LMFDB - Embedded newform 300.2.o.a.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(109,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("300.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.o (of order $10$, degree $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	300.289
Dual form			300.2.o.a.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{3} +(-1.64247 - 1.51733i) q^{5} -3.78808i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{3} +(-1.64247 - 1.51733i) q^{5} -3.78808i q^{7} +(0.809017 + 0.587785i) q^{9} +(0.653426 - 0.474742i) q^{11} +(2.79168 - 3.84242i) q^{13} +(-1.09320 - 1.95062i) q^{15} +(-1.09262 + 0.355012i) q^{17} +(-0.00463870 - 0.0142765i) q^{19} +(1.17058 - 3.60268i) q^{21} +(3.68422 + 5.07089i) q^{23} +(0.395416 + 4.98434i) q^{25} +(0.587785 + 0.809017i) q^{27} +(-1.14365 + 3.51978i) q^{29} +(-0.488893 - 1.50466i) q^{31} +(0.768148 - 0.249586i) q^{33} +(-5.74777 + 6.22181i) q^{35} +(5.02074 - 6.91045i) q^{37} +(3.84242 - 2.79168i) q^{39} +(-9.30279 - 6.75887i) q^{41} +10.2458i q^{43} +(-0.436922 - 2.19297i) q^{45} +(0.500524 + 0.162630i) q^{47} -7.34957 q^{49} -1.14884 q^{51} +(-2.80539 - 0.911527i) q^{53} +(-1.79357 - 0.211714i) q^{55} -0.0150112i q^{57} +(9.25803 + 6.72635i) q^{59} +(-2.54203 + 1.84689i) q^{61} +(2.22658 - 3.06462i) q^{63} +(-10.4155 + 2.07516i) q^{65} +(12.6312 - 4.10412i) q^{67} +(1.93691 + 5.96119i) q^{69} +(-1.51826 + 4.67271i) q^{71} +(2.75001 + 3.78507i) q^{73} +(-1.16418 + 4.86258i) q^{75} +(-1.79836 - 2.47523i) q^{77} +(-2.86507 + 8.81777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.35402 + 0.439947i) q^{83} +(2.33326 + 1.07476i) q^{85} +(-2.17534 + 2.99410i) q^{87} +(-13.0306 + 9.46730i) q^{89} +(-14.5554 - 10.5751i) q^{91} -1.58209i q^{93} +(-0.0140432 + 0.0304871i) q^{95} +(-7.66744 - 2.49130i) q^{97} +0.807679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^5 + 6 * q^9	$ 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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			0
$2$		0			0
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$		0			0
$5$	−1.64247	−	1.51733i	−0.734535	−	0.678571i
$5$	−1.64247	−	1.51733i	−0.734535	−	0.678571i
$6$		0			0
$7$		−	3.78808i		−	1.43176i	−0.698223	−	0.715880i	$-0.746026\pi$
$7$		−	3.78808i		−	1.43176i	0.698223	−	0.715880i	$-0.253974\pi$
$8$		0			0
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	0.653426	−	0.474742i	0.197015	−	0.143140i	−0.484904	−	0.874567i	$-0.661145\pi$
$11$	0.653426	−	0.474742i	0.197015	−	0.143140i	0.681919	+	0.731427i	$0.261145\pi$
$12$		0			0
$13$	2.79168	−	3.84242i	0.774274	−	1.06570i	−0.221617	−	0.975134i	$-0.571133\pi$
$13$	2.79168	−	3.84242i	0.774274	−	1.06570i	0.995891	−	0.0905626i	$-0.0288665\pi$
$14$		0			0
$15$	−1.09320	−	1.95062i	−0.282263	−	0.503647i
$16$		0			0
$17$	−1.09262	+	0.355012i	−0.264998	+	0.0861032i	−0.438503	−	0.898730i	$-0.644491\pi$
$17$	−1.09262	+	0.355012i	−0.264998	+	0.0861032i	0.173504	+	0.984833i	$0.444491\pi$
$18$		0			0
$19$	−0.00463870	−	0.0142765i	−0.00106419	−	0.00327524i	0.950523	−	0.310654i	$-0.100548\pi$
$19$	−0.00463870	−	0.0142765i	−0.00106419	−	0.00327524i	−0.951587	+	0.307379i	$0.900548\pi$
$20$		0			0
$21$	1.17058	−	3.60268i	0.255442	−	0.786169i
$22$		0			0
$23$	3.68422	+	5.07089i	0.768213	+	1.05735i	0.996486	+	0.0837569i	$0.0266919\pi$
$23$	3.68422	+	5.07089i	0.768213	+	1.05735i	−0.228274	+	0.973597i	$0.573308\pi$
$24$		0			0
$25$	0.395416	+	4.98434i	0.0790832	+	0.996868i
$26$		0			0
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$		0			0
$29$	−1.14365	+	3.51978i	−0.212370	+	0.653607i	0.786960	+	0.617004i	$0.211654\pi$
$29$	−1.14365	+	3.51978i	−0.212370	+	0.653607i	−0.999330	+	0.0366030i	$0.988346\pi$
$30$		0			0
$31$	−0.488893	−	1.50466i	−0.0878078	−	0.270245i	0.897505	−	0.441005i	$-0.145378\pi$
$31$	−0.488893	−	1.50466i	−0.0878078	−	0.270245i	−0.985313	+	0.170760i	$0.945378\pi$
$32$		0			0
$33$	0.768148	−	0.249586i	0.133717	−	0.0434474i
$34$		0			0
$35$	−5.74777	+	6.22181i	−0.971551	+	1.05168i
$36$		0			0
$37$	5.02074	−	6.91045i	0.825404	−	1.13607i	−0.163357	−	0.986567i	$-0.552232\pi$
$37$	5.02074	−	6.91045i	0.825404	−	1.13607i	0.988761	−	0.149504i	$-0.0477678\pi$
$38$		0			0
$39$	3.84242	−	2.79168i	0.615280	−	0.447027i
$40$		0			0
$41$	−9.30279	−	6.75887i	−1.45285	−	1.05556i	−0.985155	−	0.171669i	$-0.945084\pi$
$41$	−9.30279	−	6.75887i	−1.45285	−	1.05556i	−0.467697	−	0.883889i	$-0.654916\pi$
$42$		0			0
$43$			10.2458i			1.56247i	0.624238	+	0.781234i	$0.285409\pi$
$43$			10.2458i			1.56247i	−0.624238	+	0.781234i	$0.714591\pi$
$44$		0			0
$45$	−0.436922	−	2.19297i	−0.0651324	−	0.326908i
$46$		0			0
$47$	0.500524	+	0.162630i	0.0730090	+	0.0237221i	0.345294	−	0.938495i	$-0.387779\pi$
$47$	0.500524	+	0.162630i	0.0730090	+	0.0237221i	−0.272285	+	0.962217i	$0.587779\pi$
$48$		0			0
$49$	−7.34957			−1.04994
$50$		0			0
$51$	−1.14884			−0.160870
$52$		0			0
$53$	−2.80539	−	0.911527i	−0.385350	−	0.125208i	0.109934	−	0.993939i	$-0.464936\pi$
$53$	−2.80539	−	0.911527i	−0.385350	−	0.125208i	−0.495284	+	0.868731i	$0.664936\pi$
$54$		0			0
$55$	−1.79357	−	0.211714i	−0.241845	−	0.0285475i
$56$		0			0
$57$		−	0.0150112i		−	0.00198828i
$58$		0			0
$59$	9.25803	+	6.72635i	1.20529	+	0.875696i	0.994795	−	0.101898i	$-0.0324916\pi$
$59$	9.25803	+	6.72635i	1.20529	+	0.875696i	0.210498	+	0.977594i	$0.432492\pi$
$60$		0			0
$61$	−2.54203	+	1.84689i	−0.325473	+	0.236470i	−0.738507	−	0.674245i	$-0.764469\pi$
$61$	−2.54203	+	1.84689i	−0.325473	+	0.236470i	0.413034	+	0.910716i	$0.364469\pi$
$62$		0			0
$63$	2.22658	−	3.06462i	0.280523	−	0.386106i
$64$		0			0
$65$	−10.4155	+	2.07516i	−1.29188	+	0.257392i
$66$		0			0
$67$	12.6312	−	4.10412i	1.54314	−	0.501398i	0.590901	−	0.806744i	$-0.298772\pi$
$67$	12.6312	−	4.10412i	1.54314	−	0.501398i	0.952241	+	0.305346i	$0.0987722\pi$
$68$		0			0
$69$	1.93691	+	5.96119i	0.233176	+	0.717643i
$70$		0			0
$71$	−1.51826	+	4.67271i	−0.180184	+	0.554549i	−0.999832	−	0.0183179i	$-0.994169\pi$
$71$	−1.51826	+	4.67271i	−0.180184	+	0.554549i	0.819648	+	0.572867i	$0.194169\pi$
$72$		0			0
$73$	2.75001	+	3.78507i	0.321865	+	0.443009i	0.939035	−	0.343820i	$-0.111721\pi$
$73$	2.75001	+	3.78507i	0.321865	+	0.443009i	−0.617171	+	0.786829i	$0.711721\pi$
$74$		0			0
$75$	−1.16418	+	4.86258i	−0.134428	+	0.561482i
$76$		0			0
$77$	−1.79836	−	2.47523i	−0.204942	−	0.282079i
$78$		0			0
$79$	−2.86507	+	8.81777i	−0.322345	+	0.992076i	0.650280	+	0.759695i	$0.274652\pi$
$79$	−2.86507	+	8.81777i	−0.322345	+	0.992076i	−0.972625	+	0.232381i	$0.925348\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−1.35402	+	0.439947i	−0.148623	+	0.0482904i	−0.382384	−	0.924004i	$-0.624897\pi$
$83$	−1.35402	+	0.439947i	−0.148623	+	0.0482904i	0.233761	+	0.972294i	$0.424897\pi$
$84$		0			0
$85$	2.33326	+	1.07476i	0.253078	+	0.116574i
$86$		0			0
$87$	−2.17534	+	2.99410i	−0.233221	+	0.321002i
$88$		0			0
$89$	−13.0306	+	9.46730i	−1.38124	+	1.00353i	−0.384480	+	0.923133i	$0.625619\pi$
$89$	−13.0306	+	9.46730i	−1.38124	+	1.00353i	−0.996763	+	0.0803985i	$0.974381\pi$
$90$		0			0
$91$	−14.5554	−	10.5751i	−1.52582	−	1.10857i
$92$		0			0
$93$		−	1.58209i		−	0.164055i
$94$		0			0
$95$	−0.0140432	+	0.0304871i	−0.00144080	+	0.00312791i
$96$		0			0
$97$	−7.66744	−	2.49130i	−0.778511	−	0.252954i	−0.107307	−	0.994226i	$-0.534223\pi$
$97$	−7.66744	−	2.49130i	−0.778511	−	0.252954i	−0.671204	+	0.741272i	$0.734223\pi$
$98$		0			0
$99$	0.807679			0.0811748
$100$		0			0
$101$	11.6496			1.15918			0.579590	−	0.814908i	$-0.303213\pi$
$101$	11.6496			1.15918			0.579590	+	0.814908i	$0.303213\pi$
$102$		0			0
$103$	17.9216	+	5.82307i	1.76587	+	0.573764i	0.997781	−	0.0665845i	$-0.0212102\pi$
$103$	17.9216	+	5.82307i	1.76587	+	0.573764i	0.768084	+	0.640349i	$0.221210\pi$
$104$		0			0
$105$	−7.38910	+	4.14114i	−0.721103	+	0.404133i
$106$		0			0
$107$			14.3957i			1.39168i	0.718195	+	0.695842i	$0.244969\pi$
$107$			14.3957i			1.39168i	−0.718195	+	0.695842i	$0.755031\pi$
$108$		0			0
$109$	−4.66144	−	3.38673i	−0.446485	−	0.324390i	0.341722	−	0.939801i	$-0.388990\pi$
$109$	−4.66144	−	3.38673i	−0.446485	−	0.324390i	−0.788206	+	0.615411i	$0.788990\pi$
$110$		0			0
$111$	6.91045	−	5.02074i	0.655911	−	0.476547i
$112$		0			0
$113$	10.5368	−	14.5027i	0.991223	−	1.36430i	0.0606641	−	0.998158i	$-0.480678\pi$
$113$	10.5368	−	14.5027i	0.991223	−	1.36430i	0.930559	−	0.366143i	$-0.119322\pi$
$114$		0			0
$115$	1.64300	−	13.9190i	0.153211	−	1.29795i
$116$		0			0
$117$	4.51704	−	1.46767i	0.417600	−	0.135687i
$118$		0			0
$119$	1.34482	+	4.13892i	0.123279	+	0.379414i
$120$		0			0
$121$	−3.19760	+	9.84120i	−0.290691	+	0.894655i
$122$		0			0
$123$	−6.75887	−	9.30279i	−0.609427	−	0.838804i
$124$		0			0
$125$	6.91343	−	8.78661i	0.618356	−	0.785898i
$126$		0			0
$127$	−1.34592	−	1.85250i	−0.119431	−	0.164382i	0.745116	−	0.666935i	$-0.232394\pi$
$127$	−1.34592	−	1.85250i	−0.119431	−	0.164382i	−0.864547	+	0.502553i	$0.832394\pi$
$128$		0			0
$129$	−3.16612	+	9.74432i	−0.278762	+	0.857940i
$130$		0			0
$131$	−2.17840	−	6.70444i	−0.190328	−	0.585769i	0.809671	−	0.586883i	$-0.199645\pi$
$131$	−2.17840	−	6.70444i	−0.190328	−	0.585769i	−0.999999	+	0.00111420i	$0.999645\pi$
$132$		0			0
$133$	−0.0540804	+	0.0175718i	−0.00468937	+	0.00152367i
$134$		0			0
$135$	0.262127	−	2.22065i	0.0225603	−	0.191123i
$136$		0			0
$137$	12.8918	−	17.7441i	1.10142	−	1.51598i	0.267940	−	0.963436i	$-0.413657\pi$
$137$	12.8918	−	17.7441i	1.10142	−	1.51598i	0.833484	−	0.552544i	$-0.186343\pi$
$138$		0			0
$139$	7.86171	−	5.71187i	0.666822	−	0.484474i	−0.202138	−	0.979357i	$-0.564789\pi$
$139$	7.86171	−	5.71187i	0.666822	−	0.484474i	0.868960	+	0.494883i	$0.164789\pi$
$140$		0			0
$141$	0.425771	+	0.309341i	0.0358564	+	0.0260512i
$142$		0			0
$143$		−	3.83607i		−	0.320788i
$144$		0			0
$145$	7.21907	−	4.04584i	0.599512	−	0.335989i
$146$		0			0
$147$	−6.98985	−	2.27114i	−0.576513	−	0.187321i
$148$		0			0
$149$	13.9712			1.14457			0.572284	−	0.820056i	$-0.306058\pi$
$149$	13.9712			1.14457			0.572284	+	0.820056i	$0.306058\pi$
$150$		0			0
$151$	−20.1871			−1.64280			−0.821400	−	0.570352i	$-0.806807\pi$
$151$	−20.1871			−1.64280			−0.821400	+	0.570352i	$0.806807\pi$
$152$		0			0
$153$	−1.09262	−	0.355012i	−0.0883328	−	0.0287011i
$154$		0			0
$155$	−1.48007	+	3.21317i	−0.118882	+	0.258088i
$156$		0			0
$157$		−	7.76546i		−	0.619751i	−0.950777	−	0.309876i	$-0.899713\pi$
$157$		−	7.76546i		−	0.619751i	0.950777	−	0.309876i	$-0.100287\pi$
$158$		0			0
$159$	−2.38641	−	1.73383i	−0.189255	−	0.137502i
$160$		0			0
$161$	19.2090	−	13.9561i	1.51388	−	1.09990i
$162$		0			0
$163$	−8.16480	+	11.2379i	−0.639517	+	0.880219i	−0.998590	−	0.0530901i	$-0.983093\pi$
$163$	−8.16480	+	11.2379i	−0.639517	+	0.880219i	0.359073	+	0.933310i	$0.383093\pi$
$164$		0			0
$165$	−1.64037	−	0.755596i	−0.127702	−	0.0588231i
$166$		0			0
$167$	−2.75604	+	0.895491i	−0.213269	+	0.0692952i	−0.413703	−	0.910412i	$-0.635765\pi$
$167$	−2.75604	+	0.895491i	−0.213269	+	0.0692952i	0.200434	+	0.979707i	$0.435765\pi$
$168$		0			0
$169$	−2.95350	−	9.08992i	−0.227192	−	0.699225i
$170$		0			0
$171$	0.00463870	−	0.0142765i	0.000354730	−	0.00109175i
$172$		0			0
$173$	−8.95423	−	12.3244i	−0.680777	−	0.937009i	0.319166	−	0.947699i	$-0.396597\pi$
$173$	−8.95423	−	12.3244i	−0.680777	−	0.937009i	−0.999943	+	0.0106895i	$0.996597\pi$
$174$		0			0
$175$	18.8811	−	1.49787i	1.42728	−	0.113228i
$176$		0			0
$177$	6.72635	+	9.25803i	0.505583	+	0.695876i
$178$		0			0
$179$	7.20182	−	22.1649i	0.538290	−	1.65669i	−0.198142	−	0.980173i	$-0.563491\pi$
$179$	7.20182	−	22.1649i	0.538290	−	1.65669i	0.736432	−	0.676512i	$-0.236509\pi$
$180$		0			0
$181$	5.46913	+	16.8322i	0.406517	+	1.25113i	0.919622	+	0.392805i	$0.128495\pi$
$181$	5.46913	+	16.8322i	0.406517	+	1.25113i	−0.513105	+	0.858326i	$0.671505\pi$
$182$		0			0
$183$	−2.98833	+	0.970968i	−0.220904	+	0.0717760i
$184$		0			0
$185$	−18.7319	+	3.73209i	−1.37719	+	0.274389i
$186$		0			0
$187$	−0.545404	+	0.750685i	−0.0398839	+	0.0548955i
$188$		0			0
$189$	3.06462	−	2.22658i	0.222919	−	0.161960i
$190$		0			0
$191$	−7.57575	−	5.50411i	−0.548162	−	0.398263i	0.278945	−	0.960307i	$-0.410015\pi$
$191$	−7.57575	−	5.50411i	−0.548162	−	0.398263i	−0.827107	+	0.562044i	$0.810015\pi$
$192$		0			0
$193$			18.9309i			1.36268i	0.731969	+	0.681338i	$0.238602\pi$
$193$			18.9309i			1.36268i	−0.731969	+	0.681338i	$0.761398\pi$
$194$		0			0
$195$	−10.5470	−	1.24497i	−0.755284	−	0.0891541i
$196$		0			0
$197$	7.17436	+	2.33109i	0.511152	+	0.166083i	0.553226	−	0.833031i	$-0.313397\pi$
$197$	7.17436	+	2.33109i	0.511152	+	0.166083i	−0.0420739	+	0.999114i	$0.513397\pi$
$198$		0			0
$199$	−3.58560			−0.254176			−0.127088	−	0.991891i	$-0.540563\pi$
$199$	−3.58560			−0.254176			−0.127088	+	0.991891i	$0.540563\pi$
$200$		0			0
$201$	13.2812			0.936783
$202$		0			0
$203$	13.3332	+	4.33223i	0.935808	+	0.304063i
$204$		0			0
$205$	5.02411	+	25.2166i	0.350899	+	1.76121i
$206$		0			0
$207$			6.26797i			0.435654i
$208$		0			0
$209$	−0.00980868	−	0.00712642i	−0.000678480	−	0.000492945i
$210$		0			0
$211$	−1.68674	+	1.22549i	−0.116120	+	0.0843663i	−0.644330	−	0.764748i	$-0.722864\pi$
$211$	−1.68674	+	1.22549i	−0.116120	+	0.0843663i	0.528210	+	0.849114i	$0.322864\pi$
$212$		0			0
$213$	−2.88790	+	3.97485i	−0.197875	+	0.272352i
$214$		0			0
$215$	15.5462	−	16.8284i	1.06025	−	1.14769i
$216$		0			0
$217$	−5.69977	+	1.85197i	−0.386926	+	0.125720i
$218$		0			0
$219$	1.44577	+	4.44962i	0.0976960	+	0.300677i
$220$		0			0
$221$	−1.68613	+	5.18938i	−0.113421	+	0.349075i
$222$		0			0
$223$	−8.25091	−	11.3564i	−0.552522	−	0.760481i	0.437830	−	0.899058i	$-0.355747\pi$
$223$	−8.25091	−	11.3564i	−0.552522	−	0.760481i	−0.990352	+	0.138577i	$0.955747\pi$
$224$		0			0
$225$	−2.60982	+	4.26484i	−0.173988	+	0.284322i
$226$		0			0
$227$	−1.48995	−	2.05074i	−0.0988915	−	0.136112i	0.756704	−	0.653758i	$-0.226809\pi$
$227$	−1.48995	−	2.05074i	−0.0988915	−	0.136112i	−0.855595	+	0.517646i	$0.826809\pi$
$228$		0			0
$229$	5.10687	−	15.7173i	0.337472	−	1.03863i	−0.628020	−	0.778197i	$-0.716134\pi$
$229$	5.10687	−	15.7173i	0.337472	−	1.03863i	0.965492	−	0.260434i	$-0.0838656\pi$
$230$		0			0
$231$	−0.945454	−	2.90981i	−0.0622063	−	0.191451i
$232$		0			0
$233$	−25.2228	+	8.19539i	−1.65240	+	0.536898i	−0.979259	−	0.202614i	$-0.935056\pi$
$233$	−25.2228	+	8.19539i	−1.65240	+	0.536898i	−0.673143	+	0.739512i	$0.735056\pi$
$234$		0			0
$235$	−0.575332	−	1.02658i	−0.0375305	−	0.0669664i
$236$		0			0
$237$	−5.44968	+	7.50084i	−0.353995	+	0.487232i
$238$		0			0
$239$	−6.03839	+	4.38714i	−0.390591	+	0.283781i	−0.765698	−	0.643201i	$-0.777606\pi$
$239$	−6.03839	+	4.38714i	−0.390591	+	0.283781i	0.375107	+	0.926982i	$0.377606\pi$
$240$		0			0
$241$	−8.33107	−	6.05288i	−0.536651	−	0.389900i	0.286189	−	0.958173i	$-0.407612\pi$
$241$	−8.33107	−	6.05288i	−0.536651	−	0.389900i	−0.822840	+	0.568273i	$0.807612\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	12.0714	+	11.1517i	0.771216	+	0.712458i
$246$		0			0
$247$	−0.0678060	−	0.0220315i	−0.00431439	−	0.00140183i
$248$		0			0
$249$	−1.42370			−0.0902231
$250$		0			0
$251$	19.5809			1.23593			0.617967	−	0.786204i	$-0.287956\pi$
$251$	19.5809			1.23593			0.617967	+	0.786204i	$0.287956\pi$
$252$		0			0
$253$	4.81473	+	1.56440i	0.302699	+	0.0983530i
$254$		0			0
$255$	1.88694	+	1.74318i	0.118165	+	0.109162i
$256$		0			0
$257$			5.98030i			0.373041i	0.982451	+	0.186520i	$0.0597210\pi$
$257$			5.98030i			0.373041i	−0.982451	+	0.186520i	$0.940279\pi$
$258$		0			0
$259$	−26.1774	−	19.0190i	−1.62658	−	1.18178i
$260$		0			0
$261$	−2.99410	+	2.17534i	−0.185330	+	0.134650i
$262$		0			0
$263$	3.56808	−	4.91104i	0.220017	−	0.302827i	−0.684713	−	0.728813i	$-0.740072\pi$
$263$	3.56808	−	4.91104i	0.220017	−	0.302827i	0.904730	+	0.425985i	$0.140072\pi$
$264$		0			0
$265$	3.22469	+	5.75386i	0.198091	+	0.353457i
$266$		0			0
$267$	−15.3184	+	4.97725i	−0.937472	+	0.304603i
$268$		0			0
$269$	−2.97152	−	9.14540i	−0.181177	−	0.557605i	0.818685	−	0.574243i	$-0.194704\pi$
$269$	−2.97152	−	9.14540i	−0.181177	−	0.557605i	−0.999862	+	0.0166382i	$0.994704\pi$
$270$		0			0
$271$	−9.40263	+	28.9383i	−0.571169	+	1.75788i	0.0776990	+	0.996977i	$0.475243\pi$
$271$	−9.40263	+	28.9383i	−0.571169	+	1.75788i	−0.648868	+	0.760901i	$0.724757\pi$
$272$		0			0
$273$	−10.5751	−	14.5554i	−0.640036	−	0.880934i
$274$		0			0
$275$	2.62465	+	3.06918i	0.158272	+	0.185078i
$276$		0			0
$277$	−4.23436	−	5.82810i	−0.254418	−	0.350176i	0.662634	−	0.748943i	$-0.269438\pi$
$277$	−4.23436	−	5.82810i	−0.254418	−	0.350176i	−0.917052	+	0.398767i	$0.869438\pi$
$278$		0			0
$279$	0.488893	−	1.50466i	0.0292693	−	0.0900815i
$280$		0			0
$281$	9.20758	+	28.3380i	0.549278	+	1.69050i	0.710594	+	0.703602i	$0.248426\pi$
$281$	9.20758	+	28.3380i	0.549278	+	1.69050i	−0.161316	+	0.986903i	$0.551574\pi$
$282$		0			0
$283$	−8.39215	+	2.72677i	−0.498861	+	0.162090i	−0.547631	−	0.836720i	$-0.684470\pi$
$283$	−8.39215	+	2.72677i	−0.498861	+	0.162090i	0.0487693	+	0.998810i	$0.484470\pi$
$284$		0			0
$285$	−0.0227769	+	0.0246554i	−0.00134919	+	0.00146046i
$286$		0			0
$287$	−25.6032	+	35.2397i	−1.51131	+	2.08014i
$288$		0			0
$289$	−12.6855	+	9.21656i	−0.746207	+	0.542151i
$290$		0			0
$291$	−6.52232	−	4.73874i	−0.382345	−	0.277790i
$292$		0			0
$293$		−	4.20743i		−	0.245800i	−0.992419	−	0.122900i	$-0.960780\pi$
$293$		−	4.20743i		−	0.245800i	0.992419	−	0.122900i	$-0.0392195\pi$
$294$		0			0
$295$	−4.99993	−	25.0953i	−0.291107	−	1.46111i
$296$		0			0
$297$	0.768148	+	0.249586i	0.0445725	+	0.0144825i
$298$		0			0
$299$	29.7697			1.72163
$300$		0			0
$301$	38.8119			2.23708
$302$		0			0
$303$	11.0794	+	3.59993i	0.636497	+	0.206811i
$304$		0			0
$305$	6.97755	+	0.823633i	0.399533	+	0.0471611i
$306$		0			0
$307$		−	4.41109i		−	0.251754i	−0.992046	−	0.125877i	$-0.959825\pi$
$307$		−	4.41109i		−	0.251754i	0.992046	−	0.125877i	$-0.0401745\pi$
$308$		0			0
$309$	15.2450	+	11.0761i	0.867258	+	0.630100i
$310$		0			0
$311$	5.11346	−	3.71514i	0.289958	−	0.210667i	−0.433291	−	0.901254i	$-0.642648\pi$
$311$	5.11346	−	3.71514i	0.289958	−	0.210667i	0.723249	+	0.690587i	$0.242648\pi$
$312$		0			0
$313$	−9.00753	+	12.3978i	−0.509136	+	0.700765i	−0.983773	−	0.179416i	$-0.942579\pi$
$313$	−9.00753	+	12.3978i	−0.509136	+	0.700765i	0.474638	+	0.880181i	$0.342579\pi$
$314$		0			0
$315$	−8.30714	+	1.65510i	−0.468054	+	0.0932541i
$316$		0			0
$317$	−20.2723	+	6.58686i	−1.13860	+	0.369955i	−0.816840	−	0.576864i	$-0.804276\pi$
$317$	−20.2723	+	6.58686i	−1.13860	+	0.369955i	−0.321765	+	0.946820i	$0.604276\pi$
$318$		0			0
$319$	0.923699	+	2.84285i	0.0517172	+	0.159169i
$320$		0			0
$321$	−4.44851	+	13.6911i	−0.248292	+	0.764164i
$322$		0			0
$323$	0.0101366	+	0.0139519i	0.000564018	+	0.000776304i
$324$		0			0
$325$	20.2558	+	12.3953i	1.12359	+	0.687570i
$326$		0			0
$327$	−3.38673	−	4.66144i	−0.187287	−	0.257778i
$328$		0			0
$329$	0.616057	−	1.89603i	0.0339643	−	0.104531i
$330$		0			0
$331$	6.12237	+	18.8427i	0.336516	+	1.03569i	0.965970	+	0.258652i	$0.0832785\pi$
$331$	6.12237	+	18.8427i	0.336516	+	1.03569i	−0.629454	+	0.777037i	$0.716722\pi$
$332$		0			0
$333$	8.12372	−	2.63956i	0.445177	−	0.144647i
$334$		0			0
$335$	−26.9736	−	12.4248i	−1.47373	−	0.678838i
$336$		0			0
$337$	5.89780	−	8.11762i	0.321274	−	0.442195i	−0.617582	−	0.786507i	$-0.711888\pi$
$337$	5.89780	−	8.11762i	0.321274	−	0.442195i	0.938856	+	0.344311i	$0.111888\pi$
$338$		0			0
$339$	14.5027	−	10.5368i	0.787680	−	0.572283i
$340$		0			0
$341$	−1.03378	−	0.751085i	−0.0559823	−	0.0406735i
$342$		0			0
$343$			1.32419i			0.0714997i
$344$		0			0
$345$	5.86378	−	12.7300i	0.315695	−	0.685361i
$346$		0			0
$347$	−13.1885	−	4.28519i	−0.707994	−	0.230041i	−0.0671837	−	0.997741i	$-0.521401\pi$
$347$	−13.1885	−	4.28519i	−0.707994	−	0.230041i	−0.640810	+	0.767700i	$0.721401\pi$
$348$		0			0
$349$	−27.2533			−1.45883			−0.729417	−	0.684069i	$-0.760209\pi$
$349$	−27.2533			−1.45883			−0.729417	+	0.684069i	$0.760209\pi$
$350$		0			0
$351$	4.74950			0.253509
$352$		0			0
$353$	−11.8063	−	3.83609i	−0.628384	−	0.204174i	−0.0225248	−	0.999746i	$-0.507170\pi$
$353$	−11.8063	−	3.83609i	−0.628384	−	0.204174i	−0.605859	+	0.795572i	$0.707170\pi$
$354$		0			0
$355$	9.58374	−	5.37110i	0.508652	−	0.285068i
$356$		0			0
$357$			4.35192i			0.230328i
$358$		0			0
$359$	−15.3910	−	11.1823i	−0.812308	−	0.590177i	0.102191	−	0.994765i	$-0.467415\pi$
$359$	−15.3910	−	11.1823i	−0.812308	−	0.590177i	−0.914499	+	0.404588i	$0.867415\pi$
$360$		0			0
$361$	15.3711	−	11.1678i	0.809007	−	0.587778i
$362$		0			0
$363$	−6.08220	+	8.37143i	−0.319233	+	0.439386i
$364$		0			0
$365$	1.22639	−	10.3895i	0.0641920	−	0.543814i
$366$		0			0
$367$	0.927465	−	0.301352i	0.0484133	−	0.0157304i	−0.284710	−	0.958614i	$-0.591897\pi$
$367$	0.927465	−	0.301352i	0.0484133	−	0.0157304i	0.333124	+	0.942883i	$0.391897\pi$
$368$		0			0
$369$	−3.55335	−	10.9361i	−0.184980	−	0.569310i
$370$		0			0
$371$	−3.45294	+	10.6271i	−0.179268	+	0.551729i
$372$		0			0
$373$	−11.0341	−	15.1871i	−0.571324	−	0.786360i	0.421387	−	0.906881i	$-0.361543\pi$
$373$	−11.0341	−	15.1871i	−0.571324	−	0.786360i	−0.992711	+	0.120521i	$0.961543\pi$
$374$		0			0
$375$	9.29028	−	6.22019i	0.479748	−	0.321209i
$376$		0			0
$377$	10.3318	+	14.2205i	0.532114	+	0.732392i
$378$		0			0
$379$	1.06536	−	3.27883i	0.0547236	−	0.168422i	−0.919959	−	0.392014i	$-0.871778\pi$
$379$	1.06536	−	3.27883i	0.0547236	−	0.168422i	0.974683	+	0.223592i	$0.0717784\pi$
$380$		0			0
$381$	−0.707591	−	2.17774i	−0.0362510	−	0.111569i
$382$		0			0
$383$	−25.9681	+	8.43755i	−1.32691	+	0.431139i	−0.884862	−	0.465854i	$-0.845747\pi$
$383$	−25.9681	+	8.43755i	−1.32691	+	0.431139i	−0.442046	+	0.896992i	$0.645747\pi$
$384$		0			0
$385$	−0.801990	+	6.79420i	−0.0408732	+	0.346264i
$386$		0			0
$387$	−6.02232	+	8.28902i	−0.306132	+	0.421354i
$388$		0			0
$389$	7.94232	−	5.77044i	0.402692	−	0.292573i	−0.367945	−	0.929848i	$-0.619938\pi$
$389$	7.94232	−	5.77044i	0.402692	−	0.292573i	0.770637	+	0.637275i	$0.219938\pi$
$390$		0			0
$391$	−5.82567	−	4.23259i	−0.294617	−	0.214051i
$392$		0			0
$393$		−	7.04946i		−	0.355598i
$394$		0			0
$395$	18.0853	−	10.1357i	0.909968	−	0.509981i
$396$		0			0
$397$	11.0447	+	3.58865i	0.554319	+	0.180109i	0.572763	−	0.819721i	$-0.305871\pi$
$397$	11.0447	+	3.58865i	0.554319	+	0.180109i	−0.0184443	+	0.999830i	$0.505871\pi$
$398$		0			0
$399$	−0.0568635			−0.00284674
$400$		0			0
$401$	−25.4145			−1.26914			−0.634570	−	0.772865i	$-0.718823\pi$
$401$	−25.4145			−1.26914			−0.634570	+	0.772865i	$0.718823\pi$
$402$		0			0
$403$	−7.14637	−	2.32200i	−0.355986	−	0.115667i
$404$		0			0
$405$	0.935516	−	2.03096i	0.0464862	−	0.100919i
$406$		0			0
$407$		−	6.89902i		−	0.341972i
$408$		0			0
$409$	13.9568	+	10.1402i	0.690117	+	0.501399i	0.876699	−	0.481040i	$-0.159741\pi$
$409$	13.9568	+	10.1402i	0.690117	+	0.501399i	−0.186582	+	0.982439i	$0.559741\pi$
$410$		0			0
$411$	17.7441	−	12.8918i	0.875251	−	0.635907i
$412$		0			0
$413$	25.4800	−	35.0702i	1.25379	−	1.72569i
$414$		0			0
$415$	2.89148	+	1.33189i	0.141937	+	0.0653800i
$416$		0			0
$417$	9.24200	−	3.00291i	0.452583	−	0.147053i
$418$		0			0
$419$	6.31956	+	19.4496i	0.308731	+	0.950176i	0.978259	+	0.207389i	$0.0664965\pi$
$419$	6.31956	+	19.4496i	0.308731	+	0.950176i	−0.669528	+	0.742787i	$0.733503\pi$
$420$		0			0
$421$	−6.46100	+	19.8849i	−0.314890	+	0.969132i	0.660910	+	0.750466i	$0.270171\pi$
$421$	−6.46100	+	19.8849i	−0.314890	+	0.969132i	−0.975800	+	0.218666i	$0.929829\pi$
$422$		0			0
$423$	0.309341	+	0.425771i	0.0150407	+	0.0207017i
$424$		0			0
$425$	−2.20154	−	5.30559i	−0.106790	−	0.257359i
$426$		0			0
$427$	6.99618	+	9.62941i	0.338569	+	0.466000i
$428$		0			0
$429$	1.18541	−	3.64832i	0.0572321	−	0.176142i
$430$		0			0
$431$	−2.85900	−	8.79908i	−0.137713	−	0.423837i	0.858289	−	0.513166i	$-0.171528\pi$
$431$	−2.85900	−	8.79908i	−0.137713	−	0.423837i	−0.996002	+	0.0893294i	$0.971528\pi$
$432$		0			0
$433$	0.223727	−	0.0726932i	0.0107516	−	0.00349341i	−0.303636	−	0.952788i	$-0.598201\pi$
$433$	0.223727	−	0.0726932i	0.0107516	−	0.00349341i	0.314388	+	0.949295i	$0.398201\pi$
$434$		0			0
$435$	8.11598	−	1.61701i	0.389132	−	0.0775297i
$436$		0			0
$437$	0.0553044	−	0.0761199i	0.00264557	−	0.00364131i
$438$		0			0
$439$	25.2424	−	18.3396i	1.20475	−	0.875304i	0.210008	−	0.977700i	$-0.432651\pi$
$439$	25.2424	−	18.3396i	1.20475	−	0.875304i	0.994744	+	0.102396i	$0.0326509\pi$
$440$		0			0
$441$	−5.94593	−	4.31997i	−0.283139	−	0.205713i
$442$		0			0
$443$			24.3862i			1.15862i	0.815106	+	0.579311i	$0.196678\pi$
$443$			24.3862i			1.15862i	−0.815106	+	0.579311i	$0.803322\pi$
$444$		0			0
$445$	35.7674	+	4.22200i	1.69554	+	0.200142i
$446$		0			0
$447$	13.2874	+	4.31735i	0.628474	+	0.204203i
$448$		0			0
$449$	−23.9483			−1.13019			−0.565096	−	0.825025i	$-0.691161\pi$
$449$	−23.9483			−1.13019			−0.565096	+	0.825025i	$0.691161\pi$
$450$		0			0
$451$	−9.28740			−0.437327
$452$		0			0
$453$	−19.1990	−	6.23815i	−0.902050	−	0.293094i
$454$		0			0
$455$	7.86087	+	39.4547i	0.368523	+	1.84967i
$456$		0			0
$457$		−	3.91244i		−	0.183016i	−0.995804	−	0.0915082i	$-0.970831\pi$
$457$		−	3.91244i		−	0.183016i	0.995804	−	0.0915082i	$-0.0291688\pi$
$458$		0			0
$459$	−0.929435	−	0.675274i	−0.0433823	−	0.0315191i
$460$		0			0
$461$	2.09170	−	1.51971i	0.0974202	−	0.0707799i	−0.538009	−	0.842939i	$-0.680823\pi$
$461$	2.09170	−	1.51971i	0.0974202	−	0.0707799i	0.635429	+	0.772159i	$0.280823\pi$
$462$		0			0
$463$	12.8777	−	17.7247i	0.598478	−	0.823734i	−0.397090	−	0.917780i	$-0.629980\pi$
$463$	12.8777	−	17.7247i	0.598478	−	0.823734i	0.995568	+	0.0940453i	$0.0299799\pi$
$464$		0			0
$465$	−2.40056	+	2.59854i	−0.111323	+	0.120504i
$466$		0			0
$467$	7.79561	−	2.53295i	0.360738	−	0.117211i	−0.123040	−	0.992402i	$-0.539264\pi$
$467$	7.79561	−	2.53295i	0.360738	−	0.117211i	0.483778	+	0.875191i	$0.339264\pi$
$468$		0			0
$469$	−15.5467	−	47.8479i	−0.717881	−	2.20941i
$470$		0			0
$471$	2.39966	−	7.38539i	0.110570	−	0.340301i
$472$		0			0
$473$	4.86410	+	6.69486i	0.223652	+	0.307830i
$474$		0			0
$475$	0.0693245	−	0.0287660i	0.00318083	−	0.00131987i
$476$		0			0
$477$	−1.73383	−	2.38641i	−0.0793865	−	0.109266i
$478$		0			0
$479$	1.90100	−	5.85067i	0.0868588	−	0.267324i	−0.898188	−	0.439612i	$-0.855116\pi$
$479$	1.90100	−	5.85067i	0.0868588	−	0.267324i	0.985047	+	0.172288i	$0.0551160\pi$
$480$		0			0
$481$	−12.5366	−	38.5836i	−0.571618	−	1.75926i
$482$		0			0
$483$	22.5815	−	7.33717i	1.02749	−	0.333853i
$484$		0			0
$485$	8.81342	+	15.7259i	0.400197	+	0.714078i
$486$		0			0
$487$	−3.69230	+	5.08201i	−0.167314	+	0.230288i	−0.884438	−	0.466658i	$-0.845458\pi$
$487$	−3.69230	+	5.08201i	−0.167314	+	0.230288i	0.717124	+	0.696945i	$0.245458\pi$
$488$		0			0
$489$	−11.2379	+	8.16480i	−0.508195	+	0.369225i
$490$		0			0
$491$	2.22591	+	1.61722i	0.100454	+	0.0729840i	0.636878	−	0.770964i	$-0.280225\pi$
$491$	2.22591	+	1.61722i	0.100454	+	0.0729840i	−0.536424	+	0.843948i	$0.680225\pi$
$492$		0			0
$493$		−	4.25178i		−	0.191490i
$494$		0			0
$495$	−1.32659	−	1.22552i	−0.0596257	−	0.0550828i
$496$		0			0
$497$	17.7006	+	5.75128i	0.793982	+	0.257980i
$498$		0			0
$499$	16.4263			0.735341			0.367670	−	0.929956i	$-0.380156\pi$
$499$	16.4263			0.735341			0.367670	+	0.929956i	$0.380156\pi$
$500$		0			0
$501$	−2.89787			−0.129467
$502$		0			0
$503$	−11.6860	−	3.79701i	−0.521053	−	0.169300i	0.0366701	−	0.999327i	$-0.488325\pi$
$503$	−11.6860	−	3.79701i	−0.521053	−	0.169300i	−0.557723	+	0.830027i	$0.688325\pi$
$504$		0			0
$505$	−19.1341	−	17.6763i	−0.851458	−	0.786586i
$506$		0			0
$507$		−	9.55771i		−	0.424473i
$508$		0			0
$509$	−8.50277	−	6.17763i	−0.376879	−	0.273818i	0.383179	−	0.923674i	$-0.374829\pi$
$509$	−8.50277	−	6.17763i	−0.376879	−	0.273818i	−0.760058	+	0.649856i	$0.774829\pi$
$510$		0			0
$511$	14.3382	−	10.4173i	0.634283	−	0.460833i
$512$		0			0
$513$	0.00882334	−	0.0121443i	0.000389560	−	0.000536183i
$514$		0			0
$515$	−20.6001	−	36.7572i	−0.907750	−	1.61971i
$516$		0			0
$517$	0.404263	−	0.131353i	0.0177795	−	0.00577690i
$518$		0			0
$519$	−4.70752	−	14.4882i	−0.206637	−	0.635963i
$520$		0			0
$521$	−2.41778	+	7.44115i	−0.105925	+	0.326003i	−0.989946	−	0.141443i	$-0.954826\pi$
$521$	−2.41778	+	7.44115i	−0.105925	+	0.326003i	0.884022	+	0.467446i	$0.154826\pi$
$522$		0			0
$523$	−12.9592	−	17.8368i	−0.566665	−	0.779947i	0.425490	−	0.904963i	$-0.360102\pi$
$523$	−12.9592	−	17.8368i	−0.566665	−	0.779947i	−0.992155	+	0.125016i	$0.960102\pi$
$524$		0			0
$525$	18.4199	+	4.41002i	0.803908	+	0.192469i
$526$		0			0
$527$	1.06834	+	1.47045i	0.0465378	+	0.0640538i
$528$		0			0
$529$	−5.03308	+	15.4902i	−0.218830	+	0.673489i
$530$		0			0
$531$	3.53625	+	10.8835i	0.153460	+	0.472302i
$532$		0			0
$533$	−51.9409	+	16.8766i	−2.24981	+	0.731007i
$534$		0			0
$535$	21.8430	−	23.6445i	0.944357	−	1.02224i
$536$		0			0
$537$	13.6987	−	18.8546i	0.591142	−	0.813637i
$538$		0			0
$539$	−4.80240	+	3.48915i	−0.206854	+	0.150288i
$540$		0			0
$541$	−10.0860	−	7.32791i	−0.433631	−	0.315052i	0.349468	−	0.936948i	$-0.386362\pi$
$541$	−10.0860	−	7.32791i	−0.433631	−	0.315052i	−0.783099	+	0.621897i	$0.786362\pi$
$542$		0			0
$543$			17.6985i			0.759514i
$544$		0			0
$545$	2.51748	+	12.6356i	0.107837	+	0.541248i
$546$		0			0
$547$	−2.39292	−	0.777505i	−0.102314	−	0.0332437i	0.257413	−	0.966302i	$-0.417130\pi$
$547$	−2.39292	−	0.777505i	−0.102314	−	0.0332437i	−0.359726	+	0.933058i	$0.617130\pi$
$548$		0			0
$549$	−3.14212			−0.134102
$550$		0			0
$551$	0.0555550			0.00236672
$552$		0			0
$553$	33.4024	+	10.8531i	1.42042	+	0.461521i
$554$		0			0
$555$	−18.9683	−	2.23903i	−0.805161	−	0.0950415i
$556$		0			0
$557$			0.262544i			0.0111244i	0.999985	+	0.00556218i	$0.00177051\pi$
$557$			0.262544i			0.0111244i	−0.999985	+	0.00556218i	$0.998229\pi$
$558$		0			0
$559$	39.3687	+	28.6030i	1.66512	+	1.20978i
$560$		0			0
$561$	−0.750685	+	0.545404i	−0.0316939	+	0.0230270i
$562$		0			0
$563$	19.0928	−	26.2790i	0.804666	−	1.10753i	−0.187459	−	0.982272i	$-0.560025\pi$
$563$	19.0928	−	26.2790i	0.804666	−	1.10753i	0.992125	−	0.125255i	$-0.0399748\pi$
$564$		0			0
$565$	−39.3119	+	7.83241i	−1.65386	+	0.329512i
$566$		0			0
$567$	3.60268	−	1.17058i	0.151298	−	0.0491598i
$568$		0			0
$569$	11.9892	+	36.8991i	0.502615	+	1.54689i	0.804743	+	0.593623i	$0.202303\pi$
$569$	11.9892	+	36.8991i	0.502615	+	1.54689i	−0.302128	+	0.953267i	$0.597697\pi$
$570$		0			0
$571$	−11.0258	+	33.9338i	−0.461414	+	1.42009i	0.402023	+	0.915629i	$0.368307\pi$
$571$	−11.0258	+	33.9338i	−0.461414	+	1.42009i	−0.863437	+	0.504456i	$0.831693\pi$
$572$		0			0
$573$	−5.50411	−	7.57575i	−0.229937	−	0.316482i
$574$		0			0
$575$	−23.8182	+	20.3685i	−0.993290	+	0.849425i
$576$		0			0
$577$	−14.8962	−	20.5029i	−0.620139	−	0.853548i	0.377224	−	0.926122i	$-0.376879\pi$
$577$	−14.8962	−	20.5029i	−0.620139	−	0.853548i	−0.997363	+	0.0725741i	$0.976879\pi$
$578$		0			0
$579$	−5.84997	+	18.0044i	−0.243116	+	0.748236i
$580$		0			0
$581$	1.66655	+	5.12913i	0.0691403	+	0.212792i
$582$		0			0
$583$	−2.26586	+	0.736221i	−0.0938422	+	0.0304912i
$584$		0			0
$585$	−9.64605	−	4.44323i	−0.398815	−	0.183705i
$586$		0			0
$587$	−0.303103	+	0.417186i	−0.0125104	+	0.0172191i	−0.815226	−	0.579142i	$-0.803388\pi$
$587$	−0.303103	+	0.417186i	−0.0125104	+	0.0172191i	0.802716	+	0.596362i	$0.203388\pi$
$588$		0			0
$589$	−0.0192134	+	0.0139593i	−0.000791673	+	0.000575184i
$590$		0			0
$591$	6.10288	+	4.43400i	0.251039	+	0.182390i
$592$		0			0
$593$			7.14389i			0.293364i	0.989184	+	0.146682i	$0.0468595\pi$
$593$			7.14389i			0.293364i	−0.989184	+	0.146682i	$0.953141\pi$
$594$		0			0
$595$	4.07129	−	8.83858i	0.166907	−	0.362347i
$596$		0			0
$597$	−3.41011	−	1.10801i	−0.139566	−	0.0453479i
$598$		0			0
$599$	−23.6627			−0.966833			−0.483417	−	0.875390i	$-0.660604\pi$
$599$	−23.6627			−0.966833			−0.483417	+	0.875390i	$0.660604\pi$
$600$		0			0
$601$	−7.98023			−0.325520			−0.162760	−	0.986666i	$-0.552040\pi$
$601$	−7.98023			−0.325520			−0.162760	+	0.986666i	$0.552040\pi$
$602$		0			0
$603$	12.6312	+	4.10412i	0.514381	+	0.167133i
$604$		0			0
$605$	20.1843	−	11.3121i	0.820610	−	0.459901i
$606$		0			0
$607$			17.2004i			0.698144i	0.937096	+	0.349072i	$0.113503\pi$
$607$			17.2004i			0.698144i	−0.937096	+	0.349072i	$0.886497\pi$
$608$		0			0
$609$	11.3419	+	8.24038i	0.459597	+	0.333917i
$610$		0			0
$611$	2.02220	−	1.46921i	0.0818094	−	0.0594380i
$612$		0			0
$613$	8.67810	−	11.9444i	0.350505	−	0.482429i	−0.596968	−	0.802265i	$-0.703628\pi$
$613$	8.67810	−	11.9444i	0.350505	−	0.482429i	0.947473	+	0.319836i	$0.103628\pi$
$614$		0			0
$615$	−3.01416	+	25.5350i	−0.121543	+	1.02967i
$616$		0			0
$617$	14.7142	−	4.78092i	0.592370	−	0.192473i	0.00253529	−	0.999997i	$-0.499193\pi$
$617$	14.7142	−	4.78092i	0.592370	−	0.192473i	0.589834	+	0.807524i	$0.299193\pi$
$618$		0			0
$619$	11.5792	+	35.6370i	0.465406	+	1.43237i	0.858471	+	0.512861i	$0.171414\pi$
$619$	11.5792	+	35.6370i	0.465406	+	1.43237i	−0.393066	+	0.919510i	$0.628586\pi$
$620$		0			0
$621$	−1.93691	+	5.96119i	−0.0777254	+	0.239214i
$622$		0			0
$623$	35.8629	+	49.3611i	1.43682	+	1.97761i
$624$		0			0
$625$	−24.6873	+	3.94177i	−0.987492	+	0.157671i
$626$		0			0
$627$	−0.00712642	−	0.00980868i	−0.000284602	−	0.000391721i
$628$		0			0
$629$	−3.03244	+	9.33290i	−0.120911	+	0.372127i
$630$		0			0
$631$	−0.468691	−	1.44248i	−0.0186583	−	0.0574244i	0.941294	−	0.337588i	$-0.109611\pi$
$631$	−0.468691	−	1.44248i	−0.0186583	−	0.0574244i	−0.959952	+	0.280164i	$0.909611\pi$
$632$		0			0
$633$	−1.98289	+	0.644279i	−0.0788126	+	0.0256078i
$634$		0			0
$635$	−0.600220	+	5.08487i	−0.0238190	+	0.201787i
$636$		0			0
$637$	−20.5177	+	28.2401i	−0.812940	+	1.11892i
$638$		0			0
$639$	−3.97485	+	2.88790i	−0.157243	+	0.114243i
$640$		0			0
$641$	3.12903	+	2.27338i	0.123589	+	0.0897930i	0.647863	−	0.761757i	$-0.275663\pi$
$641$	3.12903	+	2.27338i	0.123589	+	0.0897930i	−0.524273	+	0.851550i	$0.675663\pi$
$642$		0			0
$643$			23.2212i			0.915756i	0.889015	+	0.457878i	$0.151390\pi$
$643$			23.2212i			0.915756i	−0.889015	+	0.457878i	$0.848610\pi$
$644$		0			0
$645$	19.9856	−	11.2007i	0.786933	−	0.441027i
$646$		0			0
$647$	−24.8795	−	8.08384i	−0.978114	−	0.317808i	−0.224027	−	0.974583i	$-0.571920\pi$
$647$	−24.8795	−	8.08384i	−0.978114	−	0.317808i	−0.754087	+	0.656775i	$0.771920\pi$
$648$		0			0
$649$	9.24271			0.362808
$650$		0			0
$651$	−5.99309			−0.234888
$652$		0			0
$653$	−8.13602	−	2.64355i	−0.318387	−	0.103450i	0.145464	−	0.989364i	$-0.453533\pi$
$653$	−8.13602	−	2.64355i	−0.318387	−	0.103450i	−0.463851	+	0.885913i	$0.653533\pi$
$654$		0			0
$655$	−6.59488	+	14.3172i	−0.257683	+	0.559419i
$656$		0			0
$657$			4.67860i			0.182530i
$658$		0			0
$659$	−33.9288	−	24.6507i	−1.32168	−	0.960255i	−0.999910	−	0.0134358i	$-0.995723\pi$
$659$	−33.9288	−	24.6507i	−1.32168	−	0.960255i	−0.321767	−	0.946819i	$-0.604277\pi$
$660$		0			0
$661$	14.1713	−	10.2961i	0.551201	−	0.400471i	−0.277027	−	0.960862i	$-0.589349\pi$
$661$	14.1713	−	10.2961i	0.551201	−	0.400471i	0.828228	+	0.560391i	$0.189349\pi$
$662$		0			0
$663$	−3.20721	+	4.41435i	−0.124558	+	0.171439i
$664$		0			0
$665$	0.115488	+	0.0531967i	0.00447842	+	0.00206288i
$666$		0			0
$667$	−22.0619	+	7.16833i	−0.854239	+	0.277559i
$668$		0			0
$669$	−4.33776	−	13.3503i	−0.167708	−	0.516151i
$670$		0			0
$671$	−0.784230	+	2.41361i	−0.0302749	+	0.0931765i
$672$		0			0
$673$	17.1017	+	23.5385i	0.659223	+	0.907343i	0.999455	−	0.0329986i	$-0.0105057\pi$
$673$	17.1017	+	23.5385i	0.659223	+	0.907343i	−0.340232	+	0.940341i	$0.610506\pi$
$674$		0			0
$675$	−3.80000	+	3.24962i	−0.146262	+	0.125078i
$676$		0			0
$677$	−17.5667	−	24.1785i	−0.675143	−	0.929255i	0.324720	−	0.945810i	$-0.394730\pi$
$677$	−17.5667	−	24.1785i	−0.675143	−	0.929255i	−0.999863	+	0.0165555i	$0.994730\pi$
$678$		0			0
$679$	−9.43726	+	29.0449i	−0.362169	+	1.11464i
$680$		0			0
$681$	−0.783313	−	2.41079i	−0.0300166	−	0.0923817i
$682$		0			0
$683$	35.3984	−	11.5016i	1.35448	−	0.440097i	0.460284	−	0.887772i	$-0.347748\pi$
$683$	35.3984	−	11.5016i	1.35448	−	0.440097i	0.894197	+	0.447674i	$0.147748\pi$
$684$		0			0
$685$	−48.0981	+	9.58296i	−1.83773	+	0.366146i
$686$		0			0
$687$	9.71385	−	13.3700i	0.370607	−	0.510096i
$688$		0			0
$689$	−11.3342	+	8.23481i	−0.431800	+	0.313721i
$690$		0			0
$691$	−13.6397	−	9.90980i	−0.518877	−	0.376986i	0.297303	−	0.954783i	$-0.403913\pi$
$691$	−13.6397	−	9.90980i	−0.518877	−	0.376986i	−0.816181	+	0.577797i	$0.803913\pi$
$692$		0			0
$693$		−	3.05955i		−	0.116223i
$694$		0			0
$695$	−21.5794	−	2.54724i	−0.818554	−	0.0966225i
$696$		0			0
$697$	12.5639	+	4.08225i	0.475890	+	0.154626i
$698$		0			0
$699$	−26.5208			−1.00311
$700$		0			0
$701$	−23.3495			−0.881898			−0.440949	−	0.897532i	$-0.645358\pi$
$701$	−23.3495			−0.881898			−0.440949	+	0.897532i	$0.645358\pi$
$702$		0			0
$703$	−0.121947	−	0.0396228i	−0.00459930	−	0.00149440i
$704$		0			0
$705$	−0.229944	−	1.15412i	−0.00866020	−	0.0434666i
$706$		0			0
$707$		−	44.1297i		−	1.65967i
$708$		0			0
$709$	15.4019	+	11.1901i	0.578429	+	0.420253i	0.838157	−	0.545428i	$-0.183633\pi$
$709$	15.4019	+	11.1901i	0.578429	+	0.420253i	−0.259728	+	0.965682i	$0.583633\pi$
$710$		0			0
$711$	−7.50084	+	5.44968i	−0.281303	+	0.204379i
$712$		0			0
$713$	5.82877	−	8.02261i	0.218289	−	0.300449i
$714$		0			0
$715$	−5.82058	+	6.30063i	−0.217677	+	0.235630i
$716$		0			0
$717$	−7.09855	+	2.30646i	−0.265100	+	0.0861363i
$718$		0			0
$719$	4.55488	+	14.0185i	0.169868	+	0.522801i	0.999362	−	0.0357149i	$-0.0113708\pi$
$719$	4.55488	+	14.0185i	0.169868	+	0.522801i	−0.829494	+	0.558516i	$0.811371\pi$
$720$		0			0
$721$	22.0583	−	67.8884i	0.821493	−	2.52830i
$722$		0			0
$723$	−6.05288	−	8.33107i	−0.225109	−	0.309836i
$724$		0			0
$725$	−17.9960	−	4.30854i	−0.668355	−	0.160015i
$726$		0			0
$727$	17.6698	+	24.3204i	0.655336	+	0.901993i	0.999316	−	0.0369839i	$-0.0117750\pi$
$727$	17.6698	+	24.3204i	0.655336	+	0.901993i	−0.343979	+	0.938977i	$0.611775\pi$
$728$		0			0
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−3.63738	−	11.1947i	−0.134533	−	0.414051i
$732$		0			0
$733$	21.5355	−	6.99732i	0.795433	−	0.258452i	0.117017	−	0.993130i	$-0.462667\pi$
$733$	21.5355	−	6.99732i	0.795433	−	0.258452i	0.678416	+	0.734678i	$0.262667\pi$
$734$		0			0
$735$	8.03455	+	14.3362i	0.296359	+	0.528799i
$736$		0			0
$737$	6.30514	−	8.67828i	0.232253	−	0.319668i
$738$		0			0
$739$	−20.7764	+	15.0949i	−0.764272	+	0.555276i	−0.900218	−	0.435440i	$-0.856593\pi$
$739$	−20.7764	+	15.0949i	−0.764272	+	0.555276i	0.135946	+	0.990716i	$0.456593\pi$
$740$		0			0
$741$	−0.0576792	−	0.0419064i	−0.00211890	−	0.00153947i
$742$		0			0
$743$		−	24.9796i		−	0.916411i	−0.888846	−	0.458205i	$-0.848492\pi$
$743$		−	24.9796i		−	0.916411i	0.888846	−	0.458205i	$-0.151508\pi$
$744$		0			0
$745$	−22.9473	−	21.1990i	−0.840725	−	0.776670i
$746$		0			0
$747$	−1.35402	−	0.439947i	−0.0495409	−	0.0160968i
$748$		0			0
$749$	54.5321			1.99256
$750$		0			0
$751$	17.9383			0.654580			0.327290	−	0.944924i	$-0.393865\pi$
$751$	17.9383			0.654580			0.327290	+	0.944924i	$0.393865\pi$
$752$		0			0
$753$	18.6225	+	6.05083i	0.678643	+	0.220504i
$754$		0			0
$755$	33.1567	+	30.6305i	1.20669	+	1.11476i
$756$		0			0
$757$			9.91474i			0.360357i	0.983634	+	0.180179i	$0.0576676\pi$
$757$			9.91474i			0.360357i	−0.983634	+	0.180179i	$0.942332\pi$
$758$		0			0
$759$	4.09565	+	2.97566i	0.148663	+	0.108010i
$760$		0			0
$761$	25.6076	−	18.6050i	0.928273	−	0.674430i	−0.0172961	−	0.999850i	$-0.505506\pi$
$761$	25.6076	−	18.6050i	0.928273	−	0.674430i	0.945569	+	0.325420i	$0.105506\pi$
$762$		0			0
$763$	−12.8292	+	17.6579i	−0.464449	+	0.639259i
$764$		0			0
$765$	1.25592	+	2.24096i	0.0454078	+	0.0810220i
$766$		0			0
$767$	51.6910	−	16.7954i	1.86645	−	0.606447i
$768$		0			0
$769$	−6.91430	−	21.2800i	−0.249336	−	0.767377i	−0.994893	−	0.100935i	$-0.967816\pi$
$769$	−6.91430	−	21.2800i	−0.249336	−	0.767377i	0.745557	−	0.666442i	$-0.232184\pi$
$770$		0			0
$771$	−1.84801	+	5.68760i	−0.0665546	+	0.204834i
$772$		0			0
$773$	28.1148	+	38.6967i	1.01122	+	1.39182i	0.918182	+	0.396160i	$0.129657\pi$
$773$	28.1148	+	38.6967i	1.01122	+	1.39182i	0.0930367	+	0.995663i	$0.470343\pi$
$774$		0			0
$775$	7.30641	−	3.03178i	0.262454	−	0.108905i
$776$		0			0
$777$	−19.0190	−	26.1774i	−0.682302	−	0.939108i
$778$		0			0
$779$	−0.0533399	+	0.164163i	−0.00191110	+	0.00588176i
$780$		0			0
$781$	1.22626	+	3.77405i	0.0438792	+	0.135046i
$782$		0			0
$783$	−3.51978	+	1.14365i	−0.125787	+	0.0408706i
$784$		0			0
$785$	−11.7828	+	12.7545i	−0.420545	+	0.455229i
$786$		0			0
$787$	16.2038	−	22.3026i	0.577603	−	0.795002i	−0.415827	−	0.909444i	$-0.636508\pi$
$787$	16.2038	−	22.3026i	0.577603	−	0.795002i	0.993430	+	0.114442i	$0.0365079\pi$
$788$		0			0
$789$	4.91104	−	3.56808i	0.174838	−	0.127027i
$790$		0			0
$791$	−54.9375	−	39.9144i	−1.95335	−	1.41919i
$792$		0			0
$793$			14.9235i			0.529948i
$794$		0			0
$795$	1.28882	+	6.46873i	0.0457096	+	0.229422i
$796$		0			0
$797$	21.9712	+	7.13887i	0.778260	+	0.252872i	0.671097	−	0.741370i	$-0.265823\pi$
$797$	21.9712	+	7.13887i	0.778260	+	0.252872i	0.107163	+	0.994241i	$0.465823\pi$
$798$		0			0
$799$	−0.604617			−0.0213898
$800$		0			0
$801$	−16.1067			−0.569103
$802$		0			0
$803$	3.59386	+	1.16772i	0.126825	+	0.0412078i
$804$		0			0
$805$	−52.7262	−	6.22382i	−1.85835	−	0.219361i
$806$		0			0
$807$		−	9.61605i		−	0.338501i
$808$		0			0
$809$	−1.36960	−	0.995071i	−0.0481525	−	0.0349848i	0.563449	−	0.826151i	$-0.309474\pi$
$809$	−1.36960	−	0.995071i	−0.0481525	−	0.0349848i	−0.611601	+	0.791166i	$0.709474\pi$
$810$		0			0
$811$	−16.6435	+	12.0922i	−0.584434	+	0.424616i	−0.840320	−	0.542091i	$-0.817633\pi$
$811$	−16.6435	+	12.0922i	−0.584434	+	0.424616i	0.255886	+	0.966707i	$0.417633\pi$
$812$		0			0
$813$	−17.8849	+	24.6164i	−0.627250	+	0.863335i
$814$		0			0
$815$	30.4620	−	6.06919i	1.06704	−	0.212594i
$816$		0			0
$817$	0.146274	−	0.0475272i	0.00511746	−	0.00166277i
$818$		0			0
$819$	−5.55967	−	17.1109i	−0.194271	−	0.597904i
$820$		0			0
$821$	−14.2235	+	43.7754i	−0.496403	+	1.52777i	0.318356	+	0.947971i	$0.396869\pi$
$821$	−14.2235	+	43.7754i	−0.496403	+	1.52777i	−0.814759	+	0.579800i	$0.803131\pi$
$822$		0			0
$823$	−32.9082	−	45.2942i	−1.14711	−	1.57886i	−0.750502	−	0.660868i	$-0.770188\pi$
$823$	−32.9082	−	45.2942i	−1.14711	−	1.57886i	−0.396605	−	0.917990i	$-0.629812\pi$
$824$		0			0
$825$	1.54776	+	3.73002i	0.0538861	+	0.129863i
$826$		0			0
$827$	12.1319	+	16.6981i	0.421866	+	0.580648i	0.966062	−	0.258309i	$-0.0831654\pi$
$827$	12.1319	+	16.6981i	0.421866	+	0.580648i	−0.544196	+	0.838958i	$0.683165\pi$
$828$		0			0
$829$	0.599179	−	1.84408i	0.0208103	−	0.0640476i	−0.940112	−	0.340866i	$-0.889280\pi$
$829$	0.599179	−	1.84408i	0.0208103	−	0.0640476i	0.960922	+	0.276818i	$0.0892799\pi$
$830$		0			0
$831$	−2.22614	−	6.85134i	−0.0772238	−	0.237670i
$832$		0			0
$833$	8.03026	−	2.60919i	0.278232	−	0.0904030i
$834$		0			0
$835$	5.88547	+	2.71100i	0.203675	+	0.0938182i
$836$		0			0
$837$	0.929930	−	1.27994i	0.0321431	−	0.0442412i
$838$		0			0
$839$	42.2783	−	30.7170i	1.45961	−	1.06047i	0.476146	−	0.879366i	$-0.342034\pi$
$839$	42.2783	−	30.7170i	1.45961	−	1.06047i	0.983464	−	0.181102i	$-0.0579665\pi$
$840$		0			0
$841$	12.3806	+	8.99501i	0.426916	+	0.310173i
$842$		0			0
$843$			29.7964i			1.02624i
$844$		0			0
$845$	−8.94139	+	19.4114i	−0.307593	+	0.667771i
$846$		0			0
$847$	37.2793	+	12.1128i	1.28093	+	0.416200i
$848$		0			0
$849$	−8.82402			−0.302840
$850$		0			0
$851$	53.5397			1.83532
$852$		0			0
$853$	−16.7010	−	5.42649i	−0.571832	−	0.185799i	0.00880614	−	0.999961i	$-0.497197\pi$
$853$	−16.7010	−	5.42649i	−0.571832	−	0.185799i	−0.580638	+	0.814162i	$0.697197\pi$
$854$		0			0
$855$	−0.0292810	+	0.0164102i	−0.00100139	+	0.000561217i
$856$		0			0
$857$		−	50.9890i		−	1.74175i	−0.491503	−	0.870876i	$-0.663552\pi$
$857$		−	50.9890i		−	1.74175i	0.491503	−	0.870876i	$-0.336448\pi$
$858$		0			0
$859$	15.0749	+	10.9525i	0.514349	+	0.373696i	0.814471	−	0.580205i	$-0.197027\pi$
$859$	15.0749	+	10.9525i	0.514349	+	0.373696i	−0.300122	+	0.953901i	$0.597027\pi$
$860$		0			0
$861$	−35.2397	+	25.6032i	−1.20097	+	0.872553i
$862$		0			0
$863$	0.171716	−	0.236347i	0.00584529	−	0.00804536i	−0.806084	−	0.591801i	$-0.798417\pi$
$863$	0.171716	−	0.236347i	0.00584529	−	0.00804536i	0.811930	+	0.583755i	$0.198417\pi$
$864$		0			0
$865$	−3.99319	+	33.8290i	−0.135773	+	1.15022i
$866$		0			0
$867$	−14.9127	+	4.84543i	−0.506462	+	0.164560i
$868$		0			0
$869$	2.31405	+	7.12192i	0.0784989	+	0.241595i
$870$		0			0
$871$	19.4925	−	59.9917i	0.660477	−	2.03274i
$872$		0			0
$873$	−4.73874	−	6.52232i	−0.160382	−	0.220747i
$874$		0			0
$875$	−33.2844	−	26.1887i	−1.12522	−	0.885338i
$876$		0			0
$877$	−22.3126	−	30.7106i	−0.753442	−	1.03702i	−0.997731	−	0.0673215i	$-0.978555\pi$
$877$	−22.3126	−	30.7106i	−0.753442	−	1.03702i	0.244289	−	0.969702i	$-0.421445\pi$
$878$		0			0
$879$	1.30017	−	4.00150i	0.0438535	−	0.134967i
$880$		0			0
$881$	−11.3378	−	34.8942i	−0.381981	−	1.17562i	−0.938647	−	0.344879i	$-0.887920\pi$
$881$	−11.3378	−	34.8942i	−0.381981	−	1.17562i	0.556666	−	0.830736i	$-0.312080\pi$
$882$		0			0
$883$	21.5128	−	6.98993i	0.723964	−	0.235230i	0.0762228	−	0.997091i	$-0.475714\pi$
$883$	21.5128	−	6.98993i	0.723964	−	0.235230i	0.647741	+	0.761861i	$0.275714\pi$
$884$		0			0
$885$	2.99966	−	25.4121i	0.100832	−	0.854219i
$886$		0			0
$887$	14.3643	−	19.7708i	0.482306	−	0.663838i	−0.496640	−	0.867957i	$-0.665433\pi$
$887$	14.3643	−	19.7708i	0.482306	−	0.663838i	0.978946	+	0.204119i	$0.0654330\pi$
$888$		0			0
$889$	−7.01741	+	5.09845i	−0.235356	+	0.170996i
$890$		0			0
$891$	0.653426	+	0.474742i	0.0218906	+	0.0159044i
$892$		0			0
$893$		−	0.00790011i		−	0.000264367i
$894$		0			0
$895$	−45.4603	+	25.4777i	−1.51957	+	0.851625i
$896$		0			0
$897$	28.3126	+	9.19934i	0.945332	+	0.307157i
$898$		0			0
$899$	5.85519			0.195281
$900$		0			0
$901$	3.38882			0.112898
$902$		0			0
$903$	36.9123	+	11.9935i	1.22836	+	0.399120i
$904$		0			0
$905$	16.5572	−	35.9449i	0.550380	−	1.19485i
$906$		0			0
$907$		−	32.7792i		−	1.08842i	−0.838950	−	0.544208i	$-0.816830\pi$
$907$		−	32.7792i		−	1.08842i	0.838950	−	0.544208i	$-0.183170\pi$
$908$		0			0
$909$	9.42474	+	6.84747i	0.312599	+	0.227116i
$910$		0			0
$911$	−22.0778	+	16.0405i	−0.731470	+	0.531444i	−0.890028	−	0.455906i	$-0.849315\pi$
$911$	−22.0778	+	16.0405i	−0.731470	+	0.531444i	0.158558	+	0.987350i	$0.449315\pi$
$912$		0			0
$913$	−0.675888	+	0.930280i	−0.0223686	+	0.0307878i
$914$		0			0
$915$	6.38153	+	2.93950i	0.210967	+	0.0971770i
$916$		0			0
$917$	−25.3970	+	8.25197i	−0.838681	+	0.272504i
$918$		0			0
$919$	12.8923	+	39.6783i	0.425277	+	1.30887i	0.902729	+	0.430209i	$0.141560\pi$
$919$	12.8923	+	39.6783i	0.425277	+	1.30887i	−0.477453	+	0.878658i	$0.658440\pi$
$920$		0			0
$921$	1.36310	−	4.19520i	0.0449158	−	0.138236i
$922$		0			0
$923$	13.7161	+	18.8785i	0.451469	+	0.621394i
$924$		0			0
$925$	36.4293	+	22.2926i	1.19779	+	0.732975i
$926$		0			0
$927$	11.0761	+	15.2450i	0.363788	+	0.500711i
$928$		0			0
$929$	10.4151	−	32.0542i	0.341707	−	1.05167i	−0.621616	−	0.783322i	$-0.713524\pi$
$929$	10.4151	−	32.0542i	0.341707	−	1.05167i	0.963323	−	0.268344i	$-0.0864763\pi$
$930$		0			0
$931$	0.0340925	+	0.104926i	0.00111734	+	0.00343880i
$932$		0			0
$933$	6.01123	−	1.95317i	0.196799	−	0.0639438i
$934$		0			0
$935$	2.03485	−	0.405418i	0.0665466	−	0.0132586i
$936$		0			0
$937$	0.614857	−	0.846278i	0.0200865	−	0.0276467i	−0.798856	−	0.601523i	$-0.794561\pi$
$937$	0.614857	−	0.846278i	0.0200865	−	0.0276467i	0.818942	+	0.573876i	$0.194561\pi$
$938$		0			0
$939$	−12.3978	+	9.00753i	−0.404587	+	0.293950i
$940$		0			0
$941$	−4.62928	−	3.36337i	−0.150910	−	0.109643i	0.509768	−	0.860312i	$-0.329731\pi$
$941$	−4.62928	−	3.36337i	−0.150910	−	0.109643i	−0.660678	+	0.750669i	$0.729731\pi$
$942$		0			0
$943$		−	72.0746i		−	2.34707i
$944$		0			0
$945$	−8.41201	−	0.992957i	−0.273643	−	0.0323009i
$946$		0			0
$947$	−11.9783	−	3.89200i	−0.389244	−	0.126473i	0.107856	−	0.994167i	$-0.465602\pi$
$947$	−11.9783	−	3.89200i	−0.389244	−	0.126473i	−0.497099	+	0.867694i	$0.665602\pi$
$948$		0			0
$949$	22.2210			0.721325
$950$		0			0
$951$	−21.3155			−0.691204
$952$		0			0
$953$	54.5813	+	17.7346i	1.76806	+	0.574479i	0.997984	−	0.0634695i	$-0.0202166\pi$
$953$	54.5813	+	17.7346i	1.76806	+	0.574479i	0.770079	+	0.637948i	$0.220217\pi$
$954$		0			0
$955$	4.09140	+	20.5352i	0.132395	+	0.664505i
$956$		0			0
$957$			2.98915i			0.0966255i
$958$		0			0
$959$	−67.2161	−	48.8353i	−2.17052	−	1.57698i
$960$		0			0
$961$	23.0545	−	16.7501i	0.743695	−	0.540326i
$962$		0			0
$963$	−8.46158	+	11.6464i	−0.272671	+	0.375299i
$964$		0			0
$965$	28.7244	−	31.0934i	0.924672	−	1.00093i
$966$		0			0
$967$	8.40935	−	2.73236i	0.270427	−	0.0878669i	−0.170665	−	0.985329i	$-0.554591\pi$
$967$	8.40935	−	2.73236i	0.270427	−	0.0878669i	0.441091	+	0.897462i	$0.354591\pi$
$968$		0			0
$969$	0.00532915	+	0.0164014i	0.000171197	+	0.000526890i
$970$		0			0
$971$	16.0493	−	49.3945i	0.515045	−	1.58515i	−0.268155	−	0.963376i	$-0.586414\pi$
$971$	16.0493	−	49.3945i	0.515045	−	1.58515i	0.783200	−	0.621770i	$-0.213586\pi$
$972$		0			0
$973$	−21.6370	−	29.7808i	−0.693651	−	0.954729i
$974$		0			0
$975$	15.4341	+	18.0481i	0.494285	+	0.578001i
$976$		0			0
$977$	21.8859	+	30.1234i	0.700193	+	0.963732i	0.999953	+	0.00971780i	$0.00309332\pi$
$977$	21.8859	+	30.1234i	0.700193	+	0.963732i	−0.299760	+	0.954015i	$0.596907\pi$
$978$		0			0
$979$	−4.02002	+	12.3724i	−0.128480	+	0.395422i
$980$		0			0
$981$	−1.78051	−	5.47985i	−0.0568473	−	0.174958i
$982$		0			0
$983$	−34.0107	+	11.0507i	−1.08477	+	0.352464i	−0.796225	−	0.605001i	$-0.793173\pi$
$983$	−34.0107	+	11.0507i	−1.08477	+	0.352464i	−0.288548	+	0.957465i	$0.593173\pi$
$984$		0			0
$985$	−8.24664	−	14.7146i	−0.262760	−	0.468847i
$986$		0			0
$987$	1.17181	−	1.61286i	0.0372991	−	0.0513378i
$988$		0			0
$989$	−51.9553	+	37.7477i	−1.65208	+	1.20031i
$990$		0			0
$991$	35.4505	+	25.7563i	1.12612	+	0.818175i	0.985126	−	0.171835i	$-0.0549697\pi$
$991$	35.4505	+	25.7563i	1.12612	+	0.818175i	0.140996	+	0.990010i	$0.454970\pi$
$992$		0			0
$993$			19.8124i			0.628728i
$994$		0			0
$995$	5.88924	+	5.44054i	0.186701	+	0.172477i
$996$		0			0
$997$	−37.5746	−	12.2087i	−1.19000	−	0.386654i	−0.353927	−	0.935273i	$-0.615154\pi$
$997$	−37.5746	−	12.2087i	−1.19000	−	0.386654i	−0.836072	+	0.548619i	$0.815154\pi$
$998$		0			0
$999$	8.54179			0.270250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.o.a.289.5	yes	24
3.2	odd	2		900.2.w.c.289.4		24
5.2	odd	4		1500.2.m.c.301.5		24
5.3	odd	4		1500.2.m.d.301.2		24
5.4	even	2		1500.2.o.c.949.1		24
25.3	odd	20		7500.2.a.m.1.4		12
25.4	even	10		7500.2.d.g.1249.9		24
25.9	even	10	inner	300.2.o.a.109.5	✓	24
25.12	odd	20		1500.2.m.c.1201.5		24
25.13	odd	20		1500.2.m.d.1201.2		24
25.16	even	5		1500.2.o.c.49.1		24
25.21	even	5		7500.2.d.g.1249.16		24
25.22	odd	20		7500.2.a.n.1.9		12
75.59	odd	10		900.2.w.c.109.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.5	✓	24	25.9	even	10	inner
300.2.o.a.289.5	yes	24	1.1	even	1	trivial
900.2.w.c.109.4		24	75.59	odd	10
900.2.w.c.289.4		24	3.2	odd	2
1500.2.m.c.301.5		24	5.2	odd	4
1500.2.m.c.1201.5		24	25.12	odd	20
1500.2.m.d.301.2		24	5.3	odd	4
1500.2.m.d.1201.2		24	25.13	odd	20
1500.2.o.c.49.1		24	25.16	even	5
1500.2.o.c.949.1		24	5.4	even	2
7500.2.a.m.1.4		12	25.3	odd	20
7500.2.a.n.1.9		12	25.22	odd	20
7500.2.d.g.1249.9		24	25.4	even	10
7500.2.d.g.1249.16		24	25.21	even	5

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{3} +(-1.64247 - 1.51733i) q^{5} -3.78808i q^{7} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{3} +(-1.64247 - 1.51733i) q^{5} -3.78808i q^{7} +(0.809017 + 0.587785i) q^{9} +(0.653426 - 0.474742i) q^{11} +(2.79168 - 3.84242i) q^{13} +(-1.09320 - 1.95062i) q^{15} +(-1.09262 + 0.355012i) q^{17} +(-0.00463870 - 0.0142765i) q^{19} +(1.17058 - 3.60268i) q^{21} +(3.68422 + 5.07089i) q^{23} +(0.395416 + 4.98434i) q^{25} +(0.587785 + 0.809017i) q^{27} +(-1.14365 + 3.51978i) q^{29} +(-0.488893 - 1.50466i) q^{31} +(0.768148 - 0.249586i) q^{33} +(-5.74777 + 6.22181i) q^{35} +(5.02074 - 6.91045i) q^{37} +(3.84242 - 2.79168i) q^{39} +(-9.30279 - 6.75887i) q^{41} +10.2458i q^{43} +(-0.436922 - 2.19297i) q^{45} +(0.500524 + 0.162630i) q^{47} -7.34957 q^{49} -1.14884 q^{51} +(-2.80539 - 0.911527i) q^{53} +(-1.79357 - 0.211714i) q^{55} -0.0150112i q^{57} +(9.25803 + 6.72635i) q^{59} +(-2.54203 + 1.84689i) q^{61} +(2.22658 - 3.06462i) q^{63} +(-10.4155 + 2.07516i) q^{65} +(12.6312 - 4.10412i) q^{67} +(1.93691 + 5.96119i) q^{69} +(-1.51826 + 4.67271i) q^{71} +(2.75001 + 3.78507i) q^{73} +(-1.16418 + 4.86258i) q^{75} +(-1.79836 - 2.47523i) q^{77} +(-2.86507 + 8.81777i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-1.35402 + 0.439947i) q^{83} +(2.33326 + 1.07476i) q^{85} +(-2.17534 + 2.99410i) q^{87} +(-13.0306 + 9.46730i) q^{89} +(-14.5554 - 10.5751i) q^{91} -1.58209i q^{93} +(-0.0140432 + 0.0304871i) q^{95} +(-7.66744 - 2.49130i) q^{97} +0.807679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^5 + 6 * q^9	\( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more