LMFDB - Embedded newform 966.2.h.b.827.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.1
Character	$\chi$	$=$	966.827
Dual form			966.2.h.b.827.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.69648 - 0.349201i) q^{3} -1.00000 q^{4} -1.62492 q^{5} +(-0.349201 + 1.69648i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(2.75612 + 1.18483i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.69648 - 0.349201i) q^{3} -1.00000 q^{4} -1.62492 q^{5} +(-0.349201 + 1.69648i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(2.75612 + 1.18483i) q^{9} +1.62492i q^{10} +3.65827 q^{11} +(1.69648 + 0.349201i) q^{12} +0.597342 q^{13} -1.00000 q^{14} +(2.75666 + 0.567425i) q^{15} +1.00000 q^{16} +3.33518 q^{17} +(1.18483 - 2.75612i) q^{18} +0.263613i q^{19} +1.62492 q^{20} +(-0.349201 + 1.69648i) q^{21} -3.65827i q^{22} +(3.04755 - 3.70303i) q^{23} +(0.349201 - 1.69648i) q^{24} -2.35962 q^{25} -0.597342i q^{26} +(-4.26197 - 2.97248i) q^{27} +1.00000i q^{28} -1.04785i q^{29} +(0.567425 - 2.75666i) q^{30} -8.47884 q^{31} -1.00000i q^{32} +(-6.20620 - 1.27747i) q^{33} -3.33518i q^{34} +1.62492i q^{35} +(-2.75612 - 1.18483i) q^{36} -7.11484i q^{37} +0.263613 q^{38} +(-1.01338 - 0.208592i) q^{39} -1.62492i q^{40} +5.26088i q^{41} +(1.69648 + 0.349201i) q^{42} +0.223081i q^{43} -3.65827 q^{44} +(-4.47848 - 1.92525i) q^{45} +(-3.70303 - 3.04755i) q^{46} -5.31374i q^{47} +(-1.69648 - 0.349201i) q^{48} -1.00000 q^{49} +2.35962i q^{50} +(-5.65807 - 1.16465i) q^{51} -0.597342 q^{52} +4.55315 q^{53} +(-2.97248 + 4.26197i) q^{54} -5.94442 q^{55} +1.00000 q^{56} +(0.0920539 - 0.447216i) q^{57} -1.04785 q^{58} -6.54561i q^{59} +(-2.75666 - 0.567425i) q^{60} -8.08845i q^{61} +8.47884i q^{62} +(1.18483 - 2.75612i) q^{63} -1.00000 q^{64} -0.970636 q^{65} +(-1.27747 + 6.20620i) q^{66} -12.2795i q^{67} -3.33518 q^{68} +(-6.46322 + 5.21793i) q^{69} +1.62492 q^{70} +3.11022i q^{71} +(-1.18483 + 2.75612i) q^{72} -7.94212 q^{73} -7.11484 q^{74} +(4.00306 + 0.823981i) q^{75} -0.263613i q^{76} -3.65827i q^{77} +(-0.208592 + 1.01338i) q^{78} -8.69069i q^{79} -1.62492 q^{80} +(6.19237 + 6.53104i) q^{81} +5.26088 q^{82} +8.43427 q^{83} +(0.349201 - 1.69648i) q^{84} -5.41941 q^{85} +0.223081 q^{86} +(-0.365909 + 1.77766i) q^{87} +3.65827i q^{88} -7.18930 q^{89} +(-1.92525 + 4.47848i) q^{90} -0.597342i q^{91} +(-3.04755 + 3.70303i) q^{92} +(14.3842 + 2.96082i) q^{93} -5.31374 q^{94} -0.428351i q^{95} +(-0.349201 + 1.69648i) q^{96} +11.3472i q^{97} +1.00000i q^{98} +(10.0826 + 4.33442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.69648	−	0.349201i	−0.979466	−	0.201611i
$3$	−1.69648	−	0.349201i	−0.979466	−	0.201611i
$4$	−1.00000			−0.500000
$5$	−1.62492			−0.726688			−0.363344	−	0.931655i	$-0.618365\pi$
$5$	−1.62492			−0.726688			−0.363344	+	0.931655i	$0.618365\pi$
$6$	−0.349201	+	1.69648i	−0.142561	+	0.692587i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.00000i			0.353553i
$9$	2.75612	+	1.18483i	0.918706	+	0.394942i
$10$			1.62492i			0.513846i
$11$	3.65827			1.10301			0.551505	−	0.834171i	$-0.314054\pi$
$11$	3.65827			1.10301			0.551505	+	0.834171i	$0.314054\pi$
$12$	1.69648	+	0.349201i	0.489733	+	0.100806i
$13$	0.597342			0.165673			0.0828364	−	0.996563i	$-0.473602\pi$
$13$	0.597342			0.165673			0.0828364	+	0.996563i	$0.473602\pi$
$14$	−1.00000			−0.267261
$15$	2.75666	+	0.567425i	0.711766	+	0.146508i
$16$	1.00000			0.250000
$17$	3.33518			0.808899			0.404449	−	0.914560i	$-0.367463\pi$
$17$	3.33518			0.808899			0.404449	+	0.914560i	$0.367463\pi$
$18$	1.18483	−	2.75612i	0.279266	−	0.649623i
$19$			0.263613i			0.0604770i	0.999543	+	0.0302385i	$0.00962668\pi$
$19$			0.263613i			0.0604770i	−0.999543	+	0.0302385i	$0.990373\pi$
$20$	1.62492			0.363344
$21$	−0.349201	+	1.69648i	−0.0762018	+	0.370203i
$22$		−	3.65827i		−	0.779946i
$23$	3.04755	−	3.70303i	0.635458	−	0.772136i
$23$	3.04755	−	3.70303i	0.635458	−	0.772136i
$24$	0.349201	−	1.69648i	0.0712803	−	0.346293i
$25$	−2.35962			−0.471924
$26$		−	0.597342i		−	0.117148i
$27$	−4.26197	−	2.97248i	−0.820216	−	0.572054i
$28$			1.00000i			0.188982i
$29$		−	1.04785i		−	0.194581i	−0.995256	−	0.0972903i	$-0.968982\pi$
$29$		−	1.04785i		−	0.194581i	0.995256	−	0.0972903i	$-0.0310175\pi$
$30$	0.567425	−	2.75666i	0.103597	−	0.503295i
$31$	−8.47884			−1.52284			−0.761422	−	0.648256i	$-0.775499\pi$
$31$	−8.47884			−1.52284			−0.761422	+	0.648256i	$0.775499\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.20620	−	1.27747i	−1.08036	−	0.222379i
$34$		−	3.33518i		−	0.571978i
$35$			1.62492i			0.274662i
$36$	−2.75612	−	1.18483i	−0.459353	−	0.197471i
$37$		−	7.11484i		−	1.16967i	−0.811151	−	0.584836i	$-0.801159\pi$
$37$		−	7.11484i		−	1.16967i	0.811151	−	0.584836i	$-0.198841\pi$
$38$	0.263613			0.0427637
$39$	−1.01338	−	0.208592i	−0.162271	−	0.0334015i
$40$		−	1.62492i		−	0.256923i
$41$			5.26088i			0.821611i	0.911723	+	0.410806i	$0.134753\pi$
$41$			5.26088i			0.821611i	−0.911723	+	0.410806i	$0.865247\pi$
$42$	1.69648	+	0.349201i	0.261773	+	0.0538828i
$43$			0.223081i			0.0340196i	0.999855	+	0.0170098i	$0.00541464\pi$
$43$			0.223081i			0.0340196i	−0.999855	+	0.0170098i	$0.994585\pi$
$44$	−3.65827			−0.551505
$45$	−4.47848	−	1.92525i	−0.667613	−	0.287000i
$46$	−3.70303	−	3.04755i	−0.545982	−	0.449337i
$47$		−	5.31374i		−	0.775089i	−0.921851	−	0.387545i	$-0.873323\pi$
$47$		−	5.31374i		−	0.775089i	0.921851	−	0.387545i	$-0.126677\pi$
$48$	−1.69648	−	0.349201i	−0.244866	−	0.0504028i
$49$	−1.00000			−0.142857
$50$			2.35962i			0.333701i
$51$	−5.65807	−	1.16465i	−0.792289	−	0.163083i
$52$	−0.597342			−0.0828364
$53$	4.55315			0.625423			0.312712	−	0.949848i	$-0.398763\pi$
$53$	4.55315			0.625423			0.312712	+	0.949848i	$0.398763\pi$
$54$	−2.97248	+	4.26197i	−0.404503	+	0.579980i
$55$	−5.94442			−0.801545
$56$	1.00000			0.133631
$57$	0.0920539	−	0.447216i	0.0121928	−	0.0592352i
$58$	−1.04785			−0.137589
$59$		−	6.54561i		−	0.852166i	−0.904684	−	0.426083i	$-0.859893\pi$
$59$		−	6.54561i		−	0.852166i	0.904684	−	0.426083i	$-0.140107\pi$
$60$	−2.75666	−	0.567425i	−0.355883	−	0.0732542i
$61$		−	8.08845i		−	1.03562i	−0.855496	−	0.517810i	$-0.826747\pi$
$61$		−	8.08845i		−	1.03562i	0.855496	−	0.517810i	$-0.173253\pi$
$62$			8.47884i			1.07681i
$63$	1.18483	−	2.75612i	0.149274	−	0.347238i
$64$	−1.00000			−0.125000
$65$	−0.970636			−0.120393
$66$	−1.27747	+	6.20620i	−0.157246	+	0.763931i
$67$		−	12.2795i		−	1.50018i	−0.661335	−	0.750090i	$-0.730010\pi$
$67$		−	12.2795i		−	1.50018i	0.661335	−	0.750090i	$-0.269990\pi$
$68$	−3.33518			−0.404449
$69$	−6.46322	+	5.21793i	−0.778080	+	0.628165i
$70$	1.62492			0.194216
$71$			3.11022i			0.369116i	0.982822	+	0.184558i	$0.0590853\pi$
$71$			3.11022i			0.369116i	−0.982822	+	0.184558i	$0.940915\pi$
$72$	−1.18483	+	2.75612i	−0.139633	+	0.324812i
$73$	−7.94212			−0.929554			−0.464777	−	0.885428i	$-0.653866\pi$
$73$	−7.94212			−0.929554			−0.464777	+	0.885428i	$0.653866\pi$
$74$	−7.11484			−0.827084
$75$	4.00306	+	0.823981i	0.462233	+	0.0951451i
$76$		−	0.263613i		−	0.0302385i
$77$		−	3.65827i		−	0.416899i
$78$	−0.208592	+	1.01338i	−0.0236184	+	0.114743i
$79$		−	8.69069i		−	0.977779i	−0.872346	−	0.488889i	$-0.837402\pi$
$79$		−	8.69069i		−	0.977779i	0.872346	−	0.488889i	$-0.162598\pi$
$80$	−1.62492			−0.181672
$81$	6.19237	+	6.53104i	0.688041	+	0.725672i
$82$	5.26088			0.580967
$83$	8.43427			0.925782			0.462891	−	0.886415i	$-0.346812\pi$
$83$	8.43427			0.925782			0.462891	+	0.886415i	$0.346812\pi$
$84$	0.349201	−	1.69648i	0.0381009	−	0.185102i
$85$	−5.41941			−0.587817
$86$	0.223081			0.0240555
$87$	−0.365909	+	1.77766i	−0.0392296	+	0.190585i
$88$			3.65827i			0.389973i
$89$	−7.18930			−0.762065			−0.381032	−	0.924562i	$-0.624431\pi$
$89$	−7.18930			−0.762065			−0.381032	+	0.924562i	$0.624431\pi$
$90$	−1.92525	+	4.47848i	−0.202940	+	0.472074i
$91$		−	0.597342i		−	0.0626185i
$92$	−3.04755	+	3.70303i	−0.317729	+	0.386068i
$93$	14.3842	+	2.96082i	1.49157	+	0.307022i
$94$	−5.31374			−0.548071
$95$		−	0.428351i		−	0.0439479i
$96$	−0.349201	+	1.69648i	−0.0356401	+	0.173147i
$97$			11.3472i			1.15213i	0.817404	+	0.576065i	$0.195413\pi$
$97$			11.3472i			1.15213i	−0.817404	+	0.576065i	$0.804587\pi$
$98$			1.00000i			0.101015i
$99$	10.0826	+	4.33442i	1.01334	+	0.435625i
$100$	2.35962			0.235962
$101$		−	1.42782i		−	0.142073i	−0.997474	−	0.0710367i	$-0.977369\pi$
$101$		−	1.42782i		−	0.142073i	0.997474	−	0.0710367i	$-0.0226307\pi$
$102$	−1.16465	+	5.65807i	−0.115317	+	0.560233i
$103$		−	7.25192i		−	0.714553i	−0.933999	−	0.357276i	$-0.883705\pi$
$103$		−	7.25192i		−	0.714553i	0.933999	−	0.357276i	$-0.116295\pi$
$104$			0.597342i			0.0585742i
$105$	0.567425	−	2.75666i	0.0553750	−	0.269022i
$106$		−	4.55315i		−	0.442241i
$107$	19.0320			1.83989			0.919946	−	0.392045i	$-0.128232\pi$
$107$	19.0320			1.83989			0.919946	+	0.392045i	$0.128232\pi$
$108$	4.26197	+	2.97248i	0.410108	+	0.286027i
$109$		−	3.88879i		−	0.372478i	−0.982504	−	0.186239i	$-0.940370\pi$
$109$		−	3.88879i		−	0.372478i	0.982504	−	0.186239i	$-0.0596299\pi$
$110$			5.94442i			0.566778i
$111$	−2.48451	+	12.0702i	−0.235819	+	1.14565i
$112$		−	1.00000i		−	0.0944911i
$113$	−15.7843			−1.48487			−0.742433	−	0.669921i	$-0.766328\pi$
$113$	−15.7843			−1.48487			−0.742433	+	0.669921i	$0.766328\pi$
$114$	−0.447216	−	0.0920539i	−0.0418856	−	0.00862164i
$115$	−4.95204	+	6.01715i	−0.461780	+	0.561102i
$116$			1.04785i			0.0972903i
$117$	1.64635	+	0.707747i	0.152205	+	0.0654312i
$118$	−6.54561			−0.602573
$119$		−	3.33518i		−	0.305735i
$120$	−0.567425	+	2.75666i	−0.0517985	+	0.251647i
$121$	2.38296			0.216632
$122$	−8.08845			−0.732294
$123$	1.83710	−	8.92500i	0.165646	−	0.804740i
$124$	8.47884			0.761422
$125$	11.9588			1.06963
$126$	−2.75612	−	1.18483i	−0.245534	−	0.105553i
$127$	8.20558			0.728128			0.364064	−	0.931374i	$-0.381389\pi$
$127$	8.20558			0.728128			0.364064	+	0.931374i	$0.381389\pi$
$128$			1.00000i			0.0883883i
$129$	0.0779001	−	0.378454i	0.00685872	−	0.0333210i
$130$			0.970636i			0.0851304i
$131$		−	15.5346i		−	1.35726i	−0.734479	−	0.678631i	$-0.762573\pi$
$131$		−	15.5346i		−	1.35726i	0.734479	−	0.678631i	$-0.237427\pi$
$132$	6.20620	+	1.27747i	0.540181	+	0.111190i
$133$	0.263613			0.0228582
$134$	−12.2795			−1.06079
$135$	6.92538	+	4.83005i	0.596042	+	0.415705i
$136$			3.33518i			0.285989i
$137$	−2.46513			−0.210610			−0.105305	−	0.994440i	$-0.533582\pi$
$137$	−2.46513			−0.210610			−0.105305	+	0.994440i	$0.533582\pi$
$138$	5.21793	+	6.46322i	0.444180	+	0.550186i
$139$	−18.8869			−1.60197			−0.800983	−	0.598688i	$-0.795689\pi$
$139$	−18.8869			−1.60197			−0.800983	+	0.598688i	$0.795689\pi$
$140$		−	1.62492i		−	0.137331i
$141$	−1.85556	+	9.01468i	−0.156267	+	0.759173i
$142$	3.11022			0.261004
$143$	2.18524			0.182739
$144$	2.75612	+	1.18483i	0.229676	+	0.0987355i
$145$			1.70267i			0.141399i
$146$			7.94212i			0.657294i
$147$	1.69648	+	0.349201i	0.139924	+	0.0288016i
$148$			7.11484i			0.584836i
$149$	5.09636			0.417510			0.208755	−	0.977968i	$-0.433059\pi$
$149$	5.09636			0.417510			0.208755	+	0.977968i	$0.433059\pi$
$150$	0.823981	−	4.00306i	0.0672778	−	0.326848i
$151$	20.4166			1.66148			0.830740	−	0.556661i	$-0.187918\pi$
$151$	20.4166			1.66148			0.830740	+	0.556661i	$0.187918\pi$
$152$	−0.263613			−0.0213819
$153$	9.19214	+	3.95160i	0.743140	+	0.319468i
$154$	−3.65827			−0.294792
$155$	13.7775			1.10663
$156$	1.01338	+	0.208592i	0.0811354	+	0.0167007i
$157$			17.2300i			1.37510i	0.726135	+	0.687552i	$0.241315\pi$
$157$			17.2300i			1.37510i	−0.726135	+	0.687552i	$0.758685\pi$
$158$	−8.69069			−0.691394
$159$	−7.72435	−	1.58996i	−0.612581	−	0.126092i
$160$			1.62492i			0.128462i
$161$	−3.70303	−	3.04755i	−0.291840	−	0.240181i
$162$	6.53104	−	6.19237i	0.513127	−	0.486519i
$163$	−7.47733			−0.585670			−0.292835	−	0.956163i	$-0.594599\pi$
$163$	−7.47733			−0.585670			−0.292835	+	0.956163i	$0.594599\pi$
$164$		−	5.26088i		−	0.410806i
$165$	10.0846	+	2.07579i	0.785086	+	0.161600i
$166$		−	8.43427i		−	0.654627i
$167$		−	14.5778i		−	1.12806i	−0.825754	−	0.564030i	$-0.809250\pi$
$167$		−	14.5778i		−	1.12806i	0.825754	−	0.564030i	$-0.190750\pi$
$168$	−1.69648	−	0.349201i	−0.130887	−	0.0269414i
$169$	−12.6432			−0.972553
$170$			5.41941i			0.415650i
$171$	−0.312336	+	0.726549i	−0.0238849	+	0.0555606i
$172$		−	0.223081i		−	0.0170098i
$173$		−	24.9204i		−	1.89466i	−0.320260	−	0.947330i	$-0.603770\pi$
$173$		−	24.9204i		−	1.89466i	0.320260	−	0.947330i	$-0.396230\pi$
$174$	1.77766	+	0.365909i	0.134764	+	0.0277395i
$175$			2.35962i			0.178371i
$176$	3.65827			0.275753
$177$	−2.28573	+	11.1045i	−0.171806	+	0.834668i
$178$			7.18930i			0.538861i
$179$			3.98382i			0.297764i	0.988855	+	0.148882i	$0.0475675\pi$
$179$			3.98382i			0.297764i	−0.988855	+	0.148882i	$0.952432\pi$
$180$	4.47848	+	1.92525i	0.333806	+	0.143500i
$181$			9.94679i			0.739339i	0.929163	+	0.369670i	$0.120529\pi$
$181$			9.94679i			0.739339i	−0.929163	+	0.369670i	$0.879471\pi$
$182$	−0.597342			−0.0442779
$183$	−2.82449	+	13.7219i	−0.208792	+	1.01435i
$184$	3.70303	+	3.04755i	0.272991	+	0.224668i
$185$			11.5611i			0.849988i
$186$	2.96082	−	14.3842i	0.217098	−	1.05470i
$187$	12.2010			0.892224
$188$			5.31374i			0.387545i
$189$	−2.97248	+	4.26197i	−0.216216	+	0.310013i
$190$	−0.428351			−0.0310759
$191$	−3.68150			−0.266384			−0.133192	−	0.991090i	$-0.542523\pi$
$191$	−3.68150			−0.266384			−0.133192	+	0.991090i	$0.542523\pi$
$192$	1.69648	+	0.349201i	0.122433	+	0.0252014i
$193$	15.8377			1.14002			0.570012	−	0.821636i	$-0.306938\pi$
$193$	15.8377			1.14002			0.570012	+	0.821636i	$0.306938\pi$
$194$	11.3472			0.814679
$195$	1.64667	+	0.338947i	0.117920	+	0.0242725i
$196$	1.00000			0.0714286
$197$		−	0.305296i		−	0.0217515i	−0.999941	−	0.0108757i	$-0.996538\pi$
$197$		−	0.305296i		−	0.0217515i	0.999941	−	0.0108757i	$-0.00346192\pi$
$198$	4.33442	−	10.0826i	0.308034	−	0.716541i
$199$		−	19.0168i		−	1.34806i	−0.738702	−	0.674032i	$-0.764561\pi$
$199$		−	19.0168i		−	1.34806i	0.738702	−	0.674032i	$-0.235439\pi$
$200$		−	2.35962i		−	0.166850i
$201$	−4.28801	+	20.8320i	−0.302453	+	1.46938i
$202$	−1.42782			−0.100461
$203$	−1.04785			−0.0735445
$204$	5.65807	+	1.16465i	0.396144	+	0.0815415i
$205$		−	8.54853i		−	0.597055i
$206$	−7.25192			−0.505265
$207$	12.7869	−	6.59518i	0.888748	−	0.458396i
$208$	0.597342			0.0414182
$209$			0.964369i			0.0667068i
$210$	−2.75666	−	0.567425i	−0.190228	−	0.0391560i
$211$	4.03120			0.277519			0.138760	−	0.990326i	$-0.455688\pi$
$211$	4.03120			0.277519			0.138760	+	0.990326i	$0.455688\pi$
$212$	−4.55315			−0.312712
$213$	1.08609	−	5.27644i	0.0744178	−	0.361536i
$214$		−	19.0320i		−	1.30100i
$215$		−	0.362490i		−	0.0247216i
$216$	2.97248	−	4.26197i	0.202251	−	0.289990i
$217$			8.47884i			0.575581i
$218$	−3.88879			−0.263382
$219$	13.4737	+	2.77339i	0.910466	+	0.187408i
$220$	5.94442			0.400772
$221$	1.99224			0.134013
$222$	12.0702	+	2.48451i	0.810100	+	0.166749i
$223$	7.73020			0.517653			0.258826	−	0.965924i	$-0.416664\pi$
$223$	7.73020			0.517653			0.258826	+	0.965924i	$0.416664\pi$
$224$	−1.00000			−0.0668153
$225$	−6.50339	−	2.79574i	−0.433560	−	0.186383i
$226$			15.7843i			1.04996i
$227$	17.5351			1.16384			0.581922	−	0.813244i	$-0.302301\pi$
$227$	17.5351			1.16384			0.581922	+	0.813244i	$0.302301\pi$
$228$	−0.0920539	+	0.447216i	−0.00609642	+	0.0296176i
$229$		−	23.2267i		−	1.53486i	−0.641130	−	0.767432i	$-0.721534\pi$
$229$		−	23.2267i		−	1.53486i	0.641130	−	0.767432i	$-0.278466\pi$
$230$	6.01715	+	4.95204i	0.396759	+	0.326528i
$231$	−1.27747	+	6.20620i	−0.0840514	+	0.408338i
$232$	1.04785			0.0687946
$233$			16.1872i			1.06046i	0.847855	+	0.530228i	$0.177894\pi$
$233$			16.1872i			1.06046i	−0.847855	+	0.530228i	$0.822106\pi$
$234$	0.707747	−	1.64635i	0.0462669	−	0.107625i
$235$			8.63443i			0.563248i
$236$			6.54561i			0.426083i
$237$	−3.03479	+	14.7436i	−0.197131	+	0.957701i
$238$	−3.33518			−0.216187
$239$			4.77505i			0.308872i	0.988003	+	0.154436i	$0.0493561\pi$
$239$			4.77505i			0.308872i	−0.988003	+	0.154436i	$0.950644\pi$
$240$	2.75666	+	0.567425i	0.177942	+	0.0366271i
$241$			19.4210i			1.25102i	0.780217	+	0.625509i	$0.215109\pi$
$241$			19.4210i			1.25102i	−0.780217	+	0.625509i	$0.784891\pi$
$242$		−	2.38296i		−	0.153182i
$243$	−8.22462	−	13.2422i	−0.527609	−	0.849487i
$244$			8.08845i			0.517810i
$245$	1.62492			0.103813
$246$	−8.92500	−	1.83710i	−0.569037	−	0.117129i
$247$			0.157467i			0.0100194i
$248$		−	8.47884i		−	0.538407i
$249$	−14.3086	−	2.94525i	−0.906772	−	0.186648i
$250$		−	11.9588i		−	0.756343i
$251$	−16.4926			−1.04100			−0.520502	−	0.853861i	$-0.674255\pi$
$251$	−16.4926			−1.04100			−0.520502	+	0.853861i	$0.674255\pi$
$252$	−1.18483	+	2.75612i	−0.0746371	+	0.173619i
$253$	11.1488	−	13.5467i	0.700917	−	0.851674i
$254$		−	8.20558i		−	0.514864i
$255$	9.19394	+	1.89246i	0.575747	+	0.118510i
$256$	1.00000			0.0625000
$257$		−	7.68831i		−	0.479583i	−0.970824	−	0.239792i	$-0.922921\pi$
$257$		−	7.68831i		−	0.479583i	0.970824	−	0.239792i	$-0.0770791\pi$
$258$	−0.378454	−	0.0779001i	−0.0235615	−	0.00484985i
$259$	−7.11484			−0.442095
$260$	0.970636			0.0601963
$261$	1.24152	−	2.88799i	0.0768481	−	0.178762i
$262$	−15.5346			−0.959729
$263$	−0.333423			−0.0205597			−0.0102799	−	0.999947i	$-0.503272\pi$
$263$	−0.333423			−0.0205597			−0.0102799	+	0.999947i	$0.503272\pi$
$264$	1.27747	−	6.20620i	0.0786229	−	0.381965i
$265$	−7.39852			−0.454488
$266$		−	0.263613i		−	0.0161632i
$267$	12.1965	+	2.51051i	0.746416	+	0.153641i
$268$			12.2795i			0.750090i
$269$			4.10364i			0.250204i	0.992144	+	0.125102i	$0.0399257\pi$
$269$			4.10364i			0.250204i	−0.992144	+	0.125102i	$0.960074\pi$
$270$	4.83005	−	6.92538i	0.293948	−	0.421465i
$271$	12.4811			0.758172			0.379086	−	0.925362i	$-0.376239\pi$
$271$	12.4811			0.758172			0.379086	+	0.925362i	$0.376239\pi$
$272$	3.33518			0.202225
$273$	−0.208592	+	1.01338i	−0.0126246	+	0.0613326i
$274$			2.46513i			0.148924i
$275$	−8.63213			−0.520537
$276$	6.46322	−	5.21793i	0.389040	−	0.314082i
$277$	−12.5108			−0.751699			−0.375849	−	0.926681i	$-0.622649\pi$
$277$	−12.5108			−0.751699			−0.375849	+	0.926681i	$0.622649\pi$
$278$			18.8869i			1.13276i
$279$	−23.3687	−	10.0460i	−1.39905	−	0.601436i
$280$	−1.62492			−0.0971078
$281$	8.24651			0.491945			0.245973	−	0.969277i	$-0.420893\pi$
$281$	8.24651			0.491945			0.245973	+	0.969277i	$0.420893\pi$
$282$	9.01468	+	1.85556i	0.536816	+	0.110497i
$283$		−	5.12713i		−	0.304776i	−0.988321	−	0.152388i	$-0.951304\pi$
$283$		−	5.12713i		−	0.304776i	0.988321	−	0.152388i	$-0.0486964\pi$
$284$		−	3.11022i		−	0.184558i
$285$	−0.149581	+	0.726692i	−0.00886039	+	0.0430455i
$286$		−	2.18524i		−	0.129216i
$287$	5.26088			0.310540
$288$	1.18483	−	2.75612i	0.0698166	−	0.162406i
$289$	−5.87660			−0.345682
$290$	1.70267			0.0999845
$291$	3.96244	−	19.2503i	0.232282	−	1.12847i
$292$	7.94212			0.464777
$293$	9.13629			0.533748			0.266874	−	0.963731i	$-0.414009\pi$
$293$	9.13629			0.533748			0.266874	+	0.963731i	$0.414009\pi$
$294$	0.349201	−	1.69648i	0.0203658	−	0.0989410i
$295$			10.6361i			0.619259i
$296$	7.11484			0.413542
$297$	−15.5914	−	10.8741i	−0.904707	−	0.630981i
$298$		−	5.09636i		−	0.295224i
$299$	1.82043	−	2.21198i	0.105278	−	0.127922i
$300$	−4.00306	−	0.823981i	−0.231117	−	0.0475726i
$301$	0.223081			0.0128582
$302$		−	20.4166i		−	1.17484i
$303$	−0.498595	+	2.42227i	−0.0286436	+	0.139156i
$304$			0.263613i			0.0151193i
$305$			13.1431i			0.752573i
$306$	3.95160	−	9.19214i	0.225898	−	0.525480i
$307$	−2.86780			−0.163674			−0.0818369	−	0.996646i	$-0.526079\pi$
$307$	−2.86780			−0.163674			−0.0818369	+	0.996646i	$0.526079\pi$
$308$			3.65827i			0.208449i
$309$	−2.53237	+	12.3028i	−0.144062	+	0.699880i
$310$		−	13.7775i		−	0.782508i
$311$			26.8944i			1.52504i	0.646962	+	0.762522i	$0.276039\pi$
$311$			26.8944i			1.52504i	−0.646962	+	0.762522i	$0.723961\pi$
$312$	0.208592	−	1.01338i	0.0118092	−	0.0573714i
$313$			20.2868i			1.14668i	0.819319	+	0.573338i	$0.194352\pi$
$313$			20.2868i			1.14668i	−0.819319	+	0.573338i	$0.805648\pi$
$314$	17.2300			0.972346
$315$	−1.92525	+	4.47848i	−0.108476	+	0.252334i
$316$			8.69069i			0.488889i
$317$		−	0.833720i		−	0.0468264i	−0.999726	−	0.0234132i	$-0.992547\pi$
$317$		−	0.833720i		−	0.0468264i	0.999726	−	0.0234132i	$-0.00745334\pi$
$318$	−1.58996	+	7.72435i	−0.0891607	+	0.433160i
$319$		−	3.83331i		−	0.214624i
$320$	1.62492			0.0908360
$321$	−32.2875	−	6.64598i	−1.80211	−	0.370943i
$322$	−3.04755	+	3.70303i	−0.169833	+	0.206362i
$323$			0.879196i			0.0489198i
$324$	−6.19237	−	6.53104i	−0.344021	−	0.362836i
$325$	−1.40950			−0.0781850
$326$			7.47733i			0.414131i
$327$	−1.35797	+	6.59727i	−0.0750957	+	0.364830i
$328$	−5.26088			−0.290483
$329$	−5.31374			−0.292956
$330$	2.07579	−	10.0846i	0.114269	−	0.555139i
$331$	7.23143			0.397475			0.198738	−	0.980053i	$-0.436316\pi$
$331$	7.23143			0.397475			0.198738	+	0.980053i	$0.436316\pi$
$332$	−8.43427			−0.462891
$333$	8.42985	−	19.6093i	0.461953	−	1.07459i
$334$	−14.5778			−0.797659
$335$			19.9533i			1.09016i
$336$	−0.349201	+	1.69648i	−0.0190505	+	0.0925508i
$337$		−	29.5714i		−	1.61086i	−0.592693	−	0.805429i	$-0.701935\pi$
$337$		−	29.5714i		−	1.61086i	0.592693	−	0.805429i	$-0.298065\pi$
$338$			12.6432i			0.687698i
$339$	26.7779	+	5.51190i	1.45437	+	0.299365i
$340$	5.41941			0.293909
$341$	−31.0179			−1.67971
$342$	0.726549	+	0.312336i	0.0392873	+	0.0168892i
$343$			1.00000i			0.0539949i
$344$	−0.223081			−0.0120277
$345$	10.5022	−	8.47874i	0.565422	−	0.456480i
$346$	−24.9204			−1.33973
$347$		−	19.4105i		−	1.04201i	−0.853554	−	0.521005i	$-0.825557\pi$
$347$		−	19.4105i		−	1.04201i	0.853554	−	0.521005i	$-0.174443\pi$
$348$	0.365909	−	1.77766i	0.0196148	−	0.0952925i
$349$	8.46750			0.453255			0.226628	−	0.973981i	$-0.427230\pi$
$349$	8.46750			0.453255			0.226628	+	0.973981i	$0.427230\pi$
$350$	2.35962			0.126127
$351$	−2.54585	−	1.77559i	−0.135888	−	0.0947738i
$352$		−	3.65827i		−	0.194987i
$353$			14.8486i			0.790313i	0.918614	+	0.395157i	$0.129310\pi$
$353$			14.8486i			0.790313i	−0.918614	+	0.395157i	$0.870690\pi$
$354$	11.1045	+	2.28573i	0.590199	+	0.121485i
$355$		−	5.05388i		−	0.268232i
$356$	7.18930			0.381032
$357$	−1.16465	+	5.65807i	−0.0616396	+	0.299457i
$358$	3.98382			0.210551
$359$	−19.1308			−1.00968			−0.504842	−	0.863212i	$-0.668449\pi$
$359$	−19.1308			−1.00968			−0.504842	+	0.863212i	$0.668449\pi$
$360$	1.92525	−	4.47848i	0.101470	−	0.236037i
$361$	18.9305			0.996343
$362$	9.94679			0.522792
$363$	−4.04265	−	0.832130i	−0.212184	−	0.0436755i
$364$			0.597342i			0.0313092i
$365$	12.9053			0.675496
$366$	13.7219	+	2.82449i	0.717257	+	0.147639i
$367$			16.9690i			0.885774i	0.896577	+	0.442887i	$0.146046\pi$
$367$			16.9690i			0.885774i	−0.896577	+	0.442887i	$0.853954\pi$
$368$	3.04755	−	3.70303i	0.158864	−	0.193034i
$369$	−6.23323	+	14.4996i	−0.324489	+	0.754819i
$370$	11.5611			0.601032
$371$		−	4.55315i		−	0.236388i
$372$	−14.3842	−	2.96082i	−0.745787	−	0.153511i
$373$			8.28644i			0.429056i	0.976718	+	0.214528i	$0.0688213\pi$
$373$			8.28644i			0.429056i	−0.976718	+	0.214528i	$0.931179\pi$
$374$		−	12.2010i		−	0.630898i
$375$	−20.2880	−	4.17603i	−1.04767	−	0.215649i
$376$	5.31374			0.274035
$377$		−	0.625924i		−	0.0322367i
$378$	4.26197	+	2.97248i	0.219212	+	0.152888i
$379$		−	11.8008i		−	0.606165i	−0.952964	−	0.303082i	$-0.901984\pi$
$379$		−	11.8008i		−	0.606165i	0.952964	−	0.303082i	$-0.0980157\pi$
$380$			0.428351i			0.0219740i
$381$	−13.9206	−	2.86539i	−0.713176	−	0.146799i
$382$			3.68150i			0.188362i
$383$	29.3281			1.49860			0.749298	−	0.662234i	$-0.230391\pi$
$383$	29.3281			1.49860			0.749298	+	0.662234i	$0.230391\pi$
$384$	0.349201	−	1.69648i	0.0178201	−	0.0865734i
$385$			5.94442i			0.302956i
$386$		−	15.8377i		−	0.806119i
$387$	−0.264313	+	0.614838i	−0.0134358	+	0.0312540i
$388$		−	11.3472i		−	0.576065i
$389$	−24.4234			−1.23832			−0.619158	−	0.785267i	$-0.712526\pi$
$389$	−24.4234			−1.23832			−0.619158	+	0.785267i	$0.712526\pi$
$390$	0.338947	−	1.64667i	0.0171632	−	0.0833823i
$391$	10.1641	−	12.3503i	0.514021	−	0.624580i
$392$		−	1.00000i		−	0.0505076i
$393$	−5.42468	+	26.3542i	−0.273639	+	1.32939i
$394$	−0.305296			−0.0153806
$395$			14.1217i			0.710540i
$396$	−10.0826	−	4.33442i	−0.506671	−	0.217813i
$397$	10.0167			0.502724			0.251362	−	0.967893i	$-0.419122\pi$
$397$	10.0167			0.502724			0.251362	+	0.967893i	$0.419122\pi$
$398$	−19.0168			−0.953226
$399$	−0.447216	−	0.0920539i	−0.0223888	−	0.00460846i
$400$	−2.35962			−0.117981
$401$	−15.2935			−0.763723			−0.381861	−	0.924220i	$-0.624717\pi$
$401$	−15.2935			−0.763723			−0.381861	+	0.924220i	$0.624717\pi$
$402$	20.8320	+	4.28801i	1.03901	+	0.213867i
$403$	−5.06477			−0.252294
$404$			1.42782i			0.0710367i
$405$	−10.0621	−	10.6125i	−0.499992	−	0.527337i
$406$			1.04785i			0.0520038i
$407$		−	26.0280i		−	1.29016i
$408$	1.16465	−	5.65807i	0.0576585	−	0.280116i
$409$	−4.70430			−0.232613			−0.116306	−	0.993213i	$-0.537105\pi$
$409$	−4.70430			−0.232613			−0.116306	+	0.993213i	$0.537105\pi$
$410$	−8.54853			−0.422182
$411$	4.18205	+	0.860824i	0.206285	+	0.0424613i
$412$			7.25192i			0.357276i
$413$	−6.54561			−0.322089
$414$	−6.59518	−	12.7869i	−0.324135	−	0.628440i
$415$	−13.7051			−0.672755
$416$		−	0.597342i		−	0.0292871i
$417$	32.0413	+	6.59531i	1.56907	+	0.322974i
$418$	0.964369			0.0471688
$419$	4.67669			0.228471			0.114236	−	0.993454i	$-0.463558\pi$
$419$	4.67669			0.228471			0.114236	+	0.993454i	$0.463558\pi$
$420$	−0.567425	+	2.75666i	−0.0276875	+	0.134511i
$421$			31.7808i			1.54890i	0.632634	+	0.774451i	$0.281974\pi$
$421$			31.7808i			1.54890i	−0.632634	+	0.774451i	$0.718026\pi$
$422$		−	4.03120i		−	0.196236i
$423$	6.29586	−	14.6453i	0.306115	−	0.712079i
$424$			4.55315i			0.221120i
$425$	−7.86975			−0.381739
$426$	−5.27644	−	1.08609i	−0.255645	−	0.0526213i
$427$	−8.08845			−0.391428
$428$	−19.0320			−0.919946
$429$	−3.70723	−	0.763087i	−0.178987	−	0.0368422i
$430$	−0.362490			−0.0174808
$431$	−15.3395			−0.738879			−0.369439	−	0.929255i	$-0.620450\pi$
$431$	−15.3395			−0.738879			−0.369439	+	0.929255i	$0.620450\pi$
$432$	−4.26197	−	2.97248i	−0.205054	−	0.143013i
$433$		−	6.23378i		−	0.299576i	−0.988718	−	0.149788i	$-0.952141\pi$
$433$		−	6.23378i		−	0.299576i	0.988718	−	0.149788i	$-0.0478592\pi$
$434$	8.47884			0.406997
$435$	0.594575	−	2.88856i	0.0285077	−	0.138496i
$436$			3.88879i			0.186239i
$437$	0.976168	+	0.803374i	0.0466964	+	0.0384306i
$438$	2.77339	−	13.4737i	0.132518	−	0.643797i
$439$	12.4195			0.592752			0.296376	−	0.955071i	$-0.404222\pi$
$439$	12.4195			0.592752			0.296376	+	0.955071i	$0.404222\pi$
$440$		−	5.94442i		−	0.283389i
$441$	−2.75612	−	1.18483i	−0.131244	−	0.0564203i
$442$		−	1.99224i		−	0.0947612i
$443$		−	12.9908i		−	0.617214i	−0.951190	−	0.308607i	$-0.900137\pi$
$443$		−	12.9908i		−	0.617214i	0.951190	−	0.308607i	$-0.0998628\pi$
$444$	2.48451	−	12.0702i	0.117909	−	0.572827i
$445$	11.6821			0.553784
$446$		−	7.73020i		−	0.366036i
$447$	−8.64589	−	1.77965i	−0.408937	−	0.0841746i
$448$			1.00000i			0.0472456i
$449$			10.8729i			0.513122i	0.966528	+	0.256561i	$0.0825895\pi$
$449$			10.8729i			0.513122i	−0.966528	+	0.256561i	$0.917411\pi$
$450$	−2.79574	+	6.50339i	−0.131793	+	0.306573i
$451$			19.2457i			0.906246i
$452$	15.7843			0.742433
$453$	−34.6365	−	7.12949i	−1.62736	−	0.334973i
$454$		−	17.5351i		−	0.822963i
$455$			0.970636i			0.0455041i
$456$	0.447216	+	0.0920539i	0.0209428	+	0.00431082i
$457$			38.8414i			1.81692i	0.417967	+	0.908462i	$0.362743\pi$
$457$			38.8414i			1.81692i	−0.417967	+	0.908462i	$0.637257\pi$
$458$	−23.2267			−1.08531
$459$	−14.2144	−	9.91374i	−0.663472	−	0.462734i
$460$	4.95204	−	6.01715i	0.230890	−	0.280551i
$461$		−	1.76466i		−	0.0821883i	−0.999155	−	0.0410941i	$-0.986916\pi$
$461$		−	1.76466i		−	0.0821883i	0.999155	−	0.0410941i	$-0.0130844\pi$
$462$	6.20620	+	1.27747i	0.288739	+	0.0594333i
$463$	−7.78106			−0.361616			−0.180808	−	0.983518i	$-0.557871\pi$
$463$	−7.78106			−0.361616			−0.180808	+	0.983518i	$0.557871\pi$
$464$		−	1.04785i		−	0.0486451i
$465$	−23.3733	−	4.81110i	−1.08391	−	0.223110i
$466$	16.1872			0.749856
$467$	−30.4169			−1.40753			−0.703764	−	0.710434i	$-0.748499\pi$
$467$	−30.4169			−1.40753			−0.703764	+	0.710434i	$0.748499\pi$
$468$	−1.64635	−	0.707747i	−0.0761023	−	0.0327156i
$469$	−12.2795			−0.567015
$470$	8.63443			0.398277
$471$	6.01673	−	29.2304i	0.277236	−	1.34687i
$472$	6.54561			0.301286
$473$			0.816092i			0.0375239i
$474$	14.7436	+	3.03479i	0.677197	+	0.139393i
$475$		−	0.622027i		−	0.0285406i
$476$			3.33518i			0.152868i
$477$	12.5490	+	5.39469i	0.574580	+	0.247006i
$478$	4.77505			0.218406
$479$	−20.8015			−0.950444			−0.475222	−	0.879866i	$-0.657632\pi$
$479$	−20.8015			−0.950444			−0.475222	+	0.879866i	$0.657632\pi$
$480$	0.567425	−	2.75666i	0.0258993	−	0.125824i
$481$		−	4.24999i		−	0.193783i
$482$	19.4210			0.884604
$483$	5.21793	+	6.46322i	0.237424	+	0.294087i
$484$	−2.38296			−0.108316
$485$		−	18.4383i		−	0.837240i
$486$	−13.2422	+	8.22462i	−0.600678	+	0.373076i
$487$	17.8807			0.810250			0.405125	−	0.914261i	$-0.367228\pi$
$487$	17.8807			0.810250			0.405125	+	0.914261i	$0.367228\pi$
$488$	8.08845			0.366147
$489$	12.6852	+	2.61109i	0.573643	+	0.118078i
$490$		−	1.62492i		−	0.0734066i
$491$			39.8488i			1.79835i	0.437587	+	0.899176i	$0.355833\pi$
$491$			39.8488i			1.79835i	−0.437587	+	0.899176i	$0.644167\pi$
$492$	−1.83710	+	8.92500i	−0.0828230	+	0.402370i
$493$		−	3.49476i		−	0.157396i
$494$	0.157467			0.00708479
$495$	−16.3835	−	7.04310i	−0.736384	−	0.316564i
$496$	−8.47884			−0.380711
$497$	3.11022			0.139513
$498$	−2.94525	+	14.3086i	−0.131980	+	0.641184i
$499$	−32.2348			−1.44303			−0.721513	−	0.692400i	$-0.756553\pi$
$499$	−32.2348			−1.44303			−0.721513	+	0.692400i	$0.756553\pi$
$500$	−11.9588			−0.534815
$501$	−5.09056	+	24.7309i	−0.227429	+	1.10490i
$502$			16.4926i			0.736100i
$503$	4.51262			0.201208			0.100604	−	0.994927i	$-0.467922\pi$
$503$	4.51262			0.201208			0.100604	+	0.994927i	$0.467922\pi$
$504$	2.75612	+	1.18483i	0.122767	+	0.0527764i
$505$			2.32010i			0.103243i
$506$	−13.5467	−	11.1488i	−0.602224	−	0.495623i
$507$	21.4490	+	4.41501i	0.952582	+	0.196077i
$508$	−8.20558			−0.364064
$509$			30.3575i			1.34557i	0.739837	+	0.672786i	$0.234903\pi$
$509$			30.3575i			1.34557i	−0.739837	+	0.672786i	$0.765097\pi$
$510$	1.89246	−	9.19394i	0.0837996	−	0.407115i
$511$			7.94212i			0.351338i
$512$		−	1.00000i		−	0.0441942i
$513$	0.783584	−	1.12351i	0.0345961	−	0.0496042i
$514$	−7.68831			−0.339117
$515$			11.7838i			0.519257i
$516$	−0.0779001	+	0.378454i	−0.00342936	+	0.0166605i
$517$		−	19.4391i		−	0.854931i
$518$			7.11484i			0.312608i
$519$	−8.70220	+	42.2770i	−0.381984	+	1.85575i
$520$		−	0.970636i		−	0.0425652i
$521$	24.6722			1.08091			0.540454	−	0.841374i	$-0.318253\pi$
$521$	24.6722			1.08091			0.540454	+	0.841374i	$0.318253\pi$
$522$	−2.88799	−	1.24152i	−0.126404	−	0.0543398i
$523$			10.8449i			0.474213i	0.971484	+	0.237107i	$0.0761990\pi$
$523$			10.8449i			0.474213i	−0.971484	+	0.237107i	$0.923801\pi$
$524$			15.5346i			0.678631i
$525$	0.823981	−	4.00306i	0.0359615	−	0.174708i
$526$			0.333423i			0.0145379i
$527$	−28.2784			−1.23183
$528$	−6.20620	−	1.27747i	−0.270090	−	0.0555948i
$529$	−4.42489	−	22.5703i	−0.192386	−	0.981319i
$530$			7.39852i			0.321371i
$531$	7.75542	−	18.0405i	0.336556	−	0.782890i
$532$	−0.263613			−0.0114291
$533$			3.14254i			0.136119i
$534$	2.51051	−	12.1965i	0.108640	−	0.527796i
$535$	−30.9255			−1.33703
$536$	12.2795			0.530394
$537$	1.39115	−	6.75848i	0.0600326	−	0.291650i
$538$	4.10364			0.176921
$539$	−3.65827			−0.157573
$540$	−6.92538	−	4.83005i	−0.298021	−	0.207852i
$541$	−9.28318			−0.399115			−0.199558	−	0.979886i	$-0.563951\pi$
$541$	−9.28318			−0.399115			−0.199558	+	0.979886i	$0.563951\pi$
$542$		−	12.4811i		−	0.536108i
$543$	3.47342	−	16.8746i	0.149059	−	0.724157i
$544$		−	3.33518i		−	0.142994i
$545$			6.31899i			0.270676i
$546$	1.01338	+	0.208592i	0.0433687	+	0.00892692i
$547$	12.9096			0.551976			0.275988	−	0.961161i	$-0.410995\pi$
$547$	12.9096			0.551976			0.275988	+	0.961161i	$0.410995\pi$
$548$	2.46513			0.105305
$549$	9.58341	−	22.2927i	0.409010	−	0.951431i
$550$			8.63213i			0.368075i
$551$	0.276227			0.0117676
$552$	−5.21793	−	6.46322i	−0.222090	−	0.275093i
$553$	−8.69069			−0.369566
$554$			12.5108i			0.531531i
$555$	4.03714	−	19.6132i	0.171367	−	0.832534i
$556$	18.8869			0.800983
$557$	36.7806			1.55844			0.779221	−	0.626749i	$-0.215615\pi$
$557$	36.7806			1.55844			0.779221	+	0.626749i	$0.215615\pi$
$558$	−10.0460	+	23.3687i	−0.425279	+	0.989275i
$559$			0.133256i			0.00563612i
$560$			1.62492i			0.0686656i
$561$	−20.6988	−	4.26059i	−0.873903	−	0.179882i
$562$		−	8.24651i		−	0.347858i
$563$	17.5140			0.738129			0.369065	−	0.929404i	$-0.379678\pi$
$563$	17.5140			0.738129			0.369065	+	0.929404i	$0.379678\pi$
$564$	1.85556	−	9.01468i	0.0781333	−	0.379587i
$565$	25.6483			1.07903
$566$	−5.12713			−0.215510
$567$	6.53104	−	6.19237i	0.274278	−	0.260055i
$568$	−3.11022			−0.130502
$569$	9.62551			0.403522			0.201761	−	0.979435i	$-0.435334\pi$
$569$	9.62551			0.403522			0.201761	+	0.979435i	$0.435334\pi$
$570$	0.726692	+	0.149581i	0.0304378	+	0.00626524i
$571$		−	10.9452i		−	0.458041i	−0.973422	−	0.229020i	$-0.926448\pi$
$571$		−	10.9452i		−	0.458041i	0.973422	−	0.229020i	$-0.0735523\pi$
$572$	−2.18524			−0.0913695
$573$	6.24560	+	1.28558i	0.260914	+	0.0537059i
$574$		−	5.26088i		−	0.219585i
$575$	−7.19106	+	8.73775i	−0.299888	+	0.364389i
$576$	−2.75612	−	1.18483i	−0.114838	−	0.0493678i
$577$	13.3327			0.555048			0.277524	−	0.960719i	$-0.410486\pi$
$577$	13.3327			0.555048			0.277524	+	0.960719i	$0.410486\pi$
$578$			5.87660i			0.244434i
$579$	−26.8685	−	5.53054i	−1.11662	−	0.229842i
$580$		−	1.70267i		−	0.0706997i
$581$		−	8.43427i		−	0.349913i
$582$	−19.2503	−	3.96244i	−0.797951	−	0.164248i
$583$	16.6567			0.689848
$584$		−	7.94212i		−	0.328647i
$585$	−2.67519	−	1.15003i	−0.110605	−	0.0475481i
$586$		−	9.13629i		−	0.377417i
$587$		−	10.3891i		−	0.428805i	−0.976745	−	0.214402i	$-0.931220\pi$
$587$		−	10.3891i		−	0.428805i	0.976745	−	0.214402i	$-0.0687804\pi$
$588$	−1.69648	−	0.349201i	−0.0699618	−	0.0144008i
$589$		−	2.23513i		−	0.0920971i
$590$	10.6361			0.437882
$591$	−0.106610	+	0.517930i	−0.00438533	+	0.0213048i
$592$		−	7.11484i		−	0.292418i
$593$		−	26.4817i		−	1.08747i	−0.839256	−	0.543736i	$-0.817009\pi$
$593$		−	26.4817i		−	1.08747i	0.839256	−	0.543736i	$-0.182991\pi$
$594$	−10.8741	+	15.5914i	−0.446171	+	0.639725i
$595$			5.41941i			0.222174i
$596$	−5.09636			−0.208755
$597$	−6.64068	+	32.2617i	−0.271785	+	1.32038i
$598$	−2.21198	−	1.82043i	−0.0904544	−	0.0744429i
$599$		−	0.618154i		−	0.0252571i	−0.999920	−	0.0126285i	$-0.995980\pi$
$599$		−	0.618154i		−	0.0252571i	0.999920	−	0.0126285i	$-0.00401990\pi$
$600$	−0.823981	+	4.00306i	−0.0336389	+	0.163424i
$601$	−25.1556			−1.02612			−0.513058	−	0.858354i	$-0.671488\pi$
$601$	−25.1556			−1.02612			−0.513058	+	0.858354i	$0.671488\pi$
$602$		−	0.223081i		−	0.00909211i
$603$	14.5491	−	33.8438i	0.592485	−	1.37823i
$604$	−20.4166			−0.830740
$605$	−3.87213			−0.157424
$606$	2.42227	+	0.498595i	0.0983981	+	0.0202541i
$607$	−4.59071			−0.186331			−0.0931657	−	0.995651i	$-0.529699\pi$
$607$	−4.59071			−0.186331			−0.0931657	+	0.995651i	$0.529699\pi$
$608$	0.263613			0.0106909
$609$	1.77766	+	0.365909i	0.0720343	+	0.0148274i
$610$	13.1431			0.532150
$611$		−	3.17412i		−	0.128411i
$612$	−9.19214	−	3.95160i	−0.371570	−	0.159734i
$613$		−	42.9903i		−	1.73636i	−0.496249	−	0.868180i	$-0.665290\pi$
$613$		−	42.9903i		−	1.73636i	0.496249	−	0.868180i	$-0.334710\pi$
$614$			2.86780i			0.115735i
$615$	−2.98515	+	14.5024i	−0.120373	+	0.584795i
$616$	3.65827			0.147396
$617$	−40.4436			−1.62820			−0.814099	−	0.580727i	$-0.802769\pi$
$617$	−40.4436			−1.62820			−0.814099	+	0.580727i	$0.802769\pi$
$618$	12.3028	+	2.53237i	0.494890	+	0.101867i
$619$		−	40.1230i		−	1.61268i	−0.591453	−	0.806340i	$-0.701445\pi$
$619$		−	40.1230i		−	1.61268i	0.591453	−	0.806340i	$-0.298555\pi$
$620$	−13.7775			−0.553317
$621$	−23.9957	+	6.72343i	−0.962916	+	0.269802i
$622$	26.8944			1.07837
$623$			7.18930i			0.288033i
$624$	−1.01338	−	0.208592i	−0.0405677	−	0.00835037i
$625$	−7.63409			−0.305364
$626$	20.2868			0.810822
$627$	0.336758	−	1.63604i	0.0134488	−	0.0653370i
$628$		−	17.2300i		−	0.687552i
$629$		−	23.7293i		−	0.946147i
$630$	4.47848	+	1.92525i	0.178427	+	0.0767039i
$631$			3.38615i			0.134801i	0.997726	+	0.0674003i	$0.0214705\pi$
$631$			3.38615i			0.134801i	−0.997726	+	0.0674003i	$0.978530\pi$
$632$	8.69069			0.345697
$633$	−6.83887	−	1.40770i	−0.271821	−	0.0559509i
$634$	−0.833720			−0.0331113
$635$	−13.3334			−0.529122
$636$	7.72435	+	1.58996i	0.306290	+	0.0630461i
$637$	−0.597342			−0.0236676
$638$	−3.83331			−0.151762
$639$	−3.68508	+	8.57214i	−0.145779	+	0.339109i
$640$		−	1.62492i		−	0.0642308i
$641$	46.3194			1.82951			0.914754	−	0.404012i	$-0.132385\pi$
$641$	46.3194			1.82951			0.914754	+	0.404012i	$0.132385\pi$
$642$	−6.64598	+	32.2875i	−0.262296	+	1.27429i
$643$			22.8137i			0.899685i	0.893108	+	0.449842i	$0.148520\pi$
$643$			22.8137i			0.899685i	−0.893108	+	0.449842i	$0.851480\pi$
$644$	3.70303	+	3.04755i	0.145920	+	0.120090i
$645$	−0.126582	+	0.614959i	−0.00498415	+	0.0242140i
$646$	0.879196			0.0345915
$647$		−	0.303115i		−	0.0119167i	−0.999982	−	0.00595834i	$-0.998103\pi$
$647$		−	0.303115i		−	0.0119167i	0.999982	−	0.00595834i	$-0.00189661\pi$
$648$	−6.53104	+	6.19237i	−0.256564	+	0.243259i
$649$		−	23.9456i		−	0.939949i
$650$			1.40950i			0.0552852i
$651$	2.96082	−	14.3842i	0.116044	−	0.563762i
$652$	7.47733			0.292835
$653$		−	23.8710i		−	0.934143i	−0.884220	−	0.467071i	$-0.845309\pi$
$653$		−	23.8710i		−	0.934143i	0.884220	−	0.467071i	$-0.154691\pi$
$654$	6.59727	+	1.35797i	0.257974	+	0.0531007i
$655$			25.2425i			0.986307i
$656$			5.26088i			0.205403i
$657$	−21.8894	−	9.41003i	−0.853987	−	0.367120i
$658$			5.31374i			0.207151i
$659$	30.8531			1.20187			0.600934	−	0.799299i	$-0.294796\pi$
$659$	30.8531			1.20187			0.600934	+	0.799299i	$0.294796\pi$
$660$	−10.0846	−	2.07579i	−0.392543	−	0.0808002i
$661$			45.6712i			1.77640i	0.459452	+	0.888202i	$0.348046\pi$
$661$			45.6712i			1.77640i	−0.459452	+	0.888202i	$0.651954\pi$
$662$		−	7.23143i		−	0.281057i
$663$	−3.37980	−	0.695692i	−0.131261	−	0.0270184i
$664$			8.43427i			0.327313i
$665$	−0.428351			−0.0166108
$666$	−19.6093	−	8.42985i	−0.759847	−	0.326650i
$667$	−3.88022	−	3.19337i	−0.150243	−	0.123648i
$668$			14.5778i			0.564030i
$669$	−13.1142	−	2.69939i	−0.507023	−	0.104364i
$670$	19.9533			0.770862
$671$		−	29.5898i		−	1.14230i
$672$	1.69648	+	0.349201i	0.0654433	+	0.0134707i
$673$	−7.97667			−0.307478			−0.153739	−	0.988112i	$-0.549131\pi$
$673$	−7.97667			−0.307478			−0.153739	+	0.988112i	$0.549131\pi$
$674$	−29.5714			−1.13905
$675$	10.0566	+	7.01392i	0.387080	+	0.269966i
$676$	12.6432			0.486276
$677$	42.8654			1.64745			0.823726	−	0.566987i	$-0.191891\pi$
$677$	42.8654			1.64745			0.823726	+	0.566987i	$0.191891\pi$
$678$	5.51190	−	26.7779i	0.211683	−	1.02840i
$679$	11.3472			0.435464
$680$		−	5.41941i		−	0.207825i
$681$	−29.7480	−	6.12326i	−1.13995	−	0.234644i
$682$			31.0179i			1.18774i
$683$		−	42.5519i		−	1.62820i	−0.580724	−	0.814101i	$-0.697230\pi$
$683$		−	42.5519i		−	1.62820i	0.580724	−	0.814101i	$-0.302770\pi$
$684$	0.312336	−	0.726549i	0.0119425	−	0.0277803i
$685$	4.00565			0.153048
$686$	1.00000			0.0381802
$687$	−8.11078	+	39.4037i	−0.309446	+	1.50335i
$688$			0.223081i			0.00850489i
$689$	2.71979			0.103616
$690$	−8.47874	−	10.5022i	−0.322780	−	0.399814i
$691$	22.0329			0.838170			0.419085	−	0.907947i	$-0.362351\pi$
$691$	22.0329			0.838170			0.419085	+	0.907947i	$0.362351\pi$
$692$			24.9204i			0.947330i
$693$	4.33442	−	10.0826i	0.164651	−	0.383007i
$694$	−19.4105			−0.736812
$695$	30.6898			1.16413
$696$	−1.77766	−	0.365909i	−0.0673819	−	0.0138698i
$697$			17.5460i			0.664601i
$698$		−	8.46750i		−	0.320500i
$699$	5.65257	−	27.4613i	0.213800	−	1.03868i
$700$		−	2.35962i		−	0.0891853i
$701$	13.6302			0.514804			0.257402	−	0.966304i	$-0.417134\pi$
$701$	13.6302			0.514804			0.257402	+	0.966304i	$0.417134\pi$
$702$	−1.77559	+	2.54585i	−0.0670152	+	0.0960870i
$703$	1.87557			0.0707383
$704$	−3.65827			−0.137876
$705$	3.01515	−	14.6482i	0.113557	−	0.551682i
$706$	14.8486			0.558836
$707$	−1.42782			−0.0536987
$708$	2.28573	−	11.1045i	0.0859031	−	0.417334i
$709$			20.8496i			0.783022i	0.920173	+	0.391511i	$0.128048\pi$
$709$			20.8496i			0.783022i	−0.920173	+	0.391511i	$0.871952\pi$
$710$	−5.05388			−0.189669
$711$	10.2970	−	23.9526i	0.386166	−	0.898291i
$712$		−	7.18930i		−	0.269431i
$713$	−25.8397	+	31.3974i	−0.967704	+	1.17584i
$714$	5.65807	+	1.16465i	0.211748	+	0.0435858i
$715$	−3.55085			−0.132794
$716$		−	3.98382i		−	0.148882i
$717$	1.66745	−	8.10079i	0.0622720	−	0.302530i
$718$			19.1308i			0.713955i
$719$			37.2938i			1.39082i	0.718611	+	0.695412i	$0.244778\pi$
$719$			37.2938i			1.39082i	−0.718611	+	0.695412i	$0.755222\pi$
$720$	−4.47848	−	1.92525i	−0.166903	−	0.0717500i
$721$	−7.25192			−0.270075
$722$		−	18.9305i		−	0.704521i
$723$	6.78184	−	32.9475i	0.252219	−	1.22533i
$724$		−	9.94679i		−	0.369670i
$725$			2.47252i			0.0918272i
$726$	−0.832130	+	4.04265i	−0.0308832	+	0.150037i
$727$			33.0405i			1.22540i	0.790314	+	0.612702i	$0.209918\pi$
$727$			33.0405i			1.22540i	−0.790314	+	0.612702i	$0.790082\pi$
$728$	0.597342			0.0221390
$729$	9.32875	+	25.3372i	0.345509	+	0.938415i
$730$		−	12.9053i		−	0.477648i
$731$			0.744015i			0.0275184i
$732$	2.82449	−	13.7219i	0.104396	−	0.507177i
$733$		−	35.8154i		−	1.32287i	−0.750002	−	0.661436i	$-0.769947\pi$
$733$		−	35.8154i		−	1.32287i	0.750002	−	0.661436i	$-0.230053\pi$
$734$	16.9690			0.626337
$735$	−2.75666	−	0.567425i	−0.101681	−	0.0209298i
$736$	−3.70303	−	3.04755i	−0.136496	−	0.112334i
$737$		−	44.9218i		−	1.65472i
$738$	14.4996	+	6.23323i	0.533738	+	0.229448i
$739$	−7.24675			−0.266576			−0.133288	−	0.991077i	$-0.542554\pi$
$739$	−7.24675			−0.266576			−0.133288	+	0.991077i	$0.542554\pi$
$740$		−	11.5611i		−	0.424994i
$741$	0.0549876	−	0.267141i	0.00202002	−	0.00981366i
$742$	−4.55315			−0.167151
$743$	16.8521			0.618244			0.309122	−	0.951022i	$-0.399965\pi$
$743$	16.8521			0.618244			0.309122	+	0.951022i	$0.399965\pi$
$744$	−2.96082	+	14.3842i	−0.108549	+	0.527351i
$745$	−8.28120			−0.303400
$746$	8.28644			0.303388
$747$	23.2459	+	9.99315i	0.850521	+	0.365630i
$748$	−12.2010			−0.446112
$749$		−	19.0320i		−	0.695414i
$750$	−4.17603	+	20.2880i	−0.152487	+	0.740812i
$751$			15.1355i			0.552303i	0.961114	+	0.276152i	$0.0890592\pi$
$751$			15.1355i			0.552303i	−0.961114	+	0.276152i	$0.910941\pi$
$752$		−	5.31374i		−	0.193772i
$753$	27.9794	+	5.75922i	1.01963	+	0.209878i
$754$	−0.625924			−0.0227948
$755$	−33.1754			−1.20738
$756$	2.97248	−	4.26197i	0.108108	−	0.155006i
$757$		−	5.04353i		−	0.183310i	−0.995791	−	0.0916552i	$-0.970784\pi$
$757$		−	5.04353i		−	0.183310i	0.995791	−	0.0916552i	$-0.0292157\pi$
$758$	−11.8008			−0.428623
$759$	−23.6442	+	19.0886i	−0.858231	+	0.692873i
$760$	0.428351			0.0155379
$761$		−	3.56552i		−	0.129250i	−0.997910	−	0.0646250i	$-0.979415\pi$
$761$		−	3.56552i		−	0.129250i	0.997910	−	0.0646250i	$-0.0205851\pi$
$762$	−2.86539	+	13.9206i	−0.103802	+	0.504292i
$763$	−3.88879			−0.140784
$764$	3.68150			0.133192
$765$	−14.9365	−	6.42106i	−0.540031	−	0.232154i
$766$		−	29.3281i		−	1.05967i
$767$		−	3.90997i		−	0.141181i
$768$	−1.69648	−	0.349201i	−0.0612166	−	0.0126007i
$769$		−	30.6344i		−	1.10471i	−0.833610	−	0.552353i	$-0.813730\pi$
$769$		−	30.6344i		−	1.10471i	0.833610	−	0.552353i	$-0.186270\pi$
$770$	5.94442			0.214222
$771$	−2.68476	+	13.0431i	−0.0966893	+	0.469735i
$772$	−15.8377			−0.570012
$773$	8.39001			0.301768			0.150884	−	0.988551i	$-0.451788\pi$
$773$	8.39001			0.301768			0.150884	+	0.988551i	$0.451788\pi$
$774$	0.614838	+	0.264313i	0.0220999	+	0.00950052i
$775$	20.0068			0.718667
$776$	−11.3472			−0.407340
$777$	12.0702	+	2.48451i	0.433017	+	0.0891312i
$778$			24.4234i			0.875621i
$779$	−1.38684			−0.0496886
$780$	−1.64667	−	0.338947i	−0.0589602	−	0.0121362i
$781$			11.3780i			0.407138i
$782$	−12.3503	−	10.1641i	−0.441644	−	0.363468i
$783$	−3.11471	+	4.46590i	−0.111310	+	0.159598i
$784$	−1.00000			−0.0357143
$785$		−	27.9975i		−	0.999272i
$786$	26.3542	+	5.42468i	0.940022	+	0.193492i
$787$			18.3373i			0.653652i	0.945084	+	0.326826i	$0.105979\pi$
$787$			18.3373i			0.653652i	−0.945084	+	0.326826i	$0.894021\pi$
$788$			0.305296i			0.0108757i
$789$	0.565646	+	0.116431i	0.0201375	+	0.00414507i
$790$	14.1217			0.502428
$791$			15.7843i			0.561226i
$792$	−4.33442	+	10.0826i	−0.154017	+	0.358271i
$793$		−	4.83157i		−	0.171574i
$794$		−	10.0167i		−	0.355479i
$795$	12.5515	+	2.58357i	0.445155	+	0.0916297i
$796$			19.0168i			0.674032i
$797$	11.1973			0.396630			0.198315	−	0.980138i	$-0.436453\pi$
$797$	11.1973			0.396630			0.198315	+	0.980138i	$0.436453\pi$
$798$	−0.0920539	+	0.447216i	−0.00325867	+	0.0158313i
$799$		−	17.7223i		−	0.626969i
$800$			2.35962i			0.0834252i
$801$	−19.8146	−	8.51808i	−0.700113	−	0.300972i
$802$			15.2935i			0.540034i
$803$	−29.0544			−1.02531
$804$	4.28801	−	20.8320i	0.151227	−	0.734688i
$805$	6.01715	+	4.95204i	0.212077	+	0.174536i
$806$			5.06477i			0.178399i
$807$	1.43299	−	6.96177i	0.0504438	−	0.245066i
$808$	1.42782			0.0502305
$809$			47.6578i			1.67556i	0.546009	+	0.837779i	$0.316146\pi$
$809$			47.6578i			1.67556i	−0.546009	+	0.837779i	$0.683854\pi$
$810$	−10.6125	+	10.0621i	−0.372884	+	0.353547i
$811$	43.1464			1.51507			0.757537	−	0.652792i	$-0.226402\pi$
$811$	43.1464			1.51507			0.757537	+	0.652792i	$0.226402\pi$
$812$	1.04785			0.0367723
$813$	−21.1740	−	4.35840i	−0.742603	−	0.152856i
$814$	−26.0280			−0.912282
$815$	12.1501			0.425599
$816$	−5.65807	−	1.16465i	−0.198072	−	0.0407707i
$817$	−0.0588071			−0.00205740
$818$			4.70430i			0.164482i
$819$	0.707747	−	1.64635i	0.0247307	−	0.0575280i
$820$			8.54853i			0.298528i
$821$			27.2143i			0.949786i	0.880043	+	0.474893i	$0.157513\pi$
$821$			27.2143i			0.949786i	−0.880043	+	0.474893i	$0.842487\pi$
$822$	0.860824	−	4.18205i	0.0300247	−	0.145866i
$823$	−48.4831			−1.69001			−0.845007	−	0.534755i	$-0.820404\pi$
$823$	−48.4831			−1.69001			−0.845007	+	0.534755i	$0.820404\pi$
$824$	7.25192			0.252632
$825$	14.6443	+	3.01435i	0.509848	+	0.104946i
$826$			6.54561i			0.227751i
$827$	13.2360			0.460261			0.230131	−	0.973160i	$-0.426085\pi$
$827$	13.2360			0.460261			0.230131	+	0.973160i	$0.426085\pi$
$828$	−12.7869	+	6.59518i	−0.444374	+	0.229198i
$829$	24.3367			0.845248			0.422624	−	0.906305i	$-0.361109\pi$
$829$	24.3367			0.845248			0.422624	+	0.906305i	$0.361109\pi$
$830$			13.7051i			0.475710i
$831$	21.2243	+	4.36876i	0.736263	+	0.151551i
$832$	−0.597342			−0.0207091
$833$	−3.33518			−0.115557
$834$	6.59531	−	32.0413i	0.228377	−	1.10950i
$835$			23.6877i			0.819748i
$836$		−	0.964369i		−	0.0333534i
$837$	36.1366	+	25.2032i	1.24906	+	0.871149i
$838$		−	4.67669i		−	0.161554i
$839$	−13.9450			−0.481435			−0.240717	−	0.970595i	$-0.577383\pi$
$839$	−13.9450			−0.481435			−0.240717	+	0.970595i	$0.577383\pi$
$840$	2.75666	+	0.567425i	0.0951138	+	0.0195780i
$841$	27.9020			0.962138
$842$	31.7808			1.09524
$843$	−13.9901	−	2.87969i	−0.481844	−	0.0991816i
$844$	−4.03120			−0.138760
$845$	20.5442			0.706743
$846$	−14.6453	−	6.29586i	−0.503516	−	0.216456i
$847$		−	2.38296i		−	0.0818794i
$848$	4.55315			0.156356
$849$	−1.79040	+	8.69810i	−0.0614463	+	0.298518i
$850$			7.86975i			0.269930i
$851$	−26.3465	−	21.6828i	−0.903146	−	0.743278i
$852$	−1.08609	+	5.27644i	−0.0372089	+	0.180768i
$853$	27.1030			0.927989			0.463995	−	0.885838i	$-0.346416\pi$
$853$	27.1030			0.927989			0.463995	+	0.885838i	$0.346416\pi$
$854$			8.08845i			0.276781i
$855$	0.507522	−	1.18059i	0.0173569	−	0.0403752i
$856$			19.0320i			0.650500i
$857$		−	14.4067i		−	0.492123i	−0.969254	−	0.246062i	$-0.920863\pi$
$857$		−	14.4067i		−	0.492123i	0.969254	−	0.246062i	$-0.0791366\pi$
$858$	−0.763087	+	3.70723i	−0.0260514	+	0.126563i
$859$	21.3818			0.729537			0.364769	−	0.931098i	$-0.381148\pi$
$859$	21.3818			0.729537			0.364769	+	0.931098i	$0.381148\pi$
$860$			0.362490i			0.0123608i
$861$	−8.92500	−	1.83710i	−0.304163	−	0.0626083i
$862$			15.3395i			0.522466i
$863$		−	21.3957i		−	0.728317i	−0.931337	−	0.364158i	$-0.881357\pi$
$863$		−	21.3957i		−	0.728317i	0.931337	−	0.364158i	$-0.118643\pi$
$864$	−2.97248	+	4.26197i	−0.101126	+	0.144995i
$865$			40.4937i			1.37683i
$866$	−6.23378			−0.211832
$867$	9.96956	+	2.05211i	0.338584	+	0.0696934i
$868$		−	8.47884i		−	0.287791i
$869$		−	31.7929i		−	1.07850i
$870$	−2.88856	−	0.594575i	−0.0979313	−	0.0201580i
$871$		−	7.33507i		−	0.248539i
$872$	3.88879			0.131691
$873$	−13.4444	+	31.2741i	−0.455025	+	1.05847i
$874$	0.803374	−	0.976168i	0.0271745	−	0.0330194i
$875$		−	11.9588i		−	0.404282i
$876$	−13.4737	−	2.77339i	−0.455233	−	0.0937042i
$877$	21.9445			0.741014			0.370507	−	0.928830i	$-0.379184\pi$
$877$	21.9445			0.741014			0.370507	+	0.928830i	$0.379184\pi$
$878$		−	12.4195i		−	0.419139i
$879$	−15.4996	−	3.19040i	−0.522788	−	0.107609i
$880$	−5.94442			−0.200386
$881$	6.85646			0.231000			0.115500	−	0.993307i	$-0.463153\pi$
$881$	6.85646			0.231000			0.115500	+	0.993307i	$0.463153\pi$
$882$	−1.18483	+	2.75612i	−0.0398952	+	0.0928033i
$883$	−35.8566			−1.20667			−0.603335	−	0.797488i	$-0.706162\pi$
$883$	−35.8566			−1.20667			−0.603335	+	0.797488i	$0.706162\pi$
$884$	−1.99224			−0.0670063
$885$	3.71414	−	18.0440i	0.124850	−	0.606543i
$886$	−12.9908			−0.436436
$887$			51.5490i			1.73085i	0.501043	+	0.865423i	$0.332950\pi$
$887$			51.5490i			1.73085i	−0.501043	+	0.865423i	$0.667050\pi$
$888$	−12.0702	−	2.48451i	−0.405050	−	0.0833746i
$889$		−	8.20558i		−	0.275206i
$890$		−	11.6821i		−	0.391584i
$891$	22.6534	+	23.8923i	0.758917	+	0.800423i
$892$	−7.73020			−0.258826
$893$	1.40077			0.0468751
$894$	−1.77965	+	8.64589i	−0.0595205	+	0.289162i
$895$		−	6.47340i		−	0.216382i
$896$	1.00000			0.0334077
$897$	−3.86075	+	3.11689i	−0.128907	+	0.104070i
$898$	10.8729			0.362832
$899$			8.88454i			0.296316i
$900$	6.50339	+	2.79574i	0.216780	+	0.0931914i
$901$	15.1856			0.505904
$902$	19.2457			0.640813
$903$	−0.378454	−	0.0779001i	−0.0125942	−	0.00259235i
$904$		−	15.7843i		−	0.524979i
$905$		−	16.1628i		−	0.537269i
$906$	−7.12949	+	34.6365i	−0.236861	+	1.15072i
$907$			43.1190i			1.43174i	0.698232	+	0.715872i	$0.253970\pi$
$907$			43.1190i			1.43174i	−0.698232	+	0.715872i	$0.746030\pi$
$908$	−17.5351			−0.581922
$909$	1.69172	−	3.93524i	0.0561108	−	0.130524i
$910$	0.970636			0.0321763
$911$	−14.9949			−0.496803			−0.248401	−	0.968657i	$-0.579905\pi$
$911$	−14.9949			−0.496803			−0.248401	+	0.968657i	$0.579905\pi$
$912$	0.0920539	−	0.447216i	0.00304821	−	0.0148088i
$913$	30.8549			1.02115
$914$	38.8414			1.28476
$915$	4.58959	−	22.2971i	0.151727	−	0.737120i
$916$			23.2267i			0.767432i
$917$	−15.5346			−0.512997
$918$	−9.91374	+	14.2144i	−0.327202	+	0.469146i
$919$			36.8676i			1.21615i	0.793880	+	0.608075i	$0.208058\pi$
$919$			36.8676i			1.21615i	−0.793880	+	0.608075i	$0.791942\pi$
$920$	−6.01715	−	4.95204i	−0.198379	−	0.163264i
$921$	4.86517	+	1.00144i	0.160313	+	0.0329985i
$922$	−1.76466			−0.0581159
$923$			1.85787i			0.0611524i
$924$	1.27747	−	6.20620i	0.0420257	−	0.204169i
$925$			16.7883i			0.551997i
$926$			7.78106i			0.255701i
$927$	8.59226	−	19.9871i	0.282207	−	0.656464i
$928$	−1.04785			−0.0343973
$929$		−	26.3917i		−	0.865884i	−0.901422	−	0.432942i	$-0.857476\pi$
$929$		−	26.3917i		−	0.865884i	0.901422	−	0.432942i	$-0.142524\pi$
$930$	−4.81110	+	23.3733i	−0.157762	+	0.766440i
$931$		−	0.263613i		−	0.00863957i
$932$		−	16.1872i		−	0.530228i
$933$	9.39155	−	45.6260i	0.307466	−	1.49373i
$934$			30.4169i			0.995272i
$935$	−19.8257			−0.648369
$936$	−0.707747	+	1.64635i	−0.0231334	+	0.0538125i
$937$		−	14.4528i		−	0.472154i	−0.971734	−	0.236077i	$-0.924138\pi$
$937$		−	14.4528i		−	0.472154i	0.971734	−	0.236077i	$-0.0758617\pi$
$938$			12.2795i			0.400940i
$939$	7.08415	−	34.4162i	0.231183	−	1.12313i
$940$		−	8.63443i		−	0.281624i
$941$	46.3805			1.51196			0.755981	−	0.654594i	$-0.227160\pi$
$941$	46.3805			1.51196			0.755981	+	0.654594i	$0.227160\pi$
$942$	−29.2304	−	6.01673i	−0.952379	−	0.196036i
$943$	19.4812	+	16.0328i	0.634395	+	0.522099i
$944$		−	6.54561i		−	0.213042i
$945$	4.83005	−	6.92538i	0.157122	−	0.225283i
$946$	0.816092			0.0265334
$947$			36.0124i			1.17024i	0.810945	+	0.585122i	$0.198953\pi$
$947$			36.0124i			1.17024i	−0.810945	+	0.585122i	$0.801047\pi$
$948$	3.03479	−	14.7436i	0.0985655	−	0.478850i
$949$	−4.74416			−0.154002
$950$	−0.622027			−0.0201812
$951$	−0.291136	+	1.41439i	−0.00944072	+	0.0458649i
$952$	3.33518			0.108094
$953$	12.5968			0.408050			0.204025	−	0.978966i	$-0.434598\pi$
$953$	12.5968			0.408050			0.204025	+	0.978966i	$0.434598\pi$
$954$	5.39469	−	12.5490i	0.174660	−	0.406289i
$955$	5.98216			0.193578
$956$		−	4.77505i		−	0.154436i
$957$	−1.33860	+	6.50316i	−0.0432706	+	0.210217i
$958$			20.8015i			0.672065i
$959$			2.46513i			0.0796032i
$960$	−2.75666	−	0.567425i	−0.0889708	−	0.0183135i
$961$	40.8907			1.31906
$962$	−4.24999			−0.137025
$963$	52.4544	+	22.5496i	1.69032	+	0.726651i
$964$		−	19.4210i		−	0.625509i
$965$	−25.7351			−0.828443
$966$	6.46322	−	5.21793i	0.207951	−	0.167884i
$967$	57.3475			1.84417			0.922086	−	0.386985i	$-0.126483\pi$
$967$	57.3475			1.84417			0.922086	+	0.386985i	$0.126483\pi$
$968$			2.38296i			0.0765911i
$969$	0.307016	−	1.49154i	0.00986277	−	0.0479153i
$970$	−18.4383			−0.592018
$971$	48.8825			1.56871			0.784357	−	0.620310i	$-0.212993\pi$
$971$	48.8825			1.56871			0.784357	+	0.620310i	$0.212993\pi$
$972$	8.22462	+	13.2422i	0.263805	+	0.424744i
$973$			18.8869i			0.605486i
$974$		−	17.8807i		−	0.572933i
$975$	2.39120	+	0.492198i	0.0765795	+	0.0157630i
$976$		−	8.08845i		−	0.258905i
$977$	45.5422			1.45702			0.728512	−	0.685033i	$-0.240212\pi$
$977$	45.5422			1.45702			0.728512	+	0.685033i	$0.240212\pi$
$978$	2.61109	−	12.6852i	0.0834934	−	0.405627i
$979$	−26.3004			−0.840565
$980$	−1.62492			−0.0519063
$981$	4.60754	−	10.7180i	0.147107	−	0.342198i
$982$	39.8488			1.27163
$983$	49.5597			1.58071			0.790354	−	0.612651i	$-0.209897\pi$
$983$	49.5597			1.58071			0.790354	+	0.612651i	$0.209897\pi$
$984$	8.92500	+	1.83710i	0.284519	+	0.0585647i
$985$			0.496083i			0.0158065i
$986$	−3.49476			−0.111296
$987$	9.01468	+	1.85556i	0.286940	+	0.0590632i
$988$		−	0.157467i		−	0.00500970i
$989$	0.826077	+	0.679851i	0.0262677	+	0.0216180i
$990$	−7.04310	+	16.3835i	−0.223844	+	0.520702i
$991$	−57.2513			−1.81865			−0.909324	−	0.416089i	$-0.863401\pi$
$991$	−57.2513			−1.81865			−0.909324	+	0.416089i	$0.863401\pi$
$992$			8.47884i			0.269203i
$993$	−12.2680	−	2.52522i	−0.389313	−	0.0801354i
$994$		−	3.11022i		−	0.0986503i
$995$			30.9009i			0.979623i
$996$	14.3086	+	2.94525i	0.453386	+	0.0933239i
$997$	19.0936			0.604699			0.302350	−	0.953197i	$-0.402229\pi$
$997$	19.0936			0.604699			0.302350	+	0.953197i	$0.402229\pi$
$998$			32.2348i			1.02037i
$999$	−21.1487	+	30.3232i	−0.669116	+	0.959385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.b.827.1	yes	24
3.2	odd	2		966.2.h.a.827.13	yes	24
23.22	odd	2		966.2.h.a.827.1	✓	24
69.68	even	2	inner	966.2.h.b.827.13	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.1	✓	24	23.22	odd	2
966.2.h.a.827.13	yes	24	3.2	odd	2
966.2.h.b.827.1	yes	24	1.1	even	1	trivial
966.2.h.b.827.13	yes	24	69.68	even	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.69648 - 0.349201i) q^{3} -1.00000 q^{4} -1.62492 q^{5} +(-0.349201 + 1.69648i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(2.75612 + 1.18483i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.69648 - 0.349201i) q^{3} -1.00000 q^{4} -1.62492 q^{5} +(-0.349201 + 1.69648i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(2.75612 + 1.18483i) q^{9} +1.62492i q^{10} +3.65827 q^{11} +(1.69648 + 0.349201i) q^{12} +0.597342 q^{13} -1.00000 q^{14} +(2.75666 + 0.567425i) q^{15} +1.00000 q^{16} +3.33518 q^{17} +(1.18483 - 2.75612i) q^{18} +0.263613i q^{19} +1.62492 q^{20} +(-0.349201 + 1.69648i) q^{21} -3.65827i q^{22} +(3.04755 - 3.70303i) q^{23} +(0.349201 - 1.69648i) q^{24} -2.35962 q^{25} -0.597342i q^{26} +(-4.26197 - 2.97248i) q^{27} +1.00000i q^{28} -1.04785i q^{29} +(0.567425 - 2.75666i) q^{30} -8.47884 q^{31} -1.00000i q^{32} +(-6.20620 - 1.27747i) q^{33} -3.33518i q^{34} +1.62492i q^{35} +(-2.75612 - 1.18483i) q^{36} -7.11484i q^{37} +0.263613 q^{38} +(-1.01338 - 0.208592i) q^{39} -1.62492i q^{40} +5.26088i q^{41} +(1.69648 + 0.349201i) q^{42} +0.223081i q^{43} -3.65827 q^{44} +(-4.47848 - 1.92525i) q^{45} +(-3.70303 - 3.04755i) q^{46} -5.31374i q^{47} +(-1.69648 - 0.349201i) q^{48} -1.00000 q^{49} +2.35962i q^{50} +(-5.65807 - 1.16465i) q^{51} -0.597342 q^{52} +4.55315 q^{53} +(-2.97248 + 4.26197i) q^{54} -5.94442 q^{55} +1.00000 q^{56} +(0.0920539 - 0.447216i) q^{57} -1.04785 q^{58} -6.54561i q^{59} +(-2.75666 - 0.567425i) q^{60} -8.08845i q^{61} +8.47884i q^{62} +(1.18483 - 2.75612i) q^{63} -1.00000 q^{64} -0.970636 q^{65} +(-1.27747 + 6.20620i) q^{66} -12.2795i q^{67} -3.33518 q^{68} +(-6.46322 + 5.21793i) q^{69} +1.62492 q^{70} +3.11022i q^{71} +(-1.18483 + 2.75612i) q^{72} -7.94212 q^{73} -7.11484 q^{74} +(4.00306 + 0.823981i) q^{75} -0.263613i q^{76} -3.65827i q^{77} +(-0.208592 + 1.01338i) q^{78} -8.69069i q^{79} -1.62492 q^{80} +(6.19237 + 6.53104i) q^{81} +5.26088 q^{82} +8.43427 q^{83} +(0.349201 - 1.69648i) q^{84} -5.41941 q^{85} +0.223081 q^{86} +(-0.365909 + 1.77766i) q^{87} +3.65827i q^{88} -7.18930 q^{89} +(-1.92525 + 4.47848i) q^{90} -0.597342i q^{91} +(-3.04755 + 3.70303i) q^{92} +(14.3842 + 2.96082i) q^{93} -5.31374 q^{94} -0.428351i q^{95} +(-0.349201 + 1.69648i) q^{96} +11.3472i q^{97} +1.00000i q^{98} +(10.0826 + 4.33442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

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