LMFDB - Embedded newform 704.2.w.b.225.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(97,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("704.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 15x^{12} - 43x^{10} - 296x^{8} - 387x^{6} + 1215x^{4} + 5103x^{2} + 6561 $ x^16 + 7x^14 + 15x^12 - 43x^10 - 296x^8 - 387x^6 + 1215x^4 + 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			225.4
Root			$0.232753 + 1.71634i$ of defining polynomial
Character	$\chi$	$=$	704.225
Dual form			704.2.w.b.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.224514 - 0.309017i) q^{3} +(3.24170 + 1.05329i) q^{5} +(1.70426 - 1.23822i) q^{7} +(0.881966 + 2.71441i) q^{9} +O(q^{10})$	\(q+(0.224514 - 0.309017i) q^{3} +(3.24170 + 1.05329i) q^{5} +(1.70426 - 1.23822i) q^{7} +(0.881966 + 2.71441i) q^{9} +(3.07768 - 1.23607i) q^{11} +(-3.24170 + 1.05329i) q^{13} +(1.05329 - 0.765261i) q^{15} +(-0.809017 + 2.48990i) q^{17} +(1.40008 - 1.92705i) q^{19} -0.804643i q^{21} -6.81705 q^{23} +(5.35410 + 3.88998i) q^{25} +(2.12663 + 0.690983i) q^{27} +(-5.24518 - 7.21937i) q^{29} +(2.35523 + 7.24866i) q^{31} +(0.309017 - 1.22857i) q^{33} +(6.82891 - 2.21885i) q^{35} +(-1.23822 - 1.70426i) q^{37} +(-0.402322 + 1.23822i) q^{39} +(6.54508 + 4.75528i) q^{41} -9.23607i q^{43} +9.72827i q^{45} +(-7.21937 - 5.24518i) q^{47} +(-0.791796 + 2.43690i) q^{49} +(0.587785 + 0.809017i) q^{51} +(7.24866 - 2.35523i) q^{53} +(11.2789 - 0.765261i) q^{55} +(-0.281153 - 0.865300i) q^{57} +(-0.673542 - 0.927051i) q^{59} +(7.24866 + 2.35523i) q^{61} +(4.86414 + 3.53400i) q^{63} -11.6180 q^{65} +3.70820i q^{67} +(-1.53052 + 2.10658i) q^{69} +(-0.248648 + 0.765261i) q^{71} +(4.16312 - 3.02468i) q^{73} +(2.40414 - 0.781153i) q^{75} +(3.71466 - 5.91743i) q^{77} +(-4.46182 - 13.7321i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(-1.76336 - 0.572949i) q^{83} +(-5.24518 + 7.21937i) q^{85} -3.40852 q^{87} +10.4721 q^{89} +(-4.22050 + 5.80902i) q^{91} +(2.76874 + 0.899619i) q^{93} +(6.56840 - 4.77222i) q^{95} +(-3.04508 - 9.37181i) q^{97} +(6.06961 + 7.26393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{9}+O(q^{10}) $ 16 * q + 32 * q^9	$ 16 q + 32 q^{9} - 4 q^{17} + 32 q^{25} - 4 q^{33} + 60 q^{41} - 120 q^{49} + 76 q^{57} - 168 q^{65} + 4 q^{73} - 64 q^{81} + 96 q^{89} - 4 q^{97}+O(q^{100}) $ 16 * q + 32 * q^9 - 4 * q^17 + 32 * q^25 - 4 * q^33 + 60 * q^41 - 120 * q^49 + 76 * q^57 - 168 * q^65 + 4 * q^73 - 64 * q^81 + 96 * q^89 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	0.224514	−	0.309017i	0.129623	−	0.178411i	−0.739272	−	0.673407i	$-0.764830\pi$
$3$	0.224514	−	0.309017i	0.129623	−	0.178411i	0.868895	+	0.494996i	$0.164830\pi$
$4$		0			0
$5$	3.24170	+	1.05329i	1.44973	+	0.471046i	0.924917	−	0.380170i	$-0.124134\pi$
$5$	3.24170	+	1.05329i	1.44973	+	0.471046i	0.524815	+	0.851216i	$0.324134\pi$
$6$		0			0
$7$	1.70426	−	1.23822i	0.644150	−	0.468003i	−0.217123	−	0.976144i	$-0.569667\pi$
$7$	1.70426	−	1.23822i	0.644150	−	0.468003i	0.861274	+	0.508142i	$0.169667\pi$
$8$		0			0
$9$	0.881966	+	2.71441i	0.293989	+	0.904804i
$10$		0			0
$11$	3.07768	−	1.23607i	0.927957	−	0.372689i
$11$	3.07768	−	1.23607i	0.927957	−	0.372689i
$12$		0			0
$13$	−3.24170	+	1.05329i	−0.899085	+	0.292131i	−0.721860	−	0.692040i	$-0.756712\pi$
$13$	−3.24170	+	1.05329i	−0.899085	+	0.292131i	−0.177226	+	0.984170i	$0.556712\pi$
$14$		0			0
$15$	1.05329	−	0.765261i	0.271959	−	0.197590i
$16$		0			0
$17$	−0.809017	+	2.48990i	−0.196215	+	0.603889i	0.803745	+	0.594974i	$0.202838\pi$
$17$	−0.809017	+	2.48990i	−0.196215	+	0.603889i	−0.999960	+	0.00891486i	$0.997162\pi$
$18$		0			0
$19$	1.40008	−	1.92705i	0.321201	−	0.442096i	−0.617632	−	0.786467i	$-0.711908\pi$
$19$	1.40008	−	1.92705i	0.321201	−	0.442096i	0.938834	+	0.344371i	$0.111908\pi$
$20$		0			0
$21$		−	0.804643i		−	0.175588i
$22$		0			0
$23$	−6.81705			−1.42145			−0.710726	−	0.703469i	$-0.751634\pi$
$23$	−6.81705			−1.42145			−0.710726	+	0.703469i	$0.751634\pi$
$24$		0			0
$25$	5.35410	+	3.88998i	1.07082	+	0.777997i
$26$		0			0
$27$	2.12663	+	0.690983i	0.409270	+	0.132980i
$28$		0			0
$29$	−5.24518	−	7.21937i	−0.974005	−	1.34060i	−0.939997	−	0.341182i	$-0.889173\pi$
$29$	−5.24518	−	7.21937i	−0.974005	−	1.34060i	−0.0340078	−	0.999422i	$-0.510827\pi$
$30$		0			0
$31$	2.35523	+	7.24866i	0.423012	+	1.30190i	0.904885	+	0.425656i	$0.139957\pi$
$31$	2.35523	+	7.24866i	0.423012	+	1.30190i	−0.481873	+	0.876241i	$0.660043\pi$
$32$		0			0
$33$	0.309017	−	1.22857i	0.0537930	−	0.213867i
$34$		0			0
$35$	6.82891	−	2.21885i	1.15430	−	0.375054i
$36$		0			0
$37$	−1.23822	−	1.70426i	−0.203562	−	0.280179i	0.695015	−	0.718995i	$-0.255398\pi$
$37$	−1.23822	−	1.70426i	−0.203562	−	0.280179i	−0.898577	+	0.438817i	$0.855398\pi$
$38$		0			0
$39$	−0.402322	+	1.23822i	−0.0644230	+	0.198274i
$40$		0			0
$41$	6.54508	+	4.75528i	1.02217	+	0.742650i	0.966727	−	0.255811i	$-0.0823426\pi$
$41$	6.54508	+	4.75528i	1.02217	+	0.742650i	0.0554438	+	0.998462i	$0.482343\pi$
$42$		0			0
$43$		−	9.23607i		−	1.40849i	−0.709958	−	0.704244i	$-0.751286\pi$
$43$		−	9.23607i		−	1.40849i	0.709958	−	0.704244i	$-0.248714\pi$
$44$		0			0
$45$			9.72827i			1.45021i
$46$		0			0
$47$	−7.21937	−	5.24518i	−1.05305	−	0.765088i	−0.0802625	−	0.996774i	$-0.525576\pi$
$47$	−7.21937	−	5.24518i	−1.05305	−	0.765088i	−0.972791	+	0.231686i	$0.925576\pi$
$48$		0			0
$49$	−0.791796	+	2.43690i	−0.113114	+	0.348128i
$50$		0			0
$51$	0.587785	+	0.809017i	0.0823064	+	0.113285i
$52$		0			0
$53$	7.24866	−	2.35523i	0.995680	−	0.323516i	0.234542	−	0.972106i	$-0.424641\pi$
$53$	7.24866	−	2.35523i	0.995680	−	0.323516i	0.761138	+	0.648590i	$0.224641\pi$
$54$		0			0
$55$	11.2789	−	0.765261i	1.52084	−	0.103188i
$56$		0			0
$57$	−0.281153	−	0.865300i	−0.0372396	−	0.114612i
$58$		0			0
$59$	−0.673542	−	0.927051i	−0.0876877	−	0.120692i	0.762919	−	0.646494i	$-0.223765\pi$
$59$	−0.673542	−	0.927051i	−0.0876877	−	0.120692i	−0.850607	+	0.525802i	$0.823765\pi$
$60$		0			0
$61$	7.24866	+	2.35523i	0.928096	+	0.301557i	0.733784	−	0.679383i	$-0.237753\pi$
$61$	7.24866	+	2.35523i	0.928096	+	0.301557i	0.194312	+	0.980940i	$0.437753\pi$
$62$		0			0
$63$	4.86414	+	3.53400i	0.612824	+	0.445242i
$64$		0			0
$65$	−11.6180			−1.44104
$66$		0			0
$67$			3.70820i			0.453029i	0.974008	+	0.226515i	$0.0727331\pi$
$67$			3.70820i			0.453029i	−0.974008	+	0.226515i	$0.927267\pi$
$68$		0			0
$69$	−1.53052	+	2.10658i	−0.184253	+	0.253603i
$70$		0			0
$71$	−0.248648	+	0.765261i	−0.0295091	+	0.0908198i	−0.964726	−	0.263255i	$-0.915204\pi$
$71$	−0.248648	+	0.765261i	−0.0295091	+	0.0908198i	0.935217	+	0.354074i	$0.115204\pi$
$72$		0			0
$73$	4.16312	−	3.02468i	0.487256	−	0.354012i	−0.316872	−	0.948468i	$-0.602633\pi$
$73$	4.16312	−	3.02468i	0.487256	−	0.354012i	0.804128	+	0.594456i	$0.202633\pi$
$74$		0			0
$75$	2.40414	−	0.781153i	0.277606	−	0.0901998i
$76$		0			0
$77$	3.71466	−	5.91743i	0.423324	−	0.674354i
$78$		0			0
$79$	−4.46182	−	13.7321i	−0.501993	−	1.54498i	−0.805767	−	0.592233i	$-0.798247\pi$
$79$	−4.46182	−	13.7321i	−0.501993	−	1.54498i	0.303773	−	0.952744i	$-0.401753\pi$
$80$		0			0
$81$	−6.23607	+	4.53077i	−0.692896	+	0.503419i
$82$		0			0
$83$	−1.76336	−	0.572949i	−0.193553	−	0.0628893i	0.210636	−	0.977565i	$-0.432446\pi$
$83$	−1.76336	−	0.572949i	−0.193553	−	0.0628893i	−0.404190	+	0.914675i	$0.632446\pi$
$84$		0			0
$85$	−5.24518	+	7.21937i	−0.568920	+	0.783051i
$86$		0			0
$87$	−3.40852			−0.365432
$88$		0			0
$89$	10.4721			1.11004			0.555022	−	0.831836i	$-0.312710\pi$
$89$	10.4721			1.11004			0.555022	+	0.831836i	$0.312710\pi$
$90$		0			0
$91$	−4.22050	+	5.80902i	−0.442428	+	0.608950i
$92$		0			0
$93$	2.76874	+	0.899619i	0.287105	+	0.0932861i
$94$		0			0
$95$	6.56840	−	4.77222i	0.673904	−	0.489620i
$96$		0			0
$97$	−3.04508	−	9.37181i	−0.309182	−	0.951563i	−0.978084	−	0.208212i	$-0.933235\pi$
$97$	−3.04508	−	9.37181i	−0.309182	−	0.951563i	0.668902	−	0.743351i	$-0.266765\pi$
$98$		0			0
$99$	6.06961	+	7.26393i	0.610019	+	0.730053i
$100$		0			0
$101$	−9.72510	+	3.15988i	−0.967683	+	0.314419i	−0.749880	−	0.661573i	$-0.769889\pi$
$101$	−9.72510	+	3.15988i	−0.967683	+	0.314419i	−0.217803	+	0.975993i	$0.569889\pi$
$102$		0			0
$103$	−1.70426	+	1.23822i	−0.167926	+	0.122005i	−0.668574	−	0.743646i	$-0.733095\pi$
$103$	−1.70426	+	1.23822i	−0.167926	+	0.122005i	0.500648	+	0.865651i	$0.333095\pi$
$104$		0			0
$105$	0.847524	−	2.60841i	0.0827099	−	0.254555i
$106$		0			0
$107$	−7.27794	+	10.0172i	−0.703585	+	0.968401i	0.296327	+	0.955087i	$0.404238\pi$
$107$	−7.27794	+	10.0172i	−0.703585	+	0.968401i	−0.999911	+	0.0133146i	$0.995762\pi$
$108$		0			0
$109$		−	6.81705i		−	0.652955i	−0.945205	−	0.326477i	$-0.894138\pi$
$109$		−	6.81705i		−	0.652955i	0.945205	−	0.326477i	$-0.105862\pi$
$110$		0			0
$111$	−0.804643			−0.0763734
$112$		0			0
$113$	−6.54508	−	4.75528i	−0.615710	−	0.447339i	0.235711	−	0.971823i	$-0.424258\pi$
$113$	−6.54508	−	4.75528i	−0.615710	−	0.447339i	−0.851420	+	0.524484i	$0.824258\pi$
$114$		0			0
$115$	−22.0988	−	7.18034i	−2.06073	−	0.669570i
$116$		0			0
$117$	−5.71814	−	7.87034i	−0.528642	−	0.727613i
$118$		0			0
$119$	1.70426	+	5.24518i	0.156229	+	0.480825i
$120$		0			0
$121$	7.94427	−	7.60845i	0.722207	−	0.691677i
$122$		0			0
$123$	2.93893	−	0.954915i	0.264994	−	0.0861018i
$124$		0			0
$125$	3.24170	+	4.46182i	0.289946	+	0.399077i
$126$		0			0
$127$	−5.76376	+	17.7390i	−0.511451	+	1.57408i	0.278198	+	0.960524i	$0.410263\pi$
$127$	−5.76376	+	17.7390i	−0.511451	+	1.57408i	−0.789649	+	0.613559i	$0.789737\pi$
$128$		0			0
$129$	−2.85410	−	2.07363i	−0.251290	−	0.182573i
$130$		0			0
$131$			0.763932i			0.0667451i	0.999443	+	0.0333725i	$0.0106248\pi$
$131$			0.763932i			0.0667451i	−0.999443	+	0.0333725i	$0.989375\pi$
$132$		0			0
$133$		−	5.01781i		−	0.435099i
$134$		0			0
$135$	6.16608	+	4.47992i	0.530691	+	0.385570i
$136$		0			0
$137$	−3.89919	+	12.0005i	−0.333130	+	1.02527i	0.634506	+	0.772918i	$0.281204\pi$
$137$	−3.89919	+	12.0005i	−0.333130	+	1.02527i	−0.967636	+	0.252351i	$0.918796\pi$
$138$		0			0
$139$	−7.55545	−	10.3992i	−0.640845	−	0.882048i	0.357815	−	0.933792i	$-0.383522\pi$
$139$	−7.55545	−	10.3992i	−0.640845	−	0.882048i	−0.998660	+	0.0517449i	$0.983522\pi$
$140$		0			0
$141$	−3.24170	+	1.05329i	−0.273000	+	0.0887032i
$142$		0			0
$143$	−8.67498	+	7.24866i	−0.725438	+	0.606163i
$144$		0			0
$145$	−9.39919	−	28.9277i	−0.780560	−	2.40232i
$146$		0			0
$147$	0.575274	+	0.791796i	0.0474478	+	0.0653062i
$148$		0			0
$149$	−0.765261	−	0.248648i	−0.0626926	−	0.0203701i	0.277503	−	0.960725i	$-0.410493\pi$
$149$	−0.765261	−	0.248648i	−0.0626926	−	0.0203701i	−0.340195	+	0.940355i	$0.610493\pi$
$150$		0			0
$151$	−18.2496	−	13.2591i	−1.48513	−	1.07901i	−0.975858	−	0.218404i	$-0.929915\pi$
$151$	−18.2496	−	13.2591i	−1.48513	−	1.07901i	−0.509272	−	0.860606i	$-0.670085\pi$
$152$		0			0
$153$	−7.47214			−0.604086
$154$		0			0
$155$			25.9787i			2.08666i
$156$		0			0
$157$	1.23822	−	1.70426i	0.0988206	−	0.136015i	−0.756743	−	0.653712i	$-0.773211\pi$
$157$	1.23822	−	1.70426i	0.0988206	−	0.136015i	0.855564	+	0.517697i	$0.173211\pi$
$158$		0			0
$159$	0.899619	−	2.76874i	0.0713444	−	0.219575i
$160$		0			0
$161$	−11.6180	+	8.44100i	−0.915629	+	0.665244i
$162$		0			0
$163$	−16.7027	+	5.42705i	−1.30826	+	0.425079i	−0.878448	−	0.477839i	$-0.841420\pi$
$163$	−16.7027	+	5.42705i	−1.30826	+	0.425079i	−0.429812	+	0.902918i	$0.641420\pi$
$164$		0			0
$165$	2.29578	−	3.65717i	0.178727	−	0.284710i
$166$		0			0
$167$	3.65717	+	11.2556i	0.283000	+	0.870986i	0.986991	+	0.160776i	$0.0513998\pi$
$167$	3.65717	+	11.2556i	0.283000	+	0.870986i	−0.703990	+	0.710210i	$0.748600\pi$
$168$		0			0
$169$	−1.11803	+	0.812299i	−0.0860026	+	0.0624846i
$170$		0			0
$171$	6.46564	+	2.10081i	0.494440	+	0.160653i
$172$		0			0
$173$	2.76874	−	3.81085i	0.210503	−	0.289733i	−0.690689	−	0.723152i	$-0.742693\pi$
$173$	2.76874	−	3.81085i	0.210503	−	0.289733i	0.901193	+	0.433418i	$0.142693\pi$
$174$		0			0
$175$	13.9414			1.05387
$176$		0			0
$177$	−0.437694			−0.0328991
$178$		0			0
$179$	−2.12663	+	2.92705i	−0.158952	+	0.218778i	−0.881063	−	0.472998i	$-0.843172\pi$
$179$	−2.12663	+	2.92705i	−0.158952	+	0.218778i	0.722112	+	0.691776i	$0.243172\pi$
$180$		0			0
$181$	−4.77222	−	1.55059i	−0.354716	−	0.115254i	0.126238	−	0.992000i	$-0.459710\pi$
$181$	−4.77222	−	1.55059i	−0.354716	−	0.115254i	−0.480954	+	0.876746i	$0.659710\pi$
$182$		0			0
$183$	2.35523	−	1.71118i	0.174104	−	0.126494i
$184$		0			0
$185$	−2.21885	−	6.82891i	−0.163133	−	0.502071i
$186$		0			0
$187$	0.587785	+	8.66312i	0.0429831	+	0.633510i
$188$		0			0
$189$	4.47992	−	1.45561i	0.325866	−	0.105880i
$190$		0			0
$191$	5.11279	−	3.71466i	0.369948	−	0.268783i	−0.387241	−	0.921978i	$-0.626572\pi$
$191$	5.11279	−	3.71466i	0.369948	−	0.268783i	0.757189	+	0.653195i	$0.226572\pi$
$192$		0			0
$193$	6.19098	−	19.0539i	0.445637	−	1.37153i	−0.436147	−	0.899875i	$-0.643657\pi$
$193$	6.19098	−	19.0539i	0.445637	−	1.37153i	0.881784	−	0.471653i	$-0.156343\pi$
$194$		0			0
$195$	−2.60841	+	3.59017i	−0.186792	+	0.257097i
$196$		0			0
$197$			17.8473i			1.27156i	0.771868	+	0.635782i	$0.219322\pi$
$197$			17.8473i			1.27156i	−0.771868	+	0.635782i	$0.780678\pi$
$198$		0			0
$199$	4.21317			0.298663			0.149332	−	0.988787i	$-0.452288\pi$
$199$	4.21317			0.298663			0.149332	+	0.988787i	$0.452288\pi$
$200$		0			0
$201$	1.14590	+	0.832544i	0.0808254	+	0.0587231i
$202$		0			0
$203$	−17.8783	−	5.80902i	−1.25481	−	0.407713i
$204$		0			0
$205$	16.2085	+	22.3091i	1.13205	+	1.55813i
$206$		0			0
$207$	−6.01240	−	18.5043i	−0.417891	−	1.28614i
$208$		0			0
$209$	1.92705	−	7.66145i	0.133297	−	0.529954i
$210$		0			0
$211$	21.4050	−	6.95492i	1.47358	−	0.478796i	0.541394	−	0.840769i	$-0.317897\pi$
$211$	21.4050	−	6.95492i	1.47358	−	0.478796i	0.932189	+	0.361973i	$0.117897\pi$
$212$		0			0
$213$	0.180654	+	0.248648i	0.0123782	+	0.0170371i
$214$		0			0
$215$	9.72827	−	29.9405i	0.663463	−	2.04193i
$216$		0			0
$217$	12.9894	+	9.43732i	0.881775	+	0.640647i
$218$		0			0
$219$		−	1.96556i		−	0.132820i
$220$		0			0
$221$		−	8.92363i		−	0.600268i
$222$		0			0
$223$	−1.70426	−	1.23822i	−0.114126	−	0.0829173i	0.529258	−	0.848461i	$-0.322470\pi$
$223$	−1.70426	−	1.23822i	−0.114126	−	0.0829173i	−0.643384	+	0.765543i	$0.722470\pi$
$224$		0			0
$225$	−5.83688	+	17.9641i	−0.389125	+	1.19760i
$226$		0			0
$227$	−3.30220	−	4.54508i	−0.219175	−	0.301668i	0.685245	−	0.728313i	$-0.259695\pi$
$227$	−3.30220	−	4.54508i	−0.219175	−	0.301668i	−0.904419	+	0.426645i	$0.859695\pi$
$228$		0			0
$229$	5.71814	−	1.85794i	0.377865	−	0.122776i	−0.113926	−	0.993489i	$-0.536343\pi$
$229$	5.71814	−	1.85794i	0.377865	−	0.122776i	0.491791	+	0.870713i	$0.336343\pi$
$230$		0			0
$231$	−0.994594	−	2.47644i	−0.0654395	−	0.162938i
$232$		0			0
$233$	−5.75329	−	17.7068i	−0.376910	−	1.16001i	−0.942181	−	0.335105i	$-0.891228\pi$
$233$	−5.75329	−	17.7068i	−0.376910	−	1.16001i	0.565270	−	0.824906i	$-0.308772\pi$
$234$		0			0
$235$	−17.8783	−	24.6074i	−1.16625	−	1.60521i
$236$		0			0
$237$	−5.24518	−	1.70426i	−0.340711	−	0.110704i
$238$		0			0
$239$	17.4449	+	12.6745i	1.12842	+	0.819845i	0.985464	−	0.169884i	$-0.0543395\pi$
$239$	17.4449	+	12.6745i	1.12842	+	0.819845i	0.142955	+	0.989729i	$0.454339\pi$
$240$		0			0
$241$	−10.2918			−0.662953			−0.331476	−	0.943463i	$-0.607547\pi$
$241$	−10.2918			−0.662953			−0.331476	+	0.943463i	$0.607547\pi$
$242$		0			0
$243$			9.65248i			0.619207i
$244$		0			0
$245$	−5.13353	+	7.06570i	−0.327969	+	0.451411i
$246$		0			0
$247$	−2.50891	+	7.72162i	−0.159638	+	0.491315i
$248$		0			0
$249$	−0.572949	+	0.416272i	−0.0363092	+	0.0263802i
$250$		0			0
$251$	23.5847	−	7.66312i	1.48865	−	0.483692i	0.551966	−	0.833867i	$-0.313878\pi$
$251$	23.5847	−	7.66312i	1.48865	−	0.483692i	0.936684	+	0.350175i	$0.113878\pi$
$252$		0			0
$253$	−20.9807	+	8.42633i	−1.31905	+	0.529759i
$254$		0			0
$255$	1.05329	+	3.24170i	0.0659597	+	0.203003i
$256$		0			0
$257$	−17.8713	+	12.9843i	−1.11478	+	0.809937i	−0.983410	−	0.181396i	$-0.941938\pi$
$257$	−17.8713	+	12.9843i	−1.11478	+	0.809937i	−0.131372	+	0.991333i	$0.541938\pi$
$258$		0			0
$259$	−4.22050	−	1.37132i	−0.262249	−	0.0852099i
$260$		0			0
$261$	14.9703	−	20.6048i	0.926637	−	1.27541i
$262$		0			0
$263$	−12.6395			−0.779385			−0.389693	−	0.920945i	$-0.627419\pi$
$263$	−12.6395			−0.779385			−0.389693	+	0.920945i	$0.627419\pi$
$264$		0			0
$265$	25.9787			1.59586
$266$		0			0
$267$	2.35114	−	3.23607i	0.143887	−	0.198044i
$268$		0			0
$269$	−20.2155	−	6.56840i	−1.23256	−	0.400482i	−0.380918	−	0.924609i	$-0.624392\pi$
$269$	−20.2155	−	6.56840i	−1.23256	−	0.400482i	−0.851640	+	0.524127i	$0.824392\pi$
$270$		0			0
$271$	−21.6581	+	15.7355i	−1.31564	+	0.955866i	−0.315661	+	0.948872i	$0.602226\pi$
$271$	−21.6581	+	15.7355i	−1.31564	+	0.955866i	−0.999976	+	0.00699364i	$0.997774\pi$
$272$		0			0
$273$	0.847524	+	2.60841i	0.0512945	+	0.157868i
$274$		0			0
$275$	21.2865	+	5.35410i	1.28363	+	0.322864i
$276$		0			0
$277$	26.6989	−	8.67498i	1.60418	−	0.521229i	0.636042	−	0.771654i	$-0.280570\pi$
$277$	26.6989	−	8.67498i	1.60418	−	0.521229i	0.968136	+	0.250425i	$0.0805703\pi$
$278$		0			0
$279$	−17.5986	+	12.7861i	−1.05360	+	0.765486i
$280$		0			0
$281$	−1.98936	+	6.12261i	−0.118675	+	0.365244i	−0.992696	−	0.120644i	$-0.961504\pi$
$281$	−1.98936	+	6.12261i	−0.118675	+	0.365244i	0.874021	+	0.485889i	$0.161504\pi$
$282$		0			0
$283$	−14.5434	+	20.0172i	−0.864513	+	1.18990i	0.115961	+	0.993254i	$0.463005\pi$
$283$	−14.5434	+	20.0172i	−0.864513	+	1.18990i	−0.980474	+	0.196647i	$0.936995\pi$
$284$		0			0
$285$		−	3.10118i		−	0.183698i
$286$		0			0
$287$	17.0426			1.00599
$288$		0			0
$289$	8.20820	+	5.96361i	0.482836	+	0.350801i
$290$		0			0
$291$	−3.57971	−	1.16312i	−0.209846	−	0.0681832i
$292$		0			0
$293$	7.72162	+	10.6279i	0.451102	+	0.620888i	0.972634	−	0.232343i	$-0.0746393\pi$
$293$	7.72162	+	10.6279i	0.451102	+	0.620888i	−0.521532	+	0.853232i	$0.674639\pi$
$294$		0			0
$295$	−1.20696	−	3.71466i	−0.0702722	−	0.216276i
$296$		0			0
$297$	7.39919	−	0.502029i	0.429344	−	0.0291307i
$298$		0			0
$299$	22.0988	−	7.18034i	1.27801	−	0.415250i
$300$		0			0
$301$	−11.4363	−	15.7407i	−0.659176	−	0.907278i
$302$		0			0
$303$	−1.20696	+	3.71466i	−0.0693383	+	0.213401i
$304$		0			0
$305$	21.0172	+	15.2699i	1.20344	+	0.874352i
$306$		0			0
$307$		−	29.1246i		−	1.66223i	−0.556101	−	0.831115i	$-0.687703\pi$
$307$		−	29.1246i		−	1.66223i	0.556101	−	0.831115i	$-0.312297\pi$
$308$		0			0
$309$			0.804643i			0.0457746i
$310$		0			0
$311$	22.9600	+	16.6815i	1.30194	+	0.945918i	0.999973	−	0.00739842i	$-0.00235501\pi$
$311$	22.9600	+	16.6815i	1.30194	+	0.945918i	0.301972	+	0.953317i	$0.402355\pi$
$312$		0			0
$313$	−2.51722	+	7.74721i	−0.142282	+	0.437898i	−0.996651	−	0.0817675i	$-0.973943\pi$
$313$	−2.51722	+	7.74721i	−0.142282	+	0.437898i	0.854370	+	0.519666i	$0.173943\pi$
$314$		0			0
$315$	12.0457	+	16.5795i	0.678700	+	0.934151i
$316$		0			0
$317$	−20.2155	+	6.56840i	−1.13541	+	0.368918i	−0.815631	−	0.578573i	$-0.803610\pi$
$317$	−20.2155	+	6.56840i	−1.13541	+	0.368918i	−0.319782	+	0.947491i	$0.603610\pi$
$318$		0			0
$319$	−25.0666	−	15.7355i	−1.40346	−	0.881021i
$320$		0			0
$321$	1.46149	+	4.49801i	0.0815726	+	0.251055i
$322$		0			0
$323$	3.66547	+	5.04508i	0.203952	+	0.280716i
$324$		0			0
$325$	−21.4537	−	6.97072i	−1.19004	−	0.386666i
$326$		0			0
$327$	−2.10658	−	1.53052i	−0.116494	−	0.0846381i
$328$		0			0
$329$	−18.7984			−1.03639
$330$		0			0
$331$		−	6.94427i		−	0.381692i	−0.981620	−	0.190846i	$-0.938877\pi$
$331$		−	6.94427i		−	0.381692i	0.981620	−	0.190846i	$-0.0611231\pi$
$332$		0			0
$333$	3.53400	−	4.86414i	0.193662	−	0.266553i
$334$		0			0
$335$	−3.90582	+	12.0209i	−0.213398	+	0.656771i
$336$		0			0
$337$	8.30902	−	6.03685i	0.452621	−	0.328848i	−0.338009	−	0.941143i	$-0.609753\pi$
$337$	8.30902	−	6.03685i	0.452621	−	0.328848i	0.790630	+	0.612295i	$0.209753\pi$
$338$		0			0
$339$	−2.93893	+	0.954915i	−0.159621	+	0.0518639i
$340$		0			0
$341$	16.2085	+	19.3979i	0.877739	+	1.05045i
$342$		0			0
$343$	6.22478	+	19.1579i	0.336106	+	1.03443i
$344$		0			0
$345$	−7.18034	+	5.21682i	−0.386577	+	0.280864i
$346$		0			0
$347$	22.3031	+	7.24671i	1.19729	+	0.389024i	0.838764	−	0.544495i	$-0.183279\pi$
$347$	22.3031	+	7.24671i	1.19729	+	0.389024i	0.358528	+	0.933519i	$0.383279\pi$
$348$		0			0
$349$	−3.71466	+	5.11279i	−0.198841	+	0.273681i	−0.896781	−	0.442475i	$-0.854100\pi$
$349$	−3.71466	+	5.11279i	−0.198841	+	0.273681i	0.697940	+	0.716157i	$0.254100\pi$
$350$		0			0
$351$	−7.62169			−0.406816
$352$		0			0
$353$	29.2361			1.55608			0.778039	−	0.628215i	$-0.216214\pi$
$353$	29.2361			1.55608			0.778039	+	0.628215i	$0.216214\pi$
$354$		0			0
$355$	−1.61209	+	2.21885i	−0.0855607	+	0.117764i
$356$		0			0
$357$	2.00348	+	0.650970i	0.106035	+	0.0344530i
$358$		0			0
$359$	0.402322	−	0.292304i	0.0212337	−	0.0154272i	−0.577118	−	0.816661i	$-0.695823\pi$
$359$	0.402322	−	0.292304i	0.0212337	−	0.0154272i	0.598351	+	0.801234i	$0.295823\pi$
$360$		0			0
$361$	4.11803	+	12.6740i	0.216739	+	0.667053i
$362$		0			0
$363$	−0.567541	−	4.16312i	−0.0297882	−	0.218507i
$364$		0			0
$365$	16.6815	−	5.42013i	0.873147	−	0.283703i
$366$		0			0
$367$	26.3686	−	19.1579i	1.37643	−	1.00003i	0.379224	−	0.925305i	$-0.376191\pi$
$367$	26.3686	−	19.1579i	1.37643	−	1.00003i	0.997204	−	0.0747289i	$-0.0238091\pi$
$368$		0			0
$369$	−7.13525	+	21.9601i	−0.371447	+	1.14319i
$370$		0			0
$371$	9.43732	−	12.9894i	0.489961	−	0.674374i
$372$		0			0
$373$		−	16.2380i		−	0.840770i	−0.907346	−	0.420385i	$-0.861895\pi$
$373$		−	16.2380i		−	0.840770i	0.907346	−	0.420385i	$-0.138105\pi$
$374$		0			0
$375$	2.10658			0.108784
$376$		0			0
$377$	24.6074	+	17.8783i	1.26735	+	0.920780i
$378$		0			0
$379$	−5.01255	−	1.62868i	−0.257478	−	0.0836595i	0.177434	−	0.984133i	$-0.443220\pi$
$379$	−5.01255	−	1.62868i	−0.257478	−	0.0836595i	−0.434912	+	0.900473i	$0.643220\pi$
$380$		0			0
$381$	4.18761	+	5.76376i	0.214538	+	0.295286i
$382$		0			0
$383$	−7.06570	−	21.7460i	−0.361040	−	1.11117i	−0.952424	−	0.304777i	$-0.901418\pi$
$383$	−7.06570	−	21.7460i	−0.361040	−	1.11117i	0.591384	−	0.806390i	$-0.298582\pi$
$384$		0			0
$385$	18.2746	−	15.2699i	0.931359	−	0.778226i
$386$		0			0
$387$	25.0705	−	8.14590i	1.27440	−	0.414079i
$388$		0			0
$389$	9.25214	+	12.7345i	0.469102	+	0.645664i	0.976365	−	0.216128i	$-0.0693427\pi$
$389$	9.25214	+	12.7345i	0.469102	+	0.645664i	−0.507263	+	0.861791i	$0.669343\pi$
$390$		0			0
$391$	5.51511	−	16.9738i	0.278911	−	0.858400i
$392$		0			0
$393$	0.236068	+	0.171513i	0.0119081	+	0.00865171i
$394$		0			0
$395$		−	49.2148i		−	2.47626i
$396$		0			0
$397$		−	4.21317i		−	0.211453i	−0.994395	−	0.105726i	$-0.966283\pi$
$397$		−	4.21317i		−	0.211453i	0.994395	−	0.105726i	$-0.0337168\pi$
$398$		0			0
$399$	−1.55059	−	1.12657i	−0.0776265	−	0.0563990i
$400$		0			0
$401$	−8.42705	+	25.9358i	−0.420827	+	1.29517i	0.486107	+	0.873899i	$0.338416\pi$
$401$	−8.42705	+	25.9358i	−0.420827	+	1.29517i	−0.906934	+	0.421273i	$0.861584\pi$
$402$		0			0
$403$	−15.2699	−	21.0172i	−0.760648	−	1.04694i
$404$		0			0
$405$	−24.9877	+	8.11899i	−1.24165	+	0.403436i
$406$		0			0
$407$	−5.91743	−	3.71466i	−0.293316	−	0.184129i
$408$		0			0
$409$	−5.42705	−	16.7027i	−0.268350	−	0.825898i	−0.990903	−	0.134581i	$-0.957031\pi$
$409$	−5.42705	−	16.7027i	−0.268350	−	0.825898i	0.722552	−	0.691316i	$-0.242969\pi$
$410$		0			0
$411$	2.83293	+	3.89919i	0.139738	+	0.192333i
$412$		0			0
$413$	−2.29578	−	0.745945i	−0.112968	−	0.0367056i
$414$		0			0
$415$	−5.11279	−	3.71466i	−0.250977	−	0.182345i
$416$		0			0
$417$	−4.90983			−0.240435
$418$		0			0
$419$			29.1246i			1.42283i	0.702772	+	0.711415i	$0.251945\pi$
$419$			29.1246i			1.42283i	−0.702772	+	0.711415i	$0.748055\pi$
$420$		0			0
$421$	8.66753	−	11.9298i	0.422430	−	0.581424i	−0.543765	−	0.839237i	$-0.683002\pi$
$421$	8.66753	−	11.9298i	0.422430	−	0.581424i	0.966195	+	0.257813i	$0.0830018\pi$
$422$		0			0
$423$	7.87034	−	24.2224i	0.382669	−	1.17773i
$424$		0			0
$425$	−14.0172	+	10.1841i	−0.679935	+	0.494002i
$426$		0			0
$427$	15.2699	−	4.96149i	0.738962	−	0.240103i
$428$		0			0
$429$	0.292304	+	4.30814i	0.0141126	+	0.207999i
$430$		0			0
$431$	1.55059	+	4.77222i	0.0746892	+	0.229870i	0.981431	−	0.191817i	$-0.0614381\pi$
$431$	1.55059	+	4.77222i	0.0746892	+	0.229870i	−0.906741	+	0.421687i	$0.861438\pi$
$432$		0			0
$433$	23.6353	−	17.1720i	1.13584	−	0.825235i	0.149304	−	0.988791i	$-0.452297\pi$
$433$	23.6353	−	17.1720i	1.13584	−	0.825235i	0.986534	+	0.163557i	$0.0522967\pi$
$434$		0			0
$435$	−11.0494	−	3.59017i	−0.529779	−	0.172135i
$436$		0			0
$437$	−9.54444	+	13.1368i	−0.456573	+	0.628418i
$438$		0			0
$439$	20.4511			0.976080			0.488040	−	0.872821i	$-0.337712\pi$
$439$	20.4511			0.976080			0.488040	+	0.872821i	$0.337712\pi$
$440$		0			0
$441$	−7.31308			−0.348242
$442$		0			0
$443$	−14.3314	+	19.7254i	−0.680903	+	0.937183i	−0.999944	−	0.0105578i	$-0.996639\pi$
$443$	−14.3314	+	19.7254i	−0.680903	+	0.937183i	0.319041	+	0.947741i	$0.396639\pi$
$444$		0			0
$445$	33.9475	+	11.0302i	1.60927	+	0.522882i
$446$		0			0
$447$	−0.248648	+	0.180654i	−0.0117607	+	0.00854463i
$448$		0			0
$449$	3.24671	+	9.99235i	0.153222	+	0.471568i	0.997976	−	0.0635857i	$-0.0202536\pi$
$449$	3.24671	+	9.99235i	0.153222	+	0.471568i	−0.844755	+	0.535154i	$0.820254\pi$
$450$		0			0
$451$	26.0216	+	6.54508i	1.22531	+	0.308196i
$452$		0			0
$453$	−8.19457	+	2.66258i	−0.385015	+	0.125099i
$454$		0			0
$455$	−19.8002	+	14.3857i	−0.928246	+	0.674410i
$456$		0			0
$457$	−2.77458	+	8.53926i	−0.129789	+	0.399450i	−0.994743	−	0.102401i	$-0.967347\pi$
$457$	−2.77458	+	8.53926i	−0.129789	+	0.399450i	0.864954	+	0.501851i	$0.167347\pi$
$458$		0			0
$459$	−3.44095	+	4.73607i	−0.160610	+	0.221061i
$460$		0			0
$461$			9.42093i			0.438776i	0.975638	+	0.219388i	$0.0704061\pi$
$461$			9.42093i			0.438776i	−0.975638	+	0.219388i	$0.929594\pi$
$462$		0			0
$463$	17.8473			0.829433			0.414716	−	0.909951i	$-0.363881\pi$
$463$	17.8473			0.829433			0.414716	+	0.909951i	$0.363881\pi$
$464$		0			0
$465$	8.02786	+	5.83258i	0.372283	+	0.270480i
$466$		0			0
$467$	−2.21238	−	0.718847i	−0.102377	−	0.0332643i	0.257381	−	0.966310i	$-0.417141\pi$
$467$	−2.21238	−	0.718847i	−0.102377	−	0.0332643i	−0.359758	+	0.933046i	$0.617141\pi$
$468$		0			0
$469$	4.59157	+	6.31975i	0.212019	+	0.291819i
$470$		0			0
$471$	−0.248648	−	0.765261i	−0.0114571	−	0.0352614i
$472$		0			0
$473$	−11.4164	−	28.4257i	−0.524927	−	1.30701i
$474$		0			0
$475$	14.9924	−	4.87132i	0.687898	−	0.223512i
$476$		0			0
$477$	12.7861	+	17.5986i	0.585437	+	0.805785i
$478$		0			0
$479$	−2.85253	+	8.77918i	−0.130335	+	0.401131i	−0.994835	−	0.101502i	$-0.967635\pi$
$479$	−2.85253	+	8.77918i	−0.130335	+	0.401131i	0.864500	+	0.502633i	$0.167635\pi$
$480$		0			0
$481$	5.80902	+	4.22050i	0.264868	+	0.192438i
$482$		0			0
$483$			5.48529i			0.249589i
$484$		0			0
$485$		−	33.5879i		−	1.52515i
$486$		0			0
$487$	−5.11279	−	3.71466i	−0.231682	−	0.168327i	0.465887	−	0.884844i	$-0.345735\pi$
$487$	−5.11279	−	3.71466i	−0.231682	−	0.168327i	−0.697570	+	0.716517i	$0.745735\pi$
$488$		0			0
$489$	−2.07295	+	6.37988i	−0.0937420	+	0.288508i
$490$		0			0
$491$	8.55951	+	11.7812i	0.386285	+	0.531676i	0.957236	−	0.289308i	$-0.0934253\pi$
$491$	8.55951	+	11.7812i	0.386285	+	0.531676i	−0.570951	+	0.820984i	$0.693425\pi$
$492$		0			0
$493$	22.2189	−	7.21937i	1.00069	−	0.325144i
$494$		0			0
$495$	12.0248	+	29.9405i	0.540475	+	1.34573i
$496$		0			0
$497$	0.523799	+	1.61209i	0.0234956	+	0.0723120i
$498$		0			0
$499$	1.40008	+	1.92705i	0.0626764	+	0.0862666i	0.839205	−	0.543816i	$-0.183021\pi$
$499$	1.40008	+	1.92705i	0.0626764	+	0.0862666i	−0.776528	+	0.630083i	$0.783021\pi$
$500$		0			0
$501$	4.29926	+	1.39692i	0.192077	+	0.0624096i
$502$		0			0
$503$	11.4325	+	8.30622i	0.509752	+	0.370356i	0.812729	−	0.582641i	$-0.197981\pi$
$503$	11.4325	+	8.30622i	0.509752	+	0.370356i	−0.302978	+	0.952998i	$0.597981\pi$
$504$		0			0
$505$	−34.8541			−1.55099
$506$		0			0
$507$			0.527864i			0.0234433i
$508$		0			0
$509$	10.1981	−	14.0364i	0.452021	−	0.622153i	−0.520809	−	0.853673i	$-0.674370\pi$
$509$	10.1981	−	14.0364i	0.452021	−	0.622153i	0.972830	+	0.231520i	$0.0743698\pi$
$510$		0			0
$511$	3.34983	−	10.3097i	0.148188	−	0.456074i
$512$		0			0
$513$	4.30902	−	3.13068i	0.190248	−	0.138223i
$514$		0			0
$515$	−6.82891	+	2.21885i	−0.300918	+	0.0977741i
$516$		0			0
$517$	−28.7023	−	7.21937i	−1.26233	−	0.317507i
$518$		0			0
$519$	−0.555995	−	1.71118i	−0.0244055	−	0.0751123i
$520$		0			0
$521$	−10.2533	+	7.44945i	−0.449205	+	0.326366i	−0.789282	−	0.614031i	$-0.789547\pi$
$521$	−10.2533	+	7.44945i	−0.449205	+	0.326366i	0.340077	+	0.940398i	$0.389547\pi$
$522$		0			0
$523$	−32.4747	−	10.5517i	−1.42002	−	0.461392i	−0.504410	−	0.863464i	$-0.668290\pi$
$523$	−32.4747	−	10.5517i	−1.42002	−	0.461392i	−0.915608	+	0.402072i	$0.868290\pi$
$524$		0			0
$525$	3.13005	−	4.30814i	0.136607	−	0.188023i
$526$		0			0
$527$	−19.9538			−0.869203
$528$		0			0
$529$	23.4721			1.02053
$530$		0			0
$531$	1.92236	−	2.64590i	0.0834232	−	0.114822i
$532$		0			0
$533$	−26.2259	−	8.52131i	−1.13597	−	0.369099i
$534$		0			0
$535$	−34.1439	+	24.8070i	−1.47617	+	1.07250i
$536$		0			0
$537$	0.427051	+	1.31433i	0.0184286	+	0.0567174i
$538$		0			0
$539$	0.575274	+	8.47871i	0.0247788	+	0.365204i
$540$		0			0
$541$	−33.1822	+	10.7816i	−1.42662	+	0.463536i	−0.917698	−	0.397279i	$-0.869955\pi$
$541$	−33.1822	+	10.7816i	−1.42662	+	0.463536i	−0.508918	+	0.860815i	$0.669955\pi$
$542$		0			0
$543$	−1.55059	+	1.12657i	−0.0665421	+	0.0483457i
$544$		0			0
$545$	7.18034	−	22.0988i	0.307572	−	0.946609i
$546$		0			0
$547$	−2.57565	+	3.54508i	−0.110127	+	0.151577i	−0.860523	−	0.509412i	$-0.829863\pi$
$547$	−2.57565	+	3.54508i	−0.110127	+	0.151577i	0.750396	+	0.660989i	$0.229863\pi$
$548$		0			0
$549$			21.7531i			0.928399i
$550$		0			0
$551$	−21.2558			−0.905527
$552$		0			0
$553$	−24.6074	−	17.8783i	−1.04641	−	0.760263i
$554$		0			0
$555$	−2.60841	−	0.847524i	−0.110721	−	0.0359754i
$556$		0			0
$557$	−16.6815	−	22.9600i	−0.706816	−	0.972848i	−0.999860	−	0.0167495i	$-0.994668\pi$
$557$	−16.6815	−	22.9600i	−0.706816	−	0.972848i	0.293044	−	0.956099i	$-0.405332\pi$
$558$		0			0
$559$	9.72827	+	29.9405i	0.411462	+	1.26635i
$560$		0			0
$561$	2.80902	+	1.76336i	0.118597	+	0.0744489i
$562$		0			0
$563$	−22.4091	+	7.28115i	−0.944430	+	0.306864i	−0.740450	−	0.672111i	$-0.765388\pi$
$563$	−22.4091	+	7.28115i	−0.944430	+	0.306864i	−0.203980	+	0.978975i	$0.565388\pi$
$564$		0			0
$565$	−16.2085	−	22.3091i	−0.681896	−	0.938550i
$566$		0			0
$567$	−5.01781	+	15.4432i	−0.210728	+	0.648555i
$568$		0			0
$569$	−20.7812	−	15.0984i	−0.871191	−	0.632957i	0.0597151	−	0.998215i	$-0.480981\pi$
$569$	−20.7812	−	15.0984i	−0.871191	−	0.632957i	−0.930906	+	0.365258i	$0.880981\pi$
$570$		0			0
$571$		−	13.1246i		−	0.549248i	−0.961552	−	0.274624i	$-0.911447\pi$
$571$		−	13.1246i		−	0.549248i	0.961552	−	0.274624i	$-0.0885534\pi$
$572$		0			0
$573$		−	2.41393i		−	0.100843i
$574$		0			0
$575$	−36.4992	−	26.5182i	−1.52212	−	1.10589i
$576$		0			0
$577$	0.392609	−	1.20833i	0.0163445	−	0.0503033i	−0.942552	−	0.334061i	$-0.891581\pi$
$577$	0.392609	−	1.20833i	0.0163445	−	0.0503033i	0.958896	+	0.283757i	$0.0915810\pi$
$578$		0			0
$579$	−4.49801	−	6.19098i	−0.186931	−	0.257288i
$580$		0			0
$581$	−3.71466	+	1.20696i	−0.154110	+	0.0500733i
$582$		0			0
$583$	19.3979	−	16.2085i	0.803377	−	0.671287i
$584$		0			0
$585$	−10.2467	−	31.5361i	−0.423649	−	1.30386i
$586$		0			0
$587$	−28.0952	−	38.6697i	−1.15961	−	1.59607i	−0.712657	−	0.701513i	$-0.752508\pi$
$587$	−28.0952	−	38.6697i	−1.15961	−	1.59607i	−0.446955	−	0.894556i	$-0.647492\pi$
$588$		0			0
$589$	17.2661	+	5.61008i	0.711436	+	0.231159i
$590$		0			0
$591$	5.51511	+	4.00696i	0.226861	+	0.164824i
$592$		0			0
$593$	−1.88854			−0.0775532			−0.0387766	−	0.999248i	$-0.512346\pi$
$593$	−1.88854			−0.0775532			−0.0387766	+	0.999248i	$0.512346\pi$
$594$		0			0
$595$			18.7984i			0.770658i
$596$		0			0
$597$	0.945915	−	1.30194i	0.0387137	−	0.0532849i
$598$		0			0
$599$	6.07110	−	18.6849i	0.248059	−	0.763446i	−0.747060	−	0.664757i	$-0.768535\pi$
$599$	6.07110	−	18.6849i	0.248059	−	0.763446i	0.995118	−	0.0986888i	$-0.0314648\pi$
$600$		0			0
$601$	2.39919	−	1.74311i	0.0978649	−	0.0711030i	−0.537777	−	0.843087i	$-0.680736\pi$
$601$	2.39919	−	1.74311i	0.0978649	−	0.0711030i	0.635642	+	0.771984i	$0.280736\pi$
$602$		0			0
$603$	−10.0656	+	3.27051i	−0.409903	+	0.133185i
$604$		0			0
$605$	33.7669	−	16.2967i	1.37282	−	0.662554i
$606$		0			0
$607$	0.555995	+	1.71118i	0.0225671	+	0.0694545i	0.961706	−	0.274084i	$-0.0883745\pi$
$607$	0.555995	+	1.71118i	0.0225671	+	0.0694545i	−0.939139	+	0.343538i	$0.888375\pi$
$608$		0			0
$609$	−5.80902	+	4.22050i	−0.235393	+	0.171023i
$610$		0			0
$611$	28.9277	+	9.39919i	1.17029	+	0.380250i
$612$		0			0
$613$	−14.2050	+	19.5515i	−0.573735	+	0.789679i	−0.992991	−	0.118189i	$-0.962291\pi$
$613$	−14.2050	+	19.5515i	−0.573735	+	0.789679i	0.419256	+	0.907868i	$0.362291\pi$
$614$		0			0
$615$	10.5329			0.424728
$616$		0			0
$617$	−3.05573			−0.123019			−0.0615095	−	0.998106i	$-0.519591\pi$
$617$	−3.05573			−0.123019			−0.0615095	+	0.998106i	$0.519591\pi$
$618$		0			0
$619$	−2.02063	+	2.78115i	−0.0812158	+	0.111784i	−0.847692	−	0.530489i	$-0.822008\pi$
$619$	−2.02063	+	2.78115i	−0.0812158	+	0.111784i	0.766476	+	0.642273i	$0.222008\pi$
$620$		0			0
$621$	−14.4973	−	4.71046i	−0.581757	−	0.189024i
$622$		0			0
$623$	17.8473	−	12.9668i	0.715035	−	0.519504i
$624$		0			0
$625$	−4.41641	−	13.5923i	−0.176656	−	0.543692i
$626$		0			0
$627$	−1.93487	−	2.31559i	−0.0772712	−	0.0924759i
$628$		0			0
$629$	5.24518	−	1.70426i	0.209139	−	0.0679534i
$630$		0			0
$631$	16.1430	−	11.7286i	0.642643	−	0.466907i	−0.218114	−	0.975923i	$-0.569991\pi$
$631$	16.1430	−	11.7286i	0.642643	−	0.466907i	0.860757	+	0.509016i	$0.169991\pi$
$632$		0			0
$633$	2.65654	−	8.17599i	0.105588	−	0.324967i
$634$		0			0
$635$	−37.3687	+	51.4336i	−1.48293	+	2.04108i
$636$		0			0
$637$		−	8.73368i		−	0.346041i
$638$		0			0
$639$	−2.29653			−0.0908495
$640$		0			0
$641$	16.0172	+	11.6372i	0.632642	+	0.459641i	0.857315	−	0.514793i	$-0.172131\pi$
$641$	16.0172	+	11.6372i	0.632642	+	0.459641i	−0.224672	+	0.974434i	$0.572131\pi$
$642$		0			0
$643$	−42.2223	−	13.7188i	−1.66508	−	0.541019i	−0.683156	−	0.730273i	$-0.739393\pi$
$643$	−42.2223	−	13.7188i	−1.66508	−	0.541019i	−0.981928	+	0.189254i	$0.939393\pi$
$644$		0			0
$645$	−7.06800	−	9.72827i	−0.278302	−	0.383050i
$646$		0			0
$647$	5.26646	+	16.2085i	0.207046	+	0.637222i	0.999623	+	0.0274502i	$0.00873877\pi$
$647$	5.26646	+	16.2085i	0.207046	+	0.637222i	−0.792577	+	0.609771i	$0.791261\pi$
$648$		0			0
$649$	−3.21885	−	2.02063i	−0.126351	−	0.0793165i
$650$		0			0
$651$	5.83258	−	1.89512i	0.228597	−	0.0742757i
$652$		0			0
$653$	10.1981	+	14.0364i	0.399081	+	0.549287i	0.960513	−	0.278235i	$-0.0897495\pi$
$653$	10.1981	+	14.0364i	0.399081	+	0.549287i	−0.561432	+	0.827523i	$0.689749\pi$
$654$		0			0
$655$	−0.804643	+	2.47644i	−0.0314400	+	0.0967624i
$656$		0			0
$657$	11.8820	+	8.63275i	0.463560	+	0.336796i
$658$		0			0
$659$			23.8197i			0.927882i	0.885866	+	0.463941i	$0.153565\pi$
$659$			23.8197i			0.927882i	−0.885866	+	0.463941i	$0.846435\pi$
$660$		0			0
$661$			45.7301i			1.77870i	0.457230	+	0.889348i	$0.348841\pi$
$661$			45.7301i			1.77870i	−0.457230	+	0.889348i	$0.651159\pi$
$662$		0			0
$663$	−2.75755	−	2.00348i	−0.107095	−	0.0778087i
$664$		0			0
$665$	5.28522	−	16.2662i	0.204952	−	0.630777i
$666$		0			0
$667$	35.7566	+	49.2148i	1.38450	+	1.90560i
$668$		0			0
$669$	−0.765261	+	0.248648i	−0.0295867	+	0.00961330i
$670$		0			0
$671$	25.2203	−	1.71118i	0.973619	−	0.0660592i
$672$		0			0
$673$	−12.1353	−	37.3485i	−0.467780	−	1.43968i	−0.855453	−	0.517881i	$-0.826721\pi$
$673$	−12.1353	−	37.3485i	−0.467780	−	1.43968i	0.387673	−	0.921797i	$-0.373279\pi$
$674$		0			0
$675$	8.69827	+	11.9721i	0.334796	+	0.460808i
$676$		0			0
$677$	29.1753	+	9.47963i	1.12130	+	0.364332i	0.810263	−	0.586067i	$-0.199324\pi$
$677$	29.1753	+	9.47963i	1.12130	+	0.364332i	0.311035	+	0.950399i	$0.399324\pi$
$678$		0			0
$679$	−16.7940	−	12.2015i	−0.644493	−	0.468252i
$680$		0			0
$681$	−2.14590			−0.0822310
$682$		0			0
$683$		−	4.47214i		−	0.171122i	−0.996333	−	0.0855608i	$-0.972732\pi$
$683$		−	4.47214i		−	0.171122i	0.996333	−	0.0855608i	$-0.0272682\pi$
$684$		0			0
$685$	−25.2800	+	34.7949i	−0.965898	+	1.32944i
$686$		0			0
$687$	0.709668	−	2.18413i	0.0270755	−	0.0833299i
$688$		0			0
$689$	−21.0172	+	15.2699i	−0.800692	+	0.581737i
$690$		0			0
$691$	−17.1518	+	5.57295i	−0.652484	+	0.212005i	−0.616509	−	0.787348i	$-0.711454\pi$
$691$	−17.1518	+	5.57295i	−0.652484	+	0.212005i	−0.0359750	+	0.999353i	$0.511454\pi$
$692$		0			0
$693$	19.3385	+	4.86414i	0.734610	+	0.184773i
$694$		0			0
$695$	−13.5391	−	41.6691i	−0.513568	−	1.58060i
$696$		0			0
$697$	−17.1353	+	12.4495i	−0.649044	+	0.471558i
$698$		0			0
$699$	−6.76340	−	2.19756i	−0.255815	−	0.0831194i
$700$		0			0
$701$	0.292304	−	0.402322i	0.0110402	−	0.0151955i	−0.803461	−	0.595357i	$-0.797011\pi$
$701$	0.292304	−	0.402322i	0.0110402	−	0.0151955i	0.814501	+	0.580162i	$0.197011\pi$
$702$		0			0
$703$	−5.01781			−0.189250
$704$		0			0
$705$	−11.6180			−0.437560
$706$		0			0
$707$	−12.6615	+	17.4271i	−0.476184	+	0.655412i
$708$		0			0
$709$	49.2101	+	15.9893i	1.84812	+	0.600492i	0.997164	+	0.0752609i	$0.0239790\pi$
$709$	49.2101	+	15.9893i	1.84812	+	0.600492i	0.850960	+	0.525231i	$0.176021\pi$
$710$		0			0
$711$	33.3393	−	24.2224i	1.25032	−	0.908411i
$712$		0			0
$713$	−16.0557	−	49.4145i	−0.601292	−	1.85059i
$714$		0			0
$715$	−35.7566	+	14.3607i	−1.33722	+	0.537059i
$716$		0			0
$717$	7.83327	−	2.54518i	0.292539	−	0.0950516i
$718$		0			0
$719$	−7.21937	+	5.24518i	−0.269237	+	0.195612i	−0.714209	−	0.699932i	$-0.753214\pi$
$719$	−7.21937	+	5.24518i	−0.269237	+	0.195612i	0.444972	+	0.895544i	$0.353214\pi$
$720$		0			0
$721$	−1.37132	+	4.22050i	−0.0510707	+	0.157180i
$722$		0			0
$723$	−2.31065	+	3.18034i	−0.0859341	+	0.118278i
$724$		0			0
$725$		−	59.0569i		−	2.19332i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−15.7254	−	11.4252i	−0.582423	−	0.423155i
$730$		0			0
$731$	22.9969	+	7.47214i	0.850570	+	0.276367i
$732$		0			0
$733$	−15.7355	−	21.6581i	−0.581205	−	0.799960i	0.412622	−	0.910903i	$-0.364613\pi$
$733$	−15.7355	−	21.6581i	−0.581205	−	0.799960i	−0.993827	+	0.110942i	$0.964613\pi$
$734$		0			0
$735$	1.03087	+	3.17270i	0.0380243	+	0.117027i
$736$		0			0
$737$	4.58359	+	11.4127i	0.168839	+	0.420391i
$738$		0			0
$739$	2.59590	−	0.843459i	0.0954917	−	0.0310271i	−0.260881	−	0.965371i	$-0.584013\pi$
$739$	2.59590	−	0.843459i	0.0954917	−	0.0310271i	0.356373	+	0.934344i	$0.384013\pi$
$740$		0			0
$741$	1.82283	+	2.50891i	0.0669632	+	0.0921669i
$742$		0			0
$743$	−6.07110	+	18.6849i	−0.222727	+	0.685484i	0.775787	+	0.630995i	$0.217353\pi$
$743$	−6.07110	+	18.6849i	−0.222727	+	0.685484i	−0.998514	+	0.0544890i	$0.982647\pi$
$744$		0			0
$745$	−2.21885	−	1.61209i	−0.0812923	−	0.0590623i
$746$		0			0
$747$		−	5.29180i		−	0.193617i
$748$		0			0
$749$			26.0836i			0.953076i
$750$		0			0
$751$	29.7771	+	21.6343i	1.08658	+	0.789448i	0.978819	−	0.204729i	$-0.0656313\pi$
$751$	29.7771	+	21.6343i	1.08658	+	0.789448i	0.107763	+	0.994177i	$0.465631\pi$
$752$		0			0
$753$	2.92705	−	9.00854i	0.106668	−	0.328289i
$754$		0			0
$755$	−45.1940	−	62.2041i	−1.64478	−	2.26384i
$756$		0			0
$757$	41.1962	−	13.3854i	1.49730	−	0.486502i	0.558071	−	0.829793i	$-0.311542\pi$
$757$	41.1962	−	13.3854i	1.49730	−	0.486502i	0.939229	+	0.343291i	$0.111542\pi$
$758$		0			0
$759$	−2.10658	+	8.37523i	−0.0764641	+	0.304001i
$760$		0			0
$761$	4.28115	+	13.1760i	0.155192	+	0.477631i	0.998180	−	0.0603006i	$-0.0192059\pi$
$761$	4.28115	+	13.1760i	0.155192	+	0.477631i	−0.842989	+	0.537931i	$0.819206\pi$
$762$		0			0
$763$	−8.44100	−	11.6180i	−0.305585	−	0.420601i
$764$		0			0
$765$	−24.2224	−	7.87034i	−0.875763	−	0.284553i
$766$		0			0
$767$	3.15988	+	2.29578i	0.114096	+	0.0828959i
$768$		0			0
$769$	38.8328			1.40035			0.700174	−	0.713973i	$-0.253106\pi$
$769$	38.8328			1.40035			0.700174	+	0.713973i	$0.253106\pi$
$770$		0			0
$771$			8.43769i			0.303876i
$772$		0			0
$773$	1.82283	−	2.50891i	0.0655625	−	0.0902390i	−0.774977	−	0.631990i	$-0.782238\pi$
$773$	1.82283	−	2.50891i	0.0655625	−	0.0902390i	0.840539	+	0.541751i	$0.182238\pi$
$774$		0			0
$775$	−15.5870	+	47.9719i	−0.559902	+	1.72320i
$776$		0			0
$777$	−1.37132	+	0.996324i	−0.0491959	+	0.0357429i
$778$		0			0
$779$	18.3273	−	5.95492i	0.656645	−	0.213357i
$780$		0			0
$781$	0.180654	+	2.66258i	0.00646430	+	0.0952745i
$782$		0			0
$783$	−6.16608	−	18.9772i	−0.220358	−	0.678191i
$784$		0			0
$785$	5.80902	−	4.22050i	0.207333	−	0.150636i
$786$		0			0
$787$	15.5272	+	5.04508i	0.553484	+	0.179838i	0.572387	−	0.819983i	$-0.306017\pi$
$787$	15.5272	+	5.04508i	0.553484	+	0.179838i	−0.0189032	+	0.999821i	$0.506017\pi$
$788$		0			0
$789$	−2.83774	+	3.90582i	−0.101026	+	0.139051i
$790$		0			0
$791$	−17.0426			−0.605966
$792$		0			0
$793$	−25.9787			−0.922531
$794$		0			0
$795$	5.83258	−	8.02786i	0.206860	−	0.284719i
$796$		0			0
$797$	9.72510	+	3.15988i	0.344481	+	0.111929i	0.476147	−	0.879366i	$-0.342033\pi$
$797$	9.72510	+	3.15988i	0.344481	+	0.111929i	−0.131667	+	0.991294i	$0.542033\pi$
$798$		0			0
$799$	18.9006	−	13.7321i	0.668654	−	0.485805i
$800$		0			0
$801$	9.23607	+	28.4257i	0.326340	+	1.00437i
$802$		0			0
$803$	9.07405	−	14.4549i	0.320216	−	0.510103i
$804$		0			0
$805$	−46.5530	+	15.1260i	−1.64078	+	0.533121i
$806$		0			0
$807$	−6.56840	+	4.77222i	−0.231219	+	0.167990i
$808$		0			0
$809$	10.7533	−	33.0952i	0.378066	−	1.16357i	−0.563322	−	0.826238i	$-0.690477\pi$
$809$	10.7533	−	33.0952i	0.378066	−	1.16357i	0.941387	−	0.337328i	$-0.109523\pi$
$810$		0			0
$811$	2.68166	−	3.69098i	0.0941657	−	0.129608i	−0.759335	−	0.650700i	$-0.774475\pi$
$811$	2.68166	−	3.69098i	0.0941657	−	0.129608i	0.853500	+	0.521093i	$0.174475\pi$
$812$		0			0
$813$			10.2256i			0.358626i
$814$		0			0
$815$	−59.8615			−2.09686
$816$		0			0
$817$	−17.7984	−	12.9313i	−0.622686	−	0.452408i
$818$		0			0
$819$	−19.4904	−	6.33282i	−0.681050	−	0.221286i
$820$		0			0
$821$	−12.3132	−	16.9476i	−0.429733	−	0.591477i	0.538159	−	0.842843i	$-0.319120\pi$
$821$	−12.3132	−	16.9476i	−0.429733	−	0.591477i	−0.967892	+	0.251367i	$0.919120\pi$
$822$		0			0
$823$	7.37304	+	22.6919i	0.257008	+	0.790990i	0.993427	+	0.114464i	$0.0365151\pi$
$823$	7.37304	+	22.6919i	0.257008	+	0.790990i	−0.736419	+	0.676525i	$0.763485\pi$
$824$		0			0
$825$	6.43363	−	5.37582i	0.223990	−	0.187162i
$826$		0			0
$827$	−10.6534	+	3.46149i	−0.370454	+	0.120368i	−0.488327	−	0.872661i	$-0.662393\pi$
$827$	−10.6534	+	3.46149i	−0.370454	+	0.120368i	0.117872	+	0.993029i	$0.462393\pi$
$828$		0			0
$829$	−22.8035	−	31.3864i	−0.792000	−	1.09009i	−0.993856	−	0.110679i	$-0.964697\pi$
$829$	−22.8035	−	31.3864i	−0.792000	−	1.09009i	0.201856	−	0.979415i	$-0.435303\pi$
$830$		0			0
$831$	3.31355	−	10.1981i	0.114946	−	0.353767i
$832$		0			0
$833$	−5.42705	−	3.94298i	−0.188036	−	0.136616i
$834$		0			0
$835$			40.3394i			1.39600i
$836$		0			0
$837$			17.0426i			0.589079i
$838$		0			0
$839$	−3.81085	−	2.76874i	−0.131565	−	0.0955876i	0.520056	−	0.854132i	$-0.325911\pi$
$839$	−3.81085	−	2.76874i	−0.131565	−	0.0955876i	−0.651621	+	0.758544i	$0.725911\pi$
$840$		0			0
$841$	−15.6459	+	48.1531i	−0.539514	+	1.66045i
$842$		0			0
$843$	1.44535	+	1.98936i	0.0497806	+	0.0685171i
$844$		0			0
$845$	−4.47992	+	1.45561i	−0.154114	+	0.0500746i
$846$		0			0
$847$	4.11819	−	22.8035i	0.141503	−	0.783539i
$848$		0			0
$849$	2.92047	+	8.98829i	0.100230	+	0.308477i
$850$		0			0
$851$	8.44100	+	11.6180i	0.289354	+	0.398261i
$852$		0			0
$853$	21.7460	+	7.06570i	0.744568	+	0.241925i	0.656642	−	0.754202i	$-0.271976\pi$
$853$	21.7460	+	7.06570i	0.744568	+	0.241925i	0.0879258	+	0.996127i	$0.471976\pi$
$854$		0			0
$855$	18.7469	+	13.6204i	0.641130	+	0.465808i
$856$		0			0
$857$	−8.65248			−0.295563			−0.147781	−	0.989020i	$-0.547213\pi$
$857$	−8.65248			−0.295563			−0.147781	+	0.989020i	$0.547213\pi$
$858$		0			0
$859$		−	10.5836i		−	0.361108i	−0.983565	−	0.180554i	$-0.942211\pi$
$859$		−	10.5836i		−	0.361108i	0.983565	−	0.180554i	$-0.0577890\pi$
$860$		0			0
$861$	3.82631	−	5.26646i	0.130400	−	0.179480i
$862$		0			0
$863$	−9.97692	+	30.7058i	−0.339618	+	1.04524i	0.624784	+	0.780798i	$0.285187\pi$
$863$	−9.97692	+	30.7058i	−0.339618	+	1.04524i	−0.964402	+	0.264440i	$0.914813\pi$
$864$		0			0
$865$	12.9894	−	9.43732i	0.441651	−	0.320879i
$866$		0			0
$867$	3.68571	−	1.19756i	0.125173	−	0.0406713i
$868$		0			0
$869$	−30.7058	−	36.7478i	−1.04162	−	1.24658i
$870$		0			0
$871$	−3.90582	−	12.0209i	−0.132344	−	0.407312i
$872$		0			0
$873$	22.7533	−	16.5312i	0.770082	−	0.559497i
$874$		0			0
$875$	11.0494	+	3.59017i	0.373538	+	0.121370i
$876$		0			0
$877$	−6.19109	+	8.52131i	−0.209058	+	0.287744i	−0.900651	−	0.434544i	$-0.856910\pi$
$877$	−6.19109	+	8.52131i	−0.209058	+	0.287744i	0.691592	+	0.722288i	$0.256910\pi$
$878$		0			0
$879$	5.01781			0.169247
$880$		0			0
$881$	39.4853			1.33029			0.665147	−	0.746713i	$-0.268369\pi$
$881$	39.4853			1.33029			0.665147	+	0.746713i	$0.268369\pi$
$882$		0			0
$883$	13.7108	−	18.8713i	0.461406	−	0.635071i	−0.513394	−	0.858153i	$-0.671612\pi$
$883$	13.7108	−	18.8713i	0.461406	−	0.635071i	0.974800	+	0.223083i	$0.0716120\pi$
$884$		0			0
$885$	−1.41887	−	0.461020i	−0.0476949	−	0.0154970i
$886$		0			0
$887$	33.9903	−	24.6954i	1.14128	−	0.829189i	0.153984	−	0.988073i	$-0.450790\pi$
$887$	33.9903	−	24.6954i	1.14128	−	0.829189i	0.987297	+	0.158884i	$0.0507896\pi$
$888$		0			0
$889$	12.1418	+	37.3687i	0.407224	+	1.25331i
$890$		0			0
$891$	−13.5923	+	21.6525i	−0.455359	+	0.725385i
$892$		0			0
$893$	−20.2155	+	6.56840i	−0.676484	+	0.219803i
$894$		0			0
$895$	−9.97692	+	7.24866i	−0.333492	+	0.242296i
$896$		0			0
$897$	2.74265	−	8.44100i	0.0915743	−	0.281837i
$898$		0			0
$899$	39.9771	−	55.0238i	1.33331	−	1.83515i
$900$		0			0
$901$			19.9538i			0.664759i
$902$		0			0
$903$	−7.43174			−0.247313
$904$		0			0
$905$	−13.8369	−	10.0531i	−0.459953	−	0.334176i
$906$		0			0
$907$	16.7027	+	5.42705i	0.554606	+	0.180202i	0.572893	−	0.819631i	$-0.305821\pi$
$907$	16.7027	+	5.42705i	0.554606	+	0.180202i	−0.0182869	+	0.999833i	$0.505821\pi$
$908$		0			0
$909$	−17.1544	−	23.6110i	−0.568976	−	0.783128i
$910$		0			0
$911$	−0.745945	−	2.29578i	−0.0247143	−	0.0760627i	0.937939	−	0.346801i	$-0.112732\pi$
$911$	−0.745945	−	2.29578i	−0.0247143	−	0.0760627i	−0.962653	+	0.270738i	$0.912732\pi$
$912$		0			0
$913$	−6.13525	+	0.416272i	−0.203047	+	0.0137766i
$914$		0			0
$915$	9.43732	−	3.06637i	0.311988	−	0.101371i
$916$		0			0
$917$	0.945915	+	1.30194i	0.0312369	+	0.0429939i
$918$		0			0
$919$	−5.76376	+	17.7390i	−0.190129	+	0.585156i	−0.999999	−	0.00145299i	$-0.999537\pi$
$919$	−5.76376	+	17.7390i	−0.190129	+	0.585156i	0.809870	+	0.586609i	$0.199537\pi$
$920$		0			0
$921$	−9.00000	−	6.53888i	−0.296560	−	0.215464i
$922$		0			0
$923$		−	2.74265i		−	0.0902753i
$924$		0			0
$925$		−	13.9414i		−	0.458392i
$926$		0			0
$927$	−4.86414	−	3.53400i	−0.159759	−	0.116072i
$928$		0			0
$929$	−2.48278	+	7.64121i	−0.0814573	+	0.250700i	−0.983488	−	0.180971i	$-0.942076\pi$
$929$	−2.48278	+	7.64121i	−0.0814573	+	0.250700i	0.902031	+	0.431671i	$0.142076\pi$
$930$		0			0
$931$	3.58744	+	4.93769i	0.117574	+	0.161826i
$932$		0			0
$933$	10.3097	−	3.34983i	0.337525	−	0.109668i
$934$		0			0
$935$	−7.21937	+	28.7023i	−0.236099	+	0.938667i
$936$		0			0
$937$	12.7533	+	39.2506i	0.416632	+	1.28226i	0.910783	+	0.412885i	$0.135479\pi$
$937$	12.7533	+	39.2506i	0.416632	+	1.28226i	−0.494151	+	0.869376i	$0.664521\pi$
$938$		0			0
$939$	1.82887	+	2.51722i	0.0596829	+	0.0821464i
$940$		0			0
$941$	−3.24170	−	1.05329i	−0.105676	−	0.0343363i	0.255702	−	0.966756i	$-0.417694\pi$
$941$	−3.24170	−	1.05329i	−0.105676	−	0.0343363i	−0.361378	+	0.932419i	$0.617694\pi$
$942$		0			0
$943$	−44.6182	−	32.4170i	−1.45297	−	1.05564i
$944$		0			0
$945$	16.0557			0.522293
$946$		0			0
$947$			8.83282i			0.287028i	0.989648	+	0.143514i	$0.0458402\pi$
$947$			8.83282i			0.287028i	−0.989648	+	0.143514i	$0.954160\pi$
$948$		0			0
$949$	−10.3097	+	14.1901i	−0.334667	+	0.460630i
$950$		0			0
$951$	−2.50891	+	7.72162i	−0.0813568	+	0.250391i
$952$		0			0
$953$	−3.30902	+	2.40414i	−0.107190	+	0.0778778i	−0.640089	−	0.768301i	$-0.721102\pi$
$953$	−3.30902	+	2.40414i	−0.107190	+	0.0778778i	0.532899	+	0.846179i	$0.321102\pi$
$954$		0			0
$955$	20.4867	−	6.65654i	0.662935	−	0.215401i
$956$		0			0
$957$	−10.4904	+	4.21317i	−0.339105	+	0.136192i
$958$		0			0
$959$	8.21396	+	25.2800i	0.265243	+	0.816333i
$960$		0			0
$961$	−21.9164	+	15.9232i	−0.706981	+	0.513652i
$962$		0			0
$963$	−33.6098	−	10.9205i	−1.08306	−	0.351907i
$964$		0			0
$965$	40.1386	−	55.2460i	1.29211	−	1.77843i
$966$		0			0
$967$	21.0658			0.677432			0.338716	−	0.940889i	$-0.390007\pi$
$967$	21.0658			0.677432			0.338716	+	0.940889i	$0.390007\pi$
$968$		0			0
$969$	2.38197			0.0765198
$970$		0			0
$971$	16.0620	−	22.1074i	0.515453	−	0.709460i	−0.469374	−	0.882999i	$-0.655520\pi$
$971$	16.0620	−	22.1074i	0.515453	−	0.709460i	0.984827	+	0.173539i	$0.0555204\pi$
$972$		0			0
$973$	−25.7529	−	8.36764i	−0.825601	−	0.268254i
$974$		0			0
$975$	−6.97072	+	5.06453i	−0.223242	+	0.162195i
$976$		0			0
$977$	−4.92047	−	15.1437i	−0.157420	−	0.484489i	0.840978	−	0.541069i	$-0.181980\pi$
$977$	−4.92047	−	15.1437i	−0.157420	−	0.484489i	−0.998398	+	0.0565805i	$0.981980\pi$
$978$		0			0
$979$	32.2299	−	12.9443i	1.03007	−	0.413701i
$980$		0			0
$981$	18.5043	−	6.01240i	0.590796	−	0.191961i
$982$		0			0
$983$	46.3224	−	33.6552i	1.47746	−	1.07343i	0.499090	−	0.866550i	$-0.333668\pi$
$983$	46.3224	−	33.6552i	1.47746	−	1.07343i	0.978365	−	0.206884i	$-0.0663324\pi$
$984$		0			0
$985$	−18.7984	+	57.8554i	−0.598966	+	1.84343i
$986$		0			0
$987$	−4.22050	+	5.80902i	−0.134340	+	0.184903i
$988$		0			0
$989$			62.9627i			2.00210i
$990$		0			0
$991$	−8.42633			−0.267671			−0.133836	−	0.991004i	$-0.542729\pi$
$991$	−8.42633			−0.267671			−0.133836	+	0.991004i	$0.542729\pi$
$992$		0			0
$993$	−2.14590	−	1.55909i	−0.0680980	−	0.0494761i
$994$		0			0
$995$	13.6578	+	4.43769i	0.432982	+	0.140684i
$996$		0			0
$997$	14.2050	+	19.5515i	0.449877	+	0.619203i	0.972371	−	0.233440i	$-0.0749983\pi$
$997$	14.2050	+	19.5515i	0.449877	+	0.619203i	−0.522494	+	0.852643i	$0.674998\pi$
$998$		0			0
$999$	−1.45561	−	4.47992i	−0.0460536	−	0.141738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.w.b.225.4	yes	16
4.3	odd	2	inner	704.2.w.b.225.2	yes	16
8.3	odd	2	inner	704.2.w.b.225.3	yes	16
8.5	even	2	inner	704.2.w.b.225.1	yes	16
11.9	even	5	inner	704.2.w.b.97.1	✓	16
44.31	odd	10	inner	704.2.w.b.97.3	yes	16
88.53	even	10	inner	704.2.w.b.97.4	yes	16
88.75	odd	10	inner	704.2.w.b.97.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
704.2.w.b.97.1	✓	16	11.9	even	5	inner
704.2.w.b.97.2	yes	16	88.75	odd	10	inner
704.2.w.b.97.3	yes	16	44.31	odd	10	inner
704.2.w.b.97.4	yes	16	88.53	even	10	inner
704.2.w.b.225.1	yes	16	8.5	even	2	inner
704.2.w.b.225.2	yes	16	4.3	odd	2	inner
704.2.w.b.225.3	yes	16	8.3	odd	2	inner
704.2.w.b.225.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.224514 - 0.309017i) q^{3} +(3.24170 + 1.05329i) q^{5} +(1.70426 - 1.23822i) q^{7} +(0.881966 + 2.71441i) q^{9} +O(q^{10})\)	\(q+(0.224514 - 0.309017i) q^{3} +(3.24170 + 1.05329i) q^{5} +(1.70426 - 1.23822i) q^{7} +(0.881966 + 2.71441i) q^{9} +(3.07768 - 1.23607i) q^{11} +(-3.24170 + 1.05329i) q^{13} +(1.05329 - 0.765261i) q^{15} +(-0.809017 + 2.48990i) q^{17} +(1.40008 - 1.92705i) q^{19} -0.804643i q^{21} -6.81705 q^{23} +(5.35410 + 3.88998i) q^{25} +(2.12663 + 0.690983i) q^{27} +(-5.24518 - 7.21937i) q^{29} +(2.35523 + 7.24866i) q^{31} +(0.309017 - 1.22857i) q^{33} +(6.82891 - 2.21885i) q^{35} +(-1.23822 - 1.70426i) q^{37} +(-0.402322 + 1.23822i) q^{39} +(6.54508 + 4.75528i) q^{41} -9.23607i q^{43} +9.72827i q^{45} +(-7.21937 - 5.24518i) q^{47} +(-0.791796 + 2.43690i) q^{49} +(0.587785 + 0.809017i) q^{51} +(7.24866 - 2.35523i) q^{53} +(11.2789 - 0.765261i) q^{55} +(-0.281153 - 0.865300i) q^{57} +(-0.673542 - 0.927051i) q^{59} +(7.24866 + 2.35523i) q^{61} +(4.86414 + 3.53400i) q^{63} -11.6180 q^{65} +3.70820i q^{67} +(-1.53052 + 2.10658i) q^{69} +(-0.248648 + 0.765261i) q^{71} +(4.16312 - 3.02468i) q^{73} +(2.40414 - 0.781153i) q^{75} +(3.71466 - 5.91743i) q^{77} +(-4.46182 - 13.7321i) q^{79} +(-6.23607 + 4.53077i) q^{81} +(-1.76336 - 0.572949i) q^{83} +(-5.24518 + 7.21937i) q^{85} -3.40852 q^{87} +10.4721 q^{89} +(-4.22050 + 5.80902i) q^{91} +(2.76874 + 0.899619i) q^{93} +(6.56840 - 4.77222i) q^{95} +(-3.04508 - 9.37181i) q^{97} +(6.06961 + 7.26393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{9}+O(q^{10}) \) 16 * q + 32 * q^9	\( 16 q + 32 q^{9} - 4 q^{17} + 32 q^{25} - 4 q^{33} + 60 q^{41} - 120 q^{49} + 76 q^{57} - 168 q^{65} + 4 q^{73} - 64 q^{81} + 96 q^{89} - 4 q^{97}+O(q^{100}) \) 16 * q + 32 * q^9 - 4 * q^17 + 32 * q^25 - 4 * q^33 + 60 * q^41 - 120 * q^49 + 76 * q^57 - 168 * q^65 + 4 * q^73 - 64 * q^81 + 96 * q^89 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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