LMFDB - Embedded newform 240.4.v.e.17.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,4,Mod(17,240)] 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("240.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 2, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	240.v (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$14.1604584014$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	240.17
Dual form			240.4.v.e.113.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89532 - 4.83816i) q^{3} +(-8.68358 - 7.04240i) q^{5} +(20.0016 + 20.0016i) q^{7} +(-19.8155 + 18.3397i) q^{9} +46.6382i q^{11} +(-20.2990 + 20.2990i) q^{13} +(-17.6141 + 55.3601i) q^{15} +(59.4675 - 59.4675i) q^{17} -81.9818i q^{19} +(58.8615 - 134.680i) q^{21} +(98.2169 + 98.2169i) q^{23} +(25.8093 + 122.307i) q^{25} +(126.287 + 61.1113i) q^{27} -18.6120 q^{29} +278.039 q^{31} +(225.643 - 88.3942i) q^{33} +(-32.8264 - 314.545i) q^{35} +(-81.9050 - 81.9050i) q^{37} +(136.683 + 59.7366i) q^{39} +211.462i q^{41} +(-168.539 + 168.539i) q^{43} +(301.225 - 19.7052i) q^{45} +(-24.9885 + 24.9885i) q^{47} +457.128i q^{49} +(-400.423 - 175.003i) q^{51} +(54.7526 + 54.7526i) q^{53} +(328.445 - 404.987i) q^{55} +(-396.641 + 155.382i) q^{57} -158.559 q^{59} +892.804 q^{61} +(-763.166 - 29.5197i) q^{63} +(319.221 - 33.3144i) q^{65} +(407.354 + 407.354i) q^{67} +(289.037 - 661.341i) q^{69} +286.035i q^{71} +(-588.912 + 588.912i) q^{73} +(542.821 - 356.679i) q^{75} +(-932.839 + 932.839i) q^{77} -693.142i q^{79} +(56.3120 - 726.822i) q^{81} +(735.453 + 735.453i) q^{83} +(-935.184 + 97.5973i) q^{85} +(35.2757 + 90.0480i) q^{87} +755.886 q^{89} -812.023 q^{91} +(-526.972 - 1345.20i) q^{93} +(-577.349 + 711.896i) q^{95} +(-760.157 - 760.157i) q^{97} +(-855.330 - 924.162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{7} + 24 q^{13} + 12 q^{15} + 32 q^{21} + 72 q^{25} + 168 q^{27} - 216 q^{31} + 204 q^{33} + 576 q^{37} - 464 q^{45} + 816 q^{51} + 372 q^{55} - 1160 q^{57} + 72 q^{61} + 628 q^{63} + 1080 q^{67}+ \cdots + 2172 q^{97}+O(q^{100}) $ 36 * q + 12 * q^7 + 24 * q^13 + 12 * q^15 + 32 * q^21 + 72 * q^25 + 168 * q^27 - 216 * q^31 + 204 * q^33 + 576 * q^37 - 464 * q^45 + 816 * q^51 + 372 * q^55 - 1160 * q^57 + 72 * q^61 + 628 * q^63 + 1080 * q^67 - 900 * q^73 - 720 * q^75 + 1196 * q^81 + 912 * q^85 - 1660 * q^87 - 4080 * q^91 + 2568 * q^93 + 2172 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.89532	−	4.83816i	−0.364754	−	0.931104i
$3$	−1.89532	−	4.83816i	−0.364754	−	0.931104i
$4$		0			0
$5$	−8.68358	−	7.04240i	−0.776683	−	0.629891i
$5$	−8.68358	−	7.04240i	−0.776683	−	0.629891i
$6$		0			0
$7$	20.0016	+	20.0016i	1.07998	+	1.07998i	0.996510	+	0.0834747i	$0.0266018\pi$
$7$	20.0016	+	20.0016i	1.07998	+	1.07998i	0.0834747	+	0.996510i	$0.473398\pi$
$8$		0			0
$9$	−19.8155	+	18.3397i	−0.733909	+	0.679248i
$10$		0			0
$11$			46.6382i			1.27836i	0.769058	+	0.639180i	$0.220726\pi$
$11$			46.6382i			1.27836i	−0.769058	+	0.639180i	$0.779274\pi$
$12$		0			0
$13$	−20.2990	+	20.2990i	−0.433071	+	0.433071i	−0.889672	−	0.456601i	$-0.849067\pi$
$13$	−20.2990	+	20.2990i	−0.433071	+	0.433071i	0.456601	+	0.889672i	$0.349067\pi$
$14$		0			0
$15$	−17.6141	+	55.3601i	−0.303196	+	0.952928i
$16$		0			0
$17$	59.4675	−	59.4675i	0.848410	−	0.848410i	−0.141524	−	0.989935i	$-0.545200\pi$
$17$	59.4675	−	59.4675i	0.848410	−	0.848410i	0.989935	+	0.141524i	$0.0452004\pi$
$18$		0			0
$19$		−	81.9818i		−	0.989891i	−0.868924	−	0.494945i	$-0.835188\pi$
$19$		−	81.9818i		−	0.989891i	0.868924	−	0.494945i	$-0.164812\pi$
$20$		0			0
$21$	58.8615	−	134.680i	0.611649	−	1.39951i
$22$		0			0
$23$	98.2169	+	98.2169i	0.890419	+	0.890419i	0.994562	−	0.104143i	$-0.0332100\pi$
$23$	98.2169	+	98.2169i	0.890419	+	0.890419i	−0.104143	+	0.994562i	$0.533210\pi$
$24$		0			0
$25$	25.8093	+	122.307i	0.206474	+	0.978452i
$26$		0			0
$27$	126.287	+	61.1113i	0.900146	+	0.435588i
$28$		0			0
$29$	−18.6120			−0.119178			−0.0595891	−	0.998223i	$-0.518979\pi$
$29$	−18.6120			−0.119178			−0.0595891	+	0.998223i	$0.518979\pi$
$30$		0			0
$31$	278.039			1.61088			0.805440	−	0.592677i	$-0.201929\pi$
$31$	278.039			1.61088			0.805440	+	0.592677i	$0.201929\pi$
$32$		0			0
$33$	225.643	−	88.3942i	1.19029	−	0.466286i
$34$		0			0
$35$	−32.8264	−	314.545i	−0.158533	−	1.51908i
$36$		0			0
$37$	−81.9050	−	81.9050i	−0.363922	−	0.363922i	0.501333	−	0.865255i	$-0.332843\pi$
$37$	−81.9050	−	81.9050i	−0.363922	−	0.363922i	−0.865255	+	0.501333i	$0.832843\pi$
$38$		0			0
$39$	136.683	+	59.7366i	0.561198	+	0.245270i
$40$		0			0
$41$			211.462i			0.805483i	0.915314	+	0.402741i	$0.131943\pi$
$41$			211.462i			0.805483i	−0.915314	+	0.402741i	$0.868057\pi$
$42$		0			0
$43$	−168.539	+	168.539i	−0.597719	+	0.597719i	−0.939705	−	0.341986i	$-0.888900\pi$
$43$	−168.539	+	168.539i	−0.597719	+	0.597719i	0.341986	+	0.939705i	$0.388900\pi$
$44$		0			0
$45$	301.225	−	19.7052i	0.997867	−	0.0652774i
$46$		0			0
$47$	−24.9885	+	24.9885i	−0.0775519	+	0.0775519i	−0.744819	−	0.667267i	$-0.767464\pi$
$47$	−24.9885	+	24.9885i	−0.0775519	+	0.0775519i	0.667267	+	0.744819i	$0.267464\pi$
$48$		0			0
$49$			457.128i			1.33273i
$50$		0			0
$51$	−400.423	−	175.003i	−1.09942	−	0.480497i
$52$		0			0
$53$	54.7526	+	54.7526i	0.141903	+	0.141903i	0.774490	−	0.632587i	$-0.218007\pi$
$53$	54.7526	+	54.7526i	0.141903	+	0.141903i	−0.632587	+	0.774490i	$0.718007\pi$
$54$		0			0
$55$	328.445	−	404.987i	0.805227	−	0.992880i
$56$		0			0
$57$	−396.641	+	155.382i	−0.921691	+	0.361066i
$58$		0			0
$59$	−158.559			−0.349875			−0.174938	−	0.984580i	$-0.555972\pi$
$59$	−158.559			−0.349875			−0.174938	+	0.984580i	$0.555972\pi$
$60$		0			0
$61$	892.804			1.87397			0.936983	−	0.349376i	$-0.113606\pi$
$61$	892.804			1.87397			0.936983	+	0.349376i	$0.113606\pi$
$62$		0			0
$63$	−763.166	−	29.5197i	−1.52619	−	0.0590338i
$64$		0			0
$65$	319.221	−	33.3144i	0.609146	−	0.0635715i
$66$		0			0
$67$	407.354	+	407.354i	0.742779	+	0.742779i	0.973112	−	0.230333i	$-0.0739815\pi$
$67$	407.354	+	407.354i	0.742779	+	0.742779i	−0.230333	+	0.973112i	$0.573982\pi$
$68$		0			0
$69$	289.037	−	661.341i	0.504289	−	1.15386i
$70$		0			0
$71$			286.035i			0.478114i	0.971005	+	0.239057i	$0.0768384\pi$
$71$			286.035i			0.478114i	−0.971005	+	0.239057i	$0.923162\pi$
$72$		0			0
$73$	−588.912	+	588.912i	−0.944205	+	0.944205i	−0.998524	−	0.0543187i	$-0.982701\pi$
$73$	−588.912	+	588.912i	−0.944205	+	0.944205i	0.0543187	+	0.998524i	$0.482701\pi$
$74$		0			0
$75$	542.821	−	356.679i	0.835728	−	0.549143i
$76$		0			0
$77$	−932.839	+	932.839i	−1.38061	+	1.38061i
$78$		0			0
$79$		−	693.142i		−	0.987147i	−0.869704	−	0.493574i	$-0.835690\pi$
$79$		−	693.142i		−	0.987147i	0.869704	−	0.493574i	$-0.164310\pi$
$80$		0			0
$81$	56.3120	−	726.822i	0.0772456	−	0.997012i
$82$		0			0
$83$	735.453	+	735.453i	0.972608	+	0.972608i	0.999635	−	0.0270266i	$-0.00860388\pi$
$83$	735.453	+	735.453i	0.972608	+	0.972608i	−0.0270266	+	0.999635i	$0.508604\pi$
$84$		0			0
$85$	−935.184	+	97.5973i	−1.19335	+	0.124540i
$86$		0			0
$87$	35.2757	+	90.0480i	0.0434707	+	0.110967i
$88$		0			0
$89$	755.886			0.900267			0.450134	−	0.892961i	$-0.351376\pi$
$89$	755.886			0.900267			0.450134	+	0.892961i	$0.351376\pi$
$90$		0			0
$91$	−812.023			−0.935420
$92$		0			0
$93$	−526.972	−	1345.20i	−0.587575	−	1.49990i
$94$		0			0
$95$	−577.349	+	711.896i	−0.623523	+	0.768832i
$96$		0			0
$97$	−760.157	−	760.157i	−0.795693	−	0.795693i	0.186720	−	0.982413i	$-0.440214\pi$
$97$	−760.157	−	760.157i	−0.795693	−	0.795693i	−0.982413	+	0.186720i	$0.940214\pi$
$98$		0			0
$99$	−855.330	−	924.162i	−0.868322	−	0.938200i
$100$		0			0
$101$			716.614i			0.705998i	0.935624	+	0.352999i	$0.114838\pi$
$101$			716.614i			0.705998i	−0.935624	+	0.352999i	$0.885162\pi$
$102$		0			0
$103$	−569.425	+	569.425i	−0.544729	+	0.544729i	−0.924912	−	0.380182i	$-0.875861\pi$
$103$	−569.425	+	569.425i	−0.544729	+	0.544729i	0.380182	+	0.924912i	$0.375861\pi$
$104$		0			0
$105$	−1459.60	+	754.981i	−1.35659	+	0.701701i
$106$		0			0
$107$	−1001.35	+	1001.35i	−0.904708	+	0.904708i	−0.995839	−	0.0911311i	$-0.970952\pi$
$107$	−1001.35	+	1001.35i	−0.904708	+	0.904708i	0.0911311	+	0.995839i	$0.470952\pi$
$108$		0			0
$109$		−	1381.20i		−	1.21372i	−0.794810	−	0.606859i	$-0.792429\pi$
$109$		−	1381.20i		−	1.21372i	0.794810	−	0.606859i	$-0.207571\pi$
$110$		0			0
$111$	−241.033	+	551.505i	−0.206107	+	0.471591i
$112$		0			0
$113$	−63.5803	−	63.5803i	−0.0529304	−	0.0529304i	0.680146	−	0.733077i	$-0.261916\pi$
$113$	−63.5803	−	63.5803i	−0.0529304	−	0.0529304i	−0.733077	+	0.680146i	$0.761916\pi$
$114$		0			0
$115$	−161.192	−	1544.56i	−0.130707	−	1.25244i
$116$		0			0
$117$	29.9586	−	774.512i	0.0236724	−	0.611997i
$118$		0			0
$119$	2378.89			1.83254
$120$		0			0
$121$	−844.123			−0.634202
$122$		0			0
$123$	1023.09	−	400.787i	0.749988	−	0.293803i
$124$		0			0
$125$	637.214	−	1243.82i	0.455953	−	0.890004i
$126$		0			0
$127$	−136.284	−	136.284i	−0.0952223	−	0.0952223i	0.657891	−	0.753113i	$-0.271449\pi$
$127$	−136.284	−	136.284i	−0.0952223	−	0.0952223i	−0.753113	+	0.657891i	$0.771449\pi$
$128$		0			0
$129$	1134.85	+	495.983i	0.774558	+	0.338518i
$130$		0			0
$131$			1841.43i			1.22814i	0.789250	+	0.614072i	$0.210469\pi$
$131$			1841.43i			1.22814i	−0.789250	+	0.614072i	$0.789531\pi$
$132$		0			0
$133$	1639.77	−	1639.77i	1.06907	−	1.06907i
$134$		0			0
$135$	−666.254	−	1420.03i	−0.424756	−	0.905308i
$136$		0			0
$137$	−981.558	+	981.558i	−0.612118	+	0.612118i	−0.943498	−	0.331380i	$-0.892486\pi$
$137$	−981.558	+	981.558i	−0.612118	+	0.612118i	0.331380	+	0.943498i	$0.392486\pi$
$138$		0			0
$139$			176.398i			0.107639i	0.998551	+	0.0538197i	$0.0171396\pi$
$139$			176.398i			0.107639i	−0.998551	+	0.0538197i	$0.982860\pi$
$140$		0			0
$141$	168.259	+	73.5371i	0.100496	+	0.0439215i
$142$		0			0
$143$	−946.708	−	946.708i	−0.553620	−	0.553620i
$144$		0			0
$145$	161.619	+	131.073i	0.0925637	+	0.0750693i
$146$		0			0
$147$	2211.66	−	866.402i	1.24091	−	0.486120i
$148$		0			0
$149$	−131.583			−0.0723472			−0.0361736	−	0.999346i	$-0.511517\pi$
$149$	−131.583			−0.0723472			−0.0361736	+	0.999346i	$0.511517\pi$
$150$		0			0
$151$	−561.623			−0.302677			−0.151338	−	0.988482i	$-0.548358\pi$
$151$	−561.623			−0.302677			−0.151338	+	0.988482i	$0.548358\pi$
$152$		0			0
$153$	−87.7660	+	2268.99i	−0.0463756	+	1.19894i
$154$		0			0
$155$	−2414.38	−	1958.06i	−1.25114	−	1.01468i
$156$		0			0
$157$	271.743	+	271.743i	0.138137	+	0.138137i	0.772794	−	0.634657i	$-0.218859\pi$
$157$	271.743	+	271.743i	0.138137	+	0.138137i	−0.634657	+	0.772794i	$0.718859\pi$
$158$		0			0
$159$	161.128	−	368.675i	0.0803667	−	0.183886i
$160$		0			0
$161$			3928.99i			1.92328i
$162$		0			0
$163$	−1418.77	+	1418.77i	−0.681758	+	0.681758i	−0.960396	−	0.278638i	$-0.910117\pi$
$163$	−1418.77	+	1418.77i	−0.681758	+	0.681758i	0.278638	+	0.960396i	$0.410117\pi$
$164$		0			0
$165$	−2581.90	−	821.490i	−1.21818	−	0.387593i
$166$		0			0
$167$	−550.935	+	550.935i	−0.255285	+	0.255285i	−0.823133	−	0.567848i	$-0.807776\pi$
$167$	−550.935	+	550.935i	−0.255285	+	0.255285i	0.567848	+	0.823133i	$0.307776\pi$
$168$		0			0
$169$			1372.90i			0.624899i
$170$		0			0
$171$	1503.52	+	1624.52i	0.672381	+	0.726490i
$172$		0			0
$173$	−1689.62	−	1689.62i	−0.742540	−	0.742540i	0.230526	−	0.973066i	$-0.425955\pi$
$173$	−1689.62	−	1689.62i	−0.742540	−	0.742540i	−0.973066	+	0.230526i	$0.925955\pi$
$174$		0			0
$175$	−1930.10	+	2962.55i	−0.833724	+	1.27970i
$176$		0			0
$177$	300.520	+	767.134i	0.127618	+	0.325770i
$178$		0			0
$179$	2315.44			0.966840			0.483420	−	0.875388i	$-0.339394\pi$
$179$	2315.44			0.966840			0.483420	+	0.875388i	$0.339394\pi$
$180$		0			0
$181$	2698.22			1.10805			0.554025	−	0.832500i	$-0.313091\pi$
$181$	2698.22			1.10805			0.554025	+	0.832500i	$0.313091\pi$
$182$		0			0
$183$	−1692.15	−	4319.53i	−0.683536	−	1.74486i
$184$		0			0
$185$	134.421	+	1288.04i	0.0534209	+	0.511883i
$186$		0			0
$187$	2773.46	+	2773.46i	1.08457	+	1.08457i
$188$		0			0
$189$	1303.62	+	3748.26i	0.501716	+	1.44257i
$190$		0			0
$191$		−	1845.08i		−	0.698982i	−0.936940	−	0.349491i	$-0.886354\pi$
$191$		−	1845.08i		−	0.698982i	0.936940	−	0.349491i	$-0.113646\pi$
$192$		0			0
$193$	124.064	−	124.064i	0.0462713	−	0.0462713i	−0.683593	−	0.729864i	$-0.739583\pi$
$193$	124.064	−	124.064i	0.0462713	−	0.0462713i	0.729864	+	0.683593i	$0.239583\pi$
$194$		0			0
$195$	−766.206	−	1481.30i	−0.281380	−	0.543991i
$196$		0			0
$197$	1972.25	−	1972.25i	0.713285	−	0.713285i	−0.253936	−	0.967221i	$-0.581725\pi$
$197$	1972.25	−	1972.25i	0.713285	−	0.713285i	0.967221	+	0.253936i	$0.0817252\pi$
$198$		0			0
$199$			375.024i			0.133592i	0.997767	+	0.0667958i	$0.0212776\pi$
$199$			375.024i			0.133592i	−0.997767	+	0.0667958i	$0.978722\pi$
$200$		0			0
$201$	1198.78	−	2742.91i	0.420673	−	0.962536i
$202$		0			0
$203$	−372.270	−	372.270i	−0.128711	−	0.128711i
$204$		0			0
$205$	1489.20	−	1836.25i	0.507366	−	0.625605i
$206$		0			0
$207$	−3747.49	−	144.955i	−1.25830	−	0.0486718i
$208$		0			0
$209$	3823.49			1.26544
$210$		0			0
$211$	1616.58			0.527441			0.263721	−	0.964599i	$-0.415050\pi$
$211$	1616.58			0.527441			0.263721	+	0.964599i	$0.415050\pi$
$212$		0			0
$213$	1383.88	−	542.127i	0.445174	−	0.174394i
$214$		0			0
$215$	2650.44	−	276.604i	0.840736	−	0.0877405i
$216$		0			0
$217$	5561.22	+	5561.22i	1.73973	+	1.73973i
$218$		0			0
$219$	3965.43	+	1733.08i	1.22356	+	0.534751i
$220$		0			0
$221$			2414.26i			0.734844i
$222$		0			0
$223$	2770.82	−	2770.82i	0.832053	−	0.832053i	−0.155744	−	0.987797i	$-0.549778\pi$
$223$	2770.82	−	2770.82i	0.832053	−	0.832053i	0.987797	+	0.155744i	$0.0497776\pi$
$224$		0			0
$225$	−2754.49	−	1950.24i	−0.816145	−	0.577848i
$226$		0			0
$227$	−1580.70	+	1580.70i	−0.462180	+	0.462180i	−0.899369	−	0.437190i	$-0.855974\pi$
$227$	−1580.70	+	1580.70i	−0.462180	+	0.462180i	0.437190	+	0.899369i	$0.355974\pi$
$228$		0			0
$229$		−	5433.47i		−	1.56792i	−0.620812	−	0.783960i	$-0.713197\pi$
$229$		−	5433.47i		−	1.56792i	0.620812	−	0.783960i	$-0.286803\pi$
$230$		0			0
$231$	6281.25	+	2745.20i	1.78907	+	0.781908i
$232$		0			0
$233$	−3500.09	−	3500.09i	−0.984115	−	0.984115i	0.0157606	−	0.999876i	$-0.494983\pi$
$233$	−3500.09	−	3500.09i	−0.984115	−	0.984115i	−0.999876	+	0.0157606i	$0.994983\pi$
$234$		0			0
$235$	392.968	−	41.0107i	0.109083	−	0.0113840i
$236$		0			0
$237$	−3353.53	+	1313.72i	−0.919137	+	0.360066i
$238$		0			0
$239$	4489.74			1.21514			0.607568	−	0.794268i	$-0.292145\pi$
$239$	4489.74			1.21514			0.607568	+	0.794268i	$0.292145\pi$
$240$		0			0
$241$	−6327.06			−1.69113			−0.845564	−	0.533874i	$-0.820736\pi$
$241$	−6327.06			−1.69113			−0.845564	+	0.533874i	$0.820736\pi$
$242$		0			0
$243$	−3623.21	+	1105.11i	−0.956498	+	0.291740i
$244$		0			0
$245$	3219.27	−	3969.51i	0.839477	−	1.03511i
$246$		0			0
$247$	1664.15	+	1664.15i	0.428693	+	0.428693i
$248$		0			0
$249$	2164.32	−	4952.16i	0.550837	−	1.26036i
$250$		0			0
$251$		−	3791.45i		−	0.953442i	−0.879055	−	0.476721i	$-0.841825\pi$
$251$		−	3791.45i		−	0.953442i	0.879055	−	0.476721i	$-0.158175\pi$
$252$		0			0
$253$	−4580.66	+	4580.66i	−1.13828	+	1.13828i
$254$		0			0
$255$	2244.66	+	4339.59i	0.551240	+	1.06571i
$256$		0			0
$257$	2100.66	−	2100.66i	0.509867	−	0.509867i	−0.404619	−	0.914486i	$-0.632596\pi$
$257$	2100.66	−	2100.66i	0.509867	−	0.509867i	0.914486	+	0.404619i	$0.132596\pi$
$258$		0			0
$259$		−	3276.46i		−	0.786060i
$260$		0			0
$261$	368.808	−	341.339i	0.0874660	−	0.0809515i
$262$		0			0
$263$	3563.87	+	3563.87i	0.835580	+	0.835580i	0.988274	−	0.152693i	$-0.0487947\pi$
$263$	3563.87	+	3563.87i	0.835580	+	0.835580i	−0.152693	+	0.988274i	$0.548795\pi$
$264$		0			0
$265$	−89.8593	−	861.039i	−0.0208302	−	0.199597i
$266$		0			0
$267$	−1432.64	−	3657.10i	−0.328376	−	0.838242i
$268$		0			0
$269$	−4230.10			−0.958787			−0.479394	−	0.877600i	$-0.659143\pi$
$269$	−4230.10			−0.958787			−0.479394	+	0.877600i	$0.659143\pi$
$270$		0			0
$271$	−1166.44			−0.261462			−0.130731	−	0.991418i	$-0.541732\pi$
$271$	−1166.44			−0.261462			−0.130731	+	0.991418i	$0.541732\pi$
$272$		0			0
$273$	1539.04	+	3928.70i	0.341198	+	0.870973i
$274$		0			0
$275$	−5704.16	+	1203.70i	−1.25081	+	0.263948i
$276$		0			0
$277$	5473.65	+	5473.65i	1.18729	+	1.18729i	0.977813	+	0.209478i	$0.0671766\pi$
$277$	5473.65	+	5473.65i	1.18729	+	1.18729i	0.209478	+	0.977813i	$0.432823\pi$
$278$		0			0
$279$	−5509.50	+	5099.15i	−1.18224	+	1.09419i
$280$		0			0
$281$		−	2933.43i		−	0.622753i	−0.950287	−	0.311376i	$-0.899210\pi$
$281$		−	2933.43i		−	0.622753i	0.950287	−	0.311376i	$-0.100790\pi$
$282$		0			0
$283$	2187.09	−	2187.09i	0.459397	−	0.459397i	−0.439061	−	0.898457i	$-0.644689\pi$
$283$	2187.09	−	2187.09i	0.459397	−	0.459397i	0.898457	+	0.439061i	$0.144689\pi$
$284$		0			0
$285$	4538.52	+	1444.04i	0.943295	+	0.300131i
$286$		0			0
$287$	−4229.57	+	4229.57i	−0.869909	+	0.869909i
$288$		0			0
$289$		−	2159.76i		−	0.439600i
$290$		0			0
$291$	−2237.02	+	5118.50i	−0.450641	+	1.03110i
$292$		0			0
$293$	−1518.21	−	1518.21i	−0.302712	−	0.302712i	0.539362	−	0.842074i	$-0.318665\pi$
$293$	−1518.21	−	1518.21i	−0.302712	−	0.302712i	−0.842074	+	0.539362i	$0.818665\pi$
$294$		0			0
$295$	1376.86	+	1116.64i	0.271742	+	0.220383i
$296$		0			0
$297$	−2850.12	+	5889.80i	−0.556837	+	1.15071i
$298$		0			0
$299$	−3987.40			−0.771229
$300$		0			0
$301$	−6742.08			−1.29105
$302$		0			0
$303$	3467.09	−	1358.21i	0.657357	−	0.257515i
$304$		0			0
$305$	−7752.74	−	6287.48i	−1.45548	−	1.18039i
$306$		0			0
$307$	−5397.25	−	5397.25i	−1.00338	−	1.00338i	−0.999994	−	0.00338426i	$-0.998923\pi$
$307$	−5397.25	−	5397.25i	−1.00338	−	1.00338i	−0.00338426	−	0.999994i	$-0.501077\pi$
$308$		0			0
$309$	3834.21	+	1675.73i	0.705892	+	0.308507i
$310$		0			0
$311$		−	8797.54i		−	1.60406i	−0.597284	−	0.802030i	$-0.703754\pi$
$311$		−	8797.54i		−	1.60406i	0.597284	−	0.802030i	$-0.296246\pi$
$312$		0			0
$313$	−368.023	+	368.023i	−0.0664597	+	0.0664597i	−0.739555	−	0.673096i	$-0.764964\pi$
$313$	−368.023	+	368.023i	−0.0664597	+	0.0664597i	0.673096	+	0.739555i	$0.264964\pi$
$314$		0			0
$315$	6419.12	+	5630.85i	1.14818	+	1.00718i
$316$		0			0
$317$	−888.667	+	888.667i	−0.157453	+	0.157453i	−0.781437	−	0.623984i	$-0.785513\pi$
$317$	−888.667	+	888.667i	−0.157453	+	0.157453i	0.623984	+	0.781437i	$0.285513\pi$
$318$		0			0
$319$		−	868.032i		−	0.152353i
$320$		0			0
$321$	6742.54	+	2946.80i	1.17237	+	0.512381i
$322$		0			0
$323$	−4875.25	−	4875.25i	−0.839834	−	0.839834i
$324$		0			0
$325$	−3006.60	−	1958.79i	−0.513157	−	0.334321i
$326$		0			0
$327$	−6682.48	+	2617.82i	−1.13010	+	0.442708i
$328$		0			0
$329$	−999.618			−0.167510
$330$		0			0
$331$	−3823.90			−0.634987			−0.317493	−	0.948260i	$-0.602841\pi$
$331$	−3823.90			−0.634987			−0.317493	+	0.948260i	$0.602841\pi$
$332$		0			0
$333$	3125.10	+	120.881i	0.514278	+	0.0198926i
$334$		0			0
$335$	−668.544	−	6406.04i	−0.109034	−	1.04477i
$336$		0			0
$337$	−7251.55	−	7251.55i	−1.17216	−	1.17216i	−0.981694	−	0.190462i	$-0.939001\pi$
$337$	−7251.55	−	7251.55i	−1.17216	−	1.17216i	−0.190462	−	0.981694i	$-0.560999\pi$
$338$		0			0
$339$	−187.107	+	428.117i	−0.0299771	+	0.0685903i
$340$		0			0
$341$			12967.2i			2.05928i
$342$		0			0
$343$	−2282.73	+	2282.73i	−0.359347	+	0.359347i
$344$		0			0
$345$	−7167.30	+	3707.30i	−1.11848	+	0.578534i
$346$		0			0
$347$	6287.76	−	6287.76i	0.972752	−	0.972752i	−0.0268868	−	0.999638i	$-0.508559\pi$
$347$	6287.76	−	6287.76i	0.972752	−	0.972752i	0.999638	+	0.0268868i	$0.00855938\pi$
$348$		0			0
$349$			1266.74i			0.194290i	0.995270	+	0.0971448i	$0.0309710\pi$
$349$			1266.74i			0.194290i	−0.995270	+	0.0971448i	$0.969029\pi$
$350$		0			0
$351$	−3803.99	+	1323.00i	−0.578467	+	0.201187i
$352$		0			0
$353$	7731.15	+	7731.15i	1.16569	+	1.16569i	0.983210	+	0.182477i	$0.0584116\pi$
$353$	7731.15	+	7731.15i	1.16569	+	1.16569i	0.182477	+	0.983210i	$0.441588\pi$
$354$		0			0
$355$	2014.37	−	2483.81i	0.301160	−	0.371344i
$356$		0			0
$357$	−4508.75	−	11509.4i	−0.668426	−	1.70629i
$358$		0			0
$359$	4860.57			0.714572			0.357286	−	0.933995i	$-0.383702\pi$
$359$	4860.57			0.714572			0.357286	+	0.933995i	$0.383702\pi$
$360$		0			0
$361$	137.979			0.0201165
$362$		0			0
$363$	1599.88	+	4084.00i	0.231328	+	0.590508i
$364$		0			0
$365$	9261.22	−	966.516i	1.32809	−	0.138602i
$366$		0			0
$367$	−8039.93	−	8039.93i	−1.14354	−	1.14354i	−0.987797	−	0.155747i	$-0.950221\pi$
$367$	−8039.93	−	8039.93i	−1.14354	−	1.14354i	−0.155747	−	0.987797i	$-0.549779\pi$
$368$		0			0
$369$	−3878.14	−	4190.23i	−0.547122	−	0.591151i
$370$		0			0
$371$			2190.28i			0.306506i
$372$		0			0
$373$	−8959.57	+	8959.57i	−1.24372	+	1.24372i	−0.285279	+	0.958444i	$0.592086\pi$
$373$	−8959.57	+	8959.57i	−1.24372	+	1.24372i	−0.958444	+	0.285279i	$0.907914\pi$
$374$		0			0
$375$	−7225.51	−	725.512i	−0.994997	−	0.0999074i
$376$		0			0
$377$	377.805	−	377.805i	0.0516126	−	0.0516126i
$378$		0			0
$379$		−	5062.47i		−	0.686126i	−0.939312	−	0.343063i	$-0.888536\pi$
$379$		−	5062.47i		−	0.686126i	0.939312	−	0.343063i	$-0.111464\pi$
$380$		0			0
$381$	−401.062	+	917.663i	−0.0539291	+	0.123395i
$382$		0			0
$383$	3779.89	+	3779.89i	0.504291	+	0.504291i	0.912768	−	0.408478i	$-0.133940\pi$
$383$	3779.89	+	3779.89i	0.504291	+	0.504291i	−0.408478	+	0.912768i	$0.633940\pi$
$384$		0			0
$385$	14669.8	−	1530.96i	1.94193	−	0.202663i
$386$		0			0
$387$	248.741	−	6430.63i	0.0326723	−	0.844670i
$388$		0			0
$389$	−10963.5			−1.42897			−0.714485	−	0.699651i	$-0.753339\pi$
$389$	−10963.5			−1.42897			−0.714485	+	0.699651i	$0.753339\pi$
$390$		0			0
$391$	11681.4			1.51088
$392$		0			0
$393$	8909.15	−	3490.10i	1.14353	−	0.447970i
$394$		0			0
$395$	−4881.38	+	6018.96i	−0.621795	+	0.766701i
$396$		0			0
$397$	2945.14	+	2945.14i	0.372323	+	0.372323i	0.868323	−	0.496000i	$-0.165198\pi$
$397$	2945.14	+	2945.14i	0.372323	+	0.372323i	−0.496000	+	0.868323i	$0.665198\pi$
$398$		0			0
$399$	−11041.3	−	4825.58i	−1.38536	−	0.605466i
$400$		0			0
$401$		−	13856.1i		−	1.72554i	−0.505601	−	0.862768i	$-0.668729\pi$
$401$		−	13856.1i		−	1.72554i	0.505601	−	0.862768i	$-0.331271\pi$
$402$		0			0
$403$	−5643.91	+	5643.91i	−0.697625	+	0.697625i
$404$		0			0
$405$	−5607.56	+	5914.85i	−0.688004	+	0.725706i
$406$		0			0
$407$	3819.90	−	3819.90i	0.465223	−	0.465223i
$408$		0			0
$409$		−	3847.31i		−	0.465128i	−0.972581	−	0.232564i	$-0.925289\pi$
$409$		−	3847.31i		−	0.465128i	0.972581	−	0.232564i	$-0.0747115\pi$
$410$		0			0
$411$	6609.30	+	2888.57i	0.793218	+	0.346673i
$412$		0			0
$413$	−3171.44	−	3171.44i	−0.377860	−	0.377860i
$414$		0			0
$415$	−1207.02	−	11565.7i	−0.142771	−	1.36805i
$416$		0			0
$417$	853.442	−	334.330i	0.100224	−	0.0392619i
$418$		0			0
$419$	−7971.58			−0.929444			−0.464722	−	0.885457i	$-0.653846\pi$
$419$	−7971.58			−0.929444			−0.464722	+	0.885457i	$0.653846\pi$
$420$		0			0
$421$	2638.67			0.305465			0.152732	−	0.988268i	$-0.451193\pi$
$421$	2638.67			0.305465			0.152732	+	0.988268i	$0.451193\pi$
$422$		0			0
$423$	36.8796	−	953.440i	0.00423912	−	0.109593i
$424$		0			0
$425$	8808.07	+	5738.44i	1.00530	+	0.654954i
$426$		0			0
$427$	17857.5	+	17857.5i	2.02385	+	2.02385i
$428$		0			0
$429$	−2786.01	+	6374.63i	−0.313543	+	0.717413i
$430$		0			0
$431$		−	1327.18i		−	0.148325i	−0.997246	−	0.0741625i	$-0.976372\pi$
$431$		−	1327.18i		−	0.148325i	0.997246	−	0.0741625i	$-0.0236283\pi$
$432$		0			0
$433$	6213.91	−	6213.91i	0.689657	−	0.689657i	−0.272499	−	0.962156i	$-0.587850\pi$
$433$	6213.91	−	6213.91i	0.689657	−	0.689657i	0.962156	+	0.272499i	$0.0878502\pi$
$434$		0			0
$435$	327.834	−	1030.36i	0.0361343	−	0.113568i
$436$		0			0
$437$	8052.00	−	8052.00i	0.881418	−	0.881418i
$438$		0			0
$439$			4083.01i			0.443899i	0.975058	+	0.221950i	$0.0712420\pi$
$439$			4083.01i			0.443899i	−0.975058	+	0.221950i	$0.928758\pi$
$440$		0			0
$441$	−8383.58	−	9058.23i	−0.905256	−	0.978105i
$442$		0			0
$443$	4181.69	+	4181.69i	0.448483	+	0.448483i	0.894850	−	0.446367i	$-0.147282\pi$
$443$	4181.69	+	4181.69i	0.448483	+	0.448483i	−0.446367	+	0.894850i	$0.647282\pi$
$444$		0			0
$445$	−6563.80	−	5323.25i	−0.699223	−	0.567070i
$446$		0			0
$447$	249.392	+	636.621i	0.0263889	+	0.0673628i
$448$		0			0
$449$	−11074.2			−1.16397			−0.581984	−	0.813200i	$-0.697723\pi$
$449$	−11074.2			−1.16397			−0.581984	+	0.813200i	$0.697723\pi$
$450$		0			0
$451$	−9862.20			−1.02970
$452$		0			0
$453$	1064.45	+	2717.22i	0.110403	+	0.281824i
$454$		0			0
$455$	7051.27	+	5718.59i	0.726525	+	0.589213i
$456$		0			0
$457$	−1208.99	−	1208.99i	−0.123751	−	0.123751i	0.642519	−	0.766270i	$-0.277890\pi$
$457$	−1208.99	−	1208.99i	−0.123751	−	0.123751i	−0.766270	+	0.642519i	$0.777890\pi$
$458$		0			0
$459$	11144.1	−	3875.84i	1.13325	−	0.394136i
$460$		0			0
$461$		−	10000.7i		−	1.01036i	−0.863013	−	0.505181i	$-0.831426\pi$
$461$		−	10000.7i		−	1.01036i	0.863013	−	0.505181i	$-0.168574\pi$
$462$		0			0
$463$	−8855.22	+	8855.22i	−0.888848	+	0.888848i	−0.994412	−	0.105564i	$-0.966335\pi$
$463$	−8855.22	+	8855.22i	−0.888848	+	0.888848i	0.105564	+	0.994412i	$0.466335\pi$
$464$		0			0
$465$	−4897.40	+	15392.3i	−0.488412	+	1.53505i
$466$		0			0
$467$	−12667.8	+	12667.8i	−1.25524	+	1.25524i	−0.301901	+	0.953339i	$0.597621\pi$
$467$	−12667.8	+	12667.8i	−1.25524	+	1.25524i	−0.953339	+	0.301901i	$0.902379\pi$
$468$		0			0
$469$			16295.5i			1.60438i
$470$		0			0
$471$	799.697	−	1829.77i	0.0782337	−	0.179005i
$472$		0			0
$473$	−7860.34	−	7860.34i	−0.764099	−	0.764099i
$474$		0			0
$475$	10026.9	−	2115.89i	0.968561	−	0.204387i
$476$		0			0
$477$	−2089.10	−	80.8076i	−0.200531	−	0.00775666i
$478$		0			0
$479$	4175.36			0.398282			0.199141	−	0.979971i	$-0.436185\pi$
$479$	4175.36			0.398282			0.199141	+	0.979971i	$0.436185\pi$
$480$		0			0
$481$	3325.17			0.315208
$482$		0			0
$483$	19009.1	−	7446.68i	1.79077	−	0.701523i
$484$		0			0
$485$	1247.56	+	11954.2i	0.116802	+	1.11920i
$486$		0			0
$487$	13693.1	+	13693.1i	1.27411	+	1.27411i	0.943909	+	0.330205i	$0.107118\pi$
$487$	13693.1	+	13693.1i	1.27411	+	1.27411i	0.330205	+	0.943909i	$0.392882\pi$
$488$		0			0
$489$	9553.25	+	4175.21i	0.883462	+	0.386114i
$490$		0			0
$491$		−	7453.35i		−	0.685061i	−0.939507	−	0.342530i	$-0.888716\pi$
$491$		−	7453.35i		−	0.685061i	0.939507	−	0.342530i	$-0.111284\pi$
$492$		0			0
$493$	−1106.81	+	1106.81i	−0.101112	+	0.101112i
$494$		0			0
$495$	919.016	+	14048.6i	0.0834479	+	1.27563i
$496$		0			0
$497$	−5721.16	+	5721.16i	−0.516356	+	0.516356i
$498$		0			0
$499$			8416.94i			0.755098i	0.925990	+	0.377549i	$0.123233\pi$
$499$			8416.94i			0.755098i	−0.925990	+	0.377549i	$0.876767\pi$
$500$		0			0
$501$	3709.71	+	1621.31i	0.330813	+	0.144581i
$502$		0			0
$503$	−4648.33	−	4648.33i	−0.412045	−	0.412045i	0.470405	−	0.882451i	$-0.344108\pi$
$503$	−4648.33	−	4648.33i	−0.412045	−	0.412045i	−0.882451	+	0.470405i	$0.844108\pi$
$504$		0			0
$505$	5046.68	−	6222.78i	0.444702	−	0.548337i
$506$		0			0
$507$	6642.33	−	2602.09i	0.581846	−	0.227934i
$508$		0			0
$509$	15771.4			1.37339			0.686696	−	0.726945i	$-0.259060\pi$
$509$	15771.4			1.37339			0.686696	+	0.726945i	$0.259060\pi$
$510$		0			0
$511$	−23558.4			−2.03945
$512$		0			0
$513$	5010.01	−	10353.2i	0.431184	−	0.891046i
$514$		0			0
$515$	8954.77	−	934.533i	0.766202	−	0.0799620i
$516$		0			0
$517$	−1165.42	−	1165.42i	−0.0991392	−	0.0991392i
$518$		0			0
$519$	−4972.28	+	11377.0i	−0.420538	+	0.962226i
$520$		0			0
$521$		−	9705.84i		−	0.816163i	−0.912946	−	0.408081i	$-0.866198\pi$
$521$		−	9705.84i		−	0.816163i	0.912946	−	0.408081i	$-0.133802\pi$
$522$		0			0
$523$	1226.21	−	1226.21i	0.102521	−	0.102521i	−0.653986	−	0.756507i	$-0.726904\pi$
$523$	1226.21	−	1226.21i	0.102521	−	0.102521i	0.756507	+	0.653986i	$0.226904\pi$
$524$		0			0
$525$	17991.4	+	3723.15i	1.49564	+	0.309507i
$526$		0			0
$527$	16534.3	−	16534.3i	1.36669	−	1.36669i
$528$		0			0
$529$			7126.12i			0.585692i
$530$		0			0
$531$	3141.94	−	2907.92i	0.256777	−	0.237652i
$532$		0			0
$533$	−4292.46	−	4292.46i	−0.348831	−	0.348831i
$534$		0			0
$535$	15747.1	−	1643.40i	1.27254	−	0.132804i
$536$		0			0
$537$	−4388.50	−	11202.5i	−0.352659	−	0.900229i
$538$		0			0
$539$	−21319.6			−1.70371
$540$		0			0
$541$	15580.8			1.23821			0.619103	−	0.785310i	$-0.287496\pi$
$541$	15580.8			1.23821			0.619103	+	0.785310i	$0.287496\pi$
$542$		0			0
$543$	−5113.98	−	13054.4i	−0.404165	−	1.03171i
$544$		0			0
$545$	−9726.98	+	11993.8i	−0.764510	+	0.942674i
$546$		0			0
$547$	−5262.41	−	5262.41i	−0.411343	−	0.411343i	0.470863	−	0.882206i	$-0.343942\pi$
$547$	−5262.41	−	5262.41i	−0.411343	−	0.411343i	−0.882206	+	0.470863i	$0.843942\pi$
$548$		0			0
$549$	−17691.4	+	16373.7i	−1.37532	+	1.27289i
$550$		0			0
$551$			1525.85i			0.117973i
$552$		0			0
$553$	13864.0	−	13864.0i	1.06610	−	1.06610i
$554$		0			0
$555$	5976.95	−	3091.59i	0.457131	−	0.236452i
$556$		0			0
$557$	−546.517	+	546.517i	−0.0415739	+	0.0415739i	−0.727588	−	0.686014i	$-0.759359\pi$
$557$	−546.517	+	546.517i	−0.0415739	+	0.0415739i	0.686014	+	0.727588i	$0.259359\pi$
$558$		0			0
$559$		−	6842.32i		−	0.517709i
$560$		0			0
$561$	8161.84	−	18675.0i	0.614248	−	1.40545i
$562$		0			0
$563$	3510.01	+	3510.01i	0.262752	+	0.262752i	0.826171	−	0.563419i	$-0.190514\pi$
$563$	3510.01	+	3510.01i	0.262752	+	0.262752i	−0.563419	+	0.826171i	$0.690514\pi$
$564$		0			0
$565$	104.347	+	999.863i	0.00776978	+	0.0744506i
$566$		0			0
$567$	15663.9	−	13411.3i	1.16018	−	0.993334i
$568$		0			0
$569$	13230.4			0.974775			0.487387	−	0.873186i	$-0.337950\pi$
$569$	13230.4			0.974775			0.487387	+	0.873186i	$0.337950\pi$
$570$		0			0
$571$	−4538.99			−0.332664			−0.166332	−	0.986070i	$-0.553192\pi$
$571$	−4538.99			−0.332664			−0.166332	+	0.986070i	$0.553192\pi$
$572$		0			0
$573$	−8926.81	+	3497.02i	−0.650825	+	0.254956i
$574$		0			0
$575$	−9477.66	+	14547.5i	−0.687384	+	1.05508i
$576$		0			0
$577$	9683.87	+	9683.87i	0.698691	+	0.698691i	0.964128	−	0.265437i	$-0.0855162\pi$
$577$	9683.87	+	9683.87i	0.698691	+	0.698691i	−0.265437	+	0.964128i	$0.585516\pi$
$578$		0			0
$579$	−835.385	−	365.102i	−0.0599610	−	0.0262057i
$580$		0			0
$581$			29420.5i			2.10080i
$582$		0			0
$583$	−2553.56	+	2553.56i	−0.181403	+	0.181403i
$584$		0			0
$585$	−5714.57	+	6514.56i	−0.403877	+	0.460417i
$586$		0			0
$587$	4116.27	−	4116.27i	0.289432	−	0.289432i	−0.547424	−	0.836856i	$-0.684391\pi$
$587$	4116.27	−	4116.27i	0.289432	−	0.289432i	0.836856	+	0.547424i	$0.184391\pi$
$588$		0			0
$589$		−	22794.2i		−	1.59460i
$590$		0			0
$591$	−13280.1	−	5804.03i	−0.924316	−	0.403969i
$592$		0			0
$593$	17390.9	+	17390.9i	1.20431	+	1.20431i	0.972841	+	0.231473i	$0.0743545\pi$
$593$	17390.9	+	17390.9i	1.20431	+	1.20431i	0.231473	+	0.972841i	$0.425645\pi$
$594$		0			0
$595$	−20657.3	−	16753.1i	−1.42330	−	1.15430i
$596$		0			0
$597$	1814.42	−	710.789i	0.124388	−	0.0487281i
$598$		0			0
$599$	752.669			0.0513409			0.0256705	−	0.999670i	$-0.491828\pi$
$599$	752.669			0.0513409			0.0256705	+	0.999670i	$0.491828\pi$
$600$		0			0
$601$	−17195.9			−1.16711			−0.583556	−	0.812073i	$-0.698339\pi$
$601$	−17195.9			−1.16711			−0.583556	+	0.812073i	$0.698339\pi$
$602$		0			0
$603$	−15542.7	−	601.200i	−1.04966	−	0.0406016i
$604$		0			0
$605$	7330.01	+	5944.65i	0.492574	+	0.399478i
$606$		0			0
$607$	7734.75	+	7734.75i	0.517206	+	0.517206i	0.916725	−	0.399519i	$-0.130823\pi$
$607$	7734.75	+	7734.75i	0.517206	+	0.517206i	−0.399519	+	0.916725i	$0.630823\pi$
$608$		0			0
$609$	−1095.53	+	2506.67i	−0.0728953	+	0.166791i
$610$		0			0
$611$		−	1014.48i		−	0.0671709i
$612$		0			0
$613$	5671.19	−	5671.19i	0.373666	−	0.373666i	−0.495145	−	0.868811i	$-0.664885\pi$
$613$	5671.19	−	5671.19i	0.373666	−	0.373666i	0.868811	+	0.495145i	$0.164885\pi$
$614$		0			0
$615$	−11706.6	−	3724.71i	−0.767567	−	0.244219i
$616$		0			0
$617$	−5008.69	+	5008.69i	−0.326811	+	0.326811i	−0.851373	−	0.524562i	$-0.824229\pi$
$617$	−5008.69	+	5008.69i	−0.326811	+	0.326811i	0.524562	+	0.851373i	$0.324229\pi$
$618$		0			0
$619$			28299.6i			1.83757i	0.394754	+	0.918787i	$0.370830\pi$
$619$			28299.6i			1.83757i	−0.394754	+	0.918787i	$0.629170\pi$
$620$		0			0
$621$	6401.36	+	18405.7i	0.413652	+	1.18936i
$622$		0			0
$623$	15118.9	+	15118.9i	0.972275	+	0.972275i
$624$		0			0
$625$	−14292.8	+	6313.29i	−0.914737	+	0.404050i
$626$		0			0
$627$	−7246.72	−	18498.6i	−0.461573	−	1.17825i
$628$		0			0
$629$	−9741.36			−0.617510
$630$		0			0
$631$	−2986.64			−0.188425			−0.0942127	−	0.995552i	$-0.530033\pi$
$631$	−2986.64			−0.188425			−0.0942127	+	0.995552i	$0.530033\pi$
$632$		0			0
$633$	−3063.94	−	7821.28i	−0.192386	−	0.491103i
$634$		0			0
$635$	223.667	+	2143.20i	0.0139779	+	0.133937i
$636$		0			0
$637$	−9279.22	−	9279.22i	−0.577168	−	0.577168i
$638$		0			0
$639$	−5245.79	−	5667.94i	−0.324758	−	0.350893i
$640$		0			0
$641$		−	6182.91i		−	0.380983i	−0.981689	−	0.190492i	$-0.938992\pi$
$641$		−	6182.91i		−	0.380983i	0.981689	−	0.190492i	$-0.0610082\pi$
$642$		0			0
$643$	1150.90	−	1150.90i	0.0705865	−	0.0705865i	−0.670932	−	0.741519i	$-0.734106\pi$
$643$	1150.90	−	1150.90i	0.0705865	−	0.0705865i	0.741519	+	0.670932i	$0.234106\pi$
$644$		0			0
$645$	−6361.67	−	12299.0i	−0.388357	−	0.750809i
$646$		0			0
$647$	12117.0	−	12117.0i	0.736270	−	0.736270i	−0.235584	−	0.971854i	$-0.575700\pi$
$647$	12117.0	−	12117.0i	0.736270	−	0.736270i	0.971854	+	0.235584i	$0.0757003\pi$
$648$		0			0
$649$		−	7394.91i		−	0.447266i
$650$		0			0
$651$	16365.8	−	37446.4i	0.985294	−	2.25444i
$652$		0			0
$653$	1911.62	+	1911.62i	0.114559	+	0.114559i	0.762063	−	0.647503i	$-0.224187\pi$
$653$	1911.62	+	1911.62i	0.114559	+	0.114559i	−0.647503	+	0.762063i	$0.724187\pi$
$654$		0			0
$655$	12968.1	−	15990.2i	0.773597	−	0.953879i
$656$		0			0
$657$	869.156	−	22470.1i	0.0516119	−	1.33431i
$658$		0			0
$659$	886.931			0.0524278			0.0262139	−	0.999656i	$-0.491655\pi$
$659$	886.931			0.0524278			0.0262139	+	0.999656i	$0.491655\pi$
$660$		0			0
$661$	−13884.6			−0.817018			−0.408509	−	0.912754i	$-0.633951\pi$
$661$	−13884.6			−0.817018			−0.408509	+	0.912754i	$0.633951\pi$
$662$		0			0
$663$	11680.6	−	4575.78i	0.684216	−	0.268037i
$664$		0			0
$665$	−25787.0	+	2691.17i	−1.50372	+	0.156931i
$666$		0			0
$667$	−1828.02	−	1828.02i	−0.106119	−	0.106119i
$668$		0			0
$669$	−18657.2	−	8154.08i	−1.07822	−	0.471233i
$670$		0			0
$671$			41638.8i			2.39560i
$672$		0			0
$673$	−13073.3	+	13073.3i	−0.748792	+	0.748792i	−0.974252	−	0.225460i	$-0.927611\pi$
$673$	−13073.3	+	13073.3i	−0.748792	+	0.748792i	0.225460	+	0.974252i	$0.427611\pi$
$674$		0			0
$675$	−4214.93	+	17023.0i	−0.240345	+	0.970688i
$676$		0			0
$677$	17707.4	−	17707.4i	1.00524	−	1.00524i	0.00525640	−	0.999986i	$-0.498327\pi$
$677$	17707.4	−	17707.4i	1.00524	−	1.00524i	0.999986	−	0.00525640i	$-0.00167317\pi$
$678$		0			0
$679$		−	30408.7i		−	1.71867i
$680$		0			0
$681$	10643.6	+	4651.75i	0.598919	+	0.261756i
$682$		0			0
$683$	−1095.51	−	1095.51i	−0.0613740	−	0.0613740i	0.675754	−	0.737128i	$-0.263818\pi$
$683$	−1095.51	−	1095.51i	−0.0613740	−	0.0613740i	−0.737128	+	0.675754i	$0.763818\pi$
$684$		0			0
$685$	15436.0	−	1610.92i	0.860989	−	0.0898542i
$686$		0			0
$687$	−26288.0	+	10298.1i	−1.45990	+	0.571905i
$688$		0			0
$689$	−2222.84			−0.122908
$690$		0			0
$691$	−7041.35			−0.387649			−0.193825	−	0.981036i	$-0.562089\pi$
$691$	−7041.35			−0.387649			−0.193825	+	0.981036i	$0.562089\pi$
$692$		0			0
$693$	1376.75	−	35592.7i	0.0754664	−	1.95102i
$694$		0			0
$695$	1242.27	−	1531.77i	0.0678012	−	0.0836018i
$696$		0			0
$697$	12575.1	+	12575.1i	0.683380	+	0.683380i
$698$		0			0
$699$	−10300.2	+	23567.8i	−0.557354	+	1.27527i
$700$		0			0
$701$		−	14448.0i		−	0.778450i	−0.921143	−	0.389225i	$-0.872743\pi$
$701$		−	14448.0i		−	0.778450i	0.921143	−	0.389225i	$-0.127257\pi$
$702$		0			0
$703$	−6714.72	+	6714.72i	−0.360243	+	0.360243i
$704$		0			0
$705$	−943.215	−	1823.51i	−0.0503880	−	0.0974148i
$706$		0			0
$707$	−14333.4	+	14333.4i	−0.762467	+	0.762467i
$708$		0			0
$709$			32313.7i			1.71166i	0.517259	+	0.855829i	$0.326953\pi$
$709$			32313.7i			1.71166i	−0.517259	+	0.855829i	$0.673047\pi$
$710$		0			0
$711$	12712.0	+	13735.0i	0.670517	+	0.724476i
$712$		0			0
$713$	27308.1	+	27308.1i	1.43436	+	1.43436i
$714$		0			0
$715$	1553.72	+	14887.9i	0.0812672	+	0.778708i
$716$		0			0
$717$	−8509.49	−	21722.1i	−0.443225	−	1.13142i
$718$		0			0
$719$	−33877.4			−1.75718			−0.878591	−	0.477576i	$-0.841516\pi$
$719$	−33877.4			−1.75718			−0.878591	+	0.477576i	$0.841516\pi$
$720$		0			0
$721$	−22778.8			−1.17660
$722$		0			0
$723$	11991.8	+	30611.3i	0.616846	+	1.57462i
$724$		0			0
$725$	−480.363	−	2276.37i	−0.0246072	−	0.116610i
$726$		0			0
$727$	−838.518	−	838.518i	−0.0427770	−	0.0427770i	0.685395	−	0.728172i	$-0.259630\pi$
$727$	−838.518	−	838.518i	−0.0427770	−	0.0427770i	−0.728172	+	0.685395i	$0.759630\pi$
$728$		0			0
$729$	12213.8	+	15435.1i	0.620527	+	0.784185i
$730$		0			0
$731$			20045.1i			1.01422i
$732$		0			0
$733$	−17368.7	+	17368.7i	−0.875209	+	0.875209i	−0.993034	−	0.117826i	$-0.962408\pi$
$733$	−17368.7	+	17368.7i	−0.875209	+	0.875209i	0.117826	+	0.993034i	$0.462408\pi$
$734$		0			0
$735$	−25306.6	−	8051.89i	−1.27000	−	0.404079i
$736$		0			0
$737$	−18998.3	+	18998.3i	−0.949538	+	0.949538i
$738$		0			0
$739$		−	37068.8i		−	1.84519i	−0.385765	−	0.922597i	$-0.626062\pi$
$739$		−	37068.8i		−	1.84519i	0.385765	−	0.922597i	$-0.373938\pi$
$740$		0			0
$741$	4897.32	−	11205.5i	0.242790	−	0.555525i
$742$		0			0
$743$	−9264.66	−	9264.66i	−0.457453	−	0.457453i	0.440366	−	0.897818i	$-0.354849\pi$
$743$	−9264.66	−	9264.66i	−0.457453	−	0.457453i	−0.897818	+	0.440366i	$0.854849\pi$
$744$		0			0
$745$	1142.62	+	926.663i	0.0561909	+	0.0455709i
$746$		0			0
$747$	−28061.4	−	1085.43i	−1.37445	−	0.0531644i
$748$		0			0
$749$	−40057.0			−1.95414
$750$		0			0
$751$	5814.52			0.282523			0.141262	−	0.989972i	$-0.454884\pi$
$751$	5814.52			0.282523			0.141262	+	0.989972i	$0.454884\pi$
$752$		0			0
$753$	−18343.6	+	7185.99i	−0.887754	+	0.347772i
$754$		0			0
$755$	4876.90	+	3955.17i	0.235084	+	0.190653i
$756$		0			0
$757$	−7605.65	−	7605.65i	−0.365168	−	0.365168i	0.500544	−	0.865711i	$-0.333134\pi$
$757$	−7605.65	−	7605.65i	−0.365168	−	0.365168i	−0.865711	+	0.500544i	$0.833134\pi$
$758$		0			0
$759$	30843.8	+	13480.2i	1.47504	+	0.644662i
$760$		0			0
$761$		−	24104.4i		−	1.14821i	−0.818783	−	0.574103i	$-0.805351\pi$
$761$		−	24104.4i		−	1.14821i	0.818783	−	0.574103i	$-0.194649\pi$
$762$		0			0
$763$	27626.3	−	27626.3i	1.31080	−	1.31080i
$764$		0			0
$765$	16741.3	−	19084.9i	0.791219	−	0.901983i
$766$		0			0
$767$	3218.59	−	3218.59i	0.151521	−	0.151521i
$768$		0			0
$769$		−	28515.1i		−	1.33717i	−0.743637	−	0.668583i	$-0.766901\pi$
$769$		−	28515.1i		−	1.33717i	0.743637	−	0.668583i	$-0.233099\pi$
$770$		0			0
$771$	−14144.8	−	6181.92i	−0.660715	−	0.288763i
$772$		0			0
$773$	−15487.0	−	15487.0i	−0.720608	−	0.720608i	0.248121	−	0.968729i	$-0.420187\pi$
$773$	−15487.0	−	15487.0i	−0.720608	−	0.720608i	−0.968729	+	0.248121i	$0.920187\pi$
$774$		0			0
$775$	7175.99	+	34006.0i	0.332605	+	1.57617i
$776$		0			0
$777$	−15852.0	+	6209.93i	−0.731903	+	0.286718i
$778$		0			0
$779$	17336.0			0.797340
$780$		0			0
$781$	−13340.2			−0.611202
$782$		0			0
$783$	−2350.46	−	1137.40i	−0.107278	−	0.0519126i
$784$		0			0
$785$	−445.981	−	4273.43i	−0.0202774	−	0.194300i
$786$		0			0
$787$	−247.704	−	247.704i	−0.0112194	−	0.0112194i	0.701475	−	0.712694i	$-0.252525\pi$
$787$	−247.704	−	247.704i	−0.0112194	−	0.0112194i	−0.712694	+	0.701475i	$0.752525\pi$
$788$		0			0
$789$	10487.9	−	23997.2i	0.473231	−	1.08279i
$790$		0			0
$791$		−	2543.42i		−	0.114328i
$792$		0			0
$793$	−18123.0	+	18123.0i	−0.811560	+	0.811560i
$794$		0			0
$795$	−3995.53	+	2066.69i	−0.178248	+	0.0921989i
$796$		0			0
$797$	−6890.52	+	6890.52i	−0.306242	+	0.306242i	−0.843450	−	0.537208i	$-0.819479\pi$
$797$	−6890.52	+	6890.52i	−0.306242	+	0.306242i	0.537208	+	0.843450i	$0.319479\pi$
$798$		0			0
$799$			2972.00i			0.131592i
$800$		0			0
$801$	−14978.3	+	13862.7i	−0.660714	+	0.611504i
$802$		0			0
$803$	−27465.8	−	27465.8i	−1.20703	−	1.20703i
$804$		0			0
$805$	27669.5	−	34117.7i	1.21146	−	1.49378i
$806$		0			0
$807$	8017.38	+	20465.9i	0.349721	+	0.892731i
$808$		0			0
$809$	18667.0			0.811243			0.405621	−	0.914041i	$-0.367055\pi$
$809$	18667.0			0.811243			0.405621	+	0.914041i	$0.367055\pi$
$810$		0			0
$811$	8766.62			0.379578			0.189789	−	0.981825i	$-0.439220\pi$
$811$	8766.62			0.379578			0.189789	+	0.981825i	$0.439220\pi$
$812$		0			0
$813$	2210.77	+	5643.41i	0.0953691	+	0.243448i
$814$		0			0
$815$	22311.5	−	2328.47i	0.958944	−	0.100077i
$816$		0			0
$817$	13817.1	+	13817.1i	0.591676	+	0.591676i
$818$		0			0
$819$	16090.7	−	14892.3i	0.686513	−	0.635381i
$820$		0			0
$821$			14743.1i			0.626722i	0.949634	+	0.313361i	$0.101455\pi$
$821$			14743.1i			0.626722i	−0.949634	+	0.313361i	$0.898545\pi$
$822$		0			0
$823$	−1071.17	+	1071.17i	−0.0453689	+	0.0453689i	−0.729427	−	0.684058i	$-0.760213\pi$
$823$	−1071.17	+	1071.17i	−0.0453689	+	0.0453689i	0.684058	+	0.729427i	$0.260213\pi$
$824$		0			0
$825$	16634.9	+	25316.2i	0.702002	+	1.06836i
$826$		0			0
$827$	−1938.09	+	1938.09i	−0.0814920	+	0.0814920i	−0.746678	−	0.665186i	$-0.768352\pi$
$827$	−1938.09	+	1938.09i	−0.0814920	+	0.0814920i	0.665186	+	0.746678i	$0.268352\pi$
$828$		0			0
$829$		−	64.9624i		−	0.00272164i	−0.999999	−	0.00136082i	$-0.999567\pi$
$829$		−	64.9624i		−	0.00272164i	0.999999	−	0.00136082i	$-0.000433162\pi$
$830$		0			0
$831$	16108.1	−	36856.7i	0.672423	−	1.53856i
$832$		0			0
$833$	27184.2	+	27184.2i	1.13070	+	1.13070i
$834$		0			0
$835$	8663.99	−	904.188i	0.359078	−	0.0374739i
$836$		0			0
$837$	35112.7	+	16991.3i	1.45003	+	0.701680i
$838$		0			0
$839$	29797.1			1.22611			0.613057	−	0.790038i	$-0.289939\pi$
$839$	29797.1			1.22611			0.613057	+	0.790038i	$0.289939\pi$
$840$		0			0
$841$	−24042.6			−0.985797
$842$		0			0
$843$	−14192.4	+	5559.77i	−0.579847	+	0.227151i
$844$		0			0
$845$	9668.53	−	11921.7i	0.393619	−	0.485349i
$846$		0			0
$847$	−16883.8	−	16883.8i	−0.684928	−	0.684928i
$848$		0			0
$849$	−14726.7	−	6436.27i	−0.595313	−	0.260179i
$850$		0			0
$851$		−	16088.9i		−	0.648086i
$852$		0			0
$853$	29726.3	−	29726.3i	1.19321	−	1.19321i	0.217050	−	0.976161i	$-0.430357\pi$
$853$	29726.3	−	29726.3i	1.19321	−	1.19321i	0.976161	−	0.217050i	$-0.0696433\pi$
$854$		0			0
$855$	−1615.47	−	24695.0i	−0.0646175	−	0.987779i
$856$		0			0
$857$	20622.9	−	20622.9i	0.822014	−	0.822014i	−0.164383	−	0.986397i	$-0.552563\pi$
$857$	20622.9	−	20622.9i	0.822014	−	0.822014i	0.986397	+	0.164383i	$0.0525632\pi$
$858$		0			0
$859$		−	958.363i		−	0.0380663i	−0.999819	−	0.0190331i	$-0.993941\pi$
$859$		−	958.363i		−	0.0380663i	0.999819	−	0.0190331i	$-0.00605880\pi$
$860$		0			0
$861$	28479.7	+	12447.0i	1.12728	+	0.492673i
$862$		0			0
$863$	1254.40	+	1254.40i	0.0494788	+	0.0494788i	0.731413	−	0.681934i	$-0.238861\pi$
$863$	1254.40	+	1254.40i	0.0494788	+	0.0494788i	−0.681934	+	0.731413i	$0.738861\pi$
$864$		0			0
$865$	2772.98	+	26570.9i	0.108999	+	1.04444i
$866$		0			0
$867$	−10449.2	+	4093.42i	−0.409314	+	0.160346i
$868$		0			0
$869$	32326.9			1.26193
$870$		0			0
$871$	−16537.7			−0.643352
$872$		0			0
$873$	29004.0	+	1121.89i	1.12444	+	0.0434939i
$874$		0			0
$875$	37623.6	−	12133.1i	1.45361	−	0.468768i
$876$		0			0
$877$	19989.5	+	19989.5i	0.769667	+	0.769667i	0.978048	−	0.208381i	$-0.0668193\pi$
$877$	19989.5	+	19989.5i	0.769667	+	0.769667i	−0.208381	+	0.978048i	$0.566819\pi$
$878$		0			0
$879$	−4467.84	+	10222.8i	−0.171441	+	0.392272i
$880$		0			0
$881$		−	20026.6i		−	0.765848i	−0.923780	−	0.382924i	$-0.874917\pi$
$881$		−	20026.6i		−	0.765848i	0.923780	−	0.382924i	$-0.125083\pi$
$882$		0			0
$883$	1578.64	−	1578.64i	0.0601648	−	0.0601648i	−0.676384	−	0.736549i	$-0.736454\pi$
$883$	1578.64	−	1578.64i	0.0601648	−	0.0601648i	0.736549	+	0.676384i	$0.236454\pi$
$884$		0			0
$885$	2792.87	−	8777.85i	0.106081	−	0.333406i
$886$		0			0
$887$	−20594.4	+	20594.4i	−0.779587	+	0.779587i	−0.979760	−	0.200173i	$-0.935849\pi$
$887$	−20594.4	+	20594.4i	−0.779587	+	0.779587i	0.200173	+	0.979760i	$0.435849\pi$
$888$		0			0
$889$		−	5451.79i		−	0.205677i
$890$		0			0
$891$	33897.7	+	2626.29i	1.27454	+	0.0987476i
$892$		0			0
$893$	2048.60	+	2048.60i	0.0767679	+	0.0767679i
$894$		0			0
$895$	−20106.4	−	16306.3i	−0.750929	−	0.609004i
$896$		0			0
$897$	7557.39	+	19291.7i	0.281309	+	0.718094i
$898$		0			0
$899$	−5174.87			−0.191982
$900$		0			0
$901$	6512.00			0.240784
$902$		0			0
$903$	12778.4	+	32619.3i	0.470917	+	1.20211i
$904$		0			0
$905$	−23430.2	−	19001.9i	−0.860604	−	0.697951i
$906$		0			0
$907$	−1320.30	−	1320.30i	−0.0483350	−	0.0483350i	0.682526	−	0.730861i	$-0.260881\pi$
$907$	−1320.30	−	1320.30i	−0.0483350	−	0.0483350i	−0.730861	+	0.682526i	$0.760881\pi$
$908$		0			0
$909$	−13142.5	−	14200.1i	−0.479547	−	0.518138i
$910$		0			0
$911$		−	38257.2i		−	1.39135i	−0.718358	−	0.695674i	$-0.755106\pi$
$911$		−	38257.2i		−	1.39135i	0.718358	−	0.695674i	$-0.244894\pi$
$912$		0			0
$913$	−34300.2	+	34300.2i	−1.24334	+	1.24334i
$914$		0			0
$915$	−15725.9	+	49425.8i	−0.568179	+	1.78575i
$916$		0			0
$917$	−36831.6	+	36831.6i	−1.32638	+	1.32638i
$918$		0			0
$919$			28818.5i			1.03442i	0.855858	+	0.517211i	$0.173030\pi$
$919$			28818.5i			1.03442i	−0.855858	+	0.517211i	$0.826970\pi$
$920$		0			0
$921$	−15883.2	+	36342.2i	−0.568264	+	1.30024i
$922$		0			0
$923$	−5806.22	−	5806.22i	−0.207057	−	0.207057i
$924$		0			0
$925$	7903.61	−	12131.4i	0.280939	−	0.431220i
$926$		0			0
$927$	840.395	−	21726.5i	0.0297758	−	0.769788i
$928$		0			0
$929$	54466.3			1.92355			0.961777	−	0.273834i	$-0.0882919\pi$
$929$	54466.3			1.92355			0.961777	+	0.273834i	$0.0882919\pi$
$930$		0			0
$931$	37476.2			1.31926
$932$		0			0
$933$	−42563.9	+	16674.1i	−1.49355	+	0.585087i
$934$		0			0
$935$	−4551.76	−	43615.3i	−0.159207	−	1.52553i
$936$		0			0
$937$	25689.0	+	25689.0i	0.895650	+	0.895650i	0.995048	−	0.0993979i	$-0.0316917\pi$
$937$	25689.0	+	25689.0i	0.895650	+	0.895650i	−0.0993979	+	0.995048i	$0.531692\pi$
$938$		0			0
$939$	2478.07	+	1083.03i	0.0861224	+	0.0376395i
$940$		0			0
$941$			25247.4i			0.874644i	0.899305	+	0.437322i	$0.144073\pi$
$941$			25247.4i			0.874644i	−0.899305	+	0.437322i	$0.855927\pi$
$942$		0			0
$943$	−20769.1	+	20769.1i	−0.717217	+	0.717217i
$944$		0			0
$945$	15076.7	−	41729.0i	0.518989	−	1.43645i
$946$		0			0
$947$	−3015.25	+	3015.25i	−0.103466	+	0.103466i	−0.756945	−	0.653479i	$-0.773309\pi$
$947$	−3015.25	+	3015.25i	−0.103466	+	0.103466i	0.653479	+	0.756945i	$0.273309\pi$
$948$		0			0
$949$		−	23908.6i		−	0.817815i
$950$		0			0
$951$	5983.82	+	2615.21i	0.204036	+	0.0891733i
$952$		0			0
$953$	−36971.0	−	36971.0i	−1.25667	−	1.25667i	−0.952672	−	0.304000i	$-0.901678\pi$
$953$	−36971.0	−	36971.0i	−1.25667	−	1.25667i	−0.304000	−	0.952672i	$-0.598322\pi$
$954$		0			0
$955$	−12993.8	+	16021.9i	−0.440283	+	0.542888i
$956$		0			0
$957$	−4199.68	+	1645.20i	−0.141856	+	0.0555712i
$958$		0			0
$959$	−39265.4			−1.32216
$960$		0			0
$961$	47514.7			1.59494
$962$		0			0
$963$	1477.85	−	38206.6i	0.0494529	−	1.27849i
$964$		0			0
$965$	−1951.03	+	203.613i	−0.0650840	+	0.00679226i
$966$		0			0
$967$	12470.4	+	12470.4i	0.414705	+	0.414705i	0.883374	−	0.468669i	$-0.155266\pi$
$967$	12470.4	+	12470.4i	0.414705	+	0.414705i	−0.468669	+	0.883374i	$0.655266\pi$
$968$		0			0
$969$	−14347.1	+	32827.4i	−0.475640	+	1.08830i
$970$		0			0
$971$			26169.1i			0.864889i	0.901660	+	0.432445i	$0.142349\pi$
$971$			26169.1i			0.864889i	−0.901660	+	0.432445i	$0.857651\pi$
$972$		0			0
$973$	−3528.24	+	3528.24i	−0.116249	+	0.116249i
$974$		0			0
$975$	−3778.50	+	18258.9i	−0.124112	+	0.599747i
$976$		0			0
$977$	−14652.3	+	14652.3i	−0.479806	+	0.479806i	−0.905069	−	0.425264i	$-0.860181\pi$
$977$	−14652.3	+	14652.3i	−0.479806	+	0.479806i	0.425264	+	0.905069i	$0.360181\pi$
$978$		0			0
$979$			35253.2i			1.15086i
$980$		0			0
$981$	25330.8	+	27369.3i	0.824415	+	0.890759i
$982$		0			0
$983$	−8853.43	−	8853.43i	−0.287264	−	0.287264i	0.548733	−	0.835997i	$-0.315110\pi$
$983$	−8853.43	−	8853.43i	−0.287264	−	0.287264i	−0.835997	+	0.548733i	$0.815110\pi$
$984$		0			0
$985$	−31015.6	+	3236.84i	−1.00329	+	0.104705i
$986$		0			0
$987$	1894.59	+	4836.31i	0.0610998	+	0.155969i
$988$		0			0
$989$	−33106.7			−1.06444
$990$		0			0
$991$	43679.4			1.40012			0.700062	−	0.714082i	$-0.253156\pi$
$991$	43679.4			1.40012			0.700062	+	0.714082i	$0.253156\pi$
$992$		0			0
$993$	7247.50	+	18500.6i	0.231614	+	0.591239i
$994$		0			0
$995$	2641.07	−	3256.55i	0.0841482	−	0.103758i
$996$		0			0
$997$	1772.56	+	1772.56i	0.0563065	+	0.0563065i	0.734699	−	0.678393i	$-0.237323\pi$
$997$	1772.56	+	1772.56i	0.0563065	+	0.0563065i	−0.678393	+	0.734699i	$0.737323\pi$
$998$		0			0
$999$	−5338.22	−	15348.9i	−0.169063	−	0.486102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.4.v.e.17.8		36
3.2	odd	2	inner	240.4.v.e.17.16		36
4.3	odd	2		120.4.r.a.17.11	yes	36
5.3	odd	4	inner	240.4.v.e.113.16		36
12.11	even	2		120.4.r.a.17.3	✓	36
15.8	even	4	inner	240.4.v.e.113.8		36
20.3	even	4		120.4.r.a.113.3	yes	36
60.23	odd	4		120.4.r.a.113.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.r.a.17.3	✓	36	12.11	even	2
120.4.r.a.17.11	yes	36	4.3	odd	2
120.4.r.a.113.3	yes	36	20.3	even	4
120.4.r.a.113.11	yes	36	60.23	odd	4
240.4.v.e.17.8		36	1.1	even	1	trivial
240.4.v.e.17.16		36	3.2	odd	2	inner
240.4.v.e.113.8		36	15.8	even	4	inner
240.4.v.e.113.16		36	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	240.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.89532 - 4.83816i) q^{3} +(-8.68358 - 7.04240i) q^{5} +(20.0016 + 20.0016i) q^{7} +(-19.8155 + 18.3397i) q^{9} +46.6382i q^{11} +(-20.2990 + 20.2990i) q^{13} +(-17.6141 + 55.3601i) q^{15} +(59.4675 - 59.4675i) q^{17} -81.9818i q^{19} +(58.8615 - 134.680i) q^{21} +(98.2169 + 98.2169i) q^{23} +(25.8093 + 122.307i) q^{25} +(126.287 + 61.1113i) q^{27} -18.6120 q^{29} +278.039 q^{31} +(225.643 - 88.3942i) q^{33} +(-32.8264 - 314.545i) q^{35} +(-81.9050 - 81.9050i) q^{37} +(136.683 + 59.7366i) q^{39} +211.462i q^{41} +(-168.539 + 168.539i) q^{43} +(301.225 - 19.7052i) q^{45} +(-24.9885 + 24.9885i) q^{47} +457.128i q^{49} +(-400.423 - 175.003i) q^{51} +(54.7526 + 54.7526i) q^{53} +(328.445 - 404.987i) q^{55} +(-396.641 + 155.382i) q^{57} -158.559 q^{59} +892.804 q^{61} +(-763.166 - 29.5197i) q^{63} +(319.221 - 33.3144i) q^{65} +(407.354 + 407.354i) q^{67} +(289.037 - 661.341i) q^{69} +286.035i q^{71} +(-588.912 + 588.912i) q^{73} +(542.821 - 356.679i) q^{75} +(-932.839 + 932.839i) q^{77} -693.142i q^{79} +(56.3120 - 726.822i) q^{81} +(735.453 + 735.453i) q^{83} +(-935.184 + 97.5973i) q^{85} +(35.2757 + 90.0480i) q^{87} +755.886 q^{89} -812.023 q^{91} +(-526.972 - 1345.20i) q^{93} +(-577.349 + 711.896i) q^{95} +(-760.157 - 760.157i) q^{97} +(-855.330 - 924.162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{7} + 24 q^{13} + 12 q^{15} + 32 q^{21} + 72 q^{25} + 168 q^{27} - 216 q^{31} + 204 q^{33} + 576 q^{37} - 464 q^{45} + 816 q^{51} + 372 q^{55} - 1160 q^{57} + 72 q^{61} + 628 q^{63} + 1080 q^{67}+ \cdots + 2172 q^{97}+O(q^{100}) \) 36 * q + 12 * q^7 + 24 * q^13 + 12 * q^15 + 32 * q^21 + 72 * q^25 + 168 * q^27 - 216 * q^31 + 204 * q^33 + 576 * q^37 - 464 * q^45 + 816 * q^51 + 372 * q^55 - 1160 * q^57 + 72 * q^61 + 628 * q^63 + 1080 * q^67 - 900 * q^73 - 720 * q^75 + 1196 * q^81 + 912 * q^85 - 1660 * q^87 - 4080 * q^91 + 2568 * q^93 + 2172 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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