LMFDB - Embedded newform 1440.2.q.n.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.3010058496.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 6x^{6} + 2x^{5} - 17x^{4} + 6x^{3} + 54x^{2} - 108x + 81 $ x^8 - 4x^7 + 6x^6 + 2x^5 - 17x^4 + 6x^3 + 54x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$1.65412 + 0.513691i$ of defining polynomial
Character	$\chi$	$=$	1440.961
Dual form			1440.2.q.n.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382191 - 1.68936i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.382191 + 0.661975i) q^{7} +(-2.70786 - 1.29132i) q^{9} +O(q^{10})$	\(q+(0.382191 - 1.68936i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.382191 + 0.661975i) q^{7} +(-2.70786 - 1.29132i) q^{9} +(-1.03631 + 1.79495i) q^{11} +(-1.97224 - 3.41602i) q^{13} +(1.65412 - 0.513691i) q^{15} +7.03221 q^{17} -1.45614 q^{19} +(0.972242 + 0.898659i) q^{21} +(-4.56229 - 7.90212i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.21642 + 4.08101i) q^{27} +(3.04386 - 5.27212i) q^{29} +(-5.21642 - 9.03510i) q^{31} +(2.63624 + 2.43672i) q^{33} -0.764383 q^{35} +4.56097 q^{37} +(-6.52466 + 2.02625i) q^{39} +(-5.54487 - 9.60400i) q^{41} +(1.72807 - 2.99310i) q^{43} +(-0.235617 - 2.99073i) q^{45} +(2.19798 - 3.80702i) q^{47} +(3.20786 + 5.55618i) q^{49} +(2.68765 - 11.8799i) q^{51} -8.36020 q^{53} -2.07263 q^{55} +(-0.556523 + 2.45994i) q^{57} +(-1.23562 - 2.14015i) q^{59} +(-3.78049 + 6.54800i) q^{61} +(1.88974 - 1.29901i) q^{63} +(1.97224 - 3.41602i) q^{65} +(1.41851 + 2.45692i) q^{67} +(-15.0932 + 4.68722i) q^{69} +9.01510 q^{71} +12.1453 q^{73} +(1.27193 + 1.17567i) q^{75} +(-0.792141 - 1.37203i) q^{77} +(0.235617 - 0.408101i) q^{79} +(5.66501 + 6.99341i) q^{81} +(-5.45482 + 9.44802i) q^{83} +(3.51610 + 6.09007i) q^{85} +(-7.74317 - 7.15713i) q^{87} +0.854744 q^{89} +3.01510 q^{91} +(-17.2572 + 5.35926i) q^{93} +(-0.728069 - 1.26105i) q^{95} +(3.16501 - 5.48195i) q^{97} +(5.12404 - 3.52226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 8 * q^9	$ 8 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 8 q^{9} + 2 q^{11} + 4 q^{15} - 8 q^{17} - 28 q^{19} - 8 q^{21} - 6 q^{23} - 4 q^{25} + 14 q^{27} + 8 q^{29} - 2 q^{31} + 8 q^{33} - 4 q^{35} - 32 q^{37} + 6 q^{39} - 8 q^{41} + 22 q^{43} - 4 q^{45} - 8 q^{47} + 12 q^{49} - 14 q^{51} - 8 q^{53} + 4 q^{55} - 16 q^{57} - 12 q^{59} + 4 q^{61} + 8 q^{63} + 12 q^{69} + 60 q^{71} + 56 q^{73} + 2 q^{75} - 20 q^{77} + 4 q^{79} + 28 q^{81} - 22 q^{83} - 4 q^{85} - 58 q^{87} + 48 q^{89} + 12 q^{91} - 8 q^{93} - 14 q^{95} + 8 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 8 * q^9 + 2 * q^11 + 4 * q^15 - 8 * q^17 - 28 * q^19 - 8 * q^21 - 6 * q^23 - 4 * q^25 + 14 * q^27 + 8 * q^29 - 2 * q^31 + 8 * q^33 - 4 * q^35 - 32 * q^37 + 6 * q^39 - 8 * q^41 + 22 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 14 * q^51 - 8 * q^53 + 4 * q^55 - 16 * q^57 - 12 * q^59 + 4 * q^61 + 8 * q^63 + 12 * q^69 + 60 * q^71 + 56 * q^73 + 2 * q^75 - 20 * q^77 + 4 * q^79 + 28 * q^81 - 22 * q^83 - 4 * q^85 - 58 * q^87 + 48 * q^89 + 12 * q^91 - 8 * q^93 - 14 * q^95 + 8 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.382191	−	1.68936i	0.220658	−	0.975351i
$3$	0.382191	−	1.68936i	0.220658	−	0.975351i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.382191	+	0.661975i	−0.144455	+	0.250203i	−0.929169	−	0.369654i	$-0.879476\pi$
$7$	−0.382191	+	0.661975i	−0.144455	+	0.250203i	0.784715	+	0.619857i	$0.212809\pi$
$8$		0			0
$9$	−2.70786	−	1.29132i	−0.902620	−	0.430439i
$10$		0			0
$11$	−1.03631	+	1.79495i	−0.312460	+	0.541197i	−0.978894	−	0.204367i	$-0.934486\pi$
$11$	−1.03631	+	1.79495i	−0.312460	+	0.541197i	0.666434	+	0.745564i	$0.267820\pi$
$12$		0			0
$13$	−1.97224	−	3.41602i	−0.547002	−	0.947435i	−0.998478	−	0.0551515i	$-0.982436\pi$
$13$	−1.97224	−	3.41602i	−0.547002	−	0.947435i	0.451476	−	0.892283i	$-0.350898\pi$
$14$		0			0
$15$	1.65412	−	0.513691i	0.427093	−	0.132635i
$16$		0			0
$17$	7.03221			1.70556			0.852781	−	0.522269i	$-0.174914\pi$
$17$	7.03221			1.70556			0.852781	+	0.522269i	$0.174914\pi$
$18$		0			0
$19$	−1.45614			−0.334061			−0.167030	−	0.985952i	$-0.553418\pi$
$19$	−1.45614			−0.334061			−0.167030	+	0.985952i	$0.553418\pi$
$20$		0			0
$21$	0.972242	+	0.898659i	0.212161	+	0.196104i
$22$		0			0
$23$	−4.56229	−	7.90212i	−0.951304	−	1.64771i	−0.742608	−	0.669726i	$-0.766412\pi$
$23$	−4.56229	−	7.90212i	−0.951304	−	1.64771i	−0.208696	−	0.977981i	$-0.566922\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−3.21642	+	4.08101i	−0.618999	+	0.785391i
$28$		0			0
$29$	3.04386	−	5.27212i	0.565231	−	0.979009i	−0.431797	−	0.901971i	$-0.642120\pi$
$29$	3.04386	−	5.27212i	0.565231	−	0.979009i	0.997028	−	0.0770381i	$-0.0245463\pi$
$30$		0			0
$31$	−5.21642	−	9.03510i	−0.936896	−	1.62275i	−0.771218	−	0.636571i	$-0.780352\pi$
$31$	−5.21642	−	9.03510i	−0.936896	−	1.62275i	−0.165678	−	0.986180i	$-0.552981\pi$
$32$		0			0
$33$	2.63624	+	2.43672i	0.458910	+	0.424178i
$34$		0			0
$35$	−0.764383			−0.129204
$36$		0			0
$37$	4.56097			0.749820			0.374910	−	0.927061i	$-0.377674\pi$
$37$	4.56097			0.749820			0.374910	+	0.927061i	$0.377674\pi$
$38$		0			0
$39$	−6.52466	+	2.02625i	−1.04478	+	0.324459i
$40$		0			0
$41$	−5.54487	−	9.60400i	−0.865963	−	1.49989i	−0.866088	−	0.499892i	$-0.833373\pi$
$41$	−5.54487	−	9.60400i	−0.865963	−	1.49989i	0.000124357	−	1.00000i	$-0.499960\pi$
$42$		0			0
$43$	1.72807	−	2.99310i	0.263528	−	0.456444i	−0.703649	−	0.710548i	$-0.748447\pi$
$43$	1.72807	−	2.99310i	0.263528	−	0.456444i	0.967177	+	0.254104i	$0.0817805\pi$
$44$		0			0
$45$	−0.235617	−	2.99073i	−0.0351237	−	0.445832i
$46$		0			0
$47$	2.19798	−	3.80702i	0.320609	−	0.555311i	−0.660005	−	0.751261i	$-0.729446\pi$
$47$	2.19798	−	3.80702i	0.320609	−	0.555311i	0.980614	+	0.195950i	$0.0627791\pi$
$48$		0			0
$49$	3.20786	+	5.55618i	0.458266	+	0.793739i
$50$		0			0
$51$	2.68765	−	11.8799i	0.376346	−	1.66352i
$52$		0			0
$53$	−8.36020			−1.14836			−0.574181	−	0.818728i	$-0.694679\pi$
$53$	−8.36020			−1.14836			−0.574181	+	0.818728i	$0.694679\pi$
$54$		0			0
$55$	−2.07263			−0.279473
$56$		0			0
$57$	−0.556523	+	2.45994i	−0.0737133	+	0.325827i
$58$		0			0
$59$	−1.23562	−	2.14015i	−0.160864	−	0.278624i	0.774315	−	0.632800i	$-0.218095\pi$
$59$	−1.23562	−	2.14015i	−0.160864	−	0.278624i	−0.935179	+	0.354176i	$0.884761\pi$
$60$		0			0
$61$	−3.78049	+	6.54800i	−0.484042	+	0.838385i	−0.999832	−	0.0183300i	$-0.994165\pi$
$61$	−3.78049	+	6.54800i	−0.484042	+	0.838385i	0.515790	+	0.856715i	$0.327498\pi$
$62$		0			0
$63$	1.88974	−	1.29901i	0.238085	−	0.163659i
$64$		0			0
$65$	1.97224	−	3.41602i	0.244627	−	0.423706i
$66$		0			0
$67$	1.41851	+	2.45692i	0.173298	+	0.300161i	0.939571	−	0.342354i	$-0.111224\pi$
$67$	1.41851	+	2.45692i	0.173298	+	0.300161i	−0.766273	+	0.642515i	$0.777891\pi$
$68$		0			0
$69$	−15.0932	+	4.68722i	−1.81701	+	0.564275i
$70$		0			0
$71$	9.01510			1.06990			0.534948	−	0.844885i	$-0.320331\pi$
$71$	9.01510			1.06990			0.534948	+	0.844885i	$0.320331\pi$
$72$		0			0
$73$	12.1453			1.42149			0.710747	−	0.703447i	$-0.248357\pi$
$73$	12.1453			1.42149			0.710747	+	0.703447i	$0.248357\pi$
$74$		0			0
$75$	1.27193	+	1.17567i	0.146870	+	0.135754i
$76$		0			0
$77$	−0.792141	−	1.37203i	−0.0902728	−	0.156357i
$78$		0			0
$79$	0.235617	−	0.408101i	0.0265090	−	0.0459149i	−0.852467	−	0.522782i	$-0.824894\pi$
$79$	0.235617	−	0.408101i	0.0265090	−	0.0459149i	0.878976	+	0.476867i	$0.158228\pi$
$80$		0			0
$81$	5.66501	+	6.99341i	0.629445	+	0.777045i
$82$		0			0
$83$	−5.45482	+	9.44802i	−0.598744	+	1.03706i	0.394263	+	0.918998i	$0.371000\pi$
$83$	−5.45482	+	9.44802i	−0.598744	+	1.03706i	−0.993007	+	0.118058i	$0.962333\pi$
$84$		0			0
$85$	3.51610	+	6.09007i	0.381375	+	0.660561i
$86$		0			0
$87$	−7.74317	−	7.15713i	−0.830154	−	0.767325i
$88$		0			0
$89$	0.854744			0.0906027			0.0453014	−	0.998973i	$-0.485575\pi$
$89$	0.854744			0.0906027			0.0453014	+	0.998973i	$0.485575\pi$
$90$		0			0
$91$	3.01510			0.316068
$92$		0			0
$93$	−17.2572	+	5.35926i	−1.78949	+	0.555729i
$94$		0			0
$95$	−0.728069	−	1.26105i	−0.0746983	−	0.129381i
$96$		0			0
$97$	3.16501	−	5.48195i	0.321358	−	0.556608i	−0.659411	−	0.751783i	$-0.729194\pi$
$97$	3.16501	−	5.48195i	0.321358	−	0.556608i	0.980768	+	0.195175i	$0.0625275\pi$
$98$		0			0
$99$	5.12404	−	3.52226i	0.514985	−	0.354000i
$100$		0			0
$101$	0.907622	−	1.57205i	0.0903118	−	0.156425i	−0.817331	−	0.576169i	$-0.804547\pi$
$101$	0.907622	−	1.57205i	0.0903118	−	0.156425i	0.907642	+	0.419744i	$0.137880\pi$
$102$		0			0
$103$	1.67255	+	2.89695i	0.164802	+	0.285445i	0.936585	−	0.350441i	$-0.113968\pi$
$103$	1.67255	+	2.89695i	0.164802	+	0.285445i	−0.771783	+	0.635886i	$0.780635\pi$
$104$		0			0
$105$	−0.292141	+	1.29132i	−0.0285100	+	0.126020i
$106$		0			0
$107$	−13.7713			−1.33132			−0.665659	−	0.746256i	$-0.731850\pi$
$107$	−13.7713			−1.33132			−0.665659	+	0.746256i	$0.731850\pi$
$108$		0			0
$109$	−9.77592			−0.936364			−0.468182	−	0.883632i	$-0.655091\pi$
$109$	−9.77592			−0.936364			−0.468182	+	0.883632i	$0.655091\pi$
$110$		0			0
$111$	1.74317	−	7.70512i	0.165454	−	0.731337i
$112$		0			0
$113$	1.10747	+	1.91820i	0.104182	+	0.180449i	0.913404	−	0.407055i	$-0.133444\pi$
$113$	1.10747	+	1.91820i	0.104182	+	0.180449i	−0.809221	+	0.587504i	$0.800111\pi$
$114$		0			0
$115$	4.56229	−	7.90212i	0.425436	−	0.736877i
$116$		0			0
$117$	0.929388	+	11.7969i	0.0859220	+	1.09062i
$118$		0			0
$119$	−2.68765	+	4.65515i	−0.246376	+	0.426737i
$120$		0			0
$121$	3.35211	+	5.80602i	0.304737	+	0.527820i
$122$		0			0
$123$	−18.3438	+	5.69670i	−1.65400	+	0.513655i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−12.1397			−1.07722			−0.538611	−	0.842554i	$-0.681051\pi$
$127$	−12.1397			−1.07722			−0.538611	+	0.842554i	$0.681051\pi$
$128$		0			0
$129$	−4.39597	−	4.06327i	−0.387043	−	0.357751i
$130$		0			0
$131$	−10.7966	−	18.7002i	−0.943303	−	1.63385i	−0.759115	−	0.650957i	$-0.774368\pi$
$131$	−10.7966	−	18.7002i	−0.943303	−	1.63385i	−0.184188	−	0.982891i	$-0.558966\pi$
$132$		0			0
$133$	0.556523	−	0.963927i	0.0482567	−	0.0835831i
$134$		0			0
$135$	−5.14247	−	0.744991i	−0.442593	−	0.0641186i
$136$		0			0
$137$	4.32334	−	7.48825i	0.369368	−	0.639764i	−0.620099	−	0.784524i	$-0.712908\pi$
$137$	4.32334	−	7.48825i	0.369368	−	0.639764i	0.989467	+	0.144760i	$0.0462409\pi$
$138$		0			0
$139$	0.0555154	+	0.0961556i	0.00470876	+	0.00815581i	0.868370	−	0.495917i	$-0.165168\pi$
$139$	0.0555154	+	0.0961556i	0.00470876	+	0.00815581i	−0.863661	+	0.504072i	$0.831834\pi$
$140$		0			0
$141$	−5.59137	−	5.16819i	−0.470878	−	0.435240i
$142$		0			0
$143$	8.17545			0.683665
$144$		0			0
$145$	6.08772			0.505558
$146$		0			0
$147$	10.6124	−	3.29570i	0.875295	−	0.271825i
$148$		0			0
$149$	−6.01610	−	10.4202i	−0.492858	−	0.853656i	0.507108	−	0.861883i	$-0.330715\pi$
$149$	−6.01610	−	10.4202i	−0.492858	−	0.853656i	−0.999966	+	0.00822679i	$0.997381\pi$
$150$		0			0
$151$	1.97878	−	3.42735i	0.161031	−	0.278914i	−0.774208	−	0.632932i	$-0.781851\pi$
$151$	1.97878	−	3.42735i	0.161031	−	0.278914i	0.935239	+	0.354018i	$0.115185\pi$
$152$		0			0
$153$	−19.0422	−	9.08080i	−1.53947	−	0.734140i
$154$		0			0
$155$	5.21642	−	9.03510i	0.418993	−	0.725716i
$156$		0			0
$157$	10.3809	+	17.9802i	0.828484	+	1.43498i	0.899227	+	0.437482i	$0.144129\pi$
$157$	10.3809	+	17.9802i	0.828484	+	1.43498i	−0.0707435	+	0.997495i	$0.522537\pi$
$158$		0			0
$159$	−3.19520	+	14.1234i	−0.253396	+	1.12006i
$160$		0			0
$161$	6.97468			0.549682
$162$		0			0
$163$	−1.37530			−0.107722			−0.0538609	−	0.998548i	$-0.517153\pi$
$163$	−1.37530			−0.107722			−0.0538609	+	0.998548i	$0.517153\pi$
$164$		0			0
$165$	−0.792141	+	3.50141i	−0.0616681	+	0.272584i
$166$		0			0
$167$	9.63082	+	16.6811i	0.745255	+	1.29082i	0.950076	+	0.312020i	$0.101006\pi$
$167$	9.63082	+	16.6811i	0.745255	+	1.29082i	−0.204821	+	0.978800i	$0.565661\pi$
$168$		0			0
$169$	−1.27948	+	2.21612i	−0.0984215	+	0.170471i
$170$		0			0
$171$	3.94302	+	1.88033i	0.301530	+	0.143793i
$172$		0			0
$173$	2.34309	−	4.05835i	0.178142	−	0.308551i	−0.763102	−	0.646278i	$-0.776325\pi$
$173$	2.34309	−	4.05835i	0.178142	−	0.308551i	0.941244	+	0.337727i	$0.109658\pi$
$174$		0			0
$175$	−0.382191	−	0.661975i	−0.0288910	−	0.0500406i
$176$		0			0
$177$	−4.08772	+	1.26945i	−0.307252	+	0.0954178i
$178$		0			0
$179$	11.9616			0.894052			0.447026	−	0.894521i	$-0.352483\pi$
$179$	11.9616			0.894052			0.447026	+	0.894521i	$0.352483\pi$
$180$		0			0
$181$	2.96981			0.220744			0.110372	−	0.993890i	$-0.464796\pi$
$181$	2.96981			0.220744			0.110372	+	0.993890i	$0.464796\pi$
$182$		0			0
$183$	9.61704	+	8.88918i	0.710912	+	0.657107i
$184$		0			0
$185$	2.28049	+	3.94992i	0.167665	+	0.290404i
$186$		0			0
$187$	−7.28758	+	12.6225i	−0.532920	+	0.923045i
$188$		0			0
$189$	−1.47224	−	3.68891i	−0.107090	−	0.268329i
$190$		0			0
$191$	6.16090	−	10.6710i	0.445787	−	0.772126i	−0.552320	−	0.833632i	$-0.686257\pi$
$191$	6.16090	−	10.6710i	0.445787	−	0.772126i	0.998107	+	0.0615066i	$0.0195905\pi$
$192$		0			0
$193$	8.07506	+	13.9864i	0.581256	+	1.00676i	0.995331	+	0.0965218i	$0.0307717\pi$
$193$	8.07506	+	13.9864i	0.581256	+	1.00676i	−0.414075	+	0.910243i	$0.635895\pi$
$194$		0			0
$195$	−5.01711	−	4.63740i	−0.359283	−	0.332091i
$196$		0			0
$197$	7.44793			0.530643			0.265321	−	0.964160i	$-0.414522\pi$
$197$	7.44793			0.530643			0.265321	+	0.964160i	$0.414522\pi$
$198$		0			0
$199$	−15.6316			−1.10809			−0.554047	−	0.832485i	$-0.686917\pi$
$199$	−15.6316			−1.10809			−0.554047	+	0.832485i	$0.686917\pi$
$200$		0			0
$201$	4.69276	−	1.45735i	0.331002	−	0.102793i
$202$		0			0
$203$	2.32668	+	4.02992i	0.163301	+	0.282845i
$204$		0			0
$205$	5.54487	−	9.60400i	0.387271	−	0.670772i
$206$		0			0
$207$	2.14991	+	27.2892i	0.149429	+	1.89673i
$208$		0			0
$209$	1.50902	−	2.61369i	0.104381	−	0.180793i
$210$		0			0
$211$	8.66790	+	15.0132i	0.596723	+	1.03355i	0.993301	+	0.115553i	$0.0368642\pi$
$211$	8.66790	+	15.0132i	0.596723	+	1.03355i	−0.396578	+	0.918001i	$0.629803\pi$
$212$		0			0
$213$	3.44549	−	15.2297i	0.236081	−	1.04352i
$214$		0			0
$215$	3.45614			0.235707
$216$		0			0
$217$	7.97468			0.541356
$218$		0			0
$219$	4.64181	−	20.5177i	0.313665	−	1.38646i
$220$		0			0
$221$	−13.8692	−	24.0222i	−0.932945	−	1.61591i
$222$		0			0
$223$	3.90685	−	6.76687i	0.261622	−	0.453143i	−0.705051	−	0.709157i	$-0.749076\pi$
$223$	3.90685	−	6.76687i	0.261622	−	0.453143i	0.966673	+	0.256014i	$0.0824092\pi$
$224$		0			0
$225$	2.47224	−	1.69942i	0.164816	−	0.113294i
$226$		0			0
$227$	−13.7603	+	23.8335i	−0.913302	+	1.58188i	−0.103933	+	0.994584i	$0.533143\pi$
$227$	−13.7603	+	23.8335i	−0.913302	+	1.58188i	−0.809369	+	0.587301i	$0.800191\pi$
$228$		0			0
$229$	1.17201	+	2.02997i	0.0774483	+	0.134144i	0.902148	−	0.431426i	$-0.141989\pi$
$229$	1.17201	+	2.02997i	0.0774483	+	0.134144i	−0.824700	+	0.565570i	$0.808656\pi$
$230$		0			0
$231$	−2.62060	+	0.813832i	−0.172422	+	0.0535462i
$232$		0			0
$233$	11.6185			0.761154			0.380577	−	0.924749i	$-0.375725\pi$
$233$	11.6185			0.761154			0.380577	+	0.924749i	$0.375725\pi$
$234$		0			0
$235$	4.39597			0.286761
$236$		0			0
$237$	−0.599378	−	0.554014i	−0.0389338	−	0.0359871i
$238$		0			0
$239$	−5.20077	−	9.00800i	−0.336410	−	0.582679i	0.647345	−	0.762197i	$-0.275879\pi$
$239$	−5.20077	−	9.00800i	−0.336410	−	0.582679i	−0.983755	+	0.179518i	$0.942546\pi$
$240$		0			0
$241$	−6.76337	+	11.7145i	−0.435667	+	0.754598i	−0.997350	−	0.0727550i	$-0.976821\pi$
$241$	−6.76337	+	11.7145i	−0.435667	+	0.754598i	0.561683	+	0.827353i	$0.310154\pi$
$242$		0			0
$243$	13.9795	−	6.89740i	0.896784	−	0.442469i
$244$		0			0
$245$	−3.20786	+	5.55618i	−0.204943	+	0.354971i
$246$		0			0
$247$	2.87186	+	4.97420i	0.182732	+	0.316501i
$248$		0			0
$249$	13.8763	+	12.8261i	0.879375	+	0.812821i
$250$		0			0
$251$	13.2300			0.835073			0.417536	−	0.908660i	$-0.362894\pi$
$251$	13.2300			0.835073			0.417536	+	0.908660i	$0.362894\pi$
$252$		0			0
$253$	18.9119			1.18898
$254$		0			0
$255$	11.6321	−	3.61239i	0.728433	−	0.226216i
$256$		0			0
$257$	−13.5055	−	23.3921i	−0.842447	−	1.45916i	−0.887820	−	0.460192i	$-0.847781\pi$
$257$	−13.5055	−	23.3921i	−0.842447	−	1.45916i	0.0453723	−	0.998970i	$-0.485553\pi$
$258$		0			0
$259$	−1.74317	+	3.01925i	−0.108315	+	0.187607i
$260$		0			0
$261$	−15.0503	+	10.3456i	−0.931592	+	0.640375i
$262$		0			0
$263$	−0.126675	+	0.219408i	−0.00781114	+	0.0135293i	−0.869905	−	0.493220i	$-0.835820\pi$
$263$	−0.126675	+	0.219408i	−0.00781114	+	0.0135293i	0.862093	+	0.506749i	$0.169153\pi$
$264$		0			0
$265$	−4.18010	−	7.24015i	−0.256782	−	0.444759i
$266$		0			0
$267$	0.326676	−	1.44397i	0.0199922	−	0.0883695i
$268$		0			0
$269$	−22.9485			−1.39920			−0.699598	−	0.714537i	$-0.746638\pi$
$269$	−22.9485			−1.39920			−0.699598	+	0.714537i	$0.746638\pi$
$270$		0			0
$271$	23.0080			1.39764			0.698818	−	0.715300i	$-0.253710\pi$
$271$	23.0080			1.39764			0.698818	+	0.715300i	$0.253710\pi$
$272$		0			0
$273$	1.15234	−	5.09358i	0.0697430	−	0.308277i
$274$		0			0
$275$	−1.03631	−	1.79495i	−0.0624921	−	0.108239i
$276$		0			0
$277$	−6.40306	+	11.0904i	−0.384722	+	0.666359i	−0.991731	−	0.128337i	$-0.959036\pi$
$277$	−6.40306	+	11.0904i	−0.384722	+	0.666359i	0.607008	+	0.794696i	$0.292370\pi$
$278$		0			0
$279$	2.45815	+	31.2018i	0.147166	+	1.86800i
$280$		0			0
$281$	15.2839	−	26.4725i	0.911763	−	1.57922i	0.100190	−	0.994968i	$-0.468055\pi$
$281$	15.2839	−	26.4725i	0.911763	−	1.57922i	0.811573	−	0.584251i	$-0.198612\pi$
$282$		0			0
$283$	8.05064	+	13.9441i	0.478561	+	0.828892i	0.999698	−	0.0245813i	$-0.00782527\pi$
$283$	8.05064	+	13.9441i	0.478561	+	0.828892i	−0.521137	+	0.853473i	$0.674492\pi$
$284$		0			0
$285$	−2.40863	+	0.748006i	−0.142675	+	0.0443080i
$286$		0			0
$287$	8.47681			0.500370
$288$		0			0
$289$	32.4520			1.90894
$290$		0			0
$291$	−8.05134	−	7.44198i	−0.471978	−	0.436257i
$292$		0			0
$293$	4.55652	+	7.89213i	0.266195	+	0.461063i	0.967876	−	0.251428i	$-0.0809002\pi$
$293$	4.55652	+	7.89213i	0.266195	+	0.461063i	−0.701681	+	0.712491i	$0.747567\pi$
$294$		0			0
$295$	1.23562	−	2.14015i	0.0719404	−	0.124604i
$296$		0			0
$297$	−3.99199	−	10.0025i	−0.231639	−	0.580405i
$298$		0			0
$299$	−17.9959	+	31.1698i	−1.04073	+	1.80260i
$300$		0			0
$301$	1.32091	+	2.28788i	0.0761358	+	0.131871i
$302$		0			0
$303$	−2.30887	−	2.13412i	−0.132641	−	0.122602i
$304$		0			0
$305$	−7.56097			−0.432940
$306$		0			0
$307$	18.2163			1.03966			0.519831	−	0.854269i	$-0.325995\pi$
$307$	18.2163			1.03966			0.519831	+	0.854269i	$0.325995\pi$
$308$		0			0
$309$	5.53322	−	1.71835i	0.314774	−	0.0977537i
$310$		0			0
$311$	−0.584829	−	1.01295i	−0.0331626	−	0.0574394i	0.848968	−	0.528445i	$-0.177225\pi$
$311$	−0.584829	−	1.01295i	−0.0331626	−	0.0574394i	−0.882130	+	0.471005i	$0.843891\pi$
$312$		0			0
$313$	5.48126	−	9.49382i	0.309819	−	0.536622i	−0.668504	−	0.743709i	$-0.733065\pi$
$313$	5.48126	−	9.49382i	0.309819	−	0.536622i	0.978323	+	0.207087i	$0.0663982\pi$
$314$		0			0
$315$	2.06984	+	0.987060i	0.116622	+	0.0556145i
$316$		0			0
$317$	11.4257	−	19.7900i	0.641734	−	1.11152i	−0.343312	−	0.939221i	$-0.611549\pi$
$317$	11.4257	−	19.7900i	0.641734	−	1.11152i	0.985046	−	0.172294i	$-0.0551179\pi$
$318$		0			0
$319$	6.30879	+	10.9272i	0.353225	+	0.611803i
$320$		0			0
$321$	−5.26326	+	23.2646i	−0.293767	+	1.29850i
$322$		0			0
$323$	−10.2399			−0.569761
$324$		0			0
$325$	3.94448			0.218801
$326$		0			0
$327$	−3.73627	+	16.5150i	−0.206616	+	0.913283i
$328$		0			0
$329$	1.68010	+	2.91002i	0.0926270	+	0.160435i
$330$		0			0
$331$	11.6383	−	20.1581i	0.639696	−	1.10799i	−0.345803	−	0.938307i	$-0.612393\pi$
$331$	11.6383	−	20.1581i	0.639696	−	1.10799i	0.985499	−	0.169679i	$-0.0542732\pi$
$332$		0			0
$333$	−12.3505	−	5.88966i	−0.676802	−	0.322751i
$334$		0			0
$335$	−1.41851	+	2.45692i	−0.0775012	+	0.134236i
$336$		0			0
$337$	−1.63422	−	2.83056i	−0.0890218	−	0.154190i	0.818076	−	0.575110i	$-0.195041\pi$
$337$	−1.63422	−	2.83056i	−0.0890218	−	0.154190i	−0.907098	+	0.420920i	$0.861707\pi$
$338$		0			0
$339$	3.66379	−	1.13780i	0.198990	−	0.0617968i
$340$		0			0
$341$	21.6234			1.17097
$342$		0			0
$343$	−10.2547			−0.553704
$344$		0			0
$345$	−11.6058	−	10.7275i	−0.624838	−	0.577548i
$346$		0			0
$347$	5.27395	+	9.13474i	0.283120	+	0.490379i	0.972152	−	0.234353i	$-0.0752971\pi$
$347$	5.27395	+	9.13474i	0.283120	+	0.490379i	−0.689031	+	0.724732i	$0.741964\pi$
$348$		0			0
$349$	6.62257	−	11.4706i	0.354498	−	0.614009i	−0.632534	−	0.774533i	$-0.717985\pi$
$349$	6.62257	−	11.4706i	0.354498	−	0.614009i	0.987032	+	0.160524i	$0.0513184\pi$
$350$		0			0
$351$	20.2844	+	2.93861i	1.08270	+	0.156851i
$352$		0			0
$353$	−8.17545	+	14.1603i	−0.435135	+	0.753676i	−0.997307	−	0.0733444i	$-0.976633\pi$
$353$	−8.17545	+	14.1603i	−0.435135	+	0.753676i	0.562171	+	0.827021i	$0.309966\pi$
$354$		0			0
$355$	4.50755	+	7.80730i	0.239236	+	0.414369i
$356$		0			0
$357$	6.83701	+	6.31956i	0.361853	+	0.334467i
$358$		0			0
$359$	25.9221			1.36812			0.684058	−	0.729428i	$-0.260214\pi$
$359$	25.9221			1.36812			0.684058	+	0.729428i	$0.260214\pi$
$360$		0			0
$361$	−16.8797			−0.888403
$362$		0			0
$363$	11.0896	−	3.44390i	0.582053	−	0.180758i
$364$		0			0
$365$	6.07263	+	10.5181i	0.317856	+	0.550543i
$366$		0			0
$367$	−11.1760	+	19.3574i	−0.583382	+	1.01045i	0.411693	+	0.911323i	$0.364938\pi$
$367$	−11.1760	+	19.3574i	−0.583382	+	1.01045i	−0.995075	+	0.0991250i	$0.968396\pi$
$368$		0			0
$369$	2.61293	+	33.1665i	0.136024	+	1.72658i
$370$		0			0
$371$	3.19520	−	5.53425i	0.165886	−	0.287324i
$372$		0			0
$373$	9.73906	+	16.8685i	0.504269	+	0.873420i	0.999988	+	0.00493694i	$0.00157148\pi$
$373$	9.73906	+	16.8685i	0.504269	+	0.873420i	−0.495718	+	0.868483i	$0.665095\pi$
$374$		0			0
$375$	−0.382191	+	1.68936i	−0.0197363	+	0.0872381i
$376$		0			0
$377$	−24.0129			−1.23673
$378$		0			0
$379$	12.5055			0.642362			0.321181	−	0.947018i	$-0.395920\pi$
$379$	12.5055			0.642362			0.321181	+	0.947018i	$0.395920\pi$
$380$		0			0
$381$	−4.63968	+	20.5083i	−0.237698	+	1.05067i
$382$		0			0
$383$	1.59993	+	2.77115i	0.0817524	+	0.141599i	0.904003	−	0.427527i	$-0.140615\pi$
$383$	1.59993	+	2.77115i	0.0817524	+	0.141599i	−0.822250	+	0.569126i	$0.807282\pi$
$384$		0			0
$385$	0.792141	−	1.37203i	0.0403712	−	0.0699250i
$386$		0			0
$387$	−8.54441	+	5.87342i	−0.434337	+	0.298563i
$388$		0			0
$389$	7.23663	−	12.5342i	0.366911	−	0.635509i	−0.622169	−	0.782883i	$-0.713749\pi$
$389$	7.23663	−	12.5342i	0.366911	−	0.635509i	0.989081	+	0.147373i	$0.0470819\pi$
$390$		0			0
$391$	−32.0830	−	55.5694i	−1.62251	−	2.81026i
$392$		0			0
$393$	−35.7178	+	11.0922i	−1.80172	+	0.559529i
$394$		0			0
$395$	0.471234			0.0237104
$396$		0			0
$397$	−37.1864			−1.86633			−0.933165	−	0.359448i	$-0.882965\pi$
$397$	−37.1864			−1.86633			−0.933165	+	0.359448i	$0.882965\pi$
$398$		0			0
$399$	−1.41572	−	1.30857i	−0.0708746	−	0.0655105i
$400$		0			0
$401$	9.52521	+	16.4981i	0.475666	+	0.823878i	0.999611	−	0.0278739i	$-0.00887368\pi$
$401$	9.52521	+	16.4981i	0.475666	+	0.823878i	−0.523945	+	0.851752i	$0.675540\pi$
$402$		0			0
$403$	−20.5761	+	35.6388i	−1.02497	+	1.77530i
$404$		0			0
$405$	−3.22396	+	8.40274i	−0.160200	+	0.417536i
$406$		0			0
$407$	−4.72660	+	8.18671i	−0.234289	+	0.405800i
$408$		0			0
$409$	−8.47325	−	14.6761i	−0.418975	−	0.725686i	0.576861	−	0.816842i	$-0.304277\pi$
$409$	−8.47325	−	14.6761i	−0.418975	−	0.725686i	−0.995837	+	0.0911556i	$0.970944\pi$
$410$		0			0
$411$	−10.9980	−	10.1656i	−0.542491	−	0.501433i
$412$		0			0
$413$	1.88897			0.0929501
$414$		0			0
$415$	−10.9096			−0.535533
$416$		0			0
$417$	0.183659	−	0.0570356i	0.00899380	−	0.00279305i
$418$		0			0
$419$	−3.97878	−	6.89145i	−0.194376	−	0.336670i	0.752320	−	0.658798i	$-0.228935\pi$
$419$	−3.97878	−	6.89145i	−0.194376	−	0.336670i	−0.946696	+	0.322129i	$0.895602\pi$
$420$		0			0
$421$	0.327995	−	0.568103i	0.0159855	−	0.0276877i	−0.857922	−	0.513780i	$-0.828245\pi$
$421$	0.327995	−	0.568103i	0.0159855	−	0.0276877i	0.873907	+	0.486092i	$0.161578\pi$
$422$		0			0
$423$	−10.8679	+	7.47058i	−0.528415	+	0.363232i
$424$		0			0
$425$	−3.51610	+	6.09007i	−0.170556	+	0.295412i
$426$		0			0
$427$	−2.88974	−	5.00518i	−0.139844	−	0.242217i
$428$		0			0
$429$	3.12459	−	13.8113i	0.150856	−	0.666814i
$430$		0			0
$431$	13.4479			0.647764			0.323882	−	0.946098i	$-0.395012\pi$
$431$	13.4479			0.647764			0.323882	+	0.946098i	$0.395012\pi$
$432$		0			0
$433$	11.3995			0.547826			0.273913	−	0.961754i	$-0.411682\pi$
$433$	11.3995			0.547826			0.273913	+	0.961754i	$0.411682\pi$
$434$		0			0
$435$	2.32668	−	10.2843i	0.111556	−	0.493097i
$436$		0			0
$437$	6.64333	+	11.5066i	0.317793	+	0.550434i
$438$		0			0
$439$	−3.36020	+	5.82004i	−0.160374	+	0.277775i	−0.935003	−	0.354640i	$-0.884603\pi$
$439$	−3.36020	+	5.82004i	−0.160374	+	0.277775i	0.774629	+	0.632416i	$0.217937\pi$
$440$		0			0
$441$	−1.51165	−	19.1877i	−0.0719835	−	0.913700i
$442$		0			0
$443$	−7.30546	+	12.6534i	−0.347093	+	0.601182i	−0.985732	−	0.168324i	$-0.946164\pi$
$443$	−7.30546	+	12.6534i	−0.347093	+	0.601182i	0.638639	+	0.769507i	$0.279498\pi$
$444$		0			0
$445$	0.427372	+	0.740230i	0.0202594	+	0.0350903i
$446$		0			0
$447$	−19.9027	+	6.18084i	−0.941368	+	0.292344i
$448$		0			0
$449$	13.4822			0.636262			0.318131	−	0.948047i	$-0.396945\pi$
$449$	13.4822			0.636262			0.318131	+	0.948047i	$0.396945\pi$
$450$		0			0
$451$	22.9849			1.08232
$452$		0			0
$453$	−5.03375	−	4.65278i	−0.236506	−	0.218606i
$454$		0			0
$455$	1.50755	+	2.61115i	0.0706749	+	0.122413i
$456$		0			0
$457$	−13.3551	+	23.1318i	−0.624727	+	1.08206i	0.363867	+	0.931451i	$0.381456\pi$
$457$	−13.3551	+	23.1318i	−0.624727	+	1.08206i	−0.988594	+	0.150607i	$0.951877\pi$
$458$		0			0
$459$	−22.6185	+	28.6985i	−1.05574	+	1.33953i
$460$		0			0
$461$	4.64324	−	8.04233i	0.216257	−	0.374569i	−0.737404	−	0.675452i	$-0.763948\pi$
$461$	4.64324	−	8.04233i	0.216257	−	0.374569i	0.953661	+	0.300884i	$0.0972817\pi$
$462$		0			0
$463$	−7.55951	−	13.0934i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$463$	−7.55951	−	13.0934i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$464$		0			0
$465$	−13.2698	−	12.2655i	−0.615374	−	0.568800i
$466$		0			0
$467$	11.3793			0.526573			0.263286	−	0.964718i	$-0.415194\pi$
$467$	11.3793			0.526573			0.263286	+	0.964718i	$0.415194\pi$
$468$		0			0
$469$	−2.16856			−0.100135
$470$		0			0
$471$	34.3425	−	10.6651i	1.58242	−	0.491423i
$472$		0			0
$473$	3.58164	+	6.20359i	0.164684	+	0.285241i
$474$		0			0
$475$	0.728069	−	1.26105i	0.0334061	−	0.0578611i
$476$		0			0
$477$	22.6383	+	10.7957i	1.03653	+	0.494300i
$478$		0			0
$479$	−8.69377	+	15.0581i	−0.397229	+	0.688020i	−0.993383	−	0.114850i	$-0.963361\pi$
$479$	−8.69377	+	15.0581i	−0.397229	+	0.688020i	0.596154	+	0.802870i	$0.296695\pi$
$480$		0			0
$481$	−8.99535	−	15.5804i	−0.410153	−	0.710405i
$482$		0			0
$483$	2.66566	−	11.7827i	0.121292	−	0.536133i
$484$		0			0
$485$	6.33001			0.287431
$486$		0			0
$487$	22.7233			1.02969			0.514846	−	0.857282i	$-0.327849\pi$
$487$	22.7233			1.02969			0.514846	+	0.857282i	$0.327849\pi$
$488$		0			0
$489$	−0.525628	+	2.32337i	−0.0237697	+	0.105067i
$490$		0			0
$491$	−2.89718	−	5.01806i	−0.130748	−	0.226462i	0.793217	−	0.608939i	$-0.208405\pi$
$491$	−2.89718	−	5.01806i	−0.130748	−	0.226462i	−0.923965	+	0.382477i	$0.875071\pi$
$492$		0			0
$493$	21.4051	−	37.0747i	0.964036	−	1.66976i
$494$		0			0
$495$	5.61238	+	2.67642i	0.252258	+	0.120296i
$496$		0			0
$497$	−3.44549	+	5.96777i	−0.154551	+	0.267691i
$498$		0			0
$499$	18.1219	+	31.3881i	0.811250	+	1.40513i	0.911990	+	0.410213i	$0.134546\pi$
$499$	18.1219	+	31.3881i	0.811250	+	1.40513i	−0.100740	+	0.994913i	$0.532121\pi$
$500$		0			0
$501$	31.8611	−	9.89453i	1.42345	−	0.442055i
$502$		0			0
$503$	42.1739			1.88044			0.940221	−	0.340566i	$-0.110619\pi$
$503$	42.1739			1.88044			0.940221	+	0.340566i	$0.110619\pi$
$504$		0			0
$505$	1.81524			0.0807773
$506$		0			0
$507$	3.25482	+	3.00848i	0.144552	+	0.133611i
$508$		0			0
$509$	2.00902	+	3.47972i	0.0890481	+	0.154236i	0.907109	−	0.420896i	$-0.138284\pi$
$509$	2.00902	+	3.47972i	0.0890481	+	0.154236i	−0.818061	+	0.575132i	$0.804951\pi$
$510$		0			0
$511$	−4.64181	+	8.03986i	−0.205342	+	0.355662i
$512$		0			0
$513$	4.68354	−	5.94252i	0.206784	−	0.262369i
$514$		0			0
$515$	−1.67255	+	2.89695i	−0.0737015	+	0.127655i
$516$		0			0
$517$	4.55560	+	7.89054i	0.200355	+	0.347025i
$518$		0			0
$519$	−5.96050	−	5.50939i	−0.261637	−	0.241835i
$520$		0			0
$521$	−28.0202			−1.22759			−0.613794	−	0.789466i	$-0.710358\pi$
$521$	−28.0202			−1.22759			−0.613794	+	0.789466i	$0.710358\pi$
$522$		0			0
$523$	23.3332			1.02029			0.510144	−	0.860089i	$-0.329592\pi$
$523$	23.3332			1.02029			0.510144	+	0.860089i	$0.329592\pi$
$524$		0			0
$525$	−1.26438	+	0.392657i	−0.0551822	+	0.0171370i
$526$		0			0
$527$	−36.6829	−	63.5367i	−1.59793	−	2.76770i
$528$		0			0
$529$	−30.1290	+	52.1850i	−1.30996	+	2.26891i
$530$		0			0
$531$	0.582265	+	7.39080i	0.0252682	+	0.320733i
$532$		0			0
$533$	−21.8717	+	37.8828i	−0.947367	+	1.64089i
$534$		0			0
$535$	−6.88563	−	11.9263i	−0.297692	−	0.515618i
$536$		0			0
$537$	4.57162	−	20.2074i	0.197280	−	0.872014i
$538$		0			0
$539$	−13.2974			−0.572759
$540$		0			0
$541$	−37.7617			−1.62350			−0.811752	−	0.584002i	$-0.801486\pi$
$541$	−37.7617			−1.62350			−0.811752	+	0.584002i	$0.801486\pi$
$542$		0			0
$543$	1.13503	−	5.01707i	0.0487090	−	0.215303i
$544$		0			0
$545$	−4.88796	−	8.46620i	−0.209377	−	0.362652i
$546$		0			0
$547$	−7.83569	+	13.5718i	−0.335030	+	0.580289i	−0.983491	−	0.180959i	$-0.942080\pi$
$547$	−7.83569	+	13.5718i	−0.335030	+	0.580289i	0.648461	+	0.761248i	$0.275413\pi$
$548$		0			0
$549$	18.6926	−	12.8492i	0.797779	−	0.548393i
$550$		0			0
$551$	−4.43228	+	7.67694i	−0.188822	+	0.327049i
$552$		0			0
$553$	0.180102	+	0.311945i	0.00765870	+	0.0132653i
$554$		0			0
$555$	7.54441	−	2.34293i	0.320242	−	0.0994520i
$556$		0			0
$557$	−7.80813			−0.330841			−0.165421	−	0.986223i	$-0.552898\pi$
$557$	−7.80813			−0.330841			−0.165421	+	0.986223i	$0.552898\pi$
$558$		0			0
$559$	−13.6327			−0.576601
$560$		0			0
$561$	18.5386	+	17.1355i	0.782700	+	0.723462i
$562$		0			0
$563$	−12.8897	−	22.3257i	−0.543238	−	0.940915i	−0.998716	−	0.0506682i	$-0.983865\pi$
$563$	−12.8897	−	22.3257i	−0.543238	−	0.940915i	0.455478	−	0.890247i	$-0.349468\pi$
$564$		0			0
$565$	−1.10747	+	1.91820i	−0.0465918	+	0.0806993i
$566$		0			0
$567$	−6.79458	+	1.07727i	−0.285345	+	0.0452412i
$568$		0			0
$569$	4.88897	−	8.46794i	0.204956	−	0.354995i	−0.745163	−	0.666883i	$-0.767628\pi$
$569$	4.88897	−	8.46794i	0.204956	−	0.354995i	0.950119	+	0.311888i	$0.100961\pi$
$570$		0			0
$571$	3.75973	+	6.51204i	0.157340	+	0.272520i	0.933909	−	0.357512i	$-0.116375\pi$
$571$	3.75973	+	6.51204i	0.157340	+	0.272520i	−0.776569	+	0.630033i	$0.783042\pi$
$572$		0			0
$573$	−15.6725	−	14.4863i	−0.654727	−	0.605175i
$574$		0			0
$575$	9.12459			0.380522
$576$		0			0
$577$	−35.6918			−1.48587			−0.742935	−	0.669363i	$-0.766567\pi$
$577$	−35.6918			−1.48587			−0.742935	+	0.669363i	$0.766567\pi$
$578$		0			0
$579$	26.7143	−	8.29618i	1.11021	−	0.344778i
$580$		0			0
$581$	−4.16957	−	7.22191i	−0.172983	−	0.299615i
$582$		0			0
$583$	8.66379	−	15.0061i	0.358818	−	0.621491i
$584$		0			0
$585$	−9.75172	+	6.70332i	−0.403184	+	0.277148i
$586$		0			0
$587$	−13.8659	+	24.0164i	−0.572306	+	0.991264i	0.424022	+	0.905652i	$0.360618\pi$
$587$	−13.8659	+	24.0164i	−0.572306	+	0.991264i	−0.996329	+	0.0856118i	$0.972716\pi$
$588$		0			0
$589$	7.59582	+	13.1563i	0.312980	+	0.542098i
$590$		0			0
$591$	2.84653	−	12.5822i	0.117091	−	0.517563i
$592$		0			0
$593$	14.2141			0.583704			0.291852	−	0.956464i	$-0.405729\pi$
$593$	14.2141			0.583704			0.291852	+	0.956464i	$0.405729\pi$
$594$		0			0
$595$	−5.37530			−0.220366
$596$		0			0
$597$	−5.97426	+	26.4073i	−0.244510	+	1.08078i
$598$		0			0
$599$	−4.49300	−	7.78210i	−0.183579	−	0.317968i	0.759518	−	0.650487i	$-0.225435\pi$
$599$	−4.49300	−	7.78210i	−0.183579	−	0.317968i	−0.943097	+	0.332518i	$0.892102\pi$
$600$		0			0
$601$	−2.33093	+	4.03729i	−0.0950806	+	0.164684i	−0.909642	−	0.415393i	$-0.863644\pi$
$601$	−2.33093	+	4.03729i	−0.0950806	+	0.164684i	0.814562	+	0.580077i	$0.196978\pi$
$602$		0			0
$603$	−0.668448	−	8.48474i	−0.0272213	−	0.345525i
$604$		0			0
$605$	−3.35211	+	5.80602i	−0.136283	+	0.236048i
$606$		0			0
$607$	7.20000	+	12.4708i	0.292239	+	0.506173i	0.974339	−	0.225086i	$-0.0722664\pi$
$607$	7.20000	+	12.4708i	0.292239	+	0.506173i	−0.682100	+	0.731259i	$0.738933\pi$
$608$		0			0
$609$	7.69721	−	2.39039i	0.311907	−	0.0968634i
$610$		0			0
$611$	−17.3398			−0.701495
$612$		0			0
$613$	24.4104			0.985929			0.492964	−	0.870050i	$-0.335913\pi$
$613$	24.4104			0.985929			0.492964	+	0.870050i	$0.335913\pi$
$614$		0			0
$615$	−14.1054	−	13.0378i	−0.568784	−	0.525736i
$616$		0			0
$617$	−18.5554	−	32.1389i	−0.747012	−	1.29386i	−0.949249	−	0.314527i	$-0.898154\pi$
$617$	−18.5554	−	32.1389i	−0.747012	−	1.29386i	0.202236	−	0.979337i	$-0.435179\pi$
$618$		0			0
$619$	15.0317	−	26.0356i	0.604173	−	1.04646i	−0.388008	−	0.921656i	$-0.626837\pi$
$619$	15.0317	−	26.0356i	0.604173	−	1.04646i	0.992182	−	0.124803i	$-0.0398299\pi$
$620$		0			0
$621$	46.9229	+	6.79773i	1.88295	+	0.272784i
$622$		0			0
$623$	−0.326676	+	0.565819i	−0.0130880	+	0.0226691i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.83873	−	3.54820i	−0.153304	−	0.141701i
$628$		0			0
$629$	32.0737			1.27886
$630$		0			0
$631$	−42.3590			−1.68628			−0.843142	−	0.537691i	$-0.819297\pi$
$631$	−42.3590			−1.68628			−0.843142	+	0.537691i	$0.819297\pi$
$632$		0			0
$633$	28.6755	−	8.90525i	1.13975	−	0.353952i
$634$		0			0
$635$	−6.06984	−	10.5133i	−0.240874	−	0.417207i
$636$		0			0
$637$	12.6534	−	21.9162i	0.501344	−	0.868353i
$638$		0			0
$639$	−24.4116	−	11.6413i	−0.965709	−	0.460524i
$640$		0			0
$641$	10.3970	−	18.0081i	0.410656	−	0.711277i	−0.584306	−	0.811534i	$-0.698633\pi$
$641$	10.3970	−	18.0081i	0.410656	−	0.711277i	0.994962	+	0.100257i	$0.0319664\pi$
$642$		0			0
$643$	−20.3246	−	35.2032i	−0.801523	−	1.38828i	−0.918613	−	0.395158i	$-0.870690\pi$
$643$	−20.3246	−	35.2032i	−0.801523	−	1.38828i	0.117090	−	0.993121i	$-0.462643\pi$
$644$		0			0
$645$	1.32091	−	5.83865i	0.0520106	−	0.229897i
$646$		0			0
$647$	25.2181			0.991426			0.495713	−	0.868486i	$-0.334907\pi$
$647$	25.2181			0.991426			0.495713	+	0.868486i	$0.334907\pi$
$648$		0			0
$649$	5.12195			0.201054
$650$		0			0
$651$	3.04785	−	13.4721i	0.119455	−	0.528013i
$652$		0			0
$653$	7.68001	+	13.3022i	0.300542	+	0.520554i	0.976259	−	0.216607i	$-0.0694991\pi$
$653$	7.68001	+	13.3022i	0.300542	+	0.520554i	−0.675717	+	0.737161i	$0.736166\pi$
$654$		0			0
$655$	10.7966	−	18.7002i	0.421858	−	0.730679i
$656$		0			0
$657$	−32.8876	−	15.6834i	−1.28307	−	0.611866i
$658$		0			0
$659$	9.30469	−	16.1162i	0.362459	−	0.627798i	−0.625906	−	0.779899i	$-0.715271\pi$
$659$	9.30469	−	16.1162i	0.362459	−	0.627798i	0.988365	+	0.152101i	$0.0486039\pi$
$660$		0			0
$661$	2.89718	+	5.01806i	0.112687	+	0.195180i	0.916853	−	0.399225i	$-0.130721\pi$
$661$	2.89718	+	5.01806i	0.112687	+	0.195180i	−0.804166	+	0.594405i	$0.797388\pi$
$662$		0			0
$663$	−45.8828	+	14.2490i	−1.78194	+	0.553385i
$664$		0			0
$665$	1.11305			0.0431621
$666$		0			0
$667$	−55.5480			−2.15083
$668$		0			0
$669$	−9.93849	−	9.18631i	−0.384244	−	0.355163i
$670$		0			0
$671$	−7.83554	−	13.5716i	−0.302488	−	0.523924i
$672$		0			0
$673$	15.3449	−	26.5782i	0.591503	−	1.02451i	−0.402528	−	0.915408i	$-0.631868\pi$
$673$	15.3449	−	26.5782i	0.591503	−	1.02451i	0.994030	−	0.109105i	$-0.0347984\pi$
$674$		0			0
$675$	−1.92605	−	4.82600i	−0.0741338	−	0.185753i
$676$		0			0
$677$	−3.80724	+	6.59433i	−0.146324	+	0.253441i	−0.929866	−	0.367898i	$-0.880078\pi$
$677$	−3.80724	+	6.59433i	−0.146324	+	0.253441i	0.783542	+	0.621339i	$0.213411\pi$
$678$		0			0
$679$	2.41928	+	4.19031i	0.0928433	+	0.160809i
$680$		0			0
$681$	35.0042	+	32.3550i	1.34137	+	1.23985i
$682$		0			0
$683$	15.6356			0.598280			0.299140	−	0.954209i	$-0.403300\pi$
$683$	15.6356			0.598280			0.299140	+	0.954209i	$0.403300\pi$
$684$		0			0
$685$	8.64668			0.330373
$686$		0			0
$687$	3.87728	−	1.20410i	0.147927	−	0.0459392i
$688$		0			0
$689$	16.4883	+	28.5587i	0.628156	+	1.08800i
$690$		0			0
$691$	−4.77948	+	8.27830i	−0.181820	+	0.314921i	−0.942500	−	0.334205i	$-0.891532\pi$
$691$	−4.77948	+	8.27830i	−0.181820	+	0.314921i	0.760680	+	0.649127i	$0.224865\pi$
$692$		0			0
$693$	0.373284	+	4.73816i	0.0141799	+	0.179988i
$694$		0			0
$695$	−0.0555154	+	0.0961556i	−0.00210582	+	0.00364739i
$696$		0			0
$697$	−38.9927	−	67.5373i	−1.47695	−	2.55816i
$698$		0			0
$699$	4.44049	−	19.6278i	0.167955	−	0.742392i
$700$		0			0
$701$	3.15943			0.119330			0.0596651	−	0.998218i	$-0.480997\pi$
$701$	3.15943			0.119330			0.0596651	+	0.998218i	$0.480997\pi$
$702$		0			0
$703$	−6.64141			−0.250485
$704$		0			0
$705$	1.68010	−	7.42636i	0.0632763	−	0.279693i
$706$		0			0
$707$	0.693771	+	1.20165i	0.0260919	+	0.0451926i
$708$		0			0
$709$	8.41916	−	14.5824i	0.316188	−	0.547654i	−0.663501	−	0.748175i	$-0.730930\pi$
$709$	8.41916	−	14.5824i	0.316188	−	0.547654i	0.979689	+	0.200521i	$0.0642635\pi$
$710$		0			0
$711$	−1.16501	+	0.800824i	−0.0436911	+	0.0300332i
$712$		0			0
$713$	−47.5976	+	82.4415i	−1.78255	+	3.08746i
$714$		0			0
$715$	4.08772	+	7.08015i	0.152872	+	0.264782i
$716$		0			0
$717$	−17.2054	+	5.34318i	−0.642548	+	0.199545i
$718$		0			0
$719$	−11.4822			−0.428212			−0.214106	−	0.976810i	$-0.568684\pi$
$719$	−11.4822			−0.428212			−0.214106	+	0.976810i	$0.568684\pi$
$720$		0			0
$721$	−2.55694			−0.0952255
$722$		0			0
$723$	17.2051	+	15.9029i	0.639864	+	0.591437i
$724$		0			0
$725$	3.04386	+	5.27212i	0.113046	+	0.195802i
$726$		0			0
$727$	11.0465	−	19.1332i	0.409693	−	0.709610i	−0.585162	−	0.810916i	$-0.698969\pi$
$727$	11.0465	−	19.1332i	0.409693	−	0.709610i	0.994855	+	0.101307i	$0.0323024\pi$
$728$		0			0
$729$	−6.30934	−	26.2525i	−0.233679	−	0.972314i
$730$		0			0
$731$	12.1521	−	21.0481i	0.449463	−	0.778493i
$732$		0			0
$733$	−23.9081	−	41.4100i	−0.883066	−	1.52951i	−0.847915	−	0.530133i	$-0.822142\pi$
$733$	−23.9081	−	41.4100i	−0.883066	−	1.52951i	−0.0351510	−	0.999382i	$-0.511191\pi$
$734$		0			0
$735$	8.16035	+	7.54274i	0.300999	+	0.278218i
$736$		0			0
$737$	−5.88007			−0.216595
$738$		0			0
$739$	−47.3973			−1.74354			−0.871769	−	0.489918i	$-0.837027\pi$
$739$	−47.3973			−1.74354			−0.871769	+	0.489918i	$0.837027\pi$
$740$		0			0
$741$	9.50081	−	2.95050i	0.349021	−	0.108389i
$742$		0			0
$743$	3.97537	+	6.88555i	0.145842	+	0.252606i	0.929687	−	0.368351i	$-0.120077\pi$
$743$	3.97537	+	6.88555i	0.145842	+	0.252606i	−0.783845	+	0.620957i	$0.786744\pi$
$744$		0			0
$745$	6.01610	−	10.4202i	0.220413	−	0.381767i
$746$		0			0
$747$	26.9713	−	18.5400i	0.986827	−	0.678344i
$748$		0			0
$749$	5.26326	−	9.11624i	0.192315	−	0.333100i
$750$		0			0
$751$	12.0150	+	20.8106i	0.438434	+	0.759391i	0.997569	−	0.0696862i	$-0.0221998\pi$
$751$	12.0150	+	20.8106i	0.438434	+	0.759391i	−0.559135	+	0.829077i	$0.688866\pi$
$752$		0			0
$753$	5.05641	−	22.3503i	0.184266	−	0.814489i
$754$		0			0
$755$	3.95756			0.144031
$756$		0			0
$757$	39.2441			1.42635			0.713175	−	0.700986i	$-0.247256\pi$
$757$	39.2441			1.42635			0.713175	+	0.700986i	$0.247256\pi$
$758$		0			0
$759$	7.22796	−	31.9489i	0.262358	−	1.15967i
$760$		0			0
$761$	−9.31370	−	16.1318i	−0.337622	−	0.584778i	0.646363	−	0.763030i	$-0.276289\pi$
$761$	−9.31370	−	16.1318i	−0.337622	−	0.584778i	−0.983985	+	0.178252i	$0.942956\pi$
$762$		0			0
$763$	3.73627	−	6.47142i	0.135262	−	0.234281i
$764$		0			0
$765$	−1.65691	−	21.0315i	−0.0599057	−	0.760394i
$766$		0			0
$767$	−4.87387	+	8.44180i	−0.175985	+	0.304816i
$768$		0			0
$769$	−3.00700	−	5.20828i	−0.108435	−	0.187815i	0.806701	−	0.590959i	$-0.201251\pi$
$769$	−3.00700	−	5.20828i	−0.108435	−	0.187815i	−0.915136	+	0.403144i	$0.867917\pi$
$770$		0			0
$771$	−44.6794	+	13.8753i	−1.60909	+	0.499706i
$772$		0			0
$773$	−14.0906			−0.506803			−0.253401	−	0.967361i	$-0.581549\pi$
$773$	−14.0906			−0.506803			−0.253401	+	0.967361i	$0.581549\pi$
$774$		0			0
$775$	10.4328			0.374758
$776$		0			0
$777$	4.43437	+	4.09876i	0.159082	+	0.147042i
$778$		0			0
$779$	8.07410	+	13.9847i	0.289284	+	0.501055i
$780$		0			0
$781$	−9.34247	+	16.1816i	−0.334300	+	0.579024i
$782$		0			0
$783$	11.7253	+	29.3794i	0.419027	+	1.04993i
$784$		0			0
$785$	−10.3809	+	17.9802i	−0.370509	+	0.641741i
$786$		0			0
$787$	−2.34456	−	4.06090i	−0.0835745	−	0.144755i	0.821208	−	0.570628i	$-0.193300\pi$
$787$	−2.34456	−	4.06090i	−0.0835745	−	0.144755i	−0.904783	+	0.425873i	$0.859967\pi$
$788$		0			0
$789$	0.322245	+	0.297856i	0.0114722	+	0.0106040i
$790$		0			0
$791$	−1.69307			−0.0601986
$792$		0			0
$793$	29.8241			1.05909
$794$		0			0
$795$	−13.8288	+	4.29456i	−0.490457	+	0.152313i
$796$		0			0
$797$	15.0413	+	26.0523i	0.532791	+	0.922820i	0.999267	+	0.0382867i	$0.0121900\pi$
$797$	15.0413	+	26.0523i	0.532791	+	0.922820i	−0.466476	+	0.884534i	$0.654477\pi$
$798$		0			0
$799$	15.4567	−	26.7718i	0.546818	−	0.947117i
$800$		0			0
$801$	−2.31453	−	1.10375i	−0.0817798	−	0.0389989i
$802$		0			0
$803$	−12.5863	+	21.8001i	−0.444161	+	0.769309i
$804$		0			0
$805$	3.48734	+	6.04025i	0.122913	+	0.212891i
$806$		0			0
$807$	−8.77073	+	38.7683i	−0.308744	+	1.36471i
$808$		0			0
$809$	6.47527			0.227658			0.113829	−	0.993500i	$-0.463688\pi$
$809$	6.47527			0.227658			0.113829	+	0.993500i	$0.463688\pi$
$810$		0			0
$811$	47.1771			1.65661			0.828305	−	0.560277i	$-0.189305\pi$
$811$	47.1771			1.65661			0.828305	+	0.560277i	$0.189305\pi$
$812$		0			0
$813$	8.79345	−	38.8687i	0.308400	−	1.36319i
$814$		0			0
$815$	−0.687650	−	1.19104i	−0.0240873	−	0.0417205i
$816$		0			0
$817$	−2.51631	+	4.35837i	−0.0880344	+	0.152480i
$818$		0			0
$819$	−8.16446	−	3.89344i	−0.285289	−	0.136048i
$820$		0			0
$821$	17.1023	−	29.6220i	0.596874	−	1.03382i	−0.396406	−	0.918076i	$-0.629743\pi$
$821$	17.1023	−	29.6220i	0.596874	−	1.03382i	0.993279	−	0.115740i	$-0.0369241\pi$
$822$		0			0
$823$	−12.6219	−	21.8618i	−0.439972	−	0.762054i	0.557715	−	0.830033i	$-0.311678\pi$
$823$	−12.6219	−	21.8618i	−0.439972	−	0.762054i	−0.997687	+	0.0679785i	$0.978345\pi$
$824$		0			0
$825$	−3.42838	+	1.06469i	−0.119361	+	0.0370678i
$826$		0			0
$827$	11.5303			0.400948			0.200474	−	0.979699i	$-0.435752\pi$
$827$	11.5303			0.400948			0.200474	+	0.979699i	$0.435752\pi$
$828$		0			0
$829$	−32.1682			−1.11725			−0.558623	−	0.829422i	$-0.688670\pi$
$829$	−32.1682			−1.11725			−0.558623	+	0.829422i	$0.688670\pi$
$830$		0			0
$831$	16.2885	+	15.0557i	0.565042	+	0.522277i
$832$		0			0
$833$	22.5583	+	39.0722i	0.781600	+	1.35377i
$834$		0			0
$835$	−9.63082	+	16.6811i	−0.333288	+	0.577272i
$836$		0			0
$837$	53.6505	+	7.77236i	1.85443	+	0.268652i
$838$		0			0
$839$	21.7692	−	37.7053i	0.751556	−	1.30173i	−0.195513	−	0.980701i	$-0.562637\pi$
$839$	21.7692	−	37.7053i	0.751556	−	1.30173i	0.947069	−	0.321031i	$-0.104029\pi$
$840$		0			0
$841$	−4.03019	−	6.98050i	−0.138972	−	0.240707i
$842$		0			0
$843$	−38.8802	−	35.9376i	−1.33911	−	1.23776i
$844$		0			0
$845$	−2.55896			−0.0880308
$846$		0			0
$847$	−5.12459			−0.176083
$848$		0			0
$849$	26.6335	−	8.27109i	0.914059	−	0.283863i
$850$		0			0
$851$	−20.8085	−	36.0414i	−0.713306	−	1.23548i
$852$		0			0
$853$	5.27939	−	9.14417i	0.180763	−	0.313091i	−0.761378	−	0.648309i	$-0.775477\pi$
$853$	5.27939	−	9.14417i	0.180763	−	0.313091i	0.942141	+	0.335218i	$0.108810\pi$
$854$		0			0
$855$	0.343091	+	4.35492i	0.0117335	+	0.148935i
$856$		0			0
$857$	12.2427	−	21.2050i	0.418203	−	0.724349i	−0.577556	−	0.816351i	$-0.695993\pi$
$857$	12.2427	−	21.2050i	0.418203	−	0.724349i	0.995759	+	0.0920025i	$0.0293268\pi$
$858$		0			0
$859$	−18.8454	−	32.6411i	−0.642996	−	1.11370i	−0.984761	−	0.173916i	$-0.944358\pi$
$859$	−18.8454	−	32.6411i	−0.642996	−	1.11370i	0.341765	−	0.939785i	$-0.388975\pi$
$860$		0			0
$861$	3.23976	−	14.3204i	0.110411	−	0.488037i
$862$		0			0
$863$	−37.7067			−1.28355			−0.641776	−	0.766892i	$-0.721802\pi$
$863$	−37.7067			−1.28355			−0.641776	+	0.766892i	$0.721802\pi$
$864$		0			0
$865$	4.68618			0.159335
$866$		0			0
$867$	12.4029	−	54.8230i	0.421223	−	1.86189i
$868$		0			0
$869$	0.488347	+	0.845841i	0.0165660	+	0.0286932i
$870$		0			0
$871$	5.59527	−	9.69130i	0.189589	−	0.328377i
$872$		0			0
$873$	−15.6493	+	10.7573i	−0.529649	+	0.364080i
$874$		0			0
$875$	0.382191	−	0.661975i	0.0129204	−	0.0223788i
$876$		0			0
$877$	14.9187	+	25.8400i	0.503770	+	0.872555i	0.999991	+	0.00435888i	$0.00138748\pi$
$877$	14.9187	+	25.8400i	0.503770	+	0.872555i	−0.496220	+	0.868197i	$0.665279\pi$
$878$		0			0
$879$	15.0741	−	4.68129i	0.508437	−	0.157896i
$880$		0			0
$881$	−42.8472			−1.44356			−0.721780	−	0.692123i	$-0.756676\pi$
$881$	−42.8472			−1.44356			−0.721780	+	0.692123i	$0.756676\pi$
$882$		0			0
$883$	41.3354			1.39105			0.695523	−	0.718504i	$-0.255173\pi$
$883$	41.3354			1.39105			0.695523	+	0.718504i	$0.255173\pi$
$884$		0			0
$885$	−3.14324	−	2.90535i	−0.105659	−	0.0976622i
$886$		0			0
$887$	−1.80070	−	3.11890i	−0.0604615	−	0.104722i	0.834210	−	0.551446i	$-0.185924\pi$
$887$	−1.80070	−	3.11890i	−0.0604615	−	0.104722i	−0.894672	+	0.446724i	$0.852591\pi$
$888$		0			0
$889$	4.63968	−	8.03617i	0.155610	−	0.269524i
$890$		0			0
$891$	−18.4235	+	2.92103i	−0.617211	+	0.0978582i
$892$		0			0
$893$	−3.20057	+	5.54355i	−0.107103	+	0.185508i
$894$		0			0
$895$	5.98080	+	10.3590i	0.199916	+	0.346265i
$896$		0			0
$897$	45.7791	+	42.3143i	1.52852	+	1.41283i
$898$		0			0
$899$	−63.5122			−2.11825
$900$		0			0
$901$	−58.7907			−1.95860
$902$		0			0
$903$	4.36988	−	1.35708i	0.145421	−	0.0451607i
$904$		0			0
$905$	1.48490	+	2.57193i	0.0493599	+	0.0854938i
$906$		0			0
$907$	23.0994	−	40.0094i	0.767003	−	1.32849i	−0.172177	−	0.985066i	$-0.555080\pi$
$907$	23.0994	−	40.0094i	0.767003	−	1.32849i	0.939181	−	0.343423i	$-0.111586\pi$
$908$		0			0
$909$	−4.48773	+	3.08486i	−0.148848	+	0.102318i
$910$		0			0
$911$	−21.2274	+	36.7669i	−0.703295	+	1.21814i	0.264008	+	0.964521i	$0.414956\pi$
$911$	−21.2274	+	36.7669i	−0.703295	+	1.21814i	−0.967303	+	0.253623i	$0.918378\pi$
$912$		0			0
$913$	−11.3058	−	19.5822i	−0.374168	−	0.648077i
$914$		0			0
$915$	−2.88974	+	12.7732i	−0.0955318	+	0.422269i
$916$		0			0
$917$	16.5055			0.545058
$918$		0			0
$919$	19.5123			0.643653			0.321826	−	0.946799i	$-0.395703\pi$
$919$	19.5123			0.643653			0.321826	+	0.946799i	$0.395703\pi$
$920$		0			0
$921$	6.96213	−	30.7739i	0.229410	−	1.01404i
$922$		0			0
$923$	−17.7800	−	30.7958i	−0.585234	−	1.01366i
$924$		0			0
$925$	−2.28049	+	3.94992i	−0.0749820	+	0.129873i
$926$		0			0
$927$	−0.788165	−	10.0043i	−0.0258867	−	0.328585i
$928$		0			0
$929$	−28.1309	+	48.7241i	−0.922943	+	1.59858i	−0.128107	+	0.991760i	$0.540890\pi$
$929$	−28.1309	+	48.7241i	−0.922943	+	1.59858i	−0.794836	+	0.606824i	$0.792443\pi$
$930$		0			0
$931$	−4.67109	−	8.09056i	−0.153089	−	0.265157i
$932$		0			0
$933$	−1.93476	+	0.600844i	−0.0633412	+	0.0196707i
$934$		0			0
$935$	−14.5752			−0.476658
$936$		0			0
$937$	−52.6041			−1.71850			−0.859251	−	0.511555i	$-0.829070\pi$
$937$	−52.6041			−1.71850			−0.859251	+	0.511555i	$0.829070\pi$
$938$		0			0
$939$	−13.9436	−	12.8883i	−0.455031	−	0.420593i
$940$		0			0
$941$	−7.40407	−	12.8242i	−0.241366	−	0.418058i	0.719738	−	0.694246i	$-0.244262\pi$
$941$	−7.40407	−	12.8242i	−0.241366	−	0.418058i	−0.961104	+	0.276188i	$0.910929\pi$
$942$		0			0
$943$	−50.5946	+	87.6325i	−1.64759	+	2.85371i
$944$		0			0
$945$	2.45857	−	3.11946i	0.0799774	−	0.101476i
$946$		0			0
$947$	−21.4330	+	37.1230i	−0.696478	+	1.20634i	0.273202	+	0.961957i	$0.411917\pi$
$947$	−21.4330	+	37.1230i	−0.696478	+	1.20634i	−0.969680	+	0.244379i	$0.921416\pi$
$948$		0			0
$949$	−23.9534	−	41.4885i	−0.777560	−	1.34677i
$950$		0			0
$951$	−29.0655	−	26.8657i	−0.942514	−	0.871181i
$952$		0			0
$953$	−18.7666			−0.607910			−0.303955	−	0.952686i	$-0.598307\pi$
$953$	−18.7666			−0.607910			−0.303955	+	0.952686i	$0.598307\pi$
$954$		0			0
$955$	12.3218			0.398724
$956$		0			0
$957$	20.8710	−	6.48155i	0.674665	−	0.209519i
$958$		0			0
$959$	3.30469	+	5.72389i	0.106714	+	0.184834i
$960$		0			0
$961$	−38.9220	+	67.4149i	−1.25555	+	2.17467i
$962$		0			0
$963$	37.2907	+	17.7831i	1.20167	+	0.573051i
$964$		0			0
$965$	−8.07506	+	13.9864i	−0.259945	+	0.450239i
$966$		0			0
$967$	−6.62448	−	11.4739i	−0.213029	−	0.368977i	0.739632	−	0.673011i	$-0.234999\pi$
$967$	−6.62448	−	11.4739i	−0.213029	−	0.368977i	−0.952661	+	0.304035i	$0.901666\pi$
$968$		0			0
$969$	−3.91359	+	17.2988i	−0.125723	+	0.555717i
$970$		0			0
$971$	50.2770			1.61347			0.806733	−	0.590916i	$-0.201233\pi$
$971$	50.2770			1.61347			0.806733	+	0.590916i	$0.201233\pi$
$972$		0			0
$973$	−0.0848701			−0.00272081
$974$		0			0
$975$	1.50755	−	6.66365i	0.0482802	−	0.213407i
$976$		0			0
$977$	16.3853	+	28.3802i	0.524213	+	0.907963i	0.999603	+	0.0281881i	$0.00897375\pi$
$977$	16.3853	+	28.3802i	0.524213	+	0.907963i	−0.475390	+	0.879775i	$0.657693\pi$
$978$		0			0
$979$	−0.885784	+	1.53422i	−0.0283098	+	0.0490339i
$980$		0			0
$981$	26.4718	+	12.6238i	0.845180	+	0.403047i
$982$		0			0
$983$	9.75951	−	16.9040i	0.311280	−	0.539153i	−0.667360	−	0.744735i	$-0.732576\pi$
$983$	9.75951	−	16.9040i	0.311280	−	0.539153i	0.978640	+	0.205583i	$0.0659090\pi$
$984$		0			0
$985$	3.72396	+	6.45009i	0.118655	+	0.205517i
$986$		0			0
$987$	5.55819	−	1.72611i	0.176919	−	0.0549426i
$988$		0			0
$989$	−31.5358			−1.00278
$990$		0			0
$991$	−41.1108			−1.30593			−0.652964	−	0.757389i	$-0.726475\pi$
$991$	−41.1108			−1.30593			−0.652964	+	0.757389i	$0.726475\pi$
$992$		0			0
$993$	−29.6061	−	27.3654i	−0.939522	−	0.868415i
$994$		0			0
$995$	−7.81579	−	13.5374i	−0.247777	−	0.429163i
$996$		0			0
$997$	−13.3405	+	23.1063i	−0.422496	+	0.731785i	−0.996183	−	0.0872897i	$-0.972179\pi$
$997$	−13.3405	+	23.1063i	−0.422496	+	0.731785i	0.573687	+	0.819075i	$0.305513\pi$
$998$		0			0
$999$	−14.6700	+	18.6134i	−0.464138	+	0.588902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.n.961.3	yes	8
3.2	odd	2		4320.2.q.i.2881.2		8
4.3	odd	2		1440.2.q.i.961.2	yes	8
9.4	even	3	inner	1440.2.q.n.481.3	yes	8
9.5	odd	6		4320.2.q.i.1441.2		8
12.11	even	2		4320.2.q.k.2881.3		8
36.23	even	6		4320.2.q.k.1441.3		8
36.31	odd	6		1440.2.q.i.481.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.i.481.2	✓	8	36.31	odd	6
1440.2.q.i.961.2	yes	8	4.3	odd	2
1440.2.q.n.481.3	yes	8	9.4	even	3	inner
1440.2.q.n.961.3	yes	8	1.1	even	1	trivial
4320.2.q.i.1441.2		8	9.5	odd	6
4320.2.q.i.2881.2		8	3.2	odd	2
4320.2.q.k.1441.3		8	36.23	even	6
4320.2.q.k.2881.3		8	12.11	even	2

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382191 - 1.68936i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.382191 + 0.661975i) q^{7} +(-2.70786 - 1.29132i) q^{9} +O(q^{10})\)	\(q+(0.382191 - 1.68936i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.382191 + 0.661975i) q^{7} +(-2.70786 - 1.29132i) q^{9} +(-1.03631 + 1.79495i) q^{11} +(-1.97224 - 3.41602i) q^{13} +(1.65412 - 0.513691i) q^{15} +7.03221 q^{17} -1.45614 q^{19} +(0.972242 + 0.898659i) q^{21} +(-4.56229 - 7.90212i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.21642 + 4.08101i) q^{27} +(3.04386 - 5.27212i) q^{29} +(-5.21642 - 9.03510i) q^{31} +(2.63624 + 2.43672i) q^{33} -0.764383 q^{35} +4.56097 q^{37} +(-6.52466 + 2.02625i) q^{39} +(-5.54487 - 9.60400i) q^{41} +(1.72807 - 2.99310i) q^{43} +(-0.235617 - 2.99073i) q^{45} +(2.19798 - 3.80702i) q^{47} +(3.20786 + 5.55618i) q^{49} +(2.68765 - 11.8799i) q^{51} -8.36020 q^{53} -2.07263 q^{55} +(-0.556523 + 2.45994i) q^{57} +(-1.23562 - 2.14015i) q^{59} +(-3.78049 + 6.54800i) q^{61} +(1.88974 - 1.29901i) q^{63} +(1.97224 - 3.41602i) q^{65} +(1.41851 + 2.45692i) q^{67} +(-15.0932 + 4.68722i) q^{69} +9.01510 q^{71} +12.1453 q^{73} +(1.27193 + 1.17567i) q^{75} +(-0.792141 - 1.37203i) q^{77} +(0.235617 - 0.408101i) q^{79} +(5.66501 + 6.99341i) q^{81} +(-5.45482 + 9.44802i) q^{83} +(3.51610 + 6.09007i) q^{85} +(-7.74317 - 7.15713i) q^{87} +0.854744 q^{89} +3.01510 q^{91} +(-17.2572 + 5.35926i) q^{93} +(-0.728069 - 1.26105i) q^{95} +(3.16501 - 5.48195i) q^{97} +(5.12404 - 3.52226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 8 * q^9	\( 8 q + 2 q^{3} + 4 q^{5} - 2 q^{7} - 8 q^{9} + 2 q^{11} + 4 q^{15} - 8 q^{17} - 28 q^{19} - 8 q^{21} - 6 q^{23} - 4 q^{25} + 14 q^{27} + 8 q^{29} - 2 q^{31} + 8 q^{33} - 4 q^{35} - 32 q^{37} + 6 q^{39} - 8 q^{41} + 22 q^{43} - 4 q^{45} - 8 q^{47} + 12 q^{49} - 14 q^{51} - 8 q^{53} + 4 q^{55} - 16 q^{57} - 12 q^{59} + 4 q^{61} + 8 q^{63} + 12 q^{69} + 60 q^{71} + 56 q^{73} + 2 q^{75} - 20 q^{77} + 4 q^{79} + 28 q^{81} - 22 q^{83} - 4 q^{85} - 58 q^{87} + 48 q^{89} + 12 q^{91} - 8 q^{93} - 14 q^{95} + 8 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^5 - 2 * q^7 - 8 * q^9 + 2 * q^11 + 4 * q^15 - 8 * q^17 - 28 * q^19 - 8 * q^21 - 6 * q^23 - 4 * q^25 + 14 * q^27 + 8 * q^29 - 2 * q^31 + 8 * q^33 - 4 * q^35 - 32 * q^37 + 6 * q^39 - 8 * q^41 + 22 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 14 * q^51 - 8 * q^53 + 4 * q^55 - 16 * q^57 - 12 * q^59 + 4 * q^61 + 8 * q^63 + 12 * q^69 + 60 * q^71 + 56 * q^73 + 2 * q^75 - 20 * q^77 + 4 * q^79 + 28 * q^81 - 22 * q^83 - 4 * q^85 - 58 * q^87 + 48 * q^89 + 12 * q^91 - 8 * q^93 - 14 * q^95 + 8 * q^97 - 2 * q^99

Introduction

L-functions

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