LMFDB - Embedded newform 936.2.g.c.469.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.2
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.c.469.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} +1.00000i q^{5} -0.146365 q^{7} +(2.81783 - 0.244644i) q^{8} +(-1.24464 - 0.671462i) q^{10} -2.68585i q^{11} +1.00000i q^{13} +(0.0982788 - 0.182173i) q^{14} +(-1.58757 + 3.67146i) q^{16} -1.00000 q^{17} +4.00000i q^{19} +(1.67146 - 1.09828i) q^{20} +(3.34292 + 1.80344i) q^{22} +6.68585 q^{23} +4.00000 q^{25} +(-1.24464 - 0.671462i) q^{26} +(0.160750 + 0.244644i) q^{28} +4.39312i q^{29} +1.31415 q^{31} +(-3.50367 - 4.44120i) q^{32} +(0.671462 - 1.24464i) q^{34} -0.146365i q^{35} +3.97858i q^{37} +(-4.97858 - 2.68585i) q^{38} +(0.244644 + 2.81783i) q^{40} +6.39312 q^{41} -6.83221i q^{43} +(-4.48929 + 2.94981i) q^{44} +(-4.48929 + 8.32150i) q^{46} +7.12494 q^{47} -6.97858 q^{49} +(-2.68585 + 4.97858i) q^{50} +(1.67146 - 1.09828i) q^{52} +8.97858i q^{53} +2.68585 q^{55} +(-0.412433 + 0.0358075i) q^{56} +(-5.46787 - 2.94981i) q^{58} +12.3503i q^{59} +8.35027i q^{61} +(-0.882404 + 1.63565i) q^{62} +(7.88030 - 1.37873i) q^{64} -1.00000 q^{65} +8.29273i q^{67} +(1.09828 + 1.67146i) q^{68} +(0.182173 + 0.0982788i) q^{70} -5.51806 q^{71} -6.97858 q^{73} +(-4.95191 - 2.67146i) q^{74} +(6.68585 - 4.39312i) q^{76} +0.393115i q^{77} +15.0361 q^{79} +(-3.67146 - 1.58757i) q^{80} +(-4.29273 + 7.95715i) q^{82} -4.29273i q^{83} -1.00000i q^{85} +(8.50367 + 4.58757i) q^{86} +(-0.657077 - 7.56825i) q^{88} +5.37169 q^{89} -0.146365i q^{91} +(-7.34292 - 11.1751i) q^{92} +(-4.78412 + 8.86802i) q^{94} -4.00000 q^{95} -10.3503 q^{97} +(4.68585 - 8.68585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$3$		0			0
$3$		0			0
$4$	−1.09828	−	1.67146i	−0.549139	−	0.835731i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$		0			0
$7$	−0.146365			−0.0553210			−0.0276605	−	0.999617i	$-0.508806\pi$
$7$	−0.146365			−0.0553210			−0.0276605	+	0.999617i	$0.508806\pi$
$8$	2.81783	−	0.244644i	0.996252	−	0.0864948i
$9$		0			0
$10$	−1.24464	−	0.671462i	−0.393591	−	0.212335i
$11$		−	2.68585i		−	0.809813i	−0.914358	−	0.404907i	$-0.867304\pi$
$11$		−	2.68585i		−	0.809813i	0.914358	−	0.404907i	$-0.132696\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.0982788	−	0.182173i	0.0262661	−	0.0486878i
$15$		0			0
$16$	−1.58757	+	3.67146i	−0.396892	+	0.917865i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	1.67146	−	1.09828i	0.373750	−	0.245583i
$21$		0			0
$22$	3.34292	+	1.80344i	0.712714	+	0.384495i
$23$	6.68585			1.39410			0.697048	−	0.717025i	$-0.254497\pi$
$23$	6.68585			1.39410			0.697048	+	0.717025i	$0.254497\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−1.24464	−	0.671462i	−0.244095	−	0.131684i
$27$		0			0
$28$	0.160750	+	0.244644i	0.0303789	+	0.0462334i
$29$			4.39312i			0.815781i	0.913031	+	0.407891i	$0.133735\pi$
$29$			4.39312i			0.815781i	−0.913031	+	0.407891i	$0.866265\pi$
$30$		0			0
$31$	1.31415			0.236029			0.118014	−	0.993012i	$-0.462347\pi$
$31$	1.31415			0.236029			0.118014	+	0.993012i	$0.462347\pi$
$32$	−3.50367	−	4.44120i	−0.619368	−	0.785101i
$33$		0			0
$34$	0.671462	−	1.24464i	0.115155	−	0.213455i
$35$		−	0.146365i		−	0.0247403i
$36$		0			0
$37$			3.97858i			0.654074i	0.945012	+	0.327037i	$0.106050\pi$
$37$			3.97858i			0.654074i	−0.945012	+	0.327037i	$0.893950\pi$
$38$	−4.97858	−	2.68585i	−0.807632	−	0.435702i
$39$		0			0
$40$	0.244644	+	2.81783i	0.0386817	+	0.445538i
$41$	6.39312			0.998437			0.499218	−	0.866476i	$-0.333621\pi$
$41$	6.39312			0.998437			0.499218	+	0.866476i	$0.333621\pi$
$42$		0			0
$43$		−	6.83221i		−	1.04190i	−0.853586	−	0.520951i	$-0.825577\pi$
$43$		−	6.83221i		−	1.04190i	0.853586	−	0.520951i	$-0.174423\pi$
$44$	−4.48929	+	2.94981i	−0.676786	+	0.444700i
$45$		0			0
$46$	−4.48929	+	8.32150i	−0.661909	+	1.22694i
$47$	7.12494			1.03928			0.519640	−	0.854385i	$-0.326066\pi$
$47$	7.12494			1.03928			0.519640	+	0.854385i	$0.326066\pi$
$48$		0			0
$49$	−6.97858			−0.996940
$50$	−2.68585	+	4.97858i	−0.379836	+	0.704077i
$51$		0			0
$52$	1.67146	−	1.09828i	0.231790	−	0.152304i
$53$			8.97858i			1.23330i	0.787236	+	0.616651i	$0.211511\pi$
$53$			8.97858i			1.23330i	−0.787236	+	0.616651i	$0.788489\pi$
$54$		0			0
$55$	2.68585			0.362159
$56$	−0.412433	+	0.0358075i	−0.0551136	+	0.00478498i
$57$		0			0
$58$	−5.46787	−	2.94981i	−0.717966	−	0.387329i
$59$			12.3503i			1.60787i	0.594718	+	0.803934i	$0.297264\pi$
$59$			12.3503i			1.60787i	−0.594718	+	0.803934i	$0.702736\pi$
$60$		0			0
$61$			8.35027i			1.06914i	0.845123	+	0.534571i	$0.179527\pi$
$61$			8.35027i			1.06914i	−0.845123	+	0.534571i	$0.820473\pi$
$62$	−0.882404	+	1.63565i	−0.112065	+	0.207728i
$63$		0			0
$64$	7.88030	−	1.37873i	0.985037	−	0.172341i
$65$	−1.00000			−0.124035
$66$		0			0
$67$			8.29273i			1.01312i	0.862205	+	0.506559i	$0.169083\pi$
$67$			8.29273i			1.01312i	−0.862205	+	0.506559i	$0.830917\pi$
$68$	1.09828	+	1.67146i	0.133186	+	0.202694i
$69$		0			0
$70$	0.182173	+	0.0982788i	0.0217738	+	0.0117466i
$71$	−5.51806			−0.654873			−0.327436	−	0.944873i	$-0.606185\pi$
$71$	−5.51806			−0.654873			−0.327436	+	0.944873i	$0.606185\pi$
$72$		0			0
$73$	−6.97858			−0.816781			−0.408390	−	0.912807i	$-0.633910\pi$
$73$	−6.97858			−0.816781			−0.408390	+	0.912807i	$0.633910\pi$
$74$	−4.95191	−	2.67146i	−0.575648	−	0.310551i
$75$		0			0
$76$	6.68585	−	4.39312i	0.766919	−	0.503925i
$77$			0.393115i			0.0447996i
$78$		0			0
$79$	15.0361			1.69170			0.845848	−	0.533425i	$-0.179095\pi$
$79$	15.0361			1.69170			0.845848	+	0.533425i	$0.179095\pi$
$80$	−3.67146	−	1.58757i	−0.410482	−	0.177495i
$81$		0			0
$82$	−4.29273	+	7.95715i	−0.474053	+	0.878721i
$83$		−	4.29273i		−	0.471188i	−0.971852	−	0.235594i	$-0.924296\pi$
$83$		−	4.29273i		−	0.471188i	0.971852	−	0.235594i	$-0.0757036\pi$
$84$		0			0
$85$		−	1.00000i		−	0.108465i
$86$	8.50367	+	4.58757i	0.916975	+	0.494690i
$87$		0			0
$88$	−0.657077	−	7.56825i	−0.0700446	−	0.806778i
$89$	5.37169			0.569398			0.284699	−	0.958617i	$-0.408106\pi$
$89$	5.37169			0.569398			0.284699	+	0.958617i	$0.408106\pi$
$90$		0			0
$91$		−	0.146365i		−	0.0153433i
$92$	−7.34292	−	11.1751i	−0.765553	−	1.16509i
$93$		0			0
$94$	−4.78412	+	8.86802i	−0.493445	+	0.914666i
$95$	−4.00000			−0.410391
$96$		0			0
$97$	−10.3503			−1.05091			−0.525455	−	0.850821i	$-0.676105\pi$
$97$	−10.3503			−1.05091			−0.525455	+	0.850821i	$0.676105\pi$
$98$	4.68585	−	8.68585i	0.473342	−	0.877403i
$99$		0			0
$100$	−4.39312	−	6.68585i	−0.439312	−	0.668585i
$101$		−	17.9572i		−	1.78680i	−0.449258	−	0.893402i	$-0.648312\pi$
$101$		−	17.9572i		−	1.78680i	0.449258	−	0.893402i	$-0.351688\pi$
$102$		0			0
$103$	10.2499			1.00995			0.504976	−	0.863134i	$-0.331501\pi$
$103$	10.2499			1.00995			0.504976	+	0.863134i	$0.331501\pi$
$104$	0.244644	+	2.81783i	0.0239893	+	0.276311i
$105$		0			0
$106$	−11.1751	−	6.02877i	−1.08543	−	0.585566i
$107$			14.6858i			1.41973i	0.704336	+	0.709867i	$0.251245\pi$
$107$			14.6858i			1.41973i	−0.704336	+	0.709867i	$0.748755\pi$
$108$		0			0
$109$			14.7648i			1.41421i	0.707108	+	0.707106i	$0.250000\pi$
$109$			14.7648i			1.41421i	−0.707108	+	0.707106i	$0.750000\pi$
$110$	−1.80344	+	3.34292i	−0.171951	+	0.318735i
$111$		0			0
$112$	0.232365	−	0.537375i	0.0219564	−	0.0507772i
$113$	−3.95715			−0.372258			−0.186129	−	0.982525i	$-0.559594\pi$
$113$	−3.95715			−0.372258			−0.186129	+	0.982525i	$0.559594\pi$
$114$		0			0
$115$			6.68585i			0.623458i
$116$	7.34292	−	4.82487i	0.681773	−	0.447977i
$117$		0			0
$118$	−15.3717	−	8.29273i	−1.41508	−	0.763408i
$119$	0.146365			0.0134173
$120$		0			0
$121$	3.78623			0.344203
$122$	−10.3931	−	5.60688i	−0.940948	−	0.507623i
$123$		0			0
$124$	−1.44331	−	2.19656i	−0.129613	−	0.197257i
$125$			9.00000i			0.804984i
$126$		0			0
$127$	−6.10038			−0.541322			−0.270661	−	0.962675i	$-0.587242\pi$
$127$	−6.10038			−0.541322			−0.270661	+	0.962675i	$0.587242\pi$
$128$	−3.57529	+	10.7339i	−0.316014	+	0.948755i
$129$		0			0
$130$	0.671462	−	1.24464i	0.0588911	−	0.109163i
$131$		−	14.8322i		−	1.29590i	−0.761684	−	0.647948i	$-0.775627\pi$
$131$		−	14.8322i		−	1.29590i	0.761684	−	0.647948i	$-0.224373\pi$
$132$		0			0
$133$		−	0.585462i		−	0.0507660i
$134$	−10.3215	−	5.56825i	−0.891642	−	0.481024i
$135$		0			0
$136$	−2.81783	+	0.244644i	−0.241627	+	0.0209781i
$137$	−9.76481			−0.834264			−0.417132	−	0.908846i	$-0.636965\pi$
$137$	−9.76481			−0.834264			−0.417132	+	0.908846i	$0.636965\pi$
$138$		0			0
$139$		−	19.4752i		−	1.65187i	−0.563768	−	0.825933i	$-0.690649\pi$
$139$		−	19.4752i		−	1.65187i	0.563768	−	0.825933i	$-0.309351\pi$
$140$	−0.244644	+	0.160750i	−0.0206762	+	0.0135859i
$141$		0			0
$142$	3.70516	−	6.86802i	0.310930	−	0.576351i
$143$	2.68585			0.224602
$144$		0			0
$145$	−4.39312			−0.364828
$146$	4.68585	−	8.68585i	0.387803	−	0.718846i
$147$		0			0
$148$	6.65004	−	4.36959i	0.546630	−	0.359178i
$149$			11.9572i			0.979568i	0.871844	+	0.489784i	$0.162924\pi$
$149$			11.9572i			0.979568i	−0.871844	+	0.489784i	$0.837076\pi$
$150$		0			0
$151$	12.7894			1.04078			0.520392	−	0.853928i	$-0.325786\pi$
$151$	12.7894			1.04078			0.520392	+	0.853928i	$0.325786\pi$
$152$	0.978577	+	11.2713i	0.0793731	+	0.914224i
$153$		0			0
$154$	−0.489289	−	0.263962i	−0.0394280	−	0.0212706i
$155$			1.31415i			0.105555i
$156$		0			0
$157$		−	21.7220i		−	1.73360i	−0.498655	−	0.866801i	$-0.666172\pi$
$157$		−	21.7220i		−	1.73360i	0.498655	−	0.866801i	$-0.333828\pi$
$158$	−10.0962	+	18.7146i	−0.803208	+	1.48885i
$159$		0			0
$160$	4.44120	−	3.50367i	0.351108	−	0.276990i
$161$	−0.978577			−0.0771227
$162$		0			0
$163$		−	20.6430i		−	1.61688i	−0.588575	−	0.808442i	$-0.700311\pi$
$163$		−	20.6430i		−	1.61688i	0.588575	−	0.808442i	$-0.299689\pi$
$164$	−7.02142	−	10.6858i	−0.548281	−	0.834424i
$165$		0			0
$166$	5.34292	+	2.88240i	0.414691	+	0.223718i
$167$	18.0147			1.39402			0.697009	−	0.717062i	$-0.254514\pi$
$167$	18.0147			1.39402			0.697009	+	0.717062i	$0.254514\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	1.24464	+	0.671462i	0.0954599	+	0.0514987i
$171$		0			0
$172$	−11.4198	+	7.50367i	−0.870750	+	0.572150i
$173$		−	6.58546i		−	0.500683i	−0.968158	−	0.250342i	$-0.919457\pi$
$173$		−	6.58546i		−	0.500683i	0.968158	−	0.250342i	$-0.0805430\pi$
$174$		0			0
$175$	−0.585462			−0.0442568
$176$	9.86098	+	4.26396i	0.743299	+	0.321408i
$177$		0			0
$178$	−3.60688	+	6.68585i	−0.270347	+	0.501125i
$179$		−	7.56090i		−	0.565128i	−0.959248	−	0.282564i	$-0.908815\pi$
$179$		−	7.56090i		−	0.565128i	0.959248	−	0.282564i	$-0.0911850\pi$
$180$		0			0
$181$		−	0.628308i		−	0.0467017i	−0.999727	−	0.0233509i	$-0.992567\pi$
$181$		−	0.628308i		−	0.0467017i	0.999727	−	0.0233509i	$-0.00743349\pi$
$182$	0.182173	+	0.0982788i	0.0135036	+	0.00728491i
$183$		0			0
$184$	18.8396	−	1.63565i	1.38887	−	0.120582i
$185$	−3.97858			−0.292511
$186$		0			0
$187$			2.68585i			0.196409i
$188$	−7.82517	−	11.9091i	−0.570709	−	0.868558i
$189$		0			0
$190$	2.68585	−	4.97858i	0.194852	−	0.361184i
$191$	10.1004			0.730838			0.365419	−	0.930843i	$-0.380926\pi$
$191$	10.1004			0.730838			0.365419	+	0.930843i	$0.380926\pi$
$192$		0			0
$193$	−3.37169			−0.242700			−0.121350	−	0.992610i	$-0.538722\pi$
$193$	−3.37169			−0.242700			−0.121350	+	0.992610i	$0.538722\pi$
$194$	6.94981	−	12.8824i	0.498967	−	0.924903i
$195$		0			0
$196$	7.66442	+	11.6644i	0.547459	+	0.833173i
$197$			14.7220i			1.04890i	0.851442	+	0.524448i	$0.175728\pi$
$197$			14.7220i			1.04890i	−0.851442	+	0.524448i	$0.824272\pi$
$198$		0			0
$199$	−13.6644			−0.968645			−0.484323	−	0.874889i	$-0.660934\pi$
$199$	−13.6644			−0.968645			−0.484323	+	0.874889i	$0.660934\pi$
$200$	11.2713	−	0.978577i	0.797002	−	0.0691959i
$201$		0			0
$202$	22.3503	+	12.0575i	1.57256	+	0.848365i
$203$		−	0.643000i		−	0.0451298i
$204$		0			0
$205$			6.39312i			0.446515i
$206$	−6.88240	+	12.7575i	−0.479520	+	0.888854i
$207$		0			0
$208$	−3.67146	−	1.58757i	−0.254570	−	0.110078i
$209$	10.7434			0.743135
$210$		0			0
$211$			1.46052i			0.100546i	0.998736	+	0.0502731i	$0.0160092\pi$
$211$			1.46052i			0.100546i	−0.998736	+	0.0502731i	$0.983991\pi$
$212$	15.0073	−	9.86098i	1.03071	−	0.677255i
$213$		0			0
$214$	−18.2787	−	9.86098i	−1.24950	−	0.674083i
$215$	6.83221			0.465953
$216$		0			0
$217$	−0.192347			−0.0130573
$218$	−18.3769	−	9.91400i	−1.24464	−	0.671461i
$219$		0			0
$220$	−2.94981	−	4.48929i	−0.198876	−	0.302668i
$221$		−	1.00000i		−	0.0672673i
$222$		0			0
$223$	7.12494			0.477121			0.238561	−	0.971128i	$-0.423324\pi$
$223$	7.12494			0.477121			0.238561	+	0.971128i	$0.423324\pi$
$224$	0.512817	+	0.650039i	0.0342640	+	0.0434325i
$225$		0			0
$226$	2.65708	−	4.92525i	0.176746	−	0.327623i
$227$		−	24.9357i		−	1.65504i	−0.561434	−	0.827521i	$-0.689750\pi$
$227$		−	24.9357i		−	1.65504i	0.561434	−	0.827521i	$-0.310250\pi$
$228$		0			0
$229$			2.95715i			0.195414i	0.995215	+	0.0977071i	$0.0311508\pi$
$229$			2.95715i			0.195414i	−0.995215	+	0.0977071i	$0.968849\pi$
$230$	−8.32150	−	4.48929i	−0.548703	−	0.296015i
$231$		0			0
$232$	1.07475	+	12.3790i	0.0705608	+	0.812724i
$233$	5.19235			0.340162			0.170081	−	0.985430i	$-0.445597\pi$
$233$	5.19235			0.340162			0.170081	+	0.985430i	$0.445597\pi$
$234$		0			0
$235$			7.12494i			0.464780i
$236$	20.6430	−	13.5640i	1.34374	−	0.882944i
$237$		0			0
$238$	−0.0982788	+	0.182173i	−0.00637047	+	0.0118085i
$239$	14.3963			0.931216			0.465608	−	0.884991i	$-0.345836\pi$
$239$	14.3963			0.931216			0.465608	+	0.884991i	$0.345836\pi$
$240$		0			0
$241$	23.3288			1.50274			0.751372	−	0.659879i	$-0.229393\pi$
$241$	23.3288			1.50274			0.751372	+	0.659879i	$0.229393\pi$
$242$	−2.54231	+	4.71251i	−0.163426	+	0.302932i
$243$		0			0
$244$	13.9572	−	9.17092i	0.893515	−	0.587108i
$245$		−	6.97858i		−	0.445845i
$246$		0			0
$247$	−4.00000			−0.254514
$248$	3.70306	−	0.321500i	0.235144	−	0.0204153i
$249$		0			0
$250$	−11.2018	−	6.04315i	−0.708464	−	0.382203i
$251$			15.2713i			0.963916i	0.876194	+	0.481958i	$0.160074\pi$
$251$			15.2713i			0.963916i	−0.876194	+	0.481958i	$0.839926\pi$
$252$		0			0
$253$		−	17.9572i		−	1.12896i
$254$	4.09617	−	7.59281i	0.257017	−	0.476415i
$255$		0			0
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$	−20.9143			−1.30460			−0.652299	−	0.757961i	$-0.726195\pi$
$257$	−20.9143			−1.30460			−0.652299	+	0.757961i	$0.726195\pi$
$258$		0			0
$259$		−	0.582326i		−	0.0361840i
$260$	1.09828	+	1.67146i	0.0681124	+	0.103660i
$261$		0			0
$262$	18.4608	+	9.95926i	1.14051	+	0.615285i
$263$	−13.0214			−0.802935			−0.401468	−	0.915873i	$-0.631500\pi$
$263$	−13.0214			−0.802935			−0.401468	+	0.915873i	$0.631500\pi$
$264$		0			0
$265$	−8.97858			−0.551550
$266$	0.728692	+	0.393115i	0.0446790	+	0.0241034i
$267$		0			0
$268$	13.8610	−	9.10773i	0.846694	−	0.556343i
$269$		−	24.3503i		−	1.48466i	−0.670033	−	0.742331i	$-0.733720\pi$
$269$		−	24.3503i		−	1.48466i	0.670033	−	0.742331i	$-0.266280\pi$
$270$		0			0
$271$	25.5756			1.55361			0.776803	−	0.629743i	$-0.216840\pi$
$271$	25.5756			1.55361			0.776803	+	0.629743i	$0.216840\pi$
$272$	1.58757	−	3.67146i	0.0962604	−	0.222615i
$273$		0			0
$274$	6.55669	−	12.1537i	0.396104	−	0.734233i
$275$		−	10.7434i		−	0.647850i
$276$		0			0
$277$			4.43596i			0.266531i	0.991080	+	0.133266i	$0.0425463\pi$
$277$			4.43596i			0.266531i	−0.991080	+	0.133266i	$0.957454\pi$
$278$	24.2397	+	13.0769i	1.45380	+	0.784298i
$279$		0			0
$280$	−0.0358075	−	0.412433i	−0.00213991	−	0.0246476i
$281$	−11.4145			−0.680934			−0.340467	−	0.940256i	$-0.610585\pi$
$281$	−11.4145			−0.680934			−0.340467	+	0.940256i	$0.610585\pi$
$282$		0			0
$283$		−	19.4721i		−	1.15749i	−0.815507	−	0.578747i	$-0.803542\pi$
$283$		−	19.4721i		−	1.15749i	0.815507	−	0.578747i	$-0.196458\pi$
$284$	6.06037	+	9.22322i	0.359617	+	0.547298i
$285$		0			0
$286$	−1.80344	+	3.34292i	−0.106640	+	0.197671i
$287$	−0.935731			−0.0552345
$288$		0			0
$289$	−16.0000			−0.941176
$290$	2.94981	−	5.46787i	0.173219	−	0.321084i
$291$		0			0
$292$	7.66442	+	11.6644i	0.448526	+	0.682609i
$293$		−	10.8077i		−	0.631390i	−0.948861	−	0.315695i	$-0.897762\pi$
$293$		−	10.8077i		−	0.631390i	0.948861	−	0.315695i	$-0.102238\pi$
$294$		0			0
$295$	−12.3503			−0.719060
$296$	0.973336	+	11.2109i	0.0565740	+	0.651623i
$297$		0			0
$298$	−14.8824	−	8.02877i	−0.862115	−	0.465094i
$299$			6.68585i			0.386652i
$300$		0			0
$301$			1.00000i			0.0576390i
$302$	−8.58757	+	15.9182i	−0.494159	+	0.915990i
$303$		0			0
$304$	−14.6858	−	6.35027i	−0.842291	−	0.364213i
$305$	−8.35027			−0.478135
$306$		0			0
$307$			4.93573i			0.281697i	0.990031	+	0.140849i	$0.0449831\pi$
$307$			4.93573i			0.281697i	−0.990031	+	0.140849i	$0.955017\pi$
$308$	0.657077	−	0.431750i	0.0374404	−	0.0246012i
$309$		0			0
$310$	−1.63565	−	0.882404i	−0.0928989	−	0.0501172i
$311$	−0.786230			−0.0445830			−0.0222915	−	0.999752i	$-0.507096\pi$
$311$	−0.786230			−0.0445830			−0.0222915	+	0.999752i	$0.507096\pi$
$312$		0			0
$313$	−13.9357			−0.787694			−0.393847	−	0.919176i	$-0.628856\pi$
$313$	−13.9357			−0.787694			−0.393847	+	0.919176i	$0.628856\pi$
$314$	27.0361	+	14.5855i	1.52574	+	0.823105i
$315$		0			0
$316$	−16.5138	−	25.1323i	−0.928976	−	1.41380i
$317$			19.9572i			1.12091i	0.828186	+	0.560453i	$0.189373\pi$
$317$			19.9572i			1.12091i	−0.828186	+	0.560453i	$0.810627\pi$
$318$		0			0
$319$	11.7992			0.660630
$320$	1.37873	+	7.88030i	0.0770734	+	0.440522i
$321$		0			0
$322$	0.657077	−	1.21798i	0.0366175	−	0.0678754i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$			4.00000i			0.221880i
$326$	25.6932	+	13.8610i	1.42301	+	0.767689i
$327$		0			0
$328$	18.0147	−	1.56404i	0.994695	−	0.0863596i
$329$	−1.04285			−0.0574939
$330$		0			0
$331$			11.7073i			0.643490i	0.946826	+	0.321745i	$0.104269\pi$
$331$			11.7073i			0.643490i	−0.946826	+	0.321745i	$0.895731\pi$
$332$	−7.17513	+	4.71462i	−0.393787	+	0.258748i
$333$		0			0
$334$	−12.0962	+	22.4219i	−0.661873	+	1.22687i
$335$	−8.29273			−0.453080
$336$		0			0
$337$	−0.807653			−0.0439957			−0.0219978	−	0.999758i	$-0.507003\pi$
$337$	−0.807653			−0.0439957			−0.0219978	+	0.999758i	$0.507003\pi$
$338$	0.671462	−	1.24464i	0.0365227	−	0.0676997i
$339$		0			0
$340$	−1.67146	+	1.09828i	−0.0906477	+	0.0595625i
$341$		−	3.52962i		−	0.191139i
$342$		0			0
$343$	2.04598			0.110473
$344$	−1.67146	−	19.2520i	−0.0901192	−	1.03800i
$345$		0			0
$346$	8.19656	+	4.42188i	0.440650	+	0.237722i
$347$		−	2.59702i		−	0.139415i	−0.997567	−	0.0697076i	$-0.977793\pi$
$347$		−	2.59702i		−	0.139415i	0.997567	−	0.0697076i	$-0.0222066\pi$
$348$		0			0
$349$		−	16.1709i		−	0.865610i	−0.901488	−	0.432805i	$-0.857524\pi$
$349$		−	16.1709i		−	0.865610i	0.901488	−	0.432805i	$-0.142476\pi$
$350$	0.393115	−	0.728692i	0.0210129	−	0.0389502i
$351$		0			0
$352$	−11.9284	+	9.41033i	−0.635785	+	0.501572i
$353$	5.32885			0.283626			0.141813	−	0.989893i	$-0.454707\pi$
$353$	5.32885			0.283626			0.141813	+	0.989893i	$0.454707\pi$
$354$		0			0
$355$		−	5.51806i		−	0.292868i
$356$	−5.89962	−	8.97858i	−0.312679	−	0.475864i
$357$		0			0
$358$	9.41064	+	5.07686i	0.497368	+	0.268320i
$359$	−34.6002			−1.82613			−0.913063	−	0.407818i	$-0.866290\pi$
$359$	−34.6002			−1.82613			−0.913063	+	0.407818i	$0.866290\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	0.782020	+	0.421884i	0.0411020	+	0.0221738i
$363$		0			0
$364$	−0.244644	+	0.160750i	−0.0128228	+	0.00842560i
$365$		−	6.97858i		−	0.365275i
$366$		0			0
$367$	−14.2499			−0.743838			−0.371919	−	0.928265i	$-0.621300\pi$
$367$	−14.2499			−0.743838			−0.371919	+	0.928265i	$0.621300\pi$
$368$	−10.6142	+	24.5468i	−0.553305	+	1.27959i
$369$		0			0
$370$	2.67146	−	4.95191i	0.138883	−	0.257438i
$371$		−	1.31415i		−	0.0682275i
$372$		0			0
$373$			15.1281i			0.783302i	0.920114	+	0.391651i	$0.128096\pi$
$373$			15.1281i			0.783302i	−0.920114	+	0.391651i	$0.871904\pi$
$374$	−3.34292	−	1.80344i	−0.172858	−	0.0932538i
$375$		0			0
$376$	20.0769	−	1.74308i	1.03538	−	0.0898923i
$377$	−4.39312			−0.226257
$378$		0			0
$379$		−	5.22846i		−	0.268568i	−0.990943	−	0.134284i	$-0.957127\pi$
$379$		−	5.22846i		−	0.268568i	0.990943	−	0.134284i	$-0.0428735\pi$
$380$	4.39312	+	6.68585i	0.225362	+	0.342977i
$381$		0			0
$382$	−6.78202	+	12.5714i	−0.346998	+	0.643208i
$383$	−27.3257			−1.39628			−0.698139	−	0.715962i	$-0.745988\pi$
$383$	−27.3257			−1.39628			−0.698139	+	0.715962i	$0.745988\pi$
$384$		0			0
$385$	−0.393115			−0.0200350
$386$	2.26396	−	4.19656i	0.115233	−	0.213599i
$387$		0			0
$388$	11.3675	+	17.3001i	0.577096	+	0.878278i
$389$		−	9.02142i		−	0.457404i	−0.973496	−	0.228702i	$-0.926552\pi$
$389$		−	9.02142i		−	0.457404i	0.973496	−	0.228702i	$-0.0734482\pi$
$390$		0			0
$391$	−6.68585			−0.338118
$392$	−19.6644	+	1.70727i	−0.993203	+	0.0862301i
$393$		0			0
$394$	−18.3236	−	9.88523i	−0.923130	−	0.498011i
$395$			15.0361i			0.756549i
$396$		0			0
$397$			35.0852i			1.76088i	0.474160	+	0.880439i	$0.342752\pi$
$397$			35.0852i			1.76088i	−0.474160	+	0.880439i	$0.657248\pi$
$398$	9.17513	−	17.0073i	0.459908	−	0.852501i
$399$		0			0
$400$	−6.35027	+	14.6858i	−0.317513	+	0.734292i
$401$	1.06427			0.0531470			0.0265735	−	0.999647i	$-0.491540\pi$
$401$	1.06427			0.0531470			0.0265735	+	0.999647i	$0.491540\pi$
$402$		0			0
$403$			1.31415i			0.0654627i
$404$	−30.0147	+	19.7220i	−1.49329	+	0.981204i
$405$		0			0
$406$	0.800307	+	0.431750i	0.0397186	+	0.0214274i
$407$	10.6858			0.529678
$408$		0			0
$409$	−31.7220			−1.56855			−0.784275	−	0.620413i	$-0.786965\pi$
$409$	−31.7220			−1.56855			−0.784275	+	0.620413i	$0.786965\pi$
$410$	−7.95715	−	4.29273i	−0.392976	−	0.212003i
$411$		0			0
$412$	−11.2572	−	17.1323i	−0.554604	−	0.844047i
$413$		−	1.80765i		−	0.0889488i
$414$		0			0
$415$	4.29273			0.210722
$416$	4.44120	−	3.50367i	0.217748	−	0.171782i
$417$		0			0
$418$	−7.21377	+	13.3717i	−0.352837	+	0.654031i
$419$		−	3.06740i		−	0.149852i	−0.997189	−	0.0749262i	$-0.976128\pi$
$419$		−	3.06740i		−	0.149852i	0.997189	−	0.0749262i	$-0.0238721\pi$
$420$		0			0
$421$			2.21377i			0.107893i	0.998544	+	0.0539463i	$0.0171800\pi$
$421$			2.21377i			0.107893i	−0.998544	+	0.0539463i	$0.982820\pi$
$422$	−1.81783	−	0.980683i	−0.0884904	−	0.0477389i
$423$		0			0
$424$	2.19656	+	25.3001i	0.106674	+	1.22868i
$425$	−4.00000			−0.194029
$426$		0			0
$427$		−	1.22219i		−	0.0591460i
$428$	24.5468	−	16.1292i	1.18652	−	0.779632i
$429$		0			0
$430$	−4.58757	+	8.50367i	−0.221232	+	0.410084i
$431$	−18.8898			−0.909887			−0.454944	−	0.890520i	$-0.650341\pi$
$431$	−18.8898			−0.909887			−0.454944	+	0.890520i	$0.650341\pi$
$432$		0			0
$433$	−21.8929			−1.05210			−0.526052	−	0.850452i	$-0.676328\pi$
$433$	−21.8929			−1.05210			−0.526052	+	0.850452i	$0.676328\pi$
$434$	0.129153	−	0.239403i	0.00619956	−	0.0114917i
$435$		0			0
$436$	24.6788	−	16.2159i	1.18190	−	0.776600i
$437$			26.7434i			1.27931i
$438$		0			0
$439$	13.8077			0.659003			0.329502	−	0.944155i	$-0.393119\pi$
$439$	13.8077			0.659003			0.329502	+	0.944155i	$0.393119\pi$
$440$	7.56825	−	0.657077i	0.360802	−	0.0313249i
$441$		0			0
$442$	1.24464	+	0.671462i	0.0592017	+	0.0319382i
$443$		−	25.5756i		−	1.21513i	−0.794269	−	0.607567i	$-0.792146\pi$
$443$		−	25.5756i		−	1.21513i	0.794269	−	0.607567i	$-0.207854\pi$
$444$		0			0
$445$			5.37169i			0.254643i
$446$	−4.78412	+	8.86802i	−0.226535	+	0.419913i
$447$		0			0
$448$	−1.15340	+	0.201799i	−0.0544932	+	0.00953409i
$449$	24.3074			1.14714			0.573569	−	0.819157i	$-0.305558\pi$
$449$	24.3074			1.14714			0.573569	+	0.819157i	$0.305558\pi$
$450$		0			0
$451$		−	17.1709i		−	0.808547i
$452$	4.34606	+	6.61423i	0.204421	+	0.311107i
$453$		0			0
$454$	31.0361	+	16.7434i	1.45660	+	0.785806i
$455$	0.146365			0.00686172
$456$		0			0
$457$	12.2008			0.570728			0.285364	−	0.958419i	$-0.407886\pi$
$457$	12.2008			0.570728			0.285364	+	0.958419i	$0.407886\pi$
$458$	−3.68061	−	1.98562i	−0.171983	−	0.0927817i
$459$		0			0
$460$	11.1751	−	7.34292i	0.521043	−	0.342366i
$461$		−	8.02142i		−	0.373595i	−0.982398	−	0.186797i	$-0.940189\pi$
$461$		−	8.02142i		−	0.373595i	0.982398	−	0.186797i	$-0.0598108\pi$
$462$		0			0
$463$	−36.0575			−1.67574			−0.837868	−	0.545873i	$-0.816198\pi$
$463$	−36.0575			−1.67574			−0.837868	+	0.545873i	$0.816198\pi$
$464$	−16.1292	−	6.97437i	−0.748777	−	0.323777i
$465$		0			0
$466$	−3.48646	+	6.46262i	−0.161507	+	0.299375i
$467$			19.1856i			0.887804i	0.896075	+	0.443902i	$0.146406\pi$
$467$			19.1856i			0.887804i	−0.896075	+	0.443902i	$0.853594\pi$
$468$		0			0
$469$		−	1.21377i		−	0.0560467i
$470$	−8.86802	−	4.78412i	−0.409051	−	0.220675i
$471$		0			0
$472$	3.02142	+	34.8009i	0.139072	+	1.60184i
$473$	−18.3503			−0.843746
$474$		0			0
$475$			16.0000i			0.734130i
$476$	−0.160750	−	0.244644i	−0.00736797	−	0.0112133i
$477$		0			0
$478$	−9.66653	+	17.9182i	−0.442137	+	0.819560i
$479$	11.9112			0.544235			0.272118	−	0.962264i	$-0.412276\pi$
$479$	11.9112			0.544235			0.272118	+	0.962264i	$0.412276\pi$
$480$		0			0
$481$	−3.97858			−0.181408
$482$	−15.6644	+	29.0361i	−0.713495	+	1.32256i
$483$		0			0
$484$	−4.15834	−	6.32854i	−0.189015	−	0.287661i
$485$		−	10.3503i		−	0.469982i
$486$		0			0
$487$	−15.8568			−0.718539			−0.359269	−	0.933234i	$-0.616974\pi$
$487$	−15.8568			−0.718539			−0.359269	+	0.933234i	$0.616974\pi$
$488$	2.04285	+	23.5296i	0.0924753	+	1.06514i
$489$		0			0
$490$	8.68585	+	4.68585i	0.392387	+	0.211685i
$491$		−	3.91117i		−	0.176509i	−0.996098	−	0.0882544i	$-0.971871\pi$
$491$		−	3.91117i		−	0.176509i	0.996098	−	0.0882544i	$-0.0281288\pi$
$492$		0			0
$493$		−	4.39312i		−	0.197856i
$494$	2.68585	−	4.97858i	0.120842	−	0.223997i
$495$		0			0
$496$	−2.08631	+	4.82487i	−0.0936780	+	0.216643i
$497$	0.807653			0.0362282
$498$		0			0
$499$		−	23.1793i		−	1.03765i	−0.854880	−	0.518825i	$-0.826370\pi$
$499$		−	23.1793i		−	1.03765i	0.854880	−	0.518825i	$-0.173630\pi$
$500$	15.0432	−	9.88451i	0.672750	−	0.442049i
$501$		0			0
$502$	−19.0073	−	10.2541i	−0.848339	−	0.457663i
$503$	−18.5426			−0.826774			−0.413387	−	0.910555i	$-0.635654\pi$
$503$	−18.5426			−0.826774			−0.413387	+	0.910555i	$0.635654\pi$
$504$		0			0
$505$	17.9572			0.799083
$506$	22.3503	+	12.0575i	0.993591	+	0.536023i
$507$		0			0
$508$	6.69992	+	10.1966i	0.297261	+	0.452399i
$509$			25.9143i			1.14863i	0.818634	+	0.574316i	$0.194732\pi$
$509$			25.9143i			1.14863i	−0.818634	+	0.574316i	$0.805268\pi$
$510$		0			0
$511$	1.02142			0.0451851
$512$	21.8680	−	5.81289i	0.966439	−	0.256896i
$513$		0			0
$514$	14.0432	−	26.0309i	0.619417	−	1.14817i
$515$			10.2499i			0.451664i
$516$		0			0
$517$		−	19.1365i		−	0.841622i
$518$	0.724789	+	0.391010i	0.0318454	+	0.0171800i
$519$		0			0
$520$	−2.81783	+	0.244644i	−0.123570	+	0.0107284i
$521$	12.7648			0.559236			0.279618	−	0.960111i	$-0.409792\pi$
$521$	12.7648			0.559236			0.279618	+	0.960111i	$0.409792\pi$
$522$		0			0
$523$			27.1856i			1.18874i	0.804190	+	0.594372i	$0.202599\pi$
$523$			27.1856i			1.18874i	−0.804190	+	0.594372i	$0.797401\pi$
$524$	−24.7915	+	16.2899i	−1.08302	+	0.711628i
$525$		0			0
$526$	8.74338	−	16.2070i	0.381230	−	0.706661i
$527$	−1.31415			−0.0572454
$528$		0			0
$529$	21.7005			0.943502
$530$	6.02877	−	11.1751i	0.261873	−	0.485417i
$531$		0			0
$532$	−0.978577	+	0.643000i	−0.0424267	+	0.0278776i
$533$			6.39312i			0.276917i
$534$		0			0
$535$	−14.6858			−0.634924
$536$	2.02877	+	23.3675i	0.0876295	+	1.00932i
$537$		0			0
$538$	30.3074	+	16.3503i	1.30665	+	0.704910i
$539$			18.7434i			0.807335i
$540$		0			0
$541$		−	6.76481i		−	0.290842i	−0.989370	−	0.145421i	$-0.953546\pi$
$541$		−	6.76481i		−	0.290842i	0.989370	−	0.145421i	$-0.0464536\pi$
$542$	−17.1730	+	31.8325i	−0.737645	+	1.36732i
$543$		0			0
$544$	3.50367	+	4.44120i	0.150219	+	0.190415i
$545$	−14.7648			−0.632455
$546$		0			0
$547$			15.3832i			0.657740i	0.944375	+	0.328870i	$0.106668\pi$
$547$			15.3832i			0.657740i	−0.944375	+	0.328870i	$0.893332\pi$
$548$	10.7245	+	16.3215i	0.458127	+	0.697220i
$549$		0			0
$550$	13.3717	+	7.21377i	0.570171	+	0.307596i
$551$	−17.5725			−0.748612
$552$		0			0
$553$	−2.20077			−0.0935862
$554$	−5.52119	−	2.97858i	−0.234573	−	0.126548i
$555$		0			0
$556$	−32.5521	+	21.3892i	−1.38052	+	0.907105i
$557$		−	7.59388i		−	0.321763i	−0.986974	−	0.160882i	$-0.948566\pi$
$557$		−	7.59388i		−	0.321763i	0.986974	−	0.160882i	$-0.0514337\pi$
$558$		0			0
$559$	6.83221			0.288972
$560$	0.537375	+	0.232365i	0.0227082	+	0.00981922i
$561$		0			0
$562$	7.66442	−	14.2070i	0.323304	−	0.599288i
$563$		−	14.9754i		−	0.631140i	−0.948902	−	0.315570i	$-0.897804\pi$
$563$		−	14.9754i		−	0.631140i	0.948902	−	0.315570i	$-0.102196\pi$
$564$		0			0
$565$		−	3.95715i		−	0.166479i
$566$	24.2358	+	13.0748i	1.01871	+	0.549573i
$567$		0			0
$568$	−15.5489	+	1.34996i	−0.652419	+	0.0566431i
$569$	4.25662			0.178447			0.0892233	−	0.996012i	$-0.471562\pi$
$569$	4.25662			0.178447			0.0892233	+	0.996012i	$0.471562\pi$
$570$		0			0
$571$			43.5903i			1.82420i	0.409971	+	0.912098i	$0.365539\pi$
$571$			43.5903i			1.82420i	−0.409971	+	0.912098i	$0.634461\pi$
$572$	−2.94981	−	4.48929i	−0.123338	−	0.187707i
$573$		0			0
$574$	0.628308	−	1.16465i	0.0262251	−	0.0486117i
$575$	26.7434			1.11528
$576$		0			0
$577$	43.5934			1.81482			0.907409	−	0.420249i	$-0.138057\pi$
$577$	43.5934			1.81482			0.907409	+	0.420249i	$0.138057\pi$
$578$	10.7434	−	19.9143i	0.446866	−	0.828326i
$579$		0			0
$580$	4.82487	+	7.34292i	0.200342	+	0.304898i
$581$			0.628308i			0.0260666i
$582$		0			0
$583$	24.1151			0.998744
$584$	−19.6644	+	1.70727i	−0.813720	+	0.0706473i
$585$		0			0
$586$	13.4517	+	7.25692i	0.555684	+	0.299781i
$587$		−	1.31415i		−	0.0542409i	−0.999632	−	0.0271205i	$-0.991366\pi$
$587$		−	1.31415i		−	0.0542409i	0.999632	−	0.0271205i	$-0.00863377\pi$
$588$		0			0
$589$			5.25662i			0.216595i
$590$	8.29273	−	15.3717i	0.341406	−	0.632843i
$591$		0			0
$592$	−14.6072	−	6.31626i	−0.600352	−	0.259597i
$593$	0.777809			0.0319408			0.0159704	−	0.999872i	$-0.494916\pi$
$593$	0.777809			0.0319408			0.0159704	+	0.999872i	$0.494916\pi$
$594$		0			0
$595$			0.146365i			0.00600040i
$596$	19.9859	−	13.1323i	0.818655	−	0.537920i
$597$		0			0
$598$	−8.32150	−	4.48929i	−0.340291	−	0.183581i
$599$	−3.36327			−0.137420			−0.0687098	−	0.997637i	$-0.521888\pi$
$599$	−3.36327			−0.137420			−0.0687098	+	0.997637i	$0.521888\pi$
$600$		0			0
$601$	4.17092			0.170136			0.0850678	−	0.996375i	$-0.472889\pi$
$601$	4.17092			0.170136			0.0850678	+	0.996375i	$0.472889\pi$
$602$	−1.24464	−	0.671462i	−0.0507279	−	0.0273667i
$603$		0			0
$604$	−14.0463	−	21.3769i	−0.571535	−	0.869815i
$605$			3.78623i			0.153932i
$606$		0			0
$607$	−34.8929			−1.41626			−0.708129	−	0.706083i	$-0.750461\pi$
$607$	−34.8929			−1.41626			−0.708129	+	0.706083i	$0.750461\pi$
$608$	17.7648	−	14.0147i	0.720458	−	0.568371i
$609$		0			0
$610$	5.60688	−	10.3931i	0.227016	−	0.420805i
$611$			7.12494i			0.288244i
$612$		0			0
$613$			17.9143i			0.723552i	0.932265	+	0.361776i	$0.117829\pi$
$613$			17.9143i			0.723552i	−0.932265	+	0.361776i	$0.882171\pi$
$614$	−6.14323	−	3.31415i	−0.247921	−	0.133748i
$615$		0			0
$616$	0.0961734	+	1.10773i	0.00387494	+	0.0446317i
$617$	−23.9143			−0.962754			−0.481377	−	0.876514i	$-0.659863\pi$
$617$	−23.9143			−0.962754			−0.481377	+	0.876514i	$0.659863\pi$
$618$		0			0
$619$			27.9656i			1.12403i	0.827127	+	0.562016i	$0.189974\pi$
$619$			27.9656i			1.12403i	−0.827127	+	0.562016i	$0.810026\pi$
$620$	2.19656	−	1.44331i	0.0882159	−	0.0579646i
$621$		0			0
$622$	0.527923	−	0.978577i	0.0211678	−	0.0392374i
$623$	−0.786230			−0.0314997
$624$		0			0
$625$	11.0000			0.440000
$626$	9.35731	−	17.3450i	0.373993	−	0.693247i
$627$		0			0
$628$	−36.3074	+	23.8568i	−1.44882	+	0.951989i
$629$		−	3.97858i		−	0.158636i
$630$		0			0
$631$	−28.4966			−1.13443			−0.567217	−	0.823569i	$-0.691980\pi$
$631$	−28.4966			−1.13443			−0.567217	+	0.823569i	$0.691980\pi$
$632$	42.3692	−	3.67850i	1.68536	−	0.146323i
$633$		0			0
$634$	−24.8396	−	13.4005i	−0.986505	−	0.532200i
$635$		−	6.10038i		−	0.242086i
$636$		0			0
$637$		−	6.97858i		−	0.276501i
$638$	−7.92273	+	14.6858i	−0.313664	+	0.581418i
$639$		0			0
$640$	−10.7339	−	3.57529i	−0.424296	−	0.141326i
$641$	−13.9143			−0.549582			−0.274791	−	0.961504i	$-0.588609\pi$
$641$	−13.9143			−0.549582			−0.274791	+	0.961504i	$0.588609\pi$
$642$		0			0
$643$		−	19.0361i		−	0.750711i	−0.926881	−	0.375356i	$-0.877521\pi$
$643$		−	19.0361i		−	0.750711i	0.926881	−	0.375356i	$-0.122479\pi$
$644$	1.07475	+	1.63565i	0.0423511	+	0.0644538i
$645$		0			0
$646$	4.97858	+	2.68585i	0.195879	+	0.105673i
$647$	17.6069			0.692198			0.346099	−	0.938198i	$-0.387506\pi$
$647$	17.6069			0.692198			0.346099	+	0.938198i	$0.387506\pi$
$648$		0			0
$649$	33.1709			1.30207
$650$	−4.97858	−	2.68585i	−0.195276	−	0.105348i
$651$		0			0
$652$	−34.5040	+	22.6718i	−1.35128	+	0.887895i
$653$		−	33.8715i		−	1.32549i	−0.748844	−	0.662746i	$-0.769391\pi$
$653$		−	33.8715i		−	1.32549i	0.748844	−	0.662746i	$-0.230609\pi$
$654$		0			0
$655$	14.8322			0.579542
$656$	−10.1495	+	23.4721i	−0.396271	+	0.916431i
$657$		0			0
$658$	0.700231	−	1.29797i	0.0272978	−	0.0506002i
$659$		−	27.1856i		−	1.05900i	−0.848310	−	0.529501i	$-0.822379\pi$
$659$		−	27.1856i		−	1.05900i	0.848310	−	0.529501i	$-0.177621\pi$
$660$		0			0
$661$		−	48.2730i		−	1.87760i	−0.344460	−	0.938801i	$-0.611938\pi$
$661$		−	48.2730i		−	1.87760i	0.344460	−	0.938801i	$-0.388062\pi$
$662$	−14.5714	−	7.86098i	−0.566333	−	0.305526i
$663$		0			0
$664$	−1.05019	−	12.0962i	−0.0407554	−	0.469423i
$665$	0.585462			0.0227032
$666$		0			0
$667$			29.3717i			1.13728i
$668$	−19.7852	−	30.1109i	−0.765511	−	1.16502i
$669$		0			0
$670$	5.56825	−	10.3215i	0.215120	−	0.398754i
$671$	22.4275			0.865806
$672$		0			0
$673$	5.78623			0.223043			0.111521	−	0.993762i	$-0.464428\pi$
$673$	5.78623			0.223043			0.111521	+	0.993762i	$0.464428\pi$
$674$	0.542308	−	1.00524i	0.0208889	−	0.0387204i
$675$		0			0
$676$	1.09828	+	1.67146i	0.0422415	+	0.0642870i
$677$		−	37.3288i		−	1.43466i	−0.696731	−	0.717332i	$-0.745363\pi$
$677$		−	37.3288i		−	1.43466i	0.696731	−	0.717332i	$-0.254637\pi$
$678$		0			0
$679$	1.51492			0.0581374
$680$	−0.244644	−	2.81783i	−0.00938168	−	0.108059i
$681$		0			0
$682$	4.39312	+	2.37000i	0.168221	+	0.0907520i
$683$		−	17.6644i		−	0.675910i	−0.941162	−	0.337955i	$-0.890265\pi$
$683$		−	17.6644i		−	0.675910i	0.941162	−	0.337955i	$-0.109735\pi$
$684$		0			0
$685$		−	9.76481i		−	0.373094i
$686$	−1.37380	+	2.54652i	−0.0524518	+	0.0972265i
$687$		0			0
$688$	25.0842	+	10.8466i	0.956326	+	0.413523i
$689$	−8.97858			−0.342057
$690$		0			0
$691$		−	44.4998i		−	1.69285i	−0.532507	−	0.846426i	$-0.678750\pi$
$691$		−	44.4998i		−	1.69285i	0.532507	−	0.846426i	$-0.321250\pi$
$692$	−11.0073	+	7.23267i	−0.418437	+	0.274945i
$693$		0			0
$694$	3.23237	+	1.74380i	0.122699	+	0.0661937i
$695$	19.4752			0.738737
$696$		0			0
$697$	−6.39312			−0.242157
$698$	20.1270	+	10.8582i	0.761820	+	0.410987i
$699$		0			0
$700$	0.643000	+	0.978577i	0.0243031	+	0.0369867i
$701$			17.0643i			0.644509i	0.946653	+	0.322254i	$0.104441\pi$
$701$			17.0643i			0.644509i	−0.946653	+	0.322254i	$0.895559\pi$
$702$		0			0
$703$	−15.9143			−0.600220
$704$	−3.70306	−	21.1653i	−0.139564	−	0.797696i
$705$		0			0
$706$	−3.57812	+	6.63252i	−0.134664	+	0.249618i
$707$			2.62831i			0.0988477i
$708$		0			0
$709$		−	0.427539i		−	0.0160566i	−0.999968	−	0.00802829i	$-0.997444\pi$
$709$		−	0.427539i		−	0.0160566i	0.999968	−	0.00802829i	$-0.00255551\pi$
$710$	6.86802	+	3.70516i	0.257752	+	0.139052i
$711$		0			0
$712$	15.1365	−	1.31415i	0.567264	−	0.0492500i
$713$	8.78623			0.329047
$714$		0			0
$715$			2.68585i			0.100445i
$716$	−12.6378	+	8.30398i	−0.472295	+	0.310334i
$717$		0			0
$718$	23.2327	−	43.0649i	0.867036	−	1.60717i
$719$	−37.3780			−1.39396			−0.696981	−	0.717089i	$-0.745474\pi$
$719$	−37.3780			−1.39396			−0.696981	+	0.717089i	$0.745474\pi$
$720$		0			0
$721$	−1.50023			−0.0558715
$722$	−2.01438	+	3.73393i	−0.0749676	+	0.138963i
$723$		0			0
$724$	−1.05019	+	0.690057i	−0.0390301	+	0.0256458i
$725$			17.5725i			0.652625i
$726$		0			0
$727$	14.4851			0.537222			0.268611	−	0.963249i	$-0.413435\pi$
$727$	14.4851			0.537222			0.268611	+	0.963249i	$0.413435\pi$
$728$	−0.0358075	−	0.412433i	−0.00132711	−	0.0152858i
$729$		0			0
$730$	8.68585	+	4.68585i	0.321478	+	0.173431i
$731$			6.83221i			0.252698i
$732$		0			0
$733$		−	0.299461i		−	0.0110608i	−0.999985	−	0.00553042i	$-0.998240\pi$
$733$		−	0.299461i		−	0.0110608i	0.999985	−	0.00553042i	$-0.00176040\pi$
$734$	9.56825	−	17.7360i	0.353171	−	0.654649i
$735$		0			0
$736$	−23.4250	−	29.6932i	−0.863458	−	1.09451i
$737$	22.2730			0.820436
$738$		0			0
$739$		−	18.9786i		−	0.698138i	−0.937097	−	0.349069i	$-0.886498\pi$
$739$		−	18.9786i		−	0.698138i	0.937097	−	0.349069i	$-0.113502\pi$
$740$	4.36959	+	6.65004i	0.160629	+	0.244460i
$741$		0			0
$742$	1.63565	+	0.882404i	0.0600467	+	0.0323941i
$743$	26.7465			0.981235			0.490617	−	0.871375i	$-0.336771\pi$
$743$	26.7465			0.981235			0.490617	+	0.871375i	$0.336771\pi$
$744$		0			0
$745$	−11.9572			−0.438076
$746$	−18.8291	−	10.1579i	−0.689381	−	0.371908i
$747$		0			0
$748$	4.48929	−	2.94981i	0.164145	−	0.107856i
$749$		−	2.14950i		−	0.0785411i
$750$		0			0
$751$	−14.1923			−0.517886			−0.258943	−	0.965893i	$-0.583374\pi$
$751$	−14.1923			−0.517886			−0.258943	+	0.965893i	$0.583374\pi$
$752$	−11.3113	+	26.1590i	−0.412482	+	0.953919i
$753$		0			0
$754$	2.94981	−	5.46787i	0.107426	−	0.199128i
$755$			12.7894i			0.465453i
$756$		0			0
$757$		−	45.5934i		−	1.65712i	−0.559899	−	0.828561i	$-0.689160\pi$
$757$		−	45.5934i		−	1.65712i	0.559899	−	0.828561i	$-0.310840\pi$
$758$	6.50758	+	3.51071i	0.236366	+	0.127515i
$759$		0			0
$760$	−11.2713	+	0.978577i	−0.408853	+	0.0354967i
$761$	37.6363			1.36431			0.682157	−	0.731206i	$-0.261042\pi$
$761$	37.6363			1.36431			0.682157	+	0.731206i	$0.261042\pi$
$762$		0			0
$763$		−	2.16106i		−	0.0782356i
$764$	−11.0930	−	16.8824i	−0.401332	−	0.610784i
$765$		0			0
$766$	18.3482	−	34.0108i	0.662946	−	1.22886i
$767$	−12.3503			−0.445942
$768$		0			0
$769$	0.700539			0.0252621			0.0126310	−	0.999920i	$-0.495979\pi$
$769$	0.700539			0.0252621			0.0126310	+	0.999920i	$0.495979\pi$
$770$	0.263962	−	0.489289i	0.00951252	−	0.0176327i
$771$		0			0
$772$	3.70306	+	5.63565i	0.133276	+	0.202832i
$773$			5.08569i			0.182920i	0.995809	+	0.0914598i	$0.0291533\pi$
$773$			5.08569i			0.182920i	−0.995809	+	0.0914598i	$0.970847\pi$
$774$		0			0
$775$	5.25662			0.188823
$776$	−29.1653	+	2.53213i	−1.04697	+	0.0908983i
$777$		0			0
$778$	11.2285	+	6.05754i	0.402560	+	0.217173i
$779$			25.5725i			0.916228i
$780$		0			0
$781$			14.8207i			0.530325i
$782$	4.48929	−	8.32150i	0.160537	−	0.297576i
$783$		0			0
$784$	11.0790	−	25.6216i	0.395677	−	0.915056i
$785$	21.7220			0.775290
$786$		0			0
$787$			14.3074i			0.510005i	0.966940	+	0.255002i	$0.0820762\pi$
$787$			14.3074i			0.510005i	−0.966940	+	0.255002i	$0.917924\pi$
$788$	24.6072	−	16.1688i	0.876595	−	0.575990i
$789$		0			0
$790$	−18.7146	−	10.0962i	−0.665836	−	0.359206i
$791$	0.579191			0.0205937
$792$		0			0
$793$	−8.35027			−0.296527
$794$	−43.6686	−	23.5584i	−1.54974	−	0.836056i
$795$		0			0
$796$	15.0073	+	22.8396i	0.531921	+	0.809527i
$797$			2.54262i			0.0900641i	0.998986	+	0.0450320i	$0.0143390\pi$
$797$			2.54262i			0.0900641i	−0.998986	+	0.0450320i	$0.985661\pi$
$798$		0			0
$799$	−7.12494			−0.252062
$800$	−14.0147	−	17.7648i	−0.495494	−	0.628081i
$801$		0			0
$802$	−0.714615	+	1.32464i	−0.0252339	+	0.0467745i
$803$			18.7434i			0.661440i
$804$		0			0
$805$		−	0.978577i		−	0.0344903i
$806$	−1.63565	−	0.882404i	−0.0576135	−	0.0310813i
$807$		0			0
$808$	−4.39312	−	50.6002i	−0.154549	−	1.78011i
$809$	33.1495			1.16547			0.582737	−	0.812661i	$-0.301982\pi$
$809$	33.1495			1.16547			0.582737	+	0.812661i	$0.301982\pi$
$810$		0			0
$811$		−	1.28600i		−	0.0451576i	−0.999745	−	0.0225788i	$-0.992812\pi$
$811$		−	1.28600i		−	0.0451576i	0.999745	−	0.0225788i	$-0.00718767\pi$
$812$	−1.07475	+	0.706194i	−0.0377163	+	0.0247825i
$813$		0			0
$814$	−7.17513	+	13.3001i	−0.251488	+	0.466167i
$815$	20.6430			0.723093
$816$		0			0
$817$	27.3288			0.956115
$818$	21.3001	−	39.4826i	0.744740	−	1.38048i
$819$		0			0
$820$	10.6858	−	7.02142i	0.373166	−	0.245199i
$821$		−	11.7005i		−	0.408352i	−0.978934	−	0.204176i	$-0.934549\pi$
$821$		−	11.7005i		−	0.408352i	0.978934	−	0.204176i	$-0.0654514\pi$
$822$		0			0
$823$	−38.9786			−1.35871			−0.679354	−	0.733811i	$-0.737740\pi$
$823$	−38.9786			−1.35871			−0.679354	+	0.733811i	$0.737740\pi$
$824$	28.8824	−	2.50758i	1.00617	−	0.0873555i
$825$		0			0
$826$	2.24989	+	1.21377i	0.0782835	+	0.0422324i
$827$			43.5296i			1.51367i	0.653604	+	0.756837i	$0.273256\pi$
$827$			43.5296i			1.51367i	−0.653604	+	0.756837i	$0.726744\pi$
$828$		0			0
$829$		−	35.0852i		−	1.21856i	−0.792955	−	0.609280i	$-0.791458\pi$
$829$		−	35.0852i		−	1.21856i	0.792955	−	0.609280i	$-0.208542\pi$
$830$	−2.88240	+	5.34292i	−0.100050	+	0.185456i
$831$		0			0
$832$	1.37873	+	7.88030i	0.0477989	+	0.273200i
$833$	6.97858			0.241793
$834$		0			0
$835$			18.0147i			0.623424i
$836$	−11.7992	−	17.9572i	−0.408085	−	0.621061i
$837$		0			0
$838$	3.81783	+	2.05964i	0.131885	+	0.0711492i
$839$	10.4851			0.361985			0.180993	−	0.983484i	$-0.442069\pi$
$839$	10.4851			0.361985			0.180993	+	0.983484i	$0.442069\pi$
$840$		0			0
$841$	9.70054			0.334501
$842$	−2.75536	−	1.48646i	−0.0949558	−	0.0512268i
$843$		0			0
$844$	2.44120	−	1.60406i	0.0840296	−	0.0552139i
$845$		−	1.00000i		−	0.0344010i
$846$		0			0
$847$	−0.554173			−0.0190416
$848$	−32.9645	−	14.2541i	−1.13201	−	0.489488i
$849$		0			0
$850$	2.68585	−	4.97858i	0.0921238	−	0.170764i
$851$			26.6002i			0.911842i
$852$		0			0
$853$			40.5296i			1.38771i	0.720116	+	0.693854i	$0.244089\pi$
$853$			40.5296i			1.38771i	−0.720116	+	0.693854i	$0.755911\pi$
$854$	1.52119	+	0.820654i	0.0520542	+	0.0280822i
$855$		0			0
$856$	3.59281	+	41.3822i	0.122800	+	1.41441i
$857$	−5.61531			−0.191815			−0.0959076	−	0.995390i	$-0.530575\pi$
$857$	−5.61531			−0.191815			−0.0959076	+	0.995390i	$0.530575\pi$
$858$		0			0
$859$		−	27.4721i		−	0.937335i	−0.883375	−	0.468668i	$-0.844734\pi$
$859$		−	27.4721i		−	0.937335i	0.883375	−	0.468668i	$-0.155266\pi$
$860$	−7.50367	−	11.4198i	−0.255873	−	0.389411i
$861$		0			0
$862$	12.6837	−	23.5110i	0.432010	−	0.800789i
$863$	−42.8898			−1.45998			−0.729992	−	0.683456i	$-0.760476\pi$
$863$	−42.8898			−1.45998			−0.729992	+	0.683456i	$0.760476\pi$
$864$		0			0
$865$	6.58546			0.223912
$866$	14.7002	−	27.2489i	0.499534	−	0.925954i
$867$		0			0
$868$	0.211250	+	0.321500i	0.00717031	+	0.0109124i
$869$		−	40.3847i		−	1.36996i
$870$		0			0
$871$	−8.29273			−0.280988
$872$	3.61213	+	41.6047i	0.122322	+	1.40891i
$873$		0			0
$874$	−33.2860	−	17.9572i	−1.12592	−	0.607410i
$875$		−	1.31729i		−	0.0445325i
$876$		0			0
$877$			31.7005i			1.07045i	0.844709	+	0.535226i	$0.179773\pi$
$877$			31.7005i			1.07045i	−0.844709	+	0.535226i	$0.820227\pi$
$878$	−9.27131	+	17.1856i	−0.312891	+	0.579986i
$879$		0			0
$880$	−4.26396	+	9.86098i	−0.143738	+	0.332414i
$881$	44.4011			1.49591			0.747955	−	0.663749i	$-0.231036\pi$
$881$	44.4011			1.49591			0.747955	+	0.663749i	$0.231036\pi$
$882$		0			0
$883$			1.28287i			0.0431719i	0.999767	+	0.0215859i	$0.00687155\pi$
$883$			1.28287i			0.0431719i	−0.999767	+	0.0215859i	$0.993128\pi$
$884$	−1.67146	+	1.09828i	−0.0562173	+	0.0369391i
$885$		0			0
$886$	31.8325	+	17.1730i	1.06943	+	0.576939i
$887$	−41.5212			−1.39415			−0.697073	−	0.717001i	$-0.745514\pi$
$887$	−41.5212			−1.39415			−0.697073	+	0.717001i	$0.745514\pi$
$888$		0			0
$889$	0.892886			0.0299464
$890$	−6.68585	−	3.60688i	−0.224110	−	0.120903i
$891$		0			0
$892$	−7.82517	−	11.9091i	−0.262006	−	0.398745i
$893$			28.4998i			0.953708i
$894$		0			0
$895$	7.56090			0.252733
$896$	0.523299	−	1.57108i	0.0174822	−	0.0524860i
$897$		0			0
$898$	−16.3215	+	30.2541i	−0.544656	+	1.00959i
$899$			5.77323i			0.192548i
$900$		0			0
$901$		−	8.97858i		−	0.299120i
$902$	21.3717	+	11.5296i	0.711600	+	0.383894i
$903$		0			0
$904$	−11.1506	+	0.968095i	−0.370863	+	0.0321984i
$905$	0.628308			0.0208857
$906$		0			0
$907$			41.9834i			1.39404i	0.717054	+	0.697018i	$0.245490\pi$
$907$			41.9834i			1.39404i	−0.717054	+	0.697018i	$0.754510\pi$
$908$	−41.6791	+	27.3864i	−1.38317	+	0.908849i
$909$		0			0
$910$	−0.0982788	+	0.182173i	−0.00325791	+	0.00603898i
$911$	37.5443			1.24390			0.621949	−	0.783058i	$-0.286341\pi$
$911$	37.5443			1.24390			0.621949	+	0.783058i	$0.286341\pi$
$912$		0			0
$913$	−11.5296			−0.381575
$914$	−8.19235	+	15.1856i	−0.270979	+	0.502296i
$915$		0			0
$916$	4.94277	−	3.24778i	0.163314	−	0.107310i
$917$			2.17092i			0.0716902i
$918$		0			0
$919$	48.7005			1.60648			0.803241	−	0.595654i	$-0.203107\pi$
$919$	48.7005			1.60648			0.803241	+	0.595654i	$0.203107\pi$
$920$	1.63565	+	18.8396i	0.0539259	+	0.621122i
$921$		0			0
$922$	9.98382	+	5.38608i	0.328800	+	0.177381i
$923$		−	5.51806i		−	0.181629i
$924$		0			0
$925$			15.9143i			0.523259i
$926$	24.2113	−	44.8788i	0.795631	−	1.47481i
$927$		0			0
$928$	19.5107	−	15.3920i	0.640470	−	0.505268i
$929$	11.1281			0.365100			0.182550	−	0.983197i	$-0.441565\pi$
$929$	11.1281			0.365100			0.182550	+	0.983197i	$0.441565\pi$
$930$		0			0
$931$		−	27.9143i		−	0.914855i
$932$	−5.70264	−	8.67881i	−0.186796	−	0.284284i
$933$		0			0
$934$	−23.8793	−	12.8824i	−0.781354	−	0.421525i
$935$	−2.68585			−0.0878366
$936$		0			0
$937$	17.6153			0.575467			0.287733	−	0.957711i	$-0.407098\pi$
$937$	17.6153			0.575467			0.287733	+	0.957711i	$0.407098\pi$
$938$	1.51071	+	0.815000i	0.0493265	+	0.0266107i
$939$		0			0
$940$	11.9091	−	7.82517i	0.388431	−	0.255229i
$941$			35.6577i			1.16241i	0.813758	+	0.581204i	$0.197418\pi$
$941$			35.6577i			1.16241i	−0.813758	+	0.581204i	$0.802582\pi$
$942$		0			0
$943$	42.7434			1.39192
$944$	−45.3435	−	19.6069i	−1.47581	−	0.638150i
$945$		0			0
$946$	12.3215	−	22.8396i	0.400607	−	0.742578i
$947$		−	22.7715i		−	0.739976i	−0.929037	−	0.369988i	$-0.879362\pi$
$947$		−	22.7715i		−	0.739976i	0.929037	−	0.369988i	$-0.120638\pi$
$948$		0			0
$949$		−	6.97858i		−	0.226534i
$950$	−19.9143	−	10.7434i	−0.646105	−	0.348561i
$951$		0			0
$952$	0.412433	−	0.0358075i	0.0133670	−	0.00116053i
$953$	1.74338			0.0564738			0.0282369	−	0.999601i	$-0.491011\pi$
$953$	1.74338			0.0564738			0.0282369	+	0.999601i	$0.491011\pi$
$954$		0			0
$955$			10.1004i			0.326841i
$956$	−15.8111	−	24.0628i	−0.511367	−	0.778246i
$957$		0			0
$958$	−7.99789	+	14.8252i	−0.258400	+	0.478980i
$959$	1.42923			0.0461523
$960$		0			0
$961$	−29.2730			−0.944290
$962$	2.67146	−	4.95191i	0.0861314	−	0.159656i
$963$		0			0
$964$	−25.6216	−	38.9933i	−0.825215	−	1.25589i
$965$		−	3.37169i		−	0.108539i
$966$		0			0
$967$	−33.8402			−1.08823			−0.544113	−	0.839012i	$-0.683134\pi$
$967$	−33.8402			−1.08823			−0.544113	+	0.839012i	$0.683134\pi$
$968$	10.6689	−	0.926280i	0.342913	−	0.0297718i
$969$		0			0
$970$	12.8824	+	6.94981i	0.413629	+	0.223145i
$971$		−	40.0031i		−	1.28376i	−0.766804	−	0.641881i	$-0.778154\pi$
$971$		−	40.0031i		−	1.28376i	0.766804	−	0.641881i	$-0.221846\pi$
$972$		0			0
$973$			2.85050i			0.0913828i
$974$	10.6472	−	19.7360i	0.341159	−	0.632383i
$975$		0			0
$976$	−30.6577	−	13.2566i	−0.981329	−	0.424334i
$977$	−38.7005			−1.23814			−0.619070	−	0.785336i	$-0.712490\pi$
$977$	−38.7005			−1.23814			−0.619070	+	0.785336i	$0.712490\pi$
$978$		0			0
$979$		−	14.4275i		−	0.461106i
$980$	−11.6644	+	7.66442i	−0.372606	+	0.244831i
$981$		0			0
$982$	4.86802	+	2.62620i	0.155345	+	0.0838055i
$983$	−23.8536			−0.760813			−0.380406	−	0.924819i	$-0.624216\pi$
$983$	−23.8536			−0.760813			−0.380406	+	0.924819i	$0.624216\pi$
$984$		0			0
$985$	−14.7220			−0.469081
$986$	5.46787	+	2.94981i	0.174132	+	0.0939410i
$987$		0			0
$988$	4.39312	+	6.68585i	0.139764	+	0.212705i
$989$		−	45.6791i		−	1.45251i
$990$		0			0
$991$	−3.01300			−0.0957111			−0.0478556	−	0.998854i	$-0.515239\pi$
$991$	−3.01300			−0.0957111			−0.0478556	+	0.998854i	$0.515239\pi$
$992$	−4.60437	−	5.83642i	−0.146189	−	0.185307i
$993$		0			0
$994$	−0.542308	+	1.00524i	−0.0172010	+	0.0318843i
$995$		−	13.6644i		−	0.433191i
$996$		0			0
$997$			7.13650i			0.226015i	0.993594	+	0.113008i	$0.0360484\pi$
$997$			7.13650i			0.226015i	−0.993594	+	0.113008i	$0.963952\pi$
$998$	28.8500	+	15.5640i	0.913232	+	0.492671i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.c.469.2		6
3.2	odd	2		104.2.b.c.53.5	✓	6
4.3	odd	2		3744.2.g.c.1873.5		6
8.3	odd	2		3744.2.g.c.1873.2		6
8.5	even	2	inner	936.2.g.c.469.1		6
12.11	even	2		416.2.b.c.209.4		6
24.5	odd	2		104.2.b.c.53.6	yes	6
24.11	even	2		416.2.b.c.209.3		6
48.5	odd	4		3328.2.a.bh.1.2		3
48.11	even	4		3328.2.a.bf.1.2		3
48.29	odd	4		3328.2.a.be.1.2		3
48.35	even	4		3328.2.a.bg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.5	✓	6	3.2	odd	2
104.2.b.c.53.6	yes	6	24.5	odd	2
416.2.b.c.209.3		6	24.11	even	2
416.2.b.c.209.4		6	12.11	even	2
936.2.g.c.469.1		6	8.5	even	2	inner
936.2.g.c.469.2		6	1.1	even	1	trivial
3328.2.a.be.1.2		3	48.29	odd	4
3328.2.a.bf.1.2		3	48.11	even	4
3328.2.a.bg.1.2		3	48.35	even	4
3328.2.a.bh.1.2		3	48.5	odd	4
3744.2.g.c.1873.2		6	8.3	odd	2
3744.2.g.c.1873.5		6	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} +1.00000i q^{5} -0.146365 q^{7} +(2.81783 - 0.244644i) q^{8} +(-1.24464 - 0.671462i) q^{10} -2.68585i q^{11} +1.00000i q^{13} +(0.0982788 - 0.182173i) q^{14} +(-1.58757 + 3.67146i) q^{16} -1.00000 q^{17} +4.00000i q^{19} +(1.67146 - 1.09828i) q^{20} +(3.34292 + 1.80344i) q^{22} +6.68585 q^{23} +4.00000 q^{25} +(-1.24464 - 0.671462i) q^{26} +(0.160750 + 0.244644i) q^{28} +4.39312i q^{29} +1.31415 q^{31} +(-3.50367 - 4.44120i) q^{32} +(0.671462 - 1.24464i) q^{34} -0.146365i q^{35} +3.97858i q^{37} +(-4.97858 - 2.68585i) q^{38} +(0.244644 + 2.81783i) q^{40} +6.39312 q^{41} -6.83221i q^{43} +(-4.48929 + 2.94981i) q^{44} +(-4.48929 + 8.32150i) q^{46} +7.12494 q^{47} -6.97858 q^{49} +(-2.68585 + 4.97858i) q^{50} +(1.67146 - 1.09828i) q^{52} +8.97858i q^{53} +2.68585 q^{55} +(-0.412433 + 0.0358075i) q^{56} +(-5.46787 - 2.94981i) q^{58} +12.3503i q^{59} +8.35027i q^{61} +(-0.882404 + 1.63565i) q^{62} +(7.88030 - 1.37873i) q^{64} -1.00000 q^{65} +8.29273i q^{67} +(1.09828 + 1.67146i) q^{68} +(0.182173 + 0.0982788i) q^{70} -5.51806 q^{71} -6.97858 q^{73} +(-4.95191 - 2.67146i) q^{74} +(6.68585 - 4.39312i) q^{76} +0.393115i q^{77} +15.0361 q^{79} +(-3.67146 - 1.58757i) q^{80} +(-4.29273 + 7.95715i) q^{82} -4.29273i q^{83} -1.00000i q^{85} +(8.50367 + 4.58757i) q^{86} +(-0.657077 - 7.56825i) q^{88} +5.37169 q^{89} -0.146365i q^{91} +(-7.34292 - 11.1751i) q^{92} +(-4.78412 + 8.86802i) q^{94} -4.00000 q^{95} -10.3503 q^{97} +(4.68585 - 8.68585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Introduction

L-functions

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