LMFDB - Embedded newform 525.2.q.e.374.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 $ x^16 + 11x^14 + 85x^12 + 332x^10 + 940x^8 + 1064x^6 + 880x^4 + 128*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.3
Root			$0.539169 + 0.933868i$ of defining polynomial
Character	$\chi$	$=$	525.374
Dual form			525.2.q.e.299.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.539169 - 0.933868i) q^{2} +(-0.0613278 + 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(-0.929227 + 2.47720i) q^{7} -3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +O(q^{10})$	\(q+(-0.539169 - 0.933868i) q^{2} +(-0.0613278 + 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(-0.929227 + 2.47720i) q^{7} -3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +(-3.84494 - 2.21988i) q^{11} +(1.22932 + 0.769035i) q^{12} -0.955682 q^{13} +(2.81439 - 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(-0.439527 - 0.253761i) q^{17} +(1.41518 + 2.90905i) q^{18} +(-4.41107 + 2.54673i) q^{19} +(-4.23096 - 1.76038i) q^{21} +4.78755i q^{22} +(-2.14856 - 3.72142i) q^{23} +(0.187629 - 5.29579i) q^{24} +(0.515274 + 0.892481i) q^{26} +(0.551027 - 5.16685i) q^{27} +(1.40707 + 1.71066i) q^{28} -6.89526i q^{29} +(5.10397 + 2.94678i) q^{31} +(-2.18344 + 3.78182i) q^{32} +(4.07833 - 6.51931i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-6.51863 + 3.76353i) q^{37} +(4.75663 + 2.74624i) q^{38} +(0.0586099 - 1.65425i) q^{39} +4.65529 q^{41} +(0.637242 + 4.90030i) q^{42} -0.492478i q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.31688 + 4.01295i) q^{46} +(-5.76715 + 3.32967i) q^{47} +(-2.48541 + 1.31989i) q^{48} +(-5.27308 - 4.60377i) q^{49} +(0.466207 - 0.745243i) q^{51} +(-0.400043 + 0.692894i) q^{52} +(-4.56616 + 7.90881i) q^{53} +(-5.12226 + 2.27122i) q^{54} +(2.84292 - 7.57887i) q^{56} +(-4.13778 - 7.79159i) q^{57} +(-6.43926 + 3.71771i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(0.399509 - 0.230657i) q^{61} -6.35524i q^{62} +(3.30663 - 7.21569i) q^{63} +7.95845 q^{64} +(-8.28709 - 0.293610i) q^{66} +(-3.20856 - 1.85246i) q^{67} +(-0.367967 + 0.212446i) q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(9.15533 + 0.649559i) q^{72} +(3.15721 - 5.46846i) q^{73} +(7.02929 + 4.05836i) q^{74} +4.26419i q^{76} +(9.07191 - 7.46193i) q^{77} +(-1.57645 + 0.837188i) q^{78} +(7.38052 + 12.7834i) q^{79} +(8.90985 + 1.27068i) q^{81} +(-2.50999 - 4.34743i) q^{82} -10.7916i q^{83} +(-3.04738 + 2.33067i) q^{84} +(-0.459909 + 0.265529i) q^{86} +(11.9355 + 0.422871i) q^{87} +(11.7634 + 6.79159i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750 q^{92} +(-5.41378 + 8.65407i) q^{93} +(6.21894 + 3.59050i) q^{94} +(-6.41230 - 4.01138i) q^{96} +6.91148 q^{97} +(-1.45623 + 7.40656i) q^{98} +(11.0346 + 7.45926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	$ 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * q^96 + 68 * 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 $

$2$	−0.539169	−	0.933868i	−0.381250	−	0.660344i	0.609991	−	0.792408i	$-0.291173\pi$
$2$	−0.539169	−	0.933868i	−0.381250	−	0.660344i	−0.991241	+	0.132064i	$0.957840\pi$
$3$	−0.0613278	+	1.73096i	−0.0354076	+	0.999373i
$3$	−0.0613278	+	1.73096i	−0.0354076	+	0.999373i
$4$	0.418594	−	0.725026i	0.209297	−	0.362513i
$5$		0			0
$5$		0			0
$6$	1.64956	−	0.876010i	0.673429	−	0.357630i
$7$	−0.929227	+	2.47720i	−0.351215	+	0.936295i
$7$	−0.929227	+	2.47720i	−0.351215	+	0.936295i
$8$	−3.05945			−1.08168
$9$	−2.99248	−	0.212312i	−0.997493	−	0.0707708i
$10$		0			0
$11$	−3.84494	−	2.21988i	−1.15929	−	0.669318i	−0.208158	−	0.978095i	$-0.566747\pi$
$11$	−3.84494	−	2.21988i	−1.15929	−	0.669318i	−0.951134	+	0.308777i	$0.900080\pi$
$12$	1.22932	+	0.769035i	0.354875	+	0.222001i
$13$	−0.955682			−0.265059			−0.132529	−	0.991179i	$-0.542310\pi$
$13$	−0.955682			−0.265059			−0.132529	+	0.991179i	$0.542310\pi$
$14$	2.81439	−	0.467856i	0.752178	−	0.125040i
$15$		0			0
$16$	0.812371	+	1.40707i	0.203093	+	0.351767i
$17$	−0.439527	−	0.253761i	−0.106601	−	0.0615461i	0.445752	−	0.895157i	$-0.352936\pi$
$17$	−0.439527	−	0.253761i	−0.106601	−	0.0615461i	−0.552353	+	0.833611i	$0.686270\pi$
$18$	1.41518	+	2.90905i	0.333561	+	0.685670i
$19$	−4.41107	+	2.54673i	−1.01197	+	0.584261i	−0.911768	−	0.410706i	$-0.865282\pi$
$19$	−4.41107	+	2.54673i	−1.01197	+	0.584261i	−0.100202	+	0.994967i	$0.531949\pi$
$20$		0			0
$21$	−4.23096	−	1.76038i	−0.923272	−	0.384146i
$22$			4.78755i			1.02071i
$23$	−2.14856	−	3.72142i	−0.448007	−	0.775970i	0.550250	−	0.835000i	$-0.314533\pi$
$23$	−2.14856	−	3.72142i	−0.448007	−	0.775970i	−0.998256	+	0.0590300i	$0.981199\pi$
$24$	0.187629	−	5.29579i	0.0382996	−	1.08100i
$25$		0			0
$26$	0.515274	+	0.892481i	0.101054	+	0.175030i
$27$	0.551027	−	5.16685i	0.106045	−	0.994361i
$28$	1.40707	+	1.71066i	0.265911	+	0.323283i
$29$		−	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	$0.489138\pi$
$32$	−2.18344	+	3.78182i	−0.385981	+	0.668538i
$33$	4.07833	−	6.51931i	0.709946	−	1.13487i
$34$			0.547280i			0.0938578i
$35$		0			0
$36$	−1.40656	+	2.08075i	−0.234427	+	0.346792i
$37$	−6.51863	+	3.76353i	−1.07166	+	0.618721i	−0.928634	−	0.370998i	$-0.879016\pi$
$37$	−6.51863	+	3.76353i	−1.07166	+	0.618721i	−0.143023	+	0.989719i	$0.545682\pi$
$38$	4.75663	+	2.74624i	0.771627	+	0.445499i
$39$	0.0586099	−	1.65425i	0.00938509	−	0.264892i
$40$		0			0
$41$	4.65529			0.727034			0.363517	−	0.931588i	$-0.381576\pi$
$41$	4.65529			0.727034			0.363517	+	0.931588i	$0.381576\pi$
$42$	0.637242	+	4.90030i	0.0983286	+	0.756133i
$43$		−	0.492478i		−	0.0751022i	−0.999295	−	0.0375511i	$-0.988044\pi$
$43$		−	0.492478i		−	0.0751022i	0.999295	−	0.0375511i	$-0.0119557\pi$
$44$	−3.21894	+	1.85845i	−0.485273	+	0.280172i
$45$		0			0
$46$	−2.31688	+	4.01295i	−0.341605	+	0.591677i
$47$	−5.76715	+	3.32967i	−0.841225	+	0.485682i	−0.857681	−	0.514183i	$-0.828095\pi$
$47$	−5.76715	+	3.32967i	−0.841225	+	0.485682i	0.0164553	+	0.999865i	$0.494762\pi$
$48$	−2.48541	+	1.31989i	−0.358737	+	0.190510i
$49$	−5.27308	−	4.60377i	−0.753297	−	0.657681i
$50$		0			0
$51$	0.466207	−	0.745243i	0.0652820	−	0.104355i
$52$	−0.400043	+	0.692894i	−0.0554759	+	0.0960871i
$53$	−4.56616	+	7.90881i	−0.627210	+	1.08636i	0.360899	+	0.932605i	$0.382470\pi$
$53$	−4.56616	+	7.90881i	−0.627210	+	1.08636i	−0.988109	+	0.153754i	$0.950864\pi$
$54$	−5.12226	+	2.27122i	−0.697051	+	0.309074i
$55$		0			0
$56$	2.84292	−	7.57887i	0.379901	−	1.01277i
$57$	−4.13778	−	7.79159i	−0.548063	−	1.03202i
$58$	−6.43926	+	3.71771i	−0.845517	+	0.488159i
$59$	−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	$0.323931\pi$
$62$		−	6.35524i		−	0.807116i
$63$	3.30663	−	7.21569i	0.416596	−	0.909092i
$64$	7.95845			0.994806
$65$		0			0
$66$	−8.28709	−	0.293610i	−1.02007	−	0.0361409i
$67$	−3.20856	−	1.85246i	−0.391988	−	0.226314i	0.291033	−	0.956713i	$-0.406001\pi$
$67$	−3.20856	−	1.85246i	−0.391988	−	0.226314i	−0.683021	+	0.730399i	$0.739334\pi$
$68$	−0.367967	+	0.212446i	−0.0446225	+	0.0257628i
$69$	6.57342	−	3.49086i	0.791346	−	0.420250i
$70$		0			0
$71$			7.90386i			0.938015i	0.883194	+	0.469008i	$0.155388\pi$
$71$			7.90386i			0.938015i	−0.883194	+	0.469008i	$0.844612\pi$
$72$	9.15533	+	0.649559i	1.07897	+	0.0765512i
$73$	3.15721	−	5.46846i	0.369524	−	0.640034i	−0.619967	−	0.784628i	$-0.712854\pi$
$73$	3.15721	−	5.46846i	0.369524	−	0.640034i	0.989491	+	0.144593i	$0.0461874\pi$
$74$	7.02929	+	4.05836i	0.817138	+	0.471775i
$75$		0			0
$76$			4.26419i			0.489136i
$77$	9.07191	−	7.46193i	1.03384	−	0.850366i
$78$	−1.57645	+	0.837188i	−0.178498	+	0.0947928i
$79$	7.38052	+	12.7834i	0.830374	+	1.43825i	0.897742	+	0.440521i	$0.145206\pi$
$79$	7.38052	+	12.7834i	0.830374	+	1.43825i	−0.0673684	+	0.997728i	$0.521460\pi$
$80$		0			0
$81$	8.90985	+	1.27068i	0.989983	+	0.141187i
$82$	−2.50999	−	4.34743i	−0.277182	−	0.480093i
$83$		−	10.7916i		−	1.18453i	−0.805743	−	0.592266i	$-0.798234\pi$
$83$		−	10.7916i		−	1.18453i	0.805743	−	0.592266i	$-0.201766\pi$
$84$	−3.04738	+	2.33067i	−0.332496	+	0.254297i
$85$		0			0
$86$	−0.459909	+	0.265529i	−0.0495933	+	0.0286327i
$87$	11.9355	+	0.422871i	1.27962	+	0.0453365i
$88$	11.7634	+	6.79159i	1.25398	+	0.723986i
$89$	−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
$92$	−3.59750			−0.375066
$93$	−5.41378	+	8.65407i	−0.561383	+	0.897385i
$94$	6.21894	+	3.59050i	0.641434	+	0.370332i
$95$		0			0
$96$	−6.41230	−	4.01138i	−0.654452	−	0.409410i
$97$	6.91148			0.701755			0.350877	−	0.936421i	$-0.385883\pi$
$97$	6.91148			0.701755			0.350877	+	0.936421i	$0.385883\pi$
$98$	−1.45623	+	7.40656i	−0.147102	+	0.748176i
$99$	11.0346	+	7.45926i	1.10902	+	0.749684i
$100$		0			0
$101$	−1.19538	+	2.07046i	−0.118945	+	0.206019i	−0.919350	−	0.393441i	$-0.871285\pi$
$101$	−1.19538	+	2.07046i	−0.118945	+	0.206019i	0.800405	+	0.599460i	$0.204618\pi$
$102$	−0.947323	−	0.0335635i	−0.0937990	−	0.00332328i
$103$	−7.48110	−	12.9577i	−0.737135	−	1.27676i	−0.953780	−	0.300505i	$-0.902845\pi$
$103$	−7.48110	−	12.9577i	−0.737135	−	1.27676i	0.216645	−	0.976250i	$-0.430489\pi$
$104$	2.92386			0.286708
$105$		0			0
$106$	9.84772			0.956495
$107$	6.78072	+	11.7445i	0.655517	+	1.13539i	0.981764	+	0.190104i	$0.0608825\pi$
$107$	6.78072	+	11.7445i	0.655517	+	1.13539i	−0.326247	+	0.945284i	$0.605784\pi$
$108$	−3.51544	−	2.56232i	−0.338274	−	0.246559i
$109$	8.06063	−	13.9614i	0.772068	−	1.33726i	−0.164359	−	0.986401i	$-0.552556\pi$
$109$	8.06063	−	13.9614i	0.772068	−	1.33726i	0.936428	−	0.350861i	$-0.114111\pi$
$110$		0			0
$111$	−6.11477	−	11.5143i	−0.580388	−	1.09289i
$112$	−4.24047	+	0.704923i	−0.400687	+	0.0666090i
$113$	5.05678			0.475702			0.237851	−	0.971302i	$-0.423557\pi$
$113$	5.05678			0.475702			0.237851	+	0.971302i	$0.423557\pi$
$114$	−5.04536	+	8.06513i	−0.472541	+	0.755369i
$115$		0			0
$116$	−4.99924	−	2.88631i	−0.464168	−	0.267987i
$117$	2.85986	+	0.202903i	0.264394	+	0.0187584i
$118$	12.5398			1.15438
$119$	1.03704	−	0.852997i	0.0950651	−	0.0781941i
$120$		0			0
$121$	4.35571	+	7.54431i	0.395973	+	0.685846i
$122$	−0.430806	−	0.248726i	−0.0390033	−	0.0225186i
$123$	−0.285499	+	8.05814i	−0.0257425	+	0.726578i
$124$	4.27298	−	2.46700i	0.383725	−	0.221544i
$125$		0			0
$126$	−8.52133	+	0.802519i	−0.759141	+	0.0714941i
$127$		−	8.05009i		−	0.714330i	−0.934041	−	0.357165i	$-0.883743\pi$
$127$		−	8.05009i		−	0.714330i	0.934041	−	0.357165i	$-0.116257\pi$
$128$	0.0759250	+	0.131506i	0.00671089	+	0.0116236i
$129$	0.852462	+	0.0302026i	0.0750551	+	0.00265919i
$130$		0			0
$131$	1.04963	+	1.81802i	0.0917069	+	0.158841i	0.908229	−	0.418473i	$-0.137434\pi$
$131$	1.04963	+	1.81802i	0.0917069	+	0.158841i	−0.816523	+	0.577314i	$0.804101\pi$
$132$	−3.01951	−	5.68584i	−0.262814	−	0.494889i
$133$	−2.20989	−	13.2936i	−0.191622	−	1.15270i
$134$			3.99516i			0.345129i
$135$		0			0
$136$	1.34471	+	0.776369i	0.115308	+	0.0665731i
$137$	2.47355	−	4.28431i	0.211329	−	0.366033i	−0.740801	−	0.671724i	$-0.765554\pi$
$137$	2.47355	−	4.28431i	0.211329	−	0.366033i	0.952131	+	0.305691i	$0.0988874\pi$
$138$	−6.80419	−	4.25654i	−0.579211	−	0.362341i
$139$			10.7217i			0.909406i	0.890643	+	0.454703i	$0.150255\pi$
$139$			10.7217i			0.909406i	−0.890643	+	0.454703i	$0.849745\pi$
$140$		0			0
$141$	−5.40985	−	10.1869i	−0.455591	−	0.857895i
$142$	7.38116	−	4.26151i	0.619413	−	0.357618i
$143$	3.67454	+	2.12150i	0.307281	+	0.177408i
$144$	−2.13226	−	4.38310i	−0.177689	−	0.365258i
$145$		0			0
$146$	−6.80909			−0.563524
$147$	8.29234	−	8.84517i	0.683941	−	0.729537i
$148$			6.30157i			0.517986i
$149$	−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	$0.0746091\pi$
$152$	13.4954	−	7.79159i	1.09462	−	0.631982i
$153$	1.26140	+	0.852692i	0.101978	+	0.0689360i
$154$	−11.8597	−	4.44872i	−0.955686	−	0.358488i
$155$		0			0
$156$	−1.17484	−	0.734953i	−0.0940626	−	0.0588434i
$157$	1.45005	−	2.51156i	0.115727	−	0.200445i	−0.802343	−	0.596863i	$-0.796414\pi$
$157$	1.45005	−	2.51156i	0.115727	−	0.200445i	0.918070	+	0.396418i	$0.129747\pi$
$158$	7.95870	−	13.7849i	0.633160	−	1.09667i
$159$	−13.4098	−	8.38889i	−1.06347	−	0.665282i
$160$		0			0
$161$	11.2152	−	1.86439i	0.883883	−	0.146934i
$162$	−3.61726	−	9.00573i	−0.284199	−	0.707557i
$163$	−11.0493	+	6.37930i	−0.865446	+	0.499665i	−0.865832	−	0.500335i	$-0.833210\pi$
$163$	−11.0493	+	6.37930i	−0.865446	+	0.499665i	0.000386523		1.00000i	$0.499877\pi$
$164$	1.94868	−	3.37521i	0.152166	−	0.263559i
$165$		0			0
$166$	−10.0779	+	5.81849i	−0.782199	+	0.451603i
$167$			15.7766i			1.22083i	0.792083	+	0.610413i	$0.208997\pi$
$167$			15.7766i			1.22083i	−0.792083	+	0.610413i	$0.791003\pi$
$168$	12.9444	+	5.38579i	0.998683	+	0.415523i
$169$	−12.0867			−0.929744
$170$		0			0
$171$	13.7407	−	6.68452i	1.05078	−	0.511178i
$172$	−0.357059	−	0.206148i	−0.0272255	−	0.0157186i
$173$	8.81037	−	5.08667i	0.669840	−	0.386732i	−0.126176	−	0.992008i	$-0.540270\pi$
$173$	8.81037	−	5.08667i	0.669840	−	0.386732i	0.796016	+	0.605275i	$0.206937\pi$
$174$	−6.04032	−	11.3741i	−0.457916	−	0.862271i
$175$		0			0
$176$		−	7.21345i		−	0.543735i
$177$	−17.0757	−	10.6821i	−1.28348	−	0.802918i
$178$	−3.85735	+	6.68113i	−0.289121	+	0.500772i
$179$	−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	$-0.117560\pi$
$182$	−2.68966	+	0.447122i	−0.199371	+	0.0331429i
$183$	0.374757	+	0.705682i	0.0277029	+	0.0521655i
$184$	6.57342	+	11.3855i	0.484599	+	0.839350i
$185$		0			0
$186$	11.0007	+	0.389753i	0.806610	+	0.0285781i
$187$	1.12664	+	1.95139i	0.0823878	+	0.142700i
$188$			5.57511i			0.406607i
$189$	12.2873	+	6.16618i	0.893771	+	0.448524i
$190$		0			0
$191$	−8.30561	+	4.79524i	−0.600973	+	0.346972i	−0.769424	−	0.638738i	$-0.779457\pi$
$191$	−8.30561	+	4.79524i	−0.600973	+	0.346972i	0.168451	+	0.985710i	$0.446123\pi$
$192$	−0.488074	+	13.7758i	−0.0352237	+	0.994182i
$193$	−7.23275	−	4.17583i	−0.520625	−	0.300583i	0.216566	−	0.976268i	$-0.430515\pi$
$193$	−7.23275	−	4.17583i	−0.520625	−	0.300583i	−0.737190	+	0.675685i	$0.763848\pi$
$194$	−3.72646	−	6.45441i	−0.267544	−	0.463400i
$195$		0			0
$196$	−5.54513	+	1.89601i	−0.396080	+	0.135429i
$197$	1.77574			0.126516			0.0632580	−	0.997997i	$-0.479851\pi$
$197$	1.77574			0.126516			0.0632580	+	0.997997i	$0.479851\pi$
$198$	1.01646	−	14.3267i	0.0722365	−	1.01815i
$199$	3.25502	+	1.87929i	0.230742	+	0.133219i	0.610915	−	0.791697i	$-0.290802\pi$
$199$	3.25502	+	1.87929i	0.230742	+	0.133219i	−0.380172	+	0.924916i	$0.624135\pi$
$200$		0			0
$201$	3.40332	−	5.44029i	0.240052	−	0.383729i
$202$	2.57805			0.181391
$203$	17.0810	+	6.40726i	1.19885	+	0.449702i
$204$	−0.345169	−	0.649966i	−0.0241667	−	0.0455067i
$205$		0			0
$206$	−8.06716	+	13.9727i	−0.562065	+	0.973526i
$207$	5.63943	+	11.5924i	0.391967	+	0.805730i
$208$	−0.776369	−	1.34471i	−0.0538315	−	0.0932388i
$209$	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	$0.601658\pi$
$212$	3.82273	+	6.62116i	0.262546	+	0.454743i
$213$	−13.6813	−	0.484726i	−0.937427	−	0.0332129i
$214$	7.31190	−	12.6646i	0.499831	−	0.865734i
$215$		0			0
$216$	−1.68584	+	15.8077i	−0.114707	+	1.07558i
$217$	−12.0425	+	9.90534i	−0.817499	+	0.672418i
$218$	−17.3842			−1.17740
$219$	9.27208	+	5.80040i	0.626549	+	0.391954i
$220$		0			0
$221$	0.420048	+	0.242515i	0.0282555	+	0.0163133i
$222$	−7.45597	+	11.9186i	−0.500412	+	0.799921i
$223$	11.7397			0.786146			0.393073	−	0.919507i	$-0.371412\pi$
$223$	11.7397			0.786146			0.393073	+	0.919507i	$0.371412\pi$
$224$	−7.33944	−	8.92299i	−0.490387	−	0.596192i
$225$		0			0
$226$	−2.72646	−	4.72236i	−0.181361	−	0.314127i
$227$	−20.9760	−	12.1105i	−1.39223	−	0.803802i	−0.398664	−	0.917097i	$-0.630526\pi$
$227$	−20.9760	−	12.1105i	−1.39223	−	0.803802i	−0.993561	+	0.113295i	$0.963859\pi$
$228$	−7.38116	−	0.261513i	−0.488829	−	0.0173191i
$229$	−18.8003	+	10.8544i	−1.24236	+	0.717278i	−0.969574	−	0.244797i	$-0.921279\pi$
$229$	−18.8003	+	10.8544i	−1.24236	+	0.717278i	−0.272787	+	0.962075i	$0.587945\pi$
$230$		0			0
$231$	12.3600	+	16.1608i	0.813227	+	1.06330i
$232$			21.0957i			1.38500i
$233$	−5.49812	−	9.52303i	−0.360194	−	0.623874i	0.627799	−	0.778376i	$-0.283956\pi$
$233$	−5.49812	−	9.52303i	−0.360194	−	0.623874i	−0.987993	+	0.154502i	$0.950623\pi$
$234$	−1.35246	−	2.78013i	−0.0884132	−	0.181743i
$235$		0			0
$236$	4.86774	+	8.43117i	0.316863	+	0.548822i
$237$	−22.5803	+	11.9914i	−1.46675	+	0.778928i
$238$	−1.35572	−	0.508547i	−0.0878786	−	0.0329642i
$239$			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	$0.718993\pi$
$242$	4.69692	−	8.13531i	0.301930	−	0.522958i
$243$	−2.74592	+	15.3447i	−0.176151	+	0.984363i
$244$		−	0.386206i		−	0.0247243i
$245$		0			0
$246$	7.67917	−	4.07808i	0.489606	−	0.260009i
$247$	4.21558	−	2.43387i	0.268231	−	0.154863i
$248$	−15.6153	−	9.01550i	−0.991573	−	0.572485i
$249$	18.6799	+	0.661824i	1.18379	+	0.0419414i
$250$		0			0
$251$	18.6748			1.17875			0.589373	−	0.807861i	$-0.299375\pi$
$251$	18.6748			1.17875			0.589373	+	0.807861i	$0.299375\pi$
$252$	−3.84743	−	5.41784i	−0.242365	−	0.341292i
$253$			19.0782i			1.19944i
$254$	−7.51772	+	4.34036i	−0.471704	+	0.272338i
$255$		0			0
$256$	8.04032	−	13.9262i	0.502520	−	0.870390i
$257$	−10.4639	+	6.04132i	−0.652718	+	0.376847i	−0.789497	−	0.613755i	$-0.789658\pi$
$257$	−10.4639	+	6.04132i	−0.652718	+	0.376847i	0.136779	+	0.990602i	$0.456325\pi$
$258$	−0.431416	−	0.812371i	−0.0268588	−	0.0505760i
$259$	−3.26575	−	19.6452i	−0.202924	−	1.22069i
$260$		0			0
$261$	−1.46395	+	20.6339i	−0.0906162	+	1.27721i
$262$	1.13186	−	1.96044i	0.0699265	−	0.121116i
$263$	−6.44388	+	11.1611i	−0.397346	+	0.688224i	−0.993398	−	0.114722i	$-0.963402\pi$
$263$	−6.44388	+	11.1611i	−0.397346	+	0.688224i	0.596051	+	0.802946i	$0.296736\pi$
$264$	−12.4774	+	19.9455i	−0.767933	+	1.22756i
$265$		0			0
$266$	−11.2230	+	9.23125i	−0.688125	+	0.566004i
$267$	10.9440	−	5.81191i	0.669764	−	0.355683i
$268$	−2.68616	+	1.55086i	−0.164084	+	0.0947337i
$269$	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	$0.583467\pi$
$272$		−	0.824593i		−	0.0499983i
$273$	4.04346	+	1.68236i	0.244721	+	0.101821i
$274$	−5.33464			−0.322277
$275$		0			0
$276$	0.220627	−	6.22715i	0.0132802	−	0.374830i
$277$	−12.0298	−	6.94543i	−0.722803	−	0.417310i	0.0929805	−	0.995668i	$-0.470361\pi$
$277$	−12.0298	−	6.94543i	−0.722803	−	0.417310i	−0.815783	+	0.578357i	$0.803694\pi$
$278$	10.0127	−	5.78083i	0.600521	−	0.346711i
$279$	−14.6479	−	9.90180i	−0.876945	−	0.592805i
$280$		0			0
$281$			6.85483i			0.408925i	0.978874	+	0.204462i	$0.0655446\pi$
$281$			6.85483i			0.408925i	−0.978874	+	0.204462i	$0.934455\pi$
$282$	−6.59643	+	10.5446i	−0.392812	+	0.627919i
$283$	−2.21825	+	3.84212i	−0.131861	+	0.228391i	−0.924394	−	0.381439i	$-0.875429\pi$
$283$	−2.21825	+	3.84212i	−0.131861	+	0.228391i	0.792533	+	0.609829i	$0.208762\pi$
$284$	5.73050	+	3.30850i	0.340043	+	0.196324i
$285$		0			0
$286$		−	4.57538i		−	0.270548i
$287$	−4.32582	+	11.5321i	−0.255345	+	0.680718i
$288$	7.33681	−	10.8534i	0.432326	−	0.639546i
$289$	−8.37121	−	14.4994i	−0.492424	−	0.852904i
$290$		0			0
$291$	−0.423866	+	11.9635i	−0.0248475	+	0.701315i
$292$	−2.64318	−	4.57812i	−0.154680	−	0.267914i
$293$			30.0822i			1.75742i	0.477357	+	0.878709i	$0.341595\pi$
$293$			30.0822i			1.75742i	−0.477357	+	0.878709i	$0.658405\pi$
$294$	−12.7312	−	2.97491i	−0.742498	−	0.173501i
$295$		0			0
$296$	19.9434	−	11.5143i	1.15919	−	0.669257i
$297$	−13.5884	+	18.6430i	−0.788481	+	1.08178i
$298$	4.91547	+	2.83795i	0.284745	+	0.164398i
$299$	2.05334	+	3.55650i	0.118748	+	0.205678i
$300$		0			0
$301$	1.21997	+	0.457623i	0.0703178	+	0.0263770i
$302$	−7.55808			−0.434919
$303$	−3.51058	−	2.19614i	−0.201678	−	0.126165i
$304$	−7.16685	−	4.13778i	−0.411047	−	0.237318i
$305$		0			0
$306$	0.116194	−	1.63772i	0.00664239	−	0.0936225i
$307$	32.8300			1.87371			0.936853	−	0.349722i	$-0.113724\pi$
$307$	32.8300			1.87371			0.936853	+	0.349722i	$0.113724\pi$
$308$	−1.61265	−	9.70088i	−0.0918891	−	0.552759i
$309$	22.8880	−	12.1549i	1.30206	−	0.691466i
$310$		0			0
$311$	8.23073	−	14.2560i	0.466722	−	0.808386i	−0.532556	−	0.846395i	$-0.678768\pi$
$311$	8.23073	−	14.2560i	0.466722	−	0.808386i	0.999277	+	0.0380092i	$0.0121016\pi$
$312$	−0.179314	+	5.06110i	−0.0101516	+	0.286528i
$313$	−2.30422	−	3.99102i	−0.130242	−	0.225586i	0.793528	−	0.608534i	$-0.208242\pi$
$313$	−2.30422	−	3.99102i	−0.130242	−	0.225586i	−0.923770	+	0.382948i	$0.874909\pi$
$314$	−3.12729			−0.176483
$315$		0			0
$316$	12.3578			0.695179
$317$	−14.7151	−	25.4873i	−0.826481	−	1.43151i	−0.900782	−	0.434272i	$-0.857006\pi$
$317$	−14.7151	−	25.4873i	−0.826481	−	1.43151i	0.0743007	−	0.997236i	$-0.476328\pi$
$318$	−0.603939	+	17.0461i	−0.0338672	+	0.955895i
$319$	−15.3066	+	26.5119i	−0.857007	+	1.48438i
$320$		0			0
$321$	−20.7452	+	11.0169i	−1.15789	+	0.614904i
$322$	−7.78799	−	9.46832i	−0.434008	−	0.527649i
$323$	2.58505			0.143836
$324$	4.65088	−	5.92797i	0.258382	−	0.329332i
$325$		0			0
$326$	11.9148	+	6.87904i	0.659902	+	0.380995i
$327$	23.6724	+	14.8089i	1.30909	+	0.818933i
$328$	−14.2426			−0.786417
$329$	−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	$0.856586\pi$
$332$	−7.82418	−	4.51729i	−0.429408	−	0.247919i
$333$	20.3059	−	9.87830i	1.11276	−	0.541328i
$334$	14.7332	−	8.50623i	0.806166	−	0.465440i
$335$		0			0
$336$	−0.960139	−	7.38334i	−0.0523799	−	0.402794i
$337$			21.4599i			1.16900i	0.811395	+	0.584499i	$0.198709\pi$
$337$			21.4599i			1.16900i	−0.811395	+	0.584499i	$0.801291\pi$
$338$	6.51676	+	11.2874i	0.354465	+	0.613951i
$339$	−0.310121	+	8.75311i	−0.0168435	+	0.475403i
$340$		0			0
$341$	−13.0830	−	22.6604i	−0.708482	−	1.22713i
$342$	−13.6510	−	9.22795i	−0.738163	−	0.498990i
$343$	16.3044	−	8.78454i	0.880352	−	0.474321i
$344$			1.50671i			0.0812363i
$345$		0			0
$346$	−9.50056	−	5.48515i	−0.510753	−	0.294883i
$347$	9.08183	−	15.7302i	0.487538	−	0.844441i	−0.512359	−	0.858771i	$-0.671228\pi$
$347$	9.08183	−	15.7302i	0.487538	−	0.844441i	0.999897	+	0.0143301i	$0.00456156\pi$
$348$	5.30270	−	8.47650i	0.284255	−	0.454388i
$349$		−	13.1543i		−	0.704135i	−0.935975	−	0.352067i	$-0.885479\pi$
$349$		−	13.1543i		−	0.704135i	0.935975	−	0.352067i	$-0.114521\pi$
$350$		0			0
$351$	−0.526607	+	4.93787i	−0.0281082	+	0.263564i
$352$	16.7904	−	9.69392i	0.894929	−	0.516688i
$353$	−8.91499	−	5.14707i	−0.474497	−	0.273951i	0.243623	−	0.969870i	$-0.421664\pi$
$353$	−8.91499	−	5.14707i	−0.474497	−	0.273951i	−0.718120	+	0.695919i	$0.754997\pi$
$354$	−0.769035	+	21.7059i	−0.0408738	+	1.15365i
$355$		0			0
$356$	−5.98946			−0.317441
$357$	1.41291	+	1.84739i	0.0747790	+	0.0977742i
$358$			5.67438i			0.299900i
$359$	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
$362$	−9.07079	+	5.23703i	−0.476750	+	0.275252i
$363$	−13.3261	+	7.07690i	−0.699436	+	0.371441i
$364$	−1.34471	−	1.63484i	−0.0704819	−	0.0856890i
$365$		0			0
$366$	0.456956	−	0.730456i	0.0238855	−	0.0381815i
$367$	7.98697	−	13.8338i	0.416916	−	0.722120i	−0.578711	−	0.815533i	$-0.696444\pi$
$367$	7.98697	−	13.8338i	0.416916	−	0.722120i	0.995628	+	0.0934122i	$0.0297774\pi$
$368$	3.49086	−	6.04635i	0.181974	−	0.315188i
$369$	−13.9309	−	0.988376i	−0.725211	−	0.0514528i
$370$		0			0
$371$	−15.3488	−	18.6604i	−0.796867	−	0.968799i
$372$	4.00825	+	7.54767i	0.207818	+	0.391328i
$373$	4.60438	−	2.65834i	0.238406	−	0.137644i	−0.376038	−	0.926604i	$-0.622714\pi$
$373$	4.60438	−	2.65834i	0.238406	−	0.137644i	0.614444	+	0.788961i	$0.289380\pi$
$374$	1.21490	−	2.10426i	0.0628207	−	0.108809i
$375$		0			0
$376$	17.6443	−	10.1869i	0.909935	−	0.525351i
$377$			6.58968i			0.339386i
$378$	−0.866538	−	14.7993i	−0.0445699	−	0.761196i
$379$	−24.0427			−1.23499			−0.617494	−	0.786575i	$-0.711852\pi$
$379$	−24.0427			−1.23499			−0.617494	+	0.786575i	$0.711852\pi$
$380$		0			0
$381$	13.9344	+	0.493694i	0.713882	+	0.0252927i
$382$	8.95625	+	5.17089i	0.458242	+	0.264566i
$383$	−16.2822	+	9.40053i	−0.831982	+	0.480345i	−0.854531	−	0.519401i	$-0.826155\pi$
$383$	−16.2822	+	9.40053i	−0.831982	+	0.480345i	0.0225490	+	0.999746i	$0.492822\pi$
$384$	−0.232289	+	0.123359i	−0.0118539	+	0.00629512i
$385$		0			0
$386$			9.00591i			0.458389i
$387$	−0.104559	+	1.47373i	−0.00531504	+	0.0749139i
$388$	2.89310	−	5.01100i	0.146875	−	0.254395i
$389$	−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
$392$	16.1327	+	14.0850i	0.814824	+	0.711399i
$393$	−3.21130	+	1.70538i	−0.161988	+	0.0860252i
$394$	−0.957422	−	1.65830i	−0.0482342	−	0.0835442i
$395$		0			0
$396$	10.0272	−	4.87796i	0.503884	−	0.245127i
$397$	−9.38254	−	16.2510i	−0.470896	−	0.815616i	0.528550	−	0.848902i	$-0.322736\pi$
$397$	−9.38254	−	16.2510i	−0.470896	−	0.815616i	−0.999446	+	0.0332862i	$0.989403\pi$
$398$		−	4.05302i		−	0.203159i
$399$	23.1463	−	3.00998i	1.15876	−	0.150687i
$400$		0			0
$401$	−20.7823	+	11.9987i	−1.03782	+	0.599184i	−0.919214	−	0.393757i	$-0.871175\pi$
$401$	−20.7823	+	11.9987i	−1.03782	+	0.599184i	−0.118603	+	0.992942i	$0.537842\pi$
$402$	−6.91548	−	0.245014i	−0.344913	−	0.0122202i
$403$	−4.87777	−	2.81618i	−0.242979	−	0.140284i
$404$	1.00076	+	1.73336i	0.0497896	+	0.0862381i
$405$		0			0
$406$	−3.22599	−	19.4060i	−0.160103	−	0.963102i
$407$	33.4183			1.65648
$408$	−1.42633	+	2.28003i	−0.0706141	+	0.112878i
$409$	14.7941	+	8.54140i	0.731523	+	0.422345i	0.818979	−	0.573823i	$-0.194540\pi$
$409$	14.7941	+	8.54140i	0.731523	+	0.422345i	−0.0874559	+	0.996168i	$0.527874\pi$
$410$		0			0
$411$	7.26429	+	4.54437i	0.358321	+	0.224157i
$412$	−12.5262			−0.617120
$413$	−19.5446	−	23.7615i	−0.961726	−	1.16923i
$414$	7.78521	−	11.5168i	0.382622	−	0.566018i
$415$		0			0
$416$	2.08667	−	3.61422i	0.102307	−	0.177202i
$417$	−18.5590	−	0.657540i	−0.908836	−	0.0321999i
$418$	−12.1926	−	21.1182i	−0.596361	−	1.03293i
$419$	−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	$0.812803\pi$
$422$	4.91790	+	8.51805i	0.239400	+	0.414652i
$423$	17.9650	−	8.73951i	0.873488	−	0.424930i
$424$	13.9699	−	24.1966i	0.678439	−	1.17509i
$425$		0			0
$426$	6.92386	+	13.0379i	0.335462	+	0.631687i
$427$	0.200149	+	1.20400i	0.00968589	+	0.0582655i
$428$	11.3535			0.548790
$429$	−3.89759	+	6.23039i	−0.188177	+	0.300806i
$430$		0			0
$431$	−22.3182	−	12.8854i	−1.07503	−	0.620668i	−0.145478	−	0.989361i	$-0.546472\pi$
$431$	−22.3182	−	12.8854i	−1.07503	−	0.620668i	−0.929551	+	0.368693i	$0.879805\pi$
$432$	7.71775	−	3.42207i	0.371320	−	0.164644i
$433$	11.9120			0.572454			0.286227	−	0.958162i	$-0.407599\pi$
$433$	11.9120			0.572454			0.286227	+	0.958162i	$0.407599\pi$
$434$	15.7432	+	5.90546i	0.755699	+	0.283471i
$435$		0			0
$436$	−6.74826	−	11.6883i	−0.323183	−	0.559769i
$437$	18.9549	+	10.9436i	0.906738	+	0.523505i
$438$	0.417586	−	11.7863i	0.0199530	−	0.563171i
$439$	14.5260	−	8.38661i	0.693290	−	0.400271i	−0.111553	−	0.993758i	$-0.535583\pi$
$439$	14.5260	−	8.38661i	0.693290	−	0.400271i	0.804843	+	0.593487i	$0.202249\pi$
$440$		0			0
$441$	14.8021	+	14.8962i	0.704863	+	0.709343i
$442$		−	0.523026i		−	0.0248778i
$443$	−1.19795	−	2.07491i	−0.0569163	−	0.0985819i	0.836163	−	0.548480i	$-0.184793\pi$
$443$	−1.19795	−	2.07491i	−0.0569163	−	0.0985819i	−0.893080	+	0.449899i	$0.851460\pi$
$444$	−10.9078	−	0.386461i	−0.517661	−	0.0183406i
$445$		0			0
$446$	−6.32967	−	10.9633i	−0.299718	−	0.519127i
$447$	−4.27596	−	8.05178i	−0.202246	−	0.380836i
$448$	−7.39520	+	19.7147i	−0.349390	+	0.931432i
$449$			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
$452$	2.11674	−	3.66629i	0.0995629	−	0.172448i
$453$	10.2920	+	6.43844i	0.483561	+	0.302504i
$454$			26.1184i			1.22580i
$455$		0			0
$456$	12.6593	+	23.8380i	0.592827	+	1.11632i
$457$	2.98078	−	1.72096i	0.139435	−	0.0805029i	−0.428660	−	0.903466i	$-0.641014\pi$
$457$	2.98078	−	1.72096i	0.139435	−	0.0805029i	0.568095	+	0.822963i	$0.307681\pi$
$458$	20.2731	+	11.7047i	0.947300	+	0.546924i
$459$	−1.55334	+	2.13114i	−0.0725036	+	0.0994732i
$460$		0			0
$461$	13.5376			0.630509			0.315254	−	0.949007i	$-0.397910\pi$
$461$	13.5376			0.630509			0.315254	+	0.949007i	$0.397910\pi$
$462$	8.42791	−	20.2560i	0.392102	−	0.942393i
$463$		−	5.13770i		−	0.238769i	−0.992848	−	0.119385i	$-0.961908\pi$
$463$		−	5.13770i		−	0.238769i	0.992848	−	0.119385i	$-0.0380921\pi$
$464$	9.70210	−	5.60151i	0.450409	−	0.260044i
$465$		0			0
$466$	−5.92883	+	10.2690i	−0.274648	+	0.475704i
$467$	−7.98292	+	4.60894i	−0.369405	+	0.213276i	−0.673199	−	0.739462i	$-0.735080\pi$
$467$	−7.98292	+	4.60894i	−0.369405	+	0.213276i	0.303793	+	0.952738i	$0.401747\pi$
$468$	1.34423	−	1.98854i	0.0621370	−	0.0919201i
$469$	7.57040	−	6.22689i	0.349569	−	0.287531i
$470$		0			0
$471$	4.25850	+	2.66402i	0.196221	+	0.122751i
$472$	17.7888	−	30.8111i	0.818797	−	1.41820i
$473$	−1.09324	+	1.89355i	−0.0502672	+	0.0870654i
$474$	23.3730	+	14.6216i	1.07356	+	0.671593i
$475$		0			0
$476$	−0.184347	−	1.10894i	−0.00844952	−	0.0508281i
$477$	15.3433	−	22.6975i	0.702520	−	1.03925i
$478$	8.42955	−	4.86680i	0.385559	−	0.222602i
$479$	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
$482$			5.47902i			0.249563i
$483$	2.53938	+	19.5275i	0.115546	+	0.888532i
$484$	7.29309			0.331504
$485$		0			0
$486$	15.8104	−	5.70906i	0.717176	−	0.258968i
$487$	2.14340	+	1.23749i	0.0971267	+	0.0560761i	0.547777	−	0.836625i	$-0.315474\pi$
$487$	2.14340	+	1.23749i	0.0971267	+	0.0560761i	−0.450650	+	0.892701i	$0.648808\pi$
$488$	−1.22228	+	0.705682i	−0.0553298	+	0.0319447i
$489$	−10.3647	−	19.5171i	−0.468709	−	0.882595i
$490$		0			0
$491$		−	21.2827i		−	0.960476i	−0.877138	−	0.480238i	$-0.840550\pi$
$491$		−	21.2827i		−	0.960476i	0.877138	−	0.480238i	$-0.159450\pi$
$492$	5.72285	+	3.58008i	0.258006	+	0.161403i
$493$	−1.74975	+	3.03065i	−0.0788047	+	0.136494i
$494$	−4.54582	−	2.62453i	−0.204526	−	0.118083i
$495$		0			0
$496$			9.57550i			0.429953i
$497$	−19.5795	−	7.34447i	−0.878259	−	0.329445i
$498$	−9.45355	−	17.8014i	−0.423624	−	0.797698i
$499$	16.3690	+	28.3519i	0.732775	+	1.26920i	0.955693	+	0.294366i	$0.0951086\pi$
$499$	16.3690	+	28.3519i	0.732775	+	1.26920i	−0.222918	+	0.974837i	$0.571558\pi$
$500$		0			0
$501$	−27.3087	−	0.967541i	−1.22006	−	0.0432265i
$502$	−10.0689	−	17.4398i	−0.449397	−	0.778378i
$503$		−	0.675693i		−	0.0301277i	−0.999887	−	0.0150638i	$-0.995205\pi$
$503$		−	0.675693i		−	0.0301277i	0.999887	−	0.0150638i	$-0.00479515\pi$
$504$	−10.1165	+	22.0760i	−0.450623	+	0.983344i
$505$		0			0
$506$	17.8165	−	10.2864i	0.792041	−	0.457285i
$507$	0.741249	−	20.9216i	0.0329200	−	0.929161i
$508$	−5.83652	−	3.36972i	−0.258954	−	0.149507i
$509$	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
$512$	−17.0367			−0.752921
$513$	10.7280	+	24.1947i	0.473652	+	1.06822i
$514$	11.2836	+	6.51458i	0.497697	+	0.287346i
$515$		0			0
$516$	0.378733	−	0.605414i	0.0166728	−	0.0266519i
$517$	29.5658			1.30030
$518$	−16.5852	+	13.6418i	−0.728711	+	0.599388i
$519$	8.26453	+	15.5624i	0.362773	+	0.683114i
$520$		0			0
$521$	−21.4725	+	37.1914i	−0.940726	+	1.62938i	−0.176634	+	0.984277i	$0.556521\pi$
$521$	−21.4725	+	37.1914i	−0.940726	+	1.62938i	−0.764092	+	0.645108i	$0.776812\pi$
$522$	20.0587	−	9.75803i	0.877944	−	0.427097i
$523$	19.0959	+	33.0751i	0.835007	+	1.44627i	0.894025	+	0.448018i	$0.147870\pi$
$523$	19.0959	+	33.0751i	0.835007	+	1.44627i	−0.0590174	+	0.998257i	$0.518797\pi$
$524$	1.75748			0.0767759
$525$		0			0
$526$	13.8974			0.605953
$527$	−1.49555	−	2.59038i	−0.0651474	−	0.112839i
$528$	12.4862	+	0.442385i	0.543394	+	0.0192523i
$529$	2.26734	−	3.92715i	0.0985802	−	0.170746i
$530$		0			0
$531$	19.5376	−	28.9022i	0.847859	−	1.25425i
$532$	−10.5633	−	3.96240i	−0.457975	−	0.171792i
$533$	−4.44898			−0.192707
$534$	−11.3282	−	7.08668i	−0.490221	−	0.306671i
$535$		0			0
$536$	9.81641	+	5.66751i	0.424004	+	0.244799i
$537$	4.83378	−	7.72692i	0.208593	−	0.333441i
$538$	−0.502984			−0.0216852
$539$	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	$0.830529\pi$
$542$	21.7504	+	12.5576i	0.934261	+	0.539396i
$543$	16.8131	+	0.595685i	0.721520	+	0.0255633i
$544$	1.91936	−	1.10814i	0.0822918	−	0.0475112i
$545$		0			0
$546$	−0.609001	−	4.68313i	−0.0260628	−	0.200420i
$547$			10.9605i			0.468638i	0.972160	+	0.234319i	$0.0752860\pi$
$547$			10.9605i			0.468638i	−0.972160	+	0.234319i	$0.924714\pi$
$548$	−2.07082	−	3.58677i	−0.0884612	−	0.153219i
$549$	−1.24449	+	0.605414i	−0.0531137	+	0.0258384i
$550$		0			0
$551$	17.5604	+	30.4155i	0.748098	+	1.29574i
$552$	−20.1110	+	10.6801i	−0.855982	+	0.454576i
$553$	−38.5254	+	6.40434i	−1.63827	+	0.272340i
$554$			14.9790i			0.636398i
$555$		0			0
$556$	7.77354	+	4.48805i	0.329671	+	0.190336i
$557$	−3.00967	+	5.21291i	−0.127524	+	0.220878i	−0.922717	−	0.385479i	$-0.874036\pi$
$557$	−3.00967	+	5.21291i	−0.127524	+	0.220878i	0.795193	+	0.606357i	$0.207370\pi$
$558$	−1.34930	+	19.0179i	−0.0571203	+	0.805093i
$559$			0.470652i			0.0199065i
$560$		0			0
$561$	−3.44689	+	1.83049i	−0.145528	+	0.0772835i
$562$	6.40150	−	3.69591i	0.270031	−	0.155903i
$563$	−12.8772	−	7.43466i	−0.542710	−	0.313334i	0.203467	−	0.979082i	$-0.434779\pi$
$563$	−12.8772	−	7.43466i	−0.542710	−	0.313334i	−0.746176	+	0.665748i	$0.768113\pi$
$564$	−9.65032	−	0.341909i	−0.406352	−	0.0143970i
$565$		0			0
$566$	4.78405			0.201089
$567$	−11.4270	+	20.8908i	−0.479889	+	0.877329i
$568$		−	24.1814i		−	1.01463i
$569$	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	$0.759918\pi$
$572$	3.07628	−	1.77609i	0.128626	−	0.0742621i
$573$	−7.79103	−	14.6708i	−0.325475	−	0.612881i
$574$	13.1018	−	2.17801i	0.546859	−	0.0909082i
$575$		0			0
$576$	−23.8155	−	1.68968i	−0.992312	−	0.0704032i
$577$	−2.51561	+	4.35716i	−0.104726	+	0.181391i	−0.913626	−	0.406555i	$-0.866730\pi$
$577$	−2.51561	+	4.35716i	−0.104726	+	0.181391i	0.808900	+	0.587946i	$0.200063\pi$
$578$	−9.02699	+	15.6352i	−0.375473	+	0.650339i
$579$	7.67178	−	12.2635i	0.318828	−	0.509655i
$580$		0			0
$581$	26.7330	+	10.0278i	1.10907	+	0.416025i
$582$	11.4009	−	6.05453i	0.472582	−	0.250968i
$583$	35.1132	−	20.2726i	1.45424	−	0.839606i
$584$	−9.65933	+	16.7305i	−0.399706	+	0.692311i
$585$		0			0
$586$	28.0928	−	16.2194i	1.16050	−	0.670016i
$587$			18.5075i			0.763887i	0.924186	+	0.381944i	$0.124745\pi$
$587$			18.5075i			0.763887i	−0.924186	+	0.381944i	$0.875255\pi$
$588$	−2.94185	−	9.71470i	−0.121320	−	0.400627i
$589$	−30.0186			−1.23690
$590$		0			0
$591$	−0.108902	+	3.07374i	−0.00447963	+	0.126437i
$592$	−10.5911	−	6.11477i	−0.435291	−	0.251316i
$593$	16.0548	−	9.26927i	0.659293	−	0.380643i	−0.132714	−	0.991154i	$-0.542369\pi$
$593$	16.0548	−	9.26927i	0.659293	−	0.380643i	0.792008	+	0.610511i	$0.209036\pi$
$594$	24.7366	+	2.63807i	1.01495	+	0.108241i
$595$		0			0
$596$			4.40658i			0.180501i
$597$	−3.45261	+	5.51908i	−0.141306	+	0.225881i
$598$	2.21420	−	3.83511i	0.0905453	−	0.156829i
$599$	−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	$-0.208447\pi$
$602$	−0.230409	−	1.38603i	−0.00939076	−	0.0564902i
$603$	9.20824	+	6.22467i	0.374988	+	0.253488i
$604$	−2.93393	−	5.08172i	−0.119380	−	0.206772i
$605$		0			0
$606$	−0.158106	+	4.46251i	−0.00642262	+	0.181277i
$607$	−12.5550	−	21.7458i	−0.509591	−	0.882637i	−0.999938	−	0.0111098i	$-0.996464\pi$
$607$	−12.5550	−	21.7458i	−0.509591	−	0.882637i	0.490348	−	0.871527i	$-0.336870\pi$
$608$		−	22.2425i		−	0.902053i
$609$	−12.1383	+	29.1736i	−0.491868	+	1.18217i
$610$		0			0
$611$	5.51156	−	3.18210i	0.222974	−	0.128734i
$612$	1.14624	−	0.557615i	0.0463339	−	0.0225402i
$613$	1.26428	+	0.729932i	0.0510638	+	0.0294817i	0.525315	−	0.850908i	$-0.323948\pi$
$613$	1.26428	+	0.729932i	0.0510638	+	0.0294817i	−0.474251	+	0.880390i	$0.657281\pi$
$614$	−17.7009	−	30.6589i	−0.714351	−	1.23729i
$615$		0			0
$616$	−27.7550	+	22.8294i	−1.11828	+	0.919822i
$617$	−6.56208			−0.264179			−0.132090	−	0.991238i	$-0.542169\pi$
$617$	−6.56208			−0.264179			−0.132090	+	0.991238i	$0.542169\pi$
$618$	−23.6916	−	14.8209i	−0.953014	−	0.596183i
$619$	−18.2419	−	10.5319i	−0.733202	−	0.423315i	0.0863902	−	0.996261i	$-0.472467\pi$
$619$	−18.2419	−	10.5319i	−0.733202	−	0.423315i	−0.819593	+	0.572947i	$0.805800\pi$
$620$		0			0
$621$	−20.4120	+	9.05071i	−0.819104	+	0.363192i
$622$	−17.7510			−0.711751
$623$	18.6721	−	3.10400i	0.748084	−	0.124359i
$624$	2.37526	−	1.26140i	0.0950864	−	0.0504964i
$625$		0			0
$626$	−2.48473	+	4.30367i	−0.0993096	+	0.172009i
$627$	−1.38685	+	39.1436i	−0.0553855	+	1.56324i
$628$	−1.21396	−	2.10265i	−0.0484425	−	0.0839048i
$629$	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	$0.386702\pi$
$632$	−22.5803	−	39.1103i	−0.898197	−	1.55572i
$633$	0.559387	−	15.7886i	0.0222336	−	0.627540i
$634$	−15.8678	+	27.4839i	−0.630192	+	1.09152i
$635$		0			0
$636$	−11.6954	+	6.21095i	−0.463754	+	0.246280i
$637$	5.03939	+	4.39974i	0.199668	+	0.174324i
$638$	33.0114			1.30694
$639$	1.67809	−	23.6521i	0.0663841	−	0.935663i
$640$		0			0
$641$	−9.98943	−	5.76740i	−0.394559	−	0.227798i	0.289575	−	0.957155i	$-0.406486\pi$
$641$	−9.98943	−	5.76740i	−0.394559	−	0.227798i	−0.684133	+	0.729357i	$0.739819\pi$
$642$	21.4735	+	13.4333i	0.847493	+	0.530172i
$643$	−17.3489			−0.684173			−0.342087	−	0.939668i	$-0.611134\pi$
$643$	−17.3489			−0.684173			−0.342087	+	0.939668i	$0.611134\pi$
$644$	3.34290	−	8.91175i	0.131729	−	0.351172i
$645$		0			0
$646$	−1.39378	−	2.41409i	−0.0548374	−	0.0949812i
$647$	6.81366	+	3.93387i	0.267873	+	0.154656i	0.627920	−	0.778278i	$-0.283906\pi$
$647$	6.81366	+	3.93387i	0.267873	+	0.154656i	−0.360048	+	0.932934i	$0.617240\pi$
$648$	−27.2592	−	3.88758i	−1.07084	−	0.152719i
$649$	44.7120	−	25.8145i	1.75510	−	1.01331i
$650$		0			0
$651$	−16.4073	−	21.4526i	−0.643051	−	0.840795i
$652$			10.6813i			0.418314i
$653$	1.00180	+	1.73516i	0.0392033	+	0.0679021i	0.884961	−	0.465665i	$-0.154185\pi$
$653$	1.00180	+	1.73516i	0.0392033	+	0.0679021i	−0.845758	+	0.533567i	$0.820851\pi$
$654$	1.06613	−	30.0914i	0.0416891	−	1.17667i
$655$		0			0
$656$	3.78182	+	6.55031i	0.147655	+	0.255747i
$657$	−10.6089	+	15.6939i	−0.413893	+	0.612278i
$658$	−14.6732	+	12.0692i	−0.572021	+	0.470506i
$659$		−	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	$0.591337\pi$
$662$	−1.43190	+	2.48012i	−0.0556523	+	0.0963926i
$663$	−0.445546	+	0.712216i	−0.0173036	+	0.0276602i
$664$			33.0163i			1.28128i
$665$		0			0
$666$	−20.1733	−	13.6370i	−0.781701	−	0.528421i
$667$	−25.6602	+	14.8149i	−0.993566	+	0.573636i
$668$	11.4384	+	6.60397i	0.442565	+	0.255515i
$669$	−0.719968	+	20.3210i	−0.0278356	+	0.785654i
$670$		0			0
$671$	−2.04812			−0.0790667
$672$	15.8955	−	12.1571i	0.613182	−	0.468970i
$673$			11.5641i			0.445763i	0.974845	+	0.222882i	$0.0715464\pi$
$673$			11.5641i			0.445763i	−0.974845	+	0.222882i	$0.928454\pi$
$674$	20.0407	−	11.5705i	0.771941	−	0.445680i
$675$		0			0
$676$	−5.05941	+	8.76315i	−0.194593	+	0.337044i
$677$	18.6138	−	10.7467i	0.715388	−	0.413029i	−0.0976651	−	0.995219i	$-0.531137\pi$
$677$	18.6138	−	10.7467i	0.715388	−	0.413029i	0.813053	+	0.582190i	$0.197804\pi$
$678$	8.34145	−	4.42979i	0.320352	−	0.170125i
$679$	−6.42234	+	17.1212i	−0.246467	+	0.657050i
$680$		0			0
$681$	22.2492	−	35.5660i	0.852593	−	1.36289i
$682$	−14.1079	+	24.4355i	−0.540218	+	0.935684i
$683$	−8.66837	+	15.0140i	−0.331686	+	0.574497i	−0.982843	−	0.184447i	$-0.940951\pi$
$683$	−8.66837	+	15.0140i	−0.331686	+	0.574497i	0.651157	+	0.758943i	$0.274284\pi$
$684$	0.905340	−	12.7605i	0.0346165	−	0.487909i
$685$		0			0
$686$	−16.9944	−	10.4898i	−0.648849	−	0.400501i
$687$	−17.6356	−	33.2084i	−0.672839	−	1.26698i
$688$	0.692950	−	0.400075i	0.0264185	−	0.0152527i
$689$	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	$0.416240\pi$
$692$		−	8.51700i		−	0.323768i
$693$	−28.7317	+	20.4036i	−1.09143	+	0.775068i
$694$	−19.5866			−0.743496
$695$		0			0
$696$	−36.5159	−	1.29375i	−1.38413	−	0.0490395i
$697$	−2.04613	−	1.18133i	−0.0775026	−	0.0447461i
$698$	−12.2844	+	7.09240i	−0.464971	+	0.268451i
$699$	16.8212	−	8.93303i	0.636237	−	0.337878i
$700$		0			0
$701$		−	41.8503i		−	1.58066i	−0.612679	−	0.790332i	$-0.709908\pi$
$701$		−	41.8503i		−	1.58066i	0.612679	−	0.790332i	$-0.290092\pi$
$702$	4.89525	−	2.17056i	0.184759	−	0.0819227i
$703$	19.1694	−	33.2024i	0.722989	−	1.25225i
$704$	−30.5998	−	17.6668i	−1.15327	−	0.665842i
$705$		0			0
$706$			11.1006i			0.417775i
$707$	−4.01817	−	4.88513i	−0.151119	−	0.183724i
$708$	−14.8926	+	7.90881i	−0.559697	+	0.297231i
$709$	−22.7397	−	39.3863i	−0.854008	−	1.47918i	−0.877563	−	0.479462i	$-0.840832\pi$
$709$	−22.7397	−	39.3863i	−0.854008	−	1.47918i	0.0235552	−	0.999723i	$-0.492501\pi$
$710$		0			0
$711$	−19.3720	−	39.8211i	−0.726506	−	1.49341i
$712$	10.9440	+	18.9556i	0.410145	+	0.710392i
$713$		−	25.3253i		−	0.948442i
$714$	0.963421	−	2.31552i	0.0360551	−	0.0866563i
$715$		0			0
$716$	−3.81519	+	2.20270i	−0.142580	+	0.0823189i
$717$	−15.6245	−	0.553574i	−0.583509	−	0.0206736i
$718$	−11.0198	−	6.36230i	−0.411256	−	0.237439i
$719$	−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
$722$	−7.48733			−0.278650
$723$	4.66737	−	7.46090i	0.173581	−	0.277474i
$724$	−7.04228	−	4.06586i	−0.261724	−	0.151107i
$725$		0			0
$726$	13.7939	+	8.62913i	0.511939	+	0.320257i
$727$	19.2284			0.713140			0.356570	−	0.934269i	$-0.383946\pi$
$727$	19.2284			0.713140			0.356570	+	0.934269i	$0.383946\pi$
$728$	−2.71693	+	7.24299i	−0.100696	+	0.268443i
$729$	−26.3927	−	5.69415i	−0.977509	−	0.210895i
$730$		0			0
$731$	−0.124972	+	0.216457i	−0.00462225	+	0.00800596i
$732$	0.668508	+	0.0236851i	0.0247088	+	0.000875428i
$733$	−4.12825	−	7.15035i	−0.152481	−	0.264104i	0.779658	−	0.626205i	$-0.215393\pi$
$733$	−4.12825	−	7.15035i	−0.152481	−	0.264104i	−0.932139	+	0.362101i	$0.882059\pi$
$734$	−17.2253			−0.635797
$735$		0			0
$736$	18.7650			0.691688
$737$	8.22447	+	14.2452i	0.302952	+	0.524729i
$738$	6.58807	+	13.5425i	0.242510	+	0.498506i
$739$	−5.17166	+	8.95758i	−0.190243	+	0.329510i	−0.945331	−	0.326114i	$-0.894261\pi$
$739$	−5.17166	+	8.95758i	−0.190243	+	0.329510i	0.755088	+	0.655623i	$0.227594\pi$
$740$		0			0
$741$	3.95441	+	7.44629i	0.145269	+	0.273546i
$742$	−9.15076	+	24.3948i	−0.335935	+	0.895561i
$743$	37.7580			1.38521			0.692604	−	0.721318i	$-0.256463\pi$
$743$	37.7580			1.38521			0.692604	+	0.721318i	$0.256463\pi$
$744$	16.5632	−	26.4767i	0.607235	−	0.970681i
$745$		0			0
$746$	−4.96508	−	2.86659i	−0.181785	−	0.104953i
$747$	−2.29119	+	32.2936i	−0.0838302	+	1.18156i
$748$	1.88641			0.0689741
$749$	−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	$0.547273\pi$
$752$	−9.37013	−	5.40985i	−0.341693	−	0.197277i
$753$	−1.14529	+	32.3255i	−0.0417365	+	1.17801i
$754$	6.15389	−	3.55295i	0.224111	−	0.129391i
$755$		0			0
$756$	9.61404	−	6.32749i	0.349659	−	0.230129i
$757$			30.1051i			1.09419i	0.837071	+	0.547094i	$0.184266\pi$
$757$			30.1051i			1.09419i	−0.837071	+	0.547094i	$0.815734\pi$
$758$	12.9631	+	22.4527i	0.470840	+	0.815518i
$759$	−33.0237	−	1.17002i	−1.19868	−	0.0424691i
$760$		0			0
$761$	18.8860	+	32.7115i	0.684618	+	1.18579i	0.973557	+	0.228445i	$0.0733641\pi$
$761$	18.8860	+	32.7115i	0.684618	+	1.18579i	−0.288939	+	0.957347i	$0.593303\pi$
$762$	−7.05196	−	13.2791i	−0.255466	−	0.481051i
$763$	27.0951	+	32.9411i	0.980910	+	1.19255i
$764$			8.02904i			0.290480i
$765$		0			0
$766$	17.5577	+	10.1370i	0.634386	+	0.366263i
$767$	5.55671	−	9.62451i	0.200641	−	0.347521i
$768$	23.6127	+	14.7716i	0.852051	+	0.533023i
$769$			33.3656i			1.20319i	0.798800	+	0.601597i	$0.205469\pi$
$769$			33.3656i			1.20319i	−0.798800	+	0.601597i	$0.794531\pi$
$770$		0			0
$771$	−9.81558	−	18.4831i	−0.353499	−	0.665652i
$772$	−6.05517	+	3.49595i	−0.217930	+	0.125822i
$773$	0.993081	+	0.573356i	0.0357186	+	0.0206222i	0.517753	−	0.855530i	$-0.326769\pi$
$773$	0.993081	+	0.573356i	0.0357186	+	0.0206222i	−0.482034	+	0.876152i	$0.660102\pi$
$774$	1.43264	−	0.696944i	0.0514953	−	0.0250511i
$775$		0			0
$776$	−21.1453			−0.759073
$777$	34.2053	−	4.44811i	1.22711	−	0.159575i
$778$			13.1743i			0.472321i
$779$	−20.5348	+	11.8558i	−0.735736	+	0.424778i
$780$		0			0
$781$	17.5456	−	30.3898i	0.627830	−	1.08743i
$782$	2.03666	−	1.17587i	0.0728309	−	0.0420489i
$783$	−35.6268	−	3.79948i	−1.27320	−	0.135782i
$784$	2.19412	−	11.1595i	0.0783614	−	0.398555i
$785$		0			0
$786$	3.32403	+	2.07944i	0.118564	+	0.0741711i
$787$	−20.7393	+	35.9215i	−0.739276	+	1.28046i	0.213546	+	0.976933i	$0.431499\pi$
$787$	−20.7393	+	35.9215i	−0.739276	+	1.28046i	−0.952822	+	0.303530i	$0.901835\pi$
$788$	0.743313	−	1.28746i	0.0264794	−	0.0458637i
$789$	−18.9243	−	11.8386i	−0.673724	−	0.421466i
$790$		0			0
$791$	−4.69889	+	12.5267i	−0.167073	+	0.445397i
$792$	−33.7597	−	22.8212i	−1.19960	−	0.810916i
$793$	−0.381804	+	0.220434i	−0.0135582	+	0.00782786i
$794$	−10.1175	+	17.5241i	−0.359058	+	0.621907i
$795$		0			0
$796$	2.72506	−	1.57332i	0.0965874	−	0.0557647i
$797$		−	49.5086i		−	1.75369i	−0.480777	−	0.876843i	$-0.659645\pi$
$797$		−	49.5086i		−	1.75369i	0.480777	−	0.876843i	$-0.340355\pi$
$798$	−15.2907	−	19.9927i	−0.541285	−	0.707734i
$799$	3.37976			0.119567
$800$		0			0
$801$	9.38904	+	19.3002i	0.331745	+	0.681938i
$802$	22.4103	+	12.9386i	0.791336	+	0.456878i
$803$	−24.2786	+	14.0173i	−0.856773	+	0.494658i
$804$	−2.51974	−	4.74477i	−0.0888645	−	0.167335i
$805$		0			0
$806$			6.07359i			0.213933i
$807$	0.684924	+	0.428472i	0.0241105	+	0.0150829i
$808$	3.65720	−	6.33446i	0.128660	−	0.222846i
$809$	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	$0.972160\pi$
$812$	11.7954	−	9.70210i	0.413938	−	0.340477i
$813$	−18.9207	−	35.6283i	−0.663577	−	1.24954i
$814$	−18.0181	−	31.2083i	−0.631535	−	1.09385i
$815$		0			0
$816$	1.42734	+	0.0505704i	0.0499669	+	0.00177032i
$817$	1.25421	+	2.17235i	0.0438792	+	0.0760011i
$818$		−	18.4210i		−	0.644076i
$819$	−3.16009	+	6.89591i	−0.110422	+	0.240963i
$820$		0			0
$821$	12.0008	−	6.92866i	0.418830	−	0.241812i	−0.275746	−	0.961230i	$-0.588925\pi$
$821$	12.0008	−	6.92866i	0.418830	−	0.241812i	0.694577	+	0.719419i	$0.255592\pi$
$822$	0.327162	−	9.23407i	0.0114111	−	0.322075i
$823$	−39.9721	−	23.0779i	−1.39334	−	0.804446i	−0.399658	−	0.916665i	$-0.630871\pi$
$823$	−39.9721	−	23.0779i	−1.39334	−	0.804446i	−0.993684	+	0.112219i	$0.964204\pi$
$824$	22.8880	+	39.6432i	0.797343	+	1.38104i
$825$		0			0
$826$	−11.6523	+	31.0635i	−0.405435	+	1.08084i
$827$	−18.6880			−0.649844			−0.324922	−	0.945741i	$-0.605338\pi$
$827$	−18.6880			−0.649844			−0.324922	+	0.945741i	$0.605338\pi$
$828$	10.7654	+	0.763794i	0.374125	+	0.0265437i
$829$	14.9458	+	8.62894i	0.519088	+	0.299695i	0.736561	−	0.676371i	$-0.236448\pi$
$829$	14.9458	+	8.62894i	0.519088	+	0.299695i	−0.217474	+	0.976066i	$0.569782\pi$
$830$		0			0
$831$	12.7601	−	20.3973i	0.442642	−	0.707574i
$832$	−7.60575			−0.263682
$833$	1.14940	+	3.36158i	0.0398244	+	0.116472i
$834$	9.39235	+	17.6861i	0.325231	+	0.612421i
$835$		0			0
$836$	9.46597	−	16.3955i	0.327387	−	0.567052i
$837$	18.0380	−	24.7477i	0.623484	−	0.855405i
$838$	21.3793	+	37.0301i	0.738536	+	1.27918i
$839$	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
$842$	18.4085	+	31.8844i	0.634398	+	1.09881i
$843$	−11.8655	−	0.420391i	−0.408668	−	0.0144790i
$844$	−3.81810	+	6.61315i	−0.131425	+	0.227634i
$845$		0			0
$846$	−17.8477	−	12.0649i	−0.613617	−	0.414798i
$847$	−22.7362	+	3.77960i	−0.781226	+	0.129869i
$848$	−14.8377			−0.509527
$849$	−6.51454	−	4.07534i	−0.223578	−	0.139865i
$850$		0			0
$851$	28.0114	+	16.1724i	0.960218	+	0.554382i
$852$	−6.07834	+	9.71639i	−0.208241	+	0.332878i
$853$	8.86218			0.303435			0.151718	−	0.988424i	$-0.451520\pi$
$853$	8.86218			0.303435			0.151718	+	0.988424i	$0.451520\pi$
$854$	1.01646	−	0.836071i	0.0347826	−	0.0286097i
$855$		0			0
$856$	−20.7452	−	35.9318i	−0.709058	−	1.22812i
$857$	0.851790	+	0.491781i	0.0290966	+	0.0167989i	0.514478	−	0.857504i	$-0.327986\pi$
$857$	0.851790	+	0.491781i	0.0290966	+	0.0167989i	−0.485381	+	0.874303i	$0.661319\pi$
$858$	7.91982	+	0.280598i	0.270378	+	0.00957945i
$859$	23.6244	−	13.6395i	0.806053	−	0.465375i	−0.0395302	−	0.999218i	$-0.512586\pi$
$859$	23.6244	−	13.6395i	0.806053	−	0.465375i	0.845583	+	0.533843i	$0.179253\pi$
$860$		0			0
$861$	−19.6964	−	8.19508i	−0.671250	−	0.279288i
$862$			27.7897i			0.946519i
$863$	2.27629	+	3.94265i	0.0774857	+	0.134209i	0.902165	−	0.431392i	$-0.141977\pi$
$863$	2.27629	+	3.94265i	0.0774857	+	0.134209i	−0.824679	+	0.565601i	$0.808644\pi$
$864$	18.3370	+	13.3654i	0.623837	+	0.454700i
$865$		0			0
$866$	−6.42257	−	11.1242i	−0.218248	−	0.378016i
$867$	25.6113	−	13.6011i	0.869804	−	0.461916i
$868$	2.14071	+	12.8774i	0.0726604	+	0.437089i
$869$		−	65.5354i		−	2.22314i
$870$		0			0
$871$	3.06636	+	1.77036i	0.103900	+	0.0599865i
$872$	−24.6611	+	42.7142i	−0.835129	+	1.44649i
$873$	−20.6825	−	1.46739i	−0.699995	−	0.0496638i
$874$		−	23.6019i		−	0.798346i
$875$		0			0
$876$	8.08667	−	4.29449i	0.273223	−	0.145097i
$877$	−18.4956	+	10.6784i	−0.624551	+	0.360584i	−0.778639	−	0.627473i	$-0.784089\pi$
$877$	−18.4956	+	10.6784i	−0.624551	+	0.360584i	0.154088	+	0.988057i	$0.450756\pi$
$878$	−15.6640	−	9.04360i	−0.528634	−	0.305207i
$879$	−52.0712	−	1.84487i	−1.75632	−	0.0622260i
$880$		0			0
$881$	−33.2551			−1.12039			−0.560196	−	0.828360i	$-0.689274\pi$
$881$	−33.2551			−1.12039			−0.560196	+	0.828360i	$0.689274\pi$
$882$	5.93025	−	21.8548i	0.199682	−	0.735890i
$883$			12.0561i			0.405721i	0.979208	+	0.202860i	$0.0650238\pi$
$883$			12.0561i			0.405721i	−0.979208	+	0.202860i	$0.934976\pi$
$884$	0.351659	−	0.203031i	0.0118276	−	0.00682866i
$885$		0			0
$886$	−1.29179	+	2.23745i	−0.0433987	+	0.0751687i
$887$	20.2760	−	11.7064i	0.680803	−	0.393062i	−0.119355	−	0.992852i	$-0.538083\pi$
$887$	20.2760	−	11.7064i	0.680803	−	0.393062i	0.800157	+	0.599790i	$0.204749\pi$
$888$	18.7078	+	35.2275i	0.627793	+	1.18216i
$889$	19.9417	+	7.48036i	0.668824	+	0.250883i
$890$		0			0
$891$	−31.4371	−	24.6645i	−1.05318	−	0.826290i
$892$	4.91415	−	8.51156i	0.164538	−	0.284988i
$893$	16.9595	−	29.3748i	0.567529	−	0.982990i
$894$	−5.21384	+	8.33445i	−0.174377	+	0.278746i
$895$		0			0
$896$	−0.396319	+	0.0658829i	−0.0132401	+	0.00220099i
$897$	−6.28210	+	3.33616i	−0.209753	+	0.111391i
$898$	23.7848	−	13.7322i	0.793711	−	0.458249i
$899$	20.3188	−	35.1932i	0.677670	−	1.17376i
$900$		0			0
$901$	4.01390	−	2.31743i	0.133722	−	0.0772046i
$902$			22.2875i			0.742091i
$903$	−0.866948	+	2.08366i	−0.0288502	+	0.0693397i
$904$	−15.4709			−0.514556
$905$		0			0
$906$	0.463521	−	13.0828i	0.0153994	−	0.434646i
$907$	−35.9415	−	20.7508i	−1.19342	−	0.689020i	−0.234338	−	0.972155i	$-0.575292\pi$
$907$	−35.9415	−	20.7508i	−1.19342	−	0.689020i	−0.959080	+	0.283135i	$0.908626\pi$
$908$	−17.5608	+	10.1388i	−0.582777	+	0.336466i
$909$	4.01674	−	5.94201i	0.133227	−	0.197084i
$910$		0			0
$911$			57.6428i			1.90979i	0.296941	+	0.954896i	$0.404034\pi$
$911$			57.6428i			1.90979i	−0.296941	+	0.954896i	$0.595966\pi$
$912$	7.60189	−	12.1518i	0.251724	−	0.402387i
$913$	−23.9560	+	41.4930i	−0.792828	+	1.37322i
$914$	−3.21429	−	1.85577i	−0.106319	−	0.0613835i
$915$		0			0
$916$			18.1743i			0.600496i
$917$	−5.47895	+	0.910804i	−0.180931	+	0.0300774i
$918$	2.82772	+	0.301566i	0.0933286	+	0.00995318i
$919$	−5.45769	−	9.45300i	−0.180033	−	0.311826i	0.761859	−	0.647743i	$-0.224287\pi$
$919$	−5.45769	−	9.45300i	−0.180033	−	0.311826i	−0.941891	+	0.335918i	$0.890954\pi$
$920$		0			0
$921$	−2.01339	+	56.8276i	−0.0663435	+	1.87253i
$922$	−7.29905	−	12.6423i	−0.240381	−	0.416353i
$923$		−	7.55357i		−	0.248629i
$924$	16.8908	−	2.19650i	0.555666	−	0.0722596i
$925$		0			0
$926$	−4.79793	+	2.77009i	−0.157670	+	0.0910307i
$927$	19.6360	+	40.3638i	0.644930	+	1.32572i
$928$	26.0767	+	15.0554i	0.856008	+	0.494217i
$929$	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
$932$	−9.20592			−0.301550
$933$	24.1719	+	15.1214i	0.791353	+	0.495052i
$934$	8.60828	+	4.96999i	0.281672	+	0.162623i
$935$		0			0
$936$	−8.74958	−	0.620772i	−0.285989	−	0.0202906i
$937$	5.67805			0.185494			0.0927468	−	0.995690i	$-0.470435\pi$
$937$	5.67805			0.185494			0.0927468	+	0.995690i	$0.470435\pi$
$938$	−9.89682	−	3.71241i	−0.323143	−	0.121214i
$939$	7.04963	−	3.74376i	0.230056	−	0.122173i
$940$		0			0
$941$	6.29634	−	10.9056i	0.205255	−	0.355512i	−0.744959	−	0.667110i	$-0.767531\pi$
$941$	6.29634	−	10.9056i	0.205255	−	0.355512i	0.950214	+	0.311598i	$0.100864\pi$
$942$	0.191790	−	5.41323i	0.00624885	−	0.176373i
$943$	−10.0022	−	17.3243i	−0.325716	−	0.564157i
$944$	−18.8938			−0.614940
$945$		0			0
$946$	2.35776			0.0766575
$947$	15.6709	+	27.1427i	0.509234	+	0.882020i	0.999943	+	0.0106960i	$0.00340470\pi$
$947$	15.6709	+	27.1427i	0.509234	+	0.882020i	−0.490708	+	0.871324i	$0.663262\pi$
$948$	−0.757874	+	21.3909i	−0.0246146	+	0.694743i
$949$	−3.01729	+	5.22611i	−0.0979455	+	0.169647i
$950$		0			0
$951$	45.0200	−	23.9082i	1.45987	−	0.775277i
$952$	−3.17276	+	2.60970i	−0.102830	+	0.0845808i
$953$	−43.7751			−1.41802			−0.709008	−	0.705200i	$-0.750857\pi$
$953$	−43.7751			−1.41802			−0.709008	+	0.705200i	$0.750857\pi$
$954$	−29.4691	−	2.09079i	−0.954097	−	0.0676919i
$955$		0			0
$956$	6.54444	+	3.77843i	0.211662	+	0.122203i
$957$	−44.9524	−	28.1212i	−1.45310	−	0.909028i
$958$	−22.2540			−0.718994
$959$	8.31462	+	10.1086i	0.268493	+	0.326423i
$960$		0			0
$961$	1.86698	+	3.23370i	0.0602251	+	0.104313i
$962$	−6.71776	−	3.87850i	−0.216589	−	0.125048i
$963$	−17.7976	−	36.5849i	−0.573521	−	1.17893i
$964$	−3.68385	+	2.12687i	−0.118649	+	0.0685019i
$965$		0			0
$966$	16.8669	−	12.9001i	0.542685	−	0.415053i
$967$		−	36.3052i		−	1.16750i	−0.811935	−	0.583748i	$-0.801585\pi$
$967$		−	36.3052i		−	1.16750i	0.811935	−	0.583748i	$-0.198415\pi$
$968$	−13.3261	−	23.0814i	−0.428316	−	0.741864i
$969$	−0.158535	+	4.47463i	−0.00509288	+	0.143746i
$970$		0			0
$971$	−24.9129	−	43.1503i	−0.799492	−	1.38476i	−0.919948	−	0.392041i	$-0.871769\pi$
$971$	−24.9129	−	43.1503i	−0.799492	−	1.38476i	0.120456	−	0.992719i	$-0.461564\pi$
$972$	9.97588	+	8.41406i	0.319976	+	0.269881i
$973$	−26.5599	−	9.96292i	−0.851472	−	0.319397i
$974$		−	2.66887i		−	0.0855161i
$975$		0			0
$976$	0.649099	+	0.374757i	0.0207772	+	0.0119957i
$977$	−13.8777	+	24.0369i	−0.443987	+	0.769008i	−0.997981	−	0.0635127i	$-0.979770\pi$
$977$	−13.8777	+	24.0369i	−0.443987	+	0.769008i	0.553994	+	0.832521i	$0.313103\pi$
$978$	−12.6381	+	20.2023i	−0.404121	+	0.645998i
$979$			31.7631i			1.01515i
$980$		0			0
$981$	−27.0854	+	40.0679i	−0.864772	+	1.27927i
$982$	−19.8753	+	11.4750i	−0.634245	+	0.366181i
$983$	36.4417	+	21.0396i	1.16231	+	0.671060i	0.951856	−	0.306544i	$-0.0991727\pi$
$983$	36.4417	+	21.0396i	1.16231	+	0.671060i	0.210453	+	0.977604i	$0.432506\pi$
$984$	0.873468	−	24.6535i	0.0278451	−	0.785924i
$985$		0			0
$986$	3.77364			0.120177
$987$	30.2621	−	3.93532i	0.963253	−	0.125263i
$988$		−	4.07521i		−	0.129650i
$989$	−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	$0.195641\pi$
$992$	−22.2884	+	12.8682i	−0.707656	+	0.408566i
$993$	4.06256	−	2.15745i	0.128922	−	0.0684647i
$994$	3.69787	+	22.2445i	0.117289	+	0.705554i
$995$		0			0
$996$	8.29912	−	13.2663i	0.262968	−	0.420360i
$997$	5.56719	−	9.64266i	0.176315	−	0.305386i	−0.764301	−	0.644860i	$-0.776916\pi$
$997$	5.56719	−	9.64266i	0.176315	−	0.305386i	0.940615	+	0.339474i	$0.110249\pi$
$998$	17.6513	−	30.5729i	0.558741	−	0.967768i
$999$	15.8537	+	35.7546i	0.501588	+	1.13123i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	35.12	even	12
105.2.s.c.101.2	yes	8	15.2	even	4
105.2.s.d.26.3	yes	8	105.47	odd	12
105.2.s.d.101.3	yes	8	5.2	odd	4
525.2.q.e.299.3		16	105.89	even	6	inner
525.2.q.e.299.6		16	21.5	even	6	inner
525.2.q.e.374.3		16	1.1	even	1	trivial
525.2.q.e.374.6		16	5.4	even	2	inner
525.2.q.f.299.3		16	7.5	odd	6
525.2.q.f.299.6		16	35.19	odd	6
525.2.q.f.374.3		16	15.14	odd	2
525.2.q.f.374.6		16	3.2	odd	2
525.2.t.f.26.2		8	105.68	odd	12
525.2.t.f.101.2		8	5.3	odd	4
525.2.t.g.26.3		8	35.33	even	12
525.2.t.g.101.3		8	15.8	even	4
735.2.b.c.146.3		8	105.17	odd	12
735.2.b.c.146.6		8	35.32	odd	12
735.2.b.d.146.3		8	105.32	even	12
735.2.b.d.146.6		8	35.17	even	12
735.2.s.k.521.2		8	105.62	odd	4
735.2.s.k.656.2		8	35.2	odd	12
735.2.s.l.521.3		8	35.27	even	4
735.2.s.l.656.3		8	105.2	even	12

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.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.539169 - 0.933868i) q^{2} +(-0.0613278 + 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(-0.929227 + 2.47720i) q^{7} -3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +O(q^{10})\)	\(q+(-0.539169 - 0.933868i) q^{2} +(-0.0613278 + 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(-0.929227 + 2.47720i) q^{7} -3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +(-3.84494 - 2.21988i) q^{11} +(1.22932 + 0.769035i) q^{12} -0.955682 q^{13} +(2.81439 - 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(-0.439527 - 0.253761i) q^{17} +(1.41518 + 2.90905i) q^{18} +(-4.41107 + 2.54673i) q^{19} +(-4.23096 - 1.76038i) q^{21} +4.78755i q^{22} +(-2.14856 - 3.72142i) q^{23} +(0.187629 - 5.29579i) q^{24} +(0.515274 + 0.892481i) q^{26} +(0.551027 - 5.16685i) q^{27} +(1.40707 + 1.71066i) q^{28} -6.89526i q^{29} +(5.10397 + 2.94678i) q^{31} +(-2.18344 + 3.78182i) q^{32} +(4.07833 - 6.51931i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-6.51863 + 3.76353i) q^{37} +(4.75663 + 2.74624i) q^{38} +(0.0586099 - 1.65425i) q^{39} +4.65529 q^{41} +(0.637242 + 4.90030i) q^{42} -0.492478i q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.31688 + 4.01295i) q^{46} +(-5.76715 + 3.32967i) q^{47} +(-2.48541 + 1.31989i) q^{48} +(-5.27308 - 4.60377i) q^{49} +(0.466207 - 0.745243i) q^{51} +(-0.400043 + 0.692894i) q^{52} +(-4.56616 + 7.90881i) q^{53} +(-5.12226 + 2.27122i) q^{54} +(2.84292 - 7.57887i) q^{56} +(-4.13778 - 7.79159i) q^{57} +(-6.43926 + 3.71771i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(0.399509 - 0.230657i) q^{61} -6.35524i q^{62} +(3.30663 - 7.21569i) q^{63} +7.95845 q^{64} +(-8.28709 - 0.293610i) q^{66} +(-3.20856 - 1.85246i) q^{67} +(-0.367967 + 0.212446i) q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(9.15533 + 0.649559i) q^{72} +(3.15721 - 5.46846i) q^{73} +(7.02929 + 4.05836i) q^{74} +4.26419i q^{76} +(9.07191 - 7.46193i) q^{77} +(-1.57645 + 0.837188i) q^{78} +(7.38052 + 12.7834i) q^{79} +(8.90985 + 1.27068i) q^{81} +(-2.50999 - 4.34743i) q^{82} -10.7916i q^{83} +(-3.04738 + 2.33067i) q^{84} +(-0.459909 + 0.265529i) q^{86} +(11.9355 + 0.422871i) q^{87} +(11.7634 + 6.79159i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750 q^{92} +(-5.41378 + 8.65407i) q^{93} +(6.21894 + 3.59050i) q^{94} +(-6.41230 - 4.01138i) q^{96} +6.91148 q^{97} +(-1.45623 + 7.40656i) q^{98} +(11.0346 + 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9	\( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 - 10 * q^6 - 8 * q^9 - 24 * q^14 + 2 * q^16 - 18 * q^19 - 44 * q^21 + 14 * q^24 + 12 * q^26 - 42 * q^31 + 18 * q^36 - 30 * q^39 + 60 * q^41 - 14 * q^46 + 8 * q^49 + 24 * q^51 - 14 * q^54 + 42 * q^56 - 24 * q^59 + 30 * q^61 - 76 * q^64 - 32 * q^66 - 26 * q^69 + 108 * q^74 + 58 * q^79 + 56 * q^81 + 102 * q^84 - 18 * q^86 - 6 * q^89 - 6 * q^91 + 48 * q^94 - 84 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

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