LMFDB - Embedded newform 416.2.ba.c.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(17,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.608487 - 1.27661i$ of defining polynomial
Character	$\chi$	$=$	416.49
Dual form			416.2.ba.c.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.28316 + 1.31818i) q^{3} -3.40672 q^{5} +(-1.30715 - 0.754684i) q^{7} +(1.97521 - 3.42116i) q^{9} +(1.69608 + 2.93770i) q^{11} +(2.16266 - 2.88494i) q^{13} +(7.77808 - 4.49068i) q^{15} +(-1.32767 + 2.29959i) q^{17} +(3.32953 - 5.76692i) q^{19} +3.97924 q^{21} +(0.307150 + 0.532000i) q^{23} +6.60576 q^{25} +2.50563i q^{27} +(2.50678 - 1.44729i) q^{29} +0.813985i q^{31} +(-7.74485 - 4.47149i) q^{33} +(4.45310 + 2.57100i) q^{35} +(2.53339 + 4.38796i) q^{37} +(-1.13482 + 9.43756i) q^{39} +(6.98302 - 4.03165i) q^{41} +(-7.93701 - 4.58243i) q^{43} +(-6.72898 + 11.6549i) q^{45} -5.88587i q^{47} +(-2.36091 - 4.08921i) q^{49} -7.00045i q^{51} -0.627889i q^{53} +(-5.77808 - 10.0079i) q^{55} +17.5557i q^{57} +(1.23678 - 2.14217i) q^{59} +(-5.75913 - 3.32504i) q^{61} +(-5.16378 + 2.98131i) q^{63} +(-7.36759 + 9.82820i) q^{65} +(0.664263 + 1.15054i) q^{67} +(-1.40255 - 0.809760i) q^{69} +(5.38030 + 3.10632i) q^{71} -10.2297i q^{73} +(-15.0820 + 8.70759i) q^{75} -5.12002i q^{77} +1.65534 q^{79} +(2.62274 + 4.54272i) q^{81} +7.81437 q^{83} +(4.52301 - 7.83408i) q^{85} +(-3.81559 + 6.60880i) q^{87} +(-1.12386 + 0.648863i) q^{89} +(-5.00414 + 2.13893i) q^{91} +(-1.07298 - 1.85846i) q^{93} +(-11.3428 + 19.6463i) q^{95} +(-12.5894 - 7.26849i) q^{97} +13.4005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) $ 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−2.28316	+	1.31818i	−1.31818	+	0.761053i	−0.983436	−	0.181256i	$-0.941984\pi$
$3$	−2.28316	+	1.31818i	−1.31818	+	0.761053i	−0.334746	+	0.942308i	$0.608650\pi$
$4$		0			0
$5$	−3.40672			−1.52353			−0.761766	−	0.647852i	$-0.775668\pi$
$5$	−3.40672			−1.52353			−0.761766	+	0.647852i	$0.775668\pi$
$6$		0			0
$7$	−1.30715	−	0.754684i	−0.494056	−	0.285244i	0.232199	−	0.972668i	$-0.425408\pi$
$7$	−1.30715	−	0.754684i	−0.494056	−	0.285244i	−0.726256	+	0.687425i	$0.758741\pi$
$8$		0			0
$9$	1.97521	−	3.42116i	0.658402	−	1.14039i
$10$		0			0
$11$	1.69608	+	2.93770i	0.511388	+	0.885751i	0.999913	+	0.0132004i	$0.00420193\pi$
$11$	1.69608	+	2.93770i	0.511388	+	0.885751i	−0.488525	+	0.872550i	$0.662465\pi$
$12$		0			0
$13$	2.16266	−	2.88494i	0.599815	−	0.800139i
$13$	2.16266	−	2.88494i	0.599815	−	0.800139i
$14$		0			0
$15$	7.77808	−	4.49068i	2.00829	−	1.15949i
$16$		0			0
$17$	−1.32767	+	2.29959i	−0.322008	+	0.557734i	−0.980902	−	0.194502i	$-0.937691\pi$
$17$	−1.32767	+	2.29959i	−0.322008	+	0.557734i	0.658894	+	0.752235i	$0.271024\pi$
$18$		0			0
$19$	3.32953	−	5.76692i	0.763847	−	1.32302i	−0.177006	−	0.984210i	$-0.556641\pi$
$19$	3.32953	−	5.76692i	0.763847	−	1.32302i	0.940854	−	0.338813i	$-0.110025\pi$
$20$		0			0
$21$	3.97924			0.868342
$22$		0			0
$23$	0.307150	+	0.532000i	0.0640453	+	0.110930i	0.896270	−	0.443509i	$-0.146266\pi$
$23$	0.307150	+	0.532000i	0.0640453	+	0.110930i	−0.832225	+	0.554438i	$0.812933\pi$
$24$		0			0
$25$	6.60576			1.32115
$26$		0			0
$27$			2.50563i			0.482209i
$28$		0			0
$29$	2.50678	−	1.44729i	0.465498	−	0.268756i	−0.248855	−	0.968541i	$-0.580054\pi$
$29$	2.50678	−	1.44729i	0.465498	−	0.268756i	0.714353	+	0.699785i	$0.246721\pi$
$30$		0			0
$31$			0.813985i			0.146196i	0.997325	+	0.0730980i	$0.0232886\pi$
$31$			0.813985i			0.146196i	−0.997325	+	0.0730980i	$0.976711\pi$
$32$		0			0
$33$	−7.74485	−	4.47149i	−1.34821	−	0.778387i
$34$		0			0
$35$	4.45310	+	2.57100i	0.752711	+	0.434578i
$36$		0			0
$37$	2.53339	+	4.38796i	0.416486	+	0.721376i	0.995583	−	0.0938831i	$-0.0299280\pi$
$37$	2.53339	+	4.38796i	0.416486	+	0.721376i	−0.579097	+	0.815259i	$0.696595\pi$
$38$		0			0
$39$	−1.13482	+	9.43756i	−0.181717	+	1.51122i
$40$		0			0
$41$	6.98302	−	4.03165i	1.09056	−	0.629637i	0.156837	−	0.987624i	$-0.449870\pi$
$41$	6.98302	−	4.03165i	1.09056	−	0.629637i	0.933726	+	0.357987i	$0.116537\pi$
$42$		0			0
$43$	−7.93701	−	4.58243i	−1.21038	−	0.698815i	−0.247540	−	0.968878i	$-0.579622\pi$
$43$	−7.93701	−	4.58243i	−1.21038	−	0.698815i	−0.962843	+	0.270063i	$0.912955\pi$
$44$		0			0
$45$	−6.72898	+	11.6549i	−1.00310	+	1.73741i
$46$		0			0
$47$		−	5.88587i		−	0.858543i	−0.903176	−	0.429271i	$-0.858770\pi$
$47$		−	5.88587i		−	0.858543i	0.903176	−	0.429271i	$-0.141230\pi$
$48$		0			0
$49$	−2.36091	−	4.08921i	−0.337272	−	0.584173i
$50$		0			0
$51$		−	7.00045i		−	0.980259i
$52$		0			0
$53$		−	0.627889i		−	0.0862472i	−0.999070	−	0.0431236i	$-0.986269\pi$
$53$		−	0.627889i		−	0.0862472i	0.999070	−	0.0431236i	$-0.0137309\pi$
$54$		0			0
$55$	−5.77808	−	10.0079i	−0.779117	−	1.34947i
$56$		0			0
$57$			17.5557i			2.32531i
$58$		0			0
$59$	1.23678	−	2.14217i	0.161015	−	0.278887i	−0.774218	−	0.632919i	$-0.781857\pi$
$59$	1.23678	−	2.14217i	0.161015	−	0.278887i	0.935233	+	0.354033i	$0.115190\pi$
$60$		0			0
$61$	−5.75913	−	3.32504i	−0.737381	−	0.425727i	0.0837352	−	0.996488i	$-0.473315\pi$
$61$	−5.75913	−	3.32504i	−0.737381	−	0.425727i	−0.821116	+	0.570761i	$0.806648\pi$
$62$		0			0
$63$	−5.16378	+	2.98131i	−0.650575	+	0.375610i
$64$		0			0
$65$	−7.36759	+	9.82820i	−0.913837	+	1.21904i
$66$		0			0
$67$	0.664263	+	1.15054i	0.0811526	+	0.140560i	0.903745	−	0.428071i	$-0.140807\pi$
$67$	0.664263	+	1.15054i	0.0811526	+	0.140560i	−0.822593	+	0.568631i	$0.807473\pi$
$68$		0			0
$69$	−1.40255	−	0.809760i	−0.168847	−	0.0974837i
$70$		0			0
$71$	5.38030	+	3.10632i	0.638524	+	0.368652i	0.784046	−	0.620703i	$-0.213153\pi$
$71$	5.38030	+	3.10632i	0.638524	+	0.368652i	−0.145521	+	0.989355i	$0.546486\pi$
$72$		0			0
$73$		−	10.2297i		−	1.19729i	−0.801014	−	0.598646i	$-0.795706\pi$
$73$		−	10.2297i		−	1.19729i	0.801014	−	0.598646i	$-0.204294\pi$
$74$		0			0
$75$	−15.0820	+	8.70759i	−1.74152	+	1.00547i
$76$		0			0
$77$		−	5.12002i		−	0.583481i
$78$		0			0
$79$	1.65534			0.186241			0.0931203	−	0.995655i	$-0.470316\pi$
$79$	1.65534			0.186241			0.0931203	+	0.995655i	$0.470316\pi$
$80$		0			0
$81$	2.62274	+	4.54272i	0.291416	+	0.504747i
$82$		0			0
$83$	7.81437			0.857738			0.428869	−	0.903367i	$-0.358912\pi$
$83$	7.81437			0.857738			0.428869	+	0.903367i	$0.358912\pi$
$84$		0			0
$85$	4.52301	−	7.83408i	0.490589	−	0.849725i
$86$		0			0
$87$	−3.81559	+	6.60880i	−0.409074	+	0.708537i
$88$		0			0
$89$	−1.12386	+	0.648863i	−0.119129	+	0.0687794i	−0.558381	−	0.829585i	$-0.688577\pi$
$89$	−1.12386	+	0.648863i	−0.119129	+	0.0687794i	0.439251	+	0.898364i	$0.355244\pi$
$90$		0			0
$91$	−5.00414	+	2.13893i	−0.524577	+	0.224220i
$92$		0			0
$93$	−1.07298	−	1.85846i	−0.111263	−	0.192713i
$94$		0			0
$95$	−11.3428	+	19.6463i	−1.16375	+	2.01567i
$96$		0			0
$97$	−12.5894	−	7.26849i	−1.27826	−	0.738004i	−0.301732	−	0.953393i	$-0.597565\pi$
$97$	−12.5894	−	7.26849i	−1.27826	−	0.738004i	−0.976528	+	0.215389i	$0.930898\pi$
$98$		0			0
$99$	13.4005			1.34680
$100$		0			0
$101$	−9.31772	+	5.37959i	−0.927148	+	0.535289i	−0.885908	−	0.463860i	$-0.846464\pi$
$101$	−9.31772	+	5.37959i	−0.927148	+	0.535289i	−0.0412395	+	0.999149i	$0.513131\pi$
$102$		0			0
$103$	3.40986			0.335984			0.167992	−	0.985788i	$-0.446272\pi$
$103$	3.40986			0.335984			0.167992	+	0.985788i	$0.446272\pi$
$104$		0			0
$105$	−13.5562			−1.32295
$106$		0			0
$107$	0.792036	−	0.457282i	0.0765690	−	0.0442071i	−0.461227	−	0.887282i	$-0.652591\pi$
$107$	0.792036	−	0.457282i	0.0765690	−	0.0442071i	0.537796	+	0.843075i	$0.319257\pi$
$108$		0			0
$109$	20.3289			1.94716			0.973578	−	0.228355i	$-0.0733348\pi$
$109$	20.3289			1.94716			0.973578	+	0.228355i	$0.0733348\pi$
$110$		0			0
$111$	−11.5682	−	6.67893i	−1.09801	−	0.633936i
$112$		0			0
$113$	−1.71337	+	2.96765i	−0.161180	+	0.279173i	−0.935292	−	0.353876i	$-0.884863\pi$
$113$	−1.71337	+	2.96765i	−0.161180	+	0.279173i	0.774112	+	0.633049i	$0.218197\pi$
$114$		0			0
$115$	−1.04638	−	1.81238i	−0.0975751	−	0.169005i
$116$		0			0
$117$	−5.59814	−	13.0972i	−0.517548	−	1.21083i
$118$		0			0
$119$	3.47093	−	2.00394i	0.318180	−	0.183701i
$120$		0			0
$121$	−0.253396	+	0.438894i	−0.0230360	+	0.0398995i
$122$		0			0
$123$	−10.6289	+	18.4098i	−0.958374	+	1.65995i
$124$		0			0
$125$	−5.47036			−0.489284
$126$		0			0
$127$	2.69954	+	4.67573i	0.239545	+	0.414904i	0.960584	−	0.277991i	$-0.0896684\pi$
$127$	2.69954	+	4.67573i	0.239545	+	0.414904i	−0.721039	+	0.692895i	$0.756335\pi$
$128$		0			0
$129$	24.1619			2.12734
$130$		0			0
$131$		−	13.5230i		−	1.18151i	−0.806850	−	0.590756i	$-0.798829\pi$
$131$		−	13.5230i		−	1.18151i	0.806850	−	0.590756i	$-0.201171\pi$
$132$		0			0
$133$	−8.70440	+	5.02549i	−0.754767	+	0.435765i
$134$		0			0
$135$		−	8.53599i		−	0.734661i
$136$		0			0
$137$	7.11430	+	4.10744i	0.607816	+	0.350923i	0.772110	−	0.635489i	$-0.219201\pi$
$137$	7.11430	+	4.10744i	0.607816	+	0.350923i	−0.164294	+	0.986411i	$0.552535\pi$
$138$		0			0
$139$	16.9128	+	9.76458i	1.43452	+	0.828221i	0.997461	−	0.0712113i	$-0.0226865\pi$
$139$	16.9128	+	9.76458i	1.43452	+	0.828221i	0.437060	+	0.899432i	$0.356020\pi$
$140$		0			0
$141$	7.75865	+	13.4384i	0.653396	+	1.13172i
$142$		0			0
$143$	12.1432	+	1.46016i	1.01546	+	0.122104i
$144$		0			0
$145$	−8.53992	+	4.93052i	−0.709202	+	0.409458i
$146$		0			0
$147$	10.7806	+	6.22420i	0.889172	+	0.513364i
$148$		0			0
$149$	6.48603	−	11.2341i	0.531356	−	0.920335i	−0.467974	−	0.883742i	$-0.655016\pi$
$149$	6.48603	−	11.2341i	0.531356	−	0.920335i	0.999330	−	0.0365934i	$-0.0116506\pi$
$150$		0			0
$151$		−	16.2580i		−	1.32306i	−0.749920	−	0.661528i	$-0.769908\pi$
$151$		−	16.2580i		−	1.32306i	0.749920	−	0.661528i	$-0.230092\pi$
$152$		0			0
$153$	5.24485	+	9.08435i	0.424021	+	0.734426i
$154$		0			0
$155$		−	2.77302i		−	0.222734i
$156$		0			0
$157$		−	8.87819i		−	0.708557i	−0.935140	−	0.354278i	$-0.884727\pi$
$157$		−	8.87819i		−	0.708557i	0.935140	−	0.354278i	$-0.115273\pi$
$158$		0			0
$159$	0.827672	+	1.43357i	0.0656386	+	0.113689i
$160$		0			0
$161$		−	0.927206i		−	0.0730740i
$162$		0			0
$163$	2.04217	−	3.53714i	0.159955	−	0.277050i	−0.774897	−	0.632087i	$-0.782198\pi$
$163$	2.04217	−	3.53714i	0.159955	−	0.277050i	0.934852	+	0.355037i	$0.115532\pi$
$164$		0			0
$165$	26.3846	+	15.2331i	2.05403	+	1.18590i
$166$		0			0
$167$	−15.0204	+	8.67204i	−1.16231	+	0.671063i	−0.951858	−	0.306540i	$-0.900829\pi$
$167$	−15.0204	+	8.67204i	−1.16231	+	0.671063i	−0.210457	+	0.977603i	$0.567495\pi$
$168$		0			0
$169$	−3.64578	−	12.4783i	−0.280445	−	0.959870i
$170$		0			0
$171$	−13.1530	−	22.7817i	−1.00584	−	1.74216i
$172$		0			0
$173$	−12.2964	−	7.09933i	−0.934878	−	0.539752i	−0.0465270	−	0.998917i	$-0.514815\pi$
$173$	−12.2964	−	7.09933i	−0.934878	−	0.539752i	−0.888351	+	0.459165i	$0.848149\pi$
$174$		0			0
$175$	−8.63472	−	4.98526i	−0.652723	−	0.376850i
$176$		0			0
$177$			6.52121i			0.490164i
$178$		0			0
$179$	−4.23741	+	2.44647i	−0.316719	+	0.182858i	−0.649929	−	0.759995i	$-0.725201\pi$
$179$	−4.23741	+	2.44647i	−0.316719	+	0.182858i	0.333210	+	0.942853i	$0.391868\pi$
$180$		0			0
$181$			21.2024i			1.57596i	0.615702	+	0.787979i	$0.288873\pi$
$181$			21.2024i			1.57596i	−0.615702	+	0.787979i	$0.711127\pi$
$182$		0			0
$183$	17.5320			1.29600
$184$		0			0
$185$	−8.63055	−	14.9486i	−0.634531	−	1.09904i
$186$		0			0
$187$	−9.00737			−0.658684
$188$		0			0
$189$	1.89096	−	3.27524i	0.137547	−	0.238238i
$190$		0			0
$191$	−0.733892	+	1.27114i	−0.0531026	+	0.0919763i	−0.891355	−	0.453306i	$-0.850244\pi$
$191$	−0.733892	+	1.27114i	−0.0531026	+	0.0919763i	0.838252	+	0.545283i	$0.183578\pi$
$192$		0			0
$193$	14.7436	−	8.51223i	1.06127	−	0.612724i	0.135486	−	0.990779i	$-0.456740\pi$
$193$	14.7436	−	8.51223i	1.06127	−	0.612724i	0.925783	+	0.378055i	$0.123407\pi$
$194$		0			0
$195$	3.86602	−	32.1511i	0.276852	−	2.30239i
$196$		0			0
$197$	−8.23055	−	14.2557i	−0.586402	−	1.01568i	−0.994699	−	0.102829i	$-0.967211\pi$
$197$	−8.23055	−	14.2557i	−0.586402	−	1.01568i	0.408297	−	0.912849i	$-0.366123\pi$
$198$		0			0
$199$	9.15170	−	15.8512i	0.648747	−	1.12366i	−0.334676	−	0.942333i	$-0.608627\pi$
$199$	9.15170	−	15.8512i	0.648747	−	1.12366i	0.983422	−	0.181329i	$-0.0580399\pi$
$200$		0			0
$201$	−3.03323	−	1.75124i	−0.213948	−	0.123523i
$202$		0			0
$203$	−4.36899			−0.306643
$204$		0			0
$205$	−23.7892	+	13.7347i	−1.66151	+	0.959273i
$206$		0			0
$207$	2.42674			0.168670
$208$		0			0
$209$	22.5887			1.56249
$210$		0			0
$211$	−3.82356	+	2.20753i	−0.263225	+	0.151973i	−0.625805	−	0.779980i	$-0.715229\pi$
$211$	−3.82356	+	2.20753i	−0.263225	+	0.151973i	0.362580	+	0.931953i	$0.381896\pi$
$212$		0			0
$213$	−16.3788			−1.12226
$214$		0			0
$215$	27.0392	+	15.6111i	1.84406	+	1.06467i
$216$		0			0
$217$	0.614301	−	1.06400i	0.0417015	−	0.0722291i
$218$		0			0
$219$	13.4846	+	23.3559i	0.911202	+	1.57825i
$220$		0			0
$221$	3.76289	+	8.80350i	0.253119	+	0.592188i
$222$		0			0
$223$	4.37362	−	2.52511i	0.292879	−	0.169094i	−0.346360	−	0.938102i	$-0.612583\pi$
$223$	4.37362	−	2.52511i	0.292879	−	0.169094i	0.639240	+	0.769008i	$0.279249\pi$
$224$		0			0
$225$	13.0477	−	22.5993i	0.869849	−	1.50662i
$226$		0			0
$227$	−7.30877	+	12.6592i	−0.485100	+	0.840219i	−0.999853	−	0.0171199i	$-0.994550\pi$
$227$	−7.30877	+	12.6592i	−0.485100	+	0.840219i	0.514753	+	0.857339i	$0.327884\pi$
$228$		0			0
$229$	12.1681			0.804089			0.402045	−	0.915620i	$-0.368300\pi$
$229$	12.1681			0.804089			0.402045	+	0.915620i	$0.368300\pi$
$230$		0			0
$231$	6.74912	+	11.6898i	0.444060	+	0.769134i
$232$		0			0
$233$	−11.4232			−0.748361			−0.374180	−	0.927356i	$-0.622076\pi$
$233$	−11.4232			−0.748361			−0.374180	+	0.927356i	$0.622076\pi$
$234$		0			0
$235$			20.0515i			1.30802i
$236$		0			0
$237$	−3.77941	+	2.18204i	−0.245499	+	0.141739i
$238$		0			0
$239$		−	24.6424i		−	1.59398i	−0.603990	−	0.796992i	$-0.706423\pi$
$239$		−	24.6424i		−	1.59398i	0.603990	−	0.796992i	$-0.293577\pi$
$240$		0			0
$241$	−0.154956	−	0.0894640i	−0.00998161	−	0.00576288i	0.495001	−	0.868892i	$-0.335168\pi$
$241$	−0.154956	−	0.0894640i	−0.00998161	−	0.00576288i	−0.504982	+	0.863130i	$0.668501\pi$
$242$		0			0
$243$	−18.4861	−	10.6729i	−1.18588	−	0.684670i
$244$		0			0
$245$	8.04295	+	13.9308i	0.513845	+	0.890006i
$246$		0			0
$247$	−9.43658	−	22.0774i	−0.600435	−	1.40475i
$248$		0			0
$249$	−17.8414	+	10.3008i	−1.13065	+	0.652784i
$250$		0			0
$251$	−17.4835	−	10.0941i	−1.10355	−	0.637134i	−0.166397	−	0.986059i	$-0.553213\pi$
$251$	−17.4835	−	10.0941i	−1.10355	−	0.637134i	−0.937151	+	0.348925i	$0.886547\pi$
$252$		0			0
$253$	−1.04191	+	1.80463i	−0.0655040	+	0.113456i
$254$		0			0
$255$			23.8486i			1.49346i
$256$		0			0
$257$	−0.0990699	−	0.171594i	−0.00617981	−	0.0107037i	0.862919	−	0.505342i	$-0.168634\pi$
$257$	−0.0990699	−	0.171594i	−0.00617981	−	0.0107037i	−0.869099	+	0.494639i	$0.835300\pi$
$258$		0			0
$259$		−	7.64763i		−	0.475200i
$260$		0			0
$261$		−	11.4348i		−	0.707797i
$262$		0			0
$263$	−3.69285	−	6.39620i	−0.227711	−	0.394407i	0.729418	−	0.684068i	$-0.239791\pi$
$263$	−3.69285	−	6.39620i	−0.227711	−	0.394407i	−0.957129	+	0.289661i	$0.906457\pi$
$264$		0			0
$265$			2.13904i			0.131400i
$266$		0			0
$267$	1.71064	−	2.96291i	0.104689	−	0.181327i
$268$		0			0
$269$	16.0265	+	9.25292i	0.977155	+	0.564161i	0.901410	−	0.432967i	$-0.142533\pi$
$269$	16.0265	+	9.25292i	0.977155	+	0.564161i	0.0757448	+	0.997127i	$0.475867\pi$
$270$		0			0
$271$	8.18255	−	4.72420i	0.497055	−	0.286975i	−0.230442	−	0.973086i	$-0.574017\pi$
$271$	8.18255	−	4.72420i	0.497055	−	0.286975i	0.727496	+	0.686112i	$0.240684\pi$
$272$		0			0
$273$	8.60576	−	11.4799i	0.520844	−	0.694794i
$274$		0			0
$275$	11.2039	+	19.4057i	0.675621	+	1.17021i
$276$		0			0
$277$	−8.64403	−	4.99063i	−0.519370	−	0.299858i	0.217307	−	0.976103i	$-0.430273\pi$
$277$	−8.64403	−	4.99063i	−0.519370	−	0.299858i	−0.736677	+	0.676245i	$0.763606\pi$
$278$		0			0
$279$	2.78477	+	1.60779i	0.166720	+	0.0962557i
$280$		0			0
$281$			11.1204i			0.663387i	0.943387	+	0.331694i	$0.107620\pi$
$281$			11.1204i			0.663387i	−0.943387	+	0.331694i	$0.892380\pi$
$282$		0			0
$283$	−1.16222	+	0.671005i	−0.0690865	+	0.0398871i	−0.534145	−	0.845393i	$-0.679367\pi$
$283$	−1.16222	+	0.671005i	−0.0690865	+	0.0398871i	0.465059	+	0.885280i	$0.346033\pi$
$284$		0			0
$285$		−	59.8075i		−	3.54269i
$286$		0			0
$287$	−12.1705			−0.718400
$288$		0			0
$289$	4.97458	+	8.61622i	0.292622	+	0.506836i
$290$		0			0
$291$	38.3248			2.24664
$292$		0			0
$293$	−4.18139	+	7.24239i	−0.244280	+	0.423105i	−0.961929	−	0.273300i	$-0.911885\pi$
$293$	−4.18139	+	7.24239i	−0.244280	+	0.423105i	0.717649	+	0.696405i	$0.245218\pi$
$294$		0			0
$295$	−4.21337	+	7.29777i	−0.245312	+	0.424893i
$296$		0			0
$297$	−7.36080	+	4.24976i	−0.427117	+	0.246596i
$298$		0			0
$299$	2.19905	+	0.264426i	0.127174	+	0.0152921i
$300$		0			0
$301$	6.91658	+	11.9799i	0.398665	+	0.690508i
$302$		0			0
$303$	14.1826	−	24.5649i	0.814766	−	1.41122i
$304$		0			0
$305$	19.6198	+	11.3275i	1.12342	+	0.648609i
$306$		0			0
$307$	19.5458			1.11554			0.557770	−	0.829996i	$-0.311657\pi$
$307$	19.5458			1.11554			0.557770	+	0.829996i	$0.311657\pi$
$308$		0			0
$309$	−7.78525	+	4.49482i	−0.442888	+	0.255701i
$310$		0			0
$311$	−24.9794			−1.41645			−0.708226	−	0.705986i	$-0.750504\pi$
$311$	−24.9794			−1.41645			−0.708226	+	0.705986i	$0.750504\pi$
$312$		0			0
$313$	4.98312			0.281663			0.140831	−	0.990034i	$-0.455022\pi$
$313$	4.98312			0.281663			0.140831	+	0.990034i	$0.455022\pi$
$314$		0			0
$315$	17.5916	−	10.1565i	0.991173	−	0.572254i
$316$		0			0
$317$	22.2072			1.24728			0.623639	−	0.781712i	$-0.285653\pi$
$317$	22.2072			1.24728			0.623639	+	0.781712i	$0.285653\pi$
$318$		0			0
$319$	8.50343	+	4.90946i	0.476101	+	0.274877i
$320$		0			0
$321$	−1.20556	+	2.08809i	−0.0672879	+	0.116546i
$322$		0			0
$323$	8.84106	+	15.3132i	0.491930	+	0.852047i
$324$		0			0
$325$	14.2860	−	19.0572i	0.792446	−	1.05710i
$326$		0			0
$327$	−46.4141	+	26.7972i	−2.56671	+	1.48189i
$328$		0			0
$329$	−4.44197	+	7.69372i	−0.244894	+	0.424169i
$330$		0			0
$331$	−6.63759	+	11.4967i	−0.364835	+	0.631913i	−0.988750	−	0.149579i	$-0.952208\pi$
$331$	−6.63759	+	11.4967i	−0.364835	+	0.631913i	0.623914	+	0.781493i	$0.285541\pi$
$332$		0			0
$333$	20.0159			1.09686
$334$		0			0
$335$	−2.26296	−	3.91956i	−0.123639	−	0.214148i
$336$		0			0
$337$	−16.5718			−0.902723			−0.451361	−	0.892341i	$-0.649061\pi$
$337$	−16.5718			−0.902723			−0.451361	+	0.892341i	$0.649061\pi$
$338$		0			0
$339$		−	9.03414i		−	0.490667i
$340$		0			0
$341$	−2.39124	+	1.38059i	−0.129493	+	0.0747629i
$342$		0			0
$343$			17.6925i			0.955306i
$344$		0			0
$345$	4.77808	+	2.75863i	0.257243	+	0.148520i
$346$		0			0
$347$	−8.74418	−	5.04846i	−0.469412	−	0.271015i	0.246581	−	0.969122i	$-0.420693\pi$
$347$	−8.74418	−	5.04846i	−0.469412	−	0.271015i	−0.715994	+	0.698107i	$0.754026\pi$
$348$		0			0
$349$	−12.5147	−	21.6761i	−0.669897	−	1.16030i	−0.977933	−	0.208921i	$-0.933005\pi$
$349$	−12.5147	−	21.6761i	−0.669897	−	1.16030i	0.308035	−	0.951375i	$-0.400328\pi$
$350$		0			0
$351$	7.22860	+	5.41884i	0.385834	+	0.289236i
$352$		0			0
$353$	−3.34290	+	1.93003i	−0.177925	+	0.102725i	−0.586317	−	0.810082i	$-0.699423\pi$
$353$	−3.34290	+	1.93003i	−0.177925	+	0.102725i	0.408393	+	0.912806i	$0.366089\pi$
$354$		0			0
$355$	−18.3292	−	10.5824i	−0.972813	−	0.561654i
$356$		0			0
$357$	−5.28313	+	9.15064i	−0.279613	+	0.484303i
$358$		0			0
$359$			14.0532i			0.741702i	0.928692	+	0.370851i	$0.120934\pi$
$359$			14.0532i			0.741702i	−0.928692	+	0.370851i	$0.879066\pi$
$360$		0			0
$361$	−12.6716	−	21.9478i	−0.666926	−	1.15515i
$362$		0			0
$363$		−	1.33609i		−	0.0701264i
$364$		0			0
$365$			34.8496i			1.82411i
$366$		0			0
$367$	10.2165	+	17.6955i	0.533298	+	0.923699i	0.999244	+	0.0388859i	$0.0123809\pi$
$367$	10.2165	+	17.6955i	0.533298	+	0.923699i	−0.465946	+	0.884813i	$0.654286\pi$
$368$		0			0
$369$		−	31.8533i		−	1.65822i
$370$		0			0
$371$	−0.473858	+	0.820745i	−0.0246015	+	0.0426110i
$372$		0			0
$373$	−9.53854	−	5.50708i	−0.493887	−	0.285146i	0.232299	−	0.972645i	$-0.425375\pi$
$373$	−9.53854	−	5.50708i	−0.493887	−	0.285146i	−0.726186	+	0.687499i	$0.758709\pi$
$374$		0			0
$375$	12.4897	−	7.21093i	0.644965	−	0.372371i
$376$		0			0
$377$	1.24597	−	10.3619i	0.0641709	−	0.533667i
$378$		0			0
$379$	−3.97232	−	6.88027i	−0.204045	−	0.353416i	0.745783	−	0.666189i	$-0.232075\pi$
$379$	−3.97232	−	6.88027i	−0.204045	−	0.353416i	−0.949828	+	0.312773i	$0.898742\pi$
$380$		0			0
$381$	−12.3269	−	7.11696i	−0.631528	−	0.364613i
$382$		0			0
$383$	−6.51992	−	3.76428i	−0.333152	−	0.192346i	0.324087	−	0.946027i	$-0.394943\pi$
$383$	−6.51992	−	3.76428i	−0.333152	−	0.192346i	−0.657240	+	0.753681i	$0.728276\pi$
$384$		0			0
$385$			17.4425i			0.888952i
$386$		0			0
$387$	−31.3545	+	18.1025i	−1.59384	+	0.920202i
$388$		0			0
$389$		−	0.770469i		−	0.0390643i	−0.999809	−	0.0195322i	$-0.993782\pi$
$389$		−	0.770469i		−	0.0390643i	0.999809	−	0.0195322i	$-0.00621768\pi$
$390$		0			0
$391$	−1.63118			−0.0824923
$392$		0			0
$393$	17.8258	+	30.8752i	0.899193	+	1.55745i
$394$		0			0
$395$	−5.63930			−0.283744
$396$		0			0
$397$	−6.90453	+	11.9590i	−0.346528	+	0.600205i	−0.985630	−	0.168917i	$-0.945973\pi$
$397$	−6.90453	+	11.9590i	−0.346528	+	0.600205i	0.639102	+	0.769122i	$0.279306\pi$
$398$		0			0
$399$	13.2490	−	22.9480i	0.663280	−	1.14884i
$400$		0			0
$401$	−31.1377	+	17.9773i	−1.55494	+	0.897745i	−0.557213	+	0.830370i	$0.688129\pi$
$401$	−31.1377	+	17.9773i	−1.55494	+	0.897745i	−0.997728	+	0.0673752i	$0.978538\pi$
$402$		0			0
$403$	2.34830	+	1.76037i	0.116977	+	0.0876905i
$404$		0			0
$405$	−8.93495	−	15.4758i	−0.443981	−	0.768998i
$406$		0			0
$407$	−8.59367	+	14.8847i	−0.425973	+	0.737806i
$408$		0			0
$409$	−3.98302	−	2.29959i	−0.196947	−	0.113708i	0.398283	−	0.917262i	$-0.369606\pi$
$409$	−3.98302	−	2.29959i	−0.196947	−	0.113708i	−0.595231	+	0.803555i	$0.702939\pi$
$410$		0			0
$411$	−21.6574			−1.06828
$412$		0			0
$413$	−3.23332	+	1.86676i	−0.159101	+	0.0918571i
$414$		0			0
$415$	−26.6214			−1.30679
$416$		0			0
$417$	−51.4860			−2.52128
$418$		0			0
$419$	−33.6915	+	19.4518i	−1.64594	+	0.950284i	−0.667277	+	0.744810i	$0.732540\pi$
$419$	−33.6915	+	19.4518i	−1.64594	+	0.950284i	−0.978663	+	0.205474i	$0.934126\pi$
$420$		0			0
$421$	−25.5891			−1.24714			−0.623568	−	0.781769i	$-0.714317\pi$
$421$	−25.5891			−1.24714			−0.623568	+	0.781769i	$0.714317\pi$
$422$		0			0
$423$	−20.1365	−	11.6258i	−0.979070	−	0.565266i
$424$		0			0
$425$	−8.77027	+	15.1906i	−0.425421	+	0.736850i
$426$		0			0
$427$	5.01870	+	8.69264i	0.242872	+	0.420666i
$428$		0			0
$429$	−29.6495	+	12.6731i	−1.43149	+	0.611864i
$430$		0			0
$431$	14.9148	−	8.61104i	0.718419	−	0.414779i	−0.0957515	−	0.995405i	$-0.530525\pi$
$431$	14.9148	−	8.61104i	0.718419	−	0.414779i	0.814170	+	0.580626i	$0.197192\pi$
$432$		0			0
$433$	−9.17891	+	15.8983i	−0.441110	+	0.764025i	−0.997772	−	0.0667139i	$-0.978749\pi$
$433$	−9.17891	+	15.8983i	−0.441110	+	0.764025i	0.556662	+	0.830739i	$0.312082\pi$
$434$		0			0
$435$	12.9987	−	22.5143i	0.623238	−	1.07948i
$436$		0			0
$437$	4.09067			0.195683
$438$		0			0
$439$	−17.6824	−	30.6269i	−0.843937	−	1.46174i	−0.886541	−	0.462650i	$-0.846899\pi$
$439$	−17.6824	−	30.6269i	−0.843937	−	1.46174i	0.0426041	−	0.999092i	$-0.486435\pi$
$440$		0			0
$441$	−18.6531			−0.888243
$442$		0			0
$443$		−	21.5119i		−	1.02206i	−0.859563	−	0.511030i	$-0.829264\pi$
$443$		−	21.5119i		−	1.02206i	0.859563	−	0.511030i	$-0.170736\pi$
$444$		0			0
$445$	3.82869	−	2.21050i	0.181497	−	0.104788i
$446$		0			0
$447$			34.1990i			1.61756i
$448$		0			0
$449$	19.2769	+	11.1295i	0.909731	+	0.525233i	0.880345	−	0.474335i	$-0.157311\pi$
$449$	19.2769	+	11.1295i	0.909731	+	0.525233i	0.0293864	+	0.999568i	$0.490645\pi$
$450$		0			0
$451$	23.6875	+	13.6760i	1.11540	+	0.643978i
$452$		0			0
$453$	21.4310	+	37.1196i	1.00692	+	1.74403i
$454$		0			0
$455$	17.0477	−	7.28673i	0.799210	−	0.341607i
$456$		0			0
$457$	15.2508	−	8.80505i	0.713402	−	0.411883i	−0.0989172	−	0.995096i	$-0.531538\pi$
$457$	15.2508	−	8.80505i	0.713402	−	0.411883i	0.812320	+	0.583213i	$0.198205\pi$
$458$		0			0
$459$	−5.76194	−	3.32666i	−0.268944	−	0.155275i
$460$		0			0
$461$	−13.2686	+	22.9818i	−0.617979	+	1.07037i	0.371875	+	0.928283i	$0.378715\pi$
$461$	−13.2686	+	22.9818i	−0.617979	+	1.07037i	−0.989854	+	0.142088i	$0.954618\pi$
$462$		0			0
$463$			24.6645i			1.14626i	0.819466	+	0.573128i	$0.194270\pi$
$463$			24.6645i			1.14626i	−0.819466	+	0.573128i	$0.805730\pi$
$464$		0			0
$465$	3.65534	+	6.33124i	0.169512	+	0.293604i
$466$		0			0
$467$		−	16.4718i		−	0.762226i	−0.924528	−	0.381113i	$-0.875541\pi$
$467$		−	16.4718i		−	0.762226i	0.924528	−	0.381113i	$-0.124459\pi$
$468$		0			0
$469$		−	2.00523i		−	0.0925931i
$470$		0			0
$471$	11.7031	+	20.2703i	0.539249	+	0.934007i
$472$		0			0
$473$		−	31.0888i		−	1.42946i
$474$		0			0
$475$	21.9941	−	38.0949i	1.00916	−	1.74791i
$476$		0			0
$477$	−2.14811	−	1.24021i	−0.0983551	−	0.0567853i
$478$		0			0
$479$	28.7794	−	16.6158i	1.31496	−	0.759194i	0.332050	−	0.943262i	$-0.392260\pi$
$479$	28.7794	−	16.6158i	1.31496	−	0.759194i	0.982914	+	0.184068i	$0.0589265\pi$
$480$		0			0
$481$	18.1379	+	2.18099i	0.827015	+	0.0994447i
$482$		0			0
$483$	1.22223	+	2.11696i	0.0556132	+	0.0963249i
$484$		0			0
$485$	42.8886	+	24.7617i	1.94747	+	1.12437i
$486$		0			0
$487$	10.7320	+	6.19614i	0.486315	+	0.280774i	0.723044	−	0.690802i	$-0.242742\pi$
$487$	10.7320	+	6.19614i	0.486315	+	0.280774i	−0.236730	+	0.971576i	$0.576076\pi$
$488$		0			0
$489$			10.7678i			0.486936i
$490$		0			0
$491$	9.13776	−	5.27569i	0.412381	−	0.238089i	−0.279431	−	0.960166i	$-0.590146\pi$
$491$	9.13776	−	5.27569i	0.412381	−	0.238089i	0.691812	+	0.722077i	$0.256813\pi$
$492$		0			0
$493$			7.68612i			0.346165i
$494$		0			0
$495$	−45.6516			−2.05189
$496$		0			0
$497$	−4.68858	−	8.12085i	−0.210311	−	0.364270i
$498$		0			0
$499$	−31.2661			−1.39966			−0.699830	−	0.714309i	$-0.746741\pi$
$499$	−31.2661			−1.39966			−0.699830	+	0.714309i	$0.746741\pi$
$500$		0			0
$501$	22.8627	−	39.5993i	1.02143	−	1.76917i
$502$		0			0
$503$	−2.06167	+	3.57092i	−0.0919253	+	0.159219i	−0.908321	−	0.418273i	$-0.862635\pi$
$503$	−2.06167	+	3.57092i	−0.0919253	+	0.159219i	0.816396	+	0.577493i	$0.195969\pi$
$504$		0			0
$505$	31.7429	−	18.3268i	1.41254	−	0.815530i
$506$		0			0
$507$	24.7726	+	23.6842i	1.10019	+	1.05185i
$508$		0			0
$509$	−11.0588	−	19.1544i	−0.490172	−	0.849002i	0.509764	−	0.860314i	$-0.329733\pi$
$509$	−11.0588	−	19.1544i	−0.490172	−	0.849002i	−0.999936	+	0.0113120i	$0.996399\pi$
$510$		0			0
$511$	−7.72016	+	13.3717i	−0.341520	+	0.591530i
$512$		0			0
$513$	14.4498	+	8.34259i	0.637973	+	0.368334i
$514$		0			0
$515$	−11.6165			−0.511882
$516$		0			0
$517$	17.2909	−	9.98293i	0.760455	−	0.439049i
$518$		0			0
$519$	37.4328			1.64312
$520$		0			0
$521$	36.7823			1.61146			0.805731	−	0.592281i	$-0.201773\pi$
$521$	36.7823			1.61146			0.805731	+	0.592281i	$0.201773\pi$
$522$		0			0
$523$	25.6362	−	14.8011i	1.12099	−	0.647205i	0.179338	−	0.983788i	$-0.442604\pi$
$523$	25.6362	−	14.8011i	1.12099	−	0.647205i	0.941654	+	0.336582i	$0.109271\pi$
$524$		0			0
$525$	26.2859			1.14721
$526$		0			0
$527$	−1.87183	−	1.08070i	−0.0815384	−	0.0470762i
$528$		0			0
$529$	11.3113	−	19.5918i	0.491796	−	0.851816i
$530$		0			0
$531$	−4.88580	−	8.46245i	−0.212026	−	0.367239i
$532$		0			0
$533$	3.47084	−	28.8647i	0.150339	−	1.25027i
$534$		0			0
$535$	−2.69825	+	1.55783i	−0.116655	+	0.0673510i
$536$		0			0
$537$	6.44978	−	11.1713i	0.278329	−	0.482079i
$538$		0			0
$539$	8.00858	−	13.8713i	0.344954	−	0.597478i
$540$		0			0
$541$	22.5906			0.971245			0.485623	−	0.874169i	$-0.338593\pi$
$541$	22.5906			0.971245			0.485623	+	0.874169i	$0.338593\pi$
$542$		0			0
$543$	−27.9486	−	48.4083i	−1.19939	−	2.07740i
$544$		0			0
$545$	−69.2549			−2.96655
$546$		0			0
$547$		−	22.1421i		−	0.946729i	−0.880867	−	0.473365i	$-0.843039\pi$
$547$		−	22.1421i		−	0.946729i	0.880867	−	0.473365i	$-0.156961\pi$
$548$		0			0
$549$	−22.7509	+	13.1353i	−0.970986	+	0.560599i
$550$		0			0
$551$		−	19.2752i		−	0.821153i
$552$		0			0
$553$	−2.16378	−	1.24926i	−0.0920134	−	0.0531240i
$554$		0			0
$555$	39.4098	+	22.7533i	1.67285	+	0.965822i
$556$		0			0
$557$	−8.54145	−	14.7942i	−0.361913	−	0.626851i	0.626363	−	0.779532i	$-0.284543\pi$
$557$	−8.54145	−	14.7942i	−0.361913	−	0.626851i	−0.988276	+	0.152680i	$0.951209\pi$
$558$		0			0
$559$	−30.3851	+	12.9876i	−1.28515	+	0.549315i
$560$		0			0
$561$	20.5652	−	11.8733i	0.868265	−	0.501293i
$562$		0			0
$563$	33.4112	+	19.2900i	1.40811	+	0.812975i	0.995206	−	0.0977986i	$-0.0311801\pi$
$563$	33.4112	+	19.2900i	1.40811	+	0.812975i	0.412907	+	0.910773i	$0.364513\pi$
$564$		0			0
$565$	5.83698	−	10.1099i	0.245564	−	0.425328i
$566$		0			0
$567$		−	7.91736i		−	0.332498i
$568$		0			0
$569$	−10.4819	−	18.1552i	−0.439424	−	0.761104i	0.558221	−	0.829692i	$-0.311484\pi$
$569$	−10.4819	−	18.1552i	−0.439424	−	0.761104i	−0.997645	+	0.0685878i	$0.978151\pi$
$570$		0			0
$571$			35.3147i			1.47787i	0.673774	+	0.738937i	$0.264672\pi$
$571$			35.3147i			1.47787i	−0.673774	+	0.738937i	$0.735328\pi$
$572$		0			0
$573$		−	3.86961i		−	0.161655i
$574$		0			0
$575$	2.02896	+	3.51426i	0.0846135	+	0.146555i
$576$		0			0
$577$			40.8549i			1.70081i	0.526128	+	0.850405i	$0.323643\pi$
$577$			40.8549i			1.70081i	−0.526128	+	0.850405i	$0.676357\pi$
$578$		0			0
$579$	−22.4413	+	38.8695i	−0.932630	+	1.61536i
$580$		0			0
$581$	−10.2146	−	5.89737i	−0.423771	−	0.244664i
$582$		0			0
$583$	1.84455	−	1.06495i	0.0763935	−	0.0441058i
$584$		0			0
$585$	19.0713	+	44.6184i	0.788501	+	1.84474i
$586$		0			0
$587$	−5.89364	−	10.2081i	−0.243256	−	0.421332i	0.718384	−	0.695647i	$-0.244882\pi$
$587$	−5.89364	−	10.2081i	−0.243256	−	0.421332i	−0.961640	+	0.274315i	$0.911549\pi$
$588$		0			0
$589$	4.69419	+	2.71019i	0.193421	+	0.111671i
$590$		0			0
$591$	37.5833	+	21.6987i	1.54597	+	0.892566i
$592$		0			0
$593$		−	37.3071i		−	1.53202i	−0.642830	−	0.766009i	$-0.722240\pi$
$593$		−	37.3071i		−	1.53202i	0.642830	−	0.766009i	$-0.277760\pi$
$594$		0			0
$595$	−11.8245	+	6.82688i	−0.484757	+	0.279875i
$596$		0			0
$597$			48.2544i			1.97492i
$598$		0			0
$599$	20.3759			0.832536			0.416268	−	0.909242i	$-0.363338\pi$
$599$	20.3759			0.832536			0.416268	+	0.909242i	$0.363338\pi$
$600$		0			0
$601$	−4.80175	−	8.31688i	−0.195868	−	0.339253i	0.751317	−	0.659942i	$-0.229419\pi$
$601$	−4.80175	−	8.31688i	−0.195868	−	0.339253i	−0.947185	+	0.320689i	$0.896086\pi$
$602$		0			0
$603$	5.24822			0.213724
$604$		0			0
$605$	0.863249	−	1.49519i	0.0350961	−	0.0607882i
$606$		0			0
$607$	13.4951	−	23.3742i	0.547749	−	0.948729i	−0.450679	−	0.892686i	$-0.648818\pi$
$607$	13.4951	−	23.3742i	0.547749	−	0.948729i	0.998428	−	0.0560433i	$-0.0178485\pi$
$608$		0			0
$609$	9.97510	−	5.75913i	0.404211	−	0.233372i
$610$		0			0
$611$	−16.9804	−	12.7292i	−0.686954	−	0.514967i
$612$		0			0
$613$	1.49345	+	2.58672i	0.0603197	+	0.104477i	0.894608	−	0.446851i	$-0.147455\pi$
$613$	1.49345	+	2.58672i	0.0603197	+	0.104477i	−0.834289	+	0.551328i	$0.814121\pi$
$614$		0			0
$615$	36.2097	−	62.7170i	1.46011	−	2.52899i
$616$		0			0
$617$	30.9399	+	17.8632i	1.24559	+	0.719144i	0.970227	−	0.242196i	$-0.0778676\pi$
$617$	30.9399	+	17.8632i	1.24559	+	0.719144i	0.275366	+	0.961339i	$0.411201\pi$
$618$		0			0
$619$	19.9292			0.801024			0.400512	−	0.916292i	$-0.368832\pi$
$619$	19.9292			0.801024			0.400512	+	0.916292i	$0.368832\pi$
$620$		0			0
$621$	−1.33300	+	0.769606i	−0.0534913	+	0.0308832i
$622$		0			0
$623$	1.95875			0.0784755
$624$		0			0
$625$	−14.3928			−0.575711
$626$		0			0
$627$	−51.5735	+	29.7760i	−2.05965	+	1.18914i
$628$		0			0
$629$	−13.4540			−0.536447
$630$		0			0
$631$	16.1192	+	9.30643i	0.641695	+	0.370483i	0.785267	−	0.619157i	$-0.212526\pi$
$631$	16.1192	+	9.30643i	0.641695	+	0.370483i	−0.143572	+	0.989640i	$0.545859\pi$
$632$		0			0
$633$	5.81986	−	10.0803i	0.231319	−	0.400656i
$634$		0			0
$635$	−9.19657	−	15.9289i	−0.364955	−	0.632120i
$636$		0			0
$637$	−16.9030	−	2.03250i	−0.669720	−	0.0805307i
$638$		0			0
$639$	21.2544	−	12.2712i	0.840812	−	0.485443i
$640$		0			0
$641$	−0.401423	+	0.695285i	−0.0158553	+	0.0274621i	−0.873844	−	0.486206i	$-0.838380\pi$
$641$	−0.401423	+	0.695285i	−0.0158553	+	0.0274621i	0.857989	+	0.513668i	$0.171714\pi$
$642$		0			0
$643$	−10.5732	+	18.3133i	−0.416965	+	0.722205i	−0.995633	−	0.0933589i	$-0.970240\pi$
$643$	−10.5732	+	18.3133i	−0.416965	+	0.722205i	0.578667	+	0.815564i	$0.303573\pi$
$644$		0			0
$645$	−82.3130			−3.24107
$646$		0			0
$647$	19.5120	+	33.7957i	0.767095	+	1.32865i	0.939132	+	0.343557i	$0.111632\pi$
$647$	19.5120	+	33.7957i	0.767095	+	1.32865i	−0.172037	+	0.985090i	$0.555035\pi$
$648$		0			0
$649$	8.39074			0.329365
$650$		0			0
$651$			3.23904i			0.126948i
$652$		0			0
$653$	41.6632	−	24.0543i	1.63041	−	0.941316i	0.646440	−	0.762965i	$-0.276257\pi$
$653$	41.6632	−	24.0543i	1.63041	−	0.941316i	0.983967	−	0.178351i	$-0.0570762\pi$
$654$		0			0
$655$			46.0692i			1.80007i
$656$		0			0
$657$	−34.9973	−	20.2057i	−1.36537	−	0.788299i
$658$		0			0
$659$	−13.6735	−	7.89443i	−0.532646	−	0.307523i	0.209447	−	0.977820i	$-0.432834\pi$
$659$	−13.6735	−	7.89443i	−0.532646	−	0.307523i	−0.742093	+	0.670297i	$0.766167\pi$
$660$		0			0
$661$	−0.142144	−	0.246200i	−0.00552876	−	0.00957608i	0.863248	−	0.504780i	$-0.168427\pi$
$661$	−0.142144	−	0.246200i	−0.00552876	−	0.00957608i	−0.868777	+	0.495204i	$0.835093\pi$
$662$		0			0
$663$	−20.1959	−	15.1396i	−0.784343	−	0.587974i
$664$		0			0
$665$	29.6535	−	17.1204i	1.14991	−	0.663902i
$666$		0			0
$667$	1.53992	+	0.889073i	0.0596259	+	0.0344251i
$668$		0			0
$669$	−6.65711	+	11.5304i	−0.257379	+	0.445793i
$670$		0			0
$671$		−	22.5581i		−	0.870848i
$672$		0			0
$673$	7.08159	+	12.2657i	0.272975	+	0.472807i	0.969622	−	0.244607i	$-0.0786589\pi$
$673$	7.08159	+	12.2657i	0.272975	+	0.472807i	−0.696647	+	0.717414i	$0.745326\pi$
$674$		0			0
$675$			16.5516i			0.637071i
$676$		0			0
$677$		−	39.2276i		−	1.50764i	−0.657081	−	0.753820i	$-0.728209\pi$
$677$		−	39.2276i		−	1.50764i	0.657081	−	0.753820i	$-0.271791\pi$
$678$		0			0
$679$	10.9708	+	19.0020i	0.421022	+	0.729231i
$680$		0			0
$681$		−	38.5372i		−	1.47675i
$682$		0			0
$683$	−3.76785	+	6.52610i	−0.144173	+	0.249714i	−0.929064	−	0.369919i	$-0.879385\pi$
$683$	−3.76785	+	6.52610i	−0.144173	+	0.249714i	0.784891	+	0.619633i	$0.212719\pi$
$684$		0			0
$685$	−24.2364	−	13.9929i	−0.926027	−	0.534642i
$686$		0			0
$687$	−27.7816	+	16.0397i	−1.05994	+	0.611954i
$688$		0			0
$689$	−1.81142	−	1.35791i	−0.0690097	−	0.0517323i
$690$		0			0
$691$	1.92252	+	3.32990i	0.0731360	+	0.126675i	0.900274	−	0.435323i	$-0.143366\pi$
$691$	1.92252	+	3.32990i	0.0731360	+	0.126675i	−0.827138	+	0.561999i	$0.810033\pi$
$692$		0			0
$693$	−17.5164	−	10.1131i	−0.665393	−	0.384165i
$694$		0			0
$695$	−57.6171	−	33.2652i	−2.18554	−	1.26182i
$696$		0			0
$697$			21.4108i			0.810992i
$698$		0			0
$699$	26.0810	−	15.0579i	0.986476	−	0.569542i
$700$		0			0
$701$		−	34.5455i		−	1.30476i	−0.757890	−	0.652382i	$-0.773770\pi$
$701$		−	34.5455i		−	1.30476i	0.757890	−	0.652382i	$-0.226230\pi$
$702$		0			0
$703$	33.7400			1.27253
$704$		0			0
$705$	−26.4316	−	45.7808i	−0.995470	−	1.72421i
$706$		0			0
$707$	16.2396			0.610751
$708$		0			0
$709$	−13.2970	+	23.0310i	−0.499378	+	0.864948i	−1.00000		0.000718230i	$-0.999771\pi$
$709$	−13.2970	+	23.0310i	−0.499378	+	0.864948i	0.500622	+	0.865666i	$0.333105\pi$
$710$		0			0
$711$	3.26964	−	5.66319i	0.122621	−	0.212386i
$712$		0			0
$713$	−0.433040	+	0.250016i	−0.0162175	+	0.00936316i
$714$		0			0
$715$	−41.3684	−	4.97435i	−1.54709	−	0.186030i
$716$		0			0
$717$	32.4831	+	56.2625i	1.21311	+	2.10116i
$718$		0			0
$719$	−19.6503	+	34.0354i	−0.732834	+	1.26931i	0.222833	+	0.974857i	$0.428469\pi$
$719$	−19.6503	+	34.0354i	−0.732834	+	1.26931i	−0.955667	+	0.294449i	$0.904864\pi$
$720$		0			0
$721$	−4.45720	−	2.57337i	−0.165995	−	0.0958372i
$722$		0			0
$723$	0.471719			0.0175434
$724$		0			0
$725$	16.5592	−	9.56046i	0.614994	−	0.355067i
$726$		0			0
$727$	28.1259			1.04313			0.521566	−	0.853211i	$-0.325348\pi$
$727$	28.1259			1.04313			0.521566	+	0.853211i	$0.325348\pi$
$728$		0			0
$729$	40.5391			1.50145
$730$		0			0
$731$	21.0755	−	12.1679i	0.779505	−	0.450047i
$732$		0			0
$733$	30.6364			1.13158			0.565791	−	0.824549i	$-0.308571\pi$
$733$	30.6364			1.13158			0.565791	+	0.824549i	$0.308571\pi$
$734$		0			0
$735$	−36.7266	−	21.2041i	−1.35468	−	0.782126i
$736$		0			0
$737$	−2.25329	+	3.90281i	−0.0830010	+	0.143762i
$738$		0			0
$739$	−13.8293	−	23.9531i	−0.508721	−	0.881130i	−0.999949	−	0.0100991i	$-0.996785\pi$
$739$	−13.8293	−	23.9531i	−0.508721	−	0.881130i	0.491228	−	0.871031i	$-0.336548\pi$
$740$		0			0
$741$	50.6472	+	37.9671i	1.86057	+	1.39476i
$742$		0			0
$743$	17.1394	−	9.89546i	0.628785	−	0.363029i	−0.151496	−	0.988458i	$-0.548409\pi$
$743$	17.1394	−	9.89546i	0.628785	−	0.363029i	0.780281	+	0.625429i	$0.215076\pi$
$744$		0			0
$745$	−22.0961	+	38.2715i	−0.809538	+	1.40216i
$746$		0			0
$747$	15.4350	−	26.7342i	0.564736	−	0.978152i
$748$		0			0
$749$	−1.38041			−0.0504392
$750$		0			0
$751$	−9.60222	−	16.6315i	−0.350390	−	0.606893i	0.635928	−	0.771749i	$-0.280618\pi$
$751$	−9.60222	−	16.6315i	−0.350390	−	0.606893i	−0.986318	+	0.164855i	$0.947284\pi$
$752$		0			0
$753$	53.2234			1.93957
$754$		0			0
$755$			55.3865i			2.01572i
$756$		0			0
$757$	8.30082	−	4.79248i	0.301698	−	0.174186i	−0.341507	−	0.939879i	$-0.610937\pi$
$757$	8.30082	−	4.79248i	0.301698	−	0.174186i	0.643206	+	0.765694i	$0.277604\pi$
$758$		0			0
$759$		−	5.49368i		−	0.199408i
$760$		0			0
$761$	−3.55022	−	2.04972i	−0.128695	−	0.0743023i	0.434270	−	0.900783i	$-0.357006\pi$
$761$	−3.55022	−	2.04972i	−0.128695	−	0.0743023i	−0.562966	+	0.826480i	$0.690340\pi$
$762$		0			0
$763$	−26.5729	−	15.3419i	−0.962005	−	0.555414i
$764$		0			0
$765$	−17.8677	−	30.9478i	−0.646010	−	1.11892i
$766$		0			0
$767$	−3.50529	−	8.20083i	−0.126569	−	0.296115i
$768$		0			0
$769$	12.3725	−	7.14328i	0.446165	−	0.257593i	−0.260044	−	0.965597i	$-0.583737\pi$
$769$	12.3725	−	7.14328i	0.446165	−	0.257593i	0.706209	+	0.708003i	$0.250404\pi$
$770$		0			0
$771$	0.452385	+	0.261184i	0.0162922	+	0.00940632i
$772$		0			0
$773$	−9.10369	+	15.7681i	−0.327437	+	0.567138i	−0.982003	−	0.188868i	$-0.939518\pi$
$773$	−9.10369	+	15.7681i	−0.327437	+	0.567138i	0.654565	+	0.756005i	$0.272852\pi$
$774$		0			0
$775$			5.37698i			0.193147i
$776$		0			0
$777$	10.0810	+	17.4607i	0.361652	+	0.626400i
$778$		0			0
$779$		−	53.6940i		−	1.92379i
$780$		0			0
$781$			21.0743i			0.754098i
$782$		0			0
$783$	3.62638	+	6.28108i	0.129596	+	0.224467i
$784$		0			0
$785$			30.2455i			1.07951i
$786$		0			0
$787$	6.01748	−	10.4226i	0.214500	−	0.371525i	−0.738618	−	0.674125i	$-0.764521\pi$
$787$	6.01748	−	10.4226i	0.214500	−	0.371525i	0.953118	+	0.302599i	$0.0978544\pi$
$788$		0			0
$789$	16.8627	+	9.73569i	0.600329	+	0.346600i
$790$		0			0
$791$	4.47927	−	2.58611i	0.159264	−	0.0919513i
$792$		0			0
$793$	−22.0476	+	9.42383i	−0.782933	+	0.334650i
$794$		0			0
$795$	−2.81965	−	4.88377i	−0.100003	−	0.173210i
$796$		0			0
$797$	−37.8735	−	21.8663i	−1.34155	−	0.774544i	−0.354514	−	0.935051i	$-0.615354\pi$
$797$	−37.8735	−	21.8663i	−1.34155	−	0.774544i	−0.987035	+	0.160507i	$0.948687\pi$
$798$		0			0
$799$	13.5351	+	7.81451i	0.478838	+	0.276457i
$800$		0			0
$801$			5.12655i			0.181138i
$802$		0			0
$803$	30.0517	−	17.3504i	1.06050	−	0.612281i
$804$		0			0
$805$			3.15873i			0.111331i
$806$		0			0
$807$	−48.7881			−1.71742
$808$		0			0
$809$	−6.93343	−	12.0090i	−0.243766	−	0.422216i	0.718018	−	0.696025i	$-0.245050\pi$
$809$	−6.93343	−	12.0090i	−0.243766	−	0.422216i	−0.961784	+	0.273809i	$0.911716\pi$
$810$		0			0
$811$	2.29509			0.0805916			0.0402958	−	0.999188i	$-0.487170\pi$
$811$	2.29509			0.0805916			0.0402958	+	0.999188i	$0.487170\pi$
$812$		0			0
$813$	−12.4547	+	21.5722i	−0.436805	+	0.756569i
$814$		0			0
$815$	−6.95710	+	12.0500i	−0.243697	+	0.422095i
$816$		0			0
$817$	−52.8531	+	30.5147i	−1.84910	+	1.06758i
$818$		0			0
$819$	−2.56661	+	21.3448i	−0.0896846	+	0.745847i
$820$		0			0
$821$	2.46599	+	4.27121i	0.0860635	+	0.149066i	0.905844	−	0.423612i	$-0.139238\pi$
$821$	2.46599	+	4.27121i	0.0860635	+	0.149066i	−0.819780	+	0.572678i	$0.805905\pi$
$822$		0			0
$823$	−20.3378	+	35.2261i	−0.708931	+	1.22790i	0.256323	+	0.966591i	$0.417489\pi$
$823$	−20.3378	+	35.2261i	−0.708931	+	1.22790i	−0.965254	+	0.261313i	$0.915845\pi$
$824$		0			0
$825$	−51.1606	−	29.5376i	−1.78118	−	1.02837i
$826$		0			0
$827$	21.5663			0.749933			0.374967	−	0.927038i	$-0.377654\pi$
$827$	21.5663			0.749933			0.374967	+	0.927038i	$0.377654\pi$
$828$		0			0
$829$	−26.5594	+	15.3341i	−0.922445	+	0.532574i	−0.884414	−	0.466702i	$-0.845442\pi$
$829$	−26.5594	+	15.3341i	−0.922445	+	0.532574i	−0.0380310	+	0.999277i	$0.512109\pi$
$830$		0			0
$831$	26.3143			0.912831
$832$		0			0
$833$	12.5380			0.434417
$834$		0			0
$835$	51.1704	−	29.5432i	1.77082	−	1.02239i
$836$		0			0
$837$	−2.03955			−0.0704970
$838$		0			0
$839$	−26.4685	−	15.2816i	−0.913793	−	0.527579i	−0.0321435	−	0.999483i	$-0.510233\pi$
$839$	−26.4685	−	15.2816i	−0.913793	−	0.527579i	−0.881650	+	0.471905i	$0.843567\pi$
$840$		0			0
$841$	−10.3107	+	17.8586i	−0.355541	+	0.615815i
$842$		0			0
$843$	−14.6587	−	25.3896i	−0.504873	−	0.874465i
$844$		0			0
$845$	12.4202	+	42.5101i	0.427267	+	1.46239i
$846$		0			0
$847$	0.662453	−	0.382467i	0.0227621	−	0.0131417i
$848$		0			0
$849$	1.76901	−	3.06402i	0.0607124	−	0.105157i
$850$		0			0
$851$	−1.55626	+	2.69553i	−0.0533480	+	0.0924014i
$852$		0			0
$853$	36.3580			1.24487			0.622437	−	0.782670i	$-0.286143\pi$
$853$	36.3580			1.24487			0.622437	+	0.782670i	$0.286143\pi$
$854$		0			0
$855$	44.8087	+	77.6110i	1.53243	+	2.65424i
$856$		0			0
$857$	−0.0833458			−0.00284704			−0.00142352	−	0.999999i	$-0.500453\pi$
$857$	−0.0833458			−0.00284704			−0.00142352	+	0.999999i	$0.500453\pi$
$858$		0			0
$859$			55.2828i			1.88622i	0.332476	+	0.943112i	$0.392116\pi$
$859$			55.2828i			1.88622i	−0.332476	+	0.943112i	$0.607884\pi$
$860$		0			0
$861$	27.7871	−	16.0429i	0.946982	−	0.546740i
$862$		0			0
$863$			14.5282i			0.494546i	0.968946	+	0.247273i	$0.0795345\pi$
$863$			14.5282i			0.494546i	−0.968946	+	0.247273i	$0.920466\pi$
$864$		0			0
$865$	41.8904	+	24.1854i	1.42432	+	0.822330i
$866$		0			0
$867$	−22.7155	−	13.1148i	−0.771458	−	0.445402i
$868$		0			0
$869$	2.80760	+	4.86291i	0.0952413	+	0.164963i
$870$		0			0
$871$	4.75581	+	0.571864i	0.161144	+	0.0193769i
$872$		0			0
$873$	−49.7333	+	28.7135i	−1.68322	+	0.971806i
$874$		0			0
$875$	7.15059	+	4.12839i	0.241734	+	0.139565i
$876$		0			0
$877$	23.5728	−	40.8294i	0.795998	−	1.37871i	−0.126205	−	0.992004i	$-0.540280\pi$
$877$	23.5728	−	40.8294i	0.795998	−	1.37871i	0.922203	−	0.386705i	$-0.126387\pi$
$878$		0			0
$879$		−	22.0474i		−	0.743639i
$880$		0			0
$881$	11.0991	+	19.2242i	0.373937	+	0.647678i	0.990167	−	0.139888i	$-0.0446742\pi$
$881$	11.0991	+	19.2242i	0.373937	+	0.647678i	−0.616230	+	0.787566i	$0.711341\pi$
$882$		0			0
$883$			23.0291i			0.774991i	0.921872	+	0.387496i	$0.126660\pi$
$883$			23.0291i			0.774991i	−0.921872	+	0.387496i	$0.873340\pi$
$884$		0			0
$885$		−	22.2160i		−	0.746781i
$886$		0			0
$887$	−27.4780	−	47.5933i	−0.922621	−	1.59803i	−0.795343	−	0.606160i	$-0.792709\pi$
$887$	−27.4780	−	47.5933i	−0.922621	−	1.59803i	−0.127278	−	0.991867i	$-0.540624\pi$
$888$		0			0
$889$		−	8.14918i		−	0.273315i
$890$		0			0
$891$	−8.89677	+	15.4097i	−0.298053	+	0.516243i
$892$		0			0
$893$	−33.9434	−	19.5972i	−1.13587	−	0.655796i
$894$		0			0
$895$	14.4357	−	8.33444i	0.482531	−	0.278590i
$896$		0			0
$897$	−5.36934	+	2.29503i	−0.179277	+	0.0766287i
$898$		0			0
$899$	1.17807	+	2.04048i	0.0392910	+	0.0680540i
$900$		0			0
$901$	1.44389	+	0.833630i	0.0481030	+	0.0277723i
$902$		0			0
$903$	−31.5833	−	18.2346i	−1.05103	−	0.606810i
$904$		0			0
$905$		−	72.2305i		−	2.40102i
$906$		0			0
$907$	27.9245	−	16.1222i	0.927217	−	0.535329i	0.0412866	−	0.999147i	$-0.486854\pi$
$907$	27.9245	−	16.1222i	0.927217	−	0.535329i	0.885930	+	0.463818i	$0.153521\pi$
$908$		0			0
$909$			42.5032i			1.40974i
$910$		0			0
$911$	6.52220			0.216090			0.108045	−	0.994146i	$-0.465541\pi$
$911$	6.52220			0.216090			0.108045	+	0.994146i	$0.465541\pi$
$912$		0			0
$913$	13.2538	+	22.9563i	0.438637	+	0.759742i
$914$		0			0
$915$	−59.7267			−1.97450
$916$		0			0
$917$	−10.2056	+	17.6766i	−0.337019	+	0.583734i
$918$		0			0
$919$	−22.7062	+	39.3283i	−0.749009	+	1.29732i	0.199289	+	0.979941i	$0.436137\pi$
$919$	−22.7062	+	39.3283i	−0.749009	+	1.29732i	−0.948298	+	0.317381i	$0.897197\pi$
$920$		0			0
$921$	−44.6262	+	25.7649i	−1.47048	+	0.848984i
$922$		0			0
$923$	20.5973	−	8.80394i	0.677969	−	0.289785i
$924$		0			0
$925$	16.7349	+	28.9858i	0.550242	+	0.953046i
$926$		0			0
$927$	6.73518	−	11.6657i	0.221212	−	0.383151i
$928$		0			0
$929$	−14.8259	−	8.55975i	−0.486423	−	0.280836i	0.236667	−	0.971591i	$-0.423945\pi$
$929$	−14.8259	−	8.55975i	−0.486423	−	0.280836i	−0.723089	+	0.690755i	$0.757278\pi$
$930$		0			0
$931$	−31.4429			−1.03050
$932$		0			0
$933$	57.0319	−	32.9274i	1.86714	−	1.07799i
$934$		0			0
$935$	30.6856			1.00353
$936$		0			0
$937$	−28.4076			−0.928036			−0.464018	−	0.885826i	$-0.653593\pi$
$937$	−28.4076			−0.928036			−0.464018	+	0.885826i	$0.653593\pi$
$938$		0			0
$939$	−11.3773	+	6.56866i	−0.371283	+	0.214360i
$940$		0			0
$941$	−18.6692			−0.608599			−0.304299	−	0.952576i	$-0.598422\pi$
$941$	−18.6692			−0.608599			−0.304299	+	0.952576i	$0.598422\pi$
$942$		0			0
$943$	4.28967	+	2.47664i	0.139691	+	0.0806506i
$944$		0			0
$945$	−6.44197	+	11.1578i	−0.209557	+	0.362964i
$946$		0			0
$947$	7.05574	+	12.2209i	0.229281	+	0.397126i	0.957595	−	0.288117i	$-0.0930293\pi$
$947$	7.05574	+	12.2209i	0.229281	+	0.397126i	−0.728314	+	0.685243i	$0.759696\pi$
$948$		0			0
$949$	−29.5120	−	22.1233i	−0.958000	−	0.718153i
$950$		0			0
$951$	−50.7025	+	29.2731i	−1.64414	+	0.949245i
$952$		0			0
$953$	9.69488	−	16.7920i	0.314048	−	0.543947i	−0.665187	−	0.746677i	$-0.731648\pi$
$953$	9.69488	−	16.7920i	0.314048	−	0.543947i	0.979235	+	0.202730i	$0.0649814\pi$
$954$		0			0
$955$	2.50017	−	4.33042i	0.0809035	−	0.140129i
$956$		0			0
$957$	−25.8862			−0.836783
$958$		0			0
$959$	−6.19964	−	10.7381i	−0.200197	−	0.346751i
$960$		0			0
$961$	30.3374			0.978627
$962$		0			0
$963$		−	3.61291i		−	0.116424i
$964$		0			0
$965$	−50.2274	+	28.9988i	−1.61688	+	0.933505i
$966$		0			0
$967$		−	4.50833i		−	0.144978i	−0.997369	−	0.0724891i	$-0.976906\pi$
$967$		−	4.50833i		−	0.144978i	0.997369	−	0.0724891i	$-0.0230943\pi$
$968$		0			0
$969$	−40.3710	−	23.3082i	−1.29690	−	0.748768i
$970$		0			0
$971$	26.6115	+	15.3641i	0.854003	+	0.493059i	0.861999	−	0.506909i	$-0.169212\pi$
$971$	26.6115	+	15.3641i	0.854003	+	0.493059i	−0.00799665	+	0.999968i	$0.502545\pi$
$972$		0			0
$973$	−14.7383	−	25.5276i	−0.472490	−	0.818376i
$974$		0			0
$975$	−7.49636	+	62.3422i	−0.240076	+	1.99655i
$976$		0			0
$977$	−8.57480	+	4.95066i	−0.274332	+	0.158386i	−0.630855	−	0.775901i	$-0.717296\pi$
$977$	−8.57480	+	4.95066i	−0.274332	+	0.158386i	0.356523	+	0.934287i	$0.383962\pi$
$978$		0			0
$979$	−3.81233	−	2.20105i	−0.121843	−	0.0703459i
$980$		0			0
$981$	40.1538	−	69.5484i	1.28201	−	2.22051i
$982$		0			0
$983$			9.87697i			0.315026i	0.987517	+	0.157513i	$0.0503477\pi$
$983$			9.87697i			0.315026i	−0.987517	+	0.157513i	$0.949652\pi$
$984$		0			0
$985$	28.0392	+	48.5653i	0.893403	+	1.54742i
$986$		0			0
$987$		−	23.4213i		−	0.745508i
$988$		0			0
$989$		−	5.62999i		−	0.179023i
$990$		0			0
$991$	−20.9826	−	36.3428i	−0.666533	−	1.15447i	−0.978867	−	0.204496i	$-0.934444\pi$
$991$	−20.9826	−	36.3428i	−0.666533	−	1.15447i	0.312335	−	0.949972i	$-0.398889\pi$
$992$		0			0
$993$		−	34.9982i		−	1.11064i
$994$		0			0
$995$	−31.1773	+	54.0007i	−0.988387	+	1.71194i
$996$		0			0
$997$	28.3587	+	16.3729i	0.898128	+	0.518534i	0.876592	−	0.481234i	$-0.159811\pi$
$997$	28.3587	+	16.3729i	0.898128	+	0.518534i	0.0215355	+	0.999768i	$0.493145\pi$
$998$		0			0
$999$	−10.9946	+	6.34774i	−0.347854	+	0.200834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.ba.c.49.1		16
4.3	odd	2		104.2.s.c.101.5	yes	16
8.3	odd	2		104.2.s.c.101.3	yes	16
8.5	even	2	inner	416.2.ba.c.49.8		16
12.11	even	2		936.2.dg.d.829.4		16
13.4	even	6	inner	416.2.ba.c.17.8		16
24.11	even	2		936.2.dg.d.829.6		16
52.43	odd	6		104.2.s.c.69.3	✓	16
104.43	odd	6		104.2.s.c.69.5	yes	16
104.69	even	6	inner	416.2.ba.c.17.1		16
156.95	even	6		936.2.dg.d.901.6		16
312.251	even	6		936.2.dg.d.901.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.3	✓	16	52.43	odd	6
104.2.s.c.69.5	yes	16	104.43	odd	6
104.2.s.c.101.3	yes	16	8.3	odd	2
104.2.s.c.101.5	yes	16	4.3	odd	2
416.2.ba.c.17.1		16	104.69	even	6	inner
416.2.ba.c.17.8		16	13.4	even	6	inner
416.2.ba.c.49.1		16	1.1	even	1	trivial
416.2.ba.c.49.8		16	8.5	even	2	inner
936.2.dg.d.829.4		16	12.11	even	2
936.2.dg.d.829.6		16	24.11	even	2
936.2.dg.d.901.4		16	312.251	even	6
936.2.dg.d.901.6		16	156.95	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.28316 + 1.31818i) q^{3} -3.40672 q^{5} +(-1.30715 - 0.754684i) q^{7} +(1.97521 - 3.42116i) q^{9} +(1.69608 + 2.93770i) q^{11} +(2.16266 - 2.88494i) q^{13} +(7.77808 - 4.49068i) q^{15} +(-1.32767 + 2.29959i) q^{17} +(3.32953 - 5.76692i) q^{19} +3.97924 q^{21} +(0.307150 + 0.532000i) q^{23} +6.60576 q^{25} +2.50563i q^{27} +(2.50678 - 1.44729i) q^{29} +0.813985i q^{31} +(-7.74485 - 4.47149i) q^{33} +(4.45310 + 2.57100i) q^{35} +(2.53339 + 4.38796i) q^{37} +(-1.13482 + 9.43756i) q^{39} +(6.98302 - 4.03165i) q^{41} +(-7.93701 - 4.58243i) q^{43} +(-6.72898 + 11.6549i) q^{45} -5.88587i q^{47} +(-2.36091 - 4.08921i) q^{49} -7.00045i q^{51} -0.627889i q^{53} +(-5.77808 - 10.0079i) q^{55} +17.5557i q^{57} +(1.23678 - 2.14217i) q^{59} +(-5.75913 - 3.32504i) q^{61} +(-5.16378 + 2.98131i) q^{63} +(-7.36759 + 9.82820i) q^{65} +(0.664263 + 1.15054i) q^{67} +(-1.40255 - 0.809760i) q^{69} +(5.38030 + 3.10632i) q^{71} -10.2297i q^{73} +(-15.0820 + 8.70759i) q^{75} -5.12002i q^{77} +1.65534 q^{79} +(2.62274 + 4.54272i) q^{81} +7.81437 q^{83} +(4.52301 - 7.83408i) q^{85} +(-3.81559 + 6.60880i) q^{87} +(-1.12386 + 0.648863i) q^{89} +(-5.00414 + 2.13893i) q^{91} +(-1.07298 - 1.85846i) q^{93} +(-11.3428 + 19.6463i) q^{95} +(-12.5894 - 7.26849i) q^{97} +13.4005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 18 q^{7} + 2 q^{9} + 36 q^{15} + 8 q^{17} + 2 q^{23} - 12 q^{25} - 30 q^{33} + 14 q^{39} + 24 q^{41} - 14 q^{49} - 4 q^{55} + 6 q^{65} - 6 q^{71} - 32 q^{79} + 12 q^{81} - 34 q^{87} - 30 q^{89} - 28 q^{95}+ \cdots - 30 q^{97}+O(q^{100}) \) 16 * q - 18 * q^7 + 2 * q^9 + 36 * q^15 + 8 * q^17 + 2 * q^23 - 12 * q^25 - 30 * q^33 + 14 * q^39 + 24 * q^41 - 14 * q^49 - 4 * q^55 + 6 * q^65 - 6 * q^71 - 32 * q^79 + 12 * q^81 - 34 * q^87 - 30 * q^89 - 28 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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