LMFDB - Embedded newform 592.2.i.f.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(417,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("592.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.27870912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} + 2x^{3} + 38x^{2} - 12x + 4 $ x^6 - x^5 + 7x^4 + 2x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 148)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$-1.08870 - 1.88569i$ of defining polynomial
Character	$\chi$	$=$	592.433
Dual form			592.2.i.f.417.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08870 + 1.88569i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.370556 - 0.641823i) q^{7} +(-0.870556 - 1.50785i) q^{9} +2.91852 q^{11} +(1.54797 - 2.68116i) q^{13} +(1.08870 + 1.88569i) q^{15} +(3.41852 + 5.92105i) q^{17} +(0.0887048 - 0.153641i) q^{19} +(0.806853 + 1.39751i) q^{21} +3.43630 q^{23} +(2.00000 + 3.46410i) q^{25} -2.74111 q^{27} -4.61371 q^{29} -2.91852 q^{31} +(-3.17741 + 5.50344i) q^{33} +(-0.370556 - 0.641823i) q^{35} +(-2.04797 + 5.72764i) q^{37} +(3.37056 + 5.83798i) q^{39} +(-0.322590 + 0.558743i) q^{41} +3.48223 q^{43} -1.74111 q^{45} +9.79112 q^{47} +(3.22538 + 5.58651i) q^{49} -14.8870 q^{51} +(-3.37056 - 5.83798i) q^{53} +(1.45926 - 2.52751i) q^{55} +(0.193147 + 0.334540i) q^{57} +(3.72538 + 6.45254i) q^{59} +(3.67741 - 6.36946i) q^{61} -1.29036 q^{63} +(-1.54797 - 2.68116i) q^{65} +(-5.18464 + 8.98005i) q^{67} +(-3.74111 + 6.47980i) q^{69} +(2.72538 - 4.72049i) q^{71} +12.3548 q^{73} -8.70964 q^{75} +(1.08148 - 1.87317i) q^{77} +(-6.26611 + 10.8532i) q^{79} +(5.59593 - 9.69244i) q^{81} +(-4.18464 - 7.24800i) q^{83} +6.83705 q^{85} +(5.02296 - 8.70003i) q^{87} +(-7.85482 - 13.6049i) q^{89} +(-1.14722 - 1.98704i) q^{91} +(3.17741 - 5.50344i) q^{93} +(-0.0887048 - 0.153641i) q^{95} -16.8056 q^{97} +(-2.54074 - 4.40069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + q^{7} - 4 q^{9} - 7 q^{13} - q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} + 8 q^{23} + 12 q^{25} - 14 q^{27} - 4 q^{33} - q^{35} + 4 q^{37} + 19 q^{39} - 17 q^{41} + 16 q^{43} - 8 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + q^7 - 4 * q^9 - 7 * q^13 - q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 + 8 * q^23 + 12 * q^25 - 14 * q^27 - 4 * q^33 - q^35 + 4 * q^37 + 19 * q^39 - 17 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 19 * q^53 + 15 * q^57 - 9 * q^59 + 7 * q^61 - 68 * q^63 + 7 * q^65 + 9 * q^67 - 20 * q^69 - 15 * q^71 + 44 * q^73 + 8 * q^75 + 24 * q^77 - 15 * q^79 + q^81 + 15 * q^83 + 6 * q^85 + 34 * q^87 - 17 * q^89 - 13 * q^91 + 4 * q^93 + 7 * q^95 - 8 * q^97 - 24 * q^99

Character values

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

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.08870	+	1.88569i	−0.628564	+	1.08870i	0.359276	+	0.933231i	$0.383024\pi$
$3$	−1.08870	+	1.88569i	−0.628564	+	1.08870i	−0.987840	+	0.155474i	$0.950310\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$		0			0
$7$	0.370556	−	0.641823i	0.140057	−	0.242586i	−0.787461	−	0.616365i	$-0.788605\pi$
$7$	0.370556	−	0.641823i	0.140057	−	0.242586i	0.927518	+	0.373779i	$0.121938\pi$
$8$		0			0
$9$	−0.870556	−	1.50785i	−0.290185	−	0.502616i
$10$		0			0
$11$	2.91852			0.879968			0.439984	−	0.898006i	$-0.354984\pi$
$11$	2.91852			0.879968			0.439984	+	0.898006i	$0.354984\pi$
$12$		0			0
$13$	1.54797	−	2.68116i	0.429329	−	0.743619i	−0.567485	−	0.823384i	$-0.692084\pi$
$13$	1.54797	−	2.68116i	0.429329	−	0.743619i	0.996814	+	0.0797647i	$0.0254169\pi$
$14$		0			0
$15$	1.08870	+	1.88569i	0.281102	+	0.486884i
$16$		0			0
$17$	3.41852	+	5.92105i	0.829114	+	1.43607i	0.898734	+	0.438493i	$0.144488\pi$
$17$	3.41852	+	5.92105i	0.829114	+	1.43607i	−0.0696210	+	0.997574i	$0.522179\pi$
$18$		0			0
$19$	0.0887048	−	0.153641i	0.0203503	−	0.0352477i	−0.855671	−	0.517520i	$-0.826855\pi$
$19$	0.0887048	−	0.153641i	0.0203503	−	0.0352477i	0.876021	+	0.482273i	$0.160189\pi$
$20$		0			0
$21$	0.806853	+	1.39751i	0.176070	+	0.304962i
$22$		0			0
$23$	3.43630			0.716517			0.358259	−	0.933622i	$-0.383371\pi$
$23$	3.43630			0.716517			0.358259	+	0.933622i	$0.383371\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$	−2.74111			−0.527527
$28$		0			0
$29$	−4.61371			−0.856744			−0.428372	−	0.903603i	$-0.640913\pi$
$29$	−4.61371			−0.856744			−0.428372	+	0.903603i	$0.640913\pi$
$30$		0			0
$31$	−2.91852			−0.524182			−0.262091	−	0.965043i	$-0.584412\pi$
$31$	−2.91852			−0.524182			−0.262091	+	0.965043i	$0.584412\pi$
$32$		0			0
$33$	−3.17741	+	5.50344i	−0.553116	+	0.958025i
$34$		0			0
$35$	−0.370556	−	0.641823i	−0.0626355	−	0.108488i
$36$		0			0
$37$	−2.04797	+	5.72764i	−0.336684	+	0.941618i
$37$	−2.04797	+	5.72764i	−0.336684	+	0.941618i
$38$		0			0
$39$	3.37056	+	5.83798i	0.539721	+	0.934824i
$40$		0			0
$41$	−0.322590	+	0.558743i	−0.0503801	+	0.0872610i	−0.890116	−	0.455735i	$-0.849377\pi$
$41$	−0.322590	+	0.558743i	−0.0503801	+	0.0872610i	0.839736	+	0.542996i	$0.182710\pi$
$42$		0			0
$43$	3.48223			0.531034			0.265517	−	0.964106i	$-0.414457\pi$
$43$	3.48223			0.531034			0.265517	+	0.964106i	$0.414457\pi$
$44$		0			0
$45$	−1.74111			−0.259550
$46$		0			0
$47$	9.79112			1.42818			0.714091	−	0.700053i	$-0.246840\pi$
$47$	9.79112			1.42818			0.714091	+	0.700053i	$0.246840\pi$
$48$		0			0
$49$	3.22538	+	5.58651i	0.460768	+	0.798074i
$50$		0			0
$51$	−14.8870			−2.08460
$52$		0			0
$53$	−3.37056	−	5.83798i	−0.462982	−	0.801908i	0.536126	−	0.844138i	$-0.319887\pi$
$53$	−3.37056	−	5.83798i	−0.462982	−	0.801908i	−0.999108	+	0.0422302i	$0.986554\pi$
$54$		0			0
$55$	1.45926	−	2.52751i	0.196767	−	0.340810i
$56$		0			0
$57$	0.193147	+	0.334540i	0.0255829	+	0.0443109i
$58$		0			0
$59$	3.72538	+	6.45254i	0.485003	+	0.840049i	0.999852	−	0.0172318i	$-0.00548531\pi$
$59$	3.72538	+	6.45254i	0.485003	+	0.840049i	−0.514849	+	0.857281i	$0.672152\pi$
$60$		0			0
$61$	3.67741	−	6.36946i	0.470844	−	0.815526i	−0.528600	−	0.848871i	$-0.677283\pi$
$61$	3.67741	−	6.36946i	0.470844	−	0.815526i	0.999444	+	0.0333453i	$0.0106161\pi$
$62$		0			0
$63$	−1.29036			−0.162570
$64$		0			0
$65$	−1.54797	−	2.68116i	−0.192002	−	0.332556i
$66$		0			0
$67$	−5.18464	+	8.98005i	−0.633404	+	1.09709i	0.353447	+	0.935455i	$0.385010\pi$
$67$	−5.18464	+	8.98005i	−0.633404	+	1.09709i	−0.986851	+	0.161634i	$0.948324\pi$
$68$		0			0
$69$	−3.74111	+	6.47980i	−0.450377	+	0.780076i
$70$		0			0
$71$	2.72538	−	4.72049i	0.323443	−	0.560219i	−0.657753	−	0.753233i	$-0.728493\pi$
$71$	2.72538	−	4.72049i	0.323443	−	0.560219i	0.981196	+	0.193014i	$0.0618264\pi$
$72$		0			0
$73$	12.3548			1.44602			0.723011	−	0.690836i	$-0.242758\pi$
$73$	12.3548			1.44602			0.723011	+	0.690836i	$0.242758\pi$
$74$		0			0
$75$	−8.70964			−1.00570
$76$		0			0
$77$	1.08148	−	1.87317i	0.123246	−	0.213468i
$78$		0			0
$79$	−6.26611	+	10.8532i	−0.704993	+	1.22108i	0.261701	+	0.965149i	$0.415717\pi$
$79$	−6.26611	+	10.8532i	−0.704993	+	1.22108i	−0.966694	+	0.255935i	$0.917617\pi$
$80$		0			0
$81$	5.59593	−	9.69244i	0.621770	−	1.07694i
$82$		0			0
$83$	−4.18464	−	7.24800i	−0.459324	−	0.795572i	0.539602	−	0.841920i	$-0.318575\pi$
$83$	−4.18464	−	7.24800i	−0.459324	−	0.795572i	−0.998925	+	0.0463486i	$0.985241\pi$
$84$		0			0
$85$	6.83705			0.741582
$86$		0			0
$87$	5.02296	−	8.70003i	0.538518	−	0.932741i
$88$		0			0
$89$	−7.85482	−	13.6049i	−0.832609	−	1.44212i	−0.895962	−	0.444130i	$-0.853513\pi$
$89$	−7.85482	−	13.6049i	−0.832609	−	1.44212i	0.0633531	−	0.997991i	$-0.479821\pi$
$90$		0			0
$91$	−1.14722	−	1.98704i	−0.120261	−	0.208298i
$92$		0			0
$93$	3.17741	−	5.50344i	0.329482	−	0.570680i
$94$		0			0
$95$	−0.0887048	−	0.153641i	−0.00910092	−	0.0157633i
$96$		0			0
$97$	−16.8056			−1.70635			−0.853174	−	0.521627i	$-0.825325\pi$
$97$	−16.8056			−1.70635			−0.853174	+	0.521627i	$0.825325\pi$
$98$		0			0
$99$	−2.54074	−	4.40069i	−0.255354	−	0.442286i
$100$		0			0
$101$	6.25889			0.622783			0.311391	−	0.950282i	$-0.399205\pi$
$101$	6.25889			0.622783			0.311391	+	0.950282i	$0.399205\pi$
$102$		0			0
$103$	20.1919			1.98956			0.994782	−	0.102026i	$-0.0325324\pi$
$103$	20.1919			1.98956			0.994782	+	0.102026i	$0.0325324\pi$
$104$		0			0
$105$	1.61371			0.157482
$106$		0			0
$107$	6.72538	−	11.6487i	0.650167	−	1.12612i	−0.332916	−	0.942957i	$-0.608032\pi$
$107$	6.72538	−	11.6487i	0.650167	−	1.12612i	0.983082	−	0.183165i	$-0.0586343\pi$
$108$		0			0
$109$	−3.24111	−	5.61377i	−0.310442	−	0.537702i	0.668016	−	0.744147i	$-0.267144\pi$
$109$	−3.24111	−	5.61377i	−0.310442	−	0.537702i	−0.978458	+	0.206445i	$0.933810\pi$
$110$		0			0
$111$	−8.57093	−	10.0975i	−0.813517	−	0.958416i
$112$		0			0
$113$	−4.80685	−	8.32571i	−0.452191	−	0.783217i	0.546331	−	0.837569i	$-0.316024\pi$
$113$	−4.80685	−	8.32571i	−0.452191	−	0.783217i	−0.998522	+	0.0543520i	$0.982691\pi$
$114$		0			0
$115$	1.71815	−	2.97592i	0.160218	−	0.277506i
$116$		0			0
$117$	−5.39037			−0.498340
$118$		0			0
$119$	5.06702			0.464493
$120$		0			0
$121$	−2.48223			−0.225657
$122$		0			0
$123$	−0.702411	−	1.21661i	−0.0633343	−	0.109698i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−2.74834	−	4.76027i	−0.243876	−	0.422405i	0.717939	−	0.696106i	$-0.245086\pi$
$127$	−2.74834	−	4.76027i	−0.243876	−	0.422405i	−0.961815	+	0.273701i	$0.911752\pi$
$128$		0			0
$129$	−3.79112	+	6.56641i	−0.333789	+	0.578140i
$130$		0			0
$131$	−0.347592	−	0.602047i	−0.0303692	−	0.0526011i	0.850441	−	0.526070i	$-0.176335\pi$
$131$	−0.347592	−	0.602047i	−0.0303692	−	0.0526011i	−0.880811	+	0.473469i	$0.843002\pi$
$132$		0			0
$133$	−0.0657403	−	0.113866i	−0.00570041	−	0.00987339i
$134$		0			0
$135$	−1.37056	+	2.37387i	−0.117959	+	0.204310i
$136$		0			0
$137$	2.25889			0.192990			0.0964949	−	0.995333i	$-0.469237\pi$
$137$	2.25889			0.192990			0.0964949	+	0.995333i	$0.469237\pi$
$138$		0			0
$139$	−7.82982	−	13.5616i	−0.664116	−	1.15028i	−0.979524	−	0.201327i	$-0.935475\pi$
$139$	−7.82982	−	13.5616i	−0.664116	−	1.15028i	0.315408	−	0.948956i	$-0.397859\pi$
$140$		0			0
$141$	−10.6596	+	18.4630i	−0.897703	+	1.55487i
$142$		0			0
$143$	4.51777	−	7.82501i	0.377795	−	0.654361i
$144$		0			0
$145$	−2.30685	+	3.99559i	−0.191574	+	0.331815i
$146$		0			0
$147$	−14.0459			−1.15849
$148$		0			0
$149$	−2.25889			−0.185055			−0.0925276	−	0.995710i	$-0.529495\pi$
$149$	−2.25889			−0.185055			−0.0925276	+	0.995710i	$0.529495\pi$
$150$		0			0
$151$	−8.92575	+	15.4599i	−0.726367	+	1.25810i	0.232042	+	0.972706i	$0.425459\pi$
$151$	−8.92575	+	15.4599i	−0.726367	+	1.25810i	−0.958409	+	0.285399i	$0.907874\pi$
$152$		0			0
$153$	5.95203	−	10.3092i	0.481193	−	0.833451i
$154$		0			0
$155$	−1.45926	+	2.52751i	−0.117211	+	0.203015i
$156$		0			0
$157$	−4.67741	−	8.10151i	−0.373298	−	0.646571i	0.616773	−	0.787141i	$-0.288440\pi$
$157$	−4.67741	−	8.10151i	−0.373298	−	0.646571i	−0.990071	+	0.140570i	$0.955106\pi$
$158$		0			0
$159$	14.6782			1.16405
$160$		0			0
$161$	1.27334	−	2.20549i	0.100353	−	0.173817i
$162$		0			0
$163$	−6.72538	−	11.6487i	−0.526772	−	0.912396i	−0.999513	−	0.0311947i	$-0.990069\pi$
$163$	−6.72538	−	11.6487i	−0.526772	−	0.912396i	0.472741	−	0.881201i	$-0.343265\pi$
$164$		0			0
$165$	3.17741	+	5.50344i	0.247361	+	0.428442i
$166$		0			0
$167$	0.984263	−	1.70479i	0.0761646	−	0.131921i	−0.825428	−	0.564508i	$-0.809066\pi$
$167$	0.984263	−	1.70479i	0.0761646	−	0.131921i	0.901592	+	0.432587i	$0.142399\pi$
$168$		0			0
$169$	1.70760	+	2.95765i	0.131354	+	0.227512i
$170$		0			0
$171$	−0.308890			−0.0236214
$172$		0			0
$173$	7.41852	+	12.8493i	0.564020	+	0.976911i	0.997140	+	0.0755749i	$0.0240792\pi$
$173$	7.41852	+	12.8493i	0.564020	+	0.976911i	−0.433120	+	0.901336i	$0.642587\pi$
$174$		0			0
$175$	2.96445			0.224091
$176$		0			0
$177$	−16.2233			−1.21942
$178$		0			0
$179$	7.67409			0.573588			0.286794	−	0.957992i	$-0.407410\pi$
$179$	7.67409			0.573588			0.286794	+	0.957992i	$0.407410\pi$
$180$		0			0
$181$	−1.75889	+	3.04648i	−0.130737	+	0.226443i	−0.923961	−	0.382487i	$-0.875068\pi$
$181$	−1.75889	+	3.04648i	−0.130737	+	0.226443i	0.793224	+	0.608930i	$0.208401\pi$
$182$		0			0
$183$	8.00723	+	13.8689i	0.591911	+	1.02522i
$184$		0			0
$185$	3.93630	+	4.63741i	0.289402	+	0.340949i
$186$		0			0
$187$	9.97704	+	17.2807i	0.729593	+	1.26369i
$188$		0			0
$189$	−1.01574	+	1.75931i	−0.0738840	+	0.127971i
$190$		0			0
$191$	−17.2733			−1.24986			−0.624928	−	0.780683i	$-0.714872\pi$
$191$	−17.2733			−1.24986			−0.624928	+	0.780683i	$0.714872\pi$
$192$		0			0
$193$	−4.09593			−0.294832			−0.147416	−	0.989075i	$-0.547096\pi$
$193$	−4.09593			−0.294832			−0.147416	+	0.989075i	$0.547096\pi$
$194$		0			0
$195$	6.74111			0.482741
$196$		0			0
$197$	−9.95075	−	17.2352i	−0.708962	−	1.22796i	−0.965243	−	0.261355i	$-0.915831\pi$
$197$	−9.95075	−	17.2352i	−0.708962	−	1.22796i	0.256281	−	0.966602i	$-0.417503\pi$
$198$		0			0
$199$	−8.51777			−0.603809			−0.301905	−	0.953338i	$-0.597622\pi$
$199$	−8.51777			−0.603809			−0.301905	+	0.953338i	$0.597622\pi$
$200$		0			0
$201$	−11.2891	−	19.5533i	−0.796270	−	1.37918i
$202$		0			0
$203$	−1.70964	+	2.96118i	−0.119993	+	0.207834i
$204$		0			0
$205$	0.322590	+	0.558743i	0.0225307	+	0.0390243i
$206$		0			0
$207$	−2.99149	−	5.18141i	−0.207923	−	0.360133i
$208$		0			0
$209$	0.258887	−	0.448406i	0.0179076	−	0.0310169i
$210$		0			0
$211$	−24.1919			−1.66544			−0.832718	−	0.553697i	$-0.813217\pi$
$211$	−24.1919			−1.66544			−0.832718	+	0.553697i	$0.813217\pi$
$212$		0			0
$213$	5.93426	+	10.2784i	0.406609	+	0.704267i
$214$		0			0
$215$	1.74111	−	3.01570i	0.118743	−	0.205669i
$216$		0			0
$217$	−1.08148	+	1.87317i	−0.0734155	+	0.127159i
$218$		0			0
$219$	−13.4508	+	23.2974i	−0.908918	+	1.57429i
$220$		0			0
$221$	21.1670			1.42385
$222$		0			0
$223$	15.1104			1.01187			0.505933	−	0.862573i	$-0.331148\pi$
$223$	15.1104			1.01187			0.505933	+	0.862573i	$0.331148\pi$
$224$		0			0
$225$	3.48223	−	6.03139i	0.232148	−	0.402093i
$226$		0			0
$227$	−8.82982	+	15.2937i	−0.586056	+	1.01508i	0.408687	+	0.912674i	$0.365987\pi$
$227$	−8.82982	+	15.2937i	−0.586056	+	1.01508i	−0.994743	+	0.102404i	$0.967347\pi$
$228$		0			0
$229$	−13.1282	+	22.7386i	−0.867533	+	1.50261i	−0.00302375	+	0.999995i	$0.500962\pi$
$229$	−13.1282	+	22.7386i	−0.867533	+	1.50261i	−0.864510	+	0.502616i	$0.832371\pi$
$230$		0			0
$231$	2.35482	+	4.07867i	0.154936	+	0.268357i
$232$		0			0
$233$	21.8411			1.43086			0.715430	−	0.698685i	$-0.246231\pi$
$233$	21.8411			1.43086			0.715430	+	0.698685i	$0.246231\pi$
$234$		0			0
$235$	4.89556	−	8.47936i	0.319351	−	0.553132i
$236$		0			0
$237$	−13.6439	−	23.6319i	−0.886266	−	1.53506i
$238$		0			0
$239$	−8.20760	−	14.2160i	−0.530906	−	0.919556i	−0.999350	−	0.0360623i	$-0.988519\pi$
$239$	−8.20760	−	14.2160i	−0.530906	−	0.919556i	0.468444	−	0.883493i	$-0.344815\pi$
$240$		0			0
$241$	2.06574	−	3.57797i	0.133066	−	0.230477i	−0.791791	−	0.610792i	$-0.790851\pi$
$241$	2.06574	−	3.57797i	0.133066	−	0.230477i	0.924857	+	0.380315i	$0.124184\pi$
$242$		0			0
$243$	8.07297	+	13.9828i	0.517881	+	0.896996i
$244$		0			0
$245$	6.45075			0.412123
$246$		0			0
$247$	−0.274624	−	0.475663i	−0.0174739	−	0.0302657i
$248$		0			0
$249$	18.2233			1.15486
$250$		0			0
$251$	−11.1563			−0.704180			−0.352090	−	0.935966i	$-0.614529\pi$
$251$	−11.1563			−0.704180			−0.352090	+	0.935966i	$0.614529\pi$
$252$		0			0
$253$	10.0289			0.630512
$254$		0			0
$255$	−7.44352	+	12.8926i	−0.466132	+	0.807364i
$256$		0			0
$257$	7.51445	+	13.0154i	0.468739	+	0.811879i	0.999362	−	0.0357287i	$-0.0113752\pi$
$257$	7.51445	+	13.0154i	0.468739	+	0.811879i	−0.530623	+	0.847608i	$0.678042\pi$
$258$		0			0
$259$	2.91724	+	3.43684i	0.181268	+	0.213555i
$260$		0			0
$261$	4.01649	+	6.95677i	0.248615	+	0.430613i
$262$		0			0
$263$	12.4665	−	21.5926i	0.768717	−	1.33146i	−0.169542	−	0.985523i	$-0.554229\pi$
$263$	12.4665	−	21.5926i	0.768717	−	1.33146i	0.938259	−	0.345933i	$-0.112438\pi$
$264$		0			0
$265$	−6.74111			−0.414103
$266$		0			0
$267$	34.2063			2.09339
$268$		0			0
$269$	14.1919			0.865293			0.432647	−	0.901564i	$-0.357580\pi$
$269$	14.1919			0.865293			0.432647	+	0.901564i	$0.357580\pi$
$270$		0			0
$271$	4.78389	+	8.28594i	0.290601	+	0.503335i	0.973952	−	0.226755i	$-0.0728116\pi$
$271$	4.78389	+	8.28594i	0.290601	+	0.503335i	−0.683351	+	0.730090i	$0.739478\pi$
$272$		0			0
$273$	4.99593			0.302367
$274$		0			0
$275$	5.83705	+	10.1101i	0.351987	+	0.609659i
$276$		0			0
$277$	3.41852	−	5.92105i	0.205399	−	0.355762i	−0.744861	−	0.667220i	$-0.767484\pi$
$277$	3.41852	−	5.92105i	0.205399	−	0.355762i	0.950260	+	0.311458i	$0.100817\pi$
$278$		0			0
$279$	2.54074	+	4.40069i	0.152110	+	0.263462i
$280$		0			0
$281$	−5.64186	−	9.77199i	−0.336565	−	0.582948i	0.647219	−	0.762304i	$-0.275932\pi$
$281$	−5.64186	−	9.77199i	−0.336565	−	0.582948i	−0.983784	+	0.179356i	$0.942599\pi$
$282$		0			0
$283$	2.37056	−	4.10592i	0.140915	−	0.244072i	−0.786926	−	0.617047i	$-0.788329\pi$
$283$	2.37056	−	4.10592i	0.140915	−	0.244072i	0.927841	+	0.372975i	$0.121662\pi$
$284$		0			0
$285$	0.386294			0.0228821
$286$		0			0
$287$	0.239076	+	0.414092i	0.0141122	+	0.0244430i
$288$		0			0
$289$	−14.8726	+	25.7601i	−0.874858	+	1.51530i
$290$		0			0
$291$	18.2963	−	31.6901i	1.07255	−	1.85771i
$292$		0			0
$293$	0.241113	−	0.417620i	0.0140860	−	0.0243976i	−0.858896	−	0.512149i	$-0.828849\pi$
$293$	0.241113	−	0.417620i	0.0140860	−	0.0243976i	0.872982	+	0.487752i	$0.162183\pi$
$294$		0			0
$295$	7.45075			0.433800
$296$		0			0
$297$	−8.00000			−0.464207
$298$		0			0
$299$	5.31927	−	9.21325i	0.307621	−	0.532816i
$300$		0			0
$301$	1.29036	−	2.23497i	0.0743752	−	0.128822i
$302$		0			0
$303$	−6.81408	+	11.8023i	−0.391459	+	0.678026i
$304$		0			0
$305$	−3.67741	−	6.36946i	−0.210568	−	0.364714i
$306$		0			0
$307$	3.80814			0.217342			0.108671	−	0.994078i	$-0.465341\pi$
$307$	3.80814			0.217342			0.108671	+	0.994078i	$0.465341\pi$
$308$		0			0
$309$	−21.9830	+	38.0756i	−1.25057	+	2.16605i
$310$		0			0
$311$	−13.4350	−	23.2701i	−0.761830	−	1.31953i	−0.941906	−	0.335875i	$-0.890968\pi$
$311$	−13.4350	−	23.2701i	−0.761830	−	1.31953i	0.180077	−	0.983653i	$-0.442365\pi$
$312$		0			0
$313$	−9.38705	−	16.2588i	−0.530587	−	0.919004i	−0.999363	−	0.0356870i	$-0.988638\pi$
$313$	−9.38705	−	16.2588i	−0.530587	−	0.919004i	0.468776	−	0.883317i	$-0.344695\pi$
$314$		0			0
$315$	−0.645181	+	1.11749i	−0.0363518	+	0.0629632i
$316$		0			0
$317$	−9.90075	−	17.1486i	−0.556081	−	0.963161i	−0.997819	−	0.0660167i	$-0.978971\pi$
$317$	−9.90075	−	17.1486i	−0.556081	−	0.963161i	0.441737	−	0.897145i	$-0.354362\pi$
$318$		0			0
$319$	−13.4652			−0.753907
$320$		0			0
$321$	14.6439	+	25.3640i	0.817343	+	1.41568i
$322$		0			0
$323$	1.21296			0.0674908
$324$		0			0
$325$	12.3837			0.686926
$326$		0			0
$327$	14.1145			0.780531
$328$		0			0
$329$	3.62816	−	6.28416i	0.200027	−	0.346457i
$330$		0			0
$331$	3.88833	+	6.73479i	0.213722	+	0.370177i	0.952876	−	0.303359i	$-0.0981080\pi$
$331$	3.88833	+	6.73479i	0.213722	+	0.370177i	−0.739154	+	0.673536i	$0.764775\pi$
$332$		0			0
$333$	10.4193	−	1.89821i	0.570973	−	0.104021i
$334$		0			0
$335$	5.18464	+	8.98005i	0.283267	+	0.490633i
$336$		0			0
$337$	−7.29112	+	12.6286i	−0.397172	+	0.687923i	−0.993376	−	0.114911i	$-0.963342\pi$
$337$	−7.29112	+	12.6286i	−0.397172	+	0.687923i	0.596203	+	0.802833i	$0.296675\pi$
$338$		0			0
$339$	20.9330			1.13692
$340$		0			0
$341$	−8.51777			−0.461263
$342$		0			0
$343$	9.96853			0.538250
$344$		0			0
$345$	3.74111	+	6.47980i	0.201415	+	0.348861i
$346$		0			0
$347$	−3.85406			−0.206897			−0.103449	−	0.994635i	$-0.532988\pi$
$347$	−3.85406			−0.206897			−0.103449	+	0.994635i	$0.532988\pi$
$348$		0			0
$349$	−8.11371	−	14.0534i	−0.434317	−	0.752259i	0.562923	−	0.826509i	$-0.309677\pi$
$349$	−8.11371	−	14.0534i	−0.434317	−	0.752259i	−0.997240	+	0.0742508i	$0.976343\pi$
$350$		0			0
$351$	−4.24315	+	7.34935i	−0.226483	+	0.392279i
$352$		0			0
$353$	11.4685	+	19.8641i	0.610408	+	1.05726i	0.991172	+	0.132585i	$0.0423278\pi$
$353$	11.4685	+	19.8641i	0.610408	+	1.05726i	−0.380764	+	0.924672i	$0.624339\pi$
$354$		0			0
$355$	−2.72538	−	4.72049i	−0.144648	−	0.250538i
$356$		0			0
$357$	−5.51649	+	9.55484i	−0.291964	+	0.505696i
$358$		0			0
$359$	−37.4193			−1.97491			−0.987457	−	0.157888i	$-0.949531\pi$
$359$	−37.4193			−1.97491			−0.987457	+	0.157888i	$0.949531\pi$
$360$		0			0
$361$	9.48426	+	16.4272i	0.499172	+	0.864591i
$362$		0			0
$363$	2.70241	−	4.68071i	0.141840	−	0.245674i
$364$		0			0
$365$	6.17741	−	10.6996i	0.323340	−	0.560042i
$366$		0			0
$367$	−3.88833	+	6.73479i	−0.202969	+	0.351553i	−0.949484	−	0.313816i	$-0.898392\pi$
$367$	−3.88833	+	6.73479i	−0.202969	+	0.351553i	0.746515	+	0.665369i	$0.231726\pi$
$368$		0			0
$369$	1.12333			0.0584783
$370$		0			0
$371$	−4.99593			−0.259376
$372$		0			0
$373$	−5.69186	+	9.85860i	−0.294714	+	0.510459i	−0.974918	−	0.222563i	$-0.928558\pi$
$373$	−5.69186	+	9.85860i	−0.294714	+	0.510459i	0.680205	+	0.733022i	$0.261891\pi$
$374$		0			0
$375$	−9.79834	+	16.9712i	−0.505984	+	0.876390i
$376$		0			0
$377$	−7.14186	+	12.3701i	−0.367825	+	0.637091i
$378$		0			0
$379$	0.756850	+	1.31090i	0.0388768	+	0.0673365i	0.884809	−	0.465954i	$-0.154289\pi$
$379$	0.756850	+	1.31090i	0.0388768	+	0.0673365i	−0.845932	+	0.533290i	$0.820955\pi$
$380$		0			0
$381$	11.9685			0.613166
$382$		0			0
$383$	11.2431	−	19.4737i	0.574498	−	0.995060i	−0.421598	−	0.906783i	$-0.638531\pi$
$383$	11.2431	−	19.4737i	0.574498	−	0.995060i	0.996096	−	0.0882770i	$-0.0281361\pi$
$384$		0			0
$385$	−1.08148	−	1.87317i	−0.0551172	−	0.0954658i
$386$		0			0
$387$	−3.03147	−	5.25067i	−0.154098	−	0.266906i
$388$		0			0
$389$	10.2241	−	17.7086i	0.518382	−	0.897864i	−0.481390	−	0.876507i	$-0.659868\pi$
$389$	10.2241	−	17.7086i	0.518382	−	0.897864i	0.999772	−	0.0213575i	$-0.00679883\pi$
$390$		0			0
$391$	11.7471	+	20.3465i	0.594074	+	1.02897i
$392$		0			0
$393$	1.51370			0.0763561
$394$		0			0
$395$	6.26611	+	10.8532i	0.315282	+	0.546085i
$396$		0			0
$397$	22.4508			1.12677			0.563385	−	0.826194i	$-0.309499\pi$
$397$	22.4508			1.12677			0.563385	+	0.826194i	$0.309499\pi$
$398$		0			0
$399$	0.286287			0.0143323
$400$		0			0
$401$	−3.64518			−0.182032			−0.0910158	−	0.995849i	$-0.529011\pi$
$401$	−3.64518			−0.182032			−0.0910158	+	0.995849i	$0.529011\pi$
$402$		0			0
$403$	−4.51777	+	7.82501i	−0.225046	+	0.389792i
$404$		0			0
$405$	−5.59593	−	9.69244i	−0.278064	−	0.481621i
$406$		0			0
$407$	−5.97704	+	16.7162i	−0.296271	+	0.828593i
$408$		0			0
$409$	−14.8693	−	25.7543i	−0.735238	−	1.27347i	−0.954619	−	0.297831i	$-0.903737\pi$
$409$	−14.8693	−	25.7543i	−0.735238	−	1.27347i	0.219380	−	0.975639i	$-0.429596\pi$
$410$		0			0
$411$	−2.45926	+	4.25957i	−0.121306	+	0.210109i
$412$		0			0
$413$	5.52185			0.271712
$414$		0			0
$415$	−8.36927			−0.410832
$416$		0			0
$417$	34.0974			1.66976
$418$		0			0
$419$	17.9843	+	31.1497i	0.878589	+	1.52176i	0.852890	+	0.522091i	$0.174848\pi$
$419$	17.9843	+	31.1497i	0.878589	+	1.52176i	0.0256987	+	0.999670i	$0.491819\pi$
$420$		0			0
$421$	−38.3167			−1.86744			−0.933721	−	0.358002i	$-0.883458\pi$
$421$	−38.3167			−1.86744			−0.933721	+	0.358002i	$0.883458\pi$
$422$		0			0
$423$	−8.52372	−	14.7635i	−0.414437	−	0.717827i
$424$		0			0
$425$	−13.6741	+	23.6842i	−0.663291	+	1.14885i
$426$		0			0
$427$	−2.72538	−	4.72049i	−0.131890	−	0.228440i
$428$		0			0
$429$	9.83705	+	17.0383i	0.474937	+	0.822615i
$430$		0			0
$431$	−5.74834	+	9.95642i	−0.276888	+	0.479584i	−0.970610	−	0.240659i	$-0.922636\pi$
$431$	−5.74834	+	9.95642i	−0.276888	+	0.479584i	0.693722	+	0.720243i	$0.255970\pi$
$432$		0			0
$433$	−5.83297			−0.280315			−0.140157	−	0.990129i	$-0.544761\pi$
$433$	−5.83297			−0.280315			−0.140157	+	0.990129i	$0.544761\pi$
$434$		0			0
$435$	−5.02296	−	8.70003i	−0.240833	−	0.417135i
$436$		0			0
$437$	0.304816	−	0.527957i	0.0145813	−	0.0252556i
$438$		0			0
$439$	−2.24315	+	3.88525i	−0.107060	+	0.185433i	−0.914578	−	0.404410i	$-0.867477\pi$
$439$	−2.24315	+	3.88525i	−0.107060	+	0.185433i	0.807518	+	0.589843i	$0.200810\pi$
$440$		0			0
$441$	5.61574	−	9.72675i	0.267416	−	0.463179i
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$	−15.7096			−0.744708
$446$		0			0
$447$	2.45926	−	4.25957i	0.116319	−	0.201471i
$448$		0			0
$449$	−1.16167	+	2.01208i	−0.0548227	+	0.0949557i	−0.892134	−	0.451770i	$-0.850793\pi$
$449$	−1.16167	+	2.01208i	−0.0548227	+	0.0949557i	0.837312	+	0.546726i	$0.184126\pi$
$450$		0			0
$451$	−0.941487	+	1.63070i	−0.0443329	+	0.0767868i
$452$		0			0
$453$	−19.4350	−	33.6624i	−0.913137	−	1.58160i
$454$		0			0
$455$	−2.29444			−0.107565
$456$		0			0
$457$	4.19518	−	7.26627i	0.196242	−	0.339902i	−0.751065	−	0.660229i	$-0.770459\pi$
$457$	4.19518	−	7.26627i	0.196242	−	0.339902i	0.947307	+	0.320327i	$0.103793\pi$
$458$		0			0
$459$	−9.37056	−	16.2303i	−0.437380	−	0.757565i
$460$		0			0
$461$	−16.9987	−	29.4426i	−0.791709	−	1.37128i	−0.924908	−	0.380191i	$-0.875858\pi$
$461$	−16.9987	−	29.4426i	−0.791709	−	1.37128i	0.133199	−	0.991089i	$-0.457475\pi$
$462$		0			0
$463$	−11.1117	+	19.2460i	−0.516403	+	0.894436i	0.483416	+	0.875391i	$0.339396\pi$
$463$	−11.1117	+	19.2460i	−0.516403	+	0.894436i	−0.999819	+	0.0190454i	$0.993937\pi$
$464$		0			0
$465$	−3.17741	−	5.50344i	−0.147349	−	0.255216i
$466$		0			0
$467$	7.29036			0.337358			0.168679	−	0.985671i	$-0.446050\pi$
$467$	7.29036			0.337358			0.168679	+	0.985671i	$0.446050\pi$
$468$		0			0
$469$	3.84240	+	6.65523i	0.177426	+	0.307310i
$470$		0			0
$471$	20.3693			0.938567
$472$		0			0
$473$	10.1630			0.467293
$474$		0			0
$475$	0.709639			0.0325605
$476$		0			0
$477$	−5.86852	+	10.1646i	−0.268701	+	0.465404i
$478$		0			0
$479$	−0.792398	−	1.37247i	−0.0362056	−	0.0627099i	0.847355	−	0.531027i	$-0.178194\pi$
$479$	−0.792398	−	1.37247i	−0.0362056	−	0.0627099i	−0.883560	+	0.468317i	$0.844860\pi$
$480$		0			0
$481$	12.1865	+	14.3571i	0.555657	+	0.654628i
$482$		0			0
$483$	2.77259	+	4.80226i	0.126157	+	0.218510i
$484$		0			0
$485$	−8.40279	+	14.5541i	−0.381551	+	0.660865i
$486$		0			0
$487$	−34.7845			−1.57624			−0.788118	−	0.615525i	$-0.788944\pi$
$487$	−34.7845			−1.57624			−0.788118	+	0.615525i	$0.788944\pi$
$488$		0			0
$489$	29.2878			1.32444
$490$		0			0
$491$	14.8267			0.669118			0.334559	−	0.942375i	$-0.391413\pi$
$491$	14.8267			0.669118			0.334559	+	0.942375i	$0.391413\pi$
$492$		0			0
$493$	−15.7721	−	27.3180i	−0.710338	−	1.23034i
$494$		0			0
$495$	−5.08148			−0.228395
$496$		0			0
$497$	−2.01981	−	3.49842i	−0.0906009	−	0.156925i
$498$		0			0
$499$	−5.39352	+	9.34185i	−0.241447	+	0.418199i	−0.961127	−	0.276108i	$-0.910955\pi$
$499$	−5.39352	+	9.34185i	−0.241447	+	0.418199i	0.719680	+	0.694306i	$0.244289\pi$
$500$		0			0
$501$	2.14314	+	3.71203i	0.0957486	+	0.165841i
$502$		0			0
$503$	−16.2806	−	28.1988i	−0.725915	−	1.25732i	−0.958596	−	0.284768i	$-0.908083\pi$
$503$	−16.2806	−	28.1988i	−0.725915	−	1.25732i	0.232682	−	0.972553i	$-0.425250\pi$
$504$		0			0
$505$	3.12944	−	5.42036i	0.139258	−	0.241203i
$506$		0			0
$507$	−7.43630			−0.330258
$508$		0			0
$509$	−10.9363	−	18.9422i	−0.484743	−	0.839599i	0.515104	−	0.857128i	$-0.327753\pi$
$509$	−10.9363	−	18.9422i	−0.484743	−	0.839599i	−0.999846	+	0.0175288i	$0.994420\pi$
$510$		0			0
$511$	4.57816	−	7.92960i	0.202526	−	0.350785i
$512$		0			0
$513$	−0.243150	+	0.421148i	−0.0107353	+	0.0185941i
$514$		0			0
$515$	10.0959	−	17.4867i	0.444880	−	0.770555i
$516$		0			0
$517$	28.5756			1.25675
$518$		0			0
$519$	−32.3063			−1.41809
$520$		0			0
$521$	18.8672	−	32.6790i	0.826589	−	1.43169i	−0.0741104	−	0.997250i	$-0.523612\pi$
$521$	18.8672	−	32.6790i	0.826589	−	1.43169i	0.900699	−	0.434444i	$-0.143055\pi$
$522$		0			0
$523$	21.6669	−	37.5281i	0.947426	−	1.64099i	0.196606	−	0.980483i	$-0.437008\pi$
$523$	21.6669	−	37.5281i	0.947426	−	1.64099i	0.750820	−	0.660507i	$-0.229659\pi$
$524$		0			0
$525$	−3.22741	+	5.59004i	−0.140856	+	0.243969i
$526$		0			0
$527$	−9.97704	−	17.2807i	−0.434606	−	0.752761i
$528$		0			0
$529$	−11.1919			−0.486603
$530$		0			0
$531$	6.48630	−	11.2346i	0.281481	−	0.487540i
$532$		0			0
$533$	0.998718	+	1.72983i	0.0432593	+	0.0749273i
$534$		0			0
$535$	−6.72538	−	11.6487i	−0.290763	−	0.503617i
$536$		0			0
$537$	−8.35482	+	14.4710i	−0.360537	+	0.624469i
$538$		0			0
$539$	9.41333	+	16.3044i	0.405461	+	0.702279i
$540$		0			0
$541$	16.1959			0.696318			0.348159	−	0.937436i	$-0.386807\pi$
$541$	16.1959			0.696318			0.348159	+	0.937436i	$0.386807\pi$
$542$		0			0
$543$	−3.82982	−	6.63344i	−0.164353	−	0.284668i
$544$		0			0
$545$	−6.48223			−0.277668
$546$		0			0
$547$	16.0459			0.686074			0.343037	−	0.939322i	$-0.388544\pi$
$547$	16.0459			0.686074			0.343037	+	0.939322i	$0.388544\pi$
$548$		0			0
$549$	−12.8056			−0.546528
$550$		0			0
$551$	−0.409258	+	0.708856i	−0.0174350	+	0.0301983i
$552$		0			0
$553$	4.64390	+	8.04347i	0.197479	+	0.342043i
$554$		0			0
$555$	−13.0302	+	2.37387i	−0.553101	+	0.100765i
$556$		0			0
$557$	15.2556	+	26.4234i	0.646399	+	1.11960i	0.983976	+	0.178298i	$0.0570592\pi$
$557$	15.2556	+	26.4234i	0.646399	+	1.11960i	−0.337577	+	0.941298i	$0.609607\pi$
$558$		0			0
$559$	5.39037	−	9.33639i	0.227988	−	0.394887i
$560$		0			0
$561$	−43.4482			−1.83438
$562$		0			0
$563$	31.1104			1.31115			0.655573	−	0.755132i	$-0.272427\pi$
$563$	31.1104			1.31115			0.655573	+	0.755132i	$0.272427\pi$
$564$		0			0
$565$	−9.61371			−0.404452
$566$		0			0
$567$	−4.14722	−	7.18319i	−0.174167	−	0.301666i
$568$		0			0
$569$	−18.4508			−0.773496			−0.386748	−	0.922185i	$-0.626402\pi$
$569$	−18.4508			−0.773496			−0.386748	+	0.922185i	$0.626402\pi$
$570$		0			0
$571$	−3.07425	−	5.32476i	−0.128653	−	0.222834i	0.794502	−	0.607262i	$-0.207732\pi$
$571$	−3.07425	−	5.32476i	−0.128653	−	0.222834i	−0.923155	+	0.384428i	$0.874399\pi$
$572$		0			0
$573$	18.8056	−	32.5722i	0.785614	−	1.36072i
$574$		0			0
$575$	6.87259	+	11.9037i	0.286607	+	0.496418i
$576$		0			0
$577$	−1.72538	−	2.98844i	−0.0718283	−	0.124410i	0.827874	−	0.560914i	$-0.189550\pi$
$577$	−1.72538	−	2.98844i	−0.0718283	−	0.124410i	−0.899703	+	0.436503i	$0.856217\pi$
$578$		0			0
$579$	4.45926	−	7.72367i	0.185321	−	0.320985i
$580$		0			0
$581$	−6.20258			−0.257326
$582$		0			0
$583$	−9.83705	−	17.0383i	−0.407409	−	0.705653i
$584$		0			0
$585$	−2.69518	+	4.66820i	−0.111432	+	0.193006i
$586$		0			0
$587$	6.91130	−	11.9707i	0.285260	−	0.494084i	−0.687412	−	0.726267i	$-0.741253\pi$
$587$	6.91130	−	11.9707i	0.285260	−	0.494084i	0.972672	+	0.232183i	$0.0745868\pi$
$588$		0			0
$589$	−0.258887	+	0.448406i	−0.0106673	+	0.0184762i
$590$		0			0
$591$	43.3337			1.78251
$592$		0			0
$593$	−32.6715			−1.34166			−0.670829	−	0.741612i	$-0.734062\pi$
$593$	−32.6715			−1.34166			−0.670829	+	0.741612i	$0.734062\pi$
$594$		0			0
$595$	2.53351	−	4.38817i	0.103864	−	0.179897i
$596$		0			0
$597$	9.27334	−	16.0619i	0.379533	−	0.657370i
$598$		0			0
$599$	7.71687	−	13.3660i	0.315303	−	0.546120i	−0.664199	−	0.747556i	$-0.731227\pi$
$599$	7.71687	−	13.3660i	0.315303	−	0.546120i	0.979502	+	0.201436i	$0.0645607\pi$
$600$		0			0
$601$	−0.744432	−	1.28939i	−0.0303660	−	0.0525955i	0.850443	−	0.526067i	$-0.176334\pi$
$601$	−0.744432	−	1.28939i	−0.0303660	−	0.0525955i	−0.880809	+	0.473472i	$0.843001\pi$
$602$		0			0
$603$	18.0541			0.735219
$604$		0			0
$605$	−1.24111	+	2.14967i	−0.0504584	+	0.0873965i
$606$		0			0
$607$	−3.12425	−	5.41137i	−0.126810	−	0.219641i	0.795629	−	0.605784i	$-0.207140\pi$
$607$	−3.12425	−	5.41137i	−0.126810	−	0.219641i	−0.922439	+	0.386143i	$0.873807\pi$
$608$		0			0
$609$	−3.72258	−	6.44770i	−0.150847	−	0.261274i
$610$		0			0
$611$	15.1563	−	26.2515i	0.613159	−	1.06202i
$612$		0			0
$613$	13.8693	+	24.0223i	0.560175	+	0.970251i	0.997481	+	0.0709383i	$0.0225993\pi$
$613$	13.8693	+	24.0223i	0.560175	+	0.970251i	−0.437306	+	0.899313i	$0.644067\pi$
$614$		0			0
$615$	−1.40482			−0.0566479
$616$		0			0
$617$	−3.72538	−	6.45254i	−0.149978	−	0.259769i	0.781241	−	0.624229i	$-0.214587\pi$
$617$	−3.72538	−	6.45254i	−0.149978	−	0.259769i	−0.931219	+	0.364460i	$0.881254\pi$
$618$		0			0
$619$	−16.1919			−0.650806			−0.325403	−	0.945575i	$-0.605500\pi$
$619$	−16.1919			−0.650806			−0.325403	+	0.945575i	$0.605500\pi$
$620$		0			0
$621$	−9.41928			−0.377983
$622$		0			0
$623$	−11.6426			−0.466452
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$	0.563703	+	0.976363i	0.0225121	+	0.0389922i
$628$		0			0
$629$	−40.9147	+	7.45394i	−1.63137	+	0.297208i
$630$		0			0
$631$	−0.393521	−	0.681598i	−0.0156658	−	0.0271340i	0.858086	−	0.513506i	$-0.171653\pi$
$631$	−0.393521	−	0.681598i	−0.0156658	−	0.0271340i	−0.873752	+	0.486372i	$0.838320\pi$
$632$		0			0
$633$	26.3378	−	45.6184i	1.04683	−	1.81317i
$634$		0			0
$635$	−5.49668			−0.218129
$636$		0			0
$637$	19.9711			0.791283
$638$		0			0
$639$	−9.49037			−0.375433
$640$		0			0
$641$	10.1741	+	17.6220i	0.401852	+	0.696029i	0.993950	−	0.109838i	$-0.0350332\pi$
$641$	10.1741	+	17.6220i	0.401852	+	0.696029i	−0.592097	+	0.805867i	$0.701700\pi$
$642$		0			0
$643$	−0.429658			−0.0169441			−0.00847203	−	0.999964i	$-0.502697\pi$
$643$	−0.429658			−0.0169441			−0.00847203	+	0.999964i	$0.502697\pi$
$644$		0			0
$645$	3.79112	+	6.56641i	0.149275	+	0.258552i
$646$		0			0
$647$	5.40610	−	9.36365i	0.212536	−	0.368123i	−0.739972	−	0.672638i	$-0.765161\pi$
$647$	5.40610	−	9.36365i	0.212536	−	0.368123i	0.952507	+	0.304515i	$0.0984944\pi$
$648$		0			0
$649$	10.8726	+	18.8319i	0.426787	+	0.739216i
$650$		0			0
$651$	−2.35482	−	4.07867i	−0.0922926	−	0.159856i
$652$		0			0
$653$	2.12816	−	3.68608i	0.0832814	−	0.144248i	−0.821376	−	0.570387i	$-0.806793\pi$
$653$	2.12816	−	3.68608i	0.0832814	−	0.144248i	0.904658	+	0.426139i	$0.140127\pi$
$654$		0			0
$655$	−0.695184			−0.0271631
$656$		0			0
$657$	−10.7556	−	18.6292i	−0.419615	−	0.726794i
$658$		0			0
$659$	−22.5980	+	39.1408i	−0.880292	+	1.52471i	−0.0292754	+	0.999571i	$0.509320\pi$
$659$	−22.5980	+	39.1408i	−0.880292	+	1.52471i	−0.851017	+	0.525139i	$0.824013\pi$
$660$		0			0
$661$	3.01777	−	5.22694i	0.117378	−	0.203304i	−0.801350	−	0.598196i	$-0.795884\pi$
$661$	3.01777	−	5.22694i	0.117378	−	0.203304i	0.918728	+	0.394891i	$0.129218\pi$
$662$		0			0
$663$	−23.0446	+	39.9145i	−0.894980	+	1.55015i
$664$		0			0
$665$	−0.131481			−0.00509860
$666$		0			0
$667$	−15.8541			−0.613872
$668$		0			0
$669$	−16.4508	+	28.4935i	−0.636023	+	1.10162i
$670$		0			0
$671$	10.7326	−	18.5894i	0.414328	−	0.717636i
$672$		0			0
$673$	23.9317	−	41.4509i	0.922499	−	1.59782i	0.126964	−	0.991907i	$-0.459477\pi$
$673$	23.9317	−	41.4509i	0.922499	−	1.59782i	0.795535	−	0.605908i	$-0.207190\pi$
$674$		0			0
$675$	−5.48223	−	9.49549i	−0.211011	−	0.365482i
$676$		0			0
$677$	45.0893			1.73292			0.866461	−	0.499244i	$-0.166389\pi$
$677$	45.0893			1.73292			0.866461	+	0.499244i	$0.166389\pi$
$678$		0			0
$679$	−6.22741	+	10.7862i	−0.238986	+	0.413936i
$680$		0			0
$681$	−19.2261	−	33.3006i	−0.736747	−	1.27608i
$682$		0			0
$683$	−4.01574	−	6.95546i	−0.153658	−	0.266143i	0.778912	−	0.627134i	$-0.215772\pi$
$683$	−4.01574	−	6.95546i	−0.153658	−	0.266143i	−0.932570	+	0.360990i	$0.882439\pi$
$684$		0			0
$685$	1.12944	−	1.95625i	0.0431538	−	0.0747446i
$686$		0			0
$687$	−28.5854	−	49.5113i	−1.09060	−	1.88898i
$688$		0			0
$689$	−20.8700			−0.795085
$690$		0			0
$691$	8.78389	+	15.2141i	0.334155	+	0.578773i	0.983322	−	0.181872i	$-0.0582158\pi$
$691$	8.78389	+	15.2141i	0.334155	+	0.578773i	−0.649167	+	0.760646i	$0.724882\pi$
$692$		0			0
$693$	−3.76595			−0.143057
$694$		0			0
$695$	−15.6596			−0.594004
$696$		0			0
$697$	−4.41113			−0.167083
$698$		0			0
$699$	−23.7785	+	41.1856i	−0.899387	+	1.55778i
$700$		0			0
$701$	2.01574	+	3.49136i	0.0761333	+	0.131867i	0.901579	−	0.432615i	$-0.142409\pi$
$701$	2.01574	+	3.49136i	0.0761333	+	0.131867i	−0.825445	+	0.564482i	$0.809076\pi$
$702$		0			0
$703$	0.698337	+	0.822721i	0.0263383	+	0.0310295i
$704$		0			0
$705$	10.6596	+	18.4630i	0.401465	+	0.695358i
$706$		0			0
$707$	2.31927	−	4.01710i	0.0872252	−	0.151078i
$708$		0			0
$709$	9.15632			0.343873			0.171936	−	0.985108i	$-0.444998\pi$
$709$	9.15632			0.343873			0.171936	+	0.985108i	$0.444998\pi$
$710$		0			0
$711$	21.8200			0.818315
$712$		0			0
$713$	−10.0289			−0.375586
$714$		0			0
$715$	−4.51777	−	7.82501i	−0.168955	−	0.292639i
$716$		0			0
$717$	35.7426			1.33483
$718$		0			0
$719$	9.11761	+	15.7922i	0.340030	+	0.588949i	0.984438	−	0.175733i	$-0.0562296\pi$
$719$	9.11761	+	15.7922i	0.340030	+	0.588949i	−0.644408	+	0.764682i	$0.722896\pi$
$720$		0			0
$721$	7.48223	−	12.9596i	0.278653	−	0.482641i
$722$		0			0
$723$	4.49796	+	7.79070i	0.167281	+	0.289739i
$724$		0			0
$725$	−9.22741	−	15.9823i	−0.342698	−	0.593570i
$726$		0			0
$727$	−3.88833	+	6.73479i	−0.144210	+	0.249779i	−0.929078	−	0.369884i	$-0.879397\pi$
$727$	−3.88833	+	6.73479i	−0.144210	+	0.249779i	0.784868	+	0.619663i	$0.212731\pi$
$728$		0			0
$729$	−1.58072			−0.0585453
$730$		0			0
$731$	11.9041	+	20.6185i	0.440288	+	0.762601i
$732$		0			0
$733$	−5.41649	+	9.38163i	−0.200062	+	0.346518i	−0.948548	−	0.316632i	$-0.897448\pi$
$733$	−5.41649	+	9.38163i	−0.200062	+	0.346518i	0.748486	+	0.663151i	$0.230781\pi$
$734$		0			0
$735$	−7.02296	+	12.1641i	−0.259046	+	0.448681i
$736$		0			0
$737$	−15.1315	+	26.2085i	−0.557375	+	0.965402i
$738$		0			0
$739$	31.9119			1.17390			0.586949	−	0.809624i	$-0.300329\pi$
$739$	31.9119			1.17390			0.586949	+	0.809624i	$0.300329\pi$
$740$		0			0
$741$	1.19594			0.0439339
$742$		0			0
$743$	−13.5395	+	23.4510i	−0.496714	+	0.860335i	−0.999993	−	0.00378964i	$-0.998794\pi$
$743$	−13.5395	+	23.4510i	−0.496714	+	0.860335i	0.503278	+	0.864124i	$0.332127\pi$
$744$		0			0
$745$	−1.12944	+	1.95625i	−0.0413796	+	0.0716716i
$746$		0			0
$747$	−7.28593	+	12.6196i	−0.266578	+	0.461727i
$748$		0			0
$749$	−4.98426	−	8.63300i	−0.182121	−	0.315443i
$750$		0			0
$751$	6.77259			0.247135			0.123568	−	0.992336i	$-0.460566\pi$
$751$	6.77259			0.247135			0.123568	+	0.992336i	$0.460566\pi$
$752$		0			0
$753$	12.1459	−	21.0374i	0.442622	−	0.766645i
$754$		0			0
$755$	8.92575	+	15.4599i	0.324841	+	0.562642i
$756$		0			0
$757$	12.2241	+	21.1728i	0.444292	+	0.769537i	0.998003	−	0.0631726i	$-0.0201219\pi$
$757$	12.2241	+	21.1728i	0.444292	+	0.769537i	−0.553710	+	0.832709i	$0.686789\pi$
$758$		0			0
$759$	−10.9185	+	18.9114i	−0.396317	+	0.686442i
$760$		0			0
$761$	0.595932	+	1.03218i	0.0216025	+	0.0374167i	0.876625	−	0.481175i	$-0.159790\pi$
$761$	0.595932	+	1.03218i	0.0216025	+	0.0374167i	−0.855022	+	0.518592i	$0.826457\pi$
$762$		0			0
$763$	−4.80406			−0.173919
$764$		0			0
$765$	−5.95203	−	10.3092i	−0.215196	−	0.372731i
$766$		0			0
$767$	23.0670			0.832902
$768$		0			0
$769$	37.7741			1.36217			0.681084	−	0.732205i	$-0.261509\pi$
$769$	37.7741			1.36217			0.681084	+	0.732205i	$0.261509\pi$
$770$		0			0
$771$	−32.7241			−1.17853
$772$		0			0
$773$	−23.6919	+	41.0355i	−0.852137	+	1.47594i	0.0271386	+	0.999632i	$0.491360\pi$
$773$	−23.6919	+	41.0355i	−0.852137	+	1.47594i	−0.879276	+	0.476313i	$0.841973\pi$
$774$		0			0
$775$	−5.83705	−	10.1101i	−0.209673	−	0.363164i
$776$		0			0
$777$	−9.65684	+	1.75931i	−0.346437	+	0.0631148i
$778$		0			0
$779$	0.0572306	+	0.0991264i	0.00205050	+	0.00355157i
$780$		0			0
$781$	7.95407	−	13.7769i	0.284619	−	0.492975i
$782$		0			0
$783$	12.6467			0.451956
$784$		0			0
$785$	−9.35482			−0.333888
$786$		0			0
$787$	28.0578			1.00015			0.500077	−	0.865981i	$-0.333305\pi$
$787$	28.0578			1.00015			0.500077	+	0.865981i	$0.333305\pi$
$788$		0			0
$789$	27.1447	+	47.0159i	0.966375	+	1.67381i
$790$		0			0
$791$	−7.12484			−0.253330
$792$		0			0
$793$	−11.3850	−	19.7194i	−0.404294	−	0.700257i
$794$		0			0
$795$	7.33908	−	12.7117i	0.260290	−	0.450836i
$796$		0			0
$797$	−4.43094	−	7.67461i	−0.156952	−	0.271849i	0.776816	−	0.629728i	$-0.216833\pi$
$797$	−4.43094	−	7.67461i	−0.156952	−	0.271849i	−0.933768	+	0.357879i	$0.883500\pi$
$798$		0			0
$799$	33.4712	+	57.9737i	1.18412	+	2.05096i
$800$		0			0
$801$	−13.6761	+	23.6877i	−0.483222	+	0.836965i
$802$		0			0
$803$	36.0578			1.27245
$804$		0			0
$805$	−1.27334	−	2.20549i	−0.0448794	−	0.0777334i
$806$		0			0
$807$	−15.4508	+	26.7615i	−0.543892	+	0.942049i
$808$		0			0
$809$	22.2076	−	38.4647i	0.780778	−	1.35235i	−0.150712	−	0.988578i	$-0.548156\pi$
$809$	22.2076	−	38.4647i	0.780778	−	1.35235i	0.931489	−	0.363769i	$-0.118510\pi$
$810$		0			0
$811$	18.0487	−	31.2613i	0.633776	−	1.09773i	−0.352997	−	0.935625i	$-0.614837\pi$
$811$	18.0487	−	31.2613i	0.633776	−	1.09773i	0.986773	−	0.162108i	$-0.0518294\pi$
$812$		0			0
$813$	−20.8330			−0.730644
$814$		0			0
$815$	−13.4508			−0.471159
$816$		0			0
$817$	0.308890	−	0.535014i	0.0108067	−	0.0187178i
$818$		0			0
$819$	−1.99744	+	3.45966i	−0.0697960	+	0.120890i
$820$		0			0
$821$	−11.8883	+	20.5912i	−0.414906	+	0.718638i	−0.995419	−	0.0956134i	$-0.969519\pi$
$821$	−11.8883	+	20.5912i	−0.414906	+	0.718638i	0.580513	+	0.814251i	$0.302852\pi$
$822$		0			0
$823$	−22.5395	−	39.0395i	−0.785676	−	1.36083i	−0.928594	−	0.371096i	$-0.878982\pi$
$823$	−22.5395	−	39.0395i	−0.785676	−	1.36083i	0.142918	−	0.989734i	$-0.454351\pi$
$824$		0			0
$825$	−25.4193			−0.884986
$826$		0			0
$827$	−26.5980	+	46.0690i	−0.924902	+	1.60198i	−0.133183	+	0.991091i	$0.542520\pi$
$827$	−26.5980	+	46.0690i	−0.924902	+	1.60198i	−0.791719	+	0.610886i	$0.790813\pi$
$828$		0			0
$829$	17.9028	+	31.0085i	0.621789	+	1.07697i	0.989152	+	0.146893i	$0.0469274\pi$
$829$	17.9028	+	31.0085i	0.621789	+	1.07697i	−0.367363	+	0.930078i	$0.619739\pi$
$830$		0			0
$831$	7.44352	+	12.8926i	0.258213	+	0.447238i
$832$		0			0
$833$	−22.0520	+	38.1953i	−0.764058	+	1.32339i
$834$		0			0
$835$	−0.984263	−	1.70479i	−0.0340618	−	0.0589968i
$836$		0			0
$837$	8.00000			0.276520
$838$		0			0
$839$	−4.23057	−	7.32756i	−0.146055	−	0.252975i	0.783711	−	0.621126i	$-0.213324\pi$
$839$	−4.23057	−	7.32756i	−0.146055	−	0.252975i	−0.929766	+	0.368151i	$0.879991\pi$
$840$		0			0
$841$	−7.71371			−0.265990
$842$		0			0
$843$	24.5693			0.846211
$844$		0			0
$845$	3.41520			0.117487
$846$		0			0
$847$	−0.919805	+	1.59315i	−0.0316049	+	0.0547412i
$848$		0			0
$849$	5.16167	+	8.94028i	0.177148	+	0.306830i
$850$		0			0
$851$	−7.03742	+	19.6819i	−0.241240	+	0.674686i
$852$		0			0
$853$	5.01777	+	8.69104i	0.171805	+	0.297576i	0.939051	−	0.343778i	$-0.111707\pi$
$853$	5.01777	+	8.69104i	0.171805	+	0.297576i	−0.767246	+	0.641353i	$0.778373\pi$
$854$		0			0
$855$	−0.154445	+	0.267507i	−0.00528191	+	0.00914854i
$856$		0			0
$857$	42.6426			1.45664			0.728322	−	0.685235i	$-0.240301\pi$
$857$	42.6426			1.45664			0.728322	+	0.685235i	$0.240301\pi$
$858$		0			0
$859$	−54.7045			−1.86649			−0.933247	−	0.359236i	$-0.883037\pi$
$859$	−54.7045			−1.86649			−0.933247	+	0.359236i	$0.883037\pi$
$860$		0			0
$861$	−1.04113			−0.0354817
$862$		0			0
$863$	0.823873	+	1.42699i	0.0280449	+	0.0485753i	0.879707	−	0.475516i	$-0.157739\pi$
$863$	0.823873	+	1.42699i	0.0280449	+	0.0485753i	−0.851662	+	0.524091i	$0.824405\pi$
$864$		0			0
$865$	14.8370			0.504475
$866$		0			0
$867$	−32.3837	−	56.0903i	−1.09981	−	1.90493i
$868$		0			0
$869$	−18.2878	+	31.6754i	−0.620371	+	1.07451i
$870$		0			0
$871$	16.0513	+	27.8016i	0.543877	+	0.942023i
$872$		0			0
$873$	14.6302	+	25.3402i	0.495157	+	0.857637i
$874$		0			0
$875$	3.33501	−	5.77640i	0.112744	−	0.195278i
$876$		0			0
$877$	−52.9056			−1.78649			−0.893247	−	0.449566i	$-0.851579\pi$
$877$	−52.9056			−1.78649			−0.893247	+	0.449566i	$0.851579\pi$
$878$		0			0
$879$	0.525002	+	0.909329i	0.0177079	+	0.0306709i
$880$		0			0
$881$	9.11371	−	15.7854i	0.307049	−	0.531824i	−0.670667	−	0.741759i	$-0.733992\pi$
$881$	9.11371	−	15.7854i	0.307049	−	0.531824i	0.977715	+	0.209935i	$0.0673253\pi$
$882$		0			0
$883$	4.65648	−	8.06526i	0.156703	−	0.271418i	−0.776975	−	0.629532i	$-0.783247\pi$
$883$	4.65648	−	8.06526i	0.156703	−	0.271418i	0.933678	+	0.358114i	$0.116580\pi$
$884$		0			0
$885$	−8.11167	+	14.0498i	−0.272671	+	0.472280i
$886$		0			0
$887$	−17.6571			−0.592866			−0.296433	−	0.955054i	$-0.595797\pi$
$887$	−17.6571			−0.592866			−0.296433	+	0.955054i	$0.595797\pi$
$888$		0			0
$889$	−4.07366			−0.136626
$890$		0			0
$891$	16.3319	−	28.2876i	0.547138	−	0.947670i
$892$		0			0
$893$	0.868519	−	1.50432i	0.0290639	−	0.0503401i
$894$		0			0
$895$	3.83705	−	6.64596i	0.128258	−	0.222150i
$896$		0			0
$897$	11.5822	+	20.0610i	0.386719	+	0.669818i
$898$		0			0
$899$	13.4652			0.449090
$900$		0			0
$901$	23.0446	−	39.9145i	0.767728	−	1.32974i
$902$		0			0
$903$	2.80965	+	4.86645i	0.0934991	+	0.161945i
$904$		0			0
$905$	1.75889	+	3.04648i	0.0584674	+	0.101268i
$906$		0			0
$907$	−7.37650	+	12.7765i	−0.244933	+	0.424236i	−0.962113	−	0.272652i	$-0.912099\pi$
$907$	−7.37650	+	12.7765i	−0.244933	+	0.424236i	0.717180	+	0.696888i	$0.245433\pi$
$908$		0			0
$909$	−5.44871	−	9.43745i	−0.180722	−	0.313020i
$910$		0			0
$911$	57.0053			1.88867			0.944334	−	0.328988i	$-0.106708\pi$
$911$	57.0053			1.88867			0.944334	+	0.328988i	$0.106708\pi$
$912$		0			0
$913$	−12.2130	−	21.1535i	−0.404190	−	0.700077i
$914$		0			0
$915$	16.0145			0.529422
$916$		0			0
$917$	−0.515210			−0.0170137
$918$		0			0
$919$	14.4007			0.475037			0.237518	−	0.971383i	$-0.423666\pi$
$919$	14.4007			0.475037			0.237518	+	0.971383i	$0.423666\pi$
$920$		0			0
$921$	−4.14594	+	7.18097i	−0.136613	+	0.236621i
$922$		0			0
$923$	−8.43758	−	14.6143i	−0.277726	−	0.481036i
$924$		0			0
$925$	−23.9371	+	4.36091i	−0.787045	+	0.143386i
$926$		0			0
$927$	−17.5782	−	30.4463i	−0.577342	−	0.999986i
$928$		0			0
$929$	−17.1782	+	29.7535i	−0.563597	+	0.976179i	0.433581	+	0.901114i	$0.357250\pi$
$929$	−17.1782	+	29.7535i	−0.563597	+	0.976179i	−0.997179	+	0.0750647i	$0.976084\pi$
$930$		0			0
$931$	1.14443			0.0375070
$932$		0			0
$933$	58.5071			1.91544
$934$		0			0
$935$	19.9541			0.652568
$936$		0			0
$937$	23.9863	+	41.5455i	0.783598	+	1.35723i	0.929833	+	0.367982i	$0.119951\pi$
$937$	23.9863	+	41.5455i	0.783598	+	1.35723i	−0.146235	+	0.989250i	$0.546715\pi$
$938$		0			0
$939$	40.8789			1.33403
$940$		0			0
$941$	25.2385	+	43.7144i	0.822753	+	1.42505i	0.903624	+	0.428326i	$0.140896\pi$
$941$	25.2385	+	43.7144i	0.822753	+	1.42505i	−0.0808712	+	0.996725i	$0.525770\pi$
$942$		0			0
$943$	−1.10852	+	1.92001i	−0.0360982	+	0.0625240i
$944$		0			0
$945$	1.01574	+	1.75931i	0.0330419	+	0.0572303i
$946$		0			0
$947$	14.0802	+	24.3876i	0.457545	+	0.792491i	0.998831	−	0.0483478i	$-0.0153956\pi$
$947$	14.0802	+	24.3876i	0.457545	+	0.792491i	−0.541286	+	0.840839i	$0.682062\pi$
$948$		0			0
$949$	19.1248	−	33.1252i	0.620819	−	1.07529i
$950$		0			0
$951$	43.1160			1.39813
$952$		0			0
$953$	0.917240	+	1.58871i	0.0297123	+	0.0514633i	0.880499	−	0.474048i	$-0.157208\pi$
$953$	0.917240	+	1.58871i	0.0297123	+	0.0514633i	−0.850787	+	0.525511i	$0.823874\pi$
$954$		0			0
$955$	−8.63667	+	14.9592i	−0.279476	+	0.484067i
$956$		0			0
$957$	14.6596	−	25.3912i	0.473879	−	0.820782i
$958$		0			0
$959$	0.837045	−	1.44980i	0.0270296	−	0.0468166i
$960$		0			0
$961$	−22.4822			−0.725233
$962$		0			0
$963$	−23.4193			−0.754676
$964$		0			0
$965$	−2.04797	+	3.54718i	−0.0659264	+	0.114188i
$966$		0			0
$967$	15.8569	−	27.4649i	0.509922	−	0.883211i	−0.490012	−	0.871716i	$-0.663008\pi$
$967$	15.8569	−	27.4649i	0.509922	−	0.883211i	0.999934	−	0.0114952i	$-0.00365913\pi$
$968$		0			0
$969$	−1.32055	+	2.28727i	−0.0424223	+	0.0734775i
$970$		0			0
$971$	4.40798	+	7.63484i	0.141459	+	0.245014i	0.928046	−	0.372465i	$-0.121487\pi$
$971$	4.40798	+	7.63484i	0.141459	+	0.245014i	−0.786587	+	0.617479i	$0.788154\pi$
$972$		0			0
$973$	−11.6056			−0.372057
$974$		0			0
$975$	−13.4822	+	23.3519i	−0.431777	+	0.747859i
$976$		0			0
$977$	−14.9698	−	25.9285i	−0.478927	−	0.829525i	0.520781	−	0.853690i	$-0.325641\pi$
$977$	−14.9698	−	25.9285i	−0.478927	−	0.829525i	−0.999708	+	0.0241649i	$0.992307\pi$
$978$		0			0
$979$	−22.9245	−	39.7063i	−0.732669	−	1.26902i
$980$		0			0
$981$	−5.64314	+	9.77421i	−0.180172	+	0.312067i
$982$		0			0
$983$	−20.7524	−	35.9442i	−0.661899	−	1.14644i	−0.980116	−	0.198425i	$-0.936417\pi$
$983$	−20.7524	−	35.9442i	−0.661899	−	1.14644i	0.318217	−	0.948018i	$-0.396916\pi$
$984$		0			0
$985$	−19.9015			−0.634115
$986$		0			0
$987$	7.89999	+	13.6832i	0.251460	+	0.435541i
$988$		0			0
$989$	11.9660			0.380495
$990$		0			0
$991$	48.0660			1.52687			0.763433	−	0.645887i	$-0.223512\pi$
$991$	48.0660			1.52687			0.763433	+	0.645887i	$0.223512\pi$
$992$		0			0
$993$	−16.9330			−0.537352
$994$		0			0
$995$	−4.25889	+	7.37661i	−0.135016	+	0.233854i
$996$		0			0
$997$	−24.3180	−	42.1200i	−0.770158	−	1.33395i	−0.937476	−	0.348050i	$-0.886844\pi$
$997$	−24.3180	−	42.1200i	−0.770158	−	1.33395i	0.167317	−	0.985903i	$-0.446490\pi$
$998$		0			0
$999$	5.61371	−	15.7001i	0.177610	−	0.496729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.i.f.433.1		6
4.3	odd	2		148.2.e.a.137.3	yes	6
12.11	even	2		1332.2.j.e.433.2		6
37.10	even	3	inner	592.2.i.f.417.1		6
148.11	odd	6		5476.2.a.g.1.1		3
148.47	odd	6		148.2.e.a.121.3	✓	6
148.63	odd	6		5476.2.a.f.1.1		3
444.47	even	6		1332.2.j.e.1009.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.e.a.121.3	✓	6	148.47	odd	6
148.2.e.a.137.3	yes	6	4.3	odd	2
592.2.i.f.417.1		6	37.10	even	3	inner
592.2.i.f.433.1		6	1.1	even	1	trivial
1332.2.j.e.433.2		6	12.11	even	2
1332.2.j.e.1009.2		6	444.47	even	6
5476.2.a.f.1.1		3	148.63	odd	6
5476.2.a.g.1.1		3	148.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08870 + 1.88569i) q^{3} +(0.500000 - 0.866025i) q^{5} +(0.370556 - 0.641823i) q^{7} +(-0.870556 - 1.50785i) q^{9} +2.91852 q^{11} +(1.54797 - 2.68116i) q^{13} +(1.08870 + 1.88569i) q^{15} +(3.41852 + 5.92105i) q^{17} +(0.0887048 - 0.153641i) q^{19} +(0.806853 + 1.39751i) q^{21} +3.43630 q^{23} +(2.00000 + 3.46410i) q^{25} -2.74111 q^{27} -4.61371 q^{29} -2.91852 q^{31} +(-3.17741 + 5.50344i) q^{33} +(-0.370556 - 0.641823i) q^{35} +(-2.04797 + 5.72764i) q^{37} +(3.37056 + 5.83798i) q^{39} +(-0.322590 + 0.558743i) q^{41} +3.48223 q^{43} -1.74111 q^{45} +9.79112 q^{47} +(3.22538 + 5.58651i) q^{49} -14.8870 q^{51} +(-3.37056 - 5.83798i) q^{53} +(1.45926 - 2.52751i) q^{55} +(0.193147 + 0.334540i) q^{57} +(3.72538 + 6.45254i) q^{59} +(3.67741 - 6.36946i) q^{61} -1.29036 q^{63} +(-1.54797 - 2.68116i) q^{65} +(-5.18464 + 8.98005i) q^{67} +(-3.74111 + 6.47980i) q^{69} +(2.72538 - 4.72049i) q^{71} +12.3548 q^{73} -8.70964 q^{75} +(1.08148 - 1.87317i) q^{77} +(-6.26611 + 10.8532i) q^{79} +(5.59593 - 9.69244i) q^{81} +(-4.18464 - 7.24800i) q^{83} +6.83705 q^{85} +(5.02296 - 8.70003i) q^{87} +(-7.85482 - 13.6049i) q^{89} +(-1.14722 - 1.98704i) q^{91} +(3.17741 - 5.50344i) q^{93} +(-0.0887048 - 0.153641i) q^{95} -16.8056 q^{97} +(-2.54074 - 4.40069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + q^{7} - 4 q^{9} - 7 q^{13} - q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} + 8 q^{23} + 12 q^{25} - 14 q^{27} - 4 q^{33} - q^{35} + 4 q^{37} + 19 q^{39} - 17 q^{41} + 16 q^{43} - 8 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + q^7 - 4 * q^9 - 7 * q^13 - q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 + 8 * q^23 + 12 * q^25 - 14 * q^27 - 4 * q^33 - q^35 + 4 * q^37 + 19 * q^39 - 17 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 19 * q^53 + 15 * q^57 - 9 * q^59 + 7 * q^61 - 68 * q^63 + 7 * q^65 + 9 * q^67 - 20 * q^69 - 15 * q^71 + 44 * q^73 + 8 * q^75 + 24 * q^77 - 15 * q^79 + q^81 + 15 * q^83 + 6 * q^85 + 34 * q^87 - 17 * q^89 - 13 * q^91 + 4 * q^93 + 7 * q^95 - 8 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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