LMFDB - Embedded newform 297.2.f.d.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 22 x^{13} + 62 x^{12} - 24 x^{11} + 152 x^{10} - 161 x^{9} + 552 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 8x^14 - 22x^13 + 62x^12 - 24x^11 + 152x^10 - 161x^9 + 552x^8 - 609x^7 + 1150x^6 - 862x^5 + 1346x^4 - 235x^3 + 340x^2 + 150*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.2
Root			$1.10209 + 0.800713i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.d.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.293070 + 0.212928i) q^{2} +(-0.577482 + 1.77731i) q^{4} +(2.17280 + 1.57863i) q^{5} +(-0.770730 + 2.37206i) q^{7} +(-0.433081 - 1.33288i) q^{8} -0.972914 q^{10} +(-1.14767 - 3.11173i) q^{11} +(-3.08851 + 2.24393i) q^{13} +(-0.279200 - 0.859290i) q^{14} +(-2.61301 - 1.89846i) q^{16} +(-0.909782 - 0.660995i) q^{17} +(2.09612 + 6.45120i) q^{19} +(-4.06046 + 2.95010i) q^{20} +(0.998921 + 0.667582i) q^{22} +6.74940 q^{23} +(0.683891 + 2.10480i) q^{25} +(0.427353 - 1.31526i) q^{26} +(-3.77080 - 2.73965i) q^{28} +(-2.29431 + 7.06116i) q^{29} +(5.42402 - 3.94078i) q^{31} +3.97298 q^{32} +0.407373 q^{34} +(-5.41925 + 3.93732i) q^{35} +(-0.0589927 + 0.181561i) q^{37} +(-1.98795 - 1.44433i) q^{38} +(1.16314 - 3.57976i) q^{40} +(0.196632 + 0.605172i) q^{41} +4.72749 q^{43} +(6.19326 - 0.242800i) q^{44} +(-1.97805 + 1.43713i) q^{46} +(-3.48969 - 10.7402i) q^{47} +(0.630458 + 0.458054i) q^{49} +(-0.648597 - 0.471233i) q^{50} +(-2.20460 - 6.78506i) q^{52} +(-4.45732 + 3.23843i) q^{53} +(2.41860 - 8.57290i) q^{55} +3.49548 q^{56} +(-0.831123 - 2.55793i) q^{58} +(2.60479 - 8.01671i) q^{59} +(-1.39299 - 1.01207i) q^{61} +(-0.750514 + 2.30984i) q^{62} +(4.06165 - 2.95096i) q^{64} -10.2530 q^{65} +4.50670 q^{67} +(1.70017 - 1.23525i) q^{68} +(0.749855 - 2.30782i) q^{70} +(9.95124 + 7.23000i) q^{71} +(-0.658284 + 2.02599i) q^{73} +(-0.0213703 - 0.0657711i) q^{74} -12.6762 q^{76} +(8.26576 - 0.324050i) q^{77} +(9.37010 - 6.80777i) q^{79} +(-2.68057 - 8.24994i) q^{80} +(-0.186485 - 0.135489i) q^{82} +(0.662117 + 0.481056i) q^{83} +(-0.933305 - 2.87242i) q^{85} +(-1.38548 + 1.00661i) q^{86} +(-3.65054 + 2.87734i) q^{88} -1.42041 q^{89} +(-2.94234 - 9.05560i) q^{91} +(-3.89766 + 11.9958i) q^{92} +(3.30960 + 2.40457i) q^{94} +(-5.62960 + 17.3261i) q^{95} +(-8.14778 + 5.91971i) q^{97} -0.282300 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31}+ \cdots + 26 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.293070	+	0.212928i	−0.207232	+	0.150563i	−0.686560	−	0.727073i	$-0.740880\pi$
$2$	−0.293070	+	0.212928i	−0.207232	+	0.150563i	0.479329	+	0.877635i	$0.340880\pi$
$3$		0			0
$3$		0			0
$4$	−0.577482	+	1.77731i	−0.288741	+	0.888654i
$5$	2.17280	+	1.57863i	0.971704	+	0.705984i	0.955839	−	0.293890i	$-0.0949498\pi$
$5$	2.17280	+	1.57863i	0.971704	+	0.705984i	0.0158649	+	0.999874i	$0.494950\pi$
$6$		0			0
$7$	−0.770730	+	2.37206i	−0.291309	+	0.896556i	0.693128	+	0.720815i	$0.256232\pi$
$7$	−0.770730	+	2.37206i	−0.291309	+	0.896556i	−0.984436	+	0.175741i	$0.943768\pi$
$8$	−0.433081	−	1.33288i	−0.153117	−	0.471246i
$9$		0			0
$10$	−0.972914			−0.307663
$11$	−1.14767	−	3.11173i	−0.346036	−	0.938221i
$11$	−1.14767	−	3.11173i	−0.346036	−	0.938221i
$12$		0			0
$13$	−3.08851	+	2.24393i	−0.856598	+	0.622355i	−0.926957	−	0.375167i	$-0.877585\pi$
$13$	−3.08851	+	2.24393i	−0.856598	+	0.622355i	0.0703593	+	0.997522i	$0.477585\pi$
$14$	−0.279200	−	0.859290i	−0.0746194	−	0.229655i
$15$		0			0
$16$	−2.61301	−	1.89846i	−0.653252	−	0.474615i
$17$	−0.909782	−	0.660995i	−0.220654	−	0.160315i	0.471967	−	0.881616i	$-0.343544\pi$
$17$	−0.909782	−	0.660995i	−0.220654	−	0.160315i	−0.692621	+	0.721301i	$0.743544\pi$
$18$		0			0
$19$	2.09612	+	6.45120i	0.480883	+	1.48001i	0.837856	+	0.545891i	$0.183809\pi$
$19$	2.09612	+	6.45120i	0.480883	+	1.48001i	−0.356973	+	0.934115i	$0.616191\pi$
$20$	−4.06046	+	2.95010i	−0.907947	+	0.659662i
$21$		0			0
$22$	0.998921	+	0.667582i	0.212971	+	0.142329i
$23$	6.74940			1.40735			0.703674	−	0.710523i	$-0.251542\pi$
$23$	6.74940			1.40735			0.703674	+	0.710523i	$0.251542\pi$
$24$		0			0
$25$	0.683891	+	2.10480i	0.136778	+	0.420960i
$26$	0.427353	−	1.31526i	0.0838108	−	0.257943i
$27$		0			0
$28$	−3.77080	−	2.73965i	−0.712615	−	0.517745i
$29$	−2.29431	+	7.06116i	−0.426043	+	1.31122i	0.475950	+	0.879472i	$0.342104\pi$
$29$	−2.29431	+	7.06116i	−0.426043	+	1.31122i	−0.901992	+	0.431752i	$0.857896\pi$
$30$		0			0
$31$	5.42402	−	3.94078i	0.974182	−	0.707785i	0.0177811	−	0.999842i	$-0.494340\pi$
$31$	5.42402	−	3.94078i	0.974182	−	0.707785i	0.956401	+	0.292057i	$0.0943398\pi$
$32$	3.97298			0.702331
$33$		0			0
$34$	0.407373			0.0698640
$35$	−5.41925	+	3.93732i	−0.916020	+	0.665528i
$36$		0			0
$37$	−0.0589927	+	0.181561i	−0.00969834	+	0.0298484i	−0.955789	−	0.294055i	$-0.904995\pi$
$37$	−0.0589927	+	0.181561i	−0.00969834	+	0.0298484i	0.946090	+	0.323903i	$0.104995\pi$
$38$	−1.98795	−	1.44433i	−0.322488	−	0.234301i
$39$		0			0
$40$	1.16314	−	3.57976i	0.183908	−	0.566010i
$41$	0.196632	+	0.605172i	0.0307088	+	0.0945121i	0.965236	−	0.261379i	$-0.0841773\pi$
$41$	0.196632	+	0.605172i	0.0307088	+	0.0945121i	−0.934527	+	0.355891i	$0.884177\pi$
$42$		0			0
$43$	4.72749			0.720936			0.360468	−	0.932772i	$-0.382617\pi$
$43$	4.72749			0.720936			0.360468	+	0.932772i	$0.382617\pi$
$44$	6.19326	−	0.242800i	0.933669	−	0.0366035i
$45$		0			0
$46$	−1.97805	+	1.43713i	−0.291647	+	0.211894i
$47$	−3.48969	−	10.7402i	−0.509024	−	1.56661i	−0.793899	−	0.608050i	$-0.791952\pi$
$47$	−3.48969	−	10.7402i	−0.509024	−	1.56661i	0.284875	−	0.958565i	$-0.408048\pi$
$48$		0			0
$49$	0.630458	+	0.458054i	0.0900654	+	0.0654363i
$50$	−0.648597	−	0.471233i	−0.0917255	−	0.0666425i
$51$		0			0
$52$	−2.20460	−	6.78506i	−0.305723	−	0.940919i
$53$	−4.45732	+	3.23843i	−0.612259	+	0.444833i	−0.850209	−	0.526445i	$-0.823525\pi$
$53$	−4.45732	+	3.23843i	−0.612259	+	0.444833i	0.237950	+	0.971277i	$0.423525\pi$
$54$		0			0
$55$	2.41860	−	8.57290i	0.326125	−	1.15597i
$56$	3.49548			0.467103
$57$		0			0
$58$	−0.831123	−	2.55793i	−0.109132	−	0.335873i
$59$	2.60479	−	8.01671i	0.339115	−	1.04369i	−0.625545	−	0.780188i	$-0.715123\pi$
$59$	2.60479	−	8.01671i	0.339115	−	1.04369i	0.964660	−	0.263499i	$-0.0848767\pi$
$60$		0			0
$61$	−1.39299	−	1.01207i	−0.178354	−	0.129582i	0.495026	−	0.868878i	$-0.335158\pi$
$61$	−1.39299	−	1.01207i	−0.178354	−	0.129582i	−0.673380	+	0.739296i	$0.735158\pi$
$62$	−0.750514	+	2.30984i	−0.0953154	+	0.293351i
$63$		0			0
$64$	4.06165	−	2.95096i	0.507706	−	0.368870i
$65$	−10.2530			−1.27173
$66$		0			0
$67$	4.50670			0.550581			0.275291	−	0.961361i	$-0.411226\pi$
$67$	4.50670			0.550581			0.275291	+	0.961361i	$0.411226\pi$
$68$	1.70017	−	1.23525i	0.206176	−	0.149796i
$69$		0			0
$70$	0.749855	−	2.30782i	0.0896248	−	0.275837i
$71$	9.95124	+	7.23000i	1.18099	+	0.858043i	0.992284	−	0.123990i	$-0.0395689\pi$
$71$	9.95124	+	7.23000i	1.18099	+	0.858043i	0.188711	+	0.982033i	$0.439569\pi$
$72$		0			0
$73$	−0.658284	+	2.02599i	−0.0770463	+	0.237124i	−0.982161	−	0.188044i	$-0.939785\pi$
$73$	−0.658284	+	2.02599i	−0.0770463	+	0.237124i	0.905114	+	0.425168i	$0.139785\pi$
$74$	−0.0213703	−	0.0657711i	−0.00248425	−	0.00764574i
$75$		0			0
$76$	−12.6762			−1.45406
$77$	8.26576	−	0.324050i	0.941971	−	0.0369290i
$78$		0			0
$79$	9.37010	−	6.80777i	1.05422	−	0.765935i	0.0812083	−	0.996697i	$-0.474122\pi$
$79$	9.37010	−	6.80777i	1.05422	−	0.765935i	0.973010	+	0.230763i	$0.0741221\pi$
$80$	−2.68057	−	8.24994i	−0.299696	−	0.922371i
$81$		0			0
$82$	−0.186485	−	0.135489i	−0.0205938	−	0.0149623i
$83$	0.662117	+	0.481056i	0.0726768	+	0.0528028i	0.623530	−	0.781799i	$-0.285698\pi$
$83$	0.662117	+	0.481056i	0.0726768	+	0.0528028i	−0.550854	+	0.834602i	$0.685698\pi$
$84$		0			0
$85$	−0.933305	−	2.87242i	−0.101231	−	0.311557i
$86$	−1.38548	+	1.00661i	−0.149401	+	0.108546i
$87$		0			0
$88$	−3.65054	+	2.87734i	−0.389149	+	0.306726i
$89$	−1.42041			−0.150564			−0.0752818	−	0.997162i	$-0.523986\pi$
$89$	−1.42041			−0.150564			−0.0752818	+	0.997162i	$0.523986\pi$
$90$		0			0
$91$	−2.94234	−	9.05560i	−0.308441	−	0.949285i
$92$	−3.89766	+	11.9958i	−0.406359	+	1.25065i
$93$		0			0
$94$	3.30960	+	2.40457i	0.341359	+	0.248012i
$95$	−5.62960	+	17.3261i	−0.577585	+	1.77762i
$96$		0			0
$97$	−8.14778	+	5.91971i	−0.827281	+	0.601055i	−0.918789	−	0.394749i	$-0.870831\pi$
$97$	−8.14778	+	5.91971i	−0.827281	+	0.601055i	0.0915074	+	0.995804i	$0.470831\pi$
$98$	−0.282300			−0.0285166
$99$		0			0
$100$	−4.13581			−0.413581
$101$	15.4878	−	11.2526i	1.54110	−	1.11967i	0.591456	−	0.806337i	$-0.298553\pi$
$101$	15.4878	−	11.2526i	1.54110	−	1.11967i	0.949642	−	0.313337i	$-0.101447\pi$
$102$		0			0
$103$	−0.959963	+	2.95446i	−0.0945880	+	0.291112i	−0.987146	−	0.159820i	$-0.948908\pi$
$103$	−0.959963	+	2.95446i	−0.0945880	+	0.291112i	0.892558	+	0.450932i	$0.148908\pi$
$104$	4.32848	+	3.14482i	0.424442	+	0.308375i
$105$		0			0
$106$	0.616753	−	1.89817i	0.0599044	−	0.184367i
$107$	−3.05389	−	9.39890i	−0.295231	−	0.908626i	−0.983144	−	0.182833i	$-0.941473\pi$
$107$	−3.05389	−	9.39890i	−0.295231	−	0.908626i	0.687913	−	0.725793i	$-0.258527\pi$
$108$		0			0
$109$	18.0851			1.73224			0.866121	−	0.499834i	$-0.166606\pi$
$109$	18.0851			1.73224			0.866121	+	0.499834i	$0.166606\pi$
$110$	1.11659	+	3.02744i	0.106462	+	0.288656i
$111$		0			0
$112$	6.51719	−	4.73502i	0.615817	−	0.447417i
$113$	−1.56978	−	4.83128i	−0.147672	−	0.454489i	0.849673	−	0.527311i	$-0.176800\pi$
$113$	−1.56978	−	4.83128i	−0.147672	−	0.454489i	−0.997345	+	0.0728217i	$0.976800\pi$
$114$		0			0
$115$	14.6651	+	10.6548i	1.36753	+	0.993566i
$116$	−11.2249	−	8.15539i	−1.04221	−	0.757209i
$117$		0			0
$118$	0.943595	+	2.90409i	0.0868650	+	0.267343i
$119$	2.26912	−	1.64861i	0.208010	−	0.151128i
$120$		0			0
$121$	−8.36569	+	7.14249i	−0.760518	+	0.649317i
$122$	0.623739			0.0564707
$123$		0			0
$124$	3.87170	+	11.9159i	0.347689	+	1.07008i
$125$	2.31293	−	7.11847i	0.206875	−	0.636695i
$126$		0			0
$127$	−0.674959	−	0.490387i	−0.0598930	−	0.0435148i	0.557436	−	0.830220i	$-0.311785\pi$
$127$	−0.674959	−	0.490387i	−0.0598930	−	0.0435148i	−0.617329	+	0.786705i	$0.711785\pi$
$128$	−3.01744	+	9.28674i	−0.266707	+	0.820839i
$129$		0			0
$130$	3.00485	−	2.18315i	0.263543	−	0.191475i
$131$	−19.7527			−1.72580			−0.862899	−	0.505376i	$-0.831354\pi$
$131$	−19.7527			−1.72580			−0.862899	+	0.505376i	$0.831354\pi$
$132$		0			0
$133$	−16.9182			−1.46699
$134$	−1.32078	+	0.959601i	−0.114098	+	0.0828969i
$135$		0			0
$136$	−0.487022	+	1.49890i	−0.0417618	+	0.128529i
$137$	3.20612	+	2.32938i	0.273918	+	0.199013i	0.716260	−	0.697833i	$-0.245852\pi$
$137$	3.20612	+	2.32938i	0.273918	+	0.199013i	−0.442343	+	0.896846i	$0.645852\pi$
$138$		0			0
$139$	−1.05212	+	3.23811i	−0.0892401	+	0.274653i	−0.985710	−	0.168452i	$-0.946123\pi$
$139$	−1.05212	+	3.23811i	−0.0892401	+	0.274653i	0.896470	+	0.443105i	$0.146123\pi$
$140$	−3.86830	−	11.9054i	−0.326931	−	1.00619i
$141$		0			0
$142$	−4.45587			−0.373929
$143$	10.5271	+	7.03530i	0.880321	+	0.588321i
$144$		0			0
$145$	−16.1320	+	11.7206i	−1.33969	+	0.973343i
$146$	−0.238466	−	0.733922i	−0.0197356	−	0.0607399i
$147$		0			0
$148$	−0.288622	−	0.209696i	−0.0237246	−	0.0172369i
$149$	−4.16967	−	3.02944i	−0.341592	−	0.248181i	0.403741	−	0.914873i	$-0.367710\pi$
$149$	−4.16967	−	3.02944i	−0.341592	−	0.248181i	−0.745333	+	0.666692i	$0.767710\pi$
$150$		0			0
$151$	−4.24751	−	13.0725i	−0.345658	−	1.06382i	−0.961231	−	0.275745i	$-0.911075\pi$
$151$	−4.24751	−	13.0725i	−0.345658	−	1.06382i	0.615573	−	0.788080i	$-0.288925\pi$
$152$	7.69091	−	5.58778i	0.623816	−	0.453229i
$153$		0			0
$154$	−2.35344	+	1.85498i	−0.189646	+	0.149478i
$155$	18.0063			1.44630
$156$		0			0
$157$	5.14028	+	15.8201i	0.410239	+	1.26258i	0.916441	+	0.400170i	$0.131049\pi$
$157$	5.14028	+	15.8201i	0.410239	+	1.26258i	−0.506202	+	0.862415i	$0.668951\pi$
$158$	−1.29653	+	3.99030i	−0.103146	+	0.317452i
$159$		0			0
$160$	8.63249	+	6.27187i	0.682458	+	0.495835i
$161$	−5.20197	+	16.0100i	−0.409973	+	1.26177i
$162$		0			0
$163$	−18.4445	+	13.4007i	−1.44469	+	1.04963i	−0.457648	+	0.889134i	$0.651308\pi$
$163$	−18.4445	+	13.4007i	−1.44469	+	1.04963i	−0.987037	+	0.160492i	$0.948692\pi$
$164$	−1.18913			−0.0928554
$165$		0			0
$166$	−0.296477			−0.0230111
$167$	−10.1932	+	7.40583i	−0.788777	+	0.573080i	−0.907600	−	0.419835i	$-0.862088\pi$
$167$	−10.1932	+	7.40583i	−0.788777	+	0.573080i	0.118823	+	0.992915i	$0.462088\pi$
$168$		0			0
$169$	0.486428	−	1.49707i	0.0374176	−	0.115159i
$170$	0.885140	+	0.643092i	0.0678871	+	0.0493229i
$171$		0			0
$172$	−2.73004	+	8.40221i	−0.208164	+	0.640662i
$173$	−2.21873	−	6.82855i	−0.168687	−	0.519165i	0.830602	−	0.556866i	$-0.187996\pi$
$173$	−2.21873	−	6.82855i	−0.168687	−	0.519165i	−0.999289	+	0.0377013i	$0.987996\pi$
$174$		0			0
$175$	−5.51981			−0.417259
$176$	−2.90861	+	10.3098i	−0.219245	+	0.777128i
$177$		0			0
$178$	0.416280	−	0.302445i	0.0312015	−	0.0226692i
$179$	2.78001	+	8.55598i	0.207788	+	0.639504i	0.999587	+	0.0287236i	$0.00914427\pi$
$179$	2.78001	+	8.55598i	0.207788	+	0.639504i	−0.791800	+	0.610781i	$0.790856\pi$
$180$		0			0
$181$	−1.51882	−	1.10349i	−0.112893	−	0.0820215i	0.529906	−	0.848056i	$-0.322227\pi$
$181$	−1.51882	−	1.10349i	−0.112893	−	0.0820215i	−0.642799	+	0.766035i	$0.722227\pi$
$182$	2.79050	+	2.02742i	0.206846	+	0.150282i
$183$		0			0
$184$	−2.92304	−	8.99618i	−0.215489	−	0.663207i
$185$	−0.414796	+	0.301367i	−0.0304964	+	0.0221570i
$186$		0			0
$187$	−1.01270	+	3.58960i	−0.0740563	+	0.262497i
$188$	21.1038			1.53915
$189$		0			0
$190$	−2.03935	−	6.27646i	−0.147950	−	0.455343i
$191$	1.97927	−	6.09158i	0.143215	−	0.440771i	−0.853562	−	0.520991i	$-0.825562\pi$
$191$	1.97927	−	6.09158i	0.143215	−	0.440771i	0.996777	+	0.0802202i	$0.0255623\pi$
$192$		0			0
$193$	−2.28013	−	1.65661i	−0.164127	−	0.119245i	0.502690	−	0.864467i	$-0.332344\pi$
$193$	−2.28013	−	1.65661i	−0.164127	−	0.119245i	−0.666817	+	0.745221i	$0.732344\pi$
$194$	1.12740	−	3.46977i	0.0809424	−	0.249115i
$195$		0			0
$196$	−1.17818	+	0.855999i	−0.0841558	+	0.0611428i
$197$	−25.7193			−1.83243			−0.916213	−	0.400692i	$-0.868770\pi$
$197$	−25.7193			−1.83243			−0.916213	+	0.400692i	$0.868770\pi$
$198$		0			0
$199$	13.3474			0.946174			0.473087	−	0.881016i	$-0.343140\pi$
$199$	13.3474			0.946174			0.473087	+	0.881016i	$0.343140\pi$
$200$	2.50927	−	1.82309i	0.177433	−	0.128912i
$201$		0			0
$202$	−2.14303	+	6.59558i	−0.150783	+	0.464063i
$203$	−14.9812	−	10.8845i	−1.05148	−	0.763942i
$204$		0			0
$205$	−0.528101	+	1.62533i	−0.0368841	+	0.113518i
$206$	−0.347751	−	1.07027i	−0.0242289	−	0.0745690i
$207$		0			0
$208$	12.3303			0.854953
$209$	17.6687	−	13.9264i	1.22217	−	0.963311i
$210$		0			0
$211$	12.7273	−	9.24690i	0.876181	−	0.636583i	−0.0560570	−	0.998428i	$-0.517853\pi$
$211$	12.7273	−	9.24690i	0.876181	−	0.636583i	0.932238	+	0.361844i	$0.117853\pi$
$212$	−3.18167	−	9.79216i	−0.218518	−	0.672528i
$213$		0			0
$214$	2.89629	+	2.10428i	0.197986	+	0.143845i
$215$	10.2719	+	7.46296i	0.700536	+	0.508969i
$216$		0			0
$217$	5.16732	+	15.9034i	0.350781	+	1.07959i
$218$	−5.30021	+	3.85083i	−0.358975	+	0.260811i
$219$		0			0
$220$	13.8400	+	9.24930i	0.933091	+	0.623588i
$221$	4.29310			0.288785
$222$		0			0
$223$	−5.83506	−	17.9585i	−0.390744	−	1.20259i	−0.932227	−	0.361875i	$-0.882137\pi$
$223$	−5.83506	−	17.9585i	−0.390744	−	1.20259i	0.541482	−	0.840712i	$-0.317863\pi$
$224$	−3.06210	+	9.42417i	−0.204595	+	0.629679i
$225$		0			0
$226$	1.48877	+	1.08165i	0.0990314	+	0.0719505i
$227$	0.333566	−	1.02661i	0.0221395	−	0.0681385i	−0.939376	−	0.342888i	$-0.888595\pi$
$227$	0.333566	−	1.02661i	0.0221395	−	0.0681385i	0.961516	+	0.274749i	$0.0885949\pi$
$228$		0			0
$229$	9.92056	−	7.20771i	0.655569	−	0.476299i	−0.209595	−	0.977788i	$-0.567214\pi$
$229$	9.92056	−	7.20771i	0.655569	−	0.476299i	0.865164	+	0.501489i	$0.167214\pi$
$230$	−6.56659			−0.432988
$231$		0			0
$232$	10.4053			0.683143
$233$	12.1863	−	8.85388i	0.798353	−	0.580037i	−0.112078	−	0.993699i	$-0.535751\pi$
$233$	12.1863	−	8.85388i	0.798353	−	0.580037i	0.910430	+	0.413662i	$0.135751\pi$
$234$		0			0
$235$	9.37235	−	28.8451i	0.611385	−	1.88165i
$236$	12.7440	+	9.25902i	0.829560	+	0.602711i
$237$		0			0
$238$	−0.313975	+	0.966316i	−0.0203520	+	0.0626370i
$239$	−4.44785	−	13.6891i	−0.287708	−	0.885473i	−0.985574	−	0.169245i	$-0.945867\pi$
$239$	−4.44785	−	13.6891i	−0.287708	−	0.885473i	0.697866	−	0.716228i	$-0.254133\pi$
$240$		0			0
$241$	−12.0283			−0.774809			−0.387404	−	0.921910i	$-0.626628\pi$
$241$	−12.0283			−0.774809			−0.387404	+	0.921910i	$0.626628\pi$
$242$	0.930898	−	3.87453i	0.0598404	−	0.249064i
$243$		0			0
$244$	2.60318	−	1.89132i	0.166651	−	0.121079i
$245$	0.646758	+	1.99052i	0.0413199	+	0.127170i
$246$		0			0
$247$	−20.9499	−	15.2210i	−1.33301	−	0.968490i
$248$	−7.60164	−	5.52291i	−0.482705	−	0.350705i
$249$		0			0
$250$	0.837868	+	2.57869i	0.0529915	+	0.163091i
$251$	−11.5075	+	8.36069i	−0.726347	+	0.527722i	−0.888406	−	0.459059i	$-0.848187\pi$
$251$	−11.5075	+	8.36069i	−0.726347	+	0.527722i	0.162058	+	0.986781i	$0.448187\pi$
$252$		0			0
$253$	−7.74611	−	21.0023i	−0.486994	−	1.32040i
$254$	0.302227			0.0189634
$255$		0			0
$256$	2.00974	+	6.18536i	0.125609	+	0.386585i
$257$	−3.35820	+	10.3355i	−0.209479	+	0.644709i	0.790021	+	0.613080i	$0.210069\pi$
$257$	−3.35820	+	10.3355i	−0.209479	+	0.644709i	−0.999500	+	0.0316290i	$0.989931\pi$
$258$		0			0
$259$	−0.385206	−	0.279869i	−0.0239356	−	0.0173902i
$260$	5.92095	−	18.2228i	0.367202	−	1.13013i
$261$		0			0
$262$	5.78891	−	4.20589i	0.357640	−	0.259841i
$263$	−2.58062			−0.159128			−0.0795640	−	0.996830i	$-0.525353\pi$
$263$	−2.58062			−0.159128			−0.0795640	+	0.996830i	$0.525353\pi$
$264$		0			0
$265$	−14.7971			−0.908980
$266$	4.95821	−	3.60235i	0.304007	−	0.220874i
$267$		0			0
$268$	−2.60254	+	8.00980i	−0.158975	+	0.489276i
$269$	4.58187	+	3.32892i	0.279361	+	0.202968i	0.718639	−	0.695383i	$-0.244765\pi$
$269$	4.58187	+	3.32892i	0.279361	+	0.202968i	−0.439277	+	0.898351i	$0.644765\pi$
$270$		0			0
$271$	0.742616	−	2.28554i	0.0451107	−	0.138836i	−0.925964	−	0.377611i	$-0.876746\pi$
$271$	0.742616	−	2.28554i	0.0451107	−	0.138836i	0.971075	+	0.238775i	$0.0767457\pi$
$272$	1.12239	+	3.45437i	0.0680550	+	0.209452i
$273$		0			0
$274$	−1.43561			−0.0867282
$275$	5.76468	−	4.54370i	0.347623	−	0.273995i
$276$		0			0
$277$	−2.11159	+	1.53416i	−0.126873	+	0.0921787i	−0.649412	−	0.760437i	$-0.724985\pi$
$277$	−2.11159	+	1.53416i	−0.126873	+	0.0921787i	0.522539	+	0.852615i	$0.324985\pi$
$278$	−0.381136	−	1.17302i	−0.0228590	−	0.0703529i
$279$		0			0
$280$	7.59496	+	5.51806i	0.453886	+	0.329767i
$281$	7.16625	+	5.20659i	0.427503	+	0.310599i	0.780650	−	0.624969i	$-0.214888\pi$
$281$	7.16625	+	5.20659i	0.427503	+	0.310599i	−0.353147	+	0.935568i	$0.614888\pi$
$282$		0			0
$283$	−4.17507	−	12.8495i	−0.248182	−	0.763826i	−0.995097	−	0.0989059i	$-0.968466\pi$
$283$	−4.17507	−	12.8495i	−0.248182	−	0.763826i	0.746915	−	0.664920i	$-0.231534\pi$
$284$	−18.5966	+	13.5112i	−1.10351	+	0.801743i
$285$		0			0
$286$	−4.58318	+	0.179679i	−0.271009	+	0.0106246i
$287$	−1.58706			−0.0936811
$288$		0			0
$289$	−4.86250	−	14.9652i	−0.286029	−	0.880308i
$290$	2.23217	−	6.86990i	0.131077	−	0.403415i
$291$		0			0
$292$	−3.22066	−	2.33995i	−0.188475	−	0.136935i
$293$	−5.47529	+	16.8512i	−0.319870	+	0.984457i	0.653834	+	0.756638i	$0.273160\pi$
$293$	−5.47529	+	16.8512i	−0.319870	+	0.984457i	−0.973703	+	0.227819i	$0.926840\pi$
$294$		0			0
$295$	18.3151	−	13.3067i	1.06635	−	0.774746i
$296$	0.267548			0.0155509
$297$		0			0
$298$	1.86705			0.108156
$299$	−20.8456	+	15.1452i	−1.20553	+	0.875870i
$300$		0			0
$301$	−3.64362	+	11.2139i	−0.210015	+	0.646359i
$302$	4.02831	+	2.92674i	0.231803	+	0.168415i
$303$		0			0
$304$	6.77016	−	20.8364i	0.388296	−	1.19505i
$305$	−1.42901	−	4.39803i	−0.0818246	−	0.251830i
$306$		0			0
$307$	11.3039			0.645145			0.322573	−	0.946545i	$-0.395452\pi$
$307$	11.3039			0.645145			0.322573	+	0.946545i	$0.395452\pi$
$308$	−4.19739	+	14.8779i	−0.239169	+	0.847749i
$309$		0			0
$310$	−5.27710	+	3.83404i	−0.299719	+	0.217759i
$311$	2.04111	+	6.28188i	0.115740	+	0.356213i	0.992101	−	0.125444i	$-0.0400354\pi$
$311$	2.04111	+	6.28188i	0.115740	+	0.356213i	−0.876360	+	0.481656i	$0.840035\pi$
$312$		0			0
$313$	−25.3217	−	18.3973i	−1.43127	−	1.03988i	−0.989779	−	0.142612i	$-0.954450\pi$
$313$	−25.3217	−	18.3973i	−1.43127	−	1.03988i	−0.441490	−	0.897266i	$-0.645550\pi$
$314$	−4.87500	−	3.54190i	−0.275112	−	0.199881i
$315$		0			0
$316$	6.68845	+	20.5849i	0.376254	+	1.15799i
$317$	10.3929	−	7.55088i	0.583723	−	0.424100i	−0.256341	−	0.966586i	$-0.582517\pi$
$317$	10.3929	−	7.55088i	0.583723	−	0.424100i	0.840064	+	0.542487i	$0.182517\pi$
$318$		0			0
$319$	24.6055	−	0.964633i	1.37764	−	0.0540091i
$320$	13.4836			0.753757
$321$		0			0
$322$	−1.88443	−	5.79969i	−0.105015	−	0.323204i
$323$	2.35720	−	7.25471i	0.131158	−	0.403663i
$324$		0			0
$325$	−6.83523	−	4.96608i	−0.379150	−	0.275469i
$326$	2.55214	−	7.85469i	0.141350	−	0.435031i
$327$		0			0
$328$	0.721468	−	0.524177i	0.0398364	−	0.0289428i
$329$	28.1660			1.55284
$330$		0			0
$331$	19.1669			1.05351			0.526755	−	0.850017i	$-0.323408\pi$
$331$	19.1669			1.05351			0.526755	+	0.850017i	$0.323408\pi$
$332$	−1.23735	+	0.898985i	−0.0679082	+	0.0493382i
$333$		0			0
$334$	1.41043	−	4.34085i	0.0771751	−	0.237521i
$335$	9.79215	+	7.11441i	0.535002	+	0.388702i
$336$		0			0
$337$	10.1049	−	31.0996i	0.550448	−	1.69410i	−0.157224	−	0.987563i	$-0.550254\pi$
$337$	10.1049	−	31.0996i	0.550448	−	1.69410i	0.707672	−	0.706542i	$-0.249746\pi$
$338$	0.176211	+	0.542321i	0.00958459	+	0.0294984i
$339$		0			0
$340$	5.64413			0.306096
$341$	−18.4876	−	12.3553i	−1.00116	−	0.669079i
$342$		0			0
$343$	−15.6970	+	11.4046i	−0.847560	+	0.615788i
$344$	−2.04738	−	6.30120i	−0.110388	−	0.339738i
$345$		0			0
$346$	2.10423	+	1.52881i	0.113124	+	0.0821894i
$347$	8.88351	+	6.45425i	0.476892	+	0.346482i	0.800121	−	0.599838i	$-0.204768\pi$
$347$	8.88351	+	6.45425i	0.476892	+	0.346482i	−0.323229	+	0.946321i	$0.604768\pi$
$348$		0			0
$349$	7.32380	+	22.5403i	0.392034	+	1.20656i	0.931247	+	0.364387i	$0.118722\pi$
$349$	7.32380	+	22.5403i	0.392034	+	1.20656i	−0.539214	+	0.842169i	$0.681278\pi$
$350$	1.61769	−	1.17532i	0.0864691	−	0.0628235i
$351$		0			0
$352$	−4.55968	−	12.3628i	−0.243032	−	0.658942i
$353$	−29.5876			−1.57479			−0.787394	−	0.616450i	$-0.788570\pi$
$353$	−29.5876			−1.57479			−0.787394	+	0.616450i	$0.788570\pi$
$354$		0			0
$355$	10.2085	+	31.4186i	0.541813	+	1.66753i
$356$	0.820264	−	2.52451i	0.0434739	−	0.133799i
$357$		0			0
$358$	−2.63654	−	1.91556i	−0.139345	−	0.101240i
$359$	−8.83869	+	27.2027i	−0.466488	+	1.43570i	0.390614	+	0.920555i	$0.372263\pi$
$359$	−8.83869	+	27.2027i	−0.466488	+	1.43570i	−0.857102	+	0.515148i	$0.827737\pi$
$360$		0			0
$361$	−21.8529	+	15.8771i	−1.15015	+	0.835635i
$362$	0.680082			0.0357443
$363$		0			0
$364$	17.7937			0.932646
$365$	−4.62860	+	3.36288i	−0.242272	+	0.176021i
$366$		0			0
$367$	−1.10625	+	3.40467i	−0.0577456	+	0.177723i	−0.975769	−	0.218804i	$-0.929785\pi$
$367$	−1.10625	+	3.40467i	−0.0577456	+	0.177723i	0.918023	+	0.396526i	$0.129785\pi$
$368$	−17.6362	−	12.8135i	−0.919352	−	0.667948i
$369$		0			0
$370$	0.0573948	−	0.176643i	0.00298382	−	0.00918324i
$371$	−4.24637	−	13.0690i	−0.220461	−	0.678508i
$372$		0			0
$373$	−36.9935			−1.91545			−0.957726	−	0.287683i	$-0.907115\pi$
$373$	−36.9935			−1.91545			−0.957726	+	0.287683i	$0.907115\pi$
$374$	−0.467531	−	1.26764i	−0.0241755	−	0.0655479i
$375$		0			0
$376$	−12.8041	+	9.30272i	−0.660320	+	0.479751i
$377$	−8.75877	−	26.9567i	−0.451100	−	1.38834i
$378$		0			0
$379$	19.4747	+	14.1492i	1.00035	+	0.726796i	0.962163	−	0.272474i	$-0.0878420\pi$
$379$	19.4747	+	14.1492i	1.00035	+	0.726796i	0.0381863	+	0.999271i	$0.487842\pi$
$380$	−27.5429	−	20.0111i	−1.41292	−	1.02655i
$381$		0			0
$382$	0.717000	+	2.20670i	0.0366849	+	0.112905i
$383$	28.3311	−	20.5837i	1.44765	−	1.05178i	0.461276	−	0.887257i	$-0.347392\pi$
$383$	28.3311	−	20.5837i	1.44765	−	1.05178i	0.986373	−	0.164522i	$-0.0526082\pi$
$384$		0			0
$385$	18.4714	+	12.3445i	0.941389	+	0.629133i
$386$	1.02097			0.0519662
$387$		0			0
$388$	−5.81594	−	17.8996i	−0.295260	−	0.908716i
$389$	1.26992	−	3.90841i	0.0643875	−	0.198164i	−0.913687	−	0.406418i	$-0.866778\pi$
$389$	1.26992	−	3.90841i	0.0643875	−	0.198164i	0.978075	+	0.208253i	$0.0667778\pi$
$390$		0			0
$391$	−6.14048	−	4.46132i	−0.310538	−	0.225619i
$392$	0.337495	−	1.03870i	0.0170461	−	0.0524624i
$393$		0			0
$394$	7.53755	−	5.47635i	0.379736	−	0.275895i
$395$	31.1063			1.56513
$396$		0			0
$397$	−23.0629			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$397$	−23.0629			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$398$	−3.91173	+	2.84203i	−0.196077	+	0.142458i
$399$		0			0
$400$	2.20887	−	6.79819i	0.110443	−	0.339910i
$401$	3.03414	+	2.20443i	0.151518	+	0.110084i	0.660961	−	0.750420i	$-0.270149\pi$
$401$	3.03414	+	2.20443i	0.151518	+	0.110084i	−0.509443	+	0.860504i	$0.670149\pi$
$402$		0			0
$403$	−7.90928	+	24.3423i	−0.393989	+	1.21257i
$404$	11.0553	+	34.0248i	0.550024	+	1.69280i
$405$		0			0
$406$	6.70815			0.332920
$407$	0.632672	−	0.0248032i	0.0313604	−	0.00122945i
$408$		0			0
$409$	22.2031	−	16.1315i	1.09787	−	0.797652i	0.117162	−	0.993113i	$-0.462620\pi$
$409$	22.2031	−	16.1315i	1.09787	−	0.797652i	0.980711	+	0.195461i	$0.0626204\pi$
$410$	−0.191307	−	0.588781i	−0.00944796	−	0.0290778i
$411$		0			0
$412$	−4.69663	−	3.41230i	−0.231386	−	0.168112i
$413$	17.0086	+	12.3574i	0.836937	+	0.608070i
$414$		0			0
$415$	0.679237	+	2.09048i	0.0333424	+	0.102617i
$416$	−12.2706	+	8.91511i	−0.601615	+	0.437099i
$417$		0			0
$418$	−2.21284	+	7.84357i	−0.108234	+	0.383641i
$419$	−21.4045			−1.04568			−0.522840	−	0.852431i	$-0.675128\pi$
$419$	−21.4045			−1.04568			−0.522840	+	0.852431i	$0.675128\pi$
$420$		0			0
$421$	3.37531	+	10.3881i	0.164502	+	0.506286i	0.998999	−	0.0447264i	$-0.0142416\pi$
$421$	3.37531	+	10.3881i	0.164502	+	0.506286i	−0.834497	+	0.551013i	$0.814242\pi$
$422$	−1.76106	+	5.41997i	−0.0857269	+	0.263840i
$423$		0			0
$424$	6.24683	+	4.53859i	0.303373	+	0.220413i
$425$	0.769071	−	2.36696i	0.0373054	−	0.114814i
$426$		0			0
$427$	3.47430	−	2.52423i	0.168133	−	0.122156i
$428$	18.4683			0.892700
$429$		0			0
$430$	−4.59944			−0.221805
$431$	9.56381	−	6.94852i	0.460673	−	0.334698i	−0.333122	−	0.942884i	$-0.608102\pi$
$431$	9.56381	−	6.94852i	0.460673	−	0.334698i	0.793795	+	0.608185i	$0.208102\pi$
$432$		0			0
$433$	−7.50566	+	23.1000i	−0.360699	+	1.11012i	0.591932	+	0.805988i	$0.298365\pi$
$433$	−7.50566	+	23.1000i	−0.360699	+	1.11012i	−0.952631	+	0.304129i	$0.901635\pi$
$434$	−4.90066	−	3.56053i	−0.235239	−	0.170911i
$435$		0			0
$436$	−10.4439	+	32.1429i	−0.500170	+	1.53936i
$437$	14.1476	+	43.5417i	0.676770	+	2.08288i
$438$		0			0
$439$	−18.5791			−0.886734			−0.443367	−	0.896340i	$-0.646216\pi$
$439$	−18.5791			−0.886734			−0.443367	+	0.896340i	$0.646216\pi$
$440$	−12.4741	+	0.489035i	−0.594681	+	0.0233139i
$441$		0			0
$442$	−1.25818	+	0.914119i	−0.0598453	+	0.0434802i
$443$	6.10193	+	18.7798i	0.289912	+	0.892256i	0.984883	+	0.173219i	$0.0554168\pi$
$443$	6.10193	+	18.7798i	0.289912	+	0.892256i	−0.694972	+	0.719037i	$0.744583\pi$
$444$		0			0
$445$	−3.08627	−	2.24231i	−0.146303	−	0.106296i
$446$	5.53393	+	4.02063i	0.262039	+	0.190383i
$447$		0			0
$448$	3.86943	+	11.9089i	0.182814	+	0.562642i
$449$	−1.68475	+	1.22404i	−0.0795083	+	0.0577662i	−0.626829	−	0.779157i	$-0.715648\pi$
$449$	−1.68475	+	1.22404i	−0.0795083	+	0.0577662i	0.547321	+	0.836923i	$0.315648\pi$
$450$		0			0
$451$	1.65746	−	1.30641i	0.0780468	−	0.0615163i
$452$	9.49320			0.446523
$453$		0			0
$454$	0.120836	+	0.371894i	0.00567109	+	0.0174538i
$455$	7.90233	−	24.3209i	0.370467	−	1.14018i
$456$		0			0
$457$	6.70503	+	4.87149i	0.313648	+	0.227879i	0.733460	−	0.679732i	$-0.237904\pi$
$457$	6.70503	+	4.87149i	0.313648	+	0.227879i	−0.419812	+	0.907611i	$0.637904\pi$
$458$	−1.37270	+	4.22472i	−0.0641418	+	0.197408i
$459$		0			0
$460$	−27.4057	+	19.9114i	−1.27780	+	0.928374i
$461$	−6.55423			−0.305261			−0.152630	−	0.988283i	$-0.548774\pi$
$461$	−6.55423			−0.305261			−0.152630	+	0.988283i	$0.548774\pi$
$462$		0			0
$463$	0.273405			0.0127062			0.00635310	−	0.999980i	$-0.497978\pi$
$463$	0.273405			0.0127062			0.00635310	+	0.999980i	$0.497978\pi$
$464$	19.4004	−	14.0952i	0.900640	−	0.654353i
$465$		0			0
$466$	−1.68621	+	5.18961i	−0.0781120	+	0.240404i
$467$	−6.19971	−	4.50435i	−0.286888	−	0.208437i	0.435028	−	0.900417i	$-0.356738\pi$
$467$	−6.19971	−	4.50435i	−0.286888	−	0.208437i	−0.721916	+	0.691980i	$0.756738\pi$
$468$		0			0
$469$	−3.47345	+	10.6902i	−0.160389	+	0.493627i
$470$	3.39517	+	10.4493i	0.156608	+	0.481989i
$471$		0			0
$472$	−11.8134			−0.543758
$473$	−5.42561	−	14.7107i	−0.249470	−	0.676397i
$474$		0			0
$475$	−12.1450	+	8.82383i	−0.557249	+	0.404865i
$476$	1.61971	+	4.98497i	0.0742395	+	0.228486i
$477$		0			0
$478$	4.21831	+	3.06478i	0.192941	+	0.140180i
$479$	−18.7751	−	13.6409i	−0.857856	−	0.623269i	0.0694449	−	0.997586i	$-0.477877\pi$
$479$	−18.7751	−	13.6409i	−0.857856	−	0.623269i	−0.927301	+	0.374317i	$0.877877\pi$
$480$		0			0
$481$	−0.225211	−	0.693128i	−0.0102687	−	0.0316039i
$482$	3.52512	−	2.56115i	0.160565	−	0.116657i
$483$		0			0
$484$	−7.86336	−	18.9931i	−0.357426	−	0.863322i
$485$	−27.0485			−1.22821
$486$		0			0
$487$	−7.44592	−	22.9162i	−0.337407	−	1.03843i	−0.965524	−	0.260313i	$-0.916174\pi$
$487$	−7.44592	−	22.9162i	−0.337407	−	1.03843i	0.628117	−	0.778119i	$-0.283826\pi$
$488$	−0.745690	+	2.29500i	−0.0337558	+	0.103890i
$489$		0			0
$490$	−0.613381	−	0.445648i	−0.0277097	−	0.0201323i
$491$	10.8675	−	33.4466i	0.490442	−	1.50942i	−0.333500	−	0.942750i	$-0.608230\pi$
$491$	10.8675	−	33.4466i	0.490442	−	1.50942i	0.823942	−	0.566675i	$-0.191770\pi$
$492$		0			0
$493$	6.75471	−	4.90759i	0.304217	−	0.221027i
$494$	9.38077			0.422061
$495$		0			0
$496$	−21.6544			−0.972311
$497$	−24.8197	+	18.0326i	−1.11332	+	0.808873i
$498$		0			0
$499$	−7.03047	+	21.6376i	−0.314727	+	0.968631i	0.661139	+	0.750263i	$0.270073\pi$
$499$	−7.03047	+	21.6376i	−0.314727	+	0.968631i	−0.975867	+	0.218368i	$0.929927\pi$
$500$	11.3160	+	8.22158i	0.506068	+	0.367680i
$501$		0			0
$502$	1.59228	−	4.90053i	0.0710669	−	0.218721i
$503$	1.55585	+	4.78840i	0.0693718	+	0.213504i	0.979732	−	0.200312i	$-0.0641956\pi$
$503$	1.55585	+	4.78840i	0.0693718	+	0.213504i	−0.910360	+	0.413816i	$0.864196\pi$
$504$		0			0
$505$	51.4156			2.28796
$506$	6.74212	+	4.50578i	0.299724	+	0.200306i
$507$		0			0
$508$	1.26135	−	0.916421i	0.0559631	−	0.0406596i
$509$	−2.87574	−	8.85063i	−0.127465	−	0.392297i	0.866877	−	0.498522i	$-0.166124\pi$
$509$	−2.87574	−	8.85063i	−0.127465	−	0.392297i	−0.994342	+	0.106225i	$0.966124\pi$
$510$		0			0
$511$	−4.29842	−	3.12298i	−0.190151	−	0.138153i
$512$	−17.7056	−	12.8639i	−0.782483	−	0.568507i
$513$		0			0
$514$	−1.21652	−	3.74406i	−0.0536584	−	0.165144i
$515$	−6.74981	+	4.90402i	−0.297432	+	0.216097i
$516$		0			0
$517$	−29.4154	+	23.1852i	−1.29369	+	1.01968i
$518$	0.172484			0.00757852
$519$		0			0
$520$	4.44039	+	13.6661i	0.194724	+	0.599299i
$521$	−3.41257	+	10.5028i	−0.149507	+	0.460136i	−0.997563	−	0.0697708i	$-0.977773\pi$
$521$	−3.41257	+	10.5028i	−0.149507	+	0.460136i	0.848056	+	0.529907i	$0.177773\pi$
$522$		0			0
$523$	15.7075	+	11.4122i	0.686841	+	0.499019i	0.875620	−	0.483001i	$-0.160453\pi$
$523$	15.7075	+	11.4122i	0.686841	+	0.499019i	−0.188779	+	0.982020i	$0.560453\pi$
$524$	11.4068	−	35.1066i	0.498309	−	1.53364i
$525$		0			0
$526$	0.756302	−	0.549486i	0.0329764	−	0.0239587i
$527$	−7.53951			−0.328426
$528$		0			0
$529$	22.5544			0.980628
$530$	4.33659	−	3.15071i	0.188369	−	0.136858i
$531$		0			0
$532$	9.76996	−	30.0688i	0.423581	−	1.30365i
$533$	−1.96527	−	1.42785i	−0.0851252	−	0.0618471i
$534$		0			0
$535$	8.20190	−	25.2429i	0.354599	−	1.09134i
$536$	−1.95176	−	6.00691i	−0.0843034	−	0.259459i
$537$		0			0
$538$	−2.05163			−0.0884519
$539$	0.701781	−	2.48751i	0.0302278	−	0.107145i
$540$		0			0
$541$	17.0772	−	12.4073i	0.734205	−	0.533431i	−0.156686	−	0.987649i	$-0.550081\pi$
$541$	17.0772	−	12.4073i	0.734205	−	0.533431i	0.890891	+	0.454217i	$0.150081\pi$
$542$	0.269015	+	0.827944i	0.0115552	+	0.0355633i
$543$		0			0
$544$	−3.61455	−	2.62612i	−0.154972	−	0.112594i
$545$	39.2953	+	28.5497i	1.68323	+	1.22294i
$546$		0			0
$547$	−4.33986	−	13.3567i	−0.185559	−	0.571092i	0.814398	−	0.580306i	$-0.197067\pi$
$547$	−4.33986	−	13.3567i	−0.185559	−	0.571092i	−0.999958	+	0.00921392i	$0.997067\pi$
$548$	−5.99151	+	4.35309i	−0.255945	+	0.185955i
$549$		0			0
$550$	−0.721973	+	2.55908i	−0.0307850	+	0.109120i
$551$	−50.3621			−2.14550
$552$		0			0
$553$	8.92666	+	27.4734i	0.379600	+	1.16829i
$554$	0.292178	−	0.899231i	0.0124134	−	0.0382047i
$555$		0			0
$556$	−5.14753	−	3.73990i	−0.218304	−	0.158607i
$557$	12.8094	−	39.4233i	0.542752	−	1.67042i	−0.183524	−	0.983015i	$-0.558751\pi$
$557$	12.8094	−	39.4233i	0.542752	−	1.67042i	0.726276	−	0.687403i	$-0.241249\pi$
$558$		0			0
$559$	−14.6009	+	10.6082i	−0.617552	+	0.448678i
$560$	21.6354			0.914261
$561$		0			0
$562$	−3.20884			−0.135357
$563$	−6.02675	+	4.37869i	−0.253997	+	0.184540i	−0.707497	−	0.706717i	$-0.750176\pi$
$563$	−6.02675	+	4.37869i	−0.253997	+	0.184540i	0.453499	+	0.891257i	$0.350176\pi$
$564$		0			0
$565$	4.21600	−	12.9755i	0.177368	−	0.545883i
$566$	3.95961	+	2.87682i	0.166435	+	0.120922i
$567$		0			0
$568$	5.32707	−	16.3950i	0.223519	−	0.687920i
$569$	7.54697	+	23.2272i	0.316385	+	0.973734i	0.975180	+	0.221412i	$0.0710664\pi$
$569$	7.54697	+	23.2272i	0.316385	+	0.973734i	−0.658795	+	0.752322i	$0.728934\pi$
$570$		0			0
$571$	−12.8161			−0.536337			−0.268169	−	0.963372i	$-0.586418\pi$
$571$	−12.8161			−0.536337			−0.268169	+	0.963372i	$0.586418\pi$
$572$	−18.5831	+	14.6471i	−0.776998	+	0.612428i
$573$		0			0
$574$	0.465119	−	0.337928i	0.0194137	−	0.0141049i
$575$	4.61585	+	14.2061i	0.192494	+	0.592437i
$576$		0			0
$577$	11.7428	+	8.53166i	0.488860	+	0.355178i	0.804746	−	0.593620i	$-0.202302\pi$
$577$	11.7428	+	8.53166i	0.488860	+	0.355178i	−0.315886	+	0.948797i	$0.602302\pi$
$578$	4.61156	+	3.35050i	0.191816	+	0.139362i
$579$		0			0
$580$	−11.5152	−	35.4400i	−0.478141	−	1.47157i
$581$	−1.65141	+	1.19982i	−0.0685120	+	0.0497769i
$582$		0			0
$583$	15.1926	+	10.1533i	0.629215	+	0.420507i
$584$	2.98550			0.123541
$585$		0			0
$586$	−1.98344	−	6.10441i	−0.0819353	−	0.252171i
$587$	6.92675	−	21.3183i	0.285897	−	0.879902i	−0.700231	−	0.713917i	$-0.746920\pi$
$587$	6.92675	−	21.3183i	0.285897	−	0.879902i	0.986128	−	0.165985i	$-0.0530805\pi$
$588$		0			0
$589$	36.7921	+	26.7311i	1.51599	+	1.10143i
$590$	−2.53424	+	7.79958i	−0.104333	+	0.321104i
$591$		0			0
$592$	0.498834	−	0.362424i	0.0205020	−	0.0148955i
$593$	−18.2533			−0.749572			−0.374786	−	0.927111i	$-0.622284\pi$
$593$	−18.2533			−0.749572			−0.374786	+	0.927111i	$0.622284\pi$
$594$		0			0
$595$	7.53288			0.308818
$596$	7.79216	−	5.66133i	0.319179	−	0.231897i
$597$		0			0
$598$	2.88438	−	8.87720i	0.117951	−	0.363016i
$599$	−21.3766	−	15.5310i	−0.873425	−	0.634581i	0.0580785	−	0.998312i	$-0.481503\pi$
$599$	−21.3766	−	15.5310i	−0.873425	−	0.634581i	−0.931504	+	0.363731i	$0.881503\pi$
$600$		0			0
$601$	4.27228	−	13.1487i	0.174270	−	0.536347i	−0.825330	−	0.564651i	$-0.809011\pi$
$601$	4.27228	−	13.1487i	0.174270	−	0.536347i	0.999599	+	0.0283041i	$0.00901067\pi$
$602$	−1.31992	−	4.06228i	−0.0537958	−	0.165566i
$603$		0			0
$604$	25.6867			1.04518
$605$	−29.4523	+	2.31285i	−1.19741	+	0.0940306i
$606$		0			0
$607$	11.7971	−	8.57109i	0.478829	−	0.347890i	−0.322043	−	0.946725i	$-0.604370\pi$
$607$	11.7971	−	8.57109i	0.478829	−	0.347890i	0.800872	+	0.598835i	$0.204370\pi$
$608$	8.32786	+	25.6305i	0.337739	+	1.03945i
$609$		0			0
$610$	1.35526	+	0.984653i	0.0548728	+	0.0398674i
$611$	34.8782	+	25.3405i	1.41102	+	1.02517i
$612$		0			0
$613$	−9.31252	−	28.6610i	−0.376129	−	1.15761i	−0.942714	−	0.333603i	$-0.891736\pi$
$613$	−9.31252	−	28.6610i	−0.376129	−	1.15761i	0.566585	−	0.824004i	$-0.308264\pi$
$614$	−3.31282	+	2.40690i	−0.133694	+	0.0971347i
$615$		0			0
$616$	−4.01166	−	10.8770i	−0.161634	−	0.438246i
$617$	19.6957			0.792918			0.396459	−	0.918052i	$-0.370239\pi$
$617$	19.6957			0.792918			0.396459	+	0.918052i	$0.370239\pi$
$618$		0			0
$619$	0.399593	+	1.22982i	0.0160610	+	0.0494306i	0.958766	−	0.284197i	$-0.0917271\pi$
$619$	0.399593	+	1.22982i	0.0160610	+	0.0494306i	−0.942705	+	0.333628i	$0.891727\pi$
$620$	−10.3983	+	32.0028i	−0.417607	+	1.28526i
$621$		0			0
$622$	−1.93577	−	1.40642i	−0.0776173	−	0.0563923i
$623$	1.09476	−	3.36931i	0.0438605	−	0.134989i
$624$		0			0
$625$	25.2152	−	18.3199i	1.00861	−	0.732797i
$626$	11.3383			0.453171
$627$		0			0
$628$	−31.0857			−1.24045
$629$	0.173681	−	0.126187i	0.00692513	−	0.00503140i
$630$		0			0
$631$	13.6277	−	41.9417i	0.542509	−	1.66967i	−0.184330	−	0.982864i	$-0.559012\pi$
$631$	13.6277	−	41.9417i	0.542509	−	1.66967i	0.726839	−	0.686808i	$-0.240988\pi$
$632$	−13.1320	−	9.54095i	−0.522362	−	0.379519i
$633$		0			0
$634$	−1.43805	+	4.42587i	−0.0571123	+	0.175774i
$635$	−0.692411	−	2.13102i	−0.0274775	−	0.0845670i
$636$		0			0
$637$	−2.97502			−0.117874
$638$	−7.00573	+	5.52190i	−0.277360	+	0.218614i
$639$		0			0
$640$	−21.2166	+	15.4148i	−0.838660	+	0.609322i
$641$	8.34164	+	25.6729i	0.329475	+	1.01402i	0.969380	+	0.245566i	$0.0789737\pi$
$641$	8.34164	+	25.6729i	0.329475	+	1.01402i	−0.639905	+	0.768454i	$0.721026\pi$
$642$		0			0
$643$	8.21678	+	5.96984i	0.324038	+	0.235428i	0.737897	−	0.674914i	$-0.235819\pi$
$643$	8.21678	+	5.96984i	0.324038	+	0.235428i	−0.413858	+	0.910341i	$0.635819\pi$
$644$	−25.4507	−	18.4910i	−1.00290	−	0.728648i
$645$		0			0
$646$	0.853904	+	2.62805i	0.0335964	+	0.103399i
$647$	27.2093	−	19.7687i	1.06971	−	0.777189i	0.0938493	−	0.995586i	$-0.470083\pi$
$647$	27.2093	−	19.7687i	1.06971	−	0.777189i	0.975860	+	0.218397i	$0.0700828\pi$
$648$		0			0
$649$	−27.9353	+	1.09517i	−1.09656	+	0.0429893i
$650$	3.06061			0.120047
$651$		0			0
$652$	−13.1658	−	40.5202i	−0.515613	−	1.58690i
$653$	−3.50045	+	10.7733i	−0.136983	+	0.421591i	−0.995893	−	0.0905356i	$-0.971142\pi$
$653$	−3.50045	+	10.7733i	−0.136983	+	0.421591i	0.858910	+	0.512127i	$0.171142\pi$
$654$		0			0
$655$	−42.9185	−	31.1821i	−1.67697	−	1.21839i
$656$	0.635094	−	1.95462i	0.0247963	−	0.0763150i
$657$		0			0
$658$	−8.25459	+	5.99731i	−0.321797	+	0.233800i
$659$	32.3806			1.26137			0.630684	−	0.776040i	$-0.282775\pi$
$659$	32.3806			1.26137			0.630684	+	0.776040i	$0.282775\pi$
$660$		0			0
$661$	3.14238			0.122225			0.0611123	−	0.998131i	$-0.480535\pi$
$661$	3.14238			0.122225			0.0611123	+	0.998131i	$0.480535\pi$
$662$	−5.61725	+	4.08117i	−0.218321	+	0.158619i
$663$		0			0
$664$	0.354443	−	1.09086i	0.0137550	−	0.0423337i
$665$	−36.7598	−	26.7076i	−1.42548	−	1.03567i
$666$		0			0
$667$	−15.4852	+	47.6586i	−0.599590	+	1.84535i
$668$	−7.27602	−	22.3933i	−0.281517	−	0.866422i
$669$		0			0
$670$	−4.38464			−0.169393
$671$	−1.55058	+	5.49612i	−0.0598594	+	0.212175i
$672$		0			0
$673$	31.2835	−	22.7288i	1.20589	−	0.876132i	0.211040	−	0.977477i	$-0.432315\pi$
$673$	31.2835	−	22.7288i	1.20589	−	0.876132i	0.994851	+	0.101346i	$0.0323149\pi$
$674$	3.66053	+	11.2660i	0.140998	+	0.433949i
$675$		0			0
$676$	2.37986	+	1.72907i	0.0915329	+	0.0665025i
$677$	36.9891	+	26.8742i	1.42161	+	1.03286i	0.991504	+	0.130078i	$0.0415229\pi$
$677$	36.9891	+	26.8742i	1.42161	+	1.03286i	0.430103	+	0.902780i	$0.358477\pi$
$678$		0			0
$679$	−7.76218	−	23.8895i	−0.297885	−	0.916797i
$680$	−3.42440	+	2.48798i	−0.131320	+	0.0954095i
$681$		0			0
$682$	8.04895	−	0.315551i	0.308210	−	0.0120831i
$683$	−11.3550			−0.434485			−0.217243	−	0.976118i	$-0.569706\pi$
$683$	−11.3550			−0.434485			−0.217243	+	0.976118i	$0.569706\pi$
$684$		0			0
$685$	3.28902	+	10.1226i	0.125667	+	0.386763i
$686$	2.17198	−	6.68466i	0.0829265	−	0.255222i
$687$		0			0
$688$	−12.3530	−	8.97495i	−0.470952	−	0.342167i
$689$	6.49964	−	20.0038i	0.247617	−	0.762085i
$690$		0			0
$691$	−7.05451	+	5.12540i	−0.268366	+	0.194979i	−0.713827	−	0.700322i	$-0.753040\pi$
$691$	−7.05451	+	5.12540i	−0.268366	+	0.194979i	0.445461	+	0.895301i	$0.353040\pi$
$692$	13.4177			0.510065
$693$		0			0
$694$	−3.97778			−0.150994
$695$	−7.39782	+	5.37483i	−0.280615	+	0.203879i
$696$		0			0
$697$	0.221123	−	0.680548i	0.00837565	−	0.0257776i
$698$	−6.94584	−	5.04645i	−0.262904	−	0.191011i
$699$		0			0
$700$	3.18759	−	9.81040i	0.120480	−	0.370798i
$701$	−12.5650	−	38.6712i	−0.474575	−	1.46059i	−0.846530	−	0.532342i	$-0.821312\pi$
$701$	−12.5650	−	38.6712i	−0.474575	−	1.46059i	0.371954	−	0.928251i	$-0.378688\pi$
$702$		0			0
$703$	−1.29494			−0.0488396
$704$	−13.8440	−	9.25201i	−0.521767	−	0.348698i
$705$		0			0
$706$	8.67122	−	6.30001i	0.326346	−	0.237104i
$707$	14.7549	+	45.4109i	0.554915	+	1.70785i
$708$		0			0
$709$	13.5448	+	9.84087i	0.508686	+	0.369582i	0.812325	−	0.583205i	$-0.198202\pi$
$709$	13.5448	+	9.84087i	0.508686	+	0.369582i	−0.303639	+	0.952787i	$0.598202\pi$
$710$	−9.68171	−	7.03417i	−0.363348	−	0.263988i
$711$		0			0
$712$	0.615154	+	1.89325i	0.0230539	+	0.0709525i
$713$	36.6089	−	26.5979i	1.37101	−	0.996099i
$714$		0			0
$715$	11.7671	+	31.9047i	0.440066	+	1.19317i
$716$	−16.8120			−0.628295
$717$		0			0
$718$	−3.20185	−	9.85428i	−0.119492	−	0.367758i
$719$	5.99373	−	18.4468i	0.223528	−	0.687949i	−0.774909	−	0.632072i	$-0.782205\pi$
$719$	5.99373	−	18.4468i	0.223528	−	0.687949i	0.998438	−	0.0558770i	$-0.0177955\pi$
$720$		0			0
$721$	−6.26830	−	4.55419i	−0.233444	−	0.169607i
$722$	3.02376	−	9.30617i	0.112533	−	0.346340i
$723$		0			0
$724$	2.83833	−	2.06216i	0.105486	−	0.0766397i
$725$	−16.4314			−0.610246
$726$		0			0
$727$	5.78433			0.214529			0.107264	−	0.994231i	$-0.465791\pi$
$727$	5.78433			0.214529			0.107264	+	0.994231i	$0.465791\pi$
$728$	−10.7958	+	7.84361i	−0.400119	+	0.290704i
$729$		0			0
$730$	0.640454	−	1.97111i	0.0237043	−	0.0729542i
$731$	−4.30099	−	3.12485i	−0.159078	−	0.115577i
$732$		0			0
$733$	7.01846	−	21.6006i	0.259233	−	0.797837i	−0.733733	−	0.679438i	$-0.762224\pi$
$733$	7.01846	−	21.6006i	0.259233	−	0.797837i	0.992966	−	0.118399i	$-0.0377762\pi$
$734$	−0.400742	−	1.23336i	−0.0147917	−	0.0455240i
$735$		0			0
$736$	26.8153			0.988424
$737$	−5.17222	−	14.0236i	−0.190521	−	0.516567i
$738$		0			0
$739$	9.31755	−	6.76960i	0.342752	−	0.249024i	−0.403070	−	0.915169i	$-0.632057\pi$
$739$	9.31755	−	6.76960i	0.342752	−	0.249024i	0.745822	+	0.666145i	$0.232057\pi$
$740$	−0.296085	−	0.911255i	−0.0108843	−	0.0334984i
$741$		0			0
$742$	4.02723	+	2.92596i	0.147844	+	0.107415i
$743$	−34.7925	−	25.2782i	−1.27641	−	0.927367i	−0.276973	−	0.960878i	$-0.589331\pi$
$743$	−34.7925	−	25.2782i	−1.27641	−	0.927367i	−0.999438	+	0.0335104i	$0.989331\pi$
$744$		0			0
$745$	−4.27747	−	13.1647i	−0.156715	−	0.482318i
$746$	10.8417	−	7.87694i	0.396942	−	0.288395i
$747$		0			0
$748$	−5.79500	−	3.87282i	−0.211886	−	0.141604i
$749$	24.6485			0.900637
$750$		0			0
$751$	1.11212	+	3.42275i	0.0405817	+	0.124898i	0.969295	−	0.245901i	$-0.0790839\pi$
$751$	1.11212	+	3.42275i	0.0405817	+	0.124898i	−0.928713	+	0.370799i	$0.879084\pi$
$752$	−11.2712	+	34.6892i	−0.411018	+	1.26498i
$753$		0			0
$754$	8.30676	+	6.03521i	0.302514	+	0.219789i
$755$	11.4076	−	35.1091i	0.415167	−	1.27775i
$756$		0			0
$757$	12.2911	−	8.93000i	0.446727	−	0.324566i	−0.341575	−	0.939855i	$-0.610960\pi$
$757$	12.2911	−	8.93000i	0.446727	−	0.324566i	0.788302	+	0.615288i	$0.210960\pi$
$758$	−8.72021			−0.316732
$759$		0			0
$760$	25.5318			0.926137
$761$	13.1992	−	9.58979i	0.478471	−	0.347630i	−0.322262	−	0.946650i	$-0.604443\pi$
$761$	13.1992	−	9.58979i	0.478471	−	0.347630i	0.800733	+	0.599021i	$0.204443\pi$
$762$		0			0
$763$	−13.9388	+	42.8991i	−0.504617	+	1.55305i
$764$	9.68362	+	7.03556i	0.350341	+	0.254538i
$765$		0			0
$766$	−3.92013	+	12.0649i	−0.141640	+	0.435923i
$767$	9.94406	+	30.6047i	0.359059	+	1.10507i
$768$		0			0
$769$	6.66672			0.240408			0.120204	−	0.992749i	$-0.461645\pi$
$769$	6.66672			0.240408			0.120204	+	0.992749i	$0.461645\pi$
$770$	−8.04188	+	0.315273i	−0.289809	+	0.0113617i
$771$		0			0
$772$	4.26104	−	3.09582i	0.153358	−	0.111421i
$773$	15.7232	+	48.3910i	0.565524	+	1.74050i	0.666389	+	0.745604i	$0.267839\pi$
$773$	15.7232	+	48.3910i	0.565524	+	1.74050i	−0.100865	+	0.994900i	$0.532161\pi$
$774$		0			0
$775$	12.0040	+	8.72140i	0.431196	+	0.313282i
$776$	11.4189	+	8.29634i	0.409916	+	0.297821i
$777$		0			0
$778$	0.460034	+	1.41584i	0.0164930	+	0.0507603i
$779$	−3.49192	+	2.53703i	−0.125111	+	0.0908985i
$780$		0			0
$781$	11.0770	−	39.2632i	0.396367	−	1.40495i
$782$	2.74953			0.0983229
$783$		0			0
$784$	−0.777792	−	2.39380i	−0.0277783	−	0.0854928i
$785$	−13.8054	+	42.4885i	−0.492735	+	1.51648i
$786$		0			0
$787$	24.5570	+	17.8417i	0.875364	+	0.635989i	0.932021	−	0.362404i	$-0.118044\pi$
$787$	24.5570	+	17.8417i	0.875364	+	0.635989i	−0.0566567	+	0.998394i	$0.518044\pi$
$788$	14.8525	−	45.7111i	0.529097	−	1.62839i
$789$		0			0
$790$	−9.11630	+	6.62338i	−0.324344	+	0.235649i
$791$	12.6700			0.450493
$792$		0			0
$793$	6.57326			0.233423
$794$	6.75904	−	4.91073i	0.239869	−	0.174275i
$795$		0			0
$796$	−7.70790	+	23.7225i	−0.273199	+	0.840821i
$797$	−3.21352	−	2.33476i	−0.113829	−	0.0827015i	0.529415	−	0.848363i	$-0.322412\pi$
$797$	−3.21352	−	2.33476i	−0.113829	−	0.0827015i	−0.643243	+	0.765662i	$0.722412\pi$
$798$		0			0
$799$	−3.92434	+	12.0779i	−0.138833	+	0.427285i
$800$	2.71709	+	8.36233i	0.0960635	+	0.295653i
$801$		0			0
$802$	−1.35860			−0.0479738
$803$	7.05982	−	0.276773i	0.249136	−	0.00976710i
$804$		0			0
$805$	−36.5767	+	26.5745i	−1.28916	+	0.936629i
$806$	−2.86517	−	8.81808i	−0.100921	−	0.310604i
$807$		0			0
$808$	−21.7059	−	15.7702i	−0.763610	−	0.554795i
$809$	4.26011	+	3.09515i	0.149778	+	0.108820i	0.660150	−	0.751133i	$-0.270493\pi$
$809$	4.26011	+	3.09515i	0.149778	+	0.108820i	−0.510373	+	0.859953i	$0.670493\pi$
$810$		0			0
$811$	11.6366	+	35.8137i	0.408615	+	1.25759i	0.917838	+	0.396954i	$0.129933\pi$
$811$	11.6366	+	35.8137i	0.408615	+	1.25759i	−0.509223	+	0.860635i	$0.670067\pi$
$812$	27.9965	−	20.3406i	0.982484	−	0.713817i
$813$		0			0
$814$	−0.180136	+	0.141982i	−0.00631375	+	0.00497648i
$815$	−61.2309			−2.14483
$816$		0			0
$817$	9.90939	+	30.4980i	0.346686	+	1.06699i
$818$	−3.07222	+	9.45531i	−0.107418	+	0.330597i
$819$		0			0
$820$	−2.58374	−	1.87719i	−0.0902280	−	0.0655545i
$821$	−0.649391	+	1.99862i	−0.0226639	+	0.0697523i	−0.961749	−	0.273933i	$-0.911675\pi$
$821$	−0.649391	+	1.99862i	−0.0226639	+	0.0697523i	0.939085	+	0.343685i	$0.111675\pi$
$822$		0			0
$823$	5.37987	−	3.90871i	0.187531	−	0.136249i	−0.490059	−	0.871689i	$-0.663025\pi$
$823$	5.37987	−	3.90871i	0.187531	−	0.136249i	0.677589	+	0.735440i	$0.263025\pi$
$824$	4.35370			0.151668
$825$		0			0
$826$	−7.61594			−0.264992
$827$	−17.8702	+	12.9834i	−0.621407	+	0.451479i	−0.853413	−	0.521236i	$-0.825471\pi$
$827$	−17.8702	+	12.9834i	−0.621407	+	0.451479i	0.232006	+	0.972714i	$0.425471\pi$
$828$		0			0
$829$	1.19544	−	3.67920i	0.0415195	−	0.127784i	−0.928148	−	0.372211i	$-0.878600\pi$
$829$	1.19544	−	3.67920i	0.0415195	−	0.127784i	0.969668	+	0.244427i	$0.0785998\pi$
$830$	−0.644184	−	0.468027i	−0.0223599	−	0.0162454i
$831$		0			0
$832$	−5.92268	+	18.2281i	−0.205332	+	0.631947i
$833$	−0.270807	−	0.833459i	−0.00938291	−	0.0288776i
$834$		0			0
$835$	−33.8389			−1.17104
$836$	14.5482	+	39.4450i	0.503159	+	1.36423i
$837$		0			0
$838$	6.27302	−	4.55762i	0.216698	−	0.157440i
$839$	7.24273	+	22.2908i	0.250047	+	0.769565i	0.994765	+	0.102186i	$0.0325837\pi$
$839$	7.24273	+	22.2908i	0.250047	+	0.769565i	−0.744719	+	0.667379i	$0.767416\pi$
$840$		0			0
$841$	−21.1346	−	15.3552i	−0.728779	−	0.529489i
$842$	−3.20112	−	2.32575i	−0.110318	−	0.0801506i
$843$		0			0
$844$	9.08482	+	27.9602i	0.312712	+	0.962430i
$845$	3.42023	−	2.48494i	0.117660	−	0.0854847i
$846$		0			0
$847$	−10.4947	−	25.3489i	−0.360604	−	0.870998i
$848$	17.7950			0.611084
$849$		0			0
$850$	0.278599	+	0.857439i	0.00955586	+	0.0294099i
$851$	−0.398165	+	1.22543i	−0.0136489	+	0.0420071i
$852$		0			0
$853$	16.9833	+	12.3391i	0.581497	+	0.422482i	0.839263	−	0.543725i	$-0.182987\pi$
$853$	16.9833	+	12.3391i	0.581497	+	0.422482i	−0.257766	+	0.966207i	$0.582987\pi$
$854$	−0.480735	+	1.47955i	−0.0164504	+	0.0506291i
$855$		0			0
$856$	−11.2051	+	8.14097i	−0.382982	+	0.278252i
$857$	−28.3180			−0.967325			−0.483662	−	0.875255i	$-0.660694\pi$
$857$	−28.3180			−0.967325			−0.483662	+	0.875255i	$0.660694\pi$
$858$		0			0
$859$	−55.7071			−1.90070			−0.950351	−	0.311179i	$-0.899276\pi$
$859$	−55.7071			−1.90070			−0.950351	+	0.311179i	$0.899276\pi$
$860$	−19.1958	+	13.9466i	−0.654571	+	0.475574i
$861$		0			0
$862$	−1.32333	+	4.07280i	−0.0450729	+	0.138720i
$863$	24.8932	+	18.0860i	0.847375	+	0.615654i	0.924421	−	0.381374i	$-0.124549\pi$
$863$	24.8932	+	18.0860i	0.847375	+	0.615654i	−0.0770462	+	0.997028i	$0.524549\pi$
$864$		0			0
$865$	5.95890	−	18.3396i	0.202609	−	0.623565i
$866$	−2.71895	−	8.36808i	−0.0923938	−	0.284359i
$867$		0			0
$868$	−31.2493			−1.06067
$869$	−31.9377	−	21.3441i	−1.08341	−	0.724049i
$870$		0			0
$871$	−13.9190	+	10.1127i	−0.471627	+	0.342657i
$872$	−7.83232	−	24.1054i	−0.265236	−	0.816312i
$873$		0			0
$874$	−13.4175	−	9.74835i	−0.453852	−	0.329743i
$875$	15.1028	+	10.9728i	0.510568	+	0.370950i
$876$		0			0
$877$	9.57738	+	29.4762i	0.323405	+	0.995339i	0.972155	+	0.234337i	$0.0752920\pi$
$877$	9.57738	+	29.4762i	0.323405	+	0.995339i	−0.648750	+	0.761002i	$0.724708\pi$
$878$	5.44498	−	3.95601i	0.183759	−	0.133509i
$879$		0			0
$880$	−22.5951	+	17.8094i	−0.761682	+	0.600355i
$881$	−29.9198			−1.00802			−0.504012	−	0.863697i	$-0.668143\pi$
$881$	−29.9198			−1.00802			−0.504012	+	0.863697i	$0.668143\pi$
$882$		0			0
$883$	4.39514	+	13.5269i	0.147908	+	0.455215i	0.997374	−	0.0724296i	$-0.0230753\pi$
$883$	4.39514	+	13.5269i	0.147908	+	0.455215i	−0.849465	+	0.527645i	$0.823075\pi$
$884$	−2.47919	+	7.63015i	−0.0833841	+	0.256630i
$885$		0			0
$886$	−5.78703	−	4.20452i	−0.194419	−	0.141254i
$887$	0.812957	−	2.50202i	0.0272964	−	0.0840097i	−0.936480	−	0.350720i	$-0.885937\pi$
$887$	0.812957	−	2.50202i	0.0272964	−	0.0840097i	0.963777	+	0.266711i	$0.0859368\pi$
$888$		0			0
$889$	1.68344	−	1.22309i	0.0564608	−	0.0410211i
$890$	1.38194			0.0463228
$891$		0			0
$892$	35.2874			1.18151
$893$	61.9721	−	45.0254i	2.07382	−	1.50672i
$894$		0			0
$895$	−7.46633	+	22.9790i	−0.249572	+	0.768104i
$896$	−19.7031	−	14.3151i	−0.658234	−	0.478235i
$897$		0			0
$898$	0.233117	−	0.717460i	0.00777921	−	0.0239419i
$899$	15.3821	+	47.3412i	0.513021	+	1.57892i
$900$		0			0
$901$	6.19577			0.206411
$902$	−0.207582	+	0.735787i	−0.00691172	+	0.0244990i
$903$		0			0
$904$	−5.75971	+	4.18467i	−0.191565	+	0.139180i
$905$	−1.55809	−	4.79530i	−0.0517926	−	0.159401i
$906$		0			0
$907$	8.22162	+	5.97336i	0.272994	+	0.198342i	0.715856	−	0.698248i	$-0.246037\pi$
$907$	8.22162	+	5.97336i	0.272994	+	0.198342i	−0.442862	+	0.896590i	$0.646037\pi$
$908$	1.63197	+	1.18570i	0.0541589	+	0.0393488i
$909$		0			0
$910$	2.86265	+	8.81033i	0.0948959	+	0.292060i
$911$	−4.76694	+	3.46339i	−0.157936	+	0.114747i	−0.663946	−	0.747780i	$-0.731120\pi$
$911$	−4.76694	+	3.46339i	−0.157936	+	0.114747i	0.506010	+	0.862527i	$0.331120\pi$
$912$		0			0
$913$	0.737022	−	2.61242i	0.0243919	−	0.0864586i
$914$	−3.00232			−0.0993078
$915$		0			0
$916$	7.08137	+	21.7942i	0.233975	+	0.720101i
$917$	15.2240	−	46.8546i	0.502740	−	1.54727i
$918$		0			0
$919$	−26.1285	−	18.9835i	−0.861899	−	0.626206i	0.0665018	−	0.997786i	$-0.478816\pi$
$919$	−26.1285	−	18.9835i	−0.861899	−	0.626206i	−0.928401	+	0.371580i	$0.878816\pi$
$920$	7.85047	−	24.1613i	0.258822	−	0.796573i
$921$		0			0
$922$	1.92085	−	1.39558i	0.0632597	−	0.0459609i
$923$	−46.9581			−1.54565
$924$		0			0
$925$	−0.422494			−0.0138915
$926$	−0.0801267	+	0.0582155i	−0.00263313	+	0.00191308i
$927$		0			0
$928$	−9.11525	+	28.0539i	−0.299223	+	0.920913i
$929$	−39.5473	−	28.7328i	−1.29751	−	0.942693i	−0.297578	−	0.954697i	$-0.596179\pi$
$929$	−39.5473	−	28.7328i	−1.29751	−	0.942693i	−0.999928	+	0.0120042i	$0.996179\pi$
$930$		0			0
$931$	−1.63348	+	5.02734i	−0.0535352	+	0.164765i
$932$	8.69869	+	26.7718i	0.284935	+	0.876940i
$933$		0			0
$934$	2.77605			0.0908350
$935$	−7.86705	+	6.20078i	−0.257280	+	0.202787i
$936$		0			0
$937$	−36.4628	+	26.4917i	−1.19119	+	0.865447i	−0.993389	−	0.114796i	$-0.963379\pi$
$937$	−36.4628	+	26.4917i	−1.19119	+	0.865447i	−0.197797	+	0.980243i	$0.563379\pi$
$938$	−1.25827	−	3.87256i	−0.0410840	−	0.126444i
$939$		0			0
$940$	45.8543	+	33.3151i	1.49560	+	1.08662i
$941$	13.3116	+	9.67142i	0.433945	+	0.315279i	0.783224	−	0.621739i	$-0.213574\pi$
$941$	13.3116	+	9.67142i	0.433945	+	0.315279i	−0.349280	+	0.937019i	$0.613574\pi$
$942$		0			0
$943$	1.32715	+	4.08455i	0.0432180	+	0.133011i
$944$	−22.0257	+	16.0026i	−0.716877	+	0.520841i
$945$		0			0
$946$	4.72239	+	3.15599i	0.153538	+	0.102610i
$947$	−7.01273			−0.227883			−0.113942	−	0.993487i	$-0.536348\pi$
$947$	−7.01273			−0.227883			−0.113942	+	0.993487i	$0.536348\pi$
$948$		0			0
$949$	−2.51307	−	7.73443i	−0.0815776	−	0.251070i
$950$	1.68048	−	5.17199i	0.0545220	−	0.167802i
$951$		0			0
$952$	−3.18012	−	2.31049i	−0.103068	−	0.0748835i
$953$	3.34588	−	10.2976i	0.108384	−	0.333571i	−0.882126	−	0.471014i	$-0.843888\pi$
$953$	3.34588	−	10.2976i	0.108384	−	0.333571i	0.990510	+	0.137443i	$0.0438883\pi$
$954$		0			0
$955$	13.9169	−	10.1112i	0.450341	−	0.327192i
$956$	26.8983			0.869952
$957$		0			0
$958$	8.40693			0.271616
$959$	−7.99650	+	5.80980i	−0.258221	+	0.187608i
$960$		0			0
$961$	4.31069	−	13.2669i	0.139054	−	0.427966i
$962$	0.213588	+	0.155181i	0.00688637	+	0.00500324i
$963$		0			0
$964$	6.94611	−	21.3779i	0.223719	−	0.688537i
$965$	−2.33908	−	7.19895i	−0.0752976	−	0.231742i
$966$		0			0
$967$	5.88206			0.189154			0.0945771	−	0.995518i	$-0.469850\pi$
$967$	5.88206			0.189154			0.0945771	+	0.995518i	$0.469850\pi$
$968$	13.1431	+	8.05723i	0.422436	+	0.258969i
$969$		0			0
$970$	7.92709	−	5.75937i	0.254524	−	0.184922i
$971$	5.64280	+	17.3667i	0.181086	+	0.557325i	0.999859	−	0.0167920i	$-0.00534530\pi$
$971$	5.64280	+	17.3667i	0.181086	+	0.557325i	−0.818773	+	0.574117i	$0.805345\pi$
$972$		0			0
$973$	−6.87009	−	4.99141i	−0.220245	−	0.160017i
$974$	7.06166	+	5.13060i	0.226270	+	0.164395i
$975$		0			0
$976$	1.71852	+	5.28907i	0.0550085	+	0.169299i
$977$	1.35784	−	0.986527i	0.0434411	−	0.0315618i	−0.565853	−	0.824506i	$-0.691453\pi$
$977$	1.35784	−	0.986527i	0.0434411	−	0.0315618i	0.609294	+	0.792944i	$0.291453\pi$
$978$		0			0
$979$	1.63017	+	4.41994i	0.0521005	+	0.141262i
$980$	−3.91125			−0.124940
$981$		0			0
$982$	3.93678	+	12.1162i	0.125628	+	0.386643i
$983$	3.46689	−	10.6700i	0.110577	−	0.340320i	−0.880422	−	0.474191i	$-0.842741\pi$
$983$	3.46689	−	10.6700i	0.110577	−	0.340320i	0.990999	+	0.133871i	$0.0427408\pi$
$984$		0			0
$985$	−55.8828	−	40.6013i	−1.78058	−	1.29366i
$986$	−0.934641	+	2.87653i	−0.0297650	+	0.0916073i
$987$		0			0
$988$	39.1507	−	28.4446i	1.24555	−	0.904944i
$989$	31.9077			1.01461
$990$		0			0
$991$	−7.78978			−0.247451			−0.123725	−	0.992317i	$-0.539484\pi$
$991$	−7.78978			−0.247451			−0.123725	+	0.992317i	$0.539484\pi$
$992$	21.5495	−	15.6566i	0.684198	−	0.497099i
$993$		0			0
$994$	3.43428	−	10.5696i	0.108929	−	0.335248i
$995$	29.0012	+	21.0706i	0.919401	+	0.667984i
$996$		0			0
$997$	−13.3876	+	41.2029i	−0.423990	+	1.30491i	0.479968	+	0.877286i	$0.340648\pi$
$997$	−13.3876	+	41.2029i	−0.423990	+	1.30491i	−0.903958	+	0.427622i	$0.859352\pi$
$998$	−2.54682	−	7.83830i	−0.0806181	−	0.248117i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.d.190.2	yes	16
3.2	odd	2		297.2.f.a.190.3	yes	16
9.2	odd	6		891.2.n.i.190.2		32
9.4	even	3		891.2.n.f.784.2		32
9.5	odd	6		891.2.n.i.784.3		32
9.7	even	3		891.2.n.f.190.3		32
11.2	odd	10		3267.2.a.bl.1.3		8
11.4	even	5	inner	297.2.f.d.136.2	yes	16
11.9	even	5		3267.2.a.be.1.6		8
33.2	even	10		3267.2.a.bf.1.6		8
33.20	odd	10		3267.2.a.bm.1.3		8
33.26	odd	10		297.2.f.a.136.3	✓	16
99.4	even	15		891.2.n.f.136.3		32
99.59	odd	30		891.2.n.i.136.2		32
99.70	even	15		891.2.n.f.433.2		32
99.92	odd	30		891.2.n.i.433.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.3	✓	16	33.26	odd	10
297.2.f.a.190.3	yes	16	3.2	odd	2
297.2.f.d.136.2	yes	16	11.4	even	5	inner
297.2.f.d.190.2	yes	16	1.1	even	1	trivial
891.2.n.f.136.3		32	99.4	even	15
891.2.n.f.190.3		32	9.7	even	3
891.2.n.f.433.2		32	99.70	even	15
891.2.n.f.784.2		32	9.4	even	3
891.2.n.i.136.2		32	99.59	odd	30
891.2.n.i.190.2		32	9.2	odd	6
891.2.n.i.433.3		32	99.92	odd	30
891.2.n.i.784.3		32	9.5	odd	6
3267.2.a.be.1.6		8	11.9	even	5
3267.2.a.bf.1.6		8	33.2	even	10
3267.2.a.bl.1.3		8	11.2	odd	10
3267.2.a.bm.1.3		8	33.20	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.293070 + 0.212928i) q^{2} +(-0.577482 + 1.77731i) q^{4} +(2.17280 + 1.57863i) q^{5} +(-0.770730 + 2.37206i) q^{7} +(-0.433081 - 1.33288i) q^{8} -0.972914 q^{10} +(-1.14767 - 3.11173i) q^{11} +(-3.08851 + 2.24393i) q^{13} +(-0.279200 - 0.859290i) q^{14} +(-2.61301 - 1.89846i) q^{16} +(-0.909782 - 0.660995i) q^{17} +(2.09612 + 6.45120i) q^{19} +(-4.06046 + 2.95010i) q^{20} +(0.998921 + 0.667582i) q^{22} +6.74940 q^{23} +(0.683891 + 2.10480i) q^{25} +(0.427353 - 1.31526i) q^{26} +(-3.77080 - 2.73965i) q^{28} +(-2.29431 + 7.06116i) q^{29} +(5.42402 - 3.94078i) q^{31} +3.97298 q^{32} +0.407373 q^{34} +(-5.41925 + 3.93732i) q^{35} +(-0.0589927 + 0.181561i) q^{37} +(-1.98795 - 1.44433i) q^{38} +(1.16314 - 3.57976i) q^{40} +(0.196632 + 0.605172i) q^{41} +4.72749 q^{43} +(6.19326 - 0.242800i) q^{44} +(-1.97805 + 1.43713i) q^{46} +(-3.48969 - 10.7402i) q^{47} +(0.630458 + 0.458054i) q^{49} +(-0.648597 - 0.471233i) q^{50} +(-2.20460 - 6.78506i) q^{52} +(-4.45732 + 3.23843i) q^{53} +(2.41860 - 8.57290i) q^{55} +3.49548 q^{56} +(-0.831123 - 2.55793i) q^{58} +(2.60479 - 8.01671i) q^{59} +(-1.39299 - 1.01207i) q^{61} +(-0.750514 + 2.30984i) q^{62} +(4.06165 - 2.95096i) q^{64} -10.2530 q^{65} +4.50670 q^{67} +(1.70017 - 1.23525i) q^{68} +(0.749855 - 2.30782i) q^{70} +(9.95124 + 7.23000i) q^{71} +(-0.658284 + 2.02599i) q^{73} +(-0.0213703 - 0.0657711i) q^{74} -12.6762 q^{76} +(8.26576 - 0.324050i) q^{77} +(9.37010 - 6.80777i) q^{79} +(-2.68057 - 8.24994i) q^{80} +(-0.186485 - 0.135489i) q^{82} +(0.662117 + 0.481056i) q^{83} +(-0.933305 - 2.87242i) q^{85} +(-1.38548 + 1.00661i) q^{86} +(-3.65054 + 2.87734i) q^{88} -1.42041 q^{89} +(-2.94234 - 9.05560i) q^{91} +(-3.89766 + 11.9958i) q^{92} +(3.30960 + 2.40457i) q^{94} +(-5.62960 + 17.3261i) q^{95} +(-8.14778 + 5.91971i) q^{97} -0.282300 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31}+ \cdots + 26 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more