LMFDB - Embedded newform 756.2.bf.b.271.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.8
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.b.703.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0660073 - 1.41267i) q^{2} +(-1.99129 - 0.186493i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(-2.50492 - 0.851694i) q^{7} +(-0.394894 + 2.80072i) q^{8} +O(q^{10})$	\(q+(0.0660073 - 1.41267i) q^{2} +(-1.99129 - 0.186493i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(-2.50492 - 0.851694i) q^{7} +(-0.394894 + 2.80072i) q^{8} +(-0.996433 + 1.55358i) q^{10} +(-1.66349 + 0.960419i) q^{11} +4.88503i q^{13} +(-1.36851 + 3.48241i) q^{14} +(3.93044 + 0.742724i) q^{16} +(7.03908 - 4.06402i) q^{17} +(-2.90712 + 5.03529i) q^{19} +(2.12893 + 1.51018i) q^{20} +(1.24695 + 2.41337i) q^{22} +(7.15864 + 4.13305i) q^{23} +(-1.64838 - 2.85507i) q^{25} +(6.90095 + 0.322448i) q^{26} +(4.82917 + 2.16312i) q^{28} -3.41373 q^{29} +(-0.682773 - 1.18260i) q^{31} +(1.30866 - 5.50340i) q^{32} +(-5.27649 - 10.2122i) q^{34} +(2.27539 + 2.59718i) q^{35} +(-5.49640 + 9.52005i) q^{37} +(6.92132 + 4.43918i) q^{38} +(2.27392 - 2.90780i) q^{40} +4.57667i q^{41} -0.547870i q^{43} +(3.49160 - 1.60224i) q^{44} +(6.31116 - 9.84001i) q^{46} +(-2.44131 + 4.22848i) q^{47} +(5.54924 + 4.26685i) q^{49} +(-4.14208 + 2.14016i) q^{50} +(0.911027 - 9.72750i) q^{52} +(2.31694 + 4.01305i) q^{53} +2.50686 q^{55} +(3.37454 - 6.67926i) q^{56} +(-0.225331 + 4.82248i) q^{58} +(-3.07108 - 5.31927i) q^{59} +(8.77355 + 5.06541i) q^{61} +(-1.71569 + 0.886475i) q^{62} +(-7.68812 - 2.21198i) q^{64} +(3.18769 - 5.52124i) q^{65} +(-6.85377 + 3.95703i) q^{67} +(-14.7747 + 6.77988i) q^{68} +(3.81916 - 3.04294i) q^{70} +4.66463i q^{71} +(-7.64041 + 4.41119i) q^{73} +(13.0859 + 8.39301i) q^{74} +(6.72796 - 9.48453i) q^{76} +(4.98490 - 0.988983i) q^{77} +(-6.79578 - 3.92355i) q^{79} +(-3.95767 - 3.40423i) q^{80} +(6.46533 + 0.302094i) q^{82} +2.23181 q^{83} -10.6078 q^{85} +(-0.773961 - 0.0361634i) q^{86} +(-2.03297 - 5.03825i) q^{88} +(-1.97649 - 1.14113i) q^{89} +(4.16055 - 12.2366i) q^{91} +(-13.4841 - 9.56512i) q^{92} +(5.81231 + 3.72788i) q^{94} +(6.57148 - 3.79404i) q^{95} +2.86429i q^{97} +(6.39395 - 7.55761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 6 q^{11} - 17 q^{14} - 4 q^{16} + 8 q^{20} + 2 q^{22} + 14 q^{25} + 15 q^{26} - 13 q^{28} + 15 q^{32} + 6 q^{35} + 4 q^{37} - q^{38} - 15 q^{40} - 42 q^{44} - 9 q^{46} - 4 q^{47} + 14 q^{49} - 9 q^{52} + 45 q^{56} + 10 q^{58} - 16 q^{59} - 42 q^{64} - 49 q^{68} - 33 q^{70} + 36 q^{73} - 54 q^{74} - 15 q^{80} - 51 q^{82} + 20 q^{83} + 16 q^{85} + 78 q^{86} - 2 q^{88} - 27 q^{94} + 24 q^{95} - 46 q^{98}+O(q^{100}) $ 32 * q - 6 * q^11 - 17 * q^14 - 4 * q^16 + 8 * q^20 + 2 * q^22 + 14 * q^25 + 15 * q^26 - 13 * q^28 + 15 * q^32 + 6 * q^35 + 4 * q^37 - q^38 - 15 * q^40 - 42 * q^44 - 9 * q^46 - 4 * q^47 + 14 * q^49 - 9 * q^52 + 45 * q^56 + 10 * q^58 - 16 * q^59 - 42 * q^64 - 49 * q^68 - 33 * q^70 + 36 * q^73 - 54 * q^74 - 15 * q^80 - 51 * q^82 + 20 * q^83 + 16 * q^85 + 78 * q^86 - 2 * q^88 - 27 * q^94 + 24 * q^95 - 46 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.0660073	−	1.41267i	0.0466742	−	0.998910i
$2$	0.0660073	−	1.41267i	0.0466742	−	0.998910i
$3$		0			0
$3$		0			0
$4$	−1.99129	−	0.186493i	−0.995643	−	0.0932467i
$5$	−1.13024	−	0.652543i	−0.505457	−	0.291826i	0.225507	−	0.974242i	$-0.427596\pi$
$5$	−1.13024	−	0.652543i	−0.505457	−	0.291826i	−0.730964	+	0.682416i	$0.760929\pi$
$6$		0			0
$7$	−2.50492	−	0.851694i	−0.946770	−	0.321910i
$7$	−2.50492	−	0.851694i	−0.946770	−	0.321910i
$8$	−0.394894	+	2.80072i	−0.139616	+	0.990206i
$9$		0			0
$10$	−0.996433	+	1.55358i	−0.315100	+	0.491286i
$11$	−1.66349	+	0.960419i	−0.501562	+	0.289577i	−0.729358	−	0.684132i	$-0.760181\pi$
$11$	−1.66349	+	0.960419i	−0.501562	+	0.289577i	0.227796	+	0.973709i	$0.426848\pi$
$12$		0			0
$13$			4.88503i			1.35486i	0.735585	+	0.677432i	$0.236907\pi$
$13$			4.88503i			1.35486i	−0.735585	+	0.677432i	$0.763093\pi$
$14$	−1.36851	+	3.48241i	−0.365749	+	0.930714i
$15$		0			0
$16$	3.93044	+	0.742724i	0.982610	+	0.185681i
$17$	7.03908	−	4.06402i	1.70723	−	0.985669i	0.769269	−	0.638925i	$-0.220621\pi$
$17$	7.03908	−	4.06402i	1.70723	−	0.985669i	0.937960	−	0.346744i	$-0.112713\pi$
$18$		0			0
$19$	−2.90712	+	5.03529i	−0.666940	+	1.15517i	0.311816	+	0.950143i	$0.399063\pi$
$19$	−2.90712	+	5.03529i	−0.666940	+	1.15517i	−0.978755	+	0.205031i	$0.934270\pi$
$20$	2.12893	+	1.51018i	0.476043	+	0.337687i
$21$		0			0
$22$	1.24695	+	2.41337i	0.265852	+	0.514531i
$23$	7.15864	+	4.13305i	1.49268	+	0.861800i	0.999965	−	0.00839082i	$-0.00267091\pi$
$23$	7.15864	+	4.13305i	1.49268	+	0.861800i	0.492716	+	0.870190i	$0.336004\pi$
$24$		0			0
$25$	−1.64838	−	2.85507i	−0.329675	−	0.571014i
$26$	6.90095	+	0.322448i	1.35339	+	0.0632373i
$27$		0			0
$28$	4.82917	+	2.16312i	0.912628	+	0.408791i
$29$	−3.41373			−0.633913			−0.316956	−	0.948440i	$-0.602661\pi$
$29$	−3.41373			−0.633913			−0.316956	+	0.948440i	$0.602661\pi$
$30$		0			0
$31$	−0.682773	−	1.18260i	−0.122630	−	0.212401i	0.798174	−	0.602427i	$-0.205799\pi$
$31$	−0.682773	−	1.18260i	−0.122630	−	0.212401i	−0.920804	+	0.390026i	$0.872466\pi$
$32$	1.30866	−	5.50340i	0.231341	−	0.972873i
$33$		0			0
$34$	−5.27649	−	10.2122i	−0.904911	−	1.75137i
$35$	2.27539	+	2.59718i	0.384610	+	0.439004i
$36$		0			0
$37$	−5.49640	+	9.52005i	−0.903603	+	1.56509i	−0.0808217	+	0.996729i	$0.525754\pi$
$37$	−5.49640	+	9.52005i	−0.903603	+	1.56509i	−0.822781	+	0.568358i	$0.807579\pi$
$38$	6.92132	+	4.43918i	1.12279	+	0.720130i
$39$		0			0
$40$	2.27392	−	2.90780i	0.359538	−	0.459763i
$41$			4.57667i			0.714756i	0.933960	+	0.357378i	$0.116329\pi$
$41$			4.57667i			0.714756i	−0.933960	+	0.357378i	$0.883671\pi$
$42$		0			0
$43$		−	0.547870i		−	0.0835494i	−0.999127	−	0.0417747i	$-0.986699\pi$
$43$		−	0.547870i		−	0.0835494i	0.999127	−	0.0417747i	$-0.0133012\pi$
$44$	3.49160	−	1.60224i	0.526379	−	0.241546i
$45$		0			0
$46$	6.31116	−	9.84001i	0.930530	−	1.45083i
$47$	−2.44131	+	4.22848i	−0.356102	+	0.616787i	−0.987306	−	0.158830i	$-0.949228\pi$
$47$	−2.44131	+	4.22848i	−0.356102	+	0.616787i	0.631204	+	0.775617i	$0.282561\pi$
$48$		0			0
$49$	5.54924	+	4.26685i	0.792748	+	0.609550i
$50$	−4.14208	+	2.14016i	−0.585779	+	0.302664i
$51$		0			0
$52$	0.911027	−	9.72750i	0.126337	−	1.34896i
$53$	2.31694	+	4.01305i	0.318256	+	0.551235i	0.980124	−	0.198385i	$-0.0635696\pi$
$53$	2.31694	+	4.01305i	0.318256	+	0.551235i	−0.661869	+	0.749620i	$0.730236\pi$
$54$		0			0
$55$	2.50686			0.338025
$56$	3.37454	−	6.67926i	0.450941	−	0.892554i
$57$		0			0
$58$	−0.225331	+	4.82248i	−0.0295874	+	0.633222i
$59$	−3.07108	−	5.31927i	−0.399821	−	0.692510i	0.593883	−	0.804552i	$-0.297594\pi$
$59$	−3.07108	−	5.31927i	−0.399821	−	0.692510i	−0.993703	+	0.112042i	$0.964261\pi$
$60$		0			0
$61$	8.77355	+	5.06541i	1.12334	+	0.648560i	0.942251	−	0.334907i	$-0.108705\pi$
$61$	8.77355	+	5.06541i	1.12334	+	0.648560i	0.181087	+	0.983467i	$0.442038\pi$
$62$	−1.71569	+	0.886475i	−0.217893	+	0.112582i
$63$		0			0
$64$	−7.68812	−	2.21198i	−0.961015	−	0.276497i
$65$	3.18769	−	5.52124i	0.395385	−	0.684826i
$66$		0			0
$67$	−6.85377	+	3.95703i	−0.837321	+	0.483428i	−0.856353	−	0.516391i	$-0.827275\pi$
$67$	−6.85377	+	3.95703i	−0.837321	+	0.483428i	0.0190314	+	0.999819i	$0.493942\pi$
$68$	−14.7747	+	6.77988i	−1.79170	+	0.822181i
$69$		0			0
$70$	3.81916	−	3.04294i	0.456477	−	0.363701i
$71$			4.66463i			0.553590i	0.960929	+	0.276795i	$0.0892723\pi$
$71$			4.66463i			0.553590i	−0.960929	+	0.276795i	$0.910728\pi$
$72$		0			0
$73$	−7.64041	+	4.41119i	−0.894242	+	0.516291i	−0.875328	−	0.483530i	$-0.839354\pi$
$73$	−7.64041	+	4.41119i	−0.894242	+	0.516291i	−0.0189144	+	0.999821i	$0.506021\pi$
$74$	13.0859	+	8.39301i	1.52121	+	0.975668i
$75$		0			0
$76$	6.72796	−	9.48453i	0.771750	−	1.08795i
$77$	4.98490	−	0.988983i	0.568082	−	0.112705i
$78$		0			0
$79$	−6.79578	−	3.92355i	−0.764585	−	0.441433i	0.0663545	−	0.997796i	$-0.478863\pi$
$79$	−6.79578	−	3.92355i	−0.764585	−	0.441433i	−0.830940	+	0.556363i	$0.812197\pi$
$80$	−3.95767	−	3.40423i	−0.442481	−	0.380605i
$81$		0			0
$82$	6.46533	+	0.302094i	0.713977	+	0.0333607i
$83$	2.23181			0.244973			0.122486	−	0.992470i	$-0.460913\pi$
$83$	2.23181			0.244973			0.122486	+	0.992470i	$0.460913\pi$
$84$		0			0
$85$	−10.6078			−1.15058
$86$	−0.773961	−	0.0361634i	−0.0834583	−	0.00389960i
$87$		0			0
$88$	−2.03297	−	5.03825i	−0.216715	−	0.537079i
$89$	−1.97649	−	1.14113i	−0.209507	−	0.120959i	0.391575	−	0.920146i	$-0.371930\pi$
$89$	−1.97649	−	1.14113i	−0.209507	−	0.120959i	−0.601082	+	0.799187i	$0.705264\pi$
$90$		0			0
$91$	4.16055	−	12.2366i	0.436144	−	1.28275i
$92$	−13.4841	−	9.56512i	−1.40582	−	0.997232i
$93$		0			0
$94$	5.81231	+	3.72788i	0.599494	+	0.384502i
$95$	6.57148	−	3.79404i	0.674219	−	0.389261i
$96$		0			0
$97$			2.86429i			0.290825i	0.989371	+	0.145412i	$0.0464509\pi$
$97$			2.86429i			0.290825i	−0.989371	+	0.145412i	$0.953549\pi$
$98$	6.39395	−	7.55761i	0.645886	−	0.763434i
$99$		0			0
$100$	2.74994	+	5.99267i	0.274994	+	0.599267i
$101$	−2.12681	+	1.22791i	−0.211625	+	0.122182i	−0.602066	−	0.798446i	$-0.705656\pi$
$101$	−2.12681	+	1.22791i	−0.211625	+	0.122182i	0.390441	+	0.920628i	$0.372322\pi$
$102$		0			0
$103$	5.93141	−	10.2735i	0.584439	−	1.01228i	−0.410506	−	0.911858i	$-0.634648\pi$
$103$	5.93141	−	10.2735i	0.584439	−	1.01228i	0.994945	−	0.100421i	$-0.0320188\pi$
$104$	−13.6816	−	1.92907i	−1.34159	−	0.189161i
$105$		0			0
$106$	5.82206	−	3.00818i	0.565489	−	0.292180i
$107$	−8.32250	−	4.80500i	−0.804566	−	0.464516i	0.0404992	−	0.999180i	$-0.487105\pi$
$107$	−8.32250	−	4.80500i	−0.804566	−	0.464516i	−0.845065	+	0.534663i	$0.820439\pi$
$108$		0			0
$109$	3.64401	+	6.31160i	0.349032	+	0.604542i	0.986078	−	0.166284i	$-0.0531770\pi$
$109$	3.64401	+	6.31160i	0.349032	+	0.604542i	−0.637045	+	0.770826i	$0.719844\pi$
$110$	0.165471	−	3.54137i	0.0157770	−	0.337656i
$111$		0			0
$112$	−9.21286	−	5.20799i	−0.870533	−	0.492109i
$113$	−8.22376			−0.773627			−0.386813	−	0.922158i	$-0.626424\pi$
$113$	−8.22376			−0.773627			−0.386813	+	0.922158i	$0.626424\pi$
$114$		0			0
$115$	−5.39398	−	9.34264i	−0.502991	−	0.871206i
$116$	6.79770	+	0.636638i	0.631151	+	0.0591103i
$117$		0			0
$118$	−7.71710	+	3.98732i	−0.710416	+	0.367063i
$119$	−21.0936	+	4.18489i	−1.93365	+	0.383628i
$120$		0			0
$121$	−3.65519	+	6.33098i	−0.332290	+	0.575543i
$122$	7.73489	−	12.0598i	0.700284	−	1.09184i
$123$		0			0
$124$	1.13905	+	2.48222i	0.102290	+	0.222910i
$125$			10.8280i			0.968483i
$126$		0			0
$127$			15.5276i			1.37786i	0.724830	+	0.688928i	$0.241918\pi$
$127$			15.5276i			1.37786i	−0.724830	+	0.688928i	$0.758082\pi$
$128$	−3.63227	+	10.7148i	−0.321050	+	0.947062i
$129$		0			0
$130$	−7.58930	−	4.86761i	−0.665625	−	0.426917i
$131$	8.33537	−	14.4373i	0.728264	−	1.26139i	−0.229352	−	0.973344i	$-0.573661\pi$
$131$	8.33537	−	14.4373i	0.728264	−	1.26139i	0.957616	−	0.288047i	$-0.0930061\pi$
$132$		0			0
$133$	11.5706	−	10.1370i	1.00330	−	0.878989i
$134$	5.13758	+	9.94333i	0.443820	+	0.858972i
$135$		0			0
$136$	8.60250	+	21.3194i	0.737659	+	1.82812i
$137$	−3.32512	−	5.75928i	−0.284084	−	0.492049i	0.688302	−	0.725424i	$-0.258356\pi$
$137$	−3.32512	−	5.75928i	−0.284084	−	0.492049i	−0.972387	+	0.233375i	$0.925023\pi$
$138$		0			0
$139$	6.19472			0.525430			0.262715	−	0.964874i	$-0.415382\pi$
$139$	6.19472			0.525430			0.262715	+	0.964874i	$0.415382\pi$
$140$	−4.04659	−	5.59608i	−0.341999	−	0.472955i
$141$		0			0
$142$	6.58960	+	0.307900i	0.552987	+	0.0258384i
$143$	−4.69168	−	8.12622i	−0.392338	−	0.679549i
$144$		0			0
$145$	3.85832	+	2.22760i	0.320416	+	0.184992i
$146$	5.72725	+	11.0846i	0.473990	+	0.917365i
$147$		0			0
$148$	12.7203	−	17.9321i	1.04561	−	1.47401i
$149$	−6.79687	+	11.7725i	−0.556822	+	0.964443i	0.440938	+	0.897538i	$0.354646\pi$
$149$	−6.79687	+	11.7725i	−0.556822	+	0.964443i	−0.997759	+	0.0669056i	$0.978687\pi$
$150$		0			0
$151$	−8.88639	+	5.13056i	−0.723164	+	0.417519i	−0.815916	−	0.578170i	$-0.803767\pi$
$151$	−8.88639	+	5.13056i	−0.723164	+	0.417519i	0.0927523	+	0.995689i	$0.470434\pi$
$152$	−12.9544	−	10.1305i	−1.05074	−	0.821688i
$153$		0			0
$154$	−1.06807	−	7.10731i	−0.0860675	−	0.572723i
$155$			1.78216i			0.143146i
$156$		0			0
$157$	8.08010	−	4.66505i	0.644862	−	0.372311i	−0.141623	−	0.989921i	$-0.545232\pi$
$157$	8.08010	−	4.66505i	0.644862	−	0.372311i	0.786485	+	0.617609i	$0.211899\pi$
$158$	−5.99126	+	9.34123i	−0.476639	+	0.743148i
$159$		0			0
$160$	−5.07030	+	5.36619i	−0.400843	+	0.424234i
$161$	−14.4117	−	16.4499i	−1.13580	−	1.29643i
$162$		0			0
$163$	−4.44216	−	2.56468i	−0.347937	−	0.200881i	0.315840	−	0.948813i	$-0.397714\pi$
$163$	−4.44216	−	2.56468i	−0.347937	−	0.200881i	−0.663776	+	0.747931i	$0.731047\pi$
$164$	0.853519	−	9.11346i	0.0666486	−	0.711641i
$165$		0			0
$166$	0.147316	−	3.15281i	0.0114339	−	0.244706i
$167$	12.6985			0.982637			0.491318	−	0.870980i	$-0.336515\pi$
$167$	12.6985			0.982637			0.491318	+	0.870980i	$0.336515\pi$
$168$		0			0
$169$	−10.8635			−0.835657
$170$	−0.700191	+	14.9853i	−0.0537022	+	1.14932i
$171$		0			0
$172$	−0.102174	+	1.09097i	−0.00779071	+	0.0831854i
$173$	−0.490752	−	0.283336i	−0.0373112	−	0.0215416i	0.481228	−	0.876595i	$-0.340191\pi$
$173$	−0.490752	−	0.283336i	−0.0373112	−	0.0215416i	−0.518540	+	0.855054i	$0.673524\pi$
$174$		0			0
$175$	1.69740	+	8.55563i	0.128312	+	0.646745i
$176$	−7.25159	+	2.53935i	−0.546609	+	0.191411i
$177$		0			0
$178$	−1.74250	+	2.71681i	−0.130606	+	0.203633i
$179$	5.70994	−	3.29664i	0.426781	−	0.246402i	−0.271193	−	0.962525i	$-0.587418\pi$
$179$	5.70994	−	3.29664i	0.426781	−	0.246402i	0.697974	+	0.716123i	$0.254085\pi$
$180$		0			0
$181$			2.90503i			0.215929i	0.994155	+	0.107965i	$0.0344333\pi$
$181$			2.90503i			0.215929i	−0.994155	+	0.107965i	$0.965567\pi$
$182$	−17.0117	−	6.68520i	−1.26099	−	0.495540i
$183$		0			0
$184$	−14.4024	+	18.4173i	−1.06176	+	1.35774i
$185$	12.4245	−	7.17328i	0.913466	−	0.527390i
$186$		0			0
$187$	−7.80632	+	13.5209i	−0.570854	+	0.988749i
$188$	5.64993	−	7.96482i	0.412064	−	0.580894i
$189$		0			0
$190$	−4.92598	−	9.53378i	−0.357368	−	0.691653i
$191$	−0.693842	−	0.400590i	−0.0502046	−	0.0289857i	0.474688	−	0.880154i	$-0.342561\pi$
$191$	−0.693842	−	0.400590i	−0.0502046	−	0.0289857i	−0.524892	+	0.851169i	$0.675894\pi$
$192$		0			0
$193$	−7.19324	−	12.4591i	−0.517781	−	0.896823i	−0.999787	−	0.0206546i	$-0.993425\pi$
$193$	−7.19324	−	12.4591i	−0.517781	−	0.896823i	0.482006	−	0.876168i	$-0.339908\pi$
$194$	4.04631	+	0.189064i	0.290508	+	0.0135740i
$195$		0			0
$196$	−10.2544	−	9.53141i	−0.732455	−	0.680815i
$197$	−12.0122			−0.855831			−0.427915	−	0.903819i	$-0.640752\pi$
$197$	−12.0122			−0.855831			−0.427915	+	0.903819i	$0.640752\pi$
$198$		0			0
$199$	5.33819	+	9.24602i	0.378414	+	0.655433i	0.990832	−	0.135102i	$-0.0431361\pi$
$199$	5.33819	+	9.24602i	0.378414	+	0.655433i	−0.612417	+	0.790535i	$0.709803\pi$
$200$	8.64720	−	3.48920i	0.611449	−	0.246724i
$201$		0			0
$202$	1.59425	+	3.08553i	0.112171	+	0.217097i
$203$	8.55111	+	2.90745i	0.600170	+	0.204063i
$204$		0			0
$205$	2.98647	−	5.17272i	0.208584	−	0.361278i
$206$	−14.1216	−	9.05727i	−0.983897	−	0.631050i
$207$		0			0
$208$	−3.62823	+	19.2003i	−0.251572	+	1.33130i
$209$		−	11.1682i		−	0.772522i
$210$		0			0
$211$			22.8497i			1.57304i	0.617567	+	0.786518i	$0.288118\pi$
$211$			22.8497i			1.57304i	−0.617567	+	0.786518i	$0.711882\pi$
$212$	−3.86528	−	8.42323i	−0.265468	−	0.578510i
$213$		0			0
$214$	−7.33723	+	11.4398i	−0.501563	+	0.782008i
$215$	−0.357509	+	0.619223i	−0.0243819	+	0.0422307i
$216$		0			0
$217$	0.703080	+	3.54383i	0.0477282	+	0.240571i
$218$	9.15676	−	4.73117i	0.620174	−	0.320435i
$219$		0			0
$220$	−4.99187	−	0.467512i	−0.336552	−	0.0315197i
$221$	19.8529	+	34.3862i	1.33545	+	2.31306i
$222$		0			0
$223$	13.8280			0.925989			0.462994	−	0.886361i	$-0.346775\pi$
$223$	13.8280			0.925989			0.462994	+	0.886361i	$0.346775\pi$
$224$	−7.96531	+	12.6710i	−0.532204	+	0.846616i
$225$		0			0
$226$	−0.542829	+	11.6175i	−0.0361084	+	0.772783i
$227$	−7.45033	−	12.9043i	−0.494496	−	0.856491i	0.505484	−	0.862836i	$-0.331314\pi$
$227$	−7.45033	−	12.9043i	−0.494496	−	0.856491i	−0.999980	+	0.00634435i	$0.997981\pi$
$228$		0			0
$229$	2.22237	+	1.28308i	0.146858	+	0.0847886i	0.571629	−	0.820512i	$-0.306312\pi$
$229$	2.22237	+	1.28308i	0.146858	+	0.0847886i	−0.424770	+	0.905301i	$0.639645\pi$
$230$	−13.5541	+	7.00324i	−0.893733	+	0.461780i
$231$		0			0
$232$	1.34806	−	9.56091i	0.0885044	−	0.627704i
$233$	−9.24865	+	16.0191i	−0.605899	+	1.04945i	0.386010	+	0.922495i	$0.373853\pi$
$233$	−9.24865	+	16.0191i	−0.605899	+	1.04945i	−0.991909	+	0.126953i	$0.959480\pi$
$234$		0			0
$235$	5.51852	−	3.18612i	0.359989	−	0.207840i
$236$	5.12339	+	11.1649i	0.333504	+	0.726774i
$237$		0			0
$238$	4.51954	+	30.0746i	0.292958	+	1.94945i
$239$		−	12.1533i		−	0.786132i	−0.919510	−	0.393066i	$-0.871414\pi$
$239$		−	12.1533i		−	0.786132i	0.919510	−	0.393066i	$-0.128586\pi$
$240$		0			0
$241$	0.0182174	−	0.0105178i	0.00117349	−	0.000677512i	−0.499413	−	0.866364i	$-0.666451\pi$
$241$	0.0182174	−	0.0105178i	0.00117349	−	0.000677512i	0.500587	+	0.865686i	$0.333118\pi$
$242$	8.70233	+	5.58148i	0.559407	+	0.358791i
$243$		0			0
$244$	−16.5260	−	11.7229i	−1.05797	−	0.750482i
$245$	−3.48765	−	8.44366i	−0.222818	−	0.539446i
$246$		0			0
$247$	−24.5975	−	14.2014i	−1.56510	−	0.903613i
$248$	3.58175	−	1.44526i	0.227442	−	0.0917741i
$249$		0			0
$250$	15.2964	+	0.714726i	0.967428	+	0.0452032i
$251$	−18.6239			−1.17553			−0.587766	−	0.809031i	$-0.699992\pi$
$251$	−18.6239			−1.17553			−0.587766	+	0.809031i	$0.699992\pi$
$252$		0			0
$253$	−15.8778			−0.998230
$254$	21.9355	+	1.02494i	1.37635	+	0.0643103i
$255$		0			0
$256$	14.8967	+	5.83846i	0.931045	+	0.364904i
$257$	1.69594	+	0.979149i	0.105790	+	0.0610777i	0.551961	−	0.833870i	$-0.313880\pi$
$257$	1.69594	+	0.979149i	0.105790	+	0.0610777i	−0.446172	+	0.894947i	$0.647213\pi$
$258$		0			0
$259$	21.8762	−	19.1657i	1.35932	−	1.19090i
$260$	−7.37728	+	10.3999i	−0.457520	+	0.644974i
$261$		0			0
$262$	−19.8450	−	12.7281i	−1.22603	−	0.786345i
$263$	−8.77023	+	5.06350i	−0.540796	+	0.312229i	−0.745401	−	0.666616i	$-0.767742\pi$
$263$	−8.77023	+	5.06350i	−0.540796	+	0.312229i	0.204606	+	0.978844i	$0.434409\pi$
$264$		0			0
$265$		−	6.04760i		−	0.371501i
$266$	−13.5565	−	17.0146i	−0.831203	−	1.04323i
$267$		0			0
$268$	14.3858	−	6.60139i	0.878751	−	0.403244i
$269$	12.8307	−	7.40783i	0.782304	−	0.451663i	−0.0549425	−	0.998490i	$-0.517498\pi$
$269$	12.8307	−	7.40783i	0.782304	−	0.451663i	0.837246	+	0.546826i	$0.184164\pi$
$270$		0			0
$271$	8.02357	−	13.8972i	0.487397	−	0.844196i	−0.512498	−	0.858688i	$-0.671280\pi$
$271$	8.02357	−	13.8972i	0.487397	−	0.844196i	0.999895	+	0.0144920i	$0.00461312\pi$
$272$	30.6851	−	10.7453i	1.86056	−	0.651528i
$273$		0			0
$274$	−8.35546	+	4.31715i	−0.504772	+	0.260809i
$275$	5.48413	+	3.16626i	0.330705	+	0.190933i
$276$		0			0
$277$	−11.9179	−	20.6424i	−0.716076	−	1.24028i	−0.962543	−	0.271129i	$-0.912603\pi$
$277$	−11.9179	−	20.6424i	−0.716076	−	1.24028i	0.246467	−	0.969151i	$-0.420730\pi$
$278$	0.408897	−	8.75112i	0.0245240	−	0.524857i
$279$		0			0
$280$	−8.17253	+	5.34712i	−0.488402	+	0.319551i
$281$	−4.18282			−0.249526			−0.124763	−	0.992187i	$-0.539817\pi$
$281$	−4.18282			−0.249526			−0.124763	+	0.992187i	$0.539817\pi$
$282$		0			0
$283$	−0.298407	−	0.516857i	−0.0177385	−	0.0307239i	0.857020	−	0.515283i	$-0.172313\pi$
$283$	−0.298407	−	0.516857i	−0.0177385	−	0.0307239i	−0.874758	+	0.484559i	$0.838980\pi$
$284$	0.869924	−	9.28862i	0.0516205	−	0.551178i
$285$		0			0
$286$	−11.7894	+	6.09141i	−0.697120	+	0.360193i
$287$	3.89792	−	11.4642i	0.230087	−	0.676709i
$288$		0			0
$289$	24.5325	−	42.4915i	1.44309	−	2.49950i
$290$	3.40155	−	5.30350i	0.199746	−	0.311432i
$291$		0			0
$292$	16.0369	−	7.35906i	0.938488	−	0.430656i
$293$		−	7.13848i		−	0.417035i	−0.978019	−	0.208517i	$-0.933136\pi$
$293$		−	7.13848i		−	0.417035i	0.978019	−	0.208517i	$-0.0668637\pi$
$294$		0			0
$295$			8.01605i			0.466712i
$296$	−24.4925	−	19.1533i	−1.42360	−	1.11326i
$297$		0			0
$298$	16.1821	+	10.3788i	0.937403	+	0.601229i
$299$	−20.1901	+	34.9702i	−1.16762	+	2.02238i
$300$		0			0
$301$	−0.466618	+	1.37237i	−0.0268954	+	0.0791021i
$302$	6.66123	+	12.8922i	0.383311	+	0.741863i
$303$		0			0
$304$	−15.1661	+	17.6317i	−0.869836	+	1.01125i
$305$	−6.61080	−	11.4502i	−0.378533	−	0.655639i
$306$		0			0
$307$	8.66748			0.494679			0.247340	−	0.968929i	$-0.420444\pi$
$307$	8.66748			0.494679			0.247340	+	0.968929i	$0.420444\pi$
$308$	−10.1108	+	1.03970i	−0.576116	+	0.0592422i
$309$		0			0
$310$	2.51760	+	0.117635i	0.142990	+	0.00668124i
$311$	−2.71078	−	4.69521i	−0.153714	−	0.266241i	0.778876	−	0.627178i	$-0.215790\pi$
$311$	−2.71078	−	4.69521i	−0.153714	−	0.266241i	−0.932590	+	0.360937i	$0.882457\pi$
$312$		0			0
$313$	3.71852	+	2.14689i	0.210183	+	0.121349i	0.601396	−	0.798951i	$-0.294611\pi$
$313$	3.71852	+	2.14689i	0.210183	+	0.121349i	−0.391213	+	0.920300i	$0.627945\pi$
$314$	−6.05684	−	11.7225i	−0.341807	−	0.661536i
$315$		0			0
$316$	12.8006	+	9.08027i	0.720092	+	0.510805i
$317$	−9.21148	+	15.9547i	−0.517368	+	0.896108i	0.482428	+	0.875935i	$0.339755\pi$
$317$	−9.21148	+	15.9547i	−0.517368	+	0.896108i	−0.999797	+	0.0201724i	$0.993578\pi$
$318$		0			0
$319$	5.67871	−	3.27861i	0.317947	−	0.183567i
$320$	7.24599	+	7.51688i	0.405063	+	0.420207i
$321$		0			0
$322$	−24.1896	+	19.2732i	−1.34803	+	1.07406i
$323$			47.2584i			2.62953i
$324$		0			0
$325$	13.9471	−	8.05237i	0.773647	−	0.446665i
$326$	−3.91627	+	6.10602i	−0.216902	+	0.338181i
$327$		0			0
$328$	−12.8180	−	1.80730i	−0.707755	−	0.0997913i
$329$	9.71665	−	8.51274i	0.535696	−	0.469322i
$330$		0			0
$331$	17.5847	+	10.1526i	0.966545	+	0.558035i	0.898181	−	0.439626i	$-0.144889\pi$
$331$	17.5847	+	10.1526i	0.966545	+	0.558035i	0.0683635	+	0.997660i	$0.478222\pi$
$332$	−4.44417	−	0.416218i	−0.243905	−	0.0228429i
$333$		0			0
$334$	0.838192	−	17.9388i	0.0458638	−	0.981566i
$335$	10.3285			0.564307
$336$		0			0
$337$	15.7982			0.860584			0.430292	−	0.902690i	$-0.358411\pi$
$337$	15.7982			0.860584			0.430292	+	0.902690i	$0.358411\pi$
$338$	−0.717073	+	15.3466i	−0.0390037	+	0.834746i
$339$		0			0
$340$	21.1231	+	1.97828i	1.14556	+	0.107287i
$341$	2.27158	+	1.31150i	0.123013	+	0.0710215i
$342$		0			0
$343$	−10.2663	−	15.4144i	−0.554330	−	0.832297i
$344$	1.53443	+	0.216350i	0.0827311	+	0.0116648i
$345$		0			0
$346$	−0.432654	+	0.674570i	−0.0232596	+	0.0362651i
$347$	23.3056	−	13.4555i	1.25111	−	0.722328i	0.279779	−	0.960064i	$-0.409739\pi$
$347$	23.3056	−	13.4555i	1.25111	−	0.722328i	0.971330	+	0.237736i	$0.0764055\pi$
$348$		0			0
$349$			2.85266i			0.152700i	0.997081	+	0.0763498i	$0.0243266\pi$
$349$			2.85266i			0.152700i	−0.997081	+	0.0763498i	$0.975673\pi$
$350$	12.1983	−	1.83314i	0.652029	−	0.0979853i
$351$		0			0
$352$	3.10861	+	10.4117i	0.165690	+	0.554947i
$353$	19.4518	−	11.2305i	1.03531	−	0.597739i	0.116812	−	0.993154i	$-0.462733\pi$
$353$	19.4518	−	11.2305i	1.03531	−	0.597739i	0.918502	+	0.395415i	$0.129399\pi$
$354$		0			0
$355$	3.04387	−	5.27214i	0.161552	−	0.279816i
$356$	3.72294	+	2.64091i	0.197315	+	0.139968i
$357$		0			0
$358$	−4.28017	−	8.28388i	−0.226214	−	0.437817i
$359$	16.0688	+	9.27735i	0.848081	+	0.489640i	0.860003	−	0.510289i	$-0.170462\pi$
$359$	16.0688	+	9.27735i	0.848081	+	0.489640i	−0.0119216	+	0.999929i	$0.503795\pi$
$360$		0			0
$361$	−7.40273	−	12.8219i	−0.389617	−	0.674837i
$362$	4.10386	+	0.191754i	0.215694	+	0.0100783i
$363$		0			0
$364$	−10.5669	+	23.5907i	−0.553856	+	1.23649i
$365$	11.5140			0.602668
$366$		0			0
$367$	−7.77468	−	13.4661i	−0.405835	−	0.702927i	0.588583	−	0.808437i	$-0.299686\pi$
$367$	−7.77468	−	13.4661i	−0.405835	−	0.702927i	−0.994418	+	0.105510i	$0.966353\pi$
$368$	25.0669	+	21.5616i	1.30670	+	1.12398i
$369$		0			0
$370$	−9.31338	−	18.0252i	−0.484180	−	0.937086i
$371$	−2.38585	−	12.0257i	−0.123867	−	0.624343i
$372$		0			0
$373$	2.48527	−	4.30461i	0.128682	−	0.222884i	−0.794484	−	0.607285i	$-0.792259\pi$
$373$	2.48527	−	4.30461i	0.128682	−	0.222884i	0.923166	+	0.384401i	$0.125592\pi$
$374$	18.5854	+	11.9202i	0.961027	+	0.616381i
$375$		0			0
$376$	−10.8787	−	8.50724i	−0.561028	−	0.438727i
$377$		−	16.6762i		−	0.858866i
$378$		0			0
$379$			4.44925i			0.228543i	0.993450	+	0.114271i	$0.0364533\pi$
$379$			4.44925i			0.228543i	−0.993450	+	0.114271i	$0.963547\pi$
$380$	−13.7933	+	6.32949i	−0.707579	+	0.324696i
$381$		0			0
$382$	−0.611701	+	0.953729i	−0.0312973	+	0.0487970i
$383$	−5.53218	+	9.58201i	−0.282681	+	0.489618i	−0.972044	−	0.234798i	$-0.924557\pi$
$383$	−5.53218	+	9.58201i	−0.282681	+	0.489618i	0.689363	+	0.724416i	$0.257890\pi$
$384$		0			0
$385$	−6.27947	−	2.13507i	−0.320032	−	0.108813i
$386$	−18.0754	+	9.33930i	−0.920012	+	0.475358i
$387$		0			0
$388$	0.534172	−	5.70363i	0.0271185	−	0.289558i
$389$	14.8606	+	25.7394i	0.753464	+	1.30504i	0.946134	+	0.323775i	$0.104952\pi$
$389$	14.8606	+	25.7394i	0.753464	+	1.30504i	−0.192670	+	0.981264i	$0.561715\pi$
$390$		0			0
$391$	67.1871			3.39780
$392$	−14.1416	+	13.8569i	−0.714260	+	0.699881i
$393$		0			0
$394$	−0.792891	+	16.9692i	−0.0399453	+	0.854898i
$395$	5.12056	+	8.86907i	0.257643	+	0.446252i
$396$		0			0
$397$	−28.6753	−	16.5557i	−1.43917	−	0.830907i	−0.441381	−	0.897320i	$-0.645511\pi$
$397$	−28.6753	−	16.5557i	−1.43917	−	0.830907i	−0.997792	+	0.0664132i	$0.978844\pi$
$398$	13.4140	−	6.93081i	0.672381	−	0.347410i
$399$		0			0
$400$	−4.35831	−	12.4460i	−0.217916	−	0.622299i
$401$	16.0777	−	27.8474i	0.802881	−	1.39063i	−0.114831	−	0.993385i	$-0.536633\pi$
$401$	16.0777	−	27.8474i	0.802881	−	1.39063i	0.917712	−	0.397246i	$-0.130034\pi$
$402$		0			0
$403$	5.77703	−	3.33537i	0.287774	−	0.166147i
$404$	4.46408	−	2.04849i	0.222096	−	0.101916i
$405$		0			0
$406$	4.67171	−	11.8880i	0.231853	−	0.589991i
$407$		−	21.1154i		−	1.04665i
$408$		0			0
$409$	12.9267	−	7.46322i	0.639183	−	0.369032i	−0.145117	−	0.989415i	$-0.546356\pi$
$409$	12.9267	−	7.46322i	0.639183	−	0.369032i	0.784300	+	0.620382i	$0.213022\pi$
$410$	−7.11023	−	4.56034i	−0.351149	−	0.225219i
$411$		0			0
$412$	−13.7271	+	19.3513i	−0.676285	+	0.953371i
$413$	3.16242	+	15.9400i	0.155613	+	0.784354i
$414$		0			0
$415$	−2.52247	−	1.45635i	−0.123823	−	0.0714894i
$416$	26.8843	+	6.39286i	1.31811	+	0.313436i
$417$		0			0
$418$	−15.7770	−	0.737185i	−0.771680	−	0.0360569i
$419$	15.9378			0.778615			0.389307	−	0.921108i	$-0.372714\pi$
$419$	15.9378			0.778615			0.389307	+	0.921108i	$0.372714\pi$
$420$		0			0
$421$	−2.56359			−0.124942			−0.0624708	−	0.998047i	$-0.519898\pi$
$421$	−2.56359			−0.124942			−0.0624708	+	0.998047i	$0.519898\pi$
$422$	32.2791	+	1.50825i	1.57132	+	0.0734203i
$423$		0			0
$424$	−12.1544	+	4.90437i	−0.590270	+	0.238177i
$425$	−23.2061	−	13.3981i	−1.12566	−	0.649901i
$426$		0			0
$427$	−17.6629	−	20.1608i	−0.854766	−	0.975651i
$428$	15.6764	+	11.1202i	0.757746	+	0.537516i
$429$		0			0
$430$	0.851161	+	0.545916i	0.0410466	+	0.0263264i
$431$	21.1223	−	12.1950i	1.01743	−	0.587411i	0.104068	−	0.994570i	$-0.466814\pi$
$431$	21.1223	−	12.1950i	1.01743	−	0.587411i	0.913357	+	0.407159i	$0.133481\pi$
$432$		0			0
$433$			22.3614i			1.07462i	0.843385	+	0.537310i	$0.180559\pi$
$433$			22.3614i			1.07462i	−0.843385	+	0.537310i	$0.819441\pi$
$434$	5.05267	−	0.759304i	0.242536	−	0.0364477i
$435$		0			0
$436$	−6.07918	−	13.2478i	−0.291140	−	0.634454i
$437$	−41.6221	+	24.0305i	−1.99106	+	1.14954i
$438$		0			0
$439$	−16.9411	+	29.3429i	−0.808555	+	1.40046i	0.105309	+	0.994440i	$0.466417\pi$
$439$	−16.9411	+	29.3429i	−0.808555	+	1.40046i	−0.913865	+	0.406019i	$0.866917\pi$
$440$	−0.989942	+	7.02102i	−0.0471936	+	0.334714i
$441$		0			0
$442$	49.8868	−	25.7758i	2.37287	−	1.22603i
$443$	6.53304	+	3.77186i	0.310394	+	0.179206i	0.647103	−	0.762403i	$-0.275980\pi$
$443$	6.53304	+	3.77186i	0.310394	+	0.179206i	−0.336709	+	0.941609i	$0.609314\pi$
$444$		0			0
$445$	1.48927	+	2.57948i	0.0705980	+	0.122279i
$446$	0.912747	−	19.5344i	0.0432198	−	0.924980i
$447$		0			0
$448$	17.3742	+	12.0887i	0.820853	+	0.571140i
$449$	29.0130			1.36921			0.684605	−	0.728915i	$-0.259975\pi$
$449$	29.0130			1.36921			0.684605	+	0.728915i	$0.259975\pi$
$450$		0			0
$451$	−4.39552	−	7.61326i	−0.206977	−	0.358494i
$452$	16.3759	+	1.53368i	0.770256	+	0.0721382i
$453$		0			0
$454$	−18.7214	+	9.67309i	−0.878638	+	0.453981i
$455$	−12.6873	+	11.1153i	−0.594791	+	0.521095i
$456$		0			0
$457$	0.958012	−	1.65933i	0.0448139	−	0.0776200i	−0.842748	−	0.538308i	$-0.819064\pi$
$457$	0.958012	−	1.65933i	0.0448139	−	0.0776200i	0.887562	+	0.460688i	$0.152397\pi$
$458$	1.95927	−	3.05478i	0.0915507	−	0.142741i
$459$		0			0
$460$	8.99861	+	19.6098i	0.419562	+	0.914312i
$461$			4.16142i			0.193817i	0.995293	+	0.0969083i	$0.0308954\pi$
$461$			4.16142i			0.193817i	−0.995293	+	0.0969083i	$0.969105\pi$
$462$		0			0
$463$			16.6614i			0.774319i	0.922013	+	0.387160i	$0.126544\pi$
$463$			16.6614i			0.774319i	−0.922013	+	0.387160i	$0.873456\pi$
$464$	−13.4174	−	2.53546i	−0.622889	−	0.117706i
$465$		0			0
$466$	22.0193	+	14.1227i	1.02002	+	0.654221i
$467$	11.8983	−	20.6084i	0.550586	−	0.953643i	−0.447646	−	0.894211i	$-0.647738\pi$
$467$	11.8983	−	20.6084i	0.550586	−	0.953643i	0.998232	−	0.0594325i	$-0.0189291\pi$
$468$		0			0
$469$	20.5383	−	4.07472i	0.948371	−	0.188153i
$470$	−4.13668	−	8.00617i	−0.190811	−	0.369297i
$471$		0			0
$472$	16.1106	−	6.50071i	0.741548	−	0.299219i
$473$	0.526185	+	0.911379i	0.0241940	+	0.0419052i
$474$		0			0
$475$	19.1681			0.879494
$476$	42.7839	−	4.39949i	1.96100	−	0.201650i
$477$		0			0
$478$	−17.1686	−	0.802207i	−0.785275	−	0.0366921i
$479$	18.2623	+	31.6312i	0.834424	+	1.44526i	0.894499	+	0.447071i	$0.147533\pi$
$479$	18.2623	+	31.6312i	0.834424	+	1.44526i	−0.0600746	+	0.998194i	$0.519134\pi$
$480$		0			0
$481$	−46.5057	−	26.8501i	−2.12048	−	1.22426i
$482$	−0.0136558	−	0.0264295i	−0.000622002	−	0.00120383i
$483$		0			0
$484$	8.45922	−	11.9251i	0.384510	−	0.542051i
$485$	1.86907	−	3.23733i	0.0848702	−	0.147000i
$486$		0			0
$487$	−27.4749	+	15.8627i	−1.24501	+	0.718806i	−0.970110	−	0.242667i	$-0.921978\pi$
$487$	−27.4749	+	15.8627i	−1.24501	+	0.718806i	−0.274899	+	0.961473i	$0.588644\pi$
$488$	−17.6515	+	22.5720i	−0.799044	+	1.02179i
$489$		0			0
$490$	−12.1583	+	4.36957i	−0.549258	+	0.197397i
$491$			37.8704i			1.70907i	0.519395	+	0.854534i	$0.326157\pi$
$491$			37.8704i			1.70907i	−0.519395	+	0.854534i	$0.673843\pi$
$492$		0			0
$493$	−24.0295	+	13.8734i	−1.08223	+	0.624828i
$494$	−21.6855	+	33.8109i	−0.975678	+	1.52122i
$495$		0			0
$496$	−1.80526	−	5.15524i	−0.0810584	−	0.231477i
$497$	3.97284	−	11.6845i	0.178206	−	0.524123i
$498$		0			0
$499$	−29.7986	−	17.2042i	−1.33397	−	0.770167i	−0.348064	−	0.937471i	$-0.613161\pi$
$499$	−29.7986	−	17.2042i	−1.33397	−	0.770167i	−0.985905	+	0.167303i	$0.946494\pi$
$500$	2.01935	−	21.5616i	0.0903079	−	0.964263i
$501$		0			0
$502$	−1.22932	+	26.3095i	−0.0548670	+	1.17425i
$503$	−37.1489			−1.65639			−0.828195	−	0.560440i	$-0.810632\pi$
$503$	−37.1489			−1.65639			−0.828195	+	0.560440i	$0.810632\pi$
$504$		0			0
$505$	3.20506			0.142623
$506$	−1.04805	+	22.4302i	−0.0465916	+	0.997142i
$507$		0			0
$508$	2.89580	−	30.9200i	0.128481	−	1.37185i
$509$	−1.75035	−	1.01056i	−0.0775828	−	0.0447924i	0.460707	−	0.887552i	$-0.347596\pi$
$509$	−1.75035	−	1.01056i	−0.0775828	−	0.0447924i	−0.538290	+	0.842760i	$0.680929\pi$
$510$		0			0
$511$	22.8956	−	4.54239i	1.01284	−	0.200943i
$512$	9.23113	−	20.6588i	0.407962	−	0.912999i
$513$		0			0
$514$	1.49516	−	2.33117i	0.0659488	−	0.102824i
$515$	−13.4078	+	7.74100i	−0.590818	+	0.341109i
$516$		0			0
$517$		−	9.37873i		−	0.412476i
$518$	−25.6309	−	32.1690i	−1.12616	−	1.41342i
$519$		0			0
$520$	14.2047	+	11.1082i	0.622917	+	0.487125i
$521$	17.2723	−	9.97217i	0.756713	−	0.436889i	−0.0714012	−	0.997448i	$-0.522747\pi$
$521$	17.2723	−	9.97217i	0.756713	−	0.436889i	0.828114	+	0.560559i	$0.189414\pi$
$522$		0			0
$523$	−17.0542	+	29.5387i	−0.745726	+	1.29164i	0.204129	+	0.978944i	$0.434564\pi$
$523$	−17.0542	+	29.5387i	−0.745726	+	1.29164i	−0.949855	+	0.312691i	$0.898769\pi$
$524$	−19.2906	+	27.1943i	−0.842712	+	1.18799i
$525$		0			0
$526$	6.57416	+	12.7237i	0.286647	+	0.554779i
$527$	−9.61220	−	5.54961i	−0.418714	−	0.241745i
$528$		0			0
$529$	22.6641	+	39.2554i	0.985397	+	1.70676i
$530$	−8.54328	−	0.399186i	−0.371096	−	0.0173395i
$531$		0			0
$532$	−24.9309	+	18.0278i	−1.08089	+	0.781605i
$533$	−22.3572			−0.968397
$534$		0			0
$535$	6.27093	+	10.8616i	0.271116	+	0.469587i
$536$	−8.37603	−	20.7581i	−0.361789	−	0.896615i
$537$		0			0
$538$	−9.61791	−	18.6146i	−0.414658	−	0.802532i
$539$	−13.3291	−	1.76829i	−0.574124	−	0.0761654i
$540$		0			0
$541$	11.5428	−	19.9928i	0.496265	−	0.859556i	−0.503726	−	0.863864i	$-0.668038\pi$
$541$	11.5428	−	19.9928i	0.496265	−	0.859556i	0.999991	+	0.00430768i	$0.00137118\pi$
$542$	−19.1026	−	12.2520i	−0.820527	−	0.526268i
$543$		0			0
$544$	−13.1541	−	44.0573i	−0.563978	−	1.88894i
$545$		−	9.51148i		−	0.407427i
$546$		0			0
$547$			15.3659i			0.657000i	0.944504	+	0.328500i	$0.106543\pi$
$547$			15.3659i			0.657000i	−0.944504	+	0.328500i	$0.893457\pi$
$548$	5.54720	+	12.0885i	0.236965	+	0.516395i
$549$		0			0
$550$	4.83488	−	7.53828i	0.206160	−	0.321433i
$551$	9.92412	−	17.1891i	0.422782	−	0.732280i
$552$		0			0
$553$	13.6812	+	15.6161i	0.581785	+	0.664064i
$554$	−29.9476	+	15.4735i	−1.27235	+	0.657407i
$555$		0			0
$556$	−12.3355	−	1.15528i	−0.523140	−	0.0489946i
$557$	−16.8263	−	29.1440i	−0.712954	−	1.23487i	−0.963743	−	0.266831i	$-0.914023\pi$
$557$	−16.8263	−	29.1440i	−0.712954	−	1.23487i	0.250789	−	0.968042i	$-0.419310\pi$
$558$		0			0
$559$	2.67636			0.113198
$560$	7.01428	+	11.8981i	0.296407	+	0.502784i
$561$		0			0
$562$	−0.276097	+	5.90895i	−0.0116464	+	0.249254i
$563$	−9.76188	−	16.9081i	−0.411414	−	0.712591i	0.583630	−	0.812019i	$-0.301632\pi$
$563$	−9.76188	−	16.9081i	−0.411414	−	0.712591i	−0.995045	+	0.0994290i	$0.968298\pi$
$564$		0			0
$565$	9.29480	+	5.36636i	0.391035	+	0.225764i
$566$	−0.749846	+	0.387435i	−0.0315184	+	0.0162851i
$567$		0			0
$568$	−13.0644	−	1.84203i	−0.548168	−	0.0772900i
$569$	10.3663	−	17.9549i	0.434578	−	0.752710i	−0.562684	−	0.826672i	$-0.690231\pi$
$569$	10.3663	−	17.9549i	0.434578	−	0.752710i	0.997261	+	0.0739620i	$0.0235644\pi$
$570$		0			0
$571$	−21.0998	+	12.1820i	−0.882998	+	0.509799i	−0.871646	−	0.490136i	$-0.836947\pi$
$571$	−21.0998	+	12.1820i	−0.882998	+	0.509799i	−0.0113526	+	0.999936i	$0.503614\pi$
$572$	7.82698	+	17.0566i	0.327263	+	0.713172i
$573$		0			0
$574$	−15.9378	−	6.26320i	−0.665233	−	0.261421i
$575$		−	27.2513i		−	1.13646i
$576$		0			0
$577$	14.0546	−	8.11442i	0.585100	−	0.337808i	−0.178058	−	0.984020i	$-0.556981\pi$
$577$	14.0546	−	8.11442i	0.585100	−	0.337808i	0.763158	+	0.646212i	$0.223648\pi$
$578$	−58.4072	−	37.4611i	−2.42942	−	1.55818i
$579$		0			0
$580$	−7.26758	−	5.15534i	−0.301770	−	0.214064i
$581$	−5.59050	−	1.90082i	−0.231933	−	0.0788592i
$582$		0			0
$583$	−7.70842	−	4.45046i	−0.319250	−	0.184319i
$584$	−9.33738	−	23.1406i	−0.386384	−	0.957566i
$585$		0			0
$586$	−10.0843	−	0.471192i	−0.416580	−	0.0194648i
$587$	14.4835			0.597799			0.298899	−	0.954285i	$-0.403380\pi$
$587$	14.4835			0.597799			0.298899	+	0.954285i	$0.403380\pi$
$588$		0			0
$589$	7.93963			0.327147
$590$	11.3240	+	0.529118i	0.466204	+	0.0217834i
$591$		0			0
$592$	−28.6741	+	33.3357i	−1.17850	+	1.37009i
$593$	17.6665	+	10.1998i	0.725477	+	0.418854i	0.816765	−	0.576970i	$-0.195765\pi$
$593$	17.6665	+	10.1998i	0.725477	+	0.418854i	−0.0912884	+	0.995824i	$0.529099\pi$
$594$		0			0
$595$	26.5716	+	9.03458i	1.08933	+	0.370382i
$596$	15.7300	−	22.1749i	0.644327	−	0.908319i
$597$		0			0
$598$	48.0688	+	30.8302i	1.96568	+	1.26074i
$599$	−24.1606	+	13.9491i	−0.987175	+	0.569946i	−0.904429	−	0.426625i	$-0.859702\pi$
$599$	−24.1606	+	13.9491i	−0.987175	+	0.569946i	−0.0827463	+	0.996571i	$0.526369\pi$
$600$		0			0
$601$			29.4377i			1.20079i	0.799704	+	0.600395i	$0.204990\pi$
$601$			29.4377i			1.20079i	−0.799704	+	0.600395i	$0.795010\pi$
$602$	1.90791	+	0.749764i	0.0777606	+	0.0305581i
$603$		0			0
$604$	18.6522	−	8.55915i	0.758945	−	0.348267i
$605$	8.26247	−	4.77034i	0.335917	−	0.193942i
$606$		0			0
$607$	9.07621	−	15.7205i	0.368392	−	0.638074i	−0.620922	−	0.783872i	$-0.713242\pi$
$607$	9.07621	−	15.7205i	0.368392	−	0.638074i	0.989314	+	0.145798i	$0.0465751\pi$
$608$	23.9067	+	22.5886i	0.969546	+	0.916087i
$609$		0			0
$610$	−16.6118	+	8.58309i	−0.672592	+	0.347519i
$611$	−20.6562	−	11.9259i	−0.835662	−	0.482470i
$612$		0			0
$613$	3.18353	+	5.51403i	0.128581	+	0.222710i	0.923127	−	0.384495i	$-0.125624\pi$
$613$	3.18353	+	5.51403i	0.128581	+	0.222710i	−0.794546	+	0.607204i	$0.792291\pi$
$614$	0.572117	−	12.2443i	0.0230888	−	0.494140i
$615$		0			0
$616$	0.801364	+	14.3519i	0.0322879	+	0.578254i
$617$	−32.1351			−1.29371			−0.646854	−	0.762613i	$-0.723916\pi$
$617$	−32.1351			−1.29371			−0.646854	+	0.762613i	$0.723916\pi$
$618$		0			0
$619$	2.96448	+	5.13463i	0.119153	+	0.206378i	0.919432	−	0.393249i	$-0.128649\pi$
$619$	2.96448	+	5.13463i	0.119153	+	0.206378i	−0.800280	+	0.599627i	$0.795316\pi$
$620$	0.332360	−	3.54878i	0.0133479	−	0.142522i
$621$		0			0
$622$	−6.81172	+	3.51952i	−0.273125	+	0.141120i
$623$	3.97905	+	4.54179i	0.159417	+	0.181963i
$624$		0			0
$625$	−1.17617	+	2.03718i	−0.0470467	+	0.0814873i
$626$	3.27830	−	5.11134i	0.131027	−	0.204290i
$627$		0			0
$628$	−16.9598	+	7.78256i	−0.676769	+	0.310558i
$629$			89.3499i			3.56261i
$630$		0			0
$631$		−	4.42267i		−	0.176064i	−0.996118	−	0.0880319i	$-0.971942\pi$
$631$		−	4.42267i		−	0.176064i	0.996118	−	0.0880319i	$-0.0280578\pi$
$632$	13.6724	−	17.4837i	0.543858	−	0.695465i
$633$		0			0
$634$	21.9308	+	14.0659i	0.870983	+	0.558629i
$635$	10.1324	−	17.5499i	0.402094	−	0.696447i
$636$		0			0
$637$	−20.8437	+	27.1082i	−0.825857	+	1.07407i
$638$	−4.25676	−	8.23857i	−0.168527	−	0.326168i
$639$		0			0
$640$	11.0972	−	9.74003i	0.438655	−	0.385009i
$641$	9.02282	+	15.6280i	0.356380	+	0.617268i	0.987353	−	0.158536i	$-0.0506775\pi$
$641$	9.02282	+	15.6280i	0.356380	+	0.617268i	−0.630973	+	0.775805i	$0.717344\pi$
$642$		0			0
$643$	−29.6357			−1.16872			−0.584358	−	0.811496i	$-0.698654\pi$
$643$	−29.6357			−1.16872			−0.584358	+	0.811496i	$0.698654\pi$
$644$	25.6301	+	35.4442i	1.00997	+	1.39670i
$645$		0			0
$646$	66.7606	+	3.11940i	2.62666	+	0.122731i
$647$	4.51555	+	7.82116i	0.177525	+	0.307482i	0.941032	−	0.338317i	$-0.109858\pi$
$647$	4.51555	+	7.82116i	0.177525	+	0.307482i	−0.763507	+	0.645799i	$0.776524\pi$
$648$		0			0
$649$	10.2174	+	5.89905i	0.401070	+	0.231558i
$650$	−10.4547	−	20.2342i	−0.410069	−	0.793651i
$651$		0			0
$652$	8.36731	+	5.93545i	0.327689	+	0.232450i
$653$	−5.38056	+	9.31941i	−0.210558	+	0.364697i	−0.951889	−	0.306442i	$-0.900861\pi$
$653$	−5.38056	+	9.31941i	−0.210558	+	0.364697i	0.741332	+	0.671139i	$0.234195\pi$
$654$		0			0
$655$	−18.8419	+	10.8784i	−0.736213	+	0.425053i
$656$	−3.39920	+	17.9883i	−0.132716	+	0.702326i
$657$		0			0
$658$	−11.3843	−	14.2884i	−0.443808	−	0.557018i
$659$		−	27.5761i		−	1.07421i	−0.843515	−	0.537106i	$-0.819518\pi$
$659$		−	27.5761i		−	1.07421i	0.843515	−	0.537106i	$-0.180482\pi$
$660$		0			0
$661$	6.77132	−	3.90942i	0.263374	−	0.152059i	−0.362499	−	0.931984i	$-0.618076\pi$
$661$	6.77132	−	3.90942i	0.263374	−	0.152059i	0.625873	+	0.779925i	$0.284743\pi$
$662$	15.5030	−	24.1713i	0.602539	−	0.939445i
$663$		0			0
$664$	−0.881327	+	6.25068i	−0.0342021	+	0.242573i
$665$	−19.6924	+	3.90689i	−0.763638	+	0.151503i
$666$		0			0
$667$	−24.4376	−	14.1091i	−0.946230	−	0.546306i
$668$	−25.2863	−	2.36818i	−0.978355	−	0.0916277i
$669$		0			0
$670$	0.681758	−	14.5908i	0.0263386	−	0.563692i
$671$	−19.4597			−0.751232
$672$		0			0
$673$	−47.9043			−1.84658			−0.923288	−	0.384108i	$-0.874509\pi$
$673$	−47.9043			−1.84658			−0.923288	+	0.384108i	$0.874509\pi$
$674$	1.04280	−	22.3177i	0.0401671	−	0.859646i
$675$		0			0
$676$	21.6324	+	2.02598i	0.832016	+	0.0779223i
$677$	21.5858	+	12.4626i	0.829610	+	0.478975i	0.853719	−	0.520734i	$-0.174342\pi$
$677$	21.5858	+	12.4626i	0.829610	+	0.478975i	−0.0241093	+	0.999709i	$0.507675\pi$
$678$		0			0
$679$	2.43950	−	7.17482i	0.0936194	−	0.275344i
$680$	4.18895	−	29.7095i	0.160639	−	1.13931i
$681$		0			0
$682$	2.00266	−	3.12243i	0.0766857	−	0.119564i
$683$	20.2982	−	11.7192i	0.776690	−	0.448422i	−0.0585660	−	0.998284i	$-0.518653\pi$
$683$	20.2982	−	11.7192i	0.776690	−	0.448422i	0.835256	+	0.549861i	$0.185319\pi$
$684$		0			0
$685$			8.67914i			0.331613i
$686$	−22.4531	+	13.4855i	−0.857263	+	0.514879i
$687$		0			0
$688$	0.406916	−	2.15337i	0.0155135	−	0.0820965i
$689$	−19.6039	+	11.3183i	−0.746849	+	0.431193i
$690$		0			0
$691$	13.3173	−	23.0662i	0.506613	−	0.877480i	−0.493358	−	0.869827i	$-0.664231\pi$
$691$	13.3173	−	23.0662i	0.506613	−	0.877480i	0.999971	−	0.00765314i	$-0.00243609\pi$
$692$	0.924388	+	0.655725i	0.0351399	+	0.0249269i
$693$		0			0
$694$	−17.4698	−	33.8113i	−0.663146	−	1.28346i
$695$	−7.00151	−	4.04232i	−0.265582	−	0.153334i
$696$		0			0
$697$	18.5997	+	32.2156i	0.704512	+	1.22025i
$698$	4.02988	+	0.188297i	0.152533	+	0.00712714i
$699$		0			0
$700$	−1.78444	−	17.3533i	−0.0674456	−	0.655892i
$701$	−8.81589			−0.332971			−0.166486	−	0.986044i	$-0.553242\pi$
$701$	−8.81589			−0.332971			−0.166486	+	0.986044i	$0.553242\pi$
$702$		0			0
$703$	−31.9574	−	55.3519i	−1.20530	−	2.08764i
$704$	14.9136	−	3.70420i	0.562076	−	0.139607i
$705$		0			0
$706$	−14.5810	−	28.2203i	−0.548765	−	1.06208i
$707$	6.37328	−	1.26443i	0.239692	−	0.0475539i
$708$		0			0
$709$	17.0196	−	29.4789i	0.639186	−	1.10710i	−0.346426	−	0.938077i	$-0.612605\pi$
$709$	17.0196	−	29.4789i	0.639186	−	1.10710i	0.985612	−	0.169025i	$-0.0540617\pi$
$710$	−7.24689	−	4.64799i	−0.271971	−	0.174436i
$711$		0			0
$712$	3.97648	−	5.08497i	0.149025	−	0.190567i
$713$		−	11.2877i		−	0.422729i
$714$		0			0
$715$			12.2461i			0.457977i
$716$	−11.9849	+	5.49968i	−0.447898	+	0.205533i
$717$		0			0
$718$	14.1665	−	22.0876i	0.528690	−	0.824304i
$719$	−13.6962	+	23.7225i	−0.510783	+	0.884701i	0.489139	+	0.872206i	$0.337311\pi$
$719$	−13.6962	+	23.7225i	−0.510783	+	0.884701i	−0.999922	+	0.0124958i	$0.996022\pi$
$720$		0			0
$721$	−23.6076	+	20.6825i	−0.879192	+	0.770258i
$722$	−18.6018	+	9.61129i	−0.692287	+	0.357695i
$723$		0			0
$724$	0.541770	−	5.78475i	0.0201347	−	0.214989i
$725$	5.62710	+	9.74643i	0.208985	+	0.361973i
$726$		0			0
$727$	−21.1585			−0.784727			−0.392364	−	0.919810i	$-0.628342\pi$
$727$	−21.1585			−0.784727			−0.392364	+	0.919810i	$0.628342\pi$
$728$	32.6284	+	16.4847i	1.20929	+	0.610964i
$729$		0			0
$730$	0.760006	−	16.2655i	0.0281291	−	0.602012i
$731$	−2.22655	−	3.85650i	−0.0823521	−	0.142638i
$732$		0			0
$733$	−8.27753	−	4.77904i	−0.305738	−	0.176518i	0.339280	−	0.940685i	$-0.389817\pi$
$733$	−8.27753	−	4.77904i	−0.305738	−	0.176518i	−0.645018	+	0.764168i	$0.723150\pi$
$734$	−19.5364	+	10.0942i	−0.721103	+	0.372584i
$735$		0			0
$736$	32.1141	−	33.9881i	1.18374	−	1.25282i
$737$	7.60080	−	13.1650i	0.279979	−	0.484938i
$738$		0			0
$739$	9.63890	−	5.56502i	0.354573	−	0.204713i	−0.312125	−	0.950041i	$-0.601041\pi$
$739$	9.63890	−	5.56502i	0.354573	−	0.204713i	0.666697	+	0.745329i	$0.267707\pi$
$740$	−26.0785	+	11.9670i	−0.958663	+	0.439914i
$741$		0			0
$742$	−17.1458	+	2.57664i	−0.629444	+	0.0945912i
$743$		−	17.6900i		−	0.648983i	−0.945889	−	0.324491i	$-0.894807\pi$
$743$		−	17.6900i		−	0.648983i	0.945889	−	0.324491i	$-0.105193\pi$
$744$		0			0
$745$	15.3642	−	8.87050i	0.562899	−	0.324990i
$746$	−5.91696	−	3.79500i	−0.216635	−	0.138945i
$747$		0			0
$748$	18.0662	−	25.4682i	0.660565	−	0.931211i
$749$	16.7548	+	19.1243i	0.612207	+	0.698788i
$750$		0			0
$751$	−10.8280	−	6.25156i	−0.395120	−	0.228123i	0.289256	−	0.957252i	$-0.406592\pi$
$751$	−10.8280	−	6.25156i	−0.395120	−	0.228123i	−0.684376	+	0.729129i	$0.739925\pi$
$752$	−12.7360	+	14.8066i	−0.464435	+	0.539939i
$753$		0			0
$754$	−23.5579	−	1.10075i	−0.857930	−	0.0400869i
$755$	13.3916			0.487371
$756$		0			0
$757$	−2.14200			−0.0778523			−0.0389261	−	0.999242i	$-0.512394\pi$
$757$	−2.14200			−0.0778523			−0.0389261	+	0.999242i	$0.512394\pi$
$758$	6.28533	+	0.293683i	0.228294	+	0.0106671i
$759$		0			0
$760$	8.03104	+	19.9031i	0.291316	+	0.721963i
$761$	−44.4637	−	25.6711i	−1.61181	−	0.930578i	−0.988951	−	0.148242i	$-0.952638\pi$
$761$	−44.4637	−	25.6711i	−1.61181	−	0.930578i	−0.622857	−	0.782336i	$-0.714028\pi$
$762$		0			0
$763$	−3.75238	−	18.9136i	−0.135845	−	0.684719i
$764$	1.30693	+	0.927086i	0.0472831	+	0.0335408i
$765$		0			0
$766$	13.1711	+	8.44764i	0.475890	+	0.305225i
$767$	25.9848	−	15.0023i	0.938257	−	0.541703i
$768$		0			0
$769$			32.6757i			1.17832i	0.808018	+	0.589158i	$0.200540\pi$
$769$			32.6757i			1.17832i	−0.808018	+	0.589158i	$0.799460\pi$
$770$	−3.43065	+	8.72991i	−0.123632	+	0.314604i
$771$		0			0
$772$	12.0003	+	26.1510i	0.431899	+	0.941197i
$773$	10.4867	−	6.05452i	0.377182	−	0.217766i	−0.299410	−	0.954125i	$-0.596790\pi$
$773$	10.4867	−	6.05452i	0.377182	−	0.217766i	0.676591	+	0.736359i	$0.263456\pi$
$774$		0			0
$775$	−2.25093	+	3.89873i	−0.0808560	+	0.140047i
$776$	−8.02210	−	1.13109i	−0.287976	−	0.0406038i
$777$		0			0
$778$	37.3422	−	19.2942i	1.33878	−	0.691731i
$779$	−23.0448	−	13.3049i	−0.825667	−	0.476699i
$780$		0			0
$781$	−4.48000	−	7.75959i	−0.160307	−	0.277660i
$782$	4.43484	−	94.9133i	0.158590	−	3.39409i
$783$		0			0
$784$	18.6418	+	20.8921i	0.665780	+	0.746148i
$785$	−12.1766			−0.434600
$786$		0			0
$787$	22.7245	+	39.3600i	0.810042	+	1.40303i	0.912834	+	0.408331i	$0.133889\pi$
$787$	22.7245	+	39.3600i	0.810042	+	1.40303i	−0.102792	+	0.994703i	$0.532778\pi$
$788$	23.9196	+	2.24019i	0.852102	+	0.0798034i
$789$		0			0
$790$	12.8671	−	6.64825i	0.457791	−	0.236534i
$791$	20.5999	+	7.00413i	0.732447	+	0.249038i
$792$		0			0
$793$	−24.7447	+	42.8591i	−0.878710	+	1.52197i
$794$	−25.2806	+	39.4160i	−0.897174	+	1.39882i
$795$		0			0
$796$	−8.90555	−	19.4070i	−0.315649	−	0.687863i
$797$		−	41.6295i		−	1.47459i	−0.675569	−	0.737296i	$-0.736102\pi$
$797$		−	41.6295i		−	1.47459i	0.675569	−	0.737296i	$-0.263898\pi$
$798$		0			0
$799$			39.6861i			1.40399i
$800$	−17.8698	+	5.33534i	−0.631792	+	0.188633i
$801$		0			0
$802$	−38.2780	−	24.5506i	−1.35164	−	0.866913i
$803$	8.47318	−	14.6760i	0.299012	−	0.517904i
$804$		0			0
$805$	5.55440	+	27.9966i	0.195767	+	0.986750i
$806$	−4.33046	−	8.38121i	−0.152534	−	0.295216i
$807$		0			0
$808$	−2.59918	−	6.44149i	−0.0914389	−	0.226611i
$809$	−22.5540	−	39.0647i	−0.792957	−	1.37344i	−0.924129	−	0.382081i	$-0.875207\pi$
$809$	−22.5540	−	39.0647i	−0.792957	−	1.37344i	0.131172	−	0.991360i	$-0.458126\pi$
$810$		0			0
$811$	22.4980			0.790010			0.395005	−	0.918679i	$-0.370743\pi$
$811$	22.4980			0.790010			0.395005	+	0.918679i	$0.370743\pi$
$812$	−16.4855	−	7.38429i	−0.578527	−	0.259138i
$813$		0			0
$814$	−29.8291	−	1.39377i	−1.04551	−	0.0488516i
$815$	3.34713	+	5.79739i	0.117245	+	0.203074i
$816$		0			0
$817$	2.75868	+	1.59273i	0.0965141	+	0.0557224i
$818$	−9.68983	−	18.7538i	−0.338797	−	0.655711i
$819$		0			0
$820$	−6.91160	+	9.74341i	−0.241363	+	0.340255i
$821$	−13.7839	+	23.8744i	−0.481061	+	0.833223i	−0.999764	−	0.0217322i	$-0.993082\pi$
$821$	−13.7839	+	23.8744i	−0.481061	+	0.833223i	0.518703	+	0.854955i	$0.326415\pi$
$822$		0			0
$823$	28.2005	−	16.2815i	0.983007	−	0.567539i	0.0798301	−	0.996808i	$-0.474562\pi$
$823$	28.2005	−	16.2815i	0.983007	−	0.567539i	0.903177	+	0.429269i	$0.141229\pi$
$824$	26.4310	+	20.6692i	0.920767	+	0.720045i
$825$		0			0
$826$	22.7267	−	3.41531i	0.790762	−	0.118834i
$827$		−	19.7347i		−	0.686243i	−0.939291	−	0.343122i	$-0.888516\pi$
$827$		−	19.7347i		−	0.686243i	0.939291	−	0.343122i	$-0.111484\pi$
$828$		0			0
$829$	−8.66870	+	5.00488i	−0.301077	+	0.173827i	−0.642926	−	0.765928i	$-0.722280\pi$
$829$	−8.66870	+	5.00488i	−0.301077	+	0.173827i	0.341850	+	0.939755i	$0.388947\pi$
$830$	−2.22385	+	3.46730i	−0.0771909	+	0.120352i
$831$		0			0
$832$	10.8056	−	37.5567i	0.374616	−	1.30204i
$833$	56.4021	+	7.48251i	1.95422	+	0.259254i
$834$		0			0
$835$	−14.3523	−	8.28629i	−0.496681	−	0.286759i
$836$	−2.08280	+	22.2391i	−0.0720352	+	0.769156i
$837$		0			0
$838$	1.05201	−	22.5149i	0.0363412	−	0.777766i
$839$	3.95140			0.136418			0.0682088	−	0.997671i	$-0.478272\pi$
$839$	3.95140			0.136418			0.0682088	+	0.997671i	$0.478272\pi$
$840$		0			0
$841$	−17.3465			−0.598154
$842$	−0.169216	+	3.62151i	−0.00583155	+	0.124805i
$843$		0			0
$844$	4.26131	−	45.5002i	0.146681	−	1.56618i
$845$	12.2784	+	7.08892i	0.422389	+	0.243866i
$846$		0			0
$847$	14.5480	−	12.7455i	0.499876	−	0.437940i
$848$	6.12599	+	17.4939i	0.210367	+	0.600743i
$849$		0			0
$850$	−20.4588	+	31.8983i	−0.701732	+	1.09410i
$851$	−78.6936	+	45.4338i	−2.69758	+	1.55745i
$852$		0			0
$853$			43.6094i			1.49316i	0.665297	+	0.746579i	$0.268305\pi$
$853$			43.6094i			1.49316i	−0.665297	+	0.746579i	$0.731695\pi$
$854$	−29.6465	+	23.6211i	−1.01448	+	0.808296i
$855$		0			0
$856$	16.7440	−	21.4116i	0.572297	−	0.731832i
$857$	−47.6767	+	27.5261i	−1.62860	+	0.940275i	−0.644093	+	0.764947i	$0.722765\pi$
$857$	−47.6767	+	27.5261i	−1.62860	+	0.940275i	−0.984510	+	0.175328i	$0.943901\pi$
$858$		0			0
$859$	−0.383633	+	0.664472i	−0.0130894	+	0.0226715i	−0.872496	−	0.488621i	$-0.837500\pi$
$859$	−0.383633	+	0.664472i	−0.0130894	+	0.0226715i	0.859407	+	0.511293i	$0.170833\pi$
$860$	0.827383	−	1.16638i	0.0282135	−	0.0397731i
$861$		0			0
$862$	−15.8333	−	30.6438i	−0.539283	−	1.04373i
$863$	6.94767	+	4.01124i	0.236501	+	0.136544i	0.613568	−	0.789642i	$-0.289734\pi$
$863$	6.94767	+	4.01124i	0.236501	+	0.136544i	−0.377066	+	0.926186i	$0.623067\pi$
$864$		0			0
$865$	0.369778	+	0.640474i	0.0125728	+	0.0217768i
$866$	31.5893	+	1.47602i	1.07345	+	0.0501571i
$867$		0			0
$868$	−0.739133	−	7.18789i	−0.0250878	−	0.243973i
$869$	15.0730			0.511316
$870$		0			0
$871$	−19.3302	−	33.4809i	−0.654979	−	1.13446i
$872$	−19.1161	+	7.71344i	−0.647351	+	0.261210i
$873$		0			0
$874$	31.1999	+	60.3846i	1.05535	+	2.04254i
$875$	9.22211	−	27.1232i	0.311764	−	0.916931i
$876$		0			0
$877$	−14.5109	+	25.1337i	−0.489999	+	0.848704i	−0.999934	−	0.0115095i	$-0.996336\pi$
$877$	−14.5109	+	25.1337i	−0.489999	+	0.848704i	0.509934	+	0.860213i	$0.329670\pi$
$878$	40.3336	+	25.8691i	1.36119	+	0.873039i
$879$		0			0
$880$	9.85305	+	1.86190i	0.332146	+	0.0627647i
$881$		−	23.0875i		−	0.777837i	−0.921272	−	0.388919i	$-0.872849\pi$
$881$		−	23.0875i		−	0.777837i	0.921272	−	0.388919i	$-0.127151\pi$
$882$		0			0
$883$			26.6902i			0.898197i	0.893482	+	0.449099i	$0.148255\pi$
$883$			26.6902i			0.898197i	−0.893482	+	0.449099i	$0.851745\pi$
$884$	−33.1199	−	72.1751i	−1.11394	−	2.42751i
$885$		0			0
$886$	5.75962	−	8.98008i	0.193498	−	0.301692i
$887$	−4.24240	+	7.34804i	−0.142446	+	0.246723i	−0.928417	−	0.371540i	$-0.878830\pi$
$887$	−4.24240	+	7.34804i	−0.142446	+	0.246723i	0.785971	+	0.618263i	$0.212163\pi$
$888$		0			0
$889$	13.2248	−	38.8955i	0.443545	−	1.30451i
$890$	3.74227	−	1.93358i	0.125441	−	0.0648137i
$891$		0			0
$892$	−27.5354	−	2.57883i	−0.921954	−	0.0863455i
$893$	−14.1944	−	24.5854i	−0.474997	−	0.822719i
$894$		0			0
$895$	−8.60478			−0.287626
$896$	18.2243	−	23.7461i	0.608830	−	0.793301i
$897$		0			0
$898$	1.91507	−	40.9859i	0.0639068	−	1.36772i
$899$	2.33080	+	4.03707i	0.0777366	+	0.134644i
$900$		0			0
$901$	32.6182	+	18.8321i	1.08667	+	0.627390i
$902$	−11.0452	+	5.70690i	−0.367764	+	0.190019i
$903$		0			0
$904$	3.24751	−	23.0325i	0.108011	−	0.766049i
$905$	1.89566	−	3.28338i	0.0630138	−	0.109143i
$906$		0			0
$907$	26.9075	−	15.5351i	0.893449	−	0.515833i	0.0183800	−	0.999831i	$-0.494149\pi$
$907$	26.9075	−	15.5351i	0.893449	−	0.515833i	0.875069	+	0.483998i	$0.160816\pi$
$908$	12.4292	+	27.0857i	0.412476	+	0.898870i
$909$		0			0
$910$	14.8649	+	18.6567i	0.492765	+	0.618464i
$911$			15.2537i			0.505377i	0.967548	+	0.252688i	$0.0813148\pi$
$911$			15.2537i			0.505377i	−0.967548	+	0.252688i	$0.918685\pi$
$912$		0			0
$913$	−3.71260	+	2.14347i	−0.122869	+	0.0709385i
$914$	−2.28085	−	1.46288i	−0.0754437	−	0.0483879i
$915$		0			0
$916$	−4.18608	−	2.96945i	−0.138312	−	0.0981133i
$917$	−33.1756	+	29.0650i	−1.09555	+	0.959812i
$918$		0			0
$919$	26.6445	+	15.3832i	0.878920	+	0.507445i	0.870302	−	0.492518i	$-0.163923\pi$
$919$	26.6445	+	15.3832i	0.878920	+	0.507445i	0.00861810	+	0.999963i	$0.497257\pi$
$920$	28.2962	−	11.4177i	0.932899	−	0.376430i
$921$		0			0
$922$	5.87872	+	0.274684i	0.193605	+	0.00904624i
$923$	−22.7869			−0.750039
$924$		0			0
$925$	36.2406			1.19158
$926$	23.5371	+	1.09977i	0.773475	+	0.0361408i
$927$		0			0
$928$	−4.46742	+	18.7871i	−0.146650	+	0.616717i
$929$	10.9345	+	6.31304i	0.358750	+	0.207124i	0.668532	−	0.743683i	$-0.266923\pi$
$929$	10.9345	+	6.31304i	0.358750	+	0.207124i	−0.309783	+	0.950807i	$0.600256\pi$
$930$		0			0
$931$	−37.6171	+	15.5377i	−1.23285	+	0.509229i
$932$	21.4042	−	30.1739i	0.701117	−	0.988377i
$933$		0			0
$934$	−28.3276	−	18.1687i	−0.926906	−	0.594497i
$935$	17.6460	−	10.1879i	0.577085	−	0.333180i
$936$		0			0
$937$		−	15.5749i		−	0.508811i	−0.967098	−	0.254405i	$-0.918120\pi$
$937$		−	15.5749i		−	0.508811i	0.967098	−	0.254405i	$-0.0818798\pi$
$938$	−4.40056	−	29.2829i	−0.143683	−	0.956120i
$939$		0			0
$940$	−11.5831	+	5.31531i	−0.377801	+	0.173366i
$941$	4.56400	−	2.63502i	0.148782	−	0.0858994i	−0.423761	−	0.905774i	$-0.639290\pi$
$941$	4.56400	−	2.63502i	0.148782	−	0.0858994i	0.572543	+	0.819875i	$0.305957\pi$
$942$		0			0
$943$	−18.9156	+	32.7627i	−0.615976	+	1.06690i
$944$	−8.11995	−	23.1880i	−0.264282	−	0.754706i
$945$		0			0
$946$	1.32221	−	0.683169i	0.0429888	−	0.0222117i
$947$	28.3259	+	16.3539i	0.920467	+	0.531432i	0.883784	−	0.467895i	$-0.154988\pi$
$947$	28.3259	+	16.3539i	0.920467	+	0.531432i	0.0366829	+	0.999327i	$0.488321\pi$
$948$		0			0
$949$	−21.5488	−	37.3236i	−0.699504	−	1.21158i
$950$	1.26524	−	27.0783i	0.0410497	−	0.878536i
$951$		0			0
$952$	−3.39098	−	60.7300i	−0.109902	−	1.96827i
$953$	18.1640			0.588389			0.294194	−	0.955746i	$-0.404949\pi$
$953$	18.1640			0.588389			0.294194	+	0.955746i	$0.404949\pi$
$954$		0			0
$955$	0.522804	+	0.905523i	0.0169175	+	0.0293020i
$956$	−2.26651	+	24.2007i	−0.0733043	+	0.782707i
$957$		0			0
$958$	45.8899	−	23.7107i	1.48264	−	0.766058i
$959$	3.42402	+	17.2585i	0.110567	+	0.557307i
$960$		0			0
$961$	14.5676	−	25.2319i	0.469924	−	0.813932i
$962$	−41.0001	+	63.9251i	−1.32190	+	2.06103i
$963$		0			0
$964$	−0.0382376	+	0.0175466i	−0.00123155	+	0.000565137i
$965$			18.7756i			0.604407i
$966$		0			0
$967$		−	19.1306i		−	0.615198i	−0.951516	−	0.307599i	$-0.900474\pi$
$967$		−	19.1306i		−	0.615198i	0.951516	−	0.307599i	$-0.0995256\pi$
$968$	−16.2879	−	12.7372i	−0.523513	−	0.409391i
$969$		0			0
$970$	−4.44991	−	2.85408i	−0.142878	−	0.0916388i
$971$	−12.6574	+	21.9233i	−0.406196	+	0.703552i	−0.994460	−	0.105117i	$-0.966478\pi$
$971$	−12.6574	+	21.9233i	−0.406196	+	0.703552i	0.588264	+	0.808669i	$0.299812\pi$
$972$		0			0
$973$	−15.5173	−	5.27601i	−0.497461	−	0.169141i
$974$	20.5952	+	39.8601i	0.659913	+	1.27720i
$975$		0			0
$976$	30.7217	+	26.4256i	0.983379	+	0.845864i
$977$	−12.8118	−	22.1908i	−0.409887	−	0.709945i	0.584990	−	0.811041i	$-0.301099\pi$
$977$	−12.8118	−	22.1908i	−0.409887	−	0.709945i	−0.994877	+	0.101096i	$0.967765\pi$
$978$		0			0
$979$	4.38383			0.140108
$980$	5.37022	+	17.4642i	0.171546	+	0.557872i
$981$		0			0
$982$	53.4985	+	2.49973i	1.70721	+	0.0797695i
$983$	−15.9395	−	27.6080i	−0.508390	−	0.880558i	−0.999953	−	0.00971556i	$-0.996907\pi$
$983$	−15.9395	−	27.6080i	−0.508390	−	0.880558i	0.491562	−	0.870842i	$-0.336426\pi$
$984$		0			0
$985$	13.5766	+	7.83845i	0.432586	+	0.249754i
$986$	18.0125	+	34.8616i	0.573635	+	1.11022i
$987$		0			0
$988$	46.3323	+	32.8663i	1.47403	+	1.04562i
$989$	2.26437	−	3.92201i	0.0720028	−	0.124713i
$990$		0			0
$991$	−45.8358	+	26.4633i	−1.45602	+	0.840635i	−0.998812	−	0.0487244i	$-0.984484\pi$
$991$	−45.8358	+	26.4633i	−1.45602	+	0.840635i	−0.457210	+	0.889359i	$0.651151\pi$
$992$	−7.40183	+	2.20995i	−0.235008	+	0.0701660i
$993$		0			0
$994$	−16.2442	−	6.38358i	−0.515234	−	0.202475i
$995$		−	13.9336i		−	0.441725i
$996$		0			0
$997$	−39.7636	+	22.9575i	−1.25933	+	0.727073i	−0.972944	−	0.231042i	$-0.925786\pi$
$997$	−39.7636	+	22.9575i	−1.25933	+	0.727073i	−0.286383	+	0.958115i	$0.592453\pi$
$998$	−26.2709	+	40.9601i	−0.831590	+	1.29657i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.b.271.8	yes	32
3.2	odd	2		756.2.bf.c.271.9	yes	32
4.3	odd	2		756.2.bf.c.271.14	yes	32
7.3	odd	6		756.2.bf.c.703.14	yes	32
12.11	even	2	inner	756.2.bf.b.271.3	✓	32
21.17	even	6	inner	756.2.bf.b.703.3	yes	32
28.3	even	6	inner	756.2.bf.b.703.8	yes	32
84.59	odd	6		756.2.bf.c.703.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.3	✓	32	12.11	even	2	inner
756.2.bf.b.271.8	yes	32	1.1	even	1	trivial
756.2.bf.b.703.3	yes	32	21.17	even	6	inner
756.2.bf.b.703.8	yes	32	28.3	even	6	inner
756.2.bf.c.271.9	yes	32	3.2	odd	2
756.2.bf.c.271.14	yes	32	4.3	odd	2
756.2.bf.c.703.9	yes	32	84.59	odd	6
756.2.bf.c.703.14	yes	32	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0660073 - 1.41267i) q^{2} +(-1.99129 - 0.186493i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(-2.50492 - 0.851694i) q^{7} +(-0.394894 + 2.80072i) q^{8} +O(q^{10})\)	\(q+(0.0660073 - 1.41267i) q^{2} +(-1.99129 - 0.186493i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(-2.50492 - 0.851694i) q^{7} +(-0.394894 + 2.80072i) q^{8} +(-0.996433 + 1.55358i) q^{10} +(-1.66349 + 0.960419i) q^{11} +4.88503i q^{13} +(-1.36851 + 3.48241i) q^{14} +(3.93044 + 0.742724i) q^{16} +(7.03908 - 4.06402i) q^{17} +(-2.90712 + 5.03529i) q^{19} +(2.12893 + 1.51018i) q^{20} +(1.24695 + 2.41337i) q^{22} +(7.15864 + 4.13305i) q^{23} +(-1.64838 - 2.85507i) q^{25} +(6.90095 + 0.322448i) q^{26} +(4.82917 + 2.16312i) q^{28} -3.41373 q^{29} +(-0.682773 - 1.18260i) q^{31} +(1.30866 - 5.50340i) q^{32} +(-5.27649 - 10.2122i) q^{34} +(2.27539 + 2.59718i) q^{35} +(-5.49640 + 9.52005i) q^{37} +(6.92132 + 4.43918i) q^{38} +(2.27392 - 2.90780i) q^{40} +4.57667i q^{41} -0.547870i q^{43} +(3.49160 - 1.60224i) q^{44} +(6.31116 - 9.84001i) q^{46} +(-2.44131 + 4.22848i) q^{47} +(5.54924 + 4.26685i) q^{49} +(-4.14208 + 2.14016i) q^{50} +(0.911027 - 9.72750i) q^{52} +(2.31694 + 4.01305i) q^{53} +2.50686 q^{55} +(3.37454 - 6.67926i) q^{56} +(-0.225331 + 4.82248i) q^{58} +(-3.07108 - 5.31927i) q^{59} +(8.77355 + 5.06541i) q^{61} +(-1.71569 + 0.886475i) q^{62} +(-7.68812 - 2.21198i) q^{64} +(3.18769 - 5.52124i) q^{65} +(-6.85377 + 3.95703i) q^{67} +(-14.7747 + 6.77988i) q^{68} +(3.81916 - 3.04294i) q^{70} +4.66463i q^{71} +(-7.64041 + 4.41119i) q^{73} +(13.0859 + 8.39301i) q^{74} +(6.72796 - 9.48453i) q^{76} +(4.98490 - 0.988983i) q^{77} +(-6.79578 - 3.92355i) q^{79} +(-3.95767 - 3.40423i) q^{80} +(6.46533 + 0.302094i) q^{82} +2.23181 q^{83} -10.6078 q^{85} +(-0.773961 - 0.0361634i) q^{86} +(-2.03297 - 5.03825i) q^{88} +(-1.97649 - 1.14113i) q^{89} +(4.16055 - 12.2366i) q^{91} +(-13.4841 - 9.56512i) q^{92} +(5.81231 + 3.72788i) q^{94} +(6.57148 - 3.79404i) q^{95} +2.86429i q^{97} +(6.39395 - 7.55761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 6 q^{11} - 17 q^{14} - 4 q^{16} + 8 q^{20} + 2 q^{22} + 14 q^{25} + 15 q^{26} - 13 q^{28} + 15 q^{32} + 6 q^{35} + 4 q^{37} - q^{38} - 15 q^{40} - 42 q^{44} - 9 q^{46} - 4 q^{47} + 14 q^{49} - 9 q^{52} + 45 q^{56} + 10 q^{58} - 16 q^{59} - 42 q^{64} - 49 q^{68} - 33 q^{70} + 36 q^{73} - 54 q^{74} - 15 q^{80} - 51 q^{82} + 20 q^{83} + 16 q^{85} + 78 q^{86} - 2 q^{88} - 27 q^{94} + 24 q^{95} - 46 q^{98}+O(q^{100}) \) 32 * q - 6 * q^11 - 17 * q^14 - 4 * q^16 + 8 * q^20 + 2 * q^22 + 14 * q^25 + 15 * q^26 - 13 * q^28 + 15 * q^32 + 6 * q^35 + 4 * q^37 - q^38 - 15 * q^40 - 42 * q^44 - 9 * q^46 - 4 * q^47 + 14 * q^49 - 9 * q^52 + 45 * q^56 + 10 * q^58 - 16 * q^59 - 42 * q^64 - 49 * q^68 - 33 * q^70 + 36 * q^73 - 54 * q^74 - 15 * q^80 - 51 * q^82 + 20 * q^83 + 16 * q^85 + 78 * q^86 - 2 * q^88 - 27 * q^94 + 24 * q^95 - 46 * q^98

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