LMFDB - Embedded newform 525.2.t.g.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-1.07834i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.g.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.933868 - 0.539169i) q^{2} +(-0.918594 - 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(2.47720 + 0.929227i) q^{7} +3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +O(q^{10})$	\(q+(0.933868 - 0.539169i) q^{2} +(-0.918594 - 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(2.47720 + 0.929227i) q^{7} +3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +(3.84494 + 2.21988i) q^{11} +(1.44914 - 0.0513428i) q^{12} -0.955682i q^{13} +(2.81439 - 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(0.253761 - 0.439527i) q^{17} +(0.228945 + 3.22690i) q^{18} +(4.41107 - 2.54673i) q^{19} +(-0.911072 - 4.49110i) q^{21} +4.78755 q^{22} +(-3.72142 + 2.14856i) q^{23} +(4.49248 - 2.81039i) q^{24} +(-0.515274 - 0.892481i) q^{26} +(5.16685 - 0.551027i) q^{27} +(-1.71066 + 1.40707i) q^{28} -6.89526i q^{29} +(5.10397 + 2.94678i) q^{31} +(-3.78182 - 2.18344i) q^{32} +(-0.272280 - 7.68506i) q^{33} -0.547280i q^{34} +(-1.40656 - 2.08075i) q^{36} +(3.76353 + 6.51863i) q^{37} +(2.74624 - 4.75663i) q^{38} +(-1.40332 + 0.877884i) q^{39} -4.65529 q^{41} +(-3.27228 - 3.70287i) q^{42} +0.492478 q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.31688 + 4.01295i) q^{46} +(-3.32967 - 5.76715i) q^{47} +(1.31989 - 2.48541i) q^{48} +(5.27308 + 4.60377i) q^{49} +(-0.878503 + 0.0311252i) q^{51} +(0.692894 + 0.400043i) q^{52} +(7.90881 + 4.56616i) q^{53} +(4.52806 - 3.30039i) q^{54} +(-2.84292 + 7.57887i) q^{56} +(-7.79159 - 4.13778i) q^{57} +(-3.71771 - 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(0.399509 - 0.230657i) q^{61} +6.35524 q^{62} +(-5.75780 + 5.46331i) q^{63} -7.95845 q^{64} +(-4.39782 - 7.03002i) q^{66} +(-1.85246 + 3.20856i) q^{67} +(0.212446 + 0.367967i) q^{68} +(6.57342 + 3.49086i) q^{69} -7.90386i q^{71} +(-8.25352 - 4.01513i) q^{72} +(5.46846 + 3.15721i) q^{73} +(7.02929 + 4.05836i) q^{74} +4.26419i q^{76} +(7.46193 + 9.07191i) q^{77} +(-0.837188 + 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-5.55536 - 7.08081i) q^{81} +(-4.34743 + 2.50999i) q^{82} -10.7916 q^{83} +(3.63753 + 1.21939i) q^{84} +(0.459909 - 0.265529i) q^{86} +(-10.1250 + 6.33394i) q^{87} +(-6.79159 + 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750i q^{92} +(-0.361438 - 10.2015i) q^{93} +(-6.21894 - 3.59050i) q^{94} +(0.267811 + 7.55890i) q^{96} -6.91148i q^{97} +(7.40656 + 1.45623i) q^{98} +(-11.0346 + 7.45926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.933868	−	0.539169i	0.660344	−	0.381250i	−0.132064	−	0.991241i	$-0.542160\pi$
$2$	0.933868	−	0.539169i	0.660344	−	0.381250i	0.792408	+	0.609991i	$0.208827\pi$
$3$	−0.918594	−	1.46840i	−0.530350	−	0.847779i
$3$	−0.918594	−	1.46840i	−0.530350	−	0.847779i
$4$	−0.418594	+	0.725026i	−0.209297	+	0.362513i
$5$		0			0
$5$		0			0
$6$	−1.64956	−	0.876010i	−0.673429	−	0.357630i
$7$	2.47720	+	0.929227i	0.936295	+	0.351215i
$7$	2.47720	+	0.929227i	0.936295	+	0.351215i
$8$			3.05945i			1.08168i
$9$	−1.31237	+	2.69772i	−0.437457	+	0.899239i
$10$		0			0
$11$	3.84494	+	2.21988i	1.15929	+	0.669318i	0.951134	−	0.308777i	$-0.0999197\pi$
$11$	3.84494	+	2.21988i	1.15929	+	0.669318i	0.208158	+	0.978095i	$0.433253\pi$
$12$	1.44914	−	0.0513428i	0.418331	−	0.0148214i
$13$		−	0.955682i		−	0.265059i	−0.991179	−	0.132529i	$-0.957690\pi$
$13$		−	0.955682i		−	0.265059i	0.991179	−	0.132529i	$-0.0423099\pi$
$14$	2.81439	−	0.467856i	0.752178	−	0.125040i
$15$		0			0
$16$	0.812371	+	1.40707i	0.203093	+	0.351767i
$17$	0.253761	−	0.439527i	0.0615461	−	0.106601i	−0.833611	−	0.552353i	$-0.813730\pi$
$17$	0.253761	−	0.439527i	0.0615461	−	0.106601i	0.895157	+	0.445752i	$0.147064\pi$
$18$	0.228945	+	3.22690i	0.0539627	+	0.760588i
$19$	4.41107	−	2.54673i	1.01197	−	0.584261i	0.100202	−	0.994967i	$-0.468051\pi$
$19$	4.41107	−	2.54673i	1.01197	−	0.584261i	0.911768	+	0.410706i	$0.134718\pi$
$20$		0			0
$21$	−0.911072	−	4.49110i	−0.198812	−	0.980038i
$22$	4.78755			1.02071
$23$	−3.72142	+	2.14856i	−0.775970	+	0.448007i	−0.835000	−	0.550250i	$-0.814533\pi$
$23$	−3.72142	+	2.14856i	−0.775970	+	0.448007i	0.0590300	+	0.998256i	$0.481199\pi$
$24$	4.49248	−	2.81039i	0.917023	−	0.573668i
$25$		0			0
$26$	−0.515274	−	0.892481i	−0.101054	−	0.175030i
$27$	5.16685	−	0.551027i	0.994361	−	0.106045i
$28$	−1.71066	+	1.40707i	−0.323283	+	0.265911i
$29$		−	6.89526i		−	1.28042i	−0.768201	−	0.640209i	$-0.778848\pi$
$29$		−	6.89526i		−	1.28042i	0.768201	−	0.640209i	$-0.221152\pi$
$30$		0			0
$31$	5.10397	+	2.94678i	0.916699	+	0.529257i	0.882581	−	0.470161i	$-0.155804\pi$
$31$	5.10397	+	2.94678i	0.916699	+	0.529257i	0.0341187	+	0.999418i	$0.489138\pi$
$32$	−3.78182	−	2.18344i	−0.668538	−	0.385981i
$33$	−0.272280	−	7.68506i	−0.0473979	−	1.33780i
$34$		−	0.547280i		−	0.0938578i
$35$		0			0
$36$	−1.40656	−	2.08075i	−0.234427	−	0.346792i
$37$	3.76353	+	6.51863i	0.618721	+	1.07166i	0.989719	+	0.143023i	$0.0456822\pi$
$37$	3.76353	+	6.51863i	0.618721	+	1.07166i	−0.370998	+	0.928634i	$0.620984\pi$
$38$	2.74624	−	4.75663i	0.445499	−	0.771627i
$39$	−1.40332	+	0.877884i	−0.224711	+	0.140574i
$40$		0			0
$41$	−4.65529			−0.727034			−0.363517	−	0.931588i	$-0.618424\pi$
$41$	−4.65529			−0.727034			−0.363517	+	0.931588i	$0.618424\pi$
$42$	−3.27228	−	3.70287i	−0.504924	−	0.571365i
$43$	0.492478			0.0751022			0.0375511	−	0.999295i	$-0.488044\pi$
$43$	0.492478			0.0751022			0.0375511	+	0.999295i	$0.488044\pi$
$44$	−3.21894	+	1.85845i	−0.485273	+	0.280172i
$45$		0			0
$46$	−2.31688	+	4.01295i	−0.341605	+	0.591677i
$47$	−3.32967	−	5.76715i	−0.485682	−	0.841225i	0.514183	−	0.857681i	$-0.328095\pi$
$47$	−3.32967	−	5.76715i	−0.485682	−	0.841225i	−0.999865	+	0.0164553i	$0.994762\pi$
$48$	1.31989	−	2.48541i	0.190510	−	0.358737i
$49$	5.27308	+	4.60377i	0.753297	+	0.657681i
$50$		0			0
$51$	−0.878503	+	0.0311252i	−0.123015	+	0.00435840i
$52$	0.692894	+	0.400043i	0.0960871	+	0.0554759i
$53$	7.90881	+	4.56616i	1.08636	+	0.627210i	0.932605	−	0.360899i	$-0.117530\pi$
$53$	7.90881	+	4.56616i	1.08636	+	0.627210i	0.153754	+	0.988109i	$0.450864\pi$
$54$	4.52806	−	3.30039i	0.616191	−	0.449127i
$55$		0			0
$56$	−2.84292	+	7.57887i	−0.379901	+	1.01277i
$57$	−7.79159	−	4.13778i	−1.03202	−	0.548063i
$58$	−3.71771	−	6.43926i	−0.488159	−	0.845517i
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	0.187420	+	0.982280i	$0.439987\pi$
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	−0.944389	+	0.328829i	$0.893346\pi$
$60$		0			0
$61$	0.399509	−	0.230657i	0.0511519	−	0.0295326i	−0.474206	−	0.880414i	$-0.657265\pi$
$61$	0.399509	−	0.230657i	0.0511519	−	0.0295326i	0.525358	+	0.850881i	$0.323931\pi$
$62$	6.35524			0.807116
$63$	−5.75780	+	5.46331i	−0.725415	+	0.688312i
$64$	−7.95845			−0.994806
$65$		0			0
$66$	−4.39782	−	7.03002i	−0.541334	−	0.865336i
$67$	−1.85246	+	3.20856i	−0.226314	+	0.391988i	−0.956713	−	0.291033i	$-0.906001\pi$
$67$	−1.85246	+	3.20856i	−0.226314	+	0.391988i	0.730399	+	0.683021i	$0.239334\pi$
$68$	0.212446	+	0.367967i	0.0257628	+	0.0446225i
$69$	6.57342	+	3.49086i	0.791346	+	0.420250i
$70$		0			0
$71$		−	7.90386i		−	0.938015i	−0.883194	−	0.469008i	$-0.844612\pi$
$71$		−	7.90386i		−	0.938015i	0.883194	−	0.469008i	$-0.155388\pi$
$72$	−8.25352	−	4.01513i	−0.972687	−	0.473187i
$73$	5.46846	+	3.15721i	0.640034	+	0.369524i	0.784628	−	0.619967i	$-0.212854\pi$
$73$	5.46846	+	3.15721i	0.640034	+	0.369524i	−0.144593	+	0.989491i	$0.546187\pi$
$74$	7.02929	+	4.05836i	0.817138	+	0.471775i
$75$		0			0
$76$			4.26419i			0.489136i
$77$	7.46193	+	9.07191i	0.850366	+	1.03384i
$78$	−0.837188	+	1.57645i	−0.0947928	+	0.178498i
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	−0.897742	−	0.440521i	$-0.854794\pi$
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	0.0673684	−	0.997728i	$-0.478540\pi$
$80$		0			0
$81$	−5.55536	−	7.08081i	−0.617263	−	0.786757i
$82$	−4.34743	+	2.50999i	−0.480093	+	0.277182i
$83$	−10.7916			−1.18453			−0.592266	−	0.805743i	$-0.701766\pi$
$83$	−10.7916			−1.18453			−0.592266	+	0.805743i	$0.701766\pi$
$84$	3.63753	+	1.21939i	0.396887	+	0.133047i
$85$		0			0
$86$	0.459909	−	0.265529i	0.0495933	−	0.0286327i
$87$	−10.1250	+	6.33394i	−1.08551	+	0.679070i
$88$	−6.79159	+	11.7634i	−0.723986	+	1.25398i
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	0.611768	−	0.791038i	$-0.290459\pi$
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	−0.990942	+	0.134287i	$0.957125\pi$
$90$		0			0
$91$	0.888045	−	2.36742i	0.0930925	−	0.248173i
$92$		−	3.59750i		−	0.375066i
$93$	−0.361438	−	10.2015i	−0.0374794	−	1.05785i
$94$	−6.21894	−	3.59050i	−0.641434	−	0.370332i
$95$		0			0
$96$	0.267811	+	7.55890i	0.0273333	+	0.771477i
$97$		−	6.91148i		−	0.701755i	−0.936421	−	0.350877i	$-0.885883\pi$
$97$		−	6.91148i		−	0.701755i	0.936421	−	0.350877i	$-0.114117\pi$
$98$	7.40656	+	1.45623i	0.748176	+	0.147102i
$99$	−11.0346	+	7.45926i	−1.10902	+	0.749684i
$100$		0			0
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	−0.800405	−	0.599460i	$-0.795382\pi$
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	0.919350	+	0.393441i	$0.128715\pi$
$102$	−0.803624	+	0.502728i	−0.0795706	+	0.0497775i
$103$	12.9577	−	7.48110i	1.27676	−	0.737135i	0.300505	−	0.953780i	$-0.402845\pi$
$103$	12.9577	−	7.48110i	1.27676	−	0.737135i	0.976250	+	0.216645i	$0.0695115\pi$
$104$	2.92386			0.286708
$105$		0			0
$106$	9.84772			0.956495
$107$	−11.7445	+	6.78072i	−1.13539	+	0.655517i	−0.945284	−	0.326247i	$-0.894216\pi$
$107$	−11.7445	+	6.78072i	−1.13539	+	0.655517i	−0.190104	+	0.981764i	$0.560882\pi$
$108$	−1.76330	+	3.97676i	−0.169674	+	0.382664i
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	0.164359	+	0.986401i	$0.447444\pi$
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	−0.936428	+	0.350861i	$0.885889\pi$
$110$		0			0
$111$	6.11477	−	11.5143i	0.580388	−	1.09289i
$112$	0.704923	+	4.24047i	0.0666090	+	0.400687i
$113$		−	5.05678i		−	0.475702i	−0.971302	−	0.237851i	$-0.923557\pi$
$113$		−	5.05678i		−	0.475702i	0.971302	−	0.237851i	$-0.0764429\pi$
$114$	−9.50729	+	0.336841i	−0.890439	+	0.0315481i
$115$		0			0
$116$	4.99924	+	2.88631i	0.464168	+	0.267987i
$117$	2.57816	+	1.25421i	0.238351	+	0.115952i
$118$			12.5398i			1.15438i
$119$	1.03704	−	0.852997i	0.0950651	−	0.0781941i
$120$		0			0
$121$	4.35571	+	7.54431i	0.395973	+	0.685846i
$122$	0.248726	−	0.430806i	0.0225186	−	0.0390033i
$123$	4.27632	+	6.83581i	0.385583	+	0.616364i
$124$	−4.27298	+	2.46700i	−0.383725	+	0.221544i
$125$		0			0
$126$	−2.43138	+	8.20643i	−0.216605	+	0.731087i
$127$	−8.05009			−0.714330			−0.357165	−	0.934041i	$-0.616257\pi$
$127$	−8.05009			−0.714330			−0.357165	+	0.934041i	$0.616257\pi$
$128$	0.131506	−	0.0759250i	0.0116236	−	0.00671089i
$129$	−0.452387	−	0.723152i	−0.0398305	−	0.0636700i
$130$		0			0
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	0.816523	−	0.577314i	$-0.195899\pi$
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	−0.908229	+	0.418473i	$0.862566\pi$
$132$	5.68584	+	3.01951i	0.494889	+	0.262814i
$133$	13.2936	−	2.20989i	1.15270	−	0.191622i
$134$			3.99516i			0.345129i
$135$		0			0
$136$	1.34471	+	0.776369i	0.115308	+	0.0665731i
$137$	4.28431	+	2.47355i	0.366033	+	0.211329i	0.671724	−	0.740801i	$-0.265554\pi$
$137$	4.28431	+	2.47355i	0.366033	+	0.211329i	−0.305691	+	0.952131i	$0.598887\pi$
$138$	8.02087	−	0.284178i	0.682782	−	0.0241908i
$139$		−	10.7217i		−	0.909406i	−0.890643	−	0.454703i	$-0.849745\pi$
$139$		−	10.7217i		−	0.909406i	0.890643	−	0.454703i	$-0.150255\pi$
$140$		0			0
$141$	−5.40985	+	10.1869i	−0.455591	+	0.857895i
$142$	−4.26151	−	7.38116i	−0.357618	−	0.619413i
$143$	2.12150	−	3.67454i	0.177408	−	0.307281i
$144$	−4.86200	+	0.344953i	−0.405167	+	0.0287461i
$145$		0			0
$146$	6.80909			0.563524
$147$	1.91634	−	11.9720i	0.158057	−	0.987430i
$148$	−6.30157			−0.517986
$149$	−4.55837	+	2.63178i	−0.373436	+	0.215604i	−0.674959	−	0.737855i	$-0.735839\pi$
$149$	−4.55837	+	2.63178i	−0.373436	+	0.215604i	0.301522	+	0.953459i	$0.402505\pi$
$150$		0			0
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	−0.687463	−	0.726219i	$-0.741276\pi$
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	0.972656	+	0.232251i	$0.0746091\pi$
$152$	7.79159	+	13.4954i	0.631982	+	1.09462i
$153$	0.852692	+	1.26140i	0.0689360	+	0.101978i
$154$	11.8597	+	4.44872i	0.955686	+	0.358488i
$155$		0			0
$156$	−0.0490674	−	1.38492i	−0.00392854	−	0.110882i
$157$	−2.51156	−	1.45005i	−0.200445	−	0.115727i	0.396418	−	0.918070i	$-0.370253\pi$
$157$	−2.51156	−	1.45005i	−0.200445	−	0.115727i	−0.596863	+	0.802343i	$0.703586\pi$
$158$	−13.7849	−	7.95870i	−1.09667	−	0.633160i
$159$	−0.560064	−	15.8077i	−0.0444160	−	1.25363i
$160$		0			0
$161$	−11.2152	+	1.86439i	−0.883883	+	0.146934i
$162$	−9.00573	−	3.61726i	−0.707557	−	0.284199i
$163$	−6.37930	−	11.0493i	−0.499665	−	0.865446i	0.500335	−	0.865832i	$-0.333210\pi$
$163$	−6.37930	−	11.0493i	−0.499665	−	0.865446i	−1.00000		0.000386523i	$0.999877\pi$
$164$	1.94868	−	3.37521i	0.152166	−	0.263559i
$165$		0			0
$166$	−10.0779	+	5.81849i	−0.782199	+	0.451603i
$167$	−15.7766			−1.22083			−0.610413	−	0.792083i	$-0.708997\pi$
$167$	−15.7766			−1.22083			−0.610413	+	0.792083i	$0.708997\pi$
$168$	13.7403	−	2.78737i	1.06008	−	0.215051i
$169$	12.0867			0.929744
$170$		0			0
$171$	1.08141	+	15.2421i	0.0826972	+	1.16559i
$172$	−0.206148	+	0.357059i	−0.0157186	+	0.0272255i
$173$	−5.08667	−	8.81037i	−0.386732	−	0.669840i	0.605275	−	0.796016i	$-0.293063\pi$
$173$	−5.08667	−	8.81037i	−0.386732	−	0.669840i	−0.992008	+	0.126176i	$0.959730\pi$
$174$	−6.04032	+	11.3741i	−0.457916	+	0.862271i
$175$		0			0
$176$			7.21345i			0.543735i
$177$	20.1290	−	0.713167i	1.51299	−	0.0536049i
$178$	−6.68113	−	3.85735i	−0.500772	−	0.289121i
$179$	−4.55716	−	2.63107i	−0.340618	−	0.196656i	0.319927	−	0.947442i	$-0.396341\pi$
$179$	−4.55716	−	2.63107i	−0.340618	−	0.196656i	−0.660545	+	0.750786i	$0.729675\pi$
$180$		0			0
$181$		−	9.71314i		−	0.721972i	−0.932571	−	0.360986i	$-0.882440\pi$
$181$		−	9.71314i		−	0.721972i	0.932571	−	0.360986i	$-0.117560\pi$
$182$	−0.447122	−	2.68966i	−0.0331429	−	0.199371i
$183$	−0.705682	−	0.374757i	−0.0521655	−	0.0277029i
$184$	−6.57342	−	11.3855i	−0.484599	−	0.839350i
$185$		0			0
$186$	−5.83788	−	9.33201i	−0.428054	−	0.684256i
$187$	1.95139	−	1.12664i	0.142700	−	0.0823878i
$188$	5.57511			0.406607
$189$	13.3114	+	3.43617i	0.968260	+	0.249945i
$190$		0			0
$191$	8.30561	−	4.79524i	0.600973	−	0.346972i	−0.168451	−	0.985710i	$-0.553877\pi$
$191$	8.30561	−	4.79524i	0.600973	−	0.346972i	0.769424	+	0.638738i	$0.220543\pi$
$192$	7.31058	+	11.6861i	0.527596	+	0.843375i
$193$	4.17583	−	7.23275i	0.300583	−	0.520625i	−0.675685	−	0.737190i	$-0.736152\pi$
$193$	4.17583	−	7.23275i	0.300583	−	0.520625i	0.976268	+	0.216566i	$0.0694855\pi$
$194$	−3.72646	−	6.45441i	−0.267544	−	0.463400i
$195$		0			0
$196$	−5.54513	+	1.89601i	−0.396080	+	0.135429i
$197$			1.77574i			0.126516i	0.997997	+	0.0632580i	$0.0201491\pi$
$197$			1.77574i			0.126516i	−0.997997	+	0.0632580i	$0.979851\pi$
$198$	−6.28305	+	12.9155i	−0.446517	+	0.917863i
$199$	−3.25502	−	1.87929i	−0.230742	−	0.133219i	0.380172	−	0.924916i	$-0.375865\pi$
$199$	−3.25502	−	1.87929i	−0.230742	−	0.133219i	−0.610915	+	0.791697i	$0.709198\pi$
$200$		0			0
$201$	6.41309	−	0.227215i	0.452345	−	0.0160265i
$202$		−	2.57805i		−	0.181391i
$203$	6.40726	−	17.0810i	0.449702	−	1.19885i
$204$	0.345169	−	0.649966i	0.0241667	−	0.0455067i
$205$		0			0
$206$	8.06716	−	13.9727i	0.562065	−	0.973526i
$207$	−0.912334	−	12.8591i	−0.0634116	−	0.893767i
$208$	1.34471	−	0.776369i	0.0932388	−	0.0538315i
$209$	22.6137			1.56422
$210$		0			0
$211$	−9.12126			−0.627933			−0.313967	−	0.949434i	$-0.601658\pi$
$211$	−9.12126			−0.627933			−0.313967	+	0.949434i	$0.601658\pi$
$212$	−6.62116	+	3.82273i	−0.454743	+	0.262546i
$213$	−11.6060	+	7.26043i	−0.795229	+	0.497477i
$214$	−7.31190	+	12.6646i	−0.499831	+	0.865734i
$215$		0			0
$216$	1.68584	+	15.8077i	0.114707	+	1.07558i
$217$	9.90534	+	12.0425i	0.672418	+	0.817499i
$218$			17.3842i			1.17740i
$219$	−0.387250	−	10.9301i	−0.0261679	−	0.738585i
$220$		0			0
$221$	−0.420048	−	0.242515i	−0.0282555	−	0.0163133i
$222$	−0.497780	−	14.0498i	−0.0334088	−	0.942958i
$223$			11.7397i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$223$			11.7397i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$224$	−7.33944	−	8.92299i	−0.490387	−	0.596192i
$225$		0			0
$226$	−2.72646	−	4.72236i	−0.181361	−	0.314127i
$227$	12.1105	−	20.9760i	0.803802	−	1.39223i	−0.113295	−	0.993561i	$-0.536141\pi$
$227$	12.1105	−	20.9760i	0.803802	−	1.39223i	0.917097	−	0.398664i	$-0.130526\pi$
$228$	6.26151	−	3.91706i	0.414679	−	0.259413i
$229$	18.8003	−	10.8544i	1.24236	−	0.717278i	0.272787	−	0.962075i	$-0.412055\pi$
$229$	18.8003	−	10.8544i	1.24236	−	0.717278i	0.969574	+	0.244797i	$0.0787213\pi$
$230$		0			0
$231$	6.46667	−	19.2905i	0.425475	−	1.26922i
$232$	21.0957			1.38500
$233$	−9.52303	+	5.49812i	−0.623874	+	0.360194i	−0.778376	−	0.627799i	$-0.783956\pi$
$233$	−9.52303	+	5.49812i	−0.623874	+	0.360194i	0.154502	+	0.987993i	$0.450623\pi$
$234$	3.08389	−	0.218798i	0.201600	−	0.0143033i
$235$		0			0
$236$	−4.86774	−	8.43117i	−0.316863	−	0.548822i
$237$	−11.9914	+	22.5803i	−0.778928	+	1.46675i
$238$	0.508547	−	1.35572i	0.0329642	−	0.0878786i
$239$			9.02649i			0.583875i	0.956437	+	0.291938i	$0.0942999\pi$
$239$			9.02649i			0.583875i	−0.956437	+	0.291938i	$0.905700\pi$
$240$		0			0
$241$	−4.40027	−	2.54050i	−0.283446	−	0.163648i	0.351536	−	0.936174i	$-0.385659\pi$
$241$	−4.40027	−	2.54050i	−0.283446	−	0.163648i	−0.634982	+	0.772527i	$0.718993\pi$
$242$	8.13531	+	4.69692i	0.522958	+	0.301930i
$243$	−5.29431	+	14.6619i	−0.339630	+	0.940559i
$244$			0.386206i			0.0247243i
$245$		0			0
$246$	7.67917	+	4.07808i	0.489606	+	0.260009i
$247$	−2.43387	−	4.21558i	−0.154863	−	0.268231i
$248$	−9.01550	+	15.6153i	−0.572485	+	0.991573i
$249$	9.91309	+	15.8463i	0.628217	+	1.00422i
$250$		0			0
$251$	−18.6748			−1.17875			−0.589373	−	0.807861i	$-0.700625\pi$
$251$	−18.6748			−1.17875			−0.589373	+	0.807861i	$0.700625\pi$
$252$	−1.55086	−	6.46146i	−0.0976949	−	0.407034i
$253$	−19.0782			−1.19944
$254$	−7.51772	+	4.34036i	−0.471704	+	0.272338i
$255$		0			0
$256$	8.04032	−	13.9262i	0.502520	−	0.870390i
$257$	−6.04132	−	10.4639i	−0.376847	−	0.652718i	0.613755	−	0.789497i	$-0.289658\pi$
$257$	−6.04132	−	10.4639i	−0.376847	−	0.652718i	−0.990602	+	0.136779i	$0.956325\pi$
$258$	−0.812371	−	0.431416i	−0.0505760	−	0.0268588i
$259$	3.26575	+	19.6452i	0.202924	+	1.22069i
$260$		0			0
$261$	18.6015	+	9.04914i	1.15140	+	0.560128i
$262$	−1.96044	−	1.13186i	−0.121116	−	0.0699265i
$263$	11.1611	+	6.44388i	0.688224	+	0.397346i	0.802946	−	0.596051i	$-0.203264\pi$
$263$	11.1611	+	6.44388i	0.688224	+	0.397346i	−0.114722	+	0.993398i	$0.536598\pi$
$264$	23.5120	−	0.833027i	1.44706	−	0.0512693i
$265$		0			0
$266$	11.2230	−	9.23125i	0.688125	−	0.566004i
$267$	−5.81191	+	10.9440i	−0.355683	+	0.669764i
$268$	−1.55086	−	2.68616i	−0.0947337	−	0.164084i
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	−0.858828	−	0.512264i	$-0.828807\pi$
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	0.873048	+	0.487635i	$0.162140\pi$
$270$		0			0
$271$	−20.1703	+	11.6453i	−1.22526	+	0.707404i	−0.966035	−	0.258413i	$-0.916801\pi$
$271$	−20.1703	+	11.6453i	−1.22526	+	0.707404i	−0.259225	+	0.965817i	$0.583467\pi$
$272$	0.824593			0.0499983
$273$	−4.29206	+	0.870695i	−0.259767	+	0.0526969i
$274$	5.33464			0.322277
$275$		0			0
$276$	−5.28256	+	3.30464i	−0.317973	+	0.198916i
$277$	−6.94543	+	12.0298i	−0.417310	+	0.722803i	−0.995668	−	0.0929805i	$-0.970361\pi$
$277$	−6.94543	+	12.0298i	−0.417310	+	0.722803i	0.578357	+	0.815783i	$0.303694\pi$
$278$	−5.78083	−	10.0127i	−0.346711	−	0.600521i
$279$	−14.6479	+	9.90180i	−0.876945	+	0.592805i
$280$		0			0
$281$		−	6.85483i		−	0.408925i	−0.978874	−	0.204462i	$-0.934455\pi$
$281$		−	6.85483i		−	0.408925i	0.978874	−	0.204462i	$-0.0655446\pi$
$282$	0.440395	+	12.4301i	0.0262252	+	0.740200i
$283$	−3.84212	−	2.21825i	−0.228391	−	0.131861i	0.381439	−	0.924394i	$-0.375429\pi$
$283$	−3.84212	−	2.21825i	−0.228391	−	0.131861i	−0.609829	+	0.792533i	$0.708762\pi$
$284$	5.73050	+	3.30850i	0.340043	+	0.196324i
$285$		0			0
$286$		−	4.57538i		−	0.270548i
$287$	−11.5321	−	4.32582i	−0.680718	−	0.255345i
$288$	10.8534	−	7.33681i	0.639546	−	0.432326i
$289$	8.37121	+	14.4994i	0.492424	+	0.852904i
$290$		0			0
$291$	−10.1488	+	6.34885i	−0.594933	+	0.372176i
$292$	−4.57812	+	2.64318i	−0.267914	+	0.154680i
$293$	30.0822			1.75742			0.878709	−	0.477357i	$-0.158405\pi$
$293$	30.0822			1.75742			0.878709	+	0.477357i	$0.158405\pi$
$294$	−4.66530	−	12.2135i	−0.272086	−	0.712303i
$295$		0			0
$296$	−19.9434	+	11.5143i	−1.15919	+	0.669257i
$297$	21.0894	+	9.35111i	1.22373	+	0.542606i
$298$	−2.83795	+	4.91547i	−0.164398	+	0.284745i
$299$	2.05334	+	3.55650i	0.118748	+	0.205678i
$300$		0			0
$301$	1.21997	+	0.457623i	0.0703178	+	0.0263770i
$302$		−	7.55808i		−	0.434919i
$303$	−4.13832	+	0.146620i	−0.237741	+	0.00842311i
$304$	7.16685	+	4.13778i	0.411047	+	0.237318i
$305$		0			0
$306$	1.47641	+	0.718235i	0.0844006	+	0.0410588i
$307$		−	32.8300i		−	1.87371i	−0.349722	−	0.936853i	$-0.613724\pi$
$307$		−	32.8300i		−	1.87371i	0.349722	−	0.936853i	$-0.386276\pi$
$308$	−9.70088	+	1.61265i	−0.552759	+	0.0918891i
$309$	−22.8880	−	12.1549i	−1.30206	−	0.691466i
$310$		0			0
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	−0.999277	−	0.0380092i	$-0.987898\pi$
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	0.532556	+	0.846395i	$0.321232\pi$
$312$	−2.68584	−	4.29338i	−0.152056	−	0.243065i
$313$	3.99102	−	2.30422i	0.225586	−	0.130242i	−0.382948	−	0.923770i	$-0.625091\pi$
$313$	3.99102	−	2.30422i	0.225586	−	0.130242i	0.608534	+	0.793528i	$0.291758\pi$
$314$	−3.12729			−0.176483
$315$		0			0
$316$	12.3578			0.695179
$317$	25.4873	−	14.7151i	1.43151	−	0.826481i	0.434272	−	0.900782i	$-0.357006\pi$
$317$	25.4873	−	14.7151i	1.43151	−	0.826481i	0.997236	+	0.0743007i	$0.0236725\pi$
$318$	−9.04605	−	14.4603i	−0.507277	−	0.810896i
$319$	15.3066	−	26.5119i	0.857007	−	1.48438i
$320$		0			0
$321$	20.7452	+	11.0169i	1.15789	+	0.614904i
$322$	−9.46832	+	7.78799i	−0.527649	+	0.434008i
$323$		−	2.58505i		−	0.143836i
$324$	7.45921	−	1.06380i	0.414401	−	0.0590999i
$325$		0			0
$326$	−11.9148	−	6.87904i	−0.659902	−	0.380995i
$327$	27.9053	−	0.988681i	1.54317	−	0.0546742i
$328$		−	14.2426i		−	0.786417i
$329$	−2.88927	−	17.3804i	−0.159291	−	0.958213i
$330$		0			0
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	0.827222	−	0.561875i	$-0.189920\pi$
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	−0.900209	+	0.435458i	$0.856586\pi$
$332$	4.51729	−	7.82418i	0.247919	−	0.429408i
$333$	−22.5246	+	1.59809i	−1.23434	+	0.0875748i
$334$	−14.7332	+	8.50623i	−0.806166	+	0.465440i
$335$		0			0
$336$	5.57915	−	4.93038i	0.304368	−	0.268974i
$337$	21.4599			1.16900			0.584499	−	0.811395i	$-0.301291\pi$
$337$	21.4599			1.16900			0.584499	+	0.811395i	$0.301291\pi$
$338$	11.2874	−	6.51676i	0.613951	−	0.354465i
$339$	−7.42535	+	4.64513i	−0.403290	+	0.252289i
$340$		0			0
$341$	13.0830	+	22.6604i	0.708482	+	1.22713i
$342$	9.22795	+	13.6510i	0.498990	+	0.738163i
$343$	8.78454	+	16.3044i	0.474321	+	0.880352i
$344$			1.50671i			0.0812363i
$345$		0			0
$346$	−9.50056	−	5.48515i	−0.510753	−	0.294883i
$347$	15.7302	+	9.08183i	0.844441	+	0.487538i	0.858771	−	0.512359i	$-0.171228\pi$
$347$	15.7302	+	9.08183i	0.844441	+	0.487538i	−0.0143301	+	0.999897i	$0.504562\pi$
$348$	−0.354022	−	9.99221i	−0.0189776	−	0.535639i
$349$			13.1543i			0.704135i	0.935975	+	0.352067i	$0.114521\pi$
$349$			13.1543i			0.704135i	−0.935975	+	0.352067i	$0.885479\pi$
$350$		0			0
$351$	−0.526607	−	4.93787i	−0.0281082	−	0.263564i
$352$	−9.69392	−	16.7904i	−0.516688	−	0.894929i
$353$	−5.14707	+	8.91499i	−0.273951	+	0.474497i	−0.969870	−	0.243623i	$-0.921664\pi$
$353$	−5.14707	+	8.91499i	−0.273951	+	0.474497i	0.695919	+	0.718120i	$0.254997\pi$
$354$	18.4133	−	11.5189i	0.978657	−	0.612225i
$355$		0			0
$356$	5.98946			0.317441
$357$	−2.20515	−	0.739225i	−0.116709	−	0.0391239i
$358$	−5.67438			−0.299900
$359$	10.2193	−	5.90010i	0.539352	−	0.311395i	−0.205464	−	0.978665i	$-0.565870\pi$
$359$	10.2193	−	5.90010i	0.539352	−	0.311395i	0.744816	+	0.667270i	$0.232537\pi$
$360$		0			0
$361$	3.47170	−	6.01316i	0.182721	−	0.316482i
$362$	−5.23703	−	9.07079i	−0.275252	−	0.476750i
$363$	7.07690	−	13.3261i	0.371441	−	0.699436i
$364$	1.34471	+	1.63484i	0.0704819	+	0.0856890i
$365$		0			0
$366$	−0.861071	+	0.0305076i	−0.0450089	+	0.00159466i
$367$	−13.8338	−	7.98697i	−0.722120	−	0.416916i	0.0934122	−	0.995628i	$-0.470223\pi$
$367$	−13.8338	−	7.98697i	−0.722120	−	0.416916i	−0.815533	+	0.578711i	$0.803556\pi$
$368$	−6.04635	−	3.49086i	−0.315188	−	0.181974i
$369$	6.10947	−	12.5587i	0.318046	−	0.653778i
$370$		0			0
$371$	15.3488	+	18.6604i	0.796867	+	0.968799i
$372$	7.54767	+	4.00825i	0.391328	+	0.207818i
$373$	2.65834	+	4.60438i	0.137644	+	0.238406i	0.926604	−	0.376038i	$-0.122714\pi$
$373$	2.65834	+	4.60438i	0.137644	+	0.238406i	−0.788961	+	0.614444i	$0.789380\pi$
$374$	1.21490	−	2.10426i	0.0628207	−	0.108809i
$375$		0			0
$376$	17.6443	−	10.1869i	0.909935	−	0.525351i
$377$	−6.58968			−0.339386
$378$	14.2837	−	3.96815i	0.734677	−	0.204100i
$379$	24.0427			1.23499			0.617494	−	0.786575i	$-0.288148\pi$
$379$	24.0427			1.23499			0.617494	+	0.786575i	$0.288148\pi$
$380$		0			0
$381$	7.39477	+	11.8207i	0.378845	+	0.605594i
$382$	5.17089	−	8.95625i	0.264566	−	0.458242i
$383$	9.40053	+	16.2822i	0.480345	+	0.831982i	0.999746	−	0.0225490i	$-0.00717818\pi$
$383$	9.40053	+	16.2822i	0.480345	+	0.831982i	−0.519401	+	0.854531i	$0.673845\pi$
$384$	−0.232289	−	0.123359i	−0.0118539	−	0.00629512i
$385$		0			0
$386$		−	9.00591i		−	0.458389i
$387$	−0.646314	+	1.32857i	−0.0328540	+	0.0675348i
$388$	5.01100	+	2.89310i	0.254395	+	0.146875i
$389$	−10.5804	−	6.10860i	−0.536448	−	0.309718i	0.207190	−	0.978301i	$-0.433568\pi$
$389$	−10.5804	−	6.10860i	−0.536448	−	0.309718i	−0.743638	+	0.668582i	$0.766901\pi$
$390$		0			0
$391$			2.18089i			0.110292i
$392$	−14.0850	+	16.1327i	−0.711399	+	0.814824i
$393$	−1.70538	+	3.21130i	−0.0860252	+	0.161988i
$394$	0.957422	+	1.65830i	0.0482342	+	0.0835442i
$395$		0			0
$396$	−0.789145	−	11.1228i	−0.0396560	−	0.558940i
$397$	−16.2510	+	9.38254i	−0.815616	+	0.470896i	−0.848902	−	0.528550i	$-0.822736\pi$
$397$	−16.2510	+	9.38254i	−0.815616	+	0.470896i	0.0332862	+	0.999446i	$0.489403\pi$
$398$	−4.05302			−0.203159
$399$	−15.4564	−	17.4903i	−0.773789	−	0.875610i
$400$		0			0
$401$	20.7823	−	11.9987i	1.03782	−	0.599184i	0.118603	−	0.992942i	$-0.462158\pi$
$401$	20.7823	−	11.9987i	1.03782	−	0.599184i	0.919214	+	0.393757i	$0.128825\pi$
$402$	5.86647	−	3.66993i	0.292593	−	0.183039i
$403$	2.81618	−	4.87777i	0.140284	−	0.242979i
$404$	1.00076	+	1.73336i	0.0497896	+	0.0862381i
$405$		0			0
$406$	−3.22599	−	19.4060i	−0.160103	−	0.963102i
$407$			33.4183i			1.65648i
$408$	−0.0952259	−	2.68773i	−0.00471438	−	0.133063i
$409$	−14.7941	−	8.54140i	−0.731523	−	0.422345i	0.0874559	−	0.996168i	$-0.472126\pi$
$409$	−14.7941	−	8.54140i	−0.731523	−	0.422345i	−0.818979	+	0.573823i	$0.805460\pi$
$410$		0			0
$411$	−0.303394	−	8.56325i	−0.0149653	−	0.422394i
$412$			12.5262i			0.617120i
$413$	−23.7615	+	19.5446i	−1.16923	+	0.961726i
$414$	−7.78521	−	11.5168i	−0.382622	−	0.566018i
$415$		0			0
$416$	−2.08667	+	3.61422i	−0.102307	+	0.177202i
$417$	−15.7438	+	9.84892i	−0.770975	+	0.482304i
$418$	21.1182	−	12.1926i	1.03293	−	0.596361i
$419$	−39.6524			−1.93714			−0.968572	−	0.248732i	$-0.919986\pi$
$419$	−39.6524			−1.93714			−0.968572	+	0.248732i	$0.919986\pi$
$420$		0			0
$421$	−34.1423			−1.66399			−0.831997	−	0.554779i	$-0.812803\pi$
$421$	−34.1423			−1.66399			−0.831997	+	0.554779i	$0.812803\pi$
$422$	−8.51805	+	4.91790i	−0.414652	+	0.239400i
$423$	19.9279	−	1.41386i	0.968928	−	0.0687442i
$424$	−13.9699	+	24.1966i	−0.678439	+	1.17509i
$425$		0			0
$426$	−6.92386	+	13.0379i	−0.335462	+	0.631687i
$427$	1.20400	−	0.200149i	0.0582655	−	0.00968589i
$428$		−	11.3535i		−	0.548790i
$429$	−7.34447	+	0.260213i	−0.354594	+	0.0125632i
$430$		0			0
$431$	22.3182	+	12.8854i	1.07503	+	0.620668i	0.929551	−	0.368693i	$-0.120195\pi$
$431$	22.3182	+	12.8854i	1.07503	+	0.620668i	0.145478	+	0.989361i	$0.453528\pi$
$432$	4.97273	+	6.82247i	0.239251	+	0.328246i
$433$			11.9120i			0.572454i	0.958162	+	0.286227i	$0.0924011\pi$
$433$			11.9120i			0.572454i	−0.958162	+	0.286227i	$0.907599\pi$
$434$	15.7432	+	5.90546i	0.755699	+	0.283471i
$435$		0			0
$436$	−6.74826	−	11.6883i	−0.323183	−	0.559769i
$437$	−10.9436	+	18.9549i	−0.523505	+	0.906738i
$438$	−6.25479	−	9.99844i	−0.298865	−	0.477744i
$439$	−14.5260	+	8.38661i	−0.693290	+	0.400271i	−0.804843	−	0.593487i	$-0.797751\pi$
$439$	−14.5260	+	8.38661i	−0.693290	+	0.400271i	0.111553	+	0.993758i	$0.464417\pi$
$440$		0			0
$441$	−19.3399	+	8.18342i	−0.920947	+	0.389687i
$442$	−0.523026			−0.0248778
$443$	−2.07491	+	1.19795i	−0.0985819	+	0.0569163i	−0.548480	−	0.836163i	$-0.684793\pi$
$443$	−2.07491	+	1.19795i	−0.0985819	+	0.0569163i	0.449899	+	0.893080i	$0.351460\pi$
$444$	5.78858	+	9.25319i	0.274714	+	0.439137i
$445$		0			0
$446$	6.32967	+	10.9633i	0.299718	+	0.519127i
$447$	8.05178	+	4.27596i	0.380836	+	0.202246i
$448$	−19.7147	−	7.39520i	−0.931432	−	0.349390i
$449$			25.4692i			1.20196i	0.799262	+	0.600982i	$0.205224\pi$
$449$			25.4692i			1.20196i	−0.799262	+	0.600982i	$0.794776\pi$
$450$		0			0
$451$	−17.8993	−	10.3342i	−0.842846	−	0.486617i
$452$	3.66629	+	2.11674i	0.172448	+	0.0995629i
$453$	−12.1324	+	0.429847i	−0.570028	+	0.0201960i
$454$		−	26.1184i		−	1.22580i
$455$		0			0
$456$	12.6593	−	23.8380i	0.592827	−	1.11632i
$457$	−1.72096	−	2.98078i	−0.0805029	−	0.139435i	0.822963	−	0.568095i	$-0.192319\pi$
$457$	−1.72096	−	2.98078i	−0.0805029	−	0.139435i	−0.903466	+	0.428660i	$0.858986\pi$
$458$	11.7047	−	20.2731i	0.546924	−	0.947300i
$459$	1.06895	−	2.41080i	0.0498945	−	0.112527i
$460$		0			0
$461$	−13.5376			−0.630509			−0.315254	−	0.949007i	$-0.602090\pi$
$461$	−13.5376			−0.630509			−0.315254	+	0.949007i	$0.602090\pi$
$462$	−4.36180	−	21.5014i	−0.202930	−	1.00033i
$463$	5.13770			0.238769			0.119385	−	0.992848i	$-0.461908\pi$
$463$	5.13770			0.238769			0.119385	+	0.992848i	$0.461908\pi$
$464$	9.70210	−	5.60151i	0.450409	−	0.260044i
$465$		0			0
$466$	−5.92883	+	10.2690i	−0.274648	+	0.475704i
$467$	−4.60894	−	7.98292i	−0.213276	−	0.369405i	0.739462	−	0.673199i	$-0.235080\pi$
$467$	−4.60894	−	7.98292i	−0.213276	−	0.369405i	−0.952738	+	0.303793i	$0.901747\pi$
$468$	−1.98854	+	1.34423i	−0.0919201	+	0.0621370i
$469$	−7.57040	+	6.22689i	−0.349569	+	0.287531i
$470$		0			0
$471$	0.177857	+	5.01998i	0.00819521	+	0.231308i
$472$	−30.8111	−	17.7888i	−1.41820	−	0.818797i
$473$	1.89355	+	1.09324i	0.0870654	+	0.0502672i
$474$	0.976178	+	27.5524i	0.0448374	+	1.26553i
$475$		0			0
$476$	0.184347	+	1.10894i	0.00844952	+	0.0508281i
$477$	−22.6975	+	15.3433i	−1.03925	+	0.702520i
$478$	4.86680	+	8.42955i	0.222602	+	0.385559i
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	−0.527996	−	0.849247i	$-0.677056\pi$
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	0.999467	+	0.0326342i	$0.0103896\pi$
$480$		0			0
$481$	6.22974	−	3.59674i	0.284052	−	0.163997i
$482$	−5.47902			−0.249563
$483$	13.0399	+	14.7558i	0.593336	+	0.671411i
$484$	−7.29309			−0.331504
$485$		0			0
$486$	2.96103	+	16.5468i	0.134315	+	0.750577i
$487$	1.23749	−	2.14340i	0.0560761	−	0.0971267i	−0.836625	−	0.547777i	$-0.815474\pi$
$487$	1.23749	−	2.14340i	0.0560761	−	0.0971267i	0.892701	+	0.450650i	$0.148808\pi$
$488$	0.705682	+	1.22228i	0.0319447	+	0.0553298i
$489$	−10.3647	+	19.5171i	−0.468709	+	0.882595i
$490$		0			0
$491$			21.2827i			0.960476i	0.877138	+	0.480238i	$0.159450\pi$
$491$			21.2827i			0.960476i	−0.877138	+	0.480238i	$0.840550\pi$
$492$	−6.74618	+	0.239016i	−0.304141	+	0.0107757i
$493$	−3.03065	−	1.74975i	−0.136494	−	0.0788047i
$494$	−4.54582	−	2.62453i	−0.204526	−	0.118083i
$495$		0			0
$496$			9.57550i			0.429953i
$497$	7.34447	−	19.5795i	0.329445	−	0.878259i
$498$	17.8014	+	9.45355i	0.797698	+	0.423624i
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	−0.955693	−	0.294366i	$-0.904891\pi$
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	0.222918	−	0.974837i	$-0.428442\pi$
$500$		0			0
$501$	14.4922	+	23.1662i	0.647466	+	1.03499i
$502$	−17.4398	+	10.0689i	−0.778378	+	0.449397i
$503$	−0.675693			−0.0301277			−0.0150638	−	0.999887i	$-0.504795\pi$
$503$	−0.675693			−0.0301277			−0.0150638	+	0.999887i	$0.504795\pi$
$504$	−16.7147	−	17.6157i	−0.744532	−	0.784665i
$505$		0			0
$506$	−17.8165	+	10.2864i	−0.792041	+	0.457285i
$507$	−11.1027	−	17.7480i	−0.493090	−	0.788217i
$508$	3.36972	−	5.83652i	0.149507	−	0.258954i
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	0.955313	+	0.295595i	$0.0955178\pi$
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	−0.221664	+	0.975123i	$0.571149\pi$
$510$		0			0
$511$	10.6127	+	12.9025i	0.469479	+	0.570773i
$512$		−	17.0367i		−	0.752921i
$513$	21.3880	−	15.5892i	0.944305	−	0.688281i
$514$	−11.2836	−	6.51458i	−0.497697	−	0.287346i
$515$		0			0
$516$	0.713670	−	0.0252852i	0.0314176	−	0.00111312i
$517$		−	29.5658i		−	1.30030i
$518$	13.6418	+	16.5852i	0.599388	+	0.728711i
$519$	−8.26453	+	15.5624i	−0.362773	+	0.683114i
$520$		0			0
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.176634	−	0.984277i	$-0.443479\pi$
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.764092	−	0.645108i	$-0.223188\pi$
$522$	22.2503	−	1.57863i	0.973871	−	0.0690949i
$523$	−33.0751	+	19.0959i	−1.44627	+	0.835007i	−0.998257	−	0.0590174i	$-0.981203\pi$
$523$	−33.0751	+	19.0959i	−1.44627	+	0.835007i	−0.448018	+	0.894025i	$0.647870\pi$
$524$	1.75748			0.0767759
$525$		0			0
$526$	13.8974			0.605953
$527$	2.59038	−	1.49555i	0.112839	−	0.0651474i
$528$	10.5922	−	6.62623i	0.460966	−	0.288370i
$529$	−2.26734	+	3.92715i	−0.0985802	+	0.170746i
$530$		0			0
$531$	−19.5376	−	28.9022i	−0.847859	−	1.25425i
$532$	−3.96240	+	10.5633i	−0.171792	+	0.457975i
$533$			4.44898i			0.192707i
$534$	0.473126	+	13.3539i	0.0204742	+	0.577879i
$535$		0			0
$536$	−9.81641	−	5.66751i	−0.424004	−	0.244799i
$537$	0.322716	+	9.10860i	0.0139262	+	0.393065i
$538$		−	0.502984i		−	0.0216852i
$539$	10.0549	+	29.4068i	0.433094	+	1.26664i
$540$		0			0
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	0.870397	−	0.492351i	$-0.163862\pi$
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	−0.861587	+	0.507611i	$0.830529\pi$
$542$	−12.5576	+	21.7504i	−0.539396	+	0.934261i
$543$	−14.2627	+	8.92243i	−0.612073	+	0.382898i
$544$	−1.91936	+	1.10814i	−0.0822918	+	0.0475112i
$545$		0			0
$546$	−3.53877	+	3.12726i	−0.151445	+	0.133834i
$547$	10.9605			0.468638			0.234319	−	0.972160i	$-0.424714\pi$
$547$	10.9605			0.468638			0.234319	+	0.972160i	$0.424714\pi$
$548$	−3.58677	+	2.07082i	−0.153219	+	0.0884612i
$549$	0.0979425	+	1.38047i	0.00418008	+	0.0589170i
$550$		0			0
$551$	−17.5604	−	30.4155i	−0.748098	−	1.29574i
$552$	−10.6801	+	20.1110i	−0.454576	+	0.855982i
$553$	−6.40434	−	38.5254i	−0.272340	−	1.63827i
$554$			14.9790i			0.636398i
$555$		0			0
$556$	7.77354	+	4.48805i	0.329671	+	0.190336i
$557$	−5.21291	−	3.00967i	−0.220878	−	0.127524i	0.385479	−	0.922717i	$-0.374036\pi$
$557$	−5.21291	−	3.00967i	−0.220878	−	0.127524i	−0.606357	+	0.795193i	$0.707370\pi$
$558$	−8.34043	+	17.1446i	−0.353079	+	0.725791i
$559$		−	0.470652i		−	0.0199065i
$560$		0			0
$561$	−3.44689	−	1.83049i	−0.145528	−	0.0772835i
$562$	−3.69591	−	6.40150i	−0.155903	−	0.270031i
$563$	−7.43466	+	12.8772i	−0.313334	+	0.542710i	−0.979082	−	0.203467i	$-0.934779\pi$
$563$	−7.43466	+	12.8772i	−0.313334	+	0.542710i	0.665748	+	0.746176i	$0.268113\pi$
$564$	−5.12126	−	8.18646i	−0.215644	−	0.344712i
$565$		0			0
$566$	−4.78405			−0.201089
$567$	−7.18209	−	22.7028i	−0.301619	−	0.953428i
$568$	24.1814			1.01463
$569$	4.55880	−	2.63203i	0.191115	−	0.110340i	−0.401389	−	0.915907i	$-0.631473\pi$
$569$	4.55880	−	2.63203i	0.191115	−	0.110340i	0.592504	+	0.805567i	$0.298139\pi$
$570$		0			0
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.228601	+	0.973520i	$0.573415\pi$
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.728793	+	0.684734i	$0.759918\pi$
$572$	1.77609	+	3.07628i	0.0742621	+	0.128626i
$573$	−14.6708	−	7.79103i	−0.612881	−	0.325475i
$574$	−13.1018	+	2.17801i	−0.546859	+	0.0909082i
$575$		0			0
$576$	10.4444	−	21.4696i	0.435185	−	0.894569i
$577$	4.35716	+	2.51561i	0.181391	+	0.104726i	0.587946	−	0.808900i	$-0.299937\pi$
$577$	4.35716	+	2.51561i	0.181391	+	0.104726i	−0.406555	+	0.913626i	$0.633270\pi$
$578$	15.6352	+	9.02699i	0.650339	+	0.375473i
$579$	−14.4564	+	0.512189i	−0.600789	+	0.0212858i
$580$		0			0
$581$	−26.7330	−	10.0278i	−1.10907	−	0.416025i
$582$	−6.05453	+	11.4009i	−0.250968	+	0.472582i
$583$	20.2726	+	35.1132i	0.839606	+	1.45424i
$584$	−9.65933	+	16.7305i	−0.399706	+	0.692311i
$585$		0			0
$586$	28.0928	−	16.2194i	1.16050	−	0.670016i
$587$	−18.5075			−0.763887			−0.381944	−	0.924186i	$-0.624745\pi$
$587$	−18.5075			−0.763887			−0.381944	+	0.924186i	$0.624745\pi$
$588$	7.87781	+	6.40078i	0.324875	+	0.263964i
$589$	30.0186			1.23690
$590$		0			0
$591$	2.60748	−	1.63118i	0.107258	−	0.0670978i
$592$	−6.11477	+	10.5911i	−0.251316	+	0.435291i
$593$	−9.26927	−	16.0548i	−0.380643	−	0.659293i	0.610511	−	0.792008i	$-0.290964\pi$
$593$	−9.26927	−	16.0548i	−0.380643	−	0.659293i	−0.991154	+	0.132714i	$0.957631\pi$
$594$	24.7366	−	2.63807i	1.01495	−	0.108241i
$595$		0			0
$596$		−	4.40658i		−	0.180501i
$597$	0.230505	+	6.50596i	0.00943395	+	0.266271i
$598$	3.83511	+	2.21420i	0.156829	+	0.0905453i
$599$	−0.501417	−	0.289493i	−0.0204873	−	0.0118284i	0.489721	−	0.871879i	$-0.337099\pi$
$599$	−0.501417	−	0.289493i	−0.0204873	−	0.0118284i	−0.510209	+	0.860051i	$0.670432\pi$
$600$		0			0
$601$		−	29.8618i		−	1.21809i	−0.793137	−	0.609044i	$-0.791553\pi$
$601$		−	29.8618i		−	1.21809i	0.793137	−	0.609044i	$-0.208447\pi$
$602$	1.38603	−	0.230409i	0.0564902	−	0.00939076i
$603$	−6.22467	−	9.20824i	−0.253488	−	0.374988i
$604$	2.93393	+	5.08172i	0.119380	+	0.206772i
$605$		0			0
$606$	−3.78560	+	2.36818i	−0.153779	+	0.0962007i
$607$	−21.7458	+	12.5550i	−0.882637	+	0.509591i	−0.871527	−	0.490348i	$-0.836870\pi$
$607$	−21.7458	+	12.5550i	−0.882637	+	0.509591i	−0.0111098	+	0.999938i	$0.503536\pi$
$608$	−22.2425			−0.902053
$609$	−30.9673	+	6.28208i	−1.25486	+	0.254563i
$610$		0			0
$611$	−5.51156	+	3.18210i	−0.222974	+	0.128734i
$612$	−1.27148	+	0.0902097i	−0.0513964	+	0.00364651i
$613$	−0.729932	+	1.26428i	−0.0294817	+	0.0510638i	−0.880390	−	0.474251i	$-0.842719\pi$
$613$	−0.729932	+	1.26428i	−0.0294817	+	0.0510638i	0.850908	+	0.525315i	$0.176052\pi$
$614$	−17.7009	−	30.6589i	−0.714351	−	1.23729i
$615$		0			0
$616$	−27.7550	+	22.8294i	−1.11828	+	0.919822i
$617$		−	6.56208i		−	0.264179i	−0.991238	−	0.132090i	$-0.957831\pi$
$617$		−	6.56208i		−	0.264179i	0.991238	−	0.132090i	$-0.0421687\pi$
$618$	−27.9279	+	0.989482i	−1.12343	+	0.0398028i
$619$	18.2419	+	10.5319i	0.733202	+	0.423315i	0.819593	−	0.572947i	$-0.194200\pi$
$619$	18.2419	+	10.5319i	0.733202	+	0.423315i	−0.0863902	+	0.996261i	$0.527533\pi$
$620$		0			0
$621$	−18.0441	+	13.1519i	−0.724086	+	0.527768i
$622$			17.7510i			0.711751i
$623$	−3.10400	−	18.6721i	−0.124359	−	0.748084i
$624$	−2.37526	−	1.26140i	−0.0950864	−	0.0504964i
$625$		0			0
$626$	2.48473	−	4.30367i	0.0993096	−	0.172009i
$627$	−20.7728	−	33.2059i	−0.829587	−	1.32612i
$628$	2.10265	−	1.21396i	0.0839048	−	0.0484425i
$629$	3.82015			0.152319
$630$		0			0
$631$	17.5069			0.696937			0.348468	−	0.937321i	$-0.386702\pi$
$631$	17.5069			0.696937			0.348468	+	0.937321i	$0.386702\pi$
$632$	39.1103	−	22.5803i	1.55572	−	0.898197i
$633$	8.37873	+	13.3936i	0.333025	+	0.532349i
$634$	15.8678	−	27.4839i	0.630192	−	1.09152i
$635$		0			0
$636$	11.6954	+	6.21095i	0.463754	+	0.246280i
$637$	4.39974	−	5.03939i	0.174324	−	0.199668i
$638$		−	33.0114i		−	1.30694i
$639$	21.3224	+	10.3728i	0.843500	+	0.410341i
$640$		0			0
$641$	9.98943	+	5.76740i	0.394559	+	0.227798i	0.684133	−	0.729357i	$-0.260181\pi$
$641$	9.98943	+	5.76740i	0.394559	+	0.227798i	−0.289575	+	0.957155i	$0.593514\pi$
$642$	25.3133	−	0.896846i	0.999036	−	0.0353957i
$643$		−	17.3489i		−	0.684173i	−0.939668	−	0.342087i	$-0.888866\pi$
$643$		−	17.3489i		−	0.684173i	0.939668	−	0.342087i	$-0.111134\pi$
$644$	3.34290	−	8.91175i	0.131729	−	0.351172i
$645$		0			0
$646$	−1.39378	−	2.41409i	−0.0548374	−	0.0949812i
$647$	−3.93387	+	6.81366i	−0.154656	+	0.267873i	−0.932934	−	0.360048i	$-0.882760\pi$
$647$	−3.93387	+	6.81366i	−0.154656	+	0.267873i	0.778278	+	0.627920i	$0.216094\pi$
$648$	21.6634	−	16.9963i	0.851018	−	0.667679i
$649$	−44.7120	+	25.8145i	−1.75510	+	1.01331i
$650$		0			0
$651$	8.58418	−	25.6071i	0.336440	−	1.00362i
$652$	10.6813			0.418314
$653$	1.73516	−	1.00180i	0.0679021	−	0.0392033i	−0.465665	−	0.884961i	$-0.654185\pi$
$653$	1.73516	−	1.00180i	0.0679021	−	0.0392033i	0.533567	+	0.845758i	$0.320851\pi$
$654$	25.5268	−	15.9690i	0.998178	−	0.624437i
$655$		0			0
$656$	−3.78182	−	6.55031i	−0.147655	−	0.255747i
$657$	−15.6939	+	10.6089i	−0.612278	+	0.413893i
$658$	−12.0692	−	14.6732i	−0.470506	−	0.572021i
$659$		−	44.8494i		−	1.74709i	−0.486747	−	0.873543i	$-0.661817\pi$
$659$		−	44.8494i		−	1.74709i	0.486747	−	0.873543i	$-0.338183\pi$
$660$		0			0
$661$	10.4404	+	6.02776i	0.406084	+	0.234453i	0.689106	−	0.724661i	$-0.258004\pi$
$661$	10.4404	+	6.02776i	0.406084	+	0.234453i	−0.283022	+	0.959113i	$0.591337\pi$
$662$	−2.48012	−	1.43190i	−0.0963926	−	0.0556523i
$663$	0.0297458	+	0.839570i	0.00115523	+	0.0326062i
$664$		−	33.0163i		−	1.28128i
$665$		0			0
$666$	−20.1733	+	13.6370i	−0.781701	+	0.528421i
$667$	14.8149	+	25.6602i	0.573636	+	0.993566i
$668$	6.60397	−	11.4384i	0.255515	−	0.442565i
$669$	17.2385	−	10.7840i	0.666478	−	0.416933i
$670$		0			0
$671$	2.04812			0.0790667
$672$	−6.36051	+	18.9738i	−0.245362	+	0.731930i
$673$	−11.5641			−0.445763			−0.222882	−	0.974845i	$-0.571546\pi$
$673$	−11.5641			−0.445763			−0.222882	+	0.974845i	$0.571546\pi$
$674$	20.0407	−	11.5705i	0.771941	−	0.445680i
$675$		0			0
$676$	−5.05941	+	8.76315i	−0.194593	+	0.337044i
$677$	10.7467	+	18.6138i	0.413029	+	0.715388i	0.995219	−	0.0976651i	$-0.0311374\pi$
$677$	10.7467	+	18.6138i	0.413029	+	0.715388i	−0.582190	+	0.813053i	$0.697804\pi$
$678$	−4.42979	+	8.34145i	−0.170125	+	0.320352i
$679$	6.42234	−	17.1212i	0.246467	−	0.657050i
$680$		0			0
$681$	−41.9257	+	1.48542i	−1.60660	+	0.0569214i
$682$	24.4355	+	14.1079i	0.935684	+	0.540218i
$683$	15.0140	+	8.66837i	0.574497	+	0.331686i	0.758943	−	0.651157i	$-0.225716\pi$
$683$	15.0140	+	8.66837i	0.574497	+	0.331686i	−0.184447	+	0.982843i	$0.559049\pi$
$684$	−11.5036	−	5.59620i	−0.439850	−	0.213976i
$685$		0			0
$686$	16.9944	+	10.4898i	0.648849	+	0.400501i
$687$	−33.2084	−	17.6356i	−1.26698	−	0.672839i
$688$	0.400075	+	0.692950i	0.0152527	+	0.0264185i
$689$	4.36379	−	7.55831i	0.166247	−	0.287949i
$690$		0			0
$691$	−11.7251	+	6.76951i	−0.446045	+	0.257524i	−0.706158	−	0.708054i	$-0.749573\pi$
$691$	−11.7251	+	6.76951i	−0.446045	+	0.257524i	0.260114	+	0.965578i	$0.416240\pi$
$692$	8.51700			0.323768
$693$	−34.2663	+	8.22447i	−1.30167	+	0.312422i
$694$	19.5866			0.743496
$695$		0			0
$696$	−19.3784	−	30.9768i	−0.734535	−	1.17417i
$697$	−1.18133	+	2.04613i	−0.0447461	+	0.0775026i
$698$	7.09240	+	12.2844i	0.268451	+	0.464971i
$699$	16.8212	+	8.93303i	0.636237	+	0.337878i
$700$		0			0
$701$			41.8503i			1.58066i	0.612679	+	0.790332i	$0.290092\pi$
$701$			41.8503i			1.58066i	−0.612679	+	0.790332i	$0.709908\pi$
$702$	−3.15413	−	4.32739i	−0.119045	−	0.163327i
$703$	33.2024	+	19.1694i	1.25225	+	0.722989i
$704$	−30.5998	−	17.6668i	−1.15327	−	0.665842i
$705$		0			0
$706$			11.1006i			0.417775i
$707$	4.88513	−	4.01817i	0.183724	−	0.151119i
$708$	−7.90881	+	14.8926i	−0.297231	+	0.559697i
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	0.877563	+	0.479462i	$0.159168\pi$
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	−0.0235552	+	0.999723i	$0.507499\pi$
$710$		0			0
$711$	44.1721	−	3.13395i	1.65658	−	0.117532i
$712$	18.9556	−	10.9440i	0.710392	−	0.410145i
$713$	−25.3253			−0.948442
$714$	−2.45789	+	0.498612i	−0.0919842	+	0.0186601i
$715$		0			0
$716$	3.81519	−	2.20270i	0.142580	−	0.0823189i
$717$	13.2545	−	8.29168i	0.494997	−	0.309658i
$718$	6.36230	−	11.0198i	0.237439	−	0.411256i
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	0.863886	−	0.503687i	$-0.168024\pi$
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	−0.868149	+	0.496304i	$0.834690\pi$
$720$		0			0
$721$	39.0504	−	6.49162i	1.45431	−	0.241761i
$722$		−	7.48733i		−	0.278650i
$723$	0.311606	+	8.79502i	0.0115887	+	0.327090i
$724$	7.04228	+	4.06586i	0.261724	+	0.151107i
$725$		0			0
$726$	−0.576104	−	16.2604i	−0.0213812	−	0.603481i
$727$		−	19.2284i		−	0.713140i	−0.934269	−	0.356570i	$-0.883946\pi$
$727$		−	19.2284i		−	0.713140i	0.934269	−	0.356570i	$-0.116054\pi$
$728$	7.24299	+	2.71693i	0.268443	+	0.100696i
$729$	26.3927	−	5.69415i	0.977509	−	0.210895i
$730$		0			0
$731$	0.124972	−	0.216457i	0.00462225	−	0.00800596i
$732$	0.567103	−	0.354766i	0.0209607	−	0.0131125i
$733$	7.15035	−	4.12825i	0.264104	−	0.152481i	−0.362101	−	0.932139i	$-0.617941\pi$
$733$	7.15035	−	4.12825i	0.264104	−	0.152481i	0.626205	+	0.779658i	$0.284607\pi$
$734$	−17.2253			−0.635797
$735$		0			0
$736$	18.7650			0.691688
$737$	−14.2452	+	8.22447i	−0.524729	+	0.302952i
$738$	−1.06580	−	15.0222i	−0.0392328	−	0.552974i
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	−0.755088	−	0.655623i	$-0.772406\pi$
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	0.945331	+	0.326114i	$0.105739\pi$
$740$		0			0
$741$	−3.95441	+	7.44629i	−0.145269	+	0.273546i
$742$	24.3948	+	9.15076i	0.895561	+	0.335935i
$743$		−	37.7580i		−	1.38521i	−0.721318	−	0.692604i	$-0.756463\pi$
$743$		−	37.7580i		−	1.38521i	0.721318	−	0.692604i	$-0.243537\pi$
$744$	31.2110	−	1.10580i	1.14425	−	0.0405407i
$745$		0			0
$746$	4.96508	+	2.86659i	0.181785	+	0.104953i
$747$	14.1626	−	29.1127i	0.518182	−	1.06518i
$748$			1.88641i			0.0689741i
$749$	−35.3945	+	5.88387i	−1.29329	+	0.214992i
$750$		0			0
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	0.930476	+	0.366352i	$0.119394\pi$
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	−0.147968	+	0.988992i	$0.547273\pi$
$752$	5.40985	−	9.37013i	0.197277	−	0.341693i
$753$	17.1546	+	27.4220i	0.625148	+	0.999315i
$754$	−6.15389	+	3.55295i	−0.224111	+	0.129391i
$755$		0			0
$756$	−8.06337	+	8.21273i	−0.293262	+	0.298694i
$757$	30.1051			1.09419			0.547094	−	0.837071i	$-0.315734\pi$
$757$	30.1051			1.09419			0.547094	+	0.837071i	$0.315734\pi$
$758$	22.4527	−	12.9631i	0.815518	−	0.470840i
$759$	17.5251	+	28.0143i	0.636121	+	1.01686i
$760$		0			0
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	−0.973557	−	0.228445i	$-0.926636\pi$
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	0.288939	−	0.957347i	$-0.406697\pi$
$762$	13.2791	+	7.05196i	0.481051	+	0.255466i
$763$	−32.9411	+	27.0951i	−1.19255	+	0.980910i
$764$			8.02904i			0.290480i
$765$		0			0
$766$	17.5577	+	10.1370i	0.634386	+	0.366263i
$767$	9.62451	+	5.55671i	0.347521	+	0.200641i
$768$	−27.8350	+	0.986190i	−1.00441	+	0.0355861i
$769$		−	33.3656i		−	1.20319i	−0.798800	−	0.601597i	$-0.794531\pi$
$769$		−	33.3656i		−	1.20319i	0.798800	−	0.601597i	$-0.205469\pi$
$770$		0			0
$771$	−9.81558	+	18.4831i	−0.353499	+	0.665652i
$772$	3.49595	+	6.05517i	0.125822	+	0.217930i
$773$	0.573356	−	0.993081i	0.0206222	−	0.0357186i	−0.855530	−	0.517753i	$-0.826769\pi$
$773$	0.573356	−	0.993081i	0.0206222	−	0.0357186i	0.876152	+	0.482034i	$0.160102\pi$
$774$	0.112750	+	1.58918i	0.00405272	+	0.0571218i
$775$		0			0
$776$	21.1453			0.759073
$777$	25.8470	−	22.8413i	0.927254	−	0.819428i
$778$	−13.1743			−0.472321
$779$	−20.5348	+	11.8558i	−0.735736	+	0.424778i
$780$		0			0
$781$	17.5456	−	30.3898i	0.627830	−	1.08743i
$782$	1.17587	+	2.03666i	0.0420489	+	0.0728309i
$783$	−3.79948	−	35.6268i	−0.135782	−	1.27320i
$784$	−2.19412	+	11.1595i	−0.0783614	+	0.398555i
$785$		0			0
$786$	0.138829	+	3.91842i	0.00495186	+	0.139765i
$787$	35.9215	+	20.7393i	1.28046	+	0.739276i	0.976933	−	0.213546i	$-0.0685014\pi$
$787$	35.9215	+	20.7393i	1.28046	+	0.739276i	0.303530	+	0.952822i	$0.401835\pi$
$788$	−1.28746	−	0.743313i	−0.0458637	−	0.0264794i
$789$	−0.790377	−	22.3082i	−0.0281382	−	0.794195i
$790$		0			0
$791$	4.69889	−	12.5267i	0.167073	−	0.445397i
$792$	−22.8212	−	33.7597i	−0.810916	−	1.19960i
$793$	−0.220434	−	0.381804i	−0.00782786	−	0.0135582i
$794$	−10.1175	+	17.5241i	−0.359058	+	0.621907i
$795$		0			0
$796$	2.72506	−	1.57332i	0.0965874	−	0.0557647i
$797$	49.5086			1.75369			0.876843	−	0.480777i	$-0.159645\pi$
$797$	49.5086			1.75369			0.876843	+	0.480777i	$0.159645\pi$
$798$	−23.8645	−	8.00000i	−0.844794	−	0.283197i
$799$	−3.37976			−0.119567
$800$		0			0
$801$	21.4090	−	1.51894i	0.756448	−	0.0536690i
$802$	12.9386	−	22.4103i	0.456878	−	0.791336i
$803$	14.0173	+	24.2786i	0.494658	+	0.856773i
$804$	−2.51974	+	4.74477i	−0.0888645	+	0.167335i
$805$		0			0
$806$		−	6.07359i		−	0.213933i
$807$	−0.807397	+	0.0286059i	−0.0284217	+	0.00100698i
$808$	6.33446	+	3.65720i	0.222846	+	0.128660i
$809$	21.7594	+	12.5628i	0.765018	+	0.441683i	0.831095	−	0.556131i	$-0.187715\pi$
$809$	21.7594	+	12.5628i	0.765018	+	0.441683i	−0.0660764	+	0.997815i	$0.521048\pi$
$810$		0			0
$811$			4.97517i			0.174702i	0.996178	+	0.0873509i	$0.0278401\pi$
$811$			4.97517i			0.174702i	−0.996178	+	0.0873509i	$0.972160\pi$
$812$	9.70210	+	11.7954i	0.340477	+	0.413938i
$813$	35.6283	+	18.9207i	1.24954	+	0.663577i
$814$	18.0181	+	31.2083i	0.631535	+	1.09385i
$815$		0			0
$816$	−0.757466	−	1.21083i	−0.0265166	−	0.0423875i
$817$	2.17235	−	1.25421i	0.0760011	−	0.0438792i
$818$	−18.4210			−0.644076
$819$	5.22119	+	5.50263i	0.182443	+	0.192277i
$820$		0			0
$821$	−12.0008	+	6.92866i	−0.418830	+	0.241812i	−0.694577	−	0.719419i	$-0.744408\pi$
$821$	−12.0008	+	6.92866i	−0.418830	+	0.241812i	0.275746	+	0.961230i	$0.411075\pi$
$822$	−4.90037	−	7.83336i	−0.170920	−	0.273220i
$823$	23.0779	−	39.9721i	0.804446	−	1.39334i	−0.112219	−	0.993684i	$-0.535796\pi$
$823$	23.0779	−	39.9721i	0.804446	−	1.39334i	0.916665	−	0.399658i	$-0.130871\pi$
$824$	22.8880	+	39.6432i	0.797343	+	1.38104i
$825$		0			0
$826$	−11.6523	+	31.0635i	−0.405435	+	1.08084i
$827$		−	18.6880i		−	0.649844i	−0.945741	−	0.324922i	$-0.894662\pi$
$827$		−	18.6880i		−	0.649844i	0.945741	−	0.324922i	$-0.105338\pi$
$828$	9.70505	+	4.72126i	0.337274	+	0.164075i
$829$	−14.9458	−	8.62894i	−0.519088	−	0.299695i	0.217474	−	0.976066i	$-0.430218\pi$
$829$	−14.9458	−	8.62894i	−0.519088	−	0.299695i	−0.736561	+	0.676371i	$0.763552\pi$
$830$		0			0
$831$	24.0446	−	0.851896i	0.834098	−	0.0295519i
$832$			7.60575i			0.263682i
$833$	3.36158	−	1.14940i	0.116472	−	0.0398244i
$834$	−9.39235	+	17.6861i	−0.325231	+	0.612421i
$835$		0			0
$836$	−9.46597	+	16.3955i	−0.327387	+	0.567052i
$837$	27.9952	+	12.4131i	0.967655	+	0.429061i
$838$	−37.0301	+	21.3793i	−1.27918	+	0.738536i
$839$	49.1689			1.69750			0.848750	−	0.528795i	$-0.177356\pi$
$839$	49.1689			1.69750			0.848750	+	0.528795i	$0.177356\pi$
$840$		0			0
$841$	−18.5446			−0.639470
$842$	−31.8844	+	18.4085i	−1.09881	+	0.634398i
$843$	−10.0656	+	6.29680i	−0.346678	+	0.216873i
$844$	3.81810	−	6.61315i	0.131425	−	0.227634i
$845$		0			0
$846$	17.8477	−	12.0649i	0.613617	−	0.414798i
$847$	3.77960	+	22.7362i	0.129869	+	0.781226i
$848$			14.8377i			0.509527i
$849$	0.272081	+	7.67943i	0.00933779	+	0.263557i
$850$		0			0
$851$	−28.0114	−	16.1724i	−0.960218	−	0.554382i
$852$	−0.405806	−	11.4538i	−0.0139027	−	0.392401i
$853$			8.86218i			0.303435i	0.988424	+	0.151718i	$0.0484804\pi$
$853$			8.86218i			0.303435i	−0.988424	+	0.151718i	$0.951520\pi$
$854$	1.01646	−	0.836071i	0.0347826	−	0.0286097i
$855$		0			0
$856$	−20.7452	−	35.9318i	−0.709058	−	1.22812i
$857$	−0.491781	+	0.851790i	−0.0167989	+	0.0290966i	−0.874303	−	0.485381i	$-0.838681\pi$
$857$	−0.491781	+	0.851790i	−0.0167989	+	0.0290966i	0.857504	+	0.514478i	$0.172014\pi$
$858$	−6.71847	+	4.20292i	−0.229365	+	0.143485i
$859$	−23.6244	+	13.6395i	−0.806053	+	0.465375i	−0.845583	−	0.533843i	$-0.820747\pi$
$859$	−23.6244	+	13.6395i	−0.806053	+	0.465375i	0.0395302	+	0.999218i	$0.487414\pi$
$860$		0			0
$861$	4.24130	+	20.9074i	0.144543	+	0.712521i
$862$	27.7897			0.946519
$863$	3.94265	−	2.27629i	0.134209	−	0.0774857i	−0.431392	−	0.902165i	$-0.641977\pi$
$863$	3.94265	−	2.27629i	0.134209	−	0.0774857i	0.565601	+	0.824679i	$0.308644\pi$
$864$	−20.7433	−	9.19761i	−0.705700	−	0.312909i
$865$		0			0
$866$	6.42257	+	11.1242i	0.218248	+	0.378016i
$867$	13.6011	−	25.6113i	0.461916	−	0.869804i
$868$	−12.8774	+	2.14071i	−0.437089	+	0.0726604i
$869$		−	65.5354i		−	2.22314i
$870$		0			0
$871$	3.06636	+	1.77036i	0.103900	+	0.0599865i
$872$	−42.7142	−	24.6611i	−1.44649	−	0.835129i
$873$	18.6452	+	9.07043i	0.631046	+	0.306988i
$874$			23.6019i			0.798346i
$875$		0			0
$876$	8.08667	+	4.29449i	0.273223	+	0.145097i
$877$	10.6784	+	18.4956i	0.360584	+	0.624551i	0.988057	−	0.154088i	$-0.0492439\pi$
$877$	10.6784	+	18.4956i	0.360584	+	0.624551i	−0.627473	+	0.778639i	$0.715911\pi$
$878$	−9.04360	+	15.6640i	−0.305207	+	0.528634i
$879$	−27.6333	−	44.1725i	−0.932047	−	1.48990i
$880$		0			0
$881$	33.2551			1.12039			0.560196	−	0.828360i	$-0.310726\pi$
$881$	33.2551			1.12039			0.560196	+	0.828360i	$0.310726\pi$
$882$	−13.6487	+	18.0697i	−0.459574	+	0.608439i
$883$	−12.0561			−0.405721			−0.202860	−	0.979208i	$-0.565024\pi$
$883$	−12.0561			−0.405721			−0.202860	+	0.979208i	$0.565024\pi$
$884$	0.351659	−	0.203031i	0.0118276	−	0.00682866i
$885$		0			0
$886$	−1.29179	+	2.23745i	−0.0433987	+	0.0751687i
$887$	11.7064	+	20.2760i	0.393062	+	0.680803i	0.992852	−	0.119355i	$-0.0380825\pi$
$887$	11.7064	+	20.2760i	0.393062	+	0.680803i	−0.599790	+	0.800157i	$0.704749\pi$
$888$	35.2275	+	18.7078i	1.18216	+	0.627793i
$889$	−19.9417	−	7.48036i	−0.668824	−	0.250883i
$890$		0			0
$891$	−5.64151	−	39.5575i	−0.188998	−	1.32523i
$892$	−8.51156	−	4.91415i	−0.284988	−	0.164538i
$893$	−29.3748	−	16.9595i	−0.982990	−	0.567529i
$894$	9.82477	−	0.348090i	0.328589	−	0.0116419i
$895$		0			0
$896$	0.396319	−	0.0658829i	0.0132401	−	0.00220099i
$897$	3.33616	−	6.28210i	0.111391	−	0.209753i
$898$	13.7322	+	23.7848i	0.458249	+	0.793711i
$899$	20.3188	−	35.1932i	0.677670	−	1.17376i
$900$		0			0
$901$	4.01390	−	2.31743i	0.133722	−	0.0772046i
$902$	−22.2875			−0.742091
$903$	−0.448683	−	2.21177i	−0.0149312	−	0.0736029i
$904$	15.4709			0.514556
$905$		0			0
$906$	−11.0983	+	6.94281i	−0.368715	+	0.230659i
$907$	−20.7508	+	35.9415i	−0.689020	+	1.19342i	0.283135	+	0.959080i	$0.408626\pi$
$907$	−20.7508	+	35.9415i	−0.689020	+	1.19342i	−0.972155	+	0.234338i	$0.924708\pi$
$908$	10.1388	+	17.5608i	0.336466	+	0.582777i
$909$	4.01674	+	5.94201i	0.133227	+	0.197084i
$910$		0			0
$911$		−	57.6428i		−	1.90979i	−0.296941	−	0.954896i	$-0.595966\pi$
$911$		−	57.6428i		−	1.90979i	0.296941	−	0.954896i	$-0.404034\pi$
$912$	−0.507522	−	14.3247i	−0.0168057	−	0.474339i
$913$	−41.4930	−	23.9560i	−1.37322	−	0.792828i
$914$	−3.21429	−	1.85577i	−0.106319	−	0.0613835i
$915$		0			0
$916$			18.1743i			0.600496i
$917$	−0.910804	−	5.47895i	−0.0300774	−	0.180931i
$918$	−0.301566	−	2.82772i	−0.00995318	−	0.0933286i
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	0.941891	−	0.335918i	$-0.109046\pi$
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	−0.761859	+	0.647743i	$0.775713\pi$
$920$		0			0
$921$	−48.2074	+	30.1574i	−1.58849	+	0.993721i
$922$	−12.6423	+	7.29905i	−0.416353	+	0.240381i
$923$	−7.55357			−0.248629
$924$	11.2792	+	12.7634i	0.371058	+	0.419884i
$925$		0			0
$926$	4.79793	−	2.77009i	0.157670	−	0.0910307i
$927$	3.17666	+	44.7741i	0.104335	+	1.47057i
$928$	−15.0554	+	26.0767i	−0.494217	+	0.856008i
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	0.979837	+	0.199799i	$0.0640289\pi$
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	−0.316887	+	0.948463i	$0.602638\pi$
$930$		0			0
$931$	34.9845	+	6.87843i	1.14657	+	0.225431i
$932$		−	9.20592i		−	0.301550i
$933$	28.4942	−	1.00954i	0.932858	−	0.0330510i
$934$	−8.60828	−	4.96999i	−0.281672	−	0.162623i
$935$		0			0
$936$	−3.83719	+	7.88775i	−0.125422	+	0.257819i
$937$		−	5.67805i		−	0.185494i	−0.995690	−	0.0927468i	$-0.970435\pi$
$937$		−	5.67805i		−	0.185494i	0.995690	−	0.0927468i	$-0.0295647\pi$
$938$	−3.71241	+	9.89682i	−0.121214	+	0.323143i
$939$	−7.04963	−	3.74376i	−0.230056	−	0.122173i
$940$		0			0
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	−0.950214	−	0.311598i	$-0.899136\pi$
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	0.744959	+	0.667110i	$0.232469\pi$
$942$	2.87271	+	4.59210i	0.0935979	+	0.149619i
$943$	17.3243	−	10.0022i	0.564157	−	0.325716i
$944$	−18.8938			−0.614940
$945$		0			0
$946$	2.35776			0.0766575
$947$	−27.1427	+	15.6709i	−0.882020	+	0.509234i	−0.871324	−	0.490708i	$-0.836738\pi$
$947$	−27.1427	+	15.6709i	−0.882020	+	0.509234i	−0.0106960	+	0.999943i	$0.503405\pi$
$948$	−11.3518	−	18.1461i	−0.368688	−	0.589357i
$949$	3.01729	−	5.22611i	0.0979455	−	0.169647i
$950$		0			0
$951$	−45.0200	−	23.9082i	−1.45987	−	0.775277i
$952$	2.60970	+	3.17276i	0.0845808	+	0.102830i
$953$			43.7751i			1.41802i	0.705200	+	0.709008i	$0.250857\pi$
$953$			43.7751i			1.41802i	−0.705200	+	0.709008i	$0.749143\pi$
$954$	−12.9239	+	26.5664i	−0.418425	+	0.860118i
$955$		0			0
$956$	−6.54444	−	3.77843i	−0.211662	−	0.122203i
$957$	−52.9905	+	1.87744i	−1.71294	+	0.0606891i
$958$		−	22.2540i		−	0.718994i
$959$	8.31462	+	10.1086i	0.268493	+	0.326423i
$960$		0			0
$961$	1.86698	+	3.23370i	0.0602251	+	0.104313i
$962$	3.87850	−	6.71776i	0.125048	−	0.216589i
$963$	−2.87926	−	40.5823i	−0.0927829	−	1.30775i
$964$	3.68385	−	2.12687i	0.118649	−	0.0685019i
$965$		0			0
$966$	20.1334	+	6.74924i	0.647781	+	0.217153i
$967$	−36.3052			−1.16750			−0.583748	−	0.811935i	$-0.698415\pi$
$967$	−36.3052			−1.16750			−0.583748	+	0.811935i	$0.698415\pi$
$968$	−23.0814	+	13.3261i	−0.741864	+	0.428316i
$969$	−3.79587	+	2.37461i	−0.121941	+	0.0762834i
$970$		0			0
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	0.919948	+	0.392041i	$0.128231\pi$
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	−0.120456	+	0.992719i	$0.538436\pi$
$972$	−8.41406	−	9.97588i	−0.269881	−	0.319976i
$973$	9.96292	−	26.5599i	0.319397	−	0.851472i
$974$		−	2.66887i		−	0.0855161i
$975$		0			0
$976$	0.649099	+	0.374757i	0.0207772	+	0.0119957i
$977$	−24.0369	−	13.8777i	−0.769008	−	0.443987i	0.0635127	−	0.997981i	$-0.479770\pi$
$977$	−24.0369	−	13.8777i	−0.769008	−	0.443987i	−0.832521	+	0.553994i	$0.813103\pi$
$978$	0.843752	+	23.8147i	0.0269802	+	0.761512i
$979$		−	31.7631i		−	1.01515i
$980$		0			0
$981$	−27.0854	−	40.0679i	−0.864772	−	1.27927i
$982$	11.4750	+	19.8753i	0.366181	+	0.634245i
$983$	21.0396	−	36.4417i	0.671060	−	1.16231i	−0.306544	−	0.951856i	$-0.599173\pi$
$983$	21.0396	−	36.4417i	0.671060	−	1.16231i	0.977604	−	0.210453i	$-0.0674940\pi$
$984$	−20.9138	+	13.0832i	−0.666707	+	0.417076i
$985$		0			0
$986$	−3.77364			−0.120177
$987$	−22.8673	+	20.2081i	−0.727873	+	0.643232i
$988$	4.07521			0.129650
$989$	−1.83272	+	1.05812i	−0.0582770	+	0.0336463i
$990$		0			0
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	−0.907890	−	0.419209i	$-0.862308\pi$
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	0.816990	+	0.576652i	$0.195641\pi$
$992$	−12.8682	−	22.2884i	−0.408566	−	0.707656i
$993$	−2.15745	+	4.06256i	−0.0684647	+	0.128922i
$994$	−3.69787	−	22.2445i	−0.117289	−	0.705554i
$995$		0			0
$996$	−15.6386	+	0.554071i	−0.495527	+	0.0175564i
$997$	−9.64266	−	5.56719i	−0.305386	−	0.176315i	0.339474	−	0.940615i	$-0.389751\pi$
$997$	−9.64266	−	5.56719i	−0.305386	−	0.176315i	−0.644860	+	0.764301i	$0.723084\pi$
$998$	−30.5729	−	17.6513i	−0.967768	−	0.558741i
$999$	23.0376	+	31.6070i	0.728876	+	1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.g.101.3		8
3.2	odd	2		525.2.t.f.101.2		8
5.2	odd	4		525.2.q.f.374.6		16
5.3	odd	4		525.2.q.f.374.3		16
5.4	even	2		105.2.s.c.101.2	yes	8
7.5	odd	6		525.2.t.f.26.2		8
15.2	even	4		525.2.q.e.374.3		16
15.8	even	4		525.2.q.e.374.6		16
15.14	odd	2		105.2.s.d.101.3	yes	8
21.5	even	6	inner	525.2.t.g.26.3		8
35.4	even	6		735.2.b.d.146.3		8
35.9	even	6		735.2.s.l.656.3		8
35.12	even	12		525.2.q.e.299.6		16
35.19	odd	6		105.2.s.d.26.3	yes	8
35.24	odd	6		735.2.b.c.146.3		8
35.33	even	12		525.2.q.e.299.3		16
35.34	odd	2		735.2.s.k.521.2		8
105.44	odd	6		735.2.s.k.656.2		8
105.47	odd	12		525.2.q.f.299.3		16
105.59	even	6		735.2.b.d.146.6		8
105.68	odd	12		525.2.q.f.299.6		16
105.74	odd	6		735.2.b.c.146.6		8
105.89	even	6		105.2.s.c.26.2	✓	8
105.104	even	2		735.2.s.l.521.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	105.89	even	6
105.2.s.c.101.2	yes	8	5.4	even	2
105.2.s.d.26.3	yes	8	35.19	odd	6
105.2.s.d.101.3	yes	8	15.14	odd	2
525.2.q.e.299.3		16	35.33	even	12
525.2.q.e.299.6		16	35.12	even	12
525.2.q.e.374.3		16	15.2	even	4
525.2.q.e.374.6		16	15.8	even	4
525.2.q.f.299.3		16	105.47	odd	12
525.2.q.f.299.6		16	105.68	odd	12
525.2.q.f.374.3		16	5.3	odd	4
525.2.q.f.374.6		16	5.2	odd	4
525.2.t.f.26.2		8	7.5	odd	6
525.2.t.f.101.2		8	3.2	odd	2
525.2.t.g.26.3		8	21.5	even	6	inner
525.2.t.g.101.3		8	1.1	even	1	trivial
735.2.b.c.146.3		8	35.24	odd	6
735.2.b.c.146.6		8	105.74	odd	6
735.2.b.d.146.3		8	35.4	even	6
735.2.b.d.146.6		8	105.59	even	6
735.2.s.k.521.2		8	35.34	odd	2
735.2.s.k.656.2		8	105.44	odd	6
735.2.s.l.521.3		8	105.104	even	2
735.2.s.l.656.3		8	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.933868 - 0.539169i) q^{2} +(-0.918594 - 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(2.47720 + 0.929227i) q^{7} +3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +O(q^{10})\)	\(q+(0.933868 - 0.539169i) q^{2} +(-0.918594 - 1.46840i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(2.47720 + 0.929227i) q^{7} +3.05945i q^{8} +(-1.31237 + 2.69772i) q^{9} +(3.84494 + 2.21988i) q^{11} +(1.44914 - 0.0513428i) q^{12} -0.955682i q^{13} +(2.81439 - 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(0.253761 - 0.439527i) q^{17} +(0.228945 + 3.22690i) q^{18} +(4.41107 - 2.54673i) q^{19} +(-0.911072 - 4.49110i) q^{21} +4.78755 q^{22} +(-3.72142 + 2.14856i) q^{23} +(4.49248 - 2.81039i) q^{24} +(-0.515274 - 0.892481i) q^{26} +(5.16685 - 0.551027i) q^{27} +(-1.71066 + 1.40707i) q^{28} -6.89526i q^{29} +(5.10397 + 2.94678i) q^{31} +(-3.78182 - 2.18344i) q^{32} +(-0.272280 - 7.68506i) q^{33} -0.547280i q^{34} +(-1.40656 - 2.08075i) q^{36} +(3.76353 + 6.51863i) q^{37} +(2.74624 - 4.75663i) q^{38} +(-1.40332 + 0.877884i) q^{39} -4.65529 q^{41} +(-3.27228 - 3.70287i) q^{42} +0.492478 q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.31688 + 4.01295i) q^{46} +(-3.32967 - 5.76715i) q^{47} +(1.31989 - 2.48541i) q^{48} +(5.27308 + 4.60377i) q^{49} +(-0.878503 + 0.0311252i) q^{51} +(0.692894 + 0.400043i) q^{52} +(7.90881 + 4.56616i) q^{53} +(4.52806 - 3.30039i) q^{54} +(-2.84292 + 7.57887i) q^{56} +(-7.79159 - 4.13778i) q^{57} +(-3.71771 - 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(0.399509 - 0.230657i) q^{61} +6.35524 q^{62} +(-5.75780 + 5.46331i) q^{63} -7.95845 q^{64} +(-4.39782 - 7.03002i) q^{66} +(-1.85246 + 3.20856i) q^{67} +(0.212446 + 0.367967i) q^{68} +(6.57342 + 3.49086i) q^{69} -7.90386i q^{71} +(-8.25352 - 4.01513i) q^{72} +(5.46846 + 3.15721i) q^{73} +(7.02929 + 4.05836i) q^{74} +4.26419i q^{76} +(7.46193 + 9.07191i) q^{77} +(-0.837188 + 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-5.55536 - 7.08081i) q^{81} +(-4.34743 + 2.50999i) q^{82} -10.7916 q^{83} +(3.63753 + 1.21939i) q^{84} +(0.459909 - 0.265529i) q^{86} +(-10.1250 + 6.33394i) q^{87} +(-6.79159 + 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750i q^{92} +(-0.361438 - 10.2015i) q^{93} +(-6.21894 - 3.59050i) q^{94} +(0.267811 + 7.55890i) q^{96} -6.91148i q^{97} +(7.40656 + 1.45623i) q^{98} +(-11.0346 + 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Introduction

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