LMFDB - Embedded newform 289.2.c.b.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(38,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("289.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.c (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1871773696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 31x^{4} + 81 $ x^8 + 31*x^4 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.1
Root			$-1.62831 - 1.62831i$ of defining polynomial
Character	$\chi$	$=$	289.251
Dual form			289.2.c.b.38.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30278i q^{2} +(-1.62831 - 1.62831i) q^{3} +0.302776 q^{4} +(-0.921201 - 0.921201i) q^{5} +(-2.12132 + 2.12132i) q^{6} +(2.33542 - 2.33542i) q^{7} -3.00000i q^{8} +2.30278i q^{9} +O(q^{10})$	\(q-1.30278i q^{2} +(-1.62831 - 1.62831i) q^{3} +0.302776 q^{4} +(-0.921201 - 0.921201i) q^{5} +(-2.12132 + 2.12132i) q^{6} +(2.33542 - 2.33542i) q^{7} -3.00000i q^{8} +2.30278i q^{9} +(-1.20012 + 1.20012i) q^{10} +(-2.12132 + 2.12132i) q^{11} +(-0.493012 - 0.493012i) q^{12} -0.302776 q^{13} +(-3.04252 - 3.04252i) q^{14} +3.00000i q^{15} -3.30278 q^{16} +3.00000 q^{18} +4.90833i q^{19} +(-0.278917 - 0.278917i) q^{20} -7.60555 q^{21} +(2.76360 + 2.76360i) q^{22} +(0.921201 - 0.921201i) q^{23} +(-4.88492 + 4.88492i) q^{24} -3.30278i q^{25} +0.394449i q^{26} +(-1.13530 + 1.13530i) q^{27} +(0.707107 - 0.707107i) q^{28} +(-0.642284 - 0.642284i) q^{29} +3.90833 q^{30} +(2.54951 + 2.54951i) q^{31} -1.69722i q^{32} +6.90833 q^{33} -4.30278 q^{35} +0.697224i q^{36} +(4.67083 + 4.67083i) q^{37} +6.39445 q^{38} +(0.493012 + 0.493012i) q^{39} +(-2.76360 + 2.76360i) q^{40} +(4.24264 - 4.24264i) q^{41} +9.90833i q^{42} -9.60555i q^{43} +(-0.642284 + 0.642284i) q^{44} +(2.12132 - 2.12132i) q^{45} +(-1.20012 - 1.20012i) q^{46} -3.00000 q^{47} +(5.37794 + 5.37794i) q^{48} -3.90833i q^{49} -4.30278 q^{50} -0.0916731 q^{52} -12.9083i q^{53} +(1.47904 + 1.47904i) q^{54} +3.90833 q^{55} +(-7.00625 - 7.00625i) q^{56} +(7.99227 - 7.99227i) q^{57} +(-0.836752 + 0.836752i) q^{58} +6.00000i q^{59} +0.908327i q^{60} +(9.06274 - 9.06274i) q^{61} +(3.32144 - 3.32144i) q^{62} +(5.37794 + 5.37794i) q^{63} -8.81665 q^{64} +(0.278917 + 0.278917i) q^{65} -9.00000i q^{66} +5.39445 q^{67} -3.00000 q^{69} +5.60555i q^{70} +(-7.92745 - 7.92745i) q^{71} +6.90833 q^{72} +(5.37794 + 5.37794i) q^{73} +(6.08504 - 6.08504i) q^{74} +(-5.37794 + 5.37794i) q^{75} +1.48612i q^{76} +9.90833i q^{77} +(0.642284 - 0.642284i) q^{78} +(2.27059 - 2.27059i) q^{79} +(3.04252 + 3.04252i) q^{80} +10.6056 q^{81} +(-5.52721 - 5.52721i) q^{82} +15.5139i q^{83} -2.30278 q^{84} -12.5139 q^{86} +2.09167i q^{87} +(6.36396 + 6.36396i) q^{88} +11.2111 q^{89} +(-2.76360 - 2.76360i) q^{90} +(-0.707107 + 0.707107i) q^{91} +(0.278917 - 0.278917i) q^{92} -8.30278i q^{93} +3.90833i q^{94} +(4.52156 - 4.52156i) q^{95} +(-2.76360 + 2.76360i) q^{96} +(-0.0648227 - 0.0648227i) q^{97} -5.09167 q^{98} +(-4.88492 - 4.88492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4}+O(q^{10}) $ 8 * q - 12 * q^4	$ 8 q - 12 q^{4} + 12 q^{13} - 12 q^{16} + 24 q^{18} - 32 q^{21} - 12 q^{30} + 12 q^{33} - 20 q^{35} + 80 q^{38} - 24 q^{47} - 20 q^{50} - 44 q^{52} - 12 q^{55} + 16 q^{64} + 72 q^{67} - 24 q^{69} + 12 q^{72} + 56 q^{81} - 4 q^{84} - 28 q^{86} + 32 q^{89} - 84 q^{98}+O(q^{100}) $ 8 * q - 12 * q^4 + 12 * q^13 - 12 * q^16 + 24 * q^18 - 32 * q^21 - 12 * q^30 + 12 * q^33 - 20 * q^35 + 80 * q^38 - 24 * q^47 - 20 * q^50 - 44 * q^52 - 12 * q^55 + 16 * q^64 + 72 * q^67 - 24 * q^69 + 12 * q^72 + 56 * q^81 - 4 * q^84 - 28 * q^86 + 32 * q^89 - 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.30278i		−	0.921201i	−0.887607	−	0.460601i	$-0.847634\pi$
$2$		−	1.30278i		−	0.921201i	0.887607	−	0.460601i	$-0.152366\pi$
$3$	−1.62831	−	1.62831i	−0.940104	−	0.940104i	0.0582007	−	0.998305i	$-0.481464\pi$
$3$	−1.62831	−	1.62831i	−0.940104	−	0.940104i	−0.998305	+	0.0582007i	$0.981464\pi$
$4$	0.302776			0.151388
$5$	−0.921201	−	0.921201i	−0.411974	−	0.411974i	0.470452	−	0.882426i	$-0.344091\pi$
$5$	−0.921201	−	0.921201i	−0.411974	−	0.411974i	−0.882426	+	0.470452i	$0.844091\pi$
$6$	−2.12132	+	2.12132i	−0.866025	+	0.866025i
$7$	2.33542	−	2.33542i	0.882704	−	0.882704i	−0.111105	−	0.993809i	$-0.535439\pi$
$7$	2.33542	−	2.33542i	0.882704	−	0.882704i	0.993809	+	0.111105i	$0.0354389\pi$
$8$		−	3.00000i		−	1.06066i
$9$			2.30278i			0.767592i
$10$	−1.20012	+	1.20012i	−0.379511	+	0.379511i
$11$	−2.12132	+	2.12132i	−0.639602	+	0.639602i	−0.950457	−	0.310855i	$-0.899385\pi$
$11$	−2.12132	+	2.12132i	−0.639602	+	0.639602i	0.310855	+	0.950457i	$0.399385\pi$
$12$	−0.493012	−	0.493012i	−0.142320	−	0.142320i
$13$	−0.302776			−0.0839749			−0.0419874	−	0.999118i	$-0.513369\pi$
$13$	−0.302776			−0.0839749			−0.0419874	+	0.999118i	$0.513369\pi$
$14$	−3.04252	−	3.04252i	−0.813148	−	0.813148i
$15$			3.00000i			0.774597i
$16$	−3.30278			−0.825694
$17$		0			0
$17$		0			0
$18$	3.00000			0.707107
$19$			4.90833i			1.12605i	0.826441	+	0.563024i	$0.190362\pi$
$19$			4.90833i			1.12605i	−0.826441	+	0.563024i	$0.809638\pi$
$20$	−0.278917	−	0.278917i	−0.0623678	−	0.0623678i
$21$	−7.60555			−1.65967
$22$	2.76360	+	2.76360i	0.589202	+	0.589202i
$23$	0.921201	−	0.921201i	0.192084	−	0.192084i	−0.604512	−	0.796596i	$-0.706632\pi$
$23$	0.921201	−	0.921201i	0.192084	−	0.192084i	0.796596	+	0.604512i	$0.206632\pi$
$24$	−4.88492	+	4.88492i	−0.997131	+	0.997131i
$25$		−	3.30278i		−	0.660555i
$26$			0.394449i			0.0773578i
$27$	−1.13530	+	1.13530i	−0.218488	+	0.218488i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−0.642284	−	0.642284i	−0.119269	−	0.119269i	0.644953	−	0.764222i	$-0.276877\pi$
$29$	−0.642284	−	0.642284i	−0.119269	−	0.119269i	−0.764222	+	0.644953i	$0.776877\pi$
$30$	3.90833			0.713560
$31$	2.54951	+	2.54951i	0.457905	+	0.457905i	0.897967	−	0.440062i	$-0.145044\pi$
$31$	2.54951	+	2.54951i	0.457905	+	0.457905i	−0.440062	+	0.897967i	$0.645044\pi$
$32$		−	1.69722i		−	0.300030i
$33$	6.90833			1.20259
$34$		0			0
$35$	−4.30278			−0.727302
$36$			0.697224i			0.116204i
$37$	4.67083	+	4.67083i	0.767880	+	0.767880i	0.977733	−	0.209853i	$-0.0672986\pi$
$37$	4.67083	+	4.67083i	0.767880	+	0.767880i	−0.209853	+	0.977733i	$0.567299\pi$
$38$	6.39445			1.03732
$39$	0.493012	+	0.493012i	0.0789451	+	0.0789451i
$40$	−2.76360	+	2.76360i	−0.436964	+	0.436964i
$41$	4.24264	−	4.24264i	0.662589	−	0.662589i	−0.293400	−	0.955990i	$-0.594787\pi$
$41$	4.24264	−	4.24264i	0.662589	−	0.662589i	0.955990	+	0.293400i	$0.0947869\pi$
$42$			9.90833i			1.52889i
$43$		−	9.60555i		−	1.46483i	−0.680857	−	0.732416i	$-0.738392\pi$
$43$		−	9.60555i		−	1.46483i	0.680857	−	0.732416i	$-0.261608\pi$
$44$	−0.642284	+	0.642284i	−0.0968280	+	0.0968280i
$45$	2.12132	−	2.12132i	0.316228	−	0.316228i
$46$	−1.20012	−	1.20012i	−0.176948	−	0.176948i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	5.37794	+	5.37794i	0.776238	+	0.776238i
$49$		−	3.90833i		−	0.558332i
$50$	−4.30278			−0.608504
$51$		0			0
$52$	−0.0916731			−0.0127128
$53$		−	12.9083i		−	1.77310i	−0.462638	−	0.886548i	$-0.653097\pi$
$53$		−	12.9083i		−	1.77310i	0.462638	−	0.886548i	$-0.346903\pi$
$54$	1.47904	+	1.47904i	0.201271	+	0.201271i
$55$	3.90833			0.526999
$56$	−7.00625	−	7.00625i	−0.936249	−	0.936249i
$57$	7.99227	−	7.99227i	1.05860	−	1.05860i
$58$	−0.836752	+	0.836752i	−0.109871	+	0.109871i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$			0.908327i			0.117265i
$61$	9.06274	−	9.06274i	1.16037	−	1.16037i	0.175970	−	0.984396i	$-0.443694\pi$
$61$	9.06274	−	9.06274i	1.16037	−	1.16037i	0.984396	−	0.175970i	$-0.0563061\pi$
$62$	3.32144	−	3.32144i	0.421823	−	0.421823i
$63$	5.37794	+	5.37794i	0.677556	+	0.677556i
$64$	−8.81665			−1.10208
$65$	0.278917	+	0.278917i	0.0345954	+	0.0345954i
$66$		−	9.00000i		−	1.10782i
$67$	5.39445			0.659037			0.329518	−	0.944149i	$-0.393114\pi$
$67$	5.39445			0.659037			0.329518	+	0.944149i	$0.393114\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$			5.60555i			0.669992i
$71$	−7.92745	−	7.92745i	−0.940815	−	0.940815i	0.0575290	−	0.998344i	$-0.481678\pi$
$71$	−7.92745	−	7.92745i	−0.940815	−	0.940815i	−0.998344	+	0.0575290i	$0.981678\pi$
$72$	6.90833			0.814154
$73$	5.37794	+	5.37794i	0.629440	+	0.629440i	0.947927	−	0.318487i	$-0.103175\pi$
$73$	5.37794	+	5.37794i	0.629440	+	0.629440i	−0.318487	+	0.947927i	$0.603175\pi$
$74$	6.08504	−	6.08504i	0.707372	−	0.707372i
$75$	−5.37794	+	5.37794i	−0.620991	+	0.620991i
$76$			1.48612i			0.170470i
$77$			9.90833i			1.12916i
$78$	0.642284	−	0.642284i	0.0727244	−	0.0727244i
$79$	2.27059	−	2.27059i	0.255462	−	0.255462i	−0.567744	−	0.823205i	$-0.692184\pi$
$79$	2.27059	−	2.27059i	0.255462	−	0.255462i	0.823205	+	0.567744i	$0.192184\pi$
$80$	3.04252	+	3.04252i	0.340164	+	0.340164i
$81$	10.6056			1.17839
$82$	−5.52721	−	5.52721i	−0.610378	−	0.610378i
$83$			15.5139i			1.70287i	0.524461	+	0.851435i	$0.324267\pi$
$83$			15.5139i			1.70287i	−0.524461	+	0.851435i	$0.675733\pi$
$84$	−2.30278			−0.251253
$85$		0			0
$86$	−12.5139			−1.34941
$87$			2.09167i			0.224251i
$88$	6.36396	+	6.36396i	0.678401	+	0.678401i
$89$	11.2111			1.18837			0.594187	−	0.804327i	$-0.297474\pi$
$89$	11.2111			1.18837			0.594187	+	0.804327i	$0.297474\pi$
$90$	−2.76360	−	2.76360i	−0.291309	−	0.291309i
$91$	−0.707107	+	0.707107i	−0.0741249	+	0.0741249i
$92$	0.278917	−	0.278917i	0.0290791	−	0.0290791i
$93$		−	8.30278i		−	0.860958i
$94$			3.90833i			0.403113i
$95$	4.52156	−	4.52156i	0.463902	−	0.463902i
$96$	−2.76360	+	2.76360i	−0.282059	+	0.282059i
$97$	−0.0648227	−	0.0648227i	−0.00658174	−	0.00658174i	0.703808	−	0.710390i	$-0.251481\pi$
$97$	−0.0648227	−	0.0648227i	−0.00658174	−	0.00658174i	−0.710390	+	0.703808i	$0.751481\pi$
$98$	−5.09167			−0.514337
$99$	−4.88492	−	4.88492i	−0.490953	−	0.490953i
$100$		−	1.00000i		−	0.100000i
$101$	−11.6056			−1.15480			−0.577398	−	0.816463i	$-0.695932\pi$
$101$	−11.6056			−1.15480			−0.577398	+	0.816463i	$0.695932\pi$
$102$		0			0
$103$	2.00000			0.197066			0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000			0.197066			0.0985329	+	0.995134i	$0.468585\pi$
$104$			0.908327i			0.0890688i
$105$	7.00625	+	7.00625i	0.683740	+	0.683740i
$106$	−16.8167			−1.63338
$107$	1.56349	+	1.56349i	0.151148	+	0.151148i	0.778631	−	0.627483i	$-0.215915\pi$
$107$	1.56349	+	1.56349i	0.151148	+	0.151148i	−0.627483	+	0.778631i	$0.715915\pi$
$108$	−0.343740	+	0.343740i	−0.0330764	+	0.0330764i
$109$	−0.149272	+	0.149272i	−0.0142977	+	0.0142977i	−0.714219	−	0.699922i	$-0.753218\pi$
$109$	−0.149272	+	0.149272i	−0.0142977	+	0.0142977i	0.699922	+	0.714219i	$0.253218\pi$
$110$		−	5.09167i		−	0.485472i
$111$		−	15.2111i		−	1.44377i
$112$	−7.71335	+	7.71335i	−0.728843	+	0.728843i
$113$	−4.60601	+	4.60601i	−0.433297	+	0.433297i	−0.889748	−	0.456452i	$-0.849120\pi$
$113$	−4.60601	+	4.60601i	−0.433297	+	0.433297i	0.456452	+	0.889748i	$0.349120\pi$
$114$	−10.4121	−	10.4121i	−0.975186	−	0.975186i
$115$	−1.69722			−0.158267
$116$	−0.194468	−	0.194468i	−0.0180559	−	0.0180559i
$117$		−	0.697224i		−	0.0644584i
$118$	7.81665			0.719581
$119$		0			0
$120$	9.00000			0.821584
$121$			2.00000i			0.181818i
$122$	−11.8067	−	11.8067i	−1.06893	−	1.06893i
$123$	−13.8167			−1.24581
$124$	0.771929	+	0.771929i	0.0693213	+	0.0693213i
$125$	−7.64853	+	7.64853i	−0.684105	+	0.684105i
$126$	7.00625	−	7.00625i	0.624166	−	0.624166i
$127$			6.81665i			0.604880i	0.953168	+	0.302440i	$0.0978012\pi$
$127$			6.81665i			0.604880i	−0.953168	+	0.302440i	$0.902199\pi$
$128$			8.09167i			0.715210i
$129$	−15.6408	+	15.6408i	−1.37710	+	1.37710i
$130$	0.363367	−	0.363367i	0.0318694	−	0.0318694i
$131$	1.84240	+	1.84240i	0.160971	+	0.160971i	0.782997	−	0.622025i	$-0.213690\pi$
$131$	1.84240	+	1.84240i	0.160971	+	0.160971i	−0.622025	+	0.782997i	$0.713690\pi$
$132$	2.09167			0.182057
$133$	11.4630	+	11.4630i	0.993966	+	0.993966i
$134$		−	7.02776i		−	0.607106i
$135$	2.09167			0.180023
$136$		0			0
$137$	19.8167			1.69305			0.846525	−	0.532348i	$-0.178690\pi$
$137$	19.8167			1.69305			0.846525	+	0.532348i	$0.178690\pi$
$138$			3.90833i			0.332699i
$139$	−1.05085	−	1.05085i	−0.0891317	−	0.0891317i	0.661135	−	0.750267i	$-0.270075\pi$
$139$	−1.05085	−	1.05085i	−0.0891317	−	0.0891317i	−0.750267	+	0.661135i	$0.770075\pi$
$140$	−1.30278			−0.110105
$141$	4.88492	+	4.88492i	0.411385	+	0.411385i
$142$	−10.3277	+	10.3277i	−0.866680	+	0.866680i
$143$	0.642284	−	0.642284i	0.0537105	−	0.0537105i
$144$		−	7.60555i		−	0.633796i
$145$			1.18335i			0.0982716i
$146$	7.00625	−	7.00625i	0.579841	−	0.579841i
$147$	−6.36396	+	6.36396i	−0.524891	+	0.524891i
$148$	1.41421	+	1.41421i	0.116248	+	0.116248i
$149$	8.60555			0.704994			0.352497	−	0.935813i	$-0.385333\pi$
$149$	8.60555			0.704994			0.352497	+	0.935813i	$0.385333\pi$
$150$	7.00625	+	7.00625i	0.572058	+	0.572058i
$151$		−	5.00000i		−	0.406894i	−0.979086	−	0.203447i	$-0.934786\pi$
$151$		−	5.00000i		−	0.406894i	0.979086	−	0.203447i	$-0.0652145\pi$
$152$	14.7250			1.19435
$153$		0			0
$154$	12.9083			1.04018
$155$		−	4.69722i		−	0.377290i
$156$	0.149272	+	0.149272i	0.0119513	+	0.0119513i
$157$	−9.30278			−0.742442			−0.371221	−	0.928544i	$-0.621061\pi$
$157$	−9.30278			−0.742442			−0.371221	+	0.928544i	$0.621061\pi$
$158$	−2.95807	−	2.95807i	−0.235332	−	0.235332i
$159$	−21.0187	+	21.0187i	−1.66689	+	1.66689i
$160$	−1.56349	+	1.56349i	−0.123604	+	0.123604i
$161$		−	4.30278i		−	0.339106i
$162$		−	13.8167i		−	1.08554i
$163$	−7.34999	+	7.34999i	−0.575695	+	0.575695i	−0.933714	−	0.358019i	$-0.883452\pi$
$163$	−7.34999	+	7.34999i	−0.575695	+	0.575695i	0.358019	+	0.933714i	$0.383452\pi$
$164$	1.28457	−	1.28457i	0.100308	−	0.100308i
$165$	−6.36396	−	6.36396i	−0.495434	−	0.495434i
$166$	20.2111			1.56869
$167$	−15.7704	−	15.7704i	−1.22035	−	1.22035i	−0.967506	−	0.252847i	$-0.918633\pi$
$167$	−15.7704	−	15.7704i	−1.22035	−	1.22035i	−0.252847	−	0.967506i	$-0.581367\pi$
$168$			22.8167i			1.76034i
$169$	−12.9083			−0.992948
$170$		0			0
$171$	−11.3028			−0.864345
$172$		−	2.90833i		−	0.221758i
$173$	0.278917	+	0.278917i	0.0212057	+	0.0212057i	0.717630	−	0.696424i	$-0.245227\pi$
$173$	0.278917	+	0.278917i	0.0212057	+	0.0212057i	−0.696424	+	0.717630i	$0.745227\pi$
$174$	2.72498			0.206580
$175$	−7.71335	−	7.71335i	−0.583075	−	0.583075i
$176$	7.00625	−	7.00625i	0.528116	−	0.528116i
$177$	9.76985	−	9.76985i	0.734347	−	0.734347i
$178$		−	14.6056i		−	1.09473i
$179$			11.7250i			0.876366i	0.898886	+	0.438183i	$0.144378\pi$
$179$			11.7250i			0.876366i	−0.898886	+	0.438183i	$0.855622\pi$
$180$	0.642284	−	0.642284i	0.0478730	−	0.0478730i
$181$	5.50758	−	5.50758i	0.409375	−	0.409375i	−0.472145	−	0.881521i	$-0.656520\pi$
$181$	5.50758	−	5.50758i	0.409375	−	0.409375i	0.881521	+	0.472145i	$0.156520\pi$
$182$	0.921201	+	0.921201i	0.0682840	+	0.0682840i
$183$	−29.5139			−2.18173
$184$	−2.76360	−	2.76360i	−0.203736	−	0.203736i
$185$		−	8.60555i		−	0.632693i
$186$	−10.8167			−0.793116
$187$		0			0
$188$	−0.908327			−0.0662465
$189$			5.30278i			0.385720i
$190$	−5.89058	−	5.89058i	−0.427347	−	0.427347i
$191$	7.69722			0.556952			0.278476	−	0.960443i	$-0.410171\pi$
$191$	7.69722			0.556952			0.278476	+	0.960443i	$0.410171\pi$
$192$	14.3562	+	14.3562i	1.03607	+	1.03607i
$193$	16.0042	−	16.0042i	1.15201	−	1.15201i	0.165855	−	0.986150i	$-0.446962\pi$
$193$	16.0042	−	16.0042i	1.15201	−	1.15201i	0.986150	−	0.165855i	$-0.0530383\pi$
$194$	−0.0844494	+	0.0844494i	−0.00606311	+	0.00606311i
$195$		−	0.908327i		−	0.0650466i
$196$		−	1.18335i		−	0.0845247i
$197$	2.76360	−	2.76360i	0.196899	−	0.196899i	−0.601770	−	0.798669i	$-0.705538\pi$
$197$	2.76360	−	2.76360i	0.196899	−	0.196899i	0.798669	+	0.601770i	$0.205538\pi$
$198$	−6.36396	+	6.36396i	−0.452267	+	0.452267i
$199$	−2.54951	−	2.54951i	−0.180730	−	0.180730i	0.610944	−	0.791674i	$-0.290790\pi$
$199$	−2.54951	−	2.54951i	−0.180730	−	0.180730i	−0.791674	+	0.610944i	$0.790790\pi$
$200$	−9.90833			−0.700625
$201$	−8.78383	−	8.78383i	−0.619563	−	0.619563i
$202$			15.1194i			1.06380i
$203$	−3.00000			−0.210559
$204$		0			0
$205$	−7.81665			−0.545939
$206$		−	2.60555i		−	0.181537i
$207$	2.12132	+	2.12132i	0.147442	+	0.147442i
$208$	1.00000			0.0693375
$209$	−10.4121	−	10.4121i	−0.720222	−	0.720222i
$210$	9.12757	−	9.12757i	0.629862	−	0.629862i
$211$	−14.0773	+	14.0773i	−0.969122	+	0.969122i	−0.999537	−	0.0304152i	$-0.990317\pi$
$211$	−14.0773	+	14.0773i	−0.969122	+	0.969122i	0.0304152	+	0.999537i	$0.490317\pi$
$212$		−	3.90833i		−	0.268425i
$213$			25.8167i			1.76893i
$214$	2.03687	−	2.03687i	0.139238	−	0.139238i
$215$	−8.84865	+	8.84865i	−0.603473	+	0.603473i
$216$	3.40589	+	3.40589i	0.231741	+	0.231741i
$217$	11.9083			0.808390
$218$	0.194468	+	0.194468i	0.0131710	+	0.0131710i
$219$		−	17.5139i		−	1.18348i
$220$	1.18335			0.0797812
$221$		0			0
$222$	−19.8167			−1.33001
$223$			9.48612i			0.635238i	0.948218	+	0.317619i	$0.102883\pi$
$223$			9.48612i			0.635238i	−0.948218	+	0.317619i	$0.897117\pi$
$224$	−3.96372	−	3.96372i	−0.264837	−	0.264837i
$225$	7.60555			0.507037
$226$	6.00059	+	6.00059i	0.399154	+	0.399154i
$227$	3.40589	−	3.40589i	0.226057	−	0.226057i	−0.584986	−	0.811043i	$-0.698900\pi$
$227$	3.40589	−	3.40589i	0.226057	−	0.226057i	0.811043	+	0.584986i	$0.198900\pi$
$228$	2.41986	−	2.41986i	0.160259	−	0.160259i
$229$			18.4222i			1.21737i	0.793411	+	0.608687i	$0.208303\pi$
$229$			18.4222i			1.21737i	−0.793411	+	0.608687i	$0.791697\pi$
$230$			2.21110i			0.145796i
$231$	16.1338	−	16.1338i	1.06153	−	1.06153i
$232$	−1.92685	+	1.92685i	−0.126504	+	0.126504i
$233$	18.2551	+	18.2551i	1.19593	+	1.19593i	0.975373	+	0.220560i	$0.0707885\pi$
$233$	18.2551	+	18.2551i	1.19593	+	1.19593i	0.220560	+	0.975373i	$0.429212\pi$
$234$	−0.908327			−0.0593792
$235$	2.76360	+	2.76360i	0.180278	+	0.180278i
$236$			1.81665i			0.118254i
$237$	−7.39445			−0.480321
$238$		0			0
$239$	8.21110			0.531132			0.265566	−	0.964093i	$-0.414441\pi$
$239$	8.21110			0.531132			0.265566	+	0.964093i	$0.414441\pi$
$240$		−	9.90833i		−	0.639580i
$241$	−6.02022	−	6.02022i	−0.387797	−	0.387797i	0.486104	−	0.873901i	$-0.338418\pi$
$241$	−6.02022	−	6.02022i	−0.387797	−	0.387797i	−0.873901	+	0.486104i	$0.838418\pi$
$242$	2.60555			0.167491
$243$	−13.8632	−	13.8632i	−0.889326	−	0.889326i
$244$	2.74398	−	2.74398i	0.175665	−	0.175665i
$245$	−3.60036	+	3.60036i	−0.230018	+	0.230018i
$246$			18.0000i			1.14764i
$247$		−	1.48612i		−	0.0945597i
$248$	7.64853	−	7.64853i	0.485682	−	0.485682i
$249$	25.2614	−	25.2614i	1.60087	−	1.60087i
$250$	9.96432	+	9.96432i	0.630199	+	0.630199i
$251$	5.09167			0.321384			0.160692	−	0.987005i	$-0.448627\pi$
$251$	5.09167			0.321384			0.160692	+	0.987005i	$0.448627\pi$
$252$	1.62831	+	1.62831i	0.102574	+	0.102574i
$253$			3.90833i			0.245714i
$254$	8.88057			0.557217
$255$		0			0
$256$	−7.09167			−0.443230
$257$			5.72498i			0.357114i	0.983930	+	0.178557i	$0.0571430\pi$
$257$			5.72498i			0.357114i	−0.983930	+	0.178557i	$0.942857\pi$
$258$	20.3765	+	20.3765i	1.26858	+	1.26858i
$259$	21.8167			1.35562
$260$	0.0844494	+	0.0844494i	0.00523733	+	0.00523733i
$261$	1.47904	−	1.47904i	0.0915500	−	0.0915500i
$262$	2.40024	−	2.40024i	0.148287	−	0.148287i
$263$			2.48612i			0.153301i	0.997058	+	0.0766504i	$0.0244225\pi$
$263$			2.48612i			0.153301i	−0.997058	+	0.0766504i	$0.975577\pi$
$264$		−	20.7250i		−	1.27553i
$265$	−11.8912	+	11.8912i	−0.730469	+	0.730469i
$266$	14.9337	−	14.9337i	0.915643	−	0.915643i
$267$	−18.2551	−	18.2551i	−1.11720	−	1.11720i
$268$	1.63331			0.0997701
$269$	17.0550	+	17.0550i	1.03986	+	1.03986i	0.999172	+	0.0406906i	$0.0129558\pi$
$269$	17.0550	+	17.0550i	1.03986	+	1.03986i	0.0406906	+	0.999172i	$0.487044\pi$
$270$		−	2.72498i		−	0.165837i
$271$	27.5416			1.67304			0.836518	−	0.547940i	$-0.184588\pi$
$271$	27.5416			1.67304			0.836518	+	0.547940i	$0.184588\pi$
$272$		0			0
$273$	2.30278			0.139370
$274$		−	25.8167i		−	1.55964i
$275$	7.00625	+	7.00625i	0.422492	+	0.422492i
$276$	−0.908327			−0.0546749
$277$	−2.82843	−	2.82843i	−0.169944	−	0.169944i	0.617011	−	0.786955i	$-0.288343\pi$
$277$	−2.82843	−	2.82843i	−0.169944	−	0.169944i	−0.786955	+	0.617011i	$0.788343\pi$
$278$	−1.36902	+	1.36902i	−0.0821082	+	0.0821082i
$279$	−5.87095	+	5.87095i	−0.351485	+	0.351485i
$280$			12.9083i			0.771420i
$281$		−	25.5416i		−	1.52369i	−0.647762	−	0.761843i	$-0.724295\pi$
$281$		−	25.5416i		−	1.52369i	0.647762	−	0.761843i	$-0.275705\pi$
$282$	6.36396	−	6.36396i	0.378968	−	0.378968i
$283$	−14.1421	+	14.1421i	−0.840663	+	0.840663i	−0.988945	−	0.148282i	$-0.952626\pi$
$283$	−14.1421	+	14.1421i	−0.840663	+	0.840663i	0.148282	+	0.988945i	$0.452626\pi$
$284$	−2.40024	−	2.40024i	−0.142428	−	0.142428i
$285$	−14.7250			−0.872233
$286$	−0.836752	−	0.836752i	−0.0494782	−	0.0494782i
$287$		−	19.8167i		−	1.16974i
$288$	3.90833			0.230300
$289$		0			0
$290$	1.54163			0.0905279
$291$			0.211103i			0.0123751i
$292$	1.62831	+	1.62831i	0.0952895	+	0.0952895i
$293$	4.18335			0.244394			0.122197	−	0.992506i	$-0.461006\pi$
$293$	4.18335			0.244394			0.122197	+	0.992506i	$0.461006\pi$
$294$	8.29081	+	8.29081i	0.483530	+	0.483530i
$295$	5.52721	−	5.52721i	0.321807	−	0.321807i
$296$	14.0125	−	14.0125i	0.814459	−	0.814459i
$297$		−	4.81665i		−	0.279491i
$298$		−	11.2111i		−	0.649442i
$299$	−0.278917	+	0.278917i	−0.0161302	+	0.0161302i
$300$	−1.62831	+	1.62831i	−0.0940104	+	0.0940104i
$301$	−22.4329	−	22.4329i	−1.29301	−	1.29301i
$302$	−6.51388			−0.374832
$303$	18.8974	+	18.8974i	1.08563	+	1.08563i
$304$		−	16.2111i		−	0.929770i
$305$	−16.6972			−0.956080
$306$		0			0
$307$	−13.1194			−0.748765			−0.374383	−	0.927274i	$-0.622145\pi$
$307$	−13.1194			−0.748765			−0.374383	+	0.927274i	$0.622145\pi$
$308$			3.00000i			0.170941i
$309$	−3.25662	−	3.25662i	−0.185262	−	0.185262i
$310$	−6.11943			−0.347560
$311$	23.6979	+	23.6979i	1.34378	+	1.34378i	0.892258	+	0.451526i	$0.149120\pi$
$311$	23.6979	+	23.6979i	1.34378	+	1.34378i	0.451526	+	0.892258i	$0.350880\pi$
$312$	1.47904	−	1.47904i	0.0837339	−	0.0837339i
$313$	−8.35564	+	8.35564i	−0.472288	+	0.472288i	−0.902654	−	0.430366i	$-0.858385\pi$
$313$	−8.35564	+	8.35564i	−0.472288	+	0.472288i	0.430366	+	0.902654i	$0.358385\pi$
$314$			12.1194i			0.683939i
$315$		−	9.90833i		−	0.558271i
$316$	0.687480	−	0.687480i	0.0386738	−	0.0386738i
$317$	19.2608	−	19.2608i	1.08179	−	1.08179i	0.0854509	−	0.996342i	$-0.472767\pi$
$317$	19.2608	−	19.2608i	1.08179	−	1.08179i	0.996342	−	0.0854509i	$-0.0272331\pi$
$318$	27.3827	+	27.3827i	1.53555	+	1.53555i
$319$	2.72498			0.152570
$320$	8.12191	+	8.12191i	0.454029	+	0.454029i
$321$		−	5.09167i		−	0.284189i
$322$	−5.60555			−0.312385
$323$		0			0
$324$	3.21110			0.178395
$325$			1.00000i			0.0554700i
$326$	9.57538	+	9.57538i	0.530331	+	0.530331i
$327$	0.486122			0.0268826
$328$	−12.7279	−	12.7279i	−0.702782	−	0.702782i
$329$	−7.00625	+	7.00625i	−0.386267	+	0.386267i
$330$	−8.29081	+	8.29081i	−0.456394	+	0.456394i
$331$			3.30278i			0.181537i	0.995872	+	0.0907685i	$0.0289323\pi$
$331$			3.30278i			0.181537i	−0.995872	+	0.0907685i	$0.971068\pi$
$332$			4.69722i			0.257794i
$333$	−10.7559	+	10.7559i	−0.589418	+	0.589418i
$334$	−20.5454	+	20.5454i	−1.12419	+	1.12419i
$335$	−4.96937	−	4.96937i	−0.271506	−	0.271506i
$336$	25.1194			1.37038
$337$	−3.17217	−	3.17217i	−0.172799	−	0.172799i	0.615409	−	0.788208i	$-0.288991\pi$
$337$	−3.17217	−	3.17217i	−0.172799	−	0.172799i	−0.788208	+	0.615409i	$0.788991\pi$
$338$			16.8167i			0.914705i
$339$	15.0000			0.814688
$340$		0			0
$341$	−10.8167			−0.585755
$342$			14.7250i			0.796236i
$343$	7.22034	+	7.22034i	0.389862	+	0.389862i
$344$	−28.8167			−1.55369
$345$	2.76360	+	2.76360i	0.148787	+	0.148787i
$346$	0.363367	−	0.363367i	0.0195347	−	0.0195347i
$347$	−9.68540	+	9.68540i	−0.519940	+	0.519940i	−0.917553	−	0.397613i	$-0.869838\pi$
$347$	−9.68540	+	9.68540i	−0.519940	+	0.519940i	0.397613	+	0.917553i	$0.369838\pi$
$348$			0.633308i			0.0339489i
$349$			13.6056i			0.728288i	0.931343	+	0.364144i	$0.118638\pi$
$349$			13.6056i			0.728288i	−0.931343	+	0.364144i	$0.881362\pi$
$350$	−10.0488	+	10.0488i	−0.537129	+	0.537129i
$351$	0.343740	−	0.343740i	0.0183475	−	0.0183475i
$352$	3.60036	+	3.60036i	0.191900	+	0.191900i
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$	−12.7279	−	12.7279i	−0.676481	−	0.676481i
$355$			14.6056i			0.775182i
$356$	3.39445			0.179905
$357$		0			0
$358$	15.2750			0.807310
$359$			21.9083i			1.15628i	0.815939	+	0.578139i	$0.196221\pi$
$359$			21.9083i			1.15628i	−0.815939	+	0.578139i	$0.803779\pi$
$360$	−6.36396	−	6.36396i	−0.335410	−	0.335410i
$361$	−5.09167			−0.267983
$362$	−7.17514	−	7.17514i	−0.377117	−	0.377117i
$363$	3.25662	−	3.25662i	0.170928	−	0.170928i
$364$	−0.214095	+	0.214095i	−0.0112216	+	0.0112216i
$365$		−	9.90833i		−	0.518626i
$366$			38.4500i			2.00981i
$367$	12.2997	−	12.2997i	0.642041	−	0.642041i	−0.309016	−	0.951057i	$-0.600000\pi$
$367$	12.2997	−	12.2997i	0.642041	−	0.642041i	0.951057	+	0.309016i	$0.0999997\pi$
$368$	−3.04252	+	3.04252i	−0.158602	+	0.158602i
$369$	9.76985	+	9.76985i	0.508598	+	0.508598i
$370$	−11.2111			−0.582837
$371$	−30.1463	−	30.1463i	−1.56512	−	1.56512i
$372$		−	2.51388i		−	0.130339i
$373$	−6.21110			−0.321599			−0.160799	−	0.986987i	$-0.551407\pi$
$373$	−6.21110			−0.321599			−0.160799	+	0.986987i	$0.551407\pi$
$374$		0			0
$375$	24.9083			1.28626
$376$			9.00000i			0.464140i
$377$	0.194468	+	0.194468i	0.0100156	+	0.0100156i
$378$	6.90833			0.355326
$379$	−11.0348	−	11.0348i	−0.566819	−	0.566819i	0.364417	−	0.931236i	$-0.381268\pi$
$379$	−11.0348	−	11.0348i	−0.566819	−	0.566819i	−0.931236	+	0.364417i	$0.881268\pi$
$380$	1.36902	−	1.36902i	0.0702291	−	0.0702291i
$381$	11.0996	−	11.0996i	0.568650	−	0.568650i
$382$		−	10.0278i		−	0.513065i
$383$		−	6.90833i		−	0.352999i	−0.984301	−	0.176500i	$-0.943523\pi$
$383$		−	6.90833i		−	0.352999i	0.984301	−	0.176500i	$-0.0564774\pi$
$384$	13.1757	−	13.1757i	0.672372	−	0.672372i
$385$	9.12757	−	9.12757i	0.465184	−	0.465184i
$386$	−20.8498	−	20.8498i	−1.06123	−	1.06123i
$387$	22.1194			1.12439
$388$	−0.0196267	−	0.0196267i	−0.000996396	−	0.000996396i
$389$			30.6333i			1.55317i	0.630012	+	0.776585i	$0.283050\pi$
$389$			30.6333i			1.55317i	−0.630012	+	0.776585i	$0.716950\pi$
$390$	−1.18335			−0.0599211
$391$		0			0
$392$	−11.7250			−0.592201
$393$		−	6.00000i		−	0.302660i
$394$	−3.60036	−	3.60036i	−0.181383	−	0.181383i
$395$	−4.18335			−0.210487
$396$	−1.47904	−	1.47904i	−0.0743244	−	0.0743244i
$397$	−5.37794	+	5.37794i	−0.269911	+	0.269911i	−0.829064	−	0.559153i	$-0.811126\pi$
$397$	−5.37794	+	5.37794i	−0.269911	+	0.269911i	0.559153	+	0.829064i	$0.311126\pi$
$398$	−3.32144	+	3.32144i	−0.166489	+	0.166489i
$399$		−	37.3305i		−	1.86886i
$400$			10.9083i			0.545416i
$401$	−13.6491	+	13.6491i	−0.681605	+	0.681605i	−0.960362	−	0.278757i	$-0.910078\pi$
$401$	−13.6491	+	13.6491i	−0.681605	+	0.681605i	0.278757	+	0.960362i	$0.410078\pi$
$402$	−11.4434	+	11.4434i	−0.570743	+	0.570743i
$403$	−0.771929	−	0.771929i	−0.0384525	−	0.0384525i
$404$	−3.51388			−0.174822
$405$	−9.76985	−	9.76985i	−0.485468	−	0.485468i
$406$			3.90833i			0.193967i
$407$	−19.8167			−0.982275
$408$		0			0
$409$	−32.8167			−1.62268			−0.811340	−	0.584575i	$-0.801261\pi$
$409$	−32.8167			−1.62268			−0.811340	+	0.584575i	$0.801261\pi$
$410$			10.1833i			0.502920i
$411$	−32.2676	−	32.2676i	−1.59164	−	1.59164i
$412$	0.605551			0.0298334
$413$	14.0125	+	14.0125i	0.689510	+	0.689510i
$414$	2.76360	−	2.76360i	0.135824	−	0.135824i
$415$	14.2914	−	14.2914i	0.701538	−	0.701538i
$416$			0.513878i			0.0251950i
$417$			3.42221i			0.167586i
$418$	−13.5647	+	13.5647i	−0.663470	+	0.663470i
$419$	−18.5340	+	18.5340i	−0.905448	+	0.905448i	−0.995901	−	0.0904532i	$-0.971168\pi$
$419$	−18.5340	+	18.5340i	−0.905448	+	0.905448i	0.0904532	+	0.995901i	$0.471168\pi$
$420$	2.12132	+	2.12132i	0.103510	+	0.103510i
$421$	−18.9361			−0.922888			−0.461444	−	0.887169i	$-0.652669\pi$
$421$	−18.9361			−0.922888			−0.461444	+	0.887169i	$0.652669\pi$
$422$	18.3396	+	18.3396i	0.892757	+	0.892757i
$423$		−	6.90833i		−	0.335894i
$424$	−38.7250			−1.88065
$425$		0			0
$426$	33.6333			1.62954
$427$		−	42.3305i		−	2.04852i
$428$	0.473385	+	0.473385i	0.0228819	+	0.0228819i
$429$	−2.09167			−0.100987
$430$	11.5278	+	11.5278i	0.555920	+	0.555920i
$431$	−15.4915	+	15.4915i	−0.746201	+	0.746201i	−0.973763	−	0.227563i	$-0.926924\pi$
$431$	−15.4915	+	15.4915i	−0.746201	+	0.746201i	0.227563	+	0.973763i	$0.426924\pi$
$432$	3.74963	−	3.74963i	0.180404	−	0.180404i
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$		−	15.5139i		−	0.744690i
$435$	1.92685	−	1.92685i	0.0923855	−	0.0923855i
$436$	−0.0451959	+	0.0451959i	−0.00216449	+	0.00216449i
$437$	4.52156	+	4.52156i	0.216295	+	0.216295i
$438$	−22.8167			−1.09022
$439$	−10.6262	−	10.6262i	−0.507162	−	0.507162i	0.406492	−	0.913654i	$-0.366752\pi$
$439$	−10.6262	−	10.6262i	−0.507162	−	0.507162i	−0.913654	+	0.406492i	$0.866752\pi$
$440$		−	11.7250i		−	0.558967i
$441$	9.00000			0.428571
$442$		0			0
$443$	15.2389			0.724020			0.362010	−	0.932174i	$-0.382091\pi$
$443$	15.2389			0.724020			0.362010	+	0.932174i	$0.382091\pi$
$444$		−	4.60555i		−	0.218570i
$445$	−10.3277	−	10.3277i	−0.489579	−	0.489579i
$446$	12.3583			0.585182
$447$	−14.0125	−	14.0125i	−0.662768	−	0.662768i
$448$	−20.5905	+	20.5905i	−0.972812	+	0.972812i
$449$	6.72733	−	6.72733i	0.317482	−	0.317482i	−0.530317	−	0.847799i	$-0.677927\pi$
$449$	6.72733	−	6.72733i	0.317482	−	0.317482i	0.847799	+	0.530317i	$0.177927\pi$
$450$		−	9.90833i		−	0.467083i
$451$			18.0000i			0.847587i
$452$	−1.39459	+	1.39459i	−0.0655958	+	0.0655958i
$453$	−8.14154	+	8.14154i	−0.382523	+	0.382523i
$454$	−4.43711	−	4.43711i	−0.208244	−	0.208244i
$455$	1.30278			0.0610751
$456$	−23.9768	−	23.9768i	−1.12282	−	1.12282i
$457$		−	8.51388i		−	0.398262i	−0.979973	−	0.199131i	$-0.936188\pi$
$457$		−	8.51388i		−	0.398262i	0.979973	−	0.199131i	$-0.0638120\pi$
$458$	24.0000			1.12145
$459$		0			0
$460$	−0.513878			−0.0239597
$461$		−	16.4222i		−	0.764858i	−0.923985	−	0.382429i	$-0.875088\pi$
$461$		−	16.4222i		−	0.764858i	0.923985	−	0.382429i	$-0.124912\pi$
$462$	−21.0187	−	21.0187i	−0.977880	−	0.977880i
$463$	5.81665			0.270323			0.135161	−	0.990824i	$-0.456845\pi$
$463$	5.81665			0.270323			0.135161	+	0.990824i	$0.456845\pi$
$464$	2.12132	+	2.12132i	0.0984798	+	0.0984798i
$465$	−7.64853	+	7.64853i	−0.354692	+	0.354692i
$466$	23.7823	−	23.7823i	1.10170	−	1.10170i
$467$			14.0917i			0.652085i	0.945355	+	0.326042i	$0.105715\pi$
$467$			14.0917i			0.652085i	−0.945355	+	0.326042i	$0.894285\pi$
$468$		−	0.211103i		−	0.00975822i
$469$	12.5983	−	12.5983i	0.581734	−	0.581734i
$470$	3.60036	−	3.60036i	0.166072	−	0.166072i
$471$	15.1478	+	15.1478i	0.697973	+	0.697973i
$472$	18.0000			0.828517
$473$	20.3765	+	20.3765i	0.936910	+	0.936910i
$474$			9.63331i			0.442472i
$475$	16.2111			0.743816
$476$		0			0
$477$	29.7250			1.36101
$478$		−	10.6972i		−	0.489280i
$479$	21.6610	+	21.6610i	0.989717	+	0.989717i	0.999948	−	0.0102304i	$-0.00325650\pi$
$479$	21.6610	+	21.6610i	0.989717	+	0.989717i	−0.0102304	+	0.999948i	$0.503257\pi$
$480$	5.09167			0.232402
$481$	−1.41421	−	1.41421i	−0.0644826	−	0.0644826i
$482$	−7.84300	+	7.84300i	−0.357239	+	0.357239i
$483$	−7.00625	+	7.00625i	−0.318795	+	0.318795i
$484$			0.605551i			0.0275251i
$485$			0.119429i			0.00542301i
$486$	−18.0607	+	18.0607i	−0.819248	+	0.819248i
$487$	16.1986	−	16.1986i	0.734030	−	0.734030i	−0.237385	−	0.971416i	$-0.576290\pi$
$487$	16.1986	−	16.1986i	0.734030	−	0.734030i	0.971416	+	0.237385i	$0.0762904\pi$
$488$	−27.1882	−	27.1882i	−1.23075	−	1.23075i
$489$	23.9361			1.08243
$490$	4.69046	+	4.69046i	0.211893	+	0.211893i
$491$		−	3.11943i		−	0.140778i	−0.997520	−	0.0703889i	$-0.977576\pi$
$491$		−	3.11943i		−	0.140778i	0.997520	−	0.0703889i	$-0.0224240\pi$
$492$	−4.18335			−0.188600
$493$		0			0
$494$	−1.93608			−0.0871085
$495$			9.00000i			0.404520i
$496$	−8.42046	−	8.42046i	−0.378090	−	0.378090i
$497$	−37.0278			−1.66092
$498$	−32.9099	−	32.9099i	−1.47473	−	1.47473i
$499$	8.55010	−	8.55010i	0.382755	−	0.382755i	−0.489339	−	0.872094i	$-0.662762\pi$
$499$	8.55010	−	8.55010i	0.382755	−	0.382755i	0.872094	+	0.489339i	$0.162762\pi$
$500$	−2.31579	+	2.31579i	−0.103565	+	0.103565i
$501$			51.3583i			2.29452i
$502$		−	6.63331i		−	0.296059i
$503$	−4.69046	+	4.69046i	−0.209137	+	0.209137i	−0.803901	−	0.594764i	$-0.797246\pi$
$503$	−4.69046	+	4.69046i	−0.209137	+	0.209137i	0.594764	+	0.803901i	$0.297246\pi$
$504$	16.1338	−	16.1338i	0.718657	−	0.718657i
$505$	10.6911	+	10.6911i	0.475746	+	0.475746i
$506$	5.09167			0.226352
$507$	21.0187	+	21.0187i	0.933475	+	0.933475i
$508$			2.06392i			0.0915715i
$509$	11.6056			0.514407			0.257204	−	0.966357i	$-0.417199\pi$
$509$	11.6056			0.514407			0.257204	+	0.966357i	$0.417199\pi$
$510$		0			0
$511$	25.1194			1.11122
$512$			25.4222i			1.12351i
$513$	−5.57240	−	5.57240i	−0.246028	−	0.246028i
$514$	7.45837			0.328974
$515$	−1.84240	−	1.84240i	−0.0811860	−	0.0811860i
$516$	−4.73565	+	4.73565i	−0.208475	+	0.208475i
$517$	6.36396	−	6.36396i	0.279887	−	0.279887i
$518$		−	28.4222i		−	1.24880i
$519$		−	0.908327i		−	0.0398711i
$520$	0.836752	−	0.836752i	0.0366940	−	0.0366940i
$521$	−31.7098	+	31.7098i	−1.38923	+	1.38923i	−0.562293	+	0.826938i	$0.690081\pi$
$521$	−31.7098	+	31.7098i	−1.38923	+	1.38923i	−0.826938	+	0.562293i	$0.809919\pi$
$522$	−1.92685	−	1.92685i	−0.0843360	−	0.0843360i
$523$	−15.4222			−0.674366			−0.337183	−	0.941439i	$-0.609474\pi$
$523$	−15.4222			−0.674366			−0.337183	+	0.941439i	$0.609474\pi$
$524$	0.557835	+	0.557835i	0.0243691	+	0.0243691i
$525$			25.1194i			1.09630i
$526$	3.23886			0.141221
$527$		0			0
$528$	−22.8167			−0.992967
$529$			21.3028i			0.926208i
$530$	15.4915	+	15.4915i	0.672909	+	0.672909i
$531$	−13.8167			−0.599592
$532$	3.47071	+	3.47071i	0.150474	+	0.150474i
$533$	−1.28457	+	1.28457i	−0.0556408	+	0.0556408i
$534$	−23.7823	+	23.7823i	−1.02916	+	1.02916i
$535$		−	2.88057i		−	0.124538i
$536$		−	16.1833i		−	0.699014i
$537$	19.0919	−	19.0919i	0.823876	−	0.823876i
$538$	22.2189	−	22.2189i	0.957923	−	0.957923i
$539$	8.29081	+	8.29081i	0.357111	+	0.357111i
$540$	0.633308			0.0272532
$541$	−8.14154	−	8.14154i	−0.350032	−	0.350032i	0.510089	−	0.860121i	$-0.329612\pi$
$541$	−8.14154	−	8.14154i	−0.350032	−	0.350032i	−0.860121	+	0.510089i	$0.829612\pi$
$542$		−	35.8806i		−	1.54120i
$543$	−17.9361			−0.769711
$544$		0			0
$545$	0.275019			0.0117805
$546$		−	3.00000i		−	0.128388i
$547$	17.8466	+	17.8466i	0.763064	+	0.763064i	0.976875	−	0.213811i	$-0.0685876\pi$
$547$	17.8466	+	17.8466i	0.763064	+	0.763064i	−0.213811	+	0.976875i	$0.568588\pi$
$548$	6.00000			0.256307
$549$	20.8695	+	20.8695i	0.890687	+	0.890687i
$550$	9.12757	−	9.12757i	0.389201	−	0.389201i
$551$	3.15254	−	3.15254i	0.134303	−	0.134303i
$552$			9.00000i			0.383065i
$553$		−	10.6056i		−	0.450994i
$554$	−3.68481	+	3.68481i	−0.156552	+	0.156552i
$555$	−14.0125	+	14.0125i	−0.594797	+	0.594797i
$556$	−0.318171	−	0.318171i	−0.0134934	−	0.0134934i
$557$	15.6333			0.662405			0.331202	−	0.943560i	$-0.392546\pi$
$557$	15.6333			0.662405			0.331202	+	0.943560i	$0.392546\pi$
$558$	7.64853	+	7.64853i	0.323788	+	0.323788i
$559$			2.90833i			0.123009i
$560$	14.2111			0.600529
$561$		0			0
$562$	−33.2750			−1.40362
$563$		−	9.39445i		−	0.395929i	−0.980209	−	0.197964i	$-0.936567\pi$
$563$		−	9.39445i		−	0.395929i	0.980209	−	0.197964i	$-0.0634330\pi$
$564$	1.47904	+	1.47904i	0.0622787	+	0.0622787i
$565$	8.48612			0.357014
$566$	18.4240	+	18.4240i	0.774420	+	0.774420i
$567$	24.7684	−	24.7684i	1.04017	−	1.04017i
$568$	−23.7823	+	23.7823i	−0.997885	+	0.997885i
$569$			17.6056i			0.738063i	0.929417	+	0.369032i	$0.120311\pi$
$569$			17.6056i			0.738063i	−0.929417	+	0.369032i	$0.879689\pi$
$570$			19.1833i			0.803502i
$571$	−18.0410	+	18.0410i	−0.754994	+	0.754994i	−0.975407	−	0.220413i	$-0.929260\pi$
$571$	−18.0410	+	18.0410i	−0.754994	+	0.754994i	0.220413	+	0.975407i	$0.429260\pi$
$572$	0.194468	−	0.194468i	0.00813111	−	0.00813111i
$573$	−12.5335	−	12.5335i	−0.523593	−	0.523593i
$574$	−25.8167			−1.07757
$575$	−3.04252	−	3.04252i	−0.126882	−	0.126882i
$576$		−	20.3028i		−	0.845949i
$577$	−13.2389			−0.551141			−0.275570	−	0.961281i	$-0.588867\pi$
$577$	−13.2389			−0.551141			−0.275570	+	0.961281i	$0.588867\pi$
$578$		0			0
$579$	−52.1194			−2.16601
$580$			0.358288i			0.0148771i
$581$	36.2313	+	36.2313i	1.50313	+	1.50313i
$582$	0.275019			0.0113999
$583$	27.3827	+	27.3827i	1.13408	+	1.13408i
$584$	16.1338	−	16.1338i	0.667622	−	0.667622i
$585$	−0.642284	+	0.642284i	−0.0265552	+	0.0265552i
$586$		−	5.44996i		−	0.225136i
$587$		−	30.1194i		−	1.24316i	−0.783350	−	0.621581i	$-0.786491\pi$
$587$		−	30.1194i		−	1.24316i	0.783350	−	0.621581i	$-0.213509\pi$
$588$	−1.92685	+	1.92685i	−0.0794621	+	0.0794621i
$589$	−12.5138	+	12.5138i	−0.515623	+	0.515623i
$590$	−7.20071	−	7.20071i	−0.296449	−	0.296449i
$591$	−9.00000			−0.370211
$592$	−15.4267	−	15.4267i	−0.634034	−	0.634034i
$593$		−	6.63331i		−	0.272397i	−0.990682	−	0.136199i	$-0.956511\pi$
$593$		−	6.63331i		−	0.272397i	0.990682	−	0.136199i	$-0.0434885\pi$
$594$	−6.27502			−0.257467
$595$		0			0
$596$	2.60555			0.106728
$597$			8.30278i			0.339810i
$598$	0.363367	+	0.363367i	0.0148592	+	0.0148592i
$599$	−30.6333			−1.25164			−0.625822	−	0.779966i	$-0.715236\pi$
$599$	−30.6333			−1.25164			−0.625822	+	0.779966i	$0.715236\pi$
$600$	16.1338	+	16.1338i	0.658660	+	0.658660i
$601$	16.7565	−	16.7565i	0.683511	−	0.683511i	−0.277279	−	0.960789i	$-0.589433\pi$
$601$	16.7565	−	16.7565i	0.683511	−	0.683511i	0.960789	+	0.277279i	$0.0894326\pi$
$602$	−29.2251	+	29.2251i	−1.19113	+	1.19113i
$603$			12.4222i			0.505871i
$604$		−	1.51388i		−	0.0615988i
$605$	1.84240	−	1.84240i	0.0749043	−	0.0749043i
$606$	24.6191	−	24.6191i	1.00008	−	1.00008i
$607$	18.8326	+	18.8326i	0.764391	+	0.764391i	0.977113	−	0.212722i	$-0.0682327\pi$
$607$	18.8326	+	18.8326i	0.764391	+	0.764391i	−0.212722	+	0.977113i	$0.568233\pi$
$608$	8.33053			0.337848
$609$	4.88492	+	4.88492i	0.197947	+	0.197947i
$610$			21.7527i			0.880743i
$611$	0.908327			0.0367470
$612$		0			0
$613$	9.02776			0.364628			0.182314	−	0.983240i	$-0.441641\pi$
$613$	9.02776			0.364628			0.182314	+	0.983240i	$0.441641\pi$
$614$			17.0917i			0.689764i
$615$	12.7279	+	12.7279i	0.513239	+	0.513239i
$616$	29.7250			1.19765
$617$	−14.8492	−	14.8492i	−0.597808	−	0.597808i	0.341921	−	0.939729i	$-0.388923\pi$
$617$	−14.8492	−	14.8492i	−0.597808	−	0.597808i	−0.939729	+	0.341921i	$0.888923\pi$
$618$	−4.24264	+	4.24264i	−0.170664	+	0.170664i
$619$	26.2022	−	26.2022i	1.05316	−	1.05316i	0.0546499	−	0.998506i	$-0.482596\pi$
$619$	26.2022	−	26.2022i	1.05316	−	1.05316i	0.998506	−	0.0546499i	$-0.0174043\pi$
$620$		−	1.42221i		−	0.0571171i
$621$			2.09167i			0.0839359i
$622$	30.8730	−	30.8730i	1.23790	−	1.23790i
$623$	26.1826	−	26.1826i	1.04898	−	1.04898i
$624$	−1.62831	−	1.62831i	−0.0651845	−	0.0651845i
$625$	−2.42221			−0.0968882
$626$	10.8855	+	10.8855i	0.435073	+	0.435073i
$627$			33.9083i			1.35417i
$628$	−2.81665			−0.112397
$629$		0			0
$630$	−12.9083			−0.514280
$631$			35.1472i			1.39919i	0.714541	+	0.699594i	$0.246636\pi$
$631$			35.1472i			1.39919i	−0.714541	+	0.699594i	$0.753364\pi$
$632$	−6.81178	−	6.81178i	−0.270958	−	0.270958i
$633$	45.8444			1.82215
$634$	−25.0925	−	25.0925i	−0.996550	−	0.996550i
$635$	6.27951	−	6.27951i	0.249195	−	0.249195i
$636$	−6.36396	+	6.36396i	−0.252347	+	0.252347i
$637$			1.18335i			0.0468859i
$638$		−	3.55004i		−	0.140547i
$639$	18.2551	−	18.2551i	0.722162	−	0.722162i
$640$	7.45406	−	7.45406i	0.294648	−	0.294648i
$641$	−0.642284	−	0.642284i	−0.0253687	−	0.0253687i	0.694309	−	0.719677i	$-0.255710\pi$
$641$	−0.642284	−	0.642284i	−0.0253687	−	0.0253687i	−0.719677	+	0.694309i	$0.755710\pi$
$642$	−6.63331			−0.261796
$643$	5.78650	+	5.78650i	0.228197	+	0.228197i	0.811939	−	0.583742i	$-0.198412\pi$
$643$	5.78650	+	5.78650i	0.228197	+	0.228197i	−0.583742	+	0.811939i	$0.698412\pi$
$644$		−	1.30278i		−	0.0513366i
$645$	28.8167			1.13465
$646$		0			0
$647$	−29.0555			−1.14229			−0.571145	−	0.820849i	$-0.693501\pi$
$647$	−29.0555			−1.14229			−0.571145	+	0.820849i	$0.693501\pi$
$648$		−	31.8167i		−	1.24988i
$649$	−12.7279	−	12.7279i	−0.499615	−	0.499615i
$650$	1.30278			0.0510991
$651$	−19.3904	−	19.3904i	−0.759971	−	0.759971i
$652$	−2.22540	+	2.22540i	−0.0871533	+	0.0871533i
$653$	−20.3765	+	20.3765i	−0.797392	+	0.797392i	−0.982684	−	0.185291i	$-0.940677\pi$
$653$	−20.3765	+	20.3765i	−0.797392	+	0.797392i	0.185291	+	0.982684i	$0.440677\pi$
$654$		−	0.633308i		−	0.0247643i
$655$		−	3.39445i		−	0.132632i
$656$	−14.0125	+	14.0125i	−0.547096	+	0.547096i
$657$	−12.3842	+	12.3842i	−0.483153	+	0.483153i
$658$	9.12757	+	9.12757i	0.355830	+	0.355830i
$659$	36.3944			1.41773			0.708863	−	0.705346i	$-0.249208\pi$
$659$	36.3944			1.41773			0.708863	+	0.705346i	$0.249208\pi$
$660$	−1.92685	−	1.92685i	−0.0750026	−	0.0750026i
$661$		−	31.7250i		−	1.23396i	−0.786979	−	0.616979i	$-0.788356\pi$
$661$		−	31.7250i		−	1.23396i	0.786979	−	0.616979i	$-0.211644\pi$
$662$	4.30278			0.167232
$663$		0			0
$664$	46.5416			1.80617
$665$		−	21.1194i		−	0.818976i
$666$	14.0125	+	14.0125i	0.542973	+	0.542973i
$667$	−1.18335			−0.0458193
$668$	−4.77491	−	4.77491i	−0.184747	−	0.184747i
$669$	15.4463	−	15.4463i	0.597190	−	0.597190i
$670$	−6.47398	+	6.47398i	−0.250112	+	0.250112i
$671$			38.4500i			1.48434i
$672$			12.9083i			0.497950i
$673$	33.6818	−	33.6818i	1.29834	−	1.29834i	0.368851	−	0.929489i	$-0.379751\pi$
$673$	33.6818	−	33.6818i	1.29834	−	1.29834i	0.929489	−	0.368851i	$-0.120249\pi$
$674$	−4.13262	+	4.13262i	−0.159183	+	0.159183i
$675$	3.74963	+	3.74963i	0.144323	+	0.144323i
$676$	−3.90833			−0.150320
$677$	0.642284	+	0.642284i	0.0246850	+	0.0246850i	0.719342	−	0.694657i	$-0.244444\pi$
$677$	0.642284	+	0.642284i	0.0246850	+	0.0246850i	−0.694657	+	0.719342i	$0.744444\pi$
$678$		−	19.5416i		−	0.750492i
$679$	−0.302776			−0.0116195
$680$		0			0
$681$	−11.0917			−0.425034
$682$			14.0917i			0.539598i
$683$	−15.3815	−	15.3815i	−0.588557	−	0.588557i	0.348683	−	0.937241i	$-0.386629\pi$
$683$	−15.3815	−	15.3815i	−0.588557	−	0.588557i	−0.937241	+	0.348683i	$0.886629\pi$
$684$	−3.42221			−0.130851
$685$	−18.2551	−	18.2551i	−0.697493	−	0.697493i
$686$	9.40648	−	9.40648i	0.359141	−	0.359141i
$687$	29.9970	−	29.9970i	1.14446	−	1.14446i
$688$			31.7250i			1.20950i
$689$			3.90833i			0.148895i
$690$	3.60036	−	3.60036i	0.137063	−	0.137063i
$691$	18.6833	−	18.6833i	0.710747	−	0.710747i	−0.255944	−	0.966691i	$-0.582386\pi$
$691$	18.6833	−	18.6833i	0.710747	−	0.710747i	0.966691	+	0.255944i	$0.0823864\pi$
$692$	0.0844494	+	0.0844494i	0.00321028	+	0.00321028i
$693$	−22.8167			−0.866733
$694$	12.6179	+	12.6179i	0.478969	+	0.478969i
$695$			1.93608i			0.0734398i
$696$	6.27502			0.237854
$697$		0			0
$698$	17.7250			0.670900
$699$		−	59.4500i		−	2.24860i
$700$	−2.33542	−	2.33542i	−0.0882704	−	0.0882704i
$701$	6.63331			0.250537			0.125268	−	0.992123i	$-0.460021\pi$
$701$	6.63331			0.250537			0.125268	+	0.992123i	$0.460021\pi$
$702$	−0.447816	−	0.447816i	−0.0169017	−	0.0169017i
$703$	−22.9260	+	22.9260i	−0.864669	+	0.864669i
$704$	18.7029	−	18.7029i	0.704894	−	0.704894i
$705$		−	9.00000i		−	0.338960i
$706$			3.90833i			0.147092i
$707$	−27.1038	+	27.1038i	−1.01934	+	1.01934i
$708$	2.95807	−	2.95807i	0.111171	−	0.111171i
$709$	24.5543	+	24.5543i	0.922155	+	0.922155i	0.997182	−	0.0750266i	$-0.0239042\pi$
$709$	24.5543	+	24.5543i	0.922155	+	0.922155i	−0.0750266	+	0.997182i	$0.523904\pi$
$710$	19.0278			0.714099
$711$	5.22866	+	5.22866i	0.196090	+	0.196090i
$712$		−	33.6333i		−	1.26046i
$713$	4.69722			0.175912
$714$		0			0
$715$	−1.18335			−0.0442546
$716$			3.55004i			0.132671i
$717$	−13.3702	−	13.3702i	−0.499319	−	0.499319i
$718$	28.5416			1.06516
$719$	29.4196	+	29.4196i	1.09716	+	1.09716i	0.994741	+	0.102424i	$0.0326598\pi$
$719$	29.4196	+	29.4196i	1.09716	+	1.09716i	0.102424	+	0.994741i	$0.467340\pi$
$720$	−7.00625	+	7.00625i	−0.261107	+	0.261107i
$721$	4.67083	−	4.67083i	0.173951	−	0.173951i
$722$			6.63331i			0.246866i
$723$			19.6056i			0.729138i
$724$	1.66756	−	1.66756i	0.0619744	−	0.0619744i
$725$	−2.12132	+	2.12132i	−0.0787839	+	0.0787839i
$726$	−4.24264	−	4.24264i	−0.157459	−	0.157459i
$727$	−43.2111			−1.60261			−0.801306	−	0.598255i	$-0.795861\pi$
$727$	−43.2111			−1.60261			−0.801306	+	0.598255i	$0.795861\pi$
$728$	2.12132	+	2.12132i	0.0786214	+	0.0786214i
$729$			13.3305i			0.493723i
$730$	−12.9083			−0.477759
$731$		0			0
$732$	−8.93608			−0.330287
$733$		−	18.3028i		−	0.676028i	−0.941141	−	0.338014i	$-0.890245\pi$
$733$		−	18.3028i		−	0.676028i	0.941141	−	0.338014i	$-0.109755\pi$
$734$	−16.0238	−	16.0238i	−0.591449	−	0.591449i
$735$	11.7250			0.432482
$736$	−1.56349	−	1.56349i	−0.0576308	−	0.0576308i
$737$	−11.4434	+	11.4434i	−0.421521	+	0.421521i
$738$	12.7279	−	12.7279i	0.468521	−	0.468521i
$739$		−	23.4222i		−	0.861600i	−0.902447	−	0.430800i	$-0.858231\pi$
$739$		−	23.4222i		−	0.861600i	0.902447	−	0.430800i	$-0.141769\pi$
$740$		−	2.60555i		−	0.0957820i
$741$	−2.41986	+	2.41986i	−0.0888959	+	0.0888959i
$742$	−39.2739	+	39.2739i	−1.44179	+	1.44179i
$743$	5.07939	+	5.07939i	0.186345	+	0.186345i	0.794114	−	0.607769i	$-0.207935\pi$
$743$	5.07939	+	5.07939i	0.186345	+	0.186345i	−0.607769	+	0.794114i	$0.707935\pi$
$744$	−24.9083			−0.913184
$745$	−7.92745	−	7.92745i	−0.290439	−	0.290439i
$746$			8.09167i			0.296257i
$747$	−35.7250			−1.30711
$748$		0			0
$749$	7.30278			0.266838
$750$		−	32.4500i		−	1.18491i
$751$	−29.8870	−	29.8870i	−1.09059	−	1.09059i	−0.995465	−	0.0951274i	$-0.969674\pi$
$751$	−29.8870	−	29.8870i	−1.09059	−	1.09059i	−0.0951274	−	0.995465i	$-0.530326\pi$
$752$	9.90833			0.361320
$753$	−8.29081	−	8.29081i	−0.302134	−	0.302134i
$754$	0.253348	−	0.253348i	0.00922640	−	0.00922640i
$755$	−4.60601	+	4.60601i	−0.167630	+	0.167630i
$756$			1.60555i			0.0583933i
$757$		−	25.7889i		−	0.937313i	−0.883380	−	0.468657i	$-0.844738\pi$
$757$		−	25.7889i		−	0.937313i	0.883380	−	0.468657i	$-0.155262\pi$
$758$	−14.3759	+	14.3759i	−0.522155	+	0.522155i
$759$	6.36396	−	6.36396i	0.230997	−	0.230997i
$760$	−13.5647	−	13.5647i	−0.492042	−	0.492042i
$761$	−26.2111			−0.950152			−0.475076	−	0.879945i	$-0.657579\pi$
$761$	−26.2111			−0.950152			−0.475076	+	0.879945i	$0.657579\pi$
$762$	−14.4603	−	14.4603i	−0.523842	−	0.523842i
$763$			0.697224i			0.0252412i
$764$	2.33053			0.0843157
$765$		0			0
$766$	−9.00000			−0.325183
$767$		−	1.81665i		−	0.0655956i
$768$	11.5474	+	11.5474i	0.416682	+	0.416682i
$769$	−27.9361			−1.00740			−0.503700	−	0.863878i	$-0.668028\pi$
$769$	−27.9361			−1.00740			−0.503700	+	0.863878i	$0.668028\pi$
$770$	−11.8912	−	11.8912i	−0.428528	−	0.428528i
$771$	9.32203	−	9.32203i	0.335725	−	0.335725i
$772$	4.84567	−	4.84567i	0.174400	−	0.174400i
$773$		−	35.8444i		−	1.28923i	−0.764506	−	0.644617i	$-0.777017\pi$
$773$		−	35.8444i		−	1.28923i	0.764506	−	0.644617i	$-0.222983\pi$
$774$		−	28.8167i		−	1.03579i
$775$	8.42046	−	8.42046i	0.302472	−	0.302472i
$776$	−0.194468	+	0.194468i	−0.00698099	+	0.00698099i
$777$	−35.5242	−	35.5242i	−1.27442	−	1.27442i
$778$	39.9083			1.43078
$779$	20.8243	+	20.8243i	0.746107	+	0.746107i
$780$		−	0.275019i		−	0.00984727i
$781$	33.6333			1.20349
$782$		0			0
$783$	1.45837			0.0521177
$784$			12.9083i			0.461012i
$785$	8.56973	+	8.56973i	0.305867	+	0.305867i
$786$	−7.81665			−0.278811
$787$	2.14095	+	2.14095i	0.0763165	+	0.0763165i	0.744235	−	0.667918i	$-0.232814\pi$
$787$	2.14095	+	2.14095i	0.0763165	+	0.0763165i	−0.667918	+	0.744235i	$0.732814\pi$
$788$	0.836752	−	0.836752i	0.0298081	−	0.0298081i
$789$	4.04817	−	4.04817i	0.144119	−	0.144119i
$790$			5.44996i			0.193901i
$791$			21.5139i			0.764945i
$792$	−14.6548	+	14.6548i	−0.520735	+	0.520735i
$793$	−2.74398	+	2.74398i	−0.0974415	+	0.0974415i
$794$	7.00625	+	7.00625i	0.248642	+	0.248642i
$795$	38.7250			1.37343
$796$	−0.771929	−	0.771929i	−0.0273603	−	0.0273603i
$797$			16.5778i			0.587216i	0.955926	+	0.293608i	$0.0948560\pi$
$797$			16.5778i			0.587216i	−0.955926	+	0.293608i	$0.905144\pi$
$798$	−48.6333			−1.72160
$799$		0			0
$800$	−5.60555			−0.198186
$801$			25.8167i			0.912187i
$802$	17.7817	+	17.7817i	0.627895	+	0.627895i
$803$	−22.8167			−0.805182
$804$	−2.65953	−	2.65953i	−0.0937943	−	0.0937943i
$805$	−3.96372	+	3.96372i	−0.139703	+	0.139703i
$806$	−1.00565	+	1.00565i	−0.0354225	+	0.0354225i
$807$		−	55.5416i		−	1.95516i
$808$			34.8167i			1.22485i
$809$	13.4547	−	13.4547i	0.473040	−	0.473040i	−0.429857	−	0.902897i	$-0.641436\pi$
$809$	13.4547	−	13.4547i	0.473040	−	0.473040i	0.902897	+	0.429857i	$0.141436\pi$
$810$	−12.7279	+	12.7279i	−0.447214	+	0.447214i
$811$	−15.7252	−	15.7252i	−0.552188	−	0.552188i	0.374884	−	0.927072i	$-0.377683\pi$
$811$	−15.7252	−	15.7252i	−0.552188	−	0.552188i	−0.927072	+	0.374884i	$0.877683\pi$
$812$	−0.908327			−0.0318760
$813$	−44.8463	−	44.8463i	−1.57283	−	1.57283i
$814$			25.8167i			0.904873i
$815$	13.5416			0.474343
$816$		0			0
$817$	47.1472			1.64947
$818$			42.7527i			1.49481i
$819$	−1.62831	−	1.62831i	−0.0568977	−	0.0568977i
$820$	−2.36669			−0.0826485
$821$	−3.40589	−	3.40589i	−0.118866	−	0.118866i	0.645171	−	0.764038i	$-0.276786\pi$
$821$	−3.40589	−	3.40589i	−0.118866	−	0.118866i	−0.764038	+	0.645171i	$0.776786\pi$
$822$	−42.0375	+	42.0375i	−1.46623	+	1.46623i
$823$	−21.5314	+	21.5314i	−0.750537	+	0.750537i	−0.974579	−	0.224043i	$-0.928074\pi$
$823$	−21.5314	+	21.5314i	−0.750537	+	0.750537i	0.224043	+	0.974579i	$0.428074\pi$
$824$		−	6.00000i		−	0.209020i
$825$		−	22.8167i		−	0.794374i
$826$	18.2551	−	18.2551i	0.635177	−	0.635177i
$827$	35.6735	−	35.6735i	1.24049	−	1.24049i	0.280691	−	0.959798i	$-0.409436\pi$
$827$	35.6735	−	35.6735i	1.24049	−	1.24049i	0.959798	−	0.280691i	$-0.0905637\pi$
$828$	0.642284	+	0.642284i	0.0223209	+	0.0223209i
$829$	33.4500			1.16177			0.580883	−	0.813987i	$-0.302708\pi$
$829$	33.4500			1.16177			0.580883	+	0.813987i	$0.302708\pi$
$830$	−18.6185	−	18.6185i	−0.646257	−	0.646257i
$831$			9.21110i			0.319530i
$832$	2.66947			0.0925472
$833$		0			0
$834$	4.45837			0.154381
$835$			29.0555i			1.00551i
$836$	−3.15254	−	3.15254i	−0.109033	−	0.109033i
$837$	−5.78890			−0.200094
$838$	24.1457	+	24.1457i	0.834100	+	0.834100i
$839$	0.168899	−	0.168899i	0.00583103	−	0.00583103i	−0.704185	−	0.710016i	$-0.748688\pi$
$839$	0.168899	−	0.168899i	0.00583103	−	0.00583103i	0.710016	+	0.704185i	$0.248688\pi$
$840$	21.0187	−	21.0187i	0.725215	−	0.725215i
$841$		−	28.1749i		−	0.971550i
$842$			24.6695i			0.850166i
$843$	−41.5897	+	41.5897i	−1.43242	+	1.43242i
$844$	−4.26227	+	4.26227i	−0.146713	+	0.146713i
$845$	11.8912	+	11.8912i	0.409069	+	0.409069i
$846$	−9.00000			−0.309426
$847$	4.67083	+	4.67083i	0.160492	+	0.160492i
$848$			42.6333i			1.46403i
$849$	46.0555			1.58062
$850$		0			0
$851$	8.60555			0.294994
$852$			7.81665i			0.267794i
$853$	−3.53553	−	3.53553i	−0.121054	−	0.121054i	0.643984	−	0.765039i	$-0.277280\pi$
$853$	−3.53553	−	3.53553i	−0.121054	−	0.121054i	−0.765039	+	0.643984i	$0.777280\pi$
$854$	−55.1472			−1.88710
$855$	10.4121	+	10.4121i	0.356087	+	0.356087i
$856$	4.69046	−	4.69046i	0.160317	−	0.160317i
$857$	−36.7892	+	36.7892i	−1.25669	+	1.25669i	−0.304033	+	0.952662i	$0.598333\pi$
$857$	−36.7892	+	36.7892i	−1.25669	+	1.25669i	−0.952662	+	0.304033i	$0.901667\pi$
$858$			2.72498i			0.0930293i
$859$			41.3944i			1.41236i	0.708032	+	0.706180i	$0.249583\pi$
$859$			41.3944i			1.41236i	−0.708032	+	0.706180i	$0.750417\pi$
$860$	−2.67916	+	2.67916i	−0.0913584	+	0.0913584i
$861$	−32.2676	+	32.2676i	−1.09968	+	1.09968i
$862$	20.1820	+	20.1820i	0.687401	+	0.687401i
$863$	9.66947			0.329153			0.164576	−	0.986364i	$-0.447374\pi$
$863$	9.66947			0.329153			0.164576	+	0.986364i	$0.447374\pi$
$864$	1.92685	+	1.92685i	0.0655528	+	0.0655528i
$865$		−	0.513878i		−	0.0174724i
$866$	−36.4777			−1.23956
$867$		0			0
$868$	3.60555			0.122380
$869$			9.63331i			0.326788i
$870$	−2.51026	−	2.51026i	−0.0851057	−	0.0851057i
$871$	−1.63331			−0.0553425
$872$	0.447816	+	0.447816i	0.0151650	+	0.0151650i
$873$	0.149272	−	0.149272i	0.00505209	−	0.00505209i
$874$	5.89058	−	5.89058i	0.199252	−	0.199252i
$875$			35.7250i			1.20772i
$876$		−	5.30278i		−	0.179164i
$877$	−26.2474	+	26.2474i	−0.886312	+	0.886312i	−0.994167	−	0.107855i	$-0.965602\pi$
$877$	−26.2474	+	26.2474i	−0.886312	+	0.886312i	0.107855	+	0.994167i	$0.465602\pi$
$878$	−13.8436	+	13.8436i	−0.467199	+	0.467199i
$879$	−6.81178	−	6.81178i	−0.229756	−	0.229756i
$880$	−12.9083			−0.435140
$881$	−4.32709	−	4.32709i	−0.145783	−	0.145783i	0.630448	−	0.776231i	$-0.282871\pi$
$881$	−4.32709	−	4.32709i	−0.145783	−	0.145783i	−0.776231	+	0.630448i	$0.782871\pi$
$882$		−	11.7250i		−	0.394801i
$883$	−14.3028			−0.481327			−0.240663	−	0.970609i	$-0.577365\pi$
$883$	−14.3028			−0.481327			−0.240663	+	0.970609i	$0.577365\pi$
$884$		0			0
$885$	−18.0000			−0.605063
$886$		−	19.8528i		−	0.666968i
$887$	−8.67975	−	8.67975i	−0.291437	−	0.291437i	0.546210	−	0.837648i	$-0.316070\pi$
$887$	−8.67975	−	8.67975i	−0.291437	−	0.291437i	−0.837648	+	0.546210i	$0.816070\pi$
$888$	−45.6333			−1.53135
$889$	15.9197	+	15.9197i	0.533930	+	0.533930i
$890$	−13.4547	+	13.4547i	−0.451001	+	0.451001i
$891$	−22.4978	+	22.4978i	−0.753704	+	0.753704i
$892$			2.87217i			0.0961673i
$893$		−	14.7250i		−	0.492753i
$894$	−18.2551	+	18.2551i	−0.610543	+	0.610543i
$895$	10.8011	−	10.8011i	0.361040	−	0.361040i
$896$	18.8974	+	18.8974i	0.631318	+	0.631318i
$897$	0.908327			0.0303282
$898$	−8.76420	−	8.76420i	−0.292465	−	0.292465i
$899$		−	3.27502i		−	0.109228i
$900$	2.30278			0.0767592
$901$		0			0
$902$	23.4500			0.780798
$903$			73.0555i			2.43114i
$904$	13.8180	+	13.8180i	0.459581	+	0.459581i
$905$	−10.1472			−0.337304
$906$	10.6066	+	10.6066i	0.352381	+	0.352381i
$907$	−4.62563	+	4.62563i	−0.153592	+	0.153592i	−0.779720	−	0.626128i	$-0.784639\pi$
$907$	−4.62563	+	4.62563i	−0.153592	+	0.153592i	0.626128	+	0.779720i	$0.284639\pi$
$908$	1.03122	−	1.03122i	0.0342222	−	0.0342222i
$909$		−	26.7250i		−	0.886412i
$910$		−	1.69722i		−	0.0562624i
$911$	19.1763	−	19.1763i	0.635340	−	0.635340i	−0.314062	−	0.949402i	$-0.601690\pi$
$911$	19.1763	−	19.1763i	0.635340	−	0.635340i	0.949402	+	0.314062i	$0.101690\pi$
$912$	−26.3967	+	26.3967i	−0.874081	+	0.874081i
$913$	−32.9099	−	32.9099i	−1.08916	−	1.08916i
$914$	−11.0917			−0.366880
$915$	27.1882	+	27.1882i	0.898815	+	0.898815i
$916$			5.57779i			0.184296i
$917$	8.60555			0.284180
$918$		0			0
$919$	21.6972			0.715725			0.357863	−	0.933774i	$-0.383506\pi$
$919$	21.6972			0.715725			0.357863	+	0.933774i	$0.383506\pi$
$920$			5.09167i			0.167867i
$921$	21.3625	+	21.3625i	0.703917	+	0.703917i
$922$	−21.3944			−0.704589
$923$	2.40024	+	2.40024i	0.0790048	+	0.0790048i
$924$	4.88492	−	4.88492i	0.160702	−	0.160702i
$925$	15.4267	−	15.4267i	0.507227	−	0.507227i
$926$		−	7.57779i		−	0.249022i
$927$			4.60555i			0.151266i
$928$	−1.09010	+	1.09010i	−0.0357843	+	0.0357843i
$929$	−19.2864	+	19.2864i	−0.632765	+	0.632765i	−0.948761	−	0.315996i	$-0.897661\pi$
$929$	−19.2864	+	19.2864i	−0.632765	+	0.632765i	0.315996	+	0.948761i	$0.397661\pi$
$930$	9.96432	+	9.96432i	0.326743	+	0.326743i
$931$	19.1833			0.628709
$932$	5.52721	+	5.52721i	0.181050	+	0.181050i
$933$		−	77.1749i		−	2.52659i
$934$	18.3583			0.600702
$935$		0			0
$936$	−2.09167			−0.0683685
$937$		−	20.7527i		−	0.677962i	−0.940793	−	0.338981i	$-0.889918\pi$
$937$		−	20.7527i		−	0.677962i	0.940793	−	0.338981i	$-0.110082\pi$
$938$	−16.4127	−	16.4127i	−0.535895	−	0.535895i
$939$	27.2111			0.888001
$940$	0.836752	+	0.836752i	0.0272918	+	0.0272918i
$941$	−26.9349	+	26.9349i	−0.878052	+	0.878052i	−0.993333	−	0.115281i	$-0.963223\pi$
$941$	−26.9349	+	26.9349i	−0.878052	+	0.878052i	0.115281	+	0.993333i	$0.463223\pi$
$942$	19.7342	−	19.7342i	0.642974	−	0.642974i
$943$		−	7.81665i		−	0.254545i
$944$		−	19.8167i		−	0.644977i
$945$	4.88492	−	4.88492i	0.158907	−	0.158907i
$946$	26.5459	−	26.5459i	0.863083	−	0.863083i
$947$	−39.1894	−	39.1894i	−1.27348	−	1.27348i	−0.944247	−	0.329238i	$-0.893208\pi$
$947$	−39.1894	−	39.1894i	−1.27348	−	1.27348i	−0.329238	−	0.944247i	$-0.606792\pi$
$948$	−2.23886			−0.0727148
$949$	−1.62831	−	1.62831i	−0.0528571	−	0.0528571i
$950$		−	21.1194i		−	0.685205i
$951$	−62.7250			−2.03400
$952$		0			0
$953$	−18.5139			−0.599723			−0.299862	−	0.953983i	$-0.596941\pi$
$953$	−18.5139			−0.599723			−0.299862	+	0.953983i	$0.596941\pi$
$954$		−	38.7250i		−	1.25377i
$955$	−7.09069	−	7.09069i	−0.229449	−	0.229449i
$956$	2.48612			0.0804069
$957$	−4.43711	−	4.43711i	−0.143431	−	0.143431i
$958$	28.2194	−	28.2194i	0.911729	−	0.911729i
$959$	46.2801	−	46.2801i	1.49446	−	1.49446i
$960$		−	26.4500i		−	0.853669i
$961$		−	18.0000i		−	0.580645i
$962$	−1.84240	+	1.84240i	−0.0594015	+	0.0594015i
$963$	−3.60036	+	3.60036i	−0.116020	+	0.116020i
$964$	−1.82278	−	1.82278i	−0.0587077	−	0.0587077i
$965$	−29.4861			−0.949192
$966$	9.12757	+	9.12757i	0.293675	+	0.293675i
$967$			44.9361i			1.44505i	0.691346	+	0.722524i	$0.257018\pi$
$967$			44.9361i			1.44505i	−0.691346	+	0.722524i	$0.742982\pi$
$968$	6.00000			0.192847
$969$		0			0
$970$	0.155590			0.00499569
$971$		−	47.7250i		−	1.53157i	−0.643098	−	0.765784i	$-0.722351\pi$
$971$		−	47.7250i		−	1.53157i	0.643098	−	0.765784i	$-0.277649\pi$
$972$	−4.19744	−	4.19744i	−0.134633	−	0.134633i
$973$	−4.90833			−0.157354
$974$	−21.1032	−	21.1032i	−0.676190	−	0.676190i
$975$	1.62831	−	1.62831i	0.0521476	−	0.0521476i
$976$	−29.9322	+	29.9322i	−0.958107	+	0.958107i
$977$			16.5416i			0.529214i	0.964356	+	0.264607i	$0.0852422\pi$
$977$			16.5416i			0.529214i	−0.964356	+	0.264607i	$0.914758\pi$
$978$		−	31.1833i		−	0.997133i
$979$	−23.7823	+	23.7823i	−0.760087	+	0.760087i
$980$	−1.09010	+	1.09010i	−0.0348220	+	0.0348220i
$981$	−0.343740	−	0.343740i	−0.0109748	−	0.0109748i
$982$	−4.06392			−0.129685
$983$	−6.81178	−	6.81178i	−0.217262	−	0.217262i	0.590082	−	0.807344i	$-0.299096\pi$
$983$	−6.81178	−	6.81178i	−0.217262	−	0.217262i	−0.807344	+	0.590082i	$0.799096\pi$
$984$			41.4500i			1.32138i
$985$	−5.09167			−0.162234
$986$		0			0
$987$	22.8167			0.726262
$988$		−	0.449961i		−	0.0143152i
$989$	−8.84865	−	8.84865i	−0.281371	−	0.281371i
$990$	11.7250			0.372644
$991$	−26.6952	−	26.6952i	−0.848001	−	0.848001i	0.141882	−	0.989884i	$-0.454685\pi$
$991$	−26.6952	−	26.6952i	−0.848001	−	0.848001i	−0.989884	+	0.141882i	$0.954685\pi$
$992$	4.32709	−	4.32709i	0.137385	−	0.137385i
$993$	5.37794	−	5.37794i	0.170664	−	0.170664i
$994$			48.2389i			1.53004i
$995$			4.69722i			0.148912i
$996$	7.64853	−	7.64853i	0.242353	−	0.242353i
$997$	11.2293	−	11.2293i	0.355634	−	0.355634i	−0.506567	−	0.862201i	$-0.669086\pi$
$997$	11.2293	−	11.2293i	0.355634	−	0.355634i	0.862201	+	0.506567i	$0.169086\pi$
$998$	−11.1389	−	11.1389i	−0.352595	−	0.352595i
$999$	−10.6056			−0.335545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.b.251.1		8
17.2	even	8		289.2.a.b.1.2	✓	2
17.3	odd	16		289.2.d.e.134.1		16
17.4	even	4	inner	289.2.c.b.38.3		8
17.5	odd	16		289.2.d.e.155.4		16
17.6	odd	16		289.2.d.e.179.3		16
17.7	odd	16		289.2.d.e.110.1		16
17.8	even	8		289.2.b.c.288.2		4
17.9	even	8		289.2.b.c.288.1		4
17.10	odd	16		289.2.d.e.110.2		16
17.11	odd	16		289.2.d.e.179.4		16
17.12	odd	16		289.2.d.e.155.3		16
17.13	even	4	inner	289.2.c.b.38.4		8
17.14	odd	16		289.2.d.e.134.2		16
17.15	even	8		289.2.a.c.1.2	yes	2
17.16	even	2	inner	289.2.c.b.251.2		8
51.2	odd	8		2601.2.a.s.1.1		2
51.32	odd	8		2601.2.a.r.1.1		2
68.15	odd	8		4624.2.a.j.1.1		2
68.19	odd	8		4624.2.a.v.1.2		2
85.19	even	8		7225.2.a.n.1.1		2
85.49	even	8		7225.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.b.1.2	✓	2	17.2	even	8
289.2.a.c.1.2	yes	2	17.15	even	8
289.2.b.c.288.1		4	17.9	even	8
289.2.b.c.288.2		4	17.8	even	8
289.2.c.b.38.3		8	17.4	even	4	inner
289.2.c.b.38.4		8	17.13	even	4	inner
289.2.c.b.251.1		8	1.1	even	1	trivial
289.2.c.b.251.2		8	17.16	even	2	inner
289.2.d.e.110.1		16	17.7	odd	16
289.2.d.e.110.2		16	17.10	odd	16
289.2.d.e.134.1		16	17.3	odd	16
289.2.d.e.134.2		16	17.14	odd	16
289.2.d.e.155.3		16	17.12	odd	16
289.2.d.e.155.4		16	17.5	odd	16
289.2.d.e.179.3		16	17.6	odd	16
289.2.d.e.179.4		16	17.11	odd	16
2601.2.a.r.1.1		2	51.32	odd	8
2601.2.a.s.1.1		2	51.2	odd	8
4624.2.a.j.1.1		2	68.15	odd	8
4624.2.a.v.1.2		2	68.19	odd	8
7225.2.a.m.1.1		2	85.49	even	8
7225.2.a.n.1.1		2	85.19	even	8

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.c (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.30278i q^{2} +(-1.62831 - 1.62831i) q^{3} +0.302776 q^{4} +(-0.921201 - 0.921201i) q^{5} +(-2.12132 + 2.12132i) q^{6} +(2.33542 - 2.33542i) q^{7} -3.00000i q^{8} +2.30278i q^{9} +O(q^{10})\)	\(q-1.30278i q^{2} +(-1.62831 - 1.62831i) q^{3} +0.302776 q^{4} +(-0.921201 - 0.921201i) q^{5} +(-2.12132 + 2.12132i) q^{6} +(2.33542 - 2.33542i) q^{7} -3.00000i q^{8} +2.30278i q^{9} +(-1.20012 + 1.20012i) q^{10} +(-2.12132 + 2.12132i) q^{11} +(-0.493012 - 0.493012i) q^{12} -0.302776 q^{13} +(-3.04252 - 3.04252i) q^{14} +3.00000i q^{15} -3.30278 q^{16} +3.00000 q^{18} +4.90833i q^{19} +(-0.278917 - 0.278917i) q^{20} -7.60555 q^{21} +(2.76360 + 2.76360i) q^{22} +(0.921201 - 0.921201i) q^{23} +(-4.88492 + 4.88492i) q^{24} -3.30278i q^{25} +0.394449i q^{26} +(-1.13530 + 1.13530i) q^{27} +(0.707107 - 0.707107i) q^{28} +(-0.642284 - 0.642284i) q^{29} +3.90833 q^{30} +(2.54951 + 2.54951i) q^{31} -1.69722i q^{32} +6.90833 q^{33} -4.30278 q^{35} +0.697224i q^{36} +(4.67083 + 4.67083i) q^{37} +6.39445 q^{38} +(0.493012 + 0.493012i) q^{39} +(-2.76360 + 2.76360i) q^{40} +(4.24264 - 4.24264i) q^{41} +9.90833i q^{42} -9.60555i q^{43} +(-0.642284 + 0.642284i) q^{44} +(2.12132 - 2.12132i) q^{45} +(-1.20012 - 1.20012i) q^{46} -3.00000 q^{47} +(5.37794 + 5.37794i) q^{48} -3.90833i q^{49} -4.30278 q^{50} -0.0916731 q^{52} -12.9083i q^{53} +(1.47904 + 1.47904i) q^{54} +3.90833 q^{55} +(-7.00625 - 7.00625i) q^{56} +(7.99227 - 7.99227i) q^{57} +(-0.836752 + 0.836752i) q^{58} +6.00000i q^{59} +0.908327i q^{60} +(9.06274 - 9.06274i) q^{61} +(3.32144 - 3.32144i) q^{62} +(5.37794 + 5.37794i) q^{63} -8.81665 q^{64} +(0.278917 + 0.278917i) q^{65} -9.00000i q^{66} +5.39445 q^{67} -3.00000 q^{69} +5.60555i q^{70} +(-7.92745 - 7.92745i) q^{71} +6.90833 q^{72} +(5.37794 + 5.37794i) q^{73} +(6.08504 - 6.08504i) q^{74} +(-5.37794 + 5.37794i) q^{75} +1.48612i q^{76} +9.90833i q^{77} +(0.642284 - 0.642284i) q^{78} +(2.27059 - 2.27059i) q^{79} +(3.04252 + 3.04252i) q^{80} +10.6056 q^{81} +(-5.52721 - 5.52721i) q^{82} +15.5139i q^{83} -2.30278 q^{84} -12.5139 q^{86} +2.09167i q^{87} +(6.36396 + 6.36396i) q^{88} +11.2111 q^{89} +(-2.76360 - 2.76360i) q^{90} +(-0.707107 + 0.707107i) q^{91} +(0.278917 - 0.278917i) q^{92} -8.30278i q^{93} +3.90833i q^{94} +(4.52156 - 4.52156i) q^{95} +(-2.76360 + 2.76360i) q^{96} +(-0.0648227 - 0.0648227i) q^{97} -5.09167 q^{98} +(-4.88492 - 4.88492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4}+O(q^{10}) \) 8 * q - 12 * q^4	\( 8 q - 12 q^{4} + 12 q^{13} - 12 q^{16} + 24 q^{18} - 32 q^{21} - 12 q^{30} + 12 q^{33} - 20 q^{35} + 80 q^{38} - 24 q^{47} - 20 q^{50} - 44 q^{52} - 12 q^{55} + 16 q^{64} + 72 q^{67} - 24 q^{69} + 12 q^{72} + 56 q^{81} - 4 q^{84} - 28 q^{86} + 32 q^{89} - 84 q^{98}+O(q^{100}) \) 8 * q - 12 * q^4 + 12 * q^13 - 12 * q^16 + 24 * q^18 - 32 * q^21 - 12 * q^30 + 12 * q^33 - 20 * q^35 + 80 * q^38 - 24 * q^47 - 20 * q^50 - 44 * q^52 - 12 * q^55 + 16 * q^64 + 72 * q^67 - 24 * q^69 + 12 * q^72 + 56 * q^81 - 4 * q^84 - 28 * q^86 + 32 * q^89 - 84 * q^98

Introduction

L-functions

Modular forms

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