LMFDB - Embedded newform 960.2.w.g.703.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(127,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("960.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.w (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			703.2
Root			$1.19252 - 0.760198i$ of defining polynomial
Character	$\chi$	$=$	960.703
Dual form			960.2.w.g.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-0.432320 + 2.19388i) q^{5} +(-0.611393 - 0.611393i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.432320 + 2.19388i) q^{5} +(-0.611393 - 0.611393i) q^{7} -1.00000i q^{9} -5.12822i q^{11} +(-1.76156 - 1.76156i) q^{13} +(-1.24561 - 1.85700i) q^{15} +(-3.76156 + 3.76156i) q^{17} -1.22279 q^{19} +0.864641 q^{21} +(1.07700 - 1.07700i) q^{23} +(-4.62620 - 1.89692i) q^{25} +(0.707107 + 0.707107i) q^{27} -0.864641i q^{29} -7.81086i q^{31} +(3.62620 + 3.62620i) q^{33} +(1.60564 - 1.07700i) q^{35} +(1.76156 - 1.76156i) q^{37} +2.49122 q^{39} +5.52311 q^{41} +(6.20522 - 6.20522i) q^{43} +(2.19388 + 0.432320i) q^{45} +(-2.29979 - 2.29979i) q^{47} -6.25240i q^{49} -5.31965i q^{51} +(2.62620 + 2.62620i) q^{53} +(11.2507 + 2.21703i) q^{55} +(0.864641 - 0.864641i) q^{57} -0.528636 q^{59} -4.98168 q^{61} +(-0.611393 + 0.611393i) q^{63} +(4.62620 - 3.10308i) q^{65} +(-6.20522 - 6.20522i) q^{67} +1.52311i q^{69} -8.10243i q^{71} +(-2.25240 - 2.25240i) q^{73} +(4.61254 - 1.92989i) q^{75} +(-3.13536 + 3.13536i) q^{77} -15.9133 q^{79} -1.00000 q^{81} +(-7.95665 + 7.95665i) q^{83} +(-6.62620 - 9.87859i) q^{85} +(0.611393 + 0.611393i) q^{87} +7.25240i q^{89} +2.15401i q^{91} +(5.52311 + 5.52311i) q^{93} +(0.528636 - 2.68264i) q^{95} +(0.793833 - 0.793833i) q^{97} -5.12822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.432320	+	2.19388i	−0.193340	+	0.981132i
$5$	−0.432320	+	2.19388i	−0.193340	+	0.981132i
$6$		0			0
$7$	−0.611393	−	0.611393i	−0.231085	−	0.231085i	0.582060	−	0.813145i	$-0.302247\pi$
$7$	−0.611393	−	0.611393i	−0.231085	−	0.231085i	−0.813145	+	0.582060i	$0.802247\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	5.12822i		−	1.54622i	−0.634274	−	0.773108i	$-0.718701\pi$
$11$		−	5.12822i		−	1.54622i	0.634274	−	0.773108i	$-0.281299\pi$
$12$		0			0
$13$	−1.76156	−	1.76156i	−0.488568	−	0.488568i	0.419286	−	0.907854i	$-0.362280\pi$
$13$	−1.76156	−	1.76156i	−0.488568	−	0.488568i	−0.907854	+	0.419286i	$0.862280\pi$
$14$		0			0
$15$	−1.24561	−	1.85700i	−0.321615	−	0.479476i
$16$		0			0
$17$	−3.76156	+	3.76156i	−0.912312	+	0.912312i	−0.996454	−	0.0841421i	$-0.973185\pi$
$17$	−3.76156	+	3.76156i	−0.912312	+	0.912312i	0.0841421	+	0.996454i	$0.473185\pi$
$18$		0			0
$19$	−1.22279			−0.280527			−0.140263	−	0.990114i	$-0.544795\pi$
$19$	−1.22279			−0.280527			−0.140263	+	0.990114i	$0.544795\pi$
$20$		0			0
$21$	0.864641			0.188680
$22$		0			0
$23$	1.07700	−	1.07700i	0.224571	−	0.224571i	−0.585849	−	0.810420i	$-0.699239\pi$
$23$	1.07700	−	1.07700i	0.224571	−	0.224571i	0.810420	+	0.585849i	$0.199239\pi$
$24$		0			0
$25$	−4.62620	−	1.89692i	−0.925240	−	0.379383i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	0.864641i		−	0.160560i	−0.996772	−	0.0802799i	$-0.974419\pi$
$29$		−	0.864641i		−	0.160560i	0.996772	−	0.0802799i	$-0.0255814\pi$
$30$		0			0
$31$		−	7.81086i		−	1.40287i	−0.712732	−	0.701436i	$-0.752543\pi$
$31$		−	7.81086i		−	1.40287i	0.712732	−	0.701436i	$-0.247457\pi$
$32$		0			0
$33$	3.62620	+	3.62620i	0.631240	+	0.631240i
$34$		0			0
$35$	1.60564	−	1.07700i	0.271403	−	0.182047i
$36$		0			0
$37$	1.76156	−	1.76156i	0.289598	−	0.289598i	−0.547323	−	0.836921i	$-0.684353\pi$
$37$	1.76156	−	1.76156i	0.289598	−	0.289598i	0.836921	+	0.547323i	$0.184353\pi$
$38$		0			0
$39$	2.49122			0.398914
$40$		0			0
$41$	5.52311			0.862566			0.431283	−	0.902217i	$-0.358061\pi$
$41$	5.52311			0.862566			0.431283	+	0.902217i	$0.358061\pi$
$42$		0			0
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	−0.0523416	−	0.998629i	$-0.516668\pi$
$43$	6.20522	−	6.20522i	0.946288	−	0.946288i	0.998629	+	0.0523416i	$0.0166685\pi$
$44$		0			0
$45$	2.19388	+	0.432320i	0.327044	+	0.0644465i
$46$		0			0
$47$	−2.29979	−	2.29979i	−0.335459	−	0.335459i	0.519196	−	0.854655i	$-0.326231\pi$
$47$	−2.29979	−	2.29979i	−0.335459	−	0.335459i	−0.854655	+	0.519196i	$0.826231\pi$
$48$		0			0
$49$		−	6.25240i		−	0.893199i
$50$		0			0
$51$		−	5.31965i		−	0.744899i
$52$		0			0
$53$	2.62620	+	2.62620i	0.360736	+	0.360736i	0.864084	−	0.503348i	$-0.167899\pi$
$53$	2.62620	+	2.62620i	0.360736	+	0.360736i	−0.503348	+	0.864084i	$0.667899\pi$
$54$		0			0
$55$	11.2507	+	2.21703i	1.51704	+	0.298945i
$56$		0			0
$57$	0.864641	−	0.864641i	0.114524	−	0.114524i
$58$		0			0
$59$	−0.528636			−0.0688225			−0.0344113	−	0.999408i	$-0.510956\pi$
$59$	−0.528636			−0.0688225			−0.0344113	+	0.999408i	$0.510956\pi$
$60$		0			0
$61$	−4.98168			−0.637838			−0.318919	−	0.947782i	$-0.603320\pi$
$61$	−4.98168			−0.637838			−0.318919	+	0.947782i	$0.603320\pi$
$62$		0			0
$63$	−0.611393	+	0.611393i	−0.0770283	+	0.0770283i
$64$		0			0
$65$	4.62620	−	3.10308i	0.573809	−	0.384890i
$66$		0			0
$67$	−6.20522	−	6.20522i	−0.758089	−	0.758089i	0.217886	−	0.975974i	$-0.430084\pi$
$67$	−6.20522	−	6.20522i	−0.758089	−	0.758089i	−0.975974	+	0.217886i	$0.930084\pi$
$68$		0			0
$69$			1.52311i			0.183361i
$70$		0			0
$71$		−	8.10243i		−	0.961581i	−0.876835	−	0.480791i	$-0.840350\pi$
$71$		−	8.10243i		−	0.961581i	0.876835	−	0.480791i	$-0.159650\pi$
$72$		0			0
$73$	−2.25240	−	2.25240i	−0.263623	−	0.263623i	0.562901	−	0.826524i	$-0.309685\pi$
$73$	−2.25240	−	2.25240i	−0.263623	−	0.263623i	−0.826524	+	0.562901i	$0.809685\pi$
$74$		0			0
$75$	4.61254	−	1.92989i	0.532610	−	0.222845i
$76$		0			0
$77$	−3.13536	+	3.13536i	−0.357307	+	0.357307i
$78$		0			0
$79$	−15.9133			−1.79039			−0.895193	−	0.445680i	$-0.852962\pi$
$79$	−15.9133			−1.79039			−0.895193	+	0.445680i	$0.852962\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	−0.992836	−	0.119481i	$-0.961877\pi$
$83$	−7.95665	+	7.95665i	−0.873355	+	0.873355i	0.119481	+	0.992836i	$0.461877\pi$
$84$		0			0
$85$	−6.62620	−	9.87859i	−0.718712	−	1.07148i
$86$		0			0
$87$	0.611393	+	0.611393i	0.0655483	+	0.0655483i
$88$		0			0
$89$			7.25240i			0.768752i	0.923177	+	0.384376i	$0.125583\pi$
$89$			7.25240i			0.768752i	−0.923177	+	0.384376i	$0.874417\pi$
$90$		0			0
$91$			2.15401i			0.225801i
$92$		0			0
$93$	5.52311	+	5.52311i	0.572720	+	0.572720i
$94$		0			0
$95$	0.528636	−	2.68264i	0.0542369	−	0.275234i
$96$		0			0
$97$	0.793833	−	0.793833i	0.0806015	−	0.0806015i	−0.665657	−	0.746258i	$-0.731848\pi$
$97$	0.793833	−	0.793833i	0.0806015	−	0.0806015i	0.746258	+	0.665657i	$0.231848\pi$
$98$		0			0
$99$	−5.12822			−0.515405
$100$		0			0
$101$	10.1170			1.00668			0.503341	−	0.864088i	$-0.332104\pi$
$101$	10.1170			1.00668			0.503341	+	0.864088i	$0.332104\pi$
$102$		0			0
$103$	−3.82267	+	3.82267i	−0.376659	+	0.376659i	−0.869895	−	0.493236i	$-0.835814\pi$
$103$	−3.82267	+	3.82267i	−0.376659	+	0.376659i	0.493236	+	0.869895i	$0.335814\pi$
$104$		0			0
$105$	−0.373802	+	1.89692i	−0.0364793	+	0.185120i
$106$		0			0
$107$	5.51107	+	5.51107i	0.532775	+	0.532775i	0.921397	−	0.388622i	$-0.127049\pi$
$107$	5.51107	+	5.51107i	0.532775	+	0.532775i	−0.388622	+	0.921397i	$0.627049\pi$
$108$		0			0
$109$		−	7.31695i		−	0.700836i	−0.936593	−	0.350418i	$-0.886039\pi$
$109$		−	7.31695i		−	0.700836i	0.936593	−	0.350418i	$-0.113961\pi$
$110$		0			0
$111$			2.49122i			0.236456i
$112$		0			0
$113$	−0.509161	−	0.509161i	−0.0478978	−	0.0478978i	0.682752	−	0.730650i	$-0.260783\pi$
$113$	−0.509161	−	0.509161i	−0.0478978	−	0.0478978i	−0.730650	+	0.682752i	$0.760783\pi$
$114$		0			0
$115$	1.89721	+	2.82843i	0.176915	+	0.263752i
$116$		0			0
$117$	−1.76156	+	1.76156i	−0.162856	+	0.162856i
$118$		0			0
$119$	4.59958			0.421643
$120$		0			0
$121$	−15.2986			−1.39078
$122$		0			0
$123$	−3.90543	+	3.90543i	−0.352141	+	0.352141i
$124$		0			0
$125$	6.16160	−	9.32924i	0.551110	−	0.834432i
$126$		0			0
$127$	7.49103	+	7.49103i	0.664722	+	0.664722i	0.956489	−	0.291767i	$-0.0942433\pi$
$127$	7.49103	+	7.49103i	0.664722	+	0.664722i	−0.291767	+	0.956489i	$0.594243\pi$
$128$		0			0
$129$			8.77551i			0.772641i
$130$		0			0
$131$		−	13.9964i		−	1.22287i	−0.791296	−	0.611434i	$-0.790593\pi$
$131$		−	13.9964i		−	1.22287i	0.791296	−	0.611434i	$-0.209407\pi$
$132$		0			0
$133$	0.747604	+	0.747604i	0.0648255	+	0.0648255i
$134$		0			0
$135$	−1.85700	+	1.24561i	−0.159825	+	0.107205i
$136$		0			0
$137$	7.01395	−	7.01395i	0.599242	−	0.599242i	−0.340869	−	0.940111i	$-0.610721\pi$
$137$	7.01395	−	7.01395i	0.599242	−	0.599242i	0.940111	+	0.340869i	$0.110721\pi$
$138$		0			0
$139$	−2.28006			−0.193392			−0.0966960	−	0.995314i	$-0.530827\pi$
$139$	−2.28006			−0.193392			−0.0966960	+	0.995314i	$0.530827\pi$
$140$		0			0
$141$	3.25240			0.273901
$142$		0			0
$143$	−9.03365	+	9.03365i	−0.755432	+	0.755432i
$144$		0			0
$145$	1.89692	+	0.373802i	0.157530	+	0.0310426i
$146$		0			0
$147$	4.42111	+	4.42111i	0.364647	+	0.364647i
$148$		0			0
$149$			10.1170i			0.828820i	0.910090	+	0.414410i	$0.136012\pi$
$149$			10.1170i			0.828820i	−0.910090	+	0.414410i	$0.863988\pi$
$150$		0			0
$151$		−	7.93691i		−	0.645897i	−0.946417	−	0.322948i	$-0.895326\pi$
$151$		−	7.93691i		−	0.645897i	0.946417	−	0.322948i	$-0.104674\pi$
$152$		0			0
$153$	3.76156	+	3.76156i	0.304104	+	0.304104i
$154$		0			0
$155$	17.1361	+	3.37680i	1.37640	+	0.271231i
$156$		0			0
$157$	−9.01395	+	9.01395i	−0.719392	+	0.719392i	−0.968481	−	0.249089i	$-0.919869\pi$
$157$	−9.01395	+	9.01395i	−0.719392	+	0.719392i	0.249089	+	0.968481i	$0.419869\pi$
$158$		0			0
$159$	−3.71400			−0.294540
$160$		0			0
$161$	−1.31695			−0.103790
$162$		0			0
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.0252033	+	0.999682i	$0.508023\pi$
$163$	−13.0849	+	13.0849i	−1.02489	+	1.02489i	−0.999682	+	0.0252033i	$0.991977\pi$
$164$		0			0
$165$	−9.52311	+	6.38776i	−0.741373	+	0.497286i
$166$		0			0
$167$	11.3334	+	11.3334i	0.877008	+	0.877008i	0.993224	−	0.116216i	$-0.0370765\pi$
$167$	11.3334	+	11.3334i	0.877008	+	0.877008i	−0.116216	+	0.993224i	$0.537076\pi$
$168$		0			0
$169$		−	6.79383i		−	0.522603i
$170$		0			0
$171$			1.22279i			0.0935088i
$172$		0			0
$173$	−7.96772	−	7.96772i	−0.605775	−	0.605775i	0.336064	−	0.941839i	$-0.390904\pi$
$173$	−7.96772	−	7.96772i	−0.605775	−	0.605775i	−0.941839	+	0.336064i	$0.890904\pi$
$174$		0			0
$175$	1.66866	+	3.98819i	0.126139	+	0.301479i
$176$		0			0
$177$	0.373802	−	0.373802i	0.0280967	−	0.0280967i
$178$		0			0
$179$	−12.6475			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$179$	−12.6475			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$180$		0			0
$181$	−7.72928			−0.574513			−0.287256	−	0.957854i	$-0.592743\pi$
$181$	−7.72928			−0.574513			−0.287256	+	0.957854i	$0.592743\pi$
$182$		0			0
$183$	3.52258	−	3.52258i	0.260396	−	0.260396i
$184$		0			0
$185$	3.10308	+	4.62620i	0.228143	+	0.340125i
$186$		0			0
$187$	19.2901	+	19.2901i	1.41063	+	1.41063i
$188$		0			0
$189$		−	0.864641i		−	0.0628934i
$190$		0			0
$191$			7.04516i			0.509770i	0.966971	+	0.254885i	$0.0820376\pi$
$191$			7.04516i			0.509770i	−0.966971	+	0.254885i	$0.917962\pi$
$192$		0			0
$193$	−11.5048	−	11.5048i	−0.828133	−	0.828133i	0.159125	−	0.987258i	$-0.449133\pi$
$193$	−11.5048	−	11.5048i	−0.828133	−	0.828133i	−0.987258	+	0.159125i	$0.949133\pi$
$194$		0			0
$195$	−1.07700	+	5.46543i	−0.0771259	+	0.391387i
$196$		0			0
$197$	−7.87859	+	7.87859i	−0.561327	+	0.561327i	−0.929684	−	0.368358i	$-0.879920\pi$
$197$	−7.87859	+	7.87859i	−0.561327	+	0.561327i	0.368358	+	0.929684i	$0.379920\pi$
$198$		0			0
$199$	11.4792			0.813741			0.406870	−	0.913486i	$-0.366620\pi$
$199$	11.4792			0.813741			0.406870	+	0.913486i	$0.366620\pi$
$200$		0			0
$201$	8.77551			0.618977
$202$		0			0
$203$	−0.528636	+	0.528636i	−0.0371030	+	0.0371030i
$204$		0			0
$205$	−2.38776	+	12.1170i	−0.166768	+	0.846291i
$206$		0			0
$207$	−1.07700	−	1.07700i	−0.0748570	−	0.0748570i
$208$		0			0
$209$			6.27072i			0.433755i
$210$		0			0
$211$		−	5.49134i		−	0.378039i	−0.981973	−	0.189020i	$-0.939469\pi$
$211$		−	5.49134i		−	0.378039i	0.981973	−	0.189020i	$-0.0605310\pi$
$212$		0			0
$213$	5.72928	+	5.72928i	0.392564	+	0.392564i
$214$		0			0
$215$	10.9309	+	16.2961i	0.745478	+	1.11139i
$216$		0			0
$217$	−4.77551	+	4.77551i	−0.324183	+	0.324183i
$218$		0			0
$219$	3.18537			0.215247
$220$		0			0
$221$	13.2524			0.891453
$222$		0			0
$223$	−10.8678	+	10.8678i	−0.727764	+	0.727764i	−0.970174	−	0.242410i	$-0.922062\pi$
$223$	−10.8678	+	10.8678i	−0.727764	+	0.727764i	0.242410	+	0.970174i	$0.422062\pi$
$224$		0			0
$225$	−1.89692	+	4.62620i	−0.126461	+	0.308413i
$226$		0			0
$227$	−4.98244	−	4.98244i	−0.330696	−	0.330696i	0.522155	−	0.852851i	$-0.325128\pi$
$227$	−4.98244	−	4.98244i	−0.330696	−	0.330696i	−0.852851	+	0.522155i	$0.825128\pi$
$228$		0			0
$229$		−	25.7572i		−	1.70208i	−0.525098	−	0.851041i	$-0.675972\pi$
$229$		−	25.7572i		−	1.70208i	0.525098	−	0.851041i	$-0.324028\pi$
$230$		0			0
$231$		−	4.43407i		−	0.291740i
$232$		0			0
$233$	−0.715328	−	0.715328i	−0.0468627	−	0.0468627i	0.683287	−	0.730150i	$-0.260550\pi$
$233$	−0.715328	−	0.715328i	−0.0468627	−	0.0468627i	−0.730150	+	0.683287i	$0.760550\pi$
$234$		0			0
$235$	6.03971	−	4.05121i	0.393987	−	0.264272i
$236$		0			0
$237$	11.2524	−	11.2524i	0.730922	−	0.730922i
$238$		0			0
$239$	−26.9354			−1.74231			−0.871154	−	0.491009i	$-0.836628\pi$
$239$	−26.9354			−1.74231			−0.871154	+	0.491009i	$0.836628\pi$
$240$		0			0
$241$	14.0925			0.907775			0.453887	−	0.891059i	$-0.350037\pi$
$241$	14.0925			0.907775			0.453887	+	0.891059i	$0.350037\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	13.7170	+	2.70304i	0.876346	+	0.172691i
$246$		0			0
$247$	2.15401	+	2.15401i	0.137056	+	0.137056i
$248$		0			0
$249$		−	11.2524i		−	0.713092i
$250$		0			0
$251$			17.2471i			1.08863i	0.838882	+	0.544314i	$0.183210\pi$
$251$			17.2471i			1.08863i	−0.838882	+	0.544314i	$0.816790\pi$
$252$		0			0
$253$	−5.52311	−	5.52311i	−0.347235	−	0.347235i
$254$		0			0
$255$	11.6707	+	2.29979i	0.730844	+	0.144019i
$256$		0			0
$257$	−15.0140	+	15.0140i	−0.936545	+	0.936545i	−0.998103	−	0.0615588i	$-0.980393\pi$
$257$	−15.0140	+	15.0140i	−0.936545	+	0.936545i	0.0615588	+	0.998103i	$0.480393\pi$
$258$		0			0
$259$	−2.15401			−0.133844
$260$		0			0
$261$	−0.864641			−0.0535199
$262$		0			0
$263$	−6.73386	+	6.73386i	−0.415228	+	0.415228i	−0.883555	−	0.468327i	$-0.844857\pi$
$263$	−6.73386	+	6.73386i	−0.415228	+	0.415228i	0.468327	+	0.883555i	$0.344857\pi$
$264$		0			0
$265$	−6.89692	+	4.62620i	−0.423674	+	0.284185i
$266$		0			0
$267$	−5.12822	−	5.12822i	−0.313842	−	0.313842i
$268$		0			0
$269$			25.7047i			1.56724i	0.621238	+	0.783622i	$0.286630\pi$
$269$			25.7047i			1.56724i	−0.621238	+	0.783622i	$0.713370\pi$
$270$		0			0
$271$			0.931222i			0.0565677i	0.999600	+	0.0282839i	$0.00900423\pi$
$271$			0.931222i			0.0565677i	−0.999600	+	0.0282839i	$0.990996\pi$
$272$		0			0
$273$	−1.52311	−	1.52311i	−0.0921831	−	0.0921831i
$274$		0			0
$275$	−9.72780	+	23.7242i	−0.586608	+	1.43062i
$276$		0			0
$277$	22.0602	−	22.0602i	1.32547	−	1.32547i	0.416190	−	0.909277i	$-0.363365\pi$
$277$	22.0602	−	22.0602i	1.32547	−	1.32547i	0.909277	−	0.416190i	$-0.136635\pi$
$278$		0			0
$279$	−7.81086			−0.467624
$280$		0			0
$281$	8.56934			0.511204			0.255602	−	0.966782i	$-0.417726\pi$
$281$	8.56934			0.511204			0.255602	+	0.966782i	$0.417726\pi$
$282$		0			0
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	−0.961744	−	0.273949i	$-0.911670\pi$
$283$	−11.5705	+	11.5705i	−0.687796	+	0.687796i	0.273949	+	0.961744i	$0.411670\pi$
$284$		0			0
$285$	1.52311	+	2.27072i	0.0902215	+	0.134506i
$286$		0			0
$287$	−3.37680	−	3.37680i	−0.199326	−	0.199326i
$288$		0			0
$289$		−	11.2986i		−	0.664625i
$290$		0			0
$291$			1.12265i			0.0658108i
$292$		0			0
$293$	−12.8969	−	12.8969i	−0.753446	−	0.753446i	0.221675	−	0.975121i	$-0.428848\pi$
$293$	−12.8969	−	12.8969i	−0.753446	−	0.753446i	−0.975121	+	0.221675i	$0.928848\pi$
$294$		0			0
$295$	0.228540	−	1.15976i	0.0133061	−	0.0675240i
$296$		0			0
$297$	3.62620	−	3.62620i	0.210413	−	0.210413i
$298$		0			0
$299$	−3.79441			−0.219436
$300$		0			0
$301$	−7.58767			−0.437346
$302$		0			0
$303$	−7.15383	+	7.15383i	−0.410977	+	0.410977i
$304$		0			0
$305$	2.15368	−	10.9292i	0.123319	−	0.625804i
$306$		0			0
$307$	−1.60564	−	1.60564i	−0.0916387	−	0.0916387i	0.659801	−	0.751440i	$-0.270640\pi$
$307$	−1.60564	−	1.60564i	−0.0916387	−	0.0916387i	−0.751440	+	0.659801i	$0.770640\pi$
$308$		0			0
$309$		−	5.40608i		−	0.307541i
$310$		0			0
$311$		−	19.4161i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$311$		−	19.4161i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$312$		0			0
$313$	17.7110	+	17.7110i	1.00108	+	1.00108i	0.999999	+	0.00108322i	$0.000344798\pi$
$313$	17.7110	+	17.7110i	1.00108	+	1.00108i	0.00108322	+	0.999999i	$0.499655\pi$
$314$		0			0
$315$	−1.07700	−	1.60564i	−0.0606823	−	0.0904676i
$316$		0			0
$317$	7.78946	−	7.78946i	0.437500	−	0.437500i	−0.453670	−	0.891170i	$-0.649885\pi$
$317$	7.78946	−	7.78946i	0.437500	−	0.437500i	0.891170	+	0.453670i	$0.149885\pi$
$318$		0			0
$319$	−4.43407			−0.248260
$320$		0			0
$321$	−7.79383			−0.435009
$322$		0			0
$323$	4.59958	−	4.59958i	0.255928	−	0.255928i
$324$		0			0
$325$	4.80779	+	11.4908i	0.266688	+	0.637397i
$326$		0			0
$327$	5.17386	+	5.17386i	0.286115	+	0.286115i
$328$		0			0
$329$			2.81215i			0.155039i
$330$		0			0
$331$		−	31.7005i		−	1.74242i	−0.490912	−	0.871209i	$-0.663336\pi$
$331$		−	31.7005i		−	1.74242i	0.490912	−	0.871209i	$-0.336664\pi$
$332$		0			0
$333$	−1.76156	−	1.76156i	−0.0965327	−	0.0965327i
$334$		0			0
$335$	16.2961	−	10.9309i	0.890353	−	0.597216i
$336$		0			0
$337$	18.9634	−	18.9634i	1.03300	−	1.03300i	0.0335632	−	0.999437i	$-0.489314\pi$
$337$	18.9634	−	18.9634i	1.03300	−	1.03300i	0.999437	−	0.0335632i	$-0.0106855\pi$
$338$		0			0
$339$	0.720062			0.0391084
$340$		0			0
$341$	−40.0558			−2.16914
$342$		0			0
$343$	−8.10243	+	8.10243i	−0.437490	+	0.437490i
$344$		0			0
$345$	−3.34153	−	0.658473i	−0.179902	−	0.0354510i
$346$		0			0
$347$	7.71957	+	7.71957i	0.414408	+	0.414408i	0.883271	−	0.468863i	$-0.155336\pi$
$347$	7.71957	+	7.71957i	0.414408	+	0.414408i	−0.468863	+	0.883271i	$0.655336\pi$
$348$		0			0
$349$			27.0741i			1.44925i	0.689146	+	0.724623i	$0.257986\pi$
$349$			27.0741i			1.44925i	−0.689146	+	0.724623i	$0.742014\pi$
$350$		0			0
$351$		−	2.49122i		−	0.132971i
$352$		0			0
$353$	−9.96772	−	9.96772i	−0.530528	−	0.530528i	0.390201	−	0.920730i	$-0.372405\pi$
$353$	−9.96772	−	9.96772i	−0.530528	−	0.530528i	−0.920730	+	0.390201i	$0.872405\pi$
$354$		0			0
$355$	17.7757	+	3.50285i	0.943438	+	0.185912i
$356$		0			0
$357$	−3.25240	+	3.25240i	−0.172135	+	0.172135i
$358$		0			0
$359$	14.2334			0.751211			0.375606	−	0.926780i	$-0.377435\pi$
$359$	14.2334			0.751211			0.375606	+	0.926780i	$0.377435\pi$
$360$		0			0
$361$	−17.5048			−0.921305
$362$		0			0
$363$	10.8178	−	10.8178i	0.567785	−	0.567785i
$364$		0			0
$365$	5.91524	−	3.96772i	0.309618	−	0.207680i
$366$		0			0
$367$	2.89145	+	2.89145i	0.150933	+	0.150933i	0.778534	−	0.627602i	$-0.215963\pi$
$367$	2.89145	+	2.89145i	0.150933	+	0.150933i	−0.627602	+	0.778534i	$0.715963\pi$
$368$		0			0
$369$		−	5.52311i		−	0.287522i
$370$		0			0
$371$		−	3.21128i		−	0.166721i
$372$		0			0
$373$	11.2847	+	11.2847i	0.584298	+	0.584298i	0.936081	−	0.351783i	$-0.114425\pi$
$373$	11.2847	+	11.2847i	0.584298	+	0.584298i	−0.351783	+	0.936081i	$0.614425\pi$
$374$		0			0
$375$	2.23986	+	10.9537i	0.115666	+	0.565645i
$376$		0			0
$377$	−1.52311	+	1.52311i	−0.0784444	+	0.0784444i
$378$		0			0
$379$	−15.4562			−0.793932			−0.396966	−	0.917833i	$-0.629937\pi$
$379$	−15.4562			−0.793932			−0.396966	+	0.917833i	$0.629937\pi$
$380$		0			0
$381$	−10.5939			−0.542743
$382$		0			0
$383$	12.5562	−	12.5562i	0.641593	−	0.641593i	−0.309354	−	0.950947i	$-0.600113\pi$
$383$	12.5562	−	12.5562i	0.641593	−	0.641593i	0.950947	+	0.309354i	$0.100113\pi$
$384$		0			0
$385$	−5.52311	−	8.23407i	−0.281484	−	0.419647i
$386$		0			0
$387$	−6.20522	−	6.20522i	−0.315429	−	0.315429i
$388$		0			0
$389$		−	5.16327i		−	0.261788i	−0.991396	−	0.130894i	$-0.958215\pi$
$389$		−	5.16327i		−	0.261788i	0.991396	−	0.130894i	$-0.0417848\pi$
$390$		0			0
$391$			8.10243i			0.409757i
$392$		0			0
$393$	9.89692	+	9.89692i	0.499233	+	0.499233i
$394$		0			0
$395$	6.87964	−	34.9118i	0.346152	−	1.75660i
$396$		0			0
$397$	3.46293	−	3.46293i	0.173800	−	0.173800i	−0.614847	−	0.788646i	$-0.710782\pi$
$397$	3.46293	−	3.46293i	0.173800	−	0.173800i	0.788646	+	0.614847i	$0.210782\pi$
$398$		0			0
$399$	−1.05727			−0.0529298
$400$		0			0
$401$	3.49521			0.174542			0.0872712	−	0.996185i	$-0.472185\pi$
$401$	3.49521			0.174542			0.0872712	+	0.996185i	$0.472185\pi$
$402$		0			0
$403$	−13.7593	+	13.7593i	−0.685399	+	0.685399i
$404$		0			0
$405$	0.432320	−	2.19388i	0.0214822	−	0.109015i
$406$		0			0
$407$	−9.03365	−	9.03365i	−0.447781	−	0.447781i
$408$		0			0
$409$			14.8034i			0.731982i	0.930618	+	0.365991i	$0.119270\pi$
$409$			14.8034i			0.731982i	−0.930618	+	0.365991i	$0.880730\pi$
$410$		0			0
$411$			9.91923i			0.489279i
$412$		0			0
$413$	0.323204	+	0.323204i	0.0159039	+	0.0159039i
$414$		0			0
$415$	−14.0161	−	20.8957i	−0.688023	−	1.02573i
$416$		0			0
$417$	1.61224	−	1.61224i	0.0789520	−	0.0789520i
$418$		0			0
$419$	19.0701			0.931634			0.465817	−	0.884881i	$-0.345760\pi$
$419$	19.0701			0.931634			0.465817	+	0.884881i	$0.345760\pi$
$420$		0			0
$421$	20.8034			1.01390			0.506948	−	0.861976i	$-0.330774\pi$
$421$	20.8034			1.01390			0.506948	+	0.861976i	$0.330774\pi$
$422$		0			0
$423$	−2.29979	+	2.29979i	−0.111820	+	0.111820i
$424$		0			0
$425$	24.5371	−	10.2663i	1.19022	−	0.497991i
$426$		0			0
$427$	3.04577	+	3.04577i	0.147395	+	0.147395i
$428$		0			0
$429$		−	12.7755i		−	0.616807i
$430$		0			0
$431$		−	15.3302i		−	0.738428i	−0.929344	−	0.369214i	$-0.879627\pi$
$431$		−	15.3302i		−	0.738428i	0.929344	−	0.369214i	$-0.120373\pi$
$432$		0			0
$433$	16.2803	+	16.2803i	0.782381	+	0.782381i	0.980232	−	0.197851i	$-0.0633961\pi$
$433$	16.2803	+	16.2803i	0.782381	+	0.782381i	−0.197851	+	0.980232i	$0.563396\pi$
$434$		0			0
$435$	−1.60564	+	1.07700i	−0.0769846	+	0.0516384i
$436$		0			0
$437$	−1.31695	+	1.31695i	−0.0629981	+	0.0629981i
$438$		0			0
$439$	24.6554			1.17674			0.588368	−	0.808593i	$-0.299770\pi$
$439$	24.6554			1.17674			0.588368	+	0.808593i	$0.299770\pi$
$440$		0			0
$441$	−6.25240			−0.297733
$442$		0			0
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	−0.747929	−	0.663779i	$-0.768952\pi$
$443$	−1.77116	+	1.77116i	−0.0841501	+	0.0841501i	0.663779	+	0.747929i	$0.268952\pi$
$444$		0			0
$445$	−15.9109	−	3.13536i	−0.754248	−	0.148630i
$446$		0			0
$447$	−7.15383	−	7.15383i	−0.338364	−	0.338364i
$448$		0			0
$449$			33.1512i			1.56450i	0.622963	+	0.782251i	$0.285929\pi$
$449$			33.1512i			1.56450i	−0.622963	+	0.782251i	$0.714071\pi$
$450$		0			0
$451$		−	28.3237i		−	1.33371i
$452$		0			0
$453$	5.61224	+	5.61224i	0.263686	+	0.263686i
$454$		0			0
$455$	−4.72563	−	0.931222i	−0.221541	−	0.0436564i
$456$		0			0
$457$	−7.50479	+	7.50479i	−0.351059	+	0.351059i	−0.860504	−	0.509444i	$-0.829851\pi$
$457$	−7.50479	+	7.50479i	−0.351059	+	0.351059i	0.509444	+	0.860504i	$0.329851\pi$
$458$		0			0
$459$	−5.31965			−0.248300
$460$		0			0
$461$	27.0216			1.25852			0.629262	−	0.777193i	$-0.283357\pi$
$461$	27.0216			1.25852			0.629262	+	0.777193i	$0.283357\pi$
$462$		0			0
$463$	27.7123	−	27.7123i	1.28790	−	1.28790i	0.351843	−	0.936059i	$-0.385555\pi$
$463$	27.7123	−	27.7123i	1.28790	−	1.28790i	0.936059	−	0.351843i	$-0.114445\pi$
$464$		0			0
$465$	−14.5048	+	9.72928i	−0.672644	+	0.451185i
$466$		0			0
$467$	2.00823	+	2.00823i	0.0929296	+	0.0929296i	0.752043	−	0.659114i	$-0.229068\pi$
$467$	2.00823	+	2.00823i	0.0929296	+	0.0929296i	−0.659114	+	0.752043i	$0.729068\pi$
$468$		0			0
$469$			7.58767i			0.350366i
$470$		0			0
$471$		−	12.7477i		−	0.587381i
$472$		0			0
$473$	−31.8217	−	31.8217i	−1.46317	−	1.46317i
$474$		0			0
$475$	5.65685	+	2.31952i	0.259554	+	0.106427i
$476$		0			0
$477$	2.62620	−	2.62620i	0.120245	−	0.120245i
$478$		0			0
$479$	−13.7593			−0.628678			−0.314339	−	0.949311i	$-0.601783\pi$
$479$	−13.7593			−0.628678			−0.314339	+	0.949311i	$0.601783\pi$
$480$		0			0
$481$	−6.20617			−0.282977
$482$		0			0
$483$	0.931222	−	0.931222i	0.0423721	−	0.0423721i
$484$		0			0
$485$	1.39838	+	2.08476i	0.0634972	+	0.0946641i
$486$		0			0
$487$	−24.3355	−	24.3355i	−1.10275	−	1.10275i	−0.994078	−	0.108671i	$-0.965340\pi$
$487$	−24.3355	−	24.3355i	−1.10275	−	1.10275i	−0.108671	−	0.994078i	$-0.534660\pi$
$488$		0			0
$489$		−	18.5048i		−	0.836816i
$490$		0			0
$491$		−	28.8918i		−	1.30387i	−0.758275	−	0.651935i	$-0.773957\pi$
$491$		−	28.8918i		−	1.30387i	0.758275	−	0.651935i	$-0.226043\pi$
$492$		0			0
$493$	3.25240	+	3.25240i	0.146481	+	0.146481i
$494$		0			0
$495$	2.21703	−	11.2507i	0.0996483	−	0.505681i
$496$		0			0
$497$	−4.95377	+	4.95377i	−0.222207	+	0.222207i
$498$		0			0
$499$	12.5365			0.561211			0.280605	−	0.959823i	$-0.409465\pi$
$499$	12.5365			0.561211			0.280605	+	0.959823i	$0.409465\pi$
$500$		0			0
$501$	−16.0279			−0.716074
$502$		0			0
$503$	−9.01392	+	9.01392i	−0.401911	+	0.401911i	−0.878906	−	0.476995i	$-0.841726\pi$
$503$	−9.01392	+	9.01392i	−0.401911	+	0.401911i	0.476995	+	0.878906i	$0.341726\pi$
$504$		0			0
$505$	−4.37380	+	22.1955i	−0.194632	+	0.987689i
$506$		0			0
$507$	4.80397	+	4.80397i	0.213352	+	0.213352i
$508$		0			0
$509$		−	22.5448i		−	0.999279i	−0.866233	−	0.499640i	$-0.833466\pi$
$509$		−	22.5448i		−	0.999279i	0.866233	−	0.499640i	$-0.166534\pi$
$510$		0			0
$511$			2.75420i			0.121839i
$512$		0			0
$513$	−0.864641	−	0.864641i	−0.0381748	−	0.0381748i
$514$		0			0
$515$	−6.73386	−	10.0391i	−0.296729	−	0.442376i
$516$		0			0
$517$	−11.7938	+	11.7938i	−0.518692	+	0.518692i
$518$		0			0
$519$	11.2681			0.494613
$520$		0			0
$521$	−18.9046			−0.828226			−0.414113	−	0.910225i	$-0.635908\pi$
$521$	−18.9046			−0.828226			−0.414113	+	0.910225i	$0.635908\pi$
$522$		0			0
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	−0.0445800	−	0.999006i	$-0.514195\pi$
$523$	21.8269	−	21.8269i	0.954426	−	0.954426i	0.999006	+	0.0445800i	$0.0141949\pi$
$524$		0			0
$525$	−4.00000	−	1.64015i	−0.174574	−	0.0715821i
$526$		0			0
$527$	29.3810	+	29.3810i	1.27986	+	1.27986i
$528$		0			0
$529$			20.6801i			0.899136i
$530$		0			0
$531$			0.528636i			0.0229408i
$532$		0			0
$533$	−9.72928	−	9.72928i	−0.421422	−	0.421422i
$534$		0			0
$535$	−14.4732	+	9.70807i	−0.625730	+	0.419716i
$536$		0			0
$537$	8.94315	−	8.94315i	0.385925	−	0.385925i
$538$		0			0
$539$	−32.0637			−1.38108
$540$		0			0
$541$	−7.85838			−0.337858			−0.168929	−	0.985628i	$-0.554031\pi$
$541$	−7.85838			−0.337858			−0.168929	+	0.985628i	$0.554031\pi$
$542$		0			0
$543$	5.46543	−	5.46543i	0.234544	−	0.234544i
$544$		0			0
$545$	16.0525	+	3.16327i	0.687613	+	0.135499i
$546$		0			0
$547$	−17.8105	−	17.8105i	−0.761522	−	0.761522i	0.215076	−	0.976597i	$-0.431000\pi$
$547$	−17.8105	−	17.8105i	−0.761522	−	0.761522i	−0.976597	+	0.215076i	$0.931000\pi$
$548$		0			0
$549$			4.98168i			0.212613i
$550$		0			0
$551$			1.05727i			0.0450413i
$552$		0			0
$553$	9.72928	+	9.72928i	0.413731	+	0.413731i
$554$		0			0
$555$	−5.46543	−	1.07700i	−0.231994	−	0.0457163i
$556$		0			0
$557$	−23.3372	+	23.3372i	−0.988827	+	0.988827i	−0.999938	−	0.0111112i	$-0.996463\pi$
$557$	−23.3372	+	23.3372i	−0.988827	+	0.988827i	0.0111112	+	0.999938i	$0.496463\pi$
$558$		0			0
$559$	−21.8617			−0.924652
$560$		0			0
$561$	−27.2803			−1.15178
$562$		0			0
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	−0.587182	−	0.809455i	$-0.699763\pi$
$563$	5.27400	−	5.27400i	0.222273	−	0.222273i	0.809455	+	0.587182i	$0.199763\pi$
$564$		0			0
$565$	1.33716	−	0.896916i	0.0562546	−	0.0377336i
$566$		0			0
$567$	0.611393	+	0.611393i	0.0256761	+	0.0256761i
$568$		0			0
$569$		−	28.5606i		−	1.19732i	−0.801002	−	0.598661i	$-0.795699\pi$
$569$		−	28.5606i		−	1.19732i	0.801002	−	0.598661i	$-0.204301\pi$
$570$		0			0
$571$			32.2837i			1.35103i	0.737347	+	0.675515i	$0.236078\pi$
$571$			32.2837i			1.35103i	−0.737347	+	0.675515i	$0.763922\pi$
$572$		0			0
$573$	−4.98168	−	4.98168i	−0.208113	−	0.208113i
$574$		0			0
$575$	−7.02542	+	2.93945i	−0.292980	+	0.122583i
$576$		0			0
$577$	27.0279	−	27.0279i	1.12519	−	1.12519i	0.134237	−	0.990949i	$-0.457142\pi$
$577$	27.0279	−	27.0279i	1.12519	−	1.12519i	0.990949	−	0.134237i	$-0.0428584\pi$
$578$		0			0
$579$	16.2702			0.676168
$580$		0			0
$581$	9.72928			0.403639
$582$		0			0
$583$	13.4677	−	13.4677i	0.557776	−	0.557776i
$584$		0			0
$585$	−3.10308	−	4.62620i	−0.128297	−	0.191270i
$586$		0			0
$587$	−17.1558	−	17.1558i	−0.708096	−	0.708096i	0.258039	−	0.966135i	$-0.416924\pi$
$587$	−17.1558	−	17.1558i	−0.708096	−	0.708096i	−0.966135	+	0.258039i	$0.916924\pi$
$588$		0			0
$589$			9.55102i			0.393543i
$590$		0			0
$591$		−	11.1420i		−	0.458321i
$592$		0			0
$593$	−21.5833	−	21.5833i	−0.886320	−	0.886320i	0.107848	−	0.994167i	$-0.465604\pi$
$593$	−21.5833	−	21.5833i	−0.886320	−	0.886320i	−0.994167	+	0.107848i	$0.965604\pi$
$594$		0			0
$595$	−1.98849	+	10.0909i	−0.0815203	+	0.413687i
$596$		0			0
$597$	−8.11704	+	8.11704i	−0.332208	+	0.332208i
$598$		0			0
$599$	−23.7636			−0.970955			−0.485478	−	0.874249i	$-0.661354\pi$
$599$	−23.7636			−0.970955			−0.485478	+	0.874249i	$0.661354\pi$
$600$		0			0
$601$	22.1695			0.904314			0.452157	−	0.891938i	$-0.350655\pi$
$601$	22.1695			0.904314			0.452157	+	0.891938i	$0.350655\pi$
$602$		0			0
$603$	−6.20522	+	6.20522i	−0.252696	+	0.252696i
$604$		0			0
$605$	6.61391	−	33.5633i	0.268894	−	1.36454i
$606$		0			0
$607$	9.35348	+	9.35348i	0.379646	+	0.379646i	0.870974	−	0.491328i	$-0.163489\pi$
$607$	9.35348	+	9.35348i	0.379646	+	0.379646i	−0.491328	+	0.870974i	$0.663489\pi$
$608$		0			0
$609$		−	0.747604i		−	0.0302944i
$610$		0			0
$611$			8.10243i			0.327789i
$612$		0			0
$613$	24.1247	+	24.1247i	0.974389	+	0.974389i	0.999680	−	0.0252913i	$-0.00805134\pi$
$613$	24.1247	+	24.1247i	0.974389	+	0.974389i	−0.0252913	+	0.999680i	$0.508051\pi$
$614$		0			0
$615$	−6.87964	−	10.2564i	−0.277414	−	0.413579i
$616$		0			0
$617$	3.82611	−	3.82611i	0.154033	−	0.154033i	−0.625883	−	0.779917i	$-0.715261\pi$
$617$	3.82611	−	3.82611i	0.154033	−	0.154033i	0.779917	+	0.625883i	$0.215261\pi$
$618$		0			0
$619$	−30.1297			−1.21101			−0.605507	−	0.795840i	$-0.707029\pi$
$619$	−30.1297			−1.21101			−0.605507	+	0.795840i	$0.707029\pi$
$620$		0			0
$621$	1.52311			0.0611205
$622$		0			0
$623$	4.43407	−	4.43407i	0.177647	−	0.177647i
$624$		0			0
$625$	17.8034	+	17.5510i	0.712137	+	0.702041i
$626$		0			0
$627$	−4.43407	−	4.43407i	−0.177080	−	0.177080i
$628$		0			0
$629$			13.2524i			0.528408i
$630$		0			0
$631$		−	21.5701i		−	0.858694i	−0.903140	−	0.429347i	$-0.858744\pi$
$631$		−	21.5701i		−	0.858694i	0.903140	−	0.429347i	$-0.141256\pi$
$632$		0			0
$633$	3.88296	+	3.88296i	0.154334	+	0.154334i
$634$		0			0
$635$	−19.6729	+	13.1959i	−0.780697	+	0.523663i
$636$		0			0
$637$	−11.0140	+	11.0140i	−0.436389	+	0.436389i
$638$		0			0
$639$	−8.10243			−0.320527
$640$		0			0
$641$	48.3911			1.91133			0.955666	−	0.294452i	$-0.0951370\pi$
$641$	48.3911			1.91133			0.955666	+	0.294452i	$0.0951370\pi$
$642$		0			0
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	−0.0765729	−	0.997064i	$-0.524398\pi$
$643$	23.3413	−	23.3413i	0.920491	−	0.920491i	0.997064	+	0.0765729i	$0.0243978\pi$
$644$		0			0
$645$	−19.2524	−	3.79383i	−0.758062	−	0.149382i
$646$		0			0
$647$	−32.4465	−	32.4465i	−1.27560	−	1.27560i	−0.943103	−	0.332501i	$-0.892108\pi$
$647$	−32.4465	−	32.4465i	−1.27560	−	1.27560i	−0.332501	−	0.943103i	$-0.607892\pi$
$648$		0			0
$649$			2.71096i			0.106414i
$650$		0			0
$651$		−	6.75359i		−	0.264694i
$652$		0			0
$653$	−18.4725	−	18.4725i	−0.722885	−	0.722885i	0.246307	−	0.969192i	$-0.420783\pi$
$653$	−18.4725	−	18.4725i	−0.722885	−	0.722885i	−0.969192	+	0.246307i	$0.920783\pi$
$654$		0			0
$655$	30.7063	+	6.05091i	1.19979	+	0.236429i
$656$		0			0
$657$	−2.25240	+	2.25240i	−0.0878743	+	0.0878743i
$658$		0			0
$659$	47.5028			1.85045			0.925223	−	0.379423i	$-0.123878\pi$
$659$	47.5028			1.85045			0.925223	+	0.379423i	$0.123878\pi$
$660$		0			0
$661$	46.1204			1.79387			0.896937	−	0.442158i	$-0.145787\pi$
$661$	46.1204			1.79387			0.896937	+	0.442158i	$0.145787\pi$
$662$		0			0
$663$	−9.37086	+	9.37086i	−0.363934	+	0.363934i
$664$		0			0
$665$	−1.96336	+	1.31695i	−0.0761357	+	0.0510690i
$666$		0			0
$667$	−0.931222	−	0.931222i	−0.0360571	−	0.0360571i
$668$		0			0
$669$		−	15.3694i		−	0.594217i
$670$		0			0
$671$			25.5471i			0.986236i
$672$		0			0
$673$	3.60599	+	3.60599i	0.139001	+	0.139001i	0.773183	−	0.634183i	$-0.218663\pi$
$673$	3.60599	+	3.60599i	0.139001	+	0.139001i	−0.634183	+	0.773183i	$0.718663\pi$
$674$		0			0
$675$	−1.92989	−	4.61254i	−0.0742816	−	0.177537i
$676$		0			0
$677$	8.26635	−	8.26635i	0.317702	−	0.317702i	−0.530182	−	0.847884i	$-0.677876\pi$
$677$	8.26635	−	8.26635i	0.317702	−	0.317702i	0.847884	+	0.530182i	$0.177876\pi$
$678$		0			0
$679$	−0.970688			−0.0372516
$680$		0			0
$681$	7.04623			0.270012
$682$		0			0
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	−0.527167	−	0.849762i	$-0.676746\pi$
$683$	8.43079	−	8.43079i	0.322595	−	0.322595i	0.849762	+	0.527167i	$0.176746\pi$
$684$		0			0
$685$	12.3555	+	18.4200i	0.472079	+	0.703793i
$686$		0			0
$687$	18.2131	+	18.2131i	0.694872	+	0.694872i
$688$		0			0
$689$		−	9.25240i		−	0.352488i
$690$		0			0
$691$			21.9182i			0.833809i	0.908950	+	0.416905i	$0.136885\pi$
$691$			21.9182i			0.833809i	−0.908950	+	0.416905i	$0.863115\pi$
$692$		0			0
$693$	3.13536	+	3.13536i	0.119102	+	0.119102i
$694$		0			0
$695$	0.985716	−	5.00217i	0.0373903	−	0.189743i
$696$		0			0
$697$	−20.7755	+	20.7755i	−0.786929	+	0.786929i
$698$		0			0
$699$	1.01163			0.0382633
$700$		0			0
$701$	21.8184			0.824070			0.412035	−	0.911168i	$-0.364818\pi$
$701$	21.8184			0.824070			0.412035	+	0.911168i	$0.364818\pi$
$702$		0			0
$703$	−2.15401	+	2.15401i	−0.0812400	+	0.0812400i
$704$		0			0
$705$	−1.40608	+	7.13536i	−0.0529559	+	0.268733i
$706$		0			0
$707$	−6.18549	−	6.18549i	−0.232629	−	0.232629i
$708$		0			0
$709$		−	31.7938i		−	1.19404i	−0.802225	−	0.597021i	$-0.796351\pi$
$709$		−	31.7938i		−	1.19404i	0.802225	−	0.597021i	$-0.203649\pi$
$710$		0			0
$711$			15.9133i			0.596795i
$712$		0			0
$713$	−8.41233	−	8.41233i	−0.315044	−	0.315044i
$714$		0			0
$715$	−15.9133	−	23.7242i	−0.595123	−	0.887233i
$716$		0			0
$717$	19.0462	−	19.0462i	0.711294	−	0.711294i
$718$		0			0
$719$	52.0874			1.94253			0.971265	−	0.237999i	$-0.0764916\pi$
$719$	52.0874			1.94253			0.971265	+	0.237999i	$0.0764916\pi$
$720$		0			0
$721$	4.67432			0.174081
$722$		0			0
$723$	−9.96487	+	9.96487i	−0.370598	+	0.370598i
$724$		0			0
$725$	−1.64015	+	4.00000i	−0.0609137	+	0.148556i
$726$		0			0
$727$	−8.13069	−	8.13069i	−0.301551	−	0.301551i	0.540070	−	0.841620i	$-0.318398\pi$
$727$	−8.13069	−	8.13069i	−0.301551	−	0.301551i	−0.841620	+	0.540070i	$0.818398\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			46.6826i			1.72662i
$732$		0			0
$733$	29.9956	+	29.9956i	1.10791	+	1.10791i	0.993424	+	0.114489i	$0.0365232\pi$
$733$	29.9956	+	29.9956i	1.10791	+	1.10791i	0.114489	+	0.993424i	$0.463477\pi$
$734$		0			0
$735$	−11.6107	+	7.78804i	−0.428268	+	0.287266i
$736$		0			0
$737$	−31.8217	+	31.8217i	−1.17217	+	1.17217i
$738$		0			0
$739$	39.4719			1.45200			0.725999	−	0.687696i	$-0.241378\pi$
$739$	39.4719			1.45200			0.725999	+	0.687696i	$0.241378\pi$
$740$		0			0
$741$	−3.04623			−0.111906
$742$		0			0
$743$	12.2252	−	12.2252i	0.448499	−	0.448499i	−0.446356	−	0.894855i	$-0.647279\pi$
$743$	12.2252	−	12.2252i	0.448499	−	0.448499i	0.894855	+	0.446356i	$0.147279\pi$
$744$		0			0
$745$	−22.1955	−	4.37380i	−0.813182	−	0.160244i
$746$		0			0
$747$	7.95665	+	7.95665i	0.291118	+	0.291118i
$748$		0			0
$749$		−	6.73887i		−	0.246233i
$750$		0			0
$751$			28.9069i			1.05483i	0.849609	+	0.527413i	$0.176838\pi$
$751$			28.9069i			1.05483i	−0.849609	+	0.527413i	$0.823162\pi$
$752$		0			0
$753$	−12.1955	−	12.1955i	−0.444430	−	0.444430i
$754$		0			0
$755$	17.4126	+	3.43129i	0.633710	+	0.124877i
$756$		0			0
$757$	16.2018	−	16.2018i	0.588864	−	0.588864i	−0.348459	−	0.937324i	$-0.613295\pi$
$757$	16.2018	−	16.2018i	0.588864	−	0.588864i	0.937324	+	0.348459i	$0.113295\pi$
$758$		0			0
$759$	7.81086			0.283516
$760$		0			0
$761$	−6.64641			−0.240932			−0.120466	−	0.992717i	$-0.538439\pi$
$761$	−6.64641			−0.240932			−0.120466	+	0.992717i	$0.538439\pi$
$762$		0			0
$763$	−4.47353	+	4.47353i	−0.161953	+	0.161953i
$764$		0			0
$765$	−9.87859	+	6.62620i	−0.357161	+	0.239571i
$766$		0			0
$767$	0.931222	+	0.931222i	0.0336245	+	0.0336245i
$768$		0			0
$769$		−	29.3449i		−	1.05820i	−0.848559	−	0.529101i	$-0.822529\pi$
$769$		−	29.3449i		−	1.05820i	0.848559	−	0.529101i	$-0.177471\pi$
$770$		0			0
$771$		−	21.2329i		−	0.764686i
$772$		0			0
$773$	−37.5833	−	37.5833i	−1.35178	−	1.35178i	−0.883674	−	0.468104i	$-0.844937\pi$
$773$	−37.5833	−	37.5833i	−1.35178	−	1.35178i	−0.468104	−	0.883674i	$-0.655063\pi$
$774$		0			0
$775$	−14.8166	+	36.1346i	−0.532226	+	1.29799i
$776$		0			0
$777$	1.52311	−	1.52311i	0.0546414	−	0.0546414i
$778$		0			0
$779$	−6.75359			−0.241973
$780$		0			0
$781$	−41.5510			−1.48681
$782$		0			0
$783$	0.611393	−	0.611393i	0.0218494	−	0.0218494i
$784$		0			0
$785$	−15.8786	−	23.6724i	−0.566731	−	0.844905i
$786$		0			0
$787$	7.59353	+	7.59353i	0.270680	+	0.270680i	0.829374	−	0.558694i	$-0.188697\pi$
$787$	7.59353	+	7.59353i	0.270680	+	0.270680i	−0.558694	+	0.829374i	$0.688697\pi$
$788$		0			0
$789$		−	9.52311i		−	0.339032i
$790$		0			0
$791$			0.622595i			0.0221369i
$792$		0			0
$793$	8.77551	+	8.77551i	0.311628	+	0.311628i
$794$		0			0
$795$	1.60564	−	8.14807i	0.0569462	−	0.288982i
$796$		0			0
$797$	−27.4908	+	27.4908i	−0.973775	+	0.973775i	−0.999665	−	0.0258893i	$-0.991758\pi$
$797$	−27.4908	+	27.4908i	−0.973775	+	0.973775i	0.0258893	+	0.999665i	$0.491758\pi$
$798$		0			0
$799$	17.3016			0.612086
$800$		0			0
$801$	7.25240			0.256251
$802$		0			0
$803$	−11.5508	+	11.5508i	−0.407618	+	0.407618i
$804$		0			0
$805$	0.569343	−	2.88922i	0.0200667	−	0.101832i
$806$		0			0
$807$	−18.1760	−	18.1760i	−0.639824	−	0.639824i
$808$		0			0
$809$			47.7205i			1.67776i	0.544313	+	0.838882i	$0.316791\pi$
$809$			47.7205i			1.67776i	−0.544313	+	0.838882i	$0.683209\pi$
$810$		0			0
$811$			37.3179i			1.31041i	0.755451	+	0.655205i	$0.227418\pi$
$811$			37.3179i			1.31041i	−0.755451	+	0.655205i	$0.772582\pi$
$812$		0			0
$813$	−0.658473	−	0.658473i	−0.0230937	−	0.0230937i
$814$		0			0
$815$	−23.0497	−	34.3634i	−0.807397	−	1.20370i
$816$		0			0
$817$	−7.58767	+	7.58767i	−0.265459	+	0.265459i
$818$		0			0
$819$	2.15401			0.0752672
$820$		0			0
$821$	0.686380			0.0239548			0.0119774	−	0.999928i	$-0.496187\pi$
$821$	0.686380			0.0239548			0.0119774	+	0.999928i	$0.496187\pi$
$822$		0			0
$823$	−27.2553	+	27.2553i	−0.950059	+	0.950059i	−0.998811	−	0.0487521i	$-0.984476\pi$
$823$	−27.2553	+	27.2553i	−0.950059	+	0.950059i	0.0487521	+	0.998811i	$0.484476\pi$
$824$		0			0
$825$	−9.89692	−	23.6541i	−0.344566	−	0.823530i
$826$		0			0
$827$	31.4437	+	31.4437i	1.09341	+	1.09341i	0.995162	+	0.0982432i	$0.0313223\pi$
$827$	31.4437	+	31.4437i	1.09341	+	1.09341i	0.0982432	+	0.995162i	$0.468678\pi$
$828$		0			0
$829$		−	0.270718i		−	0.00940243i	−0.999989	−	0.00470122i	$-0.998504\pi$
$829$		−	0.270718i		−	0.00940243i	0.999989	−	0.00470122i	$-0.00149645\pi$
$830$		0			0
$831$			31.1978i			1.08224i
$832$		0			0
$833$	23.5187	+	23.5187i	0.814876	+	0.814876i
$834$		0			0
$835$	−29.7639	+	19.9645i	−1.03002	+	0.690900i
$836$		0			0
$837$	5.52311	−	5.52311i	0.190907	−	0.190907i
$838$		0			0
$839$	31.0214			1.07098			0.535489	−	0.844542i	$-0.320127\pi$
$839$	31.0214			1.07098			0.535489	+	0.844542i	$0.320127\pi$
$840$		0			0
$841$	28.2524			0.974221
$842$		0			0
$843$	−6.05944	+	6.05944i	−0.208698	+	0.208698i
$844$		0			0
$845$	14.9048	+	2.93711i	0.512742	+	0.101040i
$846$		0			0
$847$	9.35348	+	9.35348i	0.321389	+	0.321389i
$848$		0			0
$849$		−	16.3632i		−	0.561583i
$850$		0			0
$851$		−	3.79441i		−	0.130071i
$852$		0			0
$853$	−3.82611	−	3.82611i	−0.131003	−	0.131003i	0.638565	−	0.769568i	$-0.279528\pi$
$853$	−3.82611	−	3.82611i	−0.131003	−	0.131003i	−0.769568	+	0.638565i	$0.779528\pi$
$854$		0			0
$855$	−2.68264	−	0.528636i	−0.0917445	−	0.0180790i
$856$		0			0
$857$	20.7711	−	20.7711i	0.709529	−	0.709529i	−0.256907	−	0.966436i	$-0.582704\pi$
$857$	20.7711	−	20.7711i	0.709529	−	0.709529i	0.966436	+	0.256907i	$0.0827035\pi$
$858$		0			0
$859$	−1.69693			−0.0578985			−0.0289492	−	0.999581i	$-0.509216\pi$
$859$	−1.69693			−0.0578985			−0.0289492	+	0.999581i	$0.509216\pi$
$860$		0			0
$861$	4.77551			0.162749
$862$		0			0
$863$	5.92869	−	5.92869i	0.201815	−	0.201815i	−0.598962	−	0.800777i	$-0.704420\pi$
$863$	5.92869	−	5.92869i	0.201815	−	0.201815i	0.800777	+	0.598962i	$0.204420\pi$
$864$		0			0
$865$	20.9248	−	14.0356i	0.711465	−	0.477225i
$866$		0			0
$867$	7.98933	+	7.98933i	0.271332	+	0.271332i
$868$		0			0
$869$			81.6068i			2.76832i
$870$		0			0
$871$			21.8617i			0.740756i
$872$		0			0
$873$	−0.793833	−	0.793833i	−0.0268672	−	0.0268672i
$874$		0			0
$875$	−9.47100	+	1.93667i	−0.320178	+	0.0654714i
$876$		0			0
$877$	10.0323	−	10.0323i	0.338766	−	0.338766i	−0.517137	−	0.855903i	$-0.673002\pi$
$877$	10.0323	−	10.0323i	0.338766	−	0.338766i	0.855903	+	0.517137i	$0.173002\pi$
$878$		0			0
$879$	18.2390			0.615186
$880$		0			0
$881$	−29.8130			−1.00443			−0.502213	−	0.864744i	$-0.667481\pi$
$881$	−29.8130			−1.00443			−0.502213	+	0.864744i	$0.667481\pi$
$882$		0			0
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	−0.607230	−	0.794526i	$-0.707719\pi$
$883$	5.56557	−	5.56557i	0.187296	−	0.187296i	0.794526	+	0.607230i	$0.207719\pi$
$884$		0			0
$885$	0.658473	+	0.981678i	0.0221343	+	0.0329987i
$886$		0			0
$887$	8.59630	+	8.59630i	0.288636	+	0.288636i	0.836541	−	0.547905i	$-0.184574\pi$
$887$	8.59630	+	8.59630i	0.288636	+	0.288636i	−0.547905	+	0.836541i	$0.684574\pi$
$888$		0			0
$889$		−	9.15994i		−	0.307214i
$890$		0			0
$891$			5.12822i			0.171802i
$892$		0			0
$893$	2.81215	+	2.81215i	0.0941052	+	0.0941052i
$894$		0			0
$895$	5.46778	−	27.7471i	0.182768	−	0.927483i
$896$		0			0
$897$	2.68305	−	2.68305i	0.0895845	−	0.0895845i
$898$		0			0
$899$	−6.75359			−0.225245
$900$		0			0
$901$	−19.7572			−0.658207
$902$		0			0
$903$	5.36529	−	5.36529i	0.178546	−	0.178546i
$904$		0			0
$905$	3.34153	−	16.9571i	0.111076	−	0.563673i
$906$		0			0
$907$	−31.6263	−	31.6263i	−1.05013	−	1.05013i	−0.998675	−	0.0514592i	$-0.983613\pi$
$907$	−31.6263	−	31.6263i	−1.05013	−	1.05013i	−0.0514592	−	0.998675i	$-0.516387\pi$
$908$		0			0
$909$		−	10.1170i		−	0.335561i
$910$		0			0
$911$			42.2656i			1.40032i	0.713985	+	0.700161i	$0.246888\pi$
$911$			42.2656i			1.40032i	−0.713985	+	0.700161i	$0.753112\pi$
$912$		0			0
$913$	40.8034	+	40.8034i	1.35040	+	1.35040i
$914$		0			0
$915$	6.20522	+	9.25099i	0.205138	+	0.305828i
$916$		0			0
$917$	−8.55728	+	8.55728i	−0.282586	+	0.282586i
$918$		0			0
$919$	−31.2829			−1.03193			−0.515964	−	0.856610i	$-0.672566\pi$
$919$	−31.2829			−1.03193			−0.515964	+	0.856610i	$0.672566\pi$
$920$		0			0
$921$	2.27072			0.0748227
$922$		0			0
$923$	−14.2729	+	14.2729i	−0.469798	+	0.469798i
$924$		0			0
$925$	−11.4908	+	4.80779i	−0.377816	+	0.158079i
$926$		0			0
$927$	3.82267	+	3.82267i	0.125553	+	0.125553i
$928$		0			0
$929$		−	22.1050i		−	0.725241i	−0.931937	−	0.362620i	$-0.881882\pi$
$929$		−	22.1050i		−	0.725241i	0.931937	−	0.362620i	$-0.118118\pi$
$930$		0			0
$931$			7.64535i			0.250566i
$932$		0			0
$933$	13.7293	+	13.7293i	0.449477	+	0.449477i
$934$		0			0
$935$	−50.6596	+	33.9806i	−1.65675	+	1.11128i
$936$		0			0
$937$	−15.2986	+	15.2986i	−0.499784	+	0.499784i	−0.911371	−	0.411586i	$-0.864975\pi$
$937$	−15.2986	+	15.2986i	−0.499784	+	0.499784i	0.411586	+	0.911371i	$0.364975\pi$
$938$		0			0
$939$	−25.0471			−0.817381
$940$		0			0
$941$	−25.5264			−0.832138			−0.416069	−	0.909333i	$-0.636593\pi$
$941$	−25.5264			−0.832138			−0.416069	+	0.909333i	$0.636593\pi$
$942$		0			0
$943$	5.94842	−	5.94842i	0.193707	−	0.193707i
$944$		0			0
$945$	1.89692	+	0.373802i	0.0617067	+	0.0121598i
$946$		0			0
$947$	−11.9881	−	11.9881i	−0.389562	−	0.389562i	0.484969	−	0.874531i	$-0.338831\pi$
$947$	−11.9881	−	11.9881i	−0.389562	−	0.389562i	−0.874531	+	0.484969i	$0.838831\pi$
$948$		0			0
$949$			7.93545i			0.257596i
$950$		0			0
$951$			11.0160i			0.357217i
$952$		0			0
$953$	5.99563	+	5.99563i	0.194218	+	0.194218i	0.797516	−	0.603298i	$-0.206147\pi$
$953$	5.99563	+	5.99563i	0.194218	+	0.194218i	−0.603298	+	0.797516i	$0.706147\pi$
$954$		0			0
$955$	−15.4562	−	3.04577i	−0.500151	−	0.0985586i
$956$		0			0
$957$	3.13536	−	3.13536i	0.101352	−	0.101352i
$958$		0			0
$959$	−8.57657			−0.276952
$960$		0			0
$961$	−30.0096			−0.968051
$962$		0			0
$963$	5.51107	−	5.51107i	0.177592	−	0.177592i
$964$		0			0
$965$	30.2139	−	20.2663i	0.972619	−	0.652397i
$966$		0			0
$967$	−1.66866	−	1.66866i	−0.0536606	−	0.0536606i	0.679767	−	0.733428i	$-0.262081\pi$
$967$	−1.66866	−	1.66866i	−0.0536606	−	0.0536606i	−0.733428	+	0.679767i	$0.762081\pi$
$968$		0			0
$969$			6.50479i			0.208964i
$970$		0			0
$971$			4.79719i			0.153949i	0.997033	+	0.0769745i	$0.0245260\pi$
$971$			4.79719i			0.153949i	−0.997033	+	0.0769745i	$0.975474\pi$
$972$		0			0
$973$	1.39401	+	1.39401i	0.0446900	+	0.0446900i
$974$		0			0
$975$	−11.5249	−	4.72563i	−0.369091	−	0.151341i
$976$		0			0
$977$	−25.0140	+	25.0140i	−0.800267	+	0.800267i	−0.983137	−	0.182870i	$-0.941461\pi$
$977$	−25.0140	+	25.0140i	−0.800267	+	0.800267i	0.182870	+	0.983137i	$0.441461\pi$
$978$		0			0
$979$	37.1919			1.18866
$980$		0			0
$981$	−7.31695			−0.233612
$982$		0			0
$983$	−30.9151	+	30.9151i	−0.986038	+	0.986038i	−0.999904	−	0.0138655i	$-0.995586\pi$
$983$	−30.9151	+	30.9151i	−0.986038	+	0.986038i	0.0138655	+	0.999904i	$0.495586\pi$
$984$		0			0
$985$	−13.8786	−	20.6907i	−0.442209	−	0.659262i
$986$		0			0
$987$	−1.98849	−	1.98849i	−0.0632945	−	0.0632945i
$988$		0			0
$989$		−	13.3661i		−	0.425017i
$990$		0			0
$991$			26.5873i			0.844575i	0.906462	+	0.422287i	$0.138773\pi$
$991$			26.5873i			0.844575i	−0.906462	+	0.422287i	$0.861227\pi$
$992$		0			0
$993$	22.4157	+	22.4157i	0.711340	+	0.711340i
$994$		0			0
$995$	−4.96270	+	25.1840i	−0.157328	+	0.798387i
$996$		0			0
$997$	2.47252	−	2.47252i	0.0783054	−	0.0783054i	−0.666869	−	0.745175i	$-0.732366\pi$
$997$	2.47252	−	2.47252i	0.0783054	−	0.0783054i	0.745175	+	0.666869i	$0.232366\pi$
$998$		0			0
$999$	2.49122			0.0788187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.w.g.703.2		12
4.3	odd	2	inner	960.2.w.g.703.5		12
5.2	odd	4	inner	960.2.w.g.127.5		12
8.3	odd	2		60.2.j.a.43.5	yes	12
8.5	even	2		60.2.j.a.43.2	yes	12
20.7	even	4	inner	960.2.w.g.127.2		12
24.5	odd	2		180.2.k.e.163.5		12
24.11	even	2		180.2.k.e.163.2		12
40.3	even	4		300.2.j.d.7.5		12
40.13	odd	4		300.2.j.d.7.2		12
40.19	odd	2		300.2.j.d.43.2		12
40.27	even	4		60.2.j.a.7.2	✓	12
40.29	even	2		300.2.j.d.43.5		12
40.37	odd	4		60.2.j.a.7.5	yes	12
120.29	odd	2		900.2.k.n.343.2		12
120.53	even	4		900.2.k.n.307.5		12
120.59	even	2		900.2.k.n.343.5		12
120.77	even	4		180.2.k.e.127.2		12
120.83	odd	4		900.2.k.n.307.2		12
120.107	odd	4		180.2.k.e.127.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.2	✓	12	40.27	even	4
60.2.j.a.7.5	yes	12	40.37	odd	4
60.2.j.a.43.2	yes	12	8.5	even	2
60.2.j.a.43.5	yes	12	8.3	odd	2
180.2.k.e.127.2		12	120.77	even	4
180.2.k.e.127.5		12	120.107	odd	4
180.2.k.e.163.2		12	24.11	even	2
180.2.k.e.163.5		12	24.5	odd	2
300.2.j.d.7.2		12	40.13	odd	4
300.2.j.d.7.5		12	40.3	even	4
300.2.j.d.43.2		12	40.19	odd	2
300.2.j.d.43.5		12	40.29	even	2
900.2.k.n.307.2		12	120.83	odd	4
900.2.k.n.307.5		12	120.53	even	4
900.2.k.n.343.2		12	120.29	odd	2
900.2.k.n.343.5		12	120.59	even	2
960.2.w.g.127.2		12	20.7	even	4	inner
960.2.w.g.127.5		12	5.2	odd	4	inner
960.2.w.g.703.2		12	1.1	even	1	trivial
960.2.w.g.703.5		12	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.w (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.432320 + 2.19388i) q^{5} +(-0.611393 - 0.611393i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.432320 + 2.19388i) q^{5} +(-0.611393 - 0.611393i) q^{7} -1.00000i q^{9} -5.12822i q^{11} +(-1.76156 - 1.76156i) q^{13} +(-1.24561 - 1.85700i) q^{15} +(-3.76156 + 3.76156i) q^{17} -1.22279 q^{19} +0.864641 q^{21} +(1.07700 - 1.07700i) q^{23} +(-4.62620 - 1.89692i) q^{25} +(0.707107 + 0.707107i) q^{27} -0.864641i q^{29} -7.81086i q^{31} +(3.62620 + 3.62620i) q^{33} +(1.60564 - 1.07700i) q^{35} +(1.76156 - 1.76156i) q^{37} +2.49122 q^{39} +5.52311 q^{41} +(6.20522 - 6.20522i) q^{43} +(2.19388 + 0.432320i) q^{45} +(-2.29979 - 2.29979i) q^{47} -6.25240i q^{49} -5.31965i q^{51} +(2.62620 + 2.62620i) q^{53} +(11.2507 + 2.21703i) q^{55} +(0.864641 - 0.864641i) q^{57} -0.528636 q^{59} -4.98168 q^{61} +(-0.611393 + 0.611393i) q^{63} +(4.62620 - 3.10308i) q^{65} +(-6.20522 - 6.20522i) q^{67} +1.52311i q^{69} -8.10243i q^{71} +(-2.25240 - 2.25240i) q^{73} +(4.61254 - 1.92989i) q^{75} +(-3.13536 + 3.13536i) q^{77} -15.9133 q^{79} -1.00000 q^{81} +(-7.95665 + 7.95665i) q^{83} +(-6.62620 - 9.87859i) q^{85} +(0.611393 + 0.611393i) q^{87} +7.25240i q^{89} +2.15401i q^{91} +(5.52311 + 5.52311i) q^{93} +(0.528636 - 2.68264i) q^{95} +(0.793833 - 0.793833i) q^{97} -5.12822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Introduction

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