LMFDB - Embedded newform 1008.2.r.f.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			337.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	1008.337
Dual form			1008.2.r.f.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +(2.18614 + 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.31386 + 0.543620i) q^{15} -4.37228 q^{17} -5.00000 q^{19} +(0.500000 - 1.65831i) q^{21} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(1.00000 - 1.73205i) q^{31} +(2.18614 - 7.25061i) q^{33} +1.37228 q^{35} +2.00000 q^{37} +(3.37228 - 0.792287i) q^{39} +(-5.18614 + 8.98266i) q^{41} +(4.55842 + 7.89542i) q^{43} +(3.43070 + 2.27567i) q^{45} +(-0.500000 + 0.866025i) q^{49} +(5.18614 + 5.51856i) q^{51} +2.74456 q^{53} +6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(3.55842 - 6.16337i) q^{59} +(7.05842 + 12.2255i) q^{61} +(-2.68614 + 1.33591i) q^{63} +(1.37228 + 2.37686i) q^{65} +(7.55842 - 13.0916i) q^{67} +(12.4307 - 2.92048i) q^{69} -10.1168 q^{71} -5.11684 q^{73} +(1.55842 - 5.16870i) q^{75} +(-2.18614 + 3.78651i) q^{77} +(6.05842 + 10.4935i) q^{79} +(-8.93070 - 1.11469i) q^{81} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-1.37228 + 4.55134i) q^{87} +3.25544 q^{89} -2.00000 q^{91} +(-3.37228 + 0.792287i) q^{93} +(-3.43070 + 5.94215i) q^{95} +(-4.55842 - 7.89542i) q^{97} +(-11.7446 + 5.84096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + 3 q^{11} - 4 q^{13} - 15 q^{15} - 6 q^{17} - 20 q^{19} + 2 q^{21} - 9 q^{23} - 11 q^{25} + 16 q^{27} + 6 q^{29} + 4 q^{31} + 3 q^{33} - 6 q^{35} + 8 q^{37} + 2 q^{39} - 15 q^{41} + q^{43} - 15 q^{45} - 2 q^{49} + 15 q^{51} - 12 q^{53} + 24 q^{55} - 5 q^{57} - 3 q^{59} + 11 q^{61} - 5 q^{63} - 6 q^{65} + 13 q^{67} + 21 q^{69} - 6 q^{71} + 14 q^{73} - 11 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} + 12 q^{83} - 12 q^{85} + 6 q^{87} + 36 q^{89} - 8 q^{91} - 2 q^{93} + 15 q^{95} - q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 + 3 * q^11 - 4 * q^13 - 15 * q^15 - 6 * q^17 - 20 * q^19 + 2 * q^21 - 9 * q^23 - 11 * q^25 + 16 * q^27 + 6 * q^29 + 4 * q^31 + 3 * q^33 - 6 * q^35 + 8 * q^37 + 2 * q^39 - 15 * q^41 + q^43 - 15 * q^45 - 2 * q^49 + 15 * q^51 - 12 * q^53 + 24 * q^55 - 5 * q^57 - 3 * q^59 + 11 * q^61 - 5 * q^63 - 6 * q^65 + 13 * q^67 + 21 * q^69 - 6 * q^71 + 14 * q^73 - 11 * q^75 - 3 * q^77 + 7 * q^79 - 7 * q^81 + 12 * q^83 - 12 * q^85 + 6 * q^87 + 36 * q^89 - 8 * q^91 - 2 * q^93 + 15 * q^95 - q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$3$	−1.18614	−	1.26217i	−0.684819	−	0.728714i
$4$		0			0
$5$	0.686141	−	1.18843i	0.306851	−	0.531482i	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	0.686141	−	1.18843i	0.306851	−	0.531482i	0.977672	+	0.210138i	$0.0673912\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$		0			0
$9$	−0.186141	+	2.99422i	−0.0620469	+	0.998073i
$10$		0			0
$11$	2.18614	+	3.78651i	0.659146	+	1.14167i	0.980837	+	0.194830i	$0.0624155\pi$
$11$	2.18614	+	3.78651i	0.659146	+	1.14167i	−0.321691	+	0.946845i	$0.604251\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	−2.31386	+	0.543620i	−0.597436	+	0.140362i
$16$		0			0
$17$	−4.37228			−1.06043			−0.530217	−	0.847862i	$-0.677890\pi$
$17$	−4.37228			−1.06043			−0.530217	+	0.847862i	$0.677890\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		0			0
$21$	0.500000	−	1.65831i	0.109109	−	0.361873i
$22$		0			0
$23$	−3.68614	+	6.38458i	−0.768613	+	1.33128i	0.169701	+	0.985496i	$0.445720\pi$
$23$	−3.68614	+	6.38458i	−0.768613	+	1.33128i	−0.938315	+	0.345782i	$0.887614\pi$
$24$		0			0
$25$	1.55842	+	2.69927i	0.311684	+	0.539853i
$26$		0			0
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$	−1.37228	−	2.37686i	−0.254826	−	0.441372i	0.710022	−	0.704179i	$-0.248685\pi$
$29$	−1.37228	−	2.37686i	−0.254826	−	0.441372i	−0.964848	+	0.262807i	$0.915352\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$		0			0
$33$	2.18614	−	7.25061i	0.380558	−	1.26217i
$34$		0			0
$35$	1.37228			0.231958
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	3.37228	−	0.792287i	0.539997	−	0.126867i
$40$		0			0
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	0.102966	+	0.994685i	$0.467167\pi$
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	−0.912906	+	0.408171i	$0.866167\pi$
$42$		0			0
$43$	4.55842	+	7.89542i	0.695153	+	1.20404i	0.970129	+	0.242589i	$0.0779967\pi$
$43$	4.55842	+	7.89542i	0.695153	+	1.20404i	−0.274976	+	0.961451i	$0.588670\pi$
$44$		0			0
$45$	3.43070	+	2.27567i	0.511419	+	0.339237i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	5.18614	+	5.51856i	0.726205	+	0.772753i
$52$		0			0
$53$	2.74456			0.376995			0.188497	−	0.982074i	$-0.439638\pi$
$53$	2.74456			0.376995			0.188497	+	0.982074i	$0.439638\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$	5.93070	+	6.31084i	0.785541	+	0.835892i
$58$		0			0
$59$	3.55842	−	6.16337i	0.463267	−	0.802402i	−0.535854	−	0.844310i	$-0.680010\pi$
$59$	3.55842	−	6.16337i	0.463267	−	0.802402i	0.999121	+	0.0419083i	$0.0133437\pi$
$60$		0			0
$61$	7.05842	+	12.2255i	0.903738	+	1.56532i	0.822602	+	0.568618i	$0.192522\pi$
$61$	7.05842	+	12.2255i	0.903738	+	1.56532i	0.0811364	+	0.996703i	$0.474145\pi$
$62$		0			0
$63$	−2.68614	+	1.33591i	−0.338422	+	0.168309i
$64$		0			0
$65$	1.37228	+	2.37686i	0.170211	+	0.294813i
$66$		0			0
$67$	7.55842	−	13.0916i	0.923408	−	1.59939i	0.129307	−	0.991605i	$-0.458725\pi$
$67$	7.55842	−	13.0916i	0.923408	−	1.59939i	0.794101	−	0.607785i	$-0.207942\pi$
$68$		0			0
$69$	12.4307	−	2.92048i	1.49648	−	0.351585i
$70$		0			0
$71$	−10.1168			−1.20065			−0.600324	−	0.799757i	$-0.704962\pi$
$71$	−10.1168			−1.20065			−0.600324	+	0.799757i	$0.704962\pi$
$72$		0			0
$73$	−5.11684			−0.598881			−0.299441	−	0.954115i	$-0.596800\pi$
$73$	−5.11684			−0.598881			−0.299441	+	0.954115i	$0.596800\pi$
$74$		0			0
$75$	1.55842	−	5.16870i	0.179951	−	0.596830i
$76$		0			0
$77$	−2.18614	+	3.78651i	−0.249134	+	0.431512i
$78$		0			0
$79$	6.05842	+	10.4935i	0.681626	+	1.18061i	0.974485	+	0.224455i	$0.0720601\pi$
$79$	6.05842	+	10.4935i	0.681626	+	1.18061i	−0.292859	+	0.956156i	$0.594607\pi$
$80$		0			0
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$		0			0
$83$	−2.74456	−	4.75372i	−0.301255	−	0.521789i	0.675166	−	0.737666i	$-0.264072\pi$
$83$	−2.74456	−	4.75372i	−0.301255	−	0.521789i	−0.976420	+	0.215877i	$0.930739\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		0			0
$87$	−1.37228	+	4.55134i	−0.147124	+	0.487955i
$88$		0			0
$89$	3.25544			0.345076			0.172538	−	0.985003i	$-0.444803\pi$
$89$	3.25544			0.345076			0.172538	+	0.985003i	$0.444803\pi$
$90$		0			0
$91$	−2.00000			−0.209657
$92$		0			0
$93$	−3.37228	+	0.792287i	−0.349689	+	0.0821563i
$94$		0			0
$95$	−3.43070	+	5.94215i	−0.351983	+	0.609652i
$96$		0			0
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	0.536263	−	0.844051i	$-0.319835\pi$
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	−0.999101	+	0.0423924i	$0.986502\pi$
$98$		0			0
$99$	−11.7446	+	5.84096i	−1.18037	+	0.587039i
$100$		0			0
$101$	−3.68614	−	6.38458i	−0.366785	−	0.635290i	0.622276	−	0.782798i	$-0.286208\pi$
$101$	−3.68614	−	6.38458i	−0.366785	−	0.635290i	−0.989061	+	0.147508i	$0.952875\pi$
$102$		0			0
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$		0			0
$105$	−1.62772	−	1.73205i	−0.158849	−	0.169031i
$106$		0			0
$107$	1.62772			0.157358			0.0786788	−	0.996900i	$-0.474930\pi$
$107$	1.62772			0.157358			0.0786788	+	0.996900i	$0.474930\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−2.37228	−	2.52434i	−0.225167	−	0.239600i
$112$		0			0
$113$	−0.686141	+	1.18843i	−0.0645467	+	0.111798i	−0.896493	−	0.443058i	$-0.853893\pi$
$113$	−0.686141	+	1.18843i	−0.0645467	+	0.111798i	0.831946	+	0.554856i	$0.187227\pi$
$114$		0			0
$115$	5.05842	+	8.76144i	0.471700	+	0.817009i
$116$		0			0
$117$	−5.00000	−	3.31662i	−0.462250	−	0.306622i
$118$		0			0
$119$	−2.18614	−	3.78651i	−0.200403	−	0.347108i
$120$		0			0
$121$	−4.05842	+	7.02939i	−0.368947	+	0.639036i
$122$		0			0
$123$	17.4891	−	4.10891i	1.57694	−	0.370488i
$124$		0			0
$125$	11.1386			0.996266
$126$		0			0
$127$	14.1168			1.25267			0.626334	−	0.779555i	$-0.284555\pi$
$127$	14.1168			1.25267			0.626334	+	0.779555i	$0.284555\pi$
$128$		0			0
$129$	4.55842	−	15.1186i	0.401347	−	1.33112i
$130$		0			0
$131$	−3.68614	+	6.38458i	−0.322060	+	0.557824i	−0.980913	−	0.194448i	$-0.937708\pi$
$131$	−3.68614	+	6.38458i	−0.322060	+	0.557824i	0.658853	+	0.752271i	$0.271042\pi$
$132$		0			0
$133$	−2.50000	−	4.33013i	−0.216777	−	0.375470i
$134$		0			0
$135$	−1.19702	−	7.02939i	−0.103023	−	0.604994i
$136$		0			0
$137$	−8.18614	−	14.1788i	−0.699389	−	1.21138i	−0.968678	−	0.248318i	$-0.920122\pi$
$137$	−8.18614	−	14.1788i	−0.699389	−	1.21138i	0.269289	−	0.963059i	$-0.413211\pi$
$138$		0			0
$139$	−10.6168	+	18.3889i	−0.900509	+	1.55973i	−0.0736742	+	0.997282i	$0.523472\pi$
$139$	−10.6168	+	18.3889i	−0.900509	+	1.55973i	−0.826835	+	0.562445i	$0.809861\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.74456			−0.731257
$144$		0			0
$145$	−3.76631			−0.312775
$146$		0			0
$147$	1.68614	−	0.396143i	0.139071	−	0.0326734i
$148$		0			0
$149$	−7.37228	+	12.7692i	−0.603961	+	1.04609i	0.388254	+	0.921552i	$0.373078\pi$
$149$	−7.37228	+	12.7692i	−0.603961	+	1.04609i	−0.992215	+	0.124538i	$0.960255\pi$
$150$		0			0
$151$	−4.05842	−	7.02939i	−0.330270	−	0.572044i	0.652295	−	0.757965i	$-0.273806\pi$
$151$	−4.05842	−	7.02939i	−0.330270	−	0.572044i	−0.982565	+	0.185921i	$0.940473\pi$
$152$		0			0
$153$	0.813859	−	13.0916i	0.0657966	−	1.05839i
$154$		0			0
$155$	−1.37228	−	2.37686i	−0.110224	−	0.190914i
$156$		0			0
$157$	4.05842	−	7.02939i	0.323897	−	0.561007i	−0.657391	−	0.753549i	$-0.728340\pi$
$157$	4.05842	−	7.02939i	0.323897	−	0.561007i	0.981289	+	0.192543i	$0.0616734\pi$
$158$		0			0
$159$	−3.25544	−	3.46410i	−0.258173	−	0.274721i
$160$		0			0
$161$	−7.37228			−0.581017
$162$		0			0
$163$	−16.2337			−1.27152			−0.635760	−	0.771887i	$-0.719313\pi$
$163$	−16.2337			−1.27152			−0.635760	+	0.771887i	$0.719313\pi$
$164$		0			0
$165$	−7.11684	−	7.57301i	−0.554046	−	0.589558i
$166$		0			0
$167$	8.74456	−	15.1460i	0.676675	−	1.17203i	−0.299302	−	0.954158i	$-0.596754\pi$
$167$	8.74456	−	15.1460i	0.676675	−	1.17203i	0.975976	−	0.217876i	$-0.0699129\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	0.930703	−	14.9711i	0.0711727	−	1.14487i
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−1.55842	+	2.69927i	−0.117806	+	0.204045i
$176$		0			0
$177$	−12.0000	+	2.81929i	−0.901975	+	0.211911i
$178$		0			0
$179$	−14.7446			−1.10206			−0.551030	−	0.834485i	$-0.685765\pi$
$179$	−14.7446			−1.10206			−0.551030	+	0.834485i	$0.685765\pi$
$180$		0			0
$181$	18.1168			1.34661			0.673307	−	0.739363i	$-0.264873\pi$
$181$	18.1168			1.34661			0.673307	+	0.739363i	$0.264873\pi$
$182$		0			0
$183$	7.05842	−	23.4101i	0.521774	−	1.73053i
$184$		0			0
$185$	1.37228	−	2.37686i	0.100892	−	0.174750i
$186$		0			0
$187$	−9.55842	−	16.5557i	−0.698981	−	1.21067i
$188$		0			0
$189$	4.87228	+	1.80579i	0.354406	+	0.131352i
$190$		0			0
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	0.829948	−	0.557841i	$-0.188370\pi$
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	−0.898078	+	0.439836i	$0.855037\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$		0			0
$195$	1.37228	−	4.55134i	0.0982711	−	0.325928i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$	−25.4891	+	5.98844i	−1.79786	+	0.422392i
$202$		0			0
$203$	1.37228	−	2.37686i	0.0963153	−	0.166823i
$204$		0			0
$205$	7.11684	+	12.3267i	0.497062	+	0.860937i
$206$		0			0
$207$	−18.4307	−	12.2255i	−1.28102	−	0.849734i
$208$		0			0
$209$	−10.9307	−	18.9325i	−0.756093	−	1.30959i
$210$		0			0
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$		0			0
$213$	12.0000	+	12.7692i	0.822226	+	0.874929i
$214$		0			0
$215$	12.5109			0.853235
$216$		0			0
$217$	2.00000			0.135769
$218$		0			0
$219$	6.06930	+	6.45832i	0.410125	+	0.436413i
$220$		0			0
$221$	4.37228	−	7.57301i	0.294111	−	0.509416i
$222$		0			0
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$		0			0
$225$	−8.37228	+	4.16381i	−0.558152	+	0.277588i
$226$		0			0
$227$	−11.8723	−	20.5634i	−0.787991	−	1.36484i	−0.927196	−	0.374577i	$-0.877788\pi$
$227$	−11.8723	−	20.5634i	−0.787991	−	1.36484i	0.139205	−	0.990264i	$-0.455545\pi$
$228$		0			0
$229$	10.0584	−	17.4217i	0.664679	−	1.15126i	−0.314693	−	0.949194i	$-0.601902\pi$
$229$	10.0584	−	17.4217i	0.664679	−	1.15126i	0.979372	−	0.202065i	$-0.0647651\pi$
$230$		0			0
$231$	7.37228	−	1.73205i	0.485060	−	0.113961i
$232$		0			0
$233$	−11.7446			−0.769412			−0.384706	−	0.923039i	$-0.625697\pi$
$233$	−11.7446			−0.769412			−0.384706	+	0.923039i	$0.625697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.05842	−	20.0935i	0.393537	−	1.30521i
$238$		0			0
$239$	−9.43070	+	16.3345i	−0.610021	+	1.05659i	0.381215	+	0.924487i	$0.375506\pi$
$239$	−9.43070	+	16.3345i	−0.610021	+	1.05659i	−0.991236	+	0.132102i	$0.957827\pi$
$240$		0			0
$241$	−0.441578	−	0.764836i	−0.0284445	−	0.0492674i	0.851453	−	0.524431i	$-0.175722\pi$
$241$	−0.441578	−	0.764836i	−0.0284445	−	0.0492674i	−0.879897	+	0.475164i	$0.842389\pi$
$242$		0			0
$243$	9.18614	+	12.5942i	0.589291	+	0.807921i
$244$		0			0
$245$	0.686141	+	1.18843i	0.0438359	+	0.0759260i
$246$		0			0
$247$	5.00000	−	8.66025i	0.318142	−	0.551039i
$248$		0			0
$249$	−2.74456	+	9.10268i	−0.173930	+	0.576859i
$250$		0			0
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	−32.2337			−2.02651
$254$		0			0
$255$	10.1168	−	2.37686i	0.633541	−	0.148845i
$256$		0			0
$257$	−10.9307	+	18.9325i	−0.681839	+	1.18098i	0.292581	+	0.956241i	$0.405486\pi$
$257$	−10.9307	+	18.9325i	−0.681839	+	1.18098i	−0.974419	+	0.224738i	$0.927847\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$		0			0
$261$	7.37228	−	3.66648i	0.456333	−	0.226949i
$262$		0			0
$263$	6.68614	+	11.5807i	0.412285	+	0.714099i	0.995139	−	0.0984781i	$-0.0313974\pi$
$263$	6.68614	+	11.5807i	0.412285	+	0.714099i	−0.582854	+	0.812577i	$0.698064\pi$
$264$		0			0
$265$	1.88316	−	3.26172i	0.115681	−	0.200366i
$266$		0			0
$267$	−3.86141	−	4.10891i	−0.236314	−	0.251461i
$268$		0			0
$269$	−7.37228			−0.449496			−0.224748	−	0.974417i	$-0.572156\pi$
$269$	−7.37228			−0.449496			−0.224748	+	0.974417i	$0.572156\pi$
$270$		0			0
$271$	18.2337			1.10762			0.553809	−	0.832644i	$-0.313174\pi$
$271$	18.2337			1.10762			0.553809	+	0.832644i	$0.313174\pi$
$272$		0			0
$273$	2.37228	+	2.52434i	0.143577	+	0.152780i
$274$		0			0
$275$	−6.81386	+	11.8020i	−0.410891	+	0.711684i
$276$		0			0
$277$	−11.1168	−	19.2549i	−0.667946	−	1.15692i	−0.978477	−	0.206354i	$-0.933840\pi$
$277$	−11.1168	−	19.2549i	−0.667946	−	1.15692i	0.310531	−	0.950563i	$-0.399493\pi$
$278$		0			0
$279$	5.00000	+	3.31662i	0.299342	+	0.198561i
$280$		0			0
$281$	−5.31386	−	9.20387i	−0.316998	−	0.549057i	0.662862	−	0.748742i	$-0.269342\pi$
$281$	−5.31386	−	9.20387i	−0.316998	−	0.549057i	−0.979860	+	0.199685i	$0.936008\pi$
$282$		0			0
$283$	4.94158	−	8.55906i	0.293746	−	0.508784i	−0.680946	−	0.732333i	$-0.738431\pi$
$283$	4.94158	−	8.55906i	0.293746	−	0.508784i	0.974692	+	0.223550i	$0.0717646\pi$
$284$		0			0
$285$	11.5693	−	2.71810i	0.685306	−	0.161006i
$286$		0			0
$287$	−10.3723			−0.612256
$288$		0			0
$289$	2.11684			0.124520
$290$		0			0
$291$	−4.55842	+	15.1186i	−0.267219	+	0.886267i
$292$		0			0
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	−0.790488	−	0.612478i	$-0.790173\pi$
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	0.925665	+	0.378344i	$0.123506\pi$
$294$		0			0
$295$	−4.88316	−	8.45787i	−0.284308	−	0.492436i
$296$		0			0
$297$	21.3030	+	7.89542i	1.23612	+	0.458139i
$298$		0			0
$299$	−7.37228	−	12.7692i	−0.426350	−	0.738460i
$300$		0			0
$301$	−4.55842	+	7.89542i	−0.262743	+	0.455084i
$302$		0			0
$303$	−3.68614	+	12.2255i	−0.211763	+	0.702339i
$304$		0			0
$305$	19.3723			1.10925
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$	16.8614	−	3.96143i	0.959212	−	0.225358i
$310$		0			0
$311$	−13.1168	+	22.7190i	−0.743788	+	1.28828i	0.206971	+	0.978347i	$0.433639\pi$
$311$	−13.1168	+	22.7190i	−0.743788	+	1.28828i	−0.950759	+	0.309931i	$0.899694\pi$
$312$		0			0
$313$	1.44158	+	2.49689i	0.0814828	+	0.141132i	0.903887	−	0.427771i	$-0.140701\pi$
$313$	1.44158	+	2.49689i	0.0814828	+	0.141132i	−0.822404	+	0.568904i	$0.807368\pi$
$314$		0			0
$315$	−0.255437	+	4.10891i	−0.0143923	+	0.231511i
$316$		0			0
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	−1.93070	−	2.05446i	−0.107761	−	0.114669i
$322$		0			0
$323$	21.8614			1.21640
$324$		0			0
$325$	−6.23369			−0.345783
$326$		0			0
$327$	−16.6060	−	17.6704i	−0.918312	−	0.977173i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.11684	−	10.5947i	−0.336212	−	0.582337i	0.647505	−	0.762061i	$-0.275813\pi$
$331$	−6.11684	−	10.5947i	−0.336212	−	0.582337i	−0.983717	+	0.179725i	$0.942479\pi$
$332$		0			0
$333$	−0.372281	+	5.98844i	−0.0204009	+	0.328164i
$334$		0			0
$335$	−10.3723	−	17.9653i	−0.566698	−	0.981550i
$336$		0			0
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	−0.963058	−	0.269294i	$-0.913210\pi$
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	0.714745	+	0.699385i	$0.246543\pi$
$338$		0			0
$339$	2.31386	−	0.543620i	0.125672	−	0.0295254i
$340$		0			0
$341$	8.74456			0.473545
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	5.05842	−	16.7769i	0.272336	−	0.903237i
$346$		0			0
$347$	3.55842	−	6.16337i	0.191026	−	0.330867i	−0.754564	−	0.656226i	$-0.772152\pi$
$347$	3.55842	−	6.16337i	0.191026	−	0.330867i	0.945591	+	0.325359i	$0.105485\pi$
$348$		0			0
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	0.994388	+	0.105797i	$0.0337393\pi$
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	−0.405571	+	0.914063i	$0.632927\pi$
$350$		0			0
$351$	1.74456	+	10.2448i	0.0931179	+	0.546828i
$352$		0			0
$353$	3.81386	+	6.60580i	0.202991	+	0.351591i	0.949491	−	0.313795i	$-0.101600\pi$
$353$	3.81386	+	6.60580i	0.202991	+	0.351591i	−0.746500	+	0.665386i	$0.768267\pi$
$354$		0			0
$355$	−6.94158	+	12.0232i	−0.368421	+	0.638123i
$356$		0			0
$357$	−2.18614	+	7.25061i	−0.115703	+	0.383743i
$358$		0			0
$359$	6.86141			0.362131			0.181066	−	0.983471i	$-0.442045\pi$
$359$	6.86141			0.362131			0.181066	+	0.983471i	$0.442045\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$		0			0
$363$	13.6861	−	3.21543i	0.718336	−	0.168767i
$364$		0			0
$365$	−3.51087	+	6.08101i	−0.183768	+	0.318295i
$366$		0			0
$367$	11.1168	+	19.2549i	0.580295	+	1.00510i	0.995444	+	0.0953465i	$0.0303959\pi$
$367$	11.1168	+	19.2549i	0.580295	+	1.00510i	−0.415150	+	0.909753i	$0.636271\pi$
$368$		0			0
$369$	−25.9307	−	17.2005i	−1.34990	−	0.895421i
$370$		0			0
$371$	1.37228	+	2.37686i	0.0712453	+	0.123400i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$	−13.2119	−	14.0588i	−0.682262	−	0.725993i
$376$		0			0
$377$	5.48913			0.282704
$378$		0			0
$379$	−9.11684			−0.468301			−0.234150	−	0.972200i	$-0.575231\pi$
$379$	−9.11684			−0.468301			−0.234150	+	0.972200i	$0.575231\pi$
$380$		0			0
$381$	−16.7446	−	17.8178i	−0.857850	−	0.912836i
$382$		0			0
$383$	−10.6277	+	18.4077i	−0.543051	+	0.940592i	0.455676	+	0.890146i	$0.349398\pi$
$383$	−10.6277	+	18.4077i	−0.543051	+	0.940592i	−0.998727	+	0.0504462i	$0.983936\pi$
$384$		0			0
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$		0			0
$387$	−24.4891	+	12.1793i	−1.24485	+	0.619107i
$388$		0			0
$389$	17.4891	+	30.2921i	0.886734	+	1.53587i	0.843713	+	0.536794i	$0.180365\pi$
$389$	17.4891	+	30.2921i	0.886734	+	1.53587i	0.0430204	+	0.999074i	$0.486302\pi$
$390$		0			0
$391$	16.1168	−	27.9152i	0.815064	−	1.41173i
$392$		0			0
$393$	12.4307	−	2.92048i	0.627046	−	0.147319i
$394$		0			0
$395$	16.6277			0.836631
$396$		0			0
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$		0			0
$399$	−2.50000	+	8.29156i	−0.125157	+	0.415097i
$400$		0			0
$401$	0.127719	−	0.221215i	0.00637797	−	0.0110470i	−0.862819	−	0.505513i	$-0.831303\pi$
$401$	0.127719	−	0.221215i	0.00637797	−	0.0110470i	0.869197	+	0.494466i	$0.164636\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$	−7.45245	+	9.84868i	−0.370315	+	0.489385i
$406$		0			0
$407$	4.37228	+	7.57301i	0.216726	+	0.375380i
$408$		0			0
$409$	−14.6753	+	25.4183i	−0.725645	+	1.25685i	0.233063	+	0.972462i	$0.425125\pi$
$409$	−14.6753	+	25.4183i	−0.725645	+	1.25685i	−0.958708	+	0.284393i	$0.908208\pi$
$410$		0			0
$411$	−8.18614	+	27.1504i	−0.403793	+	1.33923i
$412$		0			0
$413$	7.11684			0.350197
$414$		0			0
$415$	−7.53262			−0.369762
$416$		0			0
$417$	35.8030	−	8.41159i	1.75328	−	0.411917i
$418$		0			0
$419$	13.8030	−	23.9075i	0.674320	−	1.16796i	−0.302347	−	0.953198i	$-0.597770\pi$
$419$	13.8030	−	23.9075i	0.674320	−	1.16796i	0.976667	−	0.214759i	$-0.0688964\pi$
$420$		0			0
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	0.868859	−	0.495060i	$-0.164854\pi$
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	−0.863164	+	0.504924i	$0.831521\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.81386	−	11.8020i	−0.330521	−	0.572479i
$426$		0			0
$427$	−7.05842	+	12.2255i	−0.341581	+	0.591636i
$428$		0			0
$429$	10.3723	+	11.0371i	0.500778	+	0.532877i
$430$		0			0
$431$	29.4891			1.42044			0.710221	−	0.703979i	$-0.248595\pi$
$431$	29.4891			1.42044			0.710221	+	0.703979i	$0.248595\pi$
$432$		0			0
$433$	−2.88316			−0.138556			−0.0692778	−	0.997597i	$-0.522069\pi$
$433$	−2.88316			−0.138556			−0.0692778	+	0.997597i	$0.522069\pi$
$434$		0			0
$435$	4.46738	+	4.75372i	0.214194	+	0.227924i
$436$		0			0
$437$	18.4307	−	31.9229i	0.881660	−	1.52708i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−2.50000	−	1.65831i	−0.119048	−	0.0789673i
$442$		0			0
$443$	−11.4416	−	19.8174i	−0.543606	−	0.941553i	−0.998693	−	0.0511061i	$-0.983725\pi$
$443$	−11.4416	−	19.8174i	−0.543606	−	0.941553i	0.455087	−	0.890447i	$-0.349608\pi$
$444$		0			0
$445$	2.23369	−	3.86886i	0.105887	−	0.183402i
$446$		0			0
$447$	24.8614	−	5.84096i	1.17590	−	0.276268i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$	−45.3505			−2.13547
$452$		0			0
$453$	−4.05842	+	13.4603i	−0.190681	+	0.632418i
$454$		0			0
$455$	−1.37228	+	2.37686i	−0.0643335	+	0.111429i
$456$		0			0
$457$	−16.7337	−	28.9836i	−0.782769	−	1.35580i	−0.930323	−	0.366742i	$-0.880473\pi$
$457$	−16.7337	−	28.9836i	−0.782769	−	1.35580i	0.147554	−	0.989054i	$-0.452860\pi$
$458$		0			0
$459$	−17.4891	+	14.5012i	−0.816322	+	0.676859i
$460$		0			0
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	−0.961523	−	0.274724i	$-0.911414\pi$
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	0.242844	−	0.970065i	$-0.421920\pi$
$462$		0			0
$463$	−2.94158	+	5.09496i	−0.136707	+	0.236783i	−0.926248	−	0.376914i	$-0.876985\pi$
$463$	−2.94158	+	5.09496i	−0.136707	+	0.236783i	0.789541	+	0.613697i	$0.210318\pi$
$464$		0			0
$465$	−1.37228	+	4.55134i	−0.0636380	+	0.211063i
$466$		0			0
$467$	30.0951			1.39263			0.696317	−	0.717734i	$-0.254821\pi$
$467$	30.0951			1.39263			0.696317	+	0.717734i	$0.254821\pi$
$468$		0			0
$469$	15.1168			0.698031
$470$		0			0
$471$	−13.6861	+	3.21543i	−0.630624	+	0.148159i
$472$		0			0
$473$	−19.9307	+	34.5210i	−0.916415	+	1.58728i
$474$		0			0
$475$	−7.79211	−	13.4963i	−0.357527	−	0.619254i
$476$		0			0
$477$	−0.510875	+	8.21782i	−0.0233913	+	0.376268i
$478$		0			0
$479$	10.6277	+	18.4077i	0.485593	+	0.841072i	0.999863	−	0.0165568i	$-0.00527043\pi$
$479$	10.6277	+	18.4077i	0.485593	+	0.841072i	−0.514270	+	0.857628i	$0.671937\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$	8.74456	+	9.30506i	0.397891	+	0.423395i
$484$		0			0
$485$	−12.5109			−0.568090
$486$		0			0
$487$	16.3505			0.740913			0.370457	−	0.928850i	$-0.379201\pi$
$487$	16.3505			0.740913			0.370457	+	0.928850i	$0.379201\pi$
$488$		0			0
$489$	19.2554	+	20.4897i	0.870761	+	0.926574i
$490$		0			0
$491$	−9.81386	+	16.9981i	−0.442893	+	0.767114i	−0.997903	−	0.0647303i	$-0.979381\pi$
$491$	−9.81386	+	16.9981i	−0.442893	+	0.767114i	0.555010	+	0.831844i	$0.312715\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$		0			0
$495$	−1.11684	+	17.9653i	−0.0501984	+	0.807481i
$496$		0			0
$497$	−5.05842	−	8.76144i	−0.226901	−	0.393004i
$498$		0			0
$499$	0.441578	−	0.764836i	0.0197677	−	0.0342387i	−0.855972	−	0.517022i	$-0.827041\pi$
$499$	0.441578	−	0.764836i	0.0197677	−	0.0342387i	0.875740	+	0.482783i	$0.160374\pi$
$500$		0			0
$501$	−29.4891	+	6.92820i	−1.31748	+	0.309529i
$502$		0			0
$503$	−2.23369			−0.0995952			−0.0497976	−	0.998759i	$-0.515858\pi$
$503$	−2.23369			−0.0995952			−0.0497976	+	0.998759i	$0.515858\pi$
$504$		0			0
$505$	−10.1168			−0.450194
$506$		0			0
$507$	4.50000	−	14.9248i	0.199852	−	0.662834i
$508$		0			0
$509$	−8.48913	+	14.7036i	−0.376274	+	0.651725i	−0.990517	−	0.137392i	$-0.956128\pi$
$509$	−8.48913	+	14.7036i	−0.376274	+	0.651725i	0.614243	+	0.789117i	$0.289461\pi$
$510$		0			0
$511$	−2.55842	−	4.43132i	−0.113178	−	0.196030i
$512$		0			0
$513$	−20.0000	+	16.5831i	−0.883022	+	0.732163i
$514$		0			0
$515$	6.86141	+	11.8843i	0.302350	+	0.523685i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	3.00000	−	9.94987i	0.131685	−	0.436751i
$520$		0			0
$521$	3.86141			0.169171			0.0845856	−	0.996416i	$-0.473043\pi$
$521$	3.86141			0.169171			0.0845856	+	0.996416i	$0.473043\pi$
$522$		0			0
$523$	17.8832			0.781976			0.390988	−	0.920396i	$-0.372133\pi$
$523$	17.8832			0.781976			0.390988	+	0.920396i	$0.372133\pi$
$524$		0			0
$525$	5.25544	−	1.23472i	0.229366	−	0.0538875i
$526$		0			0
$527$	−4.37228	+	7.57301i	−0.190460	+	0.329886i
$528$		0			0
$529$	−15.6753	−	27.1504i	−0.681533	−	1.18045i
$530$		0			0
$531$	17.7921	+	11.8020i	0.772112	+	0.512161i
$532$		0			0
$533$	−10.3723	−	17.9653i	−0.449273	−	0.778164i
$534$		0			0
$535$	1.11684	−	1.93443i	0.0482854	−	0.0836327i
$536$		0			0
$537$	17.4891	+	18.6101i	0.754711	+	0.803086i
$538$		0			0
$539$	−4.37228			−0.188327
$540$		0			0
$541$	28.2337			1.21386			0.606931	−	0.794755i	$-0.292401\pi$
$541$	28.2337			1.21386			0.606931	+	0.794755i	$0.292401\pi$
$542$		0			0
$543$	−21.4891	−	22.8665i	−0.922187	−	0.981296i
$544$		0			0
$545$	9.60597	−	16.6380i	0.411475	−	0.712695i
$546$		0			0
$547$	0.441578	+	0.764836i	0.0188805	+	0.0327020i	0.875311	−	0.483560i	$-0.160656\pi$
$547$	0.441578	+	0.764836i	0.0188805	+	0.0327020i	−0.856431	+	0.516262i	$0.827323\pi$
$548$		0			0
$549$	−37.9198	+	18.8588i	−1.61838	+	0.804874i
$550$		0			0
$551$	6.86141	+	11.8843i	0.292306	+	0.506288i
$552$		0			0
$553$	−6.05842	+	10.4935i	−0.257630	+	0.446229i
$554$		0			0
$555$	−4.62772	+	1.08724i	−0.196436	+	0.0461508i
$556$		0			0
$557$	6.51087			0.275875			0.137937	−	0.990441i	$-0.455953\pi$
$557$	6.51087			0.275875			0.137937	+	0.990441i	$0.455953\pi$
$558$		0			0
$559$	−18.2337			−0.771203
$560$		0			0
$561$	−9.55842	+	31.7017i	−0.403557	+	1.33845i
$562$		0			0
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	−0.832684	−	0.553748i	$-0.813197\pi$
$563$	1.50000	−	2.59808i	0.0632175	−	0.109496i	0.895902	+	0.444252i	$0.146530\pi$
$564$		0			0
$565$	0.941578	+	1.63086i	0.0396125	+	0.0686108i
$566$		0			0
$567$	−3.50000	−	8.29156i	−0.146986	−	0.348213i
$568$		0			0
$569$	0.558422	+	0.967215i	0.0234103	+	0.0405478i	0.877493	−	0.479589i	$-0.159214\pi$
$569$	0.558422	+	0.967215i	0.0234103	+	0.0405478i	−0.854083	+	0.520137i	$0.825881\pi$
$570$		0			0
$571$	14.6753	−	25.4183i	0.614141	−	1.06372i	−0.376394	−	0.926460i	$-0.622836\pi$
$571$	14.6753	−	25.4183i	0.614141	−	1.06372i	0.990535	−	0.137263i	$-0.0438306\pi$
$572$		0			0
$573$	−0.941578	+	3.12286i	−0.0393350	+	0.130459i
$574$		0			0
$575$	−22.9783			−0.958259
$576$		0			0
$577$	27.1168			1.12889			0.564444	−	0.825471i	$-0.309090\pi$
$577$	27.1168			1.12889			0.564444	+	0.825471i	$0.309090\pi$
$578$		0			0
$579$	−11.8030	+	2.77300i	−0.490515	+	0.115242i
$580$		0			0
$581$	2.74456	−	4.75372i	0.113864	−	0.197218i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$	−7.37228	+	3.66648i	−0.304806	+	0.151590i
$586$		0			0
$587$	−4.24456	−	7.35180i	−0.175192	−	0.303441i	0.765036	−	0.643988i	$-0.222721\pi$
$587$	−4.24456	−	7.35180i	−0.175192	−	0.303441i	−0.940228	+	0.340547i	$0.889388\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$		0			0
$591$	7.11684	+	7.57301i	0.292748	+	0.311512i
$592$		0			0
$593$	3.25544			0.133685			0.0668424	−	0.997764i	$-0.478708\pi$
$593$	3.25544			0.133685			0.0668424	+	0.997764i	$0.478708\pi$
$594$		0			0
$595$	−6.00000			−0.245976
$596$		0			0
$597$	−11.8614	−	12.6217i	−0.485455	−	0.516571i
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	0.787257	−	0.616625i	$-0.211501\pi$
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	−0.927642	+	0.373472i	$0.878167\pi$
$602$		0			0
$603$	37.7921	+	25.0684i	1.53901	+	1.02087i
$604$		0			0
$605$	5.56930	+	9.64630i	0.226424	+	0.392178i
$606$		0			0
$607$	−6.11684	+	10.5947i	−0.248275	+	0.430025i	−0.963047	−	0.269332i	$-0.913197\pi$
$607$	−6.11684	+	10.5947i	−0.248275	+	0.430025i	0.714772	+	0.699357i	$0.246530\pi$
$608$		0			0
$609$	−4.62772	+	1.08724i	−0.187525	+	0.0440572i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.76631			−0.0713407			−0.0356703	−	0.999364i	$-0.511357\pi$
$613$	−1.76631			−0.0713407			−0.0356703	+	0.999364i	$0.511357\pi$
$614$		0			0
$615$	7.11684	−	23.6039i	0.286979	−	0.951801i
$616$		0			0
$617$	4.93070	−	8.54023i	0.198503	−	0.343817i	−0.749540	−	0.661959i	$-0.769725\pi$
$617$	4.93070	−	8.54023i	0.198503	−	0.343817i	0.948043	+	0.318142i	$0.103059\pi$
$618$		0			0
$619$	−11.7337	−	20.3233i	−0.471617	−	0.816864i	0.527856	−	0.849334i	$-0.322996\pi$
$619$	−11.7337	−	20.3233i	−0.471617	−	0.816864i	−0.999473	+	0.0324697i	$0.989663\pi$
$620$		0			0
$621$	6.43070	+	37.7639i	0.258055	+	1.51541i
$622$		0			0
$623$	1.62772	+	2.81929i	0.0652132	+	0.112953i
$624$		0			0
$625$	−0.149468	+	0.258886i	−0.00597872	+	0.0103555i
$626$		0			0
$627$	−10.9307	+	36.2530i	−0.436530	+	1.44781i
$628$		0			0
$629$	−8.74456			−0.348669
$630$		0			0
$631$	−14.3505			−0.571286			−0.285643	−	0.958336i	$-0.592207\pi$
$631$	−14.3505			−0.571286			−0.285643	+	0.958336i	$0.592207\pi$
$632$		0			0
$633$	26.9783	−	6.33830i	1.07229	−	0.251925i
$634$		0			0
$635$	9.68614	−	16.7769i	0.384383	−	0.665770i
$636$		0			0
$637$	−1.00000	−	1.73205i	−0.0396214	−	0.0686264i
$638$		0			0
$639$	1.88316	−	30.2921i	0.0744965	−	1.19834i
$640$		0			0
$641$	23.1060	+	40.0207i	0.912631	+	1.58072i	0.810333	+	0.585969i	$0.199286\pi$
$641$	23.1060	+	40.0207i	0.912631	+	1.58072i	0.102298	+	0.994754i	$0.467381\pi$
$642$		0			0
$643$	−12.6753	+	21.9542i	−0.499864	+	0.865789i	−1.00000		0.000157386i	$-0.999950\pi$
$643$	−12.6753	+	21.9542i	−0.499864	+	0.865789i	0.500136	+	0.865947i	$0.333283\pi$
$644$		0			0
$645$	−14.8397	−	15.7908i	−0.584311	−	0.621764i
$646$		0			0
$647$	17.4891			0.687568			0.343784	−	0.939049i	$-0.388291\pi$
$647$	17.4891			0.687568			0.343784	+	0.939049i	$0.388291\pi$
$648$		0			0
$649$	31.1168			1.22144
$650$		0			0
$651$	−2.37228	−	2.52434i	−0.0929770	−	0.0989366i
$652$		0			0
$653$	7.62772	−	13.2116i	0.298496	−	0.517010i	−0.677296	−	0.735710i	$-0.736848\pi$
$653$	7.62772	−	13.2116i	0.298496	−	0.517010i	0.975792	+	0.218701i	$0.0701818\pi$
$654$		0			0
$655$	5.05842	+	8.76144i	0.197649	+	0.342338i
$656$		0			0
$657$	0.952453	−	15.3210i	0.0371587	−	0.597727i
$658$		0			0
$659$	−4.62772	−	8.01544i	−0.180270	−	0.312237i	0.761702	−	0.647927i	$-0.224364\pi$
$659$	−4.62772	−	8.01544i	−0.180270	−	0.312237i	−0.941973	+	0.335690i	$0.891031\pi$
$660$		0			0
$661$	−4.94158	+	8.55906i	−0.192205	+	0.332909i	−0.945981	−	0.324223i	$-0.894897\pi$
$661$	−4.94158	+	8.55906i	−0.192205	+	0.332909i	0.753776	+	0.657132i	$0.228231\pi$
$662$		0			0
$663$	−14.7446	+	3.46410i	−0.572631	+	0.134535i
$664$		0			0
$665$	−6.86141			−0.266074
$666$		0			0
$667$	20.2337			0.783452
$668$		0			0
$669$	−2.00000	+	6.63325i	−0.0773245	+	0.256456i
$670$		0			0
$671$	−30.8614	+	53.4535i	−1.19139	+	2.06355i
$672$		0			0
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	0.992143	−	0.125109i	$-0.0399281\pi$
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	−0.604419	+	0.796666i	$0.706595\pi$
$674$		0			0
$675$	15.1861	+	5.62836i	0.584515	+	0.216636i
$676$		0			0
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	0.979998	+	0.199007i	$0.0637718\pi$
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	−0.317654	+	0.948207i	$0.602895\pi$
$678$		0			0
$679$	4.55842	−	7.89542i	0.174936	−	0.302998i
$680$		0			0
$681$	−11.8723	+	39.3759i	−0.454947	+	1.50889i
$682$		0			0
$683$	44.8397			1.71574			0.857871	−	0.513865i	$-0.171787\pi$
$683$	44.8397			1.71574			0.857871	+	0.513865i	$0.171787\pi$
$684$		0			0
$685$	−22.4674			−0.858434
$686$		0			0
$687$	−33.9198	+	7.96916i	−1.29412	+	0.304042i
$688$		0			0
$689$	−2.74456	+	4.75372i	−0.104560	+	0.181102i
$690$		0			0
$691$	−2.94158	−	5.09496i	−0.111903	−	0.193822i	0.804635	−	0.593770i	$-0.202361\pi$
$691$	−2.94158	−	5.09496i	−0.111903	−	0.193822i	−0.916537	+	0.399949i	$0.869028\pi$
$692$		0			0
$693$	−10.9307	−	7.25061i	−0.415223	−	0.275428i
$694$		0			0
$695$	14.5693	+	25.2348i	0.552645	+	0.957209i
$696$		0			0
$697$	22.6753	−	39.2747i	0.858887	−	1.48764i
$698$		0			0
$699$	13.9307	+	14.8236i	0.526908	+	0.560681i
$700$		0			0
$701$	−3.76631			−0.142252			−0.0711258	−	0.997467i	$-0.522659\pi$
$701$	−3.76631			−0.142252			−0.0711258	+	0.997467i	$0.522659\pi$
$702$		0			0
$703$	−10.0000			−0.377157
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.68614	−	6.38458i	0.138632	−	0.240117i
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$		0			0
$711$	−32.5475	+	16.1870i	−1.22063	+	0.607059i
$712$		0			0
$713$	7.37228	+	12.7692i	0.276094	+	0.478209i
$714$		0			0
$715$	−6.00000	+	10.3923i	−0.224387	+	0.388650i
$716$		0			0
$717$	31.8030	−	7.47182i	1.18770	−	0.279040i
$718$		0			0
$719$	8.74456			0.326117			0.163059	−	0.986616i	$-0.447864\pi$
$719$	8.74456			0.326117			0.163059	+	0.986616i	$0.447864\pi$
$720$		0			0
$721$	−10.0000			−0.372419
$722$		0			0
$723$	−0.441578	+	1.46455i	−0.0164225	+	0.0544671i
$724$		0			0
$725$	4.27719	−	7.40830i	0.158851	−	0.275138i
$726$		0			0
$727$	−0.883156	−	1.52967i	−0.0327544	−	0.0567324i	0.849183	−	0.528098i	$-0.177095\pi$
$727$	−0.883156	−	1.52967i	−0.0327544	−	0.0567324i	−0.881938	+	0.471366i	$0.843761\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$		0			0
$731$	−19.9307	−	34.5210i	−0.737164	−	1.27680i
$732$		0			0
$733$	11.9416	−	20.6834i	0.441072	−	0.763960i	−0.556697	−	0.830716i	$-0.687932\pi$
$733$	11.9416	−	20.6834i	0.441072	−	0.763960i	0.997769	+	0.0667560i	$0.0212649\pi$
$734$		0			0
$735$	0.686141	−	2.27567i	0.0253087	−	0.0839394i
$736$		0			0
$737$	66.0951			2.43464
$738$		0			0
$739$	−9.11684			−0.335369			−0.167684	−	0.985841i	$-0.553629\pi$
$739$	−9.11684			−0.335369			−0.167684	+	0.985841i	$0.553629\pi$
$740$		0			0
$741$	−16.8614	+	3.96143i	−0.619419	+	0.145527i
$742$		0			0
$743$	21.8614	−	37.8651i	0.802017	−	1.38913i	−0.116269	−	0.993218i	$-0.537094\pi$
$743$	21.8614	−	37.8651i	0.802017	−	1.38913i	0.918286	−	0.395917i	$-0.129573\pi$
$744$		0			0
$745$	10.1168	+	17.5229i	0.370652	+	0.641989i
$746$		0			0
$747$	14.7446	−	7.33296i	0.539475	−	0.268299i
$748$		0			0
$749$	0.813859	+	1.40965i	0.0297378	+	0.0515073i
$750$		0			0
$751$	0.0584220	−	0.101190i	0.00213185	−	0.00369247i	−0.864958	−	0.501845i	$-0.832655\pi$
$751$	0.0584220	−	0.101190i	0.00213185	−	0.00369247i	0.867089	+	0.498153i	$0.165988\pi$
$752$		0			0
$753$	−10.6753	−	11.3595i	−0.389028	−	0.413964i
$754$		0			0
$755$	−11.1386			−0.405375
$756$		0			0
$757$	11.7663			0.427654			0.213827	−	0.976872i	$-0.431407\pi$
$757$	11.7663			0.427654			0.213827	+	0.976872i	$0.431407\pi$
$758$		0			0
$759$	38.2337	+	40.6844i	1.38779	+	1.47675i
$760$		0			0
$761$	−6.25544	+	10.8347i	−0.226759	+	0.392759i	−0.956846	−	0.290596i	$-0.906146\pi$
$761$	−6.25544	+	10.8347i	−0.226759	+	0.392759i	0.730086	+	0.683355i	$0.239480\pi$
$762$		0			0
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$		0			0
$765$	−15.0000	−	9.94987i	−0.542326	−	0.359738i
$766$		0			0
$767$	7.11684	+	12.3267i	0.256974	+	0.445093i
$768$		0			0
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$		0			0
$771$	36.8614	−	8.66025i	1.32753	−	0.311891i
$772$		0			0
$773$	−11.1386			−0.400627			−0.200314	−	0.979732i	$-0.564196\pi$
$773$	−11.1386			−0.400627			−0.200314	+	0.979732i	$0.564196\pi$
$774$		0			0
$775$	6.23369			0.223921
$776$		0			0
$777$	1.00000	−	3.31662i	0.0358748	−	0.118983i
$778$		0			0
$779$	25.9307	−	44.9133i	0.929064	−	1.60919i
$780$		0			0
$781$	−22.1168	−	38.3075i	−0.791403	−	1.37075i
$782$		0			0
$783$	−13.3723	−	4.95610i	−0.477886	−	0.177117i
$784$		0			0
$785$	−5.56930	−	9.64630i	−0.198777	−	0.344291i
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$		0			0
$789$	6.68614	−	22.1754i	0.238033	−	0.789466i
$790$		0			0
$791$	−1.37228			−0.0487927
$792$		0			0
$793$	−28.2337			−1.00261
$794$		0			0
$795$	−6.35053	+	1.49200i	−0.225230	+	0.0529158i
$796$		0			0
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	−0.329579	−	0.944128i	$-0.606907\pi$
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	0.982428	−	0.186640i	$-0.0597597\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.605969	+	9.74749i	−0.0214109	+	0.344411i
$802$		0			0
$803$	−11.1861	−	19.3750i	−0.394750	−	0.683728i
$804$		0			0
$805$	−5.05842	+	8.76144i	−0.178286	+	0.308800i
$806$		0			0
$807$	8.74456	+	9.30506i	0.307823	+	0.327554i
$808$		0			0
$809$	21.8614			0.768606			0.384303	−	0.923207i	$-0.374442\pi$
$809$	21.8614			0.768606			0.384303	+	0.923207i	$0.374442\pi$
$810$		0			0
$811$	−24.8832			−0.873766			−0.436883	−	0.899518i	$-0.643918\pi$
$811$	−24.8832			−0.873766			−0.436883	+	0.899518i	$0.643918\pi$
$812$		0			0
$813$	−21.6277	−	23.0140i	−0.758517	−	0.807136i
$814$		0			0
$815$	−11.1386	+	19.2926i	−0.390168	+	0.675791i
$816$		0			0
$817$	−22.7921	−	39.4771i	−0.797395	−	1.38113i
$818$		0			0
$819$	0.372281	−	5.98844i	0.0130086	−	0.209253i
$820$		0			0
$821$	19.1168	+	33.1113i	0.667182	+	1.15559i	0.978689	+	0.205350i	$0.0658332\pi$
$821$	19.1168	+	33.1113i	0.667182	+	1.15559i	−0.311506	+	0.950244i	$0.600833\pi$
$822$		0			0
$823$	11.1168	−	19.2549i	0.387509	−	0.671185i	−0.604605	−	0.796525i	$-0.706669\pi$
$823$	11.1168	−	19.2549i	0.387509	−	0.671185i	0.992114	+	0.125341i	$0.0400023\pi$
$824$		0			0
$825$	22.9783	−	5.39853i	0.800000	−	0.187953i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−48.2337			−1.67523			−0.837613	−	0.546265i	$-0.816049\pi$
$829$	−48.2337			−1.67523			−0.837613	+	0.546265i	$0.816049\pi$
$830$		0			0
$831$	−11.1168	+	36.8704i	−0.385639	+	1.27902i
$832$		0			0
$833$	2.18614	−	3.78651i	0.0757453	−	0.131195i
$834$		0			0
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$		0			0
$837$	−1.74456	−	10.2448i	−0.0603009	−	0.354113i
$838$		0			0
$839$	−8.74456	−	15.1460i	−0.301896	−	0.522899i	0.674670	−	0.738120i	$-0.264286\pi$
$839$	−8.74456	−	15.1460i	−0.301896	−	0.522899i	−0.976565	+	0.215221i	$0.930953\pi$
$840$		0			0
$841$	10.7337	−	18.5913i	0.370127	−	0.641079i
$842$		0			0
$843$	−5.31386	+	17.6241i	−0.183019	+	0.607005i
$844$		0			0
$845$	12.3505			0.424871
$846$		0			0
$847$	−8.11684			−0.278898
$848$		0			0
$849$	−16.6644	+	3.91515i	−0.571920	+	0.134368i
$850$		0			0
$851$	−7.37228	+	12.7692i	−0.252719	+	0.437721i
$852$		0			0
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	0.977518	−	0.210854i	$-0.0676245\pi$
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	−0.671364	+	0.741128i	$0.734291\pi$
$854$		0			0
$855$	−17.1535	−	11.3784i	−0.586638	−	0.389132i
$856$		0			0
$857$	−25.9783	−	44.9956i	−0.887400	−	1.53702i	−0.842938	−	0.538011i	$-0.819176\pi$
$857$	−25.9783	−	44.9956i	−0.887400	−	1.53702i	−0.0444624	−	0.999011i	$-0.514157\pi$
$858$		0			0
$859$	25.5584	−	44.2685i	0.872042	−	1.51042i	0.0121615	−	0.999926i	$-0.496129\pi$
$859$	25.5584	−	44.2685i	0.872042	−	1.51042i	0.859881	−	0.510495i	$-0.170538\pi$
$860$		0			0
$861$	12.3030	+	13.0916i	0.419285	+	0.446160i
$862$		0			0
$863$	18.8614			0.642050			0.321025	−	0.947071i	$-0.395973\pi$
$863$	18.8614			0.642050			0.321025	+	0.947071i	$0.395973\pi$
$864$		0			0
$865$	8.23369			0.279954
$866$		0			0
$867$	−2.51087	−	2.67181i	−0.0852738	−	0.0907396i
$868$		0			0
$869$	−26.4891	+	45.8805i	−0.898582	+	1.55639i
$870$		0			0
$871$	15.1168	+	26.1831i	0.512215	+	0.887182i
$872$		0			0
$873$	24.4891	−	12.1793i	0.828831	−	0.412205i
$874$		0			0
$875$	5.56930	+	9.64630i	0.188277	+	0.326105i
$876$		0			0
$877$	−22.3505	+	38.7123i	−0.754724	+	1.30722i	0.190788	+	0.981631i	$0.438896\pi$
$877$	−22.3505	+	38.7123i	−0.754724	+	1.30722i	−0.945512	+	0.325589i	$0.894438\pi$
$878$		0			0
$879$	−7.80298	+	1.83324i	−0.263188	+	0.0618337i
$880$		0			0
$881$	14.2337			0.479545			0.239773	−	0.970829i	$-0.422927\pi$
$881$	14.2337			0.479545			0.239773	+	0.970829i	$0.422927\pi$
$882$		0			0
$883$	−11.3505			−0.381976			−0.190988	−	0.981592i	$-0.561169\pi$
$883$	−11.3505			−0.381976			−0.190988	+	0.981592i	$0.561169\pi$
$884$		0			0
$885$	−4.88316	+	16.1956i	−0.164145	+	0.544409i
$886$		0			0
$887$	−15.8614	+	27.4728i	−0.532574	+	0.922445i	0.466703	+	0.884414i	$0.345442\pi$
$887$	−15.8614	+	27.4728i	−0.532574	+	0.922445i	−0.999277	+	0.0380308i	$0.987892\pi$
$888$		0			0
$889$	7.05842	+	12.2255i	0.236732	+	0.410032i
$890$		0			0
$891$	−15.3030	−	36.2530i	−0.512669	−	1.21452i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−10.1168	+	17.5229i	−0.338169	+	0.585726i
$896$		0			0
$897$	−7.37228	+	24.4511i	−0.246153	+	0.816398i
$898$		0			0
$899$	−5.48913			−0.183073
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$	15.3723	−	3.61158i	0.511557	−	0.120186i
$904$		0			0
$905$	12.4307	−	21.5306i	0.413211	−	0.715702i
$906$		0			0
$907$	−4.44158	−	7.69304i	−0.147480	−	0.255443i	0.782815	−	0.622254i	$-0.213783\pi$
$907$	−4.44158	−	7.69304i	−0.147480	−	0.255443i	−0.930296	+	0.366811i	$0.880450\pi$
$908$		0			0
$909$	19.8030	−	9.84868i	0.656824	−	0.326660i
$910$		0			0
$911$	−21.6861	−	37.5615i	−0.718494	−	1.24447i	−0.961596	−	0.274467i	$-0.911498\pi$
$911$	−21.6861	−	37.5615i	−0.718494	−	1.24447i	0.243103	−	0.970001i	$-0.421835\pi$
$912$		0			0
$913$	12.0000	−	20.7846i	0.397142	−	0.687870i
$914$		0			0
$915$	−22.9783	−	24.4511i	−0.759638	−	0.808328i
$916$		0			0
$917$	−7.37228			−0.243454
$918$		0			0
$919$	29.8832			0.985754			0.492877	−	0.870099i	$-0.335945\pi$
$919$	29.8832			0.985754			0.492877	+	0.870099i	$0.335945\pi$
$920$		0			0
$921$	−15.4198	−	16.4082i	−0.508101	−	0.540668i
$922$		0			0
$923$	10.1168	−	17.5229i	0.333000	−	0.576773i
$924$		0			0
$925$	3.11684	+	5.39853i	0.102481	+	0.177503i
$926$		0			0
$927$	−25.0000	−	16.5831i	−0.821108	−	0.544661i
$928$		0			0
$929$	−4.88316	−	8.45787i	−0.160211	−	0.277494i	0.774733	−	0.632288i	$-0.217884\pi$
$929$	−4.88316	−	8.45787i	−0.160211	−	0.277494i	−0.934944	+	0.354794i	$0.884551\pi$
$930$		0			0
$931$	2.50000	−	4.33013i	0.0819342	−	0.141914i
$932$		0			0
$933$	44.2337	−	10.3923i	1.44815	−	0.340229i
$934$		0			0
$935$	−26.2337			−0.857933
$936$		0			0
$937$	−38.4674			−1.25667			−0.628337	−	0.777941i	$-0.716264\pi$
$937$	−38.4674			−1.25667			−0.628337	+	0.777941i	$0.716264\pi$
$938$		0			0
$939$	1.44158	−	4.78117i	0.0470441	−	0.156028i
$940$		0			0
$941$	−0.941578	+	1.63086i	−0.0306946	+	0.0531645i	−0.880965	−	0.473182i	$-0.843105\pi$
$941$	−0.941578	+	1.63086i	−0.0306946	+	0.0531645i	0.850270	+	0.526347i	$0.176439\pi$
$942$		0			0
$943$	−38.2337	−	66.2227i	−1.24506	−	2.15651i
$944$		0			0
$945$	5.48913	−	4.55134i	0.178561	−	0.148055i
$946$		0			0
$947$	8.44158	+	14.6212i	0.274314	+	0.475127i	0.969962	−	0.243257i	$-0.0782158\pi$
$947$	8.44158	+	14.6212i	0.274314	+	0.475127i	−0.695648	+	0.718383i	$0.744882\pi$
$948$		0			0
$949$	5.11684	−	8.86263i	0.166100	−	0.287693i
$950$		0			0
$951$	3.00000	−	9.94987i	0.0972817	−	0.322647i
$952$		0			0
$953$	10.8832			0.352540			0.176270	−	0.984342i	$-0.443597\pi$
$953$	10.8832			0.352540			0.176270	+	0.984342i	$0.443597\pi$
$954$		0			0
$955$	−2.58422			−0.0836234
$956$		0			0
$957$	−20.2337	+	4.75372i	−0.654062	+	0.153666i
$958$		0			0
$959$	8.18614	−	14.1788i	0.264344	−	0.457858i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−0.302985	+	4.87375i	−0.00976354	+	0.157054i
$964$		0			0
$965$	−4.80298	−	8.31901i	−0.154614	−	0.267799i
$966$		0			0
$967$	24.0584	−	41.6704i	0.773667	−	1.34003i	−0.161874	−	0.986811i	$-0.551754\pi$
$967$	24.0584	−	41.6704i	0.773667	−	1.34003i	0.935541	−	0.353219i	$-0.114913\pi$
$968$		0			0
$969$	−25.9307	−	27.5928i	−0.833014	−	0.886408i
$970$		0			0
$971$	−7.37228			−0.236588			−0.118294	−	0.992979i	$-0.537742\pi$
$971$	−7.37228			−0.236588			−0.118294	+	0.992979i	$0.537742\pi$
$972$		0			0
$973$	−21.2337			−0.680721
$974$		0			0
$975$	7.39403	+	7.86797i	0.236798	+	0.251977i
$976$		0			0
$977$	−11.4416	+	19.8174i	−0.366049	+	0.634015i	−0.988944	−	0.148291i	$-0.952623\pi$
$977$	−11.4416	+	19.8174i	−0.366049	+	0.634015i	0.622895	+	0.782305i	$0.285956\pi$
$978$		0			0
$979$	7.11684	+	12.3267i	0.227455	+	0.393964i
$980$		0			0
$981$	−2.60597	+	41.9191i	−0.0832022	+	1.33837i
$982$		0			0
$983$	−25.3723	−	43.9461i	−0.809250	−	1.40166i	−0.913384	−	0.407099i	$-0.866540\pi$
$983$	−25.3723	−	43.9461i	−0.809250	−	1.40166i	0.104134	−	0.994563i	$-0.466793\pi$
$984$		0			0
$985$	−4.11684	+	7.13058i	−0.131174	+	0.227199i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−67.2119			−2.13722
$990$		0			0
$991$	20.4674			0.650168			0.325084	−	0.945685i	$-0.394607\pi$
$991$	20.4674			0.650168			0.325084	+	0.945685i	$0.394607\pi$
$992$		0			0
$993$	−6.11684	+	20.2873i	−0.194112	+	0.643797i
$994$		0			0
$995$	6.86141	−	11.8843i	0.217521	−	0.376758i
$996$		0			0
$997$	−6.05842	−	10.4935i	−0.191872	−	0.332332i	0.753999	−	0.656876i	$-0.228123\pi$
$997$	−6.05842	−	10.4935i	−0.191872	−	0.332332i	−0.945871	+	0.324544i	$0.894789\pi$
$998$		0			0
$999$	8.00000	−	6.63325i	0.253109	−	0.209867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.f.337.1		4
3.2	odd	2		3024.2.r.f.1009.1		4
4.3	odd	2		126.2.f.d.85.2	yes	4
9.2	odd	6		3024.2.r.f.2017.1		4
9.4	even	3		9072.2.a.bm.1.1		2
9.5	odd	6		9072.2.a.bb.1.2		2
9.7	even	3	inner	1008.2.r.f.673.1		4
12.11	even	2		378.2.f.c.253.1		4
28.3	even	6		882.2.e.k.373.2		4
28.11	odd	6		882.2.e.l.373.1		4
28.19	even	6		882.2.h.n.67.2		4
28.23	odd	6		882.2.h.m.67.1		4
28.27	even	2		882.2.f.k.589.1		4
36.7	odd	6		126.2.f.d.43.2	✓	4
36.11	even	6		378.2.f.c.127.1		4
36.23	even	6		1134.2.a.n.1.2		2
36.31	odd	6		1134.2.a.k.1.1		2
84.11	even	6		2646.2.e.n.1549.1		4
84.23	even	6		2646.2.h.k.361.2		4
84.47	odd	6		2646.2.h.l.361.1		4
84.59	odd	6		2646.2.e.m.1549.2		4
84.83	odd	2		2646.2.f.j.1765.2		4
252.11	even	6		2646.2.h.k.667.2		4
252.47	odd	6		2646.2.e.m.2125.2		4
252.79	odd	6		882.2.e.l.655.2		4
252.83	odd	6		2646.2.f.j.883.2		4
252.115	even	6		882.2.h.n.79.2		4
252.139	even	6		7938.2.a.bh.1.2		2
252.151	odd	6		882.2.h.m.79.1		4
252.167	odd	6		7938.2.a.bs.1.1		2
252.187	even	6		882.2.e.k.655.1		4
252.191	even	6		2646.2.e.n.2125.1		4
252.223	even	6		882.2.f.k.295.1		4
252.227	odd	6		2646.2.h.l.667.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.2	✓	4	36.7	odd	6
126.2.f.d.85.2	yes	4	4.3	odd	2
378.2.f.c.127.1		4	36.11	even	6
378.2.f.c.253.1		4	12.11	even	2
882.2.e.k.373.2		4	28.3	even	6
882.2.e.k.655.1		4	252.187	even	6
882.2.e.l.373.1		4	28.11	odd	6
882.2.e.l.655.2		4	252.79	odd	6
882.2.f.k.295.1		4	252.223	even	6
882.2.f.k.589.1		4	28.27	even	2
882.2.h.m.67.1		4	28.23	odd	6
882.2.h.m.79.1		4	252.151	odd	6
882.2.h.n.67.2		4	28.19	even	6
882.2.h.n.79.2		4	252.115	even	6
1008.2.r.f.337.1		4	1.1	even	1	trivial
1008.2.r.f.673.1		4	9.7	even	3	inner
1134.2.a.k.1.1		2	36.31	odd	6
1134.2.a.n.1.2		2	36.23	even	6
2646.2.e.m.1549.2		4	84.59	odd	6
2646.2.e.m.2125.2		4	252.47	odd	6
2646.2.e.n.1549.1		4	84.11	even	6
2646.2.e.n.2125.1		4	252.191	even	6
2646.2.f.j.883.2		4	252.83	odd	6
2646.2.f.j.1765.2		4	84.83	odd	2
2646.2.h.k.361.2		4	84.23	even	6
2646.2.h.k.667.2		4	252.11	even	6
2646.2.h.l.361.1		4	84.47	odd	6
2646.2.h.l.667.1		4	252.227	odd	6
3024.2.r.f.1009.1		4	3.2	odd	2
3024.2.r.f.2017.1		4	9.2	odd	6
7938.2.a.bh.1.2		2	252.139	even	6
7938.2.a.bs.1.1		2	252.167	odd	6
9072.2.a.bb.1.2		2	9.5	odd	6
9072.2.a.bm.1.1		2	9.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+(-1.18614 - 1.26217i) q^{3} +(0.686141 - 1.18843i) q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.186141 + 2.99422i) q^{9} +(2.18614 + 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.31386 + 0.543620i) q^{15} -4.37228 q^{17} -5.00000 q^{19} +(0.500000 - 1.65831i) q^{21} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-1.37228 - 2.37686i) q^{29} +(1.00000 - 1.73205i) q^{31} +(2.18614 - 7.25061i) q^{33} +1.37228 q^{35} +2.00000 q^{37} +(3.37228 - 0.792287i) q^{39} +(-5.18614 + 8.98266i) q^{41} +(4.55842 + 7.89542i) q^{43} +(3.43070 + 2.27567i) q^{45} +(-0.500000 + 0.866025i) q^{49} +(5.18614 + 5.51856i) q^{51} +2.74456 q^{53} +6.00000 q^{55} +(5.93070 + 6.31084i) q^{57} +(3.55842 - 6.16337i) q^{59} +(7.05842 + 12.2255i) q^{61} +(-2.68614 + 1.33591i) q^{63} +(1.37228 + 2.37686i) q^{65} +(7.55842 - 13.0916i) q^{67} +(12.4307 - 2.92048i) q^{69} -10.1168 q^{71} -5.11684 q^{73} +(1.55842 - 5.16870i) q^{75} +(-2.18614 + 3.78651i) q^{77} +(6.05842 + 10.4935i) q^{79} +(-8.93070 - 1.11469i) q^{81} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-1.37228 + 4.55134i) q^{87} +3.25544 q^{89} -2.00000 q^{91} +(-3.37228 + 0.792287i) q^{93} +(-3.43070 + 5.94215i) q^{95} +(-4.55842 - 7.89542i) q^{97} +(-11.7446 + 5.84096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} + 3 q^{11} - 4 q^{13} - 15 q^{15} - 6 q^{17} - 20 q^{19} + 2 q^{21} - 9 q^{23} - 11 q^{25} + 16 q^{27} + 6 q^{29} + 4 q^{31} + 3 q^{33} - 6 q^{35} + 8 q^{37} + 2 q^{39} - 15 q^{41} + q^{43} - 15 q^{45} - 2 q^{49} + 15 q^{51} - 12 q^{53} + 24 q^{55} - 5 q^{57} - 3 q^{59} + 11 q^{61} - 5 q^{63} - 6 q^{65} + 13 q^{67} + 21 q^{69} - 6 q^{71} + 14 q^{73} - 11 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} + 12 q^{83} - 12 q^{85} + 6 q^{87} + 36 q^{89} - 8 q^{91} - 2 q^{93} + 15 q^{95} - q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 + 3 * q^11 - 4 * q^13 - 15 * q^15 - 6 * q^17 - 20 * q^19 + 2 * q^21 - 9 * q^23 - 11 * q^25 + 16 * q^27 + 6 * q^29 + 4 * q^31 + 3 * q^33 - 6 * q^35 + 8 * q^37 + 2 * q^39 - 15 * q^41 + q^43 - 15 * q^45 - 2 * q^49 + 15 * q^51 - 12 * q^53 + 24 * q^55 - 5 * q^57 - 3 * q^59 + 11 * q^61 - 5 * q^63 - 6 * q^65 + 13 * q^67 + 21 * q^69 - 6 * q^71 + 14 * q^73 - 11 * q^75 - 3 * q^77 + 7 * q^79 - 7 * q^81 + 12 * q^83 - 12 * q^85 + 6 * q^87 + 36 * q^89 - 8 * q^91 - 2 * q^93 + 15 * q^95 - q^97 - 24 * q^99

Introduction

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