LMFDB - Embedded newform 289.3.e.g.158.1

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)

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);

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")

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 = [8,0,0,-8,24] 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:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			158.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.158
Dual form			289.3.e.g.75.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08979 + 2.63099i) q^{2} +(2.88669 + 4.32023i) q^{3} +(-2.90602 + 2.90602i) q^{4} +(0.711297 - 3.57593i) q^{5} +(-8.22059 + 12.3030i) q^{6} +(0.644047 + 3.23784i) q^{7} +(-0.288703 - 0.119585i) q^{8} +(-6.88730 + 16.6274i) q^{9} +(10.1834 - 2.02560i) q^{10} +(-2.02046 - 1.35003i) q^{11} +(-20.9434 - 4.16591i) q^{12} +(-7.73173 - 7.73173i) q^{13} +(-7.81684 + 5.22304i) q^{14} +(17.5022 - 7.24963i) q^{15} +15.5490i q^{16} -51.2522 q^{18} +(-3.50319 - 8.45745i) q^{19} +(8.32469 + 12.4588i) q^{20} +(-12.1291 + 12.1291i) q^{21} +(1.35003 - 6.78704i) q^{22} +(1.91942 - 2.87262i) q^{23} +(-0.316761 - 1.59247i) q^{24} +(10.8156 + 4.47998i) q^{25} +(11.9161 - 28.7680i) q^{26} +(-45.8512 + 9.12037i) q^{27} +(-11.2808 - 7.53762i) q^{28} +(23.5861 + 4.69157i) q^{29} +(38.1474 + 38.1474i) q^{30} +(23.0300 - 15.3882i) q^{31} +(-42.0641 + 17.4235i) q^{32} -12.6260i q^{33} +12.0364 q^{35} +(-28.3049 - 68.3342i) q^{36} +(21.3995 + 32.0267i) q^{37} +(18.4337 - 18.4337i) q^{38} +(11.0838 - 55.7219i) q^{39} +(-0.632980 + 0.947321i) q^{40} +(-15.0157 - 75.4890i) q^{41} +(-45.1295 - 18.6933i) q^{42} +(20.7301 - 50.0470i) q^{43} +(9.79469 - 1.94829i) q^{44} +(54.5596 + 36.4555i) q^{45} +(9.64960 + 1.91942i) q^{46} +(-5.13810 - 5.13810i) q^{47} +(-67.1754 + 44.8852i) q^{48} +(35.2013 - 14.5808i) q^{49} +33.3380i q^{50} +44.9371 q^{52} +(21.8223 + 52.6837i) q^{53} +(-73.9637 - 110.695i) q^{54} +(-6.26475 + 6.26475i) q^{55} +(0.201258 - 1.01179i) q^{56} +(26.4255 - 39.5486i) q^{57} +(13.3605 + 67.1676i) q^{58} +(-21.2985 - 8.82213i) q^{59} +(-29.7940 + 71.9292i) q^{60} +(-40.6888 + 8.09351i) q^{61} +(65.5839 + 43.8218i) q^{62} +(-58.2726 - 11.5911i) q^{63} +(-47.7028 - 47.7028i) q^{64} +(-33.1477 + 22.1486i) q^{65} +(33.2187 - 13.7596i) q^{66} +17.3637i q^{67} +17.9512 q^{69} +(13.1172 + 31.6676i) q^{70} +(28.6631 + 42.8974i) q^{71} +(3.97676 - 3.97676i) q^{72} +(-12.1277 + 60.9700i) q^{73} +(-60.9407 + 91.2042i) q^{74} +(11.8668 + 59.6583i) q^{75} +(34.7579 + 14.3972i) q^{76} +(3.06990 - 7.41140i) q^{77} +(158.683 - 31.5639i) q^{78} +(-98.5655 - 65.8593i) q^{79} +(55.6023 + 11.0600i) q^{80} +(-57.2255 - 57.2255i) q^{81} +(182.247 - 121.773i) q^{82} +(-86.9369 + 36.0104i) q^{83} -70.4946i q^{84} +154.264 q^{86} +(47.8171 + 115.441i) q^{87} +(0.421869 + 0.631372i) q^{88} +(19.6021 - 19.6021i) q^{89} +(-36.4555 + 183.274i) q^{90} +(20.0545 - 30.0137i) q^{91} +(2.77001 + 13.9258i) q^{92} +(132.961 + 55.0742i) q^{93} +(7.91883 - 19.1177i) q^{94} +(-32.7351 + 6.51142i) q^{95} +(-196.700 - 131.430i) q^{96} +(-14.9417 - 2.97209i) q^{97} +(76.7240 + 76.7240i) q^{98} +(36.3629 - 24.2969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 24 q^{5} + 16 q^{7} + 16 q^{8} + 8 q^{9} - 40 q^{11} - 40 q^{12} - 16 q^{14} + 32 q^{15} - 136 q^{18} - 32 q^{19} + 40 q^{20} - 64 q^{21} + 8 q^{23} - 24 q^{24} + 16 q^{25} - 96 q^{27} - 80 q^{28}+ \cdots - 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 24 * q^5 + 16 * q^7 + 16 * q^8 + 8 * q^9 - 40 * q^11 - 40 * q^12 - 16 * q^14 + 32 * q^15 - 136 * q^18 - 32 * q^19 + 40 * q^20 - 64 * q^21 + 8 * q^23 - 24 * q^24 + 16 * q^25 - 96 * q^27 - 80 * q^28 - 24 * q^29 + 168 * q^30 - 32 * q^31 - 24 * q^32 + 80 * q^35 - 104 * q^36 + 168 * q^37 + 8 * q^38 + 72 * q^39 + 200 * q^40 - 72 * q^42 + 96 * q^43 + 96 * q^44 + 88 * q^45 - 80 * q^47 - 88 * q^48 + 8 * q^49 + 240 * q^52 + 96 * q^53 - 208 * q^54 - 8 * q^55 - 72 * q^56 - 248 * q^57 + 8 * q^59 + 16 * q^60 - 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 32 * q^65 + 8 * q^66 - 208 * q^69 - 80 * q^70 - 32 * q^71 + 24 * q^72 - 24 * q^73 - 176 * q^74 + 192 * q^75 - 80 * q^76 - 216 * q^77 + 368 * q^78 + 96 * q^79 - 24 * q^80 - 224 * q^81 + 408 * q^82 - 88 * q^83 + 288 * q^86 + 312 * q^87 - 176 * q^88 + 288 * q^89 - 256 * q^90 + 24 * q^91 - 336 * q^92 + 280 * q^93 - 8 * q^94 + 152 * q^95 - 328 * q^96 + 344 * q^97 + 16 * q^98 - 136 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{16}\right)$

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 $

$2$	1.08979	+	2.63099i	0.544895	+	1.31549i	0.921233	+	0.389011i	$0.127183\pi$
$2$	1.08979	+	2.63099i	0.544895	+	1.31549i	−0.376338	+	0.926482i	$0.622817\pi$
$3$	2.88669	+	4.32023i	0.962229	+	1.44008i	0.896910	+	0.442213i	$0.145807\pi$
$3$	2.88669	+	4.32023i	0.962229	+	1.44008i	0.0653191	+	0.997864i	$0.479193\pi$
$4$	−2.90602	+	2.90602i	−0.726505	+	0.726505i
$5$	0.711297	−	3.57593i	0.142259	−	0.715187i	−0.842143	−	0.539255i	$-0.818706\pi$
$5$	0.711297	−	3.57593i	0.142259	−	0.715187i	0.984402	−	0.175932i	$-0.0562939\pi$
$6$	−8.22059	+	12.3030i	−1.37010	+	2.05050i
$7$	0.644047	+	3.23784i	0.0920066	+	0.462549i	0.999131	+	0.0416855i	$0.0132727\pi$
$7$	0.644047	+	3.23784i	0.0920066	+	0.462549i	−0.907124	+	0.420863i	$0.861727\pi$
$8$	−0.288703	−	0.119585i	−0.0360878	−	0.0149481i
$9$	−6.88730	+	16.6274i	−0.765255	+	1.84749i
$10$	10.1834	−	2.02560i	1.01834	−	0.202560i
$11$	−2.02046	−	1.35003i	−0.183678	−	0.122730i	0.460332	−	0.887747i	$-0.347730\pi$
$11$	−2.02046	−	1.35003i	−0.183678	−	0.122730i	−0.644010	+	0.765017i	$0.722730\pi$
$12$	−20.9434	−	4.16591i	−1.74529	−	0.347159i
$13$	−7.73173	−	7.73173i	−0.594748	−	0.594748i	0.344162	−	0.938910i	$-0.388163\pi$
$13$	−7.73173	−	7.73173i	−0.594748	−	0.594748i	−0.938910	+	0.344162i	$0.888163\pi$
$14$	−7.81684	+	5.22304i	−0.558346	+	0.373075i
$15$	17.5022	−	7.24963i	1.16681	−	0.483309i
$16$			15.5490i			0.971815i
$17$		0			0
$17$		0			0
$18$	−51.2522			−2.84734
$19$	−3.50319	−	8.45745i	−0.184379	−	0.445129i	0.804481	−	0.593978i	$-0.202443\pi$
$19$	−3.50319	−	8.45745i	−0.184379	−	0.445129i	−0.988860	+	0.148849i	$0.952443\pi$
$20$	8.32469	+	12.4588i	0.416234	+	0.622939i
$21$	−12.1291	+	12.1291i	−0.577574	+	0.577574i
$22$	1.35003	−	6.78704i	0.0613649	−	0.308502i
$23$	1.91942	−	2.87262i	0.0834532	−	0.124897i	−0.787395	−	0.616449i	$-0.788571\pi$
$23$	1.91942	−	2.87262i	0.0834532	−	0.124897i	0.870848	+	0.491553i	$0.163571\pi$
$24$	−0.316761	−	1.59247i	−0.0131984	−	0.0663527i
$25$	10.8156	+	4.47998i	0.432625	+	0.179199i
$26$	11.9161	−	28.7680i	0.458312	−	1.10646i
$27$	−45.8512	+	9.12037i	−1.69819	+	0.337791i
$28$	−11.2808	−	7.53762i	−0.402887	−	0.269201i
$29$	23.5861	+	4.69157i	0.813314	+	0.161778i	0.584188	−	0.811618i	$-0.301413\pi$
$29$	23.5861	+	4.69157i	0.813314	+	0.161778i	0.229126	+	0.973397i	$0.426413\pi$
$30$	38.1474	+	38.1474i	1.27158	+	1.27158i
$31$	23.0300	−	15.3882i	0.742903	−	0.496392i	−0.125597	−	0.992081i	$-0.540085\pi$
$31$	23.0300	−	15.3882i	0.742903	−	0.496392i	0.868500	+	0.495689i	$0.165085\pi$
$32$	−42.0641	+	17.4235i	−1.31450	+	0.544485i
$33$		−	12.6260i		−	0.382605i
$34$		0			0
$35$	12.0364			0.343897
$36$	−28.3049	−	68.3342i	−0.786248	−	1.89817i
$37$	21.3995	+	32.0267i	0.578366	+	0.865586i	0.999135	−	0.0415820i	$-0.0132398\pi$
$37$	21.3995	+	32.0267i	0.578366	+	0.865586i	−0.420769	+	0.907168i	$0.638240\pi$
$38$	18.4337	−	18.4337i	0.485097	−	0.485097i
$39$	11.0838	−	55.7219i	0.284200	−	1.42877i
$40$	−0.632980	+	0.947321i	−0.0158245	+	0.0236830i
$41$	−15.0157	−	75.4890i	−0.366237	−	1.84120i	−0.521407	−	0.853308i	$-0.674593\pi$
$41$	−15.0157	−	75.4890i	−0.366237	−	1.84120i	0.155171	−	0.987888i	$-0.450407\pi$
$42$	−45.1295	−	18.6933i	−1.07451	−	0.445078i
$43$	20.7301	−	50.0470i	0.482096	−	1.16388i	−0.476515	−	0.879166i	$-0.658100\pi$
$43$	20.7301	−	50.0470i	0.482096	−	1.16388i	0.958612	−	0.284717i	$-0.0918996\pi$
$44$	9.79469	−	1.94829i	0.222607	−	0.0442792i
$45$	54.5596	+	36.4555i	1.21244	+	0.810123i
$46$	9.64960	+	1.91942i	0.209774	+	0.0417266i
$47$	−5.13810	−	5.13810i	−0.109321	−	0.109321i	0.650330	−	0.759652i	$-0.274631\pi$
$47$	−5.13810	−	5.13810i	−0.109321	−	0.109321i	−0.759652	+	0.650330i	$0.774631\pi$
$48$	−67.1754	+	44.8852i	−1.39949	+	0.935108i
$49$	35.2013	−	14.5808i	0.718394	−	0.297568i
$50$			33.3380i			0.666760i
$51$		0			0
$52$	44.9371			0.864175
$53$	21.8223	+	52.6837i	0.411742	+	0.994033i	0.984670	+	0.174427i	$0.0558074\pi$
$53$	21.8223	+	52.6837i	0.411742	+	0.994033i	−0.572928	+	0.819606i	$0.694193\pi$
$54$	−73.9637	−	110.695i	−1.36970	−	2.04990i
$55$	−6.26475	+	6.26475i	−0.113905	+	0.113905i
$56$	0.201258	−	1.01179i	0.00359389	−	0.0180677i
$57$	26.4255	−	39.5486i	0.463606	−	0.693836i
$58$	13.3605	+	67.1676i	0.230353	+	1.15806i
$59$	−21.2985	−	8.82213i	−0.360992	−	0.149528i	0.194813	−	0.980840i	$-0.437590\pi$
$59$	−21.2985	−	8.82213i	−0.360992	−	0.149528i	−0.555805	+	0.831313i	$0.687590\pi$
$60$	−29.7940	+	71.9292i	−0.496567	+	1.19882i
$61$	−40.6888	+	8.09351i	−0.667030	+	0.132680i	−0.516979	−	0.855998i	$-0.672944\pi$
$61$	−40.6888	+	8.09351i	−0.667030	+	0.132680i	−0.150050	+	0.988678i	$0.547944\pi$
$62$	65.5839	+	43.8218i	1.05780	+	0.706803i
$63$	−58.2726	−	11.5911i	−0.924962	−	0.183986i
$64$	−47.7028	−	47.7028i	−0.745356	−	0.745356i
$65$	−33.1477	+	22.1486i	−0.509965	+	0.340747i
$66$	33.2187	−	13.7596i	0.503314	−	0.208479i
$67$			17.3637i			0.259160i	0.991569	+	0.129580i	$0.0413630\pi$
$67$			17.3637i			0.259160i	−0.991569	+	0.129580i	$0.958637\pi$
$68$		0			0
$69$	17.9512			0.260162
$70$	13.1172	+	31.6676i	0.187388	+	0.452395i
$71$	28.6631	+	42.8974i	0.403706	+	0.604188i	0.976502	−	0.215510i	$-0.0691413\pi$
$71$	28.6631	+	42.8974i	0.403706	+	0.604188i	−0.572796	+	0.819698i	$0.694141\pi$
$72$	3.97676	−	3.97676i	0.0552328	−	0.0552328i
$73$	−12.1277	+	60.9700i	−0.166133	+	0.835206i	0.804372	+	0.594126i	$0.202502\pi$
$73$	−12.1277	+	60.9700i	−0.166133	+	0.835206i	−0.970505	+	0.241080i	$0.922498\pi$
$74$	−60.9407	+	91.2042i	−0.823523	+	1.23249i
$75$	11.8668	+	59.6583i	0.158224	+	0.795445i
$76$	34.7579	+	14.3972i	0.457340	+	0.189437i
$77$	3.06990	−	7.41140i	0.0398689	−	0.0962520i
$78$	158.683	−	31.5639i	2.03439	−	0.404666i
$79$	−98.5655	−	65.8593i	−1.24766	−	0.833662i	−0.256531	−	0.966536i	$-0.582580\pi$
$79$	−98.5655	−	65.8593i	−1.24766	−	0.833662i	−0.991133	+	0.132874i	$0.957580\pi$
$80$	55.6023	+	11.0600i	0.695029	+	0.138250i
$81$	−57.2255	−	57.2255i	−0.706488	−	0.706488i
$82$	182.247	−	121.773i	2.22252	−	1.48504i
$83$	−86.9369	+	36.0104i	−1.04743	+	0.433861i	−0.838975	−	0.544171i	$-0.816844\pi$
$83$	−86.9369	+	36.0104i	−1.04743	+	0.433861i	−0.208458	+	0.978031i	$0.566844\pi$
$84$		−	70.4946i		−	0.839221i
$85$		0			0
$86$	154.264			1.79377
$87$	47.8171	+	115.441i	0.549621	+	1.32690i
$88$	0.421869	+	0.631372i	0.00479397	+	0.00717468i
$89$	19.6021	−	19.6021i	0.220248	−	0.220248i	−0.588355	−	0.808603i	$-0.700224\pi$
$89$	19.6021	−	19.6021i	0.220248	−	0.220248i	0.808603	+	0.588355i	$0.200224\pi$
$90$	−36.4555	+	183.274i	−0.405062	+	2.03638i
$91$	20.0545	−	30.0137i	0.220379	−	0.329821i
$92$	2.77001	+	13.9258i	0.0301088	+	0.151367i
$93$	132.961	+	55.0742i	1.42969	+	0.592195i
$94$	7.91883	−	19.1177i	0.0842428	−	0.203380i
$95$	−32.7351	+	6.51142i	−0.344580	+	0.0685412i
$96$	−196.700	−	131.430i	−2.04895	−	1.36907i
$97$	−14.9417	−	2.97209i	−0.154038	−	0.0306401i	0.117469	−	0.993077i	$-0.462522\pi$
$97$	−14.9417	−	2.97209i	−0.154038	−	0.0306401i	−0.271507	+	0.962437i	$0.587522\pi$
$98$	76.7240	+	76.7240i	0.782898	+	0.782898i
$99$	36.3629	−	24.2969i	0.367302	−	0.245424i
$100$	−44.4493	+	18.4115i	−0.444493	+	0.184115i
$101$		−	132.191i		−	1.30882i	−0.756140	−	0.654410i	$-0.772917\pi$
$101$		−	132.191i		−	1.30882i	0.756140	−	0.654410i	$-0.227083\pi$
$102$		0			0
$103$	−185.135			−1.79743			−0.898713	−	0.438536i	$-0.855497\pi$
$103$	−185.135			−1.79743			−0.898713	+	0.438536i	$0.855497\pi$
$104$	1.30757	+	3.15676i	0.0125728	+	0.0303535i
$105$	34.7454	+	52.0001i	0.330908	+	0.495239i
$106$	−114.828	+	114.828i	−1.08329	+	1.08329i
$107$	7.23785	−	36.3871i	0.0676434	−	0.340066i	−0.932112	−	0.362169i	$-0.882036\pi$
$107$	7.23785	−	36.3871i	0.0676434	−	0.340066i	0.999756	+	0.0221030i	$0.00703617\pi$
$108$	106.740	−	159.748i	0.988337	−	1.47915i
$109$	8.89084	+	44.6973i	0.0815673	+	0.410067i	0.999898	+	0.0142535i	$0.00453719\pi$
$109$	8.89084	+	44.6973i	0.0815673	+	0.410067i	−0.918331	+	0.395813i	$0.870463\pi$
$110$	−23.3097	−	9.65521i	−0.211907	−	0.0877747i
$111$	−76.5889	+	184.902i	−0.689990	+	1.66578i
$112$	−50.3453	+	10.0143i	−0.449511	+	0.0894134i
$113$	72.6645	+	48.5529i	0.643049	+	0.429671i	0.833876	−	0.551952i	$-0.186117\pi$
$113$	72.6645	+	48.5529i	0.643049	+	0.429671i	−0.190827	+	0.981624i	$0.561117\pi$
$114$	132.850	+	26.4255i	1.16535	+	0.231803i
$115$	−8.90702	−	8.90702i	−0.0774524	−	0.0774524i
$116$	−82.1755	+	54.9079i	−0.708409	+	0.473344i
$117$	181.809	−	75.3079i	1.55393	−	0.643657i
$118$		−	65.6503i		−	0.556359i
$119$		0			0
$120$	−5.91986			−0.0493322
$121$	−44.0450	−	106.334i	−0.364008	−	0.878794i
$122$	−65.6362	−	98.2315i	−0.538001	−	0.805176i
$123$	282.785	−	282.785i	2.29906	−	2.29906i
$124$	−22.2074	+	111.644i	−0.179092	+	0.900354i
$125$	74.3533	−	111.278i	0.594827	−	0.890221i
$126$	−33.0088	−	165.946i	−0.261975	−	1.31703i
$127$	102.264	+	42.3590i	0.805226	+	0.333535i	0.747047	−	0.664771i	$-0.231471\pi$
$127$	102.264	+	42.3590i	0.805226	+	0.333535i	0.0581782	+	0.998306i	$0.481471\pi$
$128$	3.82526	−	9.23501i	0.0298849	−	0.0721485i
$129$	276.056	−	54.9109i	2.13997	−	0.425666i
$130$	−94.3967	−	63.0738i	−0.726128	−	0.485183i
$131$	44.0168	+	8.75549i	0.336006	+	0.0668358i	0.360210	−	0.932871i	$-0.382705\pi$
$131$	44.0168	+	8.75549i	0.336006	+	0.0668358i	−0.0242037	+	0.999707i	$0.507705\pi$
$132$	36.6913	+	36.6913i	0.277964	+	0.277964i
$133$	25.1277	−	16.7898i	0.188930	−	0.126239i
$134$	−45.6838	+	18.9228i	−0.340924	+	0.141215i
$135$			170.448i			1.26258i
$136$		0			0
$137$	61.5009			0.448911			0.224456	−	0.974484i	$-0.427940\pi$
$137$	61.5009			0.448911			0.224456	+	0.974484i	$0.427940\pi$
$138$	19.5630	+	47.2293i	0.141761	+	0.342241i
$139$	−48.5334	−	72.6354i	−0.349161	−	0.522557i	0.614770	−	0.788706i	$-0.289249\pi$
$139$	−48.5334	−	72.6354i	−0.349161	−	0.522557i	−0.963932	+	0.266149i	$0.914249\pi$
$140$	−34.9780	+	34.9780i	−0.249843	+	0.249843i
$141$	7.36571	−	37.0299i	0.0522391	−	0.262623i
$142$	−81.6256	+	122.161i	−0.574828	+	0.860291i
$143$	5.18359	+	26.0597i	0.0362489	+	0.182235i
$144$	−258.540	−	107.091i	−1.79542	−	0.743686i
$145$	33.5535	−	81.0053i	0.231403	−	0.558657i
$146$	−173.628	+	34.5368i	−1.18923	+	0.236553i
$147$	164.608	+	109.987i	1.11978	+	0.748213i
$148$	−155.258	−	30.8827i	−1.04904	−	0.208667i
$149$	132.640	+	132.640i	0.890200	+	0.890200i	0.994541	−	0.104342i	$-0.0332736\pi$
$149$	132.640	+	132.640i	0.890200	+	0.890200i	−0.104342	+	0.994541i	$0.533274\pi$
$150$	−144.028	+	96.2364i	−0.960187	+	0.641576i
$151$	−199.707	+	82.7215i	−1.32257	+	0.547824i	−0.928525	−	0.371269i	$-0.878923\pi$
$151$	−199.707	+	82.7215i	−1.32257	+	0.547824i	−0.394040	+	0.919093i	$0.628923\pi$
$152$			2.86062i			0.0188198i
$153$		0			0
$154$	22.8448			0.148343
$155$	−38.6458	−	93.2993i	−0.249328	−	0.601931i
$156$	129.719	+	194.139i	0.831534	+	1.24448i
$157$	−111.042	+	111.042i	−0.707276	+	0.707276i	−0.965961	−	0.258686i	$-0.916711\pi$
$157$	−111.042	+	111.042i	−0.707276	+	0.707276i	0.258686	+	0.965961i	$0.416711\pi$
$158$	65.8593	−	331.097i	0.416831	−	2.09555i
$159$	−164.612	+	246.359i	−1.03529	+	1.54943i
$160$	32.3853	+	162.812i	0.202408	+	1.01757i
$161$	10.5373	+	4.36469i	0.0654490	+	0.0271099i
$162$	88.1957	−	212.923i	0.544418	−	1.31434i
$163$	−163.655	+	32.5530i	−1.00402	+	0.199712i	−0.669607	−	0.742715i	$-0.733538\pi$
$163$	−163.655	+	32.5530i	−1.00402	+	0.199712i	−0.334412	+	0.942427i	$0.608538\pi$
$164$	263.008	+	175.737i	1.60371	+	1.07156i
$165$	−45.1496	−	8.98081i	−0.273634	−	0.0544291i
$166$	−189.486	−	189.486i	−1.14148	−	1.14148i
$167$	44.7752	−	29.9178i	0.268115	−	0.179149i	−0.414244	−	0.910166i	$-0.635954\pi$
$167$	44.7752	−	29.9178i	0.268115	−	0.179149i	0.682359	+	0.731017i	$0.260954\pi$
$168$	4.95214	−	2.05124i	0.0294770	−	0.0122098i
$169$		−	49.4408i		−	0.292549i
$170$		0			0
$171$	164.753			0.963468
$172$	85.1953	+	205.680i	0.495321	+	1.19581i
$173$	−37.3651	−	55.9209i	−0.215983	−	0.323242i	0.707619	−	0.706594i	$-0.249769\pi$
$173$	−37.3651	−	55.9209i	−0.215983	−	0.323242i	−0.923602	+	0.383352i	$0.874769\pi$
$174$	−251.612	+	251.612i	−1.44605	+	1.44605i
$175$	−7.53969	+	37.9046i	−0.0430840	+	0.216598i
$176$	20.9916	−	31.4162i	0.119271	−	0.178501i
$177$	−23.3685	−	117.481i	−0.132025	−	0.663736i
$178$	72.9349	+	30.2106i	0.409747	+	0.169723i
$179$	96.0193	−	231.811i	0.536421	−	1.29503i	−0.390785	−	0.920482i	$-0.627797\pi$
$179$	96.0193	−	231.811i	0.536421	−	1.29503i	0.927206	−	0.374552i	$-0.122203\pi$
$180$	−264.492	+	52.6107i	−1.46940	+	0.292282i
$181$	14.2421	+	9.51629i	0.0786859	+	0.0525762i	0.594291	−	0.804250i	$-0.297433\pi$
$181$	14.2421	+	9.51629i	0.0786859	+	0.0525762i	−0.515605	+	0.856826i	$0.672433\pi$
$182$	100.821	+	20.0545i	0.553961	+	0.110190i
$183$	−152.422	−	152.422i	−0.832905	−	0.832905i
$184$	−0.897664	+	0.599800i	−0.00487861	+	0.00325978i
$185$	129.747	−	53.7428i	0.701333	−	0.290502i
$186$			409.837i			2.20343i
$187$		0			0
$188$	29.8629			0.158845
$189$	−59.0606	−	142.585i	−0.312490	−	0.754417i
$190$	−52.8058	−	79.0295i	−0.277925	−	0.415945i
$191$	79.7646	−	79.7646i	0.417615	−	0.417615i	−0.466766	−	0.884381i	$-0.654581\pi$
$191$	79.7646	−	79.7646i	0.417615	−	0.417615i	0.884381	+	0.466766i	$0.154581\pi$
$192$	68.3841	−	343.790i	0.356167	−	1.79057i
$193$	11.3804	−	17.0319i	0.0589656	−	0.0882482i	−0.800815	−	0.598911i	$-0.795600\pi$
$193$	11.3804	−	17.0319i	0.0589656	−	0.0882482i	0.859781	+	0.510663i	$0.170600\pi$
$194$	−8.46379	−	42.5503i	−0.0436278	−	0.219332i
$195$	−191.374	−	79.2697i	−0.981406	−	0.406511i
$196$	−59.9234	+	144.668i	−0.305732	+	0.738101i
$197$	40.4361	−	8.04325i	0.205260	−	0.0408287i	−0.0913895	−	0.995815i	$-0.529131\pi$
$197$	40.4361	−	8.04325i	0.205260	−	0.0408287i	0.296649	+	0.954987i	$0.404131\pi$
$198$	103.553	+	69.1918i	0.522994	+	0.349454i
$199$	−359.028	−	71.4150i	−1.80416	−	0.358870i	−0.825507	−	0.564392i	$-0.809110\pi$
$199$	−359.028	−	71.4150i	−1.80416	−	0.358870i	−0.978652	+	0.205523i	$0.934110\pi$
$200$	−2.58676	−	2.58676i	−0.0129338	−	0.0129338i
$201$	−75.0154	+	50.1237i	−0.373211	+	0.249372i
$202$	347.792	−	144.060i	1.72174	−	0.713170i
$203$			79.3897i			0.391082i
$204$		0			0
$205$	−280.624			−1.36890
$206$	−201.758	−	487.088i	−0.979409	−	2.36450i
$207$	34.5446	+	51.6997i	0.166882	+	0.249757i
$208$	120.221	−	120.221i	0.577985	−	0.577985i
$209$	−4.33974	+	21.8173i	−0.0207643	+	0.104389i
$210$	−98.9464	+	148.084i	−0.471173	+	0.705161i
$211$	−62.5770	−	314.596i	−0.296574	−	1.49098i	−0.785615	−	0.618716i	$-0.787653\pi$
$211$	−62.5770	−	314.596i	−0.296574	−	1.49098i	0.489041	−	0.872261i	$-0.337347\pi$
$212$	−216.516	−	89.6839i	−1.02130	−	0.423037i
$213$	−102.585	+	247.663i	−0.481621	+	1.16274i
$214$	103.622	−	20.6116i	0.484214	−	0.0963161i
$215$	−164.219	−	109.728i	−0.763811	−	0.510362i
$216$	14.3280	+	2.85002i	0.0663334	+	0.0131945i
$217$	64.6568	+	64.6568i	0.297958	+	0.297958i
$218$	−107.909	+	72.1023i	−0.494994	+	0.330745i
$219$	−298.414	+	123.607i	−1.36262	+	0.564415i
$220$		−	36.4110i		−	0.165504i
$221$		0			0
$222$	−569.940			−2.56730
$223$	−41.5859	−	100.397i	−0.186484	−	0.450211i	0.802794	−	0.596256i	$-0.203346\pi$
$223$	−41.5859	−	100.397i	−0.186484	−	0.450211i	−0.989278	+	0.146045i	$0.953346\pi$
$224$	−83.5058	−	124.975i	−0.372794	−	0.557925i
$225$	−148.981	+	148.981i	−0.662137	+	0.662137i
$226$	−48.5529	+	244.092i	−0.214836	+	1.08005i
$227$	109.633	−	164.078i	0.482966	−	0.722810i	−0.507335	−	0.861749i	$-0.669369\pi$
$227$	109.633	−	164.078i	0.482966	−	0.722810i	0.990301	+	0.138939i	$0.0443693\pi$
$228$	38.1359	+	191.722i	0.167263	+	0.840887i
$229$	−167.322	−	69.3072i	−0.730665	−	0.302651i	−0.0138399	−	0.999904i	$-0.504406\pi$
$229$	−167.322	−	69.3072i	−0.730665	−	0.302651i	−0.716825	+	0.697253i	$0.754406\pi$
$230$	13.7275	−	33.1410i	0.0596847	−	0.144091i
$231$	40.8808	−	8.13170i	0.176973	−	0.0352022i
$232$	−6.24833	−	4.17500i	−0.0269325	−	0.0179957i
$233$	−5.74492	−	1.14274i	−0.0246563	−	0.00490444i	0.182747	−	0.983160i	$-0.441501\pi$
$233$	−5.74492	−	1.14274i	−0.0246563	−	0.00490444i	−0.207403	+	0.978256i	$0.566501\pi$
$234$	396.268	+	396.268i	1.69345	+	1.69345i
$235$	−22.0282	+	14.7188i	−0.0937372	+	0.0626332i
$236$	87.5311	−	36.2566i	0.370895	−	0.153630i
$237$		−	615.941i		−	2.59891i
$238$		0			0
$239$	68.9414			0.288458			0.144229	−	0.989544i	$-0.453930\pi$
$239$	68.9414			0.288458			0.144229	+	0.989544i	$0.453930\pi$
$240$	112.725	+	272.142i	0.469686	+	1.13392i
$241$	172.160	+	257.655i	0.714355	+	1.06911i	0.994040	+	0.109016i	$0.0347700\pi$
$241$	172.160	+	257.655i	0.714355	+	1.06911i	−0.279685	+	0.960092i	$0.590230\pi$
$242$	231.764	−	231.764i	0.957701	−	0.957701i
$243$	−0.0479123	+	0.240872i	−0.000197170	+	0.000991241i
$244$	94.7226	−	141.762i	0.388207	−	0.580993i
$245$	−27.1016	−	136.249i	−0.110619	−	0.556117i
$246$	1052.18	+	435.826i	4.27715	+	1.77165i
$247$	−38.3050	+	92.4764i	−0.155081	+	0.374399i
$248$	−8.48901	+	1.68857i	−0.0342299	+	0.00680874i
$249$	−406.533	−	271.637i	−1.63266	−	1.09091i
$250$	373.799	+	74.3533i	1.49520	+	0.297413i
$251$	149.892	+	149.892i	0.597178	+	0.597178i	0.939561	−	0.342382i	$-0.111234\pi$
$251$	149.892	+	149.892i	0.597178	+	0.597178i	−0.342382	+	0.939561i	$0.611234\pi$
$252$	203.025	−	135.657i	0.805657	−	0.538323i
$253$	−7.75623	+	3.21274i	−0.0306571	+	0.0126986i
$254$			315.217i			1.24101i
$255$		0			0
$256$	−241.382			−0.942898
$257$	92.4689	+	223.240i	0.359801	+	0.868637i	0.995327	+	0.0965575i	$0.0307832\pi$
$257$	92.4689	+	223.240i	0.359801	+	0.868637i	−0.635526	+	0.772079i	$0.719217\pi$
$258$	445.313	+	666.458i	1.72602	+	2.58317i
$259$	−89.9150	+	89.9150i	−0.347162	+	0.347162i
$260$	31.9636	−	160.692i	0.122937	−	0.618046i
$261$	−240.453	+	359.864i	−0.921277	+	1.37879i
$262$	24.9335	+	125.349i	0.0951661	+	0.478432i
$263$	−221.046	−	91.5602i	−0.840479	−	0.348138i	−0.0794365	−	0.996840i	$-0.525312\pi$
$263$	−221.046	−	91.5602i	−0.840479	−	0.348138i	−0.761042	+	0.648702i	$0.775312\pi$
$264$	−1.50987	+	3.64515i	−0.00571920	+	0.0138074i
$265$	203.916	−	40.5614i	0.769493	−	0.153062i
$266$	71.5575	+	47.8132i	0.269013	+	0.179749i
$267$	141.271	+	28.1005i	0.529103	+	0.105245i
$268$	−50.4594	−	50.4594i	−0.188281	−	0.188281i
$269$	−9.41947	+	6.29389i	−0.0350166	+	0.0233973i	−0.572955	−	0.819587i	$-0.694203\pi$
$269$	−9.41947	+	6.29389i	−0.0350166	+	0.0233973i	0.537939	+	0.842984i	$0.319203\pi$
$270$	−448.446	+	185.753i	−1.66091	+	0.687973i
$271$			352.304i			1.30001i	0.759929	+	0.650007i	$0.225234\pi$
$271$			352.304i			1.30001i	−0.759929	+	0.650007i	$0.774766\pi$
$272$		0			0
$273$	187.557			0.687023
$274$	67.0230	+	161.808i	0.244610	+	0.590540i
$275$	−15.8044	−	23.6530i	−0.0574707	−	0.0860109i
$276$	−52.1665	+	52.1665i	−0.189009	+	0.189009i
$277$	18.1940	−	91.4673i	0.0656823	−	0.330207i	−0.933948	−	0.357410i	$-0.883660\pi$
$277$	18.1940	−	91.4673i	0.0656823	−	0.330207i	0.999630	+	0.0272028i	$0.00865997\pi$
$278$	138.212	−	206.848i	0.497164	−	0.744058i
$279$	97.2506	+	488.912i	0.348569	+	1.75237i
$280$	−3.47494	−	1.43937i	−0.0124105	−	0.00514060i
$281$	85.1913	−	205.670i	0.303172	−	0.731922i	−0.696722	−	0.717341i	$-0.745359\pi$
$281$	85.1913	−	205.670i	0.303172	−	0.731922i	0.999894	−	0.0145802i	$-0.00464119\pi$
$282$	105.452	−	20.9758i	0.373944	−	0.0743821i
$283$	−104.017	−	69.5017i	−0.367550	−	0.245589i	0.358055	−	0.933700i	$-0.383440\pi$
$283$	−104.017	−	69.5017i	−0.367550	−	0.245589i	−0.725605	+	0.688111i	$0.758440\pi$
$284$	−207.956	−	41.3650i	−0.732240	−	0.145652i
$285$	−122.627	−	122.627i	−0.430270	−	0.430270i
$286$	−62.9136	+	42.0375i	−0.219978	+	0.146984i
$287$	234.751	−	97.2369i	0.817946	−	0.338804i
$288$		−	819.418i		−	2.84520i
$289$		0			0
$290$	249.690			0.861000
$291$	−30.2919	−	73.1311i	−0.104096	−	0.251309i
$292$	−141.937	−	212.423i	−0.486085	−	0.727477i
$293$	−84.7101	+	84.7101i	−0.289113	+	0.289113i	−0.836729	−	0.547617i	$-0.815535\pi$
$293$	−84.7101	+	84.7101i	−0.289113	+	0.289113i	0.547617	+	0.836729i	$0.315535\pi$
$294$	−109.987	+	552.944i	−0.374107	+	1.88076i
$295$	−46.6969	+	69.8869i	−0.158295	+	0.236905i
$296$	−2.34821	−	11.8052i	−0.00793313	−	0.0398826i
$297$	104.953	+	43.4730i	0.353378	+	0.146374i
$298$	−204.424	+	493.523i	−0.685986	+	1.65612i
$299$	−37.0508	+	7.36986i	−0.123916	+	0.0246484i
$300$	−207.853	−	138.883i	−0.692845	−	0.462944i
$301$	175.395	+	34.8883i	0.582709	+	0.115908i
$302$	−435.278	−	435.278i	−1.44132	−	1.44132i
$303$	571.095	−	381.594i	1.88480	−	1.25938i
$304$	131.505	−	54.4712i	0.432583	−	0.179182i
$305$			151.257i			0.495926i
$306$		0			0
$307$	237.264			0.772846			0.386423	−	0.922322i	$-0.373711\pi$
$307$	237.264			0.772846			0.386423	+	0.922322i	$0.373711\pi$
$308$	12.6165	+	30.4589i	0.0409626	+	0.0988924i
$309$	−534.427	−	799.826i	−1.72954	−	2.58843i
$310$	203.353	−	203.353i	0.655979	−	0.655979i
$311$	−62.8072	+	315.753i	−0.201953	+	1.01528i	0.738213	+	0.674567i	$0.235670\pi$
$311$	−62.8072	+	315.753i	−0.201953	+	1.01528i	−0.940166	+	0.340717i	$0.889330\pi$
$312$	−9.86340	+	14.7616i	−0.0316135	+	0.0473129i
$313$	−61.4642	−	309.001i	−0.196371	−	0.987225i	−0.945703	−	0.325031i	$-0.894625\pi$
$313$	−61.4642	−	309.001i	−0.196371	−	0.987225i	0.749332	−	0.662194i	$-0.230375\pi$
$314$	−413.163	−	171.138i	−1.31581	−	0.545025i
$315$	−82.8983	+	200.134i	−0.263169	+	0.635347i
$316$	477.822	−	95.0446i	1.51209	−	0.300774i
$317$	266.949	+	178.370i	0.842111	+	0.562681i	0.900123	−	0.435635i	$-0.143476\pi$
$317$	266.949	+	178.370i	0.842111	+	0.562681i	−0.0580122	+	0.998316i	$0.518476\pi$
$318$	−827.559	−	164.612i	−2.60239	−	0.517647i
$319$	−41.3210	−	41.3210i	−0.129533	−	0.129533i
$320$	−204.513	+	136.651i	−0.639103	+	0.427035i
$321$	178.094	−	73.7690i	0.554811	−	0.229810i
$322$			32.4801i			0.100870i
$323$		0			0
$324$	332.597			1.02653
$325$	−48.9855	−	118.262i	−0.150725	−	0.363882i
$326$	−263.996	−	395.098i	−0.809805	−	1.21196i
$327$	−167.437	+	167.437i	−0.512041	+	0.512041i
$328$	−4.69225	+	23.5895i	−0.0143056	+	0.0719193i
$329$	13.3272	−	19.9455i	0.0405082	−	0.0606247i
$330$	−25.5752	−	128.575i	−0.0775006	−	0.389622i
$331$	24.6962	+	10.2295i	0.0746109	+	0.0309049i	0.419677	−	0.907674i	$-0.362143\pi$
$331$	24.6962	+	10.2295i	0.0746109	+	0.0309049i	−0.345066	+	0.938578i	$0.612143\pi$
$332$	147.993	−	357.287i	0.445763	−	1.07617i
$333$	−679.905	+	135.242i	−2.04176	+	0.406131i
$334$	127.509	+	85.1987i	0.381763	+	0.255086i
$335$	62.0916	+	12.3508i	0.185348	+	0.0368680i
$336$	−188.595	−	188.595i	−0.561295	−	0.561295i
$337$	−406.888	+	271.874i	−1.20738	+	0.806748i	−0.985723	−	0.168375i	$-0.946148\pi$
$337$	−406.888	+	271.874i	−1.20738	+	0.806748i	−0.221661	+	0.975124i	$0.571148\pi$
$338$	130.078	−	53.8801i	0.384846	−	0.159409i
$339$			454.084i			1.33948i
$340$		0			0
$341$	−67.3056			−0.197377
$342$	179.546	+	433.463i	0.524989	+	1.26744i
$343$	159.752	+	239.086i	0.465750	+	0.697043i
$344$	−11.9697	+	11.9697i	−0.0347956	+	0.0347956i
$345$	12.7686	−	64.1922i	0.0370105	−	0.186064i
$346$	106.407	−	159.249i	0.307534	−	0.460258i
$347$	47.1829	+	237.204i	0.135974	+	0.683586i	0.987289	+	0.158932i	$0.0508052\pi$
$347$	47.1829	+	237.204i	0.135974	+	0.683586i	−0.851316	+	0.524654i	$0.824195\pi$
$348$	−474.430	−	196.515i	−1.36330	−	0.564699i
$349$	−15.1979	+	36.6909i	−0.0435470	+	0.105132i	−0.944156	−	0.329498i	$-0.893121\pi$
$349$	−15.1979	+	36.6909i	−0.0435470	+	0.105132i	0.900609	+	0.434629i	$0.143121\pi$
$350$	−107.943	+	21.4712i	−0.308409	+	0.0613464i
$351$	425.025	+	283.993i	1.21090	+	0.809096i
$352$	108.511	+	21.5842i	0.308270	+	0.0613187i
$353$	−451.955	−	451.955i	−1.28033	−	1.28033i	−0.940482	−	0.339843i	$-0.889626\pi$
$353$	−451.955	−	451.955i	−1.28033	−	1.28033i	−0.339843	−	0.940482i	$-0.610374\pi$
$354$	283.625	−	189.512i	0.801200	−	0.535345i
$355$	173.786	−	71.9846i	0.489538	−	0.202773i
$356$			113.928i			0.320022i
$357$		0			0
$358$	714.533			1.99590
$359$	78.0349	+	188.393i	0.217367	+	0.524771i	0.994521	−	0.104540i	$-0.0333370\pi$
$359$	78.0349	+	188.393i	0.217367	+	0.524771i	−0.777153	+	0.629311i	$0.783337\pi$
$360$	−11.3920	−	17.0493i	−0.0316444	−	0.0473591i
$361$	196.009	−	196.009i	0.542962	−	0.542962i
$362$	−9.51629	+	47.8416i	−0.0262881	+	0.132159i
$363$	332.244	−	497.238i	0.915272	−	1.36980i
$364$	28.9416	+	145.499i	0.0795098	+	0.399723i
$365$	209.398	+	86.7357i	0.573694	+	0.237632i
$366$	234.912	−	567.127i	0.641835	−	1.54953i
$367$	276.557	−	55.0107i	0.753563	−	0.149893i	0.196661	−	0.980472i	$-0.436990\pi$
$367$	276.557	−	55.0107i	0.753563	−	0.149893i	0.556901	+	0.830579i	$0.311990\pi$
$368$	44.6665	+	29.8452i	0.121376	+	0.0811011i
$369$	1358.60	+	270.243i	3.68185	+	0.732366i
$370$	282.793	+	282.793i	0.764306	+	0.764306i
$371$	−156.527	+	104.588i	−0.421906	+	0.281908i
$372$	−546.433	+	226.340i	−1.46891	+	0.608441i
$373$		−	340.976i		−	0.914144i	−0.889430	−	0.457072i	$-0.848898\pi$
$373$		−	340.976i		−	0.914144i	0.889430	−	0.457072i	$-0.151102\pi$
$374$		0			0
$375$	695.380			1.85435
$376$	0.868946	+	2.09782i	0.00231103	+	0.00557931i
$377$	−146.087	−	218.635i	−0.387500	−	0.579935i
$378$	310.775	−	310.775i	0.822156	−	0.822156i
$379$	69.8686	−	351.253i	0.184350	−	0.926790i	−0.772235	−	0.635337i	$-0.780861\pi$
$379$	69.8686	−	351.253i	0.184350	−	0.926790i	0.956585	−	0.291453i	$-0.0941387\pi$
$380$	76.2065	−	114.051i	0.200544	−	0.300135i
$381$	112.202	+	564.080i	0.294495	+	1.48052i
$382$	296.786	+	122.933i	0.776927	+	0.321814i
$383$	92.5645	−	223.470i	0.241683	−	0.583474i	−0.755767	−	0.654840i	$-0.772736\pi$
$383$	92.5645	−	223.470i	0.241683	−	0.583474i	0.997450	+	0.0713664i	$0.0227360\pi$
$384$	50.9397	−	10.1325i	0.132656	−	0.0263868i
$385$	−24.3191	−	16.2495i	−0.0631664	−	0.0422064i
$386$	57.2129	+	11.3804i	0.148220	+	0.0294828i
$387$	689.377	+	689.377i	1.78134	+	1.78134i
$388$	52.0578	−	34.7839i	0.134170	−	0.0896492i
$389$	−619.174	+	256.470i	−1.59171	+	0.659307i	−0.990212	−	0.139570i	$-0.955428\pi$
$389$	−619.174	+	256.470i	−1.59171	+	0.659307i	−0.601495	+	0.798877i	$0.705428\pi$
$390$		−	589.890i		−	1.51254i
$391$		0			0
$392$	−11.9063			−0.0303733
$393$	89.2370	+	215.437i	0.227066	+	0.548186i
$394$	65.2286	+	97.6215i	0.165555	+	0.247770i
$395$	−305.618	+	305.618i	−0.773716	+	0.773716i
$396$	−35.0640	+	176.279i	−0.0885455	+	0.445148i
$397$	−248.868	+	372.457i	−0.626871	+	0.938179i	0.373075	+	0.927801i	$0.378303\pi$
$397$	−248.868	+	372.457i	−0.626871	+	0.938179i	−0.999946	+	0.0103776i	$0.996697\pi$
$398$	−203.373	−	1022.42i	−0.510987	−	2.56890i
$399$	145.071	+	60.0906i	0.363588	+	0.150603i
$400$	−69.6594	+	168.173i	−0.174148	+	0.420431i
$401$	−136.334	+	27.1185i	−0.339985	+	0.0676272i	−0.362130	−	0.932128i	$-0.617950\pi$
$401$	−136.334	+	27.1185i	−0.339985	+	0.0676272i	0.0221452	+	0.999755i	$0.492950\pi$
$402$	−213.626	−	142.740i	−0.531407	−	0.355075i
$403$	−297.039	−	59.0847i	−0.737069	−	0.146612i
$404$	384.149	+	384.149i	0.950864	+	0.950864i
$405$	−245.339	+	163.930i	−0.605775	+	0.404766i
$406$	−208.873	+	86.5181i	−0.514466	+	0.213099i
$407$		−	93.5985i		−	0.229972i
$408$		0			0
$409$	−404.559			−0.989142			−0.494571	−	0.869137i	$-0.664675\pi$
$409$	−404.559			−0.989142			−0.494571	+	0.869137i	$0.664675\pi$
$410$	−305.822	−	738.319i	−0.745907	−	1.80078i
$411$	177.534	+	265.698i	0.431956	+	0.646467i
$412$	538.006	−	538.006i	1.30584	−	1.30584i
$413$	14.8474	−	74.6430i	0.0359502	−	0.180734i
$414$	−98.3747	+	147.228i	−0.237620	+	0.355624i
$415$	66.9330	+	336.495i	0.161284	+	0.810831i
$416$	459.942	+	190.514i	1.10563	+	0.457967i
$417$	173.701	−	419.352i	0.416549	−	1.00564i
$418$	−62.1305	+	12.3585i	−0.148638	+	0.0295659i
$419$	217.250	+	145.162i	0.518496	+	0.346448i	0.787123	−	0.616796i	$-0.211570\pi$
$419$	217.250	+	145.162i	0.518496	+	0.346448i	−0.268627	+	0.963244i	$0.586570\pi$
$420$	−252.084	−	50.1426i	−0.600200	−	0.119387i
$421$	429.955	+	429.955i	1.02127	+	1.02127i	0.999769	+	0.0215010i	$0.00684449\pi$
$421$	429.955	+	429.955i	1.02127	+	1.02127i	0.0215010	+	0.999769i	$0.493156\pi$
$422$	759.502	−	507.483i	1.79977	−	1.20257i
$423$	120.821	−	50.0457i	0.285629	−	0.118311i
$424$		−	17.8195i		−	0.0420272i
$425$		0			0
$426$	−763.393			−1.79200
$427$	−52.4110	−	126.531i	−0.122742	−	0.296326i
$428$	84.7083	+	126.775i	0.197917	+	0.296203i
$429$	−97.6204	+	97.6204i	−0.227553	+	0.227553i
$430$	109.728	−	551.639i	0.255181	−	1.28288i
$431$	355.752	−	532.421i	0.825412	−	1.23532i	−0.143927	−	0.989588i	$-0.545973\pi$
$431$	355.752	−	532.421i	0.825412	−	1.23532i	0.969339	−	0.245728i	$-0.0790269\pi$
$432$	−141.813	−	712.941i	−0.328271	−	1.65033i
$433$	−590.594	−	244.632i	−1.36396	−	0.564971i	−0.423816	−	0.905748i	$-0.639310\pi$
$433$	−590.594	−	244.632i	−1.36396	−	0.564971i	−0.940144	+	0.340778i	$0.889310\pi$
$434$	−99.6488	+	240.573i	−0.229605	+	0.554317i
$435$	446.820	−	88.8780i	1.02717	−	0.204317i
$436$	−155.728	−	104.054i	−0.357174	−	0.238656i
$437$	−31.0192	−	6.17010i	−0.0709821	−	0.0141192i
$438$	−650.416	−	650.416i	−1.48497	−	1.48497i
$439$	−586.307	+	391.758i	−1.33555	+	0.892386i	−0.998789	−	0.0492039i	$-0.984332\pi$
$439$	−586.307	+	391.758i	−1.33555	+	0.892386i	−0.336761	+	0.941590i	$0.609332\pi$
$440$	2.55782	−	1.05948i	0.00581322	−	0.00240792i
$441$			685.729i			1.55494i
$442$		0			0
$443$	−317.185			−0.715994			−0.357997	−	0.933723i	$-0.616540\pi$
$443$	−317.185			−0.715994			−0.357997	+	0.933723i	$0.616540\pi$
$444$	−314.760	−	759.898i	−0.708919	−	1.71148i
$445$	−56.1528	−	84.0386i	−0.126186	−	0.188851i
$446$	218.824	−	218.824i	0.490636	−	0.490636i
$447$	−190.145	+	955.924i	−0.425381	+	2.13853i
$448$	123.731	−	185.177i	0.276186	−	0.413341i
$449$	47.9801	+	241.212i	0.106860	+	0.537222i	0.996716	+	0.0809796i	$0.0258049\pi$
$449$	47.9801	+	241.212i	0.106860	+	0.537222i	−0.889856	+	0.456242i	$0.849195\pi$
$450$	−554.325	−	229.609i	−1.23183	−	0.510242i
$451$	−71.5736	+	172.794i	−0.158700	+	0.383135i
$452$	−352.260	+	70.0689i	−0.779336	+	0.155020i
$453$	−933.869	−	623.991i	−2.06152	−	1.37746i
$454$	551.164	+	109.633i	1.21402	+	0.241483i
$455$	−93.0622	−	93.0622i	−0.204532	−	0.204532i
$456$	−12.3585	+	8.25770i	−0.0271020	+	0.0181090i
$457$	343.798	−	142.406i	0.752293	−	0.311610i	0.0266163	−	0.999646i	$-0.491527\pi$
$457$	343.798	−	142.406i	0.752293	−	0.311610i	0.725677	+	0.688036i	$0.241527\pi$
$458$		−	515.753i		−	1.12610i
$459$		0			0
$460$	51.7680			0.112539
$461$	329.689	+	795.940i	0.715161	+	1.72655i	0.686683	+	0.726957i	$0.259066\pi$
$461$	329.689	+	795.940i	0.715161	+	1.72655i	0.0284783	+	0.999594i	$0.490934\pi$
$462$	65.9459	+	98.6951i	0.142740	+	0.213626i
$463$	−386.172	+	386.172i	−0.834065	+	0.834065i	−0.988070	−	0.154005i	$-0.950783\pi$
$463$	−386.172	+	386.172i	−0.834065	+	0.834065i	0.154005	+	0.988070i	$0.450783\pi$
$464$	−72.9494	+	366.741i	−0.157218	+	0.790391i
$465$	291.516	−	436.285i	0.626917	−	0.938247i
$466$	−3.25423	−	16.3601i	−0.00698333	−	0.0351076i
$467$	374.194	+	154.996i	0.801272	+	0.331898i	0.745466	−	0.666544i	$-0.232227\pi$
$467$	374.194	+	154.996i	0.801272	+	0.331898i	0.0558061	+	0.998442i	$0.482227\pi$
$468$	−309.495	+	747.187i	−0.661314	+	1.59655i
$469$	−56.2210	+	11.1831i	−0.119874	+	0.0238445i
$470$	−62.7311	−	41.9156i	−0.133470	−	0.0891821i
$471$	−800.273	−	159.184i	−1.69909	−	0.337971i
$472$	5.09394	+	5.09394i	0.0107922	+	0.0107922i
$473$	−109.449	+	73.1316i	−0.231394	+	0.154612i
$474$	1620.53	−	671.246i	3.41884	−	1.41613i
$475$		−	107.167i		−	0.225615i
$476$		0			0
$477$	−1026.29			−2.15155
$478$	75.1317	+	181.384i	0.157179	+	0.379464i
$479$	−66.8122	−	99.9916i	−0.139483	−	0.208751i	0.755151	−	0.655551i	$-0.227564\pi$
$479$	−66.8122	−	99.9916i	−0.139483	−	0.208751i	−0.894634	+	0.446800i	$0.852564\pi$
$480$	−609.898	+	609.898i	−1.27062	+	1.27062i
$481$	82.1661	−	413.077i	0.170823	−	0.858788i
$482$	−490.269	+	733.739i	−1.01716	+	1.52228i
$483$	11.5614	+	58.1230i	0.0239366	+	0.120338i
$484$	437.005	+	181.013i	0.902902	+	0.373994i
$485$	−21.2560	+	51.3164i	−0.0438267	+	0.105807i
$486$	−0.685944	+	0.136443i	−0.00141141	+	0.000280747i
$487$	673.901	+	450.287i	1.38378	+	0.924613i	0.999999	+	0.00118928i	$0.000378561\pi$
$487$	673.901	+	450.287i	1.38378	+	0.924613i	0.383782	+	0.923424i	$0.374621\pi$
$488$	12.7148	+	2.52914i	0.0260550	+	0.00518265i
$489$	−613.058	−	613.058i	−1.25370	−	1.25370i
$490$	328.934	−	219.786i	0.671293	−	0.448544i
$491$	−139.166	+	57.6444i	−0.283433	+	0.117402i	−0.519871	−	0.854245i	$-0.674020\pi$
$491$	−139.166	+	57.6444i	−0.283433	+	0.117402i	0.236438	+	0.971647i	$0.424020\pi$
$492$			1643.55i			3.34056i
$493$		0			0
$494$	−285.049			−0.577022
$495$	−61.0194	−	147.314i	−0.123271	−	0.297604i
$496$	239.271	+	358.094i	0.482401	+	0.721964i
$497$	−120.434	+	120.434i	−0.242323	+	0.242323i
$498$	271.637	−	1365.61i	0.545455	−	2.74219i
$499$	−457.780	+	685.116i	−0.917394	+	1.37298i	0.0104246	+	0.999946i	$0.496682\pi$
$499$	−457.780	+	685.116i	−0.917394	+	1.37298i	−0.927819	+	0.373032i	$0.878318\pi$
$500$	107.303	+	539.447i	0.214605	+	1.07889i
$501$	258.504	+	107.076i	0.515976	+	0.213724i
$502$	−231.013	+	557.714i	−0.460185	+	1.11098i
$503$	−663.866	+	132.051i	−1.31981	+	0.262527i	−0.804233	−	0.594314i	$-0.797424\pi$
$503$	−663.866	+	132.051i	−1.31981	+	0.262527i	−0.515580	+	0.856841i	$0.672424\pi$
$504$	15.4373	+	10.3149i	0.0306296	+	0.0204661i
$505$	−472.706	−	94.0270i	−0.936051	−	0.186192i
$506$	−16.9053	−	16.9053i	−0.0334098	−	0.0334098i
$507$	213.596	−	142.720i	0.421293	−	0.281499i
$508$	−420.276	+	174.084i	−0.827315	+	0.342685i
$509$		−	340.603i		−	0.669161i	−0.942367	−	0.334581i	$-0.891405\pi$
$509$		−	340.603i		−	0.669161i	0.942367	−	0.334581i	$-0.108595\pi$
$510$		0			0
$511$	−205.222			−0.401609
$512$	−278.357	−	672.012i	−0.543665	−	1.31252i
$513$	237.761	+	355.834i	0.463471	+	0.693633i
$514$	−486.569	+	486.569i	−0.946632	+	0.946632i
$515$	−131.686	+	662.030i	−0.255701	+	1.28550i
$516$	−642.652	+	961.796i	−1.24545	+	1.86395i
$517$	3.44475	+	17.3179i	0.00666295	+	0.0334969i
$518$	−334.553	−	138.577i	−0.645856	−	0.267522i
$519$	133.730	−	322.852i	0.257668	−	0.622066i
$520$	12.2185	−	2.43040i	0.0234970	−	0.00467385i
$521$	−374.731	−	250.387i	−0.719253	−	0.480590i	0.141289	−	0.989968i	$-0.454875\pi$
$521$	−374.731	−	250.387i	−0.719253	−	0.480590i	−0.860542	+	0.509379i	$0.829875\pi$
$522$	−1208.84	−	240.453i	−2.31579	−	0.460638i
$523$	425.914	+	425.914i	0.814367	+	0.814367i	0.985285	−	0.170918i	$-0.0546734\pi$
$523$	425.914	+	425.914i	0.814367	+	0.814367i	−0.170918	+	0.985285i	$0.554673\pi$
$524$	−153.357	+	102.470i	−0.292667	+	0.195554i
$525$	−185.521	+	76.8455i	−0.353374	+	0.146372i
$526$		−	681.350i		−	1.29534i
$527$		0			0
$528$	196.321			0.371821
$529$	197.872	+	477.705i	0.374049	+	0.903033i
$530$	328.942	+	492.296i	0.620645	+	0.928861i
$531$	293.378	−	293.378i	0.552501	−	0.552501i
$532$	−24.2301	+	121.813i	−0.0455453	+	0.228972i
$533$	−467.563	+	699.758i	−0.877229	+	1.31287i
$534$	80.0234	+	402.305i	0.149856	+	0.753379i
$535$	−124.970	−	51.7641i	−0.233588	−	0.0967554i
$536$	2.07643	−	5.01296i	0.00387395	−	0.00935253i
$537$	1278.66	−	254.340i	2.38111	−	0.473632i
$538$	−26.8244	−	17.9235i	−0.0498594	−	0.0333150i
$539$	−90.8073	−	18.0627i	−0.168474	−	0.0335115i
$540$	−495.325	−	495.325i	−0.917269	−	0.917269i
$541$	406.212	−	271.422i	0.750855	−	0.501705i	−0.120286	−	0.992739i	$-0.538381\pi$
$541$	406.212	−	271.422i	0.750855	−	0.501705i	0.871140	+	0.491034i	$0.163381\pi$
$542$	−926.906	+	383.937i	−1.71016	+	0.708371i
$543$			88.9999i			0.163904i
$544$		0			0
$545$	166.158			0.304878
$546$	204.398	+	493.460i	0.374355	+	0.903774i
$547$	209.264	+	313.185i	0.382566	+	0.572551i	0.971916	−	0.235327i	$-0.0756161\pi$
$547$	209.264	+	313.185i	0.382566	+	0.572551i	−0.589350	+	0.807878i	$0.700616\pi$
$548$	−178.723	+	178.723i	−0.326136	+	0.326136i
$549$	145.662	−	732.292i	0.265322	−	1.33386i
$550$	45.0072	−	67.3581i	0.0818313	−	0.122469i
$551$	−42.9480	−	215.914i	−0.0779455	−	0.391858i
$552$	−5.18255	−	2.14668i	−0.00938868	−	0.00388892i
$553$	149.761	−	361.556i	0.270816	−	0.653808i
$554$	260.477	−	51.8121i	0.470175	−	0.0935236i
$555$	606.720	+	405.397i	1.09319	+	0.730445i
$556$	352.119	+	70.0408i	0.633308	+	0.125973i
$557$	58.1418	+	58.1418i	0.104384	+	0.104384i	0.757370	−	0.652986i	$-0.226484\pi$
$557$	58.1418	+	58.1418i	0.104384	+	0.104384i	−0.652986	+	0.757370i	$0.726484\pi$
$558$	−1180.34	+	788.677i	−2.11530	+	1.41340i
$559$	−547.229	+	226.670i	−0.978943	+	0.405492i
$560$			187.155i			0.334205i
$561$		0			0
$562$	633.956			1.12803
$563$	93.7832	+	226.413i	0.166578	+	0.402154i	0.985021	−	0.172433i	$-0.0551628\pi$
$563$	93.7832	+	226.413i	0.166578	+	0.402154i	−0.818444	+	0.574587i	$0.805163\pi$
$564$	86.2047	+	129.015i	0.152845	+	0.228749i
$565$	225.308	−	225.308i	0.398775	−	0.398775i
$566$	69.5017	−	349.409i	0.122794	−	0.617330i
$567$	148.431	−	222.143i	0.261783	−	0.391787i
$568$	−3.14525	−	15.8122i	−0.00553741	−	0.0278385i
$569$	−35.1685	−	14.5673i	−0.0618076	−	0.0256015i	0.351565	−	0.936163i	$-0.385649\pi$
$569$	−35.1685	−	14.5673i	−0.0618076	−	0.0256015i	−0.413373	+	0.910562i	$0.635649\pi$
$570$	188.992	−	456.267i	0.331565	−	0.800469i
$571$	55.6344	−	11.0664i	0.0974332	−	0.0193807i	−0.146133	−	0.989265i	$-0.546683\pi$
$571$	55.6344	−	11.0664i	0.0974332	−	0.0193807i	0.243566	+	0.969884i	$0.421683\pi$
$572$	−90.7935	−	60.6663i	−0.158730	−	0.106060i
$573$	574.857	+	114.346i	1.00324	+	0.199557i
$574$	511.658	+	511.658i	0.891390	+	0.891390i
$575$	33.6291	−	22.4702i	0.0584854	−	0.0390787i
$576$	1121.72	−	464.630i	1.94743	−	0.806650i
$577$			711.158i			1.23251i	0.787547	+	0.616255i	$0.211351\pi$
$577$			711.158i			1.23251i	−0.787547	+	0.616255i	$0.788649\pi$
$578$		0			0
$579$	106.433			0.183823
$580$	137.896	+	332.910i	0.237751	+	0.573983i
$581$	−172.587	−	258.295i	−0.297052	−	0.444570i
$582$	159.395	−	159.395i	0.273875	−	0.273875i
$583$	27.0334	−	135.906i	0.0463694	−	0.233115i
$584$	10.7924	−	16.1519i	0.0184801	−	0.0276574i
$585$	−139.975	−	703.704i	−0.239274	−	1.20291i
$586$	−315.187	−	130.555i	−0.537862	−	0.222790i
$587$	−358.692	+	865.959i	−0.611060	+	1.47523i	0.250778	+	0.968045i	$0.419314\pi$
$587$	−358.692	+	865.959i	−0.611060	+	1.47523i	−0.861838	+	0.507184i	$0.830686\pi$
$588$	−797.979	+	158.728i	−1.35711	+	0.269945i
$589$	−210.823	−	140.868i	−0.357934	−	0.239164i
$590$	−234.761	−	46.6969i	−0.397900	−	0.0791473i
$591$	151.475	+	151.475i	0.256303	+	0.256303i
$592$	−497.984	+	332.742i	−0.841189	+	0.562064i
$593$	858.785	−	355.720i	1.44820	−	0.599865i	0.486432	−	0.873719i	$-0.338298\pi$
$593$	858.785	−	355.720i	1.44820	−	0.599865i	0.961772	+	0.273853i	$0.0882982\pi$
$594$			323.507i			0.544624i
$595$		0			0
$596$	−770.907			−1.29347
$597$	−727.871	−	1757.24i	−1.21921	−	2.94344i
$598$	−59.7676	−	89.4485i	−0.0999458	−	0.149579i
$599$	−278.647	+	278.647i	−0.465187	+	0.465187i	−0.900351	−	0.435164i	$-0.856690\pi$
$599$	−278.647	+	278.647i	−0.465187	+	0.465187i	0.435164	+	0.900351i	$0.356690\pi$
$600$	3.70824	−	18.6426i	0.00618041	−	0.0310710i
$601$	−280.477	+	419.764i	−0.466684	+	0.698442i	−0.987919	−	0.154971i	$-0.950472\pi$
$601$	−280.477	+	419.764i	−0.466684	+	0.698442i	0.521235	+	0.853413i	$0.325472\pi$
$602$	99.3534	+	499.484i	0.165039	+	0.829707i
$603$	−288.714	−	119.589i	−0.478796	−	0.198324i
$604$	339.963	−	820.744i	0.562853	−	1.35885i
$605$	−411.573	+	81.8669i	−0.680285	+	0.135317i
$606$	1626.34	+	1086.69i	2.68373	+	1.79321i
$607$	302.742	+	60.2190i	0.498750	+	0.0992076i	0.438054	−	0.898949i	$-0.355668\pi$
$607$	302.742	+	60.2190i	0.498750	+	0.0992076i	0.0606964	+	0.998156i	$0.480668\pi$
$608$	294.717	+	294.717i	0.484732	+	0.484732i
$609$	−342.982	+	229.173i	−0.563189	+	0.376311i
$610$	−397.956	+	164.839i	−0.652387	+	0.270228i
$611$			79.4528i			0.130037i
$612$		0			0
$613$	116.450			0.189967			0.0949835	−	0.995479i	$-0.469720\pi$
$613$	116.450			0.189967			0.0949835	+	0.995479i	$0.469720\pi$
$614$	258.568	+	624.237i	0.421120	+	1.01667i
$615$	−810.075	−	1212.36i	−1.31719	−	1.97132i
$616$	−1.77258	+	1.77258i	−0.00287756	+	0.00287756i
$617$	124.062	−	623.701i	0.201073	−	1.01086i	−0.739987	−	0.672621i	$-0.765169\pi$
$617$	124.062	−	623.701i	0.201073	−	1.01086i	0.941060	−	0.338239i	$-0.109831\pi$
$618$	1521.92	−	2277.71i	2.46265	−	3.68562i
$619$	−114.897	−	577.626i	−0.185617	−	0.933160i	−0.955504	−	0.294980i	$-0.904687\pi$
$619$	−114.897	−	577.626i	−0.185617	−	0.933160i	0.769886	−	0.638181i	$-0.220313\pi$
$620$	383.435	+	158.824i	0.618444	+	0.256168i
$621$	−61.8085	+	149.219i	−0.0995306	+	0.240288i
$622$	−899.189	+	178.860i	−1.44564	+	0.287556i
$623$	76.0930	+	50.8437i	0.122140	+	0.0816111i
$624$	866.422	+	172.342i	1.38850	+	0.276189i
$625$	−138.086	−	138.086i	−0.220938	−	0.220938i
$626$	745.995	−	498.458i	1.19169	−	0.796259i
$627$	−106.783	+	44.2311i	−0.170309	+	0.0705441i
$628$		−	645.382i		−	1.02768i
$629$		0			0
$630$	−616.892			−0.979194
$631$	−414.694	−	1001.16i	−0.657201	−	1.58662i	−0.802108	−	0.597179i	$-0.796288\pi$
$631$	−414.694	−	1001.16i	−0.657201	−	1.58662i	0.144906	−	0.989445i	$-0.453712\pi$
$632$	20.5803	+	30.8007i	0.0325638	+	0.0487352i
$633$	1178.49	−	1178.49i	1.86175	−	1.86175i
$634$	−178.370	+	896.725i	−0.281340	+	1.41439i
$635$	224.213	−	335.558i	0.353091	−	0.528438i
$636$	−237.559	−	1194.29i	−0.373520	−	1.87781i
$637$	−384.902	−	159.432i	−0.604242	−	0.250285i
$638$	63.6838	−	153.746i	0.0998178	−	0.240982i
$639$	−910.683	+	181.146i	−1.42517	+	0.283484i
$640$	−30.3029	−	20.2477i	−0.0473482	−	0.0316371i
$641$	545.664	+	108.539i	0.851269	+	0.169328i	0.601397	−	0.798951i	$-0.294611\pi$
$641$	545.664	+	108.539i	0.851269	+	0.169328i	0.249873	+	0.968279i	$0.419611\pi$
$642$	388.171	+	388.171i	0.604627	+	0.604627i
$643$	90.3509	−	60.3706i	0.140515	−	0.0938889i	−0.483326	−	0.875440i	$-0.660571\pi$
$643$	90.3509	−	60.3706i	0.140515	−	0.0938889i	0.623841	+	0.781552i	$0.285571\pi$
$644$	−43.3054	+	17.9377i	−0.0672445	+	0.0278536i
$645$		−	1026.22i		−	1.59103i
$646$		0			0
$647$	1175.55			1.81693			0.908463	−	0.417966i	$-0.137257\pi$
$647$	1175.55			1.81693			0.908463	+	0.417966i	$0.137257\pi$
$648$	9.67787	+	23.3644i	0.0149350	+	0.0360562i
$649$	31.1226	+	46.5783i	0.0479547	+	0.0717693i
$650$	257.760	−	257.760i	0.396555	−	0.396555i
$651$	−92.6884	+	465.976i	−0.142379	+	0.715785i
$652$	380.985	−	570.185i	0.584333	−	0.874516i
$653$	132.779	+	667.525i	0.203337	+	1.02224i	0.938743	+	0.344617i	$0.111991\pi$
$653$	132.779	+	667.525i	0.203337	+	1.02224i	−0.735407	+	0.677626i	$0.763009\pi$
$654$	−622.997	−	258.054i	−0.952596	−	0.394578i
$655$	62.6181	−	151.173i	0.0956001	−	0.230799i
$656$	1173.78	−	233.480i	1.78930	−	0.355914i
$657$	−930.246	−	621.571i	−1.41590	−	0.946074i
$658$	67.0003	+	13.3272i	0.101824	+	0.0202541i
$659$	−542.829	−	542.829i	−0.823716	−	0.823716i	0.162923	−	0.986639i	$-0.447908\pi$
$659$	−542.829	−	542.829i	−0.823716	−	0.823716i	−0.986639	+	0.162923i	$0.947908\pi$
$660$	157.304	−	105.107i	0.238339	−	0.159253i
$661$	84.7509	−	35.1050i	0.128216	−	0.0531089i	−0.317653	−	0.948207i	$-0.602895\pi$
$661$	84.7509	−	35.1050i	0.128216	−	0.0531089i	0.445869	+	0.895098i	$0.352895\pi$
$662$			76.1234i			0.114990i
$663$		0			0
$664$	29.4052			0.0442849
$665$	−42.1659	−	101.797i	−0.0634073	−	0.153079i
$666$	−1096.77	−	1641.44i	−1.64681	−	2.46462i
$667$	58.7489	−	58.7489i	0.0880793	−	0.0880793i
$668$	−43.1758	+	217.059i	−0.0646344	+	0.324939i
$669$	313.694	−	469.476i	0.468899	−	0.701757i
$670$	35.1721	+	176.822i	0.0524956	+	0.263913i
$671$	93.1365	+	38.5784i	0.138803	+	0.0574939i
$672$	298.867	−	721.529i	0.444743	−	1.07370i
$673$	166.460	−	33.1109i	0.247340	−	0.0491990i	−0.0698631	−	0.997557i	$-0.522256\pi$
$673$	166.460	−	33.1109i	0.247340	−	0.0491990i	0.317203	+	0.948358i	$0.397256\pi$
$674$	−1158.72	−	774.232i	−1.71917	−	1.14871i
$675$	−536.768	−	106.770i	−0.795213	−	0.158178i
$676$	143.676	+	143.676i	0.212538	+	0.212538i
$677$	378.084	−	252.628i	0.558470	−	0.373158i	−0.244068	−	0.969758i	$-0.578482\pi$
$677$	378.084	−	252.628i	0.558470	−	0.373158i	0.802539	+	0.596600i	$0.203482\pi$
$678$	−1194.69	+	494.857i	−1.76208	+	0.729877i
$679$		−	50.2930i		−	0.0740692i
$680$		0			0
$681$	1025.33			1.50563
$682$	−73.3490	−	177.080i	−0.107550	−	0.259648i
$683$	746.009	+	1116.48i	1.09225	+	1.63467i	0.698779	+	0.715337i	$0.253727\pi$
$683$	746.009	+	1116.48i	1.09225	+	1.63467i	0.393474	+	0.919336i	$0.371273\pi$
$684$	−478.775	+	478.775i	−0.699964	+	0.699964i
$685$	43.7454	−	219.923i	0.0638619	−	0.321055i
$686$	−454.935	+	680.859i	−0.663171	+	0.992506i
$687$	−183.584	−	922.940i	−0.267226	−	1.34343i
$688$	778.182	+	322.334i	1.13108	+	0.468508i
$689$	238.612	−	576.061i	0.346317	−	0.836082i
$690$	182.804	−	36.3620i	0.264933	−	0.0526985i
$691$	163.058	+	108.952i	0.235975	+	0.157673i	0.667936	−	0.744219i	$-0.267178\pi$
$691$	163.058	+	108.952i	0.235975	+	0.157673i	−0.431961	+	0.901892i	$0.642178\pi$
$692$	271.091	+	53.9233i	0.391750	+	0.0779239i
$693$	102.089	+	102.089i	0.147315	+	0.147315i
$694$	−572.662	+	382.641i	−0.825161	+	0.551355i
$695$	−294.261	+	121.887i	−0.423397	+	0.175377i
$696$		−	39.0462i		−	0.0561008i
$697$		0			0
$698$	−113.096			−0.162028
$699$	−11.6469	−	28.1181i	−0.0166622	−	0.0402262i
$700$	−88.2410	−	132.062i	−0.126059	−	0.188660i
$701$	−164.717	+	164.717i	−0.234975	+	0.234975i	−0.814766	−	0.579791i	$-0.803134\pi$
$701$	−164.717	+	164.717i	−0.234975	+	0.234975i	0.579791	+	0.814766i	$0.303134\pi$
$702$	−283.993	+	1427.73i	−0.404548	+	2.03380i
$703$	195.897	−	293.181i	0.278659	−	0.417043i
$704$	31.9814	+	160.782i	0.0454282	+	0.228383i
$705$	−127.177	−	52.6786i	−0.180393	−	0.0747214i
$706$	696.551	−	1681.62i	0.986616	−	2.38190i
$707$	428.013	−	85.1370i	0.605393	−	0.120420i
$708$	409.312	+	273.493i	0.578124	+	0.386290i
$709$	−737.675	−	146.733i	−1.04044	−	0.206957i	−0.354836	−	0.934928i	$-0.615463\pi$
$709$	−737.675	−	146.733i	−1.04044	−	0.206957i	−0.685608	+	0.727971i	$0.740463\pi$
$710$	378.781	+	378.781i	0.533494	+	0.533494i
$711$	1773.92	−	1185.29i	2.49496	−	1.66708i
$712$	−8.00327	+	3.31506i	−0.0112406	+	0.00465599i
$713$		−	95.6929i		−	0.134212i
$714$		0			0
$715$	96.8747			0.135489
$716$	394.613	+	952.681i	0.551136	+	1.33056i
$717$	199.012	+	297.843i	0.277562	+	0.415402i
$718$	−410.618	+	410.618i	−0.571891	+	0.571891i
$719$	104.310	−	524.403i	0.145077	−	0.729351i	−0.837929	−	0.545779i	$-0.816234\pi$
$719$	104.310	−	524.403i	0.145077	−	0.729351i	0.983006	−	0.183572i	$-0.0587661\pi$
$720$	−566.848	+	848.349i	−0.787290	+	1.17826i
$721$	−119.236	−	599.437i	−0.165375	−	0.831397i
$722$	729.307	+	302.089i	1.01012	+	0.418406i
$723$	−616.159	+	1487.54i	−0.852225	+	2.05745i
$724$	−69.0425	+	13.7334i	−0.0953625	+	0.0189688i
$725$	234.081	+	156.408i	0.322870	+	0.215735i
$726$	1670.30	+	332.244i	2.30069	+	0.457636i
$727$	−883.793	−	883.793i	−1.21567	−	1.21567i	−0.969133	−	0.246538i	$-0.920707\pi$
$727$	−883.793	−	883.793i	−1.21567	−	1.21567i	−0.246538	−	0.969133i	$-0.579293\pi$
$728$	−9.37896	+	6.26682i	−0.0128832	+	0.00860827i
$729$	−674.098	+	279.220i	−0.924688	+	0.383018i
$730$			645.448i			0.884175i
$731$		0			0
$732$	885.881			1.21022
$733$	249.714	+	602.864i	0.340674	+	0.822460i	0.997648	+	0.0685469i	$0.0218363\pi$
$733$	249.714	+	602.864i	0.340674	+	0.822460i	−0.656974	+	0.753914i	$0.728164\pi$
$734$	446.122	+	667.669i	0.607796	+	0.909631i
$735$	510.393	−	510.393i	0.694412	−	0.694412i
$736$	−30.6877	+	154.277i	−0.0416952	+	0.209616i
$737$	23.4415	−	35.0827i	0.0318067	−	0.0476021i
$738$	769.587	+	3868.98i	1.04280	+	5.24252i
$739$	710.562	+	294.324i	0.961518	+	0.398274i	0.807548	−	0.589802i	$-0.200794\pi$
$739$	710.562	+	294.324i	0.961518	+	0.398274i	0.153970	+	0.988075i	$0.450794\pi$
$740$	−220.869	+	533.224i	−0.298471	+	0.720573i
$741$	−510.094	+	101.464i	−0.688386	+	0.136929i
$742$	−445.751	−	297.841i	−0.600743	−	0.401403i
$743$	−66.1835	−	13.1647i	−0.0890760	−	0.0177183i	0.150351	−	0.988633i	$-0.451960\pi$
$743$	−66.1835	−	13.1647i	−0.0890760	−	0.0177183i	−0.239427	+	0.970914i	$0.576960\pi$
$744$	−31.8001	−	31.8001i	−0.0427421	−	0.0427421i
$745$	568.657	−	379.965i	0.763298	−	0.510020i
$746$	897.102	−	371.592i	1.20255	−	0.498113i
$747$		−	1693.55i		−	2.26713i
$748$		0			0
$749$	122.477			0.163521
$750$	757.818	+	1829.54i	1.01042	+	2.43938i
$751$	−155.202	−	232.276i	−0.206660	−	0.309289i	0.713632	−	0.700521i	$-0.247049\pi$
$751$	−155.202	−	232.276i	−0.206660	−	0.309289i	−0.920292	+	0.391232i	$0.872049\pi$
$752$	79.8926	−	79.8926i	0.106240	−	0.106240i
$753$	−214.877	+	1080.26i	−0.285361	+	1.43461i
$754$	416.022	−	622.621i	0.551753	−	0.825757i
$755$	153.755	+	772.980i	0.203649	+	1.02381i
$756$	585.985	+	242.723i	0.775113	+	0.321062i
$757$	−222.495	+	537.150i	−0.293917	+	0.709577i	0.706082	+	0.708130i	$0.250461\pi$
$757$	−222.495	+	537.150i	−0.293917	+	0.709577i	−0.999999	+	0.00144764i	$0.999539\pi$
$758$	1000.29	−	198.969i	1.31964	−	0.262492i
$759$	−36.2696	−	24.2346i	−0.0477860	−	0.0319296i
$760$	10.2294	+	2.03475i	0.0134597	+	0.00267730i
$761$	−64.7670	−	64.7670i	−0.0851078	−	0.0851078i	0.663271	−	0.748379i	$-0.269168\pi$
$761$	−64.7670	−	64.7670i	−0.0851078	−	0.0851078i	−0.748379	+	0.663271i	$0.769168\pi$
$762$	−1361.81	+	909.932i	−1.78715	+	1.19414i
$763$	−138.996	+	57.5742i	−0.182171	+	0.0754577i
$764$			463.595i			0.606799i
$765$		0			0
$766$	688.823			0.899247
$767$	96.4639	+	232.884i	0.125768	+	0.303630i
$768$	−696.794	−	1042.83i	−0.907284	−	1.35785i
$769$	−8.68658	+	8.68658i	−0.0112959	+	0.0112959i	−0.712732	−	0.701436i	$-0.752543\pi$
$769$	−8.68658	+	8.68658i	−0.0112959	+	0.0112959i	0.701436	+	0.712732i	$0.252543\pi$
$770$	16.2495	−	81.6917i	0.0211032	−	0.106093i
$771$	−697.518	+	1043.91i	−0.904693	+	1.35397i
$772$	16.4235	+	82.5666i	0.0212740	+	0.106952i
$773$	−256.725	−	106.339i	−0.332115	−	0.137567i	0.210393	−	0.977617i	$-0.432526\pi$
$773$	−256.725	−	106.339i	−0.332115	−	0.137567i	−0.542509	+	0.840050i	$0.682526\pi$
$774$	−1062.46	+	2565.02i	−1.37269	+	3.31397i
$775$	318.023	−	63.2586i	0.410352	−	0.0816240i
$776$	3.95829	+	2.64484i	0.00510089	+	0.00340830i
$777$	−648.010	−	128.897i	−0.833990	−	0.165891i
$778$	−1349.54	−	1349.54i	−1.73463	−	1.73463i
$779$	−585.842	+	391.447i	−0.752044	+	0.502500i
$780$	786.496	−	325.777i	1.00833	−	0.417663i
$781$		−	125.368i		−	0.160523i
$782$		0			0
$783$	−1124.24			−1.43581
$784$	226.718	+	547.346i	0.289181	+	0.698145i
$785$	318.096	+	476.064i	0.405217	+	0.606451i
$786$	−469.563	+	469.563i	−0.597408	+	0.597408i
$787$	25.8529	−	129.971i	0.0328499	−	0.165148i	−0.960878	−	0.276971i	$-0.910669\pi$
$787$	25.8529	−	129.971i	0.0328499	−	0.165148i	0.993728	+	0.111824i	$0.0356692\pi$
$788$	−94.1343	+	140.882i	−0.119460	+	0.178784i
$789$	−242.529	−	1219.28i	−0.307388	−	1.54534i
$790$	−1137.14	−	471.017i	−1.43941	−	0.596224i
$791$	−110.407	+	266.546i	−0.139579	+	0.336974i
$792$	−13.4036	+	2.66614i	−0.0169238	+	0.00336634i
$793$	377.172	+	252.018i	0.475626	+	0.317803i
$794$	−1251.14	−	248.868i	−1.57575	−	0.313435i
$795$	763.875	+	763.875i	0.960850	+	0.960850i
$796$	1250.87	−	835.808i	1.57145	−	1.05001i
$797$	1137.33	−	471.097i	1.42701	−	0.591087i	0.470400	−	0.882453i	$-0.344110\pi$
$797$	1137.33	−	471.097i	1.42701	−	0.591087i	0.956612	+	0.291366i	$0.0941097\pi$
$798$			447.167i			0.560360i
$799$		0			0
$800$	−533.007			−0.666259
$801$	190.926	+	460.937i	0.238360	+	0.575452i
$802$	−219.924	−	329.139i	−0.274219	−	0.410398i
$803$	106.815	−	106.815i	0.133020	−	0.133020i
$804$	72.3358	−	363.657i	0.0899699	−	0.452309i
$805$	23.1030	−	34.5761i	0.0286994	−	0.0429516i
$806$	−168.259	−	845.895i	−0.208758	−	1.04950i
$807$	−54.3821	−	22.5258i	−0.0673880	−	0.0279130i
$808$	−15.8080	+	38.1638i	−0.0195643	+	0.0472325i
$809$	1547.48	−	307.812i	1.91282	−	0.380485i	0.913191	−	0.407532i	$-0.133611\pi$
$809$	1547.48	−	307.812i	1.91282	−	0.380485i	0.999634	+	0.0270477i	$0.00861059\pi$
$810$	−698.666	−	466.834i	−0.862551	−	0.576338i
$811$	−590.002	−	117.359i	−0.727499	−	0.144709i	−0.182573	−	0.983192i	$-0.558442\pi$
$811$	−590.002	−	117.359i	−0.727499	−	0.144709i	−0.544926	+	0.838484i	$0.683442\pi$
$812$	−230.708	−	230.708i	−0.284123	−	0.284123i
$813$	−1522.03	+	1016.99i	−1.87212	+	1.25091i
$814$	246.256	−	102.003i	0.302526	−	0.125310i
$815$			608.375i			0.746472i
$816$		0			0
$817$	−495.892			−0.606966
$818$	−440.884	−	1064.39i	−0.538978	−	1.30121i
$819$	360.928	+	540.168i	0.440694	+	0.659545i
$820$	815.500	−	815.500i	0.994512	−	0.994512i
$821$	−153.360	+	770.993i	−0.186797	+	0.939090i	0.767687	+	0.640826i	$0.221408\pi$
$821$	−153.360	+	770.993i	−0.186797	+	0.939090i	−0.954483	+	0.298265i	$0.903592\pi$
$822$	−505.573	+	756.644i	−0.615053	+	0.920491i
$823$	54.7382	+	275.188i	0.0665106	+	0.334371i	0.999686	−	0.0250494i	$-0.00797432\pi$
$823$	54.7382	+	275.188i	0.0665106	+	0.334371i	−0.933176	+	0.359421i	$0.882974\pi$
$824$	53.4489	+	22.1393i	0.0648652	+	0.0268681i
$825$	56.5640	−	136.558i	0.0685625	−	0.165524i
$826$	212.565	−	42.2819i	0.257343	−	0.0511887i
$827$	−1229.32	−	821.409i	−1.48649	−	0.993239i	−0.992297	−	0.123886i	$-0.960464\pi$
$827$	−1229.32	−	821.409i	−1.48649	−	0.993239i	−0.494191	−	0.869354i	$-0.664536\pi$
$828$	−250.627	−	49.8529i	−0.302690	−	0.0602088i
$829$	−331.030	−	331.030i	−0.399312	−	0.399312i	0.478678	−	0.877990i	$-0.341116\pi$
$829$	−331.030	−	331.030i	−0.399312	−	0.399312i	−0.877990	+	0.478678i	$0.841116\pi$
$830$	−812.370	+	542.808i	−0.978759	+	0.653986i
$831$	447.681	−	185.435i	0.538725	−	0.223147i
$832$			737.650i			0.886598i
$833$		0			0
$834$	1292.61			1.54989
$835$	−75.1357	−	181.394i	−0.0899828	−	0.217238i
$836$	−50.7902	−	76.0130i	−0.0607539	−	0.0909246i
$837$	−915.607	+	915.607i	−1.09392	+	1.09392i
$838$	−145.162	+	729.778i	−0.173224	+	0.870856i
$839$	117.506	−	175.861i	0.140055	−	0.209608i	−0.754810	−	0.655943i	$-0.772271\pi$
$839$	117.506	−	175.861i	0.140055	−	0.209608i	0.894866	+	0.446335i	$0.147271\pi$
$840$	−3.81267	−	19.1676i	−0.00453889	−	0.0228185i
$841$	−242.689	−	100.525i	−0.288572	−	0.119530i
$842$	−662.644	+	1599.76i	−0.786988	+	1.89996i
$843$	1134.46	−	225.659i	1.34574	−	0.267685i
$844$	1096.07	+	732.372i	1.29866	+	0.867739i
$845$	−176.797	−	35.1671i	−0.209227	−	0.0416179i
$846$	263.339	+	263.339i	0.311276	+	0.311276i
$847$	315.926	−	211.095i	0.372994	−	0.249226i
$848$	−819.181	+	339.316i	−0.966016	+	0.400137i
$849$		−	650.006i		−	0.765613i
$850$		0			0
$851$	133.075			0.156375
$852$	−421.598	−	1017.83i	−0.494833	−	1.19463i
$853$	−556.064	−	832.209i	−0.651892	−	0.975626i	−0.999281	−	0.0379048i	$-0.987932\pi$
$853$	−556.064	−	832.209i	−0.651892	−	0.975626i	0.347389	−	0.937721i	$-0.387068\pi$
$854$	275.785	−	275.785i	0.322933	−	0.322933i
$855$	117.188	−	589.146i	0.137062	−	0.689060i
$856$	−6.44092	+	9.63952i	−0.00752444	+	0.0112611i
$857$	−145.210	−	730.021i	−0.169440	−	0.851833i	−0.968199	−	0.250181i	$-0.919510\pi$
$857$	−145.210	−	730.021i	−0.169440	−	0.851833i	0.798759	−	0.601651i	$-0.205490\pi$
$858$	−363.224	−	150.452i	−0.423338	−	0.175352i
$859$	374.100	−	903.157i	0.435506	−	1.05141i	−0.541977	−	0.840393i	$-0.682324\pi$
$859$	374.100	−	903.157i	0.435506	−	1.05141i	0.977483	−	0.211012i	$-0.0676759\pi$
$860$	796.096	−	158.353i	0.925693	−	0.184132i
$861$	1097.74	+	733.485i	1.27496	+	0.851899i
$862$	1788.49	+	355.752i	2.07481	+	0.412706i
$863$	799.269	+	799.269i	0.926152	+	0.926152i	0.997455	−	0.0713024i	$-0.0227155\pi$
$863$	799.269	+	799.269i	0.926152	+	0.926152i	−0.0713024	+	0.997455i	$0.522716\pi$
$864$	1769.78	−	1182.53i	2.04836	−	1.36867i
$865$	−226.547	+	93.8388i	−0.261904	+	0.108484i
$866$		−	1820.44i		−	2.10213i
$867$		0			0
$868$	−375.788			−0.432935
$869$	110.236	+	266.132i	0.126853	+	0.306251i
$870$	720.777	+	1078.72i	0.828479	+	1.23991i
$871$	134.252	−	134.252i	0.154135	−	0.154135i
$872$	2.77829	−	13.9674i	0.00318612	−	0.0160177i
$873$	152.326	−	227.972i	0.174486	−	0.261136i
$874$	−17.5710	−	88.3352i	−0.0201041	−	0.101070i
$875$	408.186	+	169.076i	0.466499	+	0.193230i
$876$	507.991	−	1226.40i	0.579899	−	1.40000i
$877$	−1320.03	+	262.571i	−1.50517	+	0.299397i	−0.877688	−	0.479233i	$-0.840915\pi$
$877$	−1320.03	+	262.571i	−1.50517	+	0.299397i	−0.627483	+	0.778630i	$0.715915\pi$
$878$	−1669.66	−	1115.63i	−1.90166	−	1.27065i
$879$	−610.499	−	121.436i	−0.694538	−	0.138152i
$880$	−97.4109	−	97.4109i	−0.110694	−	0.110694i
$881$	880.918	−	588.611i	0.999907	−	0.668116i	0.0560352	−	0.998429i	$-0.482154\pi$
$881$	880.918	−	588.611i	0.999907	−	0.668116i	0.943872	+	0.330312i	$0.107154\pi$
$882$	−1804.14	+	747.300i	−2.04551	+	0.847279i
$883$			658.553i			0.745813i	0.927869	+	0.372907i	$0.121639\pi$
$883$			658.553i			0.745813i	−0.927869	+	0.372907i	$0.878361\pi$
$884$		0			0
$885$	−436.727			−0.493477
$886$	−345.665	−	834.510i	−0.390142	−	0.941885i
$887$	370.614	+	554.662i	0.417828	+	0.625324i	0.979358	−	0.202132i	$-0.0647871\pi$
$887$	370.614	+	554.662i	0.417828	+	0.625324i	−0.561530	+	0.827456i	$0.689787\pi$
$888$	44.2228	−	44.2228i	0.0498005	−	0.0498005i
$889$	−71.2891	+	358.395i	−0.0801902	+	0.403143i
$890$	159.910	−	239.322i	0.179674	−	0.268901i
$891$	38.3658	+	192.878i	0.0430592	+	0.216473i
$892$	412.605	+	170.907i	0.462562	+	0.191599i
$893$	−25.4555	+	61.4550i	−0.0285056	+	0.0688186i
$894$	−2722.24	+	541.487i	−3.04501	+	0.605691i
$895$	−760.643	−	508.245i	−0.849880	−	0.567872i
$896$	32.3651	+	6.43782i	0.0361218	+	0.00718507i
$897$	−138.794	−	138.794i	−0.154731	−	0.154731i
$898$	−582.338	+	389.106i	−0.648484	+	0.433303i
$899$	615.383	−	254.900i	0.684519	−	0.283537i
$900$		−	865.883i		−	0.962092i
$901$		0			0
$902$	−532.619			−0.590487
$903$	355.586	+	858.460i	0.393783	+	0.950676i
$904$	−15.1723	−	22.7069i	−0.0167835	−	0.0251182i
$905$	44.1600	−	44.1600i	0.0487956	−	0.0487956i
$906$	623.991	−	3137.01i	0.688732	−	3.46249i
$907$	100.245	−	150.028i	0.110524	−	0.165411i	−0.772084	−	0.635521i	$-0.780786\pi$
$907$	100.245	−	150.028i	0.110524	−	0.165411i	0.882608	+	0.470109i	$0.155786\pi$
$908$	158.217	+	795.410i	0.174248	+	0.876002i
$909$	2197.99	+	910.437i	2.41803	+	1.00158i
$910$	143.427	−	346.264i	0.157612	−	0.380510i
$911$	−1620.68	+	322.374i	−1.77901	+	0.353868i	−0.971693	−	0.236246i	$-0.924083\pi$
$911$	−1620.68	+	322.374i	−1.77901	+	0.353868i	−0.807320	+	0.590114i	$0.799083\pi$
$912$	614.943	+	410.892i	0.674279	+	0.450539i
$913$	224.267	+	44.6096i	0.245638	+	0.0488604i
$914$	749.335	+	749.335i	0.819842	+	0.819842i
$915$	−653.467	+	436.633i	−0.714172	+	0.477194i
$916$	687.650	−	284.834i	0.750709	−	0.310954i
$917$			148.158i			0.161569i
$918$		0			0
$919$	−630.155			−0.685697			−0.342848	−	0.939391i	$-0.611392\pi$
$919$	−630.155			−0.685697			−0.342848	+	0.939391i	$0.611392\pi$
$920$	1.50634	+	3.63662i	0.00163732	+	0.00395285i
$921$	684.906	+	1025.03i	0.743655	+	1.11296i
$922$	−1734.82	+	1734.82i	−1.88158	+	1.88158i
$923$	110.055	−	553.286i	0.119237	−	0.599443i
$924$	−95.1696	+	142.431i	−0.102997	+	0.154146i
$925$	87.9706	+	442.258i	0.0951034	+	0.478117i
$926$	−1436.86	−	595.167i	−1.55169	−	0.642729i
$927$	1275.08	−	3078.31i	1.37549	−	3.32073i
$928$	−1073.87	+	213.607i	−1.15719	+	0.230179i
$929$	1303.36	+	870.877i	1.40297	+	0.937435i	0.999751	+	0.0223314i	$0.00710891\pi$
$929$	1303.36	+	870.877i	1.40297	+	0.937435i	0.403220	+	0.915103i	$0.367891\pi$
$930$	1465.55	+	291.516i	1.57586	+	0.313458i
$931$	−246.634	−	246.634i	−0.264913	−	0.264913i
$932$	20.0156	−	13.3740i	0.0214760	−	0.0143498i
$933$	−1545.43	+	640.139i	−1.65641	+	0.686109i
$934$			1153.41i			1.23492i
$935$		0			0
$936$	−61.4945			−0.0656992
$937$	−291.961	−	704.857i	−0.311591	−	0.752248i	−0.999646	−	0.0265897i	$-0.991535\pi$
$937$	−291.961	−	704.857i	−0.311591	−	0.752248i	0.688055	−	0.725659i	$-0.258465\pi$
$938$	−90.6916	−	135.730i	−0.0966861	−	0.144701i
$939$	1157.53	−	1157.53i	1.23273	−	1.23273i
$940$	21.2414	−	106.788i	0.0225972	−	0.113604i
$941$	656.274	−	982.184i	0.697422	−	1.04377i	−0.298575	−	0.954386i	$-0.596511\pi$
$941$	656.274	−	982.184i	0.697422	−	1.04377i	0.995998	−	0.0893803i	$-0.0284886\pi$
$942$	−453.318	−	2278.98i	−0.481229	−	2.41930i
$943$	−245.673	−	101.761i	−0.260523	−	0.107912i
$944$	137.176	−	331.171i	0.145313	−	0.350817i
$945$	−551.884	+	109.776i	−0.584004	+	0.116166i
$946$	−311.685	−	208.261i	−0.329476	−	0.220149i
$947$	1709.91	+	340.121i	1.80560	+	0.359157i	0.979037	−	0.203684i	$-0.0652914\pi$
$947$	1709.91	+	340.121i	1.80560	+	0.359157i	0.826566	+	0.562840i	$0.190291\pi$
$948$	1789.94	+	1789.94i	1.88812	+	1.88812i
$949$	565.172	−	377.636i	0.595544	−	0.397930i
$950$	281.955	−	116.789i	0.296794	−	0.122936i
$951$			1668.18i			1.75413i
$952$		0			0
$953$	−1007.14			−1.05681			−0.528405	−	0.848992i	$-0.677210\pi$
$953$	−1007.14			−1.05681			−0.528405	+	0.848992i	$0.677210\pi$
$954$	−1118.44	−	2700.16i	−1.17237	−	2.83035i
$955$	−228.496	−	341.969i	−0.239263	−	0.358083i
$956$	−200.345	+	200.345i	−0.209566	+	0.209566i
$957$	59.2356	−	297.797i	0.0618971	−	0.311178i
$958$	190.265	−	284.752i	0.198607	−	0.297236i
$959$	39.6094	+	199.130i	0.0413028	+	0.207643i
$960$	−1180.73	−	489.074i	−1.22993	−	0.509452i
$961$	−74.1731	+	179.070i	−0.0771833	+	0.186337i
$962$	1176.34	−	233.989i	1.22281	−	0.243232i
$963$	555.174	+	370.955i	0.576505	+	0.385208i
$964$	−1249.05	−	248.451i	−1.29569	−	0.257730i
$965$	−52.8101	−	52.8101i	−0.0547255	−	0.0547255i
$966$	−140.321	+	93.7598i	−0.145260	+	0.0970598i
$967$	499.135	−	206.749i	0.516169	−	0.213804i	−0.109364	−	0.994002i	$-0.534882\pi$
$967$	499.135	−	206.749i	0.516169	−	0.213804i	0.625533	+	0.780198i	$0.284882\pi$
$968$			35.9660i			0.0371550i
$969$		0			0
$970$	−158.177			−0.163069
$971$	153.655	+	370.956i	0.158244	+	0.382035i	0.983039	−	0.183397i	$-0.0587095\pi$
$971$	153.655	+	370.956i	0.158244	+	0.382035i	−0.824795	+	0.565432i	$0.808709\pi$
$972$	−0.560743	−	0.839212i	−0.000576896	−	0.000863387i
$973$	203.924	−	203.924i	0.209583	−	0.209583i
$974$	−450.287	+	2263.74i	−0.462307	+	2.32417i
$975$	369.511	−	553.013i	0.378986	−	0.567193i
$976$	−125.846	−	632.672i	−0.128941	−	0.648229i
$977$	880.902	+	364.881i	0.901639	+	0.373471i	0.784850	−	0.619686i	$-0.212740\pi$
$977$	880.902	+	364.881i	0.901639	+	0.373471i	0.116789	+	0.993157i	$0.462740\pi$
$978$	944.842	−	2281.05i	0.966096	−	2.33236i
$979$	−66.0685	+	13.1418i	−0.0674857	+	0.0134237i
$980$	474.699	+	317.184i	0.484387	+	0.323657i
$981$	−804.433	−	160.012i	−0.820014	−	0.163111i
$982$	−303.323	−	303.323i	−0.308883	−	0.308883i
$983$	−1186.50	+	792.797i	−1.20702	+	0.806507i	−0.985670	−	0.168686i	$-0.946048\pi$
$983$	−1186.50	+	792.797i	−1.20702	+	0.806507i	−0.221354	+	0.975194i	$0.571048\pi$
$984$	−115.457	+	47.8240i	−0.117335	+	0.0486016i
$985$		−	150.318i		−	0.152607i
$986$		0			0
$987$	124.641			0.126282
$988$	−157.423	−	380.053i	−0.159335	−	0.384669i
$989$	−103.976	−	155.611i	−0.105133	−	0.157342i
$990$	321.082	−	321.082i	0.324326	−	0.324326i
$991$	−54.9030	+	276.016i	−0.0554016	+	0.278523i	−0.998549	−	0.0538524i	$-0.982850\pi$
$991$	−54.9030	+	276.016i	−0.0554016	+	0.278523i	0.943147	+	0.332375i	$0.107850\pi$
$992$	−700.620	+	1048.55i	−0.706271	+	1.05701i
$993$	27.0964	+	136.223i	0.0272874	+	0.137183i
$994$	−448.110	−	185.613i	−0.450815	−	0.186734i
$995$	−510.751	+	1233.06i	−0.513317	+	1.23926i
$996$	1970.77	−	392.011i	1.97869	−	0.393586i
$997$	447.153	+	298.778i	0.448499	+	0.299677i	0.759232	−	0.650820i	$-0.225575\pi$
$997$	447.153	+	298.778i	0.448499	+	0.299677i	−0.310734	+	0.950497i	$0.600575\pi$
$998$	−2301.41	−	457.780i	−2.30603	−	0.458697i
$999$	−1273.29	−	1273.29i	−1.27456	−	1.27456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.g.158.1		8
17.2	even	8		289.3.e.e.224.1		8
17.3	odd	16		289.3.e.j.249.1		8
17.4	even	4		289.3.e.h.131.1		8
17.5	odd	16		289.3.e.a.40.1		8
17.6	odd	16		289.3.e.h.214.1		8
17.7	odd	16	inner	289.3.e.g.75.1		8
17.8	even	8		289.3.e.j.65.1		8
17.9	even	8		289.3.e.n.65.1		8
17.10	odd	16		17.3.e.b.7.1	yes	8
17.11	odd	16		289.3.e.f.214.1		8
17.12	odd	16		289.3.e.e.40.1		8
17.13	even	4		289.3.e.f.131.1		8
17.14	odd	16		289.3.e.n.249.1		8
17.15	even	8		289.3.e.a.224.1		8
17.16	even	2		17.3.e.b.5.1	✓	8
51.44	even	16		153.3.p.a.109.1		8
51.50	odd	2		153.3.p.a.73.1		8
68.27	even	16		272.3.bh.b.177.1		8
68.67	odd	2		272.3.bh.b.209.1		8
85.27	even	16		425.3.t.d.24.1		8
85.33	odd	4		425.3.t.d.124.1		8
85.44	odd	16		425.3.u.a.126.1		8
85.67	odd	4		425.3.t.b.124.1		8
85.78	even	16		425.3.t.b.24.1		8
85.84	even	2		425.3.u.a.226.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.5.1	✓	8	17.16	even	2
17.3.e.b.7.1	yes	8	17.10	odd	16
153.3.p.a.73.1		8	51.50	odd	2
153.3.p.a.109.1		8	51.44	even	16
272.3.bh.b.177.1		8	68.27	even	16
272.3.bh.b.209.1		8	68.67	odd	2
289.3.e.a.40.1		8	17.5	odd	16
289.3.e.a.224.1		8	17.15	even	8
289.3.e.e.40.1		8	17.12	odd	16
289.3.e.e.224.1		8	17.2	even	8
289.3.e.f.131.1		8	17.13	even	4
289.3.e.f.214.1		8	17.11	odd	16
289.3.e.g.75.1		8	17.7	odd	16	inner
289.3.e.g.158.1		8	1.1	even	1	trivial
289.3.e.h.131.1		8	17.4	even	4
289.3.e.h.214.1		8	17.6	odd	16
289.3.e.j.65.1		8	17.8	even	8
289.3.e.j.249.1		8	17.3	odd	16
289.3.e.n.65.1		8	17.9	even	8
289.3.e.n.249.1		8	17.14	odd	16
425.3.t.b.24.1		8	85.78	even	16
425.3.t.b.124.1		8	85.67	odd	4
425.3.t.d.24.1		8	85.27	even	16
425.3.t.d.124.1		8	85.33	odd	4
425.3.u.a.126.1		8	85.44	odd	16
425.3.u.a.226.1		8	85.84	even	2

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+(1.08979 + 2.63099i) q^{2} +(2.88669 + 4.32023i) q^{3} +(-2.90602 + 2.90602i) q^{4} +(0.711297 - 3.57593i) q^{5} +(-8.22059 + 12.3030i) q^{6} +(0.644047 + 3.23784i) q^{7} +(-0.288703 - 0.119585i) q^{8} +(-6.88730 + 16.6274i) q^{9} +(10.1834 - 2.02560i) q^{10} +(-2.02046 - 1.35003i) q^{11} +(-20.9434 - 4.16591i) q^{12} +(-7.73173 - 7.73173i) q^{13} +(-7.81684 + 5.22304i) q^{14} +(17.5022 - 7.24963i) q^{15} +15.5490i q^{16} -51.2522 q^{18} +(-3.50319 - 8.45745i) q^{19} +(8.32469 + 12.4588i) q^{20} +(-12.1291 + 12.1291i) q^{21} +(1.35003 - 6.78704i) q^{22} +(1.91942 - 2.87262i) q^{23} +(-0.316761 - 1.59247i) q^{24} +(10.8156 + 4.47998i) q^{25} +(11.9161 - 28.7680i) q^{26} +(-45.8512 + 9.12037i) q^{27} +(-11.2808 - 7.53762i) q^{28} +(23.5861 + 4.69157i) q^{29} +(38.1474 + 38.1474i) q^{30} +(23.0300 - 15.3882i) q^{31} +(-42.0641 + 17.4235i) q^{32} -12.6260i q^{33} +12.0364 q^{35} +(-28.3049 - 68.3342i) q^{36} +(21.3995 + 32.0267i) q^{37} +(18.4337 - 18.4337i) q^{38} +(11.0838 - 55.7219i) q^{39} +(-0.632980 + 0.947321i) q^{40} +(-15.0157 - 75.4890i) q^{41} +(-45.1295 - 18.6933i) q^{42} +(20.7301 - 50.0470i) q^{43} +(9.79469 - 1.94829i) q^{44} +(54.5596 + 36.4555i) q^{45} +(9.64960 + 1.91942i) q^{46} +(-5.13810 - 5.13810i) q^{47} +(-67.1754 + 44.8852i) q^{48} +(35.2013 - 14.5808i) q^{49} +33.3380i q^{50} +44.9371 q^{52} +(21.8223 + 52.6837i) q^{53} +(-73.9637 - 110.695i) q^{54} +(-6.26475 + 6.26475i) q^{55} +(0.201258 - 1.01179i) q^{56} +(26.4255 - 39.5486i) q^{57} +(13.3605 + 67.1676i) q^{58} +(-21.2985 - 8.82213i) q^{59} +(-29.7940 + 71.9292i) q^{60} +(-40.6888 + 8.09351i) q^{61} +(65.5839 + 43.8218i) q^{62} +(-58.2726 - 11.5911i) q^{63} +(-47.7028 - 47.7028i) q^{64} +(-33.1477 + 22.1486i) q^{65} +(33.2187 - 13.7596i) q^{66} +17.3637i q^{67} +17.9512 q^{69} +(13.1172 + 31.6676i) q^{70} +(28.6631 + 42.8974i) q^{71} +(3.97676 - 3.97676i) q^{72} +(-12.1277 + 60.9700i) q^{73} +(-60.9407 + 91.2042i) q^{74} +(11.8668 + 59.6583i) q^{75} +(34.7579 + 14.3972i) q^{76} +(3.06990 - 7.41140i) q^{77} +(158.683 - 31.5639i) q^{78} +(-98.5655 - 65.8593i) q^{79} +(55.6023 + 11.0600i) q^{80} +(-57.2255 - 57.2255i) q^{81} +(182.247 - 121.773i) q^{82} +(-86.9369 + 36.0104i) q^{83} -70.4946i q^{84} +154.264 q^{86} +(47.8171 + 115.441i) q^{87} +(0.421869 + 0.631372i) q^{88} +(19.6021 - 19.6021i) q^{89} +(-36.4555 + 183.274i) q^{90} +(20.0545 - 30.0137i) q^{91} +(2.77001 + 13.9258i) q^{92} +(132.961 + 55.0742i) q^{93} +(7.91883 - 19.1177i) q^{94} +(-32.7351 + 6.51142i) q^{95} +(-196.700 - 131.430i) q^{96} +(-14.9417 - 2.97209i) q^{97} +(76.7240 + 76.7240i) q^{98} +(36.3629 - 24.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 24 q^{5} + 16 q^{7} + 16 q^{8} + 8 q^{9} - 40 q^{11} - 40 q^{12} - 16 q^{14} + 32 q^{15} - 136 q^{18} - 32 q^{19} + 40 q^{20} - 64 q^{21} + 8 q^{23} - 24 q^{24} + 16 q^{25} - 96 q^{27} - 80 q^{28}+ \cdots - 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 24 * q^5 + 16 * q^7 + 16 * q^8 + 8 * q^9 - 40 * q^11 - 40 * q^12 - 16 * q^14 + 32 * q^15 - 136 * q^18 - 32 * q^19 + 40 * q^20 - 64 * q^21 + 8 * q^23 - 24 * q^24 + 16 * q^25 - 96 * q^27 - 80 * q^28 - 24 * q^29 + 168 * q^30 - 32 * q^31 - 24 * q^32 + 80 * q^35 - 104 * q^36 + 168 * q^37 + 8 * q^38 + 72 * q^39 + 200 * q^40 - 72 * q^42 + 96 * q^43 + 96 * q^44 + 88 * q^45 - 80 * q^47 - 88 * q^48 + 8 * q^49 + 240 * q^52 + 96 * q^53 - 208 * q^54 - 8 * q^55 - 72 * q^56 - 248 * q^57 + 8 * q^59 + 16 * q^60 - 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 32 * q^65 + 8 * q^66 - 208 * q^69 - 80 * q^70 - 32 * q^71 + 24 * q^72 - 24 * q^73 - 176 * q^74 + 192 * q^75 - 80 * q^76 - 216 * q^77 + 368 * q^78 + 96 * q^79 - 24 * q^80 - 224 * q^81 + 408 * q^82 - 88 * q^83 + 288 * q^86 + 312 * q^87 - 176 * q^88 + 288 * q^89 - 256 * q^90 + 24 * q^91 - 336 * q^92 + 280 * q^93 - 8 * q^94 + 152 * q^95 - 328 * q^96 + 344 * q^97 + 16 * q^98 - 136 * q^99

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