LMFDB - Embedded newform 240.4.v.c.113.3

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)

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")

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);

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 = [8,0,6] 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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.3
Root			$-2.66260 + 2.66260i$ of defining polynomial
Character	$\chi$	$=$	240.113
Dual form			240.4.v.c.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.80471 + 4.37420i) q^{3} +(-9.55729 + 5.80157i) q^{5} +(-9.35782 + 9.35782i) q^{7} +(-11.2672 + 24.5367i) q^{9} -34.1375i q^{11} +(2.82109 + 2.82109i) q^{13} +(-52.1826 - 25.5337i) q^{15} +(-64.2384 - 64.2384i) q^{17} -19.0735i q^{19} +(-67.1789 - 14.6869i) q^{21} +(-51.4018 + 51.4018i) q^{23} +(57.6836 - 110.895i) q^{25} +(-138.930 + 19.5337i) q^{27} -50.5042 q^{29} +93.3673 q^{31} +(149.324 - 95.7458i) q^{33} +(35.1454 - 143.725i) q^{35} +(-161.537 + 161.537i) q^{37} +(-4.42765 + 20.2524i) q^{39} -88.7935i q^{41} +(-176.399 - 176.399i) q^{43} +(-34.6678 - 299.872i) q^{45} +(38.2843 + 38.2843i) q^{47} +167.863i q^{49} +(100.821 - 461.162i) q^{51} +(-344.569 + 344.569i) q^{53} +(198.051 + 326.262i) q^{55} +(83.4310 - 53.4956i) q^{57} -421.133 q^{59} +2.00000 q^{61} +(-124.174 - 335.046i) q^{63} +(-43.3287 - 10.5952i) q^{65} +(-430.987 + 430.987i) q^{67} +(-369.009 - 80.6742i) q^{69} +733.866i q^{71} +(-348.073 - 348.073i) q^{73} +(646.860 - 58.7079i) q^{75} +(319.452 + 319.452i) q^{77} -588.019i q^{79} +(-475.102 - 552.919i) q^{81} +(-217.997 + 217.997i) q^{83} +(986.629 + 241.262i) q^{85} +(-141.650 - 220.915i) q^{87} +1272.00 q^{89} -52.7985 q^{91} +(261.868 + 408.407i) q^{93} +(110.656 + 182.291i) q^{95} +(-432.111 + 432.111i) q^{97} +(837.622 + 384.633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 16 q^{7} + 68 q^{13} - 90 q^{15} - 492 q^{21} - 220 q^{25} - 702 q^{27} - 616 q^{31} - 240 q^{33} - 1156 q^{37} - 548 q^{43} + 180 q^{45} + 852 q^{51} - 460 q^{55} + 684 q^{57} + 16 q^{61}+ \cdots + 1904 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 + 16 * q^7 + 68 * q^13 - 90 * q^15 - 492 * q^21 - 220 * q^25 - 702 * q^27 - 616 * q^31 - 240 * q^33 - 1156 * q^37 - 548 * q^43 + 180 * q^45 + 852 * q^51 - 460 * q^55 + 684 * q^57 + 16 * q^61 - 1428 * q^63 - 404 * q^67 - 2512 * q^73 + 2910 * q^75 + 288 * q^81 + 4940 * q^85 + 1680 * q^87 + 1304 * q^91 + 3408 * q^93 + 1904 * q^97

Character values

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

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	2.80471	+	4.37420i	0.539767	+	0.841814i
$3$	2.80471	+	4.37420i	0.539767	+	0.841814i
$4$		0			0
$5$	−9.55729	+	5.80157i	−0.854830	+	0.518908i
$5$	−9.55729	+	5.80157i	−0.854830	+	0.518908i
$6$		0			0
$7$	−9.35782	+	9.35782i	−0.505275	+	0.505275i	−0.913072	−	0.407798i	$-0.866297\pi$
$7$	−9.35782	+	9.35782i	−0.505275	+	0.505275i	0.407798	+	0.913072i	$0.366297\pi$
$8$		0			0
$9$	−11.2672	+	24.5367i	−0.417303	+	0.908768i
$10$		0			0
$11$		−	34.1375i		−	0.935712i	−0.883805	−	0.467856i	$-0.845027\pi$
$11$		−	34.1375i		−	0.935712i	0.883805	−	0.467856i	$-0.154973\pi$
$12$		0			0
$13$	2.82109	+	2.82109i	0.0601869	+	0.0601869i	0.736560	−	0.676373i	$-0.236449\pi$
$13$	2.82109	+	2.82109i	0.0601869	+	0.0601869i	−0.676373	+	0.736560i	$0.736449\pi$
$14$		0			0
$15$	−52.1826	−	25.5337i	−0.898233	−	0.439519i
$16$		0			0
$17$	−64.2384	−	64.2384i	−0.916477	−	0.916477i	0.0802942	−	0.996771i	$-0.474414\pi$
$17$	−64.2384	−	64.2384i	−0.916477	−	0.916477i	−0.996771	+	0.0802942i	$0.974414\pi$
$18$		0			0
$19$		−	19.0735i		−	0.230303i	−0.993348	−	0.115151i	$-0.963265\pi$
$19$		−	19.0735i		−	0.230303i	0.993348	−	0.115151i	$-0.0367353\pi$
$20$		0			0
$21$	−67.1789	−	14.6869i	−0.698078	−	0.152617i
$22$		0			0
$23$	−51.4018	+	51.4018i	−0.466001	+	0.466001i	−0.900616	−	0.434616i	$-0.856884\pi$
$23$	−51.4018	+	51.4018i	−0.466001	+	0.466001i	0.434616	+	0.900616i	$0.356884\pi$
$24$		0			0
$25$	57.6836	−	110.895i	0.461469	−	0.887156i
$26$		0			0
$27$	−138.930	+	19.5337i	−0.990260	+	0.139232i
$28$		0			0
$29$	−50.5042			−0.323393			−0.161697	−	0.986841i	$-0.551697\pi$
$29$	−50.5042			−0.323393			−0.161697	+	0.986841i	$0.551697\pi$
$30$		0			0
$31$	93.3673			0.540944			0.270472	−	0.962728i	$-0.412820\pi$
$31$	93.3673			0.540944			0.270472	+	0.962728i	$0.412820\pi$
$32$		0			0
$33$	149.324	−	95.7458i	0.787696	−	0.505067i
$34$		0			0
$35$	35.1454	−	143.725i	0.169733	−	0.694115i
$36$		0			0
$37$	−161.537	+	161.537i	−0.717743	+	0.717743i	−0.968142	−	0.250400i	$-0.919438\pi$
$37$	−161.537	+	161.537i	−0.717743	+	0.717743i	0.250400	+	0.968142i	$0.419438\pi$
$38$		0			0
$39$	−4.42765	+	20.2524i	−0.0181793	+	0.0831531i
$40$		0			0
$41$		−	88.7935i		−	0.338225i	−0.985597	−	0.169112i	$-0.945910\pi$
$41$		−	88.7935i		−	0.338225i	0.985597	−	0.169112i	$-0.0540901\pi$
$42$		0			0
$43$	−176.399	−	176.399i	−0.625596	−	0.625596i	0.321361	−	0.946957i	$-0.395860\pi$
$43$	−176.399	−	176.399i	−0.625596	−	0.625596i	−0.946957	+	0.321361i	$0.895860\pi$
$44$		0			0
$45$	−34.6678	−	299.872i	−0.114844	−	0.993384i
$46$		0			0
$47$	38.2843	+	38.2843i	0.118816	+	0.118816i	0.764015	−	0.645199i	$-0.223225\pi$
$47$	38.2843	+	38.2843i	0.118816	+	0.118816i	−0.645199	+	0.764015i	$0.723225\pi$
$48$		0			0
$49$			167.863i			0.489395i
$50$		0			0
$51$	100.821	−	461.162i	0.276819	−	1.26619i
$52$		0			0
$53$	−344.569	+	344.569i	−0.893022	+	0.893022i	−0.994806	−	0.101784i	$-0.967545\pi$
$53$	−344.569	+	344.569i	−0.893022	+	0.893022i	0.101784	+	0.994806i	$0.467545\pi$
$54$		0			0
$55$	198.051	+	326.262i	0.485549	+	0.799875i
$56$		0			0
$57$	83.4310	−	53.4956i	0.193872	−	0.124310i
$58$		0			0
$59$	−421.133			−0.929268			−0.464634	−	0.885503i	$-0.653814\pi$
$59$	−421.133			−0.929268			−0.464634	+	0.885503i	$0.653814\pi$
$60$		0			0
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$		0			0
$63$	−124.174	−	335.046i	−0.248325	−	0.670030i
$64$		0			0
$65$	−43.3287	−	10.5952i	−0.0826811	−	0.0202181i
$66$		0			0
$67$	−430.987	+	430.987i	−0.785872	+	0.785872i	−0.980815	−	0.194943i	$-0.937548\pi$
$67$	−430.987	+	430.987i	−0.785872	+	0.785872i	0.194943	+	0.980815i	$0.437548\pi$
$68$		0			0
$69$	−369.009	−	80.6742i	−0.643818	−	0.140754i
$70$		0			0
$71$			733.866i			1.22667i	0.789822	+	0.613337i	$0.210173\pi$
$71$			733.866i			1.22667i	−0.789822	+	0.613337i	$0.789827\pi$
$72$		0			0
$73$	−348.073	−	348.073i	−0.558067	−	0.558067i	0.370690	−	0.928757i	$-0.379121\pi$
$73$	−348.073	−	348.073i	−0.558067	−	0.558067i	−0.928757	+	0.370690i	$0.879121\pi$
$74$		0			0
$75$	646.860	−	58.7079i	0.995907	−	0.0903867i
$76$		0			0
$77$	319.452	+	319.452i	0.472792	+	0.472792i
$78$		0			0
$79$		−	588.019i		−	0.837434i	−0.908117	−	0.418717i	$-0.862480\pi$
$79$		−	588.019i		−	0.837434i	0.908117	−	0.418717i	$-0.137520\pi$
$80$		0			0
$81$	−475.102	−	552.919i	−0.651717	−	0.758462i
$82$		0			0
$83$	−217.997	+	217.997i	−0.288293	+	0.288293i	−0.836405	−	0.548112i	$-0.815347\pi$
$83$	−217.997	+	217.997i	−0.288293	+	0.288293i	0.548112	+	0.836405i	$0.315347\pi$
$84$		0			0
$85$	986.629	+	241.262i	1.25900	+	0.307865i
$86$		0			0
$87$	−141.650	−	220.915i	−0.174557	−	0.272237i
$88$		0			0
$89$	1272.00			1.51497			0.757483	−	0.652855i	$-0.226429\pi$
$89$	1272.00			1.51497			0.757483	+	0.652855i	$0.226429\pi$
$90$		0			0
$91$	−52.7985			−0.0608219
$92$		0			0
$93$	261.868	+	408.407i	0.291984	+	0.455374i
$94$		0			0
$95$	110.656	+	182.291i	0.119506	+	0.196870i
$96$		0			0
$97$	−432.111	+	432.111i	−0.452312	+	0.452312i	−0.896121	−	0.443809i	$-0.853627\pi$
$97$	−432.111	+	432.111i	−0.452312	+	0.452312i	0.443809	+	0.896121i	$0.353627\pi$
$98$		0			0
$99$	837.622	+	384.633i	0.850345	+	0.390475i
$100$		0			0
$101$			1662.30i			1.63767i	0.574029	+	0.818835i	$0.305380\pi$
$101$			1662.30i			1.63767i	−0.574029	+	0.818835i	$0.694620\pi$
$102$		0			0
$103$	774.495	+	774.495i	0.740906	+	0.740906i	0.972752	−	0.231847i	$-0.0744768\pi$
$103$	774.495	+	774.495i	0.740906	+	0.740906i	−0.231847	+	0.972752i	$0.574477\pi$
$104$		0			0
$105$	727.256	−	249.376i	0.675932	−	0.231777i
$106$		0			0
$107$	1170.26	+	1170.26i	1.05732	+	1.05732i	0.998254	+	0.0590633i	$0.0188114\pi$
$107$	1170.26	+	1170.26i	1.05732	+	1.05732i	0.0590633	+	0.998254i	$0.481189\pi$
$108$		0			0
$109$		−	1264.60i		−	1.11125i	−0.831432	−	0.555627i	$-0.812478\pi$
$109$		−	1264.60i		−	1.11125i	0.831432	−	0.555627i	$-0.187522\pi$
$110$		0			0
$111$	−1159.66	−	253.529i	−0.991620	−	0.216792i
$112$		0			0
$113$	381.173	−	381.173i	0.317325	−	0.317325i	−0.530414	−	0.847739i	$-0.677963\pi$
$113$	381.173	−	381.173i	0.317325	−	0.317325i	0.847739	+	0.530414i	$0.177963\pi$
$114$		0			0
$115$	193.051	−	789.473i	0.156540	−	0.640163i
$116$		0			0
$117$	−101.006	+	37.4346i	−0.0798121	+	0.0295798i
$118$		0			0
$119$	1202.26			0.926145
$120$		0			0
$121$	165.633			0.124442
$122$		0			0
$123$	388.400	−	249.040i	0.284722	−	0.182563i
$124$		0			0
$125$	92.0630	+	1394.51i	0.0658749	+	0.997828i
$126$		0			0
$127$	439.588	−	439.588i	0.307142	−	0.307142i	−0.536658	−	0.843800i	$-0.680313\pi$
$127$	439.588	−	439.588i	0.307142	−	0.307142i	0.843800	+	0.536658i	$0.180313\pi$
$128$		0			0
$129$	276.856	−	1266.35i	0.188959	−	0.864312i
$130$		0			0
$131$			1399.28i			0.933247i	0.884456	+	0.466623i	$0.154530\pi$
$131$			1399.28i			0.933247i	−0.884456	+	0.466623i	$0.845470\pi$
$132$		0			0
$133$	178.486	+	178.486i	0.116366	+	0.116366i
$134$		0			0
$135$	1214.46	−	992.698i	0.774255	−	0.632873i
$136$		0			0
$137$	1092.28	+	1092.28i	0.681169	+	0.681169i	0.960264	−	0.279095i	$-0.0900344\pi$
$137$	1092.28	+	1092.28i	0.681169	+	0.681169i	−0.279095	+	0.960264i	$0.590034\pi$
$138$		0			0
$139$		−	2498.43i		−	1.52456i	−0.647245	−	0.762282i	$-0.724079\pi$
$139$		−	2498.43i		−	1.52456i	0.647245	−	0.762282i	$-0.275921\pi$
$140$		0			0
$141$	−60.0866	+	274.840i	−0.0358880	+	0.164154i
$142$		0			0
$143$	96.3049	−	96.3049i	0.0563177	−	0.0563177i
$144$		0			0
$145$	482.684	−	293.004i	0.276446	−	0.167811i
$146$		0			0
$147$	−734.264	+	470.806i	−0.411980	+	0.264159i
$148$		0			0
$149$	−3570.40			−1.96308			−0.981538	−	0.191270i	$-0.938739\pi$
$149$	−3570.40			−1.96308			−0.981538	+	0.191270i	$0.938739\pi$
$150$		0			0
$151$	−2687.14			−1.44819			−0.724094	−	0.689701i	$-0.757742\pi$
$151$	−2687.14			−1.44819			−0.724094	+	0.689701i	$0.757742\pi$
$152$		0			0
$153$	2299.99	−	852.415i	1.21531	−	0.450416i
$154$		0			0
$155$	−892.338	+	541.676i	−0.462415	+	0.280700i
$156$		0			0
$157$	−1810.48	+	1810.48i	−0.920333	+	0.920333i	−0.997053	−	0.0767201i	$-0.975555\pi$
$157$	−1810.48	+	1810.48i	−0.920333	+	0.920333i	0.0767201	+	0.997053i	$0.475555\pi$
$158$		0			0
$159$	−2473.63	−	540.795i	−1.23378	−	0.269735i
$160$		0			0
$161$		−	962.017i		−	0.470916i
$162$		0			0
$163$	2679.06	+	2679.06i	1.28736	+	1.28736i	0.936382	+	0.350982i	$0.114152\pi$
$163$	2679.06	+	2679.06i	1.28736	+	1.28736i	0.350982	+	0.936382i	$0.385848\pi$
$164$		0			0
$165$	−871.657	+	1781.38i	−0.411263	+	0.840488i
$166$		0			0
$167$	−139.543	−	139.543i	−0.0646597	−	0.0646597i	0.674037	−	0.738697i	$-0.264559\pi$
$167$	−139.543	−	139.543i	−0.0646597	−	0.0646597i	−0.738697	+	0.674037i	$0.764559\pi$
$168$		0			0
$169$		−	2181.08i		−	0.992755i
$170$		0			0
$171$	468.000	+	214.904i	0.209292	+	0.0961059i
$172$		0			0
$173$	−881.613	+	881.613i	−0.387444	+	0.387444i	−0.873775	−	0.486331i	$-0.838335\pi$
$173$	−881.613	+	881.613i	−0.387444	+	0.387444i	0.486331	+	0.873775i	$0.338335\pi$
$174$		0			0
$175$	497.938	+	1577.52i	0.215089	+	0.681426i
$176$		0			0
$177$	−1181.16	−	1842.12i	−0.501588	−	0.782271i
$178$		0			0
$179$	−2512.87			−1.04928			−0.524638	−	0.851325i	$-0.675799\pi$
$179$	−2512.87			−1.04928			−0.524638	+	0.851325i	$0.675799\pi$
$180$		0			0
$181$	269.796			0.110795			0.0553973	−	0.998464i	$-0.482357\pi$
$181$	269.796			0.110795			0.0553973	+	0.998464i	$0.482357\pi$
$182$		0			0
$183$	5.60943	+	8.74839i	0.00226591	+	0.00353388i
$184$		0			0
$185$	606.687	−	2481.02i	0.241106	−	0.985990i
$186$		0			0
$187$	−2192.94	+	2192.94i	−0.857559	+	0.857559i
$188$		0			0
$189$	1117.29	−	1482.87i	0.430003	−	0.570703i
$190$		0			0
$191$		−	2420.22i		−	0.916864i	−0.888729	−	0.458432i	$-0.848411\pi$
$191$		−	2420.22i		−	0.916864i	0.888729	−	0.458432i	$-0.151589\pi$
$192$		0			0
$193$	1965.28	+	1965.28i	0.732973	+	0.732973i	0.971208	−	0.238234i	$-0.0765686\pi$
$193$	1965.28	+	1965.28i	0.732973	+	0.732973i	−0.238234	+	0.971208i	$0.576569\pi$
$194$		0			0
$195$	−75.1791	−	219.245i	−0.0276086	−	0.0805152i
$196$		0			0
$197$	−832.602	−	832.602i	−0.301119	−	0.301119i	0.540333	−	0.841452i	$-0.318298\pi$
$197$	−832.602	−	832.602i	−0.301119	−	0.301119i	−0.841452	+	0.540333i	$0.818298\pi$
$198$		0			0
$199$		−	1540.54i		−	0.548775i	−0.961619	−	0.274387i	$-0.911525\pi$
$199$		−	1540.54i		−	0.548775i	0.961619	−	0.274387i	$-0.0884750\pi$
$200$		0			0
$201$	−3094.02	−	676.426i	−1.08575	−	0.237370i
$202$		0			0
$203$	472.609	−	472.609i	0.163402	−	0.163402i
$204$		0			0
$205$	515.142	+	848.625i	0.175508	+	0.289125i
$206$		0			0
$207$	−682.079	−	1840.38i	−0.229023	−	0.617949i
$208$		0			0
$209$	−651.119			−0.215497
$210$		0			0
$211$	10.9380			0.00356874			0.00178437	−	0.999998i	$-0.499432\pi$
$211$	10.9380			0.00356874			0.00178437	+	0.999998i	$0.499432\pi$
$212$		0			0
$213$	−3210.07	+	2058.28i	−1.03263	+	0.662118i
$214$		0			0
$215$	2709.29	+	662.507i	0.859405	+	0.210152i
$216$		0			0
$217$	−873.714	+	873.714i	−0.273325	+	0.273325i
$218$		0			0
$219$	546.295	−	2498.79i	0.168563	−	0.771016i
$220$		0			0
$221$		−	362.445i		−	0.110320i
$222$		0			0
$223$	−831.512	−	831.512i	−0.249696	−	0.249696i	0.571150	−	0.820846i	$-0.306497\pi$
$223$	−831.512	−	831.512i	−0.249696	−	0.249696i	−0.820846	+	0.571150i	$0.806497\pi$
$224$		0			0
$225$	2071.06	+	2664.83i	0.613647	+	0.789581i
$226$		0			0
$227$	−3441.18	−	3441.18i	−1.00616	−	1.00616i	−0.999981	−	0.00618314i	$-0.998032\pi$
$227$	−3441.18	−	3441.18i	−1.00616	−	1.00616i	−0.00618314	−	0.999981i	$-0.501968\pi$
$228$		0			0
$229$		−	1680.38i		−	0.484903i	−0.970164	−	0.242451i	$-0.922049\pi$
$229$		−	1680.38i		−	0.484903i	0.970164	−	0.242451i	$-0.0779515\pi$
$230$		0			0
$231$	−501.375	+	2293.32i	−0.142805	+	0.653200i
$232$		0			0
$233$	2106.74	−	2106.74i	0.592348	−	0.592348i	−0.345917	−	0.938265i	$-0.612432\pi$
$233$	2106.74	−	2106.74i	0.592348	−	0.592348i	0.938265	+	0.345917i	$0.112432\pi$
$234$		0			0
$235$	−588.004	−	143.785i	−0.163222	−	0.0399129i
$236$		0			0
$237$	2572.11	−	1649.22i	0.704964	−	0.452019i
$238$		0			0
$239$	261.125			0.0706728			0.0353364	−	0.999375i	$-0.488750\pi$
$239$	261.125			0.0706728			0.0353364	+	0.999375i	$0.488750\pi$
$240$		0			0
$241$	−6001.45			−1.60410			−0.802048	−	0.597259i	$-0.796256\pi$
$241$	−6001.45			−1.60410			−0.802048	+	0.597259i	$0.796256\pi$
$242$		0			0
$243$	1086.05	−	3628.97i	0.286709	−	0.958018i
$244$		0			0
$245$	−973.866	−	1604.31i	−0.253951	−	0.418350i
$246$		0			0
$247$	53.8080	−	53.8080i	0.0138612	−	0.0138612i
$248$		0			0
$249$	−1564.98	−	342.143i	−0.398300	−	0.0870781i
$250$		0			0
$251$		−	3044.59i		−	0.765630i	−0.923825	−	0.382815i	$-0.874955\pi$
$251$		−	3044.59i		−	0.765630i	0.923825	−	0.382815i	$-0.125045\pi$
$252$		0			0
$253$	1754.73	+	1754.73i	0.436042	+	0.436042i
$254$		0			0
$255$	1711.89	+	4992.38i	0.420402	+	1.22602i
$256$		0			0
$257$	−946.317	−	946.317i	−0.229687	−	0.229687i	0.582875	−	0.812562i	$-0.301928\pi$
$257$	−946.317	−	946.317i	−0.229687	−	0.229687i	−0.812562	+	0.582875i	$0.801928\pi$
$258$		0			0
$259$		−	3023.26i		−	0.725314i
$260$		0			0
$261$	569.040	−	1239.21i	0.134953	−	0.293889i
$262$		0			0
$263$	−67.0257	+	67.0257i	−0.0157148	+	0.0157148i	−0.714921	−	0.699206i	$-0.753537\pi$
$263$	−67.0257	+	67.0257i	−0.0157148	+	0.0157148i	0.699206	+	0.714921i	$0.253537\pi$
$264$		0			0
$265$	1294.11	−	5292.18i	0.299986	−	1.22678i
$266$		0			0
$267$	3567.60	+	5563.99i	0.817729	+	1.27532i
$268$		0			0
$269$	2658.15			0.602492			0.301246	−	0.953546i	$-0.402597\pi$
$269$	2658.15			0.602492			0.301246	+	0.953546i	$0.402597\pi$
$270$		0			0
$271$	−145.673			−0.0326530			−0.0163265	−	0.999867i	$-0.505197\pi$
$271$	−145.673			−0.0326530			−0.0163265	+	0.999867i	$0.505197\pi$
$272$		0			0
$273$	−148.085	−	230.951i	−0.0328296	−	0.0512007i
$274$		0			0
$275$	−3785.66	−	1969.17i	−0.830123	−	0.431802i
$276$		0			0
$277$	−1074.57	+	1074.57i	−0.233085	+	0.233085i	−0.813979	−	0.580894i	$-0.802703\pi$
$277$	−1074.57	+	1074.57i	−0.233085	+	0.233085i	0.580894	+	0.813979i	$0.302703\pi$
$278$		0			0
$279$	−1051.98	+	2290.93i	−0.225737	+	0.491592i
$280$		0			0
$281$			2020.29i			0.428898i	0.976735	+	0.214449i	$0.0687956\pi$
$281$			2020.29i			0.428898i	−0.976735	+	0.214449i	$0.931204\pi$
$282$		0			0
$283$	2400.34	+	2400.34i	0.504189	+	0.504189i	0.912737	−	0.408548i	$-0.133965\pi$
$283$	2400.34	+	2400.34i	0.504189	+	0.504189i	−0.408548	+	0.912737i	$0.633965\pi$
$284$		0			0
$285$	−487.016	+	995.303i	−0.101222	+	0.206866i
$286$		0			0
$287$	830.913	+	830.913i	0.170896	+	0.170896i
$288$		0			0
$289$			3340.15i			0.679860i
$290$		0			0
$291$	−3102.09	−	678.191i	−0.624906	−	0.136619i
$292$		0			0
$293$	2533.13	−	2533.13i	0.505075	−	0.505075i	−0.407936	−	0.913011i	$-0.633751\pi$
$293$	2533.13	−	2533.13i	0.505075	−	0.505075i	0.913011	+	0.407936i	$0.133751\pi$
$294$		0			0
$295$	4024.89	−	2443.23i	0.794366	−	0.482204i
$296$		0			0
$297$	666.830	+	4742.71i	0.130281	+	0.926598i
$298$		0			0
$299$	−290.018			−0.0560943
$300$		0			0
$301$	3301.42			0.632196
$302$		0			0
$303$	−7271.21	+	4662.27i	−1.37861	+	0.883961i
$304$		0			0
$305$	−19.1146	+	11.6031i	−0.00358852	+	0.00217834i
$306$		0			0
$307$	−3159.93	+	3159.93i	−0.587449	+	0.587449i	−0.936940	−	0.349491i	$-0.886355\pi$
$307$	−3159.93	+	3159.93i	−0.587449	+	0.587449i	0.349491	+	0.936940i	$0.386355\pi$
$308$		0			0
$309$	−1215.56	+	5560.03i	−0.223788	+	1.02362i
$310$		0			0
$311$			7206.19i			1.31391i	0.753931	+	0.656954i	$0.228155\pi$
$311$			7206.19i			1.31391i	−0.753931	+	0.656954i	$0.771845\pi$
$312$		0			0
$313$	2029.31	+	2029.31i	0.366464	+	0.366464i	0.866186	−	0.499722i	$-0.166564\pi$
$313$	2029.31	+	2029.31i	0.366464	+	0.366464i	−0.499722	+	0.866186i	$0.666564\pi$
$314$		0			0
$315$	3130.56	+	2481.73i	0.559959	+	0.443904i
$316$		0			0
$317$	−689.223	−	689.223i	−0.122116	−	0.122116i	0.643408	−	0.765524i	$-0.277520\pi$
$317$	−689.223	−	689.223i	−0.122116	−	0.122116i	−0.765524	+	0.643408i	$0.777520\pi$
$318$		0			0
$319$			1724.09i			0.302603i
$320$		0			0
$321$	−1836.70	+	8401.16i	−0.319360	+	1.46077i
$322$		0			0
$323$	−1225.25	+	1225.25i	−0.211067	+	0.211067i
$324$		0			0
$325$	475.574	−	150.113i	0.0811696	−	0.0256208i
$326$		0			0
$327$	5531.60	−	3546.84i	0.935469	−	0.599818i
$328$		0			0
$329$	−716.516			−0.120069
$330$		0			0
$331$	8226.53			1.36608			0.683038	−	0.730383i	$-0.260658\pi$
$331$	8226.53			1.36608			0.683038	+	0.730383i	$0.260658\pi$
$332$		0			0
$333$	−2143.52	−	5783.64i	−0.352745	−	0.951777i
$334$		0			0
$335$	1618.67	−	6619.47i	0.263992	−	1.07958i
$336$		0			0
$337$	1777.34	−	1777.34i	0.287294	−	0.287294i	−0.548715	−	0.836009i	$-0.684883\pi$
$337$	1777.34	−	1777.34i	0.287294	−	0.287294i	0.836009	+	0.548715i	$0.184883\pi$
$338$		0			0
$339$	2736.41	+	598.245i	0.438411	+	0.0958472i
$340$		0			0
$341$		−	3187.32i		−	0.506168i
$342$		0			0
$343$	−4780.56	−	4780.56i	−0.752554	−	0.752554i
$344$		0			0
$345$	3994.76	−	1369.80i	0.623393	−	0.213761i
$346$		0			0
$347$	1715.22	+	1715.22i	0.265354	+	0.265354i	0.827225	−	0.561871i	$-0.189918\pi$
$347$	1715.22	+	1715.22i	0.265354	+	0.265354i	−0.561871	+	0.827225i	$0.689918\pi$
$348$		0			0
$349$		−	8603.96i		−	1.31965i	−0.751417	−	0.659827i	$-0.770629\pi$
$349$		−	8603.96i		−	1.31965i	0.751417	−	0.659827i	$-0.229371\pi$
$350$		0			0
$351$	−447.039	−	336.827i	−0.0679806	−	0.0512208i
$352$		0			0
$353$	−5425.13	+	5425.13i	−0.817990	+	0.817990i	−0.985816	−	0.167827i	$-0.946325\pi$
$353$	−5425.13	+	5425.13i	−0.817990	+	0.817990i	0.167827	+	0.985816i	$0.446325\pi$
$354$		0			0
$355$	−4257.57	−	7013.77i	−0.636531	−	1.04860i
$356$		0			0
$357$	3372.00	+	5258.93i	0.499903	+	0.779642i
$358$		0			0
$359$	11418.9			1.67874			0.839370	−	0.543560i	$-0.182924\pi$
$359$	11418.9			1.67874			0.839370	+	0.543560i	$0.182924\pi$
$360$		0			0
$361$	6495.20			0.946961
$362$		0			0
$363$	464.552	+	724.510i	0.0671699	+	0.104757i
$364$		0			0
$365$	5346.01	+	1307.27i	0.766638	+	0.187467i
$366$		0			0
$367$	−6554.73	+	6554.73i	−0.932299	+	0.932299i	−0.997849	−	0.0655499i	$-0.979120\pi$
$367$	−6554.73	+	6554.73i	−0.932299	+	0.932299i	0.0655499	+	0.997849i	$0.479120\pi$
$368$		0			0
$369$	2178.70	+	1000.45i	0.307368	+	0.141142i
$370$		0			0
$371$		−	6448.83i		−	0.902443i
$372$		0			0
$373$	−5967.46	−	5967.46i	−0.828374	−	0.828374i	0.158918	−	0.987292i	$-0.449199\pi$
$373$	−5967.46	−	5967.46i	−0.828374	−	0.828374i	−0.987292	+	0.158918i	$0.949199\pi$
$374$		0			0
$375$	−5841.64	+	4313.89i	−0.804429	+	0.594049i
$376$		0			0
$377$	−142.477	−	142.477i	−0.0194640	−	0.0194640i
$378$		0			0
$379$			1680.48i			0.227758i	0.993495	+	0.113879i	$0.0363276\pi$
$379$			1680.48i			0.227758i	−0.993495	+	0.113879i	$0.963672\pi$
$380$		0			0
$381$	3155.76	+	689.925i	0.424342	+	0.0927715i
$382$		0			0
$383$	7493.42	−	7493.42i	0.999728	−	0.999728i	−0.000271480	−	1.00000i	$-0.500086\pi$
$383$	7493.42	−	7493.42i	0.999728	−	0.999728i	1.00000		0.000271480i	$8.64148e-5\pi$
$384$		0			0
$385$	−4906.42	−	1199.77i	−0.649492	−	0.158821i
$386$		0			0
$387$	6315.78	−	2340.74i	0.829584	−	0.307459i
$388$		0			0
$389$	7966.97			1.03841			0.519205	−	0.854650i	$-0.326228\pi$
$389$	7966.97			1.03841			0.519205	+	0.854650i	$0.326228\pi$
$390$		0			0
$391$	6603.94			0.854158
$392$		0			0
$393$	−6120.71	+	3924.57i	−0.785620	+	0.503736i
$394$		0			0
$395$	3411.43	+	5619.87i	0.434551	+	0.715864i
$396$		0			0
$397$	−8188.88	+	8188.88i	−1.03523	+	1.03523i	−0.0358786	+	0.999356i	$0.511423\pi$
$397$	−8188.88	+	8188.88i	−1.03523	+	1.03523i	−0.999356	+	0.0358786i	$0.988577\pi$
$398$		0			0
$399$	−280.130	+	1281.33i	−0.0351480	+	0.160769i
$400$		0			0
$401$		−	5167.66i		−	0.643542i	−0.946817	−	0.321771i	$-0.895722\pi$
$401$		−	5167.66i		−	0.643542i	0.946817	−	0.321771i	$-0.104278\pi$
$402$		0			0
$403$	263.398	+	263.398i	0.0325577	+	0.0325577i
$404$		0			0
$405$	7748.48	+	2528.07i	0.950679	+	0.310175i
$406$		0			0
$407$	5514.46	+	5514.46i	0.671601	+	0.671601i
$408$		0			0
$409$			8514.82i			1.02941i	0.857366	+	0.514707i	$0.172099\pi$
$409$			8514.82i			1.02941i	−0.857366	+	0.514707i	$0.827901\pi$
$410$		0			0
$411$	−1714.32	+	7841.41i	−0.205745	+	0.941090i
$412$		0			0
$413$	3940.88	−	3940.88i	0.469535	−	0.469535i
$414$		0			0
$415$	818.738	−	3348.19i	0.0968440	−	0.396039i
$416$		0			0
$417$	10928.6	−	7007.39i	1.28340	−	0.822910i
$418$		0			0
$419$	−11939.7			−1.39211			−0.696053	−	0.717990i	$-0.745062\pi$
$419$	−11939.7			−1.39211			−0.696053	+	0.717990i	$0.745062\pi$
$420$		0			0
$421$	10873.3			1.25875			0.629373	−	0.777103i	$-0.283312\pi$
$421$	10873.3			1.25875			0.629373	+	0.777103i	$0.283312\pi$
$422$		0			0
$423$	−1370.73	+	508.016i	−0.157558	+	0.0583938i
$424$		0			0
$425$	−10829.2	+	3418.19i	−1.23598	+	0.390133i
$426$		0			0
$427$	−18.7156	+	18.7156i	−0.00212111	+	0.00212111i
$428$		0			0
$429$	691.364	+	151.149i	0.0778074	+	0.0170106i
$430$		0			0
$431$		−	7603.48i		−	0.849760i	−0.905250	−	0.424880i	$-0.860316\pi$
$431$		−	7603.48i		−	0.849760i	0.905250	−	0.424880i	$-0.139684\pi$
$432$		0			0
$433$	4681.19	+	4681.19i	0.519547	+	0.519547i	0.917434	−	0.397887i	$-0.130257\pi$
$433$	4681.19	+	4681.19i	0.519547	+	0.519547i	−0.397887	+	0.917434i	$0.630257\pi$
$434$		0			0
$435$	2635.44	+	1289.56i	0.290483	+	0.142137i
$436$		0			0
$437$	980.409	+	980.409i	0.107321	+	0.107321i
$438$		0			0
$439$			8608.08i			0.935857i	0.883766	+	0.467929i	$0.155000\pi$
$439$			8608.08i			0.935857i	−0.883766	+	0.467929i	$0.845000\pi$
$440$		0			0
$441$	−4118.80	−	1891.34i	−0.444746	−	0.204226i
$442$		0			0
$443$	−6466.81	+	6466.81i	−0.693561	+	0.693561i	−0.963014	−	0.269453i	$-0.913157\pi$
$443$	−6466.81	+	6466.81i	−0.693561	+	0.693561i	0.269453	+	0.963014i	$0.413157\pi$
$444$		0			0
$445$	−12156.9	+	7379.61i	−1.29504	+	0.786128i
$446$		0			0
$447$	−10013.9	−	15617.6i	−1.05960	−	1.65254i
$448$		0			0
$449$	356.370			0.0374569			0.0187284	−	0.999825i	$-0.494038\pi$
$449$	356.370			0.0374569			0.0187284	+	0.999825i	$0.494038\pi$
$450$		0			0
$451$	−3031.19			−0.316481
$452$		0			0
$453$	−7536.66	−	11754.1i	−0.781685	−	1.21911i
$454$		0			0
$455$	504.611	−	306.314i	0.0519923	−	0.0315609i
$456$		0			0
$457$	1512.80	−	1512.80i	0.154849	−	0.154849i	−0.625431	−	0.780280i	$-0.715077\pi$
$457$	1512.80	−	1512.80i	0.154849	−	0.154849i	0.780280	+	0.625431i	$0.215077\pi$
$458$		0			0
$459$	10179.4	+	7669.81i	1.03515	+	0.779948i
$460$		0			0
$461$		−	13307.9i		−	1.34449i	−0.740327	−	0.672246i	$-0.765330\pi$
$461$		−	13307.9i		−	1.34449i	0.740327	−	0.672246i	$-0.234670\pi$
$462$		0			0
$463$	1237.43	+	1237.43i	0.124208	+	0.124208i	0.766478	−	0.642270i	$-0.222007\pi$
$463$	1237.43	+	1237.43i	0.124208	+	0.124208i	−0.642270	+	0.766478i	$0.722007\pi$
$464$		0			0
$465$	−4872.15	−	2384.01i	−0.485894	−	0.237755i
$466$		0			0
$467$	−8201.87	−	8201.87i	−0.812713	−	0.812713i	0.172327	−	0.985040i	$-0.444872\pi$
$467$	−8201.87	−	8201.87i	−0.812713	−	0.812713i	−0.985040	+	0.172327i	$0.944872\pi$
$468$		0			0
$469$		−	8066.19i		−	0.794162i
$470$		0			0
$471$	−12997.3	−	2841.52i	−1.27151	−	0.277984i
$472$		0			0
$473$	−6021.83	+	6021.83i	−0.585378	+	0.585378i
$474$		0			0
$475$	−2115.14	−	1100.23i	−0.204314	−	0.106278i
$476$		0			0
$477$	−4572.28	−	12336.9i	−0.438889	−	1.18421i
$478$		0			0
$479$	−11419.1			−1.08926			−0.544629	−	0.838677i	$-0.683329\pi$
$479$	−11419.1			−1.08926			−0.544629	+	0.838677i	$0.683329\pi$
$480$		0			0
$481$	−911.420			−0.0863974
$482$		0			0
$483$	4208.05	−	2698.18i	0.396424	−	0.254185i
$484$		0			0
$485$	1622.89	−	6636.73i	0.151942	−	0.621358i
$486$		0			0
$487$	6066.93	−	6066.93i	0.564515	−	0.564515i	−0.366071	−	0.930587i	$-0.619297\pi$
$487$	6066.93	−	6066.93i	0.564515	−	0.564515i	0.930587	+	0.366071i	$0.119297\pi$
$488$		0			0
$489$	−4204.74	+	19232.7i	−0.388845	+	1.77860i
$490$		0			0
$491$			8978.88i			0.825277i	0.910895	+	0.412639i	$0.135393\pi$
$491$			8978.88i			0.825277i	−0.910895	+	0.412639i	$0.864607\pi$
$492$		0			0
$493$	3244.31	+	3244.31i	0.296382	+	0.296382i
$494$		0			0
$495$	−10236.9	+	1183.47i	−0.929521	+	0.107461i
$496$		0			0
$497$	−6867.38	−	6867.38i	−0.619807	−	0.619807i
$498$		0			0
$499$			7674.34i			0.688478i	0.938882	+	0.344239i	$0.111863\pi$
$499$			7674.34i			0.688478i	−0.938882	+	0.344239i	$0.888137\pi$
$500$		0			0
$501$	219.010	−	1001.77i	0.0195303	−	0.0893326i
$502$		0			0
$503$	4044.23	−	4044.23i	0.358496	−	0.358496i	−0.504762	−	0.863258i	$-0.668420\pi$
$503$	4044.23	−	4044.23i	0.358496	−	0.358496i	0.863258	+	0.504762i	$0.168420\pi$
$504$		0			0
$505$	−9643.93	−	15887.1i	−0.849800	−	1.39993i
$506$		0			0
$507$	9540.48	−	6117.31i	0.835715	−	0.535857i
$508$		0			0
$509$	−12532.5			−1.09134			−0.545672	−	0.837999i	$-0.683725\pi$
$509$	−12532.5			−1.09134			−0.545672	+	0.837999i	$0.683725\pi$
$510$		0			0
$511$	6514.42			0.563955
$512$		0			0
$513$	372.574	+	2649.87i	0.0320654	+	0.228059i
$514$		0			0
$515$	−11895.4	−	2908.79i	−1.01781	−	0.248887i
$516$		0			0
$517$	1306.93	−	1306.93i	0.111177	−	0.111177i
$518$		0			0
$519$	−6329.02	−	1383.68i	−0.535285	−	0.117026i
$520$		0			0
$521$			19201.8i			1.61468i	0.590089	+	0.807338i	$0.299093\pi$
$521$			19201.8i			1.61468i	−0.590089	+	0.807338i	$0.700907\pi$
$522$		0			0
$523$	−5472.69	−	5472.69i	−0.457560	−	0.457560i	0.440294	−	0.897854i	$-0.354874\pi$
$523$	−5472.69	−	5472.69i	−0.457560	−	0.457560i	−0.897854	+	0.440294i	$0.854874\pi$
$524$		0			0
$525$	−5503.82	+	6602.58i	−0.457536	+	0.548877i
$526$		0			0
$527$	−5997.77	−	5997.77i	−0.495762	−	0.495762i
$528$		0			0
$529$			6882.71i			0.565687i
$530$		0			0
$531$	4744.97	−	10333.2i	0.387786	−	0.844488i
$532$		0			0
$533$	250.495	−	250.495i	0.0203567	−	0.0203567i
$534$		0			0
$535$	−17973.8	−	4395.16i	−1.45248	−	0.355176i
$536$		0			0
$537$	−7047.87	−	10991.8i	−0.566365	−	0.883295i
$538$		0			0
$539$	5730.40			0.457933
$540$		0			0
$541$	12778.2			1.01548			0.507741	−	0.861510i	$-0.330481\pi$
$541$	12778.2			1.01548			0.507741	+	0.861510i	$0.330481\pi$
$542$		0			0
$543$	756.702	+	1180.14i	0.0598033	+	0.0932684i
$544$		0			0
$545$	7336.66	+	12086.1i	0.576638	+	0.949933i
$546$		0			0
$547$	2414.12	−	2414.12i	0.188702	−	0.188702i	−0.606433	−	0.795135i	$-0.707400\pi$
$547$	2414.12	−	2414.12i	0.188702	−	0.188702i	0.795135	+	0.606433i	$0.207400\pi$
$548$		0			0
$549$	−22.5343	+	49.0735i	−0.00175181	+	0.00381494i
$550$		0			0
$551$			963.290i			0.0744783i
$552$		0			0
$553$	5502.57	+	5502.57i	0.423134	+	0.423134i
$554$		0			0
$555$	12554.0	−	4304.78i	0.960162	−	0.329239i
$556$		0			0
$557$	5573.05	+	5573.05i	0.423946	+	0.423946i	0.886560	−	0.462614i	$-0.153088\pi$
$557$	5573.05	+	5573.05i	0.423946	+	0.423946i	−0.462614	+	0.886560i	$0.653088\pi$
$558$		0			0
$559$		−	995.277i		−	0.0753054i
$560$		0			0
$561$	−15742.9	−	3441.78i	−1.18479	−	0.259023i
$562$		0			0
$563$	−3488.75	+	3488.75i	−0.261160	+	0.261160i	−0.825525	−	0.564365i	$-0.809121\pi$
$563$	−3488.75	+	3488.75i	−0.261160	+	0.261160i	0.564365	+	0.825525i	$0.309121\pi$
$564$		0			0
$565$	−1431.58	+	5854.39i	−0.106597	+	0.435922i
$566$		0			0
$567$	9620.03	+	728.199i	0.712528	+	0.0539356i
$568$		0			0
$569$	−4924.15			−0.362796			−0.181398	−	0.983410i	$-0.558062\pi$
$569$	−4924.15			−0.362796			−0.181398	+	0.983410i	$0.558062\pi$
$570$		0			0
$571$	5642.12			0.413512			0.206756	−	0.978393i	$-0.433709\pi$
$571$	5642.12			0.413512			0.206756	+	0.978393i	$0.433709\pi$
$572$		0			0
$573$	10586.5	−	6788.02i	0.771829	−	0.494893i
$574$		0			0
$575$	2735.14	+	8665.22i	0.198371	+	0.628460i
$576$		0			0
$577$	8505.39	−	8505.39i	0.613663	−	0.613663i	−0.330235	−	0.943899i	$-0.607128\pi$
$577$	8505.39	−	8505.39i	0.613663	−	0.613663i	0.943899	+	0.330235i	$0.107128\pi$
$578$		0			0
$579$	−3084.47	+	14108.6i	−0.221392	+	1.01266i
$580$		0			0
$581$		−	4079.96i		−	0.291334i
$582$		0			0
$583$	11762.7	+	11762.7i	0.835612	+	0.835612i
$584$		0			0
$585$	748.165	−	943.767i	0.0528766	−	0.0667008i
$586$		0			0
$587$	1464.72	+	1464.72i	0.102990	+	0.102990i	0.756724	−	0.653734i	$-0.226798\pi$
$587$	1464.72	+	1464.72i	0.102990	+	0.102990i	−0.653734	+	0.756724i	$0.726798\pi$
$588$		0			0
$589$		−	1780.84i		−	0.124581i
$590$		0			0
$591$	1306.75	−	5977.17i	0.0909521	−	0.416020i
$592$		0			0
$593$	18086.4	−	18086.4i	1.25248	−	1.25248i	0.297871	−	0.954606i	$-0.403723\pi$
$593$	18086.4	−	18086.4i	1.25248	−	1.25248i	0.954606	−	0.297871i	$-0.0962766\pi$
$594$		0			0
$595$	−11490.4	+	6975.01i	−0.791697	+	0.480584i
$596$		0			0
$597$	6738.63	−	4320.78i	0.461966	−	0.296211i
$598$		0			0
$599$	21899.3			1.49379			0.746897	−	0.664940i	$-0.231543\pi$
$599$	21899.3			1.49379			0.746897	+	0.664940i	$0.231543\pi$
$600$		0			0
$601$	−12431.8			−0.843766			−0.421883	−	0.906650i	$-0.638631\pi$
$601$	−12431.8			−0.843766			−0.421883	+	0.906650i	$0.638631\pi$
$602$		0			0
$603$	−5719.00	−	15431.0i	−0.386229	−	1.04212i
$604$		0			0
$605$	−1583.00	+	960.930i	−0.106377	+	0.0645741i
$606$		0			0
$607$	−8237.79	+	8237.79i	−0.550843	+	0.550843i	−0.926684	−	0.375841i	$-0.877354\pi$
$607$	−8237.79	+	8237.79i	−0.550843	+	0.550843i	0.375841	+	0.926684i	$0.377354\pi$
$608$		0			0
$609$	3392.82	+	741.752i	0.225754	+	0.0493552i
$610$		0			0
$611$			216.007i			0.0143023i
$612$		0			0
$613$	−8913.02	−	8913.02i	−0.587265	−	0.587265i	0.349625	−	0.936890i	$-0.386309\pi$
$613$	−8913.02	−	8913.02i	−0.587265	−	0.587265i	−0.936890	+	0.349625i	$0.886309\pi$
$614$		0			0
$615$	−2267.23	+	4633.48i	−0.148656	+	0.303805i
$616$		0			0
$617$	1378.18	+	1378.18i	0.0899244	+	0.0899244i	0.750638	−	0.660714i	$-0.229746\pi$
$617$	1378.18	+	1378.18i	0.0899244	+	0.0899244i	−0.660714	+	0.750638i	$0.729746\pi$
$618$		0			0
$619$		−	18926.2i		−	1.22893i	−0.788945	−	0.614464i	$-0.789372\pi$
$619$		−	18926.2i		−	1.22893i	0.788945	−	0.614464i	$-0.210628\pi$
$620$		0			0
$621$	6137.16	−	8145.29i	0.396580	−	0.526344i
$622$		0			0
$623$	−11903.2	+	11903.2i	−0.765474	+	0.765474i
$624$		0			0
$625$	−8970.20	−	12793.6i	−0.574093	−	0.818790i
$626$		0			0
$627$	−1826.20	−	2848.12i	−0.116318	−	0.181408i
$628$		0			0
$629$	20753.7			1.31559
$630$		0			0
$631$	26118.8			1.64782			0.823909	−	0.566723i	$-0.191789\pi$
$631$	26118.8			1.64782			0.823909	+	0.566723i	$0.191789\pi$
$632$		0			0
$633$	30.6780	+	47.8450i	0.00192629	+	0.00300421i
$634$		0			0
$635$	−1650.97	+	6751.56i	−0.103176	+	0.421933i
$636$		0			0
$637$	−473.556	+	473.556i	−0.0294552	+	0.0294552i
$638$		0			0
$639$	−18006.7	−	8268.59i	−1.11476	−	0.511894i
$640$		0			0
$641$			15846.5i			0.976442i	0.872720	+	0.488221i	$0.162354\pi$
$641$			15846.5i			0.976442i	−0.872720	+	0.488221i	$0.837646\pi$
$642$		0			0
$643$	−89.9404	−	89.9404i	−0.00551618	−	0.00551618i	0.704343	−	0.709859i	$-0.251242\pi$
$643$	−89.9404	−	89.9404i	−0.00551618	−	0.00551618i	−0.709859	+	0.704343i	$0.751242\pi$
$644$		0			0
$645$	4700.85	+	13709.1i	0.286970	+	0.836893i
$646$		0			0
$647$	20057.0	+	20057.0i	1.21874	+	1.21874i	0.968074	+	0.250665i	$0.0806492\pi$
$647$	20057.0	+	20057.0i	1.21874	+	1.21874i	0.250665	+	0.968074i	$0.419351\pi$
$648$		0			0
$649$			14376.4i			0.869527i
$650$		0			0
$651$	−6272.31	−	1371.28i	−0.377621	−	0.0825570i
$652$		0			0
$653$	−20478.4	+	20478.4i	−1.22723	+	1.22723i	−0.262225	+	0.965007i	$0.584456\pi$
$653$	−20478.4	+	20478.4i	−1.22723	+	1.22723i	−0.965007	+	0.262225i	$0.915544\pi$
$654$		0			0
$655$	−8117.99	−	13373.3i	−0.484269	−	0.797767i
$656$		0			0
$657$	12462.4	−	4618.78i	0.740036	−	0.274271i
$658$		0			0
$659$	−1169.87			−0.0691529			−0.0345765	−	0.999402i	$-0.511008\pi$
$659$	−1169.87			−0.0691529			−0.0345765	+	0.999402i	$0.511008\pi$
$660$		0			0
$661$	19622.6			1.15466			0.577329	−	0.816511i	$-0.304095\pi$
$661$	19622.6			1.15466			0.577329	+	0.816511i	$0.304095\pi$
$662$		0			0
$663$	1585.41	−	1016.55i	0.0928688	−	0.0595471i
$664$		0			0
$665$	−2741.34	−	670.343i	−0.159856	−	0.0390899i
$666$		0			0
$667$	2596.01	−	2596.01i	0.150701	−	0.150701i
$668$		0			0
$669$	1305.04	−	5969.35i	0.0754199	−	0.344975i
$670$		0			0
$671$		−	68.2750i		−	0.00392806i
$672$		0			0
$673$	15256.3	+	15256.3i	0.873830	+	0.873830i	0.992887	−	0.119057i	$-0.0379872\pi$
$673$	15256.3	+	15256.3i	0.873830	+	0.873830i	−0.119057	+	0.992887i	$0.537987\pi$
$674$		0			0
$675$	−5847.79	+	16533.3i	−0.333454	+	0.942766i
$676$		0			0
$677$	−16.1429	−	16.1429i	−0.000916428	−	0.000916428i	0.706648	−	0.707565i	$-0.250206\pi$
$677$	−16.1429	−	16.1429i	−0.000916428	−	0.000916428i	−0.707565	+	0.706648i	$0.750206\pi$
$678$		0			0
$679$		−	8087.23i		−	0.457083i
$680$		0			0
$681$	5400.87	−	24703.9i	0.303909	−	1.39010i
$682$		0			0
$683$	3894.05	−	3894.05i	0.218157	−	0.218157i	−0.589564	−	0.807722i	$-0.700700\pi$
$683$	3894.05	−	3894.05i	0.218157	−	0.218157i	0.807722	+	0.589564i	$0.200700\pi$
$684$		0			0
$685$	−16776.2	−	4102.32i	−0.935747	−	0.228820i
$686$		0			0
$687$	7350.31	−	4712.99i	0.408198	−	0.261735i
$688$		0			0
$689$	−1944.12			−0.107497
$690$		0			0
$691$	1041.11			0.0573163			0.0286581	−	0.999589i	$-0.490877\pi$
$691$	1041.11			0.0573163			0.0286581	+	0.999589i	$0.490877\pi$
$692$		0			0
$693$	−11437.6	+	4238.99i	−0.626955	+	0.232361i
$694$		0			0
$695$	14494.8	+	23878.3i	0.791108	+	1.30324i
$696$		0			0
$697$	−5703.96	+	5703.96i	−0.309975	+	0.309975i
$698$		0			0
$699$	15124.1	+	3306.49i	0.818378	+	0.178917i
$700$		0			0
$701$			29885.3i			1.61020i	0.593138	+	0.805101i	$0.297889\pi$
$701$			29885.3i			1.61020i	−0.593138	+	0.805101i	$0.702111\pi$
$702$		0			0
$703$	3081.06	+	3081.06i	0.165298	+	0.165298i
$704$		0			0
$705$	−1020.24	−	2975.32i	−0.0545026	−	0.158946i
$706$		0			0
$707$	−15555.5	−	15555.5i	−0.827473	−	0.827473i
$708$		0			0
$709$			12115.0i			0.641734i	0.947124	+	0.320867i	$0.103974\pi$
$709$			12115.0i			0.641734i	−0.947124	+	0.320867i	$0.896026\pi$
$710$		0			0
$711$	14428.1	+	6625.31i	0.761033	+	0.349463i
$712$		0			0
$713$	−4799.24	+	4799.24i	−0.252080	+	0.252080i
$714$		0			0
$715$	−361.695	+	1479.13i	−0.0189183	+	0.0773657i
$716$		0			0
$717$	732.381	+	1142.21i	0.0381468	+	0.0594933i
$718$		0			0
$719$	6371.24			0.330469			0.165234	−	0.986254i	$-0.447162\pi$
$719$	6371.24			0.330469			0.165234	+	0.986254i	$0.447162\pi$
$720$		0			0
$721$	−14495.2			−0.748722
$722$		0			0
$723$	−16832.3	−	26251.5i	−0.865839	−	1.35035i
$724$		0			0
$725$	−2913.27	+	5600.64i	−0.149236	+	0.286900i
$726$		0			0
$727$	−15771.9	+	15771.9i	−0.804604	+	0.804604i	−0.983811	−	0.179207i	$-0.942647\pi$
$727$	−15771.9	+	15771.9i	−0.804604	+	0.804604i	0.179207	+	0.983811i	$0.442647\pi$
$728$		0			0
$729$	18919.9	−	5427.61i	0.961229	−	0.275751i
$730$		0			0
$731$			22663.2i			1.14669i
$732$		0			0
$733$	−5626.05	−	5626.05i	−0.283496	−	0.283496i	0.551005	−	0.834502i	$-0.314244\pi$
$733$	−5626.05	−	5626.05i	−0.283496	−	0.283496i	−0.834502	+	0.551005i	$0.814244\pi$
$734$		0			0
$735$	4286.16	−	8759.51i	0.215098	−	0.439591i
$736$		0			0
$737$	14712.8	+	14712.8i	0.735350	+	0.735350i
$738$		0			0
$739$			30340.1i			1.51026i	0.655577	+	0.755129i	$0.272426\pi$
$739$			30340.1i			1.51026i	−0.655577	+	0.755129i	$0.727574\pi$
$740$		0			0
$741$	386.282	+	84.4506i	0.0191504	+	0.00418674i
$742$		0			0
$743$	2368.77	−	2368.77i	0.116961	−	0.116961i	−0.646204	−	0.763165i	$-0.723645\pi$
$743$	2368.77	−	2368.77i	0.116961	−	0.116961i	0.763165	+	0.646204i	$0.223645\pi$
$744$		0			0
$745$	34123.3	−	20713.9i	1.67810	−	1.01866i
$746$		0			0
$747$	−2892.73	−	7805.16i	−0.141686	−	0.382297i
$748$		0			0
$749$	−21902.1			−1.06847
$750$		0			0
$751$	−10606.2			−0.515346			−0.257673	−	0.966232i	$-0.582956\pi$
$751$	−10606.2			−0.515346			−0.257673	+	0.966232i	$0.582956\pi$
$752$		0			0
$753$	13317.6	−	8539.21i	0.644518	−	0.413262i
$754$		0			0
$755$	25681.8	−	15589.6i	1.23796	−	0.751477i
$756$		0			0
$757$	−18470.4	+	18470.4i	−0.886812	+	0.886812i	−0.994215	−	0.107404i	$-0.965746\pi$
$757$	−18470.4	+	18470.4i	−0.886812	+	0.886812i	0.107404	+	0.994215i	$0.465746\pi$
$758$		0			0
$759$	−2754.01	+	12597.0i	−0.131705	+	0.602428i
$760$		0			0
$761$		−	13568.0i		−	0.646307i	−0.946347	−	0.323153i	$-0.895257\pi$
$761$		−	13568.0i		−	0.646307i	0.946347	−	0.323153i	$-0.104743\pi$
$762$		0			0
$763$	11833.9	+	11833.9i	0.561488	+	0.561488i
$764$		0			0
$765$	−17036.3	+	21490.3i	−0.805161	+	1.01566i
$766$		0			0
$767$	−1188.05	−	1188.05i	−0.0559298	−	0.0559298i
$768$		0			0
$769$		−	11029.1i		−	0.517190i	−0.965986	−	0.258595i	$-0.916741\pi$
$769$		−	11029.1i		−	0.517190i	0.965986	−	0.258595i	$-0.0832594\pi$
$770$		0			0
$771$	1485.23	−	6793.52i	0.0693764	−	0.317332i
$772$		0			0
$773$	−7090.94	+	7090.94i	−0.329940	+	0.329940i	−0.852563	−	0.522624i	$-0.824953\pi$
$773$	−7090.94	+	7090.94i	−0.329940	+	0.329940i	0.522624	+	0.852563i	$0.324953\pi$
$774$		0			0
$775$	5385.76	−	10353.9i	0.249629	−	0.479902i
$776$		0			0
$777$	13224.3	−	8479.38i	0.610580	−	0.391501i
$778$		0			0
$779$	−1693.60			−0.0778940
$780$		0			0
$781$	25052.3			1.14781
$782$		0			0
$783$	7016.53	−	986.533i	0.320243	−	0.0450266i
$784$		0			0
$785$	6799.67	−	27806.9i	0.309160	−	1.26430i
$786$		0			0
$787$	17915.0	−	17915.0i	0.811437	−	0.811437i	−0.173412	−	0.984849i	$-0.555479\pi$
$787$	17915.0	−	17915.0i	0.811437	−	0.811437i	0.984849	+	0.173412i	$0.0554793\pi$
$788$		0			0
$789$	−481.172	−	105.196i	−0.0217112	−	0.00474660i
$790$		0			0
$791$			7133.90i			0.320673i
$792$		0			0
$793$	5.64218	+	5.64218i	0.000252661	+	0.000252661i
$794$		0			0
$795$	26778.6	−	9182.39i	1.19464	−	0.409643i
$796$		0			0
$797$	6043.79	+	6043.79i	0.268610	+	0.268610i	0.828540	−	0.559930i	$-0.189172\pi$
$797$	6043.79	+	6043.79i	0.268610	+	0.268610i	−0.559930	+	0.828540i	$0.689172\pi$
$798$		0			0
$799$		−	4918.65i		−	0.217784i
$800$		0			0
$801$	−14331.9	+	31210.8i	−0.632199	+	1.37675i
$802$		0			0
$803$	−11882.3	+	11882.3i	−0.522191	+	0.522191i
$804$		0			0
$805$	5581.21	+	9194.28i	0.244362	+	0.402554i
$806$		0			0
$807$	7455.35	+	11627.3i	0.325205	+	0.507186i
$808$		0			0
$809$	35063.4			1.52381			0.761905	−	0.647689i	$-0.224264\pi$
$809$	35063.4			1.52381			0.761905	+	0.647689i	$0.224264\pi$
$810$		0			0
$811$	−24621.3			−1.06605			−0.533027	−	0.846098i	$-0.678946\pi$
$811$	−24621.3			−1.06605			−0.533027	+	0.846098i	$0.678946\pi$
$812$		0			0
$813$	−408.570	−	637.200i	−0.0176250	−	0.0274878i
$814$		0			0
$815$	−41147.3	−	10061.8i	−1.76850	−	0.432454i
$816$		0			0
$817$	−3364.54	+	3364.54i	−0.144076	+	0.144076i
$818$		0			0
$819$	594.890	−	1295.50i	0.0253811	−	0.0552729i
$820$		0			0
$821$		−	14268.3i		−	0.606538i	−0.952905	−	0.303269i	$-0.901922\pi$
$821$		−	14268.3i		−	0.606538i	0.952905	−	0.303269i	$-0.0980781\pi$
$822$		0			0
$823$	−13764.1	−	13764.1i	−0.582972	−	0.582972i	0.352747	−	0.935719i	$-0.385248\pi$
$823$	−13764.1	−	13764.1i	−0.582972	−	0.582972i	−0.935719	+	0.352747i	$0.885248\pi$
$824$		0			0
$825$	−2004.14	−	22082.2i	−0.0845760	−	0.931882i
$826$		0			0
$827$	27442.5	+	27442.5i	1.15389	+	1.15389i	0.985765	+	0.168128i	$0.0537721\pi$
$827$	27442.5	+	27442.5i	1.15389	+	1.15389i	0.168128	+	0.985765i	$0.446228\pi$
$828$		0			0
$829$		−	12176.9i		−	0.510159i	−0.966920	−	0.255080i	$-0.917898\pi$
$829$		−	12176.9i		−	0.510159i	0.966920	−	0.255080i	$-0.0821016\pi$
$830$		0			0
$831$	−7714.23	−	1686.52i	−0.322026	−	0.0704027i
$832$		0			0
$833$	10783.2	−	10783.2i	0.448519	−	0.448519i
$834$		0			0
$835$	2143.22	+	524.085i	0.0888255	+	0.0217206i
$836$		0			0
$837$	−12971.5	+	1823.80i	−0.535675	+	0.0753165i
$838$		0			0
$839$	−13942.3			−0.573710			−0.286855	−	0.957974i	$-0.592610\pi$
$839$	−13942.3			−0.573710			−0.286855	+	0.957974i	$0.592610\pi$
$840$		0			0
$841$	−21838.3			−0.895417
$842$		0			0
$843$	−8837.14	+	5666.33i	−0.361053	+	0.231505i
$844$		0			0
$845$	12653.7	+	20845.2i	0.515149	+	0.848637i
$846$		0			0
$847$	−1549.96	+	1549.96i	−0.0628776	+	0.0628776i
$848$		0			0
$849$	−3767.30	+	17231.8i	−0.152289	+	0.696579i
$850$		0			0
$851$		−	16606.6i		−	0.668937i
$852$		0			0
$853$	−32654.2	−	32654.2i	−1.31074	−	1.31074i	−0.920871	−	0.389866i	$-0.872521\pi$
$853$	−32654.2	−	32654.2i	−1.31074	−	1.31074i	−0.389866	−	0.920871i	$-0.627479\pi$
$854$		0			0
$855$	−5719.59	+	661.235i	−0.228779	+	0.0264489i
$856$		0			0
$857$	−10358.9	−	10358.9i	−0.412898	−	0.412898i	0.469849	−	0.882747i	$-0.344308\pi$
$857$	−10358.9	−	10358.9i	−0.412898	−	0.412898i	−0.882747	+	0.469849i	$0.844308\pi$
$858$		0			0
$859$		−	14100.5i		−	0.560072i	−0.959990	−	0.280036i	$-0.909654\pi$
$859$		−	14100.5i		−	0.560072i	0.959990	−	0.280036i	$-0.0903464\pi$
$860$		0			0
$861$	−1304.10	+	5965.05i	−0.0516187	+	0.236107i
$862$		0			0
$863$	16830.6	−	16830.6i	0.663872	−	0.663872i	−0.292419	−	0.956290i	$-0.594460\pi$
$863$	16830.6	−	16830.6i	0.663872	−	0.663872i	0.956290	+	0.292419i	$0.0944601\pi$
$864$		0			0
$865$	3311.09	−	13540.6i	0.130151	−	0.532246i
$866$		0			0
$867$	−14610.5	+	9368.17i	−0.572316	+	0.366966i
$868$		0			0
$869$	−20073.5			−0.783597
$870$		0			0
$871$	−2431.71			−0.0945984
$872$		0			0
$873$	−5733.92	−	15471.3i	−0.222295	−	0.599797i
$874$		0			0
$875$	−13911.0	−	12188.0i	−0.537462	−	0.470892i
$876$		0			0
$877$	9832.57	−	9832.57i	0.378589	−	0.378589i	−0.492004	−	0.870593i	$-0.663736\pi$
$877$	9832.57	−	9832.57i	0.378589	−	0.378589i	0.870593	+	0.492004i	$0.163736\pi$
$878$		0			0
$879$	18185.1	+	3975.70i	0.697802	+	0.152556i
$880$		0			0
$881$		−	41729.4i		−	1.59580i	−0.602789	−	0.797900i	$-0.705944\pi$
$881$		−	41729.4i		−	1.59580i	0.602789	−	0.797900i	$-0.294056\pi$
$882$		0			0
$883$	11757.3	+	11757.3i	0.448090	+	0.448090i	0.894719	−	0.446629i	$-0.147376\pi$
$883$	11757.3	+	11757.3i	0.448090	+	0.448090i	−0.446629	+	0.894719i	$0.647376\pi$
$884$		0			0
$885$	21975.8	+	10753.1i	0.834699	+	0.408431i
$886$		0			0
$887$	−24303.5	−	24303.5i	−0.919989	−	0.919989i	0.0770388	−	0.997028i	$-0.475453\pi$
$887$	−24303.5	−	24303.5i	−0.919989	−	0.919989i	−0.997028	+	0.0770388i	$0.975453\pi$
$888$		0			0
$889$			8227.16i			0.310383i
$890$		0			0
$891$	−18875.3	+	16218.8i	−0.709702	+	0.609820i
$892$		0			0
$893$	730.214	−	730.214i	0.0273636	−	0.0273636i
$894$		0			0
$895$	24016.2	−	14578.6i	0.896953	−	0.544478i
$896$		0			0
$897$	−813.418	−	1268.60i	−0.0302779	−	0.0472210i
$898$		0			0
$899$	−4715.44			−0.174937
$900$		0			0
$901$	44269.1			1.63687
$902$		0			0
$903$	9259.55	+	14441.1i	0.341239	+	0.532191i
$904$		0			0
$905$	−2578.52	+	1565.24i	−0.0947105	+	0.0574922i
$906$		0			0
$907$	−1017.75	+	1017.75i	−0.0372589	+	0.0372589i	−0.725491	−	0.688232i	$-0.758387\pi$
$907$	−1017.75	+	1017.75i	−0.0372589	+	0.0372589i	0.688232	+	0.725491i	$0.258387\pi$
$908$		0			0
$909$	−40787.3	−	18729.4i	−1.48826	−	0.683404i
$910$		0			0
$911$		−	33165.2i		−	1.20616i	−0.797681	−	0.603080i	$-0.793940\pi$
$911$		−	33165.2i		−	1.20616i	0.797681	−	0.603080i	$-0.206060\pi$
$912$		0			0
$913$	7441.88	+	7441.88i	0.269759	+	0.269759i
$914$		0			0
$915$	−104.365	−	51.0675i	−0.00377072	−	0.00184507i
$916$		0			0
$917$	−13094.2	−	13094.2i	−0.471546	−	0.471546i
$918$		0			0
$919$		−	2162.18i		−	0.0776103i	−0.999247	−	0.0388051i	$-0.987645\pi$
$919$		−	2162.18i		−	0.0776103i	0.999247	−	0.0388051i	$-0.0123552\pi$
$920$		0			0
$921$	−22684.9	−	4959.46i	−0.811609	−	0.177437i
$922$		0			0
$923$	−2070.30	+	2070.30i	−0.0738297	+	0.0738297i
$924$		0			0
$925$	8595.52	+	27231.6i	0.305534	+	0.967966i
$926$		0			0
$927$	−27729.9	+	10277.2i	−0.982493	+	0.364129i
$928$		0			0
$929$	−17695.1			−0.624929			−0.312464	−	0.949930i	$-0.601154\pi$
$929$	−17695.1			−0.624929			−0.312464	+	0.949930i	$0.601154\pi$
$930$		0			0
$931$	3201.72			0.112709
$932$		0			0
$933$	−31521.3	+	20211.3i	−1.10607	+	0.709204i
$934$		0			0
$935$	8236.07	−	33681.0i	0.288073	−	1.17806i
$936$		0			0
$937$	−30208.0	+	30208.0i	−1.05320	+	1.05320i	−0.0547017	+	0.998503i	$0.517421\pi$
$937$	−30208.0	+	30208.0i	−1.05320	+	1.05320i	−0.998503	+	0.0547017i	$0.982579\pi$
$938$		0			0
$939$	−3184.96	+	14568.2i	−0.110689	+	0.506300i
$940$		0			0
$941$			1499.59i			0.0519503i	0.999663	+	0.0259752i	$0.00826908\pi$
$941$			1499.59i			0.0519503i	−0.999663	+	0.0259752i	$0.991731\pi$
$942$		0			0
$943$	4564.14	+	4564.14i	0.157613	+	0.157613i
$944$		0			0
$945$	−2075.25	+	20654.2i	−0.0714369	+	0.710986i
$946$		0			0
$947$	−13763.8	−	13763.8i	−0.472294	−	0.472294i	0.430362	−	0.902656i	$-0.358386\pi$
$947$	−13763.8	−	13763.8i	−0.472294	−	0.472294i	−0.902656	+	0.430362i	$0.858386\pi$
$948$		0			0
$949$		−	1963.89i		−	0.0671767i
$950$		0			0
$951$	1081.72	−	4947.87i	0.0368847	−	0.168713i
$952$		0			0
$953$	14570.7	−	14570.7i	0.495268	−	0.495268i	−0.414693	−	0.909961i	$-0.636111\pi$
$953$	14570.7	−	14570.7i	0.495268	−	0.495268i	0.909961	+	0.414693i	$0.136111\pi$
$954$		0			0
$955$	14041.1	+	23130.8i	0.475768	+	0.783763i
$956$		0			0
$957$	−7541.49	+	4835.57i	−0.254735	+	0.163335i
$958$		0			0
$959$	−20442.8			−0.688355
$960$		0			0
$961$	−21073.6			−0.707380
$962$		0			0
$963$	−41899.7	+	15528.8i	−1.40208	+	0.519635i
$964$		0			0
$965$	−30184.4	−	7381.04i	−1.00691	−	0.246222i
$966$		0			0
$967$	−28409.1	+	28409.1i	−0.944752	+	0.944752i	−0.998552	−	0.0538000i	$-0.982867\pi$
$967$	−28409.1	+	28409.1i	−0.944752	+	0.944752i	0.0538000	+	0.998552i	$0.482867\pi$
$968$		0			0
$969$	−8795.95	−	1923.01i	−0.291606	−	0.0637522i
$970$		0			0
$971$		−	18059.4i		−	0.596864i	−0.954431	−	0.298432i	$-0.903536\pi$
$971$		−	18059.4i		−	0.596864i	0.954431	−	0.298432i	$-0.0964637\pi$
$972$		0			0
$973$	23379.9	+	23379.9i	0.770323	+	0.770323i
$974$		0			0
$975$	1990.47	+	1659.23i	0.0653807	+	0.0545005i
$976$		0			0
$977$	−31166.3	−	31166.3i	−1.02057	−	1.02057i	−0.999784	−	0.0207872i	$-0.993383\pi$
$977$	−31166.3	−	31166.3i	−1.02057	−	1.02057i	−0.0207872	−	0.999784i	$-0.506617\pi$
$978$		0			0
$979$		−	43422.9i		−	1.41757i
$980$		0			0
$981$	31029.1	+	14248.5i	1.00987	+	0.463729i
$982$		0			0
$983$	−13839.4	+	13839.4i	−0.449042	+	0.449042i	−0.895036	−	0.445994i	$-0.852850\pi$
$983$	−13839.4	+	13839.4i	−0.449042	+	0.449042i	0.445994	+	0.895036i	$0.352850\pi$
$984$		0			0
$985$	12787.8	+	3127.02i	0.413659	+	0.101153i
$986$		0			0
$987$	−2009.62	−	3134.18i	−0.0648095	−	0.101076i
$988$		0			0
$989$	18134.5			0.583056
$990$		0			0
$991$	−17820.9			−0.571242			−0.285621	−	0.958343i	$-0.592200\pi$
$991$	−17820.9			−0.571242			−0.285621	+	0.958343i	$0.592200\pi$
$992$		0			0
$993$	23073.1	+	35984.5i	0.737363	+	1.14998i
$994$		0			0
$995$	8937.56	+	14723.4i	0.284764	+	0.469109i
$996$		0			0
$997$	−36985.0	+	36985.0i	−1.17485	+	1.17485i	−0.193814	+	0.981038i	$0.562086\pi$
$997$	−36985.0	+	36985.0i	−1.17485	+	1.17485i	−0.981038	+	0.193814i	$0.937914\pi$
$998$		0			0
$999$	19286.8	−	25597.6i	0.610819	−	0.810684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.4.v.c.113.3		8
3.2	odd	2	inner	240.4.v.c.113.4		8
4.3	odd	2		15.4.e.a.8.4	yes	8
5.2	odd	4	inner	240.4.v.c.17.4		8
12.11	even	2		15.4.e.a.8.1	yes	8
15.2	even	4	inner	240.4.v.c.17.3		8
20.3	even	4		75.4.e.c.32.4		8
20.7	even	4		15.4.e.a.2.1	✓	8
20.19	odd	2		75.4.e.c.68.1		8
60.23	odd	4		75.4.e.c.32.1		8
60.47	odd	4		15.4.e.a.2.4	yes	8
60.59	even	2		75.4.e.c.68.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.1	✓	8	20.7	even	4
15.4.e.a.2.4	yes	8	60.47	odd	4
15.4.e.a.8.1	yes	8	12.11	even	2
15.4.e.a.8.4	yes	8	4.3	odd	2
75.4.e.c.32.1		8	60.23	odd	4
75.4.e.c.32.4		8	20.3	even	4
75.4.e.c.68.1		8	20.19	odd	2
75.4.e.c.68.4		8	60.59	even	2
240.4.v.c.17.3		8	15.2	even	4	inner
240.4.v.c.17.4		8	5.2	odd	4	inner
240.4.v.c.113.3		8	1.1	even	1	trivial
240.4.v.c.113.4		8	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(2.80471 + 4.37420i) q^{3} +(-9.55729 + 5.80157i) q^{5} +(-9.35782 + 9.35782i) q^{7} +(-11.2672 + 24.5367i) q^{9} -34.1375i q^{11} +(2.82109 + 2.82109i) q^{13} +(-52.1826 - 25.5337i) q^{15} +(-64.2384 - 64.2384i) q^{17} -19.0735i q^{19} +(-67.1789 - 14.6869i) q^{21} +(-51.4018 + 51.4018i) q^{23} +(57.6836 - 110.895i) q^{25} +(-138.930 + 19.5337i) q^{27} -50.5042 q^{29} +93.3673 q^{31} +(149.324 - 95.7458i) q^{33} +(35.1454 - 143.725i) q^{35} +(-161.537 + 161.537i) q^{37} +(-4.42765 + 20.2524i) q^{39} -88.7935i q^{41} +(-176.399 - 176.399i) q^{43} +(-34.6678 - 299.872i) q^{45} +(38.2843 + 38.2843i) q^{47} +167.863i q^{49} +(100.821 - 461.162i) q^{51} +(-344.569 + 344.569i) q^{53} +(198.051 + 326.262i) q^{55} +(83.4310 - 53.4956i) q^{57} -421.133 q^{59} +2.00000 q^{61} +(-124.174 - 335.046i) q^{63} +(-43.3287 - 10.5952i) q^{65} +(-430.987 + 430.987i) q^{67} +(-369.009 - 80.6742i) q^{69} +733.866i q^{71} +(-348.073 - 348.073i) q^{73} +(646.860 - 58.7079i) q^{75} +(319.452 + 319.452i) q^{77} -588.019i q^{79} +(-475.102 - 552.919i) q^{81} +(-217.997 + 217.997i) q^{83} +(986.629 + 241.262i) q^{85} +(-141.650 - 220.915i) q^{87} +1272.00 q^{89} -52.7985 q^{91} +(261.868 + 408.407i) q^{93} +(110.656 + 182.291i) q^{95} +(-432.111 + 432.111i) q^{97} +(837.622 + 384.633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 16 q^{7} + 68 q^{13} - 90 q^{15} - 492 q^{21} - 220 q^{25} - 702 q^{27} - 616 q^{31} - 240 q^{33} - 1156 q^{37} - 548 q^{43} + 180 q^{45} + 852 q^{51} - 460 q^{55} + 684 q^{57} + 16 q^{61}+ \cdots + 1904 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 + 16 * q^7 + 68 * q^13 - 90 * q^15 - 492 * q^21 - 220 * q^25 - 702 * q^27 - 616 * q^31 - 240 * q^33 - 1156 * q^37 - 548 * q^43 + 180 * q^45 + 852 * q^51 - 460 * q^55 + 684 * q^57 + 16 * q^61 - 1428 * q^63 - 404 * q^67 - 2512 * q^73 + 2910 * q^75 + 288 * q^81 + 4940 * q^85 + 1680 * q^87 + 1304 * q^91 + 3408 * q^93 + 1904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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