LMFDB - Embedded newform 592.2.be.e.399.1

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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.1
Root			$3.11417i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.e.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55708 + 2.69695i) q^{3} +(-0.386109 - 1.44098i) q^{5} +(-1.53894 - 0.888509i) q^{7} +(-3.34902 - 5.80068i) q^{9} +O(q^{10})$	\(q+(-1.55708 + 2.69695i) q^{3} +(-0.386109 - 1.44098i) q^{5} +(-1.53894 - 0.888509i) q^{7} +(-3.34902 - 5.80068i) q^{9} +4.50616 q^{11} +(-0.816471 - 3.04711i) q^{13} +(4.48745 + 1.20241i) q^{15} +(1.00420 + 0.269074i) q^{17} +(2.33013 - 0.624355i) q^{19} +(4.79253 - 2.76697i) q^{21} +(-5.24867 - 5.24867i) q^{23} +(2.40279 - 1.38725i) q^{25} +11.5163 q^{27} +(3.77549 + 3.77549i) q^{29} +(-4.22131 + 4.22131i) q^{31} +(-7.01647 + 12.1529i) q^{33} +(-0.686123 + 2.56065i) q^{35} +(1.55878 - 5.87964i) q^{37} +(9.48921 + 2.54263i) q^{39} +(7.21484 + 4.16549i) q^{41} +(7.73682 + 7.73682i) q^{43} +(-7.06556 + 7.06556i) q^{45} -5.13543i q^{47} +(-1.92110 - 3.32745i) q^{49} +(-2.28930 + 2.28930i) q^{51} +(-3.45764 - 5.98880i) q^{53} +(-1.73987 - 6.49328i) q^{55} +(-1.94435 + 7.25640i) q^{57} +(2.71617 - 10.1369i) q^{59} +(4.78954 - 1.28335i) q^{61} +11.9025i q^{63} +(-4.07557 + 2.35303i) q^{65} +(6.03004 - 10.4443i) q^{67} +(22.3280 - 5.98278i) q^{69} +(-5.09087 - 2.93921i) q^{71} -1.33259i q^{73} +8.64026i q^{75} +(-6.93472 - 4.00376i) q^{77} +(-6.53795 + 1.75184i) q^{79} +(-7.88483 + 13.6569i) q^{81} +(-4.89869 + 2.82826i) q^{83} -1.55092i q^{85} +(-16.0610 + 4.30354i) q^{87} +(1.46168 - 5.45505i) q^{89} +(-1.45088 + 5.41477i) q^{91} +(-4.81172 - 17.9576i) q^{93} +(-1.79937 - 3.11659i) q^{95} +(-1.23082 + 1.23082i) q^{97} +(-15.0912 - 26.1388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

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
$3$	−1.55708	+	2.69695i	−0.898983	+	1.55708i	−0.0701865	+	0.997534i	$0.522359\pi$
$3$	−1.55708	+	2.69695i	−0.898983	+	1.55708i	−0.828796	+	0.559550i	$0.810974\pi$
$4$		0			0
$5$	−0.386109	−	1.44098i	−0.172673	−	0.644425i	−0.996936	−	0.0782183i	$-0.975077\pi$
$5$	−0.386109	−	1.44098i	−0.172673	−	0.644425i	0.824263	−	0.566207i	$-0.191590\pi$
$6$		0			0
$7$	−1.53894	−	0.888509i	−0.581666	−	0.335825i	0.180129	−	0.983643i	$-0.442348\pi$
$7$	−1.53894	−	0.888509i	−0.581666	−	0.335825i	−0.761795	+	0.647818i	$0.775682\pi$
$8$		0			0
$9$	−3.34902	−	5.80068i	−1.11634	−	1.93356i
$10$		0			0
$11$	4.50616			1.35866			0.679329	−	0.733834i	$-0.262271\pi$
$11$	4.50616			1.35866			0.679329	+	0.733834i	$0.262271\pi$
$12$		0			0
$13$	−0.816471	−	3.04711i	−0.226448	−	0.845116i	−0.981819	−	0.189819i	$-0.939210\pi$
$13$	−0.816471	−	3.04711i	−0.226448	−	0.845116i	0.755371	−	0.655297i	$-0.227457\pi$
$14$		0			0
$15$	4.48745	+	1.20241i	1.15865	+	0.310461i
$16$		0			0
$17$	1.00420	+	0.269074i	0.243554	+	0.0652602i	0.378531	−	0.925589i	$-0.376429\pi$
$17$	1.00420	+	0.269074i	0.243554	+	0.0652602i	−0.134977	+	0.990849i	$0.543096\pi$
$18$		0			0
$19$	2.33013	−	0.624355i	0.534568	−	0.143237i	0.0185709	−	0.999828i	$-0.494088\pi$
$19$	2.33013	−	0.624355i	0.534568	−	0.143237i	0.515997	+	0.856591i	$0.327422\pi$
$20$		0			0
$21$	4.79253	−	2.76697i	1.04582	−	0.603802i
$22$		0			0
$23$	−5.24867	−	5.24867i	−1.09442	−	1.09442i	−0.995050	−	0.0993737i	$-0.968316\pi$
$23$	−5.24867	−	5.24867i	−1.09442	−	1.09442i	−0.0993737	−	0.995050i	$-0.531684\pi$
$24$		0			0
$25$	2.40279	−	1.38725i	0.480557	−	0.277450i
$26$		0			0
$27$	11.5163			2.21632
$28$		0			0
$29$	3.77549	+	3.77549i	0.701090	+	0.701090i	0.964645	−	0.263554i	$-0.0848949\pi$
$29$	3.77549	+	3.77549i	0.701090	+	0.701090i	−0.263554	+	0.964645i	$0.584895\pi$
$30$		0			0
$31$	−4.22131	+	4.22131i	−0.758169	+	0.758169i	−0.975989	−	0.217820i	$-0.930105\pi$
$31$	−4.22131	+	4.22131i	−0.758169	+	0.758169i	0.217820	+	0.975989i	$0.430105\pi$
$32$		0			0
$33$	−7.01647	+	12.1529i	−1.22141	+	2.11554i
$34$		0			0
$35$	−0.686123	+	2.56065i	−0.115976	+	0.432828i
$36$		0			0
$37$	1.55878	−	5.87964i	0.256263	−	0.966607i
$37$	1.55878	−	5.87964i	0.256263	−	0.966607i
$38$		0			0
$39$	9.48921	+	2.54263i	1.51949	+	0.407146i
$40$		0			0
$41$	7.21484	+	4.16549i	1.12677	+	0.650541i	0.943120	−	0.332451i	$-0.107876\pi$
$41$	7.21484	+	4.16549i	1.12677	+	0.650541i	0.183649	+	0.982992i	$0.441209\pi$
$42$		0			0
$43$	7.73682	+	7.73682i	1.17985	+	1.17985i	0.979781	+	0.200073i	$0.0641180\pi$
$43$	7.73682	+	7.73682i	1.17985	+	1.17985i	0.200073	+	0.979781i	$0.435882\pi$
$44$		0			0
$45$	−7.06556	+	7.06556i	−1.05327	+	1.05327i
$46$		0			0
$47$		−	5.13543i		−	0.749080i	−0.927211	−	0.374540i	$-0.877801\pi$
$47$		−	5.13543i		−	0.749080i	0.927211	−	0.374540i	$-0.122199\pi$
$48$		0			0
$49$	−1.92110	−	3.32745i	−0.274443	−	0.475350i
$50$		0			0
$51$	−2.28930	+	2.28930i	−0.320567	+	0.320567i
$52$		0			0
$53$	−3.45764	−	5.98880i	−0.474943	−	0.822625i	0.524645	−	0.851321i	$-0.324198\pi$
$53$	−3.45764	−	5.98880i	−0.474943	−	0.822625i	−0.999588	+	0.0286958i	$0.990865\pi$
$54$		0			0
$55$	−1.73987	−	6.49328i	−0.234604	−	0.875553i
$56$		0			0
$57$	−1.94435	+	7.25640i	−0.257535	+	0.961134i
$58$		0			0
$59$	2.71617	−	10.1369i	0.353616	−	1.31971i	−0.528602	−	0.848870i	$-0.677284\pi$
$59$	2.71617	−	10.1369i	0.353616	−	1.31971i	0.882218	−	0.470842i	$-0.156050\pi$
$60$		0			0
$61$	4.78954	−	1.28335i	0.613238	−	0.164317i	0.0611861	−	0.998126i	$-0.480512\pi$
$61$	4.78954	−	1.28335i	0.613238	−	0.164317i	0.552052	+	0.833810i	$0.313845\pi$
$62$		0			0
$63$			11.9025i			1.49958i
$64$		0			0
$65$	−4.07557	+	2.35303i	−0.505513	+	0.291858i
$66$		0			0
$67$	6.03004	−	10.4443i	0.736687	−	1.27598i	−0.217292	−	0.976107i	$-0.569722\pi$
$67$	6.03004	−	10.4443i	0.736687	−	1.27598i	0.953979	−	0.299873i	$-0.0969443\pi$
$68$		0			0
$69$	22.3280	−	5.98278i	2.68798	−	0.720242i
$70$		0			0
$71$	−5.09087	−	2.93921i	−0.604175	−	0.348820i	0.166507	−	0.986040i	$-0.446751\pi$
$71$	−5.09087	−	2.93921i	−0.604175	−	0.348820i	−0.770682	+	0.637220i	$0.780084\pi$
$72$		0			0
$73$		−	1.33259i		−	0.155968i	−0.996955	−	0.0779842i	$-0.975152\pi$
$73$		−	1.33259i		−	0.155968i	0.996955	−	0.0779842i	$-0.0248484\pi$
$74$		0			0
$75$			8.64026i			0.997691i
$76$		0			0
$77$	−6.93472	−	4.00376i	−0.790285	−	0.456271i
$78$		0			0
$79$	−6.53795	+	1.75184i	−0.735577	+	0.197097i	−0.607111	−	0.794617i	$-0.707672\pi$
$79$	−6.53795	+	1.75184i	−0.735577	+	0.197097i	−0.128466	+	0.991714i	$0.541005\pi$
$80$		0			0
$81$	−7.88483	+	13.6569i	−0.876092	+	1.51744i
$82$		0			0
$83$	−4.89869	+	2.82826i	−0.537702	+	0.310442i	−0.744147	−	0.668016i	$-0.767144\pi$
$83$	−4.89869	+	2.82826i	−0.537702	+	0.310442i	0.206445	+	0.978458i	$0.433810\pi$
$84$		0			0
$85$		−	1.55092i		−	0.168221i
$86$		0			0
$87$	−16.0610	+	4.30354i	−1.72192	+	0.461388i
$88$		0			0
$89$	1.46168	−	5.45505i	0.154937	−	0.578234i	−0.844173	−	0.536070i	$-0.819908\pi$
$89$	1.46168	−	5.45505i	0.154937	−	0.578234i	0.999111	−	0.0421636i	$-0.0134251\pi$
$90$		0			0
$91$	−1.45088	+	5.41477i	−0.152094	+	0.567622i
$92$		0			0
$93$	−4.81172	−	17.9576i	−0.498952	−	1.86211i
$94$		0			0
$95$	−1.79937	−	3.11659i	−0.184611	−	0.319756i
$96$		0			0
$97$	−1.23082	+	1.23082i	−0.124971	+	0.124971i	−0.766826	−	0.641855i	$-0.778165\pi$
$97$	−1.23082	+	1.23082i	−0.124971	+	0.124971i	0.641855	+	0.766826i	$0.278165\pi$
$98$		0			0
$99$	−15.0912	−	26.1388i	−1.51672	−	2.62704i
$100$		0			0
$101$			7.97888i			0.793928i	0.917834	+	0.396964i	$0.129936\pi$
$101$			7.97888i			0.793928i	−0.917834	+	0.396964i	$0.870064\pi$
$102$		0			0
$103$	−1.81696	+	1.81696i	−0.179031	+	0.179031i	−0.790933	−	0.611902i	$-0.790404\pi$
$103$	−1.81696	+	1.81696i	−0.179031	+	0.179031i	0.611902	+	0.790933i	$0.290404\pi$
$104$		0			0
$105$	−5.83758	−	5.83758i	−0.569690	−	0.569690i
$106$		0			0
$107$	−12.3662	−	7.13965i	−1.19549	−	0.690216i	−0.235943	−	0.971767i	$-0.575818\pi$
$107$	−12.3662	−	7.13965i	−1.19549	−	0.690216i	−0.959546	+	0.281551i	$0.909151\pi$
$108$		0			0
$109$	14.1264	+	3.78516i	1.35306	+	0.362552i	0.861264	−	0.508157i	$-0.169673\pi$
$109$	14.1264	+	3.78516i	1.35306	+	0.362552i	0.491798	+	0.870709i	$0.336340\pi$
$110$		0			0
$111$	13.4299	+	13.3591i	1.27471	+	1.26799i
$112$		0			0
$113$	4.29710	−	16.0370i	0.404237	−	1.50863i	−0.401222	−	0.915981i	$-0.631415\pi$
$113$	4.29710	−	16.0370i	0.404237	−	1.50863i	0.805459	−	0.592651i	$-0.201919\pi$
$114$		0			0
$115$	−5.53667	+	9.58979i	−0.516297	+	0.894252i
$116$		0			0
$117$	−14.9409	+	14.9409i	−1.38129	+	1.38129i
$118$		0			0
$119$	−1.30633	−	1.30633i	−0.119751	−	0.119751i
$120$		0			0
$121$	9.30545			0.845950
$122$		0			0
$123$	−22.4682	+	12.9720i	−2.02589	+	1.16965i
$124$		0			0
$125$	−8.20109	−	8.20109i	−0.733527	−	0.733527i
$126$		0			0
$127$	15.7276	−	9.08036i	1.39560	−	0.805751i	0.401674	−	0.915783i	$-0.368428\pi$
$127$	15.7276	−	9.08036i	1.39560	−	0.805751i	0.993928	+	0.110031i	$0.0350951\pi$
$128$		0			0
$129$	−32.9127	+	8.81893i	−2.89780	+	0.776463i
$130$		0			0
$131$	−12.9139	−	3.46027i	−1.12829	−	0.302325i	−0.354058	−	0.935224i	$-0.615198\pi$
$131$	−12.9139	−	3.46027i	−1.12829	−	0.302325i	−0.774235	+	0.632899i	$0.781865\pi$
$132$		0			0
$133$	−4.14068	−	1.10949i	−0.359042	−	0.0962051i
$134$		0			0
$135$	−4.44656	−	16.5948i	−0.382699	−	1.42825i
$136$		0			0
$137$	−16.6081			−1.41893			−0.709464	−	0.704741i	$-0.751063\pi$
$137$	−16.6081			−1.41893			−0.709464	+	0.704741i	$0.751063\pi$
$138$		0			0
$139$	6.27427	+	10.8674i	0.532176	+	0.921757i	0.999294	+	0.0375616i	$0.0119590\pi$
$139$	6.27427	+	10.8674i	0.532176	+	0.921757i	−0.467118	+	0.884195i	$0.654708\pi$
$140$		0			0
$141$	13.8500	+	7.99630i	1.16638	+	0.673410i
$142$		0			0
$143$	−3.67914	−	13.7308i	−0.307666	−	1.14822i
$144$		0			0
$145$	3.98265	−	6.89815i	0.330741	−	0.572860i
$146$		0			0
$147$	11.9653			0.986879
$148$		0			0
$149$	14.8042			1.21280			0.606402	−	0.795158i	$-0.292612\pi$
$149$	14.8042			1.21280			0.606402	+	0.795158i	$0.292612\pi$
$150$		0			0
$151$	2.15321	−	3.72947i	0.175226	−	0.303500i	−0.765013	−	0.644014i	$-0.777268\pi$
$151$	2.15321	−	3.72947i	0.175226	−	0.303500i	0.940239	+	0.340514i	$0.110601\pi$
$152$		0			0
$153$	−1.80227	−	6.72617i	−0.145705	−	0.543779i
$154$		0			0
$155$	7.71270	+	4.45293i	0.619499	+	0.357668i
$156$		0			0
$157$	11.9714	+	20.7351i	0.955425	+	1.65484i	0.733393	+	0.679804i	$0.237935\pi$
$157$	11.9714	+	20.7351i	0.955425	+	1.65484i	0.222031	+	0.975040i	$0.428731\pi$
$158$		0			0
$159$	21.5353			1.70786
$160$		0			0
$161$	3.41391	+	12.7409i	0.269054	+	1.00412i
$162$		0			0
$163$	−20.2462	−	5.42496i	−1.58581	−	0.424916i	−0.645089	−	0.764107i	$-0.723180\pi$
$163$	−20.2462	−	5.42496i	−1.58581	−	0.424916i	−0.940717	+	0.339191i	$0.889847\pi$
$164$		0			0
$165$	20.2212	+	5.41824i	1.57422	+	0.421810i
$166$		0			0
$167$	−1.00006	+	0.267964i	−0.0773867	+	0.0207357i	−0.297305	−	0.954783i	$-0.596088\pi$
$167$	−1.00006	+	0.267964i	−0.0773867	+	0.0207357i	0.219918	+	0.975518i	$0.429421\pi$
$168$		0			0
$169$	2.64008	−	1.52425i	0.203083	−	0.117250i
$170$		0			0
$171$	−11.4253	−	11.4253i	−0.873716	−	0.873716i
$172$		0			0
$173$	−8.83349	+	5.10002i	−0.671598	+	0.387747i	−0.796682	−	0.604399i	$-0.793413\pi$
$173$	−8.83349	+	5.10002i	−0.671598	+	0.387747i	0.125084	+	0.992146i	$0.460080\pi$
$174$		0			0
$175$	−4.93034			−0.372698
$176$		0			0
$177$	23.1094	+	23.1094i	1.73701	+	1.73701i
$178$		0			0
$179$	0.932835	−	0.932835i	0.0697234	−	0.0697234i	−0.671385	−	0.741109i	$-0.734300\pi$
$179$	0.932835	−	0.932835i	0.0697234	−	0.0697234i	0.741109	+	0.671385i	$0.234300\pi$
$180$		0			0
$181$	−8.16068	+	14.1347i	−0.606579	+	1.05063i	0.385221	+	0.922824i	$0.374125\pi$
$181$	−8.16068	+	14.1347i	−0.606579	+	1.05063i	−0.991800	+	0.127801i	$0.959208\pi$
$182$		0			0
$183$	−3.99658	+	14.9154i	−0.295436	+	1.10258i
$184$		0			0
$185$	−9.07430	+	0.0240085i	−0.667156	+	0.00176514i
$186$		0			0
$187$	4.52508	+	1.21249i	0.330907	+	0.0886662i
$188$		0			0
$189$	−17.7230	−	10.2324i	−1.28916	−	0.744295i
$190$		0			0
$191$	7.38978	+	7.38978i	0.534706	+	0.534706i	0.921969	−	0.387263i	$-0.126580\pi$
$191$	7.38978	+	7.38978i	0.534706	+	0.534706i	−0.387263	+	0.921969i	$0.626580\pi$
$192$		0			0
$193$	−6.37281	+	6.37281i	−0.458725	+	0.458725i	−0.898237	−	0.439512i	$-0.855151\pi$
$193$	−6.37281	+	6.37281i	−0.458725	+	0.458725i	0.439512	+	0.898237i	$0.355151\pi$
$194$		0			0
$195$		−	14.6555i		−	1.04950i
$196$		0			0
$197$	−5.36425	−	9.29115i	−0.382187	−	0.661967i	0.609188	−	0.793026i	$-0.291496\pi$
$197$	−5.36425	−	9.29115i	−0.382187	−	0.661967i	−0.991375	+	0.131059i	$0.958162\pi$
$198$		0			0
$199$	1.51856	−	1.51856i	0.107648	−	0.107648i	−0.651231	−	0.758879i	$-0.725747\pi$
$199$	1.51856	−	1.51856i	0.107648	−	0.107648i	0.758879	+	0.651231i	$0.225747\pi$
$200$		0			0
$201$	18.7786	+	32.5254i	1.32454	+	2.29417i
$202$		0			0
$203$	−2.45570	−	9.16481i	−0.172357	−	0.643244i
$204$		0			0
$205$	3.21667	−	12.0048i	0.224662	−	0.838450i
$206$		0			0
$207$	−12.8679	+	48.0238i	−0.894383	+	3.33788i
$208$		0			0
$209$	10.4999	−	2.81344i	0.726294	−	0.194610i
$210$		0			0
$211$			17.9619i			1.23655i	0.785962	+	0.618274i	$0.212168\pi$
$211$			17.9619i			1.23655i	−0.785962	+	0.618274i	$0.787832\pi$
$212$		0			0
$213$	15.8538	−	9.15320i	1.08629	−	0.627167i
$214$		0			0
$215$	8.16134	−	14.1359i	0.556599	−	0.964057i
$216$		0			0
$217$	10.2470	−	2.74568i	0.695613	−	0.186389i
$218$		0			0
$219$	3.59394	+	2.07496i	0.242856	+	0.140213i
$220$		0			0
$221$		−	3.27960i		−	0.220610i
$222$		0			0
$223$			4.09362i			0.274129i	0.990562	+	0.137065i	$0.0437668\pi$
$223$			4.09362i			0.274129i	−0.990562	+	0.137065i	$0.956233\pi$
$224$		0			0
$225$	−16.0940	−	9.29186i	−1.07293	−	0.619457i
$226$		0			0
$227$	19.3365	−	5.18119i	1.28341	−	0.343888i	0.448254	−	0.893906i	$-0.352046\pi$
$227$	19.3365	−	5.18119i	1.28341	−	0.343888i	0.835152	+	0.550019i	$0.185379\pi$
$228$		0			0
$229$	−12.6060	+	21.8342i	−0.833025	+	1.44284i	0.0626028	+	0.998039i	$0.480060\pi$
$229$	−12.6060	+	21.8342i	−0.833025	+	1.44284i	−0.895628	+	0.444804i	$0.853273\pi$
$230$		0			0
$231$	21.5959	−	12.4684i	1.42090	−	0.820360i
$232$		0			0
$233$			29.1142i			1.90734i	0.300860	+	0.953668i	$0.402726\pi$
$233$			29.1142i			1.90734i	−0.300860	+	0.953668i	$0.597274\pi$
$234$		0			0
$235$	−7.40005	+	1.98284i	−0.482726	+	0.129346i
$236$		0			0
$237$	5.45552	−	20.3603i	0.354374	−	1.32254i
$238$		0			0
$239$	1.47175	−	5.49263i	0.0951994	−	0.355289i	−0.901850	−	0.432049i	$-0.857791\pi$
$239$	1.47175	−	5.49263i	0.0951994	−	0.355289i	0.997050	+	0.0767598i	$0.0244575\pi$
$240$		0			0
$241$	−4.86393	−	18.1524i	−0.313313	−	1.16930i	−0.925550	−	0.378626i	$-0.876397\pi$
$241$	−4.86393	−	18.1524i	−0.313313	−	1.16930i	0.612237	−	0.790674i	$-0.290270\pi$
$242$		0			0
$243$	−7.28019	−	12.6097i	−0.467024	−	0.808910i
$244$		0			0
$245$	−4.05303	+	4.05303i	−0.258938	+	0.258938i
$246$		0			0
$247$	−3.80496	−	6.59038i	−0.242104	−	0.419336i
$248$		0			0
$249$		−	17.6154i		−	1.11633i
$250$		0			0
$251$	17.3059	−	17.3059i	1.09234	−	1.09234i	0.0970593	−	0.995279i	$-0.469056\pi$
$251$	17.3059	−	17.3059i	1.09234	−	1.09234i	0.995279	−	0.0970593i	$-0.0309437\pi$
$252$		0			0
$253$	−23.6513	−	23.6513i	−1.48695	−	1.48695i
$254$		0			0
$255$	4.18276	+	2.41492i	0.261935	+	0.151228i
$256$		0			0
$257$	−13.4767	−	3.61108i	−0.840654	−	0.225253i	−0.187298	−	0.982303i	$-0.559973\pi$
$257$	−13.4767	−	3.61108i	−0.840654	−	0.225253i	−0.653356	+	0.757050i	$0.726640\pi$
$258$		0			0
$259$	−7.62300	+	7.66344i	−0.473670	+	0.476183i
$260$		0			0
$261$	9.25618	−	34.5446i	0.572943	−	2.13825i
$262$		0			0
$263$	−0.377548	+	0.653932i	−0.0232806	+	0.0403232i	−0.877431	−	0.479703i	$-0.840744\pi$
$263$	−0.377548	+	0.653932i	−0.0232806	+	0.0403232i	0.854150	+	0.520026i	$0.174078\pi$
$264$		0			0
$265$	−7.29471	+	7.29471i	−0.448111	+	0.448111i
$266$		0			0
$267$	12.4360	+	12.4360i	0.761073	+	0.761073i
$268$		0			0
$269$	−22.9471			−1.39911			−0.699555	−	0.714578i	$-0.746619\pi$
$269$	−22.9471			−1.39911			−0.699555	+	0.714578i	$0.746619\pi$
$270$		0			0
$271$	10.2100	−	5.89476i	0.620215	−	0.358081i	−0.156738	−	0.987640i	$-0.550098\pi$
$271$	10.2100	−	5.89476i	0.620215	−	0.358081i	0.776953	+	0.629559i	$0.216764\pi$
$272$		0			0
$273$	−12.3442	−	12.3442i	−0.747106	−	0.747106i
$274$		0			0
$275$	10.8273	−	6.25116i	0.652913	−	0.376959i
$276$		0			0
$277$	30.1787	−	8.08636i	1.81326	−	0.485862i	0.817346	−	0.576148i	$-0.195445\pi$
$277$	30.1787	−	8.08636i	1.81326	−	0.485862i	0.995916	+	0.0902856i	$0.0287780\pi$
$278$		0			0
$279$	38.6237	+	10.3492i	2.31234	+	0.619590i
$280$		0			0
$281$	0.193586	+	0.0518713i	0.0115484	+	0.00309438i	0.264589	−	0.964361i	$-0.414764\pi$
$281$	0.193586	+	0.0518713i	0.0115484	+	0.00309438i	−0.253040	+	0.967456i	$0.581431\pi$
$282$		0			0
$283$	3.60439	+	13.4518i	0.214259	+	0.799624i	0.986426	+	0.164205i	$0.0525059\pi$
$283$	3.60439	+	13.4518i	0.214259	+	0.799624i	−0.772168	+	0.635419i	$0.780827\pi$
$284$		0			0
$285$	11.2071			0.663849
$286$		0			0
$287$	−7.40216	−	12.8209i	−0.436935	−	0.756794i
$288$		0			0
$289$	−13.7864	−	7.95959i	−0.810966	−	0.468211i
$290$		0			0
$291$	−1.40297	−	5.23596i	−0.0822436	−	0.306937i
$292$		0			0
$293$	2.63678	−	4.56703i	0.154042	−	0.266809i	−0.778668	−	0.627436i	$-0.784104\pi$
$293$	2.63678	−	4.56703i	0.154042	−	0.266809i	0.932710	+	0.360628i	$0.117438\pi$
$294$		0			0
$295$	−15.6558			−0.911515
$296$		0			0
$297$	51.8944			3.01122
$298$		0			0
$299$	−11.7079	+	20.2787i	−0.677085	+	1.17275i
$300$		0			0
$301$	−5.03229	−	18.7808i	−0.290056	−	1.08251i
$302$		0			0
$303$	−21.5186	−	12.4238i	−1.23621	−	0.713728i
$304$		0			0
$305$	−3.69857	−	6.40612i	−0.211780	−	0.366813i
$306$		0			0
$307$	−12.9562			−0.739447			−0.369724	−	0.929142i	$-0.620548\pi$
$307$	−12.9562			−0.739447			−0.369724	+	0.929142i	$0.620548\pi$
$308$		0			0
$309$	−2.07109	−	7.72942i	−0.117820	−	0.439712i
$310$		0			0
$311$	−10.3402	−	2.77065i	−0.586340	−	0.157109i	−0.0465598	−	0.998916i	$-0.514826\pi$
$311$	−10.3402	−	2.77065i	−0.586340	−	0.157109i	−0.539780	+	0.841806i	$0.681492\pi$
$312$		0			0
$313$	1.84596	+	0.494623i	0.104340	+	0.0279578i	0.310611	−	0.950537i	$-0.399466\pi$
$313$	1.84596	+	0.494623i	0.104340	+	0.0279578i	−0.206271	+	0.978495i	$0.566133\pi$
$314$		0			0
$315$	17.1513	−	4.59568i	0.966367	−	0.258937i
$316$		0			0
$317$	4.48468	−	2.58923i	0.251885	−	0.145426i	−0.368742	−	0.929532i	$-0.620211\pi$
$317$	4.48468	−	2.58923i	0.251885	−	0.145426i	0.620627	+	0.784106i	$0.286878\pi$
$318$		0			0
$319$	17.0129	+	17.0129i	0.952541	+	0.952541i
$320$		0			0
$321$	38.5105	−	22.2341i	2.14945	−	1.24098i
$322$		0			0
$323$	2.50791			0.139544
$324$		0			0
$325$	−6.18891	−	6.18891i	−0.343299	−	0.343299i
$326$		0			0
$327$	−32.2043	+	32.2043i	−1.78090	+	1.78090i
$328$		0			0
$329$	−4.56288	+	7.90314i	−0.251560	+	0.435714i
$330$		0			0
$331$	1.79053	−	6.68236i	0.0984166	−	0.367296i	−0.899099	−	0.437746i	$-0.855777\pi$
$331$	1.79053	−	6.68236i	0.0984166	−	0.367296i	0.997515	+	0.0704502i	$0.0224436\pi$
$332$		0			0
$333$	−39.3263	+	10.6490i	−2.15507	+	0.583564i
$334$		0			0
$335$	−17.3783	−	4.65651i	−0.949480	−	0.254412i
$336$		0			0
$337$	16.8160	+	9.70871i	0.916025	+	0.528867i	0.882365	−	0.470566i	$-0.155950\pi$
$337$	16.8160	+	9.70871i	0.916025	+	0.528867i	0.0336599	+	0.999433i	$0.489284\pi$
$338$		0			0
$339$	36.5600	+	36.5600i	1.98566	+	1.98566i
$340$		0			0
$341$	−19.0219	+	19.0219i	−1.03009	+	1.03009i
$342$		0			0
$343$			19.2668i			1.04031i
$344$		0			0
$345$	−17.2421	−	29.8642i	−0.928284	−	1.60784i
$346$		0			0
$347$	−12.1668	+	12.1668i	−0.653148	+	0.653148i	−0.953750	−	0.300602i	$-0.902812\pi$
$347$	−12.1668	+	12.1668i	−0.653148	+	0.653148i	0.300602	+	0.953750i	$0.402812\pi$
$348$		0			0
$349$	11.4784	+	19.8812i	0.614426	+	1.06422i	0.990485	+	0.137621i	$0.0439457\pi$
$349$	11.4784	+	19.8812i	0.614426	+	1.06422i	−0.376059	+	0.926596i	$0.622721\pi$
$350$		0			0
$351$	−9.40275	−	35.0915i	−0.501881	−	1.87305i
$352$		0			0
$353$	−2.76543	+	10.3207i	−0.147189	+	0.549316i	0.852459	+	0.522793i	$0.175110\pi$
$353$	−2.76543	+	10.3207i	−0.147189	+	0.549316i	−0.999648	+	0.0265227i	$0.991557\pi$
$354$		0			0
$355$	−2.26971	+	8.47069i	−0.120464	+	0.449578i
$356$		0			0
$357$	5.55717	−	1.48904i	0.294117	−	0.0788084i
$358$		0			0
$359$			4.51041i			0.238050i	0.992891	+	0.119025i	$0.0379769\pi$
$359$			4.51041i			0.238050i	−0.992891	+	0.119025i	$0.962023\pi$
$360$		0			0
$361$	−11.4148	+	6.59035i	−0.600780	+	0.346860i
$362$		0			0
$363$	−14.4894	+	25.0963i	−0.760495	+	1.31722i
$364$		0			0
$365$	−1.92024	+	0.514527i	−0.100510	+	0.0269316i
$366$		0			0
$367$	12.0895	+	6.97989i	0.631068	+	0.364347i	0.781165	−	0.624324i	$-0.214625\pi$
$367$	12.0895	+	6.97989i	0.631068	+	0.364347i	−0.150098	+	0.988671i	$0.547959\pi$
$368$		0			0
$369$		−	55.8013i		−	2.90490i
$370$		0			0
$371$			12.2886i			0.637990i
$372$		0			0
$373$	16.9389	+	9.77966i	0.877061	+	0.506371i	0.869688	−	0.493601i	$-0.164320\pi$
$373$	16.9389	+	9.77966i	0.877061	+	0.506371i	0.00737276	+	0.999973i	$0.497653\pi$
$374$		0			0
$375$	34.8877	−	9.34813i	1.80159	−	0.482735i
$376$		0			0
$377$	8.42175	−	14.5869i	0.433742	−	0.751263i
$378$		0			0
$379$	21.2874	−	12.2903i	1.09346	−	0.631310i	0.158965	−	0.987284i	$-0.449184\pi$
$379$	21.2874	−	12.2903i	1.09346	−	0.631310i	0.934496	+	0.355975i	$0.115851\pi$
$380$		0			0
$381$			56.5555i			2.89743i
$382$		0			0
$383$	10.7014	−	2.86742i	0.546814	−	0.146518i	0.0251723	−	0.999683i	$-0.491987\pi$
$383$	10.7014	−	2.86742i	0.546814	−	0.146518i	0.521641	+	0.853165i	$0.325320\pi$
$384$		0			0
$385$	−3.09178	+	11.5387i	−0.157572	+	0.588065i
$386$		0			0
$387$	18.9680	−	70.7896i	0.964198	−	3.59844i
$388$		0			0
$389$	−2.68859	−	10.0340i	−0.136317	−	0.508742i	−0.999989	−	0.00468798i	$-0.998508\pi$
$389$	−2.68859	−	10.0340i	−0.136317	−	0.508742i	0.863672	−	0.504054i	$-0.168159\pi$
$390$		0			0
$391$	−3.85843	−	6.68300i	−0.195129	−	0.337974i
$392$		0			0
$393$	29.4402	−	29.4402i	1.48506	−	1.48506i
$394$		0			0
$395$	5.04873	+	8.74465i	0.254029	+	0.439991i
$396$		0			0
$397$			35.4744i			1.78041i	0.455562	+	0.890204i	$0.349438\pi$
$397$			35.4744i			1.78041i	−0.455562	+	0.890204i	$0.650562\pi$
$398$		0			0
$399$	9.43962	−	9.43962i	0.472572	−	0.472572i
$400$		0			0
$401$	8.16954	+	8.16954i	0.407967	+	0.407967i	0.881029	−	0.473062i	$-0.156851\pi$
$401$	8.16954	+	8.16954i	0.407967	+	0.407967i	−0.473062	+	0.881029i	$0.656851\pi$
$402$		0			0
$403$	16.3094	+	9.41621i	0.812427	+	0.469055i
$404$		0			0
$405$	22.7237	+	6.08881i	1.12915	+	0.302555i
$406$		0			0
$407$	7.02413	−	26.4946i	0.348173	−	1.31329i
$408$		0			0
$409$	−1.89340	+	7.06627i	−0.0936227	+	0.349405i	−0.996807	−	0.0798483i	$-0.974556\pi$
$409$	−1.89340	+	7.06627i	−0.0936227	+	0.349405i	0.903184	+	0.429253i	$0.141223\pi$
$410$		0			0
$411$	25.8603	−	44.7913i	1.27559	−	2.20939i
$412$		0			0
$413$	−13.1868	+	13.1868i	−0.648878	+	0.648878i
$414$		0			0
$415$	5.96690	+	5.96690i	0.292904	+	0.292904i
$416$		0			0
$417$	−39.0782			−1.91367
$418$		0			0
$419$	−8.85347	+	5.11155i	−0.432520	+	0.249716i	−0.700420	−	0.713731i	$-0.747004\pi$
$419$	−8.85347	+	5.11155i	−0.432520	+	0.249716i	0.267900	+	0.963447i	$0.413670\pi$
$420$		0			0
$421$	2.97382	+	2.97382i	0.144935	+	0.144935i	0.775851	−	0.630916i	$-0.217321\pi$
$421$	2.97382	+	2.97382i	0.144935	+	0.144935i	−0.630916	+	0.775851i	$0.717321\pi$
$422$		0			0
$423$	−29.7890	+	17.1987i	−1.44839	+	0.836228i
$424$		0			0
$425$	2.78615	−	0.746547i	0.135148	−	0.0362128i
$426$		0			0
$427$	−8.51110	−	2.28054i	−0.411881	−	0.110363i
$428$		0			0
$429$	42.7599	+	11.4575i	2.06447	+	0.553172i
$430$		0			0
$431$	−6.50047	−	24.2601i	−0.313117	−	1.16857i	−0.925730	−	0.378185i	$-0.876548\pi$
$431$	−6.50047	−	24.2601i	−0.313117	−	1.16857i	0.612613	−	0.790383i	$-0.290118\pi$
$432$		0			0
$433$	−14.9790			−0.719843			−0.359922	−	0.932983i	$-0.617197\pi$
$433$	−14.9790			−0.719843			−0.359922	+	0.932983i	$0.617197\pi$
$434$		0			0
$435$	12.4026	+	21.4820i	0.594661	+	1.02998i
$436$		0			0
$437$	−15.5071	−	8.95303i	−0.741805	−	0.428282i
$438$		0			0
$439$	−2.17158	−	8.10445i	−0.103644	−	0.386804i	0.894544	−	0.446980i	$-0.147501\pi$
$439$	−2.17158	−	8.10445i	−0.103644	−	0.386804i	−0.998188	+	0.0601758i	$0.980834\pi$
$440$		0			0
$441$	−12.8676	+	22.2874i	−0.612744	+	1.06130i
$442$		0			0
$443$	−7.29372			−0.346535			−0.173268	−	0.984875i	$-0.555433\pi$
$443$	−7.29372			−0.346535			−0.173268	+	0.984875i	$0.555433\pi$
$444$		0			0
$445$	−8.42497			−0.399382
$446$		0			0
$447$	−23.0513	+	39.9261i	−1.09029	+	1.88844i
$448$		0			0
$449$	5.79578	+	21.6301i	0.273520	+	1.02079i	0.956827	+	0.290659i	$0.0938744\pi$
$449$	5.79578	+	21.6301i	0.273520	+	1.02079i	−0.683307	+	0.730131i	$0.739459\pi$
$450$		0			0
$451$	32.5112	+	18.7704i	1.53089	+	0.883862i
$452$		0			0
$453$	6.70547	+	11.6142i	0.315050	+	0.545683i
$454$		0			0
$455$	8.36277			0.392053
$456$		0			0
$457$	−8.94483	−	33.3825i	−0.418421	−	1.56157i	−0.777883	−	0.628410i	$-0.783706\pi$
$457$	−8.94483	−	33.3825i	−0.418421	−	1.56157i	0.359461	−	0.933160i	$-0.382960\pi$
$458$		0			0
$459$	11.5647	+	3.09875i	0.539794	+	0.144637i
$460$		0			0
$461$	−15.4870	−	4.14973i	−0.721302	−	0.193272i	−0.120549	−	0.992707i	$-0.538466\pi$
$461$	−15.4870	−	4.14973i	−0.721302	−	0.193272i	−0.600752	+	0.799435i	$0.705132\pi$
$462$		0			0
$463$	9.86040	−	2.64209i	0.458252	−	0.122788i	−0.0223062	−	0.999751i	$-0.507101\pi$
$463$	9.86040	−	2.64209i	0.458252	−	0.122788i	0.480558	+	0.876963i	$0.340434\pi$
$464$		0			0
$465$	−24.0186	+	13.8672i	−1.11384	+	0.643075i
$466$		0			0
$467$	12.6736	+	12.6736i	0.586466	+	0.586466i	0.936673	−	0.350206i	$-0.113889\pi$
$467$	12.6736	+	12.6736i	0.586466	+	0.586466i	−0.350206	+	0.936673i	$0.613889\pi$
$468$		0			0
$469$	−18.5598	+	10.7155i	−0.857011	+	0.494796i
$470$		0			0
$471$	−74.5621			−3.43564
$472$		0			0
$473$	34.8633	+	34.8633i	1.60302	+	1.60302i
$474$		0			0
$475$	4.73266	−	4.73266i	0.217149	−	0.217149i
$476$		0			0
$477$	−23.1594	+	40.1133i	−1.06040	+	1.83666i
$478$		0			0
$479$	8.66955	−	32.3552i	0.396122	−	1.47835i	−0.423739	−	0.905784i	$-0.639283\pi$
$479$	8.66955	−	32.3552i	0.396122	−	1.47835i	0.819861	−	0.572562i	$-0.194051\pi$
$480$		0			0
$481$	−19.1886	+	0.0507686i	−0.874926	+	0.00231485i
$482$		0			0
$483$	−39.6773	−	10.6315i	−1.80538	−	0.483750i
$484$		0			0
$485$	2.24882	+	1.29836i	0.102114	+	0.0589554i
$486$		0			0
$487$	−2.86756	−	2.86756i	−0.129942	−	0.129942i	0.639145	−	0.769086i	$-0.279288\pi$
$487$	−2.86756	−	2.86756i	−0.129942	−	0.129942i	−0.769086	+	0.639145i	$0.779288\pi$
$488$		0			0
$489$	46.1559	−	46.1559i	2.08724	−	2.08724i
$490$		0			0
$491$		−	15.2148i		−	0.686633i	−0.939220	−	0.343317i	$-0.888450\pi$
$491$		−	15.2148i		−	0.686633i	0.939220	−	0.343317i	$-0.111550\pi$
$492$		0			0
$493$	2.77545	+	4.80723i	0.125000	+	0.216507i
$494$		0			0
$495$	−31.8385	+	31.8385i	−1.43104	+	1.43104i
$496$		0			0
$497$	5.22304	+	9.04656i	0.234285	+	0.405794i
$498$		0			0
$499$	−2.55672	−	9.54180i	−0.114454	−	0.427150i	0.884791	−	0.465988i	$-0.154301\pi$
$499$	−2.55672	−	9.54180i	−0.114454	−	0.427150i	−0.999246	+	0.0388383i	$0.987634\pi$
$500$		0			0
$501$	0.834486	−	3.11434i	0.0372821	−	0.139139i
$502$		0			0
$503$	−9.13964	+	34.1096i	−0.407516	+	1.52087i	0.391850	+	0.920029i	$0.371835\pi$
$503$	−9.13964	+	34.1096i	−0.407516	+	1.52087i	−0.799367	+	0.600843i	$0.794832\pi$
$504$		0			0
$505$	11.4974	−	3.08072i	0.511627	−	0.137090i
$506$		0			0
$507$			9.49353i			0.421623i
$508$		0			0
$509$	−31.8302	+	18.3772i	−1.41085	+	0.814554i	−0.995468	−	0.0950946i	$-0.969685\pi$
$509$	−31.8302	+	18.3772i	−1.41085	+	0.814554i	−0.415380	+	0.909648i	$0.636351\pi$
$510$		0			0
$511$	−1.18402	+	2.05079i	−0.0523781	+	0.0907215i
$512$		0			0
$513$	26.8345	−	7.19028i	1.18477	−	0.317459i
$514$		0			0
$515$	3.31975	+	1.91666i	0.146286	+	0.0844582i
$516$		0			0
$517$		−	23.1411i		−	1.01774i
$518$		0			0
$519$		−	31.7646i		−	1.39431i
$520$		0			0
$521$	13.8864	+	8.01731i	0.608374	+	0.351245i	0.772329	−	0.635223i	$-0.219092\pi$
$521$	13.8864	+	8.01731i	0.608374	+	0.351245i	−0.163955	+	0.986468i	$0.552425\pi$
$522$		0			0
$523$	13.4676	−	3.60864i	0.588899	−	0.157795i	0.0479489	−	0.998850i	$-0.484732\pi$
$523$	13.4676	−	3.60864i	0.588899	−	0.157795i	0.540950	+	0.841055i	$0.318065\pi$
$524$		0			0
$525$	7.67695	−	13.2969i	0.335049	−	0.580323i
$526$		0			0
$527$	−5.37488	+	3.10319i	−0.234134	+	0.135177i
$528$		0			0
$529$			32.0971i			1.39553i
$530$		0			0
$531$	−67.8974	+	18.1930i	−2.94649	+	0.789511i
$532$		0			0
$533$	6.80200	−	25.3854i	0.294628	−	1.09956i
$534$		0			0
$535$	−5.51337	+	20.5762i	−0.238364	+	0.889585i
$536$		0			0
$537$	1.06331	+	3.96831i	0.0458850	+	0.171245i
$538$		0			0
$539$	−8.65679	−	14.9940i	−0.372874	−	0.645837i
$540$		0			0
$541$	20.5067	−	20.5067i	0.881654	−	0.881654i	−0.112049	−	0.993703i	$-0.535741\pi$
$541$	20.5067	−	20.5067i	0.881654	−	0.881654i	0.993703	+	0.112049i	$0.0357414\pi$
$542$		0			0
$543$	−25.4137	−	44.0179i	−1.09061	−	1.88899i
$544$		0			0
$545$		−	21.8173i		−	0.934551i
$546$		0			0
$547$	−4.78520	+	4.78520i	−0.204601	+	0.204601i	−0.801968	−	0.597367i	$-0.796213\pi$
$547$	−4.78520	+	4.78520i	−0.204601	+	0.204601i	0.597367	+	0.801968i	$0.296213\pi$
$548$		0			0
$549$	−23.4846	−	23.4846i	−1.00230	−	1.00230i
$550$		0			0
$551$	11.1546	+	6.44011i	0.475202	+	0.274358i
$552$		0			0
$553$	11.6181	+	3.11305i	0.494050	+	0.132380i
$554$		0			0
$555$	14.0647	−	24.5103i	0.597013	−	1.04040i
$556$		0			0
$557$	−1.93726	+	7.22994i	−0.0820842	+	0.306343i	−0.994746	−	0.102373i	$-0.967356\pi$
$557$	−1.93726	+	7.22994i	−0.0820842	+	0.306343i	0.912662	+	0.408715i	$0.134023\pi$
$558$		0			0
$559$	17.2581	−	29.8918i	0.729938	−	1.26429i
$560$		0			0
$561$	−10.3160	+	10.3160i	−0.435540	+	0.435540i
$562$		0			0
$563$	17.7178	+	17.7178i	0.746715	+	0.746715i	0.973861	−	0.227145i	$-0.0729393\pi$
$563$	17.7178	+	17.7178i	0.746715	+	0.746715i	−0.227145	+	0.973861i	$0.572939\pi$
$564$		0			0
$565$	−24.7681			−1.04200
$566$		0			0
$567$	24.2686	−	14.0115i	1.01919	−	0.588427i
$568$		0			0
$569$	−23.4963	−	23.4963i	−0.985016	−	0.985016i	0.0148732	−	0.999889i	$-0.495266\pi$
$569$	−23.4963	−	23.4963i	−0.985016	−	0.985016i	−0.999889	+	0.0148732i	$0.995266\pi$
$570$		0			0
$571$	−29.3682	+	16.9558i	−1.22902	+	0.709577i	−0.966826	−	0.255438i	$-0.917780\pi$
$571$	−29.3682	+	16.9558i	−1.22902	+	0.709577i	−0.262197	+	0.965014i	$0.584447\pi$
$572$		0			0
$573$	−31.4364	+	8.42335i	−1.31327	+	0.351890i
$574$		0			0
$575$	−19.8927	−	5.33022i	−0.829581	−	0.222286i
$576$		0			0
$577$	−2.76034	−	0.739632i	−0.114915	−	0.0307913i	0.200903	−	0.979611i	$-0.435612\pi$
$577$	−2.76034	−	0.739632i	−0.114915	−	0.0307913i	−0.315818	+	0.948820i	$0.602279\pi$
$578$		0			0
$579$	−7.26414	−	27.1101i	−0.301887	−	1.12666i
$580$		0			0
$581$	10.0517			0.417017
$582$		0			0
$583$	−15.5807	−	26.9865i	−0.645285	−	1.11767i
$584$		0			0
$585$	27.2984	+	15.7607i	1.12865	+	0.651626i
$586$		0			0
$587$	1.03447	+	3.86071i	0.0426973	+	0.159349i	0.983983	−	0.178263i	$-0.0570477\pi$
$587$	1.03447	+	3.86071i	0.0426973	+	0.159349i	−0.941286	+	0.337611i	$0.890381\pi$
$588$		0			0
$589$	−7.20058	+	12.4718i	−0.296695	+	0.513890i
$590$		0			0
$591$	33.4103			1.37432
$592$		0			0
$593$	−1.96925			−0.0808674			−0.0404337	−	0.999182i	$-0.512874\pi$
$593$	−1.96925			−0.0808674			−0.0404337	+	0.999182i	$0.512874\pi$
$594$		0			0
$595$	−1.37801	+	2.38678i	−0.0564929	+	0.0978485i
$596$		0			0
$597$	1.73096	+	6.46002i	0.0708433	+	0.264391i
$598$		0			0
$599$	4.10805	+	2.37179i	0.167851	+	0.0969086i	0.581572	−	0.813495i	$-0.302438\pi$
$599$	4.10805	+	2.37179i	0.167851	+	0.0969086i	−0.413721	+	0.910404i	$0.635771\pi$
$600$		0			0
$601$	−2.32332	−	4.02410i	−0.0947700	−	0.164146i	0.814743	−	0.579823i	$-0.196878\pi$
$601$	−2.32332	−	4.02410i	−0.0947700	−	0.164146i	−0.909513	+	0.415676i	$0.863545\pi$
$602$		0			0
$603$	−80.7790			−3.28957
$604$		0			0
$605$	−3.59292	−	13.4090i	−0.146073	−	0.545152i
$606$		0			0
$607$	−35.5442	−	9.52403i	−1.44269	−	0.386568i	−0.549217	−	0.835680i	$-0.685074\pi$
$607$	−35.5442	−	9.52403i	−1.44269	−	0.386568i	−0.893476	+	0.449111i	$0.851741\pi$
$608$		0			0
$609$	28.5408	+	7.64747i	1.15653	+	0.309891i
$610$		0			0
$611$	−15.6482	+	4.19293i	−0.633060	+	0.169628i
$612$		0			0
$613$	10.4656	−	6.04232i	0.422702	−	0.244047i	−0.273531	−	0.961863i	$-0.588191\pi$
$613$	10.4656	−	6.04232i	0.422702	−	0.244047i	0.696233	+	0.717816i	$0.254858\pi$
$614$		0			0
$615$	27.3676	+	27.3676i	1.10357	+	1.10357i
$616$		0			0
$617$	2.52892	−	1.46008i	0.101811	−	0.0587804i	−0.448230	−	0.893918i	$-0.647945\pi$
$617$	2.52892	−	1.46008i	0.101811	−	0.0587804i	0.550041	+	0.835138i	$0.314612\pi$
$618$		0			0
$619$	10.5302			0.423243			0.211622	−	0.977352i	$-0.432126\pi$
$619$	10.5302			0.423243			0.211622	+	0.977352i	$0.432126\pi$
$620$		0			0
$621$	−60.4454	−	60.4454i	−2.42559	−	2.42559i
$622$		0			0
$623$	−7.09629	+	7.09629i	−0.284307	+	0.284307i
$624$		0			0
$625$	−1.71483	+	2.97017i	−0.0685932	+	0.118807i
$626$		0			0
$627$	−8.76154	+	32.6985i	−0.349902	+	1.30585i
$628$		0			0
$629$	3.14739	−	5.48491i	0.125495	−	0.218698i
$630$		0			0
$631$	17.7309	+	4.75099i	0.705858	+	0.189134i	0.593853	−	0.804574i	$-0.297606\pi$
$631$	17.7309	+	4.75099i	0.705858	+	0.189134i	0.112005	+	0.993708i	$0.464273\pi$
$632$		0			0
$633$	−48.4423	−	27.9682i	−1.92541	−	1.11164i
$634$		0			0
$635$	−19.1572	−	19.1572i	−0.760230	−	0.760230i
$636$		0			0
$637$	−8.57058	+	8.57058i	−0.339579	+	0.339579i
$638$		0			0
$639$			39.3740i			1.55761i
$640$		0			0
$641$	−1.11808	−	1.93658i	−0.0441616	−	0.0764902i	0.843100	−	0.537757i	$-0.180728\pi$
$641$	−1.11808	−	1.93658i	−0.0441616	−	0.0764902i	−0.887261	+	0.461267i	$0.847395\pi$
$642$		0			0
$643$	−13.7492	+	13.7492i	−0.542215	+	0.542215i	−0.924178	−	0.381963i	$-0.875248\pi$
$643$	−13.7492	+	13.7492i	−0.542215	+	0.542215i	0.381963	+	0.924178i	$0.375248\pi$
$644$		0			0
$645$	25.4158	+	44.0214i	1.00075	+	1.73334i
$646$		0			0
$647$	11.2945	+	42.1517i	0.444034	+	1.65716i	0.718476	+	0.695552i	$0.244840\pi$
$647$	11.2945	+	42.1517i	0.444034	+	1.65716i	−0.274442	+	0.961604i	$0.588493\pi$
$648$		0			0
$649$	12.2395	−	45.6784i	0.480442	−	1.79304i
$650$		0			0
$651$	−8.55051	+	31.9109i	−0.335121	+	1.25069i
$652$		0			0
$653$	−14.4892	+	3.88236i	−0.567004	+	0.151928i	−0.530922	−	0.847420i	$-0.678154\pi$
$653$	−14.4892	+	3.88236i	−0.567004	+	0.151928i	−0.0360820	+	0.999349i	$0.511488\pi$
$654$		0			0
$655$			19.9447i			0.779304i
$656$		0			0
$657$	−7.72995	+	4.46289i	−0.301574	+	0.174114i
$658$		0			0
$659$	−20.0040	+	34.6479i	−0.779243	+	1.34969i	0.153135	+	0.988205i	$0.451063\pi$
$659$	−20.0040	+	34.6479i	−0.779243	+	1.34969i	−0.932378	+	0.361484i	$0.882270\pi$
$660$		0			0
$661$	38.3302	−	10.2705i	1.49087	−	0.399478i	0.580841	−	0.814017i	$-0.302724\pi$
$661$	38.3302	−	10.2705i	1.49087	−	0.399478i	0.910032	+	0.414539i	$0.136057\pi$
$662$		0			0
$663$	8.84491	+	5.10661i	0.343508	+	0.198324i
$664$		0			0
$665$			6.39501i			0.247988i
$666$		0			0
$667$		−	39.6326i		−	1.53458i
$668$		0			0
$669$	−11.0403	−	6.37411i	−0.426842	−	0.246437i
$670$		0			0
$671$	21.5824	−	5.78299i	0.833180	−	0.223250i
$672$		0			0
$673$	−9.53886	+	16.5218i	−0.367696	+	0.636868i	−0.989205	−	0.146539i	$-0.953187\pi$
$673$	−9.53886	+	16.5218i	−0.367696	+	0.636868i	0.621509	+	0.783407i	$0.286520\pi$
$674$		0			0
$675$	27.6713	−	15.9760i	1.06507	−	0.614917i
$676$		0			0
$677$		−	6.71399i		−	0.258040i	−0.991642	−	0.129020i	$-0.958817\pi$
$677$		−	6.71399i		−	0.258040i	0.991642	−	0.129020i	$-0.0411831\pi$
$678$		0			0
$679$	2.98776	−	0.800569i	0.114660	−	0.0307230i
$680$		0			0
$681$	−16.1351	+	60.2170i	−0.618298	+	2.30752i
$682$		0			0
$683$	7.21292	−	26.9190i	0.275995	−	1.03003i	−0.679177	−	0.733975i	$-0.737663\pi$
$683$	7.21292	−	26.9190i	0.275995	−	1.03003i	0.955172	−	0.296052i	$-0.0956703\pi$
$684$		0			0
$685$	6.41255	+	23.9320i	0.245011	+	0.914394i
$686$		0			0
$687$	−39.2571	−	67.9953i	−1.49775	−	2.59418i
$688$		0			0
$689$	−15.4255	+	15.4255i	−0.587664	+	0.587664i
$690$		0			0
$691$	−1.43551	−	2.48638i	−0.0546096	−	0.0945865i	0.837428	−	0.546547i	$-0.184058\pi$
$691$	−1.43551	−	2.48638i	−0.0546096	−	0.0945865i	−0.892038	+	0.451961i	$0.850725\pi$
$692$		0			0
$693$			53.6347i			2.03742i
$694$		0			0
$695$	13.2371	−	13.2371i	0.502111	−	0.502111i
$696$		0			0
$697$	6.12432	+	6.12432i	0.231975	+	0.231975i
$698$		0			0
$699$	−78.5196	−	45.3333i	−2.96988	−	1.71466i
$700$		0			0
$701$	−5.31685	−	1.42465i	−0.200815	−	0.0538082i	0.157010	−	0.987597i	$-0.449815\pi$
$701$	−5.31685	−	1.42465i	−0.200815	−	0.0538082i	−0.357824	+	0.933789i	$0.616481\pi$
$702$		0			0
$703$	−0.0388227	−	14.6735i	−0.00146423	−	0.553423i
$704$		0			0
$705$	6.17489	−	23.0450i	0.232560	−	0.867925i
$706$		0			0
$707$	7.08931	−	12.2790i	0.266621	−	0.461801i
$708$		0			0
$709$	12.6964	−	12.6964i	0.476822	−	0.476822i	−0.427292	−	0.904114i	$-0.640532\pi$
$709$	12.6964	−	12.6964i	0.476822	−	0.476822i	0.904114	+	0.427292i	$0.140532\pi$
$710$		0			0
$711$	32.0576	+	32.0576i	1.20225	+	1.20225i
$712$		0			0
$713$	44.3125			1.65952
$714$		0			0
$715$	−18.3652	+	10.6031i	−0.686819	+	0.396535i
$716$		0			0
$717$	12.5217	+	12.5217i	0.467632	+	0.467632i
$718$		0			0
$719$	2.76653	−	1.59726i	0.103174	−	0.0595676i	−0.447525	−	0.894271i	$-0.647694\pi$
$719$	2.76653	−	1.59726i	0.103174	−	0.0595676i	0.550699	+	0.834704i	$0.314361\pi$
$720$		0			0
$721$	4.41059	−	1.18181i	0.164259	−	0.0440131i
$722$		0			0
$723$	56.5297	+	15.1471i	2.10236	+	0.563326i
$724$		0			0
$725$	14.3092	+	3.83415i	0.531431	+	0.142397i
$726$		0			0
$727$	5.26607	+	19.6532i	0.195308	+	0.728898i	0.992187	+	0.124759i	$0.0398159\pi$
$727$	5.26607	+	19.6532i	0.195308	+	0.728898i	−0.796879	+	0.604138i	$0.793517\pi$
$728$		0			0
$729$	−1.96551			−0.0727965
$730$		0			0
$731$	5.68753	+	9.85110i	0.210361	+	0.364356i
$732$		0			0
$733$	28.5519	+	16.4844i	1.05459	+	0.608866i	0.923930	−	0.382561i	$-0.124958\pi$
$733$	28.5519	+	16.4844i	1.05459	+	0.608866i	0.130657	+	0.991428i	$0.458291\pi$
$734$		0			0
$735$	−4.61990	−	17.2417i	−0.170408	−	0.635970i
$736$		0			0
$737$	27.1723	−	47.0638i	1.00091	−	1.73362i
$738$		0			0
$739$	40.5426			1.49139			0.745693	−	0.666290i	$-0.232119\pi$
$739$	40.5426			1.49139			0.745693	+	0.666290i	$0.232119\pi$
$740$		0			0
$741$	23.6986			0.870588
$742$		0			0
$743$	4.50095	−	7.79588i	0.165124	−	0.286003i	−0.771575	−	0.636138i	$-0.780531\pi$
$743$	4.50095	−	7.79588i	0.165124	−	0.286003i	0.936699	+	0.350135i	$0.113864\pi$
$744$		0			0
$745$	−5.71602	−	21.3325i	−0.209419	−	0.781562i
$746$		0			0
$747$	32.8117	+	18.9438i	1.20052	+	0.693118i
$748$		0			0
$749$	12.6873	+	21.9750i	0.463583	+	0.802950i
$750$		0			0
$751$	12.3370			0.450185			0.225092	−	0.974337i	$-0.427732\pi$
$751$	12.3370			0.450185			0.225092	+	0.974337i	$0.427732\pi$
$752$		0			0
$753$	19.7264	+	73.6198i	0.718869	+	2.68286i
$754$		0			0
$755$	−6.20547	−	1.66275i	−0.225840	−	0.0605137i
$756$		0			0
$757$	−42.6200	−	11.4200i	−1.54905	−	0.415067i	−0.619874	−	0.784701i	$-0.712816\pi$
$757$	−42.6200	−	11.4200i	−1.54905	−	0.415067i	−0.929177	+	0.369634i	$0.879483\pi$
$758$		0			0
$759$	100.614	−	26.9593i	3.65204	−	0.978562i
$760$		0			0
$761$	−15.5736	+	8.99141i	−0.564542	+	0.325938i	−0.754966	−	0.655763i	$-0.772347\pi$
$761$	−15.5736	+	8.99141i	−0.564542	+	0.325938i	0.190425	+	0.981702i	$0.439014\pi$
$762$		0			0
$763$	−18.3766	−	18.3766i	−0.665276	−	0.665276i
$764$		0			0
$765$	−8.99640	+	5.19407i	−0.325266	+	0.187792i
$766$		0			0
$767$	−33.1059			−1.19538
$768$		0			0
$769$	−12.8686	−	12.8686i	−0.464055	−	0.464055i	0.435927	−	0.899982i	$-0.356421\pi$
$769$	−12.8686	−	12.8686i	−0.464055	−	0.464055i	−0.899982	+	0.435927i	$0.856421\pi$
$770$		0			0
$771$	30.7233	−	30.7233i	1.10647	−	1.10647i
$772$		0			0
$773$	−6.96009	+	12.0552i	−0.250337	+	0.433597i	−0.963619	−	0.267281i	$-0.913875\pi$
$773$	−6.96009	+	12.0552i	−0.250337	+	0.433597i	0.713282	+	0.700878i	$0.247208\pi$
$774$		0			0
$775$	−4.28689	+	15.9989i	−0.153990	+	0.574698i
$776$		0			0
$777$	−8.79826	−	32.4914i	−0.315636	−	1.16562i
$778$		0			0
$779$	19.4122	+	5.20149i	0.695516	+	0.186363i
$780$		0			0
$781$	−22.9402	−	13.2446i	−0.820866	−	0.473927i
$782$		0			0
$783$	43.4797	+	43.4797i	1.55384	+	1.55384i
$784$		0			0
$785$	25.2566	−	25.2566i	0.901447	−	0.901447i
$786$		0			0
$787$		−	15.8890i		−	0.566383i	−0.959063	−	0.283192i	$-0.908607\pi$
$787$		−	15.8890i		−	0.566383i	0.959063	−	0.283192i	$-0.0913933\pi$
$788$		0			0
$789$	−1.17575	−	2.03645i	−0.0418577	−	0.0724997i
$790$		0			0
$791$	−20.8620	+	20.8620i	−0.741767	+	0.741767i
$792$		0			0
$793$	−7.82104	−	13.5464i	−0.277733	−	0.481048i
$794$		0			0
$795$	−8.31499	−	31.0319i	−0.294902	−	1.10059i
$796$		0			0
$797$	5.41293	−	20.2013i	0.191736	−	0.715568i	−0.801352	−	0.598193i	$-0.795886\pi$
$797$	5.41293	−	20.2013i	0.191736	−	0.715568i	0.993088	−	0.117375i	$-0.0374478\pi$
$798$		0			0
$799$	1.38181	−	5.15700i	0.0488851	−	0.182442i
$800$		0			0
$801$	−36.5381	+	9.79036i	−1.29101	+	0.345925i
$802$		0			0
$803$		−	6.00488i		−	0.211908i
$804$		0			0
$805$	17.0412	−	9.83876i	0.600624	−	0.346771i
$806$		0			0
$807$	35.7306	−	61.8872i	1.25778	−	2.17853i
$808$		0			0
$809$	18.1514	−	4.86365i	0.638168	−	0.170997i	0.0747947	−	0.997199i	$-0.476170\pi$
$809$	18.1514	−	4.86365i	0.638168	−	0.170997i	0.563374	+	0.826202i	$0.309503\pi$
$810$		0			0
$811$	−4.60001	−	2.65582i	−0.161528	−	0.0932584i	0.417057	−	0.908880i	$-0.363062\pi$
$811$	−4.60001	−	2.65582i	−0.161528	−	0.0932584i	−0.578585	+	0.815622i	$0.696395\pi$
$812$		0			0
$813$			36.7146i			1.28764i
$814$		0			0
$815$			31.2690i			1.09531i
$816$		0			0
$817$	22.8583	+	13.1972i	0.799710	+	0.461713i
$818$		0			0
$819$	36.2684	−	9.71808i	1.26732	−	0.339577i
$820$		0			0
$821$	−6.72579	+	11.6494i	−0.234732	+	0.406567i	−0.959195	−	0.282746i	$-0.908754\pi$
$821$	−6.72579	+	11.6494i	−0.234732	+	0.406567i	0.724463	+	0.689314i	$0.242088\pi$
$822$		0			0
$823$	18.5474	−	10.7083i	0.646521	−	0.373269i	−0.140601	−	0.990066i	$-0.544904\pi$
$823$	18.5474	−	10.7083i	0.646521	−	0.373269i	0.787122	+	0.616797i	$0.211570\pi$
$824$		0			0
$825$			38.9343i			1.35552i
$826$		0			0
$827$	31.5309	−	8.44868i	1.09644	−	0.293790i	0.335124	−	0.942174i	$-0.391222\pi$
$827$	31.5309	−	8.44868i	1.09644	−	0.293790i	0.761313	+	0.648384i	$0.224555\pi$
$828$		0			0
$829$	11.8338	−	44.1642i	0.411004	−	1.53389i	−0.381704	−	0.924285i	$-0.624663\pi$
$829$	11.8338	−	44.1642i	0.411004	−	1.53389i	0.792707	−	0.609602i	$-0.208671\pi$
$830$		0			0
$831$	−25.1823	+	93.9815i	−0.873563	+	3.26018i
$832$		0			0
$833$	−1.03384	−	3.85834i	−0.0358204	−	0.133684i
$834$		0			0
$835$	0.772262	+	1.33760i	0.0267252	+	0.0462895i
$836$		0			0
$837$	−48.6140	+	48.6140i	−1.68034	+	1.68034i
$838$		0			0
$839$	20.6049	+	35.6888i	0.711362	+	1.23211i	0.964346	+	0.264644i	$0.0852545\pi$
$839$	20.6049	+	35.6888i	0.711362	+	1.23211i	−0.252985	+	0.967470i	$0.581412\pi$
$840$		0			0
$841$		−	0.491417i		−	0.0169454i
$842$		0			0
$843$	−0.441325	+	0.441325i	−0.0152000	+	0.0152000i
$844$		0			0
$845$	−3.21577	−	3.21577i	−0.110626	−	0.110626i
$846$		0			0
$847$	−14.3206	−	8.26798i	−0.492060	−	0.284091i
$848$		0			0
$849$	−41.8910	−	11.2247i	−1.43770	−	0.385230i
$850$		0			0
$851$	−39.0419	+	22.6788i	−1.33834	+	0.777418i
$852$		0			0
$853$	−5.01442	+	18.7141i	−0.171691	+	0.640758i	0.825401	+	0.564547i	$0.190949\pi$
$853$	−5.01442	+	18.7141i	−0.171691	+	0.640758i	−0.997092	+	0.0762111i	$0.975718\pi$
$854$		0			0
$855$	−12.0522	+	20.8751i	−0.412178	+	0.713913i
$856$		0			0
$857$	32.4869	−	32.4869i	1.10973	−	1.10973i	0.116546	−	0.993185i	$-0.462818\pi$
$857$	32.4869	−	32.4869i	1.10973	−	1.10973i	0.993185	−	0.116546i	$-0.0371821\pi$
$858$		0			0
$859$	−7.99636	−	7.99636i	−0.272832	−	0.272832i	0.557407	−	0.830239i	$-0.311796\pi$
$859$	−7.99636	−	7.99636i	−0.272832	−	0.272832i	−0.830239	+	0.557407i	$0.811796\pi$
$860$		0			0
$861$	46.1031			1.57119
$862$		0			0
$863$	11.1398	−	6.43156i	0.379203	−	0.218933i	−0.298269	−	0.954482i	$-0.596409\pi$
$863$	11.1398	−	6.43156i	0.379203	−	0.218933i	0.677471	+	0.735549i	$0.263076\pi$
$864$		0			0
$865$	10.7597	+	10.7597i	0.365841	+	0.365841i
$866$		0			0
$867$	42.9332	−	24.7875i	1.45809	−	0.841828i
$868$		0			0
$869$	−29.4610	+	7.89406i	−0.999397	+	0.267788i
$870$		0			0
$871$	−36.7484	−	9.84671i	−1.24517	−	0.333643i
$872$		0			0
$873$	11.2617	+	3.01755i	0.381149	+	0.102129i
$874$		0			0
$875$	5.33426	+	19.9077i	0.180331	+	0.673004i
$876$		0			0
$877$	21.5818			0.728765			0.364383	−	0.931249i	$-0.381280\pi$
$877$	21.5818			0.728765			0.364383	+	0.931249i	$0.381280\pi$
$878$		0			0
$879$	8.21136	+	14.2225i	0.276962	+	0.479713i
$880$		0			0
$881$	−14.8709	−	8.58569i	−0.501012	−	0.289259i	0.228119	−	0.973633i	$-0.426742\pi$
$881$	−14.8709	−	8.58569i	−0.501012	−	0.289259i	−0.729131	+	0.684374i	$0.760076\pi$
$882$		0			0
$883$	1.53404	+	5.72511i	0.0516245	+	0.192665i	0.986922	−	0.161196i	$-0.0515352\pi$
$883$	1.53404	+	5.72511i	0.0516245	+	0.192665i	−0.935298	+	0.353861i	$0.884869\pi$
$884$		0			0
$885$	24.3774	−	42.2229i	0.819437	−	1.41931i
$886$		0			0
$887$	9.47818			0.318246			0.159123	−	0.987259i	$-0.449133\pi$
$887$	9.47818			0.318246			0.159123	+	0.987259i	$0.449133\pi$
$888$		0			0
$889$	−32.2719			−1.08237
$890$		0			0
$891$	−35.5303	+	61.5402i	−1.19031	+	2.06168i
$892$		0			0
$893$	−3.20634	−	11.9662i	−0.107296	−	0.400434i
$894$		0			0
$895$	−1.70437	−	0.984020i	−0.0569709	−	0.0328922i
$896$		0			0
$897$	−36.4604	−	63.1512i	−1.21738	−	2.10856i
$898$		0			0
$899$	−31.8750			−1.06309
$900$		0			0
$901$	−1.86072	−	6.94431i	−0.0619897	−	0.231349i
$902$		0			0
$903$	58.4865	+	15.6714i	1.94631	+	0.521512i
$904$		0			0
$905$	23.5188	+	6.30183i	0.781790	+	0.209480i
$906$		0			0
$907$	−15.8609	+	4.24992i	−0.526653	+	0.141116i	−0.512342	−	0.858781i	$-0.671222\pi$
$907$	−15.8609	+	4.24992i	−0.526653	+	0.141116i	−0.0143105	+	0.999898i	$0.504555\pi$
$908$		0			0
$909$	46.2829	−	26.7214i	1.53511	−	0.886294i
$910$		0			0
$911$	−29.1197	−	29.1197i	−0.964780	−	0.964780i	0.0346208	−	0.999401i	$-0.488978\pi$
$911$	−29.1197	−	29.1197i	−0.964780	−	0.964780i	−0.999401	+	0.0346208i	$0.988978\pi$
$912$		0			0
$913$	−22.0743	+	12.7446i	−0.730552	+	0.421785i
$914$		0			0
$915$	23.0360			0.761545
$916$		0			0
$917$	16.7993	+	16.7993i	0.554761	+	0.554761i
$918$		0			0
$919$	−0.834279	+	0.834279i	−0.0275203	+	0.0275203i	−0.720733	−	0.693213i	$-0.756195\pi$
$919$	−0.834279	+	0.834279i	−0.0275203	+	0.0275203i	0.693213	+	0.720733i	$0.256195\pi$
$920$		0			0
$921$	20.1738	−	34.9421i	0.664751	−	1.15138i
$922$		0			0
$923$	−4.79956	+	17.9122i	−0.157980	+	0.589588i
$924$		0			0
$925$	−4.41110	−	16.2899i	−0.145036	−	0.535610i
$926$		0			0
$927$	16.6247	+	4.45457i	0.546026	+	0.146307i
$928$		0			0
$929$	32.9911	+	19.0474i	1.08240	+	0.624925i	0.931543	−	0.363631i	$-0.118463\pi$
$929$	32.9911	+	19.0474i	1.08240	+	0.624925i	0.150858	+	0.988555i	$0.451796\pi$
$930$		0			0
$931$	−6.55392	−	6.55392i	−0.214796	−	0.214796i
$932$		0			0
$933$	23.5729	−	23.5729i	0.771742	−	0.771742i
$934$		0			0
$935$		−	6.98870i		−	0.228555i
$936$		0			0
$937$	6.18754	+	10.7171i	0.202138	+	0.350113i	0.949217	−	0.314622i	$-0.101878\pi$
$937$	6.18754	+	10.7171i	0.202138	+	0.350113i	−0.747079	+	0.664735i	$0.768544\pi$
$938$		0			0
$939$	−4.20829	+	4.20829i	−0.137332	+	0.137332i
$940$		0			0
$941$	−17.6865	−	30.6339i	−0.576564	−	0.998637i	−0.995870	−	0.0907926i	$-0.971060\pi$
$941$	−17.6865	−	30.6339i	−0.576564	−	0.998637i	0.419306	−	0.907845i	$-0.362273\pi$
$942$		0			0
$943$	−16.0051	−	59.7317i	−0.521196	−	1.94513i
$944$		0			0
$945$	−7.90162	+	29.4892i	−0.257040	+	0.959285i
$946$		0			0
$947$	−7.27244	+	27.1411i	−0.236323	+	0.881968i	0.741225	+	0.671256i	$0.234245\pi$
$947$	−7.27244	+	27.1411i	−0.236323	+	0.881968i	−0.977548	+	0.210712i	$0.932422\pi$
$948$		0			0
$949$	−4.06056	+	1.08802i	−0.131811	+	0.0353188i
$950$		0			0
$951$			16.1266i			0.522941i
$952$		0			0
$953$	5.43084	−	3.13550i	0.175922	−	0.101569i	−0.409453	−	0.912331i	$-0.634280\pi$
$953$	5.43084	−	3.13550i	0.175922	−	0.101569i	0.585375	+	0.810762i	$0.300947\pi$
$954$		0			0
$955$	7.79526	−	13.5018i	0.252249	−	0.436907i
$956$		0			0
$957$	−72.3736	+	19.3924i	−2.33951	+	0.626869i
$958$		0			0
$959$	25.5590	+	14.7565i	0.825342	+	0.476512i
$960$		0			0
$961$		−	4.63887i		−	0.149641i
$962$		0			0
$963$			95.6434i			3.08206i
$964$		0			0
$965$	11.6437	+	6.72248i	0.374823	+	0.216404i
$966$		0			0
$967$	−56.2752	+	15.0789i	−1.80969	+	0.484905i	−0.995421	−	0.0955853i	$-0.969528\pi$
$967$	−56.2752	+	15.0789i	−1.80969	+	0.484905i	−0.814267	+	0.580490i	$0.802861\pi$
$968$		0			0
$969$	−3.90503	+	6.76370i	−0.125448	+	0.217281i
$970$		0			0
$971$	15.7082	−	9.06912i	0.504099	−	0.291042i	−0.226305	−	0.974056i	$-0.572665\pi$
$971$	15.7082	−	9.06912i	0.504099	−	0.291042i	0.730405	+	0.683014i	$0.239331\pi$
$972$		0			0
$973$		−	22.2990i		−	0.714872i
$974$		0			0
$975$	26.3278	−	7.05452i	0.843165	−	0.225925i
$976$		0			0
$977$	5.32062	−	19.8568i	0.170222	−	0.635276i	−0.827095	−	0.562063i	$-0.810008\pi$
$977$	5.32062	−	19.8568i	0.170222	−	0.635276i	0.997316	−	0.0732132i	$-0.0233254\pi$
$978$		0			0
$979$	6.58654	−	24.5813i	0.210507	−	0.785621i
$980$		0			0
$981$	−25.3531	−	94.6192i	−0.809463	−	3.02096i
$982$		0			0
$983$	1.43413	+	2.48399i	0.0457416	+	0.0792268i	0.887990	−	0.459863i	$-0.152102\pi$
$983$	1.43413	+	2.48399i	0.0457416	+	0.0792268i	−0.842248	+	0.539090i	$0.818768\pi$
$984$		0			0
$985$	−11.3172	+	11.3172i	−0.360595	+	0.360595i
$986$		0			0
$987$	−14.2096	−	24.6117i	−0.452296	−	0.783399i
$988$		0			0
$989$		−	81.2161i		−	2.58252i
$990$		0			0
$991$	6.33954	−	6.33954i	0.201382	−	0.201382i	−0.599210	−	0.800592i	$-0.704518\pi$
$991$	6.33954	−	6.33954i	0.201382	−	0.201382i	0.800592	+	0.599210i	$0.204518\pi$
$992$		0			0
$993$	15.2340	+	15.2340i	0.483436	+	0.483436i
$994$		0			0
$995$	−2.77455	−	1.60189i	−0.0879591	−	0.0507832i
$996$		0			0
$997$	33.4847	+	8.97220i	1.06047	+	0.284153i	0.746573	−	0.665304i	$-0.231698\pi$
$997$	33.4847	+	8.97220i	1.06047	+	0.284153i	0.313899	+	0.949456i	$0.398365\pi$
$998$		0			0
$999$	17.9515	−	67.7119i	0.567959	−	2.14231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.399.1	yes	20
4.3	odd	2		592.2.be.f.399.5	yes	20
37.23	odd	12		592.2.be.f.319.5	yes	20
148.23	even	12	inner	592.2.be.e.319.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.319.1	✓	20	148.23	even	12	inner
592.2.be.e.399.1	yes	20	1.1	even	1	trivial
592.2.be.f.319.5	yes	20	37.23	odd	12
592.2.be.f.399.5	yes	20	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.55708 + 2.69695i) q^{3} +(-0.386109 - 1.44098i) q^{5} +(-1.53894 - 0.888509i) q^{7} +(-3.34902 - 5.80068i) q^{9} +O(q^{10})\)	\(q+(-1.55708 + 2.69695i) q^{3} +(-0.386109 - 1.44098i) q^{5} +(-1.53894 - 0.888509i) q^{7} +(-3.34902 - 5.80068i) q^{9} +4.50616 q^{11} +(-0.816471 - 3.04711i) q^{13} +(4.48745 + 1.20241i) q^{15} +(1.00420 + 0.269074i) q^{17} +(2.33013 - 0.624355i) q^{19} +(4.79253 - 2.76697i) q^{21} +(-5.24867 - 5.24867i) q^{23} +(2.40279 - 1.38725i) q^{25} +11.5163 q^{27} +(3.77549 + 3.77549i) q^{29} +(-4.22131 + 4.22131i) q^{31} +(-7.01647 + 12.1529i) q^{33} +(-0.686123 + 2.56065i) q^{35} +(1.55878 - 5.87964i) q^{37} +(9.48921 + 2.54263i) q^{39} +(7.21484 + 4.16549i) q^{41} +(7.73682 + 7.73682i) q^{43} +(-7.06556 + 7.06556i) q^{45} -5.13543i q^{47} +(-1.92110 - 3.32745i) q^{49} +(-2.28930 + 2.28930i) q^{51} +(-3.45764 - 5.98880i) q^{53} +(-1.73987 - 6.49328i) q^{55} +(-1.94435 + 7.25640i) q^{57} +(2.71617 - 10.1369i) q^{59} +(4.78954 - 1.28335i) q^{61} +11.9025i q^{63} +(-4.07557 + 2.35303i) q^{65} +(6.03004 - 10.4443i) q^{67} +(22.3280 - 5.98278i) q^{69} +(-5.09087 - 2.93921i) q^{71} -1.33259i q^{73} +8.64026i q^{75} +(-6.93472 - 4.00376i) q^{77} +(-6.53795 + 1.75184i) q^{79} +(-7.88483 + 13.6569i) q^{81} +(-4.89869 + 2.82826i) q^{83} -1.55092i q^{85} +(-16.0610 + 4.30354i) q^{87} +(1.46168 - 5.45505i) q^{89} +(-1.45088 + 5.41477i) q^{91} +(-4.81172 - 17.9576i) q^{93} +(-1.79937 - 3.11659i) q^{95} +(-1.23082 + 1.23082i) q^{97} +(-15.0912 - 26.1388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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