LMFDB - Embedded newform 1512.2.c.d.757.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.3
Root			$-0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.d.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} -2.63506i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +O(q^{10})$	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} -2.63506i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +(2.19041 + 3.01484i) q^{10} -4.29757i q^{11} -0.0480111i q^{13} +(1.14412 - 0.831254i) q^{14} +(-3.23607 - 2.35114i) q^{16} -3.16228 q^{17} -0.726543i q^{19} +(-5.01219 - 1.62856i) q^{20} +(3.57237 + 4.91695i) q^{22} -5.28146 q^{23} -1.94356 q^{25} +(0.0399094 + 0.0549306i) q^{26} +(-0.618034 + 1.90211i) q^{28} -8.00208i q^{29} +4.90868 q^{31} +5.65685 q^{32} +(3.61803 - 2.62866i) q^{34} +2.63506i q^{35} +9.10736i q^{37} +(0.603941 + 0.831254i) q^{38} +(7.08831 - 2.30313i) q^{40} +1.45412 q^{41} +8.85816i q^{43} +(-8.17447 - 2.65605i) q^{44} +(6.04264 - 4.39024i) q^{46} -9.23016 q^{47} +1.00000 q^{49} +(2.22367 - 1.61559i) q^{50} +(-0.0913225 - 0.0296725i) q^{52} -3.14726i q^{53} -11.3244 q^{55} +(-0.874032 - 2.68999i) q^{56} +(6.65176 + 9.15537i) q^{58} +5.90515i q^{59} -2.19577i q^{61} +(-5.61613 + 4.08036i) q^{62} +(-6.47214 + 4.70228i) q^{64} -0.126512 q^{65} -8.55452i q^{67} +(-1.95440 + 6.01501i) q^{68} +(-2.19041 - 3.01484i) q^{70} -3.86725 q^{71} -7.56044 q^{73} +(-7.57052 - 10.4199i) q^{74} +(-1.38197 - 0.449028i) q^{76} +4.29757i q^{77} -14.6139 q^{79} +(-6.19541 + 8.52724i) q^{80} +(-1.66370 + 1.20875i) q^{82} +9.05240i q^{83} +8.33280i q^{85} +(-7.36338 - 10.1348i) q^{86} +(11.5604 - 3.75621i) q^{88} +5.15394 q^{89} +0.0480111i q^{91} +(-3.26412 + 10.0459i) q^{92} +(10.5604 - 7.67261i) q^{94} -1.91449 q^{95} +12.1803 q^{97} +(-1.14412 + 0.831254i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) $ 16 * q - 8 * q^4 - 16 * q^7	$ 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−1.14412	+	0.831254i	−0.809017	+	0.587785i
$2$	−1.14412	+	0.831254i	−0.809017	+	0.587785i
$3$		0			0
$3$		0			0
$4$	0.618034	−	1.90211i	0.309017	−	0.951057i
$5$		−	2.63506i		−	1.17844i	−0.807974	−	0.589218i	$-0.799436\pi$
$5$		−	2.63506i		−	1.17844i	0.807974	−	0.589218i	$-0.200564\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.874032	+	2.68999i	0.309017	+	0.951057i
$9$		0			0
$10$	2.19041	+	3.01484i	0.692667	+	0.953375i
$11$		−	4.29757i		−	1.29577i	−0.761740	−	0.647883i	$-0.775654\pi$
$11$		−	4.29757i		−	1.29577i	0.761740	−	0.647883i	$-0.224346\pi$
$12$		0			0
$13$		−	0.0480111i		−	0.0133159i	−0.999978	−	0.00665794i	$-0.997881\pi$
$13$		−	0.0480111i		−	0.0133159i	0.999978	−	0.00665794i	$-0.00211930\pi$
$14$	1.14412	−	0.831254i	0.305780	−	0.222162i
$15$		0			0
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	−3.16228			−0.766965			−0.383482	−	0.923548i	$-0.625275\pi$
$17$	−3.16228			−0.766965			−0.383482	+	0.923548i	$0.625275\pi$
$18$		0			0
$19$		−	0.726543i		−	0.166680i	−0.996521	−	0.0833401i	$-0.973441\pi$
$19$		−	0.726543i		−	0.166680i	0.996521	−	0.0833401i	$-0.0265588\pi$
$20$	−5.01219	−	1.62856i	−1.12076	−	0.364157i
$21$		0			0
$22$	3.57237	+	4.91695i	0.761632	+	1.04830i
$23$	−5.28146			−1.10126			−0.550631	−	0.834749i	$-0.685613\pi$
$23$	−5.28146			−1.10126			−0.550631	+	0.834749i	$0.685613\pi$
$24$		0			0
$25$	−1.94356			−0.388712
$26$	0.0399094	+	0.0549306i	0.00782687	+	0.0107728i
$27$		0			0
$28$	−0.618034	+	1.90211i	−0.116797	+	0.359466i
$29$		−	8.00208i		−	1.48595i	−0.669319	−	0.742975i	$-0.733414\pi$
$29$		−	8.00208i		−	1.48595i	0.669319	−	0.742975i	$-0.266586\pi$
$30$		0			0
$31$	4.90868			0.881625			0.440812	−	0.897599i	$-0.354690\pi$
$31$	4.90868			0.881625			0.440812	+	0.897599i	$0.354690\pi$
$32$	5.65685			1.00000
$33$		0			0
$34$	3.61803	−	2.62866i	0.620488	−	0.450811i
$35$			2.63506i			0.445407i
$36$		0			0
$37$			9.10736i			1.49724i	0.662999	+	0.748620i	$0.269283\pi$
$37$			9.10736i			1.49724i	−0.662999	+	0.748620i	$0.730717\pi$
$38$	0.603941	+	0.831254i	0.0979722	+	0.134847i
$39$		0			0
$40$	7.08831	−	2.30313i	1.12076	−	0.364157i
$41$	1.45412			0.227096			0.113548	−	0.993533i	$-0.463778\pi$
$41$	1.45412			0.227096			0.113548	+	0.993533i	$0.463778\pi$
$42$		0			0
$43$			8.85816i			1.35086i	0.737426	+	0.675428i	$0.236041\pi$
$43$			8.85816i			1.35086i	−0.737426	+	0.675428i	$0.763959\pi$
$44$	−8.17447	−	2.65605i	−1.23235	−	0.400414i
$45$		0			0
$46$	6.04264	−	4.39024i	0.890939	−	0.647305i
$47$	−9.23016			−1.34636			−0.673179	−	0.739480i	$-0.735072\pi$
$47$	−9.23016			−1.34636			−0.673179	+	0.739480i	$0.735072\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	2.22367	−	1.61559i	0.314475	−	0.228479i
$51$		0			0
$52$	−0.0913225	−	0.0296725i	−0.0126641	−	0.00411483i
$53$		−	3.14726i		−	0.432309i	−0.976359	−	0.216154i	$-0.930649\pi$
$53$		−	3.14726i		−	0.432309i	0.976359	−	0.216154i	$-0.0693515\pi$
$54$		0			0
$55$	−11.3244			−1.52698
$56$	−0.874032	−	2.68999i	−0.116797	−	0.359466i
$57$		0			0
$58$	6.65176	+	9.15537i	0.873419	+	1.20216i
$59$			5.90515i			0.768785i	0.923170	+	0.384392i	$0.125589\pi$
$59$			5.90515i			0.768785i	−0.923170	+	0.384392i	$0.874411\pi$
$60$		0			0
$61$		−	2.19577i		−	0.281140i	−0.990071	−	0.140570i	$-0.955106\pi$
$61$		−	2.19577i		−	0.281140i	0.990071	−	0.140570i	$-0.0448935\pi$
$62$	−5.61613	+	4.08036i	−0.713249	+	0.518206i
$63$		0			0
$64$	−6.47214	+	4.70228i	−0.809017	+	0.587785i
$65$	−0.126512			−0.0156919
$66$		0			0
$67$		−	8.55452i		−	1.04510i	−0.852608	−	0.522550i	$-0.824981\pi$
$67$		−	8.55452i		−	1.04510i	0.852608	−	0.522550i	$-0.175019\pi$
$68$	−1.95440	+	6.01501i	−0.237005	+	0.729427i
$69$		0			0
$70$	−2.19041	−	3.01484i	−0.261804	−	0.360342i
$71$	−3.86725			−0.458958			−0.229479	−	0.973314i	$-0.573702\pi$
$71$	−3.86725			−0.458958			−0.229479	+	0.973314i	$0.573702\pi$
$72$		0			0
$73$	−7.56044			−0.884883			−0.442441	−	0.896797i	$-0.645888\pi$
$73$	−7.56044			−0.884883			−0.442441	+	0.896797i	$0.645888\pi$
$74$	−7.57052	−	10.4199i	−0.880056	−	1.21129i
$75$		0			0
$76$	−1.38197	−	0.449028i	−0.158522	−	0.0515070i
$77$			4.29757i			0.489754i
$78$		0			0
$79$	−14.6139			−1.64419			−0.822094	−	0.569352i	$-0.807194\pi$
$79$	−14.6139			−1.64419			−0.822094	+	0.569352i	$0.807194\pi$
$80$	−6.19541	+	8.52724i	−0.692667	+	0.953375i
$81$		0			0
$82$	−1.66370	+	1.20875i	−0.183724	+	0.133484i
$83$			9.05240i			0.993631i	0.867856	+	0.496815i	$0.165497\pi$
$83$			9.05240i			0.993631i	−0.867856	+	0.496815i	$0.834503\pi$
$84$		0			0
$85$			8.33280i			0.903819i
$86$	−7.36338	−	10.1348i	−0.794014	−	1.09287i
$87$		0			0
$88$	11.5604	−	3.75621i	1.23235	−	0.400414i
$89$	5.15394			0.546317			0.273159	−	0.961969i	$-0.411932\pi$
$89$	5.15394			0.546317			0.273159	+	0.961969i	$0.411932\pi$
$90$		0			0
$91$			0.0480111i			0.00503293i
$92$	−3.26412	+	10.0459i	−0.340309	+	1.04736i
$93$		0			0
$94$	10.5604	−	7.67261i	1.08923	−	0.791369i
$95$	−1.91449			−0.196422
$96$		0			0
$97$	12.1803			1.23673			0.618363	−	0.785893i	$-0.287796\pi$
$97$	12.1803			1.23673			0.618363	+	0.785893i	$0.287796\pi$
$98$	−1.14412	+	0.831254i	−0.115574	+	0.0839693i
$99$		0			0
$100$	−1.20119	+	3.69687i	−0.120119	+	0.369687i
$101$			4.35250i			0.433090i	0.976273	+	0.216545i	$0.0694788\pi$
$101$			4.35250i			0.433090i	−0.976273	+	0.216545i	$0.930521\pi$
$102$		0			0
$103$	−12.3214			−1.21406			−0.607030	−	0.794679i	$-0.707639\pi$
$103$	−12.3214			−1.21406			−0.607030	+	0.794679i	$0.707639\pi$
$104$	0.129149	−	0.0419632i	0.0126641	−	0.00411483i
$105$		0			0
$106$	2.61617	+	3.60085i	0.254105	+	0.349745i
$107$			9.69053i			0.936819i	0.883512	+	0.468409i	$0.155173\pi$
$107$			9.69053i			0.936819i	−0.883512	+	0.468409i	$0.844827\pi$
$108$		0			0
$109$			9.08902i			0.870570i	0.900293	+	0.435285i	$0.143352\pi$
$109$			9.08902i			0.870570i	−0.900293	+	0.435285i	$0.856648\pi$
$110$	12.9565	−	9.41343i	1.23535	−	0.897535i
$111$		0			0
$112$	3.23607	+	2.35114i	0.305780	+	0.222162i
$113$	−13.5205			−1.27190			−0.635951	−	0.771729i	$-0.719392\pi$
$113$	−13.5205			−1.27190			−0.635951	+	0.771729i	$0.719392\pi$
$114$		0			0
$115$			13.9170i			1.29777i
$116$	−15.2209	−	4.94556i	−1.41322	−	0.459184i
$117$		0			0
$118$	−4.90868	−	6.75621i	−0.451880	−	0.621960i
$119$	3.16228			0.289886
$120$		0			0
$121$	−7.46912			−0.679011
$122$	1.82525	+	2.51224i	0.165250	+	0.227447i
$123$		0			0
$124$	3.03373	−	9.33686i	0.272437	−	0.838475i
$125$		−	8.05391i		−	0.720364i
$126$		0			0
$127$	−10.9792			−0.974242			−0.487121	−	0.873334i	$-0.661953\pi$
$127$	−10.9792			−0.974242			−0.487121	+	0.873334i	$0.661953\pi$
$128$	3.49613	−	10.7600i	0.309017	−	0.951057i
$129$		0			0
$130$	0.144746	−	0.105164i	0.0126950	−	0.00922347i
$131$		−	0.770817i		−	0.0673466i	−0.999433	−	0.0336733i	$-0.989279\pi$
$131$		−	0.770817i		−	0.0673466i	0.999433	−	0.0336733i	$-0.0107206\pi$
$132$		0			0
$133$			0.726543i			0.0629992i
$134$	7.11098	+	9.78742i	0.614295	+	0.845504i
$135$		0			0
$136$	−2.76393	−	8.50651i	−0.237005	−	0.729427i
$137$	10.9782			0.937933			0.468967	−	0.883216i	$-0.344626\pi$
$137$	10.9782			0.937933			0.468967	+	0.883216i	$0.344626\pi$
$138$		0			0
$139$		−	22.0189i		−	1.86762i	−0.357767	−	0.933811i	$-0.616462\pi$
$139$		−	22.0189i		−	1.86762i	0.357767	−	0.933811i	$-0.383538\pi$
$140$	5.01219	+	1.62856i	0.423607	+	0.137638i
$141$		0			0
$142$	4.42461	−	3.21467i	0.371305	−	0.269769i
$143$	−0.206331			−0.0172543
$144$		0			0
$145$	−21.0860			−1.75110
$146$	8.65007	−	6.28465i	0.715885	−	0.520121i
$147$		0			0
$148$	17.3232	+	5.62866i	1.42396	+	0.462673i
$149$		−	5.06643i		−	0.415058i	−0.978229	−	0.207529i	$-0.933458\pi$
$149$		−	5.06643i		−	0.415058i	0.978229	−	0.207529i	$-0.0665422\pi$
$150$		0			0
$151$	−6.94054			−0.564813			−0.282407	−	0.959295i	$-0.591133\pi$
$151$	−6.94054			−0.564813			−0.282407	+	0.959295i	$0.591133\pi$
$152$	1.95440	−	0.635021i	0.158522	−	0.0515070i
$153$		0			0
$154$	−3.57237	−	4.91695i	−0.287870	−	0.396219i
$155$		−	12.9347i		−	1.03894i
$156$		0			0
$157$		−	18.4181i		−	1.46992i	−0.678109	−	0.734962i	$-0.737200\pi$
$157$		−	18.4181i		−	1.46992i	0.678109	−	0.734962i	$-0.262800\pi$
$158$	16.7201	−	12.1478i	1.33018	−	0.966430i
$159$		0			0
$160$		−	14.9062i		−	1.17844i
$161$	5.28146			0.416238
$162$		0			0
$163$		−	10.5949i		−	0.829859i	−0.909854	−	0.414929i	$-0.863806\pi$
$163$		−	10.5949i		−	0.829859i	0.909854	−	0.414929i	$-0.136194\pi$
$164$	0.898697	−	2.76591i	0.0701765	−	0.215981i
$165$		0			0
$166$	−7.52485	−	10.3571i	−0.584041	−	0.803864i
$167$	−17.3800			−1.34490			−0.672451	−	0.740142i	$-0.734758\pi$
$167$	−17.3800			−1.34490			−0.672451	+	0.740142i	$0.734758\pi$
$168$		0			0
$169$	12.9977			0.999823
$170$	−6.92667	−	9.53375i	−0.531252	−	0.731205i
$171$		0			0
$172$	16.8492	+	5.47464i	1.28474	+	0.417438i
$173$		−	22.9078i		−	1.74165i	−0.491595	−	0.870824i	$-0.663586\pi$
$173$		−	22.9078i		−	1.74165i	0.491595	−	0.870824i	$-0.336414\pi$
$174$		0			0
$175$	1.94356			0.146919
$176$	−10.1042	+	13.9072i	−0.761632	+	1.04830i
$177$		0			0
$178$	−5.89675	+	4.28424i	−0.441980	+	0.321117i
$179$			21.6267i			1.61646i	0.588869	+	0.808228i	$0.299573\pi$
$179$			21.6267i			1.61646i	−0.588869	+	0.808228i	$0.700427\pi$
$180$		0			0
$181$		−	12.6144i		−	0.937619i	−0.883299	−	0.468810i	$-0.844683\pi$
$181$		−	12.6144i		−	0.937619i	0.883299	−	0.468810i	$-0.155317\pi$
$182$	−0.0399094	−	0.0549306i	−0.00295828	−	0.00407172i
$183$		0			0
$184$	−4.61617	−	14.2071i	−0.340309	−	1.04736i
$185$	23.9985			1.76440
$186$		0			0
$187$			13.5901i			0.993808i
$188$	−5.70456	+	17.5568i	−0.416047	+	1.28046i
$189$		0			0
$190$	2.19041	−	1.59142i	0.158909	−	0.115454i
$191$	−13.5578			−0.981006			−0.490503	−	0.871439i	$-0.663187\pi$
$191$	−13.5578			−0.981006			−0.490503	+	0.871439i	$0.663187\pi$
$192$		0			0
$193$	−26.0614			−1.87594			−0.937971	−	0.346713i	$-0.887298\pi$
$193$	−26.0614			−1.87594			−0.937971	+	0.346713i	$0.887298\pi$
$194$	−13.9358	+	10.1250i	−1.00053	+	0.726929i
$195$		0			0
$196$	0.618034	−	1.90211i	0.0441453	−	0.135865i
$197$			3.18922i			0.227222i	0.993525	+	0.113611i	$0.0362418\pi$
$197$			3.18922i			0.227222i	−0.993525	+	0.113611i	$0.963758\pi$
$198$		0			0
$199$	25.2129			1.78730			0.893648	−	0.448768i	$-0.148137\pi$
$199$	25.2129			1.78730			0.893648	+	0.448768i	$0.148137\pi$
$200$	−1.69873	−	5.22816i	−0.120119	−	0.369687i
$201$		0			0
$202$	−3.61803	−	4.97980i	−0.254564	−	0.350377i
$203$			8.00208i			0.561636i
$204$		0			0
$205$		−	3.83171i		−	0.267618i
$206$	14.0971	−	10.2422i	0.982195	−	0.713606i
$207$		0			0
$208$	−0.112881	+	0.155367i	−0.00782687	+	0.0107728i
$209$	−3.12237			−0.215979
$210$		0			0
$211$		−	5.25731i		−	0.361928i	−0.983490	−	0.180964i	$-0.942078\pi$
$211$		−	5.25731i		−	0.361928i	0.983490	−	0.180964i	$-0.0579218\pi$
$212$	−5.98644	−	1.94511i	−0.411150	−	0.133591i
$213$		0			0
$214$	−8.05529	−	11.0872i	−0.550648	−	0.757902i
$215$	23.3418			1.59190
$216$		0			0
$217$	−4.90868			−0.333223
$218$	−7.55528	−	10.3990i	−0.511708	−	0.704306i
$219$		0			0
$220$	−6.99885	+	21.5402i	−0.471862	+	1.45224i
$221$			0.151824i			0.0102128i
$222$		0			0
$223$	2.27095			0.152074			0.0760370	−	0.997105i	$-0.475773\pi$
$223$	2.27095			0.152074			0.0760370	+	0.997105i	$0.475773\pi$
$224$	−5.65685			−0.377964
$225$		0			0
$226$	15.4691	−	11.2390i	1.02899	−	0.747605i
$227$		−	1.44780i		−	0.0960940i	−0.998845	−	0.0480470i	$-0.984700\pi$
$227$		−	1.44780i		−	0.0960940i	0.998845	−	0.0480470i	$-0.0152997\pi$
$228$		0			0
$229$		−	13.1128i		−	0.866516i	−0.901270	−	0.433258i	$-0.857364\pi$
$229$		−	13.1128i		−	0.866516i	0.901270	−	0.433258i	$-0.142636\pi$
$230$	−11.5686	−	15.9228i	−0.762808	−	1.04992i
$231$		0			0
$232$	21.5256	−	6.99408i	1.41322	−	0.459184i
$233$	−12.6984			−0.831903			−0.415951	−	0.909387i	$-0.636551\pi$
$233$	−12.6984			−0.831903			−0.415951	+	0.909387i	$0.636551\pi$
$234$		0			0
$235$			24.3221i			1.58660i
$236$	11.2323	+	3.64958i	0.731158	+	0.237568i
$237$		0			0
$238$	−3.61803	+	2.62866i	−0.234522	+	0.170390i
$239$	−15.1437			−0.979564			−0.489782	−	0.871845i	$-0.662924\pi$
$239$	−15.1437			−0.979564			−0.489782	+	0.871845i	$0.662924\pi$
$240$		0			0
$241$	−17.0920			−1.10099			−0.550497	−	0.834837i	$-0.685562\pi$
$241$	−17.0920			−1.10099			−0.550497	+	0.834837i	$0.685562\pi$
$242$	8.54559	−	6.20873i	0.549331	−	0.399113i
$243$		0			0
$244$	−4.17661	−	1.35706i	−0.267380	−	0.0868771i
$245$		−	2.63506i		−	0.168348i
$246$		0			0
$247$	−0.0348821			−0.00221949
$248$	4.29034	+	13.2043i	0.272437	+	0.838475i
$249$		0			0
$250$	6.69485	+	9.21467i	0.423419	+	0.582787i
$251$			11.7844i			0.743822i	0.928268	+	0.371911i	$0.121297\pi$
$251$			11.7844i			0.743822i	−0.928268	+	0.371911i	$0.878703\pi$
$252$		0			0
$253$			22.6975i			1.42698i
$254$	12.5615	−	9.12646i	0.788179	−	0.572645i
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	14.8905			0.928847			0.464423	−	0.885613i	$-0.346262\pi$
$257$	14.8905			0.928847			0.464423	+	0.885613i	$0.346262\pi$
$258$		0			0
$259$		−	9.10736i		−	0.565904i
$260$	−0.0781888	+	0.240641i	−0.00484907	+	0.0149239i
$261$		0			0
$262$	0.640745	+	0.881910i	0.0395853	+	0.0544846i
$263$	17.1032			1.05463			0.527315	−	0.849670i	$-0.323199\pi$
$263$	17.1032			1.05463			0.527315	+	0.849670i	$0.323199\pi$
$264$		0			0
$265$	−8.29322			−0.509448
$266$	−0.603941	−	0.831254i	−0.0370300	−	0.0509674i
$267$		0			0
$268$	−16.2717	−	5.28698i	−0.993950	−	0.322954i
$269$			2.32461i			0.141734i	0.997486	+	0.0708670i	$0.0225766\pi$
$269$			2.32461i			0.141734i	−0.997486	+	0.0708670i	$0.977423\pi$
$270$		0			0
$271$	12.4721			0.757628			0.378814	−	0.925473i	$-0.376332\pi$
$271$	12.4721			0.757628			0.378814	+	0.925473i	$0.376332\pi$
$272$	10.2333	+	7.43496i	0.620488	+	0.450811i
$273$		0			0
$274$	−12.5604	+	9.12569i	−0.758804	+	0.551303i
$275$			8.35259i			0.503680i
$276$		0			0
$277$			15.6257i			0.938858i	0.882970	+	0.469429i	$0.155540\pi$
$277$			15.6257i			0.938858i	−0.882970	+	0.469429i	$0.844460\pi$
$278$	18.3033	+	25.1924i	1.09776	+	1.51094i
$279$		0			0
$280$	−7.08831	+	2.30313i	−0.423607	+	0.137638i
$281$	26.0872			1.55623			0.778115	−	0.628122i	$-0.216176\pi$
$281$	26.0872			1.55623			0.778115	+	0.628122i	$0.216176\pi$
$282$		0			0
$283$			17.4083i			1.03482i	0.855739	+	0.517408i	$0.173103\pi$
$283$			17.4083i			1.03482i	−0.855739	+	0.517408i	$0.826897\pi$
$284$	−2.39009	+	7.35595i	−0.141826	+	0.436495i
$285$		0			0
$286$	0.236068	−	0.171513i	0.0139590	−	0.0101418i
$287$	−1.45412			−0.0858342
$288$		0			0
$289$	−7.00000			−0.411765
$290$	24.1250	−	17.5278i	1.41667	−	1.02927i
$291$		0			0
$292$	−4.67261	+	14.3808i	−0.273444	+	0.841573i
$293$		−	13.6647i		−	0.798299i	−0.916886	−	0.399149i	$-0.869305\pi$
$293$		−	13.6647i		−	0.798299i	0.916886	−	0.399149i	$-0.130695\pi$
$294$		0			0
$295$	15.5604			0.905964
$296$	−24.4987	+	7.96012i	−1.42396	+	0.462673i
$297$		0			0
$298$	4.21149	+	5.79662i	0.243965	+	0.335789i
$299$			0.253569i			0.0146643i
$300$		0			0
$301$		−	8.85816i		−	0.510576i
$302$	7.94083	−	5.76935i	0.456944	−	0.331989i
$303$		0			0
$304$	−1.70820	+	2.35114i	−0.0979722	+	0.134847i
$305$	−5.78600			−0.331306
$306$		0			0
$307$			8.43102i			0.481184i	0.970626	+	0.240592i	$0.0773415\pi$
$307$			8.43102i			0.481184i	−0.970626	+	0.240592i	$0.922659\pi$
$308$	8.17447	+	2.65605i	0.465783	+	0.151342i
$309$		0			0
$310$	10.7520	+	14.7989i	0.610673	+	0.840519i
$311$	25.4195			1.44141			0.720703	−	0.693244i	$-0.243819\pi$
$311$	25.4195			1.44141			0.720703	+	0.693244i	$0.243819\pi$
$312$		0			0
$313$	−24.3183			−1.37455			−0.687277	−	0.726396i	$-0.741194\pi$
$313$	−24.3183			−1.37455			−0.687277	+	0.726396i	$0.741194\pi$
$314$	15.3101	+	21.0726i	0.863999	+	1.18919i
$315$		0			0
$316$	−9.03186	+	27.7972i	−0.508082	+	1.56372i
$317$		−	15.2593i		−	0.857047i	−0.903531	−	0.428523i	$-0.859034\pi$
$317$		−	15.2593i		−	0.857047i	0.903531	−	0.428523i	$-0.140966\pi$
$318$		0			0
$319$	−34.3895			−1.92544
$320$	12.3908	+	17.0545i	0.692667	+	0.953375i
$321$		0			0
$322$	−6.04264	+	4.39024i	−0.336743	+	0.244658i
$323$			2.29753i			0.127838i
$324$		0			0
$325$			0.0933124i			0.00517604i
$326$	8.80707	+	12.1219i	0.487779	+	0.671370i
$327$		0			0
$328$	1.27095	+	3.91158i	0.0701765	+	0.215981i
$329$	9.23016			0.508875
$330$		0			0
$331$			22.9170i			1.25963i	0.776744	+	0.629816i	$0.216870\pi$
$331$			22.9170i			1.25963i	−0.776744	+	0.629816i	$0.783130\pi$
$332$	17.2187	+	5.59469i	0.944999	+	0.307049i
$333$		0			0
$334$	19.8848	−	14.4472i	1.08805	−	0.790514i
$335$	−22.5417			−1.23158
$336$		0			0
$337$	34.0474			1.85468			0.927340	−	0.374221i	$-0.122090\pi$
$337$	34.0474			1.85468			0.927340	+	0.374221i	$0.122090\pi$
$338$	−14.8710	+	10.8044i	−0.808874	+	0.587681i
$339$		0			0
$340$	15.8499	+	5.14996i	0.859583	+	0.279296i
$341$		−	21.0954i		−	1.14238i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−23.8284	+	7.74231i	−1.28474	+	0.417438i
$345$		0			0
$346$	19.0422	+	26.2093i	1.02372	+	1.40902i
$347$		−	1.72245i		−	0.0924662i	−0.998931	−	0.0462331i	$-0.985278\pi$
$347$		−	1.72245i		−	0.0924662i	0.998931	−	0.0462331i	$-0.0147217\pi$
$348$		0			0
$349$			7.95586i			0.425868i	0.977067	+	0.212934i	$0.0683019\pi$
$349$			7.95586i			0.425868i	−0.977067	+	0.212934i	$0.931698\pi$
$350$	−2.22367	+	1.61559i	−0.118860	+	0.0863570i
$351$		0			0
$352$		−	24.3107i		−	1.29577i
$353$	23.1711			1.23327			0.616637	−	0.787247i	$-0.288495\pi$
$353$	23.1711			1.23327			0.616637	+	0.787247i	$0.288495\pi$
$354$		0			0
$355$			10.1905i			0.540853i
$356$	3.18531	−	9.80339i	0.168821	−	0.519578i
$357$		0			0
$358$	−17.9773	−	24.7436i	−0.950129	−	1.30774i
$359$	−18.7889			−0.991640			−0.495820	−	0.868425i	$-0.665133\pi$
$359$	−18.7889			−0.991640			−0.495820	+	0.868425i	$0.665133\pi$
$360$		0			0
$361$	18.4721			0.972218
$362$	10.4857	+	14.4324i	0.551119	+	0.758550i
$363$		0			0
$364$	0.0913225	+	0.0296725i	0.00478660	+	0.00155526i
$365$			19.9222i			1.04278i
$366$		0			0
$367$	25.1394			1.31227			0.656134	−	0.754645i	$-0.272191\pi$
$367$	25.1394			1.31227			0.656134	+	0.754645i	$0.272191\pi$
$368$	17.0912	+	12.4175i	0.890939	+	0.647305i
$369$		0			0
$370$	−27.4572	+	19.9488i	−1.42743	+	1.03709i
$371$			3.14726i			0.163397i
$372$		0			0
$373$		−	25.0530i		−	1.29719i	−0.761132	−	0.648597i	$-0.775356\pi$
$373$		−	25.0530i		−	1.29719i	0.761132	−	0.648597i	$-0.224644\pi$
$374$	−11.2968	−	15.5488i	−0.584145	−	0.804007i
$375$		0			0
$376$	−8.06746	−	24.8291i	−0.416047	−	1.28046i
$377$	−0.384189			−0.0197867
$378$		0			0
$379$		−	15.2282i		−	0.782222i	−0.920344	−	0.391111i	$-0.872091\pi$
$379$		−	15.2282i		−	0.782222i	0.920344	−	0.391111i	$-0.127909\pi$
$380$	−1.18322	+	3.64157i	−0.0606978	+	0.186809i
$381$		0			0
$382$	15.5118	−	11.2700i	0.793651	−	0.576621i
$383$	−29.5703			−1.51097			−0.755487	−	0.655164i	$-0.772600\pi$
$383$	−29.5703			−1.51097			−0.755487	+	0.655164i	$0.772600\pi$
$384$		0			0
$385$	11.3244			0.577143
$386$	29.8175	−	21.6637i	1.51767	−	1.10265i
$387$		0			0
$388$	7.52786	−	23.1684i	0.382169	−	1.17620i
$389$			1.90315i			0.0964934i	0.998835	+	0.0482467i	$0.0153634\pi$
$389$			1.90315i			0.0964934i	−0.998835	+	0.0482467i	$0.984637\pi$
$390$		0			0
$391$	16.7015			0.844629
$392$	0.874032	+	2.68999i	0.0441453	+	0.135865i
$393$		0			0
$394$	−2.65105	−	3.64886i	−0.133558	−	0.183827i
$395$			38.5085i			1.93757i
$396$		0			0
$397$		−	16.7660i		−	0.841462i	−0.907185	−	0.420731i	$-0.861774\pi$
$397$		−	16.7660i		−	0.841462i	0.907185	−	0.420731i	$-0.138226\pi$
$398$	−28.8467	+	20.9583i	−1.44595	+	1.05055i
$399$		0			0
$400$	6.28949	+	4.56958i	0.314475	+	0.228479i
$401$	17.2567			0.861759			0.430880	−	0.902409i	$-0.358203\pi$
$401$	17.2567			0.861759			0.430880	+	0.902409i	$0.358203\pi$
$402$		0			0
$403$		−	0.235671i		−	0.0117396i
$404$	8.27895	+	2.68999i	0.411893	+	0.133832i
$405$		0			0
$406$	−6.65176	−	9.15537i	−0.330121	−	0.454373i
$407$	39.1395			1.94007
$408$		0			0
$409$	1.55671			0.0769744			0.0384872	−	0.999259i	$-0.487746\pi$
$409$	1.55671			0.0769744			0.0384872	+	0.999259i	$0.487746\pi$
$410$	3.18512	+	4.38394i	0.157302	+	0.216507i
$411$		0			0
$412$	−7.61502	+	23.4366i	−0.375165	+	1.15464i
$413$		−	5.90515i		−	0.290573i
$414$		0			0
$415$	23.8537			1.17093
$416$		−	0.271592i		−	0.0133159i
$417$		0			0
$418$	3.57237	−	2.59548i	0.174730	−	0.126949i
$419$		−	26.1570i		−	1.27785i	−0.769268	−	0.638926i	$-0.779379\pi$
$419$		−	26.1570i		−	1.27785i	0.769268	−	0.638926i	$-0.220621\pi$
$420$		0			0
$421$		−	0.696870i		−	0.0339634i	−0.999856	−	0.0169817i	$-0.994594\pi$
$421$		−	0.696870i		−	0.0339634i	0.999856	−	0.0169817i	$-0.00540570\pi$
$422$	4.37016	+	6.01501i	0.212736	+	0.292806i
$423$		0			0
$424$	8.46610	−	2.75080i	0.411150	−	0.133591i
$425$	6.14608			0.298128
$426$		0			0
$427$			2.19577i			0.106261i
$428$	18.4325	+	5.98907i	0.890967	+	0.289493i
$429$		0			0
$430$	−26.7059	+	19.4030i	−1.28787	+	0.935694i
$431$	−7.65116			−0.368543			−0.184272	−	0.982875i	$-0.558993\pi$
$431$	−7.65116			−0.368543			−0.184272	+	0.982875i	$0.558993\pi$
$432$		0			0
$433$	17.0860			0.821101			0.410550	−	0.911838i	$-0.365337\pi$
$433$	17.0860			0.821101			0.410550	+	0.911838i	$0.365337\pi$
$434$	5.61613	−	4.08036i	0.269583	−	0.195863i
$435$		0			0
$436$	17.2883	+	5.61732i	0.827961	+	0.269021i
$437$			3.83721i			0.183559i
$438$		0			0
$439$	−3.23837			−0.154559			−0.0772796	−	0.997009i	$-0.524623\pi$
$439$	−3.23837			−0.154559			−0.0772796	+	0.997009i	$0.524623\pi$
$440$	−9.89787	−	30.4625i	−0.471862	−	1.45224i
$441$		0			0
$442$	−0.126205	−	0.173706i	−0.00600294	−	0.00826234i
$443$		−	3.42501i		−	0.162727i	−0.996684	−	0.0813636i	$-0.974073\pi$
$443$		−	3.42501i		−	0.162727i	0.996684	−	0.0813636i	$-0.0259275\pi$
$444$		0			0
$445$		−	13.5810i		−	0.643800i
$446$	−2.59825	+	1.88774i	−0.123031	+	0.0893869i
$447$		0			0
$448$	6.47214	−	4.70228i	0.305780	−	0.222162i
$449$	−39.7647			−1.87661			−0.938305	−	0.345808i	$-0.887605\pi$
$449$	−39.7647			−1.87661			−0.938305	+	0.345808i	$0.887605\pi$
$450$		0			0
$451$		−	6.24920i		−	0.294263i
$452$	−8.35613	+	25.7175i	−0.393039	+	1.20965i
$453$		0			0
$454$	1.20349	+	1.65646i	0.0564826	+	0.0777417i
$455$	0.126512			0.00593098
$456$		0			0
$457$	7.46983			0.349424			0.174712	−	0.984620i	$-0.444101\pi$
$457$	7.46983			0.349424			0.174712	+	0.984620i	$0.444101\pi$
$458$	10.9000	+	15.0026i	0.509325	+	0.701026i
$459$		0			0
$460$	26.4717	+	8.60118i	1.23425	+	0.401032i
$461$		−	15.0075i		−	0.698967i	−0.936942	−	0.349484i	$-0.886357\pi$
$461$		−	15.0075i		−	0.698967i	0.936942	−	0.349484i	$-0.113643\pi$
$462$		0			0
$463$	−4.29553			−0.199630			−0.0998150	−	0.995006i	$-0.531825\pi$
$463$	−4.29553			−0.199630			−0.0998150	+	0.995006i	$0.531825\pi$
$464$	−18.8140	+	25.8953i	−0.873419	+	1.20216i
$465$		0			0
$466$	14.5286	−	10.5556i	0.673023	−	0.488980i
$467$			26.3945i			1.22139i	0.791865	+	0.610696i	$0.209110\pi$
$467$			26.3945i			1.22139i	−0.791865	+	0.610696i	$0.790890\pi$
$468$		0			0
$469$			8.55452i			0.395011i
$470$	−20.2178	−	27.8274i	−0.932578	−	1.28358i
$471$		0			0
$472$	−15.8848	+	5.16129i	−0.731158	+	0.237568i
$473$	38.0686			1.75039
$474$		0			0
$475$			1.41208i			0.0647906i
$476$	1.95440	−	6.01501i	0.0895796	−	0.275698i
$477$		0			0
$478$	17.3262	−	12.5882i	0.792484	−	0.575773i
$479$	−6.66267			−0.304425			−0.152213	−	0.988348i	$-0.548640\pi$
$479$	−6.66267			−0.304425			−0.152213	+	0.988348i	$0.548640\pi$
$480$		0			0
$481$	0.437254			0.0199371
$482$	19.5554	−	14.2078i	0.890723	−	0.647148i
$483$		0			0
$484$	−4.61617	+	14.2071i	−0.209826	+	0.645778i
$485$		−	32.0960i		−	1.45740i
$486$		0			0
$487$	−36.6813			−1.66219			−0.831095	−	0.556131i	$-0.812285\pi$
$487$	−36.6813			−1.66219			−0.831095	+	0.556131i	$0.812285\pi$
$488$	5.90662	−	1.91918i	0.267380	−	0.0868771i
$489$		0			0
$490$	2.19041	+	3.01484i	0.0989525	+	0.136196i
$491$			4.38460i			0.197874i	0.995094	+	0.0989371i	$0.0315443\pi$
$491$			4.38460i			0.197874i	−0.995094	+	0.0989371i	$0.968456\pi$
$492$		0			0
$493$			25.3048i			1.13967i
$494$	0.0399094	−	0.0289959i	0.00179561	−	0.00130459i
$495$		0			0
$496$	−15.8848	−	11.5410i	−0.713249	−	0.518206i
$497$	3.86725			0.173470
$498$		0			0
$499$		−	35.6754i		−	1.59705i	−0.601961	−	0.798525i	$-0.705614\pi$
$499$		−	35.6754i		−	1.59705i	0.601961	−	0.798525i	$-0.294386\pi$
$500$	−15.3195	−	4.97759i	−0.685107	−	0.222605i
$501$		0			0
$502$	−9.79580	−	13.4828i	−0.437208	−	0.601765i
$503$	11.3657			0.506770			0.253385	−	0.967365i	$-0.418456\pi$
$503$	11.3657			0.506770			0.253385	+	0.967365i	$0.418456\pi$
$504$		0			0
$505$	11.4691			0.510369
$506$	−18.8674	−	25.9687i	−0.838756	−	1.15445i
$507$		0			0
$508$	−6.78549	+	20.8836i	−0.301057	+	0.926560i
$509$			2.78884i			0.123613i	0.998088	+	0.0618066i	$0.0196862\pi$
$509$			2.78884i			0.123613i	−0.998088	+	0.0618066i	$0.980314\pi$
$510$		0			0
$511$	7.56044			0.334454
$512$	−18.3060	−	13.3001i	−0.809017	−	0.587785i
$513$		0			0
$514$	−17.0366	+	12.3778i	−0.751453	+	0.545962i
$515$			32.4676i			1.43069i
$516$		0			0
$517$			39.6673i			1.74457i
$518$	7.57052	+	10.4199i	0.332630	+	0.457826i
$519$		0			0
$520$	−0.110576	−	0.340317i	−0.00484907	−	0.0149239i
$521$	−40.3056			−1.76582			−0.882910	−	0.469542i	$-0.844419\pi$
$521$	−40.3056			−1.76582			−0.882910	+	0.469542i	$0.844419\pi$
$522$		0			0
$523$		−	35.9726i		−	1.57297i	−0.617608	−	0.786486i	$-0.711898\pi$
$523$		−	35.9726i		−	1.57297i	0.617608	−	0.786486i	$-0.288102\pi$
$524$	−1.46618	−	0.476391i	−0.0640504	−	0.0208112i
$525$		0			0
$526$	−19.5682	+	14.2171i	−0.853214	+	0.619896i
$527$	−15.5226			−0.676175
$528$		0			0
$529$	4.89387			0.212777
$530$	9.48846	−	6.89377i	0.412152	−	0.299446i
$531$		0			0
$532$	1.38197	+	0.449028i	0.0599158	+	0.0194678i
$533$		−	0.0698140i		−	0.00302398i
$534$		0			0
$535$	25.5352			1.10398
$536$	23.0116	−	7.47692i	0.993950	−	0.322954i
$537$		0			0
$538$	−1.93234	−	2.65964i	−0.0833091	−	0.114665i
$539$		−	4.29757i		−	0.185109i
$540$		0			0
$541$		−	10.1931i		−	0.438234i	−0.975699	−	0.219117i	$-0.929682\pi$
$541$		−	10.1931i		−	0.438234i	0.975699	−	0.219117i	$-0.0703177\pi$
$542$	−14.2697	+	10.3675i	−0.612934	+	0.445323i
$543$		0			0
$544$	−17.8885			−0.766965
$545$	23.9501			1.02591
$546$		0			0
$547$		−	12.3063i		−	0.526182i	−0.964771	−	0.263091i	$-0.915258\pi$
$547$		−	12.3063i		−	0.526182i	0.964771	−	0.263091i	$-0.0847419\pi$
$548$	6.78492	−	20.8818i	0.289837	−	0.892028i
$549$		0			0
$550$	−6.94312	−	9.55638i	−0.296056	−	0.407486i
$551$	−5.81385			−0.247679
$552$		0			0
$553$	14.6139			0.621445
$554$	−12.9889	−	17.8777i	−0.551847	−	0.759552i
$555$		0			0
$556$	−41.8825	−	13.6085i	−1.77621	−	0.577127i
$557$			27.2392i			1.15416i	0.816687	+	0.577082i	$0.195809\pi$
$557$			27.2392i			1.15416i	−0.816687	+	0.577082i	$0.804191\pi$
$558$		0			0
$559$	0.425290			0.0179878
$560$	6.19541	−	8.52724i	0.261804	−	0.360342i
$561$		0			0
$562$	−29.8469	+	21.6851i	−1.25902	+	0.914729i
$563$		−	32.9187i		−	1.38736i	−0.720285	−	0.693678i	$-0.755989\pi$
$563$		−	32.9187i		−	1.38736i	0.720285	−	0.693678i	$-0.244011\pi$
$564$		0			0
$565$			35.6274i			1.49886i
$566$	−14.4707	−	19.9172i	−0.608249	−	0.837183i
$567$		0			0
$568$	−3.38010	−	10.4029i	−0.141826	−	0.436495i
$569$	−25.9554			−1.08811			−0.544053	−	0.839051i	$-0.683111\pi$
$569$	−25.9554			−1.08811			−0.544053	+	0.839051i	$0.683111\pi$
$570$		0			0
$571$			0.527977i			0.0220951i	0.999939	+	0.0110476i	$0.00351662\pi$
$571$			0.527977i			0.0220951i	−0.999939	+	0.0110476i	$0.996483\pi$
$572$	−0.127520	+	0.392465i	−0.00533186	+	0.0164098i
$573$		0			0
$574$	1.66370	−	1.20875i	0.0694413	−	0.0504521i
$575$	10.2648			0.428073
$576$		0			0
$577$	43.1860			1.79786			0.898929	−	0.438094i	$-0.144346\pi$
$577$	43.1860			1.79786			0.898929	+	0.438094i	$0.144346\pi$
$578$	8.00886	−	5.81878i	0.333125	−	0.242029i
$579$		0			0
$580$	−13.0319	+	40.1080i	−0.541119	+	1.66539i
$581$		−	9.05240i		−	0.375557i
$582$		0			0
$583$	−13.5256			−0.560171
$584$	−6.60807	−	20.3375i	−0.273444	−	0.841573i
$585$		0			0
$586$	11.3588	+	15.6341i	0.469228	+	0.645837i
$587$			20.5375i			0.847675i	0.905738	+	0.423837i	$0.139317\pi$
$587$			20.5375i			0.847675i	−0.905738	+	0.423837i	$0.860683\pi$
$588$		0			0
$589$		−	3.56636i		−	0.146949i
$590$	−17.8031	+	12.9347i	−0.732940	+	0.532512i
$591$		0			0
$592$	21.4127	−	29.4720i	0.880056	−	1.21129i
$593$	47.4930			1.95030			0.975152	−	0.221537i	$-0.0711073\pi$
$593$	47.4930			1.95030			0.975152	+	0.221537i	$0.0711073\pi$
$594$		0			0
$595$		−	8.33280i		−	0.341612i
$596$	−9.63693	−	3.13123i	−0.394744	−	0.128260i
$597$		0			0
$598$	−0.210780	−	0.290114i	−0.00861944	−	0.0118636i
$599$	5.31521			0.217174			0.108587	−	0.994087i	$-0.465367\pi$
$599$	5.31521			0.217174			0.108587	+	0.994087i	$0.465367\pi$
$600$		0			0
$601$	29.9137			1.22020			0.610102	−	0.792323i	$-0.291129\pi$
$601$	29.9137			1.22020			0.610102	+	0.792323i	$0.291129\pi$
$602$	7.36338	+	10.1348i	0.300109	+	0.413064i
$603$		0			0
$604$	−4.28949	+	13.2017i	−0.174537	+	0.537169i
$605$			19.6816i			0.800171i
$606$		0			0
$607$	−17.3429			−0.703927			−0.351964	−	0.936014i	$-0.614486\pi$
$607$	−17.3429			−0.703927			−0.351964	+	0.936014i	$0.614486\pi$
$608$		−	4.10995i		−	0.166680i
$609$		0			0
$610$	6.61990	−	4.80964i	0.268032	−	0.194737i
$611$			0.443150i			0.0179279i
$612$		0			0
$613$			17.8469i			0.720830i	0.932792	+	0.360415i	$0.117365\pi$
$613$			17.8469i			0.720830i	−0.932792	+	0.360415i	$0.882635\pi$
$614$	−7.00832	−	9.64612i	−0.282833	−	0.389286i
$615$		0			0
$616$	−11.5604	+	3.75621i	−0.465783	+	0.151342i
$617$	−3.51870			−0.141658			−0.0708289	−	0.997488i	$-0.522564\pi$
$617$	−3.51870			−0.141658			−0.0708289	+	0.997488i	$0.522564\pi$
$618$		0			0
$619$			5.33557i			0.214455i	0.994235	+	0.107227i	$0.0341973\pi$
$619$			5.33557i			0.214455i	−0.994235	+	0.107227i	$0.965803\pi$
$620$	−24.6032	−	7.99407i	−0.988089	−	0.321050i
$621$		0			0
$622$	−29.0830	+	21.1300i	−1.16612	+	0.847237i
$623$	−5.15394			−0.206488
$624$		0			0
$625$	−30.9404			−1.23761
$626$	27.8232	−	20.2147i	1.11204	−	0.807942i
$627$		0			0
$628$	−35.0333	−	11.3830i	−1.39798	−	0.454231i
$629$		−	28.8000i		−	1.14833i
$630$		0			0
$631$	13.1520			0.523574			0.261787	−	0.965126i	$-0.415688\pi$
$631$	13.1520			0.523574			0.261787	+	0.965126i	$0.415688\pi$
$632$	−12.7730	−	39.3112i	−0.508082	−	1.56372i
$633$		0			0
$634$	12.6843	+	17.4585i	0.503760	+	0.693365i
$635$			28.9308i			1.14808i
$636$		0			0
$637$		−	0.0480111i		−	0.00190227i
$638$	39.3458	−	28.5864i	1.55772	−	1.13175i
$639$		0			0
$640$	−28.3532	−	9.21252i	−1.12076	−	0.364157i
$641$	−8.20177			−0.323950			−0.161975	−	0.986795i	$-0.551786\pi$
$641$	−8.20177			−0.323950			−0.161975	+	0.986795i	$0.551786\pi$
$642$		0			0
$643$		−	32.8167i		−	1.29416i	−0.762421	−	0.647082i	$-0.775989\pi$
$643$		−	32.8167i		−	1.29416i	0.762421	−	0.647082i	$-0.224011\pi$
$644$	3.26412	−	10.0459i	0.128625	−	0.395866i
$645$		0			0
$646$	−1.90983	−	2.62866i	−0.0751413	−	0.103423i
$647$	38.7207			1.52227			0.761134	−	0.648595i	$-0.224643\pi$
$647$	38.7207			1.52227			0.761134	+	0.648595i	$0.224643\pi$
$648$		0			0
$649$	25.3778			0.996166
$650$	−0.0775663	−	0.106761i	−0.00304240	−	0.00418750i
$651$		0			0
$652$	−20.1527	−	6.54802i	−0.789242	−	0.256440i
$653$			28.7630i			1.12558i	0.826598	+	0.562792i	$0.190273\pi$
$653$			28.7630i			1.12558i	−0.826598	+	0.562792i	$0.809727\pi$
$654$		0			0
$655$	−2.03115			−0.0793637
$656$	−4.70564	−	3.41885i	−0.183724	−	0.133484i
$657$		0			0
$658$	−10.5604	+	7.67261i	−0.411689	+	0.299109i
$659$		−	30.6124i		−	1.19249i	−0.802803	−	0.596244i	$-0.796659\pi$
$659$		−	30.6124i		−	1.19249i	0.802803	−	0.596244i	$-0.203341\pi$
$660$		0			0
$661$		−	44.1975i		−	1.71908i	−0.511066	−	0.859541i	$-0.670749\pi$
$661$		−	44.1975i		−	1.71908i	0.511066	−	0.859541i	$-0.329251\pi$
$662$	−19.0498	−	26.2199i	−0.740393	−	1.01906i
$663$		0			0
$664$	−24.3509	+	7.91209i	−0.944999	+	0.307049i
$665$	1.91449			0.0742406
$666$		0			0
$667$			42.2627i			1.63642i
$668$	−10.7414	+	33.0587i	−0.415598	+	1.27908i
$669$		0			0
$670$	25.7905	−	18.7379i	0.996373	−	0.723907i
$671$	−9.43649			−0.364292
$672$		0			0
$673$	17.0117			0.655754			0.327877	−	0.944720i	$-0.393667\pi$
$673$	17.0117			0.655754			0.327877	+	0.944720i	$0.393667\pi$
$674$	−38.9544	+	28.3020i	−1.50047	+	1.09015i
$675$		0			0
$676$	8.03302	−	24.7231i	0.308962	−	0.950888i
$677$			45.4750i			1.74775i	0.486155	+	0.873873i	$0.338399\pi$
$677$			45.4750i			1.74775i	−0.486155	+	0.873873i	$0.661601\pi$
$678$		0			0
$679$	−12.1803			−0.467439
$680$	−22.4152	+	7.28314i	−0.859583	+	0.279296i
$681$		0			0
$682$	17.5356	+	24.1357i	0.671474	+	0.924204i
$683$		−	34.4287i		−	1.31738i	−0.752416	−	0.658689i	$-0.771111\pi$
$683$		−	34.4287i		−	1.31738i	0.752416	−	0.658689i	$-0.228889\pi$
$684$		0			0
$685$		−	28.9283i		−	1.10529i
$686$	1.14412	−	0.831254i	0.0436828	−	0.0317374i
$687$		0			0
$688$	20.8268	−	28.6656i	0.794014	−	1.09287i
$689$	−0.151103			−0.00575657
$690$		0			0
$691$		−	28.9692i		−	1.10204i	−0.834491	−	0.551021i	$-0.814238\pi$
$691$		−	28.9692i		−	1.10204i	0.834491	−	0.551021i	$-0.185762\pi$
$692$	−43.5732	−	14.1578i	−1.65641	−	0.538199i
$693$		0			0
$694$	1.43180	+	1.97070i	0.0543503	+	0.0748067i
$695$	−58.0213			−2.20087
$696$		0			0
$697$	−4.59834			−0.174175
$698$	−6.61334	−	9.10248i	−0.250319	−	0.344534i
$699$		0			0
$700$	1.20119	−	3.69687i	0.0454006	−	0.139729i
$701$			12.9846i			0.490421i	0.969470	+	0.245211i	$0.0788571\pi$
$701$			12.9846i			0.490421i	−0.969470	+	0.245211i	$0.921143\pi$
$702$		0			0
$703$	6.61688			0.249560
$704$	20.2084	+	27.8145i	0.761632	+	1.04830i
$705$		0			0
$706$	−26.5106	+	19.2611i	−0.997740	+	0.724901i
$707$		−	4.35250i		−	0.163693i
$708$		0			0
$709$		−	5.62511i		−	0.211255i	−0.994406	−	0.105628i	$-0.966315\pi$
$709$		−	5.62511i		−	0.211255i	0.994406	−	0.105628i	$-0.0336852\pi$
$710$	−8.47085	−	11.6591i	−0.317905	−	0.437559i
$711$		0			0
$712$	4.50471	+	13.8641i	0.168821	+	0.519578i
$713$	−25.9250			−0.970899
$714$		0			0
$715$			0.543695i			0.0203330i
$716$	41.1365	+	13.3660i	1.53734	+	0.499513i
$717$		0			0
$718$	21.4968	−	15.6183i	0.802254	−	0.582872i
$719$	13.3194			0.496732			0.248366	−	0.968666i	$-0.420106\pi$
$719$	13.3194			0.496732			0.248366	+	0.968666i	$0.420106\pi$
$720$		0			0
$721$	12.3214			0.458871
$722$	−21.1344	+	15.3550i	−0.786541	+	0.571455i
$723$		0			0
$724$	−23.9940	−	7.79611i	−0.891729	−	0.289740i
$725$			15.5525i			0.577606i
$726$		0			0
$727$	20.0614			0.744037			0.372019	−	0.928225i	$-0.378666\pi$
$727$	20.0614			0.744037			0.372019	+	0.928225i	$0.378666\pi$
$728$	−0.129149	+	0.0419632i	−0.00478660	+	0.00155526i
$729$		0			0
$730$	−16.5604	−	22.7935i	−0.612929	−	0.843625i
$731$		−	28.0120i		−	1.03606i
$732$		0			0
$733$			4.06695i			0.150216i	0.997175	+	0.0751081i	$0.0239302\pi$
$733$			4.06695i			0.150216i	−0.997175	+	0.0751081i	$0.976070\pi$
$734$	−28.7626	+	20.8972i	−1.06165	+	0.771331i
$735$		0			0
$736$	−29.8765			−1.10126
$737$	−36.7637			−1.35421
$738$		0			0
$739$			2.22283i			0.0817680i	0.999164	+	0.0408840i	$0.0130174\pi$
$739$			2.22283i			0.0817680i	−0.999164	+	0.0408840i	$0.986983\pi$
$740$	14.8319	−	45.6478i	0.545230	−	1.67805i
$741$		0			0
$742$	−2.61617	−	3.60085i	−0.0960426	−	0.132191i
$743$	−28.6763			−1.05203			−0.526015	−	0.850475i	$-0.676314\pi$
$743$	−28.6763			−1.05203			−0.526015	+	0.850475i	$0.676314\pi$
$744$		0			0
$745$	−13.3504			−0.489120
$746$	20.8254	+	28.6637i	0.762472	+	1.04945i
$747$		0			0
$748$	25.8499	+	8.39915i	0.945167	+	0.307103i
$749$		−	9.69053i		−	0.354084i
$750$		0			0
$751$	8.61386			0.314324			0.157162	−	0.987573i	$-0.449765\pi$
$751$	8.61386			0.314324			0.157162	+	0.987573i	$0.449765\pi$
$752$	29.8694	+	21.7014i	1.08923	+	0.791369i
$753$		0			0
$754$	0.439559	−	0.319358i	0.0160078	−	0.0116303i
$755$			18.2888i			0.665596i
$756$		0			0
$757$		−	27.8835i		−	1.01344i	−0.862109	−	0.506722i	$-0.830857\pi$
$757$		−	27.8835i		−	1.01344i	0.862109	−	0.506722i	$-0.169143\pi$
$758$	12.6585	+	17.4230i	0.459779	+	0.632831i
$759$		0			0
$760$	−1.67332	−	5.14996i	−0.0606978	−	0.186809i
$761$	−4.20889			−0.152572			−0.0762861	−	0.997086i	$-0.524306\pi$
$761$	−4.20889			−0.152572			−0.0762861	+	0.997086i	$0.524306\pi$
$762$		0			0
$763$		−	9.08902i		−	0.329045i
$764$	−8.37917	+	25.7884i	−0.303148	+	0.932992i
$765$		0			0
$766$	33.8321	−	24.5805i	1.22240	−	0.888128i
$767$	0.283512			0.0102370
$768$		0			0
$769$	21.5187			0.775986			0.387993	−	0.921662i	$-0.373168\pi$
$769$	21.5187			0.775986			0.387993	+	0.921662i	$0.373168\pi$
$770$	−12.9565	+	9.41343i	−0.466919	+	0.339236i
$771$		0			0
$772$	−16.1068	+	49.5718i	−0.579698	+	1.78413i
$773$		−	30.1139i		−	1.08312i	−0.840661	−	0.541562i	$-0.817833\pi$
$773$		−	30.1139i		−	1.08312i	0.840661	−	0.541562i	$-0.182167\pi$
$774$		0			0
$775$	−9.54031			−0.342698
$776$	10.6460	+	32.7650i	0.382169	+	1.17620i
$777$		0			0
$778$	−1.58200	−	2.17744i	−0.0567174	−	0.0780648i
$779$		−	1.05648i		−	0.0378524i
$780$		0			0
$781$			16.6198i			0.594703i
$782$	−19.1085	+	13.8832i	−0.683319	+	0.496460i
$783$		0			0
$784$	−3.23607	−	2.35114i	−0.115574	−	0.0839693i
$785$	−48.5328			−1.73221
$786$		0			0
$787$		−	48.9845i		−	1.74611i	−0.487624	−	0.873054i	$-0.662136\pi$
$787$		−	48.9845i		−	1.74611i	0.487624	−	0.873054i	$-0.337864\pi$
$788$	6.06626	+	1.97105i	0.216101	+	0.0702156i
$789$		0			0
$790$	−32.0103	−	44.0584i	−1.13888	−	1.56753i
$791$	13.5205			0.480734
$792$		0			0
$793$	−0.105421			−0.00374363
$794$	13.9368	+	19.1824i	0.494599	+	0.680757i
$795$		0			0
$796$	15.5824	−	47.9578i	0.552305	−	1.69982i
$797$		−	47.5262i		−	1.68347i	−0.539894	−	0.841733i	$-0.681536\pi$
$797$		−	47.5262i		−	1.68347i	0.539894	−	0.841733i	$-0.318464\pi$
$798$		0			0
$799$	29.1883			1.03261
$800$	−10.9944			−0.388712
$801$		0			0
$802$	−19.7438	+	14.3447i	−0.697178	+	0.506529i
$803$			32.4915i			1.14660i
$804$		0			0
$805$		−	13.9170i		−	0.490510i
$806$	0.195902	+	0.269636i	0.00690036	+	0.00949754i
$807$		0			0
$808$	−11.7082	+	3.80423i	−0.411893	+	0.133832i
$809$	−30.1063			−1.05848			−0.529240	−	0.848472i	$-0.677523\pi$
$809$	−30.1063			−1.05848			−0.529240	+	0.848472i	$0.677523\pi$
$810$		0			0
$811$			30.2492i			1.06219i	0.847311	+	0.531096i	$0.178220\pi$
$811$			30.2492i			1.06219i	−0.847311	+	0.531096i	$0.821780\pi$
$812$	15.2209	+	4.94556i	0.534148	+	0.173555i
$813$		0			0
$814$	−44.7804	+	32.5349i	−1.56955	+	1.14035i
$815$	−27.9183			−0.977935
$816$		0			0
$817$	6.43583			0.225161
$818$	−1.78107	+	1.29402i	−0.0622736	+	0.0452444i
$819$		0			0
$820$	−7.28834	−	2.36812i	−0.254520	−	0.0826985i
$821$		−	15.4111i		−	0.537851i	−0.963161	−	0.268926i	$-0.913331\pi$
$821$		−	15.4111i		−	0.537851i	0.963161	−	0.268926i	$-0.0866686\pi$
$822$		0			0
$823$	−20.0591			−0.699217			−0.349608	−	0.936896i	$-0.613685\pi$
$823$	−20.0591			−0.699217			−0.349608	+	0.936896i	$0.613685\pi$
$824$	−10.7693	−	33.1444i	−0.375165	−	1.15464i
$825$		0			0
$826$	4.90868	+	6.75621i	0.170795	+	0.235079i
$827$		−	35.3363i		−	1.22876i	−0.789009	−	0.614382i	$-0.789406\pi$
$827$		−	35.3363i		−	1.22876i	0.789009	−	0.614382i	$-0.210594\pi$
$828$		0			0
$829$		−	52.3976i		−	1.81985i	−0.414778	−	0.909923i	$-0.636141\pi$
$829$		−	52.3976i		−	1.81985i	0.414778	−	0.909923i	$-0.363859\pi$
$830$	−27.2915	+	19.8284i	−0.947302	+	0.688256i
$831$		0			0
$832$	0.225762	+	0.310734i	0.00782687	+	0.0107728i
$833$	−3.16228			−0.109566
$834$		0			0
$835$			45.7973i			1.58488i
$836$	−1.92973	+	5.93910i	−0.0667411	+	0.205408i
$837$		0			0
$838$	21.7431	+	29.9268i	0.751102	+	1.03380i
$839$	−43.5132			−1.50224			−0.751121	−	0.660164i	$-0.770487\pi$
$839$	−43.5132			−1.50224			−0.751121	+	0.660164i	$0.770487\pi$
$840$		0			0
$841$	−35.0334			−1.20805
$842$	0.579276	+	0.797305i	0.0199632	+	0.0274769i
$843$		0			0
$844$	−10.0000	−	3.24920i	−0.344214	−	0.111842i
$845$		−	34.2498i		−	1.17823i
$846$		0			0
$847$	7.46912			0.256642
$848$	−7.39964	+	10.1847i	−0.254105	+	0.349745i
$849$		0			0
$850$	−7.03186	+	5.10895i	−0.241191	+	0.175235i
$851$		−	48.1002i		−	1.64885i
$852$		0			0
$853$		−	28.8647i		−	0.988310i	−0.869374	−	0.494155i	$-0.835478\pi$
$853$		−	28.8647i		−	0.988310i	0.869374	−	0.494155i	$-0.164522\pi$
$854$	−1.82525	−	2.51224i	−0.0624586	−	0.0859669i
$855$		0			0
$856$	−26.0675	+	8.46983i	−0.890967	+	0.289493i
$857$	10.7856			0.368429			0.184214	−	0.982886i	$-0.441026\pi$
$857$	10.7856			0.368429			0.184214	+	0.982886i	$0.441026\pi$
$858$		0			0
$859$			47.7595i			1.62953i	0.579789	+	0.814767i	$0.303135\pi$
$859$			47.7595i			1.62953i	−0.579789	+	0.814767i	$0.696865\pi$
$860$	14.4260	−	44.3988i	0.491924	−	1.51399i
$861$		0			0
$862$	8.75387	−	6.36006i	0.298158	−	0.216624i
$863$	41.2620			1.40457			0.702287	−	0.711894i	$-0.252162\pi$
$863$	41.2620			1.40457			0.702287	+	0.711894i	$0.252162\pi$
$864$		0			0
$865$	−60.3635			−2.05242
$866$	−19.5485	+	14.2028i	−0.664284	+	0.482631i
$867$		0			0
$868$	−3.03373	+	9.33686i	−0.102971	+	0.316914i
$869$			62.8041i			2.13048i
$870$		0			0
$871$	−0.410712			−0.0139164
$872$	−24.4494	+	7.94409i	−0.827961	+	0.269021i
$873$		0			0
$874$	−3.18969	−	4.39024i	−0.107893	−	0.148502i
$875$			8.05391i			0.272272i
$876$		0			0
$877$			34.8776i			1.17773i	0.808230	+	0.588867i	$0.200426\pi$
$877$			34.8776i			1.17773i	−0.808230	+	0.588867i	$0.799574\pi$
$878$	3.70510	−	2.69191i	0.125041	−	0.0908476i
$879$		0			0
$880$	36.6464	+	26.6252i	1.23535	+	0.897535i
$881$	6.15123			0.207240			0.103620	−	0.994617i	$-0.466957\pi$
$881$	6.15123			0.207240			0.103620	+	0.994617i	$0.466957\pi$
$882$		0			0
$883$		−	24.2713i		−	0.816796i	−0.912804	−	0.408398i	$-0.866088\pi$
$883$		−	24.2713i		−	0.816796i	0.912804	−	0.408398i	$-0.133912\pi$
$884$	0.288787	+	0.0938326i	0.00971296	+	0.00315593i
$885$		0			0
$886$	2.84705	+	3.91863i	0.0956486	+	0.131649i
$887$	12.8061			0.429987			0.214994	−	0.976615i	$-0.431027\pi$
$887$	12.8061			0.429987			0.214994	+	0.976615i	$0.431027\pi$
$888$		0			0
$889$	10.9792			0.368229
$890$	11.2892	+	15.5383i	0.378416	+	0.520845i
$891$		0			0
$892$	1.40352	−	4.31960i	0.0469935	−	0.144631i
$893$			6.70611i			0.224411i
$894$		0			0
$895$	56.9878			1.90489
$896$	−3.49613	+	10.7600i	−0.116797	+	0.359466i
$897$		0			0
$898$	45.4957	−	33.0545i	1.51821	−	1.10304i
$899$		−	39.2797i		−	1.31005i
$900$		0			0
$901$			9.95250i			0.331566i
$902$	5.19467	+	7.14985i	0.172964	+	0.238064i
$903$		0			0
$904$	−11.8174	−	36.3701i	−0.393039	−	1.20965i
$905$	−33.2397			−1.10492
$906$		0			0
$907$		−	26.7650i		−	0.888717i	−0.895849	−	0.444358i	$-0.853432\pi$
$907$		−	26.7650i		−	0.888717i	0.895849	−	0.444358i	$-0.146568\pi$
$908$	−2.75388	−	0.894791i	−0.0913908	−	0.0296947i
$909$		0			0
$910$	−0.144746	+	0.105164i	−0.00479827	+	0.00348614i
$911$	34.9594			1.15826			0.579128	−	0.815237i	$-0.303393\pi$
$911$	34.9594			1.15826			0.579128	+	0.815237i	$0.303393\pi$
$912$		0			0
$913$	38.9034			1.28751
$914$	−8.54640	+	6.20933i	−0.282690	+	0.205386i
$915$		0			0
$916$	−24.9420	−	8.10414i	−0.824106	−	0.267768i
$917$			0.770817i			0.0254546i
$918$		0			0
$919$	17.3058			0.570867			0.285433	−	0.958399i	$-0.407862\pi$
$919$	17.3058			0.570867			0.285433	+	0.958399i	$0.407862\pi$
$920$	−37.4366	+	12.1639i	−1.23425	+	0.401032i
$921$		0			0
$922$	12.4750	+	17.1704i	0.410843	+	0.565477i
$923$			0.185671i			0.00611143i
$924$		0			0
$925$		−	17.7007i		−	0.581995i
$926$	4.91461	−	3.57067i	0.161504	−	0.117340i
$927$		0			0
$928$		−	45.2666i		−	1.48595i
$929$	8.69526			0.285282			0.142641	−	0.989774i	$-0.454441\pi$
$929$	8.69526			0.285282			0.142641	+	0.989774i	$0.454441\pi$
$930$		0			0
$931$		−	0.726543i		−	0.0238115i
$932$	−7.84807	+	24.1539i	−0.257072	+	0.791186i
$933$		0			0
$934$	−21.9405	−	30.1986i	−0.717916	−	0.988127i
$935$	35.8108			1.17114
$936$		0			0
$937$	24.8633			0.812249			0.406125	−	0.913818i	$-0.366880\pi$
$937$	24.8633			0.812249			0.406125	+	0.913818i	$0.366880\pi$
$938$	−7.11098	−	9.78742i	−0.232182	−	0.319571i
$939$		0			0
$940$	46.2633	+	15.0319i	1.50894	+	0.490285i
$941$			15.1562i			0.494078i	0.969006	+	0.247039i	$0.0794575\pi$
$941$			15.1562i			0.494078i	−0.969006	+	0.247039i	$0.920542\pi$
$942$		0			0
$943$	−7.67990			−0.250092
$944$	13.8838	−	19.1095i	0.451880	−	0.621960i
$945$		0			0
$946$	−43.5551	+	31.6446i	−1.41610	+	1.02886i
$947$		−	25.6626i		−	0.833922i	−0.908924	−	0.416961i	$-0.863095\pi$
$947$		−	25.6626i		−	0.833922i	0.908924	−	0.416961i	$-0.136905\pi$
$948$		0			0
$949$			0.362985i			0.0117830i
$950$	−1.17380	−	1.61559i	−0.0380830	−	0.0524167i
$951$		0			0
$952$	2.76393	+	8.50651i	0.0895796	+	0.275698i
$953$	−9.66478			−0.313073			−0.156536	−	0.987672i	$-0.550033\pi$
$953$	−9.66478			−0.313073			−0.156536	+	0.987672i	$0.550033\pi$
$954$		0			0
$955$			35.7256i			1.15605i
$956$	−9.35931	+	28.8050i	−0.302702	+	0.931620i
$957$		0			0
$958$	7.62292	−	5.53837i	0.246285	−	0.178937i
$959$	−10.9782			−0.354505
$960$		0			0
$961$	−6.90488			−0.222738
$962$	−0.500272	+	0.363469i	−0.0161294	+	0.0117187i
$963$		0			0
$964$	−10.5635	+	32.5110i	−0.340226	+	1.04711i
$965$			68.6735i			2.21068i
$966$		0			0
$967$	6.28949			0.202256			0.101128	−	0.994873i	$-0.467755\pi$
$967$	6.28949			0.202256			0.101128	+	0.994873i	$0.467755\pi$
$968$	−6.52825	−	20.0919i	−0.209826	−	0.645778i
$969$		0			0
$970$	26.6799	+	36.7217i	0.856640	+	1.17906i
$971$			28.3396i			0.909462i	0.890629	+	0.454731i	$0.150265\pi$
$971$			28.3396i			0.909462i	−0.890629	+	0.454731i	$0.849735\pi$
$972$		0			0
$973$			22.0189i			0.705895i
$974$	41.9679	−	30.4915i	1.34474	−	0.977010i
$975$		0			0
$976$	−5.16257	+	7.10567i	−0.165250	+	0.227447i
$977$	−28.0973			−0.898911			−0.449455	−	0.893303i	$-0.648382\pi$
$977$	−28.0973			−0.898911			−0.449455	+	0.893303i	$0.648382\pi$
$978$		0			0
$979$		−	22.1494i		−	0.707899i
$980$	−5.01219	−	1.62856i	−0.160108	−	0.0520224i
$981$		0			0
$982$	−3.64471	−	5.01652i	−0.116307	−	0.160084i
$983$	38.4571			1.22659			0.613296	−	0.789853i	$-0.289843\pi$
$983$	38.4571			1.22659			0.613296	+	0.789853i	$0.289843\pi$
$984$		0			0
$985$	8.40380			0.267767
$986$	−21.0347	−	28.9518i	−0.669882	−	0.922014i
$987$		0			0
$988$	−0.0215583	+	0.0663497i	−0.000685861	+	0.00211086i
$989$		−	46.7841i		−	1.48765i
$990$		0			0
$991$	−30.2448			−0.960759			−0.480380	−	0.877061i	$-0.659501\pi$
$991$	−30.2448			−0.960759			−0.480380	+	0.877061i	$0.659501\pi$
$992$	27.7677			0.881625
$993$		0			0
$994$	−4.42461	+	3.21467i	−0.140340	+	0.101963i
$995$		−	66.4376i		−	2.10621i
$996$		0			0
$997$			17.2007i			0.544751i	0.962191	+	0.272375i	$0.0878093\pi$
$997$			17.2007i			0.544751i	−0.962191	+	0.272375i	$0.912191\pi$
$998$	29.6553	+	40.8170i	0.938723	+	1.29204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.d.757.3	yes	16
3.2	odd	2	inner	1512.2.c.d.757.14	yes	16
4.3	odd	2		6048.2.c.d.3025.3		16
8.3	odd	2		6048.2.c.d.3025.14		16
8.5	even	2	inner	1512.2.c.d.757.2	✓	16
12.11	even	2		6048.2.c.d.3025.13		16
24.5	odd	2	inner	1512.2.c.d.757.15	yes	16
24.11	even	2		6048.2.c.d.3025.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.d.757.2	✓	16	8.5	even	2	inner
1512.2.c.d.757.3	yes	16	1.1	even	1	trivial
1512.2.c.d.757.14	yes	16	3.2	odd	2	inner
1512.2.c.d.757.15	yes	16	24.5	odd	2	inner
6048.2.c.d.3025.3		16	4.3	odd	2
6048.2.c.d.3025.4		16	24.11	even	2
6048.2.c.d.3025.13		16	12.11	even	2
6048.2.c.d.3025.14		16	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} -2.63506i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +O(q^{10})\)	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} -2.63506i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +(2.19041 + 3.01484i) q^{10} -4.29757i q^{11} -0.0480111i q^{13} +(1.14412 - 0.831254i) q^{14} +(-3.23607 - 2.35114i) q^{16} -3.16228 q^{17} -0.726543i q^{19} +(-5.01219 - 1.62856i) q^{20} +(3.57237 + 4.91695i) q^{22} -5.28146 q^{23} -1.94356 q^{25} +(0.0399094 + 0.0549306i) q^{26} +(-0.618034 + 1.90211i) q^{28} -8.00208i q^{29} +4.90868 q^{31} +5.65685 q^{32} +(3.61803 - 2.62866i) q^{34} +2.63506i q^{35} +9.10736i q^{37} +(0.603941 + 0.831254i) q^{38} +(7.08831 - 2.30313i) q^{40} +1.45412 q^{41} +8.85816i q^{43} +(-8.17447 - 2.65605i) q^{44} +(6.04264 - 4.39024i) q^{46} -9.23016 q^{47} +1.00000 q^{49} +(2.22367 - 1.61559i) q^{50} +(-0.0913225 - 0.0296725i) q^{52} -3.14726i q^{53} -11.3244 q^{55} +(-0.874032 - 2.68999i) q^{56} +(6.65176 + 9.15537i) q^{58} +5.90515i q^{59} -2.19577i q^{61} +(-5.61613 + 4.08036i) q^{62} +(-6.47214 + 4.70228i) q^{64} -0.126512 q^{65} -8.55452i q^{67} +(-1.95440 + 6.01501i) q^{68} +(-2.19041 - 3.01484i) q^{70} -3.86725 q^{71} -7.56044 q^{73} +(-7.57052 - 10.4199i) q^{74} +(-1.38197 - 0.449028i) q^{76} +4.29757i q^{77} -14.6139 q^{79} +(-6.19541 + 8.52724i) q^{80} +(-1.66370 + 1.20875i) q^{82} +9.05240i q^{83} +8.33280i q^{85} +(-7.36338 - 10.1348i) q^{86} +(11.5604 - 3.75621i) q^{88} +5.15394 q^{89} +0.0480111i q^{91} +(-3.26412 + 10.0459i) q^{92} +(10.5604 - 7.67261i) q^{94} -1.91449 q^{95} +12.1803 q^{97} +(-1.14412 + 0.831254i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) \) 16 * q - 8 * q^4 - 16 * q^7	\( 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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