
$477$	16.0000	−	5.65685i	0.732590	−	0.259010i
$478$	16.0000			0.731823
$479$	8.48528	−	8.48528i	0.387702	−	0.387702i	−0.486165	−	0.873867i	$-0.661605\pi$
$479$	8.48528	−	8.48528i	0.387702	−	0.387702i	0.873867	+	0.486165i	$0.161605\pi$
$480$	−1.41421	−	1.00000i	−0.0645497	−	0.0456435i
$481$	−15.0000	+	21.0000i	−0.683941	+	0.957518i
$482$			7.07107i			0.322078i
$483$	27.3137	−	4.68629i	1.24282	−	0.213234i
$484$		−	3.00000i		−	0.136364i
$485$	4.24264			0.192648
$486$	11.7071	+	10.2929i	0.531045	+	0.466895i
$487$	−5.00000	−	5.00000i	−0.226572	−	0.226572i	0.584687	−	0.811259i	$-0.301217\pi$
$487$	−5.00000	−	5.00000i	−0.226572	−	0.226572i	−0.811259	+	0.584687i	$0.801217\pi$
$488$			12.7279i			0.576166i
$489$	7.24264	−	1.24264i	0.327524	−	0.0561942i
$490$	3.00000			0.135526
$491$		−	33.9411i		−	1.53174i	−0.642995	−	0.765871i	$-0.722308\pi$
$491$		−	33.9411i		−	1.53174i	0.642995	−	0.765871i	$-0.277692\pi$
$492$		0			0
$493$	4.00000			0.180151
$494$	−4.24264	+	4.24264i	−0.190885	+	0.190885i
$495$	−7.65685	−	3.65685i	−0.344150	−	0.164363i
$496$	−1.00000	+	1.00000i	−0.0449013	+	0.0449013i
$497$		−	5.65685i		−	0.253745i
$498$	4.82843	−	0.828427i	0.216367	−	0.0371227i
$499$	21.0000	−	21.0000i	0.940089	−	0.940089i	−0.0582150	−	0.998304i	$-0.518541\pi$
$499$	21.0000	−	21.0000i	0.940089	−	0.940089i	0.998304	+	0.0582150i	$0.0185409\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−20.4853	+	3.51472i	−0.915215	+	0.157026i
$502$		−	24.0000i		−	1.07117i
$503$	31.1127	−	31.1127i	1.38725	−	1.38725i	0.556195	−	0.831052i	$-0.312261\pi$
$503$	31.1127	−	31.1127i	1.38725	−	1.38725i	0.831052	−	0.556195i	$-0.187739\pi$
$504$	5.41421	+	2.58579i	0.241168	+	0.115180i
$505$	4.00000	−	4.00000i	0.177998	−	0.177998i
$506$	22.6274			1.00591
$507$	5.00000	−	7.07107i	0.222058	−	0.314037i
$508$			16.0000i			0.709885i
$509$	8.48528			0.376103			0.188052	−	0.982159i	$-0.439783\pi$
$509$	8.48528			0.376103			0.188052	+	0.982159i	$0.439783\pi$
$510$	−3.41421	+	0.585786i	−0.151184	+	0.0259391i
$511$			20.0000i			0.884748i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−6.41421	+	3.58579i	−0.283194	+	0.158316i
$514$	−18.0000			−0.793946
$515$		−	9.89949i		−	0.436224i
$516$	−12.0711	+	2.07107i	−0.531399	+	0.0911737i
$517$		0			0
$518$	−7.07107	+	9.89949i	−0.310685	+	0.434959i
$519$	16.0000	+	11.3137i	0.702322	+	0.496617i
$520$	−3.00000	+	3.00000i	−0.131559	+	0.131559i
$521$	−28.2843			−1.23916			−0.619578	−	0.784935i	$-0.712696\pi$
$521$	−28.2843			−1.23916			−0.619578	+	0.784935i	$0.712696\pi$
$522$	5.65685	−	2.00000i	0.247594	−	0.0875376i
$523$	−17.0000	−	17.0000i	−0.743358	−	0.743358i	0.229865	−	0.973223i	$-0.426172\pi$
$523$	−17.0000	−	17.0000i	−0.743358	−	0.743358i	−0.973223	+	0.229865i	$0.926172\pi$
$524$	8.48528	−	8.48528i	0.370681	−	0.370681i
$525$	2.00000	−	2.82843i	0.0872872	−	0.123443i
$526$	−12.0000	−	12.0000i	−0.523225	−	0.523225i
$527$			2.82843i			0.123208i
$528$	4.00000	+	2.82843i	0.174078	+	0.123091i
$529$		−	41.0000i		−	1.78261i
$530$			5.65685i			0.245718i
$531$	10.8284	+	5.17157i	0.469914	+	0.224427i
$532$	−2.00000	+	2.00000i	−0.0867110	+	0.0867110i
$533$		0			0
$534$	−10.0000	+	14.1421i	−0.432742	+	0.611990i
$535$	−8.00000	−	8.00000i	−0.345870	−	0.345870i
$536$	2.82843	+	2.82843i	0.122169	+	0.122169i
$537$	−7.02944	−	40.9706i	−0.303343	−	1.76801i
$538$		0			0
$539$	−8.48528			−0.365487
$540$	−4.53553	+	2.53553i	−0.195178	+	0.109112i
$541$	31.0000	+	31.0000i	1.33279	+	1.33279i	0.902861	+	0.429934i	$0.141463\pi$
$541$	31.0000	+	31.0000i	1.33279	+	1.33279i	0.429934	+	0.902861i	$0.358537\pi$
$542$	−4.24264	−	4.24264i	−0.182237	−	0.182237i
$543$	28.2843	+	20.0000i	1.21379	+	0.858282i
$544$	2.00000			0.0857493
$545$	−4.24264			−0.181735
$546$	8.48528	−	12.0000i	0.363137	−	0.513553i
$547$	−17.0000	+	17.0000i	−0.726868	+	0.726868i	−0.969994	−	0.243127i	$-0.921827\pi$
$547$	−17.0000	+	17.0000i	−0.726868	+	0.726868i	0.243127	+	0.969994i	$0.421827\pi$
$548$	−5.65685			−0.241649
$549$	34.4558	+	16.4558i	1.47054	+	0.702318i
$550$	2.00000	−	2.00000i	0.0852803	−	0.0852803i
$551$			2.82843i			0.120495i
$552$	8.00000	−	11.3137i	0.340503	−	0.481543i
$553$	−6.00000	−	6.00000i	−0.255146	−	0.255146i
$554$	15.5563			0.660926
$555$	−3.46447	−	9.94975i	−0.147058	−	0.422343i
$556$	−4.00000			−0.169638
$557$	29.6985	+	29.6985i	1.25837	+	1.25837i	0.951873	+	0.306492i	$0.0991552\pi$
$557$	29.6985	+	29.6985i	1.25837	+	1.25837i	0.306492	+	0.951873i	$0.400845\pi$
$558$	1.41421	+	4.00000i	0.0598684	+	0.169334i
$559$			30.0000i			1.26886i
$560$	−1.41421	+	1.41421i	−0.0597614	+	0.0597614i
$561$	9.65685	−	1.65685i	0.407713	−	0.0699524i
$562$	−18.0000			−0.759284
$563$	19.7990	−	19.7990i	0.834428	−	0.834428i	−0.153691	−	0.988119i	$-0.549116\pi$
$563$	19.7990	−	19.7990i	0.834428	−	0.834428i	0.988119	+	0.153691i	$0.0491160\pi$
$564$		0			0
$565$	−6.00000			−0.252422
$566$	−1.41421			−0.0594438
$567$	14.0000	−	11.3137i	0.587945	−	0.475131i
$568$	−2.00000	−	2.00000i	−0.0839181	−	0.0839181i
$569$	−21.2132	−	21.2132i	−0.889304	−	0.889304i	0.105152	−	0.994456i	$-0.466467\pi$
$569$	−21.2132	−	21.2132i	−0.889304	−	0.889304i	−0.994456	+	0.105152i	$0.966467\pi$
$570$	−0.414214	−	2.41421i	−0.0173495	−	0.101120i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	8.48528	−	8.48528i	0.354787	−	0.354787i
$573$	20.4853	−	3.51472i	0.855785	−	0.146829i
$574$		0			0
$575$	−5.65685	−	5.65685i	−0.235907	−	0.235907i
$576$	2.82843	−	1.00000i	0.117851	−	0.0416667i
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	0.869177	−	0.494502i	$-0.164649\pi$
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	−0.494502	+	0.869177i	$0.664649\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$	6.21320	+	36.2132i	0.258212	+	1.50497i
$580$			2.00000i			0.0830455i
$581$		−	5.65685i		−	0.234686i
$582$	−4.24264	+	6.00000i	−0.175863	+	0.248708i
$583$		−	16.0000i		−	0.662652i
$584$	7.07107	+	7.07107i	0.292603	+	0.292603i
$585$	4.24264	+	12.0000i	0.175412	+	0.496139i
$586$	4.00000	−	4.00000i	0.165238	−	0.165238i
$587$	31.1127	+	31.1127i	1.28416	+	1.28416i	0.938279	+	0.345880i	$0.112419\pi$
$587$	31.1127	+	31.1127i	1.28416	+	1.28416i	0.345880	+	0.938279i	$0.387581\pi$
$588$	−3.00000	+	4.24264i	−0.123718	+	0.174964i
$589$	−2.00000			−0.0824086
$590$	−2.82843	+	2.82843i	−0.116445	+	0.116445i
$591$	19.7990	−	28.0000i	0.814422	−	1.15177i
$592$	1.00000	+	6.00000i	0.0410997	+	0.246598i
$593$			36.7696i			1.50994i	0.655757	+	0.754972i	$0.272350\pi$
$593$			36.7696i			1.50994i	−0.655757	+	0.754972i	$0.727650\pi$
$594$	12.8284	−	7.17157i	0.526357	−	0.294253i
$595$			4.00000i			0.163984i
$596$	11.3137			0.463428
$597$	−31.3848	+	5.38478i	−1.28449	+	0.220384i
$598$	−24.0000	−	24.0000i	−0.981433	−	0.981433i
$599$			2.82843i			0.115566i	0.998329	+	0.0577832i	$0.0184032\pi$
$599$			2.82843i			0.115566i	−0.998329	+	0.0577832i	$0.981597\pi$
$600$	−0.292893	−	1.70711i	−0.0119573	−	0.0696923i
$601$	−12.0000			−0.489490			−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000			−0.489490			−0.244745	+	0.969587i	$0.578704\pi$
$602$			14.1421i			0.576390i
$603$	11.3137	−	4.00000i	0.460730	−	0.162893i
$604$	−10.0000			−0.406894
$605$	2.12132	−	2.12132i	0.0862439	−	0.0862439i
$606$	1.65685	+	9.65685i	0.0673051	+	0.392283i
$607$	−19.0000	+	19.0000i	−0.771186	+	0.771186i	−0.978314	−	0.207128i	$-0.933588\pi$
$607$	−19.0000	+	19.0000i	−0.771186	+	0.771186i	0.207128	+	0.978314i	$0.433588\pi$
$608$			1.41421i			0.0573539i
$609$	−1.17157	−	6.82843i	−0.0474745	−	0.276702i
$610$	−9.00000	+	9.00000i	−0.364399	+	0.364399i
$611$		0			0
$612$	2.58579	−	5.41421i	0.104524	−	0.218857i
$613$		−	4.00000i		−	0.161558i	−0.996732	−	0.0807792i	$-0.974259\pi$
$613$		−	4.00000i		−	0.161558i	0.996732	−	0.0807792i	$-0.0257409\pi$
$614$	15.5563	−	15.5563i	0.627803	−	0.627803i
$615$		0			0
$616$	4.00000	−	4.00000i	0.161165	−	0.161165i
$617$	−5.65685			−0.227736			−0.113868	−	0.993496i	$-0.536324\pi$
$617$	−5.65685			−0.227736			−0.113868	+	0.993496i	$0.536324\pi$
$618$	14.0000	+	9.89949i	0.563163	+	0.398216i
$619$		−	10.0000i		−	0.401934i	−0.979598	−	0.200967i	$-0.935592\pi$
$619$		−	10.0000i		−	0.401934i	0.979598	−	0.200967i	$-0.0644084\pi$
$620$	−1.41421			−0.0567962
$621$	−20.2843	−	36.2843i	−0.813980	−	1.45604i
$622$		0			0
$623$	14.1421	+	14.1421i	0.566593	+	0.566593i
$624$	−1.24264	−	7.24264i	−0.0497454	−	0.289938i
$625$	−1.00000			−0.0400000
$626$		−	12.7279i		−	0.508710i
$627$	1.17157	+	6.82843i	0.0467881	+	0.272701i
$628$			4.00000i			0.159617i
$629$	9.89949	+	7.07107i	0.394719	+	0.281942i
$630$	2.00000	+	5.65685i	0.0796819	+	0.225374i
$631$	−31.0000	+	31.0000i	−1.23409	+	1.23409i	−0.271712	+	0.962379i	$0.587590\pi$
$631$	−31.0000	+	31.0000i	−1.23409	+	1.23409i	−0.962379	+	0.271712i	$0.912410\pi$
$632$	−4.24264			−0.168763
$633$	−39.5980	−	28.0000i	−1.57388	−	1.11290i
$634$	−12.0000	−	12.0000i	−0.476581	−	0.476581i
$635$	−11.3137	+	11.3137i	−0.448971	+	0.448971i
$636$	−8.00000	−	5.65685i	−0.317221	−	0.224309i
$637$	9.00000	+	9.00000i	0.356593	+	0.356593i
$638$		−	5.65685i		−	0.223957i
$639$	−8.00000	+	2.82843i	−0.316475	+	0.111891i
$640$			1.00000i			0.0395285i
$641$		−	5.65685i		−	0.223432i	−0.993740	−	0.111716i	$-0.964365\pi$
$641$		−	5.65685i		−	0.223432i	0.993740	−	0.111716i	$-0.0356347\pi$
$642$	19.3137	−	3.31371i	0.762251	−	0.130782i
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	−0.987262	−	0.159103i	$-0.949140\pi$
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	0.159103	+	0.987262i	$0.449140\pi$
$644$	−11.3137	−	11.3137i	−0.445823	−	0.445823i
$645$	−10.0000	−	7.07107i	−0.393750	−	0.278423i
$646$	2.00000	+	2.00000i	0.0786889	+	0.0786889i
$647$	8.48528	+	8.48528i	0.333591	+	0.333591i	0.853948	−	0.520358i	$-0.174201\pi$
$647$	8.48528	+	8.48528i	0.333591	+	0.333591i	−0.520358	+	0.853948i	$0.674201\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$	8.00000	−	8.00000i	0.314027	−	0.314027i
$650$	−4.24264			−0.166410
$651$	4.82843	−	0.828427i	0.189241	−	0.0324686i
$652$	−3.00000	−	3.00000i	−0.117489	−	0.117489i
$653$	12.7279	+	12.7279i	0.498082	+	0.498082i	0.910841	−	0.412758i	$-0.135435\pi$
$653$	12.7279	+	12.7279i	0.498082	+	0.498082i	−0.412758	+	0.910841i	$0.635435\pi$
$654$	4.24264	−	6.00000i	0.165900	−	0.234619i
$655$	12.0000			0.468879
$656$		0			0
$657$	28.2843	−	10.0000i	1.10347	−	0.390137i
$658$		0			0
$659$	2.82843			0.110180			0.0550899	−	0.998481i	$-0.482455\pi$
$659$	2.82843			0.110180			0.0550899	+	0.998481i	$0.482455\pi$
$660$	0.828427	+	4.82843i	0.0322465	+	0.187946i
$661$	1.00000	−	1.00000i	0.0388955	−	0.0388955i	−0.687392	−	0.726287i	$-0.741244\pi$
$661$	1.00000	−	1.00000i	0.0388955	−	0.0388955i	0.726287	+	0.687392i	$0.241244\pi$
$662$		−	32.5269i		−	1.26419i
$663$	−12.0000	−	8.48528i	−0.466041	−	0.329541i
$664$	−2.00000	−	2.00000i	−0.0776151	−	0.0776151i
$665$	−2.82843			−0.109682
$666$	17.5355	+	5.05025i	0.679488	+	0.195693i
$667$	−16.0000			−0.619522
$668$	8.48528	+	8.48528i	0.328305	+	0.328305i
$669$	−11.3137	−	8.00000i	−0.437413	−	0.309298i
$670$			4.00000i			0.154533i
$671$	25.4558	−	25.4558i	0.982712	−	0.982712i
$672$	−0.585786	−	3.41421i	−0.0225972	−	0.131706i
$673$	−48.0000			−1.85026			−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000			−1.85026			−0.925132	+	0.379646i	$0.876046\pi$
$674$	−11.3137	+	11.3137i	−0.435788	+	0.435788i
$675$	−5.00000	−	1.41421i	−0.192450	−	0.0544331i
$676$	−5.00000			−0.192308
$677$	−22.6274			−0.869642			−0.434821	−	0.900517i	$-0.643188\pi$
$677$	−22.6274			−0.869642			−0.434821	+	0.900517i	$0.643188\pi$
$678$	6.00000	−	8.48528i	0.230429	−	0.325875i
$679$	6.00000	+	6.00000i	0.230259	+	0.230259i
$680$	1.41421	+	1.41421i	0.0542326	+	0.0542326i
$681$	34.1421	−	5.85786i	1.30833	−	0.224474i
$682$	4.00000			0.153168
$683$	14.1421	−	14.1421i	0.541134	−	0.541134i	−0.382727	−	0.923861i	$-0.625015\pi$
$683$	14.1421	−	14.1421i	0.541134	−	0.541134i	0.923861	+	0.382727i	$0.125015\pi$
$684$	3.82843	+	1.82843i	0.146384	+	0.0699117i
$685$	−4.00000	−	4.00000i	−0.152832	−	0.152832i
$686$	14.1421	+	14.1421i	0.539949	+	0.539949i
$687$	−8.48528	−	6.00000i	−0.323734	−	0.228914i
$688$	5.00000	+	5.00000i	0.190623	+	0.190623i
$689$	−16.9706	+	16.9706i	−0.646527	+	0.646527i
$690$	13.6569	−	2.34315i	0.519908	−	0.0892020i
$691$		−	20.0000i		−	0.760836i	−0.924815	−	0.380418i	$-0.875780\pi$
$691$		−	20.0000i		−	0.760836i	0.924815	−	0.380418i	$-0.124220\pi$
$692$		−	11.3137i		−	0.430083i
$693$	−5.65685	−	16.0000i	−0.214886	−	0.607790i
$694$		−	28.0000i		−	1.06287i
$695$	−2.82843	−	2.82843i	−0.107288	−	0.107288i
$696$	−2.82843	−	2.00000i	−0.107211	−	0.0758098i
$697$		0			0
$698$	−2.82843	−	2.82843i	−0.107058	−	0.107058i
$699$	20.0000	+	14.1421i	0.756469	+	0.534905i
$700$	−2.00000			−0.0755929
$701$	15.5563	−	15.5563i	0.587555	−	0.587555i	−0.349413	−	0.936969i	$-0.613619\pi$
$701$	15.5563	−	15.5563i	0.587555	−	0.587555i	0.936969	+	0.349413i	$0.113619\pi$
$702$	−21.2132	−	6.00000i	−0.800641	−	0.226455i
$703$	−5.00000	+	7.00000i	−0.188579	+	0.264010i
$704$		−	2.82843i		−	0.106600i
$705$		0			0
$706$		−	18.0000i		−	0.677439i
$707$	11.3137			0.425496
$708$	−1.17157	−	6.82843i	−0.0440304	−	0.256628i
$709$	9.00000	+	9.00000i	0.338002	+	0.338002i	0.855615	−	0.517613i	$-0.173179\pi$
$709$	9.00000	+	9.00000i	0.338002	+	0.338002i	−0.517613	+	0.855615i	$0.673179\pi$
$710$		−	2.82843i		−	0.106149i
$711$	−5.48528	+	11.4853i	−0.205714	+	0.430732i
$712$	10.0000			0.374766
$713$		−	11.3137i		−	0.423702i
$714$	−5.65685	−	4.00000i	−0.211702	−	0.149696i
$715$	12.0000			0.448775
$716$	−16.9706	+	16.9706i	−0.634220	+	0.634220i
$717$	−27.3137	+	4.68629i	−1.02005	+	0.175013i
$718$	−12.0000	+	12.0000i	−0.447836	+	0.447836i
$719$		−	16.9706i		−	0.632895i	−0.948610	−	0.316448i	$-0.897510\pi$
$719$		−	16.9706i		−	0.632895i	0.948610	−	0.316448i	$-0.102490\pi$
$720$	2.70711	+	1.29289i	0.100888	+	0.0481833i
$721$	14.0000	−	14.0000i	0.521387	−	0.521387i
$722$	12.0208	−	12.0208i	0.447368	−	0.447368i
$723$	−2.07107	−	12.0711i	−0.0770238	−	0.448928i
$724$		−	20.0000i		−	0.743294i
$725$	−1.41421	+	1.41421i	−0.0525226	+	0.0525226i
$726$	0.878680	+	5.12132i	0.0326109	+	0.190070i
$727$	−37.0000	+	37.0000i	−1.37225	+	1.37225i	−0.515160	+	0.857094i	$0.672268\pi$
$727$	−37.0000	+	37.0000i	−1.37225	+	1.37225i	−0.857094	+	0.515160i	$0.827732\pi$
$728$	−8.48528			−0.314485
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$			10.0000i			0.370117i
$731$	14.1421			0.523066
$732$	−3.72792	−	21.7279i	−0.137788	−	0.803087i
$733$			28.0000i			1.03420i	0.855924	+	0.517102i	$0.172989\pi$
$733$			28.0000i			1.03420i	−0.855924	+	0.517102i	$0.827011\pi$
$734$	−5.65685	−	5.65685i	−0.208798	−	0.208798i
$735$	−5.12132	+	0.878680i	−0.188903	+	0.0324106i
$736$	−8.00000			−0.294884
$737$		−	11.3137i		−	0.416746i
$738$		0			0
$739$		−	34.0000i		−	1.25071i	−0.780340	−	0.625355i	$-0.784954\pi$
$739$		−	34.0000i		−	1.25071i	0.780340	−	0.625355i	$-0.215046\pi$
$740$	−3.53553	+	4.94975i	−0.129969	+	0.181956i
$741$	6.00000	−	8.48528i	0.220416	−	0.311715i
$742$	−8.00000	+	8.00000i	−0.293689	+	0.293689i
$743$	−22.6274			−0.830119			−0.415060	−	0.909794i	$-0.636239\pi$
$743$	−22.6274			−0.830119			−0.415060	+	0.909794i	$0.636239\pi$
$744$	1.41421	−	2.00000i	0.0518476	−	0.0733236i
$745$	8.00000	+	8.00000i	0.293097	+	0.293097i
$746$	12.7279	−	12.7279i	0.466002	−	0.466002i
$747$	−8.00000	+	2.82843i	−0.292705	+	0.103487i
$748$	−4.00000	−	4.00000i	−0.146254	−	0.146254i
$749$		−	22.6274i		−	0.826788i
$750$	1.00000	−	1.41421i	0.0365148	−	0.0516398i
$751$			40.0000i			1.45962i	0.683650	+	0.729810i	$0.260392\pi$
$751$			40.0000i			1.45962i	−0.683650	+	0.729810i	$0.739608\pi$
$752$		0			0
$753$	7.02944	+	40.9706i	0.256167	+	1.49305i
$754$	−6.00000	+	6.00000i	−0.218507	+	0.218507i
$755$	−7.07107	−	7.07107i	−0.257343	−	0.257343i
$756$	−10.0000	−	2.82843i	−0.363696	−	0.102869i
$757$	11.0000	+	11.0000i	0.399802	+	0.399802i	0.878163	−	0.478361i	$-0.158769\pi$
$757$	11.0000	+	11.0000i	0.399802	+	0.399802i	−0.478361	+	0.878163i	$0.658769\pi$
$758$	−1.41421	−	1.41421i	−0.0513665	−	0.0513665i
$759$	−38.6274	+	6.62742i	−1.40209	+	0.240560i
$760$	−1.00000	+	1.00000i	−0.0362738	+	0.0362738i
$761$	−36.7696			−1.33290			−0.666448	−	0.745552i	$-0.732186\pi$
$761$	−36.7696			−1.33290			−0.666448	+	0.745552i	$0.732186\pi$
$762$	−4.68629	−	27.3137i	−0.169766	−	0.989471i
$763$	−6.00000	−	6.00000i	−0.217215	−	0.217215i
$764$	−8.48528	−	8.48528i	−0.306987	−	0.306987i
$765$	5.65685	−	2.00000i	0.204524	−	0.0723102i
$766$	12.0000			0.433578
$767$	−16.9706			−0.612772
$768$	−1.41421	−	1.00000i	−0.0510310	−	0.0360844i
$769$	19.0000	−	19.0000i	0.685158	−	0.685158i	−0.276000	−	0.961158i	$-0.589009\pi$
$769$	19.0000	−	19.0000i	0.685158	−	0.685158i	0.961158	+	0.276000i	$0.0890090\pi$
$770$	5.65685			0.203859
$771$	30.7279	−	5.27208i	1.10664	−	0.189869i
$772$	15.0000	−	15.0000i	0.539862	−	0.539862i
$773$		−	19.7990i		−	0.712120i	−0.934463	−	0.356060i	$-0.884120\pi$
$773$		−	19.7990i		−	0.712120i	0.934463	−	0.356060i	$-0.115880\pi$
$774$	20.0000	−	7.07107i	0.718885	−	0.254164i
$775$	−1.00000	−	1.00000i	−0.0359211	−	0.0359211i
$776$	4.24264			0.152302
$777$	9.17157	−	18.9706i	0.329028	−	0.680565i
$778$	34.0000			1.21896
$779$		0			0
$780$	4.24264	−	6.00000i	0.151911	−	0.214834i
$781$			8.00000i			0.286263i
$782$	−11.3137	+	11.3137i	−0.404577	+	0.404577i
$783$	−9.07107	+	5.07107i	−0.324174	+	0.181225i
$784$	3.00000			0.107143
$785$	−2.82843	+	2.82843i	−0.100951	+	0.100951i
$786$	−12.0000	+	16.9706i	−0.428026	+	0.605320i
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−19.7990			−0.705310
$789$	24.0000	+	16.9706i	0.854423	+	0.604168i
$790$	−3.00000	−	3.00000i	−0.106735	−	0.106735i
$791$	−8.48528	−	8.48528i	−0.301702	−	0.301702i
$792$	−7.65685	−	3.65685i	−0.272074	−	0.129941i
$793$	−54.0000			−1.91760
$794$	24.0416	−	24.0416i	0.853206	−	0.853206i
$795$	−1.65685	−	9.65685i	−0.0587626	−	0.342493i
$796$	13.0000	+	13.0000i	0.460773	+	0.460773i
$797$	12.7279	+	12.7279i	0.450846	+	0.450846i	0.895635	−	0.444789i	$-0.146721\pi$
$797$	12.7279	+	12.7279i	0.450846	+	0.450846i	−0.444789	+	0.895635i	$0.646721\pi$
$798$	2.82843	−	4.00000i	0.100125	−	0.141598i
$799$		0			0
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	12.9289	−	27.0711i	0.456821	−	0.956509i
$802$			30.0000i			1.05934i
$803$		−	28.2843i		−	0.998130i
$804$	−5.65685	−	4.00000i	−0.199502	−	0.141069i
$805$		−	16.0000i		−	0.563926i
$806$	−4.24264	−	4.24264i	−0.149441	−	0.149441i
$807$		0			0
$808$	4.00000	−	4.00000i	0.140720	−	0.140720i
$809$	7.07107	+	7.07107i	0.248606	+	0.248606i	0.820398	−	0.571793i	$-0.193752\pi$
$809$	7.07107	+	7.07107i	0.248606	+	0.248606i	−0.571793	+	0.820398i	$0.693752\pi$
$810$	7.00000	−	5.65685i	0.245955	−	0.198762i
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$	−2.82843	+	2.82843i	−0.0992583	+	0.0992583i
$813$	8.48528	+	6.00000i	0.297592	+	0.210429i
$814$	10.0000	−	14.0000i	0.350500	−	0.490700i
$815$		−	4.24264i		−	0.148613i
$816$	−3.41421	+	0.585786i	−0.119521	+	0.0205066i
$817$			10.0000i			0.349856i
$818$	−24.0416			−0.840596
$819$	−10.9706	+	22.9706i	−0.383342	+	0.802656i
$820$		0			0
$821$			2.82843i			0.0987128i	0.998781	+	0.0493564i	$0.0157170\pi$
$821$			2.82843i			0.0987128i	−0.998781	+	0.0493564i	$0.984283\pi$
$822$	9.65685	−	1.65685i	0.336821	−	0.0577894i
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$		−	9.89949i		−	0.344865i
$825$	−2.82843	+	4.00000i	−0.0984732	+	0.139262i
$826$	−8.00000			−0.278356
$827$	−33.9411	+	33.9411i	−1.18025	+	1.18025i	−0.200569	+	0.979680i	$0.564279\pi$
$827$	−33.9411	+	33.9411i	−1.18025	+	1.18025i	−0.979680	+	0.200569i	$0.935721\pi$
$828$	−10.3431	+	21.6569i	−0.359449	+	0.752628i
$829$	19.0000	−	19.0000i	0.659897	−	0.659897i	−0.295458	−	0.955356i	$-0.595472\pi$
$829$	19.0000	−	19.0000i	0.659897	−	0.659897i	0.955356	+	0.295458i	$0.0954724\pi$
$830$		−	2.82843i		−	0.0981761i
$831$	−26.5563	+	4.55635i	−0.921230	+	0.158058i
$832$	−3.00000	+	3.00000i	−0.104006	+	0.104006i
$833$	4.24264	−	4.24264i	0.146999	−	0.146999i
$834$	6.82843	−	1.17157i	0.236449	−	0.0405683i
$835$			12.0000i			0.415277i
$836$	2.82843	−	2.82843i	0.0978232	−	0.0978232i
$837$	−3.58579	−	6.41421i	−0.123943	−	0.221708i
$838$	−8.00000	+	8.00000i	−0.276355	+	0.276355i
$839$	−2.82843			−0.0976481			−0.0488241	−	0.998807i	$-0.515547\pi$
$839$	−2.82843			−0.0976481			−0.0488241	+	0.998807i	$0.515547\pi$
$840$	2.00000	−	2.82843i	0.0690066	−	0.0975900i
$841$		−	25.0000i		−	0.862069i
$842$	15.5563			0.536107
$843$	30.7279	−	5.27208i	1.05833	−	0.181580i
$844$			28.0000i			0.963800i
$845$	−3.53553	−	3.53553i	−0.121626	−	0.121626i
$846$		0			0
$847$	6.00000			0.206162
$848$			5.65685i			0.194257i
$849$	2.41421	−	0.414214i	0.0828556	−	0.0142158i
$850$			2.00000i			0.0685994i
$851$	−39.5980	−	28.2843i	−1.35740	−	0.969572i
$852$	4.00000	+	2.82843i	0.137038	+	0.0969003i
$853$	−27.0000	+	27.0000i	−0.924462	+	0.924462i	−0.997341	−	0.0728784i	$-0.976781\pi$
$853$	−27.0000	+	27.0000i	−0.924462	+	0.924462i	0.0728784	+	0.997341i	$0.476781\pi$
$854$	−25.4558			−0.871081
$855$	1.41421	+	4.00000i	0.0483651	+	0.136797i
$856$	−8.00000	−	8.00000i	−0.273434	−	0.273434i
$857$	−15.5563	+	15.5563i	−0.531395	+	0.531395i	−0.920987	−	0.389593i	$-0.872616\pi$
$857$	−15.5563	+	15.5563i	−0.531395	+	0.531395i	0.389593	+	0.920987i	$0.372616\pi$
$858$	−12.0000	+	16.9706i	−0.409673	+	0.579365i
$859$	27.0000	+	27.0000i	0.921228	+	0.921228i	0.997116	−	0.0758882i	$-0.0241792\pi$
$859$	27.0000	+	27.0000i	0.921228	+	0.921228i	−0.0758882	+	0.997116i	$0.524179\pi$
$860$			7.07107i			0.241121i
$861$		0			0
$862$			16.0000i			0.544962i
$863$		−	19.7990i		−	0.673965i	−0.941511	−	0.336983i	$-0.890594\pi$
$863$		−	19.7990i		−	0.673965i	0.941511	−	0.336983i	$-0.109406\pi$
$864$	−4.53553	+	2.53553i	−0.154302	+	0.0862606i
$865$	8.00000	−	8.00000i	0.272008	−	0.272008i
$866$	19.7990	+	19.7990i	0.672797	+	0.672797i
$867$	13.0000	−	18.3848i	0.441503	−	0.624380i
$868$	−2.00000	−	2.00000i	−0.0678844	−	0.0678844i
$869$	8.48528	+	8.48528i	0.287843	+	0.287843i
$870$	−0.585786	−	3.41421i	−0.0198600	−	0.115753i
$871$	−12.0000	+	12.0000i	−0.406604	+	0.406604i
$872$	−4.24264			−0.143674
$873$	5.48528	−	11.4853i	0.185649	−	0.388718i
$874$	−8.00000	−	8.00000i	−0.270604	−	0.270604i
$875$	−1.41421	−	1.41421i	−0.0478091	−	0.0478091i
$876$	−14.1421	−	10.0000i	−0.477818	−	0.337869i
$877$	44.0000			1.48577			0.742887	−	0.669417i	$-0.233456\pi$
$877$	44.0000			1.48577			0.742887	+	0.669417i	$0.233456\pi$
$878$	−12.7279			−0.429547
$879$	−5.65685	+	8.00000i	−0.190801	+	0.269833i
$880$	2.00000	−	2.00000i	0.0674200	−	0.0674200i
$881$	19.7990			0.667045			0.333522	−	0.942742i	$-0.391763\pi$
$881$	19.7990			0.667045			0.333522	+	0.942742i	$0.391763\pi$
$882$	3.87868	−	8.12132i	0.130602	−	0.273459i
$883$	19.0000	−	19.0000i	0.639401	−	0.639401i	−0.311007	−	0.950408i	$-0.600666\pi$
$883$	19.0000	−	19.0000i	0.639401	−	0.639401i	0.950408	+	0.311007i	$0.100666\pi$
$884$			8.48528i			0.285391i
$885$	4.00000	−	5.65685i	0.134459	−	0.190153i
$886$	22.0000	+	22.0000i	0.739104	+	0.739104i
$887$	−50.9117			−1.70945			−0.854724	−	0.519083i	$-0.826273\pi$
$887$	−50.9117			−1.70945			−0.854724	+	0.519083i	$0.826273\pi$
$888$	−3.46447	−	9.94975i	−0.116260	−	0.333892i
$889$	−32.0000			−1.07325
$890$	7.07107	+	7.07107i	0.237023	+	0.237023i
$891$	−19.7990	+	16.0000i	−0.663291	+	0.536020i
$892$			8.00000i			0.267860i
$893$		0			0
$894$	−19.3137	+	3.31371i	−0.645947	+	0.110827i
$895$	−24.0000			−0.802232
$896$	−1.41421	+	1.41421i	−0.0472456	+	0.0472456i
$897$	48.0000	+	33.9411i	1.60267	+	1.13326i
$898$	34.0000			1.13459
$899$	−2.82843			−0.0943333
$900$	1.00000	+	2.82843i	0.0333333	+	0.0942809i
$901$	8.00000	+	8.00000i	0.266519	+	0.266519i
$902$		0			0
$903$	−4.14214	−	24.1421i	−0.137842	−	0.803400i
$904$	−6.00000			−0.199557
$905$	14.1421	−	14.1421i	0.470100	−	0.470100i
$906$	17.0711	−	2.92893i	0.567148	−	0.0973073i
$907$	−17.0000	−	17.0000i	−0.564476	−	0.564476i	0.366100	−	0.930576i	$-0.380693\pi$
$907$	−17.0000	−	17.0000i	−0.564476	−	0.564476i	−0.930576	+	0.366100i	$0.880693\pi$
$908$	−14.1421	−	14.1421i	−0.469323	−	0.469323i
$909$	−5.65685	−	16.0000i	−0.187626	−	0.530687i
$910$	−6.00000	−	6.00000i	−0.198898	−	0.198898i
$911$	−5.65685	+	5.65685i	−0.187420	+	0.187420i	−0.794580	−	0.607160i	$-0.792309\pi$
$911$	−5.65685	+	5.65685i	−0.187420	+	0.187420i	0.607160	+	0.794580i	$0.292309\pi$
$912$	−0.414214	−	2.41421i	−0.0137160	−	0.0799426i
$913$			8.00000i			0.264761i
$914$		−	7.07107i		−	0.233890i
$915$	12.7279	−	18.0000i	0.420772	−	0.595062i
$916$			6.00000i			0.198246i
$917$	16.9706	+	16.9706i	0.560417	+	0.560417i
$918$	−2.82843	+	10.0000i	−0.0933520	+	0.330049i
$919$	31.0000	−	31.0000i	1.02260	−	1.02260i	0.0228569	−	0.999739i	$-0.492724\pi$
$919$	31.0000	−	31.0000i	1.02260	−	1.02260i	0.999739	−	0.0228569i	$-0.00727621\pi$
$920$	−5.65685	−	5.65685i	−0.186501	−	0.186501i
$921$	−22.0000	+	31.1127i	−0.724925	+	1.02520i
$922$	−30.0000			−0.987997
$923$	8.48528	−	8.48528i	0.279296	−	0.279296i
$924$	−5.65685	+	8.00000i	−0.186097	+	0.263181i
$925$	−6.00000	+	1.00000i	−0.197279	+	0.0328798i
$926$			24.0416i			0.790057i
$927$	−26.7990	−	12.7990i	−0.880194	−	0.420374i
$928$			2.00000i			0.0656532i
$929$	−45.2548			−1.48476			−0.742381	−	0.669977i	$-0.766304\pi$
$929$	−45.2548			−1.48476			−0.742381	+	0.669977i	$0.766304\pi$
$930$	2.41421	−	0.414214i	0.0791652	−	0.0135826i
$931$	3.00000	+	3.00000i	0.0983210	+	0.0983210i
$932$		−	14.1421i		−	0.463241i
$933$		0			0
$934$	28.0000			0.916188
$935$		−	5.65685i		−	0.184999i
$936$	4.24264	+	12.0000i	0.138675	+	0.392232i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−5.65685	+	5.65685i	−0.184703	+	0.184703i
$939$	3.72792	+	21.7279i	0.121656	+	0.709064i
$940$		0			0
$941$		−	25.4558i		−	0.829837i	−0.909859	−	0.414918i	$-0.863810\pi$
$941$		−	25.4558i		−	0.829837i	0.909859	−	0.414918i	$-0.136190\pi$
$942$	−1.17157	−	6.82843i	−0.0381719	−	0.222482i
$943$		0			0
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$	−5.07107	−	9.07107i	−0.164962	−	0.295082i
$946$		−	20.0000i		−	0.650256i
$947$	19.7990	−	19.7990i	0.643381	−	0.643381i	−0.308004	−	0.951385i	$-0.599661\pi$
$947$	19.7990	−	19.7990i	0.643381	−	0.643381i	0.951385	+	0.308004i	$0.0996611\pi$
$948$	7.24264	−	1.24264i	0.235230	−	0.0403591i
$949$	−30.0000	+	30.0000i	−0.973841	+	0.973841i
$950$	−1.41421			−0.0458831
$951$	24.0000	+	16.9706i	0.778253	+	0.550308i
$952$			4.00000i			0.129641i
$953$	33.9411			1.09946			0.549730	−	0.835342i	$-0.314730\pi$
$953$	33.9411			1.09946			0.549730	+	0.835342i	$0.314730\pi$
$954$	15.3137	+	7.31371i	0.495800	+	0.236790i
$955$		−	12.0000i		−	0.388311i
$956$	11.3137	+	11.3137i	0.365911	+	0.365911i
$957$	1.65685	+	9.65685i	0.0535585	+	0.312162i
$958$	12.0000			0.387702
$959$		−	11.3137i		−	0.365339i
$960$	−0.292893	−	1.70711i	−0.00945309	−	0.0550966i
$961$			29.0000i			0.935484i
$962$	−25.4558	+	4.24264i	−0.820729	+	0.136788i
$963$	−32.0000	+	11.3137i	−1.03119	+	0.364579i
$964$	−5.00000	+	5.00000i	−0.161039	+	0.161039i
$965$	21.2132			0.682877
$966$	22.6274	+	16.0000i	0.728025	+	0.514792i
$967$	−27.0000	−	27.0000i	−0.868261	−	0.868261i	0.124018	−	0.992280i	$-0.460422\pi$
$967$	−27.0000	−	27.0000i	−0.868261	−	0.868261i	−0.992280	+	0.124018i	$0.960422\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$	−4.00000	−	2.82843i	−0.128499	−	0.0908622i
$970$	3.00000	+	3.00000i	0.0963242	+	0.0963242i
$971$			22.6274i			0.726148i	0.931760	+	0.363074i	$0.118273\pi$
$971$			22.6274i			0.726148i	−0.931760	+	0.363074i	$0.881727\pi$
$972$	1.00000	+	15.5563i	0.0320750	+	0.498970i
$973$		−	8.00000i		−	0.256468i
$974$		−	7.07107i		−	0.226572i
$975$	7.24264	−	1.24264i	0.231950	−	0.0397964i
$976$	−9.00000	+	9.00000i	−0.288083	+	0.288083i
$977$	12.7279	+	12.7279i	0.407202	+	0.407202i	0.880762	−	0.473560i	$-0.157031\pi$
$977$	12.7279	+	12.7279i	0.407202	+	0.407202i	−0.473560	+	0.880762i	$0.657031\pi$
$978$	6.00000	+	4.24264i	0.191859	+	0.135665i
$979$	−20.0000	−	20.0000i	−0.639203	−	0.639203i
$980$	2.12132	+	2.12132i	0.0677631	+	0.0677631i
$981$	−5.48528	+	11.4853i	−0.175132	+	0.366697i
$982$	24.0000	−	24.0000i	0.765871	−	0.765871i
$983$	16.9706			0.541277			0.270638	−	0.962681i	$-0.412765\pi$
$983$	16.9706			0.541277			0.270638	+	0.962681i	$0.412765\pi$
$984$		0			0
$985$	−14.0000	−	14.0000i	−0.446077	−	0.446077i
$986$	2.82843	+	2.82843i	0.0900755	+	0.0900755i
$987$		0			0
$988$	−6.00000			−0.190885
$989$	−56.5685			−1.79878
$990$	−2.82843	−	8.00000i	−0.0898933	−	0.254257i
$991$	31.0000	−	31.0000i	0.984747	−	0.984747i	−0.0151380	−	0.999885i	$-0.504819\pi$
$991$	31.0000	−	31.0000i	0.984747	−	0.984747i	0.999885	+	0.0151380i	$0.00481875\pi$
$992$	−1.41421			−0.0449013
$993$	9.52691	+	55.5269i	0.302327	+	1.76209i
$994$	4.00000	−	4.00000i	0.126872	−	0.126872i
$995$			18.3848i			0.582837i
$996$	4.00000	+	2.82843i	0.126745	+	0.0896221i
$997$	33.0000	+	33.0000i	1.04512	+	1.04512i	0.998933	+	0.0461877i	$0.0147072\pi$
$997$	33.0000	+	33.0000i	1.04512	+	1.04512i	0.0461877	+	0.998933i	$0.485293\pi$
$998$	29.6985			0.940089
$999$	−31.4142	−	3.48528i	−0.993902	−	0.110269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.a.191.2	yes	4
3.2	odd	2	inner	1110.2.u.a.191.1	✓	4
37.31	odd	4	inner	1110.2.u.a.401.1	yes	4
111.68	even	4	inner	1110.2.u.a.401.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.a.191.1	✓	4	3.2	odd	2	inner
1110.2.u.a.191.2	yes	4	1.1	even	1	trivial
1110.2.u.a.401.1	yes	4	37.31	odd	4	inner
1110.2.u.a.401.2	yes	4	111.68	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} -2.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} -2.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} -1.00000 q^{10} +2.82843 q^{11} +(1.00000 - 1.41421i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(-1.41421 - 1.41421i) q^{14} +(1.70711 - 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-1.00000 - 1.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(2.82843 + 2.00000i) q^{21} +(2.00000 + 2.00000i) q^{22} +(5.65685 - 5.65685i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -4.24264i q^{26} +(1.41421 - 5.00000i) q^{27} -2.00000i q^{28} +(-1.41421 - 1.41421i) q^{29} +(1.41421 + 1.00000i) q^{30} +(1.00000 - 1.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.00000 - 2.82843i) q^{33} -2.00000 q^{34} +(1.41421 - 1.41421i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-1.00000 - 6.00000i) q^{37} -1.41421i q^{38} +(1.24264 + 7.24264i) q^{39} -1.00000i q^{40} +(0.585786 + 3.41421i) q^{42} +(-5.00000 - 5.00000i) q^{43} +2.82843i q^{44} +(-2.70711 - 1.29289i) q^{45} +8.00000 q^{46} +(1.41421 + 1.00000i) q^{48} -3.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(3.00000 - 3.00000i) q^{52} -5.65685i q^{53} +(4.53553 - 2.53553i) q^{54} +(-2.00000 + 2.00000i) q^{55} +(1.41421 - 1.41421i) q^{56} +(0.414214 + 2.41421i) q^{57} -2.00000i q^{58} +(2.82843 - 2.82843i) q^{59} +(0.292893 + 1.70711i) q^{60} +(9.00000 - 9.00000i) q^{61} +1.41421 q^{62} +(-2.00000 - 5.65685i) q^{63} -1.00000i q^{64} +4.24264 q^{65} +(-0.828427 - 4.82843i) q^{66} -4.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(-13.6569 + 2.34315i) q^{69} +2.00000 q^{70} +2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -10.0000i q^{73} +(3.53553 - 4.94975i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(1.00000 - 1.00000i) q^{76} -5.65685 q^{77} +(-4.24264 + 6.00000i) q^{78} +(3.00000 + 3.00000i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +2.82843i q^{83} +(-2.00000 + 2.82843i) q^{84} -2.00000i q^{85} -7.07107i q^{86} +(0.585786 + 3.41421i) q^{87} +(-2.00000 + 2.00000i) q^{88} +(-7.07107 - 7.07107i) q^{89} +(-1.00000 - 2.82843i) q^{90} +(6.00000 + 6.00000i) q^{91} +(5.65685 + 5.65685i) q^{92} +(-2.41421 + 0.414214i) q^{93} +1.41421 q^{95} +(0.292893 + 1.70711i) q^{96} +(-3.00000 - 3.00000i) q^{97} +(-2.12132 - 2.12132i) q^{98} +(2.82843 + 8.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^6 - 8 * q^7 + 4 * q^9	\( 4 q - 4 q^{6} - 8 q^{7} + 4 q^{9} - 4 q^{10} + 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 4 q^{19} + 8 q^{22} + 4 q^{24} + 4 q^{31} - 16 q^{33} - 8 q^{34} - 4 q^{37} - 12 q^{39} + 8 q^{42} - 20 q^{43} - 8 q^{45} + 32 q^{46} - 12 q^{49} + 8 q^{51} + 12 q^{52} + 4 q^{54} - 8 q^{55} - 4 q^{57} + 4 q^{60} + 36 q^{61} - 8 q^{63} + 8 q^{66} - 32 q^{69} + 8 q^{70} - 8 q^{72} - 4 q^{75} + 4 q^{76} + 12 q^{79} - 28 q^{81} - 8 q^{84} + 8 q^{87} - 8 q^{88} - 4 q^{90} + 24 q^{91} - 4 q^{93} + 4 q^{96} - 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^6 - 8 * q^7 + 4 * q^9 - 4 * q^10 + 4 * q^12 - 12 * q^13 + 4 * q^15 - 4 * q^16 - 8 * q^18 - 4 * q^19 + 8 * q^22 + 4 * q^24 + 4 * q^31 - 16 * q^33 - 8 * q^34 - 4 * q^37 - 12 * q^39 + 8 * q^42 - 20 * q^43 - 8 * q^45 + 32 * q^46 - 12 * q^49 + 8 * q^51 + 12 * q^52 + 4 * q^54 - 8 * q^55 - 4 * q^57 + 4 * q^60 + 36 * q^61 - 8 * q^63 + 8 * q^66 - 32 * q^69 + 8 * q^70 - 8 * q^72 - 4 * q^75 + 4 * q^76 + 12 * q^79 - 28 * q^81 - 8 * q^84 + 8 * q^87 - 8 * q^88 - 4 * q^90 + 24 * q^91 - 4 * q^93 + 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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