LMFDB - Embedded newform 294.3.h.d.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(263,294)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("294.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$2.23256 + 1.28897i$ of defining polynomial
Character	$\chi$	$=$	294.275
Dual form			294.3.h.d.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(-0.0981308 - 2.99839i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.790881 + 0.456615i) q^{5} +(-2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 + 0.588470i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.0981308 - 2.99839i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.790881 + 0.456615i) q^{5} +(-2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 + 0.588470i) q^{9} +(-0.645751 - 1.11847i) q^{10} +(-12.6045 + 7.27719i) q^{11} +(5.09524 - 3.16836i) q^{12} -0.583005 q^{13} +(1.29150 - 2.41618i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-18.6513 + 10.7684i) q^{17} +(11.4152 + 5.62962i) q^{18} +(8.00000 - 13.8564i) q^{19} +1.82646i q^{20} +20.5830 q^{22} +(-33.6284 - 19.4154i) q^{23} +(-8.48074 + 0.277556i) q^{24} +(-12.0830 - 20.9284i) q^{25} +(0.714033 + 0.412247i) q^{26} +(2.64575 + 26.8701i) q^{27} +35.7676i q^{29} +(-3.29026 + 2.04597i) q^{30} +(29.2288 + 50.6257i) q^{31} +(4.89898 - 2.82843i) q^{32} +(23.0568 + 37.0790i) q^{33} +30.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +(-10.0000 + 17.3205i) q^{37} +(-19.5959 + 11.3137i) q^{38} +(0.0572108 + 1.74808i) q^{39} +(1.29150 - 2.23695i) q^{40} -8.75149i q^{41} -11.7490 q^{43} +(-25.2089 - 14.5544i) q^{44} +(-7.37140 - 3.63533i) q^{45} +(27.4575 + 47.5578i) q^{46} +(7.34847 + 4.24264i) q^{47} +(10.5830 + 5.65685i) q^{48} +34.1759i q^{50} +(34.1181 + 54.8674i) q^{51} +(-0.583005 - 1.00979i) q^{52} +(-44.0908 + 25.4558i) q^{53} +(15.7596 - 34.7798i) q^{54} -13.2915 q^{55} +(-42.3320 - 22.6274i) q^{57} +(25.2915 - 43.8062i) q^{58} +(50.4179 - 29.1088i) q^{59} +(5.47645 - 0.179232i) q^{60} +(-19.4575 + 33.7014i) q^{61} -82.6714i q^{62} -8.00000 q^{64} +(-0.461088 - 0.266209i) q^{65} +(-2.01983 - 61.7160i) q^{66} +(-35.2915 - 61.1267i) q^{67} +(-37.3027 - 21.5367i) q^{68} +(-54.9150 + 102.737i) q^{69} -17.0279i q^{71} +(1.66444 + 25.4014i) q^{72} +(-36.1660 - 62.6414i) q^{73} +(24.4949 - 14.1421i) q^{74} +(-61.5658 + 38.2833i) q^{75} +32.0000 q^{76} +(1.16601 - 2.18141i) q^{78} +(-10.4575 + 18.1129i) q^{79} +(-3.16352 + 1.82646i) q^{80} +(80.3074 - 10.5698i) q^{81} +(-6.18824 + 10.7183i) q^{82} -145.544i q^{83} -19.6680 q^{85} +(14.3895 + 8.30781i) q^{86} +(107.245 - 3.50990i) q^{87} +(20.5830 + 35.6508i) q^{88} +(-46.4635 - 26.8257i) q^{89} +(6.45751 + 9.66472i) q^{90} -77.6616i q^{92} +(148.928 - 92.6073i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(12.6541 - 7.30584i) q^{95} +(-8.96148 - 14.4115i) q^{96} -111.166 q^{97} +(108.915 - 72.7719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 16 q^{6} - 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 16 * q^6 - 20 * q^9	$ 8 q + 8 q^{4} - 16 q^{6} - 20 q^{9} + 16 q^{10} + 80 q^{13} - 32 q^{15} - 16 q^{16} + 64 q^{19} + 80 q^{22} - 16 q^{24} - 12 q^{25} - 56 q^{30} + 128 q^{31} - 40 q^{33} + 32 q^{34} - 80 q^{36} - 80 q^{37} + 112 q^{39} - 32 q^{40} + 160 q^{43} - 112 q^{45} + 8 q^{46} - 16 q^{51} + 80 q^{52} + 152 q^{54} - 64 q^{55} + 160 q^{58} - 32 q^{60} + 56 q^{61} - 64 q^{64} - 112 q^{66} - 240 q^{67} - 16 q^{69} - 120 q^{73} - 224 q^{75} + 256 q^{76} - 160 q^{78} + 128 q^{79} + 124 q^{81} - 240 q^{82} - 496 q^{85} + 160 q^{87} + 80 q^{88} - 160 q^{90} + 280 q^{93} - 48 q^{94} + 32 q^{96} - 720 q^{97} + 448 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^6 - 20 * q^9 + 16 * q^10 + 80 * q^13 - 32 * q^15 - 16 * q^16 + 64 * q^19 + 80 * q^22 - 16 * q^24 - 12 * q^25 - 56 * q^30 + 128 * q^31 - 40 * q^33 + 32 * q^34 - 80 * q^36 - 80 * q^37 + 112 * q^39 - 32 * q^40 + 160 * q^43 - 112 * q^45 + 8 * q^46 - 16 * q^51 + 80 * q^52 + 152 * q^54 - 64 * q^55 + 160 * q^58 - 32 * q^60 + 56 * q^61 - 64 * q^64 - 112 * q^66 - 240 * q^67 - 16 * q^69 - 120 * q^73 - 224 * q^75 + 256 * q^76 - 160 * q^78 + 128 * q^79 + 124 * q^81 - 240 * q^82 - 496 * q^85 + 160 * q^87 + 80 * q^88 - 160 * q^90 + 280 * q^93 - 48 * q^94 + 32 * q^96 - 720 * q^97 + 448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	−0.0981308	−	2.99839i	−0.0327103	−	0.999465i
$3$	−0.0981308	−	2.99839i	−0.0327103	−	0.999465i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	0.790881	+	0.456615i	0.158176	+	0.0913230i	0.576999	−	0.816745i	$-0.304224\pi$
$5$	0.790881	+	0.456615i	0.158176	+	0.0913230i	−0.418823	+	0.908068i	$0.637557\pi$
$6$	−2.00000	+	3.74166i	−0.333333	+	0.623610i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	−8.98074	+	0.588470i	−0.997860	+	0.0653855i
$10$	−0.645751	−	1.11847i	−0.0645751	−	0.111847i
$11$	−12.6045	+	7.27719i	−1.14586	+	0.661563i	−0.947875	−	0.318642i	$-0.896773\pi$
$11$	−12.6045	+	7.27719i	−1.14586	+	0.661563i	−0.197985	+	0.980205i	$0.563440\pi$
$12$	5.09524	−	3.16836i	0.424603	−	0.264030i
$13$	−0.583005			−0.0448466			−0.0224233	−	0.999749i	$-0.507138\pi$
$13$	−0.583005			−0.0448466			−0.0224233	+	0.999749i	$0.507138\pi$
$14$		0			0
$15$	1.29150	−	2.41618i	0.0861002	−	0.161079i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−18.6513	+	10.7684i	−1.09714	+	0.633433i	−0.935468	−	0.353412i	$-0.885021\pi$
$17$	−18.6513	+	10.7684i	−1.09714	+	0.633433i	−0.161670	+	0.986845i	$0.551688\pi$
$18$	11.4152	+	5.62962i	0.634179	+	0.312757i
$19$	8.00000	−	13.8564i	0.421053	−	0.729285i	−0.574990	−	0.818160i	$-0.694994\pi$
$19$	8.00000	−	13.8564i	0.421053	−	0.729285i	0.996043	+	0.0888758i	$0.0283274\pi$
$20$			1.82646i			0.0913230i
$21$		0			0
$22$	20.5830			0.935591
$23$	−33.6284	−	19.4154i	−1.46211	−	0.844148i	−0.462998	−	0.886359i	$-0.653226\pi$
$23$	−33.6284	−	19.4154i	−1.46211	−	0.844148i	−0.999109	+	0.0422119i	$0.986560\pi$
$24$	−8.48074	+	0.277556i	−0.353364	+	0.0115648i
$25$	−12.0830	−	20.9284i	−0.483320	−	0.837135i
$26$	0.714033	+	0.412247i	0.0274628	+	0.0158557i
$27$	2.64575	+	26.8701i	0.0979908	+	0.995187i
$28$		0			0
$29$			35.7676i			1.23337i	0.787212	+	0.616683i	$0.211524\pi$
$29$			35.7676i			1.23337i	−0.787212	+	0.616683i	$0.788476\pi$
$30$	−3.29026	+	2.04597i	−0.109675	+	0.0681991i
$31$	29.2288	+	50.6257i	0.942863	+	1.63309i	0.759974	+	0.649953i	$0.225212\pi$
$31$	29.2288	+	50.6257i	0.942863	+	1.63309i	0.182889	+	0.983134i	$0.441455\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	23.0568	+	37.0790i	0.698690	+	1.12361i
$34$	30.4575			0.895809
$35$		0			0
$36$	−10.0000	−	14.9666i	−0.277778	−	0.415740i
$37$	−10.0000	+	17.3205i	−0.270270	+	0.468122i	−0.968931	−	0.247331i	$-0.920446\pi$
$37$	−10.0000	+	17.3205i	−0.270270	+	0.468122i	0.698661	+	0.715453i	$0.253780\pi$
$38$	−19.5959	+	11.3137i	−0.515682	+	0.297729i
$39$	0.0572108	+	1.74808i	0.00146694	+	0.0448226i
$40$	1.29150	−	2.23695i	0.0322876	−	0.0559237i
$41$		−	8.75149i		−	0.213451i	−0.994289	−	0.106725i	$-0.965963\pi$
$41$		−	8.75149i		−	0.213451i	0.994289	−	0.106725i	$-0.0340366\pi$
$42$		0			0
$43$	−11.7490			−0.273233			−0.136616	−	0.990624i	$-0.543623\pi$
$43$	−11.7490			−0.273233			−0.136616	+	0.990624i	$0.543623\pi$
$44$	−25.2089	−	14.5544i	−0.572930	−	0.330781i
$45$	−7.37140	−	3.63533i	−0.163809	−	0.0807852i
$46$	27.4575	+	47.5578i	0.596902	+	1.03387i
$47$	7.34847	+	4.24264i	0.156350	+	0.0902690i	0.576134	−	0.817355i	$-0.304561\pi$
$47$	7.34847	+	4.24264i	0.156350	+	0.0902690i	−0.419784	+	0.907624i	$0.637894\pi$
$48$	10.5830	+	5.65685i	0.220479	+	0.117851i
$49$		0			0
$50$			34.1759i			0.683518i
$51$	34.1181	+	54.8674i	0.668981	+	1.07583i
$52$	−0.583005	−	1.00979i	−0.0112116	−	0.0194191i
$53$	−44.0908	+	25.4558i	−0.831902	+	0.480299i	−0.854504	−	0.519446i	$-0.826138\pi$
$53$	−44.0908	+	25.4558i	−0.831902	+	0.480299i	0.0226013	+	0.999745i	$0.492805\pi$
$54$	15.7596	−	34.7798i	0.291845	−	0.644070i
$55$	−13.2915			−0.241664
$56$		0			0
$57$	−42.3320	−	22.6274i	−0.742667	−	0.396972i
$58$	25.2915	−	43.8062i	0.436060	−	0.755279i
$59$	50.4179	−	29.1088i	0.854540	−	0.493369i	−0.00764008	−	0.999971i	$-0.502432\pi$
$59$	50.4179	−	29.1088i	0.854540	−	0.493369i	0.862180	+	0.506602i	$0.169099\pi$
$60$	5.47645	−	0.179232i	0.0912742	−	0.00298720i
$61$	−19.4575	+	33.7014i	−0.318976	+	0.552482i	−0.980275	−	0.197640i	$-0.936672\pi$
$61$	−19.4575	+	33.7014i	−0.318976	+	0.552482i	0.661299	+	0.750122i	$0.270005\pi$
$62$		−	82.6714i		−	1.33341i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−0.461088	−	0.266209i	−0.00709365	−	0.00409552i
$66$	−2.01983	−	61.7160i	−0.0306034	−	0.935090i
$67$	−35.2915	−	61.1267i	−0.526739	−	0.912338i	−0.999515	−	0.0311556i	$-0.990081\pi$
$67$	−35.2915	−	61.1267i	−0.526739	−	0.912338i	0.472776	−	0.881183i	$-0.343252\pi$
$68$	−37.3027	−	21.5367i	−0.548569	−	0.316716i
$69$	−54.9150	+	102.737i	−0.795870	+	1.48894i
$70$		0			0
$71$		−	17.0279i		−	0.239829i	−0.992784	−	0.119915i	$-0.961738\pi$
$71$		−	17.0279i		−	0.239829i	0.992784	−	0.119915i	$-0.0382621\pi$
$72$	1.66444	+	25.4014i	0.0231173	+	0.352797i
$73$	−36.1660	−	62.6414i	−0.495425	−	0.858101i	0.504561	−	0.863376i	$-0.331654\pi$
$73$	−36.1660	−	62.6414i	−0.495425	−	0.858101i	−0.999986	+	0.00527495i	$0.998321\pi$
$74$	24.4949	−	14.1421i	0.331012	−	0.191110i
$75$	−61.5658	+	38.2833i	−0.820878	+	0.510444i
$76$	32.0000			0.421053
$77$		0			0
$78$	1.16601	−	2.18141i	0.0149489	−	0.0279667i
$79$	−10.4575	+	18.1129i	−0.132374	+	0.229278i	−0.924591	−	0.380961i	$-0.875593\pi$
$79$	−10.4575	+	18.1129i	−0.132374	+	0.229278i	0.792217	+	0.610239i	$0.208927\pi$
$80$	−3.16352	+	1.82646i	−0.0395440	+	0.0228308i
$81$	80.3074	−	10.5698i	0.991449	−	0.130491i
$82$	−6.18824	+	10.7183i	−0.0754663	+	0.130711i
$83$		−	145.544i		−	1.75354i	−0.480910	−	0.876770i	$-0.659694\pi$
$83$		−	145.544i		−	1.75354i	0.480910	−	0.876770i	$-0.340306\pi$
$84$		0			0
$85$	−19.6680			−0.231388
$86$	14.3895	+	8.30781i	0.167320	+	0.0966024i
$87$	107.245	−	3.50990i	1.23271	−	0.0403437i
$88$	20.5830	+	35.6508i	0.233898	+	0.405123i
$89$	−46.4635	−	26.8257i	−0.522061	−	0.301412i	0.215716	−	0.976456i	$-0.430791\pi$
$89$	−46.4635	−	26.8257i	−0.522061	−	0.301412i	−0.737778	+	0.675044i	$0.764125\pi$
$90$	6.45751	+	9.66472i	0.0717501	+	0.107386i
$91$		0			0
$92$		−	77.6616i		−	0.844148i
$93$	148.928	−	92.6073i	1.60137	−	0.995777i
$94$	−6.00000	−	10.3923i	−0.0638298	−	0.110556i
$95$	12.6541	−	7.30584i	0.133201	−	0.0769036i
$96$	−8.96148	−	14.4115i	−0.0933488	−	0.150120i
$97$	−111.166			−1.14604			−0.573021	−	0.819541i	$-0.694229\pi$
$97$	−111.166			−1.14604			−0.573021	+	0.819541i	$0.694229\pi$
$98$		0			0
$99$	108.915	−	72.7719i	1.10015	−	0.735070i
$100$	24.1660	−	41.8568i	0.241660	−	0.418568i
$101$	−50.0881	+	28.9184i	−0.495921	+	0.286320i	−0.727028	−	0.686608i	$-0.759099\pi$
$101$	−50.0881	+	28.9184i	−0.495921	+	0.286320i	0.231106	+	0.972929i	$0.425766\pi$
$102$	−2.98882	−	91.3236i	−0.0293022	−	0.895330i
$103$	59.6863	−	103.380i	0.579478	−	1.00369i	−0.416061	−	0.909337i	$-0.636590\pi$
$103$	59.6863	−	103.380i	0.579478	−	1.00369i	0.995539	−	0.0943492i	$-0.0300770\pi$
$104$			1.64899i			0.0158557i
$105$		0			0
$106$	72.0000			0.679245
$107$	100.885	+	58.2462i	0.942854	+	0.544357i	0.890854	−	0.454290i	$-0.150107\pi$
$107$	100.885	+	58.2462i	0.942854	+	0.544357i	0.0520000	+	0.998647i	$0.483440\pi$
$108$	−43.8946	+	31.4526i	−0.406431	+	0.291228i
$109$	−43.9150	−	76.0631i	−0.402890	−	0.697826i	0.591183	−	0.806537i	$-0.298661\pi$
$109$	−43.9150	−	76.0631i	−0.402890	−	0.697826i	−0.994073	+	0.108711i	$0.965328\pi$
$110$	16.2787	+	9.39851i	0.147988	+	0.0854410i
$111$	52.9150	+	28.2843i	0.476712	+	0.254813i
$112$		0			0
$113$			69.1763i			0.612180i	0.952003	+	0.306090i	$0.0990208\pi$
$113$			69.1763i			0.612180i	−0.952003	+	0.306090i	$0.900979\pi$
$114$	35.8459	+	57.6461i	0.314438	+	0.505667i
$115$	−17.7307	−	30.7105i	−0.154180	−	0.267048i
$116$	−61.9513	+	35.7676i	−0.534063	+	0.308341i
$117$	5.23582	−	0.343081i	0.0447506	−	0.00293232i
$118$	−82.3320			−0.697729
$119$		0			0
$120$	−6.83399	−	3.65292i	−0.0569499	−	0.0304410i
$121$	45.4150	−	78.6611i	0.375331	−	0.650092i
$122$	47.6610	−	27.5171i	0.390664	−	0.225550i
$123$	−26.2404	+	0.858791i	−0.213337	+	0.00698204i
$124$	−58.4575	+	101.251i	−0.471432	+	0.816543i
$125$		−	44.8999i		−	0.359199i
$126$		0			0
$127$	−27.0850			−0.213268			−0.106634	−	0.994298i	$-0.534007\pi$
$127$	−27.0850			−0.213268			−0.106634	+	0.994298i	$0.534007\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	1.15294	+	35.2282i	0.00893752	+	0.273087i
$130$	0.376476	+	0.652076i	0.00289597	+	0.00501597i
$131$	−126.045	−	72.7719i	−0.962173	−	0.555511i	−0.0653318	−	0.997864i	$-0.520811\pi$
$131$	−126.045	−	72.7719i	−0.962173	−	0.555511i	−0.896841	+	0.442353i	$0.854144\pi$
$132$	−41.1660	+	77.0146i	−0.311864	+	0.583444i
$133$		0			0
$134$			99.8194i			0.744921i
$135$	−10.1768	+	22.4591i	−0.0753837	+	0.166364i
$136$	30.4575	+	52.7540i	0.223952	+	0.387897i
$137$	21.4851	−	12.4044i	0.156825	−	0.0905431i	−0.419534	−	0.907740i	$-0.637806\pi$
$137$	21.4851	−	12.4044i	0.156825	−	0.0905431i	0.576359	+	0.817197i	$0.304473\pi$
$138$	139.903	−	86.9953i	1.01379	−	0.630401i
$139$	146.458			1.05365			0.526826	−	0.849973i	$-0.323382\pi$
$139$	146.458			1.05365			0.526826	+	0.849973i	$0.323382\pi$
$140$		0			0
$141$	12.0000	−	22.4499i	0.0851064	−	0.159219i
$142$	−12.0405	+	20.8548i	−0.0847924	+	0.146865i
$143$	7.34847	−	4.24264i	0.0513879	−	0.0296688i
$144$	15.9230	−	32.2871i	0.110576	−	0.224216i
$145$	−16.3320	+	28.2879i	−0.112635	+	0.195089i
$146$			102.293i			0.700636i
$147$		0			0
$148$	−40.0000			−0.270270
$149$	−190.138	−	109.776i	−1.27609	−	0.736753i	−0.299966	−	0.953950i	$-0.596975\pi$
$149$	−190.138	−	109.776i	−1.27609	−	0.736753i	−0.976128	+	0.217197i	$0.930309\pi$
$150$	102.473	−	3.35371i	0.683152	−	0.0223581i
$151$	105.830	+	183.303i	0.700861	+	1.21393i	0.968164	+	0.250315i	$0.0805341\pi$
$151$	105.830	+	183.303i	0.700861	+	1.21393i	−0.267303	+	0.963612i	$0.586133\pi$
$152$	−39.1918	−	22.6274i	−0.257841	−	0.148865i
$153$	161.166	−	107.684i	1.05337	−	0.703814i
$154$		0			0
$155$			53.3852i			0.344420i
$156$	−2.97055	+	1.84717i	−0.0190420	+	0.0118408i
$157$	−104.373	−	180.779i	−0.664793	−	1.15146i	−0.979341	−	0.202214i	$-0.935186\pi$
$157$	−104.373	−	180.779i	−0.664793	−	1.15146i	0.314548	−	0.949242i	$-0.398147\pi$
$158$	25.6156	−	14.7892i	0.162124	−	0.0936023i
$159$	80.6533	+	129.704i	0.507254	+	0.815746i
$160$	5.16601			0.0322876
$161$		0			0
$162$	−105.830	−	43.8406i	−0.653272	−	0.270621i
$163$	−133.498	+	231.225i	−0.819006	+	1.41856i	0.0874088	+	0.996173i	$0.472141\pi$
$163$	−133.498	+	231.225i	−0.819006	+	1.41856i	−0.906415	+	0.422388i	$0.861192\pi$
$164$	15.1580	−	8.75149i	0.0924270	−	0.0533627i
$165$	1.30431	+	39.8532i	0.00790488	+	0.241534i
$166$	−102.915	+	178.254i	−0.619970	+	1.07382i
$167$		−	7.19124i		−	0.0430613i	−0.999768	−	0.0215307i	$-0.993146\pi$
$167$		−	7.19124i		−	0.0430613i	0.999768	−	0.0215307i	$-0.00685395\pi$
$168$		0			0
$169$	−168.660			−0.997989
$170$	24.0883	+	13.9074i	0.141696	+	0.0818080i
$171$	−63.6919	+	129.149i	−0.372467	+	0.755255i
$172$	−11.7490	−	20.3499i	−0.0683082	−	0.118313i
$173$	166.741	+	96.2682i	0.963823	+	0.556464i	0.897348	−	0.441325i	$-0.145491\pi$
$173$	166.741	+	96.2682i	0.963823	+	0.556464i	0.0664755	+	0.997788i	$0.478825\pi$
$174$	−133.830	−	71.5352i	−0.769138	−	0.411122i
$175$		0			0
$176$		−	58.2175i		−	0.330781i
$177$	−92.2271	−	148.316i	−0.521057	−	0.837944i
$178$	37.9373	+	65.7093i	0.213131	+	0.369153i
$179$	−37.8134	+	21.8316i	−0.211248	+	0.121964i	−0.601891	−	0.798578i	$-0.705586\pi$
$179$	−37.8134	+	21.8316i	−0.211248	+	0.121964i	0.390643	+	0.920542i	$0.372253\pi$
$180$	−1.07482	−	16.4030i	−0.00597120	−	0.0911276i
$181$	−81.0850			−0.447983			−0.223992	−	0.974591i	$-0.571909\pi$
$181$	−81.0850			−0.447983			−0.223992	+	0.974591i	$0.571909\pi$
$182$		0			0
$183$	102.959	+	55.0342i	0.562620	+	0.300733i
$184$	−54.9150	+	95.1156i	−0.298451	+	0.516933i
$185$	−15.8176	+	9.13230i	−0.0855006	+	0.0493638i
$186$	−247.882	+	8.11261i	−1.33270	+	0.0436162i
$187$	156.727	−	271.459i	0.838111	−	1.45165i
$188$			16.9706i			0.0902690i
$189$		0			0
$190$	−20.6640			−0.108758
$191$	−46.3818	−	26.7785i	−0.242837	−	0.140202i	0.373643	−	0.927573i	$-0.378108\pi$
$191$	−46.3818	−	26.7785i	−0.242837	−	0.140202i	−0.616480	+	0.787371i	$0.711442\pi$
$192$	0.785046	+	23.9872i	0.00408878	+	0.124933i
$193$	55.2470	+	95.6907i	0.286254	+	0.495807i	0.972913	−	0.231174i	$-0.0742565\pi$
$193$	55.2470	+	95.6907i	0.286254	+	0.495807i	−0.686658	+	0.726980i	$0.740923\pi$
$194$	136.150	+	78.6062i	0.701804	+	0.405187i
$195$	−0.752953	+	1.40865i	−0.00386130	+	0.00722382i
$196$		0			0
$197$		−	86.1469i		−	0.437294i	−0.975804	−	0.218647i	$-0.929836\pi$
$197$		−	86.1469i		−	0.437294i	0.975804	−	0.218647i	$-0.0701643\pi$
$198$	−184.851	+	12.1125i	−0.933589	+	0.0611741i
$199$	44.0000	+	76.2102i	0.221106	+	0.382966i	0.955144	−	0.296142i	$-0.0957001\pi$
$199$	44.0000	+	76.2102i	0.221106	+	0.382966i	−0.734038	+	0.679108i	$0.762367\pi$
$200$	−59.1944	+	34.1759i	−0.295972	+	0.170879i
$201$	−179.819	+	111.816i	−0.894620	+	0.556300i
$202$	81.7935			0.404918
$203$		0			0
$204$	−60.9150	+	113.962i	−0.298603	+	0.558635i
$205$	3.99606	−	6.92138i	0.0194930	−	0.0337628i
$206$	−146.201	+	84.4091i	−0.709713	+	0.409753i
$207$	313.434	+	154.575i	1.51417	+	0.746741i
$208$	1.16601	−	2.01959i	0.00560582	−	0.00970956i
$209$			232.870i			1.11421i
$210$		0			0
$211$	−61.2549			−0.290308			−0.145154	−	0.989409i	$-0.546368\pi$
$211$	−61.2549			−0.290308			−0.145154	+	0.989409i	$0.546368\pi$
$212$	−88.1816	−	50.9117i	−0.415951	−	0.240149i
$213$	−51.0563	+	1.67096i	−0.239701	+	0.00784487i
$214$	−82.3725	−	142.673i	−0.384918	−	0.666698i
$215$	−9.29207	−	5.36478i	−0.0432189	−	0.0249525i
$216$	76.0000	−	7.48331i	0.351852	−	0.0346450i
$217$		0			0
$218$			124.210i			0.569773i
$219$	−184.275	+	114.587i	−0.841436	+	0.523228i
$220$	−13.2915	−	23.0216i	−0.0604159	−	0.104643i
$221$	10.8738	−	6.27801i	0.0492029	−	0.0284073i
$222$	−44.8074	−	72.0576i	−0.201835	−	0.324584i
$223$	150.494			0.674861			0.337431	−	0.941350i	$-0.390442\pi$
$223$	150.494			0.674861			0.337431	+	0.941350i	$0.390442\pi$
$224$		0			0
$225$	120.830	+	180.842i	0.537022	+	0.803742i
$226$	48.9150	−	84.7233i	0.216438	−	0.374882i
$227$	−165.028	+	95.2792i	−0.726997	+	0.419732i	−0.817323	−	0.576180i	$-0.804543\pi$
$227$	−165.028	+	95.2792i	−0.726997	+	0.419732i	0.0903255	+	0.995912i	$0.471209\pi$
$228$	−3.14019	−	95.9486i	−0.0137727	−	0.420827i
$229$	71.4575	−	123.768i	0.312042	−	0.540472i	−0.666763	−	0.745270i	$-0.732321\pi$
$229$	71.4575	−	123.768i	0.312042	−	0.540472i	0.978804	+	0.204798i	$0.0656539\pi$
$230$			50.1501i			0.218044i
$231$		0			0
$232$	101.166			0.436060
$233$	6.78813	+	3.91913i	0.0291336	+	0.0168203i	0.514496	−	0.857493i	$-0.327979\pi$
$233$	6.78813	+	3.91913i	0.0291336	+	0.0168203i	−0.485362	+	0.874313i	$0.661312\pi$
$234$	−6.65514	−	3.28210i	−0.0284408	−	0.0140261i
$235$	3.87451	+	6.71084i	0.0164873	+	0.0285568i
$236$	100.836	+	58.2175i	0.427270	+	0.246684i
$237$	55.3360	+	29.5783i	0.233485	+	0.124803i
$238$		0			0
$239$		−	213.369i		−	0.892756i	−0.894844	−	0.446378i	$-0.852714\pi$
$239$		−	213.369i		−	0.892756i	0.894844	−	0.446378i	$-0.147286\pi$
$240$	5.78689	+	9.30626i	0.0241120	+	0.0387761i
$241$	65.0000	+	112.583i	0.269710	+	0.467151i	0.968787	−	0.247896i	$-0.0797390\pi$
$241$	65.0000	+	112.583i	0.269710	+	0.467151i	−0.699077	+	0.715046i	$0.746406\pi$
$242$	−111.244	+	64.2265i	−0.459684	+	0.265399i
$243$	−39.5730	−	239.756i	−0.162852	−	0.986651i
$244$	−77.8301			−0.318976
$245$		0			0
$246$	32.7451	+	17.5030i	0.133110	+	0.0711503i
$247$	−4.66404	+	8.07836i	−0.0188828	+	0.0327059i
$248$	143.191	−	82.6714i	0.577383	−	0.333352i
$249$	−436.398	+	14.2823i	−1.75260	+	0.0573588i
$250$	−31.7490	+	54.9909i	−0.126996	+	0.219964i
$251$			389.258i			1.55083i	0.631453	+	0.775415i	$0.282459\pi$
$251$			389.258i			1.55083i	−0.631453	+	0.775415i	$0.717541\pi$
$252$		0			0
$253$	565.158			2.23383
$254$	33.1722	+	19.1520i	0.130599	+	0.0754015i
$255$	1.93003	+	58.9724i	0.00756876	+	0.231264i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	291.105	+	168.070i	1.13270	+	0.653967i	0.944614	−	0.328184i	$-0.106437\pi$
$257$	291.105	+	168.070i	1.13270	+	0.653967i	0.188091	+	0.982152i	$0.439770\pi$
$258$	23.4980	−	43.9608i	0.0910776	−	0.170391i
$259$		0			0
$260$		−	1.06484i		−	0.00409552i
$261$	−21.0481	−	321.219i	−0.0806442	−	1.23073i
$262$	102.915	+	178.254i	0.392805	+	0.680359i
$263$	380.127	−	219.467i	1.44535	−	0.834473i	0.447151	−	0.894458i	$-0.352439\pi$
$263$	380.127	−	219.467i	1.44535	−	0.834473i	0.998199	+	0.0599849i	$0.0191053\pi$
$264$	104.875	−	65.2144i	0.397255	−	0.247024i
$265$	−46.4941			−0.175449
$266$		0			0
$267$	−75.8745	+	141.948i	−0.284174	+	0.531641i
$268$	70.5830	−	122.253i	0.263369	−	0.456169i
$269$	12.5228	−	7.23004i	0.0465531	−	0.0268775i	−0.476543	−	0.879151i	$-0.658110\pi$
$269$	12.5228	−	7.23004i	0.0465531	−	0.0268775i	0.523096	+	0.852274i	$0.324777\pi$
$270$	28.3450	−	20.3106i	0.104981	−	0.0752244i
$271$	−30.7712	+	53.2974i	−0.113547	+	0.196669i	−0.917198	−	0.398432i	$-0.869555\pi$
$271$	−30.7712	+	53.2974i	−0.113547	+	0.196669i	0.803651	+	0.595101i	$0.202888\pi$
$272$		−	86.1469i		−	0.316716i
$273$		0			0
$274$	−35.0850			−0.128047
$275$	304.600	+	175.861i	1.10764	+	0.639493i
$276$	−232.860	+	7.62099i	−0.843696	+	0.0276123i
$277$	−75.2470	−	130.332i	−0.271650	−	0.470512i	0.697634	−	0.716454i	$-0.254236\pi$
$277$	−75.2470	−	130.332i	−0.271650	−	0.470512i	−0.969284	+	0.245942i	$0.920903\pi$
$278$	−179.373	−	103.561i	−0.645227	−	0.372522i
$279$	−292.288	−	437.456i	−1.04763	−	1.56794i
$280$		0			0
$281$		−	300.220i		−	1.06840i	−0.845359	−	0.534199i	$-0.820613\pi$
$281$		−	300.220i		−	1.06840i	0.845359	−	0.534199i	$-0.179387\pi$
$282$	−30.5714	+	19.0102i	−0.108409	+	0.0674120i
$283$	−49.4170	−	85.5927i	−0.174618	−	0.302448i	0.765411	−	0.643542i	$-0.222536\pi$
$283$	−49.4170	−	85.5927i	−0.174618	−	0.302448i	−0.940029	+	0.341094i	$0.889202\pi$
$284$	29.4931	−	17.0279i	0.103849	−	0.0599573i
$285$	−23.1476	−	37.2250i	−0.0812195	−	0.130614i
$286$	−12.0000			−0.0419580
$287$		0			0
$288$	−42.3320	+	28.2843i	−0.146986	+	0.0982093i
$289$	87.4150	−	151.407i	0.302474	−	0.523901i
$290$	40.0051	−	23.0970i	0.137949	−	0.0796447i
$291$	10.9088	+	333.320i	0.0374873	+	1.14543i
$292$	72.3320	−	125.283i	0.247712	−	0.429050i
$293$		−	7.15424i		−	0.0244172i	−0.999925	−	0.0122086i	$-0.996114\pi$
$293$		−	7.15424i		−	0.0244172i	0.999925	−	0.0122086i	$-0.00388621\pi$
$294$		0			0
$295$	53.1660			0.180224
$296$	48.9898	+	28.2843i	0.165506	+	0.0955550i
$297$	−228.887	−	319.429i	−0.770663	−	1.07552i
$298$	155.247	+	268.896i	0.520963	+	0.902335i
$299$	19.6056	+	11.3193i	0.0655704	+	0.0378571i
$300$	−127.875	−	68.3518i	−0.426248	−	0.227839i
$301$		0			0
$302$		−	299.333i		−	0.991168i
$303$	91.6238	+	147.346i	0.302389	+	0.486290i
$304$	32.0000	+	55.4256i	0.105263	+	0.182321i
$305$	−30.7771	+	17.7692i	−0.100909	+	0.0582596i
$306$	−273.531	+	17.9233i	−0.893892	+	0.0585729i
$307$	105.830			0.344723			0.172362	−	0.985034i	$-0.444860\pi$
$307$	105.830			0.344723			0.172362	+	0.985034i	$0.444860\pi$
$308$		0			0
$309$	−315.830	−	168.818i	−1.02210	−	0.546337i
$310$	37.7490	−	65.3832i	0.121771	−	0.210914i
$311$	229.845	−	132.701i	0.739053	−	0.426692i	−0.0826721	−	0.996577i	$-0.526345\pi$
$311$	229.845	−	132.701i	0.739053	−	0.426692i	0.821725	+	0.569885i	$0.193012\pi$
$312$	4.94432	−	0.161816i	0.0158472	−	0.000518643i
$313$	−129.664	+	224.585i	−0.414262	+	0.717523i	−0.995351	−	0.0963173i	$-0.969294\pi$
$313$	−129.664	+	224.585i	−0.414262	+	0.717523i	0.581089	+	0.813840i	$0.302627\pi$
$314$			295.210i			0.940160i
$315$		0			0
$316$	−41.8301			−0.132374
$317$	32.7559	+	18.9116i	0.103331	+	0.0596581i	0.550775	−	0.834654i	$-0.314332\pi$
$317$	32.7559	+	18.9116i	0.103331	+	0.0596581i	−0.447444	+	0.894312i	$0.647666\pi$
$318$	−7.06542	−	215.884i	−0.0222183	−	0.678882i
$319$	−260.288	−	450.831i	−0.815948	−	1.41326i
$320$	−6.32704	−	3.65292i	−0.0197720	−	0.0114154i
$321$	164.745	−	308.210i	0.513225	−	0.960155i
$322$		0			0
$323$			344.587i			1.06683i
$324$	98.6148	+	128.527i	0.304367	+	0.396687i
$325$	7.04446	+	12.2014i	0.0216752	+	0.0375426i
$326$	327.002	−	188.795i	1.00307	−	0.579125i
$327$	−223.758	+	139.139i	−0.684274	+	0.425501i
$328$	−24.7530			−0.0754663
$329$		0			0
$330$	26.5830	−	49.7322i	0.0805546	−	0.150704i
$331$	−72.7451	+	125.998i	−0.219774	+	0.380659i	−0.954739	−	0.297446i	$-0.903865\pi$
$331$	−72.7451	+	125.998i	−0.219774	+	0.380659i	0.734965	+	0.678105i	$0.237199\pi$
$332$	252.089	−	145.544i	0.759305	−	0.438385i
$333$	79.6148	−	161.436i	0.239084	−	0.484792i
$334$	−5.08497	+	8.80743i	−0.0152245	+	0.0263696i
$335$		−	64.4585i		−	0.192414i
$336$		0			0
$337$	−600.316			−1.78135			−0.890677	−	0.454637i	$-0.849769\pi$
$337$	−600.316			−1.78135			−0.890677	+	0.454637i	$0.849769\pi$
$338$	206.566	+	119.261i	0.611141	+	0.352842i
$339$	207.418	−	6.78832i	0.611852	−	0.0200246i
$340$	−19.6680	−	34.0659i	−0.0578470	−	0.100194i
$341$	−736.826	−	425.407i	−2.16078	−	1.24753i
$342$	169.328	−	113.137i	0.495111	−	0.330810i
$343$		0			0
$344$			33.2312i			0.0966024i
$345$	−90.3423	+	56.1774i	−0.261862	+	0.162833i
$346$	−136.144	−	235.808i	−0.393479	−	0.681526i
$347$	−27.4007	+	15.8198i	−0.0789644	+	0.0455901i	−0.538962	−	0.842330i	$-0.681183\pi$
$347$	−27.4007	+	15.8198i	−0.0789644	+	0.0455901i	0.459998	+	0.887920i	$0.347850\pi$
$348$	113.325	+	182.244i	0.325646	+	0.523691i
$349$	−592.405			−1.69744			−0.848718	−	0.528846i	$-0.822625\pi$
$349$	−592.405			−1.69744			−0.848718	+	0.528846i	$0.822625\pi$
$350$		0			0
$351$	−1.54249	−	15.6654i	−0.00439455	−	0.0446307i
$352$	−41.1660	+	71.3016i	−0.116949	+	0.202561i
$353$	538.648	−	310.988i	1.52591	−	0.880987i	0.526386	−	0.850245i	$-0.323547\pi$
$353$	538.648	−	310.988i	1.52591	−	0.880987i	0.999527	−	0.0307412i	$-0.00978678\pi$
$354$	8.07931	+	246.864i	0.0228229	+	0.697356i
$355$	7.77518	−	13.4670i	0.0219019	−	0.0379352i
$356$		−	107.303i		−	0.301412i
$357$		0			0
$358$	61.7490			0.172483
$359$	432.588	+	249.755i	1.20498	+	0.695696i	0.961658	−	0.274250i	$-0.0884296\pi$
$359$	432.588	+	249.755i	1.20498	+	0.695696i	0.243322	+	0.969946i	$0.421763\pi$
$360$	−10.2823	+	20.8495i	−0.0285619	+	0.0579152i
$361$	52.5000	+	90.9327i	0.145429	+	0.251891i
$362$	99.3084	+	57.3357i	0.274333	+	0.158386i
$363$	−240.314	−	128.453i	−0.662021	−	0.353865i
$364$		0			0
$365$		−	66.0558i		−	0.180975i
$366$	−87.1841	−	140.206i	−0.238208	−	0.383077i
$367$	−36.5020	−	63.2233i	−0.0994604	−	0.172270i	0.812001	−	0.583656i	$-0.198378\pi$
$367$	−36.5020	−	63.2233i	−0.0994604	−	0.172270i	−0.911461	+	0.411386i	$0.865045\pi$
$368$	134.514	−	77.6616i	0.365527	−	0.211037i
$369$	5.14999	+	78.5949i	0.0139566	+	0.212994i
$370$	25.8301			0.0698110
$371$		0			0
$372$	309.328	+	165.343i	0.831527	+	0.444470i
$373$	237.332	−	411.071i	0.636279	−	1.10207i	−0.349964	−	0.936763i	$-0.613806\pi$
$373$	237.332	−	411.071i	0.636279	−	1.10207i	0.986243	−	0.165304i	$-0.0528606\pi$
$374$	−383.901	+	221.645i	−1.02647	+	0.592634i
$375$	−134.628	+	4.40606i	−0.359007	+	0.0117495i
$376$	12.0000	−	20.7846i	0.0319149	−	0.0552782i
$377$		−	20.8527i		−	0.0553122i
$378$		0			0
$379$	−223.660			−0.590132			−0.295066	−	0.955477i	$-0.595342\pi$
$379$	−223.660			−0.590132			−0.295066	+	0.955477i	$0.595342\pi$
$380$	25.3082	+	14.6117i	0.0666005	+	0.0384518i
$381$	2.65787	+	81.2114i	0.00697604	+	0.213153i
$382$	37.8706	+	65.5938i	0.0991376	+	0.171711i
$383$	448.753	+	259.088i	1.17168	+	0.676469i	0.954075	−	0.299568i	$-0.0968426\pi$
$383$	448.753	+	259.088i	1.17168	+	0.676469i	0.217604	+	0.976037i	$0.430176\pi$
$384$	16.0000	−	29.9333i	0.0416667	−	0.0779512i
$385$		0			0
$386$		−	156.262i		−	0.404824i
$387$	105.515	−	6.91394i	0.272648	−	0.0178655i
$388$	−111.166	−	192.545i	−0.286510	−	0.496250i
$389$	−38.2249	+	22.0691i	−0.0982644	+	0.0567330i	−0.548327	−	0.836264i	$-0.684735\pi$
$389$	−38.2249	+	22.0691i	−0.0982644	+	0.0567330i	0.450062	+	0.892997i	$0.351402\pi$
$390$	1.91824	−	1.19281i	0.00491856	−	0.00305850i
$391$	836.288			2.13884
$392$		0			0
$393$	−205.830	+	385.073i	−0.523741	+	0.979829i
$394$	−60.9150	+	105.508i	−0.154607	+	0.267787i
$395$	−16.5413	+	9.55012i	−0.0418767	+	0.0241775i
$396$	234.960	+	115.874i	0.593333	+	0.292612i
$397$	−149.708	+	259.303i	−0.377099	+	0.653155i	−0.990639	−	0.136509i	$-0.956412\pi$
$397$	−149.708	+	259.303i	−0.377099	+	0.653155i	0.613539	+	0.789664i	$0.289745\pi$
$398$		−	124.451i		−	0.312690i
$399$		0			0
$400$	96.6640			0.241660
$401$	239.896	+	138.504i	0.598245	+	0.345397i	0.768351	−	0.640029i	$-0.221078\pi$
$401$	239.896	+	138.504i	0.598245	+	0.345397i	−0.170106	+	0.985426i	$0.554411\pi$
$402$	299.298	−	9.79536i	0.744523	−	0.0243666i
$403$	−17.0405	−	29.5150i	−0.0422842	−	0.0732383i
$404$	−100.176	−	57.8367i	−0.247961	−	0.143160i
$405$	68.3399	+	28.3101i	0.168740	+	0.0699016i
$406$		0			0
$407$		−	291.088i		−	0.715203i
$408$	155.188	−	96.5004i	0.380364	−	0.236521i
$409$	370.490	+	641.708i	0.905844	+	1.56897i	0.819780	+	0.572678i	$0.194095\pi$
$409$	370.490	+	641.708i	0.905844	+	1.56897i	0.0860635	+	0.996290i	$0.472571\pi$
$410$	−9.78832	+	5.65129i	−0.0238739	+	0.0137836i
$411$	−39.3017	−	63.2035i	−0.0956245	−	0.153780i
$412$	238.745			0.579478
$413$		0			0
$414$	−274.575	−	410.946i	−0.663225	−	0.992624i
$415$	66.4575	−	115.108i	0.160139	−	0.277368i
$416$	−2.85613	+	1.64899i	−0.00686570	+	0.00396391i
$417$	−14.3720	−	439.137i	−0.0344652	−	1.05309i
$418$	164.664	−	285.206i	0.393933	−	0.682312i
$419$		−	89.7998i		−	0.214319i	−0.994242	−	0.107160i	$-0.965824\pi$
$419$		−	89.7998i		−	0.214319i	0.994242	−	0.107160i	$-0.0341756\pi$
$420$		0			0
$421$	281.150			0.667815			0.333908	−	0.942606i	$-0.391633\pi$
$421$	281.150			0.667815			0.333908	+	0.942606i	$0.391633\pi$
$422$	75.0217	+	43.3138i	0.177776	+	0.102639i
$423$	−68.4914	−	33.7777i	−0.161918	−	0.0798527i
$424$	72.0000	+	124.708i	0.169811	+	0.294122i
$425$	450.729	+	260.228i	1.06054	+	0.612302i
$426$	63.7124	+	34.0557i	0.149560	+	0.0799430i
$427$		0			0
$428$			232.985i			0.544357i
$429$	−13.4422	−	21.6173i	−0.0313339	−	0.0503899i
$430$	7.58694	+	13.1410i	0.0176441	+	0.0305604i
$431$	−485.148	+	280.100i	−1.12563	+	0.649885i	−0.942833	−	0.333266i	$-0.891849\pi$
$431$	−485.148	+	280.100i	−1.12563	+	0.649885i	−0.182800	+	0.983150i	$0.558516\pi$
$432$	−98.3721	−	44.5750i	−0.227713	−	0.103183i
$433$	−543.004			−1.25405			−0.627025	−	0.778999i	$-0.715728\pi$
$433$	−543.004			−1.25405			−0.627025	+	0.778999i	$0.715728\pi$
$434$		0			0
$435$	86.4209	+	46.1939i	0.198669	+	0.106193i
$436$	87.8301	−	152.126i	0.201445	−	0.348913i
$437$	−538.055	+	310.646i	−1.23125	+	0.710861i
$438$	306.715	−	10.0381i	0.700262	−	0.0229180i
$439$	−171.085	+	296.328i	−0.389715	+	0.675007i	−0.992411	−	0.122964i	$-0.960760\pi$
$439$	−171.085	+	296.328i	−0.389715	+	0.675007i	0.602696	+	0.797971i	$0.294093\pi$
$440$			37.5940i			0.0854410i
$441$		0			0
$442$	−17.7569			−0.0401740
$443$	−346.251	−	199.908i	−0.781604	−	0.451259i	0.0553944	−	0.998465i	$-0.482358\pi$
$443$	−346.251	−	199.908i	−0.781604	−	0.451259i	−0.836998	+	0.547205i	$0.815692\pi$
$444$	3.92523	+	119.936i	0.00884061	+	0.270126i
$445$	−24.4980	−	42.4318i	−0.0550518	−	0.0953524i
$446$	−184.317	−	106.415i	−0.413267	−	0.238600i
$447$	−310.494	+	580.881i	−0.694618	+	1.29951i
$448$		0			0
$449$			737.040i			1.64151i	0.571277	+	0.820757i	$0.306448\pi$
$449$			737.040i			1.64151i	−0.571277	+	0.820757i	$0.693552\pi$
$450$	−20.1115	−	306.925i	−0.0446922	−	0.682055i
$451$	63.6863	+	110.308i	0.141211	+	0.244585i
$452$	−119.817	+	69.1763i	−0.265082	+	0.153045i
$453$	539.230	−	335.308i	1.19035	−	0.740194i
$454$	269.490			0.593591
$455$		0			0
$456$	−64.0000	+	119.733i	−0.140351	+	0.262572i
$457$	−332.668	+	576.198i	−0.727939	+	1.26083i	0.229814	+	0.973235i	$0.426188\pi$
$457$	−332.668	+	576.198i	−0.727939	+	1.26083i	−0.957753	+	0.287592i	$0.907145\pi$
$458$	−175.034	+	101.056i	−0.382171	+	0.220647i
$459$	−338.693	−	472.672i	−0.737894	−	1.02979i
$460$	35.4615	−	61.4210i	0.0770901	−	0.133524i
$461$			318.865i			0.691682i	0.938293	+	0.345841i	$0.112406\pi$
$461$			318.865i			0.691682i	−0.938293	+	0.345841i	$0.887594\pi$
$462$		0			0
$463$	402.332			0.868968			0.434484	−	0.900680i	$-0.356931\pi$
$463$	402.332			0.868968			0.434484	+	0.900680i	$0.356931\pi$
$464$	−123.903	−	71.5352i	−0.267031	−	0.154171i
$465$	160.070	−	5.23873i	0.344236	−	0.0112661i
$466$	−5.54249	−	9.59987i	−0.0118937	−	0.0206006i
$467$	−603.695	−	348.544i	−1.29271	−	0.746346i	−0.313575	−	0.949563i	$-0.601527\pi$
$467$	−603.695	−	348.544i	−1.29271	−	0.746346i	−0.979134	+	0.203217i	$0.934860\pi$
$468$	5.83005	+	8.72562i	0.0124574	+	0.0186445i
$469$		0			0
$470$		−	10.9588i		−	0.0233165i
$471$	−531.803	+	330.690i	−1.12909	+	0.702102i
$472$	−82.3320	−	142.603i	−0.174432	−	0.302126i
$473$	148.090	−	85.4998i	0.313087	−	0.180761i
$474$	−46.8574	−	75.3543i	−0.0988553	−	0.158975i
$475$	−386.656			−0.814013
$476$		0			0
$477$	380.988	−	254.558i	0.798717	−	0.533665i
$478$	−150.875	+	261.322i	−0.315637	+	0.546699i
$479$	141.862	−	81.9042i	0.296163	−	0.170990i	−0.344555	−	0.938766i	$-0.611970\pi$
$479$	141.862	−	81.9042i	0.296163	−	0.170990i	0.640718	+	0.767776i	$0.278637\pi$
$480$	−0.506945	−	15.4897i	−0.00105613	−	0.0322703i
$481$	5.83005	−	10.0979i	0.0121207	−	0.0209937i
$482$		−	183.848i		−	0.381427i
$483$		0			0
$484$	181.660			0.375331
$485$	−87.9190	−	50.7601i	−0.181276	−	0.104660i
$486$	−121.066	+	321.622i	−0.249108	+	0.661774i
$487$	51.7490	+	89.6319i	0.106261	+	0.184049i	0.914253	−	0.405145i	$-0.132779\pi$
$487$	51.7490	+	89.6319i	0.106261	+	0.184049i	−0.807992	+	0.589194i	$0.799445\pi$
$488$	95.3220	+	55.0342i	0.195332	+	0.112775i
$489$	706.405	+	377.589i	1.44459	+	0.772167i
$490$		0			0
$491$		−	570.094i		−	1.16109i	−0.814229	−	0.580544i	$-0.802840\pi$
$491$		−	570.094i		−	1.16109i	0.814229	−	0.580544i	$-0.197160\pi$
$492$	−27.7279	−	44.5910i	−0.0563575	−	0.0906320i
$493$	−385.158	−	667.113i	−0.781254	−	1.35317i
$494$	11.4245	−	6.59595i	0.0231266	−	0.0133521i
$495$	119.368	−	7.82165i	0.241147	−	0.0158013i
$496$	−233.830			−0.471432
$497$		0			0
$498$	544.575	+	291.088i	1.09352	+	0.584513i
$499$	243.830	−	422.326i	0.488637	−	0.846345i	−0.511277	−	0.859416i	$-0.670827\pi$
$499$	243.830	−	422.326i	0.488637	−	0.846345i	0.999915	+	0.0130711i	$0.00416078\pi$
$500$	77.7689	−	44.8999i	0.155538	−	0.0897998i
$501$	−21.5622	+	0.705682i	−0.0430383	+	0.00140855i
$502$	275.247	−	476.742i	0.548301	−	0.949685i
$503$		−	97.9412i		−	0.194714i	−0.995250	−	0.0973571i	$-0.968961\pi$
$503$		−	97.9412i		−	0.194714i	0.995250	−	0.0973571i	$-0.0310389\pi$
$504$		0			0
$505$	−52.8182			−0.104591
$506$	−692.175	−	399.627i	−1.36793	−	0.789777i
$507$	16.5507	+	505.710i	0.0326445	+	0.997455i
$508$	−27.0850	−	46.9126i	−0.0533169	−	0.0923475i
$509$	275.486	+	159.052i	0.541230	+	0.312479i	0.745577	−	0.666419i	$-0.232174\pi$
$509$	275.486	+	159.052i	0.541230	+	0.312479i	−0.204347	+	0.978898i	$0.565507\pi$
$510$	39.3360	−	73.5908i	0.0771293	−	0.144296i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	393.488	+	178.300i	0.767034	+	0.347563i
$514$	−237.686	−	411.685i	−0.462425	−	0.800943i
$515$	94.4094	−	54.5073i	0.183319	−	0.105839i
$516$	−59.8641	+	37.2251i	−0.116016	+	0.0721417i
$517$	−123.498			−0.238874
$518$		0			0
$519$	272.288	−	509.403i	0.524639	−	0.981509i
$520$	−0.752953	+	1.30415i	−0.00144799	+	0.00250799i
$521$	−629.730	+	363.575i	−1.20870	+	0.697840i	−0.962474	−	0.271373i	$-0.912522\pi$
$521$	−629.730	+	363.575i	−1.20870	+	0.697840i	−0.246221	+	0.969214i	$0.579189\pi$
$522$	−201.358	+	408.295i	−0.385743	+	0.782175i
$523$	103.812	−	179.807i	0.198493	−	0.343800i	−0.749547	−	0.661951i	$-0.769729\pi$
$523$	103.812	−	179.807i	0.198493	−	0.343800i	0.948040	+	0.318151i	$0.103062\pi$
$524$		−	291.088i		−	0.555511i
$525$		0			0
$526$	−620.745			−1.18012
$527$	−1090.31	−	629.491i	−2.06890	−	1.19448i
$528$	−174.559	+	5.71293i	−0.330604	+	0.0108199i
$529$	489.415	+	847.692i	0.925170	+	1.60244i
$530$	56.9434	+	32.8763i	0.107440	+	0.0620307i
$531$	−435.660	+	291.088i	−0.820452	+	0.548188i
$532$		0			0
$533$			5.10216i			0.00957254i
$534$	193.299	−	120.199i	0.361984	−	0.225092i
$535$	53.1922	+	92.1316i	0.0994246	+	0.172209i
$536$	−172.892	+	99.8194i	−0.322560	+	0.186230i
$537$	69.1703	+	111.237i	0.128809	+	0.207145i
$538$	−20.4496			−0.0380105
$539$		0			0
$540$	−49.0771	+	4.83236i	−0.0908835	+	0.00894882i
$541$	−512.575	+	887.806i	−0.947459	+	1.64105i	−0.196707	+	0.980462i	$0.563025\pi$
$541$	−512.575	+	887.806i	−0.947459	+	1.64105i	−0.750752	+	0.660584i	$0.770309\pi$
$542$	75.3738	−	43.5171i	0.139066	−	0.0802899i
$543$	7.95693	+	243.125i	0.0146537	+	0.447744i
$544$	−60.9150	+	105.508i	−0.111976	+	0.193948i
$545$		−	80.2091i		−	0.147173i
$546$		0			0
$547$	−560.089			−1.02393			−0.511964	−	0.859007i	$-0.671082\pi$
$547$	−560.089			−1.02393			−0.511964	+	0.859007i	$0.671082\pi$
$548$	42.9701	+	24.8088i	0.0784127	+	0.0452716i
$549$	154.911	−	314.114i	0.282169	−	0.572156i
$550$	−248.705	−	430.769i	−0.452190	−	0.783216i
$551$	495.610	+	286.141i	0.899474	+	0.519312i
$552$	290.583	+	155.323i	0.526418	+	0.281383i
$553$		0			0
$554$			212.831i			0.384171i
$555$	28.9344	+	46.5313i	0.0521341	+	0.0838401i
$556$	146.458	+	253.672i	0.263413	+	0.456244i
$557$	−498.575	+	287.853i	−0.895108	+	0.516791i	−0.875610	−	0.483019i	$-0.839540\pi$
$557$	−498.575	+	287.853i	−0.895108	+	0.516791i	−0.0194983	+	0.999810i	$0.506207\pi$
$558$	48.6496	+	742.450i	0.0871857	+	1.33056i
$559$	6.84974			0.0122536
$560$		0			0
$561$	−829.320	−	443.290i	−1.47829	−	0.790179i
$562$	−212.288	+	367.693i	−0.377736	+	0.654258i
$563$	405.783	−	234.279i	0.720751	−	0.416126i	−0.0942781	−	0.995546i	$-0.530054\pi$
$563$	405.783	−	234.279i	0.720751	−	0.416126i	0.815029	+	0.579420i	$0.196721\pi$
$564$	50.8844	−	1.66533i	0.0902206	−	0.00295272i
$565$	−31.5869	+	54.7102i	−0.0559061	+	0.0968322i
$566$			139.772i			0.246948i
$567$		0			0
$568$	−48.1621			−0.0847924
$569$	−438.603	−	253.227i	−0.770831	−	0.445039i	0.0623401	−	0.998055i	$-0.480144\pi$
$569$	−438.603	−	253.227i	−0.770831	−	0.445039i	−0.833171	+	0.553016i	$0.813477\pi$
$570$	2.02778	+	61.9590i	0.00355751	+	0.108700i
$571$	−16.4575	−	28.5052i	−0.0288223	−	0.0499216i	0.851254	−	0.524753i	$-0.175842\pi$
$571$	−16.4575	−	28.5052i	−0.0288223	−	0.0499216i	−0.880077	+	0.474831i	$0.842509\pi$
$572$	14.6969	+	8.48528i	0.0256939	+	0.0148344i
$573$	−75.7411	+	141.699i	−0.132183	+	0.247293i
$574$		0			0
$575$			938.385i			1.63197i
$576$	71.8459	−	4.70776i	0.124733	−	0.00817319i
$577$	126.077	+	218.372i	0.218505	+	0.378461i	0.954351	−	0.298688i	$-0.0965488\pi$
$577$	126.077	+	218.372i	0.218505	+	0.378461i	−0.735846	+	0.677148i	$0.763215\pi$
$578$	−214.122	+	123.624i	−0.370454	+	0.213882i
$579$	281.497	−	175.043i	0.486178	−	0.302319i
$580$	−65.3281			−0.112635
$581$		0			0
$582$	222.332	−	415.945i	0.382014	−	0.714682i
$583$	370.494	−	641.715i	0.635496	−	1.10071i
$584$	−177.177	+	102.293i	−0.303384	+	0.175159i
$585$	4.29756	+	2.11942i	0.00734626	+	0.00362294i
$586$	−5.05881	+	8.76211i	−0.00863278	+	0.0149524i
$587$		−	366.882i		−	0.625012i	−0.949916	−	0.312506i	$-0.898832\pi$
$587$		−	366.882i		−	0.625012i	0.949916	−	0.312506i	$-0.101168\pi$
$588$		0			0
$589$	935.320			1.58798
$590$	−65.1148	−	37.5940i	−0.110364	−	0.0637187i
$591$	−258.302	+	8.45366i	−0.437060	+	0.0143040i
$592$	−40.0000	−	69.2820i	−0.0675676	−	0.117030i
$593$	−537.591	−	310.378i	−0.906562	−	0.523404i	−0.0272383	−	0.999629i	$-0.508671\pi$
$593$	−537.591	−	310.378i	−0.906562	−	0.523404i	−0.879323	+	0.476225i	$0.842005\pi$
$594$	54.4575	+	553.067i	0.0916793	+	0.931088i
$595$		0			0
$596$		−	439.105i		−	0.736753i
$597$	224.191	−	139.408i	0.375529	−	0.233514i
$598$	−16.0079	−	27.7265i	−0.0267690	−	0.0463653i
$599$	22.8187	−	13.1744i	0.0380947	−	0.0219940i	−0.480832	−	0.876813i	$-0.659665\pi$
$599$	22.8187	−	13.1744i	0.0380947	−	0.0219940i	0.518926	+	0.854819i	$0.326332\pi$
$600$	108.282	+	174.134i	0.180469	+	0.290224i
$601$	930.470			1.54820			0.774102	−	0.633061i	$-0.218202\pi$
$601$	930.470			1.54820			0.774102	+	0.633061i	$0.218202\pi$
$602$		0			0
$603$	352.915	+	528.195i	0.585265	+	0.875945i
$604$	−211.660	+	366.606i	−0.350431	+	0.606964i
$605$	71.8357	−	41.4744i	0.118737	−	0.0685527i
$606$	−8.02646	−	245.249i	−0.0132450	−	0.404701i
$607$	−108.073	+	187.188i	−0.178045	+	0.308383i	−0.941211	−	0.337820i	$-0.890311\pi$
$607$	−108.073	+	187.188i	−0.178045	+	0.308383i	0.763166	+	0.646202i	$0.223644\pi$
$608$		−	90.5097i		−	0.148865i
$609$		0			0
$610$	50.2589			0.0823916
$611$	−4.28420	−	2.47348i	−0.00701178	−	0.00404825i
$612$	347.679	+	171.464i	0.568104	+	0.280170i
$613$	134.417	+	232.817i	0.219277	+	0.379799i	0.954587	−	0.297932i	$-0.0962967\pi$
$613$	134.417	+	232.817i	0.219277	+	0.379799i	−0.735310	+	0.677731i	$0.762963\pi$
$614$	−129.615	−	74.8331i	−0.211099	−	0.121878i
$615$	−21.1452	−	11.3026i	−0.0343824	−	0.0183782i
$616$		0			0
$617$			531.338i			0.861163i	0.902552	+	0.430582i	$0.141692\pi$
$617$			531.338i			0.861163i	−0.902552	+	0.430582i	$0.858308\pi$
$618$	267.439	+	430.085i	0.432749	+	0.695930i
$619$	−212.601	−	368.236i	−0.343459	−	0.594889i	0.641613	−	0.767028i	$-0.278265\pi$
$619$	−212.601	−	368.236i	−0.343459	−	0.594889i	−0.985073	+	0.172139i	$0.944932\pi$
$620$	−92.4658	+	53.3852i	−0.149138	+	0.0861051i
$621$	432.720	−	954.967i	0.696812	−	1.53779i
$622$	−375.336			−0.603434
$623$		0			0
$624$	−6.16995	−	3.29798i	−0.00988774	−	0.00528522i
$625$	−281.573	+	487.699i	−0.450517	+	0.780318i
$626$	317.611	−	183.373i	0.507365	−	0.292928i
$627$	698.237	−	22.8517i	1.11361	−	0.0364461i
$628$	208.745	−	361.557i	0.332397	−	0.575728i
$629$		−	430.734i		−	0.684792i
$630$		0			0
$631$	−453.490			−0.718685			−0.359342	−	0.933206i	$-0.616999\pi$
$631$	−453.490			−0.718685			−0.359342	+	0.933206i	$0.616999\pi$
$632$	51.2311	+	29.5783i	0.0810619	+	0.0468011i
$633$	6.01099	+	183.666i	0.00949604	+	0.290152i
$634$	−26.7451	−	46.3238i	−0.0421847	−	0.0730660i
$635$	−21.4210	−	12.3674i	−0.0337338	−	0.0194762i
$636$	−144.000	+	269.399i	−0.226415	+	0.423584i
$637$		0			0
$638$			736.204i			1.15393i
$639$	10.0204	+	152.923i	0.0156813	+	0.239316i
$640$	5.16601	+	8.94779i	0.00807189	+	0.0139809i
$641$	401.364	−	231.728i	0.626153	−	0.361510i	−0.153108	−	0.988210i	$-0.548928\pi$
$641$	401.364	−	231.728i	0.626153	−	0.361510i	0.779261	+	0.626700i	$0.215595\pi$
$642$	−419.708	+	260.986i	−0.653751	+	0.406520i
$643$	820.988			1.27681			0.638405	−	0.769701i	$-0.279595\pi$
$643$	820.988			1.27681			0.638405	+	0.769701i	$0.279595\pi$
$644$		0			0
$645$	−15.1739	+	28.3877i	−0.0235254	+	0.0440120i
$646$	243.660	−	422.032i	0.377183	−	0.653300i
$647$	−863.133	+	498.330i	−1.33405	+	0.770216i	−0.985918	−	0.167228i	$-0.946518\pi$
$647$	−863.133	+	498.330i	−1.33405	+	0.770216i	−0.348136	+	0.937444i	$0.613185\pi$
$648$	−29.8959	−	227.144i	−0.0461356	−	0.350530i
$649$	−423.660	+	733.801i	−0.652789	+	1.13066i
$650$		−	19.9247i		−	0.0306534i
$651$		0			0
$652$	−533.992			−0.819006
$653$	309.692	+	178.801i	0.474261	+	0.273815i	0.718022	−	0.696021i	$-0.245048\pi$
$653$	309.692	+	178.801i	0.474261	+	0.273815i	−0.243761	+	0.969835i	$0.578381\pi$
$654$	372.432	−	12.1889i	0.569468	−	0.0186374i
$655$	−66.4575	−	115.108i	−0.101462	−	0.175737i
$656$	30.3161	+	17.5030i	0.0462135	+	0.0266814i
$657$	361.660	+	541.283i	0.550472	+	0.823871i
$658$		0			0
$659$		−	131.562i		−	0.199640i	−0.995006	−	0.0998198i	$-0.968173\pi$
$659$		−	131.562i		−	0.199640i	0.995006	−	0.0998198i	$-0.0318266\pi$
$660$	−67.7234	+	42.1123i	−0.102611	+	0.0638065i
$661$	125.458	+	217.299i	0.189800	+	0.328742i	0.945183	−	0.326540i	$-0.105883\pi$
$661$	125.458	+	217.299i	0.189800	+	0.328742i	−0.755384	+	0.655283i	$0.772550\pi$
$662$	178.188	−	102.877i	0.269167	−	0.155403i
$663$	−19.8910	−	31.9880i	−0.0300015	−	0.0482473i
$664$	−411.660			−0.619970
$665$		0			0
$666$	−211.660	+	141.421i	−0.317808	+	0.212344i
$667$	694.442	−	1202.81i	1.04114	−	1.80331i
$668$	12.4556	−	7.19124i	0.0186461	−	0.0107653i
$669$	−14.7681	−	451.241i	−0.0220749	−	0.674500i
$670$	−45.5791	+	78.9453i	−0.0680285	+	0.117829i
$671$		−	566.384i		−	0.844090i
$672$		0			0
$673$	196.502			0.291979			0.145990	−	0.989286i	$-0.453363\pi$
$673$	196.502			0.291979			0.145990	+	0.989286i	$0.453363\pi$
$674$	735.234	+	424.488i	1.09085	+	0.629804i
$675$	530.378	−	380.042i	0.785745	−	0.563026i
$676$	−168.660	−	292.128i	−0.249497	−	0.432142i
$677$	−46.9245	−	27.0919i	−0.0693125	−	0.0400176i	0.464943	−	0.885340i	$-0.346075\pi$
$677$	−46.9245	−	27.0919i	−0.0693125	−	0.0400176i	−0.534256	+	0.845323i	$0.679408\pi$
$678$	−258.834	−	138.353i	−0.381761	−	0.204060i
$679$		0			0
$680$			55.6294i			0.0818080i
$681$	301.879	+	485.470i	0.443288	+	0.712879i
$682$	601.616	+	1042.03i	0.882134	+	1.52790i
$683$	−648.659	+	374.503i	−0.949720	+	0.548321i	−0.892994	−	0.450069i	$-0.851399\pi$
$683$	−648.659	+	374.503i	−0.949720	+	0.548321i	−0.0567258	+	0.998390i	$0.518066\pi$
$684$	−287.384	+	18.8310i	−0.420152	+	0.0275307i
$685$	22.6562			0.0330747
$686$		0			0
$687$	−378.118	−	202.112i	−0.550390	−	0.294196i
$688$	23.4980	−	40.6998i	0.0341541	−	0.0591567i
$689$	25.7052	−	14.8409i	0.0373079	−	0.0215398i
$690$	150.370	−	4.92127i	0.217927	−	0.00713227i
$691$	−237.569	+	411.481i	−0.343804	+	0.595486i	−0.985136	−	0.171778i	$-0.945049\pi$
$691$	−237.569	+	411.481i	−0.343804	+	0.595486i	0.641332	+	0.767264i	$0.278382\pi$
$692$			385.073i			0.556464i
$693$		0			0
$694$	44.7451			0.0644742
$695$	115.830	+	66.8747i	0.166662	+	0.0962226i
$696$	−9.92750	−	303.336i	−0.0142636	−	0.435827i
$697$	94.2392	+	163.227i	0.135207	+	0.234185i
$698$	725.545	+	418.894i	1.03946	+	0.600134i
$699$	11.0850	−	20.7381i	0.0158583	−	0.0296682i
$700$		0			0
$701$		−	1251.49i		−	1.78529i	−0.450760	−	0.892645i	$-0.648847\pi$
$701$		−	1251.49i		−	1.78529i	0.450760	−	0.892645i	$-0.351153\pi$
$702$	−9.18795	+	20.2768i	−0.0130882	+	0.0288843i
$703$	160.000	+	277.128i	0.227596	+	0.394208i
$704$	100.836	−	58.2175i	0.143233	−	0.0826954i
$705$	19.7416	−	12.2758i	0.0280022	−	0.0174125i
$706$	−879.608			−1.24590
$707$		0			0
$708$	164.664	−	308.058i	0.232576	−	0.435110i
$709$	8.25492	−	14.2979i	0.0116430	−	0.0201664i	−0.860145	−	0.510049i	$-0.829627\pi$
$709$	8.25492	−	14.2979i	0.0116430	−	0.0201664i	0.871788	+	0.489883i	$0.162960\pi$
$710$	−19.0452	+	10.9958i	−0.0268243	+	0.0154870i
$711$	83.2573	−	168.822i	0.117099	−	0.237442i
$712$	−75.8745	+	131.419i	−0.106565	+	0.184577i
$713$		−	2269.95i		−	3.18366i
$714$		0			0
$715$	7.74902			0.0108378
$716$	−75.6268	−	43.6631i	−0.105624	−	0.0609820i
$717$	−639.764	+	20.9380i	−0.892279	+	0.0292023i
$718$	−353.207	−	611.772i	−0.491931	−	0.852050i
$719$	−1149.72	−	663.793i	−1.59906	−	0.923217i	−0.991669	−	0.128813i	$-0.958883\pi$
$719$	−1149.72	−	663.793i	−1.59906	−	0.923217i	−0.607390	−	0.794404i	$-0.707783\pi$
$720$	27.3360	−	18.2646i	0.0379666	−	0.0253675i
$721$		0			0
$722$		−	148.492i		−	0.205668i
$723$	331.191	−	205.944i	0.458078	−	0.284846i
$724$	−81.0850	−	140.443i	−0.111996	−	0.193982i
$725$	748.558	−	432.180i	1.03249	−	0.596110i
$726$	203.493	+	327.250i	0.280293	+	0.450757i
$727$	−202.782			−0.278929			−0.139465	−	0.990227i	$-0.544538\pi$
$727$	−202.782			−0.278929			−0.139465	+	0.990227i	$0.544538\pi$
$728$		0			0
$729$	−715.000	+	142.183i	−0.980796	+	0.195038i
$730$	−46.7085	+	80.9015i	−0.0639842	+	0.110824i
$731$	219.135	−	126.518i	0.299774	−	0.173075i
$732$	7.63752	+	233.365i	0.0104338	+	0.318805i
$733$	291.280	−	504.511i	0.397380	−	0.688283i	−0.596022	−	0.802968i	$-0.703253\pi$
$733$	291.280	−	504.511i	0.397380	−	0.688283i	0.993402	+	0.114686i	$0.0365861\pi$
$734$			103.243i			0.140658i
$735$		0			0
$736$	−219.660			−0.298451
$737$	889.661	+	513.646i	1.20714	+	0.696942i
$738$	49.2675	−	99.9002i	0.0667582	−	0.135366i
$739$	128.405	+	222.404i	0.173755	+	0.300953i	0.939730	−	0.341918i	$-0.111076\pi$
$739$	128.405	+	222.404i	0.173755	+	0.300953i	−0.765975	+	0.642871i	$0.777743\pi$
$740$	−31.6352	−	18.2646i	−0.0427503	−	0.0246819i
$741$	24.6798	+	13.1919i	0.0333061	+	0.0178028i
$742$		0			0
$743$			573.256i			0.771542i	0.922595	+	0.385771i	$0.126064\pi$
$743$			573.256i			0.771542i	−0.922595	+	0.385771i	$0.873936\pi$
$744$	−261.933	−	421.231i	−0.352060	−	0.566170i
$745$	−100.251	−	173.640i	−0.134565	−	0.233074i
$746$	−581.342	+	335.638i	−0.779279	+	0.449917i
$747$	85.6481	+	1307.09i	0.114656	+	1.74979i
$748$	626.907			0.838111
$749$		0			0
$750$	168.000	+	89.7998i	0.224000	+	0.119733i
$751$	289.542	−	501.502i	0.385543	−	0.667779i	−0.606302	−	0.795235i	$-0.707348\pi$
$751$	289.542	−	501.502i	0.385543	−	0.667779i	0.991844	+	0.127455i	$0.0406809\pi$
$752$	−29.3939	+	16.9706i	−0.0390876	+	0.0225672i
$753$	1167.15	−	38.1982i	1.55000	−	0.0507280i
$754$	−14.7451	+	25.5392i	−0.0195558	+	0.0338717i
$755$			193.294i			0.256019i
$756$		0			0
$757$	1167.13			1.54179			0.770895	−	0.636963i	$-0.219809\pi$
$757$	1167.13			1.54179			0.770895	+	0.636963i	$0.219809\pi$
$758$	273.927	+	158.152i	0.361381	+	0.208643i
$759$	−55.4594	−	1694.57i	−0.0730691	−	2.23263i
$760$	−20.6640	−	35.7912i	−0.0271895	−	0.0470936i
$761$	−693.660	−	400.485i	−0.911511	−	0.526261i	−0.0305942	−	0.999532i	$-0.509740\pi$
$761$	−693.660	−	400.485i	−0.911511	−	0.526261i	−0.880917	+	0.473271i	$0.843073\pi$
$762$	54.1699	−	101.343i	0.0710892	−	0.132996i
$763$		0			0
$764$		−	107.114i		−	0.140202i
$765$	176.633	−	11.5740i	0.230893	−	0.0151294i
$766$	−366.405	−	634.632i	−0.478336	−	0.828502i
$767$	−29.3939	+	16.9706i	−0.0383232	+	0.0221259i
$768$	−40.7619	+	25.3469i	−0.0530754	+	0.0330038i
$769$	−242.680			−0.315578			−0.157789	−	0.987473i	$-0.550437\pi$
$769$	−242.680			−0.315578			−0.157789	+	0.987473i	$0.550437\pi$
$770$		0			0
$771$	475.373	−	889.341i	0.616566	−	1.15349i
$772$	−110.494	+	191.381i	−0.143127	+	0.247903i
$773$	1093.64	−	631.414i	1.41480	−	0.816836i	0.418965	−	0.908002i	$-0.362393\pi$
$773$	1093.64	−	631.414i	1.41480	−	0.816836i	0.995836	+	0.0911667i	$0.0290596\pi$
$774$	−134.118	−	66.1425i	−0.173279	−	0.0854554i
$775$	706.342	−	1223.42i	0.911410	−	1.57861i
$776$			314.425i			0.405187i
$777$		0			0
$778$	62.4209			0.0802326
$779$	−121.264	−	70.0119i	−0.155667	−	0.0898741i
$780$	−3.19280	+	0.104493i	−0.00409333	+	0.000133966i
$781$	123.915	+	214.627i	0.158662	+	0.274811i
$782$	−1024.24	−	591.345i	−1.30977	−	0.756195i
$783$	−961.077	+	94.6321i	−1.22743	+	0.120858i
$784$		0			0
$785$		−	190.632i		−	0.242844i
$786$	524.377	−	326.072i	0.667146	−	0.414850i
$787$	−673.501	−	1166.54i	−0.855782	−	1.48226i	−0.875917	−	0.482461i	$-0.839743\pi$
$787$	−673.501	−	1166.54i	−0.855782	−	1.48226i	0.0201353	−	0.999797i	$-0.493590\pi$
$788$	149.211	−	86.1469i	0.189354	−	0.109323i
$789$	−695.349	−	1118.23i	−0.881305	−	1.41728i
$790$	27.0118			0.0341922
$791$		0			0
$792$	−205.830	−	308.058i	−0.259886	−	0.388962i
$793$	11.3438	−	19.6481i	0.0143050	−	0.0247769i
$794$	366.709	−	211.720i	0.461851	−	0.266650i
$795$	4.56250	+	139.408i	0.00573900	+	0.175356i
$796$	−88.0000	+	152.420i	−0.110553	+	0.191483i
$797$			1210.62i			1.51897i	0.650523	+	0.759487i	$0.274550\pi$
$797$			1210.62i			1.51897i	−0.650523	+	0.759487i	$0.725450\pi$
$798$		0			0
$799$	−182.745			−0.228717
$800$	−118.389	−	68.3518i	−0.147986	−	0.0854397i
$801$	433.062	+	213.572i	0.540652	+	0.266632i
$802$	−195.875	−	339.265i	−0.244233	−	0.423023i
$803$	911.706	+	526.374i	1.13538	+	0.655509i
$804$	−373.490	−	199.639i	−0.464540	−	0.248307i
$805$		0			0
$806$			48.1979i			0.0597988i
$807$	−22.9074	−	36.8388i	−0.0283859	−	0.0456491i
$808$	81.7935	+	141.670i	0.101230	+	0.175335i
$809$	−269.226	+	155.438i	−0.332789	+	0.192136i	−0.657079	−	0.753822i	$-0.728208\pi$
$809$	−269.226	+	155.438i	−0.332789	+	0.192136i	0.324290	+	0.945958i	$0.394875\pi$
$810$	−63.6806	−	82.9963i	−0.0786181	−	0.102465i
$811$	−65.7777			−0.0811069			−0.0405535	−	0.999177i	$-0.512912\pi$
$811$	−65.7777			−0.0811069			−0.0405535	+	0.999177i	$0.512912\pi$
$812$		0			0
$813$	162.826	+	87.0342i	0.200278	+	0.107053i
$814$	−205.830	+	356.508i	−0.252862	+	0.437971i
$815$	−211.162	+	121.914i	−0.259094	+	0.149588i
$816$	−258.302	+	8.45366i	−0.316547	+	0.0103599i
$817$	−93.9921	+	162.799i	−0.115045	+	0.199265i
$818$		−	1047.90i		−	1.28106i
$819$		0			0
$820$	15.9843			0.0194930
$821$	−321.290	−	185.497i	−0.391340	−	0.225940i	0.291401	−	0.956601i	$-0.405879\pi$
$821$	−321.290	−	185.497i	−0.391340	−	0.225940i	−0.682740	+	0.730661i	$0.739212\pi$
$822$	3.44292	+	105.199i	0.00418846	+	0.127979i
$823$	−220.539	−	381.984i	−0.267969	−	0.464136i	0.700368	−	0.713782i	$-0.253019\pi$
$823$	−220.539	−	381.984i	−0.267969	−	0.464136i	−0.968337	+	0.249646i	$0.919686\pi$
$824$	−292.402	−	168.818i	−0.354857	−	0.204877i
$825$	497.409	−	930.567i	0.602920	−	1.12796i
$826$		0			0
$827$			116.492i			0.140861i	0.997517	+	0.0704307i	$0.0224374\pi$
$827$			116.492i			0.140861i	−0.997517	+	0.0704307i	$0.977563\pi$
$828$	45.7015	+	697.458i	0.0551950	+	0.842341i
$829$	440.712	+	763.336i	0.531619	+	0.920792i	0.999319	+	0.0369042i	$0.0117496\pi$
$829$	440.712	+	763.336i	0.531619	+	0.920792i	−0.467699	+	0.883888i	$0.654917\pi$
$830$	−162.787	+	93.9851i	−0.196129	+	0.113235i
$831$	−383.402	+	238.410i	−0.461374	+	0.286895i
$832$	4.66404			0.00560582
$833$		0			0
$834$	−292.915	+	547.994i	−0.351217	+	0.657067i
$835$	3.28363	−	5.68741i	0.00393249	−	0.00681127i
$836$	−403.343	+	232.870i	−0.482468	+	0.278553i
$837$	−1282.98	+	919.321i	−1.53284	+	1.09835i
$838$	−63.4980	+	109.982i	−0.0757733	+	0.131243i
$839$			1346.42i			1.60480i	0.596789	+	0.802398i	$0.296443\pi$
$839$			1346.42i			1.60480i	−0.596789	+	0.802398i	$0.703557\pi$
$840$		0			0
$841$	−438.320			−0.521189
$842$	−344.337	−	198.803i	−0.408952	−	0.236108i
$843$	−900.178	+	29.4608i	−1.06783	+	0.0349476i
$844$	−61.2549	−	106.097i	−0.0725769	−	0.125707i
$845$	−133.390	−	77.0128i	−0.157858	−	0.0911394i
$846$	60.0000	+	89.7998i	0.0709220	+	0.106146i
$847$		0			0
$848$		−	203.647i		−	0.240149i
$849$	−251.792	+	156.571i	−0.296574	+	0.184418i
$850$	−368.018	−	637.426i	−0.432963	−	0.749913i
$851$	672.569	−	388.308i	0.790328	−	0.456296i
$852$	−53.9504	−	86.7611i	−0.0633221	−	0.101832i
$853$	−966.235			−1.13275			−0.566375	−	0.824148i	$-0.691654\pi$
$853$	−966.235			−1.13275			−0.566375	+	0.824148i	$0.691654\pi$
$854$		0			0
$855$	−109.344	+	73.0584i	−0.127888	+	0.0854484i
$856$	164.745	−	285.347i	0.192459	−	0.333349i
$857$	850.645	−	491.120i	0.992585	−	0.573069i	0.0865390	−	0.996248i	$-0.472419\pi$
$857$	850.645	−	491.120i	0.992585	−	0.573069i	0.906046	+	0.423179i	$0.139086\pi$
$858$	1.17757	+	35.9807i	0.00137246	+	0.0419356i
$859$	−654.745	+	1134.05i	−0.762218	+	1.32020i	0.179487	+	0.983760i	$0.442556\pi$
$859$	−654.745	+	1134.05i	−0.762218	+	1.32020i	−0.941705	+	0.336440i	$0.890777\pi$
$860$		−	21.4591i		−	0.0249525i
$861$		0			0
$862$	792.243			0.919076
$863$	867.367	+	500.775i	1.00506	+	0.580272i	0.909742	−	0.415175i	$-0.136280\pi$
$863$	867.367	+	500.775i	1.00506	+	0.580272i	0.0953191	+	0.995447i	$0.469613\pi$
$864$	88.9615	+	124.153i	0.102965	+	0.143695i
$865$	87.9150	+	152.273i	0.101636	+	0.176038i
$866$	665.041	+	383.962i	0.767946	+	0.443374i
$867$	−462.557	−	247.247i	−0.533514	−	0.285175i
$868$		0			0
$869$		−	304.405i		−	0.350294i
$870$	−73.1796	−	117.685i	−0.0841144	−	0.135270i
$871$	20.5751	+	35.6372i	0.0236224	+	0.0409152i
$872$	−215.139	+	124.210i	−0.246719	+	0.142443i
$873$	998.353	−	65.4178i	1.14359	−	0.0749345i
$874$	878.640			1.00531
$875$		0			0
$876$	−382.745	−	204.586i	−0.436924	−	0.233545i
$877$	16.5712	−	28.7022i	0.0188953	−	0.0327277i	−0.856423	−	0.516275i	$-0.827318\pi$
$877$	16.5712	−	28.7022i	0.0188953	−	0.0327277i	0.875318	+	0.483547i	$0.160652\pi$
$878$	419.071	−	241.951i	0.477302	−	0.275570i
$879$	−21.4512	+	0.702051i	−0.0244041	+	0.000798693i
$880$	26.5830	−	46.0431i	0.0302080	−	0.0523217i
$881$			944.040i			1.07156i	0.844359	+	0.535778i	$0.179981\pi$
$881$			944.040i			1.07156i	−0.844359	+	0.535778i	$0.820019\pi$
$882$		0			0
$883$	55.5138			0.0628695			0.0314348	−	0.999506i	$-0.489992\pi$
$883$	55.5138			0.0628695			0.0314348	+	0.999506i	$0.489992\pi$
$884$	21.7477	+	12.5560i	0.0246014	+	0.0142036i
$885$	−5.21722	−	159.413i	−0.00589517	−	0.180127i
$886$	282.712	+	489.672i	0.319089	+	0.552678i
$887$	−17.4345	−	10.0658i	−0.0196556	−	0.0113482i	0.490140	−	0.871644i	$-0.336946\pi$
$887$	−17.4345	−	10.0658i	−0.0196556	−	0.0113482i	−0.509796	+	0.860296i	$0.670279\pi$
$888$	80.0000	−	149.666i	0.0900901	−	0.168543i
$889$		0			0
$890$			69.2909i			0.0778549i
$891$	−935.314	+	717.639i	−1.04973	+	0.805431i
$892$	150.494	+	260.663i	0.168715	+	0.292224i
$893$	117.576	−	67.8823i	0.131664	−	0.0760160i
$894$	791.021	−	491.879i	0.884811	−	0.550200i
$895$	−39.8745			−0.0445525
$896$		0			0
$897$	32.0157	−	59.8960i	0.0356920	−	0.0667737i
$898$	521.166	−	902.686i	0.580363	−	1.00522i
$899$	−1810.76	+	1045.44i	−2.01419	+	1.16289i
$900$	−192.397	+	390.126i	−0.213775	+	0.433473i
$901$	548.235	−	949.571i	0.608474	−	1.05391i
$902$		−	180.132i		−	0.199703i
$903$		0			0
$904$	195.660			0.216438
$905$	−64.1285	−	37.0246i	−0.0708603	−	0.0409112i
$906$	−897.517	+	29.3737i	−0.990637	+	0.0324213i
$907$	−109.822	−	190.218i	−0.121083	−	0.209722i	0.799112	−	0.601182i	$-0.205303\pi$
$907$	−109.822	−	190.218i	−0.121083	−	0.209722i	−0.920195	+	0.391460i	$0.871970\pi$
$908$	−330.057	−	190.558i	−0.363499	−	0.209866i
$909$	432.810	−	289.184i	0.476139	−	0.318134i
$910$		0			0
$911$		−	827.126i		−	0.907932i	−0.891019	−	0.453966i	$-0.850009\pi$
$911$		−	827.126i		−	0.907932i	0.891019	−	0.453966i	$-0.149991\pi$
$912$	163.048	−	101.388i	0.178780	−	0.111171i
$913$	1059.15	+	1834.50i	1.16008	+	2.00931i
$914$	814.867	−	470.464i	0.891539	−	0.514730i
$915$	56.2992	+	90.5383i	0.0615292	+	0.0989490i
$916$	285.830			0.312042
$917$		0			0
$918$	80.5830	+	818.395i	0.0877811	+	0.891498i
$919$	514.693	−	891.474i	0.560057	−	0.970048i	−0.437433	−	0.899251i	$-0.644112\pi$
$919$	514.693	−	891.474i	0.560057	−	0.970048i	0.997491	−	0.0707970i	$-0.0225543\pi$
$920$	−86.8625	+	50.1501i	−0.0944157	+	0.0545109i
$921$	−10.3852	−	317.320i	−0.0112760	−	0.344539i
$922$	225.472	−	390.529i	0.244546	−	0.423567i
$923$			9.92733i			0.0107555i
$924$		0			0
$925$	483.320			0.522508
$926$	−492.754	−	284.492i	−0.532132	−	0.307226i
$927$	−475.191	+	963.549i	−0.512612	+	1.03943i
$928$	101.166	+	175.225i	0.109015	+	0.188820i
$929$	1247.92	+	720.489i	1.34330	+	0.775553i	0.987290	−	0.158930i	$-0.0508043\pi$
$929$	1247.92	+	720.489i	1.34330	+	0.775553i	0.356008	+	0.934483i	$0.384138\pi$
$930$	−199.749	−	106.770i	−0.214784	−	0.114807i
$931$		0			0
$932$			15.6765i			0.0168203i
$933$	−420.446	−	676.145i	−0.450639	−	0.724700i
$934$	492.915	+	853.754i	0.527746	+	0.914083i
$935$	247.904	−	143.128i	0.265138	−	0.153078i
$936$	−0.970379	−	14.8091i	−0.00103673	−	0.0158217i
$937$	1010.00			1.07791			0.538954	−	0.842335i	$-0.318820\pi$
$937$	1010.00			1.07791			0.538954	+	0.842335i	$0.318820\pi$
$938$		0			0
$939$	686.118	+	366.745i	0.730690	+	0.390570i
$940$	−7.74902	+	13.4217i	−0.00824363	+	0.0142784i
$941$	166.082	−	95.8874i	0.176495	−	0.101899i	−0.409150	−	0.912467i	$-0.634175\pi$
$941$	166.082	−	95.8874i	0.176495	−	0.101899i	0.585645	+	0.810568i	$0.300841\pi$
$942$	885.156	−	28.9692i	0.939657	−	0.0307529i
$943$	−169.914	+	294.299i	−0.180184	+	0.312088i
$944$			232.870i			0.246684i
$945$		0			0
$946$	−241.830			−0.255634
$947$	−773.454	−	446.554i	−0.816742	−	0.471546i	0.0325499	−	0.999470i	$-0.489637\pi$
$947$	−773.454	−	446.554i	−0.816742	−	0.471546i	−0.849292	+	0.527924i	$0.822971\pi$
$948$	4.10482	+	125.423i	0.00432997	+	0.132303i
$949$	21.0850	+	36.5202i	0.0222181	+	0.0384829i
$950$	473.555	+	273.407i	0.498479	+	0.287797i
$951$	53.4902	−	100.071i	0.0562462	−	0.105227i
$952$		0			0
$953$			1300.12i			1.36423i	0.731243	+	0.682117i	$0.238941\pi$
$953$			1300.12i			1.36423i	−0.731243	+	0.682117i	$0.761059\pi$
$954$	−646.613	+	42.3698i	−0.677792	+	0.0444128i
$955$	−24.4550	−	42.3573i	−0.0256073	−	0.0443531i
$956$	369.566	−	213.369i	0.386575	−	0.223189i
$957$	−1326.23	+	824.685i	−1.38582	+	0.861740i
$958$	−231.660			−0.241816
$959$		0			0
$960$	−10.3320	+	19.3294i	−0.0107625	+	0.0201348i
$961$	−1228.14	+	2127.20i	−1.27798	+	2.21353i
$962$	−14.2807	+	8.24494i	−0.0148448	+	0.00857062i
$963$	−940.301	−	463.726i	−0.976429	−	0.481543i
$964$	−130.000	+	225.167i	−0.134855	+	0.233575i
$965$			100.907i			0.104566i
$966$		0			0
$967$	−375.247			−0.388053			−0.194026	−	0.980996i	$-0.562155\pi$
$967$	−375.247			−0.388053			−0.194026	+	0.980996i	$0.562155\pi$
$968$	−222.487	−	128.453i	−0.229842	−	0.132699i
$969$	1033.21	−	33.8146i	1.06626	−	0.0348964i
$970$	71.7856	+	124.336i	0.0740058	+	0.128182i
$971$	905.053	+	522.532i	0.932083	+	0.538138i	0.887470	−	0.460866i	$-0.152461\pi$
$971$	905.053	+	522.532i	0.932083	+	0.538138i	0.0446133	+	0.999004i	$0.485794\pi$
$972$	375.697	−	308.299i	0.386519	−	0.317180i
$973$		0			0
$974$		−	146.368i		−	0.150275i
$975$	35.8932	−	22.3194i	0.0368135	−	0.0228917i
$976$	−77.8301	−	134.806i	−0.0797439	−	0.138120i
$977$	−397.874	+	229.713i	−0.407240	+	0.235120i	−0.689603	−	0.724187i	$-0.742215\pi$
$977$	−397.874	+	229.713i	−0.407240	+	0.235120i	0.282363	+	0.959308i	$0.408882\pi$
$978$	−598.170	−	961.955i	−0.611626	−	0.983594i
$979$	780.863			0.797613
$980$		0			0
$981$	439.150	+	657.260i	0.447656	+	0.669990i
$982$	−403.118	+	698.220i	−0.410507	+	0.711019i
$983$	89.4305	−	51.6327i	0.0909771	−	0.0525257i	−0.453821	−	0.891093i	$-0.649940\pi$
$983$	89.4305	−	51.6327i	0.0909771	−	0.0525257i	0.544798	+	0.838567i	$0.316606\pi$
$984$	2.42903	+	74.2191i	0.00246852	+	0.0754259i
$985$	39.3360	−	68.1319i	0.0399350	−	0.0691694i
$986$			1089.39i			1.10486i
$987$		0			0
$988$	−18.6562			−0.0188828
$989$	395.101	+	228.112i	0.399496	+	0.230649i
$990$	−151.726	−	74.8261i	−0.153258	−	0.0755819i
$991$	−664.863	−	1151.58i	−0.670901	−	1.16203i	−0.977649	−	0.210244i	$-0.932574\pi$
$991$	−664.863	−	1151.58i	−0.670901	−	1.16203i	0.306748	−	0.951791i	$-0.400759\pi$
$992$	286.382	+	165.343i	0.288692	+	0.166676i
$993$	384.931	+	205.754i	0.387644	+	0.207205i
$994$		0			0
$995$			80.3643i			0.0807681i
$996$	−461.136	−	741.581i	−0.462987	−	0.744559i
$997$	−332.129	−	575.265i	−0.333129	−	0.576996i	0.649995	−	0.759939i	$-0.274771\pi$
$997$	−332.129	−	575.265i	−0.333129	−	0.576996i	−0.983124	+	0.182943i	$0.941438\pi$
$998$	−597.259	+	344.828i	−0.598456	+	0.345519i
$999$	−491.861	−	222.875i	−0.492353	−	0.223098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.h.d.275.1		8
3.2	odd	2	inner	294.3.h.d.275.3		8
7.2	even	3		42.3.b.a.29.4	yes	4
7.3	odd	6		294.3.h.g.263.4		8
7.4	even	3	inner	294.3.h.d.263.3		8
7.5	odd	6		294.3.b.h.197.3		4
7.6	odd	2		294.3.h.g.275.2		8
21.2	odd	6		42.3.b.a.29.2	✓	4
21.5	even	6		294.3.b.h.197.1		4
21.11	odd	6	inner	294.3.h.d.263.1		8
21.17	even	6		294.3.h.g.263.2		8
21.20	even	2		294.3.h.g.275.4		8
28.23	odd	6		336.3.d.b.113.1		4
35.2	odd	12		1050.3.c.a.449.1		8
35.9	even	6		1050.3.e.a.701.1		4
35.23	odd	12		1050.3.c.a.449.7		8
56.37	even	6		1344.3.d.c.449.1		4
56.51	odd	6		1344.3.d.e.449.4		4
63.2	odd	6		1134.3.q.a.701.1		8
63.16	even	3		1134.3.q.a.701.4		8
63.23	odd	6		1134.3.q.a.1079.4		8
63.58	even	3		1134.3.q.a.1079.1		8
84.23	even	6		336.3.d.b.113.2		4
105.2	even	12		1050.3.c.a.449.6		8
105.23	even	12		1050.3.c.a.449.4		8
105.44	odd	6		1050.3.e.a.701.3		4
168.107	even	6		1344.3.d.e.449.3		4
168.149	odd	6		1344.3.d.c.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.2	✓	4	21.2	odd	6
42.3.b.a.29.4	yes	4	7.2	even	3
294.3.b.h.197.1		4	21.5	even	6
294.3.b.h.197.3		4	7.5	odd	6
294.3.h.d.263.1		8	21.11	odd	6	inner
294.3.h.d.263.3		8	7.4	even	3	inner
294.3.h.d.275.1		8	1.1	even	1	trivial
294.3.h.d.275.3		8	3.2	odd	2	inner
294.3.h.g.263.2		8	21.17	even	6
294.3.h.g.263.4		8	7.3	odd	6
294.3.h.g.275.2		8	7.6	odd	2
294.3.h.g.275.4		8	21.20	even	2
336.3.d.b.113.1		4	28.23	odd	6
336.3.d.b.113.2		4	84.23	even	6
1050.3.c.a.449.1		8	35.2	odd	12
1050.3.c.a.449.4		8	105.23	even	12
1050.3.c.a.449.6		8	105.2	even	12
1050.3.c.a.449.7		8	35.23	odd	12
1050.3.e.a.701.1		4	35.9	even	6
1050.3.e.a.701.3		4	105.44	odd	6
1134.3.q.a.701.1		8	63.2	odd	6
1134.3.q.a.701.4		8	63.16	even	3
1134.3.q.a.1079.1		8	63.58	even	3
1134.3.q.a.1079.4		8	63.23	odd	6
1344.3.d.c.449.1		4	56.37	even	6
1344.3.d.c.449.2		4	168.149	odd	6
1344.3.d.e.449.3		4	168.107	even	6
1344.3.d.e.449.4		4	56.51	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.0981308 - 2.99839i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.790881 + 0.456615i) q^{5} +(-2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 + 0.588470i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.0981308 - 2.99839i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.790881 + 0.456615i) q^{5} +(-2.00000 + 3.74166i) q^{6} -2.82843i q^{8} +(-8.98074 + 0.588470i) q^{9} +(-0.645751 - 1.11847i) q^{10} +(-12.6045 + 7.27719i) q^{11} +(5.09524 - 3.16836i) q^{12} -0.583005 q^{13} +(1.29150 - 2.41618i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-18.6513 + 10.7684i) q^{17} +(11.4152 + 5.62962i) q^{18} +(8.00000 - 13.8564i) q^{19} +1.82646i q^{20} +20.5830 q^{22} +(-33.6284 - 19.4154i) q^{23} +(-8.48074 + 0.277556i) q^{24} +(-12.0830 - 20.9284i) q^{25} +(0.714033 + 0.412247i) q^{26} +(2.64575 + 26.8701i) q^{27} +35.7676i q^{29} +(-3.29026 + 2.04597i) q^{30} +(29.2288 + 50.6257i) q^{31} +(4.89898 - 2.82843i) q^{32} +(23.0568 + 37.0790i) q^{33} +30.4575 q^{34} +(-10.0000 - 14.9666i) q^{36} +(-10.0000 + 17.3205i) q^{37} +(-19.5959 + 11.3137i) q^{38} +(0.0572108 + 1.74808i) q^{39} +(1.29150 - 2.23695i) q^{40} -8.75149i q^{41} -11.7490 q^{43} +(-25.2089 - 14.5544i) q^{44} +(-7.37140 - 3.63533i) q^{45} +(27.4575 + 47.5578i) q^{46} +(7.34847 + 4.24264i) q^{47} +(10.5830 + 5.65685i) q^{48} +34.1759i q^{50} +(34.1181 + 54.8674i) q^{51} +(-0.583005 - 1.00979i) q^{52} +(-44.0908 + 25.4558i) q^{53} +(15.7596 - 34.7798i) q^{54} -13.2915 q^{55} +(-42.3320 - 22.6274i) q^{57} +(25.2915 - 43.8062i) q^{58} +(50.4179 - 29.1088i) q^{59} +(5.47645 - 0.179232i) q^{60} +(-19.4575 + 33.7014i) q^{61} -82.6714i q^{62} -8.00000 q^{64} +(-0.461088 - 0.266209i) q^{65} +(-2.01983 - 61.7160i) q^{66} +(-35.2915 - 61.1267i) q^{67} +(-37.3027 - 21.5367i) q^{68} +(-54.9150 + 102.737i) q^{69} -17.0279i q^{71} +(1.66444 + 25.4014i) q^{72} +(-36.1660 - 62.6414i) q^{73} +(24.4949 - 14.1421i) q^{74} +(-61.5658 + 38.2833i) q^{75} +32.0000 q^{76} +(1.16601 - 2.18141i) q^{78} +(-10.4575 + 18.1129i) q^{79} +(-3.16352 + 1.82646i) q^{80} +(80.3074 - 10.5698i) q^{81} +(-6.18824 + 10.7183i) q^{82} -145.544i q^{83} -19.6680 q^{85} +(14.3895 + 8.30781i) q^{86} +(107.245 - 3.50990i) q^{87} +(20.5830 + 35.6508i) q^{88} +(-46.4635 - 26.8257i) q^{89} +(6.45751 + 9.66472i) q^{90} -77.6616i q^{92} +(148.928 - 92.6073i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(12.6541 - 7.30584i) q^{95} +(-8.96148 - 14.4115i) q^{96} -111.166 q^{97} +(108.915 - 72.7719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 16 q^{6} - 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 16 * q^6 - 20 * q^9	\( 8 q + 8 q^{4} - 16 q^{6} - 20 q^{9} + 16 q^{10} + 80 q^{13} - 32 q^{15} - 16 q^{16} + 64 q^{19} + 80 q^{22} - 16 q^{24} - 12 q^{25} - 56 q^{30} + 128 q^{31} - 40 q^{33} + 32 q^{34} - 80 q^{36} - 80 q^{37} + 112 q^{39} - 32 q^{40} + 160 q^{43} - 112 q^{45} + 8 q^{46} - 16 q^{51} + 80 q^{52} + 152 q^{54} - 64 q^{55} + 160 q^{58} - 32 q^{60} + 56 q^{61} - 64 q^{64} - 112 q^{66} - 240 q^{67} - 16 q^{69} - 120 q^{73} - 224 q^{75} + 256 q^{76} - 160 q^{78} + 128 q^{79} + 124 q^{81} - 240 q^{82} - 496 q^{85} + 160 q^{87} + 80 q^{88} - 160 q^{90} + 280 q^{93} - 48 q^{94} + 32 q^{96} - 720 q^{97} + 448 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^6 - 20 * q^9 + 16 * q^10 + 80 * q^13 - 32 * q^15 - 16 * q^16 + 64 * q^19 + 80 * q^22 - 16 * q^24 - 12 * q^25 - 56 * q^30 + 128 * q^31 - 40 * q^33 + 32 * q^34 - 80 * q^36 - 80 * q^37 + 112 * q^39 - 32 * q^40 + 160 * q^43 - 112 * q^45 + 8 * q^46 - 16 * q^51 + 80 * q^52 + 152 * q^54 - 64 * q^55 + 160 * q^58 - 32 * q^60 + 56 * q^61 - 64 * q^64 - 112 * q^66 - 240 * q^67 - 16 * q^69 - 120 * q^73 - 224 * q^75 + 256 * q^76 - 160 * q^78 + 128 * q^79 + 124 * q^81 - 240 * q^82 - 496 * q^85 + 160 * q^87 + 80 * q^88 - 160 * q^90 + 280 * q^93 - 48 * q^94 + 32 * q^96 - 720 * q^97 + 448 * q^99

Introduction

L-functions

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