LMFDB - Embedded newform 1470.2.m.e.1273.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.8
Root			$-0.424637 + 3.22544i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.e.97.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.15899 + 0.582041i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.15899 + 0.582041i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.93820 - 1.11507i) q^{10} +0.461115 q^{11} +(-0.707107 - 0.707107i) q^{12} +(4.00275 - 4.00275i) q^{13} +(1.93820 - 1.11507i) q^{15} -1.00000 q^{16} +(-1.15953 - 1.15953i) q^{17} +(-0.707107 - 0.707107i) q^{18} -5.82646 q^{19} +(0.582041 - 2.15899i) q^{20} +(0.326057 - 0.326057i) q^{22} +(3.11997 + 3.11997i) q^{23} -1.00000 q^{24} +(4.32246 + 2.51324i) q^{25} -5.66074i q^{26} +(-0.707107 - 0.707107i) q^{27} -5.53773i q^{29} +(0.582041 - 2.15899i) q^{30} -0.0324420i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.326057 - 0.326057i) q^{33} -1.63982 q^{34} -1.00000 q^{36} +(5.70242 - 5.70242i) q^{37} +(-4.11993 + 4.11993i) q^{38} -5.66074i q^{39} +(-1.11507 - 1.93820i) q^{40} +10.9453i q^{41} +(4.75146 + 4.75146i) q^{43} -0.461115i q^{44} +(0.582041 - 2.15899i) q^{45} +4.41231 q^{46} +(-6.39241 - 6.39241i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(4.83357 - 1.27931i) q^{50} -1.63982 q^{51} +(-4.00275 - 4.00275i) q^{52} +(1.94214 + 1.94214i) q^{53} -1.00000 q^{54} +(0.995541 + 0.268388i) q^{55} +(-4.11993 + 4.11993i) q^{57} +(-3.91576 - 3.91576i) q^{58} +1.91758 q^{59} +(-1.11507 - 1.93820i) q^{60} -13.5554i q^{61} +(-0.0229400 - 0.0229400i) q^{62} +1.00000i q^{64} +(10.9716 - 6.31212i) q^{65} -0.461115i q^{66} +(-2.69424 + 2.69424i) q^{67} +(-1.15953 + 1.15953i) q^{68} +4.41231 q^{69} +8.85877 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-2.86894 + 2.86894i) q^{73} -8.06444i q^{74} +(4.83357 - 1.27931i) q^{75} +5.82646i q^{76} +(-4.00275 - 4.00275i) q^{78} +5.06128i q^{79} +(-2.15899 - 0.582041i) q^{80} -1.00000 q^{81} +(7.73949 + 7.73949i) q^{82} +(-1.08813 + 1.08813i) q^{83} +(-1.82851 - 3.17829i) q^{85} +6.71958 q^{86} +(-3.91576 - 3.91576i) q^{87} +(-0.326057 - 0.326057i) q^{88} -11.4285 q^{89} +(-1.11507 - 1.93820i) q^{90} +(3.11997 - 3.11997i) q^{92} +(-0.0229400 - 0.0229400i) q^{93} -9.04024 q^{94} +(-12.5793 - 3.39124i) q^{95} +1.00000i q^{96} +(-2.51799 - 2.51799i) q^{97} -0.461115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	2.15899	+	0.582041i	0.965529	+	0.260297i
$5$	2.15899	+	0.582041i	0.965529	+	0.260297i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	1.93820	−	1.11507i	0.612913	−	0.352616i
$11$	0.461115			0.139031			0.0695156	−	0.997581i	$-0.477855\pi$
$11$	0.461115			0.139031			0.0695156	+	0.997581i	$0.477855\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	4.00275	−	4.00275i	1.11016	−	1.11016i	0.117035	−	0.993128i	$-0.462661\pi$
$13$	4.00275	−	4.00275i	1.11016	−	1.11016i	0.993128	−	0.117035i	$-0.0373389\pi$
$14$		0			0
$15$	1.93820	−	1.11507i	0.500441	−	0.287910i
$16$	−1.00000			−0.250000
$17$	−1.15953	−	1.15953i	−0.281226	−	0.281226i	0.552372	−	0.833598i	$-0.313723\pi$
$17$	−1.15953	−	1.15953i	−0.281226	−	0.281226i	−0.833598	+	0.552372i	$0.813723\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−5.82646			−1.33668			−0.668341	−	0.743855i	$-0.732995\pi$
$19$	−5.82646			−1.33668			−0.668341	+	0.743855i	$0.732995\pi$
$20$	0.582041	−	2.15899i	0.130148	−	0.482764i
$21$		0			0
$22$	0.326057	−	0.326057i	0.0695156	−	0.0695156i
$23$	3.11997	+	3.11997i	0.650559	+	0.650559i	0.953128	−	0.302568i	$-0.0978441\pi$
$23$	3.11997	+	3.11997i	0.650559	+	0.650559i	−0.302568	+	0.953128i	$0.597844\pi$
$24$	−1.00000			−0.204124
$25$	4.32246	+	2.51324i	0.864491	+	0.502648i
$26$		−	5.66074i		−	1.11016i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	5.53773i		−	1.02833i	−0.857691	−	0.514165i	$-0.828102\pi$
$29$		−	5.53773i		−	1.02833i	0.857691	−	0.514165i	$-0.171898\pi$
$30$	0.582041	−	2.15899i	0.106266	−	0.394175i
$31$		−	0.0324420i		−	0.00582676i	−0.999996	−	0.00291338i	$-0.999073\pi$
$31$		−	0.0324420i		−	0.00582676i	0.999996	−	0.00291338i	$-0.000927359\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.326057	−	0.326057i	0.0567593	−	0.0567593i
$34$	−1.63982			−0.281226
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.70242	−	5.70242i	0.937473	−	0.937473i	−0.0606844	−	0.998157i	$-0.519328\pi$
$37$	5.70242	−	5.70242i	0.937473	−	0.937473i	0.998157	+	0.0606844i	$0.0193283\pi$
$38$	−4.11993	+	4.11993i	−0.668341	+	0.668341i
$39$		−	5.66074i		−	0.906444i
$40$	−1.11507	−	1.93820i	−0.176308	−	0.306456i
$41$			10.9453i			1.70937i	0.519149	+	0.854684i	$0.326249\pi$
$41$			10.9453i			1.70937i	−0.519149	+	0.854684i	$0.673751\pi$
$42$		0			0
$43$	4.75146	+	4.75146i	0.724591	+	0.724591i	0.969537	−	0.244946i	$-0.0787703\pi$
$43$	4.75146	+	4.75146i	0.724591	+	0.724591i	−0.244946	+	0.969537i	$0.578770\pi$
$44$		−	0.461115i		−	0.0695156i
$45$	0.582041	−	2.15899i	0.0867655	−	0.321843i
$46$	4.41231			0.650559
$47$	−6.39241	−	6.39241i	−0.932429	−	0.932429i	0.0654279	−	0.997857i	$-0.479159\pi$
$47$	−6.39241	−	6.39241i	−0.932429	−	0.932429i	−0.997857	+	0.0654279i	$0.979159\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		0			0
$50$	4.83357	−	1.27931i	0.683570	−	0.180922i
$51$	−1.63982			−0.229620
$52$	−4.00275	−	4.00275i	−0.555081	−	0.555081i
$53$	1.94214	+	1.94214i	0.266773	+	0.266773i	0.827799	−	0.561025i	$-0.189593\pi$
$53$	1.94214	+	1.94214i	0.266773	+	0.266773i	−0.561025	+	0.827799i	$0.689593\pi$
$54$	−1.00000			−0.136083
$55$	0.995541	+	0.268388i	0.134239	+	0.0361894i
$56$		0			0
$57$	−4.11993	+	4.11993i	−0.545698	+	0.545698i
$58$	−3.91576	−	3.91576i	−0.514165	−	0.514165i
$59$	1.91758			0.249648			0.124824	−	0.992179i	$-0.460163\pi$
$59$	1.91758			0.249648			0.124824	+	0.992179i	$0.460163\pi$
$60$	−1.11507	−	1.93820i	−0.143955	−	0.250221i
$61$		−	13.5554i		−	1.73559i	−0.496925	−	0.867793i	$-0.665538\pi$
$61$		−	13.5554i		−	1.73559i	0.496925	−	0.867793i	$-0.334462\pi$
$62$	−0.0229400	−	0.0229400i	−0.00291338	−	0.00291338i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	10.9716	−	6.31212i	1.36087	−	0.782922i
$66$		−	0.461115i		−	0.0567593i
$67$	−2.69424	+	2.69424i	−0.329154	+	0.329154i	−0.852265	−	0.523111i	$-0.824771\pi$
$67$	−2.69424	+	2.69424i	−0.329154	+	0.329154i	0.523111	+	0.852265i	$0.324771\pi$
$68$	−1.15953	+	1.15953i	−0.140613	+	0.140613i
$69$	4.41231			0.531179
$70$		0			0
$71$	8.85877			1.05134			0.525671	−	0.850688i	$-0.323814\pi$
$71$	8.85877			1.05134			0.525671	+	0.850688i	$0.323814\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−2.86894	+	2.86894i	−0.335784	+	0.335784i	−0.854778	−	0.518994i	$-0.826307\pi$
$73$	−2.86894	+	2.86894i	−0.335784	+	0.335784i	0.518994	+	0.854778i	$0.326307\pi$
$74$		−	8.06444i		−	0.937473i
$75$	4.83357	−	1.27931i	0.558132	−	0.147722i
$76$			5.82646i			0.668341i
$77$		0			0
$78$	−4.00275	−	4.00275i	−0.453222	−	0.453222i
$79$			5.06128i			0.569438i	0.958611	+	0.284719i	$0.0919003\pi$
$79$			5.06128i			0.569438i	−0.958611	+	0.284719i	$0.908100\pi$
$80$	−2.15899	−	0.582041i	−0.241382	−	0.0650741i
$81$	−1.00000			−0.111111
$82$	7.73949	+	7.73949i	0.854684	+	0.854684i
$83$	−1.08813	+	1.08813i	−0.119438	+	0.119438i	−0.764299	−	0.644861i	$-0.776915\pi$
$83$	−1.08813	+	1.08813i	−0.119438	+	0.119438i	0.644861	+	0.764299i	$0.276915\pi$
$84$		0			0
$85$	−1.82851	−	3.17829i	−0.198330	−	0.344734i
$86$	6.71958			0.724591
$87$	−3.91576	−	3.91576i	−0.419814	−	0.419814i
$88$	−0.326057	−	0.326057i	−0.0347578	−	0.0347578i
$89$	−11.4285			−1.21142			−0.605708	−	0.795687i	$-0.707110\pi$
$89$	−11.4285			−1.21142			−0.605708	+	0.795687i	$0.707110\pi$
$90$	−1.11507	−	1.93820i	−0.117539	−	0.204304i
$91$		0			0
$92$	3.11997	−	3.11997i	0.325280	−	0.325280i
$93$	−0.0229400	−	0.0229400i	−0.00237876	−	0.00237876i
$94$	−9.04024			−0.932429
$95$	−12.5793	−	3.39124i	−1.29060	−	0.347934i
$96$			1.00000i			0.102062i
$97$	−2.51799	−	2.51799i	−0.255663	−	0.255663i	0.567624	−	0.823288i	$-0.307863\pi$
$97$	−2.51799	−	2.51799i	−0.255663	−	0.255663i	−0.823288	+	0.567624i	$0.807863\pi$
$98$		0			0
$99$		−	0.461115i		−	0.0463438i
$100$	2.51324	−	4.32246i	0.251324	−	0.432246i
$101$		−	4.51181i		−	0.448942i	−0.974481	−	0.224471i	$-0.927935\pi$
$101$		−	4.51181i		−	0.448942i	0.974481	−	0.224471i	$-0.0720654\pi$
$102$	−1.15953	+	1.15953i	−0.114810	+	0.114810i
$103$	−10.4477	+	10.4477i	−1.02945	+	1.02945i	−0.0298934	+	0.999553i	$0.509517\pi$
$103$	−10.4477	+	10.4477i	−1.02945	+	1.02945i	−0.999553	+	0.0298934i	$0.990483\pi$
$104$	−5.66074			−0.555081
$105$		0			0
$106$	2.74660			0.266773
$107$	4.17138	−	4.17138i	0.403262	−	0.403262i	−0.476119	−	0.879381i	$-0.657957\pi$
$107$	4.17138	−	4.17138i	0.403262	−	0.403262i	0.879381	+	0.476119i	$0.157957\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$			16.6187i			1.59179i	0.605437	+	0.795893i	$0.292998\pi$
$109$			16.6187i			1.59179i	−0.605437	+	0.795893i	$0.707002\pi$
$110$	0.893732	−	0.514175i	0.0852140	−	0.0490247i
$111$		−	8.06444i		−	0.765443i
$112$		0			0
$113$	6.35390	+	6.35390i	0.597724	+	0.597724i	0.939706	−	0.341982i	$-0.111098\pi$
$113$	6.35390	+	6.35390i	0.597724	+	0.597724i	−0.341982	+	0.939706i	$0.611098\pi$
$114$			5.82646i			0.545698i
$115$	4.92003	+	8.55193i	0.458795	+	0.797472i
$116$	−5.53773			−0.514165
$117$	−4.00275	−	4.00275i	−0.370054	−	0.370054i
$118$	1.35593	−	1.35593i	0.124824	−	0.124824i
$119$		0			0
$120$	−2.15899	−	0.582041i	−0.197088	−	0.0531328i
$121$	−10.7874			−0.980670
$122$	−9.58509	−	9.58509i	−0.867793	−	0.867793i
$123$	7.73949	+	7.73949i	0.697847	+	0.697847i
$124$	−0.0324420			−0.00291338
$125$	7.86932	+	7.94190i	0.703854	+	0.710345i
$126$		0			0
$127$	−11.7757	+	11.7757i	−1.04493	+	1.04493i	−0.0459856	+	0.998942i	$0.514643\pi$
$127$	−11.7757	+	11.7757i	−1.04493	+	1.04493i	−0.998942	+	0.0459856i	$0.985357\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	6.71958			0.591626
$130$	3.29478	−	12.2215i	0.288972	−	1.07189i
$131$			18.9765i			1.65798i	0.559261	+	0.828992i	$0.311085\pi$
$131$			18.9765i			1.65798i	−0.559261	+	0.828992i	$0.688915\pi$
$132$	−0.326057	−	0.326057i	−0.0283796	−	0.0283796i
$133$		0			0
$134$			3.81023i			0.329154i
$135$	−1.11507	−	1.93820i	−0.0959699	−	0.166814i
$136$			1.63982i			0.140613i
$137$	−3.13179	+	3.13179i	−0.267567	+	0.267567i	−0.828119	−	0.560552i	$-0.810589\pi$
$137$	−3.13179	+	3.13179i	−0.267567	+	0.267567i	0.560552	+	0.828119i	$0.310589\pi$
$138$	3.11997	−	3.11997i	0.265590	−	0.265590i
$139$	4.35020			0.368979			0.184489	−	0.982835i	$-0.440937\pi$
$139$	4.35020			0.368979			0.184489	+	0.982835i	$0.440937\pi$
$140$		0			0
$141$	−9.04024			−0.761325
$142$	6.26410	−	6.26410i	0.525671	−	0.525671i
$143$	1.84573	−	1.84573i	0.154347	−	0.154347i
$144$			1.00000i			0.0833333i
$145$	3.22318	−	11.9559i	0.267671	−	0.992882i
$146$			4.05729i			0.335784i
$147$		0			0
$148$	−5.70242	−	5.70242i	−0.468736	−	0.468736i
$149$		−	4.34052i		−	0.355589i	−0.984068	−	0.177794i	$-0.943104\pi$
$149$		−	4.34052i		−	0.355589i	0.984068	−	0.177794i	$-0.0568962\pi$
$150$	2.51324	−	4.32246i	0.205205	−	0.352927i
$151$	8.18514			0.666098			0.333049	−	0.942910i	$-0.391923\pi$
$151$	8.18514			0.666098			0.333049	+	0.942910i	$0.391923\pi$
$152$	4.11993	+	4.11993i	0.334170	+	0.334170i
$153$	−1.15953	+	1.15953i	−0.0937421	+	0.0937421i
$154$		0			0
$155$	0.0188826	−	0.0700419i	0.00151669	−	0.00562590i
$156$	−5.66074			−0.453222
$157$	−15.3974	−	15.3974i	−1.22885	−	1.22885i	−0.964399	−	0.264451i	$-0.914809\pi$
$157$	−15.3974	−	15.3974i	−1.22885	−	1.22885i	−0.264451	−	0.964399i	$-0.585191\pi$
$158$	3.57886	+	3.57886i	0.284719	+	0.284719i
$159$	2.74660			0.217820
$160$	−1.93820	+	1.11507i	−0.153228	+	0.0881540i
$161$		0			0
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−8.25527	−	8.25527i	−0.646602	−	0.646602i	0.305568	−	0.952170i	$-0.401154\pi$
$163$	−8.25527	−	8.25527i	−0.646602	−	0.646602i	−0.952170	+	0.305568i	$0.901154\pi$
$164$	10.9453			0.854684
$165$	0.893732	−	0.514175i	0.0695770	−	0.0400285i
$166$			1.53885i			0.119438i
$167$	15.5061	+	15.5061i	1.19990	+	1.19990i	0.974196	+	0.225703i	$0.0724679\pi$
$167$	15.5061	+	15.5061i	1.19990	+	1.19990i	0.225703	+	0.974196i	$0.427532\pi$
$168$		0			0
$169$		−	19.0440i		−	1.46492i
$170$	−3.54035	−	0.954441i	−0.271532	−	0.0732023i
$171$			5.82646i			0.445560i
$172$	4.75146	−	4.75146i	0.362295	−	0.362295i
$173$	6.89034	−	6.89034i	0.523863	−	0.523863i	−0.394873	−	0.918736i	$-0.629211\pi$
$173$	6.89034	−	6.89034i	0.523863	−	0.523863i	0.918736	+	0.394873i	$0.129211\pi$
$174$	−5.53773			−0.419814
$175$		0			0
$176$	−0.461115			−0.0347578
$177$	1.35593	−	1.35593i	0.101918	−	0.101918i
$178$	−8.08115	+	8.08115i	−0.605708	+	0.605708i
$179$			1.61515i			0.120722i	0.998177	+	0.0603611i	$0.0192252\pi$
$179$			1.61515i			0.120722i	−0.998177	+	0.0603611i	$0.980775\pi$
$180$	−2.15899	−	0.582041i	−0.160921	−	0.0433828i
$181$		−	12.8519i		−	0.955277i	−0.878556	−	0.477639i	$-0.841493\pi$
$181$		−	12.8519i		−	0.955277i	0.878556	−	0.477639i	$-0.158507\pi$
$182$		0			0
$183$	−9.58509	−	9.58509i	−0.708550	−	0.708550i
$184$		−	4.41231i		−	0.325280i
$185$	15.6305	−	8.99242i	1.14918	−	0.661136i
$186$	−0.0324420			−0.00237876
$187$	−0.534674	−	0.534674i	−0.0390993	−	0.0390993i
$188$	−6.39241	+	6.39241i	−0.466215	+	0.466215i
$189$		0			0
$190$	−11.2928	+	6.49691i	−0.819269	+	0.471335i
$191$	−10.6007			−0.767036			−0.383518	−	0.923533i	$-0.625288\pi$
$191$	−10.6007			−0.767036			−0.383518	+	0.923533i	$0.625288\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	5.10254	+	5.10254i	0.367289	+	0.367289i	0.866487	−	0.499199i	$-0.166372\pi$
$193$	5.10254	+	5.10254i	0.367289	+	0.367289i	−0.499199	+	0.866487i	$0.666372\pi$
$194$	−3.56097			−0.255663
$195$	3.29478	−	12.2215i	0.235944	−	0.875198i
$196$		0			0
$197$	−9.72803	+	9.72803i	−0.693093	+	0.693093i	−0.962911	−	0.269818i	$-0.913036\pi$
$197$	−9.72803	+	9.72803i	−0.693093	+	0.693093i	0.269818	+	0.962911i	$0.413036\pi$
$198$	−0.326057	−	0.326057i	−0.0231719	−	0.0231719i
$199$	9.65296			0.684280			0.342140	−	0.939649i	$-0.388848\pi$
$199$	9.65296			0.684280			0.342140	+	0.939649i	$0.388848\pi$
$200$	−1.27931	−	4.83357i	−0.0904609	−	0.341785i
$201$			3.81023i			0.268753i
$202$	−3.19033	−	3.19033i	−0.224471	−	0.224471i
$203$		0			0
$204$			1.63982i			0.114810i
$205$	−6.37061	+	23.6308i	−0.444943	+	1.65044i
$206$			14.7753i			1.02945i
$207$	3.11997	−	3.11997i	0.216853	−	0.216853i
$208$	−4.00275	+	4.00275i	−0.277541	+	0.277541i
$209$	−2.68667			−0.185841
$210$		0			0
$211$	1.33273			0.0917487			0.0458744	−	0.998947i	$-0.485393\pi$
$211$	1.33273			0.0917487			0.0458744	+	0.998947i	$0.485393\pi$
$212$	1.94214	−	1.94214i	0.133387	−	0.133387i
$213$	6.26410	−	6.26410i	0.429209	−	0.429209i
$214$		−	5.89922i		−	0.403262i
$215$	7.49280	+	13.0239i	0.511005	+	0.888221i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	11.7512	+	11.7512i	0.795893	+	0.795893i
$219$			4.05729i			0.274166i
$220$	0.268388	−	0.995541i	0.0180947	−	0.0671193i
$221$	−9.28258			−0.624414
$222$	−5.70242	−	5.70242i	−0.382722	−	0.382722i
$223$	−8.25284	+	8.25284i	−0.552651	+	0.552651i	−0.927205	−	0.374554i	$-0.877796\pi$
$223$	−8.25284	+	8.25284i	−0.552651	+	0.552651i	0.374554	+	0.927205i	$0.377796\pi$
$224$		0			0
$225$	2.51324	−	4.32246i	0.167549	−	0.288164i
$226$	8.98577			0.597724
$227$	15.8128	+	15.8128i	1.04953	+	1.04953i	0.998708	+	0.0508215i	$0.0161840\pi$
$227$	15.8128	+	15.8128i	1.04953	+	1.04953i	0.0508215	+	0.998708i	$0.483816\pi$
$228$	4.11993	+	4.11993i	0.272849	+	0.272849i
$229$	4.96622			0.328177			0.164088	−	0.986446i	$-0.447532\pi$
$229$	4.96622			0.328177			0.164088	+	0.986446i	$0.447532\pi$
$230$	9.52612	+	2.56814i	0.628134	+	0.169338i
$231$		0			0
$232$	−3.91576	+	3.91576i	−0.257082	+	0.257082i
$233$	20.2472	+	20.2472i	1.32644	+	1.32644i	0.908456	+	0.417980i	$0.137262\pi$
$233$	20.2472	+	20.2472i	1.32644	+	1.32644i	0.417980	+	0.908456i	$0.362738\pi$
$234$	−5.66074			−0.370054
$235$	−10.0805	−	17.5218i	−0.657579	−	1.14300i
$236$		−	1.91758i		−	0.124824i
$237$	3.57886	+	3.57886i	0.232472	+	0.232472i
$238$		0			0
$239$		−	13.9230i		−	0.900603i	−0.892877	−	0.450302i	$-0.851316\pi$
$239$		−	13.9230i		−	0.900603i	0.892877	−	0.450302i	$-0.148684\pi$
$240$	−1.93820	+	1.11507i	−0.125110	+	0.0719775i
$241$		−	1.05757i		−	0.0681239i	−0.999420	−	0.0340620i	$-0.989156\pi$
$241$		−	1.05757i		−	0.0681239i	0.999420	−	0.0340620i	$-0.0108444\pi$
$242$	−7.62782	+	7.62782i	−0.490335	+	0.490335i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−13.5554			−0.867793
$245$		0			0
$246$	10.9453			0.697847
$247$	−23.3218	+	23.3218i	−1.48393	+	1.48393i
$248$	−0.0229400	+	0.0229400i	−0.00145669	+	0.00145669i
$249$			1.53885i			0.0975207i
$250$	11.1802	+	0.0513167i	0.707099	+	0.00324555i
$251$		−	6.36260i		−	0.401604i	−0.979632	−	0.200802i	$-0.935645\pi$
$251$		−	6.36260i		−	0.401604i	0.979632	−	0.200802i	$-0.0643548\pi$
$252$		0			0
$253$	1.43866	+	1.43866i	0.0904481	+	0.0904481i
$254$			16.6534i			1.04493i
$255$	−3.54035	−	0.954441i	−0.221705	−	0.0597694i
$256$	1.00000			0.0625000
$257$	7.34052	+	7.34052i	0.457889	+	0.457889i	0.897962	−	0.440073i	$-0.145047\pi$
$257$	7.34052	+	7.34052i	0.457889	+	0.457889i	−0.440073	+	0.897962i	$0.645047\pi$
$258$	4.75146	−	4.75146i	0.295813	−	0.295813i
$259$		0			0
$260$	−6.31212	−	10.9716i	−0.391461	−	0.680433i
$261$	−5.53773			−0.342777
$262$	13.4184	+	13.4184i	0.828992	+	0.828992i
$263$	16.8022	+	16.8022i	1.03607	+	1.03607i	0.999325	+	0.0367463i	$0.0116993\pi$
$263$	16.8022	+	16.8022i	1.03607	+	1.03607i	0.0367463	+	0.999325i	$0.488301\pi$
$264$	−0.461115			−0.0283796
$265$	3.06265	+	5.32346i	0.188137	+	0.327018i
$266$		0			0
$267$	−8.08115	+	8.08115i	−0.494558	+	0.494558i
$268$	2.69424	+	2.69424i	0.164577	+	0.164577i
$269$	−1.42007			−0.0865833			−0.0432917	−	0.999062i	$-0.513784\pi$
$269$	−1.42007			−0.0865833			−0.0432917	+	0.999062i	$0.513784\pi$
$270$	−2.15899	−	0.582041i	−0.131392	−	0.0354219i
$271$		−	0.353601i		−	0.0214797i	−0.999942	−	0.0107399i	$-0.996581\pi$
$271$		−	0.353601i		−	0.0214797i	0.999942	−	0.0107399i	$-0.00341867\pi$
$272$	1.15953	+	1.15953i	0.0703066	+	0.0703066i
$273$		0			0
$274$			4.42902i			0.267567i
$275$	1.99315	+	1.15889i	0.120191	+	0.0698837i
$276$		−	4.41231i		−	0.265590i
$277$	−16.6182	+	16.6182i	−0.998492	+	0.998492i	−0.999999	−	0.00150661i	$-0.999520\pi$
$277$	−16.6182	+	16.6182i	−0.998492	+	0.998492i	0.00150661	+	0.999999i	$0.499520\pi$
$278$	3.07605	−	3.07605i	0.184489	−	0.184489i
$279$	−0.0324420			−0.00194225
$280$		0			0
$281$	28.4747			1.69866			0.849330	−	0.527862i	$-0.177006\pi$
$281$	28.4747			1.69866			0.849330	+	0.527862i	$0.177006\pi$
$282$	−6.39241	+	6.39241i	−0.380663	+	0.380663i
$283$	−2.65722	+	2.65722i	−0.157956	+	0.157956i	−0.781660	−	0.623705i	$-0.785627\pi$
$283$	−2.65722	+	2.65722i	−0.157956	+	0.157956i	0.623705	+	0.781660i	$0.285627\pi$
$284$		−	8.85877i		−	0.525671i
$285$	−11.2928	+	6.49691i	−0.668930	+	0.384844i
$286$		−	2.61025i		−	0.154347i
$287$		0			0
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	14.3110i		−	0.841823i
$290$	−6.17495	−	10.7332i	−0.362606	−	0.630276i
$291$	−3.56097			−0.208748
$292$	2.86894	+	2.86894i	0.167892	+	0.167892i
$293$	−4.18500	+	4.18500i	−0.244490	+	0.244490i	−0.818705	−	0.574215i	$-0.805308\pi$
$293$	−4.18500	+	4.18500i	−0.244490	+	0.244490i	0.574215	+	0.818705i	$0.305308\pi$
$294$		0			0
$295$	4.14003	+	1.11611i	0.241042	+	0.0649825i
$296$	−8.06444			−0.468736
$297$	−0.326057	−	0.326057i	−0.0189198	−	0.0189198i
$298$	−3.06921	−	3.06921i	−0.177794	−	0.177794i
$299$	24.9769			1.44445
$300$	−1.27931	−	4.83357i	−0.0738610	−	0.279066i
$301$		0			0
$302$	5.78777	−	5.78777i	0.333049	−	0.333049i
$303$	−3.19033	−	3.19033i	−0.183280	−	0.183280i
$304$	5.82646			0.334170
$305$	7.88978	−	29.2659i	0.451767	−	1.67576i
$306$			1.63982i			0.0937421i
$307$	−18.0884	−	18.0884i	−1.03236	−	1.03236i	−0.999459	−	0.0329031i	$-0.989525\pi$
$307$	−18.0884	−	18.0884i	−1.03236	−	1.03236i	−0.0329031	−	0.999459i	$-0.510475\pi$
$308$		0			0
$309$			14.7753i			0.840540i
$310$	−0.0361751	−	0.0628791i	−0.00205461	−	0.00357130i
$311$			33.6176i			1.90628i	0.302531	+	0.953139i	$0.402168\pi$
$311$			33.6176i			1.90628i	−0.302531	+	0.953139i	$0.597832\pi$
$312$	−4.00275	+	4.00275i	−0.226611	+	0.226611i
$313$	−16.2383	+	16.2383i	−0.917843	+	0.917843i	−0.996872	−	0.0790289i	$-0.974818\pi$
$313$	−16.2383	+	16.2383i	−0.917843	+	0.917843i	0.0790289	+	0.996872i	$0.474818\pi$
$314$	−21.7753			−1.22885
$315$		0			0
$316$	5.06128			0.284719
$317$	18.1316	−	18.1316i	1.01837	−	1.01837i	0.0185453	−	0.999828i	$-0.494096\pi$
$317$	18.1316	−	18.1316i	1.01837	−	1.01837i	0.999828	−	0.0185453i	$-0.00590350\pi$
$318$	1.94214	−	1.94214i	0.108910	−	0.108910i
$319$		−	2.55353i		−	0.142970i
$320$	−0.582041	+	2.15899i	−0.0325371	+	0.120691i
$321$		−	5.89922i		−	0.329262i
$322$		0			0
$323$	6.75593	+	6.75593i	0.375910	+	0.375910i
$324$			1.00000i			0.0555556i
$325$	27.3616	−	7.24185i	1.51775	−	0.401705i
$326$	−11.6747			−0.646602
$327$	11.7512	+	11.7512i	0.649844	+	0.649844i
$328$	7.73949	−	7.73949i	0.427342	−	0.427342i
$329$		0			0
$330$	0.268388	−	0.995541i	0.0147742	−	0.0548027i
$331$	−11.8648			−0.652151			−0.326076	−	0.945344i	$-0.605726\pi$
$331$	−11.8648			−0.652151			−0.326076	+	0.945344i	$0.605726\pi$
$332$	1.08813	+	1.08813i	0.0597190	+	0.0597190i
$333$	−5.70242	−	5.70242i	−0.312491	−	0.312491i
$334$	21.9290			1.19990
$335$	−7.38499	+	4.24868i	−0.403485	+	0.232130i
$336$		0			0
$337$	−3.18746	+	3.18746i	−0.173632	+	0.173632i	−0.788573	−	0.614941i	$-0.789180\pi$
$337$	−3.18746	+	3.18746i	−0.173632	+	0.173632i	0.614941	+	0.788573i	$0.289180\pi$
$338$	−13.4661	−	13.4661i	−0.732461	−	0.732461i
$339$	8.98577			0.488040
$340$	−3.17829	+	1.82851i	−0.172367	+	0.0991649i
$341$		−	0.0149595i		−	0.000810102i
$342$	4.11993	+	4.11993i	0.222780	+	0.222780i
$343$		0			0
$344$		−	6.71958i		−	0.362295i
$345$	9.52612	+	2.56814i	0.512869	+	0.138264i
$346$		−	9.74441i		−	0.523863i
$347$	−15.1477	+	15.1477i	−0.813172	+	0.813172i	−0.985108	−	0.171936i	$-0.944998\pi$
$347$	−15.1477	+	15.1477i	−0.813172	+	0.813172i	0.171936	+	0.985108i	$0.444998\pi$
$348$	−3.91576	+	3.91576i	−0.209907	+	0.209907i
$349$	16.0682			0.860113			0.430056	−	0.902802i	$-0.358494\pi$
$349$	16.0682			0.860113			0.430056	+	0.902802i	$0.358494\pi$
$350$		0			0
$351$	−5.66074			−0.302148
$352$	−0.326057	+	0.326057i	−0.0173789	+	0.0173789i
$353$	−20.7861	+	20.7861i	−1.10633	+	1.10633i	−0.112703	+	0.993629i	$0.535951\pi$
$353$	−20.7861	+	20.7861i	−1.10633	+	1.10633i	−0.993629	+	0.112703i	$0.964049\pi$
$354$		−	1.91758i		−	0.101918i
$355$	19.1260	+	5.15617i	1.01510	+	0.273661i
$356$			11.4285i			0.605708i
$357$		0			0
$358$	1.14209	+	1.14209i	0.0603611	+	0.0603611i
$359$			13.6274i			0.719226i	0.933102	+	0.359613i	$0.117091\pi$
$359$			13.6274i			0.719226i	−0.933102	+	0.359613i	$0.882909\pi$
$360$	−1.93820	+	1.11507i	−0.102152	+	0.0587693i
$361$	14.9476			0.786717
$362$	−9.08769	−	9.08769i	−0.477639	−	0.477639i
$363$	−7.62782	+	7.62782i	−0.400357	+	0.400357i
$364$		0			0
$365$	−7.86384	+	4.52416i	−0.411612	+	0.236805i
$366$	−13.5554			−0.708550
$367$	−9.02205	−	9.02205i	−0.470947	−	0.470947i	0.431274	−	0.902221i	$-0.358064\pi$
$367$	−9.02205	−	9.02205i	−0.470947	−	0.470947i	−0.902221	+	0.431274i	$0.858064\pi$
$368$	−3.11997	−	3.11997i	−0.162640	−	0.162640i
$369$	10.9453			0.569789
$370$	4.69384	−	17.4110i	0.244021	−	0.905157i
$371$		0			0
$372$	−0.0229400	+	0.0229400i	−0.00118938	+	0.00118938i
$373$	2.82938	+	2.82938i	0.146500	+	0.146500i	0.776552	−	0.630053i	$-0.216967\pi$
$373$	2.82938	+	2.82938i	0.146500	+	0.146500i	−0.630053	+	0.776552i	$0.716967\pi$
$374$	−0.756144			−0.0390993
$375$	11.1802	+	0.0513167i	0.577344	+	0.00264998i
$376$			9.04024i			0.466215i
$377$	−22.1661	−	22.1661i	−1.14161	−	1.14161i
$378$		0			0
$379$		−	1.00281i		−	0.0515109i	−0.999668	−	0.0257555i	$-0.991801\pi$
$379$		−	1.00281i		−	0.0515109i	0.999668	−	0.0257555i	$-0.00819912\pi$
$380$	−3.39124	+	12.5793i	−0.173967	+	0.645302i
$381$			16.6534i			0.853180i
$382$	−7.49579	+	7.49579i	−0.383518	+	0.383518i
$383$	12.5887	−	12.5887i	0.643255	−	0.643255i	−0.308100	−	0.951354i	$-0.599693\pi$
$383$	12.5887	−	12.5887i	0.643255	−	0.643255i	0.951354	+	0.308100i	$0.0996930\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	7.21608			0.367289
$387$	4.75146	−	4.75146i	0.241530	−	0.241530i
$388$	−2.51799	+	2.51799i	−0.127832	+	0.127832i
$389$		−	11.2587i		−	0.570839i	−0.958403	−	0.285419i	$-0.907867\pi$
$389$		−	11.2587i		−	0.570839i	0.958403	−	0.285419i	$-0.0921329\pi$
$390$	−6.31212	−	10.9716i	−0.319627	−	0.555571i
$391$		−	7.23538i		−	0.365909i
$392$		0			0
$393$	13.4184	+	13.4184i	0.676869	+	0.676869i
$394$			13.7575i			0.693093i
$395$	−2.94587	+	10.9272i	−0.148223	+	0.549809i
$396$	−0.461115			−0.0231719
$397$	−2.71023	−	2.71023i	−0.136022	−	0.136022i	0.635817	−	0.771840i	$-0.280663\pi$
$397$	−2.71023	−	2.71023i	−0.136022	−	0.136022i	−0.771840	+	0.635817i	$0.780663\pi$
$398$	6.82567	−	6.82567i	0.342140	−	0.342140i
$399$		0			0
$400$	−4.32246	−	2.51324i	−0.216123	−	0.125662i
$401$	0.900044			0.0449461			0.0224730	−	0.999747i	$-0.492846\pi$
$401$	0.900044			0.0449461			0.0224730	+	0.999747i	$0.492846\pi$
$402$	2.69424	+	2.69424i	0.134377	+	0.134377i
$403$	−0.129857	−	0.129857i	−0.00646865	−	0.00646865i
$404$	−4.51181			−0.224471
$405$	−2.15899	−	0.582041i	−0.107281	−	0.0289218i
$406$		0			0
$407$	2.62947	−	2.62947i	0.130338	−	0.130338i
$408$	1.15953	+	1.15953i	0.0574051	+	0.0574051i
$409$	12.8927			0.637501			0.318751	−	0.947839i	$-0.396737\pi$
$409$	12.8927			0.637501			0.318751	+	0.947839i	$0.396737\pi$
$410$	12.2048	+	21.2142i	0.602751	+	1.04769i
$411$			4.42902i			0.218468i
$412$	10.4477	+	10.4477i	0.514723	+	0.514723i
$413$		0			0
$414$		−	4.41231i		−	0.216853i
$415$	−2.98260	+	1.71593i	−0.146410	+	0.0842315i
$416$			5.66074i			0.277541i
$417$	3.07605	−	3.07605i	0.150635	−	0.150635i
$418$	−1.89976	+	1.89976i	−0.0929203	+	0.0929203i
$419$	19.8918			0.971777			0.485888	−	0.874021i	$-0.338496\pi$
$419$	19.8918			0.971777			0.485888	+	0.874021i	$0.338496\pi$
$420$		0			0
$421$	−12.6339			−0.615740			−0.307870	−	0.951428i	$-0.599616\pi$
$421$	−12.6339			−0.615740			−0.307870	+	0.951428i	$0.599616\pi$
$422$	0.942380	−	0.942380i	0.0458744	−	0.0458744i
$423$	−6.39241	+	6.39241i	−0.310810	+	0.310810i
$424$		−	2.74660i		−	0.133387i
$425$	−2.09784	−	7.92617i	−0.101760	−	0.384476i
$426$		−	8.85877i		−	0.429209i
$427$		0			0
$428$	−4.17138	−	4.17138i	−0.201631	−	0.201631i
$429$		−	2.61025i		−	0.126024i
$430$	14.5075	+	3.91107i	0.699613	+	0.188608i
$431$	30.7701			1.48215			0.741073	−	0.671425i	$-0.234317\pi$
$431$	30.7701			1.48215			0.741073	+	0.671425i	$0.234317\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−3.04743	+	3.04743i	−0.146450	+	0.146450i	−0.776530	−	0.630080i	$-0.783022\pi$
$433$	−3.04743	+	3.04743i	−0.146450	+	0.146450i	0.630080	+	0.776530i	$0.283022\pi$
$434$		0			0
$435$	−6.17495	−	10.7332i	−0.296066	−	0.514618i
$436$	16.6187			0.795893
$437$	−18.1784	−	18.1784i	−0.869590	−	0.869590i
$438$	2.86894	+	2.86894i	0.137083	+	0.137083i
$439$	−36.9987			−1.76585			−0.882926	−	0.469513i	$-0.844430\pi$
$439$	−36.9987			−1.76585			−0.882926	+	0.469513i	$0.844430\pi$
$440$	−0.514175	−	0.893732i	−0.0245123	−	0.0426070i
$441$		0			0
$442$	−6.56378	+	6.56378i	−0.312207	+	0.312207i
$443$	−12.5847	−	12.5847i	−0.597919	−	0.597919i	0.341839	−	0.939758i	$-0.388950\pi$
$443$	−12.5847	−	12.5847i	−0.597919	−	0.597919i	−0.939758	+	0.341839i	$0.888950\pi$
$444$	−8.06444			−0.382722
$445$	−24.6739	−	6.65183i	−1.16966	−	0.315327i
$446$			11.6713i			0.552651i
$447$	−3.06921	−	3.06921i	−0.145169	−	0.145169i
$448$		0			0
$449$		−	2.41945i		−	0.114181i	−0.998369	−	0.0570904i	$-0.981818\pi$
$449$		−	2.41945i		−	0.114181i	0.998369	−	0.0570904i	$-0.0181823\pi$
$450$	−1.27931	−	4.83357i	−0.0603073	−	0.227857i
$451$			5.04704i			0.237656i
$452$	6.35390	−	6.35390i	0.298862	−	0.298862i
$453$	5.78777	−	5.78777i	0.271933	−	0.271933i
$454$	22.3626			1.04953
$455$		0			0
$456$	5.82646			0.272849
$457$	−19.4870	+	19.4870i	−0.911565	+	0.911565i	−0.996395	−	0.0848308i	$-0.972965\pi$
$457$	−19.4870	+	19.4870i	−0.911565	+	0.911565i	0.0848308	+	0.996395i	$0.472965\pi$
$458$	3.51165	−	3.51165i	0.164088	−	0.164088i
$459$			1.63982i			0.0765401i
$460$	8.55193	−	4.92003i	0.398736	−	0.229398i
$461$			1.02712i			0.0478378i	0.999714	+	0.0239189i	$0.00761434\pi$
$461$			1.02712i			0.0478378i	−0.999714	+	0.0239189i	$0.992386\pi$
$462$		0			0
$463$	−8.26507	−	8.26507i	−0.384111	−	0.384111i	0.488470	−	0.872581i	$-0.337555\pi$
$463$	−8.26507	−	8.26507i	−0.384111	−	0.384111i	−0.872581	+	0.488470i	$0.837555\pi$
$464$			5.53773i			0.257082i
$465$	−0.0361751	−	0.0628791i	−0.00167758	−	0.00291595i
$466$	28.6338			1.32644
$467$	−13.1131	−	13.1131i	−0.606804	−	0.606804i	0.335305	−	0.942109i	$-0.391160\pi$
$467$	−13.1131	−	13.1131i	−0.606804	−	0.606804i	−0.942109	+	0.335305i	$0.891160\pi$
$468$	−4.00275	+	4.00275i	−0.185027	+	0.185027i
$469$		0			0
$470$	−19.5178	−	5.26179i	−0.900287	−	0.242708i
$471$	−21.7753			−1.00335
$472$	−1.35593	−	1.35593i	−0.0624120	−	0.0624120i
$473$	2.19097	+	2.19097i	0.100741	+	0.100741i
$474$	5.06128			0.232472
$475$	−25.1846	−	14.6433i	−1.15555	−	0.671880i
$476$		0			0
$477$	1.94214	−	1.94214i	0.0889245	−	0.0889245i
$478$	−9.84504	−	9.84504i	−0.450302	−	0.450302i
$479$	8.47745			0.387344			0.193672	−	0.981066i	$-0.437960\pi$
$479$	8.47745			0.387344			0.193672	+	0.981066i	$0.437960\pi$
$480$	−0.582041	+	2.15899i	−0.0265664	+	0.0985439i
$481$		−	45.6507i		−	2.08149i
$482$	−0.747813	−	0.747813i	−0.0340620	−	0.0340620i
$483$		0			0
$484$			10.7874i			0.490335i
$485$	−3.97074	−	6.90188i	−0.180302	−	0.313398i
$486$			1.00000i			0.0453609i
$487$	−3.43393	+	3.43393i	−0.155606	+	0.155606i	−0.780617	−	0.625010i	$-0.785095\pi$
$487$	−3.43393	+	3.43393i	−0.155606	+	0.155606i	0.625010	+	0.780617i	$0.285095\pi$
$488$	−9.58509	+	9.58509i	−0.433897	+	0.433897i
$489$	−11.6747			−0.527949
$490$		0			0
$491$	−37.8594			−1.70857			−0.854286	−	0.519803i	$-0.826005\pi$
$491$	−37.8594			−1.70857			−0.854286	+	0.519803i	$0.826005\pi$
$492$	7.73949	−	7.73949i	0.348923	−	0.348923i
$493$	−6.42114	+	6.42114i	−0.289193	+	0.289193i
$494$			32.9821i			1.48393i
$495$	0.268388	−	0.995541i	0.0120631	−	0.0447462i
$496$			0.0324420i			0.00145669i
$497$		0			0
$498$	1.08813	+	1.08813i	0.0487604	+	0.0487604i
$499$			0.512196i			0.0229290i	0.999934	+	0.0114645i	$0.00364935\pi$
$499$			0.512196i			0.0229290i	−0.999934	+	0.0114645i	$0.996351\pi$
$500$	7.94190	−	7.86932i	0.355172	−	0.351927i
$501$	21.9290			0.979714
$502$	−4.49904	−	4.49904i	−0.200802	−	0.200802i
$503$	8.58209	−	8.58209i	0.382657	−	0.382657i	−0.489402	−	0.872058i	$-0.662785\pi$
$503$	8.58209	−	8.58209i	0.382657	−	0.382657i	0.872058	+	0.489402i	$0.162785\pi$
$504$		0			0
$505$	2.62606	−	9.74094i	0.116858	−	0.433466i
$506$	2.03458			0.0904481
$507$	−13.4661	−	13.4661i	−0.598052	−	0.598052i
$508$	11.7757	+	11.7757i	0.522464	+	0.522464i
$509$	11.3876			0.504748			0.252374	−	0.967630i	$-0.418789\pi$
$509$	11.3876			0.504748			0.252374	+	0.967630i	$0.418789\pi$
$510$	−3.17829	+	1.82851i	−0.140737	+	0.0809678i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	4.11993	+	4.11993i	0.181899	+	0.181899i
$514$	10.3811			0.457889
$515$	−28.6376	+	16.4755i	−1.26192	+	0.725999i
$516$		−	6.71958i		−	0.295813i
$517$	−2.94764	−	2.94764i	−0.129637	−	0.129637i
$518$		0			0
$519$		−	9.74441i		−	0.427732i
$520$	−12.2215	−	3.29478i	−0.535947	−	0.144486i
$521$		−	19.5013i		−	0.854365i	−0.904165	−	0.427183i	$-0.859506\pi$
$521$		−	19.5013i		−	0.854365i	0.904165	−	0.427183i	$-0.140494\pi$
$522$	−3.91576	+	3.91576i	−0.171388	+	0.171388i
$523$	10.5304	−	10.5304i	0.460462	−	0.460462i	−0.438345	−	0.898807i	$-0.644435\pi$
$523$	10.5304	−	10.5304i	0.460462	−	0.460462i	0.898807	+	0.438345i	$0.144435\pi$
$524$	18.9765			0.828992
$525$		0			0
$526$	23.7620			1.03607
$527$	−0.0376174	+	0.0376174i	−0.00163864	+	0.00163864i
$528$	−0.326057	+	0.326057i	−0.0141898	+	0.0141898i
$529$		−	3.53155i		−	0.153546i
$530$	5.92988	+	1.59863i	0.257577	+	0.0694402i
$531$		−	1.91758i		−	0.0832159i
$532$		0			0
$533$	43.8113	+	43.8113i	1.89768	+	1.89768i
$534$			11.4285i			0.494558i
$535$	11.4339	−	6.57804i	0.494329	−	0.284394i
$536$	3.81023			0.164577
$537$	1.14209	+	1.14209i	0.0492846	+	0.0492846i
$538$	−1.00414	+	1.00414i	−0.0432917	+	0.0432917i
$539$		0			0
$540$	−1.93820	+	1.11507i	−0.0834068	+	0.0479850i
$541$	43.8119			1.88362			0.941810	−	0.336145i	$-0.109123\pi$
$541$	43.8119			1.88362			0.941810	+	0.336145i	$0.109123\pi$
$542$	−0.250034	−	0.250034i	−0.0107399	−	0.0107399i
$543$	−9.08769	−	9.08769i	−0.389990	−	0.389990i
$544$	1.63982			0.0703066
$545$	−9.67279	+	35.8797i	−0.414337	+	1.53692i
$546$		0			0
$547$	8.59346	−	8.59346i	0.367430	−	0.367430i	−0.499109	−	0.866539i	$-0.666339\pi$
$547$	8.59346	−	8.59346i	0.367430	−	0.367430i	0.866539	+	0.499109i	$0.166339\pi$
$548$	3.13179	+	3.13179i	0.133784	+	0.133784i
$549$	−13.5554			−0.578529
$550$	2.22883	−	0.589909i	0.0950375	−	0.0251538i
$551$			32.2653i			1.37455i
$552$	−3.11997	−	3.11997i	−0.132795	−	0.132795i
$553$		0			0
$554$			23.5017i			0.998492i
$555$	4.69384	−	17.4110i	0.199242	−	0.739057i
$556$		−	4.35020i		−	0.184489i
$557$	6.03331	−	6.03331i	0.255640	−	0.255640i	−0.567638	−	0.823278i	$-0.692143\pi$
$557$	6.03331	−	6.03331i	0.255640	−	0.255640i	0.823278	+	0.567638i	$0.192143\pi$
$558$	−0.0229400	+	0.0229400i	−0.000971127	+	0.000971127i
$559$	38.0378			1.60883
$560$		0			0
$561$	−0.756144			−0.0319244
$562$	20.1347	−	20.1347i	0.849330	−	0.849330i
$563$	−0.0998745	+	0.0998745i	−0.00420921	+	0.00420921i	−0.709208	−	0.704999i	$-0.750947\pi$
$563$	−0.0998745	+	0.0998745i	−0.00420921	+	0.00420921i	0.704999	+	0.709208i	$0.250947\pi$
$564$			9.04024i			0.380663i
$565$	10.0198	+	17.4162i	0.421534	+	0.732706i
$566$			3.75788i			0.157956i
$567$		0			0
$568$	−6.26410	−	6.26410i	−0.262836	−	0.262836i
$569$		−	4.19043i		−	0.175672i	−0.996135	−	0.0878359i	$-0.972005\pi$
$569$		−	4.19043i		−	0.175672i	0.996135	−	0.0878359i	$-0.0279951\pi$
$570$	−3.39124	+	12.5793i	−0.142043	+	0.526887i
$571$	−9.79512			−0.409913			−0.204957	−	0.978771i	$-0.565705\pi$
$571$	−9.79512			−0.409913			−0.204957	+	0.978771i	$0.565705\pi$
$572$	−1.84573	−	1.84573i	−0.0771737	−	0.0771737i
$573$	−7.49579	+	7.49579i	−0.313141	+	0.313141i
$574$		0			0
$575$	5.64471	+	21.3272i	0.235401	+	0.889405i
$576$	1.00000			0.0416667
$577$	−5.75211	−	5.75211i	−0.239464	−	0.239464i	0.577164	−	0.816628i	$-0.304159\pi$
$577$	−5.75211	−	5.75211i	−0.239464	−	0.239464i	−0.816628	+	0.577164i	$0.804159\pi$
$578$	−10.1194	−	10.1194i	−0.420912	−	0.420912i
$579$	7.21608			0.299890
$580$	−11.9559	−	3.22318i	−0.496441	−	0.133835i
$581$		0			0
$582$	−2.51799	+	2.51799i	−0.104374	+	0.104374i
$583$	0.895549	+	0.895549i	0.0370899	+	0.0370899i
$584$	4.05729			0.167892
$585$	−6.31212	−	10.9716i	−0.260974	−	0.453622i
$586$			5.91848i			0.244490i
$587$	−20.3618	−	20.3618i	−0.840423	−	0.840423i	0.148491	−	0.988914i	$-0.452558\pi$
$587$	−20.3618	−	20.3618i	−0.840423	−	0.840423i	−0.988914	+	0.148491i	$0.952558\pi$
$588$		0			0
$589$			0.189022i			0.00778852i
$590$	3.71666	−	2.13824i	0.153012	−	0.0880298i
$591$			13.7575i			0.565908i
$592$	−5.70242	+	5.70242i	−0.234368	+	0.234368i
$593$	−13.2775	+	13.2775i	−0.545242	+	0.545242i	−0.925061	−	0.379819i	$-0.875986\pi$
$593$	−13.2775	+	13.2775i	−0.545242	+	0.545242i	0.379819	+	0.925061i	$0.375986\pi$
$594$	−0.461115			−0.0189198
$595$		0			0
$596$	−4.34052			−0.177794
$597$	6.82567	−	6.82567i	0.279356	−	0.279356i
$598$	17.6614	−	17.6614i	0.722226	−	0.722226i
$599$		−	24.2998i		−	0.992862i	−0.868076	−	0.496431i	$-0.834644\pi$
$599$		−	24.2998i		−	0.992862i	0.868076	−	0.496431i	$-0.165356\pi$
$600$	−4.32246	−	2.51324i	−0.176464	−	0.102603i
$601$			21.1930i			0.864481i	0.901758	+	0.432241i	$0.142277\pi$
$601$			21.1930i			0.864481i	−0.901758	+	0.432241i	$0.857723\pi$
$602$		0			0
$603$	2.69424	+	2.69424i	0.109718	+	0.109718i
$604$		−	8.18514i		−	0.333049i
$605$	−23.2898	−	6.27869i	−0.946865	−	0.255265i
$606$	−4.51181			−0.183280
$607$	6.74182	+	6.74182i	0.273642	+	0.273642i	0.830564	−	0.556923i	$-0.188018\pi$
$607$	6.74182	+	6.74182i	0.273642	+	0.273642i	−0.556923	+	0.830564i	$0.688018\pi$
$608$	4.11993	−	4.11993i	0.167085	−	0.167085i
$609$		0			0
$610$	−15.1152	−	26.2730i	−0.611996	−	1.06376i
$611$	−51.1744			−2.07030
$612$	1.15953	+	1.15953i	0.0468711	+	0.0468711i
$613$	−15.7821	−	15.7821i	−0.637431	−	0.637431i	0.312490	−	0.949921i	$-0.398837\pi$
$613$	−15.7821	−	15.7821i	−0.637431	−	0.637431i	−0.949921	+	0.312490i	$0.898837\pi$
$614$	−25.5809			−1.03236
$615$	12.2048	+	21.2142i	0.492144	+	0.855438i
$616$		0			0
$617$	15.4571	−	15.4571i	0.622278	−	0.622278i	−0.323836	−	0.946113i	$-0.604973\pi$
$617$	15.4571	−	15.4571i	0.622278	−	0.622278i	0.946113	+	0.323836i	$0.104973\pi$
$618$	10.4477	+	10.4477i	0.420270	+	0.420270i
$619$	−24.7191			−0.993543			−0.496772	−	0.867881i	$-0.665481\pi$
$619$	−24.7191			−0.993543			−0.496772	+	0.867881i	$0.665481\pi$
$620$	−0.0700419	−	0.0188826i	−0.00281295	−	0.000758343i
$621$		−	4.41231i		−	0.177060i
$622$	23.7712	+	23.7712i	0.953139	+	0.953139i
$623$		0			0
$624$			5.66074i			0.226611i
$625$	12.3673	+	21.7267i	0.494691	+	0.869069i
$626$			22.9644i			0.917843i
$627$	−1.89976	+	1.89976i	−0.0758691	+	0.0758691i
$628$	−15.3974	+	15.3974i	−0.614425	+	0.614425i
$629$	−13.2242			−0.527284
$630$		0			0
$631$	34.7305			1.38260			0.691299	−	0.722569i	$-0.257039\pi$
$631$	34.7305			1.38260			0.691299	+	0.722569i	$0.257039\pi$
$632$	3.57886	−	3.57886i	0.142359	−	0.142359i
$633$	0.942380	−	0.942380i	0.0374563	−	0.0374563i
$634$		−	25.6420i		−	1.01837i
$635$	−32.2776	+	18.5697i	−1.28090	+	0.736917i
$636$		−	2.74660i		−	0.108910i
$637$		0			0
$638$	−1.80562	−	1.80562i	−0.0714850	−	0.0714850i
$639$		−	8.85877i		−	0.350448i
$640$	1.11507	+	1.93820i	0.0440770	+	0.0766141i
$641$	11.6521			0.460229			0.230115	−	0.973164i	$-0.426090\pi$
$641$	11.6521			0.460229			0.230115	+	0.973164i	$0.426090\pi$
$642$	−4.17138	−	4.17138i	−0.164631	−	0.164631i
$643$	−21.8198	+	21.8198i	−0.860489	+	0.860489i	−0.991395	−	0.130906i	$-0.958211\pi$
$643$	−21.8198	+	21.8198i	−0.860489	+	0.860489i	0.130906	+	0.991395i	$0.458211\pi$
$644$		0			0
$645$	14.5075	+	3.91107i	0.571232	+	0.153998i
$646$	9.55433			0.375910
$647$	−26.2680	−	26.2680i	−1.03270	−	1.03270i	−0.999447	−	0.0332527i	$-0.989413\pi$
$647$	−26.2680	−	26.2680i	−1.03270	−	1.03270i	−0.0332527	−	0.999447i	$-0.510587\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	0.884225			0.0347089
$650$	14.2268	−	24.4683i	0.558021	−	0.959726i
$651$		0			0
$652$	−8.25527	+	8.25527i	−0.323301	+	0.323301i
$653$	22.3571	+	22.3571i	0.874903	+	0.874903i	0.993002	−	0.118099i	$-0.0376801\pi$
$653$	22.3571	+	22.3571i	0.874903	+	0.874903i	−0.118099	+	0.993002i	$0.537680\pi$
$654$	16.6187			0.649844
$655$	−11.0451	+	40.9700i	−0.431568	+	1.60083i
$656$		−	10.9453i		−	0.427342i
$657$	2.86894	+	2.86894i	0.111928	+	0.111928i
$658$		0			0
$659$		−	38.7284i		−	1.50864i	−0.656504	−	0.754322i	$-0.727966\pi$
$659$		−	38.7284i		−	1.50864i	0.656504	−	0.754322i	$-0.272034\pi$
$660$	−0.514175	−	0.893732i	−0.0200142	−	0.0347885i
$661$		−	33.8658i		−	1.31723i	−0.752482	−	0.658613i	$-0.771143\pi$
$661$		−	33.8658i		−	1.31723i	0.752482	−	0.658613i	$-0.228857\pi$
$662$	−8.38971	+	8.38971i	−0.326076	+	0.326076i
$663$	−6.56378	+	6.56378i	−0.254916	+	0.254916i
$664$	1.53885			0.0597190
$665$		0			0
$666$	−8.06444			−0.312491
$667$	17.2775	−	17.2775i	0.668989	−	0.668989i
$668$	15.5061	−	15.5061i	0.599950	−	0.599950i
$669$			11.6713i			0.451238i
$670$	−2.21771	+	8.22625i	−0.0856777	+	0.317808i
$671$		−	6.25058i		−	0.241301i
$672$		0			0
$673$	−24.7046	−	24.7046i	−0.952294	−	0.952294i	0.0466190	−	0.998913i	$-0.485155\pi$
$673$	−24.7046	−	24.7046i	−0.952294	−	0.952294i	−0.998913	+	0.0466190i	$0.985155\pi$
$674$			4.50775i			0.173632i
$675$	−1.27931	−	4.83357i	−0.0492407	−	0.186044i
$676$	−19.0440			−0.732461
$677$	−12.4482	−	12.4482i	−0.478425	−	0.478425i	0.426203	−	0.904628i	$-0.359851\pi$
$677$	−12.4482	−	12.4482i	−0.478425	−	0.478425i	−0.904628	+	0.426203i	$0.859851\pi$
$678$	6.35390	−	6.35390i	0.244020	−	0.244020i
$679$		0			0
$680$	−0.954441	+	3.54035i	−0.0366011	+	0.135766i
$681$	22.3626			0.856937
$682$	−0.0105780	−	0.0105780i	−0.000405051	−	0.000405051i
$683$	−17.0933	−	17.0933i	−0.654057	−	0.654057i	0.299910	−	0.953967i	$-0.403043\pi$
$683$	−17.0933	−	17.0933i	−0.654057	−	0.654057i	−0.953967	+	0.299910i	$0.903043\pi$
$684$	5.82646			0.222780
$685$	−8.58433	+	4.93867i	−0.327991	+	0.188697i
$686$		0			0
$687$	3.51165	−	3.51165i	0.133978	−	0.133978i
$688$	−4.75146	−	4.75146i	−0.181148	−	0.181148i
$689$	15.5478			0.592324
$690$	8.55193	−	4.92003i	0.325567	−	0.187302i
$691$		−	2.96578i		−	0.112824i	−0.998408	−	0.0564118i	$-0.982034\pi$
$691$		−	2.96578i		−	0.112824i	0.998408	−	0.0564118i	$-0.0179660\pi$
$692$	−6.89034	−	6.89034i	−0.261931	−	0.261931i
$693$		0			0
$694$			21.4221i			0.813172i
$695$	9.39202	+	2.53199i	0.356260	+	0.0960439i
$696$			5.53773i			0.209907i
$697$	12.6914	−	12.6914i	0.480719	−	0.480719i
$698$	11.3620	−	11.3620i	0.430056	−	0.430056i
$699$	28.6338			1.08303
$700$		0			0
$701$	−18.6815			−0.705591			−0.352795	−	0.935701i	$-0.614769\pi$
$701$	−18.6815			−0.705591			−0.352795	+	0.935701i	$0.614769\pi$
$702$	−4.00275	+	4.00275i	−0.151074	+	0.151074i
$703$	−33.2249	+	33.2249i	−1.25310	+	1.25310i
$704$			0.461115i			0.0173789i
$705$	−19.5178	−	5.26179i	−0.735082	−	0.198170i
$706$			29.3960i			1.10633i
$707$		0			0
$708$	−1.35593	−	1.35593i	−0.0509592	−	0.0509592i
$709$		−	21.1525i		−	0.794401i	−0.917732	−	0.397200i	$-0.869982\pi$
$709$		−	21.1525i		−	0.794401i	0.917732	−	0.397200i	$-0.130018\pi$
$710$	17.1701	−	9.87815i	0.644381	−	0.370720i
$711$	5.06128			0.189813
$712$	8.08115	+	8.08115i	0.302854	+	0.302854i
$713$	0.101218	−	0.101218i	0.00379065	−	0.00379065i
$714$		0			0
$715$	5.05919	−	2.91061i	0.189203	−	0.108851i
$716$	1.61515			0.0603611
$717$	−9.84504	−	9.84504i	−0.367670	−	0.367670i
$718$	9.63602	+	9.63602i	0.359613	+	0.359613i
$719$	8.61250			0.321192			0.160596	−	0.987020i	$-0.448658\pi$
$719$	8.61250			0.321192			0.160596	+	0.987020i	$0.448658\pi$
$720$	−0.582041	+	2.15899i	−0.0216914	+	0.0804607i
$721$		0			0
$722$	10.5696	−	10.5696i	0.393359	−	0.393359i
$723$	−0.747813	−	0.747813i	−0.0278115	−	0.0278115i
$724$	−12.8519			−0.477639
$725$	13.9176	−	23.9366i	0.516888	−	0.888982i
$726$			10.7874i			0.400357i
$727$	−12.8013	−	12.8013i	−0.474774	−	0.474774i	0.428682	−	0.903455i	$-0.358978\pi$
$727$	−12.8013	−	12.8013i	−0.474774	−	0.474774i	−0.903455	+	0.428682i	$0.858978\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−2.36151	+	8.75964i	−0.0874033	+	0.324209i
$731$		−	11.0189i		−	0.407548i
$732$	−9.58509	+	9.58509i	−0.354275	+	0.354275i
$733$	23.3893	−	23.3893i	0.863903	−	0.863903i	−0.127886	−	0.991789i	$-0.540819\pi$
$733$	23.3893	−	23.3893i	0.863903	−	0.863903i	0.991789	+	0.127886i	$0.0408192\pi$
$734$	−12.7591			−0.470947
$735$		0			0
$736$	−4.41231			−0.162640
$737$	−1.24235	+	1.24235i	−0.0457627	+	0.0457627i
$738$	7.73949	−	7.73949i	0.284895	−	0.284895i
$739$		−	47.3172i		−	1.74059i	−0.492528	−	0.870296i	$-0.663927\pi$
$739$		−	47.3172i		−	1.74059i	0.492528	−	0.870296i	$-0.336073\pi$
$740$	−8.99242	−	15.6305i	−0.330568	−	0.574589i
$741$			32.9821i			1.21163i
$742$		0			0
$743$	−21.5587	−	21.5587i	−0.790914	−	0.790914i	0.190729	−	0.981643i	$-0.438915\pi$
$743$	−21.5587	−	21.5587i	−0.790914	−	0.790914i	−0.981643	+	0.190729i	$0.938915\pi$
$744$			0.0324420i			0.00118938i
$745$	2.52636	−	9.37112i	0.0925586	−	0.343331i
$746$	4.00135			0.146500
$747$	1.08813	+	1.08813i	0.0398127	+	0.0398127i
$748$	−0.534674	+	0.534674i	−0.0195496	+	0.0195496i
$749$		0			0
$750$	7.94190	−	7.86932i	0.289997	−	0.287347i
$751$	31.0138			1.13171			0.565854	−	0.824505i	$-0.308547\pi$
$751$	31.0138			1.13171			0.565854	+	0.824505i	$0.308547\pi$
$752$	6.39241	+	6.39241i	0.233107	+	0.233107i
$753$	−4.49904	−	4.49904i	−0.163954	−	0.163954i
$754$	−31.3476			−1.14161
$755$	17.6716	+	4.76409i	0.643136	+	0.173383i
$756$		0			0
$757$	−16.7486	+	16.7486i	−0.608738	+	0.608738i	−0.942616	−	0.333879i	$-0.891642\pi$
$757$	−16.7486	+	16.7486i	−0.608738	+	0.608738i	0.333879	+	0.942616i	$0.391642\pi$
$758$	−0.709094	−	0.709094i	−0.0257555	−	0.0257555i
$759$	2.03458			0.0738505
$760$	6.49691	+	11.2928i	0.235668	+	0.409634i
$761$		−	17.0155i		−	0.616813i	−0.951255	−	0.308406i	$-0.900204\pi$
$761$		−	17.0155i		−	0.616813i	0.951255	−	0.308406i	$-0.0997956\pi$
$762$	11.7757	+	11.7757i	0.426590	+	0.426590i
$763$		0			0
$764$			10.6007i			0.383518i
$765$	−3.17829	+	1.82851i	−0.114911	+	0.0661100i
$766$		−	17.8032i		−	0.643255i
$767$	7.67560	−	7.67560i	0.277150	−	0.277150i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−7.70275			−0.277768			−0.138884	−	0.990309i	$-0.544352\pi$
$769$	−7.70275			−0.277768			−0.138884	+	0.990309i	$0.544352\pi$
$770$		0			0
$771$	10.3811			0.373865
$772$	5.10254	−	5.10254i	0.183644	−	0.183644i
$773$	2.13982	−	2.13982i	0.0769640	−	0.0769640i	−0.667577	−	0.744541i	$-0.732668\pi$
$773$	2.13982	−	2.13982i	0.0769640	−	0.0769640i	0.744541	+	0.667577i	$0.232668\pi$
$774$		−	6.71958i		−	0.241530i
$775$	0.0815345	−	0.140229i	0.00292881	−	0.00503718i
$776$			3.56097i			0.127832i
$777$		0			0
$778$	−7.96110	−	7.96110i	−0.285419	−	0.285419i
$779$		−	63.7723i		−	2.28488i
$780$	−12.2215	−	3.29478i	−0.437599	−	0.117972i
$781$	4.08491			0.146170
$782$	−5.11618	−	5.11618i	−0.182954	−	0.182954i
$783$	−3.91576	+	3.91576i	−0.139938	+	0.139938i
$784$		0			0
$785$	−24.2810	−	42.2048i	−0.866624	−	1.50636i
$786$	18.9765			0.676869
$787$	15.8501	+	15.8501i	0.564996	+	0.564996i	0.930722	−	0.365726i	$-0.119179\pi$
$787$	15.8501	+	15.8501i	0.564996	+	0.564996i	−0.365726	+	0.930722i	$0.619179\pi$
$788$	9.72803	+	9.72803i	0.346547	+	0.346547i
$789$	23.7620			0.845948
$790$	5.64368	+	9.80976i	0.200793	+	0.349016i
$791$		0			0
$792$	−0.326057	+	0.326057i	−0.0115859	+	0.0115859i
$793$	−54.2587	−	54.2587i	−1.92678	−	1.92678i
$794$	−3.83284			−0.136022
$795$	5.92988	+	1.59863i	0.210311	+	0.0566977i
$796$		−	9.65296i		−	0.342140i
$797$	21.8939	+	21.8939i	0.775520	+	0.775520i	0.979066	−	0.203545i	$-0.0652464\pi$
$797$	21.8939	+	21.8939i	0.775520	+	0.775520i	−0.203545	+	0.979066i	$0.565246\pi$
$798$		0			0
$799$			14.8243i			0.524447i
$800$	−4.83357	+	1.27931i	−0.170892	+	0.0452305i
$801$			11.4285i			0.403805i
$802$	0.636428	−	0.636428i	0.0224730	−	0.0224730i
$803$	−1.32291	+	1.32291i	−0.0466844	+	0.0466844i
$804$	3.81023			0.134377
$805$		0			0
$806$	−0.183646			−0.00646865
$807$	−1.00414	+	1.00414i	−0.0353475	+	0.0353475i
$808$	−3.19033	+	3.19033i	−0.112235	+	0.112235i
$809$		−	1.08401i		−	0.0381118i	−0.999818	−	0.0190559i	$-0.993934\pi$
$809$		−	1.08401i		−	0.0381118i	0.999818	−	0.0190559i	$-0.00606605\pi$
$810$	−1.93820	+	1.11507i	−0.0681014	+	0.0391796i
$811$			33.8754i			1.18953i	0.803901	+	0.594763i	$0.202754\pi$
$811$			33.8754i			1.18953i	−0.803901	+	0.594763i	$0.797246\pi$
$812$		0			0
$813$	−0.250034	−	0.250034i	−0.00876907	−	0.00876907i
$814$		−	3.71863i		−	0.130338i
$815$	−13.0181	−	22.6279i	−0.456005	−	0.792622i
$816$	1.63982			0.0574051
$817$	−27.6842	−	27.6842i	−0.968547	−	0.968547i
$818$	9.11649	−	9.11649i	0.318751	−	0.318751i
$819$		0			0
$820$	23.6308	+	6.37061i	0.825222	+	0.222471i
$821$	4.86638			0.169838			0.0849190	−	0.996388i	$-0.472937\pi$
$821$	4.86638			0.169838			0.0849190	+	0.996388i	$0.472937\pi$
$822$	3.13179	+	3.13179i	0.109234	+	0.109234i
$823$	−24.5590	−	24.5590i	−0.856072	−	0.856072i	0.134801	−	0.990873i	$-0.456961\pi$
$823$	−24.5590	−	24.5590i	−0.856072	−	0.856072i	−0.990873	+	0.134801i	$0.956961\pi$
$824$	14.7753			0.514723
$825$	2.22883	−	0.589909i	0.0775978	−	0.0205380i
$826$		0			0
$827$	−38.4936	+	38.4936i	−1.33855	+	1.33855i	−0.441093	+	0.897461i	$0.645409\pi$
$827$	−38.4936	+	38.4936i	−1.33855	+	1.33855i	−0.897461	+	0.441093i	$0.854591\pi$
$828$	−3.11997	−	3.11997i	−0.108427	−	0.108427i
$829$	−40.1305			−1.39379			−0.696895	−	0.717173i	$-0.745436\pi$
$829$	−40.1305			−1.39379			−0.696895	+	0.717173i	$0.745436\pi$
$830$	−0.895674	+	3.32236i	−0.0310893	+	0.115321i
$831$			23.5017i			0.815266i
$832$	4.00275	+	4.00275i	0.138770	+	0.138770i
$833$		0			0
$834$		−	4.35020i		−	0.150635i
$835$	24.4523	+	42.5027i	0.846207	+	1.47087i
$836$			2.68667i			0.0929203i
$837$	−0.0229400	+	0.0229400i	−0.000792922	+	0.000792922i
$838$	14.0656	−	14.0656i	0.485888	−	0.485888i
$839$	−27.8082			−0.960044			−0.480022	−	0.877256i	$-0.659371\pi$
$839$	−27.8082			−0.960044			−0.480022	+	0.877256i	$0.659371\pi$
$840$		0			0
$841$	−1.66640			−0.0574621
$842$	−8.93353	+	8.93353i	−0.307870	+	0.307870i
$843$	20.1347	−	20.1347i	0.693475	−	0.693475i
$844$		−	1.33273i		−	0.0458744i
$845$	11.0844	−	41.1157i	0.381314	−	1.41442i
$846$			9.04024i			0.310810i
$847$		0			0
$848$	−1.94214	−	1.94214i	−0.0666934	−	0.0666934i
$849$			3.75788i			0.128970i
$850$	−7.08804	−	4.12125i	−0.243118	−	0.141358i
$851$	35.5828			1.21976
$852$	−6.26410	−	6.26410i	−0.214604	−	0.214604i
$853$	19.0929	−	19.0929i	0.653729	−	0.653729i	−0.300160	−	0.953889i	$-0.597040\pi$
$853$	19.0929	−	19.0929i	0.653729	−	0.653729i	0.953889	+	0.300160i	$0.0970400\pi$
$854$		0			0
$855$	−3.39124	+	12.5793i	−0.115978	+	0.430201i
$856$	−5.89922			−0.201631
$857$	14.4167	+	14.4167i	0.492465	+	0.492465i	0.909082	−	0.416617i	$-0.136784\pi$
$857$	14.4167	+	14.4167i	0.492465	+	0.492465i	−0.416617	+	0.909082i	$0.636784\pi$
$858$	−1.84573	−	1.84573i	−0.0630120	−	0.0630120i
$859$	4.48341			0.152972			0.0764860	−	0.997071i	$-0.475630\pi$
$859$	4.48341			0.152972			0.0764860	+	0.997071i	$0.475630\pi$
$860$	13.0239	−	7.49280i	0.444111	−	0.255502i
$861$		0			0
$862$	21.7578	−	21.7578i	0.741073	−	0.741073i
$863$	−13.8924	−	13.8924i	−0.472902	−	0.472902i	0.429951	−	0.902852i	$-0.358531\pi$
$863$	−13.8924	−	13.8924i	−0.472902	−	0.472902i	−0.902852	+	0.429951i	$0.858531\pi$
$864$	1.00000			0.0340207
$865$	18.8866	−	10.8657i	0.642164	−	0.369445i
$866$			4.30971i			0.146450i
$867$	−10.1194	−	10.1194i	−0.343673	−	0.343673i
$868$		0			0
$869$			2.33383i			0.0791697i
$870$	−11.9559	−	3.22318i	−0.405342	−	0.109276i
$871$			21.5687i			0.730829i
$872$	11.7512	−	11.7512i	0.397947	−	0.397947i
$873$	−2.51799	+	2.51799i	−0.0852210	+	0.0852210i
$874$	−25.7081			−0.869590
$875$		0			0
$876$	4.05729			0.137083
$877$	9.52443	−	9.52443i	0.321617	−	0.321617i	−0.527770	−	0.849387i	$-0.676972\pi$
$877$	9.52443	−	9.52443i	0.321617	−	0.321617i	0.849387	+	0.527770i	$0.176972\pi$
$878$	−26.1620	+	26.1620i	−0.882926	+	0.882926i
$879$			5.91848i			0.199625i
$880$	−0.995541	−	0.268388i	−0.0335597	−	0.00904734i
$881$		−	55.0357i		−	1.85420i	−0.374813	−	0.927100i	$-0.622293\pi$
$881$		−	55.0357i		−	1.85420i	0.374813	−	0.927100i	$-0.377707\pi$
$882$		0			0
$883$	3.82147	+	3.82147i	0.128603	+	0.128603i	0.768478	−	0.639876i	$-0.221014\pi$
$883$	3.82147	+	3.82147i	0.128603	+	0.128603i	−0.639876	+	0.768478i	$0.721014\pi$
$884$			9.28258i			0.312207i
$885$	3.71666	−	2.13824i	0.124934	−	0.0718761i
$886$	−17.7975			−0.597919
$887$	−16.1865	−	16.1865i	−0.543489	−	0.543489i	0.381061	−	0.924550i	$-0.375559\pi$
$887$	−16.1865	−	16.1865i	−0.543489	−	0.543489i	−0.924550	+	0.381061i	$0.875559\pi$
$888$	−5.70242	+	5.70242i	−0.191361	+	0.191361i
$889$		0			0
$890$	−22.1507	+	12.7435i	−0.742492	+	0.427164i
$891$	−0.461115			−0.0154479
$892$	8.25284	+	8.25284i	0.276326	+	0.276326i
$893$	37.2451	+	37.2451i	1.24636	+	1.24636i
$894$	−4.34052			−0.145169
$895$	−0.940085	+	3.48710i	−0.0314236	+	0.116561i
$896$		0			0
$897$	17.6614	−	17.6614i	0.589695	−	0.589695i
$898$	−1.71081	−	1.71081i	−0.0570904	−	0.0570904i
$899$	−0.179655			−0.00599183
$900$	−4.32246	−	2.51324i	−0.144082	−	0.0837746i
$901$		−	4.50392i		−	0.150047i
$902$	3.56879	+	3.56879i	0.118828	+	0.118828i
$903$		0			0
$904$		−	8.98577i		−	0.298862i
$905$	7.48035	−	27.7472i	0.248655	−	0.922347i
$906$		−	8.18514i		−	0.271933i
$907$	19.3481	−	19.3481i	0.642444	−	0.642444i	−0.308712	−	0.951156i	$-0.599898\pi$
$907$	19.3481	−	19.3481i	0.642444	−	0.642444i	0.951156	+	0.308712i	$0.0998979\pi$
$908$	15.8128	−	15.8128i	0.524765	−	0.524765i
$909$	−4.51181			−0.149647
$910$		0			0
$911$	−55.5763			−1.84132			−0.920662	−	0.390360i	$-0.872350\pi$
$911$	−55.5763			−1.84132			−0.920662	+	0.390360i	$0.872350\pi$
$912$	4.11993	−	4.11993i	0.136424	−	0.136424i
$913$	−0.501754	+	0.501754i	−0.0166056	+	0.0166056i
$914$			27.5588i			0.911565i
$915$	−15.1152	−	26.2730i	−0.499692	−	0.868559i
$916$		−	4.96622i		−	0.164088i
$917$		0			0
$918$	1.15953	+	1.15953i	0.0382701	+	0.0382701i
$919$		−	20.1259i		−	0.663893i	−0.943298	−	0.331947i	$-0.892295\pi$
$919$		−	20.1259i		−	0.663893i	0.943298	−	0.331947i	$-0.107705\pi$
$920$	2.56814	−	9.52612i	0.0846692	−	0.314067i
$921$	−25.5809			−0.842920
$922$	0.726284	+	0.726284i	0.0239189	+	0.0239189i
$923$	35.4594	−	35.4594i	1.16716	−	1.16716i
$924$		0			0
$925$	38.9800	−	10.3169i	1.28166	−	0.339219i
$926$	−11.6886			−0.384111
$927$	10.4477	+	10.4477i	0.343149	+	0.343149i
$928$	3.91576	+	3.91576i	0.128541	+	0.128541i
$929$	26.0224			0.853766			0.426883	−	0.904307i	$-0.359612\pi$
$929$	26.0224			0.853766			0.426883	+	0.904307i	$0.359612\pi$
$930$	−0.0700419	−	0.0188826i	−0.00229677	−	0.000619184i
$931$		0			0
$932$	20.2472	−	20.2472i	0.663218	−	0.663218i
$933$	23.7712	+	23.7712i	0.778235	+	0.778235i
$934$	−18.5448			−0.606804
$935$	−0.843153	−	1.46556i	−0.0275741	−	0.0479289i
$936$			5.66074i			0.185027i
$937$	17.1515	+	17.1515i	0.560314	+	0.560314i	0.929397	−	0.369082i	$-0.120328\pi$
$937$	17.1515	+	17.1515i	0.560314	+	0.560314i	−0.369082	+	0.929397i	$0.620328\pi$
$938$		0			0
$939$			22.9644i			0.749416i
$940$	−17.5218	+	10.0805i	−0.571498	+	0.328790i
$941$		−	16.6306i		−	0.542143i	−0.962559	−	0.271071i	$-0.912622\pi$
$941$		−	16.6306i		−	0.542143i	0.962559	−	0.271071i	$-0.0873779\pi$
$942$	−15.3974	+	15.3974i	−0.501676	+	0.501676i
$943$	−34.1490	+	34.1490i	−1.11204	+	1.11204i
$944$	−1.91758			−0.0624120
$945$		0			0
$946$	3.09849			0.100741
$947$	−20.9961	+	20.9961i	−0.682281	+	0.682281i	−0.960514	−	0.278233i	$-0.910251\pi$
$947$	−20.9961	+	20.9961i	−0.682281	+	0.682281i	0.278233	+	0.960514i	$0.410251\pi$
$948$	3.57886	−	3.57886i	0.116236	−	0.116236i
$949$			22.9673i			0.745549i
$950$	−28.1626	+	7.45385i	−0.913715	+	0.241835i
$951$		−	25.6420i		−	0.831498i
$952$		0			0
$953$	−30.9752	−	30.9752i	−1.00339	−	1.00339i	−0.999994	−	0.00339090i	$-0.998921\pi$
$953$	−30.9752	−	30.9752i	−1.00339	−	1.00339i	−0.00339090	−	0.999994i	$-0.501079\pi$
$954$		−	2.74660i		−	0.0889245i
$955$	−22.8867	−	6.17001i	−0.740595	−	0.199657i
$956$	−13.9230			−0.450302
$957$	−1.80562	−	1.80562i	−0.0583673	−	0.0583673i
$958$	5.99446	−	5.99446i	0.193672	−	0.193672i
$959$		0			0
$960$	1.11507	+	1.93820i	0.0359887	+	0.0625551i
$961$	30.9989			0.999966
$962$	−32.2799	−	32.2799i	−1.04075	−	1.04075i
$963$	−4.17138	−	4.17138i	−0.134421	−	0.134421i
$964$	−1.05757			−0.0340620
$965$	8.04643	+	13.9862i	0.259024	+	0.450232i
$966$		0			0
$967$	−9.23140	+	9.23140i	−0.296862	+	0.296862i	−0.839783	−	0.542922i	$-0.817318\pi$
$967$	−9.23140	+	9.23140i	−0.296862	+	0.296862i	0.542922	+	0.839783i	$0.317318\pi$
$968$	7.62782	+	7.62782i	0.245168	+	0.245168i
$969$	9.55433			0.306929
$970$	−7.68810	−	2.07263i	−0.246850	−	0.0665482i
$971$			24.4464i			0.784522i	0.919854	+	0.392261i	$0.128307\pi$
$971$			24.4464i			0.784522i	−0.919854	+	0.392261i	$0.871693\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$		0			0
$974$			4.85631i			0.155606i
$975$	14.2268	−	24.4683i	0.455622	−	0.783613i
$976$			13.5554i			0.433897i
$977$	−19.8040	+	19.8040i	−0.633585	+	0.633585i	−0.948965	−	0.315380i	$-0.897868\pi$
$977$	−19.8040	+	19.8040i	−0.633585	+	0.633585i	0.315380	+	0.948965i	$0.397868\pi$
$978$	−8.25527	+	8.25527i	−0.263974	+	0.263974i
$979$	−5.26983			−0.168425
$980$		0			0
$981$	16.6187			0.530596
$982$	−26.7707	+	26.7707i	−0.854286	+	0.854286i
$983$	29.1748	−	29.1748i	0.930531	−	0.930531i	−0.0672080	−	0.997739i	$-0.521409\pi$
$983$	29.1748	−	29.1748i	0.930531	−	0.930531i	0.997739	+	0.0672080i	$0.0214091\pi$
$984$		−	10.9453i		−	0.348923i
$985$	−26.6648	+	15.3406i	−0.849611	+	0.488792i
$986$			9.08086i			0.289193i
$987$		0			0
$988$	23.3218	+	23.3218i	0.741967	+	0.741967i
$989$			29.6488i			0.942778i
$990$	−0.514175	−	0.893732i	−0.0163416	−	0.0284047i
$991$	−36.3648			−1.15516			−0.577582	−	0.816332i	$-0.696004\pi$
$991$	−36.3648			−1.15516			−0.577582	+	0.816332i	$0.696004\pi$
$992$	0.0229400	+	0.0229400i	0.000728345	+	0.000728345i
$993$	−8.38971	+	8.38971i	−0.266240	+	0.266240i
$994$		0			0
$995$	20.8406	+	5.61842i	0.660692	+	0.178116i
$996$	1.53885			0.0487604
$997$	12.7033	+	12.7033i	0.402317	+	0.402317i	0.879049	−	0.476732i	$-0.158179\pi$
$997$	12.7033	+	12.7033i	0.402317	+	0.402317i	−0.476732	+	0.879049i	$0.658179\pi$
$998$	0.362177	+	0.362177i	0.0114645	+	0.0114645i
$999$	−8.06444			−0.255148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.e.1273.8		16
5.2	odd	4		1470.2.m.d.97.5		16
7.2	even	3		210.2.u.b.73.1	yes	16
7.3	odd	6		210.2.u.a.103.4	✓	16
7.6	odd	2		1470.2.m.d.1273.5		16
21.2	odd	6		630.2.bv.b.73.4		16
21.17	even	6		630.2.bv.a.523.1		16
35.2	odd	12		210.2.u.a.157.4	yes	16
35.3	even	12		1050.2.bc.g.607.3		16
35.9	even	6		1050.2.bc.g.493.3		16
35.17	even	12		210.2.u.b.187.1	yes	16
35.23	odd	12		1050.2.bc.h.157.1		16
35.24	odd	6		1050.2.bc.h.943.1		16
35.27	even	4	inner	1470.2.m.e.97.8		16
105.2	even	12		630.2.bv.a.577.1		16
105.17	odd	12		630.2.bv.b.397.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.4	✓	16	7.3	odd	6
210.2.u.a.157.4	yes	16	35.2	odd	12
210.2.u.b.73.1	yes	16	7.2	even	3
210.2.u.b.187.1	yes	16	35.17	even	12
630.2.bv.a.523.1		16	21.17	even	6
630.2.bv.a.577.1		16	105.2	even	12
630.2.bv.b.73.4		16	21.2	odd	6
630.2.bv.b.397.4		16	105.17	odd	12
1050.2.bc.g.493.3		16	35.9	even	6
1050.2.bc.g.607.3		16	35.3	even	12
1050.2.bc.h.157.1		16	35.23	odd	12
1050.2.bc.h.943.1		16	35.24	odd	6
1470.2.m.d.97.5		16	5.2	odd	4
1470.2.m.d.1273.5		16	7.6	odd	2
1470.2.m.e.97.8		16	35.27	even	4	inner
1470.2.m.e.1273.8		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.15899 + 0.582041i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(2.15899 + 0.582041i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.93820 - 1.11507i) q^{10} +0.461115 q^{11} +(-0.707107 - 0.707107i) q^{12} +(4.00275 - 4.00275i) q^{13} +(1.93820 - 1.11507i) q^{15} -1.00000 q^{16} +(-1.15953 - 1.15953i) q^{17} +(-0.707107 - 0.707107i) q^{18} -5.82646 q^{19} +(0.582041 - 2.15899i) q^{20} +(0.326057 - 0.326057i) q^{22} +(3.11997 + 3.11997i) q^{23} -1.00000 q^{24} +(4.32246 + 2.51324i) q^{25} -5.66074i q^{26} +(-0.707107 - 0.707107i) q^{27} -5.53773i q^{29} +(0.582041 - 2.15899i) q^{30} -0.0324420i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.326057 - 0.326057i) q^{33} -1.63982 q^{34} -1.00000 q^{36} +(5.70242 - 5.70242i) q^{37} +(-4.11993 + 4.11993i) q^{38} -5.66074i q^{39} +(-1.11507 - 1.93820i) q^{40} +10.9453i q^{41} +(4.75146 + 4.75146i) q^{43} -0.461115i q^{44} +(0.582041 - 2.15899i) q^{45} +4.41231 q^{46} +(-6.39241 - 6.39241i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(4.83357 - 1.27931i) q^{50} -1.63982 q^{51} +(-4.00275 - 4.00275i) q^{52} +(1.94214 + 1.94214i) q^{53} -1.00000 q^{54} +(0.995541 + 0.268388i) q^{55} +(-4.11993 + 4.11993i) q^{57} +(-3.91576 - 3.91576i) q^{58} +1.91758 q^{59} +(-1.11507 - 1.93820i) q^{60} -13.5554i q^{61} +(-0.0229400 - 0.0229400i) q^{62} +1.00000i q^{64} +(10.9716 - 6.31212i) q^{65} -0.461115i q^{66} +(-2.69424 + 2.69424i) q^{67} +(-1.15953 + 1.15953i) q^{68} +4.41231 q^{69} +8.85877 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-2.86894 + 2.86894i) q^{73} -8.06444i q^{74} +(4.83357 - 1.27931i) q^{75} +5.82646i q^{76} +(-4.00275 - 4.00275i) q^{78} +5.06128i q^{79} +(-2.15899 - 0.582041i) q^{80} -1.00000 q^{81} +(7.73949 + 7.73949i) q^{82} +(-1.08813 + 1.08813i) q^{83} +(-1.82851 - 3.17829i) q^{85} +6.71958 q^{86} +(-3.91576 - 3.91576i) q^{87} +(-0.326057 - 0.326057i) q^{88} -11.4285 q^{89} +(-1.11507 - 1.93820i) q^{90} +(3.11997 - 3.11997i) q^{92} +(-0.0229400 - 0.0229400i) q^{93} -9.04024 q^{94} +(-12.5793 - 3.39124i) q^{95} +1.00000i q^{96} +(-2.51799 - 2.51799i) q^{97} -0.461115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more