LMFDB - Embedded newform 756.2.bf.c.271.14

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			271.14
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19041 - 0.763500i) q^{2} +(0.834135 - 1.81775i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(2.50492 + 0.851694i) q^{7} +(-0.394894 - 2.80072i) q^{8} +O(q^{10})$	\(q+(1.19041 - 0.763500i) q^{2} +(0.834135 - 1.81775i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(2.50492 + 0.851694i) q^{7} +(-0.394894 - 2.80072i) q^{8} +(-1.84366 + 0.0861452i) q^{10} +(1.66349 - 0.960419i) q^{11} +4.88503i q^{13} +(3.63214 - 0.898644i) q^{14} +(-2.60844 - 3.03250i) q^{16} +(7.03908 - 4.06402i) q^{17} +(2.90712 - 5.03529i) q^{19} +(-2.12893 + 1.51018i) q^{20} +(1.24695 - 2.41337i) q^{22} +(-7.15864 - 4.13305i) q^{23} +(-1.64838 - 2.85507i) q^{25} +(3.72972 + 5.81517i) q^{26} +(3.63761 - 3.84289i) q^{28} -3.41373 q^{29} +(0.682773 + 1.18260i) q^{31} +(-5.42041 - 1.61836i) q^{32} +(5.27649 - 10.2122i) q^{34} +(-2.27539 - 2.59718i) q^{35} +(-5.49640 + 9.52005i) q^{37} +(-0.383783 - 8.21363i) q^{38} +(-1.38127 + 3.42317i) q^{40} +4.57667i q^{41} +0.547870i q^{43} +(-0.358224 - 3.82494i) q^{44} +(-11.6773 + 0.545623i) q^{46} +(2.44131 - 4.22848i) q^{47} +(5.54924 + 4.26685i) q^{49} +(-4.14208 - 2.14016i) q^{50} +(8.87977 + 4.07478i) q^{52} +(2.31694 + 4.01305i) q^{53} -2.50686 q^{55} +(1.39618 - 7.35192i) q^{56} +(-4.06372 + 2.60638i) q^{58} +(3.07108 + 5.31927i) q^{59} +(8.77355 + 5.06541i) q^{61} +(1.71569 + 0.886475i) q^{62} +(-7.68812 + 2.21198i) q^{64} +(3.18769 - 5.52124i) q^{65} +(6.85377 - 3.95703i) q^{67} +(-1.51583 - 16.1852i) q^{68} +(-4.69158 - 1.35445i) q^{70} -4.66463i q^{71} +(-7.64041 + 4.41119i) q^{73} +(0.725606 + 15.5292i) q^{74} +(-6.72796 - 9.48453i) q^{76} +(4.98490 - 0.988983i) q^{77} +(6.79578 + 3.92355i) q^{79} +(0.969318 + 5.12956i) q^{80} +(3.49429 + 5.44810i) q^{82} -2.23181 q^{83} -10.6078 q^{85} +(0.418299 + 0.652188i) q^{86} +(-3.34677 - 4.27973i) q^{88} +(-1.97649 - 1.14113i) q^{89} +(-4.16055 + 12.2366i) q^{91} +(-13.4841 + 9.56512i) q^{92} +(-0.322289 - 6.89755i) q^{94} +(-6.57148 + 3.79404i) q^{95} +2.86429i q^{97} +(9.86358 + 0.842440i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.19041	−	0.763500i	0.841744	−	0.539876i
$2$	1.19041	−	0.763500i	0.841744	−	0.539876i
$3$		0			0
$3$		0			0
$4$	0.834135	−	1.81775i	0.417067	−	0.908876i
$5$	−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
$10$	−1.84366	+	0.0861452i	−0.583016	+	0.0272415i
$11$	1.66349	−	0.960419i	0.501562	−	0.289577i	−0.227796	−	0.973709i	$-0.573152\pi$
$11$	1.66349	−	0.960419i	0.501562	−	0.289577i	0.729358	+	0.684132i	$0.239819\pi$
$12$		0			0
$13$			4.88503i			1.35486i	0.735585	+	0.677432i	$0.236907\pi$
$13$			4.88503i			1.35486i	−0.735585	+	0.677432i	$0.763093\pi$
$14$	3.63214	−	0.898644i	0.970730	−	0.240173i
$15$		0			0
$16$	−2.60844	−	3.03250i	−0.652109	−	0.758125i
$17$	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	$-0.600937\pi$
$19$	2.90712	−	5.03529i	0.666940	−	1.15517i	0.978755	−	0.205031i	$-0.0657295\pi$
$20$	−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	−0.492716	−	0.870190i	$-0.663996\pi$
$23$	−7.15864	−	4.13305i	−1.49268	−	0.861800i	−0.999965	+	0.00839082i	$0.997329\pi$
$24$		0			0
$25$	−1.64838	−	2.85507i	−0.329675	−	0.571014i
$26$	3.72972	+	5.81517i	0.731459	+	1.14045i
$27$		0			0
$28$	3.63761	−	3.84289i	0.687443	−	0.726238i
$29$	−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	0.920804	−	0.390026i	$-0.127534\pi$
$31$	0.682773	+	1.18260i	0.122630	+	0.212401i	−0.798174	+	0.602427i	$0.794201\pi$
$32$	−5.42041	−	1.61836i	−0.958203	−	0.286089i
$33$		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	$0.807579\pi$
$38$	−0.383783	−	8.21363i	−0.0622578	−	1.33243i
$39$		0			0
$40$	−1.38127	+	3.42317i	−0.218398	+	0.541250i
$41$			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	$0.0133012\pi$
$43$			0.547870i			0.0835494i	−0.999127	+	0.0417747i	$0.986699\pi$
$44$	−0.358224	−	3.82494i	−0.0540043	−	0.576631i
$45$		0			0
$46$	−11.6773	+	0.545623i	−1.72172	+	0.0804477i
$47$	2.44131	−	4.22848i	0.356102	−	0.616787i	−0.631204	−	0.775617i	$-0.717439\pi$
$47$	2.44131	−	4.22848i	0.356102	−	0.616787i	0.987306	+	0.158830i	$0.0507723\pi$
$48$		0			0
$49$	5.54924	+	4.26685i	0.792748	+	0.609550i
$50$	−4.14208	−	2.14016i	−0.585779	−	0.302664i
$51$		0			0
$52$	8.87977	+	4.07478i	1.23140	+	0.565070i
$53$	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
$56$	1.39618	−	7.35192i	0.186573	−	0.982441i
$57$		0			0
$58$	−4.06372	+	2.60638i	−0.533593	+	0.342234i
$59$	3.07108	+	5.31927i	0.399821	+	0.692510i	0.993703	−	0.112042i	$-0.0357391\pi$
$59$	3.07108	+	5.31927i	0.399821	+	0.692510i	−0.593883	+	0.804552i	$0.702406\pi$
$60$		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	−0.0190314	−	0.999819i	$-0.506058\pi$
$67$	6.85377	−	3.95703i	0.837321	−	0.483428i	0.856353	+	0.516391i	$0.172725\pi$
$68$	−1.51583	−	16.1852i	−0.183821	−	1.96275i
$69$		0			0
$70$	−4.69158	−	1.35445i	−0.560751	−	0.161887i
$71$		−	4.66463i		−	0.553590i	−0.960929	−	0.276795i	$-0.910728\pi$
$71$		−	4.66463i		−	0.553590i	0.960929	−	0.276795i	$-0.0892723\pi$
$72$		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	$0.506021\pi$
$74$	0.725606	+	15.5292i	0.0843500	+	1.80524i
$75$		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	0.830940	−	0.556363i	$-0.187803\pi$
$79$	6.79578	+	3.92355i	0.764585	+	0.441433i	−0.0663545	+	0.997796i	$0.521137\pi$
$80$	0.969318	+	5.12956i	0.108373	+	0.573502i
$81$		0			0
$82$	3.49429	+	5.44810i	0.385879	+	0.601641i
$83$	−2.23181			−0.244973			−0.122486	−	0.992470i	$-0.539087\pi$
$83$	−2.23181			−0.244973			−0.122486	+	0.992470i	$0.539087\pi$
$84$		0			0
$85$	−10.6078			−1.15058
$86$	0.418299	+	0.652188i	0.0451063	+	0.0703272i
$87$		0			0
$88$	−3.34677	−	4.27973i	−0.356767	−	0.456220i
$89$	−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
$94$	−0.322289	−	6.89755i	−0.0332416	−	0.711428i
$95$	−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	$0.953549\pi$
$98$	9.86358	+	0.842440i	0.996372	+	0.0850993i
$99$		0			0
$100$	−6.56478	+	0.614823i	−0.656478	+	0.0614823i
$101$	−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	$0.365352\pi$
$103$	−5.93141	+	10.2735i	−0.584439	+	1.01228i	−0.994945	+	0.100421i	$0.967981\pi$
$104$	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	0.845065	−	0.534663i	$-0.179561\pi$
$107$	8.32250	+	4.80500i	0.804566	+	0.464516i	−0.0404992	+	0.999180i	$0.512895\pi$
$108$		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	$0.719844\pi$
$110$	−2.98418	+	1.91399i	−0.284530	+	0.182491i
$111$		0			0
$112$	−3.95116	−	9.81775i	−0.373350	−	0.927691i
$113$	−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
$116$	−2.84751	+	6.20530i	−0.264384	+	0.576148i
$117$		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
$122$	14.3115	−	0.668709i	1.29571	−	0.0605421i
$123$		0			0
$124$	2.71919	−	0.254666i	0.244191	−	0.0228696i
$125$			10.8280i			0.968483i
$126$		0			0
$127$		−	15.5276i		−	1.37786i	−0.724830	−	0.688928i	$-0.758082\pi$
$127$		−	15.5276i		−	1.37786i	0.724830	−	0.688928i	$-0.241918\pi$
$128$	−7.46314	+	8.50303i	−0.659655	+	0.751569i
$129$		0			0
$130$	−0.420822	−	9.00633i	−0.0369085	−	0.789907i
$131$	−8.33537	+	14.4373i	−0.728264	+	1.26139i	0.229352	+	0.973344i	$0.426339\pi$
$131$	−8.33537	+	14.4373i	−0.728264	+	1.26139i	−0.957616	+	0.288047i	$0.906994\pi$
$132$		0			0
$133$	11.5706	−	10.1370i	1.00330	−	0.878989i
$134$	5.13758	−	9.94333i	0.443820	−	0.858972i
$135$		0			0
$136$	−14.1619	−	18.1097i	−1.21437	−	1.55289i
$137$	−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	$-0.584618\pi$
$139$	−6.19472			−0.525430			−0.262715	+	0.964874i	$0.584618\pi$
$140$	−6.61901	+	1.96968i	−0.559408	+	0.166469i
$141$		0			0
$142$	−3.56145	−	5.55281i	−0.298870	−	0.465981i
$143$	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	−0.0927523	−	0.995689i	$-0.529566\pi$
$151$	8.88639	−	5.13056i	0.723164	−	0.417519i	0.815916	+	0.578170i	$0.196233\pi$
$152$	−15.2505	−	6.15365i	−1.23698	−	0.499127i
$153$		0			0
$154$	5.17897	−	4.98326i	0.417333	−	0.401563i
$155$		−	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	$0.211899\pi$
$158$	11.0854	−	0.517966i	0.881905	−	0.0412071i
$159$		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	0.663776	−	0.747931i	$-0.268953\pi$
$163$	4.44216	+	2.56468i	0.347937	+	0.200881i	−0.315840	+	0.948813i	$0.602286\pi$
$164$	8.31924	+	3.81756i	0.649624	+	0.298101i
$165$		0			0
$166$	−2.65676	+	1.70399i	−0.206204	+	0.132255i
$167$	−12.6985			−0.982637			−0.491318	−	0.870980i	$-0.663485\pi$
$167$	−12.6985			−0.982637			−0.491318	+	0.870980i	$0.663485\pi$
$168$		0			0
$169$	−10.8635			−0.835657
$170$	−12.6276	+	8.09904i	−0.968490	+	0.621168i
$171$		0			0
$172$	0.995891	+	0.456998i	0.0759360	+	0.0348457i
$173$	−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
$178$	−3.22407	+	0.150645i	−0.241654	+	0.0112913i
$179$	−5.70994	+	3.29664i	−0.426781	+	0.246402i	−0.697974	−	0.716123i	$-0.745915\pi$
$179$	−5.70994	+	3.29664i	−0.426781	+	0.246402i	0.271193	+	0.962525i	$0.412582\pi$
$180$		0			0
$181$			2.90503i			0.215929i	0.994155	+	0.107965i	$0.0344333\pi$
$181$			2.90503i			0.215929i	−0.994155	+	0.107965i	$0.965567\pi$
$182$	4.38991	+	17.7431i	0.325401	+	1.31521i
$183$		0			0
$184$	−8.74862	+	21.6815i	−0.644957	+	1.59838i
$185$	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	0.524892	−	0.851169i	$-0.324106\pi$
$191$	0.693842	+	0.400590i	0.0502046	+	0.0289857i	−0.474688	+	0.880154i	$0.657439\pi$
$192$		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	$-0.339908\pi$
$194$	2.18689	+	3.40967i	0.157009	+	0.244800i
$195$		0			0
$196$	12.3849	−	6.52800i	0.884634	−	0.466286i
$197$	−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	0.612417	−	0.790535i	$-0.290197\pi$
$199$	−5.33819	−	9.24602i	−0.378414	−	0.655433i	−0.990832	+	0.135102i	$0.956864\pi$
$200$	−7.34534	+	5.74410i	−0.519394	+	0.406169i
$201$		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
$206$	0.783033	+	16.7583i	0.0545565	+	1.16760i
$207$		0			0
$208$	14.8139	−	12.7423i	1.02716	−	0.883520i
$209$		−	11.1682i		−	0.772522i
$210$		0			0
$211$		−	22.8497i		−	1.57304i	−0.617567	−	0.786518i	$-0.711882\pi$
$211$		−	22.8497i		−	1.57304i	0.617567	−	0.786518i	$-0.288118\pi$
$212$	9.22737	−	0.864187i	0.633738	−	0.0593526i
$213$		0			0
$214$	13.5758	−	0.634330i	0.928020	−	0.0433619i
$215$	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
$220$	−2.09106	+	4.55684i	−0.140979	+	0.307222i
$221$	19.8529	+	34.3862i	1.33545	+	2.31306i
$222$		0			0
$223$	−13.8280			−0.925989			−0.462994	−	0.886361i	$-0.653225\pi$
$223$	−13.8280			−0.925989			−0.462994	+	0.886361i	$0.653225\pi$
$224$	−12.1993	−	8.67040i	−0.815103	−	0.579316i
$225$		0			0
$226$	−9.78962	+	6.27884i	−0.651196	+	0.417663i
$227$	7.45033	+	12.9043i	0.494496	+	0.856491i	0.999980	−	0.00634435i	$-0.00201948\pi$
$227$	7.45033	+	12.9043i	0.494496	+	0.856491i	−0.505484	+	0.862836i	$0.668686\pi$
$228$		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
$236$	12.2308	−	1.14547i	0.796157	−	0.0745640i
$237$		0			0
$238$	21.9148	−	21.0867i	1.42053	−	1.36685i
$239$			12.1533i			0.786132i	0.919510	+	0.393066i	$0.128586\pi$
$239$			12.1533i			0.786132i	−0.919510	+	0.393066i	$0.871414\pi$
$240$		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	$0.333118\pi$
$242$	0.482539	+	10.3272i	0.0310188	+	0.663856i
$243$		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
$248$	3.04251	−	2.37926i	0.193200	−	0.151083i
$249$		0			0
$250$	8.26716	+	12.8897i	0.522861	+	0.815215i
$251$	18.6239			1.17553			0.587766	−	0.809031i	$-0.300008\pi$
$251$	18.6239			1.17553			0.587766	+	0.809031i	$0.300008\pi$
$252$		0			0
$253$	−15.8778			−0.998230
$254$	−11.8554	−	18.4842i	−0.743871	−	1.15980i
$255$		0			0
$256$	−2.39210	+	15.8202i	−0.149507	+	0.988761i
$257$	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
$262$	1.10039	+	23.5503i	0.0679824	+	1.45494i
$263$	8.77023	−	5.06350i	0.540796	−	0.312229i	−0.204606	−	0.978844i	$-0.565591\pi$
$263$	8.77023	−	5.06350i	0.540796	−	0.312229i	0.745401	+	0.666616i	$0.232258\pi$
$264$		0			0
$265$		−	6.04760i		−	0.371501i
$266$	6.03415	−	20.9013i	0.369977	−	1.28154i
$267$		0			0
$268$	−1.47592	−	15.7591i	−0.0901561	−	0.962643i
$269$	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	−0.999895	−	0.0144920i	$-0.995387\pi$
$271$	−8.02357	+	13.8972i	−0.487397	+	0.844196i	0.512498	+	0.858688i	$0.328720\pi$
$272$	−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	$-0.420730\pi$
$278$	−7.37424	+	4.72967i	−0.442278	+	0.283667i
$279$		0			0
$280$	−6.37546	+	7.39834i	−0.381006	+	0.442135i
$281$	−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	0.874758	−	0.484559i	$-0.161020\pi$
$283$	0.298407	+	0.516857i	0.0177385	+	0.0307239i	−0.857020	+	0.515283i	$0.827687\pi$
$284$	−8.47914	−	3.89093i	−0.503145	−	0.230884i
$285$		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
$290$	6.29374	−	0.294076i	0.369581	−	0.0172687i
$291$		0			0
$292$	1.64532	+	17.5679i	0.0962849	+	1.02808i
$293$		−	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
$296$	28.8335	+	11.6345i	1.67592	+	0.676242i
$297$		0			0
$298$	0.897287	+	19.2035i	0.0519784	+	1.11243i
$299$	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
$304$	−22.8525	+	4.31838i	−1.31068	+	0.247676i
$305$	−6.61080	−	11.4502i	−0.378533	−	0.655639i
$306$		0			0
$307$	−8.66748			−0.494679			−0.247340	−	0.968929i	$-0.579556\pi$
$307$	−8.66748			−0.494679			−0.247340	+	0.968929i	$0.579556\pi$
$308$	2.36035	−	9.88625i	0.134494	−	0.563322i
$309$		0			0
$310$	−1.36068	−	2.12149i	−0.0772812	−	0.120492i
$311$	2.71078	+	4.69521i	0.153714	+	0.266241i	0.932590	−	0.360937i	$-0.117543\pi$
$311$	2.71078	+	4.69521i	0.153714	+	0.266241i	−0.778876	+	0.627178i	$0.784210\pi$
$312$		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
$320$	10.1328	+	2.51677i	0.566441	+	0.140692i
$321$		0			0
$322$	−29.7153	−	8.57872i	−1.65597	−	0.478074i
$323$		−	47.2584i		−	2.62953i
$324$		0			0
$325$	13.9471	−	8.05237i	0.773647	−	0.446665i
$326$	7.24611	−	0.338575i	0.401325	−	0.0187520i
$327$		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	−0.0683635	−	0.997660i	$-0.521778\pi$
$331$	−17.5847	−	10.1526i	−0.966545	−	0.558035i	−0.898181	+	0.439626i	$0.855111\pi$
$332$	−1.86163	+	4.05687i	−0.102170	+	0.222650i
$333$		0			0
$334$	−15.1163	+	9.69528i	−0.827129	+	0.530502i
$335$	−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	$0.358411\pi$
$338$	−12.9320	+	8.29432i	−0.703410	+	0.451151i
$339$		0			0
$340$	−8.84832	+	19.2823i	−0.479867	+	1.04573i
$341$	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
$346$	−0.800522	+	0.0374045i	−0.0430363	+	0.00201088i
$347$	−23.3056	+	13.4555i	−1.25111	+	0.722328i	−0.971330	−	0.237736i	$-0.923595\pi$
$347$	−23.3056	+	13.4555i	−1.25111	+	0.722328i	−0.279779	+	0.960064i	$0.590261\pi$
$348$		0			0
$349$			2.85266i			0.152700i	0.997081	+	0.0763498i	$0.0243266\pi$
$349$			2.85266i			0.152700i	−0.997081	+	0.0763498i	$0.975673\pi$
$350$	−8.55283	−	8.88871i	−0.457168	−	0.475122i
$351$		0			0
$352$	−10.5711	+	2.51373i	−0.563443	+	0.133982i
$353$	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	0.0119216	−	0.999929i	$-0.496205\pi$
$359$	−16.0688	−	9.27735i	−0.848081	−	0.489640i	−0.860003	+	0.510289i	$0.829538\pi$
$360$		0			0
$361$	−7.40273	−	12.8219i	−0.389617	−	0.674837i
$362$	2.21799	+	3.45817i	0.116575	+	0.181757i
$363$		0			0
$364$	18.7726	+	17.7698i	0.983954	+	0.931392i
$365$	11.5140			0.602668
$366$		0			0
$367$	7.77468	+	13.4661i	0.405835	+	0.702927i	0.994418	−	0.105510i	$-0.0336474\pi$
$367$	7.77468	+	13.4661i	0.405835	+	0.702927i	−0.588583	+	0.808437i	$0.700314\pi$
$368$	6.13942	+	32.4894i	0.320039	+	1.69363i
$369$		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	$0.125592\pi$
$374$	−1.03055	−	22.0555i	−0.0532884	−	1.14046i
$375$		0			0
$376$	−12.8069	−	5.16764i	−0.660463	−	0.266501i
$377$		−	16.6762i		−	0.858866i
$378$		0			0
$379$		−	4.44925i		−	0.228543i	−0.993450	−	0.114271i	$-0.963547\pi$
$379$		−	4.44925i		−	0.228543i	0.993450	−	0.114271i	$-0.0364533\pi$
$380$	1.41513	+	15.1101i	0.0725946	+	0.775129i
$381$		0			0
$382$	1.13180	−	0.0528837i	0.0579081	−	0.00270577i
$383$	5.53218	−	9.58201i	0.282681	−	0.489618i	−0.689363	−	0.724416i	$-0.742110\pi$
$383$	5.53218	−	9.58201i	0.282681	−	0.489618i	0.972044	+	0.234798i	$0.0754429\pi$
$384$		0			0
$385$	−6.27947	−	2.13507i	−0.320032	−	0.108813i
$386$	−18.0754	−	9.33930i	−0.920012	−	0.475358i
$387$		0			0
$388$	5.20657	+	2.38921i	0.264324	+	0.121294i
$389$	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
$392$	9.75891	−	17.2268i	0.492899	−	0.870086i
$393$		0			0
$394$	−14.2993	+	9.17128i	−0.720391	+	0.462043i
$395$	−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
$404$	0.457995	+	4.89025i	0.0227861	+	0.243299i
$405$		0			0
$406$	−12.3991	+	3.06772i	−0.615358	+	0.152249i
$407$			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	$0.213022\pi$
$410$	−0.394258	−	8.43781i	−0.0194710	−	0.416714i
$411$		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
$416$	7.90576	−	26.4789i	0.387612	−	1.29823i
$417$		0			0
$418$	−8.52694	−	13.2947i	−0.417066	−	0.650266i
$419$	−15.9378			−0.778615			−0.389307	−	0.921108i	$-0.627286\pi$
$419$	−15.9378			−0.778615			−0.389307	+	0.921108i	$0.627286\pi$
$420$		0			0
$421$	−2.56359			−0.124942			−0.0624708	−	0.998047i	$-0.519898\pi$
$421$	−2.56359			−0.124942			−0.0624708	+	0.998047i	$0.519898\pi$
$422$	−17.4457	−	27.2004i	−0.849245	−	1.32409i
$423$		0			0
$424$	10.3245	−	8.07383i	0.501402	−	0.392100i
$425$	−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
$430$	−0.0471964	−	1.01008i	−0.00227601	−	0.0487106i
$431$	−21.1223	+	12.1950i	−1.01743	+	0.587411i	−0.913357	−	0.407159i	$-0.866519\pi$
$431$	−21.1223	+	12.1950i	−1.01743	+	0.587411i	−0.104068	+	0.994570i	$0.533186\pi$
$432$		0			0
$433$			22.3614i			1.07462i	0.843385	+	0.537310i	$0.180559\pi$
$433$			22.3614i			1.07462i	−0.843385	+	0.537310i	$0.819441\pi$
$434$	3.54266	+	3.68179i	0.170053	+	0.176732i
$435$		0			0
$436$	14.5125	−	1.35917i	0.695023	−	0.0650923i
$437$	−41.6221	+	24.0305i	−1.99106	+	1.14954i
$438$		0			0
$439$	16.9411	−	29.3429i	0.808555	−	1.40046i	−0.105309	−	0.994440i	$-0.533583\pi$
$439$	16.9411	−	29.3429i	0.808555	−	1.40046i	0.913865	−	0.406019i	$-0.133083\pi$
$440$	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	0.336709	−	0.941609i	$-0.390686\pi$
$443$	−6.53304	−	3.77186i	−0.310394	−	0.179206i	−0.647103	+	0.762403i	$0.724020\pi$
$444$		0			0
$445$	1.48927	+	2.57948i	0.0705980	+	0.122279i
$446$	−16.4609	+	10.5577i	−0.779446	+	0.499919i
$447$		0			0
$448$	−21.1420	−	1.00710i	−0.998867	−	0.0475810i
$449$	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
$452$	−6.85973	+	14.9488i	−0.322654	+	0.703130i
$453$		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	$0.152397\pi$
$458$	3.62516	−	0.169386i	0.169392	−	0.00791489i
$459$		0			0
$460$	21.4819	−	2.01188i	1.00160	−	0.0938045i
$461$			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	$-0.873456\pi$
$463$		−	16.6614i		−	0.774319i	0.922013	−	0.387160i	$-0.126544\pi$
$464$	8.90449	+	10.3521i	0.413381	+	0.480585i
$465$		0			0
$466$	1.22096	+	26.1306i	0.0565598	+	1.21048i
$467$	−11.8983	+	20.6084i	−0.550586	+	0.953643i	0.447646	+	0.894211i	$0.352262\pi$
$467$	−11.8983	+	20.6084i	−0.550586	+	0.953643i	−0.998232	+	0.0594325i	$0.981071\pi$
$468$		0			0
$469$	20.5383	−	4.07472i	0.948371	−	0.188153i
$470$	−4.13668	+	8.00617i	−0.190811	+	0.369297i
$471$		0			0
$472$	13.6851	−	10.7018i	0.629906	−	0.492590i
$473$	0.526185	+	0.911379i	0.0241940	+	0.0419052i
$474$		0			0
$475$	−19.1681			−0.879494
$476$	9.98785	−	41.8337i	0.457792	−	1.91745i
$477$		0			0
$478$	9.27905	+	14.4674i	0.424414	+	0.661722i
$479$	−18.2623	−	31.6312i	−0.834424	−	1.44526i	−0.894499	−	0.447071i	$-0.852467\pi$
$479$	−18.2623	−	31.6312i	−0.834424	−	1.44526i	0.0600746	−	0.998194i	$-0.480866\pi$
$480$		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	0.274899	−	0.961473i	$-0.411356\pi$
$487$	27.4749	−	15.8627i	1.24501	−	0.718806i	0.970110	+	0.242667i	$0.0780223\pi$
$488$	10.7222	−	26.5726i	0.485372	−	1.20289i
$489$		0			0
$490$	−10.5985	−	7.38857i	−0.478790	−	0.333781i
$491$		−	37.8704i		−	1.70907i	−0.519395	−	0.854534i	$-0.673843\pi$
$491$		−	37.8704i		−	1.70907i	0.519395	−	0.854534i	$-0.326157\pi$
$492$		0			0
$493$	−24.0295	+	13.8734i	−1.08223	+	0.624828i
$494$	40.1238	−	1.87479i	1.80526	−	0.0843509i
$495$		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	0.985905	−	0.167303i	$-0.0535059\pi$
$499$	29.7986	+	17.2042i	1.33397	+	0.770167i	0.348064	+	0.937471i	$0.386839\pi$
$500$	19.6826	+	9.03199i	0.880231	+	0.403923i
$501$		0			0
$502$	22.1700	−	14.2194i	0.989497	−	0.634641i
$503$	37.1489			1.65639			0.828195	−	0.560440i	$-0.189368\pi$
$503$	37.1489			1.65639			0.828195	+	0.560440i	$0.189368\pi$
$504$		0			0
$505$	3.20506			0.142623
$506$	−18.9011	+	12.1227i	−0.840254	+	0.538920i
$507$		0			0
$508$	−28.2254	−	12.9521i	−1.25230	−	0.574659i
$509$	−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
$514$	2.76643	−	0.129262i	0.122022	−	0.00570151i
$515$	13.4078	−	7.74100i	0.590818	−	0.341109i
$516$		0			0
$517$		−	9.37873i		−	0.412476i
$518$	−11.4086	+	39.5175i	−0.501264	+	1.73630i
$519$		0			0
$520$	−16.7223	−	6.74754i	−0.733321	−	0.295899i
$521$	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	$-0.565436\pi$
$523$	17.0542	−	29.5387i	0.745726	−	1.29164i	0.949855	−	0.312691i	$-0.101231\pi$
$524$	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
$530$	−4.61734	−	7.19910i	−0.200565	−	0.312709i
$531$		0			0
$532$	−8.77508	−	29.4881i	−0.380448	−	1.27847i
$533$	−22.3572			−0.968397
$534$		0			0
$535$	−6.27093	−	10.8616i	−0.271116	−	0.469587i
$536$	−13.7891	−	17.6329i	−0.595596	−	0.761626i
$537$		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	$0.00137118\pi$
$542$	1.05923	+	22.6693i	0.0454978	+	0.973732i
$543$		0			0
$544$	−44.7318	+	10.6369i	−1.91786	+	0.456052i
$545$		−	9.51148i		−	0.407427i
$546$		0			0
$547$		−	15.3659i		−	0.657000i	−0.944504	−	0.328500i	$-0.893457\pi$
$547$		−	15.3659i		−	0.657000i	0.944504	−	0.328500i	$-0.106543\pi$
$548$	−13.2425	+	1.24023i	−0.565693	+	0.0529799i
$549$		0			0
$550$	−8.94578	+	0.417993i	−0.381449	+	0.0178233i
$551$	−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
$556$	−5.16724	+	11.2605i	−0.219140	+	0.477550i
$557$	−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
$560$	−1.94075	+	13.6747i	−0.0820117	+	0.577861i
$561$		0			0
$562$	−4.97925	+	3.19358i	−0.210037	+	0.134713i
$563$	9.76188	+	16.9081i	0.411414	+	0.712591i	0.995045	−	0.0994290i	$-0.0317016\pi$
$563$	9.76188	+	16.9081i	0.411414	+	0.712591i	−0.583630	+	0.812019i	$0.698368\pi$
$564$		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	0.0113526	−	0.999936i	$-0.496386\pi$
$571$	21.0998	−	12.1820i	0.882998	−	0.509799i	0.871646	+	0.490136i	$0.163053\pi$
$572$	18.6849	−	1.74993i	0.781257	−	0.0731684i
$573$		0			0
$574$	4.11280	+	16.6231i	0.171665	+	0.693835i
$575$			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	$0.223648\pi$
$578$	−3.23865	−	69.3127i	−0.134710	−	2.88303i
$579$		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
$584$	15.3717	+	19.6567i	0.636085	+	0.813401i
$585$		0			0
$586$	−5.45023	−	8.49769i	−0.225147	−	0.351037i
$587$	−14.4835			−0.597799			−0.298899	−	0.954285i	$-0.596620\pi$
$587$	−14.4835			−0.597799			−0.298899	+	0.954285i	$0.596620\pi$
$588$		0			0
$589$	7.93963			0.327147
$590$	−6.12025	−	9.54235i	−0.251967	−	0.392852i
$591$		0			0
$592$	43.2066	−	8.16462i	1.77578	−	0.335564i
$593$	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
$598$	−2.66538	−	57.0439i	−0.108996	−	2.33270i
$599$	24.1606	−	13.9491i	0.987175	−	0.569946i	0.0827463	−	0.996571i	$-0.473631\pi$
$599$	24.1606	−	13.9491i	0.987175	−	0.569946i	0.904429	+	0.426625i	$0.140298\pi$
$600$		0			0
$601$			29.4377i			1.20079i	0.799704	+	0.600395i	$0.204990\pi$
$601$			29.4377i			1.20079i	−0.799704	+	0.600395i	$0.795010\pi$
$602$	0.492340	+	1.98994i	0.0200663	+	0.0811039i
$603$		0			0
$604$	−1.91363	−	20.4328i	−0.0778645	−	0.831399i
$605$	8.26247	−	4.77034i	0.335917	−	0.193942i
$606$		0			0
$607$	−9.07621	+	15.7205i	−0.368392	+	0.638074i	−0.989314	−	0.145798i	$-0.953425\pi$
$607$	−9.07621	+	15.7205i	−0.368392	+	0.638074i	0.620922	+	0.783872i	$0.286758\pi$
$608$	−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	$0.792291\pi$
$614$	−10.3178	+	6.61762i	−0.416393	+	0.267065i
$615$		0			0
$616$	−4.73838	−	13.5708i	−0.190915	−	0.546783i
$617$	−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	0.800280	−	0.599627i	$-0.204684\pi$
$619$	−2.96448	−	5.13463i	−0.119153	−	0.206378i	−0.919432	+	0.393249i	$0.871351\pi$
$620$	−3.23951	−	1.48656i	−0.130102	−	0.0597016i
$621$		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
$626$	6.06570	−	0.283421i	0.242434	−	0.0113278i
$627$		0			0
$628$	−1.74000	−	18.5789i	−0.0694336	−	0.741378i
$629$			89.3499i			3.56261i
$630$		0			0
$631$			4.42267i			0.176064i	0.996118	+	0.0880319i	$0.0280578\pi$
$631$			4.42267i			0.176064i	−0.996118	+	0.0880319i	$0.971942\pi$
$632$	8.30516	−	20.5825i	0.330362	−	0.818728i
$633$		0			0
$634$	1.21605	+	26.0256i	0.0482955	+	1.03361i
$635$	−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
$640$	13.9837	−	4.74042i	0.552755	−	0.187382i
$641$	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	$-0.301346\pi$
$643$	29.6357			1.16872			0.584358	+	0.811496i	$0.301346\pi$
$644$	−41.9232	+	12.4755i	−1.65200	+	0.491603i
$645$		0			0
$646$	−36.0818	−	56.2567i	−1.41962	−	2.21339i
$647$	−4.51555	−	7.82116i	−0.177525	−	0.307482i	0.763507	−	0.645799i	$-0.223476\pi$
$647$	−4.51555	−	7.82116i	−0.177525	−	0.307482i	−0.941032	+	0.338317i	$0.890142\pi$
$648$		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
$656$	13.8787	−	11.9380i	0.541874	−	0.466099i
$657$		0			0
$658$	5.06729	−	17.5523i	0.197544	−	0.684259i
$659$			27.5761i			1.07421i	0.843515	+	0.537106i	$0.180482\pi$
$659$			27.5761i			1.07421i	−0.843515	+	0.537106i	$0.819518\pi$
$660$		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	$0.284743\pi$
$662$	−28.6845	+	1.34029i	−1.11485	+	0.0520917i
$663$		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
$668$	−10.5922	+	23.0826i	−0.409826	+	0.893095i
$669$		0			0
$670$	−12.2951	+	7.88582i	−0.475002	+	0.304656i
$671$	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	$0.874509\pi$
$674$	18.8063	−	12.0619i	0.724392	−	0.464609i
$675$		0			0
$676$	−9.06166	+	19.7472i	−0.348525	+	0.759508i
$677$	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
$682$	3.70543	−	0.173137i	0.141888	−	0.00662975i
$683$	−20.2982	+	11.7192i	−0.776690	+	0.448422i	−0.835256	−	0.549861i	$-0.814681\pi$
$683$	−20.2982	+	11.7192i	−0.776690	+	0.448422i	0.0585660	+	0.998284i	$0.481347\pi$
$684$		0			0
$685$			8.67914i			0.331613i
$686$	23.9900	+	10.5110i	0.915942	+	0.401312i
$687$		0			0
$688$	1.66142	−	1.42908i	0.0633409	−	0.0544834i
$689$	−19.6039	+	11.3183i	−0.746849	+	0.431193i
$690$		0			0
$691$	−13.3173	+	23.0662i	−0.506613	+	0.877480i	0.493358	+	0.869827i	$0.335769\pi$
$691$	−13.3173	+	23.0662i	−0.506613	+	0.877480i	−0.999971	+	0.00765314i	$0.997564\pi$
$692$	−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
$698$	2.17801	+	3.39583i	0.0824388	+	0.128534i
$699$		0			0
$700$	−16.9679	−	4.05110i	−0.641325	−	0.153117i
$701$	−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
$704$	−10.6647	+	11.0634i	−0.401942	+	0.416968i
$705$		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	$-0.0540617\pi$
$710$	0.401836	+	8.59999i	0.0150806	+	0.322752i
$711$		0			0
$712$	−2.41548	+	5.98622i	−0.0905238	+	0.224343i
$713$		−	11.2877i		−	0.422729i
$714$		0			0
$715$		−	12.2461i		−	0.457977i
$716$	1.22960	+	13.1291i	0.0459524	+	0.490657i
$717$		0			0
$718$	−26.2117	+	1.22475i	−0.978213	+	0.0457072i
$719$	13.6962	−	23.7225i	0.510783	−	0.884701i	−0.489139	−	0.872206i	$-0.662689\pi$
$719$	13.6962	−	23.7225i	0.510783	−	0.884701i	0.999922	−	0.0124958i	$-0.00397763\pi$
$720$		0			0
$721$	−23.6076	+	20.6825i	−0.879192	+	0.770258i
$722$	−18.6018	−	9.61129i	−0.692287	−	0.357695i
$723$		0			0
$724$	5.28063	+	2.42319i	0.196253	+	0.0900571i
$725$	5.62710	+	9.74643i	0.208985	+	0.361973i
$726$		0			0
$727$	21.1585			0.784727			0.392364	−	0.919810i	$-0.371658\pi$
$727$	21.1585			0.784727			0.392364	+	0.919810i	$0.371658\pi$
$728$	35.9143	+	6.82040i	1.33107	+	0.252781i
$729$		0			0
$730$	13.7063	−	8.79091i	0.507293	−	0.325366i
$731$	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	−0.666697	−	0.745329i	$-0.732293\pi$
$739$	−9.63890	+	5.56502i	−0.354573	+	0.204713i	0.312125	+	0.950041i	$0.398959\pi$
$740$	−2.67554	−	28.5681i	−0.0983547	−	1.05018i
$741$		0			0
$742$	12.0217	+	12.4939i	0.441332	+	0.458664i
$743$			17.6900i			0.648983i	0.945889	+	0.324491i	$0.105193\pi$
$743$			17.6900i			0.648983i	−0.945889	+	0.324491i	$0.894807\pi$
$744$		0			0
$745$	15.3642	−	8.87050i	0.562899	−	0.324990i
$746$	−0.328092	−	7.02174i	−0.0120123	−	0.257084i
$747$		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	0.684376	−	0.729129i	$-0.260075\pi$
$751$	10.8280	+	6.25156i	0.395120	+	0.228123i	−0.289256	+	0.957252i	$0.593408\pi$
$752$	−19.1909	+	3.62644i	−0.699819	+	0.132243i
$753$		0			0
$754$	−12.7323	−	19.8514i	−0.463681	−	0.722946i
$755$	−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	$0.512394\pi$
$758$	−3.39700	−	5.29642i	−0.123385	−	0.192375i
$759$		0			0
$760$	13.2211	+	16.9067i	0.479580	+	0.613269i
$761$	−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
$766$	−0.730329	−	15.6303i	−0.0263878	−	0.564746i
$767$	−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	$0.799460\pi$
$770$	−9.10525	+	2.25277i	−0.328131	+	0.0811843i
$771$		0			0
$772$	−28.6476	+	2.68299i	−1.03105	+	0.0965627i
$773$	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
$782$	−79.9799	+	51.2973i	−2.86008	+	1.83439i
$783$		0			0
$784$	−1.53562	−	27.9579i	−0.0548437	−	0.998495i
$785$	−12.1766			−0.434600
$786$		0			0
$787$	−22.7245	−	39.3600i	−0.810042	−	1.40303i	−0.912834	−	0.408331i	$-0.866111\pi$
$787$	−22.7245	−	39.3600i	−0.810042	−	1.40303i	0.102792	−	0.994703i	$-0.467222\pi$
$788$	−10.0198	+	21.8351i	−0.356939	+	0.777844i
$789$		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
$794$	−46.7756	+	2.18560i	−1.66000	+	0.0775639i
$795$		0			0
$796$	−21.2597	+	1.99108i	−0.753531	+	0.0705718i
$797$		−	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
$800$	4.31434	+	18.1433i	0.152535	+	0.641464i
$801$		0			0
$802$	−2.12249	−	45.4250i	−0.0749478	−	1.60401i
$803$	−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
$808$	4.27891	+	5.47170i	0.150531	+	0.192494i
$809$	−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	$-0.629257\pi$
$811$	−22.4980			−0.790010			−0.395005	+	0.918679i	$0.629257\pi$
$812$	−12.4178	+	13.1186i	−0.435779	+	0.460372i
$813$		0			0
$814$	16.1216	+	25.1359i	0.565062	+	0.881013i
$815$	−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	−0.903177	−	0.429269i	$-0.858771\pi$
$823$	−28.2005	+	16.2815i	−0.983007	+	0.567539i	−0.0798301	+	0.996808i	$0.525438\pi$
$824$	31.1155	+	12.5553i	1.08396	+	0.437385i
$825$		0			0
$826$	15.9347	+	16.5605i	0.554440	+	0.576214i
$827$			19.7347i			0.686243i	0.939291	+	0.343122i	$0.111484\pi$
$827$			19.7347i			0.686243i	−0.939291	+	0.343122i	$0.888516\pi$
$828$		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	$0.388947\pi$
$830$	4.11469	−	0.192260i	0.142823	−	0.00667343i
$831$		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
$836$	−20.3010	−	9.31580i	−0.702126	−	0.322194i
$837$		0			0
$838$	−18.9725	+	12.1685i	−0.655395	+	0.420355i
$839$	−3.95140			−0.136418			−0.0682088	−	0.997671i	$-0.521728\pi$
$839$	−3.95140			−0.136418			−0.0682088	+	0.997671i	$0.521728\pi$
$840$		0			0
$841$	−17.3465			−0.598154
$842$	−3.05171	+	1.95730i	−0.105169	+	0.0674530i
$843$		0			0
$844$	−41.5350	−	19.0597i	−1.42969	−	0.656062i
$845$	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
$850$	−37.8541	+	1.76874i	−1.29839	+	0.0606673i
$851$	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	$0.731695\pi$
$854$	36.4188	+	10.5140i	1.24622	+	0.359781i
$855$		0			0
$856$	10.1710	−	25.2065i	0.347637	−	0.861540i
$857$	−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	−0.859407	−	0.511293i	$-0.829167\pi$
$859$	0.383633	−	0.664472i	0.0130894	−	0.0226715i	0.872496	+	0.488621i	$0.162500\pi$
$860$	−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	0.377066	−	0.926186i	$-0.376933\pi$
$863$	−6.94767	−	4.01124i	−0.236501	−	0.136544i	−0.613568	+	0.789642i	$0.710266\pi$
$864$		0			0
$865$	0.369778	+	0.640474i	0.0125728	+	0.0217768i
$866$	17.0729	+	26.6191i	0.580162	+	0.904555i
$867$		0			0
$868$	7.02826	+	1.67800i	0.238555	+	0.0569552i
$869$	15.0730			0.511316
$870$		0			0
$871$	19.3302	+	33.4809i	0.654979	+	1.13446i
$872$	16.2381	−	12.6983i	0.549890	−	0.430018i
$873$		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	$0.329670\pi$
$878$	−2.23648	−	47.8645i	−0.0754774	−	1.61535i
$879$		0			0
$880$	6.53898	+	7.60204i	0.220429	+	0.256265i
$881$		−	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	$-0.851745\pi$
$883$		−	26.6902i		−	0.898197i	0.893482	−	0.449099i	$-0.148255\pi$
$884$	79.0654	−	7.40486i	2.65926	−	0.249052i
$885$		0			0
$886$	−10.6568	+	0.497940i	−0.358022	+	0.0167286i
$887$	4.24240	−	7.34804i	0.142446	−	0.246723i	−0.785971	−	0.618263i	$-0.787837\pi$
$887$	4.24240	−	7.34804i	0.142446	−	0.246723i	0.928417	+	0.371540i	$0.121170\pi$
$888$		0			0
$889$	13.2248	−	38.8955i	0.443545	−	1.30451i
$890$	3.74227	+	1.93358i	0.125441	+	0.0648137i
$891$		0			0
$892$	−11.5344	+	25.1358i	−0.386200	+	0.841609i
$893$	−14.1944	−	24.5854i	−0.474997	−	0.822719i
$894$		0			0
$895$	8.60478			0.287626
$896$	−25.9365	+	14.9431i	−0.866479	+	0.499214i
$897$		0			0
$898$	34.5373	−	22.1515i	1.15252	−	0.739204i
$899$	−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	−0.875069	−	0.483998i	$-0.839184\pi$
$907$	−26.9075	+	15.5351i	−0.893449	+	0.515833i	−0.0183800	+	0.999831i	$0.505851\pi$
$908$	29.6715	−	2.77887i	0.984682	−	0.0922202i
$909$		0			0
$910$	6.61651	−	22.9185i	0.219335	−	0.759742i
$911$		−	15.2537i		−	0.505377i	−0.967548	−	0.252688i	$-0.918685\pi$
$911$		−	15.2537i		−	0.505377i	0.967548	−	0.252688i	$-0.0813148\pi$
$912$		0			0
$913$	−3.71260	+	2.14347i	−0.122869	+	0.0709385i
$914$	−0.126472	−	2.70671i	−0.00418331	−	0.0895302i
$915$		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	−0.00861810	−	0.999963i	$-0.502743\pi$
$919$	−26.6445	−	15.3832i	−0.878920	−	0.507445i	−0.870302	+	0.492518i	$0.836077\pi$
$920$	24.0361	−	18.7964i	0.792447	−	0.619699i
$921$		0			0
$922$	3.17724	+	4.95378i	0.104637	+	0.163144i
$923$	22.7869			0.750039
$924$		0			0
$925$	36.2406			1.19158
$926$	−12.7210	−	19.8338i	−0.418037	−	0.651779i
$927$		0			0
$928$	18.5038	+	5.52465i	0.607417	+	0.181356i
$929$	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
$934$	1.57075	+	33.6167i	0.0513964	+	1.09997i
$935$	−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	$-0.0818798\pi$
$938$	21.3379	−	20.5316i	0.696707	−	0.670380i
$939$		0			0
$940$	1.18838	+	12.6890i	0.0387607	+	0.413868i
$941$	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	−0.0366829	−	0.999327i	$-0.511679\pi$
$947$	−28.3259	−	16.3539i	−0.920467	−	0.531432i	−0.883784	+	0.467895i	$0.845012\pi$
$948$		0			0
$949$	−21.5488	−	37.3236i	−0.699504	−	1.21158i
$950$	−22.8179	+	14.6349i	−0.740309	+	0.474818i
$951$		0			0
$952$	−20.0505	−	57.4249i	−0.649839	−	1.86115i
$953$	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
$956$	22.0917	+	10.1375i	0.714496	+	0.327870i
$957$		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
$962$	−75.8608	+	3.54461i	−2.44585	+	0.114283i
$963$		0			0
$964$	−0.00392301	−	0.0418880i	−0.000126352	−	0.00134912i
$965$			18.7756i			0.604407i
$966$		0			0
$967$			19.1306i			0.615198i	0.951516	+	0.307599i	$0.0995256\pi$
$967$			19.1306i			0.615198i	−0.951516	+	0.307599i	$0.900474\pi$
$968$	19.1747	+	7.73712i	0.616299	+	0.248681i
$969$		0			0
$970$	−0.246745	−	5.28078i	−0.00792251	−	0.169556i
$971$	12.6574	−	21.9233i	0.406196	−	0.703552i	−0.588264	−	0.808669i	$-0.700188\pi$
$971$	12.6574	−	21.9233i	0.406196	−	0.703552i	0.994460	+	0.105117i	$0.0335218\pi$
$972$		0			0
$973$	−15.5173	−	5.27601i	−0.497461	−	0.169141i
$974$	20.5952	−	39.8601i	0.659913	−	1.27720i
$975$		0			0
$976$	−7.52441	−	39.8186i	−0.240850	−	1.27456i
$977$	−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
$980$	−18.2576	−	0.703471i	−0.583219	−	0.0224716i
$981$		0			0
$982$	−28.9141	−	45.0812i	−0.922685	−	1.43860i
$983$	15.9395	+	27.6080i	0.508390	+	0.880558i	0.999953	+	0.00971556i	$0.00309261\pi$
$983$	15.9395	+	27.6080i	0.508390	+	0.880558i	−0.491562	+	0.870842i	$0.663574\pi$
$984$		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	0.457210	−	0.889359i	$-0.348849\pi$
$991$	45.8358	−	26.4633i	1.45602	−	0.840635i	0.998812	+	0.0487244i	$0.0155156\pi$
$992$	−1.78704	−	7.51515i	−0.0567386	−	0.238606i
$993$		0			0
$994$	−4.19185	−	16.9426i	−0.132957	−	0.537387i
$995$			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	$0.592453\pi$
$998$	48.6079	−	2.27121i	1.53866	−	0.0718940i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.19041 - 0.763500i) q^{2} +(0.834135 - 1.81775i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(2.50492 + 0.851694i) q^{7} +(-0.394894 - 2.80072i) q^{8} +O(q^{10})\)	\(q+(1.19041 - 0.763500i) q^{2} +(0.834135 - 1.81775i) q^{4} +(-1.13024 - 0.652543i) q^{5} +(2.50492 + 0.851694i) q^{7} +(-0.394894 - 2.80072i) q^{8} +(-1.84366 + 0.0861452i) q^{10} +(1.66349 - 0.960419i) q^{11} +4.88503i q^{13} +(3.63214 - 0.898644i) q^{14} +(-2.60844 - 3.03250i) q^{16} +(7.03908 - 4.06402i) q^{17} +(2.90712 - 5.03529i) q^{19} +(-2.12893 + 1.51018i) q^{20} +(1.24695 - 2.41337i) q^{22} +(-7.15864 - 4.13305i) q^{23} +(-1.64838 - 2.85507i) q^{25} +(3.72972 + 5.81517i) q^{26} +(3.63761 - 3.84289i) q^{28} -3.41373 q^{29} +(0.682773 + 1.18260i) q^{31} +(-5.42041 - 1.61836i) q^{32} +(5.27649 - 10.2122i) q^{34} +(-2.27539 - 2.59718i) q^{35} +(-5.49640 + 9.52005i) q^{37} +(-0.383783 - 8.21363i) q^{38} +(-1.38127 + 3.42317i) q^{40} +4.57667i q^{41} +0.547870i q^{43} +(-0.358224 - 3.82494i) q^{44} +(-11.6773 + 0.545623i) q^{46} +(2.44131 - 4.22848i) q^{47} +(5.54924 + 4.26685i) q^{49} +(-4.14208 - 2.14016i) q^{50} +(8.87977 + 4.07478i) q^{52} +(2.31694 + 4.01305i) q^{53} -2.50686 q^{55} +(1.39618 - 7.35192i) q^{56} +(-4.06372 + 2.60638i) q^{58} +(3.07108 + 5.31927i) q^{59} +(8.77355 + 5.06541i) q^{61} +(1.71569 + 0.886475i) q^{62} +(-7.68812 + 2.21198i) q^{64} +(3.18769 - 5.52124i) q^{65} +(6.85377 - 3.95703i) q^{67} +(-1.51583 - 16.1852i) q^{68} +(-4.69158 - 1.35445i) q^{70} -4.66463i q^{71} +(-7.64041 + 4.41119i) q^{73} +(0.725606 + 15.5292i) q^{74} +(-6.72796 - 9.48453i) q^{76} +(4.98490 - 0.988983i) q^{77} +(6.79578 + 3.92355i) q^{79} +(0.969318 + 5.12956i) q^{80} +(3.49429 + 5.44810i) q^{82} -2.23181 q^{83} -10.6078 q^{85} +(0.418299 + 0.652188i) q^{86} +(-3.34677 - 4.27973i) q^{88} +(-1.97649 - 1.14113i) q^{89} +(-4.16055 + 12.2366i) q^{91} +(-13.4841 + 9.56512i) q^{92} +(-0.322289 - 6.89755i) q^{94} +(-6.57148 + 3.79404i) q^{95} +2.86429i q^{97} +(9.86358 + 0.842440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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