LMFDB - Embedded newform 592.2.be.d.399.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 14x^{14} + 135x^{12} - 686x^{10} + 2521x^{8} - 4452x^{6} + 5592x^{4} - 2016x^{2} + 576 $ x^16 - 14x^14 + 135x^12 - 686x^10 + 2521x^8 - 4452x^6 + 5592x^4 - 2016*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.4
Root			$2.22768 - 1.28615i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.d.319.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28615 - 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(0.256864 + 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} +O(q^{10})$	\(q+(1.28615 - 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(0.256864 + 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} +4.15876 q^{11} +(-0.973243 - 3.63219i) q^{13} +(-1.28615 - 0.344623i) q^{15} +(-3.07454 - 0.823821i) q^{17} +(0.880988 - 0.236060i) q^{19} +(0.660731 - 0.381473i) q^{21} +(-1.05009 - 1.05009i) q^{23} +(4.09808 - 2.36603i) q^{25} -1.58646 q^{27} +(-2.32382 - 2.32382i) q^{29} +(-4.09452 + 4.09452i) q^{31} +(5.34880 - 9.26439i) q^{33} +(0.0397369 - 0.148300i) q^{35} +(-4.04778 + 4.54042i) q^{37} +(-9.34310 - 2.50348i) q^{39} +(-2.06087 - 1.18985i) q^{41} +(5.44121 + 5.44121i) q^{43} +(-1.32382 + 1.32382i) q^{45} +5.23149i q^{47} +(-3.45601 - 5.98599i) q^{49} +(-5.78953 + 5.78953i) q^{51} +(3.22396 + 5.58407i) q^{53} +(-0.557168 - 2.07938i) q^{55} +(0.607218 - 2.26617i) q^{57} +(-0.837547 + 3.12577i) q^{59} +(3.80659 - 1.01997i) q^{61} -1.07273i q^{63} +(-1.68571 + 0.973243i) q^{65} +(0.0605407 - 0.104859i) q^{67} +(-3.68985 + 0.988691i) q^{69} +(1.18587 + 0.684665i) q^{71} +3.46410i q^{73} -12.1723i q^{75} +(1.06823 + 0.616745i) q^{77} +(10.4241 - 2.79313i) q^{79} +(3.38469 - 5.86246i) q^{81} +(10.4366 - 6.02559i) q^{83} +1.64764i q^{85} +(-8.16552 + 2.18794i) q^{87} +(-2.86010 + 10.6741i) q^{89} +(0.288665 - 1.07731i) q^{91} +(3.85510 + 14.3874i) q^{93} +(-0.236060 - 0.408868i) q^{95} +(9.25847 - 9.25847i) q^{97} +(-7.52059 - 13.0260i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{5} - 4 q^{9}+O(q^{10}) $ 16 * q - 16 * q^5 - 4 * q^9	$ 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89} - 60 q^{93} - 4 q^{97}+O(q^{100}) $ 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	1.28615	−	2.22768i	0.742560	−	1.28615i	−0.208766	−	0.977966i	$-0.566945\pi$
$3$	1.28615	−	2.22768i	0.742560	−	1.28615i	0.951326	−	0.308186i	$-0.0997220\pi$
$4$		0			0
$5$	−0.133975	−	0.500000i	−0.0599153	−	0.223607i	0.929476	−	0.368883i	$-0.120260\pi$
$5$	−0.133975	−	0.500000i	−0.0599153	−	0.223607i	−0.989391	+	0.145276i	$0.953593\pi$
$6$		0			0
$7$	0.256864	+	0.148300i	0.0970853	+	0.0560522i	0.547757	−	0.836638i	$-0.315482\pi$
$7$	0.256864	+	0.148300i	0.0970853	+	0.0560522i	−0.450671	+	0.892690i	$0.648815\pi$
$8$		0			0
$9$	−1.80837	−	3.13219i	−0.602791	−	1.04406i
$10$		0			0
$11$	4.15876			1.25391			0.626957	−	0.779054i	$-0.284300\pi$
$11$	4.15876			1.25391			0.626957	+	0.779054i	$0.284300\pi$
$12$		0			0
$13$	−0.973243	−	3.63219i	−0.269929	−	1.00739i	−0.959164	−	0.282851i	$-0.908720\pi$
$13$	−0.973243	−	3.63219i	−0.269929	−	1.00739i	0.689235	−	0.724538i	$-0.257947\pi$
$14$		0			0
$15$	−1.28615	−	0.344623i	−0.332083	−	0.0889814i
$16$		0			0
$17$	−3.07454	−	0.823821i	−0.745686	−	0.199806i	−0.134082	−	0.990970i	$-0.542809\pi$
$17$	−3.07454	−	0.823821i	−0.745686	−	0.199806i	−0.611604	+	0.791164i	$0.709475\pi$
$18$		0			0
$19$	0.880988	−	0.236060i	0.202112	−	0.0541559i	−0.156342	−	0.987703i	$-0.549970\pi$
$19$	0.880988	−	0.236060i	0.202112	−	0.0541559i	0.358455	+	0.933547i	$0.383304\pi$
$20$		0			0
$21$	0.660731	−	0.381473i	0.144183	−	0.0832443i
$22$		0			0
$23$	−1.05009	−	1.05009i	−0.218959	−	0.218959i	0.589101	−	0.808060i	$-0.299482\pi$
$23$	−1.05009	−	1.05009i	−0.218959	−	0.218959i	−0.808060	+	0.589101i	$0.799482\pi$
$24$		0			0
$25$	4.09808	−	2.36603i	0.819615	−	0.473205i
$26$		0			0
$27$	−1.58646			−0.305314
$28$		0			0
$29$	−2.32382	−	2.32382i	−0.431523	−	0.431523i	0.457623	−	0.889146i	$-0.348701\pi$
$29$	−2.32382	−	2.32382i	−0.431523	−	0.431523i	−0.889146	+	0.457623i	$0.848701\pi$
$30$		0			0
$31$	−4.09452	+	4.09452i	−0.735397	+	0.735397i	−0.971683	−	0.236287i	$-0.924070\pi$
$31$	−4.09452	+	4.09452i	−0.735397	+	0.735397i	0.236287	+	0.971683i	$0.424070\pi$
$32$		0			0
$33$	5.34880	−	9.26439i	0.931106	−	1.61272i
$34$		0			0
$35$	0.0397369	−	0.148300i	0.00671677	−	0.0250673i
$36$		0			0
$37$	−4.04778	+	4.54042i	−0.665452	+	0.746441i
$37$	−4.04778	+	4.54042i	−0.665452	+	0.746441i
$38$		0			0
$39$	−9.34310	−	2.50348i	−1.49609	−	0.400877i
$40$		0			0
$41$	−2.06087	−	1.18985i	−0.321854	−	0.185823i	0.330364	−	0.943853i	$-0.392828\pi$
$41$	−2.06087	−	1.18985i	−0.321854	−	0.185823i	−0.652219	+	0.758031i	$0.726162\pi$
$42$		0			0
$43$	5.44121	+	5.44121i	0.829776	+	0.829776i	0.987486	−	0.157709i	$-0.0504109\pi$
$43$	5.44121	+	5.44121i	0.829776	+	0.829776i	−0.157709	+	0.987486i	$0.550411\pi$
$44$		0			0
$45$	−1.32382	+	1.32382i	−0.197344	+	0.197344i
$46$		0			0
$47$			5.23149i			0.763091i	0.924350	+	0.381546i	$0.124608\pi$
$47$			5.23149i			0.763091i	−0.924350	+	0.381546i	$0.875392\pi$
$48$		0			0
$49$	−3.45601	−	5.98599i	−0.493716	−	0.855142i
$50$		0			0
$51$	−5.78953	+	5.78953i	−0.810697	+	0.810697i
$52$		0			0
$53$	3.22396	+	5.58407i	0.442845	+	0.767031i	0.997899	−	0.0647836i	$-0.0206357\pi$
$53$	3.22396	+	5.58407i	0.442845	+	0.767031i	−0.555054	+	0.831814i	$0.687302\pi$
$54$		0			0
$55$	−0.557168	−	2.07938i	−0.0751285	−	0.280384i
$56$		0			0
$57$	0.607218	−	2.26617i	0.0804280	−	0.300161i
$58$		0			0
$59$	−0.837547	+	3.12577i	−0.109039	+	0.406940i	−0.998772	−	0.0495415i	$-0.984224\pi$
$59$	−0.837547	+	3.12577i	−0.109039	+	0.406940i	0.889733	+	0.456482i	$0.150891\pi$
$60$		0			0
$61$	3.80659	−	1.01997i	0.487384	−	0.130594i	−0.00675473	−	0.999977i	$-0.502150\pi$
$61$	3.80659	−	1.01997i	0.487384	−	0.130594i	0.494139	+	0.869383i	$0.335483\pi$
$62$		0			0
$63$		−	1.07273i		−	0.135151i
$64$		0			0
$65$	−1.68571	+	0.973243i	−0.209086	+	0.120716i
$66$		0			0
$67$	0.0605407	−	0.104859i	0.00739622	−	0.0128106i	−0.862304	−	0.506392i	$-0.830979\pi$
$67$	0.0605407	−	0.104859i	0.00739622	−	0.0128106i	0.869700	+	0.493581i	$0.164312\pi$
$68$		0			0
$69$	−3.68985	+	0.988691i	−0.444205	+	0.119024i
$70$		0			0
$71$	1.18587	+	0.684665i	0.140737	+	0.0812548i	0.568715	−	0.822534i	$-0.307441\pi$
$71$	1.18587	+	0.684665i	0.140737	+	0.0812548i	−0.427978	+	0.903789i	$0.640774\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$		0			0
$75$		−	12.1723i		−	1.40553i
$76$		0			0
$77$	1.06823	+	0.616745i	0.121737	+	0.0702847i
$78$		0			0
$79$	10.4241	−	2.79313i	1.17280	−	0.314252i	0.380736	−	0.924684i	$-0.375671\pi$
$79$	10.4241	−	2.79313i	1.17280	−	0.314252i	0.792069	+	0.610432i	$0.209004\pi$
$80$		0			0
$81$	3.38469	−	5.86246i	0.376077	−	0.651385i
$82$		0			0
$83$	10.4366	−	6.02559i	1.14557	−	0.661395i	0.197766	−	0.980249i	$-0.436631\pi$
$83$	10.4366	−	6.02559i	1.14557	−	0.661395i	0.947804	+	0.318854i	$0.103298\pi$
$84$		0			0
$85$			1.64764i			0.178712i
$86$		0			0
$87$	−8.16552	+	2.18794i	−0.875435	+	0.234572i
$88$		0			0
$89$	−2.86010	+	10.6741i	−0.303171	+	1.13145i	0.631338	+	0.775508i	$0.282506\pi$
$89$	−2.86010	+	10.6741i	−0.303171	+	1.13145i	−0.934509	+	0.355940i	$0.884161\pi$
$90$		0			0
$91$	0.288665	−	1.07731i	0.0302603	−	0.112933i
$92$		0			0
$93$	3.85510	+	14.3874i	0.399756	+	1.49191i
$94$		0			0
$95$	−0.236060	−	0.408868i	−0.0242192	−	0.0419490i
$96$		0			0
$97$	9.25847	−	9.25847i	0.940055	−	0.940055i	−0.0582474	−	0.998302i	$-0.518551\pi$
$97$	9.25847	−	9.25847i	0.940055	−	0.940055i	0.998302	+	0.0582474i	$0.0185512\pi$
$98$		0			0
$99$	−7.52059	−	13.0260i	−0.755847	−	1.30917i
$100$		0			0
$101$			15.6096i			1.55322i	0.629985	+	0.776608i	$0.283061\pi$
$101$			15.6096i			1.55322i	−0.629985	+	0.776608i	$0.716939\pi$
$102$		0			0
$103$	10.1932	−	10.1932i	1.00436	−	1.00436i	0.00437231	−	0.999990i	$-0.498608\pi$
$103$	10.1932	−	10.1932i	1.00436	−	1.00436i	0.999990	−	0.00437231i	$-0.00139175\pi$
$104$		0			0
$105$	−0.279258	−	0.279258i	−0.0272528	−	0.0272528i
$106$		0			0
$107$	15.5794	+	8.99478i	1.50612	+	0.869558i	0.999975	+	0.00710869i	$0.00226279\pi$
$107$	15.5794	+	8.99478i	1.50612	+	0.869558i	0.506144	+	0.862449i	$0.331071\pi$
$108$		0			0
$109$	−2.86603	−	0.767949i	−0.274515	−	0.0735562i	0.118935	−	0.992902i	$-0.462052\pi$
$109$	−2.86603	−	0.767949i	−0.274515	−	0.0735562i	−0.393450	+	0.919346i	$0.628719\pi$
$110$		0			0
$111$	4.90855	+	14.8568i	0.465899	+	1.41015i
$112$		0			0
$113$	−3.13850	+	11.7130i	−0.295245	+	1.10187i	0.645777	+	0.763526i	$0.276533\pi$
$113$	−3.13850	+	11.7130i	−0.295245	+	1.10187i	−0.941022	+	0.338344i	$0.890133\pi$
$114$		0			0
$115$	−0.384360	+	0.665732i	−0.0358418	+	0.0620798i
$116$		0			0
$117$	−9.61675	+	9.61675i	−0.889068	+	0.889068i
$118$		0			0
$119$	−0.667565	−	0.667565i	−0.0611956	−	0.0611956i
$120$		0			0
$121$	6.29528			0.572298
$122$		0			0
$123$	−5.30119	+	3.06065i	−0.477992	+	0.275969i
$124$		0			0
$125$	−3.56218	−	3.56218i	−0.318611	−	0.318611i
$126$		0			0
$127$	12.2554	−	7.07569i	1.08750	−	0.627866i	0.154587	−	0.987979i	$-0.450595\pi$
$127$	12.2554	−	7.07569i	1.08750	−	0.627866i	0.932908	+	0.360114i	$0.117262\pi$
$128$		0			0
$129$	19.1195	−	5.12305i	1.68338	−	0.451060i
$130$		0			0
$131$	−9.49511	−	2.54421i	−0.829591	−	0.222288i	−0.181056	−	0.983473i	$-0.557952\pi$
$131$	−9.49511	−	2.54421i	−0.829591	−	0.222288i	−0.648535	+	0.761184i	$0.724618\pi$
$132$		0			0
$133$	0.261302	+	0.0700155i	0.0226577	+	0.00607112i
$134$		0			0
$135$	0.212545	+	0.793228i	0.0182929	+	0.0682702i
$136$		0			0
$137$	−13.3614			−1.14154			−0.570771	−	0.821109i	$-0.693356\pi$
$137$	−13.3614			−1.14154			−0.570771	+	0.821109i	$0.693356\pi$
$138$		0			0
$139$	3.40897	+	5.90451i	0.289145	+	0.500814i	0.973606	−	0.228235i	$-0.0732956\pi$
$139$	3.40897	+	5.90451i	0.289145	+	0.500814i	−0.684461	+	0.729050i	$0.739962\pi$
$140$		0			0
$141$	11.6541	+	6.72849i	0.981451	+	0.566641i
$142$		0			0
$143$	−4.04748	−	15.1054i	−0.338468	−	1.26318i
$144$		0			0
$145$	−0.850577	+	1.47324i	−0.0706366	+	0.122346i
$146$		0			0
$147$	−17.7798			−1.46646
$148$		0			0
$149$	−20.4832			−1.67805			−0.839023	−	0.544096i	$-0.816873\pi$
$149$	−20.4832			−1.67805			−0.839023	+	0.544096i	$0.816873\pi$
$150$		0			0
$151$	−5.38067	+	9.31959i	−0.437872	+	0.758417i	−0.997525	−	0.0703099i	$-0.977601\pi$
$151$	−5.38067	+	9.31959i	−0.437872	+	0.758417i	0.559653	+	0.828727i	$0.310935\pi$
$152$		0			0
$153$	2.97955	+	11.1198i	0.240882	+	0.898985i
$154$		0			0
$155$	2.59582	+	1.49870i	0.208501	+	0.120378i
$156$		0			0
$157$	7.84880	+	13.5945i	0.626402	+	1.08496i	0.988268	+	0.152730i	$0.0488065\pi$
$157$	7.84880	+	13.5945i	0.626402	+	1.08496i	−0.361866	+	0.932230i	$0.617860\pi$
$158$		0			0
$159$	16.5860			1.31536
$160$		0			0
$161$	−0.114001	−	0.425459i	−0.00898458	−	0.0335309i
$162$		0			0
$163$	−6.34300	−	1.69960i	−0.496822	−	0.133123i	0.00170268	−	0.999999i	$-0.499458\pi$
$163$	−6.34300	−	1.69960i	−0.496822	−	0.133123i	−0.498525	+	0.866875i	$0.666125\pi$
$164$		0			0
$165$	−5.34880	−	1.43321i	−0.416403	−	0.111575i
$166$		0			0
$167$	−11.9053	+	3.19001i	−0.921259	+	0.246851i	−0.688123	−	0.725594i	$-0.741565\pi$
$167$	−11.9053	+	3.19001i	−0.921259	+	0.246851i	−0.233135	+	0.972444i	$0.574899\pi$
$168$		0			0
$169$	−0.987296	+	0.570016i	−0.0759458	+	0.0438473i
$170$		0			0
$171$	−2.33254	−	2.33254i	−0.178374	−	0.178374i
$172$		0			0
$173$	0.642639	−	0.371028i	0.0488589	−	0.0282087i	−0.475372	−	0.879785i	$-0.657686\pi$
$173$	0.642639	−	0.371028i	0.0488589	−	0.0282087i	0.524230	+	0.851576i	$0.324353\pi$
$174$		0			0
$175$	1.40353			0.106097
$176$		0			0
$177$	5.88600	+	5.88600i	0.442419	+	0.442419i
$178$		0			0
$179$	−16.8448	+	16.8448i	−1.25904	+	1.25904i	−0.307483	+	0.951554i	$0.599487\pi$
$179$	−16.8448	+	16.8448i	−1.25904	+	1.25904i	−0.951554	+	0.307483i	$0.900513\pi$
$180$		0			0
$181$	4.98908	−	8.64134i	0.370835	−	0.642305i	−0.618859	−	0.785502i	$-0.712405\pi$
$181$	4.98908	−	8.64134i	0.370835	−	0.642305i	0.989694	+	0.143197i	$0.0457381\pi$
$182$		0			0
$183$	2.62368	−	9.79171i	0.193948	−	0.723824i
$184$		0			0
$185$	2.81251	+	1.41559i	0.206780	+	0.104076i
$186$		0			0
$187$	−12.7863	−	3.42607i	−0.935025	−	0.250539i
$188$		0			0
$189$	−0.407503	−	0.235272i	−0.0296415	−	0.0171135i
$190$		0			0
$191$	14.7128	+	14.7128i	1.06458	+	1.06458i	0.997765	+	0.0668134i	$0.0212832\pi$
$191$	14.7128	+	14.7128i	1.06458	+	1.06458i	0.0668134	+	0.997765i	$0.478717\pi$
$192$		0			0
$193$	7.47290	−	7.47290i	0.537911	−	0.537911i	−0.385004	−	0.922915i	$-0.625800\pi$
$193$	7.47290	−	7.47290i	0.537911	−	0.537911i	0.922915	+	0.385004i	$0.125800\pi$
$194$		0			0
$195$			5.00695i			0.358555i
$196$		0			0
$197$	2.30029	+	3.98421i	0.163889	+	0.283863i	0.936260	−	0.351308i	$-0.114263\pi$
$197$	2.30029	+	3.98421i	0.163889	+	0.283863i	−0.772371	+	0.635171i	$0.780930\pi$
$198$		0			0
$199$	−14.1514	+	14.1514i	−1.00316	+	1.00316i	−0.00316927	+	0.999995i	$0.501009\pi$
$199$	−14.1514	+	14.1514i	−1.00316	+	1.00316i	−0.999995	+	0.00316927i	$0.998991\pi$
$200$		0			0
$201$	−0.155729	−	0.269730i	−0.0109843	−	0.0190253i
$202$		0			0
$203$	−0.252282	−	0.941528i	−0.0177067	−	0.0660823i
$204$		0			0
$205$	−0.318818	+	1.18985i	−0.0222672	+	0.0831025i
$206$		0			0
$207$	−1.39013	+	5.18805i	−0.0966209	+	0.360594i
$208$		0			0
$209$	3.66382	−	0.981717i	0.253431	−	0.0679068i
$210$		0			0
$211$			23.7513i			1.63511i	0.575851	+	0.817555i	$0.304671\pi$
$211$			23.7513i			1.63511i	−0.575851	+	0.817555i	$0.695329\pi$
$212$		0			0
$213$	3.05043	−	1.76117i	0.209012	−	0.120673i
$214$		0			0
$215$	1.99162	−	3.44959i	0.135827	−	0.235260i
$216$		0			0
$217$	−1.65895	+	0.444514i	−0.112617	+	0.0301756i
$218$		0			0
$219$	7.71691	+	4.45536i	0.521460	+	0.301065i
$220$		0			0
$221$			11.9691i			0.805129i
$222$		0			0
$223$		−	14.7990i		−	0.991015i	−0.868604	−	0.495508i	$-0.834982\pi$
$223$		−	14.7990i		−	0.991015i	0.868604	−	0.495508i	$-0.165018\pi$
$224$		0			0
$225$	−14.8217	−	8.55731i	−0.988113	−	0.570487i
$226$		0			0
$227$	−7.85181	+	2.10389i	−0.521143	+	0.139640i	−0.509795	−	0.860296i	$-0.670279\pi$
$227$	−7.85181	+	2.10389i	−0.521143	+	0.139640i	−0.0113479	+	0.999936i	$0.503612\pi$
$228$		0			0
$229$	0.883255	−	1.52984i	0.0583671	−	0.101095i	−0.835365	−	0.549695i	$-0.814744\pi$
$229$	0.883255	−	1.52984i	0.0583671	−	0.101095i	0.893733	+	0.448600i	$0.148077\pi$
$230$		0			0
$231$	2.74782	−	1.58646i	0.180793	−	0.104381i
$232$		0			0
$233$		−	1.60386i		−	0.105072i	−0.998619	−	0.0525362i	$-0.983270\pi$
$233$		−	1.60386i		−	0.105072i	0.998619	−	0.0525362i	$-0.0167305\pi$
$234$		0			0
$235$	2.61574	−	0.700887i	0.170632	−	0.0457208i
$236$		0			0
$237$	7.18479	−	26.8140i	0.466702	−	1.74176i
$238$		0			0
$239$	4.74131	−	17.6948i	0.306690	−	1.14458i	−0.624791	−	0.780792i	$-0.714816\pi$
$239$	4.74131	−	17.6948i	0.306690	−	1.14458i	0.931481	−	0.363791i	$-0.118518\pi$
$240$		0			0
$241$	0.0702654	+	0.262234i	0.00452619	+	0.0168920i	0.968152	−	0.250363i	$-0.0805500\pi$
$241$	0.0702654	+	0.262234i	0.00452619	+	0.0168920i	−0.963626	+	0.267255i	$0.913883\pi$
$242$		0			0
$243$	−11.0861	−	19.2018i	−0.711177	−	1.23179i
$244$		0			0
$245$	−2.52998	+	2.52998i	−0.161634	+	0.161634i
$246$		0			0
$247$	−1.71483	−	2.97017i	−0.109112	−	0.188988i
$248$		0			0
$249$		−	30.9993i		−	1.96450i
$250$		0			0
$251$	7.36587	−	7.36587i	0.464930	−	0.464930i	−0.435338	−	0.900267i	$-0.643371\pi$
$251$	7.36587	−	7.36587i	0.464930	−	0.464930i	0.900267	+	0.435338i	$0.143371\pi$
$252$		0			0
$253$	−4.36708	−	4.36708i	−0.274556	−	0.274556i
$254$		0			0
$255$	3.67042	+	2.11912i	0.229850	+	0.132704i
$256$		0			0
$257$	−23.4198	−	6.27531i	−1.46089	−	0.391443i	−0.561090	−	0.827755i	$-0.689618\pi$
$257$	−23.4198	−	6.27531i	−1.46089	−	0.391443i	−0.899796	+	0.436312i	$0.856284\pi$
$258$		0			0
$259$	−1.71307	+	0.565982i	−0.106445	+	0.0351684i
$260$		0			0
$261$	−3.07632	+	11.4810i	−0.190420	+	0.710655i
$262$		0			0
$263$	8.44589	−	14.6287i	0.520796	−	0.902045i	−0.478911	−	0.877863i	$-0.658968\pi$
$263$	8.44589	−	14.6287i	0.520796	−	0.902045i	0.999708	−	0.0241822i	$-0.00769817\pi$
$264$		0			0
$265$	2.36010	−	2.36010i	0.144980	−	0.144980i
$266$		0			0
$267$	20.0999	+	20.0999i	1.23009	+	1.23009i
$268$		0			0
$269$	−2.50355			−0.152644			−0.0763220	−	0.997083i	$-0.524318\pi$
$269$	−2.50355			−0.152644			−0.0763220	+	0.997083i	$0.524318\pi$
$270$		0			0
$271$	−22.5697	+	13.0306i	−1.37101	+	0.791554i	−0.991055	−	0.133451i	$-0.957394\pi$
$271$	−22.5697	+	13.0306i	−1.37101	+	0.791554i	−0.379956	+	0.925005i	$0.624061\pi$
$272$		0			0
$273$	−2.02864	−	2.02864i	−0.122779	−	0.122779i
$274$		0			0
$275$	17.0429	−	9.83973i	1.02773	−	0.593358i
$276$		0			0
$277$	17.6416	−	4.72705i	1.05998	−	0.284021i	0.313610	−	0.949552i	$-0.398462\pi$
$277$	17.6416	−	4.72705i	1.05998	−	0.284021i	0.746370	+	0.665531i	$0.231795\pi$
$278$		0			0
$279$	20.2292	+	5.42040i	1.21109	+	0.324511i
$280$		0			0
$281$	−29.5227	−	7.91059i	−1.76118	−	0.471906i	−0.774224	−	0.632912i	$-0.781860\pi$
$281$	−29.5227	−	7.91059i	−1.76118	−	0.471906i	−0.986954	+	0.161005i	$0.948526\pi$
$282$		0			0
$283$	−7.89701	−	29.4720i	−0.469429	−	1.75193i	−0.641773	−	0.766895i	$-0.721801\pi$
$283$	−7.89701	−	29.4720i	−0.469429	−	1.75193i	0.172344	−	0.985037i	$-0.444866\pi$
$284$		0			0
$285$	−1.21444			−0.0719370
$286$		0			0
$287$	−0.352909	−	0.611256i	−0.0208316	−	0.0360813i
$288$		0			0
$289$	−5.94831	−	3.43426i	−0.349901	−	0.202015i
$290$		0			0
$291$	−8.71711	−	32.5327i	−0.511006	−	1.90710i
$292$		0			0
$293$	−2.12267	+	3.67657i	−0.124007	+	0.214787i	−0.921345	−	0.388747i	$-0.872908\pi$
$293$	−2.12267	+	3.67657i	−0.124007	+	0.214787i	0.797337	+	0.603534i	$0.206241\pi$
$294$		0			0
$295$	1.67509			0.0975277
$296$		0			0
$297$	−6.59769			−0.382837
$298$		0			0
$299$	−2.79214	+	4.83613i	−0.161474	+	0.279681i
$300$		0			0
$301$	0.590716	+	2.20458i	0.0340483	+	0.127070i
$302$		0			0
$303$	34.7732	+	20.0763i	1.99767	+	1.15336i
$304$		0			0
$305$	−1.01997	−	1.76665i	−0.0584035	−	0.101158i
$306$		0			0
$307$	34.4112			1.96395			0.981976	−	0.189008i	$-0.0605271\pi$
$307$	34.4112			1.96395			0.981976	+	0.189008i	$0.0605271\pi$
$308$		0			0
$309$	−9.59716	−	35.8171i	−0.545963	−	2.03756i
$310$		0			0
$311$	−23.9565	−	6.41912i	−1.35845	−	0.363995i	−0.495201	−	0.868778i	$-0.664906\pi$
$311$	−23.9565	−	6.41912i	−1.35845	−	0.363995i	−0.863246	+	0.504783i	$0.831572\pi$
$312$		0			0
$313$	10.0995	+	2.70616i	0.570858	+	0.152961i	0.532690	−	0.846310i	$-0.321181\pi$
$313$	10.0995	+	2.70616i	0.570858	+	0.152961i	0.0381681	+	0.999271i	$0.487848\pi$
$314$		0			0
$315$	−0.536364	+	0.143718i	−0.0302207	+	0.00809762i
$316$		0			0
$317$	22.7109	−	13.1121i	1.27557	−	0.736451i	0.299539	−	0.954084i	$-0.403167\pi$
$317$	22.7109	−	13.1121i	1.27557	−	0.736451i	0.976031	+	0.217633i	$0.0698337\pi$
$318$		0			0
$319$	−9.66421	−	9.66421i	−0.541092	−	0.541092i
$320$		0			0
$321$	40.0750	−	23.1373i	2.23677	−	1.29140i
$322$		0			0
$323$	−2.90310			−0.161533
$324$		0			0
$325$	−12.5823	−	12.5823i	−0.697940	−	0.697940i
$326$		0			0
$327$	−5.39689	+	5.39689i	−0.298449	+	0.298449i
$328$		0			0
$329$	−0.775831	+	1.34378i	−0.0427730	+	0.0740850i
$330$		0			0
$331$	−2.78485	+	10.3932i	−0.153069	+	0.571262i	0.846194	+	0.532875i	$0.178888\pi$
$331$	−2.78485	+	10.3932i	−0.153069	+	0.571262i	−0.999263	+	0.0383865i	$0.987778\pi$
$332$		0			0
$333$	21.5414	+	4.46766i	1.18046	+	0.244826i
$334$		0			0
$335$	−0.0605407	−	0.0162218i	−0.00330769	−	0.000886293i
$336$		0			0
$337$	24.2316	+	13.9901i	1.31998	+	0.762091i	0.983725	−	0.179680i	$-0.0575062\pi$
$337$	24.2316	+	13.9901i	1.31998	+	0.762091i	0.336255	+	0.941771i	$0.390840\pi$
$338$		0			0
$339$	22.0563	+	22.0563i	1.19793	+	1.19793i
$340$		0			0
$341$	−17.0281	+	17.0281i	−0.922124	+	0.922124i
$342$		0			0
$343$		−	4.12632i		−	0.222800i
$344$		0			0
$345$	0.988691	+	1.71246i	0.0532293	+	0.0921959i
$346$		0			0
$347$	1.52962	−	1.52962i	0.0821143	−	0.0821143i	−0.664857	−	0.746971i	$-0.731507\pi$
$347$	1.52962	−	1.52962i	0.0821143	−	0.0821143i	0.746971	+	0.664857i	$0.231507\pi$
$348$		0			0
$349$	−15.9693	−	27.6597i	−0.854819	−	1.48059i	−0.876813	−	0.480832i	$-0.840335\pi$
$349$	−15.9693	−	27.6597i	−0.854819	−	1.48059i	0.0219936	−	0.999758i	$-0.492999\pi$
$350$		0			0
$351$	1.54401	+	5.76232i	0.0824130	+	0.307570i
$352$		0			0
$353$	−3.41689	+	12.7520i	−0.181863	+	0.678722i	0.813417	+	0.581680i	$0.197605\pi$
$353$	−3.41689	+	12.7520i	−0.181863	+	0.678722i	−0.995280	+	0.0970413i	$0.969062\pi$
$354$		0			0
$355$	0.183455	−	0.684665i	0.00973680	−	0.0363382i
$356$		0			0
$357$	−2.34571	+	0.628531i	−0.124148	+	0.0332654i
$358$		0			0
$359$			10.5767i			0.558214i	0.960260	+	0.279107i	$0.0900385\pi$
$359$			10.5767i			0.558214i	−0.960260	+	0.279107i	$0.909962\pi$
$360$		0			0
$361$	−15.7341	+	9.08407i	−0.828109	+	0.478109i
$362$		0			0
$363$	8.09669	−	14.0239i	0.424966	−	0.736063i
$364$		0			0
$365$	1.73205	−	0.464102i	0.0906597	−	0.0242922i
$366$		0			0
$367$	−24.3917	−	14.0825i	−1.27324	−	0.735103i	−0.297640	−	0.954678i	$-0.596200\pi$
$367$	−24.3917	−	14.0825i	−1.27324	−	0.735103i	−0.975596	+	0.219575i	$0.929533\pi$
$368$		0			0
$369$			8.60674i			0.448049i
$370$		0			0
$371$			1.91246i			0.0992899i
$372$		0			0
$373$	6.02617	+	3.47921i	0.312023	+	0.180147i	0.647831	−	0.761784i	$-0.275676\pi$
$373$	6.02617	+	3.47921i	0.312023	+	0.180147i	−0.335808	+	0.941930i	$0.609009\pi$
$374$		0			0
$375$	−12.5169	+	3.35389i	−0.646370	+	0.173194i
$376$		0			0
$377$	−6.17892	+	10.7022i	−0.318231	+	0.551192i
$378$		0			0
$379$	−1.08743	+	0.627828i	−0.0558575	+	0.0322494i	−0.527669	−	0.849450i	$-0.676934\pi$
$379$	−1.08743	+	0.627828i	−0.0558575	+	0.0322494i	0.471811	+	0.881700i	$0.343600\pi$
$380$		0			0
$381$		−	36.4016i		−	1.86491i
$382$		0			0
$383$	−29.3066	+	7.85269i	−1.49750	+	0.401254i	−0.912262	−	0.409608i	$-0.865666\pi$
$383$	−29.3066	+	7.85269i	−1.49750	+	0.401254i	−0.585238	+	0.810862i	$0.698999\pi$
$384$		0			0
$385$	0.165256	−	0.616745i	0.00842225	−	0.0314323i
$386$		0			0
$387$	7.20318	−	26.8826i	0.366158	−	1.36652i
$388$		0			0
$389$	−0.663952	−	2.47790i	−0.0336637	−	0.125635i	0.947049	−	0.321089i	$-0.104049\pi$
$389$	−0.663952	−	2.47790i	−0.0336637	−	0.125635i	−0.980713	+	0.195454i	$0.937382\pi$
$390$		0			0
$391$	2.36346	+	4.09364i	0.119525	+	0.207024i
$392$		0			0
$393$	−17.8798	+	17.8798i	−0.901918	+	0.901918i
$394$		0			0
$395$	−2.79313	−	4.83785i	−0.140538	−	0.243419i
$396$		0			0
$397$		−	27.6714i		−	1.38879i	−0.719595	−	0.694394i	$-0.755672\pi$
$397$		−	27.6714i		−	1.38879i	0.719595	−	0.694394i	$-0.244328\pi$
$398$		0			0
$399$	0.492046	−	0.492046i	0.0246331	−	0.0246331i
$400$		0			0
$401$	−1.74389	−	1.74389i	−0.0870858	−	0.0870858i	0.662222	−	0.749308i	$-0.269614\pi$
$401$	−1.74389	−	1.74389i	−0.0870858	−	0.0870858i	−0.749308	+	0.662222i	$0.769614\pi$
$402$		0			0
$403$	18.8570	+	10.8871i	0.939336	+	0.542326i
$404$		0			0
$405$	−3.38469	−	0.906926i	−0.168187	−	0.0450655i
$406$		0			0
$407$	−16.8338	+	18.8825i	−0.834419	+	0.935972i
$408$		0			0
$409$	2.12805	−	7.94201i	0.105226	−	0.392707i	−0.893145	−	0.449769i	$-0.851506\pi$
$409$	2.12805	−	7.94201i	0.105226	−	0.392707i	0.998371	+	0.0570616i	$0.0181731\pi$
$410$		0			0
$411$	−17.1848	+	29.7649i	−0.847664	+	1.46820i
$412$		0			0
$413$	−0.678688	+	0.678688i	−0.0333960	+	0.0333960i
$414$		0			0
$415$	−4.41104	−	4.41104i	−0.216530	−	0.216530i
$416$		0			0
$417$	17.5378			0.858831
$418$		0			0
$419$	−19.8643	+	11.4686i	−0.970433	+	0.560280i	−0.899368	−	0.437192i	$-0.855973\pi$
$419$	−19.8643	+	11.4686i	−0.970433	+	0.560280i	−0.0710645	+	0.997472i	$0.522640\pi$
$420$		0			0
$421$	−4.36261	−	4.36261i	−0.212621	−	0.212621i	0.592759	−	0.805380i	$-0.298039\pi$
$421$	−4.36261	−	4.36261i	−0.212621	−	0.212621i	−0.805380	+	0.592759i	$0.798039\pi$
$422$		0			0
$423$	16.3860	−	9.46048i	0.796716	−	0.459984i
$424$		0			0
$425$	−14.5489	+	3.89836i	−0.705724	+	0.189098i
$426$		0			0
$427$	1.12904	+	0.302525i	0.0546379	+	0.0146402i
$428$		0			0
$429$	−38.8557	−	10.4114i	−1.87597	−	0.502665i
$430$		0			0
$431$	−2.77321	−	10.3498i	−0.133581	−	0.498530i	0.866419	−	0.499318i	$-0.166416\pi$
$431$	−2.77321	−	10.3498i	−0.133581	−	0.498530i	−1.00000		0.000787611i	$0.999749\pi$
$432$		0			0
$433$	−6.55679			−0.315099			−0.157550	−	0.987511i	$-0.550359\pi$
$433$	−6.55679			−0.315099			−0.157550	+	0.987511i	$0.550359\pi$
$434$		0			0
$435$	2.18794	+	3.78963i	0.104904	+	0.181699i
$436$		0			0
$437$	−1.17300	−	0.677233i	−0.0561123	−	0.0323965i
$438$		0			0
$439$	−5.37238	−	20.0500i	−0.256410	−	0.956934i	−0.967301	−	0.253632i	$-0.918375\pi$
$439$	−5.37238	−	20.0500i	−0.256410	−	0.956934i	0.710891	−	0.703302i	$-0.248292\pi$
$440$		0			0
$441$	−12.4995	+	21.6498i	−0.595215	+	1.03094i
$442$		0			0
$443$	−8.86545			−0.421210			−0.210605	−	0.977571i	$-0.567543\pi$
$443$	−8.86545			−0.421210			−0.210605	+	0.977571i	$0.567543\pi$
$444$		0			0
$445$	5.72021			0.271164
$446$		0			0
$447$	−26.3444	+	45.6299i	−1.24605	+	2.15822i
$448$		0			0
$449$	5.78614	+	21.5942i	0.273065	+	1.01909i	0.957127	+	0.289668i	$0.0935450\pi$
$449$	5.78614	+	21.5942i	0.273065	+	1.01909i	−0.684062	+	0.729424i	$0.739788\pi$
$450$		0			0
$451$	−8.57068	−	4.94828i	−0.403578	−	0.233006i
$452$		0			0
$453$	13.8407	+	23.9728i	0.650293	+	1.12634i
$454$		0			0
$455$	−0.577329			−0.0270656
$456$		0			0
$457$	3.18628	+	11.8914i	0.149048	+	0.556255i	0.999542	+	0.0302697i	$0.00963662\pi$
$457$	3.18628	+	11.8914i	0.149048	+	0.556255i	−0.850494	+	0.525985i	$0.823697\pi$
$458$		0			0
$459$	4.87762	+	1.30696i	0.227668	+	0.0610035i
$460$		0			0
$461$	41.1652	+	11.0302i	1.91725	+	0.513726i	0.990385	+	0.138336i	$0.0441753\pi$
$461$	41.1652	+	11.0302i	1.91725	+	0.513726i	0.926867	+	0.375390i	$0.122491\pi$
$462$		0			0
$463$	−29.8430	+	7.99641i	−1.38692	+	0.371625i	−0.873631	−	0.486589i	$-0.838241\pi$
$463$	−29.8430	+	7.99641i	−1.38692	+	0.371625i	−0.513292	+	0.858214i	$0.671574\pi$
$464$		0			0
$465$	6.67723	−	3.85510i	0.309649	−	0.178776i
$466$		0			0
$467$	11.3491	+	11.3491i	0.525174	+	0.525174i	0.919130	−	0.393955i	$-0.128894\pi$
$467$	11.3491	+	11.3491i	0.525174	+	0.525174i	−0.393955	+	0.919130i	$0.628894\pi$
$468$		0			0
$469$	0.0311014	−	0.0179564i	0.00143613	−	0.000829149i
$470$		0			0
$471$	40.3790			1.86056
$472$		0			0
$473$	22.6287	+	22.6287i	1.04047	+	1.04047i
$474$		0			0
$475$	3.05183	−	3.05183i	0.140028	−	0.140028i
$476$		0			0
$477$	11.6603	−	20.1962i	0.533886	−	0.924718i
$478$		0			0
$479$	3.75547	−	14.0156i	0.171592	−	0.640389i	−0.825515	−	0.564379i	$-0.809115\pi$
$479$	3.75547	−	14.0156i	0.171592	−	0.640389i	0.997107	−	0.0760092i	$-0.0242178\pi$
$480$		0			0
$481$	20.4312	+	10.2834i	0.931581	+	0.468883i
$482$		0			0
$483$	−1.09441	−	0.293246i	−0.0497974	−	0.0133432i
$484$		0			0
$485$	−5.86963	−	3.38883i	−0.266526	−	0.153879i
$486$		0			0
$487$	2.12282	+	2.12282i	0.0961942	+	0.0961942i	0.753566	−	0.657372i	$-0.228332\pi$
$487$	2.12282	+	2.12282i	0.0961942	+	0.0961942i	−0.657372	+	0.753566i	$0.728332\pi$
$488$		0			0
$489$	−11.9442	+	11.9442i	−0.540137	+	0.540137i
$490$		0			0
$491$			5.86263i			0.264577i	0.991211	+	0.132288i	$0.0422325\pi$
$491$			5.86263i			0.264577i	−0.991211	+	0.132288i	$0.957767\pi$
$492$		0			0
$493$	5.23027	+	9.05909i	0.235559	+	0.408001i
$494$		0			0
$495$	−5.50545	+	5.50545i	−0.247452	+	0.247452i
$496$		0			0
$497$	0.203072	+	0.351731i	0.00910902	+	0.0157773i
$498$		0			0
$499$	6.82612	+	25.4754i	0.305579	+	1.14044i	0.932446	+	0.361310i	$0.117670\pi$
$499$	6.82612	+	25.4754i	0.305579	+	1.14044i	−0.626867	+	0.779126i	$0.715663\pi$
$500$		0			0
$501$	−8.20568	+	30.6240i	−0.366603	+	1.36818i
$502$		0			0
$503$	1.01864	−	3.80162i	0.0454189	−	0.169506i	−0.939491	−	0.342574i	$-0.888701\pi$
$503$	1.01864	−	3.80162i	0.0454189	−	0.169506i	0.984910	+	0.173068i	$0.0553680\pi$
$504$		0			0
$505$	7.80481	−	2.09129i	0.347309	−	0.0930613i
$506$		0			0
$507$			2.93251i			0.130237i
$508$		0			0
$509$	14.7791	−	8.53272i	0.655072	−	0.378206i	−0.135324	−	0.990801i	$-0.543208\pi$
$509$	14.7791	−	8.53272i	0.655072	−	0.378206i	0.790397	+	0.612595i	$0.209874\pi$
$510$		0			0
$511$	−0.513727	+	0.889802i	−0.0227260	+	0.0393625i
$512$		0			0
$513$	−1.39765	+	0.374499i	−0.0617077	+	0.0165345i
$514$		0			0
$515$	−6.46221	−	3.73096i	−0.284759	−	0.164406i
$516$		0			0
$517$			21.7565i			0.956850i
$518$		0			0
$519$		−	1.90879i		−	0.0837867i
$520$		0			0
$521$	−35.2639	−	20.3596i	−1.54494	−	0.891971i	−0.998516	−	0.0544629i	$-0.982655\pi$
$521$	−35.2639	−	20.3596i	−1.54494	−	0.891971i	−0.546424	−	0.837509i	$-0.684011\pi$
$522$		0			0
$523$	−8.32393	+	2.23039i	−0.363980	+	0.0975282i	−0.436174	−	0.899862i	$-0.643667\pi$
$523$	−8.32393	+	2.23039i	−0.363980	+	0.0975282i	0.0721936	+	0.997391i	$0.477000\pi$
$524$		0			0
$525$	1.80515	−	3.12661i	0.0787833	−	0.136457i
$526$		0			0
$527$	15.9619	−	9.21561i	0.695311	−	0.401438i
$528$		0			0
$529$		−	20.7946i		−	0.904114i
$530$		0			0
$531$	11.3051	−	3.02919i	0.490600	−	0.131456i
$532$		0			0
$533$	−2.31602	+	8.64350i	−0.100318	+	0.374392i
$534$		0			0
$535$	2.41014	−	8.99478i	0.104200	−	0.388878i
$536$		0			0
$537$	15.8598	+	59.1896i	0.684402	+	2.55422i
$538$		0			0
$539$	−14.3727	−	24.8943i	−0.619077	−	1.07227i
$540$		0			0
$541$	−17.0279	+	17.0279i	−0.732085	+	0.732085i	−0.971032	−	0.238948i	$-0.923198\pi$
$541$	−17.0279	+	17.0279i	−0.732085	+	0.732085i	0.238948	+	0.971032i	$0.423198\pi$
$542$		0			0
$543$	−12.8334	−	22.2281i	−0.550735	−	0.953901i
$544$		0			0
$545$			1.53590i			0.0657907i
$546$		0			0
$547$	28.0196	−	28.0196i	1.19803	−	1.19803i	0.223277	−	0.974755i	$-0.428324\pi$
$547$	28.0196	−	28.0196i	1.19803	−	1.19803i	0.974755	−	0.223277i	$-0.0716756\pi$
$548$		0			0
$549$	−10.0785	−	10.0785i	−0.430139	−	0.430139i
$550$		0			0
$551$	−2.59582	−	1.49870i	−0.110586	−	0.0638466i
$552$		0			0
$553$	3.09180	+	0.828445i	0.131477	+	0.0352291i
$554$		0			0
$555$	6.77080	−	4.44471i	0.287404	−	0.188668i
$556$		0			0
$557$	0.681281	−	2.54258i	0.0288668	−	0.107732i	−0.949989	−	0.312282i	$-0.898906\pi$
$557$	0.681281	−	2.54258i	0.0288668	−	0.107732i	0.978856	+	0.204550i	$0.0655731\pi$
$558$		0			0
$559$	14.4679	−	25.0591i	0.611927	−	1.05989i
$560$		0			0
$561$	−24.0773	+	24.0773i	−1.01654	+	1.01654i
$562$		0			0
$563$	26.9635	+	26.9635i	1.13637	+	1.13637i	0.989095	+	0.147280i	$0.0470517\pi$
$563$	26.9635	+	26.9635i	1.13637	+	1.13637i	0.147280	+	0.989095i	$0.452948\pi$
$564$		0			0
$565$	6.27700			0.264075
$566$		0			0
$567$	1.73881	−	1.00390i	0.0730232	−	0.0421599i
$568$		0			0
$569$	−13.5552	−	13.5552i	−0.568264	−	0.568264i	0.363378	−	0.931642i	$-0.381623\pi$
$569$	−13.5552	−	13.5552i	−0.568264	−	0.568264i	−0.931642	+	0.363378i	$0.881623\pi$
$570$		0			0
$571$	12.0499	−	6.95700i	0.504272	−	0.291142i	−0.226204	−	0.974080i	$-0.572632\pi$
$571$	12.0499	−	6.95700i	0.504272	−	0.291142i	0.730476	+	0.682938i	$0.239298\pi$
$572$		0			0
$573$	51.6982	−	13.8525i	2.15972	−	0.578696i
$574$		0			0
$575$	−6.78790	−	1.81881i	−0.283075	−	0.0758497i
$576$		0			0
$577$	−27.3782	−	7.33596i	−1.13977	−	0.305400i	−0.360910	−	0.932601i	$-0.617534\pi$
$577$	−27.3782	−	7.33596i	−1.13977	−	0.305400i	−0.778858	+	0.627201i	$0.784201\pi$
$578$		0			0
$579$	−7.03595	−	26.2585i	−0.292404	−	1.09127i
$580$		0			0
$581$	3.57439			0.148291
$582$		0			0
$583$	13.4077	+	23.2228i	0.555290	+	0.961790i
$584$		0			0
$585$	6.09677	+	3.51997i	0.252071	+	0.145533i
$586$		0			0
$587$	−6.20176	−	23.1453i	−0.255974	−	0.955308i	−0.967546	−	0.252695i	$-0.918683\pi$
$587$	−6.20176	−	23.1453i	−0.255974	−	0.955308i	0.711572	−	0.702613i	$-0.247983\pi$
$588$		0			0
$589$	−2.64067	+	4.57377i	−0.108807	+	0.188459i
$590$		0			0
$591$	11.8341			0.486788
$592$		0			0
$593$	−30.2397			−1.24179			−0.620897	−	0.783892i	$-0.713231\pi$
$593$	−30.2397			−1.24179			−0.620897	+	0.783892i	$0.713231\pi$
$594$		0			0
$595$	−0.244346	+	0.423219i	−0.0100172	+	0.0173503i
$596$		0			0
$597$	13.3239	+	49.7255i	0.545312	+	2.03513i
$598$		0			0
$599$	27.9974	+	16.1643i	1.14394	+	0.660456i	0.947404	−	0.320039i	$-0.103696\pi$
$599$	27.9974	+	16.1643i	1.14394	+	0.660456i	0.196540	+	0.980496i	$0.437029\pi$
$600$		0			0
$601$	4.56535	+	7.90743i	0.186225	+	0.322551i	0.943989	−	0.329978i	$-0.107041\pi$
$601$	4.56535	+	7.90743i	0.186225	+	0.322551i	−0.757764	+	0.652529i	$0.773708\pi$
$602$		0			0
$603$	−0.437920			−0.0178335
$604$		0			0
$605$	−0.843408	−	3.14764i	−0.0342894	−	0.127970i
$606$		0			0
$607$	−5.63295	−	1.50934i	−0.228634	−	0.0612624i	0.142683	−	0.989768i	$-0.454427\pi$
$607$	−5.63295	−	1.50934i	−0.228634	−	0.0612624i	−0.371317	+	0.928506i	$0.621094\pi$
$608$		0			0
$609$	−2.42190	−	0.648945i	−0.0981402	−	0.0262966i
$610$		0			0
$611$	19.0018	−	5.09151i	0.768730	−	0.205980i
$612$		0			0
$613$	13.7965	−	7.96541i	0.557235	−	0.321720i	−0.194800	−	0.980843i	$-0.562406\pi$
$613$	13.7965	−	7.96541i	0.557235	−	0.321720i	0.752035	+	0.659123i	$0.229072\pi$
$614$		0			0
$615$	2.24055	+	2.24055i	0.0903476	+	0.0903476i
$616$		0			0
$617$	−27.2288	+	15.7205i	−1.09619	+	0.632885i	−0.935217	−	0.354074i	$-0.884796\pi$
$617$	−27.2288	+	15.7205i	−1.09619	+	0.632885i	−0.160972	+	0.986959i	$0.551463\pi$
$618$		0			0
$619$	−39.5031			−1.58776			−0.793881	−	0.608073i	$-0.791943\pi$
$619$	−39.5031			−1.58776			−0.793881	+	0.608073i	$0.791943\pi$
$620$		0			0
$621$	1.66592	+	1.66592i	0.0668513	+	0.0668513i
$622$		0			0
$623$	−2.31762	+	2.31762i	−0.0928536	+	0.0928536i
$624$		0			0
$625$	10.5263	−	18.2321i	0.421051	−	0.729282i
$626$		0			0
$627$	2.52527	−	9.42445i	0.100850	−	0.376376i
$628$		0			0
$629$	16.1856	−	10.6251i	0.645361	−	0.423649i
$630$		0			0
$631$	10.5720	+	2.83276i	0.420864	+	0.112770i	0.463035	−	0.886340i	$-0.346761\pi$
$631$	10.5720	+	2.83276i	0.420864	+	0.112770i	−0.0421703	+	0.999110i	$0.513427\pi$
$632$		0			0
$633$	52.9104	+	30.5478i	2.10300	+	1.21417i
$634$		0			0
$635$	−5.17976	−	5.17976i	−0.205553	−	0.205553i
$636$		0			0
$637$	−18.3787	+	18.3787i	−0.728192	+	0.728192i
$638$		0			0
$639$		−	4.95252i		−	0.195919i
$640$		0			0
$641$	9.98316	+	17.2913i	0.394311	+	0.682967i	0.993013	−	0.118005i	$-0.0376500\pi$
$641$	9.98316	+	17.2913i	0.394311	+	0.682967i	−0.598702	+	0.800972i	$0.704317\pi$
$642$		0			0
$643$	−7.33949	+	7.33949i	−0.289441	+	0.289441i	−0.836859	−	0.547418i	$-0.815611\pi$
$643$	−7.33949	+	7.33949i	−0.289441	+	0.289441i	0.547418	+	0.836859i	$0.315611\pi$
$644$		0			0
$645$	−5.12305	−	8.87339i	−0.201720	−	0.349389i
$646$		0			0
$647$	−4.21236	−	15.7207i	−0.165605	−	0.618046i	−0.997962	−	0.0638065i	$-0.979676\pi$
$647$	−4.21236	−	15.7207i	−0.165605	−	0.618046i	0.832357	−	0.554239i	$-0.186991\pi$
$648$		0			0
$649$	−3.48316	+	12.9993i	−0.136726	+	0.510268i
$650$		0			0
$651$	−1.14343	+	4.26732i	−0.0448144	+	0.167250i
$652$		0			0
$653$	13.0872	−	3.50669i	0.512140	−	0.137227i	0.00651143	−	0.999979i	$-0.497927\pi$
$653$	13.0872	−	3.50669i	0.512140	−	0.137227i	0.505628	+	0.862751i	$0.331261\pi$
$654$		0			0
$655$			5.08841i			0.198821i
$656$		0			0
$657$	10.8502	−	6.26439i	0.423308	−	0.244397i
$658$		0			0
$659$	−1.66039	+	2.87588i	−0.0646797	+	0.112029i	−0.896552	−	0.442939i	$-0.853936\pi$
$659$	−1.66039	+	2.87588i	−0.0646797	+	0.112029i	0.831872	+	0.554967i	$0.187269\pi$
$660$		0			0
$661$	8.81827	−	2.36285i	0.342991	−	0.0919042i	−0.0832116	−	0.996532i	$-0.526518\pi$
$661$	8.81827	−	2.36285i	0.342991	−	0.0919042i	0.426203	+	0.904628i	$0.359851\pi$
$662$		0			0
$663$	26.6633	+	15.3941i	1.03552	+	0.597857i
$664$		0			0
$665$		−	0.140031i		−	0.00543017i
$666$		0			0
$667$			4.88045i			0.188972i
$668$		0			0
$669$	−32.9675	−	19.0338i	−1.27460	−	0.735888i
$670$		0			0
$671$	15.8307	−	4.24182i	0.611137	−	0.163754i
$672$		0			0
$673$	−2.14668	+	3.71816i	−0.0827484	+	0.143324i	−0.904430	−	0.426623i	$-0.859703\pi$
$673$	−2.14668	+	3.71816i	−0.0827484	+	0.143324i	0.821681	+	0.569947i	$0.193036\pi$
$674$		0			0
$675$	−6.50142	+	3.75360i	−0.250240	+	0.144476i
$676$		0			0
$677$		−	33.2544i		−	1.27807i	−0.769178	−	0.639035i	$-0.779334\pi$
$677$		−	33.2544i		−	1.27807i	0.769178	−	0.639035i	$-0.220666\pi$
$678$		0			0
$679$	3.75120	−	1.00513i	0.143958	−	0.0385734i
$680$		0			0
$681$	−5.41184	+	20.1973i	−0.207382	+	0.773960i
$682$		0			0
$683$	−12.4399	+	46.4263i	−0.475999	+	1.77645i	0.141560	+	0.989930i	$0.454788\pi$
$683$	−12.4399	+	46.4263i	−0.475999	+	1.77645i	−0.617559	+	0.786524i	$0.711878\pi$
$684$		0			0
$685$	1.79009	+	6.68070i	0.0683958	+	0.255257i
$686$		0			0
$687$	−2.27200	−	3.93522i	−0.0866822	−	0.150138i
$688$		0			0
$689$	17.1447	−	17.1447i	0.653162	−	0.653162i
$690$		0			0
$691$	0.893506	+	1.54760i	0.0339906	+	0.0588734i	0.882520	−	0.470274i	$-0.155845\pi$
$691$	0.893506	+	1.54760i	0.0339906	+	0.0588734i	−0.848530	+	0.529148i	$0.822512\pi$
$692$		0			0
$693$		−	4.46122i		−	0.169468i
$694$		0			0
$695$	2.49554	−	2.49554i	0.0946613	−	0.0946613i
$696$		0			0
$697$	5.35602	+	5.35602i	0.202874	+	0.202874i
$698$		0			0
$699$	−3.57289	−	2.06281i	−0.135139	−	0.0780226i
$700$		0			0
$701$	42.8692	+	11.4868i	1.61915	+	0.433849i	0.950751	−	0.309957i	$-0.100314\pi$
$701$	42.8692	+	11.4868i	1.61915	+	0.433849i	0.668396	+	0.743806i	$0.266981\pi$
$702$		0			0
$703$	−2.49424	+	4.95558i	−0.0940719	+	0.186903i
$704$		0			0
$705$	1.80289	−	6.72849i	0.0679009	−	0.253410i
$706$		0			0
$707$	−2.31491	+	4.00954i	−0.0870612	+	0.150794i
$708$		0			0
$709$	−25.7523	+	25.7523i	−0.967146	+	0.967146i	−0.999477	−	0.0323308i	$-0.989707\pi$
$709$	−25.7523	+	25.7523i	−0.967146	+	0.967146i	0.0323308	+	0.999477i	$0.489707\pi$
$710$		0			0
$711$	−27.5993	−	27.5993i	−1.03506	−	1.03506i
$712$		0			0
$713$	8.59923			0.322044
$714$		0			0
$715$	−7.01045	+	4.04748i	−0.262176	+	0.151367i
$716$		0			0
$717$	−33.3204	−	33.3204i	−1.24437	−	1.24437i
$718$		0			0
$719$	−17.8103	+	10.2828i	−0.664213	+	0.383484i	−0.793880	−	0.608074i	$-0.791942\pi$
$719$	−17.8103	+	10.2828i	−0.664213	+	0.383484i	0.129667	+	0.991558i	$0.458609\pi$
$720$		0			0
$721$	4.12990	−	1.10660i	0.153806	−	0.0412121i
$722$		0			0
$723$	0.674546	+	0.180744i	0.0250866	+	0.00672194i
$724$		0			0
$725$	−15.0214	−	4.02498i	−0.557881	−	0.149484i
$726$		0			0
$727$	10.5396	+	39.3344i	0.390893	+	1.45883i	0.828664	+	0.559746i	$0.189101\pi$
$727$	10.5396	+	39.3344i	0.390893	+	1.45883i	−0.437771	+	0.899087i	$0.644232\pi$
$728$		0			0
$729$	−36.7257			−1.36021
$730$		0			0
$731$	−12.2466	−	21.2118i	−0.452958	−	0.784547i
$732$		0			0
$733$	−5.51097	−	3.18176i	−0.203552	−	0.117521i	0.394759	−	0.918785i	$-0.370828\pi$
$733$	−5.51097	−	3.18176i	−0.203552	−	0.117521i	−0.598311	+	0.801264i	$0.704161\pi$
$734$		0			0
$735$	2.38205	+	8.88992i	0.0878631	+	0.327910i
$736$		0			0
$737$	0.251774	−	0.436085i	0.00927422	−	0.0160634i
$738$		0			0
$739$	−23.0713			−0.848690			−0.424345	−	0.905501i	$-0.639496\pi$
$739$	−23.0713			−0.848690			−0.424345	+	0.905501i	$0.639496\pi$
$740$		0			0
$741$	−8.82213			−0.324089
$742$		0			0
$743$	14.2247	−	24.6380i	0.521855	−	0.903880i	−0.477822	−	0.878457i	$-0.658573\pi$
$743$	14.2247	−	24.6380i	0.521855	−	0.903880i	0.999677	−	0.0254229i	$-0.00809323\pi$
$744$		0			0
$745$	2.74422	+	10.2416i	0.100541	+	0.375222i
$746$		0			0
$747$	−37.7467	−	21.7930i	−1.38108	−	0.797366i
$748$		0			0
$749$	2.66786	+	4.62086i	0.0974813	+	0.168843i
$750$		0			0
$751$	10.7992			0.394068			0.197034	−	0.980397i	$-0.436869\pi$
$751$	10.7992			0.394068			0.197034	+	0.980397i	$0.436869\pi$
$752$		0			0
$753$	−6.93518	−	25.8824i	−0.252732	−	0.943208i
$754$		0			0
$755$	5.38067	+	1.44175i	0.195823	+	0.0524705i
$756$		0			0
$757$	−41.0579	−	11.0014i	−1.49228	−	0.399854i	−0.581771	−	0.813353i	$-0.697640\pi$
$757$	−41.0579	−	11.0014i	−1.49228	−	0.399854i	−0.910505	+	0.413498i	$0.864307\pi$
$758$		0			0
$759$	−15.3452	+	4.11173i	−0.556995	+	0.149246i
$760$		0			0
$761$	9.19288	−	5.30751i	0.333242	−	0.192397i	−0.324038	−	0.946044i	$-0.605041\pi$
$761$	9.19288	−	5.30751i	0.333242	−	0.192397i	0.657279	+	0.753647i	$0.271707\pi$
$762$		0			0
$763$	−0.622291	−	0.622291i	−0.0225284	−	0.0225284i
$764$		0			0
$765$	5.16073	−	2.97955i	0.186587	−	0.107726i
$766$		0			0
$767$	12.1685			0.439380
$768$		0			0
$769$	10.2432	+	10.2432i	0.369380	+	0.369380i	0.867251	−	0.497871i	$-0.165885\pi$
$769$	10.2432	+	10.2432i	0.369380	+	0.369380i	−0.497871	+	0.867251i	$0.665885\pi$
$770$		0			0
$771$	−44.1008	+	44.1008i	−1.58825	+	1.58825i
$772$		0			0
$773$	13.6617	−	23.6627i	0.491377	−	0.851090i	−0.508574	−	0.861018i	$-0.669827\pi$
$773$	13.6617	−	23.6627i	0.491377	−	0.851090i	0.999951	+	0.00992855i	$0.00316041\pi$
$774$		0			0
$775$	−7.09191	+	26.4674i	−0.254749	+	0.950736i
$776$		0			0
$777$	−0.942447	+	4.54412i	−0.0338101	+	0.163019i
$778$		0			0
$779$	−2.09648	−	0.561750i	−0.0751142	−	0.0201268i
$780$		0			0
$781$	4.93177	+	2.84736i	0.176472	+	0.101886i
$782$		0			0
$783$	3.68664	+	3.68664i	0.131750	+	0.131750i
$784$		0			0
$785$	5.74572	−	5.74572i	0.205073	−	0.205073i
$786$		0			0
$787$		−	2.90029i		−	0.103384i	−0.998663	−	0.0516921i	$-0.983539\pi$
$787$		−	2.90029i		−	0.103384i	0.998663	−	0.0516921i	$-0.0164614\pi$
$788$		0			0
$789$	−21.7254	−	37.6295i	−0.773445	−	1.33965i
$790$		0			0
$791$	−2.54321	+	2.54321i	−0.0904263	+	0.0904263i
$792$		0			0
$793$	−7.40948	−	12.8336i	−0.263118	−	0.455734i
$794$		0			0
$795$	−2.22211	−	8.29301i	−0.0788100	−	0.294123i
$796$		0			0
$797$	10.3694	−	38.6991i	0.367302	−	1.37079i	−0.496970	−	0.867768i	$-0.665554\pi$
$797$	10.3694	−	38.6991i	0.367302	−	1.37079i	0.864273	−	0.503024i	$-0.167779\pi$
$798$		0			0
$799$	4.30981	−	16.0844i	0.152470	−	0.569026i
$800$		0			0
$801$	38.6053	−	10.3443i	1.36405	−	0.365497i
$802$		0			0
$803$			14.4064i			0.508390i
$804$		0			0
$805$	−0.197456	+	0.114001i	−0.00695942	+	0.00401802i
$806$		0			0
$807$	−3.21994	+	5.57710i	−0.113347	+	0.196323i
$808$		0			0
$809$	−21.1055	+	5.65519i	−0.742029	+	0.198826i	−0.609980	−	0.792417i	$-0.708822\pi$
$809$	−21.1055	+	5.65519i	−0.742029	+	0.198826i	−0.132049	+	0.991243i	$0.542156\pi$
$810$		0			0
$811$	2.77274	+	1.60084i	0.0973642	+	0.0562133i	0.547892	−	0.836549i	$-0.315431\pi$
$811$	2.77274	+	1.60084i	0.0973642	+	0.0562133i	−0.450527	+	0.892763i	$0.648764\pi$
$812$		0			0
$813$			67.0374i			2.35111i
$814$		0			0
$815$			3.39920i			0.119069i
$816$		0			0
$817$	6.07809	+	3.50919i	0.212645	+	0.122771i
$818$		0			0
$819$	−3.89636	+	1.04403i	−0.136150	+	0.0364812i
$820$		0			0
$821$	10.5454	−	18.2652i	0.368038	−	0.637460i	−0.621221	−	0.783636i	$-0.713363\pi$
$821$	10.5454	−	18.2652i	0.368038	−	0.637460i	0.989259	+	0.146175i	$0.0466963\pi$
$822$		0			0
$823$	−13.8815	+	8.01450i	−0.483880	+	0.279368i	−0.722032	−	0.691860i	$-0.756792\pi$
$823$	−13.8815	+	8.01450i	−0.483880	+	0.279368i	0.238152	+	0.971228i	$0.423458\pi$
$824$		0			0
$825$		−	50.6216i		−	1.76242i
$826$		0			0
$827$	31.9156	−	8.55175i	1.10981	−	0.297373i	0.343058	−	0.939314i	$-0.388537\pi$
$827$	31.9156	−	8.55175i	1.10981	−	0.297373i	0.766754	+	0.641941i	$0.221871\pi$
$828$		0			0
$829$	7.48085	−	27.9189i	0.259821	−	0.969664i	−0.705524	−	0.708686i	$-0.749288\pi$
$829$	7.48085	−	27.9189i	0.259821	−	0.969664i	0.965345	−	0.260978i	$-0.0840451\pi$
$830$		0			0
$831$	12.1594	−	45.3795i	0.421805	−	1.57420i
$832$		0			0
$833$	5.69427	+	21.2513i	0.197295	+	0.736314i
$834$		0			0
$835$	3.19001	+	5.52526i	0.110395	+	0.191210i
$836$		0			0
$837$	6.49577	−	6.49577i	0.224527	−	0.224527i
$838$		0			0
$839$	14.2369	+	24.6591i	0.491514	+	0.851327i	0.999952	−	0.00977112i	$-0.00311029\pi$
$839$	14.2369	+	24.6591i	0.491514	+	0.851327i	−0.508438	+	0.861098i	$0.669777\pi$
$840$		0			0
$841$		−	18.1997i		−	0.627576i
$842$		0			0
$843$	−55.5930	+	55.5930i	−1.91472	+	1.91472i
$844$		0			0
$845$	0.417280	+	0.417280i	0.0143549	+	0.0143549i
$846$		0			0
$847$	1.61703	+	0.933592i	0.0555618	+	0.0320786i
$848$		0			0
$849$	−75.8111	−	20.3135i	−2.60183	−	0.697158i
$850$		0			0
$851$	9.01841	−	0.517317i	0.309147	−	0.0177334i
$852$		0			0
$853$	−4.99961	+	18.6588i	−0.171184	+	0.638866i	0.825987	+	0.563690i	$0.190619\pi$
$853$	−4.99961	+	18.6588i	−0.171184	+	0.638866i	−0.997170	+	0.0751761i	$0.976048\pi$
$854$		0			0
$855$	−0.853769	+	1.47877i	−0.0291983	+	0.0505729i
$856$		0			0
$857$	9.55942	−	9.55942i	0.326544	−	0.326544i	−0.524727	−	0.851271i	$-0.675833\pi$
$857$	9.55942	−	9.55942i	0.326544	−	0.326544i	0.851271	+	0.524727i	$0.175833\pi$
$858$		0			0
$859$	−17.1237	−	17.1237i	−0.584254	−	0.584254i	0.351815	−	0.936069i	$-0.385565\pi$
$859$	−17.1237	−	17.1237i	−0.584254	−	0.584254i	−0.936069	+	0.351815i	$0.885565\pi$
$860$		0			0
$861$	−1.81558			−0.0618748
$862$		0			0
$863$	2.25254	−	1.30050i	0.0766773	−	0.0442696i	−0.461171	−	0.887311i	$-0.652571\pi$
$863$	2.25254	−	1.30050i	0.0766773	−	0.0442696i	0.537848	+	0.843042i	$0.319237\pi$
$864$		0			0
$865$	−0.271611	−	0.271611i	−0.00923506	−	0.00923506i
$866$		0			0
$867$	−15.3009	+	8.83396i	−0.519645	+	0.300017i
$868$		0			0
$869$	43.3514	−	11.6160i	1.47060	−	0.394045i
$870$		0			0
$871$	−0.439791	−	0.117842i	−0.0149017	−	0.00399291i
$872$		0			0
$873$	−45.7421	−	12.2565i	−1.54813	−	0.414821i
$874$		0			0
$875$	−0.386722	−	1.44327i	−0.0130736	−	0.0487913i
$876$		0			0
$877$	−26.8250			−0.905816			−0.452908	−	0.891557i	$-0.649613\pi$
$877$	−26.8250			−0.905816			−0.452908	+	0.891557i	$0.649613\pi$
$878$		0			0
$879$	5.46014	+	9.45724i	0.184166	+	0.318985i
$880$		0			0
$881$	8.84197	+	5.10491i	0.297894	+	0.171989i	0.641496	−	0.767126i	$-0.278314\pi$
$881$	8.84197	+	5.10491i	0.297894	+	0.171989i	−0.343603	+	0.939115i	$0.611647\pi$
$882$		0			0
$883$	8.91107	+	33.2566i	0.299881	+	1.11917i	0.937263	+	0.348624i	$0.113351\pi$
$883$	8.91107	+	33.2566i	0.299881	+	1.11917i	−0.637381	+	0.770549i	$0.719982\pi$
$884$		0			0
$885$	2.15442	−	3.73157i	0.0724202	−	0.125435i
$886$		0			0
$887$	24.5451			0.824144			0.412072	−	0.911151i	$-0.364805\pi$
$887$	24.5451			0.824144			0.412072	+	0.911151i	$0.364805\pi$
$888$		0			0
$889$	4.19731			0.140773
$890$		0			0
$891$	14.0761	−	24.3806i	0.471568	−	0.816780i
$892$		0			0
$893$	1.23495	+	4.60888i	0.0413259	+	0.154230i
$894$		0			0
$895$	10.6791	+	6.16561i	0.356965	+	0.206094i
$896$		0			0
$897$	7.18224	+	12.4400i	0.239808	+	0.415359i
$898$		0			0
$899$	19.0298			0.634681
$900$		0			0
$901$	−5.31194	−	19.8244i	−0.176966	−	0.660447i
$902$		0			0
$903$	5.67085	+	1.51950i	0.188714	+	0.0505658i
$904$		0			0
$905$	−4.98908	−	1.33682i	−0.165843	−	0.0444374i
$906$		0			0
$907$	46.9660	−	12.5845i	1.55948	−	0.417861i	0.626981	−	0.779035i	$-0.284290\pi$
$907$	46.9660	−	12.5845i	1.55948	−	0.417861i	0.932499	+	0.361174i	$0.117624\pi$
$908$		0			0
$909$	48.8923	−	28.2280i	1.62166	−	0.936264i
$910$		0			0
$911$	−25.0804	−	25.0804i	−0.830951	−	0.830951i	0.156696	−	0.987647i	$-0.449916\pi$
$911$	−25.0804	−	25.0804i	−0.830951	−	0.830951i	−0.987647	+	0.156696i	$0.949916\pi$
$912$		0			0
$913$	43.4035	−	25.0590i	1.43644	−	0.829332i
$914$		0			0
$915$	−5.24736			−0.173472
$916$		0			0
$917$	−2.06164	−	2.06164i	−0.0680814	−	0.0680814i
$918$		0			0
$919$	40.2335	−	40.2335i	1.32718	−	1.32718i	0.419361	−	0.907820i	$-0.362254\pi$
$919$	40.2335	−	40.2335i	1.32718	−	1.32718i	0.907820	−	0.419361i	$-0.137746\pi$
$920$		0			0
$921$	44.2580	−	76.6572i	1.45835	−	2.52594i
$922$		0			0
$923$	1.33269	−	4.97367i	0.0438661	−	0.163710i
$924$		0			0
$925$	−5.84537	+	28.1842i	−0.192195	+	0.926690i
$926$		0			0
$927$	−50.3600	−	13.4939i	−1.65404	−	0.443199i
$928$		0			0
$929$	−4.20850	−	2.42978i	−0.138076	−	0.0797185i	0.429370	−	0.903128i	$-0.358735\pi$
$929$	−4.20850	−	2.42978i	−0.138076	−	0.0797185i	−0.567447	+	0.823410i	$0.692069\pi$
$930$		0			0
$931$	−4.45776	−	4.45776i	−0.146097	−	0.146097i
$932$		0			0
$933$	−45.1114	+	45.1114i	−1.47688	+	1.47688i
$934$		0			0
$935$			6.85214i			0.224089i
$936$		0			0
$937$	−19.0638	−	33.0194i	−0.622786	−	1.07870i	−0.988965	−	0.148152i	$-0.952668\pi$
$937$	−19.0638	−	33.0194i	−0.622786	−	1.07870i	0.366179	−	0.930544i	$-0.380666\pi$
$938$		0			0
$939$	19.0180	−	19.0180i	0.620628	−	0.620628i
$940$		0			0
$941$	13.5124	+	23.4041i	0.440490	+	0.762952i	0.997726	−	0.0674027i	$-0.0214712\pi$
$941$	13.5124	+	23.4041i	0.440490	+	0.762952i	−0.557235	+	0.830355i	$0.688138\pi$
$942$		0			0
$943$	0.914659	+	3.41355i	0.0297854	+	0.111161i
$944$		0			0
$945$	−0.0630409	+	0.235272i	−0.00205072	+	0.00765340i
$946$		0			0
$947$	−3.97061	+	14.8185i	−0.129027	+	0.481537i	−0.999951	−	0.00988126i	$-0.996855\pi$
$947$	−3.97061	+	14.8185i	−0.129027	+	0.481537i	0.870924	+	0.491418i	$0.163521\pi$
$948$		0			0
$949$	12.5823	−	3.37141i	0.408438	−	0.109441i
$950$		0			0
$951$		−	67.4567i		−	2.18743i
$952$		0			0
$953$	6.95313	−	4.01439i	0.225234	−	0.130039i	−0.383137	−	0.923691i	$-0.625156\pi$
$953$	6.95313	−	4.01439i	0.225234	−	0.130039i	0.608371	+	0.793652i	$0.291823\pi$
$954$		0			0
$955$	5.38525	−	9.32752i	0.174263	−	0.301832i
$956$		0			0
$957$	−33.9584	+	9.09913i	−1.09772	+	0.294133i
$958$		0			0
$959$	−3.43206	−	1.98150i	−0.110827	−	0.0639860i
$960$		0			0
$961$		−	2.53011i		−	0.0816165i
$962$		0			0
$963$		−	65.0636i		−	2.09665i
$964$		0			0
$965$	−4.73763	−	2.73527i	−0.152510	−	0.0880515i
$966$		0			0
$967$	53.7080	−	14.3910i	1.72713	−	0.462784i	0.747614	−	0.664133i	$-0.231199\pi$
$967$	53.7080	−	14.3910i	1.72713	−	0.462784i	0.979520	+	0.201349i	$0.0645326\pi$
$968$		0			0
$969$	−3.73383	+	6.46719i	−0.119948	+	0.207756i
$970$		0			0
$971$	6.25891	−	3.61358i	0.200858	−	0.115965i	−0.396198	−	0.918165i	$-0.629671\pi$
$971$	6.25891	−	3.61358i	0.200858	−	0.115965i	0.597056	+	0.802200i	$0.296337\pi$
$972$		0			0
$973$			2.02221i			0.0648290i
$974$		0			0
$975$	−44.2120	+	11.8466i	−1.41592	+	0.379394i
$976$		0			0
$977$	1.91222	−	7.13651i	0.0611774	−	0.228317i	−0.928567	−	0.371164i	$-0.878959\pi$
$977$	1.91222	−	7.13651i	0.0611774	−	0.228317i	0.989745	+	0.142846i	$0.0456255\pi$
$978$		0			0
$979$	−11.8945	+	44.3908i	−0.380150	+	1.41874i
$980$		0			0
$981$	2.77748	+	10.3657i	0.0886780	+	0.330951i
$982$		0			0
$983$	16.5421	+	28.6517i	0.527610	+	0.913847i	0.999482	+	0.0321798i	$0.0102449\pi$
$983$	16.5421	+	28.6517i	0.527610	+	0.913847i	−0.471872	+	0.881667i	$0.656422\pi$
$984$		0			0
$985$	1.68393	−	1.68393i	0.0536543	−	0.0536543i
$986$		0			0
$987$	1.99567	+	3.45661i	0.0635230	+	0.110025i
$988$		0			0
$989$		−	11.4275i		−	0.363374i
$990$		0			0
$991$	19.2544	−	19.2544i	0.611635	−	0.611635i	−0.331737	−	0.943372i	$-0.607635\pi$
$991$	19.2544	−	19.2544i	0.611635	−	0.611635i	0.943372	+	0.331737i	$0.107635\pi$
$992$		0			0
$993$	19.5710	+	19.5710i	0.621066	+	0.621066i
$994$		0			0
$995$	8.97161	+	5.17976i	0.284419	+	0.164209i
$996$		0			0
$997$	−28.3214	−	7.58868i	−0.896946	−	0.240336i	−0.219242	−	0.975671i	$-0.570358\pi$
$997$	−28.3214	−	7.58868i	−0.896946	−	0.240336i	−0.677704	+	0.735334i	$0.737025\pi$
$998$		0			0
$999$	6.42163	−	7.20318i	0.203171	−	0.227899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.d.399.4	yes	16
4.3	odd	2	inner	592.2.be.d.399.1	yes	16
37.23	odd	12	inner	592.2.be.d.319.1	✓	16
148.23	even	12	inner	592.2.be.d.319.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.d.319.1	✓	16	37.23	odd	12	inner
592.2.be.d.319.4	yes	16	148.23	even	12	inner
592.2.be.d.399.1	yes	16	4.3	odd	2	inner
592.2.be.d.399.4	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28615 - 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(0.256864 + 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} +O(q^{10})\)	\(q+(1.28615 - 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(0.256864 + 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} +4.15876 q^{11} +(-0.973243 - 3.63219i) q^{13} +(-1.28615 - 0.344623i) q^{15} +(-3.07454 - 0.823821i) q^{17} +(0.880988 - 0.236060i) q^{19} +(0.660731 - 0.381473i) q^{21} +(-1.05009 - 1.05009i) q^{23} +(4.09808 - 2.36603i) q^{25} -1.58646 q^{27} +(-2.32382 - 2.32382i) q^{29} +(-4.09452 + 4.09452i) q^{31} +(5.34880 - 9.26439i) q^{33} +(0.0397369 - 0.148300i) q^{35} +(-4.04778 + 4.54042i) q^{37} +(-9.34310 - 2.50348i) q^{39} +(-2.06087 - 1.18985i) q^{41} +(5.44121 + 5.44121i) q^{43} +(-1.32382 + 1.32382i) q^{45} +5.23149i q^{47} +(-3.45601 - 5.98599i) q^{49} +(-5.78953 + 5.78953i) q^{51} +(3.22396 + 5.58407i) q^{53} +(-0.557168 - 2.07938i) q^{55} +(0.607218 - 2.26617i) q^{57} +(-0.837547 + 3.12577i) q^{59} +(3.80659 - 1.01997i) q^{61} -1.07273i q^{63} +(-1.68571 + 0.973243i) q^{65} +(0.0605407 - 0.104859i) q^{67} +(-3.68985 + 0.988691i) q^{69} +(1.18587 + 0.684665i) q^{71} +3.46410i q^{73} -12.1723i q^{75} +(1.06823 + 0.616745i) q^{77} +(10.4241 - 2.79313i) q^{79} +(3.38469 - 5.86246i) q^{81} +(10.4366 - 6.02559i) q^{83} +1.64764i q^{85} +(-8.16552 + 2.18794i) q^{87} +(-2.86010 + 10.6741i) q^{89} +(0.288665 - 1.07731i) q^{91} +(3.85510 + 14.3874i) q^{93} +(-0.236060 - 0.408868i) q^{95} +(9.25847 - 9.25847i) q^{97} +(-7.52059 - 13.0260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{5} - 4 q^{9}+O(q^{10}) \) 16 * q - 16 * q^5 - 4 * q^9	\( 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89} - 60 q^{93} - 4 q^{97}+O(q^{100}) \) 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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