LMFDB - Embedded newform 1344.2.q.x.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	1344.961
Dual form			1344.2.q.x.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} +1.27492 q^{13} -4.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-0.637459 + 1.10411i) q^{19} +(-1.13746 + 2.38876i) q^{21} +(2.00000 - 3.46410i) q^{23} +(-6.63746 - 11.4964i) q^{25} -1.00000 q^{27} +2.27492 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-2.13746 + 3.70219i) q^{33} +(-11.2749 + 0.894797i) q^{35} +(2.63746 - 4.56821i) q^{37} +(0.637459 + 1.10411i) q^{39} +10.5498 q^{41} -7.27492 q^{43} +(-2.13746 - 3.70219i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(0.862541 + 1.49397i) q^{53} -18.2749 q^{55} -1.27492 q^{57} +(-3.13746 - 5.43424i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-2.63746 + 0.209313i) q^{63} +(-2.72508 + 4.71998i) q^{65} +(-3.63746 - 6.30026i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(-1.63746 - 2.83616i) q^{73} +(6.63746 - 11.4964i) q^{75} +(-4.86254 + 10.2118i) q^{77} +(-1.77492 + 3.07425i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.274917 q^{83} -17.0997 q^{85} +(1.13746 + 1.97014i) q^{87} +(-2.27492 + 3.94027i) q^{89} +(1.91238 + 2.77862i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-2.72508 - 4.71998i) q^{95} +16.2749 q^{97} -4.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - q^5 + 6 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} - q^{5} + 6 q^{7} - 2 q^{9} + q^{11} - 10 q^{13} - 2 q^{15} + 8 q^{17} + 5 q^{19} + 3 q^{21} + 8 q^{23} - 19 q^{25} - 4 q^{27} - 6 q^{29} - 2 q^{31} - q^{33} - 30 q^{35} + 3 q^{37} - 5 q^{39} + 12 q^{41} - 14 q^{43} - q^{45} - 12 q^{47} - 10 q^{49} - 8 q^{51} + 11 q^{53} - 58 q^{55} + 10 q^{57} - 5 q^{59} + 20 q^{61} - 3 q^{63} - 26 q^{65} - 7 q^{67} + 16 q^{69} - 8 q^{71} + q^{73} + 19 q^{75} - 27 q^{77} + 8 q^{79} - 2 q^{81} + 14 q^{83} - 8 q^{85} - 3 q^{87} + 6 q^{89} - 15 q^{91} + 2 q^{93} - 26 q^{95} + 50 q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - q^5 + 6 * q^7 - 2 * q^9 + q^11 - 10 * q^13 - 2 * q^15 + 8 * q^17 + 5 * q^19 + 3 * q^21 + 8 * q^23 - 19 * q^25 - 4 * q^27 - 6 * q^29 - 2 * q^31 - q^33 - 30 * q^35 + 3 * q^37 - 5 * q^39 + 12 * q^41 - 14 * q^43 - q^45 - 12 * q^47 - 10 * q^49 - 8 * q^51 + 11 * q^53 - 58 * q^55 + 10 * q^57 - 5 * q^59 + 20 * q^61 - 3 * q^63 - 26 * q^65 - 7 * q^67 + 16 * q^69 - 8 * q^71 + q^73 + 19 * q^75 - 27 * q^77 + 8 * q^79 - 2 * q^81 + 14 * q^83 - 8 * q^85 - 3 * q^87 + 6 * q^89 - 15 * q^91 + 2 * q^93 - 26 * q^95 + 50 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

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
$5$	−2.13746	+	3.70219i	−0.955901	+	1.65567i	−0.223607	+	0.974679i	$0.571783\pi$
$5$	−2.13746	+	3.70219i	−0.955901	+	1.65567i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	1.50000	+	2.17945i	0.566947	+	0.823754i
$7$	1.50000	+	2.17945i	0.566947	+	0.823754i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.13746	+	3.70219i	0.644468	+	1.11625i	0.984424	+	0.175810i	$0.0562545\pi$
$11$	2.13746	+	3.70219i	0.644468	+	1.11625i	−0.339956	+	0.940441i	$0.610412\pi$
$12$		0			0
$13$	1.27492			0.353598			0.176799	−	0.984247i	$-0.443426\pi$
$13$	1.27492			0.353598			0.176799	+	0.984247i	$0.443426\pi$
$14$		0			0
$15$	−4.27492			−1.10378
$16$		0			0
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	−0.637459	+	1.10411i	−0.146243	+	0.253300i	−0.929836	−	0.367974i	$-0.880051\pi$
$19$	−0.637459	+	1.10411i	−0.146243	+	0.253300i	0.783593	+	0.621275i	$0.213385\pi$
$20$		0			0
$21$	−1.13746	+	2.38876i	−0.248214	+	0.521271i
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	−6.63746	−	11.4964i	−1.32749	−	2.29928i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.27492			0.422442			0.211221	−	0.977438i	$-0.432256\pi$
$29$	2.27492			0.422442			0.211221	+	0.977438i	$0.432256\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$		0			0
$33$	−2.13746	+	3.70219i	−0.372084	+	0.644468i
$34$		0			0
$35$	−11.2749	+	0.894797i	−1.90581	+	0.151248i
$36$		0			0
$37$	2.63746	−	4.56821i	0.433596	−	0.751009i	−0.563584	−	0.826059i	$-0.690578\pi$
$37$	2.63746	−	4.56821i	0.433596	−	0.751009i	0.997180	+	0.0750491i	$0.0239113\pi$
$38$		0			0
$39$	0.637459	+	1.10411i	0.102075	+	0.176799i
$40$		0			0
$41$	10.5498			1.64761			0.823804	−	0.566875i	$-0.191848\pi$
$41$	10.5498			1.64761			0.823804	+	0.566875i	$0.191848\pi$
$42$		0			0
$43$	−7.27492			−1.10941			−0.554707	−	0.832046i	$-0.687170\pi$
$43$	−7.27492			−1.10941			−0.554707	+	0.832046i	$0.687170\pi$
$44$		0			0
$45$	−2.13746	−	3.70219i	−0.318634	−	0.551889i
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	−2.50000	+	6.53835i	−0.357143	+	0.934050i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	0.862541	+	1.49397i	0.118479	+	0.205212i	0.919165	−	0.393872i	$-0.128865\pi$
$53$	0.862541	+	1.49397i	0.118479	+	0.205212i	−0.800686	+	0.599084i	$0.795531\pi$
$54$		0			0
$55$	−18.2749			−2.46419
$56$		0			0
$57$	−1.27492			−0.168867
$58$		0			0
$59$	−3.13746	−	5.43424i	−0.408462	−	0.707477i	0.586255	−	0.810126i	$-0.300602\pi$
$59$	−3.13746	−	5.43424i	−0.408462	−	0.707477i	−0.994718	+	0.102649i	$0.967268\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$		0			0
$63$	−2.63746	+	0.209313i	−0.332289	+	0.0263710i
$64$		0			0
$65$	−2.72508	+	4.71998i	−0.338005	+	0.585442i
$66$		0			0
$67$	−3.63746	−	6.30026i	−0.444386	−	0.769700i	0.553623	−	0.832767i	$-0.313245\pi$
$67$	−3.63746	−	6.30026i	−0.444386	−	0.769700i	−0.998009	+	0.0630678i	$0.979912\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	−1.63746	−	2.83616i	−0.191650	−	0.331948i	0.754147	−	0.656705i	$-0.228051\pi$
$73$	−1.63746	−	2.83616i	−0.191650	−	0.331948i	−0.945797	+	0.324758i	$0.894717\pi$
$74$		0			0
$75$	6.63746	−	11.4964i	0.766428	−	1.32749i
$76$		0			0
$77$	−4.86254	+	10.2118i	−0.554138	+	1.16374i
$78$		0			0
$79$	−1.77492	+	3.07425i	−0.199694	+	0.345880i	−0.948429	−	0.316989i	$-0.897328\pi$
$79$	−1.77492	+	3.07425i	−0.199694	+	0.345880i	0.748735	+	0.662869i	$0.230661\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.274917			−0.0301761			−0.0150880	−	0.999886i	$-0.504803\pi$
$83$	−0.274917			−0.0301761			−0.0150880	+	0.999886i	$0.504803\pi$
$84$		0			0
$85$	−17.0997			−1.85472
$86$		0			0
$87$	1.13746	+	1.97014i	0.121948	+	0.211221i
$88$		0			0
$89$	−2.27492	+	3.94027i	−0.241141	+	0.417668i	−0.961040	−	0.276411i	$-0.910855\pi$
$89$	−2.27492	+	3.94027i	−0.241141	+	0.417668i	0.719899	+	0.694079i	$0.244188\pi$
$90$		0			0
$91$	1.91238	+	2.77862i	0.200471	+	0.291278i
$92$		0			0
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$		0			0
$95$	−2.72508	−	4.71998i	−0.279588	−	0.484260i
$96$		0			0
$97$	16.2749			1.65247			0.826234	−	0.563327i	$-0.190479\pi$
$97$	16.2749			1.65247			0.826234	+	0.563327i	$0.190479\pi$
$98$		0			0
$99$	−4.27492			−0.429645
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−5.91238	+	10.2405i	−0.582564	+	1.00903i	0.412611	+	0.910907i	$0.364617\pi$
$103$	−5.91238	+	10.2405i	−0.582564	+	1.00903i	−0.995174	+	0.0981224i	$0.968716\pi$
$104$		0			0
$105$	−6.41238	−	9.31697i	−0.625784	−	0.909243i
$106$		0			0
$107$	−3.41238	+	5.91041i	−0.329887	+	0.571381i	−0.982489	−	0.186320i	$-0.940344\pi$
$107$	−3.41238	+	5.91041i	−0.329887	+	0.571381i	0.652602	+	0.757701i	$0.273677\pi$
$108$		0			0
$109$	−2.91238	−	5.04438i	−0.278955	−	0.483164i	0.692170	−	0.721734i	$-0.256655\pi$
$109$	−2.91238	−	5.04438i	−0.278955	−	0.483164i	−0.971125	+	0.238570i	$0.923321\pi$
$110$		0			0
$111$	5.27492			0.500673
$112$		0			0
$113$	10.5498			0.992445			0.496222	−	0.868195i	$-0.334720\pi$
$113$	10.5498			0.992445			0.496222	+	0.868195i	$0.334720\pi$
$114$		0			0
$115$	8.54983	+	14.8087i	0.797276	+	1.38092i
$116$		0			0
$117$	−0.637459	+	1.10411i	−0.0589331	+	0.102075i
$118$		0			0
$119$	−4.54983	+	9.55505i	−0.417083	+	0.875910i
$120$		0			0
$121$	−3.63746	+	6.30026i	−0.330678	+	0.572751i
$122$		0			0
$123$	5.27492	+	9.13642i	0.475623	+	0.823804i
$124$		0			0
$125$	35.3746			3.16400
$126$		0			0
$127$	21.5498			1.91224			0.956119	−	0.292978i	$-0.0946462\pi$
$127$	21.5498			1.91224			0.956119	+	0.292978i	$0.0946462\pi$
$128$		0			0
$129$	−3.63746	−	6.30026i	−0.320260	−	0.554707i
$130$		0			0
$131$	0.137459	−	0.238085i	0.0120098	−	0.0208016i	−0.859958	−	0.510365i	$-0.829510\pi$
$131$	0.137459	−	0.238085i	0.0120098	−	0.0208016i	0.871968	+	0.489563i	$0.162844\pi$
$132$		0			0
$133$	−3.36254	+	0.266857i	−0.291569	+	0.0231395i
$134$		0			0
$135$	2.13746	−	3.70219i	0.183963	−	0.318634i
$136$		0			0
$137$	−8.27492	−	14.3326i	−0.706974	−	1.22451i	−0.965974	−	0.258638i	$-0.916726\pi$
$137$	−8.27492	−	14.3326i	−0.706974	−	1.22451i	0.259001	−	0.965877i	$-0.416607\pi$
$138$		0			0
$139$	0.725083			0.0615007			0.0307504	−	0.999527i	$-0.490210\pi$
$139$	0.725083			0.0615007			0.0307504	+	0.999527i	$0.490210\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	2.72508	+	4.71998i	0.227883	+	0.394705i
$144$		0			0
$145$	−4.86254	+	8.42217i	−0.403812	+	0.699423i
$146$		0			0
$147$	−6.91238	+	1.10411i	−0.570123	+	0.0910655i
$148$		0			0
$149$	0.274917	−	0.476171i	0.0225221	−	0.0390094i	−0.854545	−	0.519378i	$-0.826164\pi$
$149$	0.274917	−	0.476171i	0.0225221	−	0.0390094i	0.877067	+	0.480368i	$0.159497\pi$
$150$		0			0
$151$	−7.68729	−	13.3148i	−0.625583	−	1.08354i	−0.988428	−	0.151692i	$-0.951528\pi$
$151$	−7.68729	−	13.3148i	−0.625583	−	1.08354i	0.362845	−	0.931850i	$-0.381806\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	4.27492			0.343370
$156$		0			0
$157$	7.27492	+	12.6005i	0.580602	+	1.00563i	0.995408	+	0.0957218i	$0.0305159\pi$
$157$	7.27492	+	12.6005i	0.580602	+	1.00563i	−0.414807	+	0.909910i	$0.636151\pi$
$158$		0			0
$159$	−0.862541	+	1.49397i	−0.0684040	+	0.118479i
$160$		0			0
$161$	10.5498	−	0.837253i	0.831443	−	0.0659848i
$162$		0			0
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$		0			0
$165$	−9.13746	−	15.8265i	−0.711350	−	1.23209i
$166$		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
$169$	−11.3746			−0.874968
$170$		0			0
$171$	−0.637459	−	1.10411i	−0.0487477	−	0.0844335i
$172$		0			0
$173$	−3.72508	+	6.45203i	−0.283213	+	0.490539i	−0.972174	−	0.234259i	$-0.924734\pi$
$173$	−3.72508	+	6.45203i	−0.283213	+	0.490539i	0.688961	+	0.724798i	$0.258067\pi$
$174$		0			0
$175$	15.0997	−	31.7106i	1.14143	−	2.39710i
$176$		0			0
$177$	3.13746	−	5.43424i	0.235826	−	0.408462i
$178$		0			0
$179$	0.725083	+	1.25588i	0.0541952	+	0.0938689i	0.891850	−	0.452331i	$-0.149407\pi$
$179$	0.725083	+	1.25588i	0.0541952	+	0.0938689i	−0.837655	+	0.546200i	$0.816074\pi$
$180$		0			0
$181$	−3.82475			−0.284292			−0.142146	−	0.989846i	$-0.545400\pi$
$181$	−3.82475			−0.284292			−0.142146	+	0.989846i	$0.545400\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	11.2749	+	19.5287i	0.828948	+	1.43578i
$186$		0			0
$187$	−8.54983	+	14.8087i	−0.625226	+	1.08292i
$188$		0			0
$189$	−1.50000	−	2.17945i	−0.109109	−	0.158532i
$190$		0			0
$191$	−5.27492	+	9.13642i	−0.381680	+	0.661088i	−0.991302	−	0.131603i	$-0.957988\pi$
$191$	−5.27492	+	9.13642i	−0.381680	+	0.661088i	0.609623	+	0.792692i	$0.291321\pi$
$192$		0			0
$193$	−7.77492	−	13.4666i	−0.559651	−	0.969344i	−0.997525	−	0.0703075i	$-0.977602\pi$
$193$	−7.77492	−	13.4666i	−0.559651	−	0.969344i	0.437875	−	0.899036i	$-0.355731\pi$
$194$		0			0
$195$	−5.45017			−0.390294
$196$		0			0
$197$	16.5498			1.17913			0.589563	−	0.807722i	$-0.299300\pi$
$197$	16.5498			1.17913			0.589563	+	0.807722i	$0.299300\pi$
$198$		0			0
$199$	12.5498	+	21.7370i	0.889634	+	1.54089i	0.840308	+	0.542109i	$0.182374\pi$
$199$	12.5498	+	21.7370i	0.889634	+	1.54089i	0.0493259	+	0.998783i	$0.484293\pi$
$200$		0			0
$201$	3.63746	−	6.30026i	0.256567	−	0.444386i
$202$		0			0
$203$	3.41238	+	4.95807i	0.239502	+	0.347988i
$204$		0			0
$205$	−22.5498	+	39.0575i	−1.57495	+	2.72789i
$206$		0			0
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$		0			0
$209$	−5.45017			−0.376996
$210$		0			0
$211$	17.6495			1.21504			0.607521	−	0.794304i	$-0.292164\pi$
$211$	17.6495			1.21504			0.607521	+	0.794304i	$0.292164\pi$
$212$		0			0
$213$	−1.00000	−	1.73205i	−0.0685189	−	0.118678i
$214$		0			0
$215$	15.5498	−	26.9331i	1.06049	−	1.83682i
$216$		0			0
$217$	1.13746	−	2.38876i	0.0772157	−	0.162160i
$218$		0			0
$219$	1.63746	−	2.83616i	0.110649	−	0.191650i
$220$		0			0
$221$	2.54983	+	4.41644i	0.171520	+	0.297082i
$222$		0			0
$223$	−6.27492			−0.420200			−0.210100	−	0.977680i	$-0.567379\pi$
$223$	−6.27492			−0.420200			−0.210100	+	0.977680i	$0.567379\pi$
$224$		0			0
$225$	13.2749			0.884994
$226$		0			0
$227$	1.86254	+	3.22602i	0.123621	+	0.214118i	0.921193	−	0.389106i	$-0.127216\pi$
$227$	1.86254	+	3.22602i	0.123621	+	0.214118i	−0.797572	+	0.603224i	$0.793883\pi$
$228$		0			0
$229$	5.36254	−	9.28819i	0.354367	−	0.613781i	−0.632643	−	0.774444i	$-0.718030\pi$
$229$	5.36254	−	9.28819i	0.354367	−	0.613781i	0.987009	+	0.160663i	$0.0513631\pi$
$230$		0			0
$231$	−11.2749	+	0.894797i	−0.741835	+	0.0588733i
$232$		0			0
$233$	−7.27492	+	12.6005i	−0.476596	+	0.825488i	−0.999640	−	0.0268173i	$-0.991463\pi$
$233$	−7.27492	+	12.6005i	−0.476596	+	0.825488i	0.523045	+	0.852305i	$0.324796\pi$
$234$		0			0
$235$	−12.8248	−	22.2131i	−0.836595	−	1.44902i
$236$		0			0
$237$	−3.54983			−0.230587
$238$		0			0
$239$	−30.5498			−1.97610			−0.988052	−	0.154119i	$-0.950746\pi$
$239$	−30.5498			−1.97610			−0.988052	+	0.154119i	$0.950746\pi$
$240$		0			0
$241$	6.41238	+	11.1066i	0.413057	+	0.715436i	0.995222	−	0.0976343i	$-0.0311275\pi$
$241$	6.41238	+	11.1066i	0.413057	+	0.715436i	−0.582165	+	0.813071i	$0.697794\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−18.8625	−	23.2309i	−1.20508	−	1.48417i
$246$		0			0
$247$	−0.812707	+	1.40765i	−0.0517113	+	0.0895666i
$248$		0			0
$249$	−0.137459	−	0.238085i	−0.00871109	−	0.0150880i
$250$		0			0
$251$	19.3746			1.22291			0.611457	−	0.791278i	$-0.290584\pi$
$251$	19.3746			1.22291			0.611457	+	0.791278i	$0.290584\pi$
$252$		0			0
$253$	17.0997			1.07505
$254$		0			0
$255$	−8.54983	−	14.8087i	−0.535411	−	0.927360i
$256$		0			0
$257$	9.54983	−	16.5408i	0.595702	−	1.03179i	−0.397745	−	0.917496i	$-0.630207\pi$
$257$	9.54983	−	16.5408i	0.595702	−	1.03179i	0.993447	−	0.114291i	$-0.0364595\pi$
$258$		0			0
$259$	13.9124	−	1.10411i	0.864473	−	0.0686061i
$260$		0			0
$261$	−1.13746	+	1.97014i	−0.0704069	+	0.121948i
$262$		0			0
$263$	−12.2749	−	21.2608i	−0.756904	−	1.31100i	−0.944422	−	0.328735i	$-0.893378\pi$
$263$	−12.2749	−	21.2608i	−0.756904	−	1.31100i	0.187518	−	0.982261i	$-0.439956\pi$
$264$		0			0
$265$	−7.37459			−0.453017
$266$		0			0
$267$	−4.54983			−0.278445
$268$		0			0
$269$	14.1375	+	24.4868i	0.861976	+	1.49299i	0.870019	+	0.493019i	$0.164107\pi$
$269$	14.1375	+	24.4868i	0.861976	+	1.49299i	−0.00804266	+	0.999968i	$0.502560\pi$
$270$		0			0
$271$	−3.13746	+	5.43424i	−0.190587	+	0.330106i	−0.945445	−	0.325782i	$-0.894372\pi$
$271$	−3.13746	+	5.43424i	−0.190587	+	0.330106i	0.754858	+	0.655888i	$0.227706\pi$
$272$		0			0
$273$	−1.45017	+	3.04547i	−0.0877680	+	0.184321i
$274$		0			0
$275$	28.3746	−	49.1462i	1.71105	−	2.96363i
$276$		0			0
$277$	−2.08762	−	3.61587i	−0.125433	−	0.217257i	0.796469	−	0.604679i	$-0.206699\pi$
$277$	−2.08762	−	3.61587i	−0.125433	−	0.217257i	−0.921902	+	0.387423i	$0.873365\pi$
$278$		0			0
$279$	1.00000			0.0598684
$280$		0			0
$281$	−11.4502			−0.683060			−0.341530	−	0.939871i	$-0.610945\pi$
$281$	−11.4502			−0.683060			−0.341530	+	0.939871i	$0.610945\pi$
$282$		0			0
$283$	−13.4622	−	23.3172i	−0.800245	−	1.38607i	−0.919454	−	0.393196i	$-0.871369\pi$
$283$	−13.4622	−	23.3172i	−0.800245	−	1.38607i	0.119209	−	0.992869i	$-0.461964\pi$
$284$		0			0
$285$	2.72508	−	4.71998i	0.161420	−	0.279588i
$286$		0			0
$287$	15.8248	+	22.9928i	0.934106	+	1.35722i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	8.13746	+	14.0945i	0.477026	+	0.826234i
$292$		0			0
$293$	5.17525			0.302341			0.151171	−	0.988508i	$-0.451696\pi$
$293$	5.17525			0.302341			0.151171	+	0.988508i	$0.451696\pi$
$294$		0			0
$295$	26.8248			1.56180
$296$		0			0
$297$	−2.13746	−	3.70219i	−0.124028	−	0.214823i
$298$		0			0
$299$	2.54983	−	4.41644i	0.147461	−	0.255409i
$300$		0			0
$301$	−10.9124	−	15.8553i	−0.628979	−	0.913885i
$302$		0			0
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$		0			0
$305$	21.3746	+	37.0219i	1.22391	+	2.11987i
$306$		0			0
$307$	−26.3746			−1.50528			−0.752639	−	0.658434i	$-0.771219\pi$
$307$	−26.3746			−1.50528			−0.752639	+	0.658434i	$0.771219\pi$
$308$		0			0
$309$	−11.8248			−0.672687
$310$		0			0
$311$	5.27492	+	9.13642i	0.299113	+	0.518079i	0.975933	−	0.218069i	$-0.0699759\pi$
$311$	5.27492	+	9.13642i	0.299113	+	0.518079i	−0.676820	+	0.736148i	$0.736643\pi$
$312$		0			0
$313$	2.22508	−	3.85396i	0.125769	−	0.217838i	−0.796264	−	0.604949i	$-0.793193\pi$
$313$	2.22508	−	3.85396i	0.125769	−	0.217838i	0.922033	+	0.387111i	$0.126527\pi$
$314$		0			0
$315$	4.86254	−	10.2118i	0.273973	−	0.575368i
$316$		0			0
$317$	−2.58762	+	4.48190i	−0.145335	+	0.251728i	−0.929498	−	0.368827i	$-0.879759\pi$
$317$	−2.58762	+	4.48190i	−0.145335	+	0.251728i	0.784163	+	0.620555i	$0.213093\pi$
$318$		0			0
$319$	4.86254	+	8.42217i	0.272250	+	0.471551i
$320$		0			0
$321$	−6.82475			−0.380920
$322$		0			0
$323$	−5.09967			−0.283753
$324$		0			0
$325$	−8.46221	−	14.6570i	−0.469399	−	0.813023i
$326$		0			0
$327$	2.91238	−	5.04438i	0.161055	−	0.278955i
$328$		0			0
$329$	−15.8248	+	1.25588i	−0.872447	+	0.0692389i
$330$		0			0
$331$	−11.9124	+	20.6328i	−0.654763	+	1.13408i	0.327190	+	0.944959i	$0.393898\pi$
$331$	−11.9124	+	20.6328i	−0.654763	+	1.13408i	−0.981953	+	0.189125i	$0.939435\pi$
$332$		0			0
$333$	2.63746	+	4.56821i	0.144532	+	0.250336i
$334$		0			0
$335$	31.0997			1.69916
$336$		0			0
$337$	6.09967			0.332270			0.166135	−	0.986103i	$-0.446871\pi$
$337$	6.09967			0.332270			0.166135	+	0.986103i	$0.446871\pi$
$338$		0			0
$339$	5.27492	+	9.13642i	0.286494	+	0.496222i
$340$		0			0
$341$	2.13746	−	3.70219i	0.115750	−	0.200485i
$342$		0			0
$343$	−18.0000	+	4.35890i	−0.971909	+	0.235358i
$344$		0			0
$345$	−8.54983	+	14.8087i	−0.460308	+	0.797276i
$346$		0			0
$347$	15.0997	+	26.1534i	0.810593	+	1.40399i	0.912450	+	0.409189i	$0.134188\pi$
$347$	15.0997	+	26.1534i	0.810593	+	1.40399i	−0.101857	+	0.994799i	$0.532478\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	−1.27492			−0.0680500
$352$		0			0
$353$	2.72508	+	4.71998i	0.145042	+	0.251219i	0.929388	−	0.369103i	$-0.120335\pi$
$353$	2.72508	+	4.71998i	0.145042	+	0.251219i	−0.784347	+	0.620322i	$0.787002\pi$
$354$		0			0
$355$	4.27492	−	7.40437i	0.226889	−	0.392983i
$356$		0			0
$357$	−10.5498	+	0.837253i	−0.558356	+	0.0443122i
$358$		0			0
$359$	12.8248	−	22.2131i	0.676865	−	1.17236i	−0.299056	−	0.954236i	$-0.596672\pi$
$359$	12.8248	−	22.2131i	0.676865	−	1.17236i	0.975920	−	0.218128i	$-0.0699950\pi$
$360$		0			0
$361$	8.68729	+	15.0468i	0.457226	+	0.791939i
$362$		0			0
$363$	−7.27492			−0.381834
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	−4.04983	−	7.01452i	−0.211400	−	0.366155i	0.740753	−	0.671777i	$-0.234469\pi$
$367$	−4.04983	−	7.01452i	−0.211400	−	0.366155i	−0.952153	+	0.305622i	$0.901135\pi$
$368$		0			0
$369$	−5.27492	+	9.13642i	−0.274601	+	0.475623i
$370$		0			0
$371$	−1.96221	+	4.12081i	−0.101873	+	0.213942i
$372$		0			0
$373$	0.637459	−	1.10411i	0.0330064	−	0.0571687i	−0.849050	−	0.528312i	$-0.822825\pi$
$373$	0.637459	−	1.10411i	0.0330064	−	0.0571687i	0.882057	+	0.471143i	$0.156159\pi$
$374$		0			0
$375$	17.6873	+	30.6353i	0.913368	+	1.58200i
$376$		0			0
$377$	2.90033			0.149375
$378$		0			0
$379$	35.8248			1.84019			0.920097	−	0.391691i	$-0.128110\pi$
$379$	35.8248			1.84019			0.920097	+	0.391691i	$0.128110\pi$
$380$		0			0
$381$	10.7749	+	18.6627i	0.552016	+	0.956119i
$382$		0			0
$383$	−2.27492	+	3.94027i	−0.116243	+	0.201339i	−0.918276	−	0.395941i	$-0.870418\pi$
$383$	−2.27492	+	3.94027i	−0.116243	+	0.201339i	0.802033	+	0.597280i	$0.203752\pi$
$384$		0			0
$385$	−27.4124	−	39.8293i	−1.39706	−	2.02989i
$386$		0			0
$387$	3.63746	−	6.30026i	0.184902	−	0.320260i
$388$		0			0
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	0.839561	−	0.543266i	$-0.182813\pi$
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	−0.890263	+	0.455448i	$0.849479\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$	0.274917			0.0138677
$394$		0			0
$395$	−7.58762	−	13.1422i	−0.381775	−	0.661253i
$396$		0			0
$397$	17.1873	−	29.7693i	0.862606	−	1.49408i	−0.00679974	−	0.999977i	$-0.502164\pi$
$397$	17.1873	−	29.7693i	0.862606	−	1.49408i	0.869405	−	0.494100i	$-0.164502\pi$
$398$		0			0
$399$	−1.91238	−	2.77862i	−0.0957385	−	0.139105i
$400$		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
$403$	−0.637459	−	1.10411i	−0.0317541	−	0.0549997i
$404$		0			0
$405$	4.27492			0.212422
$406$		0			0
$407$	22.5498			1.11775
$408$		0			0
$409$	−12.7749	−	22.1268i	−0.631679	−	1.09410i	−0.987208	−	0.159435i	$-0.949033\pi$
$409$	−12.7749	−	22.1268i	−0.631679	−	1.09410i	0.355529	−	0.934665i	$-0.384301\pi$
$410$		0			0
$411$	8.27492	−	14.3326i	0.408172	−	0.706974i
$412$		0			0
$413$	7.13746	−	14.9893i	0.351211	−	0.737575i
$414$		0			0
$415$	0.587624	−	1.01779i	0.0288453	−	0.0499616i
$416$		0			0
$417$	0.362541	+	0.627940i	0.0177537	+	0.0307504i
$418$		0			0
$419$	13.4502			0.657084			0.328542	−	0.944489i	$-0.393443\pi$
$419$	13.4502			0.657084			0.328542	+	0.944489i	$0.393443\pi$
$420$		0			0
$421$	13.8248			0.673777			0.336889	−	0.941545i	$-0.390625\pi$
$421$	13.8248			0.673777			0.336889	+	0.941545i	$0.390625\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	26.5498	−	45.9857i	1.28786	−	2.23063i
$426$		0			0
$427$	26.3746	−	2.09313i	1.27636	−	0.101294i
$428$		0			0
$429$	−2.72508	+	4.71998i	−0.131568	+	0.227883i
$430$		0			0
$431$	13.8248	+	23.9452i	0.665915	+	1.15340i	0.979036	+	0.203685i	$0.0652919\pi$
$431$	13.8248	+	23.9452i	0.665915	+	1.15340i	−0.313122	+	0.949713i	$0.601375\pi$
$432$		0			0
$433$	25.8248			1.24106			0.620529	−	0.784183i	$-0.286918\pi$
$433$	25.8248			1.24106			0.620529	+	0.784183i	$0.286918\pi$
$434$		0			0
$435$	−9.72508			−0.466282
$436$		0			0
$437$	2.54983	+	4.41644i	0.121975	+	0.211267i
$438$		0			0
$439$	4.86254	−	8.42217i	0.232076	−	0.401968i	−0.726343	−	0.687333i	$-0.758781\pi$
$439$	4.86254	−	8.42217i	0.232076	−	0.401968i	0.958419	+	0.285365i	$0.0921147\pi$
$440$		0			0
$441$	−4.41238	−	5.43424i	−0.210113	−	0.258773i
$442$		0			0
$443$	−15.6873	+	27.1712i	−0.745326	+	1.29094i	0.204717	+	0.978821i	$0.434373\pi$
$443$	−15.6873	+	27.1712i	−0.745326	+	1.29094i	−0.950042	+	0.312121i	$0.898961\pi$
$444$		0			0
$445$	−9.72508	−	16.8443i	−0.461013	−	0.798498i
$446$		0			0
$447$	0.549834			0.0260063
$448$		0			0
$449$	5.45017			0.257209			0.128605	−	0.991696i	$-0.458950\pi$
$449$	5.45017			0.257209			0.128605	+	0.991696i	$0.458950\pi$
$450$		0			0
$451$	22.5498	+	39.0575i	1.06183	+	1.83914i
$452$		0			0
$453$	7.68729	−	13.3148i	0.361181	−	0.625583i
$454$		0			0
$455$	−14.3746	+	1.14079i	−0.673891	+	0.0534812i
$456$		0			0
$457$	4.32475	−	7.49069i	0.202303	−	0.350400i	−0.746967	−	0.664861i	$-0.768491\pi$
$457$	4.32475	−	7.49069i	0.202303	−	0.350400i	0.949270	+	0.314462i	$0.101824\pi$
$458$		0			0
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−41.6495			−1.93981			−0.969905	−	0.243482i	$-0.921710\pi$
$461$	−41.6495			−1.93981			−0.969905	+	0.243482i	$0.921710\pi$
$462$		0			0
$463$	−35.8248			−1.66492			−0.832459	−	0.554087i	$-0.813067\pi$
$463$	−35.8248			−1.66492			−0.832459	+	0.554087i	$0.813067\pi$
$464$		0			0
$465$	2.13746	+	3.70219i	0.0991223	+	0.171685i
$466$		0			0
$467$	−12.7251	+	22.0405i	−0.588847	+	1.01991i	0.405537	+	0.914079i	$0.367084\pi$
$467$	−12.7251	+	22.0405i	−0.588847	+	1.01991i	−0.994384	+	0.105834i	$0.966249\pi$
$468$		0			0
$469$	8.27492	−	17.3781i	0.382100	−	0.802444i
$470$		0			0
$471$	−7.27492	+	12.6005i	−0.335210	+	0.580602i
$472$		0			0
$473$	−15.5498	−	26.9331i	−0.714982	−	1.23839i
$474$		0			0
$475$	16.9244			0.776546
$476$		0			0
$477$	−1.72508			−0.0789861
$478$		0			0
$479$	−10.2749	−	17.7967i	−0.469473	−	0.813151i	0.529918	−	0.848049i	$-0.322223\pi$
$479$	−10.2749	−	17.7967i	−0.469473	−	0.813151i	−0.999391	+	0.0348979i	$0.988889\pi$
$480$		0			0
$481$	3.36254	−	5.82409i	0.153319	−	0.265556i
$482$		0			0
$483$	6.00000	+	8.71780i	0.273009	+	0.396674i
$484$		0			0
$485$	−34.7870	+	60.2528i	−1.57959	+	2.73594i
$486$		0			0
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−15.9244			−0.718659			−0.359330	−	0.933211i	$-0.616995\pi$
$491$	−15.9244			−0.718659			−0.359330	+	0.933211i	$0.616995\pi$
$492$		0			0
$493$	4.54983	+	7.88054i	0.204914	+	0.354922i
$494$		0			0
$495$	9.13746	−	15.8265i	0.410698	−	0.711350i
$496$		0			0
$497$	−3.00000	−	4.35890i	−0.134568	−	0.195523i
$498$		0			0
$499$	−12.3625	+	21.4125i	−0.553423	+	0.958557i	0.444601	+	0.895729i	$0.353345\pi$
$499$	−12.3625	+	21.4125i	−0.553423	+	0.958557i	−0.998024	+	0.0628286i	$0.979988\pi$
$500$		0			0
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$		0			0
$503$	−7.64950			−0.341074			−0.170537	−	0.985351i	$-0.554550\pi$
$503$	−7.64950			−0.341074			−0.170537	+	0.985351i	$0.554550\pi$
$504$		0			0
$505$	25.6495			1.14139
$506$		0			0
$507$	−5.68729	−	9.85068i	−0.252582	−	0.437484i
$508$		0			0
$509$	−1.86254	+	3.22602i	−0.0825557	+	0.142991i	−0.904347	−	0.426798i	$-0.859642\pi$
$509$	−1.86254	+	3.22602i	−0.0825557	+	0.142991i	0.821791	+	0.569789i	$0.192975\pi$
$510$		0			0
$511$	3.72508	−	7.82300i	0.164788	−	0.346069i
$512$		0			0
$513$	0.637459	−	1.10411i	0.0281445	−	0.0487477i
$514$		0			0
$515$	−25.2749	−	43.7774i	−1.11375	−	1.92906i
$516$		0			0
$517$	−25.6495			−1.12806
$518$		0			0
$519$	−7.45017			−0.327026
$520$		0			0
$521$	−0.274917	−	0.476171i	−0.0120443	−	0.0208614i	0.859940	−	0.510394i	$-0.170501\pi$
$521$	−0.274917	−	0.476171i	−0.0120443	−	0.0208614i	−0.871985	+	0.489533i	$0.837167\pi$
$522$		0			0
$523$	12.6375	−	21.8887i	0.552597	−	0.957127i	−0.445489	−	0.895288i	$-0.646970\pi$
$523$	12.6375	−	21.8887i	0.552597	−	0.957127i	0.998086	−	0.0618393i	$-0.0196966\pi$
$524$		0			0
$525$	35.0120	−	2.77862i	1.52805	−	0.121269i
$526$		0			0
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	6.27492			0.272308
$532$		0			0
$533$	13.4502			0.582591
$534$		0			0
$535$	−14.5876	−	25.2665i	−0.630678	−	1.09237i
$536$		0			0
$537$	−0.725083	+	1.25588i	−0.0312896	+	0.0541952i
$538$		0			0
$539$	−29.5498	+	4.71998i	−1.27280	+	0.203304i
$540$		0			0
$541$	−0.362541	+	0.627940i	−0.0155869	+	0.0269973i	−0.873714	−	0.486441i	$-0.838295\pi$
$541$	−0.362541	+	0.627940i	−0.0155869	+	0.0269973i	0.858127	+	0.513438i	$0.171628\pi$
$542$		0			0
$543$	−1.91238	−	3.31233i	−0.0820679	−	0.142146i
$544$		0			0
$545$	24.9003			1.06661
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$		0			0
$551$	−1.45017	+	2.51176i	−0.0617791	+	0.107005i
$552$		0			0
$553$	−9.36254	+	0.743028i	−0.398136	+	0.0315968i
$554$		0			0
$555$	−11.2749	+	19.5287i	−0.478594	+	0.828948i
$556$		0			0
$557$	−3.58762	−	6.21395i	−0.152013	−	0.263293i	0.779955	−	0.625836i	$-0.215242\pi$
$557$	−3.58762	−	6.21395i	−0.152013	−	0.263293i	−0.931967	+	0.362543i	$0.881909\pi$
$558$		0			0
$559$	−9.27492			−0.392287
$560$		0			0
$561$	−17.0997			−0.721949
$562$		0			0
$563$	−3.86254	−	6.69012i	−0.162787	−	0.281955i	0.773080	−	0.634308i	$-0.218715\pi$
$563$	−3.86254	−	6.69012i	−0.162787	−	0.281955i	−0.935867	+	0.352353i	$0.885382\pi$
$564$		0			0
$565$	−22.5498	+	39.0575i	−0.948679	+	1.64316i
$566$		0			0
$567$	1.13746	−	2.38876i	0.0477688	−	0.100319i
$568$		0			0
$569$	−13.2749	+	22.9928i	−0.556513	+	0.963910i	0.441271	+	0.897374i	$0.354528\pi$
$569$	−13.2749	+	22.9928i	−0.556513	+	0.963910i	−0.997784	+	0.0665355i	$0.978805\pi$
$570$		0			0
$571$	−0.362541	−	0.627940i	−0.0151719	−	0.0262785i	0.858340	−	0.513082i	$-0.171496\pi$
$571$	−0.362541	−	0.627940i	−0.0151719	−	0.0262785i	−0.873512	+	0.486803i	$0.838163\pi$
$572$		0			0
$573$	−10.5498			−0.440726
$574$		0			0
$575$	−53.0997			−2.21441
$576$		0			0
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$		0			0
$579$	7.77492	−	13.4666i	0.323115	−	0.559651i
$580$		0			0
$581$	−0.412376	−	0.599168i	−0.0171082	−	0.0248577i
$582$		0			0
$583$	−3.68729	+	6.38658i	−0.152712	+	0.264505i
$584$		0			0
$585$	−2.72508	−	4.71998i	−0.112668	−	0.195147i
$586$		0			0
$587$	1.72508			0.0712018			0.0356009	−	0.999366i	$-0.488665\pi$
$587$	1.72508			0.0712018			0.0356009	+	0.999366i	$0.488665\pi$
$588$		0			0
$589$	1.27492			0.0525320
$590$		0			0
$591$	8.27492	+	14.3326i	0.340385	+	0.589563i
$592$		0			0
$593$	−7.27492	+	12.6005i	−0.298745	+	0.517442i	−0.975849	−	0.218446i	$-0.929901\pi$
$593$	−7.27492	+	12.6005i	−0.298745	+	0.517442i	0.677104	+	0.735887i	$0.263235\pi$
$594$		0			0
$595$	−25.6495	−	37.2679i	−1.05153	−	1.52783i
$596$		0			0
$597$	−12.5498	+	21.7370i	−0.513631	+	0.889634i
$598$		0			0
$599$	3.72508	+	6.45203i	0.152203	+	0.263623i	0.932037	−	0.362363i	$-0.118030\pi$
$599$	3.72508	+	6.45203i	0.152203	+	0.263623i	−0.779834	+	0.625986i	$0.784697\pi$
$600$		0			0
$601$	−26.0997			−1.06463			−0.532314	−	0.846547i	$-0.678677\pi$
$601$	−26.0997			−1.06463			−0.532314	+	0.846547i	$0.678677\pi$
$602$		0			0
$603$	7.27492			0.296258
$604$		0			0
$605$	−15.5498	−	26.9331i	−0.632191	−	1.09499i
$606$		0			0
$607$	−3.50000	+	6.06218i	−0.142061	+	0.246056i	−0.928272	−	0.371901i	$-0.878706\pi$
$607$	−3.50000	+	6.06218i	−0.142061	+	0.246056i	0.786212	+	0.617957i	$0.212039\pi$
$608$		0			0
$609$	−2.58762	+	5.43424i	−0.104856	+	0.220206i
$610$		0			0
$611$	−3.82475	+	6.62466i	−0.154733	+	0.268005i
$612$		0			0
$613$	3.27492	+	5.67232i	0.132273	+	0.229103i	0.924552	−	0.381055i	$-0.124439\pi$
$613$	3.27492	+	5.67232i	0.132273	+	0.229103i	−0.792280	+	0.610158i	$0.791106\pi$
$614$		0			0
$615$	−45.0997			−1.81859
$616$		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
$619$	−3.08762	−	5.34792i	−0.124102	−	0.214951i	0.797280	−	0.603610i	$-0.206272\pi$
$619$	−3.08762	−	5.34792i	−0.124102	−	0.214951i	−0.921382	+	0.388659i	$0.872938\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$		0			0
$623$	−12.0000	+	0.952341i	−0.480770	+	0.0381547i
$624$		0			0
$625$	−42.4244	+	73.4813i	−1.69698	+	2.93925i
$626$		0			0
$627$	−2.72508	−	4.71998i	−0.108829	−	0.188498i
$628$		0			0
$629$	21.0997			0.841299
$630$		0			0
$631$	2.82475			0.112452			0.0562258	−	0.998418i	$-0.482093\pi$
$631$	2.82475			0.112452			0.0562258	+	0.998418i	$0.482093\pi$
$632$		0			0
$633$	8.82475	+	15.2849i	0.350752	+	0.607521i
$634$		0			0
$635$	−46.0619	+	79.7815i	−1.82791	+	3.16603i
$636$		0			0
$637$	−3.18729	+	8.33585i	−0.126285	+	0.330279i
$638$		0			0
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$		0			0
$641$	−20.8248	−	36.0695i	−0.822528	−	1.42466i	−0.903794	−	0.427968i	$-0.859230\pi$
$641$	−20.8248	−	36.0695i	−0.822528	−	1.42466i	0.0812655	−	0.996692i	$-0.474104\pi$
$642$		0			0
$643$	−32.3746			−1.27673			−0.638365	−	0.769734i	$-0.720389\pi$
$643$	−32.3746			−1.27673			−0.638365	+	0.769734i	$0.720389\pi$
$644$		0			0
$645$	31.0997			1.22455
$646$		0			0
$647$	−17.0000	−	29.4449i	−0.668339	−	1.15760i	−0.978368	−	0.206870i	$-0.933672\pi$
$647$	−17.0000	−	29.4449i	−0.668339	−	1.15760i	0.310029	−	0.950727i	$-0.399661\pi$
$648$		0			0
$649$	13.4124	−	23.2309i	0.526482	−	0.911893i
$650$		0			0
$651$	2.63746	−	0.209313i	0.103370	−	0.00820364i
$652$		0			0
$653$	22.9622	−	39.7717i	0.898581	−	1.55639i	0.0692713	−	0.997598i	$-0.477933\pi$
$653$	22.9622	−	39.7717i	0.898581	−	1.55639i	0.829309	−	0.558790i	$-0.188734\pi$
$654$		0			0
$655$	0.587624	+	1.01779i	0.0229604	+	0.0397685i
$656$		0			0
$657$	3.27492			0.127767
$658$		0			0
$659$	18.1993			0.708946			0.354473	−	0.935066i	$-0.384660\pi$
$659$	18.1993			0.708946			0.354473	+	0.935066i	$0.384660\pi$
$660$		0			0
$661$	14.9124	+	25.8290i	0.580024	+	1.00463i	0.995476	+	0.0950161i	$0.0302902\pi$
$661$	14.9124	+	25.8290i	0.580024	+	1.00463i	−0.415452	+	0.909615i	$0.636376\pi$
$662$		0			0
$663$	−2.54983	+	4.41644i	−0.0990274	+	0.171520i
$664$		0			0
$665$	6.19934	−	13.0192i	0.240400	−	0.504861i
$666$		0			0
$667$	4.54983	−	7.88054i	0.176170	−	0.305136i
$668$		0			0
$669$	−3.13746	−	5.43424i	−0.121301	−	0.210100i
$670$		0			0
$671$	42.7492			1.65031
$672$		0			0
$673$	26.4502			1.01958			0.509789	−	0.860299i	$-0.329723\pi$
$673$	26.4502			1.01958			0.509789	+	0.860299i	$0.329723\pi$
$674$		0			0
$675$	6.63746	+	11.4964i	0.255476	+	0.442497i
$676$		0			0
$677$	−2.86254	+	4.95807i	−0.110016	+	0.190554i	−0.915777	−	0.401688i	$-0.868424\pi$
$677$	−2.86254	+	4.95807i	−0.110016	+	0.190554i	0.805760	+	0.592242i	$0.201757\pi$
$678$		0			0
$679$	24.4124	+	35.4704i	0.936861	+	1.36123i
$680$		0			0
$681$	−1.86254	+	3.22602i	−0.0713727	+	0.123621i
$682$		0			0
$683$	−17.4124	−	30.1591i	−0.666266	−	1.15401i	−0.978940	−	0.204146i	$-0.934558\pi$
$683$	−17.4124	−	30.1591i	−0.666266	−	1.15401i	0.312674	−	0.949860i	$-0.398775\pi$
$684$		0			0
$685$	70.7492			2.70319
$686$		0			0
$687$	10.7251			0.409187
$688$		0			0
$689$	1.09967	+	1.90468i	0.0418940	+	0.0725626i
$690$		0			0
$691$	−5.91238	+	10.2405i	−0.224917	+	0.389568i	−0.956295	−	0.292405i	$-0.905545\pi$
$691$	−5.91238	+	10.2405i	−0.224917	+	0.389568i	0.731377	+	0.681973i	$0.238878\pi$
$692$		0			0
$693$	−6.41238	−	9.31697i	−0.243586	−	0.353922i
$694$		0			0
$695$	−1.54983	+	2.68439i	−0.0587886	+	0.101825i
$696$		0			0
$697$	21.0997	+	36.5457i	0.799207	+	1.38427i
$698$		0			0
$699$	−14.5498			−0.550325
$700$		0			0
$701$	−39.9244			−1.50792			−0.753962	−	0.656918i	$-0.771860\pi$
$701$	−39.9244			−1.50792			−0.753962	+	0.656918i	$0.771860\pi$
$702$		0			0
$703$	3.36254	+	5.82409i	0.126821	+	0.219660i
$704$		0			0
$705$	12.8248	−	22.2131i	0.483008	−	0.836595i
$706$		0			0
$707$	6.82475	−	14.3326i	0.256671	−	0.539032i
$708$		0			0
$709$	16.0997	−	27.8854i	0.604636	−	1.04726i	−0.387473	−	0.921881i	$-0.626652\pi$
$709$	16.0997	−	27.8854i	0.604636	−	1.04726i	0.992109	−	0.125379i	$-0.0400146\pi$
$710$		0			0
$711$	−1.77492	−	3.07425i	−0.0665646	−	0.115293i
$712$		0			0
$713$	−4.00000			−0.149801
$714$		0			0
$715$	−23.2990			−0.871333
$716$		0			0
$717$	−15.2749	−	26.4569i	−0.570452	−	0.988052i
$718$		0			0
$719$	−16.0997	+	27.8854i	−0.600416	+	1.03995i	0.392342	+	0.919820i	$0.371665\pi$
$719$	−16.0997	+	27.8854i	−0.600416	+	1.03995i	−0.992758	+	0.120132i	$0.961668\pi$
$720$		0			0
$721$	−31.1873	+	2.47508i	−1.16148	+	0.0921767i
$722$		0			0
$723$	−6.41238	+	11.1066i	−0.238479	+	0.413057i
$724$		0			0
$725$	−15.0997	−	26.1534i	−0.560788	−	0.971313i
$726$		0			0
$727$	−16.4502			−0.610103			−0.305051	−	0.952336i	$-0.598674\pi$
$727$	−16.4502			−0.610103			−0.305051	+	0.952336i	$0.598674\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−14.5498	−	25.2011i	−0.538145	−	0.932095i
$732$		0			0
$733$	−23.4622	+	40.6377i	−0.866597	+	1.50099i	−0.00114334	+	0.999999i	$0.500364\pi$
$733$	−23.4622	+	40.6377i	−0.866597	+	1.50099i	−0.865453	+	0.500990i	$0.832969\pi$
$734$		0			0
$735$	10.6873	−	27.9509i	0.394207	−	1.03098i
$736$		0			0
$737$	15.5498	−	26.9331i	0.572786	−	0.992094i
$738$		0			0
$739$	18.1873	+	31.5013i	0.669030	+	1.15879i	0.978176	+	0.207780i	$0.0666237\pi$
$739$	18.1873	+	31.5013i	0.669030	+	1.15879i	−0.309145	+	0.951015i	$0.600043\pi$
$740$		0			0
$741$	−1.62541			−0.0597111
$742$		0			0
$743$	−16.1993			−0.594296			−0.297148	−	0.954831i	$-0.596035\pi$
$743$	−16.1993			−0.594296			−0.297148	+	0.954831i	$0.596035\pi$
$744$		0			0
$745$	1.17525	+	2.03559i	0.0430578	+	0.0745782i
$746$		0			0
$747$	0.137459	−	0.238085i	0.00502935	−	0.00871109i
$748$		0			0
$749$	−18.0000	+	1.42851i	−0.657706	+	0.0521967i
$750$		0			0
$751$	−12.7749	+	22.1268i	−0.466163	+	0.807419i	−0.999253	−	0.0386400i	$-0.987697\pi$
$751$	−12.7749	+	22.1268i	−0.466163	+	0.807419i	0.533090	+	0.846059i	$0.321031\pi$
$752$		0			0
$753$	9.68729	+	16.7789i	0.353025	+	0.611457i
$754$		0			0
$755$	65.7251			2.39198
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$		0			0
$759$	8.54983	+	14.8087i	0.310339	+	0.537523i
$760$		0			0
$761$	−2.54983	+	4.41644i	−0.0924314	+	0.160096i	−0.908534	−	0.417812i	$-0.862797\pi$
$761$	−2.54983	+	4.41644i	−0.0924314	+	0.160096i	0.816102	+	0.577907i	$0.196131\pi$
$762$		0			0
$763$	6.62541	−	13.9140i	0.239856	−	0.503719i
$764$		0			0
$765$	8.54983	−	14.8087i	0.309120	−	0.535411i
$766$		0			0
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$		0			0
$769$	12.6495			0.456153			0.228076	−	0.973643i	$-0.426756\pi$
$769$	12.6495			0.456153			0.228076	+	0.973643i	$0.426756\pi$
$770$		0			0
$771$	19.0997			0.687858
$772$		0			0
$773$	−13.5498	−	23.4690i	−0.487354	−	0.844121i	0.512541	−	0.858663i	$-0.328704\pi$
$773$	−13.5498	−	23.4690i	−0.487354	−	0.844121i	−0.999894	+	0.0145417i	$0.995371\pi$
$774$		0			0
$775$	−6.63746	+	11.4964i	−0.238425	+	0.412963i
$776$		0			0
$777$	7.91238	+	11.4964i	0.283855	+	0.412432i
$778$		0			0
$779$	−6.72508	+	11.6482i	−0.240951	+	0.417340i
$780$		0			0
$781$	−4.27492	−	7.40437i	−0.152969	−	0.264949i
$782$		0			0
$783$	−2.27492			−0.0812989
$784$		0			0
$785$	−62.1993			−2.21999
$786$		0			0
$787$	6.27492	+	10.8685i	0.223677	+	0.387419i	0.955922	−	0.293622i	$-0.0948607\pi$
$787$	6.27492	+	10.8685i	0.223677	+	0.387419i	−0.732245	+	0.681041i	$0.761527\pi$
$788$		0			0
$789$	12.2749	−	21.2608i	0.436999	−	0.756904i
$790$		0			0
$791$	15.8248	+	22.9928i	0.562663	+	0.817531i
$792$		0			0
$793$	6.37459	−	11.0411i	0.226368	−	0.392081i
$794$		0			0
$795$	−3.68729	−	6.38658i	−0.130775	−	0.226509i
$796$		0			0
$797$	−36.4743			−1.29198			−0.645992	−	0.763344i	$-0.723556\pi$
$797$	−36.4743			−1.29198			−0.645992	+	0.763344i	$0.723556\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$		0			0
$801$	−2.27492	−	3.94027i	−0.0803802	−	0.139223i
$802$		0			0
$803$	7.00000	−	12.1244i	0.247025	−	0.427859i
$804$		0			0
$805$	−19.4502	+	40.8471i	−0.685528	+	1.43967i
$806$		0			0
$807$	−14.1375	+	24.4868i	−0.497662	+	0.861976i
$808$		0			0
$809$	−7.82475	−	13.5529i	−0.275104	−	0.476493i	0.695058	−	0.718954i	$-0.255379\pi$
$809$	−7.82475	−	13.5529i	−0.275104	−	0.476493i	−0.970161	+	0.242461i	$0.922045\pi$
$810$		0			0
$811$	−27.4502			−0.963906			−0.481953	−	0.876197i	$-0.660072\pi$
$811$	−27.4502			−0.963906			−0.481953	+	0.876197i	$0.660072\pi$
$812$		0			0
$813$	−6.27492			−0.220071
$814$		0			0
$815$	25.6495	+	44.4262i	0.898463	+	1.55618i
$816$		0			0
$817$	4.63746	−	8.03231i	0.162244	−	0.281015i
$818$		0			0
$819$	−3.36254	+	0.266857i	−0.117497	+	0.00932475i
$820$		0			0
$821$	10.1375	−	17.5586i	0.353800	−	0.612799i	−0.633112	−	0.774060i	$-0.718223\pi$
$821$	10.1375	−	17.5586i	0.353800	−	0.612799i	0.986912	+	0.161261i	$0.0515561\pi$
$822$		0			0
$823$	13.0997	+	22.6893i	0.456626	+	0.790899i	0.998780	−	0.0493799i	$-0.0157245\pi$
$823$	13.0997	+	22.6893i	0.456626	+	0.790899i	−0.542154	+	0.840279i	$0.682391\pi$
$824$		0			0
$825$	56.7492			1.97575
$826$		0			0
$827$	39.0241			1.35700			0.678500	−	0.734600i	$-0.262630\pi$
$827$	39.0241			1.35700			0.678500	+	0.734600i	$0.262630\pi$
$828$		0			0
$829$	11.3625	+	19.6805i	0.394637	+	0.683532i	0.993055	−	0.117652i	$-0.0375369\pi$
$829$	11.3625	+	19.6805i	0.394637	+	0.683532i	−0.598417	+	0.801184i	$0.704204\pi$
$830$		0			0
$831$	2.08762	−	3.61587i	0.0724189	−	0.125433i
$832$		0			0
$833$	−27.6495	+	4.41644i	−0.957999	+	0.153021i
$834$		0			0
$835$	−12.8248	+	22.2131i	−0.443819	+	0.768717i
$836$		0			0
$837$	0.500000	+	0.866025i	0.0172825	+	0.0299342i
$838$		0			0
$839$	−30.1993			−1.04260			−0.521298	−	0.853374i	$-0.674552\pi$
$839$	−30.1993			−1.04260			−0.521298	+	0.853374i	$0.674552\pi$
$840$		0			0
$841$	−23.8248			−0.821543
$842$		0			0
$843$	−5.72508	−	9.91613i	−0.197182	−	0.341530i
$844$		0			0
$845$	24.3127	−	42.1108i	0.836383	−	1.44866i
$846$		0			0
$847$	−19.1873	+	1.52274i	−0.659283	+	0.0523219i
$848$		0			0
$849$	13.4622	−	23.3172i	0.462022	−	0.800245i
$850$		0			0
$851$	−10.5498	−	18.2728i	−0.361644	−	0.626385i
$852$		0			0
$853$	24.3746			0.834570			0.417285	−	0.908776i	$-0.362982\pi$
$853$	24.3746			0.834570			0.417285	+	0.908776i	$0.362982\pi$
$854$		0			0
$855$	5.45017			0.186392
$856$		0			0
$857$	14.2749	+	24.7249i	0.487622	+	0.844586i	0.999899	−	0.0142345i	$-0.00453114\pi$
$857$	14.2749	+	24.7249i	0.487622	+	0.844586i	−0.512277	+	0.858820i	$0.671198\pi$
$858$		0			0
$859$	5.17525	−	8.96379i	0.176577	−	0.305841i	−0.764129	−	0.645064i	$-0.776831\pi$
$859$	5.17525	−	8.96379i	0.176577	−	0.305841i	0.940706	+	0.339223i	$0.110164\pi$
$860$		0			0
$861$	−12.0000	+	25.2011i	−0.408959	+	0.858850i
$862$		0			0
$863$	−5.54983	+	9.61260i	−0.188919	+	0.327217i	−0.944890	−	0.327388i	$-0.893832\pi$
$863$	−5.54983	+	9.61260i	−0.188919	+	0.327217i	0.755971	+	0.654605i	$0.227165\pi$
$864$		0			0
$865$	−15.9244	−	27.5819i	−0.541447	−	0.937813i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−15.1752			−0.514785
$870$		0			0
$871$	−4.63746	−	8.03231i	−0.157134	−	0.272165i
$872$		0			0
$873$	−8.13746	+	14.0945i	−0.275411	+	0.477026i
$874$		0			0
$875$	53.0619	+	77.0971i	1.79382	+	2.60636i
$876$		0			0
$877$	−14.3746	+	24.8975i	−0.485395	+	0.840729i	−0.999859	−	0.0167828i	$-0.994658\pi$
$877$	−14.3746	+	24.8975i	−0.485395	+	0.840729i	0.514464	+	0.857512i	$0.327991\pi$
$878$		0			0
$879$	2.58762	+	4.48190i	0.0872784	+	0.151171i
$880$		0			0
$881$	24.5498			0.827105			0.413552	−	0.910480i	$-0.364288\pi$
$881$	24.5498			0.827105			0.413552	+	0.910480i	$0.364288\pi$
$882$		0			0
$883$	−30.3746			−1.02219			−0.511093	−	0.859525i	$-0.670759\pi$
$883$	−30.3746			−1.02219			−0.511093	+	0.859525i	$0.670759\pi$
$884$		0			0
$885$	13.4124	+	23.2309i	0.450852	+	0.780899i
$886$		0			0
$887$	−5.82475	+	10.0888i	−0.195576	+	0.338748i	−0.947089	−	0.320970i	$-0.895991\pi$
$887$	−5.82475	+	10.0888i	−0.195576	+	0.338748i	0.751513	+	0.659718i	$0.229324\pi$
$888$		0			0
$889$	32.3248	+	46.9668i	1.08414	+	1.57522i
$890$		0			0
$891$	2.13746	−	3.70219i	0.0716076	−	0.124028i
$892$		0			0
$893$	−3.82475	−	6.62466i	−0.127990	−	0.221686i
$894$		0			0
$895$	−6.19934			−0.207221
$896$		0			0
$897$	5.09967			0.170273
$898$		0			0
$899$	−1.13746	−	1.97014i	−0.0379364	−	0.0657077i
$900$		0			0
$901$	−3.45017	+	5.97586i	−0.114942	+	0.199085i
$902$		0			0
$903$	8.27492	−	17.3781i	0.275372	−	0.578305i
$904$		0			0
$905$	8.17525	−	14.1599i	0.271754	−	0.470693i
$906$		0			0
$907$	18.6375	+	32.2810i	0.618847	+	1.07187i	0.989697	+	0.143181i	$0.0457331\pi$
$907$	18.6375	+	32.2810i	0.618847	+	1.07187i	−0.370850	+	0.928693i	$0.620934\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	51.8488			1.71783			0.858914	−	0.512119i	$-0.171139\pi$
$911$	51.8488			1.71783			0.858914	+	0.512119i	$0.171139\pi$
$912$		0			0
$913$	−0.587624	−	1.01779i	−0.0194475	−	0.0336841i
$914$		0			0
$915$	−21.3746	+	37.0219i	−0.706622	+	1.22391i
$916$		0			0
$917$	0.725083	−	0.0575438i	0.0239443	−	0.00190027i
$918$		0			0
$919$	9.91238	−	17.1687i	0.326979	−	0.566344i	−0.654932	−	0.755688i	$-0.727303\pi$
$919$	9.91238	−	17.1687i	0.326979	−	0.566344i	0.981911	+	0.189344i	$0.0606360\pi$
$920$		0			0
$921$	−13.1873	−	22.8411i	−0.434536	−	0.752639i
$922$		0			0
$923$	−2.54983			−0.0839288
$924$		0			0
$925$	−70.0241			−2.30238
$926$		0			0
$927$	−5.91238	−	10.2405i	−0.194188	−	0.336343i
$928$		0			0
$929$	−10.0997	+	17.4931i	−0.331359	+	0.573931i	−0.982779	−	0.184787i	$-0.940841\pi$
$929$	−10.0997	+	17.4931i	−0.331359	+	0.573931i	0.651419	+	0.758718i	$0.274174\pi$
$930$		0			0
$931$	−5.62541	−	6.92820i	−0.184365	−	0.227063i
$932$		0			0
$933$	−5.27492	+	9.13642i	−0.172693	+	0.299113i
$934$		0			0
$935$	−36.5498	−	63.3062i	−1.19531	−	2.07033i
$936$		0			0
$937$	24.0997			0.787302			0.393651	−	0.919260i	$-0.371212\pi$
$937$	24.0997			0.787302			0.393651	+	0.919260i	$0.371212\pi$
$938$		0			0
$939$	4.45017			0.145226
$940$		0			0
$941$	14.5876	+	25.2665i	0.475543	+	0.823665i	0.999608	−	0.0280140i	$-0.00891829\pi$
$941$	14.5876	+	25.2665i	0.475543	+	0.823665i	−0.524065	+	0.851679i	$0.675585\pi$
$942$		0			0
$943$	21.0997	−	36.5457i	0.687100	−	1.19009i
$944$		0			0
$945$	11.2749	−	0.894797i	0.366773	−	0.0291078i
$946$		0			0
$947$	17.2749	−	29.9210i	0.561359	−	0.972303i	−0.436019	−	0.899938i	$-0.643612\pi$
$947$	17.2749	−	29.9210i	0.561359	−	0.972303i	0.997378	−	0.0723654i	$-0.0230548\pi$
$948$		0			0
$949$	−2.08762	−	3.61587i	−0.0677671	−	0.117376i
$950$		0			0
$951$	−5.17525			−0.167819
$952$		0			0
$953$	10.3505			0.335285			0.167643	−	0.985848i	$-0.446384\pi$
$953$	10.3505			0.335285			0.167643	+	0.985848i	$0.446384\pi$
$954$		0			0
$955$	−22.5498	−	39.0575i	−0.729696	−	1.26387i
$956$		0			0
$957$	−4.86254	+	8.42217i	−0.157184	+	0.272250i
$958$		0			0
$959$	18.8248	−	39.5336i	0.607883	−	1.27661i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$	−3.41238	−	5.91041i	−0.109962	−	0.190460i
$964$		0			0
$965$	66.4743			2.13988
$966$		0			0
$967$	38.4502			1.23647			0.618237	−	0.785992i	$-0.287847\pi$
$967$	38.4502			1.23647			0.618237	+	0.785992i	$0.287847\pi$
$968$		0			0
$969$	−2.54983	−	4.41644i	−0.0819125	−	0.141877i
$970$		0			0
$971$	20.7870	−	36.0041i	0.667085	−	1.15543i	−0.311630	−	0.950204i	$-0.600875\pi$
$971$	20.7870	−	36.0041i	0.667085	−	1.15543i	0.978715	−	0.205222i	$-0.0657917\pi$
$972$		0			0
$973$	1.08762	+	1.58028i	0.0348676	+	0.0506615i
$974$		0			0
$975$	8.46221	−	14.6570i	0.271008	−	0.469399i
$976$		0			0
$977$	−19.5498	−	33.8613i	−0.625455	−	1.08332i	−0.988453	−	0.151529i	$-0.951580\pi$
$977$	−19.5498	−	33.8613i	−0.625455	−	1.08332i	0.362998	−	0.931790i	$-0.381753\pi$
$978$		0			0
$979$	−19.4502			−0.621630
$980$		0			0
$981$	5.82475			0.185970
$982$		0			0
$983$	−25.6495	−	44.4262i	−0.818092	−	1.41698i	−0.907086	−	0.420945i	$-0.861699\pi$
$983$	−25.6495	−	44.4262i	−0.818092	−	1.41698i	0.0889941	−	0.996032i	$-0.471635\pi$
$984$		0			0
$985$	−35.3746	+	61.2706i	−1.12713	+	1.95224i
$986$		0			0
$987$	−9.00000	−	13.0767i	−0.286473	−	0.416236i
$988$		0			0
$989$	−14.5498	+	25.2011i	−0.462658	+	0.801347i
$990$		0			0
$991$	8.04983	+	13.9427i	0.255711	+	0.442905i	0.965089	−	0.261924i	$-0.0843570\pi$
$991$	8.04983	+	13.9427i	0.255711	+	0.442905i	−0.709377	+	0.704829i	$0.751024\pi$
$992$		0			0
$993$	−23.8248			−0.756056
$994$		0			0
$995$	−107.299			−3.40161
$996$		0			0
$997$	−11.0876	−	19.2043i	−0.351149	−	0.608207i	0.635302	−	0.772263i	$-0.280875\pi$
$997$	−11.0876	−	19.2043i	−0.351149	−	0.608207i	−0.986451	+	0.164056i	$0.947542\pi$
$998$		0			0
$999$	−2.63746	+	4.56821i	−0.0834455	+	0.144532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.x.961.1		4
4.3	odd	2		1344.2.q.w.961.1		4
7.2	even	3		9408.2.a.dp.1.2		2
7.4	even	3	inner	1344.2.q.x.193.1		4
7.5	odd	6		9408.2.a.dw.1.1		2
8.3	odd	2		168.2.q.c.121.2	yes	4
8.5	even	2		336.2.q.g.289.2		4
24.5	odd	2		1008.2.s.r.289.1		4
24.11	even	2		504.2.s.i.289.1		4
28.11	odd	6		1344.2.q.w.193.1		4
28.19	even	6		9408.2.a.dj.1.1		2
28.23	odd	6		9408.2.a.ec.1.2		2
56.3	even	6		1176.2.q.l.361.1		4
56.5	odd	6		2352.2.a.ba.1.2		2
56.11	odd	6		168.2.q.c.25.2	✓	4
56.13	odd	2		2352.2.q.bf.961.1		4
56.19	even	6		1176.2.a.n.1.2		2
56.27	even	2		1176.2.q.l.961.1		4
56.37	even	6		2352.2.a.bf.1.1		2
56.45	odd	6		2352.2.q.bf.1537.1		4
56.51	odd	6		1176.2.a.k.1.1		2
56.53	even	6		336.2.q.g.193.2		4
168.5	even	6		7056.2.a.ch.1.1		2
168.11	even	6		504.2.s.i.361.1		4
168.53	odd	6		1008.2.s.r.865.1		4
168.59	odd	6		3528.2.s.bk.361.2		4
168.83	odd	2		3528.2.s.bk.3313.2		4
168.107	even	6		3528.2.a.bk.1.2		2
168.131	odd	6		3528.2.a.bd.1.1		2
168.149	odd	6		7056.2.a.cu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.q.c.25.2	✓	4	56.11	odd	6
168.2.q.c.121.2	yes	4	8.3	odd	2
336.2.q.g.193.2		4	56.53	even	6
336.2.q.g.289.2		4	8.5	even	2
504.2.s.i.289.1		4	24.11	even	2
504.2.s.i.361.1		4	168.11	even	6
1008.2.s.r.289.1		4	24.5	odd	2
1008.2.s.r.865.1		4	168.53	odd	6
1176.2.a.k.1.1		2	56.51	odd	6
1176.2.a.n.1.2		2	56.19	even	6
1176.2.q.l.361.1		4	56.3	even	6
1176.2.q.l.961.1		4	56.27	even	2
1344.2.q.w.193.1		4	28.11	odd	6
1344.2.q.w.961.1		4	4.3	odd	2
1344.2.q.x.193.1		4	7.4	even	3	inner
1344.2.q.x.961.1		4	1.1	even	1	trivial
2352.2.a.ba.1.2		2	56.5	odd	6
2352.2.a.bf.1.1		2	56.37	even	6
2352.2.q.bf.961.1		4	56.13	odd	2
2352.2.q.bf.1537.1		4	56.45	odd	6
3528.2.a.bd.1.1		2	168.131	odd	6
3528.2.a.bk.1.2		2	168.107	even	6
3528.2.s.bk.361.2		4	168.59	odd	6
3528.2.s.bk.3313.2		4	168.83	odd	2
7056.2.a.ch.1.1		2	168.5	even	6
7056.2.a.cu.1.2		2	168.149	odd	6
9408.2.a.dj.1.1		2	28.19	even	6
9408.2.a.dp.1.2		2	7.2	even	3
9408.2.a.dw.1.1		2	7.5	odd	6
9408.2.a.ec.1.2		2	28.23	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-2.13746 + 3.70219i) q^{5} +(1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.13746 + 3.70219i) q^{11} +1.27492 q^{13} -4.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-0.637459 + 1.10411i) q^{19} +(-1.13746 + 2.38876i) q^{21} +(2.00000 - 3.46410i) q^{23} +(-6.63746 - 11.4964i) q^{25} -1.00000 q^{27} +2.27492 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-2.13746 + 3.70219i) q^{33} +(-11.2749 + 0.894797i) q^{35} +(2.63746 - 4.56821i) q^{37} +(0.637459 + 1.10411i) q^{39} +10.5498 q^{41} -7.27492 q^{43} +(-2.13746 - 3.70219i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-2.50000 + 6.53835i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(0.862541 + 1.49397i) q^{53} -18.2749 q^{55} -1.27492 q^{57} +(-3.13746 - 5.43424i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-2.63746 + 0.209313i) q^{63} +(-2.72508 + 4.71998i) q^{65} +(-3.63746 - 6.30026i) q^{67} +4.00000 q^{69} -2.00000 q^{71} +(-1.63746 - 2.83616i) q^{73} +(6.63746 - 11.4964i) q^{75} +(-4.86254 + 10.2118i) q^{77} +(-1.77492 + 3.07425i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.274917 q^{83} -17.0997 q^{85} +(1.13746 + 1.97014i) q^{87} +(-2.27492 + 3.94027i) q^{89} +(1.91238 + 2.77862i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-2.72508 - 4.71998i) q^{95} +16.2749 q^{97} -4.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - q^5 + 6 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} - q^{5} + 6 q^{7} - 2 q^{9} + q^{11} - 10 q^{13} - 2 q^{15} + 8 q^{17} + 5 q^{19} + 3 q^{21} + 8 q^{23} - 19 q^{25} - 4 q^{27} - 6 q^{29} - 2 q^{31} - q^{33} - 30 q^{35} + 3 q^{37} - 5 q^{39} + 12 q^{41} - 14 q^{43} - q^{45} - 12 q^{47} - 10 q^{49} - 8 q^{51} + 11 q^{53} - 58 q^{55} + 10 q^{57} - 5 q^{59} + 20 q^{61} - 3 q^{63} - 26 q^{65} - 7 q^{67} + 16 q^{69} - 8 q^{71} + q^{73} + 19 q^{75} - 27 q^{77} + 8 q^{79} - 2 q^{81} + 14 q^{83} - 8 q^{85} - 3 q^{87} + 6 q^{89} - 15 q^{91} + 2 q^{93} - 26 q^{95} + 50 q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - q^5 + 6 * q^7 - 2 * q^9 + q^11 - 10 * q^13 - 2 * q^15 + 8 * q^17 + 5 * q^19 + 3 * q^21 + 8 * q^23 - 19 * q^25 - 4 * q^27 - 6 * q^29 - 2 * q^31 - q^33 - 30 * q^35 + 3 * q^37 - 5 * q^39 + 12 * q^41 - 14 * q^43 - q^45 - 12 * q^47 - 10 * q^49 - 8 * q^51 + 11 * q^53 - 58 * q^55 + 10 * q^57 - 5 * q^59 + 20 * q^61 - 3 * q^63 - 26 * q^65 - 7 * q^67 + 16 * q^69 - 8 * q^71 + q^73 + 19 * q^75 - 27 * q^77 + 8 * q^79 - 2 * q^81 + 14 * q^83 - 8 * q^85 - 3 * q^87 + 6 * q^89 - 15 * q^91 + 2 * q^93 - 26 * q^95 + 50 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more