LMFDB - Embedded newform 216.3.h.c.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.121670000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} - 6x^{3} + 16x^{2} - 16x + 64 $ x^6 - x^5 + 4x^4 - 6x^3 + 16x^2 - 16x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.4
Root			$0.122180 - 1.99626i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.c.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.122180 + 1.99626i) q^{2} +(-3.97014 - 0.487807i) q^{4} +5.18465 q^{5} +3.67337 q^{7} +(1.45886 - 7.86586i) q^{8} +O(q^{10})$	\(q+(-0.122180 + 1.99626i) q^{2} +(-3.97014 - 0.487807i) q^{4} +5.18465 q^{5} +3.67337 q^{7} +(1.45886 - 7.86586i) q^{8} +(-0.633460 + 10.3499i) q^{10} +12.8806 q^{11} +8.72227i q^{13} +(-0.448812 + 7.33301i) q^{14} +(15.5241 + 3.87333i) q^{16} -18.6586i q^{17} +30.7262i q^{19} +(-20.5838 - 2.52911i) q^{20} +(-1.57375 + 25.7130i) q^{22} +20.7899i q^{23} +1.88058 q^{25} +(-17.4120 - 1.06569i) q^{26} +(-14.5838 - 1.79189i) q^{28} +27.8806 q^{29} -16.6216 q^{31} +(-9.62892 + 30.5169i) q^{32} +(37.2474 + 2.27970i) q^{34} +19.0451 q^{35} -60.5351i q^{37} +(-61.3377 - 3.75413i) q^{38} +(7.56370 - 40.7817i) q^{40} +28.2982i q^{41} +51.8128i q^{43} +(-51.1377 - 6.28324i) q^{44} +(-41.5022 - 2.54011i) q^{46} -69.2573i q^{47} -35.5064 q^{49} +(-0.229769 + 3.75413i) q^{50} +(4.25479 - 34.6287i) q^{52} +28.5022 q^{53} +66.7813 q^{55} +(5.35894 - 28.8942i) q^{56} +(-3.40645 + 55.6570i) q^{58} +61.1030 q^{59} -105.460i q^{61} +(2.03083 - 33.1812i) q^{62} +(-59.7434 - 22.9504i) q^{64} +45.2219i q^{65} +16.9237i q^{67} +(-9.10178 + 74.0772i) q^{68} +(-2.32693 + 38.0191i) q^{70} -26.1668i q^{71} +102.299 q^{73} +(120.844 + 7.39617i) q^{74} +(14.9885 - 121.988i) q^{76} +47.3151 q^{77} -92.2317 q^{79} +(80.4869 + 20.0818i) q^{80} +(-56.4907 - 3.45747i) q^{82} -36.4161 q^{83} -96.7381i q^{85} +(-103.432 - 6.33049i) q^{86} +(18.7910 - 101.317i) q^{88} -73.5201i q^{89} +32.0401i q^{91} +(10.1415 - 82.5390i) q^{92} +(138.256 + 8.46186i) q^{94} +159.305i q^{95} -186.818 q^{97} +(4.33817 - 70.8801i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 7 q^{4} - 2 q^{5} - 10 q^{7} - 7 q^{8}+O(q^{10}) $ 6 * q - q^2 - 7 * q^4 - 2 * q^5 - 10 * q^7 - 7 * q^8	$ 6 q - q^{2} - 7 q^{4} - 2 q^{5} - 10 q^{7} - 7 q^{8} - 3 q^{10} + 10 q^{11} - 35 q^{14} - 23 q^{16} - 41 q^{20} + 25 q^{22} - 56 q^{25} + 60 q^{26} - 5 q^{28} + 100 q^{29} + 6 q^{31} + 29 q^{32} - 4 q^{34} + 110 q^{35} - 132 q^{38} + 59 q^{40} - 125 q^{44} - 76 q^{46} - 24 q^{49} + 36 q^{50} + 80 q^{52} - 2 q^{53} + 170 q^{55} + 175 q^{56} + 10 q^{58} - 20 q^{59} - 191 q^{62} - 151 q^{64} - 312 q^{68} + 115 q^{70} + 130 q^{73} + 300 q^{74} - 176 q^{76} + 50 q^{77} - 76 q^{79} + 331 q^{80} + 100 q^{82} - 38 q^{83} - 360 q^{86} - 5 q^{88} - 408 q^{92} + 240 q^{94} - 70 q^{97} + 324 q^{98}+O(q^{100}) $ 6 * q - q^2 - 7 * q^4 - 2 * q^5 - 10 * q^7 - 7 * q^8 - 3 * q^10 + 10 * q^11 - 35 * q^14 - 23 * q^16 - 41 * q^20 + 25 * q^22 - 56 * q^25 + 60 * q^26 - 5 * q^28 + 100 * q^29 + 6 * q^31 + 29 * q^32 - 4 * q^34 + 110 * q^35 - 132 * q^38 + 59 * q^40 - 125 * q^44 - 76 * q^46 - 24 * q^49 + 36 * q^50 + 80 * q^52 - 2 * q^53 + 170 * q^55 + 175 * q^56 + 10 * q^58 - 20 * q^59 - 191 * q^62 - 151 * q^64 - 312 * q^68 + 115 * q^70 + 130 * q^73 + 300 * q^74 - 176 * q^76 + 50 * q^77 - 76 * q^79 + 331 * q^80 + 100 * q^82 - 38 * q^83 - 360 * q^86 - 5 * q^88 - 408 * q^92 + 240 * q^94 - 70 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.122180	+	1.99626i	−0.0610900	+	0.998132i
$2$	−0.122180	+	1.99626i	−0.0610900	+	0.998132i
$3$		0			0
$3$		0			0
$4$	−3.97014	−	0.487807i	−0.992536	−	0.121952i
$5$	5.18465			1.03693			0.518465	−	0.855099i	$-0.326504\pi$
$5$	5.18465			1.03693			0.518465	+	0.855099i	$0.326504\pi$
$6$		0			0
$7$	3.67337			0.524767			0.262383	−	0.964964i	$-0.415491\pi$
$7$	3.67337			0.524767			0.262383	+	0.964964i	$0.415491\pi$
$8$	1.45886	−	7.86586i	0.182358	−	0.983232i
$9$		0			0
$10$	−0.633460	+	10.3499i	−0.0633460	+	1.03499i
$11$	12.8806			1.17096			0.585481	−	0.810686i	$-0.300906\pi$
$11$	12.8806			1.17096			0.585481	+	0.810686i	$0.300906\pi$
$12$		0			0
$13$			8.72227i			0.670944i	0.942050	+	0.335472i	$0.108896\pi$
$13$			8.72227i			0.670944i	−0.942050	+	0.335472i	$0.891104\pi$
$14$	−0.448812	+	7.33301i	−0.0320580	+	0.523787i
$15$		0			0
$16$	15.5241	+	3.87333i	0.970256	+	0.242083i
$17$		−	18.6586i		−	1.09756i	−0.835966	−	0.548781i	$-0.815092\pi$
$17$		−	18.6586i		−	1.09756i	0.835966	−	0.548781i	$-0.184908\pi$
$18$		0			0
$19$			30.7262i			1.61717i	0.588380	+	0.808585i	$0.299766\pi$
$19$			30.7262i			1.61717i	−0.588380	+	0.808585i	$0.700234\pi$
$20$	−20.5838	−	2.52911i	−1.02919	−	0.126455i
$21$		0			0
$22$	−1.57375	+	25.7130i	−0.0715340	+	1.16877i
$23$			20.7899i			0.903910i	0.892041	+	0.451955i	$0.149273\pi$
$23$			20.7899i			0.903910i	−0.892041	+	0.451955i	$0.850727\pi$
$24$		0			0
$25$	1.88058			0.0752231
$26$	−17.4120	−	1.06569i	−0.669691	−	0.0409880i
$27$		0			0
$28$	−14.5838	−	1.79189i	−0.520850	−	0.0639962i
$29$	27.8806			0.961399			0.480700	−	0.876885i	$-0.340383\pi$
$29$	27.8806			0.961399			0.480700	+	0.876885i	$0.340383\pi$
$30$		0			0
$31$	−16.6216			−0.536181			−0.268091	−	0.963394i	$-0.586393\pi$
$31$	−16.6216			−0.536181			−0.268091	+	0.963394i	$0.586393\pi$
$32$	−9.62892	+	30.5169i	−0.300904	+	0.953655i
$33$		0			0
$34$	37.2474	+	2.27970i	1.09551	+	0.0670501i
$35$	19.0451			0.544146
$36$		0			0
$37$		−	60.5351i		−	1.63608i	−0.575159	−	0.818042i	$-0.695060\pi$
$37$		−	60.5351i		−	1.63608i	0.575159	−	0.818042i	$-0.304940\pi$
$38$	−61.3377	−	3.75413i	−1.61415	−	0.0987928i
$39$		0			0
$40$	7.56370	−	40.7817i	0.189092	−	1.01954i
$41$			28.2982i			0.690200i	0.938566	+	0.345100i	$0.112155\pi$
$41$			28.2982i			0.690200i	−0.938566	+	0.345100i	$0.887845\pi$
$42$		0			0
$43$			51.8128i			1.20495i	0.798138	+	0.602474i	$0.205818\pi$
$43$			51.8128i			1.20495i	−0.798138	+	0.602474i	$0.794182\pi$
$44$	−51.1377	−	6.28324i	−1.16222	−	0.142801i
$45$		0			0
$46$	−41.5022	−	2.54011i	−0.902222	−	0.0552198i
$47$		−	69.2573i		−	1.47356i	−0.676132	−	0.736780i	$-0.736345\pi$
$47$		−	69.2573i		−	1.47356i	0.676132	−	0.736780i	$-0.263655\pi$
$48$		0			0
$49$	−35.5064			−0.724620
$50$	−0.229769	+	3.75413i	−0.00459538	+	0.0750826i
$51$		0			0
$52$	4.25479	−	34.6287i	0.0818228	−	0.665936i
$53$	28.5022			0.537777			0.268889	−	0.963171i	$-0.413344\pi$
$53$	28.5022			0.537777			0.268889	+	0.963171i	$0.413344\pi$
$54$		0			0
$55$	66.7813			1.21420
$56$	5.35894	−	28.8942i	0.0956954	−	0.515968i
$57$		0			0
$58$	−3.40645	+	55.6570i	−0.0587319	+	0.959604i
$59$	61.1030			1.03564			0.517822	−	0.855488i	$-0.326743\pi$
$59$	61.1030			1.03564			0.517822	+	0.855488i	$0.326743\pi$
$60$		0			0
$61$		−	105.460i		−	1.72886i	−0.502755	−	0.864429i	$-0.667680\pi$
$61$		−	105.460i		−	1.72886i	0.502755	−	0.864429i	$-0.332320\pi$
$62$	2.03083	−	33.1812i	0.0327553	−	0.535180i
$63$		0			0
$64$	−59.7434	−	22.9504i	−0.933491	−	0.358601i
$65$			45.2219i			0.695722i
$66$		0			0
$67$			16.9237i			0.252593i	0.991993	+	0.126296i	$0.0403090\pi$
$67$			16.9237i			0.252593i	−0.991993	+	0.126296i	$0.959691\pi$
$68$	−9.10178	+	74.0772i	−0.133850	+	1.08937i
$69$		0			0
$70$	−2.32693	+	38.0191i	−0.0332419	+	0.543130i
$71$		−	26.1668i		−	0.368547i	−0.982875	−	0.184273i	$-0.941007\pi$
$71$		−	26.1668i		−	0.368547i	0.982875	−	0.184273i	$-0.0589932\pi$
$72$		0			0
$73$	102.299			1.40136			0.700681	−	0.713475i	$-0.252880\pi$
$73$	102.299			1.40136			0.700681	+	0.713475i	$0.252880\pi$
$74$	120.844	+	7.39617i	1.63303	+	0.0999483i
$75$		0			0
$76$	14.9885	−	121.988i	0.197217	−	1.60510i
$77$	47.3151			0.614482
$78$		0			0
$79$	−92.2317			−1.16749			−0.583745	−	0.811937i	$-0.698413\pi$
$79$	−92.2317			−1.16749			−0.583745	+	0.811937i	$0.698413\pi$
$80$	80.4869	+	20.0818i	1.00609	+	0.251023i
$81$		0			0
$82$	−56.4907	−	3.45747i	−0.688911	−	0.0421643i
$83$	−36.4161			−0.438749			−0.219374	−	0.975641i	$-0.570402\pi$
$83$	−36.4161			−0.438749			−0.219374	+	0.975641i	$0.570402\pi$
$84$		0			0
$85$		−	96.7381i		−	1.13809i
$86$	−103.432	−	6.33049i	−1.20270	−	0.0736103i
$87$		0			0
$88$	18.7910	−	101.317i	0.213534	−	1.15133i
$89$		−	73.5201i		−	0.826068i	−0.910715	−	0.413034i	$-0.864469\pi$
$89$		−	73.5201i		−	0.826068i	0.910715	−	0.413034i	$-0.135531\pi$
$90$		0			0
$91$			32.0401i			0.352089i
$92$	10.1415	−	82.5390i	0.110233	−	0.897163i
$93$		0			0
$94$	138.256	+	8.46186i	1.47081	+	0.0900198i
$95$			159.305i			1.67689i
$96$		0			0
$97$	−186.818			−1.92596			−0.962982	−	0.269566i	$-0.913120\pi$
$97$	−186.818			−1.92596			−0.962982	+	0.269566i	$0.913120\pi$
$98$	4.33817	−	70.8801i	0.0442670	−	0.723266i
$99$		0			0
$100$	−7.46616	−	0.917358i	−0.0746616	−	0.00917358i
$101$	−112.768			−1.11651			−0.558257	−	0.829668i	$-0.688530\pi$
$101$	−112.768			−1.11651			−0.558257	+	0.829668i	$0.688530\pi$
$102$		0			0
$103$	−14.2548			−0.138396			−0.0691980	−	0.997603i	$-0.522044\pi$
$103$	−14.2548			−0.138396			−0.0691980	+	0.997603i	$0.522044\pi$
$104$	68.6081	+	12.7246i	0.659694	+	0.122352i
$105$		0			0
$106$	−3.48240	+	56.8979i	−0.0328528	+	0.536773i
$107$	−58.8965			−0.550435			−0.275217	−	0.961382i	$-0.588750\pi$
$107$	−58.8965			−0.550435			−0.275217	+	0.961382i	$0.588750\pi$
$108$		0			0
$109$		−	58.7004i		−	0.538535i	−0.963065	−	0.269268i	$-0.913218\pi$
$109$		−	58.7004i		−	0.538535i	0.963065	−	0.269268i	$-0.0867816\pi$
$110$	−8.15933	+	133.313i	−0.0741757	+	1.21194i
$111$		0			0
$112$	57.0257	+	14.2282i	0.509158	+	0.127037i
$113$		−	118.742i		−	1.05081i	−0.850851	−	0.525407i	$-0.823913\pi$
$113$		−	118.742i		−	1.05081i	0.850851	−	0.525407i	$-0.176087\pi$
$114$		0			0
$115$			107.788i			0.937291i
$116$	−110.690	−	13.6003i	−0.954223	−	0.117244i
$117$		0			0
$118$	−7.46556	+	121.978i	−0.0632675	+	1.03371i
$119$		−	68.5397i		−	0.575964i
$120$		0			0
$121$	44.9092			0.371151
$122$	210.527	+	12.8851i	1.72563	+	0.105616i
$123$		0			0
$124$	65.9902	+	8.10815i	0.532179	+	0.0653883i
$125$	−119.866			−0.958929
$126$		0			0
$127$	176.105			1.38665			0.693326	−	0.720624i	$-0.256144\pi$
$127$	176.105			1.38665			0.693326	+	0.720624i	$0.256144\pi$
$128$	53.1146	−	116.460i	0.414958	−	0.909841i
$129$		0			0
$130$	−90.2749	−	5.52521i	−0.694422	−	0.0425016i
$131$	−178.760			−1.36458			−0.682291	−	0.731081i	$-0.739016\pi$
$131$	−178.760			−1.36458			−0.682291	+	0.731081i	$0.739016\pi$
$132$		0			0
$133$			112.869i			0.848637i
$134$	−33.7842	−	2.06774i	−0.252121	−	0.0154309i
$135$		0			0
$136$	−146.766	−	27.2203i	−1.07916	−	0.200149i
$137$			182.002i			1.32848i	0.747519	+	0.664240i	$0.231245\pi$
$137$			182.002i			1.32848i	−0.747519	+	0.664240i	$0.768755\pi$
$138$		0			0
$139$			208.293i			1.49851i	0.662282	+	0.749255i	$0.269588\pi$
$139$			208.293i			1.49851i	−0.662282	+	0.749255i	$0.730412\pi$
$140$	−75.6119	−	9.29034i	−0.540085	−	0.0663596i
$141$		0			0
$142$	52.2359	+	3.19706i	0.367858	+	0.0225145i
$143$			112.348i			0.785650i
$144$		0			0
$145$	144.551			0.996903
$146$	−12.4989	+	204.217i	−0.0856092	+	1.39874i
$147$		0			0
$148$	−29.5294	+	240.333i	−0.199523	+	1.62387i
$149$	−230.862			−1.54941			−0.774704	−	0.632325i	$-0.782101\pi$
$149$	−230.862			−1.54941			−0.774704	+	0.632325i	$0.782101\pi$
$150$		0			0
$151$	−103.666			−0.686531			−0.343266	−	0.939238i	$-0.611533\pi$
$151$	−103.666			−0.686531			−0.343266	+	0.939238i	$0.611533\pi$
$152$	241.688	+	44.8254i	1.59005	+	0.294904i
$153$		0			0
$154$	−5.78096	+	94.4535i	−0.0375387	+	0.613334i
$155$	−86.1773			−0.555982
$156$		0			0
$157$		−	17.4445i		−	0.111112i	−0.998456	−	0.0555559i	$-0.982307\pi$
$157$		−	17.4445i		−	0.111112i	0.998456	−	0.0555559i	$-0.0176931\pi$
$158$	11.2689	−	184.119i	0.0713219	−	1.16531i
$159$		0			0
$160$	−49.9226	+	158.220i	−0.312016	+	0.988873i
$161$			76.3691i			0.474342i
$162$		0			0
$163$		−	1.80733i		−	0.0110879i	−0.999985	−	0.00554395i	$-0.998235\pi$
$163$		−	1.80733i		−	0.0110879i	0.999985	−	0.00554395i	$-0.00176470\pi$
$164$	13.8041	−	112.348i	0.0841711	−	0.685048i
$165$		0			0
$166$	4.44932	−	72.6962i	0.0268031	−	0.437929i
$167$		−	13.1093i		−	0.0784988i	−0.999229	−	0.0392494i	$-0.987503\pi$
$167$		−	13.1093i		−	0.0784988i	0.999229	−	0.0392494i	$-0.0124967\pi$
$168$		0			0
$169$	92.9220			0.549834
$170$	193.115	+	11.8195i	1.13597	+	0.0695262i
$171$		0			0
$172$	25.2747	−	205.704i	0.146946	−	1.19596i
$173$	190.710			1.10237			0.551186	−	0.834382i	$-0.314175\pi$
$173$	190.710			1.10237			0.551186	+	0.834382i	$0.314175\pi$
$174$		0			0
$175$	6.90805			0.0394746
$176$	199.959	+	49.8907i	1.13613	+	0.283470i
$177$		0			0
$178$	146.766	+	8.98268i	0.824526	+	0.0504645i
$179$	3.96761			0.0221654			0.0110827	−	0.999939i	$-0.496472\pi$
$179$	3.96761			0.0221654			0.0110827	+	0.999939i	$0.496472\pi$
$180$		0			0
$181$			122.905i			0.679032i	0.940600	+	0.339516i	$0.110263\pi$
$181$			122.905i			0.679032i	−0.940600	+	0.339516i	$0.889737\pi$
$182$	−63.9605	−	3.91466i	−0.351432	−	0.0215091i
$183$		0			0
$184$	163.531	+	30.3297i	0.888753	+	0.164835i
$185$		−	313.853i		−	1.69650i
$186$		0			0
$187$		−	240.333i		−	1.28520i
$188$	−33.7842	+	274.962i	−0.179703	+	1.46256i
$189$		0			0
$190$	−318.014	−	19.4638i	−1.67376	−	0.102441i
$191$		−	345.569i		−	1.80926i	−0.426195	−	0.904631i	$-0.640146\pi$
$191$		−	345.569i		−	1.80926i	0.426195	−	0.904631i	$-0.359854\pi$
$192$		0			0
$193$	−236.253			−1.22411			−0.612055	−	0.790815i	$-0.709657\pi$
$193$	−236.253			−1.22411			−0.612055	+	0.790815i	$0.709657\pi$
$194$	22.8255	−	372.939i	0.117657	−	1.92237i
$195$		0			0
$196$	140.965	+	17.3203i	0.719211	+	0.0883687i
$197$	8.25131			0.0418848			0.0209424	−	0.999781i	$-0.493333\pi$
$197$	8.25131			0.0418848			0.0209424	+	0.999781i	$0.493333\pi$
$198$		0			0
$199$	−26.1913			−0.131614			−0.0658072	−	0.997832i	$-0.520962\pi$
$199$	−26.1913			−0.131614			−0.0658072	+	0.997832i	$0.520962\pi$
$200$	2.74351	−	14.7923i	0.0137175	−	0.0739617i
$201$		0			0
$202$	13.7780	−	225.115i	0.0682079	−	1.11443i
$203$	102.416			0.504510
$204$		0			0
$205$			146.716i			0.715689i
$206$	1.74165	−	28.4563i	0.00845461	−	0.138137i
$207$		0			0
$208$	−33.7842	+	135.405i	−0.162424	+	0.650987i
$209$			395.771i			1.89364i
$210$		0			0
$211$		−	169.241i		−	0.802090i	−0.916058	−	0.401045i	$-0.868647\pi$
$211$		−	169.241i		−	0.802090i	0.916058	−	0.401045i	$-0.131353\pi$
$212$	−113.158	−	13.9036i	−0.533763	−	0.0655829i
$213$		0			0
$214$	7.19597	−	117.573i	0.0336260	−	0.549407i
$215$			268.631i			1.24945i
$216$		0			0
$217$	−61.0573			−0.281370
$218$	117.181	+	7.17201i	0.537530	+	0.0328991i
$219$		0			0
$220$	−265.131	−	32.5764i	−1.20514	−	0.148074i
$221$	162.745			0.736403
$222$		0			0
$223$	107.627			0.482634			0.241317	−	0.970446i	$-0.422421\pi$
$223$	107.627			0.482634			0.241317	+	0.970446i	$0.422421\pi$
$224$	−35.3706	+	112.100i	−0.157904	+	0.500446i
$225$		0			0
$226$	237.040	+	14.5079i	1.04885	+	0.0641942i
$227$	213.657			0.941219			0.470609	−	0.882342i	$-0.344034\pi$
$227$	213.657			0.941219			0.470609	+	0.882342i	$0.344034\pi$
$228$		0			0
$229$			87.4950i			0.382074i	0.981583	+	0.191037i	$0.0611851\pi$
$229$			87.4950i			0.382074i	−0.981583	+	0.191037i	$0.938815\pi$
$230$	−215.174	−	13.1696i	−0.935540	−	0.0572591i
$231$		0			0
$232$	40.6740	−	219.305i	0.175319	−	0.945279i
$233$		−	8.39823i		−	0.0360439i	−0.999838	−	0.0180219i	$-0.994263\pi$
$233$		−	8.39823i		−	0.0360439i	0.999838	−	0.0180219i	$-0.00573687\pi$
$234$		0			0
$235$		−	359.075i		−	1.52798i
$236$	−242.588	−	29.8065i	−1.02791	−	0.126299i
$237$		0			0
$238$	136.823	+	8.37418i	0.574889	+	0.0351856i
$239$		−	61.5767i		−	0.257643i	−0.991668	−	0.128822i	$-0.958881\pi$
$239$		−	61.5767i		−	0.257643i	0.991668	−	0.128822i	$-0.0411195\pi$
$240$		0			0
$241$	68.1354			0.282719			0.141360	−	0.989958i	$-0.454853\pi$
$241$	68.1354			0.282719			0.141360	+	0.989958i	$0.454853\pi$
$242$	−5.48701	+	89.6507i	−0.0226736	+	0.370458i
$243$		0			0
$244$	−51.4443	+	418.693i	−0.210837	+	1.71595i
$245$	−184.088			−0.751380
$246$		0			0
$247$	−268.002			−1.08503
$248$	−24.2487	+	130.743i	−0.0977770	+	0.527191i
$249$		0			0
$250$	14.6452	−	239.284i	0.0585809	−	0.957138i
$251$	−23.3408			−0.0929913			−0.0464956	−	0.998918i	$-0.514805\pi$
$251$	−23.3408			−0.0929913			−0.0464956	+	0.998918i	$0.514805\pi$
$252$		0			0
$253$			267.786i			1.05844i
$254$	−21.5165	+	351.552i	−0.0847106	+	1.38406i
$255$		0			0
$256$	225.995	+	120.260i	0.882792	+	0.469765i
$257$		−	201.774i		−	0.785115i	−0.919728	−	0.392557i	$-0.871590\pi$
$257$		−	201.774i		−	0.785115i	0.919728	−	0.392557i	$-0.128410\pi$
$258$		0			0
$259$		−	222.368i		−	0.858562i
$260$	22.0596	−	179.537i	0.0848445	−	0.690529i
$261$		0			0
$262$	21.8409	−	356.853i	0.0833622	−	1.36203i
$263$		−	259.261i		−	0.985783i	−0.870091	−	0.492891i	$-0.835940\pi$
$263$		−	259.261i		−	0.985783i	0.870091	−	0.492891i	$-0.164060\pi$
$264$		0			0
$265$	147.774			0.557637
$266$	−225.316	−	13.7903i	−0.847052	−	0.0518432i
$267$		0			0
$268$	8.25551	−	67.1896i	0.0308041	−	0.250707i
$269$	317.109			1.17884			0.589422	−	0.807825i	$-0.299356\pi$
$269$	317.109			1.17884			0.589422	+	0.807825i	$0.299356\pi$
$270$		0			0
$271$	−155.556			−0.574009			−0.287004	−	0.957929i	$-0.592659\pi$
$271$	−155.556			−0.574009			−0.287004	+	0.957929i	$0.592659\pi$
$272$	72.2707	−	289.657i	0.265701	−	1.06492i
$273$		0			0
$274$	−363.324	−	22.2370i	−1.32600	−	0.0811568i
$275$	24.2229			0.0880833
$276$		0			0
$277$		−	191.890i		−	0.692744i	−0.938097	−	0.346372i	$-0.887414\pi$
$277$		−	191.890i		−	0.692744i	0.938097	−	0.346372i	$-0.112586\pi$
$278$	−415.808	−	25.4492i	−1.49571	−	0.0915439i
$279$		0			0
$280$	27.7842	−	149.806i	0.0992294	−	0.535022i
$281$			339.302i			1.20748i	0.797181	+	0.603741i	$0.206324\pi$
$281$			339.302i			1.20748i	−0.797181	+	0.603741i	$0.793676\pi$
$282$		0			0
$283$		−	360.882i		−	1.27520i	−0.770367	−	0.637601i	$-0.779927\pi$
$283$		−	360.882i		−	1.27520i	0.770367	−	0.637601i	$-0.220073\pi$
$284$	−12.7644	+	103.886i	−0.0449449	+	0.365796i
$285$		0			0
$286$	−224.276	−	13.7267i	−0.784182	−	0.0479953i
$287$			103.950i			0.362194i
$288$		0			0
$289$	−59.1418			−0.204643
$290$	−17.6612	+	288.562i	−0.0609008	+	0.995041i
$291$		0			0
$292$	−406.143	−	49.9024i	−1.39090	−	0.170899i
$293$	−27.4171			−0.0935739			−0.0467869	−	0.998905i	$-0.514898\pi$
$293$	−27.4171			−0.0935739			−0.0467869	+	0.998905i	$0.514898\pi$
$294$		0			0
$295$	316.797			1.07389
$296$	−476.160	−	88.3124i	−1.60865	−	0.298353i
$297$		0			0
$298$	28.2067	−	460.861i	0.0946533	−	1.54651i
$299$	−181.335			−0.606473
$300$		0			0
$301$			190.327i			0.632317i
$302$	12.6659	−	206.945i	0.0419402	−	0.685249i
$303$		0			0
$304$	−119.013	+	476.997i	−0.391489	+	1.56907i
$305$		−	546.775i		−	1.79270i
$306$		0			0
$307$		−	200.788i		−	0.654031i	−0.945019	−	0.327016i	$-0.893957\pi$
$307$		−	200.788i		−	0.654031i	0.945019	−	0.327016i	$-0.106043\pi$
$308$	−187.848	−	23.0806i	−0.609895	−	0.0749371i
$309$		0			0
$310$	10.5291	−	172.033i	0.0339650	−	0.554944i
$311$			441.838i			1.42070i	0.703848	+	0.710351i	$0.251464\pi$
$311$			441.838i			1.42070i	−0.703848	+	0.710351i	$0.748536\pi$
$312$		0			0
$313$	−7.18318			−0.0229494			−0.0114747	−	0.999934i	$-0.503653\pi$
$313$	−7.18318			−0.0229494			−0.0114747	+	0.999934i	$0.503653\pi$
$314$	34.8239	+	2.13137i	0.110904	+	0.00678781i
$315$		0			0
$316$	366.173	+	44.9913i	1.15878	+	0.142377i
$317$	431.934			1.36257			0.681284	−	0.732019i	$-0.261422\pi$
$317$	431.934			1.36257			0.681284	+	0.732019i	$0.261422\pi$
$318$		0			0
$319$	359.118			1.12576
$320$	−309.749	−	118.990i	−0.967965	−	0.371843i
$321$		0			0
$322$	−152.453	−	9.33077i	−0.473456	−	0.0289775i
$323$	573.307			1.77494
$324$		0			0
$325$			16.4029i			0.0504705i
$326$	3.60791	+	0.220819i	0.0110672	+	0.000677360i
$327$		0			0
$328$	222.590	+	41.2832i	0.678627	+	0.125863i
$329$		−	254.408i		−	0.773276i
$330$		0			0
$331$			221.602i			0.669492i	0.942308	+	0.334746i	$0.108651\pi$
$331$			221.602i			0.669492i	−0.942308	+	0.334746i	$0.891349\pi$
$332$	144.577	+	17.7640i	0.435474	+	0.0535062i
$333$		0			0
$334$	26.1696	+	1.60169i	0.0783522	+	0.00479549i
$335$			87.7435i			0.261921i
$336$		0			0
$337$	380.043			1.12772			0.563862	−	0.825869i	$-0.309315\pi$
$337$	380.043			1.12772			0.563862	+	0.825869i	$0.309315\pi$
$338$	−11.3532	+	185.497i	−0.0335894	+	0.548807i
$339$		0			0
$340$	−47.1895	+	384.064i	−0.138793	+	1.12960i
$341$	−214.096			−0.627848
$342$		0			0
$343$	−310.423			−0.905023
$344$	407.552	+	75.5878i	1.18474	+	0.219732i
$345$		0			0
$346$	−23.3010	+	380.708i	−0.0673439	+	1.10031i
$347$	526.595			1.51756			0.758782	−	0.651345i	$-0.225795\pi$
$347$	526.595			1.51756			0.758782	+	0.651345i	$0.225795\pi$
$348$		0			0
$349$			452.198i			1.29570i	0.761769	+	0.647849i	$0.224331\pi$
$349$			452.198i			1.29570i	−0.761769	+	0.647849i	$0.775669\pi$
$350$	−0.844025	+	13.7903i	−0.00241150	+	0.0394008i
$351$		0			0
$352$	−124.026	+	393.076i	−0.352347	+	1.11669i
$353$		−	90.5925i		−	0.256636i	−0.991733	−	0.128318i	$-0.959042\pi$
$353$		−	90.5925i		−	0.256636i	0.991733	−	0.128318i	$-0.0409578\pi$
$354$		0			0
$355$		−	135.666i		−	0.382157i
$356$	−35.8636	+	291.885i	−0.100741	+	0.819903i
$357$		0			0
$358$	−0.484763	+	7.92041i	−0.00135409	+	0.0221240i
$359$		−	96.2690i		−	0.268159i	−0.990971	−	0.134079i	$-0.957192\pi$
$359$		−	96.2690i		−	0.268159i	0.990971	−	0.134079i	$-0.0428077\pi$
$360$		0			0
$361$	−583.100			−1.61524
$362$	−245.351	−	15.0165i	−0.677764	−	0.0414821i
$363$		0			0
$364$	15.6294	−	127.204i	0.0429379	−	0.349461i
$365$	530.386			1.45311
$366$		0			0
$367$	−517.326			−1.40961			−0.704804	−	0.709402i	$-0.748965\pi$
$367$	−517.326			−1.40961			−0.704804	+	0.709402i	$0.748965\pi$
$368$	−80.5262	+	322.745i	−0.218821	+	0.877024i
$369$		0			0
$370$	626.534	+	38.3466i	1.69333	+	0.103639i
$371$	104.699			0.282208
$372$		0			0
$373$			727.914i			1.95151i	0.218862	+	0.975756i	$0.429766\pi$
$373$			727.914i			1.95151i	−0.218862	+	0.975756i	$0.570234\pi$
$374$	479.768	+	29.3639i	1.28280	+	0.0785130i
$375$		0			0
$376$	−544.768	−	101.037i	−1.44885	−	0.268716i
$377$			243.182i			0.645045i
$378$		0			0
$379$			635.832i			1.67766i	0.544396	+	0.838829i	$0.316759\pi$
$379$			635.832i			1.67766i	−0.544396	+	0.838829i	$0.683241\pi$
$380$	77.7099	−	632.462i	0.204500	−	1.66437i
$381$		0			0
$382$	689.847	+	42.2216i	1.80588	+	0.110528i
$383$			151.699i			0.396082i	0.980194	+	0.198041i	$0.0634579\pi$
$383$			151.699i			0.396082i	−0.980194	+	0.198041i	$0.936542\pi$
$384$		0			0
$385$	245.312			0.637174
$386$	28.8654	−	471.624i	0.0747809	−	1.22182i
$387$		0			0
$388$	741.696	+	91.1314i	1.91159	+	0.234875i
$389$	−337.972			−0.868823			−0.434411	−	0.900715i	$-0.643044\pi$
$389$	−337.972			−0.868823			−0.434411	+	0.900715i	$0.643044\pi$
$390$		0			0
$391$	387.910			0.992098
$392$	−51.7990	+	279.288i	−0.132140	+	0.712469i
$393$		0			0
$394$	−1.00814	+	16.4718i	−0.00255874	+	0.0418066i
$395$	−478.189			−1.21061
$396$		0			0
$397$		−	225.147i		−	0.567121i	−0.958954	−	0.283561i	$-0.908484\pi$
$397$		−	225.147i		−	0.567121i	0.958954	−	0.283561i	$-0.0915157\pi$
$398$	3.20005	−	52.2847i	0.00804032	−	0.131369i
$399$		0			0
$400$	29.1942	+	7.28409i	0.0729856	+	0.0182102i
$401$			342.151i			0.853245i	0.904430	+	0.426623i	$0.140297\pi$
$401$			342.151i			0.853245i	−0.904430	+	0.426623i	$0.859703\pi$
$402$		0			0
$403$		−	144.978i		−	0.359748i
$404$	447.705	+	55.0090i	1.10818	+	0.136161i
$405$		0			0
$406$	−12.5131	+	204.449i	−0.0308205	+	0.503568i
$407$		−	779.727i		−	1.91579i
$408$		0			0
$409$	−247.089			−0.604130			−0.302065	−	0.953287i	$-0.597676\pi$
$409$	−247.089			−0.604130			−0.302065	+	0.953287i	$0.597676\pi$
$410$	−292.884	−	17.9258i	−0.714352	−	0.0437214i
$411$		0			0
$412$	56.5936	+	6.95358i	0.137363	+	0.0168776i
$413$	224.454			0.543471
$414$		0			0
$415$	−188.805			−0.454951
$416$	−266.177	−	83.9861i	−0.639849	−	0.201890i
$417$		0			0
$418$	−790.064	−	48.3553i	−1.89011	−	0.115683i
$419$	−650.435			−1.55235			−0.776175	−	0.630517i	$-0.782843\pi$
$419$	−650.435			−1.55235			−0.776175	+	0.630517i	$0.782843\pi$
$420$		0			0
$421$		−	17.1960i		−	0.0408455i	−0.999791	−	0.0204228i	$-0.993499\pi$
$421$		−	17.1960i		−	0.0408455i	0.999791	−	0.0204228i	$-0.00650122\pi$
$422$	337.850	+	20.6778i	0.800592	+	0.0489996i
$423$		0			0
$424$	41.5808	−	224.194i	0.0980680	−	0.528760i
$425$		−	35.0888i		−	0.0825620i
$426$		0			0
$427$		−	387.395i		−	0.907247i
$428$	233.828	+	28.7301i	0.546326	+	0.0671265i
$429$		0			0
$430$	−536.259	−	32.8213i	−1.24711	−	0.0763287i
$431$		−	312.439i		−	0.724917i	−0.932000	−	0.362459i	$-0.881937\pi$
$431$		−	312.439i		−	0.724917i	0.932000	−	0.362459i	$-0.118063\pi$
$432$		0			0
$433$	164.038			0.378841			0.189421	−	0.981896i	$-0.439339\pi$
$433$	164.038			0.378841			0.189421	+	0.981896i	$0.439339\pi$
$434$	7.45998	−	121.887i	0.0171889	−	0.280845i
$435$		0			0
$436$	−28.6344	+	233.049i	−0.0656753	+	0.534516i
$437$	−638.796			−1.46178
$438$		0			0
$439$	614.082			1.39882			0.699410	−	0.714721i	$-0.253446\pi$
$439$	614.082			1.39882			0.699410	+	0.714721i	$0.253446\pi$
$440$	97.4248	−	525.292i	0.221420	−	1.19385i
$441$		0			0
$442$	−19.8842	+	324.882i	−0.0449868	+	0.735027i
$443$	−4.75963			−0.0107441			−0.00537204	−	0.999986i	$-0.501710\pi$
$443$	−4.75963			−0.0107441			−0.00537204	+	0.999986i	$0.501710\pi$
$444$		0			0
$445$		−	381.176i		−	0.856575i
$446$	−13.1499	+	214.853i	−0.0294841	+	0.481733i
$447$		0			0
$448$	−219.460	−	84.3054i	−0.489865	−	0.188182i
$449$			370.195i			0.824488i	0.911074	+	0.412244i	$0.135255\pi$
$449$			370.195i			0.824488i	−0.911074	+	0.412244i	$0.864745\pi$
$450$		0			0
$451$			364.497i			0.808197i
$452$	−57.9232	+	471.423i	−0.128149	+	1.04297i
$453$		0			0
$454$	−26.1046	+	426.515i	−0.0574990	+	0.939461i
$455$			166.117i			0.365092i
$456$		0			0
$457$	172.960			0.378469			0.189234	−	0.981932i	$-0.439399\pi$
$457$	172.960			0.378469			0.189234	+	0.981932i	$0.439399\pi$
$458$	−174.663	−	10.6901i	−0.381360	−	0.0233409i
$459$		0			0
$460$	52.5800	−	427.936i	0.114304	−	0.930295i
$461$	17.8691			0.0387617			0.0193808	−	0.999812i	$-0.493831\pi$
$461$	17.8691			0.0387617			0.0193808	+	0.999812i	$0.493831\pi$
$462$		0			0
$463$	−265.709			−0.573886			−0.286943	−	0.957948i	$-0.592639\pi$
$463$	−265.709			−0.573886			−0.286943	+	0.957948i	$0.592639\pi$
$464$	432.821	+	107.991i	0.932803	+	0.232738i
$465$		0			0
$466$	16.7651	+	1.02609i	0.0359766	+	0.00220192i
$467$	−282.686			−0.605323			−0.302661	−	0.953098i	$-0.597875\pi$
$467$	−282.686			−0.605323			−0.302661	+	0.953098i	$0.597875\pi$
$468$		0			0
$469$			62.1671i			0.132552i
$470$	716.809	+	43.8718i	1.52512	+	0.0933442i
$471$		0			0
$472$	89.1409	−	480.627i	0.188858	−	1.01828i
$473$			667.379i			1.41095i
$474$		0			0
$475$			57.7830i			0.121648i
$476$	−33.4342	+	272.113i	−0.0702399	+	0.571665i
$477$		0			0
$478$	122.923	+	7.52344i	0.257162	+	0.0157394i
$479$			415.417i			0.867258i	0.901091	+	0.433629i	$0.142767\pi$
$479$			415.417i			0.867258i	−0.901091	+	0.433629i	$0.857233\pi$
$480$		0			0
$481$	528.003			1.09772
$482$	−8.32478	+	136.016i	−0.0172713	+	0.282191i
$483$		0			0
$484$	−178.296	−	21.9070i	−0.368381	−	0.0452625i
$485$	−968.588			−1.99709
$486$		0			0
$487$	−133.938			−0.275027			−0.137513	−	0.990500i	$-0.543911\pi$
$487$	−133.938			−0.275027			−0.137513	+	0.990500i	$0.543911\pi$
$488$	−829.536	−	153.852i	−1.69987	−	0.315271i
$489$		0			0
$490$	22.4919	−	367.488i	0.0459018	−	0.749976i
$491$	−147.872			−0.301164			−0.150582	−	0.988598i	$-0.548115\pi$
$491$	−147.872			−0.301164			−0.150582	+	0.988598i	$0.548115\pi$
$492$		0			0
$493$		−	520.211i		−	1.05520i
$494$	32.7445	−	535.004i	0.0662845	−	1.08300i
$495$		0			0
$496$	−258.036	−	64.3810i	−0.520233	−	0.129800i
$497$		−	96.1203i		−	0.193401i
$498$		0			0
$499$			786.614i			1.57638i	0.615431	+	0.788191i	$0.288982\pi$
$499$			786.614i			1.57638i	−0.615431	+	0.788191i	$0.711018\pi$
$500$	475.886	+	58.4715i	0.951771	+	0.116943i
$501$		0			0
$502$	2.85178	−	46.5944i	0.00568083	−	0.0928176i
$503$		−	306.345i		−	0.609035i	−0.952507	−	0.304518i	$-0.901505\pi$
$503$		−	306.345i		−	0.609035i	0.952507	−	0.304518i	$-0.0984953\pi$
$504$		0			0
$505$	−584.662			−1.15775
$506$	−534.572	−	32.7181i	−1.05647	−	0.0646603i
$507$		0			0
$508$	−699.162	−	85.9052i	−1.37630	−	0.169105i
$509$	−319.082			−0.626880			−0.313440	−	0.949608i	$-0.601481\pi$
$509$	−319.082			−0.626880			−0.313440	+	0.949608i	$0.601481\pi$
$510$		0			0
$511$	375.783			0.735388
$512$	−267.682	+	436.452i	−0.522817	+	0.852445i
$513$		0			0
$514$	402.795	+	24.6528i	0.783648	+	0.0479626i
$515$	−73.9060			−0.143507
$516$		0			0
$517$		−	892.075i		−	1.72548i
$518$	443.905	+	27.1689i	0.856959	+	0.0524495i
$519$		0			0
$520$	355.709	+	65.9726i	0.684056	+	0.126870i
$521$		−	890.788i		−	1.70977i	−0.518821	−	0.854883i	$-0.673629\pi$
$521$		−	890.788i		−	1.70977i	0.518821	−	0.854883i	$-0.326371\pi$
$522$		0			0
$523$		−	370.577i		−	0.708560i	−0.935139	−	0.354280i	$-0.884726\pi$
$523$		−	370.577i		−	0.708560i	0.935139	−	0.354280i	$-0.115274\pi$
$524$	709.703	+	87.2005i	1.35440	+	0.166413i
$525$		0			0
$526$	517.553	+	31.6765i	0.983941	+	0.0602214i
$527$			310.136i			0.588493i
$528$		0			0
$529$	96.7788			0.182947
$530$	−18.0550	+	294.996i	−0.0340661	+	0.556596i
$531$		0			0
$532$	55.0581	−	448.105i	0.103493	−	0.842303i
$533$	−246.824			−0.463085
$534$		0			0
$535$	−305.358			−0.570762
$536$	133.120	+	24.6894i	0.248357	+	0.0460623i
$537$		0			0
$538$	−38.7444	+	633.034i	−0.0720156	+	1.17664i
$539$	−457.342			−0.848502
$540$		0			0
$541$		−	553.017i		−	1.02221i	−0.859517	−	0.511106i	$-0.829236\pi$
$541$		−	553.017i		−	1.02221i	0.859517	−	0.511106i	$-0.170764\pi$
$542$	19.0059	−	310.532i	0.0350662	−	0.572937i
$543$		0			0
$544$	569.402	+	179.662i	1.04670	+	0.330261i
$545$		−	304.341i		−	0.558423i
$546$		0			0
$547$			306.986i			0.561218i	0.959822	+	0.280609i	$0.0905364\pi$
$547$			306.986i			0.561218i	−0.959822	+	0.280609i	$0.909464\pi$
$548$	88.7817	−	722.573i	0.162010	−	1.31856i
$549$		0			0
$550$	−2.95955	+	48.3553i	−0.00538101	+	0.0879188i
$551$			856.665i			1.55475i
$552$		0			0
$553$	−338.801			−0.612660
$554$	383.063	+	23.4451i	0.691450	+	0.0423197i
$555$		0			0
$556$	101.607	−	826.953i	0.182746	−	1.48732i
$557$	954.484			1.71362			0.856808	−	0.515636i	$-0.172444\pi$
$557$	954.484			1.71362			0.856808	+	0.515636i	$0.172444\pi$
$558$		0			0
$559$	−451.925			−0.808453
$560$	295.658	+	73.7680i	0.527961	+	0.131729i
$561$		0			0
$562$	−677.337	−	41.4559i	−1.20523	−	0.0737650i
$563$	−129.049			−0.229217			−0.114609	−	0.993411i	$-0.536561\pi$
$563$	−129.049			−0.229217			−0.114609	+	0.993411i	$0.536561\pi$
$564$		0			0
$565$		−	615.636i		−	1.08962i
$566$	720.417	+	44.0926i	1.27282	+	0.0779021i
$567$		0			0
$568$	−205.824	−	38.1738i	−0.362367	−	0.0672074i
$569$		−	511.940i		−	0.899719i	−0.893099	−	0.449860i	$-0.851474\pi$
$569$		−	511.940i		−	0.899719i	0.893099	−	0.449860i	$-0.148526\pi$
$570$		0			0
$571$			781.355i			1.36840i	0.729296	+	0.684199i	$0.239848\pi$
$571$			781.355i			1.36840i	−0.729296	+	0.684199i	$0.760152\pi$
$572$	54.8041	−	446.037i	0.0958113	−	0.779785i
$573$		0			0
$574$	−207.511	−	12.7006i	−0.361517	−	0.0221264i
$575$			39.0971i			0.0679949i
$576$		0			0
$577$	−364.123			−0.631062			−0.315531	−	0.948915i	$-0.602183\pi$
$577$	−364.123			−0.631062			−0.315531	+	0.948915i	$0.602183\pi$
$578$	7.22594	−	118.063i	0.0125016	−	0.204261i
$579$		0			0
$580$	−573.888	−	70.5130i	−0.989462	−	0.121574i
$581$	−133.770			−0.230241
$582$		0			0
$583$	367.125			0.629717
$584$	149.241	−	804.672i	0.255549	−	1.37786i
$585$		0			0
$586$	3.34983	−	54.7319i	0.00571643	−	0.0933991i
$587$	−297.832			−0.507380			−0.253690	−	0.967286i	$-0.581644\pi$
$587$	−297.832			−0.507380			−0.253690	+	0.967286i	$0.581644\pi$
$588$		0			0
$589$		−	510.720i		−	0.867096i
$590$	−38.7063	+	632.411i	−0.0656039	+	1.07188i
$591$		0			0
$592$	234.472	−	939.752i	0.396068	−	1.58742i
$593$			358.088i			0.603859i	0.953330	+	0.301929i	$0.0976306\pi$
$593$			358.088i			0.603859i	−0.953330	+	0.301929i	$0.902369\pi$
$594$		0			0
$595$		−	355.354i		−	0.597234i
$596$	916.554	+	112.616i	1.53784	+	0.188953i
$597$		0			0
$598$	22.1556	−	361.993i	0.0370494	−	0.605340i
$599$		−	339.451i		−	0.566696i	−0.959017	−	0.283348i	$-0.908555\pi$
$599$		−	339.451i		−	0.566696i	0.959017	−	0.283348i	$-0.0914452\pi$
$600$		0			0
$601$	23.3185			0.0387996			0.0193998	−	0.999812i	$-0.493824\pi$
$601$	23.3185			0.0387996			0.0193998	+	0.999812i	$0.493824\pi$
$602$	−379.944	−	23.2542i	−0.631136	−	0.0386283i
$603$		0			0
$604$	411.570	+	50.5691i	0.681407	+	0.0837237i
$605$	232.839			0.384857
$606$		0			0
$607$	676.105			1.11385			0.556924	−	0.830564i	$-0.311982\pi$
$607$	676.105			1.11385			0.556924	+	0.830564i	$0.311982\pi$
$608$	−937.670	−	295.860i	−1.54222	−	0.486612i
$609$		0			0
$610$	1091.51	+	66.8049i	1.78936	+	0.109516i
$611$	604.081			0.988677
$612$		0			0
$613$			86.7019i			0.141439i	0.997496	+	0.0707193i	$0.0225295\pi$
$613$			86.7019i			0.141439i	−0.997496	+	0.0707193i	$0.977471\pi$
$614$	400.825	+	24.5322i	0.652810	+	0.0399548i
$615$		0			0
$616$	69.0263	−	372.174i	0.112056	−	0.604178i
$617$			284.165i			0.460559i	0.973125	+	0.230279i	$0.0739640\pi$
$617$			284.165i			0.460559i	−0.973125	+	0.230279i	$0.926036\pi$
$618$		0			0
$619$			195.090i			0.315169i	0.987506	+	0.157585i	$0.0503707\pi$
$619$			195.090i			0.315169i	−0.987506	+	0.157585i	$0.949629\pi$
$620$	342.136	+	42.0379i	0.551833	+	0.0678030i
$621$		0			0
$622$	−882.026	−	53.9838i	−1.41805	−	0.0867906i
$623$		−	270.066i		−	0.433493i
$624$		0			0
$625$	−668.478			−1.06956
$626$	0.877640	−	14.3395i	0.00140198	−	0.0229066i
$627$		0			0
$628$	−8.50957	+	69.2573i	−0.0135503	+	0.110282i
$629$	−1129.50			−1.79570
$630$		0			0
$631$	−432.949			−0.686132			−0.343066	−	0.939311i	$-0.611465\pi$
$631$	−432.949			−0.686132			−0.343066	+	0.939311i	$0.611465\pi$
$632$	−134.554	+	725.482i	−0.212901	+	1.14791i
$633$		0			0
$634$	−52.7737	+	862.255i	−0.0832393	+	1.36002i
$635$	913.042			1.43786
$636$		0			0
$637$		−	309.696i		−	0.486179i
$638$	−43.8770	+	716.894i	−0.0687727	+	1.12366i
$639$		0			0
$640$	275.380	−	603.802i	0.430282	−	0.943441i
$641$		−	375.595i		−	0.585952i	−0.956120	−	0.292976i	$-0.905354\pi$
$641$		−	375.595i		−	0.585952i	0.956120	−	0.292976i	$-0.0946457\pi$
$642$		0			0
$643$			309.345i			0.481097i	0.970637	+	0.240549i	$0.0773273\pi$
$643$			309.345i			0.481097i	−0.970637	+	0.240549i	$0.922673\pi$
$644$	37.2534	−	303.196i	0.0578468	−	0.470802i
$645$		0			0
$646$	−70.0466	+	1144.47i	−0.108431	+	1.77163i
$647$			595.742i			0.920776i	0.887718	+	0.460388i	$0.152290\pi$
$647$			595.742i			0.920776i	−0.887718	+	0.460388i	$0.847710\pi$
$648$		0			0
$649$	787.042			1.21270
$650$	−32.7445	−	2.00411i	−0.0503762	−	0.00308324i
$651$		0			0
$652$	−0.881628	+	7.17535i	−0.00135219	+	0.0110051i
$653$	1031.59			1.57977			0.789884	−	0.613256i	$-0.210141\pi$
$653$	1031.59			1.57977			0.789884	+	0.613256i	$0.210141\pi$
$654$		0			0
$655$	−926.808			−1.41497
$656$	−109.608	+	439.304i	−0.167086	+	0.669670i
$657$		0			0
$658$	507.865	+	31.0835i	0.771831	+	0.0472394i
$659$	−524.843			−0.796423			−0.398211	−	0.917294i	$-0.630369\pi$
$659$	−524.843			−0.796423			−0.398211	+	0.917294i	$0.630369\pi$
$660$		0			0
$661$		−	846.380i		−	1.28045i	−0.768186	−	0.640227i	$-0.778840\pi$
$661$		−	846.380i		−	1.28045i	0.768186	−	0.640227i	$-0.221160\pi$
$662$	−442.376	−	27.0753i	−0.668242	−	0.0408993i
$663$		0			0
$664$	−53.1262	+	286.444i	−0.0800093	+	0.431392i
$665$			585.185i			0.879977i
$666$		0			0
$667$			579.635i			0.869018i
$668$	−6.39481	+	52.0458i	−0.00957307	+	0.0779129i
$669$		0			0
$670$	−175.159	−	10.7205i	−0.261432	−	0.0160007i
$671$		−	1358.39i		−	2.02443i
$672$		0			0
$673$	729.874			1.08451			0.542254	−	0.840214i	$-0.317571\pi$
$673$	729.874			1.08451			0.542254	+	0.840214i	$0.317571\pi$
$674$	−46.4336	+	758.667i	−0.0688927	+	1.12562i
$675$		0			0
$676$	−368.914	−	45.3280i	−0.545730	−	0.0670533i
$677$	−393.764			−0.581631			−0.290816	−	0.956779i	$-0.593927\pi$
$677$	−393.764			−0.581631			−0.290816	+	0.956779i	$0.593927\pi$
$678$		0			0
$679$	−686.253			−1.01068
$680$	−760.928	−	141.128i	−1.11901	−	0.207541i
$681$		0			0
$682$	26.1583	−	427.392i	0.0383552	−	0.626675i
$683$	570.113			0.834718			0.417359	−	0.908742i	$-0.362956\pi$
$683$	570.113			0.834718			0.417359	+	0.908742i	$0.362956\pi$
$684$		0			0
$685$			943.615i			1.37754i
$686$	37.9275	−	619.686i	0.0552879	−	0.903333i
$687$		0			0
$688$	−200.688	+	804.347i	−0.291698	+	1.16911i
$689$			248.604i			0.360818i
$690$		0			0
$691$			434.769i			0.629188i	0.949226	+	0.314594i	$0.101868\pi$
$691$			434.769i			0.629188i	−0.949226	+	0.314594i	$0.898132\pi$
$692$	−757.148	−	93.0299i	−1.09414	−	0.134436i
$693$		0			0
$694$	−64.3393	+	1051.22i	−0.0927079	+	1.51473i
$695$			1079.93i			1.55385i
$696$		0			0
$697$	528.003			0.757537
$698$	−902.708	−	55.2496i	−1.29328	−	0.0791541i
$699$		0			0
$700$	−27.4260	−	3.36980i	−0.0391799	−	0.00481399i
$701$	1218.27			1.73791			0.868955	−	0.494891i	$-0.164792\pi$
$701$	1218.27			1.73791			0.868955	+	0.494891i	$0.164792\pi$
$702$		0			0
$703$	1860.01			2.64582
$704$	−769.530	−	295.615i	−1.09308	−	0.419907i
$705$		0			0
$706$	180.847	+	11.0686i	0.256157	+	0.0156779i
$707$	−414.238			−0.585910
$708$		0			0
$709$			877.234i			1.23728i	0.785673	+	0.618642i	$0.212317\pi$
$709$			877.234i			1.23728i	−0.785673	+	0.618642i	$0.787683\pi$
$710$	270.825	+	16.5756i	0.381443	+	0.0233460i
$711$		0			0
$712$	−578.299	−	107.256i	−0.812217	−	0.150640i
$713$		−	345.562i		−	0.484660i
$714$		0			0
$715$			582.484i			0.814663i
$716$	−15.7520	−	1.93543i	−0.0220000	−	0.00270311i
$717$		0			0
$718$	192.178	+	11.7621i	0.267658	+	0.0163818i
$719$		−	91.5816i		−	0.127374i	−0.997970	−	0.0636868i	$-0.979714\pi$
$719$		−	91.5816i		−	0.127374i	0.997970	−	0.0636868i	$-0.0202859\pi$
$720$		0			0
$721$	−52.3631			−0.0726256
$722$	71.2432	−	1164.02i	0.0986748	−	1.61222i
$723$		0			0
$724$	59.9539	−	487.950i	0.0828092	−	0.673964i
$725$	52.4316			0.0723194
$726$		0			0
$727$	429.043			0.590155			0.295078	−	0.955473i	$-0.404655\pi$
$727$	429.043			0.590155			0.295078	+	0.955473i	$0.404655\pi$
$728$	252.023	+	46.7422i	0.346185	+	0.0642063i
$729$		0			0
$730$	−64.8026	+	1058.79i	−0.0887707	+	1.45040i
$731$	966.752			1.32251
$732$		0			0
$733$			890.582i			1.21498i	0.794327	+	0.607491i	$0.207824\pi$
$733$			890.582i			1.21498i	−0.794327	+	0.607491i	$0.792176\pi$
$734$	63.2069	−	1032.72i	0.0861130	−	1.40698i
$735$		0			0
$736$	−634.445	−	200.185i	−0.862018	−	0.271990i
$737$			217.987i			0.295776i
$738$		0			0
$739$			294.501i			0.398513i	0.979947	+	0.199257i	$0.0638527\pi$
$739$			294.501i			0.398513i	−0.979947	+	0.199257i	$0.936147\pi$
$740$	−153.100	+	1246.04i	−0.206892	+	1.68384i
$741$		0			0
$742$	−12.7921	+	209.007i	−0.0172401	+	0.281681i
$743$		−	1159.61i		−	1.56071i	−0.625338	−	0.780354i	$-0.715039\pi$
$743$		−	1159.61i		−	1.56071i	0.625338	−	0.780354i	$-0.284961\pi$
$744$		0			0
$745$	−1196.94			−1.60663
$746$	−1453.11	−	88.9365i	−1.94787	−	0.119218i
$747$		0			0
$748$	−117.236	+	954.157i	−0.156733	+	1.27561i
$749$	−216.349			−0.288850
$750$		0			0
$751$	900.292			1.19879			0.599396	−	0.800453i	$-0.295408\pi$
$751$	900.292			1.19879			0.599396	+	0.800453i	$0.295408\pi$
$752$	268.256	−	1075.16i	0.356724	−	1.42973i
$753$		0			0
$754$	−485.455	−	29.7120i	−0.643840	−	0.0394058i
$755$	−537.473			−0.711885
$756$		0			0
$757$		−	960.950i		−	1.26942i	−0.772751	−	0.634709i	$-0.781120\pi$
$757$		−	960.950i		−	1.26942i	0.772751	−	0.634709i	$-0.218880\pi$
$758$	−1269.29	−	77.6859i	−1.67452	−	0.102488i
$759$		0			0
$760$	1253.07	+	232.404i	1.64877	+	0.305794i
$761$		−	469.313i		−	0.616706i	−0.951272	−	0.308353i	$-0.900222\pi$
$761$		−	469.313i		−	0.616706i	0.951272	−	0.308353i	$-0.0997777\pi$
$762$		0			0
$763$		−	215.628i		−	0.282606i
$764$	−168.571	+	1371.96i	−0.220643	+	1.79576i
$765$		0			0
$766$	−302.832	−	18.5346i	−0.395342	−	0.0241967i
$767$			532.957i			0.694859i
$768$		0			0
$769$	25.4553			0.0331019			0.0165509	−	0.999863i	$-0.494731\pi$
$769$	25.4553			0.0331019			0.0165509	+	0.999863i	$0.494731\pi$
$770$	−29.9722	+	489.708i	−0.0389250	+	0.635984i
$771$		0			0
$772$	937.959	+	115.246i	1.21497	+	0.149282i
$773$	298.091			0.385629			0.192815	−	0.981235i	$-0.438238\pi$
$773$	298.091			0.385629			0.192815	+	0.981235i	$0.438238\pi$
$774$		0			0
$775$	−31.2582			−0.0403332
$776$	−272.543	+	1469.49i	−0.351215	+	1.89367i
$777$		0			0
$778$	41.2934	−	674.682i	0.0530764	−	0.867200i
$779$	−869.496			−1.11617
$780$		0			0
$781$		−	337.044i		−	0.431554i
$782$	−47.3948	+	774.371i	−0.0606072	+	0.990245i
$783$		0			0
$784$	−551.204	−	137.528i	−0.703066	−	0.175418i
$785$		−	90.4438i		−	0.115215i
$786$		0			0
$787$		−	543.215i		−	0.690235i	−0.938560	−	0.345117i	$-0.887839\pi$
$787$		−	543.215i		−	0.690235i	0.938560	−	0.345117i	$-0.112161\pi$
$788$	−32.7589	−	4.02505i	−0.0415722	−	0.00510793i
$789$		0			0
$790$	58.4251	−	954.592i	0.0739558	−	1.20834i
$791$		−	436.183i		−	0.551432i
$792$		0			0
$793$	919.854			1.15997
$794$	449.453	+	27.5085i	0.566062	+	0.0346454i
$795$		0			0
$796$	103.983	+	12.7763i	0.130632	+	0.0160506i
$797$	248.119			0.311316			0.155658	−	0.987811i	$-0.450250\pi$
$797$	248.119			0.311316			0.155658	+	0.987811i	$0.450250\pi$
$798$		0			0
$799$	−1292.24			−1.61732
$800$	−18.1079	+	57.3894i	−0.0226349	+	0.0717368i
$801$		0			0
$802$	−683.024	−	41.8040i	−0.851651	−	0.0521247i
$803$	1317.68			1.64094
$804$		0			0
$805$			395.947i			0.491859i
$806$	289.415	+	17.7134i	0.359076	+	0.0219770i
$807$		0			0
$808$	−164.513	+	887.017i	−0.203605	+	1.09779i
$809$			1181.89i			1.46093i	0.682950	+	0.730465i	$0.260697\pi$
$809$			1181.89i			1.46093i	−0.682950	+	0.730465i	$0.739303\pi$
$810$		0			0
$811$			414.119i			0.510627i	0.966858	+	0.255314i	$0.0821787\pi$
$811$			414.119i			0.510627i	−0.966858	+	0.255314i	$0.917821\pi$
$812$	−406.605	−	49.9591i	−0.500745	−	0.0615259i
$813$		0			0
$814$	1556.54	+	95.2670i	1.91221	+	0.117036i
$815$		−	9.37036i		−	0.0114974i
$816$		0			0
$817$	−1592.01			−1.94861
$818$	30.1894	−	493.255i	0.0369063	−	0.603002i
$819$		0			0
$820$	71.5692	−	582.484i	0.0872795	−	0.710347i
$821$	672.119			0.818659			0.409329	−	0.912387i	$-0.365763\pi$
$821$	672.119			0.818659			0.409329	+	0.912387i	$0.365763\pi$
$822$		0			0
$823$	−1427.52			−1.73453			−0.867265	−	0.497848i	$-0.834124\pi$
$823$	−1427.52			−1.73453			−0.867265	+	0.497848i	$0.834124\pi$
$824$	−20.7958	+	112.126i	−0.0252376	+	0.136075i
$825$		0			0
$826$	−27.4237	+	448.069i	−0.0332007	+	0.542456i
$827$	1018.10			1.23108			0.615538	−	0.788107i	$-0.288939\pi$
$827$	1018.10			1.23108			0.615538	+	0.788107i	$0.288939\pi$
$828$		0			0
$829$		−	538.177i		−	0.649188i	−0.945853	−	0.324594i	$-0.894772\pi$
$829$		−	538.177i		−	0.649188i	0.945853	−	0.324594i	$-0.105228\pi$
$830$	23.0682	−	376.904i	0.0277930	−	0.454102i
$831$		0			0
$832$	200.180	−	521.098i	0.240601	−	0.626320i
$833$			662.498i			0.795315i
$834$		0			0
$835$		−	67.9671i		−	0.0813978i
$836$	193.060	−	1571.27i	0.230933	−	1.87951i
$837$		0			0
$838$	79.4701	−	1298.44i	0.0948331	−	1.54945i
$839$			365.236i			0.435323i	0.976024	+	0.217661i	$0.0698429\pi$
$839$			365.236i			0.435323i	−0.976024	+	0.217661i	$0.930157\pi$
$840$		0			0
$841$	−63.6735			−0.0757116
$842$	34.3277	+	2.10100i	0.0407692	+	0.00249525i
$843$		0			0
$844$	−82.5569	+	671.911i	−0.0978162	+	0.796103i
$845$	481.768			0.570139
$846$		0			0
$847$	164.968			0.194768
$848$	442.471	+	110.398i	0.521781	+	0.130187i
$849$		0			0
$850$	70.0466	+	4.28715i	0.0824078	+	0.00504371i
$851$	1258.52			1.47887
$852$		0			0
$853$			1017.25i			1.19255i	0.802779	+	0.596277i	$0.203354\pi$
$853$			1017.25i			1.19255i	−0.802779	+	0.596277i	$0.796646\pi$
$854$	773.342	+	47.3319i	0.905553	+	0.0554237i
$855$		0			0
$856$	−85.9220	+	463.272i	−0.100376	+	0.541205i
$857$		−	1363.62i		−	1.59115i	−0.605853	−	0.795576i	$-0.707168\pi$
$857$		−	1363.62i		−	1.59115i	0.605853	−	0.795576i	$-0.292832\pi$
$858$		0			0
$859$		−	1157.63i		−	1.34765i	−0.738892	−	0.673824i	$-0.764651\pi$
$859$		−	1157.63i		−	1.34765i	0.738892	−	0.673824i	$-0.235349\pi$
$860$	131.040	−	1066.50i	0.152372	−	1.24012i
$861$		0			0
$862$	623.711	+	38.1738i	0.723563	+	0.0442852i
$863$		−	55.8935i		−	0.0647665i	−0.999476	−	0.0323833i	$-0.989690\pi$
$863$		−	55.8935i		−	0.0647665i	0.999476	−	0.0323833i	$-0.0103097\pi$
$864$		0			0
$865$	988.766			1.14308
$866$	−20.0422	+	327.464i	−0.0231434	+	0.378134i
$867$		0			0
$868$	242.406	+	29.7842i	0.279270	+	0.0343136i
$869$	−1188.00			−1.36709
$870$		0			0
$871$	−147.613			−0.169476
$872$	−461.729	−	85.6358i	−0.529505	−	0.0982062i
$873$		0			0
$874$	78.0481	−	1275.21i	0.0892998	−	1.45905i
$875$	−440.312			−0.503214
$876$		0			0
$877$			804.852i			0.917733i	0.888505	+	0.458867i	$0.151744\pi$
$877$			804.852i			0.917733i	−0.888505	+	0.458867i	$0.848256\pi$
$878$	−75.0285	+	1225.87i	−0.0854539	+	1.39621i
$879$		0			0
$880$	1036.72	+	258.666i	1.17809	+	0.293938i
$881$		−	56.8723i		−	0.0645543i	−0.999479	−	0.0322771i	$-0.989724\pi$
$881$		−	56.8723i		−	0.0645543i	0.999479	−	0.0322771i	$-0.0102759\pi$
$882$		0			0
$883$		−	219.243i		−	0.248293i	−0.992264	−	0.124146i	$-0.960381\pi$
$883$		−	219.243i		−	0.248293i	0.992264	−	0.124146i	$-0.0396193\pi$
$884$	−646.121	−	79.3882i	−0.730906	−	0.0898056i
$885$		0			0
$886$	0.581531	−	9.50147i	0.000656355	−	0.0107240i
$887$		−	1247.63i		−	1.40657i	−0.710908	−	0.703285i	$-0.751716\pi$
$887$		−	1247.63i		−	1.40657i	0.710908	−	0.703285i	$-0.248284\pi$
$888$		0			0
$889$	646.898			0.727670
$890$	760.928	+	46.5720i	0.854975	+	0.0523281i
$891$		0			0
$892$	−427.297	−	52.5014i	−0.479032	−	0.0588581i
$893$	2128.02			2.38300
$894$		0			0
$895$	20.5707			0.0229840
$896$	195.109	−	427.799i	0.217756	−	0.477454i
$897$		0			0
$898$	−739.007	−	45.2304i	−0.822948	−	0.0503679i
$899$	−463.420			−0.515484
$900$		0			0
$901$		−	531.810i		−	0.590244i
$902$	−727.632	−	44.5342i	−0.806688	−	0.0493728i
$903$		0			0
$904$	−934.008	−	173.228i	−1.03319	−	0.191624i
$905$			637.219i			0.704109i
$906$		0			0
$907$		−	236.058i		−	0.260263i	−0.991497	−	0.130131i	$-0.958460\pi$
$907$		−	236.058i		−	0.260263i	0.991497	−	0.130131i	$-0.0415399\pi$
$908$	−848.248	−	104.223i	−0.934193	−	0.114783i
$909$		0			0
$910$	−331.613	−	20.2961i	−0.364410	−	0.0223034i
$911$			1513.83i			1.66172i	0.556480	+	0.830861i	$0.312151\pi$
$911$			1513.83i			1.66172i	−0.556480	+	0.830861i	$0.687849\pi$
$912$		0			0
$913$	−469.061			−0.513758
$914$	−21.1323	+	345.274i	−0.0231207	+	0.377762i
$915$		0			0
$916$	42.6807	−	347.368i	0.0465946	−	0.379222i
$917$	−656.652			−0.716087
$918$		0			0
$919$	1401.43			1.52495			0.762477	−	0.647015i	$-0.223983\pi$
$919$	1401.43			1.52495			0.762477	+	0.647015i	$0.223983\pi$
$920$	847.849	+	157.249i	0.921575	+	0.170923i
$921$		0			0
$922$	−2.18325	+	35.6715i	−0.00236795	+	0.0386893i
$923$	228.234			0.247274
$924$		0			0
$925$		−	113.841i		−	0.123071i
$926$	32.4644	−	530.426i	0.0350587	−	0.572814i
$927$		0			0
$928$	−268.460	+	850.830i	−0.289289	+	0.916843i
$929$		−	1241.19i		−	1.33605i	−0.744140	−	0.668024i	$-0.767140\pi$
$929$		−	1241.19i		−	1.33605i	0.744140	−	0.668024i	$-0.232860\pi$
$930$		0			0
$931$		−	1090.98i		−	1.17183i
$932$	−4.09671	+	33.3422i	−0.00439562	+	0.0357749i
$933$		0			0
$934$	34.5385	−	564.316i	0.0369792	−	0.604192i
$935$		−	1246.04i		−	1.33267i
$936$		0			0
$937$	723.373			0.772009			0.386005	−	0.922497i	$-0.373855\pi$
$937$	723.373			0.772009			0.386005	+	0.922497i	$0.373855\pi$
$938$	−124.102	−	7.59557i	−0.132305	−	0.00809762i
$939$		0			0
$940$	−175.159	+	1425.58i	−0.186340	+	1.51657i
$941$	491.200			0.521997			0.260999	−	0.965339i	$-0.415948\pi$
$941$	491.200			0.521997			0.260999	+	0.965339i	$0.415948\pi$
$942$		0			0
$943$	−588.317			−0.623878
$944$	948.568	+	236.672i	1.00484	+	0.250712i
$945$		0			0
$946$	−1332.26	−	81.5403i	−1.40831	−	0.0861948i
$947$	−729.946			−0.770798			−0.385399	−	0.922750i	$-0.625936\pi$
$947$	−729.946			−0.770798			−0.385399	+	0.922750i	$0.625936\pi$
$948$		0			0
$949$			892.283i			0.940235i
$950$	−115.350	−	7.05992i	−0.121421	−	0.00743150i
$951$		0			0
$952$	−539.124	−	99.9902i	−0.566307	−	0.105032i
$953$		−	503.118i		−	0.527930i	−0.964532	−	0.263965i	$-0.914970\pi$
$953$		−	503.118i		−	0.527930i	0.964532	−	0.263965i	$-0.0850304\pi$
$954$		0			0
$955$		−	1791.65i		−	1.87608i
$956$	−30.0376	+	244.468i	−0.0314200	+	0.255720i
$957$		0			0
$958$	−829.282	−	50.7556i	−0.865639	−	0.0529808i
$959$			668.559i			0.697142i
$960$		0			0
$961$	−684.722			−0.712509
$962$	−64.5114	+	1054.03i	−0.0670597	+	1.09567i
$963$		0			0
$964$	−270.507	−	33.2369i	−0.280609	−	0.0344781i
$965$	−1224.89			−1.26932
$966$		0			0
$967$	684.220			0.707570			0.353785	−	0.935327i	$-0.384894\pi$
$967$	684.220			0.707570			0.353785	+	0.935327i	$0.384894\pi$
$968$	65.5165	−	353.250i	0.0676823	−	0.364927i
$969$		0			0
$970$	118.342	−	1933.56i	0.122002	−	1.99336i
$971$	−710.914			−0.732146			−0.366073	−	0.930586i	$-0.619298\pi$
$971$	−710.914			−0.732146			−0.366073	+	0.930586i	$0.619298\pi$
$972$		0			0
$973$			765.136i			0.786368i
$974$	16.3645	−	267.376i	0.0168014	−	0.274513i
$975$		0			0
$976$	408.482	−	1637.18i	0.418527	−	1.67743i
$977$		−	520.084i		−	0.532328i	−0.963928	−	0.266164i	$-0.914244\pi$
$977$		−	520.084i		−	0.532328i	0.963928	−	0.266164i	$-0.0857562\pi$
$978$		0			0
$979$		−	946.981i		−	0.967294i
$980$	730.856	+	89.7994i	0.745771	+	0.0916321i
$981$		0			0
$982$	18.0669	−	295.191i	0.0183981	−	0.300602i
$983$			1483.80i			1.50946i	0.656038	+	0.754728i	$0.272231\pi$
$983$			1483.80i			1.50946i	−0.656038	+	0.754728i	$0.727769\pi$
$984$		0			0
$985$	42.7801			0.0434316
$986$	1038.48	+	63.5594i	1.05322	+	0.0644619i
$987$		0			0
$988$	1064.01	+	130.733i	1.07693	+	0.132321i
$989$	−1077.18			−1.08917
$990$		0			0
$991$	128.402			0.129568			0.0647839	−	0.997899i	$-0.479364\pi$
$991$	128.402			0.129568			0.0647839	+	0.997899i	$0.479364\pi$
$992$	160.048	−	507.241i	0.161339	−	0.511332i
$993$		0			0
$994$	191.882	+	11.7440i	0.193040	+	0.0118149i
$995$	−135.793			−0.136475
$996$		0			0
$997$		−	433.440i		−	0.434744i	−0.976089	−	0.217372i	$-0.930252\pi$
$997$		−	433.440i		−	0.434744i	0.976089	−	0.217372i	$-0.0697485\pi$
$998$	−1570.29	−	96.1085i	−1.57344	−	0.0963011i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.c.53.4	yes	6
3.2	odd	2		216.3.h.d.53.3	yes	6
4.3	odd	2		864.3.h.c.593.6		6
8.3	odd	2		864.3.h.d.593.1		6
8.5	even	2		216.3.h.d.53.4	yes	6
12.11	even	2		864.3.h.d.593.2		6
24.5	odd	2	inner	216.3.h.c.53.3	✓	6
24.11	even	2		864.3.h.c.593.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.c.53.3	✓	6	24.5	odd	2	inner
216.3.h.c.53.4	yes	6	1.1	even	1	trivial
216.3.h.d.53.3	yes	6	3.2	odd	2
216.3.h.d.53.4	yes	6	8.5	even	2
864.3.h.c.593.5		6	24.11	even	2
864.3.h.c.593.6		6	4.3	odd	2
864.3.h.d.593.1		6	8.3	odd	2
864.3.h.d.593.2		6	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.122180 + 1.99626i) q^{2} +(-3.97014 - 0.487807i) q^{4} +5.18465 q^{5} +3.67337 q^{7} +(1.45886 - 7.86586i) q^{8} +O(q^{10})\)	\(q+(-0.122180 + 1.99626i) q^{2} +(-3.97014 - 0.487807i) q^{4} +5.18465 q^{5} +3.67337 q^{7} +(1.45886 - 7.86586i) q^{8} +(-0.633460 + 10.3499i) q^{10} +12.8806 q^{11} +8.72227i q^{13} +(-0.448812 + 7.33301i) q^{14} +(15.5241 + 3.87333i) q^{16} -18.6586i q^{17} +30.7262i q^{19} +(-20.5838 - 2.52911i) q^{20} +(-1.57375 + 25.7130i) q^{22} +20.7899i q^{23} +1.88058 q^{25} +(-17.4120 - 1.06569i) q^{26} +(-14.5838 - 1.79189i) q^{28} +27.8806 q^{29} -16.6216 q^{31} +(-9.62892 + 30.5169i) q^{32} +(37.2474 + 2.27970i) q^{34} +19.0451 q^{35} -60.5351i q^{37} +(-61.3377 - 3.75413i) q^{38} +(7.56370 - 40.7817i) q^{40} +28.2982i q^{41} +51.8128i q^{43} +(-51.1377 - 6.28324i) q^{44} +(-41.5022 - 2.54011i) q^{46} -69.2573i q^{47} -35.5064 q^{49} +(-0.229769 + 3.75413i) q^{50} +(4.25479 - 34.6287i) q^{52} +28.5022 q^{53} +66.7813 q^{55} +(5.35894 - 28.8942i) q^{56} +(-3.40645 + 55.6570i) q^{58} +61.1030 q^{59} -105.460i q^{61} +(2.03083 - 33.1812i) q^{62} +(-59.7434 - 22.9504i) q^{64} +45.2219i q^{65} +16.9237i q^{67} +(-9.10178 + 74.0772i) q^{68} +(-2.32693 + 38.0191i) q^{70} -26.1668i q^{71} +102.299 q^{73} +(120.844 + 7.39617i) q^{74} +(14.9885 - 121.988i) q^{76} +47.3151 q^{77} -92.2317 q^{79} +(80.4869 + 20.0818i) q^{80} +(-56.4907 - 3.45747i) q^{82} -36.4161 q^{83} -96.7381i q^{85} +(-103.432 - 6.33049i) q^{86} +(18.7910 - 101.317i) q^{88} -73.5201i q^{89} +32.0401i q^{91} +(10.1415 - 82.5390i) q^{92} +(138.256 + 8.46186i) q^{94} +159.305i q^{95} -186.818 q^{97} +(4.33817 - 70.8801i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 7 q^{4} - 2 q^{5} - 10 q^{7} - 7 q^{8}+O(q^{10}) \) 6 * q - q^2 - 7 * q^4 - 2 * q^5 - 10 * q^7 - 7 * q^8	\( 6 q - q^{2} - 7 q^{4} - 2 q^{5} - 10 q^{7} - 7 q^{8} - 3 q^{10} + 10 q^{11} - 35 q^{14} - 23 q^{16} - 41 q^{20} + 25 q^{22} - 56 q^{25} + 60 q^{26} - 5 q^{28} + 100 q^{29} + 6 q^{31} + 29 q^{32} - 4 q^{34} + 110 q^{35} - 132 q^{38} + 59 q^{40} - 125 q^{44} - 76 q^{46} - 24 q^{49} + 36 q^{50} + 80 q^{52} - 2 q^{53} + 170 q^{55} + 175 q^{56} + 10 q^{58} - 20 q^{59} - 191 q^{62} - 151 q^{64} - 312 q^{68} + 115 q^{70} + 130 q^{73} + 300 q^{74} - 176 q^{76} + 50 q^{77} - 76 q^{79} + 331 q^{80} + 100 q^{82} - 38 q^{83} - 360 q^{86} - 5 q^{88} - 408 q^{92} + 240 q^{94} - 70 q^{97} + 324 q^{98}+O(q^{100}) \) 6 * q - q^2 - 7 * q^4 - 2 * q^5 - 10 * q^7 - 7 * q^8 - 3 * q^10 + 10 * q^11 - 35 * q^14 - 23 * q^16 - 41 * q^20 + 25 * q^22 - 56 * q^25 + 60 * q^26 - 5 * q^28 + 100 * q^29 + 6 * q^31 + 29 * q^32 - 4 * q^34 + 110 * q^35 - 132 * q^38 + 59 * q^40 - 125 * q^44 - 76 * q^46 - 24 * q^49 + 36 * q^50 + 80 * q^52 - 2 * q^53 + 170 * q^55 + 175 * q^56 + 10 * q^58 - 20 * q^59 - 191 * q^62 - 151 * q^64 - 312 * q^68 + 115 * q^70 + 130 * q^73 + 300 * q^74 - 176 * q^76 + 50 * q^77 - 76 * q^79 + 331 * q^80 + 100 * q^82 - 38 * q^83 - 360 * q^86 - 5 * q^88 - 408 * q^92 + 240 * q^94 - 70 * q^97 + 324 * q^98

Introduction

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