LMFDB - Embedded newform 1008.2.q.h.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.h.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09097 + 1.34528i) q^{3} +(-0.880438 + 1.52496i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})$	\(q+(-1.09097 + 1.34528i) q^{3} +(-0.880438 + 1.52496i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} +(3.06238 + 5.30420i) q^{11} +(-0.380438 - 0.658939i) q^{13} +(-1.09097 - 2.84813i) q^{15} +(-3.42107 + 5.92546i) q^{17} +(-0.971410 - 1.68253i) q^{19} +(2.65335 + 3.73627i) q^{21} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} -7.70370 q^{31} +(-10.4766 - 1.66697i) q^{33} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +(1.30150 + 0.207087i) q^{39} +(-3.47141 - 6.01266i) q^{41} +(-4.33009 + 7.49994i) q^{43} +(5.02175 + 1.63957i) q^{45} -1.66019 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-4.23912 - 11.0668i) q^{51} +(-0.112725 + 0.195246i) q^{53} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} -1.98633 q^{59} -10.3502 q^{61} +(-7.92107 - 0.506659i) q^{63} +1.33981 q^{65} -6.78495 q^{67} +(-0.260877 - 0.681054i) q^{69} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +(-3.24884 - 0.516934i) q^{75} +(15.6940 - 4.03584i) q^{77} +13.4451 q^{79} +(-8.23229 + 3.63723i) q^{81} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(0.907394 + 2.36887i) q^{87} +(1.30150 + 2.25427i) q^{89} +(-1.94966 + 0.501371i) q^{91} +(8.40451 - 10.3636i) q^{93} +3.42107 q^{95} +(-1.81806 + 3.14897i) q^{97} +(13.6722 - 12.2754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9	$ 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} - 2 q^{25} - 7 q^{27} - 5 q^{29} - 28 q^{31} - 19 q^{33} + 19 q^{35} - 9 q^{37} - 9 q^{39} - 12 q^{41} - 18 q^{43} + 29 q^{45} + 6 q^{47} - 12 q^{49} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} + 8 q^{59} - 8 q^{61} - 31 q^{63} + 24 q^{65} + 10 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} - 44 q^{75} + 52 q^{77} + 14 q^{79} - 40 q^{81} - 8 q^{83} + 14 q^{85} - 31 q^{87} - 9 q^{89} - 4 q^{91} + 4 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9 + q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 - 2 * q^25 - 7 * q^27 - 5 * q^29 - 28 * q^31 - 19 * q^33 + 19 * q^35 - 9 * q^37 - 9 * q^39 - 12 * q^41 - 18 * q^43 + 29 * q^45 + 6 * q^47 - 12 * q^49 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 + 8 * q^59 - 8 * q^61 - 31 * q^63 + 24 * q^65 + 10 * q^67 - q^69 - 14 * q^71 - 25 * q^73 - 44 * q^75 + 52 * q^77 + 14 * q^79 - 40 * q^81 - 8 * q^83 + 14 * q^85 - 31 * q^87 - 9 * q^89 - 4 * q^91 + 4 * q^95 - 28 * q^97 + 41 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$3$	−1.09097	+	1.34528i	−0.629873	+	0.776698i
$4$		0			0
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	−0.992940	−	0.118618i	$-0.962154\pi$
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	0.599196	+	0.800602i	$0.295487\pi$
$6$		0			0
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$7$	0.710533	−	2.54856i	0.268556	−	0.963264i
$8$		0			0
$9$	−0.619562	−	2.93533i	−0.206521	−	0.978442i
$10$		0			0
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.794205	+	0.607650i	$0.207888\pi$
$11$	3.06238	+	5.30420i	0.923343	+	1.59928i	0.129138	+	0.991627i	$0.458779\pi$
$12$		0			0
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	0.808434	−	0.588587i	$-0.200316\pi$
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	−0.913948	+	0.405831i	$0.866982\pi$
$14$		0			0
$15$	−1.09097	−	2.84813i	−0.281688	−	0.735384i
$16$		0			0
$17$	−3.42107	+	5.92546i	−0.829731	+	1.43714i	0.0685191	+	0.997650i	$0.478173\pi$
$17$	−3.42107	+	5.92546i	−0.829731	+	1.43714i	−0.898250	+	0.439486i	$0.855161\pi$
$18$		0			0
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	0.732818	−	0.680425i	$-0.238205\pi$
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	−0.955674	+	0.294426i	$0.904872\pi$
$20$		0			0
$21$	2.65335	+	3.73627i	0.579009	+	0.815321i
$22$		0			0
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	−0.887140	−	0.461500i	$-0.847311\pi$
$23$	−0.210533	+	0.364654i	−0.0438992	+	0.0760357i	0.843241	+	0.537536i	$0.180645\pi$
$24$		0			0
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$		0			0
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$		0			0
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	−0.789990	−	0.613120i	$-0.789914\pi$
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	0.925972	+	0.377592i	$0.123248\pi$
$30$		0			0
$31$	−7.70370			−1.38362			−0.691812	−	0.722077i	$-0.743187\pi$
$31$	−7.70370			−1.38362			−0.691812	+	0.722077i	$0.743187\pi$
$32$		0			0
$33$	−10.4766	−	1.66697i	−1.82374	−	0.290182i
$34$		0			0
$35$	3.26088	+	3.32738i	0.551189	+	0.562431i
$36$		0			0
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	0.959909	−	0.280311i	$-0.0904376\pi$
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	−0.722711	+	0.691150i	$0.757104\pi$
$38$		0			0
$39$	1.30150	+	0.207087i	0.208408	+	0.0331604i
$40$		0			0
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	−0.998781	−	0.0493667i	$-0.984280\pi$
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	0.456638	−	0.889653i	$-0.349054\pi$
$42$		0			0
$43$	−4.33009	+	7.49994i	−0.660333	+	1.14373i	0.320195	+	0.947352i	$0.396252\pi$
$43$	−4.33009	+	7.49994i	−0.660333	+	1.14373i	−0.980528	+	0.196379i	$0.937082\pi$
$44$		0			0
$45$	5.02175	+	1.63957i	0.748599	+	0.244412i
$46$		0			0
$47$	−1.66019			−0.242164			−0.121082	−	0.992643i	$-0.538636\pi$
$47$	−1.66019			−0.242164			−0.121082	+	0.992643i	$0.538636\pi$
$48$		0			0
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$		0			0
$51$	−4.23912	−	11.0668i	−0.593596	−	1.54966i
$52$		0			0
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	−0.873664	−	0.486531i	$-0.838262\pi$
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	0.858180	+	0.513350i	$0.171596\pi$
$54$		0			0
$55$	−10.7850			−1.45424
$56$		0			0
$57$	3.32326	+	0.528775i	0.440176	+	0.0700379i
$58$		0			0
$59$	−1.98633			−0.258598			−0.129299	−	0.991606i	$-0.541273\pi$
$59$	−1.98633			−0.258598			−0.129299	+	0.991606i	$0.541273\pi$
$60$		0			0
$61$	−10.3502			−1.32521			−0.662605	−	0.748969i	$-0.730549\pi$
$61$	−10.3502			−1.32521			−0.662605	+	0.748969i	$0.730549\pi$
$62$		0			0
$63$	−7.92107	−	0.506659i	−0.997961	−	0.0638331i
$64$		0			0
$65$	1.33981			0.166183
$66$		0			0
$67$	−6.78495			−0.828914			−0.414457	−	0.910069i	$-0.636028\pi$
$67$	−6.78495			−0.828914			−0.414457	+	0.910069i	$0.636028\pi$
$68$		0			0
$69$	−0.260877	−	0.681054i	−0.0314059	−	0.0819893i
$70$		0			0
$71$	−10.7850			−1.27994			−0.639969	−	0.768401i	$-0.721053\pi$
$71$	−10.7850			−1.27994			−0.639969	+	0.768401i	$0.721053\pi$
$72$		0			0
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	−0.856912	−	0.515463i	$-0.827620\pi$
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	0.874860	+	0.484375i	$0.160953\pi$
$74$		0			0
$75$	−3.24884	−	0.516934i	−0.375144	−	0.0596904i
$76$		0			0
$77$	15.6940	−	4.03584i	1.78850	−	0.459927i
$78$		0			0
$79$	13.4451			1.51270			0.756348	−	0.654169i	$-0.226982\pi$
$79$	13.4451			1.51270			0.756348	+	0.654169i	$0.226982\pi$
$80$		0			0
$81$	−8.23229	+	3.63723i	−0.914699	+	0.404137i
$82$		0			0
$83$	1.56238	−	2.70612i	0.171494	−	0.297036i	−0.767449	−	0.641110i	$-0.778474\pi$
$83$	1.56238	−	2.70612i	0.171494	−	0.297036i	0.938942	+	0.344075i	$0.111807\pi$
$84$		0			0
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$		0			0
$87$	0.907394	+	2.36887i	0.0972828	+	0.253970i
$88$		0			0
$89$	1.30150	+	2.25427i	0.137959	+	0.238952i	0.926724	−	0.375743i	$-0.122612\pi$
$89$	1.30150	+	2.25427i	0.137959	+	0.238952i	−0.788765	+	0.614695i	$0.789279\pi$
$90$		0			0
$91$	−1.94966	+	0.501371i	−0.204380	+	0.0525580i
$92$		0			0
$93$	8.40451	−	10.3636i	0.871508	−	1.07466i
$94$		0			0
$95$	3.42107			0.350994
$96$		0			0
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	−0.943440	−	0.331543i	$-0.892431\pi$
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	0.758845	+	0.651272i	$0.225764\pi$
$98$		0			0
$99$	13.6722	−	12.2754i	1.37411	−	1.23372i
$100$		0			0
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	0.993545	−	0.113438i	$-0.0361863\pi$
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	−0.595013	+	0.803716i	$0.702853\pi$
$102$		0			0
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	−0.983755	−	0.179514i	$-0.942548\pi$
$103$	−3.41423	+	5.91362i	−0.336414	+	0.582686i	0.647341	+	0.762200i	$0.275881\pi$
$104$		0			0
$105$	−8.03379	+	0.756713i	−0.784018	+	0.0738476i
$106$		0			0
$107$	−1.77292	−	3.07078i	−0.171394	−	0.296863i	0.767513	−	0.641033i	$-0.221494\pi$
$107$	−1.77292	−	3.07078i	−0.171394	−	0.296863i	−0.938908	+	0.344170i	$0.888160\pi$
$108$		0			0
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	−0.848683	−	0.528902i	$-0.822604\pi$
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	0.882384	+	0.470530i	$0.155937\pi$
$110$		0			0
$111$	−4.93598	−	0.785381i	−0.468503	−	0.0745451i
$112$		0			0
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	0.993715	−	0.111939i	$-0.0357061\pi$
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	−0.593799	+	0.804613i	$0.702373\pi$
$114$		0			0
$115$	−0.370723	−	0.642111i	−0.0345701	−	0.0598772i
$116$		0			0
$117$	−1.69850	+	1.52496i	−0.157026	+	0.140983i
$118$		0			0
$119$	12.6706	+	12.9290i	1.16151	+	1.18520i
$120$		0			0
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$		0			0
$123$	11.8759	+	1.88962i	1.07082	+	0.170381i
$124$		0			0
$125$	−12.1488			−1.08663
$126$		0			0
$127$	18.9532			1.68183			0.840913	−	0.541170i	$-0.182018\pi$
$127$	18.9532			1.68183			0.840913	+	0.541170i	$0.182018\pi$
$128$		0			0
$129$	−5.36552	−	14.0074i	−0.472408	−	1.23328i
$130$		0			0
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	−0.980196	−	0.198031i	$-0.936545\pi$
$131$	−3.64652	+	6.31595i	−0.318598	+	0.551827i	0.661598	+	0.749859i	$0.269879\pi$
$132$		0			0
$133$	−4.97825	+	1.28020i	−0.431669	+	0.111007i
$134$		0			0
$135$	−7.68427	+	4.96695i	−0.661356	+	0.427487i
$136$		0			0
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	0.986163	−	0.165776i	$-0.0530129\pi$
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	−0.636648	+	0.771154i	$0.719680\pi$
$138$		0			0
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	0.999443	+	0.0333640i	$0.0106220\pi$
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	−0.470828	+	0.882225i	$0.656045\pi$
$140$		0			0
$141$	1.81122	−	2.23342i	0.152532	−	0.188088i
$142$		0			0
$143$	2.33009	−	4.03584i	0.194852	−	0.337494i
$144$		0			0
$145$	1.28947	+	2.23342i	0.107084	+	0.185476i
$146$		0			0
$147$	11.4074	−	4.10748i	0.940866	−	0.338779i
$148$		0			0
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	−0.988229	−	0.152982i	$-0.951112\pi$
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	0.626601	+	0.779340i	$0.284446\pi$
$150$		0			0
$151$	−7.49316	−	12.9785i	−0.609785	−	1.05618i	−0.991276	−	0.131806i	$-0.957922\pi$
$151$	−7.49316	−	12.9785i	−0.609785	−	1.05618i	0.381491	−	0.924373i	$-0.375411\pi$
$152$		0			0
$153$	19.5127	+	6.37076i	1.57751	+	0.515045i
$154$		0			0
$155$	6.78263	−	11.7479i	0.544794	−	0.943611i
$156$		0			0
$157$	18.9806			1.51481			0.757407	−	0.652943i	$-0.226466\pi$
$157$	18.9806			1.51481			0.757407	+	0.652943i	$0.226466\pi$
$158$		0			0
$159$	−0.139680	−	0.364654i	−0.0110774	−	0.0289190i
$160$		0			0
$161$	0.779752	+	0.795655i	0.0614530	+	0.0627064i
$162$		0			0
$163$	7.51887	+	13.0231i	0.588924	+	1.02005i	0.994374	+	0.105929i	$0.0337815\pi$
$163$	7.51887	+	13.0231i	0.588924	+	1.02005i	−0.405450	+	0.914117i	$0.632885\pi$
$164$		0			0
$165$	11.7661	−	14.5088i	0.915988	−	1.12951i
$166$		0			0
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	0.843041	−	0.537849i	$-0.180763\pi$
$167$	−0.572097	−	0.990901i	−0.0442702	−	0.0766782i	−0.887311	+	0.461171i	$0.847430\pi$
$168$		0			0
$169$	6.21053	−	10.7570i	0.477733	−	0.827458i
$170$		0			0
$171$	−4.33693	+	3.89384i	−0.331653	+	0.297769i
$172$		0			0
$173$	0.497677			0.0378377			0.0189188	−	0.999821i	$-0.493978\pi$
$173$	0.497677			0.0378377			0.0189188	+	0.999821i	$0.493978\pi$
$174$		0			0
$175$	4.86677	−	1.25153i	0.367893	−	0.0946068i
$176$		0			0
$177$	2.16703	−	2.67217i	0.162884	−	0.200852i
$178$		0			0
$179$	−4.41423	+	7.64567i	−0.329935	+	0.571464i	−0.982499	−	0.186270i	$-0.940360\pi$
$179$	−4.41423	+	7.64567i	−0.329935	+	0.571464i	0.652564	+	0.757734i	$0.273694\pi$
$180$		0			0
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$		0			0
$183$	11.2918	−	13.9239i	0.834713	−	1.02929i
$184$		0			0
$185$	−5.08126			−0.373581
$186$		0			0
$187$	−41.9064			−3.06450
$188$		0			0
$189$	9.32326	−	10.1033i	0.678167	−	0.734908i
$190$		0			0
$191$	16.1683			1.16989			0.584947	−	0.811071i	$-0.301115\pi$
$191$	16.1683			1.16989			0.584947	+	0.811071i	$0.301115\pi$
$192$		0			0
$193$	−14.1683			−1.01985			−0.509927	−	0.860218i	$-0.670328\pi$
$193$	−14.1683			−1.01985			−0.509927	+	0.860218i	$0.670328\pi$
$194$		0			0
$195$	−1.46169	+	1.80242i	−0.104674	+	0.129074i
$196$		0			0
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$		0			0
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	−0.662884	−	0.748722i	$-0.730668\pi$
$199$	4.47141	−	7.74471i	0.316970	−	0.549008i	0.979854	+	0.199714i	$0.0640013\pi$
$200$		0			0
$201$	7.40219	−	9.12767i	0.522110	−	0.643816i
$202$		0			0
$203$	−2.71217	−	2.76748i	−0.190357	−	0.194239i
$204$		0			0
$205$	12.2255			0.853862
$206$		0			0
$207$	1.20082	+	0.392058i	0.0834626	+	0.0272499i
$208$		0			0
$209$	5.94966	−	10.3051i	0.411546	−	0.712819i
$210$		0			0
$211$	−11.3856	−	19.7205i	−0.783820	−	1.35762i	−0.929702	−	0.368314i	$-0.879935\pi$
$211$	−11.3856	−	19.7205i	−0.783820	−	1.35762i	0.145882	−	0.989302i	$-0.453398\pi$
$212$		0			0
$213$	11.7661	−	14.5088i	0.806198	−	0.994126i
$214$		0			0
$215$	−7.62476	−	13.2065i	−0.520005	−	0.900674i
$216$		0			0
$217$	−5.47373	+	19.6333i	−0.371581	+	1.33280i
$218$		0			0
$219$	0.190024	+	0.496083i	0.0128406	+	0.0335222i
$220$		0			0
$221$	5.20602			0.350195
$222$		0			0
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	−0.565555	−	0.824711i	$-0.691338\pi$
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	0.996998	+	0.0774293i	$0.0246712\pi$
$224$		0			0
$225$	4.23981	−	3.80664i	0.282654	−	0.253776i
$226$		0			0
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	0.956888	+	0.290457i	$0.0938073\pi$
$227$	10.9984	+	19.0497i	0.729987	+	1.26437i	−0.226901	+	0.973918i	$0.572859\pi$
$228$		0			0
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	−0.796422	−	0.604741i	$-0.793277\pi$
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	0.921932	+	0.387351i	$0.126610\pi$
$230$		0			0
$231$	−11.6923	+	25.5158i	−0.769300	+	1.67882i
$232$		0			0
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	0.735848	−	0.677147i	$-0.236784\pi$
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	−0.954350	+	0.298689i	$0.903451\pi$
$234$		0			0
$235$	1.46169	−	2.53173i	0.0953505	−	0.165152i
$236$		0			0
$237$	−14.6683	+	18.0875i	−0.952807	+	1.17491i
$238$		0			0
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	0.999977	+	0.00677786i	$0.00215748\pi$
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	−0.494119	+	0.869394i	$0.664509\pi$
$240$		0			0
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	−0.971956	−	0.235163i	$-0.924437\pi$
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	0.282320	−	0.959320i	$-0.408896\pi$
$242$		0			0
$243$	4.08809	−	15.0429i	0.262251	−	0.965000i
$244$		0			0
$245$	10.7970	−	5.94631i	0.689794	−	0.379896i
$246$		0			0
$247$	−0.739123	+	1.28020i	−0.0470293	+	0.0814571i
$248$		0			0
$249$	1.93598	+	5.05415i	0.122688	+	0.320294i
$250$		0			0
$251$	23.6030			1.48981			0.744904	−	0.667171i	$-0.232495\pi$
$251$	23.6030			1.48981			0.744904	+	0.667171i	$0.232495\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$		0			0
$255$	20.6088	+	3.27913i	1.29057	+	0.205347i
$256$		0			0
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	0.355275	+	0.934762i	$0.384387\pi$
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	−0.987165	+	0.159704i	$0.948946\pi$
$258$		0			0
$259$	7.39411	−	1.90146i	0.459448	−	0.118151i
$260$		0			0
$261$	−4.17674	−	1.36368i	−0.258534	−	0.0844094i
$262$		0			0
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	−0.970732	−	0.240165i	$-0.922799\pi$
$263$	−11.2443	−	19.4757i	−0.693355	−	1.20093i	0.277377	−	0.960761i	$-0.410535\pi$
$264$		0			0
$265$	−0.198495	−	0.343803i	−0.0121935	−	0.0211197i
$266$		0			0
$267$	−4.45254	−	0.708458i	−0.272491	−	0.0433569i
$268$		0			0
$269$	−12.6706	+	21.9461i	−0.772540	+	1.33808i	0.163627	+	0.986522i	$0.447681\pi$
$269$	−12.6706	+	21.9461i	−0.772540	+	1.33808i	−0.936167	+	0.351556i	$0.885653\pi$
$270$		0			0
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	0.995724	−	0.0923810i	$-0.0294478\pi$
$271$	6.87880	+	11.9144i	0.417858	+	0.723751i	−0.577866	+	0.816132i	$0.696114\pi$
$272$		0			0
$273$	1.45254	−	3.16982i	0.0879114	−	0.191846i
$274$		0			0
$275$	−5.81642	+	10.0743i	−0.350743	+	0.607505i
$276$		0			0
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$		0			0
$279$	4.77292	+	22.6129i	0.285747	+	1.35380i
$280$		0			0
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	−0.846480	−	0.532421i	$-0.821282\pi$
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	0.884330	+	0.466863i	$0.154616\pi$
$282$		0			0
$283$	8.19235			0.486984			0.243492	−	0.969903i	$-0.421707\pi$
$283$	8.19235			0.486984			0.243492	+	0.969903i	$0.421707\pi$
$284$		0			0
$285$	−3.73229	+	4.60230i	−0.221082	+	0.272616i
$286$		0			0
$287$	−17.7902	+	4.57489i	−1.05012	+	0.270047i
$288$		0			0
$289$	−14.9074	−	25.8204i	−0.876906	−	1.51884i
$290$		0			0
$291$	−2.25280	−	5.88123i	−0.132061	−	0.344764i
$292$		0			0
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	0.998469	−	0.0553202i	$-0.0176180\pi$
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	−0.547143	+	0.837039i	$0.684285\pi$
$294$		0			0
$295$	1.74884	−	3.02908i	0.101821	−	0.176360i
$296$		0			0
$297$	1.59781	+	31.7851i	0.0927142	+	1.84436i
$298$		0			0
$299$	0.320380			0.0185280
$300$		0			0
$301$	16.0374	+	16.3645i	0.924378	+	0.943231i
$302$		0			0
$303$	−13.7021	−	2.18018i	−0.787163	−	0.125248i
$304$		0			0
$305$	9.11273	−	15.7837i	0.521793	−	0.903772i
$306$		0			0
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$	−4.23065	−	11.0447i	−0.240673	−	0.628310i
$310$		0			0
$311$	7.69002			0.436061			0.218031	−	0.975942i	$-0.430037\pi$
$311$	7.69002			0.436061			0.218031	+	0.975942i	$0.430037\pi$
$312$		0			0
$313$	−1.72313			−0.0973969			−0.0486985	−	0.998814i	$-0.515507\pi$
$313$	−1.72313			−0.0973969			−0.0486985	+	0.998814i	$0.515507\pi$
$314$		0			0
$315$	7.74665	−	11.6333i	0.436474	−	0.655460i
$316$		0			0
$317$	33.2028			1.86485			0.932426	−	0.361361i	$-0.117688\pi$
$317$	33.2028			1.86485			0.932426	+	0.361361i	$0.117688\pi$
$318$		0			0
$319$	8.97017			0.502233
$320$		0			0
$321$	6.06526	+	0.965064i	0.338530	+	0.0538646i
$322$		0			0
$323$	13.2930			0.739644
$324$		0			0
$325$	0.722572	−	1.25153i	0.0400811	−	0.0694224i
$326$		0			0
$327$	0.435984	+	1.13819i	0.0241099	+	0.0629423i
$328$		0			0
$329$	−1.17962	+	4.23109i	−0.0650346	+	0.233267i
$330$		0			0
$331$	−2.88891			−0.158789			−0.0793944	−	0.996843i	$-0.525299\pi$
$331$	−2.88891			−0.158789			−0.0793944	+	0.996843i	$0.525299\pi$
$332$		0			0
$333$	6.44158	−	5.78346i	0.352996	−	0.316931i
$334$		0			0
$335$	5.97373	−	10.3468i	0.326380	−	0.565307i
$336$		0			0
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$		0			0
$339$	−14.5435	−	2.31407i	−0.789895	−	0.125683i
$340$		0			0
$341$	−23.5917	−	40.8620i	−1.27756	−	2.21280i
$342$		0			0
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$		0			0
$345$	1.26827	+	0.201799i	0.0682813	+	0.0108645i
$346$		0			0
$347$	−9.69467			−0.520437			−0.260219	−	0.965550i	$-0.583795\pi$
$347$	−9.69467			−0.520437			−0.260219	+	0.965550i	$0.583795\pi$
$348$		0			0
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	−0.182752	−	0.983159i	$-0.558500\pi$
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	0.942817	−	0.333312i	$-0.108166\pi$
$350$		0			0
$351$	−0.198495	−	3.94865i	−0.0105949	−	0.210763i
$352$		0			0
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	0.918548	−	0.395308i	$-0.129362\pi$
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	−0.801621	+	0.597832i	$0.796029\pi$
$354$		0			0
$355$	9.49549	−	16.4467i	0.503968	−	0.872898i
$356$		0			0
$357$	−31.2164	+	2.94031i	−1.65215	+	0.155618i
$358$		0			0
$359$	−16.0796	−	27.8507i	−0.848650	−	1.46990i	−0.882413	−	0.470475i	$-0.844083\pi$
$359$	−16.0796	−	27.8507i	−0.848650	−	1.46990i	0.0337633	−	0.999430i	$-0.489251\pi$
$360$		0			0
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$		0			0
$363$	−16.4263	−	42.8830i	−0.862155	−	2.25077i
$364$		0			0
$365$	0.270036	+	0.467717i	0.0141343	+	0.0244814i
$366$		0			0
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.823406	+	0.567452i	$0.192071\pi$
$367$	17.3015	+	29.9671i	0.903131	+	1.56427i	0.0797249	+	0.996817i	$0.474596\pi$
$368$		0			0
$369$	−15.4984	+	13.9149i	−0.806813	+	0.724383i
$370$		0			0
$371$	0.417500	+	0.426015i	0.0216755	+	0.0221176i
$372$		0			0
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$		0			0
$375$	13.2540	−	16.3436i	0.684436	−	0.843980i
$376$		0			0
$377$	−1.11436			−0.0573925
$378$		0			0
$379$	−33.9877			−1.74583			−0.872916	−	0.487871i	$-0.837774\pi$
$379$	−33.9877			−1.74583			−0.872916	+	0.487871i	$0.837774\pi$
$380$		0			0
$381$	−20.6774	+	25.4974i	−1.05934	+	1.30627i
$382$		0			0
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	0.461916	+	0.886923i	$0.347162\pi$
$383$	−10.5120	+	18.2074i	−0.537140	+	0.930354i	−0.999056	+	0.0434304i	$0.986171\pi$
$384$		0			0
$385$	−7.66307	+	27.4861i	−0.390546	+	1.40082i
$386$		0			0
$387$	24.6975	+	8.06357i	1.25545	+	0.409894i
$388$		0			0
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	0.637667	−	0.770312i	$-0.279900\pi$
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	−0.985943	+	0.167080i	$0.946566\pi$
$390$		0			0
$391$	−1.44050	−	2.49501i	−0.0728491	−	0.126178i
$392$		0			0
$393$	−4.51848	−	11.7961i	−0.227927	−	0.595035i
$394$		0			0
$395$	−11.8376	+	20.5034i	−0.595615	+	1.03164i
$396$		0			0
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	0.762129	−	0.647425i	$-0.224154\pi$
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$398$		0			0
$399$	3.70890	−	8.09380i	0.185677	−	0.405197i
$400$		0			0
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	−0.726612	−	0.687048i	$-0.758906\pi$
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	0.958307	+	0.285741i	$0.0922397\pi$
$402$		0			0
$403$	2.93078	+	5.07626i	0.145993	+	0.252867i
$404$		0			0
$405$	1.70137	−	15.7563i	0.0845419	−	0.782937i
$406$		0			0
$407$	−8.83693	+	15.3060i	−0.438030	+	0.758691i
$408$		0			0
$409$	15.1683			0.750023			0.375011	−	0.927020i	$-0.377639\pi$
$409$	15.1683			0.750023			0.375011	+	0.927020i	$0.377639\pi$
$410$		0			0
$411$	−13.9955	−	2.22687i	−0.690346	−	0.109843i
$412$		0			0
$413$	−1.41135	+	5.06227i	−0.0694481	+	0.249098i
$414$		0			0
$415$	2.75116	+	4.76515i	0.135049	+	0.233912i
$416$		0			0
$417$	−21.3211	−	3.39247i	−1.04410	−	0.166130i
$418$		0			0
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	0.949696	−	0.313172i	$-0.101392\pi$
$419$	4.16827	+	7.21966i	0.203633	+	0.352703i	−0.746063	+	0.665875i	$0.768058\pi$
$420$		0			0
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$		0			0
$423$	1.02859	+	4.87320i	0.0500118	+	0.236943i
$424$		0			0
$425$	−12.9954			−0.630367
$426$		0			0
$427$	−7.35417	+	26.3781i	−0.355893	+	1.27653i
$428$		0			0
$429$	2.88727	+	7.53762i	0.139399	+	0.363920i
$430$		0			0
$431$	1.72545	−	2.98857i	0.0831120	−	0.143954i	−0.821473	−	0.570247i	$-0.806847\pi$
$431$	1.72545	−	2.98857i	0.0831120	−	0.143954i	0.904585	+	0.426293i	$0.140181\pi$
$432$		0			0
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$		0			0
$435$	−4.41135	−	0.701905i	−0.211508	−	0.0336538i
$436$		0			0
$437$	0.818057			0.0391330
$438$		0			0
$439$	28.8960			1.37913			0.689566	−	0.724222i	$-0.257801\pi$
$439$	28.8960			1.37913			0.689566	+	0.724222i	$0.257801\pi$
$440$		0			0
$441$	−6.91943	+	19.8273i	−0.329497	+	0.944157i
$442$		0			0
$443$	13.7609			0.653799			0.326899	−	0.945059i	$-0.393996\pi$
$443$	13.7609			0.653799			0.326899	+	0.945059i	$0.393996\pi$
$444$		0			0
$445$	−4.58358			−0.217283
$446$		0			0
$447$	−5.46978	−	14.2796i	−0.258711	−	0.675401i
$448$		0			0
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$		0			0
$451$	21.2616	−	36.8261i	1.00117	−	1.73407i
$452$		0			0
$453$	25.6346	+	4.07881i	1.20442	+	0.191639i
$454$		0			0
$455$	0.951980	−	3.41458i	0.0446295	−	0.160078i
$456$		0			0
$457$	20.0298			0.936956			0.468478	−	0.883475i	$-0.344803\pi$
$457$	20.0298			0.936956			0.468478	+	0.883475i	$0.344803\pi$
$458$		0			0
$459$	−29.8583	+	19.2998i	−1.39367	+	0.900837i
$460$		0			0
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	−0.692618	−	0.721304i	$-0.743543\pi$
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	0.970977	+	0.239173i	$0.0768763\pi$
$462$		0			0
$463$	−6.64527	−	11.5100i	−0.308832	−	0.534913i	0.669275	−	0.743015i	$-0.266605\pi$
$463$	−6.64527	−	11.5100i	−0.308832	−	0.534913i	−0.978107	+	0.208102i	$0.933271\pi$
$464$		0			0
$465$	8.40451	+	21.9411i	0.389750	+	1.01750i
$466$		0			0
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	0.966197	−	0.257804i	$-0.0829990\pi$
$467$	5.61505	+	9.72555i	0.259833	+	0.450045i	−0.706364	+	0.707849i	$0.749666\pi$
$468$		0			0
$469$	−4.82094	+	17.2918i	−0.222610	+	0.798463i
$470$		0			0
$471$	−20.7073	+	25.5342i	−0.954140	+	1.17655i
$472$		0			0
$473$	−53.0416			−2.43886
$474$		0			0
$475$	1.84501	−	3.19565i	0.0846550	−	0.146627i
$476$		0			0
$477$	0.642950	+	0.209918i	0.0294387	+	0.00961150i
$478$		0			0
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	−0.950015	−	0.312205i	$-0.898932\pi$
$479$	−16.3135	−	28.2559i	−0.745385	−	1.29104i	0.204630	−	0.978839i	$-0.434401\pi$
$480$		0			0
$481$	1.09781	−	1.90146i	0.0500557	−	0.0866991i
$482$		0			0
$483$	−1.92107	+	0.180948i	−0.0874116	+	0.00823340i
$484$		0			0
$485$	−3.20137	−	5.54494i	−0.145367	−	0.251783i
$486$		0			0
$487$	−1.84897	+	3.20251i	−0.0837848	+	0.145120i	−0.904873	−	0.425682i	$-0.860034\pi$
$487$	−1.84897	+	3.20251i	−0.0837848	+	0.145120i	0.821088	+	0.570802i	$0.193368\pi$
$488$		0			0
$489$	−25.7226	−	4.09280i	−1.16321	−	0.185083i
$490$		0			0
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	0.883389	+	0.468641i	$0.155256\pi$
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	−0.0358393	+	0.999358i	$0.511410\pi$
$492$		0			0
$493$	5.01040	+	8.67827i	0.225657	+	0.390850i
$494$		0			0
$495$	6.68194	+	31.6574i	0.300331	+	1.42289i
$496$		0			0
$497$	−7.66307	+	27.4861i	−0.343736	+	1.23292i
$498$		0			0
$499$	−15.8977	+	27.5356i	−0.711678	+	1.23266i	0.252549	+	0.967584i	$0.418731\pi$
$499$	−15.8977	+	27.5356i	−0.711678	+	1.23266i	−0.964227	+	0.265078i	$0.914602\pi$
$500$		0			0
$501$	1.95718	+	0.311414i	0.0874404	+	0.0139129i
$502$		0			0
$503$	−30.8252			−1.37443			−0.687214	−	0.726455i	$-0.741166\pi$
$503$	−30.8252			−1.37443			−0.687214	+	0.726455i	$0.741166\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$		0			0
$507$	7.69562	+	20.0904i	0.341774	+	0.892248i
$508$		0			0
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	−0.941077	−	0.338193i	$-0.890184\pi$
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	0.763422	+	0.645900i	$0.223518\pi$
$510$		0			0
$511$	−0.567974	−	0.579559i	−0.0251257	−	0.0256382i
$512$		0			0
$513$	−0.506837	−	10.0825i	−0.0223774	−	0.445151i
$514$		0			0
$515$	−6.01204	−	10.4132i	−0.264922	−	0.458858i
$516$		0			0
$517$	−5.08414	−	8.80598i	−0.223600	−	0.387287i
$518$		0			0
$519$	−0.542951	+	0.669515i	−0.0238329	+	0.0293885i
$520$		0			0
$521$	14.8646	−	25.7462i	0.651229	−	1.12796i	−0.331596	−	0.943421i	$-0.607587\pi$
$521$	14.8646	−	25.7462i	0.651229	−	1.12796i	0.982825	−	0.184540i	$-0.0590795\pi$
$522$		0			0
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	−0.994365	−	0.106013i	$-0.966192\pi$
$523$	−13.4698	−	23.3303i	−0.588992	−	1.02016i	0.405373	−	0.914152i	$-0.367142\pi$
$524$		0			0
$525$	−3.62584	+	7.91255i	−0.158245	+	0.345332i
$526$		0			0
$527$	26.3549	−	45.6480i	1.14804	−	1.98846i
$528$		0			0
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$		0			0
$531$	1.23065	+	5.83052i	0.0534057	+	0.253023i
$532$		0			0
$533$	−2.64132	+	4.57489i	−0.114408	+	0.198161i
$534$		0			0
$535$	6.24377			0.269942
$536$		0			0
$537$	−5.46978	−	14.2796i	−0.236038	−	0.616210i
$538$		0			0
$539$	0.865521	−	42.8646i	0.0372806	−	1.84631i
$540$		0			0
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	0.977847	−	0.209321i	$-0.0671252\pi$
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	−0.670201	+	0.742180i	$0.733792\pi$
$542$		0			0
$543$	−1.45034	+	1.78843i	−0.0622403	+	0.0767487i
$544$		0			0
$545$	0.619562	+	1.07311i	0.0265391	+	0.0459671i
$546$		0			0
$547$	−1.02463	+	1.77471i	−0.0438101	+	0.0758813i	−0.887099	−	0.461579i	$-0.847283\pi$
$547$	−1.02463	+	1.77471i	−0.0438101	+	0.0758813i	0.843289	+	0.537461i	$0.180616\pi$
$548$		0			0
$549$	6.41260	+	30.3813i	0.273683	+	1.29664i
$550$		0			0
$551$	−2.84540			−0.121218
$552$		0			0
$553$	9.55322	−	34.2657i	0.406244	−	1.45713i
$554$		0			0
$555$	5.54351	−	6.83572i	0.235309	−	0.290160i
$556$		0			0
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	−0.615577	−	0.788077i	$-0.711077\pi$
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	0.990283	+	0.139067i	$0.0444103\pi$
$558$		0			0
$559$	6.58934			0.278699
$560$		0			0
$561$	45.7187	−	56.3759i	1.93025	−	2.38019i
$562$		0			0
$563$	−0.937063			−0.0394925			−0.0197462	−	0.999805i	$-0.506286\pi$
$563$	−0.937063			−0.0394925			−0.0197462	+	0.999805i	$0.506286\pi$
$564$		0			0
$565$	−14.9715			−0.629858
$566$		0			0
$567$	3.42038	+	23.5648i	0.143642	+	0.989630i
$568$		0			0
$569$	23.5264			0.986278			0.493139	−	0.869951i	$-0.335849\pi$
$569$	23.5264			0.986278			0.493139	+	0.869951i	$0.335849\pi$
$570$		0			0
$571$	0.484004			0.0202549			0.0101275	−	0.999949i	$-0.496776\pi$
$571$	0.484004			0.0202549			0.0101275	+	0.999949i	$0.496776\pi$
$572$		0			0
$573$	−17.6391	+	21.7509i	−0.736885	+	0.908655i
$574$		0			0
$575$	−0.799737			−0.0333514
$576$		0			0
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	−0.908715	−	0.417417i	$-0.862935\pi$
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	0.815852	+	0.578261i	$0.196269\pi$
$578$		0			0
$579$	15.4572	−	19.0603i	0.642379	−	0.792119i
$580$		0			0
$581$	−5.78659	−	5.90461i	−0.240068	−	0.244965i
$582$		0			0
$583$	−1.38083			−0.0571881
$584$		0			0
$585$	−0.830095	−	3.93278i	−0.0343202	−	0.162600i
$586$		0			0
$587$	−8.31518	+	14.4023i	−0.343204	+	0.594447i	−0.985026	−	0.172407i	$-0.944846\pi$
$587$	−8.31518	+	14.4023i	−0.343204	+	0.594447i	0.641822	+	0.766854i	$0.278179\pi$
$588$		0			0
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$		0			0
$591$	−17.2833	+	21.3121i	−0.710941	+	0.876663i
$592$		0			0
$593$	20.7632	+	35.9629i	0.852642	+	1.47682i	0.878815	+	0.477163i	$0.158335\pi$
$593$	20.7632	+	35.9629i	0.852642	+	1.47682i	−0.0261726	+	0.999657i	$0.508332\pi$
$594$		0			0
$595$	−30.8720	+	7.93899i	−1.26563	+	0.325467i
$596$		0			0
$597$	5.54063	+	14.4646i	0.226763	+	0.591995i
$598$		0			0
$599$	−15.0766			−0.616014			−0.308007	−	0.951384i	$-0.599662\pi$
$599$	−15.0766			−0.616014			−0.308007	+	0.951384i	$0.599662\pi$
$600$		0			0
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$602$		0			0
$603$	4.20370	+	19.9161i	0.171188	+	0.811044i
$604$		0			0
$605$	−23.3428	−	40.4310i	−0.949021	−	1.64375i
$606$		0			0
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	−0.596157	−	0.802868i	$-0.703306\pi$
$607$	9.78659	−	16.9509i	0.397225	−	0.688014i	0.993382	+	0.114853i	$0.0366398\pi$
$608$		0			0
$609$	6.68194	−	0.629380i	0.270766	−	0.0255038i
$610$		0			0
$611$	0.631600	+	1.09396i	0.0255518	+	0.0442570i
$612$		0			0
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	−0.916622	−	0.399755i	$-0.869095\pi$
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	0.804509	+	0.593941i	$0.202429\pi$
$614$		0			0
$615$	−13.3376	+	16.4467i	−0.537825	+	0.663194i
$616$		0			0
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	0.878514	−	0.477716i	$-0.158535\pi$
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	−0.852971	+	0.521958i	$0.825202\pi$
$618$		0			0
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	0.907714	−	0.419589i	$-0.137826\pi$
$619$	2.25116	+	3.89913i	0.0904818	+	0.156719i	−0.817232	+	0.576309i	$0.804493\pi$
$620$		0			0
$621$	−1.83749	+	1.18771i	−0.0737358	+	0.0476613i
$622$		0			0
$623$	6.66991	−	1.71522i	0.267224	−	0.0687190i
$624$		0			0
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$		0			0
$627$	7.37236	+	19.2465i	0.294424	+	0.768633i
$628$		0			0
$629$	−19.7439			−0.787242
$630$		0			0
$631$	1.69905			0.0676381			0.0338191	−	0.999428i	$-0.489233\pi$
$631$	1.69905			0.0676381			0.0338191	+	0.999428i	$0.489233\pi$
$632$		0			0
$633$	38.9510	+	6.19763i	1.54816	+	0.246334i
$634$		0			0
$635$	−16.6871	+	28.9030i	−0.662209	+	1.14698i
$636$		0			0
$637$	−0.107523	+	5.32505i	−0.00426023	+	0.210986i
$638$		0			0
$639$	6.68194	+	31.6574i	0.264334	+	1.25235i
$640$		0			0
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	0.875240	−	0.483689i	$-0.160703\pi$
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	−0.856507	+	0.516136i	$0.827370\pi$
$642$		0			0
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	0.992235	−	0.124375i	$-0.0396927\pi$
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	−0.603830	+	0.797113i	$0.706359\pi$
$644$		0			0
$645$	26.0848	+	4.15044i	1.02709	+	0.163424i
$646$		0			0
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	−0.999013	−	0.0444181i	$-0.985857\pi$
$647$	−11.7271	+	20.3119i	−0.461039	+	0.798543i	0.537974	+	0.842962i	$0.319190\pi$
$648$		0			0
$649$	−6.08289	−	10.5359i	−0.238774	−	0.413569i
$650$		0			0
$651$	−20.4406	−	28.7831i	−0.801131	−	1.12810i
$652$		0			0
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	−0.998117	−	0.0613420i	$-0.980462\pi$
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	0.552182	+	0.833724i	$0.313795\pi$
$654$		0			0
$655$	−6.42107	−	11.1216i	−0.250892	−	0.434557i
$656$		0			0
$657$	−0.874681	−	0.285577i	−0.0341246	−	0.0111414i
$658$		0			0
$659$	13.2398	−	22.9320i	0.515750	−	0.893305i	−0.484083	−	0.875022i	$-0.660847\pi$
$659$	13.2398	−	22.9320i	0.515750	−	0.893305i	0.999833	−	0.0182828i	$-0.00581993\pi$
$660$		0			0
$661$	−26.7382			−1.03999			−0.519997	−	0.854168i	$-0.674067\pi$
$661$	−26.7382			−1.03999			−0.519997	+	0.854168i	$0.674067\pi$
$662$		0			0
$663$	−5.67962	+	7.00356i	−0.220578	+	0.271996i
$664$		0			0
$665$	2.43078	−	8.71878i	0.0942617	−	0.338100i
$666$		0			0
$667$	0.308342	+	0.534063i	0.0119390	+	0.0206790i
$668$		0			0
$669$	7.98345	+	20.8419i	0.308658	+	0.805793i
$670$		0			0
$671$	−31.6963	−	54.8996i	−1.22362	−	2.11938i
$672$		0			0
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$		0			0
$675$	0.495487	+	9.85667i	0.0190713	+	0.379384i
$676$		0			0
$677$	−20.6979			−0.795486			−0.397743	−	0.917497i	$-0.630207\pi$
$677$	−20.6979			−0.795486			−0.397743	+	0.917497i	$0.630207\pi$
$678$		0			0
$679$	6.73353	+	6.87087i	0.258409	+	0.263680i
$680$		0			0
$681$	−37.6261	−	5.98682i	−1.44184	−	0.229416i
$682$		0			0
$683$	−14.2918	+	24.7541i	−0.546860	+	0.947190i	0.451627	+	0.892207i	$0.350844\pi$
$683$	−14.2918	+	24.7541i	−0.546860	+	0.947190i	−0.998487	+	0.0549828i	$0.982490\pi$
$684$		0			0
$685$	−14.4074			−0.550478
$686$		0			0
$687$	2.35348	+	6.14409i	0.0897910	+	0.234412i
$688$		0			0
$689$	0.171540			0.00653515
$690$		0			0
$691$	6.69794			0.254802			0.127401	−	0.991851i	$-0.459337\pi$
$691$	6.69794			0.254802			0.127401	+	0.991851i	$0.459337\pi$
$692$		0			0
$693$	−21.5699	−	43.5665i	−0.819373	−	1.65495i
$694$		0			0
$695$	−21.9486			−0.832557
$696$		0			0
$697$	47.5037			1.79933
$698$		0			0
$699$	11.4103	+	1.81553i	0.431576	+	0.0686695i
$700$		0			0
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$		0			0
$703$	2.80314	−	4.85518i	0.105722	−	0.183117i
$704$		0			0
$705$	1.81122	+	4.72844i	0.0682145	+	0.178083i
$706$		0			0
$707$	20.5257	−	5.27836i	0.771949	−	0.198513i
$708$		0			0
$709$	8.86621			0.332977			0.166489	−	0.986043i	$-0.446757\pi$
$709$	8.86621			0.332977			0.166489	+	0.986043i	$0.446757\pi$
$710$		0			0
$711$	−8.33009	−	39.4659i	−0.312403	−	1.48009i
$712$		0			0
$713$	1.62188	−	2.80919i	0.0607401	−	0.105205i
$714$		0			0
$715$	4.10301	+	7.10662i	0.153444	+	0.265773i
$716$		0			0
$717$	−26.7540	−	4.25693i	−0.999148	−	0.158978i
$718$		0			0
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	0.557576	−	0.830126i	$-0.311731\pi$
$719$	−11.8015	−	20.4408i	−0.440122	−	0.762313i	−0.997698	+	0.0678123i	$0.978398\pi$
$720$		0			0
$721$	12.6453	+	12.9032i	0.470935	+	0.480540i
$722$		0			0
$723$	36.6260	+	5.82769i	1.36214	+	0.216734i
$724$		0			0
$725$	2.78168			0.103309
$726$		0			0
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	−0.920080	−	0.391730i	$-0.871877\pi$
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	0.799288	+	0.600948i	$0.205210\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$		0			0
$731$	−29.6271	−	51.3156i	−1.09580	−	1.89798i
$732$		0			0
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	−0.568312	−	0.822813i	$-0.692403\pi$
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	0.996733	+	0.0807664i	$0.0257368\pi$
$734$		0			0
$735$	−3.77975	+	21.0122i	−0.139418	+	0.775048i
$736$		0			0
$737$	−20.7781	−	35.9888i	−0.765372	−	1.32566i
$738$		0			0
$739$	7.57838	−	13.1261i	0.278775	−	0.482853i	−0.692305	−	0.721605i	$-0.743405\pi$
$739$	7.57838	−	13.1261i	0.278775	−	0.482853i	0.971081	+	0.238752i	$0.0767383\pi$
$740$		0			0
$741$	−0.915865	−	2.39099i	−0.0336451	−	0.0878352i
$742$		0			0
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	0.945717	−	0.324992i	$-0.105362\pi$
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	−0.754310	+	0.656518i	$0.772028\pi$
$744$		0			0
$745$	−7.77292	−	13.4631i	−0.284778	−	0.493249i
$746$		0			0
$747$	−8.91135	−	2.90949i	−0.326049	−	0.106453i
$748$		0			0
$749$	−9.08577	+	2.33648i	−0.331987	+	0.0853733i
$750$		0			0
$751$	20.1059	−	34.8244i	0.733674	−	1.27076i	−0.221628	−	0.975131i	$-0.571137\pi$
$751$	20.1059	−	34.8244i	0.733674	−	1.27076i	0.955303	−	0.295630i	$-0.0955295\pi$
$752$		0			0
$753$	−25.7502	+	31.7527i	−0.938390	+	1.15713i
$754$		0			0
$755$	26.3891			0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$		0			0
$759$	2.81354	−	3.46939i	0.102125	−	0.125931i
$760$		0			0
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	−0.567889	−	0.823105i	$-0.692240\pi$
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	0.996774	+	0.0802535i	$0.0255730\pi$
$762$		0			0
$763$	−1.30314	−	1.32972i	−0.0471768	−	0.0481390i
$764$		0			0
$765$	−26.8949	+	24.1471i	−0.972388	+	0.873042i
$766$		0			0
$767$	0.755675	+	1.30887i	0.0272858	+	0.0472605i
$768$		0			0
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	0.746536	−	0.665345i	$-0.231716\pi$
$769$	−5.62764	−	9.74736i	−0.202938	−	0.351499i	−0.949474	+	0.313846i	$0.898382\pi$
$770$		0			0
$771$	−12.5523	−	32.7694i	−0.452059	−	1.18016i
$772$		0			0
$773$	0.138992	−	0.240741i	0.00499919	−	0.00865886i	−0.863515	−	0.504323i	$-0.831742\pi$
$773$	0.138992	−	0.240741i	0.00499919	−	0.00865886i	0.868514	+	0.495664i	$0.165075\pi$
$774$		0			0
$775$	−7.31587	−	12.6715i	−0.262794	−	0.455172i
$776$		0			0
$777$	−5.50877	+	12.0216i	−0.197626	+	0.431272i
$778$		0			0
$779$	−6.74433	+	11.6815i	−0.241641	+	0.418534i
$780$		0			0
$781$	−33.0276	−	57.2056i	−1.18182	−	2.04698i
$782$		0			0
$783$	6.39123	−	4.13116i	0.228404	−	0.147636i
$784$		0			0
$785$	−16.7112	+	28.9447i	−0.596449	+	1.03308i
$786$		0			0
$787$	29.3880			1.04757			0.523784	−	0.851851i	$-0.324520\pi$
$787$	29.3880			1.04757			0.523784	+	0.851851i	$0.324520\pi$
$788$		0			0
$789$	38.4676	+	6.12071i	1.36948	+	0.217903i
$790$		0			0
$791$	21.7862	−	5.60251i	0.774628	−	0.199202i
$792$		0			0
$793$	3.93762	+	6.82015i	0.139829	+	0.242191i
$794$		0			0
$795$	0.679065	+	0.108048i	0.0240839	+	0.00383208i
$796$		0			0
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	0.873594	−	0.486655i	$-0.161783\pi$
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	−0.858253	+	0.513227i	$0.828450\pi$
$798$		0			0
$799$	5.67962	−	9.83739i	0.200931	−	0.348022i
$800$		0			0
$801$	5.81066	−	5.21700i	0.205310	−	0.184334i
$802$		0			0
$803$	1.87851			0.0662910
$804$		0			0
$805$	−1.89987	+	0.488568i	−0.0669616	+	0.0172197i
$806$		0			0
$807$	−15.7004	−	40.9881i	−0.552681	−	1.44285i
$808$		0			0
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	−0.644534	−	0.764575i	$-0.722949\pi$
$809$	9.66703	−	16.7438i	0.339875	−	0.588680i	0.984409	+	0.175895i	$0.0562820\pi$
$810$		0			0
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$	−23.5328	−	3.74439i	−0.825333	−	0.131321i
$814$		0			0
$815$	−26.4796			−0.927541
$816$		0			0
$817$	16.8252			0.588639
$818$		0			0
$819$	2.67962	+	5.41225i	0.0936335	+	0.189119i
$820$		0			0
$821$	1.41066			0.0492325			0.0246162	−	0.999697i	$-0.492164\pi$
$821$	1.41066			0.0492325			0.0246162	+	0.999697i	$0.492164\pi$
$822$		0			0
$823$	35.0391			1.22139			0.610694	−	0.791867i	$-0.290891\pi$
$823$	35.0391			1.22139			0.610694	+	0.791867i	$0.290891\pi$
$824$		0			0
$825$	−7.20726	−	18.8155i	−0.250925	−	0.655073i
$826$		0			0
$827$	18.5997			0.646776			0.323388	−	0.946266i	$-0.395178\pi$
$827$	18.5997			0.646776			0.323388	+	0.946266i	$0.395178\pi$
$828$		0			0
$829$	19.0848	−	33.0559i	0.662843	−	1.14808i	−0.317022	−	0.948418i	$-0.602683\pi$
$829$	19.0848	−	33.0559i	0.662843	−	1.14808i	0.979865	−	0.199660i	$-0.0639838\pi$
$830$		0			0
$831$	−5.61505	−	0.893429i	−0.194784	−	0.0309927i
$832$		0			0
$833$	41.9532	−	23.1052i	1.45359	−	0.800549i
$834$		0			0
$835$	2.01478			0.0697245
$836$		0			0
$837$	−35.6278	−	18.2491i	−1.23148	−	0.630781i
$838$		0			0
$839$	−17.3691	+	30.0841i	−0.599648	+	1.03862i	0.393225	+	0.919442i	$0.371359\pi$
$839$	−17.3691	+	30.0841i	−0.599648	+	1.03862i	−0.992873	+	0.119178i	$0.961974\pi$
$840$		0			0
$841$	13.4275	+	23.2571i	0.463018	+	0.801970i
$842$		0			0
$843$	0.786197	+	2.05247i	0.0270781	+	0.0706910i
$844$		0			0
$845$	10.9360	+	18.9417i	0.376209	+	0.651614i
$846$		0			0
$847$	49.0976	+	50.0989i	1.68701	+	1.72142i
$848$		0			0
$849$	−8.93762	+	11.0210i	−0.306738	+	0.378240i
$850$		0			0
$851$	−1.21505			−0.0416513
$852$		0			0
$853$	−21.1586	+	36.6477i	−0.724455	+	1.25479i	0.234743	+	0.972058i	$0.424575\pi$
$853$	−21.1586	+	36.6477i	−0.724455	+	1.25479i	−0.959198	+	0.282736i	$0.908758\pi$
$854$		0			0
$855$	−2.11956	−	10.0419i	−0.0724875	−	0.343427i
$856$		0			0
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	0.709978	−	0.704224i	$-0.248705\pi$
$857$	−7.46169	−	12.9240i	−0.254887	−	0.441477i	−0.964865	+	0.262747i	$0.915371\pi$
$858$		0			0
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	−0.651560	−	0.758597i	$-0.725885\pi$
$859$	9.70658	−	16.8123i	0.331184	−	0.573628i	0.982744	+	0.184969i	$0.0592186\pi$
$860$		0			0
$861$	13.2540	−	28.9238i	0.451696	−	0.985722i
$862$		0			0
$863$	0.542263	+	0.939227i	0.0184588	+	0.0319717i	0.875107	−	0.483929i	$-0.160791\pi$
$863$	0.542263	+	0.939227i	0.0184588	+	0.0319717i	−0.856648	+	0.515901i	$0.827457\pi$
$864$		0			0
$865$	−0.438174	+	0.758939i	−0.0148984	+	0.0258047i
$866$		0			0
$867$	50.9992	+	8.11465i	1.73202	+	0.275588i
$868$		0			0
$869$	41.1742	+	71.3157i	1.39674	+	2.41922i
$870$		0			0
$871$	2.58126	+	4.47087i	0.0874625	+	0.151490i
$872$		0			0
$873$	10.3696	+	3.38561i	0.350959	+	0.114586i
$874$		0			0
$875$	−8.63216	+	30.9620i	−0.291820	+	1.04671i
$876$		0			0
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	−0.517427	−	0.855728i	$-0.673110\pi$
$877$	14.2850	−	24.7423i	0.482369	−	0.835487i	0.999795	+	0.0202407i	$0.00644326\pi$
$878$		0			0
$879$	−26.4293	−	4.20525i	−0.891437	−	0.141840i
$880$		0			0
$881$	45.9967			1.54967			0.774835	−	0.632164i	$-0.217833\pi$
$881$	45.9967			1.54967			0.774835	+	0.632164i	$0.217833\pi$
$882$		0			0
$883$	−32.9384			−1.10847			−0.554233	−	0.832361i	$-0.686988\pi$
$883$	−32.9384			−1.10847			−0.554233	+	0.832361i	$0.686988\pi$
$884$		0			0
$885$	2.16703	+	5.65732i	0.0728438	+	0.190169i
$886$		0			0
$887$	−14.1699	+	24.5430i	−0.475779	+	0.824073i	−0.999615	−	0.0277459i	$-0.991167\pi$
$887$	−14.1699	+	24.5430i	−0.475779	+	0.824073i	0.523836	+	0.851819i	$0.324500\pi$
$888$		0			0
$889$	13.4669	−	48.3034i	0.451665	−	1.62004i
$890$		0			0
$891$	−44.5030	−	32.5271i	−1.49091	−	1.08970i
$892$		0			0
$893$	1.61273	+	2.79332i	0.0539678	+	0.0934750i
$894$		0			0
$895$	−7.77292	−	13.4631i	−0.259820	−	0.450021i
$896$		0			0
$897$	−0.349525	+	0.431001i	−0.0116703	+	0.0143907i
$898$		0			0
$899$	−5.64132	+	9.77104i	−0.188148	+	0.325883i
$900$		0			0
$901$	−0.771280	−	1.33590i	−0.0256951	−	0.0445052i
$902$		0			0
$903$	−39.5111	+	3.72160i	−1.31485	+	0.123847i
$904$		0			0
$905$	−1.17046	+	2.02730i	−0.0389074	+	0.0673896i
$906$		0			0
$907$	3.97373	+	6.88271i	0.131946	+	0.228537i	0.924427	−	0.381360i	$-0.124544\pi$
$907$	3.97373	+	6.88271i	0.131946	+	0.228537i	−0.792481	+	0.609897i	$0.791211\pi$
$908$		0			0
$909$	17.8815	−	16.0546i	0.593093	−	0.532498i
$910$		0			0
$911$	4.00808	−	6.94220i	0.132794	−	0.230005i	−0.791959	−	0.610575i	$-0.790939\pi$
$911$	4.00808	−	6.94220i	0.132794	−	0.230005i	0.924752	+	0.380569i	$0.124272\pi$
$912$		0			0
$913$	19.1384			0.633390
$914$		0			0
$915$	11.2918	+	29.4787i	0.373295	+	0.974537i
$916$		0			0
$917$	13.5056	+	13.7811i	0.445994	+	0.455090i
$918$		0			0
$919$	12.0224	+	20.8235i	0.396584	+	0.686903i	0.993302	−	0.115548i	$-0.0368623\pi$
$919$	12.0224	+	20.8235i	0.396584	+	0.686903i	−0.596718	+	0.802451i	$0.703529\pi$
$920$		0			0
$921$	5.34501	−	6.59095i	0.176124	−	0.217179i
$922$		0			0
$923$	4.10301	+	7.10662i	0.135052	+	0.233917i
$924$		0			0
$925$	−2.74037	+	4.74646i	−0.0901027	+	0.156062i
$926$		0			0
$927$	19.4737	+	6.35803i	0.639601	+	0.208825i
$928$		0			0
$929$	27.8662			0.914261			0.457130	−	0.889400i	$-0.348877\pi$
$929$	27.8662			0.914261			0.457130	+	0.889400i	$0.348877\pi$
$930$		0			0
$931$	−0.274550	+	13.5970i	−0.00899801	+	0.445623i
$932$		0			0
$933$	−8.38960	+	10.3452i	−0.274663	+	0.338688i
$934$		0			0
$935$	36.8960	−	63.9058i	1.20663	−	2.08994i
$936$		0			0
$937$	53.2211			1.73866			0.869328	−	0.494235i	$-0.164552\pi$
$937$	53.2211			1.73866			0.869328	+	0.494235i	$0.164552\pi$
$938$		0			0
$939$	1.87988	−	2.31809i	0.0613477	−	0.0756480i
$940$		0			0
$941$	−30.0482			−0.979542			−0.489771	−	0.871851i	$-0.662920\pi$
$941$	−30.0482			−0.979542			−0.489771	+	0.871851i	$0.662920\pi$
$942$		0			0
$943$	2.92339			0.0951987
$944$		0			0
$945$	7.19863	+	23.1130i	0.234171	+	0.751865i
$946$		0			0
$947$	39.6889			1.28972			0.644858	−	0.764302i	$-0.276916\pi$
$947$	39.6889			1.28972			0.644858	+	0.764302i	$0.276916\pi$
$948$		0			0
$949$	−0.233366			−0.00757538
$950$		0			0
$951$	−36.2233	+	44.6670i	−1.17462	+	1.44843i
$952$		0			0
$953$	23.0643			0.747126			0.373563	−	0.927605i	$-0.378136\pi$
$953$	23.0643			0.747126			0.373563	+	0.927605i	$0.378136\pi$
$954$		0			0
$955$	−14.2352	+	24.6560i	−0.460639	+	0.797850i
$956$		0			0
$957$	−9.78620	+	12.0674i	−0.316343	+	0.390083i
$958$		0			0
$959$	20.9653	−	5.39140i	0.677004	−	0.174097i
$960$		0			0
$961$	28.3469			0.914418
$962$		0			0
$963$	−7.91531	+	7.10662i	−0.255067	+	0.229008i
$964$		0			0
$965$	12.4743	−	21.6061i	0.401562	−	0.695525i
$966$		0			0
$967$	−15.2902	−	26.4833i	−0.491698	−	0.851646i	0.508256	−	0.861206i	$-0.330290\pi$
$967$	−15.2902	−	26.4833i	−0.491698	−	0.851646i	−0.999954	+	0.00955967i	$0.996957\pi$
$968$		0			0
$969$	−14.5023	+	17.8829i	−0.465882	+	0.574480i
$970$		0			0
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	0.575492	−	0.817807i	$-0.304810\pi$
$971$	−13.1030	−	22.6951i	−0.420496	−	0.728320i	−0.995988	+	0.0894874i	$0.971477\pi$
$972$		0			0
$973$	31.9390	−	8.21339i	1.02392	−	0.263309i
$974$		0			0
$975$	0.895355	+	2.33745i	0.0286743	+	0.0748582i
$976$		0			0
$977$	21.0539			0.673574			0.336787	−	0.941581i	$-0.390660\pi$
$977$	21.0539			0.673574			0.336787	+	0.941581i	$0.390660\pi$
$978$		0			0
$979$	−7.97141	+	13.8069i	−0.254767	+	0.441270i
$980$		0			0
$981$	−2.00684	−	0.655217i	−0.0640734	−	0.0209195i
$982$		0			0
$983$	−9.76483	−	16.9132i	−0.311450	−	0.539447i	0.667227	−	0.744855i	$-0.267481\pi$
$983$	−9.76483	−	16.9132i	−0.311450	−	0.539447i	−0.978676	+	0.205408i	$0.934148\pi$
$984$		0			0
$985$	−13.9480	+	24.1587i	−0.444421	+	0.769760i
$986$		0			0
$987$	−4.40507	−	6.20292i	−0.140215	−	0.197441i
$988$		0			0
$989$	−1.82326	−	3.15798i	−0.0579762	−	0.100418i
$990$		0			0
$991$	7.49837	−	12.9875i	0.238193	−	0.412563i	−0.722003	−	0.691890i	$-0.756778\pi$
$991$	7.49837	−	12.9875i	0.238193	−	0.412563i	0.960196	+	0.279327i	$0.0901114\pi$
$992$		0			0
$993$	3.15172	−	3.88640i	0.100017	−	0.123331i
$994$		0			0
$995$	7.87360	+	13.6375i	0.249610	+	0.432337i
$996$		0			0
$997$	29.2821	+	50.7180i	0.927373	+	1.60626i	0.787700	+	0.616059i	$0.211272\pi$
$997$	29.2821	+	50.7180i	0.927373	+	1.60626i	0.139672	+	0.990198i	$0.455395\pi$
$998$		0			0
$999$	0.752796	+	14.9753i	0.0238174	+	0.473798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.h.529.1		6
3.2	odd	2		3024.2.q.h.2881.2		6
4.3	odd	2		126.2.e.d.25.3	✓	6
7.2	even	3		1008.2.t.g.961.2		6
9.4	even	3		1008.2.t.g.193.2		6
9.5	odd	6		3024.2.t.g.1873.2		6
12.11	even	2		378.2.e.c.235.2		6
21.2	odd	6		3024.2.t.g.289.2		6
28.3	even	6		882.2.f.m.295.3		6
28.11	odd	6		882.2.f.l.295.1		6
28.19	even	6		882.2.h.o.79.2		6
28.23	odd	6		126.2.h.c.79.2	yes	6
28.27	even	2		882.2.e.p.655.1		6
36.7	odd	6		1134.2.g.k.487.2		6
36.11	even	6		1134.2.g.n.487.2		6
36.23	even	6		378.2.h.d.361.2		6
36.31	odd	6		126.2.h.c.67.2	yes	6
63.23	odd	6		3024.2.q.h.2305.2		6
63.58	even	3	inner	1008.2.q.h.625.1		6
84.11	even	6		2646.2.f.o.883.2		6
84.23	even	6		378.2.h.d.289.2		6
84.47	odd	6		2646.2.h.p.667.2		6
84.59	odd	6		2646.2.f.n.883.2		6
84.83	odd	2		2646.2.e.o.2125.2		6
252.11	even	6		7938.2.a.bu.1.2		3
252.23	even	6		378.2.e.c.37.2		6
252.31	even	6		882.2.f.m.589.3		6
252.59	odd	6		2646.2.f.n.1765.2		6
252.67	odd	6		882.2.f.l.589.1		6
252.79	odd	6		1134.2.g.k.163.2		6
252.95	even	6		2646.2.f.o.1765.2		6
252.103	even	6		882.2.e.p.373.1		6
252.115	even	6		7938.2.a.by.1.2		3
252.131	odd	6		2646.2.e.o.1549.2		6
252.139	even	6		882.2.h.o.67.2		6
252.151	odd	6		7938.2.a.cb.1.2		3
252.167	odd	6		2646.2.h.p.361.2		6
252.191	even	6		1134.2.g.n.163.2		6
252.227	odd	6		7938.2.a.bx.1.2		3
252.247	odd	6		126.2.e.d.121.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	4.3	odd	2
126.2.e.d.121.3	yes	6	252.247	odd	6
126.2.h.c.67.2	yes	6	36.31	odd	6
126.2.h.c.79.2	yes	6	28.23	odd	6
378.2.e.c.37.2		6	252.23	even	6
378.2.e.c.235.2		6	12.11	even	2
378.2.h.d.289.2		6	84.23	even	6
378.2.h.d.361.2		6	36.23	even	6
882.2.e.p.373.1		6	252.103	even	6
882.2.e.p.655.1		6	28.27	even	2
882.2.f.l.295.1		6	28.11	odd	6
882.2.f.l.589.1		6	252.67	odd	6
882.2.f.m.295.3		6	28.3	even	6
882.2.f.m.589.3		6	252.31	even	6
882.2.h.o.67.2		6	252.139	even	6
882.2.h.o.79.2		6	28.19	even	6
1008.2.q.h.529.1		6	1.1	even	1	trivial
1008.2.q.h.625.1		6	63.58	even	3	inner
1008.2.t.g.193.2		6	9.4	even	3
1008.2.t.g.961.2		6	7.2	even	3
1134.2.g.k.163.2		6	252.79	odd	6
1134.2.g.k.487.2		6	36.7	odd	6
1134.2.g.n.163.2		6	252.191	even	6
1134.2.g.n.487.2		6	36.11	even	6
2646.2.e.o.1549.2		6	252.131	odd	6
2646.2.e.o.2125.2		6	84.83	odd	2
2646.2.f.n.883.2		6	84.59	odd	6
2646.2.f.n.1765.2		6	252.59	odd	6
2646.2.f.o.883.2		6	84.11	even	6
2646.2.f.o.1765.2		6	252.95	even	6
2646.2.h.p.361.2		6	252.167	odd	6
2646.2.h.p.667.2		6	84.47	odd	6
3024.2.q.h.2305.2		6	63.23	odd	6
3024.2.q.h.2881.2		6	3.2	odd	2
3024.2.t.g.289.2		6	21.2	odd	6
3024.2.t.g.1873.2		6	9.5	odd	6
7938.2.a.bu.1.2		3	252.11	even	6
7938.2.a.bx.1.2		3	252.227	odd	6
7938.2.a.by.1.2		3	252.115	even	6
7938.2.a.cb.1.2		3	252.151	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09097 + 1.34528i) q^{3} +(-0.880438 + 1.52496i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})\)	\(q+(-1.09097 + 1.34528i) q^{3} +(-0.880438 + 1.52496i) q^{5} +(0.710533 - 2.54856i) q^{7} +(-0.619562 - 2.93533i) q^{9} +(3.06238 + 5.30420i) q^{11} +(-0.380438 - 0.658939i) q^{13} +(-1.09097 - 2.84813i) q^{15} +(-3.42107 + 5.92546i) q^{17} +(-0.971410 - 1.68253i) q^{19} +(2.65335 + 3.73627i) q^{21} +(-0.210533 + 0.364654i) q^{23} +(0.949657 + 1.64485i) q^{25} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} -7.70370 q^{31} +(-10.4766 - 1.66697i) q^{33} +(3.26088 + 3.32738i) q^{35} +(1.44282 + 2.49904i) q^{37} +(1.30150 + 0.207087i) q^{39} +(-3.47141 - 6.01266i) q^{41} +(-4.33009 + 7.49994i) q^{43} +(5.02175 + 1.63957i) q^{45} -1.66019 q^{47} +(-5.99028 - 3.62167i) q^{49} +(-4.23912 - 11.0668i) q^{51} +(-0.112725 + 0.195246i) q^{53} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} -1.98633 q^{59} -10.3502 q^{61} +(-7.92107 - 0.506659i) q^{63} +1.33981 q^{65} -6.78495 q^{67} +(-0.260877 - 0.681054i) q^{69} -10.7850 q^{71} +(0.153353 - 0.265616i) q^{73} +(-3.24884 - 0.516934i) q^{75} +(15.6940 - 4.03584i) q^{77} +13.4451 q^{79} +(-8.23229 + 3.63723i) q^{81} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(0.907394 + 2.36887i) q^{87} +(1.30150 + 2.25427i) q^{89} +(-1.94966 + 0.501371i) q^{91} +(8.40451 - 10.3636i) q^{93} +3.42107 q^{95} +(-1.81806 + 3.14897i) q^{97} +(13.6722 - 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9	\( 6 q + 2 q^{3} - 5 q^{5} - 4 q^{7} - 4 q^{9} + q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 10 q^{21} + 7 q^{23} - 2 q^{25} - 7 q^{27} - 5 q^{29} - 28 q^{31} - 19 q^{33} + 19 q^{35} - 9 q^{37} - 9 q^{39} - 12 q^{41} - 18 q^{43} + 29 q^{45} + 6 q^{47} - 12 q^{49} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} + 8 q^{59} - 8 q^{61} - 31 q^{63} + 24 q^{65} + 10 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} - 44 q^{75} + 52 q^{77} + 14 q^{79} - 40 q^{81} - 8 q^{83} + 14 q^{85} - 31 q^{87} - 9 q^{89} - 4 q^{91} + 4 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 - 5 * q^5 - 4 * q^7 - 4 * q^9 + q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 10 * q^21 + 7 * q^23 - 2 * q^25 - 7 * q^27 - 5 * q^29 - 28 * q^31 - 19 * q^33 + 19 * q^35 - 9 * q^37 - 9 * q^39 - 12 * q^41 - 18 * q^43 + 29 * q^45 + 6 * q^47 - 12 * q^49 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 + 8 * q^59 - 8 * q^61 - 31 * q^63 + 24 * q^65 + 10 * q^67 - q^69 - 14 * q^71 - 25 * q^73 - 44 * q^75 + 52 * q^77 + 14 * q^79 - 40 * q^81 - 8 * q^83 + 14 * q^85 - 31 * q^87 - 9 * q^89 - 4 * q^91 + 4 * q^95 - 28 * q^97 + 41 * q^99

Introduction

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