LMFDB - Embedded newform 1450.2.j.i.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(157,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1450.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.j (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:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 36 x^{18} + 534 x^{16} + 4248 x^{14} + 19701 x^{12} + 54104 x^{10} + 85176 x^{8} + 70068 x^{6} + \cdots + 100 $ x^20 + 36x^18 + 534x^16 + 4248x^14 + 19701x^12 + 54104x^10 + 85176x^8 + 70068x^6 + 24828x^4 + 3384*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.5
Root			$0.525625i$ of defining polynomial
Character	$\chi$	$=$	1450.157
Dual form			1450.2.j.i.1293.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.525625 q^{3} -1.00000 q^{4} -0.525625i q^{6} +(1.99569 + 1.99569i) q^{7} -1.00000i q^{8} -2.72372 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.525625 q^{3} -1.00000 q^{4} -0.525625i q^{6} +(1.99569 + 1.99569i) q^{7} -1.00000i q^{8} -2.72372 q^{9} +(4.00099 + 4.00099i) q^{11} +0.525625 q^{12} +(1.85043 + 1.85043i) q^{13} +(-1.99569 + 1.99569i) q^{14} +1.00000 q^{16} -4.25603i q^{17} -2.72372i q^{18} +(-0.197135 + 0.197135i) q^{19} +(-1.04898 - 1.04898i) q^{21} +(-4.00099 + 4.00099i) q^{22} +(3.84799 - 3.84799i) q^{23} +0.525625i q^{24} +(-1.85043 + 1.85043i) q^{26} +3.00853 q^{27} +(-1.99569 - 1.99569i) q^{28} +(0.248111 + 5.37945i) q^{29} +(0.499611 + 0.499611i) q^{31} +1.00000i q^{32} +(-2.10302 - 2.10302i) q^{33} +4.25603 q^{34} +2.72372 q^{36} -6.77511 q^{37} +(-0.197135 - 0.197135i) q^{38} +(-0.972633 - 0.972633i) q^{39} +(-3.62348 + 3.62348i) q^{41} +(1.04898 - 1.04898i) q^{42} -6.41041 q^{43} +(-4.00099 - 4.00099i) q^{44} +(3.84799 + 3.84799i) q^{46} +9.69432 q^{47} -0.525625 q^{48} +0.965542i q^{49} +2.23707i q^{51} +(-1.85043 - 1.85043i) q^{52} +(-5.52014 + 5.52014i) q^{53} +3.00853i q^{54} +(1.99569 - 1.99569i) q^{56} +(0.103619 - 0.103619i) q^{57} +(-5.37945 + 0.248111i) q^{58} +10.5354i q^{59} +(7.92394 + 7.92394i) q^{61} +(-0.499611 + 0.499611i) q^{62} +(-5.43569 - 5.43569i) q^{63} -1.00000 q^{64} +(2.10302 - 2.10302i) q^{66} +(0.259532 - 0.259532i) q^{67} +4.25603i q^{68} +(-2.02260 + 2.02260i) q^{69} +12.3264i q^{71} +2.72372i q^{72} +2.56003i q^{73} -6.77511i q^{74} +(0.197135 - 0.197135i) q^{76} +15.9695i q^{77} +(0.972633 - 0.972633i) q^{78} +(0.678650 - 0.678650i) q^{79} +6.58980 q^{81} +(-3.62348 - 3.62348i) q^{82} +(-3.66587 + 3.66587i) q^{83} +(1.04898 + 1.04898i) q^{84} -6.41041i q^{86} +(-0.130413 - 2.82757i) q^{87} +(4.00099 - 4.00099i) q^{88} +(-12.5804 + 12.5804i) q^{89} +7.38577i q^{91} +(-3.84799 + 3.84799i) q^{92} +(-0.262608 - 0.262608i) q^{93} +9.69432i q^{94} -0.525625i q^{96} +11.3437 q^{97} -0.965542 q^{98} +(-10.8976 - 10.8976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{3} - 20 q^{4} + 8 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 8 * q^3 - 20 * q^4 + 8 * q^7 + 12 * q^9	$ 20 q - 8 q^{3} - 20 q^{4} + 8 q^{7} + 12 q^{9} - 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{14} + 20 q^{16} + 4 q^{19} + 4 q^{21} + 8 q^{22} - 12 q^{23} + 4 q^{26} - 32 q^{27} - 8 q^{28} - 8 q^{29} + 28 q^{31} + 16 q^{34} - 12 q^{36} + 20 q^{37} + 4 q^{38} + 24 q^{39} + 24 q^{41} - 4 q^{42} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 28 q^{47} - 8 q^{48} + 4 q^{52} + 8 q^{56} - 8 q^{57} - 8 q^{58} + 24 q^{61} - 28 q^{62} + 20 q^{63} - 20 q^{64} + 12 q^{67} + 28 q^{69} - 4 q^{76} - 24 q^{78} - 32 q^{79} - 12 q^{81} + 24 q^{82} + 20 q^{83} - 4 q^{84} + 36 q^{87} - 8 q^{88} - 4 q^{89} + 12 q^{92} + 12 q^{93} - 48 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) $ 20 * q - 8 * q^3 - 20 * q^4 + 8 * q^7 + 12 * q^9 - 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^14 + 20 * q^16 + 4 * q^19 + 4 * q^21 + 8 * q^22 - 12 * q^23 + 4 * q^26 - 32 * q^27 - 8 * q^28 - 8 * q^29 + 28 * q^31 + 16 * q^34 - 12 * q^36 + 20 * q^37 + 4 * q^38 + 24 * q^39 + 24 * q^41 - 4 * q^42 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 28 * q^47 - 8 * q^48 + 4 * q^52 + 8 * q^56 - 8 * q^57 - 8 * q^58 + 24 * q^61 - 28 * q^62 + 20 * q^63 - 20 * q^64 + 12 * q^67 + 28 * q^69 - 4 * q^76 - 24 * q^78 - 32 * q^79 - 12 * q^81 + 24 * q^82 + 20 * q^83 - 4 * q^84 + 36 * q^87 - 8 * q^88 - 4 * q^89 + 12 * q^92 + 12 * q^93 - 48 * q^97 - 20 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.525625			−0.303469			−0.151735	−	0.988421i	$-0.548486\pi$
$3$	−0.525625			−0.303469			−0.151735	+	0.988421i	$0.548486\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	0.525625i		−	0.214585i
$7$	1.99569	+	1.99569i	0.754299	+	0.754299i	0.975279	−	0.220979i	$-0.0709253\pi$
$7$	1.99569	+	1.99569i	0.754299	+	0.754299i	−0.220979	+	0.975279i	$0.570925\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.72372			−0.907906
$10$		0			0
$11$	4.00099	+	4.00099i	1.20634	+	1.20634i	0.972203	+	0.234141i	$0.0752277\pi$
$11$	4.00099	+	4.00099i	1.20634	+	1.20634i	0.234141	+	0.972203i	$0.424772\pi$
$12$	0.525625			0.151735
$13$	1.85043	+	1.85043i	0.513218	+	0.513218i	0.915511	−	0.402293i	$-0.131787\pi$
$13$	1.85043	+	1.85043i	0.513218	+	0.513218i	−0.402293	+	0.915511i	$0.631787\pi$
$14$	−1.99569	+	1.99569i	−0.533370	+	0.533370i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.25603i		−	1.03224i	−0.856517	−	0.516119i	$-0.827376\pi$
$17$		−	4.25603i		−	1.03224i	0.856517	−	0.516119i	$-0.172624\pi$
$18$		−	2.72372i		−	0.641987i
$19$	−0.197135	+	0.197135i	−0.0452258	+	0.0452258i	−0.729358	−	0.684132i	$-0.760181\pi$
$19$	−0.197135	+	0.197135i	−0.0452258	+	0.0452258i	0.684132	+	0.729358i	$0.260181\pi$
$20$		0			0
$21$	−1.04898	−	1.04898i	−0.228907	−	0.228907i
$22$	−4.00099	+	4.00099i	−0.853014	+	0.853014i
$23$	3.84799	−	3.84799i	0.802362	−	0.802362i	−0.181102	−	0.983464i	$-0.557966\pi$
$23$	3.84799	−	3.84799i	0.802362	−	0.802362i	0.983464	+	0.181102i	$0.0579665\pi$
$24$			0.525625i			0.107293i
$25$		0			0
$26$	−1.85043	+	1.85043i	−0.362900	+	0.362900i
$27$	3.00853			0.578991
$28$	−1.99569	−	1.99569i	−0.377150	−	0.377150i
$29$	0.248111	+	5.37945i	0.0460730	+	0.998938i
$29$	0.248111	+	5.37945i	0.0460730	+	0.998938i
$30$		0			0
$31$	0.499611	+	0.499611i	0.0897328	+	0.0897328i	0.750548	−	0.660816i	$-0.229789\pi$
$31$	0.499611	+	0.499611i	0.0897328	+	0.0897328i	−0.660816	+	0.750548i	$0.729789\pi$
$32$			1.00000i			0.176777i
$33$	−2.10302	−	2.10302i	−0.366088	−	0.366088i
$34$	4.25603			0.729903
$35$		0			0
$36$	2.72372			0.453953
$37$	−6.77511			−1.11382			−0.556910	−	0.830573i	$-0.688013\pi$
$37$	−6.77511			−1.11382			−0.556910	+	0.830573i	$0.688013\pi$
$38$	−0.197135	−	0.197135i	−0.0319795	−	0.0319795i
$39$	−0.972633	−	0.972633i	−0.155746	−	0.155746i
$40$		0			0
$41$	−3.62348	+	3.62348i	−0.565892	+	0.565892i	−0.930975	−	0.365083i	$-0.881041\pi$
$41$	−3.62348	+	3.62348i	−0.565892	+	0.565892i	0.365083	+	0.930975i	$0.381041\pi$
$42$	1.04898	−	1.04898i	0.161862	−	0.161862i
$43$	−6.41041			−0.977578			−0.488789	−	0.872402i	$-0.662561\pi$
$43$	−6.41041			−0.977578			−0.488789	+	0.872402i	$0.662561\pi$
$44$	−4.00099	−	4.00099i	−0.603172	−	0.603172i
$45$		0			0
$46$	3.84799	+	3.84799i	0.567356	+	0.567356i
$47$	9.69432			1.41406			0.707031	−	0.707183i	$-0.250034\pi$
$47$	9.69432			1.41406			0.707031	+	0.707183i	$0.250034\pi$
$48$	−0.525625			−0.0758674
$49$			0.965542i			0.137935i
$50$		0			0
$51$			2.23707i			0.313253i
$52$	−1.85043	−	1.85043i	−0.256609	−	0.256609i
$53$	−5.52014	+	5.52014i	−0.758250	+	0.758250i	−0.976004	−	0.217754i	$-0.930127\pi$
$53$	−5.52014	+	5.52014i	−0.758250	+	0.758250i	0.217754	+	0.976004i	$0.430127\pi$
$54$			3.00853i			0.409409i
$55$		0			0
$56$	1.99569	−	1.99569i	0.266685	−	0.266685i
$57$	0.103619	−	0.103619i	0.0137247	−	0.0137247i
$58$	−5.37945	+	0.248111i	−0.706356	+	0.0325785i
$59$			10.5354i			1.37160i	0.727791	+	0.685799i	$0.240547\pi$
$59$			10.5354i			1.37160i	−0.727791	+	0.685799i	$0.759453\pi$
$60$		0			0
$61$	7.92394	+	7.92394i	1.01456	+	1.01456i	0.999892	+	0.0146635i	$0.00466770\pi$
$61$	7.92394	+	7.92394i	1.01456	+	1.01456i	0.0146635	+	0.999892i	$0.495332\pi$
$62$	−0.499611	+	0.499611i	−0.0634507	+	0.0634507i
$63$	−5.43569	−	5.43569i	−0.684833	−	0.684833i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.10302	−	2.10302i	0.258864	−	0.258864i
$67$	0.259532	−	0.259532i	0.0317069	−	0.0317069i	−0.691076	−	0.722782i	$-0.742863\pi$
$67$	0.259532	−	0.259532i	0.0317069	−	0.0317069i	0.722782	+	0.691076i	$0.242863\pi$
$68$			4.25603i			0.516119i
$69$	−2.02260	+	2.02260i	−0.243492	+	0.243492i
$70$		0			0
$71$			12.3264i			1.46287i	0.681909	+	0.731437i	$0.261150\pi$
$71$			12.3264i			1.46287i	−0.681909	+	0.731437i	$0.738850\pi$
$72$			2.72372i			0.320993i
$73$			2.56003i			0.299629i	0.988714	+	0.149814i	$0.0478676\pi$
$73$			2.56003i			0.299629i	−0.988714	+	0.149814i	$0.952132\pi$
$74$		−	6.77511i		−	0.787590i
$75$		0			0
$76$	0.197135	−	0.197135i	0.0226129	−	0.0226129i
$77$			15.9695i			1.81989i
$78$	0.972633	−	0.972633i	0.110129	−	0.110129i
$79$	0.678650	−	0.678650i	0.0763541	−	0.0763541i	−0.667898	−	0.744252i	$-0.732806\pi$
$79$	0.678650	−	0.678650i	0.0763541	−	0.0763541i	0.744252	+	0.667898i	$0.232806\pi$
$80$		0			0
$81$	6.58980			0.732200
$82$	−3.62348	−	3.62348i	−0.400146	−	0.400146i
$83$	−3.66587	+	3.66587i	−0.402381	+	0.402381i	−0.879071	−	0.476690i	$-0.841836\pi$
$83$	−3.66587	+	3.66587i	−0.402381	+	0.402381i	0.476690	+	0.879071i	$0.341836\pi$
$84$	1.04898	+	1.04898i	0.114453	+	0.114453i
$85$		0			0
$86$		−	6.41041i		−	0.691252i
$87$	−0.130413	−	2.82757i	−0.0139817	−	0.303147i
$88$	4.00099	−	4.00099i	0.426507	−	0.426507i
$89$	−12.5804	+	12.5804i	−1.33352	+	1.33352i	−0.431316	+	0.902201i	$0.641950\pi$
$89$	−12.5804	+	12.5804i	−1.33352	+	1.33352i	−0.902201	+	0.431316i	$0.858050\pi$
$90$		0			0
$91$			7.38577i			0.774240i
$92$	−3.84799	+	3.84799i	−0.401181	+	0.401181i
$93$	−0.262608	−	0.262608i	−0.0272312	−	0.0272312i
$94$			9.69432i			0.999893i
$95$		0			0
$96$		−	0.525625i		−	0.0536463i
$97$	11.3437			1.15177			0.575887	−	0.817529i	$-0.304657\pi$
$97$	11.3437			1.15177			0.575887	+	0.817529i	$0.304657\pi$
$98$	−0.965542			−0.0975345
$99$	−10.8976	−	10.8976i	−1.09525	−	1.09525i
$100$		0			0
$101$	−11.4898	−	11.4898i	−1.14327	−	1.14327i	−0.987848	−	0.155425i	$-0.950325\pi$
$101$	−11.4898	−	11.4898i	−1.14327	−	1.14327i	−0.155425	−	0.987848i	$-0.549675\pi$
$102$	−2.23707			−0.221503
$103$	2.95200	−	2.95200i	0.290869	−	0.290869i	−0.546555	−	0.837424i	$-0.684061\pi$
$103$	2.95200	−	2.95200i	0.290869	−	0.290869i	0.837424	+	0.546555i	$0.184061\pi$
$104$	1.85043	−	1.85043i	0.181450	−	0.181450i
$105$		0			0
$106$	−5.52014	−	5.52014i	−0.536163	−	0.536163i
$107$	−7.14252	−	7.14252i	−0.690493	−	0.690493i	0.271847	−	0.962340i	$-0.412365\pi$
$107$	−7.14252	−	7.14252i	−0.690493	−	0.690493i	−0.962340	+	0.271847i	$0.912365\pi$
$108$	−3.00853			−0.289496
$109$	2.06917			0.198190			0.0990951	−	0.995078i	$-0.468405\pi$
$109$	2.06917			0.198190			0.0990951	+	0.995078i	$0.468405\pi$
$110$		0			0
$111$	3.56116			0.338010
$112$	1.99569	+	1.99569i	0.188575	+	0.188575i
$113$		−	8.62412i		−	0.811289i	−0.914031	−	0.405645i	$-0.867047\pi$
$113$		−	8.62412i		−	0.811289i	0.914031	−	0.405645i	$-0.132953\pi$
$114$	0.103619	+	0.103619i	0.00970479	+	0.00970479i
$115$		0			0
$116$	−0.248111	−	5.37945i	−0.0230365	−	0.499469i
$117$	−5.04006	−	5.04006i	−0.465954	−	0.465954i
$118$	−10.5354			−0.969866
$119$	8.49371	−	8.49371i	0.778617	−	0.778617i
$120$		0			0
$121$			21.0158i			1.91053i
$122$	−7.92394	+	7.92394i	−0.717399	+	0.717399i
$123$	1.90459	−	1.90459i	0.171731	−	0.171731i
$124$	−0.499611	−	0.499611i	−0.0448664	−	0.0448664i
$125$		0			0
$126$	5.43569	−	5.43569i	0.484250	−	0.484250i
$127$			1.71279i			0.151986i	0.997108	+	0.0759928i	$0.0242126\pi$
$127$			1.71279i			0.151986i	−0.997108	+	0.0759928i	$0.975787\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.36947			0.296665
$130$		0			0
$131$	−11.9198	+	11.9198i	−1.04143	+	1.04143i	−0.0423310	+	0.999104i	$0.513478\pi$
$131$	−11.9198	+	11.9198i	−1.04143	+	1.04143i	−0.999104	+	0.0423310i	$0.986522\pi$
$132$	2.10302	+	2.10302i	0.183044	+	0.183044i
$133$	−0.786839			−0.0682276
$134$	0.259532	+	0.259532i	0.0224201	+	0.0224201i
$135$		0			0
$136$	−4.25603			−0.364952
$137$		−	17.2523i		−	1.47396i	−0.675914	−	0.736980i	$-0.736251\pi$
$137$		−	17.2523i		−	1.47396i	0.675914	−	0.736980i	$-0.263749\pi$
$138$	−2.02260	−	2.02260i	−0.172175	−	0.172175i
$139$		−	15.5459i		−	1.31858i	−0.751887	−	0.659292i	$-0.770856\pi$
$139$		−	15.5459i		−	1.31858i	0.751887	−	0.659292i	$-0.229144\pi$
$140$		0			0
$141$	−5.09557			−0.429124
$142$	−12.3264			−1.03441
$143$			14.8071i			1.23823i
$144$	−2.72372			−0.226977
$145$		0			0
$146$	−2.56003			−0.211870
$147$		−	0.507513i		−	0.0418589i
$148$	6.77511			0.556910
$149$	5.74010			0.470247			0.235124	−	0.971965i	$-0.424450\pi$
$149$	5.74010			0.470247			0.235124	+	0.971965i	$0.424450\pi$
$150$		0			0
$151$		−	4.34872i		−	0.353894i	−0.984220	−	0.176947i	$-0.943378\pi$
$151$		−	4.34872i		−	0.353894i	0.984220	−	0.176947i	$-0.0566220\pi$
$152$	0.197135	+	0.197135i	0.0159897	+	0.0159897i
$153$			11.5922i			0.937176i
$154$	−15.9695			−1.28686
$155$		0			0
$156$	0.972633	+	0.972633i	0.0778730	+	0.0778730i
$157$	19.2755			1.53836			0.769178	−	0.639035i	$-0.220666\pi$
$157$	19.2755			1.53836			0.769178	+	0.639035i	$0.220666\pi$
$158$	0.678650	+	0.678650i	0.0539905	+	0.0539905i
$159$	2.90152	−	2.90152i	0.230106	−	0.230106i
$160$		0			0
$161$	15.3588			1.21044
$162$			6.58980i			0.517744i
$163$			18.5680i			1.45436i	0.686448	+	0.727179i	$0.259169\pi$
$163$			18.5680i			1.45436i	−0.686448	+	0.727179i	$0.740831\pi$
$164$	3.62348	−	3.62348i	0.282946	−	0.282946i
$165$		0			0
$166$	−3.66587	−	3.66587i	−0.284526	−	0.284526i
$167$	−5.50661	+	5.50661i	−0.426114	+	0.426114i	−0.887302	−	0.461188i	$-0.847423\pi$
$167$	−5.50661	+	5.50661i	−0.426114	+	0.426114i	0.461188	+	0.887302i	$0.347423\pi$
$168$	−1.04898	+	1.04898i	−0.0809308	+	0.0809308i
$169$		−	6.15179i		−	0.473215i
$170$		0			0
$171$	0.536940	−	0.536940i	0.0410608	−	0.0410608i
$172$	6.41041			0.488789
$173$	−4.46207	−	4.46207i	−0.339245	−	0.339245i	0.516838	−	0.856083i	$-0.327109\pi$
$173$	−4.46207	−	4.46207i	−0.339245	−	0.339245i	−0.856083	+	0.516838i	$0.827109\pi$
$174$	2.82757	−	0.130413i	0.214357	−	0.00988658i
$175$		0			0
$176$	4.00099	+	4.00099i	0.301586	+	0.301586i
$177$		−	5.53769i		−	0.416238i
$178$	−12.5804	−	12.5804i	−0.942939	−	0.942939i
$179$	20.3959			1.52446			0.762230	−	0.647307i	$-0.224105\pi$
$179$	20.3959			1.52446			0.762230	+	0.647307i	$0.224105\pi$
$180$		0			0
$181$	3.67401			0.273087			0.136544	−	0.990634i	$-0.456401\pi$
$181$	3.67401			0.273087			0.136544	+	0.990634i	$0.456401\pi$
$182$	−7.38577			−0.547470
$183$	−4.16501	−	4.16501i	−0.307887	−	0.307887i
$184$	−3.84799	−	3.84799i	−0.283678	−	0.283678i
$185$		0			0
$186$	0.262608	−	0.262608i	0.0192553	−	0.0192553i
$187$	17.0283	−	17.0283i	1.24523	−	1.24523i
$188$	−9.69432			−0.707031
$189$	6.00408	+	6.00408i	0.436733	+	0.436733i
$190$		0			0
$191$	−15.9172	−	15.9172i	−1.15173	−	1.15173i	−0.986206	−	0.165521i	$-0.947069\pi$
$191$	−15.9172	−	15.9172i	−1.15173	−	1.15173i	−0.165521	−	0.986206i	$-0.552931\pi$
$192$	0.525625			0.0379337
$193$	11.4353			0.823133			0.411567	−	0.911380i	$-0.364982\pi$
$193$	11.4353			0.823133			0.411567	+	0.911380i	$0.364982\pi$
$194$			11.3437i			0.814428i
$195$		0			0
$196$		−	0.965542i		−	0.0689673i
$197$	6.93809	+	6.93809i	0.494318	+	0.494318i	0.909664	−	0.415345i	$-0.136339\pi$
$197$	6.93809	+	6.93809i	0.494318	+	0.494318i	−0.415345	+	0.909664i	$0.636339\pi$
$198$	10.8976	−	10.8976i	0.774457	−	0.774457i
$199$			6.08686i			0.431486i	0.976450	+	0.215743i	$0.0692174\pi$
$199$			6.08686i			0.431486i	−0.976450	+	0.215743i	$0.930783\pi$
$200$		0			0
$201$	−0.136416	+	0.136416i	−0.00962207	+	0.00962207i
$202$	11.4898	−	11.4898i	0.808416	−	0.808416i
$203$	−10.2405	+	11.2308i	−0.718745	+	0.788251i
$204$		−	2.23707i		−	0.156626i
$205$		0			0
$206$	2.95200	+	2.95200i	0.205675	+	0.205675i
$207$	−10.4809	+	10.4809i	−0.728470	+	0.728470i
$208$	1.85043	+	1.85043i	0.128304	+	0.128304i
$209$	−1.57747			−0.109116
$210$		0			0
$211$	2.18584	−	2.18584i	0.150479	−	0.150479i	−0.627853	−	0.778332i	$-0.716066\pi$
$211$	2.18584	−	2.18584i	0.150479	−	0.150479i	0.778332	+	0.627853i	$0.216066\pi$
$212$	5.52014	−	5.52014i	0.379125	−	0.379125i
$213$		−	6.47906i		−	0.443938i
$214$	7.14252	−	7.14252i	0.488252	−	0.488252i
$215$		0			0
$216$		−	3.00853i		−	0.204704i
$217$			1.99414i			0.135371i
$218$			2.06917i			0.140142i
$219$		−	1.34561i		−	0.0909282i
$220$		0			0
$221$	7.87550	−	7.87550i	0.529763	−	0.529763i
$222$			3.56116i			0.239010i
$223$	−10.3129	+	10.3129i	−0.690605	+	0.690605i	−0.962365	−	0.271760i	$-0.912394\pi$
$223$	−10.3129	+	10.3129i	−0.690605	+	0.690605i	0.271760	+	0.962365i	$0.412394\pi$
$224$	−1.99569	+	1.99569i	−0.133343	+	0.133343i
$225$		0			0
$226$	8.62412			0.573668
$227$	−18.6177	−	18.6177i	−1.23570	−	1.23570i	−0.961742	−	0.273956i	$-0.911668\pi$
$227$	−18.6177	−	18.6177i	−1.23570	−	1.23570i	−0.273956	−	0.961742i	$-0.588332\pi$
$228$	−0.103619	+	0.103619i	−0.00686233	+	0.00686233i
$229$	−4.04389	−	4.04389i	−0.267228	−	0.267228i	0.560754	−	0.827982i	$-0.310511\pi$
$229$	−4.04389	−	4.04389i	−0.267228	−	0.267228i	−0.827982	+	0.560754i	$0.810511\pi$
$230$		0			0
$231$		−	8.39394i		−	0.552280i
$232$	5.37945	−	0.248111i	0.353178	−	0.0162893i
$233$	10.2570	−	10.2570i	0.671956	−	0.671956i	−0.286210	−	0.958167i	$-0.592396\pi$
$233$	10.2570	−	10.2570i	0.671956	−	0.671956i	0.958167	+	0.286210i	$0.0923956\pi$
$234$	5.04006	−	5.04006i	0.329479	−	0.329479i
$235$		0			0
$236$		−	10.5354i		−	0.685799i
$237$	−0.356715	+	0.356715i	−0.0231711	+	0.0231711i
$238$	8.49371	+	8.49371i	0.550565	+	0.550565i
$239$		−	22.6323i		−	1.46396i	−0.681324	−	0.731982i	$-0.738595\pi$
$239$		−	22.6323i		−	1.46396i	0.681324	−	0.731982i	$-0.261405\pi$
$240$		0			0
$241$			8.27343i			0.532938i	0.963843	+	0.266469i	$0.0858570\pi$
$241$			8.27343i			0.532938i	−0.963843	+	0.266469i	$0.914143\pi$
$242$	−21.0158			−1.35095
$243$	−12.4893			−0.801192
$244$	−7.92394	−	7.92394i	−0.507278	−	0.507278i
$245$		0			0
$246$	1.90459	+	1.90459i	0.121432	+	0.121432i
$247$	−0.729569			−0.0464214
$248$	0.499611	−	0.499611i	0.0317253	−	0.0317253i
$249$	1.92687	−	1.92687i	0.122110	−	0.122110i
$250$		0			0
$251$	−6.96217	−	6.96217i	−0.439448	−	0.439448i	0.452378	−	0.891826i	$-0.350576\pi$
$251$	−6.96217	−	6.96217i	−0.439448	−	0.439448i	−0.891826	+	0.452378i	$0.850576\pi$
$252$	5.43569	+	5.43569i	0.342416	+	0.342416i
$253$	30.7916			1.93585
$254$	−1.71279			−0.107470
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.588484	−	0.588484i	−0.0367086	−	0.0367086i	0.688514	−	0.725223i	$-0.258263\pi$
$257$	−0.588484	−	0.588484i	−0.0367086	−	0.0367086i	−0.725223	+	0.688514i	$0.758263\pi$
$258$			3.36947i			0.209774i
$259$	−13.5210	−	13.5210i	−0.840154	−	0.840154i
$260$		0			0
$261$	−0.675783	−	14.6521i	−0.0418299	−	0.906942i
$262$	−11.9198	−	11.9198i	−0.736405	−	0.736405i
$263$	20.7698			1.28072			0.640362	−	0.768073i	$-0.278784\pi$
$263$	20.7698			1.28072			0.640362	+	0.768073i	$0.278784\pi$
$264$	−2.10302	+	2.10302i	−0.129432	+	0.129432i
$265$		0			0
$266$		−	0.786839i		−	0.0482442i
$267$	6.61255	−	6.61255i	0.404682	−	0.404682i
$268$	−0.259532	+	0.259532i	−0.0158534	+	0.0158534i
$269$	16.9924	+	16.9924i	1.03604	+	1.03604i	0.999326	+	0.0367193i	$0.0116907\pi$
$269$	16.9924	+	16.9924i	1.03604	+	1.03604i	0.0367193	+	0.999326i	$0.488309\pi$
$270$		0			0
$271$	11.9538	−	11.9538i	0.726140	−	0.726140i	−0.243709	−	0.969848i	$-0.578364\pi$
$271$	11.9538	−	11.9538i	0.726140	−	0.726140i	0.969848	+	0.243709i	$0.0783641\pi$
$272$		−	4.25603i		−	0.258060i
$273$		−	3.88214i		−	0.234958i
$274$	17.2523			1.04225
$275$		0			0
$276$	2.02260	−	2.02260i	0.121746	−	0.121746i
$277$	20.1950	+	20.1950i	1.21340	+	1.21340i	0.969901	+	0.243499i	$0.0782954\pi$
$277$	20.1950	+	20.1950i	1.21340	+	1.21340i	0.243499	+	0.969901i	$0.421705\pi$
$278$	15.5459			0.932379
$279$	−1.36080	−	1.36080i	−0.0814690	−	0.0814690i
$280$		0			0
$281$	−20.5557			−1.22625			−0.613125	−	0.789986i	$-0.710088\pi$
$281$	−20.5557			−1.22625			−0.613125	+	0.789986i	$0.710088\pi$
$282$		−	5.09557i		−	0.303437i
$283$	0.884450	+	0.884450i	0.0525751	+	0.0525751i	0.732906	−	0.680330i	$-0.238164\pi$
$283$	0.884450	+	0.884450i	0.0525751	+	0.0525751i	−0.680330	+	0.732906i	$0.738164\pi$
$284$		−	12.3264i		−	0.731437i
$285$		0			0
$286$	−14.8071			−0.875564
$287$	−14.4627			−0.853704
$288$		−	2.72372i		−	0.160497i
$289$	−1.11379			−0.0655170
$290$		0			0
$291$	−5.96251			−0.349528
$292$		−	2.56003i		−	0.149814i
$293$	15.7737			0.921511			0.460755	−	0.887527i	$-0.347579\pi$
$293$	15.7737			0.921511			0.460755	+	0.887527i	$0.347579\pi$
$294$	0.507513			0.0295987
$295$		0			0
$296$			6.77511i			0.393795i
$297$	12.0371	+	12.0371i	0.698462	+	0.698462i
$298$			5.74010i			0.332515i
$299$	14.2409			0.823573
$300$		0			0
$301$	−12.7932	−	12.7932i	−0.737386	−	0.737386i
$302$	4.34872			0.250241
$303$	6.03929	+	6.03929i	0.346948	+	0.346948i
$304$	−0.197135	+	0.197135i	−0.0113065	+	0.0113065i
$305$		0			0
$306$	−11.5922			−0.662684
$307$			2.24543i			0.128153i	0.997945	+	0.0640767i	$0.0204102\pi$
$307$			2.24543i			0.128153i	−0.997945	+	0.0640767i	$0.979590\pi$
$308$		−	15.9695i		−	0.909944i
$309$	−1.55164	+	1.55164i	−0.0882698	+	0.0882698i
$310$		0			0
$311$	0.158505	+	0.158505i	0.00898800	+	0.00898800i	0.711586	−	0.702599i	$-0.247977\pi$
$311$	0.158505	+	0.158505i	0.00898800	+	0.00898800i	−0.702599	+	0.711586i	$0.747977\pi$
$312$	−0.972633	+	0.972633i	−0.0550645	+	0.0550645i
$313$	17.4806	−	17.4806i	0.988060	−	0.988060i	−0.0118697	−	0.999930i	$-0.503778\pi$
$313$	17.4806	−	17.4806i	0.988060	−	0.988060i	0.999930	+	0.0118697i	$0.00377832\pi$
$314$			19.2755i			1.08778i
$315$		0			0
$316$	−0.678650	+	0.678650i	−0.0381770	+	0.0381770i
$317$	−17.6454			−0.991065			−0.495532	−	0.868589i	$-0.665027\pi$
$317$	−17.6454			−0.991065			−0.495532	+	0.868589i	$0.665027\pi$
$318$	2.90152	+	2.90152i	0.162709	+	0.162709i
$319$	−20.5304	+	22.5158i	−1.14948	+	1.26064i
$320$		0			0
$321$	3.75428	+	3.75428i	0.209544	+	0.209544i
$322$			15.3588i			0.855912i
$323$	0.839011	+	0.839011i	0.0466838	+	0.0466838i
$324$	−6.58980			−0.366100
$325$		0			0
$326$	−18.5680			−1.02839
$327$	−1.08760			−0.0601447
$328$	3.62348	+	3.62348i	0.200073	+	0.200073i
$329$	19.3468	+	19.3468i	1.06663	+	1.06663i
$330$		0			0
$331$	2.77539	−	2.77539i	0.152549	−	0.152549i	−0.626706	−	0.779255i	$-0.715597\pi$
$331$	2.77539	−	2.77539i	0.152549	−	0.152549i	0.779255	+	0.626706i	$0.215597\pi$
$332$	3.66587	−	3.66587i	0.201191	−	0.201191i
$333$	18.4535			1.01124
$334$	−5.50661	−	5.50661i	−0.301308	−	0.301308i
$335$		0			0
$336$	−1.04898	−	1.04898i	−0.0572267	−	0.0572267i
$337$	16.8845			0.919757			0.459878	−	0.887982i	$-0.347893\pi$
$337$	16.8845			0.919757			0.459878	+	0.887982i	$0.347893\pi$
$338$	6.15179			0.334614
$339$			4.53305i			0.246201i
$340$		0			0
$341$			3.99788i			0.216497i
$342$	0.536940	+	0.536940i	0.0290344	+	0.0290344i
$343$	12.0429	−	12.0429i	0.650255	−	0.650255i
$344$			6.41041i			0.345626i
$345$		0			0
$346$	4.46207	−	4.46207i	0.239882	−	0.239882i
$347$	−8.18092	+	8.18092i	−0.439175	+	0.439175i	−0.891734	−	0.452560i	$-0.850511\pi$
$347$	−8.18092	+	8.18092i	−0.439175	+	0.439175i	0.452560	+	0.891734i	$0.350511\pi$
$348$	0.130413	+	2.82757i	0.00699087	+	0.151574i
$349$			13.8212i			0.739833i	0.929065	+	0.369916i	$0.120614\pi$
$349$			13.8212i			0.739833i	−0.929065	+	0.369916i	$0.879386\pi$
$350$		0			0
$351$	5.56708	+	5.56708i	0.297149	+	0.297149i
$352$	−4.00099	+	4.00099i	−0.213253	+	0.213253i
$353$	16.5789	+	16.5789i	0.882408	+	0.882408i	0.993779	−	0.111371i	$-0.0355241\pi$
$353$	16.5789	+	16.5789i	0.882408	+	0.882408i	−0.111371	+	0.993779i	$0.535524\pi$
$354$	5.53769			0.294325
$355$		0			0
$356$	12.5804	−	12.5804i	0.666758	−	0.666758i
$357$	−4.46450	+	4.46450i	−0.236286	+	0.236286i
$358$			20.3959i			1.07796i
$359$	1.51633	−	1.51633i	0.0800288	−	0.0800288i	−0.665959	−	0.745988i	$-0.731978\pi$
$359$	1.51633	−	1.51633i	0.0800288	−	0.0800288i	0.745988	+	0.665959i	$0.231978\pi$
$360$		0			0
$361$			18.9223i			0.995909i
$362$			3.67401i			0.193102i
$363$		−	11.0464i		−	0.579787i
$364$		−	7.38577i		−	0.387120i
$365$		0			0
$366$	4.16501	−	4.16501i	0.217709	−	0.217709i
$367$		−	19.7813i		−	1.03258i	−0.856415	−	0.516288i	$-0.827313\pi$
$367$		−	19.7813i		−	1.03258i	0.856415	−	0.516288i	$-0.172687\pi$
$368$	3.84799	−	3.84799i	0.200591	−	0.200591i
$369$	9.86933	−	9.86933i	0.513777	−	0.513777i
$370$		0			0
$371$	−22.0330			−1.14389
$372$	0.262608	+	0.262608i	0.0136156	+	0.0136156i
$373$	−3.15011	+	3.15011i	−0.163107	+	0.163107i	−0.783941	−	0.620835i	$-0.786794\pi$
$373$	−3.15011	+	3.15011i	−0.163107	+	0.163107i	0.620835	+	0.783941i	$0.286794\pi$
$374$	17.0283	+	17.0283i	0.880514	+	0.880514i
$375$		0			0
$376$		−	9.69432i		−	0.499946i
$377$	−9.49519	+	10.4134i	−0.489027	+	0.536318i
$378$	−6.00408	+	6.00408i	−0.308817	+	0.308817i
$379$	12.0938	−	12.0938i	0.621215	−	0.621215i	−0.324627	−	0.945842i	$-0.605239\pi$
$379$	12.0938	−	12.0938i	0.621215	−	0.621215i	0.945842	+	0.324627i	$0.105239\pi$
$380$		0			0
$381$		−	0.900285i		−	0.0461230i
$382$	15.9172	−	15.9172i	0.814394	−	0.814394i
$383$	2.80067	+	2.80067i	0.143108	+	0.143108i	0.775031	−	0.631923i	$-0.217734\pi$
$383$	2.80067	+	2.80067i	0.143108	+	0.143108i	−0.631923	+	0.775031i	$0.717734\pi$
$384$			0.525625i			0.0268232i
$385$		0			0
$386$			11.4353i			0.582043i
$387$	17.4601			0.887549
$388$	−11.3437			−0.575887
$389$	−7.12003	−	7.12003i	−0.361000	−	0.361000i	0.503181	−	0.864181i	$-0.332163\pi$
$389$	−7.12003	−	7.12003i	−0.361000	−	0.361000i	−0.864181	+	0.503181i	$0.832163\pi$
$390$		0			0
$391$	−16.3772	−	16.3772i	−0.828229	−	0.828229i
$392$	0.965542			0.0487673
$393$	6.26532	−	6.26532i	0.316044	−	0.316044i
$394$	−6.93809	+	6.93809i	−0.349536	+	0.349536i
$395$		0			0
$396$	10.8976	+	10.8976i	0.547623	+	0.547623i
$397$	−12.3293	−	12.3293i	−0.618788	−	0.618788i	0.326432	−	0.945221i	$-0.394153\pi$
$397$	−12.3293	−	12.3293i	−0.618788	−	0.618788i	−0.945221	+	0.326432i	$0.894153\pi$
$398$	−6.08686			−0.305107
$399$	0.413582			0.0207050
$400$		0			0
$401$	9.70554			0.484672			0.242336	−	0.970192i	$-0.422086\pi$
$401$	9.70554			0.484672			0.242336	+	0.970192i	$0.422086\pi$
$402$	−0.136416	−	0.136416i	−0.00680383	−	0.00680383i
$403$			1.84899i			0.0921050i
$404$	11.4898	+	11.4898i	0.571636	+	0.571636i
$405$		0			0
$406$	−11.2308	−	10.2405i	−0.557378	−	0.508230i
$407$	−27.1071	−	27.1071i	−1.34365	−	1.34365i
$408$	2.23707			0.110752
$409$	−14.2026	+	14.2026i	−0.702272	+	0.702272i	−0.964898	−	0.262626i	$-0.915412\pi$
$409$	−14.2026	+	14.2026i	−0.702272	+	0.702272i	0.262626	+	0.964898i	$0.415412\pi$
$410$		0			0
$411$			9.06822i			0.447302i
$412$	−2.95200	+	2.95200i	−0.145434	+	0.145434i
$413$	−21.0255	+	21.0255i	−1.03460	+	1.03460i
$414$	−10.4809	−	10.4809i	−0.515106	−	0.515106i
$415$		0			0
$416$	−1.85043	+	1.85043i	−0.0907249	+	0.0907249i
$417$			8.17129i			0.400150i
$418$		−	1.57747i		−	0.0771565i
$419$	−10.9032			−0.532657			−0.266328	−	0.963882i	$-0.585811\pi$
$419$	−10.9032			−0.532657			−0.266328	+	0.963882i	$0.585811\pi$
$420$		0			0
$421$	17.1886	−	17.1886i	0.837723	−	0.837723i	−0.150836	−	0.988559i	$-0.548197\pi$
$421$	17.1886	−	17.1886i	0.837723	−	0.837723i	0.988559	+	0.150836i	$0.0481965\pi$
$422$	2.18584	+	2.18584i	0.106405	+	0.106405i
$423$	−26.4046			−1.28384
$424$	5.52014	+	5.52014i	0.268082	+	0.268082i
$425$		0			0
$426$	6.47906			0.313911
$427$			31.6274i			1.53056i
$428$	7.14252	+	7.14252i	0.345247	+	0.345247i
$429$		−	7.78299i		−	0.375766i
$430$		0			0
$431$	23.8776			1.15014			0.575071	−	0.818103i	$-0.304974\pi$
$431$	23.8776			1.15014			0.575071	+	0.818103i	$0.304974\pi$
$432$	3.00853			0.144748
$433$		−	11.1605i		−	0.536342i	−0.963371	−	0.268171i	$-0.913581\pi$
$433$		−	11.1605i		−	0.536342i	0.963371	−	0.268171i	$-0.0864192\pi$
$434$	−1.99414			−0.0957216
$435$		0			0
$436$	−2.06917			−0.0990951
$437$			1.51715i			0.0725750i
$438$	1.34561			0.0642959
$439$	21.3926			1.02101			0.510507	−	0.859874i	$-0.329458\pi$
$439$	21.3926			1.02101			0.510507	+	0.859874i	$0.329458\pi$
$440$		0			0
$441$		−	2.62987i		−	0.125232i
$442$	7.87550	+	7.87550i	0.374599	+	0.374599i
$443$		−	5.95373i		−	0.282870i	−0.989948	−	0.141435i	$-0.954828\pi$
$443$		−	5.95373i		−	0.282870i	0.989948	−	0.141435i	$-0.0451717\pi$
$444$	−3.56116			−0.169005
$445$		0			0
$446$	−10.3129	−	10.3129i	−0.488331	−	0.488331i
$447$	−3.01714			−0.142706
$448$	−1.99569	−	1.99569i	−0.0942874	−	0.0942874i
$449$	−13.4108	+	13.4108i	−0.632896	+	0.632896i	−0.948793	−	0.315897i	$-0.897695\pi$
$449$	−13.4108	+	13.4108i	−0.632896	+	0.632896i	0.315897	+	0.948793i	$0.397695\pi$
$450$		0			0
$451$	−28.9950			−1.36532
$452$			8.62412i			0.405645i
$453$			2.28579i			0.107396i
$454$	18.6177	−	18.6177i	0.873771	−	0.873771i
$455$		0			0
$456$	−0.103619	−	0.103619i	−0.00485240	−	0.00485240i
$457$	16.7887	−	16.7887i	0.785343	−	0.785343i	−0.195384	−	0.980727i	$-0.562595\pi$
$457$	16.7887	−	16.7887i	0.785343	−	0.785343i	0.980727	+	0.195384i	$0.0625953\pi$
$458$	4.04389	−	4.04389i	0.188959	−	0.188959i
$459$		−	12.8044i		−	0.597657i
$460$		0			0
$461$	12.7770	−	12.7770i	0.595083	−	0.595083i	−0.343917	−	0.939000i	$-0.611754\pi$
$461$	12.7770	−	12.7770i	0.595083	−	0.595083i	0.939000	+	0.343917i	$0.111754\pi$
$462$	8.39394			0.390521
$463$	−6.84002	−	6.84002i	−0.317883	−	0.317883i	0.530071	−	0.847953i	$-0.322165\pi$
$463$	−6.84002	−	6.84002i	−0.317883	−	0.317883i	−0.847953	+	0.530071i	$0.822165\pi$
$464$	0.248111	+	5.37945i	0.0115182	+	0.249735i
$465$		0			0
$466$	10.2570	+	10.2570i	0.475145	+	0.475145i
$467$		−	33.8234i		−	1.56516i	−0.622551	−	0.782579i	$-0.713904\pi$
$467$		−	33.8234i		−	1.56516i	0.622551	−	0.782579i	$-0.286096\pi$
$468$	5.04006	+	5.04006i	0.232977	+	0.232977i
$469$	1.03589			0.0478329
$470$		0			0
$471$	−10.1317			−0.466844
$472$	10.5354			0.484933
$473$	−25.6480	−	25.6480i	−1.17930	−	1.17930i
$474$	−0.356715	−	0.356715i	−0.0163845	−	0.0163845i
$475$		0			0
$476$	−8.49371	+	8.49371i	−0.389308	+	0.389308i
$477$	15.0353	−	15.0353i	0.688420	−	0.688420i
$478$	22.6323			1.03518
$479$	−13.2884	−	13.2884i	−0.607161	−	0.607161i	0.335042	−	0.942203i	$-0.391250\pi$
$479$	−13.2884	−	13.2884i	−0.607161	−	0.607161i	−0.942203	+	0.335042i	$0.891250\pi$
$480$		0			0
$481$	−12.5369	−	12.5369i	−0.571632	−	0.571632i
$482$	−8.27343			−0.376844
$483$	−8.07296			−0.367332
$484$		−	21.0158i		−	0.955265i
$485$		0			0
$486$		−	12.4893i		−	0.566528i
$487$	20.5484	+	20.5484i	0.931139	+	0.931139i	0.997777	−	0.0666381i	$-0.0212273\pi$
$487$	20.5484	+	20.5484i	0.931139	+	0.931139i	−0.0666381	+	0.997777i	$0.521227\pi$
$488$	7.92394	−	7.92394i	0.358700	−	0.358700i
$489$		−	9.75980i		−	0.441353i
$490$		0			0
$491$	9.25965	−	9.25965i	0.417882	−	0.417882i	−0.466591	−	0.884473i	$-0.654518\pi$
$491$	9.25965	−	9.25965i	0.417882	−	0.417882i	0.884473	+	0.466591i	$0.154518\pi$
$492$	−1.90459	+	1.90459i	−0.0858654	+	0.0858654i
$493$	22.8951	−	1.05597i	1.03114	−	0.0475583i
$494$		−	0.729569i		−	0.0328249i
$495$		0			0
$496$	0.499611	+	0.499611i	0.0224332	+	0.0224332i
$497$	−24.5996	+	24.5996i	−1.10344	+	1.10344i
$498$	1.92687	+	1.92687i	0.0863451	+	0.0863451i
$499$	16.1174			0.721513			0.360757	−	0.932660i	$-0.382519\pi$
$499$	16.1174			0.721513			0.360757	+	0.932660i	$0.382519\pi$
$500$		0			0
$501$	2.89441	−	2.89441i	0.129313	−	0.129313i
$502$	6.96217	−	6.96217i	0.310737	−	0.310737i
$503$		−	13.4803i		−	0.601058i	−0.953773	−	0.300529i	$-0.902837\pi$
$503$		−	13.4803i		−	0.601058i	0.953773	−	0.300529i	$-0.0971633\pi$
$504$	−5.43569	+	5.43569i	−0.242125	+	0.242125i
$505$		0			0
$506$			30.7916i			1.36885i
$507$			3.23353i			0.143606i
$508$		−	1.71279i		−	0.0759928i
$509$			8.96501i			0.397367i	0.980064	+	0.198684i	$0.0636666\pi$
$509$			8.96501i			0.397367i	−0.980064	+	0.198684i	$0.936333\pi$
$510$		0			0
$511$	−5.10902	+	5.10902i	−0.226010	+	0.226010i
$512$			1.00000i			0.0441942i
$513$	−0.593085	+	0.593085i	−0.0261854	+	0.0261854i
$514$	0.588484	−	0.588484i	0.0259569	−	0.0259569i
$515$		0			0
$516$	−3.36947			−0.148333
$517$	38.7869	+	38.7869i	1.70584	+	1.70584i
$518$	13.5210	−	13.5210i	0.594079	−	0.594079i
$519$	2.34537	+	2.34537i	0.102950	+	0.102950i
$520$		0			0
$521$		−	22.0170i		−	0.964581i	−0.876011	−	0.482290i	$-0.839805\pi$
$521$		−	22.0170i		−	0.964581i	0.876011	−	0.482290i	$-0.160195\pi$
$522$	14.6521	−	0.675783i	0.641305	−	0.0295782i
$523$	11.0816	−	11.0816i	0.484565	−	0.484565i	−0.422021	−	0.906586i	$-0.638679\pi$
$523$	11.0816	−	11.0816i	0.484565	−	0.484565i	0.906586	+	0.422021i	$0.138679\pi$
$524$	11.9198	−	11.9198i	0.520717	−	0.520717i
$525$		0			0
$526$			20.7698i			0.905608i
$527$	2.12636	−	2.12636i	0.0926257	−	0.0926257i
$528$	−2.10302	−	2.10302i	−0.0915221	−	0.0915221i
$529$		−	6.61411i		−	0.287570i
$530$		0			0
$531$		−	28.6956i		−	1.24528i
$532$	0.786839			0.0341138
$533$	−13.4100			−0.580852
$534$	6.61255	+	6.61255i	0.286153	+	0.286153i
$535$		0			0
$536$	−0.259532	−	0.259532i	−0.0112101	−	0.0112101i
$537$	−10.7206			−0.462627
$538$	−16.9924	+	16.9924i	−0.732594	+	0.732594i
$539$	−3.86312	+	3.86312i	−0.166397	+	0.166397i
$540$		0			0
$541$	16.7675	+	16.7675i	0.720893	+	0.720893i	0.968787	−	0.247894i	$-0.0797385\pi$
$541$	16.7675	+	16.7675i	0.720893	+	0.720893i	−0.247894	+	0.968787i	$0.579738\pi$
$542$	11.9538	+	11.9538i	0.513458	+	0.513458i
$543$	−1.93115			−0.0828736
$544$	4.25603			0.182476
$545$		0			0
$546$	3.88214			0.166140
$547$	−23.1264	−	23.1264i	−0.988814	−	0.988814i	0.0111242	−	0.999938i	$-0.496459\pi$
$547$	−23.1264	−	23.1264i	−0.988814	−	0.988814i	−0.999938	+	0.0111242i	$0.996459\pi$
$548$			17.2523i			0.736980i
$549$	−21.5826	−	21.5826i	−0.921122	−	0.921122i
$550$		0			0
$551$	−1.10939	−	1.01156i	−0.0472615	−	0.0430941i
$552$	2.02260	+	2.02260i	0.0860876	+	0.0860876i
$553$	2.70875			0.115188
$554$	−20.1950	+	20.1950i	−0.858004	+	0.858004i
$555$		0			0
$556$			15.5459i			0.659292i
$557$	−17.2548	+	17.2548i	−0.731110	+	0.731110i	−0.970840	−	0.239730i	$-0.922941\pi$
$557$	−17.2548	+	17.2548i	−0.731110	+	0.731110i	0.239730	+	0.970840i	$0.422941\pi$
$558$	1.36080	−	1.36080i	0.0576073	−	0.0576073i
$559$	−11.8620	−	11.8620i	−0.501710	−	0.501710i
$560$		0			0
$561$	−8.95051	+	8.95051i	−0.377891	+	0.377891i
$562$		−	20.5557i		−	0.867089i
$563$			23.2190i			0.978565i	0.872125	+	0.489282i	$0.162741\pi$
$563$			23.2190i			0.978565i	−0.872125	+	0.489282i	$0.837259\pi$
$564$	5.09557			0.214562
$565$		0			0
$566$	−0.884450	+	0.884450i	−0.0371762	+	0.0371762i
$567$	13.1512	+	13.1512i	0.552298	+	0.552298i
$568$	12.3264			0.517204
$569$	−10.8123	−	10.8123i	−0.453274	−	0.453274i	0.443166	−	0.896440i	$-0.353855\pi$
$569$	−10.8123	−	10.8123i	−0.453274	−	0.453274i	−0.896440	+	0.443166i	$0.853855\pi$
$570$		0			0
$571$	12.2970			0.514612			0.257306	−	0.966330i	$-0.417165\pi$
$571$	12.2970			0.514612			0.257306	+	0.966330i	$0.417165\pi$
$572$		−	14.8071i		−	0.619117i
$573$	8.36647	+	8.36647i	0.349514	+	0.349514i
$574$		−	14.4627i		−	0.603660i
$575$		0			0
$576$	2.72372			0.113488
$577$	−38.9130			−1.61997			−0.809985	−	0.586451i	$-0.800525\pi$
$577$	−38.9130			−1.61997			−0.809985	+	0.586451i	$0.800525\pi$
$578$		−	1.11379i		−	0.0463275i
$579$	−6.01069			−0.249796
$580$		0			0
$581$	−14.6318			−0.607031
$582$		−	5.96251i		−	0.247154i
$583$	−44.1720			−1.82942
$584$	2.56003			0.105935
$585$		0			0
$586$			15.7737i			0.651606i
$587$	6.17514	+	6.17514i	0.254875	+	0.254875i	0.822966	−	0.568091i	$-0.192318\pi$
$587$	6.17514	+	6.17514i	0.254875	+	0.254875i	−0.568091	+	0.822966i	$0.692318\pi$
$588$			0.507513i			0.0209295i
$589$	−0.196981			−0.00811648
$590$		0			0
$591$	−3.64683	−	3.64683i	−0.150011	−	0.150011i
$592$	−6.77511			−0.278455
$593$	−1.97670	−	1.97670i	−0.0811735	−	0.0811735i	0.665354	−	0.746528i	$-0.268281\pi$
$593$	−1.97670	−	1.97670i	−0.0811735	−	0.0811735i	−0.746528	+	0.665354i	$0.768281\pi$
$594$	−12.0371	+	12.0371i	−0.493888	+	0.493888i
$595$		0			0
$596$	−5.74010			−0.235124
$597$		−	3.19940i		−	0.130943i
$598$			14.2409i			0.582354i
$599$	−29.5374	+	29.5374i	−1.20686	+	1.20686i	−0.234826	+	0.972037i	$0.575452\pi$
$599$	−29.5374	+	29.5374i	−1.20686	+	1.20686i	−0.972037	+	0.234826i	$0.924548\pi$
$600$		0			0
$601$	15.7916	+	15.7916i	0.644151	+	0.644151i	0.951573	−	0.307422i	$-0.0994664\pi$
$601$	15.7916	+	15.7916i	0.644151	+	0.644151i	−0.307422	+	0.951573i	$0.599466\pi$
$602$	12.7932	−	12.7932i	0.521411	−	0.521411i
$603$	−0.706892	+	0.706892i	−0.0287869	+	0.0287869i
$604$			4.34872i			0.176947i
$605$		0			0
$606$	−6.03929	+	6.03929i	−0.245330	+	0.245330i
$607$	−25.6141			−1.03965			−0.519823	−	0.854274i	$-0.674002\pi$
$607$	−25.6141			−1.03965			−0.519823	+	0.854274i	$0.674002\pi$
$608$	−0.197135	−	0.197135i	−0.00799487	−	0.00799487i
$609$	5.38268	−	5.90321i	0.218117	−	0.239210i
$610$		0			0
$611$	17.9387	+	17.9387i	0.725722	+	0.725722i
$612$		−	11.5922i		−	0.468588i
$613$	7.44159	+	7.44159i	0.300563	+	0.300563i	0.841234	−	0.540671i	$-0.181830\pi$
$613$	7.44159	+	7.44159i	0.300563	+	0.300563i	−0.540671	+	0.841234i	$0.681830\pi$
$614$	−2.24543			−0.0906182
$615$		0			0
$616$	15.9695			0.643428
$617$	−14.5318			−0.585027			−0.292514	−	0.956261i	$-0.594492\pi$
$617$	−14.5318			−0.585027			−0.292514	+	0.956261i	$0.594492\pi$
$618$	−1.55164	−	1.55164i	−0.0624162	−	0.0624162i
$619$	26.5990	+	26.5990i	1.06910	+	1.06910i	0.997428	+	0.0716754i	$0.0228346\pi$
$619$	26.5990	+	26.5990i	1.06910	+	1.06910i	0.0716754	+	0.997428i	$0.477165\pi$
$620$		0			0
$621$	11.5768	−	11.5768i	0.464561	−	0.464561i
$622$	−0.158505	+	0.158505i	−0.00635547	+	0.00635547i
$623$	−50.2130			−2.01174
$624$	−0.972633	−	0.972633i	−0.0389365	−	0.0389365i
$625$		0			0
$626$	17.4806	+	17.4806i	0.698664	+	0.698664i
$627$	0.829156			0.0331133
$628$	−19.2755			−0.769178
$629$			28.8350i			1.14973i
$630$		0			0
$631$		−	32.6472i		−	1.29966i	−0.760078	−	0.649832i	$-0.774839\pi$
$631$		−	32.6472i		−	1.29966i	0.760078	−	0.649832i	$-0.225161\pi$
$632$	−0.678650	−	0.678650i	−0.0269952	−	0.0269952i
$633$	−1.14893	+	1.14893i	−0.0456659	+	0.0456659i
$634$		−	17.6454i		−	0.700789i
$635$		0			0
$636$	−2.90152	+	2.90152i	−0.115053	+	0.115053i
$637$	−1.78667	+	1.78667i	−0.0707905	+	0.0707905i
$638$	−22.5158	−	20.5304i	−0.891409	−	0.812807i
$639$		−	33.5736i		−	1.32815i
$640$		0			0
$641$	−29.0493	−	29.0493i	−1.14738	−	1.14738i	−0.987066	−	0.160313i	$-0.948750\pi$
$641$	−29.0493	−	29.0493i	−1.14738	−	1.14738i	−0.160313	−	0.987066i	$-0.551250\pi$
$642$	−3.75428	+	3.75428i	−0.148170	+	0.148170i
$643$	23.8741	+	23.8741i	0.941504	+	0.941504i	0.998381	−	0.0568775i	$-0.0181145\pi$
$643$	23.8741	+	23.8741i	0.941504	+	0.941504i	−0.0568775	+	0.998381i	$0.518114\pi$
$644$	−15.3588			−0.605221
$645$		0			0
$646$	−0.839011	+	0.839011i	−0.0330105	+	0.0330105i
$647$	−21.3178	+	21.3178i	−0.838089	+	0.838089i	−0.988607	−	0.150518i	$-0.951906\pi$
$647$	−21.3178	+	21.3178i	−0.838089	+	0.838089i	0.150518	+	0.988607i	$0.451906\pi$
$648$		−	6.58980i		−	0.258872i
$649$	−42.1522	+	42.1522i	−1.65462	+	1.65462i
$650$		0			0
$651$		−	1.04817i		−	0.0410809i
$652$		−	18.5680i		−	0.727179i
$653$			12.0344i			0.470942i	0.971881	+	0.235471i	$0.0756632\pi$
$653$			12.0344i			0.470942i	−0.971881	+	0.235471i	$0.924337\pi$
$654$		−	1.08760i		−	0.0425287i
$655$		0			0
$656$	−3.62348	+	3.62348i	−0.141473	+	0.141473i
$657$		−	6.97280i		−	0.272035i
$658$	−19.3468	+	19.3468i	−0.754218	+	0.754218i
$659$	24.8319	−	24.8319i	0.967313	−	0.967313i	−0.0321690	−	0.999482i	$-0.510241\pi$
$659$	24.8319	−	24.8319i	0.967313	−	0.967313i	0.999482	+	0.0321690i	$0.0102415\pi$
$660$		0			0
$661$	30.3843			1.18181			0.590906	−	0.806740i	$-0.298770\pi$
$661$	30.3843			1.18181			0.590906	+	0.806740i	$0.298770\pi$
$662$	2.77539	+	2.77539i	0.107868	+	0.107868i
$663$	−4.13955	+	4.13955i	−0.160767	+	0.160767i
$664$	3.66587	+	3.66587i	0.142263	+	0.142263i
$665$		0			0
$666$			18.4535i			0.715058i
$667$	21.6548	+	19.7453i	0.838477	+	0.764543i
$668$	5.50661	−	5.50661i	0.213057	−	0.213057i
$669$	5.42073	−	5.42073i	0.209577	−	0.209577i
$670$		0			0
$671$			63.4072i			2.44781i
$672$	1.04898	−	1.04898i	0.0404654	−	0.0404654i
$673$	−27.6644	−	27.6644i	−1.06638	−	1.06638i	−0.997634	−	0.0687508i	$-0.978099\pi$
$673$	−27.6644	−	27.6644i	−1.06638	−	1.06638i	−0.0687508	−	0.997634i	$-0.521901\pi$
$674$			16.8845i			0.650366i
$675$		0			0
$676$			6.15179i			0.236607i
$677$	−33.6291			−1.29247			−0.646236	−	0.763138i	$-0.723658\pi$
$677$	−33.6291			−1.29247			−0.646236	+	0.763138i	$0.723658\pi$
$678$	−4.53305			−0.174091
$679$	22.6384	+	22.6384i	0.868783	+	0.868783i
$680$		0			0
$681$	9.78591	+	9.78591i	0.374997	+	0.374997i
$682$	−3.99788			−0.153087
$683$	−31.5697	+	31.5697i	−1.20798	+	1.20798i	−0.236302	+	0.971680i	$0.575936\pi$
$683$	−31.5697	+	31.5697i	−1.20798	+	1.20798i	−0.971680	+	0.236302i	$0.924064\pi$
$684$	−0.536940	+	0.536940i	−0.0205304	+	0.0205304i
$685$		0			0
$686$	12.0429	+	12.0429i	0.459800	+	0.459800i
$687$	2.12557	+	2.12557i	0.0810955	+	0.0810955i
$688$	−6.41041			−0.244395
$689$	−20.4293			−0.778294
$690$		0			0
$691$	35.2173			1.33973			0.669864	−	0.742484i	$-0.266352\pi$
$691$	35.2173			1.33973			0.669864	+	0.742484i	$0.266352\pi$
$692$	4.46207	+	4.46207i	0.169622	+	0.169622i
$693$		−	43.4963i		−	1.65229i
$694$	−8.18092	−	8.18092i	−0.310543	−	0.310543i
$695$		0			0
$696$	−2.82757	+	0.130413i	−0.107179	+	0.00494329i
$697$	15.4216	+	15.4216i	0.584136	+	0.584136i
$698$	−13.8212			−0.523141
$699$	−5.39131	+	5.39131i	−0.203918	+	0.203918i
$700$		0			0
$701$			2.32524i			0.0878229i	0.999035	+	0.0439115i	$0.0139820\pi$
$701$			2.32524i			0.0878229i	−0.999035	+	0.0439115i	$0.986018\pi$
$702$	−5.56708	+	5.56708i	−0.210116	+	0.210116i
$703$	1.33561	−	1.33561i	0.0503734	−	0.0503734i
$704$	−4.00099	−	4.00099i	−0.150793	−	0.150793i
$705$		0			0
$706$	−16.5789	+	16.5789i	−0.623957	+	0.623957i
$707$		−	45.8599i		−	1.72474i
$708$			5.53769i			0.208119i
$709$	22.8118			0.856715			0.428358	−	0.903609i	$-0.359092\pi$
$709$	22.8118			0.856715			0.428358	+	0.903609i	$0.359092\pi$
$710$		0			0
$711$	−1.84845	+	1.84845i	−0.0693223	+	0.0693223i
$712$	12.5804	+	12.5804i	0.471469	+	0.471469i
$713$	3.84500			0.143996
$714$	−4.46450	−	4.46450i	−0.167080	−	0.167080i
$715$		0			0
$716$	−20.3959			−0.762230
$717$			11.8961i			0.444269i
$718$	1.51633	+	1.51633i	0.0565889	+	0.0565889i
$719$		−	7.58333i		−	0.282811i	−0.989952	−	0.141405i	$-0.954838\pi$
$719$		−	7.58333i		−	0.282811i	0.989952	−	0.141405i	$-0.0451621\pi$
$720$		0			0
$721$	11.7825			0.438804
$722$	−18.9223			−0.704214
$723$		−	4.34872i		−	0.161730i
$724$	−3.67401			−0.136544
$725$		0			0
$726$	11.0464			0.409972
$727$		−	16.3822i		−	0.607583i	−0.952739	−	0.303791i	$-0.901747\pi$
$727$		−	16.3822i		−	0.607583i	0.952739	−	0.303791i	$-0.0982526\pi$
$728$	7.38577			0.273735
$729$	−13.2047			−0.489063
$730$		0			0
$731$			27.2829i			1.00909i
$732$	4.16501	+	4.16501i	0.153943	+	0.153943i
$733$		−	38.4679i		−	1.42084i	−0.703776	−	0.710422i	$-0.748504\pi$
$733$		−	38.4679i		−	1.42084i	0.703776	−	0.710422i	$-0.251496\pi$
$734$	19.7813			0.730142
$735$		0			0
$736$	3.84799	+	3.84799i	0.141839	+	0.141839i
$737$	2.07677			0.0764988
$738$	9.86933	+	9.86933i	0.363295	+	0.363295i
$739$	4.44183	−	4.44183i	0.163396	−	0.163396i	−0.620674	−	0.784069i	$-0.713141\pi$
$739$	4.44183	−	4.44183i	0.163396	−	0.163396i	0.784069	+	0.620674i	$0.213141\pi$
$740$		0			0
$741$	0.383480			0.0140875
$742$		−	22.0330i		−	0.808855i
$743$		−	44.3880i		−	1.62844i	−0.580557	−	0.814220i	$-0.697165\pi$
$743$		−	44.3880i		−	1.62844i	0.580557	−	0.814220i	$-0.302835\pi$
$744$	−0.262608	+	0.262608i	−0.00962767	+	0.00962767i
$745$		0			0
$746$	−3.15011	−	3.15011i	−0.115334	−	0.115334i
$747$	9.98479	−	9.98479i	0.365324	−	0.365324i
$748$	−17.0283	+	17.0283i	−0.622617	+	0.622617i
$749$		−	28.5085i		−	1.04168i
$750$		0			0
$751$	14.4207	−	14.4207i	0.526217	−	0.526217i	−0.393225	−	0.919442i	$-0.628641\pi$
$751$	14.4207	−	14.4207i	0.526217	−	0.526217i	0.919442	+	0.393225i	$0.128641\pi$
$752$	9.69432			0.353515
$753$	3.65949	+	3.65949i	0.133359	+	0.133359i
$754$	−10.4134	−	9.49519i	−0.379234	−	0.345795i
$755$		0			0
$756$	−6.00408	−	6.00408i	−0.218366	−	0.218366i
$757$		−	51.7937i		−	1.88247i	−0.337748	−	0.941237i	$-0.609665\pi$
$757$		−	51.7937i		−	1.88247i	0.337748	−	0.941237i	$-0.390335\pi$
$758$	12.0938	+	12.0938i	0.439266	+	0.439266i
$759$	−16.1848			−0.587471
$760$		0			0
$761$	7.44094			0.269734			0.134867	−	0.990864i	$-0.456939\pi$
$761$	7.44094			0.269734			0.134867	+	0.990864i	$0.456939\pi$
$762$	0.900285			0.0326139
$763$	4.12941	+	4.12941i	0.149495	+	0.149495i
$764$	15.9172	+	15.9172i	0.575864	+	0.575864i
$765$		0			0
$766$	−2.80067	+	2.80067i	−0.101192	+	0.101192i
$767$	−19.4951	+	19.4951i	−0.703929	+	0.703929i
$768$	−0.525625			−0.0189668
$769$	−19.2415	−	19.2415i	−0.693867	−	0.693867i	0.269214	−	0.963080i	$-0.413236\pi$
$769$	−19.2415	−	19.2415i	−0.693867	−	0.693867i	−0.963080	+	0.269214i	$0.913236\pi$
$770$		0			0
$771$	0.309322	+	0.309322i	0.0111400	+	0.0111400i
$772$	−11.4353			−0.411567
$773$	−15.9006			−0.571904			−0.285952	−	0.958244i	$-0.592310\pi$
$773$	−15.9006			−0.571904			−0.285952	+	0.958244i	$0.592310\pi$
$774$			17.4601i			0.627592i
$775$		0			0
$776$		−	11.3437i		−	0.407214i
$777$	7.10697	+	7.10697i	0.254961	+	0.254961i
$778$	7.12003	−	7.12003i	0.255265	−	0.255265i
$779$		−	1.42863i		−	0.0511858i
$780$		0			0
$781$	−49.3178	+	49.3178i	−1.76473	+	1.76473i
$782$	16.3772	−	16.3772i	0.585647	−	0.585647i
$783$	0.746447	+	16.1842i	0.0266758	+	0.578376i
$784$			0.965542i			0.0344837i
$785$		0			0
$786$	6.26532	+	6.26532i	0.223477	+	0.223477i
$787$	−10.0290	+	10.0290i	−0.357497	+	0.357497i	−0.862889	−	0.505393i	$-0.831348\pi$
$787$	−10.0290	+	10.0290i	−0.357497	+	0.357497i	0.505393	+	0.862889i	$0.331348\pi$
$788$	−6.93809	−	6.93809i	−0.247159	−	0.247159i
$789$	−10.9171			−0.388660
$790$		0			0
$791$	17.2111	−	17.2111i	0.611955	−	0.611955i
$792$	−10.8976	+	10.8976i	−0.387228	+	0.387228i
$793$			29.3254i			1.04138i
$794$	12.3293	−	12.3293i	0.437549	−	0.437549i
$795$		0			0
$796$		−	6.08686i		−	0.215743i
$797$		−	2.50059i		−	0.0885755i	−0.999019	−	0.0442878i	$-0.985898\pi$
$797$		−	2.50059i		−	0.0885755i	0.999019	−	0.0442878i	$-0.0141018\pi$
$798$			0.413582i			0.0146406i
$799$		−	41.2593i		−	1.45965i
$800$		0			0
$801$	34.2654	−	34.2654i	1.21071	−	1.21071i
$802$			9.70554i			0.342715i
$803$	−10.2426	+	10.2426i	−0.361455	+	0.361455i
$804$	0.136416	−	0.136416i	0.00481103	−	0.00481103i
$805$		0			0
$806$	−1.84899			−0.0651280
$807$	−8.93162	−	8.93162i	−0.314408	−	0.314408i
$808$	−11.4898	+	11.4898i	−0.404208	+	0.404208i
$809$	27.3039	+	27.3039i	0.959953	+	0.959953i	0.999228	−	0.0392758i	$-0.0125051\pi$
$809$	27.3039	+	27.3039i	0.959953	+	0.959953i	−0.0392758	+	0.999228i	$0.512505\pi$
$810$		0			0
$811$			23.1263i			0.812075i	0.913856	+	0.406037i	$0.133090\pi$
$811$			23.1263i			0.812075i	−0.913856	+	0.406037i	$0.866910\pi$
$812$	10.2405	−	11.2308i	0.359373	−	0.394126i
$813$	−6.28319	+	6.28319i	−0.220361	+	0.220361i
$814$	27.1071	−	27.1071i	0.950104	−	0.950104i
$815$		0			0
$816$			2.23707i			0.0783132i
$817$	1.26371	−	1.26371i	0.0442118	−	0.0442118i
$818$	−14.2026	−	14.2026i	−0.496581	−	0.496581i
$819$		−	20.1168i		−	0.702937i
$820$		0			0
$821$			31.4535i			1.09773i	0.835910	+	0.548867i	$0.184941\pi$
$821$			31.4535i			1.09773i	−0.835910	+	0.548867i	$0.815059\pi$
$822$	−9.06822			−0.316290
$823$	−21.2810			−0.741810			−0.370905	−	0.928671i	$-0.620952\pi$
$823$	−21.2810			−0.741810			−0.370905	+	0.928671i	$0.620952\pi$
$824$	−2.95200	−	2.95200i	−0.102838	−	0.102838i
$825$		0			0
$826$	−21.0255	−	21.0255i	−0.731569	−	0.731569i
$827$	37.6296			1.30851			0.654255	−	0.756274i	$-0.272982\pi$
$827$	37.6296			1.30851			0.654255	+	0.756274i	$0.272982\pi$
$828$	10.4809	−	10.4809i	0.364235	−	0.364235i
$829$	−15.0280	+	15.0280i	−0.521946	+	0.521946i	−0.918159	−	0.396213i	$-0.870324\pi$
$829$	−15.0280	+	15.0280i	−0.521946	+	0.521946i	0.396213	+	0.918159i	$0.370324\pi$
$830$		0			0
$831$	−10.6150	−	10.6150i	−0.368230	−	0.368230i
$832$	−1.85043	−	1.85043i	−0.0641522	−	0.0641522i
$833$	4.10938			0.142381
$834$	−8.17129			−0.282949
$835$		0			0
$836$	1.57747			0.0545579
$837$	1.50309	+	1.50309i	0.0519545	+	0.0519545i
$838$		−	10.9032i		−	0.376645i
$839$	31.2050	+	31.2050i	1.07732	+	1.07732i	0.996749	+	0.0805679i	$0.0256734\pi$
$839$	31.2050	+	31.2050i	1.07732	+	1.07732i	0.0805679	+	0.996749i	$0.474327\pi$
$840$		0			0
$841$	−28.8769	+	2.66939i	−0.995755	+	0.0920481i
$842$	17.1886	+	17.1886i	0.592359	+	0.592359i
$843$	10.8046			0.372129
$844$	−2.18584	+	2.18584i	−0.0752397	+	0.0752397i
$845$		0			0
$846$		−	26.4046i		−	0.907809i
$847$	−41.9410	+	41.9410i	−1.44111	+	1.44111i
$848$	−5.52014	+	5.52014i	−0.189562	+	0.189562i
$849$	−0.464888	−	0.464888i	−0.0159549	−	0.0159549i
$850$		0			0
$851$	−26.0706	+	26.0706i	−0.893687	+	0.893687i
$852$			6.47906i			0.221969i
$853$		−	41.2866i		−	1.41362i	−0.707401	−	0.706812i	$-0.750132\pi$
$853$		−	41.2866i		−	1.41362i	0.707401	−	0.706812i	$-0.249868\pi$
$854$	−31.6274			−1.08227
$855$		0			0
$856$	−7.14252	+	7.14252i	−0.244126	+	0.244126i
$857$	4.90811	+	4.90811i	0.167658	+	0.167658i	0.785949	−	0.618291i	$-0.212175\pi$
$857$	4.90811	+	4.90811i	0.167658	+	0.167658i	−0.618291	+	0.785949i	$0.712175\pi$
$858$	7.78299			0.265707
$859$	−34.3576	−	34.3576i	−1.17226	−	1.17226i	−0.981669	−	0.190596i	$-0.938958\pi$
$859$	−34.3576	−	34.3576i	−1.17226	−	1.17226i	−0.190596	−	0.981669i	$-0.561042\pi$
$860$		0			0
$861$	7.60193			0.259073
$862$			23.8776i			0.813274i
$863$	−23.7860	−	23.7860i	−0.809683	−	0.809683i	0.174902	−	0.984586i	$-0.444039\pi$
$863$	−23.7860	−	23.7860i	−0.809683	−	0.809683i	−0.984586	+	0.174902i	$0.944039\pi$
$864$			3.00853i			0.102352i
$865$		0			0
$866$	11.1605			0.379251
$867$	0.585434			0.0198824
$868$		−	1.99414i		−	0.0676854i
$869$	5.43054			0.184218
$870$		0			0
$871$	0.960493			0.0325451
$872$		−	2.06917i		−	0.0700708i
$873$	−30.8970			−1.04570
$874$	−1.51715			−0.0513182
$875$		0			0
$876$			1.34561i			0.0454641i
$877$	−1.29421	−	1.29421i	−0.0437023	−	0.0437023i	0.684918	−	0.728620i	$-0.259838\pi$
$877$	−1.29421	−	1.29421i	−0.0437023	−	0.0437023i	−0.728620	+	0.684918i	$0.759838\pi$
$878$			21.3926i			0.721966i
$879$	−8.29105			−0.279650
$880$		0			0
$881$	−25.0178	−	25.0178i	−0.842870	−	0.842870i	0.146361	−	0.989231i	$-0.453244\pi$
$881$	−25.0178	−	25.0178i	−0.842870	−	0.842870i	−0.989231	+	0.146361i	$0.953244\pi$
$882$	2.62987			0.0885522
$883$	−27.3498	−	27.3498i	−0.920393	−	0.920393i	0.0766643	−	0.997057i	$-0.475573\pi$
$883$	−27.3498	−	27.3498i	−0.920393	−	0.920393i	−0.997057	+	0.0766643i	$0.975573\pi$
$884$	−7.87550	+	7.87550i	−0.264882	+	0.264882i
$885$		0			0
$886$	5.95373			0.200020
$887$		−	46.1404i		−	1.54924i	−0.632426	−	0.774621i	$-0.717941\pi$
$887$		−	46.1404i		−	1.54924i	0.632426	−	0.774621i	$-0.282059\pi$
$888$		−	3.56116i		−	0.119505i
$889$	−3.41820	+	3.41820i	−0.114643	+	0.114643i
$890$		0			0
$891$	26.3657	+	26.3657i	0.883285	+	0.883285i
$892$	10.3129	−	10.3129i	0.345302	−	0.345302i
$893$	−1.91109	+	1.91109i	−0.0639521	+	0.0639521i
$894$		−	3.01714i		−	0.100908i
$895$		0			0
$896$	1.99569	−	1.99569i	0.0666713	−	0.0666713i
$897$	−7.48537			−0.249929
$898$	−13.4108	−	13.4108i	−0.447525	−	0.447525i
$899$	−2.56367	+	2.81159i	−0.0855033	+	0.0937718i
$900$		0			0
$901$	23.4939	+	23.4939i	0.782695	+	0.782695i
$902$		−	28.9950i		−	0.965427i
$903$	6.72441	+	6.72441i	0.223774	+	0.223774i
$904$	−8.62412			−0.286834
$905$		0			0
$906$	−2.28579			−0.0759404
$907$	25.8559			0.858532			0.429266	−	0.903178i	$-0.358772\pi$
$907$	25.8559			0.858532			0.429266	+	0.903178i	$0.358772\pi$
$908$	18.6177	+	18.6177i	0.617849	+	0.617849i
$909$	31.2949	+	31.2949i	1.03798	+	1.03798i
$910$		0			0
$911$	30.2093	−	30.2093i	1.00088	−	1.00088i	0.000879468	−	1.00000i	$-0.499720\pi$
$911$	30.2093	−	30.2093i	1.00088	−	1.00088i	1.00000		0.000879468i	$-0.000279944\pi$
$912$	0.103619	−	0.103619i	0.00343116	−	0.00343116i
$913$	−29.3342			−0.970820
$914$	16.7887	+	16.7887i	0.555321	+	0.555321i
$915$		0			0
$916$	4.04389	+	4.04389i	0.133614	+	0.133614i
$917$	−47.5763			−1.57111
$918$	12.8044			0.422608
$919$			4.54181i			0.149820i	0.997190	+	0.0749102i	$0.0238670\pi$
$919$			4.54181i			0.149820i	−0.997190	+	0.0749102i	$0.976133\pi$
$920$		0			0
$921$		−	1.18025i		−	0.0388907i
$922$	12.7770	+	12.7770i	0.420787	+	0.420787i
$923$	−22.8092	+	22.8092i	−0.750773	+	0.750773i
$924$			8.39394i			0.276140i
$925$		0			0
$926$	6.84002	−	6.84002i	0.224777	−	0.224777i
$927$	−8.04041	+	8.04041i	−0.264082	+	0.264082i
$928$	−5.37945	+	0.248111i	−0.176589	+	0.00814463i
$929$			53.0665i			1.74106i	0.492120	+	0.870528i	$0.336222\pi$
$929$			53.0665i			1.74106i	−0.492120	+	0.870528i	$0.663778\pi$
$930$		0			0
$931$	−0.190342	−	0.190342i	−0.00623820	−	0.00623820i
$932$	−10.2570	+	10.2570i	−0.335978	+	0.335978i
$933$	−0.0833142	−	0.0833142i	−0.00272758	−	0.00272758i
$934$	33.8234			1.10673
$935$		0			0
$936$	−5.04006	+	5.04006i	−0.164739	+	0.164739i
$937$	−21.9690	+	21.9690i	−0.717697	+	0.717697i	−0.968133	−	0.250436i	$-0.919426\pi$
$937$	−21.9690	+	21.9690i	−0.717697	+	0.717697i	0.250436	+	0.968133i	$0.419426\pi$
$938$			1.03589i			0.0338230i
$939$	−9.18821	+	9.18821i	−0.299846	+	0.299846i
$940$		0			0
$941$			55.7801i			1.81838i	0.416383	+	0.909189i	$0.363298\pi$
$941$			55.7801i			1.81838i	−0.416383	+	0.909189i	$0.636702\pi$
$942$		−	10.1317i		−	0.330108i
$943$			27.8862i			0.908100i
$944$			10.5354i			0.342900i
$945$		0			0
$946$	25.6480	−	25.6480i	0.833888	−	0.833888i
$947$			31.1858i			1.01340i	0.862122	+	0.506701i	$0.169135\pi$
$947$			31.1858i			1.01340i	−0.862122	+	0.506701i	$0.830865\pi$
$948$	0.356715	−	0.356715i	0.0115856	−	0.0115856i
$949$	−4.73716	+	4.73716i	−0.153775	+	0.153775i
$950$		0			0
$951$	9.27486			0.300758
$952$	−8.49371	−	8.49371i	−0.275283	−	0.275283i
$953$	17.2077	−	17.2077i	0.557412	−	0.557412i	−0.371158	−	0.928570i	$-0.621039\pi$
$953$	17.2077	−	17.2077i	0.557412	−	0.557412i	0.928570	+	0.371158i	$0.121039\pi$
$954$	15.0353	+	15.0353i	0.486786	+	0.486786i
$955$		0			0
$956$			22.6323i			0.731982i
$957$	10.7913	−	11.8349i	0.348833	−	0.382566i
$958$	13.2884	−	13.2884i	0.429328	−	0.429328i
$959$	34.4302	−	34.4302i	1.11181	−	1.11181i
$960$		0			0
$961$		−	30.5008i		−	0.983896i
$962$	12.5369	−	12.5369i	0.404205	−	0.404205i
$963$	19.4542	+	19.4542i	0.626903	+	0.626903i
$964$		−	8.27343i		−	0.266469i
$965$		0			0
$966$		−	8.07296i		−	0.259743i
$967$	−29.6674			−0.954039			−0.477019	−	0.878893i	$-0.658283\pi$
$967$	−29.6674			−0.954039			−0.477019	+	0.878893i	$0.658283\pi$
$968$	21.0158			0.675474
$969$	−0.441005	−	0.441005i	−0.0141671	−	0.0141671i
$970$		0			0
$971$	−5.56780	−	5.56780i	−0.178679	−	0.178679i	0.612101	−	0.790780i	$-0.290325\pi$
$971$	−5.56780	−	5.56780i	−0.178679	−	0.178679i	−0.790780	+	0.612101i	$0.790325\pi$
$972$	12.4893			0.400596
$973$	31.0247	−	31.0247i	0.994607	−	0.994607i
$974$	−20.5484	+	20.5484i	−0.658415	+	0.658415i
$975$		0			0
$976$	7.92394	+	7.92394i	0.253639	+	0.253639i
$977$	30.8380	+	30.8380i	0.986595	+	0.986595i	0.999911	−	0.0133160i	$-0.00423875\pi$
$977$	30.8380	+	30.8380i	0.986595	+	0.986595i	−0.0133160	+	0.999911i	$0.504239\pi$
$978$	9.75980			0.312084
$979$	−100.668			−3.21736
$980$		0			0
$981$	−5.63583			−0.179938
$982$	9.25965	+	9.25965i	0.295487	+	0.295487i
$983$			36.4826i			1.16361i	0.813327	+	0.581807i	$0.197654\pi$
$983$			36.4826i			1.16361i	−0.813327	+	0.581807i	$0.802346\pi$
$984$	−1.90459	−	1.90459i	−0.0607160	−	0.0607160i
$985$		0			0
$986$	1.05597	+	22.8951i	0.0336288	+	0.729128i
$987$	−10.1692	−	10.1692i	−0.323688	−	0.323688i
$988$	0.729569			0.0232107
$989$	−24.6672	+	24.6672i	−0.784372	+	0.784372i
$990$		0			0
$991$		−	28.8229i		−	0.915589i	−0.889058	−	0.457794i	$-0.848640\pi$
$991$		−	28.8229i		−	0.915589i	0.889058	−	0.457794i	$-0.151360\pi$
$992$	−0.499611	+	0.499611i	−0.0158627	+	0.0158627i
$993$	−1.45881	+	1.45881i	−0.0462940	+	0.0462940i
$994$	−24.5996	−	24.5996i	−0.780253	−	0.780253i
$995$		0			0
$996$	−1.92687	+	1.92687i	−0.0610552	+	0.0610552i
$997$			27.1866i			0.861009i	0.902588	+	0.430504i	$0.141664\pi$
$997$			27.1866i			0.861009i	−0.902588	+	0.430504i	$0.858336\pi$
$998$			16.1174i			0.510187i
$999$	−20.3831			−0.644892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.j.i.157.5	yes	20
5.2	odd	4		1450.2.e.i.1143.6	yes	20
5.3	odd	4		1450.2.e.j.1143.5	yes	20
5.4	even	2		1450.2.j.j.157.6	yes	20
29.17	odd	4		1450.2.e.j.307.6	yes	20
145.17	even	4		1450.2.j.j.1293.6	yes	20
145.104	odd	4		1450.2.e.i.307.5	✓	20
145.133	even	4	inner	1450.2.j.i.1293.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.e.i.307.5	✓	20	145.104	odd	4
1450.2.e.i.1143.6	yes	20	5.2	odd	4
1450.2.e.j.307.6	yes	20	29.17	odd	4
1450.2.e.j.1143.5	yes	20	5.3	odd	4
1450.2.j.i.157.5	yes	20	1.1	even	1	trivial
1450.2.j.i.1293.5	yes	20	145.133	even	4	inner
1450.2.j.j.157.6	yes	20	5.4	even	2
1450.2.j.j.1293.6	yes	20	145.17	even	4

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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.525625 q^{3} -1.00000 q^{4} -0.525625i q^{6} +(1.99569 + 1.99569i) q^{7} -1.00000i q^{8} -2.72372 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.525625 q^{3} -1.00000 q^{4} -0.525625i q^{6} +(1.99569 + 1.99569i) q^{7} -1.00000i q^{8} -2.72372 q^{9} +(4.00099 + 4.00099i) q^{11} +0.525625 q^{12} +(1.85043 + 1.85043i) q^{13} +(-1.99569 + 1.99569i) q^{14} +1.00000 q^{16} -4.25603i q^{17} -2.72372i q^{18} +(-0.197135 + 0.197135i) q^{19} +(-1.04898 - 1.04898i) q^{21} +(-4.00099 + 4.00099i) q^{22} +(3.84799 - 3.84799i) q^{23} +0.525625i q^{24} +(-1.85043 + 1.85043i) q^{26} +3.00853 q^{27} +(-1.99569 - 1.99569i) q^{28} +(0.248111 + 5.37945i) q^{29} +(0.499611 + 0.499611i) q^{31} +1.00000i q^{32} +(-2.10302 - 2.10302i) q^{33} +4.25603 q^{34} +2.72372 q^{36} -6.77511 q^{37} +(-0.197135 - 0.197135i) q^{38} +(-0.972633 - 0.972633i) q^{39} +(-3.62348 + 3.62348i) q^{41} +(1.04898 - 1.04898i) q^{42} -6.41041 q^{43} +(-4.00099 - 4.00099i) q^{44} +(3.84799 + 3.84799i) q^{46} +9.69432 q^{47} -0.525625 q^{48} +0.965542i q^{49} +2.23707i q^{51} +(-1.85043 - 1.85043i) q^{52} +(-5.52014 + 5.52014i) q^{53} +3.00853i q^{54} +(1.99569 - 1.99569i) q^{56} +(0.103619 - 0.103619i) q^{57} +(-5.37945 + 0.248111i) q^{58} +10.5354i q^{59} +(7.92394 + 7.92394i) q^{61} +(-0.499611 + 0.499611i) q^{62} +(-5.43569 - 5.43569i) q^{63} -1.00000 q^{64} +(2.10302 - 2.10302i) q^{66} +(0.259532 - 0.259532i) q^{67} +4.25603i q^{68} +(-2.02260 + 2.02260i) q^{69} +12.3264i q^{71} +2.72372i q^{72} +2.56003i q^{73} -6.77511i q^{74} +(0.197135 - 0.197135i) q^{76} +15.9695i q^{77} +(0.972633 - 0.972633i) q^{78} +(0.678650 - 0.678650i) q^{79} +6.58980 q^{81} +(-3.62348 - 3.62348i) q^{82} +(-3.66587 + 3.66587i) q^{83} +(1.04898 + 1.04898i) q^{84} -6.41041i q^{86} +(-0.130413 - 2.82757i) q^{87} +(4.00099 - 4.00099i) q^{88} +(-12.5804 + 12.5804i) q^{89} +7.38577i q^{91} +(-3.84799 + 3.84799i) q^{92} +(-0.262608 - 0.262608i) q^{93} +9.69432i q^{94} -0.525625i q^{96} +11.3437 q^{97} -0.965542 q^{98} +(-10.8976 - 10.8976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{3} - 20 q^{4} + 8 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 8 * q^3 - 20 * q^4 + 8 * q^7 + 12 * q^9	\( 20 q - 8 q^{3} - 20 q^{4} + 8 q^{7} + 12 q^{9} - 8 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{14} + 20 q^{16} + 4 q^{19} + 4 q^{21} + 8 q^{22} - 12 q^{23} + 4 q^{26} - 32 q^{27} - 8 q^{28} - 8 q^{29} + 28 q^{31} + 16 q^{34} - 12 q^{36} + 20 q^{37} + 4 q^{38} + 24 q^{39} + 24 q^{41} - 4 q^{42} - 8 q^{43} + 8 q^{44} - 12 q^{46} + 28 q^{47} - 8 q^{48} + 4 q^{52} + 8 q^{56} - 8 q^{57} - 8 q^{58} + 24 q^{61} - 28 q^{62} + 20 q^{63} - 20 q^{64} + 12 q^{67} + 28 q^{69} - 4 q^{76} - 24 q^{78} - 32 q^{79} - 12 q^{81} + 24 q^{82} + 20 q^{83} - 4 q^{84} + 36 q^{87} - 8 q^{88} - 4 q^{89} + 12 q^{92} + 12 q^{93} - 48 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) \) 20 * q - 8 * q^3 - 20 * q^4 + 8 * q^7 + 12 * q^9 - 8 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^14 + 20 * q^16 + 4 * q^19 + 4 * q^21 + 8 * q^22 - 12 * q^23 + 4 * q^26 - 32 * q^27 - 8 * q^28 - 8 * q^29 + 28 * q^31 + 16 * q^34 - 12 * q^36 + 20 * q^37 + 4 * q^38 + 24 * q^39 + 24 * q^41 - 4 * q^42 - 8 * q^43 + 8 * q^44 - 12 * q^46 + 28 * q^47 - 8 * q^48 + 4 * q^52 + 8 * q^56 - 8 * q^57 - 8 * q^58 + 24 * q^61 - 28 * q^62 + 20 * q^63 - 20 * q^64 + 12 * q^67 + 28 * q^69 - 4 * q^76 - 24 * q^78 - 32 * q^79 - 12 * q^81 + 24 * q^82 + 20 * q^83 - 4 * q^84 + 36 * q^87 - 8 * q^88 - 4 * q^89 + 12 * q^92 + 12 * q^93 - 48 * q^97 - 20 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more