LMFDB - Embedded newform 483.3.b.a.323.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.15
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.74

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.85750i q^{2} +(-1.75729 - 2.43145i) q^{3} -4.16533 q^{4} -5.17933i q^{5} +(-6.94788 + 5.02145i) q^{6} -2.64575 q^{7} +0.472440i q^{8} +(-2.82389 + 8.54551i) q^{9} +O(q^{10})$	\(q-2.85750i q^{2} +(-1.75729 - 2.43145i) q^{3} -4.16533 q^{4} -5.17933i q^{5} +(-6.94788 + 5.02145i) q^{6} -2.64575 q^{7} +0.472440i q^{8} +(-2.82389 + 8.54551i) q^{9} -14.8000 q^{10} +4.51004i q^{11} +(7.31968 + 10.1278i) q^{12} +0.104362 q^{13} +7.56025i q^{14} +(-12.5933 + 9.10157i) q^{15} -15.3113 q^{16} +10.0444i q^{17} +(24.4188 + 8.06927i) q^{18} -19.4307 q^{19} +21.5736i q^{20} +(4.64934 + 6.43301i) q^{21} +12.8875 q^{22} -4.79583i q^{23} +(1.14871 - 0.830213i) q^{24} -1.82546 q^{25} -0.298216i q^{26} +(25.7403 - 8.15076i) q^{27} +11.0204 q^{28} -3.74791i q^{29} +(26.0078 + 35.9853i) q^{30} -37.7648 q^{31} +45.6420i q^{32} +(10.9659 - 7.92544i) q^{33} +28.7020 q^{34} +13.7032i q^{35} +(11.7624 - 35.5949i) q^{36} +19.5299 q^{37} +55.5234i q^{38} +(-0.183394 - 0.253751i) q^{39} +2.44692 q^{40} -11.9288i q^{41} +(18.3824 - 13.2855i) q^{42} +16.6104 q^{43} -18.7858i q^{44} +(44.2600 + 14.6258i) q^{45} -13.7041 q^{46} -64.8406i q^{47} +(26.9064 + 37.2287i) q^{48} +7.00000 q^{49} +5.21626i q^{50} +(24.4225 - 17.6509i) q^{51} -0.434703 q^{52} +7.40726i q^{53} +(-23.2908 - 73.5531i) q^{54} +23.3590 q^{55} -1.24996i q^{56} +(34.1454 + 47.2448i) q^{57} -10.7097 q^{58} +11.2757i q^{59} +(52.4552 - 37.9111i) q^{60} -47.5042 q^{61} +107.913i q^{62} +(7.47131 - 22.6093i) q^{63} +69.1768 q^{64} -0.540526i q^{65} +(-22.6470 - 31.3352i) q^{66} -40.1639 q^{67} -41.8383i q^{68} +(-11.6608 + 8.42765i) q^{69} +39.1570 q^{70} +41.2532i q^{71} +(-4.03724 - 1.33412i) q^{72} +27.1251 q^{73} -55.8066i q^{74} +(3.20786 + 4.43851i) q^{75} +80.9355 q^{76} -11.9325i q^{77} +(-0.725096 + 0.524050i) q^{78} +11.4925 q^{79} +79.3024i q^{80} +(-65.0513 - 48.2631i) q^{81} -34.0866 q^{82} -36.0723i q^{83} +(-19.3661 - 26.7956i) q^{84} +52.0233 q^{85} -47.4643i q^{86} +(-9.11285 + 6.58615i) q^{87} -2.13073 q^{88} -113.863i q^{89} +(41.7934 - 126.473i) q^{90} -0.276116 q^{91} +19.9762i q^{92} +(66.3635 + 91.8231i) q^{93} -185.282 q^{94} +100.638i q^{95} +(110.976 - 80.2060i) q^{96} -51.8908 q^{97} -20.0025i q^{98} +(-38.5406 - 12.7359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.85750i		−	1.42875i	−0.699762	−	0.714376i	$-0.746711\pi$
$2$		−	2.85750i		−	1.42875i	0.699762	−	0.714376i	$-0.253289\pi$
$3$	−1.75729	−	2.43145i	−0.585762	−	0.810483i
$3$	−1.75729	−	2.43145i	−0.585762	−	0.810483i
$4$	−4.16533			−1.04133
$5$		−	5.17933i		−	1.03587i	−0.855421	−	0.517933i	$-0.826702\pi$
$5$		−	5.17933i		−	1.03587i	0.855421	−	0.517933i	$-0.173298\pi$
$6$	−6.94788	+	5.02145i	−1.15798	+	0.836909i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$			0.472440i			0.0590550i
$9$	−2.82389	+	8.54551i	−0.313765	+	0.949501i
$10$	−14.8000			−1.48000
$11$			4.51004i			0.410004i	0.978762	+	0.205002i	$0.0657201\pi$
$11$			4.51004i			0.410004i	−0.978762	+	0.205002i	$0.934280\pi$
$12$	7.31968	+	10.1278i	0.609974	+	0.843983i
$13$	0.104362			0.00802786			0.00401393	−	0.999992i	$-0.498722\pi$
$13$	0.104362			0.00802786			0.00401393	+	0.999992i	$0.498722\pi$
$14$			7.56025i			0.540018i
$15$	−12.5933	+	9.10157i	−0.839552	+	0.606771i
$16$	−15.3113			−0.956958
$17$			10.0444i			0.590848i	0.955366	+	0.295424i	$0.0954609\pi$
$17$			10.0444i			0.590848i	−0.955366	+	0.295424i	$0.904539\pi$
$18$	24.4188	+	8.06927i	1.35660	+	0.448293i
$19$	−19.4307			−1.02267			−0.511335	−	0.859381i	$-0.670849\pi$
$19$	−19.4307			−1.02267			−0.511335	+	0.859381i	$0.670849\pi$
$20$			21.5736i			1.07868i
$21$	4.64934	+	6.43301i	0.221397	+	0.306334i
$22$	12.8875			0.585794
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	1.14871	−	0.830213i	0.0478631	−	0.0345922i
$25$	−1.82546			−0.0730184
$26$		−	0.298216i		−	0.0114698i
$27$	25.7403	−	8.15076i	0.953346	−	0.301880i
$28$	11.0204			0.393587
$29$		−	3.74791i		−	0.129238i	−0.997910	−	0.0646191i	$-0.979417\pi$
$29$		−	3.74791i		−	0.129238i	0.997910	−	0.0646191i	$-0.0205833\pi$
$30$	26.0078	+	35.9853i	0.866926	+	1.19951i
$31$	−37.7648			−1.21822			−0.609109	−	0.793087i	$-0.708473\pi$
$31$	−37.7648			−1.21822			−0.609109	+	0.793087i	$0.708473\pi$
$32$			45.6420i			1.42631i
$33$	10.9659	−	7.92544i	0.332301	−	0.240165i
$34$	28.7020			0.844176
$35$			13.7032i			0.391521i
$36$	11.7624	−	35.5949i	0.326734	−	0.988747i
$37$	19.5299			0.527834			0.263917	−	0.964545i	$-0.414986\pi$
$37$	19.5299			0.527834			0.263917	+	0.964545i	$0.414986\pi$
$38$			55.5234i			1.46114i
$39$	−0.183394	−	0.253751i	−0.00470242	−	0.00650645i
$40$	2.44692			0.0611731
$41$		−	11.9288i		−	0.290947i	−0.989362	−	0.145473i	$-0.953530\pi$
$41$		−	11.9288i		−	0.290947i	0.989362	−	0.145473i	$-0.0464705\pi$
$42$	18.3824	−	13.2855i	0.437675	−	0.316322i
$43$	16.6104			0.386289			0.193144	−	0.981170i	$-0.438131\pi$
$43$	16.6104			0.386289			0.193144	+	0.981170i	$0.438131\pi$
$44$		−	18.7858i		−	0.426951i
$45$	44.2600	+	14.6258i	0.983555	+	0.325019i
$46$	−13.7041			−0.297915
$47$		−	64.8406i		−	1.37959i	−0.724007	−	0.689793i	$-0.757701\pi$
$47$		−	64.8406i		−	1.37959i	0.724007	−	0.689793i	$-0.242299\pi$
$48$	26.9064	+	37.2287i	0.560550	+	0.775598i
$49$	7.00000			0.142857
$50$			5.21626i			0.104325i
$51$	24.4225	−	17.6509i	0.478872	−	0.346096i
$52$	−0.434703			−0.00835968
$53$			7.40726i			0.139760i	0.997555	+	0.0698798i	$0.0222616\pi$
$53$			7.40726i			0.139760i	−0.997555	+	0.0698798i	$0.977738\pi$
$54$	−23.2908	−	73.5531i	−0.431312	−	1.36210i
$55$	23.3590			0.424709
$56$		−	1.24996i		−	0.0223207i
$57$	34.1454	+	47.2448i	0.599042	+	0.828857i
$58$	−10.7097			−0.184650
$59$			11.2757i			0.191113i	0.995424	+	0.0955565i	$0.0304631\pi$
$59$			11.2757i			0.191113i	−0.995424	+	0.0955565i	$0.969537\pi$
$60$	52.4552	−	37.9111i	0.874253	−	0.631851i
$61$	−47.5042			−0.778757			−0.389378	−	0.921078i	$-0.627310\pi$
$61$	−47.5042			−0.778757			−0.389378	+	0.921078i	$0.627310\pi$
$62$			107.913i			1.74053i
$63$	7.47131	−	22.6093i	0.118592	−	0.358877i
$64$	69.1768			1.08089
$65$		−	0.540526i		−	0.00831579i
$66$	−22.6470	−	31.3352i	−0.343136	−	0.474776i
$67$	−40.1639			−0.599461			−0.299731	−	0.954024i	$-0.596897\pi$
$67$	−40.1639			−0.599461			−0.299731	+	0.954024i	$0.596897\pi$
$68$		−	41.8383i		−	0.615270i
$69$	−11.6608	+	8.42765i	−0.168997	+	0.122140i
$70$	39.1570			0.559386
$71$			41.2532i			0.581031i	0.956870	+	0.290516i	$0.0938269\pi$
$71$			41.2532i			0.581031i	−0.956870	+	0.290516i	$0.906173\pi$
$72$	−4.03724	−	1.33412i	−0.0560728	−	0.0185294i
$73$	27.1251			0.371576			0.185788	−	0.982590i	$-0.440516\pi$
$73$	27.1251			0.371576			0.185788	+	0.982590i	$0.440516\pi$
$74$		−	55.8066i		−	0.754144i
$75$	3.20786	+	4.43851i	0.0427714	+	0.0591801i
$76$	80.9355			1.06494
$77$		−	11.9325i		−	0.154967i
$78$	−0.725096	+	0.524050i	−0.00929610	+	0.00671859i
$79$	11.4925			0.145475			0.0727373	−	0.997351i	$-0.476827\pi$
$79$	11.4925			0.145475			0.0727373	+	0.997351i	$0.476827\pi$
$80$			79.3024i			0.991281i
$81$	−65.0513	−	48.2631i	−0.803103	−	0.595841i
$82$	−34.0866			−0.415691
$83$		−	36.0723i		−	0.434606i	−0.976104	−	0.217303i	$-0.930274\pi$
$83$		−	36.0723i		−	0.434606i	0.976104	−	0.217303i	$-0.0697260\pi$
$84$	−19.3661	−	26.7956i	−0.230548	−	0.318996i
$85$	52.0233			0.612039
$86$		−	47.4643i		−	0.551911i
$87$	−9.11285	+	6.58615i	−0.104745	+	0.0757029i
$88$	−2.13073			−0.0242128
$89$		−	113.863i		−	1.27936i	−0.768643	−	0.639678i	$-0.779068\pi$
$89$		−	113.863i		−	1.27936i	0.768643	−	0.639678i	$-0.220932\pi$
$90$	41.7934	−	126.473i	0.464371	−	1.40526i
$91$	−0.276116			−0.00303425
$92$			19.9762i			0.217133i
$93$	66.3635	+	91.8231i	0.713586	+	0.987345i
$94$	−185.282			−1.97109
$95$			100.638i			1.05935i
$96$	110.976	−	80.2060i	1.15600	−	0.835479i
$97$	−51.8908			−0.534957			−0.267478	−	0.963564i	$-0.586190\pi$
$97$	−51.8908			−0.534957			−0.267478	+	0.963564i	$0.586190\pi$
$98$		−	20.0025i		−	0.204107i
$99$	−38.5406	−	12.7359i	−0.389299	−	0.128645i
$100$	7.60365			0.0760365
$101$			76.8146i			0.760540i	0.924875	+	0.380270i	$0.124169\pi$
$101$			76.8146i			0.760540i	−0.924875	+	0.380270i	$0.875831\pi$
$102$	−50.4376	−	69.7874i	−0.494486	−	0.684190i
$103$	−78.1734			−0.758965			−0.379482	−	0.925199i	$-0.623898\pi$
$103$	−78.1734			−0.758965			−0.379482	+	0.925199i	$0.623898\pi$
$104$			0.0493049i			0.000474086i
$105$	33.3187	−	24.0805i	0.317321	−	0.229338i
$106$	21.1663			0.199682
$107$			81.1111i			0.758048i	0.925387	+	0.379024i	$0.123740\pi$
$107$			81.1111i			0.758048i	−0.925387	+	0.379024i	$0.876260\pi$
$108$	−107.217	+	33.9506i	−0.992751	+	0.314358i
$109$	−191.309			−1.75513			−0.877564	−	0.479460i	$-0.840832\pi$
$109$	−191.309			−1.75513			−0.877564	+	0.479460i	$0.840832\pi$
$110$		−	66.7485i		−	0.606804i
$111$	−34.3195	−	47.4858i	−0.309185	−	0.427800i
$112$	40.5100			0.361696
$113$			58.0554i			0.513765i	0.966443	+	0.256883i	$0.0826953\pi$
$113$			58.0554i			0.513765i	−0.966443	+	0.256883i	$0.917305\pi$
$114$	135.002	−	97.5706i	1.18423	−	0.855882i
$115$	−24.8392			−0.215993
$116$			15.6113i			0.134580i
$117$	−0.294707	+	0.891828i	−0.00251886	+	0.00762246i
$118$	32.2203			0.273053
$119$		−	26.5750i		−	0.223320i
$120$	−4.29995	−	5.94957i	−0.0358329	−	0.0495798i
$121$	100.660			0.831897
$122$			135.743i			1.11265i
$123$	−29.0043	+	20.9623i	−0.235807	+	0.170425i
$124$	157.303			1.26857
$125$		−	120.029i		−	0.960229i
$126$	−64.6061	−	21.3493i	−0.512747	−	0.169439i
$127$	−230.070			−1.81158			−0.905788	−	0.423731i	$-0.860720\pi$
$127$	−230.070			−1.81158			−0.905788	+	0.423731i	$0.860720\pi$
$128$		−	15.1052i		−	0.118009i
$129$	−29.1892	−	40.3874i	−0.226273	−	0.313080i
$130$	−1.54456			−0.0118812
$131$			13.6376i			0.104104i	0.998644	+	0.0520518i	$0.0165761\pi$
$131$			13.6376i			0.104104i	−0.998644	+	0.0520518i	$0.983424\pi$
$132$	−45.6768	+	33.0121i	−0.346036	+	0.250092i
$133$	51.4089			0.386533
$134$			114.769i			0.856482i
$135$	−42.2155	−	133.318i	−0.312707	−	0.987539i
$136$	−4.74539			−0.0348926
$137$			115.845i			0.845587i	0.906226	+	0.422794i	$0.138950\pi$
$137$			115.845i			0.845587i	−0.906226	+	0.422794i	$0.861050\pi$
$138$	24.0821	+	33.3208i	0.174508	+	0.241455i
$139$	124.795			0.897803			0.448902	−	0.893581i	$-0.351815\pi$
$139$	124.795			0.897803			0.448902	+	0.893581i	$0.351815\pi$
$140$		−	57.0785i		−	0.407703i
$141$	−157.656	+	113.943i	−1.11813	+	0.808109i
$142$	117.881			0.830150
$143$			0.470678i			0.00329146i
$144$	43.2375	−	130.843i	0.300260	−	0.908632i
$145$	−19.4117			−0.133874
$146$		−	77.5100i		−	0.530890i
$147$	−12.3010	−	17.0201i	−0.0836803	−	0.115783i
$148$	−81.3483			−0.549651
$149$			211.033i			1.41633i	0.706046	+	0.708166i	$0.250477\pi$
$149$			211.033i			1.41633i	−0.706046	+	0.708166i	$0.749523\pi$
$150$	12.6831	−	9.16646i	0.0845538	−	0.0611097i
$151$	−128.437			−0.850574			−0.425287	−	0.905059i	$-0.639827\pi$
$151$	−128.437			−0.850574			−0.425287	+	0.905059i	$0.639827\pi$
$152$		−	9.17986i		−	0.0603938i
$153$	−85.8346	−	28.3643i	−0.561011	−	0.185388i
$154$	−34.0970			−0.221409
$155$			195.596i			1.26191i
$156$	0.763898	+	1.05696i	0.00489678	+	0.00677538i
$157$	−145.825			−0.928821			−0.464411	−	0.885620i	$-0.653734\pi$
$157$	−145.825			−0.928821			−0.464411	+	0.885620i	$0.653734\pi$
$158$		−	32.8398i		−	0.207847i
$159$	18.0104	−	13.0167i	0.113273	−	0.0818659i
$160$	236.395			1.47747
$161$			12.6886i			0.0788110i
$162$	−137.912	+	185.884i	−0.851309	+	1.14743i
$163$	−280.558			−1.72121			−0.860607	−	0.509270i	$-0.829916\pi$
$163$	−280.558			−1.72121			−0.860607	+	0.509270i	$0.829916\pi$
$164$			49.6875i			0.302972i
$165$	−41.0485	−	56.7962i	−0.248779	−	0.344220i
$166$	−103.077			−0.620945
$167$		−	148.319i		−	0.888135i	−0.895993	−	0.444067i	$-0.853535\pi$
$167$		−	148.319i		−	0.888135i	0.895993	−	0.444067i	$-0.146465\pi$
$168$	−3.03921	+	2.19654i	−0.0180906	+	0.0130746i
$169$	−168.989			−0.999936
$170$		−	148.657i		−	0.874453i
$171$	54.8702	−	166.045i	0.320879	−	0.971026i
$172$	−69.1879			−0.402255
$173$			112.504i			0.650311i	0.945661	+	0.325155i	$0.105417\pi$
$173$			112.504i			0.650311i	−0.945661	+	0.325155i	$0.894583\pi$
$174$	18.8200	+	26.0400i	0.108161	+	0.149655i
$175$	4.82971			0.0275984
$176$		−	69.0548i		−	0.392357i
$177$	27.4162	−	19.8146i	0.154894	−	0.111947i
$178$	−325.363			−1.82788
$179$			35.7186i			0.199545i	0.995010	+	0.0997726i	$0.0318115\pi$
$179$			35.7186i			0.199545i	−0.995010	+	0.0997726i	$0.968188\pi$
$180$	−184.358	−	60.9215i	−1.02421	−	0.338453i
$181$	98.0897			0.541932			0.270966	−	0.962589i	$-0.412657\pi$
$181$	98.0897			0.541932			0.270966	+	0.962589i	$0.412657\pi$
$182$			0.789004i			0.00433519i
$183$	83.4784	+	115.504i	0.456166	+	0.631169i
$184$	2.26574			0.0123138
$185$		−	101.152i		−	0.546765i
$186$	262.385	−	189.634i	1.41067	−	1.01954i
$187$	−45.3007			−0.242250
$188$			270.082i			1.43661i
$189$	−68.1025	+	21.5649i	−0.360331	+	0.114100i
$190$	287.574			1.51355
$191$			57.9900i			0.303613i	0.988410	+	0.151806i	$0.0485090\pi$
$191$			57.9900i			0.303613i	−0.988410	+	0.151806i	$0.951491\pi$
$192$	−121.563	−	168.200i	−0.633143	−	0.876041i
$193$	198.515			1.02857			0.514287	−	0.857618i	$-0.328057\pi$
$193$	198.515			1.02857			0.514287	+	0.857618i	$0.328057\pi$
$194$			148.278i			0.764321i
$195$	−1.31426	+	0.949860i	−0.00673981	+	0.00487108i
$196$	−29.1573			−0.148762
$197$			43.3935i			0.220272i	0.993917	+	0.110136i	$0.0351286\pi$
$197$			43.3935i			0.220272i	−0.993917	+	0.110136i	$0.964871\pi$
$198$	−36.3928	+	110.130i	−0.183802	+	0.556212i
$199$	−258.069			−1.29683			−0.648414	−	0.761288i	$-0.724567\pi$
$199$	−258.069			−1.29683			−0.648414	+	0.761288i	$0.724567\pi$
$200$		−	0.862421i		−	0.00431210i
$201$	70.5795	+	97.6565i	0.351142	+	0.485853i
$202$	219.498			1.08662
$203$			9.91604i			0.0488475i
$204$	−101.728	+	73.5220i	−0.498666	+	0.360402i
$205$	−61.7832			−0.301382
$206$			223.381i			1.08437i
$207$	40.9828	+	13.5429i	0.197985	+	0.0654246i
$208$	−1.59792			−0.00768233
$209$		−	87.6335i		−	0.419299i
$210$	−68.8101	−	95.2083i	−0.327667	−	0.453373i
$211$	80.9414			0.383609			0.191804	−	0.981433i	$-0.438566\pi$
$211$	80.9414			0.383609			0.191804	+	0.981433i	$0.438566\pi$
$212$		−	30.8537i		−	0.145536i
$213$	100.305	−	72.4938i	0.470916	−	0.340346i
$214$	231.775			1.08306
$215$		−	86.0308i		−	0.400143i
$216$	3.85075	+	12.1608i	0.0178275	+	0.0562999i
$217$	99.9161			0.460443
$218$			546.666i			2.50764i
$219$	−47.6665	−	65.9532i	−0.217655	−	0.301156i
$220$	−97.2980			−0.442264
$221$			1.04826i			0.00474325i
$222$	−135.691	+	98.0683i	−0.611221	+	0.441749i
$223$	277.936			1.24635			0.623174	−	0.782083i	$-0.285843\pi$
$223$	277.936			1.24635			0.623174	+	0.782083i	$0.285843\pi$
$224$		−	120.757i		−	0.539095i
$225$	5.15489	−	15.5995i	0.0229106	−	0.0693310i
$226$	165.894			0.734043
$227$		−	249.477i		−	1.09902i	−0.835488	−	0.549509i	$-0.814815\pi$
$227$		−	249.477i		−	1.09902i	0.835488	−	0.549509i	$-0.185185\pi$
$228$	−142.227	−	196.791i	−0.623802	−	0.863116i
$229$	112.418			0.490908			0.245454	−	0.969408i	$-0.421063\pi$
$229$	112.418			0.490908			0.245454	+	0.969408i	$0.421063\pi$
$230$			70.9781i			0.308600i
$231$	−29.0131	+	20.9687i	−0.125598	+	0.0907738i
$232$	1.77066			0.00763217
$233$		−	209.239i		−	0.898022i	−0.893526	−	0.449011i	$-0.851776\pi$
$233$		−	209.239i		−	0.898022i	0.893526	−	0.449011i	$-0.148224\pi$
$234$	2.54840	+	0.842127i	0.0108906	+	0.00359883i
$235$	−335.831			−1.42907
$236$		−	46.9669i		−	0.199012i
$237$	−20.1956	−	27.9434i	−0.0852135	−	0.117905i
$238$	−75.9383			−0.319068
$239$		−	447.303i		−	1.87156i	−0.352583	−	0.935781i	$-0.614696\pi$
$239$		−	447.303i		−	1.87156i	0.352583	−	0.935781i	$-0.385304\pi$
$240$	192.820	−	139.357i	0.803416	−	0.580655i
$241$	92.7145			0.384708			0.192354	−	0.981326i	$-0.438388\pi$
$241$	92.7145			0.384708			0.192354	+	0.981326i	$0.438388\pi$
$242$		−	287.635i		−	1.18857i
$243$	−3.03546	+	242.981i	−0.0124916	+	0.999922i
$244$	197.871			0.810946
$245$		−	36.2553i		−	0.147981i
$246$	59.9000	+	82.8799i	0.243496	+	0.336910i
$247$	−2.02783			−0.00820986
$248$		−	17.8416i		−	0.0719419i
$249$	−87.7080	+	63.3894i	−0.352241	+	0.254576i
$250$	−342.982			−1.37193
$251$		−	335.906i		−	1.33827i	−0.743141	−	0.669135i	$-0.766665\pi$
$251$		−	335.906i		−	1.33827i	0.743141	−	0.669135i	$-0.233335\pi$
$252$	−31.1205	+	94.1752i	−0.123494	+	0.373711i
$253$	21.6294			0.0854917
$254$			657.427i			2.58829i
$255$	−91.4199	−	126.492i	−0.358510	−	0.496048i
$256$	233.544			0.912282
$257$		−	493.068i		−	1.91855i	−0.282470	−	0.959276i	$-0.591154\pi$
$257$		−	493.068i		−	1.91855i	0.282470	−	0.959276i	$-0.408846\pi$
$258$	−115.407	+	83.4084i	−0.447314	+	0.323288i
$259$	−51.6711			−0.199502
$260$			2.25147i			0.00865951i
$261$	32.0278	+	10.5837i	0.122712	+	0.0405505i
$262$	38.9694			0.148738
$263$			172.635i			0.656407i	0.944607	+	0.328203i	$0.106443\pi$
$263$			172.635i			0.656407i	−0.944607	+	0.328203i	$0.893557\pi$
$264$	3.74430	+	5.18075i	0.0141829	+	0.0196241i
$265$	38.3646			0.144772
$266$		−	146.901i		−	0.552260i
$267$	−276.851	+	200.089i	−1.03690	+	0.749398i
$268$	167.296			0.624239
$269$		−	471.994i		−	1.75462i	−0.479920	−	0.877312i	$-0.659334\pi$
$269$		−	471.994i		−	1.75462i	0.479920	−	0.877312i	$-0.340666\pi$
$270$	−380.956	+	120.631i	−1.41095	+	0.446781i
$271$	78.1542			0.288392			0.144196	−	0.989549i	$-0.453940\pi$
$271$	78.1542			0.288392			0.144196	+	0.989549i	$0.453940\pi$
$272$		−	153.793i		−	0.565417i
$273$	0.485216	+	0.671363i	0.00177735	+	0.00245921i
$274$	331.029			1.20813
$275$		−	8.23290i		−	0.0299378i
$276$	48.5712	−	35.1040i	0.175983	−	0.127188i
$277$	22.2952			0.0804879			0.0402440	−	0.999190i	$-0.487186\pi$
$277$	22.2952			0.0804879			0.0402440	+	0.999190i	$0.487186\pi$
$278$		−	356.601i		−	1.28274i
$279$	106.643	−	322.719i	0.382235	−	1.15670i
$280$	−6.47395			−0.0231213
$281$		−	445.483i		−	1.58535i	−0.609646	−	0.792674i	$-0.708689\pi$
$281$		−	445.483i		−	1.58535i	0.609646	−	0.792674i	$-0.291311\pi$
$282$	325.594	+	450.504i	1.15459	+	1.59753i
$283$	−341.664			−1.20729			−0.603647	−	0.797252i	$-0.706286\pi$
$283$	−341.664			−1.20729			−0.603647	+	0.797252i	$0.706286\pi$
$284$		−	171.833i		−	0.605047i
$285$	244.697	−	176.850i	0.858585	−	0.620527i
$286$	1.34496			0.00470267
$287$			31.5607i			0.109967i
$288$	−390.034	−	128.888i	−1.35428	−	0.447527i
$289$	188.110			0.650899
$290$			55.4689i			0.191272i
$291$	91.1870	+	126.170i	0.313357	+	0.433573i
$292$	−112.985			−0.386935
$293$			298.928i			1.02023i	0.860106	+	0.510116i	$0.170397\pi$
$293$			298.928i			1.02023i	−0.860106	+	0.510116i	$0.829603\pi$
$294$	−48.6351	+	35.1502i	−0.165426	+	0.119558i
$295$	58.4004			0.197967
$296$			9.22669i			0.0311712i
$297$	36.7603	+	116.090i	0.123772	+	0.390876i
$298$	603.029			2.02359
$299$		−	0.500504i		−	0.00167393i
$300$	−13.3618	−	18.4879i	−0.0445393	−	0.0616263i
$301$	−43.9470			−0.146003
$302$			367.008i			1.21526i
$303$	186.771	−	134.985i	0.616405	−	0.445496i
$304$	297.510			0.978653
$305$			246.040i			0.806688i
$306$	−81.0511	+	245.273i	−0.264873	+	0.801545i
$307$	−431.487			−1.40550			−0.702748	−	0.711439i	$-0.748044\pi$
$307$	−431.487			−1.40550			−0.702748	+	0.711439i	$0.748044\pi$
$308$			49.7026i			0.161372i
$309$	137.373	+	190.075i	0.444573	+	0.615128i
$310$	558.917			1.80296
$311$		−	470.458i		−	1.51273i	−0.654152	−	0.756363i	$-0.726975\pi$
$311$		−	470.458i		−	1.51273i	0.654152	−	0.756363i	$-0.273025\pi$
$312$	0.119882	−	0.0866429i	0.000384238	−	0.000277701i
$313$	512.346			1.63689			0.818444	−	0.574586i	$-0.194837\pi$
$313$	512.346			1.63689			0.818444	+	0.574586i	$0.194837\pi$
$314$			416.695i			1.32706i
$315$	−117.101	−	38.6964i	−0.371749	−	0.122846i
$316$	−47.8700			−0.151487
$317$			564.038i			1.77930i	0.456643	+	0.889650i	$0.349052\pi$
$317$			564.038i			1.77930i	−0.456643	+	0.889650i	$0.650948\pi$
$318$	−37.1952	−	51.4647i	−0.116966	−	0.161839i
$319$	16.9032			0.0529882
$320$		−	358.289i		−	1.11965i
$321$	197.218	−	142.536i	0.614385	−	0.444036i
$322$	36.2577			0.112601
$323$		−	195.170i		−	0.604243i
$324$	270.960	+	201.032i	0.836298	+	0.620469i
$325$	−0.190509			−0.000586181
$326$			801.695i			2.45919i
$327$	336.185	+	465.158i	1.02809	+	1.42250i
$328$	5.63565			0.0171819
$329$			171.552i			0.521435i
$330$	−162.295	+	117.296i	−0.491804	+	0.355443i
$331$	406.464			1.22799			0.613994	−	0.789310i	$-0.289562\pi$
$331$	406.464			1.22799			0.613994	+	0.789310i	$0.289562\pi$
$332$			150.253i			0.452570i
$333$	−55.1501	+	166.892i	−0.165616	+	0.501179i
$334$	−423.821			−1.26892
$335$			208.022i			0.620961i
$336$	−71.1876	−	98.4979i	−0.211868	−	0.293149i
$337$	643.215			1.90865			0.954325	−	0.298771i	$-0.0965766\pi$
$337$	643.215			1.90865			0.954325	+	0.298771i	$0.0965766\pi$
$338$			482.887i			1.42866i
$339$	141.159	−	102.020i	0.416398	−	0.300944i
$340$	−216.695			−0.637337
$341$		−	170.321i		−	0.499474i
$342$	−474.476	−	156.792i	−1.38736	−	0.458456i
$343$	−18.5203			−0.0539949
$344$			7.84743i			0.0228123i
$345$	43.6496	+	60.3952i	0.126521	+	0.175059i
$346$	321.480			0.929133
$347$		−	346.936i		−	0.999816i	−0.866078	−	0.499908i	$-0.833367\pi$
$347$		−	346.936i		−	0.999816i	0.866078	−	0.499908i	$-0.166633\pi$
$348$	37.9581	−	27.4335i	0.109075	−	0.0788320i
$349$	−87.8421			−0.251697			−0.125848	−	0.992049i	$-0.540165\pi$
$349$	−87.8421			−0.251697			−0.125848	+	0.992049i	$0.540165\pi$
$350$		−	13.8009i		−	0.0394312i
$351$	2.68632	−	0.850632i	0.00765333	−	0.00242345i
$352$	−205.847			−0.584793
$353$			100.317i			0.284184i	0.989853	+	0.142092i	$0.0453829\pi$
$353$			100.317i			0.284184i	−0.989853	+	0.142092i	$0.954617\pi$
$354$	−56.6202	−	78.3419i	−0.159944	−	0.221305i
$355$	213.664			0.601871
$356$			474.276i			1.33224i
$357$	−64.6158	+	46.6999i	−0.180997	+	0.130812i
$358$	102.066			0.285101
$359$		−	236.827i		−	0.659684i	−0.944036	−	0.329842i	$-0.893005\pi$
$359$		−	236.827i		−	0.659684i	0.944036	−	0.329842i	$-0.106995\pi$
$360$	−6.90984	+	20.9102i	−0.0191940	+	0.0580839i
$361$	16.5536			0.0458548
$362$		−	280.292i		−	0.774287i
$363$	−176.888	−	244.748i	−0.487294	−	0.674238i
$364$	1.15012			0.00315966
$365$		−	140.490i		−	0.384903i
$366$	330.053	−	238.540i	0.901785	−	0.651749i
$367$	−449.428			−1.22460			−0.612299	−	0.790626i	$-0.709755\pi$
$367$	−449.428			−1.22460			−0.612299	+	0.790626i	$0.709755\pi$
$368$			73.4306i			0.199540i
$369$	101.938	+	33.6856i	0.276254	+	0.0912889i
$370$	−289.041			−0.781192
$371$		−	19.5978i		−	0.0528242i
$372$	−276.426	−	382.474i	−0.743081	−	1.02816i
$373$	−32.5920			−0.0873781			−0.0436891	−	0.999045i	$-0.513911\pi$
$373$	−32.5920			−0.0873781			−0.0436891	+	0.999045i	$0.513911\pi$
$374$			129.447i			0.346115i
$375$	−291.843	+	210.925i	−0.778249	+	0.562466i
$376$	30.6333			0.0814715
$377$		−	0.391140i		−	0.00103751i
$378$	61.6218	+	194.603i	0.163021	+	0.514824i
$379$	−497.826			−1.31353			−0.656763	−	0.754097i	$-0.728075\pi$
$379$	−497.826			−1.31353			−0.656763	+	0.754097i	$0.728075\pi$
$380$		−	419.192i		−	1.10314i
$381$	404.299	+	559.404i	1.06115	+	1.46825i
$382$	165.707			0.433787
$383$			565.733i			1.47711i	0.674194	+	0.738554i	$0.264491\pi$
$383$			565.733i			1.47711i	−0.674194	+	0.738554i	$0.735509\pi$
$384$	−36.7275	+	26.5441i	−0.0956444	+	0.0691253i
$385$	−61.8021			−0.160525
$386$		−	567.256i		−	1.46958i
$387$	−46.9059	+	141.944i	−0.121204	+	0.366781i
$388$	216.143			0.557068
$389$			56.1192i			0.144265i	0.997395	+	0.0721327i	$0.0229805\pi$
$389$			56.1192i			0.144265i	−0.997395	+	0.0721327i	$0.977019\pi$
$390$	2.71423	+	3.75551i	0.00695956	+	0.00962951i
$391$	48.1713			0.123200
$392$			3.30708i			0.00843643i
$393$	33.1591	−	23.9651i	0.0843742	−	0.0609800i
$394$	123.997			0.314714
$395$		−	59.5234i		−	0.150692i
$396$	160.534	+	53.0491i	0.405390	+	0.133962i
$397$	−472.761			−1.19083			−0.595417	−	0.803417i	$-0.703013\pi$
$397$	−472.761			−1.19083			−0.595417	+	0.803417i	$0.703013\pi$
$398$			737.433i			1.85285i
$399$	−90.3402	−	124.998i	−0.226416	−	0.313278i
$400$	27.9502			0.0698755
$401$			360.051i			0.897882i	0.893561	+	0.448941i	$0.148199\pi$
$401$			360.051i			0.897882i	−0.893561	+	0.448941i	$0.851801\pi$
$402$	279.054	−	201.681i	0.694164	−	0.501695i
$403$	−3.94121			−0.00977969
$404$		−	319.958i		−	0.791976i
$405$	−249.971	+	336.922i	−0.617211	+	0.831907i
$406$	28.3351			0.0697910
$407$			88.0805i			0.216414i
$408$	8.33900	+	11.5382i	0.0204387	+	0.0282798i
$409$	−117.315			−0.286834			−0.143417	−	0.989662i	$-0.545809\pi$
$409$	−117.315			−0.286834			−0.143417	+	0.989662i	$0.545809\pi$
$410$			176.546i			0.430600i
$411$	281.672	−	203.574i	0.685334	−	0.495313i
$412$	325.618			0.790335
$413$		−	29.8326i		−	0.0722339i
$414$	38.6989	−	117.109i	0.0934755	−	0.282871i
$415$	−186.830			−0.450194
$416$			4.76330i			0.0114502i
$417$	−219.300	−	303.432i	−0.525899	−	0.727654i
$418$	−250.413			−0.599074
$419$		−	45.4820i		−	0.108549i	−0.998526	−	0.0542745i	$-0.982715\pi$
$419$		−	45.4820i		−	0.108549i	0.998526	−	0.0542745i	$-0.0172846\pi$
$420$	−138.783	+	100.303i	−0.330437	+	0.238817i
$421$	329.422			0.782476			0.391238	−	0.920290i	$-0.372047\pi$
$421$	329.422			0.782476			0.391238	+	0.920290i	$0.372047\pi$
$422$		−	231.291i		−	0.548082i
$423$	554.095	+	183.102i	1.30992	+	0.432866i
$424$	−3.49949			−0.00825351
$425$		−	18.3357i		−	0.0431428i
$426$	−207.151	−	286.622i	−0.486271	−	0.672823i
$427$	125.684			0.294342
$428$		−	337.855i		−	0.789381i
$429$	1.14443	−	0.827116i	0.00266767	−	0.00192801i
$430$	−245.833			−0.571705
$431$		−	228.376i		−	0.529875i	−0.964266	−	0.264938i	$-0.914649\pi$
$431$		−	228.376i		−	0.529875i	0.964266	−	0.264938i	$-0.0853514\pi$
$432$	−394.119	+	124.799i	−0.912312	+	0.288887i
$433$	376.144			0.868692			0.434346	−	0.900746i	$-0.356979\pi$
$433$	376.144			0.868692			0.434346	+	0.900746i	$0.356979\pi$
$434$		−	285.511i		−	0.657859i
$435$	34.1119	+	47.1985i	0.0784181	+	0.108502i
$436$	796.865			1.82767
$437$			93.1865i			0.213242i
$438$	−188.462	+	136.207i	−0.430278	+	0.310976i
$439$	−802.365			−1.82771			−0.913856	−	0.406039i	$-0.866910\pi$
$439$	−802.365			−1.82771			−0.913856	+	0.406039i	$0.866910\pi$
$440$			11.0357i			0.0250812i
$441$	−19.7672	+	59.8185i	−0.0448236	+	0.135643i
$442$	2.99540			0.00677693
$443$			45.2110i			0.102057i	0.998697	+	0.0510283i	$0.0162499\pi$
$443$			45.2110i			0.102057i	−0.998697	+	0.0510283i	$0.983750\pi$
$444$	142.952	+	197.794i	0.321965	+	0.445483i
$445$	−589.732			−1.32524
$446$		−	794.202i		−	1.78072i
$447$	513.117	−	370.846i	1.14791	−	0.829634i
$448$	−183.025			−0.408537
$449$		−	739.546i		−	1.64710i	−0.567247	−	0.823548i	$-0.691992\pi$
$449$		−	739.546i		−	1.64710i	0.567247	−	0.823548i	$-0.308008\pi$
$450$	−44.5756	−	14.7301i	−0.0990568	−	0.0327336i
$451$	53.7994			0.119289
$452$		−	241.820i		−	0.535001i
$453$	225.700	+	312.287i	0.498234	+	0.689376i
$454$	−712.882			−1.57022
$455$			1.43010i			0.00314307i
$456$	−22.3204	+	16.1317i	−0.0489482	+	0.0353764i
$457$	606.571			1.32729			0.663644	−	0.748049i	$-0.269009\pi$
$457$	606.571			1.32729			0.663644	+	0.748049i	$0.269009\pi$
$458$		−	321.235i		−	0.701386i
$459$	81.8696	+	258.547i	0.178365	+	0.563283i
$460$	103.464			0.224921
$461$		−	46.1395i		−	0.100086i	−0.998747	−	0.0500429i	$-0.984064\pi$
$461$		−	46.1395i		−	0.100086i	0.998747	−	0.0500429i	$-0.0159358\pi$
$462$	59.9183	+	82.9052i	0.129693	+	0.179448i
$463$	−424.488			−0.916821			−0.458410	−	0.888741i	$-0.651581\pi$
$463$	−424.488			−0.916821			−0.458410	+	0.888741i	$0.651581\pi$
$464$			57.3855i			0.123676i
$465$	475.582	−	343.718i	1.02276	−	0.739179i
$466$	−597.902			−1.28305
$467$			308.599i			0.660811i	0.943839	+	0.330405i	$0.107185\pi$
$467$			308.599i			0.660811i	−0.943839	+	0.330405i	$0.892815\pi$
$468$	1.22755	−	3.71476i	0.00262298	−	0.00793752i
$469$	106.264			0.226575
$470$			959.638i			2.04178i
$471$	256.256	+	354.566i	0.544068	+	0.752794i
$472$	−5.32708			−0.0112862
$473$			74.9136i			0.158380i
$474$	−79.8484	+	57.7090i	−0.168456	+	0.121749i
$475$	35.4700			0.0746737
$476$			110.694i			0.232550i
$477$	−63.2988	−	20.9173i	−0.132702	−	0.0438517i
$478$	−1278.17			−2.67400
$479$		−	472.310i		−	0.986033i	−0.870020	−	0.493016i	$-0.835894\pi$
$479$		−	472.310i		−	0.986033i	0.870020	−	0.493016i	$-0.164106\pi$
$480$	−415.413	−	574.782i	−0.865445	−	1.19746i
$481$	2.03818			0.00423738
$482$		−	264.932i		−	0.549652i
$483$	30.8516	−	22.2975i	0.0638750	−	0.0461645i
$484$	−419.280			−0.866282
$485$			268.760i			0.554144i
$486$	694.319	+	8.67383i	1.42864	+	0.0178474i
$487$	−359.862			−0.738936			−0.369468	−	0.929243i	$-0.620460\pi$
$487$	−359.862			−0.738936			−0.369468	+	0.929243i	$0.620460\pi$
$488$		−	22.4429i		−	0.0459895i
$489$	493.021	+	682.162i	1.00822	+	1.39501i
$490$	−103.600			−0.211428
$491$			67.9890i			0.138471i	0.997600	+	0.0692353i	$0.0220559\pi$
$491$			67.9890i			0.138471i	−0.997600	+	0.0692353i	$0.977944\pi$
$492$	120.813	−	87.3151i	0.245554	−	0.177470i
$493$	37.6456			0.0763602
$494$			5.79455i			0.0117299i
$495$	−65.9632	+	199.614i	−0.133259	+	0.403262i
$496$	578.229			1.16578
$497$		−	109.146i		−	0.219609i
$498$	181.136	+	250.626i	0.363726	+	0.503265i
$499$	−73.0292			−0.146351			−0.0731755	−	0.997319i	$-0.523313\pi$
$499$	−73.0292			−0.146351			−0.0731755	+	0.997319i	$0.523313\pi$
$500$			499.959i			0.999918i
$501$	−360.629	+	260.638i	−0.719818	+	0.520236i
$502$	−959.852			−1.91206
$503$			922.602i			1.83420i	0.398658	+	0.917100i	$0.369476\pi$
$503$			922.602i			1.83420i	−0.398658	+	0.917100i	$0.630524\pi$
$504$	10.6815	+	3.52975i	0.0211935	+	0.00700346i
$505$	397.848			0.787818
$506$		−	61.8061i		−	0.122147i
$507$	296.962	+	410.888i	0.585724	+	0.810431i
$508$	958.319			1.88645
$509$		−	339.384i		−	0.666765i	−0.942792	−	0.333383i	$-0.891810\pi$
$509$		−	339.384i		−	0.666765i	0.942792	−	0.333383i	$-0.108190\pi$
$510$	−361.452	+	261.233i	−0.708729	+	0.512221i
$511$	−71.7662			−0.140443
$512$		−	727.774i		−	1.42143i
$513$	−500.154	+	158.375i	−0.974959	+	0.308724i
$514$	−1408.94			−2.74114
$515$			404.886i			0.786186i
$516$	121.583	+	168.227i	0.235626	+	0.326021i
$517$	292.434			0.565636
$518$			147.651i			0.285040i
$519$	273.547	−	197.701i	0.527066	−	0.380927i
$520$	0.255366			0.000491089
$521$		−	212.314i		−	0.407513i	−0.979022	−	0.203756i	$-0.934685\pi$
$521$		−	212.314i		−	0.407513i	0.979022	−	0.203756i	$-0.0653151\pi$
$522$	30.2429	−	91.5196i	0.0579366	−	0.175325i
$523$	−79.4284			−0.151871			−0.0759354	−	0.997113i	$-0.524194\pi$
$523$	−79.4284			−0.151871			−0.0759354	+	0.997113i	$0.524194\pi$
$524$		−	56.8050i		−	0.108407i
$525$	−8.48719	−	11.7432i	−0.0161661	−	0.0223680i
$526$	493.305			0.937843
$527$		−	379.325i		−	0.719782i
$528$	−167.903	+	121.349i	−0.317998	+	0.229828i
$529$	−23.0000			−0.0434783
$530$		−	109.627i		−	0.206844i
$531$	−96.3562	−	31.8412i	−0.181462	−	0.0599646i
$532$	−214.135			−0.402510
$533$		−	1.24492i		−	0.00233568i
$534$	571.756	+	791.104i	1.07070	+	1.48147i
$535$	420.101			0.785236
$536$		−	18.9750i		−	0.0354012i
$537$	86.8480	−	62.7678i	0.161728	−	0.116886i
$538$	−1348.73			−2.50692
$539$			31.5703i			0.0585720i
$540$	175.842	+	555.313i	0.325633	+	1.02836i
$541$	−388.731			−0.718541			−0.359271	−	0.933233i	$-0.616975\pi$
$541$	−388.731			−0.718541			−0.359271	+	0.933233i	$0.616975\pi$
$542$		−	223.326i		−	0.412040i
$543$	−172.372	−	238.500i	−0.317443	−	0.439227i
$544$	−458.447			−0.842733
$545$			990.852i			1.81808i
$546$	1.91842	−	1.38651i	0.00351360	−	0.00253939i
$547$	615.373			1.12500			0.562498	−	0.826798i	$-0.309840\pi$
$547$	615.373			1.12500			0.562498	+	0.826798i	$0.309840\pi$
$548$		−	482.535i		−	0.880538i
$549$	134.146	−	405.947i	0.244347	−	0.739430i
$550$	−23.5255			−0.0427737
$551$			72.8247i			0.132168i
$552$	−3.98156	−	5.50904i	−0.00721297	−	0.00998015i
$553$	−30.4063			−0.0549842
$554$		−	63.7085i		−	0.114997i
$555$	−245.945	+	177.752i	−0.443144	+	0.320274i
$556$	−519.811			−0.934913
$557$		−	922.995i		−	1.65708i	−0.559929	−	0.828541i	$-0.689171\pi$
$557$		−	922.995i		−	1.65708i	0.559929	−	0.828541i	$-0.310829\pi$
$558$	−922.171	−	304.734i	−1.65264	−	0.546118i
$559$	1.73350			0.00310107
$560$		−	209.815i		−	0.374669i
$561$	79.6064	+	110.146i	0.141901	+	0.196340i
$562$	−1272.97			−2.26507
$563$			720.353i			1.27949i	0.768587	+	0.639745i	$0.220960\pi$
$563$			720.353i			1.27949i	−0.768587	+	0.639745i	$0.779040\pi$
$564$	656.692	−	474.612i	1.16435	−	0.841511i
$565$	300.688			0.532192
$566$			976.306i			1.72492i
$567$	172.110	+	127.692i	0.303544	+	0.225207i
$568$	−19.4897			−0.0343128
$569$		−	766.567i		−	1.34722i	−0.739088	−	0.673609i	$-0.764743\pi$
$569$		−	766.567i		−	1.34722i	0.739088	−	0.673609i	$-0.235257\pi$
$570$	−505.350	−	699.222i	−0.886579	−	1.22670i
$571$	−442.635			−0.775193			−0.387597	−	0.921829i	$-0.626695\pi$
$571$	−442.635			−0.775193			−0.387597	+	0.921829i	$0.626695\pi$
$572$		−	1.96053i		−	0.00342750i
$573$	141.000	−	101.905i	0.246073	−	0.177845i
$574$	90.1847			0.157116
$575$			8.75460i			0.0152254i
$576$	−195.348	+	591.151i	−0.339145	+	1.02630i
$577$	−935.321			−1.62101			−0.810503	−	0.585734i	$-0.800806\pi$
$577$	−935.321			−1.62101			−0.810503	+	0.585734i	$0.800806\pi$
$578$		−	537.524i		−	0.929973i
$579$	−348.847	−	482.678i	−0.602499	−	0.833641i
$580$	80.8561			0.139407
$581$			95.4384i			0.164266i
$582$	360.531	−	260.567i	0.619469	−	0.447710i
$583$	−33.4070			−0.0573020
$584$			12.8150i			0.0219435i
$585$	4.61907	+	1.52639i	0.00789585	+	0.00260921i
$586$	854.188			1.45766
$587$		−	576.488i		−	0.982092i	−0.871134	−	0.491046i	$-0.836615\pi$
$587$		−	576.488i		−	0.982092i	0.871134	−	0.491046i	$-0.163385\pi$
$588$	51.2378	+	70.8946i	0.0871391	+	0.120569i
$589$	733.797			1.24584
$590$		−	166.879i		−	0.282846i
$591$	105.509	−	76.2549i	0.178526	−	0.129027i
$592$	−299.028			−0.505115
$593$		−	635.853i		−	1.07226i	−0.844134	−	0.536132i	$-0.819885\pi$
$593$		−	635.853i		−	1.07226i	0.844134	−	0.536132i	$-0.180115\pi$
$594$	331.728	−	105.043i	0.558464	−	0.176840i
$595$	−137.641			−0.231329
$596$		−	879.025i		−	1.47487i
$597$	453.501	+	627.481i	0.759633	+	1.05106i
$598$	−1.43019			−0.00239162
$599$			90.4343i			0.150976i	0.997147	+	0.0754878i	$0.0240514\pi$
$599$			90.4343i			0.150976i	−0.997147	+	0.0754878i	$0.975949\pi$
$600$	−2.09693	+	1.51552i	−0.00349489	+	0.00252587i
$601$	435.626			0.724835			0.362418	−	0.932016i	$-0.381951\pi$
$601$	435.626			0.724835			0.362418	+	0.932016i	$0.381951\pi$
$602$			125.579i			0.208603i
$603$	113.418	−	343.221i	0.188090	−	0.569189i
$604$	534.981			0.885731
$605$		−	521.349i		−	0.861734i
$606$	−385.721	−	533.698i	−0.636503	−	0.880690i
$607$	−172.419			−0.284052			−0.142026	−	0.989863i	$-0.545362\pi$
$607$	−172.419			−0.284052			−0.142026	+	0.989863i	$0.545362\pi$
$608$		−	886.857i		−	1.45865i
$609$	24.1103	−	17.4253i	0.0395901	−	0.0286130i
$610$	703.060			1.15256
$611$		−	6.76690i		−	0.0110751i
$612$	357.530	+	118.147i	0.584199	+	0.193050i
$613$	213.715			0.348638			0.174319	−	0.984689i	$-0.444228\pi$
$613$	213.715			0.348638			0.174319	+	0.984689i	$0.444228\pi$
$614$			1232.98i			2.00810i
$615$	108.571	+	150.223i	0.176538	+	0.244265i
$616$	5.63737			0.00915158
$617$		−	942.326i		−	1.52727i	−0.645648	−	0.763635i	$-0.723413\pi$
$617$		−	942.326i		−	1.52727i	0.645648	−	0.763635i	$-0.276587\pi$
$618$	543.139	−	392.544i	0.878866	−	0.635185i
$619$	−845.871			−1.36651			−0.683256	−	0.730179i	$-0.739437\pi$
$619$	−845.871			−1.36651			−0.683256	+	0.730179i	$0.739437\pi$
$620$		−	814.723i		−	1.31407i
$621$	−39.0897	−	123.446i	−0.0629463	−	0.198786i
$622$	−1344.33			−2.16131
$623$			301.252i			0.483551i
$624$	2.80801	+	3.88527i	0.00450002	+	0.00622640i
$625$	−667.304			−1.06769
$626$		−	1464.03i		−	2.33871i
$627$	−213.076	+	153.997i	−0.339835	+	0.245609i
$628$	607.410			0.967213
$629$			196.166i			0.311870i
$630$	−110.575	+	334.616i	−0.175516	+	0.531137i
$631$	12.9692			0.0205534			0.0102767	−	0.999947i	$-0.496729\pi$
$631$	12.9692			0.0205534			0.0102767	+	0.999947i	$0.496729\pi$
$632$			5.42951i			0.00859100i
$633$	−142.237	−	196.805i	−0.224704	−	0.310908i
$634$	1611.74			2.54218
$635$			1191.61i			1.87655i
$636$	−75.0192	+	54.2188i	−0.117955	+	0.0852497i
$637$	0.730536			0.00114684
$638$		−	48.3011i		−	0.0757070i
$639$	−352.530	−	116.495i	−0.551690	−	0.182308i
$640$	−78.2347			−0.122242
$641$			906.275i			1.41385i	0.707291	+	0.706923i	$0.249917\pi$
$641$			906.275i			1.41385i	−0.707291	+	0.706923i	$0.750083\pi$
$642$	−407.296	−	563.550i	−0.634417	−	0.877804i
$643$	528.879			0.822519			0.411259	−	0.911518i	$-0.365089\pi$
$643$	528.879			0.822519			0.411259	+	0.911518i	$0.365089\pi$
$644$		−	52.8522i		−	0.0820686i
$645$	−209.179	+	151.181i	−0.324309	+	0.234389i
$646$	−557.700			−0.863313
$647$		−	835.562i		−	1.29144i	−0.763574	−	0.645720i	$-0.776557\pi$
$647$		−	835.562i		−	1.29144i	0.763574	−	0.645720i	$-0.223443\pi$
$648$	22.8014	−	30.7329i	0.0351874	−	0.0474273i
$649$	−50.8537			−0.0783571
$650$			0.544380i			0.000837508i
$651$	−175.581	−	242.941i	−0.269710	−	0.373181i
$652$	1168.62			1.79236
$653$		−	331.155i		−	0.507128i	−0.967319	−	0.253564i	$-0.918397\pi$
$653$		−	331.155i		−	0.507128i	0.967319	−	0.253564i	$-0.0816029\pi$
$654$	1329.19	−	960.649i	2.03240	−	1.46888i
$655$	70.6335			0.107837
$656$			182.646i			0.278424i
$657$	−76.5982	+	231.797i	−0.116588	+	0.352812i
$658$	490.211			0.745001
$659$		−	795.950i		−	1.20782i	−0.797054	−	0.603908i	$-0.793610\pi$
$659$		−	795.950i		−	1.20782i	0.797054	−	0.603908i	$-0.206390\pi$
$660$	170.981	+	236.575i	0.259061	+	0.358447i
$661$	507.374			0.767586			0.383793	−	0.923419i	$-0.374618\pi$
$661$	507.374			0.767586			0.383793	+	0.923419i	$0.374618\pi$
$662$		−	1161.47i		−	1.75449i
$663$	2.54878	−	1.84209i	0.00384432	−	0.00277841i
$664$	17.0420			0.0256657
$665$		−	266.264i		−	0.400396i
$666$	476.896	+	157.592i	0.716060	+	0.236624i
$667$	−17.9743			−0.0269480
$668$			617.796i			0.924844i
$669$	−488.412	−	675.786i	−0.730064	−	1.01014i
$670$	594.424			0.887200
$671$		−	214.246i		−	0.319293i
$672$	−293.615	+	212.205i	−0.436927	+	0.315781i
$673$	−127.283			−0.189127			−0.0945637	−	0.995519i	$-0.530146\pi$
$673$	−127.283			−0.189127			−0.0945637	+	0.995519i	$0.530146\pi$
$674$		−	1837.99i		−	2.72699i
$675$	−46.9879	+	14.8789i	−0.0696118	+	0.0220428i
$676$	703.896			1.04127
$677$			1040.30i			1.53664i	0.640067	+	0.768319i	$0.278907\pi$
$677$			1040.30i			1.53664i	−0.640067	+	0.768319i	$0.721093\pi$
$678$	−291.523	−	403.362i	−0.429975	−	0.594929i
$679$	137.290			0.202195
$680$			24.5779i			0.0361440i
$681$	−606.591	+	438.403i	−0.890735	+	0.643763i
$682$	−486.692			−0.713625
$683$			7.64329i			0.0111908i	0.999984	+	0.00559538i	$0.00178107\pi$
$683$			7.64329i			0.0111908i	−0.999984	+	0.00559538i	$0.998219\pi$
$684$	−228.553	+	691.635i	−0.334141	+	1.01116i
$685$	600.002			0.875915
$686$			52.9217i			0.0771454i
$687$	−197.551	−	273.338i	−0.287555	−	0.397873i
$688$	−254.327			−0.369662
$689$			0.773038i			0.00112197i
$690$	172.580	−	124.729i	0.250115	−	0.180767i
$691$	−1020.22			−1.47644			−0.738220	−	0.674560i	$-0.764333\pi$
$691$	−1020.22			−1.47644			−0.738220	+	0.674560i	$0.764333\pi$
$692$		−	468.616i		−	0.677190i
$693$	101.969	+	33.6959i	0.147141	+	0.0486232i
$694$	−991.372			−1.42849
$695$		−	646.353i		−	0.930004i
$696$	−3.11156	−	4.30528i	−0.00447064	−	0.00618575i
$697$	119.818			0.171905
$698$			251.009i			0.359612i
$699$	−508.754	+	367.693i	−0.727832	+	0.526028i
$700$	−20.1174			−0.0287391
$701$			315.718i			0.450382i	0.974315	+	0.225191i	$0.0723007\pi$
$701$			315.718i			0.450382i	−0.974315	+	0.225191i	$0.927699\pi$
$702$	−2.43068	−	7.67617i	−0.00346251	−	0.0109347i
$703$	−379.479			−0.539800
$704$			311.990i			0.443168i
$705$	590.151	+	816.555i	0.837093	+	1.15823i
$706$	286.656			0.406029
$707$		−	203.232i		−	0.287457i
$708$	−114.198	+	82.5343i	−0.161296	+	0.116574i
$709$	241.328			0.340379			0.170189	−	0.985411i	$-0.445562\pi$
$709$	241.328			0.340379			0.170189	+	0.985411i	$0.445562\pi$
$710$		−	610.546i		−	0.859924i
$711$	−32.4535	+	98.2091i	−0.0456449	+	0.138128i
$712$	53.7933			0.0755524
$713$			181.113i			0.254016i
$714$	133.445	+	184.640i	0.186898	+	0.258599i
$715$	2.43780			0.00340951
$716$		−	148.780i		−	0.207793i
$717$	−1087.59	+	786.040i	−1.51687	+	1.09629i
$718$	−676.733			−0.942525
$719$			224.025i			0.311579i	0.987790	+	0.155790i	$0.0497922\pi$
$719$			224.025i			0.311579i	−0.987790	+	0.155790i	$0.950208\pi$
$720$	−677.679	−	223.941i	−0.941221	−	0.311029i
$721$	206.827			0.286862
$722$		−	47.3019i		−	0.0655151i
$723$	−162.926	−	225.431i	−0.225347	−	0.311799i
$724$	−408.576			−0.564332
$725$			6.84166i			0.00943677i
$726$	−699.370	+	505.457i	−0.963319	+	0.696222i
$727$	−70.1113			−0.0964393			−0.0482196	−	0.998837i	$-0.515355\pi$
$727$	−70.1113			−0.0964393			−0.0482196	+	0.998837i	$0.515355\pi$
$728$		−	0.130449i		−	0.000179188i
$729$	596.130	−	419.607i	0.817737	−	0.575592i
$730$	−401.450			−0.549931
$731$			166.842i			0.228238i
$732$	−347.716	−	481.113i	−0.475021	−	0.657258i
$733$	547.069			0.746343			0.373171	−	0.927762i	$-0.378270\pi$
$733$	547.069			0.746343			0.373171	+	0.927762i	$0.378270\pi$
$734$			1284.24i			1.74965i
$735$	−88.1529	+	63.7110i	−0.119936	+	0.0866816i
$736$	218.891			0.297406
$737$		−	181.141i		−	0.245781i
$738$	96.2568	−	291.287i	0.130429	−	0.394698i
$739$	545.722			0.738459			0.369230	−	0.929338i	$-0.379622\pi$
$739$	545.722			0.738459			0.369230	+	0.929338i	$0.379622\pi$
$740$			421.330i			0.569365i
$741$	3.56349	+	4.93058i	0.00480902	+	0.00665395i
$742$	−56.0007			−0.0754726
$743$		−	509.832i		−	0.686181i	−0.939302	−	0.343090i	$-0.888526\pi$
$743$		−	509.832i		−	0.686181i	0.939302	−	0.343090i	$-0.111474\pi$
$744$	−43.3809	+	31.3528i	−0.0583077	+	0.0421408i
$745$	1093.01			1.46713
$746$			93.1319i			0.124842i
$747$	308.256	+	101.864i	0.412659	+	0.136364i
$748$	188.693			0.252263
$749$		−	214.600i		−	0.286515i
$750$	602.718	+	833.944i	0.803624	+	1.11193i
$751$	577.684			0.769220			0.384610	−	0.923079i	$-0.374336\pi$
$751$	577.684			0.769220			0.384610	+	0.923079i	$0.374336\pi$
$752$			992.795i			1.32021i
$753$	−816.737	+	590.282i	−1.08464	+	0.783908i
$754$	−1.11769			−0.00148234
$755$			665.216i			0.881081i
$756$	283.670	−	89.8249i	0.375225	−	0.118816i
$757$	−723.297			−0.955478			−0.477739	−	0.878502i	$-0.658544\pi$
$757$	−723.297			−0.955478			−0.477739	+	0.878502i	$0.658544\pi$
$758$			1422.54i			1.87670i
$759$	−38.0091	−	52.5908i	−0.0500778	−	0.0692896i
$760$	−47.5455			−0.0625599
$761$			973.741i			1.27955i	0.768560	+	0.639777i	$0.220973\pi$
$761$			973.741i			1.27955i	−0.768560	+	0.639777i	$0.779027\pi$
$762$	1598.50	−	1155.29i	2.09777	−	1.51612i
$763$	506.156			0.663376
$764$		−	241.548i		−	0.316162i
$765$	−146.908	+	444.566i	−0.192037	+	0.581132i
$766$	1616.58			2.11042
$767$			1.17675i			0.00153423i
$768$	−410.404	−	567.851i	−0.534380	−	0.739389i
$769$	494.571			0.643135			0.321568	−	0.946887i	$-0.395790\pi$
$769$	494.571			0.643135			0.321568	+	0.946887i	$0.395790\pi$
$770$			176.600i			0.229350i
$771$	−1198.87	+	866.462i	−1.55495	+	1.12382i
$772$	−826.879			−1.07109
$773$			328.066i			0.424407i	0.977226	+	0.212203i	$0.0680639\pi$
$773$			328.066i			0.424407i	−0.977226	+	0.212203i	$0.931936\pi$
$774$	405.607	+	134.034i	0.524039	+	0.173170i
$775$	68.9380			0.0889523
$776$		−	24.5153i		−	0.0315919i
$777$	90.8010	+	125.636i	0.116861	+	0.161693i
$778$	160.361			0.206119
$779$			231.786i			0.297542i
$780$	5.47434	−	3.95648i	0.00701838	−	0.00507241i
$781$	−186.054			−0.238225
$782$		−	137.650i		−	0.176023i
$783$	−30.5483	−	96.4725i	−0.0390145	−	0.123209i
$784$	−107.179			−0.136708
$785$			755.276i			0.962134i
$786$	−68.4805	−	94.7522i	−0.0871253	−	0.120550i
$787$	686.300			0.872046			0.436023	−	0.899936i	$-0.356387\pi$
$787$	686.300			0.872046			0.436023	+	0.899936i	$0.356387\pi$
$788$		−	180.749i		−	0.229376i
$789$	419.753	−	303.369i	0.532006	−	0.384498i
$790$	−170.088			−0.215302
$791$		−	153.600i		−	0.194185i
$792$	6.01693	−	18.2081i	0.00759714	−	0.0229901i
$793$	−4.95764			−0.00625175
$794$			1350.92i			1.70141i
$795$	−67.4176	−	93.2816i	−0.0848021	−	0.117335i
$796$	1074.94			1.35043
$797$			425.036i			0.533295i	0.963794	+	0.266648i	$0.0859160\pi$
$797$			425.036i			0.533295i	−0.963794	+	0.266648i	$0.914084\pi$
$798$	−357.183	+	258.147i	−0.447597	+	0.323493i
$799$	651.286			0.815126
$800$		−	83.3175i		−	0.104147i
$801$	973.014	+	321.535i	1.21475	+	0.401417i
$802$	1028.85			1.28285
$803$			122.335i			0.152348i
$804$	−293.987	−	406.772i	−0.365656	−	0.505935i
$805$	65.7183			0.0816377
$806$			11.2620i			0.0139727i
$807$	−1147.63	+	829.429i	−1.42209	+	1.02779i
$808$	−36.2903			−0.0449137
$809$			1081.40i			1.33672i	0.743839	+	0.668358i	$0.233003\pi$
$809$			1081.40i			1.33672i	−0.743839	+	0.668358i	$0.766997\pi$
$810$	962.757	+	714.292i	1.18859	+	0.881842i
$811$	791.945			0.976504			0.488252	−	0.872703i	$-0.337635\pi$
$811$	791.945			0.976504			0.488252	+	0.872703i	$0.337635\pi$
$812$		−	41.3036i		−	0.0508665i
$813$	−137.339	−	190.028i	−0.168929	−	0.233737i
$814$	251.690			0.309202
$815$			1453.10i			1.78295i
$816$	−373.941	+	270.259i	−0.458261	+	0.331200i
$817$	−322.752			−0.395046
$818$			335.228i			0.409814i
$819$	0.779722	−	2.35955i	0.000952041	−	0.00288102i
$820$	257.348			0.313839
$821$			444.407i			0.541300i	0.962678	+	0.270650i	$0.0872386\pi$
$821$			444.407i			0.541300i	−0.962678	+	0.270650i	$0.912761\pi$
$822$	−581.713	−	804.880i	−0.707680	−	0.979173i
$823$	1496.62			1.81849			0.909245	−	0.416261i	$-0.136660\pi$
$823$	1496.62			1.81849			0.909245	+	0.416261i	$0.136660\pi$
$824$		−	36.9322i		−	0.0448207i
$825$	−20.0179	+	14.4676i	−0.0242641	+	0.0175364i
$826$	−85.2468			−0.103204
$827$		−	656.566i		−	0.793913i	−0.917837	−	0.396956i	$-0.870066\pi$
$827$		−	656.566i		−	0.793913i	0.917837	−	0.396956i	$-0.129934\pi$
$828$	−170.707	−	56.4107i	−0.206168	−	0.0681288i
$829$	−1170.40			−1.41183			−0.705913	−	0.708298i	$-0.749463\pi$
$829$	−1170.40			−1.41183			−0.705913	+	0.708298i	$0.749463\pi$
$830$			533.869i			0.643216i
$831$	−39.1790	−	54.2095i	−0.0471468	−	0.0652341i
$832$	7.21944			0.00867722
$833$			70.3109i			0.0844069i
$834$	−867.058	+	626.651i	−1.03964	+	0.751380i
$835$	−768.191			−0.919989
$836$			365.023i			0.436630i
$837$	−972.078	+	307.812i	−1.16138	+	0.367756i
$838$	−129.965			−0.155090
$839$		−	488.998i		−	0.582834i	−0.956596	−	0.291417i	$-0.905873\pi$
$839$		−	488.998i		−	0.582834i	0.956596	−	0.291417i	$-0.0941267\pi$
$840$	11.3766	+	15.7411i	0.0135436	+	0.0187394i
$841$	826.953			0.983297
$842$		−	941.326i		−	1.11796i
$843$	−1083.17	+	782.840i	−1.28490	+	0.928636i
$844$	−337.148			−0.399465
$845$			875.250i			1.03580i
$846$	523.216	−	1583.33i	0.618459	−	1.87155i
$847$	−266.320			−0.314427
$848$		−	113.415i		−	0.133744i
$849$	600.402	+	830.739i	0.707187	+	0.978491i
$850$	−52.3943			−0.0616403
$851$		−	93.6619i		−	0.110061i
$852$	−417.804	+	301.961i	−0.490381	+	0.354414i
$853$	−404.319			−0.473997			−0.236998	−	0.971510i	$-0.576164\pi$
$853$	−404.319			−0.473997			−0.236998	+	0.971510i	$0.576164\pi$
$854$		−	359.143i		−	0.420542i
$855$	−860.004	−	284.191i	−1.00585	−	0.332387i
$856$	−38.3202			−0.0447666
$857$		−	458.894i		−	0.535466i	−0.963493	−	0.267733i	$-0.913726\pi$
$857$		−	458.894i		−	0.535466i	0.963493	−	0.267733i	$-0.0862744\pi$
$858$	−2.36349	−	3.27021i	−0.00275465	−	0.00381144i
$859$	−231.190			−0.269139			−0.134569	−	0.990904i	$-0.542965\pi$
$859$	−231.190			−0.269139			−0.134569	+	0.990904i	$0.542965\pi$
$860$			358.347i			0.416682i
$861$	76.7381	−	55.4611i	0.0891267	−	0.0644148i
$862$	−652.586			−0.757061
$863$			100.008i			0.115884i	0.998320	+	0.0579418i	$0.0184538\pi$
$863$			100.008i			0.115884i	−0.998320	+	0.0579418i	$0.981546\pi$
$864$	372.017	+	1174.84i	0.430575	+	1.35977i
$865$	582.694			0.673635
$866$		−	1074.83i		−	1.24115i
$867$	−330.563	−	457.379i	−0.381272	−	0.527542i
$868$	−416.184			−0.479475
$869$			51.8316i			0.0596451i
$870$	134.870	−	97.4748i	0.155023	−	0.112040i
$871$	−4.19159			−0.00481239
$872$		−	90.3820i		−	0.103649i
$873$	146.534	−	443.433i	0.167851	−	0.507942i
$874$	266.281			0.304669
$875$			317.566i			0.362932i
$876$	198.547	+	274.717i	0.226652	+	0.313604i
$877$	839.337			0.957055			0.478527	−	0.878073i	$-0.341171\pi$
$877$	839.337			0.957055			0.478527	+	0.878073i	$0.341171\pi$
$878$			2292.76i			2.61135i
$879$	726.828	−	525.302i	0.826880	−	0.597613i
$880$	−357.657			−0.406429
$881$			5.71965i			0.00649222i	0.999995	+	0.00324611i	$0.00103327\pi$
$881$			5.71965i			0.00649222i	−0.999995	+	0.00324611i	$0.998967\pi$
$882$	170.932	+	56.4849i	0.193800	+	0.0640418i
$883$	−393.472			−0.445609			−0.222804	−	0.974863i	$-0.571521\pi$
$883$	−393.472			−0.445609			−0.222804	+	0.974863i	$0.571521\pi$
$884$		−	4.36634i		−	0.00493930i
$885$	−102.626	−	141.998i	−0.115962	−	0.160449i
$886$	129.191			0.145813
$887$			689.862i			0.777748i	0.921291	+	0.388874i	$0.127136\pi$
$887$			689.862i			0.777748i	−0.921291	+	0.388874i	$0.872864\pi$
$888$	22.4342	−	16.2139i	0.0252638	−	0.0182589i
$889$	608.708			0.684711
$890$			1685.16i			1.89344i
$891$	217.669	−	293.384i	0.244297	−	0.329275i
$892$	−1157.69			−1.29786
$893$			1259.90i			1.41086i
$894$	−1059.69	−	1466.23i	−1.18534	−	1.64008i
$895$	184.998			0.206702
$896$			39.9645i			0.0446033i
$897$	−1.21695	+	0.879528i	−0.00135669	+	0.000980522i
$898$	−2113.26			−2.35329
$899$			141.539i			0.157440i
$900$	−21.4718	+	64.9770i	−0.0238576	+	0.0721967i
$901$	−74.4016			−0.0825767
$902$		−	153.732i		−	0.170435i
$903$	77.2275	+	106.855i	0.0855232	+	0.118333i
$904$	−27.4277			−0.0303404
$905$		−	508.039i		−	0.561369i
$906$	892.362	−	644.939i	0.984947	−	0.711853i
$907$	450.916			0.497151			0.248576	−	0.968613i	$-0.420038\pi$
$907$	450.916			0.497151			0.248576	+	0.968613i	$0.420038\pi$
$908$			1039.15i			1.14444i
$909$	−656.419	−	216.916i	−0.722133	−	0.238631i
$910$	4.08651			0.00449067
$911$		−	1411.17i		−	1.54904i	−0.632551	−	0.774518i	$-0.717992\pi$
$911$		−	1411.17i		−	1.54904i	0.632551	−	0.774518i	$-0.282008\pi$
$912$	−522.811	−	723.382i	−0.573258	−	0.793182i
$913$	162.688			0.178190
$914$		−	1733.28i		−	1.89637i
$915$	598.233	−	432.362i	0.653807	−	0.472527i
$916$	−468.258			−0.511199
$917$		−	36.0816i		−	0.0393475i
$918$	738.798	−	233.943i	0.804791	−	0.254840i
$919$	290.846			0.316481			0.158240	−	0.987401i	$-0.449418\pi$
$919$	290.846			0.316481			0.158240	+	0.987401i	$0.449418\pi$
$920$		−	11.7350i		−	0.0127555i
$921$	758.246	+	1049.14i	0.823286	+	1.13913i
$922$	−131.844			−0.142998
$923$			4.30528i			0.00466444i
$924$	120.849	−	87.3418i	0.130789	−	0.0945257i
$925$	−35.6510			−0.0385416
$926$			1212.98i			1.30991i
$927$	220.753	−	668.031i	0.238137	−	0.720637i
$928$	171.062			0.184334
$929$		−	539.564i		−	0.580801i	−0.956905	−	0.290400i	$-0.906211\pi$
$929$		−	539.564i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$930$	−982.177	−	1358.98i	−1.05610	−	1.46127i
$931$	−136.015			−0.146096
$932$			871.551i			0.935141i
$933$	−1143.89	+	826.729i	−1.22604	+	0.886097i
$934$	881.822			0.944135
$935$			234.628i			0.250939i
$936$	−0.421335	−	0.139232i	−0.000450145	−	0.000148752i
$937$	401.836			0.428853			0.214427	−	0.976740i	$-0.431212\pi$
$937$	401.836			0.428853			0.214427	+	0.976740i	$0.431212\pi$
$938$		−	303.649i		−	0.323720i
$939$	−900.339	−	1245.74i	−0.958827	−	1.32667i
$940$	1398.85			1.48813
$941$			339.213i			0.360482i	0.983622	+	0.180241i	$0.0576877\pi$
$941$			339.213i			0.360482i	−0.983622	+	0.180241i	$0.942312\pi$
$942$	1013.17	−	732.253i	1.07556	−	0.777339i
$943$	−57.2086			−0.0606665
$944$		−	172.645i		−	0.182887i
$945$	111.692	+	352.726i	0.118192	+	0.373255i
$946$	214.066			0.226286
$947$		−	889.175i		−	0.938938i	−0.882949	−	0.469469i	$-0.844445\pi$
$947$		−	889.175i		−	0.938938i	0.882949	−	0.469469i	$-0.155555\pi$
$948$	84.1214	+	116.394i	0.0887356	+	0.122778i
$949$	2.83083			0.00298296
$950$		−	101.356i		−	0.106690i
$951$	1371.43	−	991.177i	1.44209	−	1.04225i
$952$	12.5551			0.0131881
$953$			1175.59i			1.23357i	0.787133	+	0.616783i	$0.211565\pi$
$953$			1175.59i			1.23357i	−0.787133	+	0.616783i	$0.788435\pi$
$954$	−59.7712	+	180.876i	−0.0626532	+	0.189598i
$955$	300.349			0.314502
$956$			1863.17i			1.94892i
$957$	−29.7038	−	41.0994i	−0.0310385	−	0.0429460i
$958$	−1349.63			−1.40880
$959$		−	306.498i		−	0.319602i
$960$	−871.163	+	629.617i	−0.907461	+	0.655851i
$961$	465.177			0.484055
$962$		−	5.82411i		−	0.00605416i
$963$	−693.136	−	229.049i	−0.719767	−	0.237849i
$964$	−386.187			−0.400609
$965$		−	1028.17i		−	1.06546i
$966$	−63.7151	−	88.1587i	−0.0659577	−	0.0912616i
$967$	−595.677			−0.616005			−0.308003	−	0.951386i	$-0.599661\pi$
$967$	−595.677			−0.616005			−0.308003	+	0.951386i	$0.599661\pi$
$968$			47.5556i			0.0491277i
$969$	−474.547	+	342.970i	−0.489729	+	0.353943i
$970$	767.982			0.791734
$971$		−	825.001i		−	0.849640i	−0.905278	−	0.424820i	$-0.860337\pi$
$971$		−	825.001i		−	0.849640i	0.905278	−	0.424820i	$-0.139663\pi$
$972$	12.6437	−	1012.10i	0.0130079	−	1.04125i
$973$	−330.176			−0.339338
$974$			1028.31i			1.05576i
$975$	0.334779	+	0.463213i	0.000343363	+	0.000475090i
$976$	727.352			0.745238
$977$			565.759i			0.579078i	0.957166	+	0.289539i	$0.0935019\pi$
$977$			565.759i			0.579078i	−0.957166	+	0.289539i	$0.906498\pi$
$978$	1949.28	−	1408.81i	1.99313	−	1.44050i
$979$	513.525			0.524541
$980$			151.015i			0.154097i
$981$	540.235	−	1634.83i	0.550698	−	1.66649i
$982$	194.279			0.197840
$983$		−	1149.18i		−	1.16905i	−0.811375	−	0.584526i	$-0.801281\pi$
$983$		−	1149.18i		−	1.16905i	0.811375	−	0.584526i	$-0.198719\pi$
$984$	−9.90345	−	13.7028i	−0.0100645	−	0.0139256i
$985$	224.749			0.228172
$986$		−	107.572i		−	0.109100i
$987$	417.120	−	301.466i	0.422614	−	0.305437i
$988$	8.44661			0.00854920
$989$		−	79.6607i		−	0.0805467i
$990$	570.399	+	188.490i	0.576161	+	0.190394i
$991$	672.510			0.678618			0.339309	−	0.940675i	$-0.389807\pi$
$991$	672.510			0.678618			0.339309	+	0.940675i	$0.389807\pi$
$992$		−	1723.66i		−	1.73756i
$993$	−714.274	−	988.297i	−0.719309	−	0.995264i
$994$	−311.885			−0.313767
$995$			1336.62i			1.34334i
$996$	365.333	−	264.038i	0.366800	−	0.265098i
$997$	−751.741			−0.754003			−0.377001	−	0.926213i	$-0.623045\pi$
$997$	−751.741			−0.754003			−0.377001	+	0.926213i	$0.623045\pi$
$998$			208.681i			0.209099i
$999$	502.705	−	159.183i	0.503208	−	0.159343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.15	✓	88
3.2	odd	2	inner	483.3.b.a.323.74	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.15	✓	88	1.1	even	1	trivial
483.3.b.a.323.74	yes	88	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.85750i q^{2} +(-1.75729 - 2.43145i) q^{3} -4.16533 q^{4} -5.17933i q^{5} +(-6.94788 + 5.02145i) q^{6} -2.64575 q^{7} +0.472440i q^{8} +(-2.82389 + 8.54551i) q^{9} +O(q^{10})\)	\(q-2.85750i q^{2} +(-1.75729 - 2.43145i) q^{3} -4.16533 q^{4} -5.17933i q^{5} +(-6.94788 + 5.02145i) q^{6} -2.64575 q^{7} +0.472440i q^{8} +(-2.82389 + 8.54551i) q^{9} -14.8000 q^{10} +4.51004i q^{11} +(7.31968 + 10.1278i) q^{12} +0.104362 q^{13} +7.56025i q^{14} +(-12.5933 + 9.10157i) q^{15} -15.3113 q^{16} +10.0444i q^{17} +(24.4188 + 8.06927i) q^{18} -19.4307 q^{19} +21.5736i q^{20} +(4.64934 + 6.43301i) q^{21} +12.8875 q^{22} -4.79583i q^{23} +(1.14871 - 0.830213i) q^{24} -1.82546 q^{25} -0.298216i q^{26} +(25.7403 - 8.15076i) q^{27} +11.0204 q^{28} -3.74791i q^{29} +(26.0078 + 35.9853i) q^{30} -37.7648 q^{31} +45.6420i q^{32} +(10.9659 - 7.92544i) q^{33} +28.7020 q^{34} +13.7032i q^{35} +(11.7624 - 35.5949i) q^{36} +19.5299 q^{37} +55.5234i q^{38} +(-0.183394 - 0.253751i) q^{39} +2.44692 q^{40} -11.9288i q^{41} +(18.3824 - 13.2855i) q^{42} +16.6104 q^{43} -18.7858i q^{44} +(44.2600 + 14.6258i) q^{45} -13.7041 q^{46} -64.8406i q^{47} +(26.9064 + 37.2287i) q^{48} +7.00000 q^{49} +5.21626i q^{50} +(24.4225 - 17.6509i) q^{51} -0.434703 q^{52} +7.40726i q^{53} +(-23.2908 - 73.5531i) q^{54} +23.3590 q^{55} -1.24996i q^{56} +(34.1454 + 47.2448i) q^{57} -10.7097 q^{58} +11.2757i q^{59} +(52.4552 - 37.9111i) q^{60} -47.5042 q^{61} +107.913i q^{62} +(7.47131 - 22.6093i) q^{63} +69.1768 q^{64} -0.540526i q^{65} +(-22.6470 - 31.3352i) q^{66} -40.1639 q^{67} -41.8383i q^{68} +(-11.6608 + 8.42765i) q^{69} +39.1570 q^{70} +41.2532i q^{71} +(-4.03724 - 1.33412i) q^{72} +27.1251 q^{73} -55.8066i q^{74} +(3.20786 + 4.43851i) q^{75} +80.9355 q^{76} -11.9325i q^{77} +(-0.725096 + 0.524050i) q^{78} +11.4925 q^{79} +79.3024i q^{80} +(-65.0513 - 48.2631i) q^{81} -34.0866 q^{82} -36.0723i q^{83} +(-19.3661 - 26.7956i) q^{84} +52.0233 q^{85} -47.4643i q^{86} +(-9.11285 + 6.58615i) q^{87} -2.13073 q^{88} -113.863i q^{89} +(41.7934 - 126.473i) q^{90} -0.276116 q^{91} +19.9762i q^{92} +(66.3635 + 91.8231i) q^{93} -185.282 q^{94} +100.638i q^{95} +(110.976 - 80.2060i) q^{96} -51.8908 q^{97} -20.0025i q^{98} +(-38.5406 - 12.7359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more