LMFDB - Embedded newform 1232.2.q.n.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} - 2x^{5} + 66x^{4} - 9x^{3} + 136x^{2} + 15x + 225 $ x^8 + 9x^6 - 2x^5 + 66x^4 - 9x^3 + 136x^2 + 15x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.4
Root			$-0.693499 - 1.20118i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.n.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03812 + 1.79807i) q^{3} +(-0.193499 + 0.335150i) q^{5} +(-1.09525 - 2.40841i) q^{7} +(-0.655380 + 1.13515i) q^{9} +O(q^{10})$	\(q+(1.03812 + 1.79807i) q^{3} +(-0.193499 + 0.335150i) q^{5} +(-1.09525 - 2.40841i) q^{7} +(-0.655380 + 1.13515i) q^{9} +(-0.500000 - 0.866025i) q^{11} +2.07624 q^{13} -0.803499 q^{15} +(3.52036 + 6.09745i) q^{17} +(-4.13337 + 7.15920i) q^{19} +(3.19350 - 4.46955i) q^{21} +(-0.731617 + 1.26720i) q^{23} +(2.42512 + 4.20042i) q^{25} +3.50726 q^{27} -2.76548 q^{29} +(3.67149 + 6.35920i) q^{31} +(1.03812 - 1.79807i) q^{33} +(1.01911 + 0.0989519i) q^{35} +(2.38700 - 4.13440i) q^{37} +(2.15538 + 3.73323i) q^{39} +11.4277 q^{41} +0.923763 q^{43} +(-0.253631 - 0.439301i) q^{45} +(-5.40611 + 9.36365i) q^{47} +(-4.60086 + 5.27561i) q^{49} +(-7.30911 + 12.6598i) q^{51} +(1.93987 + 3.35995i) q^{53} +0.386998 q^{55} -17.1637 q^{57} +(-4.75063 - 8.22833i) q^{59} +(4.56149 - 7.90072i) q^{61} +(3.45171 + 0.335150i) q^{63} +(-0.401750 + 0.695851i) q^{65} +(-2.75198 - 4.76657i) q^{67} -3.03802 q^{69} +7.04073 q^{71} +(-2.34162 - 4.05580i) q^{73} +(-5.03512 + 8.72108i) q^{75} +(-1.53812 + 2.15272i) q^{77} +(8.15673 - 14.1279i) q^{79} +(5.60709 + 9.71177i) q^{81} -11.8147 q^{83} -2.72475 q^{85} +(-2.87089 - 4.97253i) q^{87} +(-4.36924 + 7.56775i) q^{89} +(-2.27400 - 5.00043i) q^{91} +(-7.62287 + 13.2032i) q^{93} +(-1.59960 - 2.77060i) q^{95} -2.45723 q^{97} +1.31076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.03812	+	1.79807i	0.599358	+	1.03812i	0.992916	+	0.118819i	$0.0379107\pi$
$3$	1.03812	+	1.79807i	0.599358	+	1.03812i	−0.393558	+	0.919300i	$0.628756\pi$
$4$		0			0
$5$	−0.193499	+	0.335150i	−0.0865353	+	0.149884i	−0.906044	−	0.423183i	$-0.860913\pi$
$5$	−0.193499	+	0.335150i	−0.0865353	+	0.149884i	0.819509	+	0.573066i	$0.194246\pi$
$6$		0			0
$7$	−1.09525	−	2.40841i	−0.413965	−	0.910293i
$7$	−1.09525	−	2.40841i	−0.413965	−	0.910293i
$8$		0			0
$9$	−0.655380	+	1.13515i	−0.218460	+	0.378384i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	2.07624			0.575845			0.287922	−	0.957654i	$-0.407036\pi$
$13$	2.07624			0.575845			0.287922	+	0.957654i	$0.407036\pi$
$14$		0			0
$15$	−0.803499			−0.207463
$16$		0			0
$17$	3.52036	+	6.09745i	0.853814	+	1.47885i	0.877741	+	0.479135i	$0.159050\pi$
$17$	3.52036	+	6.09745i	0.853814	+	1.47885i	−0.0239272	+	0.999714i	$0.507617\pi$
$18$		0			0
$19$	−4.13337	+	7.15920i	−0.948259	+	1.64243i	−0.199170	+	0.979965i	$0.563824\pi$
$19$	−4.13337	+	7.15920i	−0.948259	+	1.64243i	−0.749090	+	0.662468i	$0.769509\pi$
$20$		0			0
$21$	3.19350	−	4.46955i	0.696879	−	0.975336i
$22$		0			0
$23$	−0.731617	+	1.26720i	−0.152553	+	0.264229i	−0.932165	−	0.362033i	$-0.882083\pi$
$23$	−0.731617	+	1.26720i	−0.152553	+	0.264229i	0.779612	+	0.626262i	$0.215416\pi$
$24$		0			0
$25$	2.42512	+	4.20042i	0.485023	+	0.840085i
$26$		0			0
$27$	3.50726			0.674973
$28$		0			0
$29$	−2.76548			−0.513536			−0.256768	−	0.966473i	$-0.582658\pi$
$29$	−2.76548			−0.513536			−0.256768	+	0.966473i	$0.582658\pi$
$30$		0			0
$31$	3.67149	+	6.35920i	0.659418	+	1.14215i	0.980766	+	0.195185i	$0.0625307\pi$
$31$	3.67149	+	6.35920i	0.659418	+	1.14215i	−0.321348	+	0.946961i	$0.604136\pi$
$32$		0			0
$33$	1.03812	−	1.79807i	0.180713	−	0.313005i
$34$		0			0
$35$	1.01911	+	0.0989519i	0.172261	+	0.0167259i
$36$		0			0
$37$	2.38700	−	4.13440i	0.392420	−	0.679691i	−0.600348	−	0.799739i	$-0.704971\pi$
$37$	2.38700	−	4.13440i	0.392420	−	0.679691i	0.992768	+	0.120047i	$0.0383046\pi$
$38$		0			0
$39$	2.15538	+	3.73323i	0.345137	+	0.597795i
$40$		0			0
$41$	11.4277			1.78471			0.892356	−	0.451333i	$-0.149051\pi$
$41$	11.4277			1.78471			0.892356	+	0.451333i	$0.149051\pi$
$42$		0			0
$43$	0.923763			0.140873			0.0704363	−	0.997516i	$-0.477561\pi$
$43$	0.923763			0.140873			0.0704363	+	0.997516i	$0.477561\pi$
$44$		0			0
$45$	−0.253631	−	0.439301i	−0.0378090	−	0.0654872i
$46$		0			0
$47$	−5.40611	+	9.36365i	−0.788561	+	1.36583i	0.138287	+	0.990392i	$0.455840\pi$
$47$	−5.40611	+	9.36365i	−0.788561	+	1.36583i	−0.926848	+	0.375436i	$0.877493\pi$
$48$		0			0
$49$	−4.60086	+	5.27561i	−0.657266	+	0.753659i
$50$		0			0
$51$	−7.30911	+	12.6598i	−1.02348	+	1.77272i
$52$		0			0
$53$	1.93987	+	3.35995i	0.266461	+	0.461525i	0.967945	−	0.251160i	$-0.0808122\pi$
$53$	1.93987	+	3.35995i	0.266461	+	0.461525i	−0.701484	+	0.712685i	$0.747479\pi$
$54$		0			0
$55$	0.386998			0.0521828
$56$		0			0
$57$	−17.1637			−2.27339
$58$		0			0
$59$	−4.75063	−	8.22833i	−0.618479	−	1.07124i	−0.989763	−	0.142718i	$-0.954416\pi$
$59$	−4.75063	−	8.22833i	−0.618479	−	1.07124i	0.371284	−	0.928519i	$-0.378918\pi$
$60$		0			0
$61$	4.56149	−	7.90072i	0.584038	−	1.01158i	−0.410956	−	0.911655i	$-0.634805\pi$
$61$	4.56149	−	7.90072i	0.584038	−	1.01158i	0.994995	−	0.0999290i	$-0.0318616\pi$
$62$		0			0
$63$	3.45171	+	0.335150i	0.434875	+	0.0422249i
$64$		0			0
$65$	−0.401750	+	0.695851i	−0.0498309	+	0.0863097i
$66$		0			0
$67$	−2.75198	−	4.76657i	−0.336208	−	0.582330i	0.647508	−	0.762059i	$-0.275811\pi$
$67$	−2.75198	−	4.76657i	−0.336208	−	0.582330i	−0.983716	+	0.179729i	$0.942478\pi$
$68$		0			0
$69$	−3.03802			−0.365735
$70$		0			0
$71$	7.04073			0.835581			0.417790	−	0.908543i	$-0.362805\pi$
$71$	7.04073			0.835581			0.417790	+	0.908543i	$0.362805\pi$
$72$		0			0
$73$	−2.34162	−	4.05580i	−0.274066	−	0.474696i	0.695833	−	0.718203i	$-0.255035\pi$
$73$	−2.34162	−	4.05580i	−0.274066	−	0.474696i	−0.969899	+	0.243508i	$0.921702\pi$
$74$		0			0
$75$	−5.03512	+	8.72108i	−0.581405	+	1.00702i
$76$		0			0
$77$	−1.53812	+	2.15272i	−0.175285	+	0.245325i
$78$		0			0
$79$	8.15673	−	14.1279i	0.917704	−	1.58951i	0.114811	−	0.993387i	$-0.463374\pi$
$79$	8.15673	−	14.1279i	0.917704	−	1.58951i	0.802893	−	0.596123i	$-0.203293\pi$
$80$		0			0
$81$	5.60709	+	9.71177i	0.623010	+	1.07909i
$82$		0			0
$83$	−11.8147			−1.29683			−0.648417	−	0.761285i	$-0.724569\pi$
$83$	−11.8147			−1.29683			−0.648417	+	0.761285i	$0.724569\pi$
$84$		0			0
$85$	−2.72475			−0.295540
$86$		0			0
$87$	−2.87089	−	4.97253i	−0.307792	−	0.533111i
$88$		0			0
$89$	−4.36924	+	7.56775i	−0.463139	+	0.802180i	−0.999115	−	0.0420528i	$-0.986610\pi$
$89$	−4.36924	+	7.56775i	−0.463139	+	0.802180i	0.535976	+	0.844233i	$0.319944\pi$
$90$		0			0
$91$	−2.27400	−	5.00043i	−0.238380	−	0.524187i
$92$		0			0
$93$	−7.62287	+	13.2032i	−0.790455	+	1.36911i
$94$		0			0
$95$	−1.59960	−	2.77060i	−0.164116	−	0.284257i
$96$		0			0
$97$	−2.45723			−0.249494			−0.124747	−	0.992189i	$-0.539812\pi$
$97$	−2.45723			−0.249494			−0.124747	+	0.992189i	$0.539812\pi$
$98$		0			0
$99$	1.31076			0.131736
$100$		0			0
$101$	1.13211	+	1.96087i	0.112649	+	0.195114i	0.916838	−	0.399260i	$-0.130733\pi$
$101$	1.13211	+	1.96087i	0.112649	+	0.195114i	−0.804188	+	0.594374i	$0.797400\pi$
$102$		0			0
$103$	−0.570624	+	0.988350i	−0.0562253	+	0.0973850i	−0.892768	−	0.450517i	$-0.851240\pi$
$103$	−0.570624	+	0.988350i	−0.0562253	+	0.0973850i	0.836543	+	0.547902i	$0.184573\pi$
$104$		0			0
$105$	0.880031	+	1.93515i	0.0858823	+	0.188852i
$106$		0			0
$107$	4.46023	−	7.72535i	0.431187	−	0.746838i	−0.565789	−	0.824550i	$-0.691428\pi$
$107$	4.46023	−	7.72535i	0.431187	−	0.746838i	0.996976	+	0.0777124i	$0.0247616\pi$
$108$		0			0
$109$	−10.0377	−	17.3859i	−0.961440	−	1.66526i	−0.718890	−	0.695124i	$-0.755349\pi$
$109$	−10.0377	−	17.3859i	−0.961440	−	1.66526i	−0.242550	−	0.970139i	$-0.577984\pi$
$110$		0			0
$111$	9.91195			0.940800
$112$		0			0
$113$	−2.07023			−0.194751			−0.0973756	−	0.995248i	$-0.531045\pi$
$113$	−2.07023			−0.194751			−0.0973756	+	0.995248i	$0.531045\pi$
$114$		0			0
$115$	−0.283134	−	0.490403i	−0.0264024	−	0.0457303i
$116$		0			0
$117$	−1.36072	+	2.35684i	−0.125799	+	0.217890i
$118$		0			0
$119$	10.8295	−	15.1567i	0.992737	−	1.38941i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	11.8633	+	20.5479i	1.06968	+	1.85274i
$124$		0			0
$125$	−3.81202			−0.340957
$126$		0			0
$127$	−12.5802			−1.11631			−0.558156	−	0.829736i	$-0.688491\pi$
$127$	−12.5802			−1.11631			−0.558156	+	0.829736i	$0.688491\pi$
$128$		0			0
$129$	0.958975	+	1.66099i	0.0844331	+	0.146242i
$130$		0			0
$131$	3.36924	−	5.83570i	0.294372	−	0.509868i	−0.680466	−	0.732779i	$-0.738223\pi$
$131$	3.36924	−	5.83570i	0.294372	−	0.509868i	0.974839	+	0.222912i	$0.0715561\pi$
$132$		0			0
$133$	21.7693	+	2.11373i	1.88764	+	0.183284i
$134$		0			0
$135$	−0.678651	+	1.17546i	−0.0584090	+	0.101167i
$136$		0			0
$137$	4.78884	+	8.29452i	0.409138	+	0.708649i	0.994793	−	0.101912i	$-0.0324960\pi$
$137$	4.78884	+	8.29452i	0.409138	+	0.708649i	−0.585655	+	0.810560i	$0.699163\pi$
$138$		0			0
$139$	8.89697			0.754631			0.377315	−	0.926085i	$-0.376847\pi$
$139$	8.89697			0.754631			0.377315	+	0.926085i	$0.376847\pi$
$140$		0			0
$141$	−22.4487			−1.89052
$142$		0			0
$143$	−1.03812	−	1.79807i	−0.0868118	−	0.150363i
$144$		0			0
$145$	0.535117	−	0.926849i	0.0444390	−	0.0769706i
$146$		0			0
$147$	−14.2622	−	2.79598i	−1.17632	−	0.230609i
$148$		0			0
$149$	−7.05548	+	12.2205i	−0.578008	+	1.00114i	0.417700	+	0.908585i	$0.362836\pi$
$149$	−7.05548	+	12.2205i	−0.578008	+	1.00114i	−0.995708	+	0.0925535i	$0.970497\pi$
$150$		0			0
$151$	−4.03812	−	6.99423i	−0.328617	−	0.569182i	0.653620	−	0.756823i	$-0.273249\pi$
$151$	−4.03812	−	6.99423i	−0.328617	−	0.569182i	−0.982238	+	0.187641i	$0.939916\pi$
$152$		0			0
$153$	−9.22871			−0.746097
$154$		0			0
$155$	−2.84171			−0.228252
$156$		0			0
$157$	1.52201	+	2.63620i	0.121470	+	0.210392i	0.920348	−	0.391102i	$-0.127906\pi$
$157$	1.52201	+	2.63620i	0.121470	+	0.210392i	−0.798878	+	0.601494i	$0.794573\pi$
$158$		0			0
$159$	−4.02763	+	6.97605i	−0.319412	+	0.553237i
$160$		0			0
$161$	3.85323	+	0.374136i	0.303677	+	0.0294861i
$162$		0			0
$163$	−7.66099	+	13.2692i	−0.600055	+	1.03933i	0.392757	+	0.919642i	$0.371521\pi$
$163$	−7.66099	+	13.2692i	−0.600055	+	1.03933i	−0.992812	+	0.119684i	$0.961812\pi$
$164$		0			0
$165$	0.401750	+	0.695851i	0.0312762	+	0.0541719i
$166$		0			0
$167$	23.6970			1.83373			0.916864	−	0.399201i	$-0.130712\pi$
$167$	23.6970			1.83373			0.916864	+	0.399201i	$0.130712\pi$
$168$		0			0
$169$	−8.68924			−0.668403
$170$		0			0
$171$	−5.41785	−	9.38400i	−0.414314	−	0.717612i
$172$		0			0
$173$	10.8121	−	18.7271i	0.822030	−	1.42380i	−0.0821385	−	0.996621i	$-0.526175\pi$
$173$	10.8121	−	18.7271i	0.822030	−	1.42380i	0.904168	−	0.427176i	$-0.140492\pi$
$174$		0			0
$175$	7.46023	−	10.4412i	0.563941	−	0.789279i
$176$		0			0
$177$	9.86343	−	17.0840i	0.741381	−	1.28411i
$178$		0			0
$179$	10.1758	+	17.6251i	0.760578	+	1.31736i	0.942553	+	0.334057i	$0.108418\pi$
$179$	10.1758	+	17.6251i	0.760578	+	1.31736i	−0.181975	+	0.983303i	$0.558249\pi$
$180$		0			0
$181$	3.15228			0.234307			0.117154	−	0.993114i	$-0.462623\pi$
$181$	3.15228			0.234307			0.117154	+	0.993114i	$0.462623\pi$
$182$		0			0
$183$	18.9415			1.40019
$184$		0			0
$185$	0.923763	+	1.60000i	0.0679164	+	0.117635i
$186$		0			0
$187$	3.52036	−	6.09745i	0.257435	−	0.445890i
$188$		0			0
$189$	−3.84132	−	8.44692i	−0.279415	−	0.614423i
$190$		0			0
$191$	7.82948	−	13.5611i	0.566521	−	0.981243i	−0.430385	−	0.902645i	$-0.641622\pi$
$191$	7.82948	−	13.5611i	0.566521	−	0.981243i	0.996906	−	0.0785980i	$-0.0250444\pi$
$192$		0			0
$193$	−2.05161	−	3.55350i	−0.147678	−	0.255786i	0.782691	−	0.622411i	$-0.213847\pi$
$193$	−2.05161	−	3.55350i	−0.147678	−	0.255786i	−0.930369	+	0.366625i	$0.880513\pi$
$194$		0			0
$195$	−1.66825			−0.119466
$196$		0			0
$197$	−1.18527			−0.0844473			−0.0422237	−	0.999108i	$-0.513444\pi$
$197$	−1.18527			−0.0844473			−0.0422237	+	0.999108i	$0.513444\pi$
$198$		0			0
$199$	5.21948	+	9.04040i	0.369999	+	0.640857i	0.989565	−	0.144088i	$-0.0460247\pi$
$199$	5.21948	+	9.04040i	0.369999	+	0.640857i	−0.619566	+	0.784945i	$0.712691\pi$
$200$		0			0
$201$	5.71377	−	9.89654i	0.403018	−	0.698048i
$202$		0			0
$203$	3.02888	+	6.66040i	0.212586	+	0.467468i
$204$		0			0
$205$	−2.21125	+	3.83000i	−0.154441	+	0.267499i
$206$		0			0
$207$	−0.958975	−	1.66099i	−0.0666534	−	0.115447i
$208$		0			0
$209$	8.26673			0.571822
$210$		0			0
$211$	−7.70047			−0.530122			−0.265061	−	0.964232i	$-0.585392\pi$
$211$	−7.70047			−0.530122			−0.265061	+	0.964232i	$0.585392\pi$
$212$		0			0
$213$	7.30911	+	12.6598i	0.500812	+	0.867432i
$214$		0			0
$215$	−0.178747	+	0.309599i	−0.0121905	+	0.0211145i
$216$		0			0
$217$	11.2944	−	15.8073i	0.766711	−	1.07307i
$218$		0			0
$219$	4.86175	−	8.42080i	0.328527	−	0.569025i
$220$		0			0
$221$	7.30911	+	12.6598i	0.491664	+	0.851587i
$222$		0			0
$223$	−2.50396			−0.167678			−0.0838389	−	0.996479i	$-0.526718\pi$
$223$	−2.50396			−0.167678			−0.0838389	+	0.996479i	$0.526718\pi$
$224$		0			0
$225$	−6.35749			−0.423833
$226$		0			0
$227$	−7.11726	−	12.3275i	−0.472389	−	0.818202i	0.527112	−	0.849796i	$-0.323275\pi$
$227$	−7.11726	−	12.3275i	−0.472389	−	0.818202i	−0.999501	+	0.0315939i	$0.989942\pi$
$228$		0			0
$229$	−5.82696	+	10.0926i	−0.385056	+	0.666937i	−0.991777	−	0.127978i	$-0.959151\pi$
$229$	−5.82696	+	10.0926i	−0.385056	+	0.666937i	0.606721	+	0.794915i	$0.292485\pi$
$230$		0			0
$231$	−5.46749	−	0.530875i	−0.359735	−	0.0349290i
$232$		0			0
$233$	−2.24947	+	3.89619i	−0.147367	+	0.255248i	−0.930254	−	0.366917i	$-0.880413\pi$
$233$	−2.24947	+	3.89619i	−0.147367	+	0.255248i	0.782886	+	0.622165i	$0.213747\pi$
$234$		0			0
$235$	−2.09215	−	3.62371i	−0.136477	−	0.236385i
$236$		0			0
$237$	33.8706			2.20013
$238$		0			0
$239$	12.7705			0.826055			0.413028	−	0.910718i	$-0.364471\pi$
$239$	12.7705			0.826055			0.413028	+	0.910718i	$0.364471\pi$
$240$		0			0
$241$	−11.9251	−	20.6549i	−0.768164	−	1.33050i	−0.938557	−	0.345123i	$-0.887837\pi$
$241$	−11.9251	−	20.6549i	−0.768164	−	1.33050i	0.170393	−	0.985376i	$-0.445496\pi$
$242$		0			0
$243$	−6.38077	+	11.0518i	−0.409326	+	0.708974i
$244$		0			0
$245$	−0.877859	−	2.56280i	−0.0560844	−	0.163731i
$246$		0			0
$247$	−8.58185	+	14.8642i	−0.546050	+	0.945786i
$248$		0			0
$249$	−12.2651	−	21.2438i	−0.777268	−	1.34627i
$250$		0			0
$251$	12.0382			0.759845			0.379923	−	0.925018i	$-0.375951\pi$
$251$	12.0382			0.759845			0.379923	+	0.925018i	$0.375951\pi$
$252$		0			0
$253$	1.46323			0.0919928
$254$		0			0
$255$	−2.82861	−	4.89930i	−0.177134	−	0.306806i
$256$		0			0
$257$	1.31250	−	2.27333i	0.0818718	−	0.141806i	−0.822182	−	0.569225i	$-0.807244\pi$
$257$	1.31250	−	2.27333i	0.0818718	−	0.141806i	0.904054	+	0.427418i	$0.140577\pi$
$258$		0			0
$259$	−12.5717	−	1.22067i	−0.781166	−	0.0758486i
$260$		0			0
$261$	1.81244	−	3.13924i	0.112187	−	0.194314i
$262$		0			0
$263$	−0.745112	−	1.29057i	−0.0459456	−	0.0795800i	0.842138	−	0.539262i	$-0.181297\pi$
$263$	−0.745112	−	1.29057i	−0.0459456	−	0.0795800i	−0.888084	+	0.459682i	$0.847963\pi$
$264$		0			0
$265$	−1.50145			−0.0922333
$266$		0			0
$267$	−18.1432			−1.11034
$268$		0			0
$269$	1.40475	+	2.43310i	0.0856492	+	0.148349i	0.905668	−	0.423988i	$-0.139370\pi$
$269$	1.40475	+	2.43310i	0.0856492	+	0.148349i	−0.820018	+	0.572337i	$0.806037\pi$
$270$		0			0
$271$	−9.45597	+	16.3782i	−0.574409	+	0.994906i	0.421696	+	0.906737i	$0.361435\pi$
$271$	−9.45597	+	16.3782i	−0.574409	+	0.994906i	−0.996106	+	0.0881691i	$0.971898\pi$
$272$		0			0
$273$	6.63046	−	9.27985i	0.401294	−	0.561642i
$274$		0			0
$275$	2.42512	−	4.20042i	0.146240	−	0.253295i
$276$		0			0
$277$	−10.1673	−	17.6103i	−0.610895	−	1.05810i	−0.991090	−	0.133195i	$-0.957476\pi$
$277$	−10.1673	−	17.6103i	−0.610895	−	1.05810i	0.380195	−	0.924906i	$-0.375857\pi$
$278$		0			0
$279$	−9.62488			−0.576226
$280$		0			0
$281$	5.37247			0.320495			0.160247	−	0.987077i	$-0.448771\pi$
$281$	5.37247			0.320495			0.160247	+	0.987077i	$0.448771\pi$
$282$		0			0
$283$	−4.88409	−	8.45950i	−0.290329	−	0.502865i	0.683558	−	0.729896i	$-0.260431\pi$
$283$	−4.88409	−	8.45950i	−0.290329	−	0.502865i	−0.973888	+	0.227031i	$0.927098\pi$
$284$		0			0
$285$	3.32116	−	5.75241i	0.196728	−	0.340744i
$286$		0			0
$287$	−12.5162	−	27.5226i	−0.738808	−	1.62461i
$288$		0			0
$289$	−16.2859	+	28.2081i	−0.957996	+	1.65930i
$290$		0			0
$291$	−2.55090	−	4.41828i	−0.149536	−	0.259004i
$292$		0			0
$293$	−16.7325			−0.977522			−0.488761	−	0.872418i	$-0.662551\pi$
$293$	−16.7325			−0.977522			−0.488761	+	0.872418i	$0.662551\pi$
$294$		0			0
$295$	3.67697			0.214081
$296$		0			0
$297$	−1.75363	−	3.03738i	−0.101756	−	0.176247i
$298$		0			0
$299$	−1.51901	+	2.63100i	−0.0878467	+	0.152155i
$300$		0			0
$301$	−1.01175	−	2.22480i	−0.0583163	−	0.128235i
$302$		0			0
$303$	−2.35053	+	4.07123i	−0.135034	+	0.233886i
$304$		0			0
$305$	1.76528	+	3.05756i	0.101080	+	0.175076i
$306$		0			0
$307$	22.5449			1.28670			0.643352	−	0.765570i	$-0.277543\pi$
$307$	22.5449			1.28670			0.643352	+	0.765570i	$0.277543\pi$
$308$		0			0
$309$	−2.36950			−0.134796
$310$		0			0
$311$	−11.2697	−	19.5198i	−0.639048	−	1.10686i	−0.985642	−	0.168849i	$-0.945995\pi$
$311$	−11.2697	−	19.5198i	−0.639048	−	1.10686i	0.346594	−	0.938015i	$-0.387338\pi$
$312$		0			0
$313$	3.30785	−	5.72937i	0.186971	−	0.323843i	−0.757268	−	0.653104i	$-0.773466\pi$
$313$	3.30785	−	5.72937i	0.186971	−	0.323843i	0.944239	+	0.329261i	$0.106800\pi$
$314$		0			0
$315$	−0.780228	+	1.09199i	−0.0439609	+	0.0615267i
$316$		0			0
$317$	2.57614	−	4.46201i	0.144691	−	0.250611i	−0.784567	−	0.620044i	$-0.787115\pi$
$317$	2.57614	−	4.46201i	0.144691	−	0.250611i	0.929257	+	0.369433i	$0.120448\pi$
$318$		0			0
$319$	1.38274	+	2.39497i	0.0774185	+	0.134093i
$320$		0			0
$321$	18.5210			1.03374
$322$		0			0
$323$	−58.2038			−3.23855
$324$		0			0
$325$	5.03512	+	8.72108i	0.279298	+	0.483758i
$326$		0			0
$327$	20.8407	−	36.0972i	1.15249	−	1.99618i
$328$		0			0
$329$	28.4725	+	2.76459i	1.56974	+	0.152417i
$330$		0			0
$331$	−0.764219	+	1.32367i	−0.0420053	+	0.0727553i	−0.886264	−	0.463181i	$-0.846708\pi$
$331$	−0.764219	+	1.32367i	−0.0420053	+	0.0727553i	0.844258	+	0.535936i	$0.180041\pi$
$332$		0			0
$333$	3.12878	+	5.41921i	0.171456	+	0.296971i
$334$		0			0
$335$	2.13002			0.116376
$336$		0			0
$337$	4.87122			0.265352			0.132676	−	0.991159i	$-0.457643\pi$
$337$	4.87122			0.265352			0.132676	+	0.991159i	$0.457643\pi$
$338$		0			0
$339$	−2.14915	−	3.72243i	−0.116726	−	0.202175i
$340$		0			0
$341$	3.67149	−	6.35920i	0.198822	−	0.344370i
$342$		0			0
$343$	17.7449	+	5.30265i	0.958135	+	0.286316i
$344$		0			0
$345$	0.587854	−	1.01819i	0.0316490	−	0.0548177i
$346$		0			0
$347$	11.9062	+	20.6221i	0.639158	+	1.10705i	0.985618	+	0.168990i	$0.0540505\pi$
$347$	11.9062	+	20.6221i	0.639158	+	1.10705i	−0.346459	+	0.938065i	$0.612616\pi$
$348$		0			0
$349$	−20.4450			−1.09439			−0.547197	−	0.837004i	$-0.684305\pi$
$349$	−20.4450			−1.09439			−0.547197	+	0.837004i	$0.684305\pi$
$350$		0			0
$351$	7.28191			0.388679
$352$		0			0
$353$	3.60212	+	6.23905i	0.191721	+	0.332071i	0.945821	−	0.324689i	$-0.105260\pi$
$353$	3.60212	+	6.23905i	0.191721	+	0.332071i	−0.754099	+	0.656760i	$0.771926\pi$
$354$		0			0
$355$	−1.36237	+	2.35970i	−0.0723073	+	0.125240i
$356$		0			0
$357$	38.4952	+	3.73775i	2.03738	+	0.197823i
$358$		0			0
$359$	−2.66887	+	4.62263i	−0.140858	+	0.243973i	−0.927820	−	0.373028i	$-0.878319\pi$
$359$	−2.66887	+	4.62263i	−0.140858	+	0.243973i	0.786962	+	0.617001i	$0.211653\pi$
$360$		0			0
$361$	−24.6694	−	42.7287i	−1.29839	−	2.24888i
$362$		0			0
$363$	−2.07624			−0.108974
$364$		0			0
$365$	1.81240			0.0948654
$366$		0			0
$367$	−16.0170	−	27.7422i	−0.836079	−	1.44813i	−0.893149	−	0.449761i	$-0.851509\pi$
$367$	−16.0170	−	27.7422i	−0.836079	−	1.44813i	0.0570696	−	0.998370i	$-0.481824\pi$
$368$		0			0
$369$	−7.48951	+	12.9722i	−0.389888	+	0.675306i
$370$		0			0
$371$	5.96749	−	8.35198i	0.309817	−	0.433613i
$372$		0			0
$373$	−0.148510	+	0.257226i	−0.00768954	+	0.0133187i	−0.869845	−	0.493326i	$-0.835781\pi$
$373$	−0.148510	+	0.257226i	−0.00768954	+	0.0133187i	0.862155	+	0.506645i	$0.169114\pi$
$374$		0			0
$375$	−3.95733	−	6.85429i	−0.204355	−	0.353954i
$376$		0			0
$377$	−5.74178			−0.295717
$378$		0			0
$379$	−5.68924			−0.292237			−0.146118	−	0.989267i	$-0.546678\pi$
$379$	−5.68924			−0.292237			−0.146118	+	0.989267i	$0.546678\pi$
$380$		0			0
$381$	−13.0597	−	22.6201i	−0.669071	−	1.15886i
$382$		0			0
$383$	−3.79010	+	6.56465i	−0.193665	+	0.335438i	−0.946462	−	0.322815i	$-0.895371\pi$
$383$	−3.79010	+	6.56465i	−0.193665	+	0.335438i	0.752797	+	0.658253i	$0.228704\pi$
$384$		0			0
$385$	−0.423859	−	0.932049i	−0.0216018	−	0.0475016i
$386$		0			0
$387$	−0.605416	+	1.04861i	−0.0307750	+	0.0533039i
$388$		0			0
$389$	−2.99077	−	5.18016i	−0.151638	−	0.262644i	0.780192	−	0.625540i	$-0.215121\pi$
$389$	−2.99077	−	5.18016i	−0.151638	−	0.262644i	−0.931830	+	0.362896i	$0.881788\pi$
$390$		0			0
$391$	−10.3022			−0.521007
$392$		0			0
$393$	13.9907			0.705737
$394$		0			0
$395$	3.15664	+	5.46746i	0.158828	+	0.275098i
$396$		0			0
$397$	2.19050	−	3.79405i	0.109938	−	0.190418i	−0.805807	−	0.592178i	$-0.798268\pi$
$397$	2.19050	−	3.79405i	0.109938	−	0.190418i	0.915745	+	0.401760i	$0.131601\pi$
$398$		0			0
$399$	18.7985	+	41.3372i	0.941103	+	2.06945i
$400$		0			0
$401$	12.3368	−	21.3680i	0.616072	−	1.06707i	−0.374123	−	0.927379i	$-0.622056\pi$
$401$	12.3368	−	21.3680i	0.616072	−	1.06707i	0.990195	−	0.139689i	$-0.0446104\pi$
$402$		0			0
$403$	7.62287	+	13.2032i	0.379722	+	0.657699i
$404$		0			0
$405$	−4.33987			−0.215650
$406$		0			0
$407$	−4.77400			−0.236638
$408$		0			0
$409$	−12.7857	−	22.1456i	−0.632214	−	1.09503i	−0.987098	−	0.160117i	$-0.948813\pi$
$409$	−12.7857	−	22.1456i	−0.632214	−	1.09503i	0.354884	−	0.934910i	$-0.384520\pi$
$410$		0			0
$411$	−9.94277	+	17.2214i	−0.490441	+	0.849469i
$412$		0			0
$413$	−14.6141	+	20.4535i	−0.719111	+	1.00645i
$414$		0			0
$415$	2.28614	−	3.95970i	0.112222	−	0.194374i
$416$		0			0
$417$	9.23611	+	15.9974i	0.452294	+	0.783396i
$418$		0			0
$419$	11.4844			0.561050			0.280525	−	0.959847i	$-0.409491\pi$
$419$	11.4844			0.561050			0.280525	+	0.959847i	$0.409491\pi$
$420$		0			0
$421$	−13.8613			−0.675557			−0.337778	−	0.941226i	$-0.609675\pi$
$421$	−13.8613			−0.675557			−0.337778	+	0.941226i	$0.609675\pi$
$422$		0			0
$423$	−7.08611	−	12.2735i	−0.344538	−	0.596758i
$424$		0			0
$425$	−17.0746	+	29.5741i	−0.828239	+	1.43455i
$426$		0			0
$427$	−24.0241	−	2.33266i	−1.16261	−	0.112885i
$428$		0			0
$429$	2.15538	−	3.73323i	0.104063	−	0.180242i
$430$		0			0
$431$	0.804757	+	1.39388i	0.0387638	+	0.0671408i	0.884756	−	0.466054i	$-0.154325\pi$
$431$	0.804757	+	1.39388i	0.0387638	+	0.0671408i	−0.845993	+	0.533195i	$0.820991\pi$
$432$		0			0
$433$	31.6124			1.51920			0.759598	−	0.650393i	$-0.225396\pi$
$433$	31.6124			1.51920			0.759598	+	0.650393i	$0.225396\pi$
$434$		0			0
$435$	2.22206			0.106540
$436$		0			0
$437$	−6.04809	−	10.4756i	−0.289319	−	0.501116i
$438$		0			0
$439$	−7.71812	+	13.3682i	−0.368366	+	0.638028i	−0.989310	−	0.145826i	$-0.953416\pi$
$439$	−7.71812	+	13.3682i	−0.368366	+	0.638028i	0.620944	+	0.783855i	$0.286749\pi$
$440$		0			0
$441$	−2.97331	−	8.68021i	−0.141586	−	0.413343i
$442$		0			0
$443$	10.5747	−	18.3159i	0.502418	−	0.870214i	−0.497578	−	0.867419i	$-0.665777\pi$
$443$	10.5747	−	18.3159i	0.502418	−	0.870214i	0.999996	−	0.00279481i	$-0.000889618\pi$
$444$		0			0
$445$	−1.69089	−	2.92870i	−0.0801558	−	0.138834i
$446$		0			0
$447$	−29.2977			−1.38573
$448$		0			0
$449$	8.51597			0.401894			0.200947	−	0.979602i	$-0.435598\pi$
$449$	8.51597			0.401894			0.200947	+	0.979602i	$0.435598\pi$
$450$		0			0
$451$	−5.71386	−	9.89670i	−0.269055	−	0.466018i
$452$		0			0
$453$	8.38409	−	14.5217i	0.393919	−	0.682288i
$454$		0			0
$455$	2.11591	+	0.205448i	0.0991953	+	0.00963153i
$456$		0			0
$457$	0.945385	−	1.63746i	0.0442233	−	0.0765969i	−0.843067	−	0.537809i	$-0.819252\pi$
$457$	0.945385	−	1.63746i	0.0442233	−	0.0765969i	0.887290	+	0.461212i	$0.152585\pi$
$458$		0			0
$459$	12.3468	+	21.3854i	0.576301	+	0.998183i
$460$		0			0
$461$	−27.9996			−1.30407			−0.652036	−	0.758188i	$-0.726085\pi$
$461$	−27.9996			−1.30407			−0.652036	+	0.758188i	$0.726085\pi$
$462$		0			0
$463$	36.4269			1.69290			0.846452	−	0.532465i	$-0.178734\pi$
$463$	36.4269			1.69290			0.846452	+	0.532465i	$0.178734\pi$
$464$		0			0
$465$	−2.95004	−	5.10961i	−0.136805	−	0.236953i
$466$		0			0
$467$	2.68508	−	4.65069i	0.124250	−	0.215208i	−0.797189	−	0.603730i	$-0.793681\pi$
$467$	2.68508	−	4.65069i	0.124250	−	0.215208i	0.921440	+	0.388521i	$0.127014\pi$
$468$		0			0
$469$	−8.46575	+	11.8485i	−0.390912	+	0.547112i
$470$		0			0
$471$	−3.16006	+	5.47339i	−0.145608	+	0.252200i
$472$		0			0
$473$	−0.461881	−	0.800002i	−0.0212373	−	0.0367841i
$474$		0			0
$475$	−40.0956			−1.83971
$476$		0			0
$477$	−5.08541			−0.232845
$478$		0			0
$479$	−1.64677	−	2.85228i	−0.0752426	−	0.130324i	0.825949	−	0.563745i	$-0.190640\pi$
$479$	−1.64677	−	2.85228i	−0.0752426	−	0.130324i	−0.901192	+	0.433421i	$0.857306\pi$
$480$		0			0
$481$	4.95597	−	8.58400i	0.225973	−	0.391397i
$482$		0			0
$483$	3.32739	+	7.31680i	0.151401	+	0.332926i
$484$		0			0
$485$	0.475471	−	0.823541i	0.0215900	−	0.0373951i
$486$		0			0
$487$	−3.81086	−	6.60060i	−0.172686	−	0.299102i	0.766672	−	0.642039i	$-0.221911\pi$
$487$	−3.81086	−	6.60060i	−0.172686	−	0.299102i	−0.939358	+	0.342938i	$0.888578\pi$
$488$		0			0
$489$	−31.8121			−1.43859
$490$		0			0
$491$	28.1454			1.27019			0.635093	−	0.772436i	$-0.280962\pi$
$491$	28.1454			1.27019			0.635093	+	0.772436i	$0.280962\pi$
$492$		0			0
$493$	−9.73549	−	16.8624i	−0.438464	−	0.759442i
$494$		0			0
$495$	−0.253631	+	0.439301i	−0.0113999	+	0.0197451i
$496$		0			0
$497$	−7.71135	−	16.9570i	−0.345901	−	0.760623i
$498$		0			0
$499$	−18.2897	+	31.6787i	−0.818760	+	1.41813i	0.0878365	+	0.996135i	$0.472005\pi$
$499$	−18.2897	+	31.6787i	−0.818760	+	1.41813i	−0.906596	+	0.421999i	$0.861329\pi$
$500$		0			0
$501$	24.6003	+	42.6089i	1.09906	+	1.90363i
$502$		0			0
$503$	41.2246			1.83812			0.919058	−	0.394123i	$-0.128952\pi$
$503$	41.2246			1.83812			0.919058	+	0.394123i	$0.128952\pi$
$504$		0			0
$505$	−0.876248			−0.0389925
$506$		0			0
$507$	−9.02046	−	15.6239i	−0.400613	−	0.693882i
$508$		0			0
$509$	−3.00416	+	5.20336i	−0.133157	+	0.230635i	−0.924892	−	0.380230i	$-0.875845\pi$
$509$	−3.00416	+	5.20336i	−0.133157	+	0.230635i	0.791735	+	0.610865i	$0.209178\pi$
$510$		0			0
$511$	−7.20337	+	10.0817i	−0.318658	+	0.445987i
$512$		0			0
$513$	−14.4968	+	25.1092i	−0.640049	+	1.10860i
$514$		0			0
$515$	−0.220830	−	0.382489i	−0.00973094	−	0.0168545i
$516$		0			0
$517$	10.8122			0.475520
$518$		0			0
$519$	44.8970			1.97076
$520$		0			0
$521$	−0.183626	−	0.318050i	−0.00804481	−	0.0139340i	0.861975	−	0.506951i	$-0.169227\pi$
$521$	−0.183626	−	0.318050i	−0.00804481	−	0.0139340i	−0.870020	+	0.493017i	$0.835894\pi$
$522$		0			0
$523$	18.4763	−	32.0020i	0.807914	−	1.39935i	−0.106392	−	0.994324i	$-0.533930\pi$
$523$	18.4763	−	32.0020i	0.807914	−	1.39935i	0.914306	−	0.405024i	$-0.132737\pi$
$524$		0			0
$525$	26.5186	+	2.57487i	1.15737	+	0.112377i
$526$		0			0
$527$	−25.8499	+	44.7734i	−1.12604	+	1.95036i
$528$		0			0
$529$	10.4295	+	18.0644i	0.453455	+	0.785408i
$530$		0			0
$531$	12.4539			0.540452
$532$		0			0
$533$	23.7267			1.02772
$534$		0			0
$535$	1.72610	+	2.98969i	0.0746258	+	0.129256i
$536$		0			0
$537$	−21.1275	+	36.5938i	−0.911717	+	1.57914i
$538$		0			0
$539$	6.86924	+	1.34666i	0.295879	+	0.0580046i
$540$		0			0
$541$	−21.4532	+	37.1580i	−0.922344	+	1.59755i	−0.126565	+	0.991958i	$0.540395\pi$
$541$	−21.4532	+	37.1580i	−0.922344	+	1.59755i	−0.795779	+	0.605588i	$0.792938\pi$
$542$		0			0
$543$	3.27244	+	5.66804i	0.140434	+	0.243239i
$544$		0			0
$545$	7.76916			0.332794
$546$		0			0
$547$	−8.87451			−0.379447			−0.189723	−	0.981838i	$-0.560759\pi$
$547$	−8.87451			−0.379447			−0.189723	+	0.981838i	$0.560759\pi$
$548$		0			0
$549$	5.97902	+	10.3560i	0.255178	+	0.441982i
$550$		0			0
$551$	11.4307	−	19.7986i	0.486965	−	0.843449i
$552$		0			0
$553$	−42.9593	−	4.17121i	−1.82682	−	0.177378i
$554$		0			0
$555$	−1.91795	+	3.32199i	−0.0814125	+	0.141011i
$556$		0			0
$557$	6.61000	+	11.4489i	0.280075	+	0.485104i	0.971403	−	0.237437i	$-0.0763074\pi$
$557$	6.61000	+	11.4489i	0.280075	+	0.485104i	−0.691328	+	0.722541i	$0.742974\pi$
$558$		0			0
$559$	1.91795			0.0811207
$560$		0			0
$561$	14.6182			0.617182
$562$		0			0
$563$	5.54499	+	9.60420i	0.233693	+	0.404769i	0.958892	−	0.283771i	$-0.0915855\pi$
$563$	5.54499	+	9.60420i	0.233693	+	0.404769i	−0.725199	+	0.688540i	$0.758252\pi$
$564$		0			0
$565$	0.400588	−	0.693839i	0.0168529	−	0.0291900i
$566$		0			0
$567$	17.2488	−	24.1410i	0.724379	−	1.01383i
$568$		0			0
$569$	−8.07459	+	13.9856i	−0.338504	+	0.586307i	−0.984152	−	0.177329i	$-0.943254\pi$
$569$	−8.07459	+	13.9856i	−0.338504	+	0.586307i	0.645647	+	0.763636i	$0.276588\pi$
$570$		0			0
$571$	−17.8903	−	30.9870i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$571$	−17.8903	−	30.9870i	−0.748687	−	1.29676i	0.199766	−	0.979844i	$-0.435982\pi$
$572$		0			0
$573$	32.5117			1.35820
$574$		0			0
$575$	−7.09703			−0.295967
$576$		0			0
$577$	−12.4603	−	21.5819i	−0.518730	−	0.898467i	−0.999763	−	0.0217646i	$-0.993072\pi$
$577$	−12.4603	−	21.5819i	−0.518730	−	0.898467i	0.481033	−	0.876703i	$-0.340262\pi$
$578$		0			0
$579$	4.25963	−	7.37790i	0.177024	−	0.306615i
$580$		0			0
$581$	12.9401	+	28.4547i	0.536844	+	1.18050i
$582$		0			0
$583$	1.93987	−	3.35995i	0.0803411	−	0.139155i
$584$		0			0
$585$	−0.526598	−	0.912094i	−0.0217721	−	0.0377104i
$586$		0			0
$587$	16.5752			0.684131			0.342065	−	0.939676i	$-0.388874\pi$
$587$	16.5752			0.684131			0.342065	+	0.939676i	$0.388874\pi$
$588$		0			0
$589$	−60.7024			−2.50120
$590$		0			0
$591$	−1.23046	−	2.13121i	−0.0506142	−	0.0876663i
$592$		0			0
$593$	−3.91724	+	6.78485i	−0.160862	+	0.278620i	−0.935178	−	0.354178i	$-0.884761\pi$
$593$	−3.91724	+	6.78485i	−0.160862	+	0.278620i	0.774316	+	0.632799i	$0.218094\pi$
$594$		0			0
$595$	2.98427	+	6.56230i	0.122343	+	0.269028i
$596$		0			0
$597$	−10.8369	+	18.7700i	−0.443524	+	0.768205i
$598$		0			0
$599$	−16.5816	−	28.7201i	−0.677504	−	1.17347i	−0.975730	−	0.218976i	$-0.929728\pi$
$599$	−16.5816	−	28.7201i	−0.677504	−	1.17347i	0.298226	−	0.954495i	$-0.403605\pi$
$600$		0			0
$601$	−2.23994			−0.0913690			−0.0456845	−	0.998956i	$-0.514547\pi$
$601$	−2.23994			−0.0913690			−0.0456845	+	0.998956i	$0.514547\pi$
$602$		0			0
$603$	7.21438			0.293792
$604$		0			0
$605$	−0.193499	−	0.335150i	−0.00786685	−	0.0136258i
$606$		0			0
$607$	−16.7081	+	28.9392i	−0.678159	+	1.17461i	0.297376	+	0.954760i	$0.403889\pi$
$607$	−16.7081	+	28.9392i	−0.678159	+	1.17461i	−0.975535	+	0.219845i	$0.929445\pi$
$608$		0			0
$609$	−8.83155	+	12.3604i	−0.357872	+	0.500870i
$610$		0			0
$611$	−11.2244	+	19.4412i	−0.454089	+	0.786505i
$612$		0			0
$613$	2.88574	+	4.99825i	0.116554	+	0.201877i	0.918400	−	0.395654i	$-0.129482\pi$
$613$	2.88574	+	4.99825i	0.116554	+	0.201877i	−0.801846	+	0.597531i	$0.796149\pi$
$614$		0			0
$615$	−9.18217			−0.370261
$616$		0			0
$617$	24.6485			0.992312			0.496156	−	0.868233i	$-0.334744\pi$
$617$	24.6485			0.992312			0.496156	+	0.868233i	$0.334744\pi$
$618$		0			0
$619$	−9.19921	−	15.9335i	−0.369747	−	0.640421i	0.619779	−	0.784777i	$-0.287222\pi$
$619$	−9.19921	−	15.9335i	−0.369747	−	0.640421i	−0.989526	+	0.144356i	$0.953889\pi$
$620$		0			0
$621$	−2.56597	+	4.44440i	−0.102969	+	0.178348i
$622$		0			0
$623$	23.0116	+	2.23435i	0.921942	+	0.0895175i
$624$		0			0
$625$	−11.3880	+	19.7245i	−0.455518	+	0.788981i
$626$		0			0
$627$	8.58185	+	14.8642i	0.342726	+	0.593619i
$628$		0			0
$629$	33.6124			1.34021
$630$		0			0
$631$	−5.60971			−0.223319			−0.111659	−	0.993747i	$-0.535617\pi$
$631$	−5.60971			−0.223319			−0.111659	+	0.993747i	$0.535617\pi$
$632$		0			0
$633$	−7.99400	−	13.8460i	−0.317733	−	0.550329i
$634$		0			0
$635$	2.43426	−	4.21625i	0.0966005	−	0.167317i
$636$		0			0
$637$	−9.55248	+	10.9534i	−0.378483	+	0.433990i
$638$		0			0
$639$	−4.61436	+	7.99230i	−0.182541	+	0.316170i
$640$		0			0
$641$	1.61455	+	2.79649i	0.0637711	+	0.110455i	0.896148	−	0.443755i	$-0.146354\pi$
$641$	1.61455	+	2.79649i	0.0637711	+	0.110455i	−0.832377	+	0.554210i	$0.813021\pi$
$642$		0			0
$643$	31.1280			1.22757			0.613784	−	0.789474i	$-0.289646\pi$
$643$	31.1280			1.22757			0.613784	+	0.789474i	$0.289646\pi$
$644$		0			0
$645$	−0.742243			−0.0292258
$646$		0			0
$647$	13.3897	+	23.1916i	0.526404	+	0.911758i	0.999527	+	0.0307615i	$0.00979323\pi$
$647$	13.3897	+	23.1916i	0.526404	+	0.911758i	−0.473123	+	0.880996i	$0.656873\pi$
$648$		0			0
$649$	−4.75063	+	8.22833i	−0.186478	+	0.322990i
$650$		0			0
$651$	40.1477	+	3.89820i	1.57351	+	0.152783i
$652$		0			0
$653$	−21.4525	+	37.1569i	−0.839503	+	1.45406i	0.0508080	+	0.998708i	$0.483820\pi$
$653$	−21.4525	+	37.1569i	−0.839503	+	1.45406i	−0.890311	+	0.455353i	$0.849513\pi$
$654$		0			0
$655$	1.30389	+	2.25840i	0.0509472	+	0.0882431i
$656$		0			0
$657$	6.13860			0.239490
$658$		0			0
$659$	31.1467			1.21330			0.606651	−	0.794968i	$-0.292513\pi$
$659$	31.1467			1.21330			0.606651	+	0.794968i	$0.292513\pi$
$660$		0			0
$661$	−8.80669	−	15.2536i	−0.342541	−	0.593298i	0.642363	−	0.766400i	$-0.277954\pi$
$661$	−8.80669	−	15.2536i	−0.342541	−	0.593298i	−0.984904	+	0.173103i	$0.944621\pi$
$662$		0			0
$663$	−15.1755	+	26.2847i	−0.589366	+	1.02081i
$664$		0			0
$665$	−4.92076	+	6.88699i	−0.190819	+	0.267066i
$666$		0			0
$667$	2.02327	−	3.50441i	0.0783414	−	0.135691i
$668$		0			0
$669$	−2.59941	−	4.50231i	−0.100499	−	0.174070i
$670$		0			0
$671$	−9.12297			−0.352188
$672$		0			0
$673$	46.3574			1.78694			0.893472	−	0.449118i	$-0.148262\pi$
$673$	46.3574			1.78694			0.893472	+	0.449118i	$0.148262\pi$
$674$		0			0
$675$	8.50552	+	14.7320i	0.327378	+	0.567034i
$676$		0			0
$677$	22.0981	−	38.2749i	0.849297	−	1.47103i	−0.0325394	−	0.999470i	$-0.510359\pi$
$677$	22.0981	−	38.2749i	0.849297	−	1.47103i	0.881837	−	0.471555i	$-0.156307\pi$
$678$		0			0
$679$	2.69128	+	5.91802i	0.103282	+	0.227113i
$680$		0			0
$681$	14.7771	−	25.5947i	0.566261	−	0.980792i
$682$		0			0
$683$	9.22532	+	15.9787i	0.352997	+	0.611409i	0.986773	−	0.162108i	$-0.0518292\pi$
$683$	9.22532	+	15.9787i	0.352997	+	0.611409i	−0.633776	+	0.773517i	$0.718496\pi$
$684$		0			0
$685$	−3.70654			−0.141620
$686$		0			0
$687$	−24.1963			−0.923147
$688$		0			0
$689$	4.02763	+	6.97605i	0.153440	+	0.265766i
$690$		0			0
$691$	22.1652	−	38.3912i	0.843203	−	1.46047i	−0.0439689	−	0.999033i	$-0.514000\pi$
$691$	22.1652	−	38.3912i	0.843203	−	1.46047i	0.887172	−	0.461438i	$-0.152666\pi$
$692$		0			0
$693$	−1.43561	−	3.15685i	−0.0545343	−	0.119919i
$694$		0			0
$695$	−1.72155	+	2.98182i	−0.0653022	+	0.113107i
$696$		0			0
$697$	40.2298	+	69.6800i	1.52381	+	2.63932i
$698$		0			0
$699$	−9.34085			−0.353304
$700$		0			0
$701$	18.5447			0.700423			0.350212	−	0.936671i	$-0.386110\pi$
$701$	18.5447			0.700423			0.350212	+	0.936671i	$0.386110\pi$
$702$		0			0
$703$	19.7327	+	34.1780i	0.744232	+	1.28905i
$704$		0			0
$705$	4.34380	−	7.52368i	0.163597	−	0.283358i
$706$		0			0
$707$	3.48264	−	4.87422i	0.130978	−	0.183314i
$708$		0			0
$709$	6.65050	−	11.5190i	0.249765	−	0.432605i	−0.713696	−	0.700456i	$-0.752980\pi$
$709$	6.65050	−	11.5190i	0.249765	−	0.432605i	0.963460	+	0.267851i	$0.0863134\pi$
$710$		0			0
$711$	10.6915	+	18.5183i	0.400964	+	0.694489i
$712$		0			0
$713$	−10.7445			−0.402384
$714$		0			0
$715$	0.803499			0.0300492
$716$		0			0
$717$	13.2573	+	22.9623i	0.495103	+	0.857543i
$718$		0			0
$719$	−1.08175	+	1.87365i	−0.0403426	+	0.0698755i	−0.885492	−	0.464655i	$-0.846178\pi$
$719$	−1.08175	+	1.87365i	−0.0403426	+	0.0698755i	0.845149	+	0.534531i	$0.179512\pi$
$720$		0			0
$721$	3.00533	+	0.291807i	0.111924	+	0.0108675i
$722$		0			0
$723$	24.7594	−	42.8845i	0.920811	−	1.59489i
$724$		0			0
$725$	−6.70660	−	11.6162i	−0.249077	−	0.431414i
$726$		0			0
$727$	25.7584			0.955327			0.477664	−	0.878543i	$-0.341484\pi$
$727$	25.7584			0.955327			0.477664	+	0.878543i	$0.341484\pi$
$728$		0			0
$729$	7.14660			0.264689
$730$		0			0
$731$	3.25198	+	5.63260i	0.120279	+	0.208329i
$732$		0			0
$733$	2.41611	−	4.18483i	0.0892411	−	0.154570i	−0.817949	−	0.575290i	$-0.804889\pi$
$733$	2.41611	−	4.18483i	0.0892411	−	0.154570i	0.907191	+	0.420720i	$0.138223\pi$
$734$		0			0
$735$	3.69679	−	4.23895i	0.136358	−	0.156356i
$736$		0			0
$737$	−2.75198	+	4.76657i	−0.101371	+	0.175579i
$738$		0			0
$739$	−12.6721	−	21.9488i	−0.466152	−	0.807398i	0.533101	−	0.846052i	$-0.321027\pi$
$739$	−12.6721	−	21.9488i	−0.466152	−	0.807398i	−0.999253	+	0.0386533i	$0.987693\pi$
$740$		0			0
$741$	−35.6359			−1.30912
$742$		0			0
$743$	−29.0605			−1.06613			−0.533063	−	0.846076i	$-0.678959\pi$
$743$	−29.0605			−1.06613			−0.533063	+	0.846076i	$0.678959\pi$
$744$		0			0
$745$	−2.73046	−	4.72929i	−0.100036	−	0.173268i
$746$		0			0
$747$	7.74314	−	13.4115i	0.283307	−	0.490701i
$748$		0			0
$749$	−23.4909	−	2.28088i	−0.858337	−	0.0833417i
$750$		0			0
$751$	10.2020	−	17.6704i	0.372277	−	0.644803i	−0.617639	−	0.786462i	$-0.711911\pi$
$751$	10.2020	−	17.6704i	0.372277	−	0.644803i	0.989915	+	0.141660i	$0.0452438\pi$
$752$		0			0
$753$	12.4971	+	21.6456i	0.455419	+	0.788810i
$754$		0			0
$755$	3.12549			0.113748
$756$		0			0
$757$	14.4739			0.526062			0.263031	−	0.964787i	$-0.415278\pi$
$757$	14.4739			0.526062			0.263031	+	0.964787i	$0.415278\pi$
$758$		0			0
$759$	1.51901	+	2.63100i	0.0551366	+	0.0954994i
$760$		0			0
$761$	−13.2626	+	22.9714i	−0.480768	+	0.832714i	−0.999756	−	0.0220668i	$-0.992975\pi$
$761$	−13.2626	+	22.9714i	−0.480768	+	0.832714i	0.518989	+	0.854781i	$0.326309\pi$
$762$		0			0
$763$	−30.8784	+	43.2168i	−1.11787	+	1.56455i
$764$		0			0
$765$	1.78575	−	3.09300i	0.0645638	−	0.111828i
$766$		0			0
$767$	−9.86343	−	17.0840i	−0.356148	−	0.616866i
$768$		0			0
$769$	20.2875			0.731584			0.365792	−	0.930697i	$-0.380798\pi$
$769$	20.2875			0.731584			0.365792	+	0.930697i	$0.380798\pi$
$770$		0			0
$771$	5.45014			0.196282
$772$		0			0
$773$	4.04861	+	7.01240i	0.145618	+	0.252218i	0.929603	−	0.368561i	$-0.120149\pi$
$773$	4.04861	+	7.01240i	0.145618	+	0.252218i	−0.783985	+	0.620780i	$0.786816\pi$
$774$		0			0
$775$	−17.8076	+	30.8436i	−0.639666	+	1.10793i
$776$		0			0
$777$	−10.8560	−	23.8720i	−0.389458	−	0.856404i
$778$		0			0
$779$	−47.2350	+	81.8134i	−1.69237	+	2.93127i
$780$		0			0
$781$	−3.52036	−	6.09745i	−0.125969	−	0.218184i
$782$		0			0
$783$	−9.69925			−0.346623
$784$		0			0
$785$	−1.17803			−0.0420457
$786$		0			0
$787$	6.48515	+	11.2326i	0.231171	+	0.400399i	0.958153	−	0.286257i	$-0.0924111\pi$
$787$	6.48515	+	11.2326i	0.231171	+	0.400399i	−0.726982	+	0.686656i	$0.759078\pi$
$788$		0			0
$789$	1.54703	−	2.67953i	0.0550757	−	0.0953939i
$790$		0			0
$791$	2.26742	+	4.98597i	0.0806202	+	0.177281i
$792$		0			0
$793$	9.47073	−	16.4038i	0.336315	−	0.582515i
$794$		0			0
$795$	−1.55868	−	2.69972i	−0.0552808	−	0.0957491i
$796$		0			0
$797$	−5.68131			−0.201242			−0.100621	−	0.994925i	$-0.532083\pi$
$797$	−5.68131			−0.201242			−0.100621	+	0.994925i	$0.532083\pi$
$798$		0			0
$799$	−76.1258			−2.69314
$800$		0			0
$801$	−5.72703	−	9.91951i	−0.202355	−	0.350489i
$802$		0			0
$803$	−2.34162	+	4.05580i	−0.0826339	+	0.143126i
$804$		0			0
$805$	−0.870988	+	1.21902i	−0.0306983	+	0.0429647i
$806$		0			0
$807$	−2.91660	+	5.05169i	−0.102669	+	0.177828i
$808$		0			0
$809$	−25.3012	−	43.8230i	−0.889544	−	1.54074i	−0.840415	−	0.541943i	$-0.817689\pi$
$809$	−25.3012	−	43.8230i	−0.889544	−	1.54074i	−0.0491285	−	0.998792i	$-0.515644\pi$
$810$		0			0
$811$	9.44349			0.331606			0.165803	−	0.986159i	$-0.446978\pi$
$811$	9.44349			0.331606			0.165803	+	0.986159i	$0.446978\pi$
$812$		0			0
$813$	−39.2657			−1.37711
$814$		0			0
$815$	−2.96479	−	5.13516i	−0.103852	−	0.179877i
$816$		0			0
$817$	−3.81825	+	6.61340i	−0.133584	+	0.231374i
$818$		0			0
$819$	7.16658	+	0.695851i	0.250420	+	0.0243150i
$820$		0			0
$821$	5.89623	−	10.2126i	0.205780	−	0.356421i	−0.744601	−	0.667510i	$-0.767360\pi$
$821$	5.89623	−	10.2126i	0.205780	−	0.356421i	0.950381	+	0.311088i	$0.100694\pi$
$822$		0			0
$823$	−0.592733	−	1.02664i	−0.0206614	−	0.0357866i	0.855510	−	0.517787i	$-0.173244\pi$
$823$	−0.592733	−	1.02664i	−0.0206614	−	0.0357866i	−0.876171	+	0.482000i	$0.839911\pi$
$824$		0			0
$825$	10.0702			0.350601
$826$		0			0
$827$	−13.7617			−0.478542			−0.239271	−	0.970953i	$-0.576908\pi$
$827$	−13.7617			−0.478542			−0.239271	+	0.970953i	$0.576908\pi$
$828$		0			0
$829$	−25.6603	−	44.4450i	−0.891219	−	1.54364i	−0.838415	−	0.545032i	$-0.816517\pi$
$829$	−25.6603	−	44.4450i	−0.891219	−	1.54364i	−0.0528042	−	0.998605i	$-0.516816\pi$
$830$		0			0
$831$	21.1098	−	36.5632i	0.732290	−	1.26836i
$832$		0			0
$833$	−48.3645	−	9.48145i	−1.67573	−	0.328513i
$834$		0			0
$835$	−4.58534	+	7.94204i	−0.158682	+	0.274846i
$836$		0			0
$837$	12.8769	+	22.3034i	0.445089	+	0.770917i
$838$		0			0
$839$	−50.1033			−1.72976			−0.864879	−	0.501980i	$-0.832605\pi$
$839$	−50.1033			−1.72976			−0.864879	+	0.501980i	$0.832605\pi$
$840$		0			0
$841$	−21.3521			−0.736281
$842$		0			0
$843$	5.57727	+	9.66011i	0.192091	+	0.332712i
$844$		0			0
$845$	1.68136	−	2.91220i	0.0578405	−	0.100183i
$846$		0			0
$847$	2.63337	+	0.255691i	0.0904836	+	0.00878565i
$848$		0			0
$849$	10.1405	−	17.5639i	0.348022	−	0.602792i
$850$		0			0
$851$	3.49274	+	6.04960i	0.119730	+	0.207378i
$852$		0			0
$853$	49.3889			1.69104			0.845522	−	0.533940i	$-0.179289\pi$
$853$	49.3889			1.69104			0.845522	+	0.533940i	$0.179289\pi$
$854$		0			0
$855$	4.19340			0.143411
$856$		0			0
$857$	15.6986	+	27.1908i	0.536255	+	0.928821i	0.999101	+	0.0423822i	$0.0134947\pi$
$857$	15.6986	+	27.1908i	0.536255	+	0.928821i	−0.462847	+	0.886438i	$0.653172\pi$
$858$		0			0
$859$	10.1933	−	17.6553i	0.347791	−	0.602392i	−0.638066	−	0.769982i	$-0.720265\pi$
$859$	10.1933	−	17.6553i	0.347791	−	0.602392i	0.985857	+	0.167590i	$0.0535986\pi$
$860$		0			0
$861$	36.4944	−	51.0768i	1.24373	−	1.74069i
$862$		0			0
$863$	−4.53647	+	7.85740i	−0.154423	+	0.267469i	−0.932849	−	0.360268i	$-0.882685\pi$
$863$	−4.53647	+	7.85740i	−0.154423	+	0.267469i	0.778426	+	0.627737i	$0.216019\pi$
$864$		0			0
$865$	4.18426	+	7.24736i	0.142269	+	0.246418i
$866$		0			0
$867$	−67.6269			−2.29673
$868$		0			0
$869$	−16.3135			−0.553396
$870$		0			0
$871$	−5.71377	−	9.89654i	−0.193604	−	0.335331i
$872$		0			0
$873$	1.61042	−	2.78933i	0.0545045	−	0.0944045i
$874$		0			0
$875$	4.17511	+	9.18090i	0.141144	+	0.310371i
$876$		0			0
$877$	13.0936	−	22.6788i	0.442139	−	0.765808i	−0.555709	−	0.831377i	$-0.687553\pi$
$877$	13.0936	−	22.6788i	0.442139	−	0.765808i	0.997848	+	0.0655692i	$0.0208863\pi$
$878$		0			0
$879$	−17.3703	−	30.0862i	−0.585886	−	1.01478i
$880$		0			0
$881$	11.2192			0.377985			0.188993	−	0.981979i	$-0.439478\pi$
$881$	11.2192			0.377985			0.188993	+	0.981979i	$0.439478\pi$
$882$		0			0
$883$	7.99321			0.268993			0.134497	−	0.990914i	$-0.457058\pi$
$883$	7.99321			0.268993			0.134497	+	0.990914i	$0.457058\pi$
$884$		0			0
$885$	3.81713	+	6.61146i	0.128311	+	0.222242i
$886$		0			0
$887$	−14.2698	+	24.7161i	−0.479134	+	0.829885i	−0.999714	−	0.0239286i	$-0.992383\pi$
$887$	−14.2698	+	24.7161i	−0.479134	+	0.829885i	0.520580	+	0.853813i	$0.325716\pi$
$888$		0			0
$889$	13.7784	+	30.2983i	0.462114	+	1.01617i
$890$		0			0
$891$	5.60709	−	9.71177i	0.187845	−	0.325357i
$892$		0			0
$893$	−44.6908	−	77.4068i	−1.49552	−	2.59032i
$894$		0			0
$895$	−7.87606			−0.263268
$896$		0			0
$897$	−6.30766			−0.210606
$898$		0			0
$899$	−10.1534	−	17.5862i	−0.338635	−	0.586533i
$900$		0			0
$901$	−13.6581	+	23.6565i	−0.455017	+	0.788112i
$902$		0			0
$903$	2.95004	−	4.12881i	0.0981710	−	0.137398i
$904$		0			0
$905$	−0.609963	+	1.05649i	−0.0202759	+	0.0351188i
$906$		0			0
$907$	−15.4695	−	26.7939i	−0.513655	−	0.889677i	−0.999875	−	0.0158402i	$-0.994958\pi$
$907$	−15.4695	−	26.7939i	−0.513655	−	0.889677i	0.486219	−	0.873837i	$-0.338376\pi$
$908$		0			0
$909$	−2.96785			−0.0984373
$910$		0			0
$911$	31.1124			1.03080			0.515400	−	0.856949i	$-0.327643\pi$
$911$	31.1124			1.03080			0.515400	+	0.856949i	$0.327643\pi$
$912$		0			0
$913$	5.90736	+	10.2319i	0.195505	+	0.338625i
$914$		0			0
$915$	−3.66515	+	6.34823i	−0.121166	+	0.209866i
$916$		0			0
$917$	−17.7449	−	1.72297i	−0.585989	−	0.0568975i
$918$		0			0
$919$	−9.99377	+	17.3097i	−0.329664	+	0.570995i	−0.982445	−	0.186552i	$-0.940269\pi$
$919$	−9.99377	+	17.3097i	−0.329664	+	0.570995i	0.652781	+	0.757547i	$0.273602\pi$
$920$		0			0
$921$	23.4043	+	40.5374i	0.771197	+	1.33575i
$922$		0			0
$923$	14.6182			0.481165
$924$		0			0
$925$	23.1550			0.761331
$926$		0			0
$927$	−0.747952	−	1.29549i	−0.0245660	−	0.0425495i
$928$		0			0
$929$	10.1300	−	17.5456i	0.332354	−	0.575653i	−0.650619	−	0.759404i	$-0.725491\pi$
$929$	10.1300	−	17.5456i	0.332354	−	0.575653i	0.982973	+	0.183751i	$0.0588239\pi$
$930$		0			0
$931$	−18.7521	−	54.7445i	−0.614576	−	1.79418i
$932$		0			0
$933$	23.3986	−	40.5276i	0.766037	−	1.32682i
$934$		0			0
$935$	1.36237	+	2.35970i	0.0445544	+	0.0771704i
$936$		0			0
$937$	−14.8320			−0.484539			−0.242269	−	0.970209i	$-0.577892\pi$
$937$	−14.8320			−0.484539			−0.242269	+	0.970209i	$0.577892\pi$
$938$		0			0
$939$	13.7358			0.448250
$940$		0			0
$941$	−17.2166	−	29.8200i	−0.561244	−	0.972103i	−0.997388	−	0.0722266i	$-0.976990\pi$
$941$	−17.2166	−	29.8200i	−0.561244	−	0.972103i	0.436144	−	0.899877i	$-0.356344\pi$
$942$		0			0
$943$	−8.36072	+	14.4812i	−0.272263	+	0.471573i
$944$		0			0
$945$	3.57428	+	0.347050i	0.116271	+	0.0112895i
$946$		0			0
$947$	6.07575	−	10.5235i	0.197435	−	0.341968i	−0.750261	−	0.661142i	$-0.770072\pi$
$947$	6.07575	−	10.5235i	0.197435	−	0.341968i	0.947696	+	0.319174i	$0.103405\pi$
$948$		0			0
$949$	−4.86175	−	8.42080i	−0.157819	−	0.273351i
$950$		0			0
$951$	10.6974			0.346886
$952$		0			0
$953$	0.0797258			0.00258257			0.00129129	−	0.999999i	$-0.499589\pi$
$953$	0.0797258			0.00258257			0.00129129	+	0.999999i	$0.499589\pi$
$954$		0			0
$955$	3.02999	+	5.24810i	0.0980482	+	0.169824i
$956$		0			0
$957$	−2.87089	+	4.97253i	−0.0928028	+	0.160739i
$958$		0			0
$959$	14.7316	−	20.6181i	0.475709	−	0.665792i
$960$		0			0
$961$	−11.4596	+	19.8486i	−0.369665	+	0.640278i
$962$		0			0
$963$	5.84630	+	10.1261i	0.188394	+	0.326309i
$964$		0			0
$965$	1.58794			0.0511176
$966$		0			0
$967$	−39.1037			−1.25749			−0.628745	−	0.777611i	$-0.716431\pi$
$967$	−39.1037			−1.25749			−0.628745	+	0.777611i	$0.716431\pi$
$968$		0			0
$969$	−60.4225	−	104.655i	−1.94105	−	3.36200i
$970$		0			0
$971$	−19.3988	+	33.5998i	−0.622539	+	1.07827i	0.366473	+	0.930429i	$0.380565\pi$
$971$	−19.3988	+	33.5998i	−0.622539	+	1.07827i	−0.989011	+	0.147840i	$0.952768\pi$
$972$		0			0
$973$	−9.74439	−	21.4275i	−0.312391	−	0.686935i
$974$		0			0
$975$	−10.4541	+	18.1070i	−0.334799	+	0.579889i
$976$		0			0
$977$	17.8596	+	30.9338i	0.571380	+	0.989659i	0.996425	+	0.0844866i	$0.0269250\pi$
$977$	17.8596	+	30.9338i	0.571380	+	0.989659i	−0.425045	+	0.905172i	$0.639742\pi$
$978$		0			0
$979$	8.73849			0.279283
$980$		0			0
$981$	26.3141			0.840145
$982$		0			0
$983$	−3.20386	−	5.54925i	−0.102187	−	0.176993i	0.810398	−	0.585879i	$-0.199251\pi$
$983$	−3.20386	−	5.54925i	−0.102187	−	0.176993i	−0.912586	+	0.408886i	$0.865917\pi$
$984$		0			0
$985$	0.229349	−	0.397245i	0.00730768	−	0.0126573i
$986$		0			0
$987$	24.5869	+	54.0657i	0.782610	+	1.72093i
$988$		0			0
$989$	−0.675841	+	1.17059i	−0.0214905	+	0.0372226i
$990$		0			0
$991$	−14.7256	−	25.5054i	−0.467773	−	0.810207i	0.531549	−	0.847028i	$-0.321610\pi$
$991$	−14.7256	−	25.5054i	−0.467773	−	0.810207i	−0.999322	+	0.0368206i	$0.988277\pi$
$992$		0			0
$993$	−3.17340			−0.100705
$994$		0			0
$995$	−4.03985			−0.128072
$996$		0			0
$997$	10.2881	+	17.8194i	0.325826	+	0.564347i	0.981679	−	0.190541i	$-0.0610242\pi$
$997$	10.2881	+	17.8194i	0.325826	+	0.564347i	−0.655853	+	0.754889i	$0.727691\pi$
$998$		0			0
$999$	8.37183	−	14.5004i	0.264873	−	0.458773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.n.177.4		8
4.3	odd	2		616.2.q.d.177.1	✓	8
7.2	even	3		8624.2.a.cz.1.1		4
7.4	even	3	inner	1232.2.q.n.529.4		8
7.5	odd	6		8624.2.a.cr.1.4		4
28.11	odd	6		616.2.q.d.529.1	yes	8
28.19	even	6		4312.2.a.bd.1.1		4
28.23	odd	6		4312.2.a.y.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.d.177.1	✓	8	4.3	odd	2
616.2.q.d.529.1	yes	8	28.11	odd	6
1232.2.q.n.177.4		8	1.1	even	1	trivial
1232.2.q.n.529.4		8	7.4	even	3	inner
4312.2.a.y.1.4		4	28.23	odd	6
4312.2.a.bd.1.1		4	28.19	even	6
8624.2.a.cr.1.4		4	7.5	odd	6
8624.2.a.cz.1.1		4	7.2	even	3

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03812 + 1.79807i) q^{3} +(-0.193499 + 0.335150i) q^{5} +(-1.09525 - 2.40841i) q^{7} +(-0.655380 + 1.13515i) q^{9} +O(q^{10})\)	\(q+(1.03812 + 1.79807i) q^{3} +(-0.193499 + 0.335150i) q^{5} +(-1.09525 - 2.40841i) q^{7} +(-0.655380 + 1.13515i) q^{9} +(-0.500000 - 0.866025i) q^{11} +2.07624 q^{13} -0.803499 q^{15} +(3.52036 + 6.09745i) q^{17} +(-4.13337 + 7.15920i) q^{19} +(3.19350 - 4.46955i) q^{21} +(-0.731617 + 1.26720i) q^{23} +(2.42512 + 4.20042i) q^{25} +3.50726 q^{27} -2.76548 q^{29} +(3.67149 + 6.35920i) q^{31} +(1.03812 - 1.79807i) q^{33} +(1.01911 + 0.0989519i) q^{35} +(2.38700 - 4.13440i) q^{37} +(2.15538 + 3.73323i) q^{39} +11.4277 q^{41} +0.923763 q^{43} +(-0.253631 - 0.439301i) q^{45} +(-5.40611 + 9.36365i) q^{47} +(-4.60086 + 5.27561i) q^{49} +(-7.30911 + 12.6598i) q^{51} +(1.93987 + 3.35995i) q^{53} +0.386998 q^{55} -17.1637 q^{57} +(-4.75063 - 8.22833i) q^{59} +(4.56149 - 7.90072i) q^{61} +(3.45171 + 0.335150i) q^{63} +(-0.401750 + 0.695851i) q^{65} +(-2.75198 - 4.76657i) q^{67} -3.03802 q^{69} +7.04073 q^{71} +(-2.34162 - 4.05580i) q^{73} +(-5.03512 + 8.72108i) q^{75} +(-1.53812 + 2.15272i) q^{77} +(8.15673 - 14.1279i) q^{79} +(5.60709 + 9.71177i) q^{81} -11.8147 q^{83} -2.72475 q^{85} +(-2.87089 - 4.97253i) q^{87} +(-4.36924 + 7.56775i) q^{89} +(-2.27400 - 5.00043i) q^{91} +(-7.62287 + 13.2032i) q^{93} +(-1.59960 - 2.77060i) q^{95} -2.45723 q^{97} +1.31076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more