LMFDB - Embedded newform 756.2.be.e.107.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.16
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.115165 - 1.40952i) q^{2} +(-1.97347 + 0.324653i) q^{4} +(-1.71449 - 0.989859i) q^{5} +(2.59406 + 0.520431i) q^{7} +(0.684877 + 2.74426i) q^{8} +O(q^{10})$	\(q+(-0.115165 - 1.40952i) q^{2} +(-1.97347 + 0.324653i) q^{4} +(-1.71449 - 0.989859i) q^{5} +(2.59406 + 0.520431i) q^{7} +(0.684877 + 2.74426i) q^{8} +(-1.19777 + 2.53059i) q^{10} +(0.764732 + 1.32456i) q^{11} +5.93917 q^{13} +(0.434812 - 3.71631i) q^{14} +(3.78920 - 1.28139i) q^{16} +(-2.22886 + 1.28683i) q^{17} +(0.124788 + 0.0720463i) q^{19} +(3.70485 + 1.39685i) q^{20} +(1.77891 - 1.23044i) q^{22} +(3.18530 - 5.51710i) q^{23} +(-0.540360 - 0.935931i) q^{25} +(-0.683981 - 8.37136i) q^{26} +(-5.28827 - 0.184888i) q^{28} -0.801493i q^{29} +(3.76992 - 2.17657i) q^{31} +(-2.24252 - 5.19337i) q^{32} +(2.07049 + 2.99341i) q^{34} +(-3.93233 - 3.46002i) q^{35} +(-3.95867 + 6.85662i) q^{37} +(0.0871793 - 0.184188i) q^{38} +(1.54221 - 5.38292i) q^{40} +1.20760i q^{41} -10.0662i q^{43} +(-1.93920 - 2.36570i) q^{44} +(-8.14327 - 3.85436i) q^{46} +(2.89176 - 5.00868i) q^{47} +(6.45830 + 2.70006i) q^{49} +(-1.25698 + 0.869432i) q^{50} +(-11.7208 + 1.92817i) q^{52} +(8.89412 - 5.13502i) q^{53} -3.02791i q^{55} +(0.348418 + 7.47520i) q^{56} +(-1.12972 + 0.0923035i) q^{58} +(-2.68157 - 4.64461i) q^{59} +(-5.22443 + 9.04898i) q^{61} +(-3.50207 - 5.06311i) q^{62} +(-7.06189 + 3.75896i) q^{64} +(-10.1826 - 5.87894i) q^{65} +(7.69547 - 4.44298i) q^{67} +(3.98082 - 3.26313i) q^{68} +(-4.42410 + 5.94115i) q^{70} +2.78520 q^{71} +(-0.0991532 - 0.171738i) q^{73} +(10.1204 + 4.79017i) q^{74} +(-0.269656 - 0.101669i) q^{76} +(1.29442 + 3.83397i) q^{77} +(7.30088 + 4.21516i) q^{79} +(-7.76492 - 1.55385i) q^{80} +(1.70213 - 0.139073i) q^{82} +12.7885 q^{83} +5.09512 q^{85} +(-14.1885 + 1.15927i) q^{86} +(-3.11117 + 3.00578i) q^{88} +(14.0488 + 8.11108i) q^{89} +(15.4066 + 3.09093i) q^{91} +(-4.49496 + 11.9220i) q^{92} +(-7.39284 - 3.49916i) q^{94} +(-0.142631 - 0.247045i) q^{95} -6.17574 q^{97} +(3.06201 - 9.41404i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) $ 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.115165	−	1.40952i	−0.0814336	−	0.996679i
$2$	−0.115165	−	1.40952i	−0.0814336	−	0.996679i
$3$		0			0
$3$		0			0
$4$	−1.97347	+	0.324653i	−0.986737	+	0.162326i
$5$	−1.71449	−	0.989859i	−0.766741	−	0.442678i	0.0649697	−	0.997887i	$-0.479305\pi$
$5$	−1.71449	−	0.989859i	−0.766741	−	0.442678i	−0.831711	+	0.555209i	$0.812638\pi$
$6$		0			0
$7$	2.59406	+	0.520431i	0.980463	+	0.196704i
$7$	2.59406	+	0.520431i	0.980463	+	0.196704i
$8$	0.684877	+	2.74426i	0.242141	+	0.970241i
$9$		0			0
$10$	−1.19777	+	2.53059i	−0.378769	+	0.800244i
$11$	0.764732	+	1.32456i	0.230575	+	0.399368i	0.957978	−	0.286843i	$-0.0926058\pi$
$11$	0.764732	+	1.32456i	0.230575	+	0.399368i	−0.727402	+	0.686211i	$0.759272\pi$
$12$		0			0
$13$	5.93917			1.64723			0.823614	−	0.567150i	$-0.191954\pi$
$13$	5.93917			1.64723			0.823614	+	0.567150i	$0.191954\pi$
$14$	0.434812	−	3.71631i	0.116208	−	0.993225i
$15$		0			0
$16$	3.78920	−	1.28139i	0.947300	−	0.320347i
$17$	−2.22886	+	1.28683i	−0.540577	+	0.312102i	−0.745313	−	0.666715i	$-0.767700\pi$
$17$	−2.22886	+	1.28683i	−0.540577	+	0.312102i	0.204736	+	0.978817i	$0.434367\pi$
$18$		0			0
$19$	0.124788	+	0.0720463i	0.0286283	+	0.0165286i	0.514246	−	0.857643i	$-0.328072\pi$
$19$	0.124788	+	0.0720463i	0.0286283	+	0.0165286i	−0.485618	+	0.874171i	$0.661405\pi$
$20$	3.70485	+	1.39685i	0.828430	+	0.312345i
$21$		0			0
$22$	1.77891	−	1.23044i	0.379265	−	0.262332i
$23$	3.18530	−	5.51710i	0.664180	−	1.15039i	−0.315326	−	0.948983i	$-0.602114\pi$
$23$	3.18530	−	5.51710i	0.664180	−	1.15039i	0.979507	−	0.201411i	$-0.0645526\pi$
$24$		0			0
$25$	−0.540360	−	0.935931i	−0.108072	−	0.187186i
$26$	−0.683981	−	8.37136i	−0.134140	−	1.64176i
$27$		0			0
$28$	−5.28827	−	0.184888i	−0.999389	−	0.0349406i
$29$		−	0.801493i		−	0.148833i	−0.997227	−	0.0744167i	$-0.976291\pi$
$29$		−	0.801493i		−	0.148833i	0.997227	−	0.0744167i	$-0.0237095\pi$
$30$		0			0
$31$	3.76992	−	2.17657i	0.677098	−	0.390923i	−0.121663	−	0.992572i	$-0.538823\pi$
$31$	3.76992	−	2.17657i	0.677098	−	0.390923i	0.798761	+	0.601649i	$0.205489\pi$
$32$	−2.24252	−	5.19337i	−0.396425	−	0.918067i
$33$		0			0
$34$	2.07049	+	2.99341i	0.355087	+	0.513366i
$35$	−3.93233	−	3.46002i	−0.664684	−	0.584851i
$36$		0			0
$37$	−3.95867	+	6.85662i	−0.650802	+	1.12722i	0.332127	+	0.943235i	$0.392234\pi$
$37$	−3.95867	+	6.85662i	−0.650802	+	1.12722i	−0.982929	+	0.183987i	$0.941100\pi$
$38$	0.0871793	−	0.184188i	0.0141424	−	0.0298792i
$39$		0			0
$40$	1.54221	−	5.38292i	0.243845	−	0.851114i
$41$			1.20760i			0.188596i	0.995544	+	0.0942978i	$0.0300606\pi$
$41$			1.20760i			0.188596i	−0.995544	+	0.0942978i	$0.969939\pi$
$42$		0			0
$43$		−	10.0662i		−	1.53508i	−0.641002	−	0.767540i	$-0.721481\pi$
$43$		−	10.0662i		−	1.53508i	0.641002	−	0.767540i	$-0.278519\pi$
$44$	−1.93920	−	2.36570i	−0.292345	−	0.356643i
$45$		0			0
$46$	−8.14327	−	3.85436i	−1.20066	−	0.568294i
$47$	2.89176	−	5.00868i	0.421807	−	0.730591i	−0.574309	−	0.818638i	$-0.694729\pi$
$47$	2.89176	−	5.00868i	0.421807	−	0.730591i	0.996116	+	0.0880475i	$0.0280627\pi$
$48$		0			0
$49$	6.45830	+	2.70006i	0.922615	+	0.385723i
$50$	−1.25698	+	0.869432i	−0.177764	+	0.122956i
$51$		0			0
$52$	−11.7208	+	1.92817i	−1.62538	+	0.267389i
$53$	8.89412	−	5.13502i	1.22170	−	0.705349i	0.256420	−	0.966565i	$-0.417457\pi$
$53$	8.89412	−	5.13502i	1.22170	−	0.705349i	0.965280	+	0.261216i	$0.0841235\pi$
$54$		0			0
$55$		−	3.02791i		−	0.408283i
$56$	0.348418	+	7.47520i	0.0465593	+	0.998916i
$57$		0			0
$58$	−1.12972	+	0.0923035i	−0.148339	+	0.0121200i
$59$	−2.68157	−	4.64461i	−0.349110	−	0.604677i	0.636981	−	0.770879i	$-0.280183\pi$
$59$	−2.68157	−	4.64461i	−0.349110	−	0.604677i	−0.986092	+	0.166202i	$0.946850\pi$
$60$		0			0
$61$	−5.22443	+	9.04898i	−0.668920	+	1.15860i	0.309286	+	0.950969i	$0.399910\pi$
$61$	−5.22443	+	9.04898i	−0.668920	+	1.15860i	−0.978206	+	0.207635i	$0.933423\pi$
$62$	−3.50207	−	5.06311i	−0.444763	−	0.643015i
$63$		0			0
$64$	−7.06189	+	3.75896i	−0.882736	+	0.469870i
$65$	−10.1826	−	5.87894i	−1.26300	−	0.729192i
$66$		0			0
$67$	7.69547	−	4.44298i	0.940152	−	0.542797i	0.0501437	−	0.998742i	$-0.484032\pi$
$67$	7.69547	−	4.44298i	0.940152	−	0.542797i	0.890008	+	0.455945i	$0.150699\pi$
$68$	3.98082	−	3.26313i	0.482745	−	0.395713i
$69$		0			0
$70$	−4.42410	+	5.94115i	−0.528781	+	0.710103i
$71$	2.78520			0.330543			0.165271	−	0.986248i	$-0.447150\pi$
$71$	2.78520			0.330543			0.165271	+	0.986248i	$0.447150\pi$
$72$		0			0
$73$	−0.0991532	−	0.171738i	−0.0116050	−	0.0201005i	0.860165	−	0.510017i	$-0.170361\pi$
$73$	−0.0991532	−	0.171738i	−0.0116050	−	0.0201005i	−0.871770	+	0.489916i	$0.837027\pi$
$74$	10.1204	+	4.79017i	1.17647	+	0.556846i
$75$		0			0
$76$	−0.269656	−	0.101669i	−0.0309316	−	0.0116622i
$77$	1.29442	+	3.83397i	0.147513	+	0.436921i
$78$		0			0
$79$	7.30088	+	4.21516i	0.821413	+	0.474243i	0.850903	−	0.525322i	$-0.176055\pi$
$79$	7.30088	+	4.21516i	0.821413	+	0.474243i	−0.0294905	+	0.999565i	$0.509388\pi$
$80$	−7.76492	−	1.55385i	−0.868145	−	0.173726i
$81$		0			0
$82$	1.70213	−	0.139073i	0.187969	−	0.0153580i
$83$	12.7885			1.40372			0.701858	−	0.712317i	$-0.252354\pi$
$83$	12.7885			1.40372			0.701858	+	0.712317i	$0.252354\pi$
$84$		0			0
$85$	5.09512			0.552644
$86$	−14.1885	+	1.15927i	−1.52998	+	0.125007i
$87$		0			0
$88$	−3.11117	+	3.00578i	−0.331652	+	0.320417i
$89$	14.0488	+	8.11108i	1.48917	+	0.859773i	0.999923	−	0.0123726i	$-0.00393841\pi$
$89$	14.0488	+	8.11108i	1.48917	+	0.859773i	0.489247	+	0.872145i	$0.337272\pi$
$90$		0			0
$91$	15.4066	+	3.09093i	1.61505	+	0.324017i
$92$	−4.49496	+	11.9220i	−0.468632	+	1.24295i
$93$		0			0
$94$	−7.39284	−	3.49916i	−0.762514	−	0.360911i
$95$	−0.142631	−	0.247045i	−0.0146337	−	0.0253462i
$96$		0			0
$97$	−6.17574			−0.627052			−0.313526	−	0.949580i	$-0.601510\pi$
$97$	−6.17574			−0.627052			−0.313526	+	0.949580i	$0.601510\pi$
$98$	3.06201	−	9.41404i	0.309310	−	0.950961i
$99$		0			0
$100$	1.37024	+	1.67161i	0.137024	+	0.167161i
$101$	−15.9254	+	9.19453i	−1.58464	+	0.914890i	−0.590467	+	0.807062i	$0.701056\pi$
$101$	−15.9254	+	9.19453i	−1.58464	+	0.914890i	−0.994170	+	0.107829i	$0.965610\pi$
$102$		0			0
$103$	−9.42859	−	5.44360i	−0.929027	−	0.536374i	−0.0425231	−	0.999095i	$-0.513540\pi$
$103$	−9.42859	−	5.44360i	−0.929027	−	0.536374i	−0.886504	+	0.462722i	$0.846873\pi$
$104$	4.06760	+	16.2986i	0.398861	+	1.59821i
$105$		0			0
$106$	−8.26218	−	11.9450i	−0.802494	−	1.16020i
$107$	−9.48166	+	16.4227i	−0.916627	+	1.58764i	−0.112124	+	0.993694i	$0.535766\pi$
$107$	−9.48166	+	16.4227i	−0.916627	+	1.58764i	−0.804502	+	0.593950i	$0.797568\pi$
$108$		0			0
$109$	−2.61792	−	4.53437i	−0.250751	−	0.434314i	0.712982	−	0.701183i	$-0.247344\pi$
$109$	−2.61792	−	4.53437i	−0.250751	−	0.434314i	−0.963733	+	0.266869i	$0.914011\pi$
$110$	−4.26789	+	0.348707i	−0.406927	+	0.0332480i
$111$		0			0
$112$	10.4963	−	1.35198i	0.991806	−	0.127750i
$113$		−	6.05957i		−	0.570036i	−0.958522	−	0.285018i	$-0.908000\pi$
$113$		−	6.05957i		−	0.570036i	0.958522	−	0.285018i	$-0.0919996\pi$
$114$		0			0
$115$	−10.9223	+	6.30599i	−1.01851	+	0.588036i
$116$	0.260207	+	1.58173i	0.0241596	+	0.146860i
$117$		0			0
$118$	−6.23784	+	4.31461i	−0.574239	+	0.397192i
$119$	−6.45150	+	2.17815i	−0.591408	+	0.199671i
$120$		0			0
$121$	4.33037	−	7.50042i	0.393670	−	0.681856i
$122$	13.3564	+	6.32180i	1.20923	+	0.572349i
$123$		0			0
$124$	−6.73322	+	5.51931i	−0.604661	+	0.495649i
$125$			12.0381i			1.07672i
$126$		0			0
$127$		−	3.11209i		−	0.276153i	−0.990422	−	0.138077i	$-0.955908\pi$
$127$		−	3.11209i		−	0.276153i	0.990422	−	0.138077i	$-0.0440920\pi$
$128$	6.11159	+	9.52095i	0.540194	+	0.841541i
$129$		0			0
$130$	−7.11378	+	15.0296i	−0.623920	+	1.31818i
$131$	−5.93677	+	10.2828i	−0.518698	+	0.898411i	0.481066	+	0.876684i	$0.340250\pi$
$131$	−5.93677	+	10.2828i	−0.518698	+	0.898411i	−0.999764	+	0.0217269i	$0.993084\pi$
$132$		0			0
$133$	0.286212	+	0.251836i	0.0248177	+	0.0218369i
$134$	−7.14870	−	10.3352i	−0.617554	−	0.892827i
$135$		0			0
$136$	−5.05789	−	5.23523i	−0.433710	−	0.448917i
$137$	12.0834	−	6.97635i	1.03235	−	0.596029i	0.114695	−	0.993401i	$-0.463411\pi$
$137$	12.0834	−	6.97635i	1.03235	−	0.596029i	0.917658	+	0.397371i	$0.130077\pi$
$138$		0			0
$139$		−	5.85806i		−	0.496874i	−0.968648	−	0.248437i	$-0.920083\pi$
$139$		−	5.85806i		−	0.496874i	0.968648	−	0.248437i	$-0.0799169\pi$
$140$	8.88365	+	5.55163i	0.750806	+	0.469198i
$141$		0			0
$142$	−0.320757	−	3.92579i	−0.0269173	−	0.329445i
$143$	4.54187	+	7.86676i	0.379811	+	0.657851i
$144$		0			0
$145$	−0.793364	+	1.37415i	−0.0658853	+	0.114117i
$146$	−0.230649	+	0.159536i	−0.0190887	+	0.0132033i
$147$		0			0
$148$	5.58632	−	14.8166i	0.459192	−	1.21791i
$149$	−17.4590	−	10.0800i	−1.43030	−	0.825784i	−0.433157	−	0.901319i	$-0.642600\pi$
$149$	−17.4590	−	10.0800i	−1.43030	−	0.825784i	−0.997143	+	0.0755346i	$0.975934\pi$
$150$		0			0
$151$	12.2111	−	7.05009i	0.993726	−	0.573728i	0.0873402	−	0.996179i	$-0.472163\pi$
$151$	12.2111	−	7.05009i	0.993726	−	0.573728i	0.906386	+	0.422450i	$0.138830\pi$
$152$	−0.112249	+	0.391793i	−0.00910461	+	0.0317786i
$153$		0			0
$154$	5.25497	−	2.26605i	0.423457	−	0.182603i
$155$	−8.61797			−0.692212
$156$		0			0
$157$	9.96820	+	17.2654i	0.795549	+	1.37793i	0.922490	+	0.386021i	$0.126151\pi$
$157$	9.96820	+	17.2654i	0.795549	+	1.37793i	−0.126941	+	0.991910i	$0.540516\pi$
$158$	5.10054	−	10.7761i	0.405777	−	0.857304i
$159$		0			0
$160$	−1.29594	+	11.1237i	−0.102453	+	0.879409i
$161$	11.1341	−	12.6540i	0.877492	−	0.997272i
$162$		0			0
$163$	3.73185	+	2.15458i	0.292301	+	0.168760i	0.638979	−	0.769224i	$-0.279357\pi$
$163$	3.73185	+	2.15458i	0.292301	+	0.168760i	−0.346678	+	0.937984i	$0.612690\pi$
$164$	−0.392051	−	2.38317i	−0.0306140	−	0.186094i
$165$		0			0
$166$	−1.47278	−	18.0255i	−0.114310	−	1.39905i
$167$	−8.13805			−0.629741			−0.314871	−	0.949135i	$-0.601961\pi$
$167$	−8.13805			−0.629741			−0.314871	+	0.949135i	$0.601961\pi$
$168$		0			0
$169$	22.2737			1.71336
$170$	−0.586777	−	7.18166i	−0.0450038	−	0.550808i
$171$		0			0
$172$	3.26801	+	19.8654i	0.249184	+	1.51472i
$173$	3.85635	+	2.22646i	0.293193	+	0.169275i	0.639381	−	0.768890i	$-0.279191\pi$
$173$	3.85635	+	2.22646i	0.293193	+	0.169275i	−0.346188	+	0.938165i	$0.612524\pi$
$174$		0			0
$175$	−0.914639	−	2.70908i	−0.0691402	−	0.204787i
$176$	4.59499	+	4.03909i	0.346361	+	0.304458i
$177$		0			0
$178$	9.81478	−	20.7361i	0.735649	−	1.55424i
$179$	3.76788	+	6.52616i	0.281625	+	0.487788i	0.971785	−	0.235868i	$-0.0757933\pi$
$179$	3.76788	+	6.52616i	0.281625	+	0.487788i	−0.690160	+	0.723657i	$0.742460\pi$
$180$		0			0
$181$	−19.6420			−1.45998			−0.729988	−	0.683460i	$-0.760474\pi$
$181$	−19.6420			−1.45998			−0.729988	+	0.683460i	$0.760474\pi$
$182$	2.58242	−	22.0718i	0.191422	−	1.63607i
$183$		0			0
$184$	17.3219	+	4.96274i	1.27698	+	0.365858i
$185$	13.5742	−	7.83705i	0.997993	−	0.576191i
$186$		0			0
$187$	−3.40896	−	1.96816i	−0.249288	−	0.143926i
$188$	−4.08074	+	10.8233i	−0.297618	+	0.789371i
$189$		0			0
$190$	−0.331787	+	0.229492i	−0.0240704	+	0.0166491i
$191$	−0.657225	+	1.13835i	−0.0475551	+	0.0823679i	−0.888823	−	0.458250i	$-0.848476\pi$
$191$	−0.657225	+	1.13835i	−0.0475551	+	0.0823679i	0.841268	+	0.540618i	$0.181810\pi$
$192$		0			0
$193$	−5.95937	−	10.3219i	−0.428965	−	0.742989i	0.567816	−	0.823155i	$-0.307788\pi$
$193$	−5.95937	−	10.3219i	−0.428965	−	0.742989i	−0.996782	+	0.0801659i	$0.974455\pi$
$194$	0.711227	+	8.70481i	0.0510631	+	0.624969i
$195$		0			0
$196$	−13.6219	−	3.23179i	−0.972991	−	0.230842i
$197$			17.5060i			1.24725i	0.781723	+	0.623626i	$0.214341\pi$
$197$			17.5060i			1.24725i	−0.781723	+	0.623626i	$0.785659\pi$
$198$		0			0
$199$	−15.7171	+	9.07427i	−1.11416	+	0.643258i	−0.939903	−	0.341443i	$-0.889085\pi$
$199$	−15.7171	+	9.07427i	−1.11416	+	0.643258i	−0.174253	+	0.984701i	$0.555751\pi$
$200$	2.19835	−	2.12388i	0.155447	−	0.150181i
$201$		0			0
$202$	14.7939	+	21.3882i	1.04089	+	1.50487i
$203$	0.417122	−	2.07912i	0.0292762	−	0.145926i
$204$		0			0
$205$	1.19535	−	2.07041i	0.0834872	−	0.144604i
$206$	−6.58701	+	13.9167i	−0.458938	+	0.969620i
$207$		0			0
$208$	22.5047	−	7.61037i	1.56042	−	0.527684i
$209$			0.220385i			0.0152443i
$210$		0			0
$211$			11.5915i			0.797995i	0.916952	+	0.398997i	$0.130642\pi$
$211$			11.5915i			0.797995i	−0.916952	+	0.398997i	$0.869358\pi$
$212$	−15.8852	+	13.0213i	−1.09100	+	0.894308i
$213$		0			0
$214$	24.2400	+	11.4732i	1.65702	+	0.784295i
$215$	−9.96410	+	17.2583i	−0.679546	+	1.17701i
$216$		0			0
$217$	10.9122	−	3.68416i	0.740766	−	0.250097i
$218$	−6.08978	+	4.21220i	−0.412452	+	0.285286i
$219$		0			0
$220$	0.983018	+	5.97550i	0.0662751	+	0.402868i
$221$	−13.2376	+	7.64271i	−0.890454	+	0.514104i
$222$		0			0
$223$			13.3702i			0.895332i	0.894201	+	0.447666i	$0.147745\pi$
$223$			13.3702i			0.895332i	−0.894201	+	0.447666i	$0.852255\pi$
$224$	−3.11444	−	14.6390i	−0.208092	−	0.978109i
$225$		0			0
$226$	−8.54106	+	0.697847i	−0.568143	+	0.0464201i
$227$	−2.24084	−	3.88126i	−0.148730	−	0.257608i	0.782028	−	0.623243i	$-0.214185\pi$
$227$	−2.24084	−	3.88126i	−0.148730	−	0.257608i	−0.930758	+	0.365635i	$0.880852\pi$
$228$		0			0
$229$	−0.501968	+	0.869434i	−0.0331710	+	0.0574538i	−0.882134	−	0.470998i	$-0.843894\pi$
$229$	−0.501968	+	0.869434i	−0.0331710	+	0.0574538i	0.848963	+	0.528452i	$0.177227\pi$
$230$	10.1463	+	14.6689i	0.669024	+	0.967240i
$231$		0			0
$232$	2.19950	−	0.548924i	0.144404	−	0.0360386i
$233$	11.2980	+	6.52291i	0.740157	+	0.427330i	0.822127	−	0.569305i	$-0.192788\pi$
$233$	11.2980	+	6.52291i	0.740157	+	0.427330i	−0.0819691	+	0.996635i	$0.526121\pi$
$234$		0			0
$235$	−9.91577	+	5.72487i	−0.646833	+	0.373449i
$236$	6.79989	+	8.29544i	0.442635	+	0.539987i
$237$		0			0
$238$	3.81312	+	8.84265i	0.247168	+	0.573184i
$239$	26.3622			1.70523			0.852614	−	0.522541i	$-0.175016\pi$
$239$	26.3622			1.70523			0.852614	+	0.522541i	$0.175016\pi$
$240$		0			0
$241$	−3.47955	−	6.02676i	−0.224138	−	0.388218i	0.731923	−	0.681388i	$-0.238623\pi$
$241$	−3.47955	−	6.02676i	−0.224138	−	0.388218i	−0.956060	+	0.293170i	$0.905290\pi$
$242$	−11.0707	−	5.23995i	−0.711650	−	0.336836i
$243$		0			0
$244$	7.37251	−	19.5541i	0.471977	−	1.25182i
$245$	−8.39999	−	11.0220i	−0.536656	−	0.704171i
$246$		0			0
$247$	0.741136	+	0.427895i	0.0471574	+	0.0272263i
$248$	8.55499	+	8.85495i	0.543242	+	0.562290i
$249$		0			0
$250$	16.9679	−	1.38636i	1.07314	−	0.0876813i
$251$	1.74359			0.110054			0.0550272	−	0.998485i	$-0.482475\pi$
$251$	1.74359			0.110054			0.0550272	+	0.998485i	$0.482475\pi$
$252$		0			0
$253$	9.74360			0.612575
$254$	−4.38654	+	0.358402i	−0.275236	+	0.0224882i
$255$		0			0
$256$	12.7161	−	9.71087i	0.794756	−	0.606929i
$257$	−0.882773	−	0.509669i	−0.0550659	−	0.0317923i	0.472214	−	0.881484i	$-0.343455\pi$
$257$	−0.882773	−	0.509669i	−0.0550659	−	0.0317923i	−0.527280	+	0.849691i	$0.676788\pi$
$258$		0			0
$259$	−13.8374	+	15.7263i	−0.859816	+	0.977183i
$260$	22.0037	+	8.29612i	1.36461	+	0.514503i
$261$		0			0
$262$	15.1775	+	7.18376i	0.937667	+	0.443814i
$263$	−12.2050	−	21.1397i	−0.752594	−	1.30353i	−0.946562	−	0.322523i	$-0.895469\pi$
$263$	−12.2050	−	21.1397i	−0.752594	−	1.30353i	0.193967	−	0.981008i	$-0.437864\pi$
$264$		0			0
$265$	−20.3318			−1.24897
$266$	0.322005	−	0.432423i	0.0197434	−	0.0265136i
$267$		0			0
$268$	−13.7444	+	11.2665i	−0.839572	+	0.688209i
$269$	−6.23825	+	3.60166i	−0.380353	+	0.219597i	−0.677972	−	0.735088i	$-0.737141\pi$
$269$	−6.23825	+	3.60166i	−0.380353	+	0.219597i	0.297619	+	0.954685i	$0.403808\pi$
$270$		0			0
$271$	−15.1954	−	8.77307i	−0.923055	−	0.532926i	−0.0384469	−	0.999261i	$-0.512241\pi$
$271$	−15.1954	−	8.77307i	−0.923055	−	0.532926i	−0.884609	+	0.466334i	$0.845574\pi$
$272$	−6.79666	+	7.73209i	−0.412108	+	0.468827i
$273$		0			0
$274$	−11.2249	−	16.2283i	−0.678118	−	0.980388i
$275$	0.826461	−	1.43147i	0.0498375	−	0.0863211i
$276$		0			0
$277$	−12.5631	−	21.7599i	−0.754842	−	1.30742i	−0.945453	−	0.325759i	$-0.894380\pi$
$277$	−12.5631	−	21.7599i	−0.754842	−	1.30742i	0.190611	−	0.981666i	$-0.438953\pi$
$278$	−8.25703	+	0.674640i	−0.495224	+	0.0404622i
$279$		0			0
$280$	6.80203	−	13.1610i	0.406499	−	0.786520i
$281$		−	9.10329i		−	0.543057i	−0.962430	−	0.271528i	$-0.912471\pi$
$281$		−	9.10329i		−	0.543057i	0.962430	−	0.271528i	$-0.0875290\pi$
$282$		0			0
$283$	−7.15520	+	4.13105i	−0.425332	+	0.245566i	−0.697356	−	0.716725i	$-0.745640\pi$
$283$	−7.15520	+	4.13105i	−0.425332	+	0.245566i	0.272024	+	0.962291i	$0.412307\pi$
$284$	−5.49653	+	0.904224i	−0.326159	+	0.0536558i
$285$		0			0
$286$	10.5653	−	7.30782i	0.624737	−	0.432120i
$287$	−0.628473	+	3.13259i	−0.0370976	+	0.184911i
$288$		0			0
$289$	−5.18813	+	8.98611i	−0.305184	+	0.528595i
$290$	2.02825	+	0.960007i	0.119103	+	0.0563736i
$291$		0			0
$292$	0.251432	+	0.306731i	0.0147139	+	0.0179501i
$293$			33.5547i			1.96029i	0.198284	+	0.980145i	$0.436463\pi$
$293$			33.5547i			1.96029i	−0.198284	+	0.980145i	$0.563537\pi$
$294$		0			0
$295$			10.6175i			0.618174i
$296$	−21.5275	−	6.16767i	−1.25126	−	0.358488i
$297$		0			0
$298$	−12.1972	+	25.7697i	−0.706567	+	1.49280i
$299$	18.9180	−	32.7670i	1.09406	−	1.89496i
$300$		0			0
$301$	5.23875	−	26.1123i	0.301957	−	1.50509i
$302$	−11.3435	−	16.3998i	−0.652745	−	0.943705i
$303$		0			0
$304$	0.565165	+	0.113096i	0.0324145	+	0.00648652i
$305$	17.9144	−	10.3429i	1.02578	−	0.592233i
$306$		0			0
$307$		−	13.8892i		−	0.792701i	−0.918099	−	0.396351i	$-0.870277\pi$
$307$		−	13.8892i		−	0.792701i	0.918099	−	0.396351i	$-0.129723\pi$
$308$	−3.79922	−	7.14600i	−0.216480	−	0.407181i
$309$		0			0
$310$	0.992484	+	12.1472i	0.0563693	+	0.689913i
$311$	8.79368	+	15.2311i	0.498644	+	0.863677i	0.999999	−	0.00156494i	$-0.000498135\pi$
$311$	8.79368	+	15.2311i	0.498644	+	0.863677i	−0.501355	+	0.865242i	$0.667165\pi$
$312$		0			0
$313$	−6.47029	+	11.2069i	−0.365722	+	0.633449i	−0.988892	−	0.148637i	$-0.952511\pi$
$313$	−6.47029	+	11.2069i	−0.365722	+	0.633449i	0.623170	+	0.782087i	$0.285845\pi$
$314$	23.1879	−	16.0387i	1.30857	−	0.905117i
$315$		0			0
$316$	−15.7766	−	5.94827i	−0.887501	−	0.334616i
$317$	−16.6065	−	9.58776i	−0.932713	−	0.538502i	−0.0450443	−	0.998985i	$-0.514343\pi$
$317$	−16.6065	−	9.58776i	−0.932713	−	0.538502i	−0.887669	+	0.460483i	$0.847676\pi$
$318$		0			0
$319$	1.06162	−	0.612927i	0.0594394	−	0.0343173i
$320$	15.8283	+	0.545589i	0.884831	+	0.0304994i
$321$		0			0
$322$	−19.1182	−	14.2364i	−1.06542	−	0.793366i
$323$	−0.370846			−0.0206344
$324$		0			0
$325$	−3.20929	−	5.55865i	−0.178019	−	0.308339i
$326$	2.60714	−	5.50823i	0.144396	−	0.305073i
$327$		0			0
$328$	−3.31397	+	0.827059i	−0.182983	+	0.0456667i
$329$	10.1081	−	11.4879i	0.557276	−	0.633346i
$330$		0			0
$331$	−12.1253	−	7.00054i	−0.666466	−	0.384784i	0.128270	−	0.991739i	$-0.459058\pi$
$331$	−12.1253	−	7.00054i	−0.666466	−	0.384784i	−0.794736	+	0.606955i	$0.792391\pi$
$332$	−25.2377	+	4.15181i	−1.38510	+	0.227860i
$333$		0			0
$334$	0.937215	+	11.4707i	0.0512821	+	0.627650i
$335$	−17.5917			−0.961137
$336$		0			0
$337$	−17.3784			−0.946660			−0.473330	−	0.880885i	$-0.656948\pi$
$337$	−17.3784			−0.946660			−0.473330	+	0.880885i	$0.656948\pi$
$338$	−2.56514	−	31.3952i	−0.139525	−	1.70767i
$339$		0			0
$340$	−10.0551	+	1.65414i	−0.545314	+	0.0897086i
$341$	5.76596	+	3.32898i	0.312244	+	0.180274i
$342$		0			0
$343$	15.3480	+	10.3652i	0.828716	+	0.559669i
$344$	27.6242	−	6.89410i	1.48940	−	0.371705i
$345$		0			0
$346$	2.69412	−	5.69200i	0.144837	−	0.306004i
$347$	−6.04552	−	10.4711i	−0.324540	−	0.562121i	0.656879	−	0.753996i	$-0.271876\pi$
$347$	−6.04552	−	10.4711i	−0.324540	−	0.562121i	−0.981419	+	0.191876i	$0.938543\pi$
$348$		0			0
$349$	9.21183			0.493098			0.246549	−	0.969130i	$-0.420703\pi$
$349$	9.21183			0.493098			0.246549	+	0.969130i	$0.420703\pi$
$350$	−3.71316	+	1.60119i	−0.198477	+	0.0855872i
$351$		0			0
$352$	5.16398	−	6.94188i	0.275241	−	0.370003i
$353$	−6.67012	+	3.85099i	−0.355014	+	0.204968i	−0.666892	−	0.745155i	$-0.732376\pi$
$353$	−6.67012	+	3.85099i	−0.355014	+	0.204968i	0.311877	+	0.950122i	$0.399042\pi$
$354$		0			0
$355$	−4.77519	−	2.75696i	−0.253441	−	0.146324i
$356$	−30.3582	−	11.4460i	−1.60898	−	0.606638i
$357$		0			0
$358$	8.76481	−	6.06248i	0.463235	−	0.320412i
$359$	1.42450	−	2.46730i	0.0751821	−	0.130219i	−0.825983	−	0.563694i	$-0.809380\pi$
$359$	1.42450	−	2.46730i	0.0751821	−	0.130219i	0.901165	+	0.433475i	$0.142713\pi$
$360$		0			0
$361$	−9.48962	−	16.4365i	−0.499454	−	0.865079i
$362$	2.26206	+	27.6857i	0.118891	+	1.45513i
$363$		0			0
$364$	−31.4079	−	1.09808i	−1.64622	−	0.0575552i
$365$			0.392591i			0.0205491i
$366$		0			0
$367$	2.33590	−	1.34863i	0.121933	−	0.0703981i	−0.437793	−	0.899076i	$-0.644240\pi$
$367$	2.33590	−	1.34863i	0.121933	−	0.0703981i	0.559726	+	0.828678i	$0.310906\pi$
$368$	5.00020	−	24.9870i	0.260653	−	1.30254i
$369$		0			0
$370$	−12.6097	−	18.2305i	−0.655548	−	0.947757i
$371$	25.7443	−	8.69178i	1.33658	−	0.451255i
$372$		0			0
$373$	−10.8471	+	18.7878i	−0.561644	+	0.972796i	0.435709	+	0.900087i	$0.356498\pi$
$373$	−10.8471	+	18.7878i	−0.561644	+	0.972796i	−0.997353	+	0.0727084i	$0.976836\pi$
$374$	−2.38157	+	5.03164i	−0.123148	+	0.260180i
$375$		0			0
$376$	15.7256	+	4.50540i	0.810986	+	0.232348i
$377$		−	4.76020i		−	0.245163i
$378$		0			0
$379$			16.8058i			0.863258i	0.902051	+	0.431629i	$0.142061\pi$
$379$			16.8058i			0.863258i	−0.902051	+	0.431629i	$0.857939\pi$
$380$	0.361683	+	0.441231i	0.0185539	+	0.0226347i
$381$		0			0
$382$	1.68021	+	0.795272i	0.0859669	+	0.0406897i
$383$	6.13532	−	10.6267i	0.313500	−	0.542998i	−0.665617	−	0.746293i	$-0.731832\pi$
$383$	6.13532	−	10.6267i	0.313500	−	0.542998i	0.979118	+	0.203295i	$0.0651650\pi$
$384$		0			0
$385$	1.57582	−	7.85458i	0.0803110	−	0.400306i
$386$	−13.8626	+	9.58856i	−0.705590	+	0.488045i
$387$		0			0
$388$	12.1877	−	2.00497i	0.618735	−	0.101787i
$389$	−11.2908	+	6.51874i	−0.572466	+	0.330513i	−0.758134	−	0.652099i	$-0.773889\pi$
$389$	−11.2908	+	6.51874i	−0.572466	+	0.330513i	0.185668	+	0.982613i	$0.440555\pi$
$390$		0			0
$391$			16.3958i			0.829169i
$392$	−2.98651	+	19.5724i	−0.150841	+	0.988558i
$393$		0			0
$394$	24.6750	−	2.01607i	1.24311	−	0.101568i
$395$	−8.34483	−	14.4537i	−0.419874	−	0.727243i
$396$		0			0
$397$	−3.44476	+	5.96650i	−0.172888	+	0.299450i	−0.939428	−	0.342746i	$-0.888643\pi$
$397$	−3.44476	+	5.96650i	−0.172888	+	0.299450i	0.766541	+	0.642196i	$0.221976\pi$
$398$	14.6004	+	21.1085i	0.731852	+	1.05807i
$399$		0			0
$400$	−3.24682	−	2.85402i	−0.162341	−	0.142701i
$401$	−24.0958	−	13.9117i	−1.20329	−	0.694719i	−0.242004	−	0.970275i	$-0.577805\pi$
$401$	−24.0958	−	13.9117i	−1.20329	−	0.694719i	−0.961285	+	0.275557i	$0.911138\pi$
$402$		0			0
$403$	22.3902	−	12.9270i	1.11534	−	0.643939i
$404$	28.4433	−	23.3154i	1.41511	−	1.15998i
$405$		0			0
$406$	−2.97859	−	0.348499i	−0.147825	−	0.0172957i
$407$	−12.1093			−0.600236
$408$		0			0
$409$	−4.46725	−	7.73750i	−0.220891	−	0.382595i	0.734188	−	0.678947i	$-0.237563\pi$
$409$	−4.46725	−	7.73750i	−0.220891	−	0.382595i	−0.955079	+	0.296352i	$0.904230\pi$
$410$	−3.05595	−	1.44643i	−0.150922	−	0.0714343i
$411$		0			0
$412$	20.3744	+	7.68179i	1.00377	+	0.378455i
$413$	−4.53895	−	13.4440i	−0.223347	−	0.661535i
$414$		0			0
$415$	−21.9256	−	12.6588i	−1.07629	−	0.621394i
$416$	−13.3187	−	30.8443i	−0.653003	−	1.51227i
$417$		0			0
$418$	0.310636	−	0.0253805i	0.0151937	−	0.00124140i
$419$	29.5362			1.44294			0.721470	−	0.692446i	$-0.243467\pi$
$419$	29.5362			1.44294			0.721470	+	0.692446i	$0.243467\pi$
$420$		0			0
$421$	−7.65150			−0.372911			−0.186456	−	0.982463i	$-0.559700\pi$
$421$	−7.65150			−0.372911			−0.186456	+	0.982463i	$0.559700\pi$
$422$	16.3385	−	1.33493i	0.795345	−	0.0649836i
$423$		0			0
$424$	20.1832	+	20.8909i	0.980182	+	1.01455i
$425$	2.40877	+	1.39070i	0.116843	+	0.0674591i
$426$		0			0
$427$	−18.2619	+	20.7547i	−0.883754	+	1.00439i
$428$	13.3801	−	35.4881i	0.646753	−	1.71538i
$429$		0			0
$430$	25.4734	+	12.0570i	1.22844	+	0.581441i
$431$	−9.04769	−	15.6711i	−0.435812	−	0.754848i	0.561550	−	0.827443i	$-0.310205\pi$
$431$	−9.04769	−	15.6711i	−0.435812	−	0.754848i	−0.997362	+	0.0725950i	$0.976872\pi$
$432$		0			0
$433$	1.17818			0.0566195			0.0283097	−	0.999599i	$-0.490988\pi$
$433$	1.17818			0.0566195			0.0283097	+	0.999599i	$0.490988\pi$
$434$	−6.44958	−	14.9566i	−0.309590	−	0.717939i
$435$		0			0
$436$	6.63849	+	8.09855i	0.317926	+	0.387850i
$437$	0.794973	−	0.458978i	0.0380287	−	0.0219559i
$438$		0			0
$439$	−33.5693	−	19.3813i	−1.60218	−	0.925017i	−0.991051	−	0.133482i	$-0.957384\pi$
$439$	−33.5693	−	19.3813i	−1.60218	−	0.925017i	−0.611125	−	0.791534i	$-0.709283\pi$
$440$	8.30935	−	2.07375i	0.396133	−	0.0988619i
$441$		0			0
$442$	12.2970	+	17.7784i	0.584910	+	0.845632i
$443$	−6.67985	+	11.5698i	−0.317369	+	0.549700i	−0.979938	−	0.199301i	$-0.936133\pi$
$443$	−6.67985	+	11.5698i	−0.317369	+	0.549700i	0.662569	+	0.749001i	$0.269466\pi$
$444$		0			0
$445$	−16.0576	−	27.8127i	−0.761205	−	1.31845i
$446$	18.8455	−	1.53977i	0.892359	−	0.0729101i
$447$		0			0
$448$	−20.2752	+	6.07574i	−0.957915	+	0.287052i
$449$			4.17243i			0.196909i	0.995142	+	0.0984546i	$0.0313899\pi$
$449$			4.17243i			0.196909i	−0.995142	+	0.0984546i	$0.968610\pi$
$450$		0			0
$451$	−1.59953	+	0.923492i	−0.0753191	+	0.0434855i
$452$	1.96725	+	11.9584i	0.0925318	+	0.562476i
$453$		0			0
$454$	−5.21263	+	3.60549i	−0.244641	+	0.169214i
$455$	−23.3547	−	20.5497i	−1.09489	−	0.963383i
$456$		0			0
$457$	−7.51668	+	13.0193i	−0.351615	+	0.609016i	−0.986533	−	0.163564i	$-0.947701\pi$
$457$	−7.51668	+	13.0193i	−0.351615	+	0.609016i	0.634917	+	0.772580i	$0.281034\pi$
$458$	1.28329	+	0.607404i	0.0599642	+	0.0283821i
$459$		0			0
$460$	19.5076	−	15.9907i	0.909547	−	0.745568i
$461$			1.66796i			0.0776847i	0.999245	+	0.0388424i	$0.0123670\pi$
$461$			1.66796i			0.0776847i	−0.999245	+	0.0388424i	$0.987633\pi$
$462$		0			0
$463$			41.5633i			1.93161i	0.259272	+	0.965804i	$0.416517\pi$
$463$			41.5633i			1.93161i	−0.259272	+	0.965804i	$0.583483\pi$
$464$	−1.02702	−	3.03702i	−0.0476783	−	0.140990i
$465$		0			0
$466$	7.89302	−	16.6759i	0.365637	−	0.772498i
$467$	−2.12072	+	3.67319i	−0.0981351	+	0.169975i	−0.910913	−	0.412599i	$-0.864621\pi$
$467$	−2.12072	+	3.67319i	−0.0981351	+	0.169975i	0.812778	+	0.582574i	$0.197954\pi$
$468$		0			0
$469$	22.2748	−	7.52041i	1.02855	−	0.347260i
$470$	9.21124	+	13.3171i	0.424883	+	0.614274i
$471$		0			0
$472$	10.9095	−	10.5399i	0.502149	−	0.485138i
$473$	13.3332	−	7.69794i	0.613062	−	0.353952i
$474$		0			0
$475$		−	0.155724i		−	0.00714510i
$476$	12.0247	−	6.39302i	0.551152	−	0.293024i
$477$		0			0
$478$	−3.03599	−	37.1579i	−0.138863	−	1.69957i
$479$	17.6039	+	30.4908i	0.804342	+	1.39316i	0.916735	+	0.399497i	$0.130815\pi$
$479$	17.6039	+	30.4908i	0.804342	+	1.39316i	−0.112393	+	0.993664i	$0.535852\pi$
$480$		0			0
$481$	−23.5112	+	40.7226i	−1.07202	+	1.85679i
$482$	−8.09409	+	5.59855i	−0.368676	+	0.255007i
$483$		0			0
$484$	−6.11084	+	16.2077i	−0.277766	+	0.736716i
$485$	10.5882	+	6.11311i	0.480786	+	0.277582i
$486$		0			0
$487$	−14.5319	+	8.39001i	−0.658504	+	0.380188i	−0.791707	−	0.610901i	$-0.790807\pi$
$487$	−14.5319	+	8.39001i	−0.658504	+	0.380188i	0.133203	+	0.991089i	$0.457474\pi$
$488$	−28.4108	−	8.13974i	−1.28610	−	0.368469i
$489$		0			0
$490$	−14.5683	+	13.1093i	−0.658130	+	0.592217i
$491$	−19.8733			−0.896869			−0.448434	−	0.893816i	$-0.648018\pi$
$491$	−19.8733			−0.896869			−0.448434	+	0.893816i	$0.648018\pi$
$492$		0			0
$493$	1.03139	+	1.78641i	0.0464513	+	0.0804560i
$494$	0.517773	−	1.09392i	0.0232957	−	0.0492179i
$495$		0			0
$496$	11.4960	−	13.0782i	0.516184	−	0.587227i
$497$	7.22499	+	1.44951i	0.324085	+	0.0650192i
$498$		0			0
$499$	−26.4656	−	15.2799i	−1.18476	−	0.684022i	−0.227650	−	0.973743i	$-0.573104\pi$
$499$	−26.4656	−	15.2799i	−1.18476	−	0.684022i	−0.957111	+	0.289721i	$0.906437\pi$
$500$	−3.90820	−	23.7569i	−0.174780	−	1.06244i
$501$		0			0
$502$	−0.200799	−	2.45762i	−0.00896212	−	0.109689i
$503$	19.4489			0.867184			0.433592	−	0.901109i	$-0.357246\pi$
$503$	19.4489			0.867184			0.433592	+	0.901109i	$0.357246\pi$
$504$		0			0
$505$	36.4052			1.62001
$506$	−1.12212	−	13.7338i	−0.0498842	−	0.610540i
$507$		0			0
$508$	1.01035	+	6.14163i	0.0448270	+	0.272491i
$509$	−34.6384	−	19.9985i	−1.53532	−	0.886417i	−0.999103	−	0.0423351i	$-0.986520\pi$
$509$	−34.6384	−	19.9985i	−1.53532	−	0.886417i	−0.536215	−	0.844081i	$-0.680146\pi$
$510$		0			0
$511$	−0.167832	−	0.497102i	−0.00742443	−	0.0219905i
$512$	−15.1521	−	16.8052i	−0.669633	−	0.742692i
$513$		0			0
$514$	−0.616723	+	1.30298i	−0.0272025	+	0.0574719i
$515$	10.7768	+	18.6659i	0.474882	+	0.822520i
$516$		0			0
$517$	8.84569			0.389033
$518$	23.7600	+	17.6930i	1.04396	+	0.777385i
$519$		0			0
$520$	9.15946	−	31.9701i	0.401669	−	1.40198i
$521$	7.91080	−	4.56730i	0.346579	−	0.200097i	−0.316599	−	0.948560i	$-0.602541\pi$
$521$	7.91080	−	4.56730i	0.346579	−	0.200097i	0.663177	+	0.748462i	$0.269208\pi$
$522$		0			0
$523$	38.4497	+	22.1989i	1.68129	+	0.970692i	0.960808	+	0.277216i	$0.0894118\pi$
$523$	38.4497	+	22.1989i	1.68129	+	0.970692i	0.720480	+	0.693476i	$0.243922\pi$
$524$	8.37773	−	22.2202i	0.365983	−	0.970694i
$525$		0			0
$526$	−28.3912	+	19.6377i	−1.23792	+	0.856246i
$527$	−5.60174	+	9.70251i	−0.244016	+	0.422648i
$528$		0			0
$529$	−8.79224	−	15.2286i	−0.382271	−	0.662113i
$530$	2.34150	+	28.6580i	0.101708	+	1.24482i
$531$		0			0
$532$	−0.646591	−	0.404072i	−0.0280333	−	0.0175188i
$533$			7.17215i			0.310660i
$534$		0			0
$535$	32.5123	−	18.7710i	1.40563	−	0.811541i
$536$	17.4631	+	18.0754i	0.754293	+	0.780741i
$537$		0			0
$538$	5.79502	+	8.37814i	0.249841	+	0.361207i
$539$	1.36250	+	10.6192i	0.0586869	+	0.457401i
$540$		0			0
$541$	18.6532	−	32.3084i	0.801965	−	1.38904i	−0.116356	−	0.993208i	$-0.537121\pi$
$541$	18.6532	−	32.3084i	0.801965	−	1.38904i	0.918321	−	0.395837i	$-0.129545\pi$
$542$	−10.6158	+	22.4285i	−0.455989	+	0.963388i
$543$		0			0
$544$	11.6812	+	8.68954i	0.500829	+	0.372561i
$545$			10.3655i			0.444008i
$546$		0			0
$547$		−	3.77104i		−	0.161238i	−0.996745	−	0.0806191i	$-0.974310\pi$
$547$		−	3.77104i		−	0.161238i	0.996745	−	0.0806191i	$-0.0256897\pi$
$548$	−21.5814	+	17.6905i	−0.921910	+	0.755703i
$549$		0			0
$550$	−2.11286	−	1.00006i	−0.0900928	−	0.0426425i
$551$	0.0577446	−	0.100017i	0.00246000	−	0.00426085i
$552$		0			0
$553$	16.7452	+	14.7340i	0.712079	+	0.626553i
$554$	−29.2241	+	20.2138i	−1.24161	+	0.858803i
$555$		0			0
$556$	1.90183	+	11.5607i	0.0806557	+	0.490284i
$557$	−35.7446	+	20.6372i	−1.51455	+	0.874425i	−0.514695	+	0.857374i	$0.672095\pi$
$557$	−35.7446	+	20.6372i	−1.51455	+	0.874425i	−0.999855	+	0.0170517i	$0.994572\pi$
$558$		0			0
$559$		−	59.7848i		−	2.52863i
$560$	−19.3340	−	8.07190i	−0.817011	−	0.341100i
$561$		0			0
$562$	−12.8312	+	1.04838i	−0.541253	+	0.0442231i
$563$	−13.0248	−	22.5597i	−0.548931	−	0.950777i	−0.998348	−	0.0574547i	$-0.981702\pi$
$563$	−13.0248	−	22.5597i	−0.548931	−	0.950777i	0.449417	−	0.893322i	$-0.351632\pi$
$564$		0			0
$565$	−5.99811	+	10.3890i	−0.252342	+	0.437070i
$566$	6.64681	+	9.60962i	0.279386	+	0.403922i
$567$		0			0
$568$	1.90752	+	7.64331i	0.0800379	+	0.320706i
$569$	22.7761	+	13.1498i	0.954824	+	0.551268i	0.894576	−	0.446915i	$-0.147478\pi$
$569$	22.7761	+	13.1498i	0.954824	+	0.551268i	0.0602479	+	0.998183i	$0.480811\pi$
$570$		0			0
$571$	23.0801	−	13.3253i	0.965873	−	0.557647i	0.0678974	−	0.997692i	$-0.478371\pi$
$571$	23.0801	−	13.3253i	0.965873	−	0.557647i	0.897976	+	0.440045i	$0.145038\pi$
$572$	−11.5172	−	14.0503i	−0.481560	−	0.587473i
$573$		0			0
$574$	4.48782	+	0.525080i	0.187318	+	0.0219164i
$575$	−6.88483			−0.287117
$576$		0			0
$577$	15.6383	+	27.0864i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589967\pi$
$577$	15.6383	+	27.0864i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$578$	13.2636	+	6.27788i	0.551691	+	0.261125i
$579$		0			0
$580$	1.11956	−	2.96941i	0.0464874	−	0.123298i
$581$	33.1740	+	6.65551i	1.37629	+	0.276117i
$582$		0			0
$583$	13.6032	+	7.85383i	0.563388	+	0.325272i
$584$	0.403386	−	0.389722i	0.0166922	−	0.0161268i
$585$		0			0
$586$	47.2960	−	3.86432i	1.95378	−	0.159633i
$587$	−10.8008			−0.445796			−0.222898	−	0.974842i	$-0.571552\pi$
$587$	−10.8008			−0.445796			−0.222898	+	0.974842i	$0.571552\pi$
$588$		0			0
$589$	0.627254			0.0258456
$590$	14.9655	−	1.22276i	0.616121	−	0.0503402i
$591$		0			0
$592$	−6.21422	+	31.0537i	−0.255403	+	1.27630i
$593$	−28.6908	−	16.5646i	−1.17819	−	0.680228i	−0.222594	−	0.974911i	$-0.571453\pi$
$593$	−28.6908	−	16.5646i	−1.17819	−	0.680228i	−0.955595	+	0.294683i	$0.904786\pi$
$594$		0			0
$595$	13.2171	+	2.65166i	0.541847	+	0.108707i
$596$	37.7274	+	14.2245i	1.54538	+	0.582656i
$597$		0			0
$598$	−48.3643	−	22.8917i	−1.97776	−	0.936110i
$599$	5.75941	+	9.97559i	0.235323	+	0.407592i	0.959367	−	0.282163i	$-0.0910518\pi$
$599$	5.75941	+	9.97559i	0.235323	+	0.407592i	−0.724043	+	0.689754i	$0.757719\pi$
$600$		0			0
$601$	8.58250			0.350088			0.175044	−	0.984561i	$-0.443993\pi$
$601$	8.58250			0.350088			0.175044	+	0.984561i	$0.443993\pi$
$602$	−37.4090	−	4.37690i	−1.52468	−	0.178389i
$603$		0			0
$604$	−21.8095	+	17.8775i	−0.887415	+	0.727427i
$605$	−14.8487	+	8.57291i	−0.603686	+	0.348538i
$606$		0			0
$607$	11.0366	+	6.37197i	0.447961	+	0.258630i	0.706969	−	0.707245i	$-0.250062\pi$
$607$	11.0366	+	6.37197i	0.447961	+	0.258630i	−0.259008	+	0.965875i	$0.583395\pi$
$608$	0.0943242	−	0.809635i	0.00382535	−	0.0328350i
$609$		0			0
$610$	−16.6416	−	24.0596i	−0.673799	−	0.974143i
$611$	17.1747	−	29.7474i	0.694812	−	1.20345i
$612$		0			0
$613$	7.23044	+	12.5235i	0.292035	+	0.505819i	0.974291	−	0.225294i	$-0.0723344\pi$
$613$	7.23044	+	12.5235i	0.292035	+	0.505819i	−0.682256	+	0.731113i	$0.739001\pi$
$614$	−19.5771	+	1.59955i	−0.790068	+	0.0645525i
$615$		0			0
$616$	−9.63487	+	6.17803i	−0.388200	+	0.248920i
$617$			25.6740i			1.03360i	0.856108	+	0.516798i	$0.172876\pi$
$617$			25.6740i			1.03360i	−0.856108	+	0.516798i	$0.827124\pi$
$618$		0			0
$619$	2.16146	−	1.24792i	0.0868766	−	0.0501582i	−0.455932	−	0.890014i	$-0.650694\pi$
$619$	2.16146	−	1.24792i	0.0868766	−	0.0501582i	0.542809	+	0.839856i	$0.317361\pi$
$620$	17.0073	−	2.79785i	0.683031	−	0.112364i
$621$		0			0
$622$	20.4558	−	14.1489i	0.820202	−	0.567320i
$623$	32.2222	+	28.3521i	1.29095	+	1.13590i
$624$		0			0
$625$	9.21422	−	15.9595i	0.368569	−	0.638380i
$626$	16.5414	+	7.82934i	0.661128	+	0.312923i
$627$		0			0
$628$	−25.2772	−	30.8367i	−1.00867	−	1.23052i
$629$		−	20.3766i		−	0.812467i
$630$		0			0
$631$			31.8112i			1.26638i	0.773995	+	0.633191i	$0.218255\pi$
$631$			31.8112i			1.26638i	−0.773995	+	0.633191i	$0.781745\pi$
$632$	−6.56728	+	22.9224i	−0.261233	+	0.911802i
$633$		0			0
$634$	−11.6016	+	24.5113i	−0.460759	+	0.973467i
$635$	−3.08053	+	5.33563i	−0.122247	+	0.211738i
$636$		0			0
$637$	38.3570	+	16.0361i	1.51976	+	0.635374i
$638$	−0.986192	−	1.42579i	−0.0390437	−	0.0564474i
$639$		0			0
$640$	−1.05385	−	22.3731i	−0.0416569	−	0.884376i
$641$	24.3597	−	14.0641i	0.962148	−	0.555497i	0.0653148	−	0.997865i	$-0.479195\pi$
$641$	24.3597	−	14.0641i	0.962148	−	0.555497i	0.896834	+	0.442368i	$0.145862\pi$
$642$		0			0
$643$		−	5.96406i		−	0.235199i	−0.993061	−	0.117600i	$-0.962480\pi$
$643$		−	5.96406i		−	0.235199i	0.993061	−	0.117600i	$-0.0375200\pi$
$644$	−17.8648	+	28.5870i	−0.703970	+	1.12648i
$645$		0			0
$646$	0.0427083	+	0.522713i	0.00168033	+	0.0205659i
$647$	−7.06054	−	12.2292i	−0.277579	−	0.480780i	0.693204	−	0.720742i	$-0.256199\pi$
$647$	−7.06054	−	12.2292i	−0.277579	−	0.480780i	−0.970782	+	0.239961i	$0.922865\pi$
$648$		0			0
$649$	4.10136	−	7.10377i	0.160993	−	0.278847i
$650$	−7.46542	+	5.16371i	−0.292818	+	0.202537i
$651$		0			0
$652$	−8.06419	−	3.04046i	−0.315818	−	0.119074i
$653$	4.99614	+	2.88452i	0.195514	+	0.112880i	0.594561	−	0.804050i	$-0.297326\pi$
$653$	4.99614	+	2.88452i	0.195514	+	0.112880i	−0.399047	+	0.916930i	$0.630659\pi$
$654$		0			0
$655$	20.3570	−	11.7531i	0.795414	−	0.459233i
$656$	1.54740	+	4.57585i	0.0604160	+	0.178657i
$657$		0			0
$658$	−17.3564	−	12.9245i	−0.676623	−	0.503850i
$659$	−17.0341			−0.663553			−0.331777	−	0.943358i	$-0.607648\pi$
$659$	−17.0341			−0.663553			−0.331777	+	0.943358i	$0.607648\pi$
$660$		0			0
$661$	−2.08067	−	3.60383i	−0.0809287	−	0.140173i	0.822720	−	0.568446i	$-0.192455\pi$
$661$	−2.08067	−	3.60383i	−0.0809287	−	0.140173i	−0.903649	+	0.428274i	$0.859122\pi$
$662$	−8.47097	+	17.8970i	−0.329234	+	0.695587i
$663$		0			0
$664$	8.75853	+	35.0948i	0.339897	+	1.36194i
$665$	−0.241425	−	0.715079i	−0.00936204	−	0.0277296i
$666$		0			0
$667$	−4.42191	−	2.55299i	−0.171217	−	0.0988523i
$668$	16.0602	−	2.64204i	0.621389	−	0.102224i
$669$		0			0
$670$	2.02594	+	24.7958i	0.0782689	+	0.957945i
$671$	−15.9812			−0.616946
$672$		0			0
$673$	−1.21451			−0.0468157			−0.0234079	−	0.999726i	$-0.507452\pi$
$673$	−1.21451			−0.0468157			−0.0234079	+	0.999726i	$0.507452\pi$
$674$	2.00137	+	24.4951i	0.0770900	+	0.943516i
$675$		0			0
$676$	−43.9566	+	7.23122i	−1.69064	+	0.278124i
$677$	33.4971	+	19.3395i	1.28740	+	0.743279i	0.978189	−	0.207716i	$-0.0666029\pi$
$677$	33.4971	+	19.3395i	1.28740	+	0.743279i	0.309208	+	0.950995i	$0.399936\pi$
$678$		0			0
$679$	−16.0203	−	3.21405i	−0.614801	−	0.123344i
$680$	3.48953	+	13.9823i	0.133818	+	0.536198i
$681$		0			0
$682$	4.02822	−	8.51060i	0.154248	−	0.325888i
$683$	19.4505	+	33.6892i	0.744253	+	1.28908i	0.950543	+	0.310592i	$0.100527\pi$
$683$	19.4505	+	33.6892i	0.744253	+	1.28908i	−0.206291	+	0.978491i	$0.566139\pi$
$684$		0			0
$685$	−27.6224			−1.05540
$686$	12.8424	−	22.8270i	0.490325	−	0.871540i
$687$		0			0
$688$	−12.8987	−	38.1428i	−0.491758	−	1.45418i
$689$	52.8237	−	30.4978i	2.01242	−	1.16187i
$690$		0			0
$691$	−11.3968	−	6.57993i	−0.433554	−	0.250312i	0.267306	−	0.963612i	$-0.413867\pi$
$691$	−11.3968	−	6.57993i	−0.433554	−	0.250312i	−0.700860	+	0.713299i	$0.747200\pi$
$692$	−8.33323	−	3.14190i	−0.316782	−	0.119437i
$693$		0			0
$694$	−14.0630	+	9.72716i	−0.533825	+	0.369238i
$695$	−5.79865	+	10.0436i	−0.219955	+	0.380974i
$696$		0			0
$697$	−1.55398	−	2.69157i	−0.0588612	−	0.101951i
$698$	−1.06088	−	12.9842i	−0.0401547	−	0.491460i
$699$		0			0
$700$	2.68453	+	5.04936i	0.101466	+	0.190848i
$701$			19.9132i			0.752111i	0.926597	+	0.376056i	$0.122720\pi$
$701$			19.9132i			0.752111i	−0.926597	+	0.376056i	$0.877280\pi$
$702$		0			0
$703$	−0.987988	+	0.570415i	−0.0372627	+	0.0215136i
$704$	−10.3794	−	6.47926i	−0.391188	−	0.244196i
$705$		0			0
$706$	6.19620	+	8.95814i	0.233197	+	0.337144i
$707$	−46.0966	+	15.5631i	−1.73364	+	0.585311i
$708$		0			0
$709$	13.9721	−	24.2004i	0.524733	−	0.908864i	−0.474852	−	0.880066i	$-0.657498\pi$
$709$	13.9721	−	24.2004i	0.524733	−	0.908864i	0.999585	−	0.0287987i	$-0.00916817\pi$
$710$	−3.33605	+	7.04822i	−0.125200	+	0.264515i
$711$		0			0
$712$	−12.6372	+	44.1086i	−0.473598	+	1.65304i
$713$		−	27.7320i		−	1.03857i
$714$		0			0
$715$		−	17.9833i		−	0.672535i
$716$	−9.55456	−	11.6560i	−0.357070	−	0.435604i
$717$		0			0
$718$	−3.64175	−	1.72371i	−0.135909	−	0.0643281i
$719$	3.03763	−	5.26133i	0.113285	−	0.196215i	−0.803808	−	0.594889i	$-0.797196\pi$
$719$	3.03763	−	5.26133i	0.113285	−	0.196215i	0.917093	+	0.398674i	$0.130529\pi$
$720$		0			0
$721$	−21.6253	−	19.0280i	−0.805369	−	0.708638i
$722$	−22.0747	+	15.2687i	−0.821534	+	0.568241i
$723$		0			0
$724$	38.7629	−	6.37681i	1.44061	−	0.236992i
$725$	−0.750142	+	0.433095i	−0.0278596	+	0.0160847i
$726$		0			0
$727$			12.7777i			0.473897i	0.971522	+	0.236949i	$0.0761473\pi$
$727$			12.7777i			0.473897i	−0.971522	+	0.236949i	$0.923853\pi$
$728$	2.06931	+	44.3965i	0.0766938	+	1.64544i
$729$		0			0
$730$	0.553363	−	0.0452125i	0.0204809	−	0.00167339i
$731$	12.9535	+	22.4361i	0.479102	+	0.829829i
$732$		0			0
$733$	−13.8210	+	23.9387i	−0.510490	+	0.884195i	0.489436	+	0.872039i	$0.337203\pi$
$733$	−13.8210	+	23.9387i	−0.510490	+	0.884195i	−0.999926	+	0.0121560i	$0.996131\pi$
$734$	−2.16993	−	3.13718i	−0.0800937	−	0.115795i
$735$		0			0
$736$	−35.7954	−	4.17025i	−1.31944	−	0.153717i
$737$	11.7700	+	6.79538i	0.433552	+	0.250311i
$738$		0			0
$739$	27.4819	−	15.8667i	1.01094	−	0.583665i	0.0994710	−	0.995040i	$-0.468285\pi$
$739$	27.4819	−	15.8667i	1.01094	−	0.583665i	0.911466	+	0.411376i	$0.134952\pi$
$740$	−24.2440	+	19.8731i	−0.891226	+	0.730550i
$741$		0			0
$742$	−15.2160	−	35.2860i	−0.558598	−	1.29539i
$743$	24.5994			0.902464			0.451232	−	0.892407i	$-0.350985\pi$
$743$	24.5994			0.902464			0.451232	+	0.892407i	$0.350985\pi$
$744$		0			0
$745$	19.9555	+	34.5640i	0.731113	+	1.26633i
$746$	27.7309	+	13.1255i	1.01530	+	0.480560i
$747$		0			0
$748$	7.36646	+	2.77739i	0.269344	+	0.101551i
$749$	−33.1429	+	37.6670i	−1.21101	+	1.37632i
$750$		0			0
$751$	26.8335	+	15.4923i	0.979169	+	0.565324i	0.902019	−	0.431696i	$-0.142085\pi$
$751$	26.8335	+	15.4923i	0.979169	+	0.565324i	0.0771499	+	0.997020i	$0.475418\pi$
$752$	4.53941	−	22.6844i	0.165535	−	0.827213i
$753$		0			0
$754$	−6.70958	+	0.548206i	−0.244349	+	0.0199645i
$755$	−27.9144			−1.01591
$756$		0			0
$757$	16.6583			0.605456			0.302728	−	0.953077i	$-0.402103\pi$
$757$	16.6583			0.605456			0.302728	+	0.953077i	$0.402103\pi$
$758$	23.6881	−	1.93544i	0.860391	−	0.0702982i
$759$		0			0
$760$	0.580269	−	0.560612i	0.0210486	−	0.0203355i
$761$	9.99942	+	5.77317i	0.362479	+	0.209277i	0.670167	−	0.742210i	$-0.266222\pi$
$761$	9.99942	+	5.77317i	0.362479	+	0.209277i	−0.307689	+	0.951487i	$0.599556\pi$
$762$		0			0
$763$	−4.43122	−	13.1249i	−0.160421	−	0.475152i
$764$	0.927449	−	2.45987i	0.0335539	−	0.0889949i
$765$		0			0
$766$	−15.6851	−	7.42402i	−0.566724	−	0.268241i
$767$	−15.9263	−	27.5851i	−0.575065	−	0.996041i
$768$		0			0
$769$	−6.25489			−0.225557			−0.112779	−	0.993620i	$-0.535975\pi$
$769$	−6.25489			−0.225557			−0.112779	+	0.993620i	$0.535975\pi$
$770$	−11.2526	−	1.31657i	−0.405517	−	0.0474459i
$771$		0			0
$772$	15.1117	+	18.4354i	0.543882	+	0.663503i
$773$	−20.8546	+	12.0404i	−0.750088	+	0.433064i	−0.825726	−	0.564072i	$-0.809234\pi$
$773$	−20.8546	+	12.0404i	−0.750088	+	0.433064i	0.0756374	+	0.997135i	$0.475901\pi$
$774$		0			0
$775$	−4.07423	−	2.35226i	−0.146351	−	0.0844956i
$776$	−4.22963	−	16.9478i	−0.151835	−	0.608392i
$777$		0			0
$778$	10.4886	+	15.1638i	0.376034	+	0.543650i
$779$	−0.0870032	+	0.150694i	−0.00311721	+	0.00539917i
$780$		0			0
$781$	2.12994	+	3.68916i	0.0762151	+	0.132008i
$782$	23.1101	−	1.88821i	0.826415	−	0.0675222i
$783$		0			0
$784$	27.9316	+	1.95548i	0.997558	+	0.0698386i
$785$		−	39.4684i		−	1.40869i
$786$		0			0
$787$	−9.00894	+	5.20131i	−0.321134	+	0.185407i	−0.651898	−	0.758307i	$-0.726027\pi$
$787$	−9.00894	+	5.20131i	−0.321134	+	0.185407i	0.330764	+	0.943714i	$0.392694\pi$
$788$	−5.68337	−	34.5477i	−0.202462	−	1.23071i
$789$		0			0
$790$	−19.4117	+	13.4267i	−0.690636	+	0.477702i
$791$	3.15359	−	15.7189i	0.112129	−	0.558899i
$792$		0			0
$793$	−31.0288	+	53.7434i	−1.10186	+	1.90849i
$794$	8.80659	+	4.16832i	0.312534	+	0.147928i
$795$		0			0
$796$	28.0713	−	23.0104i	0.994961	−	0.815584i
$797$		−	15.2010i		−	0.538447i	−0.963078	−	0.269224i	$-0.913233\pi$
$797$		−	15.2010i		−	0.538447i	0.963078	−	0.269224i	$-0.0867671\pi$
$798$		0			0
$799$			14.8848i			0.526588i
$800$	−3.64887	+	4.90513i	−0.129007	+	0.173423i
$801$		0			0
$802$	−16.8338	+	35.5656i	−0.594423	+	1.25587i
$803$	0.151651	−	0.262668i	0.00535166	−	0.00926935i
$804$		0			0
$805$	−31.6149	+	10.6738i	−1.11428	+	0.376203i
$806$	−20.7994	−	30.0706i	−0.732626	−	1.05919i
$807$		0			0
$808$	−36.1391	−	37.4063i	−1.27137	−	1.31595i
$809$	7.98096	−	4.60781i	0.280595	−	0.162002i	−0.353097	−	0.935587i	$-0.614872\pi$
$809$	7.98096	−	4.60781i	0.280595	−	0.162002i	0.633693	+	0.773585i	$0.281538\pi$
$810$		0			0
$811$		−	36.7250i		−	1.28959i	−0.764356	−	0.644794i	$-0.776943\pi$
$811$		−	36.7250i		−	1.28959i	0.764356	−	0.644794i	$-0.223057\pi$
$812$	−0.148187	+	4.23851i	−0.00520033	+	0.148743i
$813$		0			0
$814$	1.39456	+	17.0683i	0.0488793	+	0.598242i
$815$	−4.26546	−	7.38800i	−0.149413	−	0.258790i
$816$		0			0
$817$	0.725231	−	1.25614i	0.0253726	−	0.0439467i
$818$	−10.3917	+	7.18775i	−0.363336	+	0.251314i
$819$		0			0
$820$	−1.68684	+	4.47399i	−0.0589069	+	0.156238i
$821$	15.2246	+	8.78995i	0.531344	+	0.306771i	0.741563	−	0.670883i	$-0.234085\pi$
$821$	15.2246	+	8.78995i	0.531344	+	0.306771i	−0.210220	+	0.977654i	$0.567418\pi$
$822$		0			0
$823$	45.3375	−	26.1756i	1.58037	−	0.912424i	0.585560	−	0.810629i	$-0.300875\pi$
$823$	45.3375	−	26.1756i	1.58037	−	0.912424i	0.994805	−	0.101795i	$-0.0324586\pi$
$824$	8.48120	−	29.6027i	0.295457	−	1.03126i
$825$		0			0
$826$	−18.4268	+	7.94600i	−0.641150	+	0.276477i
$827$	−0.811503			−0.0282187			−0.0141094	−	0.999900i	$-0.504491\pi$
$827$	−0.811503			−0.0282187			−0.0141094	+	0.999900i	$0.504491\pi$
$828$		0			0
$829$	13.7687	+	23.8481i	0.478206	+	0.828278i	0.999688	−	0.0249848i	$-0.00795373\pi$
$829$	13.7687	+	23.8481i	0.478206	+	0.828278i	−0.521481	+	0.853263i	$0.674620\pi$
$830$	−15.3177	+	32.3624i	−0.531685	+	1.12331i
$831$		0			0
$832$	−41.9417	+	22.3251i	−1.45407	+	0.773983i
$833$	−17.8692	+	2.29270i	−0.619129	+	0.0794374i
$834$		0			0
$835$	13.9526	+	8.05552i	0.482849	+	0.278773i
$836$	−0.0715484	−	0.434923i	−0.00247455	−	0.0150421i
$837$		0			0
$838$	−3.40153	−	41.6318i	−0.117504	−	1.43815i
$839$	−3.84381			−0.132703			−0.0663515	−	0.997796i	$-0.521136\pi$
$839$	−3.84381			−0.132703			−0.0663515	+	0.997796i	$0.521136\pi$
$840$		0			0
$841$	28.3576			0.977849
$842$	0.881181	+	10.7849i	0.0303675	+	0.371673i
$843$		0			0
$844$	−3.76323	−	22.8756i	−0.129536	−	0.787411i
$845$	−38.1880	−	22.0478i	−1.31371	−	0.758469i
$846$		0			0
$847$	15.1367	−	17.2029i	0.520103	−	0.591098i
$848$	27.1216	−	30.8544i	0.931361	−	1.05955i
$849$		0			0
$850$	1.68282	−	3.55536i	0.0577201	−	0.121948i
$851$	25.2191	+	43.6807i	0.864499	+	1.49736i
$852$		0			0
$853$	−27.3448			−0.936268			−0.468134	−	0.883658i	$-0.655073\pi$
$853$	−27.3448			−0.936268			−0.468134	+	0.883658i	$0.655073\pi$
$854$	31.3572	+	23.3502i	1.07302	+	0.799028i
$855$		0			0
$856$	−51.5619	−	14.7726i	−1.76235	−	0.504916i
$857$	2.98741	−	1.72478i	0.102048	−	0.0589174i	−0.448107	−	0.893980i	$-0.647902\pi$
$857$	2.98741	−	1.72478i	0.102048	−	0.0589174i	0.550155	+	0.835062i	$0.314568\pi$
$858$		0			0
$859$	−17.7558	−	10.2513i	−0.605819	−	0.349770i	0.165508	−	0.986208i	$-0.447074\pi$
$859$	−17.7558	−	10.2513i	−0.605819	−	0.349770i	−0.771328	+	0.636438i	$0.780407\pi$
$860$	14.0609	−	37.2937i	0.479474	−	1.27171i
$861$		0			0
$862$	−21.0466	+	14.5576i	−0.716851	+	0.495834i
$863$	3.52476	−	6.10506i	0.119984	−	0.207819i	−0.799777	−	0.600297i	$-0.795049\pi$
$863$	3.52476	−	6.10506i	0.119984	−	0.207819i	0.919761	+	0.392479i	$0.128382\pi$
$864$		0			0
$865$	−4.40777	−	7.63448i	−0.149869	−	0.259580i
$866$	−0.135684	−	1.66066i	−0.00461073	−	0.0564314i
$867$		0			0
$868$	−20.3388	+	10.8133i	−0.690344	+	0.367026i
$869$			12.8939i			0.437395i
$870$		0			0
$871$	45.7047	−	26.3876i	1.54864	−	0.894111i
$872$	10.6505	−	10.2897i	0.360672	−	0.348454i
$873$		0			0
$874$	−0.738489	−	1.06767i	−0.0249798	−	0.0361145i
$875$	−6.26500	+	31.2276i	−0.211796	+	1.05568i
$876$		0			0
$877$	−2.86574	+	4.96361i	−0.0967691	+	0.167609i	−0.910346	−	0.413849i	$-0.864184\pi$
$877$	−2.86574	+	4.96361i	−0.0967691	+	0.167609i	0.813576	+	0.581458i	$0.197518\pi$
$878$	−23.4522	+	49.5485i	−0.791473	+	1.67218i
$879$		0			0
$880$	−3.87992	−	11.4734i	−0.130792	−	0.386767i
$881$		−	17.8606i		−	0.601739i	−0.953665	−	0.300870i	$-0.902723\pi$
$881$		−	17.8606i		−	0.601739i	0.953665	−	0.300870i	$-0.0972769\pi$
$882$		0			0
$883$		−	1.77852i		−	0.0598520i	−0.999552	−	0.0299260i	$-0.990473\pi$
$883$		−	1.77852i		−	0.0598520i	0.999552	−	0.0299260i	$-0.00952716\pi$
$884$	23.6428	−	19.3803i	0.795192	−	0.651830i
$885$		0			0
$886$	17.0772	+	8.08293i	0.573719	+	0.271551i
$887$	−26.0789	+	45.1700i	−0.875645	+	1.51666i	−0.0195702	+	0.999808i	$0.506230\pi$
$887$	−26.0789	+	45.1700i	−0.875645	+	1.51666i	−0.856074	+	0.516853i	$0.827104\pi$
$888$		0			0
$889$	1.61963	−	8.07295i	0.0543206	−	0.270758i
$890$	−37.3531	+	25.8365i	−1.25208	+	0.866043i
$891$		0			0
$892$	−4.34066	−	26.3857i	−0.145336	−	0.883457i
$893$	0.721713	−	0.416681i	0.0241512	−	0.0139437i
$894$		0			0
$895$		−	14.9187i		−	0.498677i
$896$	10.8988	+	27.8786i	0.364105	+	0.931358i
$897$		0			0
$898$	5.88111	−	0.480516i	0.196255	−	0.0160350i
$899$	−1.74450	−	3.02157i	−0.0581824	−	0.100775i
$900$		0			0
$901$	−13.2158	+	22.8904i	−0.440282	+	0.762591i
$902$	1.48589	+	2.14822i	0.0494746	+	0.0715278i
$903$		0			0
$904$	16.6290	−	4.15006i	0.553072	−	0.138029i
$905$	33.6759	+	19.4428i	1.11942	+	0.646299i
$906$		0			0
$907$	2.37104	−	1.36892i	0.0787292	−	0.0454543i	−0.460119	−	0.887857i	$-0.652193\pi$
$907$	2.37104	−	1.36892i	0.0787292	−	0.0454543i	0.538848	+	0.842403i	$0.318860\pi$
$908$	5.68231	+	6.93207i	0.188574	+	0.230049i
$909$		0			0
$910$	−26.2755	+	35.2855i	−0.871023	+	1.16970i
$911$	−30.6139			−1.01428			−0.507142	−	0.861863i	$-0.669298\pi$
$911$	−30.6139			−1.01428			−0.507142	+	0.861863i	$0.669298\pi$
$912$		0			0
$913$	9.77975	+	16.9390i	0.323662	+	0.560600i
$914$	19.2165	+	9.09553i	0.635626	+	0.300853i
$915$		0			0
$916$	0.708357	−	1.87877i	0.0234048	−	0.0620763i
$917$	−20.7518	+	23.5845i	−0.685286	+	0.778829i
$918$		0			0
$919$	−38.8003	−	22.4014i	−1.27990	−	0.738953i	−0.303074	−	0.952967i	$-0.598013\pi$
$919$	−38.8003	−	22.4014i	−1.27990	−	0.738953i	−0.976831	+	0.214014i	$0.931346\pi$
$920$	−24.7857	−	25.6547i	−0.817160	−	0.845812i
$921$		0			0
$922$	2.35102	−	0.192090i	0.0774267	−	0.00632615i
$923$	16.5418			0.544480
$924$		0			0
$925$	8.55643			0.281334
$926$	58.5841	−	4.78661i	1.92519	−	0.157298i
$927$		0			0
$928$	−4.16245	+	1.79736i	−0.136639	+	0.0590013i
$929$	40.9962	+	23.6692i	1.34504	+	0.776561i	0.987542	−	0.157353i	$-0.0502959\pi$
$929$	40.9962	+	23.6692i	1.34504	+	0.776561i	0.357500	+	0.933913i	$0.383629\pi$
$930$		0			0
$931$	0.611389	+	0.802231i	0.0200374	+	0.0262921i
$932$	−24.4140	−	9.20487i	−0.799708	−	0.301515i
$933$		0			0
$934$	5.42165	+	2.56616i	0.177402	+	0.0839675i
$935$	3.89640	+	6.74877i	0.127426	+	0.220708i
$936$		0			0
$937$	−1.08271			−0.0353707			−0.0176853	−	0.999844i	$-0.505630\pi$
$937$	−1.08271			−0.0353707			−0.0176853	+	0.999844i	$0.505630\pi$
$938$	−13.1654	−	30.5306i	−0.429866	−	0.996859i
$939$		0			0
$940$	17.7099	−	14.5171i	0.577634	−	0.473494i
$941$	−35.6464	+	20.5804i	−1.16204	+	0.670903i	−0.951792	−	0.306745i	$-0.900760\pi$
$941$	−35.6464	+	20.5804i	−1.16204	+	0.670903i	−0.210247	+	0.977648i	$0.567427\pi$
$942$		0			0
$943$	6.66245	+	3.84657i	0.216959	+	0.125262i
$944$	−16.1125	−	14.1632i	−0.524419	−	0.460974i
$945$		0			0
$946$	−12.3859	−	17.9069i	−0.402700	−	0.582202i
$947$	−12.5525	+	21.7416i	−0.407903	+	0.706508i	−0.994655	−	0.103259i	$-0.967073\pi$
$947$	−12.5525	+	21.7416i	−0.407903	+	0.706508i	0.586752	+	0.809767i	$0.300406\pi$
$948$		0			0
$949$	−0.588888	−	1.01998i	−0.0191161	−	0.0331101i
$950$	−0.219495	+	0.0179338i	−0.00712136	+	0.000581851i
$951$		0			0
$952$	−10.3959	−	16.2128i	−0.336933	−	0.525460i
$953$		−	51.5822i		−	1.67091i	−0.549559	−	0.835455i	$-0.685204\pi$
$953$		−	51.5822i		−	1.67091i	0.549559	−	0.835455i	$-0.314796\pi$
$954$		0			0
$955$	2.25361	−	1.30112i	0.0729250	−	0.0421032i
$956$	−52.0251	+	8.55855i	−1.68261	+	0.276803i
$957$		0			0
$958$	40.9500	−	28.3244i	1.32303	−	0.915120i
$959$	34.9757	−	11.8085i	1.12943	−	0.381316i
$960$		0			0
$961$	−6.02512	+	10.4358i	−0.194359	+	0.336639i
$962$	60.1069	+	28.4497i	1.93792	+	0.917254i
$963$		0			0
$964$	8.82340	+	10.7640i	0.284183	+	0.346685i
$965$			23.5957i			0.759574i
$966$		0			0
$967$		−	39.1641i		−	1.25943i	−0.776825	−	0.629716i	$-0.783171\pi$
$967$		−	39.1641i		−	1.25943i	0.776825	−	0.629716i	$-0.216829\pi$
$968$	23.5488	+	6.74677i	0.756889	+	0.216850i
$969$		0			0
$970$	7.39715	−	15.6283i	0.237508	−	0.501794i
$971$	17.8757	−	30.9616i	0.573659	−	0.993607i	−0.422527	−	0.906350i	$-0.638857\pi$
$971$	17.8757	−	30.9616i	0.573659	−	0.993607i	0.996186	−	0.0872562i	$-0.0278099\pi$
$972$		0			0
$973$	3.04871	−	15.1962i	0.0977373	−	0.487167i
$974$	13.4994	+	19.5168i	0.432549	+	0.625357i
$975$		0			0
$976$	−8.20118	+	40.9829i	−0.262513	+	1.31183i
$977$	−32.9104	+	19.0008i	−1.05290	+	0.607890i	−0.923459	−	0.383698i	$-0.874650\pi$
$977$	−32.9104	+	19.0008i	−1.05290	+	0.607890i	−0.129437	+	0.991588i	$0.541317\pi$
$978$		0			0
$979$			24.8112i			0.792970i
$980$	20.1555	+	19.0246i	0.643844	+	0.607718i
$981$		0			0
$982$	2.28870	+	28.0117i	0.0730353	+	0.893890i
$983$	0.539311	+	0.934113i	0.0172013	+	0.0297936i	0.874498	−	0.485029i	$-0.161191\pi$
$983$	0.539311	+	0.934113i	0.0172013	+	0.0297936i	−0.857297	+	0.514823i	$0.827858\pi$
$984$		0			0
$985$	17.3285	−	30.0138i	0.552131	−	0.956320i
$986$	2.39920	−	1.65949i	0.0764061	−	0.0528488i
$987$		0			0
$988$	−1.60153	−	0.603828i	−0.0509515	−	0.0192103i
$989$	−55.5361	−	32.0638i	−1.76595	−	1.01957i
$990$		0			0
$991$	−41.0362	+	23.6923i	−1.30356	+	0.752609i	−0.981012	−	0.193945i	$-0.937872\pi$
$991$	−41.0362	+	23.6923i	−1.30356	+	0.752609i	−0.322545	+	0.946554i	$0.604538\pi$
$992$	−19.7578	−	14.6976i	−0.627312	−	0.466650i
$993$		0			0
$994$	1.21104	−	10.3507i	0.0384119	−	0.328303i
$995$	35.9290			1.13903
$996$		0			0
$997$	4.17406	+	7.22968i	0.132194	+	0.228966i	0.924522	−	0.381129i	$-0.124465\pi$
$997$	4.17406	+	7.22968i	0.132194	+	0.228966i	−0.792328	+	0.610095i	$0.791131\pi$
$998$	−18.4894	+	39.0633i	−0.585271	+	1.23653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.16	yes	64
3.2	odd	2	inner	756.2.be.e.107.17	yes	64
4.3	odd	2	inner	756.2.be.e.107.6	✓	64
7.4	even	3	inner	756.2.be.e.431.27	yes	64
12.11	even	2	inner	756.2.be.e.107.27	yes	64
21.11	odd	6	inner	756.2.be.e.431.6	yes	64
28.11	odd	6	inner	756.2.be.e.431.17	yes	64
84.11	even	6	inner	756.2.be.e.431.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.6	✓	64	4.3	odd	2	inner
756.2.be.e.107.16	yes	64	1.1	even	1	trivial
756.2.be.e.107.17	yes	64	3.2	odd	2	inner
756.2.be.e.107.27	yes	64	12.11	even	2	inner
756.2.be.e.431.6	yes	64	21.11	odd	6	inner
756.2.be.e.431.16	yes	64	84.11	even	6	inner
756.2.be.e.431.17	yes	64	28.11	odd	6	inner
756.2.be.e.431.27	yes	64	7.4	even	3	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.115165 - 1.40952i) q^{2} +(-1.97347 + 0.324653i) q^{4} +(-1.71449 - 0.989859i) q^{5} +(2.59406 + 0.520431i) q^{7} +(0.684877 + 2.74426i) q^{8} +O(q^{10})\)	\(q+(-0.115165 - 1.40952i) q^{2} +(-1.97347 + 0.324653i) q^{4} +(-1.71449 - 0.989859i) q^{5} +(2.59406 + 0.520431i) q^{7} +(0.684877 + 2.74426i) q^{8} +(-1.19777 + 2.53059i) q^{10} +(0.764732 + 1.32456i) q^{11} +5.93917 q^{13} +(0.434812 - 3.71631i) q^{14} +(3.78920 - 1.28139i) q^{16} +(-2.22886 + 1.28683i) q^{17} +(0.124788 + 0.0720463i) q^{19} +(3.70485 + 1.39685i) q^{20} +(1.77891 - 1.23044i) q^{22} +(3.18530 - 5.51710i) q^{23} +(-0.540360 - 0.935931i) q^{25} +(-0.683981 - 8.37136i) q^{26} +(-5.28827 - 0.184888i) q^{28} -0.801493i q^{29} +(3.76992 - 2.17657i) q^{31} +(-2.24252 - 5.19337i) q^{32} +(2.07049 + 2.99341i) q^{34} +(-3.93233 - 3.46002i) q^{35} +(-3.95867 + 6.85662i) q^{37} +(0.0871793 - 0.184188i) q^{38} +(1.54221 - 5.38292i) q^{40} +1.20760i q^{41} -10.0662i q^{43} +(-1.93920 - 2.36570i) q^{44} +(-8.14327 - 3.85436i) q^{46} +(2.89176 - 5.00868i) q^{47} +(6.45830 + 2.70006i) q^{49} +(-1.25698 + 0.869432i) q^{50} +(-11.7208 + 1.92817i) q^{52} +(8.89412 - 5.13502i) q^{53} -3.02791i q^{55} +(0.348418 + 7.47520i) q^{56} +(-1.12972 + 0.0923035i) q^{58} +(-2.68157 - 4.64461i) q^{59} +(-5.22443 + 9.04898i) q^{61} +(-3.50207 - 5.06311i) q^{62} +(-7.06189 + 3.75896i) q^{64} +(-10.1826 - 5.87894i) q^{65} +(7.69547 - 4.44298i) q^{67} +(3.98082 - 3.26313i) q^{68} +(-4.42410 + 5.94115i) q^{70} +2.78520 q^{71} +(-0.0991532 - 0.171738i) q^{73} +(10.1204 + 4.79017i) q^{74} +(-0.269656 - 0.101669i) q^{76} +(1.29442 + 3.83397i) q^{77} +(7.30088 + 4.21516i) q^{79} +(-7.76492 - 1.55385i) q^{80} +(1.70213 - 0.139073i) q^{82} +12.7885 q^{83} +5.09512 q^{85} +(-14.1885 + 1.15927i) q^{86} +(-3.11117 + 3.00578i) q^{88} +(14.0488 + 8.11108i) q^{89} +(15.4066 + 3.09093i) q^{91} +(-4.49496 + 11.9220i) q^{92} +(-7.39284 - 3.49916i) q^{94} +(-0.142631 - 0.247045i) q^{95} -6.17574 q^{97} +(3.06201 - 9.41404i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) \) 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

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