LMFDB - Embedded newform 289.2.c.d.251.3

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
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			251.3
Root			$1.32893 - 1.32893i$ of defining polynomial
Character	$\chi$	$=$	289.251
Dual form			289.2.c.d.38.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.347296i q^{2} +(-0.621819 - 0.621819i) q^{3} +1.87939 q^{4} +(-1.65979 - 1.65979i) q^{5} +(-0.215956 + 0.215956i) q^{6} +(-1.32893 + 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +O(q^{10})$	\(q-0.347296i q^{2} +(-0.621819 - 0.621819i) q^{3} +1.87939 q^{4} +(-1.65979 - 1.65979i) q^{5} +(-0.215956 + 0.215956i) q^{6} +(-1.32893 + 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +(-0.576439 + 0.576439i) q^{10} +(3.58091 - 3.58091i) q^{11} +(-1.16864 - 1.16864i) q^{12} -4.71688 q^{13} +(0.461531 + 0.461531i) q^{14} +2.06418i q^{15} +3.29086 q^{16} -0.773318 q^{18} -0.347296i q^{19} +(-3.11938 - 3.11938i) q^{20} +1.65270 q^{21} +(-1.24364 - 1.24364i) q^{22} +(1.25393 - 1.25393i) q^{23} +(-0.837775 + 0.837775i) q^{24} +0.509800i q^{25} +1.63816i q^{26} +(-3.25005 + 3.25005i) q^{27} +(-2.49756 + 2.49756i) q^{28} +(1.57450 + 1.57450i) q^{29} +0.716881 q^{30} +(-1.37431 - 1.37431i) q^{31} -3.83750i q^{32} -4.45336 q^{33} +4.41147 q^{35} -4.18479i q^{36} +(4.36302 + 4.36302i) q^{37} -0.120615 q^{38} +(2.93305 + 2.93305i) q^{39} +(-2.23623 + 2.23623i) q^{40} +(3.65592 - 3.65592i) q^{41} -0.573978i q^{42} -1.47565i q^{43} +(6.72992 - 6.72992i) q^{44} +(-3.69582 + 3.69582i) q^{45} +(-0.435484 - 0.435484i) q^{46} +8.53209 q^{47} +(-2.04632 - 2.04632i) q^{48} +3.46791i q^{49} +0.177052 q^{50} -8.86484 q^{52} +10.4534i q^{53} +(1.12873 + 1.12873i) q^{54} -11.8871 q^{55} +(1.79046 + 1.79046i) q^{56} +(-0.215956 + 0.215956i) q^{57} +(0.546819 - 0.546819i) q^{58} +5.00774i q^{59} +3.87939i q^{60} +(-0.130668 + 0.130668i) q^{61} +(-0.477292 + 0.477292i) q^{62} +(2.95910 + 2.95910i) q^{63} +5.24897 q^{64} +(7.82903 + 7.82903i) q^{65} +1.54664i q^{66} -2.44831 q^{67} -1.55943 q^{69} -1.53209i q^{70} +(7.01540 + 7.01540i) q^{71} -3.00000 q^{72} +(7.70865 + 7.70865i) q^{73} +(1.51526 - 1.51526i) q^{74} +(0.317004 - 0.317004i) q^{75} -0.652704i q^{76} +9.51754i q^{77} +(1.01864 - 1.01864i) q^{78} +(-3.13514 + 3.13514i) q^{79} +(-5.46213 - 5.46213i) q^{80} -2.63816 q^{81} +(-1.26969 - 1.26969i) q^{82} -13.5817i q^{83} +3.10607 q^{84} -0.512489 q^{86} -1.95811i q^{87} +(-4.82455 - 4.82455i) q^{88} +6.32770 q^{89} +(1.28355 + 1.28355i) q^{90} +(6.26839 - 6.26839i) q^{91} +(2.35661 - 2.35661i) q^{92} +1.70914i q^{93} -2.96316i q^{94} +(-0.576439 + 0.576439i) q^{95} +(-2.38623 + 2.38623i) q^{96} +(6.55934 + 6.55934i) q^{97} +1.20439 q^{98} +(-7.97356 - 7.97356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84} + 24 q^{86} + 60 q^{89} + 12 q^{98}+O(q^{100}) $ 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * 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 $

$2$		−	0.347296i		−	0.245576i	−0.992433	−	0.122788i	$-0.960817\pi$
$2$		−	0.347296i		−	0.245576i	0.992433	−	0.122788i	$-0.0391835\pi$
$3$	−0.621819	−	0.621819i	−0.359008	−	0.359008i	0.504440	−	0.863447i	$-0.331699\pi$
$3$	−0.621819	−	0.621819i	−0.359008	−	0.359008i	−0.863447	+	0.504440i	$0.831699\pi$
$4$	1.87939			0.939693
$5$	−1.65979	−	1.65979i	−0.742280	−	0.742280i	0.230736	−	0.973016i	$-0.425887\pi$
$5$	−1.65979	−	1.65979i	−0.742280	−	0.742280i	−0.973016	+	0.230736i	$0.925887\pi$
$6$	−0.215956	+	0.215956i	−0.0881635	+	0.0881635i
$7$	−1.32893	+	1.32893i	−0.502287	+	0.502287i	−0.912148	−	0.409861i	$-0.865577\pi$
$7$	−1.32893	+	1.32893i	−0.502287	+	0.502287i	0.409861	+	0.912148i	$0.365577\pi$
$8$		−	1.34730i		−	0.476341i
$9$		−	2.22668i		−	0.742227i
$10$	−0.576439	+	0.576439i	−0.182286	+	0.182286i
$11$	3.58091	−	3.58091i	1.07969	−	1.07969i	0.0831492	−	0.996537i	$-0.473502\pi$
$11$	3.58091	−	3.58091i	1.07969	−	1.07969i	0.996537	−	0.0831492i	$-0.0264978\pi$
$12$	−1.16864	−	1.16864i	−0.337357	−	0.337357i
$13$	−4.71688			−1.30823			−0.654114	−	0.756396i	$-0.726958\pi$
$13$	−4.71688			−1.30823			−0.654114	+	0.756396i	$0.726958\pi$
$14$	0.461531	+	0.461531i	0.123349	+	0.123349i
$15$			2.06418i			0.532968i
$16$	3.29086			0.822715
$17$		0			0
$17$		0			0
$18$	−0.773318			−0.182273
$19$		−	0.347296i		−	0.0796752i	−0.999206	−	0.0398376i	$-0.987316\pi$
$19$		−	0.347296i		−	0.0796752i	0.999206	−	0.0398376i	$-0.0126841\pi$
$20$	−3.11938	−	3.11938i	−0.697515	−	0.697515i
$21$	1.65270			0.360650
$22$	−1.24364	−	1.24364i	−0.265145	−	0.265145i
$23$	1.25393	−	1.25393i	0.261462	−	0.261462i	−0.564186	−	0.825648i	$-0.690810\pi$
$23$	1.25393	−	1.25393i	0.261462	−	0.261462i	0.825648	+	0.564186i	$0.190810\pi$
$24$	−0.837775	+	0.837775i	−0.171010	+	0.171010i
$25$			0.509800i			0.101960i
$26$			1.63816i			0.321269i
$27$	−3.25005	+	3.25005i	−0.625473	+	0.625473i
$28$	−2.49756	+	2.49756i	−0.471995	+	0.471995i
$29$	1.57450	+	1.57450i	0.292378	+	0.292378i	0.838019	−	0.545641i	$-0.183714\pi$
$29$	1.57450	+	1.57450i	0.292378	+	0.292378i	−0.545641	+	0.838019i	$0.683714\pi$
$30$	0.716881			0.130884
$31$	−1.37431	−	1.37431i	−0.246833	−	0.246833i	0.572837	−	0.819669i	$-0.305843\pi$
$31$	−1.37431	−	1.37431i	−0.246833	−	0.246833i	−0.819669	+	0.572837i	$0.805843\pi$
$32$		−	3.83750i		−	0.678380i
$33$	−4.45336			−0.775231
$34$		0			0
$35$	4.41147			0.745675
$36$		−	4.18479i		−	0.697465i
$37$	4.36302	+	4.36302i	0.717276	+	0.717276i	0.968047	−	0.250770i	$-0.0806839\pi$
$37$	4.36302	+	4.36302i	0.717276	+	0.717276i	−0.250770	+	0.968047i	$0.580684\pi$
$38$	−0.120615			−0.0195663
$39$	2.93305	+	2.93305i	0.469664	+	0.469664i
$40$	−2.23623	+	2.23623i	−0.353579	+	0.353579i
$41$	3.65592	−	3.65592i	0.570958	−	0.570958i	−0.361438	−	0.932396i	$-0.617714\pi$
$41$	3.65592	−	3.65592i	0.570958	−	0.570958i	0.932396	+	0.361438i	$0.117714\pi$
$42$		−	0.573978i		−	0.0885667i
$43$		−	1.47565i		−	0.225035i	−0.993650	−	0.112517i	$-0.964109\pi$
$43$		−	1.47565i		−	0.225035i	0.993650	−	0.112517i	$-0.0358914\pi$
$44$	6.72992	−	6.72992i	1.01457	−	1.01457i
$45$	−3.69582	+	3.69582i	−0.550941	+	0.550941i
$46$	−0.435484	−	0.435484i	−0.0642086	−	0.0642086i
$47$	8.53209			1.24453			0.622267	−	0.782805i	$-0.286212\pi$
$47$	8.53209			1.24453			0.622267	+	0.782805i	$0.286212\pi$
$48$	−2.04632	−	2.04632i	−0.295361	−	0.295361i
$49$			3.46791i			0.495416i
$50$	0.177052			0.0250389
$51$		0			0
$52$	−8.86484			−1.22933
$53$			10.4534i			1.43588i	0.696105	+	0.717940i	$0.254915\pi$
$53$			10.4534i			1.43588i	−0.696105	+	0.717940i	$0.745085\pi$
$54$	1.12873	+	1.12873i	0.153601	+	0.153601i
$55$	−11.8871			−1.60286
$56$	1.79046	+	1.79046i	0.239260	+	0.239260i
$57$	−0.215956	+	0.215956i	−0.0286040	+	0.0286040i
$58$	0.546819	−	0.546819i	0.0718008	−	0.0718008i
$59$			5.00774i			0.651952i	0.945378	+	0.325976i	$0.105693\pi$
$59$			5.00774i			0.651952i	−0.945378	+	0.325976i	$0.894307\pi$
$60$			3.87939i			0.500826i
$61$	−0.130668	+	0.130668i	−0.0167303	+	0.0167303i	−0.715422	−	0.698692i	$-0.753766\pi$
$61$	−0.130668	+	0.130668i	−0.0167303	+	0.0167303i	0.698692	+	0.715422i	$0.253766\pi$
$62$	−0.477292	+	0.477292i	−0.0606161	+	0.0606161i
$63$	2.95910	+	2.95910i	0.372811	+	0.372811i
$64$	5.24897			0.656121
$65$	7.82903	+	7.82903i	0.971071	+	0.971071i
$66$			1.54664i			0.190378i
$67$	−2.44831			−0.299109			−0.149554	−	0.988754i	$-0.547784\pi$
$67$	−2.44831			−0.299109			−0.149554	+	0.988754i	$0.547784\pi$
$68$		0			0
$69$	−1.55943			−0.187733
$70$		−	1.53209i		−	0.183120i
$71$	7.01540	+	7.01540i	0.832575	+	0.832575i	0.987868	−	0.155294i	$-0.0496323\pi$
$71$	7.01540	+	7.01540i	0.832575	+	0.832575i	−0.155294	+	0.987868i	$0.549632\pi$
$72$	−3.00000			−0.353553
$73$	7.70865	+	7.70865i	0.902229	+	0.902229i	0.995629	−	0.0933997i	$-0.0297735\pi$
$73$	7.70865	+	7.70865i	0.902229	+	0.902229i	−0.0933997	+	0.995629i	$0.529773\pi$
$74$	1.51526	−	1.51526i	0.176146	−	0.176146i
$75$	0.317004	−	0.317004i	0.0366044	−	0.0366044i
$76$		−	0.652704i		−	0.0748702i
$77$			9.51754i			1.08462i
$78$	1.01864	−	1.01864i	0.115338	−	0.115338i
$79$	−3.13514	+	3.13514i	−0.352731	+	0.352731i	−0.861125	−	0.508394i	$-0.830240\pi$
$79$	−3.13514	+	3.13514i	−0.352731	+	0.352731i	0.508394	+	0.861125i	$0.330240\pi$
$80$	−5.46213	−	5.46213i	−0.610685	−	0.610685i
$81$	−2.63816			−0.293128
$82$	−1.26969	−	1.26969i	−0.140213	−	0.140213i
$83$		−	13.5817i		−	1.49079i	−0.666625	−	0.745394i	$-0.732262\pi$
$83$		−	13.5817i		−	1.49079i	0.666625	−	0.745394i	$-0.267738\pi$
$84$	3.10607			0.338900
$85$		0			0
$86$	−0.512489			−0.0552631
$87$		−	1.95811i		−	0.209932i
$88$	−4.82455	−	4.82455i	−0.514299	−	0.514299i
$89$	6.32770			0.670734			0.335367	−	0.942087i	$-0.391140\pi$
$89$	6.32770			0.670734			0.335367	+	0.942087i	$0.391140\pi$
$90$	1.28355	+	1.28355i	0.135298	+	0.135298i
$91$	6.26839	−	6.26839i	0.657105	−	0.657105i
$92$	2.35661	−	2.35661i	0.245693	−	0.245693i
$93$			1.70914i			0.177230i
$94$		−	2.96316i		−	0.305627i
$95$	−0.576439	+	0.576439i	−0.0591414	+	0.0591414i
$96$	−2.38623	+	2.38623i	−0.243543	+	0.243543i
$97$	6.55934	+	6.55934i	0.666000	+	0.666000i	0.956788	−	0.290787i	$-0.0939172\pi$
$97$	6.55934	+	6.55934i	0.666000	+	0.666000i	−0.290787	+	0.956788i	$0.593917\pi$
$98$	1.20439			0.121662
$99$	−7.97356	−	7.97356i	−0.801373	−	0.801373i
$100$			0.958111i			0.0958111i
$101$	−7.04963			−0.701464			−0.350732	−	0.936476i	$-0.614067\pi$
$101$	−7.04963			−0.701464			−0.350732	+	0.936476i	$0.614067\pi$
$102$		0			0
$103$	5.29860			0.522087			0.261043	−	0.965327i	$-0.415933\pi$
$103$	5.29860			0.522087			0.261043	+	0.965327i	$0.415933\pi$
$104$			6.35504i			0.623163i
$105$	−2.74314	−	2.74314i	−0.267703	−	0.267703i
$106$	3.63041			0.352617
$107$	−11.0282	−	11.0282i	−1.06614	−	1.06614i	−0.997652	−	0.0684868i	$-0.978183\pi$
$107$	−11.0282	−	11.0282i	−1.06614	−	1.06614i	−0.0684868	−	0.997652i	$-0.521817\pi$
$108$	−6.10810	+	6.10810i	−0.587752	+	0.587752i
$109$	1.32345	−	1.32345i	0.126764	−	0.126764i	−0.640879	−	0.767642i	$-0.721430\pi$
$109$	1.32345	−	1.32345i	0.126764	−	0.126764i	0.767642	+	0.640879i	$0.221430\pi$
$110$			4.12836i			0.393623i
$111$		−	5.42602i		−	0.515015i
$112$	−4.37331	+	4.37331i	−0.413239	+	0.413239i
$113$	8.56576	−	8.56576i	0.805798	−	0.805798i	−0.178196	−	0.983995i	$-0.557026\pi$
$113$	8.56576	−	8.56576i	0.805798	−	0.805798i	0.983995	+	0.178196i	$0.0570262\pi$
$114$	0.0750006	+	0.0750006i	0.00702445	+	0.00702445i
$115$	−4.16250			−0.388155
$116$	2.95910	+	2.95910i	0.274745	+	0.274745i
$117$			10.5030i			0.971002i
$118$	1.73917			0.160104
$119$		0			0
$120$	2.78106			0.253875
$121$		−	14.6459i		−	1.33145i
$122$	0.0453805	+	0.0453805i	0.00410856	+	0.00410856i
$123$	−4.54664			−0.409956
$124$	−2.58285	−	2.58285i	−0.231947	−	0.231947i
$125$	−7.45279	+	7.45279i	−0.666597	+	0.666597i
$126$	1.02768	−	1.02768i	0.0915533	−	0.0915533i
$127$		−	11.5398i		−	1.02399i	−0.858987	−	0.511997i	$-0.828906\pi$
$127$		−	11.5398i		−	1.02399i	0.858987	−	0.511997i	$-0.171094\pi$
$128$		−	9.49794i		−	0.839507i
$129$	−0.917589	+	0.917589i	−0.0807892	+	0.0807892i
$130$	2.71899	−	2.71899i	0.238471	−	0.238471i
$131$	−13.6999	−	13.6999i	−1.19697	−	1.19697i	−0.975070	−	0.221900i	$-0.928774\pi$
$131$	−13.6999	−	13.6999i	−1.19697	−	1.19697i	−0.221900	−	0.975070i	$-0.571226\pi$
$132$	−8.36959			−0.728479
$133$	0.461531	+	0.461531i	0.0400198	+	0.0400198i
$134$			0.850289i			0.0734538i
$135$	10.7888			0.928552
$136$		0			0
$137$	−0.448311			−0.0383018			−0.0191509	−	0.999817i	$-0.506096\pi$
$137$	−0.448311			−0.0383018			−0.0191509	+	0.999817i	$0.506096\pi$
$138$			0.541584i			0.0461027i
$139$	−8.25904	−	8.25904i	−0.700523	−	0.700523i	0.264000	−	0.964523i	$-0.414958\pi$
$139$	−8.25904	−	8.25904i	−0.700523	−	0.700523i	−0.964523	+	0.264000i	$0.914958\pi$
$140$	8.29086			0.700706
$141$	−5.30542	−	5.30542i	−0.446797	−	0.446797i
$142$	2.43642	−	2.43642i	0.204460	−	0.204460i
$143$	−16.8907	+	16.8907i	−1.41248	+	1.41248i
$144$		−	7.32770i		−	0.610641i
$145$		−	5.22668i		−	0.434052i
$146$	2.67719	−	2.67719i	0.221565	−	0.221565i
$147$	2.15641	−	2.15641i	0.177858	−	0.177858i
$148$	8.19980	+	8.19980i	0.674019	+	0.674019i
$149$	−8.46791			−0.693718			−0.346859	−	0.937917i	$-0.612752\pi$
$149$	−8.46791			−0.693718			−0.346859	+	0.937917i	$0.612752\pi$
$150$	−0.110094	−	0.110094i	−0.00898915	−	0.00898915i
$151$			13.7665i			1.12030i	0.828390	+	0.560151i	$0.189257\pi$
$151$			13.7665i			1.12030i	−0.828390	+	0.560151i	$0.810743\pi$
$152$	−0.467911			−0.0379526
$153$		0			0
$154$	3.30541			0.266357
$155$			4.56212i			0.366438i
$156$	5.51233	+	5.51233i	0.441339	+	0.441339i
$157$	17.9786			1.43485			0.717426	−	0.696635i	$-0.245320\pi$
$157$	17.9786			1.43485			0.717426	+	0.696635i	$0.245320\pi$
$158$	1.08882	+	1.08882i	0.0866222	+	0.0866222i
$159$	6.50010	−	6.50010i	0.515492	−	0.515492i
$160$	−6.36943	+	6.36943i	−0.503548	+	0.503548i
$161$			3.33275i			0.262657i
$162$			0.916222i			0.0719852i
$163$	−5.11551	+	5.11551i	−0.400678	+	0.400678i	−0.878472	−	0.477794i	$-0.841436\pi$
$163$	−5.11551	+	5.11551i	−0.400678	+	0.400678i	0.477794	+	0.878472i	$0.341436\pi$
$164$	6.87087	−	6.87087i	0.536525	−	0.536525i
$165$	7.39164	+	7.39164i	0.575439	+	0.575439i
$166$	−4.71688			−0.366101
$167$	3.61053	+	3.61053i	0.279392	+	0.279392i	0.832866	−	0.553475i	$-0.186698\pi$
$167$	3.61053	+	3.61053i	0.279392	+	0.279392i	−0.553475	+	0.832866i	$0.686698\pi$
$168$		−	2.22668i		−	0.171792i
$169$	9.24897			0.711459
$170$		0			0
$171$	−0.773318			−0.0591371
$172$		−	2.77332i		−	0.211464i
$173$	−9.06909	−	9.06909i	−0.689510	−	0.689510i	0.272613	−	0.962124i	$-0.412112\pi$
$173$	−9.06909	−	9.06909i	−0.689510	−	0.689510i	−0.962124	+	0.272613i	$0.912112\pi$
$174$	−0.680045			−0.0515541
$175$	−0.677487	−	0.677487i	−0.0512132	−	0.0512132i
$176$	11.7843	−	11.7843i	0.888274	−	0.888274i
$177$	3.11391	−	3.11391i	0.234056	−	0.234056i
$178$		−	2.19759i		−	0.164716i
$179$			4.27126i			0.319249i	0.987178	+	0.159624i	$0.0510283\pi$
$179$			4.27126i			0.319249i	−0.987178	+	0.159624i	$0.948972\pi$
$180$	−6.94587	+	6.94587i	−0.517715	+	0.517715i
$181$	0.327291	−	0.327291i	0.0243273	−	0.0243273i	−0.694838	−	0.719166i	$-0.744524\pi$
$181$	0.327291	−	0.327291i	0.0243273	−	0.0243273i	0.719166	+	0.694838i	$0.244524\pi$
$182$	−2.17699	−	2.17699i	−0.161369	−	0.161369i
$183$	0.162504			0.0120126
$184$	−1.68941	−	1.68941i	−0.124545	−	0.124545i
$185$		−	14.4834i		−	1.06484i
$186$	0.593578			0.0435233
$187$		0			0
$188$	16.0351			1.16948
$189$		−	8.63816i		−	0.628333i
$190$	0.200195	+	0.200195i	0.0145237	+	0.0145237i
$191$	1.43107			0.103549			0.0517745	−	0.998659i	$-0.483512\pi$
$191$	1.43107			0.103549			0.0517745	+	0.998659i	$0.483512\pi$
$192$	−3.26391	−	3.26391i	−0.235552	−	0.235552i
$193$	−17.4829	+	17.4829i	−1.25845	+	1.25845i	−0.306617	+	0.951833i	$0.599197\pi$
$193$	−17.4829	+	17.4829i	−1.25845	+	1.25845i	−0.951833	+	0.306617i	$0.900803\pi$
$194$	2.27804	−	2.27804i	0.163553	−	0.163553i
$195$		−	9.73648i		−	0.697244i
$196$			6.51754i			0.465539i
$197$	8.31661	−	8.31661i	0.592534	−	0.592534i	−0.345781	−	0.938315i	$-0.612386\pi$
$197$	8.31661	−	8.31661i	0.592534	−	0.592534i	0.938315	+	0.345781i	$0.112386\pi$
$198$	−2.76919	+	2.76919i	−0.196798	+	0.196798i
$199$	−14.5100	−	14.5100i	−1.02859	−	1.02859i	−0.999579	−	0.0290069i	$-0.990766\pi$
$199$	−14.5100	−	14.5100i	−1.02859	−	1.02859i	−0.0290069	−	0.999579i	$-0.509234\pi$
$200$	0.686852			0.0485678
$201$	1.52241	+	1.52241i	0.107382	+	0.107382i
$202$			2.44831i			0.172263i
$203$	−4.18479			−0.293715
$204$		0			0
$205$	−12.1361			−0.847622
$206$		−	1.84018i		−	0.128212i
$207$	−2.79209	−	2.79209i	−0.194064	−	0.194064i
$208$	−15.5226			−1.07630
$209$	−1.24364	−	1.24364i	−0.0860243	−	0.0860243i
$210$	−0.952682	+	0.952682i	−0.0657413	+	0.0657413i
$211$	15.3568	−	15.3568i	1.05721	−	1.05721i	0.0589455	−	0.998261i	$-0.481226\pi$
$211$	15.3568	−	15.3568i	1.05721	−	1.05721i	0.998261	−	0.0589455i	$-0.0187738\pi$
$212$			19.6459i			1.34929i
$213$		−	8.72462i		−	0.597801i
$214$	−3.83006	+	3.83006i	−0.261818	+	0.261818i
$215$	−2.44927	+	2.44927i	−0.167039	+	0.167039i
$216$	4.37878	+	4.37878i	0.297938	+	0.297938i
$217$	3.65270			0.247962
$218$	−0.459630	−	0.459630i	−0.0311301	−	0.0311301i
$219$		−	9.58677i		−	0.647814i
$220$	−22.3405			−1.50620
$221$		0			0
$222$	−1.88444			−0.126475
$223$			19.9513i			1.33604i	0.744144	+	0.668019i	$0.232858\pi$
$223$			19.9513i			1.33604i	−0.744144	+	0.668019i	$0.767142\pi$
$224$	5.09975	+	5.09975i	0.340741	+	0.340741i
$225$	1.13516			0.0756775
$226$	−2.97486	−	2.97486i	−0.197884	−	0.197884i
$227$	2.98514	−	2.98514i	0.198131	−	0.198131i	−0.601067	−	0.799198i	$-0.705258\pi$
$227$	2.98514	−	2.98514i	0.198131	−	0.198131i	0.799198	+	0.601067i	$0.205258\pi$
$228$	−0.405864	+	0.405864i	−0.0268790	+	0.0268790i
$229$			14.5057i			0.958562i	0.877661	+	0.479281i	$0.159103\pi$
$229$			14.5057i			0.958562i	−0.877661	+	0.479281i	$0.840897\pi$
$230$			1.44562i			0.0953215i
$231$	5.91819	−	5.91819i	0.389388	−	0.389388i
$232$	2.12132	−	2.12132i	0.139272	−	0.139272i
$233$	3.62563	+	3.62563i	0.237523	+	0.237523i	0.815824	−	0.578301i	$-0.196284\pi$
$233$	3.62563	+	3.62563i	0.237523	+	0.237523i	−0.578301	+	0.815824i	$0.696284\pi$
$234$	3.64765			0.238454
$235$	−14.1615	−	14.1615i	−0.923792	−	0.923792i
$236$			9.41147i			0.612635i
$237$	3.89899			0.253266
$238$		0			0
$239$	−15.8503			−1.02527			−0.512635	−	0.858607i	$-0.671331\pi$
$239$	−15.8503			−1.02527			−0.512635	+	0.858607i	$0.671331\pi$
$240$			6.79292i			0.438481i
$241$	12.8103	+	12.8103i	0.825184	+	0.825184i	0.986846	−	0.161662i	$-0.0516855\pi$
$241$	12.8103	+	12.8103i	0.825184	+	0.825184i	−0.161662	+	0.986846i	$0.551686\pi$
$242$	−5.08647			−0.326970
$243$	11.3906	+	11.3906i	0.730708	+	0.730708i
$244$	−0.245576	+	0.245576i	−0.0157214	+	0.0157214i
$245$	5.75600	−	5.75600i	0.367737	−	0.367737i
$246$			1.57903i			0.100675i
$247$			1.63816i			0.104233i
$248$	−1.85160	+	1.85160i	−0.117577	+	0.117577i
$249$	−8.44537	+	8.44537i	−0.535204	+	0.535204i
$250$	2.58833	+	2.58833i	0.163700	+	0.163700i
$251$	29.6810			1.87345			0.936723	−	0.350070i	$-0.113842\pi$
$251$	29.6810			1.87345			0.936723	+	0.350070i	$0.113842\pi$
$252$	5.56128	+	5.56128i	0.350328	+	0.350328i
$253$		−	8.98040i		−	0.564593i
$254$	−4.00774			−0.251468
$255$		0			0
$256$	7.19934			0.449959
$257$		−	7.39693i		−	0.461408i	−0.973024	−	0.230704i	$-0.925897\pi$
$257$		−	7.39693i		−	0.461408i	0.973024	−	0.230704i	$-0.0741028\pi$
$258$	0.318675	+	0.318675i	0.0198399	+	0.0198399i
$259$	−11.5963			−0.720557
$260$	14.7138	+	14.7138i	0.912509	+	0.912509i
$261$	3.50591	−	3.50591i	0.217011	−	0.217011i
$262$	−4.75794	+	4.75794i	−0.293946	+	0.293946i
$263$		−	23.1908i		−	1.43000i	−0.699122	−	0.715002i	$-0.746426\pi$
$263$		−	23.1908i		−	1.43000i	0.699122	−	0.715002i	$-0.253574\pi$
$264$			6.00000i			0.369274i
$265$	17.3504	−	17.3504i	1.06583	−	1.06583i
$266$	0.160288	−	0.160288i	0.00982789	−	0.00982789i
$267$	−3.93468	−	3.93468i	−0.240799	−	0.240799i
$268$	−4.60132			−0.281070
$269$	11.2478	+	11.2478i	0.685788	+	0.685788i	0.961298	−	0.275510i	$-0.0888469\pi$
$269$	11.2478	+	11.2478i	0.685788	+	0.685788i	−0.275510	+	0.961298i	$0.588847\pi$
$270$		−	3.74691i		−	0.228030i
$271$	17.0000			1.03268			0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000			1.03268			0.516338	+	0.856385i	$0.327295\pi$
$272$		0			0
$273$	−7.79561			−0.471812
$274$			0.155697i			0.00940598i
$275$	1.82555	+	1.82555i	0.110085	+	0.110085i
$276$	−2.93077			−0.176412
$277$	11.8834	+	11.8834i	0.714006	+	0.714006i	0.967371	−	0.253365i	$-0.0815372\pi$
$277$	11.8834	+	11.8834i	0.714006	+	0.714006i	−0.253365	+	0.967371i	$0.581537\pi$
$278$	−2.86833	+	2.86833i	−0.172031	+	0.172031i
$279$	−3.06014	+	3.06014i	−0.183206	+	0.183206i
$280$		−	5.94356i		−	0.355196i
$281$			28.3209i			1.68948i	0.535175	+	0.844741i	$0.320246\pi$
$281$			28.3209i			1.68948i	−0.535175	+	0.844741i	$0.679754\pi$
$282$	−1.84255	+	1.84255i	−0.109722	+	0.109722i
$283$	−22.7932	+	22.7932i	−1.35491	+	1.35491i	−0.474844	+	0.880070i	$0.657495\pi$
$283$	−22.7932	+	22.7932i	−1.35491	+	1.35491i	−0.880070	+	0.474844i	$0.842505\pi$
$284$	13.1846	+	13.1846i	0.782364	+	0.782364i
$285$	0.716881			0.0424644
$286$	5.86610	+	5.86610i	0.346869	+	0.346869i
$287$			9.71688i			0.573569i
$288$	−8.54488			−0.503512
$289$		0			0
$290$	−1.81521			−0.106593
$291$		−	8.15745i		−	0.478198i
$292$	14.4875	+	14.4875i	0.847818	+	0.847818i
$293$	−13.9709			−0.816189			−0.408094	−	0.912940i	$-0.633807\pi$
$293$	−13.9709			−0.816189			−0.408094	+	0.912940i	$0.633807\pi$
$294$	−0.748915	−	0.748915i	−0.0436776	−	0.0436776i
$295$	8.31179	−	8.31179i	0.483931	−	0.483931i
$296$	5.87828	−	5.87828i	0.341668	−	0.341668i
$297$			23.2763i			1.35063i
$298$			2.94087i			0.170360i
$299$	−5.91462	+	5.91462i	−0.342051	+	0.342051i
$300$	0.595772	−	0.595772i	0.0343969	−	0.0343969i
$301$	1.96103	+	1.96103i	0.113032	+	0.113032i
$302$	4.78106			0.275119
$303$	4.38360	+	4.38360i	0.251831	+	0.251831i
$304$		−	1.14290i		−	0.0655500i
$305$	0.433763			0.0248372
$306$		0			0
$307$	9.04963			0.516490			0.258245	−	0.966080i	$-0.416856\pi$
$307$	9.04963			0.516490			0.258245	+	0.966080i	$0.416856\pi$
$308$			17.8871i			1.01921i
$309$	−3.29477	−	3.29477i	−0.187433	−	0.187433i
$310$	1.58441			0.0899883
$311$	−1.65979	−	1.65979i	−0.0941180	−	0.0941180i	0.658480	−	0.752598i	$-0.271200\pi$
$311$	−1.65979	−	1.65979i	−0.0941180	−	0.0941180i	−0.752598	+	0.658480i	$0.771200\pi$
$312$	3.95168	−	3.95168i	0.223720	−	0.223720i
$313$	−10.6974	+	10.6974i	−0.604651	+	0.604651i	−0.941543	−	0.336892i	$-0.890624\pi$
$313$	−10.6974	+	10.6974i	−0.604651	+	0.604651i	0.336892	+	0.941543i	$0.390624\pi$
$314$		−	6.24392i		−	0.352365i
$315$		−	9.82295i		−	0.553460i
$316$	−5.89214	+	5.89214i	−0.331459	+	0.331459i
$317$	−7.30993	+	7.30993i	−0.410567	+	0.410567i	−0.881936	−	0.471369i	$-0.843760\pi$
$317$	−7.30993	+	7.30993i	−0.410567	+	0.410567i	0.471369	+	0.881936i	$0.343760\pi$
$318$	−2.25746	−	2.25746i	−0.126592	−	0.126592i
$319$	11.2763			0.631352
$320$	−8.71218	−	8.71218i	−0.487026	−	0.487026i
$321$			13.7151i			0.765504i
$322$	1.15745			0.0645022
$323$		0			0
$324$	−4.95811			−0.275451
$325$		−	2.40467i		−	0.133387i
$326$	1.77660	+	1.77660i	0.0983966	+	0.0983966i
$327$	−1.64590			−0.0910183
$328$	−4.92560	−	4.92560i	−0.271971	−	0.271971i
$329$	−11.3385	+	11.3385i	−0.625113	+	0.625113i
$330$	2.56709	−	2.56709i	0.141314	−	0.141314i
$331$			18.2567i			1.00348i	0.865019	+	0.501740i	$0.167307\pi$
$331$			18.2567i			1.00348i	−0.865019	+	0.501740i	$0.832693\pi$
$332$		−	25.5253i		−	1.40088i
$333$	9.71506	−	9.71506i	0.532382	−	0.532382i
$334$	1.25393	−	1.25393i	0.0686117	−	0.0686117i
$335$	4.06368	+	4.06368i	0.222023	+	0.222023i
$336$	5.43882			0.296712
$337$	−11.6639	−	11.6639i	−0.635373	−	0.635373i	0.314037	−	0.949411i	$-0.398318\pi$
$337$	−11.6639	−	11.6639i	−0.635373	−	0.635373i	−0.949411	+	0.314037i	$0.898318\pi$
$338$		−	3.21213i		−	0.174717i
$339$	−10.6527			−0.578575
$340$		0			0
$341$	−9.84255			−0.533004
$342$			0.268571i			0.0145226i
$343$	−13.9111	−	13.9111i	−0.751128	−	0.751128i
$344$	−1.98814			−0.107193
$345$	2.58833	+	2.58833i	0.139351	+	0.139351i
$346$	−3.14966	+	3.14966i	−0.169327	+	0.169327i
$347$	14.5468	−	14.5468i	0.780911	−	0.780911i	−0.199074	−	0.979985i	$-0.563793\pi$
$347$	14.5468	−	14.5468i	0.780911	−	0.780911i	0.979985	+	0.199074i	$0.0637933\pi$
$348$		−	3.68004i		−	0.197271i
$349$			6.42427i			0.343883i	0.985107	+	0.171942i	$0.0550040\pi$
$349$			6.42427i			0.343883i	−0.985107	+	0.171942i	$0.944996\pi$
$350$	−0.235289	+	0.235289i	−0.0125767	+	0.0125767i
$351$	15.3301	−	15.3301i	0.818261	−	0.818261i
$352$	−13.7417	−	13.7417i	−0.732437	−	0.732437i
$353$	−27.1685			−1.44603			−0.723016	−	0.690831i	$-0.757245\pi$
$353$	−27.1685			−1.44603			−0.723016	+	0.690831i	$0.757245\pi$
$354$	−1.08145	−	1.08145i	−0.0574784	−	0.0574784i
$355$		−	23.2882i		−	1.23601i
$356$	11.8922			0.630284
$357$		0			0
$358$	1.48339			0.0783997
$359$		−	16.8949i		−	0.891677i	−0.895113	−	0.445838i	$-0.852906\pi$
$359$		−	16.8949i		−	0.891677i	0.895113	−	0.445838i	$-0.147094\pi$
$360$	4.97937	+	4.97937i	0.262436	+	0.262436i
$361$	18.8794			0.993652
$362$	−0.113667	−	0.113667i	−0.00597419	−	0.00597419i
$363$	−9.10710	+	9.10710i	−0.477999	+	0.477999i
$364$	11.7807	−	11.7807i	0.617477	−	0.617477i
$365$		−	25.5895i		−	1.33941i
$366$		−	0.0564370i		−	0.00295001i
$367$	−1.05183	+	1.05183i	−0.0549051	+	0.0549051i	−0.734026	−	0.679121i	$-0.762361\pi$
$367$	−1.05183	+	1.05183i	−0.0549051	+	0.0549051i	0.679121	+	0.734026i	$0.262361\pi$
$368$	4.12649	−	4.12649i	0.215108	−	0.215108i
$369$	−8.14056	−	8.14056i	−0.423781	−	0.423781i
$370$	−5.03003			−0.261499
$371$	−13.8917	−	13.8917i	−0.721224	−	0.721224i
$372$			3.21213i			0.166541i
$373$	−24.0496			−1.24524			−0.622621	−	0.782523i	$-0.713932\pi$
$373$	−24.0496			−1.24524			−0.622621	+	0.782523i	$0.713932\pi$
$374$		0			0
$375$	9.26857			0.478627
$376$		−	11.4953i		−	0.592822i
$377$	−7.42674	−	7.42674i	−0.382496	−	0.382496i
$378$	−3.00000			−0.154303
$379$	−14.2818	−	14.2818i	−0.733609	−	0.733609i	0.237724	−	0.971333i	$-0.423599\pi$
$379$	−14.2818	−	14.2818i	−0.733609	−	0.733609i	−0.971333	+	0.237724i	$0.923599\pi$
$380$	−1.08335	+	1.08335i	−0.0555747	+	0.0555747i
$381$	−7.17569	+	7.17569i	−0.367622	+	0.367622i
$382$		−	0.497007i		−	0.0254291i
$383$		−	8.52528i		−	0.435622i	−0.975991	−	0.217811i	$-0.930108\pi$
$383$		−	8.52528i		−	0.435622i	0.975991	−	0.217811i	$-0.0698916\pi$
$384$	−5.90600	+	5.90600i	−0.301389	+	0.301389i
$385$	15.7971	−	15.7971i	0.805095	−	0.805095i
$386$	6.07176	+	6.07176i	0.309045	+	0.309045i
$387$	−3.28581			−0.167027
$388$	12.3275	+	12.3275i	0.625836	+	0.625836i
$389$			12.9162i			0.654878i	0.944872	+	0.327439i	$0.106186\pi$
$389$			12.9162i			0.654878i	−0.944872	+	0.327439i	$0.893814\pi$
$390$	−3.38144			−0.171226
$391$		0			0
$392$	4.67230			0.235987
$393$			17.0378i			0.859442i
$394$	−2.88833	−	2.88833i	−0.145512	−	0.145512i
$395$	10.4074			0.523651
$396$	−14.9854	−	14.9854i	−0.753044	−	0.753044i
$397$	17.1296	−	17.1296i	0.859710	−	0.859710i	−0.131593	−	0.991304i	$-0.542009\pi$
$397$	17.1296	−	17.1296i	0.859710	−	0.859710i	0.991304	+	0.131593i	$0.0420093\pi$
$398$	−5.03927	+	5.03927i	−0.252596	+	0.252596i
$399$		−	0.573978i		−	0.0287348i
$400$			1.67768i			0.0838840i
$401$	−18.0575	+	18.0575i	−0.901748	+	0.901748i	−0.995587	−	0.0938395i	$-0.970086\pi$
$401$	−18.0575	+	18.0575i	−0.901748	+	0.901748i	0.0938395	+	0.995587i	$0.470086\pi$
$402$	0.528726	−	0.528726i	0.0263705	−	0.0263705i
$403$	6.48244	+	6.48244i	0.322913	+	0.322913i
$404$	−13.2490			−0.659161
$405$	4.37878	+	4.37878i	0.217583	+	0.217583i
$406$			1.45336i			0.0721292i
$407$	31.2472			1.54887
$408$		0			0
$409$	10.3523			0.511891			0.255945	−	0.966691i	$-0.417613\pi$
$409$	10.3523			0.511891			0.255945	+	0.966691i	$0.417613\pi$
$410$			4.21482i			0.208155i
$411$	0.278768	+	0.278768i	0.0137506	+	0.0137506i
$412$	9.95811			0.490601
$413$	−6.65492	−	6.65492i	−0.327467	−	0.327467i
$414$	−0.969684	+	0.969684i	−0.0476574	+	0.0476574i
$415$	−22.5428	+	22.5428i	−1.10658	+	1.10658i
$416$			18.1010i			0.887475i
$417$			10.2713i			0.502986i
$418$	−0.431911	+	0.431911i	−0.0211255	+	0.0211255i
$419$	0.928536	−	0.928536i	0.0453619	−	0.0453619i	−0.684062	−	0.729424i	$-0.739788\pi$
$419$	0.928536	−	0.928536i	0.0453619	−	0.0453619i	0.729424	+	0.684062i	$0.239788\pi$
$420$	−5.15542	−	5.15542i	−0.251559	−	0.251559i
$421$	−8.01548			−0.390651			−0.195325	−	0.980739i	$-0.562576\pi$
$421$	−8.01548			−0.390651			−0.195325	+	0.980739i	$0.562576\pi$
$422$	−5.33337	−	5.33337i	−0.259624	−	0.259624i
$423$		−	18.9982i		−	0.923726i
$424$	14.0838			0.683969
$425$		0			0
$426$	−3.03003			−0.146805
$427$		−	0.347296i		−	0.0168068i
$428$	−20.7263	−	20.7263i	−1.00184	−	1.00184i
$429$	21.0060			1.01418
$430$	0.850623	+	0.850623i	0.0410207	+	0.0410207i
$431$	10.4136	−	10.4136i	0.501603	−	0.501603i	−0.410333	−	0.911936i	$-0.634587\pi$
$431$	10.4136	−	10.4136i	0.501603	−	0.501603i	0.911936	+	0.410333i	$0.134587\pi$
$432$	−10.6955	+	10.6955i	−0.514586	+	0.514586i
$433$		−	8.24123i		−	0.396048i	−0.980197	−	0.198024i	$-0.936548\pi$
$433$		−	8.24123i		−	0.396048i	0.980197	−	0.198024i	$-0.0634524\pi$
$434$		−	1.26857i		−	0.0608933i
$435$	−3.25005	+	3.25005i	−0.155828	+	0.155828i
$436$	2.48728	−	2.48728i	0.119119	−	0.119119i
$437$	−0.435484	−	0.435484i	−0.0208320	−	0.0208320i
$438$	−3.32945			−0.159087
$439$	28.2534	+	28.2534i	1.34846	+	1.34846i	0.887334	+	0.461128i	$0.152555\pi$
$439$	28.2534	+	28.2534i	1.34846	+	1.34846i	0.461128	+	0.887334i	$0.347445\pi$
$440$			16.0155i			0.763508i
$441$	7.72193			0.367711
$442$		0			0
$443$	13.9463			0.662606			0.331303	−	0.943524i	$-0.392512\pi$
$443$	13.9463			0.662606			0.331303	+	0.943524i	$0.392512\pi$
$444$		−	10.1976i		−	0.483956i
$445$	−10.5026	−	10.5026i	−0.497873	−	0.497873i
$446$	6.92902			0.328098
$447$	5.26551	+	5.26551i	0.249050	+	0.249050i
$448$	−6.97549	+	6.97549i	−0.329561	+	0.329561i
$449$	−7.23493	+	7.23493i	−0.341437	+	0.341437i	−0.856908	−	0.515470i	$-0.827617\pi$
$449$	−7.23493	+	7.23493i	−0.341437	+	0.341437i	0.515470	+	0.856908i	$0.327617\pi$
$450$		−	0.394238i		−	0.0185846i
$451$		−	26.1830i		−	1.23291i
$452$	16.0984	−	16.0984i	0.757203	−	0.757203i
$453$	8.56028	−	8.56028i	0.402197	−	0.402197i
$454$	−1.03673	−	1.03673i	−0.0486561	−	0.0486561i
$455$	−20.8084			−0.975513
$456$	0.290956	+	0.290956i	0.0136253	+	0.0136253i
$457$			11.7706i			0.550607i	0.961357	+	0.275303i	$0.0887783\pi$
$457$			11.7706i			0.550607i	−0.961357	+	0.275303i	$0.911222\pi$
$458$	5.03777			0.235400
$459$		0			0
$460$	−7.82295			−0.364747
$461$		−	19.5003i		−	0.908220i	−0.890946	−	0.454110i	$-0.849957\pi$
$461$		−	19.5003i		−	0.908220i	0.890946	−	0.454110i	$-0.150043\pi$
$462$	−2.05537	−	2.05537i	−0.0956243	−	0.0956243i
$463$	1.43107			0.0665077			0.0332538	−	0.999447i	$-0.489413\pi$
$463$	1.43107			0.0665077			0.0332538	+	0.999447i	$0.489413\pi$
$464$	5.18146	+	5.18146i	0.240543	+	0.240543i
$465$	2.83681	−	2.83681i	0.131554	−	0.131554i
$466$	1.25917	−	1.25917i	0.0583299	−	0.0583299i
$467$		−	10.6895i		−	0.494653i	−0.968932	−	0.247326i	$-0.920448\pi$
$467$		−	10.6895i		−	0.494653i	0.968932	−	0.247326i	$-0.0795520\pi$
$468$			19.7392i			0.912443i
$469$	3.25362	−	3.25362i	0.150238	−	0.150238i
$470$	−4.91823	+	4.91823i	−0.226861	+	0.226861i
$471$	−11.1795	−	11.1795i	−0.515123	−	0.515123i
$472$	6.74691			0.310552
$473$	−5.28418	−	5.28418i	−0.242967	−	0.242967i
$474$		−	1.35410i		−	0.0621960i
$475$	0.177052			0.00812369
$476$		0			0
$477$	23.2763			1.06575
$478$			5.50475i			0.251781i
$479$	27.4835	+	27.4835i	1.25575	+	1.25575i	0.953101	+	0.302651i	$0.0978718\pi$
$479$	27.4835	+	27.4835i	1.25575	+	1.25575i	0.302651	+	0.953101i	$0.402128\pi$
$480$	7.92127			0.361555
$481$	−20.5799	−	20.5799i	−0.938361	−	0.938361i
$482$	4.44897	−	4.44897i	0.202645	−	0.202645i
$483$	2.07237	−	2.07237i	0.0942960	−	0.0942960i
$484$		−	27.5253i		−	1.25115i
$485$		−	21.7743i		−	0.988718i
$486$	3.95592	−	3.95592i	0.179444	−	0.179444i
$487$	26.1727	−	26.1727i	1.18600	−	1.18600i	0.207832	−	0.978165i	$-0.433359\pi$
$487$	26.1727	−	26.1727i	1.18600	−	1.18600i	0.978165	−	0.207832i	$-0.0666406\pi$
$488$	0.176049	+	0.176049i	0.00796935	+	0.00796935i
$489$	6.36184			0.287693
$490$	−1.99904	−	1.99904i	−0.0903073	−	0.0903073i
$491$			25.4175i			1.14707i	0.819180	+	0.573537i	$0.194429\pi$
$491$			25.4175i			1.14707i	−0.819180	+	0.573537i	$0.805571\pi$
$492$	−8.54488			−0.385233
$493$		0			0
$494$	0.568926			0.0255972
$495$			26.4688i			1.18969i
$496$	−4.52265	−	4.52265i	−0.203073	−	0.203073i
$497$	−18.6459			−0.836383
$498$	2.93305	+	2.93305i	0.131433	+	0.131433i
$499$	−15.4318	+	15.4318i	−0.690823	+	0.690823i	−0.962413	−	0.271590i	$-0.912451\pi$
$499$	−15.4318	+	15.4318i	−0.690823	+	0.690823i	0.271590	+	0.962413i	$0.412451\pi$
$500$	−14.0067	+	14.0067i	−0.626397	+	0.626397i
$501$		−	4.49020i		−	0.200607i
$502$		−	10.3081i		−	0.460073i
$503$	−23.6436	+	23.6436i	−1.05421	+	1.05421i	−0.0557712	+	0.998444i	$0.517762\pi$
$503$	−23.6436	+	23.6436i	−1.05421	+	1.05421i	−0.998444	+	0.0557712i	$0.982238\pi$
$504$	3.98678	−	3.98678i	0.177585	−	0.177585i
$505$	11.7009	+	11.7009i	0.520683	+	0.520683i
$506$	−3.11886			−0.138650
$507$	−5.75119	−	5.75119i	−0.255419	−	0.255419i
$508$		−	21.6878i		−	0.962240i
$509$	−19.1530			−0.848942			−0.424471	−	0.905441i	$-0.639540\pi$
$509$	−19.1530			−0.848942			−0.424471	+	0.905441i	$0.639540\pi$
$510$		0			0
$511$	−20.4884			−0.906355
$512$		−	21.4962i		−	0.950006i
$513$	1.12873	+	1.12873i	0.0498347	+	0.0498347i
$514$	−2.56893			−0.113310
$515$	−8.79456	−	8.79456i	−0.387535	−	0.387535i
$516$	−1.72450	+	1.72450i	−0.0759170	+	0.0759170i
$517$	30.5527	−	30.5527i	1.34371	−	1.34371i
$518$			4.02734i			0.176951i
$519$			11.2787i			0.495079i
$520$	10.5480	−	10.5480i	0.462561	−	0.462561i
$521$	−25.1256	+	25.1256i	−1.10077	+	1.10077i	−0.106457	+	0.994317i	$0.533951\pi$
$521$	−25.1256	+	25.1256i	−1.10077	+	1.10077i	−0.994317	+	0.106457i	$0.966049\pi$
$522$	−1.21759	−	1.21759i	−0.0532925	−	0.0532925i
$523$	11.8307			0.517320			0.258660	−	0.965968i	$-0.416719\pi$
$523$	11.8307			0.517320			0.258660	+	0.965968i	$0.416719\pi$
$524$	−25.7475	−	25.7475i	−1.12478	−	1.12478i
$525$			0.842549i			0.0367718i
$526$	−8.05407			−0.351174
$527$		0			0
$528$	−14.6554			−0.637794
$529$			19.8553i			0.863276i
$530$	−6.02572	−	6.02572i	−0.261741	−	0.261741i
$531$	11.1506			0.483897
$532$	0.867395	+	0.867395i	0.0376063	+	0.0376063i
$533$	−17.2445	+	17.2445i	−0.746943	+	0.746943i
$534$	−1.36650	+	1.36650i	−0.0591343	+	0.0591343i
$535$			36.6091i			1.58275i
$536$			3.29860i			0.142478i
$537$	2.65595	−	2.65595i	0.114613	−	0.114613i
$538$	3.90630	−	3.90630i	0.168413	−	0.168413i
$539$	12.4183	+	12.4183i	0.534894	+	0.534894i
$540$	20.2763			0.872554
$541$	3.93045	+	3.93045i	0.168983	+	0.168983i	0.786532	−	0.617549i	$-0.211874\pi$
$541$	3.93045	+	3.93045i	0.168983	+	0.168983i	−0.617549	+	0.786532i	$0.711874\pi$
$542$		−	5.90404i		−	0.253600i
$543$	−0.407031			−0.0174674
$544$		0			0
$545$	−4.39330			−0.188188
$546$			2.70739i			0.115865i
$547$	3.55297	+	3.55297i	0.151914	+	0.151914i	0.778972	−	0.627058i	$-0.215741\pi$
$547$	3.55297	+	3.55297i	0.151914	+	0.151914i	−0.627058	+	0.778972i	$0.715741\pi$
$548$	−0.842549			−0.0359919
$549$	0.290956	+	0.290956i	0.0124177	+	0.0124177i
$550$	0.634007	−	0.634007i	0.0270342	−	0.0270342i
$551$	0.546819	−	0.546819i	0.0232953	−	0.0232953i
$552$			2.10101i			0.0894251i
$553$		−	8.33275i		−	0.354345i
$554$	4.12707	−	4.12707i	0.175343	−	0.175343i
$555$	−9.00605	+	9.00605i	−0.382286	+	0.382286i
$556$	−15.5219	−	15.5219i	−0.658276	−	0.658276i
$557$	−3.86659			−0.163833			−0.0819164	−	0.996639i	$-0.526104\pi$
$557$	−3.86659			−0.163833			−0.0819164	+	0.996639i	$0.526104\pi$
$558$	1.06278	+	1.06278i	0.0449909	+	0.0449909i
$559$			6.96048i			0.294397i
$560$	14.5175			0.613478
$561$		0			0
$562$	9.83574			0.414896
$563$		−	28.8411i		−	1.21551i	−0.794125	−	0.607754i	$-0.792071\pi$
$563$		−	28.8411i		−	1.21551i	0.794125	−	0.607754i	$-0.207929\pi$
$564$	−9.97092	−	9.97092i	−0.419852	−	0.419852i
$565$	−28.4347			−1.19626
$566$	7.91599	+	7.91599i	0.332734	+	0.332734i
$567$	3.50591	−	3.50591i	0.147235	−	0.147235i
$568$	9.45182	−	9.45182i	0.396590	−	0.396590i
$569$			2.16157i			0.0906177i	0.998973	+	0.0453089i	$0.0144272\pi$
$569$			2.16157i			0.0906177i	−0.998973	+	0.0453089i	$0.985573\pi$
$570$		−	0.248970i		−	0.0104282i
$571$	4.04412	−	4.04412i	0.169241	−	0.169241i	−0.617405	−	0.786646i	$-0.711816\pi$
$571$	4.04412	−	4.04412i	0.169241	−	0.169241i	0.786646	+	0.617405i	$0.211816\pi$
$572$	−31.7442	+	31.7442i	−1.32729	+	1.32729i
$573$	−0.889870	−	0.889870i	−0.0371748	−	0.0371748i
$574$	3.37464			0.140855
$575$	0.639251	+	0.639251i	0.0266586	+	0.0266586i
$576$		−	11.6878i		−	0.486991i
$577$	−10.8007			−0.449637			−0.224819	−	0.974401i	$-0.572179\pi$
$577$	−10.8007			−0.449637			−0.224819	+	0.974401i	$0.572179\pi$
$578$		0			0
$579$	21.7425			0.903586
$580$		−	9.82295i		−	0.407876i
$581$	18.0491	+	18.0491i	0.748803	+	0.748803i
$582$	−2.83305			−0.117434
$583$	37.4326	+	37.4326i	1.55030	+	1.55030i
$584$	10.3858	−	10.3858i	0.429769	−	0.429769i
$585$	17.4328	−	17.4328i	0.720756	−	0.720756i
$586$			4.85204i			0.200436i
$587$			20.8188i			0.859285i	0.902999	+	0.429643i	$0.141360\pi$
$587$			20.8188i			0.859285i	−0.902999	+	0.429643i	$0.858640\pi$
$588$	4.05273	−	4.05273i	0.167132	−	0.167132i
$589$	−0.477292	+	0.477292i	−0.0196665	+	0.0196665i
$590$	−2.88666	−	2.88666i	−0.118842	−	0.118842i
$591$	−10.3429			−0.425448
$592$	14.3581	+	14.3581i	0.590114	+	0.590114i
$593$		−	20.6313i		−	0.847228i	−0.905843	−	0.423614i	$-0.860761\pi$
$593$		−	20.6313i		−	0.847228i	0.905843	−	0.423614i	$-0.139239\pi$
$594$	8.08378			0.331681
$595$		0			0
$596$	−15.9145			−0.651882
$597$			18.0452i			0.738540i
$598$	2.05413	+	2.05413i	0.0839994	+	0.0839994i
$599$	−31.8212			−1.30018			−0.650089	−	0.759858i	$-0.725269\pi$
$599$	−31.8212			−1.30018			−0.650089	+	0.759858i	$0.725269\pi$
$600$	−0.427098	−	0.427098i	−0.0174362	−	0.0174362i
$601$	34.0242	−	34.0242i	1.38787	−	1.38787i	0.558102	−	0.829772i	$-0.311530\pi$
$601$	34.0242	−	34.0242i	1.38787	−	1.38787i	0.829772	−	0.558102i	$-0.188470\pi$
$602$	0.681059	−	0.681059i	0.0277579	−	0.0277579i
$603$			5.45161i			0.222007i
$604$			25.8726i			1.05274i
$605$	−24.3091	+	24.3091i	−0.988305	+	0.988305i
$606$	1.52241	−	1.52241i	0.0618435	−	0.0618435i
$607$	10.9429	+	10.9429i	0.444160	+	0.444160i	0.893407	−	0.449247i	$-0.148308\pi$
$607$	10.9429	+	10.9429i	0.444160	+	0.444160i	−0.449247	+	0.893407i	$0.648308\pi$
$608$	−1.33275			−0.0540501
$609$	2.60218	+	2.60218i	0.105446	+	0.105446i
$610$		−	0.150644i		−	0.00609941i
$611$	−40.2449			−1.62813
$612$		0			0
$613$	−5.04963			−0.203953			−0.101976	−	0.994787i	$-0.532517\pi$
$613$	−5.04963			−0.203953			−0.101976	+	0.994787i	$0.532517\pi$
$614$		−	3.14290i		−	0.126837i
$615$	7.54646	+	7.54646i	0.304303	+	0.304303i
$616$	12.8229			0.516651
$617$	19.5207	+	19.5207i	0.785872	+	0.785872i	0.980815	−	0.194943i	$-0.0624521\pi$
$617$	19.5207	+	19.5207i	0.785872	+	0.785872i	−0.194943	+	0.980815i	$0.562452\pi$
$618$	−1.14426	+	1.14426i	−0.0460290	+	0.0460290i
$619$	−10.4886	+	10.4886i	−0.421571	+	0.421571i	−0.885744	−	0.464174i	$-0.846351\pi$
$619$	−10.4886	+	10.4886i	−0.421571	+	0.421571i	0.464174	+	0.885744i	$0.346351\pi$
$620$			8.57398i			0.344339i
$621$			8.15064i			0.327074i
$622$	−0.576439	+	0.576439i	−0.0231131	+	0.0231131i
$623$	−8.40904	+	8.40904i	−0.336901	+	0.336901i
$624$	9.65225	+	9.65225i	0.386399	+	0.386399i
$625$	27.2891			1.09156
$626$	3.71516	+	3.71516i	0.148487	+	0.148487i
$627$			1.54664i			0.0617667i
$628$	33.7888			1.34832
$629$		0			0
$630$	−3.41147			−0.135916
$631$			34.0506i			1.35553i	0.735278	+	0.677766i	$0.237052\pi$
$631$			34.0506i			1.35553i	−0.735278	+	0.677766i	$0.762948\pi$
$632$	4.22397	+	4.22397i	0.168020	+	0.168020i
$633$	−19.0983			−0.759090
$634$	2.53871	+	2.53871i	0.100825	+	0.100825i
$635$	−19.1537	+	19.1537i	−0.760091	+	0.760091i
$636$	12.2162	−	12.2162i	0.484404	−	0.484404i
$637$		−	16.3577i		−	0.648117i
$638$		−	3.91622i		−	0.155045i
$639$	15.6211	−	15.6211i	0.617960	−	0.617960i
$640$	−15.7646	+	15.7646i	−0.623150	+	0.623150i
$641$	10.6230	+	10.6230i	0.419584	+	0.419584i	0.885060	−	0.465476i	$-0.154117\pi$
$641$	10.6230	+	10.6230i	0.419584	+	0.419584i	−0.465476	+	0.885060i	$0.654117\pi$
$642$	4.76321			0.187989
$643$	−12.5851	−	12.5851i	−0.496307	−	0.496307i	0.413980	−	0.910286i	$-0.364138\pi$
$643$	−12.5851	−	12.5851i	−0.496307	−	0.496307i	−0.910286	+	0.413980i	$0.864138\pi$
$644$			6.26352i			0.246817i
$645$	3.04601			0.119936
$646$		0			0
$647$	−46.4971			−1.82799			−0.913995	−	0.405725i	$-0.867019\pi$
$647$	−46.4971			−1.82799			−0.913995	+	0.405725i	$0.867019\pi$
$648$			3.55438i			0.139629i
$649$	17.9323	+	17.9323i	0.703904	+	0.703904i
$650$	−0.835132			−0.0327566
$651$	−2.27132	−	2.27132i	−0.0890201	−	0.0890201i
$652$	−9.61401	+	9.61401i	−0.376514	+	0.376514i
$653$	−21.5882	+	21.5882i	−0.844812	+	0.844812i	−0.989480	−	0.144668i	$-0.953788\pi$
$653$	−21.5882	+	21.5882i	−0.844812	+	0.844812i	0.144668	+	0.989480i	$0.453788\pi$
$654$			0.571614i			0.0223519i
$655$			45.4780i			1.77697i
$656$	12.0311	−	12.0311i	0.469736	−	0.469736i
$657$	17.1647	−	17.1647i	0.669659	−	0.669659i
$658$	3.93782	+	3.93782i	0.153512	+	0.153512i
$659$	9.83481			0.383110			0.191555	−	0.981482i	$-0.438647\pi$
$659$	9.83481			0.383110			0.191555	+	0.981482i	$0.438647\pi$
$660$	13.8917	+	13.8917i	0.540736	+	0.540736i
$661$		−	12.4361i		−	0.483709i	−0.970312	−	0.241855i	$-0.922244\pi$
$661$		−	12.4361i		−	0.483709i	0.970312	−	0.241855i	$-0.0777557\pi$
$662$	6.34049			0.246430
$663$		0			0
$664$	−18.2986			−0.710123
$665$		−	1.53209i		−	0.0594119i
$666$	−3.37401	−	3.37401i	−0.130740	−	0.130740i
$667$	3.94862			0.152891
$668$	6.78559	+	6.78559i	0.262542	+	0.262542i
$669$	12.4061	−	12.4061i	0.479648	−	0.479648i
$670$	1.41130	−	1.41130i	0.0545233	−	0.0545233i
$671$			0.935822i			0.0361270i
$672$		−	6.34224i		−	0.244657i
$673$	8.91785	−	8.91785i	0.343758	−	0.343758i	−0.514020	−	0.857778i	$-0.671844\pi$
$673$	8.91785	−	8.91785i	0.343758	−	0.343758i	0.857778	+	0.514020i	$0.171844\pi$
$674$	−4.05083	+	4.05083i	−0.156032	+	0.156032i
$675$	−1.65688	−	1.65688i	−0.0637732	−	0.0637732i
$676$	17.3824			0.668553
$677$	−3.21663	−	3.21663i	−0.123625	−	0.123625i	0.642587	−	0.766212i	$-0.277861\pi$
$677$	−3.21663	−	3.21663i	−0.123625	−	0.123625i	−0.766212	+	0.642587i	$0.777861\pi$
$678$			3.69965i			0.142084i
$679$	−17.4338			−0.669046
$680$		0			0
$681$	−3.71244			−0.142261
$682$			3.41828i			0.130893i
$683$	3.44186	+	3.44186i	0.131699	+	0.131699i	0.769884	−	0.638184i	$-0.220314\pi$
$683$	3.44186	+	3.44186i	0.131699	+	0.131699i	−0.638184	+	0.769884i	$0.720314\pi$
$684$	−1.45336			−0.0555707
$685$	0.744101	+	0.744101i	0.0284307	+	0.0284307i
$686$	−4.83127	+	4.83127i	−0.184459	+	0.184459i
$687$	9.01991	−	9.01991i	0.344131	−	0.344131i
$688$		−	4.85616i		−	0.185139i
$689$		−	49.3073i		−	1.87846i
$690$	0.898916	−	0.898916i	0.0342211	−	0.0342211i
$691$	3.90083	−	3.90083i	0.148395	−	0.148395i	−0.629006	−	0.777401i	$-0.716538\pi$
$691$	3.90083	−	3.90083i	0.148395	−	0.148395i	0.777401	+	0.629006i	$0.216538\pi$
$692$	−17.0443	−	17.0443i	−0.647928	−	0.647928i
$693$	21.1925			0.805038
$694$	−5.05204	−	5.05204i	−0.191773	−	0.191773i
$695$			27.4165i			1.03997i
$696$	−2.63816			−0.0999990
$697$		0			0
$698$	2.23112			0.0844493
$699$		−	4.50898i		−	0.170545i
$700$	−1.27326	−	1.27326i	−0.0481247	−	0.0481247i
$701$	−22.3233			−0.843138			−0.421569	−	0.906796i	$-0.638520\pi$
$701$	−22.3233			−0.843138			−0.421569	+	0.906796i	$0.638520\pi$
$702$	−5.32409	−	5.32409i	−0.200945	−	0.200945i
$703$	1.51526	−	1.51526i	0.0571492	−	0.0571492i
$704$	18.7961	−	18.7961i	0.708405	−	0.708405i
$705$			17.6117i			0.663297i
$706$			9.43552i			0.355110i
$707$	9.36844	−	9.36844i	0.352336	−	0.352336i
$708$	5.85224	−	5.85224i	0.219940	−	0.219940i
$709$	−24.5908	−	24.5908i	−0.923526	−	0.923526i	0.0737506	−	0.997277i	$-0.476503\pi$
$709$	−24.5908	−	24.5908i	−0.923526	−	0.923526i	−0.997277	+	0.0737506i	$0.976503\pi$
$710$	−8.08790			−0.303533
$711$	6.98097	+	6.98097i	0.261807	+	0.261807i
$712$		−	8.52528i		−	0.319498i
$713$	−3.44656			−0.129075
$714$		0			0
$715$	56.0702			2.09691
$716$			8.02734i			0.299996i
$717$	9.85602	+	9.85602i	0.368080	+	0.368080i
$718$	−5.86753			−0.218974
$719$	3.00514	+	3.00514i	0.112073	+	0.112073i	0.760919	−	0.648847i	$-0.224748\pi$
$719$	3.00514	+	3.00514i	0.112073	+	0.112073i	−0.648847	+	0.760919i	$0.724748\pi$
$720$	−12.1624	+	12.1624i	−0.453267	+	0.453267i
$721$	−7.04145	+	7.04145i	−0.262237	+	0.262237i
$722$		−	6.55674i		−	0.244017i
$723$		−	15.9314i		−	0.592494i
$724$	0.615105	−	0.615105i	0.0228602	−	0.0228602i
$725$	−0.802681	+	0.802681i	−0.0298108	+	0.0298108i
$726$	3.16286	+	3.16286i	0.117385	+	0.117385i
$727$	−29.1644			−1.08165			−0.540823	−	0.841136i	$-0.681887\pi$
$727$	−29.1644			−1.08165			−0.540823	+	0.841136i	$0.681887\pi$
$728$	−8.44537	−	8.44537i	−0.313006	−	0.313006i
$729$		−	6.25133i		−	0.231531i
$730$	−8.88713			−0.328927
$731$		0			0
$732$	0.305407			0.0112882
$733$			0.502993i			0.0185785i	0.999957	+	0.00928924i	$0.00295690\pi$
$733$			0.502993i			0.0185785i	−0.999957	+	0.00928924i	$0.997043\pi$
$734$	0.365297	+	0.365297i	0.0134833	+	0.0134833i
$735$	−7.15839			−0.264041
$736$	−4.81193	−	4.81193i	−0.177370	−	0.177370i
$737$	−8.76719	+	8.76719i	−0.322944	+	0.322944i
$738$	−2.82719	+	2.82719i	−0.104070	+	0.104070i
$739$			14.9581i			0.550243i	0.961409	+	0.275122i	$0.0887181\pi$
$739$			14.9581i			0.550243i	−0.961409	+	0.275122i	$0.911282\pi$
$740$		−	27.2199i		−	1.00062i
$741$	1.01864	−	1.01864i	0.0374206	−	0.0374206i
$742$	−4.82455	+	4.82455i	−0.177115	+	0.177115i
$743$	16.5290	+	16.5290i	0.606391	+	0.606391i	0.942001	−	0.335610i	$-0.108942\pi$
$743$	16.5290	+	16.5290i	0.606391	+	0.606391i	−0.335610	+	0.942001i	$0.608942\pi$
$744$	2.30272			0.0844218
$745$	14.0549	+	14.0549i	0.514933	+	0.514933i
$746$			8.35235i			0.305801i
$747$	−30.2422			−1.10650
$748$		0			0
$749$	29.3114			1.07102
$750$		−	3.21894i		−	0.117539i
$751$	−12.0414	−	12.0414i	−0.439397	−	0.439397i	0.452412	−	0.891809i	$-0.350564\pi$
$751$	−12.0414	−	12.0414i	−0.439397	−	0.439397i	−0.891809	+	0.452412i	$0.850564\pi$
$752$	28.0779			1.02390
$753$	−18.4562	−	18.4562i	−0.672581	−	0.672581i
$754$	−2.57928	+	2.57928i	−0.0939318	+	0.0939318i
$755$	22.8495	−	22.8495i	0.831579	−	0.831579i
$756$		−	16.2344i		−	0.590440i
$757$			16.3746i			0.595146i	0.954699	+	0.297573i	$0.0961772\pi$
$757$			16.3746i			0.595146i	−0.954699	+	0.297573i	$0.903823\pi$
$758$	−4.96003	+	4.96003i	−0.180157	+	0.180157i
$759$	−5.58419	+	5.58419i	−0.202693	+	0.202693i
$760$	0.776634	+	0.776634i	0.0281715	+	0.0281715i
$761$	18.8803			0.684411			0.342206	−	0.939625i	$-0.388826\pi$
$761$	18.8803			0.684411			0.342206	+	0.939625i	$0.388826\pi$
$762$	2.49209	+	2.49209i	0.0902789	+	0.0902789i
$763$			3.51754i			0.127344i
$764$	2.68954			0.0973042
$765$		0			0
$766$	−2.96080			−0.106978
$767$		−	23.6209i		−	0.852902i
$768$	−4.47669	−	4.47669i	−0.161539	−	0.161539i
$769$	27.4766			0.990831			0.495416	−	0.868656i	$-0.335016\pi$
$769$	27.4766			0.990831			0.495416	+	0.868656i	$0.335016\pi$
$770$	−5.48628	−	5.48628i	−0.197712	−	0.197712i
$771$	−4.59955	+	4.59955i	−0.165649	+	0.165649i
$772$	−32.8572	+	32.8572i	−1.18256	+	1.18256i
$773$			9.90436i			0.356235i	0.984009	+	0.178118i	$0.0570007\pi$
$773$			9.90436i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$774$			1.14115i			0.0410177i
$775$	0.700622	−	0.700622i	0.0251671	−	0.0251671i
$776$	8.83738	−	8.83738i	0.317243	−	0.317243i
$777$	7.21078	+	7.21078i	0.258685	+	0.258685i
$778$	4.48576			0.160822
$779$	−1.26969	−	1.26969i	−0.0454912	−	0.0454912i
$780$		−	18.2986i		−	0.655195i
$781$	50.2431			1.79784
$782$		0			0
$783$	−10.2344			−0.365748
$784$			11.4124i			0.407586i
$785$	−29.8408	−	29.8408i	−1.06506	−	1.06506i
$786$	5.91716			0.211058
$787$	−35.9524	−	35.9524i	−1.28157	−	1.28157i	−0.939777	−	0.341789i	$-0.888967\pi$
$787$	−35.9524	−	35.9524i	−1.28157	−	1.28157i	−0.341789	−	0.939777i	$-0.611033\pi$
$788$	15.6301	−	15.6301i	0.556800	−	0.556800i
$789$	−14.4205	+	14.4205i	−0.513382	+	0.513382i
$790$		−	3.61444i		−	0.128596i
$791$			22.7665i			0.809484i
$792$	−10.7427	+	10.7427i	−0.381727	+	0.381727i
$793$	0.616346	−	0.616346i	0.0218871	−	0.0218871i
$794$	−5.94905	−	5.94905i	−0.211124	−	0.211124i
$795$	−21.5776			−0.765279
$796$	−27.2699	−	27.2699i	−0.966555	−	0.966555i
$797$		−	5.38650i		−	0.190800i	−0.995439	−	0.0953998i	$-0.969587\pi$
$797$		−	5.38650i		−	0.190800i	0.995439	−	0.0953998i	$-0.0304129\pi$
$798$	−0.199340			−0.00705658
$799$		0			0
$800$	1.95636			0.0691676
$801$		−	14.0898i		−	0.497837i
$802$	6.27130	+	6.27130i	0.221447	+	0.221447i
$803$	55.2080			1.94825
$804$	2.86119	+	2.86119i	0.100906	+	0.100906i
$805$	5.53166	−	5.53166i	0.194965	−	0.194965i
$806$	2.25133	−	2.25133i	0.0792997	−	0.0792997i
$807$		−	13.9881i		−	0.492406i
$808$			9.49794i			0.334136i
$809$	−34.4233	+	34.4233i	−1.21026	+	1.21026i	−0.239318	+	0.970941i	$0.576924\pi$
$809$	−34.4233	+	34.4233i	−1.21026	+	1.21026i	−0.970941	+	0.239318i	$0.923076\pi$
$810$	1.52074	−	1.52074i	0.0534332	−	0.0534332i
$811$	11.2629	+	11.2629i	0.395492	+	0.395492i	0.876640	−	0.481147i	$-0.159780\pi$
$811$	11.2629	+	11.2629i	0.395492	+	0.395492i	−0.481147	+	0.876640i	$0.659780\pi$
$812$	−7.86484			−0.276002
$813$	−10.5709	−	10.5709i	−0.370739	−	0.370739i
$814$		−	10.8520i		−	0.380364i
$815$	16.9813			0.594830
$816$		0			0
$817$	−0.512489			−0.0179297
$818$		−	3.59533i		−	0.125708i
$819$	−13.9577	−	13.9577i	−0.487722	−	0.487722i
$820$	−22.8084			−0.796504
$821$	12.0922	+	12.0922i	0.422022	+	0.422022i	0.885899	−	0.463877i	$-0.153542\pi$
$821$	12.0922	+	12.0922i	0.422022	+	0.422022i	−0.463877	+	0.885899i	$0.653542\pi$
$822$	0.0968152	−	0.0968152i	0.00337682	−	0.00337682i
$823$	3.97583	−	3.97583i	0.138589	−	0.138589i	−0.634409	−	0.772998i	$-0.718756\pi$
$823$	3.97583	−	3.97583i	0.138589	−	0.138589i	0.772998	+	0.634409i	$0.218756\pi$
$824$		−	7.13878i		−	0.248691i
$825$		−	2.27033i		−	0.0790426i
$826$	−2.31123	+	2.31123i	−0.0804179	+	0.0804179i
$827$	12.6294	−	12.6294i	0.439168	−	0.439168i	−0.452564	−	0.891732i	$-0.649490\pi$
$827$	12.6294	−	12.6294i	0.439168	−	0.439168i	0.891732	+	0.452564i	$0.149490\pi$
$828$	−5.24742	−	5.24742i	−0.182360	−	0.182360i
$829$	−35.8161			−1.24395			−0.621973	−	0.783039i	$-0.713669\pi$
$829$	−35.8161			−1.24395			−0.621973	+	0.783039i	$0.713669\pi$
$830$	7.82903	+	7.82903i	0.271750	+	0.271750i
$831$		−	14.7787i		−	0.512667i
$832$	−24.7588			−0.858356
$833$		0			0
$834$	3.56717			0.123521
$835$		−	11.9855i		−	0.414774i
$836$	−2.33728	−	2.33728i	−0.0808364	−	0.0808364i
$837$	8.93313			0.308774
$838$	−0.322477	−	0.322477i	−0.0111398	−	0.0111398i
$839$	25.2956	−	25.2956i	0.873300	−	0.873300i	−0.119531	−	0.992830i	$-0.538139\pi$
$839$	25.2956	−	25.2956i	0.873300	−	0.873300i	0.992830	+	0.119531i	$0.0381391\pi$
$840$	−3.69582	+	3.69582i	−0.127518	+	0.127518i
$841$		−	24.0419i		−	0.829031i
$842$			2.78375i			0.0959343i
$843$	17.6105	−	17.6105i	0.606537	−	0.606537i
$844$	28.8614	−	28.8614i	0.993449	−	0.993449i
$845$	−15.3513	−	15.3513i	−0.528102	−	0.528102i
$846$	−6.59802			−0.226845
$847$	19.4633	+	19.4633i	0.668767	+	0.668767i
$848$			34.4005i			1.18132i
$849$	28.3465			0.972849
$850$		0			0
$851$	10.9418			0.375080
$852$		−	16.3969i		−	0.561749i
$853$	7.82546	+	7.82546i	0.267939	+	0.267939i	0.828269	−	0.560331i	$-0.189326\pi$
$853$	7.82546	+	7.82546i	0.267939	+	0.267939i	−0.560331	+	0.828269i	$0.689326\pi$
$854$	−0.120615			−0.00412735
$855$	1.28355	+	1.28355i	0.0438963	+	0.0438963i
$856$	−14.8583	+	14.8583i	−0.507846	+	0.507846i
$857$	−19.1446	+	19.1446i	−0.653968	+	0.653968i	−0.953946	−	0.299978i	$-0.903021\pi$
$857$	−19.1446	+	19.1446i	−0.653968	+	0.653968i	0.299978	+	0.953946i	$0.403021\pi$
$858$		−	7.29530i		−	0.249058i
$859$		−	51.7279i		−	1.76493i	−0.470374	−	0.882467i	$-0.655881\pi$
$859$		−	51.7279i		−	1.76493i	0.470374	−	0.882467i	$-0.344119\pi$
$860$	−4.60312	+	4.60312i	−0.156965	+	0.156965i
$861$	6.04214	−	6.04214i	0.205916	−	0.205916i
$862$	−3.61659	−	3.61659i	−0.123181	−	0.123181i
$863$	−45.4712			−1.54786			−0.773929	−	0.633272i	$-0.781711\pi$
$863$	−45.4712			−1.54786			−0.773929	+	0.633272i	$0.781711\pi$
$864$	12.4721	+	12.4721i	0.424308	+	0.424308i
$865$			30.1056i			1.02362i
$866$	−2.86215			−0.0972598
$867$		0			0
$868$	6.86484			0.233008
$869$			22.4534i			0.761678i
$870$	1.12873	+	1.12873i	0.0382676	+	0.0382676i
$871$	11.5484			0.391302
$872$	−1.78308	−	1.78308i	−0.0603828	−	0.0603828i
$873$	14.6056	−	14.6056i	0.494324	−	0.494324i
$874$	−0.151242	+	0.151242i	−0.00511583	+	0.00511583i
$875$		−	19.8084i		−	0.669646i
$876$		−	18.0172i		−	0.608746i
$877$	−26.5048	+	26.5048i	−0.895002	+	0.895002i	−0.994989	−	0.0999866i	$-0.968120\pi$
$877$	−26.5048	+	26.5048i	−0.895002	+	0.895002i	0.0999866	+	0.994989i	$0.468120\pi$
$878$	9.81231	−	9.81231i	0.331149	−	0.331149i
$879$	8.68738	+	8.68738i	0.293018	+	0.293018i
$880$	−39.1189			−1.31870
$881$	−12.8664	−	12.8664i	−0.433480	−	0.433480i	0.456330	−	0.889810i	$-0.349163\pi$
$881$	−12.8664	−	12.8664i	−0.433480	−	0.433480i	−0.889810	+	0.456330i	$0.849163\pi$
$882$		−	2.68180i		−	0.0903009i
$883$	0.397860			0.0133891			0.00669453	−	0.999978i	$-0.497869\pi$
$883$	0.397860			0.0133891			0.00669453	+	0.999978i	$0.497869\pi$
$884$		0			0
$885$	−10.3369			−0.347470
$886$		−	4.84348i		−	0.162720i
$887$	−16.8174	−	16.8174i	−0.564674	−	0.564674i	0.365958	−	0.930631i	$-0.380741\pi$
$887$	−16.8174	−	16.8174i	−0.564674	−	0.564674i	−0.930631	+	0.365958i	$0.880741\pi$
$888$	−7.31046			−0.245323
$889$	15.3356	+	15.3356i	0.514339	+	0.514339i
$890$	−3.64753	+	3.64753i	−0.122265	+	0.122265i
$891$	−9.44701	+	9.44701i	−0.316487	+	0.316487i
$892$			37.4962i			1.25547i
$893$		−	2.96316i		−	0.0991585i
$894$	1.82869	−	1.82869i	0.0611606	−	0.0611606i
$895$	7.08939	−	7.08939i	0.236972	−	0.236972i
$896$	12.6221	+	12.6221i	0.421673	+	0.421673i
$897$	7.35565			0.245598
$898$	2.51266	+	2.51266i	0.0838487	+	0.0838487i
$899$		−	4.32770i		−	0.144337i
$900$	2.13341			0.0711136
$901$		0			0
$902$	−9.09327			−0.302773
$903$		−	2.43882i		−	0.0811587i
$904$	−11.5406	−	11.5406i	−0.383835	−	0.383835i
$905$	−1.08647			−0.0361154
$906$	−2.97295	−	2.97295i	−0.0987698	−	0.0987698i
$907$	−26.5315	+	26.5315i	−0.880963	+	0.880963i	−0.993633	−	0.112670i	$-0.964060\pi$
$907$	−26.5315	+	26.5315i	−0.880963	+	0.880963i	0.112670	+	0.993633i	$0.464060\pi$
$908$	5.61023	−	5.61023i	0.186182	−	0.186182i
$909$			15.6973i			0.520646i
$910$			7.22668i			0.239562i
$911$	10.4403	−	10.4403i	0.345901	−	0.345901i	−0.512679	−	0.858580i	$-0.671347\pi$
$911$	10.4403	−	10.4403i	0.345901	−	0.345901i	0.858580	+	0.512679i	$0.171347\pi$
$912$	−0.710679	+	0.710679i	−0.0235329	+	0.0235329i
$913$	−48.6350	−	48.6350i	−1.60958	−	1.60958i
$914$	4.08790			0.135216
$915$	−0.269722	−	0.269722i	−0.00891674	−	0.00891674i
$916$			27.2618i			0.900754i
$917$	36.4124			1.20244
$918$		0			0
$919$	−48.5476			−1.60144			−0.800718	−	0.599041i	$-0.795549\pi$
$919$	−48.5476			−1.60144			−0.800718	+	0.599041i	$0.795549\pi$
$920$			5.60813i			0.184894i
$921$	−5.62723	−	5.62723i	−0.185424	−	0.185424i
$922$	−6.77238			−0.223037
$923$	−33.0908	−	33.0908i	−1.08920	−	1.08920i
$924$	11.1226	−	11.1226i	0.365905	−	0.365905i
$925$	−2.22427	+	2.22427i	−0.0731335	+	0.0731335i
$926$		−	0.497007i		−	0.0163327i
$927$		−	11.7983i		−	0.387507i
$928$	6.04214	−	6.04214i	0.198343	−	0.198343i
$929$	7.96451	−	7.96451i	0.261307	−	0.261307i	−0.564278	−	0.825585i	$-0.690845\pi$
$929$	7.96451	−	7.96451i	0.261307	−	0.261307i	0.825585	+	0.564278i	$0.190845\pi$
$930$	−0.985215	−	0.985215i	−0.0323065	−	0.0323065i
$931$	1.20439			0.0394724
$932$	6.81396	+	6.81396i	0.223199	+	0.223199i
$933$			2.06418i			0.0675781i
$934$	−3.71244			−0.121475
$935$		0			0
$936$	14.1506			0.462528
$937$		−	2.39775i		−	0.0783310i	−0.999233	−	0.0391655i	$-0.987530\pi$
$937$		−	2.39775i		−	0.0783310i	0.999233	−	0.0391655i	$-0.0124700\pi$
$938$	−1.12997	−	1.12997i	−0.0368949	−	0.0368949i
$939$	13.3037			0.434148
$940$	−26.6149	−	26.6149i	−0.868081	−	0.868081i
$941$	−24.3101	+	24.3101i	−0.792487	+	0.792487i	−0.981898	−	0.189411i	$-0.939342\pi$
$941$	−24.3101	+	24.3101i	−0.792487	+	0.792487i	0.189411	+	0.981898i	$0.439342\pi$
$942$	−3.88259	+	3.88259i	−0.126502	+	0.126502i
$943$		−	9.16849i		−	0.298567i
$944$			16.4798i			0.536371i
$945$	−14.3375	+	14.3375i	−0.466399	+	0.466399i
$946$	−1.83518	+	1.83518i	−0.0596668	+	0.0596668i
$947$	14.5165	+	14.5165i	0.471722	+	0.471722i	0.902472	−	0.430749i	$-0.141751\pi$
$947$	14.5165	+	14.5165i	0.471722	+	0.471722i	−0.430749	+	0.902472i	$0.641751\pi$
$948$	7.32770			0.237993
$949$	−36.3608	−	36.3608i	−1.18032	−	1.18032i
$950$		−	0.0614894i		−	0.00199498i
$951$	9.09091			0.294793
$952$		0			0
$953$	16.5517			0.536162			0.268081	−	0.963396i	$-0.413611\pi$
$953$	16.5517			0.536162			0.268081	+	0.963396i	$0.413611\pi$
$954$		−	8.08378i		−	0.261722i
$955$	−2.37528	−	2.37528i	−0.0768623	−	0.0768623i
$956$	−29.7888			−0.963439
$957$	−7.01183	−	7.01183i	−0.226660	−	0.226660i
$958$	9.54492	−	9.54492i	0.308382	−	0.308382i
$959$	0.595772	−	0.595772i	0.0192385	−	0.0192385i
$960$			10.8348i			0.349692i
$961$		−	27.2226i		−	0.878147i
$962$	−7.14731	+	7.14731i	−0.230438	+	0.230438i
$963$	−24.5563	+	24.5563i	−0.791317	+	0.791317i
$964$	24.0755	+	24.0755i	0.775419	+	0.775419i
$965$	58.0360			1.86825
$966$	−0.719726	−	0.719726i	−0.0231568	−	0.0231568i
$967$		−	3.92665i		−	0.126273i	−0.998005	−	0.0631363i	$-0.979890\pi$
$967$		−	3.92665i		−	0.126273i	0.998005	−	0.0631363i	$-0.0201103\pi$
$968$	−19.7324			−0.634222
$969$		0			0
$970$	−7.56212			−0.242805
$971$			4.25402i			0.136518i	0.997668	+	0.0682590i	$0.0217444\pi$
$971$			4.25402i			0.136518i	−0.997668	+	0.0682590i	$0.978256\pi$
$972$	21.4073	+	21.4073i	0.686641	+	0.686641i
$973$	21.9513			0.703726
$974$	−9.08967	−	9.08967i	−0.291252	−	0.291252i
$975$	−1.49527	+	1.49527i	−0.0478869	+	0.0478869i
$976$	−0.430010	+	0.430010i	−0.0137643	+	0.0137643i
$977$		−	48.5431i		−	1.55303i	−0.630097	−	0.776516i	$-0.716985\pi$
$977$		−	48.5431i		−	1.55303i	0.630097	−	0.776516i	$-0.283015\pi$
$978$		−	2.20945i		−	0.0706503i
$979$	22.6589	−	22.6589i	0.724183	−	0.724183i
$980$	10.8177	−	10.8177i	0.345560	−	0.345560i
$981$	−2.94691	−	2.94691i	−0.0940875	−	0.0940875i
$982$	8.82739			0.281693
$983$	24.7910	+	24.7910i	0.790709	+	0.790709i	0.981609	−	0.190900i	$-0.0611407\pi$
$983$	24.7910	+	24.7910i	0.790709	+	0.790709i	−0.190900	+	0.981609i	$0.561141\pi$
$984$			6.12567i			0.195279i
$985$	−27.6076			−0.879652
$986$		0			0
$987$	14.1010			0.448840
$988$			3.07873i			0.0979473i
$989$	−1.85036	−	1.85036i	−0.0588379	−	0.0588379i
$990$	9.19253			0.292158
$991$	37.6177	+	37.6177i	1.19497	+	1.19497i	0.975655	+	0.219310i	$0.0703807\pi$
$991$	37.6177	+	37.6177i	1.19497	+	1.19497i	0.219310	+	0.975655i	$0.429619\pi$
$992$	−5.27390	+	5.27390i	−0.167446	+	0.167446i
$993$	11.3524	−	11.3524i	0.360257	−	0.360257i
$994$			6.47565i			0.205395i
$995$			48.1671i			1.52700i
$996$	−15.8721	+	15.8721i	−0.502927	+	0.502927i
$997$	−15.9660	+	15.9660i	−0.505649	+	0.505649i	−0.913188	−	0.407539i	$-0.866387\pi$
$997$	−15.9660	+	15.9660i	−0.505649	+	0.505649i	0.407539	+	0.913188i	$0.366387\pi$
$998$	5.35941	+	5.35941i	0.169649	+	0.169649i
$999$	−28.3601			−0.897274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.c.d.251.3		12
17.2	even	8		289.2.a.e.1.2	yes	3
17.3	odd	16		289.2.d.f.134.3		24
17.4	even	4	inner	289.2.c.d.38.3		12
17.5	odd	16		289.2.d.f.155.4		24
17.6	odd	16		289.2.d.f.179.3		24
17.7	odd	16		289.2.d.f.110.3		24
17.8	even	8		289.2.b.d.288.4		6
17.9	even	8		289.2.b.d.288.3		6
17.10	odd	16		289.2.d.f.110.4		24
17.11	odd	16		289.2.d.f.179.4		24
17.12	odd	16		289.2.d.f.155.3		24
17.13	even	4	inner	289.2.c.d.38.4		12
17.14	odd	16		289.2.d.f.134.4		24
17.15	even	8		289.2.a.d.1.2	✓	3
17.16	even	2	inner	289.2.c.d.251.4		12
51.2	odd	8		2601.2.a.w.1.2		3
51.32	odd	8		2601.2.a.x.1.2		3
68.15	odd	8		4624.2.a.bg.1.1		3
68.19	odd	8		4624.2.a.bd.1.3		3
85.19	even	8		7225.2.a.s.1.2		3
85.49	even	8		7225.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.2	✓	3	17.15	even	8
289.2.a.e.1.2	yes	3	17.2	even	8
289.2.b.d.288.3		6	17.9	even	8
289.2.b.d.288.4		6	17.8	even	8
289.2.c.d.38.3		12	17.4	even	4	inner
289.2.c.d.38.4		12	17.13	even	4	inner
289.2.c.d.251.3		12	1.1	even	1	trivial
289.2.c.d.251.4		12	17.16	even	2	inner
289.2.d.f.110.3		24	17.7	odd	16
289.2.d.f.110.4		24	17.10	odd	16
289.2.d.f.134.3		24	17.3	odd	16
289.2.d.f.134.4		24	17.14	odd	16
289.2.d.f.155.3		24	17.12	odd	16
289.2.d.f.155.4		24	17.5	odd	16
289.2.d.f.179.3		24	17.6	odd	16
289.2.d.f.179.4		24	17.11	odd	16
2601.2.a.w.1.2		3	51.2	odd	8
2601.2.a.x.1.2		3	51.32	odd	8
4624.2.a.bd.1.3		3	68.19	odd	8
4624.2.a.bg.1.1		3	68.15	odd	8
7225.2.a.s.1.2		3	85.19	even	8
7225.2.a.t.1.2		3	85.49	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)

\(f(q)\)	\(=\)	\(q-0.347296i q^{2} +(-0.621819 - 0.621819i) q^{3} +1.87939 q^{4} +(-1.65979 - 1.65979i) q^{5} +(-0.215956 + 0.215956i) q^{6} +(-1.32893 + 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +O(q^{10})\)	\(q-0.347296i q^{2} +(-0.621819 - 0.621819i) q^{3} +1.87939 q^{4} +(-1.65979 - 1.65979i) q^{5} +(-0.215956 + 0.215956i) q^{6} +(-1.32893 + 1.32893i) q^{7} -1.34730i q^{8} -2.22668i q^{9} +(-0.576439 + 0.576439i) q^{10} +(3.58091 - 3.58091i) q^{11} +(-1.16864 - 1.16864i) q^{12} -4.71688 q^{13} +(0.461531 + 0.461531i) q^{14} +2.06418i q^{15} +3.29086 q^{16} -0.773318 q^{18} -0.347296i q^{19} +(-3.11938 - 3.11938i) q^{20} +1.65270 q^{21} +(-1.24364 - 1.24364i) q^{22} +(1.25393 - 1.25393i) q^{23} +(-0.837775 + 0.837775i) q^{24} +0.509800i q^{25} +1.63816i q^{26} +(-3.25005 + 3.25005i) q^{27} +(-2.49756 + 2.49756i) q^{28} +(1.57450 + 1.57450i) q^{29} +0.716881 q^{30} +(-1.37431 - 1.37431i) q^{31} -3.83750i q^{32} -4.45336 q^{33} +4.41147 q^{35} -4.18479i q^{36} +(4.36302 + 4.36302i) q^{37} -0.120615 q^{38} +(2.93305 + 2.93305i) q^{39} +(-2.23623 + 2.23623i) q^{40} +(3.65592 - 3.65592i) q^{41} -0.573978i q^{42} -1.47565i q^{43} +(6.72992 - 6.72992i) q^{44} +(-3.69582 + 3.69582i) q^{45} +(-0.435484 - 0.435484i) q^{46} +8.53209 q^{47} +(-2.04632 - 2.04632i) q^{48} +3.46791i q^{49} +0.177052 q^{50} -8.86484 q^{52} +10.4534i q^{53} +(1.12873 + 1.12873i) q^{54} -11.8871 q^{55} +(1.79046 + 1.79046i) q^{56} +(-0.215956 + 0.215956i) q^{57} +(0.546819 - 0.546819i) q^{58} +5.00774i q^{59} +3.87939i q^{60} +(-0.130668 + 0.130668i) q^{61} +(-0.477292 + 0.477292i) q^{62} +(2.95910 + 2.95910i) q^{63} +5.24897 q^{64} +(7.82903 + 7.82903i) q^{65} +1.54664i q^{66} -2.44831 q^{67} -1.55943 q^{69} -1.53209i q^{70} +(7.01540 + 7.01540i) q^{71} -3.00000 q^{72} +(7.70865 + 7.70865i) q^{73} +(1.51526 - 1.51526i) q^{74} +(0.317004 - 0.317004i) q^{75} -0.652704i q^{76} +9.51754i q^{77} +(1.01864 - 1.01864i) q^{78} +(-3.13514 + 3.13514i) q^{79} +(-5.46213 - 5.46213i) q^{80} -2.63816 q^{81} +(-1.26969 - 1.26969i) q^{82} -13.5817i q^{83} +3.10607 q^{84} -0.512489 q^{86} -1.95811i q^{87} +(-4.82455 - 4.82455i) q^{88} +6.32770 q^{89} +(1.28355 + 1.28355i) q^{90} +(6.26839 - 6.26839i) q^{91} +(2.35661 - 2.35661i) q^{92} +1.70914i q^{93} -2.96316i q^{94} +(-0.576439 + 0.576439i) q^{95} +(-2.38623 + 2.38623i) q^{96} +(6.55934 + 6.55934i) q^{97} +1.20439 q^{98} +(-7.97356 - 7.97356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 24 q^{13} - 24 q^{16} - 36 q^{18} + 24 q^{21} - 24 q^{30} + 12 q^{35} - 24 q^{38} + 84 q^{47} + 84 q^{50} - 12 q^{52} - 24 q^{55} + 12 q^{64} - 36 q^{67} + 84 q^{69} - 36 q^{72} + 36 q^{81} - 12 q^{84} + 24 q^{86} + 60 q^{89} + 12 q^{98}+O(q^{100}) \) 12 * q - 24 * q^13 - 24 * q^16 - 36 * q^18 + 24 * q^21 - 24 * q^30 + 12 * q^35 - 24 * q^38 + 84 * q^47 + 84 * q^50 - 12 * q^52 - 24 * q^55 + 12 * q^64 - 36 * q^67 + 84 * q^69 - 36 * q^72 + 36 * q^81 - 12 * q^84 + 24 * q^86 + 60 * q^89 + 12 * q^98

Introduction

L-functions

Modular forms

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