LMFDB - Embedded newform 2646.2.l.b.1097.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.1
Root			$-1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	2646.1097
Dual form			2646.2.l.b.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +1.00000i q^{8} +(-1.55049 + 0.895175i) q^{10} +(-2.07976 - 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +1.00000 q^{16} +(-1.83233 - 3.17369i) q^{17} +(-2.61281 - 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(3.26178 - 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(2.44566 - 4.23601i) q^{26} +(5.68202 - 3.28052i) q^{29} -4.64661i q^{31} -1.00000i q^{32} +(-3.17369 + 1.83233i) q^{34} +(-4.68202 + 8.10950i) q^{37} +(-1.50851 + 2.61281i) q^{38} +(1.55049 - 0.895175i) q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(2.07976 + 1.20075i) q^{44} +(-1.88319 - 3.26178i) q^{46} -5.13604 q^{47} +(-1.55421 - 0.897324i) q^{50} +(-4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(-3.28052 - 5.68202i) q^{58} -14.5900 q^{59} -11.3283i q^{61} -4.64661 q^{62} -1.00000 q^{64} -8.75718i q^{65} +0.570231 q^{67} +(1.83233 + 3.17369i) q^{68} +5.96254i q^{71} +(-10.7226 + 6.19070i) q^{73} +(8.10950 + 4.68202i) q^{74} +(2.61281 + 1.50851i) q^{76} +3.03663 q^{79} +(-0.895175 - 1.55049i) q^{80} +(6.99911 + 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(-6.02973 + 3.48127i) q^{86} +(1.20075 - 2.07976i) q^{88} +(1.87432 - 3.24641i) q^{89} +(-3.26178 + 1.88319i) q^{92} +5.13604i q^{94} +5.40150i q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	0.593432	−	0.804884i	$-0.297773\pi$
$5$	−0.895175	−	1.55049i	−0.400334	−	0.693399i	−0.993766	+	0.111485i	$0.964439\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.55049	+	0.895175i	−0.490307	+	0.283079i
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	0.152545	−	0.988297i	$-0.451253\pi$
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	−0.779617	+	0.626256i	$0.784586\pi$
$12$		0			0
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.83233	−	3.17369i	−0.444406	−	0.769734i	0.553605	−	0.832780i	$-0.313252\pi$
$17$	−1.83233	−	3.17369i	−0.444406	−	0.769734i	−0.998011	+	0.0630460i	$0.979919\pi$
$18$		0			0
$19$	−2.61281	−	1.50851i	−0.599419	−	0.346075i	0.169394	−	0.985548i	$-0.445819\pi$
$19$	−2.61281	−	1.50851i	−0.599419	−	0.346075i	−0.768813	+	0.639474i	$0.779152\pi$
$20$	0.895175	+	1.55049i	0.200167	+	0.346700i
$21$		0			0
$22$	−1.20075	+	2.07976i	−0.256001	+	0.443407i
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	−0.119775	−	0.992801i	$-0.538217\pi$
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	0.799904	+	0.600128i	$0.204884\pi$
$24$		0			0
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$	2.44566	−	4.23601i	0.479634	−	0.830750i
$27$		0			0
$28$		0			0
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.131045	−	0.991376i	$-0.458167\pi$
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.924080	+	0.382200i	$0.124833\pi$
$30$		0			0
$31$		−	4.64661i		−	0.834556i	−0.908779	−	0.417278i	$-0.862984\pi$
$31$		−	4.64661i		−	0.834556i	0.908779	−	0.417278i	$-0.137016\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−3.17369	+	1.83233i	−0.544284	+	0.314242i
$35$		0			0
$36$		0			0
$37$	−4.68202	+	8.10950i	−0.769719	+	1.33319i	0.167996	+	0.985788i	$0.446271\pi$
$37$	−4.68202	+	8.10950i	−0.769719	+	1.33319i	−0.937715	+	0.347405i	$0.887063\pi$
$38$	−1.50851	+	2.61281i	−0.244712	+	0.423853i
$39$		0			0
$40$	1.55049	−	0.895175i	0.245154	−	0.141540i
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	0.356241	+	0.934394i	$0.384058\pi$
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	−0.987330	+	0.158683i	$0.949275\pi$
$42$		0			0
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	−0.999350	−	0.0360419i	$-0.988525\pi$
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$44$	2.07976	+	1.20075i	0.313536	+	0.181020i
$45$		0			0
$46$	−1.88319	−	3.26178i	−0.277661	−	0.480924i
$47$	−5.13604			−0.749169			−0.374584	−	0.927193i	$-0.622215\pi$
$47$	−5.13604			−0.749169			−0.374584	+	0.927193i	$0.622215\pi$
$48$		0			0
$49$		0			0
$50$	−1.55421	−	0.897324i	−0.219799	−	0.126901i
$51$		0			0
$52$	−4.23601	−	2.44566i	−0.587429	−	0.339152i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$			4.29953i			0.579749i
$56$		0			0
$57$		0			0
$58$	−3.28052	−	5.68202i	−0.430753	−	0.746086i
$59$	−14.5900			−1.89946			−0.949729	−	0.313073i	$-0.898641\pi$
$59$	−14.5900			−1.89946			−0.949729	+	0.313073i	$0.898641\pi$
$60$		0			0
$61$		−	11.3283i		−	1.45044i	−0.688518	−	0.725219i	$-0.741738\pi$
$61$		−	11.3283i		−	1.45044i	0.688518	−	0.725219i	$-0.258262\pi$
$62$	−4.64661			−0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	8.75718i		−	1.08619i
$66$		0			0
$67$	0.570231			0.0696648			0.0348324	−	0.999393i	$-0.488910\pi$
$67$	0.570231			0.0696648			0.0348324	+	0.999393i	$0.488910\pi$
$68$	1.83233	+	3.17369i	0.222203	+	0.384867i
$69$		0			0
$70$		0			0
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$		0			0
$73$	−10.7226	+	6.19070i	−1.25499	+	0.724567i	−0.972096	−	0.234585i	$-0.924627\pi$
$73$	−10.7226	+	6.19070i	−1.25499	+	0.724567i	−0.282891	+	0.959152i	$0.591294\pi$
$74$	8.10950	+	4.68202i	0.942710	+	0.544274i
$75$		0			0
$76$	2.61281	+	1.50851i	0.299710	+	0.173037i
$77$		0			0
$78$		0			0
$79$	3.03663			0.341647			0.170824	−	0.985302i	$-0.445357\pi$
$79$	3.03663			0.341647			0.170824	+	0.985302i	$0.445357\pi$
$80$	−0.895175	−	1.55049i	−0.100084	−	0.173350i
$81$		0			0
$82$	6.99911	+	4.04094i	0.772922	+	0.446247i
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	−0.938297	−	0.345830i	$-0.887597\pi$
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	0.169651	−	0.985504i	$-0.445736\pi$
$84$		0			0
$85$	−3.28052	+	5.68202i	−0.355822	+	0.616302i
$86$	−6.02973	+	3.48127i	−0.650203	+	0.375395i
$87$		0			0
$88$	1.20075	−	2.07976i	0.128001	−	0.221704i
$89$	1.87432	−	3.24641i	0.198677	−	0.344119i	−0.749423	−	0.662092i	$-0.769669\pi$
$89$	1.87432	−	3.24641i	0.198677	−	0.344119i	0.948100	+	0.317973i	$0.103002\pi$
$90$		0			0
$91$		0			0
$92$	−3.26178	+	1.88319i	−0.340064	+	0.196336i
$93$		0			0
$94$			5.13604i			0.529742i
$95$			5.40150i			0.554183i
$96$		0			0
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	−0.722323	−	0.691556i	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$		0			0
$99$		0			0
$100$	−0.897324	+	1.55421i	−0.0897324	+	0.155421i
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	−0.872185	−	0.489176i	$-0.837298\pi$
$101$	−0.125162	+	0.216787i	−0.0124541	+	0.0215711i	0.859731	+	0.510747i	$0.170631\pi$
$102$		0			0
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	−0.492818	−	0.870132i	$-0.664033\pi$
$103$	0.145433	−	0.0839657i	0.0143299	−	0.00827339i	0.507148	+	0.861859i	$0.330700\pi$
$104$	−2.44566	+	4.23601i	−0.239817	+	0.415375i
$105$		0			0
$106$		0			0
$107$	6.92024	+	3.99540i	0.669004	+	0.386250i	0.795699	−	0.605692i	$-0.207104\pi$
$107$	6.92024	+	3.99540i	0.669004	+	0.386250i	−0.126695	+	0.991942i	$0.540437\pi$
$108$		0			0
$109$	9.47667	+	16.4141i	0.907700	+	1.57218i	0.817251	+	0.576282i	$0.195497\pi$
$109$	9.47667	+	16.4141i	0.907700	+	1.57218i	0.0904491	+	0.995901i	$0.471170\pi$
$110$	4.29953			0.409944
$111$		0			0
$112$		0			0
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	0.546488	−	0.837467i	$-0.315964\pi$
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	−0.452023	+	0.892006i	$0.649298\pi$
$114$		0			0
$115$	−5.83973	−	3.37157i	−0.544558	−	0.314401i
$116$	−5.68202	+	3.28052i	−0.527562	+	0.304588i
$117$		0			0
$118$			14.5900i			1.34312i
$119$		0			0
$120$		0			0
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$	−11.3283			−1.02561
$123$		0			0
$124$			4.64661i			0.417278i
$125$	−12.1648			−1.08805
$126$		0			0
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−8.75718			−0.768056
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	0.540538	−	0.841320i	$-0.318221\pi$
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	−0.998873	+	0.0474597i	$0.984887\pi$
$132$		0			0
$133$		0			0
$134$		−	0.570231i		−	0.0492604i
$135$		0			0
$136$	3.17369	−	1.83233i	0.272142	−	0.157121i
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	0.315093	−	0.949061i	$-0.397964\pi$
$137$	−4.08812	−	2.36028i	−0.349272	−	0.201652i	−0.664365	+	0.747409i	$0.731298\pi$
$138$		0			0
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	0.584296	−	0.811540i	$-0.301371\pi$
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	−0.410666	+	0.911786i	$0.634704\pi$
$140$		0			0
$141$		0			0
$142$	5.96254			0.500365
$143$	−5.87327	−	10.1728i	−0.491148	−	0.850692i
$144$		0			0
$145$	−10.1728	−	5.87327i	−0.844805	−	0.487749i
$146$	6.19070	+	10.7226i	0.512346	+	0.887410i
$147$		0			0
$148$	4.68202	−	8.10950i	0.384860	−	0.666597i
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.967433	−	0.253126i	$-0.918541\pi$
$149$	−15.0377	+	8.68202i	−1.23194	+	0.711259i	−0.264503	+	0.964385i	$0.585208\pi$
$150$		0			0
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	−0.541749	−	0.840541i	$-0.682238\pi$
$151$	5.61639	−	9.72787i	0.457055	−	0.791643i	0.998804	+	0.0488977i	$0.0155708\pi$
$152$	1.50851	−	2.61281i	0.122356	−	0.211927i
$153$		0			0
$154$		0			0
$155$	−7.20451	+	4.15953i	−0.578680	+	0.334101i
$156$		0			0
$157$			13.8431i			1.10480i	0.833580	+	0.552399i	$0.186287\pi$
$157$			13.8431i			1.10480i	−0.833580	+	0.552399i	$0.813713\pi$
$158$		−	3.03663i		−	0.241581i
$159$		0			0
$160$	−1.55049	+	0.895175i	−0.122577	+	0.0707698i
$161$		0			0
$162$		0			0
$163$	2.16789	−	3.75489i	0.169802	−	0.294106i	−0.768548	−	0.639792i	$-0.779020\pi$
$163$	2.16789	−	3.75489i	0.169802	−	0.294106i	0.938350	+	0.345686i	$0.112354\pi$
$164$	4.04094	−	6.99911i	0.315544	−	0.546539i
$165$		0			0
$166$	−12.1290	+	7.00270i	−0.941395	+	0.543515i
$167$	−6.20756	+	10.7518i	−0.480355	+	0.832000i	−0.999746	−	0.0225370i	$-0.992826\pi$
$167$	−6.20756	+	10.7518i	−0.480355	+	0.832000i	0.519391	+	0.854537i	$0.326159\pi$
$168$		0			0
$169$	5.46254	+	9.46139i	0.420195	+	0.727799i
$170$	5.68202	+	3.28052i	0.435791	+	0.251604i
$171$		0			0
$172$	3.48127	+	6.02973i	0.265444	+	0.459763i
$173$	−17.4182			−1.32428			−0.662139	−	0.749381i	$-0.730351\pi$
$173$	−17.4182			−1.32428			−0.662139	+	0.749381i	$0.730351\pi$
$174$		0			0
$175$		0			0
$176$	−2.07976	−	1.20075i	−0.156768	−	0.0905101i
$177$		0			0
$178$	−3.24641	−	1.87432i	−0.243329	−	0.140486i
$179$	11.3640	−	6.56103i	0.849388	−	0.490395i	−0.0110562	−	0.999939i	$-0.503519\pi$
$179$	11.3640	−	6.56103i	0.849388	−	0.490395i	0.860444	+	0.509544i	$0.170186\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$		0			0
$183$		0			0
$184$	1.88319	+	3.26178i	0.138831	+	0.240462i
$185$	16.7649			1.23258
$186$		0			0
$187$			8.80071i			0.643572i
$188$	5.13604			0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$			9.25333i			0.669547i	0.942299	+	0.334774i	$0.108660\pi$
$191$			9.25333i			0.669547i	−0.942299	+	0.334774i	$0.891340\pi$
$192$		0			0
$193$	−24.5602			−1.76788			−0.883941	−	0.467599i	$-0.845119\pi$
$193$	−24.5602			−1.76788			−0.883941	+	0.467599i	$0.845119\pi$
$194$	2.75544	+	4.77256i	0.197829	+	0.342650i
$195$		0			0
$196$		0			0
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$		0			0
$199$	0.155144	−	0.0895727i	0.0109979	−	0.00634964i	−0.494491	−	0.869183i	$-0.664645\pi$
$199$	0.155144	−	0.0895727i	0.0109979	−	0.00634964i	0.505489	+	0.862833i	$0.331312\pi$
$200$	1.55421	+	0.897324i	0.109899	+	0.0634504i
$201$		0			0
$202$	0.216787	+	0.125162i	0.0152531	+	0.00880637i
$203$		0			0
$204$		0			0
$205$	14.4694			1.01059
$206$	−0.0839657	−	0.145433i	−0.00585017	−	0.0101328i
$207$		0			0
$208$	4.23601	+	2.44566i	0.293715	+	0.169576i
$209$	3.62268	+	6.27467i	0.250586	+	0.434028i
$210$		0			0
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	−0.479192	−	0.877710i	$-0.659070\pi$
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	0.999715	−	0.0238622i	$-0.00759629\pi$
$212$		0			0
$213$		0			0
$214$	3.99540	−	6.92024i	0.273120	−	0.473058i
$215$	−6.23269	+	10.7953i	−0.425066	+	0.736235i
$216$		0			0
$217$		0			0
$218$	16.4141	−	9.47667i	1.11170	−	0.641841i
$219$		0			0
$220$		−	4.29953i		−	0.289874i
$221$		−	17.9251i		−	1.20577i
$222$		0			0
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	−0.236406	−	0.971654i	$-0.575970\pi$
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	0.723274	+	0.690561i	$0.242636\pi$
$224$		0			0
$225$		0			0
$226$	0.579764	−	1.00418i	0.0385653	−	0.0667971i
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	−0.822974	−	0.568079i	$-0.807687\pi$
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	0.903458	+	0.428677i	$0.141020\pi$
$228$		0			0
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$	−3.37157	+	5.83973i	−0.222315	+	0.385061i
$231$		0			0
$232$	3.28052	+	5.68202i	0.215376	+	0.373043i
$233$	−11.0236	−	6.36446i	−0.722178	−	0.416950i	0.0933759	−	0.995631i	$-0.470234\pi$
$233$	−11.0236	−	6.36446i	−0.722178	−	0.416950i	−0.815554	+	0.578681i	$0.803568\pi$
$234$		0			0
$235$	4.59766	+	7.96337i	0.299918	+	0.519473i
$236$	14.5900			0.949729
$237$		0			0
$238$		0			0
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.0759814	−	0.997109i	$-0.524209\pi$
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.901513	+	0.432753i	$0.857542\pi$
$240$		0			0
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$	−4.53172	+	2.61639i	−0.291310	+	0.168188i
$243$		0			0
$244$			11.3283i			0.725219i
$245$		0			0
$246$		0			0
$247$	−7.37859	−	12.7801i	−0.469489	−	0.813178i
$248$	4.64661			0.295060
$249$		0			0
$250$			12.1648i			0.769369i
$251$	−27.3560			−1.72669			−0.863347	−	0.504611i	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$		−	1.40150i		−	0.0879382i
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	0.915390	−	0.402569i	$-0.131883\pi$
$257$	1.74837	+	3.02826i	0.109060	+	0.188898i	−0.806330	+	0.591466i	$0.798549\pi$
$258$		0			0
$259$		0			0
$260$			8.75718i			0.543097i
$261$		0			0
$262$	−9.08614	+	5.24589i	−0.561344	+	0.324092i
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	0.219901	−	0.975522i	$-0.429427\pi$
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	−0.734877	+	0.678201i	$0.762760\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.570231			−0.0348324
$269$	3.45554	+	5.98517i	0.210688	+	0.364922i	0.951930	−	0.306316i	$-0.0990963\pi$
$269$	3.45554	+	5.98517i	0.210688	+	0.364922i	−0.741242	+	0.671238i	$0.765763\pi$
$270$		0			0
$271$	−17.8672	−	10.3156i	−1.08535	−	0.626629i	−0.153017	−	0.988224i	$-0.548899\pi$
$271$	−17.8672	−	10.3156i	−1.08535	−	0.626629i	−0.932335	+	0.361595i	$0.882232\pi$
$272$	−1.83233	−	3.17369i	−0.111101	−	0.192433i
$273$		0			0
$274$	−2.36028	+	4.08812i	−0.142590	+	0.246973i
$275$	−3.73244	+	2.15493i	−0.225075	+	0.129947i
$276$		0			0
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$	1.18187	−	2.04707i	0.0708841	−	0.122775i
$279$		0			0
$280$		0			0
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	−0.808275	−	0.588805i	$-0.799599\pi$
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	0.105783	+	0.994389i	$0.466265\pi$
$282$		0			0
$283$		−	5.44783i		−	0.323840i	−0.986804	−	0.161920i	$-0.948231\pi$
$283$		−	5.44783i		−	0.323840i	0.986804	−	0.161920i	$-0.0517687\pi$
$284$		−	5.96254i		−	0.353811i
$285$		0			0
$286$	−10.1728	+	5.87327i	−0.601530	+	0.347294i
$287$		0			0
$288$		0			0
$289$	1.78512	−	3.09191i	0.105007	−	0.181877i
$290$	−5.87327	+	10.1728i	−0.344890	+	0.597368i
$291$		0			0
$292$	10.7226	−	6.19070i	0.627493	−	0.362284i
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	−0.248583	−	0.968610i	$-0.579965\pi$
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	0.963133	−	0.269026i	$-0.0867017\pi$
$294$		0			0
$295$	13.0606	+	22.6216i	0.760418	+	1.31708i
$296$	−8.10950	−	4.68202i	−0.471355	−	0.272137i
$297$		0			0
$298$	8.68202	+	15.0377i	0.502936	+	0.871111i
$299$	18.4226			1.06541
$300$		0			0
$301$		0			0
$302$	−9.72787	−	5.61639i	−0.559776	−	0.323187i
$303$		0			0
$304$	−2.61281	−	1.50851i	−0.149855	−	0.0865187i
$305$	−17.5644	+	10.1408i	−1.00573	+	0.580660i
$306$		0			0
$307$		−	31.2223i		−	1.78195i	−0.454053	−	0.890975i	$-0.650022\pi$
$307$		−	31.2223i		−	1.78195i	0.454053	−	0.890975i	$-0.349978\pi$
$308$		0			0
$309$		0			0
$310$	4.15953	+	7.20451i	0.236245	+	0.409189i
$311$	10.9100			0.618651			0.309325	−	0.950956i	$-0.399897\pi$
$311$	10.9100			0.618651			0.309325	+	0.950956i	$0.399897\pi$
$312$		0			0
$313$		−	3.42405i		−	0.193539i	−0.995307	−	0.0967694i	$-0.969149\pi$
$313$		−	3.42405i		−	0.193539i	0.995307	−	0.0967694i	$-0.0308509\pi$
$314$	13.8431			0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$		−	19.0471i		−	1.06979i	−0.844917	−	0.534897i	$-0.820350\pi$
$317$		−	19.0471i		−	1.06979i	0.844917	−	0.534897i	$-0.179650\pi$
$318$		0			0
$319$	−15.7563			−0.882186
$320$	0.895175	+	1.55049i	0.0500418	+	0.0866749i
$321$		0			0
$322$		0			0
$323$			11.0563i			0.615191i
$324$		0			0
$325$	7.60215	−	4.38910i	0.421692	−	0.243464i
$326$	−3.75489	−	2.16789i	−0.207964	−	0.120068i
$327$		0			0
$328$	−6.99911	−	4.04094i	−0.386461	−	0.223123i
$329$		0			0
$330$		0			0
$331$	0.0732502			0.00402620			0.00201310	−	0.999998i	$-0.499359\pi$
$331$	0.0732502			0.00402620			0.00201310	+	0.999998i	$0.499359\pi$
$332$	7.00270	+	12.1290i	0.384323	+	0.665667i
$333$		0			0
$334$	10.7518	+	6.20756i	0.588313	+	0.339663i
$335$	−0.510456	−	0.884136i	−0.0278892	−	0.0483055i
$336$		0			0
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$	9.46139	−	5.46254i	0.514632	−	0.297123i
$339$		0			0
$340$	3.28052	−	5.68202i	0.177911	−	0.308151i
$341$	−5.57943	+	9.66385i	−0.302143	+	0.523327i
$342$		0			0
$343$		0			0
$344$	6.02973	−	3.48127i	0.325101	−	0.187697i
$345$		0			0
$346$			17.4182i			0.936406i
$347$			31.8409i			1.70931i	0.519195	+	0.854656i	$0.326232\pi$
$347$			31.8409i			1.70931i	−0.519195	+	0.854656i	$0.673768\pi$
$348$		0			0
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$		0			0
$351$		0			0
$352$	−1.20075	+	2.07976i	−0.0640003	+	0.110852i
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	−0.893330	−	0.449402i	$-0.851637\pi$
$353$	−1.07979	+	1.87025i	−0.0574713	+	0.0995431i	0.835858	+	0.548945i	$0.184970\pi$
$354$		0			0
$355$	9.24484	−	5.33751i	0.490665	−	0.283286i
$356$	−1.87432	+	3.24641i	−0.0993385	+	0.172059i
$357$		0			0
$358$	−6.56103	−	11.3640i	−0.346761	−	0.600608i
$359$	28.2712	+	16.3224i	1.49210	+	0.861463i	0.999959	−	0.00905364i	$-0.00288190\pi$
$359$	28.2712	+	16.3224i	1.49210	+	0.861463i	0.492139	+	0.870517i	$0.336215\pi$
$360$		0			0
$361$	−4.94882	−	8.57161i	−0.260464	−	0.451138i
$362$	13.3577			0.702067
$363$		0			0
$364$		0			0
$365$	19.1972	+	11.0835i	1.00483	+	0.580138i
$366$		0			0
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.987194	−	0.159527i	$-0.0509969\pi$
$367$	25.7212	+	14.8501i	1.34264	+	0.775171i	0.355442	+	0.934698i	$0.384330\pi$
$368$	3.26178	−	1.88319i	0.170032	−	0.0981682i
$369$		0			0
$370$		−	16.7649i		−	0.871566i
$371$		0			0
$372$		0			0
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$	8.80071			0.455074
$375$		0			0
$376$		−	5.13604i		−	0.264871i
$377$	32.0921			1.65283
$378$		0			0
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$		−	5.40150i		−	0.277091i
$381$		0			0
$382$	9.25333			0.473441
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	0.855142	−	0.518394i	$-0.173470\pi$
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	−0.876514	+	0.481377i	$0.840137\pi$
$384$		0			0
$385$		0			0
$386$			24.5602i			1.25008i
$387$		0			0
$388$	4.77256	−	2.75544i	0.242290	−	0.139886i
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.933552	−	0.358441i	$-0.116692\pi$
$389$	21.4964	+	12.4109i	1.08991	+	0.629260i	0.156357	+	0.987701i	$0.450025\pi$
$390$		0			0
$391$	−11.9533	−	6.90127i	−0.604507	−	0.349012i
$392$		0			0
$393$		0			0
$394$	−12.4861			−0.629041
$395$	−2.71831	−	4.70825i	−0.136773	−	0.236898i
$396$		0			0
$397$	2.62744	+	1.51695i	0.131867	+	0.0761336i	0.564482	−	0.825445i	$-0.309076\pi$
$397$	2.62744	+	1.51695i	0.131867	+	0.0761336i	−0.432615	+	0.901579i	$0.642409\pi$
$398$	−0.0895727	−	0.155144i	−0.00448987	−	0.00777669i
$399$		0			0
$400$	0.897324	−	1.55421i	0.0448662	−	0.0777105i
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	−0.189822	−	0.981819i	$-0.560791\pi$
$401$	11.3251	−	6.53854i	0.565548	−	0.326519i	0.755369	+	0.655300i	$0.227458\pi$
$402$		0			0
$403$	11.3640	−	19.6831i	0.566083	−	0.980485i
$404$	0.125162	−	0.216787i	0.00622705	−	0.0107856i
$405$		0			0
$406$		0			0
$407$	19.4750	−	11.2439i	0.965339	−	0.557339i
$408$		0			0
$409$			5.56709i			0.275275i	0.990483	+	0.137637i	$0.0439508\pi$
$409$			5.56709i			0.275275i	−0.990483	+	0.137637i	$0.956049\pi$
$410$		−	14.4694i		−	0.714592i
$411$		0			0
$412$	−0.145433	+	0.0839657i	−0.00716496	+	0.00413669i
$413$		0			0
$414$		0			0
$415$	−12.5373	+	21.7152i	−0.615431	+	1.06596i
$416$	2.44566	−	4.23601i	0.119908	−	0.207688i
$417$		0			0
$418$	6.27467	−	3.62268i	0.306904	−	0.177191i
$419$	8.19938	−	14.2017i	0.400566	−	0.693800i	−0.593228	−	0.805034i	$-0.702147\pi$
$419$	8.19938	−	14.2017i	0.400566	−	0.693800i	0.993794	+	0.111234i	$0.0354802\pi$
$420$		0			0
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$	−13.0961	−	7.56103i	−0.637508	−	0.368065i
$423$		0			0
$424$		0			0
$425$	−6.57678			−0.319021
$426$		0			0
$427$		0			0
$428$	−6.92024	−	3.99540i	−0.334502	−	0.193125i
$429$		0			0
$430$	10.7953	+	6.23269i	0.520597	+	0.300567i
$431$	21.6737	−	12.5133i	1.04398	−	0.602744i	0.123024	−	0.992404i	$-0.460741\pi$
$431$	21.6737	−	12.5133i	1.04398	−	0.602744i	0.920959	+	0.389660i	$0.127407\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$		0			0
$435$		0			0
$436$	−9.47667	−	16.4141i	−0.453850	−	0.786091i
$437$	−11.3632			−0.543576
$438$		0			0
$439$		−	18.7400i		−	0.894412i	−0.894431	−	0.447206i	$-0.852419\pi$
$439$		−	18.7400i		−	0.894412i	0.894431	−	0.447206i	$-0.147581\pi$
$440$	−4.29953			−0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$			1.20451i			0.0572281i	0.999591	+	0.0286141i	$0.00910938\pi$
$443$			1.20451i			0.0572281i	−0.999591	+	0.0286141i	$0.990891\pi$
$444$		0			0
$445$	−6.71136			−0.318149
$446$	−4.19762	−	7.27049i	−0.198763	−	0.344268i
$447$		0			0
$448$		0			0
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$		0			0
$451$	16.8084	−	9.70433i	0.791476	−	0.456959i
$452$	−1.00418	−	0.579764i	−0.0472327	−	0.0272698i
$453$		0			0
$454$	−2.10030	−	1.21261i	−0.0985719	−	0.0569105i
$455$		0			0
$456$		0			0
$457$	13.8488			0.647821			0.323911	−	0.946088i	$-0.395002\pi$
$457$	13.8488			0.647821			0.323911	+	0.946088i	$0.395002\pi$
$458$	−1.00987	−	1.74915i	−0.0471883	−	0.0817326i
$459$		0			0
$460$	5.83973	+	3.37157i	0.272279	+	0.157200i
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	0.916533	−	0.399959i	$-0.130976\pi$
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	−0.804641	+	0.593761i	$0.797642\pi$
$462$		0			0
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	−0.511041	−	0.859556i	$-0.670740\pi$
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	0.999918	+	0.0127960i	$0.00407321\pi$
$464$	5.68202	−	3.28052i	0.263781	−	0.152294i
$465$		0			0
$466$	−6.36446	+	11.0236i	−0.294828	+	0.510657i
$467$	−2.91151	+	5.04288i	−0.134729	+	0.233357i	−0.925494	−	0.378763i	$-0.876350\pi$
$467$	−2.91151	+	5.04288i	−0.134729	+	0.233357i	0.790765	+	0.612120i	$0.209683\pi$
$468$		0			0
$469$		0			0
$470$	7.96337	−	4.59766i	0.367323	−	0.212074i
$471$		0			0
$472$		−	14.5900i		−	0.671560i
$473$			16.7206i			0.768812i
$474$		0			0
$475$	−4.68907	+	2.70724i	−0.215149	+	0.124217i
$476$		0			0
$477$		0			0
$478$	−8.72474	+	15.1117i	−0.399060	+	0.691193i
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	−0.374411	−	0.927263i	$-0.622155\pi$
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	0.990239	−	0.139382i	$-0.0445117\pi$
$480$		0			0
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$	5.71659	−	9.90142i	0.260383	−	0.450997i
$483$		0			0
$484$	2.61639	+	4.53172i	0.118927	+	0.205987i
$485$	8.54455	+	4.93320i	0.387988	+	0.224005i
$486$		0			0
$487$	6.81338	+	11.8011i	0.308744	+	0.534760i	0.978088	−	0.208193i	$-0.0667581\pi$
$487$	6.81338	+	11.8011i	0.308744	+	0.534760i	−0.669344	+	0.742953i	$0.733425\pi$
$488$	11.3283			0.512807
$489$		0			0
$490$		0			0
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.999637	+	0.0269544i	$0.00858088\pi$
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.523162	+	0.852234i	$0.324752\pi$
$492$		0			0
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$	−12.7801	+	7.37859i	−0.575004	+	0.331979i
$495$		0			0
$496$		−	4.64661i		−	0.208639i
$497$		0			0
$498$		0			0
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	−0.995221	−	0.0976483i	$-0.968868\pi$
$499$	−13.0048	−	22.5250i	−0.582176	−	1.00836i	0.413045	−	0.910711i	$-0.364465\pi$
$500$	12.1648			0.544026
$501$		0			0
$502$			27.3560i			1.22096i
$503$	10.5271			0.469378			0.234689	−	0.972070i	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$			9.04499i			0.402099i
$507$		0			0
$508$	−1.40150			−0.0621817
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	0.876242	−	0.481872i	$-0.160043\pi$
$509$	0.469435	+	0.813086i	0.0208074	+	0.0360394i	−0.855434	+	0.517911i	$0.826710\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	3.02826	−	1.74837i	0.133571	−	0.0771172i
$515$	−0.260376	−	0.150328i	−0.0114735	−	0.00662424i
$516$		0			0
$517$	10.6818	+	6.16711i	0.469783	+	0.271229i
$518$		0			0
$519$		0			0
$520$	8.75718			0.384028
$521$	19.7527	+	34.2127i	0.865382	+	1.49889i	0.866667	+	0.498887i	$0.166258\pi$
$521$	19.7527	+	34.2127i	0.865382	+	1.49889i	−0.00128461	+	0.999999i	$0.500409\pi$
$522$		0			0
$523$	21.0697	+	12.1646i	0.921315	+	0.531922i	0.884054	−	0.467384i	$-0.154803\pi$
$523$	21.0697	+	12.1646i	0.921315	+	0.531922i	0.0372609	+	0.999306i	$0.488137\pi$
$524$	5.24589	+	9.08614i	0.229168	+	0.396930i
$525$		0			0
$526$	−4.82174	+	8.35150i	−0.210238	+	0.364143i
$527$	−14.7469	+	8.51413i	−0.642385	+	0.370881i
$528$		0			0
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−34.2349	+	19.7655i	−1.48288	+	0.856141i
$534$		0			0
$535$		−	14.3063i		−	0.618516i
$536$			0.570231i			0.0246302i
$537$		0			0
$538$	5.98517	−	3.45554i	0.258039	−	0.148979i
$539$		0			0
$540$		0			0
$541$	−21.3640	+	37.0036i	−0.918512	+	1.59091i	−0.116835	+	0.993151i	$0.537275\pi$
$541$	−21.3640	+	37.0036i	−0.918512	+	1.59091i	−0.801677	+	0.597758i	$0.796058\pi$
$542$	−10.3156	+	17.8672i	−0.443093	+	0.767460i
$543$		0			0
$544$	−3.17369	+	1.83233i	−0.136071	+	0.0785606i
$545$	16.9665	−	29.3869i	0.726767	−	1.25880i
$546$		0			0
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	−0.999620	−	0.0275530i	$-0.991229\pi$
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	0.475949	−	0.879473i	$-0.342105\pi$
$548$	4.08812	+	2.36028i	0.174636	+	0.100826i
$549$		0			0
$550$	2.15493	+	3.73244i	0.0918864	+	0.159152i
$551$	−19.7947			−0.843283
$552$		0			0
$553$		0			0
$554$	−13.4358	−	7.75718i	−0.570834	−	0.329571i
$555$		0			0
$556$	−2.04707	−	1.18187i	−0.0868150	−	0.0501227i
$557$	2.20344	−	1.27216i	0.0933627	−	0.0539030i	−0.452592	−	0.891718i	$-0.649501\pi$
$557$	2.20344	−	1.27216i	0.0933627	−	0.0539030i	0.545954	+	0.837815i	$0.316167\pi$
$558$		0			0
$559$		−	34.0560i		−	1.44042i
$560$		0			0
$561$		0			0
$562$	6.79883	+	11.7759i	0.286791	+	0.496737i
$563$	15.8141			0.666487			0.333243	−	0.942841i	$-0.391857\pi$
$563$	15.8141			0.666487			0.333243	+	0.942841i	$0.391857\pi$
$564$		0			0
$565$		−	2.07596i		−	0.0873363i
$566$	−5.44783			−0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$			6.38311i			0.267594i	0.991009	+	0.133797i	$0.0427170\pi$
$569$			6.38311i			0.267594i	−0.991009	+	0.133797i	$0.957283\pi$
$570$		0			0
$571$	−7.82375			−0.327414			−0.163707	−	0.986509i	$-0.552345\pi$
$571$	−7.82375			−0.327414			−0.163707	+	0.986509i	$0.552345\pi$
$572$	5.87327	+	10.1728i	0.245574	+	0.425346i
$573$		0			0
$574$		0			0
$575$		−	6.75933i		−	0.281884i
$576$		0			0
$577$	12.4012	−	7.15986i	0.516270	−	0.298069i	−0.219137	−	0.975694i	$-0.570324\pi$
$577$	12.4012	−	7.15986i	0.516270	−	0.298069i	0.735407	+	0.677625i	$0.236991\pi$
$578$	−3.09191	−	1.78512i	−0.128607	−	0.0742510i
$579$		0			0
$580$	10.1728	+	5.87327i	0.422403	+	0.243874i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−6.19070	−	10.7226i	−0.256173	−	0.443705i
$585$		0			0
$586$	−21.1849	−	12.2311i	−0.875141	−	0.505263i
$587$	−2.37575	−	4.11492i	−0.0980577	−	0.169841i	0.812823	−	0.582511i	$-0.197930\pi$
$587$	−2.37575	−	4.11492i	−0.0980577	−	0.169841i	−0.910881	+	0.412670i	$0.864596\pi$
$588$		0			0
$589$	−7.00943	+	12.1407i	−0.288819	+	0.500249i
$590$	22.6216	−	13.0606i	0.931318	−	0.537697i
$591$		0			0
$592$	−4.68202	+	8.10950i	−0.192430	+	0.333298i
$593$	−1.79035	+	3.10098i	−0.0735208	+	0.127342i	−0.900442	−	0.434976i	$-0.856757\pi$
$593$	−1.79035	+	3.10098i	−0.0735208	+	0.127342i	0.826921	+	0.562318i	$0.190090\pi$
$594$		0			0
$595$		0			0
$596$	15.0377	−	8.68202i	0.615968	−	0.355629i
$597$		0			0
$598$		−	18.4226i		−	0.753357i
$599$		−	15.0655i		−	0.615561i	−0.951457	−	0.307780i	$-0.900414\pi$
$599$		−	15.0655i		−	0.615561i	0.951457	−	0.307780i	$-0.0995862\pi$
$600$		0			0
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$		0			0
$603$		0			0
$604$	−5.61639	+	9.72787i	−0.228528	+	0.395821i
$605$	−4.68425	+	8.11336i	−0.190442	+	0.329855i
$606$		0			0
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	−0.00360990	−	0.999993i	$-0.501149\pi$
$607$	21.2030	−	12.2416i	0.860605	−	0.496870i	0.864215	+	0.503123i	$0.167816\pi$
$608$	−1.50851	+	2.61281i	−0.0611780	+	0.105963i
$609$		0			0
$610$	10.1408	+	17.5644i	0.410589	+	0.711161i
$611$	−21.7563	−	12.5610i	−0.880167	−	0.508165i
$612$		0			0
$613$	0.440043	+	0.762177i	0.0177732	+	0.0307840i	0.874775	−	0.484529i	$-0.161009\pi$
$613$	0.440043	+	0.762177i	0.0177732	+	0.0307840i	−0.857002	+	0.515313i	$0.827676\pi$
$614$	−31.2223			−1.26003
$615$		0			0
$616$		0			0
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	0.717690	−	0.696362i	$-0.245199\pi$
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	−0.244222	+	0.969719i	$0.578533\pi$
$618$		0			0
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.267126	−	0.963662i	$-0.586074\pi$
$619$	−30.7325	−	17.7434i	−1.23524	−	0.713169i	−0.968118	+	0.250493i	$0.919407\pi$
$620$	7.20451	−	4.15953i	0.289340	−	0.167051i
$621$		0			0
$622$		−	10.9100i		−	0.437452i
$623$		0			0
$624$		0			0
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$	−3.42405			−0.136853
$627$		0			0
$628$		−	13.8431i		−	0.552399i
$629$	34.3161			1.36827
$630$		0			0
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$			3.03663i			0.120790i
$633$		0			0
$634$	−19.0471			−0.756458
$635$	−1.25459	−	2.17302i	−0.0497869	−	0.0862335i
$636$		0			0
$637$		0			0
$638$			15.7563i			0.623800i
$639$		0			0
$640$	1.55049	−	0.895175i	0.0612884	−	0.0353849i
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	0.518308	−	0.855194i	$-0.326562\pi$
$641$	0.932777	+	0.538539i	0.0368425	+	0.0212710i	−0.481466	+	0.876465i	$0.659895\pi$
$642$		0			0
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.331010	−	0.943627i	$-0.607389\pi$
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.982710	+	0.185150i	$0.940723\pi$
$644$		0			0
$645$		0			0
$646$	11.0563			0.435006
$647$	4.47605	+	7.75275i	0.175972	+	0.304792i	0.940497	−	0.339802i	$-0.110360\pi$
$647$	4.47605	+	7.75275i	0.175972	+	0.304792i	−0.764525	+	0.644594i	$0.777027\pi$
$648$		0			0
$649$	30.3438	+	17.5190i	1.19110	+	0.687680i
$650$	−4.38910	−	7.60215i	−0.172155	−	0.298181i
$651$		0			0
$652$	−2.16789	+	3.75489i	−0.0849010	+	0.147053i
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	−0.680350	−	0.732887i	$-0.738172\pi$
$653$	−9.85934	+	5.69229i	−0.385826	+	0.222757i	0.294524	+	0.955644i	$0.404839\pi$
$654$		0			0
$655$	−9.39197	+	16.2674i	−0.366975	+	0.635619i
$656$	−4.04094	+	6.99911i	−0.157772	+	0.273269i
$657$		0			0
$658$		0			0
$659$	−31.4373	+	18.1503i	−1.22462	+	0.707036i	−0.965900	−	0.258915i	$-0.916635\pi$
$659$	−31.4373	+	18.1503i	−1.22462	+	0.707036i	−0.258723	+	0.965952i	$0.583302\pi$
$660$		0			0
$661$		−	36.0758i		−	1.40319i	−0.712578	−	0.701593i	$-0.752473\pi$
$661$		−	36.0758i		−	1.40319i	0.712578	−	0.701593i	$-0.247527\pi$
$662$		−	0.0732502i		−	0.00284695i
$663$		0			0
$664$	12.1290	−	7.00270i	0.470698	−	0.271757i
$665$		0			0
$666$		0			0
$667$	12.3557	−	21.4007i	0.478414	−	0.828637i
$668$	6.20756	−	10.7518i	0.240178	−	0.416000i
$669$		0			0
$670$	−0.884136	+	0.510456i	−0.0341572	+	0.0197206i
$671$	−13.6025	+	23.5602i	−0.525117	+	0.909530i
$672$		0			0
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$	−1.93364	−	1.11639i	−0.0744811	−	0.0430017i
$675$		0			0
$676$	−5.46254	−	9.46139i	−0.210098	−	0.363900i
$677$	−15.6282			−0.600639			−0.300320	−	0.953839i	$-0.597093\pi$
$677$	−15.6282			−0.600639			−0.300320	+	0.953839i	$0.597093\pi$
$678$		0			0
$679$		0			0
$680$	−5.68202	−	3.28052i	−0.217896	−	0.125802i
$681$		0			0
$682$	9.66385	+	5.57943i	0.370048	+	0.213647i
$683$	−9.63996	+	5.56563i	−0.368863	+	0.212963i	−0.672961	−	0.739678i	$-0.734978\pi$
$683$	−9.63996	+	5.56563i	−0.368863	+	0.212963i	0.304099	+	0.952640i	$0.401645\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$		0			0
$687$		0			0
$688$	−3.48127	−	6.02973i	−0.132722	−	0.229881i
$689$		0			0
$690$		0			0
$691$		−	3.02419i		−	0.115046i	−0.998344	−	0.0575228i	$-0.981680\pi$
$691$		−	3.02419i		−	0.115046i	0.998344	−	0.0575228i	$-0.0183202\pi$
$692$	17.4182			0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$		−	4.23194i		−	0.160527i
$696$		0			0
$697$	29.6174			1.12184
$698$	−7.36772	−	12.7613i	−0.278872	−	0.483021i
$699$		0			0
$700$		0			0
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$		0			0
$703$	24.4664	−	14.1257i	0.922769	−	0.532761i
$704$	2.07976	+	1.20075i	0.0783840	+	0.0452550i
$705$		0			0
$706$	1.87025	+	1.07979i	0.0703876	+	0.0406383i
$707$		0			0
$708$		0			0
$709$	−3.60770			−0.135490			−0.0677449	−	0.997703i	$-0.521580\pi$
$709$	−3.60770			−0.135490			−0.0677449	+	0.997703i	$0.521580\pi$
$710$	−5.33751	−	9.24484i	−0.200313	−	0.346953i
$711$		0			0
$712$	3.24641	+	1.87432i	0.121664	+	0.0702429i
$713$	−8.75046	−	15.1562i	−0.327707	−	0.567605i
$714$		0			0
$715$	−10.5152	+	18.2129i	−0.393246	+	0.681123i
$716$	−11.3640	+	6.56103i	−0.424694	+	0.245197i
$717$		0			0
$718$	16.3224	−	28.2712i	0.609146	−	1.05507i
$719$	17.1580	−	29.7186i	0.639887	−	1.10832i	−0.345571	−	0.938393i	$-0.612315\pi$
$719$	17.1580	−	29.7186i	0.639887	−	1.10832i	0.985457	−	0.169924i	$-0.0543521\pi$
$720$		0			0
$721$		0			0
$722$	−8.57161	+	4.94882i	−0.319002	+	0.184176i
$723$		0			0
$724$		−	13.3577i		−	0.496437i
$725$		−	11.7747i		−	0.437303i
$726$		0			0
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	0.0932892	+	0.995639i	$0.470262\pi$
$728$		0			0
$729$		0			0
$730$	11.0835	−	19.1972i	0.410220	−	0.710521i
$731$	−12.7577	+	22.0970i	−0.471860	+	0.817285i
$732$		0			0
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$	14.8501	−	25.7212i	0.548129	−	0.949387i
$735$		0			0
$736$	−1.88319	−	3.26178i	−0.0694154	−	0.120231i
$737$	−1.18595	−	0.684706i	−0.0436849	−	0.0252215i
$738$		0			0
$739$	−2.04314	−	3.53882i	−0.0751581	−	0.130178i	0.825997	−	0.563675i	$-0.190613\pi$
$739$	−2.04314	−	3.53882i	−0.0751581	−	0.130178i	−0.901155	+	0.433497i	$0.857279\pi$
$740$	−16.7649			−0.616290
$741$		0			0
$742$		0			0
$743$	1.78246	+	1.02910i	0.0653921	+	0.0377542i	0.532340	−	0.846531i	$-0.321313\pi$
$743$	1.78246	+	1.02910i	0.0653921	+	0.0377542i	−0.466947	+	0.884285i	$0.654646\pi$
$744$		0			0
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$	1.74653	−	1.00836i	0.0639450	−	0.0369187i
$747$		0			0
$748$		−	8.80071i		−	0.321786i
$749$		0			0
$750$		0			0
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	0.562820	−	0.826580i	$-0.309717\pi$
$751$	−11.9053	−	20.6205i	−0.434429	−	0.752454i	−0.997249	+	0.0741262i	$0.976383\pi$
$752$	−5.13604			−0.187292
$753$		0			0
$754$		−	32.0921i		−	1.16873i
$755$	−20.1106			−0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$			18.8709i			0.685421i
$759$		0			0
$760$	−5.40150			−0.195933
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	0.999982	+	0.00602283i	$0.00191714\pi$
$761$	13.9368	+	24.1392i	0.505207	+	0.875044i	−0.494775	+	0.869021i	$0.664750\pi$
$762$		0			0
$763$		0			0
$764$		−	9.25333i		−	0.334774i
$765$		0			0
$766$	−0.724440	+	0.418256i	−0.0261751	+	0.0151122i
$767$	−61.8035	−	35.6823i	−2.23159	−	1.28841i
$768$		0			0
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	0.607800	−	0.794090i	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$		0			0
$771$		0			0
$772$	24.5602			0.883941
$773$	1.07077	+	1.85462i	0.0385128	+	0.0667061i	0.884639	−	0.466276i	$-0.154405\pi$
$773$	1.07077	+	1.85462i	0.0385128	+	0.0667061i	−0.846127	+	0.532982i	$0.821071\pi$
$774$		0			0
$775$	−7.22181	−	4.16951i	−0.259415	−	0.149773i
$776$	−2.75544	−	4.77256i	−0.0989144	−	0.171325i
$777$		0			0
$778$	12.4109	−	21.4964i	0.444954	−	0.770682i
$779$	21.1164	−	12.1916i	0.756573	−	0.436808i
$780$		0			0
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$	−6.90127	+	11.9533i	−0.246789	+	0.427451i
$783$		0			0
$784$		0			0
$785$	21.4635	−	12.3920i	0.766066	−	0.442288i
$786$		0			0
$787$			18.3552i			0.654292i	0.944974	+	0.327146i	$0.106087\pi$
$787$			18.3552i			0.654292i	−0.944974	+	0.327146i	$0.893913\pi$
$788$			12.4861i			0.444799i
$789$		0			0
$790$	−4.70825	+	2.71831i	−0.167512	+	0.0967131i
$791$		0			0
$792$		0			0
$793$	27.7052	−	47.9868i	0.983839	−	1.70406i
$794$	1.51695	−	2.62744i	0.0538346	−	0.0932442i
$795$		0			0
$796$	−0.155144	+	0.0895727i	−0.00549895	+	0.00317482i
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	−0.557660	−	0.830069i	$-0.688301\pi$
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	0.997691	+	0.0679130i	$0.0216340\pi$
$798$		0			0
$799$	9.41094	+	16.3002i	0.332935	+	0.576660i
$800$	−1.55421	−	0.897324i	−0.0549497	−	0.0317252i
$801$		0			0
$802$	−6.53854	−	11.3251i	−0.230884	−	0.399903i
$803$	29.7340			1.04929
$804$		0			0
$805$		0			0
$806$	−19.6831	−	11.3640i	−0.693307	−	0.400281i
$807$		0			0
$808$	−0.216787	−	0.125162i	−0.00762654	−	0.00440319i
$809$	32.7237	−	18.8930i	1.15050	−	0.664244i	0.201494	−	0.979490i	$-0.435420\pi$
$809$	32.7237	−	18.8930i	1.15050	−	0.664244i	0.949010	+	0.315246i	$0.102087\pi$
$810$		0			0
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$		0			0
$813$		0			0
$814$	−11.2439	−	19.4750i	−0.394098	−	0.682598i
$815$	−7.76255			−0.271910
$816$		0			0
$817$			21.0060i			0.734909i
$818$	5.56709			0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$			6.37558i			0.222509i	0.993792	+	0.111255i	$0.0354869\pi$
$821$			6.37558i			0.222509i	−0.993792	+	0.111255i	$0.964513\pi$
$822$		0			0
$823$	28.0587			0.978064			0.489032	−	0.872266i	$-0.337350\pi$
$823$	28.0587			0.978064			0.489032	+	0.872266i	$0.337350\pi$
$824$	0.0839657	+	0.145433i	0.00292508	+	0.00506639i
$825$		0			0
$826$		0			0
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$		0			0
$829$	−44.9680	+	25.9623i	−1.56180	+	0.901708i	−0.564729	+	0.825276i	$0.691019\pi$
$829$	−44.9680	+	25.9623i	−1.56180	+	0.901708i	−0.997075	+	0.0764314i	$0.975647\pi$
$830$	21.7152	+	12.5373i	0.753746	+	0.435175i
$831$		0			0
$832$	−4.23601	−	2.44566i	−0.146857	−	0.0847881i
$833$		0			0
$834$		0			0
$835$	22.2274			0.769211
$836$	−3.62268	−	6.27467i	−0.125293	−	0.217014i
$837$		0			0
$838$	−14.2017	−	8.19938i	−0.490591	−	0.283243i
$839$	−3.33038	−	5.76838i	−0.114977	−	0.199147i	0.802793	−	0.596257i	$-0.203346\pi$
$839$	−3.33038	−	5.76838i	−0.114977	−	0.199147i	−0.917771	+	0.397111i	$0.870013\pi$
$840$		0			0
$841$	7.02357	−	12.1652i	0.242192	−	0.419489i
$842$	−13.3869	+	7.72892i	−0.461342	+	0.266356i
$843$		0			0
$844$	−7.56103	+	13.0961i	−0.260261	+	0.450786i
$845$	9.77985	−	16.9392i	0.336437	−	0.582726i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$			6.57678i			0.225582i
$851$			35.2686i			1.20899i
$852$		0			0
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	−0.133281	−	0.991078i	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$		0			0
$855$		0			0
$856$	−3.99540	+	6.92024i	−0.136560	+	0.236529i
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	−0.966577	−	0.256375i	$-0.917472\pi$
$857$	−7.64830	+	13.2472i	−0.261261	+	0.452517i	0.705316	+	0.708893i	$0.250805\pi$
$858$		0			0
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	−0.435794	−	0.900046i	$-0.643532\pi$
$859$	3.68620	−	2.12823i	0.125772	−	0.0726143i	0.561566	+	0.827432i	$0.310199\pi$
$860$	6.23269	−	10.7953i	0.212533	−	0.368118i
$861$		0			0
$862$	−12.5133	−	21.6737i	−0.426204	−	0.738208i
$863$	−20.4922	−	11.8312i	−0.697562	−	0.402738i	0.108876	−	0.994055i	$-0.465275\pi$
$863$	−20.4922	−	11.8312i	−0.697562	−	0.402738i	−0.806439	+	0.591317i	$0.798608\pi$
$864$		0			0
$865$	15.5923	+	27.0067i	0.530154	+	0.918254i
$866$	−2.25168			−0.0765151
$867$		0			0
$868$		0			0
$869$	−6.31546	−	3.64623i	−0.214237	−	0.123690i
$870$		0			0
$871$	2.41551	+	1.39459i	0.0818463	+	0.0472540i
$872$	−16.4141	+	9.47667i	−0.555851	+	0.320920i
$873$		0			0
$874$			11.3632i			0.384367i
$875$		0			0
$876$		0			0
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	−18.7400			−0.632445
$879$		0			0
$880$			4.29953i			0.144937i
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		0			0
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$			17.9251i			0.602885i
$885$		0			0
$886$	1.20451			0.0404664
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	0.772813	−	0.634634i	$-0.218849\pi$
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	−0.936016	+	0.351959i	$0.885516\pi$
$888$		0			0
$889$		0			0
$890$			6.71136i			0.224965i
$891$		0			0
$892$	−7.27049	+	4.19762i	−0.243434	+	0.140547i
$893$	13.4195	+	7.74775i	0.449066	+	0.259269i
$894$		0			0
$895$	−20.3456	−	11.7465i	−0.680079	−	0.392644i
$896$		0			0
$897$		0			0
$898$	−26.8022			−0.894400
$899$	−15.2433	−	26.4021i	−0.508392	−	0.880560i
$900$		0			0
$901$		0			0
$902$	−9.70433	−	16.8084i	−0.323119	−	0.559658i
$903$		0			0
$904$	−0.579764	+	1.00418i	−0.0192827	+	0.0333985i
$905$	20.7110	−	11.9575i	0.688458	−	0.397481i
$906$		0			0
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	−0.701035	−	0.713127i	$-0.747278\pi$
$907$	8.04314	−	13.9311i	0.267068	−	0.462575i	0.968103	+	0.250551i	$0.0806118\pi$
$908$	−1.21261	+	2.10030i	−0.0402418	+	0.0697009i
$909$		0			0
$910$		0			0
$911$	−27.0087	+	15.5935i	−0.894838	+	0.516635i	−0.875522	−	0.483179i	$-0.839482\pi$
$911$	−27.0087	+	15.5935i	−0.894838	+	0.516635i	−0.0193161	+	0.999813i	$0.506149\pi$
$912$		0			0
$913$			33.6340i			1.11312i
$914$		−	13.8488i		−	0.458079i
$915$		0			0
$916$	−1.74915	+	1.00987i	−0.0577936	+	0.0333672i
$917$		0			0
$918$		0			0
$919$	−12.8832	+	22.3143i	−0.424977	+	0.736082i	−0.996418	−	0.0845609i	$-0.973051\pi$
$919$	−12.8832	+	22.3143i	−0.424977	+	0.736082i	0.571441	+	0.820643i	$0.306385\pi$
$920$	3.37157	−	5.83973i	0.111157	−	0.192530i
$921$		0			0
$922$	4.16110	−	2.40241i	0.137039	−	0.0791193i
$923$	−14.5824	+	25.2574i	−0.479984	+	0.831357i
$924$		0			0
$925$	8.40258	+	14.5537i	0.276275	+	0.478522i
$926$	−18.2201	−	10.5194i	−0.598750	−	0.345689i
$927$		0			0
$928$	−3.28052	−	5.68202i	−0.107688	−	0.186521i
$929$	54.7487			1.79625			0.898124	−	0.439743i	$-0.144931\pi$
$929$	54.7487			1.79625			0.898124	+	0.439743i	$0.144931\pi$
$930$		0			0
$931$		0			0
$932$	11.0236	+	6.36446i	0.361089	+	0.208475i
$933$		0			0
$934$	5.04288	+	2.91151i	0.165008	+	0.0952675i
$935$	13.6454	−	7.87817i	0.446252	−	0.257644i
$936$		0			0
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$		0			0
$939$		0			0
$940$	−4.59766	−	7.96337i	−0.149959	−	0.259737i
$941$	−33.3316			−1.08658			−0.543289	−	0.839545i	$-0.682821\pi$
$941$	−33.3316			−1.08658			−0.543289	+	0.839545i	$0.682821\pi$
$942$		0			0
$943$			30.4394i			0.991245i
$944$	−14.5900			−0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$			7.61522i			0.247461i	0.992316	+	0.123731i	$0.0394859\pi$
$947$			7.61522i			0.247461i	−0.992316	+	0.123731i	$0.960514\pi$
$948$		0			0
$949$	−60.5615			−1.96591
$950$	2.70724	+	4.68907i	0.0878344	+	0.152134i
$951$		0			0
$952$		0			0
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$	14.3472	−	8.28334i	0.464264	−	0.268043i
$956$	15.1117	+	8.72474i	0.488747	+	0.282178i
$957$		0			0
$958$	−23.3447	−	13.4781i	−0.754232	−	0.435456i
$959$		0			0
$960$		0			0
$961$	9.40903			0.303517
$962$	22.9013	+	39.6662i	0.738367	+	1.27889i
$963$		0			0
$964$	−9.90142	−	5.71659i	−0.318903	−	0.184119i
$965$	21.9857	+	38.0803i	0.707744	+	1.22585i
$966$		0			0
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	−0.996775	−	0.0802517i	$-0.974428\pi$
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$968$	4.53172	−	2.61639i	0.145655	−	0.0840939i
$969$		0			0
$970$	4.93320	−	8.54455i	0.158395	−	0.274349i
$971$	4.29971	−	7.44731i	0.137984	−	0.238996i	−0.788749	−	0.614715i	$-0.789271\pi$
$971$	4.29971	−	7.44731i	0.137984	−	0.238996i	0.926733	+	0.375719i	$0.122604\pi$
$972$		0			0
$973$		0			0
$974$	11.8011	−	6.81338i	0.378132	−	0.218315i
$975$		0			0
$976$		−	11.3283i		−	0.362610i
$977$		−	14.7771i		−	0.472761i	−0.971661	−	0.236380i	$-0.924039\pi$
$977$		−	14.7771i		−	0.472761i	0.971661	−	0.236380i	$-0.0759612\pi$
$978$		0			0
$979$	−7.79627	+	4.50118i	−0.249170	+	0.143858i
$980$		0			0
$981$		0			0
$982$	19.4815	−	33.7430i	0.621680	−	1.07678i
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	−0.654803	−	0.755800i	$-0.727248\pi$
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	0.981943	+	0.189176i	$0.0605818\pi$
$984$		0			0
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$	−12.0220	+	20.8227i	−0.382858	+	0.663130i
$987$		0			0
$988$	7.37859	+	12.7801i	0.234744	+	0.406589i
$989$	−22.7103	−	13.1118i	−0.722145	−	0.416931i
$990$		0			0
$991$	4.64647	+	8.04792i	0.147600	+	0.255651i	0.930340	−	0.366698i	$-0.119512\pi$
$991$	4.64647	+	8.04792i	0.147600	+	0.255651i	−0.782740	+	0.622349i	$0.786179\pi$
$992$	−4.64661			−0.147530
$993$		0			0
$994$		0			0
$995$	−0.277763	−	0.160366i	−0.00880567	−	0.00508396i
$996$		0			0
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$	−22.5250	+	13.0048i	−0.713018	+	0.411661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.b.1097.1		16
3.2	odd	2		882.2.l.a.509.7		16
7.2	even	3		378.2.m.a.125.1		16
7.3	odd	6		2646.2.t.a.2285.5		16
7.4	even	3		2646.2.t.a.2285.8		16
7.5	odd	6		378.2.m.a.125.4		16
7.6	odd	2	inner	2646.2.l.b.1097.4		16
9.2	odd	6		2646.2.t.a.1979.5		16
9.7	even	3		882.2.t.b.803.2		16
21.2	odd	6		126.2.m.a.41.5	✓	16
21.5	even	6		126.2.m.a.41.8	yes	16
21.11	odd	6		882.2.t.b.815.3		16
21.17	even	6		882.2.t.b.815.2		16
21.20	even	2		882.2.l.a.509.6		16
28.19	even	6		3024.2.cc.b.881.6		16
28.23	odd	6		3024.2.cc.b.881.3		16
63.2	odd	6		378.2.m.a.251.4		16
63.5	even	6		1134.2.d.a.1133.14		16
63.11	odd	6	inner	2646.2.l.b.521.8		16
63.16	even	3		126.2.m.a.83.8	yes	16
63.20	even	6		2646.2.t.a.1979.8		16
63.23	odd	6		1134.2.d.a.1133.11		16
63.25	even	3		882.2.l.a.227.2		16
63.34	odd	6		882.2.t.b.803.3		16
63.38	even	6	inner	2646.2.l.b.521.5		16
63.40	odd	6		1134.2.d.a.1133.3		16
63.47	even	6		378.2.m.a.251.1		16
63.52	odd	6		882.2.l.a.227.3		16
63.58	even	3		1134.2.d.a.1133.6		16
63.61	odd	6		126.2.m.a.83.5	yes	16
84.23	even	6		1008.2.cc.b.545.8		16
84.47	odd	6		1008.2.cc.b.545.1		16
252.47	odd	6		3024.2.cc.b.2897.3		16
252.79	odd	6		1008.2.cc.b.209.1		16
252.187	even	6		1008.2.cc.b.209.8		16
252.191	even	6		3024.2.cc.b.2897.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	21.2	odd	6
126.2.m.a.41.8	yes	16	21.5	even	6
126.2.m.a.83.5	yes	16	63.61	odd	6
126.2.m.a.83.8	yes	16	63.16	even	3
378.2.m.a.125.1		16	7.2	even	3
378.2.m.a.125.4		16	7.5	odd	6
378.2.m.a.251.1		16	63.47	even	6
378.2.m.a.251.4		16	63.2	odd	6
882.2.l.a.227.2		16	63.25	even	3
882.2.l.a.227.3		16	63.52	odd	6
882.2.l.a.509.6		16	21.20	even	2
882.2.l.a.509.7		16	3.2	odd	2
882.2.t.b.803.2		16	9.7	even	3
882.2.t.b.803.3		16	63.34	odd	6
882.2.t.b.815.2		16	21.17	even	6
882.2.t.b.815.3		16	21.11	odd	6
1008.2.cc.b.209.1		16	252.79	odd	6
1008.2.cc.b.209.8		16	252.187	even	6
1008.2.cc.b.545.1		16	84.47	odd	6
1008.2.cc.b.545.8		16	84.23	even	6
1134.2.d.a.1133.3		16	63.40	odd	6
1134.2.d.a.1133.6		16	63.58	even	3
1134.2.d.a.1133.11		16	63.23	odd	6
1134.2.d.a.1133.14		16	63.5	even	6
2646.2.l.b.521.5		16	63.38	even	6	inner
2646.2.l.b.521.8		16	63.11	odd	6	inner
2646.2.l.b.1097.1		16	1.1	even	1	trivial
2646.2.l.b.1097.4		16	7.6	odd	2	inner
2646.2.t.a.1979.5		16	9.2	odd	6
2646.2.t.a.1979.8		16	63.20	even	6
2646.2.t.a.2285.5		16	7.3	odd	6
2646.2.t.a.2285.8		16	7.4	even	3
3024.2.cc.b.881.3		16	28.23	odd	6
3024.2.cc.b.881.6		16	28.19	even	6
3024.2.cc.b.2897.3		16	252.47	odd	6
3024.2.cc.b.2897.6		16	252.191	even	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.895175 - 1.55049i) q^{5} +1.00000i q^{8} +(-1.55049 + 0.895175i) q^{10} +(-2.07976 - 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +1.00000 q^{16} +(-1.83233 - 3.17369i) q^{17} +(-2.61281 - 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +(3.26178 - 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(2.44566 - 4.23601i) q^{26} +(5.68202 - 3.28052i) q^{29} -4.64661i q^{31} -1.00000i q^{32} +(-3.17369 + 1.83233i) q^{34} +(-4.68202 + 8.10950i) q^{37} +(-1.50851 + 2.61281i) q^{38} +(1.55049 - 0.895175i) q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(2.07976 + 1.20075i) q^{44} +(-1.88319 - 3.26178i) q^{46} -5.13604 q^{47} +(-1.55421 - 0.897324i) q^{50} +(-4.23601 - 2.44566i) q^{52} +4.29953i q^{55} +(-3.28052 - 5.68202i) q^{58} -14.5900 q^{59} -11.3283i q^{61} -4.64661 q^{62} -1.00000 q^{64} -8.75718i q^{65} +0.570231 q^{67} +(1.83233 + 3.17369i) q^{68} +5.96254i q^{71} +(-10.7226 + 6.19070i) q^{73} +(8.10950 + 4.68202i) q^{74} +(2.61281 + 1.50851i) q^{76} +3.03663 q^{79} +(-0.895175 - 1.55049i) q^{80} +(6.99911 + 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} +(-6.02973 + 3.48127i) q^{86} +(1.20075 - 2.07976i) q^{88} +(1.87432 - 3.24641i) q^{89} +(-3.26178 + 1.88319i) q^{92} +5.13604i q^{94} +5.40150i q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Introduction

L-functions

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