LMFDB - Embedded newform 1350.2.f.f.593.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(107,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("1350.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.4
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.593
Dual form			1350.2.f.f.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.44949 - 3.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.44949 - 3.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +4.56048i q^{11} +(-1.77526 - 1.77526i) q^{13} +4.87832 q^{14} -1.00000 q^{16} +(2.75699 + 2.75699i) q^{17} -0.449490i q^{19} +(-3.22474 + 3.22474i) q^{22} +(5.90326 - 5.90326i) q^{23} -2.51059i q^{26} +(3.44949 + 3.44949i) q^{28} +0.317837 q^{29} +3.44949 q^{31} +(-0.707107 - 0.707107i) q^{32} +3.89898i q^{34} +(0.317837 - 0.317837i) q^{38} +2.04989i q^{41} +(4.77526 + 4.77526i) q^{43} -4.56048 q^{44} +8.34847 q^{46} +(3.07483 + 3.07483i) q^{47} -16.7980i q^{49} +(1.77526 - 1.77526i) q^{52} +(5.65685 - 5.65685i) q^{53} +4.87832i q^{56} +(0.224745 + 0.224745i) q^{58} +2.82843 q^{59} -3.55051 q^{61} +(2.43916 + 2.43916i) q^{62} -1.00000i q^{64} +(-2.00000 + 2.00000i) q^{67} +(-2.75699 + 2.75699i) q^{68} -0.142865i q^{71} +(-0.449490 - 0.449490i) q^{73} +0.449490 q^{76} +(15.7313 + 15.7313i) q^{77} +0.550510i q^{79} +(-1.44949 + 1.44949i) q^{82} +(-6.75323 + 6.75323i) q^{83} +6.75323i q^{86} +(-3.22474 - 3.22474i) q^{88} +3.32124 q^{89} -12.2474 q^{91} +(5.90326 + 5.90326i) q^{92} +4.34847i q^{94} +(-3.55051 + 3.55051i) q^{97} +(11.8780 - 11.8780i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} - 24 q^{13} - 8 q^{16} - 16 q^{22} + 8 q^{28} + 8 q^{31} + 48 q^{43} + 8 q^{46} + 24 q^{52} - 8 q^{58} - 48 q^{61} - 16 q^{67} + 16 q^{73} - 16 q^{76} + 8 q^{82} - 16 q^{88} - 48 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 - 24 * q^13 - 8 * q^16 - 16 * q^22 + 8 * q^28 + 8 * q^31 + 48 * q^43 + 8 * q^46 + 24 * q^52 - 8 * q^58 - 48 * q^61 - 16 * q^67 + 16 * q^73 - 16 * q^76 + 8 * q^82 - 16 * q^88 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.44949	−	3.44949i	1.30378	−	1.30378i	0.377964	−	0.925820i	$-0.376624\pi$
$7$	3.44949	−	3.44949i	1.30378	−	1.30378i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			4.56048i			1.37504i	0.726167	+	0.687518i	$0.241300\pi$
$11$			4.56048i			1.37504i	−0.726167	+	0.687518i	$0.758700\pi$
$12$		0			0
$13$	−1.77526	−	1.77526i	−0.492367	−	0.492367i	0.416684	−	0.909051i	$-0.363192\pi$
$13$	−1.77526	−	1.77526i	−0.492367	−	0.492367i	−0.909051	+	0.416684i	$0.863192\pi$
$14$	4.87832			1.30378
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.75699	+	2.75699i	0.668669	+	0.668669i	0.957408	−	0.288739i	$-0.0932358\pi$
$17$	2.75699	+	2.75699i	0.668669	+	0.668669i	−0.288739	+	0.957408i	$0.593236\pi$
$18$		0			0
$19$		−	0.449490i		−	0.103120i	−0.998670	−	0.0515600i	$-0.983581\pi$
$19$		−	0.449490i		−	0.103120i	0.998670	−	0.0515600i	$-0.0164193\pi$
$20$		0			0
$21$		0			0
$22$	−3.22474	+	3.22474i	−0.687518	+	0.687518i
$23$	5.90326	−	5.90326i	1.23091	−	1.23091i	0.267302	−	0.963613i	$-0.413868\pi$
$23$	5.90326	−	5.90326i	1.23091	−	1.23091i	0.963613	−	0.267302i	$-0.0861320\pi$
$24$		0			0
$25$		0			0
$26$		−	2.51059i		−	0.492367i
$27$		0			0
$28$	3.44949	+	3.44949i	0.651892	+	0.651892i
$29$	0.317837			0.0590209			0.0295104	−	0.999564i	$-0.490605\pi$
$29$	0.317837			0.0590209			0.0295104	+	0.999564i	$0.490605\pi$
$30$		0			0
$31$	3.44949			0.619547			0.309773	−	0.950810i	$-0.399747\pi$
$31$	3.44949			0.619547			0.309773	+	0.950810i	$0.399747\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$			3.89898i			0.668669i
$35$		0			0
$36$		0			0
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	0.317837	−	0.317837i	0.0515600	−	0.0515600i
$39$		0			0
$40$		0			0
$41$			2.04989i			0.320139i	0.987106	+	0.160069i	$0.0511718\pi$
$41$			2.04989i			0.320139i	−0.987106	+	0.160069i	$0.948828\pi$
$42$		0			0
$43$	4.77526	+	4.77526i	0.728220	+	0.728220i	0.970265	−	0.242045i	$-0.0778183\pi$
$43$	4.77526	+	4.77526i	0.728220	+	0.728220i	−0.242045	+	0.970265i	$0.577818\pi$
$44$	−4.56048			−0.687518
$45$		0			0
$46$	8.34847			1.23091
$47$	3.07483	+	3.07483i	0.448510	+	0.448510i	0.894859	−	0.446349i	$-0.147276\pi$
$47$	3.07483	+	3.07483i	0.448510	+	0.448510i	−0.446349	+	0.894859i	$0.647276\pi$
$48$		0			0
$49$		−	16.7980i		−	2.39971i
$50$		0			0
$51$		0			0
$52$	1.77526	−	1.77526i	0.246184	−	0.246184i
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	−0.202296	−	0.979324i	$-0.564840\pi$
$53$	5.65685	−	5.65685i	0.777029	−	0.777029i	0.979324	+	0.202296i	$0.0648402\pi$
$54$		0			0
$55$		0			0
$56$			4.87832i			0.651892i
$57$		0			0
$58$	0.224745	+	0.224745i	0.0295104	+	0.0295104i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	−3.55051			−0.454596			−0.227298	−	0.973825i	$-0.572989\pi$
$61$	−3.55051			−0.454596			−0.227298	+	0.973825i	$0.572989\pi$
$62$	2.43916	+	2.43916i	0.309773	+	0.309773i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−2.00000	+	2.00000i	−0.244339	+	0.244339i	−0.818642	−	0.574304i	$-0.805273\pi$
$67$	−2.00000	+	2.00000i	−0.244339	+	0.244339i	0.574304	+	0.818642i	$0.305273\pi$
$68$	−2.75699	+	2.75699i	−0.334335	+	0.334335i
$69$		0			0
$70$		0			0
$71$		−	0.142865i		−	0.0169549i	−0.999964	−	0.00847745i	$-0.997302\pi$
$71$		−	0.142865i		−	0.0169549i	0.999964	−	0.00847745i	$-0.00269849\pi$
$72$		0			0
$73$	−0.449490	−	0.449490i	−0.0526088	−	0.0526088i	0.680313	−	0.732922i	$-0.261844\pi$
$73$	−0.449490	−	0.449490i	−0.0526088	−	0.0526088i	−0.732922	+	0.680313i	$0.761844\pi$
$74$		0			0
$75$		0			0
$76$	0.449490			0.0515600
$77$	15.7313	+	15.7313i	1.79275	+	1.79275i
$78$		0			0
$79$			0.550510i			0.0619372i	0.999520	+	0.0309686i	$0.00985919\pi$
$79$			0.550510i			0.0619372i	−0.999520	+	0.0309686i	$0.990141\pi$
$80$		0			0
$81$		0			0
$82$	−1.44949	+	1.44949i	−0.160069	+	0.160069i
$83$	−6.75323	+	6.75323i	−0.741263	+	0.741263i	−0.972821	−	0.231558i	$-0.925618\pi$
$83$	−6.75323	+	6.75323i	−0.741263	+	0.741263i	0.231558	+	0.972821i	$0.425618\pi$
$84$		0			0
$85$		0			0
$86$			6.75323i			0.728220i
$87$		0			0
$88$	−3.22474	−	3.22474i	−0.343759	−	0.343759i
$89$	3.32124			0.352050			0.176025	−	0.984386i	$-0.443676\pi$
$89$	3.32124			0.352050			0.176025	+	0.984386i	$0.443676\pi$
$90$		0			0
$91$	−12.2474			−1.28388
$92$	5.90326	+	5.90326i	0.615457	+	0.615457i
$93$		0			0
$94$			4.34847i			0.448510i
$95$		0			0
$96$		0			0
$97$	−3.55051	+	3.55051i	−0.360500	+	0.360500i	−0.863997	−	0.503497i	$-0.832046\pi$
$97$	−3.55051	+	3.55051i	−0.360500	+	0.360500i	0.503497	+	0.863997i	$0.332046\pi$
$98$	11.8780	−	11.8780i	1.19985	−	1.19985i
$99$		0			0
$100$		0			0
$101$			11.6315i			1.15738i	0.815547	+	0.578691i	$0.196436\pi$
$101$			11.6315i			1.15738i	−0.815547	+	0.578691i	$0.803564\pi$
$102$		0			0
$103$	−6.44949	−	6.44949i	−0.635487	−	0.635487i	0.313952	−	0.949439i	$-0.398347\pi$
$103$	−6.44949	−	6.44949i	−0.635487	−	0.635487i	−0.949439	+	0.313952i	$0.898347\pi$
$104$	2.51059			0.246184
$105$		0			0
$106$	8.00000			0.777029
$107$	−10.5352	−	10.5352i	−1.01847	−	1.01847i	−0.999826	−	0.0186471i	$-0.994064\pi$
$107$	−10.5352	−	10.5352i	−1.01847	−	1.01847i	−0.0186471	−	0.999826i	$-0.505936\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$		0			0
$112$	−3.44949	+	3.44949i	−0.325946	+	0.325946i
$113$	−12.6565	+	12.6565i	−1.19062	+	1.19062i	−0.213730	+	0.976893i	$0.568561\pi$
$113$	−12.6565	+	12.6565i	−1.19062	+	1.19062i	−0.976893	+	0.213730i	$0.931439\pi$
$114$		0			0
$115$		0			0
$116$			0.317837i			0.0295104i
$117$		0			0
$118$	2.00000	+	2.00000i	0.184115	+	0.184115i
$119$	19.0205			1.74360
$120$		0			0
$121$	−9.79796			−0.890724
$122$	−2.51059	−	2.51059i	−0.227298	−	0.227298i
$123$		0			0
$124$			3.44949i			0.309773i
$125$		0			0
$126$		0			0
$127$	9.44949	−	9.44949i	0.838507	−	0.838507i	−0.150156	−	0.988662i	$-0.547978\pi$
$127$	9.44949	−	9.44949i	0.838507	−	0.838507i	0.988662	+	0.150156i	$0.0479775\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			14.9528i			1.30643i	0.757172	+	0.653215i	$0.226580\pi$
$131$			14.9528i			1.30643i	−0.757172	+	0.653215i	$0.773420\pi$
$132$		0			0
$133$	−1.55051	−	1.55051i	−0.134446	−	0.134446i
$134$	−2.82843			−0.244339
$135$		0			0
$136$	−3.89898			−0.334335
$137$	1.55708	+	1.55708i	0.133030	+	0.133030i	0.770486	−	0.637456i	$-0.220013\pi$
$137$	1.55708	+	1.55708i	0.133030	+	0.133030i	−0.637456	+	0.770486i	$0.720013\pi$
$138$		0			0
$139$			16.2474i			1.37809i	0.724718	+	0.689045i	$0.241970\pi$
$139$			16.2474i			1.37809i	−0.724718	+	0.689045i	$0.758030\pi$
$140$		0			0
$141$		0			0
$142$	0.101021	−	0.101021i	0.00847745	−	0.00847745i
$143$	8.09601	−	8.09601i	0.677023	−	0.677023i
$144$		0			0
$145$		0			0
$146$		−	0.635674i		−	0.0526088i
$147$		0			0
$148$		0			0
$149$	−12.9029			−1.05705			−0.528523	−	0.848919i	$-0.677254\pi$
$149$	−12.9029			−1.05705			−0.528523	+	0.848919i	$0.677254\pi$
$150$		0			0
$151$	−10.1464			−0.825705			−0.412852	−	0.910798i	$-0.635467\pi$
$151$	−10.1464			−0.825705			−0.412852	+	0.910798i	$0.635467\pi$
$152$	0.317837	+	0.317837i	0.0257800	+	0.0257800i
$153$		0			0
$154$			22.2474i			1.79275i
$155$		0			0
$156$		0			0
$157$	14.0227	−	14.0227i	1.11913	−	1.11913i	0.127265	−	0.991869i	$-0.459380\pi$
$157$	14.0227	−	14.0227i	1.11913	−	1.11913i	0.991869	−	0.127265i	$-0.0406198\pi$
$158$	−0.389270	+	0.389270i	−0.0309686	+	0.0309686i
$159$		0			0
$160$		0			0
$161$		−	40.7265i		−	3.20970i
$162$		0			0
$163$	−8.12372	−	8.12372i	−0.636299	−	0.636299i	0.313341	−	0.949641i	$-0.398552\pi$
$163$	−8.12372	−	8.12372i	−0.636299	−	0.636299i	−0.949641	+	0.313341i	$0.898552\pi$
$164$	−2.04989			−0.160069
$165$		0			0
$166$	−9.55051			−0.741263
$167$	−8.34242	−	8.34242i	−0.645556	−	0.645556i	0.306360	−	0.951916i	$-0.400889\pi$
$167$	−8.34242	−	8.34242i	−0.645556	−	0.645556i	−0.951916	+	0.306360i	$0.900889\pi$
$168$		0			0
$169$		−	6.69694i		−	0.515149i
$170$		0			0
$171$		0			0
$172$	−4.77526	+	4.77526i	−0.364110	+	0.364110i
$173$	8.80312	−	8.80312i	0.669289	−	0.669289i	−0.288263	−	0.957551i	$-0.593078\pi$
$173$	8.80312	−	8.80312i	0.669289	−	0.669289i	0.957551	+	0.288263i	$0.0930776\pi$
$174$		0			0
$175$		0			0
$176$		−	4.56048i		−	0.343759i
$177$		0			0
$178$	2.34847	+	2.34847i	0.176025	+	0.176025i
$179$	−14.7778			−1.10455			−0.552273	−	0.833664i	$-0.686239\pi$
$179$	−14.7778			−1.10455			−0.552273	+	0.833664i	$0.686239\pi$
$180$		0			0
$181$	20.2474			1.50498			0.752491	−	0.658603i	$-0.228852\pi$
$181$	20.2474			1.50498			0.752491	+	0.658603i	$0.228852\pi$
$182$	−8.66025	−	8.66025i	−0.641941	−	0.641941i
$183$		0			0
$184$			8.34847i			0.615457i
$185$		0			0
$186$		0			0
$187$	−12.5732	+	12.5732i	−0.919444	+	0.919444i
$188$	−3.07483	+	3.07483i	−0.224255	+	0.224255i
$189$		0			0
$190$		0			0
$191$		−	4.73545i		−	0.342645i	−0.985215	−	0.171323i	$-0.945196\pi$
$191$		−	4.73545i		−	0.342645i	0.985215	−	0.171323i	$-0.0548040\pi$
$192$		0			0
$193$	−12.7980	−	12.7980i	−0.921217	−	0.921217i	0.0758983	−	0.997116i	$-0.475818\pi$
$193$	−12.7980	−	12.7980i	−0.921217	−	0.921217i	−0.997116	+	0.0758983i	$0.975818\pi$
$194$	−5.02118			−0.360500
$195$		0			0
$196$	16.7980			1.19985
$197$	−10.2173	−	10.2173i	−0.727955	−	0.727955i	0.242257	−	0.970212i	$-0.422112\pi$
$197$	−10.2173	−	10.2173i	−0.727955	−	0.727955i	−0.970212	+	0.242257i	$0.922112\pi$
$198$		0			0
$199$		−	17.4495i		−	1.23696i	−0.785800	−	0.618481i	$-0.787748\pi$
$199$		−	17.4495i		−	1.23696i	0.785800	−	0.618481i	$-0.212252\pi$
$200$		0			0
$201$		0			0
$202$	−8.22474	+	8.22474i	−0.578691	+	0.578691i
$203$	1.09638	−	1.09638i	0.0769505	−	0.0769505i
$204$		0			0
$205$		0			0
$206$		−	9.12096i		−	0.635487i
$207$		0			0
$208$	1.77526	+	1.77526i	0.123092	+	0.123092i
$209$	2.04989			0.141794
$210$		0			0
$211$	−16.2474			−1.11852			−0.559260	−	0.828992i	$-0.688915\pi$
$211$	−16.2474			−1.11852			−0.559260	+	0.828992i	$0.688915\pi$
$212$	5.65685	+	5.65685i	0.388514	+	0.388514i
$213$		0			0
$214$		−	14.8990i		−	1.01847i
$215$		0			0
$216$		0			0
$217$	11.8990	−	11.8990i	0.807755	−	0.807755i
$218$	−2.82843	+	2.82843i	−0.191565	+	0.191565i
$219$		0			0
$220$		0			0
$221$		−	9.78874i		−	0.658462i
$222$		0			0
$223$	−6.79796	−	6.79796i	−0.455225	−	0.455225i	0.441859	−	0.897084i	$-0.354319\pi$
$223$	−6.79796	−	6.79796i	−0.455225	−	0.455225i	−0.897084	+	0.441859i	$0.854319\pi$
$224$	−4.87832			−0.325946
$225$		0			0
$226$	−17.8990			−1.19062
$227$	8.80312	+	8.80312i	0.584284	+	0.584284i	0.936077	−	0.351794i	$-0.114428\pi$
$227$	8.80312	+	8.80312i	0.584284	+	0.584284i	−0.351794	+	0.936077i	$0.614428\pi$
$228$		0			0
$229$		−	19.3485i		−	1.27858i	−0.768965	−	0.639291i	$-0.779228\pi$
$229$		−	19.3485i		−	1.27858i	0.768965	−	0.639291i	$-0.220772\pi$
$230$		0			0
$231$		0			0
$232$	−0.224745	+	0.224745i	−0.0147552	+	0.0147552i
$233$	−3.46410	+	3.46410i	−0.226941	+	0.226941i	−0.811413	−	0.584473i	$-0.801301\pi$
$233$	−3.46410	+	3.46410i	−0.226941	+	0.226941i	0.584473	+	0.811413i	$0.301301\pi$
$234$		0			0
$235$		0			0
$236$			2.82843i			0.184115i
$237$		0			0
$238$	13.4495	+	13.4495i	0.871801	+	0.871801i
$239$	14.6349			0.946656			0.473328	−	0.880886i	$-0.343053\pi$
$239$	14.6349			0.946656			0.473328	+	0.880886i	$0.343053\pi$
$240$		0			0
$241$	9.69694			0.624635			0.312317	−	0.949978i	$-0.398895\pi$
$241$	9.69694			0.624635			0.312317	+	0.949978i	$0.398895\pi$
$242$	−6.92820	−	6.92820i	−0.445362	−	0.445362i
$243$		0			0
$244$		−	3.55051i		−	0.227298i
$245$		0			0
$246$		0			0
$247$	−0.797959	+	0.797959i	−0.0507729	+	0.0507729i
$248$	−2.43916	+	2.43916i	−0.154887	+	0.154887i
$249$		0			0
$250$		0			0
$251$		−	1.73205i		−	0.109326i	−0.998505	−	0.0546630i	$-0.982592\pi$
$251$		−	1.73205i		−	0.109326i	0.998505	−	0.0546630i	$-0.0174085\pi$
$252$		0			0
$253$	26.9217	+	26.9217i	1.69255	+	1.69255i
$254$	13.3636			0.838507
$255$		0			0
$256$	1.00000			0.0625000
$257$	−18.1705	−	18.1705i	−1.13344	−	1.13344i	−0.989601	−	0.143843i	$-0.954054\pi$
$257$	−18.1705	−	18.1705i	−1.13344	−	1.13344i	−0.143843	−	0.989601i	$-0.545946\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−10.5732	+	10.5732i	−0.653215	+	0.653215i
$263$	−21.7060	+	21.7060i	−1.33845	+	1.33845i	−0.440888	+	0.897562i	$0.645336\pi$
$263$	−21.7060	+	21.7060i	−1.33845	+	1.33845i	−0.897562	+	0.440888i	$0.854664\pi$
$264$		0			0
$265$		0			0
$266$		−	2.19275i		−	0.134446i
$267$		0			0
$268$	−2.00000	−	2.00000i	−0.122169	−	0.122169i
$269$	−27.3950			−1.67030			−0.835151	−	0.550021i	$-0.814620\pi$
$269$	−27.3950			−1.67030			−0.835151	+	0.550021i	$0.814620\pi$
$270$		0			0
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	−2.75699	−	2.75699i	−0.167167	−	0.167167i
$273$		0			0
$274$			2.20204i			0.133030i
$275$		0			0
$276$		0			0
$277$	−14.4495	+	14.4495i	−0.868186	+	0.868186i	−0.992271	−	0.124086i	$-0.960400\pi$
$277$	−14.4495	+	14.4495i	−0.868186	+	0.868186i	0.124086	+	0.992271i	$0.460400\pi$
$278$	−11.4887	+	11.4887i	−0.689045	+	0.689045i
$279$		0			0
$280$		0			0
$281$			25.8058i			1.53944i	0.638379	+	0.769722i	$0.279605\pi$
$281$			25.8058i			1.53944i	−0.638379	+	0.769722i	$0.720395\pi$
$282$		0			0
$283$	8.89898	+	8.89898i	0.528989	+	0.528989i	0.920271	−	0.391282i	$-0.127968\pi$
$283$	8.89898	+	8.89898i	0.528989	+	0.528989i	−0.391282	+	0.920271i	$0.627968\pi$
$284$	0.142865			0.00847745
$285$		0			0
$286$	11.4495			0.677023
$287$	7.07107	+	7.07107i	0.417392	+	0.417392i
$288$		0			0
$289$		−	1.79796i		−	0.105762i
$290$		0			0
$291$		0			0
$292$	0.449490	−	0.449490i	0.0263044	−	0.0263044i
$293$	4.24264	−	4.24264i	0.247858	−	0.247858i	−0.572233	−	0.820091i	$-0.693923\pi$
$293$	4.24264	−	4.24264i	0.247858	−	0.247858i	0.820091	+	0.572233i	$0.193923\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−9.12372	−	9.12372i	−0.528523	−	0.528523i
$299$	−20.9596			−1.21212
$300$		0			0
$301$	32.9444			1.89888
$302$	−7.17461	−	7.17461i	−0.412852	−	0.412852i
$303$		0			0
$304$			0.449490i			0.0257800i
$305$		0			0
$306$		0			0
$307$	−14.3258	+	14.3258i	−0.817615	+	0.817615i	−0.985762	−	0.168147i	$-0.946222\pi$
$307$	−14.3258	+	14.3258i	−0.817615	+	0.817615i	0.168147	+	0.985762i	$0.446222\pi$
$308$	−15.7313	+	15.7313i	−0.896375	+	0.896375i
$309$		0			0
$310$		0			0
$311$			4.52837i			0.256780i	0.991724	+	0.128390i	$0.0409810\pi$
$311$			4.52837i			0.256780i	−0.991724	+	0.128390i	$0.959019\pi$
$312$		0			0
$313$	21.2474	+	21.2474i	1.20098	+	1.20098i	0.973870	+	0.227107i	$0.0729267\pi$
$313$	21.2474	+	21.2474i	1.20098	+	1.20098i	0.227107	+	0.973870i	$0.427073\pi$
$314$	19.8311			1.11913
$315$		0			0
$316$	−0.550510			−0.0309686
$317$	−15.4135	−	15.4135i	−0.865708	−	0.865708i	0.126286	−	0.991994i	$-0.459694\pi$
$317$	−15.4135	−	15.4135i	−0.865708	−	0.865708i	−0.991994	+	0.126286i	$0.959694\pi$
$318$		0			0
$319$			1.44949i			0.0811558i
$320$		0			0
$321$		0			0
$322$	28.7980	−	28.7980i	1.60485	−	1.60485i
$323$	1.23924	−	1.23924i	0.0689532	−	0.0689532i
$324$		0			0
$325$		0			0
$326$		−	11.4887i		−	0.636299i
$327$		0			0
$328$	−1.44949	−	1.44949i	−0.0800347	−	0.0800347i
$329$	21.2132			1.16952
$330$		0			0
$331$	−30.8990			−1.69836			−0.849181	−	0.528102i	$-0.822904\pi$
$331$	−30.8990			−1.69836			−0.849181	+	0.528102i	$0.822904\pi$
$332$	−6.75323	−	6.75323i	−0.370632	−	0.370632i
$333$		0			0
$334$		−	11.7980i		−	0.645556i
$335$		0			0
$336$		0			0
$337$	16.8990	−	16.8990i	0.920546	−	0.920546i	−0.0765218	−	0.997068i	$-0.524381\pi$
$337$	16.8990	−	16.8990i	0.920546	−	0.920546i	0.997068	+	0.0765218i	$0.0243815\pi$
$338$	4.73545	−	4.73545i	0.257575	−	0.257575i
$339$		0			0
$340$		0			0
$341$			15.7313i			0.851899i
$342$		0			0
$343$	−33.7980	−	33.7980i	−1.82492	−	1.82492i
$344$	−6.75323			−0.364110
$345$		0			0
$346$	12.4495			0.669289
$347$	−7.24604	−	7.24604i	−0.388988	−	0.388988i	0.485339	−	0.874326i	$-0.338696\pi$
$347$	−7.24604	−	7.24604i	−0.388988	−	0.388988i	−0.874326	+	0.485339i	$0.838696\pi$
$348$		0			0
$349$			24.0454i			1.28712i	0.765395	+	0.643561i	$0.222544\pi$
$349$			24.0454i			1.28712i	−0.765395	+	0.643561i	$0.777456\pi$
$350$		0			0
$351$		0			0
$352$	3.22474	−	3.22474i	0.171879	−	0.171879i
$353$	−5.58542	+	5.58542i	−0.297282	+	0.297282i	−0.839948	−	0.542666i	$-0.817415\pi$
$353$	−5.58542	+	5.58542i	−0.297282	+	0.297282i	0.542666	+	0.839948i	$0.317415\pi$
$354$		0			0
$355$		0			0
$356$			3.32124i			0.176025i
$357$		0			0
$358$	−10.4495	−	10.4495i	−0.552273	−	0.552273i
$359$	−24.0416			−1.26887			−0.634434	−	0.772977i	$-0.718767\pi$
$359$	−24.0416			−1.26887			−0.634434	+	0.772977i	$0.718767\pi$
$360$		0			0
$361$	18.7980			0.989366
$362$	14.3171	+	14.3171i	0.752491	+	0.752491i
$363$		0			0
$364$		−	12.2474i		−	0.641941i
$365$		0			0
$366$		0			0
$367$	4.24745	−	4.24745i	0.221715	−	0.221715i	−0.587505	−	0.809220i	$-0.699890\pi$
$367$	4.24745	−	4.24745i	0.221715	−	0.221715i	0.809220	+	0.587505i	$0.199890\pi$
$368$	−5.90326	+	5.90326i	−0.307729	+	0.307729i
$369$		0			0
$370$		0			0
$371$		−	39.0265i		−	2.02616i
$372$		0			0
$373$	17.3712	+	17.3712i	0.899445	+	0.899445i	0.995387	−	0.0959417i	$-0.0305862\pi$
$373$	17.3712	+	17.3712i	0.899445	+	0.899445i	−0.0959417	+	0.995387i	$0.530586\pi$
$374$	−17.7812			−0.919444
$375$		0			0
$376$	−4.34847			−0.224255
$377$	−0.564242	−	0.564242i	−0.0290600	−	0.0290600i
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$		0			0
$381$		0			0
$382$	3.34847	−	3.34847i	0.171323	−	0.171323i
$383$	−10.0030	+	10.0030i	−0.511131	+	0.511131i	−0.914873	−	0.403742i	$-0.867709\pi$
$383$	−10.0030	+	10.0030i	−0.511131	+	0.511131i	0.403742	+	0.914873i	$0.367709\pi$
$384$		0			0
$385$		0			0
$386$		−	18.0990i		−	0.921217i
$387$		0			0
$388$	−3.55051	−	3.55051i	−0.180250	−	0.180250i
$389$	0.953512			0.0483450			0.0241725	−	0.999708i	$-0.492305\pi$
$389$	0.953512			0.0483450			0.0241725	+	0.999708i	$0.492305\pi$
$390$		0			0
$391$	32.5505			1.64615
$392$	11.8780	+	11.8780i	0.599927	+	0.599927i
$393$		0			0
$394$		−	14.4495i		−	0.727955i
$395$		0			0
$396$		0			0
$397$	2.42679	−	2.42679i	0.121797	−	0.121797i	−0.643581	−	0.765378i	$-0.722552\pi$
$397$	2.42679	−	2.42679i	0.121797	−	0.121797i	0.765378	+	0.643581i	$0.222552\pi$
$398$	12.3387	−	12.3387i	0.618481	−	0.618481i
$399$		0			0
$400$		0			0
$401$		−	23.8988i		−	1.19345i	−0.802447	−	0.596724i	$-0.796469\pi$
$401$		−	23.8988i		−	1.19345i	0.802447	−	0.596724i	$-0.203531\pi$
$402$		0			0
$403$	−6.12372	−	6.12372i	−0.305044	−	0.305044i
$404$	−11.6315			−0.578691
$405$		0			0
$406$	1.55051			0.0769505
$407$		0			0
$408$		0			0
$409$			11.2020i			0.553905i	0.960884	+	0.276953i	$0.0893245\pi$
$409$			11.2020i			0.553905i	−0.960884	+	0.276953i	$0.910675\pi$
$410$		0			0
$411$		0			0
$412$	6.44949	−	6.44949i	0.317744	−	0.317744i
$413$	9.75663	−	9.75663i	0.480092	−	0.480092i
$414$		0			0
$415$		0			0
$416$			2.51059i			0.123092i
$417$		0			0
$418$	1.44949	+	1.44949i	0.0708969	+	0.0708969i
$419$	−16.7956			−0.820518			−0.410259	−	0.911969i	$-0.634562\pi$
$419$	−16.7956			−0.820518			−0.410259	+	0.911969i	$0.634562\pi$
$420$		0			0
$421$	−18.4495			−0.899173			−0.449587	−	0.893237i	$-0.648429\pi$
$421$	−18.4495			−0.899173			−0.449587	+	0.893237i	$0.648429\pi$
$422$	−11.4887	−	11.4887i	−0.559260	−	0.559260i
$423$		0			0
$424$			8.00000i			0.388514i
$425$		0			0
$426$		0			0
$427$	−12.2474	+	12.2474i	−0.592696	+	0.592696i
$428$	10.5352	−	10.5352i	0.509237	−	0.509237i
$429$		0			0
$430$		0			0
$431$		−	22.6274i		−	1.08992i	−0.838461	−	0.544962i	$-0.816544\pi$
$431$		−	22.6274i		−	1.08992i	0.838461	−	0.544962i	$-0.183456\pi$
$432$		0			0
$433$	10.2474	+	10.2474i	0.492461	+	0.492461i	0.909081	−	0.416620i	$-0.136785\pi$
$433$	10.2474	+	10.2474i	0.492461	+	0.492461i	−0.416620	+	0.909081i	$0.636785\pi$
$434$	16.8277			0.807755
$435$		0			0
$436$	−4.00000			−0.191565
$437$	−2.65345	−	2.65345i	−0.126932	−	0.126932i
$438$		0			0
$439$			35.5959i			1.69890i	0.527669	+	0.849450i	$0.323066\pi$
$439$			35.5959i			1.69890i	−0.527669	+	0.849450i	$0.676934\pi$
$440$		0			0
$441$		0			0
$442$	6.92168	−	6.92168i	0.329231	−	0.329231i
$443$	12.9029	−	12.9029i	0.613035	−	0.613035i	−0.330701	−	0.943736i	$-0.607285\pi$
$443$	12.9029	−	12.9029i	0.613035	−	0.613035i	0.943736	+	0.330701i	$0.107285\pi$
$444$		0			0
$445$		0			0
$446$		−	9.61377i		−	0.455225i
$447$		0			0
$448$	−3.44949	−	3.44949i	−0.162973	−	0.162973i
$449$	15.5563			0.734150			0.367075	−	0.930191i	$-0.380359\pi$
$449$	15.5563			0.734150			0.367075	+	0.930191i	$0.380359\pi$
$450$		0			0
$451$	−9.34847			−0.440202
$452$	−12.6565	−	12.6565i	−0.595311	−	0.595311i
$453$		0			0
$454$			12.4495i			0.584284i
$455$		0			0
$456$		0			0
$457$	14.6969	−	14.6969i	0.687494	−	0.687494i	−0.274184	−	0.961677i	$-0.588408\pi$
$457$	14.6969	−	14.6969i	0.687494	−	0.687494i	0.961677	+	0.274184i	$0.0884076\pi$
$458$	13.6814	−	13.6814i	0.639291	−	0.639291i
$459$		0			0
$460$		0			0
$461$			2.82843i			0.131733i	0.997828	+	0.0658665i	$0.0209811\pi$
$461$			2.82843i			0.131733i	−0.997828	+	0.0658665i	$0.979019\pi$
$462$		0			0
$463$	−3.34847	−	3.34847i	−0.155617	−	0.155617i	0.625005	−	0.780621i	$-0.285097\pi$
$463$	−3.34847	−	3.34847i	−0.155617	−	0.155617i	−0.780621	+	0.625005i	$0.785097\pi$
$464$	−0.317837			−0.0147552
$465$		0			0
$466$	−4.89898			−0.226941
$467$	−3.78194	−	3.78194i	−0.175007	−	0.175007i	0.614168	−	0.789175i	$-0.289492\pi$
$467$	−3.78194	−	3.78194i	−0.175007	−	0.175007i	−0.789175	+	0.614168i	$0.789492\pi$
$468$		0			0
$469$			13.7980i			0.637131i
$470$		0			0
$471$		0			0
$472$	−2.00000	+	2.00000i	−0.0920575	+	0.0920575i
$473$	−21.7774	+	21.7774i	−1.00133	+	1.00133i
$474$		0			0
$475$		0			0
$476$			19.0205i			0.871801i
$477$		0			0
$478$	10.3485	+	10.3485i	0.473328	+	0.473328i
$479$	−18.3848			−0.840022			−0.420011	−	0.907519i	$-0.637974\pi$
$479$	−18.3848			−0.840022			−0.420011	+	0.907519i	$0.637974\pi$
$480$		0			0
$481$		0			0
$482$	6.85677	+	6.85677i	0.312317	+	0.312317i
$483$		0			0
$484$		−	9.79796i		−	0.445362i
$485$		0			0
$486$		0			0
$487$	−14.6969	+	14.6969i	−0.665982	+	0.665982i	−0.956783	−	0.290802i	$-0.906078\pi$
$487$	−14.6969	+	14.6969i	−0.665982	+	0.665982i	0.290802	+	0.956783i	$0.406078\pi$
$488$	2.51059	−	2.51059i	0.113649	−	0.113649i
$489$		0			0
$490$		0			0
$491$			2.54270i			0.114750i	0.998353	+	0.0573752i	$0.0182731\pi$
$491$			2.54270i			0.114750i	−0.998353	+	0.0573752i	$0.981727\pi$
$492$		0			0
$493$	0.876276	+	0.876276i	0.0394655	+	0.0394655i
$494$	−1.12848			−0.0507729
$495$		0			0
$496$	−3.44949			−0.154887
$497$	−0.492810	−	0.492810i	−0.0221055	−	0.0221055i
$498$		0			0
$499$			13.7980i			0.617681i	0.951114	+	0.308841i	$0.0999410\pi$
$499$			13.7980i			0.617681i	−0.951114	+	0.308841i	$0.900059\pi$
$500$		0			0
$501$		0			0
$502$	1.22474	−	1.22474i	0.0546630	−	0.0546630i
$503$	4.98186	−	4.98186i	0.222130	−	0.222130i	−0.587265	−	0.809395i	$-0.699795\pi$
$503$	4.98186	−	4.98186i	0.222130	−	0.222130i	0.809395	+	0.587265i	$0.199795\pi$
$504$		0			0
$505$		0			0
$506$			38.0730i			1.69255i
$507$		0			0
$508$	9.44949	+	9.44949i	0.419253	+	0.419253i
$509$	29.2378			1.29594			0.647971	−	0.761665i	$-0.275618\pi$
$509$	29.2378			1.29594			0.647971	+	0.761665i	$0.275618\pi$
$510$		0			0
$511$	−3.10102			−0.137181
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	25.6969i		−	1.13344i
$515$		0			0
$516$		0			0
$517$	−14.0227	+	14.0227i	−0.616718	+	0.616718i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			30.0484i			1.31645i	0.752823	+	0.658223i	$0.228692\pi$
$521$			30.0484i			1.31645i	−0.752823	+	0.658223i	$0.771308\pi$
$522$		0			0
$523$	−7.22474	−	7.22474i	−0.315916	−	0.315916i	0.531280	−	0.847196i	$-0.321711\pi$
$523$	−7.22474	−	7.22474i	−0.315916	−	0.315916i	−0.847196	+	0.531280i	$0.821711\pi$
$524$	−14.9528			−0.653215
$525$		0			0
$526$	−30.6969			−1.33845
$527$	9.51023	+	9.51023i	0.414272	+	0.414272i
$528$		0			0
$529$		−	46.6969i		−	2.03030i
$530$		0			0
$531$		0			0
$532$	1.55051	−	1.55051i	0.0672231	−	0.0672231i
$533$	3.63907	−	3.63907i	0.157626	−	0.157626i
$534$		0			0
$535$		0			0
$536$		−	2.82843i		−	0.122169i
$537$		0			0
$538$	−19.3712	−	19.3712i	−0.835151	−	0.835151i
$539$	76.6067			3.29969
$540$		0			0
$541$	29.5959			1.27243			0.636214	−	0.771513i	$-0.280500\pi$
$541$	29.5959			1.27243			0.636214	+	0.771513i	$0.280500\pi$
$542$	−4.24264	−	4.24264i	−0.182237	−	0.182237i
$543$		0			0
$544$		−	3.89898i		−	0.167167i
$545$		0			0
$546$		0			0
$547$	−13.4722	+	13.4722i	−0.576029	+	0.576029i	−0.933807	−	0.357777i	$-0.883535\pi$
$547$	−13.4722	+	13.4722i	−0.576029	+	0.576029i	0.357777	+	0.933807i	$0.383535\pi$
$548$	−1.55708	+	1.55708i	−0.0665151	+	0.0665151i
$549$		0			0
$550$		0			0
$551$		−	0.142865i		−	0.00608624i
$552$		0			0
$553$	1.89898	+	1.89898i	0.0807528	+	0.0807528i
$554$	−20.4347			−0.868186
$555$		0			0
$556$	−16.2474			−0.689045
$557$	12.1244	+	12.1244i	0.513725	+	0.513725i	0.915666	−	0.401940i	$-0.131664\pi$
$557$	12.1244	+	12.1244i	0.513725	+	0.513725i	−0.401940	+	0.915666i	$0.631664\pi$
$558$		0			0
$559$		−	16.9546i		−	0.717103i
$560$		0			0
$561$		0			0
$562$	−18.2474	+	18.2474i	−0.769722	+	0.769722i
$563$	3.28913	−	3.28913i	0.138620	−	0.138620i	−0.634392	−	0.773012i	$-0.718749\pi$
$563$	3.28913	−	3.28913i	0.138620	−	0.138620i	0.773012	+	0.634392i	$0.218749\pi$
$564$		0			0
$565$		0			0
$566$			12.5851i			0.528989i
$567$		0			0
$568$	0.101021	+	0.101021i	0.00423873	+	0.00423873i
$569$	33.3697			1.39893			0.699465	−	0.714667i	$-0.253422\pi$
$569$	33.3697			1.39893			0.699465	+	0.714667i	$0.253422\pi$
$570$		0			0
$571$	−6.44949			−0.269903			−0.134951	−	0.990852i	$-0.543088\pi$
$571$	−6.44949			−0.269903			−0.134951	+	0.990852i	$0.543088\pi$
$572$	8.09601	+	8.09601i	0.338511	+	0.338511i
$573$		0			0
$574$			10.0000i			0.417392i
$575$		0			0
$576$		0			0
$577$	−4.00000	+	4.00000i	−0.166522	+	0.166522i	−0.785449	−	0.618927i	$-0.787568\pi$
$577$	−4.00000	+	4.00000i	−0.166522	+	0.166522i	0.618927	+	0.785449i	$0.287568\pi$
$578$	1.27135	−	1.27135i	0.0528811	−	0.0528811i
$579$		0			0
$580$		0			0
$581$			46.5904i			1.93290i
$582$		0			0
$583$	25.7980	+	25.7980i	1.06844	+	1.06844i
$584$	0.635674			0.0263044
$585$		0			0
$586$	6.00000			0.247858
$587$	7.10318	+	7.10318i	0.293179	+	0.293179i	0.838335	−	0.545156i	$-0.183529\pi$
$587$	7.10318	+	7.10318i	0.293179	+	0.293179i	−0.545156	+	0.838335i	$0.683529\pi$
$588$		0			0
$589$		−	1.55051i		−	0.0638877i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−17.0420	+	17.0420i	−0.699831	+	0.699831i	−0.964374	−	0.264543i	$-0.914779\pi$
$593$	−17.0420	+	17.0420i	−0.699831	+	0.699831i	0.264543	+	0.964374i	$0.414779\pi$
$594$		0			0
$595$		0			0
$596$		−	12.9029i		−	0.528523i
$597$		0			0
$598$	−14.8207	−	14.8207i	−0.606062	−	0.606062i
$599$	−29.9056			−1.22191			−0.610954	−	0.791666i	$-0.709214\pi$
$599$	−29.9056			−1.22191			−0.610954	+	0.791666i	$0.709214\pi$
$600$		0			0
$601$	40.3939			1.64770			0.823850	−	0.566807i	$-0.191822\pi$
$601$	40.3939			1.64770			0.823850	+	0.566807i	$0.191822\pi$
$602$	23.2952	+	23.2952i	0.949441	+	0.949441i
$603$		0			0
$604$		−	10.1464i		−	0.412852i
$605$		0			0
$606$		0			0
$607$	31.3485	−	31.3485i	1.27240	−	1.27240i	0.327567	−	0.944828i	$-0.393771\pi$
$607$	31.3485	−	31.3485i	1.27240	−	1.27240i	0.944828	−	0.327567i	$-0.106229\pi$
$608$	−0.317837	+	0.317837i	−0.0128900	+	0.0128900i
$609$		0			0
$610$		0			0
$611$		−	10.9172i		−	0.441664i
$612$		0			0
$613$	−16.4722	−	16.4722i	−0.665306	−	0.665306i	0.291320	−	0.956626i	$-0.405906\pi$
$613$	−16.4722	−	16.4722i	−0.665306	−	0.665306i	−0.956626	+	0.291320i	$0.905906\pi$
$614$	−20.2597			−0.817615
$615$		0			0
$616$	−22.2474			−0.896375
$617$	17.5348	+	17.5348i	0.705925	+	0.705925i	0.965676	−	0.259751i	$-0.0836405\pi$
$617$	17.5348	+	17.5348i	0.705925	+	0.705925i	−0.259751	+	0.965676i	$0.583640\pi$
$618$		0			0
$619$			20.6969i			0.831880i	0.909392	+	0.415940i	$0.136547\pi$
$619$			20.6969i			0.831880i	−0.909392	+	0.415940i	$0.863453\pi$
$620$		0			0
$621$		0			0
$622$	−3.20204	+	3.20204i	−0.128390	+	0.128390i
$623$	11.4566	−	11.4566i	0.458998	−	0.458998i
$624$		0			0
$625$		0			0
$626$			30.0484i			1.20098i
$627$		0			0
$628$	14.0227	+	14.0227i	0.559567	+	0.559567i
$629$		0			0
$630$		0			0
$631$	−44.4949			−1.77131			−0.885657	−	0.464340i	$-0.846292\pi$
$631$	−44.4949			−1.77131			−0.885657	+	0.464340i	$0.846292\pi$
$632$	−0.389270	−	0.389270i	−0.0154843	−	0.0154843i
$633$		0			0
$634$		−	21.7980i		−	0.865708i
$635$		0			0
$636$		0			0
$637$	−29.8207	+	29.8207i	−1.18154	+	1.18154i
$638$	−1.02494	+	1.02494i	−0.0405779	+	0.0405779i
$639$		0			0
$640$		0			0
$641$			13.7135i			0.541652i	0.962628	+	0.270826i	$0.0872969\pi$
$641$			13.7135i			0.541652i	−0.962628	+	0.270826i	$0.912703\pi$
$642$		0			0
$643$	−8.82066	−	8.82066i	−0.347853	−	0.347853i	0.511456	−	0.859309i	$-0.329106\pi$
$643$	−8.82066	−	8.82066i	−0.347853	−	0.347853i	−0.859309	+	0.511456i	$0.829106\pi$
$644$	40.7265			1.60485
$645$		0			0
$646$	1.75255			0.0689532
$647$	28.6342	+	28.6342i	1.12573	+	1.12573i	0.990864	+	0.134863i	$0.0430594\pi$
$647$	28.6342	+	28.6342i	1.12573	+	1.12573i	0.134863	+	0.990864i	$0.456941\pi$
$648$		0			0
$649$			12.8990i			0.506329i
$650$		0			0
$651$		0			0
$652$	8.12372	−	8.12372i	0.318150	−	0.318150i
$653$	27.5378	−	27.5378i	1.07764	−	1.07764i	0.0809182	−	0.996721i	$-0.474215\pi$
$653$	27.5378	−	27.5378i	1.07764	−	1.07764i	0.996721	−	0.0809182i	$-0.0257853\pi$
$654$		0			0
$655$		0			0
$656$		−	2.04989i		−	0.0800347i
$657$		0			0
$658$	15.0000	+	15.0000i	0.584761	+	0.584761i
$659$	9.47090			0.368934			0.184467	−	0.982839i	$-0.440944\pi$
$659$	9.47090			0.368934			0.184467	+	0.982839i	$0.440944\pi$
$660$		0			0
$661$	24.0454			0.935258			0.467629	−	0.883925i	$-0.345108\pi$
$661$	24.0454			0.935258			0.467629	+	0.883925i	$0.345108\pi$
$662$	−21.8489	−	21.8489i	−0.849181	−	0.849181i
$663$		0			0
$664$		−	9.55051i		−	0.370632i
$665$		0			0
$666$		0			0
$667$	1.87628	−	1.87628i	0.0726497	−	0.0726497i
$668$	8.34242	−	8.34242i	0.322778	−	0.322778i
$669$		0			0
$670$		0			0
$671$		−	16.1920i		−	0.625086i
$672$		0			0
$673$	−15.2020	−	15.2020i	−0.585996	−	0.585996i	0.350549	−	0.936544i	$-0.385995\pi$
$673$	−15.2020	−	15.2020i	−0.585996	−	0.585996i	−0.936544	+	0.350549i	$0.885995\pi$
$674$	23.8988			0.920546
$675$		0			0
$676$	6.69694			0.257575
$677$	−5.94258	−	5.94258i	−0.228392	−	0.228392i	0.583629	−	0.812021i	$-0.301632\pi$
$677$	−5.94258	−	5.94258i	−0.228392	−	0.228392i	−0.812021	+	0.583629i	$0.801632\pi$
$678$		0			0
$679$			24.4949i			0.940028i
$680$		0			0
$681$		0			0
$682$	−11.1237	+	11.1237i	−0.425949	+	0.425949i
$683$	−6.92820	+	6.92820i	−0.265100	+	0.265100i	−0.827122	−	0.562022i	$-0.810024\pi$
$683$	−6.92820	+	6.92820i	−0.265100	+	0.265100i	0.562022	+	0.827122i	$0.310024\pi$
$684$		0			0
$685$		0			0
$686$		−	47.7975i		−	1.82492i
$687$		0			0
$688$	−4.77526	−	4.77526i	−0.182055	−	0.182055i
$689$	−20.0847			−0.765167
$690$		0			0
$691$	13.1010			0.498386			0.249193	−	0.968454i	$-0.419835\pi$
$691$	13.1010			0.498386			0.249193	+	0.968454i	$0.419835\pi$
$692$	8.80312	+	8.80312i	0.334644	+	0.334644i
$693$		0			0
$694$		−	10.2474i		−	0.388988i
$695$		0			0
$696$		0			0
$697$	−5.65153	+	5.65153i	−0.214067	+	0.214067i
$698$	−17.0027	+	17.0027i	−0.643561	+	0.643561i
$699$		0			0
$700$		0			0
$701$			17.2884i			0.652974i	0.945202	+	0.326487i	$0.105865\pi$
$701$			17.2884i			0.652974i	−0.945202	+	0.326487i	$0.894135\pi$
$702$		0			0
$703$		0			0
$704$	4.56048			0.171879
$705$		0			0
$706$	−7.89898			−0.297282
$707$	40.1229	+	40.1229i	1.50898	+	1.50898i
$708$		0			0
$709$			8.00000i			0.300446i	0.988652	+	0.150223i	$0.0479992\pi$
$709$			8.00000i			0.300446i	−0.988652	+	0.150223i	$0.952001\pi$
$710$		0			0
$711$		0			0
$712$	−2.34847	+	2.34847i	−0.0880126	+	0.0880126i
$713$	20.3632	−	20.3632i	0.762609	−	0.762609i
$714$		0			0
$715$		0			0
$716$		−	14.7778i		−	0.552273i
$717$		0			0
$718$	−17.0000	−	17.0000i	−0.634434	−	0.634434i
$719$	−32.5911			−1.21544			−0.607722	−	0.794150i	$-0.707916\pi$
$719$	−32.5911			−1.21544			−0.607722	+	0.794150i	$0.707916\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	13.2922	+	13.2922i	0.494683	+	0.494683i
$723$		0			0
$724$			20.2474i			0.752491i
$725$		0			0
$726$		0			0
$727$	−24.4949	+	24.4949i	−0.908465	+	0.908465i	−0.996148	−	0.0876830i	$-0.972054\pi$
$727$	−24.4949	+	24.4949i	−0.908465	+	0.908465i	0.0876830	+	0.996148i	$0.472054\pi$
$728$	8.66025	−	8.66025i	0.320970	−	0.320970i
$729$		0			0
$730$		0			0
$731$			26.3307i			0.973876i
$732$		0			0
$733$	15.5959	+	15.5959i	0.576048	+	0.576048i	0.933812	−	0.357764i	$-0.116461\pi$
$733$	15.5959	+	15.5959i	0.576048	+	0.576048i	−0.357764	+	0.933812i	$0.616461\pi$
$734$	6.00680			0.221715
$735$		0			0
$736$	−8.34847			−0.307729
$737$	−9.12096	−	9.12096i	−0.335975	−	0.335975i
$738$		0			0
$739$			53.8434i			1.98066i	0.138731	+	0.990330i	$0.455698\pi$
$739$			53.8434i			1.98066i	−0.138731	+	0.990330i	$0.544302\pi$
$740$		0			0
$741$		0			0
$742$	27.5959	−	27.5959i	1.01308	−	1.01308i
$743$	18.3455	−	18.3455i	0.673029	−	0.673029i	−0.285384	−	0.958413i	$-0.592121\pi$
$743$	18.3455	−	18.3455i	0.673029	−	0.673029i	0.958413	+	0.285384i	$0.0921211\pi$
$744$		0			0
$745$		0			0
$746$			24.5665i			0.899445i
$747$		0			0
$748$	−12.5732	−	12.5732i	−0.459722	−	0.459722i
$749$	−72.6819			−2.65574
$750$		0			0
$751$	−19.0454			−0.694977			−0.347488	−	0.937684i	$-0.612965\pi$
$751$	−19.0454			−0.694977			−0.347488	+	0.937684i	$0.612965\pi$
$752$	−3.07483	−	3.07483i	−0.112128	−	0.112128i
$753$		0			0
$754$		−	0.797959i		−	0.0290600i
$755$		0			0
$756$		0			0
$757$	20.0227	−	20.0227i	0.727738	−	0.727738i	−0.242431	−	0.970169i	$-0.577945\pi$
$757$	20.0227	−	20.0227i	0.727738	−	0.727738i	0.970169	+	0.242431i	$0.0779448\pi$
$758$	2.82843	−	2.82843i	0.102733	−	0.102733i
$759$		0			0
$760$		0			0
$761$		−	32.2412i		−	1.16874i	−0.811487	−	0.584371i	$-0.801341\pi$
$761$		−	32.2412i		−	1.16874i	0.811487	−	0.584371i	$-0.198659\pi$
$762$		0			0
$763$	13.7980	+	13.7980i	0.499520	+	0.499520i
$764$	4.73545			0.171323
$765$		0			0
$766$	−14.1464			−0.511131
$767$	−5.02118	−	5.02118i	−0.181304	−	0.181304i
$768$		0			0
$769$		−	2.30306i		−	0.0830505i	−0.999137	−	0.0415253i	$-0.986778\pi$
$769$		−	2.30306i		−	0.0830505i	0.999137	−	0.0415253i	$-0.0132217\pi$
$770$		0			0
$771$		0			0
$772$	12.7980	−	12.7980i	0.460609	−	0.460609i
$773$	−26.5843	+	26.5843i	−0.956172	+	0.956172i	−0.999079	−	0.0429072i	$-0.986338\pi$
$773$	−26.5843	+	26.5843i	−0.956172	+	0.956172i	0.0429072	+	0.999079i	$0.486338\pi$
$774$		0			0
$775$		0			0
$776$		−	5.02118i		−	0.180250i
$777$		0			0
$778$	0.674235	+	0.674235i	0.0241725	+	0.0241725i
$779$	0.921404			0.0330127
$780$		0			0
$781$	0.651531			0.0233136
$782$	23.0167	+	23.0167i	0.823075	+	0.823075i
$783$		0			0
$784$			16.7980i			0.599927i
$785$		0			0
$786$		0			0
$787$	4.57321	−	4.57321i	0.163017	−	0.163017i	−0.620885	−	0.783902i	$-0.713226\pi$
$787$	4.57321	−	4.57321i	0.163017	−	0.163017i	0.783902	+	0.620885i	$0.213226\pi$
$788$	10.2173	−	10.2173i	0.363977	−	0.363977i
$789$		0			0
$790$		0			0
$791$			87.3169i			3.10463i
$792$		0			0
$793$	6.30306	+	6.30306i	0.223828	+	0.223828i
$794$	3.43199			0.121797
$795$		0			0
$796$	17.4495			0.618481
$797$	−15.2385	−	15.2385i	−0.539776	−	0.539776i	0.383687	−	0.923463i	$-0.374654\pi$
$797$	−15.2385	−	15.2385i	−0.539776	−	0.539776i	−0.923463	+	0.383687i	$0.874654\pi$
$798$		0			0
$799$			16.9546i			0.599810i
$800$		0			0
$801$		0			0
$802$	16.8990	−	16.8990i	0.596724	−	0.596724i
$803$	2.04989	−	2.04989i	0.0723390	−	0.0723390i
$804$		0			0
$805$		0			0
$806$		−	8.66025i		−	0.305044i
$807$		0			0
$808$	−8.22474	−	8.22474i	−0.289346	−	0.289346i
$809$	29.5556			1.03912			0.519560	−	0.854434i	$-0.326096\pi$
$809$	29.5556			1.03912			0.519560	+	0.854434i	$0.326096\pi$
$810$		0			0
$811$	21.1010			0.740957			0.370479	−	0.928841i	$-0.379194\pi$
$811$	21.1010			0.740957			0.370479	+	0.928841i	$0.379194\pi$
$812$	1.09638	+	1.09638i	0.0384753	+	0.0384753i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.14643	−	2.14643i	0.0750940	−	0.0750940i
$818$	−7.92104	+	7.92104i	−0.276953	+	0.276953i
$819$		0			0
$820$		0			0
$821$		−	50.3402i		−	1.75689i	−0.477847	−	0.878443i	$-0.658583\pi$
$821$		−	50.3402i		−	1.75689i	0.477847	−	0.878443i	$-0.341417\pi$
$822$		0			0
$823$	4.00000	+	4.00000i	0.139431	+	0.139431i	0.773377	−	0.633946i	$-0.218566\pi$
$823$	4.00000	+	4.00000i	0.139431	+	0.139431i	−0.633946	+	0.773377i	$0.718566\pi$
$824$	9.12096			0.317744
$825$		0			0
$826$	13.7980			0.480092
$827$	−24.6773	−	24.6773i	−0.858114	−	0.858114i	0.133002	−	0.991116i	$-0.457538\pi$
$827$	−24.6773	−	24.6773i	−0.858114	−	0.858114i	−0.991116	+	0.133002i	$0.957538\pi$
$828$		0			0
$829$			6.20204i			0.215406i	0.994183	+	0.107703i	$0.0343495\pi$
$829$			6.20204i			0.215406i	−0.994183	+	0.107703i	$0.965650\pi$
$830$		0			0
$831$		0			0
$832$	−1.77526	+	1.77526i	−0.0615459	+	0.0615459i
$833$	46.3119	−	46.3119i	1.60461	−	1.60461i
$834$		0			0
$835$		0			0
$836$			2.04989i			0.0708969i
$837$		0			0
$838$	−11.8763	−	11.8763i	−0.410259	−	0.410259i
$839$	53.8043			1.85753			0.928766	−	0.370667i	$-0.120871\pi$
$839$	53.8043			1.85753			0.928766	+	0.370667i	$0.120871\pi$
$840$		0			0
$841$	−28.8990			−0.996517
$842$	−13.0458	−	13.0458i	−0.449587	−	0.449587i
$843$		0			0
$844$		−	16.2474i		−	0.559260i
$845$		0			0
$846$		0			0
$847$	−33.7980	+	33.7980i	−1.16131	+	1.16131i
$848$	−5.65685	+	5.65685i	−0.194257	+	0.194257i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−33.5732	−	33.5732i	−1.14952	−	1.14952i	−0.986646	−	0.162879i	$-0.947922\pi$
$853$	−33.5732	−	33.5732i	−1.14952	−	1.14952i	−0.162879	−	0.986646i	$-0.552078\pi$
$854$	−17.3205			−0.592696
$855$		0			0
$856$	14.8990			0.509237
$857$	24.2487	+	24.2487i	0.828320	+	0.828320i	0.987284	−	0.158964i	$-0.0508154\pi$
$857$	24.2487	+	24.2487i	0.828320	+	0.828320i	−0.158964	+	0.987284i	$0.550815\pi$
$858$		0			0
$859$		−	6.89898i		−	0.235390i	−0.993050	−	0.117695i	$-0.962449\pi$
$859$		−	6.89898i		−	0.235390i	0.993050	−	0.117695i	$-0.0375505\pi$
$860$		0			0
$861$		0			0
$862$	16.0000	−	16.0000i	0.544962	−	0.544962i
$863$	9.36736	−	9.36736i	0.318869	−	0.318869i	−0.529464	−	0.848333i	$-0.677607\pi$
$863$	9.36736	−	9.36736i	0.318869	−	0.318869i	0.848333	+	0.529464i	$0.177607\pi$
$864$		0			0
$865$		0			0
$866$			14.4921i			0.492461i
$867$		0			0
$868$	11.8990	+	11.8990i	0.403878	+	0.403878i
$869$	−2.51059			−0.0851659
$870$		0			0
$871$	7.10102			0.240609
$872$	−2.82843	−	2.82843i	−0.0957826	−	0.0957826i
$873$		0			0
$874$		−	3.75255i		−	0.126932i
$875$		0			0
$876$		0			0
$877$	−6.92168	+	6.92168i	−0.233729	+	0.233729i	−0.814247	−	0.580518i	$-0.802850\pi$
$877$	−6.92168	+	6.92168i	−0.233729	+	0.233729i	0.580518	+	0.814247i	$0.302850\pi$
$878$	−25.1701	+	25.1701i	−0.849450	+	0.849450i
$879$		0			0
$880$		0			0
$881$			33.3055i			1.12209i	0.827786	+	0.561045i	$0.189600\pi$
$881$			33.3055i			1.12209i	−0.827786	+	0.561045i	$0.810400\pi$
$882$		0			0
$883$	1.14643	+	1.14643i	0.0385804	+	0.0385804i	0.726134	−	0.687553i	$-0.241315\pi$
$883$	1.14643	+	1.14643i	0.0385804	+	0.0385804i	−0.687553	+	0.726134i	$0.741315\pi$
$884$	9.78874			0.329231
$885$		0			0
$886$	18.2474			0.613035
$887$	−27.7521	−	27.7521i	−0.931826	−	0.931826i	0.0659944	−	0.997820i	$-0.478978\pi$
$887$	−27.7521	−	27.7521i	−0.931826	−	0.931826i	−0.997820	+	0.0659944i	$0.978978\pi$
$888$		0			0
$889$		−	65.1918i		−	2.18646i
$890$		0			0
$891$		0			0
$892$	6.79796	−	6.79796i	0.227613	−	0.227613i
$893$	1.38211	−	1.38211i	0.0462504	−	0.0462504i
$894$		0			0
$895$		0			0
$896$		−	4.87832i		−	0.162973i
$897$		0			0
$898$	11.0000	+	11.0000i	0.367075	+	0.367075i
$899$	1.09638			0.0365662
$900$		0			0
$901$	31.1918			1.03915
$902$	−6.61037	−	6.61037i	−0.220101	−	0.220101i
$903$		0			0
$904$		−	17.8990i		−	0.595311i
$905$		0			0
$906$		0			0
$907$	38.3712	−	38.3712i	1.27409	−	1.27409i	0.330174	−	0.943920i	$-0.392893\pi$
$907$	38.3712	−	38.3712i	1.27409	−	1.27409i	0.943920	−	0.330174i	$-0.107107\pi$
$908$	−8.80312	+	8.80312i	−0.292142	+	0.292142i
$909$		0			0
$910$		0			0
$911$			1.84281i			0.0610549i	0.999534	+	0.0305275i	$0.00971870\pi$
$911$			1.84281i			0.0610549i	−0.999534	+	0.0305275i	$0.990281\pi$
$912$		0			0
$913$	−30.7980	−	30.7980i	−1.01926	−	1.01926i
$914$	20.7846			0.687494
$915$		0			0
$916$	19.3485			0.639291
$917$	51.5795	+	51.5795i	1.70330	+	1.70330i
$918$		0			0
$919$			20.3485i			0.671234i	0.941999	+	0.335617i	$0.108945\pi$
$919$			20.3485i			0.671234i	−0.941999	+	0.335617i	$0.891055\pi$
$920$		0			0
$921$		0			0
$922$	−2.00000	+	2.00000i	−0.0658665	+	0.0658665i
$923$	−0.253621	+	0.253621i	−0.00834804	+	0.00834804i
$924$		0			0
$925$		0			0
$926$		−	4.73545i		−	0.155617i
$927$		0			0
$928$	−0.224745	−	0.224745i	−0.00737761	−	0.00737761i
$929$	−8.69236			−0.285187			−0.142594	−	0.989781i	$-0.545544\pi$
$929$	−8.69236			−0.285187			−0.142594	+	0.989781i	$0.545544\pi$
$930$		0			0
$931$	−7.55051			−0.247458
$932$	−3.46410	−	3.46410i	−0.113470	−	0.113470i
$933$		0			0
$934$		−	5.34847i		−	0.175007i
$935$		0			0
$936$		0			0
$937$	29.4949	−	29.4949i	0.963556	−	0.963556i	−0.0358026	−	0.999359i	$-0.511399\pi$
$937$	29.4949	−	29.4949i	0.963556	−	0.963556i	0.999359	+	0.0358026i	$0.0113988\pi$
$938$	−9.75663	+	9.75663i	−0.318565	+	0.318565i
$939$		0			0
$940$		0			0
$941$		−	9.08885i		−	0.296288i	−0.988966	−	0.148144i	$-0.952670\pi$
$941$		−	9.08885i		−	0.296288i	0.988966	−	0.148144i	$-0.0473299\pi$
$942$		0			0
$943$	12.1010	+	12.1010i	0.394063	+	0.394063i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	−30.7980			−1.00133
$947$	23.0881	+	23.0881i	0.750263	+	0.750263i	0.974528	−	0.224265i	$-0.0719982\pi$
$947$	23.0881	+	23.0881i	0.750263	+	0.750263i	−0.224265	+	0.974528i	$0.571998\pi$
$948$		0			0
$949$			1.59592i			0.0518057i
$950$		0			0
$951$		0			0
$952$	−13.4495	+	13.4495i	−0.435900	+	0.435900i
$953$	−17.5348	+	17.5348i	−0.568008	+	0.568008i	−0.931570	−	0.363562i	$-0.881560\pi$
$953$	−17.5348	+	17.5348i	−0.568008	+	0.568008i	0.363562	+	0.931570i	$0.381560\pi$
$954$		0			0
$955$		0			0
$956$			14.6349i			0.473328i
$957$		0			0
$958$	−13.0000	−	13.0000i	−0.420011	−	0.420011i
$959$	10.7423			0.346885
$960$		0			0
$961$	−19.1010			−0.616162
$962$		0			0
$963$		0			0
$964$			9.69694i			0.312317i
$965$		0			0
$966$		0			0
$967$	3.34847	−	3.34847i	0.107680	−	0.107680i	−0.651214	−	0.758894i	$-0.725740\pi$
$967$	3.34847	−	3.34847i	0.107680	−	0.107680i	0.758894	+	0.651214i	$0.225740\pi$
$968$	6.92820	−	6.92820i	0.222681	−	0.222681i
$969$		0			0
$970$		0			0
$971$			41.3300i			1.32634i	0.748467	+	0.663172i	$0.230790\pi$
$971$			41.3300i			1.32634i	−0.748467	+	0.663172i	$0.769210\pi$
$972$		0			0
$973$	56.0454	+	56.0454i	1.79673	+	1.79673i
$974$	−20.7846			−0.665982
$975$		0			0
$976$	3.55051			0.113649
$977$	7.14250	+	7.14250i	0.228509	+	0.228509i	0.812070	−	0.583561i	$-0.198341\pi$
$977$	7.14250	+	7.14250i	0.228509	+	0.228509i	−0.583561	+	0.812070i	$0.698341\pi$
$978$		0			0
$979$			15.1464i			0.484082i
$980$		0			0
$981$		0			0
$982$	−1.79796	+	1.79796i	−0.0573752	+	0.0573752i
$983$	−5.12472	+	5.12472i	−0.163453	+	0.163453i	−0.784095	−	0.620641i	$-0.786872\pi$
$983$	−5.12472	+	5.12472i	−0.163453	+	0.163453i	0.620641	+	0.784095i	$0.286872\pi$
$984$		0			0
$985$		0			0
$986$			1.23924i			0.0394655i
$987$		0			0
$988$	−0.797959	−	0.797959i	−0.0253865	−	0.0253865i
$989$	56.3791			1.79275
$990$		0			0
$991$	31.7423			1.00833			0.504164	−	0.863608i	$-0.331801\pi$
$991$	31.7423			1.00833			0.504164	+	0.863608i	$0.331801\pi$
$992$	−2.43916	−	2.43916i	−0.0774433	−	0.0774433i
$993$		0			0
$994$		−	0.696938i		−	0.0221055i
$995$		0			0
$996$		0			0
$997$	−16.9217	+	16.9217i	−0.535915	+	0.535915i	−0.922327	−	0.386411i	$-0.873714\pi$
$997$	−16.9217	+	16.9217i	−0.535915	+	0.535915i	0.386411	+	0.922327i	$0.373714\pi$
$998$	−9.75663	+	9.75663i	−0.308841	+	0.308841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.f.f.593.4		8
3.2	odd	2	inner	1350.2.f.f.593.2		8
5.2	odd	4	inner	1350.2.f.f.107.2		8
5.3	odd	4		270.2.f.a.107.3	yes	8
5.4	even	2		270.2.f.a.53.1	✓	8
15.2	even	4	inner	1350.2.f.f.107.4		8
15.8	even	4		270.2.f.a.107.2	yes	8
15.14	odd	2		270.2.f.a.53.4	yes	8
20.3	even	4		2160.2.w.f.1457.3		8
20.19	odd	2		2160.2.w.f.593.1		8
45.4	even	6		810.2.m.a.593.2		8
45.13	odd	12		810.2.m.a.107.2		8
45.14	odd	6		810.2.m.h.593.1		8
45.23	even	12		810.2.m.h.107.1		8
45.29	odd	6		810.2.m.a.53.2		8
45.34	even	6		810.2.m.h.53.1		8
45.38	even	12		810.2.m.a.377.2		8
45.43	odd	12		810.2.m.h.377.1		8
60.23	odd	4		2160.2.w.f.1457.2		8
60.59	even	2		2160.2.w.f.593.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.f.a.53.1	✓	8	5.4	even	2
270.2.f.a.53.4	yes	8	15.14	odd	2
270.2.f.a.107.2	yes	8	15.8	even	4
270.2.f.a.107.3	yes	8	5.3	odd	4
810.2.m.a.53.2		8	45.29	odd	6
810.2.m.a.107.2		8	45.13	odd	12
810.2.m.a.377.2		8	45.38	even	12
810.2.m.a.593.2		8	45.4	even	6
810.2.m.h.53.1		8	45.34	even	6
810.2.m.h.107.1		8	45.23	even	12
810.2.m.h.377.1		8	45.43	odd	12
810.2.m.h.593.1		8	45.14	odd	6
1350.2.f.f.107.2		8	5.2	odd	4	inner
1350.2.f.f.107.4		8	15.2	even	4	inner
1350.2.f.f.593.2		8	3.2	odd	2	inner
1350.2.f.f.593.4		8	1.1	even	1	trivial
2160.2.w.f.593.1		8	20.19	odd	2
2160.2.w.f.593.4		8	60.59	even	2
2160.2.w.f.1457.2		8	60.23	odd	4
2160.2.w.f.1457.3		8	20.3	even	4

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.44949 - 3.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(3.44949 - 3.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +4.56048i q^{11} +(-1.77526 - 1.77526i) q^{13} +4.87832 q^{14} -1.00000 q^{16} +(2.75699 + 2.75699i) q^{17} -0.449490i q^{19} +(-3.22474 + 3.22474i) q^{22} +(5.90326 - 5.90326i) q^{23} -2.51059i q^{26} +(3.44949 + 3.44949i) q^{28} +0.317837 q^{29} +3.44949 q^{31} +(-0.707107 - 0.707107i) q^{32} +3.89898i q^{34} +(0.317837 - 0.317837i) q^{38} +2.04989i q^{41} +(4.77526 + 4.77526i) q^{43} -4.56048 q^{44} +8.34847 q^{46} +(3.07483 + 3.07483i) q^{47} -16.7980i q^{49} +(1.77526 - 1.77526i) q^{52} +(5.65685 - 5.65685i) q^{53} +4.87832i q^{56} +(0.224745 + 0.224745i) q^{58} +2.82843 q^{59} -3.55051 q^{61} +(2.43916 + 2.43916i) q^{62} -1.00000i q^{64} +(-2.00000 + 2.00000i) q^{67} +(-2.75699 + 2.75699i) q^{68} -0.142865i q^{71} +(-0.449490 - 0.449490i) q^{73} +0.449490 q^{76} +(15.7313 + 15.7313i) q^{77} +0.550510i q^{79} +(-1.44949 + 1.44949i) q^{82} +(-6.75323 + 6.75323i) q^{83} +6.75323i q^{86} +(-3.22474 - 3.22474i) q^{88} +3.32124 q^{89} -12.2474 q^{91} +(5.90326 + 5.90326i) q^{92} +4.34847i q^{94} +(-3.55051 + 3.55051i) q^{97} +(11.8780 - 11.8780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} - 24 q^{13} - 8 q^{16} - 16 q^{22} + 8 q^{28} + 8 q^{31} + 48 q^{43} + 8 q^{46} + 24 q^{52} - 8 q^{58} - 48 q^{61} - 16 q^{67} + 16 q^{73} - 16 q^{76} + 8 q^{82} - 16 q^{88} - 48 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 - 24 * q^13 - 8 * q^16 - 16 * q^22 + 8 * q^28 + 8 * q^31 + 48 * q^43 + 8 * q^46 + 24 * q^52 - 8 * q^58 - 48 * q^61 - 16 * q^67 + 16 * q^73 - 16 * q^76 + 8 * q^82 - 16 * q^88 - 48 * q^97

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