LMFDB - Embedded newform 1344.2.q.v.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(193,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1344.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1344.961
Dual form			1344.2.q.v.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-2.00000 - 3.46410i) q^{25} -1.00000 q^{27} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(6.00000 - 5.19615i) q^{35} +(4.00000 - 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{39} +10.0000 q^{43} +(1.50000 + 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(-2.00000 + 1.73205i) q^{63} +(6.00000 - 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.00000 q^{83} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(10.0000 + 3.46410i) q^{91} +(-0.500000 + 0.866025i) q^{93} +(6.00000 + 10.3923i) q^{95} -1.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 3 q^{11} + 8 q^{13} + 6 q^{15} - 4 q^{19} + q^{21} - 4 q^{25} - 2 q^{27} - 18 q^{29} + q^{31} - 3 q^{33} + 12 q^{35} + 8 q^{37} + 4 q^{39} + 20 q^{43} + 3 q^{45}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 3 * q^11 + 8 * q^13 + 6 * q^15 - 4 * q^19 + q^21 - 4 * q^25 - 2 * q^27 - 18 * q^29 + q^31 - 3 * q^33 + 12 * q^35 + 8 * q^37 + 4 * q^39 + 20 * q^43 + 3 * q^45 + 6 * q^47 + 11 * q^49 - 3 * q^53 + 18 * q^55 - 8 * q^57 + 3 * q^59 - 10 * q^61 - 4 * q^63 + 12 * q^65 - 10 * q^67 - 12 * q^71 - 2 * q^73 + 4 * q^75 + 3 * q^77 + q^79 - q^81 + 18 * q^83 - 9 * q^87 - 6 * q^89 + 20 * q^91 - q^93 + 12 * q^95 - 2 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$		0			0
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$	6.00000	−	5.19615i	1.01419	−	0.878310i
$36$		0			0
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$	−4.00000			−0.529813
$58$		0			0
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		0			0
$63$	−2.00000	+	1.73205i	−0.251976	+	0.218218i
$64$		0			0
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$		0			0
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.50000	−	7.79423i	−0.482451	−	0.835629i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	10.0000	+	3.46410i	1.04828	+	0.363137i
$92$		0			0
$93$	−0.500000	+	0.866025i	−0.0518476	+	0.0898027i
$94$		0			0
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$	7.50000	+	2.59808i	0.731925	+	0.253546i
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$		0			0
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$	−8.00000	+	6.92820i	−0.693688	+	0.600751i
$134$		0			0
$135$	−1.50000	+	2.59808i	−0.129099	+	0.223607i
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$		0			0
$145$	−13.5000	+	23.3827i	−1.12111	+	1.94183i
$146$		0			0
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$		0			0
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.00000			0.240966
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$		0			0
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$		0			0
$165$	4.50000	+	7.79423i	0.350325	+	0.606780i
$166$		0			0
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$		0			0
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$		0			0
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	−12.0000	−	20.7846i	−0.882258	−	1.52811i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730182\pi$
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$194$		0			0
$195$	12.0000			0.859338
$196$		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	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$		0			0
$201$	5.00000	−	8.66025i	0.352673	−	0.610847i
$202$		0			0
$203$	−22.5000	−	7.79423i	−1.57919	−	0.547048i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$		0			0
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$		0			0
$215$	15.0000	−	25.9808i	1.02299	−	1.77187i
$216$		0			0
$217$	0.500000	+	2.59808i	0.0339422	+	0.176369i
$218$		0			0
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$		0			0
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.832529	−	0.553981i	$-0.813108\pi$
$227$	−13.5000	−	23.3827i	−0.896026	−	1.55196i	−0.0634974	−	0.997982i	$-0.520225\pi$
$228$		0			0
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$		0			0
$231$	−6.00000	+	5.19615i	−0.394771	+	0.341882i
$232$		0			0
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$		0			0
$235$	−9.00000	−	15.5885i	−0.587095	−	1.01688i
$236$		0			0
$237$	1.00000			0.0649570
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	19.5000	−	7.79423i	1.24581	−	0.497955i
$246$		0			0
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$		0			0
$249$	4.50000	+	7.79423i	0.285176	+	0.493939i
$250$		0			0
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	16.0000	−	13.8564i	0.994192	−	0.860995i
$260$		0			0
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$		0			0
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$		0			0
$267$	−6.00000			−0.367194
$268$		0			0
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$	2.00000	+	10.3923i	0.121046	+	0.628971i
$274$		0			0
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	0.960810	−	0.277207i	$-0.0894088\pi$
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	−0.720473	+	0.693482i	$0.756075\pi$
$278$		0			0
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$		0			0
$285$	−6.00000	+	10.3923i	−0.355409	+	0.615587i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−0.500000	−	0.866025i	−0.0293105	−	0.0507673i
$292$		0			0
$293$	−33.0000			−1.92788			−0.963940	−	0.266119i	$-0.914259\pi$
$293$	−33.0000			−1.92788			−0.963940	+	0.266119i	$0.914259\pi$
$294$		0			0
$295$	9.00000			0.524000
$296$		0			0
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	25.0000	+	8.66025i	1.44098	+	0.499169i
$302$		0			0
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$		0			0
$305$	15.0000	+	25.9808i	0.858898	+	1.48765i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	15.5000	−	26.8468i	0.876112	−	1.51747i	0.0205381	−	0.999789i	$-0.493462\pi$
$313$	15.5000	−	26.8468i	0.876112	−	1.51747i	0.855574	−	0.517681i	$-0.173205\pi$
$314$		0			0
$315$	1.50000	+	7.79423i	0.0845154	+	0.439155i
$316$		0			0
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$		0			0
$319$	−13.5000	−	23.3827i	−0.755855	−	1.30918i
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.00000	−	13.8564i	−0.443760	−	0.768615i
$326$		0			0
$327$	−7.00000	+	12.1244i	−0.387101	+	0.670478i
$328$		0			0
$329$	12.0000	−	10.3923i	0.661581	−	0.572946i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$		0			0
$333$	4.00000	+	6.92820i	0.219199	+	0.379663i
$334$		0			0
$335$	−30.0000			−1.63908
$336$		0			0
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.50000	+	2.59808i	−0.0812296	+	0.140694i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$	−9.00000	+	15.5885i	−0.477670	+	0.827349i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.50000	−	7.79423i	−0.0778761	−	0.404656i
$372$		0			0
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	−0.743691	−	0.668523i	$-0.766927\pi$
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	0.950804	+	0.309794i	$0.100260\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$	−36.0000			−1.85409
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	2.50000	+	4.33013i	0.128079	+	0.221839i
$382$		0			0
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$		0			0
$385$	22.5000	+	7.79423i	1.14671	+	0.397231i
$386$		0			0
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$		0			0
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−9.00000			−0.453990
$394$		0			0
$395$	−1.50000	−	2.59808i	−0.0754732	−	0.130723i
$396$		0			0
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	−0.911840	−	0.410546i	$-0.865338\pi$
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	0.811463	+	0.584404i	$0.198672\pi$
$398$		0			0
$399$	−10.0000	−	3.46410i	−0.500626	−	0.173422i
$400$		0			0
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$	−3.00000			−0.149071
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$		0			0
$413$	1.50000	+	7.79423i	0.0738102	+	0.383529i
$414$		0			0
$415$	13.5000	−	23.3827i	0.662689	−	1.14781i
$416$		0			0
$417$	−1.00000	−	1.73205i	−0.0489702	−	0.0848189i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$		0			0
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.0000	+	17.3205i	−0.967868	+	0.838198i
$428$		0			0
$429$	−6.00000	+	10.3923i	−0.289683	+	0.501745i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	−27.0000			−1.29455
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$		0			0
$443$	−16.5000	+	28.5788i	−0.783939	+	1.35782i	0.145692	+	0.989330i	$0.453459\pi$
$443$	−16.5000	+	28.5788i	−0.783939	+	1.35782i	−0.929631	+	0.368492i	$0.879874\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−0.500000	+	0.866025i	−0.0234920	+	0.0406894i
$454$		0			0
$455$	24.0000	−	20.7846i	1.12514	−	0.974398i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$	1.50000	+	2.59808i	0.0695608	+	0.120483i
$466$		0			0
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$		0			0
$469$	−5.00000	−	25.9808i	−0.230879	−	1.19968i
$470$		0			0
$471$	2.00000	−	3.46410i	0.0921551	−	0.159617i
$472$		0			0
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$		0			0
$475$	16.0000			0.734130
$476$		0			0
$477$	3.00000			0.137361
$478$		0			0
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.50000	+	2.59808i	−0.0681115	+	0.117973i
$486$		0			0
$487$	−20.5000	−	35.5070i	−0.928944	−	1.60898i	−0.785093	−	0.619378i	$-0.787385\pi$
$487$	−20.5000	−	35.5070i	−0.928944	−	1.60898i	−0.143851	−	0.989599i	$-0.545949\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	33.0000			1.48927			0.744635	−	0.667472i	$-0.232624\pi$
$491$	33.0000			1.48927			0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$		0			0
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$		0			0
$499$	1.00000	−	1.73205i	0.0447661	−	0.0775372i	−0.842774	−	0.538267i	$-0.819079\pi$
$499$	1.00000	−	1.73205i	0.0447661	−	0.0775372i	0.887540	+	0.460730i	$0.152412\pi$
$500$		0			0
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$		0			0
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$		0			0
$511$	−1.00000	−	5.19615i	−0.0442374	−	0.229864i
$512$		0			0
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$		0			0
$515$	12.0000	+	20.7846i	0.528783	+	0.915879i
$516$		0			0
$517$	18.0000			0.791639
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	−0.906434	−	0.422347i	$-0.861206\pi$
$523$	−2.00000	+	3.46410i	−0.0874539	+	0.151475i	0.818980	+	0.573822i	$0.194540\pi$
$524$		0			0
$525$	8.00000	−	6.92820i	0.349149	−	0.302372i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−3.00000			−0.130189
$532$		0			0
$533$		0			0
$534$		0			0
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$		0			0
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$		0			0
$539$	−3.00000	+	20.7846i	−0.129219	+	0.895257i
$540$		0			0
$541$	13.0000	−	22.5167i	0.558914	−	0.968067i	−0.438674	−	0.898646i	$-0.644552\pi$
$541$	13.0000	−	22.5167i	0.558914	−	0.968067i	0.997587	−	0.0694205i	$-0.0221150\pi$
$542$		0			0
$543$	−4.00000	−	6.92820i	−0.171656	−	0.297318i
$544$		0			0
$545$	42.0000			1.79908
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$		0			0
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$	18.0000	−	31.1769i	0.766826	−	1.32818i
$552$		0			0
$553$	2.00000	−	1.73205i	0.0850487	−	0.0736543i
$554$		0			0
$555$	12.0000	−	20.7846i	0.509372	−	0.882258i
$556$		0			0
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.500000	−	2.59808i	−0.0209980	−	0.109109i
$568$		0			0
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$570$		0			0
$571$	−17.0000	−	29.4449i	−0.711428	−	1.23223i	−0.964321	−	0.264735i	$-0.914716\pi$
$571$	−17.0000	−	29.4449i	−0.711428	−	1.23223i	0.252893	−	0.967494i	$-0.418618\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$		0			0
$579$	−9.50000	+	16.4545i	−0.394807	+	0.683825i
$580$		0			0
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$		0			0
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$		0			0
$585$	6.00000	+	10.3923i	0.248069	+	0.429669i
$586$		0			0
$587$	−21.0000			−0.866763			−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000			−0.866763			−0.433381	+	0.901211i	$0.642680\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$		0			0
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	−0.999965	−	0.00831589i	$-0.997353\pi$
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	0.507184	+	0.861838i	$0.330686\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.0000	−	17.3205i	0.409273	−	0.708881i
$598$		0			0
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	0.989210	−	0.146503i	$-0.0468017\pi$
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$		0			0
$603$	10.0000			0.407231
$604$		0			0
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	−0.786212	−	0.617957i	$-0.787961\pi$
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	0.928272	+	0.371901i	$0.121294\pi$
$608$		0			0
$609$	−4.50000	−	23.3827i	−0.182349	−	0.947514i
$610$		0			0
$611$	12.0000	−	20.7846i	0.485468	−	0.840855i
$612$		0			0
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	0.658012	−	0.753007i	$-0.271397\pi$
$613$	−8.00000	−	13.8564i	−0.323117	−	0.559655i	−0.981129	+	0.193352i	$0.938064\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	−0.973972	−	0.226670i	$-0.927216\pi$
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	0.290684	−	0.956819i	$-0.406117\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.0000	+	10.3923i	−0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$		0			0
$633$	−7.00000	−	12.1244i	−0.278225	−	0.481900i
$634$		0			0
$635$	7.50000	−	12.9904i	0.297628	−	0.515508i
$636$		0			0
$637$	22.0000	+	17.3205i	0.871672	+	0.686264i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$		0			0
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$	30.0000			1.18125
$646$		0			0
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$	−2.00000	+	1.73205i	−0.0783862	+	0.0678844i
$652$		0			0
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		0			0
$655$	13.5000	+	23.3827i	0.527489	+	0.913637i
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.00000	+	31.1769i	0.232670	+	1.20899i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$		0			0
$671$	−30.0000			−1.15814
$672$		0			0
$673$	29.0000			1.11787			0.558934	−	0.829212i	$-0.311211\pi$
$673$	29.0000			1.11787			0.558934	+	0.829212i	$0.311211\pi$
$674$		0			0
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$		0			0
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	0.352549	+	0.935793i	$0.385315\pi$
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	−0.986695	+	0.162581i	$0.948018\pi$
$678$		0			0
$679$	−2.50000	−	0.866025i	−0.0959412	−	0.0332350i
$680$		0			0
$681$	13.5000	−	23.3827i	0.517321	−	0.896026i
$682$		0			0
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	0.987275	+	0.159022i	$0.0508342\pi$
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	−0.355920	+	0.934516i	$0.615832\pi$
$684$		0			0
$685$	−54.0000			−2.06323
$686$		0			0
$687$	−4.00000			−0.152610
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		0			0
$693$	−7.50000	−	2.59808i	−0.284901	−	0.0986928i
$694$		0			0
$695$	−3.00000	+	5.19615i	−0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	24.0000			0.907763
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$		0			0
$705$	9.00000	−	15.5885i	0.338960	−	0.587095i
$706$		0			0
$707$	−9.00000	−	46.7654i	−0.338480	−	1.75879i
$708$		0			0
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	−0.944509	−	0.328484i	$-0.893462\pi$
$709$	−5.00000	+	8.66025i	−0.187779	+	0.325243i	0.756730	+	0.653727i	$0.226796\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	36.0000			1.34632
$716$		0			0
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$		0			0
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$		0			0
$721$	−16.0000	+	13.8564i	−0.595871	+	0.516040i
$722$		0			0
$723$	−0.500000	+	0.866025i	−0.0185952	+	0.0322078i
$724$		0			0
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−5.00000	+	8.66025i	−0.184679	+	0.319874i	−0.943468	−	0.331463i	$-0.892458\pi$
$733$	−5.00000	+	8.66025i	−0.184679	+	0.319874i	0.758789	+	0.651336i	$0.225791\pi$
$734$		0			0
$735$	16.5000	+	12.9904i	0.608612	+	0.479157i
$736$		0			0
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$		0			0
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.799962	+	0.600050i	$0.204853\pi$
$739$	25.0000	+	43.3013i	0.919640	+	1.59286i	0.119677	+	0.992813i	$0.461814\pi$
$740$		0			0
$741$	−16.0000			−0.587775
$742$		0			0
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$		0			0
$745$	−27.0000	−	46.7654i	−0.989203	−	1.71335i
$746$		0			0
$747$	−4.50000	+	7.79423i	−0.164646	+	0.285176i
$748$		0			0
$749$	−6.00000	+	5.19615i	−0.219235	+	0.189863i
$750$		0			0
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	−0.795075	−	0.606511i	$-0.792568\pi$
$751$	3.50000	−	6.06218i	0.127717	−	0.221212i	0.922792	+	0.385299i	$0.125902\pi$
$752$		0			0
$753$	−13.5000	−	23.3827i	−0.491967	−	0.852112i
$754$		0			0
$755$	3.00000			0.109181
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	−0.954043	−	0.299670i	$-0.903123\pi$
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	0.736543	+	0.676391i	$0.236457\pi$
$762$		0			0
$763$	7.00000	+	36.3731i	0.253417	+	1.31679i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000	+	10.3923i	0.216647	+	0.375244i
$768$		0			0
$769$	−19.0000			−0.685158			−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$		0			0
$777$	20.0000	+	6.92820i	0.717496	+	0.248548i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$		0			0
$783$	9.00000			0.321634
$784$		0			0
$785$	−12.0000			−0.428298
$786$		0			0
$787$	25.0000	+	43.3013i	0.891154	+	1.54352i	0.838494	+	0.544911i	$0.183437\pi$
$787$	25.0000	+	43.3013i	0.891154	+	1.54352i	0.0526599	+	0.998613i	$0.483230\pi$
$788$		0			0
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$		0			0
$795$	−4.50000	−	7.79423i	−0.159599	−	0.276433i
$796$		0			0
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−10.5000	+	18.1865i	−0.369618	+	0.640196i
$808$		0			0
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	−11.0000			−0.385787
$814$		0			0
$815$	24.0000	+	41.5692i	0.840683	+	1.45611i
$816$		0			0
$817$	−20.0000	+	34.6410i	−0.699711	+	1.21194i
$818$		0			0
$819$	−8.00000	+	6.92820i	−0.279543	+	0.242091i
$820$		0			0
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	−0.891013	−	0.453978i	$-0.850005\pi$
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	0.838663	+	0.544651i	$0.183338\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$	12.0000			0.417786
$826$		0			0
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		0			0
$829$	−2.00000	−	3.46410i	−0.0694629	−	0.120313i	0.829202	−	0.558949i	$-0.188795\pi$
$829$	−2.00000	−	3.46410i	−0.0694629	−	0.120313i	−0.898665	+	0.438636i	$0.855462\pi$
$830$		0			0
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$		0			0
$837$	−0.500000	−	0.866025i	−0.0172825	−	0.0299342i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$		0			0
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$		0			0
$849$	−7.00000	+	12.1244i	−0.240239	+	0.416107i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	−0.0255092	−	0.999675i	$-0.508121\pi$
$859$	25.0000	−	43.3013i	0.852989	−	1.47742i	0.878498	−	0.477746i	$-0.158546\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$		0			0
$865$	−27.0000	−	46.7654i	−0.918028	−	1.59007i
$866$		0			0
$867$	17.0000			0.577350
$868$		0			0
$869$	3.00000			0.101768
$870$		0			0
$871$	−20.0000	−	34.6410i	−0.677674	−	1.17377i
$872$		0			0
$873$	0.500000	−	0.866025i	0.0169224	−	0.0293105i
$874$		0			0
$875$	7.50000	+	2.59808i	0.253546	+	0.0878310i
$876$		0			0
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$		0			0
$879$	−16.5000	−	28.5788i	−0.556531	−	0.963940i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$		0			0
$885$	4.50000	+	7.79423i	0.151266	+	0.262000i
$886$		0			0
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$		0			0
$889$	12.5000	+	4.33013i	0.419237	+	0.145228i
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		0			0
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	36.0000			1.20335
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.50000	−	7.79423i	−0.150083	−	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	5.00000	+	25.9808i	0.166390	+	0.864586i
$904$		0			0
$905$	−12.0000	+	20.7846i	−0.398893	+	0.690904i
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$		0			0
$915$	−15.0000	+	25.9808i	−0.495885	+	0.858898i
$916$		0			0
$917$	−18.0000	+	15.5885i	−0.594412	+	0.514776i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−32.0000			−1.05215
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	−26.0000	+	10.3923i	−0.852116	+	0.340594i
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$		0			0
$939$	31.0000			1.01165
$940$		0			0
$941$	−4.50000	−	7.79423i	−0.146696	−	0.254085i	0.783309	−	0.621633i	$-0.213531\pi$
$941$	−4.50000	−	7.79423i	−0.146696	−	0.254085i	−0.930004	+	0.367549i	$0.880197\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−6.00000	+	5.19615i	−0.195180	+	0.169031i
$946$		0			0
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$		0			0
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$	9.00000			0.291845
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	13.5000	−	23.3827i	0.436393	−	0.755855i
$958$		0			0
$959$	−9.00000	−	46.7654i	−0.290625	−	1.51013i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$	−1.50000	−	2.59808i	−0.0483368	−	0.0837218i
$964$		0			0
$965$	57.0000			1.83489
$966$		0			0
$967$	−1.00000			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	0.362604	+	0.931943i	$0.381888\pi$
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	−0.988389	+	0.151948i	$0.951445\pi$
$972$		0			0
$973$	−5.00000	−	1.73205i	−0.160293	−	0.0555270i
$974$		0			0
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$		0			0
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$	15.0000	+	5.19615i	0.477455	+	0.165395i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$		0			0
$995$	−60.0000			−1.90213
$996$		0			0
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	0.955322	−	0.295567i	$-0.0955086\pi$
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	−0.733630	+	0.679549i	$0.762175\pi$
$998$		0			0
$999$	−4.00000	+	6.92820i	−0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.v.961.1		2
4.3	odd	2		1344.2.q.j.961.1		2
7.2	even	3		9408.2.a.d.1.1		1
7.4	even	3	inner	1344.2.q.v.193.1		2
7.5	odd	6		9408.2.a.db.1.1		1
8.3	odd	2		336.2.q.d.289.1		2
8.5	even	2		42.2.e.b.37.1	yes	2
24.5	odd	2		126.2.g.b.37.1		2
24.11	even	2		1008.2.s.n.289.1		2
28.11	odd	6		1344.2.q.j.193.1		2
28.19	even	6		9408.2.a.bm.1.1		1
28.23	odd	6		9408.2.a.bu.1.1		1
40.13	odd	4		1050.2.o.b.499.1		4
40.29	even	2		1050.2.i.e.751.1		2
40.37	odd	4		1050.2.o.b.499.2		4
56.3	even	6		2352.2.q.m.1537.1		2
56.5	odd	6		294.2.a.a.1.1		1
56.11	odd	6		336.2.q.d.193.1		2
56.13	odd	2		294.2.e.f.79.1		2
56.19	even	6		2352.2.a.n.1.1		1
56.27	even	2		2352.2.q.m.961.1		2
56.37	even	6		294.2.a.d.1.1		1
56.45	odd	6		294.2.e.f.67.1		2
56.51	odd	6		2352.2.a.m.1.1		1
56.53	even	6		42.2.e.b.25.1	✓	2
72.5	odd	6		1134.2.h.a.541.1		2
72.13	even	6		1134.2.h.p.541.1		2
72.29	odd	6		1134.2.e.p.919.1		2
72.61	even	6		1134.2.e.a.919.1		2
168.5	even	6		882.2.a.k.1.1		1
168.11	even	6		1008.2.s.n.865.1		2
168.53	odd	6		126.2.g.b.109.1		2
168.101	even	6		882.2.g.b.361.1		2
168.107	even	6		7056.2.a.g.1.1		1
168.125	even	2		882.2.g.b.667.1		2
168.131	odd	6		7056.2.a.bz.1.1		1
168.149	odd	6		882.2.a.g.1.1		1
280.53	odd	12		1050.2.o.b.949.2		4
280.109	even	6		1050.2.i.e.151.1		2
280.149	even	6		7350.2.a.ce.1.1		1
280.229	odd	6		7350.2.a.cw.1.1		1
280.277	odd	12		1050.2.o.b.949.1		4
504.221	odd	6		1134.2.e.p.865.1		2
504.277	even	6		1134.2.h.p.109.1		2
504.389	odd	6		1134.2.h.a.109.1		2
504.445	even	6		1134.2.e.a.865.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	56.53	even	6
42.2.e.b.37.1	yes	2	8.5	even	2
126.2.g.b.37.1		2	24.5	odd	2
126.2.g.b.109.1		2	168.53	odd	6
294.2.a.a.1.1		1	56.5	odd	6
294.2.a.d.1.1		1	56.37	even	6
294.2.e.f.67.1		2	56.45	odd	6
294.2.e.f.79.1		2	56.13	odd	2
336.2.q.d.193.1		2	56.11	odd	6
336.2.q.d.289.1		2	8.3	odd	2
882.2.a.g.1.1		1	168.149	odd	6
882.2.a.k.1.1		1	168.5	even	6
882.2.g.b.361.1		2	168.101	even	6
882.2.g.b.667.1		2	168.125	even	2
1008.2.s.n.289.1		2	24.11	even	2
1008.2.s.n.865.1		2	168.11	even	6
1050.2.i.e.151.1		2	280.109	even	6
1050.2.i.e.751.1		2	40.29	even	2
1050.2.o.b.499.1		4	40.13	odd	4
1050.2.o.b.499.2		4	40.37	odd	4
1050.2.o.b.949.1		4	280.277	odd	12
1050.2.o.b.949.2		4	280.53	odd	12
1134.2.e.a.865.1		2	504.445	even	6
1134.2.e.a.919.1		2	72.61	even	6
1134.2.e.p.865.1		2	504.221	odd	6
1134.2.e.p.919.1		2	72.29	odd	6
1134.2.h.a.109.1		2	504.389	odd	6
1134.2.h.a.541.1		2	72.5	odd	6
1134.2.h.p.109.1		2	504.277	even	6
1134.2.h.p.541.1		2	72.13	even	6
1344.2.q.j.193.1		2	28.11	odd	6
1344.2.q.j.961.1		2	4.3	odd	2
1344.2.q.v.193.1		2	7.4	even	3	inner
1344.2.q.v.961.1		2	1.1	even	1	trivial
2352.2.a.m.1.1		1	56.51	odd	6
2352.2.a.n.1.1		1	56.19	even	6
2352.2.q.m.961.1		2	56.27	even	2
2352.2.q.m.1537.1		2	56.3	even	6
7056.2.a.g.1.1		1	168.107	even	6
7056.2.a.bz.1.1		1	168.131	odd	6
7350.2.a.ce.1.1		1	280.149	even	6
7350.2.a.cw.1.1		1	280.229	odd	6
9408.2.a.d.1.1		1	7.2	even	3
9408.2.a.bm.1.1		1	28.19	even	6
9408.2.a.bu.1.1		1	28.23	odd	6
9408.2.a.db.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-2.00000 - 3.46410i) q^{25} -1.00000 q^{27} -9.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(6.00000 - 5.19615i) q^{35} +(4.00000 - 6.92820i) q^{37} +(2.00000 + 3.46410i) q^{39} +10.0000 q^{43} +(1.50000 + 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} -4.00000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(-2.00000 + 1.73205i) q^{63} +(6.00000 - 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} -6.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +9.00000 q^{83} +(-4.50000 - 7.79423i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(10.0000 + 3.46410i) q^{91} +(-0.500000 + 0.866025i) q^{93} +(6.00000 + 10.3923i) q^{95} -1.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 3 q^{5} + 5 q^{7} - q^{9} + 3 q^{11} + 8 q^{13} + 6 q^{15} - 4 q^{19} + q^{21} - 4 q^{25} - 2 q^{27} - 18 q^{29} + q^{31} - 3 q^{33} + 12 q^{35} + 8 q^{37} + 4 q^{39} + 20 q^{43} + 3 q^{45}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^3 + 3 * q^5 + 5 * q^7 - q^9 + 3 * q^11 + 8 * q^13 + 6 * q^15 - 4 * q^19 + q^21 - 4 * q^25 - 2 * q^27 - 18 * q^29 + q^31 - 3 * q^33 + 12 * q^35 + 8 * q^37 + 4 * q^39 + 20 * q^43 + 3 * q^45 + 6 * q^47 + 11 * q^49 - 3 * q^53 + 18 * q^55 - 8 * q^57 + 3 * q^59 - 10 * q^61 - 4 * q^63 + 12 * q^65 - 10 * q^67 - 12 * q^71 - 2 * q^73 + 4 * q^75 + 3 * q^77 + q^79 - q^81 + 18 * q^83 - 9 * q^87 - 6 * q^89 + 20 * q^91 - q^93 + 12 * q^95 - 2 * q^97 - 6 * q^99

Introduction

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