LMFDB - Embedded newform 289.3.e.q.214.2

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			214.2
Character	$\chi$	$=$	289.214
Dual form			289.3.e.q.131.2

$q$-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} +(3.14642 + 2.10237i) q^{3} +(-5.40099 - 5.40099i) q^{4} +(3.98752 - 0.793166i) q^{5} +(-10.7339 + 7.17219i) q^{6} +(7.05618 + 1.40356i) q^{7} +(11.4667 - 4.74967i) q^{8} +(2.03586 + 4.91500i) q^{9} +(-2.70587 + 13.6033i) q^{10} +(5.66504 + 8.47833i) q^{11} +(-5.63891 - 28.3487i) q^{12} +(6.16377 - 6.16377i) q^{13} +(-13.6357 + 20.4072i) q^{14} +(14.2139 + 5.88761i) q^{15} +11.7888i q^{16} -18.1489 q^{18} +(-12.4979 + 30.1727i) q^{19} +(-25.8204 - 17.2527i) q^{20} +(19.2509 + 19.2509i) q^{21} +(-34.1177 + 6.78644i) q^{22} +(-1.02127 + 0.682389i) q^{23} +(46.0647 + 9.16284i) q^{24} +(-7.82581 + 3.24156i) q^{25} +(11.3800 + 27.4738i) q^{26} +(2.71681 - 13.6583i) q^{27} +(-30.5298 - 45.6910i) q^{28} +(4.44769 + 22.3601i) q^{29} +(-37.1130 + 37.1130i) q^{30} +(15.3310 - 22.9445i) q^{31} +(8.71099 + 3.60821i) q^{32} +38.5864i q^{33} +29.2499 q^{35} +(15.5502 - 37.5415i) q^{36} +(-35.4305 - 23.6739i) q^{37} +(-78.7818 - 78.7818i) q^{38} +(32.3524 - 6.43528i) q^{39} +(41.9564 - 28.0344i) q^{40} +(-21.1933 - 4.21560i) q^{41} +(-85.8073 + 35.5425i) q^{42} +(-9.49830 - 22.9309i) q^{43} +(15.1946 - 76.3882i) q^{44} +(12.0164 + 17.9839i) q^{45} +(-0.817468 - 4.10969i) q^{46} +(44.1371 - 44.1371i) q^{47} +(-24.7845 + 37.0926i) q^{48} +(2.54963 + 1.05609i) q^{49} -28.8972i q^{50} -66.5809 q^{52} +(32.5495 - 78.5814i) q^{53} +(39.5014 + 26.3940i) q^{54} +(29.3142 + 29.3142i) q^{55} +(87.5776 - 17.4203i) q^{56} +(-102.758 + 68.6608i) q^{57} +(-76.2808 - 15.1732i) q^{58} +(-36.1126 + 14.9583i) q^{59} +(-44.9705 - 108.568i) q^{60} +(1.44491 - 7.26406i) q^{61} +(52.3015 + 78.2747i) q^{62} +(7.46689 + 37.5386i) q^{63} +(-56.0884 + 56.0884i) q^{64} +(19.6892 - 29.4670i) q^{65} +(-121.616 - 50.3752i) q^{66} +99.8893i q^{67} -4.64798 q^{69} +(-38.1862 + 92.1896i) q^{70} +(-3.91793 - 2.61787i) q^{71} +(46.6892 + 46.6892i) q^{72} +(-100.718 + 20.0340i) q^{73} +(120.870 - 80.7630i) q^{74} +(-31.4383 - 6.25346i) q^{75} +(230.464 - 95.4612i) q^{76} +(28.0737 + 67.7759i) q^{77} +(-21.9538 + 110.369i) q^{78} +(-32.6757 - 48.9026i) q^{79} +(9.35048 + 47.0080i) q^{80} +(71.1192 - 71.1192i) q^{81} +(40.9548 - 61.2932i) q^{82} +(83.6340 + 34.6423i) q^{83} -207.948i q^{84} +84.6737 q^{86} +(-33.0149 + 79.7050i) q^{87} +(105.229 + 70.3115i) q^{88} +(5.23601 + 5.23601i) q^{89} +(-72.3690 + 14.3951i) q^{90} +(52.1439 - 34.8414i) q^{91} +(9.20143 + 1.83028i) q^{92} +(96.4760 - 39.9616i) q^{93} +(81.4892 + 196.732i) q^{94} +(-25.9038 + 130.227i) q^{95} +(19.8227 + 29.6667i) q^{96} +(18.9779 + 95.4085i) q^{97} +(-6.65717 + 6.65717i) q^{98} +(-30.1378 + 45.1043i) 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 $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

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

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	$0.450139\pi$
$2$	−1.30551	+	3.15179i	−0.652757	+	1.57590i	−0.808760	+	0.588139i	$0.799861\pi$
$3$	3.14642	+	2.10237i	1.04881	+	0.700791i	0.955543	−	0.294850i	$-0.0952698\pi$
$3$	3.14642	+	2.10237i	1.04881	+	0.700791i	0.0932645	+	0.995641i	$0.470270\pi$
$4$	−5.40099	−	5.40099i	−1.35025	−	1.35025i
$5$	3.98752	−	0.793166i	0.797503	−	0.158633i	0.220513	−	0.975384i	$-0.429227\pi$
$5$	3.98752	−	0.793166i	0.797503	−	0.158633i	0.576991	+	0.816751i	$0.304227\pi$
$6$	−10.7339	+	7.17219i	−1.78899	+	1.19537i
$7$	7.05618	+	1.40356i	1.00803	+	0.200509i	0.671373	−	0.741120i	$-0.265705\pi$
$7$	7.05618	+	1.40356i	1.00803	+	0.200509i	0.336653	+	0.941629i	$0.390705\pi$
$8$	11.4667	−	4.74967i	1.43334	−	0.593708i
$9$	2.03586	+	4.91500i	0.226207	+	0.546111i
$10$	−2.70587	+	13.6033i	−0.270587	+	1.36033i
$11$	5.66504	+	8.47833i	0.515004	+	0.770757i	0.994268	−	0.106913i	$-0.0340966\pi$
$11$	5.66504	+	8.47833i	0.515004	+	0.770757i	−0.479265	+	0.877670i	$0.659097\pi$
$12$	−5.63891	−	28.3487i	−0.469909	−	2.36239i
$13$	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	$0.141174\pi$
$14$	−13.6357	+	20.4072i	−0.973977	+	1.45766i
$15$	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	$0.454187\pi$
$19$	−12.4979	+	30.1727i	−0.657786	+	1.58804i	−0.801215	+	0.598376i	$0.795813\pi$
$20$	−25.8204	−	17.2527i	−1.29102	−	0.862633i
$21$	19.2509	+	19.2509i	0.916711	+	0.916711i
$22$	−34.1177	+	6.78644i	−1.55081	+	0.308474i
$23$	−1.02127	+	0.682389i	−0.0444029	+	0.0296691i	−0.577574	−	0.816339i	$-0.696000\pi$
$23$	−1.02127	+	0.682389i	−0.0444029	+	0.0296691i	0.533171	+	0.846008i	$0.321000\pi$
$24$	46.0647	+	9.16284i	1.91936	+	0.381785i
$25$	−7.82581	+	3.24156i	−0.313033	+	0.129662i
$26$	11.3800	+	27.4738i	0.437693	+	1.05668i
$27$	2.71681	−	13.6583i	0.100623	−	0.505864i
$28$	−30.5298	−	45.6910i	−1.09035	−	1.63182i
$29$	4.44769	+	22.3601i	0.153369	+	0.771037i	0.978524	+	0.206131i	$0.0660874\pi$
$29$	4.44769	+	22.3601i	0.153369	+	0.771037i	−0.825156	+	0.564906i	$0.808913\pi$
$30$	−37.1130	+	37.1130i	−1.23710	+	1.23710i
$31$	15.3310	−	22.9445i	0.494550	−	0.740146i	−0.497297	−	0.867580i	$-0.665674\pi$
$31$	15.3310	−	22.9445i	0.494550	−	0.740146i	0.991847	+	0.127434i	$0.0406741\pi$
$32$	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
$37$	−35.4305	−	23.6739i	−0.957582	−	0.639836i	−0.0245764	−	0.999698i	$-0.507824\pi$
$37$	−35.4305	−	23.6739i	−0.957582	−	0.639836i	−0.933005	+	0.359862i	$0.882824\pi$
$38$	−78.7818	−	78.7818i	−2.07320	−	2.07320i
$39$	32.3524	−	6.43528i	0.829548	−	0.165007i
$40$	41.9564	−	28.0344i	1.04891	−	0.700859i
$41$	−21.1933	−	4.21560i	−0.516909	−	0.102820i	−0.0702597	−	0.997529i	$-0.522383\pi$
$41$	−21.1933	−	4.21560i	−0.516909	−	0.102820i	−0.446649	+	0.894709i	$0.647383\pi$
$42$	−85.8073	+	35.5425i	−2.04303	+	0.846251i
$43$	−9.49830	−	22.9309i	−0.220891	−	0.533277i	0.774121	−	0.633038i	$-0.218192\pi$
$43$	−9.49830	−	22.9309i	−0.220891	−	0.533277i	−0.995011	+	0.0997606i	$0.968192\pi$
$44$	15.1946	−	76.3882i	0.345331	−	1.73610i
$45$	12.0164	+	17.9839i	0.267032	+	0.399641i
$46$	−0.817468	−	4.10969i	−0.0177710	−	0.0893411i
$47$	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	$0.0188429\pi$
$48$	−24.7845	+	37.0926i	−0.516343	+	0.772762i
$49$	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	$-0.578548\pi$
$53$	32.5495	−	78.5814i	0.614141	−	1.48267i	0.858412	−	0.512961i	$-0.171452\pi$
$54$	39.5014	+	26.3940i	0.731507	+	0.488778i
$55$	29.3142	+	29.3142i	0.532985	+	0.532985i
$56$	87.5776	−	17.4203i	1.56389	−	0.311076i
$57$	−102.758	+	68.6608i	−1.80277	+	1.20457i
$58$	−76.2808	−	15.1732i	−1.31519	−	0.261607i
$59$	−36.1126	+	14.9583i	−0.612078	+	0.253531i	−0.667117	−	0.744953i	$-0.732472\pi$
$59$	−36.1126	+	14.9583i	−0.612078	+	0.253531i	0.0550386	+	0.998484i	$0.482472\pi$
$60$	−44.9705	−	108.568i	−0.749508	−	1.80947i
$61$	1.44491	−	7.26406i	0.0236871	−	0.119083i	−0.967133	−	0.254272i	$-0.918164\pi$
$61$	1.44491	−	7.26406i	0.0236871	−	0.119083i	0.990820	+	0.135189i	$0.0431642\pi$
$62$	52.3015	+	78.2747i	0.843572	+	1.26249i
$63$	7.46689	+	37.5386i	0.118522	+	0.595850i
$64$	−56.0884	+	56.0884i	−0.876382	+	0.876382i
$65$	19.6892	−	29.4670i	0.302911	−	0.453339i
$66$	−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
$71$	−3.91793	−	2.61787i	−0.0551821	−	0.0368715i	0.527673	−	0.849447i	$-0.323065\pi$
$71$	−3.91793	−	2.61787i	−0.0551821	−	0.0368715i	−0.582855	+	0.812576i	$0.698065\pi$
$72$	46.6892	+	46.6892i	0.648461	+	0.648461i
$73$	−100.718	+	20.0340i	−1.37969	+	0.274438i	−0.828524	−	0.559954i	$-0.810819\pi$
$73$	−100.718	+	20.0340i	−1.37969	+	0.274438i	−0.551171	+	0.834392i	$0.685819\pi$
$74$	120.870	−	80.7630i	1.63338	−	1.09139i
$75$	−31.4383	−	6.25346i	−0.419177	−	0.0833795i
$76$	230.464	−	95.4612i	3.03242	−	1.25607i
$77$	28.0737	+	67.7759i	0.364593	+	0.880206i
$78$	−21.9538	+	110.369i	−0.281459	+	1.41499i
$79$	−32.6757	−	48.9026i	−0.413616	−	0.619021i	0.564907	−	0.825154i	$-0.308912\pi$
$79$	−32.6757	−	48.9026i	−0.413616	−	0.619021i	−0.978524	+	0.206134i	$0.933912\pi$
$80$	9.35048	+	47.0080i	0.116881	+	0.587600i
$81$	71.1192	−	71.1192i	0.878014	−	0.878014i
$82$	40.9548	−	61.2932i	0.499449	−	0.747478i
$83$	83.6340	+	34.6423i	1.00764	+	0.417378i	0.824593	−	0.565727i	$-0.191404\pi$
$83$	83.6340	+	34.6423i	1.00764	+	0.417378i	0.183046	+	0.983104i	$0.441404\pi$
$84$		−	207.948i		−	2.47557i
$85$		0			0
$86$	84.6737			0.984578
$87$	−33.0149	+	79.7050i	−0.379481	+	0.916149i
$88$	105.229	+	70.3115i	1.19578	+	0.798994i
$89$	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	$0.736754\pi$
$90$	−72.3690	+	14.3951i	−0.804100	+	0.159945i
$91$	52.1439	−	34.8414i	0.573010	−	0.382873i
$92$	9.20143	+	1.83028i	0.100016	+	0.0198943i
$93$	96.4760	−	39.9616i	1.03738	−	0.429695i
$94$	81.4892	+	196.732i	0.866906	+	2.09290i
$95$	−25.9038	+	130.227i	−0.272671	+	1.37081i
$96$	19.8227	+	29.6667i	0.206486	+	0.309028i
$97$	18.9779	+	95.4085i	0.195649	+	0.983593i	0.946397	+	0.323005i	$0.104693\pi$
$97$	18.9779	+	95.4085i	0.195649	+	0.983593i	−0.750748	+	0.660588i	$0.770307\pi$
$98$	−6.65717	+	6.65717i	−0.0679303	+	0.0679303i
$99$	−30.1378	+	45.1043i	−0.304422	+	0.455599i
$100$	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
$105$	92.0326	+	61.4942i	0.876501	+	0.585659i
$106$	205.178	+	205.178i	1.93565	+	1.93565i
$107$	111.497	−	22.1781i	1.04203	−	0.207272i	0.355726	−	0.934590i	$-0.384234\pi$
$107$	111.497	−	22.1781i	1.04203	−	0.207272i	0.686300	+	0.727319i	$0.259234\pi$
$108$	−88.4421	+	59.0951i	−0.818908	+	0.547177i
$109$	98.3600	+	19.5650i	0.902386	+	0.179496i	0.624414	−	0.781094i	$-0.285338\pi$
$109$	98.3600	+	19.5650i	0.902386	+	0.179496i	0.277972	+	0.960589i	$0.410338\pi$
$110$	−130.662	+	54.1221i	−1.18784	+	0.492019i
$111$	−61.7080	−	148.976i	−0.555928	−	1.34213i
$112$	−16.5463	+	83.1839i	−0.147735	+	0.742714i
$113$	−81.8476	−	122.494i	−0.724315	−	1.08401i	−0.992689	−	0.120699i	$-0.961486\pi$
$113$	−81.8476	−	122.494i	−0.724315	−	1.08401i	0.268375	−	0.963315i	$-0.413514\pi$
$114$	−82.2522	−	413.510i	−0.721510	−	3.62728i
$115$	−3.53107	+	3.53107i	−0.0307050	+	0.0307050i
$116$	96.7446	−	144.788i	0.834005	−	1.24818i
$117$	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
$122$	21.0084	+	14.0374i	0.172200	+	0.115061i
$123$	−57.8202	−	57.8202i	−0.470083	−	0.470083i
$124$	−206.726	+	41.1204i	−1.66715	+	0.331616i
$125$	−113.146	+	75.6016i	−0.905166	+	0.604813i
$126$	−128.062	−	25.4731i	−1.01636	−	0.202167i
$127$	−45.2810	+	18.7560i	−0.356543	+	0.147685i	−0.553763	−	0.832674i	$-0.686809\pi$
$127$	−45.2810	+	18.7560i	−0.356543	+	0.147685i	0.197220	+	0.980359i	$0.436809\pi$
$128$	−89.1219	−	215.159i	−0.696265	−	1.68093i
$129$	18.3237	−	92.1194i	0.142044	−	0.714104i
$130$	67.1693	+	100.526i	0.516687	+	0.773276i
$131$	4.52419	+	22.7447i	0.0345358	+	0.173623i	0.994204	−	0.107513i	$-0.0342887\pi$
$131$	4.52419	+	22.7447i	0.0345358	+	0.173623i	−0.959668	+	0.281136i	$0.909289\pi$
$132$	208.405	−	208.405i	1.57883	−	1.57883i
$133$	−130.537	+	195.362i	−0.981481	+	1.46889i
$134$	−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
$139$	−32.1068	−	21.4531i	−0.230984	−	0.154339i	0.434693	−	0.900579i	$-0.356857\pi$
$139$	−32.1068	−	21.4531i	−0.230984	−	0.154339i	−0.665677	+	0.746240i	$0.731857\pi$
$140$	−157.978	−	157.978i	−1.12842	−	1.12842i
$141$	231.666	−	46.0813i	1.64302	−	0.326818i
$142$	13.3659	−	8.93081i	0.0941261	−	0.0628930i
$143$	87.1764	+	17.3405i	0.609625	+	0.121262i
$144$	−57.9419	+	24.0003i	−0.402374	+	0.166669i
$145$	35.4705	+	85.6334i	0.244624	+	0.590575i
$146$	68.3455	−	343.596i	0.468120	−	2.35340i
$147$	5.80193	+	8.68320i	0.0394689	+	0.0590694i
$148$	63.4973	+	319.223i	0.429036	+	2.15691i
$149$	−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	$0.971998\pi$
$150$	60.7528	−	90.9229i	0.405018	−	0.606153i
$151$	29.5306	+	12.2320i	0.195567	+	0.0810066i	0.478318	−	0.878187i	$-0.341247\pi$
$151$	29.5306	+	12.2320i	0.195567	+	0.0810066i	−0.282750	+	0.959194i	$0.591247\pi$
$152$			405.342i			2.66673i
$153$		0			0
$154$	−250.266			−1.62510
$155$	42.9340	−	103.652i	0.276993	−	0.668721i
$156$	−209.492	−	139.978i	−1.34290	−	0.897294i
$157$	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	$0.737680\pi$
$158$	196.789	−	39.1439i	1.24550	−	0.247746i
$159$	267.622	−	178.819i	1.68316	−	1.12465i
$160$	37.5971	+	7.47854i	0.234982	+	0.0467408i
$161$	−8.16402	+	3.38165i	−0.0507082	+	0.0210040i
$162$	131.306	+	317.000i	0.810529	+	1.95679i
$163$	−34.8710	+	175.308i	−0.213932	+	1.07551i	0.713253	+	0.700907i	$0.247221\pi$
$163$	−34.8710	+	175.308i	−0.213932	+	1.07551i	−0.927185	+	0.374603i	$0.877779\pi$
$164$	91.6962	+	137.233i	0.559123	+	0.836787i
$165$	30.6055	+	153.864i	0.185488	+	0.932510i
$166$	−218.371	+	218.371i	−1.31549	+	1.31549i
$167$	49.6728	−	74.3406i	0.297442	−	0.445153i	−0.652404	−	0.757871i	$-0.726239\pi$
$167$	49.6728	−	74.3406i	0.297442	−	0.445153i	0.949846	+	0.312718i	$0.101239\pi$
$168$	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
$173$	78.0218	+	52.1325i	0.450993	+	0.301344i	0.760245	−	0.649636i	$-0.225079\pi$
$173$	78.0218	+	52.1325i	0.450993	+	0.301344i	−0.309252	+	0.950980i	$0.600079\pi$
$174$	−208.112	−	208.112i	−1.19605	−	1.19605i
$175$	−59.7701	+	11.8890i	−0.341543	+	0.0679372i
$176$	−99.9493	+	66.7840i	−0.567894	+	0.379455i
$177$	−145.074	−	28.8569i	−0.819625	−	0.163033i
$178$	−23.3385	+	9.66713i	−0.131115	+	0.0543097i
$179$	−110.449	−	266.646i	−0.617031	−	1.48964i	−0.855135	−	0.518405i	$-0.826526\pi$
$179$	−110.449	−	266.646i	−0.617031	−	1.48964i	0.238104	−	0.971240i	$-0.423474\pi$
$180$	32.2300	−	162.031i	0.179056	−	0.900174i
$181$	−96.6838	−	144.698i	−0.534165	−	0.799434i	0.462005	−	0.886877i	$-0.347130\pi$
$181$	−96.6838	−	144.698i	−0.534165	−	0.799434i	−0.996169	+	0.0874435i	$0.972130\pi$
$182$	41.7383	+	209.833i	0.229331	+	1.15293i
$183$	19.8181	−	19.8181i	0.108295	−	0.108295i
$184$	−8.46945	+	12.6754i	−0.0460296	+	0.0688882i
$185$	−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
$190$	−376.631	−	251.657i	−1.98227	−	1.32451i
$191$	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	$0.727461\pi$
$192$	−294.397	+	58.5591i	−1.53332	+	0.304996i
$193$	155.664	−	104.011i	0.806548	−	0.538918i	−0.0825761	−	0.996585i	$-0.526315\pi$
$193$	155.664	−	104.011i	0.806548	−	0.538918i	0.889124	+	0.457667i	$0.151315\pi$
$194$	−325.484	−	64.7427i	−1.67775	−	0.333726i
$195$	123.901	−	51.3216i	0.635391	−	0.263188i
$196$	−8.06660	−	19.4745i	−0.0411561	−	0.0993597i
$197$	51.9872	−	261.357i	0.263894	−	1.32669i	−0.590490	−	0.807045i	$-0.701066\pi$
$197$	51.9872	−	261.357i	0.263894	−	1.32669i	0.854384	−	0.519641i	$-0.173934\pi$
$198$	−102.814	−	153.872i	−0.519264	−	0.777133i
$199$	−68.2994	−	343.364i	−0.343213	−	1.72545i	−0.638132	−	0.769927i	$-0.720293\pi$
$199$	−68.2994	−	343.364i	−0.343213	−	1.72545i	0.294919	−	0.955522i	$-0.404707\pi$
$200$	−74.3400	+	74.3400i	−0.371700	+	0.371700i
$201$	−210.005	+	314.294i	−1.04480	+	1.56365i
$202$	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
$207$	−5.43310	−	3.63028i	−0.0262468	−	0.0175376i
$208$	72.6634	+	72.6634i	0.349343	+	0.349343i
$209$	−326.615	+	64.9678i	−1.56275	+	0.310851i
$210$	−313.967	+	209.786i	−1.49508	+	0.998981i
$211$	224.669	+	44.6895i	1.06478	+	0.211799i	0.696238	−	0.717811i	$-0.254856\pi$
$211$	224.669	+	44.6895i	1.06478	+	0.211799i	0.368545	+	0.929610i	$0.379856\pi$
$212$	−600.217	+	248.618i	−2.83121	+	1.17273i
$213$	−6.82371	−	16.4739i	−0.0320362	−	0.0773422i
$214$	−75.6600	+	380.368i	−0.353551	+	1.77742i
$215$	−56.0627	−	83.9037i	−0.260757	−	0.390250i
$216$	−33.7196	−	169.520i	−0.156109	−	0.784815i
$217$	140.383	−	140.383i	0.646925	−	0.646925i
$218$	−190.075	+	284.468i	−0.871905	+	1.30490i
$219$	−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	−0.720153	−	0.693815i	$-0.755928\pi$
$223$	62.3672	−	150.568i	0.279674	−	0.675192i	0.999827	+	0.0186236i	$0.00592843\pi$
$224$	56.4020	+	37.6866i	0.251795	+	0.168244i
$225$	−31.8645	−	31.8645i	−0.141620	−	0.141620i
$226$	492.927	−	98.0493i	2.18109	−	0.433847i
$227$	−110.101	+	73.5668i	−0.485025	+	0.324083i	−0.773926	−	0.633276i	$-0.781710\pi$
$227$	−110.101	+	73.5668i	−0.485025	+	0.324083i	0.288902	+	0.957359i	$0.406710\pi$
$228$	925.832	+	184.159i	4.06067	+	0.807717i
$229$	149.442	−	61.9007i	0.652583	−	0.270309i	−0.0317307	−	0.999496i	$-0.510102\pi$
$229$	149.442	−	61.9007i	0.652583	−	0.270309i	0.684314	+	0.729188i	$0.260102\pi$
$230$	−6.51933	−	15.7391i	−0.0283449	−	0.0684307i
$231$	−54.1585	+	272.273i	−0.234452	+	1.17867i
$232$	157.203	+	235.271i	0.677600	+	1.01410i
$233$	−33.4057	−	167.942i	−0.143372	−	0.720780i	−0.983859	−	0.178948i	$-0.942731\pi$
$233$	−33.4057	−	167.942i	−0.143372	−	0.720780i	0.840486	−	0.541833i	$-0.182269\pi$
$234$	−111.866	+	111.866i	−0.478058	+	0.478058i
$235$	140.989	−	211.005i	0.599954	−	0.897895i
$236$	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
$241$	−104.944	−	70.1215i	−0.435453	−	0.290961i	0.318458	−	0.947937i	$-0.396835\pi$
$241$	−104.944	−	70.1215i	−0.435453	−	0.290961i	−0.753911	+	0.656976i	$0.771835\pi$
$242$	41.0696	+	41.0696i	0.169709	+	0.169709i
$243$	250.365	−	49.8007i	1.03031	−	0.204941i
$244$	−47.0371	+	31.4292i	−0.192775	+	0.128808i
$245$	11.0044	+	2.18890i	0.0449158	+	0.00893430i
$246$	257.722	−	106.752i	1.04765	−	0.433952i
$247$	108.943	+	263.012i	0.441065	+	1.06483i
$248$	66.8178	−	335.916i	0.269426	−	1.35450i
$249$	190.317	+	284.829i	0.764325	+	1.14389i
$250$	−90.5670	−	455.311i	−0.362268	−	1.82124i
$251$	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	$0.130033\pi$
$252$	162.417	−	243.074i	0.644512	−	0.964580i
$253$	−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	−0.969201	−	0.246272i	$-0.920794\pi$
$257$	−28.2011	+	68.0835i	−0.109732	+	0.264916i	0.859469	+	0.511188i	$0.170794\pi$
$258$	266.419	+	178.016i	1.03263	+	0.689983i
$259$	−216.776	−	216.776i	−0.836975	−	0.836975i
$260$	−265.492	+	52.8097i	−1.02112	+	0.203114i
$261$	−100.845	+	67.3823i	−0.386379	+	0.258170i
$262$	−77.5928	−	15.4342i	−0.296156	−	0.0589091i
$263$	142.799	−	59.1494i	0.542963	−	0.224903i	−0.0943069	−	0.995543i	$-0.530063\pi$
$263$	142.799	−	59.1494i	0.542963	−	0.224903i	0.637270	+	0.770640i	$0.280063\pi$
$264$	183.273	+	442.459i	0.694215	+	1.67598i
$265$	67.4635	−	339.162i	0.254579	−	1.27986i
$266$	−445.324	−	666.474i	−1.67415	−	2.50554i
$267$	5.46666	+	27.4828i	0.0204744	+	0.102932i
$268$	539.501	−	539.501i	2.01306	−	2.01306i
$269$	113.488	−	169.847i	0.421890	−	0.631403i	−0.558259	−	0.829667i	$-0.688530\pi$
$269$	113.488	−	169.847i	0.421890	−	0.631403i	0.980149	+	0.198264i	$0.0635304\pi$
$270$	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
$275$	−71.8165	−	47.9863i	−0.261151	−	0.174496i
$276$	25.1037	+	25.1037i	0.0909554	+	0.0909554i
$277$	−172.498	+	34.3119i	−0.622735	+	0.123870i	−0.496366	−	0.868113i	$-0.665333\pi$
$277$	−172.498	+	34.3119i	−0.622735	+	0.123870i	−0.126370	+	0.991983i	$0.540333\pi$
$278$	109.532	−	73.1867i	0.393998	−	0.263261i
$279$	143.984	+	28.6402i	0.516072	+	0.102653i
$280$	335.400	−	138.927i	1.19786	−	0.496169i
$281$	53.9707	+	130.297i	0.192067	+	0.463690i	0.990349	−	0.138593i	$-0.0442580\pi$
$281$	53.9707	+	130.297i	0.192067	+	0.463690i	−0.798283	+	0.602283i	$0.794258\pi$
$282$	−157.205	+	790.324i	−0.557465	+	2.80257i
$283$	−15.4868	−	23.1776i	−0.0547237	−	0.0818998i	0.803099	−	0.595846i	$-0.203183\pi$
$283$	−15.4868	−	23.1776i	−0.0547237	−	0.0818998i	−0.857822	+	0.513946i	$0.828183\pi$
$284$	7.02157	+	35.2998i	0.0247238	+	0.124295i
$285$	−355.290	+	355.290i	−1.24663	+	1.24663i
$286$	−168.464	+	252.124i	−0.589034	+	0.881551i
$287$	−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
$292$	652.179	+	435.772i	2.23349	+	1.49237i
$293$	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	$0.417042\pi$
$294$	−34.9421	+	6.95042i	−0.118851	+	0.0236409i
$295$	−132.135	+	88.2899i	−0.447916	+	0.299288i
$296$	−518.715	−	103.179i	−1.75241	−	0.348577i
$297$	131.191	−	54.3410i	0.441720	−	0.182966i
$298$	−298.200	−	719.919i	−1.00067	−	2.41584i
$299$	−2.08877	+	10.5009i	−0.00698584	+	0.0351202i
$300$	136.023	+	203.573i	0.453410	+	0.678576i
$301$	−34.8368	−	175.136i	−0.115737	−	0.581848i
$302$	−77.1054	+	77.1054i	−0.255316	+	0.255316i
$303$	204.659	−	306.294i	0.675443	−	1.01087i
$304$	−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
$309$	124.851	+	83.4225i	0.404047	+	0.269976i
$310$	270.638	+	270.638i	0.873025	+	0.873025i
$311$	40.1945	−	7.99518i	0.129243	−	0.0257080i	−0.130045	−	0.991508i	$-0.541512\pi$
$311$	40.1945	−	7.99518i	0.129243	−	0.0257080i	0.259288	+	0.965800i	$0.416512\pi$
$312$	340.410	−	227.454i	1.09106	−	0.729020i
$313$	−171.992	−	34.2114i	−0.549496	−	0.109302i	−0.0874689	−	0.996167i	$-0.527878\pi$
$313$	−171.992	−	34.2114i	−0.549496	−	0.109302i	−0.462027	+	0.886866i	$0.652878\pi$
$314$	−38.2954	+	15.8625i	−0.121960	+	0.0505174i
$315$	59.5487	+	143.763i	0.189043	+	0.456391i
$316$	−87.6416	+	440.604i	−0.277347	+	1.39432i
$317$	245.733	+	367.766i	0.775184	+	1.16014i	0.983291	+	0.182039i	$0.0582696\pi$
$317$	245.733	+	367.766i	0.775184	+	1.16014i	−0.208108	+	0.978106i	$0.566730\pi$
$318$	214.217	+	1076.94i	0.673637	+	3.38660i
$319$	−164.380	+	164.380i	−0.515297	+	0.515297i
$320$	−179.166	+	268.141i	−0.559894	+	0.837940i
$321$	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
$326$	−507.010	−	338.773i	−1.55525	−	1.03918i
$327$	268.349	+	268.349i	0.820640	+	0.820640i
$328$	−263.040	+	52.3218i	−0.801950	+	0.159518i
$329$	373.388	−	249.490i	1.13492	−	0.758328i
$330$	−524.903	−	104.410i	−1.59062	−	0.316393i
$331$	−495.359	+	205.184i	−1.49655	+	0.619893i	−0.972731	−	0.231935i	$-0.925494\pi$
$331$	−495.359	+	205.184i	−1.49655	+	0.619893i	−0.523822	+	0.851828i	$0.675494\pi$
$332$	−264.604	−	638.809i	−0.796999	−	1.92412i
$333$	44.2257	−	222.338i	0.132810	−	0.667681i
$334$	169.458	+	253.611i	0.507358	+	0.759315i
$335$	79.2288	+	398.310i	0.236504	+	1.18899i
$336$	−226.945	+	226.945i	−0.675433	+	0.675433i
$337$	−322.911	+	483.271i	−0.958194	+	1.43404i	−0.0581152	+	0.998310i	$0.518509\pi$
$337$	−322.911	+	483.271i	−0.958194	+	1.43404i	−0.900078	+	0.435728i	$0.856491\pi$
$338$	−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
$343$	−276.607	−	184.823i	−0.806434	−	0.538842i
$344$	−217.828	−	217.828i	−0.633222	−	0.633222i
$345$	−18.5339	+	3.68662i	−0.0537214	+	0.0106858i
$346$	−266.169	+	177.849i	−0.769276	+	0.514014i
$347$	−532.385	−	105.898i	−1.53425	−	0.305181i	−0.645568	−	0.763703i	$-0.723379\pi$
$347$	−532.385	−	105.898i	−1.53425	−	0.305181i	−0.888683	+	0.458522i	$0.848379\pi$
$348$	608.799	−	252.173i	1.74942	−	0.724634i
$349$	12.4247	+	29.9960i	0.0356010	+	0.0859484i	0.940680	−	0.339295i	$-0.110188\pi$
$349$	12.4247	+	29.9960i	0.0356010	+	0.0859484i	−0.905079	+	0.425243i	$0.860188\pi$
$350$	40.5591	−	203.904i	0.115883	−	0.582583i
$351$	−67.4410	−	100.933i	−0.192140	−	0.287557i
$352$	18.7565	+	94.2953i	0.0532855	+	0.267884i
$353$	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	$0.0888922\pi$
$354$	280.347	−	419.568i	0.791940	−	1.18522i
$355$	−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	$0.275251\pi$
$359$	−124.934	+	301.618i	−0.348007	+	0.840162i	−0.996855	+	0.0792446i	$0.974749\pi$
$360$	223.206	+	149.142i	0.620017	+	0.414282i
$361$	−498.927	−	498.927i	−1.38207	−	1.38207i
$362$	582.278	−	115.822i	1.60850	−	0.319951i
$363$	53.5686	−	35.7934i	0.147572	−	0.0986044i
$364$	−469.807	−	93.4504i	−1.29068	−	0.256732i
$365$	−385.723	+	159.772i	−1.05678	+	0.437731i
$366$	36.5896	+	88.3352i	0.0999717	+	0.241353i
$367$	58.1740	−	292.460i	0.158512	−	0.796894i	−0.816947	−	0.576713i	$-0.804335\pi$
$367$	58.1740	−	292.460i	0.158512	−	0.796894i	0.975459	−	0.220181i	$-0.0706649\pi$
$368$	−8.04455	−	12.0395i	−0.0218602	−	0.0327161i
$369$	−22.4268	−	112.747i	−0.0607773	−	0.305548i
$370$	417.914	−	417.914i	1.12950	−	1.12950i
$371$	339.969	−	508.800i	0.916359	−	1.37143i
$372$	−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
$377$	165.237	+	110.408i	0.438294	+	0.292859i
$378$	241.683	+	241.683i	0.639374	+	0.639374i
$379$	235.191	−	46.7824i	0.620557	−	0.123436i	0.125208	−	0.992131i	$-0.460040\pi$
$379$	235.191	−	46.7824i	0.620557	−	0.123436i	0.495349	+	0.868694i	$0.335040\pi$
$380$	843.261	−	563.449i	2.21911	−	1.48276i
$381$	−181.905	−	36.1832i	−0.477442	−	0.0949691i
$382$	−85.1804	+	35.2829i	−0.222985	+	0.0923635i
$383$	8.96693	+	21.6481i	0.0234123	+	0.0565224i	0.935153	−	0.354243i	$-0.115261\pi$
$383$	8.96693	+	21.6481i	0.0234123	+	0.0565224i	−0.911741	+	0.410766i	$0.865261\pi$
$384$	171.930	−	864.350i	0.447734	−	2.25091i
$385$	165.702	+	247.990i	0.430394	+	0.644131i
$386$	124.600	+	626.408i	0.322798	+	1.62282i
$387$	93.3683	−	93.3683i	0.241262	−	0.241262i
$388$	412.801	−	617.800i	1.06392	−	1.59227i
$389$	352.455	+	145.991i	0.906053	+	0.375299i	0.786544	−	0.617534i	$-0.211868\pi$
$389$	352.455	+	145.991i	0.906053	+	0.375299i	0.119509	+	0.992833i	$0.461868\pi$
$390$			457.512i			1.17311i
$391$		0			0
$392$	34.2520			0.0873775
$393$	−33.5827	+	81.0759i	−0.0854522	+	0.206300i
$394$	755.873	+	505.058i	1.91846	+	1.28187i
$395$	−169.083	−	169.083i	−0.428058	−	0.428058i
$396$	406.382	−	80.8344i	1.02622	−	0.204127i
$397$	−598.911	+	400.180i	−1.50859	+	1.00801i	−0.520549	+	0.853832i	$0.674273\pi$
$397$	−598.911	+	400.180i	−1.50859	+	1.00801i	−0.988043	+	0.154177i	$0.950727\pi$
$398$	1171.38	+	233.002i	2.94316	+	0.585431i
$399$	−821.449	+	340.255i	−2.05877	+	0.852771i
$400$	−38.2141	−	92.2569i	−0.0955352	−	0.230642i
$401$	−72.6009	+	364.990i	−0.181050	+	0.910198i	0.778282	+	0.627915i	$0.216092\pi$
$401$	−72.6009	+	364.990i	−0.181050	+	0.910198i	−0.959331	+	0.282283i	$0.908908\pi$
$402$	−716.425	−	1072.21i	−1.78215	−	2.66718i
$403$	−46.9278	−	235.922i	−0.116446	−	0.585414i
$404$	−525.769	+	525.769i	−1.30141	+	1.30141i
$405$	227.179	−	339.998i	0.560937	−	0.839502i
$406$	−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
$411$	170.216	+	113.735i	0.414151	+	0.276727i
$412$	−214.312	−	214.312i	−0.520175	−	0.520175i
$413$	−275.812	+	54.8624i	−0.667826	+	0.132839i
$414$	18.5349	−	12.3846i	0.0447702	−	0.0299145i
$415$	360.969	+	71.8012i	0.869805	+	0.173015i
$416$	75.9327	−	31.4523i	0.182531	−	0.0756066i
$417$	−55.9192	−	135.001i	−0.134099	−	0.323743i
$418$	221.636	−	1114.24i	0.530230	−	2.66565i
$419$	438.200	+	655.813i	1.04582	+	1.56519i	0.803785	+	0.594920i	$0.202816\pi$
$419$	438.200	+	655.813i	1.04582	+	1.56519i	0.242039	+	0.970267i	$0.422184\pi$
$420$	−164.938	−	829.197i	−0.392708	−	1.97428i
$421$	−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	$0.962828\pi$
$422$	−434.161	+	649.768i	−1.02882	+	1.53973i
$423$	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
$428$	−721.977	−	482.409i	−1.68686	−	1.12712i
$429$	237.838	+	237.838i	0.554401	+	0.554401i
$430$	337.638	−	67.1603i	0.785204	−	0.156187i
$431$	−110.627	+	73.9183i	−0.256674	+	0.171504i	−0.677250	−	0.735753i	$-0.736828\pi$
$431$	−110.627	+	73.9183i	−0.256674	+	0.171504i	0.420575	+	0.907258i	$0.361828\pi$
$432$	161.015	+	32.0280i	0.372721	+	0.0741388i
$433$	−25.8940	+	10.7257i	−0.0598015	+	0.0247706i	−0.412384	−	0.911010i	$-0.635304\pi$
$433$	−25.8940	+	10.7257i	−0.0598015	+	0.0247706i	0.352582	+	0.935781i	$0.385304\pi$
$434$	259.185	+	625.729i	0.597201	+	1.44177i
$435$	−68.4281	+	344.011i	−0.157306	+	0.790830i
$436$	−425.571	−	636.912i	−0.976081	−	1.46081i
$437$	−7.82578	−	39.3428i	−0.0179080	−	0.0900294i
$438$	937.410	−	937.410i	2.14021	−	2.14021i
$439$	3.34293	−	5.00305i	0.00761488	−	0.0113965i	−0.827643	−	0.561255i	$-0.810319\pi$
$439$	3.34293	−	5.00305i	0.00761488	−	0.0113965i	0.835258	+	0.549859i	$0.185319\pi$
$440$	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
$445$	25.0317	+	16.7257i	0.0562510	+	0.0375857i
$446$	393.137	+	393.137i	0.881473	+	0.881473i
$447$	−847.757	+	168.629i	−1.89655	+	0.377247i
$448$	−474.494	+	317.047i	−1.05914	+	0.707693i
$449$	−733.471	−	145.896i	−1.63356	−	0.324936i	−0.708781	−	0.705429i	$-0.750754\pi$
$449$	−733.471	−	145.896i	−1.63356	−	0.324936i	−0.924784	+	0.380493i	$0.875754\pi$
$450$	142.030	−	58.8307i	0.315622	−	0.130735i
$451$	−84.3194	−	203.565i	−0.186961	−	0.451364i
$452$	−219.529	+	1103.64i	−0.485683	+	2.44169i
$453$	67.1997	+	100.571i	0.148344	+	0.222012i
$454$	−88.1294	−	443.057i	−0.194118	−	0.975896i
$455$	180.290	−	180.290i	0.396241	−	0.396241i
$456$	−852.181	+	1275.38i	−1.86882	+	2.79688i
$457$	6.44295	+	2.66876i	0.0140984	+	0.00583973i	0.389721	−	0.920933i	$-0.372571\pi$
$457$	6.44295	+	2.66876i	0.0140984	+	0.00583973i	−0.375623	+	0.926773i	$0.622571\pi$
$458$			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	$-0.638811\pi$
$461$	238.435	−	575.633i	0.517213	−	1.24866i	0.939609	−	0.342251i	$-0.111189\pi$
$462$	−787.443	−	526.153i	−1.70442	−	1.13886i
$463$	−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	$0.790353\pi$
$464$	−263.598	+	52.4330i	−0.568100	+	0.113002i
$465$	353.003	−	235.869i	0.759147	−	0.507246i
$466$	572.929	+	113.963i	1.22946	+	0.244555i
$467$	549.497	−	227.609i	1.17665	−	0.487386i	0.293267	−	0.956031i	$-0.405258\pi$
$467$	549.497	−	227.609i	1.17665	−	0.487386i	0.883387	+	0.468645i	$0.155258\pi$
$468$	−135.549	−	327.245i	−0.289635	−	0.699241i
$469$	−140.201	+	704.837i	−0.298936	+	1.50285i
$470$	480.981	+	719.839i	1.02336	+	1.53157i
$471$	8.97007	+	45.0956i	0.0190447	+	0.0957443i
$472$	−343.046	+	343.046i	−0.726792	+	0.726792i
$473$	140.608	−	210.434i	0.297268	−	0.444893i
$474$	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
$479$	−614.473	−	410.578i	−1.28282	−	0.857156i	−0.287888	−	0.957664i	$-0.592953\pi$
$479$	−614.473	−	410.578i	−1.28282	−	0.857156i	−0.994936	+	0.100508i	$0.967953\pi$
$480$	102.574	+	102.574i	0.213696	+	0.213696i
$481$	−364.306	+	72.4650i	−0.757393	+	0.150655i
$482$	358.015	−	239.218i	0.742769	−	0.496302i
$483$	−32.7970	−	6.52372i	−0.0679026	−	0.0135067i
$484$	−120.143	+	49.7647i	−0.248229	+	0.102820i
$485$	151.350	+	365.390i	0.312061	+	0.753382i
$486$	−169.894	+	854.114i	−0.349576	+	1.75744i
$487$	−432.464	−	647.229i	−0.888017	−	1.32901i	−0.943782	−	0.330568i	$-0.892760\pi$
$487$	−432.464	−	647.229i	−0.888017	−	1.32901i	0.0557647	−	0.998444i	$-0.482240\pi$
$488$	−17.9335	−	90.1577i	−0.0367489	−	0.184749i
$489$	−478.282	+	478.282i	−0.978082	+	0.978082i
$490$	−21.2653	+	31.8258i	−0.0433986	+	0.0649506i
$491$	45.4991	+	18.8463i	0.0926661	+	0.0383836i	0.428535	−	0.903525i	$-0.359030\pi$
$491$	45.4991	+	18.8463i	0.0926661	+	0.0383836i	−0.335869	+	0.941909i	$0.609030\pi$
$492$			624.573i			1.26946i
$493$		0			0
$494$	−971.185			−1.96596
$495$	−84.3996	+	203.759i	−0.170504	+	0.411633i
$496$	270.489	+	180.735i	0.545340	+	0.364384i
$497$	−23.9713	−	23.9713i	−0.0482319	−	0.0482319i
$498$	−1146.18	+	227.990i	−2.30157	+	0.457812i
$499$	−757.858	+	506.384i	−1.51875	+	1.01480i	−0.533092	+	0.846057i	$0.678970\pi$
$499$	−757.858	+	506.384i	−1.51875	+	1.01480i	−0.985660	+	0.168741i	$0.946030\pi$
$500$	1019.42	+	202.776i	2.03885	+	0.405552i
$501$	312.583	−	129.476i	0.623919	−	0.258436i
$502$	241.194	+	582.293i	0.480466	+	1.15995i
$503$	−74.4193	+	374.131i	−0.147951	+	0.743799i	0.833565	+	0.552421i	$0.186296\pi$
$503$	−74.4193	+	374.131i	−0.147951	+	0.743799i	−0.981516	+	0.191378i	$0.938704\pi$
$504$	263.916	+	394.979i	0.523643	+	0.783688i
$505$	−77.2122	−	388.172i	−0.152895	−	0.768657i
$506$	30.2123	−	30.2123i	0.0597081	−	0.0597081i
$507$	−195.554	+	292.668i	−0.385709	+	0.577254i
$508$	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
$513$	378.154	+	252.675i	0.737143	+	0.492543i
$514$	−177.768	−	177.768i	−0.345852	−	0.345852i
$515$	158.225	−	31.4730i	0.307234	−	0.0611126i
$516$	−596.502	+	398.570i	−1.15601	+	0.772423i
$517$	624.247	+	124.170i	1.20744	+	0.240175i
$518$	966.239	−	400.229i	1.86533	−	0.772643i
$519$	135.888	+	328.062i	0.261826	+	0.632104i
$520$	85.8121	−	431.407i	0.165023	−	0.829628i
$521$	−194.505	−	291.097i	−0.373330	−	0.558728i	0.596468	−	0.802637i	$-0.296570\pi$
$521$	−194.505	−	291.097i	−0.373330	−	0.558728i	−0.969798	+	0.243909i	$0.921570\pi$
$522$	−80.7207	−	405.810i	−0.154637	−	0.777414i
$523$	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	$0.115999\pi$
$524$	98.4086	−	147.279i	0.187803	−	0.281067i
$525$	−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
$530$	980.893	+	655.412i	1.85074	+	1.23663i
$531$	−147.040	−	147.040i	−0.276912	−	0.276912i
$532$	1760.18	−	350.122i	3.30861	−	0.658123i
$533$	−156.614	+	104.646i	−0.293835	+	0.196335i
$534$	−93.7567	−	18.6494i	−0.175574	−	0.0349239i
$535$	427.004	−	176.871i	0.798139	−	0.330600i
$536$	474.441	+	1145.40i	0.885151	+	2.13694i
$537$	213.072	−	1071.19i	0.396783	−	1.99476i
$538$	387.163	+	579.430i	0.719633	+	1.07701i
$539$	5.48987	+	27.5994i	0.0101853	+	0.0512049i
$540$	−305.792	+	305.792i	−0.566281	+	0.566281i
$541$	194.202	−	290.644i	0.358969	−	0.537236i	−0.607399	−	0.794397i	$-0.707787\pi$
$541$	194.202	−	290.644i	0.358969	−	0.537236i	0.966369	+	0.257161i	$0.0827871\pi$
$542$	−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
$547$	−86.7357	−	57.9550i	−0.158566	−	0.105951i	0.473756	−	0.880656i	$-0.342898\pi$
$547$	−86.7357	−	57.9550i	−0.158566	−	0.105951i	−0.632322	+	0.774706i	$0.717898\pi$
$548$	−292.184	−	292.184i	−0.533183	−	0.533183i
$549$	38.6445	−	7.68686i	0.0703907	−	0.0140016i
$550$	245.000	−	163.704i	0.445455	−	0.297644i
$551$	−730.250	−	145.256i	−1.32532	−	0.263622i
$552$	−53.2970	+	22.0763i	−0.0965525	+	0.0399933i
$553$	−161.928	−	390.928i	−0.292817	−	0.706923i
$554$	117.054	−	588.472i	0.211289	−	1.06222i
$555$	−364.225	−	545.101i	−0.656261	−	0.982164i
$556$	57.5407	+	289.277i	0.103490	+	0.520282i
$557$	−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	$0.344620\pi$
$558$	−278.242	+	416.418i	−0.498641	+	0.746269i
$559$	−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	−0.985305	−	0.170807i	$-0.945363\pi$
$563$	−94.4773	+	228.088i	−0.167811	+	0.405130i	0.817494	+	0.575937i	$0.195363\pi$
$564$	−1500.11	−	1002.34i	−2.65978	−	1.77720i
$565$	−423.526	−	423.526i	−0.749604	−	0.749604i
$566$	93.2693	−	18.5524i	0.164787	−	0.0327781i
$567$	601.650	−	402.010i	1.06111	−	0.709012i
$568$	−57.3597	−	11.4096i	−0.100985	−	0.0200873i
$569$	−123.790	+	51.2755i	−0.217557	+	0.0901150i	−0.488800	−	0.872396i	$-0.662565\pi$
$569$	−123.790	+	51.2755i	−0.217557	+	0.0901150i	0.271243	+	0.962511i	$0.412565\pi$
$570$	−655.964	−	1583.64i	−1.15081	−	2.77831i
$571$	38.1020	−	191.552i	0.0667286	−	0.335467i	−0.932972	−	0.359950i	$-0.882794\pi$
$571$	38.1020	−	191.552i	0.0667286	−	0.335467i	0.999700	+	0.0244826i	$0.00779382\pi$
$572$	−377.183	−	564.495i	−0.659412	−	0.986879i
$573$	19.9521	+	100.306i	0.0348204	+	0.175054i
$574$	375.013	−	375.013i	0.653334	−	0.653334i
$575$	5.78024	−	8.65075i	0.0100526	−	0.0150448i
$576$	−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
$581$	541.514	+	361.828i	0.932038	+	0.622768i
$582$	−887.996	−	887.996i	−1.52577	−	1.52577i
$583$	850.634	−	169.202i	1.45906	−	0.290226i
$584$	−1059.75	+	708.099i	−1.81463	+	1.21250i
$585$	184.915	+	36.7818i	0.316094	+	0.0628749i
$586$	−1598.42	+	662.086i	−2.72767	+	1.12984i
$587$	81.3118	+	196.304i	0.138521	+	0.334419i	0.977883	−	0.209154i	$-0.0670710\pi$
$587$	81.3118	+	196.304i	0.138521	+	0.334419i	−0.839362	+	0.543573i	$0.817071\pi$
$588$	15.5617	−	78.2340i	0.0264655	−	0.133051i
$589$	500.692	+	749.338i	0.850071	+	1.27222i
$590$	−105.767	−	531.726i	−0.179266	−	0.901231i
$591$	713.044	−	713.044i	1.20650	−	1.20650i
$592$	279.087	−	417.683i	0.471431	−	0.705546i
$593$	442.361	+	183.232i	0.745972	+	0.308992i	0.723097	−	0.690747i	$-0.242718\pi$
$593$	442.361	+	183.232i	0.745972	+	0.308992i	0.0228751	+	0.999738i	$0.492718\pi$
$594$			484.429i			0.815537i
$595$		0			0
$596$	1744.68			2.92731
$597$	506.981	−	1223.96i	0.849215	−	2.05019i
$598$	−30.3698	−	20.2925i	−0.0507857	−	0.0339339i
$599$	−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	$0.768777\pi$
$600$	−390.196	+	77.6147i	−0.650326	+	0.129358i
$601$	619.543	−	413.966i	1.03085	−	0.688795i	0.0794811	−	0.996836i	$-0.474674\pi$
$601$	619.543	−	413.966i	1.03085	−	0.688795i	0.951373	+	0.308042i	$0.0996737\pi$
$602$	597.473	+	118.845i	0.992480	+	0.197417i
$603$	−490.956	+	203.361i	−0.814189	+	0.337248i
$604$	−93.4299	−	225.560i	−0.154685	−	0.373443i
$605$	13.5038	−	67.8884i	0.0223204	−	0.112212i
$606$	698.190	+	1044.91i	1.15213	+	1.72428i
$607$	12.9870	+	65.2902i	0.0213954	+	0.107562i	0.990007	−	0.141016i	$-0.0450368\pi$
$607$	12.9870	+	65.2902i	0.0213954	+	0.107562i	−0.968612	+	0.248578i	$0.920037\pi$
$608$	−217.739	+	217.739i	−0.358123	+	0.358123i
$609$	−344.830	+	516.074i	−0.566223	+	0.847413i
$610$	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
$615$	−276.420	−	184.698i	−0.449464	−	0.300322i
$616$	643.826	+	643.826i	1.04517	+	1.04517i
$617$	159.075	−	31.6420i	0.257820	−	0.0512837i	−0.0644877	−	0.997919i	$-0.520541\pi$
$617$	159.075	−	31.6420i	0.257820	−	0.0512837i	0.322308	+	0.946635i	$0.395541\pi$
$618$	−425.925	+	284.594i	−0.689198	+	0.460508i
$619$	472.862	+	94.0581i	0.763913	+	0.151952i	0.561645	−	0.827378i	$-0.310169\pi$
$619$	472.862	+	94.0581i	0.763913	+	0.151952i	0.202268	+	0.979330i	$0.435169\pi$
$620$	−791.708	+	327.936i	−1.27695	+	0.528930i
$621$	6.54571	+	15.8027i	0.0105406	+	0.0254472i
$622$	−27.2754	+	137.122i	−0.0438511	+	0.220454i
$623$	29.5972	+	44.2953i	0.0475075	+	0.0711000i
$624$	75.8643	+	381.395i	0.121577	+	0.611211i
$625$	−241.466	+	241.466i	−0.386345	+	0.386345i
$626$	332.366	−	497.420i	0.530936	−	0.794601i
$627$	−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	−0.911287	−	0.411772i	$-0.864910\pi$
$631$	15.3062	−	36.9525i	0.0242571	−	0.0585618i	0.935544	+	0.353210i	$0.114910\pi$
$632$	−606.954	−	405.554i	−0.960370	−	0.641699i
$633$	612.951	+	612.951i	0.968326	+	0.968326i
$634$	−1479.93	+	294.376i	−2.33427	+	0.464316i
$635$	−165.682	+	110.705i	−0.260917	+	0.174339i
$636$	−2411.23	−	479.623i	−3.79124	−	0.754124i
$637$	22.2249	−	9.20584i	0.0348899	−	0.0144519i
$638$	−303.490	−	732.690i	−0.475690	−	1.14842i
$639$	4.89050	−	24.5862i	0.00765337	−	0.0384761i
$640$	−526.032	−	787.263i	−0.821925	−	1.23010i
$641$	100.822	+	506.864i	0.157288	+	0.790740i	0.976209	+	0.216833i	$0.0695728\pi$
$641$	100.822	+	506.864i	0.157288	+	0.790740i	−0.818921	+	0.573907i	$0.805427\pi$
$642$	−1037.73	+	1037.73i	−1.61641	+	1.61641i
$643$	−405.187	+	606.405i	−0.630151	+	0.943088i	0.369752	+	0.929131i	$0.379443\pi$
$643$	−405.187	+	606.405i	−0.630151	+	0.943088i	−0.999903	+	0.0139570i	$0.995557\pi$
$644$	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
$649$	−331.401	−	221.435i	−0.510633	−	0.341194i
$650$	−178.116	−	178.116i	−0.274024	−	0.274024i
$651$	736.841	−	146.567i	1.13186	−	0.225141i
$652$	1135.18	−	758.500i	1.74107	−	1.16334i
$653$	742.889	+	147.770i	1.13766	+	0.226294i	0.727756	−	0.685836i	$-0.240563\pi$
$653$	742.889	+	147.770i	1.13766	+	0.226294i	0.409900	+	0.912130i	$0.365563\pi$
$654$	−1196.12	+	495.447i	−1.82892	+	0.757564i
$655$	36.0806	+	87.1063i	0.0550849	+	0.132987i
$656$	49.6969	−	249.843i	0.0757575	−	0.380858i
$657$	−303.514	−	454.241i	−0.461970	−	0.691386i
$658$	298.877	+	1502.55i	0.454220	+	2.28352i
$659$	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	$0.180409\pi$
$660$	665.719	−	996.319i	1.00866	−	1.50957i
$661$	−558.348	−	231.275i	−0.844702	−	0.349887i	−0.0819961	−	0.996633i	$-0.526130\pi$
$661$	−558.348	−	231.275i	−0.844702	−	0.349887i	−0.762706	+	0.646746i	$0.776130\pi$
$662$		−	1829.14i		−	2.76305i
$663$		0			0
$664$	1123.55			1.69209
$665$	−365.564	+	882.548i	−0.549720	+	1.32714i
$666$	643.025	+	429.655i	0.965503	+	0.645128i
$667$	−19.8005	−	19.8005i	−0.0296860	−	0.0296860i
$668$	−669.796	+	133.231i	−1.00269	+	0.199447i
$669$	512.783	−	342.631i	0.766492	−	0.512154i
$670$	−1358.83	−	270.287i	−2.02810	−	0.403414i
$671$	69.7726	−	28.9008i	0.103983	−	0.0430712i
$672$	98.2333	+	237.156i	0.146180	+	0.352911i
$673$	136.428	−	685.871i	0.202717	−	1.01913i	−0.736667	−	0.676256i	$-0.763601\pi$
$673$	136.428	−	685.871i	0.202717	−	1.01913i	0.939383	−	0.342869i	$-0.111399\pi$
$674$	−1101.60	−	1648.67i	−1.63443	−	2.44609i
$675$	23.0130	+	115.694i	0.0340934	+	0.171399i
$676$	502.379	−	502.379i	0.743164	−	0.743164i
$677$	−572.702	+	857.109i	−0.845941	+	1.26604i	0.116128	+	0.993234i	$0.462952\pi$
$677$	−572.702	+	857.109i	−0.845941	+	1.26604i	−0.962069	+	0.272806i	$0.912048\pi$
$678$	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
$683$	426.344	+	284.874i	0.624223	+	0.417092i	0.827055	−	0.562121i	$-0.190015\pi$
$683$	426.344	+	284.874i	0.624223	+	0.417092i	−0.202832	+	0.979214i	$0.565015\pi$
$684$	938.383	+	938.383i	1.37191	+	1.37191i
$685$	215.718	−	42.9089i	0.314917	−	0.0626408i
$686$	943.637	−	630.518i	1.37556	−	0.919123i
$687$	600.345	+	119.416i	0.873864	+	0.173822i
$688$	270.328	−	111.974i	0.392919	−	0.162752i
$689$	−283.730	−	684.985i	−0.411800	−	0.994173i
$690$	12.5768	−	63.2278i	0.0182272	−	0.0916346i
$691$	−181.822	−	272.116i	−0.263129	−	0.393800i	0.676255	−	0.736667i	$-0.263602\pi$
$691$	−181.822	−	272.116i	−0.263129	−	0.393800i	−0.939384	+	0.342868i	$0.888602\pi$
$692$	−139.828	−	702.963i	−0.202063	−	1.01584i
$693$	−275.964	+	275.964i	−0.398217	+	0.398217i
$694$	1028.80	−	1539.71i	1.48243	−	2.21861i
$695$	−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
$700$	387.030	+	258.605i	0.552900	+	0.369436i
$701$	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	$0.471423\pi$
$702$	406.164	−	80.7910i	0.578581	−	0.115087i
$703$	1157.11	−	773.159i	1.64597	−	1.09980i
$704$	−793.279	−	157.793i	−1.12682	−	0.224138i
$705$	887.223	−	367.500i	1.25847	−	0.521277i
$706$	446.837	+	1078.76i	0.632914	+	1.52799i
$707$	136.632	−	686.897i	0.193256	−	0.971565i
$708$	627.685	+	939.397i	0.886561	+	1.32683i
$709$	111.088	+	558.478i	0.156683	+	0.787698i	0.976575	+	0.215179i	$0.0690336\pi$
$709$	111.088	+	558.478i	0.156683	+	0.787698i	−0.819892	+	0.572519i	$0.805966\pi$
$710$	46.2131	−	46.2131i	0.0650889	−	0.0650889i
$711$	173.833	−	260.160i	0.244491	−	0.365907i
$712$	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
$717$	368.403	+	246.159i	0.513811	+	0.343318i
$718$	−787.534	−	787.534i	−1.09684	−	1.09684i
$719$	−779.636	+	155.079i	−1.08433	+	0.215687i	−0.704740	−	0.709466i	$-0.748936\pi$
$719$	−779.636	+	155.079i	−1.08433	+	0.215687i	−0.379594	+	0.925153i	$0.623936\pi$
$720$	−212.008	+	141.659i	−0.294456	+	0.196749i
$721$	279.990	+	55.6936i	0.388336	+	0.0772449i
$722$	2223.87	−	921.158i	3.08016	−	1.27584i
$723$	−182.778	−	441.264i	−0.252804	−	0.610324i
$724$	−259.322	+	1303.70i	−0.358179	+	1.80069i
$725$	−107.288	−	160.568i	−0.147984	−	0.221473i
$726$	42.8787	+	215.566i	0.0590616	+	0.296923i
$727$	−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	$0.441007\pi$
$728$	432.434	−	647.183i	0.594002	−	0.888987i
$729$	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	−0.778588	−	0.627535i	$-0.784064\pi$
$733$	158.102	−	381.691i	0.215691	−	0.520725i	0.994279	+	0.106810i	$0.0340638\pi$
$734$	845.827	+	565.163i	1.15235	+	0.769977i
$735$	30.0225	+	30.0225i	0.0408469	+	0.0408469i
$736$	−11.3585	+	2.25934i	−0.0154327	+	0.00306975i
$737$	−846.895	+	565.877i	−1.14911	+	0.767811i
$738$	384.634	+	76.5085i	0.521185	+	0.103670i
$739$	1135.74	−	470.438i	1.53686	−	0.636587i	0.555976	−	0.831198i	$-0.312345\pi$
$739$	1135.74	−	470.438i	1.53686	−	0.636587i	0.980880	+	0.194612i	$0.0623447\pi$
$740$	506.393	+	1222.54i	0.684315	+	1.65208i
$741$	−210.168	+	1056.59i	−0.283627	+	1.42589i
$742$	1159.80	+	1735.76i	1.56307	+	2.33930i
$743$	17.0906	+	85.9201i	0.0230021	+	0.115639i	0.990581	−	0.136931i	$-0.0437240\pi$
$743$	17.0906	+	85.9201i	0.0230021	+	0.115639i	−0.967578	+	0.252571i	$0.918724\pi$
$744$	916.457	−	916.457i	1.23180	−	1.23180i
$745$	−515.934	+	772.150i	−0.692529	+	1.03644i
$746$	−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
$751$	−789.674	−	527.643i	−1.05150	−	0.702588i	−0.0953406	−	0.995445i	$-0.530394\pi$
$751$	−789.674	−	527.643i	−1.05150	−	0.702588i	−0.956156	+	0.292857i	$0.905394\pi$
$752$	520.323	+	520.323i	0.691919	+	0.691919i
$753$	685.692	−	136.393i	0.910614	−	0.181132i
$754$	−563.701	+	376.653i	−0.747614	+	0.499540i
$755$	127.456	+	25.3526i	0.168816	+	0.0335795i
$756$	−707.007	+	292.852i	−0.935194	+	0.387370i
$757$	38.5085	+	92.9677i	0.0508699	+	0.122811i	0.947272	−	0.320432i	$-0.103828\pi$
$757$	38.5085	+	92.9677i	0.0508699	+	0.122811i	−0.896402	+	0.443243i	$0.853828\pi$
$758$	−159.597	+	802.348i	−0.210550	+	1.05851i
$759$	−26.3310	−	39.4071i	−0.0346917	−	0.0519197i
$760$	321.504	+	1616.31i	0.423032	+	2.12672i
$761$	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	$-0.0642738\pi$
$762$	351.522	−	526.090i	0.461315	−	0.690407i
$763$	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
$768$	1501.48	+	1003.26i	1.95506	+	1.30633i
$769$	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	$0.643647\pi$
$770$	−997.940	+	198.503i	−1.29603	+	0.257796i
$771$	−231.870	+	154.930i	−0.300739	+	0.200947i
$772$	−1402.50	−	278.975i	−1.81671	−	0.361366i
$773$	−561.790	+	232.701i	−0.726766	+	0.301036i	−0.715222	−	0.698897i	$-0.753675\pi$
$773$	−561.790	+	232.701i	−0.726766	+	0.301036i	−0.0115436	+	0.999933i	$0.503675\pi$
$774$	172.384	+	416.171i	0.222718	+	0.537689i
$775$	−45.6019	+	229.256i	−0.0588411	+	0.295814i
$776$	670.773	+	1003.88i	0.864398	+	1.29366i
$777$	−226.326	−	1137.82i	−0.291281	−	1.46437i
$778$	−920.269	+	920.269i	−1.18287	+	1.18287i
$779$	392.068	−	586.772i	0.503297	−	0.753237i
$780$	−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
$785$	41.0737	+	27.4446i	0.0523232	+	0.0349613i
$786$	−211.692	−	211.692i	−0.269328	−	0.269328i
$787$	151.027	−	30.0411i	0.191902	−	0.0381717i	−0.0982034	−	0.995166i	$-0.531310\pi$
$787$	151.027	−	30.0411i	0.191902	−	0.0381717i	0.290106	+	0.956995i	$0.406310\pi$
$788$	−1692.37	+	1130.81i	−2.14768	+	1.43503i
$789$	573.662	+	114.108i	0.727074	+	0.144624i
$790$	753.654	−	312.174i	0.953992	−	0.395156i
$791$	−405.604	−	979.215i	−0.512774	−	1.23795i
$792$	−131.350	+	660.342i	−0.165846	+	0.833766i
$793$	−35.8679	−	53.6801i	−0.0452306	−	0.0676924i
$794$	−479.395	−	2410.08i	−0.603772	−	3.03537i
$795$	925.314	−	925.314i	1.16392	−	1.16392i
$796$	−1485.62	+	2223.39i	−1.86636	+	2.79321i
$797$	−155.316	−	64.3339i	−0.194876	−	0.0807201i	0.283111	−	0.959087i	$-0.408633\pi$
$797$	−155.316	−	64.3339i	−0.194876	−	0.0807201i	−0.477987	+	0.878367i	$0.658633\pi$
$798$		−	3033.25i		−	3.80106i
$799$		0			0
$800$	−79.8668			−0.0998335
$801$	−15.0752	+	36.3948i	−0.0188205	+	0.0454367i
$802$	−1055.59	−	705.322i	−1.31620	−	0.879454i
$803$	−740.425	−	740.425i	−0.922073	−	0.922073i
$804$	2831.73	−	563.267i	3.52206	−	0.700581i
$805$	−29.8720	+	19.9598i	−0.0371080	+	0.0247948i
$806$	804.841	+	160.093i	0.998562	+	0.198626i
$807$	714.165	−	295.817i	0.884963	−	0.366564i
$808$	−462.365	−	1116.25i	−0.572233	−	1.38149i
$809$	−92.6641	+	465.854i	−0.114542	+	0.575839i	0.880302	+	0.474414i	$0.157340\pi$
$809$	−92.6641	+	465.854i	−0.114542	+	0.575839i	−0.994843	+	0.101425i	$0.967660\pi$
$810$	775.017	+	1159.89i	0.956811	+	1.43197i
$811$	−305.365	−	1535.18i	−0.376530	−	1.89294i	−0.445427	−	0.895318i	$-0.646948\pi$
$811$	−305.365	−	1535.18i	−0.376530	−	1.89294i	0.0688973	−	0.997624i	$-0.478052\pi$
$812$	885.867	−	885.867i	1.09097	−	1.09097i
$813$	−24.6310	+	36.8629i	−0.0302964	+	0.0453418i
$814$	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
$819$	277.403	+	185.355i	0.338710	+	0.226319i
$820$	474.489	+	474.489i	0.578645	+	0.578645i
$821$	742.932	−	147.778i	0.904911	−	0.179998i	0.279365	−	0.960185i	$-0.409876\pi$
$821$	742.932	−	147.778i	0.904911	−	0.179998i	0.625546	+	0.780187i	$0.284876\pi$
$822$	−580.688	+	388.003i	−0.706433	+	0.472023i
$823$	−993.171	−	197.554i	−1.20677	−	0.240041i	−0.449582	−	0.893239i	$-0.648427\pi$
$823$	−993.171	−	197.554i	−1.20677	−	0.240041i	−0.757187	+	0.653198i	$0.773427\pi$
$824$	455.001	−	188.467i	0.552185	−	0.228723i
$825$	−125.080	−	301.970i	−0.151612	−	0.366025i
$826$	187.162	−	940.926i	0.226588	−	1.13914i
$827$	−96.9624	−	145.114i	−0.117246	−	0.175471i	0.768205	−	0.640204i	$-0.221150\pi$
$827$	−96.9624	−	145.114i	−0.117246	−	0.175471i	−0.885451	+	0.464733i	$0.846150\pi$
$828$	9.73700	+	48.9512i	0.0117597	+	0.0591198i
$829$	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	$0.183800\pi$
$830$	−697.553	+	1043.96i	−0.840425	+	1.25779i
$831$	−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
$836$	2114.94	+	1413.16i	2.52983	+	1.69038i
$837$	−271.733	−	271.733i	−0.324651	−	0.324651i
$838$	−2639.06	+	524.942i	−3.14924	+	0.626423i
$839$	−318.409	+	212.754i	−0.379511	+	0.253581i	−0.730664	−	0.682737i	$-0.760789\pi$
$839$	−318.409	+	212.754i	−0.379511	+	0.253581i	0.351154	+	0.936318i	$0.385789\pi$
$840$	1347.39	+	268.012i	1.60403	+	0.319062i
$841$	296.792	−	122.935i	0.352904	−	0.146178i
$842$	−862.553	−	2082.39i	−1.02441	−	2.47314i
$843$	−104.118	+	523.436i	−0.123509	+	0.620920i
$844$	−972.069	−	1454.80i	−1.15174	−	1.72370i
$845$	73.7771	+	370.903i	0.0873102	+	0.438938i
$846$	−801.038	+	801.038i	−0.946854	+	0.946854i
$847$	68.0500	−	101.844i	0.0803424	−	0.120241i
$848$	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
$853$	234.986	+	157.013i	0.275482	+	0.184071i	0.685635	−	0.727946i	$-0.259525\pi$
$853$	234.986	+	157.013i	0.275482	+	0.184071i	−0.410153	+	0.912017i	$0.634525\pi$
$854$	128.537	+	128.537i	0.150512	+	0.150512i
$855$	−692.802	+	137.807i	−0.810295	+	0.161178i
$856$	1173.16	−	783.882i	1.37052	−	0.915750i
$857$	−1085.10	−	215.840i	−1.26616	−	0.251855i	−0.484075	−	0.875027i	$-0.660844\pi$
$857$	−1085.10	−	215.840i	−1.26616	−	0.251855i	−0.782085	+	0.623172i	$0.785844\pi$
$858$	−1060.12	+	439.114i	−1.23557	+	0.511788i
$859$	67.0359	+	161.839i	0.0780395	+	0.188404i	0.958084	−	0.286487i	$-0.0924875\pi$
$859$	67.0359	+	161.839i	0.0780395	+	0.188404i	−0.880045	+	0.474891i	$0.842487\pi$
$860$	−150.369	+	755.957i	−0.174848	+	0.879020i
$861$	−326.836	−	489.144i	−0.379600	−	0.568112i
$862$	−88.5505	−	445.173i	−0.102727	−	0.516442i
$863$	−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	$0.418040\pi$
$864$	72.9483	−	109.175i	0.0844309	−	0.126360i
$865$	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
$870$	−994.917	−	664.782i	−1.14358	−	0.764118i
$871$	615.694	+	615.694i	0.706882	+	0.706882i
$872$	1220.79	−	242.831i	1.39999	−	0.278476i
$873$	−430.296	+	287.515i	−0.492894	+	0.329341i
$874$	134.217	+	26.6974i	0.153566	+	0.0305463i
$875$	−904.489	+	374.652i	−1.03370	+	0.428173i
$876$	1135.88	+	2742.25i	1.29666	+	3.13042i
$877$	56.1031	−	282.049i	0.0639716	−	0.321607i	−0.935528	−	0.353254i	$-0.885075\pi$
$877$	56.1031	−	282.049i	0.0639716	−	0.321607i	0.999499	+	0.0316469i	$0.0100752\pi$
$878$	11.4043	+	17.0678i	0.0129890	+	0.0194394i
$879$	374.403	+	1882.25i	0.425942	+	2.14135i
$880$	−345.579	+	345.579i	−0.392703	+	0.392703i
$881$	607.696	−	909.481i	0.689780	−	1.03233i	−0.306966	−	0.951720i	$-0.599314\pi$
$881$	607.696	−	909.481i	0.689780	−	1.03233i	0.996746	−	0.0806078i	$-0.0256861\pi$
$882$	−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
$887$	874.942	+	584.618i	0.986406	+	0.659096i	0.940480	−	0.339849i	$-0.110376\pi$
$887$	874.942	+	584.618i	0.986406	+	0.659096i	0.0459263	+	0.998945i	$0.485376\pi$
$888$	−1415.18	−	1415.18i	−1.59367	−	1.59367i
$889$	−345.836	+	68.7911i	−0.389017	+	0.0773803i
$890$	−85.3950	+	57.0591i	−0.0959495	+	0.0641114i
$891$	1005.86	+	200.079i	1.12892	+	0.224555i
$892$	−1150.06	+	476.370i	−1.28930	+	0.534047i
$893$	780.112	+	1883.36i	0.873585	+	2.10902i
$894$	575.274	−	2892.10i	0.643484	−	3.23501i
$895$	−651.910	−	975.653i	−0.728391	−	1.09011i
$896$	−326.871	−	1643.29i	−0.364811	−	1.83403i
$897$	−28.6490	+	28.6490i	−0.0319387	+	0.0319387i
$898$	1417.39	−	2121.28i	1.57839	−	2.36222i
$899$	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
$904$	−1520.33	−	1015.85i	−1.68178	−	1.12373i
$905$	−500.297	−	500.297i	−0.552815	−	0.552815i
$906$	−404.710	+	80.5019i	−0.446700	+	0.0888542i
$907$	213.141	−	142.416i	0.234995	−	0.157019i	−0.432497	−	0.901635i	$-0.642367\pi$
$907$	213.141	−	142.416i	0.234995	−	0.157019i	0.667493	+	0.744616i	$0.267367\pi$
$908$	991.986	+	197.318i	1.09250	+	0.217311i
$909$	478.459	−	198.184i	0.526358	−	0.218024i
$910$	332.864	+	803.606i	0.365785	+	0.883083i
$911$	−211.821	+	1064.90i	−0.232515	+	1.16893i	0.671359	+	0.741133i	$0.265711\pi$
$911$	−211.821	+	1064.90i	−0.232515	+	1.16893i	−0.903874	+	0.427800i	$0.859289\pi$
$912$	−809.428	−	1211.39i	−0.887531	−	1.32828i
$913$	180.081	+	905.327i	0.197241	+	0.991596i
$914$	−16.8227	+	16.8227i	−0.0184056	+	0.0184056i
$915$	63.3059	−	94.7439i	0.0691867	−	0.103545i
$916$	−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
$921$	−1465.66	−	979.326i	−1.59138	−	1.06333i
$922$	1503.00	+	1503.00i	1.63015	+	1.63015i
$923$	−40.2851	+	8.01321i	−0.0436459	+	0.00868171i
$924$	1763.05	−	1178.03i	1.90807	−	1.27493i
$925$	354.013	+	70.4176i	0.382717	+	0.0761271i
$926$	369.004	−	152.846i	0.398493	−	0.165061i
$927$	80.7832	+	195.028i	0.0871448	+	0.210386i
$928$	−41.9360	+	210.827i	−0.0451897	+	0.227184i
$929$	42.5550	+	63.6881i	0.0458074	+	0.0685556i	0.853666	−	0.520820i	$-0.174374\pi$
$929$	42.5550	+	63.6881i	0.0458074	+	0.0685556i	−0.807859	+	0.589376i	$0.799374\pi$
$930$	282.560	+	1420.52i	0.303828	+	1.52744i
$931$	−63.7303	+	63.7303i	−0.0684536	+	0.0684536i
$932$	−726.628	+	1087.48i	−0.779644	+	1.16682i
$933$	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	−0.940019	−	0.341122i	$-0.889193\pi$
$937$	−31.9660	+	77.1728i	−0.0341153	+	0.0823616i	0.905904	+	0.423484i	$0.139193\pi$
$938$	−2038.47	−	1362.06i	−2.17320	−	1.45209i
$939$	−469.236	−	469.236i	−0.499718	−	0.499718i
$940$	−1901.12	+	378.156i	−2.02247	+	0.402294i
$941$	−4.64679	+	3.10489i	−0.00493814	+	0.00329956i	−0.558037	−	0.829816i	$-0.688445\pi$
$941$	−4.64679	+	3.10489i	−0.00493814	+	0.00329956i	0.553099	+	0.833116i	$0.313445\pi$
$942$	−153.842	−	30.6012i	−0.163315	−	0.0324853i
$943$	24.5207	−	10.1568i	0.0260028	−	0.0107707i
$944$	−176.341	−	425.724i	−0.186802	−	0.450979i
$945$	79.4665	−	399.505i	0.0840915	−	0.422757i
$946$	479.680	+	717.891i	0.507061	+	0.758870i
$947$	179.695	+	903.388i	0.189752	+	0.953947i	0.951868	+	0.306507i	$0.0991604\pi$
$947$	179.695	+	903.388i	0.189752	+	0.953947i	−0.762116	+	0.647440i	$0.775840\pi$
$948$	−1202.07	+	1202.07i	−1.26801	+	1.26801i
$949$	−497.315	+	744.285i	−0.524042	+	0.784284i
$950$	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
$955$	91.3602	+	61.0449i	0.0956651	+	0.0639214i
$956$	−632.381	−	632.381i	−0.661487	−	0.661487i
$957$	−862.795	+	171.621i	−0.901563	+	0.179332i
$958$	2096.26	−	1400.68i	2.18816	−	1.46208i
$959$	381.727	+	75.9303i	0.398047	+	0.0791765i
$960$	−1127.46	+	467.011i	−1.17444	+	0.486470i
$961$	76.3481	+	184.321i	0.0794465	+	0.191801i
$962$	247.212	−	1242.82i	0.256978	−	1.29191i
$963$	335.997	+	502.855i	0.348906	+	0.522175i
$964$	188.077	+	945.529i	0.195101	+	0.980839i
$965$	538.213	−	538.213i	0.557734	−	0.557734i
$966$	63.3783	−	94.8524i	0.0656090	−	0.0981909i
$967$	1542.05	+	638.737i	1.59467	+	0.660534i	0.990649	−	0.136434i	$-0.0435642\pi$
$967$	1542.05	+	638.737i	1.59467	+	0.660534i	0.604021	+	0.796968i	$0.293564\pi$
$968$		−	211.308i		−	0.218294i
$969$		0			0
$970$	−1349.22			−1.39095
$971$	−108.360	+	261.605i	−0.111597	+	0.269419i	−0.969804	−	0.243884i	$-0.921578\pi$
$971$	−108.360	+	261.605i	−0.111597	+	0.269419i	0.858208	+	0.513303i	$0.171578\pi$
$972$	−1621.19	−	1083.25i	−1.66789	−	1.11445i
$973$	−196.441	−	196.441i	−0.201892	−	0.201892i
$974$	2604.52	−	518.071i	2.67404	−	0.531900i
$975$	−232.323	+	155.233i	−0.238280	+	0.159214i
$976$	85.6346	+	17.0338i	0.0877403	+	0.0174526i
$977$	−1350.75	+	559.500i	−1.38255	+	0.572671i	−0.945162	−	0.326601i	$-0.894097\pi$
$977$	−1350.75	+	559.500i	−1.38255	+	0.572671i	−0.437389	+	0.899272i	$0.644097\pi$
$978$	−883.041	−	2131.85i	−0.902904	−	2.17980i
$979$	−14.7304	+	74.0549i	−0.0150464	+	0.0756434i
$980$	−47.6122	−	71.2567i	−0.0485839	−	0.0727110i
$981$	104.085	+	523.271i	0.106101	+	0.533406i
$982$	−118.799	+	118.799i	−0.120977	+	0.120977i
$983$	−75.4993	+	112.993i	−0.0768050	+	0.114947i	−0.867883	−	0.496768i	$-0.834520\pi$
$983$	−75.4993	+	112.993i	−0.0768050	+	0.114947i	0.791078	+	0.611715i	$0.209520\pi$
$984$	−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
$989$	25.3481	+	16.9371i	0.0256300	+	0.0171255i
$990$	−532.020	−	532.020i	−0.537393	−	0.537393i
$991$	73.4596	−	14.6120i	0.0741267	−	0.0147447i	−0.157888	−	0.987457i	$-0.550468\pi$
$991$	73.4596	−	14.6120i	0.0741267	−	0.0147447i	0.232014	+	0.972712i	$0.425468\pi$
$992$	216.337	−	144.552i	0.218082	−	0.145718i
$993$	−1989.98	−	395.832i	−2.00401	−	0.398623i
$994$	106.847	−	44.2576i	0.107492	−	0.0445247i
$995$	−544.690	−	1315.00i	−0.547427	−	1.32161i
$996$	510.461	−	2566.26i	0.512511	−	2.57657i
$997$	−257.592	−	385.513i	−0.258367	−	0.386674i	0.679496	−	0.733679i	$-0.262198\pi$
$997$	−257.592	−	385.513i	−0.258367	−	0.386674i	−0.937863	+	0.347006i	$0.887198\pi$
$998$	−606.623	−	3049.70i	−0.607839	−	3.05581i
$999$	−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.214.2	yes	48
17.2	even	8	inner	289.3.e.q.40.2	yes	48
17.3	odd	16	inner	289.3.e.q.158.6	yes	48
17.4	even	4	inner	289.3.e.q.75.6	yes	48
17.5	odd	16	inner	289.3.e.q.131.1	yes	48
17.6	odd	16	inner	289.3.e.q.224.2	yes	48
17.7	odd	16	inner	289.3.e.q.65.6	yes	48
17.8	even	8	inner	289.3.e.q.249.5	yes	48
17.9	even	8	inner	289.3.e.q.249.6	yes	48
17.10	odd	16	inner	289.3.e.q.65.5	yes	48
17.11	odd	16	inner	289.3.e.q.224.1	yes	48
17.12	odd	16	inner	289.3.e.q.131.2	yes	48
17.13	even	4	inner	289.3.e.q.75.5	yes	48
17.14	odd	16	inner	289.3.e.q.158.5	yes	48
17.15	even	8	inner	289.3.e.q.40.1	✓	48
17.16	even	2	inner	289.3.e.q.214.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.q.40.1	✓	48	17.15	even	8	inner
289.3.e.q.40.2	yes	48	17.2	even	8	inner
289.3.e.q.65.5	yes	48	17.10	odd	16	inner
289.3.e.q.65.6	yes	48	17.7	odd	16	inner
289.3.e.q.75.5	yes	48	17.13	even	4	inner
289.3.e.q.75.6	yes	48	17.4	even	4	inner
289.3.e.q.131.1	yes	48	17.5	odd	16	inner
289.3.e.q.131.2	yes	48	17.12	odd	16	inner
289.3.e.q.158.5	yes	48	17.14	odd	16	inner
289.3.e.q.158.6	yes	48	17.3	odd	16	inner
289.3.e.q.214.1	yes	48	17.16	even	2	inner
289.3.e.q.214.2	yes	48	1.1	even	1	trivial
289.3.e.q.224.1	yes	48	17.11	odd	16	inner
289.3.e.q.224.2	yes	48	17.6	odd	16	inner
289.3.e.q.249.5	yes	48	17.8	even	8	inner
289.3.e.q.249.6	yes	48	17.9	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} +(3.14642 + 2.10237i) q^{3} +(-5.40099 - 5.40099i) q^{4} +(3.98752 - 0.793166i) q^{5} +(-10.7339 + 7.17219i) q^{6} +(7.05618 + 1.40356i) q^{7} +(11.4667 - 4.74967i) q^{8} +(2.03586 + 4.91500i) q^{9} +(-2.70587 + 13.6033i) q^{10} +(5.66504 + 8.47833i) q^{11} +(-5.63891 - 28.3487i) q^{12} +(6.16377 - 6.16377i) q^{13} +(-13.6357 + 20.4072i) q^{14} +(14.2139 + 5.88761i) q^{15} +11.7888i q^{16} -18.1489 q^{18} +(-12.4979 + 30.1727i) q^{19} +(-25.8204 - 17.2527i) q^{20} +(19.2509 + 19.2509i) q^{21} +(-34.1177 + 6.78644i) q^{22} +(-1.02127 + 0.682389i) q^{23} +(46.0647 + 9.16284i) q^{24} +(-7.82581 + 3.24156i) q^{25} +(11.3800 + 27.4738i) q^{26} +(2.71681 - 13.6583i) q^{27} +(-30.5298 - 45.6910i) q^{28} +(4.44769 + 22.3601i) q^{29} +(-37.1130 + 37.1130i) q^{30} +(15.3310 - 22.9445i) q^{31} +(8.71099 + 3.60821i) q^{32} +38.5864i q^{33} +29.2499 q^{35} +(15.5502 - 37.5415i) q^{36} +(-35.4305 - 23.6739i) q^{37} +(-78.7818 - 78.7818i) q^{38} +(32.3524 - 6.43528i) q^{39} +(41.9564 - 28.0344i) q^{40} +(-21.1933 - 4.21560i) q^{41} +(-85.8073 + 35.5425i) q^{42} +(-9.49830 - 22.9309i) q^{43} +(15.1946 - 76.3882i) q^{44} +(12.0164 + 17.9839i) q^{45} +(-0.817468 - 4.10969i) q^{46} +(44.1371 - 44.1371i) q^{47} +(-24.7845 + 37.0926i) q^{48} +(2.54963 + 1.05609i) q^{49} -28.8972i q^{50} -66.5809 q^{52} +(32.5495 - 78.5814i) q^{53} +(39.5014 + 26.3940i) q^{54} +(29.3142 + 29.3142i) q^{55} +(87.5776 - 17.4203i) q^{56} +(-102.758 + 68.6608i) q^{57} +(-76.2808 - 15.1732i) q^{58} +(-36.1126 + 14.9583i) q^{59} +(-44.9705 - 108.568i) q^{60} +(1.44491 - 7.26406i) q^{61} +(52.3015 + 78.2747i) q^{62} +(7.46689 + 37.5386i) q^{63} +(-56.0884 + 56.0884i) q^{64} +(19.6892 - 29.4670i) q^{65} +(-121.616 - 50.3752i) q^{66} +99.8893i q^{67} -4.64798 q^{69} +(-38.1862 + 92.1896i) q^{70} +(-3.91793 - 2.61787i) q^{71} +(46.6892 + 46.6892i) q^{72} +(-100.718 + 20.0340i) q^{73} +(120.870 - 80.7630i) q^{74} +(-31.4383 - 6.25346i) q^{75} +(230.464 - 95.4612i) q^{76} +(28.0737 + 67.7759i) q^{77} +(-21.9538 + 110.369i) q^{78} +(-32.6757 - 48.9026i) q^{79} +(9.35048 + 47.0080i) q^{80} +(71.1192 - 71.1192i) q^{81} +(40.9548 - 61.2932i) q^{82} +(83.6340 + 34.6423i) q^{83} -207.948i q^{84} +84.6737 q^{86} +(-33.0149 + 79.7050i) q^{87} +(105.229 + 70.3115i) q^{88} +(5.23601 + 5.23601i) q^{89} +(-72.3690 + 14.3951i) q^{90} +(52.1439 - 34.8414i) q^{91} +(9.20143 + 1.83028i) q^{92} +(96.4760 - 39.9616i) q^{93} +(81.4892 + 196.732i) q^{94} +(-25.9038 + 130.227i) q^{95} +(19.8227 + 29.6667i) q^{96} +(18.9779 + 95.4085i) q^{97} +(-6.65717 + 6.65717i) q^{98} +(-30.1378 + 45.1043i) 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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