LMFDB - Embedded newform 2340.2.g.b.1691.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(1691,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2340.1691"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-4,0,0,0,0,0,-4,0,0,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1691.26
Character	$\chi$	$=$	2340.1691
Dual form			2340.2.g.b.1691.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.273967 + 1.38742i) q^{2} +(-1.84988 + 0.760217i) q^{4} +1.00000i q^{5} +1.96615i q^{7} +(-1.56155 - 2.35830i) q^{8} +(-1.38742 + 0.273967i) q^{10} +4.36912 q^{11} +1.00000 q^{13} +(-2.72788 + 0.538660i) q^{14} +(2.84414 - 2.81263i) q^{16} +0.0716155i q^{17} +5.97650i q^{19} +(-0.760217 - 1.84988i) q^{20} +(1.19700 + 6.06182i) q^{22} +2.51552 q^{23} -1.00000 q^{25} +(0.273967 + 1.38742i) q^{26} +(-1.49470 - 3.63714i) q^{28} +8.97749i q^{29} -8.59947i q^{31} +(4.68150 + 3.17546i) q^{32} +(-0.0993610 + 0.0196203i) q^{34} -1.96615 q^{35} +7.61005 q^{37} +(-8.29193 + 1.63737i) q^{38} +(2.35830 - 1.56155i) q^{40} -0.210511i q^{41} +3.48595i q^{43} +(-8.08237 + 3.32148i) q^{44} +(0.689170 + 3.49009i) q^{46} -6.45364 q^{47} +3.13427 q^{49} +(-0.273967 - 1.38742i) q^{50} +(-1.84988 + 0.760217i) q^{52} +12.4170i q^{53} +4.36912i q^{55} +(4.63675 - 3.07023i) q^{56} +(-12.4556 + 2.45954i) q^{58} -4.78803 q^{59} -1.86816 q^{61} +(11.9311 - 2.35597i) q^{62} +(-3.12312 + 7.36520i) q^{64} +1.00000i q^{65} -1.41578i q^{67} +(-0.0544433 - 0.132480i) q^{68} +(-0.538660 - 2.72788i) q^{70} -5.02207 q^{71} -1.40955 q^{73} +(2.08490 + 10.5584i) q^{74} +(-4.54344 - 11.0558i) q^{76} +8.59033i q^{77} -8.61213i q^{79} +(2.81263 + 2.84414i) q^{80} +(0.292068 - 0.0576731i) q^{82} -5.88367 q^{83} -0.0716155 q^{85} +(-4.83648 + 0.955035i) q^{86} +(-6.82261 - 10.3037i) q^{88} +6.62764i q^{89} +1.96615i q^{91} +(-4.65342 + 1.91234i) q^{92} +(-1.76809 - 8.95393i) q^{94} -5.97650 q^{95} -9.32275 q^{97} +(0.858688 + 4.34856i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 4 q^{10} + 48 q^{13} - 36 q^{16} - 8 q^{22} - 48 q^{25} + 8 q^{28} + 8 q^{34} + 16 q^{37} + 4 q^{40} + 32 q^{46} - 64 q^{49} - 4 q^{52} + 72 q^{58} - 32 q^{61} - 28 q^{64} - 24 q^{70} - 48 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 - 4 * q^10 + 48 * q^13 - 36 * q^16 - 8 * q^22 - 48 * q^25 + 8 * q^28 + 8 * q^34 + 16 * q^37 + 4 * q^40 + 32 * q^46 - 64 * q^49 - 4 * q^52 + 72 * q^58 - 32 * q^61 - 28 * q^64 - 24 * q^70 - 48 * q^73 - 72 * q^76 + 48 * q^82 + 32 * q^85 - 24 * q^88 - 56 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	0.273967	+	1.38742i	0.193724	+	0.981056i
$2$	0.273967	+	1.38742i	0.193724	+	0.981056i
$3$		0			0
$3$		0			0
$4$	−1.84988	+	0.760217i	−0.924942	+	0.380108i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			1.96615i			0.743133i	0.928406	+	0.371567i	$0.121179\pi$
$7$			1.96615i			0.743133i	−0.928406	+	0.371567i	$0.878821\pi$
$8$	−1.56155	−	2.35830i	−0.552091	−	0.833784i
$9$		0			0
$10$	−1.38742	+	0.273967i	−0.438742	+	0.0866361i
$11$	4.36912			1.31734			0.658670	−	0.752432i	$-0.271119\pi$
$11$	4.36912			1.31734			0.658670	+	0.752432i	$0.271119\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−2.72788	+	0.538660i	−0.729055	+	0.143963i
$15$		0			0
$16$	2.84414	−	2.81263i	0.711035	−	0.703157i
$17$			0.0716155i			0.0173693i	0.999962	+	0.00868465i	$0.00276445\pi$
$17$			0.0716155i			0.0173693i	−0.999962	+	0.00868465i	$0.997236\pi$
$18$		0			0
$19$			5.97650i			1.37110i	0.728024	+	0.685552i	$0.240439\pi$
$19$			5.97650i			1.37110i	−0.728024	+	0.685552i	$0.759561\pi$
$20$	−0.760217	−	1.84988i	−0.169990	−	0.413647i
$21$		0			0
$22$	1.19700	+	6.06182i	0.255201	+	1.29238i
$23$	2.51552			0.524522			0.262261	−	0.964997i	$-0.415532\pi$
$23$	2.51552			0.524522			0.262261	+	0.964997i	$0.415532\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	0.273967	+	1.38742i	0.0537294	+	0.272096i
$27$		0			0
$28$	−1.49470	−	3.63714i	−0.282471	−	0.687355i
$29$			8.97749i			1.66708i	0.552461	+	0.833539i	$0.313689\pi$
$29$			8.97749i			1.66708i	−0.552461	+	0.833539i	$0.686311\pi$
$30$		0			0
$31$		−	8.59947i		−	1.54451i	−0.635313	−	0.772255i	$-0.719129\pi$
$31$		−	8.59947i		−	1.54451i	0.635313	−	0.772255i	$-0.280871\pi$
$32$	4.68150	+	3.17546i	0.827581	+	0.561347i
$33$		0			0
$34$	−0.0993610	+	0.0196203i	−0.0170403	+	0.00336485i
$35$	−1.96615			−0.332339
$36$		0			0
$37$	7.61005			1.25108			0.625542	−	0.780191i	$-0.284878\pi$
$37$	7.61005			1.25108			0.625542	+	0.780191i	$0.284878\pi$
$38$	−8.29193	+	1.63737i	−1.34513	+	0.265616i
$39$		0			0
$40$	2.35830	−	1.56155i	0.372879	−	0.246903i
$41$		−	0.210511i		−	0.0328763i	−0.999865	−	0.0164381i	$-0.994767\pi$
$41$		−	0.210511i		−	0.0328763i	0.999865	−	0.0164381i	$-0.00523266\pi$
$42$		0			0
$43$			3.48595i			0.531602i	0.964028	+	0.265801i	$0.0856364\pi$
$43$			3.48595i			0.531602i	−0.964028	+	0.265801i	$0.914364\pi$
$44$	−8.08237	+	3.32148i	−1.21846	+	0.500732i
$45$		0			0
$46$	0.689170	+	3.49009i	0.101613	+	0.514585i
$47$	−6.45364			−0.941361			−0.470680	−	0.882304i	$-0.655992\pi$
$47$	−6.45364			−0.941361			−0.470680	+	0.882304i	$0.655992\pi$
$48$		0			0
$49$	3.13427			0.447753
$50$	−0.273967	−	1.38742i	−0.0387448	−	0.196211i
$51$		0			0
$52$	−1.84988	+	0.760217i	−0.256533	+	0.105423i
$53$			12.4170i			1.70560i	0.522236	+	0.852801i	$0.325098\pi$
$53$			12.4170i			1.70560i	−0.522236	+	0.852801i	$0.674902\pi$
$54$		0			0
$55$			4.36912i			0.589133i
$56$	4.63675	−	3.07023i	0.619612	−	0.410277i
$57$		0			0
$58$	−12.4556	+	2.45954i	−1.63550	+	0.322953i
$59$	−4.78803			−0.623349			−0.311674	−	0.950189i	$-0.600890\pi$
$59$	−4.78803			−0.623349			−0.311674	+	0.950189i	$0.600890\pi$
$60$		0			0
$61$	−1.86816			−0.239193			−0.119597	−	0.992823i	$-0.538160\pi$
$61$	−1.86816			−0.239193			−0.119597	+	0.992823i	$0.538160\pi$
$62$	11.9311	−	2.35597i	1.51525	−	0.299209i
$63$		0			0
$64$	−3.12312	+	7.36520i	−0.390390	+	0.920649i
$65$			1.00000i			0.124035i
$66$		0			0
$67$		−	1.41578i		−	0.172965i	−0.996253	−	0.0864824i	$-0.972437\pi$
$67$		−	1.41578i		−	0.172965i	0.996253	−	0.0864824i	$-0.0275626\pi$
$68$	−0.0544433	−	0.132480i	−0.00660222	−	0.0160656i
$69$		0			0
$70$	−0.538660	−	2.72788i	−0.0643821	−	0.326043i
$71$	−5.02207			−0.596010			−0.298005	−	0.954564i	$-0.596321\pi$
$71$	−5.02207			−0.596010			−0.298005	+	0.954564i	$0.596321\pi$
$72$		0			0
$73$	−1.40955			−0.164975			−0.0824876	−	0.996592i	$-0.526286\pi$
$73$	−1.40955			−0.164975			−0.0824876	+	0.996592i	$0.526286\pi$
$74$	2.08490	+	10.5584i	0.242365	+	1.22738i
$75$		0			0
$76$	−4.54344	−	11.0558i	−0.521168	−	1.26819i
$77$			8.59033i			0.978959i
$78$		0			0
$79$		−	8.61213i		−	0.968940i	−0.874808	−	0.484470i	$-0.839012\pi$
$79$		−	8.61213i		−	0.968940i	0.874808	−	0.484470i	$-0.160988\pi$
$80$	2.81263	+	2.84414i	0.314461	+	0.317985i
$81$		0			0
$82$	0.292068	−	0.0576731i	0.0322535	−	0.00636893i
$83$	−5.88367			−0.645817			−0.322908	−	0.946430i	$-0.604661\pi$
$83$	−5.88367			−0.645817			−0.322908	+	0.946430i	$0.604661\pi$
$84$		0			0
$85$	−0.0716155			−0.00776779
$86$	−4.83648	+	0.955035i	−0.521531	+	0.102984i
$87$		0			0
$88$	−6.82261	−	10.3037i	−0.727292	−	1.09838i
$89$			6.62764i			0.702528i	0.936276	+	0.351264i	$0.114248\pi$
$89$			6.62764i			0.702528i	−0.936276	+	0.351264i	$0.885752\pi$
$90$		0			0
$91$			1.96615i			0.206108i
$92$	−4.65342	+	1.91234i	−0.485152	+	0.199375i
$93$		0			0
$94$	−1.76809	−	8.95393i	−0.182364	−	0.923528i
$95$	−5.97650			−0.613176
$96$		0			0
$97$	−9.32275			−0.946582			−0.473291	−	0.880906i	$-0.656934\pi$
$97$	−9.32275			−0.946582			−0.473291	+	0.880906i	$0.656934\pi$
$98$	0.858688	+	4.34856i	0.0867406	+	0.439271i
$99$		0			0
$100$	1.84988	−	0.760217i	0.184988	−	0.0760217i
$101$		−	3.75790i		−	0.373925i	−0.982367	−	0.186963i	$-0.940136\pi$
$101$		−	3.75790i		−	0.373925i	0.982367	−	0.186963i	$-0.0598643\pi$
$102$		0			0
$103$		−	14.8434i		−	1.46256i	−0.682077	−	0.731281i	$-0.738923\pi$
$103$		−	14.8434i		−	1.46256i	0.682077	−	0.731281i	$-0.261077\pi$
$104$	−1.56155	−	2.35830i	−0.153123	−	0.231250i
$105$		0			0
$106$	−17.2276	+	3.40184i	−1.67329	+	0.330416i
$107$	−14.1755			−1.37039			−0.685197	−	0.728357i	$-0.740284\pi$
$107$	−14.1755			−1.37039			−0.685197	+	0.728357i	$0.740284\pi$
$108$		0			0
$109$	8.37528			0.802206			0.401103	−	0.916033i	$-0.368627\pi$
$109$	8.37528			0.802206			0.401103	+	0.916033i	$0.368627\pi$
$110$	−6.06182	+	1.19700i	−0.577972	+	0.114129i
$111$		0			0
$112$	5.53003	+	5.59199i	0.522539	+	0.528394i
$113$			1.62190i			0.152575i	0.997086	+	0.0762876i	$0.0243067\pi$
$113$			1.62190i			0.152575i	−0.997086	+	0.0762876i	$0.975693\pi$
$114$		0			0
$115$			2.51552i			0.234573i
$116$	−6.82484	−	16.6073i	−0.633670	−	1.54195i
$117$		0			0
$118$	−1.31176	−	6.64302i	−0.120758	−	0.611540i
$119$	−0.140806			−0.0129077
$120$		0			0
$121$	8.08925			0.735386
$122$	−0.511814	−	2.59192i	−0.0463375	−	0.234662i
$123$		0			0
$124$	6.53746	+	15.9080i	0.587081	+	1.42858i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			6.46594i			0.573759i	0.957967	+	0.286880i	$0.0926179\pi$
$127$			6.46594i			0.573759i	−0.957967	+	0.286880i	$0.907382\pi$
$128$	−11.0743	−	2.31527i	−0.978837	−	0.204643i
$129$		0			0
$130$	−1.38742	+	0.273967i	−0.121685	+	0.0240285i
$131$	3.74851			0.327509			0.163754	−	0.986501i	$-0.447640\pi$
$131$	3.74851			0.327509			0.163754	+	0.986501i	$0.447640\pi$
$132$		0			0
$133$	−11.7507			−1.01891
$134$	1.96428	−	0.387877i	0.169688	−	0.0335074i
$135$		0			0
$136$	0.168891	−	0.111831i	0.0144822	−	0.00958944i
$137$			20.1321i			1.72000i	0.510293	+	0.860000i	$0.329537\pi$
$137$			20.1321i			1.72000i	−0.510293	+	0.860000i	$0.670463\pi$
$138$		0			0
$139$		−	22.0701i		−	1.87196i	−0.352051	−	0.935981i	$-0.614516\pi$
$139$		−	22.0701i		−	1.87196i	0.352051	−	0.935981i	$-0.385484\pi$
$140$	3.63714	−	1.49470i	0.307395	−	0.126325i
$141$		0			0
$142$	−1.37588	−	6.96774i	−0.115462	−	0.584720i
$143$	4.36912			0.365365
$144$		0			0
$145$	−8.97749			−0.745540
$146$	−0.386170	−	1.95564i	−0.0319597	−	0.161850i
$147$		0			0
$148$	−14.0777	+	5.78529i	−1.15718	+	0.475548i
$149$			6.70578i			0.549359i	0.961536	+	0.274680i	$0.0885718\pi$
$149$			6.70578i			0.549359i	−0.961536	+	0.274680i	$0.911428\pi$
$150$		0			0
$151$			14.6433i			1.19165i	0.803112	+	0.595827i	$0.203176\pi$
$151$			14.6433i			1.19165i	−0.803112	+	0.595827i	$0.796824\pi$
$152$	14.0944	−	9.33260i	1.14320	−	0.756974i
$153$		0			0
$154$	−11.9184	+	2.35347i	−0.960414	+	0.189648i
$155$	8.59947			0.690726
$156$		0			0
$157$	−7.75689			−0.619067			−0.309534	−	0.950888i	$-0.600173\pi$
$157$	−7.75689			−0.619067			−0.309534	+	0.950888i	$0.600173\pi$
$158$	11.9487	−	2.35944i	0.950585	−	0.187707i
$159$		0			0
$160$	−3.17546	+	4.68150i	−0.251042	+	0.370105i
$161$			4.94587i			0.389789i
$162$		0			0
$163$			3.65693i			0.286433i	0.989691	+	0.143217i	$0.0457445\pi$
$163$			3.65693i			0.286433i	−0.989691	+	0.143217i	$0.954255\pi$
$164$	0.160034	+	0.389421i	0.0124966	+	0.0304086i
$165$		0			0
$166$	−1.61193	−	8.16314i	−0.125110	−	0.633582i
$167$	14.8809			1.15152			0.575760	−	0.817619i	$-0.304706\pi$
$167$	14.8809			1.15152			0.575760	+	0.817619i	$0.304706\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−0.0196203	−	0.0993610i	−0.00150481	−	0.00762064i
$171$		0			0
$172$	−2.65008	−	6.44859i	−0.202066	−	0.491701i
$173$			2.65773i			0.202064i	0.994883	+	0.101032i	$0.0322144\pi$
$173$			2.65773i			0.202064i	−0.994883	+	0.101032i	$0.967786\pi$
$174$		0			0
$175$		−	1.96615i		−	0.148627i
$176$	12.4264	−	12.2887i	0.936675	−	0.926297i
$177$		0			0
$178$	−9.19534	+	1.81576i	−0.689220	+	0.136097i
$179$	−4.15872			−0.310837			−0.155419	−	0.987849i	$-0.549673\pi$
$179$	−4.15872			−0.310837			−0.155419	+	0.987849i	$0.549673\pi$
$180$		0			0
$181$	−6.25207			−0.464712			−0.232356	−	0.972631i	$-0.574644\pi$
$181$	−6.25207			−0.464712			−0.232356	+	0.972631i	$0.574644\pi$
$182$	−2.72788	+	0.538660i	−0.202204	+	0.0399281i
$183$		0			0
$184$	−3.92811	−	5.93234i	−0.289584	−	0.437338i
$185$			7.61005i			0.559502i
$186$		0			0
$187$			0.312897i			0.0228813i
$188$	11.9385	−	4.90617i	0.870704	−	0.357819i
$189$		0			0
$190$	−1.63737	−	8.29193i	−0.118787	−	0.601560i
$191$	11.0501			0.799556			0.399778	−	0.916612i	$-0.369087\pi$
$191$	11.0501			0.799556			0.399778	+	0.916612i	$0.369087\pi$
$192$		0			0
$193$	−16.9753			−1.22191			−0.610954	−	0.791666i	$-0.709214\pi$
$193$	−16.9753			−1.22191			−0.610954	+	0.791666i	$0.709214\pi$
$194$	−2.55413	−	12.9346i	−0.183376	−	0.928650i
$195$		0			0
$196$	−5.79804	+	2.38273i	−0.414146	+	0.170195i
$197$			6.51969i			0.464509i	0.972655	+	0.232255i	$0.0746102\pi$
$197$			6.51969i			0.464509i	−0.972655	+	0.232255i	$0.925390\pi$
$198$		0			0
$199$			11.3778i			0.806548i	0.915079	+	0.403274i	$0.132128\pi$
$199$			11.3778i			0.806548i	−0.915079	+	0.403274i	$0.867872\pi$
$200$	1.56155	+	2.35830i	0.110418	+	0.166757i
$201$		0			0
$202$	5.21380	−	1.02954i	0.366841	−	0.0724383i
$203$	−17.6510			−1.23886
$204$		0			0
$205$	0.210511			0.0147027
$206$	20.5940	−	4.06660i	1.43485	−	0.283333i
$207$		0			0
$208$	2.84414	−	2.81263i	0.197206	−	0.195021i
$209$			26.1121i			1.80621i
$210$		0			0
$211$			21.5436i			1.48312i	0.670886	+	0.741560i	$0.265914\pi$
$211$			21.5436i			1.48312i	−0.670886	+	0.741560i	$0.734086\pi$
$212$	−9.43959	−	22.9699i	−0.648314	−	1.57758i
$213$		0			0
$214$	−3.88362	−	19.6674i	−0.265479	−	1.34443i
$215$	−3.48595			−0.237740
$216$		0			0
$217$	16.9078			1.14778
$218$	2.29455	+	11.6201i	0.155407	+	0.787009i
$219$		0			0
$220$	−3.32148	−	8.08237i	−0.223934	−	0.544913i
$221$			0.0716155i			0.00481738i
$222$		0			0
$223$		−	25.1026i		−	1.68099i	−0.541816	−	0.840497i	$-0.682263\pi$
$223$		−	25.1026i		−	1.68099i	0.541816	−	0.840497i	$-0.317737\pi$
$224$	−6.24341	+	9.20452i	−0.417155	+	0.615003i
$225$		0			0
$226$	−2.25026	+	0.444346i	−0.149685	+	0.0295575i
$227$	−22.7277			−1.50849			−0.754246	−	0.656592i	$-0.771997\pi$
$227$	−22.7277			−1.50849			−0.754246	+	0.656592i	$0.771997\pi$
$228$		0			0
$229$	22.5945			1.49308			0.746542	−	0.665338i	$-0.231712\pi$
$229$	22.5945			1.49308			0.746542	+	0.665338i	$0.231712\pi$
$230$	−3.49009	+	0.689170i	−0.230129	+	0.0454425i
$231$		0			0
$232$	21.1716	−	14.0188i	1.38998	−	0.920379i
$233$		−	22.6564i		−	1.48427i	−0.670249	−	0.742136i	$-0.733813\pi$
$233$		−	22.6564i		−	1.48427i	0.670249	−	0.742136i	$-0.266187\pi$
$234$		0			0
$235$		−	6.45364i		−	0.420989i
$236$	8.85730	−	3.63994i	0.576561	−	0.236940i
$237$		0			0
$238$	−0.0385764	−	0.195358i	−0.00250053	−	0.0126632i
$239$	−13.0926			−0.846889			−0.423444	−	0.905922i	$-0.639179\pi$
$239$	−13.0926			−0.846889			−0.423444	+	0.905922i	$0.639179\pi$
$240$		0			0
$241$	4.59983			0.296301			0.148151	−	0.988965i	$-0.452668\pi$
$241$	4.59983			0.296301			0.148151	+	0.988965i	$0.452668\pi$
$242$	2.21619	+	11.2232i	0.142462	+	0.721455i
$243$		0			0
$244$	3.45587	−	1.42020i	0.221240	−	0.0909193i
$245$			3.13427i			0.200241i
$246$		0			0
$247$			5.97650i			0.380276i
$248$	−20.2801	+	13.4285i	−1.28779	+	0.852710i
$249$		0			0
$250$	1.38742	−	0.273967i	0.0877483	−	0.0173272i
$251$	28.8981			1.82403			0.912016	−	0.410155i	$-0.134525\pi$
$251$	28.8981			1.82403			0.912016	+	0.410155i	$0.134525\pi$
$252$		0			0
$253$	10.9906			0.690974
$254$	−8.97099	+	1.77146i	−0.562890	+	0.111151i
$255$		0			0
$256$	0.178269	−	15.9990i	0.0111418	−	0.999938i
$257$			12.6201i			0.787222i	0.919277	+	0.393611i	$0.128774\pi$
$257$			12.6201i			0.787222i	−0.919277	+	0.393611i	$0.871226\pi$
$258$		0			0
$259$			14.9625i			0.929722i
$260$	−0.760217	−	1.84988i	−0.0471467	−	0.114725i
$261$		0			0
$262$	1.02697	+	5.20077i	0.0634464	+	0.321305i
$263$	9.23080			0.569196			0.284598	−	0.958647i	$-0.408140\pi$
$263$	9.23080			0.569196			0.284598	+	0.958647i	$0.408140\pi$
$264$		0			0
$265$	−12.4170			−0.762768
$266$	−3.21930	−	16.3031i	−0.197388	−	0.999610i
$267$		0			0
$268$	1.07630	+	2.61902i	0.0657454	+	0.159982i
$269$		−	30.2419i		−	1.84388i	−0.387330	−	0.921941i	$-0.626603\pi$
$269$		−	30.2419i		−	1.84388i	0.387330	−	0.921941i	$-0.373397\pi$
$270$		0			0
$271$			14.1029i			0.856689i	0.903616	+	0.428344i	$0.140903\pi$
$271$			14.1029i			0.856689i	−0.903616	+	0.428344i	$0.859097\pi$
$272$	0.201428	+	0.203685i	0.0122133	+	0.0123502i
$273$		0			0
$274$	−27.9317	+	5.51554i	−1.68742	+	0.333206i
$275$	−4.36912			−0.263468
$276$		0			0
$277$	13.1165			0.788097			0.394048	−	0.919090i	$-0.371074\pi$
$277$	13.1165			0.788097			0.394048	+	0.919090i	$0.371074\pi$
$278$	30.6206	−	6.04649i	1.83650	−	0.362644i
$279$		0			0
$280$	3.07023	+	4.63675i	0.183482	+	0.277099i
$281$		−	8.11697i		−	0.484218i	−0.970249	−	0.242109i	$-0.922161\pi$
$281$		−	8.11697i		−	0.484218i	0.970249	−	0.242109i	$-0.0778392\pi$
$282$		0			0
$283$			1.08934i			0.0647546i	0.999476	+	0.0323773i	$0.0103078\pi$
$283$			1.08934i			0.0647546i	−0.999476	+	0.0323773i	$0.989692\pi$
$284$	9.29025	−	3.81787i	0.551275	−	0.226549i
$285$		0			0
$286$	1.19700	+	6.06182i	0.0707799	+	0.358443i
$287$	0.413895			0.0244315
$288$		0			0
$289$	16.9949			0.999698
$290$	−2.45954	−	12.4556i	−0.144429	−	0.731416i
$291$		0			0
$292$	2.60750	−	1.07156i	0.152593	−	0.0627085i
$293$			22.9490i			1.34070i	0.742047	+	0.670348i	$0.233855\pi$
$293$			22.9490i			1.34070i	−0.742047	+	0.670348i	$0.766145\pi$
$294$		0			0
$295$		−	4.78803i		−	0.278770i
$296$	−11.8835	−	17.9467i	−0.690713	−	1.04313i
$297$		0			0
$298$	−9.30376	+	1.83717i	−0.538952	+	0.106424i
$299$	2.51552			0.145476
$300$		0			0
$301$	−6.85388			−0.395051
$302$	−20.3164	+	4.01179i	−1.16908	+	0.230852i
$303$		0			0
$304$	16.8097	+	16.9980i	0.964100	+	0.974903i
$305$		−	1.86816i		−	0.106970i
$306$		0			0
$307$		−	24.5145i		−	1.39912i	−0.714575	−	0.699558i	$-0.753380\pi$
$307$		−	24.5145i		−	1.39912i	0.714575	−	0.699558i	$-0.246620\pi$
$308$	−6.53052	−	15.8911i	−0.372111	−	0.905481i
$309$		0			0
$310$	2.35597	+	11.9311i	0.133810	+	0.677641i
$311$	29.0810			1.64903			0.824517	−	0.565837i	$-0.191447\pi$
$311$	29.0810			1.64903			0.824517	+	0.565837i	$0.191447\pi$
$312$		0			0
$313$	7.12171			0.402543			0.201271	−	0.979535i	$-0.435493\pi$
$313$	7.12171			0.402543			0.201271	+	0.979535i	$0.435493\pi$
$314$	−2.12513	−	10.7621i	−0.119928	−	0.607340i
$315$		0			0
$316$	6.54709	+	15.9314i	0.368302	+	0.896213i
$317$			13.3640i			0.750598i	0.926904	+	0.375299i	$0.122460\pi$
$317$			13.3640i			0.750598i	−0.926904	+	0.375299i	$0.877540\pi$
$318$		0			0
$319$			39.2238i			2.19611i
$320$	−7.36520	−	3.12312i	−0.411727	−	0.174588i
$321$		0			0
$322$	−6.86202	+	1.35501i	−0.382405	+	0.0755116i
$323$	−0.428010			−0.0238151
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−5.07371	+	1.00188i	−0.281007	+	0.0554890i
$327$		0			0
$328$	−0.496447	+	0.328723i	−0.0274117	+	0.0181507i
$329$		−	12.6888i		−	0.699556i
$330$		0			0
$331$		−	26.6953i		−	1.46731i	−0.679525	−	0.733653i	$-0.737814\pi$
$331$		−	26.6953i		−	1.46731i	0.679525	−	0.733653i	$-0.262186\pi$
$332$	10.8841	−	4.47286i	0.597343	−	0.245480i
$333$		0			0
$334$	4.07688	+	20.6461i	0.223077	+	1.12971i
$335$	1.41578			0.0773522
$336$		0			0
$337$	−25.3169			−1.37910			−0.689549	−	0.724239i	$-0.742191\pi$
$337$	−25.3169			−1.37910			−0.689549	+	0.724239i	$0.742191\pi$
$338$	0.273967	+	1.38742i	0.0149019	+	0.0754658i
$339$		0			0
$340$	0.132480	−	0.0544433i	0.00718476	−	0.00295260i
$341$		−	37.5721i		−	2.03465i
$342$		0			0
$343$			19.9255i			1.07587i
$344$	8.22089	−	5.44348i	0.443241	−	0.293493i
$345$		0			0
$346$	−3.68740	+	0.728132i	−0.198236	+	0.0391446i
$347$	−16.5210			−0.886894			−0.443447	−	0.896301i	$-0.646244\pi$
$347$	−16.5210			−0.886894			−0.443447	+	0.896301i	$0.646244\pi$
$348$		0			0
$349$	21.7411			1.16377			0.581887	−	0.813270i	$-0.302315\pi$
$349$	21.7411			1.16377			0.581887	+	0.813270i	$0.302315\pi$
$350$	2.72788	−	0.538660i	0.145811	−	0.0287926i
$351$		0			0
$352$	20.4541	+	13.8740i	1.09021	+	0.739485i
$353$			29.0213i			1.54465i	0.635230	+	0.772323i	$0.280905\pi$
$353$			29.0213i			1.54465i	−0.635230	+	0.772323i	$0.719095\pi$
$354$		0			0
$355$		−	5.02207i		−	0.266544i
$356$	−5.03844	−	12.2604i	−0.267037	−	0.649798i
$357$		0			0
$358$	−1.13935	−	5.76991i	−0.0602167	−	0.304949i
$359$	31.0955			1.64116			0.820580	−	0.571532i	$-0.193651\pi$
$359$	31.0955			1.64116			0.820580	+	0.571532i	$0.193651\pi$
$360$		0			0
$361$	−16.7186			−0.879924
$362$	−1.71286	−	8.67426i	−0.0900260	−	0.455909i
$363$		0			0
$364$	−1.49470	−	3.63714i	−0.0783434	−	0.190638i
$365$		−	1.40955i		−	0.0737792i
$366$		0			0
$367$		−	21.0100i		−	1.09671i	−0.836245	−	0.548356i	$-0.815254\pi$
$367$		−	21.0100i		−	1.09671i	0.836245	−	0.548356i	$-0.184746\pi$
$368$	7.15449	−	7.07521i	0.372953	−	0.368821i
$369$		0			0
$370$	−10.5584	+	2.08490i	−0.548903	+	0.108389i
$371$	−24.4136			−1.26749
$372$		0			0
$373$	21.0508			1.08997			0.544984	−	0.838446i	$-0.316536\pi$
$373$	21.0508			1.08997			0.544984	+	0.838446i	$0.316536\pi$
$374$	−0.434120	+	0.0857235i	−0.0224478	+	0.00443266i
$375$		0			0
$376$	10.0777	+	15.2196i	0.519717	+	0.784891i
$377$			8.97749i			0.462364i
$378$		0			0
$379$		−	11.5894i		−	0.595310i	−0.954674	−	0.297655i	$-0.903795\pi$
$379$		−	11.5894i		−	0.595310i	0.954674	−	0.297655i	$-0.0962045\pi$
$380$	11.0558	−	4.54344i	0.567152	−	0.233073i
$381$		0			0
$382$	3.02736	+	15.3311i	0.154893	+	0.784409i
$383$	9.87863			0.504774			0.252387	−	0.967626i	$-0.418784\pi$
$383$	9.87863			0.504774			0.252387	+	0.967626i	$0.418784\pi$
$384$		0			0
$385$	−8.59033			−0.437804
$386$	−4.65068	−	23.5519i	−0.236713	−	1.19876i
$387$		0			0
$388$	17.2460	−	7.08731i	0.875534	−	0.359804i
$389$		−	1.06843i		−	0.0541716i	−0.999633	−	0.0270858i	$-0.991377\pi$
$389$		−	1.06843i		−	0.0541716i	0.999633	−	0.0270858i	$-0.00862274\pi$
$390$		0			0
$391$			0.180150i			0.00911058i
$392$	−4.89432	−	7.39154i	−0.247201	−	0.373329i
$393$		0			0
$394$	−9.04557	+	1.78618i	−0.455709	+	0.0899866i
$395$	8.61213			0.433323
$396$		0			0
$397$	32.7236			1.64235			0.821174	−	0.570677i	$-0.193319\pi$
$397$	32.7236			1.64235			0.821174	+	0.570677i	$0.193319\pi$
$398$	−15.7858	+	3.11713i	−0.791269	+	0.156248i
$399$		0			0
$400$	−2.84414	+	2.81263i	−0.142207	+	0.140631i
$401$		−	23.5346i		−	1.17526i	−0.809130	−	0.587630i	$-0.800061\pi$
$401$		−	23.5346i		−	1.17526i	0.809130	−	0.587630i	$-0.199939\pi$
$402$		0			0
$403$		−	8.59947i		−	0.428370i
$404$	2.85682	+	6.95168i	0.142132	+	0.345859i
$405$		0			0
$406$	−4.83581	−	24.4895i	−0.239997	−	1.21539i
$407$	33.2492			1.64810
$408$		0			0
$409$	18.4855			0.914047			0.457023	−	0.889455i	$-0.348916\pi$
$409$	18.4855			0.914047			0.457023	+	0.889455i	$0.348916\pi$
$410$	0.0576731	+	0.292068i	0.00284827	+	0.0144242i
$411$		0			0
$412$	11.2842	+	27.4585i	0.555932	+	1.35278i
$413$		−	9.41397i		−	0.463231i
$414$		0			0
$415$		−	5.88367i		−	0.288818i
$416$	4.68150	+	3.17546i	0.229530	+	0.155690i
$417$		0			0
$418$	−36.2285	+	7.15385i	−1.77199	+	0.349906i
$419$	2.83618			0.138557			0.0692783	−	0.997597i	$-0.477930\pi$
$419$	2.83618			0.138557			0.0692783	+	0.997597i	$0.477930\pi$
$420$		0			0
$421$	23.3525			1.13813			0.569066	−	0.822292i	$-0.307305\pi$
$421$	23.3525			1.13813			0.569066	+	0.822292i	$0.307305\pi$
$422$	−29.8900	+	5.90223i	−1.45502	+	0.287316i
$423$		0			0
$424$	29.2829	−	19.3897i	1.42210	−	0.941648i
$425$		−	0.0716155i		−	0.00347386i
$426$		0			0
$427$		−	3.67307i		−	0.177752i
$428$	26.2230	−	10.7764i	1.26754	−	0.520899i
$429$		0			0
$430$	−0.955035	−	4.83648i	−0.0460559	−	0.233236i
$431$	−27.5094			−1.32508			−0.662540	−	0.749027i	$-0.730521\pi$
$431$	−27.5094			−1.32508			−0.662540	+	0.749027i	$0.730521\pi$
$432$		0			0
$433$	31.5459			1.51600			0.757999	−	0.652256i	$-0.226177\pi$
$433$	31.5459			1.51600			0.757999	+	0.652256i	$0.226177\pi$
$434$	4.63219	+	23.4583i	0.222352	+	1.12603i
$435$		0			0
$436$	−15.4933	+	6.36703i	−0.741994	+	0.304925i
$437$			15.0340i			0.719173i
$438$		0			0
$439$			4.09067i			0.195237i	0.995224	+	0.0976186i	$0.0311225\pi$
$439$			4.09067i			0.195237i	−0.995224	+	0.0976186i	$0.968877\pi$
$440$	10.3037	−	6.82261i	0.491209	−	0.325255i
$441$		0			0
$442$	−0.0993610	+	0.0196203i	−0.00472612	+	0.000933243i
$443$	−28.1549			−1.33768			−0.668840	−	0.743406i	$-0.733209\pi$
$443$	−28.1549			−1.33768			−0.668840	+	0.743406i	$0.733209\pi$
$444$		0			0
$445$	−6.62764			−0.314180
$446$	34.8279	−	6.87729i	1.64915	−	0.325649i
$447$		0			0
$448$	−14.4810	−	6.14051i	−0.684165	−	0.290112i
$449$		−	22.3195i		−	1.05332i	−0.850076	−	0.526660i	$-0.823444\pi$
$449$		−	22.3195i		−	1.05332i	0.850076	−	0.526660i	$-0.176556\pi$
$450$		0			0
$451$		−	0.919748i		−	0.0433093i
$452$	−1.23299	−	3.00032i	−0.0579951	−	0.141123i
$453$		0			0
$454$	−6.22665	−	31.5330i	−0.292231	−	1.47992i
$455$	−1.96615			−0.0921743
$456$		0			0
$457$	−15.4945			−0.724800			−0.362400	−	0.932023i	$-0.618043\pi$
$457$	−15.4945			−0.724800			−0.362400	+	0.932023i	$0.618043\pi$
$458$	6.19015	+	31.3481i	0.289247	+	1.46480i
$459$		0			0
$460$	−1.91234	−	4.65342i	−0.0891633	−	0.216967i
$461$		−	7.45662i		−	0.347290i	−0.984808	−	0.173645i	$-0.944446\pi$
$461$		−	7.45662i		−	0.347290i	0.984808	−	0.173645i	$-0.0555545\pi$
$462$		0			0
$463$		−	32.9618i		−	1.53186i	−0.642922	−	0.765931i	$-0.722278\pi$
$463$		−	32.9618i		−	1.53186i	0.642922	−	0.765931i	$-0.277722\pi$
$464$	25.2503	+	25.5332i	1.17222	+	1.18535i
$465$		0			0
$466$	31.4341	−	6.20712i	1.45615	−	0.287539i
$467$	−2.89190			−0.133821			−0.0669105	−	0.997759i	$-0.521314\pi$
$467$	−2.89190			−0.133821			−0.0669105	+	0.997759i	$0.521314\pi$
$468$		0			0
$469$	2.78362			0.128536
$470$	8.95393	−	1.76809i	0.413014	−	0.0815558i
$471$		0			0
$472$	7.47675	+	11.2916i	0.344145	+	0.519738i
$473$			15.2305i			0.700301i
$474$		0			0
$475$		−	5.97650i		−	0.274221i
$476$	0.260476	−	0.107043i	0.0119389	−	0.00490633i
$477$		0			0
$478$	−3.58694	−	18.1649i	−0.164063	−	0.830845i
$479$	−32.3122			−1.47638			−0.738191	−	0.674591i	$-0.764320\pi$
$479$	−32.3122			−1.47638			−0.738191	+	0.674591i	$0.764320\pi$
$480$		0			0
$481$	7.61005			0.346988
$482$	1.26020	+	6.38191i	0.0574007	+	0.290688i
$483$		0			0
$484$	−14.9642	+	6.14958i	−0.680189	+	0.279526i
$485$		−	9.32275i		−	0.423324i
$486$		0			0
$487$			35.2835i			1.59885i	0.600766	+	0.799425i	$0.294862\pi$
$487$			35.2835i			1.59885i	−0.600766	+	0.799425i	$0.705138\pi$
$488$	2.91722	+	4.40567i	0.132056	+	0.199435i
$489$		0			0
$490$	−4.34856	+	0.858688i	−0.196448	+	0.0387916i
$491$	37.3751			1.68672			0.843358	−	0.537353i	$-0.180576\pi$
$491$	37.3751			1.68672			0.843358	+	0.537353i	$0.180576\pi$
$492$		0			0
$493$	−0.642927			−0.0289560
$494$	−8.29193	+	1.63737i	−0.373072	+	0.0736686i
$495$		0			0
$496$	−24.1871	−	24.4581i	−1.08603	−	1.09820i
$497$		−	9.87413i		−	0.442915i
$498$		0			0
$499$			22.3917i			1.00239i	0.865334	+	0.501196i	$0.167106\pi$
$499$			22.3917i			1.00239i	−0.865334	+	0.501196i	$0.832894\pi$
$500$	0.760217	+	1.84988i	0.0339979	+	0.0827293i
$501$		0			0
$502$	7.91713	+	40.0939i	0.353359	+	1.78948i
$503$	11.2378			0.501069			0.250534	−	0.968108i	$-0.419394\pi$
$503$	11.2378			0.501069			0.250534	+	0.968108i	$0.419394\pi$
$504$		0			0
$505$	3.75790			0.167224
$506$	3.01107	+	15.2486i	0.133858	+	0.677884i
$507$		0			0
$508$	−4.91551	−	11.9612i	−0.218091	−	0.530694i
$509$		−	17.1041i		−	0.758128i	−0.925371	−	0.379064i	$-0.876246\pi$
$509$		−	17.1041i		−	0.758128i	0.925371	−	0.379064i	$-0.123754\pi$
$510$		0			0
$511$		−	2.77138i		−	0.122599i
$512$	22.2462	−	4.13587i	0.983154	−	0.182781i
$513$		0			0
$514$	−17.5095	+	3.45750i	−0.772309	+	0.152504i
$515$	14.8434			0.654077
$516$		0			0
$517$	−28.1968			−1.24009
$518$	−20.7593	+	4.09922i	−0.912109	+	0.180110i
$519$		0			0
$520$	2.35830	−	1.56155i	0.103418	−	0.0684785i
$521$		−	1.92405i		−	0.0842940i	−0.999111	−	0.0421470i	$-0.986580\pi$
$521$		−	1.92405i		−	0.0842940i	0.999111	−	0.0421470i	$-0.0134198\pi$
$522$		0			0
$523$			22.4875i			0.983308i	0.870791	+	0.491654i	$0.163607\pi$
$523$			22.4875i			0.983308i	−0.870791	+	0.491654i	$0.836393\pi$
$524$	−6.93431	+	2.84968i	−0.302927	+	0.124489i
$525$		0			0
$526$	2.52894	+	12.8070i	0.110267	+	0.558413i
$527$	0.615855			0.0268271
$528$		0			0
$529$	−16.6722			−0.724877
$530$	−3.40184	−	17.2276i	−0.147767	−	0.748318i
$531$		0			0
$532$	21.7374	−	8.93306i	0.942435	−	0.387297i
$533$		−	0.210511i		−	0.00911824i
$534$		0			0
$535$		−	14.1755i		−	0.612859i
$536$	−3.33882	+	2.21081i	−0.144215	+	0.0954923i
$537$		0			0
$538$	41.9583	−	8.28530i	1.80895	−	0.357204i
$539$	13.6940			0.589843
$540$		0			0
$541$	4.58442			0.197099			0.0985497	−	0.995132i	$-0.468580\pi$
$541$	4.58442			0.197099			0.0985497	+	0.995132i	$0.468580\pi$
$542$	−19.5667	+	3.86373i	−0.840460	+	0.165961i
$543$		0			0
$544$	−0.227412	+	0.335268i	−0.00975021	+	0.0143745i
$545$			8.37528i			0.358758i
$546$		0			0
$547$		−	2.52726i		−	0.108058i	−0.998539	−	0.0540289i	$-0.982794\pi$
$547$		−	2.52726i		−	0.108058i	0.998539	−	0.0540289i	$-0.0172063\pi$
$548$	−15.3048	−	37.2420i	−0.653787	−	1.59090i
$549$		0			0
$550$	−1.19700	−	6.06182i	−0.0510401	−	0.258477i
$551$	−53.6540			−2.28574
$552$		0			0
$553$	16.9327			0.720052
$554$	3.59350	+	18.1982i	0.152673	+	0.773167i
$555$		0			0
$556$	16.7781	+	40.8271i	0.711548	+	1.73146i
$557$			35.7483i			1.51470i	0.653007	+	0.757352i	$0.273507\pi$
$557$			35.7483i			1.51470i	−0.653007	+	0.757352i	$0.726493\pi$
$558$		0			0
$559$			3.48595i			0.147440i
$560$	−5.59199	+	5.53003i	−0.236305	+	0.233687i
$561$		0			0
$562$	11.2617	−	2.22379i	0.475045	−	0.0938047i
$563$	−1.75915			−0.0741392			−0.0370696	−	0.999313i	$-0.511802\pi$
$563$	−1.75915			−0.0741392			−0.0370696	+	0.999313i	$0.511802\pi$
$564$		0			0
$565$	−1.62190			−0.0682337
$566$	−1.51138	+	0.298444i	−0.0635279	+	0.0125445i
$567$		0			0
$568$	7.84222	+	11.8435i	0.329052	+	0.496944i
$569$			10.1398i			0.425083i	0.977152	+	0.212541i	$0.0681740\pi$
$569$			10.1398i			0.425083i	−0.977152	+	0.212541i	$0.931826\pi$
$570$		0			0
$571$			19.5224i			0.816986i	0.912762	+	0.408493i	$0.133946\pi$
$571$			19.5224i			0.816986i	−0.912762	+	0.408493i	$0.866054\pi$
$572$	−8.08237	+	3.32148i	−0.337941	+	0.138878i
$573$		0			0
$574$	0.113394	+	0.574247i	0.00473296	+	0.0239686i
$575$	−2.51552			−0.104904
$576$		0			0
$577$	3.12050			0.129908			0.0649541	−	0.997888i	$-0.479310\pi$
$577$	3.12050			0.129908			0.0649541	+	0.997888i	$0.479310\pi$
$578$	4.65604	+	23.5791i	0.193666	+	0.980760i
$579$		0			0
$580$	16.6073	−	6.82484i	0.689581	−	0.283386i
$581$		−	11.5681i		−	0.479928i
$582$		0			0
$583$			54.2513i			2.24686i
$584$	2.20108	+	3.32414i	0.0910814	+	0.137554i
$585$		0			0
$586$	−31.8400	+	6.28728i	−1.31530	+	0.259725i
$587$	24.6002			1.01536			0.507679	−	0.861546i	$-0.330504\pi$
$587$	24.6002			1.01536			0.507679	+	0.861546i	$0.330504\pi$
$588$		0			0
$589$	51.3947			2.11768
$590$	6.64302	−	1.31176i	0.273489	−	0.0540045i
$591$		0			0
$592$	21.6440	−	21.4042i	0.889565	−	0.879708i
$593$		−	18.2108i		−	0.747826i	−0.927464	−	0.373913i	$-0.878016\pi$
$593$		−	18.2108i		−	0.747826i	0.927464	−	0.373913i	$-0.121984\pi$
$594$		0			0
$595$		−	0.140806i		−	0.00577250i
$596$	−5.09785	−	12.4049i	−0.208816	−	0.508125i
$597$		0			0
$598$	0.689170	+	3.49009i	0.0281822	+	0.142720i
$599$	−12.0439			−0.492102			−0.246051	−	0.969257i	$-0.579133\pi$
$599$	−12.0439			−0.492102			−0.246051	+	0.969257i	$0.579133\pi$
$600$		0			0
$601$	−14.6433			−0.597312			−0.298656	−	0.954361i	$-0.596538\pi$
$601$	−14.6433			−0.597312			−0.298656	+	0.954361i	$0.596538\pi$
$602$	−1.87774	−	9.50922i	−0.0765309	−	0.387567i
$603$		0			0
$604$	−11.1321	−	27.0884i	−0.452958	−	1.10221i
$605$			8.08925i			0.328875i
$606$		0			0
$607$			35.1183i			1.42541i	0.701465	+	0.712703i	$0.252529\pi$
$607$			35.1183i			1.42541i	−0.701465	+	0.712703i	$0.747471\pi$
$608$	−18.9781	+	27.9790i	−0.769665	+	1.13470i
$609$		0			0
$610$	2.59192	−	0.511814i	0.104944	−	0.0207227i
$611$	−6.45364			−0.261087
$612$		0			0
$613$	−15.3549			−0.620180			−0.310090	−	0.950707i	$-0.600359\pi$
$613$	−15.3549			−0.620180			−0.310090	+	0.950707i	$0.600359\pi$
$614$	34.0120	−	6.71617i	1.37261	−	0.271043i
$615$		0			0
$616$	20.2586	−	13.4142i	0.816240	−	0.540475i
$617$			36.4231i			1.46634i	0.680046	+	0.733170i	$0.261960\pi$
$617$			36.4231i			1.46634i	−0.680046	+	0.733170i	$0.738040\pi$
$618$		0			0
$619$			18.6214i			0.748459i	0.927336	+	0.374230i	$0.122093\pi$
$619$			18.6214i			0.748459i	−0.927336	+	0.374230i	$0.877907\pi$
$620$	−15.9080	+	6.53746i	−0.638881	+	0.262551i
$621$		0			0
$622$	7.96726	+	40.3477i	0.319458	+	1.61780i
$623$	−13.0309			−0.522072
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.95112	+	9.88083i	0.0779823	+	0.394917i
$627$		0			0
$628$	14.3493	−	5.89692i	0.572601	−	0.235313i
$629$			0.544997i			0.0217305i
$630$		0			0
$631$		−	46.0313i		−	1.83248i	−0.400635	−	0.916238i	$-0.631210\pi$
$631$		−	46.0313i		−	1.83248i	0.400635	−	0.916238i	$-0.368790\pi$
$632$	−20.3100	+	13.4483i	−0.807886	+	0.534943i
$633$		0			0
$634$	−18.5415	+	3.66130i	−0.736379	+	0.145409i
$635$	−6.46594			−0.256593
$636$		0			0
$637$	3.13427			0.124184
$638$	−54.4199	+	10.7460i	−2.15451	+	0.425439i
$639$		0			0
$640$	2.31527	−	11.0743i	0.0915191	−	0.437749i
$641$		−	27.4870i		−	1.08567i	−0.839840	−	0.542835i	$-0.817351\pi$
$641$		−	27.4870i		−	1.08567i	0.839840	−	0.542835i	$-0.182649\pi$
$642$		0			0
$643$			10.8672i			0.428561i	0.976772	+	0.214280i	$0.0687406\pi$
$643$			10.8672i			0.428561i	−0.976772	+	0.214280i	$0.931259\pi$
$644$	−3.75994	−	9.14929i	−0.148162	−	0.360533i
$645$		0			0
$646$	−0.117261	−	0.593831i	−0.00461356	−	0.0233640i
$647$	−31.4787			−1.23756			−0.618778	−	0.785566i	$-0.712372\pi$
$647$	−31.4787			−1.23756			−0.618778	+	0.785566i	$0.712372\pi$
$648$		0			0
$649$	−20.9195			−0.821162
$650$	−0.273967	−	1.38742i	−0.0107459	−	0.0544192i
$651$		0			0
$652$	−2.78006	−	6.76490i	−0.108876	−	0.264934i
$653$		−	3.96525i		−	0.155172i	−0.996986	−	0.0775861i	$-0.975279\pi$
$653$		−	3.96525i		−	0.155172i	0.996986	−	0.0775861i	$-0.0247213\pi$
$654$		0			0
$655$			3.74851i			0.146466i
$656$	−0.592088	−	0.598722i	−0.0231172	−	0.0233762i
$657$		0			0
$658$	17.6047	−	3.47632i	0.686304	−	0.135521i
$659$	−3.47093			−0.135208			−0.0676041	−	0.997712i	$-0.521535\pi$
$659$	−3.47093			−0.135208			−0.0676041	+	0.997712i	$0.521535\pi$
$660$		0			0
$661$	28.5987			1.11236			0.556180	−	0.831062i	$-0.312267\pi$
$661$	28.5987			1.11236			0.556180	+	0.831062i	$0.312267\pi$
$662$	37.0376	−	7.31364i	1.43951	−	0.284253i
$663$		0			0
$664$	9.18764	+	13.8754i	0.356550	+	0.538471i
$665$		−	11.7507i		−	0.455671i
$666$		0			0
$667$			22.5830i			0.874418i
$668$	−27.5280	+	11.3127i	−1.06509	+	0.437702i
$669$		0			0
$670$	0.387877	+	1.96428i	0.0149850	+	0.0758868i
$671$	−8.16221			−0.315099
$672$		0			0
$673$	−18.7837			−0.724059			−0.362029	−	0.932167i	$-0.617916\pi$
$673$	−18.7837			−0.724059			−0.362029	+	0.932167i	$0.617916\pi$
$674$	−6.93599	−	35.1252i	−0.267164	−	1.35297i
$675$		0			0
$676$	−1.84988	+	0.760217i	−0.0711494	+	0.0292391i
$677$			27.7053i			1.06480i	0.846493	+	0.532400i	$0.178710\pi$
$677$			27.7053i			1.06480i	−0.846493	+	0.532400i	$0.821290\pi$
$678$		0			0
$679$		−	18.3299i		−	0.703437i
$680$	0.111831	+	0.168891i	0.00428853	+	0.00647666i
$681$		0			0
$682$	52.1284	−	10.2935i	1.99610	−	0.394160i
$683$	20.1958			0.772771			0.386386	−	0.922337i	$-0.373723\pi$
$683$	20.1958			0.772771			0.386386	+	0.922337i	$0.373723\pi$
$684$		0			0
$685$	−20.1321			−0.769208
$686$	−27.6450	+	5.45892i	−1.05549	+	0.208423i
$687$		0			0
$688$	9.80466	+	9.91452i	0.373799	+	0.377988i
$689$			12.4170i			0.473049i
$690$		0			0
$691$		−	9.80840i		−	0.373129i	−0.982443	−	0.186565i	$-0.940265\pi$
$691$		−	9.80840i		−	0.373129i	0.982443	−	0.186565i	$-0.0597354\pi$
$692$	−2.02045	−	4.91649i	−0.0768061	−	0.186897i
$693$		0			0
$694$	−4.52621	−	22.9216i	−0.171813	−	0.870092i
$695$	22.0701			0.837167
$696$		0			0
$697$	0.0150758			0.000571038
$698$	5.95634	+	30.1641i	0.225451	+	1.14173i
$699$		0			0
$700$	1.49470	+	3.63714i	0.0564942	+	0.137471i
$701$		−	30.5947i		−	1.15555i	−0.816198	−	0.577773i	$-0.803922\pi$
$701$		−	30.5947i		−	1.15555i	0.816198	−	0.577773i	$-0.196078\pi$
$702$		0			0
$703$			45.4814i			1.71537i
$704$	−13.6453	+	32.1795i	−0.514277	+	1.21281i
$705$		0			0
$706$	−40.2648	+	7.95088i	−1.51538	+	0.299235i
$707$	7.38858			0.277876
$708$		0			0
$709$	13.1974			0.495639			0.247819	−	0.968806i	$-0.420286\pi$
$709$	13.1974			0.495639			0.247819	+	0.968806i	$0.420286\pi$
$710$	6.96774	−	1.37588i	0.261495	−	0.0516360i
$711$		0			0
$712$	15.6299	−	10.3494i	0.585757	−	0.387860i
$713$		−	21.6321i		−	0.810129i
$714$		0			0
$715$			4.36912i			0.163396i
$716$	7.69315	−	3.16153i	0.287507	−	0.118152i
$717$		0			0
$718$	8.51916	+	43.1427i	0.317932	+	1.61007i
$719$	−4.65845			−0.173731			−0.0868654	−	0.996220i	$-0.527685\pi$
$719$	−4.65845			−0.173731			−0.0868654	+	0.996220i	$0.527685\pi$
$720$		0			0
$721$	29.1842			1.08688
$722$	−4.58034	−	23.1957i	−0.170463	−	0.863255i
$723$		0			0
$724$	11.5656	−	4.75293i	0.429832	−	0.176641i
$725$		−	8.97749i		−	0.333416i
$726$		0			0
$727$		−	24.8319i		−	0.920966i	−0.887669	−	0.460483i	$-0.847676\pi$
$727$		−	24.8319i		−	0.920966i	0.887669	−	0.460483i	$-0.152324\pi$
$728$	4.63675	−	3.07023i	0.171850	−	0.113790i
$729$		0			0
$730$	1.95564	−	0.386170i	0.0723815	−	0.0142928i
$731$	−0.249648			−0.00923356
$732$		0			0
$733$	33.3378			1.23136			0.615680	−	0.787996i	$-0.288881\pi$
$733$	33.3378			1.23136			0.615680	+	0.787996i	$0.288881\pi$
$734$	29.1497	−	5.75605i	1.07594	−	0.212460i
$735$		0			0
$736$	11.7764	+	7.98792i	0.434084	+	0.294439i
$737$		−	6.18571i		−	0.227853i
$738$		0			0
$739$		−	37.3362i		−	1.37343i	−0.726925	−	0.686717i	$-0.759051\pi$
$739$		−	37.3362i		−	1.37343i	0.726925	−	0.686717i	$-0.240949\pi$
$740$	−5.78529	−	14.0777i	−0.212671	−	0.517507i
$741$		0			0
$742$	−6.68852	−	33.8719i	−0.245543	−	1.24348i
$743$	−20.2606			−0.743290			−0.371645	−	0.928375i	$-0.621206\pi$
$743$	−20.2606			−0.743290			−0.371645	+	0.928375i	$0.621206\pi$
$744$		0			0
$745$	−6.70578			−0.245681
$746$	5.76723	+	29.2063i	0.211153	+	1.06932i
$747$		0			0
$748$	−0.237870	−	0.578823i	−0.00869737	−	0.0211639i
$749$		−	27.8710i		−	1.01839i
$750$		0			0
$751$		−	20.3727i		−	0.743410i	−0.928351	−	0.371705i	$-0.878773\pi$
$751$		−	20.3727i		−	0.743410i	0.928351	−	0.371705i	$-0.121227\pi$
$752$	−18.3551	+	18.1517i	−0.669341	+	0.661924i
$753$		0			0
$754$	−12.4556	+	2.45954i	−0.453605	+	0.0895711i
$755$	−14.6433			−0.532924
$756$		0			0
$757$	−23.6535			−0.859702			−0.429851	−	0.902900i	$-0.641434\pi$
$757$	−23.6535			−0.859702			−0.429851	+	0.902900i	$0.641434\pi$
$758$	16.0795	−	3.17513i	0.584032	−	0.115326i
$759$		0			0
$760$	9.33260	+	14.0944i	0.338529	+	0.511256i
$761$			21.7465i			0.788311i	0.919044	+	0.394156i	$0.128963\pi$
$761$			21.7465i			0.788311i	−0.919044	+	0.394156i	$0.871037\pi$
$762$		0			0
$763$			16.4670i			0.596146i
$764$	−20.4414	+	8.40046i	−0.739543	+	0.303918i
$765$		0			0
$766$	2.70642	+	13.7058i	0.0977870	+	0.495212i
$767$	−4.78803			−0.172886
$768$		0			0
$769$	−18.5715			−0.669705			−0.334852	−	0.942271i	$-0.608686\pi$
$769$	−18.5715			−0.669705			−0.334852	+	0.942271i	$0.608686\pi$
$770$	−2.35347	−	11.9184i	−0.0848132	−	0.429510i
$771$		0			0
$772$	31.4023	−	12.9049i	1.13019	−	0.464458i
$773$		−	18.5196i		−	0.666102i	−0.942909	−	0.333051i	$-0.891922\pi$
$773$		−	18.5196i		−	0.666102i	0.942909	−	0.333051i	$-0.108078\pi$
$774$		0			0
$775$			8.59947i			0.308902i
$776$	14.5579	+	21.9858i	0.522600	+	0.789245i
$777$		0			0
$778$	1.48237	−	0.292715i	0.0531454	−	0.0104944i
$779$	1.25812			0.0450768
$780$		0			0
$781$	−21.9421			−0.785149
$782$	−0.249944	+	0.0493552i	−0.00893799	+	0.00176494i
$783$		0			0
$784$	8.91431	−	8.81553i	0.318368	−	0.314841i
$785$		−	7.75689i		−	0.276855i
$786$		0			0
$787$		−	0.0382658i		−	0.00136403i	−1.00000		0.000682015i	$-0.999783\pi$
$787$		−	0.0382658i		−	0.00136403i	1.00000		0.000682015i	$-0.000217092\pi$
$788$	−4.95638	−	12.0607i	−0.176564	−	0.429644i
$789$		0			0
$790$	2.35944	+	11.9487i	0.0839452	+	0.425114i
$791$	−3.18888			−0.113384
$792$		0			0
$793$	−1.86816			−0.0663402
$794$	8.96519	+	45.4014i	0.318163	+	1.61124i
$795$		0			0
$796$	−8.64957	−	21.0475i	−0.306576	−	0.746010i
$797$		−	15.3623i		−	0.544160i	−0.962275	−	0.272080i	$-0.912288\pi$
$797$		−	15.3623i		−	0.544160i	0.962275	−	0.272080i	$-0.0877115\pi$
$798$		0			0
$799$		−	0.462181i		−	0.0163508i
$800$	−4.68150	−	3.17546i	−0.165516	−	0.112269i
$801$		0			0
$802$	32.6524	−	6.44770i	1.15300	−	0.227676i
$803$	−6.15850			−0.217329
$804$		0			0
$805$	−4.94587			−0.174319
$806$	11.9311	−	2.35597i	0.420255	−	0.0829856i
$807$		0			0
$808$	−8.86224	+	5.86815i	−0.311773	+	0.206441i
$809$		−	15.0561i		−	0.529344i	−0.964338	−	0.264672i	$-0.914736\pi$
$809$		−	15.0561i		−	0.529344i	0.964338	−	0.264672i	$-0.0852637\pi$
$810$		0			0
$811$		−	22.8262i		−	0.801537i	−0.916179	−	0.400769i	$-0.868743\pi$
$811$		−	22.8262i		−	0.801537i	0.916179	−	0.400769i	$-0.131257\pi$
$812$	32.6524	−	13.4186i	1.14587	−	0.470901i
$813$		0			0
$814$	9.10920	+	46.1307i	0.319277	+	1.61688i
$815$	−3.65693			−0.128097
$816$		0			0
$817$	−20.8338			−0.728881
$818$	5.06441	+	25.6471i	0.177073	+	0.896731i
$819$		0			0
$820$	−0.389421	+	0.160034i	−0.0135992	+	0.00558863i
$821$			4.29951i			0.150054i	0.997181	+	0.0750271i	$0.0239043\pi$
$821$			4.29951i			0.150054i	−0.997181	+	0.0750271i	$0.976096\pi$
$822$		0			0
$823$		−	36.9597i		−	1.28833i	−0.764885	−	0.644167i	$-0.777204\pi$
$823$		−	36.9597i		−	1.28833i	0.764885	−	0.644167i	$-0.222796\pi$
$824$	−35.0051	+	23.1787i	−1.21946	+	0.807467i
$825$		0			0
$826$	13.0611	−	2.57912i	0.454456	−	0.0897390i
$827$	41.1068			1.42942			0.714711	−	0.699419i	$-0.246558\pi$
$827$	41.1068			1.42942			0.714711	+	0.699419i	$0.246558\pi$
$828$		0			0
$829$	50.0130			1.73702			0.868512	−	0.495668i	$-0.165077\pi$
$829$	50.0130			1.73702			0.868512	+	0.495668i	$0.165077\pi$
$830$	8.16314	−	1.61193i	0.283347	−	0.0559510i
$831$		0			0
$832$	−3.12312	+	7.36520i	−0.108275	+	0.255342i
$833$			0.224462i			0.00777716i
$834$		0			0
$835$			14.8809i			0.514975i
$836$	−19.8508	−	48.3043i	−0.686556	−	1.67064i
$837$		0			0
$838$	0.777021	+	3.93498i	0.0268418	+	0.135932i
$839$	31.5788			1.09022			0.545111	−	0.838364i	$-0.316488\pi$
$839$	31.5788			1.09022			0.545111	+	0.838364i	$0.316488\pi$
$840$		0			0
$841$	−51.5953			−1.77915
$842$	6.39783	+	32.3998i	0.220484	+	1.11657i
$843$		0			0
$844$	−16.3778	−	39.8531i	−0.563747	−	1.37180i
$845$			1.00000i			0.0344010i
$846$		0			0
$847$			15.9046i			0.546490i
$848$	34.9243	+	35.3156i	1.19930	+	1.21274i
$849$		0			0
$850$	0.0993610	−	0.0196203i	0.00340805	−	0.000672971i
$851$	19.1432			0.656221
$852$		0			0
$853$	−7.10627			−0.243314			−0.121657	−	0.992572i	$-0.538821\pi$
$853$	−7.10627			−0.243314			−0.121657	+	0.992572i	$0.538821\pi$
$854$	5.09610	−	1.00630i	0.174385	−	0.0344349i
$855$		0			0
$856$	22.1357	+	33.4300i	0.756583	+	1.14261i
$857$		−	9.93212i		−	0.339275i	−0.985507	−	0.169637i	$-0.945740\pi$
$857$		−	9.93212i		−	0.339275i	0.985507	−	0.169637i	$-0.0542597\pi$
$858$		0			0
$859$		−	49.8487i		−	1.70082i	−0.526123	−	0.850408i	$-0.676355\pi$
$859$		−	49.8487i		−	1.70082i	0.526123	−	0.850408i	$-0.323645\pi$
$860$	6.44859	−	2.65008i	0.219895	−	0.0903668i
$861$		0			0
$862$	−7.53667	−	38.1671i	−0.256700	−	1.29998i
$863$	10.5237			0.358232			0.179116	−	0.983828i	$-0.442676\pi$
$863$	10.5237			0.358232			0.179116	+	0.983828i	$0.442676\pi$
$864$		0			0
$865$	−2.65773			−0.0903656
$866$	8.64253	+	43.7674i	0.293685	+	1.48728i
$867$		0			0
$868$	−31.2775	+	12.8536i	−1.06163	+	0.436280i
$869$		−	37.6275i		−	1.27642i
$870$		0			0
$871$		−	1.41578i		−	0.0479718i
$872$	−13.0784	−	19.7514i	−0.442891	−	0.668866i
$873$		0			0
$874$	−20.8585	+	4.11882i	−0.705549	+	0.139321i
$875$	1.96615			0.0664679
$876$		0			0
$877$	20.6188			0.696248			0.348124	−	0.937448i	$-0.386819\pi$
$877$	20.6188			0.696248			0.348124	+	0.937448i	$0.386819\pi$
$878$	−5.67549	+	1.12071i	−0.191539	+	0.0378221i
$879$		0			0
$880$	12.2887	+	12.4264i	0.414252	+	0.418894i
$881$			44.6191i			1.50326i	0.659587	+	0.751628i	$0.270731\pi$
$881$			44.6191i			1.50326i	−0.659587	+	0.751628i	$0.729269\pi$
$882$		0			0
$883$		−	39.5436i		−	1.33075i	−0.746510	−	0.665374i	$-0.768272\pi$
$883$		−	39.5436i		−	1.33075i	0.746510	−	0.665374i	$-0.231728\pi$
$884$	−0.0544433	−	0.132480i	−0.00183113	−	0.00445580i
$885$		0			0
$886$	−7.71352	−	39.0628i	−0.259141	−	1.31234i
$887$	13.9851			0.469572			0.234786	−	0.972047i	$-0.424561\pi$
$887$	13.9851			0.469572			0.234786	+	0.972047i	$0.424561\pi$
$888$		0			0
$889$	−12.7130			−0.426379
$890$	−1.81576	−	9.19534i	−0.0608643	−	0.308228i
$891$		0			0
$892$	19.0834	+	46.4369i	0.638960	+	1.55482i
$893$		−	38.5702i		−	1.29070i
$894$		0			0
$895$		−	4.15872i		−	0.139011i
$896$	4.55216	−	21.7736i	0.152077	−	0.727406i
$897$		0			0
$898$	30.9665	−	6.11480i	1.03337	−	0.204054i
$899$	77.2016			2.57482
$900$		0			0
$901$	−0.889247			−0.0296251
$902$	1.27608	−	0.251981i	0.0424888	−	0.00839005i
$903$		0			0
$904$	3.82491	−	2.53267i	0.127215	−	0.0842354i
$905$		−	6.25207i		−	0.207826i
$906$		0			0
$907$		−	20.0084i		−	0.664369i	−0.943215	−	0.332184i	$-0.892214\pi$
$907$		−	20.0084i		−	0.664369i	0.943215	−	0.332184i	$-0.107786\pi$
$908$	42.0437	−	17.2780i	1.39527	−	0.573391i
$909$		0			0
$910$	−0.538660	−	2.72788i	−0.0178564	−	0.0904282i
$911$	25.4179			0.842133			0.421067	−	0.907030i	$-0.361656\pi$
$911$	25.4179			0.842133			0.421067	+	0.907030i	$0.361656\pi$
$912$		0			0
$913$	−25.7065			−0.850760
$914$	−4.24497	−	21.4974i	−0.140411	−	0.711069i
$915$		0			0
$916$	−41.7972	+	17.1767i	−1.38102	+	0.567534i
$917$			7.37012i			0.243383i
$918$		0			0
$919$			29.8031i			0.983113i	0.870846	+	0.491556i	$0.163572\pi$
$919$			29.8031i			0.983113i	−0.870846	+	0.491556i	$0.836428\pi$
$920$	5.93234	−	3.92811i	0.195583	−	0.129506i
$921$		0			0
$922$	10.3455	−	2.04287i	0.340711	−	0.0672784i
$923$	−5.02207			−0.165304
$924$		0			0
$925$	−7.61005			−0.250217
$926$	45.7319	−	9.03044i	1.50284	−	0.296759i
$927$		0			0
$928$	−28.5076	+	42.0281i	−0.935809	+	1.37964i
$929$		−	29.4051i		−	0.964751i	−0.875965	−	0.482375i	$-0.839774\pi$
$929$		−	29.4051i		−	0.964751i	0.875965	−	0.482375i	$-0.160226\pi$
$930$		0			0
$931$			18.7320i			0.613916i
$932$	17.2238	+	41.9118i	0.564185	+	1.37287i
$933$		0			0
$934$	−0.792285	−	4.01228i	−0.0259244	−	0.131286i
$935$	−0.312897			−0.0102328
$936$		0			0
$937$	−53.4921			−1.74751			−0.873755	−	0.486366i	$-0.838322\pi$
$937$	−53.4921			−1.74751			−0.873755	+	0.486366i	$0.838322\pi$
$938$	0.762622	+	3.86206i	0.0249005	+	0.126101i
$939$		0			0
$940$	4.90617	+	11.9385i	0.160022	+	0.389391i
$941$		−	1.22264i		−	0.0398570i	−0.999801	−	0.0199285i	$-0.993656\pi$
$941$		−	1.22264i		−	0.0398570i	0.999801	−	0.0199285i	$-0.00634385\pi$
$942$		0			0
$943$		−	0.529544i		−	0.0172443i
$944$	−13.6178	+	13.4669i	−0.443223	+	0.438312i
$945$		0			0
$946$	−21.1312	+	4.17267i	−0.687034	+	0.135665i
$947$	−20.3261			−0.660510			−0.330255	−	0.943892i	$-0.607135\pi$
$947$	−20.3261			−0.660510			−0.330255	+	0.943892i	$0.607135\pi$
$948$		0			0
$949$	−1.40955			−0.0457559
$950$	8.29193	−	1.63737i	0.269026	−	0.0531232i
$951$		0			0
$952$	0.219876	+	0.332063i	0.00712623	+	0.0107622i
$953$		−	28.0582i		−	0.908895i	−0.890774	−	0.454448i	$-0.849837\pi$
$953$		−	28.0582i		−	0.908895i	0.890774	−	0.454448i	$-0.150163\pi$
$954$		0			0
$955$			11.0501i			0.357572i
$956$	24.2198	−	9.95320i	0.783323	−	0.321910i
$957$		0			0
$958$	−8.85249	−	44.8307i	−0.286011	−	1.44841i
$959$	−39.5826			−1.27819
$960$		0			0
$961$	−42.9508			−1.38551
$962$	2.08490	+	10.5584i	0.0672200	+	0.340415i
$963$		0			0
$964$	−8.50915	+	3.49687i	−0.274061	+	0.112627i
$965$		−	16.9753i		−	0.546454i
$966$		0			0
$967$		−	2.24165i		−	0.0720867i	−0.999350	−	0.0360433i	$-0.988525\pi$
$967$		−	2.24165i		−	0.0720867i	0.999350	−	0.0360433i	$-0.0114754\pi$
$968$	−12.6318	−	19.0768i	−0.406000	−	0.613153i
$969$		0			0
$970$	12.9346	−	2.55413i	0.415305	−	0.0820082i
$971$	33.9202			1.08855			0.544275	−	0.838907i	$-0.316805\pi$
$971$	33.9202			1.08855			0.544275	+	0.838907i	$0.316805\pi$
$972$		0			0
$973$	43.3930			1.39112
$974$	−48.9532	+	9.66653i	−1.56856	+	0.309736i
$975$		0			0
$976$	−5.31330	+	5.25443i	−0.170075	+	0.168190i
$977$			54.6863i			1.74957i	0.484510	+	0.874786i	$0.338998\pi$
$977$			54.6863i			1.74957i	−0.484510	+	0.874786i	$0.661002\pi$
$978$		0			0
$979$			28.9570i			0.925469i
$980$	−2.38273	−	5.79804i	−0.0761134	−	0.185212i
$981$		0			0
$982$	10.2396	+	51.8551i	0.326757	+	1.65476i
$983$	22.4014			0.714495			0.357247	−	0.934010i	$-0.383715\pi$
$983$	22.4014			0.714495			0.357247	+	0.934010i	$0.383715\pi$
$984$		0			0
$985$	−6.51969			−0.207735
$986$	−0.176141	−	0.892012i	−0.00560947	−	0.0284074i
$987$		0			0
$988$	−4.54344	−	11.0558i	−0.144546	−	0.351733i
$989$			8.76896i			0.278837i
$990$		0			0
$991$		−	28.1329i		−	0.893671i	−0.894616	−	0.446835i	$-0.852551\pi$
$991$		−	28.1329i		−	0.893671i	0.894616	−	0.446835i	$-0.147449\pi$
$992$	27.3072	−	40.2584i	0.867006	−	1.27821i
$993$		0			0
$994$	13.6996	−	2.70519i	0.434525	−	0.0858034i
$995$	−11.3778			−0.360699
$996$		0			0
$997$	−34.5199			−1.09326			−0.546628	−	0.837375i	$-0.684089\pi$
$997$	−34.5199			−1.09326			−0.546628	+	0.837375i	$0.684089\pi$
$998$	−31.0668	+	6.13460i	−0.983403	+	0.194187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.g.b.1691.26	yes	48
3.2	odd	2	inner	2340.2.g.b.1691.23	✓	48
4.3	odd	2	inner	2340.2.g.b.1691.24	yes	48
12.11	even	2	inner	2340.2.g.b.1691.25	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2340.2.g.b.1691.23	✓	48	3.2	odd	2	inner
2340.2.g.b.1691.24	yes	48	4.3	odd	2	inner
2340.2.g.b.1691.25	yes	48	12.11	even	2	inner
2340.2.g.b.1691.26	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273967 + 1.38742i) q^{2} +(-1.84988 + 0.760217i) q^{4} +1.00000i q^{5} +1.96615i q^{7} +(-1.56155 - 2.35830i) q^{8} +(-1.38742 + 0.273967i) q^{10} +4.36912 q^{11} +1.00000 q^{13} +(-2.72788 + 0.538660i) q^{14} +(2.84414 - 2.81263i) q^{16} +0.0716155i q^{17} +5.97650i q^{19} +(-0.760217 - 1.84988i) q^{20} +(1.19700 + 6.06182i) q^{22} +2.51552 q^{23} -1.00000 q^{25} +(0.273967 + 1.38742i) q^{26} +(-1.49470 - 3.63714i) q^{28} +8.97749i q^{29} -8.59947i q^{31} +(4.68150 + 3.17546i) q^{32} +(-0.0993610 + 0.0196203i) q^{34} -1.96615 q^{35} +7.61005 q^{37} +(-8.29193 + 1.63737i) q^{38} +(2.35830 - 1.56155i) q^{40} -0.210511i q^{41} +3.48595i q^{43} +(-8.08237 + 3.32148i) q^{44} +(0.689170 + 3.49009i) q^{46} -6.45364 q^{47} +3.13427 q^{49} +(-0.273967 - 1.38742i) q^{50} +(-1.84988 + 0.760217i) q^{52} +12.4170i q^{53} +4.36912i q^{55} +(4.63675 - 3.07023i) q^{56} +(-12.4556 + 2.45954i) q^{58} -4.78803 q^{59} -1.86816 q^{61} +(11.9311 - 2.35597i) q^{62} +(-3.12312 + 7.36520i) q^{64} +1.00000i q^{65} -1.41578i q^{67} +(-0.0544433 - 0.132480i) q^{68} +(-0.538660 - 2.72788i) q^{70} -5.02207 q^{71} -1.40955 q^{73} +(2.08490 + 10.5584i) q^{74} +(-4.54344 - 11.0558i) q^{76} +8.59033i q^{77} -8.61213i q^{79} +(2.81263 + 2.84414i) q^{80} +(0.292068 - 0.0576731i) q^{82} -5.88367 q^{83} -0.0716155 q^{85} +(-4.83648 + 0.955035i) q^{86} +(-6.82261 - 10.3037i) q^{88} +6.62764i q^{89} +1.96615i q^{91} +(-4.65342 + 1.91234i) q^{92} +(-1.76809 - 8.95393i) q^{94} -5.97650 q^{95} -9.32275 q^{97} +(0.858688 + 4.34856i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 4 q^{10} + 48 q^{13} - 36 q^{16} - 8 q^{22} - 48 q^{25} + 8 q^{28} + 8 q^{34} + 16 q^{37} + 4 q^{40} + 32 q^{46} - 64 q^{49} - 4 q^{52} + 72 q^{58} - 32 q^{61} - 28 q^{64} - 24 q^{70} - 48 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 - 4 * q^10 + 48 * q^13 - 36 * q^16 - 8 * q^22 - 48 * q^25 + 8 * q^28 + 8 * q^34 + 16 * q^37 + 4 * q^40 + 32 * q^46 - 64 * q^49 - 4 * q^52 + 72 * q^58 - 32 * q^61 - 28 * q^64 - 24 * q^70 - 48 * q^73 - 72 * q^76 + 48 * q^82 + 32 * q^85 - 24 * q^88 - 56 * q^94 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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