LMFDB - Embedded newform 1344.2.bb.e.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(31,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))

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

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

chi := DirichletCharacter("1344.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bb (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 84x^{8} - 187x^{6} + 141x^{4} + 108x^{2} + 16 $ x^12 - 15x^10 + 84x^8 - 187x^6 + 141x^4 + 108*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.5
Root			$1.51496 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1344.31
Dual form			1344.2.bb.e.607.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-0.727452 - 1.25998i) q^{5} +(1.51496 - 2.16908i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(-0.727452 - 1.25998i) q^{5} +(1.51496 - 2.16908i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.12100 + 1.94163i) q^{11} +4.88325 q^{13} -1.45490i q^{15} +(-4.12398 - 2.38098i) q^{17} +(-0.393958 + 0.227452i) q^{19} +(2.39653 - 1.12100i) q^{21} +(4.62298 - 2.66908i) q^{23} +(1.44163 - 2.49697i) q^{25} +1.00000i q^{27} +1.22210i q^{29} +(-0.217093 + 0.376017i) q^{31} +(-1.94163 + 1.12100i) q^{33} +(-3.83506 - 0.330921i) q^{35} +(4.80634 - 2.77494i) q^{37} +(4.22902 + 2.44163i) q^{39} -6.05983i q^{41} +5.27191 q^{43} +(0.727452 - 1.25998i) q^{45} +(1.59307 + 2.75927i) q^{47} +(-2.40981 - 6.57212i) q^{49} +(-2.38098 - 4.12398i) q^{51} +(-9.06561 - 5.23403i) q^{53} +3.26189 q^{55} -0.454904 q^{57} +(7.82976 + 4.52051i) q^{59} +(-2.45490 - 4.25202i) q^{61} +(2.63596 + 0.227452i) q^{63} +(-3.55233 - 6.15282i) q^{65} +(-2.12601 + 3.68236i) q^{67} +5.33816 q^{69} -11.3382i q^{71} +(-11.6896 - 6.74899i) q^{73} +(2.49697 - 1.44163i) q^{75} +(2.51328 + 5.37302i) q^{77} +(10.5289 - 6.07889i) q^{79} +(-0.500000 + 0.866025i) q^{81} +15.0410i q^{83} +6.92820i q^{85} +(-0.611052 + 1.05837i) q^{87} +(13.7665 - 7.94810i) q^{89} +(7.39792 - 10.5922i) q^{91} +(-0.376017 + 0.217093i) q^{93} +(0.573172 + 0.330921i) q^{95} +10.7460i q^{97} -2.24200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^5 + 6 * q^9	$ 12 q - 6 q^{5} + 6 q^{9} - 12 q^{17} - 6 q^{21} - 12 q^{25} + 6 q^{33} + 12 q^{37} + 6 q^{45} - 18 q^{49} - 42 q^{53} - 24 q^{61} + 48 q^{65} - 36 q^{73} + 54 q^{77} - 6 q^{81} + 48 q^{89} - 42 q^{93}+O(q^{100}) $ 12 * q - 6 * q^5 + 6 * q^9 - 12 * q^17 - 6 * q^21 - 12 * q^25 + 6 * q^33 + 12 * q^37 + 6 * q^45 - 18 * q^49 - 42 * q^53 - 24 * q^61 + 48 * q^65 - 36 * q^73 + 54 * q^77 - 6 * q^81 + 48 * q^89 - 42 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−0.727452	−	1.25998i	−0.325326	−	0.563482i	0.656252	−	0.754542i	$-0.272141\pi$
$5$	−0.727452	−	1.25998i	−0.325326	−	0.563482i	−0.981578	+	0.191060i	$0.938808\pi$
$6$		0			0
$7$	1.51496	−	2.16908i	0.572600	−	0.819835i
$7$	1.51496	−	2.16908i	0.572600	−	0.819835i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.12100	+	1.94163i	−0.337994	+	0.585423i	−0.984055	−	0.177863i	$-0.943082\pi$
$11$	−1.12100	+	1.94163i	−0.337994	+	0.585423i	0.646061	+	0.763285i	$0.276415\pi$
$12$		0			0
$13$	4.88325			1.35437			0.677185	−	0.735812i	$-0.263199\pi$
$13$	4.88325			1.35437			0.677185	+	0.735812i	$0.263199\pi$
$14$		0			0
$15$		−	1.45490i		−	0.375655i
$16$		0			0
$17$	−4.12398	−	2.38098i	−1.00021	−	0.577473i	−0.0919016	−	0.995768i	$-0.529295\pi$
$17$	−4.12398	−	2.38098i	−1.00021	−	0.577473i	−0.908311	+	0.418295i	$0.862628\pi$
$18$		0			0
$19$	−0.393958	+	0.227452i	−0.0903803	+	0.0521811i	−0.544509	−	0.838755i	$-0.683284\pi$
$19$	−0.393958	+	0.227452i	−0.0903803	+	0.0521811i	0.454129	+	0.890936i	$0.349951\pi$
$20$		0			0
$21$	2.39653	−	1.12100i	0.522966	−	0.244622i
$22$		0			0
$23$	4.62298	−	2.66908i	0.963958	−	0.556541i	0.0665691	−	0.997782i	$-0.478795\pi$
$23$	4.62298	−	2.66908i	0.963958	−	0.556541i	0.897389	+	0.441240i	$0.145461\pi$
$24$		0			0
$25$	1.44163	−	2.49697i	0.288325	−	0.499394i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$			1.22210i			0.226939i	0.993541	+	0.113469i	$0.0361964\pi$
$29$			1.22210i			0.226939i	−0.993541	+	0.113469i	$0.963804\pi$
$30$		0			0
$31$	−0.217093	+	0.376017i	−0.0389911	+	0.0675346i	−0.884862	−	0.465852i	$-0.845748\pi$
$31$	−0.217093	+	0.376017i	−0.0389911	+	0.0675346i	0.845871	+	0.533387i	$0.179081\pi$
$32$		0			0
$33$	−1.94163	+	1.12100i	−0.337994	+	0.195141i
$34$		0			0
$35$	−3.83506	−	0.330921i	−0.648244	−	0.0559358i
$36$		0			0
$37$	4.80634	−	2.77494i	0.790157	−	0.456198i	−0.0498606	−	0.998756i	$-0.515878\pi$
$37$	4.80634	−	2.77494i	0.790157	−	0.456198i	0.840018	+	0.542559i	$0.182544\pi$
$38$		0			0
$39$	4.22902	+	2.44163i	0.677185	+	0.390973i
$40$		0			0
$41$		−	6.05983i		−	0.946386i	−0.880959	−	0.473193i	$-0.843101\pi$
$41$		−	6.05983i		−	0.946386i	0.880959	−	0.473193i	$-0.156899\pi$
$42$		0			0
$43$	5.27191			0.803959			0.401980	−	0.915649i	$-0.368322\pi$
$43$	5.27191			0.803959			0.401980	+	0.915649i	$0.368322\pi$
$44$		0			0
$45$	0.727452	−	1.25998i	0.108442	−	0.187827i
$46$		0			0
$47$	1.59307	+	2.75927i	0.232373	+	0.402481i	0.958506	−	0.285073i	$-0.0920178\pi$
$47$	1.59307	+	2.75927i	0.232373	+	0.402481i	−0.726133	+	0.687554i	$0.758684\pi$
$48$		0			0
$49$	−2.40981	−	6.57212i	−0.344258	−	0.938875i
$50$		0			0
$51$	−2.38098	−	4.12398i	−0.333404	−	0.577473i
$52$		0			0
$53$	−9.06561	−	5.23403i	−1.24526	−	0.718950i	−0.275098	−	0.961416i	$-0.588710\pi$
$53$	−9.06561	−	5.23403i	−1.24526	−	0.718950i	−0.970160	+	0.242467i	$0.922044\pi$
$54$		0			0
$55$	3.26189			0.439833
$56$		0			0
$57$	−0.454904			−0.0602535
$58$		0			0
$59$	7.82976	+	4.52051i	1.01935	+	0.588521i	0.913915	−	0.405906i	$-0.133044\pi$
$59$	7.82976	+	4.52051i	1.01935	+	0.588521i	0.105433	+	0.994426i	$0.466377\pi$
$60$		0			0
$61$	−2.45490	−	4.25202i	−0.314318	−	0.544415i	0.664974	−	0.746866i	$-0.268443\pi$
$61$	−2.45490	−	4.25202i	−0.314318	−	0.544415i	−0.979292	+	0.202451i	$0.935109\pi$
$62$		0			0
$63$	2.63596	+	0.227452i	0.332099	+	0.0286563i
$64$		0			0
$65$	−3.55233	−	6.15282i	−0.440613	−	0.763164i
$66$		0			0
$67$	−2.12601	+	3.68236i	−0.259733	+	0.449871i	−0.966170	−	0.257904i	$-0.916968\pi$
$67$	−2.12601	+	3.68236i	−0.259733	+	0.449871i	0.706437	+	0.707776i	$0.250301\pi$
$68$		0			0
$69$	5.33816			0.642639
$70$		0			0
$71$		−	11.3382i		−	1.34559i	−0.739828	−	0.672796i	$-0.765093\pi$
$71$		−	11.3382i		−	1.34559i	0.739828	−	0.672796i	$-0.234907\pi$
$72$		0			0
$73$	−11.6896	−	6.74899i	−1.36816	−	0.789910i	−0.377470	−	0.926022i	$-0.623206\pi$
$73$	−11.6896	−	6.74899i	−1.36816	−	0.789910i	−0.990693	+	0.136112i	$0.956539\pi$
$74$		0			0
$75$	2.49697	−	1.44163i	0.288325	−	0.166465i
$76$		0			0
$77$	2.51328	+	5.37302i	0.286415	+	0.612312i
$78$		0			0
$79$	10.5289	−	6.07889i	1.18460	−	0.683928i	0.227525	−	0.973772i	$-0.426937\pi$
$79$	10.5289	−	6.07889i	1.18460	−	0.683928i	0.957074	+	0.289844i	$0.0936035\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			15.0410i			1.65097i	0.564426	+	0.825484i	$0.309098\pi$
$83$			15.0410i			1.65097i	−0.564426	+	0.825484i	$0.690902\pi$
$84$		0			0
$85$			6.92820i			0.751469i
$86$		0			0
$87$	−0.611052	+	1.05837i	−0.0655116	+	0.113469i
$88$		0			0
$89$	13.7665	−	7.94810i	1.45925	−	0.842497i	0.460273	−	0.887778i	$-0.347752\pi$
$89$	13.7665	−	7.94810i	1.45925	−	0.842497i	0.998974	+	0.0452810i	$0.0144183\pi$
$90$		0			0
$91$	7.39792	−	10.5922i	0.775513	−	1.11036i
$92$		0			0
$93$	−0.376017	+	0.217093i	−0.0389911	+	0.0225115i
$94$		0			0
$95$	0.573172	+	0.330921i	0.0588062	+	0.0339518i
$96$		0			0
$97$			10.7460i			1.09109i	0.838080	+	0.545547i	$0.183678\pi$
$97$			10.7460i			1.09109i	−0.838080	+	0.545547i	$0.816322\pi$
$98$		0			0
$99$	−2.24200			−0.225329
$100$		0			0
$101$	0.0901918	−	0.156217i	0.00897442	−	0.0155442i	−0.861503	−	0.507752i	$-0.830477\pi$
$101$	0.0901918	−	0.156217i	0.00897442	−	0.0155442i	0.870478	+	0.492208i	$0.163810\pi$
$102$		0			0
$103$	−2.12601	−	3.68236i	−0.209482	−	0.362833i	0.742070	−	0.670323i	$-0.233844\pi$
$103$	−2.12601	−	3.68236i	−0.209482	−	0.362833i	−0.951551	+	0.307490i	$0.900511\pi$
$104$		0			0
$105$	−3.15580	−	2.20412i	−0.307975	−	0.215100i
$106$		0			0
$107$	9.71803	+	16.8321i	0.939477	+	1.62722i	0.766449	+	0.642305i	$0.222022\pi$
$107$	9.71803	+	16.8321i	0.939477	+	1.62722i	0.173029	+	0.984917i	$0.444645\pi$
$108$		0			0
$109$	9.57285	+	5.52689i	0.916912	+	0.529380i	0.882649	−	0.470033i	$-0.155758\pi$
$109$	9.57285	+	5.52689i	0.916912	+	0.529380i	0.0342637	+	0.999413i	$0.489091\pi$
$110$		0			0
$111$	5.54988			0.526772
$112$		0			0
$113$	−8.06758			−0.758934			−0.379467	−	0.925205i	$-0.623893\pi$
$113$	−8.06758			−0.758934			−0.379467	+	0.925205i	$0.623893\pi$
$114$		0			0
$115$	−6.72599	−	3.88325i	−0.627202	−	0.362115i
$116$		0			0
$117$	2.44163	+	4.22902i	0.225728	+	0.390973i
$118$		0			0
$119$	−11.4122	+	5.33816i	−1.04615	+	0.489348i
$120$		0			0
$121$	2.98672	+	5.17316i	0.271520	+	0.470287i
$122$		0			0
$123$	3.02991	−	5.24797i	0.273198	−	0.473193i
$124$		0			0
$125$	−11.4694			−1.02585
$126$		0			0
$127$			1.24797i			0.110739i	0.998466	+	0.0553696i	$0.0176337\pi$
$127$			1.24797i			0.110739i	−0.998466	+	0.0553696i	$0.982366\pi$
$128$		0			0
$129$	4.56561	+	2.63596i	0.401980	+	0.232083i
$130$		0			0
$131$	−4.73662	+	2.73469i	−0.413840	+	0.238931i	−0.692439	−	0.721477i	$-0.743464\pi$
$131$	−4.73662	+	2.73469i	−0.413840	+	0.238931i	0.278598	+	0.960408i	$0.410130\pi$
$132$		0			0
$133$	−0.103469	+	1.19911i	−0.00897189	+	0.103976i
$134$		0			0
$135$	1.25998	−	0.727452i	0.108442	−	0.0626091i
$136$		0			0
$137$	−4.54510	+	7.87234i	−0.388314	+	0.672579i	−0.992223	−	0.124474i	$-0.960276\pi$
$137$	−4.54510	+	7.87234i	−0.388314	+	0.672579i	0.603909	+	0.797053i	$0.293609\pi$
$138$		0			0
$139$			6.63529i			0.562798i	0.959591	+	0.281399i	$0.0907984\pi$
$139$			6.63529i			0.562798i	−0.959591	+	0.281399i	$0.909202\pi$
$140$		0			0
$141$			3.18613i			0.268321i
$142$		0			0
$143$	−5.47412	+	9.48146i	−0.457769	+	0.792879i
$144$		0			0
$145$	1.53983	−	0.889022i	0.127876	−	0.0738293i
$146$		0			0
$147$	1.19911	−	6.89653i	0.0989007	−	0.568816i
$148$		0			0
$149$	3.75203	−	2.16624i	0.307379	−	0.177465i	−0.338374	−	0.941012i	$-0.609877\pi$
$149$	3.75203	−	2.16624i	0.307379	−	0.177465i	0.645753	+	0.763547i	$0.276544\pi$
$150$		0			0
$151$	18.0073	+	10.3965i	1.46541	+	0.846058i	0.999253	−	0.0386418i	$-0.0123031\pi$
$151$	18.0073	+	10.3965i	1.46541	+	0.846058i	0.466162	+	0.884699i	$0.345636\pi$
$152$		0			0
$153$		−	4.76197i		−	0.384982i
$154$		0			0
$155$	0.631700			0.0507394
$156$		0			0
$157$	8.88325	−	15.3862i	0.708961	−	1.22796i	−0.256282	−	0.966602i	$-0.582498\pi$
$157$	8.88325	−	15.3862i	0.708961	−	1.22796i	0.965243	−	0.261354i	$-0.0841691\pi$
$158$		0			0
$159$	−5.23403	−	9.06561i	−0.415086	−	0.718950i
$160$		0			0
$161$	1.21417	−	14.0712i	0.0956904	−	1.10896i
$162$		0			0
$163$	−3.02991	−	5.24797i	−0.237321	−	0.411052i	0.722623	−	0.691242i	$-0.242936\pi$
$163$	−3.02991	−	5.24797i	−0.237321	−	0.411052i	−0.959945	+	0.280189i	$0.909603\pi$
$164$		0			0
$165$	2.82488	+	1.63095i	0.219917	+	0.126969i
$166$		0			0
$167$	−10.2659			−0.794396			−0.397198	−	0.917733i	$-0.630017\pi$
$167$	−10.2659			−0.794396			−0.397198	+	0.917733i	$0.630017\pi$
$168$		0			0
$169$	10.8462			0.834321
$170$		0			0
$171$	−0.393958	−	0.227452i	−0.0301268	−	0.0173937i
$172$		0			0
$173$	−8.66908	−	15.0153i	−0.659098	−	1.14159i	−0.980850	−	0.194767i	$-0.937605\pi$
$173$	−8.66908	−	15.0153i	−0.659098	−	1.14159i	0.321752	−	0.946824i	$-0.395728\pi$
$174$		0			0
$175$	−3.23212	−	6.90981i	−0.244326	−	0.522332i
$176$		0			0
$177$	4.52051	+	7.82976i	0.339783	+	0.588521i
$178$		0			0
$179$	−5.41090	+	9.37195i	−0.404429	+	0.700492i	−0.994255	−	0.107038i	$-0.965863\pi$
$179$	−5.41090	+	9.37195i	−0.404429	+	0.700492i	0.589825	+	0.807531i	$0.299197\pi$
$180$		0			0
$181$	−4.88325			−0.362969			−0.181485	−	0.983394i	$-0.558090\pi$
$181$	−4.88325			−0.362969			−0.181485	+	0.983394i	$0.558090\pi$
$182$		0			0
$183$		−	4.90981i		−	0.362943i
$184$		0			0
$185$	−6.99276	−	4.03727i	−0.514118	−	0.296826i
$186$		0			0
$187$	9.24596	−	5.33816i	0.676132	−	0.390365i
$188$		0			0
$189$	2.16908	+	1.51496i	0.157777	+	0.110197i
$190$		0			0
$191$	−13.7127	+	7.91705i	−0.992218	+	0.572857i	−0.905937	−	0.423414i	$-0.860832\pi$
$191$	−13.7127	+	7.91705i	−0.992218	+	0.572857i	−0.0862814	+	0.996271i	$0.527498\pi$
$192$		0			0
$193$	−8.92835	+	15.4644i	−0.642677	+	1.11315i	0.342156	+	0.939643i	$0.388843\pi$
$193$	−8.92835	+	15.4644i	−0.642677	+	1.11315i	−0.984833	+	0.173506i	$0.944491\pi$
$194$		0			0
$195$		−	7.10467i		−	0.508776i
$196$		0			0
$197$			11.6902i			0.832890i	0.909161	+	0.416445i	$0.136724\pi$
$197$			11.6902i			0.832890i	−0.909161	+	0.416445i	$0.863276\pi$
$198$		0			0
$199$	−9.68015	+	16.7665i	−0.686207	+	1.18855i	0.286848	+	0.957976i	$0.407392\pi$
$199$	−9.68015	+	16.7665i	−0.686207	+	1.18855i	−0.973056	+	0.230570i	$0.925941\pi$
$200$		0			0
$201$	−3.68236	+	2.12601i	−0.259733	+	0.149957i
$202$		0			0
$203$	2.65084	+	1.85144i	0.186052	+	0.129945i
$204$		0			0
$205$	−7.63529	+	4.40824i	−0.533272	+	0.307885i
$206$		0			0
$207$	4.62298	+	2.66908i	0.321319	+	0.185514i
$208$		0			0
$209$		−	1.01989i		−	0.0705475i
$210$		0			0
$211$	−22.6635			−1.56022			−0.780109	−	0.625643i	$-0.784837\pi$
$211$	−22.6635			−1.56022			−0.780109	+	0.625643i	$0.784837\pi$
$212$		0			0
$213$	5.66908	−	9.81913i	0.388439	−	0.672796i
$214$		0			0
$215$	−3.83506	−	6.64252i	−0.261549	−	0.453016i
$216$		0			0
$217$	0.486723	+	1.04054i	0.0330409	+	0.0706366i
$218$		0			0
$219$	−6.74899	−	11.6896i	−0.456054	−	0.789910i
$220$		0			0
$221$	−20.1385	−	11.6269i	−1.35466	−	0.782113i
$222$		0			0
$223$	−5.39367			−0.361187			−0.180593	−	0.983558i	$-0.557802\pi$
$223$	−5.39367			−0.361187			−0.180593	+	0.983558i	$0.557802\pi$
$224$		0			0
$225$	2.88325			0.192217
$226$		0			0
$227$	−25.5212	−	14.7347i	−1.69390	−	0.977976i	−0.951311	−	0.308232i	$-0.900263\pi$
$227$	−25.5212	−	14.7347i	−1.69390	−	0.977976i	−0.742592	−	0.669744i	$-0.766404\pi$
$228$		0			0
$229$	6.01328	+	10.4153i	0.397369	+	0.688262i	0.993400	−	0.114698i	$-0.0365901\pi$
$229$	6.01328	+	10.4153i	0.397369	+	0.688262i	−0.596032	+	0.802961i	$0.703257\pi$
$230$		0			0
$231$	−0.509947	+	5.90981i	−0.0335520	+	0.388837i
$232$		0			0
$233$	11.0072	+	19.0651i	0.721108	+	1.24900i	0.960556	+	0.278087i	$0.0897002\pi$
$233$	11.0072	+	19.0651i	0.721108	+	1.24900i	−0.239448	+	0.970909i	$0.576966\pi$
$234$		0			0
$235$	2.31776	−	4.01447i	0.151194	−	0.261875i
$236$		0			0
$237$	12.1578			0.789732
$238$		0			0
$239$		−	18.0000i		−	1.16432i	−0.813073	−	0.582162i	$-0.802207\pi$
$239$		−	18.0000i		−	1.16432i	0.813073	−	0.582162i	$-0.197793\pi$
$240$		0			0
$241$	7.32081	+	4.22667i	0.471575	+	0.272264i	0.716899	−	0.697177i	$-0.245561\pi$
$241$	7.32081	+	4.22667i	0.471575	+	0.272264i	−0.245324	+	0.969441i	$0.578894\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−6.52775	+	7.81723i	−0.417043	+	0.499424i
$246$		0			0
$247$	−1.92380	+	1.11071i	−0.122408	+	0.0706725i
$248$		0			0
$249$	−7.52051	+	13.0259i	−0.476593	+	0.825484i
$250$		0			0
$251$		−	4.54510i		−	0.286884i	−0.989659	−	0.143442i	$-0.954183\pi$
$251$		−	4.54510i		−	0.286884i	0.989659	−	0.143442i	$-0.0458170\pi$
$252$		0			0
$253$			11.9681i			0.752430i
$254$		0			0
$255$	−3.46410	+	6.00000i	−0.216930	+	0.375735i
$256$		0			0
$257$	9.24073	−	5.33514i	0.576421	−	0.332797i	−0.183289	−	0.983059i	$-0.558674\pi$
$257$	9.24073	−	5.33514i	0.576421	−	0.332797i	0.759710	+	0.650262i	$0.225341\pi$
$258$		0			0
$259$	1.26233	−	14.6292i	0.0784375	−	0.909017i
$260$		0			0
$261$	−1.05837	+	0.611052i	−0.0655116	+	0.0378232i
$262$		0			0
$263$	9.01868	+	5.20694i	0.556116	+	0.321074i	0.751585	−	0.659636i	$-0.229290\pi$
$263$	9.01868	+	5.20694i	0.556116	+	0.321074i	−0.195469	+	0.980710i	$0.562623\pi$
$264$		0			0
$265$			15.2300i			0.935573i
$266$		0			0
$267$	15.8962			0.972831
$268$		0			0
$269$	−7.27979	+	12.6090i	−0.443856	+	0.768782i	−0.997972	−	0.0636581i	$-0.979723\pi$
$269$	−7.27979	+	12.6090i	−0.443856	+	0.768782i	0.554115	+	0.832440i	$0.313057\pi$
$270$		0			0
$271$	4.93883	+	8.55431i	0.300013	+	0.519637i	0.976138	−	0.217149i	$-0.0696758\pi$
$271$	4.93883	+	8.55431i	0.300013	+	0.519637i	−0.676126	+	0.736786i	$0.736342\pi$
$272$		0			0
$273$	11.7029	−	5.47412i	0.708290	−	0.331309i
$274$		0			0
$275$	3.23212	+	5.59820i	0.194904	+	0.337584i
$276$		0			0
$277$	−15.4416	−	8.91523i	−0.927797	−	0.535664i	−0.0416832	−	0.999131i	$-0.513272\pi$
$277$	−15.4416	−	8.91523i	−0.927797	−	0.535664i	−0.886114	+	0.463467i	$0.846605\pi$
$278$		0			0
$279$	−0.434187			−0.0259941
$280$		0			0
$281$	27.6537			1.64968			0.824841	−	0.565365i	$-0.191265\pi$
$281$	27.6537			1.64968			0.824841	+	0.565365i	$0.191265\pi$
$282$		0			0
$283$	2.08002	+	1.20090i	0.123644	+	0.0713860i	0.560546	−	0.828123i	$-0.310591\pi$
$283$	2.08002	+	1.20090i	0.123644	+	0.0713860i	−0.436902	+	0.899509i	$0.643924\pi$
$284$		0			0
$285$	0.330921	+	0.573172i	0.0196021	+	0.0339518i
$286$		0			0
$287$	−13.1442	−	9.18038i	−0.775881	−	0.541901i
$288$		0			0
$289$	2.83816	+	4.91583i	0.166950	+	0.289167i
$290$		0			0
$291$	−5.37302	+	9.30634i	−0.314972	+	0.545547i
$292$		0			0
$293$	−12.7931			−0.747379			−0.373689	−	0.927554i	$-0.621907\pi$
$293$	−12.7931			−0.747379			−0.373689	+	0.927554i	$0.621907\pi$
$294$		0			0
$295$		−	13.1538i		−	0.765846i
$296$		0			0
$297$	−1.94163	−	1.12100i	−0.112665	−	0.0650470i
$298$		0			0
$299$	22.5752	−	13.0338i	1.30556	−	0.753764i
$300$		0			0
$301$	7.98672	−	11.4352i	0.460347	−	0.659114i
$302$		0			0
$303$	0.156217	−	0.0901918i	0.00897442	−	0.00518138i
$304$		0			0
$305$	−3.57165	+	6.18628i	−0.204512	+	0.354225i
$306$		0			0
$307$		−	20.7173i		−	1.18240i	−0.806525	−	0.591201i	$-0.798654\pi$
$307$		−	20.7173i		−	1.18240i	0.806525	−	0.591201i	$-0.201346\pi$
$308$		0			0
$309$		−	4.25202i		−	0.241889i
$310$		0			0
$311$	−7.51391	+	13.0145i	−0.426075	+	0.737983i	−0.996520	−	0.0833524i	$-0.973437\pi$
$311$	−7.51391	+	13.0145i	−0.426075	+	0.737983i	0.570445	+	0.821336i	$0.306771\pi$
$312$		0			0
$313$	−8.11268	+	4.68386i	−0.458556	+	0.264747i	−0.711437	−	0.702750i	$-0.751955\pi$
$313$	−8.11268	+	4.68386i	−0.458556	+	0.264747i	0.252881	+	0.967497i	$0.418622\pi$
$314$		0			0
$315$	−1.63095	−	3.48672i	−0.0918934	−	0.196455i
$316$		0			0
$317$	−19.8023	+	11.4328i	−1.11221	+	0.642133i	−0.939400	−	0.342823i	$-0.888617\pi$
$317$	−19.8023	+	11.4328i	−1.11221	+	0.642133i	−0.172806	+	0.984956i	$0.555284\pi$
$318$		0			0
$319$	−2.37287	−	1.36998i	−0.132855	−	0.0767040i
$320$		0			0
$321$			19.4361i			1.08481i
$322$		0			0
$323$	2.16624			0.120533
$324$		0			0
$325$	7.03983	−	12.1933i	0.390500	−	0.676365i
$326$		0			0
$327$	5.52689	+	9.57285i	0.305637	+	0.529380i
$328$		0			0
$329$	8.39850	+	0.724692i	0.463024	+	0.0399536i
$330$		0			0
$331$	0.671929	+	1.16381i	0.0369325	+	0.0639690i	0.883901	−	0.467674i	$-0.154908\pi$
$331$	0.671929	+	1.16381i	0.0369325	+	0.0639690i	−0.846968	+	0.531643i	$0.821575\pi$
$332$		0			0
$333$	4.80634	+	2.77494i	0.263386	+	0.152066i
$334$		0			0
$335$	6.18628			0.337993
$336$		0			0
$337$	31.2624			1.70297			0.851487	−	0.524376i	$-0.175701\pi$
$337$	31.2624			1.70297			0.851487	+	0.524376i	$0.175701\pi$
$338$		0			0
$339$	−6.98673	−	4.03379i	−0.379467	−	0.219085i
$340$		0			0
$341$	−0.486723	−	0.843029i	−0.0263575	−	0.0456526i
$342$		0			0
$343$	−17.9062	−	4.72942i	−0.966845	−	0.255365i
$344$		0			0
$345$	−3.88325	−	6.72599i	−0.209067	−	0.362115i
$346$		0			0
$347$	−6.51125	+	11.2778i	−0.349542	+	0.605425i	−0.986168	−	0.165748i	$-0.946996\pi$
$347$	−6.51125	+	11.2778i	−0.349542	+	0.605425i	0.636626	+	0.771173i	$0.280330\pi$
$348$		0			0
$349$	4.18038			0.223771			0.111885	−	0.993721i	$-0.464311\pi$
$349$	4.18038			0.223771			0.111885	+	0.993721i	$0.464311\pi$
$350$		0			0
$351$			4.88325i			0.260649i
$352$		0			0
$353$	−30.7737	−	17.7672i	−1.63792	−	0.945654i	−0.981548	−	0.191218i	$-0.938756\pi$
$353$	−30.7737	−	17.7672i	−1.63792	−	0.945654i	−0.656374	−	0.754436i	$-0.727911\pi$
$354$		0			0
$355$	−14.2859	+	8.24797i	−0.758217	+	0.437757i
$356$		0			0
$357$	−12.5523	−	1.08312i	−0.664340	−	0.0573247i
$358$		0			0
$359$	−16.8059	+	9.70287i	−0.886980	+	0.512098i	−0.872953	−	0.487804i	$-0.837798\pi$
$359$	−16.8059	+	9.70287i	−0.886980	+	0.512098i	−0.0140263	+	0.999902i	$0.504465\pi$
$360$		0			0
$361$	−9.39653	+	16.2753i	−0.494554	+	0.856593i
$362$		0			0
$363$			5.97345i			0.313525i
$364$		0			0
$365$			19.6383i			1.02791i
$366$		0			0
$367$	−15.8813	+	27.5072i	−0.828998	+	1.43587i	0.0698276	+	0.997559i	$0.477755\pi$
$367$	−15.8813	+	27.5072i	−0.828998	+	1.43587i	−0.898825	+	0.438307i	$0.855578\pi$
$368$		0			0
$369$	5.24797	−	3.02991i	0.273198	−	0.157731i
$370$		0			0
$371$	−25.0870	+	11.7347i	−1.30245	+	0.609235i
$372$		0			0
$373$	−2.28780	+	1.32086i	−0.118458	+	0.0683916i	−0.558058	−	0.829802i	$-0.688453\pi$
$373$	−2.28780	+	1.32086i	−0.118458	+	0.0683916i	0.439600	+	0.898193i	$0.355120\pi$
$374$		0			0
$375$	−9.93277	−	5.73469i	−0.512926	−	0.296138i
$376$		0			0
$377$			5.96784i			0.307360i
$378$		0			0
$379$	30.1361			1.54799			0.773994	−	0.633193i	$-0.218256\pi$
$379$	30.1361			1.54799			0.773994	+	0.633193i	$0.218256\pi$
$380$		0			0
$381$	−0.623983	+	1.08077i	−0.0319676	+	0.0553696i
$382$		0			0
$383$	1.36109	+	2.35748i	0.0695484	+	0.120461i	0.898703	−	0.438559i	$-0.144511\pi$
$383$	1.36109	+	2.35748i	0.0695484	+	0.120461i	−0.829154	+	0.559020i	$0.811178\pi$
$384$		0			0
$385$	4.94163	−	7.07530i	0.251849	−	0.360591i
$386$		0			0
$387$	2.63596	+	4.56561i	0.133993	+	0.232083i
$388$		0			0
$389$	−12.5113	−	7.22341i	−0.634348	−	0.366241i	0.148086	−	0.988975i	$-0.452689\pi$
$389$	−12.5113	−	7.22341i	−0.634348	−	0.366241i	−0.782434	+	0.622733i	$0.786022\pi$
$390$		0			0
$391$	−25.4201			−1.28555
$392$		0			0
$393$	−5.46938			−0.275894
$394$		0			0
$395$	−15.3186	−	8.84420i	−0.770762	−	0.445000i
$396$		0			0
$397$	18.8208	+	32.5986i	0.944590	+	1.63608i	0.756571	+	0.653912i	$0.226873\pi$
$397$	18.8208	+	32.5986i	0.944590	+	1.63608i	0.188019	+	0.982165i	$0.439793\pi$
$398$		0			0
$399$	−0.689160	+	0.986723i	−0.0345012	+	0.0493979i
$400$		0			0
$401$	10.3044	+	17.8477i	0.514576	+	0.891271i	0.999857	+	0.0169129i	$0.00538381\pi$
$401$	10.3044	+	17.8477i	0.514576	+	0.891271i	−0.485281	+	0.874358i	$0.661283\pi$
$402$		0			0
$403$	−1.06012	+	1.83619i	−0.0528085	+	0.0914669i
$404$		0			0
$405$	1.45490			0.0722948
$406$		0			0
$407$			12.4428i			0.616768i
$408$		0			0
$409$	−17.3833	−	10.0362i	−0.859547	−	0.496259i	0.00431383	−	0.999991i	$-0.498627\pi$
$409$	−17.3833	−	10.0362i	−0.859547	−	0.496259i	−0.863860	+	0.503731i	$0.831960\pi$
$410$		0			0
$411$	−7.87234	+	4.54510i	−0.388314	+	0.224193i
$412$		0			0
$413$	21.6671	−	10.1350i	1.06617	−	0.498710i
$414$		0			0
$415$	18.9515	−	10.9416i	0.930290	−	0.537103i
$416$		0			0
$417$	−3.31764	+	5.74633i	−0.162466	+	0.281399i
$418$		0			0
$419$			1.76651i			0.0862996i	0.999069	+	0.0431498i	$0.0137393\pi$
$419$			1.76651i			0.0862996i	−0.999069	+	0.0431498i	$0.986261\pi$
$420$		0			0
$421$		−	1.37832i		−	0.0671752i	−0.999436	−	0.0335876i	$-0.989307\pi$
$421$		−	1.37832i		−	0.0671752i	0.999436	−	0.0335876i	$-0.0106933\pi$
$422$		0			0
$423$	−1.59307	+	2.75927i	−0.0774575	+	0.134160i
$424$		0			0
$425$	−11.8905	+	6.86498i	−0.576774	+	0.333000i
$426$		0			0
$427$	−12.9420	−	1.11675i	−0.626309	−	0.0540431i
$428$		0			0
$429$	−9.48146	+	5.47412i	−0.457769	+	0.264293i
$430$		0			0
$431$	7.29917	+	4.21417i	0.351588	+	0.202990i	0.665385	−	0.746501i	$-0.268268\pi$
$431$	7.29917	+	4.21417i	0.351588	+	0.202990i	−0.313796	+	0.949490i	$0.601601\pi$
$432$		0			0
$433$			15.6298i			0.751118i	0.926798	+	0.375559i	$0.122549\pi$
$433$			15.6298i			0.751118i	−0.926798	+	0.375559i	$0.877451\pi$
$434$		0			0
$435$	1.77804			0.0852507
$436$		0			0
$437$	−1.21417	+	2.10301i	−0.0580819	+	0.100601i
$438$		0			0
$439$	−10.2912	−	17.8249i	−0.491172	−	0.850735i	0.508776	−	0.860899i	$-0.330098\pi$
$439$	−10.2912	−	17.8249i	−0.491172	−	0.850735i	−0.999948	+	0.0101637i	$0.996765\pi$
$440$		0			0
$441$	4.48672	−	5.37302i	0.213653	−	0.255858i
$442$		0			0
$443$	10.8644	+	18.8176i	0.516182	+	0.894053i	0.999824	+	0.0187871i	$0.00598048\pi$
$443$	10.8644	+	18.8176i	0.516182	+	0.894053i	−0.483642	+	0.875266i	$0.660686\pi$
$444$		0			0
$445$	−20.0289	−	11.5637i	−0.949463	−	0.548173i
$446$		0			0
$447$	4.33248			0.204919
$448$		0			0
$449$	−6.74390			−0.318264			−0.159132	−	0.987257i	$-0.550870\pi$
$449$	−6.74390			−0.318264			−0.159132	+	0.987257i	$0.550870\pi$
$450$		0			0
$451$	11.7659	+	6.79306i	0.554036	+	0.319873i
$452$		0			0
$453$	10.3965	+	18.0073i	0.488472	+	0.846058i
$454$		0			0
$455$	−18.7276	−	1.61597i	−0.877963	−	0.0757579i
$456$		0			0
$457$	−14.6312	−	25.3420i	−0.684420	−	1.18545i	−0.973619	−	0.228181i	$-0.926722\pi$
$457$	−14.6312	−	25.3420i	−0.684420	−	1.18545i	0.289199	−	0.957269i	$-0.406611\pi$
$458$		0			0
$459$	2.38098	−	4.12398i	0.111135	−	0.192491i
$460$		0			0
$461$	18.0821			0.842165			0.421083	−	0.907022i	$-0.361650\pi$
$461$	18.0821			0.842165			0.421083	+	0.907022i	$0.361650\pi$
$462$		0			0
$463$		−	7.13122i		−	0.331416i	−0.986175	−	0.165708i	$-0.947009\pi$
$463$		−	7.13122i		−	0.331416i	0.986175	−	0.165708i	$-0.0529909\pi$
$464$		0			0
$465$	0.547068	+	0.315850i	0.0253697	+	0.0146472i
$466$		0			0
$467$	29.4574	−	17.0072i	1.36313	−	0.787001i	0.373087	−	0.927796i	$-0.378299\pi$
$467$	29.4574	−	17.0072i	1.36313	−	0.787001i	0.990039	+	0.140795i	$0.0449659\pi$
$468$		0			0
$469$	4.76651	+	10.1901i	0.220097	+	0.470535i
$470$		0			0
$471$	15.3862	−	8.88325i	0.708961	−	0.409319i
$472$		0			0
$473$	−5.90981	+	10.2361i	−0.271733	+	0.470656i
$474$		0			0
$475$			1.31160i			0.0601805i
$476$		0			0
$477$		−	10.4681i		−	0.479300i
$478$		0			0
$479$	−6.51125	+	11.2778i	−0.297507	+	0.515296i	−0.975565	−	0.219712i	$-0.929488\pi$
$479$	−6.51125	+	11.2778i	−0.297507	+	0.515296i	0.678058	+	0.735008i	$0.262822\pi$
$480$		0			0
$481$	23.4706	−	13.5507i	1.07017	−	0.617861i
$482$		0			0
$483$	8.08708	−	11.5789i	0.367975	−	0.526858i
$484$		0			0
$485$	13.5398	−	7.81723i	0.614812	−	0.354962i
$486$		0			0
$487$	30.9551	+	17.8719i	1.40271	+	0.809855i	0.994670	−	0.103109i	$-0.0328789\pi$
$487$	30.9551	+	17.8719i	1.40271	+	0.809855i	0.408040	+	0.912964i	$0.366212\pi$
$488$		0			0
$489$		−	6.05983i		−	0.274035i
$490$		0			0
$491$	3.11037			0.140369			0.0701845	−	0.997534i	$-0.477641\pi$
$491$	3.11037			0.140369			0.0701845	+	0.997534i	$0.477641\pi$
$492$		0			0
$493$	2.90981	−	5.03994i	0.131051	−	0.226987i
$494$		0			0
$495$	1.63095	+	2.82488i	0.0733056	+	0.126969i
$496$		0			0
$497$	−24.5934	−	17.1768i	−1.10316	−	0.770486i
$498$		0			0
$499$	−2.28223	−	3.95293i	−0.102166	−	0.176958i	0.810411	−	0.585862i	$-0.199244\pi$
$499$	−2.28223	−	3.95293i	−0.102166	−	0.176958i	−0.912577	+	0.408905i	$0.865911\pi$
$500$		0			0
$501$	−8.89049	−	5.13293i	−0.397198	−	0.229322i
$502$		0			0
$503$	42.8922			1.91247			0.956233	−	0.292605i	$-0.0945222\pi$
$503$	42.8922			1.91247			0.956233	+	0.292605i	$0.0945222\pi$
$504$		0			0
$505$	−0.262441			−0.0116785
$506$		0			0
$507$	9.39306	+	5.42309i	0.417160	+	0.240848i
$508$		0			0
$509$	−16.1292	−	27.9367i	−0.714916	−	1.23827i	−0.962992	−	0.269531i	$-0.913131\pi$
$509$	−16.1292	−	27.9367i	−0.714916	−	1.23827i	0.248075	−	0.968741i	$-0.420202\pi$
$510$		0			0
$511$	−32.3483	+	15.1312i	−1.43101	+	0.669366i
$512$		0			0
$513$	−0.227452	−	0.393958i	−0.0100423	−	0.0173937i
$514$		0			0
$515$	−3.09314	+	5.35748i	−0.136300	+	0.236079i
$516$		0			0
$517$	−7.14330			−0.314162
$518$		0			0
$519$		−	17.3382i		−	0.761061i
$520$		0			0
$521$	10.1457	+	5.85762i	0.444491	+	0.256627i	0.705501	−	0.708709i	$-0.250722\pi$
$521$	10.1457	+	5.85762i	0.444491	+	0.256627i	−0.261010	+	0.965336i	$0.584055\pi$
$522$		0			0
$523$	8.38335	−	4.84013i	0.366578	−	0.211644i	−0.305384	−	0.952229i	$-0.598785\pi$
$523$	8.38335	−	4.84013i	0.366578	−	0.211644i	0.671963	+	0.740585i	$0.265452\pi$
$524$		0			0
$525$	0.655802	−	7.60013i	0.0286215	−	0.331697i
$526$		0			0
$527$	1.79058	−	1.03379i	0.0779989	−	0.0450327i
$528$		0			0
$529$	2.74797	−	4.75962i	0.119477	−	0.206940i
$530$		0			0
$531$			9.04103i			0.392347i
$532$		0			0
$533$		−	29.5917i		−	1.28176i
$534$		0			0
$535$	14.1388	−	24.4891i	0.611274	−	1.05876i
$536$		0			0
$537$	−9.37195	+	5.41090i	−0.404429	+	0.233497i
$538$		0			0
$539$	15.4620	+	2.68840i	0.665996	+	0.115797i
$540$		0			0
$541$	−39.5728	+	22.8474i	−1.70137	+	0.982286i	−0.756991	+	0.653425i	$0.773332\pi$
$541$	−39.5728	+	22.8474i	−1.70137	+	0.982286i	−0.944378	+	0.328861i	$0.893335\pi$
$542$		0			0
$543$	−4.22902	−	2.44163i	−0.181485	−	0.104780i
$544$		0			0
$545$		−	16.0822i		−	0.688885i
$546$		0			0
$547$	5.35237			0.228851			0.114425	−	0.993432i	$-0.463497\pi$
$547$	5.35237			0.228851			0.114425	+	0.993432i	$0.463497\pi$
$548$		0			0
$549$	2.45490	−	4.25202i	0.104773	−	0.181472i
$550$		0			0
$551$	−0.277970	−	0.481458i	−0.0118419	−	0.0205108i
$552$		0			0
$553$	2.76531	−	32.0474i	0.117593	−	1.36279i
$554$		0			0
$555$	−4.03727	−	6.99276i	−0.171373	−	0.296826i
$556$		0			0
$557$	37.8538	+	21.8549i	1.60392	+	0.926023i	0.990693	+	0.136114i	$0.0434615\pi$
$557$	37.8538	+	21.8549i	1.60392	+	0.926023i	0.613225	+	0.789908i	$0.289872\pi$
$558$		0			0
$559$	25.7441			1.08886
$560$		0			0
$561$	10.6763			0.450754
$562$		0			0
$563$	−24.5646	−	14.1824i	−1.03527	−	0.597715i	−0.116782	−	0.993158i	$-0.537258\pi$
$563$	−24.5646	−	14.1824i	−1.03527	−	0.597715i	−0.918491	+	0.395443i	$0.870591\pi$
$564$		0			0
$565$	5.86878	+	10.1650i	0.246901	+	0.427646i
$566$		0			0
$567$	1.12100	+	2.39653i	0.0470775	+	0.100645i
$568$		0			0
$569$	15.7931	+	27.3544i	0.662080	+	1.14676i	0.980068	+	0.198661i	$0.0636593\pi$
$569$	15.7931	+	27.3544i	0.662080	+	1.14676i	−0.317989	+	0.948095i	$0.603007\pi$
$570$		0			0
$571$	−14.9578	+	25.9077i	−0.625966	+	1.08420i	0.362388	+	0.932027i	$0.381962\pi$
$571$	−14.9578	+	25.9077i	−0.625966	+	1.08420i	−0.988353	+	0.152177i	$0.951372\pi$
$572$		0			0
$573$	−15.8341			−0.661479
$574$		0			0
$575$		−	15.3913i		−	0.641860i
$576$		0			0
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	0.530898	−	0.847436i	$-0.321855\pi$
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	−0.468452	+	0.883489i	$0.655188\pi$
$578$		0			0
$579$	−15.4644	+	8.92835i	−0.642677	+	0.371050i
$580$		0			0
$581$	32.6252	+	22.7865i	1.35352	+	0.945344i
$582$		0			0
$583$	20.3251	−	11.7347i	0.841779	−	0.486001i
$584$		0			0
$585$	3.55233	−	6.15282i	0.146871	−	0.254388i
$586$		0			0
$587$		−	17.6498i		−	0.728484i	−0.931304	−	0.364242i	$-0.881328\pi$
$587$		−	17.6498i		−	0.728484i	0.931304	−	0.364242i	$-0.118672\pi$
$588$		0			0
$589$		−	0.197513i		−	0.00813840i
$590$		0			0
$591$	−5.84508	+	10.1240i	−0.240435	+	0.416445i
$592$		0			0
$593$	−3.74390	+	2.16154i	−0.153744	+	0.0887639i	−0.574898	−	0.818225i	$-0.694958\pi$
$593$	−3.74390	+	2.16154i	−0.153744	+	0.0887639i	0.421155	+	0.906989i	$0.361625\pi$
$594$		0			0
$595$	15.0278	+	10.4959i	0.616081	+	0.430291i
$596$		0			0
$597$	−16.7665	+	9.68015i	−0.686207	+	0.396182i
$598$		0			0
$599$	26.3643	+	15.2214i	1.07721	+	0.621930i	0.930144	−	0.367196i	$-0.119682\pi$
$599$	26.3643	+	15.2214i	1.07721	+	0.621930i	0.147071	+	0.989126i	$0.453015\pi$
$600$		0			0
$601$		−	28.8795i		−	1.17802i	−0.808126	−	0.589010i	$-0.799518\pi$
$601$		−	28.8795i		−	1.17802i	0.808126	−	0.589010i	$-0.200482\pi$
$602$		0			0
$603$	−4.25202			−0.173156
$604$		0			0
$605$	4.34540	−	7.52645i	0.176665	−	0.305994i
$606$		0			0
$607$	−7.49903	−	12.9887i	−0.304376	−	0.527195i	0.672746	−	0.739873i	$-0.265115\pi$
$607$	−7.49903	−	12.9887i	−0.304376	−	0.527195i	−0.977122	+	0.212679i	$0.931781\pi$
$608$		0			0
$609$	1.36998	+	2.92881i	0.0555143	+	0.118681i
$610$		0			0
$611$	7.77935	+	13.4742i	0.314719	+	0.545109i
$612$		0			0
$613$	8.37919	+	4.83773i	0.338432	+	0.195394i	0.659579	−	0.751636i	$-0.270735\pi$
$613$	8.37919	+	4.83773i	0.338432	+	0.195394i	−0.321146	+	0.947030i	$0.604068\pi$
$614$		0			0
$615$	−8.81647			−0.355514
$616$		0			0
$617$	35.1191			1.41384			0.706922	−	0.707292i	$-0.250083\pi$
$617$	35.1191			1.41384			0.706922	+	0.707292i	$0.250083\pi$
$618$		0			0
$619$	−27.7483	−	16.0205i	−1.11530	−	0.643919i	−0.175103	−	0.984550i	$-0.556026\pi$
$619$	−27.7483	−	16.0205i	−1.11530	−	0.643919i	−0.940197	+	0.340631i	$0.889359\pi$
$620$		0			0
$621$	2.66908	+	4.62298i	0.107106	+	0.185514i
$622$		0			0
$623$	3.61562	−	41.9017i	0.144857	−	1.67876i
$624$		0			0
$625$	1.13529	+	1.96638i	0.0454115	+	0.0786550i
$626$		0			0
$627$	0.509947	−	0.883254i	0.0203653	−	0.0352738i
$628$		0			0
$629$	−26.4283			−1.05377
$630$		0			0
$631$			1.64976i			0.0656760i	0.999461	+	0.0328380i	$0.0104545\pi$
$631$			1.64976i			0.0656760i	−0.999461	+	0.0328380i	$0.989545\pi$
$632$		0			0
$633$	−19.6272	−	11.3317i	−0.780109	−	0.450396i
$634$		0			0
$635$	1.57242	−	0.907836i	0.0623995	−	0.0360264i
$636$		0			0
$637$	−11.7677	−	32.0934i	−0.466253	−	1.27159i
$638$		0			0
$639$	9.81913	−	5.66908i	0.388439	−	0.224265i
$640$		0			0
$641$	4.12398	−	7.14295i	0.162888	−	0.282129i	−0.773016	−	0.634387i	$-0.781253\pi$
$641$	4.12398	−	7.14295i	0.162888	−	0.282129i	0.935903	+	0.352258i	$0.114586\pi$
$642$		0			0
$643$			17.6272i			0.695147i	0.937653	+	0.347574i	$0.112994\pi$
$643$			17.6272i			0.695147i	−0.937653	+	0.347574i	$0.887006\pi$
$644$		0			0
$645$		−	7.67013i		−	0.302011i
$646$		0			0
$647$	17.9820	−	31.1457i	0.706944	−	1.22446i	−0.259041	−	0.965866i	$-0.583406\pi$
$647$	17.9820	−	31.1457i	0.706944	−	1.22446i	0.965985	−	0.258597i	$-0.0832602\pi$
$648$		0			0
$649$	−17.5543	+	10.1350i	−0.689067	+	0.397833i
$650$		0			0
$651$	−0.0987567	+	1.14450i	−0.00387058	+	0.0448564i
$652$		0			0
$653$	38.9480	−	22.4866i	1.52415	−	0.879969i	0.524561	−	0.851373i	$-0.324230\pi$
$653$	38.9480	−	22.4866i	1.52415	−	0.879969i	0.999591	−	0.0285964i	$-0.00910374\pi$
$654$		0			0
$655$	6.89133	+	3.97871i	0.269267	+	0.155461i
$656$		0			0
$657$		−	13.4980i		−	0.526606i
$658$		0			0
$659$	25.6981			1.00106			0.500528	−	0.865720i	$-0.333139\pi$
$659$	25.6981			1.00106			0.500528	+	0.865720i	$0.333139\pi$
$660$		0			0
$661$	15.2983	−	26.4975i	0.595036	−	1.03063i	−0.398506	−	0.917166i	$-0.630471\pi$
$661$	15.2983	−	26.4975i	0.595036	−	1.03063i	0.993542	−	0.113467i	$-0.0361955\pi$
$662$		0			0
$663$	−11.6269	−	20.1385i	−0.451553	−	0.782113i
$664$		0			0
$665$	1.58612	−	0.741924i	0.0615073	−	0.0287706i
$666$		0			0
$667$	3.26189	+	5.64976i	0.126301	+	0.218760i
$668$		0			0
$669$	−4.67105	−	2.69683i	−0.180593	−	0.104266i
$670$		0			0
$671$	11.0078			0.424951
$672$		0			0
$673$	−13.2624			−0.511230			−0.255615	−	0.966779i	$-0.582278\pi$
$673$	−13.2624			−0.511230			−0.255615	+	0.966779i	$0.582278\pi$
$674$		0			0
$675$	2.49697	+	1.44163i	0.0961085	+	0.0554883i
$676$		0			0
$677$	11.2532	+	19.4912i	0.432497	+	0.749106i	0.997088	−	0.0762645i	$-0.0242993\pi$
$677$	11.2532	+	19.4912i	0.432497	+	0.749106i	−0.564591	+	0.825371i	$0.690966\pi$
$678$		0			0
$679$	23.3090	+	16.2798i	0.894517	+	0.624761i
$680$		0			0
$681$	−14.7347	−	25.5212i	−0.564635	−	0.977976i
$682$		0			0
$683$	9.99600	−	17.3136i	0.382486	−	0.662486i	−0.608931	−	0.793223i	$-0.708401\pi$
$683$	9.99600	−	17.3136i	0.382486	−	0.662486i	0.991417	+	0.130738i	$0.0417346\pi$
$684$		0			0
$685$	13.2254			0.505315
$686$		0			0
$687$			12.0266i			0.458842i
$688$		0			0
$689$	−44.2697	−	25.5591i	−1.68654	−	0.973725i
$690$		0			0
$691$	−33.6864	+	19.4489i	−1.28149	+	0.739870i	−0.977121	−	0.212684i	$-0.931780\pi$
$691$	−33.6864	+	19.4489i	−1.28149	+	0.739870i	−0.304371	+	0.952554i	$0.598446\pi$
$692$		0			0
$693$	−3.39653	+	4.86307i	−0.129024	+	0.184733i
$694$		0			0
$695$	8.36036	−	4.82685i	0.317126	−	0.183093i
$696$		0			0
$697$	−14.4283	+	24.9906i	−0.546513	+	0.946588i
$698$		0			0
$699$			22.0145i			0.832664i
$700$		0			0
$701$			14.8005i			0.559009i	0.960144	+	0.279504i	$0.0901701\pi$
$701$			14.8005i			0.559009i	−0.960144	+	0.279504i	$0.909830\pi$
$702$		0			0
$703$	−1.26233	+	2.18642i	−0.0476098	+	0.0824625i
$704$		0			0
$705$	4.01447	−	2.31776i	0.151194	−	0.0872918i
$706$		0			0
$707$	−0.202210	−	0.432295i	−0.00760488	−	0.0162581i
$708$		0			0
$709$	29.7810	−	17.1941i	1.11845	−	0.645736i	0.177444	−	0.984131i	$-0.443217\pi$
$709$	29.7810	−	17.1941i	1.11845	−	0.645736i	0.941004	+	0.338394i	$0.109884\pi$
$710$		0			0
$711$	10.5289	+	6.07889i	0.394866	+	0.227976i
$712$		0			0
$713$			2.31776i			0.0868007i
$714$		0			0
$715$	15.9286			0.595698
$716$		0			0
$717$	9.00000	−	15.5885i	0.336111	−	0.582162i
$718$		0			0
$719$	6.41826	+	11.1167i	0.239361	+	0.414585i	0.960531	−	0.278173i	$-0.0897289\pi$
$719$	6.41826	+	11.1167i	0.239361	+	0.414585i	−0.721170	+	0.692758i	$0.756396\pi$
$720$		0			0
$721$	−11.2081	−	0.967130i	−0.417413	−	0.0360178i
$722$		0			0
$723$	4.22667	+	7.32081i	0.157192	+	0.272264i
$724$		0			0
$725$	3.05156	+	1.76182i	0.113332	+	0.0654323i
$726$		0			0
$727$	4.04981			0.150199			0.0750995	−	0.997176i	$-0.476073\pi$
$727$	4.04981			0.150199			0.0750995	+	0.997176i	$0.476073\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−21.7413	−	12.5523i	−0.804130	−	0.464265i
$732$		0			0
$733$	−26.5237	−	45.9404i	−0.979675	−	1.69685i	−0.663556	−	0.748127i	$-0.730954\pi$
$733$	−26.5237	−	45.9404i	−0.979675	−	1.69685i	−0.316119	−	0.948720i	$-0.602380\pi$
$734$		0			0
$735$	−9.56181	+	3.50604i	−0.352693	+	0.129322i
$736$		0			0
$737$	−4.76651	−	8.25583i	−0.175577	−	0.304108i
$738$		0			0
$739$	−4.68044	+	8.10676i	−0.172173	+	0.298212i	−0.939179	−	0.343427i	$-0.888412\pi$
$739$	−4.68044	+	8.10676i	−0.172173	+	0.298212i	0.767006	+	0.641639i	$0.221745\pi$
$740$		0			0
$741$	−2.22141			−0.0816056
$742$		0			0
$743$		−	30.5249i		−	1.11985i	−0.828544	−	0.559925i	$-0.810830\pi$
$743$		−	30.5249i		−	1.11985i	0.828544	−	0.559925i	$-0.189170\pi$
$744$		0			0
$745$	−5.45885	−	3.15167i	−0.199997	−	0.115468i
$746$		0			0
$747$	−13.0259	+	7.52051i	−0.476593	+	0.275161i
$748$		0			0
$749$	51.2326	+	4.42077i	1.87200	+	0.161531i
$750$		0			0
$751$	7.57948	−	4.37602i	0.276579	−	0.159683i	−0.355295	−	0.934754i	$-0.615619\pi$
$751$	7.57948	−	4.37602i	0.276579	−	0.159683i	0.631874	+	0.775071i	$0.282286\pi$
$752$		0			0
$753$	2.27255	−	3.93617i	0.0828163	−	0.143442i
$754$		0			0
$755$		−	30.2519i		−	1.10098i
$756$		0			0
$757$		−	9.22089i		−	0.335139i	−0.985860	−	0.167569i	$-0.946408\pi$
$757$		−	9.22089i		−	0.335139i	0.985860	−	0.167569i	$-0.0535919\pi$
$758$		0			0
$759$	−5.98407	+	10.3647i	−0.217208	+	0.376215i
$760$		0			0
$761$	25.4661	−	14.7029i	0.923145	−	0.532978i	0.0385079	−	0.999258i	$-0.487740\pi$
$761$	25.4661	−	14.7029i	0.923145	−	0.532978i	0.884637	+	0.466280i	$0.154406\pi$
$762$		0			0
$763$	26.4907	−	12.3913i	0.959028	−	0.448594i
$764$		0			0
$765$	−6.00000	+	3.46410i	−0.216930	+	0.125245i
$766$		0			0
$767$	38.2347	+	22.0748i	1.38058	+	0.797076i
$768$		0			0
$769$		−	23.9316i		−	0.862995i	−0.902114	−	0.431497i	$-0.857985\pi$
$769$		−	23.9316i		−	0.862995i	0.902114	−	0.431497i	$-0.142015\pi$
$770$		0			0
$771$	10.6703			0.384281
$772$		0			0
$773$	9.26244	−	16.0430i	0.333147	−	0.577027i	−0.649980	−	0.759951i	$-0.725223\pi$
$773$	9.26244	−	16.0430i	0.333147	−	0.577027i	0.983127	+	0.182924i	$0.0585562\pi$
$774$		0			0
$775$	0.625935	+	1.08415i	0.0224843	+	0.0389439i
$776$		0			0
$777$	8.40784	−	12.0381i	0.301629	−	0.431866i
$778$		0			0
$779$	1.37832	+	2.38732i	0.0493835	+	0.0855347i
$780$		0			0
$781$	22.0145	+	12.7101i	0.787740	+	0.454802i
$782$		0			0
$783$	−1.22210			−0.0436744
$784$		0			0
$785$	−25.8486			−0.922575
$786$		0			0
$787$	18.5839	+	10.7294i	0.662445	+	0.382463i	0.793208	−	0.608951i	$-0.208409\pi$
$787$	18.5839	+	10.7294i	0.662445	+	0.382463i	−0.130763	+	0.991414i	$0.541743\pi$
$788$		0			0
$789$	5.20694	+	9.01868i	0.185372	+	0.321074i
$790$		0			0
$791$	−12.2220	+	17.4992i	−0.434566	+	0.622201i
$792$		0			0
$793$	−11.9879	−	20.7637i	−0.425704	−	0.737340i
$794$		0			0
$795$	−7.61502	+	13.1896i	−0.270077	+	0.467787i
$796$		0			0
$797$	−14.5982			−0.517095			−0.258547	−	0.965999i	$-0.583244\pi$
$797$	−14.5982			−0.517095			−0.258547	+	0.965999i	$0.583244\pi$
$798$		0			0
$799$		−	15.1722i		−	0.536756i
$800$		0			0
$801$	13.7665	+	7.94810i	0.486416	+	0.280832i
$802$		0			0
$803$	26.2080	−	15.1312i	0.924862	−	0.533969i
$804$		0			0
$805$	−18.6127	+	8.70625i	−0.656011	+	0.306855i
$806$		0			0
$807$	−12.6090	+	7.27979i	−0.443856	+	0.256261i
$808$		0			0
$809$	−2.75927	+	4.77920i	−0.0970108	+	0.168028i	−0.910446	−	0.413628i	$-0.864261\pi$
$809$	−2.75927	+	4.77920i	−0.0970108	+	0.168028i	0.813435	+	0.581655i	$0.197595\pi$
$810$		0			0
$811$			12.7294i			0.446991i	0.974705	+	0.223495i	$0.0717467\pi$
$811$			12.7294i			0.446991i	−0.974705	+	0.223495i	$0.928253\pi$
$812$		0			0
$813$			9.87766i			0.346425i
$814$		0			0
$815$	−4.40824	+	7.63529i	−0.154414	+	0.267452i
$816$		0			0
$817$	−2.07691	+	1.19911i	−0.0726620	+	0.0419515i
$818$		0			0
$819$	12.8720	+	1.11071i	0.449786	+	0.0388112i
$820$		0			0
$821$	39.9489	−	23.0645i	1.39422	−	0.804956i	0.400445	−	0.916321i	$-0.368855\pi$
$821$	39.9489	−	23.0645i	1.39422	−	0.804956i	0.993780	+	0.111364i	$0.0355221\pi$
$822$		0			0
$823$	−33.2073	−	19.1722i	−1.15753	−	0.668303i	−0.206822	−	0.978379i	$-0.566312\pi$
$823$	−33.2073	−	19.1722i	−1.15753	−	0.668303i	−0.950712	+	0.310076i	$0.899646\pi$
$824$		0			0
$825$			6.46425i			0.225056i
$826$		0			0
$827$	−53.9162			−1.87485			−0.937424	−	0.348189i	$-0.886797\pi$
$827$	−53.9162			−1.87485			−0.937424	+	0.348189i	$0.886797\pi$
$828$		0			0
$829$	−11.9376	+	20.6765i	−0.414609	+	0.718123i	−0.995387	−	0.0959384i	$-0.969415\pi$
$829$	−11.9376	+	20.6765i	−0.414609	+	0.718123i	0.580779	+	0.814061i	$0.302748\pi$
$830$		0			0
$831$	−8.91523	−	15.4416i	−0.309266	−	0.535664i
$832$		0			0
$833$	−5.71011	+	32.8410i	−0.197844	+	1.13787i
$834$		0			0
$835$	7.46792	+	12.9348i	0.258438	+	0.447628i
$836$		0			0
$837$	−0.376017	−	0.217093i	−0.0129970	−	0.00750385i
$838$		0			0
$839$	3.77654			0.130380			0.0651902	−	0.997873i	$-0.479235\pi$
$839$	3.77654			0.130380			0.0651902	+	0.997873i	$0.479235\pi$
$840$		0			0
$841$	27.5065			0.948499
$842$		0			0
$843$	23.9488	+	13.8269i	0.824841	+	0.476222i
$844$		0			0
$845$	−7.89007	−	13.6660i	−0.271427	−	0.470125i
$846$		0			0
$847$	15.7457	+	1.35867i	0.541030	+	0.0466845i
$848$		0			0
$849$	1.20090	+	2.08002i	0.0412147	+	0.0713860i
$850$		0			0
$851$	14.8131	−	25.6570i	0.507786	−	0.879511i
$852$		0			0
$853$	−0.469379			−0.0160712			−0.00803561	−	0.999968i	$-0.502558\pi$
$853$	−0.469379			−0.0160712			−0.00803561	+	0.999968i	$0.502558\pi$
$854$		0			0
$855$			0.661842i			0.0226345i
$856$		0			0
$857$	0.262441	+	0.151520i	0.00896481	+	0.00517584i	0.504476	−	0.863426i	$-0.331686\pi$
$857$	0.262441	+	0.151520i	0.00896481	+	0.00517584i	−0.495511	+	0.868602i	$0.665019\pi$
$858$		0			0
$859$	−48.0078	+	27.7173i	−1.63801	+	0.945704i	−0.656488	+	0.754336i	$0.727959\pi$
$859$	−48.0078	+	27.7173i	−1.63801	+	0.945704i	−0.981518	+	0.191367i	$0.938708\pi$
$860$		0			0
$861$	−6.79306	−	14.5226i	−0.231507	−	0.494928i
$862$		0			0
$863$	23.9154	−	13.8075i	0.814088	−	0.470014i	−0.0342854	−	0.999412i	$-0.510916\pi$
$863$	23.9154	−	13.8075i	0.814088	−	0.470014i	0.848374	+	0.529398i	$0.177582\pi$
$864$		0			0
$865$	−12.6127	+	21.8458i	−0.428844	+	0.742779i
$866$		0			0
$867$			5.67632i			0.192778i
$868$		0			0
$869$			27.2577i			0.924654i
$870$		0			0
$871$	−10.3818	+	17.9819i	−0.351775	+	0.609293i
$872$		0			0
$873$	−9.30634	+	5.37302i	−0.314972	+	0.181849i
$874$		0			0
$875$	−17.3756	+	24.8780i	−0.587403	+	0.841030i
$876$		0			0
$877$	−29.0371	+	16.7646i	−0.980513	+	0.566099i	−0.902425	−	0.430847i	$-0.858215\pi$
$877$	−29.0371	+	16.7646i	−0.980513	+	0.566099i	−0.0780878	+	0.996946i	$0.524881\pi$
$878$		0			0
$879$	−11.0791	−	6.39653i	−0.373689	−	0.215750i
$880$		0			0
$881$		−	23.6583i		−	0.797069i	−0.917153	−	0.398534i	$-0.869519\pi$
$881$		−	23.6583i		−	0.797069i	0.917153	−	0.398534i	$-0.130481\pi$
$882$		0			0
$883$	55.3953			1.86420			0.932100	−	0.362200i	$-0.117974\pi$
$883$	55.3953			1.86420			0.932100	+	0.362200i	$0.117974\pi$
$884$		0			0
$885$	6.57691	−	11.3916i	0.221081	−	0.382923i
$886$		0			0
$887$	14.5936	+	25.2769i	0.490006	+	0.848716i	0.999934	−	0.0115016i	$-0.00366115\pi$
$887$	14.5936	+	25.2769i	0.490006	+	0.848716i	−0.509928	+	0.860217i	$0.670328\pi$
$888$		0			0
$889$	2.70694	+	1.89062i	0.0907878	+	0.0634092i
$890$		0			0
$891$	−1.12100	−	1.94163i	−0.0375549	−	0.0650470i
$892$		0			0
$893$	−1.25520	−	0.724692i	−0.0420038	−	0.0242509i
$894$		0			0
$895$	15.7447			0.526286
$896$		0			0
$897$	26.0676			0.870371
$898$		0			0
$899$	−0.459532	−	0.265311i	−0.0153262	−	0.00884861i
$900$		0			0
$901$	24.9243	+	43.1701i	0.830348	+	1.43821i
$902$		0			0
$903$	12.6343	−	5.90981i	0.420443	−	0.196666i
$904$		0			0
$905$	3.55233	+	6.15282i	0.118084	+	0.204527i
$906$		0			0
$907$	−26.1678	+	45.3240i	−0.868888	+	1.50496i	−0.00575389	+	0.999983i	$0.501832\pi$
$907$	−26.1678	+	45.3240i	−0.868888	+	1.50496i	−0.863134	+	0.504975i	$0.831502\pi$
$908$		0			0
$909$	0.180384			0.00598295
$910$		0			0
$911$		−	19.6458i		−	0.650895i	−0.945560	−	0.325447i	$-0.894485\pi$
$911$		−	19.6458i		−	0.650895i	0.945560	−	0.325447i	$-0.105515\pi$
$912$		0			0
$913$	−29.2041	−	16.8610i	−0.966514	−	0.558017i
$914$		0			0
$915$	−6.18628	+	3.57165i	−0.204512	+	0.118075i
$916$		0			0
$917$	−1.24402	+	14.4170i	−0.0410812	+	0.476093i
$918$		0			0
$919$	−17.3560	+	10.0205i	−0.572523	+	0.330546i	−0.758156	−	0.652073i	$-0.773900\pi$
$919$	−17.3560	+	10.0205i	−0.572523	+	0.330546i	0.185633	+	0.982619i	$0.440566\pi$
$920$		0			0
$921$	10.3587	−	17.9417i	0.341330	−	0.591201i
$922$		0			0
$923$		−	55.3671i		−	1.82243i
$924$		0			0
$925$		−	16.0017i		−	0.526133i
$926$		0			0
$927$	2.12601	−	3.68236i	0.0698273	−	0.120944i
$928$		0			0
$929$	7.66513	−	4.42547i	0.251485	−	0.145195i	−0.368959	−	0.929446i	$-0.620286\pi$
$929$	7.66513	−	4.42547i	0.251485	−	0.145195i	0.620444	+	0.784251i	$0.286952\pi$
$930$		0			0
$931$	2.44421	+	2.04103i	0.0801057	+	0.0668920i
$932$		0			0
$933$	−13.0145	+	7.51391i	−0.426075	+	0.245994i
$934$		0			0
$935$	−13.4520	−	7.76651i	−0.439927	−	0.253992i
$936$		0			0
$937$		−	15.7400i		−	0.514203i	−0.966384	−	0.257101i	$-0.917233\pi$
$937$		−	15.7400i		−	0.514203i	0.966384	−	0.257101i	$-0.0827674\pi$
$938$		0			0
$939$	−9.36771			−0.305704
$940$		0			0
$941$	−16.7009	+	28.9268i	−0.544434	+	0.942987i	0.454209	+	0.890895i	$0.349922\pi$
$941$	−16.7009	+	28.9268i	−0.544434	+	0.942987i	−0.998642	+	0.0520915i	$0.983411\pi$
$942$		0			0
$943$	−16.1742	−	28.0145i	−0.526703	−	0.912277i
$944$		0			0
$945$	0.330921	−	3.83506i	0.0107649	−	0.124755i
$946$		0			0
$947$	−1.69759	−	2.94031i	−0.0551642	−	0.0955471i	0.837125	−	0.547012i	$-0.184235\pi$
$947$	−1.69759	−	2.94031i	−0.0551642	−	0.0955471i	−0.892289	+	0.451465i	$0.850902\pi$
$948$		0			0
$949$	−57.0833	−	32.9570i	−1.85300	−	1.06983i
$950$		0			0
$951$	−22.8657			−0.741471
$952$		0			0
$953$	−21.2319			−0.687770			−0.343885	−	0.939012i	$-0.611743\pi$
$953$	−21.2319			−0.687770			−0.343885	+	0.939012i	$0.611743\pi$
$954$		0			0
$955$	19.9507	+	11.5185i	0.645589	+	0.372731i
$956$		0			0
$957$	−1.36998	−	2.37287i	−0.0442851	−	0.0767040i
$958$		0			0
$959$	10.1901	+	21.7849i	0.329055	+	0.703472i
$960$		0			0
$961$	15.4057	+	26.6835i	0.496959	+	0.860759i
$962$		0			0
$963$	−9.71803	+	16.8321i	−0.313159	+	0.542407i
$964$		0			0
$965$	25.9798			0.836319
$966$		0			0
$967$			5.37524i			0.172856i	0.996258	+	0.0864281i	$0.0275453\pi$
$967$			5.37524i			0.172856i	−0.996258	+	0.0864281i	$0.972455\pi$
$968$		0			0
$969$	1.87602	+	1.08312i	0.0602663	+	0.0347948i
$970$		0			0
$971$	5.39495	−	3.11477i	0.173132	−	0.0999578i	−0.410930	−	0.911667i	$-0.634796\pi$
$971$	5.39495	−	3.11477i	0.173132	−	0.0999578i	0.584062	+	0.811709i	$0.301463\pi$
$972$		0			0
$973$	14.3925	+	10.0522i	0.461401	+	0.322258i
$974$		0			0
$975$	12.1933	−	7.03983i	0.390500	−	0.225455i
$976$		0			0
$977$	−19.4959	+	33.7679i	−0.623730	+	1.08033i	0.365055	+	0.930986i	$0.381050\pi$
$977$	−19.4959	+	33.7679i	−0.623730	+	1.08033i	−0.988785	+	0.149346i	$0.952283\pi$
$978$		0			0
$979$			35.6392i			1.13903i
$980$		0			0
$981$			11.0538i			0.352920i
$982$		0			0
$983$	14.7373	−	25.5258i	0.470047	−	0.814146i	−0.529366	−	0.848394i	$-0.677570\pi$
$983$	14.7373	−	25.5258i	0.470047	−	0.814146i	0.999413	+	0.0342476i	$0.0109035\pi$
$984$		0			0
$985$	14.7294	−	8.50404i	0.469318	−	0.270961i
$986$		0			0
$987$	6.91097	+	4.82685i	0.219979	+	0.153640i
$988$		0			0
$989$	24.3719	−	14.0712i	0.774983	−	0.447437i
$990$		0			0
$991$	1.35404	+	0.781758i	0.0430126	+	0.0248334i	0.521352	−	0.853342i	$-0.325428\pi$
$991$	1.35404	+	0.781758i	0.0430126	+	0.0248334i	−0.478339	+	0.878175i	$0.658761\pi$
$992$		0			0
$993$			1.34386i			0.0426460i
$994$		0			0
$995$	28.1674			0.892966
$996$		0			0
$997$	−20.2757	+	35.1186i	−0.642138	+	1.11222i	0.342816	+	0.939403i	$0.388619\pi$
$997$	−20.2757	+	35.1186i	−0.642138	+	1.11222i	−0.984955	+	0.172814i	$0.944714\pi$
$998$		0			0
$999$	2.77494	+	4.80634i	0.0877953	+	0.152066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bb.e.31.5	yes	12
4.3	odd	2	inner	1344.2.bb.e.31.2	✓	12
7.5	odd	6		1344.2.bb.h.607.5	yes	12
8.3	odd	2		1344.2.bb.h.31.5	yes	12
8.5	even	2		1344.2.bb.h.31.2	yes	12
28.19	even	6		1344.2.bb.h.607.2	yes	12
56.5	odd	6	inner	1344.2.bb.e.607.2	yes	12
56.19	even	6	inner	1344.2.bb.e.607.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1344.2.bb.e.31.2	✓	12	4.3	odd	2	inner
1344.2.bb.e.31.5	yes	12	1.1	even	1	trivial
1344.2.bb.e.607.2	yes	12	56.5	odd	6	inner
1344.2.bb.e.607.5	yes	12	56.19	even	6	inner
1344.2.bb.h.31.2	yes	12	8.5	even	2
1344.2.bb.h.31.5	yes	12	8.3	odd	2
1344.2.bb.h.607.2	yes	12	28.19	even	6
1344.2.bb.h.607.5	yes	12	7.5	odd	6

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.727452 - 1.25998i) q^{5} +(1.51496 - 2.16908i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.727452 - 1.25998i) q^{5} +(1.51496 - 2.16908i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-1.12100 + 1.94163i) q^{11} +4.88325 q^{13} -1.45490i q^{15} +(-4.12398 - 2.38098i) q^{17} +(-0.393958 + 0.227452i) q^{19} +(2.39653 - 1.12100i) q^{21} +(4.62298 - 2.66908i) q^{23} +(1.44163 - 2.49697i) q^{25} +1.00000i q^{27} +1.22210i q^{29} +(-0.217093 + 0.376017i) q^{31} +(-1.94163 + 1.12100i) q^{33} +(-3.83506 - 0.330921i) q^{35} +(4.80634 - 2.77494i) q^{37} +(4.22902 + 2.44163i) q^{39} -6.05983i q^{41} +5.27191 q^{43} +(0.727452 - 1.25998i) q^{45} +(1.59307 + 2.75927i) q^{47} +(-2.40981 - 6.57212i) q^{49} +(-2.38098 - 4.12398i) q^{51} +(-9.06561 - 5.23403i) q^{53} +3.26189 q^{55} -0.454904 q^{57} +(7.82976 + 4.52051i) q^{59} +(-2.45490 - 4.25202i) q^{61} +(2.63596 + 0.227452i) q^{63} +(-3.55233 - 6.15282i) q^{65} +(-2.12601 + 3.68236i) q^{67} +5.33816 q^{69} -11.3382i q^{71} +(-11.6896 - 6.74899i) q^{73} +(2.49697 - 1.44163i) q^{75} +(2.51328 + 5.37302i) q^{77} +(10.5289 - 6.07889i) q^{79} +(-0.500000 + 0.866025i) q^{81} +15.0410i q^{83} +6.92820i q^{85} +(-0.611052 + 1.05837i) q^{87} +(13.7665 - 7.94810i) q^{89} +(7.39792 - 10.5922i) q^{91} +(-0.376017 + 0.217093i) q^{93} +(0.573172 + 0.330921i) q^{95} +10.7460i q^{97} -2.24200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^5 + 6 * q^9	\( 12 q - 6 q^{5} + 6 q^{9} - 12 q^{17} - 6 q^{21} - 12 q^{25} + 6 q^{33} + 12 q^{37} + 6 q^{45} - 18 q^{49} - 42 q^{53} - 24 q^{61} + 48 q^{65} - 36 q^{73} + 54 q^{77} - 6 q^{81} + 48 q^{89} - 42 q^{93}+O(q^{100}) \) 12 * q - 6 * q^5 + 6 * q^9 - 12 * q^17 - 6 * q^21 - 12 * q^25 + 6 * q^33 + 12 * q^37 + 6 * q^45 - 18 * q^49 - 42 * q^53 - 24 * q^61 + 48 * q^65 - 36 * q^73 + 54 * q^77 - 6 * q^81 + 48 * q^89 - 42 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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