LMFDB - Embedded newform 1134.2.g.m.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1134 = 2 \cdot 3^{4} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1134.g (of order $3$ , 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3$ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.m.487.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.59097 - 2.75564i) q^{5} +(1.85185 - 1.88962i) q^{7} -1.00000 q^{8} +(-1.59097 - 2.75564i) q^{10} +(-1.59097 - 2.75564i) q^{11} -5.70370 q^{13} +(-0.710533 - 2.54856i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.760877 - 1.31788i) q^{17} +(-0.641315 + 1.11079i) q^{19} -3.18194 q^{20} -3.18194 q^{22} +(-1.11956 + 1.93914i) q^{23} +(-2.56238 - 4.43818i) q^{25} +(-2.85185 + 4.93955i) q^{26} +(-2.56238 - 0.658939i) q^{28} +7.08126 q^{29} +(4.71053 + 8.15888i) q^{31} +(0.500000 + 0.866025i) q^{32} -1.52175 q^{34} +(-2.26088 - 8.10936i) q^{35} +(0.500000 - 0.866025i) q^{37} +(0.641315 + 1.11079i) q^{38} +(-1.59097 + 2.75564i) q^{40} +5.60301 q^{41} -6.82846 q^{43} +(-1.59097 + 2.75564i) q^{44} +(1.11956 + 1.93914i) q^{46} +(2.91423 - 5.04759i) q^{47} +(-0.141315 - 6.99857i) q^{49} -5.12476 q^{50} +(2.85185 + 4.93955i) q^{52} +(1.02859 + 1.78157i) q^{53} -10.1248 q^{55} +(-1.85185 + 1.88962i) q^{56} +(3.54063 - 6.13255i) q^{58} +(0.562382 + 0.974074i) q^{59} +(-1.56238 + 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(-9.07442 + 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} +(-0.760877 + 1.31788i) q^{68} +(-8.15335 - 2.09671i) q^{70} +8.69002 q^{71} +(-2.48345 - 4.30146i) q^{73} +(-0.500000 - 0.866025i) q^{74} +1.28263 q^{76} +(-8.15335 - 2.09671i) q^{77} +(2.06922 - 3.58399i) q^{79} +(1.59097 + 2.75564i) q^{80} +(2.80150 - 4.85235i) q^{82} +8.06758 q^{83} -4.84213 q^{85} +(-3.41423 + 5.91362i) q^{86} +(1.59097 + 2.75564i) q^{88} +(0.112725 - 0.195246i) q^{89} +(-10.5624 + 10.7778i) q^{91} +2.23912 q^{92} +(-2.91423 - 5.04759i) q^{94} +(2.04063 + 3.53447i) q^{95} -14.8421 q^{97} +(-6.13160 - 3.37690i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 3 q^{2} - 3 q^{4} + q^{5} + 2 q^{7} - 6 q^{8} - q^{10} - q^{11} - 16 q^{13} + 4 q^{14} - 3 q^{16} - 4 q^{17} - 3 q^{19} - 2 q^{20} - 2 q^{22} - 7 q^{23} + 2 q^{25} - 8 q^{26} + 2 q^{28} + 10 q^{29}+ \cdots - 12 q^{98}+O(q^{100})$ 6 * q + 3 * q^2 - 3 * q^4 + q^5 + 2 * q^7 - 6 * q^8 - q^10 - q^11 - 16 * q^13 + 4 * q^14 - 3 * q^16 - 4 * q^17 - 3 * q^19 - 2 * q^20 - 2 * q^22 - 7 * q^23 + 2 * q^25 - 8 * q^26 + 2 * q^28 + 10 * q^29 + 20 * q^31 + 3 * q^32 - 8 * q^34 - 13 * q^35 + 3 * q^37 + 3 * q^38 - q^40 + 12 * q^43 - q^44 + 7 * q^46 - 9 * q^47 + 4 * q^50 + 8 * q^52 + 15 * q^53 - 26 * q^55 - 2 * q^56 + 5 * q^58 - 14 * q^59 + 8 * q^61 + 40 * q^62 + 6 * q^64 - 12 * q^65 + q^67 - 4 * q^68 - 23 * q^70 + 14 * q^71 + 19 * q^73 - 3 * q^74 + 6 * q^76 - 23 * q^77 + 5 * q^79 + q^80 - 4 * q^83 + 4 * q^85 + 6 * q^86 + q^88 - 9 * q^89 - 46 * q^91 + 14 * q^92 + 9 * q^94 - 4 * q^95 - 56 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$ .

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	−0.252788	−	0.967522i	$-0.581348\pi$
$5$	1.59097	−	2.75564i	0.711504	−	1.23236i	0.964292	−	0.264840i	$-0.0853191\pi$
$6$		0			0
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.59097	−	2.75564i	−0.503109	−	0.871411i
$11$	−1.59097	−	2.75564i	−0.479696	−	0.830858i	0.520033	−	0.854146i	$-0.325920\pi$
$11$	−1.59097	−	2.75564i	−0.479696	−	0.830858i	−0.999729	+	0.0232884i	$0.992586\pi$
$12$		0			0
$13$	−5.70370			−1.58192			−0.790960	−	0.611867i	$-0.790419\pi$
$13$	−5.70370			−1.58192			−0.790960	+	0.611867i	$0.790419\pi$
$14$	−0.710533	−	2.54856i	−0.189898	−	0.681130i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	0.758882	−	0.651229i	$-0.225746\pi$
$17$	−0.760877	−	1.31788i	−0.184540	−	0.319632i	−0.943421	+	0.331596i	$0.892413\pi$
$18$		0			0
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	−0.930165	−	0.367142i	$-0.880336\pi$
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	0.783037	+	0.621975i	$0.213670\pi$
$20$	−3.18194			−0.711504
$21$		0			0
$22$	−3.18194			−0.678393
$23$	−1.11956	+	1.93914i	−0.233445	+	0.404338i	−0.958820	−	0.284016i	$-0.908333\pi$
$23$	−1.11956	+	1.93914i	−0.233445	+	0.404338i	0.725375	+	0.688354i	$0.241666\pi$
$24$		0			0
$25$	−2.56238	−	4.43818i	−0.512476	−	0.887635i
$26$	−2.85185	+	4.93955i	−0.559293	+	0.968725i
$27$		0			0
$28$	−2.56238	−	0.658939i	−0.484245	−	0.124528i
$29$	7.08126			1.31496			0.657478	−	0.753474i	$-0.271623\pi$
$29$	7.08126			1.31496			0.657478	+	0.753474i	$0.271623\pi$
$30$		0			0
$31$	4.71053	+	8.15888i	0.846037	+	1.46538i	0.884718	+	0.466127i	$0.154351\pi$
$31$	4.71053	+	8.15888i	0.846037	+	1.46538i	−0.0386810	+	0.999252i	$0.512316\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.52175			−0.260979
$35$	−2.26088	−	8.10936i	−0.382158	−	1.37073i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	0.641315	+	1.11079i	0.104035	+	0.180194i
$39$		0			0
$40$	−1.59097	+	2.75564i	−0.251555	+	0.435706i
$41$	5.60301			0.875043			0.437522	−	0.899208i	$-0.355856\pi$
$41$	5.60301			0.875043			0.437522	+	0.899208i	$0.355856\pi$
$42$		0			0
$43$	−6.82846			−1.04133			−0.520665	−	0.853761i	$-0.674316\pi$
$43$	−6.82846			−1.04133			−0.520665	+	0.853761i	$0.674316\pi$
$44$	−1.59097	+	2.75564i	−0.239848	+	0.415429i
$45$		0			0
$46$	1.11956	+	1.93914i	0.165070	+	0.285910i
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	−0.571344	−	0.820711i	$-0.693578\pi$
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	0.996428	+	0.0844432i	$0.0269112\pi$
$48$		0			0
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$	−5.12476			−0.724751
$51$		0			0
$52$	2.85185	+	4.93955i	0.395480	+	0.684992i
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	0.927982	−	0.372626i	$-0.121542\pi$
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	−0.786694	+	0.617343i	$0.788209\pi$
$54$		0			0
$55$	−10.1248			−1.36522
$56$	−1.85185	+	1.88962i	−0.247464	+	0.252511i
$57$		0			0
$58$	3.54063	−	6.13255i	0.464907	−	0.805243i
$59$	0.562382	+	0.974074i	0.0732159	+	0.126814i	0.900309	−	0.435251i	$-0.143340\pi$
$59$	0.562382	+	0.974074i	0.0732159	+	0.126814i	−0.827093	+	0.562065i	$0.810007\pi$
$60$		0			0
$61$	−1.56238	+	2.70612i	−0.200042	+	0.346484i	−0.948542	−	0.316652i	$-0.897441\pi$
$61$	−1.56238	+	2.70612i	−0.200042	+	0.346484i	0.748499	+	0.663135i	$0.230775\pi$
$62$	9.42107			1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	−9.07442	+	15.7174i	−1.12554	+	1.94950i
$66$		0			0
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	−0.977929	−	0.208938i	$-0.932999\pi$
$67$	−5.48345	−	9.49761i	−0.669910	−	1.16032i	0.308019	−	0.951380i	$-0.400334\pi$
$68$	−0.760877	+	1.31788i	−0.0922699	+	0.159816i
$69$		0			0
$70$	−8.15335	−	2.09671i	−0.974512	−	0.250604i
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$		0			0
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	0.683302	−	0.730136i	$-0.260543\pi$
$73$	−2.48345	−	4.30146i	−0.290666	−	0.503448i	−0.973967	+	0.226689i	$0.927210\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	1.28263			0.147128
$77$	−8.15335	−	2.09671i	−0.929161	−	0.238942i
$78$		0			0
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	−0.725827	−	0.687877i	$-0.758543\pi$
$79$	2.06922	−	3.58399i	0.232805	−	0.403231i	0.958633	+	0.284646i	$0.0918762\pi$
$80$	1.59097	+	2.75564i	0.177876	+	0.308090i
$81$		0			0
$82$	2.80150	−	4.85235i	0.309374	−	0.535852i
$83$	8.06758			0.885532			0.442766	−	0.896637i	$-0.353997\pi$
$83$	8.06758			0.885532			0.442766	+	0.896637i	$0.353997\pi$
$84$		0			0
$85$	−4.84213			−0.525203
$86$	−3.41423	+	5.91362i	−0.368166	+	0.637682i
$87$		0			0
$88$	1.59097	+	2.75564i	0.169598	+	0.293753i
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	−0.859989	−	0.510312i	$-0.829530\pi$
$89$	0.112725	−	0.195246i	0.0119488	−	0.0206960i	0.871938	+	0.489616i	$0.162863\pi$
$90$		0			0
$91$	−10.5624	+	10.7778i	−1.10724	+	1.12982i
$92$	2.23912			0.233445
$93$		0			0
$94$	−2.91423	−	5.04759i	−0.300580	−	0.520620i
$95$	2.04063	+	3.53447i	0.209364	+	0.362629i
$96$		0			0
$97$	−14.8421			−1.50699			−0.753495	−	0.657453i	$-0.771634\pi$
$97$	−14.8421			−1.50699			−0.753495	+	0.657453i	$0.771634\pi$
$98$	−6.13160	−	3.37690i	−0.619385	−	0.341119i
$99$		0			0
$100$	−2.56238	+	4.43818i	−0.256238	+	0.443818i
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.791796	−	0.610786i	$-0.790854\pi$
$101$	−9.29467	−	16.0988i	−0.924854	−	1.60189i	−0.133058	−	0.991108i	$-0.542480\pi$
$102$		0			0
$103$	0.141315	−	0.244765i	0.0139242	−	0.0241174i	−0.858979	−	0.512010i	$-0.828901\pi$
$103$	0.141315	−	0.244765i	0.0139242	−	0.0241174i	0.872904	+	0.487893i	$0.162234\pi$
$104$	5.70370			0.559293
$105$		0			0
$106$	2.05718			0.199811
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	−0.448322	−	0.893872i	$-0.647978\pi$
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	0.998277	−	0.0586780i	$-0.0186885\pi$
$108$		0			0
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$	−5.06238	+	8.76830i	−0.482679	+	0.836025i
$111$		0			0
$112$	0.710533	+	2.54856i	0.0671391	+	0.240816i
$113$	3.21505			0.302446			0.151223	−	0.988500i	$-0.451679\pi$
$113$	3.21505			0.302446			0.151223	+	0.988500i	$0.451679\pi$
$114$		0			0
$115$	3.56238	+	6.17023i	0.332194	+	0.575377i
$116$	−3.54063	−	6.13255i	−0.328739	−	0.569393i
$117$		0			0
$118$	1.12476			0.103543
$119$	−3.89931	−	1.00274i	−0.357449	−	0.0919212i
$120$		0			0
$121$	0.437618	−	0.757977i	0.0397835	−	0.0689070i
$122$	1.56238	+	2.70612i	0.141451	+	0.245001i
$123$		0			0
$124$	4.71053	−	8.15888i	0.423018	−	0.732689i
$125$	−0.396990			−0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	9.07442	+	15.7174i	0.795879	+	1.37850i
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	−0.970890	−	0.239528i	$-0.923007\pi$
$131$	−3.18194	+	5.51129i	−0.278008	+	0.481523i	0.692882	+	0.721051i	$0.256341\pi$
$132$		0			0
$133$	0.911351	+	3.26886i	0.0790242	+	0.283446i
$134$	−10.9669			−0.947396
$135$		0			0
$136$	0.760877	+	1.31788i	0.0652446	+	0.113007i
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	0.801512	−	0.597979i	$-0.204029\pi$
$137$	−1.37072	−	2.37416i	−0.117109	−	0.202838i	−0.918621	+	0.395140i	$0.870696\pi$
$138$		0			0
$139$	7.96690			0.675743			0.337872	−	0.941192i	$-0.390293\pi$
$139$	7.96690			0.675743			0.337872	+	0.941192i	$0.390293\pi$
$140$	−5.89248	+	6.01266i	−0.498005	+	0.508162i
$141$		0			0
$142$	4.34501	−	7.52578i	0.364625	−	0.631550i
$143$	9.07442	+	15.7174i	0.758841	+	1.31435i
$144$		0			0
$145$	11.2661	−	19.5134i	0.935597	−	1.62050i
$146$	−4.96690			−0.411063
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.213360	−	0.976974i	$-0.431559\pi$
$149$	11.6300	−	20.1437i	0.952764	−	1.65024i	0.739404	−	0.673262i	$-0.235107\pi$
$150$		0			0
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	0.982628	−	0.185586i	$-0.0594183\pi$
$151$	4.06238	+	7.03625i	0.330592	+	0.572602i	−0.652036	+	0.758188i	$0.726085\pi$
$152$	0.641315	−	1.11079i	0.0520175	−	0.0900970i
$153$		0			0
$154$	−5.89248	+	6.01266i	−0.474829	+	0.484514i
$155$	29.9773			2.40783
$156$		0			0
$157$	5.63160	+	9.75422i	0.449451	+	0.778471i	0.998350	−	0.0574170i	$-0.0182864\pi$
$157$	5.63160	+	9.75422i	0.449451	+	0.778471i	−0.548900	+	0.835888i	$0.684953\pi$
$158$	−2.06922	−	3.58399i	−0.164618	−	0.285127i
$159$		0			0
$160$	3.18194			0.251555
$161$	1.59097	+	5.70653i	0.125386	+	0.449738i
$162$		0			0
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	−0.933383	−	0.358881i	$-0.883158\pi$
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	0.777492	+	0.628893i	$0.216492\pi$
$164$	−2.80150	−	4.85235i	−0.218761	−	0.378905i
$165$		0			0
$166$	4.03379	−	6.98673i	0.313083	−	0.542276i
$167$	−5.23912			−0.405416			−0.202708	−	0.979239i	$-0.564974\pi$
$167$	−5.23912			−0.405416			−0.202708	+	0.979239i	$0.564974\pi$
$168$		0			0
$169$	19.5322			1.50247
$170$	−2.42107	+	4.19341i	−0.185687	+	0.321620i
$171$		0			0
$172$	3.41423	+	5.91362i	0.260333	+	0.450909i
$173$	−1.27579	+	2.20974i	−0.0969968	+	0.168003i	−0.910440	−	0.413641i	$-0.864257\pi$
$173$	−1.27579	+	2.20974i	−0.0969968	+	0.168003i	0.813443	+	0.581644i	$0.197590\pi$
$174$		0			0
$175$	−13.1316	−	3.37690i	−0.992656	−	0.255270i
$176$	3.18194			0.239848
$177$		0			0
$178$	−0.112725	−	0.195246i	−0.00844910	−	0.0146343i
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	0.967041	−	0.254620i	$-0.0819504\pi$
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	−0.704028	+	0.710172i	$0.748617\pi$
$180$		0			0
$181$	−12.9669			−0.963822			−0.481911	−	0.876220i	$-0.660057\pi$
$181$	−12.9669			−0.963822			−0.481911	+	0.876220i	$0.660057\pi$
$182$	4.05267	+	14.5362i	0.300404	+	1.07749i
$183$		0			0
$184$	1.11956	−	1.93914i	0.0825352	−	0.142955i
$185$	−1.59097	−	2.75564i	−0.116971	−	0.202599i
$186$		0			0
$187$	−2.42107	+	4.19341i	−0.177046	+	0.306653i
$188$	−5.82846			−0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	−0.990285	+	1.71522i	−0.0716545	+	0.124109i	−0.899627	−	0.436660i	$-0.856161\pi$
$191$	−0.990285	+	1.71522i	−0.0716545	+	0.124109i	0.827972	+	0.560769i	$0.189495\pi$
$192$		0			0
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	0.936160	−	0.351574i	$-0.114353\pi$
$193$	2.27292	+	3.93680i	0.163608	+	0.283377i	−0.772552	+	0.634951i	$0.781020\pi$
$194$	−7.42107	+	12.8537i	−0.532802	+	0.922839i
$195$		0			0
$196$	−5.99028	+	3.62167i	−0.427877	+	0.258691i
$197$	−21.8148			−1.55424			−0.777120	−	0.629353i	$-0.783320\pi$
$197$	−21.8148			−1.55424			−0.777120	+	0.629353i	$0.783320\pi$
$198$		0			0
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	0.997324	−	0.0731106i	$-0.0232926\pi$
$199$	6.14132	+	10.6371i	0.435346	+	0.754042i	−0.561978	+	0.827152i	$0.689959\pi$
$200$	2.56238	+	4.43818i	0.181188	+	0.313826i
$201$		0			0
$202$	−18.5893			−1.30794
$203$	13.1134	−	13.3809i	0.920381	−	0.939153i
$204$		0			0
$205$	8.91423	−	15.4399i	0.622597	−	1.07837i
$206$	−0.141315	−	0.244765i	−0.00984589	−	0.0170536i
$207$		0			0
$208$	2.85185	−	4.93955i	0.197740	−	0.342496i
$209$	4.08126			0.282306
$210$		0			0
$211$	16.6569			1.14671			0.573355	−	0.819307i	$-0.305642\pi$
$211$	16.6569			1.14671			0.573355	+	0.819307i	$0.305642\pi$
$212$	1.02859	−	1.78157i	0.0706438	−	0.122359i
$213$		0			0
$214$	−5.68878	−	9.85326i	−0.388877	−	0.673555i
$215$	−10.8639	+	18.8168i	−0.740911	+	1.28330i
$216$		0			0
$217$	24.1404	+	6.20790i	1.63876	+	0.421420i
$218$	−4.42107			−0.299432
$219$		0			0
$220$	5.06238	+	8.76830i	0.341306	+	0.591159i
$221$	4.33981	+	7.51677i	0.291927	+	0.505633i
$222$		0			0
$223$	10.6569			0.713640			0.356820	−	0.934173i	$-0.383861\pi$
$223$	10.6569			0.713640			0.356820	+	0.934173i	$0.383861\pi$
$224$	2.56238	+	0.658939i	0.171206	+	0.0440272i
$225$		0			0
$226$	1.60752	−	2.78431i	0.106931	−	0.185210i
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	0.999774	−	0.0212688i	$-0.00677059\pi$
$227$	7.25404	+	12.5644i	0.481468	+	0.833926i	−0.518306	+	0.855195i	$0.673437\pi$
$228$		0			0
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	−0.984180	−	0.177173i	$-0.943305\pi$
$229$	−5.12476	+	8.87635i	−0.338654	+	0.586566i	0.645526	+	0.763738i	$0.276638\pi$
$230$	7.12476			0.469793
$231$		0			0
$232$	−7.08126			−0.464907
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	−0.847773	−	0.530359i	$-0.822057\pi$
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	0.883191	+	0.469014i	$0.155390\pi$
$234$		0			0
$235$	−9.27292	−	16.0612i	−0.604898	−	1.04771i
$236$	0.562382	−	0.974074i	0.0366079	−	0.0634068i
$237$		0			0
$238$	−2.81806	+	2.87553i	−0.182667	+	0.186393i
$239$	12.3204			0.796939			0.398470	−	0.917182i	$-0.369541\pi$
$239$	12.3204			0.796939			0.398470	+	0.917182i	$0.369541\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	−0.437618	−	0.757977i	−0.0281312	−	0.0487246i
$243$		0			0
$244$	3.12476			0.200042
$245$	−19.5104	−	10.7451i	−1.24647	−	0.686480i
$246$		0			0
$247$	3.65787	−	6.33561i	0.232744	−	0.403125i
$248$	−4.71053	−	8.15888i	−0.299119	−	0.518090i
$249$		0			0
$250$	−0.198495	+	0.343803i	−0.0125539	+	0.0217440i
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$	10.0527	−	17.4117i	0.630760	−	1.09251i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	−0.960403	−	0.278614i	$-0.910125\pi$
$257$	−3.83009	+	6.63392i	−0.238915	+	0.413813i	0.721488	+	0.692427i	$0.243458\pi$
$258$		0			0
$259$	−0.710533	−	2.54856i	−0.0441504	−	0.158360i
$260$	18.1488			1.12554
$261$		0			0
$262$	3.18194	+	5.51129i	0.196581	+	0.340488i
$263$	1.54746	+	2.68029i	0.0954208	+	0.165274i	0.909784	−	0.415082i	$-0.136247\pi$
$263$	1.54746	+	2.68029i	0.0954208	+	0.165274i	−0.814363	+	0.580355i	$0.802914\pi$
$264$		0			0
$265$	6.54583			0.402107
$266$	3.28659	+	0.845174i	0.201514	+	0.0518210i
$267$		0			0
$268$	−5.48345	+	9.49761i	−0.334955	+	0.580159i
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	−0.905855	−	0.423587i	$-0.860771\pi$
$269$	−13.4451	−	23.2877i	−0.819765	−	1.41987i	0.0860906	−	0.996287i	$-0.472563\pi$
$270$		0			0
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	0.301759	+	0.953384i	$0.402426\pi$
$271$	−11.1082	+	19.2400i	−0.674776	+	1.16875i	−0.976534	+	0.215362i	$0.930907\pi$
$272$	1.52175			0.0922699
$273$		0			0
$274$	−2.74145			−0.165617
$275$	−8.15335	+	14.1220i	−0.491666	+	0.851590i
$276$		0			0
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	0.997669	−	0.0682357i	$-0.0217370\pi$
$277$	7.31875	+	12.6764i	0.439741	+	0.761653i	−0.557928	+	0.829889i	$0.688404\pi$
$278$	3.98345	−	6.89953i	0.238911	−	0.413807i
$279$		0			0
$280$	2.26088	+	8.10936i	0.135113	+	0.484627i
$281$	−23.3984			−1.39583			−0.697915	−	0.716181i	$-0.745889\pi$
$281$	−23.3984			−1.39583			−0.697915	+	0.716181i	$0.745889\pi$
$282$		0			0
$283$	13.0624	+	22.6247i	0.776478	+	1.34490i	0.933960	+	0.357377i	$0.116329\pi$
$283$	13.0624	+	22.6247i	0.776478	+	1.34490i	−0.157482	+	0.987522i	$0.550338\pi$
$284$	−4.34501	−	7.52578i	−0.257829	−	0.446573i
$285$		0			0
$286$	18.1488			1.07316
$287$	10.3759	−	10.5876i	0.612471	−	0.624963i
$288$		0			0
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$	−11.2661	−	19.5134i	−0.661567	−	1.14587i
$291$		0			0
$292$	−2.48345	+	4.30146i	−0.145333	+	0.251724i
$293$	−25.8629			−1.51093			−0.755465	−	0.655190i	$-0.772589\pi$
$293$	−25.8629			−1.51093			−0.755465	+	0.655190i	$0.772589\pi$
$294$		0			0
$295$	3.57893			0.208374
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$		0			0
$298$	−11.6300	−	20.1437i	−0.673706	−	1.16689i
$299$	6.38564	−	11.0603i	0.369291	−	0.639631i
$300$		0			0
$301$	−12.6453	+	12.9032i	−0.728861	+	0.743727i
$302$	8.12476			0.467528
$303$		0			0
$304$	−0.641315	−	1.11079i	−0.0367819	−	0.0637082i
$305$	4.97141	+	8.61073i	0.284662	+	0.493049i
$306$		0			0
$307$	3.53216			0.201591			0.100795	−	0.994907i	$-0.467861\pi$
$307$	3.53216			0.201591			0.100795	+	0.994907i	$0.467861\pi$
$308$	2.26088	+	8.10936i	0.128825	+	0.462074i
$309$		0			0
$310$	14.9887	−	25.9611i	0.851298	−	1.47449i
$311$	−0.851848	−	1.47544i	−0.0483039	−	0.0836648i	0.840863	−	0.541249i	$-0.182048\pi$
$311$	−0.851848	−	1.47544i	−0.0483039	−	0.0836648i	−0.889166	+	0.457584i	$0.848715\pi$
$312$		0			0
$313$	1.42107	−	2.46136i	0.0803234	−	0.139124i	−0.823065	−	0.567947i	$-0.807738\pi$
$313$	1.42107	−	2.46136i	0.0803234	−	0.139124i	0.903389	+	0.428822i	$0.141071\pi$
$314$	11.2632			0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	12.4601	−	21.5815i	0.699827	−	1.21214i	−0.268700	−	0.963224i	$-0.586594\pi$
$317$	12.4601	−	21.5815i	0.699827	−	1.21214i	0.968526	−	0.248911i	$-0.0800728\pi$
$318$		0			0
$319$	−11.2661	−	19.5134i	−0.630779	−	1.09254i
$320$	1.59097	−	2.75564i	0.0889380	−	0.154045i
$321$		0			0
$322$	5.73749	+	1.47544i	0.319738	+	0.0822233i
$323$	1.95185			0.108604
$324$		0			0
$325$	14.6150	+	25.3140i	0.810697	+	1.40417i
$326$	1.99028	+	3.44727i	0.110232	+	0.190927i
$327$		0			0
$328$	−5.60301			−0.309374
$329$	−4.14132	−	14.8542i	−0.228318	−	0.818936i
$330$		0			0
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	−0.750492	−	0.660879i	$-0.770184\pi$
$331$	3.58577	−	6.21074i	0.197092	−	0.341373i	0.947584	+	0.319506i	$0.103517\pi$
$332$	−4.03379	−	6.98673i	−0.221383	−	0.383447i
$333$		0			0
$334$	−2.61956	+	4.53721i	−0.143336	+	0.248265i
$335$	−34.8960			−1.90657
$336$		0			0
$337$	21.8421			1.18982			0.594908	−	0.803793i	$-0.297188\pi$
$337$	21.8421			1.18982			0.594908	+	0.803793i	$0.297188\pi$
$338$	9.76608	−	16.9153i	0.531205	−	0.920073i
$339$		0			0
$340$	2.42107	+	4.19341i	0.131301	+	0.227420i
$341$	14.9887	−	25.9611i	0.811681	−	1.40587i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$	6.82846			0.368166
$345$		0			0
$346$	1.27579	+	2.20974i	0.0685871	+	0.118796i
$347$	1.05555	+	1.82826i	0.0566646	+	0.0981460i	0.892966	−	0.450124i	$-0.148620\pi$
$347$	1.05555	+	1.82826i	0.0566646	+	0.0981460i	−0.836302	+	0.548270i	$0.815287\pi$
$348$		0			0
$349$	−36.2164			−1.93862			−0.969310	−	0.245840i	$-0.920936\pi$
$349$	−36.2164			−1.93862			−0.969310	+	0.245840i	$0.920936\pi$
$350$	−9.49028	+	9.68385i	−0.507277	+	0.517623i
$351$		0			0
$352$	1.59097	−	2.75564i	0.0847991	−	0.146876i
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	0.971168	−	0.238396i	$-0.0766215\pi$
$353$	5.24433	+	9.08344i	0.279127	+	0.483463i	−0.692041	+	0.721858i	$0.743288\pi$
$354$		0			0
$355$	13.8256	−	23.9466i	0.733786	−	1.27095i
$356$	−0.225450			−0.0119488
$357$		0			0
$358$	7.03775			0.371957
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	−0.0195047	−	0.999810i	$-0.506209\pi$
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	0.875613	−	0.483013i	$-0.160458\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$	−6.48345	+	11.2297i	−0.340762	+	0.590218i
$363$		0			0
$364$	14.6150	+	3.75839i	0.766037	+	0.196993i
$365$	−15.8044			−0.827239
$366$		0			0
$367$	9.05555	+	15.6847i	0.472696	+	0.818733i	0.999512	−	0.0312465i	$-0.00994768\pi$
$367$	9.05555	+	15.6847i	0.472696	+	0.818733i	−0.526816	+	0.849979i	$0.676614\pi$
$368$	−1.11956	−	1.93914i	−0.0583612	−	0.101085i
$369$		0			0
$370$	−3.18194			−0.165421
$371$	5.27128	+	1.35556i	0.273671	+	0.0703769i
$372$		0			0
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	−0.674480	−	0.738293i	$-0.735632\pi$
$373$	5.83530	−	10.1070i	0.302140	−	0.523322i	0.976621	+	0.214971i	$0.0689656\pi$
$374$	2.42107	+	4.19341i	0.125190	+	0.216836i
$375$		0			0
$376$	−2.91423	+	5.04759i	−0.150290	+	0.260310i
$377$	−40.3893			−2.08016
$378$		0			0
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	2.04063	−	3.53447i	0.104682	−	0.181315i
$381$		0			0
$382$	0.990285	+	1.71522i	0.0506674	+	0.0877585i
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	−0.844181	−	0.536059i	$-0.819913\pi$
$383$	0.824893	−	1.42876i	0.0421501	−	0.0730061i	0.886331	+	0.463053i	$0.153246\pi$
$384$		0			0
$385$	−18.7495	+	19.1319i	−0.955564	+	0.975054i
$386$	4.54583			0.231377
$387$		0			0
$388$	7.42107	+	12.8537i	0.376748	+	0.652546i
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	0.910794	+	0.412862i	$0.135471\pi$
$389$	16.0338	+	27.7713i	0.812946	+	1.40806i	−0.0978483	+	0.995201i	$0.531196\pi$
$390$		0			0
$391$	3.40739			0.172319
$392$	0.141315	+	6.99857i	0.00713749	+	0.353481i
$393$		0			0
$394$	−10.9074	+	18.8922i	−0.549507	+	0.951773i
$395$	−6.58414	−	11.4041i	−0.331284	−	0.573800i
$396$		0			0
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.210660	+	0.977559i	$0.567561\pi$
$397$	−18.9669	+	32.8516i	−0.951921	+	1.64878i	−0.741261	+	0.671217i	$0.765772\pi$
$398$	12.2826			0.615673
$399$		0			0
$400$	5.12476			0.256238
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	−0.967602	−	0.252479i	$-0.918754\pi$
$401$	−5.30959	+	9.19647i	−0.265148	+	0.459250i	0.702454	+	0.711729i	$0.252087\pi$
$402$		0			0
$403$	−26.8675	−	46.5358i	−1.33836	−	2.31811i
$404$	−9.29467	+	16.0988i	−0.462427	+	0.800947i
$405$		0			0
$406$	−5.03147	−	18.0470i	−0.249708	−	0.895657i
$407$	−3.18194			−0.157723
$408$		0			0
$409$	−2.77292	−	4.80283i	−0.137112	−	0.237485i	0.789290	−	0.614020i	$-0.210449\pi$
$409$	−2.77292	−	4.80283i	−0.137112	−	0.237485i	−0.926402	+	0.376535i	$0.877115\pi$
$410$	−8.91423	−	15.4399i	−0.440242	−	0.762522i
$411$		0			0
$412$	−0.282630			−0.0139242
$413$	2.88207	+	0.741150i	0.141818	+	0.0364696i
$414$		0			0
$415$	12.8353	−	22.2314i	0.630060	−	1.09130i
$416$	−2.85185	−	4.93955i	−0.139823	−	0.242181i
$417$		0			0
$418$	2.04063	−	3.53447i	0.0998104	−	0.172877i
$419$	−5.54910			−0.271091			−0.135546	−	0.990771i	$-0.543279\pi$
$419$	−5.54910			−0.271091			−0.135546	+	0.990771i	$0.543279\pi$
$420$		0			0
$421$	6.84213			0.333465			0.166733	−	0.986002i	$-0.446678\pi$
$421$	6.84213			0.333465			0.166733	+	0.986002i	$0.446678\pi$
$422$	8.32846	−	14.4253i	0.405423	−	0.702213i
$423$		0			0
$424$	−1.02859	−	1.78157i	−0.0499527	−	0.0865207i
$425$	−3.89931	+	6.75381i	−0.189144	+	0.327608i
$426$		0			0
$427$	2.22025	+	7.96364i	0.107445	+	0.385387i
$428$	−11.3776			−0.549955
$429$		0			0
$430$	10.8639	+	18.8168i	0.523903	+	0.907427i
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	0.921321	+	0.388803i	$0.127111\pi$
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	−0.123947	+	0.992289i	$0.539555\pi$
$432$		0			0
$433$	−12.1111			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$433$	−12.1111			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$434$	17.4464	−	17.8022i	0.837453	−	0.854534i
$435$		0			0
$436$	−2.21053	+	3.82876i	−0.105865	+	0.183364i
$437$	−1.43598	−	2.48720i	−0.0686924	−	0.118979i
$438$		0			0
$439$	4.41711	−	7.65066i	0.210817	−	0.365146i	−0.741153	−	0.671336i	$-0.765721\pi$
$439$	4.41711	−	7.65066i	0.210817	−	0.365146i	0.951970	+	0.306190i	$0.0990542\pi$
$440$	10.1248			0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	−8.75924	+	15.1715i	−0.416164	+	0.720817i	−0.995550	−	0.0942360i	$-0.969959\pi$
$443$	−8.75924	+	15.1715i	−0.416164	+	0.720817i	0.579386	+	0.815053i	$0.303292\pi$
$444$		0			0
$445$	−0.358685	−	0.621261i	−0.0170033	−	0.0294506i
$446$	5.32846	−	9.22916i	0.252310	−	0.437014i
$447$		0			0
$448$	1.85185	−	1.88962i	0.0874916	−	0.0892761i
$449$	31.2301			1.47384			0.736920	−	0.675980i	$-0.236280\pi$
$449$	31.2301			1.47384			0.736920	+	0.675980i	$0.236280\pi$
$450$		0			0
$451$	−8.91423	−	15.4399i	−0.419755	−	0.727036i
$452$	−1.60752	−	2.78431i	−0.0756115	−	0.130963i
$453$		0			0
$454$	14.5081			0.680898
$455$	12.8954	+	46.2534i	0.604544	+	2.16839i
$456$		0			0
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	−0.195794	−	0.980645i	$-0.562728\pi$
$457$	16.0624	−	27.8209i	0.751367	−	1.30140i	0.947161	−	0.320760i	$-0.103938\pi$
$458$	5.12476	+	8.87635i	0.239464	+	0.414765i
$459$		0			0
$460$	3.56238	−	6.17023i	0.166097	−	0.287688i
$461$	−2.46457			−0.114787			−0.0573933	−	0.998352i	$-0.518279\pi$
$461$	−2.46457			−0.114787			−0.0573933	+	0.998352i	$0.518279\pi$
$462$		0			0
$463$	−30.3469			−1.41034			−0.705171	−	0.709037i	$-0.749130\pi$
$463$	−30.3469			−1.41034			−0.705171	+	0.709037i	$0.749130\pi$
$464$	−3.54063	+	6.13255i	−0.164370	+	0.284696i
$465$		0			0
$466$	−0.540628	−	0.936396i	−0.0250441	−	0.0433777i
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	−0.989465	−	0.144774i	$-0.953754\pi$
$467$	−7.98181	+	13.8249i	−0.369354	+	0.639740i	0.620110	+	0.784515i	$0.287088\pi$
$468$		0			0
$469$	−28.1014	−	7.22651i	−1.29760	−	0.333689i
$470$	−18.5458			−0.855455
$471$		0			0
$472$	−0.562382	−	0.974074i	−0.0258857	−	0.0448354i
$473$	10.8639	+	18.8168i	0.499522	+	0.865198i
$474$		0			0
$475$	6.57318			0.301598
$476$	1.08126	+	3.87828i	0.0495593	+	0.177760i
$477$		0			0
$478$	6.16019	−	10.6698i	0.281761	−	0.488024i
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	0.999412	+	0.0342863i	$0.0109158\pi$
$479$	11.5865	+	20.0683i	0.529399	+	0.916946i	−0.470013	+	0.882659i	$0.655751\pi$
$480$		0			0
$481$	−2.85185	+	4.93955i	−0.130033	+	0.225224i
$482$	13.0000			0.592134
$483$		0			0
$484$	−0.875237			−0.0397835
$485$	−23.6134	+	40.8996i	−1.07223	+	1.85716i
$486$		0			0
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	0.902098	−	0.431531i	$-0.142026\pi$
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	−0.824766	+	0.565474i	$0.808693\pi$
$488$	1.56238	−	2.70612i	0.0707257	−	0.122500i
$489$		0			0
$490$	−19.0607	+	11.5239i	−0.861077	+	0.520599i
$491$	19.1683			0.865052			0.432526	−	0.901621i	$-0.357622\pi$
$491$	19.1683			0.865052			0.432526	+	0.901621i	$0.357622\pi$
$492$		0			0
$493$	−5.38796	−	9.33223i	−0.242662	−	0.420302i
$494$	−3.65787	−	6.33561i	−0.164575	−	0.285053i
$495$		0			0
$496$	−9.42107			−0.423018
$497$	16.0926	−	16.4208i	0.721852	−	0.736575i
$498$		0			0
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.124413	+	0.992231i	$0.539705\pi$
$499$	−20.5848	+	35.6540i	−0.921503	+	1.59609i	−0.797090	+	0.603860i	$0.793629\pi$
$500$	0.198495	+	0.343803i	0.00887697	+	0.0153754i
$501$		0			0
$502$	2.55555	−	4.42633i	0.114060	−	0.197557i
$503$	−26.4542			−1.17953			−0.589767	−	0.807574i	$-0.700780\pi$
$503$	−26.4542			−1.17953			−0.589767	+	0.807574i	$0.700780\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$	3.56238	−	6.17023i	0.158367	−	0.274300i
$507$		0			0
$508$	−10.0527	−	17.4117i	−0.446015	−	0.772521i
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	−0.972132	−	0.234436i	$-0.924676\pi$
$509$	−6.38564	+	11.0603i	−0.283039	+	0.490237i	0.689093	+	0.724673i	$0.258009\pi$
$510$		0			0
$511$	−12.7271	−	3.27288i	−0.563013	−	0.144784i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.83009	+	6.63392i	0.168938	+	0.292610i
$515$	−0.449657	−	0.778828i	−0.0198142	−	0.0343193i
$516$		0			0
$517$	−18.5458			−0.815645
$518$	−2.56238	−	0.658939i	−0.112585	−	0.0289521i
$519$		0			0
$520$	9.07442	−	15.7174i	0.397940	−	0.689252i
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	0.781716	−	0.623635i	$-0.214345\pi$
$521$	−3.40615	−	5.89962i	−0.149226	−	0.258467i	−0.930942	+	0.365168i	$0.881012\pi$
$522$		0			0
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	−0.339148	−	0.940733i	$-0.610139\pi$
$523$	14.7535	−	25.5538i	0.645125	−	1.11739i	0.984273	−	0.176656i	$-0.0565280\pi$
$524$	6.36389			0.278008
$525$		0			0
$526$	3.09493			0.134945
$527$	7.16827	−	12.4158i	0.312255	−	0.540841i
$528$		0			0
$529$	8.99316	+	15.5766i	0.391007	+	0.677244i
$530$	3.27292	−	5.66886i	0.142166	−	0.246239i
$531$		0			0
$532$	2.37524	−	2.42368i	0.102980	−	0.105080i
$533$	−31.9579			−1.38425
$534$		0			0
$535$	−18.1014	−	31.3525i	−0.782591	−	1.35549i
$536$	5.48345	+	9.49761i	0.236849	+	0.410234i
$537$		0			0
$538$	−26.8903			−1.15932
$539$	−19.0607	+	11.5239i	−0.821004	+	0.496371i
$540$		0			0
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$	11.1082	+	19.2400i	0.477139	+	0.826428i
$543$		0			0
$544$	0.760877	−	1.31788i	0.0326223	−	0.0565035i
$545$	−14.0676			−0.602589
$546$		0			0
$547$	−35.2301			−1.50633			−0.753165	−	0.657832i	$-0.771474\pi$
$547$	−35.2301			−1.50633			−0.753165	+	0.657832i	$0.771474\pi$
$548$	−1.37072	+	2.37416i	−0.0585544	+	0.101419i
$549$		0			0
$550$	8.15335	+	14.1220i	0.347660	+	0.602165i
$551$	−4.54132	+	7.86579i	−0.193467	+	0.335094i
$552$		0			0
$553$	−2.94050	−	10.5470i	−0.125043	−	0.448506i
$554$	14.6375			0.621887
$555$		0			0
$556$	−3.98345	−	6.89953i	−0.168936	−	0.292605i
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	0.785779	−	0.618507i	$-0.212262\pi$
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	−0.928532	+	0.371252i	$0.878929\pi$
$558$		0			0
$559$	38.9475			1.64730
$560$	8.15335	+	2.09671i	0.344542	+	0.0886020i
$561$		0			0
$562$	−11.6992	+	20.2636i	−0.493500	+	0.854768i
$563$	0.729964	+	1.26433i	0.0307643	+	0.0532853i	0.880998	−	0.473121i	$-0.156873\pi$
$563$	0.729964	+	1.26433i	0.0307643	+	0.0532853i	−0.850233	+	0.526406i	$0.823539\pi$
$564$		0			0
$565$	5.11505	−	8.85952i	0.215192	−	0.372723i
$566$	26.1248			1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	−9.78263	+	16.9440i	−0.410109	+	0.710330i	−0.994901	−	0.100853i	$-0.967843\pi$
$569$	−9.78263	+	16.9440i	−0.410109	+	0.710330i	0.584792	+	0.811183i	$0.301176\pi$
$570$		0			0
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	0.998897	−	0.0469545i	$-0.0149516\pi$
$571$	10.9629	+	18.9884i	0.458785	+	0.794638i	−0.540112	+	0.841593i	$0.681618\pi$
$572$	9.07442	−	15.7174i	0.379421	−	0.657176i
$573$		0			0
$574$	−3.98113	−	14.2796i	−0.166169	−	0.596019i
$575$	11.4750			0.478540
$576$		0			0
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	0.999853	+	0.0171554i	$0.00546099\pi$
$577$	12.3655	+	21.4177i	0.514783	+	0.891631i	−0.485069	+	0.874476i	$0.661206\pi$
$578$	−7.34213	−	12.7169i	−0.305392	−	0.528955i
$579$		0			0
$580$	−22.5322			−0.935597
$581$	14.9399	−	15.2447i	0.619813	−	0.632455i
$582$		0			0
$583$	3.27292	−	5.66886i	0.135550	−	0.234780i
$584$	2.48345	+	4.30146i	0.102766	+	0.177996i
$585$		0			0
$586$	−12.9315	+	22.3980i	−0.534194	+	0.925251i
$587$	36.1592			1.49245			0.746226	−	0.665693i	$-0.231864\pi$
$587$	36.1592			1.49245			0.746226	+	0.665693i	$0.231864\pi$
$588$		0			0
$589$	−12.0837			−0.497902
$590$	1.78947	−	3.09945i	0.0736712	−	0.127602i
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	−0.978406	−	0.206693i	$-0.933730\pi$
$593$	−7.55391	+	13.0838i	−0.310202	+	0.537285i	0.668204	+	0.743978i	$0.267063\pi$
$594$		0			0
$595$	−8.96690	+	9.14978i	−0.367607	+	0.375105i
$596$	−23.2599			−0.952764
$597$		0			0
$598$	−6.38564	−	11.0603i	−0.261128	−	0.452287i
$599$	2.72708	+	4.72345i	0.111426	+	0.192995i	0.916345	−	0.400389i	$-0.131125\pi$
$599$	2.72708	+	4.72345i	0.111426	+	0.192995i	−0.804920	+	0.593384i	$0.797792\pi$
$600$		0			0
$601$	6.73680			0.274800			0.137400	−	0.990516i	$-0.456125\pi$
$601$	6.73680			0.274800			0.137400	+	0.990516i	$0.456125\pi$
$602$	4.85185	+	17.4027i	0.197747	+	0.709282i
$603$		0			0
$604$	4.06238	−	7.03625i	0.165296	−	0.286301i
$605$	−1.39248	−	2.41184i	−0.0566122	−	0.0980553i
$606$		0			0
$607$	−3.33530	+	5.77690i	−0.135376	+	0.234477i	−0.925741	−	0.378159i	$-0.876557\pi$
$607$	−3.33530	+	5.77690i	−0.135376	+	0.234477i	0.790365	+	0.612636i	$0.209891\pi$
$608$	−1.28263			−0.0520175
$609$		0			0
$610$	9.94282			0.402573
$611$	−16.6219	+	28.7899i	−0.672449	+	1.16472i
$612$		0			0
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$	1.76608	−	3.05894i	0.0712731	−	0.123449i
$615$		0			0
$616$	8.15335	+	2.09671i	0.328508	+	0.0844787i
$617$	−34.4966			−1.38878			−0.694390	−	0.719599i	$-0.744326\pi$
$617$	−34.4966			−1.38878			−0.694390	+	0.719599i	$0.744326\pi$
$618$		0			0
$619$	8.22421	+	14.2447i	0.330559	+	0.572545i	0.982622	−	0.185620i	$-0.0594295\pi$
$619$	8.22421	+	14.2447i	0.330559	+	0.572545i	−0.652063	+	0.758165i	$0.726096\pi$
$620$	−14.9887	−	25.9611i	−0.601959	−	1.04262i
$621$		0			0
$622$	−1.70370			−0.0683120
$623$	−0.160190	−	0.574573i	−0.00641787	−	0.0230198i
$624$		0			0
$625$	12.1803	−	21.0969i	0.487212	−	0.843877i
$626$	−1.42107	−	2.46136i	−0.0567972	−	0.0983757i
$627$		0			0
$628$	5.63160	−	9.75422i	0.224725	−	0.389236i
$629$	−1.52175			−0.0606763
$630$		0			0
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	−2.06922	+	3.58399i	−0.0823091	+	0.142564i
$633$		0			0
$634$	−12.4601	−	21.5815i	−0.494852	−	0.857109i
$635$	31.9870	−	55.4031i	1.26937	−	2.19861i
$636$		0			0
$637$	0.806018	+	39.9177i	0.0319356	+	1.58160i
$638$	−22.5322			−0.892057
$639$		0			0
$640$	−1.59097	−	2.75564i	−0.0628887	−	0.108926i
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	−0.998204	−	0.0599014i	$-0.980921\pi$
$641$	−13.9497	−	24.1615i	−0.550978	−	0.954322i	0.447226	−	0.894421i	$-0.352412\pi$
$642$		0			0
$643$	−28.5048			−1.12412			−0.562060	−	0.827096i	$-0.689991\pi$
$643$	−28.5048			−1.12412			−0.562060	+	0.827096i	$0.689991\pi$
$644$	4.14652	−	4.23109i	0.163396	−	0.166728i
$645$		0			0
$646$	0.975923	−	1.69035i	0.0383972	−	0.0665059i
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	0.982224	−	0.187711i	$-0.0601069\pi$
$647$	8.35705	+	14.4748i	0.328550	+	0.569065i	−0.653675	+	0.756776i	$0.726774\pi$
$648$		0			0
$649$	1.78947	−	3.09945i	0.0702427	−	0.121664i
$650$	29.2301			1.14650
$651$		0			0
$652$	3.98057			0.155891
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	0.202614	+	0.979259i	$0.435056\pi$
$653$	−19.0825	+	33.0519i	−0.746756	+	1.29342i	−0.949370	+	0.314161i	$0.898277\pi$
$654$		0			0
$655$	10.1248	+	17.5366i	0.395607	+	0.685212i
$656$	−2.80150	+	4.85235i	−0.109380	+	0.189452i
$657$		0			0
$658$	−14.9347	−	3.84060i	−0.582217	−	0.149722i
$659$	−8.74145			−0.340518			−0.170259	−	0.985399i	$-0.554461\pi$
$659$	−8.74145			−0.340518			−0.170259	+	0.985399i	$0.554461\pi$
$660$		0			0
$661$	10.0419	+	17.3930i	0.390584	+	0.676511i	0.992527	−	0.122028i	$-0.0389399\pi$
$661$	10.0419	+	17.3930i	0.390584	+	0.676511i	−0.601943	+	0.798539i	$0.705607\pi$
$662$	−3.58577	−	6.21074i	−0.139365	−	0.241387i
$663$		0			0
$664$	−8.06758			−0.313083
$665$	10.4577	+	2.68930i	0.405534	+	0.104286i
$666$		0			0
$667$	−7.92790	+	13.7315i	−0.306970	+	0.531687i
$668$	2.61956	+	4.53721i	0.101354	+	0.175550i
$669$		0			0
$670$	−17.4480	+	30.2209i	−0.674076	+	1.16753i
$671$	9.94282			0.383838
$672$		0			0
$673$	34.0528			1.31264			0.656319	−	0.754483i	$-0.272112\pi$
$673$	34.0528			1.31264			0.656319	+	0.754483i	$0.272112\pi$
$674$	10.9211	−	18.9158i	0.420664	−	0.728611i
$675$		0			0
$676$	−9.76608	−	16.9153i	−0.375618	−	0.650590i
$677$	0.358685	−	0.621261i	0.0137854	−	0.0238770i	−0.859050	−	0.511891i	$-0.828945\pi$
$677$	0.358685	−	0.621261i	0.0137854	−	0.0238770i	0.872836	+	0.488014i	$0.162279\pi$
$678$		0			0
$679$	−27.4854	+	28.0460i	−1.05479	+	1.07631i
$680$	4.84213			0.185687
$681$		0			0
$682$	−14.9887	−	25.9611i	−0.573945	−	0.994102i
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	0.591260	−	0.806481i	$-0.298631\pi$
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	−0.994063	+	0.108806i	$0.965297\pi$
$684$		0			0
$685$	−8.72313			−0.333294
$686$	−17.7359	+	5.33287i	−0.677158	+	0.203610i
$687$		0			0
$688$	3.41423	−	5.91362i	0.130166	−	0.225455i
$689$	−5.86677	−	10.1615i	−0.223506	−	0.387124i
$690$		0			0
$691$	−2.92395	+	5.06442i	−0.111232	+	0.192660i	−0.916267	−	0.400567i	$-0.868813\pi$
$691$	−2.92395	+	5.06442i	−0.111232	+	0.192660i	0.805035	+	0.593227i	$0.202146\pi$
$692$	2.55159			0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	12.6751	−	21.9539i	0.480794	−	0.832760i
$696$		0			0
$697$	−4.26320	−	7.38408i	−0.161480	−	0.279692i
$698$	−18.1082	+	31.3643i	−0.685406	+	1.18716i
$699$		0			0
$700$	3.64132	+	13.0608i	0.137629	+	0.493650i
$701$	10.2711			0.387935			0.193967	−	0.981008i	$-0.437864\pi$
$701$	10.2711			0.387935			0.193967	+	0.981008i	$0.437864\pi$
$702$		0			0
$703$	0.641315	+	1.11079i	0.0241877	+	0.0418942i
$704$	−1.59097	−	2.75564i	−0.0599620	−	0.103857i
$705$		0			0
$706$	10.4887			0.394746
$707$	−47.6330	−	12.2492i	−1.79142	−	0.460680i
$708$		0			0
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	0.0916356	+	0.995793i	$0.470790\pi$
$709$	−21.7427	+	37.6594i	−0.816564	+	1.41433i	−0.908200	+	0.418538i	$0.862543\pi$
$710$	−13.8256	−	23.9466i	−0.518865	−	0.898700i
$711$		0			0
$712$	−0.112725	+	0.195246i	−0.00422455	+	0.00731714i
$713$	−21.0949			−0.790011
$714$		0			0
$715$	57.7486			2.15967
$716$	3.51887	−	6.09487i	0.131507	−	0.227776i
$717$		0			0
$718$	−16.2209	−	28.0955i	−0.605360	−	1.04851i
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.200830	−	0.979626i	$-0.435636\pi$
$719$	25.4412	−	44.0654i	0.948796	−	1.64336i	0.747966	−	0.663737i	$-0.231031\pi$
$720$		0			0
$721$	−0.200818	−	0.720299i	−0.00747886	−	0.0268253i
$722$	17.3549			0.645881
$723$		0			0
$724$	6.48345	+	11.2297i	0.240955	+	0.417347i
$725$	−18.1449	−	31.4279i	−0.673884	−	1.16720i
$726$		0			0
$727$	−12.1442			−0.450403			−0.225202	−	0.974312i	$-0.572304\pi$
$727$	−12.1442			−0.450403			−0.225202	+	0.974312i	$0.572304\pi$
$728$	10.5624	−	10.7778i	0.391468	−	0.399452i
$729$		0			0
$730$	−7.90219	+	13.6870i	−0.292473	+	0.506579i
$731$	5.19562	+	8.99907i	0.192167	+	0.332843i
$732$		0			0
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	−0.0261440	−	0.999658i	$-0.508323\pi$
$733$	23.0848	−	39.9841i	0.852657	−	1.47685i	0.878801	−	0.477188i	$-0.158344\pi$
$734$	18.1111			0.668493
$735$		0			0
$736$	−2.23912			−0.0825352
$737$	−17.4480	+	30.2209i	−0.642706	+	1.11320i
$738$		0			0
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	0.816458	−	0.577405i	$-0.195935\pi$
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	−0.908276	+	0.418371i	$0.862601\pi$
$740$	−1.59097	+	2.75564i	−0.0584853	+	0.101299i
$741$		0			0
$742$	3.80959	−	3.88728i	0.139854	−	0.142707i
$743$	31.4120			1.15240			0.576198	−	0.817310i	$-0.304536\pi$
$743$	31.4120			1.15240			0.576198	+	0.817310i	$0.304536\pi$
$744$		0			0
$745$	−37.0059	−	64.0961i	−1.35579	−	2.34830i
$746$	−5.83530	−	10.1070i	−0.213645	−	0.370045i
$747$		0			0
$748$	4.84213			0.177046
$749$	−8.08414	−	28.9964i	−0.295388	−	1.05950i
$750$		0			0
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	−0.894529	−	0.447010i	$-0.852489\pi$
$751$	−1.64815	+	2.85468i	−0.0601419	+	0.104169i	0.834387	+	0.551179i	$0.185822\pi$
$752$	2.91423	+	5.04759i	0.106271	+	0.184067i
$753$		0			0
$754$	−20.1947	+	34.9782i	−0.735447	+	1.27383i
$755$	25.8525			0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	7.13448	−	12.3573i	0.259136	−	0.448837i
$759$		0			0
$760$	−2.04063	−	3.53447i	−0.0740214	−	0.128209i
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	−0.964889	−	0.262659i	$-0.915400\pi$
$761$	−7.03379	+	12.1829i	−0.254975	+	0.441629i	0.709914	+	0.704288i	$0.248734\pi$
$762$		0			0
$763$	−11.3285	−	2.91321i	−0.410118	−	0.105465i
$764$	1.98057			0.0716545
$765$		0			0
$766$	−0.824893	−	1.42876i	−0.0298046	−	0.0516231i
$767$	−3.20765	−	5.55582i	−0.115822	−	0.200609i
$768$		0			0
$769$	−22.6922			−0.818301			−0.409151	−	0.912467i	$-0.634175\pi$
$769$	−22.6922			−0.818301			−0.409151	+	0.912467i	$0.634175\pi$
$770$	7.19398	+	25.8035i	0.259253	+	0.929895i
$771$		0			0
$772$	2.27292	−	3.93680i	0.0818040	−	0.141689i
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	0.871860	−	0.489756i	$-0.162914\pi$
$773$	0.327772	+	0.567717i	0.0117891	+	0.0204194i	−0.860071	+	0.510175i	$0.829581\pi$
$774$		0			0
$775$	24.1404	−	41.8123i	0.867148	−	1.50194i
$776$	14.8421			0.532802
$777$		0			0
$778$	32.0676			1.14968
$779$	−3.59329	+	6.22377i	−0.128743	+	0.222990i
$780$		0			0
$781$	−13.8256	−	23.9466i	−0.494718	−	0.856877i
$782$	1.70370	−	2.95089i	0.0609241	−	0.105524i
$783$		0			0
$784$	6.13160	+	3.37690i	0.218986	+	0.120604i
$785$	35.8389			1.27914
$786$		0			0
$787$	−0.270036	−	0.467717i	−0.00962576	−	0.0166723i	0.861172	−	0.508313i	$-0.169731\pi$
$787$	−0.270036	−	0.467717i	−0.00962576	−	0.0166723i	−0.870798	+	0.491641i	$0.836397\pi$
$788$	10.9074	+	18.8922i	0.388560	+	0.673005i
$789$		0			0
$790$	−13.1683			−0.468506
$791$	5.95378	−	6.07521i	0.211692	−	0.216010i
$792$		0			0
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$	18.9669	+	32.8516i	0.673110	+	1.16586i
$795$		0			0
$796$	6.14132	−	10.6371i	0.217673	−	0.377021i
$797$	25.1100			0.889441			0.444721	−	0.895669i	$-0.353303\pi$
$797$	25.1100			0.889441			0.444721	+	0.895669i	$0.353303\pi$
$798$		0			0
$799$	−8.86948			−0.313780
$800$	2.56238	−	4.43818i	0.0905939	−	0.156913i
$801$		0			0
$802$	5.30959	+	9.19647i	0.187488	+	0.324739i
$803$	−7.90219	+	13.6870i	−0.278862	+	0.483004i
$804$		0			0
$805$	18.2564	+	4.69478i	0.643452	+	0.165469i
$806$	−53.7349			−1.89273
$807$		0			0
$808$	9.29467	+	16.0988i	0.326985	+	0.566355i
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	−0.999889	−	0.0148817i	$-0.995263\pi$
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	0.487057	−	0.873370i	$-0.338071\pi$
$810$		0			0
$811$	−15.4290			−0.541785			−0.270892	−	0.962610i	$-0.587319\pi$
$811$	−15.4290			−0.541785			−0.270892	+	0.962610i	$0.587319\pi$
$812$	−18.1449	−	4.66611i	−0.636761	−	0.163748i
$813$		0			0
$814$	−1.59097	+	2.75564i	−0.0557635	+	0.0965853i
$815$	6.33297	+	10.9690i	0.221834	+	0.384228i
$816$		0			0
$817$	4.37919	−	7.58499i	0.153209	−	0.265365i
$818$	−5.54583			−0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	−4.24364	+	7.35019i	−0.148104	+	0.256524i	−0.930527	−	0.366224i	$-0.880650\pi$
$821$	−4.24364	+	7.35019i	−0.148104	+	0.256524i	0.782423	+	0.622748i	$0.213984\pi$
$822$		0			0
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	−0.999966	−	0.00825976i	$-0.997371\pi$
$823$	−14.5487	−	25.1991i	−0.507136	−	0.878385i	0.492830	−	0.870126i	$-0.335963\pi$
$824$	−0.141315	+	0.244765i	−0.00492294	+	0.00852679i
$825$		0			0
$826$	2.08289	−	2.12537i	0.0724731	−	0.0739512i
$827$	−25.9396			−0.902007			−0.451003	−	0.892522i	$-0.648934\pi$
$827$	−25.9396			−0.902007			−0.451003	+	0.892522i	$0.648934\pi$
$828$		0			0
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	0.914941	−	0.403588i	$-0.132237\pi$
$829$	3.10821	+	5.38358i	0.107953	+	0.186979i	−0.806988	+	0.590568i	$0.798904\pi$
$830$	−12.8353	−	22.2314i	−0.445520	−	0.771663i
$831$		0			0
$832$	−5.70370			−0.197740
$833$	−9.11574	+	5.51129i	−0.315842	+	0.190955i
$834$		0			0
$835$	−8.33530	+	14.4372i	−0.288455	+	0.499618i
$836$	−2.04063	−	3.53447i	−0.0705766	−	0.122242i
$837$		0			0
$838$	−2.77455	+	4.80566i	−0.0958452	+	0.166009i
$839$	−42.5893			−1.47035			−0.735174	−	0.677879i	$-0.762899\pi$
$839$	−42.5893			−1.47035			−0.735174	+	0.677879i	$0.762899\pi$
$840$		0			0
$841$	21.1442			0.729110
$842$	3.42107	−	5.92546i	0.117898	−	0.204205i
$843$		0			0
$844$	−8.32846	−	14.4253i	−0.286677	−	0.496540i
$845$	31.0751	−	53.8237i	1.06902	−	1.85159i
$846$		0			0
$847$	−0.621885	−	2.23059i	−0.0213682	−	0.0766440i
$848$	−2.05718			−0.0706438
$849$		0			0
$850$	3.89931	+	6.75381i	0.133745	+	0.231654i
$851$	1.11956	+	1.93914i	0.0383781	+	0.0664728i
$852$		0			0
$853$	21.3937			0.732507			0.366254	−	0.930515i	$-0.380640\pi$
$853$	21.3937			0.732507			0.366254	+	0.930515i	$0.380640\pi$
$854$	8.00684	+	2.05903i	0.273988	+	0.0704585i
$855$		0			0
$856$	−5.68878	+	9.85326i	−0.194438	+	0.336777i
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	0.987697	+	0.156377i	$0.0499815\pi$
$857$	18.4218	+	31.9074i	0.629275	+	1.08994i	−0.358422	+	0.933560i	$0.616685\pi$
$858$		0			0
$859$	8.81875	−	15.2745i	0.300892	−	0.521160i	−0.675446	−	0.737409i	$-0.736049\pi$
$859$	8.81875	−	15.2745i	0.300892	−	0.521160i	0.976338	+	0.216249i	$0.0693824\pi$
$860$	21.7278			0.740911
$861$		0			0
$862$	33.1078			1.12766
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	−0.872428	−	0.488743i	$-0.837456\pi$
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	0.859478	+	0.511173i	$0.170789\pi$
$864$		0			0
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$	−6.05555	+	10.4885i	−0.205776	+	0.356414i
$867$		0			0
$868$	−6.69398	−	24.0101i	−0.227209	−	0.814957i
$869$	−13.1683			−0.446703
$870$		0			0
$871$	31.2759	+	54.1715i	1.05974	+	1.83553i
$872$	2.21053	+	3.82876i	0.0748581	+	0.129658i
$873$		0			0
$874$	−2.87197			−0.0971457
$875$	−0.735165	+	0.750160i	−0.0248531	+	0.0253600i
$876$		0			0
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	−0.267573	−	0.963538i	$-0.586222\pi$
$877$	20.7495	−	35.9392i	0.700662	−	1.21358i	0.968234	−	0.250044i	$-0.0804451\pi$
$878$	−4.41711	−	7.65066i	−0.149070	−	0.258197i
$879$		0			0
$880$	5.06238	−	8.76830i	0.170653	−	0.295579i
$881$	8.35486			0.281482			0.140741	−	0.990046i	$-0.455051\pi$
$881$	8.35486			0.281482			0.140741	+	0.990046i	$0.455051\pi$
$882$		0			0
$883$	35.6181			1.19864			0.599322	−	0.800508i	$-0.295437\pi$
$883$	35.6181			1.19864			0.599322	+	0.800508i	$0.295437\pi$
$884$	4.33981	−	7.51677i	0.145964	−	0.252816i
$885$		0			0
$886$	8.75924	+	15.1715i	0.294272	+	0.509695i
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	−0.365905	−	0.930652i	$-0.619241\pi$
$887$	18.5550	−	32.1382i	0.623016	−	1.07909i	0.988921	−	0.148443i	$-0.0474260\pi$
$888$		0			0
$889$	37.2320	−	37.9914i	1.24872	−	1.27419i
$890$	−0.717370			−0.0240463
$891$		0			0
$892$	−5.32846	−	9.22916i	−0.178410	−	0.309015i
$893$	3.73788	+	6.47420i	0.125083	+	0.216651i
$894$		0			0
$895$	22.3937			0.748540
$896$	−0.710533	−	2.54856i	−0.0237373	−	0.0851413i
$897$		0			0
$898$	15.6150	−	27.0461i	0.521081	−	0.902539i
$899$	33.3565	+	57.7751i	1.11250	+	1.92691i
$900$		0			0
$901$	1.56526	−	2.71111i	0.0521464	−	0.0903202i
$902$	−17.8285			−0.593623
$903$		0			0
$904$	−3.21505			−0.106931
$905$	−20.6300	+	35.7321i	−0.685763	+	1.18778i
$906$		0			0
$907$	24.0751	+	41.6993i	0.799401	+	1.38460i	0.920007	+	0.391902i	$0.128183\pi$
$907$	24.0751	+	41.6993i	0.799401	+	1.38460i	−0.120606	+	0.992700i	$0.538484\pi$
$908$	7.25404	−	12.5644i	0.240734	−	0.416963i
$909$		0			0
$910$	46.5043	+	11.9590i	1.54160	+	0.396436i
$911$	−34.8856			−1.15581			−0.577906	−	0.816103i	$-0.696130\pi$
$911$	−34.8856			−1.15581			−0.577906	+	0.816103i	$0.696130\pi$
$912$		0			0
$913$	−12.8353	−	22.2314i	−0.424786	−	0.735751i
$914$	−16.0624	−	27.8209i	−0.531296	−	0.920232i
$915$		0			0
$916$	10.2495			0.338654
$917$	4.52175	+	16.2187i	0.149321	+	0.535590i
$918$		0			0
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	0.0249351	+	0.999689i	$0.492062\pi$
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	−0.878224	+	0.478250i	$0.841271\pi$
$920$	−3.56238	−	6.17023i	−0.117448	−	0.203426i
$921$		0			0
$922$	−1.23229	+	2.13438i	−0.0405832	+	0.0702922i
$923$	−49.5653			−1.63146
$924$		0			0
$925$	−5.12476			−0.168501
$926$	−15.1735	+	26.2812i	−0.498631	+	0.863655i
$927$		0			0
$928$	3.54063	+	6.13255i	0.116227	+	0.201311i
$929$	25.4142	−	44.0187i	0.833814	−	1.44421i	−0.0611787	−	0.998127i	$-0.519486\pi$
$929$	25.4142	−	44.0187i	0.833814	−	1.44421i	0.894993	−	0.446081i	$-0.147181\pi$
$930$		0			0
$931$	7.86458	+	4.33132i	0.257751	+	0.141953i
$932$	−1.08126			−0.0354177
$933$		0			0
$934$	7.98181	+	13.8249i	0.261173	+	0.452365i
$935$	7.70370	+	13.3432i	0.251938	+	0.436369i
$936$		0			0
$937$	2.54583			0.0831686			0.0415843	−	0.999135i	$-0.486759\pi$
$937$	2.54583			0.0831686			0.0415843	+	0.999135i	$0.486759\pi$
$938$	−20.3090	+	20.7232i	−0.663113	+	0.676638i
$939$		0			0
$940$	−9.27292	+	16.0612i	−0.302449	+	0.523857i
$941$	−0.578933	−	1.00274i	−0.0188727	−	0.0326885i	0.856435	−	0.516255i	$-0.172674\pi$
$941$	−0.578933	−	1.00274i	−0.0188727	−	0.0326885i	−0.875308	+	0.483567i	$0.839341\pi$
$942$		0			0
$943$	−6.27292	+	10.8650i	−0.204274	+	0.353813i
$944$	−1.12476			−0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	−4.90739	+	8.49985i	−0.159469	+	0.276208i	−0.934677	−	0.355497i	$-0.884311\pi$
$947$	−4.90739	+	8.49985i	−0.159469	+	0.276208i	0.775208	+	0.631706i	$0.217645\pi$
$948$		0			0
$949$	14.1648	+	24.5342i	0.459810	+	0.796414i
$950$	3.28659	−	5.69254i	0.106631	−	0.184690i
$951$		0			0
$952$	3.89931	+	1.00274i	0.126377	+	0.0324991i
$953$	6.53791			0.211784			0.105892	−	0.994378i	$-0.466230\pi$
$953$	6.53791			0.211784			0.105892	+	0.994378i	$0.466230\pi$
$954$		0			0
$955$	3.15103	+	5.45774i	0.101965	+	0.176608i
$956$	−6.16019	−	10.6698i	−0.199235	−	0.345085i
$957$		0			0
$958$	23.1729			0.748683
$959$	−7.02463	−	1.80644i	−0.226837	−	0.0583331i
$960$		0			0
$961$	−28.8782	+	50.0186i	−0.931556	+	1.61350i
$962$	2.85185	+	4.93955i	0.0919473	+	0.159257i
$963$		0			0
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$	14.4646			0.465631
$966$		0			0
$967$	−28.8889			−0.929005			−0.464502	−	0.885572i	$-0.653767\pi$
$967$	−28.8889			−0.929005			−0.464502	+	0.885572i	$0.653767\pi$
$968$	−0.437618	+	0.757977i	−0.0140656	+	0.0243623i
$969$		0			0
$970$	23.6134	+	40.8996i	0.758181	+	1.31321i
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	−0.820030	−	0.572320i	$-0.806043\pi$
$971$	2.66827	−	4.62158i	0.0856289	−	0.148314i	0.905659	+	0.424007i	$0.139377\pi$
$972$		0			0
$973$	14.7535	−	15.0544i	0.472975	−	0.482622i
$974$	3.41315			0.109364
$975$		0			0
$976$	−1.56238	−	2.70612i	−0.0500106	−	0.0866209i
$977$	24.0361	+	41.6318i	0.768983	+	1.33192i	0.938115	+	0.346325i	$0.112571\pi$
$977$	24.0361	+	41.6318i	0.768983	+	1.33192i	−0.169131	+	0.985594i	$0.554096\pi$
$978$		0			0
$979$	−0.717370			−0.0229272
$980$	0.449657	+	22.2691i	0.0143638	+	0.711359i
$981$		0			0
$982$	9.58414	−	16.6002i	0.305842	−	0.529734i
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	0.529549	−	0.848279i	$-0.322361\pi$
$983$	−14.7313	−	25.5154i	−0.469857	−	0.813816i	−0.999406	+	0.0344634i	$0.989028\pi$
$984$		0			0
$985$	−34.7067	+	60.1138i	−1.10585	+	1.91538i
$986$	−10.7759			−0.343175
$987$		0			0
$988$	−7.31573			−0.232744
$989$	7.64488	−	13.2413i	0.243093	−	0.421050i
$990$		0			0
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	0.999929	−	0.0119112i	$-0.00379153\pi$
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	−0.510280	+	0.860008i	$0.670458\pi$
$992$	−4.71053	+	8.15888i	−0.149560	+	0.259045i
$993$		0			0
$994$	−6.17455	−	22.1470i	−0.195845	−	0.702461i
$995$	39.0826			1.23900
$996$		0			0
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	0.818770	−	0.574122i	$-0.194656\pi$
$997$	−2.77292	−	4.80283i	−0.0878191	−	0.152107i	−0.906589	+	0.422015i	$0.861323\pi$
$998$	20.5848	+	35.6540i	0.651601	+	1.12861i
$999$		0			0

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	1134.2.g.m.163.3		6
3.2	odd	2		1134.2.g.l.163.1		6
7.2	even	3		7938.2.a.bv.1.1		3
7.4	even	3	inner	1134.2.g.m.487.3		6
7.5	odd	6		7938.2.a.bw.1.3		3
9.2	odd	6		378.2.e.d.37.1		6
9.4	even	3		126.2.h.d.79.1	yes	6
9.5	odd	6		378.2.h.c.289.3		6
9.7	even	3		126.2.e.c.121.3	yes	6
21.2	odd	6		7938.2.a.ca.1.3		3
21.5	even	6		7938.2.a.bz.1.1		3
21.11	odd	6		1134.2.g.l.487.1		6
36.7	odd	6		1008.2.q.g.625.1		6
36.11	even	6		3024.2.q.g.2305.1		6
36.23	even	6		3024.2.t.h.289.3		6
36.31	odd	6		1008.2.t.h.961.3		6
63.2	odd	6		2646.2.f.l.1765.1		6
63.4	even	3		126.2.e.c.25.3	✓	6
63.5	even	6		2646.2.f.m.883.3		6
63.11	odd	6		378.2.h.c.361.3		6
63.13	odd	6		882.2.h.p.79.3		6
63.16	even	3		882.2.f.n.589.2		6
63.20	even	6		2646.2.e.p.1549.3		6
63.23	odd	6		2646.2.f.l.883.1		6
63.25	even	3		126.2.h.d.67.1	yes	6
63.31	odd	6		882.2.e.o.655.1		6
63.32	odd	6		378.2.e.d.235.1		6
63.34	odd	6		882.2.e.o.373.1		6
63.38	even	6		2646.2.h.o.361.1		6
63.40	odd	6		882.2.f.o.295.2		6
63.41	even	6		2646.2.h.o.667.1		6
63.47	even	6		2646.2.f.m.1765.3		6
63.52	odd	6		882.2.h.p.67.3		6
63.58	even	3		882.2.f.n.295.2		6
63.59	even	6		2646.2.e.p.2125.3		6
63.61	odd	6		882.2.f.o.589.2		6
252.11	even	6		3024.2.t.h.1873.3		6
252.67	odd	6		1008.2.q.g.529.1		6
252.95	even	6		3024.2.q.g.2881.1		6
252.151	odd	6		1008.2.t.h.193.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	63.4	even	3
126.2.e.c.121.3	yes	6	9.7	even	3
126.2.h.d.67.1	yes	6	63.25	even	3
126.2.h.d.79.1	yes	6	9.4	even	3
378.2.e.d.37.1		6	9.2	odd	6
378.2.e.d.235.1		6	63.32	odd	6
378.2.h.c.289.3		6	9.5	odd	6
378.2.h.c.361.3		6	63.11	odd	6
882.2.e.o.373.1		6	63.34	odd	6
882.2.e.o.655.1		6	63.31	odd	6
882.2.f.n.295.2		6	63.58	even	3
882.2.f.n.589.2		6	63.16	even	3
882.2.f.o.295.2		6	63.40	odd	6
882.2.f.o.589.2		6	63.61	odd	6
882.2.h.p.67.3		6	63.52	odd	6
882.2.h.p.79.3		6	63.13	odd	6
1008.2.q.g.529.1		6	252.67	odd	6
1008.2.q.g.625.1		6	36.7	odd	6
1008.2.t.h.193.3		6	252.151	odd	6
1008.2.t.h.961.3		6	36.31	odd	6
1134.2.g.l.163.1		6	3.2	odd	2
1134.2.g.l.487.1		6	21.11	odd	6
1134.2.g.m.163.3		6	1.1	even	1	trivial
1134.2.g.m.487.3		6	7.4	even	3	inner
2646.2.e.p.1549.3		6	63.20	even	6
2646.2.e.p.2125.3		6	63.59	even	6
2646.2.f.l.883.1		6	63.23	odd	6
2646.2.f.l.1765.1		6	63.2	odd	6
2646.2.f.m.883.3		6	63.5	even	6
2646.2.f.m.1765.3		6	63.47	even	6
2646.2.h.o.361.1		6	63.38	even	6
2646.2.h.o.667.1		6	63.41	even	6
3024.2.q.g.2305.1		6	36.11	even	6
3024.2.q.g.2881.1		6	252.95	even	6
3024.2.t.h.289.3		6	36.23	even	6
3024.2.t.h.1873.3		6	252.11	even	6
7938.2.a.bv.1.1		3	7.2	even	3
7938.2.a.bw.1.3		3	7.5	odd	6
7938.2.a.bz.1.1		3	21.5	even	6
7938.2.a.ca.1.3		3	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	1134.2.g.m.163.3

Level	$1134$
Weight	$2$
Character	1134.163
Analytic conductor	$9.055$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$