LMFDB - Embedded newform 896.2.q.d.831.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(703,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("896.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.q (of order $6$, degree $2$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 24x^{14} + 226x^{12} - 972x^{10} + 1575x^{8} + 252x^{6} + 550x^{4} + 156x^{2} + 49 $ x^16 - 24x^14 + 226x^12 - 972x^10 + 1575x^8 + 252x^6 + 550x^4 + 156*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			831.8
Root			$2.37177 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.831
Dual form			896.2.q.d.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.80401 - 1.61890i) q^{3} +(1.53015 - 2.65030i) q^{5} +(-2.57882 - 0.591357i) q^{7} +(3.74165 - 6.48073i) q^{9} +O(q^{10})$	\(q+(2.80401 - 1.61890i) q^{3} +(1.53015 - 2.65030i) q^{5} +(-2.57882 - 0.591357i) q^{7} +(3.74165 - 6.48073i) q^{9} +(1.21265 + 2.10038i) q^{11} -0.365284 q^{13} -9.90862i q^{15} +(-3.79168 + 2.18913i) q^{17} +(4.27065 + 2.46566i) q^{19} +(-8.18838 + 2.51667i) q^{21} +(-0.108007 - 0.0623577i) q^{23} +(-2.18271 - 3.78057i) q^{25} -14.5160i q^{27} +1.73274i q^{29} +(4.01507 + 6.95431i) q^{31} +(6.80059 + 3.92632i) q^{33} +(-5.51325 + 5.92976i) q^{35} +(-6.87043 - 3.96664i) q^{37} +(-1.02426 + 0.591357i) q^{39} -6.84087i q^{41} -2.36543 q^{43} +(-11.4506 - 19.8330i) q^{45} +(-0.550970 + 0.954308i) q^{47} +(6.30059 + 3.05000i) q^{49} +(-7.08794 + 12.2767i) q^{51} +(11.2872 - 6.51667i) q^{53} +7.42217 q^{55} +15.9666 q^{57} +(-2.41203 + 1.39259i) q^{59} +(-6.45633 + 11.1827i) q^{61} +(-13.4815 + 14.5000i) q^{63} +(-0.558939 + 0.968111i) q^{65} +(2.25399 + 3.90402i) q^{67} -0.403803 q^{69} +7.46548i q^{71} +(-4.41545 + 2.54926i) q^{73} +(-12.2407 - 7.06718i) q^{75} +(-1.88514 - 6.13360i) q^{77} +(10.3420 + 5.97097i) q^{79} +(-12.2750 - 21.2609i) q^{81} +0.730568i q^{83} +13.3988i q^{85} +(2.80512 + 4.85862i) q^{87} +(-9.10119 - 5.25457i) q^{89} +(0.942001 + 0.216013i) q^{91} +(22.5166 + 13.0000i) q^{93} +(13.0695 - 7.54567i) q^{95} -12.9615i q^{97} +18.1493 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 + 8 * q^9	$ 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.80401	−	1.61890i	1.61890	−	0.934671i	0.631691	−	0.775220i	$-0.282361\pi$
$3$	2.80401	−	1.61890i	1.61890	−	0.934671i	0.987206	−	0.159450i	$-0.0509721\pi$
$4$		0			0
$5$	1.53015	−	2.65030i	0.684304	−	1.18525i	−0.289351	−	0.957223i	$-0.593440\pi$
$5$	1.53015	−	2.65030i	0.684304	−	1.18525i	0.973655	−	0.228026i	$-0.0732270\pi$
$6$		0			0
$7$	−2.57882	−	0.591357i	−0.974701	−	0.223512i
$7$	−2.57882	−	0.591357i	−0.974701	−	0.223512i
$8$		0			0
$9$	3.74165	−	6.48073i	1.24722	−	2.16024i
$10$		0			0
$11$	1.21265	+	2.10038i	0.365629	+	0.633288i	0.988877	−	0.148736i	$-0.0475206\pi$
$11$	1.21265	+	2.10038i	0.365629	+	0.633288i	−0.623248	+	0.782024i	$0.714187\pi$
$12$		0			0
$13$	−0.365284			−0.101312			−0.0506558	−	0.998716i	$-0.516131\pi$
$13$	−0.365284			−0.101312			−0.0506558	+	0.998716i	$0.516131\pi$
$14$		0			0
$15$		−	9.90862i		−	2.55839i
$16$		0			0
$17$	−3.79168	+	2.18913i	−0.919617	+	0.530941i	−0.883513	−	0.468407i	$-0.844828\pi$
$17$	−3.79168	+	2.18913i	−0.919617	+	0.530941i	−0.0361041	+	0.999348i	$0.511495\pi$
$18$		0			0
$19$	4.27065	+	2.46566i	0.979755	+	0.565662i	0.902196	−	0.431326i	$-0.141954\pi$
$19$	4.27065	+	2.46566i	0.979755	+	0.565662i	0.0775589	+	0.996988i	$0.475287\pi$
$20$		0			0
$21$	−8.18838	+	2.51667i	−1.78685	+	0.549182i
$22$		0			0
$23$	−0.108007	−	0.0623577i	−0.0225210	−	0.0130025i	0.488697	−	0.872453i	$-0.337472\pi$
$23$	−0.108007	−	0.0623577i	−0.0225210	−	0.0130025i	−0.511218	+	0.859451i	$0.670806\pi$
$24$		0			0
$25$	−2.18271	−	3.78057i	−0.436543	−	0.756115i
$26$		0			0
$27$		−	14.5160i		−	2.79361i
$28$		0			0
$29$			1.73274i			0.321761i	0.986974	+	0.160881i	$0.0514334\pi$
$29$			1.73274i			0.321761i	−0.986974	+	0.160881i	$0.948567\pi$
$30$		0			0
$31$	4.01507	+	6.95431i	0.721128	+	1.24903i	0.960548	+	0.278114i	$0.0897095\pi$
$31$	4.01507	+	6.95431i	0.721128	+	1.24903i	−0.239420	+	0.970916i	$0.576957\pi$
$32$		0			0
$33$	6.80059	+	3.92632i	1.18383	+	0.683485i
$34$		0			0
$35$	−5.51325	+	5.92976i	−0.931909	+	1.00231i
$36$		0			0
$37$	−6.87043	−	3.96664i	−1.12949	−	0.652112i	−0.185684	−	0.982609i	$-0.559450\pi$
$37$	−6.87043	−	3.96664i	−1.12949	−	0.652112i	−0.943807	+	0.330498i	$0.892783\pi$
$38$		0			0
$39$	−1.02426	+	0.591357i	−0.164013	+	0.0946930i
$40$		0			0
$41$		−	6.84087i		−	1.06836i	−0.845369	−	0.534182i	$-0.820620\pi$
$41$		−	6.84087i		−	1.06836i	0.845369	−	0.534182i	$-0.179380\pi$
$42$		0			0
$43$	−2.36543			−0.360725			−0.180362	−	0.983600i	$-0.557727\pi$
$43$	−2.36543			−0.360725			−0.180362	+	0.983600i	$0.557727\pi$
$44$		0			0
$45$	−11.4506	−	19.8330i	−1.70695	−	2.95653i
$46$		0			0
$47$	−0.550970	+	0.954308i	−0.0803672	+	0.139200i	−0.903408	−	0.428783i	$-0.858943\pi$
$47$	−0.550970	+	0.954308i	−0.0803672	+	0.139200i	0.823040	+	0.567983i	$0.192276\pi$
$48$		0			0
$49$	6.30059	+	3.05000i	0.900085	+	0.435715i
$50$		0			0
$51$	−7.08794	+	12.2767i	−0.992510	+	1.71908i
$52$		0			0
$53$	11.2872	−	6.51667i	1.55042	−	0.895133i	0.552308	−	0.833640i	$-0.313747\pi$
$53$	11.2872	−	6.51667i	1.55042	−	0.895133i	0.998108	−	0.0614928i	$-0.0195861\pi$
$54$		0			0
$55$	7.42217			1.00081
$56$		0			0
$57$	15.9666			2.11483
$58$		0			0
$59$	−2.41203	+	1.39259i	−0.314020	+	0.181300i	−0.648724	−	0.761024i	$-0.724697\pi$
$59$	−2.41203	+	1.39259i	−0.314020	+	0.181300i	0.334704	+	0.942323i	$0.391364\pi$
$60$		0			0
$61$	−6.45633	+	11.1827i	−0.826648	+	1.43180i	0.0740051	+	0.997258i	$0.476422\pi$
$61$	−6.45633	+	11.1827i	−0.826648	+	1.43180i	−0.900653	+	0.434539i	$0.856911\pi$
$62$		0			0
$63$	−13.4815	+	14.5000i	−1.69851	+	1.82682i
$64$		0			0
$65$	−0.558939	+	0.968111i	−0.0693279	+	0.120079i
$66$		0			0
$67$	2.25399	+	3.90402i	0.275368	+	0.476952i	0.970228	−	0.242193i	$-0.0778668\pi$
$67$	2.25399	+	3.90402i	0.275368	+	0.476952i	−0.694860	+	0.719145i	$0.744533\pi$
$68$		0			0
$69$	−0.403803			−0.0486121
$70$		0			0
$71$			7.46548i			0.885989i	0.896524	+	0.442995i	$0.146084\pi$
$71$			7.46548i			0.885989i	−0.896524	+	0.442995i	$0.853916\pi$
$72$		0			0
$73$	−4.41545	+	2.54926i	−0.516790	+	0.298369i	−0.735620	−	0.677394i	$-0.763109\pi$
$73$	−4.41545	+	2.54926i	−0.516790	+	0.298369i	0.218831	+	0.975763i	$0.429776\pi$
$74$		0			0
$75$	−12.2407	−	7.06718i	−1.41344	−	0.816048i
$76$		0			0
$77$	−1.88514	−	6.13360i	−0.214832	−	0.698989i
$78$		0			0
$79$	10.3420	+	5.97097i	1.16357	+	0.671787i	0.952157	−	0.305610i	$-0.0988603\pi$
$79$	10.3420	+	5.97097i	1.16357	+	0.671787i	0.211412	+	0.977397i	$0.432194\pi$
$80$		0			0
$81$	−12.2750	−	21.2609i	−1.36389	−	2.36232i
$82$		0			0
$83$			0.730568i			0.0801903i	0.999196	+	0.0400951i	$0.0127661\pi$
$83$			0.730568i			0.0801903i	−0.999196	+	0.0400951i	$0.987234\pi$
$84$		0			0
$85$			13.3988i			1.45330i
$86$		0			0
$87$	2.80512	+	4.85862i	0.300741	+	0.520899i
$88$		0			0
$89$	−9.10119	−	5.25457i	−0.964724	−	0.556984i	−0.0671001	−	0.997746i	$-0.521375\pi$
$89$	−9.10119	−	5.25457i	−0.964724	−	0.556984i	−0.897624	+	0.440763i	$0.854708\pi$
$90$		0			0
$91$	0.942001	+	0.216013i	0.0987485	+	0.0226444i
$92$		0			0
$93$	22.5166	+	13.0000i	2.33486	+	1.34803i
$94$		0			0
$95$	13.0695	−	7.54567i	1.34090	−	0.774169i
$96$		0			0
$97$		−	12.9615i		−	1.31604i	−0.753001	−	0.658019i	$-0.771395\pi$
$97$		−	12.9615i		−	1.31604i	0.753001	−	0.658019i	$-0.228605\pi$
$98$		0			0
$99$	18.1493			1.82408
$100$		0			0
$101$	−1.48134	−	2.56575i	−0.147398	−	0.255302i	0.782867	−	0.622189i	$-0.213757\pi$
$101$	−1.48134	−	2.56575i	−0.147398	−	0.255302i	−0.930265	+	0.366888i	$0.880423\pi$
$102$		0			0
$103$	6.45491	−	11.1802i	0.636021	−	1.10162i	−0.350276	−	0.936646i	$-0.613912\pi$
$103$	6.45491	−	11.1802i	0.636021	−	1.10162i	0.986298	−	0.164975i	$-0.0527543\pi$
$104$		0			0
$105$	−5.85953	+	25.5525i	−0.571832	+	2.49367i
$106$		0			0
$107$	−3.33737	+	5.78049i	−0.322636	+	0.558821i	−0.981031	−	0.193851i	$-0.937902\pi$
$107$	−3.33737	+	5.78049i	−0.322636	+	0.558821i	0.658395	+	0.752672i	$0.271236\pi$
$108$		0			0
$109$	2.39549	−	1.38304i	0.229446	−	0.132471i	−0.380870	−	0.924628i	$-0.624376\pi$
$109$	2.39549	−	1.38304i	0.229446	−	0.132471i	0.610316	+	0.792158i	$0.291042\pi$
$110$		0			0
$111$	−25.6863			−2.43804
$112$		0			0
$113$	12.9488			1.21812			0.609060	−	0.793124i	$-0.291547\pi$
$113$	12.9488			1.21812			0.609060	+	0.793124i	$0.291547\pi$
$114$		0			0
$115$	−0.330533	+	0.190833i	−0.0308223	+	0.0177953i
$116$		0			0
$117$	−1.36677	+	2.36731i	−0.126358	+	0.218858i
$118$		0			0
$119$	11.0726	−	3.40312i	1.01502	−	0.311963i
$120$		0			0
$121$	2.55894	−	4.43221i	0.232631	−	0.402928i
$122$		0			0
$123$	−11.0747	−	19.1819i	−0.998569	−	1.72957i
$124$		0			0
$125$	1.94198			0.173696
$126$		0			0
$127$		−	3.46548i		−	0.307511i	−0.988109	−	0.153756i	$-0.950863\pi$
$127$		−	3.46548i		−	0.307511i	0.988109	−	0.153756i	$-0.0491369\pi$
$128$		0			0
$129$	−6.63269	+	3.82939i	−0.583976	+	0.337159i
$130$		0			0
$131$	−11.4966	−	6.63755i	−1.00446	−	0.579926i	−0.0948959	−	0.995487i	$-0.530252\pi$
$131$	−11.4966	−	6.63755i	−1.00446	−	0.579926i	−0.909565	+	0.415561i	$0.863585\pi$
$132$		0			0
$133$	−9.55515	−	8.88398i	−0.828536	−	0.770338i
$134$		0			0
$135$	−38.4718	−	22.2117i	−3.31112	−	1.91168i
$136$		0			0
$137$	2.69163	+	4.66204i	0.229961	+	0.398305i	0.957796	−	0.287447i	$-0.0928067\pi$
$137$	2.69163	+	4.66204i	0.229961	+	0.398305i	−0.727835	+	0.685752i	$0.759473\pi$
$138$		0			0
$139$			8.67947i			0.736183i	0.929790	+	0.368091i	$0.119989\pi$
$139$			8.67947i			0.736183i	−0.929790	+	0.368091i	$0.880011\pi$
$140$		0			0
$141$			3.56785i			0.300468i
$142$		0			0
$143$	−0.442963	−	0.767235i	−0.0370425	−	0.0641594i
$144$		0			0
$145$	4.59227	+	2.65135i	0.381367	+	0.220183i
$146$		0			0
$147$	22.6046	−	1.64776i	1.86439	−	0.135905i
$148$		0			0
$149$	5.68630	+	3.28299i	0.465840	+	0.268953i	0.714497	−	0.699639i	$-0.246656\pi$
$149$	5.68630	+	3.28299i	0.465840	+	0.268953i	−0.248657	+	0.968592i	$0.579989\pi$
$150$		0			0
$151$	−3.28450	+	1.89631i	−0.267289	+	0.154319i	−0.627655	−	0.778492i	$-0.715985\pi$
$151$	−3.28450	+	1.89631i	−0.267289	+	0.154319i	0.360366	+	0.932811i	$0.382652\pi$
$152$		0			0
$153$			32.7638i			2.64880i
$154$		0			0
$155$	24.5746			1.97388
$156$		0			0
$157$	−0.423062	−	0.732765i	−0.0337640	−	0.0584810i	0.848650	−	0.528955i	$-0.177416\pi$
$157$	−0.423062	−	0.732765i	−0.0337640	−	0.0584810i	−0.882414	+	0.470474i	$0.844083\pi$
$158$		0			0
$159$	21.0996	−	36.5456i	1.67331	−	2.89826i
$160$		0			0
$161$	0.241654	+	0.224680i	0.0190450	+	0.0177072i
$162$		0			0
$163$	−3.19599	+	5.53561i	−0.250329	+	0.433583i	−0.963616	−	0.267289i	$-0.913872\pi$
$163$	−3.19599	+	5.53561i	−0.250329	+	0.433583i	0.713287	+	0.700872i	$0.247205\pi$
$164$		0			0
$165$	20.8118	−	12.0157i	1.62020	−	0.935423i
$166$		0			0
$167$	16.6477			1.28824			0.644118	−	0.764926i	$-0.277225\pi$
$167$	16.6477			1.28824			0.644118	+	0.764926i	$0.277225\pi$
$168$		0			0
$169$	−12.8666			−0.989736
$170$		0			0
$171$	31.9586	−	18.4513i	2.44394	−	1.41101i
$172$		0			0
$173$	5.12808	−	8.88209i	0.389881	−	0.675293i	−0.602552	−	0.798079i	$-0.705850\pi$
$173$	5.12808	−	8.88209i	0.389881	−	0.675293i	0.992433	+	0.122786i	$0.0391829\pi$
$174$		0			0
$175$	3.39315	+	11.0402i	0.256498	+	0.834558i
$176$		0			0
$177$	−4.50892	+	7.80967i	−0.338911	+	0.587011i
$178$		0			0
$179$	7.24599	+	12.5504i	0.541590	+	0.938062i	0.998813	+	0.0487098i	$0.0155109\pi$
$179$	7.24599	+	12.5504i	0.541590	+	0.938062i	−0.457223	+	0.889352i	$0.651156\pi$
$180$		0			0
$181$	−3.56173			−0.264741			−0.132371	−	0.991200i	$-0.542259\pi$
$181$	−3.56173			−0.264741			−0.132371	+	0.991200i	$0.542259\pi$
$182$		0			0
$183$			41.8085i			3.09057i
$184$		0			0
$185$	−21.0256	+	12.1391i	−1.54583	+	0.892485i
$186$		0			0
$187$	−9.19599	−	5.30931i	−0.672477	−	0.388255i
$188$		0			0
$189$	−8.58416	+	37.4342i	−0.624406	+	2.72294i
$190$		0			0
$191$	−11.4123	−	6.58888i	−0.825763	−	0.476755i	0.0266367	−	0.999645i	$-0.491520\pi$
$191$	−11.4123	−	6.58888i	−0.825763	−	0.476755i	−0.852400	+	0.522891i	$0.824854\pi$
$192$		0			0
$193$	−1.50892	−	2.61352i	−0.108614	−	0.188125i	0.806595	−	0.591105i	$-0.201308\pi$
$193$	−1.50892	−	2.61352i	−0.108614	−	0.188125i	−0.915209	+	0.402979i	$0.867975\pi$
$194$		0			0
$195$			3.61946i			0.259195i
$196$		0			0
$197$			15.9685i			1.13771i	0.822438	+	0.568854i	$0.192613\pi$
$197$			15.9685i			1.13771i	−0.822438	+	0.568854i	$0.807387\pi$
$198$		0			0
$199$	−6.07389	−	10.5203i	−0.430567	−	0.745763i	0.566356	−	0.824161i	$-0.308353\pi$
$199$	−6.07389	−	10.5203i	−0.430567	−	0.745763i	−0.996922	+	0.0783979i	$0.975020\pi$
$200$		0			0
$201$	12.6404	+	7.29795i	0.891586	+	0.514757i
$202$		0			0
$203$	1.02467	−	4.46842i	0.0719176	−	0.313621i
$204$		0			0
$205$	−18.1303	−	10.4676i	−1.26628	−	0.731086i
$206$		0			0
$207$	−0.808247	+	0.466642i	−0.0561771	+	0.0324339i
$208$		0			0
$209$			11.9600i			0.827290i
$210$		0			0
$211$	−15.8172			−1.08890			−0.544452	−	0.838792i	$-0.683262\pi$
$211$	−15.8172			−1.08890			−0.544452	+	0.838792i	$0.683262\pi$
$212$		0			0
$213$	12.0858	+	20.9333i	0.828108	+	1.43432i
$214$		0			0
$215$	−3.61946	+	6.26909i	−0.246845	+	0.427548i
$216$		0			0
$217$	−6.24165	−	20.3082i	−0.423711	−	1.37861i
$218$		0			0
$219$	−8.25399	+	14.2963i	−0.557753	+	0.966056i
$220$		0			0
$221$	1.38504	−	0.799653i	0.0931678	−	0.0537905i
$222$		0			0
$223$	−2.18329			−0.146204			−0.0731020	−	0.997324i	$-0.523290\pi$
$223$	−2.18329			−0.146204			−0.0731020	+	0.997324i	$0.523290\pi$
$224$		0			0
$225$	−32.6678			−2.17786
$226$		0			0
$227$	−1.81880	+	1.05008i	−0.120718	+	0.0696965i	−0.559143	−	0.829071i	$-0.688870\pi$
$227$	−1.81880	+	1.05008i	−0.120718	+	0.0696965i	0.438425	+	0.898768i	$0.355536\pi$
$228$		0			0
$229$	−10.5172	+	18.2163i	−0.694994	+	1.20377i	0.275189	+	0.961390i	$0.411260\pi$
$229$	−10.5172	+	18.2163i	−0.694994	+	1.20377i	−0.970183	+	0.242375i	$0.922074\pi$
$230$		0			0
$231$	−15.2156	−	14.1469i	−1.00111	−	0.930795i
$232$		0			0
$233$	−0.391037	+	0.677296i	−0.0256177	+	0.0443711i	−0.878550	−	0.477650i	$-0.841489\pi$
$233$	−0.391037	+	0.677296i	−0.0256177	+	0.0443711i	0.852932	+	0.522021i	$0.174822\pi$
$234$		0			0
$235$	1.68613	+	2.92047i	0.109991	+	0.190510i
$236$		0			0
$237$	38.6656			2.51160
$238$		0			0
$239$		−	7.54814i		−	0.488249i	−0.969744	−	0.244124i	$-0.921499\pi$
$239$		−	7.54814i		−	0.488249i	0.969744	−	0.244124i	$-0.0785005\pi$
$240$		0			0
$241$	−14.9499	+	8.63134i	−0.963009	+	0.555994i	−0.897098	−	0.441832i	$-0.854329\pi$
$241$	−14.9499	+	8.63134i	−0.963009	+	0.555994i	−0.0659113	+	0.997825i	$0.520995\pi$
$242$		0			0
$243$	−31.1247	−	17.9698i	−1.99665	−	1.15277i
$244$		0			0
$245$	17.7243	−	12.0315i	1.13236	−	0.768663i
$246$		0			0
$247$	−1.56000	−	0.900667i	−0.0992605	−	0.0573081i
$248$		0			0
$249$	1.18271	+	2.04852i	0.0749515	+	0.129820i
$250$		0			0
$251$			17.0438i			1.07580i	0.843009	+	0.537899i	$0.180782\pi$
$251$			17.0438i			1.07580i	−0.843009	+	0.537899i	$0.819218\pi$
$252$		0			0
$253$		−	0.302473i		−	0.0190163i
$254$		0			0
$255$	21.6912	+	37.5703i	1.35836	+	2.35274i
$256$		0			0
$257$	14.0571	+	8.11585i	0.876855	+	0.506253i	0.869620	−	0.493721i	$-0.164364\pi$
$257$	14.0571	+	8.11585i	0.876855	+	0.506253i	0.00723501	+	0.999974i	$0.497697\pi$
$258$		0			0
$259$	15.3719	+	14.2921i	0.955161	+	0.888069i
$260$		0			0
$261$	11.2294	+	6.48331i	0.695084	+	0.401307i
$262$		0			0
$263$	−10.2383	+	5.91109i	−0.631322	+	0.364494i	−0.781264	−	0.624201i	$-0.785425\pi$
$263$	−10.2383	+	5.91109i	−0.631322	+	0.364494i	0.149942	+	0.988695i	$0.452091\pi$
$264$		0			0
$265$		−	39.8859i		−	2.45017i
$266$		0			0
$267$	−34.0264			−2.08238
$268$		0			0
$269$	6.41781	+	11.1160i	0.391301	+	0.677753i	0.992621	−	0.121255i	$-0.0386919\pi$
$269$	6.41781	+	11.1160i	0.391301	+	0.677753i	−0.601321	+	0.799008i	$0.705359\pi$
$270$		0			0
$271$	−2.67717	+	4.63700i	−0.162627	+	0.281677i	−0.935810	−	0.352505i	$-0.885330\pi$
$271$	−2.67717	+	4.63700i	−0.162627	+	0.281677i	0.773183	+	0.634183i	$0.218663\pi$
$272$		0			0
$273$	2.99108	−	0.919298i	0.181029	−	0.0556384i
$274$		0			0
$275$	5.29376	−	9.16905i	0.319226	−	0.552915i
$276$		0			0
$277$	−10.7087	+	6.18269i	−0.643425	+	0.371482i	−0.785933	−	0.618312i	$-0.787817\pi$
$277$	−10.7087	+	6.18269i	−0.643425	+	0.371482i	0.142508	+	0.989794i	$0.454483\pi$
$278$		0			0
$279$	60.0920			3.59762
$280$		0			0
$281$	16.4499			0.981320			0.490660	−	0.871351i	$-0.336756\pi$
$281$	16.4499			0.981320			0.490660	+	0.871351i	$0.336756\pi$
$282$		0			0
$283$	−20.4620	+	11.8138i	−1.21634	+	0.702255i	−0.964133	−	0.265418i	$-0.914490\pi$
$283$	−20.4620	+	11.8138i	−1.21634	+	0.702255i	−0.252208	+	0.967673i	$0.581157\pi$
$284$		0			0
$285$	24.4313	−	42.3163i	1.44719	−	2.50660i
$286$		0			0
$287$	−4.04540	+	17.6414i	−0.238792	+	1.04134i
$288$		0			0
$289$	1.08455	−	1.87849i	0.0637969	−	0.110499i
$290$		0			0
$291$	−20.9833	−	36.3441i	−1.23006	−	2.13053i
$292$		0			0
$293$	−7.00524			−0.409251			−0.204625	−	0.978840i	$-0.565598\pi$
$293$	−7.00524			−0.409251			−0.204625	+	0.978840i	$0.565598\pi$
$294$		0			0
$295$			8.52348i			0.496256i
$296$		0			0
$297$	30.4892	−	17.6029i	1.76916	−	1.02143i
$298$		0			0
$299$	0.0394531	+	0.0227783i	0.00228163	+	0.00131730i
$300$		0			0
$301$	6.10001	+	1.39881i	0.351599	+	0.0806263i
$302$		0			0
$303$	−8.30737	−	4.79626i	−0.477246	−	0.275538i
$304$		0			0
$305$	19.7583	+	34.2224i	1.13136	+	1.95957i
$306$		0			0
$307$		−	23.7191i		−	1.35372i	−0.736113	−	0.676859i	$-0.763341\pi$
$307$		−	23.7191i		−	1.35372i	0.736113	−	0.676859i	$-0.236659\pi$
$308$		0			0
$309$		−	41.7993i		−	2.37788i
$310$		0			0
$311$	11.0149	+	19.0783i	0.624596	+	1.08183i	0.988619	+	0.150442i	$0.0480696\pi$
$311$	11.0149	+	19.0783i	0.624596	+	1.08183i	−0.364023	+	0.931390i	$0.618597\pi$
$312$		0			0
$313$	−27.4981	−	15.8760i	−1.55428	−	0.897365i	−0.997785	−	0.0665161i	$-0.978812\pi$
$313$	−27.4981	−	15.8760i	−1.55428	−	0.897365i	−0.556497	−	0.830849i	$-0.687855\pi$
$314$		0			0
$315$	17.8006	+	57.9170i	1.00295	+	3.26325i
$316$		0			0
$317$	−12.2366	−	7.06481i	−0.687276	−	0.396799i	0.115314	−	0.993329i	$-0.463212\pi$
$317$	−12.2366	−	7.06481i	−0.687276	−	0.396799i	−0.802591	+	0.596530i	$0.796546\pi$
$318$		0			0
$319$	−3.63941	+	2.10121i	−0.203768	+	0.117645i
$320$		0			0
$321$			21.6114i			1.20623i
$322$		0			0
$323$	−21.5906			−1.20133
$324$		0			0
$325$	0.797311	+	1.38098i	0.0442269	+	0.0766032i
$326$		0			0
$327$	4.47798	−	7.75609i	0.247633	−	0.428913i
$328$		0			0
$329$	1.98519	−	2.13517i	0.109447	−	0.117715i
$330$		0			0
$331$	−8.25399	+	14.2963i	−0.453680	+	0.785797i	−0.998611	−	0.0526837i	$-0.983222\pi$
$331$	−8.25399	+	14.2963i	−0.453680	+	0.785797i	0.544931	+	0.838481i	$0.316556\pi$
$332$		0			0
$333$	−51.4135	+	29.6836i	−2.81744	+	1.62665i
$334$		0			0
$335$	13.7958			0.753742
$336$		0			0
$337$	20.6190			1.12319			0.561595	−	0.827412i	$-0.310188\pi$
$337$	20.6190			1.12319			0.561595	+	0.827412i	$0.310188\pi$
$338$		0			0
$339$	36.3085	−	20.9627i	1.97201	−	1.13854i
$340$		0			0
$341$	−9.73779	+	16.8663i	−0.527331	+	0.913364i
$342$		0			0
$343$	−14.4444	−	11.5913i	−0.779926	−	0.625872i
$344$		0			0
$345$	−0.617879	+	1.07020i	−0.0332655	+	0.0576175i
$346$		0			0
$347$	4.69713	+	8.13566i	0.252155	+	0.436745i	0.964119	−	0.265471i	$-0.0855274\pi$
$347$	4.69713	+	8.13566i	0.252155	+	0.436745i	−0.711964	+	0.702216i	$0.752194\pi$
$348$		0			0
$349$	−9.89354			−0.529589			−0.264794	−	0.964305i	$-0.585304\pi$
$349$	−9.89354			−0.529589			−0.264794	+	0.964305i	$0.585304\pi$
$350$		0			0
$351$			5.30247i			0.283025i
$352$		0			0
$353$	18.5737	−	10.7235i	0.988578	−	0.570756i	0.0837292	−	0.996489i	$-0.473317\pi$
$353$	18.5737	−	10.7235i	0.988578	−	0.570756i	0.904849	+	0.425733i	$0.139984\pi$
$354$		0			0
$355$	19.7857	+	11.4233i	1.05012	+	0.606286i
$356$		0			0
$357$	25.5384	−	27.4678i	1.35164	−	1.45375i
$358$		0			0
$359$	−24.7329	−	14.2796i	−1.30535	−	0.753647i	−0.324037	−	0.946044i	$-0.605040\pi$
$359$	−24.7329	−	14.2796i	−1.30535	−	0.753647i	−0.981317	+	0.192397i	$0.938374\pi$
$360$		0			0
$361$	2.65899	+	4.60550i	0.139947	+	0.242395i
$362$		0			0
$363$		−	16.5706i		−	0.869733i
$364$		0			0
$365$			15.6030i			0.816699i
$366$		0			0
$367$	−11.1599	−	19.3296i	−0.582544	−	1.00900i	−0.995177	−	0.0980979i	$-0.968724\pi$
$367$	−11.1599	−	19.3296i	−0.582544	−	1.00900i	0.412633	−	0.910897i	$-0.364609\pi$
$368$		0			0
$369$	−44.3339	−	25.5962i	−2.30793	−	1.33248i
$370$		0			0
$371$	−32.9613	+	10.1305i	−1.71126	+	0.525951i
$372$		0			0
$373$	5.83231	+	3.36728i	0.301985	+	0.174351i	0.643334	−	0.765585i	$-0.277551\pi$
$373$	5.83231	+	3.36728i	0.301985	+	0.174351i	−0.341349	+	0.939937i	$0.610884\pi$
$374$		0			0
$375$	5.44532	−	3.14386i	0.281195	−	0.162348i
$376$		0			0
$377$		−	0.632942i		−	0.0325982i
$378$		0			0
$379$	5.26305			0.270345			0.135172	−	0.990822i	$-0.456841\pi$
$379$	5.26305			0.270345			0.135172	+	0.990822i	$0.456841\pi$
$380$		0			0
$381$	−5.61025	−	9.71724i	−0.287422	−	0.497829i
$382$		0			0
$383$	−16.7605	+	29.0301i	−0.856423	+	1.48337i	0.0188957	+	0.999821i	$0.493985\pi$
$383$	−16.7605	+	29.0301i	−0.856423	+	1.48337i	−0.875319	+	0.483547i	$0.839348\pi$
$384$		0			0
$385$	−19.1404	−	4.38915i	−0.975486	−	0.223692i
$386$		0			0
$387$	−8.85062	+	15.3297i	−0.449902	+	0.779253i
$388$		0			0
$389$	−10.4773	+	6.04906i	−0.531219	+	0.306699i	−0.741513	−	0.670939i	$-0.765891\pi$
$389$	−10.4773	+	6.04906i	−0.531219	+	0.306699i	0.210294	+	0.977638i	$0.432558\pi$
$390$		0			0
$391$	0.546036			0.0276142
$392$		0			0
$393$	−42.9821			−2.16816
$394$		0			0
$395$	31.6497	−	18.2730i	1.59247	−	0.919413i
$396$		0			0
$397$	−2.76077	+	4.78180i	−0.138559	+	0.239991i	−0.926951	−	0.375181i	$-0.877580\pi$
$397$	−2.76077	+	4.78180i	−0.138559	+	0.239991i	0.788392	+	0.615173i	$0.210914\pi$
$398$		0			0
$399$	−41.1750	−	9.44197i	−2.06133	−	0.472690i
$400$		0			0
$401$	−14.5244	+	25.1570i	−0.725315	+	1.25628i	0.233530	+	0.972350i	$0.424972\pi$
$401$	−14.5244	+	25.1570i	−0.725315	+	1.25628i	−0.958844	+	0.283932i	$0.908361\pi$
$402$		0			0
$403$	−1.46664	−	2.54030i	−0.0730586	−	0.126541i
$404$		0			0
$405$	−75.1302			−3.73325
$406$		0			0
$407$		−	19.2407i		−	0.953724i
$408$		0			0
$409$	27.9941	−	16.1624i	1.38422	−	0.799178i	0.391561	−	0.920152i	$-0.371935\pi$
$409$	27.9941	−	16.1624i	1.38422	−	0.799178i	0.992656	+	0.120974i	$0.0386018\pi$
$410$		0			0
$411$	15.0947	+	8.71494i	0.744568	+	0.429876i
$412$		0			0
$413$	7.04371	−	2.16486i	0.346598	−	0.106526i
$414$		0			0
$415$	1.93622	+	1.11788i	0.0950454	+	0.0548745i
$416$		0			0
$417$	14.0512	+	24.3373i	0.688088	+	1.19180i
$418$		0			0
$419$		−	21.0832i		−	1.02998i	−0.857196	−	0.514990i	$-0.827796\pi$
$419$		−	21.0832i		−	1.02998i	0.857196	−	0.514990i	$-0.172204\pi$
$420$		0			0
$421$		−	13.9685i		−	0.680783i	−0.940284	−	0.340391i	$-0.889440\pi$
$421$		−	13.9685i		−	0.680783i	0.940284	−	0.340391i	$-0.110560\pi$
$422$		0			0
$423$	4.12308	+	7.14138i	0.200471	+	0.347226i
$424$		0			0
$425$	16.5523	+	9.55648i	0.802905	+	0.463557i
$426$		0			0
$427$	23.2627	−	25.0201i	1.12576	−	1.21081i
$428$		0			0
$429$	−2.48415	−	1.43422i	−0.119936	−	0.0692450i
$430$		0			0
$431$	26.2063	−	15.1302i	1.26231	−	0.728795i	0.288790	−	0.957393i	$-0.406747\pi$
$431$	26.2063	−	15.1302i	1.26231	−	0.728795i	0.973521	+	0.228597i	$0.0734139\pi$
$432$		0			0
$433$		−	28.2790i		−	1.35900i	−0.733674	−	0.679501i	$-0.762196\pi$
$433$		−	28.2790i		−	1.35900i	0.733674	−	0.679501i	$-0.237804\pi$
$434$		0			0
$435$	17.1690			0.823193
$436$		0			0
$437$	−0.307506	−	0.532616i	−0.0147100	−	0.0254785i
$438$		0			0
$439$	11.4433	−	19.8204i	0.546160	−	0.945977i	−0.452373	−	0.891829i	$-0.649422\pi$
$439$	11.4433	−	19.8204i	0.546160	−	0.945977i	0.998533	−	0.0541483i	$-0.0172444\pi$
$440$		0			0
$441$	43.3409	−	29.4204i	2.06385	−	1.40097i
$442$		0			0
$443$	18.1527	−	31.4414i	0.862462	−	1.49383i	−0.00708366	−	0.999975i	$-0.502255\pi$
$443$	18.1527	−	31.4414i	0.862462	−	1.49383i	0.869546	−	0.493853i	$-0.164412\pi$
$444$		0			0
$445$	−27.8523	+	16.0806i	−1.32033	+	0.762292i
$446$		0			0
$447$	21.2593			1.00553
$448$		0			0
$449$	−0.147503			−0.00696108			−0.00348054	−	0.999994i	$-0.501108\pi$
$449$	−0.147503			−0.00696108			−0.00348054	+	0.999994i	$0.501108\pi$
$450$		0			0
$451$	14.3684	−	8.29561i	0.676583	−	0.390625i
$452$		0			0
$453$	−6.13986	+	10.6345i	−0.288476	+	0.499654i
$454$		0			0
$455$	2.01390	−	2.16605i	0.0944132	−	0.101546i
$456$		0			0
$457$	−14.7513	+	25.5499i	−0.690035	+	1.19518i	0.281791	+	0.959476i	$0.409071\pi$
$457$	−14.7513	+	25.5499i	−0.690035	+	1.19518i	−0.971826	+	0.235699i	$0.924262\pi$
$458$		0			0
$459$	31.7774	+	55.0401i	1.48324	+	2.56905i
$460$		0			0
$461$	36.1246			1.68249			0.841246	−	0.540653i	$-0.181823\pi$
$461$	36.1246			1.68249			0.841246	+	0.540653i	$0.181823\pi$
$462$		0			0
$463$		−	13.4518i		−	0.625158i	−0.949892	−	0.312579i	$-0.898807\pi$
$463$		−	13.4518i		−	0.625158i	0.949892	−	0.312579i	$-0.101193\pi$
$464$		0			0
$465$	68.9076	−	39.7838i	3.19551	−	1.84493i
$466$		0			0
$467$	−18.3878	−	10.6162i	−0.850887	−	0.491260i	0.0100632	−	0.999949i	$-0.496797\pi$
$467$	−18.3878	−	10.6162i	−0.850887	−	0.491260i	−0.860950	+	0.508690i	$0.830130\pi$
$468$		0			0
$469$	−3.50395	−	11.4007i	−0.161797	−	0.526434i
$470$		0			0
$471$	−2.37254	−	1.36979i	−0.109321	−	0.0631165i
$472$		0			0
$473$	−2.86845	−	4.96830i	−0.131891	−	0.228443i
$474$		0			0
$475$		−	21.5274i		−	0.987743i
$476$		0			0
$477$		−	97.5324i		−	4.46570i
$478$		0			0
$479$	−6.50656	−	11.2697i	−0.297292	−	0.514925i	0.678223	−	0.734856i	$-0.262750\pi$
$479$	−6.50656	−	11.2697i	−0.297292	−	0.514925i	−0.975515	+	0.219931i	$0.929417\pi$
$480$		0			0
$481$	2.50966	+	1.44895i	0.114431	+	0.0660665i
$482$		0			0
$483$	1.04133	+	0.238792i	0.0473823	+	0.0108654i
$484$		0			0
$485$	−34.3517	−	19.8330i	−1.55983	−	0.900569i
$486$		0			0
$487$	−25.5103	+	14.7284i	−1.15598	+	0.667407i	−0.950338	−	0.311220i	$-0.899262\pi$
$487$	−25.5103	+	14.7284i	−1.15598	+	0.667407i	−0.205644	+	0.978627i	$0.565929\pi$
$488$		0			0
$489$			20.6959i			0.935901i
$490$		0			0
$491$	13.3344			0.601772			0.300886	−	0.953660i	$-0.402718\pi$
$491$	13.3344			0.601772			0.300886	+	0.953660i	$0.402718\pi$
$492$		0			0
$493$	−3.79318	−	6.56999i	−0.170836	−	0.295897i
$494$		0			0
$495$	27.7712	−	48.1011i	1.24822	−	2.16198i
$496$		0			0
$497$	4.41476	−	19.2521i	0.198029	−	0.863575i
$498$		0			0
$499$	1.13611	−	1.96780i	0.0508592	−	0.0880908i	−0.839475	−	0.543398i	$-0.817137\pi$
$499$	1.13611	−	1.96780i	0.0508592	−	0.0880908i	0.890334	+	0.455308i	$0.150471\pi$
$500$		0			0
$501$	46.6803	−	26.9509i	2.08552	−	1.20408i
$502$		0			0
$503$	−39.0610			−1.74164			−0.870821	−	0.491600i	$-0.836412\pi$
$503$	−39.0610			−1.74164			−0.870821	+	0.491600i	$0.836412\pi$
$504$		0			0
$505$	−9.06666			−0.403461
$506$		0			0
$507$	−36.0780	+	20.8296i	−1.60228	+	0.925077i
$508$		0			0
$509$	1.16487	−	2.01761i	0.0516317	−	0.0894288i	−0.839054	−	0.544048i	$-0.816891\pi$
$509$	1.16487	−	2.01761i	0.0516317	−	0.0894288i	0.890686	+	0.454619i	$0.150224\pi$
$510$		0			0
$511$	12.8942	−	3.96297i	0.570405	−	0.175312i
$512$		0			0
$513$	35.7916	−	61.9929i	1.58024	−	2.73705i
$514$		0			0
$515$	−19.7540	−	34.2149i	−0.870464	−	1.50769i
$516$		0			0
$517$	−2.67254			−0.117538
$518$		0			0
$519$		−	33.2073i		−	1.45764i
$520$		0			0
$521$	7.48217	−	4.31983i	0.327800	−	0.189255i	−0.327064	−	0.945002i	$-0.606059\pi$
$521$	7.48217	−	4.31983i	0.327800	−	0.189255i	0.654864	+	0.755747i	$0.272726\pi$
$522$		0			0
$523$	−22.4935	−	12.9866i	−0.983574	−	0.567867i	−0.0802265	−	0.996777i	$-0.525564\pi$
$523$	−22.4935	−	12.9866i	−0.983574	−	0.567867i	−0.903347	+	0.428910i	$0.858898\pi$
$524$		0			0
$525$	27.3873	+	25.4636i	1.19528	+	1.11132i
$526$		0			0
$527$	−30.4477	−	17.5790i	−1.32632	−	0.765753i
$528$		0			0
$529$	−11.4922	−	19.9051i	−0.499662	−	0.865440i
$530$		0			0
$531$			20.8423i			0.904481i
$532$		0			0
$533$			2.49886i			0.108238i
$534$		0			0
$535$	10.2133	+	17.6900i	0.441562	+	0.764807i
$536$		0			0
$537$	40.6357	+	23.4610i	1.75356	+	1.01242i
$538$		0			0
$539$	1.23428	+	16.9322i	0.0531641	+	0.729323i
$540$		0			0
$541$	−18.3004	−	10.5657i	−0.786796	−	0.454257i	0.0520372	−	0.998645i	$-0.483429\pi$
$541$	−18.3004	−	10.5657i	−0.786796	−	0.454257i	−0.838833	+	0.544388i	$0.816762\pi$
$542$		0			0
$543$	−9.98713	+	5.76607i	−0.428589	+	0.247446i
$544$		0			0
$545$		−	8.46500i		−	0.362601i
$546$		0			0
$547$	21.8999			0.936372			0.468186	−	0.883630i	$-0.344908\pi$
$547$	21.8999			0.936372			0.468186	+	0.883630i	$0.344908\pi$
$548$		0			0
$549$	48.3147	+	83.6835i	2.06202	+	3.57152i
$550$		0			0
$551$	−4.27235	+	7.39993i	−0.182008	+	0.315247i
$552$		0			0
$553$	−23.1392	−	21.5139i	−0.983980	−	0.914863i
$554$		0			0
$555$	−39.3039	+	68.0764i	−1.66836	+	2.88968i
$556$		0			0
$557$	−13.9992	+	8.08244i	−0.593165	+	0.342464i	−0.766348	−	0.642426i	$-0.777928\pi$
$557$	−13.9992	+	8.08244i	−0.593165	+	0.342464i	0.173183	+	0.984890i	$0.444595\pi$
$558$		0			0
$559$	0.864054			0.0365456
$560$		0			0
$561$	−34.3809			−1.45156
$562$		0			0
$563$	6.51396	−	3.76084i	0.274531	−	0.158500i	−0.356414	−	0.934328i	$-0.616001\pi$
$563$	6.51396	−	3.76084i	0.274531	−	0.158500i	0.630945	+	0.775828i	$0.282667\pi$
$564$		0			0
$565$	19.8136	−	34.3181i	0.833563	−	1.44377i
$566$		0			0
$567$	19.0822	+	62.0869i	0.801375	+	2.60740i
$568$		0			0
$569$	−12.0166	+	20.8134i	−0.503764	+	0.872544i	0.496227	+	0.868193i	$0.334718\pi$
$569$	−12.0166	+	20.8134i	−0.503764	+	0.872544i	−0.999991	+	0.00435144i	$0.998615\pi$
$570$		0			0
$571$	−18.9700	−	32.8570i	−0.793870	−	1.37502i	−0.923554	−	0.383468i	$-0.874730\pi$
$571$	−18.9700	−	32.8570i	−0.793870	−	1.37502i	0.129684	−	0.991555i	$-0.458604\pi$
$572$		0			0
$573$	−42.6669			−1.78243
$574$		0			0
$575$			0.544436i			0.0227046i
$576$		0			0
$577$	−9.23462	+	5.33161i	−0.384442	+	0.221958i	−0.679749	−	0.733445i	$-0.737911\pi$
$577$	−9.23462	+	5.33161i	−0.384442	+	0.221958i	0.295307	+	0.955402i	$0.404578\pi$
$578$		0			0
$579$	−8.46203	−	4.88556i	−0.351670	−	0.203037i
$580$		0			0
$581$	0.432027	−	1.88400i	0.0179235	−	0.0781616i
$582$		0			0
$583$	27.3749	+	15.8049i	1.13375	+	0.654573i
$584$		0			0
$585$	4.18271	+	7.24467i	0.172934	+	0.299530i
$586$		0			0
$587$			22.2579i			0.918683i	0.888260	+	0.459341i	$0.151915\pi$
$587$			22.2579i			0.918683i	−0.888260	+	0.459341i	$0.848085\pi$
$588$		0			0
$589$			39.5993i			1.63166i
$590$		0			0
$591$	25.8513	+	44.7758i	1.06338	+	1.84183i
$592$		0			0
$593$	−22.5089	−	12.9955i	−0.924330	−	0.533662i	−0.0393164	−	0.999227i	$-0.512518\pi$
$593$	−22.5089	−	12.9955i	−0.924330	−	0.533662i	−0.885014	+	0.465564i	$0.845851\pi$
$594$		0			0
$595$	7.92345	−	34.5530i	0.324830	−	1.41653i
$596$		0			0
$597$	−34.0625	−	19.6660i	−1.39409	−	0.804876i
$598$		0			0
$599$	33.9427	−	19.5968i	1.38686	−	0.800705i	0.393901	−	0.919153i	$-0.371125\pi$
$599$	33.9427	−	19.5968i	1.38686	−	0.800705i	0.992960	+	0.118448i	$0.0377920\pi$
$600$		0			0
$601$			5.30270i			0.216302i	0.994135	+	0.108151i	$0.0344929\pi$
$601$			5.30270i			0.216302i	−0.994135	+	0.108151i	$0.965507\pi$
$602$		0			0
$603$	33.7346			1.37378
$604$		0			0
$605$	−7.83112	−	13.5639i	−0.318380	−	0.551451i
$606$		0			0
$607$	0.781485	−	1.35357i	0.0317195	−	0.0549398i	−0.849730	−	0.527218i	$-0.823235\pi$
$607$	0.781485	−	1.35357i	0.0317195	−	0.0549398i	0.881449	+	0.472279i	$0.156568\pi$
$608$		0			0
$609$	−4.36072	−	14.1883i	−0.176705	−	0.574940i
$610$		0			0
$611$	0.201261	−	0.348594i	0.00814213	−	0.0141026i
$612$		0			0
$613$	−35.1311	+	20.2829i	−1.41893	+	0.819220i	−0.996205	−	0.0870377i	$-0.972260\pi$
$613$	−35.1311	+	20.2829i	−1.41893	+	0.819220i	−0.422726	+	0.906258i	$0.638927\pi$
$614$		0			0
$615$	−67.7836			−2.73330
$616$		0			0
$617$	19.1141			0.769505			0.384753	−	0.923020i	$-0.374287\pi$
$617$	19.1141			0.769505			0.384753	+	0.923020i	$0.374287\pi$
$618$		0			0
$619$	−4.87118	+	2.81238i	−0.195789	+	0.113039i	−0.594690	−	0.803955i	$-0.702725\pi$
$619$	−4.87118	+	2.81238i	−0.195789	+	0.113039i	0.398901	+	0.916994i	$0.369392\pi$
$620$		0			0
$621$	−0.905186	+	1.56783i	−0.0363239	+	0.0629148i
$622$		0			0
$623$	20.3630	+	18.9326i	0.815825	+	0.758520i
$624$		0			0
$625$	13.8851	−	24.0497i	0.555403	−	0.961987i
$626$		0			0
$627$	19.3620	+	33.5359i	0.773243	+	1.33930i
$628$		0			0
$629$	34.7339			1.38493
$630$		0			0
$631$			42.5344i			1.69327i	0.532175	+	0.846634i	$0.321375\pi$
$631$			42.5344i			1.69327i	−0.532175	+	0.846634i	$0.678625\pi$
$632$		0			0
$633$	−44.3517	+	25.6065i	−1.76282	+	1.01777i
$634$		0			0
$635$	−9.18454	−	5.30270i	−0.364477	−	0.210431i
$636$		0			0
$637$	−2.30151	−	1.11412i	−0.0911890	−	0.0441430i
$638$		0			0
$639$	48.3818	+	27.9332i	1.91395	+	1.10502i
$640$		0			0
$641$	6.25057	+	10.8263i	0.246883	+	0.427613i	0.962659	−	0.270716i	$-0.0872604\pi$
$641$	6.25057	+	10.8263i	0.246883	+	0.427613i	−0.715777	+	0.698329i	$0.753927\pi$
$642$		0			0
$643$		−	6.94038i		−	0.273702i	−0.990592	−	0.136851i	$-0.956302\pi$
$643$		−	6.94038i		−	0.273702i	0.990592	−	0.136851i	$-0.0436981\pi$
$644$		0			0
$645$			23.4381i			0.922875i
$646$		0			0
$647$	−15.7363	−	27.2560i	−0.618656	−	1.07154i	−0.989731	−	0.142941i	$-0.954344\pi$
$647$	−15.7363	−	27.2560i	−0.618656	−	1.07154i	0.371075	−	0.928603i	$-0.378989\pi$
$648$		0			0
$649$	−5.84993	−	3.37746i	−0.229630	−	0.132577i
$650$		0			0
$651$	−50.3786	−	46.8399i	−1.97449	−	1.83580i
$652$		0			0
$653$	25.7765	+	14.8821i	1.00871	+	0.582381i	0.910815	−	0.412815i	$-0.135454\pi$
$653$	25.7765	+	14.8821i	1.00871	+	0.582381i	0.0978992	+	0.995196i	$0.468788\pi$
$654$		0			0
$655$	−35.1830	+	20.3129i	−1.37471	+	0.793691i
$656$		0			0
$657$			38.1538i			1.48852i
$658$		0			0
$659$	−12.9803			−0.505640			−0.252820	−	0.967513i	$-0.581358\pi$
$659$	−12.9803			−0.505640			−0.252820	+	0.967513i	$0.581358\pi$
$660$		0			0
$661$	13.7986	+	23.8999i	0.536704	+	0.929599i	0.999079	+	0.0429145i	$0.0136643\pi$
$661$	13.7986	+	23.8999i	0.536704	+	0.929599i	−0.462374	+	0.886685i	$0.653002\pi$
$662$		0			0
$663$	2.58911	−	4.48447i	0.100553	−	0.174162i
$664$		0			0
$665$	−38.1660	+	11.7302i	−1.48001	+	0.454876i
$666$		0			0
$667$	0.108050	−	0.187147i	0.00418370	−	0.00724638i
$668$		0			0
$669$	−6.12197	+	3.53452i	−0.236689	+	0.136653i
$670$		0			0
$671$	−31.3172			−1.20899
$672$		0			0
$673$	36.2178			1.39609			0.698047	−	0.716052i	$-0.254053\pi$
$673$	36.2178			1.39609			0.698047	+	0.716052i	$0.254053\pi$
$674$		0			0
$675$	−54.8789	+	31.6843i	−2.11229	+	1.21953i
$676$		0			0
$677$	23.4401	−	40.5995i	0.900877	−	1.56036i	0.0745189	−	0.997220i	$-0.476258\pi$
$677$	23.4401	−	40.5995i	0.900877	−	1.56036i	0.826358	−	0.563145i	$-0.190409\pi$
$678$		0			0
$679$	−7.66486	+	33.4253i	−0.294150	+	1.28274i
$680$		0			0
$681$	−3.39995	+	5.88889i	−0.130286	+	0.225663i
$682$		0			0
$683$	8.75584	+	15.1656i	0.335033	+	0.580294i	0.983491	−	0.180956i	$-0.0579192\pi$
$683$	8.75584	+	15.1656i	0.335033	+	0.580294i	−0.648458	+	0.761250i	$0.724586\pi$
$684$		0			0
$685$	16.4744			0.629454
$686$		0			0
$687$			68.1048i			2.59836i
$688$		0			0
$689$	−4.12303	+	2.38043i	−0.157075	+	0.0906873i
$690$		0			0
$691$	−7.12882	−	4.11583i	−0.271193	−	0.156573i	0.358237	−	0.933631i	$-0.383378\pi$
$691$	−7.12882	−	4.11583i	−0.271193	−	0.156573i	−0.629430	+	0.777057i	$0.716711\pi$
$692$		0			0
$693$	−46.8038	−	10.7327i	−1.77793	−	0.407703i
$694$		0			0
$695$	23.0032	+	13.2809i	0.872560	+	0.503773i
$696$		0			0
$697$	14.9755	+	25.9384i	0.567239	+	0.982486i
$698$		0			0
$699$			2.53219i			0.0957763i
$700$		0			0
$701$		−	16.4359i		−	0.620774i	−0.950610	−	0.310387i	$-0.899541\pi$
$701$		−	16.4359i		−	0.620774i	0.950610	−	0.310387i	$-0.100459\pi$
$702$		0			0
$703$	−19.5608	−	33.8803i	−0.737750	−	1.27782i
$704$		0			0
$705$	9.45587	+	5.45935i	0.356129	+	0.205611i
$706$		0			0
$707$	2.30282	+	7.49260i	0.0866065	+	0.281788i
$708$		0			0
$709$	−29.5058	−	17.0352i	−1.10811	−	0.639770i	−0.169774	−	0.985483i	$-0.554304\pi$
$709$	−29.5058	−	17.0352i	−1.10811	−	0.639770i	−0.938340	+	0.345713i	$0.887637\pi$
$710$		0			0
$711$	77.3926	−	44.6826i	2.90245	−	1.67573i
$712$		0			0
$713$		−	1.00148i		−	0.0375058i
$714$		0			0
$715$	−2.71120			−0.101393
$716$		0			0
$717$	−12.2197	−	21.1651i	−0.456352	−	0.790424i
$718$		0			0
$719$	−6.67093	+	11.5544i	−0.248784	+	0.430906i	−0.963189	−	0.268827i	$-0.913364\pi$
$719$	−6.67093	+	11.5544i	−0.248784	+	0.430906i	0.714405	+	0.699732i	$0.246697\pi$
$720$		0			0
$721$	−23.2576	+	25.0146i	−0.866156	+	0.931593i
$722$		0			0
$723$	−27.9465	+	48.4048i	−1.03934	+	1.80019i
$724$		0			0
$725$	6.55074	−	3.78207i	0.243289	−	0.140463i
$726$		0			0
$727$	−16.5956			−0.615497			−0.307748	−	0.951468i	$-0.599576\pi$
$727$	−16.5956			−0.615497			−0.307748	+	0.951468i	$0.599576\pi$
$728$		0			0
$729$	−42.7153			−1.58205
$730$		0			0
$731$	8.96895	−	5.17822i	0.331728	−	0.191523i
$732$		0			0
$733$	−1.35780	+	2.35178i	−0.0501516	+	0.0868650i	−0.890011	−	0.455938i	$-0.849304\pi$
$733$	−1.35780	+	2.35178i	−0.0501516	+	0.0868650i	0.839860	+	0.542803i	$0.182637\pi$
$734$		0			0
$735$	30.2213	−	62.4302i	1.11473	−	2.30277i
$736$		0			0
$737$	−5.46662	+	9.46846i	−0.201365	+	0.348775i
$738$		0			0
$739$	24.5064	+	42.4463i	0.901483	+	1.56141i	0.825570	+	0.564300i	$0.190854\pi$
$739$	24.5064	+	42.4463i	0.901483	+	1.56141i	0.0759129	+	0.997114i	$0.475813\pi$
$740$		0			0
$741$	−5.83235			−0.214257
$742$		0			0
$743$		−	10.8013i		−	0.396261i	−0.980176	−	0.198130i	$-0.936513\pi$
$743$		−	10.8013i		−	0.396261i	0.980176	−	0.198130i	$-0.0634869\pi$
$744$		0			0
$745$	17.4018	−	10.0469i	0.637552	−	0.368091i
$746$		0			0
$747$	4.73462	+	2.73353i	0.173231	+	0.100015i
$748$		0			0
$749$	12.0248	−	12.9333i	0.439377	−	0.472571i
$750$		0			0
$751$	−42.5550	−	24.5691i	−1.55285	−	0.896540i	−0.997908	−	0.0646524i	$-0.979406\pi$
$751$	−42.5550	−	24.5691i	−1.55285	−	0.896540i	−0.554945	−	0.831887i	$-0.687261\pi$
$752$		0			0
$753$	27.5922	+	47.7911i	1.00552	+	1.74161i
$754$		0			0
$755$			11.6065i			0.422405i
$756$		0			0
$757$			26.4006i			0.959546i	0.877393	+	0.479773i	$0.159281\pi$
$757$			26.4006i			0.959546i	−0.877393	+	0.479773i	$0.840719\pi$
$758$		0			0
$759$	−0.489673	−	0.848139i	−0.0177740	−	0.0307855i
$760$		0			0
$761$	23.8565	+	13.7735i	0.864796	+	0.499290i	0.865615	−	0.500709i	$-0.166927\pi$
$761$	23.8565	+	13.7735i	0.864796	+	0.499290i	−0.000819389		1.00000i	$0.500261\pi$
$762$		0			0
$763$	−6.99539	+	2.15001i	−0.253250	+	0.0778354i
$764$		0			0
$765$	86.8338	+	50.1335i	3.13948	+	1.81258i
$766$		0			0
$767$	0.881078	−	0.508691i	0.0318139	−	0.0183678i
$768$		0			0
$769$			9.18665i			0.331279i	0.986186	+	0.165640i	$0.0529688\pi$
$769$			9.18665i			0.331279i	−0.986186	+	0.165640i	$0.947031\pi$
$770$		0			0
$771$	52.5549			1.89272
$772$		0			0
$773$	−5.68818	−	9.85222i	−0.204590	−	0.354360i	0.745412	−	0.666604i	$-0.232253\pi$
$773$	−5.68818	−	9.85222i	−0.204590	−	0.354360i	−0.950002	+	0.312244i	$0.898919\pi$
$774$		0			0
$775$	17.5275	−	30.3585i	0.629607	−	1.09051i
$776$		0			0
$777$	66.2404	+	15.1898i	2.37636	+	0.544931i
$778$		0			0
$779$	16.8673	−	29.2150i	0.604333	−	1.04674i
$780$		0			0
$781$	−15.6803	+	9.05304i	−0.561086	+	0.323943i
$782$		0			0
$783$	25.1525			0.898876
$784$		0			0
$785$	−2.58939			−0.0924194
$786$		0			0
$787$	−31.1823	+	18.0031i	−1.11153	+	0.641742i	−0.939225	−	0.343302i	$-0.888455\pi$
$787$	−31.1823	+	18.0031i	−1.11153	+	0.641742i	−0.172304	+	0.985044i	$0.555121\pi$
$788$		0			0
$789$	−19.1389	+	33.1496i	−0.681363	+	1.18016i
$790$		0			0
$791$	−33.3925	−	7.65736i	−1.18730	−	0.272264i
$792$		0			0
$793$	2.35839	−	4.08486i	0.0837490	−	0.145058i
$794$		0			0
$795$	−64.5711	−	111.840i	−2.29010	−	3.96657i
$796$		0			0
$797$	36.8346			1.30475			0.652374	−	0.757897i	$-0.273773\pi$
$797$	36.8346			1.30475			0.652374	+	0.757897i	$0.273773\pi$
$798$		0			0
$799$		−	4.82457i		−	0.170681i
$800$		0			0
$801$	−68.1070	+	39.3216i	−2.40644	+	1.38936i
$802$		0			0
$803$	−10.7088	−	6.18275i	−0.377907	−	0.218184i
$804$		0			0
$805$	0.965234	−	0.296661i	0.0340200	−	0.0104559i
$806$		0			0
$807$	35.9912	+	20.7795i	1.26695	+	0.731475i
$808$		0			0
$809$	−23.4018	−	40.5331i	−0.822763	−	1.42507i	−0.903617	−	0.428341i	$-0.859098\pi$
$809$	−23.4018	−	40.5331i	−0.822763	−	1.42507i	0.0808544	−	0.996726i	$-0.474235\pi$
$810$		0			0
$811$		−	8.13198i		−	0.285552i	−0.989755	−	0.142776i	$-0.954397\pi$
$811$		−	8.13198i		−	0.285552i	0.989755	−	0.142776i	$-0.0456029\pi$
$812$		0			0
$813$			17.3363i			0.608009i
$814$		0			0
$815$	9.78068	+	16.9406i	0.342602	+	0.593405i
$816$		0			0
$817$	−10.1019	−	5.83235i	−0.353422	−	0.204048i
$818$		0			0
$819$	4.92457	−	5.29661i	0.172078	−	0.185079i
$820$		0			0
$821$	−4.70275	−	2.71513i	−0.164127	−	0.0947588i	0.415687	−	0.909508i	$-0.363541\pi$
$821$	−4.70275	−	2.71513i	−0.164127	−	0.0947588i	−0.579814	+	0.814749i	$0.696875\pi$
$822$		0			0
$823$	−24.2839	+	14.0203i	−0.846483	+	0.488717i	−0.859463	−	0.511199i	$-0.829202\pi$
$823$	−24.2839	+	14.0203i	−0.846483	+	0.488717i	0.0129796	+	0.999916i	$0.495868\pi$
$824$		0			0
$825$		−	34.2802i		−	1.19348i
$826$		0			0
$827$	53.9999			1.87776			0.938880	−	0.344244i	$-0.111865\pi$
$827$	53.9999			1.87776			0.938880	+	0.344244i	$0.111865\pi$
$828$		0			0
$829$	−24.6534	−	42.7010i	−0.856248	−	1.48307i	−0.875482	−	0.483251i	$-0.839456\pi$
$829$	−24.6534	−	42.7010i	−0.856248	−	1.48307i	0.0192339	−	0.999815i	$-0.493877\pi$
$830$		0			0
$831$	−20.0183	+	34.6727i	−0.694426	+	1.20278i
$832$		0			0
$833$	−30.5667	+	2.22816i	−1.05907	+	0.0772012i
$834$		0			0
$835$	25.4734	−	44.1213i	0.881544	−	1.52688i
$836$		0			0
$837$	100.949	−	58.2829i	3.48930	−	2.01455i
$838$		0			0
$839$	−23.2253			−0.801825			−0.400913	−	0.916116i	$-0.631307\pi$
$839$	−23.2253			−0.801825			−0.400913	+	0.916116i	$0.631307\pi$
$840$		0			0
$841$	25.9976			0.896470
$842$		0			0
$843$	46.1258	−	26.6307i	1.58866	−	0.917211i
$844$		0			0
$845$	−19.6878	+	34.1002i	−0.677280	+	1.17308i
$846$		0			0
$847$	−9.22006	+	9.91662i	−0.316805	+	0.340739i
$848$		0			0
$849$	−38.2505	+	66.2518i	−1.31275	+	2.27376i
$850$		0			0
$851$	0.494701	+	0.856848i	0.0169581	+	0.0293724i
$852$		0			0
$853$	39.9494			1.36784			0.683920	−	0.729557i	$-0.260274\pi$
$853$	39.9494			1.36784			0.683920	+	0.729557i	$0.260274\pi$
$854$		0			0
$855$		−	112.933i		−	3.86223i
$856$		0			0
$857$	8.54740	−	4.93484i	0.291974	−	0.168571i	−0.346858	−	0.937918i	$-0.612751\pi$
$857$	8.54740	−	4.93484i	0.291974	−	0.168571i	0.638832	+	0.769347i	$0.279418\pi$
$858$		0			0
$859$	27.4794	+	15.8652i	0.937585	+	0.541315i	0.889203	−	0.457514i	$-0.151260\pi$
$859$	27.4794	+	15.8652i	0.937585	+	0.541315i	0.0483829	+	0.998829i	$0.484593\pi$
$860$		0			0
$861$	17.2162	+	56.0156i	0.586726	+	1.90901i
$862$		0			0
$863$	−28.7124	−	16.5771i	−0.977382	−	0.564292i	−0.0759031	−	0.997115i	$-0.524184\pi$
$863$	−28.7124	−	16.5771i	−0.977382	−	0.564292i	−0.901479	+	0.432824i	$0.857517\pi$
$864$		0			0
$865$	−15.6935	−	27.1819i	−0.533594	−	0.924211i
$866$		0			0
$867$		−	7.02308i		−	0.238516i
$868$		0			0
$869$			28.9629i			0.982499i
$870$		0			0
$871$	−0.823346	−	1.42608i	−0.0278980	−	0.0483208i
$872$		0			0
$873$	−83.9998	−	48.4973i	−2.84296	−	1.64139i
$874$		0			0
$875$	−5.00800	−	1.14840i	−0.169301	−	0.0388231i
$876$		0			0
$877$	22.9522	+	13.2515i	0.775042	+	0.447471i	0.834670	−	0.550750i	$-0.185658\pi$
$877$	22.9522	+	13.2515i	0.775042	+	0.447471i	−0.0596282	+	0.998221i	$0.518992\pi$
$878$		0			0
$879$	−19.6428	+	11.3408i	−0.662534	+	0.382514i
$880$		0			0
$881$		−	43.7082i		−	1.47257i	−0.676673	−	0.736284i	$-0.736579\pi$
$881$		−	43.7082i		−	1.47257i	0.676673	−	0.736284i	$-0.263421\pi$
$882$		0			0
$883$	−0.654282			−0.0220183			−0.0110092	−	0.999939i	$-0.503504\pi$
$883$	−0.654282			−0.0220183			−0.0110092	+	0.999939i	$0.503504\pi$
$884$		0			0
$885$	13.7986	+	23.8999i	0.463836	+	0.803387i
$886$		0			0
$887$	5.01939	−	8.69383i	0.168534	−	0.291910i	−0.769370	−	0.638803i	$-0.779430\pi$
$887$	5.01939	−	8.69383i	0.168534	−	0.291910i	0.937905	+	0.346893i	$0.112763\pi$
$888$		0			0
$889$	−2.04934	+	8.93683i	−0.0687325	+	0.299732i
$890$		0			0
$891$	29.7706	−	51.5642i	0.997354	−	1.72747i
$892$		0			0
$893$	−4.70600	+	2.71701i	−0.157480	+	0.0909214i
$894$		0			0
$895$	44.3498			1.48245
$896$		0			0
$897$	0.147503			0.00492497
$898$		0			0
$899$	−12.0500	+	6.95707i	−0.401890	+	0.232031i
$900$		0			0
$901$	−28.5316	+	49.4182i	−0.950526	+	1.64636i
$902$		0			0
$903$	19.3690	−	5.95299i	0.644561	−	0.198103i
$904$		0			0
$905$	−5.44998	+	9.43964i	−0.181163	+	0.313784i
$906$		0			0
$907$	26.7281	+	46.2945i	0.887493	+	1.53718i	0.842829	+	0.538181i	$0.180888\pi$
$907$	26.7281	+	46.2945i	0.887493	+	1.53718i	0.0446635	+	0.999002i	$0.485778\pi$
$908$		0			0
$909$	−22.1706			−0.735352
$910$		0			0
$911$		−	8.48143i		−	0.281002i	−0.990081	−	0.140501i	$-0.955129\pi$
$911$		−	8.48143i		−	0.281002i	0.990081	−	0.140501i	$-0.0448714\pi$
$912$		0			0
$913$	−1.53447	+	0.885927i	−0.0507835	+	0.0293199i
$914$		0			0
$915$	110.805	+	63.9733i	3.66310	+	2.11489i
$916$		0			0
$917$	25.7224	+	23.9156i	0.849429	+	0.789764i
$918$		0			0
$919$	18.3096	+	10.5710i	0.603978	+	0.348707i	0.770605	−	0.637313i	$-0.219954\pi$
$919$	18.3096	+	10.5710i	0.603978	+	0.348707i	−0.166627	+	0.986020i	$0.553288\pi$
$920$		0			0
$921$	−38.3987	−	66.5085i	−1.26528	−	2.19153i
$922$		0			0
$923$		−	2.72702i		−	0.0897610i
$924$		0			0
$925$			34.6322i			1.13870i
$926$		0			0
$927$	−48.3041	−	83.6651i	−1.58651	−	2.74792i
$928$		0			0
$929$	20.1816	+	11.6518i	0.662136	+	0.382284i	0.793090	−	0.609104i	$-0.208471\pi$
$929$	20.1816	+	11.6518i	0.662136	+	0.382284i	−0.130954	+	0.991388i	$0.541804\pi$
$930$		0			0
$931$	19.3874	+	28.5607i	0.635395	+	0.936038i
$932$		0			0
$933$	61.7716	+	35.6639i	2.02231	+	1.16758i
$934$		0			0
$935$	−28.1425	+	16.2481i	−0.920357	+	0.531369i
$936$		0			0
$937$			25.2541i			0.825017i	0.910954	+	0.412508i	$0.135347\pi$
$937$			25.2541i			0.825017i	−0.910954	+	0.412508i	$0.864653\pi$
$938$		0			0
$939$	−102.807			−3.35496
$940$		0			0
$941$	−23.0655	−	39.9506i	−0.751913	−	1.30235i	−0.946894	−	0.321545i	$-0.895798\pi$
$941$	−23.0655	−	39.9506i	−0.751913	−	1.30235i	0.194981	−	0.980807i	$-0.437535\pi$
$942$		0			0
$943$	−0.426581	+	0.738860i	−0.0138914	+	0.0240606i
$944$		0			0
$945$	86.0766	+	80.0304i	2.80007	+	2.60339i
$946$		0			0
$947$	1.74601	−	3.02418i	0.0567378	−	0.0982727i	−0.836261	−	0.548331i	$-0.815263\pi$
$947$	1.74601	−	3.02418i	0.0567378	−	0.0982727i	0.892999	+	0.450058i	$0.148597\pi$
$948$		0			0
$949$	1.61289	−	0.931205i	0.0523568	−	0.0302282i
$950$		0			0
$951$	−45.7488			−1.48351
$952$		0			0
$953$	8.18227			0.265050			0.132525	−	0.991180i	$-0.457692\pi$
$953$	8.18227			0.265050			0.132525	+	0.991180i	$0.457692\pi$
$954$		0			0
$955$	−34.9250	+	20.1639i	−1.13015	+	0.652490i
$956$		0			0
$957$	−6.80329	+	11.7836i	−0.219919	+	0.380911i
$958$		0			0
$959$	−4.18429	−	13.6143i	−0.135118	−	0.439627i
$960$		0			0
$961$	−16.7416	+	28.9973i	−0.540052	+	0.935397i
$962$		0			0
$963$	24.9746	+	43.2572i	0.804794	+	1.39394i
$964$		0			0
$965$	−9.23546			−0.297300
$966$		0			0
$967$		−	48.4950i		−	1.55949i	−0.626095	−	0.779747i	$-0.715348\pi$
$967$		−	48.4950i		−	1.55949i	0.626095	−	0.779747i	$-0.284652\pi$
$968$		0			0
$969$	−60.5403	+	34.9529i	−1.94483	+	1.12285i
$970$		0			0
$971$	−2.87563	−	1.66025i	−0.0922834	−	0.0532798i	0.453148	−	0.891435i	$-0.350301\pi$
$971$	−2.87563	−	1.66025i	−0.0922834	−	0.0532798i	−0.545432	+	0.838155i	$0.683634\pi$
$972$		0			0
$973$	5.13267	−	22.3828i	0.164546	−	0.717558i
$974$		0			0
$975$	4.47134	+	2.58153i	0.143197	+	0.0826751i
$976$		0			0
$977$	−26.3064	−	45.5641i	−0.841617	−	1.45772i	−0.888527	−	0.458825i	$-0.848270\pi$
$977$	−26.3064	−	45.5641i	−0.841617	−	1.45772i	0.0469091	−	0.998899i	$-0.485063\pi$
$978$		0			0
$979$		−	25.4879i		−	0.814597i
$980$		0			0
$981$		−	20.6994i		−	0.660880i
$982$		0			0
$983$	9.53987	+	16.5235i	0.304275	+	0.527019i	0.977100	−	0.212783i	$-0.0682526\pi$
$983$	9.53987	+	16.5235i	0.304275	+	0.527019i	−0.672825	+	0.739802i	$0.734919\pi$
$984$		0			0
$985$	42.3212	+	24.4342i	1.34847	+	0.778538i
$986$		0			0
$987$	2.10988	−	9.20084i	0.0671581	−	0.292866i
$988$		0			0
$989$	0.255482	+	0.147503i	0.00812386	+	0.00469031i
$990$		0			0
$991$	23.1184	−	13.3474i	0.734379	−	0.423994i	−0.0856429	−	0.996326i	$-0.527294\pi$
$991$	23.1184	−	13.3474i	0.734379	−	0.423994i	0.820022	+	0.572332i	$0.193961\pi$
$992$		0			0
$993$			53.4494i			1.69617i
$994$		0			0
$995$	−37.1758			−1.17855
$996$		0			0
$997$	−29.9801	−	51.9271i	−0.949480	−	1.64455i	−0.746522	−	0.665361i	$-0.768278\pi$
$997$	−29.9801	−	51.9271i	−0.949480	−	1.64455i	−0.202958	−	0.979187i	$-0.565056\pi$
$998$		0			0
$999$	−57.5799	+	99.7313i	−1.82175	+	3.15536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.q.d.831.8	yes	16
4.3	odd	2		896.2.q.a.831.2	yes	16
7.3	odd	6	inner	896.2.q.d.703.7	yes	16
8.3	odd	2	inner	896.2.q.d.831.7	yes	16
8.5	even	2		896.2.q.a.831.1	yes	16
28.3	even	6		896.2.q.a.703.1	✓	16
56.3	even	6	inner	896.2.q.d.703.8	yes	16
56.45	odd	6		896.2.q.a.703.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.q.a.703.1	✓	16	28.3	even	6
896.2.q.a.703.2	yes	16	56.45	odd	6
896.2.q.a.831.1	yes	16	8.5	even	2
896.2.q.a.831.2	yes	16	4.3	odd	2
896.2.q.d.703.7	yes	16	7.3	odd	6	inner
896.2.q.d.703.8	yes	16	56.3	even	6	inner
896.2.q.d.831.7	yes	16	8.3	odd	2	inner
896.2.q.d.831.8	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.80401 - 1.61890i) q^{3} +(1.53015 - 2.65030i) q^{5} +(-2.57882 - 0.591357i) q^{7} +(3.74165 - 6.48073i) q^{9} +O(q^{10})\)	\(q+(2.80401 - 1.61890i) q^{3} +(1.53015 - 2.65030i) q^{5} +(-2.57882 - 0.591357i) q^{7} +(3.74165 - 6.48073i) q^{9} +(1.21265 + 2.10038i) q^{11} -0.365284 q^{13} -9.90862i q^{15} +(-3.79168 + 2.18913i) q^{17} +(4.27065 + 2.46566i) q^{19} +(-8.18838 + 2.51667i) q^{21} +(-0.108007 - 0.0623577i) q^{23} +(-2.18271 - 3.78057i) q^{25} -14.5160i q^{27} +1.73274i q^{29} +(4.01507 + 6.95431i) q^{31} +(6.80059 + 3.92632i) q^{33} +(-5.51325 + 5.92976i) q^{35} +(-6.87043 - 3.96664i) q^{37} +(-1.02426 + 0.591357i) q^{39} -6.84087i q^{41} -2.36543 q^{43} +(-11.4506 - 19.8330i) q^{45} +(-0.550970 + 0.954308i) q^{47} +(6.30059 + 3.05000i) q^{49} +(-7.08794 + 12.2767i) q^{51} +(11.2872 - 6.51667i) q^{53} +7.42217 q^{55} +15.9666 q^{57} +(-2.41203 + 1.39259i) q^{59} +(-6.45633 + 11.1827i) q^{61} +(-13.4815 + 14.5000i) q^{63} +(-0.558939 + 0.968111i) q^{65} +(2.25399 + 3.90402i) q^{67} -0.403803 q^{69} +7.46548i q^{71} +(-4.41545 + 2.54926i) q^{73} +(-12.2407 - 7.06718i) q^{75} +(-1.88514 - 6.13360i) q^{77} +(10.3420 + 5.97097i) q^{79} +(-12.2750 - 21.2609i) q^{81} +0.730568i q^{83} +13.3988i q^{85} +(2.80512 + 4.85862i) q^{87} +(-9.10119 - 5.25457i) q^{89} +(0.942001 + 0.216013i) q^{91} +(22.5166 + 13.0000i) q^{93} +(13.0695 - 7.54567i) q^{95} -12.9615i q^{97} +18.1493 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} + 8 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 + 8 * q^9	\( 16 q + 12 q^{3} + 8 q^{9} - 4 q^{11} - 12 q^{19} - 16 q^{25} + 24 q^{33} + 20 q^{35} + 16 q^{49} - 52 q^{51} + 48 q^{57} + 60 q^{59} + 24 q^{65} + 12 q^{67} - 24 q^{73} - 120 q^{75} - 32 q^{81} + 24 q^{89} + 72 q^{91} + 64 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 + 8 * q^9 - 4 * q^11 - 12 * q^19 - 16 * q^25 + 24 * q^33 + 20 * q^35 + 16 * q^49 - 52 * q^51 + 48 * q^57 + 60 * q^59 + 24 * q^65 + 12 * q^67 - 24 * q^73 - 120 * q^75 - 32 * q^81 + 24 * q^89 + 72 * q^91 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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