LMFDB - Embedded newform 180.3.c.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, 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("180.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.c (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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.3.c.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} -2.23607 q^{5} +8.50651i q^{7} +(-2.47214 + 7.60845i) q^{8} +O(q^{10})$	\(q+(1.61803 + 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} -2.23607 q^{5} +8.50651i q^{7} +(-2.47214 + 7.60845i) q^{8} +(-3.61803 - 2.62866i) q^{10} +1.79611i q^{11} +0.472136 q^{13} +(-10.0000 + 13.7638i) q^{14} +(-12.9443 + 9.40456i) q^{16} +23.8885 q^{17} +9.40456i q^{19} +(-2.76393 - 8.50651i) q^{20} +(-2.11146 + 2.90617i) q^{22} -16.1150i q^{23} +5.00000 q^{25} +(0.763932 + 0.555029i) q^{26} +(-32.3607 + 10.5146i) q^{28} -6.94427 q^{29} -47.4468i q^{31} -32.0000 q^{32} +(38.6525 + 28.0827i) q^{34} -19.0211i q^{35} +26.3607 q^{37} +(-11.0557 + 15.2169i) q^{38} +(5.52786 - 17.0130i) q^{40} +41.4164 q^{41} +2.00811i q^{43} +(-6.83282 + 2.22012i) q^{44} +(18.9443 - 26.0746i) q^{46} -35.3481i q^{47} -23.3607 q^{49} +(8.09017 + 5.87785i) q^{50} +(0.583592 + 1.79611i) q^{52} +21.6393 q^{53} -4.01623i q^{55} +(-64.7214 - 21.0292i) q^{56} +(-11.2361 - 8.16348i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(55.7771 - 76.7706i) q^{62} +(-51.7771 - 37.6183i) q^{64} -1.05573 q^{65} -88.8693i q^{67} +(29.5279 + 90.8774i) q^{68} +(22.3607 - 30.7768i) q^{70} -39.4144i q^{71} +137.554 q^{73} +(42.6525 + 30.9888i) q^{74} +(-35.7771 + 11.6247i) q^{76} -15.2786 q^{77} +113.703i q^{79} +(28.9443 - 21.0292i) q^{80} +(67.0132 + 48.6879i) q^{82} +21.2412i q^{83} -53.4164 q^{85} +(-2.36068 + 3.24920i) q^{86} +(-13.6656 - 4.44023i) q^{88} -67.4427 q^{89} +4.01623i q^{91} +(61.3050 - 19.9192i) q^{92} +(41.5542 - 57.1944i) q^{94} -21.0292i q^{95} -39.1672 q^{97} +(-37.7984 - 27.4621i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 10 q^{10} - 16 q^{13} - 40 q^{14} - 16 q^{16} + 24 q^{17} - 20 q^{20} - 80 q^{22} + 20 q^{25} + 12 q^{26} - 40 q^{28} + 8 q^{29} - 128 q^{32} + 92 q^{34} + 16 q^{37} - 80 q^{38} + 40 q^{40} + 112 q^{41} + 80 q^{44} + 40 q^{46} - 4 q^{49} + 10 q^{50} + 56 q^{52} + 176 q^{53} - 80 q^{56} - 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} - 40 q^{65} + 136 q^{68} + 264 q^{73} + 108 q^{74} - 240 q^{77} + 80 q^{80} + 116 q^{82} - 160 q^{85} + 80 q^{86} + 160 q^{88} + 88 q^{89} + 120 q^{92} - 120 q^{94} - 264 q^{97} - 102 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 10 * q^10 - 16 * q^13 - 40 * q^14 - 16 * q^16 + 24 * q^17 - 20 * q^20 - 80 * q^22 + 20 * q^25 + 12 * q^26 - 40 * q^28 + 8 * q^29 - 128 * q^32 + 92 * q^34 + 16 * q^37 - 80 * q^38 + 40 * q^40 + 112 * q^41 + 80 * q^44 + 40 * q^46 - 4 * q^49 + 10 * q^50 + 56 * q^52 + 176 * q^53 - 80 * q^56 - 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 - 40 * q^65 + 136 * q^68 + 264 * q^73 + 108 * q^74 - 240 * q^77 + 80 * q^80 + 116 * q^82 - 160 * q^85 + 80 * q^86 + 160 * q^88 + 88 * q^89 + 120 * q^92 - 120 * q^94 - 264 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.61803	+	1.17557i	0.809017	+	0.587785i
$2$	1.61803	+	1.17557i	0.809017	+	0.587785i
$3$		0			0
$3$		0			0
$4$	1.23607	+	3.80423i	0.309017	+	0.951057i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		0			0
$7$			8.50651i			1.21522i	0.794237	+	0.607608i	$0.207871\pi$
$7$			8.50651i			1.21522i	−0.794237	+	0.607608i	$0.792129\pi$
$8$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$9$		0			0
$10$	−3.61803	−	2.62866i	−0.361803	−	0.262866i
$11$			1.79611i			0.163283i	0.996662	+	0.0816415i	$0.0260162\pi$
$11$			1.79611i			0.163283i	−0.996662	+	0.0816415i	$0.973984\pi$
$12$		0			0
$13$	0.472136			0.0363182			0.0181591	−	0.999835i	$-0.494219\pi$
$13$	0.472136			0.0363182			0.0181591	+	0.999835i	$0.494219\pi$
$14$	−10.0000	+	13.7638i	−0.714286	+	0.983130i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$17$	23.8885			1.40521			0.702604	−	0.711581i	$-0.252020\pi$
$17$	23.8885			1.40521			0.702604	+	0.711581i	$0.252020\pi$
$18$		0			0
$19$			9.40456i			0.494977i	0.968891	+	0.247489i	$0.0796053\pi$
$19$			9.40456i			0.494977i	−0.968891	+	0.247489i	$0.920395\pi$
$20$	−2.76393	−	8.50651i	−0.138197	−	0.425325i
$21$		0			0
$22$	−2.11146	+	2.90617i	−0.0959753	+	0.132099i
$23$		−	16.1150i		−	0.700650i	−0.936628	−	0.350325i	$-0.886071\pi$
$23$		−	16.1150i		−	0.700650i	0.936628	−	0.350325i	$-0.113929\pi$
$24$		0			0
$25$	5.00000			0.200000
$26$	0.763932	+	0.555029i	0.0293820	+	0.0213473i
$27$		0			0
$28$	−32.3607	+	10.5146i	−1.15574	+	0.375522i
$29$	−6.94427			−0.239458			−0.119729	−	0.992807i	$-0.538203\pi$
$29$	−6.94427			−0.239458			−0.119729	+	0.992807i	$0.538203\pi$
$30$		0			0
$31$		−	47.4468i		−	1.53054i	−0.643708	−	0.765271i	$-0.722605\pi$
$31$		−	47.4468i		−	1.53054i	0.643708	−	0.765271i	$-0.277395\pi$
$32$	−32.0000			−1.00000
$33$		0			0
$34$	38.6525	+	28.0827i	1.13684	+	0.825961i
$35$		−	19.0211i		−	0.543461i
$36$		0			0
$37$	26.3607			0.712451			0.356225	−	0.934400i	$-0.384064\pi$
$37$	26.3607			0.712451			0.356225	+	0.934400i	$0.384064\pi$
$38$	−11.0557	+	15.2169i	−0.290940	+	0.400445i
$39$		0			0
$40$	5.52786	−	17.0130i	0.138197	−	0.425325i
$41$	41.4164			1.01016			0.505078	−	0.863074i	$-0.331464\pi$
$41$	41.4164			1.01016			0.505078	+	0.863074i	$0.331464\pi$
$42$		0			0
$43$			2.00811i			0.0467003i	0.999727	+	0.0233502i	$0.00743326\pi$
$43$			2.00811i			0.0467003i	−0.999727	+	0.0233502i	$0.992567\pi$
$44$	−6.83282	+	2.22012i	−0.155291	+	0.0504572i
$45$		0			0
$46$	18.9443	−	26.0746i	0.411832	−	0.566838i
$47$		−	35.3481i		−	0.752087i	−0.926602	−	0.376044i	$-0.877284\pi$
$47$		−	35.3481i		−	0.752087i	0.926602	−	0.376044i	$-0.122716\pi$
$48$		0			0
$49$	−23.3607			−0.476749
$50$	8.09017	+	5.87785i	0.161803	+	0.117557i
$51$		0			0
$52$	0.583592	+	1.79611i	0.0112229	+	0.0345406i
$53$	21.6393			0.408289			0.204145	−	0.978941i	$-0.434559\pi$
$53$	21.6393			0.408289			0.204145	+	0.978941i	$0.434559\pi$
$54$		0			0
$55$		−	4.01623i		−	0.0730223i
$56$	−64.7214	−	21.0292i	−1.15574	−	0.375522i
$57$		0			0
$58$	−11.2361	−	8.16348i	−0.193725	−	0.140750i
$59$			73.8644i			1.25194i	0.779848	+	0.625970i	$0.215297\pi$
$59$			73.8644i			1.25194i	−0.779848	+	0.625970i	$0.784703\pi$
$60$		0			0
$61$	−26.1378			−0.428488			−0.214244	−	0.976780i	$-0.568729\pi$
$61$	−26.1378			−0.428488			−0.214244	+	0.976780i	$0.568729\pi$
$62$	55.7771	−	76.7706i	0.899630	−	1.23824i
$63$		0			0
$64$	−51.7771	−	37.6183i	−0.809017	−	0.587785i
$65$	−1.05573			−0.0162420
$66$		0			0
$67$		−	88.8693i		−	1.32641i	−0.748439	−	0.663204i	$-0.769196\pi$
$67$		−	88.8693i		−	1.32641i	0.748439	−	0.663204i	$-0.230804\pi$
$68$	29.5279	+	90.8774i	0.434233	+	1.33643i
$69$		0			0
$70$	22.3607	−	30.7768i	0.319438	−	0.439669i
$71$		−	39.4144i		−	0.555132i	−0.960707	−	0.277566i	$-0.910472\pi$
$71$		−	39.4144i		−	0.555132i	0.960707	−	0.277566i	$-0.0895277\pi$
$72$		0			0
$73$	137.554			1.88430			0.942152	−	0.335186i	$-0.108799\pi$
$73$	137.554			1.88430			0.942152	+	0.335186i	$0.108799\pi$
$74$	42.6525	+	30.9888i	0.576385	+	0.418768i
$75$		0			0
$76$	−35.7771	+	11.6247i	−0.470751	+	0.152956i
$77$	−15.2786			−0.198424
$78$		0			0
$79$			113.703i			1.43928i	0.694350	+	0.719638i	$0.255692\pi$
$79$			113.703i			1.43928i	−0.694350	+	0.719638i	$0.744308\pi$
$80$	28.9443	−	21.0292i	0.361803	−	0.262866i
$81$		0			0
$82$	67.0132	+	48.6879i	0.817234	+	0.593755i
$83$			21.2412i			0.255919i	0.991779	+	0.127959i	$0.0408427\pi$
$83$			21.2412i			0.255919i	−0.991779	+	0.127959i	$0.959157\pi$
$84$		0			0
$85$	−53.4164			−0.628428
$86$	−2.36068	+	3.24920i	−0.0274498	+	0.0377814i
$87$		0			0
$88$	−13.6656	−	4.44023i	−0.155291	−	0.0504572i
$89$	−67.4427			−0.757783			−0.378892	−	0.925441i	$-0.623695\pi$
$89$	−67.4427			−0.757783			−0.378892	+	0.925441i	$0.623695\pi$
$90$		0			0
$91$			4.01623i			0.0441344i
$92$	61.3050	−	19.9192i	0.666358	−	0.216513i
$93$		0			0
$94$	41.5542	−	57.1944i	0.442066	−	0.608451i
$95$		−	21.0292i		−	0.221360i
$96$		0			0
$97$	−39.1672			−0.403785			−0.201893	−	0.979408i	$-0.564709\pi$
$97$	−39.1672			−0.403785			−0.201893	+	0.979408i	$0.564709\pi$
$98$	−37.7984	−	27.4621i	−0.385698	−	0.280226i
$99$		0			0
$100$	6.18034	+	19.0211i	0.0618034	+	0.190211i
$101$	−99.8885			−0.988995			−0.494498	−	0.869179i	$-0.664648\pi$
$101$	−99.8885			−0.988995			−0.494498	+	0.869179i	$0.664648\pi$
$102$		0			0
$103$			35.7721i			0.347302i	0.984807	+	0.173651i	$0.0555565\pi$
$103$			35.7721i			0.347302i	−0.984807	+	0.173651i	$0.944444\pi$
$104$	−1.16718	+	3.59222i	−0.0112229	+	0.0345406i
$105$		0			0
$106$	35.0132	+	25.4385i	0.330313	+	0.239986i
$107$		−	121.099i		−	1.13177i	−0.824485	−	0.565884i	$-0.808535\pi$
$107$		−	121.099i		−	1.13177i	0.824485	−	0.565884i	$-0.191465\pi$
$108$		0			0
$109$	−197.469			−1.81164			−0.905821	−	0.423660i	$-0.860745\pi$
$109$	−197.469			−1.81164			−0.905821	+	0.423660i	$0.860745\pi$
$110$	4.72136	−	6.49839i	0.0429215	−	0.0590763i
$111$		0			0
$112$	−80.0000	−	110.111i	−0.714286	−	0.983130i
$113$	−81.2786			−0.719280			−0.359640	−	0.933091i	$-0.617100\pi$
$113$	−81.2786			−0.719280			−0.359640	+	0.933091i	$0.617100\pi$
$114$		0			0
$115$			36.0341i			0.313340i
$116$	−8.58359	−	26.4176i	−0.0739965	−	0.227738i
$117$		0			0
$118$	−86.8328	+	119.515i	−0.735871	+	1.01284i
$119$			203.208i			1.70763i
$120$		0			0
$121$	117.774			0.973339
$122$	−42.2918	−	30.7268i	−0.346654	−	0.251859i
$123$		0			0
$124$	180.498	−	58.6475i	1.45563	−	0.472964i
$125$	−11.1803			−0.0894427
$126$		0			0
$127$			1.84616i			0.0145367i	0.999974	+	0.00726834i	$0.00231361\pi$
$127$			1.84616i			0.0145367i	−0.999974	+	0.00726834i	$0.997686\pi$
$128$	−39.5542	−	121.735i	−0.309017	−	0.951057i
$129$		0			0
$130$	−1.70820	−	1.24108i	−0.0131400	−	0.00954679i
$131$			225.609i			1.72221i	0.508428	+	0.861105i	$0.330227\pi$
$131$			225.609i			1.72221i	−0.508428	+	0.861105i	$0.669773\pi$
$132$		0			0
$133$	−80.0000			−0.601504
$134$	104.472	−	143.794i	0.779643	−	1.07309i
$135$		0			0
$136$	−59.0557	+	181.755i	−0.434233	+	1.33643i
$137$	52.8328			0.385641			0.192820	−	0.981234i	$-0.438236\pi$
$137$	52.8328			0.385641			0.192820	+	0.981234i	$0.438236\pi$
$138$		0			0
$139$			125.852i			0.905407i	0.891661	+	0.452703i	$0.149540\pi$
$139$			125.852i			0.905407i	−0.891661	+	0.452703i	$0.850460\pi$
$140$	72.3607	−	23.5114i	0.516862	−	0.167939i
$141$		0			0
$142$	46.3344	−	63.7738i	0.326298	−	0.449111i
$143$			0.848009i			0.00593013i
$144$		0			0
$145$	15.5279			0.107089
$146$	222.567	+	161.705i	1.52443	+	1.10757i
$147$		0			0
$148$	32.5836	+	100.282i	0.220159	+	0.677581i
$149$	−132.971			−0.892420			−0.446210	−	0.894928i	$-0.647227\pi$
$149$	−132.971			−0.892420			−0.446210	+	0.894928i	$0.647227\pi$
$150$		0			0
$151$			151.221i			1.00146i	0.865603	+	0.500732i	$0.166936\pi$
$151$			151.221i			1.00146i	−0.865603	+	0.500732i	$0.833064\pi$
$152$	−71.5542	−	23.2494i	−0.470751	−	0.152956i
$153$		0			0
$154$	−24.7214	−	17.9611i	−0.160528	−	0.116631i
$155$			106.094i			0.684480i
$156$		0			0
$157$	−36.7477			−0.234062			−0.117031	−	0.993128i	$-0.537338\pi$
$157$	−36.7477			−0.234062			−0.117031	+	0.993128i	$0.537338\pi$
$158$	−133.666	+	183.975i	−0.845985	+	1.16440i
$159$		0			0
$160$	71.5542			0.447214
$161$	137.082			0.851441
$162$		0			0
$163$		−	302.854i		−	1.85800i	−0.370079	−	0.929000i	$-0.620669\pi$
$163$		−	302.854i		−	1.85800i	0.370079	−	0.929000i	$-0.379331\pi$
$164$	51.1935	+	157.557i	0.312155	+	0.960716i
$165$		0			0
$166$	−24.9706	+	34.3691i	−0.150425	+	0.207043i
$167$			99.3839i			0.595113i	0.954704	+	0.297557i	$0.0961717\pi$
$167$			99.3839i			0.595113i	−0.954704	+	0.297557i	$0.903828\pi$
$168$		0			0
$169$	−168.777			−0.998681
$170$	−86.4296	−	62.7948i	−0.508409	−	0.369381i
$171$		0			0
$172$	−7.63932	+	2.48217i	−0.0444147	+	0.0144312i
$173$	181.639			1.04994			0.524969	−	0.851121i	$-0.324077\pi$
$173$	181.639			1.04994			0.524969	+	0.851121i	$0.324077\pi$
$174$		0			0
$175$			42.5325i			0.243043i
$176$	−16.8916	−	23.2494i	−0.0959753	−	0.132099i
$177$		0			0
$178$	−109.125	−	79.2837i	−0.613060	−	0.445414i
$179$		−	260.907i		−	1.45758i	−0.684735	−	0.728792i	$-0.740082\pi$
$179$		−	260.907i		−	1.45758i	0.684735	−	0.728792i	$-0.259918\pi$
$180$		0			0
$181$	157.777			0.871697			0.435848	−	0.900020i	$-0.356448\pi$
$181$	157.777			0.871697			0.435848	+	0.900020i	$0.356448\pi$
$182$	−4.72136	+	6.49839i	−0.0259415	+	0.0357055i
$183$		0			0
$184$	122.610	+	39.8384i	0.666358	+	0.216513i
$185$	−58.9443			−0.318618
$186$		0			0
$187$			42.9065i			0.229447i
$188$	134.472	−	43.6926i	0.715277	−	0.232408i
$189$		0			0
$190$	24.7214	−	34.0260i	0.130112	−	0.179084i
$191$		−	324.095i		−	1.69683i	−0.529328	−	0.848417i	$-0.677556\pi$
$191$		−	324.095i		−	1.69683i	0.529328	−	0.848417i	$-0.322444\pi$
$192$		0			0
$193$	181.777			0.941850			0.470925	−	0.882173i	$-0.343920\pi$
$193$	181.777			0.941850			0.470925	+	0.882173i	$0.343920\pi$
$194$	−63.3738	−	46.0438i	−0.326669	−	0.237339i
$195$		0			0
$196$	−28.8754	−	88.8693i	−0.147323	−	0.453415i
$197$	−140.525			−0.713324			−0.356662	−	0.934234i	$-0.616085\pi$
$197$	−140.525			−0.713324			−0.356662	+	0.934234i	$0.616085\pi$
$198$		0			0
$199$		−	168.234i		−	0.845397i	−0.906270	−	0.422698i	$-0.861083\pi$
$199$		−	168.234i		−	0.845397i	0.906270	−	0.422698i	$-0.138917\pi$
$200$	−12.3607	+	38.0423i	−0.0618034	+	0.190211i
$201$		0			0
$202$	−161.623	−	117.426i	−0.800114	−	0.581317i
$203$		−	59.0715i		−	0.290993i
$204$		0			0
$205$	−92.6099			−0.451756
$206$	−42.0526	+	57.8805i	−0.204139	+	0.280973i
$207$		0			0
$208$	−6.11146	+	4.44023i	−0.0293820	+	0.0213473i
$209$	−16.8916			−0.0808213
$210$		0			0
$211$		−	93.9455i		−	0.445240i	−0.974905	−	0.222620i	$-0.928539\pi$
$211$		−	93.9455i		−	0.445240i	0.974905	−	0.222620i	$-0.0714608\pi$
$212$	26.7477	+	82.3209i	0.126168	+	0.388306i
$213$		0			0
$214$	142.361	−	195.943i	0.665237	−	0.915620i
$215$		−	4.49028i		−	0.0208850i
$216$		0			0
$217$	403.607			1.85994
$218$	−319.512	−	232.139i	−1.46565	−	1.06486i
$219$		0			0
$220$	15.2786	−	4.96433i	0.0694484	−	0.0225651i
$221$	11.2786			0.0510346
$222$		0			0
$223$		−	214.035i		−	0.959797i	−0.877324	−	0.479899i	$-0.840673\pi$
$223$		−	214.035i		−	0.959797i	0.877324	−	0.479899i	$-0.159327\pi$
$224$		−	272.208i		−	1.21522i
$225$		0			0
$226$	−131.512	−	95.5488i	−0.581910	−	0.422782i
$227$		−	41.4225i		−	0.182478i	−0.995829	−	0.0912389i	$-0.970917\pi$
$227$		−	41.4225i		−	0.182478i	0.995829	−	0.0912389i	$-0.0290827\pi$
$228$		0			0
$229$	73.2786			0.319994			0.159997	−	0.987117i	$-0.448852\pi$
$229$	73.2786			0.319994			0.159997	+	0.987117i	$0.448852\pi$
$230$	−42.3607	+	58.3045i	−0.184177	+	0.253498i
$231$		0			0
$232$	17.1672	−	52.8352i	0.0739965	−	0.227738i
$233$	307.050			1.31781			0.658905	−	0.752227i	$-0.271020\pi$
$233$	307.050			1.31781			0.658905	+	0.752227i	$0.271020\pi$
$234$		0			0
$235$			79.0407i			0.336344i
$236$	−280.997	+	91.3014i	−1.19066	+	0.386870i
$237$		0			0
$238$	−238.885	+	328.798i	−1.00372	+	1.38150i
$239$		−	42.9065i		−	0.179525i	−0.995963	−	0.0897625i	$-0.971389\pi$
$239$		−	42.9065i		−	0.179525i	0.995963	−	0.0897625i	$-0.0286108\pi$
$240$		0			0
$241$	−135.082			−0.560506			−0.280253	−	0.959926i	$-0.590418\pi$
$241$	−135.082			−0.560506			−0.280253	+	0.959926i	$0.590418\pi$
$242$	190.562	+	138.452i	0.787448	+	0.572114i
$243$		0			0
$244$	−32.3081	−	99.4340i	−0.132410	−	0.407516i
$245$	52.2361			0.213208
$246$		0			0
$247$			4.44023i			0.0179767i
$248$	360.997	+	117.295i	1.45563	+	0.472964i
$249$		0			0
$250$	−18.0902	−	13.1433i	−0.0723607	−	0.0525731i
$251$		−	221.169i		−	0.881152i	−0.897715	−	0.440576i	$-0.854774\pi$
$251$		−	221.169i		−	0.881152i	0.897715	−	0.440576i	$-0.145226\pi$
$252$		0			0
$253$	28.9443			0.114404
$254$	−2.17029	+	2.98715i	−0.00854445	+	0.0117604i
$255$		0			0
$256$	79.1084	−	243.470i	0.309017	−	0.951057i
$257$	257.056			1.00022			0.500108	−	0.865963i	$-0.333293\pi$
$257$	257.056			1.00022			0.500108	+	0.865963i	$0.333293\pi$
$258$		0			0
$259$			224.237i			0.865781i
$260$	−1.30495	−	4.01623i	−0.00501904	−	0.0154470i
$261$		0			0
$262$	−265.220	+	365.044i	−1.01229	+	1.39330i
$263$		−	164.168i		−	0.624212i	−0.950047	−	0.312106i	$-0.898966\pi$
$263$		−	164.168i		−	0.624212i	0.950047	−	0.312106i	$-0.101034\pi$
$264$		0			0
$265$	−48.3870			−0.182592
$266$	−129.443	−	94.0456i	−0.486627	−	0.353555i
$267$		0			0
$268$	338.079	−	109.849i	1.26149	−	0.409882i
$269$	35.4752			0.131878			0.0659391	−	0.997824i	$-0.478996\pi$
$269$	35.4752			0.131878			0.0659391	+	0.997824i	$0.478996\pi$
$270$		0			0
$271$		−	298.950i		−	1.10314i	−0.834130	−	0.551568i	$-0.814030\pi$
$271$		−	298.950i		−	1.10314i	0.834130	−	0.551568i	$-0.185970\pi$
$272$	−309.220	+	224.661i	−1.13684	+	0.825961i
$273$		0			0
$274$	85.4853	+	62.1087i	0.311990	+	0.226674i
$275$			8.98056i			0.0326566i
$276$		0			0
$277$	−457.246			−1.65071			−0.825354	−	0.564616i	$-0.809024\pi$
$277$	−457.246			−1.65071			−0.825354	+	0.564616i	$0.809024\pi$
$278$	−147.947	+	203.632i	−0.532185	+	0.732490i
$279$		0			0
$280$	144.721	+	47.0228i	0.516862	+	0.167939i
$281$	5.63932			0.0200688			0.0100344	−	0.999950i	$-0.496806\pi$
$281$	5.63932			0.0200688			0.0100344	+	0.999950i	$0.496806\pi$
$282$		0			0
$283$			169.918i			0.600418i	0.953874	+	0.300209i	$0.0970563\pi$
$283$			169.918i			0.600418i	−0.953874	+	0.300209i	$0.902944\pi$
$284$	149.941	−	48.7188i	0.527962	−	0.171545i
$285$		0			0
$286$	−0.996894	+	1.37211i	−0.00348564	+	0.00479758i
$287$			352.309i			1.22756i
$288$		0			0
$289$	281.663			0.974611
$290$	25.1246	+	18.2541i	0.0866366	+	0.0629452i
$291$		0			0
$292$	170.026	+	523.287i	0.582282	+	1.79208i
$293$	26.8591			0.0916694			0.0458347	−	0.998949i	$-0.485405\pi$
$293$	26.8591			0.0916694			0.0458347	+	0.998949i	$0.485405\pi$
$294$		0			0
$295$		−	165.166i		−	0.559884i
$296$	−65.1672	+	200.564i	−0.220159	+	0.677581i
$297$		0			0
$298$	−215.151	−	156.316i	−0.721983	−	0.524551i
$299$		−	7.60845i		−	0.0254463i
$300$		0			0
$301$	−17.0820			−0.0567510
$302$	−177.771	+	244.681i	−0.588645	+	0.810201i
$303$		0			0
$304$	−88.4458	−	121.735i	−0.290940	−	0.400445i
$305$	58.4458			0.191626
$306$		0			0
$307$			118.031i			0.384466i	0.981349	+	0.192233i	$0.0615730\pi$
$307$			118.031i			0.384466i	−0.981349	+	0.192233i	$0.938427\pi$
$308$	−18.8854	−	58.1234i	−0.0613164	−	0.188712i
$309$		0			0
$310$	−124.721	+	171.664i	−0.402327	+	0.553756i
$311$			121.835i			0.391753i	0.980629	+	0.195877i	$0.0627552\pi$
$311$			121.835i			0.391753i	−0.980629	+	0.195877i	$0.937245\pi$
$312$		0			0
$313$	219.548			0.701431			0.350716	−	0.936482i	$-0.385938\pi$
$313$	219.548			0.701431			0.350716	+	0.936482i	$0.385938\pi$
$314$	−59.4590	−	43.1995i	−0.189360	−	0.137578i
$315$		0			0
$316$	−432.551	+	140.544i	−1.36883	+	0.444761i
$317$	−366.859			−1.15728			−0.578642	−	0.815582i	$-0.696417\pi$
$317$	−366.859			−1.15728			−0.578642	+	0.815582i	$0.696417\pi$
$318$		0			0
$319$		−	12.4727i		−	0.0390993i
$320$	115.777	+	84.1170i	0.361803	+	0.262866i
$321$		0			0
$322$	221.803	+	161.150i	0.688830	+	0.500465i
$323$			224.661i			0.695546i
$324$		0			0
$325$	2.36068			0.00726363
$326$	356.026	−	490.028i	1.09211	−	1.50315i
$327$		0			0
$328$	−102.387	+	315.115i	−0.312155	+	0.960716i
$329$	300.689			0.913948
$330$		0			0
$331$			162.846i			0.491981i	0.969272	+	0.245990i	$0.0791132\pi$
$331$			162.846i			0.491981i	−0.969272	+	0.245990i	$0.920887\pi$
$332$	−80.8065	+	26.2556i	−0.243393	+	0.0790832i
$333$		0			0
$334$	−116.833	+	160.807i	−0.349799	+	0.481457i
$335$			198.718i			0.593187i
$336$		0			0
$337$	17.1084			0.0507666			0.0253833	−	0.999678i	$-0.491919\pi$
$337$	17.1084			0.0507666			0.0253833	+	0.999678i	$0.491919\pi$
$338$	−273.087	−	198.409i	−0.807950	−	0.587010i
$339$		0			0
$340$	−66.0263	−	203.208i	−0.194195	−	0.597671i
$341$	85.2198			0.249911
$342$		0			0
$343$			218.101i			0.635863i
$344$	−15.2786	−	4.96433i	−0.0444147	−	0.0144312i
$345$		0			0
$346$	293.899	+	213.530i	0.849418	+	0.617138i
$347$			167.498i			0.482703i	0.970438	+	0.241351i	$0.0775906\pi$
$347$			167.498i			0.482703i	−0.970438	+	0.241351i	$0.922409\pi$
$348$		0			0
$349$	−483.495			−1.38537			−0.692687	−	0.721239i	$-0.743573\pi$
$349$	−483.495			−1.38537			−0.692687	+	0.721239i	$0.743573\pi$
$350$	−50.0000	+	68.8191i	−0.142857	+	0.196626i
$351$		0			0
$352$		−	57.4756i		−	0.163283i
$353$	−307.994			−0.872504			−0.436252	−	0.899825i	$-0.643694\pi$
$353$	−307.994			−0.872504			−0.436252	+	0.899825i	$0.643694\pi$
$354$		0			0
$355$			88.1332i			0.248263i
$356$	−83.3638	−	256.567i	−0.234168	−	0.720695i
$357$		0			0
$358$	306.715	−	422.157i	0.856746	−	1.17921i
$359$		−	23.2494i		−	0.0647615i	−0.999476	−	0.0323807i	$-0.989691\pi$
$359$		−	23.2494i		−	0.0647615i	0.999476	−	0.0323807i	$-0.0103089\pi$
$360$		0			0
$361$	272.554			0.754998
$362$	255.289	+	185.478i	0.705217	+	0.512370i
$363$		0			0
$364$	−15.2786	+	4.96433i	−0.0419743	+	0.0136383i
$365$	−307.580			−0.842686
$366$		0			0
$367$			517.325i			1.40960i	0.709404	+	0.704802i	$0.248964\pi$
$367$			517.325i			1.40960i	−0.709404	+	0.704802i	$0.751036\pi$
$368$	151.554	+	208.596i	0.411832	+	0.566838i
$369$		0			0
$370$	−95.3738	−	69.2931i	−0.257767	−	0.187279i
$371$			184.075i			0.496159i
$372$		0			0
$373$	−88.3545			−0.236875			−0.118438	−	0.992961i	$-0.537789\pi$
$373$	−88.3545			−0.236875			−0.118438	+	0.992961i	$0.537789\pi$
$374$	−50.4396	+	69.4242i	−0.134865	+	0.185626i
$375$		0			0
$376$	268.944	+	87.3853i	0.715277	+	0.232408i
$377$	−3.27864			−0.00869666
$378$		0			0
$379$		−	19.3332i		−	0.0510112i	−0.999675	−	0.0255056i	$-0.991880\pi$
$379$		−	19.3332i		−	0.0510112i	0.999675	−	0.0255056i	$-0.00811956\pi$
$380$	80.0000	−	25.9936i	0.210526	−	0.0684041i
$381$		0			0
$382$	380.997	−	524.397i	0.997374	−	1.37277i
$383$		−	431.612i		−	1.12692i	−0.826142	−	0.563462i	$-0.809469\pi$
$383$		−	431.612i		−	1.12692i	0.826142	−	0.563462i	$-0.190531\pi$
$384$		0			0
$385$	34.1641			0.0887379
$386$	294.122	+	213.692i	0.761973	+	0.553606i
$387$		0			0
$388$	−48.4133	−	149.001i	−0.124777	−	0.384023i
$389$	296.354			0.761837			0.380918	−	0.924609i	$-0.375608\pi$
$389$	296.354			0.761837			0.380918	+	0.924609i	$0.375608\pi$
$390$		0			0
$391$		−	384.963i		−	0.984560i
$392$	57.7508	−	177.739i	0.147323	−	0.453415i
$393$		0			0
$394$	−227.374	−	165.197i	−0.577091	−	0.419281i
$395$		−	254.247i		−	0.643664i
$396$		0			0
$397$	−86.1904			−0.217104			−0.108552	−	0.994091i	$-0.534621\pi$
$397$	−86.1904			−0.217104			−0.108552	+	0.994091i	$0.534621\pi$
$398$	197.771	−	272.208i	0.496912	−	0.683940i
$399$		0			0
$400$	−64.7214	+	47.0228i	−0.161803	+	0.117557i
$401$	−442.997			−1.10473			−0.552365	−	0.833602i	$-0.686275\pi$
$401$	−442.997			−1.10473			−0.552365	+	0.833602i	$0.686275\pi$
$402$		0			0
$403$		−	22.4014i		−	0.0555865i
$404$	−123.469	−	379.999i	−0.305616	−	0.940591i
$405$		0			0
$406$	69.4427	−	95.5797i	0.171041	−	0.235418i
$407$			47.3467i			0.116331i
$408$		0			0
$409$	63.4102			0.155037			0.0775186	−	0.996991i	$-0.475300\pi$
$409$	63.4102			0.155037			0.0775186	+	0.996991i	$0.475300\pi$
$410$	−149.846	−	108.869i	−0.365478	−	0.265535i
$411$		0			0
$412$	−136.085	+	44.2167i	−0.330304	+	0.107322i
$413$	−628.328			−1.52138
$414$		0			0
$415$		−	47.4969i		−	0.114450i
$416$	−15.1084			−0.0363182
$417$		0			0
$418$	−27.3313	−	19.8573i	−0.0653858	−	0.0475056i
$419$		−	435.678i		−	1.03980i	−0.854226	−	0.519902i	$-0.825968\pi$
$419$		−	435.678i		−	1.03980i	0.854226	−	0.519902i	$-0.174032\pi$
$420$		0			0
$421$	−582.912			−1.38459			−0.692294	−	0.721615i	$-0.743400\pi$
$421$	−582.912			−1.38459			−0.692294	+	0.721615i	$0.743400\pi$
$422$	110.440	−	152.007i	0.261705	−	0.360206i
$423$		0			0
$424$	−53.4953	+	164.642i	−0.126168	+	0.388306i
$425$	119.443			0.281042
$426$		0			0
$427$		−	222.341i		−	0.520705i
$428$	460.689	−	149.687i	1.07638	−	0.349736i
$429$		0			0
$430$	5.27864	−	7.26543i	0.0122759	−	0.0168963i
$431$			375.882i			0.872117i	0.899918	+	0.436058i	$0.143626\pi$
$431$			375.882i			0.872117i	−0.899918	+	0.436058i	$0.856374\pi$
$432$		0			0
$433$	−368.164			−0.850263			−0.425132	−	0.905131i	$-0.639772\pi$
$433$	−368.164			−0.850263			−0.425132	+	0.905131i	$0.639772\pi$
$434$	653.050	+	474.468i	1.50472	+	1.09324i
$435$		0			0
$436$	−244.085	−	751.217i	−0.559828	−	1.72297i
$437$	151.554			0.346806
$438$		0			0
$439$		−	483.549i		−	1.10148i	−0.834677	−	0.550739i	$-0.814346\pi$
$439$		−	483.549i		−	1.10148i	0.834677	−	0.550739i	$-0.185654\pi$
$440$	30.5573	+	9.92866i	0.0694484	+	0.0225651i
$441$		0			0
$442$	18.2492	+	13.2588i	0.0412878	+	0.0299974i
$443$		−	279.181i		−	0.630205i	−0.949058	−	0.315102i	$-0.897961\pi$
$443$		−	279.181i		−	0.630205i	0.949058	−	0.315102i	$-0.102039\pi$
$444$		0			0
$445$	150.807			0.338891
$446$	251.613	−	346.316i	0.564155	−	0.776492i
$447$		0			0
$448$	320.000	−	440.442i	0.714286	−	0.983130i
$449$	−756.079			−1.68392			−0.841959	−	0.539542i	$-0.818597\pi$
$449$	−756.079			−1.68392			−0.841959	+	0.539542i	$0.818597\pi$
$450$		0			0
$451$			74.3885i			0.164941i
$452$	−100.466	−	309.202i	−0.222270	−	0.684076i
$453$		0			0
$454$	48.6950	−	67.0230i	0.107258	−	0.147628i
$455$		−	8.98056i		−	0.0197375i
$456$		0			0
$457$	285.672			0.625103			0.312551	−	0.949901i	$-0.398816\pi$
$457$	285.672			0.625103			0.312551	+	0.949901i	$0.398816\pi$
$458$	118.567	+	86.1442i	0.258881	+	0.188088i
$459$		0			0
$460$	−137.082	+	44.5407i	−0.298004	+	0.0968275i
$461$	99.1146			0.214999			0.107500	−	0.994205i	$-0.465716\pi$
$461$	99.1146			0.214999			0.107500	+	0.994205i	$0.465716\pi$
$462$		0			0
$463$			630.603i			1.36199i	0.732286	+	0.680997i	$0.238453\pi$
$463$			630.603i			1.36199i	−0.732286	+	0.680997i	$0.761547\pi$
$464$	89.8885	−	65.3078i	0.193725	−	0.140750i
$465$		0			0
$466$	496.817	+	360.958i	1.06613	+	0.774589i
$467$			496.010i			1.06212i	0.847334	+	0.531060i	$0.178206\pi$
$467$			496.010i			1.06212i	−0.847334	+	0.531060i	$0.821794\pi$
$468$		0			0
$469$	755.967			1.61187
$470$	−92.9180	+	127.891i	−0.197698	+	0.272108i
$471$		0			0
$472$	−561.994	−	182.603i	−1.19066	−	0.386870i
$473$	−3.60680			−0.00762537
$474$		0			0
$475$			47.0228i			0.0989954i
$476$	−773.050	+	251.179i	−1.62405	+	0.527687i
$477$		0			0
$478$	50.4396	−	69.4242i	0.105522	−	0.145239i
$479$			579.090i			1.20896i	0.796621	+	0.604478i	$0.206618\pi$
$479$			579.090i			1.20896i	−0.796621	+	0.604478i	$0.793382\pi$
$480$		0			0
$481$	12.4458			0.0258749
$482$	−218.567	−	158.798i	−0.453459	−	0.329457i
$483$		0			0
$484$	145.577	+	448.039i	0.300778	+	0.925700i
$485$	87.5805			0.180578
$486$		0			0
$487$		−	626.363i		−	1.28617i	−0.765796	−	0.643084i	$-0.777655\pi$
$487$		−	626.363i		−	1.28617i	0.765796	−	0.643084i	$-0.222345\pi$
$488$	64.6161	−	198.868i	0.132410	−	0.407516i
$489$		0			0
$490$	84.5197	+	61.4072i	0.172489	+	0.125321i
$491$			22.3013i			0.0454201i	0.999742	+	0.0227100i	$0.00722945\pi$
$491$			22.3013i			0.0454201i	−0.999742	+	0.0227100i	$0.992771\pi$
$492$		0			0
$493$	−165.889			−0.336488
$494$	−5.21981	+	7.18445i	−0.0105664	+	0.0145434i
$495$		0			0
$496$	446.217	+	614.165i	0.899630	+	1.23824i
$497$	335.279			0.674605
$498$		0			0
$499$		−	627.362i		−	1.25724i	−0.777714	−	0.628619i	$-0.783621\pi$
$499$		−	627.362i		−	1.25724i	0.777714	−	0.628619i	$-0.216379\pi$
$500$	−13.8197	−	42.5325i	−0.0276393	−	0.0850651i
$501$		0			0
$502$	260.000	−	357.859i	0.517928	−	0.712867i
$503$			780.853i			1.55239i	0.630492	+	0.776196i	$0.282853\pi$
$503$			780.853i			1.55239i	−0.630492	+	0.776196i	$0.717147\pi$
$504$		0			0
$505$	223.358			0.442292
$506$	46.8328	+	34.0260i	0.0925550	+	0.0672451i
$507$		0			0
$508$	−7.02321	+	2.28198i	−0.0138252	+	0.00449208i
$509$	288.950			0.567683			0.283841	−	0.958871i	$-0.408391\pi$
$509$	288.950			0.567683			0.283841	+	0.958871i	$0.408391\pi$
$510$		0			0
$511$			1170.11i			2.28984i
$512$	414.217	−	300.946i	0.809017	−	0.587785i
$513$		0			0
$514$	415.925	+	302.187i	0.809192	+	0.587913i
$515$		−	79.9888i		−	0.155318i
$516$		0			0
$517$	63.4891			0.122803
$518$	−263.607	+	362.824i	−0.508893	+	0.700432i
$519$		0			0
$520$	2.60990	−	8.03246i	0.00501904	−	0.0154470i
$521$	602.984			1.15736			0.578680	−	0.815555i	$-0.303568\pi$
$521$	602.984			1.15736			0.578680	+	0.815555i	$0.303568\pi$
$522$		0			0
$523$		−	367.962i		−	0.703560i	−0.936083	−	0.351780i	$-0.885577\pi$
$523$		−	367.962i		−	0.703560i	0.936083	−	0.351780i	$-0.114423\pi$
$524$	−858.269	+	278.869i	−1.63792	+	0.532192i
$525$		0			0
$526$	192.991	−	265.629i	0.366902	−	0.504998i
$527$		−	1133.44i		−	2.15073i
$528$		0			0
$529$	269.308			0.509089
$530$	−78.2918	−	56.8823i	−0.147720	−	0.107325i
$531$		0			0
$532$	−98.8854	−	304.338i	−0.185875	−	0.572064i
$533$	19.5542			0.0366870
$534$		0			0
$535$			270.786i			0.506142i
$536$	676.158	+	219.697i	1.26149	+	0.409882i
$537$		0			0
$538$	57.4001	+	41.7036i	0.106692	+	0.0775161i
$539$		−	41.9584i		−	0.0778449i
$540$		0			0
$541$	−616.885			−1.14027			−0.570134	−	0.821551i	$-0.693109\pi$
$541$	−616.885			−1.14027			−0.570134	+	0.821551i	$0.693109\pi$
$542$	351.437	−	483.711i	0.648407	−	0.892455i
$543$		0			0
$544$	−764.433			−1.40521
$545$	441.554			0.810191
$546$		0			0
$547$			97.8499i			0.178885i	0.995992	+	0.0894423i	$0.0285085\pi$
$547$			97.8499i			0.178885i	−0.995992	+	0.0894423i	$0.971492\pi$
$548$	65.3050	+	200.988i	0.119170	+	0.366766i
$549$		0			0
$550$	−10.5573	+	14.5309i	−0.0191951	+	0.0264197i
$551$		−	65.3078i		−	0.118526i
$552$		0			0
$553$	−967.214			−1.74903
$554$	−739.840	−	537.525i	−1.33545	−	0.970262i
$555$		0			0
$556$	−478.768	+	155.561i	−0.861093	+	0.279786i
$557$	−896.302			−1.60916			−0.804580	−	0.593845i	$-0.797609\pi$
$557$	−896.302			−1.60916			−0.804580	+	0.593845i	$0.797609\pi$
$558$		0			0
$559$			0.948103i			0.00169607i
$560$	178.885	+	246.215i	0.319438	+	0.439669i
$561$		0			0
$562$	9.12461	+	6.62942i	0.0162360	+	0.0117961i
$563$			771.186i			1.36978i	0.728647	+	0.684890i	$0.240150\pi$
$563$			771.186i			1.36978i	−0.728647	+	0.684890i	$0.759850\pi$
$564$		0			0
$565$	181.745			0.321672
$566$	−199.751	+	274.933i	−0.352917	+	0.485748i
$567$		0			0
$568$	299.882	+	97.4377i	0.527962	+	0.171545i
$569$	−8.74767			−0.0153738			−0.00768688	−	0.999970i	$-0.502447\pi$
$569$	−8.74767			−0.0153738			−0.00768688	+	0.999970i	$0.502447\pi$
$570$		0			0
$571$		−	511.138i		−	0.895164i	−0.894243	−	0.447582i	$-0.852285\pi$
$571$		−	511.138i		−	0.895164i	0.894243	−	0.447582i	$-0.147715\pi$
$572$	−3.22602	+	1.04820i	−0.00563989	+	0.00183251i
$573$		0			0
$574$	−414.164	+	570.048i	−0.721540	+	0.993115i
$575$		−	80.5748i		−	0.140130i
$576$		0			0
$577$	−713.712			−1.23694			−0.618468	−	0.785810i	$-0.712246\pi$
$577$	−713.712			−1.23694			−0.618468	+	0.785810i	$0.712246\pi$
$578$	455.740	+	331.114i	0.788477	+	0.572862i
$579$		0			0
$580$	19.1935	+	59.0715i	0.0330922	+	0.101847i
$581$	−180.689			−0.310996
$582$		0			0
$583$			38.8666i			0.0666666i
$584$	−340.053	+	1046.57i	−0.582282	+	1.79208i
$585$		0			0
$586$	43.4590	+	31.5748i	0.0741621	+	0.0538819i
$587$		−	422.169i		−	0.719198i	−0.933107	−	0.359599i	$-0.882914\pi$
$587$		−	422.169i		−	0.719198i	0.933107	−	0.359599i	$-0.117086\pi$
$588$		0			0
$589$	446.217			0.757584
$590$	194.164	−	267.244i	0.329092	−	0.452956i
$591$		0			0
$592$	−341.220	+	247.911i	−0.576385	+	0.418768i
$593$	308.663			0.520510			0.260255	−	0.965540i	$-0.416193\pi$
$593$	308.663			0.520510			0.260255	+	0.965540i	$0.416193\pi$
$594$		0			0
$595$		−	454.387i		−	0.763676i
$596$	−164.361	−	505.850i	−0.275773	−	0.848742i
$597$		0			0
$598$	8.94427	−	12.3107i	0.0149570	−	0.0205865i
$599$		−	462.196i		−	0.771612i	−0.922580	−	0.385806i	$-0.873923\pi$
$599$		−	462.196i		−	0.771612i	0.922580	−	0.385806i	$-0.126077\pi$
$600$		0			0
$601$	355.358			0.591277			0.295639	−	0.955300i	$-0.404468\pi$
$601$	355.358			0.591277			0.295639	+	0.955300i	$0.404468\pi$
$602$	−27.6393	−	20.0811i	−0.0459125	−	0.0333574i
$603$		0			0
$604$	−575.279	+	186.919i	−0.952448	+	0.309469i
$605$	−263.351			−0.435290
$606$		0			0
$607$		−	630.403i		−	1.03856i	−0.854605	−	0.519278i	$-0.826201\pi$
$607$		−	630.403i		−	1.03856i	0.854605	−	0.519278i	$-0.173799\pi$
$608$		−	300.946i		−	0.494977i
$609$		0			0
$610$	94.5673	+	68.7072i	0.155028	+	0.112635i
$611$		−	16.6891i		−	0.0273144i
$612$		0			0
$613$	812.525			1.32549			0.662745	−	0.748846i	$-0.269392\pi$
$613$	812.525			1.32549			0.662745	+	0.748846i	$0.269392\pi$
$614$	−138.754	+	190.978i	−0.225984	+	0.311040i
$615$		0			0
$616$	37.7709	−	116.247i	0.0613164	−	0.188712i
$617$	437.935			0.709781			0.354891	−	0.934908i	$-0.384518\pi$
$617$	437.935			0.709781			0.354891	+	0.934908i	$0.384518\pi$
$618$		0			0
$619$			770.250i			1.24435i	0.782880	+	0.622173i	$0.213750\pi$
$619$			770.250i			1.24435i	−0.782880	+	0.622173i	$0.786250\pi$
$620$	−403.607	+	131.140i	−0.650979	+	0.211516i
$621$		0			0
$622$	−143.226	+	197.134i	−0.230267	+	0.316935i
$623$		−	573.702i		−	0.920870i
$624$		0			0
$625$	25.0000			0.0400000
$626$	355.236	+	258.094i	0.567470	+	0.412291i
$627$		0			0
$628$	−45.4226	−	139.796i	−0.0723290	−	0.222606i
$629$	629.718			1.00114
$630$		0			0
$631$			875.496i			1.38747i	0.720228	+	0.693737i	$0.244037\pi$
$631$			875.496i			1.38747i	−0.720228	+	0.693737i	$0.755963\pi$
$632$	−865.102	−	281.089i	−1.36883	−	0.444761i
$633$		0			0
$634$	−593.591	−	431.269i	−0.936263	−	0.680235i
$635$		−	4.12814i		−	0.00650100i
$636$		0			0
$637$	−11.0294			−0.0173146
$638$	14.6625	−	20.1812i	0.0229820	−	0.0316320i
$639$		0			0
$640$	88.4458	+	272.208i	0.138197	+	0.425325i
$641$	−842.571			−1.31446			−0.657232	−	0.753689i	$-0.728273\pi$
$641$	−842.571			−1.31446			−0.657232	+	0.753689i	$0.728273\pi$
$642$		0			0
$643$			1153.20i			1.79348i	0.442563	+	0.896738i	$0.354069\pi$
$643$			1153.20i			1.79348i	−0.442563	+	0.896738i	$0.645931\pi$
$644$	169.443	+	521.491i	0.263110	+	0.809769i
$645$		0			0
$646$	−264.105	+	363.510i	−0.408832	+	0.562708i
$647$		−	355.751i		−	0.549847i	−0.961466	−	0.274924i	$-0.911347\pi$
$647$		−	355.751i		−	0.549847i	0.961466	−	0.274924i	$-0.0886526\pi$
$648$		0			0
$649$	−132.669			−0.204420
$650$	3.81966	+	2.77515i	0.00587640	+	0.00426945i
$651$		0			0
$652$	1152.13	−	374.348i	1.76706	−	0.574154i
$653$	557.915			0.854387			0.427194	−	0.904160i	$-0.359502\pi$
$653$	557.915			0.854387			0.427194	+	0.904160i	$0.359502\pi$
$654$		0			0
$655$		−	504.478i		−	0.770195i
$656$	−536.105	+	389.503i	−0.817234	+	0.593755i
$657$		0			0
$658$	486.525	+	353.481i	0.739399	+	0.537205i
$659$			284.157i			0.431194i	0.976482	+	0.215597i	$0.0691697\pi$
$659$			284.157i			0.431194i	−0.976482	+	0.215597i	$0.930830\pi$
$660$		0			0
$661$	716.735			1.08432			0.542160	−	0.840275i	$-0.317607\pi$
$661$	716.735			1.08432			0.542160	+	0.840275i	$0.317607\pi$
$662$	−191.437	+	263.490i	−0.289179	+	0.398021i
$663$		0			0
$664$	−161.613	−	52.5112i	−0.243393	−	0.0790832i
$665$	178.885			0.269001
$666$		0			0
$667$			111.907i			0.167776i
$668$	−378.079	+	122.845i	−0.565986	+	0.183900i
$669$		0			0
$670$	−233.607	+	321.532i	−0.348667	+	0.479899i
$671$		−	46.9464i		−	0.0699648i
$672$		0			0
$673$	−695.378			−1.03325			−0.516625	−	0.856212i	$-0.672812\pi$
$673$	−695.378			−1.03325			−0.516625	+	0.856212i	$0.672812\pi$
$674$	27.6819	+	20.1121i	0.0410711	+	0.0298399i
$675$		0			0
$676$	−208.620	−	642.066i	−0.308609	−	0.949802i
$677$	820.237			1.21158			0.605788	−	0.795626i	$-0.292858\pi$
$677$	820.237			1.21158			0.605788	+	0.795626i	$0.292858\pi$
$678$		0			0
$679$		−	333.176i		−	0.490686i
$680$	132.053	−	406.416i	0.194195	−	0.597671i
$681$		0			0
$682$	137.889	+	100.182i	0.202183	+	0.146894i
$683$			335.508i			0.491227i	0.969368	+	0.245613i	$0.0789894\pi$
$683$			335.508i			0.491227i	−0.969368	+	0.245613i	$0.921011\pi$
$684$		0			0
$685$	−118.138			−0.172464
$686$	−256.393	+	352.895i	−0.373751	+	0.514424i
$687$		0			0
$688$	−18.8854	−	25.9936i	−0.0274498	−	0.0377814i
$689$	10.2167			0.0148283
$690$		0			0
$691$		−	336.568i		−	0.487074i	−0.969892	−	0.243537i	$-0.921692\pi$
$691$		−	336.568i		−	0.487074i	0.969892	−	0.243537i	$-0.0783077\pi$
$692$	224.519	+	690.997i	0.324449	+	0.998551i
$693$		0			0
$694$	−196.906	+	271.017i	−0.283726	+	0.390515i
$695$		−	281.413i		−	0.404910i
$696$		0			0
$697$	989.378			1.41948
$698$	−782.312	−	568.383i	−1.12079	−	0.814302i
$699$		0			0
$700$	−161.803	+	52.5731i	−0.231148	+	0.0751044i
$701$	429.364			0.612502			0.306251	−	0.951951i	$-0.400925\pi$
$701$	429.364			0.612502			0.306251	+	0.951951i	$0.400925\pi$
$702$		0			0
$703$			247.911i			0.352647i
$704$	67.5666	−	92.9974i	0.0959753	−	0.132099i
$705$		0			0
$706$	−498.344	−	362.068i	−0.705870	−	0.512845i
$707$		−	849.703i		−	1.20184i
$708$		0			0
$709$	1224.60			1.72722			0.863609	−	0.504162i	$-0.168199\pi$
$709$	1224.60			1.72722			0.863609	+	0.504162i	$0.168199\pi$
$710$	−103.607	+	142.603i	−0.145925	+	0.200849i
$711$		0			0
$712$	166.728	−	513.135i	0.234168	−	0.720695i
$713$	−764.604			−1.07238
$714$		0			0
$715$		−	1.89621i		−	0.00265204i
$716$	992.551	−	322.499i	1.38624	−	0.450418i
$717$		0			0
$718$	27.3313	−	37.6183i	0.0380658	−	0.0523931i
$719$			496.022i			0.689877i	0.938625	+	0.344939i	$0.112100\pi$
$719$			496.022i			0.689877i	−0.938625	+	0.344939i	$0.887900\pi$
$720$		0			0
$721$	−304.296			−0.422047
$722$	441.002	+	320.407i	0.610806	+	0.443777i
$723$		0			0
$724$	195.023	+	600.220i	0.269369	+	0.829033i
$725$	−34.7214			−0.0478915
$726$		0			0
$727$			152.843i			0.210238i	0.994460	+	0.105119i	$0.0335224\pi$
$727$			152.843i			0.210238i	−0.994460	+	0.105119i	$0.966478\pi$
$728$	−30.5573	−	9.92866i	−0.0419743	−	0.0136383i
$729$		0			0
$730$	−497.676	−	361.583i	−0.681748	−	0.495319i
$731$			47.9709i			0.0656237i
$732$		0			0
$733$	−761.286			−1.03859			−0.519295	−	0.854595i	$-0.673805\pi$
$733$	−761.286			−1.03859			−0.519295	+	0.854595i	$0.673805\pi$
$734$	−608.152	+	837.049i	−0.828544	+	1.14039i
$735$		0			0
$736$			515.679i			0.700650i
$737$	159.619			0.216580
$738$		0			0
$739$			183.975i			0.248951i	0.992223	+	0.124476i	$0.0397249\pi$
$739$			183.975i			0.248951i	−0.992223	+	0.124476i	$0.960275\pi$
$740$	−72.8591	−	224.237i	−0.0984583	−	0.303023i
$741$		0			0
$742$	−216.393	+	297.840i	−0.291635	+	0.401401i
$743$			495.247i			0.666551i	0.942830	+	0.333275i	$0.108154\pi$
$743$			495.247i			0.666551i	−0.942830	+	0.333275i	$0.891846\pi$
$744$		0			0
$745$	297.331			0.399102
$746$	−142.961	−	103.867i	−0.191636	−	0.139232i
$747$		0			0
$748$	−163.226	+	53.0353i	−0.218217	+	0.0709029i
$749$	1030.13			1.37534
$750$		0			0
$751$		−	800.059i		−	1.06533i	−0.846328	−	0.532663i	$-0.821191\pi$
$751$		−	800.059i		−	1.06533i	0.846328	−	0.532663i	$-0.178809\pi$
$752$	332.433	+	457.555i	0.442066	+	0.608451i
$753$		0			0
$754$	−5.30495	−	3.85427i	−0.00703574	−	0.00511177i
$755$		−	338.140i		−	0.447868i
$756$		0			0
$757$	−276.367			−0.365082			−0.182541	−	0.983198i	$-0.558432\pi$
$757$	−276.367			−0.365082			−0.182541	+	0.983198i	$0.558432\pi$
$758$	22.7276	−	31.2818i	0.0299836	−	0.0412689i
$759$		0			0
$760$	160.000	+	51.9872i	0.210526	+	0.0684041i
$761$	−891.207			−1.17110			−0.585550	−	0.810636i	$-0.699121\pi$
$761$	−891.207			−1.17110			−0.585550	+	0.810636i	$0.699121\pi$
$762$		0			0
$763$		−	1679.77i		−	2.20154i
$764$	1232.93	−	400.604i	1.61379	−	0.524351i
$765$		0			0
$766$	507.390	−	698.363i	0.662389	−	0.911700i
$767$			34.8740i			0.0454681i
$768$		0			0
$769$	−835.430			−1.08639			−0.543193	−	0.839608i	$-0.682785\pi$
$769$	−835.430			−1.08639			−0.543193	+	0.839608i	$0.682785\pi$
$770$	55.2786	+	40.1623i	0.0717904	+	0.0521588i
$771$		0			0
$772$	224.689	+	691.521i	0.291048	+	0.895753i
$773$	−213.522			−0.276225			−0.138112	−	0.990417i	$-0.544103\pi$
$773$	−213.522			−0.276225			−0.138112	+	0.990417i	$0.544103\pi$
$774$		0			0
$775$		−	237.234i		−	0.306109i
$776$	96.8266	−	298.002i	0.124777	−	0.384023i
$777$		0			0
$778$	479.512	+	348.386i	0.616339	+	0.447796i
$779$			389.503i			0.500004i
$780$		0			0
$781$	70.7926			0.0906436
$782$	452.551	−	622.883i	0.578710	−	0.796526i
$783$		0			0
$784$	302.387	−	219.697i	0.385698	−	0.280226i
$785$	82.1703			0.104676
$786$		0			0
$787$			370.182i			0.470371i	0.971951	+	0.235185i	$0.0755697\pi$
$787$			370.182i			0.470371i	−0.971951	+	0.235185i	$0.924430\pi$
$788$	−173.698	−	534.588i	−0.220429	−	0.678411i
$789$		0			0
$790$	298.885	−	411.381i	0.378336	−	0.520735i
$791$		−	691.397i		−	0.874080i
$792$		0			0
$793$	−12.3406			−0.0155619
$794$	−139.459	−	101.323i	−0.175641	−	0.127611i
$795$		0			0
$796$	640.000	−	207.949i	0.804020	−	0.261242i
$797$	−274.426			−0.344323			−0.172162	−	0.985069i	$-0.555075\pi$
$797$	−274.426			−0.344323			−0.172162	+	0.985069i	$0.555075\pi$
$798$		0			0
$799$		−	844.414i		−	1.05684i
$800$	−160.000			−0.200000
$801$		0			0
$802$	−716.784	−	520.774i	−0.893746	−	0.649344i
$803$			247.063i			0.307675i
$804$		0			0
$805$	−306.525			−0.380776
$806$	26.3344	−	36.2461i	0.0326729	−	0.0449704i
$807$		0			0
$808$	246.938	−	759.997i	0.305616	−	0.940591i
$809$	−665.214			−0.822266			−0.411133	−	0.911575i	$-0.634867\pi$
$809$	−665.214			−0.822266			−0.411133	+	0.911575i	$0.634867\pi$
$810$		0			0
$811$			360.665i			0.444717i	0.974965	+	0.222358i	$0.0713755\pi$
$811$			360.665i			0.444717i	−0.974965	+	0.222358i	$0.928624\pi$
$812$	224.721	−	73.0164i	0.276750	−	0.0899217i
$813$		0			0
$814$	−55.6594	+	76.6086i	−0.0683777	+	0.0941138i
$815$			677.202i			0.830923i
$816$		0			0
$817$	−18.8854			−0.0231156
$818$	102.600	+	74.5432i	0.125428	+	0.0911286i
$819$		0			0
$820$	−114.472	−	352.309i	−0.139600	−	0.429645i
$821$	666.899			0.812301			0.406151	−	0.913806i	$-0.366871\pi$
$821$	666.899			0.812301			0.406151	+	0.913806i	$0.366871\pi$
$822$		0			0
$823$			122.433i			0.148764i	0.997230	+	0.0743822i	$0.0236985\pi$
$823$			122.433i			0.148764i	−0.997230	+	0.0743822i	$0.976302\pi$
$824$	−272.170	−	88.4335i	−0.330304	−	0.107322i
$825$		0			0
$826$	−1016.66	−	738.644i	−1.23082	−	0.894242i
$827$			1532.98i			1.85366i	0.375477	+	0.926832i	$0.377479\pi$
$827$			1532.98i			1.85366i	−0.375477	+	0.926832i	$0.622521\pi$
$828$		0			0
$829$	−195.475			−0.235796			−0.117898	−	0.993026i	$-0.537616\pi$
$829$	−195.475			−0.235796			−0.117898	+	0.993026i	$0.537616\pi$
$830$	55.8359	−	76.8516i	0.0672722	−	0.0925922i
$831$		0			0
$832$	−24.4458	−	17.7609i	−0.0293820	−	0.0213473i
$833$	−558.053			−0.669931
$834$		0			0
$835$		−	222.229i		−	0.266143i
$836$	−20.8792	−	64.2597i	−0.0249752	−	0.0768656i
$837$		0			0
$838$	512.170	−	704.942i	0.611182	−	0.841219i
$839$		−	1325.97i		−	1.58041i	−0.612840	−	0.790207i	$-0.709973\pi$
$839$		−	1325.97i		−	1.58041i	0.612840	−	0.790207i	$-0.290027\pi$
$840$		0			0
$841$	−792.777			−0.942660
$842$	−943.171	−	685.254i	−1.12016	−	0.813841i
$843$		0			0
$844$	357.390	−	116.123i	0.423448	−	0.137587i
$845$	377.397			0.446624
$846$		0			0
$847$			1001.85i			1.18282i
$848$	−280.105	+	203.508i	−0.330313	+	0.239986i
$849$		0			0
$850$	193.262	+	140.413i	0.227368	+	0.165192i
$851$		−	424.801i		−	0.499179i
$852$		0			0
$853$	1055.28			1.23714			0.618570	−	0.785730i	$-0.287712\pi$
$853$	1055.28			1.23714			0.618570	+	0.785730i	$0.287712\pi$
$854$	261.378	−	359.756i	0.306063	−	0.421259i
$855$		0			0
$856$	921.378	+	299.374i	1.07638	+	0.349736i
$857$	−155.378			−0.181304			−0.0906521	−	0.995883i	$-0.528895\pi$
$857$	−155.378			−0.181304			−0.0906521	+	0.995883i	$0.528895\pi$
$858$		0			0
$859$		−	226.033i		−	0.263136i	−0.991307	−	0.131568i	$-0.957999\pi$
$859$		−	226.033i		−	0.263136i	0.991307	−	0.131568i	$-0.0420011\pi$
$860$	17.0820	−	5.55029i	0.0198628	−	0.00645383i
$861$		0			0
$862$	−441.876	+	608.190i	−0.512617	+	0.705557i
$863$		−	930.702i		−	1.07845i	−0.842162	−	0.539225i	$-0.818717\pi$
$863$		−	930.702i		−	1.07845i	0.842162	−	0.539225i	$-0.181283\pi$
$864$		0			0
$865$	−406.158			−0.469547
$866$	−595.702	−	432.803i	−0.687878	−	0.499772i
$867$		0			0
$868$	498.885	+	1535.41i	0.574753	+	1.76891i
$869$	−204.223			−0.235009
$870$		0			0
$871$		−	41.9584i		−	0.0481727i
$872$	488.170	−	1502.43i	0.559828	−	1.72297i
$873$		0			0
$874$	245.220	+	178.163i	0.280572	+	0.203847i
$875$		−	95.1057i		−	0.108692i
$876$		0			0
$877$	−33.5217			−0.0382231			−0.0191115	−	0.999817i	$-0.506084\pi$
$877$	−33.5217			−0.0382231			−0.0191115	+	0.999817i	$0.506084\pi$
$878$	568.446	−	782.399i	0.647433	−	0.891115i
$879$		0			0
$880$	37.7709	+	51.9872i	0.0429215	+	0.0590763i
$881$	933.850			1.05999			0.529994	−	0.848001i	$-0.322194\pi$
$881$	933.850			1.05999			0.529994	+	0.848001i	$0.322194\pi$
$882$		0			0
$883$			542.308i			0.614166i	0.951683	+	0.307083i	$0.0993529\pi$
$883$			542.308i			0.614166i	−0.951683	+	0.307083i	$0.900647\pi$
$884$	13.9412	+	42.9065i	0.0157706	+	0.0485368i
$885$		0			0
$886$	328.197	−	451.724i	0.370425	−	0.509846i
$887$			714.720i			0.805773i	0.915250	+	0.402886i	$0.131993\pi$
$887$			714.720i			0.805773i	−0.915250	+	0.402886i	$0.868007\pi$
$888$		0			0
$889$	−15.7044			−0.0176652
$890$	244.010	+	177.284i	0.274169	+	0.199195i
$891$		0			0
$892$	814.237	−	264.562i	0.912822	−	0.296594i
$893$	332.433			0.372266
$894$		0			0
$895$			583.407i			0.651851i
$896$	1035.54	−	336.468i	1.15574	−	0.375522i
$897$		0			0
$898$	−1223.36	−	888.824i	−1.36232	−	0.989782i
$899$			329.484i			0.366500i
$900$		0			0
$901$	516.932			0.573731
$902$	−87.4489	+	120.363i	−0.0969500	+	0.133440i
$903$		0			0
$904$	200.932	−	618.405i	0.222270	−	0.684076i
$905$	−352.800			−0.389835
$906$		0			0
$907$		−	347.233i		−	0.382837i	−0.981509	−	0.191418i	$-0.938691\pi$
$907$		−	347.233i		−	0.382837i	0.981509	−	0.191418i	$-0.0613087\pi$
$908$	157.580	−	51.2010i	0.173547	−	0.0563888i
$909$		0			0
$910$	10.5573	−	14.5309i	0.0116014	−	0.0159680i
$911$			1427.54i			1.56701i	0.621386	+	0.783504i	$0.286570\pi$
$911$			1427.54i			1.56701i	−0.621386	+	0.783504i	$0.713430\pi$
$912$		0			0
$913$	−38.1517			−0.0417871
$914$	462.227	+	335.827i	0.505719	+	0.367426i
$915$		0			0
$916$	90.5774	+	278.769i	0.0988836	+	0.304332i
$917$	−1919.15			−2.09286
$918$		0			0
$919$			569.162i			0.619327i	0.950846	+	0.309664i	$0.100216\pi$
$919$			569.162i			0.619327i	−0.950846	+	0.309664i	$0.899784\pi$
$920$	−274.164	−	89.0813i	−0.298004	−	0.0968275i
$921$		0			0
$922$	160.371	+	116.516i	0.173938	+	0.126373i
$923$		−	18.6089i		−	0.0201614i
$924$		0			0
$925$	131.803			0.142490
$926$	−741.319	+	1020.34i	−0.800560	+	1.10188i
$927$		0			0
$928$	222.217			0.239458
$929$	−1535.96			−1.65335			−0.826675	−	0.562680i	$-0.809770\pi$
$929$	−1535.96			−1.65335			−0.826675	+	0.562680i	$0.809770\pi$
$930$		0			0
$931$		−	219.697i		−	0.235980i
$932$	379.534	+	1168.09i	0.407225	+	1.25331i
$933$		0			0
$934$	−583.094	+	802.561i	−0.624298	+	0.859273i
$935$		−	95.9418i		−	0.102612i
$936$		0			0
$937$	338.721			0.361496			0.180748	−	0.983529i	$-0.442148\pi$
$937$	338.721			0.361496			0.180748	+	0.983529i	$0.442148\pi$
$938$	1223.18	+	888.693i	1.30403	+	0.947434i
$939$		0			0
$940$	−300.689	+	97.6997i	−0.319882	+	0.103936i
$941$	−1439.77			−1.53004			−0.765022	−	0.644004i	$-0.777272\pi$
$941$	−1439.77			−1.53004			−0.765022	+	0.644004i	$0.777272\pi$
$942$		0			0
$943$		−	667.424i		−	0.707766i
$944$	−694.663	−	956.121i	−0.735871	−	1.01284i
$945$		0			0
$946$	−5.83592	−	4.24005i	−0.00616905	−	0.00448208i
$947$			656.135i			0.692856i	0.938077	+	0.346428i	$0.112606\pi$
$947$			656.135i			0.692856i	−0.938077	+	0.346428i	$0.887394\pi$
$948$		0			0
$949$	64.9443			0.0684344
$950$	−55.2786	+	76.0845i	−0.0581880	+	0.0800890i
$951$		0			0
$952$	−1546.10	−	502.358i	−1.62405	−	0.527687i
$953$	−436.675			−0.458211			−0.229105	−	0.973402i	$-0.573580\pi$
$953$	−436.675			−0.458211			−0.229105	+	0.973402i	$0.573580\pi$
$954$		0			0
$955$			724.699i			0.758847i
$956$	163.226	−	53.0353i	0.170739	−	0.0554763i
$957$		0			0
$958$	−680.762	+	936.988i	−0.710607	+	0.978067i
$959$			449.423i			0.468637i
$960$		0			0
$961$	−1290.20			−1.34256
$962$	20.1378	+	14.6309i	0.0209332	+	0.0152089i
$963$		0			0
$964$	−166.971	−	513.883i	−0.173206	−	0.533073i
$965$	−406.466			−0.421208
$966$		0			0
$967$			903.436i			0.934267i	0.884187	+	0.467133i	$0.154713\pi$
$967$			903.436i			0.934267i	−0.884187	+	0.467133i	$0.845287\pi$
$968$	−291.153	+	896.078i	−0.300778	+	0.925700i
$969$		0			0
$970$	141.708	+	102.957i	0.146091	+	0.106141i
$971$		−	1866.89i		−	1.92265i	−0.275420	−	0.961324i	$-0.588817\pi$
$971$		−	1866.89i		−	1.92265i	0.275420	−	0.961324i	$-0.411183\pi$
$972$		0			0
$973$	−1070.56			−1.10026
$974$	736.334	−	1013.48i	0.755990	−	1.04053i
$975$		0			0
$976$	338.334	−	245.814i	0.346654	−	0.251859i
$977$	1073.95			1.09923			0.549615	−	0.835418i	$-0.314774\pi$
$977$	1073.95			1.09923			0.549615	+	0.835418i	$0.314774\pi$
$978$		0			0
$979$		−	121.135i		−	0.123733i
$980$	64.5673	+	198.718i	0.0658850	+	0.202773i
$981$		0			0
$982$	−26.2167	+	36.0842i	−0.0266973	+	0.0367456i
$983$			534.114i			0.543351i	0.962389	+	0.271675i	$0.0875777\pi$
$983$			534.114i			0.543351i	−0.962389	+	0.271675i	$0.912422\pi$
$984$		0			0
$985$	314.223			0.319008
$986$	−268.413	−	195.014i	−0.272224	−	0.197783i
$987$		0			0
$988$	−16.8916	+	5.48843i	−0.0170968	+	0.00555509i
$989$	32.3607			0.0327206
$990$		0			0
$991$		−	520.419i		−	0.525146i	−0.964912	−	0.262573i	$-0.915429\pi$
$991$		−	520.419i		−	0.525146i	0.964912	−	0.262573i	$-0.0845710\pi$
$992$			1518.30i			1.53054i
$993$		0			0
$994$	542.492	+	394.144i	0.545767	+	0.396523i
$995$			376.183i			0.378073i
$996$		0			0
$997$	457.680			0.459057			0.229528	−	0.973302i	$-0.426282\pi$
$997$	457.680			0.459057			0.229528	+	0.973302i	$0.426282\pi$
$998$	737.508	−	1015.09i	0.738986	−	1.01713i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.c.a.91.4		4
3.2	odd	2		20.3.b.a.11.1	✓	4
4.3	odd	2	inner	180.3.c.a.91.3		4
5.2	odd	4		900.3.f.e.199.4		8
5.3	odd	4		900.3.f.e.199.5		8
5.4	even	2		900.3.c.k.451.1		4
8.3	odd	2		2880.3.e.e.2431.3		4
8.5	even	2		2880.3.e.e.2431.4		4
12.11	even	2		20.3.b.a.11.2	yes	4
15.2	even	4		100.3.d.b.99.5		8
15.8	even	4		100.3.d.b.99.4		8
15.14	odd	2		100.3.b.f.51.4		4
20.3	even	4		900.3.f.e.199.3		8
20.7	even	4		900.3.f.e.199.6		8
20.19	odd	2		900.3.c.k.451.2		4
24.5	odd	2		320.3.b.c.191.4		4
24.11	even	2		320.3.b.c.191.1		4
48.5	odd	4		1280.3.g.e.1151.2		8
48.11	even	4		1280.3.g.e.1151.8		8
48.29	odd	4		1280.3.g.e.1151.7		8
48.35	even	4		1280.3.g.e.1151.1		8
60.23	odd	4		100.3.d.b.99.6		8
60.47	odd	4		100.3.d.b.99.3		8
60.59	even	2		100.3.b.f.51.3		4
120.29	odd	2		1600.3.b.s.1151.1		4
120.53	even	4		1600.3.h.n.1599.2		8
120.59	even	2		1600.3.b.s.1151.4		4
120.77	even	4		1600.3.h.n.1599.8		8
120.83	odd	4		1600.3.h.n.1599.7		8
120.107	odd	4		1600.3.h.n.1599.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.1	✓	4	3.2	odd	2
20.3.b.a.11.2	yes	4	12.11	even	2
100.3.b.f.51.3		4	60.59	even	2
100.3.b.f.51.4		4	15.14	odd	2
100.3.d.b.99.3		8	60.47	odd	4
100.3.d.b.99.4		8	15.8	even	4
100.3.d.b.99.5		8	15.2	even	4
100.3.d.b.99.6		8	60.23	odd	4
180.3.c.a.91.3		4	4.3	odd	2	inner
180.3.c.a.91.4		4	1.1	even	1	trivial
320.3.b.c.191.1		4	24.11	even	2
320.3.b.c.191.4		4	24.5	odd	2
900.3.c.k.451.1		4	5.4	even	2
900.3.c.k.451.2		4	20.19	odd	2
900.3.f.e.199.3		8	20.3	even	4
900.3.f.e.199.4		8	5.2	odd	4
900.3.f.e.199.5		8	5.3	odd	4
900.3.f.e.199.6		8	20.7	even	4
1280.3.g.e.1151.1		8	48.35	even	4
1280.3.g.e.1151.2		8	48.5	odd	4
1280.3.g.e.1151.7		8	48.29	odd	4
1280.3.g.e.1151.8		8	48.11	even	4
1600.3.b.s.1151.1		4	120.29	odd	2
1600.3.b.s.1151.4		4	120.59	even	2
1600.3.h.n.1599.1		8	120.107	odd	4
1600.3.h.n.1599.2		8	120.53	even	4
1600.3.h.n.1599.7		8	120.83	odd	4
1600.3.h.n.1599.8		8	120.77	even	4
2880.3.e.e.2431.3		4	8.3	odd	2
2880.3.e.e.2431.4		4	8.5	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 + 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} -2.23607 q^{5} +8.50651i q^{7} +(-2.47214 + 7.60845i) q^{8} +O(q^{10})\)	\(q+(1.61803 + 1.17557i) q^{2} +(1.23607 + 3.80423i) q^{4} -2.23607 q^{5} +8.50651i q^{7} +(-2.47214 + 7.60845i) q^{8} +(-3.61803 - 2.62866i) q^{10} +1.79611i q^{11} +0.472136 q^{13} +(-10.0000 + 13.7638i) q^{14} +(-12.9443 + 9.40456i) q^{16} +23.8885 q^{17} +9.40456i q^{19} +(-2.76393 - 8.50651i) q^{20} +(-2.11146 + 2.90617i) q^{22} -16.1150i q^{23} +5.00000 q^{25} +(0.763932 + 0.555029i) q^{26} +(-32.3607 + 10.5146i) q^{28} -6.94427 q^{29} -47.4468i q^{31} -32.0000 q^{32} +(38.6525 + 28.0827i) q^{34} -19.0211i q^{35} +26.3607 q^{37} +(-11.0557 + 15.2169i) q^{38} +(5.52786 - 17.0130i) q^{40} +41.4164 q^{41} +2.00811i q^{43} +(-6.83282 + 2.22012i) q^{44} +(18.9443 - 26.0746i) q^{46} -35.3481i q^{47} -23.3607 q^{49} +(8.09017 + 5.87785i) q^{50} +(0.583592 + 1.79611i) q^{52} +21.6393 q^{53} -4.01623i q^{55} +(-64.7214 - 21.0292i) q^{56} +(-11.2361 - 8.16348i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(55.7771 - 76.7706i) q^{62} +(-51.7771 - 37.6183i) q^{64} -1.05573 q^{65} -88.8693i q^{67} +(29.5279 + 90.8774i) q^{68} +(22.3607 - 30.7768i) q^{70} -39.4144i q^{71} +137.554 q^{73} +(42.6525 + 30.9888i) q^{74} +(-35.7771 + 11.6247i) q^{76} -15.2786 q^{77} +113.703i q^{79} +(28.9443 - 21.0292i) q^{80} +(67.0132 + 48.6879i) q^{82} +21.2412i q^{83} -53.4164 q^{85} +(-2.36068 + 3.24920i) q^{86} +(-13.6656 - 4.44023i) q^{88} -67.4427 q^{89} +4.01623i q^{91} +(61.3050 - 19.9192i) q^{92} +(41.5542 - 57.1944i) q^{94} -21.0292i q^{95} -39.1672 q^{97} +(-37.7984 - 27.4621i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 10 q^{10} - 16 q^{13} - 40 q^{14} - 16 q^{16} + 24 q^{17} - 20 q^{20} - 80 q^{22} + 20 q^{25} + 12 q^{26} - 40 q^{28} + 8 q^{29} - 128 q^{32} + 92 q^{34} + 16 q^{37} - 80 q^{38} + 40 q^{40} + 112 q^{41} + 80 q^{44} + 40 q^{46} - 4 q^{49} + 10 q^{50} + 56 q^{52} + 176 q^{53} - 80 q^{56} - 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} - 40 q^{65} + 136 q^{68} + 264 q^{73} + 108 q^{74} - 240 q^{77} + 80 q^{80} + 116 q^{82} - 160 q^{85} + 80 q^{86} + 160 q^{88} + 88 q^{89} + 120 q^{92} - 120 q^{94} - 264 q^{97} - 102 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 10 * q^10 - 16 * q^13 - 40 * q^14 - 16 * q^16 + 24 * q^17 - 20 * q^20 - 80 * q^22 + 20 * q^25 + 12 * q^26 - 40 * q^28 + 8 * q^29 - 128 * q^32 + 92 * q^34 + 16 * q^37 - 80 * q^38 + 40 * q^40 + 112 * q^41 + 80 * q^44 + 40 * q^46 - 4 * q^49 + 10 * q^50 + 56 * q^52 + 176 * q^53 - 80 * q^56 - 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 - 40 * q^65 + 136 * q^68 + 264 * q^73 + 108 * q^74 - 240 * q^77 + 80 * q^80 + 116 * q^82 - 160 * q^85 + 80 * q^86 + 160 * q^88 + 88 * q^89 + 120 * q^92 - 120 * q^94 - 264 * q^97 - 102 * q^98

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