LMFDB - Embedded newform 675.2.y.a.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0134680 - 0.0633621i) q^{2} +(1.82326 + 0.811767i) q^{4} +(-1.33347 + 1.79495i) q^{5} +(0.0617846 + 0.0356713i) q^{7} +(0.152142 - 0.209405i) q^{8} +O(q^{10})$	\(q+(0.0134680 - 0.0633621i) q^{2} +(1.82326 + 0.811767i) q^{4} +(-1.33347 + 1.79495i) q^{5} +(0.0617846 + 0.0356713i) q^{7} +(0.152142 - 0.209405i) q^{8} +(0.0957728 + 0.108666i) q^{10} +(-1.44247 - 0.306606i) q^{11} +(0.827777 + 3.89439i) q^{13} +(0.00309233 - 0.00343438i) q^{14} +(2.65969 + 2.95388i) q^{16} +(-0.372547 + 0.512767i) q^{17} +(1.33258 + 0.968174i) q^{19} +(-3.88834 + 2.19019i) q^{20} +(-0.0388544 + 0.0872684i) q^{22} +(-0.0818713 - 0.0737173i) q^{23} +(-1.44371 - 4.78704i) q^{25} +0.257905 q^{26} +(0.0836924 + 0.115193i) q^{28} +(0.817041 + 7.77363i) q^{29} +(-0.614550 + 5.84705i) q^{31} +(0.671307 - 0.387579i) q^{32} +(0.0274725 + 0.0305114i) q^{34} +(-0.146416 + 0.0633337i) q^{35} +(-3.33257 - 1.08282i) q^{37} +(0.0792927 - 0.0713955i) q^{38} +(0.172996 + 0.552323i) q^{40} +(3.85961 - 0.820385i) q^{41} +(-9.25438 - 5.34302i) q^{43} +(-2.38110 - 1.72997i) q^{44} +(-0.00577353 + 0.00419471i) q^{46} +(-5.48189 + 0.576170i) q^{47} +(-3.49746 - 6.05777i) q^{49} +(-0.322761 + 0.0270045i) q^{50} +(-1.65208 + 7.77243i) q^{52} +(6.09380 + 8.38739i) q^{53} +(2.47383 - 2.18031i) q^{55} +(0.0168698 - 0.00751091i) q^{56} +(0.503558 + 0.0529260i) q^{58} +(12.5288 - 2.66308i) q^{59} +(12.1362 + 2.57963i) q^{61} +(0.362205 + 0.117688i) q^{62} +(2.44107 + 7.51284i) q^{64} +(-8.09406 - 3.70723i) q^{65} +(-1.49035 - 0.156642i) q^{67} +(-1.09550 + 0.632485i) q^{68} +(0.00204102 + 0.0101302i) q^{70} +(6.20729 - 4.50986i) q^{71} +(7.85987 - 2.55383i) q^{73} +(-0.113493 + 0.196576i) q^{74} +(1.64370 + 2.84697i) q^{76} +(-0.0781852 - 0.0703983i) q^{77} +(-0.144654 - 1.37629i) q^{79} +(-8.84870 + 0.835096i) q^{80} -0.255602i q^{82} +(-3.66568 - 8.23326i) q^{83} +(-0.423612 - 1.35246i) q^{85} +(-0.463184 + 0.514418i) q^{86} +(-0.283664 + 0.255412i) q^{88} +(3.48501 + 10.7258i) q^{89} +(-0.0877741 + 0.270141i) q^{91} +(-0.0894313 - 0.200866i) q^{92} +(-0.0373229 + 0.355104i) q^{94} +(-3.51478 + 1.10088i) q^{95} +(-1.81309 + 0.190563i) q^{97} +(-0.430937 + 0.140020i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.0134680	−	0.0633621i	0.00952334	−	0.0448038i	−0.973129	−	0.230259i	$-0.926043\pi$
$2$	0.0134680	−	0.0633621i	0.00952334	−	0.0448038i	0.982653	+	0.185455i	$0.0593760\pi$
$3$		0			0
$3$		0			0
$4$	1.82326	+	0.811767i	0.911629	+	0.405883i
$5$	−1.33347	+	1.79495i	−0.596346	+	0.802727i
$5$	−1.33347	+	1.79495i	−0.596346	+	0.802727i
$6$		0			0
$7$	0.0617846	+	0.0356713i	0.0233524	+	0.0134825i	0.511631	−	0.859205i	$-0.329042\pi$
$7$	0.0617846	+	0.0356713i	0.0233524	+	0.0134825i	−0.488278	+	0.872688i	$0.662375\pi$
$8$	0.152142	−	0.209405i	0.0537902	−	0.0740359i
$9$		0			0
$10$	0.0957728	+	0.108666i	0.0302860	+	0.0343632i
$11$	−1.44247	−	0.306606i	−0.434920	−	0.0924452i	−0.0147516	−	0.999891i	$-0.504696\pi$
$11$	−1.44247	−	0.306606i	−0.434920	−	0.0924452i	−0.420169	+	0.907446i	$0.638029\pi$
$12$		0			0
$13$	0.827777	+	3.89439i	0.229584	+	1.08011i	0.930337	+	0.366705i	$0.119514\pi$
$13$	0.827777	+	3.89439i	0.229584	+	1.08011i	−0.700753	+	0.713404i	$0.747153\pi$
$14$	0.00309233	−	0.00343438i	0.000826460	−	0.000917877i
$15$		0			0
$16$	2.65969	+	2.95388i	0.664922	+	0.738471i
$17$	−0.372547	+	0.512767i	−0.0903560	+	0.124364i	−0.851802	−	0.523864i	$-0.824490\pi$
$17$	−0.372547	+	0.512767i	−0.0903560	+	0.124364i	0.761446	+	0.648229i	$0.224490\pi$
$18$		0			0
$19$	1.33258	+	0.968174i	0.305714	+	0.222114i	0.730055	−	0.683388i	$-0.239494\pi$
$19$	1.33258	+	0.968174i	0.305714	+	0.222114i	−0.424341	+	0.905502i	$0.639494\pi$
$20$	−3.88834	+	2.19019i	−0.869460	+	0.489742i
$21$		0			0
$22$	−0.0388544	+	0.0872684i	−0.00828379	+	0.0186057i
$23$	−0.0818713	−	0.0737173i	−0.0170714	−	0.0153711i	0.660551	−	0.750781i	$-0.270323\pi$
$23$	−0.0818713	−	0.0737173i	−0.0170714	−	0.0153711i	−0.677622	+	0.735410i	$0.736989\pi$
$24$		0			0
$25$	−1.44371	−	4.78704i	−0.288742	−	0.957407i
$26$	0.257905			0.0505794
$27$		0			0
$28$	0.0836924	+	0.115193i	0.0158164	+	0.0217694i
$29$	0.817041	+	7.77363i	0.151721	+	1.44353i	0.760062	+	0.649851i	$0.225169\pi$
$29$	0.817041	+	7.77363i	0.151721	+	1.44353i	−0.608341	+	0.793676i	$0.708165\pi$
$30$		0			0
$31$	−0.614550	+	5.84705i	−0.110376	+	1.05016i	0.789420	+	0.613853i	$0.210381\pi$
$31$	−0.614550	+	5.84705i	−0.110376	+	1.05016i	−0.899797	+	0.436309i	$0.856285\pi$
$32$	0.671307	−	0.387579i	0.118671	−	0.0685150i
$33$		0			0
$34$	0.0274725	+	0.0305114i	0.00471150	+	0.00523265i
$35$	−0.146416	+	0.0633337i	−0.0247489	+	0.0107053i
$36$		0			0
$37$	−3.33257	−	1.08282i	−0.547872	−	0.178014i	0.0219851	−	0.999758i	$-0.493001\pi$
$37$	−3.33257	−	1.08282i	−0.547872	−	0.178014i	−0.569857	+	0.821744i	$0.693001\pi$
$38$	0.0792927	−	0.0713955i	0.0128630	−	0.0115819i
$39$		0			0
$40$	0.172996	+	0.552323i	0.0273530	+	0.0873299i
$41$	3.85961	−	0.820385i	0.602770	−	0.128123i	0.103588	−	0.994620i	$-0.466968\pi$
$41$	3.85961	−	0.820385i	0.602770	−	0.128123i	0.499181	+	0.866498i	$0.333634\pi$
$42$		0			0
$43$	−9.25438	−	5.34302i	−1.41128	−	0.814803i	−0.415771	−	0.909469i	$-0.636488\pi$
$43$	−9.25438	−	5.34302i	−1.41128	−	0.814803i	−0.995509	+	0.0946660i	$0.969822\pi$
$44$	−2.38110	−	1.72997i	−0.358964	−	0.260803i
$45$		0			0
$46$	−0.00577353	+	0.00419471i	−0.000851261	+	0.000618477i
$47$	−5.48189	+	0.576170i	−0.799616	+	0.0840430i	−0.495518	−	0.868598i	$-0.665022\pi$
$47$	−5.48189	+	0.576170i	−0.799616	+	0.0840430i	−0.304098	+	0.952641i	$0.598355\pi$
$48$		0			0
$49$	−3.49746	−	6.05777i	−0.499636	−	0.865396i
$50$	−0.322761	+	0.0270045i	−0.0456453	+	0.00381901i
$51$		0			0
$52$	−1.65208	+	7.77243i	−0.229102	+	1.07784i
$53$	6.09380	+	8.38739i	0.837048	+	1.15210i	0.986570	+	0.163339i	$0.0522264\pi$
$53$	6.09380	+	8.38739i	0.837048	+	1.15210i	−0.149522	+	0.988758i	$0.547774\pi$
$54$		0			0
$55$	2.47383	−	2.18031i	0.333571	−	0.293993i
$56$	0.0168698	−	0.00751091i	0.00225432	−	0.00100369i
$57$		0			0
$58$	0.503558	+	0.0529260i	0.0661204	+	0.00694953i
$59$	12.5288	−	2.66308i	1.63111	−	0.346704i	0.700769	−	0.713388i	$-0.252840\pi$
$59$	12.5288	−	2.66308i	1.63111	−	0.346704i	0.930345	+	0.366684i	$0.119507\pi$
$60$		0			0
$61$	12.1362	+	2.57963i	1.55388	+	0.330288i	0.903254	−	0.429106i	$-0.141171\pi$
$61$	12.1362	+	2.57963i	1.55388	+	0.330288i	0.650631	+	0.759394i	$0.274505\pi$
$62$	0.362205	+	0.117688i	0.0460001	+	0.0149463i
$63$		0			0
$64$	2.44107	+	7.51284i	0.305134	+	0.939105i
$65$	−8.09406	−	3.70723i	−1.00394	−	0.459825i
$66$		0			0
$67$	−1.49035	−	0.156642i	−0.182075	−	0.0191369i	0.0130521	−	0.999915i	$-0.495845\pi$
$67$	−1.49035	−	0.156642i	−0.182075	−	0.0191369i	−0.195127	+	0.980778i	$0.562512\pi$
$68$	−1.09550	+	0.632485i	−0.132848	+	0.0767001i
$69$		0			0
$70$	0.00204102	+	0.0101302i	0.000243948	+	0.00121079i
$71$	6.20729	−	4.50986i	0.736670	−	0.535222i	−0.154997	−	0.987915i	$-0.549537\pi$
$71$	6.20729	−	4.50986i	0.736670	−	0.535222i	0.891666	+	0.452693i	$0.149537\pi$
$72$		0			0
$73$	7.85987	−	2.55383i	0.919928	−	0.298903i	0.189491	−	0.981882i	$-0.439316\pi$
$73$	7.85987	−	2.55383i	0.919928	−	0.298903i	0.730437	+	0.682980i	$0.239316\pi$
$74$	−0.113493	+	0.196576i	−0.0131933	+	0.0228514i
$75$		0			0
$76$	1.64370	+	2.84697i	0.188545	+	0.326570i
$77$	−0.0781852	−	0.0703983i	−0.00891003	−	0.00802263i
$78$		0			0
$79$	−0.144654	−	1.37629i	−0.0162748	−	0.154845i	0.983366	−	0.181634i	$-0.0581385\pi$
$79$	−0.144654	−	1.37629i	−0.0162748	−	0.154845i	−0.999641	+	0.0267890i	$0.991472\pi$
$80$	−8.84870	+	0.835096i	−0.989314	+	0.0933665i
$81$		0			0
$82$		−	0.255602i		−	0.0282265i
$83$	−3.66568	−	8.23326i	−0.402361	−	0.903717i	−0.995151	−	0.0983603i	$-0.968640\pi$
$83$	−3.66568	−	8.23326i	−0.402361	−	0.903717i	0.592790	−	0.805357i	$-0.298026\pi$
$84$		0			0
$85$	−0.423612	−	1.35246i	−0.0459471	−	0.146695i
$86$	−0.463184	+	0.514418i	−0.0499464	+	0.0554711i
$87$		0			0
$88$	−0.283664	+	0.255412i	−0.0302387	+	0.0272271i
$89$	3.48501	+	10.7258i	0.369411	+	1.13693i	0.947173	+	0.320724i	$0.103926\pi$
$89$	3.48501	+	10.7258i	0.369411	+	1.13693i	−0.577762	+	0.816205i	$0.696074\pi$
$90$		0			0
$91$	−0.0877741	+	0.270141i	−0.00920123	+	0.0283185i
$92$	−0.0894313	−	0.200866i	−0.00932386	−	0.0209417i
$93$		0			0
$94$	−0.0373229	+	0.355104i	−0.00384957	+	0.0366262i
$95$	−3.51478	+	1.10088i	−0.360609	+	0.112948i
$96$		0			0
$97$	−1.81309	+	0.190563i	−0.184091	+	0.0193488i	−0.196125	−	0.980579i	$-0.562836\pi$
$97$	−1.81309	+	0.190563i	−0.184091	+	0.0193488i	0.0120342	+	0.999928i	$0.496169\pi$
$98$	−0.430937	+	0.140020i	−0.0435312	+	0.0141442i
$99$		0			0
$100$	1.25370	−	9.89995i	0.125370	−	0.989995i
$101$	5.57600	−	9.65791i	0.554832	−	0.960998i	−0.443084	−	0.896480i	$-0.646116\pi$
$101$	5.57600	−	9.65791i	0.554832	−	0.960998i	0.997917	−	0.0645179i	$-0.0205510\pi$
$102$		0			0
$103$	5.33010	−	11.9716i	0.525191	−	1.17960i	−0.435045	−	0.900409i	$-0.643268\pi$
$103$	5.33010	−	11.9716i	0.525191	−	1.17960i	0.960236	−	0.279189i	$-0.0900657\pi$
$104$	0.941444	+	0.419158i	0.0923162	+	0.0411018i
$105$		0			0
$106$	0.613515	−	0.273154i	0.0595898	−	0.0265311i
$107$			4.16072i			0.402232i	0.979567	+	0.201116i	$0.0644568\pi$
$107$			4.16072i			0.402232i	−0.979567	+	0.201116i	$0.935543\pi$
$108$		0			0
$109$	−2.72812	+	8.39629i	−0.261307	+	0.804219i	0.731215	+	0.682147i	$0.238954\pi$
$109$	−2.72812	+	8.39629i	−0.261307	+	0.804219i	−0.992521	+	0.122072i	$0.961046\pi$
$110$	−0.104831	−	0.186112i	−0.00999529	−	0.0177451i
$111$		0			0
$112$	0.0589587	+	0.277379i	0.00557108	+	0.0262099i
$113$	−3.50202	−	16.4757i	−0.329442	−	1.54990i	−0.761566	−	0.648088i	$-0.775569\pi$
$113$	−3.50202	−	16.4757i	−0.329442	−	1.54990i	0.432124	−	0.901814i	$-0.357764\pi$
$114$		0			0
$115$	0.241492	−	0.0486553i	0.0225192	−	0.00453713i
$116$	−4.82070	+	14.8366i	−0.447590	+	1.37754i
$117$		0			0
$118$		−	0.829720i		−	0.0763819i
$119$	−0.0413088	+	0.0183918i	−0.00378677	+	0.00168598i
$120$		0			0
$121$	−8.06230	−	3.58957i	−0.732936	−	0.326324i
$122$	0.326902	−	0.734235i	0.0295963	−	0.0664745i
$123$		0			0
$124$	−5.86693	+	10.1618i	−0.526866	+	0.912558i
$125$	10.5176	+	3.79199i	0.940727	+	0.339165i
$126$		0			0
$127$	−13.1962	+	4.28772i	−1.17098	+	0.380473i	−0.829007	−	0.559238i	$-0.811094\pi$
$127$	−13.1962	+	4.28772i	−1.17098	+	0.380473i	−0.341969	+	0.939711i	$0.611094\pi$
$128$	2.05073	−	0.215541i	0.181261	−	0.0190513i
$129$		0			0
$130$	−0.343909	+	0.462928i	−0.0301628	+	0.0406014i
$131$	2.01563	−	19.1774i	0.176106	−	1.67554i	−0.447871	−	0.894098i	$-0.647818\pi$
$131$	2.01563	−	19.1774i	0.176106	−	1.67554i	0.623978	−	0.781442i	$-0.285516\pi$
$132$		0			0
$133$	0.0477966	+	0.107353i	0.00414449	+	0.00930869i
$134$	−0.0299972	+	0.0923220i	−0.00259137	+	0.00797541i
$135$		0			0
$136$	0.0506961	+	0.156027i	0.00434715	+	0.0133792i
$137$	−6.24272	+	5.62097i	−0.533352	+	0.480232i	−0.891240	−	0.453532i	$-0.850164\pi$
$137$	−6.24272	+	5.62097i	−0.533352	+	0.480232i	0.357888	+	0.933765i	$0.383497\pi$
$138$		0			0
$139$	4.95172	−	5.49944i	0.420000	−	0.466457i	−0.495598	−	0.868552i	$-0.665051\pi$
$139$	4.95172	−	5.49944i	0.420000	−	0.466457i	0.915598	+	0.402095i	$0.131718\pi$
$140$	−0.318367	−	0.00338229i	−0.0269069	−	0.000285855i
$141$		0			0
$142$	−0.202154	−	0.454046i	−0.0169644	−	0.0381027i
$143$		−	5.87133i		−	0.490985i
$144$		0			0
$145$	−15.0428	−	8.89936i	−1.24924	−	0.739052i
$146$	−0.0559589	−	0.532413i	−0.00463119	−	0.0440628i
$147$		0			0
$148$	−5.19714	−	4.67953i	−0.427203	−	0.384655i
$149$	−3.11548	−	5.39616i	−0.255230	−	0.442071i	0.709728	−	0.704476i	$-0.248818\pi$
$149$	−3.11548	−	5.39616i	−0.255230	−	0.442071i	−0.964958	+	0.262405i	$0.915484\pi$
$150$		0			0
$151$	7.95472	−	13.7780i	0.647346	−	1.12124i	−0.336408	−	0.941716i	$-0.609212\pi$
$151$	7.95472	−	13.7780i	0.647346	−	1.12124i	0.983754	−	0.179520i	$-0.0574545\pi$
$152$	0.405481	−	0.131749i	0.0328889	−	0.0106862i
$153$		0			0
$154$	−0.00551359	+	0.00400585i	−0.000444297	+	0.000322801i
$155$	−9.67570	−	8.89997i	−0.777171	−	0.714863i
$156$		0			0
$157$	−1.02843	+	0.593765i	−0.0820777	+	0.0473876i	−0.540477	−	0.841359i	$-0.681756\pi$
$157$	−1.02843	+	0.593765i	−0.0820777	+	0.0473876i	0.458399	+	0.888746i	$0.348423\pi$
$158$	−0.0891528	−	0.00937033i	−0.00709261	−	0.000745464i
$159$		0			0
$160$	−0.199482	+	1.72179i	−0.0157705	+	0.136120i
$161$	−0.00242879	−	0.00747505i	−0.000191416	−	0.000589117i
$162$		0			0
$163$	21.7996	+	7.08313i	1.70748	+	0.554794i	0.989911	−	0.141693i	$-0.0452547\pi$
$163$	21.7996	+	7.08313i	1.70748	+	0.554794i	0.717569	+	0.696487i	$0.245255\pi$
$164$	7.70302	+	1.63733i	0.601505	+	0.127854i
$165$		0			0
$166$	−0.571046	+	0.121380i	−0.0443218	+	0.00942089i
$167$	14.9139	+	1.56751i	1.15407	+	0.121298i	0.662171	−	0.749353i	$-0.269635\pi$
$167$	14.9139	+	1.56751i	1.15407	+	0.121298i	0.491902	+	0.870651i	$0.336302\pi$
$168$		0			0
$169$	−2.60494	+	1.15979i	−0.200380	+	0.0892149i
$170$	−0.0914003	+	0.00862590i	−0.00701008	+	0.000661576i
$171$		0			0
$172$	−12.5358	−	17.2541i	−0.955849	−	1.31561i
$173$	4.30502	−	20.2535i	0.327304	−	1.53985i	−0.439665	−	0.898162i	$-0.644903\pi$
$173$	4.30502	−	20.2535i	0.327304	−	1.53985i	0.766969	−	0.641684i	$-0.221764\pi$
$174$		0			0
$175$	0.0815611	−	0.347264i	0.00616544	−	0.0262507i
$176$	−2.93083	−	5.07635i	−0.220920	−	0.382645i
$177$		0			0
$178$	0.726544	−	0.0763628i	0.0544568	−	0.00572364i
$179$	−0.431280	+	0.313343i	−0.0322354	+	0.0234204i	−0.603786	−	0.797146i	$-0.706342\pi$
$179$	−0.431280	+	0.313343i	−0.0322354	+	0.0234204i	0.571551	+	0.820567i	$0.306342\pi$
$180$		0			0
$181$	−1.18446	−	0.860558i	−0.0880400	−	0.0639648i	0.542895	−	0.839801i	$-0.317328\pi$
$181$	−1.18446	−	0.860558i	−0.0880400	−	0.0639648i	−0.630934	+	0.775836i	$0.717328\pi$
$182$	0.0159346	+	0.00919983i	0.00118115	+	0.000681937i
$183$		0			0
$184$	−0.0278928	+	0.00592880i	−0.00205629	+	0.000437077i
$185$	6.38750	−	4.53790i	0.469618	−	0.333633i
$186$		0			0
$187$	0.694605	−	0.625425i	0.0507945	−	0.0457356i
$188$	−10.4626	−	3.39951i	−0.763064	−	0.247935i
$189$		0			0
$190$	0.0224169	+	0.237531i	0.00162630	+	0.0172323i
$191$	5.03144	+	5.58798i	0.364062	+	0.404332i	0.897149	−	0.441729i	$-0.145635\pi$
$191$	5.03144	+	5.58798i	0.364062	+	0.404332i	−0.533087	+	0.846061i	$0.678968\pi$
$192$		0			0
$193$	10.1650	−	5.86874i	0.731690	−	0.422441i	−0.0873503	−	0.996178i	$-0.527840\pi$
$193$	10.1650	−	5.86874i	0.731690	−	0.422441i	0.819040	+	0.573736i	$0.194507\pi$
$194$	−0.0123442	+	0.117448i	−0.000886265	+	0.00843225i
$195$		0			0
$196$	−1.45927	−	13.8840i	−0.104233	−	0.991714i
$197$	−0.302676	−	0.416597i	−0.0215647	−	0.0296813i	0.798098	−	0.602527i	$-0.205839\pi$
$197$	−0.302676	−	0.416597i	−0.0215647	−	0.0296813i	−0.819663	+	0.572846i	$0.805839\pi$
$198$		0			0
$199$	−22.1619			−1.57101			−0.785507	−	0.618853i	$-0.787598\pi$
$199$	−22.1619			−1.57101			−0.785507	+	0.618853i	$0.787598\pi$
$200$	−1.22208	−	0.425988i	−0.0864140	−	0.0301219i
$201$		0			0
$202$	−0.536848	−	0.483380i	−0.0377725	−	0.0340105i
$203$	−0.226815	+	0.509435i	−0.0159193	+	0.0357554i
$204$		0			0
$205$	−3.67412	+	8.02177i	−0.256612	+	0.560265i
$206$	−0.686761	−	0.498961i	−0.0478489	−	0.0347643i
$207$		0			0
$208$	−9.30193	+	12.8030i	−0.644973	+	0.887729i
$209$	−1.62535	−	1.80513i	−0.112428	−	0.124864i
$210$		0			0
$211$	−7.63244	+	8.47668i	−0.525439	+	0.583559i	−0.946188	−	0.323618i	$-0.895101\pi$
$211$	−7.63244	+	8.47668i	−0.525439	+	0.583559i	0.420749	+	0.907177i	$0.361767\pi$
$212$	4.30196	+	20.2391i	0.295460	+	1.39003i
$213$		0			0
$214$	0.263632	+	0.0560368i	0.0180215	+	0.00383059i
$215$	21.9309	−	9.48641i	1.49568	−	0.646968i
$216$		0			0
$217$	−0.246542	+	0.339336i	−0.0167364	+	0.0230356i
$218$	0.495265	+	0.285941i	0.0335436	+	0.0193664i
$219$		0			0
$220$	6.28033	−	1.96709i	0.423420	−	0.132621i
$221$	−2.30530	−	1.02639i	−0.155071	−	0.0690422i
$222$		0			0
$223$	4.55331	−	21.4216i	0.304912	−	1.43450i	−0.512620	−	0.858616i	$-0.671325\pi$
$223$	4.55331	−	21.4216i	0.304912	−	1.43450i	0.817532	−	0.575883i	$-0.195342\pi$
$224$	0.0553019			0.00369502
$225$		0			0
$226$	−1.09110			−0.0725789
$227$	−3.46715	+	16.3117i	−0.230123	+	1.08264i	0.699643	+	0.714493i	$0.253342\pi$
$227$	−3.46715	+	16.3117i	−0.230123	+	1.08264i	−0.929766	+	0.368151i	$0.879991\pi$
$228$		0			0
$229$	−3.10203	−	1.38111i	−0.204988	−	0.0912666i	0.301675	−	0.953411i	$-0.402454\pi$
$229$	−3.10203	−	1.38111i	−0.204988	−	0.0912666i	−0.506663	+	0.862144i	$0.669121\pi$
$230$	0.000169522	−	0.0159567i	1.11780e−5	−	0.00105216i
$231$		0			0
$232$	1.75214	+	1.01160i	0.115034	+	0.0664148i
$233$	5.63449	−	7.75521i	0.369128	−	0.508061i	−0.583536	−	0.812087i	$-0.698331\pi$
$233$	5.63449	−	7.75521i	0.369128	−	0.508061i	0.952663	+	0.304027i	$0.0983312\pi$
$234$		0			0
$235$	6.27575	−	10.6080i	0.409384	−	0.691992i
$236$	25.0051	+	5.31499i	1.62769	+	0.345977i
$237$		0			0
$238$	0.000608999		0.00286511i	3.94755e−5		0.000185718i
$239$	−11.0876	+	12.3140i	−0.717198	+	0.796529i	−0.986014	−	0.166663i	$-0.946701\pi$
$239$	−11.0876	+	12.3140i	−0.717198	+	0.796529i	0.268816	+	0.963192i	$0.413368\pi$
$240$		0			0
$241$	11.5289	+	12.8041i	0.742639	+	0.824785i	0.989540	−	0.144256i	$-0.0460789\pi$
$241$	11.5289	+	12.8041i	0.742639	+	0.824785i	−0.246901	+	0.969041i	$0.579412\pi$
$242$	−0.336026	+	0.462500i	−0.0216006	+	0.0297306i
$243$		0			0
$244$	20.0334	+	14.5551i	1.28251	+	0.931796i
$245$	15.5372	+	1.80010i	0.992633	+	0.115004i
$246$		0			0
$247$	−2.66737	+	5.99100i	−0.169720	+	0.381198i
$248$	1.13090	+	1.01827i	0.0718125	+	0.0646603i
$249$		0			0
$250$	0.381920	−	0.615350i	0.0241548	−	0.0389181i
$251$	2.98431			0.188368			0.0941841	−	0.995555i	$-0.469976\pi$
$251$	2.98431			0.188368			0.0941841	+	0.995555i	$0.469976\pi$
$252$		0			0
$253$	0.0954946	+	0.131437i	0.00600369	+	0.00826337i
$254$	0.0939515	+	0.893889i	0.00589504	+	0.0560876i
$255$		0			0
$256$	−1.63748	+	15.5795i	−0.102342	+	0.973722i
$257$	−23.0388	+	13.3014i	−1.43712	+	0.829721i	−0.997649	−	0.0685352i	$-0.978167\pi$
$257$	−23.0388	+	13.3014i	−1.43712	+	0.829721i	−0.439471	+	0.898257i	$0.644834\pi$
$258$		0			0
$259$	−0.167276	−	0.185779i	−0.0103940	−	0.0115437i
$260$	−11.7481	−	13.3297i	−0.728589	−	0.826674i
$261$		0			0
$262$	−1.18798	−	0.385997i	−0.0733934	−	0.0238470i
$263$	−15.4480	+	13.9095i	−0.952567	+	0.857695i	−0.989923	−	0.141607i	$-0.954773\pi$
$263$	−15.4480	+	13.9095i	−0.952567	+	0.857695i	0.0373560	+	0.999302i	$0.488106\pi$
$264$		0			0
$265$	−23.1809	−	0.246270i	−1.42399	−	0.0151283i
$266$	0.00744584	−	0.00158266i	0.000456534	−	9.70393e-5i
$267$		0			0
$268$	−2.59013	−	1.49541i	−0.158218	−	0.0913469i
$269$	−1.14544	−	0.832213i	−0.0698389	−	0.0507410i	0.552318	−	0.833634i	$-0.313743\pi$
$269$	−1.14544	−	0.832213i	−0.0698389	−	0.0507410i	−0.622157	+	0.782893i	$0.713743\pi$
$270$		0			0
$271$	12.5405	−	9.11118i	0.761779	−	0.553464i	−0.137677	−	0.990477i	$-0.543964\pi$
$271$	12.5405	−	9.11118i	0.761779	−	0.553464i	0.899455	+	0.437013i	$0.143964\pi$
$272$	−2.50551	+	0.263340i	−0.151919	+	0.0159673i
$273$		0			0
$274$	0.272080	+	0.471256i	0.0164369	+	0.0284696i
$275$	0.614769	+	7.34779i	0.0370720	+	0.443088i
$276$		0			0
$277$	2.38077	−	11.2007i	0.143047	−	0.672982i	−0.846924	−	0.531713i	$-0.821548\pi$
$277$	2.38077	−	11.2007i	0.143047	−	0.672982i	0.989971	−	0.141269i	$-0.0451183\pi$
$278$	−0.281767	−	0.387818i	−0.0168992	−	0.0232598i
$279$		0			0
$280$	−0.00901364	+	0.0402960i	−0.000538668	+	0.00240815i
$281$	−11.1952	+	4.98444i	−0.667852	+	0.297347i	−0.712517	−	0.701655i	$-0.752445\pi$
$281$	−11.1952	+	4.98444i	−0.667852	+	0.297347i	0.0446648	+	0.999002i	$0.485778\pi$
$282$		0			0
$283$	14.6841	+	1.54337i	0.872882	+	0.0917435i	0.530366	−	0.847769i	$-0.322054\pi$
$283$	14.6841	+	1.54337i	0.872882	+	0.0917435i	0.342515	+	0.939512i	$0.388721\pi$
$284$	14.9784	−	3.18377i	0.888807	−	0.188922i
$285$		0			0
$286$	−0.372020	−	0.0790753i	−0.0219980	−	0.00467582i
$287$	0.267729	+	0.0869903i	0.0158035	+	0.00513487i
$288$		0			0
$289$	5.12915	+	15.7859i	0.301715	+	0.928582i
$290$	−0.766479	+	0.833287i	−0.0450092	+	0.0489323i
$291$		0			0
$292$	16.4037	+	1.72410i	0.959953	+	0.100895i
$293$	−20.3267	+	11.7356i	−1.18750	+	0.685602i	−0.957737	−	0.287645i	$-0.907128\pi$
$293$	−20.3267	+	11.7356i	−1.18750	+	0.685602i	−0.229760	+	0.973247i	$0.573794\pi$
$294$		0			0
$295$	−11.9267	+	26.0398i	−0.694401	+	1.51610i
$296$	−0.733771	+	0.533116i	−0.0426496	+	0.0309867i
$297$		0			0
$298$	−0.383872	+	0.124727i	−0.0222371	+	0.00722527i
$299$	0.219312	−	0.379860i	0.0126832	−	0.0219679i
$300$		0			0
$301$	−0.381186	−	0.660233i	−0.0219712	−	0.0380552i
$302$	−0.765868	−	0.689591i	−0.0440707	−	0.0396815i
$303$		0			0
$304$	0.684367	+	6.51131i	0.0392511	+	0.373449i
$305$	−20.8136	+	18.3441i	−1.19179	+	1.05038i
$306$		0			0
$307$			20.5467i			1.17266i	0.810071	+	0.586332i	$0.199429\pi$
$307$			20.5467i			1.17266i	−0.810071	+	0.586332i	$0.800571\pi$
$308$	−0.0854048	−	0.191822i	−0.00486639	−	0.0109301i
$309$		0			0
$310$	−0.694234	+	0.493208i	−0.0394298	+	0.0280123i
$311$	2.64525	−	2.93785i	0.149999	−	0.166590i	−0.663463	−	0.748209i	$-0.730914\pi$
$311$	2.64525	−	2.93785i	0.149999	−	0.166590i	0.813461	+	0.581619i	$0.197581\pi$
$312$		0			0
$313$	2.57780	−	2.32106i	0.145706	−	0.131194i	−0.593054	−	0.805162i	$-0.702078\pi$
$313$	2.57780	−	2.32106i	0.145706	−	0.131194i	0.738761	+	0.673968i	$0.235411\pi$
$314$	0.0237713	+	0.0731604i	0.00134149	+	0.00412868i
$315$		0			0
$316$	0.853484	−	2.62675i	0.0480122	−	0.147766i
$317$	4.28304	+	9.61987i	0.240560	+	0.540306i	0.992967	−	0.118392i	$-0.0377741\pi$
$317$	4.28304	+	9.61987i	0.240560	+	0.540306i	−0.752407	+	0.658698i	$0.771107\pi$
$318$		0			0
$319$	1.20488	−	11.4637i	0.0674606	−	0.641845i
$320$	−16.7403	−	5.63655i	−0.935811	−	0.315093i
$321$		0			0
$322$	−0.000506346	0	5.32191e-5i	−2.82176e−5	0	2.96579e-6i
$323$	−0.992895	+	0.322611i	−0.0552462	+	0.0179506i
$324$		0			0
$325$	17.4475	−	9.58496i	0.967813	−	0.531678i
$326$	0.742401	−	1.28588i	0.0411178	−	0.0712181i
$327$		0			0
$328$	0.415415	−	0.933036i	0.0229374	−	0.0515183i
$329$	−0.359249	−	0.159948i	−0.0198060	−	0.00881822i
$330$		0			0
$331$	1.04027	−	0.463156i	0.0571782	−	0.0254574i	−0.377948	−	0.925827i	$-0.623370\pi$
$331$	1.04027	−	0.463156i	0.0571782	−	0.0254574i	0.435127	+	0.900369i	$0.356704\pi$
$332$		−	17.9870i		−	0.987166i
$333$		0			0
$334$	0.300182	−	0.923866i	0.0164252	−	0.0505517i
$335$	2.26850	−	2.46623i	0.123942	−	0.134744i
$336$		0			0
$337$	3.20482	+	15.0775i	0.174578	+	0.821323i	0.975056	+	0.221961i	$0.0712457\pi$
$337$	3.20482	+	15.0775i	0.174578	+	0.821323i	−0.800478	+	0.599362i	$0.795421\pi$
$338$	0.0384036	+	0.180675i	0.00208888	+	0.00982741i
$339$		0			0
$340$	0.325532	−	2.80977i	0.0176545	−	0.152381i
$341$	2.67921	−	8.24576i	0.145087	−	0.446533i
$342$		0			0
$343$		−	0.998435i		−	0.0539104i
$344$	−2.52683	+	1.12502i	−0.136238	+	0.0606570i
$345$		0			0
$346$	−1.22533	−	0.545550i	−0.0658739	−	0.0293290i
$347$	10.2423	−	23.0045i	0.549834	−	1.23495i	−0.398353	−	0.917232i	$-0.630418\pi$
$347$	10.2423	−	23.0045i	0.549834	−	1.23495i	0.948187	−	0.317714i	$-0.102915\pi$
$348$		0			0
$349$	−18.1802	+	31.4890i	−0.973163	+	1.68557i	−0.287296	+	0.957842i	$0.592756\pi$
$349$	−18.1802	+	31.4890i	−0.973163	+	1.68557i	−0.685867	+	0.727727i	$0.740577\pi$
$350$	−0.0209049	−	0.00984485i	−0.00111742	−	0.000526229i
$351$		0			0
$352$	−1.08717	+	0.353244i	−0.0579465	+	0.0188280i
$353$	2.01200	−	0.211470i	0.107088	−	0.0112554i	−0.0508329	−	0.998707i	$-0.516188\pi$
$353$	2.01200	−	0.211470i	0.107088	−	0.0112554i	0.157921	+	0.987452i	$0.449521\pi$
$354$		0			0
$355$	−0.182258	+	17.1556i	−0.00967327	+	0.910523i
$356$	−2.35274	+	22.3848i	−0.124695	+	1.18639i
$357$		0			0
$358$	0.0140456	+	0.0315469i	0.000742333	+	0.00166731i
$359$	4.58912	−	14.1239i	0.242204	−	0.745429i	−0.753879	−	0.657013i	$-0.771820\pi$
$359$	4.58912	−	14.1239i	0.242204	−	0.745429i	0.996084	−	0.0884156i	$-0.0281804\pi$
$360$		0			0
$361$	−5.03292	−	15.4897i	−0.264891	−	0.815250i
$362$	−0.0704791	+	0.0634597i	−0.00370430	+	0.00333537i
$363$		0			0
$364$	−0.379326	+	0.421285i	−0.0198821	+	0.0220813i
$365$	−5.89691	+	17.5135i	−0.308659	+	0.916701i
$366$		0			0
$367$	−8.77789	−	19.7155i	−0.458202	−	1.02914i	−0.983941	−	0.178493i	$-0.942878\pi$
$367$	−8.77789	−	19.7155i	−0.458202	−	1.02914i	0.525739	−	0.850646i	$-0.323789\pi$
$368$		−	0.437903i		−	0.0228273i
$369$		0			0
$370$	−0.201504	−	0.465842i	−0.0104757	−	0.0242180i
$371$	0.0773132	+	0.735586i	0.00401390	+	0.0381897i
$372$		0			0
$373$	18.6065	+	16.7533i	0.963406	+	0.867455i	0.991229	−	0.132158i	$-0.0421906\pi$
$373$	18.6065	+	16.7533i	0.963406	+	0.867455i	−0.0278223	+	0.999613i	$0.508857\pi$
$374$	−0.0302733	−	0.0524349i	−0.00156539	−	0.00271134i
$375$		0			0
$376$	−0.713371	+	1.23560i	−0.0367893	+	0.0637210i
$377$	−29.5972	+	9.61671i	−1.52433	+	0.495286i
$378$		0			0
$379$	24.0385	−	17.4650i	1.23477	−	0.897115i	0.237534	−	0.971379i	$-0.423661\pi$
$379$	24.0385	−	17.4650i	1.23477	−	0.897115i	0.997239	+	0.0742645i	$0.0236609\pi$
$380$	−7.30200	−	0.845992i	−0.374585	−	0.0433985i
$381$		0			0
$382$	0.421830	−	0.243543i	0.0215827	−	0.0124608i
$383$	11.9861	+	1.25979i	0.612460	+	0.0643722i	0.405680	−	0.914015i	$-0.367035\pi$
$383$	11.9861	+	1.25979i	0.612460	+	0.0643722i	0.206780	+	0.978387i	$0.433701\pi$
$384$		0			0
$385$	0.230619	−	0.0464646i	0.0117534	−	0.00236806i
$386$	−0.234954	−	0.723114i	−0.0119588	−	0.0368055i
$387$		0			0
$388$	−3.46042	−	1.12436i	−0.175676	−	0.0570807i
$389$	0.667516	+	0.141885i	0.0338444	+	0.00719384i	0.224803	−	0.974404i	$-0.427826\pi$
$389$	0.667516	+	0.141885i	0.0338444	+	0.00719384i	−0.190958	+	0.981598i	$0.561160\pi$
$390$		0			0
$391$	0.0683007	−	0.0145178i	0.00345412	−	0.000734195i
$392$	−1.80064	−	0.189255i	−0.0909459	−	0.00955880i
$393$		0			0
$394$	−0.0304729	+	0.0135674i	−0.00153520	+	0.000683517i
$395$	2.66326	+	1.57559i	0.134003	+	0.0792768i
$396$		0			0
$397$	−1.78022	−	2.45027i	−0.0893469	−	0.122975i	0.762004	−	0.647573i	$-0.224216\pi$
$397$	−1.78022	−	2.45027i	−0.0893469	−	0.122975i	−0.851350	+	0.524597i	$0.824216\pi$
$398$	−0.298477	+	1.40422i	−0.0149613	+	0.0703874i
$399$		0			0
$400$	10.3005	−	16.9966i	0.515026	−	0.849828i
$401$	11.0554	+	19.1486i	0.552082	+	0.956235i	0.998124	+	0.0612227i	$0.0195000\pi$
$401$	11.0554	+	19.1486i	0.552082	+	0.956235i	−0.446042	+	0.895012i	$0.647167\pi$
$402$		0			0
$403$	−23.2794	+	2.44676i	−1.15963	+	0.121882i
$404$	18.0064	−	13.0824i	0.895854	−	0.650876i
$405$		0			0
$406$	0.0292242	+	0.0212326i	0.00145037	+	0.00105376i
$407$	4.47513	+	2.58372i	0.221824	+	0.128070i
$408$		0			0
$409$	3.05277	−	0.648886i	0.150950	−	0.0320854i	−0.131817	−	0.991274i	$-0.542081\pi$
$409$	3.05277	−	0.648886i	0.150950	−	0.0320854i	0.282767	+	0.959189i	$0.408748\pi$
$410$	0.458793	+	0.340838i	0.0226582	+	0.0168328i
$411$		0			0
$412$	19.4363	−	17.5005i	0.957558	−	0.862189i
$413$	0.869084	+	0.282383i	0.0427648	+	0.0138951i
$414$		0			0
$415$	19.6664	+	4.39909i	0.965385	+	0.215943i
$416$	2.06508	+	2.29350i	0.101249	+	0.112448i
$417$		0			0
$418$	−0.136267	+	0.0786741i	−0.00666506	+	0.00384807i
$419$	0.959503	−	9.12906i	0.0468748	−	0.445984i	−0.945763	−	0.324859i	$-0.894683\pi$
$419$	0.959503	−	9.12906i	0.0468748	−	0.445984i	0.992637	−	0.121125i	$-0.0386501\pi$
$420$		0			0
$421$	2.60521	+	24.7869i	0.126970	+	1.20804i	0.853570	+	0.520978i	$0.174433\pi$
$421$	2.60521	+	24.7869i	0.126970	+	1.20804i	−0.726600	+	0.687061i	$0.758901\pi$
$422$	0.434307	+	0.597772i	0.0211417	+	0.0290991i
$423$		0			0
$424$	2.68348			0.130322
$425$	2.99248	+	1.04311i	0.145157	+	0.0505983i
$426$		0			0
$427$	0.657813	+	0.592297i	0.0318338	+	0.0286633i
$428$	−3.37754	+	7.58607i	−0.163259	+	0.366686i
$429$		0			0
$430$	−0.305713	−	1.51735i	−0.0147428	−	0.0731733i
$431$	−7.49000	−	5.44180i	−0.360780	−	0.262122i	0.392597	−	0.919711i	$-0.371577\pi$
$431$	−7.49000	−	5.44180i	−0.360780	−	0.262122i	−0.753378	+	0.657588i	$0.771577\pi$
$432$		0			0
$433$	−10.2213	+	14.0684i	−0.491203	+	0.676083i	−0.980609	−	0.195973i	$-0.937213\pi$
$433$	−10.2213	+	14.0684i	−0.491203	+	0.676083i	0.489407	+	0.872056i	$0.337213\pi$
$434$	0.0181806	+	0.0201916i	0.000872698	+	0.000969229i
$435$		0			0
$436$	−11.7899	+	13.0940i	−0.564634	+	0.627089i
$437$	−0.0377287	−	0.177500i	−0.00180481	−	0.00849096i
$438$		0			0
$439$	21.4445	+	4.55817i	1.02349	+	0.217550i	0.688933	−	0.724825i	$-0.258080\pi$
$439$	21.4445	+	4.55817i	1.02349	+	0.217550i	0.334558	+	0.942375i	$0.391413\pi$
$440$	−0.0801951	−	0.849749i	−0.00382315	−	0.0405102i
$441$		0			0
$442$	−0.0960819	+	0.132245i	−0.00457015	+	0.00629027i
$443$	13.0284	+	7.52198i	0.619000	+	0.357380i	0.776480	−	0.630142i	$-0.217004\pi$
$443$	13.0284	+	7.52198i	0.619000	+	0.357380i	−0.157480	+	0.987522i	$0.550337\pi$
$444$		0			0
$445$	−23.8994	−	8.04707i	−1.13294	−	0.381468i
$446$	−1.29600	−	0.577015i	−0.0613672	−	0.0273225i
$447$		0			0
$448$	−0.117173	+	0.551254i	−0.00553589	+	0.0260443i
$449$	−38.0675			−1.79651			−0.898257	−	0.439470i	$-0.855166\pi$
$449$	−38.0675			−1.79651			−0.898257	+	0.439470i	$0.855166\pi$
$450$		0			0
$451$	−5.81889			−0.274001
$452$	6.98934	−	32.8822i	0.328751	−	1.54665i
$453$		0			0
$454$	0.986846	+	0.439372i	0.0463150	+	0.0206208i
$455$	−0.367846	−	0.517776i	−0.0172449	−	0.0242737i
$456$		0			0
$457$	5.80372	+	3.35078i	0.271487	+	0.156743i	0.629563	−	0.776949i	$-0.283234\pi$
$457$	5.80372	+	3.35078i	0.271487	+	0.156743i	−0.358076	+	0.933692i	$0.616567\pi$
$458$	−0.129289	+	0.177951i	−0.00604126	+	0.00831508i
$459$		0			0
$460$	0.479799	+	0.107324i	0.0223707	+	0.00500401i
$461$	−17.1454	−	3.64437i	−0.798542	−	0.169735i	−0.209469	−	0.977815i	$-0.567174\pi$
$461$	−17.1454	−	3.64437i	−0.798542	−	0.169735i	−0.589073	+	0.808080i	$0.700507\pi$
$462$		0			0
$463$	4.01215	+	18.8757i	0.186461	+	0.877228i	0.967525	+	0.252777i	$0.0813439\pi$
$463$	4.01215	+	18.8757i	0.186461	+	0.877228i	−0.781064	+	0.624451i	$0.785323\pi$
$464$	−20.7893	+	23.0889i	−0.965119	+	1.07187i
$465$		0			0
$466$	−0.415501	−	0.461461i	−0.0192477	−	0.0213768i
$467$	19.6880	−	27.0982i	0.911052	−	1.25396i	−0.0557537	−	0.998445i	$-0.517756\pi$
$467$	19.6880	−	27.0982i	0.911052	−	1.25396i	0.966806	−	0.255511i	$-0.0822438\pi$
$468$		0			0
$469$	−0.0864930	−	0.0628408i	−0.00399387	−	0.00290172i
$470$	−0.587626	−	0.540514i	−0.0271052	−	0.0249321i
$471$		0			0
$472$	1.34849	−	3.02877i	0.0620695	−	0.139410i
$473$	11.7109	+	10.5446i	0.538470	+	0.484840i
$474$		0			0
$475$	2.71083	−	7.77685i	0.124381	−	0.356826i
$476$	−0.0902464			−0.00413644
$477$		0			0
$478$	0.630915	+	0.868381i	0.0288574	+	0.0397188i
$479$	2.68283	+	25.5254i	0.122582	+	1.16629i	0.866907	+	0.498470i	$0.166104\pi$
$479$	2.68283	+	25.5254i	0.122582	+	1.16629i	−0.744326	+	0.667817i	$0.767229\pi$
$480$		0			0
$481$	1.45829	−	13.8747i	0.0664921	−	0.632630i
$482$	0.966566	−	0.558047i	0.0440259	−	0.0254184i
$483$		0			0
$484$	−11.7858	−	13.0894i	−0.535716	−	0.594973i
$485$	2.07565	−	3.50852i	0.0942504	−	0.159314i
$486$		0			0
$487$	8.05547	+	2.61738i	0.365028	+	0.118605i	0.485788	−	0.874077i	$-0.338533\pi$
$487$	8.05547	+	2.61738i	0.365028	+	0.118605i	−0.120759	+	0.992682i	$0.538533\pi$
$488$	2.38661	−	2.14892i	0.108037	−	0.0972769i
$489$		0			0
$490$	0.323313	−	0.960224i	0.0146058	−	0.0433785i
$491$	−7.10605	+	1.51044i	−0.320691	+	0.0681651i	−0.365445	−	0.930833i	$-0.619083\pi$
$491$	−7.10605	+	1.51044i	−0.320691	+	0.0681651i	0.0447535	+	0.998998i	$0.485750\pi$
$492$		0			0
$493$	−4.29045	−	2.47709i	−0.193232	−	0.111563i
$494$	0.343678	+	0.249697i	0.0154628	+	0.0112344i
$495$		0			0
$496$	−18.9060	+	13.7360i	−0.848906	+	0.616766i
$497$	0.544388	−	0.0572175i	0.0244191	−	0.00256655i
$498$		0			0
$499$	−18.5403	−	32.1127i	−0.829978	−	1.43756i	−0.898055	−	0.439884i	$-0.855020\pi$
$499$	−18.5403	−	32.1127i	−0.829978	−	1.43756i	0.0680767	−	0.997680i	$-0.478314\pi$
$500$	16.0982	+	15.4516i	0.719932	+	0.691018i
$501$		0			0
$502$	0.0401929	−	0.189093i	0.00179390	−	0.00843961i
$503$	13.4772	+	18.5497i	0.600917	+	0.827092i	0.995792	−	0.0916433i	$-0.0292120\pi$
$503$	13.4772	+	18.5497i	0.600917	+	0.827092i	−0.394875	+	0.918735i	$0.629212\pi$
$504$		0			0
$505$	9.90006	+	22.8872i	0.440547	+	1.01847i
$506$	0.00961425	−	0.00428054i	0.000427406	−	0.000190293i
$507$		0			0
$508$	−27.5408	−	2.89465i	−1.22192	−	0.128429i
$509$	14.4344	−	3.06813i	0.639795	−	0.135993i	0.123419	−	0.992355i	$-0.460614\pi$
$509$	14.4344	−	3.06813i	0.639795	−	0.135993i	0.516376	+	0.856362i	$0.327281\pi$
$510$		0			0
$511$	0.576717	+	0.122585i	0.0255125	+	0.00542284i
$512$	4.88731	+	1.58798i	0.215991	+	0.0701796i
$513$		0			0
$514$	0.532521	+	1.63893i	0.0234885	+	0.0722901i
$515$	14.3809	+	25.5311i	0.633700	+	1.12503i
$516$		0			0
$517$	8.08410	+	0.849674i	0.355538	+	0.0373686i
$518$	−0.0140242	+	0.00809689i	−0.000616189	+	0.000355757i
$519$		0			0
$520$	−2.00776	+	1.13091i	−0.0880460	+	0.0495938i
$521$	7.19138	−	5.22484i	0.315060	−	0.228904i	−0.419005	−	0.907984i	$-0.637621\pi$
$521$	7.19138	−	5.22484i	0.315060	−	0.228904i	0.734065	+	0.679080i	$0.237621\pi$
$522$		0			0
$523$	−33.6275	+	10.9262i	−1.47043	+	0.477771i	−0.931237	−	0.364413i	$-0.881270\pi$
$523$	−33.6275	+	10.9262i	−1.47043	+	0.477771i	−0.539190	+	0.842184i	$0.681270\pi$
$524$	19.2426	−	33.3292i	0.840617	−	1.45599i
$525$		0			0
$526$	0.673279	+	1.16615i	0.0293564	+	0.0508467i
$527$	−2.76923	−	2.49342i	−0.120630	−	0.108615i
$528$		0			0
$529$	−2.40289	−	22.8619i	−0.104473	−	0.993997i
$530$	−0.327805	+	1.46547i	−0.0142389	+	0.0636561i
$531$		0			0
$532$			0.234532i			0.0101682i
$533$	6.38979	+	14.3517i	0.276773	+	0.621642i
$534$		0			0
$535$	−7.46830	−	5.54820i	−0.322883	−	0.239870i
$536$	−0.259546	+	0.288255i	−0.0112107	+	0.0124507i
$537$		0			0
$538$	−0.0681577	+	0.0613695i	−0.00293849	+	0.00264583i
$539$	3.18762	+	9.81048i	0.137300	+	0.422567i
$540$		0			0
$541$	2.03061	−	6.24956i	0.0873025	−	0.268690i	−0.897869	−	0.440263i	$-0.854885\pi$
$541$	2.03061	−	6.24956i	0.0873025	−	0.268690i	0.985171	+	0.171574i	$0.0548851\pi$
$542$	−0.408408	−	0.917300i	−0.0175426	−	0.0394014i
$543$		0			0
$544$	−0.0513556	+	0.488616i	−0.00220185	+	0.0209492i
$545$	−11.4331	−	16.0931i	−0.489739	−	0.689351i
$546$		0			0
$547$	−13.6647	+	1.43622i	−0.584260	+	0.0614082i	−0.392047	−	0.919945i	$-0.628233\pi$
$547$	−13.6647	+	1.43622i	−0.584260	+	0.0614082i	−0.192213	+	0.981353i	$0.561566\pi$
$548$	−15.9450	+	5.18085i	−0.681137	+	0.221315i
$549$		0			0
$550$	0.473851	+	0.0600072i	0.0202051	+	0.00255872i
$551$	−6.43745	+	11.1500i	−0.274245	+	0.475006i
$552$		0			0
$553$	0.0401567	−	0.0901934i	0.00170764	−	0.00383541i
$554$	−0.677633	−	0.301702i	−0.0287899	−	0.0128181i
$555$		0			0
$556$	13.4925	−	6.00726i	0.572211	−	0.254765i
$557$			43.4297i			1.84017i	0.391714	+	0.920087i	$0.371882\pi$
$557$			43.4297i			1.84017i	−0.391714	+	0.920087i	$0.628118\pi$
$558$		0			0
$559$	13.1472	−	40.4630i	0.556068	−	1.71140i
$560$	−0.576502	−	0.264049i	−0.0243617	−	0.0111581i
$561$		0			0
$562$	0.165047	+	0.776485i	0.00696208	+	0.0327540i
$563$	1.18046	+	5.55363i	0.0497505	+	0.234058i	0.995997	−	0.0893894i	$-0.0284915\pi$
$563$	1.18046	+	5.55363i	0.0497505	+	0.234058i	−0.946246	+	0.323447i	$0.895158\pi$
$564$		0			0
$565$	34.2429	+	15.6839i	1.44061	+	0.659827i
$566$	0.295557	−	0.909632i	0.0124232	−	0.0382347i
$567$		0			0
$568$		−	1.98598i		−	0.0833297i
$569$	−10.9814	+	4.88922i	−0.460363	+	0.204967i	−0.623795	−	0.781588i	$-0.714410\pi$
$569$	−10.9814	+	4.88922i	−0.460363	+	0.204967i	0.163432	+	0.986555i	$0.447743\pi$
$570$		0			0
$571$	33.0181	+	14.7006i	1.38177	+	0.615202i	0.956996	−	0.290100i	$-0.0936884\pi$
$571$	33.0181	+	14.7006i	1.38177	+	0.615202i	0.424770	+	0.905301i	$0.360355\pi$
$572$	4.76615	−	10.7049i	0.199283	−	0.447596i
$573$		0			0
$574$	0.00911767	−	0.0157923i	0.000380564	−	0.000659156i
$575$	−0.234689	+	0.498347i	−0.00978720	+	0.0207825i
$576$		0			0
$577$	−37.3374	+	12.1317i	−1.55438	+	0.505048i	−0.955299	−	0.295642i	$-0.904467\pi$
$577$	−37.3374	+	12.1317i	−1.55438	+	0.505048i	−0.599079	+	0.800690i	$0.704467\pi$
$578$	1.06931	−	0.112389i	0.0444774	−	0.00467476i
$579$		0			0
$580$	−20.2027	−	28.4371i	−0.838871	−	1.18078i
$581$	0.0672087	−	0.639448i	0.00278829	−	0.0265288i
$582$		0			0
$583$	−6.21848	−	13.9669i	−0.257543	−	0.578451i
$584$	0.661030	−	2.03444i	0.0273536	−	0.0841858i
$585$		0			0
$586$	0.469833	+	1.44600i	0.0194086	+	0.0597336i
$587$	30.7302	−	27.6696i	1.26837	−	1.14205i	0.285377	−	0.958415i	$-0.407881\pi$
$587$	30.7302	−	27.6696i	1.26837	−	1.14205i	0.982995	−	0.183632i	$-0.0587855\pi$
$588$		0			0
$589$	−6.47990	+	7.19666i	−0.267000	+	0.296533i
$590$	1.48931	+	1.10641i	0.0613138	+	0.0455501i
$591$		0			0
$592$	−5.66509	−	12.7240i	−0.232834	−	0.522953i
$593$		−	15.9649i		−	0.655601i	−0.944747	−	0.327801i	$-0.893693\pi$
$593$		−	15.9649i		−	0.655601i	0.944747	−	0.327801i	$-0.106307\pi$
$594$		0			0
$595$	0.0220716	−	0.0986723i	0.000904846	−	0.00404517i
$596$	−1.29989	−	12.3676i	−0.0532456	−	0.506598i
$597$		0			0
$598$	−0.0211150	−	0.0190121i	−0.000863458	−	0.000777461i
$599$	−17.0464	−	29.5252i	−0.696496	−	1.20637i	−0.969674	−	0.244403i	$-0.921408\pi$
$599$	−17.0464	−	29.5252i	−0.696496	−	1.20637i	0.273178	−	0.961964i	$-0.411925\pi$
$600$		0			0
$601$	−7.15065	+	12.3853i	−0.291681	+	0.505207i	−0.974207	−	0.225655i	$-0.927548\pi$
$601$	−7.15065	+	12.3853i	−0.291681	+	0.505207i	0.682526	+	0.730861i	$0.260881\pi$
$602$	−0.0469676	+	0.0152607i	−0.00191426	+	0.000621979i
$603$		0			0
$604$	25.6880	−	18.6634i	1.04523	−	0.759404i
$605$	17.1939	−	9.68485i	0.699033	−	0.393745i
$606$		0			0
$607$	13.9372	−	8.04665i	0.565694	−	0.326604i	−0.189734	−	0.981836i	$-0.560762\pi$
$607$	13.9372	−	8.04665i	0.565694	−	0.326604i	0.755428	+	0.655232i	$0.227429\pi$
$608$	1.26981	+	0.133463i	0.0514977	+	0.00541263i
$609$		0			0
$610$	0.882001	+	1.56586i	0.0357112	+	0.0633996i
$611$	−6.78161	−	20.8717i	−0.274355	−	0.844377i
$612$		0			0
$613$	−22.5773	−	7.33580i	−0.911887	−	0.296290i	−0.184753	−	0.982785i	$-0.559148\pi$
$613$	−22.5773	−	7.33580i	−0.911887	−	0.296290i	−0.727135	+	0.686495i	$0.759148\pi$
$614$	1.30189	+	0.276724i	0.0525398	+	0.0111677i
$615$		0			0
$616$	−0.0266370	+	0.00566187i	−0.00107323	+	0.000228123i
$617$	−33.8202	−	3.55464i	−1.36155	−	0.143105i	−0.604574	−	0.796549i	$-0.706657\pi$
$617$	−33.8202	−	3.55464i	−1.36155	−	0.143105i	−0.756975	+	0.653444i	$0.773323\pi$
$618$		0			0
$619$	−5.73259	+	2.55232i	−0.230412	+	0.102586i	−0.518696	−	0.854959i	$-0.673582\pi$
$619$	−5.73259	+	2.55232i	−0.230412	+	0.102586i	0.288283	+	0.957545i	$0.406916\pi$
$620$	−10.4166	−	24.0813i	−0.418341	−	0.967130i
$621$		0			0
$622$	−0.150522	−	0.207176i	−0.00603539	−	0.00830700i
$623$	−0.167282	+	0.787002i	−0.00670203	+	0.0315306i
$624$		0			0
$625$	−20.8314	+	13.8222i	−0.833256	+	0.552887i
$626$	−0.112350	−	0.194595i	−0.00449040	−	0.00777759i
$627$		0			0
$628$	−2.35709	+	0.247740i	−0.0940582	+	0.00988592i
$629$	1.79677	−	1.30543i	0.0716421	−	0.0520510i
$630$		0			0
$631$	−25.3592	−	18.4245i	−1.00953	−	0.733469i	−0.0454228	−	0.998968i	$-0.514463\pi$
$631$	−25.3592	−	18.4245i	−1.00953	−	0.733469i	−0.964111	+	0.265498i	$0.914463\pi$
$632$	−0.310210	−	0.179100i	−0.0123395	−	0.00712420i
$633$		0			0
$634$	0.667220	−	0.141822i	0.0264987	−	0.00563247i
$635$	9.90055	−	29.4042i	0.392891	−	1.16687i
$636$		0			0
$637$	20.6962	−	18.6349i	0.820013	−	0.738343i
$638$	−0.710138	−	0.230738i	−0.0281146	−	0.00913500i
$639$		0			0
$640$	−2.34771	+	3.96838i	−0.0928012	+	0.156864i
$641$	−26.9261	−	29.9045i	−1.06352	−	1.18116i	−0.982848	−	0.184415i	$-0.940961\pi$
$641$	−26.9261	−	29.9045i	−1.06352	−	1.18116i	−0.0806690	−	0.996741i	$-0.525706\pi$
$642$		0			0
$643$	9.56983	−	5.52514i	0.377397	−	0.217890i	−0.299288	−	0.954163i	$-0.596749\pi$
$643$	9.56983	−	5.52514i	0.377397	−	0.217890i	0.676685	+	0.736272i	$0.263416\pi$
$644$	0.00163968	−	0.0156006i	6.46126e−5	−	0.000614748i
$645$		0			0
$646$	0.00706899	+	0.0672569i	0.000278126	+	0.00264619i
$647$	0.882610	+	1.21481i	0.0346990	+	0.0477591i	0.826014	−	0.563650i	$-0.190603\pi$
$647$	0.882610	+	1.21481i	0.0346990	+	0.0477591i	−0.791315	+	0.611409i	$0.790603\pi$
$648$		0			0
$649$	−18.8889			−0.741456
$650$	−0.372340	−	1.23460i	−0.0146044	−	0.0484250i
$651$		0			0
$652$	33.9965	+	30.6106i	1.33141	+	1.19880i
$653$	12.0567	−	27.0799i	0.471817	−	1.05972i	−0.508279	−	0.861192i	$-0.669718\pi$
$653$	12.0567	−	27.0799i	0.471817	−	1.05972i	0.980096	−	0.198525i	$-0.0636152\pi$
$654$		0			0
$655$	31.7348	+	29.1905i	1.23998	+	1.14057i
$656$	12.6887	+	9.21886i	0.495409	+	0.359936i
$657$		0			0
$658$	−0.0149730	+	0.0206086i	−0.000583709	+	0.000803407i
$659$	−8.36033	−	9.28509i	−0.325672	−	0.361696i	0.557968	−	0.829863i	$-0.311581\pi$
$659$	−8.36033	−	9.28509i	−0.325672	−	0.361696i	−0.883640	+	0.468167i	$0.844915\pi$
$660$		0			0
$661$	16.2741	−	18.0743i	0.632991	−	0.703007i	−0.338264	−	0.941051i	$-0.609840\pi$
$661$	16.2741	−	18.0743i	0.632991	−	0.703007i	0.971254	+	0.238044i	$0.0765062\pi$
$662$	−0.0153362	−	0.0721513i	−0.000596060	−	0.00280424i
$663$		0			0
$664$	−2.28179	−	0.485009i	−0.0885506	−	0.0188220i
$665$	−0.256429	−	0.0573595i	−0.00994389	−	0.00222430i
$666$		0			0
$667$	0.506158	−	0.696667i	0.0195985	−	0.0269751i
$668$	25.9194	+	14.9646i	1.00285	+	0.578998i
$669$		0			0
$670$	−0.125713	−	0.176952i	−0.00485672	−	0.00683627i
$671$	−16.7152	−	7.44208i	−0.645282	−	0.287298i
$672$		0			0
$673$	−7.77394	+	36.5735i	−0.299664	+	1.40981i	0.528316	+	0.849048i	$0.322824\pi$
$673$	−7.77394	+	36.5735i	−0.299664	+	1.40981i	−0.827980	+	0.560758i	$0.810510\pi$
$674$	0.998504			0.0384610
$675$		0			0
$676$	−5.69096			−0.218883
$677$	8.33296	−	39.2035i	0.320262	−	1.50671i	−0.463750	−	0.885966i	$-0.653496\pi$
$677$	8.33296	−	39.2035i	0.320262	−	1.50671i	0.784012	−	0.620746i	$-0.213170\pi$
$678$		0			0
$679$	−0.118819	−	0.0529014i	−0.00455984	−	0.00203017i
$680$	−0.347662	−	0.117060i	−0.0133322	−	0.00448904i
$681$		0			0
$682$	−0.486385	−	0.280815i	−0.0186247	−	0.0107530i
$683$	8.38112	−	11.5356i	0.320694	−	0.441398i	−0.617985	−	0.786190i	$-0.712051\pi$
$683$	8.38112	−	11.5356i	0.320694	−	0.441398i	0.938679	+	0.344792i	$0.112051\pi$
$684$		0			0
$685$	−1.76489	−	18.7008i	−0.0674329	−	0.714521i
$686$	−0.0632630	−	0.0134470i	−0.00241539	−	0.000513407i
$687$		0			0
$688$	−8.83112	−	41.5471i	−0.336683	−	1.58397i
$689$	−27.6194	+	30.6745i	−1.05222	+	1.16861i
$690$		0			0
$691$	−20.1988	−	22.4331i	−0.768399	−	0.853394i	0.224236	−	0.974535i	$-0.428011\pi$
$691$	−20.1988	−	22.4331i	−0.768399	−	0.853394i	−0.992635	+	0.121141i	$0.961345\pi$
$692$	24.2903	−	33.4327i	0.923378	−	1.27092i
$693$		0			0
$694$	−1.31967	−	0.958797i	−0.0500940	−	0.0363955i
$695$	3.26826	+	16.2215i	0.123972	+	0.615315i
$696$		0			0
$697$	−1.01722	+	2.28471i	−0.0385299	+	0.0865397i
$698$	1.75036	+	1.57603i	0.0662521	+	0.0596537i
$699$		0			0
$700$	0.430604	−	0.566943i	0.0162753	−	0.0214284i
$701$	−34.3156			−1.29608			−0.648041	−	0.761606i	$-0.724411\pi$
$701$	−34.3156			−1.29608			−0.648041	+	0.761606i	$0.724411\pi$
$702$		0			0
$703$	−3.39255	−	4.66945i	−0.127953	−	0.176112i
$704$	−1.21768	−	11.5855i	−0.0458931	−	0.436644i
$705$		0			0
$706$	0.0136985	−	0.130333i	0.000515550	−	0.00490514i
$707$	0.689021	−	0.397807i	0.0259133	−	0.0149611i
$708$		0			0
$709$	−23.9795	−	26.6319i	−0.900567	−	1.00018i	−0.999987	−	0.00513589i	$-0.998365\pi$
$709$	−23.9795	−	26.6319i	−0.900567	−	1.00018i	0.0994193	−	0.995046i	$-0.468301\pi$
$710$	1.08456	+	0.242600i	0.0407028	+	0.00910462i
$711$		0			0
$712$	2.77625	+	0.902057i	0.104044	+	0.0338060i
$713$	0.481343	−	0.433403i	0.0180264	−	0.0162311i
$714$		0			0
$715$	10.5388	+	7.82925i	0.394127	+	0.292797i
$716$	−1.04070	+	0.221207i	−0.0388926	+	0.00826688i
$717$		0			0
$718$	−0.833111	−	0.480997i	−0.0310914	−	0.0179506i
$719$	9.66447	+	7.02165i	0.360424	+	0.261863i	0.753229	−	0.657758i	$-0.228495\pi$
$719$	9.66447	+	7.02165i	0.360424	+	0.261863i	−0.392805	+	0.919622i	$0.628495\pi$
$720$		0			0
$721$	0.756362	−	0.549529i	0.0281684	−	0.0204655i
$722$	−1.04925	+	0.110280i	−0.0390489	+	0.00410421i
$723$		0			0
$724$	−1.46100	−	2.53052i	−0.0542975	−	0.0940461i
$725$	36.0331	−	15.1341i	1.33823	−	0.562065i
$726$		0			0
$727$	−0.115720	+	0.544418i	−0.00429180	+	0.0201913i	−0.980241	−	0.197805i	$-0.936619\pi$
$727$	−0.115720	+	0.544418i	−0.00429180	+	0.0201913i	0.975950	+	0.217996i	$0.0699521\pi$
$728$	0.0432148	+	0.0594801i	0.00160165	+	0.00220448i
$729$		0			0
$730$	1.03028	+	0.609514i	0.0381322	+	0.0225591i
$731$	6.18742	−	2.75482i	0.228850	−	0.101891i
$732$		0			0
$733$	29.4740	+	3.09784i	1.08865	+	0.114421i	0.631806	−	0.775127i	$-0.282314\pi$
$733$	29.4740	+	3.09784i	1.08865	+	0.114421i	0.456842	+	0.889548i	$0.348981\pi$
$734$	−1.36744	+	0.290657i	−0.0504730	+	0.0107284i
$735$		0			0
$736$	−0.0835321	−	0.0177553i	−0.00307903	−	0.000654469i
$737$	2.10175	+	0.682901i	0.0774190	+	0.0251550i
$738$		0			0
$739$	6.51854	+	20.0620i	0.239788	+	0.737993i	0.996450	+	0.0841861i	$0.0268290\pi$
$739$	6.51854	+	20.0620i	0.239788	+	0.737993i	−0.756662	+	0.653807i	$0.773171\pi$
$740$	15.3298	−	3.08861i	0.563534	−	0.113539i
$741$		0			0
$742$	0.0476495	+	0.00500817i	0.00174927	+	0.000183856i
$743$	4.00757	−	2.31377i	0.147023	−	0.0848840i	−0.424684	−	0.905342i	$-0.639615\pi$
$743$	4.00757	−	2.31377i	0.147023	−	0.0848840i	0.571707	+	0.820458i	$0.306281\pi$
$744$		0			0
$745$	13.8403	+	1.60350i	0.507068	+	0.0587476i
$746$	1.31212	−	0.953311i	0.0480401	−	0.0349032i
$747$		0			0
$748$	1.77414	−	0.576454i	0.0648690	−	0.0210772i
$749$	−0.148419	+	0.257069i	−0.00542310	+	0.00939308i
$750$		0			0
$751$	−11.3178	−	19.6029i	−0.412991	−	0.715322i	0.582224	−	0.813028i	$-0.302183\pi$
$751$	−11.3178	−	19.6029i	−0.412991	−	0.715322i	−0.995215	+	0.0977067i	$0.968849\pi$
$752$	−16.2821	−	14.6604i	−0.593745	−	0.534611i
$753$		0			0
$754$	0.210719	+	2.00486i	0.00767394	+	0.0730127i
$755$	14.1234	+	32.6509i	0.514004	+	1.18829i
$756$		0			0
$757$			21.3063i			0.774391i	0.921998	+	0.387195i	$0.126556\pi$
$757$			21.3063i			0.774391i	−0.921998	+	0.387195i	$0.873444\pi$
$758$	−0.782866	−	1.75835i	−0.0284350	−	0.0638660i
$759$		0			0
$760$	−0.304214	+	0.903502i	−0.0110350	+	0.0327735i
$761$	−30.3715	+	33.7310i	−1.10097	+	1.22275i	−0.128007	+	0.991773i	$0.540858\pi$
$761$	−30.3715	+	33.7310i	−1.10097	+	1.22275i	−0.972960	+	0.230974i	$0.925809\pi$
$762$		0			0
$763$	−0.468063	+	0.421446i	−0.0169450	+	0.0152574i
$764$	4.63747	+	14.2727i	0.167778	+	0.516367i
$765$		0			0
$766$	0.241252	−	0.742497i	0.00871679	−	0.0268275i
$767$	20.7422	+	46.5877i	0.748956	+	1.68218i
$768$		0			0
$769$	0.155093	−	1.47562i	0.00559281	−	0.0532120i	−0.991370	−	0.131097i	$-0.958150\pi$
$769$	0.155093	−	1.47562i	0.00559281	−	0.0532120i	0.996962	+	0.0778850i	$0.0248167\pi$
$770$	0.000161890	−	0.0152383i	5.83410e−6	−	0.000549151i
$771$		0			0
$772$	23.2974	−	2.44865i	0.838491	−	0.0881290i
$773$	−30.3917	+	9.87486i	−1.09311	+	0.355174i	−0.799449	−	0.600734i	$-0.794875\pi$
$773$	−30.3917	+	9.87486i	−1.09311	+	0.355174i	−0.293665	+	0.955908i	$0.594875\pi$
$774$		0			0
$775$	28.8773	−	5.49957i	1.03730	−	0.197550i
$776$	−0.235941	+	0.408663i	−0.00846980	+	0.0146701i
$777$		0			0
$778$	0.0179802	−	0.0403843i	0.000644623	−	0.00144785i
$779$	5.93750	+	2.64355i	0.212733	+	0.0947148i
$780$		0			0
$781$	−10.3366	+	4.60213i	−0.369871	+	0.164677i
$782$		−	0.00452321i		−	0.000161750i
$783$		0			0
$784$	8.59180	−	26.4428i	0.306850	−	0.944387i
$785$	0.305603	−	2.63775i	0.0109074	−	0.0941454i
$786$		0			0
$787$	5.04974	+	23.7572i	0.180004	+	0.846851i	0.971752	+	0.236004i	$0.0758378\pi$
$787$	5.04974	+	23.7572i	0.180004	+	0.846851i	−0.791748	+	0.610847i	$0.790829\pi$
$788$	−0.213676	−	1.00527i	−0.00761189	−	0.0358111i
$789$		0			0
$790$	0.135702	−	0.147530i	0.00482806	−	0.00524888i
$791$	0.371339	−	1.14287i	0.0132033	−	0.0406356i
$792$		0			0
$793$			49.3985i			1.75419i
$794$	−0.179230	+	0.0797985i	−0.00636065	+	0.00283194i
$795$		0			0
$796$	−40.4068	−	17.9903i	−1.43218	−	0.637648i
$797$	15.4295	−	34.6551i	0.546540	−	1.22755i	−0.403374	−	0.915035i	$-0.632163\pi$
$797$	15.4295	−	34.6551i	0.546540	−	1.22755i	0.949913	−	0.312513i	$-0.101171\pi$
$798$		0			0
$799$	1.74682	−	3.02558i	0.0617981	−	0.107037i
$800$	−2.82453	−	2.65402i	−0.0998622	−	0.0938338i
$801$		0			0
$802$	1.36219	−	0.442603i	0.0481006	−	0.0156288i
$803$	−12.1206	+	1.27393i	−0.427728	+	0.0449560i
$804$		0			0
$805$	0.0166561	+	0.00560820i	0.000587050	+	0.000197663i
$806$	−0.158496	+	1.50799i	−0.00558277	+	0.0531165i
$807$		0			0
$808$	−1.17407	−	2.63701i	−0.0413038	−	0.0927698i
$809$	7.34319	−	22.6000i	0.258173	−	0.794575i	−0.735015	−	0.678051i	$-0.762825\pi$
$809$	7.34319	−	22.6000i	0.258173	−	0.794575i	0.993188	−	0.116524i	$-0.0371751\pi$
$810$		0			0
$811$	−5.82121	−	17.9158i	−0.204410	−	0.629111i	−0.999737	−	0.0229295i	$-0.992701\pi$
$811$	−5.82121	−	17.9158i	−0.204410	−	0.629111i	0.795327	−	0.606181i	$-0.207299\pi$
$812$	−0.827085	+	0.744711i	−0.0290250	+	0.0261342i
$813$		0			0
$814$	0.223981	−	0.248756i	0.00785053	−	0.00871890i
$815$	−41.7831	+	29.6842i	−1.46360	+	1.03979i
$816$		0			0
$817$	−7.15920	−	16.0798i	−0.250469	−	0.562562i
$818$		−	0.202169i		−	0.00706868i
$819$		0			0
$820$	−13.2107	+	11.6432i	−0.461337	+	0.406599i
$821$	5.63534	+	53.6167i	0.196675	+	1.87123i	0.435523	+	0.900177i	$0.356563\pi$
$821$	5.63534	+	53.6167i	0.196675	+	1.87123i	−0.238849	+	0.971057i	$0.576770\pi$
$822$		0			0
$823$	−6.35539	−	5.72242i	−0.221535	−	0.199471i	0.550888	−	0.834579i	$-0.314289\pi$
$823$	−6.35539	−	5.72242i	−0.221535	−	0.199471i	−0.772423	+	0.635108i	$0.780956\pi$
$824$	−1.69599	−	2.93753i	−0.0590824	−	0.102334i
$825$		0			0
$826$	0.0295972	−	0.0512639i	0.00102982	−	0.00178370i
$827$	2.74216	−	0.890981i	0.0953542	−	0.0309825i	−0.260951	−	0.965352i	$-0.584036\pi$
$827$	2.74216	−	0.890981i	0.0953542	−	0.0309825i	0.356306	+	0.934369i	$0.384036\pi$
$828$		0			0
$829$	−4.16387	+	3.02523i	−0.144617	+	0.105070i	−0.657741	−	0.753244i	$-0.728488\pi$
$829$	−4.16387	+	3.02523i	−0.144617	+	0.105070i	0.513124	+	0.858314i	$0.328488\pi$
$830$	0.543603	−	1.18686i	0.0188687	−	0.0411964i
$831$		0			0
$832$	−27.2372	+	15.7254i	−0.944282	+	0.545181i
$833$	4.40919	+	0.463425i	0.152769	+	0.0160567i
$834$		0			0
$835$	−22.7009	+	24.6795i	−0.785596	+	0.854070i
$836$	−1.49808	−	4.61063i	−0.0518123	−	0.159462i
$837$		0			0
$838$	−0.565514	−	0.183747i	−0.0195354	−	0.00634742i
$839$	−29.1968	−	6.20596i	−1.00798	−	0.214254i	−0.325804	−	0.945438i	$-0.605635\pi$
$839$	−29.1968	−	6.20596i	−1.00798	−	0.214254i	−0.682180	+	0.731184i	$0.738968\pi$
$840$		0			0
$841$	−31.3955	+	6.67331i	−1.08260	+	0.230114i
$842$	1.60564	+	0.168759i	0.0553339	+	0.00581583i
$843$		0			0
$844$	−20.7970	+	9.25941i	−0.715862	+	0.318722i
$845$	1.39184	−	6.22230i	0.0478807	−	0.214054i
$846$		0			0
$847$	−0.370081	−	0.509373i	−0.0127161	−	0.0175023i
$848$	−8.56777	+	40.3082i	−0.294219	+	1.38419i
$849$		0			0
$850$	0.106397	−	0.175562i	0.00364937	−	0.00602171i
$851$	0.193020	+	0.334320i	0.00661663	+	0.0114603i
$852$		0			0
$853$	32.1569	−	3.37983i	1.10103	−	0.115723i	0.463463	−	0.886116i	$-0.346607\pi$
$853$	32.1569	−	3.37983i	1.10103	−	0.115723i	0.637569	+	0.770393i	$0.279940\pi$
$854$	0.0463887	−	0.0337033i	0.00158739	−	0.00115330i
$855$		0			0
$856$	0.871276	+	0.633019i	0.0297796	+	0.0216362i
$857$	−22.3973	−	12.9311i	−0.765078	−	0.441718i	0.0660377	−	0.997817i	$-0.478964\pi$
$857$	−22.3973	−	12.9311i	−0.765078	−	0.441718i	−0.831116	+	0.556099i	$0.812298\pi$
$858$		0			0
$859$	0.289557	−	0.0615473i	0.00987957	−	0.00209997i	−0.202969	−	0.979185i	$-0.565059\pi$
$859$	0.289557	−	0.0615473i	0.00987957	−	0.00209997i	0.212849	+	0.977085i	$0.431726\pi$
$860$	47.6865	+	0.506615i	1.62610	+	0.0172754i
$861$		0			0
$862$	−0.445680	+	0.401292i	−0.0151799	+	0.0136681i
$863$	51.9067	+	16.8655i	1.76692	+	0.574108i	0.997880	−	0.0650883i	$-0.0207329\pi$
$863$	51.9067	+	16.8655i	1.76692	+	0.574108i	0.769044	+	0.639196i	$0.220733\pi$
$864$		0			0
$865$	30.6135	+	34.7348i	1.04089	+	1.18102i
$866$	0.753741	+	0.837115i	0.0256132	+	0.0284463i
$867$		0			0
$868$	−0.724971	+	0.418562i	−0.0246071	+	0.0142069i
$869$	−0.213320	+	2.02960i	−0.00723638	+	0.0688495i
$870$		0			0
$871$	−0.623653	−	5.93366i	−0.0211317	−	0.201054i
$872$	1.34317	+	1.84871i	0.0454853	+	0.0626052i
$873$		0			0
$874$	−0.0117549			−0.000397615
$875$	0.514563	+	0.609465i	0.0173954	+	0.0206037i
$876$		0			0
$877$	−16.0777	−	14.4764i	−0.542905	−	0.488834i	0.351441	−	0.936210i	$-0.385692\pi$
$877$	−16.0777	−	14.4764i	−0.542905	−	0.488834i	−0.894346	+	0.447376i	$0.852359\pi$
$878$	0.577631	−	1.29738i	0.0194941	−	0.0437845i
$879$		0			0
$880$	13.0200	+	1.50846i	0.438904	+	0.0508503i
$881$	31.9847	+	23.2382i	1.07759	+	0.782916i	0.977261	−	0.212038i	$-0.0680100\pi$
$881$	31.9847	+	23.2382i	1.07759	+	0.782916i	0.100330	+	0.994954i	$0.468010\pi$
$882$		0			0
$883$	−2.46210	+	3.38880i	−0.0828564	+	0.114042i	−0.848433	−	0.529302i	$-0.822454\pi$
$883$	−2.46210	+	3.38880i	−0.0828564	+	0.114042i	0.765577	+	0.643345i	$0.222454\pi$
$884$	−3.36997	−	3.74273i	−0.113344	−	0.125882i
$885$		0			0
$886$	0.652076	−	0.724204i	0.0219069	−	0.0243301i
$887$	8.72061	+	41.0272i	0.292809	+	1.37756i	0.840923	+	0.541156i	$0.182013\pi$
$887$	8.72061	+	41.0272i	0.292809	+	1.37756i	−0.548113	+	0.836404i	$0.684654\pi$
$888$		0			0
$889$	−0.968273	−	0.205813i	−0.0324748	−	0.00690274i
$890$	−0.831758	+	1.40594i	−0.0278806	+	0.0471272i
$891$		0			0
$892$	25.6912	−	35.3609i	0.860206	−	1.18397i
$893$	−7.86287	−	4.53963i	−0.263121	−	0.151913i
$894$		0			0
$895$	0.0126632	−	1.19196i	0.000423285	−	0.0398429i
$896$	0.134392	+	0.0598353i	0.00448973	+	0.00199896i
$897$		0			0
$898$	−0.512694	+	2.41204i	−0.0171088	+	0.0804907i
$899$	−45.9549			−1.53268
$900$		0			0
$901$	−6.57101			−0.218912
$902$	−0.0783691	+	0.368698i	−0.00260941	+	0.0122763i
$903$		0			0
$904$	−3.98290	−	1.77330i	−0.132469	−	0.0589791i
$905$	3.12410	−	0.978514i	0.103849	−	0.0325269i
$906$		0			0
$907$	9.21024	+	5.31754i	0.305821	+	0.176566i	0.645055	−	0.764136i	$-0.276834\pi$
$907$	9.21024	+	5.31754i	0.305821	+	0.176566i	−0.339234	+	0.940702i	$0.610168\pi$
$908$	−19.5628	+	26.9259i	−0.649214	+	0.893566i
$909$		0			0
$910$	−0.0377615	+	0.0163341i	−0.00125178	+	0.000541470i
$911$	−30.8364	−	6.55448i	−1.02166	−	0.217160i	−0.333521	−	0.942743i	$-0.608237\pi$
$911$	−30.8364	−	6.55448i	−1.02166	−	0.217160i	−0.688135	+	0.725583i	$0.741570\pi$
$912$		0			0
$913$	2.76326	+	13.0001i	0.0914506	+	0.430241i
$914$	0.290477	−	0.322608i	0.00960814	−	0.0106709i
$915$		0			0
$916$	−4.53466	−	5.03625i	−0.149829	−	0.166402i
$917$	0.808620	−	1.11297i	0.0267030	−	0.0367535i
$918$		0			0
$919$	−1.89004	−	1.37319i	−0.0623466	−	0.0452974i	0.556175	−	0.831065i	$-0.312268\pi$
$919$	−1.89004	−	1.37319i	−0.0623466	−	0.0452974i	−0.618522	+	0.785767i	$0.712268\pi$
$920$	0.0265524	−	0.0579722i	0.000875405	−	0.00191129i
$921$		0			0
$922$	−0.461831	+	1.03729i	−0.0152096	+	0.0341613i
$923$	22.7014	+	20.4404i	0.747226	+	0.672805i
$924$		0			0
$925$	−0.372226	+	17.5164i	−0.0122387	+	0.575936i
$926$	1.25004			0.0410789
$927$		0			0
$928$	3.56138	+	4.90182i	0.116908	+	0.160910i
$929$	−4.88986	−	46.5239i	−0.160431	−	1.52640i	−0.717867	−	0.696180i	$-0.754882\pi$
$929$	−4.88986	−	46.5239i	−0.160431	−	1.52640i	0.557436	−	0.830220i	$-0.311785\pi$
$930$		0			0
$931$	1.20435	−	11.4586i	0.0394708	−	0.375540i
$932$	16.5685	−	9.56585i	0.542721	−	0.313340i
$933$		0			0
$934$	−1.45184	−	1.61243i	−0.0475057	−	0.0527605i
$935$	0.196372	+	2.08077i	0.00642207	+	0.0680484i
$936$		0			0
$937$	41.9492	+	13.6301i	1.37042	+	0.445277i	0.899509	−	0.436902i	$-0.143924\pi$
$937$	41.9492	+	13.6301i	1.37042	+	0.445277i	0.470913	+	0.882180i	$0.343924\pi$
$938$	−0.00514662	+	0.00463404i	−0.000168043	+	0.000151307i
$939$		0			0
$940$	20.0535	−	14.2467i	0.654075	−	0.464678i
$941$	44.5927	−	9.47847i	1.45368	−	0.308989i	0.587705	−	0.809075i	$-0.300032\pi$
$941$	44.5927	−	9.47847i	1.45368	−	0.308989i	0.865976	+	0.500086i	$0.166698\pi$
$942$		0			0
$943$	−0.376468	−	0.217354i	−0.0122595	−	0.00707801i
$944$	41.1892	+	29.9257i	1.34059	+	0.973999i
$945$		0			0
$946$	0.825851	−	0.600016i	0.0268507	−	0.0195082i
$947$	−16.3141	+	1.71469i	−0.530138	+	0.0557198i	−0.365817	−	0.930687i	$-0.619210\pi$
$947$	−16.3141	+	1.71469i	−0.530138	+	0.0557198i	−0.164322	+	0.986407i	$0.552544\pi$
$948$		0			0
$949$	16.4518	+	28.4954i	0.534048	+	0.924999i
$950$	−0.456248	−	0.276503i	−0.0148027	−	0.00897094i
$951$		0			0
$952$	−0.00243344	+	0.0114484i	−7.88682e−5	+	0.000371046i
$953$	−34.2399	−	47.1272i	−1.10914	−	1.52660i	−0.822678	−	0.568508i	$-0.807521\pi$
$953$	−34.2399	−	47.1272i	−1.10914	−	1.52660i	−0.286462	−	0.958092i	$-0.592479\pi$
$954$		0			0
$955$	−16.7394	+	1.57978i	−0.541675	+	0.0511206i
$956$	−30.2117	+	13.4511i	−0.977116	+	0.435040i
$957$		0			0
$958$	1.65348	+	0.173788i	0.0534215	+	0.00561482i
$959$	−0.586212	+	0.124603i	−0.0189298	+	0.00402365i
$960$		0			0
$961$	−3.48780	−	0.741355i	−0.112510	−	0.0239147i
$962$	−0.859488	−	0.279265i	−0.0277110	−	0.00900385i
$963$		0			0
$964$	10.6261	+	32.7039i	0.342245	+	1.05332i
$965$	−3.02057	+	26.0714i	−0.0972355	+	0.839269i
$966$		0			0
$967$	3.54196	+	0.372275i	0.113902	+	0.0119715i	0.161308	−	0.986904i	$-0.448429\pi$
$967$	3.54196	+	0.372275i	0.113902	+	0.0119715i	−0.0474061	+	0.998876i	$0.515095\pi$
$968$	−1.97828	+	1.14216i	−0.0635845	+	0.0367105i
$969$		0			0
$970$	−0.194352	−	0.178770i	−0.00624028	−	0.00573997i
$971$	−21.5571	+	15.6621i	−0.691799	+	0.502621i	−0.877251	−	0.480032i	$-0.840625\pi$
$971$	−21.5571	+	15.6621i	−0.691799	+	0.502621i	0.185452	+	0.982653i	$0.440625\pi$
$972$		0			0
$973$	0.502113	−	0.163146i	0.0160970	−	0.00523023i
$974$	0.274334	−	0.475161i	0.00879024	−	0.0152251i
$975$		0			0
$976$	24.6586	+	42.7100i	0.789304	+	1.36711i
$977$	11.6480	+	10.4879i	0.372652	+	0.335537i	0.834083	−	0.551639i	$-0.185997\pi$
$977$	11.6480	+	10.4879i	0.372652	+	0.335537i	−0.461431	+	0.887176i	$0.652664\pi$
$978$		0			0
$979$	−1.73843	−	16.5401i	−0.0555606	−	0.528624i
$980$	26.8670	+	15.8946i	0.858235	+	0.507734i
$981$		0			0
$982$			0.470597i			0.0150173i
$983$	−2.33894	−	5.25335i	−0.0746007	−	0.167556i	0.872396	−	0.488801i	$-0.162565\pi$
$983$	−2.33894	−	5.25335i	−0.0746007	−	0.167556i	−0.946996	+	0.321245i	$0.895899\pi$
$984$		0			0
$985$	1.15138	+	0.0122321i	0.0366861	+	0.000389748i
$986$	−0.214738	+	0.238490i	−0.00683864	+	0.00759508i
$987$		0			0
$988$	−9.72659	+	8.75786i	−0.309444	+	0.278625i
$989$	0.363796	+	1.11965i	0.0115680	+	0.0356027i
$990$		0			0
$991$	12.0898	−	37.2087i	0.384046	−	1.18197i	−0.553124	−	0.833099i	$-0.686564\pi$
$991$	12.0898	−	37.2087i	0.384046	−	1.18197i	0.937170	−	0.348873i	$-0.113436\pi$
$992$	1.85365	+	4.16336i	0.0588533	+	0.132187i
$993$		0			0
$994$	0.00370641	−	0.0352642i	0.000117560	−	0.00111851i
$995$	29.5522	−	39.7795i	0.936869	−	1.26110i
$996$		0			0
$997$	−24.2200	+	2.54562i	−0.767054	+	0.0806207i	−0.479970	−	0.877285i	$-0.659353\pi$
$997$	−24.2200	+	2.54562i	−0.767054	+	0.0806207i	−0.287084	+	0.957905i	$0.592686\pi$
$998$	−2.28443	+	0.742258i	−0.0723125	+	0.0234958i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.15		224
3.2	odd	2		225.2.u.a.169.14	yes	224
9.4	even	3	inner	675.2.y.a.469.15		224
9.5	odd	6		225.2.u.a.94.14	yes	224
25.4	even	10	inner	675.2.y.a.154.15		224
75.29	odd	10		225.2.u.a.79.14	yes	224
225.4	even	30	inner	675.2.y.a.604.15		224
225.104	odd	30		225.2.u.a.4.14	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.14	✓	224	225.104	odd	30
225.2.u.a.79.14	yes	224	75.29	odd	10
225.2.u.a.94.14	yes	224	9.5	odd	6
225.2.u.a.169.14	yes	224	3.2	odd	2
675.2.y.a.19.15		224	1.1	even	1	trivial
675.2.y.a.154.15		224	25.4	even	10	inner
675.2.y.a.469.15		224	9.4	even	3	inner
675.2.y.a.604.15		224	225.4	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0134680 - 0.0633621i) q^{2} +(1.82326 + 0.811767i) q^{4} +(-1.33347 + 1.79495i) q^{5} +(0.0617846 + 0.0356713i) q^{7} +(0.152142 - 0.209405i) q^{8} +O(q^{10})\)	\(q+(0.0134680 - 0.0633621i) q^{2} +(1.82326 + 0.811767i) q^{4} +(-1.33347 + 1.79495i) q^{5} +(0.0617846 + 0.0356713i) q^{7} +(0.152142 - 0.209405i) q^{8} +(0.0957728 + 0.108666i) q^{10} +(-1.44247 - 0.306606i) q^{11} +(0.827777 + 3.89439i) q^{13} +(0.00309233 - 0.00343438i) q^{14} +(2.65969 + 2.95388i) q^{16} +(-0.372547 + 0.512767i) q^{17} +(1.33258 + 0.968174i) q^{19} +(-3.88834 + 2.19019i) q^{20} +(-0.0388544 + 0.0872684i) q^{22} +(-0.0818713 - 0.0737173i) q^{23} +(-1.44371 - 4.78704i) q^{25} +0.257905 q^{26} +(0.0836924 + 0.115193i) q^{28} +(0.817041 + 7.77363i) q^{29} +(-0.614550 + 5.84705i) q^{31} +(0.671307 - 0.387579i) q^{32} +(0.0274725 + 0.0305114i) q^{34} +(-0.146416 + 0.0633337i) q^{35} +(-3.33257 - 1.08282i) q^{37} +(0.0792927 - 0.0713955i) q^{38} +(0.172996 + 0.552323i) q^{40} +(3.85961 - 0.820385i) q^{41} +(-9.25438 - 5.34302i) q^{43} +(-2.38110 - 1.72997i) q^{44} +(-0.00577353 + 0.00419471i) q^{46} +(-5.48189 + 0.576170i) q^{47} +(-3.49746 - 6.05777i) q^{49} +(-0.322761 + 0.0270045i) q^{50} +(-1.65208 + 7.77243i) q^{52} +(6.09380 + 8.38739i) q^{53} +(2.47383 - 2.18031i) q^{55} +(0.0168698 - 0.00751091i) q^{56} +(0.503558 + 0.0529260i) q^{58} +(12.5288 - 2.66308i) q^{59} +(12.1362 + 2.57963i) q^{61} +(0.362205 + 0.117688i) q^{62} +(2.44107 + 7.51284i) q^{64} +(-8.09406 - 3.70723i) q^{65} +(-1.49035 - 0.156642i) q^{67} +(-1.09550 + 0.632485i) q^{68} +(0.00204102 + 0.0101302i) q^{70} +(6.20729 - 4.50986i) q^{71} +(7.85987 - 2.55383i) q^{73} +(-0.113493 + 0.196576i) q^{74} +(1.64370 + 2.84697i) q^{76} +(-0.0781852 - 0.0703983i) q^{77} +(-0.144654 - 1.37629i) q^{79} +(-8.84870 + 0.835096i) q^{80} -0.255602i q^{82} +(-3.66568 - 8.23326i) q^{83} +(-0.423612 - 1.35246i) q^{85} +(-0.463184 + 0.514418i) q^{86} +(-0.283664 + 0.255412i) q^{88} +(3.48501 + 10.7258i) q^{89} +(-0.0877741 + 0.270141i) q^{91} +(-0.0894313 - 0.200866i) q^{92} +(-0.0373229 + 0.355104i) q^{94} +(-3.51478 + 1.10088i) q^{95} +(-1.81309 + 0.190563i) q^{97} +(-0.430937 + 0.140020i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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