LMFDB - Embedded newform 414.2.p.a.113.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.19
Character	$\chi$	$=$	414.113
Dual form			414.2.p.a.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998867 + 0.0475819i) q^{2} +(0.528452 - 1.64947i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.691050 + 0.658915i) q^{5} +(0.606339 - 1.62245i) q^{6} +(0.416494 - 2.16098i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.44148 - 1.74333i) q^{9} +O(q^{10})$	\(q+(0.998867 + 0.0475819i) q^{2} +(0.528452 - 1.64947i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.691050 + 0.658915i) q^{5} +(0.606339 - 1.62245i) q^{6} +(0.416494 - 2.16098i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.44148 - 1.74333i) q^{9} +(-0.721620 + 0.625287i) q^{10} +(-0.655914 - 0.338147i) q^{11} +(0.682851 - 1.59176i) q^{12} +(4.85504 - 0.935732i) q^{13} +(0.518846 - 2.13871i) q^{14} +(0.721671 + 1.48807i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.66314 - 3.64176i) q^{17} +(-2.35576 - 1.85752i) q^{18} +(0.529556 - 0.241840i) q^{19} +(-0.750555 + 0.590243i) q^{20} +(-3.34436 - 1.82897i) q^{21} +(-0.639082 - 0.368974i) q^{22} +(-4.76578 - 0.536043i) q^{23} +(0.757817 - 1.55747i) q^{24} +(-0.194528 + 4.08365i) q^{25} +(4.89406 - 0.703660i) q^{26} +(-4.16576 + 3.10587i) q^{27} +(0.620023 - 2.11160i) q^{28} +(0.917207 + 9.60542i) q^{29} +(0.650048 + 1.52072i) q^{30} +(-0.120727 - 0.0949405i) q^{31} +(0.971812 + 0.235759i) q^{32} +(-0.904382 + 0.903214i) q^{33} +(1.83453 - 3.55850i) q^{34} +(1.13608 + 1.76778i) q^{35} +(-2.26471 - 1.96751i) q^{36} +(-0.607266 - 2.06816i) q^{37} +(0.540464 - 0.216369i) q^{38} +(1.02220 - 8.50271i) q^{39} +(-0.777790 + 0.553861i) q^{40} +(3.01873 + 3.16595i) q^{41} +(-3.25355 - 1.98603i) q^{42} +(0.165565 + 0.210533i) q^{43} +(-0.620801 - 0.398965i) q^{44} +(2.83589 - 0.403998i) q^{45} +(-4.73488 - 0.762201i) q^{46} +(-6.99317 + 4.03751i) q^{47} +(0.831066 - 1.51965i) q^{48} +(2.00221 + 0.801566i) q^{49} +(-0.388616 + 4.06977i) q^{50} +(-5.12807 - 4.66779i) q^{51} +(4.92200 - 0.469994i) q^{52} +(3.10406 - 3.58228i) q^{53} +(-4.30883 + 2.90413i) q^{54} +(0.676080 - 0.198515i) q^{55} +(0.719794 - 2.07971i) q^{56} +(-0.119062 - 1.00129i) q^{57} +(0.459123 + 9.63819i) q^{58} +(1.64391 + 8.52943i) q^{59} +(0.576953 + 1.54993i) q^{60} +(4.64436 + 11.6010i) q^{61} +(-0.116072 - 0.100577i) q^{62} +(-4.78416 + 4.54989i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.73851 + 3.84570i) q^{65} +(-0.946334 + 0.859158i) q^{66} +(-7.23072 - 14.0256i) q^{67} +(2.00178 - 3.46718i) q^{68} +(-3.40267 + 7.57772i) q^{69} +(1.05068 + 1.81983i) q^{70} +(-1.03028 + 1.60314i) q^{71} +(-2.16852 - 2.07304i) q^{72} +(-1.80797 - 3.95890i) q^{73} +(-0.508171 - 2.09471i) q^{74} +(6.63304 + 2.47888i) q^{75} +(0.550147 - 0.190408i) q^{76} +(-1.00391 + 1.27658i) q^{77} +(1.42562 - 8.44444i) q^{78} +(11.8552 + 4.10314i) q^{79} +(-0.803262 + 0.516225i) q^{80} +(2.92161 + 8.51259i) q^{81} +(2.86467 + 3.30600i) q^{82} +(0.124068 + 0.118299i) q^{83} +(-3.15537 - 2.13859i) q^{84} +(1.25030 + 3.61251i) q^{85} +(0.155360 + 0.218172i) q^{86} +(16.3285 + 3.56311i) q^{87} +(-0.601115 - 0.428052i) q^{88} +(-0.286790 - 1.99467i) q^{89} +(2.85190 - 0.268603i) q^{90} -10.8814i q^{91} +(-4.69325 - 0.986632i) q^{92} +(-0.220399 + 0.148963i) q^{93} +(-7.17736 + 3.70019i) q^{94} +(-0.206598 + 0.516056i) q^{95} +(0.902432 - 1.47838i) q^{96} +(-10.6880 + 2.59288i) q^{97} +(1.96181 + 0.895927i) q^{98} +(1.01190 + 1.96905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{22}\right)$

Coefficient data

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

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

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

$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$2$	0.998867	+	0.0475819i	0.706306	+	0.0336455i
$3$	0.528452	−	1.64947i	0.305102	−	0.952320i
$3$	0.528452	−	1.64947i	0.305102	−	0.952320i
$4$	0.995472	+	0.0950560i	0.497736	+	0.0475280i
$5$	−0.691050	+	0.658915i	−0.309047	+	0.294676i	−0.828690	−	0.559708i	$-0.810913\pi$
$5$	−0.691050	+	0.658915i	−0.309047	+	0.294676i	0.519643	+	0.854383i	$0.326065\pi$
$6$	0.606339	−	1.62245i	0.247537	−	0.662364i
$7$	0.416494	−	2.16098i	0.157420	−	0.816773i	−0.814265	−	0.580493i	$-0.802860\pi$
$7$	0.416494	−	2.16098i	0.157420	−	0.816773i	0.971685	−	0.236280i	$-0.0759282\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	−2.44148	−	1.74333i	−0.813825	−	0.581109i
$10$	−0.721620	+	0.625287i	−0.228196	+	0.197733i
$11$	−0.655914	−	0.338147i	−0.197766	−	0.101955i	0.356499	−	0.934296i	$-0.383970\pi$
$11$	−0.655914	−	0.338147i	−0.197766	−	0.101955i	−0.554265	+	0.832340i	$0.687001\pi$
$12$	0.682851	−	1.59176i	0.197122	−	0.459503i
$13$	4.85504	−	0.935732i	1.34655	−	0.259525i	0.535513	−	0.844527i	$-0.320118\pi$
$13$	4.85504	−	0.935732i	1.34655	−	0.259525i	0.811032	+	0.585001i	$0.198906\pi$
$14$	0.518846	−	2.13871i	0.138667	−	0.571595i
$15$	0.721671	+	1.48807i	0.186335	+	0.384218i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	1.66314	−	3.64176i	0.403370	−	0.883257i	−0.593548	−	0.804799i	$-0.702273\pi$
$17$	1.66314	−	3.64176i	0.403370	−	0.883257i	0.996917	−	0.0784580i	$-0.0249996\pi$
$18$	−2.35576	−	1.85752i	−0.555258	−	0.437823i
$19$	0.529556	−	0.241840i	0.121489	−	0.0554820i	−0.353743	−	0.935342i	$-0.615091\pi$
$19$	0.529556	−	0.241840i	0.121489	−	0.0554820i	0.475232	+	0.879861i	$0.342364\pi$
$20$	−0.750555	+	0.590243i	−0.167829	+	0.131982i
$21$	−3.34436	−	1.82897i	−0.729800	−	0.399113i
$22$	−0.639082	−	0.368974i	−0.136253	−	0.0786655i
$23$	−4.76578	−	0.536043i	−0.993734	−	0.111773i
$23$	−4.76578	−	0.536043i	−0.993734	−	0.111773i
$24$	0.757817	−	1.55747i	0.154689	−	0.317917i
$25$	−0.194528	+	4.08365i	−0.0389056	+	0.816730i
$26$	4.89406	−	0.703660i	0.959805	−	0.137999i
$27$	−4.16576	+	3.10587i	−0.801702	+	0.597724i
$28$	0.620023	−	2.11160i	0.117173	−	0.399055i
$29$	0.917207	+	9.60542i	0.170321	+	1.78368i	0.527409	+	0.849612i	$0.323164\pi$
$29$	0.917207	+	9.60542i	0.170321	+	1.78368i	−0.357088	+	0.934071i	$0.616230\pi$
$30$	0.650048	+	1.52072i	0.118682	+	0.277645i
$31$	−0.120727	−	0.0949405i	−0.0216831	−	0.0170518i	0.607259	−	0.794504i	$-0.292269\pi$
$31$	−0.120727	−	0.0949405i	−0.0216831	−	0.0170518i	−0.628942	+	0.777452i	$0.716512\pi$
$32$	0.971812	+	0.235759i	0.171794	+	0.0416767i
$33$	−0.904382	+	0.903214i	−0.157433	+	0.157229i
$34$	1.83453	−	3.55850i	0.314620	−	0.610278i
$35$	1.13608	+	1.76778i	0.192033	+	0.298809i
$36$	−2.26471	−	1.96751i	−0.377451	−	0.327919i
$37$	−0.607266	−	2.06816i	−0.0998339	−	0.340003i	0.894396	−	0.447277i	$-0.147606\pi$
$37$	−0.607266	−	2.06816i	−0.0998339	−	0.340003i	−0.994230	+	0.107274i	$0.965788\pi$
$38$	0.540464	−	0.216369i	0.0876748	−	0.0350997i
$39$	1.02220	−	8.50271i	0.163683	−	1.36152i
$40$	−0.777790	+	0.553861i	−0.122979	+	0.0875732i
$41$	3.01873	+	3.16595i	0.471446	+	0.494438i	0.915924	−	0.401351i	$-0.131459\pi$
$41$	3.01873	+	3.16595i	0.471446	+	0.494438i	−0.444478	+	0.895790i	$0.646611\pi$
$42$	−3.25355	−	1.98603i	−0.502034	−	0.306451i
$43$	0.165565	+	0.210533i	0.0252484	+	0.0321059i	0.798513	−	0.601977i	$-0.205620\pi$
$43$	0.165565	+	0.210533i	0.0252484	+	0.0321059i	−0.773265	+	0.634083i	$0.781378\pi$
$44$	−0.620801	−	0.398965i	−0.0935893	−	0.0601462i
$45$	2.83589	−	0.403998i	0.422749	−	0.0602244i
$46$	−4.73488	−	0.762201i	−0.698119	−	0.112380i
$47$	−6.99317	+	4.03751i	−1.02006	+	0.588931i	−0.914121	−	0.405441i	$-0.867118\pi$
$47$	−6.99317	+	4.03751i	−1.02006	+	0.588931i	−0.105938	+	0.994373i	$0.533785\pi$
$48$	0.831066	−	1.51965i	0.119954	−	0.219342i
$49$	2.00221	+	0.801566i	0.286031	+	0.114509i
$50$	−0.388616	+	4.06977i	−0.0549586	+	0.575552i
$51$	−5.12807	−	4.66779i	−0.718074	−	0.653621i
$52$	4.92200	−	0.469994i	0.682559	−	0.0651765i
$53$	3.10406	−	3.58228i	0.426376	−	0.492064i	−0.501393	−	0.865220i	$-0.667179\pi$
$53$	3.10406	−	3.58228i	0.426376	−	0.492064i	0.927769	+	0.373156i	$0.121724\pi$
$54$	−4.30883	+	2.90413i	−0.586357	+	0.395202i
$55$	0.676080	−	0.198515i	0.0911626	−	0.0267678i
$56$	0.719794	−	2.07971i	0.0961866	−	0.277913i
$57$	−0.119062	−	1.00129i	−0.0157701	−	0.132624i
$58$	0.459123	+	9.63819i	0.0602859	+	1.26556i
$59$	1.64391	+	8.52943i	0.214019	+	1.11044i	0.916896	+	0.399126i	$0.130686\pi$
$59$	1.64391	+	8.52943i	0.214019	+	1.11044i	−0.702877	+	0.711312i	$0.748101\pi$
$60$	0.576953	+	1.54993i	0.0744843	+	0.200095i
$61$	4.64436	+	11.6010i	0.594649	+	1.48536i	0.854363	+	0.519676i	$0.173947\pi$
$61$	4.64436	+	11.6010i	0.594649	+	1.48536i	−0.259714	+	0.965685i	$0.583628\pi$
$62$	−0.116072	−	0.100577i	−0.0147412	−	0.0127733i
$63$	−4.78416	+	4.54989i	−0.602747	+	0.573232i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−2.73851	+	3.84570i	−0.339670	+	0.477000i
$66$	−0.946334	+	0.859158i	−0.116486	+	0.105755i
$67$	−7.23072	−	14.0256i	−0.883373	−	1.71351i	−0.678337	−	0.734751i	$-0.737299\pi$
$67$	−7.23072	−	14.0256i	−0.883373	−	1.71351i	−0.205036	−	0.978754i	$-0.565731\pi$
$68$	2.00178	−	3.46718i	0.242751	−	0.420457i
$69$	−3.40267	+	7.57772i	−0.409634	+	0.912250i
$70$	1.05068	+	1.81983i	0.125580	+	0.217512i
$71$	−1.03028	+	1.60314i	−0.122271	+	0.190258i	−0.896993	−	0.442044i	$-0.854253\pi$
$71$	−1.03028	+	1.60314i	−0.122271	+	0.190258i	0.774722	+	0.632302i	$0.217890\pi$
$72$	−2.16852	−	2.07304i	−0.255563	−	0.244310i
$73$	−1.80797	−	3.95890i	−0.211607	−	0.463354i	0.773831	−	0.633393i	$-0.218338\pi$
$73$	−1.80797	−	3.95890i	−0.211607	−	0.463354i	−0.985437	+	0.170038i	$0.945611\pi$
$74$	−0.508171	−	2.09471i	−0.0590737	−	0.243505i
$75$	6.63304	+	2.47888i	0.765918	+	0.286237i
$76$	0.550147	−	0.190408i	0.0631062	−	0.0218413i
$77$	−1.00391	+	1.27658i	−0.114407	+	0.145480i
$78$	1.42562	−	8.44444i	0.161419	−	0.956145i
$79$	11.8552	+	4.10314i	1.33382	+	0.461639i	0.898633	−	0.438702i	$-0.144562\pi$
$79$	11.8552	+	4.10314i	1.33382	+	0.461639i	0.435185	+	0.900341i	$0.356683\pi$
$80$	−0.803262	+	0.516225i	−0.0898075	+	0.0577158i
$81$	2.92161	+	8.51259i	0.324624	+	0.945843i
$82$	2.86467	+	3.30600i	0.316350	+	0.365087i
$83$	0.124068	+	0.118299i	0.0136183	+	0.0129850i	0.696858	−	0.717210i	$-0.254581\pi$
$83$	0.124068	+	0.118299i	0.0136183	+	0.0129850i	−0.683239	+	0.730195i	$0.739429\pi$
$84$	−3.15537	−	2.13859i	−0.344279	−	0.233339i
$85$	1.25030	+	3.61251i	0.135614	+	0.391831i
$86$	0.155360	+	0.218172i	0.0167529	+	0.0235261i
$87$	16.3285	+	3.56311i	1.75060	+	0.382005i
$88$	−0.601115	−	0.428052i	−0.0640790	−	0.0456305i
$89$	−0.286790	−	1.99467i	−0.0303997	−	0.211435i	0.968960	−	0.247218i	$-0.0795164\pi$
$89$	−0.286790	−	1.99467i	−0.0303997	−	0.211435i	−0.999360	+	0.0357835i	$0.988607\pi$
$90$	2.85190	−	0.268603i	0.300616	−	0.0283133i
$91$		−	10.8814i		−	1.14068i
$92$	−4.69325	−	0.986632i	−0.489305	−	0.102863i
$93$	−0.220399	+	0.148963i	−0.0228543	+	0.0154467i
$94$	−7.17736	+	3.70019i	−0.740289	+	0.381645i
$95$	−0.206598	+	0.516056i	−0.0211965	+	0.0529463i
$96$	0.902432	−	1.47838i	0.0921041	−	0.150887i
$97$	−10.6880	+	2.59288i	−1.08520	+	0.263267i	−0.738189	−	0.674594i	$-0.764319\pi$
$97$	−10.6880	+	2.59288i	−1.08520	+	0.263267i	−0.347012	+	0.937861i	$0.612804\pi$
$98$	1.96181	+	0.895927i	0.198172	+	0.0905023i
$99$	1.01190	+	1.96905i	0.101699	+	0.197897i
$100$	−0.581823	+	4.04667i	−0.0581823	+	0.404667i
$101$	−3.30053	+	3.46149i	−0.328415	+	0.344431i	−0.867153	−	0.498042i	$-0.834053\pi$
$101$	−3.30053	+	3.46149i	−0.328415	+	0.344431i	0.538738	+	0.842473i	$0.318901\pi$
$102$	−4.90016	−	4.90650i	−0.485188	−	0.485816i
$103$	10.7662	−	0.512859i	1.06083	−	0.0505335i	0.490095	−	0.871669i	$-0.336962\pi$
$103$	10.7662	−	0.512859i	1.06083	−	0.0505335i	0.570734	+	0.821135i	$0.306659\pi$
$104$	4.93879	−	0.235264i	0.484288	−	0.0230695i
$105$	3.51626	−	0.939743i	0.343152	−	0.0917095i
$106$	3.27100	−	3.43053i	0.317708	−	0.333202i
$107$	0.0443043	−	0.308143i	0.00428306	−	0.0297894i	−0.987568	−	0.157193i	$-0.949755\pi$
$107$	0.0443043	−	0.308143i	0.00428306	−	0.0297894i	0.991851	+	0.127404i	$0.0406645\pi$
$108$	−4.44213	+	2.69582i	−0.427444	+	0.259406i
$109$	3.06729	+	1.40079i	0.293793	+	0.134171i	0.556859	−	0.830607i	$-0.312006\pi$
$109$	3.06729	+	1.40079i	0.293793	+	0.134171i	−0.263066	+	0.964778i	$0.584734\pi$
$110$	0.684760	−	0.166121i	0.0652893	−	0.0158390i
$111$	−3.73227	−	0.0912584i	−0.354251	−	0.00866186i
$112$	0.817936	−	2.04310i	0.0772877	−	0.193055i
$113$	−14.9344	+	7.69922i	−1.40491	+	0.724282i	−0.983214	−	0.182455i	$-0.941596\pi$
$113$	−14.9344	+	7.69922i	−1.40491	+	0.724282i	−0.421697	+	0.906737i	$0.638565\pi$
$114$	−0.0712840	−	1.00582i	−0.00667636	−	0.0942034i
$115$	3.64660	−	2.76981i	0.340047	−	0.258286i
$116$			9.64912i			0.895898i
$117$	−13.4847	−	6.17936i	−1.24667	−	0.571282i
$118$	1.23620	+	8.59799i	0.113802	+	0.791510i
$119$	−7.17708	−	5.11078i	−0.657922	−	0.468504i
$120$	0.502551	+	1.57563i	0.0458764	+	0.143834i
$121$	−6.06475	−	8.51674i	−0.551341	−	0.774249i
$122$	4.08710	+	11.8089i	0.370028	+	1.06913i
$123$	6.81738	−	3.30624i	0.614703	−	0.298113i
$124$	−0.111155	−	0.105986i	−0.00998204	−	0.00951786i
$125$	−5.68278	−	6.55828i	−0.508284	−	0.586591i
$126$	−4.99523	+	4.31710i	−0.445010	+	0.384598i
$127$	−1.75202	+	1.12595i	−0.155466	+	0.0999122i	−0.616061	−	0.787698i	$-0.711273\pi$
$127$	−1.75202	+	1.12595i	−0.155466	+	0.0999122i	0.460595	+	0.887611i	$0.347636\pi$
$128$	0.945001	+	0.327068i	0.0835271	+	0.0289090i
$129$	0.434759	−	0.161837i	0.0382784	−	0.0142489i
$130$	−2.91839	+	3.71104i	−0.255960	+	0.325479i
$131$	−10.4938	+	3.63196i	−0.916852	+	0.317325i	−0.744432	−	0.667698i	$-0.767280\pi$
$131$	−10.4938	+	3.63196i	−0.916852	+	0.317325i	−0.172420	+	0.985024i	$0.555159\pi$
$132$	−0.986143	+	0.813157i	−0.0858327	+	0.0707762i
$133$	−0.302054	−	1.24509i	−0.0261914	−	0.107963i
$134$	−6.55517	−	14.3538i	−0.566280	−	1.23998i
$135$	0.832251	−	4.89119i	0.0716287	−	0.420967i
$136$	2.16449	−	3.36800i	0.185603	−	0.288804i
$137$	3.17587	+	5.50077i	0.271333	+	0.469962i	0.969203	−	0.246262i	$-0.0792022\pi$
$137$	3.17587	+	5.50077i	0.271333	+	0.469962i	−0.697870	+	0.716224i	$0.745869\pi$
$138$	−3.75938	+	7.40723i	−0.320020	+	0.630545i
$139$	0.127920	−	0.221564i	0.0108500	−	0.0187928i	−0.860549	−	0.509367i	$-0.829880\pi$
$139$	0.127920	−	0.221564i	0.0108500	−	0.0187928i	0.871399	+	0.490574i	$0.163213\pi$
$140$	0.962900	+	1.86777i	0.0813799	+	0.157855i
$141$	2.96418	+	13.6686i	0.249629	+	1.15111i
$142$	−1.10539	+	1.55230i	−0.0927624	+	0.130267i
$143$	−3.50090	−	1.02796i	−0.292760	−	0.0859622i
$144$	−2.06743	−	2.17388i	−0.172286	−	0.181156i
$145$	−6.96299	−	6.03347i	−0.578245	−	0.501052i
$146$	−1.61755	−	4.04044i	−0.133869	−	0.334390i
$147$	2.38023	−	2.87900i	0.196318	−	0.237456i
$148$	−0.407925	−	2.11652i	−0.0335313	−	0.173977i
$149$	−0.176471	−	3.70459i	−0.0144571	−	0.303491i	−0.994502	−	0.104716i	$-0.966607\pi$
$149$	−0.176471	−	3.70459i	−0.0144571	−	0.303491i	0.980045	−	0.198775i	$-0.0636964\pi$
$150$	6.50758	+	2.79169i	0.531342	+	0.227940i
$151$	5.51225	−	15.9266i	0.448580	−	1.29609i	−0.463507	−	0.886093i	$-0.653409\pi$
$151$	5.51225	−	15.9266i	0.448580	−	1.29609i	0.912088	−	0.409995i	$-0.134470\pi$
$152$	0.558584	−	0.164015i	0.0453071	−	0.0133034i
$153$	−10.4093	+	5.99188i	−0.841542	+	0.484415i
$154$	−1.06352	+	1.22737i	−0.0857008	+	0.0989040i
$155$	0.145986	−	0.0139400i	0.0117259	−	0.00111968i
$156$	1.82580	−	8.36704i	0.146181	−	0.669900i
$157$	2.04797	−	21.4473i	0.163446	−	1.71168i	−0.426706	−	0.904390i	$-0.640326\pi$
$157$	2.04797	−	21.4473i	0.163446	−	1.71168i	0.590152	−	0.807292i	$-0.299068\pi$
$158$	11.6466	+	4.66258i	0.926551	+	0.370935i
$159$	−4.26850	−	7.01311i	−0.338514	−	0.556176i
$160$	−0.826916	+	0.477420i	−0.0653734	+	0.0377434i
$161$	−3.14330	+	10.0755i	−0.247727	+	0.794060i
$162$	2.51326	+	8.64196i	0.197460	+	0.678977i
$163$	−0.827743	−	0.531958i	−0.0648338	−	0.0416662i	0.507822	−	0.861462i	$-0.330451\pi$
$163$	−0.827743	−	0.531958i	−0.0648338	−	0.0416662i	−0.572656	+	0.819796i	$0.694087\pi$
$164$	2.70412	+	3.43856i	0.211156	+	0.268507i
$165$	0.0298323	−	1.22008i	0.00232244	−	0.0949828i
$166$	0.118299	+	0.124068i	0.00918178	+	0.00962958i
$167$	10.6700	−	7.59804i	0.825666	−	0.587954i	−0.0872103	−	0.996190i	$-0.527795\pi$
$167$	10.6700	−	7.59804i	0.825666	−	0.587954i	0.912877	+	0.408236i	$0.133856\pi$
$168$	−3.05003	−	2.28630i	−0.235315	−	0.176392i
$169$	10.6270	−	4.25442i	0.817463	−	0.327263i
$170$	1.07699	+	3.66791i	0.0826017	+	0.281315i
$171$	−1.71451	−	0.332743i	−0.131112	−	0.0254455i
$172$	0.144803	+	0.225317i	0.0110411	+	0.0171803i
$173$	1.97460	−	3.83018i	0.150126	−	0.291203i	−0.801766	−	0.597638i	$-0.796106\pi$
$173$	1.97460	−	3.83018i	0.150126	−	0.291203i	0.951892	+	0.306435i	$0.0991362\pi$
$174$	16.1405	+	4.33601i	1.22361	+	0.328712i
$175$	8.74366	+	2.12119i	0.660959	+	0.160347i
$176$	−0.580066	−	0.456169i	−0.0437241	−	0.0343850i
$177$	14.9377	+	1.79582i	1.12279	+	0.134982i
$178$	−0.191555	−	2.00606i	−0.0143577	−	0.150360i
$179$	3.87999	−	13.2140i	0.290004	−	0.987663i	−0.677651	−	0.735384i	$-0.737002\pi$
$179$	3.87999	−	13.2140i	0.290004	−	0.987663i	0.967655	−	0.252279i	$-0.0811800\pi$
$180$	2.86145	−	0.132600i	0.213280	−	0.00988344i
$181$	−13.2393	+	1.90352i	−0.984070	+	0.141488i	−0.615521	−	0.788121i	$-0.711054\pi$
$181$	−13.2393	+	1.90352i	−0.984070	+	0.141488i	−0.368549	+	0.929608i	$0.620145\pi$
$182$	0.517756	−	10.8690i	0.0383786	−	0.805667i
$183$	21.5899	−	1.53011i	1.59597	−	0.113109i
$184$	−4.64098	−	1.20883i	−0.342138	−	0.0891160i
$185$	1.78239	+	1.02906i	0.131044	+	0.0756583i
$186$	−0.227238	+	0.138307i	−0.0166619	+	0.0101412i
$187$	−2.32233	+	1.82630i	−0.169825	+	0.133552i
$188$	−7.34530	+	3.35448i	−0.535711	+	0.244651i
$189$	4.97669	+	10.2957i	0.362001	+	0.748902i
$190$	−0.230919	+	0.505641i	−0.0167526	+	0.0366831i
$191$	−24.4742	−	4.71701i	−1.77089	−	0.341311i	−0.803636	−	0.595122i	$-0.797104\pi$
$191$	−24.4742	−	4.71701i	−1.77089	−	0.341311i	−0.967254	+	0.253811i	$0.918316\pi$
$192$	0.971755	−	1.43377i	0.0701303	−	0.103473i
$193$	−3.47624	+	14.3293i	−0.250225	+	1.03144i	0.698567	+	0.715544i	$0.253821\pi$
$193$	−3.47624	+	14.3293i	−0.250225	+	1.03144i	−0.948793	+	0.315899i	$0.897694\pi$
$194$	−10.7993	+	2.08139i	−0.775341	+	0.149435i
$195$	4.89617	+	6.54934i	0.350622	+	0.469008i
$196$	1.91695	+	0.988259i	0.136925	+	0.0705899i
$197$	17.8053	−	15.4284i	1.26858	−	1.09923i	0.278243	−	0.960511i	$-0.410248\pi$
$197$	17.8053	−	15.4284i	1.26858	−	1.09923i	0.990332	−	0.138716i	$-0.0442974\pi$
$198$	0.917060	+	2.01497i	0.0651726	+	0.143198i
$199$	7.47699	+	1.07503i	0.530030	+	0.0762068i	0.402134	−	0.915581i	$-0.368269\pi$
$199$	7.47699	+	1.07503i	0.530030	+	0.0762068i	0.127896	+	0.991788i	$0.459178\pi$
$200$	−0.773712	+	4.01440i	−0.0547097	+	0.283861i
$201$	−26.9559	+	4.51495i	−1.90132	+	0.318460i
$202$	−3.46149	+	3.30053i	−0.243550	+	0.232224i
$203$	21.1391	+	2.01854i	1.48368	+	0.141674i
$204$	−4.66115	−	5.13410i	−0.326346	−	0.359459i
$205$	−4.17218	−	0.198746i	−0.291398	−	0.0138810i
$206$	10.7784			0.750970
$207$	10.7010	+	9.61706i	0.743774	+	0.668432i
$208$	4.94439			0.342832
$209$	−0.429121	−	0.0204416i	−0.0296829	−	0.00141397i
$210$	3.55699	−	0.771368i	0.245456	−	0.0532294i
$211$	−1.17467	−	0.112167i	−0.0808674	−	0.00772190i	0.0545439	−	0.998511i	$-0.482630\pi$
$211$	−1.17467	−	0.112167i	−0.0808674	−	0.00772190i	−0.135411	+	0.990789i	$0.543236\pi$
$212$	3.43053	−	3.27100i	0.235609	−	0.224653i
$213$	2.09988	+	2.54659i	0.143881	+	0.174490i
$214$	0.0589162	−	0.305686i	0.00402743	−	0.0208963i
$215$	−0.253137	−	0.0363955i	−0.0172638	−	0.00248216i
$216$	−4.56537	+	2.48140i	−0.310634	+	0.168838i
$217$	−0.255446	+	0.221345i	−0.0173408	+	0.0150259i
$218$	2.99717	+	1.54515i	0.202994	+	0.104651i
$219$	−7.48550	+	0.890094i	−0.505823	+	0.0601470i
$220$	0.691889	−	0.133351i	0.0466471	−	0.00899050i
$221$	4.66688	−	19.2371i	0.313928	−	1.29403i
$222$	−3.72370	−	0.268744i	−0.249918	−	0.0180369i
$223$	−22.6473	−	4.36491i	−1.51658	−	0.292296i	−0.638052	−	0.769993i	$-0.720260\pi$
$223$	−22.6473	−	4.36491i	−1.51658	−	0.292296i	−0.878525	+	0.477697i	$0.841472\pi$
$224$	0.914224	−	2.00187i	0.0610842	−	0.133756i
$225$	7.59408	−	9.63101i	0.506272	−	0.642067i
$226$	−15.2838	+	6.97989i	−1.01667	+	0.464296i
$227$	8.70859	−	6.84851i	0.578009	−	0.454552i	−0.285857	−	0.958272i	$-0.592278\pi$
$227$	8.70859	−	6.84851i	0.578009	−	0.454552i	0.863867	+	0.503721i	$0.168036\pi$
$228$	−0.0233446	−	1.00807i	−0.00154603	−	0.0667611i
$229$	11.4460	+	6.60836i	0.756374	+	0.436693i	0.827992	−	0.560740i	$-0.189483\pi$
$229$	11.4460	+	6.60836i	0.756374	+	0.436693i	−0.0716185	+	0.997432i	$0.522816\pi$
$230$	3.77426	−	2.59316i	0.248867	−	0.170988i
$231$	1.57515	+	2.33053i	0.103638	+	0.153338i
$232$	−0.459123	+	9.63819i	−0.0301429	+	0.632778i
$233$	12.4694	−	1.79284i	0.816901	−	0.117453i	0.278817	−	0.960344i	$-0.410058\pi$
$233$	12.4694	−	1.79284i	0.816901	−	0.117453i	0.538083	+	0.842892i	$0.319149\pi$
$234$	−13.1754	−	6.81399i	−0.861306	−	0.445444i
$235$	2.17226	−	7.39803i	0.141702	−	0.482594i
$236$	0.825696	+	8.64708i	0.0537482	+	0.562877i
$237$	13.0329	−	17.3865i	0.846578	−	1.12937i
$238$	−6.92577	−	5.44649i	−0.448931	−	0.353043i
$239$	17.9609	+	4.35727i	1.16180	+	0.281849i	0.769902	−	0.638162i	$-0.220305\pi$
$239$	17.9609	+	4.35727i	1.16180	+	0.281849i	0.391894	+	0.920011i	$0.371820\pi$
$240$	0.427010	+	1.59775i	0.0275634	+	0.103135i
$241$	−11.8649	+	23.0146i	−0.764284	+	1.48250i	0.108342	+	0.994114i	$0.465446\pi$
$241$	−11.8649	+	23.0146i	−0.764284	+	1.48250i	−0.872626	+	0.488390i	$0.837584\pi$
$242$	−5.65263	−	8.79567i	−0.363365	−	0.565407i
$243$	15.5852	−	0.320602i	0.999788	−	0.0205666i
$244$	3.52058	+	11.9900i	0.225382	+	0.767580i
$245$	−1.91179	+	0.765367i	−0.122140	+	0.0488975i
$246$	6.96698	−	2.97811i	0.444198	−	0.189877i
$247$	2.34472	−	1.66967i	0.149191	−	0.106238i
$248$	−0.105986	−	0.111155i	−0.00673014	−	0.00705837i
$249$	0.260694	−	0.142131i	0.0165208	−	0.00900720i
$250$	−5.36429	−	6.82125i	−0.339268	−	0.431414i
$251$	−23.1478	−	14.8762i	−1.46108	−	0.938978i	−0.998630	−	0.0523319i	$-0.983335\pi$
$251$	−23.1478	−	14.8762i	−1.46108	−	0.938978i	−0.462449	−	0.886646i	$-0.653029\pi$
$252$	−5.19499	+	4.07453i	−0.327254	+	0.256671i
$253$	2.94468	+	1.96313i	0.185131	+	0.123421i
$254$	−1.80361	+	1.04131i	−0.113168	+	0.0653379i
$255$	6.61943	−	0.153291i	0.414525	−	0.00959944i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−0.558130	+	5.84500i	−0.0348152	+	0.364601i	0.961230	+	0.275749i	$0.0889259\pi$
$257$	−0.558130	+	5.84500i	−0.0348152	+	0.364601i	−0.996045	+	0.0888521i	$0.971680\pi$
$258$	0.441968	−	0.140967i	0.0275157	−	0.00877621i
$259$	−4.72217	+	0.450912i	−0.293421	+	0.0280183i
$260$	−3.09166	+	3.56797i	−0.191737	+	0.221276i
$261$	14.5061	−	25.0504i	0.897903	−	1.55058i
$262$	−10.6548	+	3.12853i	−0.658254	+	0.193281i
$263$	−2.35353	+	6.80009i	−0.145125	+	0.419311i	−0.994013	−	0.109261i	$-0.965151\pi$
$263$	−2.35353	+	6.80009i	−0.145125	+	0.419311i	0.848888	+	0.528573i	$0.177273\pi$
$264$	−1.02372	+	0.765313i	−0.0630054	+	0.0471018i
$265$	0.215355	+	4.52085i	0.0132291	+	0.277714i
$266$	−0.242469	−	1.25805i	−0.0148667	−	0.0771358i
$267$	−3.44170	−	0.581037i	−0.210628	−	0.0355589i
$268$	−5.86476	−	14.6495i	−0.358247	−	0.894858i
$269$	−7.23732	−	6.27117i	−0.441267	−	0.382360i	0.405699	−	0.914007i	$-0.367028\pi$
$269$	−7.23732	−	6.27117i	−0.441267	−	0.382360i	−0.846966	+	0.531647i	$0.821573\pi$
$270$	1.06404	−	4.84605i	0.0647554	−	0.294921i
$271$	3.45106	+	1.01332i	0.209637	+	0.0615550i	0.384865	−	0.922973i	$-0.374248\pi$
$271$	3.45106	+	1.01332i	0.209637	+	0.0615550i	−0.175228	+	0.984528i	$0.556066\pi$
$272$	2.32229	−	3.26120i	0.140809	−	0.197739i
$273$	−17.9484	−	5.75028i	−1.08629	−	0.348023i
$274$	2.91054	+	5.64565i	0.175832	+	0.341066i
$275$	1.50847	−	2.61275i	0.0909641	−	0.157554i
$276$	−4.10757	+	7.21996i	−0.247247	+	0.434591i
$277$	−5.83707	−	10.1101i	−0.350715	−	0.607457i	0.635660	−	0.771969i	$-0.280728\pi$
$277$	−5.83707	−	10.1101i	−0.350715	−	0.607457i	−0.986375	+	0.164513i	$0.947395\pi$
$278$	0.138317	−	0.215226i	0.00829572	−	0.0129084i
$279$	0.129239	+	0.442261i	0.00773732	+	0.0264775i
$280$	0.872938	+	1.91147i	0.0521680	+	0.114232i
$281$	−5.16344	−	21.2840i	−0.308025	−	1.26970i	−0.889801	−	0.456348i	$-0.849157\pi$
$281$	−5.16344	−	21.2840i	−0.308025	−	1.26970i	0.581776	−	0.813349i	$-0.302358\pi$
$282$	2.31044	+	13.7942i	0.137585	+	0.821432i
$283$	9.75253	−	3.37538i	0.579727	−	0.200646i	−0.0214380	−	0.999770i	$-0.506824\pi$
$283$	9.75253	−	3.37538i	0.579727	−	0.200646i	0.601165	+	0.799125i	$0.294703\pi$
$284$	−1.17800	+	1.49795i	−0.0699015	+	0.0888870i
$285$	0.742040	+	0.613487i	0.0439547	+	0.0363398i
$286$	−3.44803	−	1.19337i	−0.203886	−	0.0705657i
$287$	8.09884	−	5.20481i	0.478059	−	0.307230i
$288$	−1.96165	−	2.26979i	−0.115591	−	0.133748i
$289$	0.636229	+	0.734248i	0.0374253	+	0.0431911i
$290$	−6.66802	−	6.35795i	−0.391560	−	0.373351i
$291$	−1.37123	+	18.9997i	−0.0803828	+	1.11378i
$292$	−1.42347	−	4.11283i	−0.0833020	−	0.240685i
$293$	6.10565	+	8.57419i	0.356696	+	0.500909i	0.953465	−	0.301504i	$-0.0974886\pi$
$293$	6.10565	+	8.57419i	0.356696	+	0.500909i	−0.596769	+	0.802413i	$0.703549\pi$
$294$	2.51452	−	2.76248i	0.146650	−	0.161111i
$295$	−6.75620	−	4.81107i	−0.393361	−	0.280111i
$296$	−0.306755	−	2.13353i	−0.0178298	−	0.124009i
$297$	3.78262	−	0.628540i	0.219490	−	0.0364716i
$298$		−	3.70879i		−	0.214844i
$299$	−23.6396	+	1.85698i	−1.36712	+	0.107392i
$300$	6.36738	+	3.09817i	0.367621	+	0.178873i
$301$	0.523913	−	0.270096i	0.0301979	−	0.0155681i
$302$	6.26382	−	15.6463i	0.360443	−	0.900342i
$303$	3.96544	+	7.27334i	0.227809	+	0.417842i
$304$	0.565755	−	0.137251i	0.0324483	−	0.00787187i
$305$	−10.8536	−	4.95667i	−0.621474	−	0.283818i
$306$	−10.6826	+	5.48980i	−0.610684	+	0.313831i
$307$	−2.30242	+	16.0137i	−0.131406	+	0.913948i	0.812318	+	0.583214i	$0.198205\pi$
$307$	−2.30242	+	16.0137i	−0.131406	+	0.913948i	−0.943724	+	0.330734i	$0.892704\pi$
$308$	−1.12071	+	1.17537i	−0.0638586	+	0.0669730i
$309$	4.84350	−	18.0296i	0.275537	−	1.02567i
$310$	0.146484	−	0.00697788i	0.00831972	−	0.000396317i
$311$	13.9836	−	0.666120i	0.792936	−	0.0377722i	0.352795	−	0.935701i	$-0.385231\pi$
$311$	13.9836	−	0.666120i	0.792936	−	0.0377722i	0.440141	+	0.897928i	$0.354928\pi$
$312$	2.22186	−	8.27069i	0.125788	−	0.468236i
$313$	−14.7078	+	15.4251i	−0.831333	+	0.871877i	−0.993376	−	0.114907i	$-0.963343\pi$
$313$	−14.7078	+	15.4251i	−0.831333	+	0.871877i	0.162043	+	0.986784i	$0.448192\pi$
$314$	3.06616	−	21.3256i	0.173033	−	1.20347i
$315$	0.308101	−	6.29655i	0.0173595	−	0.354771i
$316$	11.4115	+	5.21147i	0.641948	+	0.293168i
$317$	5.70793	−	1.38473i	0.320589	−	0.0777741i	−0.0722350	−	0.997388i	$-0.523013\pi$
$317$	5.70793	−	1.38473i	0.320589	−	0.0777741i	0.392824	+	0.919614i	$0.371498\pi$
$318$	−3.92997	−	7.20827i	−0.220382	−	0.404220i
$319$	2.64644	−	6.61049i	0.148172	−	0.370116i
$320$	−0.848695	+	0.437533i	−0.0474435	+	0.0244588i
$321$	−0.484859	−	0.235918i	−0.0270622	−	0.0131676i
$322$	−3.61915	+	9.91451i	−0.201687	+	0.552514i
$323$		−	2.33073i		−	0.129685i
$324$	2.09921	+	8.75176i	0.116623	+	0.486209i
$325$	2.87676	+	20.0083i	0.159574	+	1.10986i
$326$	−0.801493	−	0.570741i	−0.0443906	−	0.0316104i
$327$	3.93147	−	4.31915i	0.217411	−	0.238849i
$328$	2.53744	+	3.56334i	0.140107	+	0.196752i
$329$	5.81236	+	16.7937i	0.320446	+	0.925867i
$330$	0.0878521	−	1.21728i	0.00483610	−	0.0670088i
$331$	−10.0652	−	9.59712i	−0.553232	−	0.527505i	0.361070	−	0.932539i	$-0.382411\pi$
$331$	−10.0652	−	9.59712i	−0.553232	−	0.527505i	−0.914302	+	0.405033i	$0.867260\pi$
$332$	0.112262	+	0.129557i	0.00616116	+	0.00711035i
$333$	−2.12285	+	6.10802i	−0.116332	+	0.334718i
$334$	11.0194	−	7.08174i	0.602955	−	0.387496i
$335$	14.2385	+	4.92799i	0.777932	+	0.269245i
$336$	−2.93779	−	2.42884i	−0.160270	−	0.132504i
$337$	−17.5555	+	22.3236i	−0.956307	+	1.21604i	0.0200324	+	0.999799i	$0.493623\pi$
$337$	−17.5555	+	22.3236i	−0.956307	+	1.21604i	−0.976339	+	0.216244i	$0.930619\pi$
$338$	10.8174	−	3.74395i	0.588390	−	0.203644i
$339$	4.80748	+	28.7025i	0.261107	+	1.55890i
$340$	0.901248	+	3.71500i	0.0488771	+	0.201474i
$341$	0.0470825	+	0.103096i	0.00254966	+	0.00558297i
$342$	−1.69673	−	0.413946i	−0.0917487	−	0.0223836i
$343$	10.8948	−	16.9526i	0.588263	−	0.915355i
$344$	0.133918	+	0.231952i	0.00722035	+	0.0125060i
$345$	−2.64166	−	7.47865i	−0.142222	−	0.402637i
$346$	2.15461	−	3.73189i	0.115832	−	0.200628i
$347$	−13.2011	−	25.6065i	−0.708671	−	1.37463i	−0.917919	−	0.396767i	$-0.870132\pi$
$347$	−13.2011	−	25.6065i	−0.708671	−	1.37463i	0.209248	−	0.977863i	$-0.432898\pi$
$348$	15.9159	+	5.09910i	0.853181	+	0.273340i
$349$	−3.41280	+	4.79261i	−0.182683	+	0.256543i	−0.895755	−	0.444549i	$-0.853364\pi$
$349$	−3.41280	+	4.79261i	−0.182683	+	0.256543i	0.713072	+	0.701091i	$0.247303\pi$
$350$	8.63283	+	2.53483i	0.461444	+	0.135492i
$351$	−17.3187	+	18.9771i	−0.924403	+	1.01292i
$352$	−0.557704	−	0.483253i	−0.0297257	−	0.0257575i
$353$	3.53497	+	8.82994i	0.188148	+	0.469970i	0.992210	−	0.124575i	$-0.0397566\pi$
$353$	3.53497	+	8.82994i	0.188148	+	0.469970i	−0.804063	+	0.594545i	$0.797332\pi$
$354$	14.8354	+	2.50455i	0.788491	+	0.133115i
$355$	−0.344362	−	1.78672i	−0.0182768	−	0.0948291i
$356$	−0.0958862	−	2.01290i	−0.00508196	−	0.106683i
$357$	−12.2228	+	9.13755i	−0.646899	+	0.483610i
$358$	4.50434	−	13.0144i	0.238062	−	0.687835i
$359$	29.7937	−	8.74822i	1.57245	−	0.461714i	0.624738	−	0.780834i	$-0.285206\pi$
$359$	29.7937	−	8.74822i	1.57245	−	0.461714i	0.947714	+	0.319121i	$0.103388\pi$
$360$	2.86452	+	0.00370310i	0.150973	+	0.000195171i
$361$	−12.2204	+	14.1031i	−0.643180	+	0.742269i
$362$	−13.3149	+	1.27142i	−0.699815	+	0.0668242i
$363$	−17.2530	+	5.50290i	−0.905548	+	0.288827i
$364$	1.03434	−	10.8321i	0.0542141	−	0.567756i
$365$	3.85798	+	1.54450i	0.201936	+	0.0808429i
$366$	21.6382	−	0.501091i	1.13105	−	0.0261925i
$367$	−12.1082	+	6.99067i	−0.632042	+	0.364910i	−0.781543	−	0.623852i	$-0.785567\pi$
$367$	−12.1082	+	6.99067i	−0.632042	+	0.364910i	0.149500	+	0.988762i	$0.452234\pi$
$368$	−4.57821	−	1.42829i	−0.238656	−	0.0744545i
$369$	−1.85086	−	12.9922i	−0.0963520	−	0.676348i
$370$	1.73141	+	1.11271i	0.0900116	+	0.0578470i
$371$	−6.44841	−	8.19981i	−0.334785	−	0.425713i
$372$	−0.233561	+	0.127338i	−0.0121096	+	0.00660218i
$373$	−11.4453	−	12.0035i	−0.592616	−	0.621518i	0.357312	−	0.933985i	$-0.383693\pi$
$373$	−11.4453	−	12.0035i	−0.592616	−	0.621518i	−0.949929	+	0.312467i	$0.898845\pi$
$374$	−2.40660	+	1.71373i	−0.124442	+	0.0886148i
$375$	−13.8207	+	5.90782i	−0.713700	+	0.305079i
$376$	−7.49659	+	3.00118i	−0.386607	+	0.154774i
$377$	13.4412	+	45.7764i	0.692256	+	2.35761i
$378$	4.48117	+	10.5208i	0.230486	+	0.541134i
$379$	−4.19804	−	6.53227i	−0.215639	−	0.335540i	0.716535	−	0.697551i	$-0.245727\pi$
$379$	−4.19804	−	6.53227i	−0.215639	−	0.335540i	−0.932174	+	0.362010i	$0.882090\pi$
$380$	−0.254717	+	0.494081i	−0.0130667	+	0.0253458i
$381$	0.931364	+	3.48491i	0.0477152	+	0.178537i
$382$	−24.2220	−	5.87620i	−1.23931	−	0.300652i
$383$	−8.55518	−	6.72786i	−0.437149	−	0.343778i	0.375206	−	0.926942i	$-0.377572\pi$
$383$	−8.55518	−	6.72786i	−0.437149	−	0.343778i	−0.812355	+	0.583164i	$0.801815\pi$
$384$	1.03888	−	1.38591i	0.0530149	−	0.0707243i
$385$	−0.147403	−	1.54367i	−0.00751235	−	0.0786729i
$386$	−4.15412	+	14.1476i	−0.211439	+	0.720096i
$387$	−0.0371947	−	0.802644i	−0.00189071	−	0.0408007i
$388$	−10.8861	+	1.56518i	−0.552656	+	0.0794599i
$389$	0.896396	−	18.8177i	0.0454491	−	0.954094i	−0.854864	−	0.518852i	$-0.826360\pi$
$389$	0.896396	−	18.8177i	0.0454491	−	0.954094i	0.900313	−	0.435242i	$-0.143337\pi$
$390$	4.57900	+	6.77489i	0.231867	+	0.343060i
$391$	−9.87828	+	16.4643i	−0.499566	+	0.832637i
$392$	1.86776	+	1.07835i	0.0943361	+	0.0544650i
$393$	0.445289	+	19.2286i	0.0224619	+	0.969953i
$394$	18.5192	−	14.5637i	0.932986	−	0.733708i
$395$	−10.8962	+	4.97612i	−0.548246	+	0.250376i
$396$	0.820145	+	2.05632i	0.0412138	+	0.103334i
$397$	−6.25228	+	13.6906i	−0.313793	+	0.687111i	−0.999155	−	0.0410913i	$-0.986917\pi$
$397$	−6.25228	+	13.6906i	−0.313793	+	0.687111i	0.685362	+	0.728202i	$0.259644\pi$
$398$	7.41737	+	1.42958i	0.371799	+	0.0716584i
$399$	−2.21335	−	0.159740i	−0.110806	−	0.00799699i
$400$	−0.963849	+	3.97304i	−0.0481924	+	0.198652i
$401$	6.29948	−	1.21413i	0.314581	−	0.0606305i	−0.0295169	−	0.999564i	$-0.509397\pi$
$401$	6.29948	−	1.21413i	0.314581	−	0.0606305i	0.344098	+	0.938934i	$0.388185\pi$
$402$	−27.1402	+	3.22722i	−1.35363	+	0.160959i
$403$	−0.674971	−	0.347972i	−0.0336227	−	0.0173337i
$404$	−3.61462	+	3.13208i	−0.179834	+	0.155827i
$405$	−7.62805	−	3.95753i	−0.379041	−	0.196651i
$406$	21.0191	+	3.02210i	1.04316	+	0.149984i
$407$	−0.301028	+	1.56188i	−0.0149214	+	0.0774195i
$408$	−4.41158	−	5.35007i	−0.218406	−	0.264868i
$409$	−23.5067	+	22.4136i	−1.16233	+	1.10828i	−0.169900	+	0.985461i	$0.554345\pi$
$409$	−23.5067	+	22.4136i	−1.16233	+	1.10828i	−0.992429	+	0.122818i	$0.960807\pi$
$410$	−4.15800	−	0.397041i	−0.205349	−	0.0196085i
$411$	10.7516	−	2.33160i	0.530339	−	0.115009i
$412$	10.7662	+	0.512859i	0.530415	+	0.0252668i
$413$	19.1166			0.940667
$414$	10.2313	+	10.1153i	0.502842	+	0.497142i
$415$	−0.163686			−0.00803505
$416$	4.93879	+	0.235264i	0.242144	+	0.0115347i
$417$	−0.297862	−	0.328085i	−0.0145864	−	0.0160664i
$418$	−0.427662	−	0.0408368i	−0.0209177	−	0.00199739i
$419$	−20.5316	+	19.5768i	−1.00303	+	0.956390i	−0.999049	−	0.0436016i	$-0.986117\pi$
$419$	−20.5316	+	19.5768i	−1.00303	+	0.956390i	−0.00398447	+	0.999992i	$0.501268\pi$
$420$	3.58966	−	0.601246i	0.175158	−	0.0293378i
$421$	−1.67850	+	8.70886i	−0.0818049	+	0.424444i	0.917818	+	0.397000i	$0.129949\pi$
$421$	−1.67850	+	8.70886i	−0.0818049	+	0.424444i	−0.999623	+	0.0274437i	$0.991263\pi$
$422$	−1.16800	−	0.167933i	−0.0568573	−	0.00817485i
$423$	24.1124	+	2.33391i	1.17238	+	0.113479i
$424$	3.58228	−	3.10406i	0.173971	−	0.150747i
$425$	14.5482	+	7.50009i	0.705689	+	0.363808i
$426$	1.97633	+	2.64362i	0.0957534	+	0.128084i
$427$	27.0040	−	5.20459i	1.30681	−	0.251868i
$428$	0.0733946	−	0.302537i	0.00354766	−	0.0146237i
$429$	−3.54564	+	5.23140i	−0.171185	+	0.252574i
$430$	−0.251118	−	0.0483990i	−0.0121100	−	0.00233401i
$431$	−15.8104	+	34.6200i	−0.761561	+	1.66759i	−0.0171594	+	0.999853i	$0.505462\pi$
$431$	−15.8104	+	34.6200i	−0.761561	+	1.66759i	−0.744401	+	0.667732i	$0.767265\pi$
$432$	−4.67827	+	2.26136i	−0.225084	+	0.108800i
$433$	23.0704	−	10.5359i	1.10869	−	0.506323i	0.224985	−	0.974362i	$-0.427767\pi$
$433$	23.0704	−	10.5359i	1.10869	−	0.506323i	0.883708	+	0.468039i	$0.155039\pi$
$434$	−0.265689	+	0.208940i	−0.0127535	+	0.0100294i
$435$	−13.6316	+	8.29682i	−0.653586	+	0.397802i
$436$	2.92025	+	1.68601i	0.139855	+	0.0807451i
$437$	−2.65339	+	0.868693i	−0.126929	+	0.0415552i
$438$	−7.51937	+	0.532911i	−0.359290	+	0.0254635i
$439$	−1.15588	+	24.2649i	−0.0551671	+	1.15810i	0.786318	+	0.617821i	$0.211985\pi$
$439$	−1.15588	+	24.2649i	−0.0551671	+	1.15810i	−0.841486	+	0.540280i	$0.818318\pi$
$440$	0.697450	−	0.100278i	0.0332496	−	0.00478057i
$441$	−3.49097	−	5.44752i	−0.166237	−	0.259406i
$442$	5.57693	−	18.9933i	0.265268	−	0.903419i
$443$	−2.14838	−	22.4988i	−0.102073	−	1.06895i	−0.890857	−	0.454283i	$-0.849896\pi$
$443$	−2.14838	−	22.4988i	−0.102073	−	1.06895i	0.788785	−	0.614669i	$-0.210711\pi$
$444$	−3.70669	−	0.445620i	−0.175912	−	0.0211482i
$445$	1.51250	+	1.18945i	0.0716996	+	0.0563852i
$446$	−22.4140	−	5.43757i	−1.06133	−	0.257477i
$447$	−6.20384	−	1.66661i	−0.293432	−	0.0788281i
$448$	1.00844	−	1.95610i	0.0476444	−	0.0924172i
$449$	−7.12071	−	11.0800i	−0.336047	−	0.522900i	0.631571	−	0.775318i	$-0.282410\pi$
$449$	−7.12071	−	11.0800i	−0.336047	−	0.522900i	−0.967618	+	0.252418i	$0.918774\pi$
$450$	8.04374	−	9.25876i	0.379186	−	0.436462i
$451$	−0.909469	−	3.09737i	−0.0428252	−	0.145849i
$452$	−15.5986	+	6.24475i	−0.733698	+	0.293729i
$453$	−23.3574	−	17.5087i	−1.09743	−	0.822631i
$454$	9.02459	−	6.42638i	0.423545	−	0.301605i
$455$	7.16989	+	7.51957i	0.336130	+	0.352523i
$456$	0.0246478	−	1.00804i	0.00115424	−	0.0472057i
$457$	5.94387	+	7.55824i	0.278042	+	0.353560i	0.904938	−	0.425544i	$-0.139917\pi$
$457$	5.94387	+	7.55824i	0.278042	+	0.353560i	−0.626895	+	0.779103i	$0.715675\pi$
$458$	11.1186	+	7.14550i	0.519538	+	0.333887i
$459$	4.38259	+	20.3362i	0.204562	+	0.949213i
$460$	3.89337	−	2.41064i	0.181530	−	0.112397i
$461$	34.5242	−	19.9325i	1.60795	−	0.928351i	0.618124	−	0.786081i	$-0.287893\pi$
$461$	34.5242	−	19.9325i	1.60795	−	0.928351i	0.989828	−	0.142271i	$-0.0454404\pi$
$462$	1.46248	+	2.40284i	0.0680407	+	0.111790i
$463$	29.7414	+	11.9067i	1.38220	+	0.553350i	0.939262	−	0.343201i	$-0.111511\pi$
$463$	29.7414	+	11.9067i	1.38220	+	0.553350i	0.442940	+	0.896551i	$0.353935\pi$
$464$	−0.917207	+	9.60542i	−0.0425803	+	0.445921i
$465$	0.0541531	−	0.248165i	0.00251129	−	0.0115084i
$466$	12.5406	−	1.19748i	0.580933	−	0.0554724i
$467$	−23.2103	+	26.7861i	−1.07405	+	1.23951i	−0.104520	+	0.994523i	$0.533331\pi$
$467$	−23.2103	+	26.7861i	−1.07405	+	1.23951i	−0.969525	+	0.244991i	$0.921215\pi$
$468$	−12.8363	−	7.43319i	−0.593358	−	0.343599i
$469$	−33.3207	+	9.78383i	−1.53861	+	0.451775i
$470$	2.52181	−	7.28629i	0.116322	−	0.336091i
$471$	−34.2944	−	14.7119i	−1.58020	−	0.677891i
$472$	0.413316	+	8.67657i	0.0190244	+	0.399372i
$473$	−0.0374052	−	0.194077i	−0.00171989	−	0.00892365i
$474$	13.8454	−	16.7467i	0.635942	−	0.769200i
$475$	0.884577	+	2.20957i	0.0405872	+	0.101382i
$476$	−6.65877	−	5.76986i	−0.305204	−	0.264461i
$477$	−13.8236	+	3.33465i	−0.632939	+	0.152683i
$478$	17.7333	+	5.20695i	0.811100	+	0.238161i
$479$	−2.43623	+	3.42121i	−0.111314	+	0.156319i	−0.866475	−	0.499221i	$-0.833620\pi$
$479$	−2.43623	+	3.42121i	−0.111314	+	0.156319i	0.755160	+	0.655540i	$0.227559\pi$
$480$	0.350502	+	1.61626i	0.0159982	+	0.0737720i
$481$	−4.88354	−	9.47275i	−0.222670	−	0.431920i
$482$	−12.9465	+	22.4240i	−0.589698	+	1.02139i
$483$	14.9581	+	10.5092i	0.680617	+	0.478184i
$484$	−5.22772	−	9.05467i	−0.237623	−	0.411576i
$485$	5.67745	−	8.83428i	0.257800	−	0.401144i
$486$	15.5828	+	0.421333i	0.706848	+	0.0191121i
$487$	−10.2097	−	22.3562i	−0.462647	−	1.01306i	−0.986876	−	0.161479i	$-0.948374\pi$
$487$	−10.2097	−	22.3562i	−0.462647	−	1.01306i	0.524229	−	0.851577i	$-0.324354\pi$
$488$	2.94608	+	12.1439i	0.133363	+	0.549730i
$489$	−1.31487	+	1.08422i	−0.0594604	+	0.0490301i
$490$	−1.94605	+	0.673533i	−0.0879134	+	0.0304271i
$491$	−6.89598	+	8.76895i	−0.311211	+	0.395737i	−0.916347	−	0.400385i	$-0.868876\pi$
$491$	−6.89598	+	8.76895i	−0.311211	+	0.395737i	0.605136	+	0.796122i	$0.293119\pi$
$492$	7.10079	−	2.64323i	0.320128	−	0.119166i
$493$	36.5061	+	12.6349i	1.64415	+	0.569047i
$494$	2.42151	−	1.55621i	0.108949	−	0.0700172i
$495$	−1.99671	−	0.693960i	−0.0897454	−	0.0311912i
$496$	−0.100577	−	0.116072i	−0.00451606	−	0.00521181i
$497$	3.03525	+	2.89411i	0.136150	+	0.129819i
$498$	0.267162	−	0.129566i	0.0119718	−	0.00580599i
$499$	9.52068	+	27.5082i	0.426204	+	1.23144i	0.929983	+	0.367603i	$0.119821\pi$
$499$	9.52068	+	27.5082i	0.426204	+	1.23144i	−0.503779	+	0.863833i	$0.668057\pi$
$500$	−5.03365	−	7.06877i	−0.225112	−	0.316125i
$501$	−6.89415	−	21.6149i	−0.308008	−	0.965684i
$502$	−22.4138	−	15.9608i	−1.00038	−	0.712364i
$503$	3.25042	+	22.6072i	0.144929	+	1.00800i	0.924362	+	0.381518i	$0.124598\pi$
$503$	3.25042	+	22.6072i	0.144929	+	1.00800i	−0.779432	+	0.626486i	$0.784492\pi$
$504$	−5.38298	+	3.82272i	−0.239777	+	0.170278i
$505$		−	4.56683i		−	0.203221i
$506$	2.84794	+	2.10102i	0.126606	+	0.0934019i
$507$	−1.40164	−	19.7772i	−0.0622491	−	0.878335i
$508$	−1.85111	+	0.954315i	−0.0821299	+	0.0423409i
$509$	−3.76704	+	9.40960i	−0.166971	+	0.417073i	−0.988129	−	0.153628i	$-0.950904\pi$
$509$	−3.76704	+	9.40960i	−0.166971	+	0.417073i	0.821158	+	0.570701i	$0.193329\pi$
$510$	6.61922	+	0.161848i	0.293104	+	0.00716675i
$511$	−9.30811	+	2.25812i	−0.411767	+	0.0998935i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	−1.45488	+	2.65218i	−0.0642347	+	0.117097i
$514$	−0.835614	+	5.81182i	−0.0368574	+	0.256349i
$515$	−7.10208	+	7.44845i	−0.312955	+	0.328218i
$516$	0.448174	−	0.119778i	0.0197298	−	0.00527291i
$517$	5.95219	−	0.283538i	0.261777	−	0.0124700i
$518$	−4.73828	+	0.225712i	−0.208188	+	0.00991721i
$519$	−5.27427	−	5.28110i	−0.231515	−	0.231814i
$520$	−3.25793	+	3.41682i	−0.142870	+	0.149838i
$521$	0.651700	−	4.53267i	0.0285515	−	0.198580i	−0.970553	−	0.240887i	$-0.922562\pi$
$521$	0.651700	−	4.53267i	0.0285515	−	0.198580i	0.999105	+	0.0423071i	$0.0134708\pi$
$522$	15.6816	−	24.3318i	0.686364	−	1.06497i
$523$	−25.4607	−	11.6275i	−1.11332	−	0.508437i	−0.228114	−	0.973634i	$-0.573256\pi$
$523$	−25.4607	−	11.6275i	−1.11332	−	0.508437i	−0.885207	+	0.465198i	$0.845983\pi$
$524$	−10.7916	+	2.61801i	−0.471432	+	0.114368i
$525$	8.11944	−	13.3014i	0.354361	−	0.580522i
$526$	−2.67443	+	6.68040i	−0.116611	+	0.291279i
$527$	−0.546535	+	0.281759i	−0.0238075	+	0.0122736i
$528$	−1.05897	+	0.715736i	−0.0460859	+	0.0311484i
$529$	22.4253	+	5.10932i	0.975014	+	0.222145i
$530$			4.52597i			0.196596i
$531$	10.8560	−	23.6903i	0.471112	−	1.02807i
$532$	−0.182334	−	1.26816i	−0.00790517	−	0.0549817i
$533$	17.6185	+	12.5461i	0.763143	+	0.543432i
$534$	−3.41015	−	0.744142i	−0.147572	−	0.0322022i
$535$	0.172424	+	0.242135i	0.00745453	+	0.0104684i
$536$	−5.16107	−	14.9119i	−0.222924	−	0.644097i
$537$	−19.7457	−	13.3829i	−0.852090	−	0.577514i
$538$	−6.93072	−	6.60843i	−0.298805	−	0.284910i
$539$	−1.04223	−	1.20280i	−0.0448922	−	0.0518083i
$540$	1.29342	−	4.78994i	0.0556599	−	0.206126i
$541$	34.2605	−	22.0179i	1.47297	−	0.946623i	0.475204	−	0.879876i	$-0.342374\pi$
$541$	34.2605	−	22.0179i	1.47297	−	0.946623i	0.997770	−	0.0667472i	$-0.0212621\pi$
$542$	3.39893	+	1.17638i	0.145997	+	0.0505300i
$543$	−3.85654	+	22.8437i	−0.165500	+	0.980317i
$544$	2.47483	−	3.14701i	0.106108	−	0.134927i
$545$	−3.04265	+	1.05307i	−0.130333	+	0.0451086i
$546$	−17.6545	−	6.59779i	−0.755543	−	0.282359i
$547$	−8.75306	−	36.0806i	−0.374254	−	1.54270i	−0.778261	−	0.627940i	$-0.783898\pi$
$547$	−8.75306	−	36.0806i	−0.374254	−	1.54270i	0.404007	−	0.914756i	$-0.367617\pi$
$548$	2.63861	+	5.77775i	0.112716	+	0.246813i
$549$	8.88534	−	36.4203i	0.379217	−	1.55438i
$550$	1.63108	−	2.53801i	0.0695495	−	0.108221i
$551$	2.80869	+	4.86480i	0.119654	+	0.207247i
$552$	−4.44646	+	7.01634i	−0.189254	+	0.298635i
$553$	13.8044	−	23.9100i	0.587024	−	1.01676i
$554$	−5.34940	−	10.3764i	−0.227274	−	0.440850i
$555$	2.63932	−	2.39618i	0.112033	−	0.101712i
$556$	0.148402	−	0.208401i	0.00629363	−	0.00883816i
$557$	−34.8106	−	10.2213i	−1.47497	−	0.433091i	−0.557260	−	0.830338i	$-0.688147\pi$
$557$	−34.8106	−	10.2213i	−1.47497	−	0.433091i	−0.917712	+	0.397247i	$0.869966\pi$
$558$	0.108049	+	0.447910i	0.00457407	+	0.0189615i
$559$	1.00083	+	0.867220i	0.0423304	+	0.0366795i
$560$	0.780998	+	1.95084i	0.0330032	+	0.0824379i
$561$	1.78518	+	4.79571i	0.0753702	+	0.202475i
$562$	−4.14486	−	21.5056i	−0.174840	−	0.907158i
$563$	−0.453049	−	9.51067i	−0.0190937	−	0.400827i	−0.988102	−	0.153799i	$-0.950849\pi$
$563$	−0.453049	−	9.51067i	−0.0190937	−	0.400827i	0.969008	−	0.247028i	$-0.0794539\pi$
$564$	1.65147	+	13.8885i	0.0695394	+	0.584811i
$565$	5.24729	−	15.1611i	0.220755	−	0.637830i
$566$	9.90209	−	2.90751i	0.416216	−	0.122212i
$567$	19.6124	−	2.76809i	0.823642	−	0.116249i
$568$	−1.24794	+	1.44020i	−0.0523625	+	0.0604295i
$569$	4.32171	−	0.412674i	0.181176	−	0.0173002i	−0.00407381	−	0.999992i	$-0.501297\pi$
$569$	4.32171	−	0.412674i	0.181176	−	0.0173002i	0.185249	+	0.982692i	$0.440691\pi$
$570$	0.712009	+	0.648100i	0.0298228	+	0.0271459i
$571$	0.910684	−	9.53711i	0.0381109	−	0.399116i	−0.956209	−	0.292684i	$-0.905451\pi$
$571$	0.910684	−	9.53711i	0.0381109	−	0.399116i	0.994320	−	0.106431i	$-0.0339425\pi$
$572$	−3.38734	−	1.35609i	−0.141632	−	0.0567008i
$573$	−20.7140	+	37.8766i	−0.865339	+	1.58232i
$574$	8.33732	−	4.81355i	0.347993	−	0.200914i
$575$	3.11609	−	19.3575i	0.129950	−	0.807264i
$576$	−1.85143	−	2.36055i	−0.0771428	−	0.0983564i
$577$	−14.4622	−	9.29427i	−0.602068	−	0.386926i	0.203807	−	0.979011i	$-0.434668\pi$
$577$	−14.4622	−	9.29427i	−0.602068	−	0.386926i	−0.805875	+	0.592085i	$0.798305\pi$
$578$	0.600572	+	0.763689i	0.0249805	+	0.0317653i
$579$	21.7986	+	13.3063i	0.905920	+	0.552990i
$580$	−6.35795	−	6.66802i	−0.263999	−	0.276875i
$581$	0.307315	−	0.218838i	0.0127496	−	0.00907894i
$582$	−2.27372	+	18.9129i	−0.0942486	+	0.783965i
$583$	−3.24734	+	1.30004i	−0.134491	+	0.0538421i
$584$	−1.22616	−	4.17591i	−0.0507387	−	0.172800i
$585$	13.3903	−	4.61506i	0.553621	−	0.190809i
$586$	5.69076	+	8.85499i	0.235083	+	0.365796i
$587$	−2.96234	+	5.74613i	−0.122269	+	0.237168i	−0.942024	−	0.335546i	$-0.891079\pi$
$587$	−2.96234	+	5.74613i	−0.122269	+	0.237168i	0.819755	+	0.572714i	$0.194110\pi$
$588$	2.64312	−	2.63970i	0.109000	−	0.108860i
$589$	−0.0868920	−	0.0210798i	−0.00358032	−	0.000868577i
$590$	−6.51963	−	5.12709i	−0.268409	−	0.211079i
$591$	−16.0393	−	37.5224i	−0.659770	−	1.54347i
$592$	−0.204890	−	2.14571i	−0.00842095	−	0.0881881i
$593$	6.13948	−	20.9092i	0.252118	−	0.858636i	−0.732028	−	0.681275i	$-0.761426\pi$
$593$	6.13948	−	20.9092i	0.252118	−	0.858636i	0.984146	−	0.177361i	$-0.0567560\pi$
$594$	3.80825	−	0.447843i	0.156254	−	0.0183752i
$595$	8.32729	−	1.19728i	0.341386	−	0.0490838i
$596$	0.176471	−	3.70459i	0.00722854	−	0.151746i
$597$	5.72446	−	11.7649i	0.234286	−	0.481507i
$598$	−23.7012	+	0.730062i	−0.969215	+	0.0298544i
$599$	−34.9300	−	20.1669i	−1.42720	−	0.823996i	−0.430304	−	0.902684i	$-0.641594\pi$
$599$	−34.9300	−	20.1669i	−1.42720	−	0.823996i	−0.996899	+	0.0786882i	$0.974927\pi$
$600$	6.21275	+	3.39763i	0.253634	+	0.138708i
$601$	5.23950	−	4.12039i	0.213724	−	0.168074i	−0.505558	−	0.862792i	$-0.668713\pi$
$601$	5.23950	−	4.12039i	0.213724	−	0.168074i	0.719282	+	0.694718i	$0.244471\pi$
$602$	0.536172	−	0.244861i	0.0218527	−	0.00997980i
$603$	−6.79767	+	46.8488i	−0.276822	+	1.90783i
$604$	7.00121	−	15.3305i	0.284875	−	0.623790i
$605$	9.80285	+	1.88935i	0.398543	+	0.0768128i
$606$	3.61487	+	7.45378i	0.146844	+	0.302789i
$607$	−7.96831	+	32.8458i	−0.323424	+	1.33317i	0.545453	+	0.838142i	$0.316358\pi$
$607$	−7.96831	+	32.8458i	−0.323424	+	1.33317i	−0.868876	+	0.495029i	$0.835157\pi$
$608$	0.571645	−	0.110176i	0.0231833	−	0.00446821i
$609$	14.5005	−	33.8016i	0.587591	−	1.36971i
$610$	−10.6054	−	5.46749i	−0.429402	−	0.221372i
$611$	−30.1741	+	26.1460i	−1.22071	+	1.05775i
$612$	−10.9317	+	4.97528i	−0.441889	+	0.201114i
$613$	22.9324	+	3.29719i	0.926233	+	0.133172i	0.588893	−	0.808211i	$-0.299564\pi$
$613$	22.9324	+	3.29719i	0.926233	+	0.133172i	0.337339	+	0.941383i	$0.390473\pi$
$614$	−3.06177	+	15.8860i	−0.123563	+	0.641106i
$615$	−2.53263	+	6.77685i	−0.102125	+	0.273269i
$616$	−1.17537	+	1.12071i	−0.0473571	+	0.0451549i
$617$	6.02049	+	0.574887i	0.242376	+	0.0231441i	0.215537	−	0.976496i	$-0.430850\pi$
$617$	6.02049	+	0.574887i	0.242376	+	0.0231441i	0.0268389	+	0.999640i	$0.491456\pi$
$618$	5.69590	−	17.7787i	0.229123	−	0.715163i
$619$	48.6741	+	2.31863i	1.95638	+	0.0931938i	0.987821	−	0.155597i	$-0.0497300\pi$
$619$	48.6741	+	2.31863i	1.95638	+	0.0931938i	0.968557	+	0.248790i	$0.0800331\pi$
$620$	0.146650			0.00588960
$621$	21.5180	−	12.5688i	0.863487	−	0.504370i
$622$	13.9994			0.561326
$623$	−4.42989	−	0.211021i	−0.177480	−	0.00845440i
$624$	2.61287	−	8.15560i	0.104599	−	0.326485i
$625$	−12.1004	−	1.15545i	−0.484016	−	0.0462179i
$626$	−15.4251	+	14.7078i	−0.616510	+	0.587841i
$627$	−0.260488	+	0.697018i	−0.0104029	+	0.0278362i
$628$	4.07739	−	21.1555i	0.162706	−	0.844198i
$629$	−8.54171	−	1.22811i	−0.340580	−	0.0489680i
$630$	0.607354	−	6.27476i	0.0241976	−	0.249993i
$631$	−22.5419	+	19.5327i	−0.897378	+	0.777583i	−0.975646	−	0.219349i	$-0.929607\pi$
$631$	−22.5419	+	19.5327i	−0.897378	+	0.777583i	0.0782679	+	0.996932i	$0.475061\pi$
$632$	11.1506	+	5.74855i	0.443548	+	0.228665i
$633$	−0.805771	+	1.87830i	−0.0320265	+	0.0746557i
$634$	5.76735	−	1.11157i	0.229051	−	0.0441459i
$635$	0.468825	−	1.93252i	0.0186047	−	0.0766898i
$636$	−3.58253	−	7.38710i	−0.142057	−	0.292918i
$637$	10.4709	+	2.01810i	0.414871	+	0.0799599i
$638$	2.95798	−	6.47708i	0.117108	−	0.256430i
$639$	5.31020	−	2.11792i	0.210068	−	0.0837838i
$640$	−0.868553	+	0.396655i	−0.0343326	+	0.0156792i
$641$	12.0975	−	9.51357i	0.477822	−	0.375764i	−0.350004	−	0.936748i	$-0.613820\pi$
$641$	12.0975	−	9.51357i	0.477822	−	0.375764i	0.827826	+	0.560985i	$0.189577\pi$
$642$	−0.473085	−	0.258721i	−0.0186712	−	0.0102109i
$643$	−5.57748	−	3.22016i	−0.219954	−	0.126991i	0.385975	−	0.922509i	$-0.373865\pi$
$643$	−5.57748	−	3.22016i	−0.219954	−	0.126991i	−0.605929	+	0.795519i	$0.707199\pi$
$644$	−4.08680	+	9.73108i	−0.161043	+	0.383458i
$645$	−0.193804	+	0.398307i	−0.00763102	+	0.0156833i
$646$	0.110901	−	2.32809i	0.00436333	−	0.0915975i
$647$	42.7362	−	6.14454i	1.68013	−	0.241567i	0.764801	−	0.644266i	$-0.222837\pi$
$647$	42.7362	−	6.14454i	1.68013	−	0.241567i	0.915332	+	0.402700i	$0.131928\pi$
$648$	1.68041	+	8.84173i	0.0660126	+	0.347336i
$649$	1.80594	−	6.15046i	0.0708893	−	0.241427i
$650$	1.92147	+	20.1225i	0.0753662	+	0.789270i
$651$	0.230111	+	0.538321i	0.00901875	+	0.0210984i
$652$	−0.773429	−	0.608231i	−0.0302898	−	0.0238202i
$653$	26.8115	+	6.50439i	1.04921	+	0.254536i	0.723064	−	0.690782i	$-0.242733\pi$
$653$	26.8115	+	6.50439i	1.04921	+	0.254536i	0.326150	+	0.945318i	$0.394249\pi$
$654$	4.13253	−	4.12719i	0.161595	−	0.161386i
$655$	4.85862	−	9.42442i	0.189842	−	0.368242i
$656$	2.36502	+	3.68004i	0.0923384	+	0.143681i
$657$	−2.48755	+	12.8175i	−0.0970486	+	0.500056i
$658$	5.00670	+	17.0512i	0.195181	+	0.664726i
$659$	16.2959	−	6.52391i	0.634800	−	0.254135i	−0.0318663	−	0.999492i	$-0.510145\pi$
$659$	16.2959	−	6.52391i	0.634800	−	0.254135i	0.666666	+	0.745357i	$0.267721\pi$
$660$	0.145673	−	1.21172i	0.00567031	−	0.0471660i
$661$	−0.838184	+	0.596868i	−0.0326016	+	0.0232155i	−0.596242	−	0.802805i	$-0.703340\pi$
$661$	−0.838184	+	0.596868i	−0.0326016	+	0.0232155i	0.563640	+	0.826021i	$0.309401\pi$
$662$	−9.59712	−	10.0652i	−0.373003	−	0.391194i
$663$	−29.2648	−	17.8638i	−1.13655	−	0.693771i
$664$	0.105970	+	0.134752i	0.00411243	+	0.00522938i
$665$	1.02914	+	0.661388i	0.0399083	+	0.0256475i
$666$	−2.41108	+	6.00010i	−0.0934275	+	0.232499i
$667$	0.777713	−	46.2690i	0.0301132	−	1.79154i
$668$	11.3439	−	6.54940i	0.438908	−	0.253404i
$669$	−19.1678	+	35.0493i	−0.741070	+	1.35509i
$670$	13.9879	+	5.59991i	0.540399	+	0.216343i
$671$	0.876562	−	9.17977i	0.0338393	−	0.354381i
$672$	−2.81890	−	2.56588i	−0.108741	−	0.0989808i
$673$	28.4929	−	2.72074i	1.09832	−	0.104877i	0.469876	−	0.882732i	$-0.344299\pi$
$673$	28.4929	−	2.72074i	1.09832	−	0.104877i	0.628443	+	0.777856i	$0.283693\pi$
$674$	−18.5978	+	21.4630i	−0.716360	+	0.826723i
$675$	−11.8729	−	17.6157i	−0.456989	−	0.678029i
$676$	10.9833	−	3.22499i	0.422435	−	0.124038i
$677$	−14.8180	+	42.8138i	−0.569502	+	1.64547i	0.180154	+	0.983638i	$0.442340\pi$
$677$	−14.8180	+	42.8138i	−0.569502	+	1.64547i	−0.749655	+	0.661828i	$0.769781\pi$
$678$	3.43632	+	28.8987i	0.131971	+	1.10985i
$679$	1.15167	+	24.1764i	0.0441968	+	0.927806i
$680$	0.723461	+	3.75367i	0.0277435	+	0.143947i
$681$	−6.69431	−	17.9836i	−0.256527	−	0.689134i
$682$	0.0421236	+	0.105220i	0.00161300	+	0.00402907i
$683$	25.0578	+	21.7127i	0.958809	+	0.830813i	0.985646	−	0.168827i	$-0.0539979\pi$
$683$	25.0578	+	21.7127i	0.958809	+	0.830813i	−0.0268366	+	0.999640i	$0.508543\pi$
$684$	−1.67511	−	0.494211i	−0.0640496	−	0.0188966i
$685$	−5.81922	−	1.70868i	−0.222341	−	0.0652853i
$686$	11.6891	−	16.4150i	0.446291	−	0.626728i
$687$	16.9489	−	15.3876i	0.646642	−	0.587074i
$688$	0.122729	+	0.238061i	0.00467901	+	0.00907600i
$689$	11.7183	−	20.2967i	0.446431	−	0.773242i
$690$	−2.28281	−	7.59588i	−0.0869053	−	0.289170i
$691$	−13.8365	−	23.9656i	−0.526367	−	0.911694i	−0.999528	−	0.0307181i	$-0.990221\pi$
$691$	−13.8365	−	23.9656i	−0.526367	−	0.911694i	0.473161	−	0.880976i	$-0.343113\pi$
$692$	2.32974	−	3.62514i	0.0885633	−	0.137807i
$693$	4.67653	−	1.36659i	0.177647	−	0.0519124i
$694$	−11.9677	−	26.2056i	−0.454288	−	0.994753i
$695$	0.0575926	+	0.237400i	0.00218461	+	0.00900509i
$696$	15.6552	+	5.85063i	0.593410	+	0.221768i
$697$	16.5502	−	5.72808i	0.626883	−	0.216966i
$698$	−3.63698	+	4.62479i	−0.137662	+	0.175051i
$699$	3.63229	−	21.5154i	0.137386	−	0.813785i
$700$	8.50244	+	2.94272i	0.321362	+	0.111224i
$701$	27.8450	−	17.8949i	1.05169	−	0.675880i	0.103839	−	0.994594i	$-0.466887\pi$
$701$	27.8450	−	17.8949i	1.05169	−	0.675880i	0.947851	+	0.318714i	$0.103251\pi$
$702$	−18.2020	+	18.1316i	−0.686992	+	0.684333i
$703$	−0.821746	−	0.948345i	−0.0309927	−	0.0357675i
$704$	−0.534078	−	0.509242i	−0.0201288	−	0.0191928i
$705$	−11.0549	−	7.49257i	−0.416350	−	0.282186i
$706$	3.11082	+	8.98814i	0.117077	+	0.338273i
$707$	6.10556	+	8.57406i	0.229623	+	0.322461i
$708$	14.6994	+	3.20761i	0.552437	+	0.120549i
$709$	7.99643	+	5.69423i	0.300312	+	0.213851i	0.720273	−	0.693691i	$-0.244017\pi$
$709$	7.99643	+	5.69423i	0.300312	+	0.213851i	−0.419961	+	0.907542i	$0.637956\pi$
$710$	−0.258956	−	1.80108i	−0.00971845	−	0.0675933i
$711$	−21.7912	−	30.6853i	−0.817232	−	1.15079i
$712$		−	2.01518i		−	0.0755221i
$713$	0.524464	+	0.517180i	0.0196413	+	0.0193685i
$714$	−12.6437	+	8.54562i	−0.473180	+	0.319812i
$715$	3.09664	−	1.59643i	0.115808	−	0.0597030i
$716$	5.11849	−	12.7854i	0.191287	−	0.477812i
$717$	16.6787	−	27.3233i	0.622876	−	1.02041i
$718$	30.1762	−	7.32067i	1.12617	−	0.273205i
$719$	−15.9404	−	7.27973i	−0.594476	−	0.271488i	0.0953727	−	0.995442i	$-0.469596\pi$
$719$	−15.9404	−	7.27973i	−0.594476	−	0.271488i	−0.689849	+	0.723954i	$0.742323\pi$
$720$	2.86110	+	0.139998i	0.106627	+	0.00521742i
$721$	3.37580	−	23.4792i	0.125721	−	0.874412i
$722$	−12.8776	+	13.5057i	−0.479255	+	0.502629i
$723$	31.6918	+	31.7328i	1.17863	+	1.18016i
$724$	−13.3603	+	0.636429i	−0.496531	+	0.0236527i
$725$	−39.4036	+	1.87703i	−1.46341	+	0.0697110i
$726$	−17.4953	+	4.67573i	−0.649312	+	0.173533i
$727$	−20.1956	+	21.1806i	−0.749015	+	0.785544i	−0.982390	−	0.186843i	$-0.940175\pi$
$727$	−20.1956	+	21.1806i	−0.749015	+	0.785544i	0.233375	+	0.972387i	$0.425023\pi$
$728$	1.54858	−	10.7706i	0.0573942	−	0.399185i
$729$	7.70719	−	25.8766i	0.285452	−	0.958393i
$730$	3.78012	+	1.72632i	0.139908	+	0.0638940i
$731$	1.04207	−	0.252803i	0.0385422	−	0.00935024i
$732$	21.6375	+	0.529064i	0.799746	+	0.0195548i
$733$	18.7350	−	46.7977i	0.691992	−	1.72851i	0.00698382	−	0.999976i	$-0.497777\pi$
$733$	18.7350	−	46.7977i	0.691992	−	1.72851i	0.685008	−	0.728536i	$-0.259799\pi$
$734$	−12.4271	+	6.40662i	−0.458693	+	0.236473i
$735$	0.252155	+	3.55790i	0.00930086	+	0.131235i
$736$	−4.50506	−	1.64451i	−0.166059	−	0.0606174i
$737$			11.6447i			0.428937i
$738$	−1.23057	−	13.0656i	−0.0452979	−	0.480951i
$739$	−2.93388	−	20.4056i	−0.107924	−	0.750631i	−0.969869	−	0.243628i	$-0.921662\pi$
$739$	−2.93388	−	20.4056i	−0.107924	−	0.750631i	0.861944	−	0.507003i	$-0.169247\pi$
$740$	1.67650	+	1.19383i	0.0616294	+	0.0438861i
$741$	−1.51499	−	4.74987i	−0.0556544	−	0.174491i
$742$	−6.05094	−	8.49735i	−0.222137	−	0.311948i
$743$	−2.65448	−	7.66962i	−0.0973835	−	0.281371i	0.885778	−	0.464109i	$-0.153625\pi$
$743$	−2.65448	−	7.66962i	−0.0973835	−	0.281371i	−0.983162	+	0.182738i	$0.941504\pi$
$744$	−0.239356	+	0.116081i	−0.00877520	+	0.00425572i
$745$	2.56296	+	2.44377i	0.0938995	+	0.0895330i
$746$	−10.8612	−	12.5345i	−0.397657	−	0.458921i
$747$	−0.0966761	−	0.505116i	−0.00353719	−	0.0184812i
$748$	−2.48541	+	1.59728i	−0.0908757	+	0.0584022i
$749$	−0.647439	−	0.224081i	−0.0236569	−	0.00818773i
$750$	−14.0862	+	5.24351i	−0.514355	+	0.191466i
$751$	4.51058	−	5.73567i	0.164593	−	0.209297i	−0.696759	−	0.717305i	$-0.745375\pi$
$751$	4.51058	−	5.73567i	0.164593	−	0.209297i	0.861353	+	0.508008i	$0.169618\pi$
$752$	−7.63090	+	2.64108i	−0.278270	+	0.0963103i
$753$	−36.7703	+	30.3202i	−1.33999	+	1.10493i
$754$	11.2478	+	46.3642i	0.409621	+	1.68848i
$755$	6.68503	+	14.6382i	0.243293	+	0.532738i
$756$	3.97549	+	10.7221i	0.144587	+	0.389961i
$757$	−16.1498	+	25.1296i	−0.586976	+	0.913352i	0.413021	+	0.910722i	$0.364474\pi$
$757$	−16.1498	+	25.1296i	−0.586976	+	0.913352i	−0.999997	+	0.00263060i	$0.999163\pi$
$758$	−3.88246	−	6.72463i	−0.141017	−	0.244249i
$759$	4.79425	−	3.81973i	0.174020	−	0.138647i
$760$	−0.277937	+	0.481402i	−0.0100818	+	0.0174623i
$761$	−11.8049	−	22.8984i	−0.427928	−	0.830065i	−0.999952	−	0.00982792i	$-0.996872\pi$
$761$	−11.8049	−	22.8984i	−0.427928	−	0.830065i	0.572023	−	0.820237i	$-0.306159\pi$
$762$	0.764491	+	3.52528i	0.0276946	+	0.127707i
$763$	4.30458	−	6.04493i	0.155836	−	0.218841i
$764$	−23.9150	−	7.02207i	−0.865214	−	0.254050i
$765$	3.24520	−	10.9995i	0.117331	−	0.397689i
$766$	−8.22536	−	7.12732i	−0.297194	−	0.257520i
$767$	15.9625	+	39.8725i	0.576374	+	1.43971i
$768$	1.10364	−	1.33491i	0.0398243	−	0.0481693i
$769$	7.13189	+	37.0037i	0.257182	+	1.33439i	0.849032	+	0.528341i	$0.177186\pi$
$769$	7.13189	+	37.0037i	0.257182	+	1.33439i	−0.591850	+	0.806048i	$0.701602\pi$
$770$	−0.0737851	−	1.54894i	−0.00265903	−	0.0558199i
$771$	9.34619	+	4.00942i	0.336595	+	0.144396i
$772$	−4.82259	+	13.9339i	−0.173569	+	0.501494i
$773$	30.6840	−	9.00963i	1.10363	−	0.324054i	0.321334	−	0.946966i	$-0.395869\pi$
$773$	30.6840	−	9.00963i	1.10363	−	0.324054i	0.782292	+	0.622912i	$0.214051\pi$
$774$	0.00103873	−	0.803505i	3.73364e−5	−	0.0288814i
$775$	0.411188	−	0.474537i	0.0147703	−	0.0170459i
$776$	−10.9482	+	1.04543i	−0.393018	+	0.0375286i
$777$	−1.75168	+	8.02734i	−0.0628410	+	0.287979i
$778$	1.79076	−	18.7537i	0.0642019	−	0.672353i
$779$	2.36424	+	0.946499i	0.0847077	+	0.0339119i
$780$	4.25145	+	6.98510i	0.152226	+	0.250107i
$781$	1.21787	−	0.703139i	0.0435789	−	0.0251603i
$782$	−10.6505	+	15.9756i	−0.380861	+	0.571288i
$783$	−33.6540	−	37.1652i	−1.20270	−	1.32818i
$784$	1.81433	+	1.16600i	0.0647977	+	0.0416429i
$785$	12.7167	+	16.1706i	0.453879	+	0.577154i
$786$	−0.470147	+	19.2280i	−0.0167696	+	0.685839i
$787$	−7.30757	−	7.66395i	−0.260487	−	0.273190i	0.580484	−	0.814272i	$-0.302864\pi$
$787$	−7.30757	−	7.66395i	−0.260487	−	0.273190i	−0.840970	+	0.541081i	$0.818015\pi$
$788$	19.1912	−	13.6660i	0.683659	−	0.486832i
$789$	9.97278	+	7.47559i	0.355040	+	0.266138i
$790$	−11.1206	+	4.45202i	−0.395654	+	0.158396i
$791$	10.4178	+	35.4796i	0.370413	+	1.26151i
$792$	0.721372	+	2.09302i	0.0256328	+	0.0743722i
$793$	33.4040	+	51.9776i	1.18621	+	1.84578i
$794$	−6.89662	+	13.3776i	−0.244752	+	0.474753i
$795$	7.57079	+	2.03383i	0.268508	+	0.0721326i
$796$	7.34094	+	1.78089i	0.260193	+	0.0631221i
$797$	−8.07243	−	6.34823i	−0.285940	−	0.224866i	0.464878	−	0.885375i	$-0.346098\pi$
$797$	−8.07243	−	6.34823i	−0.285940	−	0.224866i	−0.750818	+	0.660509i	$0.770341\pi$
$798$	−2.20324	−	0.264874i	−0.0779938	−	0.00937644i
$799$	3.07305	+	32.1824i	0.108717	+	1.13853i
$800$	−1.15180	+	3.92268i	−0.0407223	+	0.138688i
$801$	−2.77717	+	5.36991i	−0.0981266	+	0.189736i
$802$	6.35011	−	0.913009i	0.224230	−	0.0322395i
$803$	−0.152819	+	3.20806i	−0.00539286	+	0.113210i
$804$	−27.2630	+	1.93218i	−0.961493	+	0.0681427i
$805$	−4.46671	−	9.03383i	−0.157431	−	0.318401i
$806$	−0.657650	−	0.379694i	−0.0231647	−	0.0133742i
$807$	−14.1687	+	8.62369i	−0.498760	+	0.303568i
$808$	−3.75955	+	2.95655i	−0.132261	+	0.104011i
$809$	−28.2429	+	12.8981i	−0.992968	+	0.453473i	−0.844565	−	0.535453i	$-0.820141\pi$
$809$	−28.2429	+	12.8981i	−0.992968	+	0.453473i	−0.148404	+	0.988927i	$0.547413\pi$
$810$	−7.43111	−	4.31601i	−0.261102	−	0.151649i
$811$	−2.47047	+	5.40958i	−0.0867501	+	0.189956i	−0.948035	−	0.318166i	$-0.896933\pi$
$811$	−2.47047	+	5.40958i	−0.0867501	+	0.189956i	0.861285	+	0.508122i	$0.169660\pi$
$812$	20.8515	+	4.01880i	0.731745	+	0.141032i
$813$	3.49516	−	5.15691i	0.122581	−	0.180861i
$814$	−0.375004	+	1.54579i	−0.0131439	+	0.0541798i
$815$	0.922527	−	0.177802i	0.0323147	−	0.00622815i
$816$	−4.15202	−	5.55393i	−0.145350	−	0.194426i
$817$	0.138591	+	0.0714487i	0.00484869	+	0.00249967i
$818$	−24.5465	+	21.2697i	−0.858249	+	0.743677i
$819$	−18.9698	+	26.5666i	−0.662858	+	0.928312i
$820$	−4.13440	−	0.594437i	−0.144380	−	0.0207586i
$821$	8.62652	−	44.7586i	0.301068	−	1.56209i	−0.444575	−	0.895742i	$-0.646645\pi$
$821$	8.62652	−	44.7586i	0.301068	−	1.56209i	0.745643	−	0.666346i	$-0.232143\pi$
$822$	10.8504	−	1.81737i	0.378451	−	0.0633881i
$823$	18.9394	−	18.0587i	0.660187	−	0.629487i	−0.284028	−	0.958816i	$-0.591671\pi$
$823$	18.9394	−	18.0587i	0.660187	−	0.629487i	0.944215	+	0.329329i	$0.106822\pi$
$824$	10.7296	+	1.02456i	0.373785	+	0.0356921i
$825$	−3.51248	−	3.86888i	−0.122289	−	0.134697i
$826$	19.0950	+	0.909605i	0.664398	+	0.0316492i
$827$	−19.3919			−0.674322			−0.337161	−	0.941447i	$-0.609467\pi$
$827$	−19.3919			−0.674322			−0.337161	+	0.941447i	$0.609467\pi$
$828$	9.73843	+	10.5907i	0.338434	+	0.368053i
$829$	−0.214723			−0.00745765			−0.00372882	−	0.999993i	$-0.501187\pi$
$829$	−0.214723			−0.00745765			−0.00372882	+	0.999993i	$0.501187\pi$
$830$	−0.163501	−	0.00778852i	−0.00567521	−	0.000270343i
$831$	−19.7609	+	4.28534i	−0.685497	+	0.148657i
$832$	4.92200	+	0.469994i	0.170640	+	0.0162941i
$833$	6.24907	−	5.95847i	0.216517	−	0.206449i
$834$	−0.281914	−	0.341886i	−0.00976188	−	0.0118386i
$835$	−2.36701	+	12.2812i	−0.0819138	+	0.425009i
$836$	−0.425235	−	0.0611396i	−0.0147071	−	0.00211456i
$837$	0.797791	+	0.0205389i	0.0275757	+	0.000709930i
$838$	−21.4398	+	18.5777i	−0.740627	+	0.641757i
$839$	−27.5707	−	14.2137i	−0.951847	−	0.490711i	−0.0889192	−	0.996039i	$-0.528341\pi$
$839$	−27.5707	−	14.2137i	−0.951847	−	0.490711i	−0.862927	+	0.505328i	$0.831372\pi$
$840$	3.61421	−	0.429762i	0.124702	−	0.0148282i
$841$	−62.9470	+	12.1320i	−2.17059	+	0.418346i
$842$	−2.09098	+	8.61913i	−0.0720599	+	0.297035i
$843$	−37.8359	−	2.73066i	−1.30314	−	0.0940488i
$844$	−1.15869	−	0.223318i	−0.0398836	−	0.00768694i
$845$	−4.54051	+	9.94232i	−0.156198	+	0.342026i
$846$	23.9740	+	3.47858i	0.824243	+	0.119596i
$847$	−20.9304	+	9.55861i	−0.719178	+	0.328438i
$848$	3.72592	−	2.93010i	0.127949	−	0.100620i
$849$	−0.413833	−	17.8702i	−0.0142027	−	0.613303i
$850$	14.1748	+	8.18383i	0.486192	+	0.280703i
$851$	1.78548	+	10.1819i	0.0612053	+	0.349031i
$852$	1.84830	+	2.73467i	0.0633217	+	0.0936882i
$853$	−1.84551	+	38.7421i	−0.0631891	+	1.32650i	0.715288	+	0.698830i	$0.246296\pi$
$853$	−1.84551	+	38.7421i	−0.0631891	+	1.32650i	−0.778477	+	0.627673i	$0.784007\pi$
$854$	27.2210	−	3.91379i	0.931484	−	0.133927i
$855$	1.40406	−	0.899771i	0.0480178	−	0.0307715i
$856$	0.0877068	−	0.298702i	0.00299776	−	0.0102094i
$857$	−0.319392	−	3.34483i	−0.0109102	−	0.114257i	0.988376	−	0.152028i	$-0.0485804\pi$
$857$	−0.319392	−	3.34483i	−0.0109102	−	0.114257i	−0.999286	+	0.0377709i	$0.987974\pi$
$858$	−3.79055	+	5.05676i	−0.129407	+	0.172635i
$859$	25.8894	+	20.3596i	0.883333	+	0.694661i	0.953020	−	0.302908i	$-0.0979575\pi$
$859$	25.8894	+	20.3596i	0.883333	+	0.694661i	−0.0696865	+	0.997569i	$0.522200\pi$
$860$	−0.248531	−	0.0602929i	−0.00847483	−	0.00205597i
$861$	−4.30530	−	16.1092i	−0.146724	−	0.549002i
$862$	−17.4398	+	33.8285i	−0.594002	+	1.15220i
$863$	−16.2411	−	25.2717i	−0.552854	−	0.860257i	0.446551	−	0.894758i	$-0.352652\pi$
$863$	−16.2411	−	25.2717i	−0.552854	−	0.860257i	−0.999405	+	0.0345010i	$0.989016\pi$
$864$	−4.78057	+	2.03620i	−0.162638	+	0.0692729i
$865$	1.15922	+	3.94794i	0.0394146	+	0.134234i
$866$	23.5456	−	9.42623i	0.800112	−	0.320316i
$867$	1.54733	−	0.661424i	0.0525502	−	0.0224631i
$868$	−0.275330	+	0.196062i	−0.00934530	+	0.00665476i
$869$	−6.38855	−	6.70012i	−0.216717	−	0.227286i
$870$	−14.0109	+	7.63880i	−0.475016	+	0.258980i
$871$	−48.2297	−	61.3290i	−1.63420	−	2.07805i
$872$	2.83672	+	1.82305i	0.0960634	+	0.0617362i
$873$	30.6147	+	12.3022i	1.03615	+	0.416367i
$874$	−2.69171	+	0.741456i	−0.0910486	+	0.0250801i
$875$	−16.5392	+	9.54889i	−0.559126	+	0.322811i
$876$	−7.53621	+	0.174521i	−0.254625	+	0.00589653i
$877$	−38.1540	−	15.2746i	−1.28837	−	0.515785i	−0.376557	−	0.926393i	$-0.622892\pi$
$877$	−38.1540	−	15.2746i	−1.28837	−	0.515785i	−0.911812	+	0.410608i	$0.865316\pi$
$878$	−2.30914	+	24.1824i	−0.0779298	+	0.816117i
$879$	17.3694	−	5.54001i	0.585854	−	0.186860i
$880$	0.701431	−	0.0669786i	0.0236452	−	0.00225785i
$881$	−21.5209	+	24.8364i	−0.725057	+	0.836761i	−0.991906	−	0.126978i	$-0.959472\pi$
$881$	−21.5209	+	24.8364i	−0.725057	+	0.836761i	0.266848	+	0.963739i	$0.414018\pi$
$882$	−3.22781	−	5.60746i	−0.108686	−	0.188813i
$883$	−38.5595	+	11.3221i	−1.29763	+	0.381019i	−0.856371	−	0.516360i	$-0.827287\pi$
$883$	−38.5595	+	11.3221i	−1.29763	+	0.381019i	−0.441260	+	0.897379i	$0.645468\pi$
$884$	6.47436	−	18.7064i	0.217756	−	0.629165i
$885$	−11.5060	+	8.60170i	−0.386771	+	0.289143i
$886$	−1.07541	−	22.5756i	−0.0361290	−	0.758442i
$887$	1.02397	+	5.31287i	0.0343816	+	0.178389i	0.995060	−	0.0992746i	$-0.0316522\pi$
$887$	1.02397	+	5.31287i	0.0343816	+	0.178389i	−0.960679	+	0.277663i	$0.910440\pi$
$888$	−3.68129	−	0.621487i	−0.123536	−	0.0208557i
$889$	1.70346	+	4.25503i	0.0571321	+	0.142709i
$890$	1.45420	+	1.26007i	0.0487447	+	0.0422376i
$891$	0.962182	−	6.57146i	0.0322343	−	0.220152i
$892$	−22.1299	−	6.49791i	−0.740963	−	0.217566i
$893$	−2.72685	+	3.82932i	−0.0912504	+	0.128143i
$894$	−6.11752	−	1.95992i	−0.204600	−	0.0655494i
$895$	6.02565	+	11.6881i	0.201415	+	0.390691i
$896$	1.10037	−	1.90590i	0.0367609	−	0.0636718i
$897$	−9.42939	+	39.9741i	−0.314838	+	1.33470i
$898$	−6.58544	−	11.4063i	−0.219759	−	0.380634i
$899$	0.801212	−	1.24671i	0.0267219	−	0.0415801i
$900$	8.47518	−	8.86554i	0.282506	−	0.295518i
$901$	−7.88333	−	17.2621i	−0.262632	−	0.575083i
$902$	−0.761060	−	3.13713i	−0.0253405	−	0.104455i
$903$	−0.168651	−	1.00691i	−0.00561236	−	0.0335079i
$904$	−15.8781	+	5.49547i	−0.528098	+	0.182777i
$905$	7.89476	−	10.0390i	0.262431	−	0.333708i
$906$	−22.4979	−	18.6003i	−0.747442	−	0.617953i
$907$	56.4888	+	19.5510i	1.87568	+	0.649179i	0.978028	+	0.208473i	$0.0668493\pi$
$907$	56.4888	+	19.5510i	1.87568	+	0.649179i	0.897651	+	0.440706i	$0.145272\pi$
$908$	9.32015	−	5.98970i	0.309300	−	0.198775i
$909$	14.0927	−	2.69725i	0.467424	−	0.0894621i
$910$	6.80398	+	7.85221i	0.225550	+	0.260298i
$911$	2.49393	+	2.37796i	0.0826276	+	0.0787853i	0.730268	−	0.683161i	$-0.239395\pi$
$911$	2.49393	+	2.37796i	0.0826276	+	0.0787853i	−0.647640	+	0.761947i	$0.724244\pi$
$912$	0.0725843	−	1.00572i	0.00240350	−	0.0333029i
$913$	−0.0413758	−	0.119547i	−0.00136934	−	0.00395644i
$914$	5.57750	+	7.83250i	0.184487	+	0.259076i
$915$	−13.9115	+	15.2833i	−0.459899	+	0.505249i
$916$	10.7660	+	7.66645i	0.355719	+	0.253307i
$917$	3.47795	+	24.1897i	0.114852	+	0.798813i
$918$	3.40999	+	20.5217i	0.112546	+	0.677317i
$919$			42.8092i			1.41215i	0.708139	+	0.706073i	$0.249535\pi$
$919$			42.8092i			1.41215i	−0.708139	+	0.706073i	$0.750465\pi$
$920$	4.00367	−	2.22265i	0.131997	−	0.0732787i
$921$	25.1973	+	12.2602i	0.830278	+	0.403988i
$922$	35.4335	−	18.2672i	1.16694	−	0.601600i
$923$	−3.50193	+	8.74739i	−0.115267	+	0.287924i
$924$	1.34649	+	2.46971i	0.0442963	+	0.0812474i
$925$	8.56377	−	2.07755i	0.281575	−	0.0683093i
$926$	29.1412	+	13.3083i	0.957640	+	0.437339i
$927$	−27.1796	−	17.5170i	−0.892695	−	0.575332i
$928$	−1.37321	+	9.55090i	−0.0450779	+	0.313524i
$929$	−4.66744	+	4.89507i	−0.153134	+	0.160602i	−0.795832	−	0.605517i	$-0.792966\pi$
$929$	−4.66744	+	4.89507i	−0.153134	+	0.160602i	0.642698	+	0.766119i	$0.277815\pi$
$930$	0.0658999	−	0.245308i	0.00216094	−	0.00804395i
$931$	1.25414	−	0.0597419i	0.0411027	−	0.00195796i
$932$	12.5834	−	0.599421i	0.412183	−	0.0196347i
$933$	6.29091	−	23.4175i	0.205955	−	0.766653i
$934$	−24.4586	+	25.6514i	−0.800308	+	0.839339i
$935$	0.401469	−	2.79228i	0.0131294	−	0.0913173i
$936$	−12.4681	−	8.03554i	−0.407532	−	0.262650i
$937$	30.2879	+	13.8320i	0.989463	+	0.451873i	0.843332	−	0.537393i	$-0.180591\pi$
$937$	30.2879	+	13.8320i	0.989463	+	0.451873i	0.146131	+	0.989265i	$0.453318\pi$
$938$	−33.7485	+	8.18729i	−1.10193	+	0.267324i
$939$	17.6708	+	32.4114i	0.576664	+	1.05771i
$940$	2.86565	−	7.15804i	0.0934671	−	0.233470i
$941$	−13.2672	+	6.83974i	−0.432500	+	0.222969i	−0.660708	−	0.750643i	$-0.729744\pi$
$941$	−13.2672	+	6.83974i	−0.432500	+	0.222969i	0.228208	+	0.973612i	$0.426713\pi$
$942$	−33.5555	−	16.3271i	−1.09330	−	0.531965i
$943$	−12.6895	−	16.7064i	−0.413227	−	0.544035i
$944$			8.68641i			0.282719i
$945$	−10.2231	−	3.83563i	−0.332559	−	0.124773i
$946$	−0.0281283	−	0.195637i	−0.000914530	−	0.00636069i
$947$	−0.668290	−	0.475887i	−0.0217165	−	0.0154643i	0.569147	−	0.822236i	$-0.307273\pi$
$947$	−0.668290	−	0.475887i	−0.0217165	−	0.0154643i	−0.590864	+	0.806771i	$0.701213\pi$
$948$	14.6266	−	16.0689i	0.475049	−	0.521894i
$949$	−12.4822	−	17.5288i	−0.405191	−	0.569010i
$950$	0.778440	+	2.24915i	0.0252559	+	0.0729722i
$951$	0.732306	−	10.1468i	0.0237467	−	0.329033i
$952$	−6.37669	−	6.08016i	−0.206670	−	0.197059i
$953$	−17.7152	−	20.4445i	−0.573852	−	0.662261i	0.392419	−	0.919786i	$-0.371638\pi$
$953$	−17.7152	−	20.4445i	−0.573852	−	0.662261i	−0.966271	+	0.257526i	$0.917093\pi$
$954$	−13.9666	+	2.67312i	−0.452185	+	0.0865455i
$955$	20.0210	−	12.8667i	0.647864	−	0.416357i
$956$	17.4654	+	6.04484i	0.564872	+	0.195504i
$957$	−9.50525	−	7.85854i	−0.307261	−	0.254030i
$958$	−2.59626	+	3.30141i	−0.0838814	+	0.106664i
$959$	13.2098	−	4.57195i	0.426566	−	0.147636i
$960$	0.273201	+	1.63111i	0.00881751	+	0.0526438i
$961$	−7.30297	−	30.1032i	−0.235580	−	0.971072i
$962$	−4.42728	−	9.69439i	−0.142741	−	0.312560i
$963$	−0.645363	+	0.675088i	−0.0207965	+	0.0217544i
$964$	−13.9988	+	21.7826i	−0.450872	+	0.701570i
$965$	−7.03951	−	12.1928i	−0.226610	−	0.392500i
$966$	14.4411	+	11.2090i	0.464635	+	0.360644i
$967$	−6.17977	+	10.7037i	−0.198728	+	0.344207i	−0.948116	−	0.317924i	$-0.897014\pi$
$967$	−6.17977	+	10.7037i	−0.198728	+	0.344207i	0.749388	+	0.662131i	$0.230348\pi$
$968$	−4.79096	−	9.29316i	−0.153987	−	0.298693i
$969$	−3.84446	−	1.23168i	−0.123502	−	0.0395673i
$970$	6.09137	−	8.55413i	0.195582	−	0.274657i
$971$	−13.4790	−	3.95780i	−0.432563	−	0.127012i	0.0582004	−	0.998305i	$-0.481464\pi$
$971$	−13.4790	−	3.95780i	−0.432563	−	0.127012i	−0.490763	+	0.871293i	$0.663282\pi$
$972$	15.5451	+	1.16231i	0.498608	+	0.0372812i
$973$	−0.425516	−	0.368712i	−0.0136414	−	0.0118204i
$974$	−9.13442	−	22.8167i	−0.292686	−	0.731093i
$975$	34.5233	+	5.82832i	1.10563	+	0.186656i
$976$	2.36492	+	12.2703i	0.0756991	+	0.392764i
$977$	−2.46977	−	51.8469i	−0.0790150	−	1.65873i	−0.596186	−	0.802846i	$-0.703318\pi$
$977$	−2.46977	−	51.8469i	−0.0790150	−	1.65873i	0.517171	−	0.855882i	$-0.326985\pi$
$978$	−1.36497	+	1.02043i	−0.0436469	+	0.0326297i
$979$	−0.486383	+	1.40531i	−0.0155449	+	0.0449139i
$980$	−1.97589	+	0.580174i	−0.0631175	+	0.0185330i
$981$	−5.04669	−	8.76728i	−0.161128	−	0.279918i
$982$	−7.30541	+	8.43089i	−0.233125	+	0.269041i
$983$	42.6520	−	4.07277i	1.36039	−	0.129901i	0.610789	−	0.791794i	$-0.290852\pi$
$983$	42.6520	−	4.07277i	1.36039	−	0.129901i	0.749599	+	0.661892i	$0.230246\pi$
$984$	7.21852	−	2.30237i	0.230118	−	0.0733968i
$985$	−2.13836	+	22.3940i	−0.0681339	+	0.713531i
$986$	35.8636	+	14.3576i	1.14213	+	0.457239i
$987$	30.7722	−	0.712613i	0.979489	−	0.0226827i
$988$	2.49281	−	1.43923i	0.0793070	−	0.0457879i
$989$	−0.676190	−	1.09210i	−0.0215016	−	0.0347268i
$990$	−1.96143	−	0.788181i	−0.0623383	−	0.0250500i
$991$	33.5409	+	21.5555i	1.06546	+	0.684732i	0.951155	−	0.308714i	$-0.0998985\pi$
$991$	33.5409	+	21.5555i	1.06546	+	0.684732i	0.114308	+	0.993445i	$0.463535\pi$
$992$	−0.0949405	−	0.120727i	−0.00301436	−	0.00383307i
$993$	−21.1491	+	11.5305i	−0.671146	+	0.365910i
$994$	2.89411	+	3.03525i	0.0917955	+	0.0962724i
$995$	−5.87533	+	4.18380i	−0.186260	+	0.132635i
$996$	0.273024	−	0.116707i	0.00865111	−	0.00369801i
$997$	37.9796	−	15.2048i	1.20283	−	0.481539i	0.318283	−	0.947996i	$-0.396894\pi$
$997$	37.9796	−	15.2048i	1.20283	−	0.481539i	0.884544	+	0.466456i	$0.154470\pi$
$998$	8.20100	+	27.9300i	0.259598	+	0.884110i
$999$	8.95315	+	6.72937i	0.283265	+	0.212908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.113.19	yes	480
9.2	odd	6	inner	414.2.p.a.389.16	yes	480
23.11	odd	22	inner	414.2.p.a.149.16	yes	480
207.11	even	66	inner	414.2.p.a.11.19	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.11.19	✓	480	207.11	even	66	inner
414.2.p.a.113.19	yes	480	1.1	even	1	trivial
414.2.p.a.149.16	yes	480	23.11	odd	22	inner
414.2.p.a.389.16	yes	480	9.2	odd	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998867 + 0.0475819i) q^{2} +(0.528452 - 1.64947i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.691050 + 0.658915i) q^{5} +(0.606339 - 1.62245i) q^{6} +(0.416494 - 2.16098i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.44148 - 1.74333i) q^{9} +O(q^{10})\)	\(q+(0.998867 + 0.0475819i) q^{2} +(0.528452 - 1.64947i) q^{3} +(0.995472 + 0.0950560i) q^{4} +(-0.691050 + 0.658915i) q^{5} +(0.606339 - 1.62245i) q^{6} +(0.416494 - 2.16098i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.44148 - 1.74333i) q^{9} +(-0.721620 + 0.625287i) q^{10} +(-0.655914 - 0.338147i) q^{11} +(0.682851 - 1.59176i) q^{12} +(4.85504 - 0.935732i) q^{13} +(0.518846 - 2.13871i) q^{14} +(0.721671 + 1.48807i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.66314 - 3.64176i) q^{17} +(-2.35576 - 1.85752i) q^{18} +(0.529556 - 0.241840i) q^{19} +(-0.750555 + 0.590243i) q^{20} +(-3.34436 - 1.82897i) q^{21} +(-0.639082 - 0.368974i) q^{22} +(-4.76578 - 0.536043i) q^{23} +(0.757817 - 1.55747i) q^{24} +(-0.194528 + 4.08365i) q^{25} +(4.89406 - 0.703660i) q^{26} +(-4.16576 + 3.10587i) q^{27} +(0.620023 - 2.11160i) q^{28} +(0.917207 + 9.60542i) q^{29} +(0.650048 + 1.52072i) q^{30} +(-0.120727 - 0.0949405i) q^{31} +(0.971812 + 0.235759i) q^{32} +(-0.904382 + 0.903214i) q^{33} +(1.83453 - 3.55850i) q^{34} +(1.13608 + 1.76778i) q^{35} +(-2.26471 - 1.96751i) q^{36} +(-0.607266 - 2.06816i) q^{37} +(0.540464 - 0.216369i) q^{38} +(1.02220 - 8.50271i) q^{39} +(-0.777790 + 0.553861i) q^{40} +(3.01873 + 3.16595i) q^{41} +(-3.25355 - 1.98603i) q^{42} +(0.165565 + 0.210533i) q^{43} +(-0.620801 - 0.398965i) q^{44} +(2.83589 - 0.403998i) q^{45} +(-4.73488 - 0.762201i) q^{46} +(-6.99317 + 4.03751i) q^{47} +(0.831066 - 1.51965i) q^{48} +(2.00221 + 0.801566i) q^{49} +(-0.388616 + 4.06977i) q^{50} +(-5.12807 - 4.66779i) q^{51} +(4.92200 - 0.469994i) q^{52} +(3.10406 - 3.58228i) q^{53} +(-4.30883 + 2.90413i) q^{54} +(0.676080 - 0.198515i) q^{55} +(0.719794 - 2.07971i) q^{56} +(-0.119062 - 1.00129i) q^{57} +(0.459123 + 9.63819i) q^{58} +(1.64391 + 8.52943i) q^{59} +(0.576953 + 1.54993i) q^{60} +(4.64436 + 11.6010i) q^{61} +(-0.116072 - 0.100577i) q^{62} +(-4.78416 + 4.54989i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.73851 + 3.84570i) q^{65} +(-0.946334 + 0.859158i) q^{66} +(-7.23072 - 14.0256i) q^{67} +(2.00178 - 3.46718i) q^{68} +(-3.40267 + 7.57772i) q^{69} +(1.05068 + 1.81983i) q^{70} +(-1.03028 + 1.60314i) q^{71} +(-2.16852 - 2.07304i) q^{72} +(-1.80797 - 3.95890i) q^{73} +(-0.508171 - 2.09471i) q^{74} +(6.63304 + 2.47888i) q^{75} +(0.550147 - 0.190408i) q^{76} +(-1.00391 + 1.27658i) q^{77} +(1.42562 - 8.44444i) q^{78} +(11.8552 + 4.10314i) q^{79} +(-0.803262 + 0.516225i) q^{80} +(2.92161 + 8.51259i) q^{81} +(2.86467 + 3.30600i) q^{82} +(0.124068 + 0.118299i) q^{83} +(-3.15537 - 2.13859i) q^{84} +(1.25030 + 3.61251i) q^{85} +(0.155360 + 0.218172i) q^{86} +(16.3285 + 3.56311i) q^{87} +(-0.601115 - 0.428052i) q^{88} +(-0.286790 - 1.99467i) q^{89} +(2.85190 - 0.268603i) q^{90} -10.8814i q^{91} +(-4.69325 - 0.986632i) q^{92} +(-0.220399 + 0.148963i) q^{93} +(-7.17736 + 3.70019i) q^{94} +(-0.206598 + 0.516056i) q^{95} +(0.902432 - 1.47838i) q^{96} +(-10.6880 + 2.59288i) q^{97} +(1.96181 + 0.895927i) q^{98} +(1.01190 + 1.96905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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