LMFDB - Embedded newform 1920.2.y.i.1567.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(223,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("1920.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1920 = 2^{7} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$ , degree $2$ , not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
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:	$x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256$ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$2^{12}$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1567.5
Root			$-1.20803 - 0.735291i$ of defining polynomial
Character	$\chi$	$=$	1920.1567
Dual form			1920.2.y.i.223.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +(1.61356 - 1.54804i) q^{5} +(0.143894 + 0.143894i) q^{7} +1.00000 q^{9} +(-0.749545 + 0.749545i) q^{11} +3.29132i q^{13} +(-1.61356 + 1.54804i) q^{15} +(1.35709 + 1.35709i) q^{17} +(-4.25468 + 4.25468i) q^{19} +(-0.143894 - 0.143894i) q^{21} +(0.837388 - 0.837388i) q^{23} +(0.207170 - 4.99571i) q^{25} -1.00000 q^{27} +(2.77462 + 2.77462i) q^{29} +6.60915i q^{31} +(0.749545 - 0.749545i) q^{33} +(0.454934 + 0.00942893i) q^{35} +10.0194i q^{37} -3.29132i q^{39} +1.72608i q^{41} -4.17171i q^{43} +(1.61356 - 1.54804i) q^{45} +(-8.54502 + 8.54502i) q^{47} -6.95859i q^{49} +(-1.35709 - 1.35709i) q^{51} +5.05524 q^{53} +(-0.0491155 + 2.36976i) q^{55} +(4.25468 - 4.25468i) q^{57} +(-3.08237 - 3.08237i) q^{59} +(5.00346 - 5.00346i) q^{61} +(0.143894 + 0.143894i) q^{63} +(5.09507 + 5.31074i) q^{65} +4.26739i q^{67} +(-0.837388 + 0.837388i) q^{69} +13.2111 q^{71} +(-11.6889 - 11.6889i) q^{73} +(-0.207170 + 4.99571i) q^{75} -0.215710 q^{77} +9.95558 q^{79} +1.00000 q^{81} +10.0134 q^{83} +(4.29056 + 0.0889259i) q^{85} +(-2.77462 - 2.77462i) q^{87} +5.76005 q^{89} +(-0.473599 + 0.473599i) q^{91} -6.60915i q^{93} +(-0.278797 + 13.4516i) q^{95} +(11.7668 + 11.7668i) q^{97} +(-0.749545 + 0.749545i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 16 q^{3} + 4 q^{5} - 4 q^{7} + 16 q^{9} - 4 q^{15} - 8 q^{17} - 8 q^{19} + 4 q^{21} + 32 q^{25} - 16 q^{27} - 12 q^{29} + 20 q^{35} + 4 q^{45} - 32 q^{47} + 8 q^{51} - 16 q^{53} - 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100})$ 16 * q - 16 * q^3 + 4 * q^5 - 4 * q^7 + 16 * q^9 - 4 * q^15 - 8 * q^17 - 8 * q^19 + 4 * q^21 + 32 * q^25 - 16 * q^27 - 12 * q^29 + 20 * q^35 + 4 * q^45 - 32 * q^47 + 8 * q^51 - 16 * q^53 - 4 * q^55 + 8 * q^57 + 24 * q^59 - 40 * q^61 - 4 * q^63 - 4 * q^65 + 8 * q^73 - 32 * q^75 + 72 * q^77 - 48 * q^79 + 16 * q^81 + 8 * q^83 + 8 * q^85 + 12 * q^87 + 40 * q^91 + 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$ .

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.61356	−	1.54804i	0.721607	−	0.692303i
$5$	1.61356	−	1.54804i	0.721607	−	0.692303i
$6$		0			0
$7$	0.143894	+	0.143894i	0.0543867	+	0.0543867i	0.733777	−	0.679390i	$-0.237756\pi$
$7$	0.143894	+	0.143894i	0.0543867	+	0.0543867i	−0.679390	+	0.733777i	$0.737756\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.749545	+	0.749545i	−0.225996	+	0.225996i	−0.811018	−	0.585021i	$-0.801086\pi$
$11$	−0.749545	+	0.749545i	−0.225996	+	0.225996i	0.585021	+	0.811018i	$0.301086\pi$
$12$		0			0
$13$			3.29132i			0.912847i	0.889763	+	0.456423i	$0.150870\pi$
$13$			3.29132i			0.912847i	−0.889763	+	0.456423i	$0.849130\pi$
$14$		0			0
$15$	−1.61356	+	1.54804i	−0.416620	+	0.399701i
$16$		0			0
$17$	1.35709	+	1.35709i	0.329142	+	0.329142i	0.852260	−	0.523118i	$-0.175231\pi$
$17$	1.35709	+	1.35709i	0.329142	+	0.329142i	−0.523118	+	0.852260i	$0.675231\pi$
$18$		0			0
$19$	−4.25468	+	4.25468i	−0.976091	+	0.976091i	−0.999721	−	0.0236300i	$-0.992478\pi$
$19$	−4.25468	+	4.25468i	−0.976091	+	0.976091i	0.0236300	+	0.999721i	$0.492478\pi$
$20$		0			0
$21$	−0.143894	−	0.143894i	−0.0314002	−	0.0314002i
$22$		0			0
$23$	0.837388	−	0.837388i	0.174608	−	0.174608i	−0.614393	−	0.789000i	$-0.710599\pi$
$23$	0.837388	−	0.837388i	0.174608	−	0.174608i	0.789000	+	0.614393i	$0.210599\pi$
$24$		0			0
$25$	0.207170	−	4.99571i	0.0414341	−	0.999141i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.77462	+	2.77462i	0.515234	+	0.515234i	0.916126	−	0.400891i	$-0.131299\pi$
$29$	2.77462	+	2.77462i	0.515234	+	0.515234i	−0.400891	+	0.916126i	$0.631299\pi$
$30$		0			0
$31$			6.60915i			1.18704i	0.804820	+	0.593520i	$0.202262\pi$
$31$			6.60915i			1.18704i	−0.804820	+	0.593520i	$0.797738\pi$
$32$		0			0
$33$	0.749545	−	0.749545i	0.130479	−	0.130479i
$34$		0			0
$35$	0.454934	+	0.00942893i	0.0768979	+	0.00159378i
$36$		0			0
$37$			10.0194i			1.64717i	0.567191	+	0.823586i	$0.308030\pi$
$37$			10.0194i			1.64717i	−0.567191	+	0.823586i	$0.691970\pi$
$38$		0			0
$39$		−	3.29132i		−	0.527032i
$40$		0			0
$41$			1.72608i			0.269569i	0.990875	+	0.134784i	$0.0430342\pi$
$41$			1.72608i			0.269569i	−0.990875	+	0.134784i	$0.956966\pi$
$42$		0			0
$43$		−	4.17171i		−	0.636180i	−0.948061	−	0.318090i	$-0.896959\pi$
$43$		−	4.17171i		−	0.636180i	0.948061	−	0.318090i	$-0.103041\pi$
$44$		0			0
$45$	1.61356	−	1.54804i	0.240536	−	0.230768i
$46$		0			0
$47$	−8.54502	+	8.54502i	−1.24642	+	1.24642i	−0.289128	+	0.957290i	$0.593365\pi$
$47$	−8.54502	+	8.54502i	−1.24642	+	1.24642i	−0.957290	+	0.289128i	$0.906635\pi$
$48$		0			0
$49$		−	6.95859i		−	0.994084i
$50$		0			0
$51$	−1.35709	−	1.35709i	−0.190030	−	0.190030i
$52$		0			0
$53$	5.05524			0.694391			0.347196	−	0.937793i	$-0.387134\pi$
$53$	5.05524			0.694391			0.347196	+	0.937793i	$0.387134\pi$
$54$		0			0
$55$	−0.0491155	+	2.36976i	−0.00662273	+	0.319538i
$56$		0			0
$57$	4.25468	−	4.25468i	0.563546	−	0.563546i
$58$		0			0
$59$	−3.08237	−	3.08237i	−0.401290	−	0.401290i	0.477398	−	0.878687i	$-0.341580\pi$
$59$	−3.08237	−	3.08237i	−0.401290	−	0.401290i	−0.878687	+	0.477398i	$0.841580\pi$
$60$		0			0
$61$	5.00346	−	5.00346i	0.640627	−	0.640627i	−0.310083	−	0.950710i	$-0.600357\pi$
$61$	5.00346	−	5.00346i	0.640627	−	0.640627i	0.950710	+	0.310083i	$0.100357\pi$
$62$		0			0
$63$	0.143894	+	0.143894i	0.0181289	+	0.0181289i
$64$		0			0
$65$	5.09507	+	5.31074i	0.631966	+	0.658717i
$66$		0			0
$67$			4.26739i			0.521345i	0.965427	+	0.260672i	$0.0839442\pi$
$67$			4.26739i			0.521345i	−0.965427	+	0.260672i	$0.916056\pi$
$68$		0			0
$69$	−0.837388	+	0.837388i	−0.100810	+	0.100810i
$70$		0			0
$71$	13.2111			1.56786			0.783932	−	0.620846i	$-0.213211\pi$
$71$	13.2111			1.56786			0.783932	+	0.620846i	$0.213211\pi$
$72$		0			0
$73$	−11.6889	−	11.6889i	−1.36808	−	1.36808i	−0.863175	−	0.504904i	$-0.831528\pi$
$73$	−11.6889	−	11.6889i	−1.36808	−	1.36808i	−0.504904	−	0.863175i	$-0.668472\pi$
$74$		0			0
$75$	−0.207170	+	4.99571i	−0.0239220	+	0.576854i
$76$		0			0
$77$	−0.215710			−0.0245824
$78$		0			0
$79$	9.95558			1.12009			0.560045	−	0.828462i	$-0.310784\pi$
$79$	9.95558			1.12009			0.560045	+	0.828462i	$0.310784\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	10.0134			1.09912			0.549559	−	0.835455i	$-0.314796\pi$
$83$	10.0134			1.09912			0.549559	+	0.835455i	$0.314796\pi$
$84$		0			0
$85$	4.29056	+	0.0889259i	0.465377	+	0.00964537i
$86$		0			0
$87$	−2.77462	−	2.77462i	−0.297471	−	0.297471i
$88$		0			0
$89$	5.76005			0.610564			0.305282	−	0.952262i	$-0.401249\pi$
$89$	5.76005			0.610564			0.305282	+	0.952262i	$0.401249\pi$
$90$		0			0
$91$	−0.473599	+	0.473599i	−0.0496467	+	0.0496467i
$92$		0			0
$93$		−	6.60915i		−	0.685337i
$94$		0			0
$95$	−0.278797	+	13.4516i	−0.0286040	+	1.38010i
$96$		0			0
$97$	11.7668	+	11.7668i	1.19474	+	1.19474i	0.975720	+	0.219021i	$0.0702865\pi$
$97$	11.7668	+	11.7668i	1.19474	+	1.19474i	0.219021	+	0.975720i	$0.429714\pi$
$98$		0			0
$99$	−0.749545	+	0.749545i	−0.0753321	+	0.0753321i
$100$		0			0
$101$	1.29314	+	1.29314i	0.128672	+	0.128672i	0.768510	−	0.639838i	$-0.220998\pi$
$101$	1.29314	+	1.29314i	0.128672	+	0.128672i	−0.639838	+	0.768510i	$0.720998\pi$
$102$		0			0
$103$	−11.2892	+	11.2892i	−1.11236	+	1.11236i	−0.119532	+	0.992830i	$0.538139\pi$
$103$	−11.2892	+	11.2892i	−1.11236	+	1.11236i	−0.992830	+	0.119532i	$0.961861\pi$
$104$		0			0
$105$	−0.454934	−	0.00942893i	−0.0443970	−	0.000920169i
$106$		0			0
$107$	−1.39451			−0.134812			−0.0674060	−	0.997726i	$-0.521472\pi$
$107$	−1.39451			−0.134812			−0.0674060	+	0.997726i	$0.521472\pi$
$108$		0			0
$109$	4.55325	+	4.55325i	0.436123	+	0.436123i	0.890705	−	0.454582i	$-0.150211\pi$
$109$	4.55325	+	4.55325i	0.436123	+	0.436123i	−0.454582	+	0.890705i	$0.650211\pi$
$110$		0			0
$111$		−	10.0194i		−	0.950995i
$112$		0			0
$113$	−11.4501	+	11.4501i	−1.07714	+	1.07714i	−0.0803726	+	0.996765i	$0.525611\pi$
$113$	−11.4501	+	11.4501i	−1.07714	+	1.07714i	−0.996765	+	0.0803726i	$0.974389\pi$
$114$		0			0
$115$	0.0548716	−	2.64749i	0.00511680	−	0.246879i
$116$		0			0
$117$			3.29132i			0.304282i
$118$		0			0
$119$			0.390552i			0.0358018i
$120$		0			0
$121$			9.87636i			0.897851i
$122$		0			0
$123$		−	1.72608i		−	0.155636i
$124$		0			0
$125$	−7.39925	−	8.38159i	−0.661809	−	0.749672i
$126$		0			0
$127$	−4.94562	+	4.94562i	−0.438853	+	0.438853i	−0.891626	−	0.452773i	$-0.850435\pi$
$127$	−4.94562	+	4.94562i	−0.438853	+	0.438853i	0.452773	+	0.891626i	$0.350435\pi$
$128$		0			0
$129$			4.17171i			0.367299i
$130$		0			0
$131$	12.7313	+	12.7313i	1.11234	+	1.11234i	0.992833	+	0.119509i	$0.0381319\pi$
$131$	12.7313	+	12.7313i	1.11234	+	1.11234i	0.119509	+	0.992833i	$0.461868\pi$
$132$		0			0
$133$	−1.22444			−0.106173
$134$		0			0
$135$	−1.61356	+	1.54804i	−0.138873	+	0.133234i
$136$		0			0
$137$	−6.06032	+	6.06032i	−0.517768	+	0.517768i	−0.916896	−	0.399127i	$-0.869313\pi$
$137$	−6.06032	+	6.06032i	−0.517768	+	0.517768i	0.399127	+	0.916896i	$0.369313\pi$
$138$		0			0
$139$	−10.3543	−	10.3543i	−0.878239	−	0.878239i	0.115114	−	0.993352i	$-0.463277\pi$
$139$	−10.3543	−	10.3543i	−0.878239	−	0.878239i	−0.993352	+	0.115114i	$0.963277\pi$
$140$		0			0
$141$	8.54502	−	8.54502i	0.719620	−	0.719620i
$142$		0			0
$143$	−2.46699	−	2.46699i	−0.206300	−	0.206300i
$144$		0			0
$145$	8.77224	+	0.181813i	0.728495	+	0.0150987i
$146$		0			0
$147$			6.95859i			0.573935i
$148$		0			0
$149$	−0.485009	+	0.485009i	−0.0397335	+	0.0397335i	−0.726694	−	0.686961i	$-0.758944\pi$
$149$	−0.485009	+	0.485009i	−0.0397335	+	0.0397335i	0.686961	+	0.726694i	$0.258944\pi$
$150$		0			0
$151$	6.47302			0.526767			0.263383	−	0.964691i	$-0.415162\pi$
$151$	6.47302			0.526767			0.263383	+	0.964691i	$0.415162\pi$
$152$		0			0
$153$	1.35709	+	1.35709i	0.109714	+	0.109714i
$154$		0			0
$155$	10.2312	+	10.6643i	0.821790	+	0.856576i
$156$		0			0
$157$	11.7463			0.937455			0.468728	−	0.883343i	$-0.344713\pi$
$157$	11.7463			0.937455			0.468728	+	0.883343i	$0.344713\pi$
$158$		0			0
$159$	−5.05524			−0.400907
$160$		0			0
$161$	0.240990			0.0189926
$162$		0			0
$163$	−1.87143			−0.146582			−0.0732908	−	0.997311i	$-0.523350\pi$
$163$	−1.87143			−0.146582			−0.0732908	+	0.997311i	$0.523350\pi$
$164$		0			0
$165$	0.0491155	−	2.36976i	0.00382364	−	0.184486i
$166$		0			0
$167$	4.79897	+	4.79897i	0.371355	+	0.371355i	0.867971	−	0.496615i	$-0.165424\pi$
$167$	4.79897	+	4.79897i	0.371355	+	0.371355i	−0.496615	+	0.867971i	$0.665424\pi$
$168$		0			0
$169$	2.16724			0.166711
$170$		0			0
$171$	−4.25468	+	4.25468i	−0.325364	+	0.325364i
$172$		0			0
$173$			12.8446i			0.976560i	0.872687	+	0.488280i	$0.162375\pi$
$173$			12.8446i			0.976560i	−0.872687	+	0.488280i	$0.837625\pi$
$174$		0			0
$175$	0.748661	−	0.689040i	0.0565934	−	0.0520865i
$176$		0			0
$177$	3.08237	+	3.08237i	0.231685	+	0.231685i
$178$		0			0
$179$	3.47791	−	3.47791i	0.259951	−	0.259951i	−0.565083	−	0.825034i	$-0.691156\pi$
$179$	3.47791	−	3.47791i	0.259951	−	0.259951i	0.825034	+	0.565083i	$0.191156\pi$
$180$		0			0
$181$	−16.3185	−	16.3185i	−1.21295	−	1.21295i	−0.970053	−	0.242893i	$-0.921903\pi$
$181$	−16.3185	−	16.3185i	−1.21295	−	1.21295i	−0.242893	−	0.970053i	$-0.578097\pi$
$182$		0			0
$183$	−5.00346	+	5.00346i	−0.369866	+	0.369866i
$184$		0			0
$185$	15.5103	+	16.1669i	1.14034	+	1.18861i
$186$		0			0
$187$	−2.03439			−0.148770
$188$		0			0
$189$	−0.143894	−	0.143894i	−0.0104667	−	0.0104667i
$190$		0			0
$191$		−	21.5483i		−	1.55918i	−0.626289	−	0.779591i	$-0.715427\pi$
$191$		−	21.5483i		−	1.55918i	0.626289	−	0.779591i	$-0.284573\pi$
$192$		0			0
$193$	11.3161	−	11.3161i	0.814552	−	0.814552i	−0.170760	−	0.985313i	$-0.554622\pi$
$193$	11.3161	−	11.3161i	0.814552	−	0.814552i	0.985313	+	0.170760i	$0.0546224\pi$
$194$		0			0
$195$	−5.09507	−	5.31074i	−0.364866	−	0.380310i
$196$		0			0
$197$			23.3109i			1.66083i	0.557142	+	0.830417i	$0.311898\pi$
$197$			23.3109i			1.66083i	−0.557142	+	0.830417i	$0.688102\pi$
$198$		0			0
$199$			2.14992i			0.152404i	0.997092	+	0.0762018i	$0.0242793\pi$
$199$			2.14992i			0.152404i	−0.997092	+	0.0762018i	$0.975721\pi$
$200$		0			0
$201$		−	4.26739i		−	0.300999i
$202$		0			0
$203$			0.798501i			0.0560438i
$204$		0			0
$205$	2.67204	+	2.78514i	0.186623	+	0.194523i
$206$		0			0
$207$	0.837388	−	0.837388i	0.0582025	−	0.0582025i
$208$		0			0
$209$		−	6.37815i		−	0.441186i
$210$		0			0
$211$	−6.27270	−	6.27270i	−0.431830	−	0.431830i	0.457420	−	0.889251i	$-0.348774\pi$
$211$	−6.27270	−	6.27270i	−0.431830	−	0.431830i	−0.889251	+	0.457420i	$0.848774\pi$
$212$		0			0
$213$	−13.2111			−0.905207
$214$		0			0
$215$	−6.45796	−	6.73132i	−0.440429	−	0.459072i
$216$		0			0
$217$	−0.951015	+	0.951015i	−0.0645591	+	0.0645591i
$218$		0			0
$219$	11.6889	+	11.6889i	0.789861	+	0.789861i
$220$		0			0
$221$	−4.46660	+	4.46660i	−0.300456	+	0.300456i
$222$		0			0
$223$	−5.00009	−	5.00009i	−0.334831	−	0.334831i	0.519587	−	0.854418i	$-0.326086\pi$
$223$	−5.00009	−	5.00009i	−0.334831	−	0.334831i	−0.854418	+	0.519587i	$0.826086\pi$
$224$		0			0
$225$	0.207170	−	4.99571i	0.0138114	−	0.333047i
$226$		0			0
$227$			22.5630i			1.49756i	0.662821	+	0.748778i	$0.269359\pi$
$227$			22.5630i			1.49756i	−0.662821	+	0.748778i	$0.730641\pi$
$228$		0			0
$229$	6.83720	−	6.83720i	0.451815	−	0.451815i	−0.444142	−	0.895957i	$-0.646491\pi$
$229$	6.83720	−	6.83720i	0.451815	−	0.451815i	0.895957	+	0.444142i	$0.146491\pi$
$230$		0			0
$231$	0.215710			0.0141926
$232$		0			0
$233$	3.10894	+	3.10894i	0.203673	+	0.203673i	0.801572	−	0.597899i	$-0.203997\pi$
$233$	3.10894	+	3.10894i	0.203673	+	0.203673i	−0.597899	+	0.801572i	$0.703997\pi$
$234$		0			0
$235$	−0.559930	+	27.0159i	−0.0365258	+	1.76232i
$236$		0			0
$237$	−9.95558			−0.646685
$238$		0			0
$239$	11.0671			0.715873			0.357937	−	0.933746i	$-0.383480\pi$
$239$	11.0671			0.715873			0.357937	+	0.933746i	$0.383480\pi$
$240$		0			0
$241$	−23.4743			−1.51211			−0.756056	−	0.654507i	$-0.772876\pi$
$241$	−23.4743			−1.51211			−0.756056	+	0.654507i	$0.772876\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−10.7721	−	11.2281i	−0.688207	−	0.717338i
$246$		0			0
$247$	−14.0035	−	14.0035i	−0.891021	−	0.891021i
$248$		0			0
$249$	−10.0134			−0.634576
$250$		0			0
$251$	1.76187	−	1.76187i	0.111209	−	0.111209i	−0.649313	−	0.760521i	$-0.724943\pi$
$251$	1.76187	−	1.76187i	0.111209	−	0.111209i	0.760521	+	0.649313i	$0.224943\pi$
$252$		0			0
$253$			1.25532i			0.0789213i
$254$		0			0
$255$	−4.29056	−	0.0889259i	−0.268685	−	0.00556875i
$256$		0			0
$257$	−4.05693	−	4.05693i	−0.253064	−	0.253064i	0.569162	−	0.822226i	$-0.307268\pi$
$257$	−4.05693	−	4.05693i	−0.253064	−	0.253064i	−0.822226	+	0.569162i	$0.807268\pi$
$258$		0			0
$259$	−1.44172	+	1.44172i	−0.0895842	+	0.0895842i
$260$		0			0
$261$	2.77462	+	2.77462i	0.171745	+	0.171745i
$262$		0			0
$263$	22.2576	−	22.2576i	1.37246	−	1.37246i	0.515676	−	0.856784i	$-0.327541\pi$
$263$	22.2576	−	22.2576i	1.37246	−	1.37246i	0.856784	−	0.515676i	$-0.172459\pi$
$264$		0			0
$265$	8.15695	−	7.82570i	0.501078	−	0.480729i
$266$		0			0
$267$	−5.76005			−0.352509
$268$		0			0
$269$	11.9600	+	11.9600i	0.729217	+	0.729217i	0.970464	−	0.241247i	$-0.0775564\pi$
$269$	11.9600	+	11.9600i	0.729217	+	0.729217i	−0.241247	+	0.970464i	$0.577556\pi$
$270$		0			0
$271$		−	15.7162i		−	0.954691i	−0.878716	−	0.477346i	$-0.841599\pi$
$271$		−	15.7162i		−	0.954691i	0.878716	−	0.477346i	$-0.158401\pi$
$272$		0			0
$273$	0.473599	−	0.473599i	0.0286635	−	0.0286635i
$274$		0			0
$275$	3.58922	+	3.89979i	0.216438	+	0.235166i
$276$		0			0
$277$		−	4.59363i		−	0.276004i	−0.990432	−	0.138002i	$-0.955932\pi$
$277$		−	4.59363i		−	0.276004i	0.990432	−	0.138002i	$-0.0440681\pi$
$278$		0			0
$279$			6.60915i			0.395680i
$280$		0			0
$281$			20.5117i			1.22363i	0.791002	+	0.611814i	$0.209560\pi$
$281$			20.5117i			1.22363i	−0.791002	+	0.611814i	$0.790440\pi$
$282$		0			0
$283$		−	28.8990i		−	1.71787i	−0.512088	−	0.858933i	$-0.671128\pi$
$283$		−	28.8990i		−	1.71787i	0.512088	−	0.858933i	$-0.328872\pi$
$284$		0			0
$285$	0.278797	−	13.4516i	0.0165145	−	0.796804i
$286$		0			0
$287$	−0.248372	+	0.248372i	−0.0146610	+	0.0146610i
$288$		0			0
$289$		−	13.3166i		−	0.783332i
$290$		0			0
$291$	−11.7668	−	11.7668i	−0.689784	−	0.689784i
$292$		0			0
$293$	−8.86723			−0.518029			−0.259014	−	0.965873i	$-0.583398\pi$
$293$	−8.86723			−0.518029			−0.259014	+	0.965873i	$0.583398\pi$
$294$		0			0
$295$	−9.74521	−	0.201978i	−0.567388	−	0.0117596i
$296$		0			0
$297$	0.749545	−	0.749545i	0.0434930	−	0.0434930i
$298$		0			0
$299$	2.75611	+	2.75611i	0.159390	+	0.159390i
$300$		0			0
$301$	0.600283	−	0.600283i	0.0345997	−	0.0345997i
$302$		0			0
$303$	−1.29314	−	1.29314i	−0.0742890	−	0.0742890i
$304$		0			0
$305$	0.327862	−	15.8189i	0.0187733	−	0.905789i
$306$		0			0
$307$		−	14.1518i		−	0.807684i	−0.914829	−	0.403842i	$-0.867675\pi$
$307$		−	14.1518i		−	0.807684i	0.914829	−	0.403842i	$-0.132325\pi$
$308$		0			0
$309$	11.2892	−	11.2892i	0.642222	−	0.642222i
$310$		0			0
$311$	7.15165			0.405533			0.202766	−	0.979227i	$-0.435007\pi$
$311$	7.15165			0.405533			0.202766	+	0.979227i	$0.435007\pi$
$312$		0			0
$313$	−5.98016	−	5.98016i	−0.338019	−	0.338019i	0.517602	−	0.855621i	$-0.326825\pi$
$313$	−5.98016	−	5.98016i	−0.338019	−	0.338019i	−0.855621	+	0.517602i	$0.826825\pi$
$314$		0			0
$315$	0.454934	+	0.00942893i	0.0256326	+	0.000531260i
$316$		0			0
$317$	−7.76996			−0.436404			−0.218202	−	0.975904i	$-0.570019\pi$
$317$	−7.76996			−0.436404			−0.218202	+	0.975904i	$0.570019\pi$
$318$		0			0
$319$	−4.15941			−0.232882
$320$		0			0
$321$	1.39451			0.0778338
$322$		0			0
$323$	−11.5479			−0.642544
$324$		0			0
$325$	16.4424	+	0.681863i	0.912063	+	0.0378229i
$326$		0			0
$327$	−4.55325	−	4.55325i	−0.251795	−	0.251795i
$328$		0			0
$329$	−2.45915			−0.135577
$330$		0			0
$331$	0.751395	−	0.751395i	0.0413004	−	0.0413004i	−0.686155	−	0.727455i	$-0.740703\pi$
$331$	0.751395	−	0.751395i	0.0413004	−	0.0413004i	0.727455	+	0.686155i	$0.240703\pi$
$332$		0			0
$333$			10.0194i			0.549057i
$334$		0			0
$335$	6.60607	+	6.88570i	0.360928	+	0.376206i
$336$		0			0
$337$	−0.379414	−	0.379414i	−0.0206680	−	0.0206680i	0.696697	−	0.717365i	$-0.254652\pi$
$337$	−0.379414	−	0.379414i	−0.0206680	−	0.0206680i	−0.717365	+	0.696697i	$0.754652\pi$
$338$		0			0
$339$	11.4501	−	11.4501i	0.621886	−	0.621886i
$340$		0			0
$341$	−4.95386	−	4.95386i	−0.268266	−	0.268266i
$342$		0			0
$343$	2.00855	−	2.00855i	0.108452	−	0.108452i
$344$		0			0
$345$	−0.0548716	+	2.64749i	−0.00295419	+	0.142536i
$346$		0			0
$347$	−16.7455			−0.898947			−0.449473	−	0.893294i	$-0.648388\pi$
$347$	−16.7455			−0.898947			−0.449473	+	0.893294i	$0.648388\pi$
$348$		0			0
$349$	−21.0019	−	21.0019i	−1.12421	−	1.12421i	−0.991102	−	0.133104i	$-0.957506\pi$
$349$	−21.0019	−	21.0019i	−1.12421	−	1.12421i	−0.133104	−	0.991102i	$-0.542494\pi$
$350$		0			0
$351$		−	3.29132i		−	0.175677i
$352$		0			0
$353$	−9.02933	+	9.02933i	−0.480583	+	0.480583i	−0.905318	−	0.424735i	$-0.860367\pi$
$353$	−9.02933	+	9.02933i	−0.480583	+	0.480583i	0.424735	+	0.905318i	$0.360367\pi$
$354$		0			0
$355$	21.3169	−	20.4512i	1.13138	−	1.08544i
$356$		0			0
$357$		−	0.390552i		−	0.0206702i
$358$		0			0
$359$			12.2651i			0.647326i	0.946172	+	0.323663i	$0.104914\pi$
$359$			12.2651i			0.647326i	−0.946172	+	0.323663i	$0.895086\pi$
$360$		0			0
$361$		−	17.2046i		−	0.905506i
$362$		0			0
$363$		−	9.87636i		−	0.518375i
$364$		0			0
$365$	−36.9555	−	0.765938i	−1.93434	−	0.0400910i
$366$		0			0
$367$	−1.25485	+	1.25485i	−0.0655025	+	0.0655025i	−0.739099	−	0.673597i	$-0.764749\pi$
$367$	−1.25485	+	1.25485i	−0.0655025	+	0.0655025i	0.673597	+	0.739099i	$0.264749\pi$
$368$		0			0
$369$			1.72608i			0.0898563i
$370$		0			0
$371$	0.727417	+	0.727417i	0.0377656	+	0.0377656i
$372$		0			0
$373$	−8.25732			−0.427548			−0.213774	−	0.976883i	$-0.568576\pi$
$373$	−8.25732			−0.427548			−0.213774	+	0.976883i	$0.568576\pi$
$374$		0			0
$375$	7.39925	+	8.38159i	0.382096	+	0.432824i
$376$		0			0
$377$	−9.13216	+	9.13216i	−0.470330	+	0.470330i
$378$		0			0
$379$	−1.03027	−	1.03027i	−0.0529214	−	0.0529214i	0.680151	−	0.733072i	$-0.261914\pi$
$379$	−1.03027	−	1.03027i	−0.0529214	−	0.0529214i	−0.733072	+	0.680151i	$0.761914\pi$
$380$		0			0
$381$	4.94562	−	4.94562i	0.253372	−	0.253372i
$382$		0			0
$383$	12.3374	+	12.3374i	0.630413	+	0.630413i	0.948172	−	0.317759i	$-0.102930\pi$
$383$	12.3374	+	12.3374i	0.630413	+	0.630413i	−0.317759	+	0.948172i	$0.602930\pi$
$384$		0			0
$385$	−0.348061	+	0.333926i	−0.0177388	+	0.0170184i
$386$		0			0
$387$		−	4.17171i		−	0.212060i
$388$		0			0
$389$	12.8354	−	12.8354i	0.650781	−	0.650781i	−0.302400	−	0.953181i	$-0.597788\pi$
$389$	12.8354	−	12.8354i	0.650781	−	0.650781i	0.953181	+	0.302400i	$0.0977880\pi$
$390$		0			0
$391$	2.27282			0.114941
$392$		0			0
$393$	−12.7313	−	12.7313i	−0.642211	−	0.642211i
$394$		0			0
$395$	16.0640	−	15.4116i	0.808266	−	0.775442i
$396$		0			0
$397$	−14.3934			−0.722383			−0.361191	−	0.932492i	$-0.617630\pi$
$397$	−14.3934			−0.722383			−0.361191	+	0.932492i	$0.617630\pi$
$398$		0			0
$399$	1.22444			0.0612988
$400$		0			0
$401$	−37.4272			−1.86902			−0.934512	−	0.355932i	$-0.884164\pi$
$401$	−37.4272			−1.86902			−0.934512	+	0.355932i	$0.884164\pi$
$402$		0			0
$403$	−21.7528			−1.08358
$404$		0			0
$405$	1.61356	−	1.54804i	0.0801786	−	0.0769225i
$406$		0			0
$407$	−7.50996	−	7.50996i	−0.372255	−	0.372255i
$408$		0			0
$409$	8.19166			0.405052			0.202526	−	0.979277i	$-0.435085\pi$
$409$	8.19166			0.405052			0.202526	+	0.979277i	$0.435085\pi$
$410$		0			0
$411$	6.06032	−	6.06032i	0.298934	−	0.298934i
$412$		0			0
$413$		−	0.887066i		−	0.0436497i
$414$		0			0
$415$	16.1573	−	15.5012i	0.793131	−	0.760922i
$416$		0			0
$417$	10.3543	+	10.3543i	0.507051	+	0.507051i
$418$		0			0
$419$	22.2183	−	22.2183i	1.08544	−	1.08544i	0.0894455	−	0.995992i	$-0.471491\pi$
$419$	22.2183	−	22.2183i	1.08544	−	1.08544i	0.995992	−	0.0894455i	$-0.0285095\pi$
$420$		0			0
$421$	2.75098	+	2.75098i	0.134074	+	0.134074i	0.770959	−	0.636885i	$-0.219777\pi$
$421$	2.75098	+	2.75098i	0.134074	+	0.134074i	−0.636885	+	0.770959i	$0.719777\pi$
$422$		0			0
$423$	−8.54502	+	8.54502i	−0.415473	+	0.415473i
$424$		0			0
$425$	7.06075	−	6.49845i	0.342497	−	0.315221i
$426$		0			0
$427$	1.43993			0.0696832
$428$		0			0
$429$	2.46699	+	2.46699i	0.119107	+	0.119107i
$430$		0			0
$431$		−	5.32770i		−	0.256626i	−0.991734	−	0.128313i	$-0.959044\pi$
$431$		−	5.32770i		−	0.256626i	0.991734	−	0.128313i	$-0.0409563\pi$
$432$		0			0
$433$	−3.38866	+	3.38866i	−0.162849	+	0.162849i	−0.783827	−	0.620979i	$-0.786735\pi$
$433$	−3.38866	+	3.38866i	−0.162849	+	0.162849i	0.620979	+	0.783827i	$0.286735\pi$
$434$		0			0
$435$	−8.77224	−	0.181813i	−0.420597	−	0.00871726i
$436$		0			0
$437$			7.12564i			0.340866i
$438$		0			0
$439$			5.99801i			0.286269i	0.989703	+	0.143135i	$0.0457182\pi$
$439$			5.99801i			0.286269i	−0.989703	+	0.143135i	$0.954282\pi$
$440$		0			0
$441$		−	6.95859i		−	0.331361i
$442$		0			0
$443$		−	13.3394i		−	0.633773i	−0.948463	−	0.316887i	$-0.897363\pi$
$443$		−	13.3394i		−	0.633773i	0.948463	−	0.316887i	$-0.102637\pi$
$444$		0			0
$445$	9.29420	−	8.91676i	0.440587	−	0.422695i
$446$		0			0
$447$	0.485009	−	0.485009i	0.0229401	−	0.0229401i
$448$		0			0
$449$		−	29.7201i		−	1.40258i	−0.712877	−	0.701289i	$-0.752608\pi$
$449$		−	29.7201i		−	1.40258i	0.712877	−	0.701289i	$-0.247392\pi$
$450$		0			0
$451$	−1.29378	−	1.29378i	−0.0609216	−	0.0609216i
$452$		0			0
$453$	−6.47302			−0.304129
$454$		0			0
$455$	−0.0310336	+	1.49733i	−0.00145488	+	0.0701960i
$456$		0			0
$457$	−13.8443	+	13.8443i	−0.647611	+	0.647611i	−0.952415	−	0.304804i	$-0.901409\pi$
$457$	−13.8443	+	13.8443i	−0.647611	+	0.647611i	0.304804	+	0.952415i	$0.401409\pi$
$458$		0			0
$459$	−1.35709	−	1.35709i	−0.0633433	−	0.0633433i
$460$		0			0
$461$	−23.8766	+	23.8766i	−1.11205	+	1.11205i	−0.119172	+	0.992874i	$0.538024\pi$
$461$	−23.8766	+	23.8766i	−1.11205	+	1.11205i	−0.992874	+	0.119172i	$0.961976\pi$
$462$		0			0
$463$	−10.5750	−	10.5750i	−0.491463	−	0.491463i	0.417304	−	0.908767i	$-0.362975\pi$
$463$	−10.5750	−	10.5750i	−0.491463	−	0.491463i	−0.908767	+	0.417304i	$0.862975\pi$
$464$		0			0
$465$	−10.2312	−	10.6643i	−0.474461	−	0.494544i
$466$		0			0
$467$		−	30.0161i		−	1.38898i	−0.719502	−	0.694491i	$-0.755630\pi$
$467$		−	30.0161i		−	1.38898i	0.719502	−	0.694491i	$-0.244370\pi$
$468$		0			0
$469$	−0.614050	+	0.614050i	−0.0283542	+	0.0283542i
$470$		0			0
$471$	−11.7463			−0.541240
$472$		0			0
$473$	3.12689	+	3.12689i	0.143774	+	0.143774i
$474$		0			0
$475$	20.3737	+	22.1366i	0.934809	+	1.01570i
$476$		0			0
$477$	5.05524			0.231464
$478$		0			0
$479$	21.9152			1.00133			0.500665	−	0.865641i	$-0.333089\pi$
$479$	21.9152			1.00133			0.500665	+	0.865641i	$0.333089\pi$
$480$		0			0
$481$	−32.9769			−1.50362
$482$		0			0
$483$	−0.240990			−0.0109654
$484$		0			0
$485$	37.2020	+	0.771047i	1.68926	+	0.0350114i
$486$		0			0
$487$	−5.66360	−	5.66360i	−0.256642	−	0.256642i	0.567045	−	0.823687i	$-0.308087\pi$
$487$	−5.66360	−	5.66360i	−0.256642	−	0.256642i	−0.823687	+	0.567045i	$0.808087\pi$
$488$		0			0
$489$	1.87143			0.0846289
$490$		0			0
$491$	25.4744	−	25.4744i	1.14964	−	1.14964i	0.163018	−	0.986623i	$-0.447877\pi$
$491$	25.4744	−	25.4744i	1.14964	−	1.14964i	0.986623	−	0.163018i	$-0.0521230\pi$
$492$		0			0
$493$			7.53080i			0.339170i
$494$		0			0
$495$	−0.0491155	+	2.36976i	−0.00220758	+	0.106513i
$496$		0			0
$497$	1.90099	+	1.90099i	0.0852709	+	0.0852709i
$498$		0			0
$499$	−18.8209	+	18.8209i	−0.842537	+	0.842537i	−0.989188	−	0.146651i	$-0.953151\pi$
$499$	−18.8209	+	18.8209i	−0.842537	+	0.842537i	0.146651	+	0.989188i	$0.453151\pi$
$500$		0			0
$501$	−4.79897	−	4.79897i	−0.214402	−	0.214402i
$502$		0			0
$503$	7.85721	−	7.85721i	0.350336	−	0.350336i	−0.509899	−	0.860234i	$-0.670317\pi$
$503$	7.85721	−	7.85721i	0.350336	−	0.350336i	0.860234	+	0.509899i	$0.170317\pi$
$504$		0			0
$505$	4.08839	+	0.0847357i	0.181931	+	0.00377069i
$506$		0			0
$507$	−2.16724			−0.0962507
$508$		0			0
$509$	10.1248	+	10.1248i	0.448776	+	0.448776i	0.894948	−	0.446171i	$-0.147213\pi$
$509$	10.1248	+	10.1248i	0.448776	+	0.448776i	−0.446171	+	0.894948i	$0.647213\pi$
$510$		0			0
$511$		−	3.36391i		−	0.148811i
$512$		0			0
$513$	4.25468	−	4.25468i	0.187849	−	0.187849i
$514$		0			0
$515$	−0.739751	+	35.6920i	−0.0325973	+	1.57278i
$516$		0			0
$517$		−	12.8097i		−	0.563372i
$518$		0			0
$519$		−	12.8446i		−	0.563817i
$520$		0			0
$521$		−	37.3503i		−	1.63634i	−0.574973	−	0.818172i	$-0.694987\pi$
$521$		−	37.3503i		−	1.63634i	0.574973	−	0.818172i	$-0.305013\pi$
$522$		0			0
$523$			8.27258i			0.361735i	0.983507	+	0.180867i	$0.0578905\pi$
$523$			8.27258i			0.361735i	−0.983507	+	0.180867i	$0.942110\pi$
$524$		0			0
$525$	−0.748661	+	0.689040i	−0.0326742	+	0.0300722i
$526$		0			0
$527$	−8.96919	+	8.96919i	−0.390704	+	0.390704i
$528$		0			0
$529$			21.5976i			0.939024i
$530$		0			0
$531$	−3.08237	−	3.08237i	−0.133763	−	0.133763i
$532$		0			0
$533$	−5.68108			−0.246075
$534$		0			0
$535$	−2.25012	+	2.15875i	−0.0972814	+	0.0933308i
$536$		0			0
$537$	−3.47791	+	3.47791i	−0.150083	+	0.150083i
$538$		0			0
$539$	5.21578	+	5.21578i	0.224659	+	0.224659i
$540$		0			0
$541$	−11.1960	+	11.1960i	−0.481352	+	0.481352i	−0.905563	−	0.424211i	$-0.860551\pi$
$541$	−11.1960	+	11.1960i	−0.481352	+	0.481352i	0.424211	+	0.905563i	$0.360551\pi$
$542$		0			0
$543$	16.3185	+	16.3185i	0.700295	+	0.700295i
$544$		0			0
$545$	14.3956	+	0.298361i	0.616638	+	0.0127804i
$546$		0			0
$547$		−	26.6966i		−	1.14147i	−0.821136	−	0.570733i	$-0.806659\pi$
$547$		−	26.6966i		−	1.14147i	0.821136	−	0.570733i	$-0.193341\pi$
$548$		0			0
$549$	5.00346	−	5.00346i	0.213542	−	0.213542i
$550$		0			0
$551$	−23.6103			−1.00583
$552$		0			0
$553$	1.43255	+	1.43255i	0.0609180	+	0.0609180i
$554$		0			0
$555$	−15.5103	−	16.1669i	−0.658377	−	0.686245i
$556$		0			0
$557$	0.715510			0.0303171			0.0151586	−	0.999885i	$-0.495175\pi$
$557$	0.715510			0.0303171			0.0151586	+	0.999885i	$0.495175\pi$
$558$		0			0
$559$	13.7304			0.580735
$560$		0			0
$561$	2.03439			0.0858922
$562$		0			0
$563$	−16.6892			−0.703364			−0.351682	−	0.936119i	$-0.614390\pi$
$563$	−16.6892			−0.703364			−0.351682	+	0.936119i	$0.614390\pi$
$564$		0			0
$565$	−0.750294	+	36.2007i	−0.0315651	+	1.52298i
$566$		0			0
$567$	0.143894	+	0.143894i	0.00604297	+	0.00604297i
$568$		0			0
$569$	−23.0249			−0.965253			−0.482626	−	0.875826i	$-0.660317\pi$
$569$	−23.0249			−0.965253			−0.482626	+	0.875826i	$0.660317\pi$
$570$		0			0
$571$	7.65518	−	7.65518i	0.320359	−	0.320359i	−0.528546	−	0.848905i	$-0.677262\pi$
$571$	7.65518	−	7.65518i	0.320359	−	0.320359i	0.848905	+	0.528546i	$0.177262\pi$
$572$		0			0
$573$			21.5483i			0.900194i
$574$		0			0
$575$	−4.00986	−	4.35683i	−0.167223	−	0.181692i
$576$		0			0
$577$	22.0343	+	22.0343i	0.917298	+	0.917298i	0.996832	−	0.0795337i	$-0.0253431\pi$
$577$	22.0343	+	22.0343i	0.917298	+	0.917298i	−0.0795337	+	0.996832i	$0.525343\pi$
$578$		0			0
$579$	−11.3161	+	11.3161i	−0.470282	+	0.470282i
$580$		0			0
$581$	1.44087	+	1.44087i	0.0597774	+	0.0597774i
$582$		0			0
$583$	−3.78913	+	3.78913i	−0.156930	+	0.156930i
$584$		0			0
$585$	5.09507	+	5.31074i	0.210655	+	0.219572i
$586$		0			0
$587$	−22.5696			−0.931547			−0.465773	−	0.884904i	$-0.654224\pi$
$587$	−22.5696			−0.931547			−0.465773	+	0.884904i	$0.654224\pi$
$588$		0			0
$589$	−28.1198	−	28.1198i	−1.15866	−	1.15866i
$590$		0			0
$591$		−	23.3109i		−	0.958883i
$592$		0			0
$593$	−26.4172	+	26.4172i	−1.08482	+	1.08482i	−0.0887706	+	0.996052i	$0.528294\pi$
$593$	−26.4172	+	26.4172i	−1.08482	+	1.08482i	−0.996052	+	0.0887706i	$0.971706\pi$
$594$		0			0
$595$	0.604589	+	0.630180i	0.0247857	+	0.0258349i
$596$		0			0
$597$		−	2.14992i		−	0.0879902i
$598$		0			0
$599$			17.4693i			0.713775i	0.934147	+	0.356888i	$0.116162\pi$
$599$			17.4693i			0.713775i	−0.934147	+	0.356888i	$0.883838\pi$
$600$		0			0
$601$			25.8843i			1.05584i	0.849294	+	0.527921i	$0.177028\pi$
$601$			25.8843i			1.05584i	−0.849294	+	0.527921i	$0.822972\pi$
$602$		0			0
$603$			4.26739i			0.173782i
$604$		0			0
$605$	15.2890	+	15.9361i	0.621585	+	0.647896i
$606$		0			0
$607$	−22.7204	+	22.7204i	−0.922193	+	0.922193i	−0.997184	−	0.0749912i	$-0.976107\pi$
$607$	−22.7204	+	22.7204i	−0.922193	+	0.922193i	0.0749912	+	0.997184i	$0.476107\pi$
$608$		0			0
$609$		−	0.798501i		−	0.0323569i
$610$		0			0
$611$	−28.1243	−	28.1243i	−1.13779	−	1.13779i
$612$		0			0
$613$	0.840532			0.0339488			0.0169744	−	0.999856i	$-0.494597\pi$
$613$	0.840532			0.0339488			0.0169744	+	0.999856i	$0.494597\pi$
$614$		0			0
$615$	−2.67204	−	2.78514i	−0.107747	−	0.112308i
$616$		0			0
$617$	7.18912	−	7.18912i	0.289423	−	0.289423i	−0.547429	−	0.836852i	$-0.684393\pi$
$617$	7.18912	−	7.18912i	0.289423	−	0.289423i	0.836852	+	0.547429i	$0.184393\pi$
$618$		0			0
$619$	31.9741	+	31.9741i	1.28515	+	1.28515i	0.937700	+	0.347447i	$0.112951\pi$
$619$	31.9741	+	31.9741i	1.28515	+	1.28515i	0.347447	+	0.937700i	$0.387049\pi$
$620$		0			0
$621$	−0.837388	+	0.837388i	−0.0336032	+	0.0336032i
$622$		0			0
$623$	0.828834	+	0.828834i	0.0332065	+	0.0332065i
$624$		0			0
$625$	−24.9142	−	2.06992i	−0.996566	−	0.0827970i
$626$		0			0
$627$			6.37815i			0.254719i
$628$		0			0
$629$	−13.5971	+	13.5971i	−0.542153	+	0.542153i
$630$		0			0
$631$	28.2004			1.12264			0.561320	−	0.827599i	$-0.310294\pi$
$631$	28.2004			1.12264			0.561320	+	0.827599i	$0.310294\pi$
$632$		0			0
$633$	6.27270	+	6.27270i	0.249317	+	0.249317i
$634$		0			0
$635$	−0.324072	+	15.6361i	−0.0128604	+	0.620498i
$636$		0			0
$637$	22.9029			0.907446
$638$		0			0
$639$	13.2111			0.522621
$640$		0			0
$641$	36.6103			1.44602			0.723011	−	0.690837i	$-0.242758\pi$
$641$	36.6103			1.44602			0.723011	+	0.690837i	$0.242758\pi$
$642$		0			0
$643$	−13.4647			−0.530996			−0.265498	−	0.964111i	$-0.585536\pi$
$643$	−13.4647			−0.530996			−0.265498	+	0.964111i	$0.585536\pi$
$644$		0			0
$645$	6.45796	+	6.73132i	0.254282	+	0.265045i
$646$		0			0
$647$	23.4382	+	23.4382i	0.921451	+	0.921451i	0.997132	−	0.0756812i	$-0.0241131\pi$
$647$	23.4382	+	23.4382i	0.921451	+	0.921451i	−0.0756812	+	0.997132i	$0.524113\pi$
$648$		0			0
$649$	4.62075			0.181380
$650$		0			0
$651$	0.951015	−	0.951015i	0.0372732	−	0.0372732i
$652$		0			0
$653$			15.0338i			0.588318i	0.955756	+	0.294159i	$0.0950396\pi$
$653$			15.0338i			0.588318i	−0.955756	+	0.294159i	$0.904960\pi$
$654$		0			0
$655$	40.2514	+	0.834247i	1.57275	+	0.0325967i
$656$		0			0
$657$	−11.6889	−	11.6889i	−0.456027	−	0.456027i
$658$		0			0
$659$	12.8233	−	12.8233i	0.499524	−	0.499524i	−0.411766	−	0.911290i	$-0.635088\pi$
$659$	12.8233	−	12.8233i	0.499524	−	0.499524i	0.911290	+	0.411766i	$0.135088\pi$
$660$		0			0
$661$	−22.6599	−	22.6599i	−0.881369	−	0.881369i	0.112305	−	0.993674i	$-0.464177\pi$
$661$	−22.6599	−	22.6599i	−0.881369	−	0.881369i	−0.993674	+	0.112305i	$0.964177\pi$
$662$		0			0
$663$	4.46660	−	4.46660i	0.173468	−	0.173468i
$664$		0			0
$665$	−1.97572	+	1.89548i	−0.0766150	+	0.0735036i
$666$		0			0
$667$	4.64687			0.179928
$668$		0			0
$669$	5.00009	+	5.00009i	0.193315	+	0.193315i
$670$		0			0
$671$			7.50063i			0.289559i
$672$		0			0
$673$	18.5901	−	18.5901i	0.716595	−	0.716595i	−0.251311	−	0.967906i	$-0.580862\pi$
$673$	18.5901	−	18.5901i	0.716595	−	0.716595i	0.967906	+	0.251311i	$0.0808617\pi$
$674$		0			0
$675$	−0.207170	+	4.99571i	−0.00797399	+	0.192285i
$676$		0			0
$677$		−	1.52496i		−	0.0586089i	−0.999571	−	0.0293044i	$-0.990671\pi$
$677$		−	1.52496i		−	0.0586089i	0.999571	−	0.0293044i	$-0.00932923\pi$
$678$		0			0
$679$			3.38635i			0.129956i
$680$		0			0
$681$		−	22.5630i		−	0.864614i
$682$		0			0
$683$			3.77382i			0.144401i	0.997390	+	0.0722006i	$0.0230022\pi$
$683$			3.77382i			0.144401i	−0.997390	+	0.0722006i	$0.976998\pi$
$684$		0			0
$685$	−0.397115	+	19.1603i	−0.0151730	+	0.732078i
$686$		0			0
$687$	−6.83720	+	6.83720i	−0.260856	+	0.260856i
$688$		0			0
$689$			16.6384i			0.633873i
$690$		0			0
$691$	15.9624	+	15.9624i	0.607239	+	0.607239i	0.942224	−	0.334984i	$-0.108731\pi$
$691$	15.9624	+	15.9624i	0.607239	+	0.607239i	−0.334984	+	0.942224i	$0.608731\pi$
$692$		0			0
$693$	−0.215710			−0.00819413
$694$		0			0
$695$	−32.7361	−	0.678486i	−1.24175	−	0.0257364i
$696$		0			0
$697$	−2.34244	+	2.34244i	−0.0887263	+	0.0887263i
$698$		0			0
$699$	−3.10894	−	3.10894i	−0.117591	−	0.117591i
$700$		0			0
$701$	20.1411	−	20.1411i	0.760717	−	0.760717i	−0.215735	−	0.976452i	$-0.569215\pi$
$701$	20.1411	−	20.1411i	0.760717	−	0.760717i	0.976452	+	0.215735i	$0.0692146\pi$
$702$		0			0
$703$	−42.6292	−	42.6292i	−1.60779	−	1.60779i
$704$		0			0
$705$	0.559930	−	27.0159i	0.0210882	−	1.01748i
$706$		0			0
$707$			0.372149i			0.0139961i
$708$		0			0
$709$	−8.20276	+	8.20276i	−0.308061	+	0.308061i	−0.844157	−	0.536096i	$-0.819899\pi$
$709$	−8.20276	+	8.20276i	−0.308061	+	0.308061i	0.536096	+	0.844157i	$0.319899\pi$
$710$		0			0
$711$	9.95558			0.373364
$712$		0			0
$713$	5.53443	+	5.53443i	0.207266	+	0.207266i
$714$		0			0
$715$	−7.79963	−	0.161655i	−0.291690	−	0.00604554i
$716$		0			0
$717$	−11.0671			−0.413310
$718$		0			0
$719$	−23.6655			−0.882576			−0.441288	−	0.897366i	$-0.645478\pi$
$719$	−23.6655			−0.882576			−0.441288	+	0.897366i	$0.645478\pi$
$720$		0			0
$721$	−3.24890			−0.120995
$722$		0			0
$723$	23.4743			0.873018
$724$		0			0
$725$	14.4360	−	13.2864i	0.536140	−	0.493444i
$726$		0			0
$727$	−1.68416	−	1.68416i	−0.0624622	−	0.0624622i	0.675186	−	0.737648i	$-0.264064\pi$
$727$	−1.68416	−	1.68416i	−0.0624622	−	0.0624622i	−0.737648	+	0.675186i	$0.764064\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.66137	−	5.66137i	0.209393	−	0.209393i
$732$		0			0
$733$		−	48.4131i		−	1.78818i	−0.447889	−	0.894089i	$-0.647824\pi$
$733$		−	48.4131i		−	1.78818i	0.447889	−	0.894089i	$-0.352176\pi$
$734$		0			0
$735$	10.7721	+	11.2281i	0.397337	+	0.414155i
$736$		0			0
$737$	−3.19860	−	3.19860i	−0.117822	−	0.117822i
$738$		0			0
$739$	−2.35313	+	2.35313i	−0.0865612	+	0.0865612i	−0.749062	−	0.662500i	$-0.769495\pi$
$739$	−2.35313	+	2.35313i	−0.0865612	+	0.0865612i	0.662500	+	0.749062i	$0.269495\pi$
$740$		0			0
$741$	14.0035	+	14.0035i	0.514431	+	0.514431i
$742$		0			0
$743$	17.6788	−	17.6788i	0.648571	−	0.648571i	−0.304076	−	0.952648i	$-0.598348\pi$
$743$	17.6788	−	17.6788i	0.648571	−	0.648571i	0.952648	+	0.304076i	$0.0983478\pi$
$744$		0			0
$745$	−0.0317812	+	1.53340i	−0.00116437	+	0.0561796i
$746$		0			0
$747$	10.0134			0.366373
$748$		0			0
$749$	−0.200661	−	0.200661i	−0.00733198	−	0.00733198i
$750$		0			0
$751$			40.8647i			1.49117i	0.666409	+	0.745587i	$0.267831\pi$
$751$			40.8647i			1.49117i	−0.666409	+	0.745587i	$0.732169\pi$
$752$		0			0
$753$	−1.76187	+	1.76187i	−0.0642063	+	0.0642063i
$754$		0			0
$755$	10.4446	−	10.0205i	0.380119	−	0.364682i
$756$		0			0
$757$			24.6892i			0.897345i	0.893696	+	0.448673i	$0.148103\pi$
$757$			24.6892i			0.897345i	−0.893696	+	0.448673i	$0.851897\pi$
$758$		0			0
$759$		−	1.25532i		−	0.0455652i
$760$		0			0
$761$		−	6.54343i		−	0.237199i	−0.992942	−	0.118600i	$-0.962160\pi$
$761$		−	6.54343i		−	0.237199i	0.992942	−	0.118600i	$-0.0378405\pi$
$762$		0			0
$763$			1.31037i			0.0474385i
$764$		0			0
$765$	4.29056	+	0.0889259i	0.155126	+	0.00321512i
$766$		0			0
$767$	10.1450	−	10.1450i	0.366316	−	0.366316i
$768$		0			0
$769$		−	26.2710i		−	0.947357i	−0.880698	−	0.473678i	$-0.842926\pi$
$769$		−	26.2710i		−	0.947357i	0.880698	−	0.473678i	$-0.157074\pi$
$770$		0			0
$771$	4.05693	+	4.05693i	0.146107	+	0.146107i
$772$		0			0
$773$	9.19242			0.330628			0.165314	−	0.986241i	$-0.447136\pi$
$773$	9.19242			0.330628			0.165314	+	0.986241i	$0.447136\pi$
$774$		0			0
$775$	33.0174	+	1.36922i	1.18602	+	0.0491839i
$776$		0			0
$777$	1.44172	−	1.44172i	0.0517215	−	0.0517215i
$778$		0			0
$779$	−7.34393	−	7.34393i	−0.263124	−	0.263124i
$780$		0			0
$781$	−9.90228	+	9.90228i	−0.354332	+	0.354332i
$782$		0			0
$783$	−2.77462	−	2.77462i	−0.0991569	−	0.0991569i
$784$		0			0
$785$	18.9534	−	18.1837i	0.676475	−	0.649003i
$786$		0			0
$787$			20.9534i			0.746908i	0.927649	+	0.373454i	$0.121827\pi$
$787$			20.9534i			0.746908i	−0.927649	+	0.373454i	$0.878173\pi$
$788$		0			0
$789$	−22.2576	+	22.2576i	−0.792390	+	0.792390i
$790$		0			0
$791$	−3.29520			−0.117164
$792$		0			0
$793$	16.4680	+	16.4680i	0.584794	+	0.584794i
$794$		0			0
$795$	−8.15695	+	7.82570i	−0.289297	+	0.277549i
$796$		0			0
$797$	25.5883			0.906384			0.453192	−	0.891413i	$-0.350285\pi$
$797$	25.5883			0.906384			0.453192	+	0.891413i	$0.350285\pi$
$798$		0			0
$799$	−23.1926			−0.820497
$800$		0			0
$801$	5.76005			0.203521
$802$		0			0
$803$	17.5227			0.618362
$804$		0			0
$805$	0.388852	−	0.373061i	0.0137052	−	0.0131487i
$806$		0			0
$807$	−11.9600	−	11.9600i	−0.421014	−	0.421014i
$808$		0			0
$809$	−4.93002			−0.173330			−0.0866652	−	0.996237i	$-0.527621\pi$
$809$	−4.93002			−0.173330			−0.0866652	+	0.996237i	$0.527621\pi$
$810$		0			0
$811$	−35.3133	+	35.3133i	−1.24002	+	1.24002i	−0.280025	+	0.959993i	$0.590343\pi$
$811$	−35.3133	+	35.3133i	−1.24002	+	1.24002i	−0.959993	+	0.280025i	$0.909657\pi$
$812$		0			0
$813$			15.7162i			0.551191i
$814$		0			0
$815$	−3.01967	+	2.89704i	−0.105774	+	0.101479i
$816$		0			0
$817$	17.7493	+	17.7493i	0.620970	+	0.620970i
$818$		0			0
$819$	−0.473599	+	0.473599i	−0.0165489	+	0.0165489i
$820$		0			0
$821$	−36.2490	−	36.2490i	−1.26510	−	1.26510i	−0.948589	−	0.316509i	$-0.897489\pi$
$821$	−36.2490	−	36.2490i	−1.26510	−	1.26510i	−0.316509	−	0.948589i	$-0.602511\pi$
$822$		0			0
$823$	23.0235	−	23.0235i	0.802548	−	0.802548i	−0.180945	−	0.983493i	$-0.557916\pi$
$823$	23.0235	−	23.0235i	0.802548	−	0.802548i	0.983493	+	0.180945i	$0.0579156\pi$
$824$		0			0
$825$	−3.58922	−	3.89979i	−0.124961	−	0.135773i
$826$		0			0
$827$	−44.8863			−1.56085			−0.780424	−	0.625250i	$-0.784997\pi$
$827$	−44.8863			−1.56085			−0.780424	+	0.625250i	$0.784997\pi$
$828$		0			0
$829$	−7.27338	−	7.27338i	−0.252615	−	0.252615i	0.569427	−	0.822042i	$-0.307165\pi$
$829$	−7.27338	−	7.27338i	−0.252615	−	0.252615i	−0.822042	+	0.569427i	$0.807165\pi$
$830$		0			0
$831$			4.59363i			0.159351i
$832$		0			0
$833$	9.44340	−	9.44340i	0.327195	−	0.327195i
$834$		0			0
$835$	15.1724	+	0.314462i	0.525063	+	0.0108824i
$836$		0			0
$837$		−	6.60915i		−	0.228446i
$838$		0			0
$839$			6.23853i			0.215378i	0.994185	+	0.107689i	$0.0343451\pi$
$839$			6.23853i			0.215378i	−0.994185	+	0.107689i	$0.965655\pi$
$840$		0			0
$841$		−	13.6029i		−	0.469067i
$842$		0			0
$843$		−	20.5117i		−	0.706462i
$844$		0			0
$845$	3.49699	−	3.35497i	0.120300	−	0.115415i
$846$		0			0
$847$	−1.42115	+	1.42115i	−0.0488312	+	0.0488312i
$848$		0			0
$849$			28.8990i			0.991811i
$850$		0			0
$851$	8.39009	+	8.39009i	0.287609	+	0.287609i
$852$		0			0
$853$	−32.1759			−1.10168			−0.550841	−	0.834610i	$-0.685693\pi$
$853$	−32.1759			−1.10168			−0.550841	+	0.834610i	$0.685693\pi$
$854$		0			0
$855$	−0.278797	+	13.4516i	−0.00953465	+	0.460035i
$856$		0			0
$857$	−11.0467	+	11.0467i	−0.377348	+	0.377348i	−0.870145	−	0.492797i	$-0.835975\pi$
$857$	−11.0467	+	11.0467i	−0.377348	+	0.377348i	0.492797	+	0.870145i	$0.335975\pi$
$858$		0			0
$859$	1.75107	+	1.75107i	0.0597457	+	0.0597457i	0.736348	−	0.676603i	$-0.236548\pi$
$859$	1.75107	+	1.75107i	0.0597457	+	0.0597457i	−0.676603	+	0.736348i	$0.736548\pi$
$860$		0			0
$861$	0.248372	−	0.248372i	0.00846451	−	0.00846451i
$862$		0			0
$863$	−4.70982	−	4.70982i	−0.160324	−	0.160324i	0.622386	−	0.782710i	$-0.286163\pi$
$863$	−4.70982	−	4.70982i	−0.160324	−	0.160324i	−0.782710	+	0.622386i	$0.786163\pi$
$864$		0			0
$865$	19.8840	+	20.7256i	0.676075	+	0.704693i
$866$		0			0
$867$			13.3166i			0.452257i
$868$		0			0
$869$	−7.46216	+	7.46216i	−0.253136	+	0.253136i
$870$		0			0
$871$	−14.0453			−0.475908
$872$		0			0
$873$	11.7668	+	11.7668i	0.398247	+	0.398247i
$874$		0			0
$875$	0.141353	−	2.27076i	0.00477860	−	0.0767658i
$876$		0			0
$877$	16.7655			0.566130			0.283065	−	0.959101i	$-0.408649\pi$
$877$	16.7655			0.566130			0.283065	+	0.959101i	$0.408649\pi$
$878$		0			0
$879$	8.86723			0.299084
$880$		0			0
$881$	50.5390			1.70270			0.851352	−	0.524595i	$-0.175783\pi$
$881$	50.5390			1.70270			0.851352	+	0.524595i	$0.175783\pi$
$882$		0			0
$883$	27.3039			0.918848			0.459424	−	0.888217i	$-0.348056\pi$
$883$	27.3039			0.918848			0.459424	+	0.888217i	$0.348056\pi$
$884$		0			0
$885$	9.74521	+	0.201978i	0.327582	+	0.00678943i
$886$		0			0
$887$	−2.95052	−	2.95052i	−0.0990688	−	0.0990688i	0.655835	−	0.754904i	$-0.272317\pi$
$887$	−2.95052	−	2.95052i	−0.0990688	−	0.0990688i	−0.754904	+	0.655835i	$0.772317\pi$
$888$		0			0
$889$	−1.42329			−0.0477355
$890$		0			0
$891$	−0.749545	+	0.749545i	−0.0251107	+	0.0251107i
$892$		0			0
$893$		−	72.7126i		−	2.43324i
$894$		0			0
$895$	0.227897	−	10.9957i	0.00761776	−	0.367547i
$896$		0			0
$897$	−2.75611	−	2.75611i	−0.0920238	−	0.0920238i
$898$		0			0
$899$	−18.3379	+	18.3379i	−0.611603	+	0.611603i
$900$		0			0
$901$	6.86040	+	6.86040i	0.228553	+	0.228553i
$902$		0			0
$903$	−0.600283	+	0.600283i	−0.0199762	+	0.0199762i
$904$		0			0
$905$	−51.5926	−	1.06931i	−1.71500	−	0.0355449i
$906$		0			0
$907$	0.0410041			0.00136152			0.000680760	−	1.00000i	$-0.499783\pi$
$907$	0.0410041			0.00136152			0.000680760		1.00000i	$0.499783\pi$
$908$		0			0
$909$	1.29314	+	1.29314i	0.0428907	+	0.0428907i
$910$		0			0
$911$		−	21.7776i		−	0.721525i	−0.932658	−	0.360763i	$-0.882516\pi$
$911$		−	21.7776i		−	0.721525i	0.932658	−	0.360763i	$-0.117484\pi$
$912$		0			0
$913$	−7.50552	+	7.50552i	−0.248397	+	0.248397i
$914$		0			0
$915$	−0.327862	+	15.8189i	−0.0108388	+	0.522957i
$916$		0			0
$917$			3.66392i			0.120993i
$918$		0			0
$919$		−	34.4842i		−	1.13753i	−0.822500	−	0.568765i	$-0.807421\pi$
$919$		−	34.4842i		−	1.13753i	0.822500	−	0.568765i	$-0.192579\pi$
$920$		0			0
$921$			14.1518i			0.466317i
$922$		0			0
$923$			43.4818i			1.43122i
$924$		0			0
$925$	50.0538	+	2.07571i	1.64576	+	0.0682490i
$926$		0			0
$927$	−11.2892	+	11.2892i	−0.370787	+	0.370787i
$928$		0			0
$929$			19.8125i			0.650028i	0.945709	+	0.325014i	$0.105369\pi$
$929$			19.8125i			0.650028i	−0.945709	+	0.325014i	$0.894631\pi$
$930$		0			0
$931$	29.6066	+	29.6066i	0.970316	+	0.970316i
$932$		0			0
$933$	−7.15165			−0.234134
$934$		0			0
$935$	−3.28262	+	3.14931i	−0.107353	+	0.102994i
$936$		0			0
$937$	20.7731	−	20.7731i	0.678628	−	0.678628i	−0.281062	−	0.959690i	$-0.590687\pi$
$937$	20.7731	−	20.7731i	0.678628	−	0.678628i	0.959690	+	0.281062i	$0.0906866\pi$
$938$		0			0
$939$	5.98016	+	5.98016i	0.195155	+	0.195155i
$940$		0			0
$941$	24.6412	−	24.6412i	0.803279	−	0.803279i	−0.180328	−	0.983607i	$-0.557716\pi$
$941$	24.6412	−	24.6412i	0.803279	−	0.803279i	0.983607	+	0.180328i	$0.0577158\pi$
$942$		0			0
$943$	1.44540	+	1.44540i	0.0470687	+	0.0470687i
$944$		0			0
$945$	−0.454934	−	0.00942893i	−0.0147990	−	0.000306723i
$946$		0			0
$947$			46.1706i			1.50034i	0.661244	+	0.750171i	$0.270029\pi$
$947$			46.1706i			1.50034i	−0.661244	+	0.750171i	$0.729971\pi$
$948$		0			0
$949$	38.4718	−	38.4718i	1.24885	−	1.24885i
$950$		0			0
$951$	7.76996			0.251958
$952$		0			0
$953$	5.45044	+	5.45044i	0.176557	+	0.176557i	0.789853	−	0.613296i	$-0.210157\pi$
$953$	5.45044	+	5.45044i	0.176557	+	0.176557i	−0.613296	+	0.789853i	$0.710157\pi$
$954$		0			0
$955$	−33.3576	−	34.7696i	−1.07943	−	1.12512i
$956$		0			0
$957$	4.15941			0.134455
$958$		0			0
$959$	−1.74408			−0.0563194
$960$		0			0
$961$	−12.6809			−0.409062
$962$		0			0
$963$	−1.39451			−0.0449374
$964$		0			0
$965$	0.741512	−	35.7770i	0.0238701	−	1.15170i
$966$		0			0
$967$	−18.1852	−	18.1852i	−0.584798	−	0.584798i	0.351420	−	0.936218i	$-0.385699\pi$
$967$	−18.1852	−	18.1852i	−0.584798	−	0.584798i	−0.936218	+	0.351420i	$0.885699\pi$
$968$		0			0
$969$	11.5479			0.370973
$970$		0			0
$971$	11.6265	−	11.6265i	0.373112	−	0.373112i	−0.495497	−	0.868609i	$-0.665014\pi$
$971$	11.6265	−	11.6265i	0.373112	−	0.373112i	0.868609	+	0.495497i	$0.165014\pi$
$972$		0			0
$973$		−	2.97983i		−	0.0955290i
$974$		0			0
$975$	−16.4424	−	0.681863i	−0.526580	−	0.0218371i
$976$		0			0
$977$	−8.35835	−	8.35835i	−0.267407	−	0.267407i	0.560647	−	0.828055i	$-0.310552\pi$
$977$	−8.35835	−	8.35835i	−0.267407	−	0.267407i	−0.828055	+	0.560647i	$0.810552\pi$
$978$		0			0
$979$	−4.31741	+	4.31741i	−0.137985	+	0.137985i
$980$		0			0
$981$	4.55325	+	4.55325i	0.145374	+	0.145374i
$982$		0			0
$983$	−18.1290	+	18.1290i	−0.578226	+	0.578226i	−0.934414	−	0.356188i	$-0.884076\pi$
$983$	−18.1290	+	18.1290i	−0.578226	+	0.578226i	0.356188	+	0.934414i	$0.384076\pi$
$984$		0			0
$985$	36.0861	+	37.6136i	1.14980	+	1.19847i
$986$		0			0
$987$	2.45915			0.0782755
$988$		0			0
$989$	−3.49334	−	3.49334i	−0.111082	−	0.111082i
$990$		0			0
$991$			28.8183i			0.915444i	0.889095	+	0.457722i	$0.151334\pi$
$991$			28.8183i			0.915444i	−0.889095	+	0.457722i	$0.848666\pi$
$992$		0			0
$993$	−0.751395	+	0.751395i	−0.0238448	+	0.0238448i
$994$		0			0
$995$	3.32815	+	3.46903i	0.105509	+	0.109975i
$996$		0			0
$997$			30.7058i			0.972463i	0.873830	+	0.486232i	$0.161629\pi$
$997$			30.7058i			0.972463i	−0.873830	+	0.486232i	$0.838371\pi$
$998$		0			0
$999$		−	10.0194i		−	0.316998i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.i.1567.5		16
4.3	odd	2		1920.2.y.j.1567.5		16
5.3	odd	4		1920.2.bc.i.1183.1		16
8.3	odd	2		960.2.y.e.847.4		16
8.5	even	2		240.2.y.e.187.7	yes	16
16.3	odd	4		1920.2.bc.i.607.1		16
16.5	even	4		960.2.bc.e.367.8		16
16.11	odd	4		240.2.bc.e.67.5	yes	16
16.13	even	4		1920.2.bc.j.607.1		16
20.3	even	4		1920.2.bc.j.1183.1		16
24.5	odd	2		720.2.z.f.667.2		16
40.3	even	4		960.2.bc.e.463.8		16
40.13	odd	4		240.2.bc.e.43.5	yes	16
48.11	even	4		720.2.bd.f.307.4		16
80.3	even	4	inner	1920.2.y.i.223.5		16
80.13	odd	4		1920.2.y.j.223.5		16
80.43	even	4		240.2.y.e.163.7	✓	16
80.53	odd	4		960.2.y.e.943.4		16
120.53	even	4		720.2.bd.f.523.4		16
240.203	odd	4		720.2.z.f.163.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.7	✓	16	80.43	even	4
240.2.y.e.187.7	yes	16	8.5	even	2
240.2.bc.e.43.5	yes	16	40.13	odd	4
240.2.bc.e.67.5	yes	16	16.11	odd	4
720.2.z.f.163.2		16	240.203	odd	4
720.2.z.f.667.2		16	24.5	odd	2
720.2.bd.f.307.4		16	48.11	even	4
720.2.bd.f.523.4		16	120.53	even	4
960.2.y.e.847.4		16	8.3	odd	2
960.2.y.e.943.4		16	80.53	odd	4
960.2.bc.e.367.8		16	16.5	even	4
960.2.bc.e.463.8		16	40.3	even	4
1920.2.y.i.223.5		16	80.3	even	4	inner
1920.2.y.i.1567.5		16	1.1	even	1	trivial
1920.2.y.j.223.5		16	80.13	odd	4
1920.2.y.j.1567.5		16	4.3	odd	2
1920.2.bc.i.607.1		16	16.3	odd	4
1920.2.bc.i.1183.1		16	5.3	odd	4
1920.2.bc.j.607.1		16	16.13	even	4
1920.2.bc.j.1183.1		16	20.3	even	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1920.2.y.i.1567.5

Level	$1920$
Weight	$2$
Character	1920.1567
Analytic conductor	$15.331$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$