LMFDB - Embedded newform 675.2.r.a.46.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, 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 $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.13
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.349998 - 0.388712i) q^{2} +(0.180458 - 1.71695i) q^{4} +(0.130882 - 2.23223i) q^{5} +(-1.68864 + 2.92481i) q^{7} +(-1.57689 + 1.14568i) q^{8} +O(q^{10})$	\(q+(-0.349998 - 0.388712i) q^{2} +(0.180458 - 1.71695i) q^{4} +(0.130882 - 2.23223i) q^{5} +(-1.68864 + 2.92481i) q^{7} +(-1.57689 + 1.14568i) q^{8} +(-0.913505 + 0.730402i) q^{10} +(-2.76572 - 3.07165i) q^{11} +(-3.39970 + 3.77575i) q^{13} +(1.72793 - 0.367283i) q^{14} +(-2.38011 - 0.505907i) q^{16} +(-0.0810977 + 0.0589209i) q^{17} +(2.55513 - 1.85641i) q^{19} +(-3.80901 - 0.627543i) q^{20} +(-0.225989 + 2.15014i) q^{22} +(-1.92791 + 0.409791i) q^{23} +(-4.96574 - 0.584319i) q^{25} +2.65757 q^{26} +(4.71702 + 3.42711i) q^{28} +(-6.19799 + 2.75952i) q^{29} +(2.22457 + 0.990444i) q^{31} +(2.58553 + 4.47827i) q^{32} +(0.0512873 + 0.0109015i) q^{34} +(6.30785 + 4.15225i) q^{35} +(0.930291 + 2.86314i) q^{37} +(-1.61590 - 0.343471i) q^{38} +(2.35104 + 3.66994i) q^{40} +(3.88818 - 4.31827i) q^{41} +(5.61908 - 9.73253i) q^{43} +(-5.77296 + 4.19430i) q^{44} +(0.834057 + 0.605978i) q^{46} +(-8.50718 + 3.78764i) q^{47} +(-2.20301 - 3.81573i) q^{49} +(1.51087 + 2.13475i) q^{50} +(5.86925 + 6.51846i) q^{52} +(-1.84804 - 1.34268i) q^{53} +(-7.21862 + 5.77172i) q^{55} +(-0.688092 - 6.54676i) q^{56} +(3.24195 + 1.44341i) q^{58} +(-5.66566 + 6.29235i) q^{59} +(2.32441 + 2.58152i) q^{61} +(-0.393599 - 1.21137i) q^{62} +(-0.668023 + 2.05596i) q^{64} +(7.98339 + 8.08310i) q^{65} +(-12.3948 - 5.51853i) q^{67} +(0.0865293 + 0.149873i) q^{68} +(-0.593706 - 3.90522i) q^{70} +(-6.75154 - 4.90528i) q^{71} +(3.28345 - 10.1054i) q^{73} +(0.787338 - 1.36371i) q^{74} +(-2.72627 - 4.72203i) q^{76} +(13.6543 - 2.90231i) q^{77} +(-13.1297 + 5.84572i) q^{79} +(-1.44082 + 5.24674i) q^{80} -3.03942 q^{82} +(-0.648356 - 6.16870i) q^{83} +(0.120911 + 0.188741i) q^{85} +(-5.74982 + 1.22216i) q^{86} +(7.88038 + 1.67503i) q^{88} +(2.14728 - 6.60864i) q^{89} +(-5.30248 - 16.3193i) q^{91} +(0.355681 + 3.38408i) q^{92} +(4.44980 + 1.98118i) q^{94} +(-3.80953 - 5.94663i) q^{95} +(-1.59492 + 0.710105i) q^{97} +(-0.712171 + 2.19184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.349998	−	0.388712i	−0.247486	−	0.274861i	0.606584	−	0.795020i	$-0.292539\pi$
$2$	−0.349998	−	0.388712i	−0.247486	−	0.274861i	−0.854070	+	0.520159i	$0.825873\pi$
$3$		0			0
$3$		0			0
$4$	0.180458	−	1.71695i	0.0902292	−	0.858473i
$5$	0.130882	−	2.23223i	0.0585323	−	0.998286i
$5$	0.130882	−	2.23223i	0.0585323	−	0.998286i
$6$		0			0
$7$	−1.68864	+	2.92481i	−0.638246	+	1.10547i	0.347571	+	0.937654i	$0.387006\pi$
$7$	−1.68864	+	2.92481i	−0.638246	+	1.10547i	−0.985817	+	0.167821i	$0.946327\pi$
$8$	−1.57689	+	1.14568i	−0.557516	+	0.405059i
$9$		0			0
$10$	−0.913505	+	0.730402i	−0.288876	+	0.230973i
$11$	−2.76572	−	3.07165i	−0.833897	−	0.926137i	0.164284	−	0.986413i	$-0.447469\pi$
$11$	−2.76572	−	3.07165i	−0.833897	−	0.926137i	−0.998182	+	0.0602761i	$0.980802\pi$
$12$		0			0
$13$	−3.39970	+	3.77575i	−0.942906	+	1.04720i	0.0559039	+	0.998436i	$0.482196\pi$
$13$	−3.39970	+	3.77575i	−0.942906	+	1.04720i	−0.998810	+	0.0487673i	$0.984471\pi$
$14$	1.72793	−	0.367283i	0.461809	−	0.0981605i
$15$		0			0
$16$	−2.38011	−	0.505907i	−0.595027	−	0.126477i
$17$	−0.0810977	+	0.0589209i	−0.0196691	+	0.0142904i	−0.597576	−	0.801812i	$-0.703870\pi$
$17$	−0.0810977	+	0.0589209i	−0.0196691	+	0.0142904i	0.577907	+	0.816102i	$0.303870\pi$
$18$		0			0
$19$	2.55513	−	1.85641i	0.586188	−	0.425890i	−0.254762	−	0.967004i	$-0.581997\pi$
$19$	2.55513	−	1.85641i	0.586188	−	0.425890i	0.840950	+	0.541113i	$0.181997\pi$
$20$	−3.80901	−	0.627543i	−0.851720	−	0.140323i
$21$		0			0
$22$	−0.225989	+	2.15014i	−0.0481810	+	0.458412i
$23$	−1.92791	+	0.409791i	−0.401998	+	0.0854473i	−0.404474	−	0.914550i	$-0.632545\pi$
$23$	−1.92791	+	0.409791i	−0.401998	+	0.0854473i	0.00247582	+	0.999997i	$0.499212\pi$
$24$		0			0
$25$	−4.96574	−	0.584319i	−0.993148	−	0.116864i
$26$	2.65757			0.521192
$27$		0			0
$28$	4.71702	+	3.42711i	0.891432	+	0.647663i
$29$	−6.19799	+	2.75952i	−1.15094	+	0.512431i	−0.891362	−	0.453292i	$-0.850250\pi$
$29$	−6.19799	+	2.75952i	−1.15094	+	0.512431i	−0.259576	+	0.965723i	$0.583583\pi$
$30$		0			0
$31$	2.22457	+	0.990444i	0.399545	+	0.177889i	0.596665	−	0.802490i	$-0.296492\pi$
$31$	2.22457	+	0.990444i	0.399545	+	0.177889i	−0.197120	+	0.980379i	$0.563159\pi$
$32$	2.58553	+	4.47827i	0.457061	+	0.791653i
$33$		0			0
$34$	0.0512873	+	0.0109015i	0.00879570	+	0.00186958i
$35$	6.30785	+	4.15225i	1.06622	+	0.701858i
$36$		0			0
$37$	0.930291	+	2.86314i	0.152939	+	0.470698i	0.997946	−	0.0640571i	$-0.0204040\pi$
$37$	0.930291	+	2.86314i	0.152939	+	0.470698i	−0.845007	+	0.534755i	$0.820404\pi$
$38$	−1.61590	−	0.343471i	−0.262134	−	0.0557183i
$39$		0			0
$40$	2.35104	+	3.66994i	0.371732	+	0.580269i
$41$	3.88818	−	4.31827i	0.607232	−	0.674400i	−0.358623	−	0.933483i	$-0.616754\pi$
$41$	3.88818	−	4.31827i	0.607232	−	0.674400i	0.965855	+	0.259083i	$0.0834203\pi$
$42$		0			0
$43$	5.61908	−	9.73253i	0.856902	−	1.48420i	−0.0179676	−	0.999839i	$-0.505720\pi$
$43$	5.61908	−	9.73253i	0.856902	−	1.48420i	0.874869	−	0.484359i	$-0.160947\pi$
$44$	−5.77296	+	4.19430i	−0.870306	+	0.632314i
$45$		0			0
$46$	0.834057	+	0.605978i	0.122975	+	0.0893465i
$47$	−8.50718	+	3.78764i	−1.24090	+	0.552484i	−0.918988	−	0.394286i	$-0.870992\pi$
$47$	−8.50718	+	3.78764i	−1.24090	+	0.552484i	−0.321912	+	0.946770i	$0.604325\pi$
$48$		0			0
$49$	−2.20301	−	3.81573i	−0.314716	−	0.545105i
$50$	1.51087	+	2.13475i	0.213669	+	0.301900i
$51$		0			0
$52$	5.86925	+	6.51846i	0.813919	+	0.903948i
$53$	−1.84804	−	1.34268i	−0.253848	−	0.184432i	0.453582	−	0.891214i	$-0.350146\pi$
$53$	−1.84804	−	1.34268i	−0.253848	−	0.184432i	−0.707431	+	0.706783i	$0.750146\pi$
$54$		0			0
$55$	−7.21862	+	5.77172i	−0.973359	+	0.778259i
$56$	−0.688092	−	6.54676i	−0.0919502	−	0.874847i
$57$		0			0
$58$	3.24195	+	1.44341i	0.425689	+	0.189529i
$59$	−5.66566	+	6.29235i	−0.737606	+	0.819195i	−0.988879	−	0.148722i	$-0.952484\pi$
$59$	−5.66566	+	6.29235i	−0.737606	+	0.819195i	0.251273	+	0.967916i	$0.419151\pi$
$60$		0			0
$61$	2.32441	+	2.58152i	0.297610	+	0.330530i	0.873341	−	0.487110i	$-0.161949\pi$
$61$	2.32441	+	2.58152i	0.297610	+	0.330530i	−0.575730	+	0.817640i	$0.695282\pi$
$62$	−0.393599	−	1.21137i	−0.0499871	−	0.153844i
$63$		0			0
$64$	−0.668023	+	2.05596i	−0.0835028	+	0.256995i
$65$	7.98339	+	8.08310i	0.990218	+	1.00258i
$66$		0			0
$67$	−12.3948	−	5.51853i	−1.51427	−	0.674195i	−0.529538	−	0.848286i	$-0.677635\pi$
$67$	−12.3948	−	5.51853i	−1.51427	−	0.674195i	−0.984730	+	0.174091i	$0.944301\pi$
$68$	0.0865293	+	0.149873i	0.0104932	+	0.0181748i
$69$		0			0
$70$	−0.593706	−	3.90522i	−0.0709615	−	0.466763i
$71$	−6.75154	−	4.90528i	−0.801260	−	0.582149i	0.110024	−	0.993929i	$-0.464907\pi$
$71$	−6.75154	−	4.90528i	−0.801260	−	0.582149i	−0.911283	+	0.411780i	$0.864907\pi$
$72$		0			0
$73$	3.28345	−	10.1054i	0.384299	−	1.18275i	−0.552689	−	0.833387i	$-0.686398\pi$
$73$	3.28345	−	10.1054i	0.384299	−	1.18275i	0.936988	−	0.349362i	$-0.113602\pi$
$74$	0.787338	−	1.36371i	0.0915262	−	0.158528i
$75$		0			0
$76$	−2.72627	−	4.72203i	−0.312724	−	0.541654i
$77$	13.6543	−	2.90231i	1.55605	−	0.330749i
$78$		0			0
$79$	−13.1297	+	5.84572i	−1.47721	+	0.657695i	−0.977965	−	0.208767i	$-0.933055\pi$
$79$	−13.1297	+	5.84572i	−1.47721	+	0.657695i	−0.499243	+	0.866462i	$0.666388\pi$
$80$	−1.44082	+	5.24674i	−0.161088	+	0.586604i
$81$		0			0
$82$	−3.03942			−0.335648
$83$	−0.648356	−	6.16870i	−0.0711664	−	0.677103i	−0.970707	−	0.240266i	$-0.922765\pi$
$83$	−0.648356	−	6.16870i	−0.0711664	−	0.677103i	0.899541	−	0.436837i	$-0.143901\pi$
$84$		0			0
$85$	0.120911	+	0.188741i	0.0131146	+	0.0204718i
$86$	−5.74982	+	1.22216i	−0.620019	+	0.131789i
$87$		0			0
$88$	7.88038	+	1.67503i	0.840051	+	0.178558i
$89$	2.14728	−	6.60864i	0.227611	−	0.700514i	−0.770405	−	0.637555i	$-0.779946\pi$
$89$	2.14728	−	6.60864i	0.227611	−	0.700514i	0.998016	−	0.0629597i	$-0.0200540\pi$
$90$		0			0
$91$	−5.30248	−	16.3193i	−0.555851	−	1.71073i
$92$	0.355681	+	3.38408i	0.0370823	+	0.352814i
$93$		0			0
$94$	4.44980	+	1.98118i	0.458962	+	0.204343i
$95$	−3.80953	−	5.94663i	−0.390849	−	0.610111i
$96$		0			0
$97$	−1.59492	+	0.710105i	−0.161940	+	0.0721002i	−0.486106	−	0.873900i	$-0.661583\pi$
$97$	−1.59492	+	0.710105i	−0.161940	+	0.0721002i	0.324166	+	0.946000i	$0.394916\pi$
$98$	−0.712171	+	2.19184i	−0.0719402	+	0.221409i
$99$		0			0
$100$	−1.89935	+	8.42047i	−0.189935	+	0.842047i
$101$	6.20087	−	10.7402i	0.617010	−	1.06869i	−0.373019	−	0.927824i	$-0.621677\pi$
$101$	6.20087	−	10.7402i	0.617010	−	1.06869i	0.990028	−	0.140868i	$-0.0449894\pi$
$102$		0			0
$103$	−0.915698	+	8.71228i	−0.0902264	+	0.858447i	0.852016	+	0.523516i	$0.175380\pi$
$103$	−0.915698	+	8.71228i	−0.0902264	+	0.858447i	−0.942243	+	0.334931i	$0.891287\pi$
$104$	1.03516	−	9.84891i	0.101506	−	0.965765i
$105$		0			0
$106$	0.124895	+	1.18829i	0.0121308	+	0.115417i
$107$	−3.09879			−0.299571			−0.149786	−	0.988718i	$-0.547858\pi$
$107$	−3.09879			−0.299571			−0.149786	+	0.988718i	$0.547858\pi$
$108$		0			0
$109$	−0.863050	−	2.65620i	−0.0826652	−	0.254417i	0.901178	−	0.433449i	$-0.142704\pi$
$109$	−0.863050	−	2.65620i	−0.0826652	−	0.254417i	−0.983843	+	0.179032i	$0.942704\pi$
$110$	4.77004	+	0.785876i	0.454806	+	0.0749303i
$111$		0			0
$112$	5.49883	−	6.10707i	0.519590	−	0.577064i
$113$	5.57890	−	6.19600i	0.524819	−	0.582870i	−0.421206	−	0.906965i	$-0.638393\pi$
$113$	5.57890	−	6.19600i	0.524819	−	0.582870i	0.946025	+	0.324095i	$0.105060\pi$
$114$		0			0
$115$	0.662419	+	4.35719i	0.0617709	+	0.406310i
$116$	3.61948	+	11.1396i	0.336060	+	1.03429i
$117$		0			0
$118$	4.42888			0.407712
$119$	−0.0353877	−	0.336692i	−0.00324399	−	0.0308645i
$120$		0			0
$121$	−0.635978	+	6.05093i	−0.0578162	+	0.550085i
$122$	0.189929	−	1.80705i	0.0171954	−	0.163603i
$123$		0			0
$124$	2.10198	−	3.64074i	0.188764	−	0.326948i
$125$	−1.95426	+	11.0082i	−0.174795	+	0.984605i
$126$		0			0
$127$	2.69804	−	8.30372i	0.239412	−	0.736836i	−0.757093	−	0.653307i	$-0.773381\pi$
$127$	2.69804	−	8.30372i	0.239412	−	0.736836i	0.996505	−	0.0835285i	$-0.0266189\pi$
$128$	10.4810	−	4.66643i	0.926396	−	0.412458i
$129$		0			0
$130$	0.347828	−	5.93231i	0.0305065	−	0.520298i
$131$	−0.853198	−	0.379868i	−0.0745443	−	0.0331893i	0.369126	−	0.929379i	$-0.379657\pi$
$131$	−0.853198	−	0.379868i	−0.0745443	−	0.0331893i	−0.443670	+	0.896190i	$0.646324\pi$
$132$		0			0
$133$	1.11496	+	10.6081i	0.0966790	+	0.919839i
$134$	2.19304	+	6.74949i	0.189450	+	0.583067i
$135$		0			0
$136$	0.0603779	−	0.185824i	0.00517736	−	0.0159343i
$137$	6.06883	+	1.28997i	0.518495	+	0.110210i	0.459724	−	0.888062i	$-0.347948\pi$
$137$	6.06883	+	1.28997i	0.518495	+	0.110210i	0.0587713	+	0.998271i	$0.481282\pi$
$138$		0			0
$139$	5.58874	−	1.18792i	0.474031	−	0.100758i	0.0352997	−	0.999377i	$-0.488761\pi$
$139$	5.58874	−	1.18792i	0.474031	−	0.100758i	0.438731	+	0.898618i	$0.355428\pi$
$140$	8.26749	−	10.0809i	0.698731	−	0.851995i
$141$		0			0
$142$	0.456283	+	4.34124i	0.0382904	+	0.364309i
$143$	21.0004			1.75614
$144$		0			0
$145$	5.34870	+	14.1965i	0.444185	+	1.17896i
$146$	−5.07730	+	2.26056i	−0.420200	+	0.187085i
$147$		0			0
$148$	5.08374	−	1.08058i	0.417881	−	0.0888234i
$149$	10.5541	+	18.2802i	0.864623	+	1.49757i	0.867421	+	0.497575i	$0.165776\pi$
$149$	10.5541	+	18.2802i	0.864623	+	1.49757i	−0.00279771	+	0.999996i	$0.500891\pi$
$150$		0			0
$151$	8.84475	−	15.3196i	0.719776	−	1.24669i	−0.241313	−	0.970447i	$-0.577578\pi$
$151$	8.84475	−	15.3196i	0.719776	−	1.24669i	0.961088	−	0.276241i	$-0.0890888\pi$
$152$	−1.90232	+	5.85473i	−0.154298	+	0.474882i
$153$		0			0
$154$	−5.90715	−	4.29179i	−0.476011	−	0.345843i
$155$	2.50206	−	4.83614i	0.200970	−	0.388448i
$156$		0			0
$157$	0.489023	+	0.847013i	0.0390283	+	0.0675990i	0.884880	−	0.465820i	$-0.154240\pi$
$157$	0.489023	+	0.847013i	0.0390283	+	0.0675990i	−0.845851	+	0.533419i	$0.820907\pi$
$158$	6.86768	+	3.05769i	0.546363	+	0.243257i
$159$		0			0
$160$	10.3349	−	5.18538i	0.817049	−	0.409940i
$161$	2.05699	−	6.33077i	0.162114	−	0.498935i
$162$		0			0
$163$	3.86004	+	11.8800i	0.302341	+	0.930511i	0.980656	+	0.195740i	$0.0627107\pi$
$163$	3.86004	+	11.8800i	0.302341	+	0.930511i	−0.678314	+	0.734772i	$0.737289\pi$
$164$	−6.71258	−	7.45507i	−0.524164	−	0.582143i
$165$		0			0
$166$	−2.17093	+	2.41106i	−0.168496	+	0.187134i
$167$	−17.9693	−	8.00045i	−1.39051	−	0.619094i	−0.431406	−	0.902158i	$-0.641982\pi$
$167$	−17.9693	−	8.00045i	−1.39051	−	0.619094i	−0.959101	+	0.283064i	$0.908649\pi$
$168$		0			0
$169$	−1.33945	−	12.7440i	−0.103034	−	0.980307i
$170$	0.0310472	−	0.113058i	0.00238121	−	0.00867119i
$171$		0			0
$172$	−15.6962	−	11.4040i	−1.19683	−	0.869545i
$173$	−2.53963	−	2.82054i	−0.193084	−	0.214442i	0.638827	−	0.769350i	$-0.279420\pi$
$173$	−2.53963	−	2.82054i	−0.193084	−	0.214442i	−0.831911	+	0.554908i	$0.812753\pi$
$174$		0			0
$175$	10.0944	−	13.5371i	0.763063	−	1.02331i
$176$	5.02875	+	8.71005i	0.379056	+	0.656545i
$177$		0			0
$178$	−3.32040	+	1.47834i	−0.248875	+	0.110806i
$179$	−3.68369	−	2.67636i	−0.275332	−	0.200040i	0.441547	−	0.897238i	$-0.354430\pi$
$179$	−3.68369	−	2.67636i	−0.275332	−	0.200040i	−0.716879	+	0.697198i	$0.754430\pi$
$180$		0			0
$181$	15.5083	−	11.2674i	1.15272	−	0.837501i	0.163881	−	0.986480i	$-0.447599\pi$
$181$	15.5083	−	11.2674i	1.15272	−	0.837501i	0.988840	+	0.148979i	$0.0475988\pi$
$182$	−4.48767	+	7.77288i	−0.332648	+	0.576164i
$183$		0			0
$184$	2.57063	−	2.85497i	0.189509	−	0.210471i
$185$	6.51296	−	1.70189i	0.478843	−	0.125126i
$186$		0			0
$187$	0.405278	+	0.0861445i	0.0296369	+	0.00629951i
$188$	4.96798	+	15.2899i	0.362328	+	1.11513i
$189$		0			0
$190$	−0.978200	+	3.56212i	−0.0709661	+	0.258423i
$191$	−17.1993	−	3.65583i	−1.24450	−	0.264526i	−0.461832	−	0.886968i	$-0.652808\pi$
$191$	−17.1993	−	3.65583i	−1.24450	−	0.264526i	−0.782666	+	0.622441i	$0.786141\pi$
$192$		0			0
$193$	−9.88753	−	17.1257i	−0.711720	−	1.23273i	−0.964211	−	0.265136i	$-0.914583\pi$
$193$	−9.88753	−	17.1257i	−0.711720	−	1.23273i	0.252491	−	0.967599i	$-0.418750\pi$
$194$	0.834246	+	0.371430i	0.0598954	+	0.0266671i
$195$		0			0
$196$	−6.94896	+	3.09388i	−0.496354	+	0.220991i
$197$	−0.487820	−	0.354422i	−0.0347558	−	0.0252515i	0.570272	−	0.821456i	$-0.306838\pi$
$197$	−0.487820	−	0.354422i	−0.0347558	−	0.0252515i	−0.605028	+	0.796205i	$0.706838\pi$
$198$		0			0
$199$	−18.7806			−1.33132			−0.665659	−	0.746256i	$-0.731850\pi$
$199$	−18.7806			−1.33132			−0.665659	+	0.746256i	$0.731850\pi$
$200$	8.49989	−	4.76774i	0.601033	−	0.337130i
$201$		0			0
$202$	−6.34515	+	1.34870i	−0.446443	+	0.0948944i
$203$	2.39510	−	22.7878i	0.168103	−	1.59939i
$204$		0			0
$205$	−9.13049	−	9.24452i	−0.637701	−	0.645665i
$206$	3.70706	−	2.69334i	0.258283	−	0.187654i
$207$		0			0
$208$	10.0018	−	7.26675i	0.693501	−	0.503858i
$209$	−12.7690	−	2.71414i	−0.883254	−	0.187741i
$210$		0			0
$211$	16.2367	−	3.45121i	1.11778	−	0.237591i	0.388259	−	0.921550i	$-0.373077\pi$
$211$	16.2367	−	3.45121i	1.11778	−	0.237591i	0.729520	+	0.683959i	$0.239743\pi$
$212$	−2.63881	+	2.93069i	−0.181234	+	0.201281i
$213$		0			0
$214$	1.08457	+	1.20454i	0.0741397	+	0.0823405i
$215$	−20.9899	−	13.8169i	−1.43150	−	0.942306i
$216$		0			0
$217$	−6.65336	+	4.83395i	−0.451660	+	0.328150i
$218$	−0.730430	+	1.26514i	−0.0494709	+	0.0856862i
$219$		0			0
$220$	8.60708	+	13.4355i	0.580289	+	0.905824i
$221$	0.0532371	−	0.506517i	0.00358112	−	0.0340720i
$222$		0			0
$223$	1.96044	+	2.17729i	0.131281	+	0.145802i	0.805201	−	0.593002i	$-0.202057\pi$
$223$	1.96044	+	2.17729i	0.131281	+	0.145802i	−0.673920	+	0.738804i	$0.735391\pi$
$224$	−17.4641			−1.16687
$225$		0			0
$226$	−4.36106			−0.290094
$227$	14.7974	+	16.4341i	0.982135	+	1.09077i	0.995863	+	0.0908658i	$0.0289634\pi$
$227$	14.7974	+	16.4341i	0.982135	+	1.09077i	−0.0137281	+	0.999906i	$0.504370\pi$
$228$		0			0
$229$	1.89375	−	18.0179i	0.125143	−	1.19065i	−0.734084	−	0.679059i	$-0.762388\pi$
$229$	1.89375	−	18.0179i	0.125143	−	1.19065i	0.859226	−	0.511595i	$-0.170945\pi$
$230$	1.46185	−	1.78250i	0.0963914	−	0.117534i
$231$		0			0
$232$	6.61204	−	11.4524i	0.434102	−	0.751887i
$233$	−6.92161	+	5.02884i	−0.453450	+	0.329450i	−0.790956	−	0.611873i	$-0.790416\pi$
$233$	−6.92161	+	5.02884i	−0.453450	+	0.329450i	0.337507	+	0.941323i	$0.390416\pi$
$234$		0			0
$235$	7.34146	+	19.4858i	0.478904	+	1.27111i
$236$	9.78122	+	10.8631i	0.636703	+	0.707131i
$237$		0			0
$238$	−0.118490	+	0.131597i	−0.00768060	+	0.00853017i
$239$	−20.8239	+	4.42625i	−1.34698	+	0.286310i	−0.824269	−	0.566198i	$-0.808414\pi$
$239$	−20.8239	+	4.42625i	−1.34698	+	0.286310i	−0.522714	+	0.852508i	$0.675080\pi$
$240$		0			0
$241$	−2.78868	−	0.592751i	−0.179634	−	0.0381825i	0.117216	−	0.993106i	$-0.462603\pi$
$241$	−2.78868	−	0.592751i	−0.179634	−	0.0381825i	−0.296851	+	0.954924i	$0.595936\pi$
$242$	2.57466	−	1.87060i	0.165506	−	0.120247i
$243$		0			0
$244$	4.85179	−	3.52503i	0.310604	−	0.225667i
$245$	−8.80594	+	4.41823i	−0.562591	+	0.282271i
$246$		0			0
$247$	−1.67734	+	15.9588i	−0.106726	+	1.01543i
$248$	−4.64265	+	0.986825i	−0.294808	+	0.0626634i
$249$		0			0
$250$	4.96302	−	3.09321i	0.313889	−	0.195632i
$251$	−1.54809			−0.0977144			−0.0488572	−	0.998806i	$-0.515558\pi$
$251$	−1.54809			−0.0977144			−0.0488572	+	0.998806i	$0.515558\pi$
$252$		0			0
$253$	6.59081	+	4.78851i	0.414361	+	0.301051i
$254$	−4.17206	+	1.85752i	−0.261779	+	0.116551i
$255$		0			0
$256$	−1.53247	−	0.682301i	−0.0957796	−	0.0426438i
$257$	5.00583	+	8.67035i	0.312255	+	0.540842i	0.978850	−	0.204578i	$-0.0655823\pi$
$257$	5.00583	+	8.67035i	0.312255	+	0.540842i	−0.666595	+	0.745420i	$0.732249\pi$
$258$		0			0
$259$	−9.94508	−	2.11389i	−0.617957	−	0.131351i
$260$	15.3189	−	12.2484i	0.950039	−	0.759613i
$261$		0			0
$262$	0.150958	+	0.464602i	0.00932623	+	0.0287032i
$263$	14.1384	+	3.00521i	0.871811	+	0.185309i	0.622030	−	0.782993i	$-0.286308\pi$
$263$	14.1384	+	3.00521i	0.871811	+	0.185309i	0.249781	+	0.968302i	$0.419641\pi$
$264$		0			0
$265$	−3.23906	+	3.94953i	−0.198974	+	0.242618i
$266$	3.73327	−	4.14621i	0.228901	−	0.254221i
$267$		0			0
$268$	−11.7118	+	20.2854i	−0.715410	+	1.23913i
$269$	24.3691	−	17.7052i	1.48581	−	1.07951i	0.510187	−	0.860064i	$-0.329576\pi$
$269$	24.3691	−	17.7052i	1.48581	−	1.07951i	0.975626	−	0.219442i	$-0.0704237\pi$
$270$		0			0
$271$	−7.60294	−	5.52386i	−0.461846	−	0.335551i	0.332409	−	0.943135i	$-0.392139\pi$
$271$	−7.60294	−	5.52386i	−0.461846	−	0.335551i	−0.794255	+	0.607585i	$0.792139\pi$
$272$	0.222830	−	0.0992101i	0.0135110	−	0.00601550i
$273$		0			0
$274$	−1.62265	−	2.81051i	−0.0980280	−	0.169789i
$275$	11.9390	+	16.8691i	0.719952	+	1.01724i
$276$		0			0
$277$	6.85333	+	7.61140i	0.411777	+	0.457324i	0.912980	−	0.408005i	$-0.133776\pi$
$277$	6.85333	+	7.61140i	0.411777	+	0.457324i	−0.501203	+	0.865330i	$0.667109\pi$
$278$	−2.41781	−	1.75664i	−0.145011	−	0.105356i
$279$		0			0
$280$	−14.7040	+	0.679129i	−0.878729	+	0.0405857i
$281$	0.158141	+	1.50461i	0.00943389	+	0.0897575i	0.998226	−	0.0595432i	$-0.0189644\pi$
$281$	0.158141	+	1.50461i	0.00943389	+	0.0897575i	−0.988792	+	0.149301i	$0.952298\pi$
$282$		0			0
$283$	−21.7756	−	9.69511i	−1.29442	−	0.576315i	−0.360158	−	0.932891i	$-0.617277\pi$
$283$	−21.7756	−	9.69511i	−1.29442	−	0.576315i	−0.934266	+	0.356577i	$0.883944\pi$
$284$	−9.64047	+	10.7068i	−0.572057	+	0.635333i
$285$		0			0
$286$	−7.35010	−	8.16311i	−0.434620	−	0.482695i
$287$	6.06437	+	18.6642i	0.357968	+	1.10171i
$288$		0			0
$289$	−5.25018	+	16.1584i	−0.308834	+	0.950494i
$290$	3.64634	−	7.04787i	0.214120	−	0.413865i
$291$		0			0
$292$	−16.7579	−	7.46111i	−0.980684	−	0.436629i
$293$	0.224026	+	0.388025i	0.0130878	+	0.0226687i	0.872495	−	0.488623i	$-0.162501\pi$
$293$	0.224026	+	0.388025i	0.0130878	+	0.0226687i	−0.859407	+	0.511292i	$0.829167\pi$
$294$		0			0
$295$	13.3045	+	13.4706i	0.774616	+	0.784291i
$296$	−4.74722	−	3.44905i	−0.275926	−	0.200472i
$297$		0			0
$298$	3.41183	−	10.5005i	0.197642	−	0.608279i
$299$	5.00706	−	8.67248i	0.289566	−	0.501542i
$300$		0			0
$301$	18.9772	+	32.8695i	1.09383	+	1.89457i
$302$	−9.05055	+	1.92375i	−0.520801	+	0.110700i
$303$		0			0
$304$	−7.02066	+	3.12580i	−0.402663	+	0.179277i
$305$	6.06678	−	4.85075i	0.347383	−	0.277753i
$306$		0			0
$307$	5.99405			0.342099			0.171049	−	0.985262i	$-0.445284\pi$
$307$	5.99405			0.342099			0.171049	+	0.985262i	$0.445284\pi$
$308$	−2.51908	−	23.9675i	−0.143538	−	1.36567i
$309$		0			0
$310$	−2.75558	+	0.720057i	−0.156506	+	0.0408965i
$311$	−21.7763	+	4.62870i	−1.23482	+	0.262469i	−0.778671	−	0.627433i	$-0.784106\pi$
$311$	−21.7763	+	4.62870i	−1.23482	+	0.262469i	−0.456151	+	0.889902i	$0.650772\pi$
$312$		0			0
$313$	−3.43837	−	0.730848i	−0.194348	−	0.0413099i	0.109709	−	0.993964i	$-0.465008\pi$
$313$	−3.43837	−	0.730848i	−0.194348	−	0.0413099i	−0.304057	+	0.952654i	$0.598341\pi$
$314$	0.158087	−	0.486542i	0.00892137	−	0.0274572i
$315$		0			0
$316$	7.66743	+	23.5979i	0.431327	+	1.32749i
$317$	0.430998	+	4.10067i	0.0242072	+	0.230317i	0.999936	+	0.0113329i	$0.00360747\pi$
$317$	0.430998	+	4.10067i	0.0242072	+	0.230317i	−0.975729	+	0.218984i	$0.929726\pi$
$318$		0			0
$319$	25.6182	+	11.4060i	1.43435	+	0.638612i
$320$	4.50196	+	1.76027i	0.251667	+	0.0984022i
$321$		0			0
$322$	−3.18079	+	1.41618i	−0.177259	+	0.0789206i
$323$	−0.0978338	+	0.301102i	−0.00544362	+	0.0167537i
$324$		0			0
$325$	19.0883	−	16.7629i	1.05883	−	0.929836i
$326$	3.26689	−	5.65841i	0.180936	−	0.313390i
$327$		0			0
$328$	−1.18390	+	11.2641i	−0.0653700	+	0.621954i
$329$	3.28744	−	31.2779i	0.181242	−	1.72440i
$330$		0			0
$331$	−1.64139	−	15.6168i	−0.0902192	−	0.858378i	−0.942255	−	0.334895i	$-0.891299\pi$
$331$	−1.64139	−	15.6168i	−0.0902192	−	0.858378i	0.852036	−	0.523483i	$-0.175368\pi$
$332$	−10.7083			−0.587696
$333$		0			0
$334$	3.17935	+	9.78504i	0.173966	+	0.535413i
$335$	−13.9409	+	26.9459i	−0.761673	+	1.47221i
$336$		0			0
$337$	−17.3925	+	19.3164i	−0.947432	+	1.05223i	0.0511340	+	0.998692i	$0.483716\pi$
$337$	−17.3925	+	19.3164i	−0.947432	+	1.05223i	−0.998566	+	0.0535378i	$0.982950\pi$
$338$	−4.48494	+	4.98103i	−0.243949	+	0.270933i
$339$		0			0
$340$	0.345877	−	0.173538i	0.0187578	−	0.00941142i
$341$	−3.11026	−	9.57240i	−0.168430	−	0.518375i
$342$		0			0
$343$	−8.76057			−0.473026
$344$	2.28968	+	21.7848i	0.123451	+	1.17456i
$345$		0			0
$346$	−0.207515	+	1.97437i	−0.0111561	+	0.106143i
$347$	−1.28335	+	12.2103i	−0.0688939	+	0.655482i	0.904520	+	0.426430i	$0.140229\pi$
$347$	−1.28335	+	12.2103i	−0.0688939	+	0.655482i	−0.973414	+	0.229051i	$0.926438\pi$
$348$		0			0
$349$	−12.3258	+	21.3489i	−0.659784	+	1.14278i	0.320888	+	0.947117i	$0.396019\pi$
$349$	−12.3258	+	21.3489i	−0.659784	+	1.14278i	−0.980671	+	0.195662i	$0.937314\pi$
$350$	−8.79507	+	0.814168i	−0.470116	+	0.0435191i
$351$		0			0
$352$	6.60480	−	20.3275i	0.352037	−	1.08346i
$353$	−23.3008	+	10.3742i	−1.24018	+	0.552162i	−0.918775	−	0.394781i	$-0.870821\pi$
$353$	−23.3008	+	10.3742i	−1.24018	+	0.552162i	−0.321401	+	0.946943i	$0.604154\pi$
$354$		0			0
$355$	−11.8334	+	14.4290i	−0.628051	+	0.765812i
$356$	−10.9592	−	4.87934i	−0.580836	−	0.258605i
$357$		0			0
$358$	0.248951	+	2.36861i	0.0131575	+	0.125185i
$359$	−2.79781	−	8.61076i	−0.147663	−	0.454459i	0.849681	−	0.527297i	$-0.176794\pi$
$359$	−2.79781	−	8.61076i	−0.147663	−	0.454459i	−0.997344	+	0.0728380i	$0.976794\pi$
$360$		0			0
$361$	−2.78888	+	8.58330i	−0.146783	+	0.451753i
$362$	−9.80765	−	2.08468i	−0.515479	−	0.109568i
$363$		0			0
$364$	−28.9763	+	6.15911i	−1.51877	+	0.322825i
$365$	−22.1279	−	8.65204i	−1.15823	−	0.452869i
$366$		0			0
$367$	2.47023	+	23.5027i	0.128945	+	1.22683i	0.847286	+	0.531137i	$0.178235\pi$
$367$	2.47023	+	23.5027i	0.128945	+	1.22683i	−0.718341	+	0.695691i	$0.755098\pi$
$368$	4.79596			0.250007
$369$		0			0
$370$	−2.94107	−	1.93601i	−0.152899	−	0.100648i
$371$	7.04777	−	3.13787i	0.365902	−	0.162910i
$372$		0			0
$373$	1.61169	−	0.342575i	0.0834500	−	0.0177378i	−0.165997	−	0.986126i	$-0.553084\pi$
$373$	1.61169	−	0.342575i	0.0834500	−	0.0177378i	0.249447	+	0.968388i	$0.419751\pi$
$374$	−0.108361	−	0.187687i	−0.00560322	−	0.00970506i
$375$		0			0
$376$	9.07549	−	15.7192i	0.468033	−	0.810656i
$377$	10.6520	−	32.7836i	0.548608	−	1.68844i
$378$		0			0
$379$	17.3280	+	12.5895i	0.890077	+	0.646679i	0.935898	−	0.352271i	$-0.114590\pi$
$379$	17.3280	+	12.5895i	0.890077	+	0.646679i	−0.0458208	+	0.998950i	$0.514590\pi$
$380$	−10.8975	+	5.46764i	−0.559030	+	0.280484i
$381$		0			0
$382$	4.59866	+	7.96511i	0.235288	+	0.407531i
$383$	10.3862	+	4.62425i	0.530712	+	0.236288i	0.654556	−	0.756013i	$-0.272856\pi$
$383$	10.3862	+	4.62425i	0.530712	+	0.236288i	−0.123844	+	0.992302i	$0.539522\pi$
$384$		0			0
$385$	−4.69154	−	30.8595i	−0.239103	−	1.57274i
$386$	−3.19635	+	9.83736i	−0.162690	+	0.500709i
$387$		0			0
$388$	0.931395	+	2.86654i	0.0472844	+	0.145527i
$389$	9.72454	+	10.8002i	0.493054	+	0.547592i	0.937396	−	0.348265i	$-0.113229\pi$
$389$	9.72454	+	10.8002i	0.493054	+	0.547592i	−0.444342	+	0.895857i	$0.646563\pi$
$390$		0			0
$391$	0.132204	−	0.146827i	0.00668585	−	0.00742538i
$392$	7.84553	+	3.49305i	0.396259	+	0.176426i
$393$		0			0
$394$	0.0329679	+	0.313669i	0.00166090	+	0.0158024i
$395$	11.3306	+	30.0737i	0.570103	+	1.51317i
$396$		0			0
$397$	−22.7814	−	16.5516i	−1.14336	−	0.830703i	−0.155780	−	0.987792i	$-0.549789\pi$
$397$	−22.7814	−	16.5516i	−1.14336	−	0.830703i	−0.987584	+	0.157089i	$0.949789\pi$
$398$	6.57316	+	7.30023i	0.329483	+	0.365928i
$399$		0			0
$400$	11.5234	+	3.90295i	0.576169	+	0.195147i
$401$	4.58244	+	7.93701i	0.228836	+	0.396356i	0.957463	−	0.288555i	$-0.0931747\pi$
$401$	4.58244	+	7.93701i	0.228836	+	0.396356i	−0.728627	+	0.684910i	$0.759841\pi$
$402$		0			0
$403$	−11.3025	+	5.03221i	−0.563019	+	0.250672i
$404$	−17.3214	−	12.5847i	−0.861772	−	0.626114i
$405$		0			0
$406$	−9.69618	+	7.04469i	−0.481213	+	0.349622i
$407$	6.22164	−	10.7762i	0.308395	−	0.534156i
$408$		0			0
$409$	10.7270	−	11.9135i	0.530416	−	0.589086i	−0.417074	−	0.908872i	$-0.636944\pi$
$409$	10.7270	−	11.9135i	0.530416	−	0.589086i	0.947490	+	0.319786i	$0.103611\pi$
$410$	−0.397806	+	6.78470i	−0.0196462	+	0.335072i
$411$		0			0
$412$	14.7933	+	3.14441i	0.728813	+	0.154914i
$413$	−8.83668	−	27.1965i	−0.434825	−	1.33825i
$414$		0			0
$415$	−13.8548	+	0.639911i	−0.680107	+	0.0314120i
$416$	−25.6988	−	5.46245i	−1.25999	−	0.267819i
$417$		0			0
$418$	3.41412	+	5.91343i	0.166990	+	0.289235i
$419$	26.9841	+	12.0141i	1.31826	+	0.586927i	0.940757	−	0.339082i	$-0.110116\pi$
$419$	26.9841	+	12.0141i	1.31826	+	0.586927i	0.377503	+	0.926009i	$0.376783\pi$
$420$		0			0
$421$	24.5088	−	10.9120i	1.19449	−	0.531820i	0.289466	−	0.957188i	$-0.406522\pi$
$421$	24.5088	−	10.9120i	1.19449	−	0.531820i	0.905020	+	0.425368i	$0.139855\pi$
$422$	−7.02433	−	5.10348i	−0.341939	−	0.248433i
$423$		0			0
$424$	4.45245			0.216230
$425$	0.437138	−	0.245199i	0.0212043	−	0.0118939i
$426$		0			0
$427$	−11.4755	+	2.43920i	−0.555341	+	0.118041i
$428$	−0.559203	+	5.32046i	−0.0270301	+	0.257174i
$429$		0			0
$430$	1.97560	+	12.9949i	0.0952721	+	0.626670i
$431$	−7.77127	+	5.64616i	−0.374329	+	0.271966i	−0.759004	−	0.651086i	$-0.774314\pi$
$431$	−7.77127	+	5.64616i	−0.374329	+	0.271966i	0.384675	+	0.923052i	$0.374314\pi$
$432$		0			0
$433$	10.7896	−	7.83912i	0.518516	−	0.376724i	−0.297529	−	0.954713i	$-0.596162\pi$
$433$	10.7896	−	7.83912i	0.518516	−	0.376724i	0.816045	+	0.577989i	$0.196162\pi$
$434$	4.20768	+	0.894370i	0.201975	+	0.0429311i
$435$		0			0
$436$	−4.71629	+	1.00248i	−0.225869	+	0.0480100i
$437$	−4.16534	+	4.62608i	−0.199255	+	0.221295i
$438$		0			0
$439$	−4.88122	−	5.42114i	−0.232968	−	0.258737i	0.615314	−	0.788282i	$-0.289029\pi$
$439$	−4.88122	−	5.42114i	−0.232968	−	0.258737i	−0.848282	+	0.529545i	$0.822363\pi$
$440$	4.77045	−	17.3716i	0.227422	−	0.828160i
$441$		0			0
$442$	−0.215522	+	0.156586i	−0.0102514	+	0.00744804i
$443$	5.86605	−	10.1603i	0.278704	−	0.482730i	−0.692359	−	0.721554i	$-0.743428\pi$
$443$	5.86605	−	10.1603i	0.278704	−	0.482730i	0.971063	+	0.238823i	$0.0767617\pi$
$444$		0			0
$445$	−14.4710	−	5.65818i	−0.685991	−	0.268223i
$446$	0.160189	−	1.52410i	0.00758517	−	0.0721680i
$447$		0			0
$448$	−4.88525	−	5.42562i	−0.230806	−	0.256337i
$449$	11.6170			0.548239			0.274120	−	0.961696i	$-0.411614\pi$
$449$	11.6170			0.548239			0.274120	+	0.961696i	$0.411614\pi$
$450$		0			0
$451$	−24.0178			−1.13096
$452$	−9.63144	−	10.6968i	−0.453025	−	0.503135i
$453$		0			0
$454$	1.20910	−	11.5038i	0.0567459	−	0.539901i
$455$	−37.1226	+	9.70046i	−1.74033	+	0.454765i
$456$		0			0
$457$	5.87515	−	10.1761i	0.274828	−	0.476016i	−0.695264	−	0.718755i	$-0.744712\pi$
$457$	5.87515	−	10.1761i	0.274828	−	0.476016i	0.970092	+	0.242739i	$0.0780457\pi$
$458$	−7.66658	+	5.57009i	−0.358236	+	0.260273i
$459$		0			0
$460$	7.60060	−	0.351047i	0.354380	−	0.0163677i
$461$	16.8831	+	18.7506i	0.786324	+	0.873301i	0.994494	−	0.104791i	$-0.0334175\pi$
$461$	16.8831	+	18.7506i	0.786324	+	0.873301i	−0.208170	+	0.978093i	$0.566751\pi$
$462$		0			0
$463$	13.7694	−	15.2924i	0.639917	−	0.710699i	−0.332722	−	0.943025i	$-0.607967\pi$
$463$	13.7694	−	15.2924i	0.639917	−	0.710699i	0.972638	+	0.232326i	$0.0746336\pi$
$464$	16.1480	−	3.43235i	0.749650	−	0.159343i
$465$		0			0
$466$	4.37732	+	0.930428i	0.202776	+	0.0431013i
$467$	−9.19766	+	6.68249i	−0.425617	+	0.309229i	−0.779894	−	0.625912i	$-0.784727\pi$
$467$	−9.19766	+	6.68249i	−0.425617	+	0.309229i	0.354277	+	0.935141i	$0.384727\pi$
$468$		0			0
$469$	37.0710	−	26.9337i	1.71178	−	1.24368i
$470$	5.00485	−	9.67369i	0.230857	−	0.446214i
$471$		0			0
$472$	1.72512	−	16.4134i	0.0794050	−	0.755488i
$473$	−45.4358	+	9.65767i	−2.08914	+	0.444060i
$474$		0			0
$475$	−13.7729	+	7.72545i	−0.631943	+	0.354468i
$476$	−0.584467			−0.0267890
$477$		0			0
$478$	9.00885	+	6.54531i	0.412055	+	0.299375i
$479$	38.5201	−	17.1502i	1.76003	−	0.783614i	0.770826	−	0.637045i	$-0.219844\pi$
$479$	38.5201	−	17.1502i	1.76003	−	0.783614i	0.989200	−	0.146569i	$-0.0468230\pi$
$480$		0			0
$481$	−13.9732	−	6.22127i	−0.637123	−	0.283666i
$482$	0.745621	+	1.29145i	0.0339621	+	0.0588241i
$483$		0			0
$484$	10.2744	+	2.18388i	0.467016	+	0.0992674i
$485$	1.37637	+	3.65318i	0.0624979	+	0.165882i
$486$		0			0
$487$	5.00668	+	15.4090i	0.226874	+	0.698248i	0.998096	+	0.0616809i	$0.0196461\pi$
$487$	5.00668	+	15.4090i	0.226874	+	0.698248i	−0.771221	+	0.636567i	$0.780354\pi$
$488$	−6.62294	−	1.40775i	−0.299806	−	0.0637258i
$489$		0			0
$490$	4.79948	+	1.87661i	0.216819	+	0.0847764i
$491$	−2.59049	+	2.87703i	−0.116907	+	0.129838i	−0.798757	−	0.601653i	$-0.794509\pi$
$491$	−2.59049	+	2.87703i	−0.116907	+	0.129838i	0.681850	+	0.731492i	$0.261176\pi$
$492$		0			0
$493$	0.340049	−	0.588982i	0.0153150	−	0.0265264i
$494$	6.79044	−	4.93354i	0.305516	−	0.221971i
$495$		0			0
$496$	−4.79365	−	3.48279i	−0.215241	−	0.156382i
$497$	25.7479	−	11.4637i	1.15495	−	0.514218i
$498$		0			0
$499$	−5.14142	−	8.90521i	−0.230162	−	0.398652i	0.727694	−	0.685902i	$-0.240592\pi$
$499$	−5.14142	−	8.90521i	−0.230162	−	0.398652i	−0.957856	+	0.287250i	$0.907259\pi$
$500$	18.5479	+	5.34189i	0.829486	+	0.238897i
$501$		0			0
$502$	0.541828	+	0.601761i	0.0241830	+	0.0268579i
$503$	−16.4188	−	11.9290i	−0.732078	−	0.531886i	0.158142	−	0.987416i	$-0.449450\pi$
$503$	−16.4188	−	11.9290i	−0.732078	−	0.531886i	−0.890220	+	0.455531i	$0.849450\pi$
$504$		0			0
$505$	−23.1631	−	15.2475i	−1.03075	−	0.678505i
$506$	−0.445421	−	4.23790i	−0.0198014	−	0.188397i
$507$		0			0
$508$	−13.7702	−	6.13087i	−0.610952	−	0.272013i
$509$	−24.7800	+	27.5210i	−1.09835	+	1.21985i	−0.124608	+	0.992206i	$0.539767\pi$
$509$	−24.7800	+	27.5210i	−1.09835	+	1.21985i	−0.973745	+	0.227640i	$0.926899\pi$
$510$		0			0
$511$	24.0119	+	26.6679i	1.06222	+	1.17972i
$512$	−6.81947	−	20.9882i	−0.301381	−	0.927555i
$513$		0			0
$514$	1.61824	−	4.98044i	0.0713776	−	0.219678i
$515$	19.3280	+	3.18434i	0.851694	+	0.140319i
$516$		0			0
$517$	35.1628	+	15.6555i	1.54646	+	0.688528i
$518$	2.65906	+	4.60563i	0.116833	+	0.202360i
$519$		0			0
$520$	−21.8496	−	3.59977i	−0.958168	−	0.157860i
$521$	11.4682	+	8.33217i	0.502433	+	0.365039i	0.809946	−	0.586505i	$-0.199497\pi$
$521$	11.4682	+	8.33217i	0.502433	+	0.365039i	−0.307513	+	0.951544i	$0.599497\pi$
$522$		0			0
$523$	−3.47821	+	10.7048i	−0.152092	+	0.468090i	−0.997855	−	0.0654688i	$-0.979146\pi$
$523$	−3.47821	+	10.7048i	−0.152092	+	0.468090i	0.845763	+	0.533559i	$0.179146\pi$
$524$	−0.806181	+	1.39635i	−0.0352182	+	0.0609996i
$525$		0			0
$526$	−3.78025	−	6.54759i	−0.164827	−	0.285488i
$527$	−0.238765	+	0.0507512i	−0.0104008	+	0.00221076i
$528$		0			0
$529$	−17.4626	+	7.77486i	−0.759244	+	0.338037i
$530$	2.66890	−	0.123268i	0.115929	−	0.00535441i
$531$		0			0
$532$	18.4147			0.798381
$533$	3.08603	+	29.3616i	0.133671	+	1.27179i
$534$		0			0
$535$	−0.405577	+	6.91723i	−0.0175346	+	0.299058i
$536$	25.8678	−	5.49836i	1.11732	−	0.237493i
$537$		0			0
$538$	−15.4114	−	3.27579i	−0.664432	−	0.141229i
$539$	−5.62766	+	17.3202i	−0.242400	+	0.746032i
$540$		0			0
$541$	−4.62861	−	14.2454i	−0.199000	−	0.612458i	−0.999907	−	0.0136691i	$-0.995649\pi$
$541$	−4.62861	−	14.2454i	−0.199000	−	0.612458i	0.800907	−	0.598789i	$-0.204351\pi$
$542$	0.513823	+	4.88870i	0.0220706	+	0.209988i
$543$		0			0
$544$	−0.473544	−	0.210835i	−0.0203030	−	0.00903949i
$545$	−6.04221	+	1.57888i	−0.258820	+	0.0676319i
$546$		0			0
$547$	12.1606	−	5.41427i	0.519951	−	0.231497i	−0.129943	−	0.991521i	$-0.541480\pi$
$547$	12.1606	−	5.41427i	0.519951	−	0.231497i	0.649895	+	0.760024i	$0.274813\pi$
$548$	3.30998	−	10.1871i	0.141395	−	0.435170i
$549$		0			0
$550$	2.37857	−	10.5450i	0.101423	−	0.449640i
$551$	−10.7139	+	18.5570i	−0.456427	+	0.790555i
$552$		0			0
$553$	5.07372	−	48.2733i	0.215757	−	2.05279i
$554$	0.559990	−	5.32795i	0.0237917	−	0.226363i
$555$		0			0
$556$	−1.03107	−	9.80994i	−0.0437269	−	0.416034i
$557$	11.7342			0.497192			0.248596	−	0.968607i	$-0.420031\pi$
$557$	11.7342			0.497192			0.248596	+	0.968607i	$0.420031\pi$
$558$		0			0
$559$	17.6444	+	54.3039i	0.746279	+	2.29681i
$560$	−12.9127	−	13.0740i	−0.545661	−	0.552476i
$561$		0			0
$562$	0.529511	−	0.588082i	0.0223361	−	0.0248067i
$563$	1.14734	−	1.27425i	0.0483544	−	0.0537030i	−0.718482	−	0.695545i	$-0.755163\pi$
$563$	1.14734	−	1.27425i	0.0483544	−	0.0537030i	0.766837	+	0.641842i	$0.221830\pi$
$564$		0			0
$565$	−13.1007	−	13.2644i	−0.551152	−	0.558036i
$566$	3.85280	+	11.8577i	0.161945	+	0.498416i
$567$		0			0
$568$	16.2663			0.682520
$569$	1.80029	+	17.1286i	0.0754722	+	0.718070i	0.965188	+	0.261556i	$0.0842356\pi$
$569$	1.80029	+	17.1286i	0.0754722	+	0.718070i	−0.889716	+	0.456514i	$0.849098\pi$
$570$		0			0
$571$	0.102140	−	0.971802i	0.00427445	−	0.0406686i	−0.992177	−	0.124841i	$-0.960158\pi$
$571$	0.102140	−	0.971802i	0.00427445	−	0.0406686i	0.996451	+	0.0841723i	$0.0268246\pi$
$572$	3.78970	−	36.0566i	0.158455	−	1.50760i
$573$		0			0
$574$	5.13249	−	8.88973i	0.214226	−	0.371050i
$575$	9.81297	−	0.908397i	0.409229	−	0.0378828i
$576$		0			0
$577$	−1.42881	+	4.39743i	−0.0594822	+	0.183067i	−0.976383	−	0.216049i	$-0.930683\pi$
$577$	−1.42881	+	4.39743i	−0.0594822	+	0.183067i	0.916900	+	0.399116i	$0.130683\pi$
$578$	8.11852	−	3.61460i	0.337686	−	0.150348i
$579$		0			0
$580$	25.3399	−	6.62155i	1.05218	−	0.274945i
$581$	19.1371	+	8.52040i	0.793942	+	0.353486i
$582$		0			0
$583$	0.986932	+	9.39003i	0.0408746	+	0.388895i
$584$	6.39992	+	19.6969i	0.264831	+	0.815065i
$585$		0			0
$586$	0.0724213	−	0.222890i	0.00299170	−	0.00920749i
$587$	−38.1643	−	8.11207i	−1.57521	−	0.334821i	−0.664313	−	0.747455i	$-0.731276\pi$
$587$	−38.1643	−	8.11207i	−1.57521	−	0.334821i	−0.910897	+	0.412634i	$0.864609\pi$
$588$		0			0
$589$	7.52275	−	1.59901i	0.309970	−	0.0658861i
$590$	0.579662	−	9.88631i	0.0238643	−	0.407013i
$591$		0			0
$592$	−0.765708	−	7.28523i	−0.0314704	−	0.299421i
$593$	0.233927			0.00960624			0.00480312	−	0.999988i	$-0.498471\pi$
$593$	0.233927			0.00960624			0.00480312	+	0.999988i	$0.498471\pi$
$594$		0			0
$595$	−0.756206	+	0.0349267i	−0.0310014	+	0.00143186i
$596$	33.2907	−	14.8220i	1.36364	−	0.607131i
$597$		0			0
$598$	−5.12356	+	1.08905i	−0.209518	+	0.0445344i
$599$	−17.3587	−	30.0662i	−0.709258	−	1.22847i	−0.965133	−	0.261761i	$-0.915697\pi$
$599$	−17.3587	−	30.0662i	−0.709258	−	1.22847i	0.255875	−	0.966710i	$-0.417637\pi$
$600$		0			0
$601$	−15.4400	+	26.7429i	−0.629811	+	1.09086i	0.357779	+	0.933806i	$0.383534\pi$
$601$	−15.4400	+	26.7429i	−0.629811	+	1.09086i	−0.987589	+	0.157058i	$0.949799\pi$
$602$	6.13479	−	18.8809i	0.250035	−	0.769530i
$603$		0			0
$604$	−24.7068	−	17.9505i	−1.00530	−	0.730396i
$605$	13.4239	+	2.21161i	0.545757	+	0.0899148i
$606$		0			0
$607$	−3.80766	−	6.59506i	−0.154548	−	0.267685i	0.778346	−	0.627835i	$-0.216059\pi$
$607$	−3.80766	−	6.59506i	−0.154548	−	0.267685i	−0.932894	+	0.360150i	$0.882725\pi$
$608$	14.9199	+	6.64276i	0.605081	+	0.269399i
$609$		0			0
$610$	−4.00891	−	0.660477i	−0.162316	−	0.0267419i
$611$	14.6207	−	44.9978i	0.591489	−	1.82041i
$612$		0			0
$613$	−9.39803	−	28.9242i	−0.379583	−	1.16824i	−0.940334	−	0.340252i	$-0.889488\pi$
$613$	−9.39803	−	28.9242i	−0.379583	−	1.16824i	0.560752	−	0.827984i	$-0.310512\pi$
$614$	−2.09791	−	2.32996i	−0.0846647	−	0.0940296i
$615$		0			0
$616$	−18.2063	+	20.2201i	−0.733551	+	0.814691i
$617$	−42.4408	−	18.8959i	−1.70860	−	0.760719i	−0.998389	−	0.0567314i	$-0.981932\pi$
$617$	−42.4408	−	18.8959i	−1.70860	−	0.760719i	−0.710213	−	0.703987i	$-0.751401\pi$
$618$		0			0
$619$	−1.33153	−	12.6687i	−0.0535187	−	0.509197i	−0.988140	−	0.153553i	$-0.950928\pi$
$619$	−1.33153	−	12.6687i	−0.0535187	−	0.509197i	0.934622	−	0.355644i	$-0.115738\pi$
$620$	−7.85187	−	5.16862i	−0.315339	−	0.207577i
$621$		0			0
$622$	9.42090	+	6.84469i	0.377744	+	0.274447i
$623$	15.7030	+	17.4400i	0.629129	+	0.698719i
$624$		0			0
$625$	24.3171	+	5.80316i	0.972686	+	0.232126i
$626$	0.919333	+	1.59233i	0.0367439	+	0.0636423i
$627$		0			0
$628$	1.54252	−	0.686776i	0.0615534	−	0.0274053i
$629$	−0.244143	−	0.177381i	−0.00973463	−	0.00707263i
$630$		0			0
$631$	−31.3529	+	22.7792i	−1.24814	+	0.906827i	−0.998113	−	0.0614115i	$-0.980440\pi$
$631$	−31.3529	+	22.7792i	−1.24814	+	0.906827i	−0.250028	+	0.968239i	$0.580440\pi$
$632$	14.0068	−	24.2605i	0.557162	−	0.965032i
$633$		0			0
$634$	1.44313	−	1.60276i	0.0573141	−	0.0636538i
$635$	−18.1827	−	7.10947i	−0.721559	−	0.282131i
$636$		0			0
$637$	21.8968	+	4.65431i	0.867583	+	0.184411i
$638$	−4.53269	−	13.9502i	−0.179451	−	0.552293i
$639$		0			0
$640$	−9.04479	−	24.0067i	−0.357527	−	0.948950i
$641$	32.7872	+	6.96913i	1.29502	+	0.275264i	0.803344	−	0.595516i	$-0.203052\pi$
$641$	32.7872	+	6.96913i	1.29502	+	0.275264i	0.491673	+	0.870780i	$0.336386\pi$
$642$		0			0
$643$	−12.4860	−	21.6263i	−0.492399	−	0.852860i	0.507563	−	0.861615i	$-0.330546\pi$
$643$	−12.4860	−	21.6263i	−0.492399	−	0.852860i	−0.999962	+	0.00875512i	$0.997213\pi$
$644$	−10.4984	−	4.67419i	−0.413695	−	0.184189i
$645$		0			0
$646$	0.151284	−	0.0673558i	0.00595217	−	0.00265008i
$647$	17.8362	+	12.9588i	0.701214	+	0.509462i	0.880327	−	0.474367i	$-0.157323\pi$
$647$	17.8362	+	12.9588i	0.701214	+	0.509462i	−0.179114	+	0.983828i	$0.557323\pi$
$648$		0			0
$649$	34.9976			1.37377
$650$	−13.1968	−	1.55287i	−0.517620	−	0.0609085i
$651$		0			0
$652$	21.0939	−	4.48364i	0.826099	−	0.175593i
$653$	−0.573436	+	5.45588i	−0.0224403	+	0.213505i	0.977556	+	0.210677i	$0.0675668\pi$
$653$	−0.573436	+	5.45588i	−0.0224403	+	0.213505i	−0.999996	+	0.00282794i	$0.999100\pi$
$654$		0			0
$655$	−0.959624	+	1.85482i	−0.0374956	+	0.0724738i
$656$	−11.4389	+	8.31087i	−0.446615	+	0.324485i
$657$		0			0
$658$	−13.3087	+	9.66932i	−0.518826	+	0.376949i
$659$	19.7873	+	4.20593i	0.770806	+	0.163840i	0.576495	−	0.817100i	$-0.304420\pi$
$659$	19.7873	+	4.20593i	0.770806	+	0.163840i	0.194310	+	0.980940i	$0.437753\pi$
$660$		0			0
$661$	−13.2971	+	2.82638i	−0.517196	+	0.109934i	−0.459112	−	0.888378i	$-0.651832\pi$
$661$	−13.2971	+	2.82638i	−0.517196	+	0.109934i	−0.0580841	+	0.998312i	$0.518499\pi$
$662$	−5.49596	+	6.10389i	−0.213607	+	0.237234i
$663$		0			0
$664$	8.08975	+	8.98457i	0.313943	+	0.348669i
$665$	23.8257	−	1.10043i	0.923921	−	0.0426729i
$666$		0			0
$667$	10.8184	−	7.86001i	0.418889	−	0.304341i
$668$	−16.9791	+	29.4086i	−0.656940	+	1.13785i
$669$		0			0
$670$	15.3535	−	4.01200i	0.593156	−	0.154997i
$671$	1.50084	−	14.2795i	0.0579393	−	0.551256i
$672$		0			0
$673$	15.9018	+	17.6607i	0.612969	+	0.680771i	0.967092	−	0.254428i	$-0.0818872\pi$
$673$	15.9018	+	17.6607i	0.612969	+	0.680771i	−0.354123	+	0.935199i	$0.615221\pi$
$674$	13.5959			0.523693
$675$		0			0
$676$	−22.1225			−0.850865
$677$	23.4852	+	26.0829i	0.902608	+	1.00245i	0.999974	+	0.00719937i	$0.00229165\pi$
$677$	23.4852	+	26.0829i	0.902608	+	1.00245i	−0.0973658	+	0.995249i	$0.531042\pi$
$678$		0			0
$679$	0.616327	−	5.86396i	0.0236524	−	0.225038i
$680$	−0.406900	−	0.159099i	−0.0156039	−	0.00610115i
$681$		0			0
$682$	−2.63232	+	4.55932i	−0.100797	+	0.174585i
$683$	−35.4803	+	25.7779i	−1.35762	+	0.986365i	−0.359023	+	0.933329i	$0.616890\pi$
$683$	−35.4803	+	25.7779i	−1.35762	+	0.986365i	−0.998593	+	0.0530363i	$0.983110\pi$
$684$		0			0
$685$	3.67382	−	13.3782i	0.140369	−	0.511155i
$686$	3.06618	+	3.40534i	0.117067	+	0.130017i
$687$		0			0
$688$	−18.2978	+	20.3217i	−0.697596	+	0.774759i
$689$	11.3524	−	2.41303i	0.432493	−	0.0919291i
$690$		0			0
$691$	24.5384	+	5.21581i	0.933486	+	0.198419i	0.649458	−	0.760397i	$-0.274996\pi$
$691$	24.5384	+	5.21581i	0.933486	+	0.198419i	0.284028	+	0.958816i	$0.408329\pi$
$692$	−5.30102	+	3.85142i	−0.201515	+	0.146409i
$693$		0			0
$694$	5.19545	−	3.77472i	0.197217	−	0.143286i
$695$	−1.92026	−	12.6309i	−0.0728395	−	0.479116i
$696$		0			0
$697$	−0.0608865	+	0.579296i	−0.00230624	+	0.0219424i
$698$	12.6126	−	2.68088i	0.477393	−	0.101473i
$699$		0			0
$700$	−21.4209	−	19.7744i	−0.809636	−	0.747402i
$701$	−4.91096			−0.185485			−0.0927423	−	0.995690i	$-0.529563\pi$
$701$	−4.91096			−0.185485			−0.0927423	+	0.995690i	$0.529563\pi$
$702$		0			0
$703$	7.69220	+	5.58871i	0.290117	+	0.210782i
$704$	8.16276	−	3.63430i	0.307646	−	0.136973i
$705$		0			0
$706$	12.1878	+	5.42636i	0.458694	+	0.204224i
$707$	20.9421	+	36.2728i	0.787608	+	1.36418i
$708$		0			0
$709$	18.2361	+	3.87619i	0.684869	+	0.145573i	0.537189	−	0.843462i	$-0.319486\pi$
$709$	18.2361	+	3.87619i	0.684869	+	0.145573i	0.147680	+	0.989035i	$0.452819\pi$
$710$	9.75039	−	0.450339i	0.365926	−	0.0169009i
$711$		0			0
$712$	4.18536	+	12.8812i	0.156853	+	0.482744i
$713$	−4.69466	−	0.997881i	−0.175816	−	0.0373709i
$714$		0			0
$715$	2.74858	−	46.8778i	0.102791	−	1.75313i
$716$	−5.25991	+	5.84172i	−0.196572	+	0.218316i
$717$		0			0
$718$	−2.36788	+	4.10129i	−0.0883686	+	0.153059i
$719$	−12.2939	+	8.93208i	−0.458487	+	0.333110i	−0.792937	−	0.609303i	$-0.791449\pi$
$719$	−12.2939	+	8.93208i	−0.458487	+	0.333110i	0.334451	+	0.942413i	$0.391449\pi$
$720$		0			0
$721$	−23.9355	−	17.3902i	−0.891405	−	0.647643i
$722$	4.31254	−	1.92007i	0.160496	−	0.0714575i
$723$		0			0
$724$	−16.5470	−	28.6602i	−0.614963	−	1.06515i
$725$	32.3901	−	10.0815i	1.20294	−	0.374417i
$726$		0			0
$727$	−21.4119	−	23.7804i	−0.794125	−	0.881965i	0.201100	−	0.979571i	$-0.435548\pi$
$727$	−21.4119	−	23.7804i	−0.794125	−	0.881965i	−0.995225	+	0.0976054i	$0.968882\pi$
$728$	27.0582	+	19.6589i	1.00284	+	0.728608i
$729$		0			0
$730$	4.38157	+	11.6296i	0.162169	+	0.430430i
$731$	0.117755	+	1.12037i	0.00435534	+	0.0414383i
$732$		0			0
$733$	18.6585	+	8.30729i	0.689167	+	0.306837i	0.721276	−	0.692648i	$-0.243556\pi$
$733$	18.6585	+	8.30729i	0.689167	+	0.306837i	−0.0321094	+	0.999484i	$0.510223\pi$
$734$	8.27119	−	9.18609i	0.305295	−	0.339065i
$735$		0			0
$736$	−6.81983	−	7.57418i	−0.251382	−	0.279188i
$737$	17.3297	+	53.3353i	0.638347	+	1.96463i
$738$		0			0
$739$	−9.35272	+	28.7847i	−0.344045	+	1.05886i	0.618048	+	0.786141i	$0.287924\pi$
$739$	−9.35272	+	28.7847i	−0.344045	+	1.05886i	−0.962093	+	0.272722i	$0.912076\pi$
$740$	−1.74674	−	11.4895i	−0.0642115	−	0.422364i
$741$		0			0
$742$	−3.68644	−	1.64131i	−0.135333	−	0.0602543i
$743$	2.81735	+	4.87980i	0.103359	+	0.179022i	0.913066	−	0.407811i	$-0.133708\pi$
$743$	2.81735	+	4.87980i	0.103359	+	0.179022i	−0.809708	+	0.586833i	$0.800374\pi$
$744$		0			0
$745$	42.1870	−	21.1666i	1.54561	−	0.775484i
$746$	−0.697250	−	0.506582i	−0.0255281	−	0.0185473i
$747$		0			0
$748$	0.221041	−	0.680295i	0.00808207	−	0.0248741i
$749$	5.23275	−	9.06338i	0.191200	−	0.331169i
$750$		0			0
$751$	11.3957	+	19.7379i	0.415835	+	0.720247i	0.995516	−	0.0945967i	$-0.0301561\pi$
$751$	11.3957	+	19.7379i	0.415835	+	0.720247i	−0.579681	+	0.814844i	$0.696823\pi$
$752$	22.1642	−	4.71114i	0.808245	−	0.171798i
$753$		0			0
$754$	−16.4716	+	7.33362i	−0.599859	+	0.267075i
$755$	−33.0392	−	21.7486i	−1.20242	−	0.791513i
$756$		0			0
$757$	41.0082			1.49047			0.745234	−	0.666803i	$-0.232338\pi$
$757$	41.0082			1.49047			0.745234	+	0.666803i	$0.232338\pi$
$758$	−1.17106	−	11.1419i	−0.0425348	−	0.404692i
$759$		0			0
$760$	12.8202	+	5.01270i	0.465036	+	0.181830i
$761$	−4.08424	+	0.868131i	−0.148053	+	0.0314697i	−0.281342	−	0.959608i	$-0.590780\pi$
$761$	−4.08424	+	0.868131i	−0.148053	+	0.0314697i	0.133289	+	0.991077i	$0.457446\pi$
$762$		0			0
$763$	9.22625	+	1.96110i	0.334013	+	0.0709966i
$764$	−9.38062	+	28.8706i	−0.339379	+	1.04450i
$765$		0			0
$766$	−1.83766	−	5.65574i	−0.0663974	−	0.204350i
$767$	−4.49680	−	42.7842i	−0.162370	−	1.54485i
$768$		0			0
$769$	−6.36851	−	2.83544i	−0.229654	−	0.102249i	0.288684	−	0.957425i	$-0.406782\pi$
$769$	−6.36851	−	2.83544i	−0.229654	−	0.102249i	−0.518338	+	0.855176i	$0.673449\pi$
$770$	−10.3534	+	12.6244i	−0.373112	+	0.454952i
$771$		0			0
$772$	−31.1882	+	13.8859i	−1.12249	+	0.499764i
$773$	3.04988	−	9.38657i	0.109697	−	0.337611i	−0.881107	−	0.472916i	$-0.843201\pi$
$773$	3.04988	−	9.38657i	0.109697	−	0.337611i	0.990804	+	0.135305i	$0.0432013\pi$
$774$		0			0
$775$	−10.4679	−	6.21815i	−0.376019	−	0.223362i
$776$	1.70147	−	2.94703i	0.0610792	−	0.105792i
$777$		0			0
$778$	0.794598	−	7.56010i	0.0284877	−	0.271043i
$779$	1.91834	−	18.2518i	0.0687318	−	0.653939i
$780$		0			0
$781$	3.60560	+	34.3050i	0.129019	+	1.22753i
$782$	−0.103345			−0.00369560
$783$		0			0
$784$	3.31300	+	10.1964i	0.118322	+	0.364156i
$785$	1.95474	−	0.980755i	0.0697675	−	0.0350047i
$786$		0			0
$787$	−23.7111	+	26.3339i	−0.845210	+	0.938701i	−0.998777	−	0.0494369i	$-0.984257\pi$
$787$	−23.7111	+	26.3339i	−0.845210	+	0.938701i	0.153567	+	0.988138i	$0.450924\pi$
$788$	−0.696555	+	0.773603i	−0.0248138	+	0.0275585i
$789$		0			0
$790$	7.72433	−	14.9301i	0.274819	−	0.531188i
$791$	8.70136	+	26.7800i	0.309385	+	0.952189i
$792$		0			0
$793$	−17.6494			−0.626750
$794$	1.53961	+	14.6484i	0.0546388	+	0.519854i
$795$		0			0
$796$	−3.38911	+	32.2452i	−0.120124	+	1.14290i
$797$	3.69661	−	35.1709i	0.130941	−	1.24582i	−0.709810	−	0.704393i	$-0.751219\pi$
$797$	3.69661	−	35.1709i	0.130941	−	1.24582i	0.840751	−	0.541423i	$-0.182114\pi$
$798$		0			0
$799$	0.466741	−	0.808419i	0.0165121	−	0.0285998i
$800$	−10.2223	−	23.7487i	−0.361414	−	0.839642i
$801$		0			0
$802$	1.48137	−	4.55919i	0.0523090	−	0.160991i
$803$	−40.1214	+	17.8632i	−1.41585	+	0.630379i
$804$		0			0
$805$	−13.8625	−	5.42028i	−0.488591	−	0.191040i
$806$	5.91195	+	2.63217i	0.208239	+	0.0927142i
$807$		0			0
$808$	2.52675	+	24.0404i	0.0888907	+	0.845738i
$809$	4.45186	+	13.7014i	0.156519	+	0.481716i	0.998312	−	0.0580852i	$-0.0184995\pi$
$809$	4.45186	+	13.7014i	0.156519	+	0.481716i	−0.841793	+	0.539801i	$0.818500\pi$
$810$		0			0
$811$	5.51450	−	16.9719i	0.193640	−	0.595964i	−0.806349	−	0.591440i	$-0.798560\pi$
$811$	5.51450	−	16.9719i	0.193640	−	0.595964i	0.999990	−	0.00452443i	$-0.00144017\pi$
$812$	−38.6932	−	8.22450i	−1.35787	−	0.288623i
$813$		0			0
$814$	−6.36640	+	1.35322i	−0.223142	+	0.0474303i
$815$	27.0241	−	7.06163i	0.946613	−	0.247358i
$816$		0			0
$817$	−3.71010	−	35.2993i	−0.129800	−	1.23496i
$818$	−8.38536			−0.293187
$819$		0			0
$820$	−17.5200	+	14.0083i	−0.611826	+	0.489191i
$821$	−24.3260	+	10.8307i	−0.848985	+	0.377992i	−0.784652	−	0.619936i	$-0.787159\pi$
$821$	−24.3260	+	10.8307i	−0.848985	+	0.377992i	−0.0643326	+	0.997929i	$0.520492\pi$
$822$		0			0
$823$	2.70123	−	0.574164i	0.0941589	−	0.0200141i	−0.160591	−	0.987021i	$-0.551340\pi$
$823$	2.70123	−	0.574164i	0.0941589	−	0.0200141i	0.254750	+	0.967007i	$0.418007\pi$
$824$	−8.53753	−	14.7874i	−0.297419	−	0.515145i
$825$		0			0
$826$	−7.47879	+	12.9537i	−0.260221	+	0.450715i
$827$	5.30684	−	16.3328i	0.184537	−	0.567946i	−0.815403	−	0.578893i	$-0.803485\pi$
$827$	5.30684	−	16.3328i	0.184537	−	0.567946i	0.999940	+	0.0109475i	$0.00348476\pi$
$828$		0			0
$829$	−7.77371	−	5.64793i	−0.269992	−	0.196161i	0.444548	−	0.895755i	$-0.353364\pi$
$829$	−7.77371	−	5.64793i	−0.269992	−	0.196161i	−0.714541	+	0.699594i	$0.753364\pi$
$830$	5.09791	+	5.16158i	0.176951	+	0.179161i
$831$		0			0
$832$	−5.49172	−	9.51193i	−0.190391	−	0.329767i
$833$	0.403486	+	0.179643i	0.0139799	+	0.00622427i
$834$		0			0
$835$	−20.2108	+	39.0646i	−0.699422	+	1.35189i
$836$	−6.96432	+	21.4340i	−0.240866	+	0.741310i
$837$		0			0
$838$	−4.77436	−	14.6940i	−0.164927	−	0.507594i
$839$	−28.5434	−	31.7007i	−0.985429	−	1.09443i	−0.995527	−	0.0944805i	$-0.969881\pi$
$839$	−28.5434	−	31.7007i	−0.985429	−	1.09443i	0.0100979	−	0.999949i	$-0.496786\pi$
$840$		0			0
$841$	11.3954	−	12.6558i	0.392944	−	0.436408i
$842$	−12.8197	−	5.70769i	−0.441795	−	0.196700i
$843$		0			0
$844$	−2.99550	−	28.5003i	−0.103109	−	0.981021i
$845$	−28.6229	+	1.32200i	−0.984658	+	0.0454782i
$846$		0			0
$847$	−16.6239	−	12.0780i	−0.571204	−	0.415004i
$848$	3.71927	+	4.13067i	0.127720	+	0.141848i
$849$		0			0
$850$	−0.248309	−	0.0841019i	−0.00851694	−	0.00288467i
$851$	−2.96681	−	5.13867i	−0.101701	−	0.176151i
$852$		0			0
$853$	−19.1682	+	8.53425i	−0.656308	+	0.292207i	−0.707744	−	0.706469i	$-0.750287\pi$
$853$	−19.1682	+	8.53425i	−0.656308	+	0.292207i	0.0514360	+	0.998676i	$0.483620\pi$
$854$	4.96457	+	3.60697i	0.169884	+	0.123428i
$855$		0			0
$856$	4.88646	−	3.55022i	0.167016	−	0.121344i
$857$	7.64159	−	13.2356i	0.261032	−	0.452120i	−0.705485	−	0.708725i	$-0.749271\pi$
$857$	7.64159	−	13.2356i	0.261032	−	0.452120i	0.966516	+	0.256605i	$0.0826040\pi$
$858$		0			0
$859$	−29.0765	+	32.2927i	−0.992077	+	1.10181i	0.00272579	+	0.999996i	$0.499132\pi$
$859$	−29.0765	+	32.2927i	−0.992077	+	1.10181i	−0.994803	+	0.101817i	$0.967534\pi$
$860$	−27.5107	+	33.5451i	−0.938107	+	1.14388i
$861$		0			0
$862$	4.91466	+	1.04464i	0.167394	+	0.0355807i
$863$	−2.99160	−	9.20721i	−0.101835	−	0.313417i	0.887139	−	0.461502i	$-0.152689\pi$
$863$	−2.99160	−	9.20721i	−0.101835	−	0.313417i	−0.988975	+	0.148085i	$0.952689\pi$
$864$		0			0
$865$	−6.62851	+	5.29989i	−0.225376	+	0.180202i
$866$	−6.82351	−	1.45038i	−0.231872	−	0.0492860i
$867$		0			0
$868$	7.09898	+	12.2958i	0.240955	+	0.417347i
$869$	54.2692	+	24.1622i	1.84096	+	0.819646i
$870$		0			0
$871$	62.9752	−	28.0384i	2.13383	−	0.950043i
$872$	4.40409	+	3.19976i	0.149141	+	0.108357i
$873$		0			0
$874$	3.25607			0.110138
$875$	−28.8969	−	24.3048i	−0.976894	−	0.821651i
$876$		0			0
$877$	13.7293	−	2.91826i	0.463607	−	0.0985427i	0.0298144	−	0.999555i	$-0.490508\pi$
$877$	13.7293	−	2.91826i	0.463607	−	0.0985427i	0.433793	+	0.901013i	$0.357175\pi$
$878$	−0.398847	+	3.79478i	−0.0134604	+	0.128068i
$879$		0			0
$880$	20.1011	−	10.0854i	0.677606	−	0.339977i
$881$	6.11208	−	4.44068i	0.205921	−	0.149610i	−0.480045	−	0.877244i	$-0.659380\pi$
$881$	6.11208	−	4.44068i	0.205921	−	0.149610i	0.685966	+	0.727633i	$0.259380\pi$
$882$		0			0
$883$	−7.80285	+	5.66910i	−0.262587	+	0.190781i	−0.711287	−	0.702902i	$-0.751887\pi$
$883$	−7.80285	+	5.66910i	−0.262587	+	0.190781i	0.448700	+	0.893683i	$0.351887\pi$
$884$	−0.860056	−	0.182811i	−0.0289268	−	0.00614859i
$885$		0			0
$886$	−6.00254	+	1.27588i	−0.201659	+	0.0428640i
$887$	22.0450	−	24.4834i	0.740198	−	0.822073i	−0.249024	−	0.968497i	$-0.580110\pi$
$887$	22.0450	−	24.4834i	0.740198	−	0.822073i	0.989222	+	0.146425i	$0.0467766\pi$
$888$		0			0
$889$	19.7308	+	21.9133i	0.661749	+	0.734947i
$890$	2.86542	+	7.60540i	0.0960489	+	0.254934i
$891$		0			0
$892$	4.09207	−	2.97307i	0.137013	−	0.0995456i
$893$	−14.7056	+	25.4708i	−0.492103	+	0.852347i
$894$		0			0
$895$	−6.45638	+	7.87257i	−0.215813	+	0.263151i
$896$	−4.05017	+	38.5348i	−0.135307	+	1.28736i
$897$		0			0
$898$	−4.06592	−	4.51566i	−0.135682	−	0.150690i
$899$	−16.5210			−0.551008
$900$		0			0
$901$	0.228984			0.00762857
$902$	8.40620	+	9.33603i	0.279896	+	0.310856i
$903$		0			0
$904$	−1.69870	+	16.1621i	−0.0564980	+	0.537542i
$905$	−23.1218	−	36.0928i	−0.768593	−	1.19977i
$906$		0			0
$907$	13.7736	−	23.8565i	0.457344	−	0.792144i	−0.541475	−	0.840717i	$-0.682134\pi$
$907$	13.7736	−	23.8565i	0.457344	−	0.792144i	0.998820	+	0.0485730i	$0.0154673\pi$
$908$	30.8868	−	22.4406i	1.02502	−	0.744717i
$909$		0			0
$910$	16.7635	+	11.0349i	0.555706	+	0.365802i
$911$	−7.57368	−	8.41143i	−0.250927	−	0.278683i	0.604501	−	0.796605i	$-0.293373\pi$
$911$	−7.57368	−	8.41143i	−0.250927	−	0.278683i	−0.855428	+	0.517921i	$0.826706\pi$
$912$		0			0
$913$	−17.1549	+	19.0524i	−0.567744	+	0.630544i
$914$	−6.01185	+	1.27786i	−0.198854	+	0.0422678i
$915$		0			0
$916$	−30.5940	−	6.50295i	−1.01085	−	0.214864i
$917$	2.55179	−	1.85398i	0.0842675	−	0.0612239i
$918$		0			0
$919$	25.7130	−	18.6816i	0.848195	−	0.616250i	−0.0764527	−	0.997073i	$-0.524359\pi$
$919$	25.7130	−	18.6816i	0.848195	−	0.616250i	0.924648	+	0.380823i	$0.124359\pi$
$920$	−6.03651	−	6.11190i	−0.199018	−	0.201503i
$921$		0			0
$922$	1.37953	−	13.1253i	0.0454323	−	0.432260i
$923$	41.4743	−	8.81562i	1.36514	−	0.290170i
$924$		0			0
$925$	−2.94660	−	14.7612i	−0.0968835	−	0.485346i
$926$	−10.7636			−0.353714
$927$		0			0
$928$	−28.3830	−	20.6214i	−0.931717	−	0.676932i
$929$	−17.7906	+	7.92089i	−0.583691	+	0.259876i	−0.677268	−	0.735736i	$-0.736836\pi$
$929$	−17.7906	+	7.92089i	−0.583691	+	0.259876i	0.0935775	+	0.995612i	$0.470170\pi$
$930$		0			0
$931$	−12.7126	−	5.66000i	−0.416638	−	0.185499i
$932$	7.38519	+	12.7915i	0.241910	+	0.419000i
$933$		0			0
$934$	5.81673	+	1.23638i	0.190329	+	0.0404557i
$935$	0.245338	−	0.893401i	0.00802342	−	0.0292173i
$936$		0			0
$937$	−6.71741	−	20.6741i	−0.219448	−	0.675393i	−0.998808	−	0.0488155i	$-0.984455\pi$
$937$	−6.71741	−	20.6741i	−0.219448	−	0.675393i	0.779359	−	0.626577i	$-0.215545\pi$
$938$	−23.4442	−	4.98323i	−0.765482	−	0.162708i
$939$		0			0
$940$	34.7808	−	9.08853i	1.13443	−	0.296435i
$941$	28.2050	−	31.3248i	0.919456	−	1.02116i	−0.0802468	−	0.996775i	$-0.525571\pi$
$941$	28.2050	−	31.3248i	0.919456	−	1.02116i	0.999703	−	0.0243841i	$-0.00776248\pi$
$942$		0			0
$943$	−5.72650	+	9.91858i	−0.186480	+	0.322994i
$944$	16.6682	−	12.1102i	0.542504	−	0.394153i
$945$		0			0
$946$	19.6565	+	14.2813i	0.639087	+	0.464324i
$947$	−3.46603	+	1.54318i	−0.112631	+	0.0501465i	−0.462279	−	0.886735i	$-0.652968\pi$
$947$	−3.46603	+	1.54318i	−0.112631	+	0.0501465i	0.349648	+	0.936881i	$0.386301\pi$
$948$		0			0
$949$	26.9927	+	46.7528i	0.876222	+	1.51766i
$950$	7.82345	+	2.64979i	0.253826	+	0.0859705i
$951$		0			0
$952$	0.441543	+	0.490384i	0.0143105	+	0.0158934i
$953$	43.1844	+	31.3753i	1.39888	+	1.01635i	0.994824	+	0.101612i	$0.0323999\pi$
$953$	43.1844	+	31.3753i	1.39888	+	1.01635i	0.404056	+	0.914734i	$0.367600\pi$
$954$		0			0
$955$	−10.4117	+	37.9144i	−0.336916	+	1.22688i
$956$	3.84179	+	36.5522i	0.124252	+	1.18218i
$957$		0			0
$958$	−20.1485	−	8.97067i	−0.650967	−	0.289829i
$959$	−14.0210	+	15.5719i	−0.452761	+	0.502842i
$960$		0			0
$961$	−16.7753	−	18.6309i	−0.541139	−	0.600996i
$962$	2.47231	+	7.60899i	0.0797105	+	0.245324i
$963$		0			0
$964$	−1.52096	+	4.68104i	−0.0489869	+	0.150766i
$965$	−39.5227	+	19.8298i	−1.27228	+	0.638345i
$966$		0			0
$967$	−13.9358	−	6.20463i	−0.448146	−	0.199528i	0.170239	−	0.985403i	$-0.445546\pi$
$967$	−13.9358	−	6.20463i	−0.448146	−	0.199528i	−0.618385	+	0.785875i	$0.712213\pi$
$968$	−5.92956	−	10.2703i	−0.190583	−	0.330100i
$969$		0			0
$970$	0.938307	−	1.81362i	0.0301272	−	0.0582318i
$971$	−15.5289	−	11.2824i	−0.498345	−	0.362069i	0.310040	−	0.950724i	$-0.399658\pi$
$971$	−15.5289	−	11.2824i	−0.498345	−	0.362069i	−0.808384	+	0.588655i	$0.799658\pi$
$972$		0			0
$973$	−5.96292	+	18.3520i	−0.191162	+	0.588338i
$974$	4.23733	−	7.33927i	0.135773	−	0.235166i
$975$		0			0
$976$	−4.22633	−	7.32023i	−0.135282	−	0.234315i
$977$	−37.3380	+	7.93643i	−1.19455	+	0.253909i	−0.761924	−	0.647666i	$-0.775745\pi$
$977$	−37.3380	+	7.93643i	−1.19455	+	0.253909i	−0.432623	+	0.901575i	$0.642412\pi$
$978$		0			0
$979$	−26.2382	+	11.6820i	−0.838576	+	0.373358i
$980$	5.99676	+	15.9166i	0.191560	+	0.508439i
$981$		0			0
$982$	2.02500			0.0646204
$983$	−4.80747	−	45.7400i	−0.153334	−	1.45888i	−0.752678	−	0.658388i	$-0.771239\pi$
$983$	−4.80747	−	45.7400i	−0.153334	−	1.45888i	0.599344	−	0.800492i	$-0.295428\pi$
$984$		0			0
$985$	−0.855001	+	1.04254i	−0.0272426	+	0.0332181i
$986$	−0.347961	+	0.0739614i	−0.0110813	+	0.00235541i
$987$		0			0
$988$	27.0977	+	5.75979i	0.862092	+	0.183243i
$989$	−6.84480	+	21.0661i	−0.217652	+	0.669864i
$990$		0			0
$991$	12.7035	+	39.0974i	0.403541	+	1.24197i	0.922107	+	0.386934i	$0.126466\pi$
$991$	12.7035	+	39.0974i	0.403541	+	1.24197i	−0.518567	+	0.855037i	$0.673534\pi$
$992$	1.31623	+	12.5230i	0.0417902	+	0.397607i
$993$		0			0
$994$	−13.4678	−	5.99626i	−0.427173	−	0.190190i
$995$	−2.45804	+	41.9226i	−0.0779251	+	1.32904i
$996$		0			0
$997$	20.2113	−	8.99863i	0.640097	−	0.284989i	−0.0609108	−	0.998143i	$-0.519401\pi$
$997$	20.2113	−	8.99863i	0.640097	−	0.284989i	0.701008	+	0.713154i	$0.252734\pi$
$998$	−1.66207	+	5.11534i	−0.0526120	+	0.161923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.13		224
3.2	odd	2		225.2.q.a.196.16	yes	224
9.4	even	3	inner	675.2.r.a.496.16		224
9.5	odd	6		225.2.q.a.121.13	yes	224
25.6	even	5	inner	675.2.r.a.181.16		224
75.56	odd	10		225.2.q.a.106.13	yes	224
225.31	even	15	inner	675.2.r.a.631.13		224
225.131	odd	30		225.2.q.a.31.16	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.16	✓	224	225.131	odd	30
225.2.q.a.106.13	yes	224	75.56	odd	10
225.2.q.a.121.13	yes	224	9.5	odd	6
225.2.q.a.196.16	yes	224	3.2	odd	2
675.2.r.a.46.13		224	1.1	even	1	trivial
675.2.r.a.181.16		224	25.6	even	5	inner
675.2.r.a.496.16		224	9.4	even	3	inner
675.2.r.a.631.13		224	225.31	even	15	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.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.349998 - 0.388712i) q^{2} +(0.180458 - 1.71695i) q^{4} +(0.130882 - 2.23223i) q^{5} +(-1.68864 + 2.92481i) q^{7} +(-1.57689 + 1.14568i) q^{8} +O(q^{10})\)	\(q+(-0.349998 - 0.388712i) q^{2} +(0.180458 - 1.71695i) q^{4} +(0.130882 - 2.23223i) q^{5} +(-1.68864 + 2.92481i) q^{7} +(-1.57689 + 1.14568i) q^{8} +(-0.913505 + 0.730402i) q^{10} +(-2.76572 - 3.07165i) q^{11} +(-3.39970 + 3.77575i) q^{13} +(1.72793 - 0.367283i) q^{14} +(-2.38011 - 0.505907i) q^{16} +(-0.0810977 + 0.0589209i) q^{17} +(2.55513 - 1.85641i) q^{19} +(-3.80901 - 0.627543i) q^{20} +(-0.225989 + 2.15014i) q^{22} +(-1.92791 + 0.409791i) q^{23} +(-4.96574 - 0.584319i) q^{25} +2.65757 q^{26} +(4.71702 + 3.42711i) q^{28} +(-6.19799 + 2.75952i) q^{29} +(2.22457 + 0.990444i) q^{31} +(2.58553 + 4.47827i) q^{32} +(0.0512873 + 0.0109015i) q^{34} +(6.30785 + 4.15225i) q^{35} +(0.930291 + 2.86314i) q^{37} +(-1.61590 - 0.343471i) q^{38} +(2.35104 + 3.66994i) q^{40} +(3.88818 - 4.31827i) q^{41} +(5.61908 - 9.73253i) q^{43} +(-5.77296 + 4.19430i) q^{44} +(0.834057 + 0.605978i) q^{46} +(-8.50718 + 3.78764i) q^{47} +(-2.20301 - 3.81573i) q^{49} +(1.51087 + 2.13475i) q^{50} +(5.86925 + 6.51846i) q^{52} +(-1.84804 - 1.34268i) q^{53} +(-7.21862 + 5.77172i) q^{55} +(-0.688092 - 6.54676i) q^{56} +(3.24195 + 1.44341i) q^{58} +(-5.66566 + 6.29235i) q^{59} +(2.32441 + 2.58152i) q^{61} +(-0.393599 - 1.21137i) q^{62} +(-0.668023 + 2.05596i) q^{64} +(7.98339 + 8.08310i) q^{65} +(-12.3948 - 5.51853i) q^{67} +(0.0865293 + 0.149873i) q^{68} +(-0.593706 - 3.90522i) q^{70} +(-6.75154 - 4.90528i) q^{71} +(3.28345 - 10.1054i) q^{73} +(0.787338 - 1.36371i) q^{74} +(-2.72627 - 4.72203i) q^{76} +(13.6543 - 2.90231i) q^{77} +(-13.1297 + 5.84572i) q^{79} +(-1.44082 + 5.24674i) q^{80} -3.03942 q^{82} +(-0.648356 - 6.16870i) q^{83} +(0.120911 + 0.188741i) q^{85} +(-5.74982 + 1.22216i) q^{86} +(7.88038 + 1.67503i) q^{88} +(2.14728 - 6.60864i) q^{89} +(-5.30248 - 16.3193i) q^{91} +(0.355681 + 3.38408i) q^{92} +(4.44980 + 1.98118i) q^{94} +(-3.80953 - 5.94663i) q^{95} +(-1.59492 + 0.710105i) q^{97} +(-0.712171 + 2.19184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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