LMFDB - Embedded newform 289.3.e.q.75.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			75.5
Character	$\chi$	$=$	289.75
Dual form			289.3.e.q.158.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30551 - 3.15179i) q^{2} +(-2.10237 + 3.14642i) q^{3} +(-5.40099 - 5.40099i) q^{4} +(0.793166 + 3.98752i) q^{5} +(7.17219 + 10.7339i) q^{6} +(1.40356 - 7.05618i) q^{7} +(-11.4667 + 4.74967i) q^{8} +(-2.03586 - 4.91500i) q^{9} +(13.6033 + 2.70587i) q^{10} +(8.47833 - 5.66504i) q^{11} +(28.3487 - 5.63891i) q^{12} +(6.16377 - 6.16377i) q^{13} +(-20.4072 - 13.6357i) q^{14} +(-14.2139 - 5.88761i) q^{15} +11.7888i q^{16} -18.1489 q^{18} +(12.4979 - 30.1727i) q^{19} +(17.2527 - 25.8204i) q^{20} +(19.2509 + 19.2509i) q^{21} +(-6.78644 - 34.1177i) q^{22} +(0.682389 + 1.02127i) q^{23} +(9.16284 - 46.0647i) q^{24} +(7.82581 - 3.24156i) q^{25} +(-11.3800 - 27.4738i) q^{26} +(-13.6583 - 2.71681i) q^{27} +(-45.6910 + 30.5298i) q^{28} +(-22.3601 + 4.44769i) q^{29} +(-37.1130 + 37.1130i) q^{30} +(22.9445 + 15.3310i) q^{31} +(-8.71099 - 3.60821i) q^{32} +38.5864i q^{33} +29.2499 q^{35} +(-15.5502 + 37.5415i) q^{36} +(23.6739 - 35.4305i) q^{37} +(-78.7818 - 78.7818i) q^{38} +(6.43528 + 32.3524i) q^{39} +(-28.0344 - 41.9564i) q^{40} +(-4.21560 + 21.1933i) q^{41} +(85.8073 - 35.5425i) q^{42} +(9.49830 + 22.9309i) q^{43} +(-76.3882 - 15.1946i) q^{44} +(17.9839 - 12.0164i) q^{45} +(4.10969 - 0.817468i) q^{46} +(44.1371 - 44.1371i) q^{47} +(-37.0926 - 24.7845i) q^{48} +(-2.54963 - 1.05609i) q^{49} -28.8972i q^{50} -66.5809 q^{52} +(-32.5495 + 78.5814i) q^{53} +(-26.3940 + 39.5014i) q^{54} +(29.3142 + 29.3142i) q^{55} +(17.4203 + 87.5776i) q^{56} +(68.6608 + 102.758i) q^{57} +(-15.1732 + 76.2808i) q^{58} +(36.1126 - 14.9583i) q^{59} +(44.9705 + 108.568i) q^{60} +(-7.26406 - 1.44491i) q^{61} +(78.2747 - 52.3015i) q^{62} +(-37.5386 + 7.46689i) q^{63} +(-56.0884 + 56.0884i) q^{64} +(29.4670 + 19.6892i) q^{65} +(121.616 + 50.3752i) q^{66} +99.8893i q^{67} -4.64798 q^{69} +(38.1862 - 92.1896i) q^{70} +(2.61787 - 3.91793i) q^{71} +(46.6892 + 46.6892i) q^{72} +(-20.0340 - 100.718i) q^{73} +(-80.7630 - 120.870i) q^{74} +(-6.25346 + 31.4383i) q^{75} +(-230.464 + 95.4612i) q^{76} +(-28.0737 - 67.7759i) q^{77} +(110.369 + 21.9538i) q^{78} +(-48.9026 + 32.6757i) q^{79} +(-47.0080 + 9.35048i) q^{80} +(71.1192 - 71.1192i) q^{81} +(61.2932 + 40.9548i) q^{82} +(-83.6340 - 34.6423i) q^{83} -207.948i q^{84} +84.6737 q^{86} +(33.0149 - 79.7050i) q^{87} +(-70.3115 + 105.229i) q^{88} +(5.23601 + 5.23601i) q^{89} +(-14.3951 - 72.3690i) q^{90} +(-34.8414 - 52.1439i) q^{91} +(1.83028 - 9.20143i) q^{92} +(-96.4760 + 39.9616i) q^{93} +(-81.4892 - 196.732i) q^{94} +(130.227 + 25.9038i) q^{95} +(29.6667 - 19.8227i) q^{96} +(-95.4085 + 18.9779i) q^{97} +(-6.65717 + 6.65717i) q^{98} +(-45.1043 - 30.1378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) $ 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	1.30551	−	3.15179i	0.652757	−	1.57590i	−0.156003	−	0.987757i	$-0.549861\pi$
$2$	1.30551	−	3.15179i	0.652757	−	1.57590i	0.808760	−	0.588139i	$-0.200139\pi$
$3$	−2.10237	+	3.14642i	−0.700791	+	1.04881i	0.294850	+	0.955543i	$0.404730\pi$
$3$	−2.10237	+	3.14642i	−0.700791	+	1.04881i	−0.995641	+	0.0932645i	$0.970270\pi$
$4$	−5.40099	−	5.40099i	−1.35025	−	1.35025i
$5$	0.793166	+	3.98752i	0.158633	+	0.797503i	0.975384	+	0.220513i	$0.0707731\pi$
$5$	0.793166	+	3.98752i	0.158633	+	0.797503i	−0.816751	+	0.576991i	$0.804227\pi$
$6$	7.17219	+	10.7339i	1.19537	+	1.78899i
$7$	1.40356	−	7.05618i	0.200509	−	1.00803i	−0.741120	−	0.671373i	$-0.765705\pi$
$7$	1.40356	−	7.05618i	0.200509	−	1.00803i	0.941629	−	0.336653i	$-0.109295\pi$
$8$	−11.4667	+	4.74967i	−1.43334	+	0.593708i
$9$	−2.03586	−	4.91500i	−0.226207	−	0.546111i
$10$	13.6033	+	2.70587i	1.36033	+	0.270587i
$11$	8.47833	−	5.66504i	0.770757	−	0.515004i	−0.106913	−	0.994268i	$-0.534097\pi$
$11$	8.47833	−	5.66504i	0.770757	−	0.515004i	0.877670	+	0.479265i	$0.159097\pi$
$12$	28.3487	−	5.63891i	2.36239	−	0.469909i
$13$	6.16377	−	6.16377i	0.474136	−	0.474136i	−0.429114	−	0.903250i	$-0.641174\pi$
$13$	6.16377	−	6.16377i	0.474136	−	0.474136i	0.903250	+	0.429114i	$0.141174\pi$
$14$	−20.4072	−	13.6357i	−1.45766	−	0.973977i
$15$	−14.2139	−	5.88761i	−0.947597	−	0.392507i
$16$			11.7888i			0.736800i
$17$		0			0
$17$		0			0
$18$	−18.1489			−1.00827
$19$	12.4979	−	30.1727i	0.657786	−	1.58804i	−0.143429	−	0.989661i	$-0.545813\pi$
$19$	12.4979	−	30.1727i	0.657786	−	1.58804i	0.801215	−	0.598376i	$-0.204187\pi$
$20$	17.2527	−	25.8204i	0.862633	−	1.29102i
$21$	19.2509	+	19.2509i	0.916711	+	0.916711i
$22$	−6.78644	−	34.1177i	−0.308474	−	1.55081i
$23$	0.682389	+	1.02127i	0.0296691	+	0.0444029i	0.846008	−	0.533171i	$-0.179000\pi$
$23$	0.682389	+	1.02127i	0.0296691	+	0.0444029i	−0.816339	+	0.577574i	$0.804000\pi$
$24$	9.16284	−	46.0647i	0.381785	−	1.91936i
$25$	7.82581	−	3.24156i	0.313033	−	0.129662i
$26$	−11.3800	−	27.4738i	−0.437693	−	1.05668i
$27$	−13.6583	−	2.71681i	−0.505864	−	0.100623i
$28$	−45.6910	+	30.5298i	−1.63182	+	1.09035i
$29$	−22.3601	+	4.44769i	−0.771037	+	0.153369i	−0.564906	−	0.825156i	$-0.691087\pi$
$29$	−22.3601	+	4.44769i	−0.771037	+	0.153369i	−0.206131	+	0.978524i	$0.566087\pi$
$30$	−37.1130	+	37.1130i	−1.23710	+	1.23710i
$31$	22.9445	+	15.3310i	0.740146	+	0.494550i	0.867580	−	0.497297i	$-0.165674\pi$
$31$	22.9445	+	15.3310i	0.740146	+	0.494550i	−0.127434	+	0.991847i	$0.540674\pi$
$32$	−8.71099	−	3.60821i	−0.272219	−	0.112757i
$33$			38.5864i			1.16929i
$34$		0			0
$35$	29.2499			0.835712
$36$	−15.5502	+	37.5415i	−0.431950	+	1.04282i
$37$	23.6739	−	35.4305i	0.639836	−	0.957582i	−0.359862	−	0.933005i	$-0.617176\pi$
$37$	23.6739	−	35.4305i	0.639836	−	0.957582i	0.999698	−	0.0245764i	$-0.00782370\pi$
$38$	−78.7818	−	78.7818i	−2.07320	−	2.07320i
$39$	6.43528	+	32.3524i	0.165007	+	0.829548i
$40$	−28.0344	−	41.9564i	−0.700859	−	1.04891i
$41$	−4.21560	+	21.1933i	−0.102820	+	0.516909i	0.894709	+	0.446649i	$0.147383\pi$
$41$	−4.21560	+	21.1933i	−0.102820	+	0.516909i	−0.997529	+	0.0702597i	$0.977617\pi$
$42$	85.8073	−	35.5425i	2.04303	−	0.846251i
$43$	9.49830	+	22.9309i	0.220891	+	0.533277i	0.995011	−	0.0997606i	$-0.0318077\pi$
$43$	9.49830	+	22.9309i	0.220891	+	0.533277i	−0.774121	+	0.633038i	$0.781808\pi$
$44$	−76.3882	−	15.1946i	−1.73610	−	0.345331i
$45$	17.9839	−	12.0164i	0.399641	−	0.267032i
$46$	4.10969	−	0.817468i	0.0893411	−	0.0177710i
$47$	44.1371	−	44.1371i	0.939086	−	0.939086i	−0.0591622	−	0.998248i	$-0.518843\pi$
$47$	44.1371	−	44.1371i	0.939086	−	0.939086i	0.998248	+	0.0591622i	$0.0188429\pi$
$48$	−37.0926	−	24.7845i	−0.772762	−	0.516343i
$49$	−2.54963	−	1.05609i	−0.0520334	−	0.0215529i
$50$		−	28.8972i		−	0.577945i
$51$		0			0
$52$	−66.5809			−1.28040
$53$	−32.5495	+	78.5814i	−0.614141	+	1.48267i	0.244270	+	0.969707i	$0.421452\pi$
$53$	−32.5495	+	78.5814i	−0.614141	+	1.48267i	−0.858412	+	0.512961i	$0.828548\pi$
$54$	−26.3940	+	39.5014i	−0.488778	+	0.731507i
$55$	29.3142	+	29.3142i	0.532985	+	0.532985i
$56$	17.4203	+	87.5776i	0.311076	+	1.56389i
$57$	68.6608	+	102.758i	1.20457	+	1.80277i
$58$	−15.1732	+	76.2808i	−0.261607	+	1.31519i
$59$	36.1126	−	14.9583i	0.612078	−	0.253531i	−0.0550386	−	0.998484i	$-0.517528\pi$
$59$	36.1126	−	14.9583i	0.612078	−	0.253531i	0.667117	+	0.744953i	$0.267528\pi$
$60$	44.9705	+	108.568i	0.749508	+	1.80947i
$61$	−7.26406	−	1.44491i	−0.119083	−	0.0236871i	0.135189	−	0.990820i	$-0.456836\pi$
$61$	−7.26406	−	1.44491i	−0.119083	−	0.0236871i	−0.254272	+	0.967133i	$0.581836\pi$
$62$	78.2747	−	52.3015i	1.26249	−	0.843572i
$63$	−37.5386	+	7.46689i	−0.595850	+	0.118522i
$64$	−56.0884	+	56.0884i	−0.876382	+	0.876382i
$65$	29.4670	+	19.6892i	0.453339	+	0.302911i
$66$	121.616	+	50.3752i	1.84267	+	0.763260i
$67$			99.8893i			1.49089i	0.666570	+	0.745443i	$0.267762\pi$
$67$			99.8893i			1.49089i	−0.666570	+	0.745443i	$0.732238\pi$
$68$		0			0
$69$	−4.64798			−0.0673620
$70$	38.1862	−	92.1896i	0.545517	−	1.31699i
$71$	2.61787	−	3.91793i	0.0368715	−	0.0551821i	−0.812576	−	0.582855i	$-0.801935\pi$
$71$	2.61787	−	3.91793i	0.0368715	−	0.0551821i	0.849447	+	0.527673i	$0.176935\pi$
$72$	46.6892	+	46.6892i	0.648461	+	0.648461i
$73$	−20.0340	−	100.718i	−0.274438	−	1.37969i	−0.834392	−	0.551171i	$-0.814181\pi$
$73$	−20.0340	−	100.718i	−0.274438	−	1.37969i	0.559954	−	0.828524i	$-0.310819\pi$
$74$	−80.7630	−	120.870i	−1.09139	−	1.63338i
$75$	−6.25346	+	31.4383i	−0.0833795	+	0.419177i
$76$	−230.464	+	95.4612i	−3.03242	+	1.25607i
$77$	−28.0737	−	67.7759i	−0.364593	−	0.880206i
$78$	110.369	+	21.9538i	1.41499	+	0.281459i
$79$	−48.9026	+	32.6757i	−0.619021	+	0.413616i	−0.825154	−	0.564907i	$-0.808912\pi$
$79$	−48.9026	+	32.6757i	−0.619021	+	0.413616i	0.206134	+	0.978524i	$0.433912\pi$
$80$	−47.0080	+	9.35048i	−0.587600	+	0.116881i
$81$	71.1192	−	71.1192i	0.878014	−	0.878014i
$82$	61.2932	+	40.9548i	0.747478	+	0.499449i
$83$	−83.6340	−	34.6423i	−1.00764	−	0.417378i	−0.183046	−	0.983104i	$-0.558596\pi$
$83$	−83.6340	−	34.6423i	−1.00764	−	0.417378i	−0.824593	+	0.565727i	$0.808596\pi$
$84$		−	207.948i		−	2.47557i
$85$		0			0
$86$	84.6737			0.984578
$87$	33.0149	−	79.7050i	0.379481	−	0.916149i
$88$	−70.3115	+	105.229i	−0.798994	+	1.19578i
$89$	5.23601	+	5.23601i	0.0588316	+	0.0588316i	0.735910	−	0.677079i	$-0.236754\pi$
$89$	5.23601	+	5.23601i	0.0588316	+	0.0588316i	−0.677079	+	0.735910i	$0.736754\pi$
$90$	−14.3951	−	72.3690i	−0.159945	−	0.804100i
$91$	−34.8414	−	52.1439i	−0.382873	−	0.573010i
$92$	1.83028	−	9.20143i	0.0198943	−	0.100016i
$93$	−96.4760	+	39.9616i	−1.03738	+	0.429695i
$94$	−81.4892	−	196.732i	−0.866906	−	2.09290i
$95$	130.227	+	25.9038i	1.37081	+	0.272671i
$96$	29.6667	−	19.8227i	0.309028	−	0.206486i
$97$	−95.4085	+	18.9779i	−0.983593	+	0.195649i	−0.660588	−	0.750748i	$-0.729693\pi$
$97$	−95.4085	+	18.9779i	−0.983593	+	0.195649i	−0.323005	+	0.946397i	$0.604693\pi$
$98$	−6.65717	+	6.65717i	−0.0679303	+	0.0679303i
$99$	−45.1043	−	30.1378i	−0.455599	−	0.304422i
$100$	−59.7748	−	24.7595i	−0.597748	−	0.247595i
$101$		−	97.3468i		−	0.963829i	−0.876218	−	0.481915i	$-0.839942\pi$
$101$		−	97.3468i		−	0.963829i	0.876218	−	0.481915i	$-0.160058\pi$
$102$		0			0
$103$	39.6802			0.385244			0.192622	−	0.981273i	$-0.438301\pi$
$103$	39.6802			0.385244			0.192622	+	0.981273i	$0.438301\pi$
$104$	−41.4023	+	99.9539i	−0.398099	+	0.961095i
$105$	−61.4942	+	92.0326i	−0.585659	+	0.876501i
$106$	205.178	+	205.178i	1.93565	+	1.93565i
$107$	22.1781	+	111.497i	0.207272	+	1.04203i	0.934590	+	0.355726i	$0.115766\pi$
$107$	22.1781	+	111.497i	0.207272	+	1.04203i	−0.727319	+	0.686300i	$0.759234\pi$
$108$	59.0951	+	88.4421i	0.547177	+	0.818908i
$109$	19.5650	−	98.3600i	0.179496	−	0.902386i	−0.781094	−	0.624414i	$-0.785338\pi$
$109$	19.5650	−	98.3600i	0.179496	−	0.902386i	0.960589	−	0.277972i	$-0.0896621\pi$
$110$	130.662	−	54.1221i	1.18784	−	0.492019i
$111$	61.7080	+	148.976i	0.555928	+	1.34213i
$112$	83.1839	+	16.5463i	0.742714	+	0.147735i
$113$	−122.494	+	81.8476i	−1.08401	+	0.724315i	−0.963315	−	0.268375i	$-0.913514\pi$
$113$	−122.494	+	81.8476i	−1.08401	+	0.724315i	−0.120699	+	0.992689i	$0.538514\pi$
$114$	413.510	−	82.2522i	3.62728	−	0.721510i
$115$	−3.53107	+	3.53107i	−0.0307050	+	0.0307050i
$116$	144.788	+	96.7446i	1.24818	+	0.834005i
$117$	−42.8435	−	17.7463i	−0.366183	−	0.151678i
$118$		−	133.348i		−	1.13007i
$119$		0			0
$120$	190.951			1.59126
$121$	−6.51528	+	15.7293i	−0.0538453	+	0.129994i
$122$	−14.0374	+	21.0084i	−0.115061	+	0.172200i
$123$	−57.8202	−	57.8202i	−0.470083	−	0.470083i
$124$	−41.1204	−	206.726i	−0.331616	−	1.66715i
$125$	75.6016	+	113.146i	0.604813	+	0.905166i
$126$	−25.4731	+	128.062i	−0.202167	+	1.01636i
$127$	45.2810	−	18.7560i	0.356543	−	0.147685i	−0.197220	−	0.980359i	$-0.563191\pi$
$127$	45.2810	−	18.7560i	0.356543	−	0.147685i	0.553763	+	0.832674i	$0.313191\pi$
$128$	89.1219	+	215.159i	0.696265	+	1.68093i
$129$	−92.1194	−	18.3237i	−0.714104	−	0.142044i
$130$	100.526	−	67.1693i	0.773276	−	0.516687i
$131$	−22.7447	+	4.52419i	−0.173623	+	0.0345358i	−0.281136	−	0.959668i	$-0.590711\pi$
$131$	−22.7447	+	4.52419i	−0.173623	+	0.0345358i	0.107513	+	0.994204i	$0.465711\pi$
$132$	208.405	−	208.405i	1.57883	−	1.57883i
$133$	−195.362	−	130.537i	−1.46889	−	0.981481i
$134$	314.830	+	130.407i	2.34948	+	0.973186i
$135$		−	56.6177i		−	0.419391i
$136$		0			0
$137$	54.0983			0.394878			0.197439	−	0.980315i	$-0.436738\pi$
$137$	54.0983			0.394878			0.197439	+	0.980315i	$0.436738\pi$
$138$	−6.06800	+	14.6494i	−0.0439710	+	0.106155i
$139$	21.4531	−	32.1068i	0.154339	−	0.230984i	−0.746240	−	0.665677i	$-0.768143\pi$
$139$	21.4531	−	32.1068i	0.154339	−	0.230984i	0.900579	+	0.434693i	$0.143143\pi$
$140$	−157.978	−	157.978i	−1.12842	−	1.12842i
$141$	46.0813	+	231.666i	0.326818	+	1.64302i
$142$	−8.93081	−	13.3659i	−0.0628930	−	0.0941261i
$143$	17.3405	−	87.1764i	0.121262	−	0.609625i
$144$	57.9419	−	24.0003i	0.402374	−	0.166669i
$145$	−35.4705	−	85.6334i	−0.244624	−	0.590575i
$146$	−343.596	−	68.3455i	−2.35340	−	0.468120i
$147$	8.68320	−	5.80193i	0.0590694	−	0.0394689i
$148$	−319.223	+	63.4973i	−2.15691	+	0.429036i
$149$	−161.514	+	161.514i	−1.08399	+	1.08399i	−0.0878567	+	0.996133i	$0.528002\pi$
$149$	−161.514	+	161.514i	−1.08399	+	1.08399i	−0.996133	+	0.0878567i	$0.971998\pi$
$150$	90.9229	+	60.7528i	0.606153	+	0.405018i
$151$	−29.5306	−	12.2320i	−0.195567	−	0.0810066i	0.282750	−	0.959194i	$-0.408753\pi$
$151$	−29.5306	−	12.2320i	−0.195567	−	0.0810066i	−0.478318	+	0.878187i	$0.658753\pi$
$152$			405.342i			2.66673i
$153$		0			0
$154$	−250.266			−1.62510
$155$	−42.9340	+	103.652i	−0.276993	+	0.668721i
$156$	139.978	−	209.492i	0.897294	−	1.34290i
$157$	8.59160	+	8.59160i	0.0547236	+	0.0547236i	0.733939	−	0.679215i	$-0.237680\pi$
$157$	8.59160	+	8.59160i	0.0547236	+	0.0547236i	−0.679215	+	0.733939i	$0.737680\pi$
$158$	39.1439	+	196.789i	0.247746	+	1.24550i
$159$	−178.819	−	267.622i	−1.12465	−	1.68316i
$160$	7.47854	−	37.5971i	0.0467408	−	0.234982i
$161$	8.16402	−	3.38165i	0.0507082	−	0.0210040i
$162$	−131.306	−	317.000i	−0.810529	−	1.95679i
$163$	175.308	+	34.8710i	1.07551	+	0.213932i	0.700907	−	0.713253i	$-0.252779\pi$
$163$	175.308	+	34.8710i	1.07551	+	0.213932i	0.374603	+	0.927185i	$0.377779\pi$
$164$	137.233	−	91.6962i	0.836787	−	0.559123i
$165$	−153.864	+	30.6055i	−0.932510	+	0.185488i
$166$	−218.371	+	218.371i	−1.31549	+	1.31549i
$167$	74.3406	+	49.6728i	0.445153	+	0.297442i	0.757871	−	0.652404i	$-0.226239\pi$
$167$	74.3406	+	49.6728i	0.445153	+	0.297442i	−0.312718	+	0.949846i	$0.601239\pi$
$168$	−312.180	−	129.309i	−1.85822	−	0.769698i
$169$			93.0160i			0.550390i
$170$		0			0
$171$	−173.743			−1.01604
$172$	72.5495	−	175.150i	0.421799	−	1.01831i
$173$	−52.1325	+	78.0218i	−0.301344	+	0.450993i	−0.950980	−	0.309252i	$-0.899921\pi$
$173$	−52.1325	+	78.0218i	−0.301344	+	0.450993i	0.649636	+	0.760245i	$0.274921\pi$
$174$	−208.112	−	208.112i	−1.19605	−	1.19605i
$175$	−11.8890	−	59.7701i	−0.0679372	−	0.341543i
$176$	66.7840	+	99.9493i	0.379455	+	0.567894i
$177$	−28.8569	+	145.074i	−0.163033	+	0.819625i
$178$	23.3385	−	9.66713i	0.131115	−	0.0543097i
$179$	110.449	+	266.646i	0.617031	+	1.48964i	0.855135	+	0.518405i	$0.173474\pi$
$179$	110.449	+	266.646i	0.617031	+	1.48964i	−0.238104	+	0.971240i	$0.576526\pi$
$180$	−162.031	−	32.2300i	−0.900174	−	0.179056i
$181$	−144.698	+	96.6838i	−0.799434	+	0.534165i	−0.886877	−	0.462005i	$-0.847130\pi$
$181$	−144.698	+	96.6838i	−0.799434	+	0.534165i	0.0874435	+	0.996169i	$0.472130\pi$
$182$	−209.833	+	41.7383i	−1.15293	+	0.229331i
$183$	19.8181	−	19.8181i	0.108295	−	0.108295i
$184$	−12.6754	−	8.46945i	−0.0688882	−	0.0460296i
$185$	160.057	+	66.2979i	0.865174	+	0.358367i
$186$			356.243i			1.91528i
$187$		0			0
$188$	−476.768			−2.53600
$189$	−38.3407	+	92.5625i	−0.202861	+	0.489749i
$190$	251.657	−	376.631i	1.32451	−	1.98227i
$191$	19.1103	+	19.1103i	0.100054	+	0.100054i	0.755362	−	0.655308i	$-0.227461\pi$
$191$	19.1103	+	19.1103i	0.100054	+	0.100054i	−0.655308	+	0.755362i	$0.727461\pi$
$192$	−58.5591	−	294.397i	−0.304996	−	1.53332i
$193$	−104.011	−	155.664i	−0.538918	−	0.806548i	0.457667	−	0.889124i	$-0.348685\pi$
$193$	−104.011	−	155.664i	−0.538918	−	0.806548i	−0.996585	+	0.0825761i	$0.973685\pi$
$194$	−64.7427	+	325.484i	−0.333726	+	1.67775i
$195$	−123.901	+	51.3216i	−0.635391	+	0.263188i
$196$	8.06660	+	19.4745i	0.0411561	+	0.0993597i
$197$	−261.357	−	51.9872i	−1.32669	−	0.263894i	−0.519641	−	0.854384i	$-0.673934\pi$
$197$	−261.357	−	51.9872i	−1.32669	−	0.263894i	−0.807045	+	0.590490i	$0.798934\pi$
$198$	−153.872	+	102.814i	−0.777133	+	0.519264i
$199$	343.364	−	68.2994i	1.72545	−	0.343213i	0.769927	−	0.638132i	$-0.220293\pi$
$199$	343.364	−	68.2994i	1.72545	−	0.343213i	0.955522	+	0.294919i	$0.0952927\pi$
$200$	−74.3400	+	74.3400i	−0.371700	+	0.371700i
$201$	−314.294	−	210.005i	−1.56365	−	1.04480i
$202$	−306.817	−	127.088i	−1.51889	−	0.629147i
$203$			164.019i			0.807977i
$204$		0			0
$205$	−87.8522			−0.428547
$206$	51.8030	−	125.064i	0.251471	−	0.607105i
$207$	3.63028	−	5.43310i	0.0175376	−	0.0262468i
$208$	72.6634	+	72.6634i	0.349343	+	0.349343i
$209$	−64.9678	−	326.615i	−0.310851	−	1.56275i
$210$	209.786	+	313.967i	0.998981	+	1.49508i
$211$	44.6895	−	224.669i	0.211799	−	1.06478i	−0.717811	−	0.696238i	$-0.754856\pi$
$211$	44.6895	−	224.669i	0.211799	−	1.06478i	0.929610	−	0.368545i	$-0.120144\pi$
$212$	600.217	−	248.618i	2.83121	−	1.17273i
$213$	6.82371	+	16.4739i	0.0320362	+	0.0773422i
$214$	380.368	+	75.6600i	1.77742	+	0.353551i
$215$	−83.9037	+	56.0627i	−0.390250	+	0.260757i
$216$	169.520	−	33.7196i	0.784815	−	0.156109i
$217$	140.383	−	140.383i	0.646925	−	0.646925i
$218$	−284.468	−	190.075i	−1.30490	−	0.871905i
$219$	359.020	+	148.711i	1.63936	+	0.679045i
$220$		−	316.651i		−	1.43932i
$221$		0			0
$222$	550.103			2.47794
$223$	−62.3672	+	150.568i	−0.279674	+	0.675192i	−0.999827	−	0.0186236i	$-0.994072\pi$
$223$	−62.3672	+	150.568i	−0.279674	+	0.675192i	0.720153	+	0.693815i	$0.244072\pi$
$224$	−37.6866	+	56.4020i	−0.168244	+	0.251795i
$225$	−31.8645	−	31.8645i	−0.141620	−	0.141620i
$226$	98.0493	+	492.927i	0.433847	+	2.18109i
$227$	73.5668	+	110.101i	0.324083	+	0.485025i	0.957359	−	0.288902i	$-0.0932901\pi$
$227$	73.5668	+	110.101i	0.324083	+	0.485025i	−0.633276	+	0.773926i	$0.718290\pi$
$228$	184.159	−	925.832i	0.807717	−	4.06067i
$229$	−149.442	+	61.9007i	−0.652583	+	0.270309i	−0.684314	−	0.729188i	$-0.739898\pi$
$229$	−149.442	+	61.9007i	−0.652583	+	0.270309i	0.0317307	+	0.999496i	$0.489898\pi$
$230$	6.51933	+	15.7391i	0.0283449	+	0.0684307i
$231$	272.273	+	54.1585i	1.17867	+	0.234452i
$232$	235.271	−	157.203i	1.01410	−	0.677600i
$233$	167.942	−	33.4057i	0.720780	−	0.143372i	0.178948	−	0.983859i	$-0.442731\pi$
$233$	167.942	−	33.4057i	0.720780	−	0.143372i	0.541833	+	0.840486i	$0.317731\pi$
$234$	−111.866	+	111.866i	−0.478058	+	0.478058i
$235$	211.005	+	140.989i	0.897895	+	0.599954i
$236$	−275.834	−	114.254i	−1.16879	−	0.484127i
$237$		−	222.565i		−	0.939092i
$238$		0			0
$239$	117.086			0.489900			0.244950	−	0.969536i	$-0.421228\pi$
$239$	117.086			0.489900			0.244950	+	0.969536i	$0.421228\pi$
$240$	69.4079	−	167.565i	0.289199	−	0.698189i
$241$	70.1215	−	104.944i	0.290961	−	0.435453i	−0.656976	−	0.753911i	$-0.728165\pi$
$241$	70.1215	−	104.944i	0.290961	−	0.435453i	0.947937	+	0.318458i	$0.103165\pi$
$242$	41.0696	+	41.0696i	0.169709	+	0.169709i
$243$	49.8007	+	250.365i	0.204941	+	1.03031i
$244$	31.4292	+	47.0371i	0.128808	+	0.192775i
$245$	2.18890	−	11.0044i	0.00893430	−	0.0449158i
$246$	−257.722	+	106.752i	−1.04765	+	0.433952i
$247$	−108.943	−	263.012i	−0.441065	−	1.06483i
$248$	−335.916	−	66.8178i	−1.35450	−	0.269426i
$249$	284.829	−	190.317i	1.14389	−	0.764325i
$250$	455.311	−	90.5670i	1.82124	−	0.362268i
$251$	130.638	−	130.638i	0.520470	−	0.520470i	−0.397243	−	0.917713i	$-0.630033\pi$
$251$	130.638	−	130.638i	0.520470	−	0.520470i	0.917713	+	0.397243i	$0.130033\pi$
$252$	243.074	+	162.417i	0.964580	+	0.644512i
$253$	11.5710	+	4.79288i	0.0457353	+	0.0189442i
$254$		−	167.202i		−	0.658278i
$255$		0			0
$256$	477.203			1.86407
$257$	28.2011	−	68.0835i	0.109732	−	0.264916i	−0.859469	−	0.511188i	$-0.829206\pi$
$257$	28.2011	−	68.0835i	0.109732	−	0.264916i	0.969201	+	0.246272i	$0.0792056\pi$
$258$	−178.016	+	266.419i	−0.689983	+	1.03263i
$259$	−216.776	−	216.776i	−0.836975	−	0.836975i
$260$	−52.8097	−	265.492i	−0.203114	−	1.02112i
$261$	67.3823	+	100.845i	0.258170	+	0.386379i
$262$	−15.4342	+	77.5928i	−0.0589091	+	0.296156i
$263$	−142.799	+	59.1494i	−0.542963	+	0.224903i	−0.637270	−	0.770640i	$-0.719937\pi$
$263$	−142.799	+	59.1494i	−0.542963	+	0.224903i	0.0943069	+	0.995543i	$0.469937\pi$
$264$	−183.273	−	442.459i	−0.694215	−	1.67598i
$265$	−339.162	−	67.4635i	−1.27986	−	0.254579i
$266$	−666.474	+	445.324i	−2.50554	+	1.67415i
$267$	−27.4828	+	5.46666i	−0.102932	+	0.0204744i
$268$	539.501	−	539.501i	2.01306	−	2.01306i
$269$	169.847	+	113.488i	0.631403	+	0.421890i	0.829667	−	0.558259i	$-0.188530\pi$
$269$	169.847	+	113.488i	0.631403	+	0.421890i	−0.198264	+	0.980149i	$0.563530\pi$
$270$	−178.447	−	73.9153i	−0.660916	−	0.273760i
$271$			11.7158i			0.0432317i	0.999766	+	0.0216159i	$0.00688108\pi$
$271$			11.7158i			0.0432317i	−0.999766	+	0.0216159i	$0.993119\pi$
$272$		0			0
$273$	237.316			0.869291
$274$	70.6261	−	170.507i	0.257760	−	0.622286i
$275$	47.9863	−	71.8165i	0.174496	−	0.261151i
$276$	25.1037	+	25.1037i	0.0909554	+	0.0909554i
$277$	−34.3119	−	172.498i	−0.123870	−	0.622735i	−0.991983	−	0.126370i	$-0.959667\pi$
$277$	−34.3119	−	172.498i	−0.123870	−	0.622735i	0.868113	−	0.496366i	$-0.165333\pi$
$278$	−73.1867	−	109.532i	−0.263261	−	0.393998i
$279$	28.6402	−	143.984i	0.102653	−	0.516072i
$280$	−335.400	+	138.927i	−1.19786	+	0.496169i
$281$	−53.9707	−	130.297i	−0.192067	−	0.463690i	0.798283	−	0.602283i	$-0.205742\pi$
$281$	−53.9707	−	130.297i	−0.192067	−	0.463690i	−0.990349	+	0.138593i	$0.955742\pi$
$282$	790.324	+	157.205i	2.80257	+	0.557465i
$283$	−23.1776	+	15.4868i	−0.0818998	+	0.0547237i	−0.595846	−	0.803099i	$-0.703183\pi$
$283$	−23.1776	+	15.4868i	−0.0818998	+	0.0547237i	0.513946	+	0.857822i	$0.328183\pi$
$284$	−35.2998	+	7.02157i	−0.124295	+	0.0247238i
$285$	−355.290	+	355.290i	−1.24663	+	1.24663i
$286$	−252.124	−	168.464i	−0.881551	−	0.589034i
$287$	143.627	+	59.4921i	0.500441	+	0.207290i
$288$			50.1603i			0.174168i
$289$		0			0
$290$	−316.206			−1.09036
$291$	140.872	−	340.094i	0.484095	−	1.16871i
$292$	−435.772	+	652.179i	−1.49237	+	2.23349i
$293$	358.606	+	358.606i	1.22391	+	1.22391i	0.966230	+	0.257681i	$0.0829583\pi$
$293$	358.606	+	358.606i	1.22391	+	1.22391i	0.257681	+	0.966230i	$0.417042\pi$
$294$	−6.95042	−	34.9421i	−0.0236409	−	0.118851i
$295$	88.2899	+	132.135i	0.299288	+	0.447916i
$296$	−103.179	+	518.715i	−0.348577	+	1.75241i
$297$	−131.191	+	54.3410i	−0.441720	+	0.182966i
$298$	298.200	+	719.919i	1.00067	+	2.41584i
$299$	10.5009	+	2.08877i	0.0351202	+	0.00698584i
$300$	203.573	−	136.023i	0.678576	−	0.453410i
$301$	175.136	−	34.8368i	0.581848	−	0.115737i
$302$	−77.1054	+	77.1054i	−0.255316	+	0.255316i
$303$	306.294	+	204.659i	1.01087	+	0.675443i
$304$	355.700	+	147.336i	1.17007	+	0.484657i
$305$		−	30.1116i		−	0.0987266i
$306$		0			0
$307$	−465.819			−1.51733			−0.758663	−	0.651483i	$-0.774147\pi$
$307$	−465.819			−1.51733			−0.758663	+	0.651483i	$0.774147\pi$
$308$	−214.431	+	517.683i	−0.696205	+	1.68079i
$309$	−83.4225	+	124.851i	−0.269976	+	0.404047i
$310$	270.638	+	270.638i	0.873025	+	0.873025i
$311$	7.99518	+	40.1945i	0.0257080	+	0.129243i	0.991508	−	0.130045i	$-0.0415122\pi$
$311$	7.99518	+	40.1945i	0.0257080	+	0.129243i	−0.965800	+	0.259288i	$0.916512\pi$
$312$	−227.454	−	340.410i	−0.729020	−	1.09106i
$313$	−34.2114	+	171.992i	−0.109302	+	0.549496i	0.886866	+	0.462027i	$0.152878\pi$
$313$	−34.2114	+	171.992i	−0.109302	+	0.549496i	−0.996167	+	0.0874689i	$0.972122\pi$
$314$	38.2954	−	15.8625i	0.121960	−	0.0505174i
$315$	−59.5487	−	143.763i	−0.189043	−	0.456391i
$316$	440.604	+	87.6416i	1.39432	+	0.277347i
$317$	367.766	−	245.733i	1.16014	−	0.775184i	0.182039	−	0.983291i	$-0.441730\pi$
$317$	367.766	−	245.733i	1.16014	−	0.775184i	0.978106	+	0.208108i	$0.0667304\pi$
$318$	−1076.94	+	214.217i	−3.38660	+	0.673637i
$319$	−164.380	+	164.380i	−0.515297	+	0.515297i
$320$	−268.141	−	179.166i	−0.837940	−	0.559894i
$321$	−397.443	−	164.626i	−1.23814	−	0.512854i
$322$		−	30.1461i		−	0.0936214i
$323$		0			0
$324$	−768.228			−2.37107
$325$	28.2563	−	68.2167i	0.0869424	−	0.209898i
$326$	338.773	−	507.010i	1.03918	−	1.55525i
$327$	268.349	+	268.349i	0.820640	+	0.820640i
$328$	−52.3218	−	263.040i	−0.159518	−	0.801950i
$329$	−249.490	−	373.388i	−0.758328	−	1.13492i
$330$	−104.410	+	524.903i	−0.316393	+	1.59062i
$331$	495.359	−	205.184i	1.49655	−	0.619893i	0.523822	−	0.851828i	$-0.324506\pi$
$331$	495.359	−	205.184i	1.49655	−	0.619893i	0.972731	+	0.231935i	$0.0745058\pi$
$332$	264.604	+	638.809i	0.796999	+	1.92412i
$333$	−222.338	−	44.2257i	−0.667681	−	0.132810i
$334$	253.611	−	169.458i	0.759315	−	0.507358i
$335$	−398.310	+	79.2288i	−1.18899	+	0.236504i
$336$	−226.945	+	226.945i	−0.675433	+	0.675433i
$337$	−483.271	−	322.911i	−1.43404	−	0.958194i	−0.998310	−	0.0581152i	$-0.981491\pi$
$337$	−483.271	−	322.911i	−1.43404	−	0.958194i	−0.435728	−	0.900078i	$-0.643509\pi$
$338$	293.167	+	121.434i	0.867358	+	0.359271i
$339$		−	557.491i		−	1.64452i
$340$		0			0
$341$	281.382			0.825168
$342$	−226.824	+	547.601i	−0.663227	+	1.60117i
$343$	184.823	−	276.607i	0.538842	−	0.806434i
$344$	−217.828	−	217.828i	−0.633222	−	0.633222i
$345$	−3.68662	−	18.5339i	−0.0106858	−	0.0537214i
$346$	177.849	+	266.169i	0.514014	+	0.769276i
$347$	−105.898	+	532.385i	−0.305181	+	1.53425i	0.458522	+	0.888683i	$0.348379\pi$
$347$	−105.898	+	532.385i	−0.305181	+	1.53425i	−0.763703	+	0.645568i	$0.776621\pi$
$348$	−608.799	+	252.173i	−1.74942	+	0.724634i
$349$	−12.4247	−	29.9960i	−0.0356010	−	0.0859484i	0.905079	−	0.425243i	$-0.139812\pi$
$349$	−12.4247	−	29.9960i	−0.0356010	−	0.0859484i	−0.940680	+	0.339295i	$0.889812\pi$
$350$	−203.904	−	40.5591i	−0.582583	−	0.115883i
$351$	−100.933	+	67.4410i	−0.287557	+	0.192140i
$352$	−94.2953	+	18.7565i	−0.267884	+	0.0532855i
$353$	242.021	−	242.021i	0.685611	−	0.685611i	−0.275647	−	0.961259i	$-0.588892\pi$
$353$	242.021	−	242.021i	0.685611	−	0.685611i	0.961259	+	0.275647i	$0.0888922\pi$
$354$	419.568	+	280.347i	1.18522	+	0.791940i
$355$	17.6992	+	7.33125i	0.0498569	+	0.0206514i
$356$		−	56.5593i		−	0.158874i
$357$		0			0
$358$	984.606			2.75030
$359$	124.934	−	301.618i	0.348007	−	0.840162i	−0.648849	−	0.760917i	$-0.724749\pi$
$359$	124.934	−	301.618i	0.348007	−	0.840162i	0.996855	−	0.0792446i	$-0.0252508\pi$
$360$	−149.142	+	223.206i	−0.414282	+	0.620017i
$361$	−498.927	−	498.927i	−1.38207	−	1.38207i
$362$	115.822	+	582.278i	0.319951	+	1.60850i
$363$	−35.7934	−	53.5686i	−0.0986044	−	0.147572i
$364$	−93.4504	+	469.807i	−0.256732	+	1.29068i
$365$	385.723	−	159.772i	1.05678	−	0.437731i
$366$	−36.5896	−	88.3352i	−0.0999717	−	0.241353i
$367$	−292.460	−	58.1740i	−0.796894	−	0.158512i	−0.220181	−	0.975459i	$-0.570665\pi$
$367$	−292.460	−	58.1740i	−0.796894	−	0.158512i	−0.576713	+	0.816947i	$0.695665\pi$
$368$	−12.0395	+	8.04455i	−0.0327161	+	0.0218602i
$369$	112.747	−	22.4268i	0.305548	−	0.0607773i
$370$	417.914	−	417.914i	1.12950	−	1.12950i
$371$	508.800	+	339.969i	1.37143	+	0.916359i
$372$	736.898	+	305.233i	1.98091	+	0.820520i
$373$			661.070i			1.77230i	0.463394	+	0.886152i	$0.346632\pi$
$373$			661.070i			1.77230i	−0.463394	+	0.886152i	$0.653368\pi$
$374$		0			0
$375$	−514.947			−1.37319
$376$	−296.470	+	715.743i	−0.788485	+	1.90357i
$377$	−110.408	+	165.237i	−0.292859	+	0.438294i
$378$	241.683	+	241.683i	0.639374	+	0.639374i
$379$	46.7824	+	235.191i	0.123436	+	0.620557i	0.992131	+	0.125208i	$0.0399598\pi$
$379$	46.7824	+	235.191i	0.123436	+	0.620557i	−0.868694	+	0.495349i	$0.835040\pi$
$380$	−563.449	−	843.261i	−1.48276	−	2.21911i
$381$	−36.1832	+	181.905i	−0.0949691	+	0.477442i
$382$	85.1804	−	35.2829i	0.222985	−	0.0923635i
$383$	−8.96693	−	21.6481i	−0.0234123	−	0.0565224i	0.911741	−	0.410766i	$-0.134739\pi$
$383$	−8.96693	−	21.6481i	−0.0234123	−	0.0565224i	−0.935153	+	0.354243i	$0.884739\pi$
$384$	−864.350	−	171.930i	−2.25091	−	0.447734i
$385$	247.990	−	165.702i	0.644131	−	0.430394i
$386$	−626.408	+	124.600i	−1.62282	+	0.322798i
$387$	93.3683	−	93.3683i	0.241262	−	0.241262i
$388$	617.800	+	412.801i	1.59227	+	1.06392i
$389$	−352.455	−	145.991i	−0.906053	−	0.375299i	−0.119509	−	0.992833i	$-0.538132\pi$
$389$	−352.455	−	145.991i	−0.906053	−	0.375299i	−0.786544	+	0.617534i	$0.788132\pi$
$390$			457.512i			1.17311i
$391$		0			0
$392$	34.2520			0.0873775
$393$	33.5827	−	81.0759i	0.0854522	−	0.206300i
$394$	−505.058	+	755.873i	−1.28187	+	1.91846i
$395$	−169.083	−	169.083i	−0.428058	−	0.428058i
$396$	80.8344	+	406.382i	0.204127	+	1.02622i
$397$	400.180	+	598.911i	1.00801	+	1.50859i	0.853832	+	0.520549i	$0.174273\pi$
$397$	400.180	+	598.911i	1.00801	+	1.50859i	0.154177	+	0.988043i	$0.450727\pi$
$398$	233.002	−	1171.38i	0.585431	−	2.94316i
$399$	821.449	−	340.255i	2.05877	−	0.852771i
$400$	38.2141	+	92.2569i	0.0955352	+	0.230642i
$401$	364.990	+	72.6009i	0.910198	+	0.181050i	0.627915	−	0.778282i	$-0.283908\pi$
$401$	364.990	+	72.6009i	0.910198	+	0.181050i	0.282283	+	0.959331i	$0.408908\pi$
$402$	−1072.21	+	716.425i	−2.66718	+	1.78215i
$403$	235.922	−	46.9278i	0.585414	−	0.116446i
$404$	−525.769	+	525.769i	−1.30141	+	1.30141i
$405$	339.998	+	227.179i	0.839502	+	0.560937i
$406$	516.955	+	214.130i	1.27329	+	0.527413i
$407$		−	434.505i		−	1.06758i
$408$		0			0
$409$	752.125			1.83894			0.919468	−	0.393165i	$-0.128620\pi$
$409$	752.125			1.83894			0.919468	+	0.393165i	$0.128620\pi$
$410$	−114.692	+	276.892i	−0.279737	+	0.675345i
$411$	−113.735	+	170.216i	−0.276727	+	0.414151i
$412$	−214.312	−	214.312i	−0.520175	−	0.520175i
$413$	−54.8624	−	275.812i	−0.132839	−	0.667826i
$414$	−12.3846	−	18.5349i	−0.0299145	−	0.0447702i
$415$	71.8012	−	360.969i	0.173015	−	0.869805i
$416$	−75.9327	+	31.4523i	−0.182531	+	0.0756066i
$417$	55.9192	+	135.001i	0.134099	+	0.323743i
$418$	−1114.24	−	221.636i	−2.66565	−	0.530230i
$419$	655.813	−	438.200i	1.56519	−	1.04582i	0.594920	−	0.803785i	$-0.297184\pi$
$419$	655.813	−	438.200i	1.56519	−	1.04582i	0.970267	−	0.242039i	$-0.0778161\pi$
$420$	829.197	−	164.938i	1.97428	−	0.392708i
$421$	−467.185	+	467.185i	−1.10970	+	1.10970i	−0.116515	+	0.993189i	$0.537172\pi$
$421$	−467.185	+	467.185i	−1.10970	+	1.10970i	−0.993189	+	0.116515i	$0.962828\pi$
$422$	−649.768	−	434.161i	−1.53973	−	1.02882i
$423$	−306.790	−	127.077i	−0.725273	−	0.300418i
$424$		−	1055.67i		−	2.48979i
$425$		0			0
$426$	60.8307			0.142795
$427$	−20.3911	+	49.2285i	−0.0477544	+	0.115289i
$428$	482.409	−	721.977i	1.12712	−	1.68686i
$429$	237.838	+	237.838i	0.554401	+	0.554401i
$430$	67.1603	+	337.638i	0.156187	+	0.785204i
$431$	73.9183	+	110.627i	0.171504	+	0.256674i	0.907258	−	0.420575i	$-0.138172\pi$
$431$	73.9183	+	110.627i	0.171504	+	0.256674i	−0.735753	+	0.677250i	$0.763172\pi$
$432$	32.0280	−	161.015i	0.0741388	−	0.372721i
$433$	25.8940	−	10.7257i	0.0598015	−	0.0247706i	−0.352582	−	0.935781i	$-0.614696\pi$
$433$	25.8940	−	10.7257i	0.0598015	−	0.0247706i	0.412384	+	0.911010i	$0.364696\pi$
$434$	−259.185	−	625.729i	−0.597201	−	1.44177i
$435$	344.011	+	68.4281i	0.790830	+	0.157306i
$436$	−636.912	+	425.571i	−1.46081	+	0.976081i
$437$	39.3428	−	7.82578i	0.0900294	−	0.0179080i
$438$	937.410	−	937.410i	2.14021	−	2.14021i
$439$	5.00305	+	3.34293i	0.0113965	+	0.00761488i	0.561255	−	0.827643i	$-0.310319\pi$
$439$	5.00305	+	3.34293i	0.0113965	+	0.00761488i	−0.549859	+	0.835258i	$0.685319\pi$
$440$	−475.369	−	196.904i	−1.08039	−	0.447510i
$441$			14.6815i			0.0332914i
$442$		0			0
$443$	−318.579			−0.719141			−0.359570	−	0.933118i	$-0.617077\pi$
$443$	−318.579			−0.719141			−0.359570	+	0.933118i	$0.617077\pi$
$444$	471.336	−	1137.90i	1.06157	−	2.56285i
$445$	−16.7257	+	25.0317i	−0.0375857	+	0.0562510i
$446$	393.137	+	393.137i	0.881473	+	0.881473i
$447$	−168.629	−	847.757i	−0.377247	−	1.89655i
$448$	317.047	+	474.494i	0.707693	+	1.05914i
$449$	−145.896	+	733.471i	−0.324936	+	1.63356i	0.380493	+	0.924784i	$0.375754\pi$
$449$	−145.896	+	733.471i	−0.324936	+	1.63356i	−0.705429	+	0.708781i	$0.749246\pi$
$450$	−142.030	+	58.8307i	−0.315622	+	0.130735i
$451$	84.3194	+	203.565i	0.186961	+	0.451364i
$452$	1103.64	+	219.529i	2.44169	+	0.485683i
$453$	100.571	−	67.1997i	0.222012	−	0.148344i
$454$	443.057	−	88.1294i	0.975896	−	0.194118i
$455$	180.290	−	180.290i	0.396241	−	0.396241i
$456$	−1275.38	−	852.181i	−2.79688	−	1.86882i
$457$	−6.44295	−	2.66876i	−0.0140984	−	0.00583973i	0.375623	−	0.926773i	$-0.377429\pi$
$457$	−6.44295	−	2.66876i	−0.0140984	−	0.00583973i	−0.389721	+	0.920933i	$0.627429\pi$
$458$			551.821i			1.20485i
$459$		0			0
$460$	38.1426			0.0829187
$461$	−238.435	+	575.633i	−0.517213	+	1.24866i	0.422396	+	0.906411i	$0.361189\pi$
$461$	−238.435	+	575.633i	−0.517213	+	1.24866i	−0.939609	+	0.342251i	$0.888811\pi$
$462$	526.153	−	787.443i	1.13886	−	1.70442i
$463$	−82.7863	−	82.7863i	−0.178804	−	0.178804i	0.612030	−	0.790834i	$-0.290353\pi$
$463$	−82.7863	−	82.7863i	−0.178804	−	0.178804i	−0.790834	+	0.612030i	$0.790353\pi$
$464$	−52.4330	−	263.598i	−0.113002	−	0.568100i
$465$	−235.869	−	353.003i	−0.507246	−	0.759147i
$466$	113.963	−	572.929i	0.244555	−	1.22946i
$467$	−549.497	+	227.609i	−1.17665	+	0.487386i	−0.883387	−	0.468645i	$-0.844742\pi$
$467$	−549.497	+	227.609i	−1.17665	+	0.487386i	−0.293267	+	0.956031i	$0.594742\pi$
$468$	135.549	+	327.245i	0.289635	+	0.699241i
$469$	704.837	+	140.201i	1.50285	+	0.298936i
$470$	719.839	−	480.981i	1.53157	−	1.02336i
$471$	−45.0956	+	8.97007i	−0.0957443	+	0.0190447i
$472$	−343.046	+	343.046i	−0.726792	+	0.726792i
$473$	210.434	+	140.608i	0.444893	+	0.297268i
$474$	−701.478	−	290.562i	−1.47991	−	0.612999i
$475$		−	276.639i		−	0.582397i
$476$		0			0
$477$	452.494			0.948624
$478$	152.858	−	369.031i	0.319786	−	0.772032i
$479$	410.578	−	614.473i	0.857156	−	1.28282i	−0.100508	−	0.994936i	$-0.532047\pi$
$479$	410.578	−	614.473i	0.857156	−	1.28282i	0.957664	−	0.287888i	$-0.0929531\pi$
$480$	102.574	+	102.574i	0.213696	+	0.213696i
$481$	−72.4650	−	364.306i	−0.150655	−	0.757393i
$482$	−239.218	−	358.015i	−0.496302	−	0.742769i
$483$	−6.52372	+	32.7970i	−0.0135067	+	0.0679026i
$484$	120.143	−	49.7647i	0.248229	−	0.102820i
$485$	−151.350	−	365.390i	−0.312061	−	0.753382i
$486$	854.114	+	169.894i	1.75744	+	0.349576i
$487$	−647.229	+	432.464i	−1.32901	+	0.888017i	−0.998444	−	0.0557647i	$-0.982240\pi$
$487$	−647.229	+	432.464i	−1.32901	+	0.888017i	−0.330568	+	0.943782i	$0.607240\pi$
$488$	90.1577	−	17.9335i	0.184749	−	0.0367489i
$489$	−478.282	+	478.282i	−0.978082	+	0.978082i
$490$	−31.8258	−	21.2653i	−0.0649506	−	0.0433986i
$491$	−45.4991	−	18.8463i	−0.0926661	−	0.0383836i	0.335869	−	0.941909i	$-0.390970\pi$
$491$	−45.4991	−	18.8463i	−0.0926661	−	0.0383836i	−0.428535	+	0.903525i	$0.640970\pi$
$492$			624.573i			1.26946i
$493$		0			0
$494$	−971.185			−1.96596
$495$	84.3996	−	203.759i	0.170504	−	0.411633i
$496$	−180.735	+	270.489i	−0.364384	+	0.545340i
$497$	−23.9713	−	23.9713i	−0.0482319	−	0.0482319i
$498$	−227.990	−	1146.18i	−0.457812	−	2.30157i
$499$	506.384	+	757.858i	1.01480	+	1.51875i	0.846057	+	0.533092i	$0.178970\pi$
$499$	506.384	+	757.858i	1.01480	+	1.51875i	0.168741	+	0.985660i	$0.446030\pi$
$500$	202.776	−	1019.42i	0.405552	−	2.03885i
$501$	−312.583	+	129.476i	−0.623919	+	0.258436i
$502$	−241.194	−	582.293i	−0.480466	−	1.15995i
$503$	374.131	+	74.4193i	0.743799	+	0.147951i	0.552421	−	0.833565i	$-0.313704\pi$
$503$	374.131	+	74.4193i	0.743799	+	0.147951i	0.191378	+	0.981516i	$0.438704\pi$
$504$	394.979	−	263.916i	0.783688	−	0.523643i
$505$	388.172	−	77.2122i	0.768657	−	0.152895i
$506$	30.2123	−	30.2123i	0.0597081	−	0.0597081i
$507$	−292.668	−	195.554i	−0.577254	−	0.385709i
$508$	−345.863	−	143.261i	−0.680833	−	0.282010i
$509$			785.473i			1.54317i	0.636126	+	0.771585i	$0.280536\pi$
$509$			785.473i			1.54317i	−0.636126	+	0.771585i	$0.719464\pi$
$510$		0			0
$511$	−738.802			−1.44580
$512$	266.508	−	643.407i	0.520523	−	1.25665i
$513$	−252.675	+	378.154i	−0.492543	+	0.737143i
$514$	−177.768	−	177.768i	−0.345852	−	0.345852i
$515$	31.4730	+	158.225i	0.0611126	+	0.307234i
$516$	398.570	+	596.502i	0.772423	+	1.15601i
$517$	124.170	−	624.247i	0.240175	−	1.20744i
$518$	−966.239	+	400.229i	−1.86533	+	0.772643i
$519$	−135.888	−	328.062i	−0.261826	−	0.632104i
$520$	−431.407	−	85.8121i	−0.829628	−	0.165023i
$521$	−291.097	+	194.505i	−0.558728	+	0.373330i	−0.802637	−	0.596468i	$-0.796570\pi$
$521$	−291.097	+	194.505i	−0.558728	+	0.373330i	0.243909	+	0.969798i	$0.421570\pi$
$522$	405.810	−	80.7207i	0.777414	−	0.154637i
$523$	302.253	−	302.253i	0.577921	−	0.577921i	−0.356409	−	0.934330i	$-0.615999\pi$
$523$	302.253	−	302.253i	0.577921	−	0.577921i	0.934330	+	0.356409i	$0.115999\pi$
$524$	147.279	+	98.4086i	0.281067	+	0.187803i
$525$	213.057	+	88.2512i	0.405823	+	0.168097i
$526$			527.294i			1.00246i
$527$		0			0
$528$	−454.888			−0.861530
$529$	201.862	−	487.338i	0.381592	−	0.921245i
$530$	−655.412	+	980.893i	−1.23663	+	1.85074i
$531$	−147.040	−	147.040i	−0.276912	−	0.276912i
$532$	350.122	+	1760.18i	0.658123	+	3.30861i
$533$	104.646	+	156.614i	0.196335	+	0.293835i
$534$	−18.6494	+	93.7567i	−0.0349239	+	0.175574i
$535$	−427.004	+	176.871i	−0.798139	+	0.330600i
$536$	−474.441	−	1145.40i	−0.885151	−	2.13694i
$537$	−1071.19	−	213.072i	−1.99476	−	0.396783i
$538$	579.430	−	387.163i	1.07701	−	0.719633i
$539$	−27.5994	+	5.48987i	−0.0512049	+	0.0101853i
$540$	−305.792	+	305.792i	−0.566281	+	0.566281i
$541$	290.644	+	194.202i	0.537236	+	0.358969i	0.794397	−	0.607399i	$-0.207787\pi$
$541$	290.644	+	194.202i	0.537236	+	0.358969i	−0.257161	+	0.966369i	$0.582787\pi$
$542$	36.9257	+	15.2951i	0.0681287	+	0.0282198i
$543$		−	658.545i		−	1.21279i
$544$		0			0
$545$	407.731			0.748130
$546$	309.820	−	747.972i	0.567436	−	1.36991i
$547$	57.9550	−	86.7357i	0.105951	−	0.158566i	−0.774706	−	0.632322i	$-0.782102\pi$
$547$	57.9550	−	86.7357i	0.105951	−	0.158566i	0.880656	+	0.473756i	$0.157102\pi$
$548$	−292.184	−	292.184i	−0.533183	−	0.533183i
$549$	7.68686	+	38.6445i	0.0140016	+	0.0703907i
$550$	−163.704	−	245.000i	−0.297644	−	0.445455i
$551$	−145.256	+	730.250i	−0.263622	+	1.32532i
$552$	53.2970	−	22.0763i	0.0965525	−	0.0399933i
$553$	161.928	+	390.928i	0.292817	+	0.706923i
$554$	−588.472	−	117.054i	−1.06222	−	0.211289i
$555$	−545.101	+	364.225i	−0.982164	+	0.656261i
$556$	−289.277	+	57.5407i	−0.520282	+	0.103490i
$557$	−230.721	+	230.721i	−0.414221	+	0.414221i	−0.883206	−	0.468985i	$-0.844620\pi$
$557$	−230.721	+	230.721i	−0.414221	+	0.414221i	0.468985	+	0.883206i	$0.344620\pi$
$558$	−416.418	−	278.242i	−0.746269	−	0.498641i
$559$	199.886	+	82.7956i	0.357578	+	0.148114i
$560$			344.821i			0.615752i
$561$		0			0
$562$	−481.128			−0.856099
$563$	94.4773	−	228.088i	0.167811	−	0.405130i	−0.817494	−	0.575937i	$-0.804637\pi$
$563$	94.4773	−	228.088i	0.167811	−	0.405130i	0.985305	+	0.170807i	$0.0546373\pi$
$564$	1002.34	−	1500.11i	1.77720	−	2.65978i
$565$	−423.526	−	423.526i	−0.749604	−	0.749604i
$566$	18.5524	+	93.2693i	0.0327781	+	0.164787i
$567$	−402.010	−	601.650i	−0.709012	−	1.06111i
$568$	−11.4096	+	57.3597i	−0.0200873	+	0.100985i
$569$	123.790	−	51.2755i	0.217557	−	0.0901150i	−0.271243	−	0.962511i	$-0.587435\pi$
$569$	123.790	−	51.2755i	0.217557	−	0.0901150i	0.488800	+	0.872396i	$0.337435\pi$
$570$	655.964	+	1583.64i	1.15081	+	2.77831i
$571$	−191.552	−	38.1020i	−0.335467	−	0.0667286i	0.0244826	−	0.999700i	$-0.492206\pi$
$571$	−191.552	−	38.1020i	−0.335467	−	0.0667286i	−0.359950	+	0.932972i	$0.617206\pi$
$572$	−564.495	+	377.183i	−0.986879	+	0.659412i
$573$	−100.306	+	19.9521i	−0.175054	+	0.0348204i
$574$	375.013	−	375.013i	0.653334	−	0.653334i
$575$	8.65075	+	5.78024i	0.0150448	+	0.0100526i
$576$	389.863	+	161.486i	0.676845	+	0.280358i
$577$			383.658i			0.664919i	0.943118	+	0.332459i	$0.107878\pi$
$577$			383.658i			0.664919i	−0.943118	+	0.332459i	$0.892122\pi$
$578$		0			0
$579$	708.454			1.22358
$580$	−270.929	+	654.081i	−0.467119	+	1.12773i
$581$	−361.828	+	541.514i	−0.622768	+	0.932038i
$582$	−887.996	−	887.996i	−1.52577	−	1.52577i
$583$	169.202	+	850.634i	0.290226	+	1.45906i
$584$	708.099	+	1059.75i	1.21250	+	1.81463i
$585$	36.7818	−	184.915i	0.0628749	−	0.316094i
$586$	1598.42	−	662.086i	2.72767	−	1.12984i
$587$	−81.3118	−	196.304i	−0.138521	−	0.334419i	0.839362	−	0.543573i	$-0.182929\pi$
$587$	−81.3118	−	196.304i	−0.138521	−	0.334419i	−0.977883	+	0.209154i	$0.932929\pi$
$588$	−78.2340	−	15.5617i	−0.133051	−	0.0264655i
$589$	749.338	−	500.692i	1.27222	−	0.850071i
$590$	531.726	−	105.767i	0.901231	−	0.179266i
$591$	713.044	−	713.044i	1.20650	−	1.20650i
$592$	417.683	+	279.087i	0.705546	+	0.471431i
$593$	−442.361	−	183.232i	−0.745972	−	0.308992i	−0.0228751	−	0.999738i	$-0.507282\pi$
$593$	−442.361	−	183.232i	−0.745972	−	0.308992i	−0.723097	+	0.690747i	$0.757282\pi$
$594$			484.429i			0.815537i
$595$		0			0
$596$	1744.68			2.92731
$597$	−506.981	+	1223.96i	−0.849215	+	2.05019i
$598$	20.2925	−	30.3698i	0.0339339	−	0.0507857i
$599$	−49.9429	−	49.9429i	−0.0833771	−	0.0833771i	0.664188	−	0.747565i	$-0.268777\pi$
$599$	−49.9429	−	49.9429i	−0.0833771	−	0.0833771i	−0.747565	+	0.664188i	$0.768777\pi$
$600$	−77.6147	−	390.196i	−0.129358	−	0.650326i
$601$	−413.966	−	619.543i	−0.688795	−	1.03085i	−0.996836	−	0.0794811i	$-0.974674\pi$
$601$	−413.966	−	619.543i	−0.688795	−	1.03085i	0.308042	−	0.951373i	$-0.400326\pi$
$602$	118.845	−	597.473i	0.197417	−	0.992480i
$603$	490.956	−	203.361i	0.814189	−	0.337248i
$604$	93.4299	+	225.560i	0.154685	+	0.373443i
$605$	−67.8884	−	13.5038i	−0.112212	−	0.0223204i
$606$	1044.91	−	698.190i	1.72428	−	1.15213i
$607$	−65.2902	+	12.9870i	−0.107562	+	0.0213954i	−0.248578	−	0.968612i	$-0.579963\pi$
$607$	−65.2902	+	12.9870i	−0.107562	+	0.0213954i	0.141016	+	0.990007i	$0.454963\pi$
$608$	−217.739	+	217.739i	−0.358123	+	0.358123i
$609$	−516.074	−	344.830i	−0.847413	−	0.566223i
$610$	−94.9055	−	39.3112i	−0.155583	−	0.0644445i
$611$		−	544.101i		−	0.890509i
$612$		0			0
$613$	−911.957			−1.48769			−0.743847	−	0.668350i	$-0.767001\pi$
$613$	−911.957			−1.48769			−0.743847	+	0.668350i	$0.767001\pi$
$614$	−608.134	+	1468.16i	−0.990446	+	2.39115i
$615$	184.698	−	276.420i	0.300322	−	0.449464i
$616$	643.826	+	643.826i	1.04517	+	1.04517i
$617$	31.6420	+	159.075i	0.0512837	+	0.257820i	0.997919	−	0.0644877i	$-0.0205413\pi$
$617$	31.6420	+	159.075i	0.0512837	+	0.257820i	−0.946635	+	0.322308i	$0.895541\pi$
$618$	284.594	+	425.925i	0.460508	+	0.689198i
$619$	94.0581	−	472.862i	0.151952	−	0.763913i	−0.827378	−	0.561645i	$-0.810169\pi$
$619$	94.0581	−	472.862i	0.151952	−	0.763913i	0.979330	−	0.202268i	$-0.0648313\pi$
$620$	791.708	−	327.936i	1.27695	−	0.528930i
$621$	−6.54571	−	15.8027i	−0.0105406	−	0.0254472i
$622$	137.122	+	27.2754i	0.220454	+	0.0438511i
$623$	44.2953	−	29.5972i	0.0711000	−	0.0475075i
$624$	−381.395	+	75.8643i	−0.611211	+	0.121577i
$625$	−241.466	+	241.466i	−0.386345	+	0.386345i
$626$	497.420	+	332.366i	0.794601	+	0.530936i
$627$	1164.26	+	482.251i	1.85687	+	0.769140i
$628$		−	92.8063i		−	0.147781i
$629$		0			0
$630$	−530.853			−0.842624
$631$	−15.3062	+	36.9525i	−0.0242571	+	0.0585618i	−0.935544	−	0.353210i	$-0.885090\pi$
$631$	−15.3062	+	36.9525i	−0.0242571	+	0.0585618i	0.911287	+	0.411772i	$0.135090\pi$
$632$	405.554	−	606.954i	0.641699	−	0.960370i
$633$	612.951	+	612.951i	0.968326	+	0.968326i
$634$	−294.376	−	1479.93i	−0.464316	−	2.33427i
$635$	110.705	+	165.682i	0.174339	+	0.260917i
$636$	−479.623	+	2411.23i	−0.754124	+	3.79124i
$637$	−22.2249	+	9.20584i	−0.0348899	+	0.0144519i
$638$	303.490	+	732.690i	0.475690	+	1.14842i
$639$	−24.5862	−	4.89050i	−0.0384761	−	0.00765337i
$640$	−787.263	+	526.032i	−1.23010	+	0.821925i
$641$	−506.864	+	100.822i	−0.790740	+	0.157288i	−0.573907	−	0.818921i	$-0.694573\pi$
$641$	−506.864	+	100.822i	−0.790740	+	0.157288i	−0.216833	+	0.976209i	$0.569573\pi$
$642$	−1037.73	+	1037.73i	−1.61641	+	1.61641i
$643$	−606.405	−	405.187i	−0.943088	−	0.630151i	−0.0139570	−	0.999903i	$-0.504443\pi$
$643$	−606.405	−	405.187i	−0.943088	−	0.630151i	−0.929131	+	0.369752i	$0.879443\pi$
$644$	−62.3581	−	25.8296i	−0.0968293	−	0.0401080i
$645$		−	381.861i		−	0.592033i
$646$		0			0
$647$	−670.058			−1.03564			−0.517819	−	0.855490i	$-0.673256\pi$
$647$	−670.058			−1.03564			−0.517819	+	0.855490i	$0.673256\pi$
$648$	−477.710	+	1153.29i	−0.737207	+	1.77978i
$649$	221.435	−	331.401i	0.341194	−	0.510633i
$650$	−178.116	−	178.116i	−0.274024	−	0.274024i
$651$	146.567	+	736.841i	0.225141	+	1.13186i
$652$	−758.500	−	1135.18i	−1.16334	−	1.74107i
$653$	147.770	−	742.889i	0.226294	−	1.13766i	−0.685836	−	0.727756i	$-0.740563\pi$
$653$	147.770	−	742.889i	0.226294	−	1.13766i	0.912130	−	0.409900i	$-0.134437\pi$
$654$	1196.12	−	495.447i	1.82892	−	0.757564i
$655$	−36.0806	−	87.1063i	−0.0550849	−	0.132987i
$656$	−249.843	−	49.6969i	−0.380858	−	0.0757575i
$657$	−454.241	+	303.514i	−0.691386	+	0.461970i
$658$	−1502.55	+	298.877i	−2.28352	+	0.454220i
$659$	202.133	−	202.133i	0.306727	−	0.306727i	−0.536911	−	0.843639i	$-0.680409\pi$
$659$	202.133	−	202.133i	0.306727	−	0.306727i	0.843639	+	0.536911i	$0.180409\pi$
$660$	996.319	+	665.719i	1.50957	+	1.00866i
$661$	558.348	+	231.275i	0.844702	+	0.349887i	0.762706	−	0.646746i	$-0.223870\pi$
$661$	558.348	+	231.275i	0.844702	+	0.349887i	0.0819961	+	0.996633i	$0.473870\pi$
$662$		−	1829.14i		−	2.76305i
$663$		0			0
$664$	1123.55			1.69209
$665$	365.564	−	882.548i	0.549720	−	1.32714i
$666$	−429.655	+	643.025i	−0.645128	+	0.965503i
$667$	−19.8005	−	19.8005i	−0.0296860	−	0.0296860i
$668$	−133.231	−	669.796i	−0.199447	−	1.00269i
$669$	−342.631	−	512.783i	−0.512154	−	0.766492i
$670$	−270.287	+	1358.83i	−0.403414	+	2.02810i
$671$	−69.7726	+	28.9008i	−0.103983	+	0.0430712i
$672$	−98.2333	−	237.156i	−0.146180	−	0.352911i
$673$	−685.871	−	136.428i	−1.01913	−	0.202717i	−0.342869	−	0.939383i	$-0.611399\pi$
$673$	−685.871	−	136.428i	−1.01913	−	0.202717i	−0.676256	+	0.736667i	$0.736399\pi$
$674$	−1648.67	+	1101.60i	−2.44609	+	1.63443i
$675$	−115.694	+	23.0130i	−0.171399	+	0.0340934i
$676$	502.379	−	502.379i	0.743164	−	0.743164i
$677$	−857.109	−	572.702i	−1.26604	−	0.845941i	−0.272806	−	0.962069i	$-0.587952\pi$
$677$	−857.109	−	572.702i	−1.26604	−	0.845941i	−0.993234	+	0.116128i	$0.962952\pi$
$678$	−1757.09	−	727.812i	−2.59158	−	1.07347i
$679$			699.857i			1.03072i
$680$		0			0
$681$	−501.088			−0.735812
$682$	367.349	−	886.858i	0.538635	−	1.30038i
$683$	−284.874	+	426.344i	−0.417092	+	0.624223i	−0.979214	−	0.202832i	$-0.934985\pi$
$683$	−284.874	+	426.344i	−0.417092	+	0.624223i	0.562121	+	0.827055i	$0.309985\pi$
$684$	938.383	+	938.383i	1.37191	+	1.37191i
$685$	42.9089	+	215.718i	0.0626408	+	0.314917i
$686$	−630.518	−	943.637i	−0.919123	−	1.37556i
$687$	119.416	−	600.345i	0.173822	−	0.873864i
$688$	−270.328	+	111.974i	−0.392919	+	0.162752i
$689$	283.730	+	684.985i	0.411800	+	0.994173i
$690$	−63.2278	−	12.5768i	−0.0916346	−	0.0182272i
$691$	−272.116	+	181.822i	−0.393800	+	0.263129i	−0.736667	−	0.676255i	$-0.763602\pi$
$691$	−272.116	+	181.822i	−0.393800	+	0.263129i	0.342868	+	0.939384i	$0.388602\pi$
$692$	702.963	−	139.828i	1.01584	−	0.202063i
$693$	−275.964	+	275.964i	−0.398217	+	0.398217i
$694$	1539.71	+	1028.80i	2.21861	+	1.48243i
$695$	145.042	+	60.0785i	0.208694	+	0.0864439i
$696$			1070.76i			1.53845i
$697$		0			0
$698$	−110.762			−0.158685
$699$	−247.968	+	598.647i	−0.354747	+	0.856434i
$700$	−258.605	+	387.030i	−0.369436	+	0.552900i
$701$	761.025	+	761.025i	1.08563	+	1.08563i	0.995973	+	0.0896553i	$0.0285765\pi$
$701$	761.025	+	761.025i	1.08563	+	1.08563i	0.0896553	+	0.995973i	$0.471423\pi$
$702$	80.7910	+	406.164i	0.115087	+	0.578581i
$703$	−773.159	−	1157.11i	−1.09980	−	1.64597i
$704$	−157.793	+	793.279i	−0.224138	+	1.12682i
$705$	−887.223	+	367.500i	−1.25847	+	0.521277i
$706$	−446.837	−	1078.76i	−0.632914	−	1.52799i
$707$	−686.897	−	136.632i	−0.971565	−	0.193256i
$708$	939.397	−	627.685i	1.32683	−	0.886561i
$709$	−558.478	+	111.088i	−0.787698	+	0.156683i	−0.572519	−	0.819892i	$-0.694034\pi$
$709$	−558.478	+	111.088i	−0.787698	+	0.156683i	−0.215179	+	0.976575i	$0.569034\pi$
$710$	46.2131	−	46.2131i	0.0650889	−	0.0650889i
$711$	260.160	+	173.833i	0.365907	+	0.244491i
$712$	−84.9091	−	35.1705i	−0.119254	−	0.0493968i
$713$			33.8942i			0.0475375i
$714$		0			0
$715$	361.371			0.505414
$716$	843.623	−	2036.69i	1.17824	−	2.84453i
$717$	−246.159	+	368.403i	−0.343318	+	0.513811i
$718$	−787.534	−	787.534i	−1.09684	−	1.09684i
$719$	−155.079	−	779.636i	−0.215687	−	1.08433i	−0.925153	−	0.379594i	$-0.876064\pi$
$719$	−155.079	−	779.636i	−0.215687	−	1.08433i	0.709466	−	0.704740i	$-0.248936\pi$
$720$	141.659	+	212.008i	0.196749	+	0.294456i
$721$	55.6936	−	279.990i	0.0772449	−	0.388336i
$722$	−2223.87	+	921.158i	−3.08016	+	1.27584i
$723$	182.778	+	441.264i	0.252804	+	0.610324i
$724$	1303.70	+	259.322i	1.80069	+	0.358179i
$725$	−160.568	+	107.288i	−0.221473	+	0.147984i
$726$	−215.566	+	42.8787i	−0.296923	+	0.0590616i
$727$	−580.585	+	580.585i	−0.798603	+	0.798603i	−0.982875	−	0.184272i	$-0.941007\pi$
$727$	−580.585	+	580.585i	−0.798603	+	0.798603i	0.184272	+	0.982875i	$0.441007\pi$
$728$	647.183	+	432.434i	0.888987	+	0.594002i
$729$	−56.1590	−	23.2618i	−0.0770356	−	0.0319092i
$730$		−	1424.30i		−	1.95110i
$731$		0			0
$732$	−214.074			−0.292451
$733$	−158.102	+	381.691i	−0.215691	+	0.520725i	−0.994279	−	0.106810i	$-0.965936\pi$
$733$	−158.102	+	381.691i	−0.215691	+	0.520725i	0.778588	+	0.627535i	$0.215936\pi$
$734$	−565.163	+	845.827i	−0.769977	+	1.15235i
$735$	30.0225	+	30.0225i	0.0408469	+	0.0408469i
$736$	−2.25934	−	11.3585i	−0.00306975	−	0.0154327i
$737$	565.877	+	846.895i	0.767811	+	1.14911i
$738$	76.5085	−	384.634i	0.103670	−	0.521185i
$739$	−1135.74	+	470.438i	−1.53686	+	0.636587i	−0.980880	−	0.194612i	$-0.937655\pi$
$739$	−1135.74	+	470.438i	−1.53686	+	0.636587i	−0.555976	+	0.831198i	$0.687655\pi$
$740$	−506.393	−	1222.54i	−0.684315	−	1.65208i
$741$	1056.59	+	210.168i	1.42589	+	0.283627i
$742$	1735.76	−	1159.80i	2.33930	−	1.56307i
$743$	−85.9201	+	17.0906i	−0.115639	+	0.0230021i	−0.252571	−	0.967578i	$-0.581276\pi$
$743$	−85.9201	+	17.0906i	−0.115639	+	0.0230021i	0.136931	+	0.990581i	$0.456276\pi$
$744$	916.457	−	916.457i	1.23180	−	1.23180i
$745$	−772.150	−	515.934i	−1.03644	−	0.692529i
$746$	2083.55	+	863.036i	2.79297	+	1.15688i
$747$			481.588i			0.644696i
$748$		0			0
$749$	817.870			1.09195
$750$	−672.271	+	1623.01i	−0.896362	+	2.16401i
$751$	527.643	−	789.674i	0.702588	−	1.05150i	−0.292857	−	0.956156i	$-0.594606\pi$
$751$	527.643	−	789.674i	0.702588	−	1.05150i	0.995445	−	0.0953406i	$-0.0303940\pi$
$752$	520.323	+	520.323i	0.691919	+	0.691919i
$753$	136.393	+	685.692i	0.181132	+	0.910614i
$754$	376.653	+	563.701i	0.499540	+	0.747614i
$755$	25.3526	−	127.456i	0.0335795	−	0.168816i
$756$	707.007	−	292.852i	0.935194	−	0.387370i
$757$	−38.5085	−	92.9677i	−0.0508699	−	0.122811i	0.896402	−	0.443243i	$-0.146172\pi$
$757$	−38.5085	−	92.9677i	−0.0508699	−	0.122811i	−0.947272	+	0.320432i	$0.896172\pi$
$758$	802.348	+	159.597i	1.05851	+	0.210550i
$759$	−39.4071	+	26.3310i	−0.0519197	+	0.0346917i
$760$	−1616.31	+	321.504i	−2.12672	+	0.423032i
$761$	898.159	−	898.159i	1.18024	−	1.18024i	0.200553	−	0.979683i	$-0.435726\pi$
$761$	898.159	−	898.159i	1.18024	−	1.18024i	0.979683	−	0.200553i	$-0.0642738\pi$
$762$	526.090	+	351.522i	0.690407	+	0.461315i
$763$	−666.586	−	276.109i	−0.873638	−	0.361873i
$764$		−	206.429i		−	0.270195i
$765$		0			0
$766$	−79.9367			−0.104356
$767$	130.390	−	314.789i	0.170000	−	0.410416i
$768$	−1003.26	+	1501.48i	−1.30633	+	1.95506i
$769$	356.640	+	356.640i	0.463771	+	0.463771i	0.899889	−	0.436118i	$-0.143647\pi$
$769$	356.640	+	356.640i	0.463771	+	0.463771i	−0.436118	+	0.899889i	$0.643647\pi$
$770$	−198.503	−	997.940i	−0.257796	−	1.29603i
$771$	154.930	+	231.870i	0.200947	+	0.300739i
$772$	−278.975	+	1402.50i	−0.361366	+	1.81671i
$773$	561.790	−	232.701i	0.726766	−	0.301036i	0.0115436	−	0.999933i	$-0.496325\pi$
$773$	561.790	−	232.701i	0.726766	−	0.301036i	0.715222	+	0.698897i	$0.246325\pi$
$774$	−172.384	−	416.171i	−0.222718	−	0.537689i
$775$	229.256	+	45.6019i	0.295814	+	0.0588411i
$776$	1003.88	−	670.773i	1.29366	−	0.864398i
$777$	1137.82	−	226.326i	1.46437	−	0.291281i
$778$	−920.269	+	920.269i	−1.18287	+	1.18287i
$779$	586.772	+	392.068i	0.753237	+	0.503297i
$780$	946.377	+	392.002i	1.21330	+	0.502567i
$781$		−	48.0478i		−	0.0615209i
$782$		0			0
$783$	317.485			0.405472
$784$	12.4501	−	30.0571i	0.0158802	−	0.0383382i
$785$	−27.4446	+	41.0737i	−0.0349613	+	0.0523232i
$786$	−211.692	−	211.692i	−0.269328	−	0.269328i
$787$	30.0411	+	151.027i	0.0381717	+	0.191902i	0.995166	−	0.0982034i	$-0.0313096\pi$
$787$	30.0411	+	151.027i	0.0381717	+	0.191902i	−0.956995	+	0.290106i	$0.906310\pi$
$788$	1130.81	+	1692.37i	1.43503	+	2.14768i
$789$	114.108	−	573.662i	0.144624	−	0.727074i
$790$	−753.654	+	312.174i	−0.953992	+	0.395156i
$791$	405.604	+	979.215i	0.512774	+	1.23795i
$792$	660.342	+	131.350i	0.833766	+	0.165846i
$793$	−53.6801	+	35.8679i	−0.0676924	+	0.0452306i
$794$	2410.08	−	479.395i	3.03537	−	0.603772i
$795$	925.314	−	925.314i	1.16392	−	1.16392i
$796$	−2223.39	−	1485.62i	−2.79321	−	1.86636i
$797$	155.316	+	64.3339i	0.194876	+	0.0807201i	0.477987	−	0.878367i	$-0.341367\pi$
$797$	155.316	+	64.3339i	0.194876	+	0.0807201i	−0.283111	+	0.959087i	$0.591367\pi$
$798$		−	3033.25i		−	3.80106i
$799$		0			0
$800$	−79.8668			−0.0998335
$801$	15.0752	−	36.3948i	0.0188205	−	0.0454367i
$802$	705.322	−	1055.59i	0.879454	−	1.31620i
$803$	−740.425	−	740.425i	−0.922073	−	0.922073i
$804$	563.267	+	2831.73i	0.700581	+	3.52206i
$805$	19.9598	+	29.8720i	0.0247948	+	0.0371080i
$806$	160.093	−	804.841i	0.198626	−	0.998562i
$807$	−714.165	+	295.817i	−0.884963	+	0.366564i
$808$	462.365	+	1116.25i	0.572233	+	1.38149i
$809$	465.854	+	92.6641i	0.575839	+	0.114542i	0.474414	−	0.880302i	$-0.342660\pi$
$809$	465.854	+	92.6641i	0.575839	+	0.114542i	0.101425	+	0.994843i	$0.467660\pi$
$810$	1159.89	−	775.017i	1.43197	−	0.956811i
$811$	1535.18	−	305.365i	1.89294	−	0.376530i	0.895318	−	0.445427i	$-0.146948\pi$
$811$	1535.18	−	305.365i	1.89294	−	0.376530i	0.997624	+	0.0688973i	$0.0219481\pi$
$812$	885.867	−	885.867i	1.09097	−	1.09097i
$813$	−36.8629	−	24.6310i	−0.0453418	−	0.0302964i
$814$	−1369.47	−	567.253i	−1.68240	−	0.696871i
$815$			726.702i			0.891659i
$816$		0			0
$817$	810.597			0.992163
$818$	981.910	−	2370.54i	1.20038	−	2.89797i
$819$	−185.355	+	277.403i	−0.226319	+	0.338710i
$820$	474.489	+	474.489i	0.578645	+	0.578645i
$821$	147.778	+	742.932i	0.179998	+	0.904911i	0.960185	+	0.279365i	$0.0901238\pi$
$821$	147.778	+	742.932i	0.179998	+	0.904911i	−0.780187	+	0.625546i	$0.784876\pi$
$822$	388.003	+	580.688i	0.472023	+	0.706433i
$823$	−197.554	+	993.171i	−0.240041	+	1.20677i	0.653198	+	0.757187i	$0.273427\pi$
$823$	−197.554	+	993.171i	−0.240041	+	1.20677i	−0.893239	+	0.449582i	$0.851573\pi$
$824$	−455.001	+	188.467i	−0.552185	+	0.228723i
$825$	125.080	+	301.970i	0.151612	+	0.366025i
$826$	−940.926	−	187.162i	−1.13914	−	0.226588i
$827$	−145.114	+	96.9624i	−0.175471	+	0.117246i	−0.640204	−	0.768205i	$-0.721150\pi$
$827$	−145.114	+	96.9624i	−0.175471	+	0.117246i	0.464733	+	0.885451i	$0.346150\pi$
$828$	−48.9512	+	9.73700i	−0.0591198	+	0.0117597i
$829$	242.070	−	242.070i	0.292002	−	0.292002i	−0.545869	−	0.837871i	$-0.683800\pi$
$829$	242.070	−	242.070i	0.292002	−	0.292002i	0.837871	+	0.545869i	$0.183800\pi$
$830$	−1043.96	−	697.553i	−1.25779	−	0.840425i
$831$	614.887	+	254.695i	0.739937	+	0.306492i
$832$			691.432i			0.831048i
$833$		0			0
$834$	498.498			0.597720
$835$	−139.107	+	335.833i	−0.166595	+	0.402195i
$836$	−1413.16	+	2114.94i	−1.69038	+	2.52983i
$837$	−271.733	−	271.733i	−0.324651	−	0.324651i
$838$	−524.942	−	2639.06i	−0.626423	−	3.14924i
$839$	212.754	+	318.409i	0.253581	+	0.379511i	0.936318	−	0.351154i	$-0.114211\pi$
$839$	212.754	+	318.409i	0.253581	+	0.379511i	−0.682737	+	0.730664i	$0.739211\pi$
$840$	268.012	−	1347.39i	0.319062	−	1.60403i
$841$	−296.792	+	122.935i	−0.352904	+	0.146178i
$842$	862.553	+	2082.39i	1.02441	+	2.47314i
$843$	523.436	+	104.118i	0.620920	+	0.123509i
$844$	−1454.80	+	972.069i	−1.72370	+	1.15174i
$845$	−370.903	+	73.7771i	−0.438938	+	0.0873102i
$846$	−801.038	+	801.038i	−0.946854	+	0.946854i
$847$	101.844	+	68.0500i	0.120241	+	0.0803424i
$848$	−926.381	−	383.720i	−1.09243	−	0.452499i
$849$		−	105.486i		−	0.124247i
$850$		0			0
$851$	52.3389			0.0615028
$852$	52.1205	−	125.830i	0.0611743	−	0.147688i
$853$	−157.013	+	234.986i	−0.184071	+	0.275482i	−0.912017	−	0.410153i	$-0.865475\pi$
$853$	−157.013	+	234.986i	−0.184071	+	0.275482i	0.727946	+	0.685635i	$0.240475\pi$
$854$	128.537	+	128.537i	0.150512	+	0.150512i
$855$	−137.807	−	692.802i	−0.161178	−	0.810295i
$856$	−783.882	−	1173.16i	−0.915750	−	1.37052i
$857$	−215.840	+	1085.10i	−0.251855	+	1.26616i	0.623172	+	0.782085i	$0.285844\pi$
$857$	−215.840	+	1085.10i	−0.251855	+	1.26616i	−0.875027	+	0.484075i	$0.839156\pi$
$858$	1060.12	−	439.114i	1.23557	−	0.511788i
$859$	−67.0359	−	161.839i	−0.0780395	−	0.188404i	0.880045	−	0.474891i	$-0.157513\pi$
$859$	−67.0359	−	161.839i	−0.0780395	−	0.188404i	−0.958084	+	0.286487i	$0.907513\pi$
$860$	755.957	+	150.369i	0.879020	+	0.174848i
$861$	−489.144	+	326.836i	−0.568112	+	0.379600i
$862$	445.173	−	88.5505i	0.516442	−	0.102727i
$863$	−614.789	+	614.789i	−0.712385	+	0.712385i	−0.967034	−	0.254648i	$-0.918040\pi$
$863$	−614.789	+	614.789i	−0.712385	+	0.712385i	0.254648	+	0.967034i	$0.418040\pi$
$864$	109.175	+	72.9483i	0.126360	+	0.0844309i
$865$	−352.463	−	145.995i	−0.407472	−	0.168780i
$866$		−	95.6151i		−	0.110410i
$867$		0			0
$868$	−1516.41			−1.74702
$869$	−229.504	+	554.071i	−0.264101	+	0.637596i
$870$	664.782	−	994.917i	0.764118	−	1.14358i
$871$	615.694	+	615.694i	0.706882	+	0.706882i
$872$	242.831	+	1220.79i	0.278476	+	1.39999i
$873$	287.515	+	430.296i	0.329341	+	0.492894i
$874$	26.6974	−	134.217i	0.0305463	−	0.153566i
$875$	904.489	−	374.652i	1.03370	−	0.428173i
$876$	−1135.88	−	2742.25i	−1.29666	−	3.13042i
$877$	−282.049	−	56.1031i	−0.321607	−	0.0639716i	0.0316469	−	0.999499i	$-0.489925\pi$
$877$	−282.049	−	56.1031i	−0.321607	−	0.0639716i	−0.353254	+	0.935528i	$0.614925\pi$
$878$	17.0678	−	11.4043i	0.0194394	−	0.0129890i
$879$	−1882.25	+	374.403i	−2.14135	+	0.425942i
$880$	−345.579	+	345.579i	−0.392703	+	0.392703i
$881$	909.481	+	607.696i	1.03233	+	0.689780i	0.951720	−	0.306966i	$-0.0993139\pi$
$881$	909.481	+	607.696i	1.03233	+	0.689780i	0.0806078	+	0.996746i	$0.474314\pi$
$882$	46.2730	+	19.1669i	0.0524638	+	0.0217312i
$883$			470.424i			0.532757i	0.963869	+	0.266378i	$0.0858271\pi$
$883$			470.424i			0.532757i	−0.963869	+	0.266378i	$0.914173\pi$
$884$		0			0
$885$	−601.372			−0.679516
$886$	−415.910	+	1004.10i	−0.469424	+	1.13329i
$887$	−584.618	+	874.942i	−0.659096	+	0.986406i	0.339849	+	0.940480i	$0.389624\pi$
$887$	−584.618	+	874.942i	−0.659096	+	0.986406i	−0.998945	+	0.0459263i	$0.985376\pi$
$888$	−1415.18	−	1415.18i	−1.59367	−	1.59367i
$889$	−68.7911	−	345.836i	−0.0773803	−	0.389017i
$890$	57.0591	+	85.3950i	0.0641114	+	0.0959495i
$891$	200.079	−	1005.86i	0.224555	−	1.12892i
$892$	1150.06	−	476.370i	1.28930	−	0.534047i
$893$	−780.112	−	1883.36i	−0.873585	−	2.10902i
$894$	−2892.10	−	575.274i	−3.23501	−	0.643484i
$895$	−975.653	+	651.910i	−1.09011	+	0.728391i
$896$	1643.29	−	326.871i	1.83403	−	0.364811i
$897$	−28.6490	+	28.6490i	−0.0319387	+	0.0319387i
$898$	2121.28	+	1417.39i	2.36222	+	1.57839i
$899$	−581.229	−	240.753i	−0.646529	−	0.267801i
$900$			344.200i			0.382444i
$901$		0			0
$902$	751.675			0.833342
$903$	−258.591	+	624.293i	−0.286368	+	0.691354i
$904$	1015.85	−	1520.33i	1.12373	−	1.68178i
$905$	−500.297	−	500.297i	−0.552815	−	0.552815i
$906$	−80.5019	−	404.710i	−0.0888542	−	0.446700i
$907$	−142.416	−	213.141i	−0.157019	−	0.234995i	0.744616	−	0.667493i	$-0.232633\pi$
$907$	−142.416	−	213.141i	−0.157019	−	0.234995i	−0.901635	+	0.432497i	$0.857633\pi$
$908$	197.318	−	991.986i	0.217311	−	1.09250i
$909$	−478.459	+	198.184i	−0.526358	+	0.218024i
$910$	−332.864	−	803.606i	−0.365785	−	0.883083i
$911$	1064.90	+	211.821i	1.16893	+	0.232515i	0.741133	−	0.671359i	$-0.234289\pi$
$911$	1064.90	+	211.821i	1.16893	+	0.232515i	0.427800	+	0.903874i	$0.359289\pi$
$912$	−1211.39	+	809.428i	−1.32828	+	0.887531i
$913$	−905.327	+	180.081i	−0.991596	+	0.197241i
$914$	−16.8227	+	16.8227i	−0.0184056	+	0.0184056i
$915$	94.7439	+	63.3059i	0.103545	+	0.0691867i
$916$	1141.46	+	472.807i	1.24613	+	0.516165i
$917$			166.840i			0.181942i
$918$		0			0
$919$	−585.165			−0.636741			−0.318371	−	0.947966i	$-0.603136\pi$
$919$	−585.165			−0.636741			−0.318371	+	0.947966i	$0.603136\pi$
$920$	23.7184	−	57.2612i	0.0257808	−	0.0622404i
$921$	979.326	−	1465.66i	1.06333	−	1.59138i
$922$	1503.00	+	1503.00i	1.63015	+	1.63015i
$923$	−8.01321	−	40.2851i	−0.00868171	−	0.0436459i
$924$	−1178.03	−	1763.05i	−1.27493	−	1.90807i
$925$	70.4176	−	354.013i	0.0761271	−	0.382717i
$926$	−369.004	+	152.846i	−0.398493	+	0.165061i
$927$	−80.7832	−	195.028i	−0.0871448	−	0.210386i
$928$	210.827	+	41.9360i	0.227184	+	0.0451897i
$929$	63.6881	−	42.5550i	0.0685556	−	0.0458074i	−0.520820	−	0.853666i	$-0.674374\pi$
$929$	63.6881	−	42.5550i	0.0685556	−	0.0458074i	0.589376	+	0.807859i	$0.299374\pi$
$930$	−1420.52	+	282.560i	−1.52744	+	0.303828i
$931$	−63.7303	+	63.7303i	−0.0684536	+	0.0684536i
$932$	−1087.48	−	726.628i	−1.16682	−	0.779644i
$933$	−143.278	−	59.3476i	−0.153567	−	0.0636094i
$934$			2029.05i			2.17243i
$935$		0			0
$936$	575.562			0.614917
$937$	31.9660	−	77.1728i	0.0341153	−	0.0823616i	−0.905904	−	0.423484i	$-0.860807\pi$
$937$	31.9660	−	77.1728i	0.0341153	−	0.0823616i	0.940019	+	0.341122i	$0.110807\pi$
$938$	1362.06	−	2038.47i	1.45209	−	2.17320i
$939$	−469.236	−	469.236i	−0.499718	−	0.499718i
$940$	−378.156	−	1901.12i	−0.402294	−	2.02247i
$941$	3.10489	+	4.64679i	0.00329956	+	0.00493814i	0.833116	−	0.553099i	$-0.186555\pi$
$941$	3.10489	+	4.64679i	0.00329956	+	0.00493814i	−0.829816	+	0.558037i	$0.811555\pi$
$942$	−30.6012	+	153.842i	−0.0324853	+	0.163315i
$943$	−24.5207	+	10.1568i	−0.0260028	+	0.0107707i
$944$	176.341	+	425.724i	0.186802	+	0.450979i
$945$	−399.505	−	79.4665i	−0.422757	−	0.0840915i
$946$	717.891	−	479.680i	0.758870	−	0.507061i
$947$	−903.388	+	179.695i	−0.953947	+	0.189752i	−0.647440	−	0.762116i	$-0.724160\pi$
$947$	−903.388	+	179.695i	−0.953947	+	0.189752i	−0.306507	+	0.951868i	$0.599160\pi$
$948$	−1202.07	+	1202.07i	−1.26801	+	1.26801i
$949$	−744.285	−	497.315i	−0.784284	−	0.524042i
$950$	−871.907	−	361.156i	−0.917797	−	0.380164i
$951$			1673.77i			1.76001i
$952$		0			0
$953$	−52.9877			−0.0556009			−0.0278005	−	0.999613i	$-0.508850\pi$
$953$	−52.9877			−0.0556009			−0.0278005	+	0.999613i	$0.508850\pi$
$954$	590.737	−	1426.17i	0.619221	−	1.49493i
$955$	−61.0449	+	91.3602i	−0.0639214	+	0.0956651i
$956$	−632.381	−	632.381i	−0.661487	−	0.661487i
$957$	−171.621	−	862.795i	−0.179332	−	0.901563i
$958$	−1400.68	−	2096.26i	−1.46208	−	2.18816i
$959$	75.9303	−	381.727i	0.0791765	−	0.398047i
$960$	1127.46	−	467.011i	1.17444	−	0.486470i
$961$	−76.3481	−	184.321i	−0.0794465	−	0.191801i
$962$	−1242.82	−	247.212i	−1.29191	−	0.256978i
$963$	502.855	−	335.997i	0.522175	−	0.348906i
$964$	−945.529	+	188.077i	−0.980839	+	0.195101i
$965$	538.213	−	538.213i	0.557734	−	0.557734i
$966$	94.8524	+	63.3783i	0.0981909	+	0.0656090i
$967$	−1542.05	−	638.737i	−1.59467	−	0.660534i	−0.604021	−	0.796968i	$-0.706436\pi$
$967$	−1542.05	−	638.737i	−1.59467	−	0.660534i	−0.990649	+	0.136434i	$0.956436\pi$
$968$		−	211.308i		−	0.218294i
$969$		0			0
$970$	−1349.22			−1.39095
$971$	108.360	−	261.605i	0.111597	−	0.269419i	−0.858208	−	0.513303i	$-0.828422\pi$
$971$	108.360	−	261.605i	0.111597	−	0.269419i	0.969804	+	0.243884i	$0.0784217\pi$
$972$	1083.25	−	1621.19i	1.11445	−	1.66789i
$973$	−196.441	−	196.441i	−0.201892	−	0.201892i
$974$	518.071	+	2604.52i	0.531900	+	2.67404i
$975$	155.233	+	232.323i	0.159214	+	0.238280i
$976$	17.0338	−	85.6346i	0.0174526	−	0.0877403i
$977$	1350.75	−	559.500i	1.38255	−	0.572671i	0.437389	−	0.899272i	$-0.355903\pi$
$977$	1350.75	−	559.500i	1.38255	−	0.572671i	0.945162	+	0.326601i	$0.105903\pi$
$978$	883.041	+	2131.85i	0.902904	+	2.17980i
$979$	74.0549	+	14.7304i	0.0756434	+	0.0150464i
$980$	−71.2567	+	47.6122i	−0.0727110	+	0.0485839i
$981$	−523.271	+	104.085i	−0.533406	+	0.106101i
$982$	−118.799	+	118.799i	−0.120977	+	0.120977i
$983$	−112.993	−	75.4993i	−0.114947	−	0.0768050i	0.496768	−	0.867883i	$-0.334520\pi$
$983$	−112.993	−	75.4993i	−0.114947	−	0.0768050i	−0.611715	+	0.791078i	$0.709520\pi$
$984$	937.634	+	388.381i	0.952880	+	0.394696i
$985$		−	1083.40i		−	1.09990i
$986$		0			0
$987$	1699.36			1.72174
$988$	−832.124	+	2008.93i	−0.842231	+	2.03333i
$989$	−16.9371	+	25.3481i	−0.0171255	+	0.0256300i
$990$	−532.020	−	532.020i	−0.537393	−	0.537393i
$991$	14.6120	+	73.4596i	0.0147447	+	0.0741267i	0.987457	−	0.157888i	$-0.0504684\pi$
$991$	14.6120	+	73.4596i	0.0147447	+	0.0741267i	−0.972712	+	0.232014i	$0.925468\pi$
$992$	−144.552	−	216.337i	−0.145718	−	0.218082i
$993$	−395.832	+	1989.98i	−0.398623	+	2.00401i
$994$	−106.847	+	44.2576i	−0.107492	+	0.0445247i
$995$	544.690	+	1315.00i	0.547427	+	1.32161i
$996$	−2566.26	−	510.461i	−2.57657	−	0.512511i
$997$	−385.513	+	257.592i	−0.386674	+	0.258367i	−0.733679	−	0.679496i	$-0.762198\pi$
$997$	−385.513	+	257.592i	−0.386674	+	0.258367i	0.347006	+	0.937863i	$0.387198\pi$
$998$	3049.70	−	606.623i	3.05581	−	0.607839i
$999$	−419.605	+	419.605i	−0.420025	+	0.420025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.q.75.5	yes	48
17.2	even	8	inner	289.3.e.q.249.6	yes	48
17.3	odd	16	inner	289.3.e.q.131.1	yes	48
17.4	even	4	inner	289.3.e.q.214.2	yes	48
17.5	odd	16	inner	289.3.e.q.158.5	yes	48
17.6	odd	16	inner	289.3.e.q.65.5	yes	48
17.7	odd	16	inner	289.3.e.q.224.2	yes	48
17.8	even	8	inner	289.3.e.q.40.2	yes	48
17.9	even	8	inner	289.3.e.q.40.1	✓	48
17.10	odd	16	inner	289.3.e.q.224.1	yes	48
17.11	odd	16	inner	289.3.e.q.65.6	yes	48
17.12	odd	16	inner	289.3.e.q.158.6	yes	48
17.13	even	4	inner	289.3.e.q.214.1	yes	48
17.14	odd	16	inner	289.3.e.q.131.2	yes	48
17.15	even	8	inner	289.3.e.q.249.5	yes	48
17.16	even	2	inner	289.3.e.q.75.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.q.40.1	✓	48	17.9	even	8	inner
289.3.e.q.40.2	yes	48	17.8	even	8	inner
289.3.e.q.65.5	yes	48	17.6	odd	16	inner
289.3.e.q.65.6	yes	48	17.11	odd	16	inner
289.3.e.q.75.5	yes	48	1.1	even	1	trivial
289.3.e.q.75.6	yes	48	17.16	even	2	inner
289.3.e.q.131.1	yes	48	17.3	odd	16	inner
289.3.e.q.131.2	yes	48	17.14	odd	16	inner
289.3.e.q.158.5	yes	48	17.5	odd	16	inner
289.3.e.q.158.6	yes	48	17.12	odd	16	inner
289.3.e.q.214.1	yes	48	17.13	even	4	inner
289.3.e.q.214.2	yes	48	17.4	even	4	inner
289.3.e.q.224.1	yes	48	17.10	odd	16	inner
289.3.e.q.224.2	yes	48	17.7	odd	16	inner
289.3.e.q.249.5	yes	48	17.15	even	8	inner
289.3.e.q.249.6	yes	48	17.2	even	8	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30551 - 3.15179i) q^{2} +(-2.10237 + 3.14642i) q^{3} +(-5.40099 - 5.40099i) q^{4} +(0.793166 + 3.98752i) q^{5} +(7.17219 + 10.7339i) q^{6} +(1.40356 - 7.05618i) q^{7} +(-11.4667 + 4.74967i) q^{8} +(-2.03586 - 4.91500i) q^{9} +(13.6033 + 2.70587i) q^{10} +(8.47833 - 5.66504i) q^{11} +(28.3487 - 5.63891i) q^{12} +(6.16377 - 6.16377i) q^{13} +(-20.4072 - 13.6357i) q^{14} +(-14.2139 - 5.88761i) q^{15} +11.7888i q^{16} -18.1489 q^{18} +(12.4979 - 30.1727i) q^{19} +(17.2527 - 25.8204i) q^{20} +(19.2509 + 19.2509i) q^{21} +(-6.78644 - 34.1177i) q^{22} +(0.682389 + 1.02127i) q^{23} +(9.16284 - 46.0647i) q^{24} +(7.82581 - 3.24156i) q^{25} +(-11.3800 - 27.4738i) q^{26} +(-13.6583 - 2.71681i) q^{27} +(-45.6910 + 30.5298i) q^{28} +(-22.3601 + 4.44769i) q^{29} +(-37.1130 + 37.1130i) q^{30} +(22.9445 + 15.3310i) q^{31} +(-8.71099 - 3.60821i) q^{32} +38.5864i q^{33} +29.2499 q^{35} +(-15.5502 + 37.5415i) q^{36} +(23.6739 - 35.4305i) q^{37} +(-78.7818 - 78.7818i) q^{38} +(6.43528 + 32.3524i) q^{39} +(-28.0344 - 41.9564i) q^{40} +(-4.21560 + 21.1933i) q^{41} +(85.8073 - 35.5425i) q^{42} +(9.49830 + 22.9309i) q^{43} +(-76.3882 - 15.1946i) q^{44} +(17.9839 - 12.0164i) q^{45} +(4.10969 - 0.817468i) q^{46} +(44.1371 - 44.1371i) q^{47} +(-37.0926 - 24.7845i) q^{48} +(-2.54963 - 1.05609i) q^{49} -28.8972i q^{50} -66.5809 q^{52} +(-32.5495 + 78.5814i) q^{53} +(-26.3940 + 39.5014i) q^{54} +(29.3142 + 29.3142i) q^{55} +(17.4203 + 87.5776i) q^{56} +(68.6608 + 102.758i) q^{57} +(-15.1732 + 76.2808i) q^{58} +(36.1126 - 14.9583i) q^{59} +(44.9705 + 108.568i) q^{60} +(-7.26406 - 1.44491i) q^{61} +(78.2747 - 52.3015i) q^{62} +(-37.5386 + 7.46689i) q^{63} +(-56.0884 + 56.0884i) q^{64} +(29.4670 + 19.6892i) q^{65} +(121.616 + 50.3752i) q^{66} +99.8893i q^{67} -4.64798 q^{69} +(38.1862 - 92.1896i) q^{70} +(2.61787 - 3.91793i) q^{71} +(46.6892 + 46.6892i) q^{72} +(-20.0340 - 100.718i) q^{73} +(-80.7630 - 120.870i) q^{74} +(-6.25346 + 31.4383i) q^{75} +(-230.464 + 95.4612i) q^{76} +(-28.0737 - 67.7759i) q^{77} +(110.369 + 21.9538i) q^{78} +(-48.9026 + 32.6757i) q^{79} +(-47.0080 + 9.35048i) q^{80} +(71.1192 - 71.1192i) q^{81} +(61.2932 + 40.9548i) q^{82} +(-83.6340 - 34.6423i) q^{83} -207.948i q^{84} +84.6737 q^{86} +(33.0149 - 79.7050i) q^{87} +(-70.3115 + 105.229i) q^{88} +(5.23601 + 5.23601i) q^{89} +(-14.3951 - 72.3690i) q^{90} +(-34.8414 - 52.1439i) q^{91} +(1.83028 - 9.20143i) q^{92} +(-96.4760 + 39.9616i) q^{93} +(-81.4892 - 196.732i) q^{94} +(130.227 + 25.9038i) q^{95} +(29.6667 - 19.8227i) q^{96} +(-95.4085 + 18.9779i) q^{97} +(-6.65717 + 6.65717i) q^{98} +(-45.1043 - 30.1378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 432 q^{18} + 144 q^{35} - 720 q^{52} - 432 q^{69}+O(q^{100}) \) 48 * q + 432 * q^18 + 144 * q^35 - 720 * q^52 - 432 * q^69

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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