LMFDB - Embedded newform 1792.2.m.f.449.3

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			449.3
Root			$2.69978 + 0.355433i$ of defining polynomial
Character	$\chi$	$=$	1792.449
Dual form			1792.2.m.f.1345.3

$q$-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	−0.998231	−	0.0594487i	$-0.981066\pi$
$3$	−1.62602	+	1.62602i	−0.938783	+	0.938783i	0.0594487	+	0.998231i	$0.481066\pi$
$4$		0			0
$5$	−1.16900	−	1.16900i	−0.522792	−	0.522792i	0.395621	−	0.918414i	$-0.370529\pi$
$5$	−1.16900	−	1.16900i	−0.522792	−	0.522792i	−0.918414	+	0.395621i	$0.870529\pi$
$6$		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	$-0.862686\pi$
$11$	−4.39956	−	4.39956i	−1.32652	−	1.32652i	−0.418130	−	0.908387i	$-0.637314\pi$
$12$		0			0
$13$	0.448377	−	0.448377i	0.124357	−	0.124357i	−0.642189	−	0.766546i	$-0.721974\pi$
$13$	0.448377	−	0.448377i	0.124357	−	0.124357i	0.766546	+	0.642189i	$0.221974\pi$
$14$		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	−0.514005	−	0.857787i	$-0.671839\pi$
$19$	1.49851	−	1.49851i	0.343782	−	0.343782i	0.857787	+	0.514005i	$0.171839\pi$
$20$		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	−0.777736	−	0.628592i	$-0.783632\pi$
$29$	−0.803165	+	0.803165i	−0.149144	+	0.149144i	0.628592	+	0.777736i	$0.283632\pi$
$30$		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	0.823059	−	0.567956i	$-0.192266\pi$
$37$	1.55173	+	1.55173i	0.255102	+	0.255102i	−0.567956	+	0.823059i	$0.692266\pi$
$38$		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	0.931922	−	0.362659i	$-0.118131\pi$
$43$	3.73291	+	3.73291i	0.569263	+	0.569263i	−0.362659	+	0.931922i	$0.618131\pi$
$44$		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	0.946253	−	0.323427i	$-0.104835\pi$
$53$	4.53424	+	4.53424i	0.622826	+	0.622826i	−0.323427	+	0.946253i	$0.604835\pi$
$54$		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	0.634219	−	0.773153i	$-0.281322\pi$
$59$	−1.06717	−	1.06717i	−0.138934	−	0.138934i	−0.773153	+	0.634219i	$0.781322\pi$
$60$		0			0
$61$	−5.11346	+	5.11346i	−0.654711	+	0.654711i	−0.954124	−	0.299413i	$-0.903209\pi$
$61$	−5.11346	+	5.11346i	−0.654711	+	0.654711i	0.299413	+	0.954124i	$0.403209\pi$
$62$		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	−0.996527	−	0.0832712i	$-0.973463\pi$
$67$	−7.47532	+	7.47532i	−0.913256	+	0.913256i	0.0832712	+	0.996527i	$0.473463\pi$
$68$		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	−0.836231	−	0.548377i	$-0.815246\pi$
$83$	−2.62248	+	2.62248i	−0.287855	+	0.287855i	0.548377	+	0.836231i	$0.315246\pi$
$84$		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	0.494686	−	0.869072i	$-0.335283\pi$
$101$	−3.76253	−	3.76253i	−0.374386	−	0.374386i	−0.869072	+	0.494686i	$0.835283\pi$
$102$		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	$0.129681\pi$
$107$	13.5961	+	13.5961i	1.31438	+	1.31438i	0.396228	+	0.918152i	$0.370319\pi$
$108$		0			0
$109$	−7.03367	+	7.03367i	−0.673704	+	0.673704i	−0.958568	−	0.284864i	$-0.908052\pi$
$109$	−7.03367	+	7.03367i	−0.673704	+	0.673704i	0.284864	+	0.958568i	$0.408052\pi$
$110$		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	−0.639190	−	0.769049i	$-0.720730\pi$
$131$	1.48631	−	1.48631i	0.129859	−	0.129859i	0.769049	+	0.639190i	$0.220730\pi$
$132$		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	0.959828	−	0.280588i	$-0.0905296\pi$
$139$	8.00812	+	8.00812i	0.679240	+	0.679240i	−0.280588	+	0.959828i	$0.590530\pi$
$140$		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	0.840206	−	0.542267i	$-0.182434\pi$
$149$	3.63681	+	3.63681i	0.297939	+	0.297939i	−0.542267	+	0.840206i	$0.682434\pi$
$150$		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	$0.541366\pi$
$157$	−14.0481	+	14.0481i	−1.12116	+	1.12116i	−0.991568	+	0.129589i	$0.958634\pi$
$158$		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	−0.983898	−	0.178729i	$-0.942801\pi$
$163$	−10.2797	+	10.2797i	−0.805169	+	0.805169i	0.178729	+	0.983898i	$0.442801\pi$
$164$		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	−0.858955	−	0.512051i	$-0.828886\pi$
$173$	−4.56281	+	4.56281i	−0.346904	+	0.346904i	0.512051	+	0.858955i	$0.328886\pi$
$174$		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	$-0.401688\pi$
$179$	16.8129	−	16.8129i	1.25665	−	1.25665i	0.952682	−	0.303970i	$-0.0983123\pi$
$180$		0			0
$181$	6.25856	+	6.25856i	0.465195	+	0.465195i	0.900354	−	0.435159i	$-0.143308\pi$
$181$	6.25856	+	6.25856i	0.465195	+	0.465195i	−0.435159	+	0.900354i	$0.643308\pi$
$182$		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	$0.0846807\pi$
$197$	17.2320	+	17.2320i	1.22773	+	1.22773i	0.262905	+	0.964822i	$0.415319\pi$
$198$		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	−0.796461	−	0.604690i	$-0.793297\pi$
$211$	−2.78563	+	2.78563i	−0.191771	+	0.191771i	0.604690	+	0.796461i	$0.293297\pi$
$212$		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	−0.545319	−	0.838228i	$-0.683592\pi$
$227$	4.41312	−	4.41312i	0.292909	−	0.292909i	0.838228	+	0.545319i	$0.183592\pi$
$228$		0			0
$229$	14.4119	+	14.4119i	0.952362	+	0.952362i	0.998916	−	0.0465535i	$-0.0148238\pi$
$229$	14.4119	+	14.4119i	0.952362	+	0.952362i	−0.0465535	+	0.998916i	$0.514824\pi$
$230$		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	0.551595	−	0.834112i	$-0.314019\pi$
$251$	−4.47591	−	4.47591i	−0.282517	−	0.282517i	−0.834112	+	0.551595i	$0.814019\pi$
$252$		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	−0.984409	−	0.175893i	$-0.943719\pi$
$269$	−13.2606	+	13.2606i	−0.808516	+	0.808516i	0.175893	+	0.984409i	$0.443719\pi$
$270$		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	0.752487	−	0.658607i	$-0.228854\pi$
$277$	1.56248	+	1.56248i	0.0938806	+	0.0938806i	−0.658607	+	0.752487i	$0.728854\pi$
$278$		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	$-0.924123\pi$
$283$	−20.3191	−	20.3191i	−1.20785	−	1.20785i	−0.236125	−	0.971723i	$-0.575877\pi$
$284$		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	$-0.879361\pi$
$293$	−22.2357	−	22.2357i	−1.29903	−	1.29903i	−0.369989	−	0.929036i	$-0.620639\pi$
$294$		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	$-0.495533\pi$
$307$	17.7656	−	17.7656i	1.01393	−	1.01393i	0.999902	−	0.0140326i	$-0.00446685\pi$
$308$		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	−0.274127	−	0.961694i	$-0.588389\pi$
$317$	12.2418	−	12.2418i	0.687567	−	0.687567i	0.961694	+	0.274127i	$0.0883888\pi$
$318$		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	0.306328	−	0.951926i	$-0.400900\pi$
$331$	−11.7456	−	11.7456i	−0.645599	−	0.645599i	−0.951926	+	0.306328i	$0.900900\pi$
$332$		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	0.862115	−	0.506713i	$-0.169140\pi$
$347$	6.62041	+	6.62041i	0.355402	+	0.355402i	−0.506713	+	0.862115i	$0.669140\pi$
$348$		0			0
$349$	14.7958	−	14.7958i	0.792001	−	0.792001i	−0.189819	−	0.981819i	$-0.560790\pi$
$349$	14.7958	−	14.7958i	0.792001	−	0.792001i	0.981819	+	0.189819i	$0.0607900\pi$
$350$		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	0.881176	−	0.472788i	$-0.156752\pi$
$373$	7.88728	+	7.88728i	0.408388	+	0.408388i	−0.472788	+	0.881176i	$0.656752\pi$
$374$		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	0.908195	−	0.418548i	$-0.137461\pi$
$379$	9.53241	+	9.53241i	0.489647	+	0.489647i	−0.418548	+	0.908195i	$0.637461\pi$
$380$		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	0.857785	−	0.514008i	$-0.171840\pi$
$389$	6.78034	+	6.78034i	0.343777	+	0.343777i	−0.514008	+	0.857785i	$0.671840\pi$
$390$		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	−0.754020	−	0.656851i	$-0.771888\pi$
$397$	−1.93608	+	1.93608i	−0.0971692	+	0.0971692i	0.656851	+	0.754020i	$0.271888\pi$
$398$		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	−0.0154368	−	0.999881i	$-0.504914\pi$
$419$	20.1511	−	20.1511i	0.984444	−	0.984444i	0.999881	+	0.0154368i	$0.00491389\pi$
$420$		0			0
$421$	6.44015	+	6.44015i	0.313874	+	0.313874i	0.846408	−	0.532535i	$-0.178760\pi$
$421$	6.44015	+	6.44015i	0.313874	+	0.313874i	−0.532535	+	0.846408i	$0.678760\pi$
$422$		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	0.989554	−	0.144160i	$-0.0460480\pi$
$443$	17.7935	+	17.7935i	0.845394	+	0.845394i	−0.144160	+	0.989554i	$0.546048\pi$
$444$		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	−0.664279	−	0.747485i	$-0.731261\pi$
$461$	1.78650	−	1.78650i	0.0832056	−	0.0832056i	0.747485	+	0.664279i	$0.231261\pi$
$462$		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	−0.495707	−	0.868490i	$-0.665091\pi$
$467$	8.05590	−	8.05590i	0.372783	−	0.372783i	0.868490	+	0.495707i	$0.165091\pi$
$468$		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	0.791818	−	0.610758i	$-0.209135\pi$
$491$	4.01202	+	4.01202i	0.181060	+	0.181060i	−0.610758	+	0.791818i	$0.709135\pi$
$492$		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	−0.609218	−	0.793003i	$-0.708516\pi$
$499$	4.10545	−	4.10545i	0.183785	−	0.183785i	0.793003	+	0.609218i	$0.208516\pi$
$500$		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	−0.863707	−	0.503995i	$-0.831863\pi$
$509$	−8.11547	+	8.11547i	−0.359712	+	0.359712i	0.503995	+	0.863707i	$0.331863\pi$
$510$		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	0.990693	−	0.136117i	$-0.0434624\pi$
$523$	19.5435	+	19.5435i	0.854575	+	0.854575i	−0.136117	+	0.990693i	$0.543462\pi$
$524$		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	$0.596078\pi$
$541$	−29.1223	+	29.1223i	−1.25207	+	1.25207i	−0.954792	+	0.297274i	$0.903922\pi$
$542$		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	−0.924440	−	0.381329i	$-0.875467\pi$
$547$	−12.7023	+	12.7023i	−0.543111	+	0.543111i	0.381329	+	0.924440i	$0.375467\pi$
$548$		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	−0.978938	−	0.204158i	$-0.934554\pi$
$557$	−18.2855	+	18.2855i	−0.774780	+	0.774780i	0.204158	+	0.978938i	$0.434554\pi$
$558$		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	−0.691739	−	0.722147i	$-0.743155\pi$
$563$	0.721510	−	0.721510i	0.0304080	−	0.0304080i	0.722147	+	0.691739i	$0.243155\pi$
$564$		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	0.623078	−	0.782159i	$-0.285882\pi$
$571$	−3.80134	−	3.80134i	−0.159081	−	0.159081i	−0.782159	+	0.623078i	$0.785882\pi$
$572$		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	0.611992	−	0.790864i	$-0.290369\pi$
$587$	−4.33373	−	4.33373i	−0.178872	−	0.178872i	−0.790864	+	0.611992i	$0.790369\pi$
$588$		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	0.522554	−	0.852606i	$-0.324979\pi$
$613$	−8.17171	−	8.17171i	−0.330052	−	0.330052i	−0.852606	+	0.522554i	$0.824979\pi$
$614$		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	0.759971	−	0.649957i	$-0.225213\pi$
$619$	2.73711	+	2.73711i	0.110014	+	0.110014i	−0.649957	+	0.759971i	$0.725213\pi$
$620$		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	−0.269284	−	0.963061i	$-0.586787\pi$
$643$	17.5924	−	17.5924i	0.693777	−	0.693777i	0.963061	+	0.269284i	$0.0867871\pi$
$644$		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	−0.712587	−	0.701583i	$-0.752477\pi$
$653$	−0.281193	+	0.281193i	−0.0110039	+	0.0110039i	0.701583	+	0.712587i	$0.252477\pi$
$654$		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	−0.731110	−	0.682259i	$-0.760997\pi$
$659$	−1.25405	+	1.25405i	−0.0488508	+	0.0488508i	0.682259	+	0.731110i	$0.260997\pi$
$660$		0			0
$661$	−30.7505	−	30.7505i	−1.19605	−	1.19605i	−0.975338	−	0.220717i	$-0.929160\pi$
$661$	−30.7505	−	30.7505i	−1.19605	−	1.19605i	−0.220717	−	0.975338i	$-0.570840\pi$
$662$		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	$-0.956078\pi$
$677$	−29.3508	−	29.3508i	−1.12804	−	1.12804i	−0.137547	−	0.990495i	$-0.543922\pi$
$678$		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	0.671918	−	0.740625i	$-0.265471\pi$
$683$	−1.79560	−	1.79560i	−0.0687066	−	0.0687066i	−0.740625	+	0.671918i	$0.765471\pi$
$684$		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	−0.447897	−	0.894085i	$-0.647827\pi$
$691$	11.7289	−	11.7289i	0.446188	−	0.446188i	0.894085	+	0.447897i	$0.147827\pi$
$692$		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	−0.994309	−	0.106536i	$-0.966024\pi$
$701$	−23.5050	+	23.5050i	−0.887772	+	0.887772i	0.106536	+	0.994309i	$0.466024\pi$
$702$		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	0.735724	−	0.677281i	$-0.236842\pi$
$709$	1.55617	+	1.55617i	0.0584430	+	0.0584430i	−0.677281	+	0.735724i	$0.736842\pi$
$710$		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	−0.397567	−	0.917573i	$-0.630145\pi$
$733$	14.0786	−	14.0786i	0.520006	−	0.520006i	0.917573	+	0.397567i	$0.130145\pi$
$734$		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	$0.661788\pi$
$739$	−36.9779	+	36.9779i	−1.36026	+	1.36026i	−0.873587	+	0.486669i	$0.838212\pi$
$740$		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	$-0.972575\pi$
$757$	−29.7792	−	29.7792i	−1.08234	−	1.08234i	−0.0860518	−	0.996291i	$-0.527425\pi$
$758$		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	0.489747	−	0.871865i	$-0.337089\pi$
$773$	−10.6240	−	10.6240i	−0.382118	−	0.382118i	−0.871865	+	0.489747i	$0.837089\pi$
$774$		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	$0.581758\pi$
$787$	−34.2598	+	34.2598i	−1.22123	+	1.22123i	−0.967195	+	0.254035i	$0.918242\pi$
$788$		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	−0.842155	−	0.539236i	$-0.818713\pi$
$797$	−8.55176	+	8.55176i	−0.302919	+	0.302919i	0.539236	+	0.842155i	$0.318713\pi$
$798$		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	0.0946041	−	0.995515i	$-0.469841\pi$
$811$	−25.6562	−	25.6562i	−0.900911	−	0.900911i	−0.995515	+	0.0946041i	$0.969841\pi$
$812$		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	0.893839	−	0.448389i	$-0.148002\pi$
$821$	12.7635	+	12.7635i	0.445450	+	0.445450i	−0.448389	+	0.893839i	$0.648002\pi$
$822$		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	0.0504301	−	0.998728i	$-0.483941\pi$
$827$	−27.2708	−	27.2708i	−0.948297	−	0.948297i	−0.998728	+	0.0504301i	$0.983941\pi$
$828$		0			0
$829$	−5.10352	+	5.10352i	−0.177253	+	0.177253i	−0.790157	−	0.612904i	$-0.790001\pi$
$829$	−5.10352	+	5.10352i	−0.177253	+	0.177253i	0.612904	+	0.790157i	$0.290001\pi$
$830$		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	$-0.895602\pi$
$853$	−37.0575	−	37.0575i	−1.26882	−	1.26882i	−0.322128	−	0.946696i	$-0.604398\pi$
$854$		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	0.943617	−	0.331039i	$-0.107399\pi$
$859$	17.9539	+	17.9539i	0.612577	+	0.612577i	−0.331039	+	0.943617i	$0.607399\pi$
$860$		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	−0.903373	−	0.428857i	$-0.858917\pi$
$877$	−14.0524	+	14.0524i	−0.474516	+	0.474516i	0.428857	+	0.903373i	$0.358917\pi$
$878$		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	−0.932606	−	0.360896i	$-0.882471\pi$
$883$	−16.9886	+	16.9886i	−0.571711	+	0.571711i	0.360896	+	0.932606i	$0.382471\pi$
$884$		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	0.606875	−	0.794797i	$-0.292423\pi$
$907$	−5.65953	−	5.65953i	−0.187922	−	0.187922i	−0.794797	+	0.606875i	$0.792423\pi$
$908$		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	−0.694470	−	0.719522i	$-0.744361\pi$
$941$	0.768500	−	0.768500i	0.0250524	−	0.0250524i	0.719522	+	0.694470i	$0.244361\pi$
$942$		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	−0.498733	−	0.866755i	$-0.666201\pi$
$947$	11.3253	−	11.3253i	0.368022	−	0.368022i	0.866755	+	0.498733i	$0.166201\pi$
$948$		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	0.459638	−	0.888106i	$-0.347979\pi$
$971$	−13.3515	−	13.3515i	−0.428469	−	0.428469i	−0.888106	+	0.459638i	$0.847979\pi$
$972$		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	0.559804	−	0.828625i	$-0.310877\pi$
$997$	−8.48812	−	8.48812i	−0.268821	−	0.268821i	−0.828625	+	0.559804i	$0.810877\pi$
$998$		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.f.449.3	yes	16
4.3	odd	2		1792.2.m.h.449.6	yes	16
8.3	odd	2		1792.2.m.e.449.3	✓	16
8.5	even	2		1792.2.m.g.449.6	yes	16
16.3	odd	4		1792.2.m.h.1345.6	yes	16
16.5	even	4		1792.2.m.g.1345.6	yes	16
16.11	odd	4		1792.2.m.e.1345.3	yes	16
16.13	even	4	inner	1792.2.m.f.1345.3	yes	16
32.3	odd	8		7168.2.a.bf.1.7		8
32.13	even	8		7168.2.a.ba.1.7		8
32.19	odd	8		7168.2.a.bb.1.2		8
32.29	even	8		7168.2.a.be.1.2		8

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more