LMFDB - Embedded newform 1008.2.t.g.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (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			961.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.g.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})$	\(q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} -6.12476 q^{11} +(-0.380438 - 0.658939i) q^{13} +(-1.09097 - 2.84813i) q^{15} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-4.20370 - 1.82454i) q^{21} +0.421067 q^{23} -1.89931 q^{25} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(3.79467 + 9.90650i) q^{33} +(3.26088 - 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(-0.830095 + 1.02359i) q^{39} +(-3.47141 - 6.01266i) q^{41} +(-4.33009 + 7.49994i) q^{43} +(-3.93078 + 3.52918i) q^{45} +(0.830095 + 1.43777i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(-7.46457 + 9.20459i) q^{51} +(-0.112725 - 0.195246i) q^{53} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} +(0.993163 - 1.72021i) q^{59} +(5.17511 + 8.96355i) q^{61} +(-0.346647 + 7.92968i) q^{63} +(-0.669905 - 1.16031i) q^{65} +(3.39248 - 5.87594i) q^{67} +(-0.260877 - 0.681054i) q^{69} -10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(1.17674 + 3.07204i) q^{75} +(-11.3421 + 11.5735i) q^{77} +(-6.72257 - 11.6438i) q^{79} +(0.966208 - 8.94799i) q^{81} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-2.50520 - 0.398611i) q^{87} +(1.30150 - 2.25427i) q^{89} +(-1.94966 - 0.501371i) q^{91} +(-13.1774 - 2.09671i) q^{93} +(-1.71053 + 2.96273i) q^{95} +(-1.81806 + 3.14897i) q^{97} +(13.6722 - 12.2754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9	$ 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$4$		0			0
$5$	1.76088			0.787488			0.393744	−	0.919220i	$-0.371180\pi$
$5$	1.76088			0.787488			0.393744	+	0.919220i	$0.371180\pi$
$6$		0			0
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$		0			0
$9$	−2.23229	+	2.00422i	−0.744096	+	0.668073i
$10$		0			0
$11$	−6.12476			−1.84669			−0.923343	−	0.383977i	$-0.874554\pi$
$11$	−6.12476			−1.84669			−0.923343	+	0.383977i	$0.874554\pi$
$12$		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	−0.898250	−	0.439486i	$-0.855161\pi$
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	0.0685191	−	0.997650i	$-0.478173\pi$
$18$		0			0
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	−0.955674	−	0.294426i	$-0.904872\pi$
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	0.732818	+	0.680425i	$0.238205\pi$
$20$		0			0
$21$	−4.20370	−	1.82454i	−0.917322	−	0.398147i
$22$		0			0
$23$	0.421067			0.0877985			0.0438992	−	0.999036i	$-0.486022\pi$
$23$	0.421067			0.0877985			0.0438992	+	0.999036i	$0.486022\pi$
$24$		0			0
$25$	−1.89931			−0.379863
$26$		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
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	−0.279431	−	0.960166i	$-0.590146\pi$
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	0.971243	−	0.238088i	$-0.0765208\pi$
$32$		0			0
$33$	3.79467	+	9.90650i	0.660567	+	1.72450i
$34$		0			0
$35$	3.26088	−	3.32738i	0.551189	−	0.562431i
$36$		0			0
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	−0.722711	−	0.691150i	$-0.757104\pi$
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	0.959909	+	0.280311i	$0.0904376\pi$
$38$		0			0
$39$	−0.830095	+	1.02359i	−0.132922	+	0.163906i
$40$		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
$45$	−3.93078	+	3.52918i	−0.585966	+	0.526100i
$46$		0			0
$47$	0.830095	+	1.43777i	0.121082	+	0.209720i	0.920195	−	0.391461i	$-0.128030\pi$
$47$	0.830095	+	1.43777i	0.121082	+	0.209720i	−0.799113	+	0.601181i	$0.794697\pi$
$48$		0			0
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$		0			0
$51$	−7.46457	+	9.20459i	−1.04525	+	1.28890i
$52$		0			0
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	0.858180	−	0.513350i	$-0.171596\pi$
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	−0.873664	+	0.486531i	$0.838262\pi$
$54$		0			0
$55$	−10.7850			−1.45424
$56$		0			0
$57$	3.32326	+	0.528775i	0.440176	+	0.0700379i
$58$		0			0
$59$	0.993163	−	1.72021i	0.129299	−	0.223952i	−0.794106	−	0.607779i	$-0.792061\pi$
$59$	0.993163	−	1.72021i	0.129299	−	0.223952i	0.923405	+	0.383827i	$0.125394\pi$
$60$		0			0
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	0.979929	+	0.199348i	$0.0638823\pi$
$61$	5.17511	+	8.96355i	0.662605	+	1.14766i	−0.317324	+	0.948317i	$0.602784\pi$
$62$		0			0
$63$	−0.346647	+	7.92968i	−0.0436734	+	0.999046i
$64$		0			0
$65$	−0.669905	−	1.16031i	−0.0830915	−	0.143919i
$66$		0			0
$67$	3.39248	−	5.87594i	0.414457	−	0.717861i	−0.580914	−	0.813965i	$-0.697305\pi$
$67$	3.39248	−	5.87594i	0.414457	−	0.717861i	0.995371	+	0.0961042i	$0.0306382\pi$
$68$		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	0.874860	−	0.484375i	$-0.160953\pi$
$73$	0.153353	+	0.265616i	0.0179487	+	0.0310880i	−0.856912	+	0.515463i	$0.827620\pi$
$74$		0			0
$75$	1.17674	+	3.07204i	0.135878	+	0.354729i
$76$		0			0
$77$	−11.3421	+	11.5735i	−1.29256	+	1.31892i
$78$		0			0
$79$	−6.72257	−	11.6438i	−0.756348	−	1.31003i	−0.944701	−	0.327932i	$-0.893648\pi$
$79$	−6.72257	−	11.6438i	−0.756348	−	1.31003i	0.188353	−	0.982101i	$-0.439685\pi$
$80$		0			0
$81$	0.966208	−	8.94799i	0.107356	−	0.994221i
$82$		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
$87$	−2.50520	−	0.398611i	−0.268586	−	0.0427356i
$88$		0			0
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	−0.788765	−	0.614695i	$-0.789279\pi$
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	0.926724	+	0.375743i	$0.122612\pi$
$90$		0			0
$91$	−1.94966	−	0.501371i	−0.204380	−	0.0525580i
$92$		0			0
$93$	−13.1774	−	2.09671i	−1.36644	−	0.217418i
$94$		0			0
$95$	−1.71053	+	2.96273i	−0.175497	+	0.303970i
$96$		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
$101$	−8.01040			−0.797065			−0.398532	−	0.917154i	$-0.630480\pi$
$101$	−8.01040			−0.797065			−0.398532	+	0.917154i	$0.630480\pi$
$102$		0			0
$103$	6.82846			0.672828			0.336414	−	0.941714i	$-0.390786\pi$
$103$	6.82846			0.672828			0.336414	+	0.941714i	$0.390786\pi$
$104$		0			0
$105$	−7.40219	−	3.21278i	−0.722380	−	0.313536i
$106$		0			0
$107$	−1.77292	+	3.07078i	−0.171394	+	0.296863i	−0.938908	−	0.344170i	$-0.888160\pi$
$107$	−1.77292	+	3.07078i	−0.171394	+	0.296863i	0.767513	+	0.641033i	$0.221494\pi$
$108$		0			0
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	0.882384	−	0.470530i	$-0.155937\pi$
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	−0.848683	+	0.528902i	$0.822604\pi$
$110$		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
$115$	0.741446			0.0691402
$116$		0			0
$117$	2.16991	+	0.708458i	0.200608	+	0.0654970i
$118$		0			0
$119$	−17.5322	−	4.50855i	−1.60717	−	0.413298i
$120$		0			0
$121$	26.5127			2.41025
$122$		0			0
$123$	−7.57442	+	9.34004i	−0.682962	+	0.842163i
$124$		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
$129$	14.8135	+	2.35703i	1.30426	+	0.207525i
$130$		0			0
$131$	7.29303			0.637195			0.318598	−	0.947890i	$-0.396788\pi$
$131$	7.29303			0.637195			0.318598	+	0.947890i	$0.396788\pi$
$132$		0			0
$133$	1.38044	+	4.95139i	0.119699	+	0.429340i
$134$		0			0
$135$	8.14364	+	4.17129i	0.700893	+	0.359008i
$136$		0			0
$137$	−8.18194			−0.699031			−0.349515	−	0.936931i	$-0.613654\pi$
$137$	−8.18194			−0.699031			−0.349515	+	0.936931i	$0.613654\pi$
$138$		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
$147$	−11.2323	+	4.56462i	−0.926423	+	0.376483i
$148$		0			0
$149$	8.82846			0.723256			0.361628	−	0.932323i	$-0.382221\pi$
$149$	8.82846			0.723256			0.361628	+	0.932323i	$0.382221\pi$
$150$		0			0
$151$	14.9863			1.21957			0.609785	−	0.792567i	$-0.291256\pi$
$151$	14.9863			1.21957			0.609785	+	0.792567i	$0.291256\pi$
$152$		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
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	0.186761	+	0.982405i	$0.440201\pi$
$157$	−9.49028	+	16.4377i	−0.757407	+	1.31187i	−0.944169	+	0.329462i	$0.893132\pi$
$158$		0			0
$159$	−0.245960	+	0.303294i	−0.0195059	+	0.0240528i
$160$		0			0
$161$	0.779752	−	0.795655i	0.0614530	−	0.0627064i
$162$		0			0
$163$	7.51887	−	13.0231i	0.588924	−	1.02005i	−0.405450	−	0.914117i	$-0.632885\pi$
$163$	7.51887	−	13.0231i	0.588924	−	1.02005i	0.994374	−	0.105929i	$-0.0337815\pi$
$164$		0			0
$165$	6.68194	+	17.4441i	0.520189	+	1.35802i
$166$		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
$171$	−1.20370	−	5.70281i	−0.0920490	−	0.436105i
$172$		0			0
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	0.856411	−	0.516295i	$-0.172689\pi$
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	−0.875330	+	0.483526i	$0.839356\pi$
$174$		0			0
$175$	−3.51724	+	3.58898i	−0.265878	+	0.271301i
$176$		0			0
$177$	−3.39768	−	0.540616i	−0.255385	−	0.0406352i
$178$		0			0
$179$	−4.41423	−	7.64567i	−0.329935	−	0.571464i	0.652564	−	0.757734i	$-0.273694\pi$
$179$	−4.41423	−	7.64567i	−0.329935	−	0.571464i	−0.982499	+	0.186270i	$0.940360\pi$
$180$		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
$185$	2.54063	−	4.40050i	0.186791	−	0.323531i
$186$		0			0
$187$	20.9532	+	36.2920i	1.53225	+	2.65394i
$188$		0			0
$189$	13.0406	−	4.35224i	0.948566	−	0.316579i
$190$		0			0
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	−0.994882	−	0.101044i	$-0.967782\pi$
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	0.409934	−	0.912115i	$-0.365552\pi$
$192$		0			0
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	−0.490007	−	0.871719i	$-0.663006\pi$
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	0.999934	−	0.0115011i	$-0.00366101\pi$
$194$		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	0.979854	−	0.199714i	$-0.0640013\pi$
$199$	4.47141	+	7.74471i	0.316970	+	0.549008i	−0.662884	+	0.748722i	$0.730668\pi$
$200$		0			0
$201$	−11.6059	−	1.84665i	−0.818616	−	0.130253i
$202$		0			0
$203$	−1.04063	−	3.73255i	−0.0730378	−	0.261974i
$204$		0			0
$205$	−6.11273	−	10.5876i	−0.426931	−	0.739467i
$206$		0			0
$207$	−0.939941	+	0.843910i	−0.0653304	+	0.0586558i
$208$		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
$213$	6.68194	+	17.4441i	0.457839	+	1.19525i
$214$		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
$219$	0.334608	−	0.412607i	0.0226107	−	0.0278814i
$220$		0			0
$221$	−2.60301	+	4.50855i	−0.175097	+	0.303278i
$222$		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
$227$	−21.9967			−1.45997			−0.729987	−	0.683461i	$-0.760474\pi$
$227$	−21.9967			−1.45997			−0.729987	+	0.683461i	$0.760474\pi$
$228$		0			0
$229$	−3.79863			−0.251020			−0.125510	−	0.992092i	$-0.540057\pi$
$229$	−3.79863			−0.251020			−0.125510	+	0.992092i	$0.540057\pi$
$230$		0			0
$231$	25.7466	+	11.1749i	1.69401	+	0.735251i
$232$		0			0
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	−0.954350	−	0.298689i	$-0.903451\pi$
$233$	−3.33530	+	5.77690i	−0.218503	+	0.378458i	0.735848	+	0.677147i	$0.236784\pi$
$234$		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
$241$	21.4120			1.37927			0.689635	−	0.724157i	$-0.257771\pi$
$241$	21.4120			1.37927			0.689635	+	0.724157i	$0.257771\pi$
$242$		0			0
$243$	−15.0715	+	3.98104i	−0.966840	+	0.255384i
$244$		0			0
$245$	−0.248838	−	12.3236i	−0.0158977	−	0.787328i
$246$		0			0
$247$	1.47825			0.0940586
$248$		0			0
$249$	−5.34501	−	0.850463i	−0.338726	−	0.0538959i
$250$		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
$255$	−13.1442	+	16.2082i	−0.823121	+	1.01499i
$256$		0			0
$257$	20.2599			1.26378			0.631890	−	0.775058i	$-0.282279\pi$
$257$	20.2599			1.26378			0.631890	+	0.775058i	$0.282279\pi$
$258$		0			0
$259$	−2.05034	−	7.35422i	−0.127402	−	0.456969i
$260$		0			0
$261$	0.907394	+	4.29900i	0.0561663	+	0.266102i
$262$		0			0
$263$	22.4887			1.38671			0.693355	−	0.720596i	$-0.256132\pi$
$263$	22.4887			1.38671			0.693355	+	0.720596i	$0.256132\pi$
$264$		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	−0.936167	−	0.351556i	$-0.885653\pi$
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	0.163627	−	0.986522i	$-0.447681\pi$
$270$		0			0
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	−0.577866	−	0.816132i	$-0.696114\pi$
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	0.995724	+	0.0923810i	$0.0294478\pi$
$272$		0			0
$273$	0.396990	+	3.46410i	0.0240269	+	0.209657i
$274$		0			0
$275$	11.6328			0.701487
$276$		0			0
$277$	−3.28263			−0.197234			−0.0986171	−	0.995125i	$-0.531442\pi$
$277$	−3.28263			−0.197234			−0.0986171	+	0.995125i	$0.531442\pi$
$278$		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
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	−0.961707	−	0.274081i	$-0.911626\pi$
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	0.718214	+	0.695822i	$0.244960\pi$
$284$		0			0
$285$	5.85185	+	0.931107i	0.346634	+	0.0551540i
$286$		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
$291$	6.21969	+	0.989636i	0.364605	+	0.0580135i
$292$		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
$297$	−28.3256	−	14.5088i	−1.64362	−	0.841886i
$298$		0			0
$299$	−0.160190	−	0.277457i	−0.00926402	−	0.0160458i
$300$		0			0
$301$	6.15335	+	22.0710i	0.354673	+	1.27215i
$302$		0			0
$303$	4.96294	+	12.9564i	0.285113	+	0.744327i
$304$		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
$311$	−3.84501	+	6.65976i	−0.218031	+	0.377640i	−0.954206	−	0.299151i	$-0.903297\pi$
$311$	−3.84501	+	6.65976i	−0.218031	+	0.377640i	0.736175	+	0.676791i	$0.236630\pi$
$312$		0			0
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	0.889347	−	0.457233i	$-0.151159\pi$
$313$	0.861564	+	1.49227i	0.0486985	+	0.0843482i	−0.840649	+	0.541581i	$0.817826\pi$
$314$		0			0
$315$	−0.610402	+	13.9632i	−0.0343923	+	0.786737i
$316$		0			0
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.779161	−	0.626824i	$-0.784354\pi$
$317$	−16.6014	−	28.7544i	−0.932426	−	1.61501i	−0.153266	−	0.988185i	$-0.548979\pi$
$318$		0			0
$319$	−4.48508	+	7.76839i	−0.251116	+	0.434946i
$320$		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
$327$	0.767713	−	0.946670i	0.0424546	−	0.0523510i
$328$		0			0
$329$	4.25404	+	1.09396i	0.234533	+	0.0603121i
$330$		0			0
$331$	1.44445	+	2.50187i	0.0793944	+	0.137515i	0.902989	−	0.429664i	$-0.141368\pi$
$331$	1.44445	+	2.50187i	0.0793944	+	0.137515i	−0.823594	+	0.567179i	$0.808035\pi$
$332$		0			0
$333$	1.78783	+	8.47030i	0.0979726	+	0.464169i
$334$		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
$339$	9.27579	−	11.4380i	0.503792	−	0.621228i
$340$		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
$345$	−0.459372	−	1.19925i	−0.0247317	−	0.0645656i
$346$		0			0
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	−0.706081	−	0.708131i	$-0.749539\pi$
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	0.966300	+	0.257419i	$0.0828720\pi$
$348$		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
$353$	−4.39372			−0.233854			−0.116927	−	0.993141i	$-0.537304\pi$
$353$	−4.39372			−0.233854			−0.116927	+	0.993141i	$0.537304\pi$
$354$		0			0
$355$	−18.9910			−1.00794
$356$		0			0
$357$	3.56991	+	31.1507i	0.188939	+	1.64867i
$358$		0			0
$359$	−16.0796	+	27.8507i	−0.848650	+	1.46990i	0.0337633	+	0.999430i	$0.489251\pi$
$359$	−16.0796	+	27.8507i	−0.848650	+	1.46990i	−0.882413	+	0.470475i	$0.844083\pi$
$360$		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
$367$	−34.6030			−1.80626			−0.903131	−	0.429365i	$-0.858738\pi$
$367$	−34.6030			−1.80626			−0.903131	+	0.429365i	$0.858738\pi$
$368$		0			0
$369$	19.7999	+	6.46451i	1.03074	+	0.336529i
$370$		0			0
$371$	−0.577690	−	0.148558i	−0.0299921	−	0.00771274i
$372$		0			0
$373$	10.9759			0.568312			0.284156	−	0.958778i	$-0.408287\pi$
$373$	10.9759			0.568312			0.284156	+	0.958778i	$0.408287\pi$
$374$		0			0
$375$	7.52696	+	19.6501i	0.388690	+	1.01473i
$376$		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
$381$	−11.7427	−	30.6559i	−0.601596	−	1.57055i
$382$		0			0
$383$	21.0241			1.07428			0.537140	−	0.843493i	$-0.319505\pi$
$383$	21.0241			1.07428			0.537140	+	0.843493i	$0.319505\pi$
$384$		0			0
$385$	−19.9721	+	20.3794i	−1.01787	+	1.03863i
$386$		0			0
$387$	−5.36552	−	25.4205i	−0.272745	−	1.29220i
$388$		0			0
$389$	13.7382			0.696553			0.348277	−	0.937392i	$-0.386767\pi$
$389$	13.7382			0.696553			0.348277	+	0.937392i	$0.386767\pi$
$390$		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	−0.941751	−	0.336311i	$-0.890821\pi$
$397$	−3.57893	+	6.19889i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$398$		0			0
$399$	7.15335	−	5.30048i	0.358116	−	0.265356i
$400$		0			0
$401$	−9.27936			−0.463389			−0.231695	−	0.972789i	$-0.574427\pi$
$401$	−9.27936			−0.463389			−0.231695	+	0.972789i	$0.574427\pi$
$402$		0			0
$403$	−5.86156			−0.291985
$404$		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
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	−0.990329	−	0.138741i	$-0.955695\pi$
$409$	−7.58414	+	13.1361i	−0.375011	+	0.649539i	0.615317	+	0.788279i	$0.289028\pi$
$410$		0			0
$411$	5.06922	+	13.2339i	0.250046	+	0.652779i
$412$		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
$417$	13.5985	−	16.7684i	0.665921	−	0.821150i
$418$		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
$423$	−4.73461	−	1.54581i	−0.230205	−	0.0751601i
$424$		0			0
$425$	6.49768	+	11.2543i	0.315184	+	0.545914i
$426$		0			0
$427$	26.5212	+	6.82015i	1.28345	+	0.330050i
$428$		0			0
$429$	5.08414	−	6.26926i	0.245464	−	0.302683i
$430$		0			0
$431$	1.72545	+	2.98857i	0.0831120	+	0.143954i	0.904585	−	0.426293i	$-0.140181\pi$
$431$	1.72545	+	2.98857i	0.0831120	+	0.143954i	−0.821473	+	0.570247i	$0.806847\pi$
$432$		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
$437$	−0.409028	+	0.708458i	−0.0195665	+	0.0338901i
$438$		0			0
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	−0.971978	−	0.235071i	$-0.924468\pi$
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	0.282412	−	0.959293i	$-0.408866\pi$
$440$		0			0
$441$	14.3421	+	15.3396i	0.682959	+	0.730457i
$442$		0			0
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	0.654995	−	0.755633i	$-0.272671\pi$
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	−0.981895	+	0.189426i	$0.939337\pi$
$444$		0			0
$445$	2.29179	−	3.96950i	0.108641	−	0.188172i
$446$		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
$453$	−9.28495	−	24.2396i	−0.436245	−	1.13888i
$454$		0			0
$455$	−3.43310	−	0.882853i	−0.160946	−	0.0413888i
$456$		0			0
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	0.530873	−	0.847451i	$-0.321864\pi$
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	−0.999351	+	0.0360237i	$0.988531\pi$
$458$		0			0
$459$	−1.78495	−	35.5079i	−0.0833145	−	1.65737i
$460$		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
$465$	−23.2038	−	3.69204i	−1.07605	−	0.171214i
$466$		0			0
$467$	5.61505	−	9.72555i	0.259833	−	0.450045i	−0.706364	−	0.707849i	$-0.749666\pi$
$467$	5.61505	−	9.72555i	0.259833	−	0.450045i	0.966197	+	0.257804i	$0.0829990\pi$
$468$		0			0
$469$	−4.82094	−	17.2918i	−0.222610	−	0.798463i
$470$		0			0
$471$	32.4669	+	5.16592i	1.49600	+	0.238033i
$472$		0			0
$473$	26.5208	−	45.9354i	1.21943	−	2.11211i
$474$		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
$479$	32.6271			1.49077			0.745385	−	0.666634i	$-0.232266\pi$
$479$	32.6271			1.49077			0.745385	+	0.666634i	$0.232266\pi$
$480$		0			0
$481$	−2.19562			−0.100111
$482$		0			0
$483$	−1.77004	−	0.768251i	−0.0805394	−	0.0349566i
$484$		0			0
$485$	−3.20137	+	5.54494i	−0.145367	+	0.251783i
$486$		0			0
$487$	−1.84897	−	3.20251i	−0.0837848	−	0.145120i	0.821088	−	0.570802i	$-0.193368\pi$
$487$	−1.84897	−	3.20251i	−0.0837848	−	0.145120i	−0.904873	+	0.425682i	$0.860034\pi$
$488$		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
$493$	−10.0208			−0.451314
$494$		0			0
$495$	24.0751	−	21.6154i	1.08210	−	0.971541i
$496$		0			0
$497$	−19.9721	+	20.3794i	−0.895871	+	0.914143i
$498$		0			0
$499$	31.7954			1.42336			0.711678	−	0.702506i	$-0.247936\pi$
$499$	31.7954			1.42336			0.711678	+	0.702506i	$0.247936\pi$
$500$		0			0
$501$	−1.24828	+	1.53926i	−0.0557692	+	0.0687692i
$502$		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
$507$	−21.2466	−	3.38063i	−0.943597	−	0.150139i
$508$		0			0
$509$	8.01616			0.355310			0.177655	−	0.984093i	$-0.443149\pi$
$509$	8.01616			0.355310			0.177655	+	0.984093i	$0.443149\pi$
$510$		0			0
$511$	0.785900	+	0.202101i	0.0347662	+	0.00894042i
$512$		0			0
$513$	−8.47825	+	5.48016i	−0.374324	+	0.241955i
$514$		0			0
$515$	12.0241			0.529844
$516$		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	0.982825	+	0.184540i	$0.0590795\pi$
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	−0.331596	+	0.943421i	$0.607587\pi$
$522$		0			0
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	0.405373	+	0.914152i	$0.367142\pi$
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	−0.994365	+	0.106013i	$0.966192\pi$
$524$		0			0
$525$	7.98414	+	3.46537i	0.348456	+	0.151241i
$526$		0			0
$527$	−52.7097			−2.29607
$528$		0			0
$529$	−22.8227			−0.992291
$530$		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
$535$	−3.12188	+	5.40726i	−0.134971	+	0.233776i
$536$		0			0
$537$	−9.63160	+	11.8768i	−0.415634	+	0.512520i
$538$		0			0
$539$	0.865521	+	42.8646i	0.0372806	+	1.84631i
$540$		0			0
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	−0.670201	−	0.742180i	$-0.733792\pi$
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	0.977847	+	0.209321i	$0.0671252\pi$
$542$		0			0
$543$	−0.823649	−	2.15025i	−0.0353462	−	0.0922760i
$544$		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
$549$	−29.5172	−	9.63716i	−1.25977	−	0.411304i
$550$		0			0
$551$	1.42270	+	2.46419i	0.0606091	+	0.104978i
$552$		0			0
$553$	−34.4516	−	8.85952i	−1.46503	−	0.376745i
$554$		0			0
$555$	−8.69166	−	1.38296i	−0.368940	−	0.0587033i
$556$		0			0
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	0.990283	−	0.139067i	$-0.0444103\pi$
$557$	8.84338	+	15.3172i	0.374706	+	0.649010i	−0.615577	+	0.788077i	$0.711077\pi$
$558$		0			0
$559$	6.58934			0.278699
$560$		0			0
$561$	45.7187	−	56.3759i	1.93025	−	2.38019i
$562$		0			0
$563$	0.468531	−	0.811520i	0.0197462	−	0.0342015i	−0.855983	−	0.517003i	$-0.827048\pi$
$563$	0.468531	−	0.811520i	0.0197462	−	0.0342015i	0.875730	+	0.482802i	$0.160381\pi$
$564$		0			0
$565$	7.48577	+	12.9657i	0.314929	+	0.545473i
$566$		0			0
$567$	−15.1190	−	18.3961i	−0.634939	−	0.772563i
$568$		0			0
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	0.506830	−	0.862046i	$-0.330817\pi$
$569$	−11.7632	−	20.3745i	−0.493139	−	0.854142i	−0.999969	+	0.00790437i	$0.997484\pi$
$570$		0			0
$571$	−0.242002	+	0.419160i	−0.0101275	+	0.0175413i	−0.871045	−	0.491204i	$-0.836557\pi$
$571$	−0.242002	+	0.419160i	−0.0101275	+	0.0175413i	0.860917	+	0.508745i	$0.169890\pi$
$572$		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	0.815852	−	0.578261i	$-0.196269\pi$
$577$	−2.23065	−	3.86360i	−0.0928633	−	0.160844i	−0.908715	+	0.417417i	$0.862935\pi$
$578$		0			0
$579$	−24.2353	−	3.85616i	−1.00718	−	0.160257i
$580$		0			0
$581$	−2.22025	−	7.96364i	−0.0921114	−	0.330387i
$582$		0			0
$583$	0.690415	+	1.19583i	0.0285941	+	0.0495264i
$584$		0			0
$585$	3.82094	+	1.24751i	0.157976	+	0.0515781i
$586$		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
$591$	−9.81518	−	25.6239i	−0.403742	−	1.05402i
$592$		0			0
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	−0.0261726	−	0.999657i	$-0.508332\pi$
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	0.878815	−	0.477163i	$-0.158335\pi$
$594$		0			0
$595$	−30.8720	−	7.93899i	−1.26563	−	0.325467i
$596$		0			0
$597$	9.75636	−	12.0306i	0.399301	−	0.492380i
$598$		0			0
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	−0.669919	−	0.742434i	$-0.733671\pi$
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	0.977926	+	0.208950i	$0.0670047\pi$
$600$		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
$605$	46.6856			1.89804
$606$		0			0
$607$	−19.5732			−0.794451			−0.397225	−	0.917721i	$-0.630027\pi$
$607$	−19.5732			−0.794451			−0.397225	+	0.917721i	$0.630027\pi$
$608$		0			0
$609$	−5.39248	+	3.99571i	−0.218514	+	0.161914i
$610$		0			0
$611$	0.631600	−	1.09396i	0.0255518	−	0.0442570i
$612$		0			0
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	0.804509	−	0.593941i	$-0.202429\pi$
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	−0.916622	+	0.399755i	$0.869095\pi$
$614$		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
$619$	−4.50232			−0.180964			−0.0904818	−	0.995898i	$-0.528841\pi$
$619$	−4.50232			−0.180964			−0.0904818	+	0.995898i	$0.528841\pi$
$620$		0			0
$621$	1.94733	+	0.997454i	0.0781438	+	0.0400264i
$622$		0			0
$623$	−1.84953	−	6.63392i	−0.0740997	−	0.265782i
$624$		0			0
$625$	−11.8960			−0.475842
$626$		0			0
$627$	−20.3542	−	3.23862i	−0.812867	−	0.129338i
$628$		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
$633$	−24.8428	+	30.6338i	−0.987414	+	1.21758i
$634$		0			0
$635$	33.3743			1.32442
$636$		0			0
$637$	−4.55787	+	2.75564i	−0.180589	+	0.109183i
$638$		0			0
$639$	24.0751	−	21.6154i	0.952397	−	0.855093i
$640$		0			0
$641$	−0.948577			−0.0374666			−0.0187333	−	0.999825i	$-0.505963\pi$
$641$	−0.948577			−0.0374666			−0.0187333	+	0.999825i	$0.505963\pi$
$642$		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	0.537974	−	0.842962i	$-0.319190\pi$
$647$	−11.7271	−	20.3119i	−0.461039	−	0.798543i	−0.999013	+	0.0444181i	$0.985857\pi$
$648$		0			0
$649$	−6.08289	+	10.5359i	−0.238774	+	0.413569i
$650$		0			0
$651$	−28.3646	+	21.0175i	−1.11170	+	0.823742i
$652$		0			0
$653$	22.7907			0.891869			0.445935	−	0.895065i	$-0.352871\pi$
$653$	22.7907			0.891869			0.445935	+	0.895065i	$0.352871\pi$
$654$		0			0
$655$	12.8421			0.501784
$656$		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
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	−0.479732	−	0.877415i	$-0.659266\pi$
$661$	13.3691	−	23.1559i	0.519997	−	0.900662i	0.999730	−	0.0232469i	$-0.00740038\pi$
$662$		0			0
$663$	8.90507	+	1.41692i	0.345844	+	0.0550284i
$664$		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
$669$	−22.0413	−	3.50707i	−0.852167	−	0.135591i
$670$		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
$675$	−8.78387	−	4.49923i	−0.338091	−	0.173176i
$676$		0			0
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	0.993447	−	0.114293i	$-0.0364602\pi$
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	−0.595704	+	0.803204i	$0.703127\pi$
$678$		0			0
$679$	2.58358	+	9.26684i	0.0991487	+	0.355629i
$680$		0			0
$681$	13.6283	+	35.5786i	0.522239	+	1.36338i
$682$		0			0
$683$	−14.2918	−	24.7541i	−0.546860	−	0.947190i	−0.998487	−	0.0549828i	$-0.982490\pi$
$683$	−14.2918	−	24.7541i	−0.546860	−	0.947190i	0.451627	−	0.892207i	$-0.350844\pi$
$684$		0			0
$685$	−14.4074			−0.550478
$686$		0			0
$687$	2.35348	+	6.14409i	0.0897910	+	0.234412i
$688$		0			0
$689$	−0.0857699	+	0.148558i	−0.00326757	+	0.00565960i
$690$		0			0
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	0.795268	−	0.606258i	$-0.207330\pi$
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	−0.922669	+	0.385593i	$0.873997\pi$
$692$		0			0
$693$	2.12313	−	48.5674i	0.0806510	−	1.84492i
$694$		0			0
$695$	10.9743	+	19.0080i	0.416278	+	0.721016i
$696$		0			0
$697$	−23.7518	+	41.1394i	−0.899665	+	1.55827i
$698$		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
$705$	3.18934	−	3.93278i	0.120117	−	0.148117i
$706$		0			0
$707$	−14.8341	+	15.1366i	−0.557892	+	0.569271i
$708$		0			0
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	0.770694	−	0.637205i	$-0.219910\pi$
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	−0.937183	+	0.348838i	$0.886576\pi$
$710$		0			0
$711$	38.3435	+	12.5189i	1.43799	+	0.469494i
$712$		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
$717$	17.0636	−	21.0412i	0.637253	−	0.785799i
$718$		0			0
$719$	−11.8015	+	20.4408i	−0.440122	+	0.762313i	−0.997698	−	0.0678123i	$-0.978398\pi$
$719$	−11.8015	+	20.4408i	−0.440122	+	0.762313i	0.557576	+	0.830126i	$0.311731\pi$
$720$		0			0
$721$	12.6453	−	12.9032i	0.470935	−	0.480540i
$722$		0			0
$723$	−13.2661	−	34.6329i	−0.493371	−	1.28801i
$724$		0			0
$725$	−1.39084	+	2.40901i	−0.0516546	+	0.0894683i
$726$		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
$731$	59.2542			2.19159
$732$		0			0
$733$	−23.1981			−0.856842			−0.428421	−	0.903579i	$-0.640930\pi$
$733$	−23.1981			−0.856842			−0.428421	+	0.903579i	$0.640930\pi$
$734$		0			0
$735$	−19.7787	+	8.03773i	−0.729547	+	0.296476i
$736$		0			0
$737$	−20.7781	+	35.9888i	−0.765372	+	1.32566i
$738$		0			0
$739$	7.57838	+	13.1261i	0.278775	+	0.482853i	0.971081	−	0.238752i	$-0.0767383\pi$
$739$	7.57838	+	13.1261i	0.278775	+	0.482853i	−0.692305	+	0.721605i	$0.743405\pi$
$740$		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
$745$	15.5458			0.569555
$746$		0			0
$747$	1.93598	+	9.17220i	0.0708339	+	0.335593i
$748$		0			0
$749$	2.51943	+	9.03675i	0.0920580	+	0.330196i
$750$		0			0
$751$	−40.2118			−1.46735			−0.733674	−	0.679501i	$-0.762196\pi$
$751$	−40.2118			−1.46735			−0.733674	+	0.679501i	$0.762196\pi$
$752$		0			0
$753$	−14.6235	−	38.1767i	−0.532911	−	1.39124i
$754$		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
$759$	1.59781	+	4.17129i	0.0579968	+	0.151408i
$760$		0			0
$761$	−23.6627			−0.857771			−0.428886	−	0.903359i	$-0.641094\pi$
$761$	−23.6627			−0.857771			−0.428886	+	0.903359i	$0.641094\pi$
$762$		0			0
$763$	1.80314	+	0.463693i	0.0652780	+	0.0167868i
$764$		0			0
$765$	34.3595	+	11.2181i	1.24227	+	0.405592i
$766$		0			0
$767$	−1.51135			−0.0545717
$768$		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	0.868514	−	0.495664i	$-0.165075\pi$
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	−0.863515	+	0.504323i	$0.831742\pi$
$774$		0			0
$775$	−7.31587	+	12.6715i	−0.262794	+	0.455172i
$776$		0			0
$777$	−10.6248	+	7.87272i	−0.381161	+	0.282432i
$778$		0			0
$779$	13.4887			0.483281
$780$		0			0
$781$	66.0553			2.36364
$782$		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
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	0.475833	+	0.879536i	$0.342147\pi$
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	−0.999617	+	0.0276845i	$0.991187\pi$
$788$		0			0
$789$	−13.9331	−	36.3743i	−0.496032	−	1.29496i
$790$		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
$795$	−0.433105	+	0.534063i	−0.0153606	+	0.0189413i
$796$		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
$801$	1.61273	+	7.64068i	0.0569828	+	0.269970i
$802$		0			0
$803$	−0.939253	−	1.62683i	−0.0331455	−	0.0574097i
$804$		0			0
$805$	1.37305	−	1.40105i	0.0483935	−	0.0493805i
$806$		0			0
$807$	−27.6465	+	34.0910i	−0.973203	+	1.20006i
$808$		0			0
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	0.984409	−	0.175895i	$-0.0562820\pi$
$809$	9.66703	+	16.7438i	0.339875	+	0.588680i	−0.644534	+	0.764575i	$0.722949\pi$
$810$		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
$815$	13.2398	−	22.9320i	0.463770	−	0.803274i
$816$		0			0
$817$	−8.41260	−	14.5710i	−0.294319	−	0.509776i
$818$		0			0
$819$	5.35705	−	2.78834i	0.187190	−	0.0974323i
$820$		0			0
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	0.853455	−	0.521167i	$-0.174503\pi$
$821$	−0.705332	−	1.22167i	−0.0246162	−	0.0426366i	−0.878071	+	0.478530i	$0.841170\pi$
$822$		0			0
$823$	−17.5196	+	30.3448i	−0.610694	+	1.05775i	0.380430	+	0.924810i	$0.375776\pi$
$823$	−17.5196	+	30.3448i	−0.610694	+	1.05775i	−0.991124	+	0.132943i	$0.957557\pi$
$824$		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	0.979865	+	0.199660i	$0.0639838\pi$
$829$	19.0848	+	33.0559i	0.662843	+	1.14808i	−0.317022	+	0.948418i	$0.602683\pi$
$830$		0			0
$831$	2.03379	+	5.30949i	0.0705515	+	0.184184i
$832$		0			0
$833$	−40.9863	+	24.7799i	−1.42009	+	0.858574i
$834$		0			0
$835$	−1.00739	−	1.74485i	−0.0348622	−	0.0603832i
$836$		0			0
$837$	33.6181	−	21.7300i	1.16201	−	0.751099i
$838$		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
$843$	−2.17059	−	0.345370i	−0.0747592	−	0.0118952i
$844$		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
$849$	14.0133	+	2.22970i	0.480935	+	0.0765231i
$850$		0			0
$851$	0.607523	−	1.05226i	0.0208256	−	0.0360711i
$852$		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
$857$	14.9234			0.509773			0.254887	−	0.966971i	$-0.417962\pi$
$857$	14.9234			0.509773			0.254887	+	0.966971i	$0.417962\pi$
$858$		0			0
$859$	−19.4132			−0.662368			−0.331184	−	0.943566i	$-0.607448\pi$
$859$	−19.4132			−0.662368			−0.331184	+	0.943566i	$0.607448\pi$
$860$		0			0
$861$	3.62244	+	31.6091i	0.123452	+	1.07724i
$862$		0			0
$863$	0.542263	−	0.939227i	0.0184588	−	0.0319717i	−0.856648	−	0.515901i	$-0.827457\pi$
$863$	0.542263	−	0.939227i	0.0184588	−	0.0319717i	0.875107	+	0.483929i	$0.160791\pi$
$864$		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
$871$	−5.16251			−0.174925
$872$		0			0
$873$	−2.25280	−	10.6732i	−0.0762456	−	0.361232i
$874$		0			0
$875$	−22.4978	+	22.9567i	−0.760565	+	0.776077i
$876$		0			0
$877$	−28.5699			−0.964737			−0.482369	−	0.875968i	$-0.660223\pi$
$877$	−28.5699			−0.964737			−0.482369	+	0.875968i	$0.660223\pi$
$878$		0			0
$879$	16.8565	−	20.7858i	0.568555	−	0.701088i
$880$		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
$885$	−5.98289	−	0.951958i	−0.201113	−	0.0319997i
$886$		0			0
$887$	28.3398			0.951558			0.475779	−	0.879565i	$-0.342166\pi$
$887$	28.3398			0.951558			0.475779	+	0.879565i	$0.342166\pi$
$888$		0			0
$889$	35.0985	−	35.8144i	1.17717	−	1.20118i
$890$		0			0
$891$	−5.91780	+	54.8043i	−0.198254	+	1.83601i
$892$		0			0
$893$	−3.22545			−0.107936
$894$		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
$903$	31.8863	−	23.6271i	1.06111	−	0.786260i
$904$		0			0
$905$	2.34092			0.0778149
$906$		0			0
$907$	−7.94747			−0.263891			−0.131946	−	0.991257i	$-0.542122\pi$
$907$	−7.94747			−0.263891			−0.131946	+	0.991257i	$0.542122\pi$
$908$		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
$913$	−9.56922	+	16.5744i	−0.316695	+	0.548532i
$914$		0			0
$915$	19.8834	−	24.5184i	0.657327	−	0.810552i
$916$		0			0
$917$	13.5056	−	13.7811i	0.445994	−	0.455090i
$918$		0			0
$919$	12.0224	−	20.8235i	0.396584	−	0.686903i	−0.596718	−	0.802451i	$-0.703529\pi$
$919$	12.0224	−	20.8235i	0.396584	−	0.686903i	0.993302	+	0.115548i	$0.0368623\pi$
$920$		0			0
$921$	3.03543	+	7.92439i	0.100021	+	0.261118i
$922$		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
$927$	−15.2431	+	13.6857i	−0.500648	+	0.449498i
$928$		0			0
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	0.541678	−	0.840586i	$-0.317789\pi$
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	−0.998808	+	0.0488134i	$0.984456\pi$
$930$		0			0
$931$	11.9126	+	6.56072i	0.390420	+	0.215019i
$932$		0			0
$933$	13.1540	+	2.09298i	0.430644	+	0.0685212i
$934$		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
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	−0.510160	−	0.860080i	$-0.670414\pi$
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	0.999931	+	0.0117715i	$0.00374709\pi$
$942$		0			0
$943$	−1.46169	−	2.53173i	−0.0475993	−	0.0824445i
$944$		0			0
$945$	22.9629	−	7.66376i	0.746984	−	0.249302i
$946$		0			0
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	−0.984334	−	0.176312i	$-0.943583\pi$
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	0.339476	−	0.940615i	$-0.389750\pi$
$948$		0			0
$949$	0.116683	−	0.202101i	0.00378769	−	0.00656047i
$950$		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
$957$	15.3438	+	2.44140i	0.495994	+	0.0789192i
$958$		0			0
$959$	−15.1517	+	15.4608i	−0.489275	+	0.499254i
$960$		0			0
$961$	−14.1735	−	24.5492i	−0.457209	−	0.791909i
$962$		0			0
$963$	−2.19686	−	10.4082i	−0.0707928	−	0.335399i
$964$		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
$969$	−8.23585	−	21.5008i	−0.264574	−	0.690706i
$970$		0			0
$971$	−13.1030	+	22.6951i	−0.420496	+	0.728320i	−0.995988	−	0.0894874i	$-0.971477\pi$
$971$	−13.1030	+	22.6951i	−0.420496	+	0.728320i	0.575492	+	0.817807i	$0.304810\pi$
$972$		0			0
$973$	31.9390	+	8.21339i	1.02392	+	0.263309i
$974$		0			0
$975$	1.57661	−	1.94412i	0.0504919	−	0.0622618i
$976$		0			0
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	−0.983826	−	0.179124i	$-0.942674\pi$
$977$	−10.5270	+	18.2332i	−0.336787	+	0.583332i	0.647039	+	0.762457i	$0.276007\pi$
$978$		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
$983$	19.5297			0.622900			0.311450	−	0.950263i	$-0.399185\pi$
$983$	19.5297			0.622900			0.311450	+	0.950263i	$0.399185\pi$
$984$		0			0
$985$	27.8960			0.888842
$986$		0			0
$987$	−0.866210	−	7.55847i	−0.0275718	−	0.240589i
$988$		0			0
$989$	−1.82326	+	3.15798i	−0.0579762	+	0.100418i
$990$		0			0
$991$	7.49837	+	12.9875i	0.238193	+	0.412563i	0.960196	−	0.279327i	$-0.0901114\pi$
$991$	7.49837	+	12.9875i	0.238193	+	0.412563i	−0.722003	+	0.691890i	$0.756778\pi$
$992$		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
$997$	−58.5641			−1.85475			−0.927373	−	0.374139i	$-0.877938\pi$
$997$	−58.5641			−1.85475			−0.927373	+	0.374139i	$0.877938\pi$
$998$		0			0
$999$	12.5926	−	8.13960i	0.398412	−	0.257526i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	28.11	odd	6
126.2.e.d.121.3	yes	6	36.31	odd	6
126.2.h.c.67.2	yes	6	252.67	odd	6
126.2.h.c.79.2	yes	6	4.3	odd	2
378.2.e.c.37.2		6	36.23	even	6
378.2.e.c.235.2		6	84.11	even	6
378.2.h.d.289.2		6	12.11	even	2
378.2.h.d.361.2		6	252.95	even	6
882.2.e.p.373.1		6	252.139	even	6
882.2.e.p.655.1		6	28.3	even	6
882.2.f.l.295.1		6	28.23	odd	6
882.2.f.l.589.1		6	252.247	odd	6
882.2.f.m.295.3		6	28.19	even	6
882.2.f.m.589.3		6	252.103	even	6
882.2.h.o.67.2		6	252.31	even	6
882.2.h.o.79.2		6	28.27	even	2
1008.2.q.h.529.1		6	7.4	even	3
1008.2.q.h.625.1		6	9.4	even	3
1008.2.t.g.193.2		6	63.4	even	3	inner
1008.2.t.g.961.2		6	1.1	even	1	trivial
1134.2.g.k.163.2		6	36.7	odd	6
1134.2.g.k.487.2		6	252.151	odd	6
1134.2.g.n.163.2		6	36.11	even	6
1134.2.g.n.487.2		6	252.11	even	6
2646.2.e.o.1549.2		6	252.167	odd	6
2646.2.e.o.2125.2		6	84.59	odd	6
2646.2.f.n.883.2		6	84.47	odd	6
2646.2.f.n.1765.2		6	252.131	odd	6
2646.2.f.o.883.2		6	84.23	even	6
2646.2.f.o.1765.2		6	252.23	even	6
2646.2.h.p.361.2		6	252.59	odd	6
2646.2.h.p.667.2		6	84.83	odd	2
3024.2.q.h.2305.2		6	9.5	odd	6
3024.2.q.h.2881.2		6	21.11	odd	6
3024.2.t.g.289.2		6	3.2	odd	2
3024.2.t.g.1873.2		6	63.32	odd	6
7938.2.a.bu.1.2		3	252.191	even	6
7938.2.a.bx.1.2		3	252.47	odd	6
7938.2.a.by.1.2		3	252.187	even	6
7938.2.a.cb.1.2		3	252.79	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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})\)	\(q+(-0.619562 - 1.61745i) q^{3} +1.76088 q^{5} +(1.85185 - 1.88962i) q^{7} +(-2.23229 + 2.00422i) q^{9} -6.12476 q^{11} +(-0.380438 - 0.658939i) q^{13} +(-1.09097 - 2.84813i) q^{15} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-4.20370 - 1.82454i) q^{21} +0.421067 q^{23} -1.89931 q^{25} +(4.62476 + 2.36887i) q^{27} +(0.732287 - 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(3.79467 + 9.90650i) q^{33} +(3.26088 - 3.32738i) q^{35} +(1.44282 - 2.49904i) q^{37} +(-0.830095 + 1.02359i) q^{39} +(-3.47141 - 6.01266i) q^{41} +(-4.33009 + 7.49994i) q^{43} +(-3.93078 + 3.52918i) q^{45} +(0.830095 + 1.43777i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(-7.46457 + 9.20459i) q^{51} +(-0.112725 - 0.195246i) q^{53} -10.7850 q^{55} +(3.32326 + 0.528775i) q^{57} +(0.993163 - 1.72021i) q^{59} +(5.17511 + 8.96355i) q^{61} +(-0.346647 + 7.92968i) q^{63} +(-0.669905 - 1.16031i) q^{65} +(3.39248 - 5.87594i) q^{67} +(-0.260877 - 0.681054i) q^{69} -10.7850 q^{71} +(0.153353 + 0.265616i) q^{73} +(1.17674 + 3.07204i) q^{75} +(-11.3421 + 11.5735i) q^{77} +(-6.72257 - 11.6438i) q^{79} +(0.966208 - 8.94799i) q^{81} +(1.56238 - 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-2.50520 - 0.398611i) q^{87} +(1.30150 - 2.25427i) q^{89} +(-1.94966 - 0.501371i) q^{91} +(-13.1774 - 2.09671i) q^{93} +(-1.71053 + 2.96273i) q^{95} +(-1.81806 + 3.14897i) q^{97} +(13.6722 - 12.2754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9	\( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

Introduction

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