LMFDB - Embedded newform 525.2.q.f.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.f.299.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.539169 - 0.933868i) q^{2} +(1.46840 - 0.918594i) q^{3} +(0.418594 - 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} -3.05945 q^{8} +(1.31237 - 2.69772i) q^{9} +O(q^{10})$	\(q+(-0.539169 - 0.933868i) q^{2} +(1.46840 - 0.918594i) q^{3} +(0.418594 - 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} -3.05945 q^{8} +(1.31237 - 2.69772i) q^{9} +(3.84494 + 2.21988i) q^{11} +(-0.0513428 - 1.44914i) q^{12} +0.955682 q^{13} +(-2.81439 + 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(-0.439527 - 0.253761i) q^{17} +(-3.22690 + 0.228945i) q^{18} +(-4.41107 + 2.54673i) q^{19} +(-0.911072 - 4.49110i) q^{21} -4.78755i q^{22} +(-2.14856 - 3.72142i) q^{23} +(-4.49248 + 2.81039i) 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} +(7.68506 - 0.272280i) q^{33} +0.547280i q^{34} +(-1.40656 - 2.08075i) q^{36} +(6.51863 - 3.76353i) q^{37} +(4.75663 + 2.74624i) q^{38} +(1.40332 - 0.877884i) q^{39} -4.65529 q^{41} +(-3.70287 + 3.27228i) 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} +(-0.878503 + 0.0311252i) q^{51} +(0.400043 - 0.692894i) q^{52} +(-4.56616 + 7.90881i) q^{53} +(-4.52806 + 3.30039i) 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} +(-5.46331 - 5.75780i) q^{63} +7.95845 q^{64} +(-4.39782 - 7.03002i) q^{66} +(3.20856 + 1.85246i) q^{67} +(-0.367967 + 0.212446i) q^{68} +(-6.57342 - 3.49086i) q^{69} -7.90386i q^{71} +(-4.01513 + 8.25352i) 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} +(-5.55536 - 7.08081i) q^{81} +(2.50999 + 4.34743i) q^{82} -10.7916i q^{83} +(-3.63753 - 1.21939i) q^{84} +(0.459909 - 0.265529i) q^{86} +(6.33394 + 10.1250i) q^{87} +(-11.7634 - 6.79159i) q^{88} +(3.57713 + 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750 q^{92} +(10.2015 - 0.361438i) q^{93} +(6.21894 + 3.59050i) q^{94} +(0.267811 + 7.55890i) 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} + 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	$ 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) $ 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * 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	$0.957840\pi$
$3$	1.46840	−	0.918594i	0.847779	−	0.530350i
$3$	1.46840	−	0.918594i	0.847779	−	0.530350i
$4$	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
$9$	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	$0.433253\pi$
$12$	−0.0513428	−	1.44914i	−0.0148214	−	0.418331i
$13$	0.955682			0.265059			0.132529	−	0.991179i	$-0.457690\pi$
$13$	0.955682			0.265059			0.132529	+	0.991179i	$0.457690\pi$
$14$	−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	$0.686270\pi$
$18$	−3.22690	+	0.228945i	−0.760588	+	0.0539627i
$19$	−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
$21$	−0.911072	−	4.49110i	−0.198812	−	0.980038i
$22$		−	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	$0.981199\pi$
$24$	−4.49248	+	2.81039i	−0.917023	+	0.573668i
$25$		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	$0.221152\pi$
$29$			6.89526i			1.28042i	−0.768201	+	0.640209i	$0.778848\pi$
$30$		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
$33$	7.68506	−	0.272280i	1.33780	−	0.0473979i
$34$			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	0.143023	−	0.989719i	$-0.454318\pi$
$37$	6.51863	−	3.76353i	1.07166	−	0.618721i	0.928634	+	0.370998i	$0.120984\pi$
$38$	4.75663	+	2.74624i	0.771627	+	0.445499i
$39$	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	$0.618424\pi$
$42$	−3.70287	+	3.27228i	−0.571365	+	0.504924i
$43$			0.492478i			0.0751022i	0.999295	+	0.0375511i	$0.0119557\pi$
$43$			0.492478i			0.0751022i	−0.999295	+	0.0375511i	$0.988044\pi$
$44$	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
$51$	−0.878503	+	0.0311252i	−0.123015	+	0.00435840i
$52$	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	$0.950864\pi$
$54$	−4.52806	+	3.30039i	−0.616191	+	0.449127i
$55$		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	$-0.560013\pi$
$59$	5.81439	−	10.0708i	0.756969	−	1.31111i	0.944389	−	0.328829i	$-0.106654\pi$
$60$		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
$63$	−5.46331	−	5.75780i	−0.688312	−	0.725415i
$64$	7.95845			0.994806
$65$		0			0
$66$	−4.39782	−	7.03002i	−0.541334	−	0.865336i
$67$	3.20856	+	1.85246i	0.391988	+	0.226314i	0.683021	−	0.730399i	$-0.260666\pi$
$67$	3.20856	+	1.85246i	0.391988	+	0.226314i	−0.291033	+	0.956713i	$0.593999\pi$
$68$	−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	$-0.844612\pi$
$71$		−	7.90386i		−	0.938015i	0.883194	−	0.469008i	$-0.155388\pi$
$72$	−4.01513	+	8.25352i	−0.473187	+	0.972687i
$73$	−3.15721	+	5.46846i	−0.369524	+	0.640034i	−0.989491	−	0.144593i	$-0.953813\pi$
$73$	−3.15721	+	5.46846i	−0.369524	+	0.640034i	0.619967	+	0.784628i	$0.287146\pi$
$74$	−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
$81$	−5.55536	−	7.08081i	−0.617263	−	0.786757i
$82$	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	$-0.201766\pi$
$84$	−3.63753	−	1.21939i	−0.396887	−	0.133047i
$85$		0			0
$86$	0.459909	−	0.265529i	0.0495933	−	0.0286327i
$87$	6.33394	+	10.1250i	0.679070	+	1.08551i
$88$	−11.7634	−	6.79159i	−1.25398	−	0.723986i
$89$	3.57713	+	6.19577i	0.379175	+	0.656750i	0.990942	−	0.134287i	$-0.0428745\pi$
$89$	3.57713	+	6.19577i	0.379175	+	0.656750i	−0.611768	+	0.791038i	$0.709541\pi$
$90$		0			0
$91$	0.888045	−	2.36742i	0.0930925	−	0.248173i
$92$	−3.59750			−0.375066
$93$	10.2015	−	0.361438i	1.05785	−	0.0374794i
$94$	6.21894	+	3.59050i	0.641434	+	0.370332i
$95$		0			0
$96$	0.267811	+	7.55890i	0.0273333	+	0.771477i
$97$	−6.91148			−0.701755			−0.350877	−	0.936421i	$-0.614117\pi$
$97$	−6.91148			−0.701755			−0.350877	+	0.936421i	$0.614117\pi$
$98$	−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	−0.800405	−	0.599460i	$-0.795382\pi$
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	0.919350	+	0.393441i	$0.128715\pi$
$102$	0.502728	+	0.803624i	0.0497775	+	0.0795706i
$103$	7.48110	+	12.9577i	0.737135	+	1.27676i	0.953780	+	0.300505i	$0.0971552\pi$
$103$	7.48110	+	12.9577i	0.737135	+	1.27676i	−0.216645	+	0.976250i	$0.569511\pi$
$104$	−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	$0.605784\pi$
$108$	−3.97676	−	1.76330i	−0.382664	−	0.169674i
$109$	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	$0.423557\pi$
$114$	9.50729	−	0.336841i	0.890439	−	0.0315481i
$115$		0			0
$116$	4.99924	+	2.88631i	0.464168	+	0.267987i
$117$	1.25421	−	2.57816i	0.115952	−	0.238351i
$118$	−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
$123$	−6.83581	+	4.27632i	−0.616364	+	0.385583i
$124$	4.27298	−	2.46700i	0.383725	−	0.221544i
$125$		0			0
$126$	−2.43138	+	8.20643i	−0.216605	+	0.731087i
$127$			8.05009i			0.714330i	0.934041	+	0.357165i	$0.116257\pi$
$127$			8.05009i			0.714330i	−0.934041	+	0.357165i	$0.883743\pi$
$128$	0.0759250	+	0.131506i	0.00671089	+	0.0116236i
$129$	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	$0.862566\pi$
$132$	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	$0.0988874\pi$
$138$	0.284178	+	8.02087i	0.0241908	+	0.682782i
$139$			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
$144$	4.86200	−	0.344953i	0.405167	−	0.0287461i
$145$		0			0
$146$	6.80909			0.563524
$147$	−11.9720	−	1.91634i	−0.987430	−	0.158057i
$148$		−	6.30157i		−	0.517986i
$149$	4.55837	−	2.63178i	0.373436	−	0.215604i	−0.301522	−	0.953459i	$-0.597495\pi$
$149$	4.55837	−	2.63178i	0.373436	−	0.215604i	0.674959	+	0.737855i	$0.264161\pi$
$150$		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
$156$	−0.0490674	−	1.38492i	−0.00392854	−	0.110882i
$157$	−1.45005	+	2.51156i	−0.115727	+	0.200445i	−0.918070	−	0.396418i	$-0.870253\pi$
$157$	−1.45005	+	2.51156i	−0.115727	+	0.200445i	0.802343	+	0.596863i	$0.203586\pi$
$158$	7.95870	−	13.7849i	0.633160	−	1.09667i
$159$	0.560064	+	15.8077i	0.0444160	+	1.25363i
$160$		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	−0.000386523	−	1.00000i	$-0.500123\pi$
$163$	11.0493	−	6.37930i	0.865446	−	0.499665i	0.865832	+	0.500335i	$0.166790\pi$
$164$	−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	$0.791003\pi$
$168$	2.78737	+	13.7403i	0.215051	+	1.06008i
$169$	−12.0867			−0.929744
$170$		0			0
$171$	1.08141	+	15.2421i	0.0826972	+	1.16559i
$172$	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
$177$	−0.713167	−	20.1290i	−0.0536049	−	1.51299i
$178$	3.85735	−	6.68113i	0.289121	−	0.500772i
$179$	4.55716	+	2.63107i	0.340618	+	0.196656i	0.660545	−	0.750786i	$-0.270325\pi$
$179$	4.55716	+	2.63107i	0.340618	+	0.196656i	−0.319927	+	0.947442i	$0.603659\pi$
$180$		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
$186$	−5.83788	−	9.33201i	−0.428054	−	0.684256i
$187$	−1.12664	−	1.95139i	−0.0823878	−	0.142700i
$188$			5.57511i			0.406607i
$189$	−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	$0.220543\pi$
$192$	11.6861	−	7.31058i	0.843375	−	0.527596i
$193$	7.23275	+	4.17583i	0.520625	+	0.300583i	0.737190	−	0.675685i	$-0.236152\pi$
$193$	7.23275	+	4.17583i	0.520625	+	0.300583i	−0.216566	+	0.976268i	$0.569485\pi$
$194$	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	$0.479851\pi$
$198$	−12.9155	−	6.28305i	−0.917863	−	0.446517i
$199$	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
$201$	6.41309	−	0.227215i	0.452345	−	0.0160265i
$202$	−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
$207$	−12.8591	+	0.912334i	−0.893767	+	0.0634116i
$208$	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
$213$	−7.26043	−	11.6060i	−0.497477	−	0.795229i
$214$	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
$219$	0.387250	+	10.9301i	0.0261679	+	0.738585i
$220$		0			0
$221$	−0.420048	−	0.242515i	−0.0282555	−	0.0163133i
$222$	−14.0498	+	0.497780i	−0.942958	+	0.0334088i
$223$	−11.7397			−0.786146			−0.393073	−	0.919507i	$-0.628588\pi$
$223$	−11.7397			−0.786146			−0.393073	+	0.919507i	$0.628588\pi$
$224$	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	$0.963859\pi$
$228$	3.91706	+	6.26151i	0.259413	+	0.414679i
$229$	−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
$231$	6.46667	−	19.2905i	0.425475	−	1.26922i
$232$		−	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	$0.950623\pi$
$234$	−3.08389	+	0.218798i	−0.201600	+	0.0143033i
$235$		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	$-0.905700\pi$
$239$		−	9.02649i		−	0.583875i	0.956437	−	0.291938i	$-0.0942999\pi$
$240$		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
$243$	−14.6619	−	5.29431i	−0.940559	−	0.339630i
$244$		−	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
$249$	−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	$0.700625\pi$
$252$	−6.46146	+	1.55086i	−0.407034	+	0.0976949i
$253$		−	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
$261$	18.6015	+	9.04914i	1.15140	+	0.560128i
$262$	−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	$0.296736\pi$
$264$	−23.5120	+	0.833027i	−1.44706	+	0.0512693i
$265$		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	−0.873048	−	0.487635i	$-0.837860\pi$
$269$	−0.233222	+	0.403952i	−0.0142198	+	0.0246294i	0.858828	+	0.512264i	$0.171193\pi$
$270$		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
$273$	−0.870695	−	4.29206i	−0.0526969	−	0.259767i
$274$	−5.33464			−0.322277
$275$		0			0
$276$	−5.28256	+	3.30464i	−0.317973	+	0.198916i
$277$	12.0298	+	6.94543i	0.722803	+	0.417310i	0.815783	−	0.578357i	$-0.196306\pi$
$277$	12.0298	+	6.94543i	0.722803	+	0.417310i	−0.0929805	+	0.995668i	$0.529639\pi$
$278$	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	$-0.934455\pi$
$281$		−	6.85483i		−	0.408925i	0.978874	−	0.204462i	$-0.0655446\pi$
$282$	12.4301	−	0.440395i	0.740200	−	0.0262252i
$283$	2.21825	−	3.84212i	0.131861	−	0.228391i	−0.792533	−	0.609829i	$-0.791238\pi$
$283$	2.21825	−	3.84212i	0.131861	−	0.228391i	0.924394	+	0.381439i	$0.124571\pi$
$284$	−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
$291$	−10.1488	+	6.34885i	−0.594933	+	0.372176i
$292$	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	$0.658405\pi$
$294$	4.66530	+	12.2135i	0.272086	+	0.712303i
$295$		0			0
$296$	−19.9434	+	11.5143i	−1.15919	+	0.669257i
$297$	9.35111	−	21.0894i	0.542606	−	1.22373i
$298$	−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
$303$	−0.146620	−	4.13832i	−0.00842311	−	0.237741i
$304$	−7.16685	−	4.13778i	−0.411047	−	0.237318i
$305$		0			0
$306$	1.47641	+	0.718235i	0.0844006	+	0.0410588i
$307$	−32.8300			−1.87371			−0.936853	−	0.349722i	$-0.886276\pi$
$307$	−32.8300			−1.87371			−0.936853	+	0.349722i	$0.886276\pi$
$308$	−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	−0.999277	−	0.0380092i	$-0.987898\pi$
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	0.532556	+	0.846395i	$0.321232\pi$
$312$	−4.29338	+	2.68584i	−0.243065	+	0.152056i
$313$	2.30422	+	3.99102i	0.130242	+	0.225586i	0.923770	−	0.382948i	$-0.125091\pi$
$313$	2.30422	+	3.99102i	0.130242	+	0.225586i	−0.793528	+	0.608534i	$0.791758\pi$
$314$	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	$-0.476328\pi$
$318$	14.4603	−	9.04605i	0.810896	−	0.507277i
$319$	−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
$324$	−7.45921	+	1.06380i	−0.414401	+	0.0590999i
$325$		0			0
$326$	−11.9148	−	6.87904i	−0.659902	−	0.380995i
$327$	−0.988681	−	27.9053i	−0.0546742	−	1.54317i
$328$	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
$333$	−1.59809	−	22.5246i	−0.0875748	−	1.23434i
$334$	14.7332	−	8.50623i	0.806166	−	0.465440i
$335$		0			0
$336$	5.57915	−	4.93038i	0.304368	−	0.268974i
$337$		−	21.4599i		−	1.16900i	−0.811395	−	0.584499i	$-0.801291\pi$
$337$		−	21.4599i		−	1.16900i	0.811395	−	0.584499i	$-0.198709\pi$
$338$	6.51676	+	11.2874i	0.354465	+	0.613951i
$339$	7.42535	−	4.64513i	0.403290	−	0.252289i
$340$		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	$0.00456156\pi$
$348$	9.99221	−	0.354022i	0.535639	−	0.0189776i
$349$		−	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	$0.754997\pi$
$354$	−18.4133	+	11.5189i	−0.978657	+	0.612225i
$355$		0			0
$356$	5.98946			0.317441
$357$	−0.739225	+	2.20515i	−0.0391239	+	0.116709i
$358$		−	5.67438i		−	0.299900i
$359$	−10.2193	+	5.90010i	−0.539352	+	0.311395i	−0.744816	−	0.667270i	$-0.767463\pi$
$359$	−10.2193	+	5.90010i	−0.539352	+	0.311395i	0.205464	+	0.978665i	$0.434130\pi$
$360$		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
$366$	−0.861071	+	0.0305076i	−0.0450089	+	0.00159466i
$367$	−7.98697	+	13.8338i	−0.416916	+	0.722120i	−0.995628	−	0.0934122i	$-0.970223\pi$
$367$	−7.98697	+	13.8338i	−0.416916	+	0.722120i	0.578711	+	0.815533i	$0.303556\pi$
$368$	3.49086	−	6.04635i	0.181974	−	0.315188i
$369$	−6.10947	+	12.5587i	−0.318046	+	0.653778i
$370$		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	−0.614444	−	0.788961i	$-0.710620\pi$
$373$	−4.60438	+	2.65834i	−0.238406	+	0.137644i	0.376038	+	0.926604i	$0.377286\pi$
$374$	−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
$378$	3.96815	+	14.2837i	0.204100	+	0.734677i
$379$	−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
$381$	7.39477	+	11.8207i	0.378845	+	0.605594i
$382$	−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
$387$	1.32857	+	0.646314i	0.0675348	+	0.0328540i
$388$	−2.89310	+	5.01100i	−0.146875	+	0.254395i
$389$	10.5804	+	6.10860i	0.536448	+	0.309718i	0.743638	−	0.668582i	$-0.233099\pi$
$389$	10.5804	+	6.10860i	0.536448	+	0.309718i	−0.207190	+	0.978301i	$0.566432\pi$
$390$		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
$396$	−0.789145	−	11.1228i	−0.0396560	−	0.558940i
$397$	9.38254	+	16.2510i	0.470896	+	0.815616i	0.999446	−	0.0332862i	$-0.0105973\pi$
$397$	9.38254	+	16.2510i	0.470896	+	0.815616i	−0.528550	+	0.848902i	$0.677264\pi$
$398$		−	4.05302i		−	0.203159i
$399$	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	$0.128825\pi$
$402$	−3.66993	−	5.86647i	−0.183039	−	0.292593i
$403$	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
$408$	2.68773	−	0.0952259i	0.133063	−	0.00471438i
$409$	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
$411$	−0.303394	−	8.56325i	−0.0149653	−	0.422394i
$412$	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
$417$	9.84892	+	15.7438i	0.482304	+	0.770975i
$418$	12.1926	+	21.1182i	0.596361	+	1.03293i
$419$	39.6524			1.93714			0.968572	−	0.248732i	$-0.0800137\pi$
$419$	39.6524			1.93714			0.968572	+	0.248732i	$0.0800137\pi$
$420$		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
$423$	1.41386	+	19.9279i	0.0687442	+	0.968928i
$424$	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
$429$	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	$0.453528\pi$
$432$	6.82247	−	4.97273i	0.328246	−	0.239251i
$433$	−11.9120			−0.572454			−0.286227	−	0.958162i	$-0.592401\pi$
$433$	−11.9120			−0.572454			−0.286227	+	0.958162i	$0.592401\pi$
$434$	−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
$438$	9.99844	−	6.25479i	0.477744	−	0.298865i
$439$	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
$441$	−19.3399	+	8.18342i	−0.920947	+	0.389687i
$442$			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	$0.851460\pi$
$444$	−5.78858	−	9.25319i	−0.274714	−	0.439137i
$445$		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	$-0.794776\pi$
$449$		−	25.4692i		−	1.20196i	0.799262	−	0.600982i	$-0.205224\pi$
$450$		0			0
$451$	−17.8993	−	10.3342i	−0.842846	−	0.486617i
$452$	2.11674	−	3.66629i	0.0995629	−	0.172448i
$453$	−0.429847	−	12.1324i	−0.0201960	−	0.570028i
$454$			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	−0.568095	−	0.822963i	$-0.692319\pi$
$457$	−2.98078	+	1.72096i	−0.139435	+	0.0805029i	0.428660	+	0.903466i	$0.358986\pi$
$458$	20.2731	+	11.7047i	0.947300	+	0.546924i
$459$	−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	$0.602090\pi$
$462$	−21.5014	+	4.36180i	−1.00033	+	0.202930i
$463$			5.13770i			0.238769i	0.992848	+	0.119385i	$0.0380921\pi$
$463$			5.13770i			0.238769i	−0.992848	+	0.119385i	$0.961908\pi$
$464$	−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
$471$	0.177857	+	5.01998i	0.00819521	+	0.231308i
$472$	−17.7888	+	30.8111i	−0.818797	+	1.41820i
$473$	−1.09324	+	1.89355i	−0.0502672	+	0.0870654i
$474$	−0.976178	−	27.5524i	−0.0448374	−	1.26553i
$475$		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	−0.999467	−	0.0326342i	$-0.989610\pi$
$479$	−10.3187	+	17.8724i	−0.471472	+	0.816613i	0.527996	+	0.849247i	$0.322944\pi$
$480$		0			0
$481$	6.22974	−	3.59674i	0.284052	−	0.163997i
$482$			5.47902i			0.249563i
$483$	−14.7558	+	13.0399i	−0.671411	+	0.593336i
$484$	7.29309			0.331504
$485$		0			0
$486$	2.96103	+	16.5468i	0.134315	+	0.750577i
$487$	−2.14340	−	1.23749i	−0.0971267	−	0.0560761i	0.450650	−	0.892701i	$-0.351192\pi$
$487$	−2.14340	−	1.23749i	−0.0971267	−	0.0560761i	−0.547777	+	0.836625i	$0.684526\pi$
$488$	−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	$0.159450\pi$
$491$			21.2827i			0.960476i	−0.877138	+	0.480238i	$0.840550\pi$
$492$	0.239016	+	6.74618i	0.0107757	+	0.304141i
$493$	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
$501$	14.4922	+	23.1662i	0.647466	+	1.03499i
$502$	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	$-0.00479515\pi$
$504$	16.7147	+	17.6157i	0.744532	+	0.784665i
$505$		0			0
$506$	−17.8165	+	10.2864i	−0.792041	+	0.457285i
$507$	−17.7480	+	11.1027i	−0.788217	+	0.493090i
$508$	5.83652	+	3.36972i	0.258954	+	0.149507i
$509$	−16.5519	−	28.6687i	−0.733649	−	1.27072i	−0.955313	−	0.295595i	$-0.904482\pi$
$509$	−16.5519	−	28.6687i	−0.733649	−	1.27072i	0.221664	−	0.975123i	$-0.428851\pi$
$510$		0			0
$511$	10.6127	+	12.9025i	0.469479	+	0.570773i
$512$	−17.0367			−0.752921
$513$	15.5892	+	21.3880i	0.688281	+	0.944305i
$514$	11.2836	+	6.51458i	0.497697	+	0.287346i
$515$		0			0
$516$	0.713670	−	0.0252852i	0.0314176	−	0.00111312i
$517$	−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	$-0.443479\pi$
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.764092	−	0.645108i	$-0.223188\pi$
$522$	−1.57863	−	22.2503i	−0.0690949	−	0.973871i
$523$	−19.0959	−	33.0751i	−0.835007	−	1.44627i	−0.894025	−	0.448018i	$-0.852130\pi$
$523$	−19.0959	−	33.0751i	−0.835007	−	1.44627i	0.0590174	−	0.998257i	$-0.481203\pi$
$524$	−1.75748			−0.0767759
$525$		0			0
$526$	13.8974			0.605953
$527$	−1.49555	−	2.59038i	−0.0651474	−	0.112839i
$528$	6.62623	+	10.5922i	0.288370	+	0.460966i
$529$	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
$534$	−0.473126	−	13.3539i	−0.0204742	−	0.577879i
$535$		0			0
$536$	−9.81641	−	5.66751i	−0.424004	−	0.244799i
$537$	9.10860	−	0.322716i	0.393065	−	0.0139262i
$538$	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
$543$	−8.92243	−	14.2627i	−0.382898	−	0.612073i
$544$	1.91936	−	1.10814i	0.0822918	−	0.0475112i
$545$		0			0
$546$	−3.53877	+	3.12726i	−0.151445	+	0.133834i
$547$		−	10.9605i		−	0.468638i	−0.972160	−	0.234319i	$-0.924714\pi$
$547$		−	10.9605i		−	0.468638i	0.972160	−	0.234319i	$-0.0752860\pi$
$548$	−2.07082	−	3.58677i	−0.0884612	−	0.153219i
$549$	−0.0979425	−	1.38047i	−0.00418008	−	0.0589170i
$550$		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	$0.207370\pi$
$558$	−17.1446	−	8.34043i	−0.725791	−	0.353079i
$559$			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	$0.768113\pi$
$564$	5.12126	+	8.18646i	0.215644	+	0.344712i
$565$		0			0
$566$	−4.78405			−0.201089
$567$	−22.7028	+	7.18209i	−0.953428	+	0.301619i
$568$			24.1814i			1.01463i
$569$	−4.55880	+	2.63203i	−0.191115	+	0.110340i	−0.592504	−	0.805567i	$-0.701861\pi$
$569$	−4.55880	+	2.63203i	−0.191115	+	0.110340i	0.401389	+	0.915907i	$0.368527\pi$
$570$		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
$576$	10.4444	−	21.4696i	0.435185	−	0.894569i
$577$	2.51561	−	4.35716i	0.104726	−	0.181391i	−0.808900	−	0.587946i	$-0.799937\pi$
$577$	2.51561	−	4.35716i	0.104726	−	0.181391i	0.913626	+	0.406555i	$0.133270\pi$
$578$	−9.02699	+	15.6352i	−0.375473	+	0.650339i
$579$	14.4564	−	0.512189i	0.600789	−	0.0212858i
$580$		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	$0.875255\pi$
$588$	−6.40078	+	7.87781i	−0.263964	+	0.324875i
$589$	−30.0186			−1.23690
$590$		0			0
$591$	2.60748	−	1.63118i	0.107258	−	0.0670978i
$592$	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
$597$	6.50596	−	0.230505i	0.266271	−	0.00943395i
$598$	−2.21420	+	3.83511i	−0.0905453	+	0.156829i
$599$	0.501417	+	0.289493i	0.0204873	+	0.0118284i	0.510209	−	0.860051i	$-0.329568\pi$
$599$	0.501417	+	0.289493i	0.0204873	+	0.0118284i	−0.489721	+	0.871879i	$0.662901\pi$
$600$		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
$606$	−3.78560	+	2.36818i	−0.153779	+	0.0962007i
$607$	12.5550	+	21.7458i	0.509591	+	0.882637i	0.999938	+	0.0111098i	$0.00353644\pi$
$607$	12.5550	+	21.7458i	0.509591	+	0.882637i	−0.490348	+	0.871527i	$0.663130\pi$
$608$		−	22.2425i		−	0.902053i
$609$	30.9673	−	6.28208i	1.25486	−	0.254563i
$610$		0			0
$611$	−5.51156	+	3.18210i	−0.222974	+	0.128734i
$612$	0.0902097	+	1.27148i	0.00364651	+	0.0513964i
$613$	−1.26428	−	0.729932i	−0.0510638	−	0.0294817i	0.474251	−	0.880390i	$-0.342719\pi$
$613$	−1.26428	−	0.729932i	−0.0510638	−	0.0294817i	−0.525315	+	0.850908i	$0.676052\pi$
$614$	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	$0.542169\pi$
$618$	−0.989482	−	27.9279i	−0.0398028	−	1.12343i
$619$	−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
$621$	−18.0441	+	13.1519i	−0.724086	+	0.527768i
$622$	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
$627$	−33.2059	+	20.7728i	−1.32612	+	0.829587i
$628$	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
$633$	−13.3936	+	8.37873i	−0.532349	+	0.333025i
$634$	−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
$639$	−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	$0.593514\pi$
$642$	−0.896846	−	25.3133i	−0.0353957	−	0.999036i
$643$	17.3489			0.684173			0.342087	−	0.939668i	$-0.388866\pi$
$643$	17.3489			0.684173			0.342087	+	0.939668i	$0.388866\pi$
$644$	−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	$0.617240\pi$
$648$	16.9963	+	21.6634i	0.667679	+	0.851018i
$649$	44.7120	−	25.8145i	1.75510	−	1.01331i
$650$		0			0
$651$	8.58418	−	25.6071i	0.336440	−	1.00362i
$652$		−	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	$0.820851\pi$
$654$	−25.5268	+	15.9690i	−0.998178	+	0.624437i
$655$		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	$0.338183\pi$
$659$			44.8494i			1.74709i	−0.486747	+	0.873543i	$0.661817\pi$
$660$		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
$663$	−0.839570	+	0.0297458i	−0.0326062	+	0.00115523i
$664$			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
$669$	−17.2385	+	10.7840i	−0.666478	+	0.416933i
$670$		0			0
$671$	2.04812			0.0790667
$672$	18.9738	+	6.36051i	0.731930	+	0.245362i
$673$		−	11.5641i		−	0.445763i	−0.974845	−	0.222882i	$-0.928454\pi$
$673$		−	11.5641i		−	0.445763i	0.974845	−	0.222882i	$-0.0715464\pi$
$674$	−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
$681$	−41.9257	+	1.48542i	−1.60660	+	0.0569214i
$682$	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	$0.274284\pi$
$684$	11.5036	+	5.59620i	0.439850	+	0.213976i
$685$		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
$693$	−8.22447	−	34.2663i	−0.312422	−	1.30167i
$694$	−19.5866			−0.743496
$695$		0			0
$696$	−19.3784	−	30.9768i	−0.734535	−	1.17417i
$697$	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	$0.290092\pi$
$701$			41.8503i			1.58066i	−0.612679	+	0.790332i	$0.709908\pi$
$702$	−4.32739	+	3.15413i	−0.163327	+	0.119045i
$703$	−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
$711$	44.1721	−	3.13395i	1.65658	−	0.117532i
$712$	−10.9440	−	18.9556i	−0.410145	−	0.710392i
$713$		−	25.3253i		−	0.948442i
$714$	2.45789	−	0.498612i	0.0919842	−	0.0186601i
$715$		0			0
$716$	3.81519	−	2.20270i	0.142580	−	0.0823189i
$717$	−8.29168	−	13.2545i	−0.309658	−	0.494997i
$718$	11.0198	+	6.36230i	0.411256	+	0.237439i
$719$	0.114311	+	0.197992i	0.00426307	+	0.00738386i	0.868149	−	0.496304i	$-0.165310\pi$
$719$	0.114311	+	0.197992i	0.00426307	+	0.00738386i	−0.863886	+	0.503687i	$0.831976\pi$
$720$		0			0
$721$	39.0504	−	6.49162i	1.45431	−	0.241761i
$722$	−7.48733			−0.278650
$723$	−8.79502	+	0.311606i	−0.327090	+	0.0115887i
$724$	−7.04228	−	4.06586i	−0.261724	−	0.151107i
$725$		0			0
$726$	−0.576104	−	16.2604i	−0.0213812	−	0.603481i
$727$	−19.2284			−0.713140			−0.356570	−	0.934269i	$-0.616054\pi$
$727$	−19.2284			−0.713140			−0.356570	+	0.934269i	$0.616054\pi$
$728$	−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
$732$	−0.354766	−	0.567103i	−0.0131125	−	0.0209607i
$733$	4.12825	+	7.15035i	0.152481	+	0.264104i	0.932139	−	0.362101i	$-0.117941\pi$
$733$	4.12825	+	7.15035i	0.152481	+	0.264104i	−0.779658	+	0.626205i	$0.784607\pi$
$734$	17.2253			0.635797
$735$		0			0
$736$	18.7650			0.691688
$737$	8.22447	+	14.2452i	0.302952	+	0.524729i
$738$	15.0222	−	1.06580i	0.552974	−	0.0392328i
$739$	−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	$0.256463\pi$
$744$	−31.2110	+	1.10580i	−1.14425	+	0.0405407i
$745$		0			0
$746$	4.96508	+	2.86659i	0.181785	+	0.104953i
$747$	−29.1127	−	14.1626i	−1.06518	−	0.518182i
$748$	−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
$753$	−27.4220	+	17.1546i	−0.999315	+	0.625148i
$754$	6.15389	−	3.55295i	0.224111	−	0.129391i
$755$		0			0
$756$	−8.06337	+	8.21273i	−0.293262	+	0.298694i
$757$		−	30.1051i		−	1.09419i	−0.837071	−	0.547094i	$-0.815734\pi$
$757$		−	30.1051i		−	1.09419i	0.837071	−	0.547094i	$-0.184266\pi$
$758$	12.9631	+	22.4527i	0.470840	+	0.815518i
$759$	−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	$-0.406697\pi$
$762$	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
$768$	−0.986190	−	27.8350i	−0.0355861	−	1.00441i
$769$			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	$0.660102\pi$
$774$	−0.112750	−	1.58918i	−0.00405272	−	0.0571218i
$775$		0			0
$776$	21.1453			0.759073
$777$	−22.8413	−	25.8470i	−0.819428	−	0.927254i
$778$		−	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
$786$	0.138829	+	3.91842i	0.00495186	+	0.139765i
$787$	20.7393	−	35.9215i	0.739276	−	1.28046i	−0.213546	−	0.976933i	$-0.568501\pi$
$787$	20.7393	−	35.9215i	0.739276	−	1.28046i	0.952822	−	0.303530i	$-0.0981653\pi$
$788$	0.743313	−	1.28746i	0.0264794	−	0.0458637i
$789$	0.790377	+	22.3082i	0.0281382	+	0.794195i
$790$		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	$-0.340355\pi$
$798$	8.00000	−	23.8645i	0.283197	−	0.844794i
$799$	3.37976			0.119567
$800$		0			0
$801$	21.4090	−	1.51894i	0.756448	−	0.0536690i
$802$	−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
$807$	0.0286059	+	0.807397i	0.00100698	+	0.0284217i
$808$	−3.65720	+	6.33446i	−0.128660	+	0.222846i
$809$	−21.7594	−	12.5628i	−0.765018	−	0.441683i	0.0660764	−	0.997815i	$-0.478952\pi$
$809$	−21.7594	−	12.5628i	−0.765018	−	0.441683i	−0.831095	+	0.556131i	$0.812285\pi$
$810$		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
$816$	−0.757466	−	1.21083i	−0.0265166	−	0.0423875i
$817$	−1.25421	−	2.17235i	−0.0438792	−	0.0760011i
$818$		−	18.4210i		−	0.644076i
$819$	−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	$0.411075\pi$
$822$	−7.83336	+	4.90037i	−0.273220	+	0.170920i
$823$	39.9721	+	23.0779i	1.39334	+	0.804446i	0.993684	−	0.112219i	$-0.0357957\pi$
$823$	39.9721	+	23.0779i	1.39334	+	0.804446i	0.399658	+	0.916665i	$0.369129\pi$
$824$	−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	$0.605338\pi$
$828$	−4.72126	+	9.70505i	−0.164075	+	0.337274i
$829$	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
$831$	24.0446	−	0.851896i	0.834098	−	0.0295519i
$832$	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
$837$	12.4131	−	27.9952i	0.429061	−	0.967655i
$838$	−21.3793	−	37.0301i	−0.738536	−	1.27918i
$839$	−49.1689			−1.69750			−0.848750	−	0.528795i	$-0.822644\pi$
$839$	−49.1689			−1.69750			−0.848750	+	0.528795i	$0.822644\pi$
$840$		0			0
$841$	−18.5446			−0.639470
$842$	18.4085	+	31.8844i	0.634398	+	1.09881i
$843$	−6.29680	−	10.0656i	−0.216873	−	0.346678i
$844$	−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
$849$	−0.272081	−	7.67943i	−0.00933779	−	0.263557i
$850$		0			0
$851$	−28.0114	−	16.1724i	−0.960218	−	0.554382i
$852$	−11.4538	+	0.405806i	−0.392401	+	0.0139027i
$853$	−8.86218			−0.303435			−0.151718	−	0.988424i	$-0.548480\pi$
$853$	−8.86218			−0.303435			−0.151718	+	0.988424i	$0.548480\pi$
$854$	−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	$0.661319\pi$
$858$	−4.20292	−	6.71847i	−0.143485	−	0.229365i
$859$	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
$861$	4.24130	+	20.9074i	0.144543	+	0.712521i
$862$		−	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	$0.808644\pi$
$864$	20.7433	+	9.19761i	0.705700	+	0.312909i
$865$		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
$873$	−9.07043	+	18.6452i	−0.306988	+	0.631046i
$874$		−	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	−0.154088	−	0.988057i	$-0.549244\pi$
$877$	18.4956	−	10.6784i	0.624551	−	0.360584i	0.778639	+	0.627473i	$0.215911\pi$
$878$	−15.6640	−	9.04360i	−0.528634	−	0.305207i
$879$	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	$0.310726\pi$
$882$	18.0697	+	13.6487i	0.608439	+	0.459574i
$883$		−	12.0561i		−	0.405721i	−0.979208	−	0.202860i	$-0.934976\pi$
$883$		−	12.0561i		−	0.405721i	0.979208	−	0.202860i	$-0.0650238\pi$
$884$	−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
$891$	−5.64151	−	39.5575i	−0.188998	−	1.32523i
$892$	−4.91415	+	8.51156i	−0.164538	+	0.284988i
$893$	16.9595	−	29.3748i	0.567529	−	0.982990i
$894$	−9.82477	+	0.348090i	−0.328589	+	0.0116419i
$895$		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
$903$	2.21177	−	0.448683i	0.0736029	−	0.0149312i
$904$	−15.4709			−0.514556
$905$		0			0
$906$	−11.0983	+	6.94281i	−0.368715	+	0.230659i
$907$	35.9415	+	20.7508i	1.19342	+	0.689020i	0.959080	−	0.283135i	$-0.0913744\pi$
$907$	35.9415	+	20.7508i	1.19342	+	0.689020i	0.234338	+	0.972155i	$0.424708\pi$
$908$	−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	$-0.595966\pi$
$911$		−	57.6428i		−	1.90979i	0.296941	−	0.954896i	$-0.404034\pi$
$912$	−14.3247	+	0.507522i	−0.474339	+	0.0168057i
$913$	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
$921$	−48.2074	+	30.1574i	−1.58849	+	0.993721i
$922$	7.29905	+	12.6423i	0.240381	+	0.416353i
$923$		−	7.55357i		−	0.248629i
$924$	−11.2792	−	12.7634i	−0.371058	−	0.419884i
$925$		0			0
$926$	4.79793	−	2.77009i	0.157670	−	0.0910307i
$927$	44.7741	−	3.17666i	1.47057	−	0.104335i
$928$	−26.0767	−	15.0554i	−0.856008	−	0.494217i
$929$	−20.2064	−	34.9985i	−0.662950	−	1.14826i	−0.979837	−	0.199799i	$-0.935971\pi$
$929$	−20.2064	−	34.9985i	−0.662950	−	1.14826i	0.316887	−	0.948463i	$-0.397362\pi$
$930$		0			0
$931$	34.9845	+	6.87843i	1.14657	+	0.225431i
$932$	−9.20592			−0.301550
$933$	1.00954	+	28.4942i	0.0330510	+	0.932858i
$934$	8.60828	+	4.96999i	0.281672	+	0.162623i
$935$		0			0
$936$	−3.83719	+	7.88775i	−0.125422	+	0.257819i
$937$	−5.67805			−0.185494			−0.0927468	−	0.995690i	$-0.529565\pi$
$937$	−5.67805			−0.185494			−0.0927468	+	0.995690i	$0.529565\pi$
$938$	−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	−0.950214	−	0.311598i	$-0.899136\pi$
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	0.744959	+	0.667110i	$0.232469\pi$
$942$	4.59210	−	2.87271i	0.149619	−	0.0935979i
$943$	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	$0.663262\pi$
$948$	18.1461	−	11.3518i	0.589357	−	0.368688i
$949$	−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	$0.750857\pi$
$954$	12.9239	−	26.5664i	0.418425	−	0.860118i
$955$		0			0
$956$	−6.54444	−	3.77843i	−0.211662	−	0.122203i
$957$	1.87744	+	52.9905i	0.0606891	+	1.71294i
$958$	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
$963$	40.5823	−	2.87926i	1.30775	−	0.0927829i
$964$	−3.68385	+	2.12687i	−0.118649	+	0.0685019i
$965$		0			0
$966$	20.1334	+	6.74924i	0.647781	+	0.217153i
$967$			36.3052i			1.16750i	0.811935	+	0.583748i	$0.198415\pi$
$967$			36.3052i			1.16750i	−0.811935	+	0.583748i	$0.801585\pi$
$968$	−13.3261	−	23.0814i	−0.428316	−	0.741864i
$969$	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	$0.538436\pi$
$972$	−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	$0.313103\pi$
$978$	−23.8147	+	0.843752i	−0.761512	+	0.0269802i
$979$			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	$0.432506\pi$
$984$	20.9138	−	13.0832i	0.666707	−	0.417076i
$985$		0			0
$986$	−3.77364			−0.120177
$987$	20.2081	+	22.8673i	0.643232	+	0.727873i
$988$			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
$996$	−15.6386	+	0.554071i	−0.495527	+	0.0175564i
$997$	−5.56719	+	9.64266i	−0.176315	+	0.305386i	−0.940615	−	0.339474i	$-0.889751\pi$
$997$	−5.56719	+	9.64266i	−0.176315	+	0.305386i	0.764301	+	0.644860i	$0.223084\pi$
$998$	17.6513	−	30.5729i	0.558741	−	0.967768i
$999$	−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.q.f.374.3		16
3.2	odd	2		525.2.q.e.374.6		16
5.2	odd	4		525.2.t.g.101.3		8
5.3	odd	4		105.2.s.c.101.2	yes	8
5.4	even	2	inner	525.2.q.f.374.6		16
7.5	odd	6		525.2.q.e.299.3		16
15.2	even	4		525.2.t.f.101.2		8
15.8	even	4		105.2.s.d.101.3	yes	8
15.14	odd	2		525.2.q.e.374.3		16
21.5	even	6	inner	525.2.q.f.299.6		16
35.3	even	12		735.2.b.c.146.3		8
35.12	even	12		525.2.t.f.26.2		8
35.13	even	4		735.2.s.k.521.2		8
35.18	odd	12		735.2.b.d.146.3		8
35.19	odd	6		525.2.q.e.299.6		16
35.23	odd	12		735.2.s.l.656.3		8
35.33	even	12		105.2.s.d.26.3	yes	8
105.23	even	12		735.2.s.k.656.2		8
105.38	odd	12		735.2.b.d.146.6		8
105.47	odd	12		525.2.t.g.26.3		8
105.53	even	12		735.2.b.c.146.6		8
105.68	odd	12		105.2.s.c.26.2	✓	8
105.83	odd	4		735.2.s.l.521.3		8
105.89	even	6	inner	525.2.q.f.299.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	105.68	odd	12
105.2.s.c.101.2	yes	8	5.3	odd	4
105.2.s.d.26.3	yes	8	35.33	even	12
105.2.s.d.101.3	yes	8	15.8	even	4
525.2.q.e.299.3		16	7.5	odd	6
525.2.q.e.299.6		16	35.19	odd	6
525.2.q.e.374.3		16	15.14	odd	2
525.2.q.e.374.6		16	3.2	odd	2
525.2.q.f.299.3		16	105.89	even	6	inner
525.2.q.f.299.6		16	21.5	even	6	inner
525.2.q.f.374.3		16	1.1	even	1	trivial
525.2.q.f.374.6		16	5.4	even	2	inner
525.2.t.f.26.2		8	35.12	even	12
525.2.t.f.101.2		8	15.2	even	4
525.2.t.g.26.3		8	105.47	odd	12
525.2.t.g.101.3		8	5.2	odd	4
735.2.b.c.146.3		8	35.3	even	12
735.2.b.c.146.6		8	105.53	even	12
735.2.b.d.146.3		8	35.18	odd	12
735.2.b.d.146.6		8	105.38	odd	12
735.2.s.k.521.2		8	35.13	even	4
735.2.s.k.656.2		8	105.23	even	12
735.2.s.l.521.3		8	105.83	odd	4
735.2.s.l.656.3		8	35.23	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.539169 - 0.933868i) q^{2} +(1.46840 - 0.918594i) q^{3} +(0.418594 - 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} -3.05945 q^{8} +(1.31237 - 2.69772i) q^{9} +O(q^{10})\)	\(q+(-0.539169 - 0.933868i) q^{2} +(1.46840 - 0.918594i) q^{3} +(0.418594 - 0.725026i) q^{4} +(-1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} -3.05945 q^{8} +(1.31237 - 2.69772i) q^{9} +(3.84494 + 2.21988i) q^{11} +(-0.0513428 - 1.44914i) q^{12} +0.955682 q^{13} +(-2.81439 + 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(-0.439527 - 0.253761i) q^{17} +(-3.22690 + 0.228945i) q^{18} +(-4.41107 + 2.54673i) q^{19} +(-0.911072 - 4.49110i) q^{21} -4.78755i q^{22} +(-2.14856 - 3.72142i) q^{23} +(-4.49248 + 2.81039i) 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} +(7.68506 - 0.272280i) q^{33} +0.547280i q^{34} +(-1.40656 - 2.08075i) q^{36} +(6.51863 - 3.76353i) q^{37} +(4.75663 + 2.74624i) q^{38} +(1.40332 - 0.877884i) q^{39} -4.65529 q^{41} +(-3.70287 + 3.27228i) 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} +(-0.878503 + 0.0311252i) q^{51} +(0.400043 - 0.692894i) q^{52} +(-4.56616 + 7.90881i) q^{53} +(-4.52806 + 3.30039i) 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} +(-5.46331 - 5.75780i) q^{63} +7.95845 q^{64} +(-4.39782 - 7.03002i) q^{66} +(3.20856 + 1.85246i) q^{67} +(-0.367967 + 0.212446i) q^{68} +(-6.57342 - 3.49086i) q^{69} -7.90386i q^{71} +(-4.01513 + 8.25352i) 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} +(-5.55536 - 7.08081i) q^{81} +(2.50999 + 4.34743i) q^{82} -10.7916i q^{83} +(-3.63753 - 1.21939i) q^{84} +(0.459909 - 0.265529i) q^{86} +(6.33394 + 10.1250i) q^{87} +(-11.7634 - 6.79159i) q^{88} +(3.57713 + 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} -3.59750 q^{92} +(10.2015 - 0.361438i) q^{93} +(6.21894 + 3.59050i) q^{94} +(0.267811 + 7.55890i) q^{96} -6.91148 q^{97} +(-1.45623 + 7.40656i) q^{98} +(11.0346 - 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9	\( 16 q - 6 q^{4} + 10 q^{6} + 10 q^{9} + 24 q^{14} + 2 q^{16} - 18 q^{19} + 38 q^{21} - 32 q^{24} - 12 q^{26} - 42 q^{31} + 18 q^{36} + 6 q^{39} - 60 q^{41} - 14 q^{46} + 8 q^{49} - 12 q^{51} - 34 q^{54} - 42 q^{56} + 24 q^{59} + 30 q^{61} - 76 q^{64} + 44 q^{66} + 26 q^{69} - 108 q^{74} + 58 q^{79} - 82 q^{81} + 6 q^{84} + 18 q^{86} + 6 q^{89} - 6 q^{91} + 48 q^{94} - 6 q^{96} + 68 q^{99}+O(q^{100}) \) 16 * q - 6 * q^4 + 10 * q^6 + 10 * q^9 + 24 * q^14 + 2 * q^16 - 18 * q^19 + 38 * q^21 - 32 * q^24 - 12 * q^26 - 42 * q^31 + 18 * q^36 + 6 * q^39 - 60 * q^41 - 14 * q^46 + 8 * q^49 - 12 * q^51 - 34 * q^54 - 42 * q^56 + 24 * q^59 + 30 * q^61 - 76 * q^64 + 44 * q^66 + 26 * q^69 - 108 * q^74 + 58 * q^79 - 82 * q^81 + 6 * q^84 + 18 * q^86 + 6 * q^89 - 6 * q^91 + 48 * q^94 - 6 * q^96 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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