LMFDB - Embedded newform 1792.2.m.g.449.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (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:	$14.3091920422$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			449.6
Root			$2.69978 + 0.355433i$ of defining polynomial
Character	$\chi$	$=$	1792.449
Dual form			1792.2.m.g.1345.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62602 - 1.62602i) q^{3} +(1.16900 + 1.16900i) q^{5} -1.00000i q^{7} -2.28788i q^{9} +O(q^{10})$	\(q+(1.62602 - 1.62602i) q^{3} +(1.16900 + 1.16900i) q^{5} -1.00000i q^{7} -2.28788i q^{9} +(4.39956 + 4.39956i) q^{11} +(-0.448377 + 0.448377i) q^{13} +3.80163 q^{15} +5.02326 q^{17} +(-1.49851 + 1.49851i) q^{19} +(-1.62602 - 1.62602i) q^{21} +8.89958i q^{23} -2.26688i q^{25} +(1.15793 + 1.15793i) q^{27} +(0.803165 - 0.803165i) q^{29} -8.27524 q^{31} +14.3075 q^{33} +(1.16900 - 1.16900i) q^{35} +(-1.55173 - 1.55173i) q^{37} +1.45814i q^{39} +4.93020i q^{41} +(-3.73291 - 3.73291i) q^{43} +(2.67453 - 2.67453i) q^{45} +6.68692 q^{47} -1.00000 q^{49} +(8.16791 - 8.16791i) q^{51} +(-4.53424 - 4.53424i) q^{53} +10.2862i q^{55} +4.87321i q^{57} +(1.06717 + 1.06717i) q^{59} +(5.11346 - 5.11346i) q^{61} -2.28788 q^{63} -1.04830 q^{65} +(7.47532 - 7.47532i) q^{67} +(14.4709 + 14.4709i) q^{69} +4.07354i q^{71} -13.5063i q^{73} +(-3.68600 - 3.68600i) q^{75} +(4.39956 - 4.39956i) q^{77} -9.19701 q^{79} +10.6293 q^{81} +(2.62248 - 2.62248i) q^{83} +(5.87218 + 5.87218i) q^{85} -2.61192i q^{87} +1.60040i q^{89} +(0.448377 + 0.448377i) q^{91} +(-13.4557 + 13.4557i) q^{93} -3.50351 q^{95} -13.0167 q^{97} +(10.0657 - 10.0657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 - 4 * q^5	$ 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.62602	−	1.62602i	0.938783	−	0.938783i	−0.0594487	−	0.998231i	$-0.518934\pi$
$3$	1.62602	−	1.62602i	0.938783	−	0.938783i	0.998231	+	0.0594487i	$0.0189343\pi$
$4$		0			0
$5$	1.16900	+	1.16900i	0.522792	+	0.522792i	0.918414	−	0.395621i	$-0.129471\pi$
$5$	1.16900	+	1.16900i	0.522792	+	0.522792i	−0.395621	+	0.918414i	$0.629471\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	2.28788i		−	0.762626i
$10$		0			0
$11$	4.39956	+	4.39956i	1.32652	+	1.32652i	0.908387	+	0.418130i	$0.137314\pi$
$11$	4.39956	+	4.39956i	1.32652	+	1.32652i	0.418130	+	0.908387i	$0.362686\pi$
$12$		0			0
$13$	−0.448377	+	0.448377i	−0.124357	+	0.124357i	−0.766546	−	0.642189i	$-0.778026\pi$
$13$	−0.448377	+	0.448377i	−0.124357	+	0.124357i	0.642189	+	0.766546i	$0.278026\pi$
$14$		0			0
$15$	3.80163			0.981576
$16$		0			0
$17$	5.02326			1.21832			0.609159	−	0.793048i	$-0.291507\pi$
$17$	5.02326			1.21832			0.609159	+	0.793048i	$0.291507\pi$
$18$		0			0
$19$	−1.49851	+	1.49851i	−0.343782	+	0.343782i	−0.857787	−	0.514005i	$-0.828161\pi$
$19$	−1.49851	+	1.49851i	−0.343782	+	0.343782i	0.514005	+	0.857787i	$0.328161\pi$
$20$		0			0
$21$	−1.62602	−	1.62602i	−0.354826	−	0.354826i
$22$		0			0
$23$			8.89958i			1.85569i	0.372965	+	0.927845i	$0.378341\pi$
$23$			8.89958i			1.85569i	−0.372965	+	0.927845i	$0.621659\pi$
$24$		0			0
$25$		−	2.26688i		−	0.453377i
$26$		0			0
$27$	1.15793	+	1.15793i	0.222843	+	0.222843i
$28$		0			0
$29$	0.803165	−	0.803165i	0.149144	−	0.149144i	−0.628592	−	0.777736i	$-0.716368\pi$
$29$	0.803165	−	0.803165i	0.149144	−	0.149144i	0.777736	+	0.628592i	$0.216368\pi$
$30$		0			0
$31$	−8.27524			−1.48628			−0.743139	−	0.669137i	$-0.766664\pi$
$31$	−8.27524			−1.48628			−0.743139	+	0.669137i	$0.766664\pi$
$32$		0			0
$33$	14.3075			2.49062
$34$		0			0
$35$	1.16900	−	1.16900i	0.197597	−	0.197597i
$36$		0			0
$37$	−1.55173	−	1.55173i	−0.255102	−	0.255102i	0.567956	−	0.823059i	$-0.307734\pi$
$37$	−1.55173	−	1.55173i	−0.255102	−	0.255102i	−0.823059	+	0.567956i	$0.807734\pi$
$38$		0			0
$39$			1.45814i			0.233489i
$40$		0			0
$41$			4.93020i			0.769968i	0.922923	+	0.384984i	$0.125793\pi$
$41$			4.93020i			0.769968i	−0.922923	+	0.384984i	$0.874207\pi$
$42$		0			0
$43$	−3.73291	−	3.73291i	−0.569263	−	0.569263i	0.362659	−	0.931922i	$-0.381869\pi$
$43$	−3.73291	−	3.73291i	−0.569263	−	0.569263i	−0.931922	+	0.362659i	$0.881869\pi$
$44$		0			0
$45$	2.67453	−	2.67453i	0.398695	−	0.398695i
$46$		0			0
$47$	6.68692			0.975387			0.487693	−	0.873015i	$-0.337838\pi$
$47$	6.68692			0.975387			0.487693	+	0.873015i	$0.337838\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	8.16791	−	8.16791i	1.14374	−	1.14374i
$52$		0			0
$53$	−4.53424	−	4.53424i	−0.622826	−	0.622826i	0.323427	−	0.946253i	$-0.395165\pi$
$53$	−4.53424	−	4.53424i	−0.622826	−	0.622826i	−0.946253	+	0.323427i	$0.895165\pi$
$54$		0			0
$55$			10.2862i			1.38699i
$56$		0			0
$57$			4.87321i			0.645473i
$58$		0			0
$59$	1.06717	+	1.06717i	0.138934	+	0.138934i	0.773153	−	0.634219i	$-0.218678\pi$
$59$	1.06717	+	1.06717i	0.138934	+	0.138934i	−0.634219	+	0.773153i	$0.718678\pi$
$60$		0			0
$61$	5.11346	−	5.11346i	0.654711	−	0.654711i	−0.299413	−	0.954124i	$-0.596791\pi$
$61$	5.11346	−	5.11346i	0.654711	−	0.654711i	0.954124	+	0.299413i	$0.0967907\pi$
$62$		0			0
$63$	−2.28788			−0.288245
$64$		0			0
$65$	−1.04830			−0.130026
$66$		0			0
$67$	7.47532	−	7.47532i	0.913256	−	0.913256i	−0.0832712	−	0.996527i	$-0.526537\pi$
$67$	7.47532	−	7.47532i	0.913256	−	0.913256i	0.996527	+	0.0832712i	$0.0265368\pi$
$68$		0			0
$69$	14.4709	+	14.4709i	1.74209	+	1.74209i
$70$		0			0
$71$			4.07354i			0.483440i	0.970346	+	0.241720i	$0.0777116\pi$
$71$			4.07354i			0.483440i	−0.970346	+	0.241720i	$0.922288\pi$
$72$		0			0
$73$		−	13.5063i		−	1.58079i	−0.612595	−	0.790397i	$-0.709874\pi$
$73$		−	13.5063i		−	1.58079i	0.612595	−	0.790397i	$-0.290126\pi$
$74$		0			0
$75$	−3.68600	−	3.68600i	−0.425622	−	0.425622i
$76$		0			0
$77$	4.39956	−	4.39956i	0.501376	−	0.501376i
$78$		0			0
$79$	−9.19701			−1.03474			−0.517372	−	0.855760i	$-0.673090\pi$
$79$	−9.19701			−1.03474			−0.517372	+	0.855760i	$0.673090\pi$
$80$		0			0
$81$	10.6293			1.18103
$82$		0			0
$83$	2.62248	−	2.62248i	0.287855	−	0.287855i	−0.548377	−	0.836231i	$-0.684754\pi$
$83$	2.62248	−	2.62248i	0.287855	−	0.287855i	0.836231	+	0.548377i	$0.184754\pi$
$84$		0			0
$85$	5.87218	+	5.87218i	0.636928	+	0.636928i
$86$		0			0
$87$		−	2.61192i		−	0.280028i
$88$		0			0
$89$			1.60040i			0.169642i	0.996396	+	0.0848209i	$0.0270318\pi$
$89$			1.60040i			0.169642i	−0.996396	+	0.0848209i	$0.972968\pi$
$90$		0			0
$91$	0.448377	+	0.448377i	0.0470027	+	0.0470027i
$92$		0			0
$93$	−13.4557	+	13.4557i	−1.39529	+	1.39529i
$94$		0			0
$95$	−3.50351			−0.359453
$96$		0			0
$97$	−13.0167			−1.32164			−0.660822	−	0.750543i	$-0.729792\pi$
$97$	−13.0167			−1.32164			−0.660822	+	0.750543i	$0.729792\pi$
$98$		0			0
$99$	10.0657	−	10.0657i	1.01164	−	1.01164i
$100$		0			0
$101$	3.76253	+	3.76253i	0.374386	+	0.374386i	0.869072	−	0.494686i	$-0.164717\pi$
$101$	3.76253	+	3.76253i	0.374386	+	0.374386i	−0.494686	+	0.869072i	$0.664717\pi$
$102$		0			0
$103$		−	7.91886i		−	0.780268i	−0.920758	−	0.390134i	$-0.872429\pi$
$103$		−	7.91886i		−	0.780268i	0.920758	−	0.390134i	$-0.127571\pi$
$104$		0			0
$105$		−	3.80163i		−	0.371001i
$106$		0			0
$107$	−13.5961	−	13.5961i	−1.31438	−	1.31438i	−0.918152	−	0.396228i	$-0.870319\pi$
$107$	−13.5961	−	13.5961i	−1.31438	−	1.31438i	−0.396228	−	0.918152i	$-0.629681\pi$
$108$		0			0
$109$	7.03367	−	7.03367i	0.673704	−	0.673704i	−0.284864	−	0.958568i	$-0.591948\pi$
$109$	7.03367	−	7.03367i	0.673704	−	0.673704i	0.958568	+	0.284864i	$0.0919485\pi$
$110$		0			0
$111$	−5.04627			−0.478971
$112$		0			0
$113$	5.62753			0.529394			0.264697	−	0.964332i	$-0.414728\pi$
$113$	5.62753			0.529394			0.264697	+	0.964332i	$0.414728\pi$
$114$		0			0
$115$	−10.4036	+	10.4036i	−0.970141	+	0.970141i
$116$		0			0
$117$	1.02583	+	1.02583i	0.0948381	+	0.0948381i
$118$		0			0
$119$		−	5.02326i		−	0.460481i
$120$		0			0
$121$			27.7123i			2.51930i
$122$		0			0
$123$	8.01660	+	8.01660i	0.722833	+	0.722833i
$124$		0			0
$125$	8.49498	−	8.49498i	0.759814	−	0.759814i
$126$		0			0
$127$	−13.5320			−1.20077			−0.600386	−	0.799710i	$-0.704987\pi$
$127$	−13.5320			−1.20077			−0.600386	+	0.799710i	$0.704987\pi$
$128$		0			0
$129$	−12.1396			−1.06883
$130$		0			0
$131$	−1.48631	+	1.48631i	−0.129859	+	0.129859i	−0.769049	−	0.639190i	$-0.779270\pi$
$131$	−1.48631	+	1.48631i	−0.129859	+	0.129859i	0.639190	+	0.769049i	$0.279270\pi$
$132$		0			0
$133$	1.49851	+	1.49851i	0.129937	+	0.129937i
$134$		0			0
$135$			2.70723i			0.233001i
$136$		0			0
$137$		−	11.7463i		−	1.00355i	−0.864998	−	0.501776i	$-0.832680\pi$
$137$		−	11.7463i		−	1.00355i	0.864998	−	0.501776i	$-0.167320\pi$
$138$		0			0
$139$	−8.00812	−	8.00812i	−0.679240	−	0.679240i	0.280588	−	0.959828i	$-0.409470\pi$
$139$	−8.00812	−	8.00812i	−0.679240	−	0.679240i	−0.959828	+	0.280588i	$0.909470\pi$
$140$		0			0
$141$	10.8731	−	10.8731i	0.915676	−	0.915676i
$142$		0			0
$143$	−3.94532			−0.329924
$144$		0			0
$145$	1.87780			0.155943
$146$		0			0
$147$	−1.62602	+	1.62602i	−0.134112	+	0.134112i
$148$		0			0
$149$	−3.63681	−	3.63681i	−0.297939	−	0.297939i	0.542267	−	0.840206i	$-0.317566\pi$
$149$	−3.63681	−	3.63681i	−0.297939	−	0.297939i	−0.840206	+	0.542267i	$0.817566\pi$
$150$		0			0
$151$			15.9697i			1.29959i	0.760108	+	0.649797i	$0.225146\pi$
$151$			15.9697i			1.29959i	−0.760108	+	0.649797i	$0.774854\pi$
$152$		0			0
$153$		−	11.4926i		−	0.929121i
$154$		0			0
$155$	−9.67375	−	9.67375i	−0.777014	−	0.777014i
$156$		0			0
$157$	14.0481	−	14.0481i	1.12116	−	1.12116i	0.129589	−	0.991568i	$-0.458634\pi$
$157$	14.0481	−	14.0481i	1.12116	−	1.12116i	0.991568	−	0.129589i	$-0.0413659\pi$
$158$		0			0
$159$	−14.7455			−1.16940
$160$		0			0
$161$	8.89958			0.701385
$162$		0			0
$163$	10.2797	−	10.2797i	0.805169	−	0.805169i	−0.178729	−	0.983898i	$-0.557199\pi$
$163$	10.2797	−	10.2797i	0.805169	−	0.805169i	0.983898	+	0.178729i	$0.0571985\pi$
$164$		0			0
$165$	16.7255	+	16.7255i	1.30208	+	1.30208i
$166$		0			0
$167$			19.4131i			1.50223i	0.660172	+	0.751115i	$0.270483\pi$
$167$			19.4131i			1.50223i	−0.660172	+	0.751115i	$0.729517\pi$
$168$		0			0
$169$			12.5979i			0.969071i
$170$		0			0
$171$	3.42841	+	3.42841i	0.262177	+	0.262177i
$172$		0			0
$173$	4.56281	−	4.56281i	0.346904	−	0.346904i	−0.512051	−	0.858955i	$-0.671114\pi$
$173$	4.56281	−	4.56281i	0.346904	−	0.346904i	0.858955	+	0.512051i	$0.171114\pi$
$174$		0			0
$175$	−2.26688			−0.171360
$176$		0			0
$177$	3.47048			0.260857
$178$		0			0
$179$	−16.8129	+	16.8129i	−1.25665	+	1.25665i	−0.303970	+	0.952682i	$0.598312\pi$
$179$	−16.8129	+	16.8129i	−1.25665	+	1.25665i	−0.952682	+	0.303970i	$0.901688\pi$
$180$		0			0
$181$	−6.25856	−	6.25856i	−0.465195	−	0.465195i	0.435159	−	0.900354i	$-0.356692\pi$
$181$	−6.25856	−	6.25856i	−0.465195	−	0.465195i	−0.900354	+	0.435159i	$0.856692\pi$
$182$		0			0
$183$		−	16.6292i		−	1.22926i
$184$		0			0
$185$		−	3.62793i		−	0.266731i
$186$		0			0
$187$	22.1001	+	22.1001i	1.61612	+	1.61612i
$188$		0			0
$189$	1.15793	−	1.15793i	0.0842267	−	0.0842267i
$190$		0			0
$191$	15.8222			1.14486			0.572428	−	0.819955i	$-0.306001\pi$
$191$	15.8222			1.14486			0.572428	+	0.819955i	$0.306001\pi$
$192$		0			0
$193$	−7.50630			−0.540315			−0.270158	−	0.962816i	$-0.587076\pi$
$193$	−7.50630			−0.540315			−0.270158	+	0.962816i	$0.587076\pi$
$194$		0			0
$195$	−1.70456	+	1.70456i	−0.122066	+	0.122066i
$196$		0			0
$197$	−17.2320	−	17.2320i	−1.22773	−	1.22773i	−0.964822	−	0.262905i	$-0.915319\pi$
$197$	−17.2320	−	17.2320i	−1.22773	−	1.22773i	−0.262905	−	0.964822i	$-0.584681\pi$
$198$		0			0
$199$		−	21.8653i		−	1.54999i	−0.631967	−	0.774995i	$-0.717752\pi$
$199$		−	21.8653i		−	1.54999i	0.631967	−	0.774995i	$-0.282248\pi$
$200$		0			0
$201$		−	24.3100i		−	1.71470i
$202$		0			0
$203$	−0.803165	−	0.803165i	−0.0563712	−	0.0563712i
$204$		0			0
$205$	−5.76340	+	5.76340i	−0.402533	+	0.402533i
$206$		0			0
$207$	20.3611			1.41520
$208$		0			0
$209$	−13.1856			−0.912065
$210$		0			0
$211$	2.78563	−	2.78563i	0.191771	−	0.191771i	−0.604690	−	0.796461i	$-0.706703\pi$
$211$	2.78563	−	2.78563i	0.191771	−	0.191771i	0.796461	+	0.604690i	$0.206703\pi$
$212$		0			0
$213$	6.62366	+	6.62366i	0.453845	+	0.453845i
$214$		0			0
$215$		−	8.72753i		−	0.595212i
$216$		0			0
$217$			8.27524i			0.561760i
$218$		0			0
$219$	−21.9615	−	21.9615i	−1.48402	−	1.48402i
$220$		0			0
$221$	−2.25231	+	2.25231i	−0.151507	+	0.151507i
$222$		0			0
$223$	4.64913			0.311329			0.155665	−	0.987810i	$-0.450248\pi$
$223$	4.64913			0.311329			0.155665	+	0.987810i	$0.450248\pi$
$224$		0			0
$225$	−5.18635			−0.345757
$226$		0			0
$227$	−4.41312	+	4.41312i	−0.292909	+	0.292909i	−0.838228	−	0.545319i	$-0.816408\pi$
$227$	−4.41312	+	4.41312i	−0.292909	+	0.292909i	0.545319	+	0.838228i	$0.316408\pi$
$228$		0			0
$229$	−14.4119	−	14.4119i	−0.952362	−	0.952362i	0.0465535	−	0.998916i	$-0.485176\pi$
$229$	−14.4119	−	14.4119i	−0.952362	−	0.952362i	−0.998916	+	0.0465535i	$0.985176\pi$
$230$		0			0
$231$		−	14.3075i		−	0.941367i
$232$		0			0
$233$			11.2765i			0.738746i	0.929281	+	0.369373i	$0.120428\pi$
$233$			11.2765i			0.738746i	−0.929281	+	0.369373i	$0.879572\pi$
$234$		0			0
$235$	7.81700	+	7.81700i	0.509925	+	0.509925i
$236$		0			0
$237$	−14.9545	+	14.9545i	−0.971400	+	0.971400i
$238$		0			0
$239$	−0.994605			−0.0643356			−0.0321678	−	0.999482i	$-0.510241\pi$
$239$	−0.994605			−0.0643356			−0.0321678	+	0.999482i	$0.510241\pi$
$240$		0			0
$241$	27.1158			1.74669			0.873343	−	0.487107i	$-0.161948\pi$
$241$	27.1158			1.74669			0.873343	+	0.487107i	$0.161948\pi$
$242$		0			0
$243$	13.8096	−	13.8096i	0.885885	−	0.885885i
$244$		0			0
$245$	−1.16900	−	1.16900i	−0.0746846	−	0.0746846i
$246$		0			0
$247$		−	1.34379i		−	0.0855036i
$248$		0			0
$249$		−	8.52841i		−	0.540466i
$250$		0			0
$251$	4.47591	+	4.47591i	0.282517	+	0.282517i	0.834112	−	0.551595i	$-0.185981\pi$
$251$	4.47591	+	4.47591i	0.282517	+	0.282517i	−0.551595	+	0.834112i	$0.685981\pi$
$252$		0			0
$253$	−39.1542	+	39.1542i	−2.46161	+	2.46161i
$254$		0			0
$255$	19.0966			1.19587
$256$		0			0
$257$	−7.08743			−0.442102			−0.221051	−	0.975262i	$-0.570949\pi$
$257$	−7.08743			−0.442102			−0.221051	+	0.975262i	$0.570949\pi$
$258$		0			0
$259$	−1.55173	+	1.55173i	−0.0964196	+	0.0964196i
$260$		0			0
$261$	−1.83754	−	1.83754i	−0.113741	−	0.113741i
$262$		0			0
$263$		−	6.95421i		−	0.428815i	−0.976744	−	0.214408i	$-0.931218\pi$
$263$		−	6.95421i		−	0.428815i	0.976744	−	0.214408i	$-0.0687821\pi$
$264$		0			0
$265$		−	10.6010i		−	0.651217i
$266$		0			0
$267$	2.60228	+	2.60228i	0.159257	+	0.159257i
$268$		0			0
$269$	13.2606	−	13.2606i	0.808516	−	0.808516i	−0.175893	−	0.984409i	$-0.556281\pi$
$269$	13.2606	−	13.2606i	0.808516	−	0.808516i	0.984409	+	0.175893i	$0.0562814\pi$
$270$		0			0
$271$	−14.2967			−0.868463			−0.434231	−	0.900801i	$-0.642980\pi$
$271$	−14.2967			−0.868463			−0.434231	+	0.900801i	$0.642980\pi$
$272$		0			0
$273$	1.45814			0.0882506
$274$		0			0
$275$	9.97329	−	9.97329i	0.601412	−	0.601412i
$276$		0			0
$277$	−1.56248	−	1.56248i	−0.0938806	−	0.0938806i	0.658607	−	0.752487i	$-0.271146\pi$
$277$	−1.56248	−	1.56248i	−0.0938806	−	0.0938806i	−0.752487	+	0.658607i	$0.771146\pi$
$278$		0			0
$279$			18.9327i			1.13347i
$280$		0			0
$281$		−	6.06619i		−	0.361879i	−0.983494	−	0.180939i	$-0.942086\pi$
$281$		−	6.06619i		−	0.361879i	0.983494	−	0.180939i	$-0.0579138\pi$
$282$		0			0
$283$	20.3191	+	20.3191i	1.20785	+	1.20785i	0.971723	+	0.236125i	$0.0758774\pi$
$283$	20.3191	+	20.3191i	1.20785	+	1.20785i	0.236125	+	0.971723i	$0.424123\pi$
$284$		0			0
$285$	−5.69678	+	5.69678i	−0.337448	+	0.337448i
$286$		0			0
$287$	4.93020			0.291021
$288$		0			0
$289$	8.23311			0.484301
$290$		0			0
$291$	−21.1654	+	21.1654i	−1.24074	+	1.24074i
$292$		0			0
$293$	22.2357	+	22.2357i	1.29903	+	1.29903i	0.929036	+	0.369989i	$0.120639\pi$
$293$	22.2357	+	22.2357i	1.29903	+	1.29903i	0.369989	+	0.929036i	$0.379361\pi$
$294$		0			0
$295$			2.49504i			0.145267i
$296$		0			0
$297$			10.1887i			0.591210i
$298$		0			0
$299$	−3.99036	−	3.99036i	−0.230769	−	0.230769i
$300$		0			0
$301$	−3.73291	+	3.73291i	−0.215161	+	0.215161i
$302$		0			0
$303$	12.2359			0.702934
$304$		0			0
$305$	11.9553			0.684556
$306$		0			0
$307$	−17.7656	+	17.7656i	−1.01393	+	1.01393i	−0.0140326	+	0.999902i	$0.504467\pi$
$307$	−17.7656	+	17.7656i	−1.01393	+	1.01393i	−0.999902	+	0.0140326i	$0.995533\pi$
$308$		0			0
$309$	−12.8762	−	12.8762i	−0.732502	−	0.732502i
$310$		0			0
$311$			31.2698i			1.77315i	0.462588	+	0.886574i	$0.346921\pi$
$311$			31.2698i			1.77315i	−0.462588	+	0.886574i	$0.653079\pi$
$312$		0			0
$313$			18.0095i			1.01796i	0.860778	+	0.508980i	$0.169977\pi$
$313$			18.0095i			1.01796i	−0.860778	+	0.508980i	$0.830023\pi$
$314$		0			0
$315$	−2.67453	−	2.67453i	−0.150692	−	0.150692i
$316$		0			0
$317$	−12.2418	+	12.2418i	−0.687567	+	0.687567i	−0.961694	−	0.274127i	$-0.911611\pi$
$317$	−12.2418	+	12.2418i	−0.687567	+	0.687567i	0.274127	+	0.961694i	$0.411611\pi$
$318$		0			0
$319$	7.06715			0.395684
$320$		0			0
$321$	−44.2149			−2.46783
$322$		0			0
$323$	−7.52740	+	7.52740i	−0.418836	+	0.418836i
$324$		0			0
$325$	1.01642	+	1.01642i	0.0563807	+	0.0563807i
$326$		0			0
$327$		−	22.8738i		−	1.26492i
$328$		0			0
$329$		−	6.68692i		−	0.368662i
$330$		0			0
$331$	11.7456	+	11.7456i	0.645599	+	0.645599i	0.951926	−	0.306328i	$-0.0991003\pi$
$331$	11.7456	+	11.7456i	0.645599	+	0.645599i	−0.306328	+	0.951926i	$0.599100\pi$
$332$		0			0
$333$	−3.55016	+	3.55016i	−0.194548	+	0.194548i
$334$		0			0
$335$	17.4773			0.954886
$336$		0			0
$337$	6.23237			0.339499			0.169750	−	0.985487i	$-0.445704\pi$
$337$	6.23237			0.339499			0.169750	+	0.985487i	$0.445704\pi$
$338$		0			0
$339$	9.15047	−	9.15047i	0.496986	−	0.496986i
$340$		0			0
$341$	−36.4074	−	36.4074i	−1.97157	−	1.97157i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			33.8329i			1.82150i
$346$		0			0
$347$	−6.62041	−	6.62041i	−0.355402	−	0.355402i	0.506713	−	0.862115i	$-0.330860\pi$
$347$	−6.62041	−	6.62041i	−0.355402	−	0.355402i	−0.862115	+	0.506713i	$0.830860\pi$
$348$		0			0
$349$	−14.7958	+	14.7958i	−0.792001	+	0.792001i	−0.981819	−	0.189819i	$-0.939210\pi$
$349$	−14.7958	+	14.7958i	−0.792001	+	0.792001i	0.189819	+	0.981819i	$0.439210\pi$
$350$		0			0
$351$	−1.03837			−0.0554243
$352$		0			0
$353$	−17.7098			−0.942599			−0.471300	−	0.881973i	$-0.656215\pi$
$353$	−17.7098			−0.942599			−0.471300	+	0.881973i	$0.656215\pi$
$354$		0			0
$355$	−4.76196	+	4.76196i	−0.252739	+	0.252739i
$356$		0			0
$357$	−8.16791	−	8.16791i	−0.432292	−	0.432292i
$358$		0			0
$359$			8.53643i			0.450535i	0.974297	+	0.225268i	$0.0723257\pi$
$359$			8.53643i			0.450535i	−0.974297	+	0.225268i	$0.927674\pi$
$360$		0			0
$361$			14.5089i			0.763628i
$362$		0			0
$363$	45.0607	+	45.0607i	2.36507	+	2.36507i
$364$		0			0
$365$	15.7889	−	15.7889i	0.826427	−	0.826427i
$366$		0			0
$367$	11.3226			0.591037			0.295519	−	0.955337i	$-0.404508\pi$
$367$	11.3226			0.591037			0.295519	+	0.955337i	$0.404508\pi$
$368$		0			0
$369$	11.2797			0.587198
$370$		0			0
$371$	−4.53424	+	4.53424i	−0.235406	+	0.235406i
$372$		0			0
$373$	−7.88728	−	7.88728i	−0.408388	−	0.408388i	0.472788	−	0.881176i	$-0.343248\pi$
$373$	−7.88728	−	7.88728i	−0.408388	−	0.408388i	−0.881176	+	0.472788i	$0.843248\pi$
$374$		0			0
$375$		−	27.6260i		−	1.42660i
$376$		0			0
$377$			0.720241i			0.0370943i
$378$		0			0
$379$	−9.53241	−	9.53241i	−0.489647	−	0.489647i	0.418548	−	0.908195i	$-0.362539\pi$
$379$	−9.53241	−	9.53241i	−0.489647	−	0.489647i	−0.908195	+	0.418548i	$0.862539\pi$
$380$		0			0
$381$	−22.0033	+	22.0033i	−1.12726	+	1.12726i
$382$		0			0
$383$	18.9261			0.967077			0.483539	−	0.875323i	$-0.339351\pi$
$383$	18.9261			0.967077			0.483539	+	0.875323i	$0.339351\pi$
$384$		0			0
$385$	10.2862			0.524231
$386$		0			0
$387$	−8.54043	+	8.54043i	−0.434134	+	0.434134i
$388$		0			0
$389$	−6.78034	−	6.78034i	−0.343777	−	0.343777i	0.514008	−	0.857785i	$-0.328160\pi$
$389$	−6.78034	−	6.78034i	−0.343777	−	0.343777i	−0.857785	+	0.514008i	$0.828160\pi$
$390$		0			0
$391$			44.7049i			2.26082i
$392$		0			0
$393$			4.83352i			0.243819i
$394$		0			0
$395$	−10.7513	−	10.7513i	−0.540956	−	0.540956i
$396$		0			0
$397$	1.93608	−	1.93608i	0.0971692	−	0.0971692i	−0.656851	−	0.754020i	$-0.728112\pi$
$397$	1.93608	−	1.93608i	0.0971692	−	0.0971692i	0.754020	+	0.656851i	$0.228112\pi$
$398$		0			0
$399$	4.87321			0.243966
$400$		0			0
$401$	−16.6483			−0.831378			−0.415689	−	0.909507i	$-0.636460\pi$
$401$	−16.6483			−0.831378			−0.415689	+	0.909507i	$0.636460\pi$
$402$		0			0
$403$	3.71043	−	3.71043i	0.184829	−	0.184829i
$404$		0			0
$405$	12.4256	+	12.4256i	0.617432	+	0.617432i
$406$		0			0
$407$		−	13.6538i		−	0.676795i
$408$		0			0
$409$		−	16.8706i		−	0.834199i	−0.908861	−	0.417100i	$-0.863047\pi$
$409$		−	16.8706i		−	0.834199i	0.908861	−	0.417100i	$-0.136953\pi$
$410$		0			0
$411$	−19.0997	−	19.0997i	−0.942117	−	0.942117i
$412$		0			0
$413$	1.06717	−	1.06717i	0.0525120	−	0.0525120i
$414$		0			0
$415$	6.13136			0.300976
$416$		0			0
$417$	−26.0427			−1.27532
$418$		0			0
$419$	−20.1511	+	20.1511i	−0.984444	+	0.984444i	−0.999881	−	0.0154368i	$-0.995086\pi$
$419$	−20.1511	+	20.1511i	−0.984444	+	0.984444i	0.0154368	+	0.999881i	$0.495086\pi$
$420$		0			0
$421$	−6.44015	−	6.44015i	−0.313874	−	0.313874i	0.532535	−	0.846408i	$-0.321240\pi$
$421$	−6.44015	−	6.44015i	−0.313874	−	0.313874i	−0.846408	+	0.532535i	$0.821240\pi$
$422$		0			0
$423$		−	15.2988i		−	0.743855i
$424$		0			0
$425$		−	11.3871i		−	0.552357i
$426$		0			0
$427$	−5.11346	−	5.11346i	−0.247458	−	0.247458i
$428$		0			0
$429$	−6.41517	+	6.41517i	−0.309727	+	0.309727i
$430$		0			0
$431$	−28.6481			−1.37993			−0.689965	−	0.723843i	$-0.742374\pi$
$431$	−28.6481			−1.37993			−0.689965	+	0.723843i	$0.742374\pi$
$432$		0			0
$433$	−4.69574			−0.225663			−0.112832	−	0.993614i	$-0.535992\pi$
$433$	−4.69574			−0.225663			−0.112832	+	0.993614i	$0.535992\pi$
$434$		0			0
$435$	3.05334	−	3.05334i	0.146396	−	0.146396i
$436$		0			0
$437$	−13.3361	−	13.3361i	−0.637953	−	0.637953i
$438$		0			0
$439$		−	22.6652i		−	1.08175i	−0.841103	−	0.540874i	$-0.818093\pi$
$439$		−	22.6652i		−	1.08175i	0.841103	−	0.540874i	$-0.181907\pi$
$440$		0			0
$441$			2.28788i			0.108947i
$442$		0			0
$443$	−17.7935	−	17.7935i	−0.845394	−	0.845394i	0.144160	−	0.989554i	$-0.453952\pi$
$443$	−17.7935	−	17.7935i	−0.845394	−	0.845394i	−0.989554	+	0.144160i	$0.953952\pi$
$444$		0			0
$445$	−1.87086	+	1.87086i	−0.0886875	+	0.0886875i
$446$		0			0
$447$	−11.8270			−0.559400
$448$		0			0
$449$	−11.2262			−0.529799			−0.264900	−	0.964276i	$-0.585339\pi$
$449$	−11.2262			−0.529799			−0.264900	+	0.964276i	$0.585339\pi$
$450$		0			0
$451$	−21.6907	+	21.6907i	−1.02138	+	1.02138i
$452$		0			0
$453$	25.9670	+	25.9670i	1.22004	+	1.22004i
$454$		0			0
$455$			1.04830i			0.0491452i
$456$		0			0
$457$		−	20.8858i		−	0.976998i	−0.872564	−	0.488499i	$-0.837545\pi$
$457$		−	20.8858i		−	0.976998i	0.872564	−	0.488499i	$-0.162455\pi$
$458$		0			0
$459$	5.81656	+	5.81656i	0.271494	+	0.271494i
$460$		0			0
$461$	−1.78650	+	1.78650i	−0.0832056	+	0.0832056i	−0.747485	−	0.664279i	$-0.768739\pi$
$461$	−1.78650	+	1.78650i	−0.0832056	+	0.0832056i	0.664279	+	0.747485i	$0.268739\pi$
$462$		0			0
$463$	21.0754			0.979457			0.489728	−	0.871875i	$-0.337096\pi$
$463$	21.0754			0.979457			0.489728	+	0.871875i	$0.337096\pi$
$464$		0			0
$465$	−31.4594			−1.45889
$466$		0			0
$467$	−8.05590	+	8.05590i	−0.372783	+	0.372783i	−0.868490	−	0.495707i	$-0.834909\pi$
$467$	−8.05590	+	8.05590i	−0.372783	+	0.372783i	0.495707	+	0.868490i	$0.334909\pi$
$468$		0			0
$469$	−7.47532	−	7.47532i	−0.345178	−	0.345178i
$470$		0			0
$471$		−	45.6848i		−	2.10505i
$472$		0			0
$473$		−	32.8463i		−	1.51027i
$474$		0			0
$475$	3.39695	+	3.39695i	0.155863	+	0.155863i
$476$		0			0
$477$	−10.3738	+	10.3738i	−0.474983	+	0.474983i
$478$		0			0
$479$	19.8741			0.908070			0.454035	−	0.890984i	$-0.349984\pi$
$479$	19.8741			0.908070			0.454035	+	0.890984i	$0.349984\pi$
$480$		0			0
$481$	1.39152			0.0634477
$482$		0			0
$483$	14.4709	−	14.4709i	0.658448	−	0.658448i
$484$		0			0
$485$	−15.2165	−	15.2165i	−0.690945	−	0.690945i
$486$		0			0
$487$			19.2744i			0.873406i	0.899606	+	0.436703i	$0.143854\pi$
$487$			19.2744i			0.873406i	−0.899606	+	0.436703i	$0.856146\pi$
$488$		0			0
$489$		−	33.4300i		−	1.51176i
$490$		0			0
$491$	−4.01202	−	4.01202i	−0.181060	−	0.181060i	0.610758	−	0.791818i	$-0.290865\pi$
$491$	−4.01202	−	4.01202i	−0.181060	−	0.181060i	−0.791818	+	0.610758i	$0.790865\pi$
$492$		0			0
$493$	4.03451	−	4.03451i	0.181705	−	0.181705i
$494$		0			0
$495$	23.5335			1.05775
$496$		0			0
$497$	4.07354			0.182723
$498$		0			0
$499$	−4.10545	+	4.10545i	−0.183785	+	0.183785i	−0.793003	−	0.609218i	$-0.791484\pi$
$499$	−4.10545	+	4.10545i	−0.183785	+	0.183785i	0.609218	+	0.793003i	$0.291484\pi$
$500$		0			0
$501$	31.5660	+	31.5660i	1.41027	+	1.41027i
$502$		0			0
$503$		−	19.8588i		−	0.885460i	−0.896655	−	0.442730i	$-0.854010\pi$
$503$		−	19.8588i		−	0.885460i	0.896655	−	0.442730i	$-0.145990\pi$
$504$		0			0
$505$			8.79680i			0.391452i
$506$		0			0
$507$	20.4845	+	20.4845i	0.909747	+	0.909747i
$508$		0			0
$509$	8.11547	−	8.11547i	0.359712	−	0.359712i	−0.503995	−	0.863707i	$-0.668137\pi$
$509$	8.11547	−	8.11547i	0.359712	−	0.359712i	0.863707	+	0.503995i	$0.168137\pi$
$510$		0			0
$511$	−13.5063			−0.597484
$512$		0			0
$513$	−3.47033			−0.153219
$514$		0			0
$515$	9.25714	−	9.25714i	0.407918	−	0.407918i
$516$		0			0
$517$	29.4195	+	29.4195i	1.29387	+	1.29387i
$518$		0			0
$519$		−	14.8384i		−	0.651335i
$520$		0			0
$521$			11.8477i			0.519059i	0.965735	+	0.259530i	$0.0835675\pi$
$521$			11.8477i			0.519059i	−0.965735	+	0.259530i	$0.916432\pi$
$522$		0			0
$523$	−19.5435	−	19.5435i	−0.854575	−	0.854575i	0.136117	−	0.990693i	$-0.456538\pi$
$523$	−19.5435	−	19.5435i	−0.854575	−	0.854575i	−0.990693	+	0.136117i	$0.956538\pi$
$524$		0			0
$525$	−3.68600	+	3.68600i	−0.160870	+	0.160870i
$526$		0			0
$527$	−41.5687			−1.81076
$528$		0			0
$529$	−56.2025			−2.44359
$530$		0			0
$531$	2.44155	−	2.44155i	0.105954	−	0.105954i
$532$		0			0
$533$	−2.21059	−	2.21059i	−0.0957512	−	0.0957512i
$534$		0			0
$535$		−	31.7876i		−	1.37430i
$536$		0			0
$537$			54.6760i			2.35945i
$538$		0			0
$539$	−4.39956	−	4.39956i	−0.189502	−	0.189502i
$540$		0			0
$541$	29.1223	−	29.1223i	1.25207	−	1.25207i	0.297274	−	0.954792i	$-0.403922\pi$
$541$	29.1223	−	29.1223i	1.25207	−	1.25207i	0.954792	−	0.297274i	$-0.0960776\pi$
$542$		0			0
$543$	−20.3531			−0.873434
$544$		0			0
$545$	16.4447			0.704414
$546$		0			0
$547$	12.7023	−	12.7023i	0.543111	−	0.543111i	−0.381329	−	0.924440i	$-0.624533\pi$
$547$	12.7023	−	12.7023i	0.543111	−	0.543111i	0.924440	+	0.381329i	$0.124533\pi$
$548$		0			0
$549$	−11.6990	−	11.6990i	−0.499299	−	0.499299i
$550$		0			0
$551$			2.40710i			0.102546i
$552$		0			0
$553$			9.19701i			0.391097i
$554$		0			0
$555$	−5.89909	−	5.89909i	−0.250402	−	0.250402i
$556$		0			0
$557$	18.2855	−	18.2855i	0.774780	−	0.774780i	−0.204158	−	0.978938i	$-0.565446\pi$
$557$	18.2855	−	18.2855i	0.774780	−	0.774780i	0.978938	+	0.204158i	$0.0654456\pi$
$558$		0			0
$559$	3.34750			0.141584
$560$		0			0
$561$	71.8704			3.03437
$562$		0			0
$563$	−0.721510	+	0.721510i	−0.0304080	+	0.0304080i	−0.722147	−	0.691739i	$-0.756845\pi$
$563$	−0.721510	+	0.721510i	−0.0304080	+	0.0304080i	0.691739	+	0.722147i	$0.256845\pi$
$564$		0			0
$565$	6.57858	+	6.57858i	0.276763	+	0.276763i
$566$		0			0
$567$		−	10.6293i		−	0.446387i
$568$		0			0
$569$		−	33.5555i		−	1.40672i	−0.710834	−	0.703360i	$-0.751682\pi$
$569$		−	33.5555i		−	1.40672i	0.710834	−	0.703360i	$-0.248318\pi$
$570$		0			0
$571$	3.80134	+	3.80134i	0.159081	+	0.159081i	0.782159	−	0.623078i	$-0.214118\pi$
$571$	3.80134	+	3.80134i	0.159081	+	0.159081i	−0.623078	+	0.782159i	$0.714118\pi$
$572$		0			0
$573$	25.7273	−	25.7273i	1.07477	−	1.07477i
$574$		0			0
$575$	20.1743			0.841327
$576$		0			0
$577$	−2.22515			−0.0926344			−0.0463172	−	0.998927i	$-0.514748\pi$
$577$	−2.22515			−0.0926344			−0.0463172	+	0.998927i	$0.514748\pi$
$578$		0			0
$579$	−12.2054	+	12.2054i	−0.507238	+	0.507238i
$580$		0			0
$581$	−2.62248	−	2.62248i	−0.108799	−	0.108799i
$582$		0			0
$583$		−	39.8973i		−	1.65238i
$584$		0			0
$585$			2.39839i			0.0991612i
$586$		0			0
$587$	4.33373	+	4.33373i	0.178872	+	0.178872i	0.790864	−	0.611992i	$-0.209631\pi$
$587$	4.33373	+	4.33373i	0.178872	+	0.178872i	−0.611992	+	0.790864i	$0.709631\pi$
$588$		0			0
$589$	12.4005	−	12.4005i	0.510955	−	0.510955i
$590$		0			0
$591$	−56.0390			−2.30514
$592$		0			0
$593$	−16.8460			−0.691784			−0.345892	−	0.938274i	$-0.612424\pi$
$593$	−16.8460			−0.691784			−0.345892	+	0.938274i	$0.612424\pi$
$594$		0			0
$595$	5.87218	−	5.87218i	0.240736	−	0.240736i
$596$		0			0
$597$	−35.5534	−	35.5534i	−1.45510	−	1.45510i
$598$		0			0
$599$			43.9075i			1.79401i	0.442018	+	0.897006i	$0.354263\pi$
$599$			43.9075i			1.79401i	−0.442018	+	0.897006i	$0.645737\pi$
$600$		0			0
$601$			35.5257i			1.44912i	0.689210	+	0.724562i	$0.257958\pi$
$601$			35.5257i			1.44912i	−0.689210	+	0.724562i	$0.742042\pi$
$602$		0			0
$603$	−17.1026	−	17.1026i	−0.696472	−	0.696472i
$604$		0			0
$605$	−32.3956	+	32.3956i	−1.31707	+	1.31707i
$606$		0			0
$607$	−15.7700			−0.640084			−0.320042	−	0.947403i	$-0.603697\pi$
$607$	−15.7700			−0.640084			−0.320042	+	0.947403i	$0.603697\pi$
$608$		0			0
$609$	−2.61192			−0.105841
$610$		0			0
$611$	−2.99826	+	2.99826i	−0.121297	+	0.121297i
$612$		0			0
$613$	8.17171	+	8.17171i	0.330052	+	0.330052i	0.852606	−	0.522554i	$-0.175021\pi$
$613$	8.17171	+	8.17171i	0.330052	+	0.330052i	−0.522554	+	0.852606i	$0.675021\pi$
$614$		0			0
$615$			18.7428i			0.755783i
$616$		0			0
$617$			23.3938i			0.941800i	0.882187	+	0.470900i	$0.156071\pi$
$617$			23.3938i			0.941800i	−0.882187	+	0.470900i	$0.843929\pi$
$618$		0			0
$619$	−2.73711	−	2.73711i	−0.110014	−	0.110014i	0.649957	−	0.759971i	$-0.274787\pi$
$619$	−2.73711	−	2.73711i	−0.110014	−	0.110014i	−0.759971	+	0.649957i	$0.774787\pi$
$620$		0			0
$621$	−10.3051	+	10.3051i	−0.413528	+	0.413528i
$622$		0			0
$623$	1.60040			0.0641186
$624$		0			0
$625$	8.52682			0.341073
$626$		0			0
$627$	−21.4400	+	21.4400i	−0.856231	+	0.856231i
$628$		0			0
$629$	−7.79472	−	7.79472i	−0.310796	−	0.310796i
$630$		0			0
$631$		−	34.9200i		−	1.39014i	−0.718941	−	0.695071i	$-0.755373\pi$
$631$		−	34.9200i		−	1.39014i	0.718941	−	0.695071i	$-0.244627\pi$
$632$		0			0
$633$		−	9.05897i		−	0.360062i
$634$		0			0
$635$	−15.8189	−	15.8189i	−0.627755	−	0.627755i
$636$		0			0
$637$	0.448377	−	0.448377i	0.0177653	−	0.0177653i
$638$		0			0
$639$	9.31976			0.368684
$640$		0			0
$641$	−42.9662			−1.69706			−0.848532	−	0.529144i	$-0.822513\pi$
$641$	−42.9662			−1.69706			−0.848532	+	0.529144i	$0.822513\pi$
$642$		0			0
$643$	−17.5924	+	17.5924i	−0.693777	+	0.693777i	−0.963061	−	0.269284i	$-0.913213\pi$
$643$	−17.5924	+	17.5924i	−0.693777	+	0.693777i	0.269284	+	0.963061i	$0.413213\pi$
$644$		0			0
$645$	−14.1911	−	14.1911i	−0.558775	−	0.558775i
$646$		0			0
$647$			33.5883i			1.32049i	0.751049	+	0.660246i	$0.229548\pi$
$647$			33.5883i			1.32049i	−0.751049	+	0.660246i	$0.770452\pi$
$648$		0			0
$649$			9.39016i			0.368596i
$650$		0			0
$651$	13.4557	+	13.4557i	0.527371	+	0.527371i
$652$		0			0
$653$	0.281193	−	0.281193i	0.0110039	−	0.0110039i	−0.701583	−	0.712587i	$-0.747523\pi$
$653$	0.281193	−	0.281193i	0.0110039	−	0.0110039i	0.712587	+	0.701583i	$0.247523\pi$
$654$		0			0
$655$	−3.47498			−0.135779
$656$		0			0
$657$	−30.9008			−1.20555
$658$		0			0
$659$	1.25405	−	1.25405i	0.0488508	−	0.0488508i	−0.682259	−	0.731110i	$-0.739003\pi$
$659$	1.25405	−	1.25405i	0.0488508	−	0.0488508i	0.731110	+	0.682259i	$0.239003\pi$
$660$		0			0
$661$	30.7505	+	30.7505i	1.19605	+	1.19605i	0.975338	+	0.220717i	$0.0708396\pi$
$661$	30.7505	+	30.7505i	1.19605	+	1.19605i	0.220717	+	0.975338i	$0.429160\pi$
$662$		0			0
$663$			7.32460i			0.284464i
$664$		0			0
$665$			3.50351i			0.135860i
$666$		0			0
$667$	7.14783	+	7.14783i	0.276765	+	0.276765i
$668$		0			0
$669$	7.55958	−	7.55958i	0.292270	−	0.292270i
$670$		0			0
$671$	44.9939			1.73697
$672$		0			0
$673$	−22.2711			−0.858486			−0.429243	−	0.903189i	$-0.641220\pi$
$673$	−22.2711			−0.858486			−0.429243	+	0.903189i	$0.641220\pi$
$674$		0			0
$675$	2.62488	−	2.62488i	0.101032	−	0.101032i
$676$		0			0
$677$	29.3508	+	29.3508i	1.12804	+	1.12804i	0.990495	+	0.137547i	$0.0439218\pi$
$677$	29.3508	+	29.3508i	1.12804	+	1.12804i	0.137547	+	0.990495i	$0.456078\pi$
$678$		0			0
$679$			13.0167i			0.499535i
$680$		0			0
$681$			14.3516i			0.549956i
$682$		0			0
$683$	1.79560	+	1.79560i	0.0687066	+	0.0687066i	0.740625	−	0.671918i	$-0.234529\pi$
$683$	1.79560	+	1.79560i	0.0687066	+	0.0687066i	−0.671918	+	0.740625i	$0.734529\pi$
$684$		0			0
$685$	13.7314	−	13.7314i	0.524649	−	0.524649i
$686$		0			0
$687$	−46.8679			−1.78812
$688$		0			0
$689$	4.06610			0.154906
$690$		0			0
$691$	−11.7289	+	11.7289i	−0.446188	+	0.446188i	−0.894085	−	0.447897i	$-0.852173\pi$
$691$	−11.7289	+	11.7289i	−0.446188	+	0.446188i	0.447897	+	0.894085i	$0.352173\pi$
$692$		0			0
$693$	−10.0657	−	10.0657i	−0.382363	−	0.382363i
$694$		0			0
$695$		−	18.7230i		−	0.710202i
$696$		0			0
$697$			24.7657i			0.938067i
$698$		0			0
$699$	18.3358	+	18.3358i	0.693522	+	0.693522i
$700$		0			0
$701$	23.5050	−	23.5050i	0.887772	−	0.887772i	−0.106536	−	0.994309i	$-0.533976\pi$
$701$	23.5050	−	23.5050i	0.887772	−	0.887772i	0.994309	+	0.106536i	$0.0339761\pi$
$702$		0			0
$703$	4.65056			0.175399
$704$		0			0
$705$	25.4212			0.957417
$706$		0			0
$707$	3.76253	−	3.76253i	0.141505	−	0.141505i
$708$		0			0
$709$	−1.55617	−	1.55617i	−0.0584430	−	0.0584430i	0.677281	−	0.735724i	$-0.263158\pi$
$709$	−1.55617	−	1.55617i	−0.0584430	−	0.0584430i	−0.735724	+	0.677281i	$0.763158\pi$
$710$		0			0
$711$			21.0416i			0.789123i
$712$		0			0
$713$		−	73.6462i		−	2.75807i
$714$		0			0
$715$	−4.61208	−	4.61208i	−0.172482	−	0.172482i
$716$		0			0
$717$	−1.61725	+	1.61725i	−0.0603972	+	0.0603972i
$718$		0			0
$719$	6.97452			0.260106			0.130053	−	0.991507i	$-0.458485\pi$
$719$	6.97452			0.260106			0.130053	+	0.991507i	$0.458485\pi$
$720$		0			0
$721$	−7.91886			−0.294914
$722$		0			0
$723$	44.0909	−	44.0909i	1.63976	−	1.63976i
$724$		0			0
$725$	−1.82068	−	1.82068i	−0.0676184	−	0.0676184i
$726$		0			0
$727$			12.7285i			0.472073i	0.971744	+	0.236037i	$0.0758485\pi$
$727$			12.7285i			0.472073i	−0.971744	+	0.236037i	$0.924151\pi$
$728$		0			0
$729$		−	13.0216i		−	0.482280i
$730$		0			0
$731$	−18.7513	−	18.7513i	−0.693544	−	0.693544i
$732$		0			0
$733$	−14.0786	+	14.0786i	−0.520006	+	0.520006i	−0.917573	−	0.397567i	$-0.869855\pi$
$733$	−14.0786	+	14.0786i	−0.520006	+	0.520006i	0.397567	+	0.917573i	$0.369855\pi$
$734$		0			0
$735$	−3.80163			−0.140225
$736$		0			0
$737$	65.7762			2.42290
$738$		0			0
$739$	36.9779	−	36.9779i	1.36026	−	1.36026i	0.486669	−	0.873587i	$-0.338212\pi$
$739$	36.9779	−	36.9779i	1.36026	−	1.36026i	0.873587	−	0.486669i	$-0.161788\pi$
$740$		0			0
$741$	−2.18504	−	2.18504i	−0.0802693	−	0.0802693i
$742$		0			0
$743$		−	10.0453i		−	0.368527i	−0.982877	−	0.184263i	$-0.941010\pi$
$743$		−	10.0453i		−	0.368527i	0.982877	−	0.184263i	$-0.0589900\pi$
$744$		0			0
$745$		−	8.50285i		−	0.311520i
$746$		0			0
$747$	−5.99992	−	5.99992i	−0.219525	−	0.219525i
$748$		0			0
$749$	−13.5961	+	13.5961i	−0.496789	+	0.496789i
$750$		0			0
$751$	−42.4776			−1.55003			−0.775014	−	0.631944i	$-0.782257\pi$
$751$	−42.4776			−1.55003			−0.775014	+	0.631944i	$0.782257\pi$
$752$		0			0
$753$	14.5558			0.530443
$754$		0			0
$755$	−18.6685	+	18.6685i	−0.679417	+	0.679417i
$756$		0			0
$757$	29.7792	+	29.7792i	1.08234	+	1.08234i	0.996291	+	0.0860518i	$0.0274251\pi$
$757$	29.7792	+	29.7792i	1.08234	+	1.08234i	0.0860518	+	0.996291i	$0.472575\pi$
$758$		0			0
$759$			127.331i			4.62183i
$760$		0			0
$761$		−	6.54784i		−	0.237359i	−0.992933	−	0.118679i	$-0.962134\pi$
$761$		−	6.54784i		−	0.237359i	0.992933	−	0.118679i	$-0.0378661\pi$
$762$		0			0
$763$	−7.03367	−	7.03367i	−0.254636	−	0.254636i
$764$		0			0
$765$	13.4348	−	13.4348i	0.485737	−	0.485737i
$766$		0			0
$767$	−0.956988			−0.0345549
$768$		0			0
$769$	31.6203			1.14026			0.570129	−	0.821555i	$-0.306893\pi$
$769$	31.6203			1.14026			0.570129	+	0.821555i	$0.306893\pi$
$770$		0			0
$771$	−11.5243	+	11.5243i	−0.415037	+	0.415037i
$772$		0			0
$773$	10.6240	+	10.6240i	0.382118	+	0.382118i	0.871865	−	0.489747i	$-0.162911\pi$
$773$	10.6240	+	10.6240i	0.382118	+	0.382118i	−0.489747	+	0.871865i	$0.662911\pi$
$774$		0			0
$775$			18.7590i			0.673843i
$776$		0			0
$777$			5.04627i			0.181034i
$778$		0			0
$779$	−7.38796	−	7.38796i	−0.264701	−	0.264701i
$780$		0			0
$781$	−17.9218	+	17.9218i	−0.641292	+	0.641292i
$782$		0			0
$783$	1.86001			0.0664714
$784$		0			0
$785$	32.8443			1.17226
$786$		0			0
$787$	34.2598	−	34.2598i	1.22123	−	1.22123i	0.254035	−	0.967195i	$-0.418242\pi$
$787$	34.2598	−	34.2598i	1.22123	−	1.22123i	0.967195	−	0.254035i	$-0.0817580\pi$
$788$		0			0
$789$	−11.3077	−	11.3077i	−0.402564	−	0.402564i
$790$		0			0
$791$		−	5.62753i		−	0.200092i
$792$		0			0
$793$			4.58551i			0.162836i
$794$		0			0
$795$	−17.2375	−	17.2375i	−0.611351	−	0.611351i
$796$		0			0
$797$	8.55176	−	8.55176i	0.302919	−	0.302919i	−0.539236	−	0.842155i	$-0.681287\pi$
$797$	8.55176	−	8.55176i	0.302919	−	0.302919i	0.842155	+	0.539236i	$0.181287\pi$
$798$		0			0
$799$	33.5901			1.18833
$800$		0			0
$801$	3.66151			0.129373
$802$		0			0
$803$	59.4218	−	59.4218i	2.09695	−	2.09695i
$804$		0			0
$805$	10.4036	+	10.4036i	0.366679	+	0.366679i
$806$		0			0
$807$		−	43.1241i		−	1.51804i
$808$		0			0
$809$		−	36.6145i		−	1.28730i	−0.765321	−	0.643649i	$-0.777420\pi$
$809$		−	36.6145i		−	1.28730i	0.765321	−	0.643649i	$-0.222580\pi$
$810$		0			0
$811$	25.6562	+	25.6562i	0.900911	+	0.900911i	0.995515	−	0.0946041i	$-0.0301585\pi$
$811$	25.6562	+	25.6562i	0.900911	+	0.900911i	−0.0946041	+	0.995515i	$0.530159\pi$
$812$		0			0
$813$	−23.2467	+	23.2467i	−0.815298	+	0.815298i
$814$		0			0
$815$	24.0340			0.841873
$816$		0			0
$817$	11.1876			0.391405
$818$		0			0
$819$	1.02583	−	1.02583i	0.0358454	−	0.0358454i
$820$		0			0
$821$	−12.7635	−	12.7635i	−0.445450	−	0.445450i	0.448389	−	0.893839i	$-0.351998\pi$
$821$	−12.7635	−	12.7635i	−0.445450	−	0.445450i	−0.893839	+	0.448389i	$0.851998\pi$
$822$		0			0
$823$		−	36.1501i		−	1.26011i	−0.776549	−	0.630057i	$-0.783032\pi$
$823$		−	36.1501i		−	1.26011i	0.776549	−	0.630057i	$-0.216968\pi$
$824$		0			0
$825$		−	32.4335i		−	1.12919i
$826$		0			0
$827$	27.2708	+	27.2708i	0.948297	+	0.948297i	0.998728	−	0.0504301i	$-0.0160592\pi$
$827$	27.2708	+	27.2708i	0.948297	+	0.948297i	−0.0504301	+	0.998728i	$0.516059\pi$
$828$		0			0
$829$	5.10352	−	5.10352i	0.177253	−	0.177253i	−0.612904	−	0.790157i	$-0.709999\pi$
$829$	5.10352	−	5.10352i	0.177253	−	0.177253i	0.790157	+	0.612904i	$0.209999\pi$
$830$		0			0
$831$	−5.08126			−0.176267
$832$		0			0
$833$	−5.02326			−0.174046
$834$		0			0
$835$	−22.6939	+	22.6939i	−0.785354	+	0.785354i
$836$		0			0
$837$	−9.58212	−	9.58212i	−0.331206	−	0.331206i
$838$		0			0
$839$			34.6198i			1.19521i	0.801791	+	0.597604i	$0.203880\pi$
$839$			34.6198i			1.19521i	−0.801791	+	0.597604i	$0.796120\pi$
$840$		0			0
$841$			27.7099i			0.955512i
$842$		0			0
$843$	−9.86374	−	9.86374i	−0.339725	−	0.339725i
$844$		0			0
$845$	−14.7270	+	14.7270i	−0.506623	+	0.506623i
$846$		0			0
$847$	27.7123			0.952205
$848$		0			0
$849$	66.0786			2.26781
$850$		0			0
$851$	13.8097	−	13.8097i	0.473391	−	0.473391i
$852$		0			0
$853$	37.0575	+	37.0575i	1.26882	+	1.26882i	0.946696	+	0.322128i	$0.104398\pi$
$853$	37.0575	+	37.0575i	1.26882	+	1.26882i	0.322128	+	0.946696i	$0.395602\pi$
$854$		0			0
$855$			8.01561i			0.274128i
$856$		0			0
$857$		−	18.9647i		−	0.647823i	−0.946087	−	0.323912i	$-0.895002\pi$
$857$		−	18.9647i		−	0.647823i	0.946087	−	0.323912i	$-0.104998\pi$
$858$		0			0
$859$	−17.9539	−	17.9539i	−0.612577	−	0.612577i	0.331039	−	0.943617i	$-0.392601\pi$
$859$	−17.9539	−	17.9539i	−0.612577	−	0.612577i	−0.943617	+	0.331039i	$0.892601\pi$
$860$		0			0
$861$	8.01660	−	8.01660i	0.273205	−	0.273205i
$862$		0			0
$863$	−11.5403			−0.392837			−0.196418	−	0.980520i	$-0.562931\pi$
$863$	−11.5403			−0.392837			−0.196418	+	0.980520i	$0.562931\pi$
$864$		0			0
$865$	10.6678			0.362717
$866$		0			0
$867$	13.3872	−	13.3872i	0.454653	−	0.454653i
$868$		0			0
$869$	−40.4628	−	40.4628i	−1.37261	−	1.37261i
$870$		0			0
$871$			6.70352i			0.227140i
$872$		0			0
$873$			29.7806i			1.00792i
$874$		0			0
$875$	−8.49498	−	8.49498i	−0.287183	−	0.287183i
$876$		0			0
$877$	14.0524	−	14.0524i	0.474516	−	0.474516i	−0.428857	−	0.903373i	$-0.641083\pi$
$877$	14.0524	−	14.0524i	0.474516	−	0.474516i	0.903373	+	0.428857i	$0.141083\pi$
$878$		0			0
$879$	72.3114			2.43900
$880$		0			0
$881$	−47.1071			−1.58708			−0.793539	−	0.608519i	$-0.791764\pi$
$881$	−47.1071			−1.58708			−0.793539	+	0.608519i	$0.791764\pi$
$882$		0			0
$883$	16.9886	−	16.9886i	0.571711	−	0.571711i	−0.360896	−	0.932606i	$-0.617529\pi$
$883$	16.9886	−	16.9886i	0.571711	−	0.571711i	0.932606	+	0.360896i	$0.117529\pi$
$884$		0			0
$885$	4.05698	+	4.05698i	0.136374	+	0.136374i
$886$		0			0
$887$			33.3126i			1.11853i	0.828990	+	0.559263i	$0.188916\pi$
$887$			33.3126i			1.11853i	−0.828990	+	0.559263i	$0.811084\pi$
$888$		0			0
$889$			13.5320i			0.453850i
$890$		0			0
$891$	46.7640	+	46.7640i	1.56665	+	1.56665i
$892$		0			0
$893$	−10.0204	+	10.0204i	−0.335320	+	0.335320i
$894$		0			0
$895$	−39.3084			−1.31394
$896$		0			0
$897$	−12.9768			−0.433283
$898$		0			0
$899$	−6.64639	+	6.64639i	−0.221669	+	0.221669i
$900$		0			0
$901$	−22.7767	−	22.7767i	−0.758801	−	0.758801i
$902$		0			0
$903$			12.1396i			0.403979i
$904$		0			0
$905$		−	14.6325i		−	0.486401i
$906$		0			0
$907$	5.65953	+	5.65953i	0.187922	+	0.187922i	0.794797	−	0.606875i	$-0.207577\pi$
$907$	5.65953	+	5.65953i	0.187922	+	0.187922i	−0.606875	+	0.794797i	$0.707577\pi$
$908$		0			0
$909$	8.60821	−	8.60821i	0.285516	−	0.285516i
$910$		0			0
$911$	41.8870			1.38778			0.693889	−	0.720082i	$-0.255896\pi$
$911$	41.8870			1.38778			0.693889	+	0.720082i	$0.255896\pi$
$912$		0			0
$913$	23.0755			0.763689
$914$		0			0
$915$	19.4395	−	19.4395i	0.642649	−	0.642649i
$916$		0			0
$917$	1.48631	+	1.48631i	0.0490821	+	0.0490821i
$918$		0			0
$919$		−	14.4978i		−	0.478237i	−0.970990	−	0.239119i	$-0.923142\pi$
$919$		−	14.4978i		−	0.478237i	0.970990	−	0.239119i	$-0.0768585\pi$
$920$		0			0
$921$			57.7743i			1.90373i
$922$		0			0
$923$	−1.82648	−	1.82648i	−0.0601193	−	0.0601193i
$924$		0			0
$925$	−3.51758	+	3.51758i	−0.115657	+	0.115657i
$926$		0			0
$927$	−18.1174			−0.595053
$928$		0			0
$929$	21.5646			0.707513			0.353756	−	0.935338i	$-0.384904\pi$
$929$	21.5646			0.707513			0.353756	+	0.935338i	$0.384904\pi$
$930$		0			0
$931$	1.49851	−	1.49851i	0.0491117	−	0.0491117i
$932$		0			0
$933$	50.8453	+	50.8453i	1.66460	+	1.66460i
$934$		0			0
$935$			51.6700i			1.68979i
$936$		0			0
$937$			3.51782i			0.114922i	0.998348	+	0.0574611i	$0.0183005\pi$
$937$			3.51782i			0.114922i	−0.998348	+	0.0574611i	$0.981699\pi$
$938$		0			0
$939$	29.2839	+	29.2839i	0.955643	+	0.955643i
$940$		0			0
$941$	−0.768500	+	0.768500i	−0.0250524	+	0.0250524i	−0.719522	−	0.694470i	$-0.755639\pi$
$941$	−0.768500	+	0.768500i	−0.0250524	+	0.0250524i	0.694470	+	0.719522i	$0.255639\pi$
$942$		0			0
$943$	−43.8767			−1.42882
$944$		0			0
$945$	2.70723			0.0880661
$946$		0			0
$947$	−11.3253	+	11.3253i	−0.368022	+	0.368022i	−0.866755	−	0.498733i	$-0.833799\pi$
$947$	−11.3253	+	11.3253i	−0.368022	+	0.368022i	0.498733	+	0.866755i	$0.333799\pi$
$948$		0			0
$949$	6.05592	+	6.05592i	0.196583	+	0.196583i
$950$		0			0
$951$			39.8107i			1.29095i
$952$		0			0
$953$		−	9.82914i		−	0.318397i	−0.987247	−	0.159199i	$-0.949109\pi$
$953$		−	9.82914i		−	0.318397i	0.987247	−	0.159199i	$-0.0508910\pi$
$954$		0			0
$955$	18.4962	+	18.4962i	0.598522	+	0.598522i
$956$		0			0
$957$	11.4913	−	11.4913i	0.371462	−	0.371462i
$958$		0			0
$959$	−11.7463			−0.379307
$960$		0			0
$961$	37.4796			1.20902
$962$		0			0
$963$	−31.1061	+	31.1061i	−1.00238	+	1.00238i
$964$		0			0
$965$	−8.77485	−	8.77485i	−0.282472	−	0.282472i
$966$		0			0
$967$			5.71372i			0.183741i	0.995771	+	0.0918705i	$0.0292846\pi$
$967$			5.71372i			0.183741i	−0.995771	+	0.0918705i	$0.970715\pi$
$968$		0			0
$969$			24.4794i			0.786392i
$970$		0			0
$971$	13.3515	+	13.3515i	0.428469	+	0.428469i	0.888106	−	0.459638i	$-0.152021\pi$
$971$	13.3515	+	13.3515i	0.428469	+	0.428469i	−0.459638	+	0.888106i	$0.652021\pi$
$972$		0			0
$973$	−8.00812	+	8.00812i	−0.256728	+	0.256728i
$974$		0			0
$975$	3.30543			0.105858
$976$		0			0
$977$	25.3043			0.809556			0.404778	−	0.914415i	$-0.367349\pi$
$977$	25.3043			0.809556			0.404778	+	0.914415i	$0.367349\pi$
$978$		0			0
$979$	−7.04105	+	7.04105i	−0.225033	+	0.225033i
$980$		0			0
$981$	−16.0922	−	16.0922i	−0.513784	−	0.513784i
$982$		0			0
$983$		−	12.4206i		−	0.396157i	−0.980186	−	0.198078i	$-0.936530\pi$
$983$		−	12.4206i		−	0.396157i	0.980186	−	0.198078i	$-0.0634701\pi$
$984$		0			0
$985$		−	40.2883i		−	1.28369i
$986$		0			0
$987$	−10.8731	−	10.8731i	−0.346093	−	0.346093i
$988$		0			0
$989$	33.2213	−	33.2213i	1.05638	−	1.05638i
$990$		0			0
$991$	−30.4013			−0.965729			−0.482865	−	0.875695i	$-0.660404\pi$
$991$	−30.4013			−0.965729			−0.482865	+	0.875695i	$0.660404\pi$
$992$		0			0
$993$	38.1973			1.21215
$994$		0			0
$995$	25.5605	−	25.5605i	0.810323	−	0.810323i
$996$		0			0
$997$	8.48812	+	8.48812i	0.268821	+	0.268821i	0.828625	−	0.559804i	$-0.189123\pi$
$997$	8.48812	+	8.48812i	0.268821	+	0.268821i	−0.559804	+	0.828625i	$0.689123\pi$
$998$		0			0
$999$		−	3.59357i		−	0.113695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.g.449.6	yes	16
4.3	odd	2		1792.2.m.e.449.3	✓	16
8.3	odd	2		1792.2.m.h.449.6	yes	16
8.5	even	2		1792.2.m.f.449.3	yes	16
16.3	odd	4		1792.2.m.e.1345.3	yes	16
16.5	even	4		1792.2.m.f.1345.3	yes	16
16.11	odd	4		1792.2.m.h.1345.6	yes	16
16.13	even	4	inner	1792.2.m.g.1345.6	yes	16
32.3	odd	8		7168.2.a.bb.1.2		8
32.13	even	8		7168.2.a.be.1.2		8
32.19	odd	8		7168.2.a.bf.1.7		8
32.29	even	8		7168.2.a.ba.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.3	✓	16	4.3	odd	2
1792.2.m.e.1345.3	yes	16	16.3	odd	4
1792.2.m.f.449.3	yes	16	8.5	even	2
1792.2.m.f.1345.3	yes	16	16.5	even	4
1792.2.m.g.449.6	yes	16	1.1	even	1	trivial
1792.2.m.g.1345.6	yes	16	16.13	even	4	inner
1792.2.m.h.449.6	yes	16	8.3	odd	2
1792.2.m.h.1345.6	yes	16	16.11	odd	4
7168.2.a.ba.1.7		8	32.29	even	8
7168.2.a.bb.1.2		8	32.3	odd	8
7168.2.a.be.1.2		8	32.13	even	8
7168.2.a.bf.1.7		8	32.19	odd	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62602 - 1.62602i) q^{3} +(1.16900 + 1.16900i) q^{5} -1.00000i q^{7} -2.28788i q^{9} +O(q^{10})\)	\(q+(1.62602 - 1.62602i) q^{3} +(1.16900 + 1.16900i) q^{5} -1.00000i q^{7} -2.28788i q^{9} +(4.39956 + 4.39956i) q^{11} +(-0.448377 + 0.448377i) q^{13} +3.80163 q^{15} +5.02326 q^{17} +(-1.49851 + 1.49851i) q^{19} +(-1.62602 - 1.62602i) q^{21} +8.89958i q^{23} -2.26688i q^{25} +(1.15793 + 1.15793i) q^{27} +(0.803165 - 0.803165i) q^{29} -8.27524 q^{31} +14.3075 q^{33} +(1.16900 - 1.16900i) q^{35} +(-1.55173 - 1.55173i) q^{37} +1.45814i q^{39} +4.93020i q^{41} +(-3.73291 - 3.73291i) q^{43} +(2.67453 - 2.67453i) q^{45} +6.68692 q^{47} -1.00000 q^{49} +(8.16791 - 8.16791i) q^{51} +(-4.53424 - 4.53424i) q^{53} +10.2862i q^{55} +4.87321i q^{57} +(1.06717 + 1.06717i) q^{59} +(5.11346 - 5.11346i) q^{61} -2.28788 q^{63} -1.04830 q^{65} +(7.47532 - 7.47532i) q^{67} +(14.4709 + 14.4709i) q^{69} +4.07354i q^{71} -13.5063i q^{73} +(-3.68600 - 3.68600i) q^{75} +(4.39956 - 4.39956i) q^{77} -9.19701 q^{79} +10.6293 q^{81} +(2.62248 - 2.62248i) q^{83} +(5.87218 + 5.87218i) q^{85} -2.61192i q^{87} +1.60040i q^{89} +(0.448377 + 0.448377i) q^{91} +(-13.4557 + 13.4557i) q^{93} -3.50351 q^{95} -13.0167 q^{97} +(10.0657 - 10.0657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 - 4 * q^5	\( 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Introduction

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