LMFDB - Embedded newform 144.3.m.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.2
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573183 - 1.91611i) q^{2} +(-3.34292 - 2.19656i) q^{4} +(-3.68585 + 3.68585i) q^{5} -9.66442 q^{7} +(-6.12494 + 5.14637i) q^{8} +O(q^{10})$	\(q+(0.573183 - 1.91611i) q^{2} +(-3.34292 - 2.19656i) q^{4} +(-3.68585 + 3.68585i) q^{5} -9.66442 q^{7} +(-6.12494 + 5.14637i) q^{8} +(4.94981 + 9.17513i) q^{10} +(-5.51806 - 5.51806i) q^{11} +(-6.27131 - 6.27131i) q^{13} +(-5.53948 + 18.5181i) q^{14} +(6.35027 + 14.6858i) q^{16} +6.78623 q^{17} +(13.5181 - 13.5181i) q^{19} +(20.4177 - 4.22533i) q^{20} +(-13.7360 + 7.41033i) q^{22} -17.0790 q^{23} -2.17092i q^{25} +(-15.6111 + 8.42188i) q^{26} +(32.3074 + 21.2285i) q^{28} +(-4.85677 - 4.85677i) q^{29} -5.25662i q^{31} +(31.7795 - 3.75011i) q^{32} +(3.88975 - 13.0031i) q^{34} +(35.6216 - 35.6216i) q^{35} +(-18.1856 + 18.1856i) q^{37} +(-18.1537 - 33.6503i) q^{38} +(3.60688 - 41.5443i) q^{40} +48.2302i q^{41} +(-54.5113 - 54.5113i) q^{43} +(6.32571 + 30.5672i) q^{44} +(-9.78937 + 32.7251i) q^{46} -40.4015i q^{47} +44.4011 q^{49} +(-4.15972 - 1.24434i) q^{50} +(7.18921 + 34.7398i) q^{52} +(-10.8996 + 10.8996i) q^{53} +40.6774 q^{55} +(59.1940 - 49.7367i) q^{56} +(-12.0899 + 6.52227i) q^{58} +(-50.8898 - 50.8898i) q^{59} +(-17.0147 - 17.0147i) q^{61} +(-10.0722 - 3.01300i) q^{62} +(11.0298 - 63.0424i) q^{64} +46.2302 q^{65} +(22.9191 - 22.9191i) q^{67} +(-22.6858 - 14.9063i) q^{68} +(-47.8370 - 88.6724i) q^{70} +51.6047 q^{71} +78.5032i q^{73} +(24.4219 + 45.2692i) q^{74} +(-74.8830 + 15.4966i) q^{76} +(53.3288 + 53.3288i) q^{77} +108.512i q^{79} +(-77.5359 - 30.7237i) q^{80} +(92.4141 + 27.6447i) q^{82} +(-57.3173 + 57.3173i) q^{83} +(-25.0130 + 25.0130i) q^{85} +(-135.694 + 73.2045i) q^{86} +(62.1957 + 5.39985i) q^{88} -44.1276i q^{89} +(60.6086 + 60.6086i) q^{91} +(57.0937 + 37.5149i) q^{92} +(-77.4136 - 23.1575i) q^{94} +99.6510i q^{95} +112.700 q^{97} +(25.4499 - 85.0772i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8	$ 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} + 36 q^{10} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 40 q^{16} + 4 q^{17} + 30 q^{19} + 84 q^{20} - 52 q^{22} - 60 q^{23} - 96 q^{26} + 56 q^{28} + 18 q^{29} - 8 q^{32} - 76 q^{34} + 100 q^{35} + 46 q^{37} - 40 q^{38} + 40 q^{40} - 114 q^{43} - 20 q^{44} + 28 q^{46} - 46 q^{49} - 46 q^{50} + 100 q^{52} - 78 q^{53} + 252 q^{55} + 168 q^{56} - 176 q^{58} - 206 q^{59} + 30 q^{61} + 144 q^{62} + 64 q^{64} - 12 q^{65} - 226 q^{67} - 112 q^{68} - 16 q^{70} + 260 q^{71} + 92 q^{74} - 188 q^{76} + 212 q^{77} - 232 q^{80} + 304 q^{82} - 318 q^{83} - 212 q^{85} - 268 q^{86} - 8 q^{88} + 188 q^{91} + 168 q^{92} + 48 q^{94} - 4 q^{97} - 10 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 + 36 * q^10 + 18 * q^11 - 2 * q^13 - 12 * q^14 - 40 * q^16 + 4 * q^17 + 30 * q^19 + 84 * q^20 - 52 * q^22 - 60 * q^23 - 96 * q^26 + 56 * q^28 + 18 * q^29 - 8 * q^32 - 76 * q^34 + 100 * q^35 + 46 * q^37 - 40 * q^38 + 40 * q^40 - 114 * q^43 - 20 * q^44 + 28 * q^46 - 46 * q^49 - 46 * q^50 + 100 * q^52 - 78 * q^53 + 252 * q^55 + 168 * q^56 - 176 * q^58 - 206 * q^59 + 30 * q^61 + 144 * q^62 + 64 * q^64 - 12 * q^65 - 226 * q^67 - 112 * q^68 - 16 * q^70 + 260 * q^71 + 92 * q^74 - 188 * q^76 + 212 * q^77 - 232 * q^80 + 304 * q^82 - 318 * q^83 - 212 * q^85 - 268 * q^86 - 8 * q^88 + 188 * q^91 + 168 * q^92 + 48 * q^94 - 4 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.573183	−	1.91611i	0.286591	−	0.958053i
$2$	0.573183	−	1.91611i	0.286591	−	0.958053i
$3$		0			0
$3$		0			0
$4$	−3.34292	−	2.19656i	−0.835731	−	0.549139i
$5$	−3.68585	+	3.68585i	−0.737169	+	0.737169i	−0.972029	−	0.234860i	$-0.924537\pi$
$5$	−3.68585	+	3.68585i	−0.737169	+	0.737169i	0.234860	+	0.972029i	$0.424537\pi$
$6$		0			0
$7$	−9.66442			−1.38063			−0.690316	−	0.723508i	$-0.742528\pi$
$7$	−9.66442			−1.38063			−0.690316	+	0.723508i	$0.742528\pi$
$8$	−6.12494	+	5.14637i	−0.765618	+	0.643296i
$9$		0			0
$10$	4.94981	+	9.17513i	0.494981	+	0.917513i
$11$	−5.51806	−	5.51806i	−0.501642	−	0.501642i	0.410306	−	0.911948i	$-0.365422\pi$
$11$	−5.51806	−	5.51806i	−0.501642	−	0.501642i	−0.911948	+	0.410306i	$0.865422\pi$
$12$		0			0
$13$	−6.27131	−	6.27131i	−0.482408	−	0.482408i	0.423492	−	0.905900i	$-0.360804\pi$
$13$	−6.27131	−	6.27131i	−0.482408	−	0.482408i	−0.905900	+	0.423492i	$0.860804\pi$
$14$	−5.53948	+	18.5181i	−0.395677	+	1.32272i
$15$		0			0
$16$	6.35027	+	14.6858i	0.396892	+	0.917865i
$17$	6.78623			0.399190			0.199595	−	0.979878i	$-0.436037\pi$
$17$	6.78623			0.399190			0.199595	+	0.979878i	$0.436037\pi$
$18$		0			0
$19$	13.5181	−	13.5181i	0.711477	−	0.711477i	−0.255367	−	0.966844i	$-0.582196\pi$
$19$	13.5181	−	13.5181i	0.711477	−	0.711477i	0.966844	+	0.255367i	$0.0821964\pi$
$20$	20.4177	−	4.22533i	1.02088	−	0.211266i
$21$		0			0
$22$	−13.7360	+	7.41033i	−0.624365	+	0.336833i
$23$	−17.0790			−0.742564			−0.371282	−	0.928520i	$-0.621082\pi$
$23$	−17.0790			−0.742564			−0.371282	+	0.928520i	$0.621082\pi$
$24$		0			0
$25$		−	2.17092i		−	0.0868370i
$26$	−15.6111	+	8.42188i	−0.600427	+	0.323919i
$27$		0			0
$28$	32.3074	+	21.2285i	1.15384	+	0.758159i
$29$	−4.85677	−	4.85677i	−0.167475	−	0.167475i	0.618394	−	0.785868i	$-0.287784\pi$
$29$	−4.85677	−	4.85677i	−0.167475	−	0.167475i	−0.785868	+	0.618394i	$0.787784\pi$
$30$		0			0
$31$		−	5.25662i		−	0.169568i	−0.996399	−	0.0847841i	$-0.972980\pi$
$31$		−	5.25662i		−	0.169568i	0.996399	−	0.0847841i	$-0.0270201\pi$
$32$	31.7795	−	3.75011i	0.993109	−	0.117191i
$33$		0			0
$34$	3.88975	−	13.0031i	0.114404	−	0.382445i
$35$	35.6216	−	35.6216i	1.01776	−	1.01776i
$36$		0			0
$37$	−18.1856	+	18.1856i	−0.491503	+	0.491503i	−0.908780	−	0.417276i	$-0.862985\pi$
$37$	−18.1856	+	18.1856i	−0.491503	+	0.491503i	0.417276	+	0.908780i	$0.362985\pi$
$38$	−18.1537	−	33.6503i	−0.477729	−	0.885535i
$39$		0			0
$40$	3.60688	−	41.5443i	0.0901721	−	1.03861i
$41$			48.2302i			1.17635i	0.808735	+	0.588173i	$0.200152\pi$
$41$			48.2302i			1.17635i	−0.808735	+	0.588173i	$0.799848\pi$
$42$		0			0
$43$	−54.5113	−	54.5113i	−1.26771	−	1.26771i	−0.947271	−	0.320435i	$-0.896171\pi$
$43$	−54.5113	−	54.5113i	−1.26771	−	1.26771i	−0.320435	−	0.947271i	$-0.603829\pi$
$44$	6.32571	+	30.5672i	0.143766	+	0.694709i
$45$		0			0
$46$	−9.78937	+	32.7251i	−0.212812	+	0.711415i
$47$		−	40.4015i		−	0.859607i	−0.902922	−	0.429804i	$-0.858583\pi$
$47$		−	40.4015i		−	0.859607i	0.902922	−	0.429804i	$-0.141417\pi$
$48$		0			0
$49$	44.4011			0.906144
$50$	−4.15972	−	1.24434i	−0.0831944	−	0.0248867i
$51$		0			0
$52$	7.18921	+	34.7398i	0.138254	+	0.668073i
$53$	−10.8996	+	10.8996i	−0.205653	+	0.205653i	−0.802417	−	0.596764i	$-0.796453\pi$
$53$	−10.8996	+	10.8996i	−0.205653	+	0.205653i	0.596764	+	0.802417i	$0.296453\pi$
$54$		0			0
$55$	40.6774			0.739590
$56$	59.1940	−	49.7367i	1.05704	−	0.888155i
$57$		0			0
$58$	−12.0899	+	6.52227i	−0.208447	+	0.112453i
$59$	−50.8898	−	50.8898i	−0.862538	−	0.862538i	0.129094	−	0.991632i	$-0.458793\pi$
$59$	−50.8898	−	50.8898i	−0.862538	−	0.862538i	−0.991632	+	0.129094i	$0.958793\pi$
$60$		0			0
$61$	−17.0147	−	17.0147i	−0.278929	−	0.278929i	0.553752	−	0.832682i	$-0.313196\pi$
$61$	−17.0147	−	17.0147i	−0.278929	−	0.278929i	−0.832682	+	0.553752i	$0.813196\pi$
$62$	−10.0722	−	3.01300i	−0.162455	−	0.0485968i
$63$		0			0
$64$	11.0298	−	63.0424i	0.172341	−	0.985037i
$65$	46.2302			0.711233
$66$		0			0
$67$	22.9191	−	22.9191i	0.342077	−	0.342077i	−0.515071	−	0.857148i	$-0.672234\pi$
$67$	22.9191	−	22.9191i	0.342077	−	0.342077i	0.857148	+	0.515071i	$0.172234\pi$
$68$	−22.6858	−	14.9063i	−0.333615	−	0.219211i
$69$		0			0
$70$	−47.8370	−	88.6724i	−0.683386	−	1.26675i
$71$	51.6047			0.726827			0.363414	−	0.931628i	$-0.381611\pi$
$71$	51.6047			0.726827			0.363414	+	0.931628i	$0.381611\pi$
$72$		0			0
$73$			78.5032i			1.07539i	0.843141	+	0.537693i	$0.180704\pi$
$73$			78.5032i			1.07539i	−0.843141	+	0.537693i	$0.819296\pi$
$74$	24.4219	+	45.2692i	0.330025	+	0.611747i
$75$		0			0
$76$	−74.8830	+	15.4966i	−0.985303	+	0.203903i
$77$	53.3288	+	53.3288i	0.692582	+	0.692582i
$78$		0			0
$79$			108.512i			1.37357i	0.726859	+	0.686787i	$0.240979\pi$
$79$			108.512i			1.37357i	−0.726859	+	0.686787i	$0.759021\pi$
$80$	−77.5359	−	30.7237i	−0.969199	−	0.384046i
$81$		0			0
$82$	92.4141	+	27.6447i	1.12700	+	0.337130i
$83$	−57.3173	+	57.3173i	−0.690570	+	0.690570i	−0.962357	−	0.271788i	$-0.912385\pi$
$83$	−57.3173	+	57.3173i	−0.690570	+	0.690570i	0.271788	+	0.962357i	$0.412385\pi$
$84$		0			0
$85$	−25.0130	+	25.0130i	−0.294271	+	0.294271i
$86$	−135.694	+	73.2045i	−1.57784	+	0.851215i
$87$		0			0
$88$	62.1957	+	5.39985i	0.706770	+	0.0613619i
$89$		−	44.1276i		−	0.495816i	−0.968784	−	0.247908i	$-0.920257\pi$
$89$		−	44.1276i		−	0.495816i	0.968784	−	0.247908i	$-0.0797431\pi$
$90$		0			0
$91$	60.6086	+	60.6086i	0.666028	+	0.666028i
$92$	57.0937	+	37.5149i	0.620583	+	0.407771i
$93$		0			0
$94$	−77.4136	−	23.1575i	−0.823549	−	0.246356i
$95$			99.6510i			1.04896i
$96$		0			0
$97$	112.700			1.16185			0.580926	−	0.813956i	$-0.302691\pi$
$97$	112.700			1.16185			0.580926	+	0.813956i	$0.302691\pi$
$98$	25.4499	−	85.0772i	0.259693	−	0.868134i
$99$		0			0
$100$	−4.76856	+	7.25723i	−0.0476856	+	0.0725723i
$101$	−97.3859	+	97.3859i	−0.964217	+	0.964217i	−0.999382	−	0.0351644i	$-0.988805\pi$
$101$	−97.3859	+	97.3859i	−0.964217	+	0.964217i	0.0351644	+	0.999382i	$0.488805\pi$
$102$		0			0
$103$	−138.698			−1.34658			−0.673290	−	0.739379i	$-0.735119\pi$
$103$	−138.698			−1.34658			−0.673290	+	0.739379i	$0.735119\pi$
$104$	70.6858	+	6.13696i	0.679672	+	0.0590092i
$105$		0			0
$106$	14.6373	+	27.1323i	0.138088	+	0.255965i
$107$	31.7386	+	31.7386i	0.296622	+	0.296622i	0.839689	−	0.543067i	$-0.182737\pi$
$107$	31.7386	+	31.7386i	0.296622	+	0.296622i	−0.543067	+	0.839689i	$0.682737\pi$
$108$		0			0
$109$	0.712308	+	0.712308i	0.00653493	+	0.00653493i	0.710367	−	0.703832i	$-0.248529\pi$
$109$	0.712308	+	0.712308i	0.00653493	+	0.00653493i	−0.703832	+	0.710367i	$0.748529\pi$
$110$	23.3156	−	77.9423i	0.211960	−	0.708566i
$111$		0			0
$112$	−61.3717	−	141.930i	−0.547962	−	1.26723i
$113$	−14.8888			−0.131759			−0.0658795	−	0.997828i	$-0.520985\pi$
$113$	−14.8888			−0.131759			−0.0658795	+	0.997828i	$0.520985\pi$
$114$		0			0
$115$	62.9504	−	62.9504i	0.547395	−	0.547395i
$116$	5.56763	+	26.9040i	0.0479968	+	0.231931i
$117$		0			0
$118$	−126.679	+	68.3410i	−1.07355	+	0.579161i
$119$	−65.5850			−0.551134
$120$		0			0
$121$		−	60.1021i		−	0.496711i
$122$	−42.3545	+	22.8494i	−0.347168	+	0.187290i
$123$		0			0
$124$	−11.5465	+	17.5725i	−0.0931166	+	0.141713i
$125$	−84.1445	−	84.1445i	−0.673156	−	0.673156i
$126$		0			0
$127$			106.861i			0.841425i	0.907194	+	0.420712i	$0.138220\pi$
$127$			106.861i			0.841425i	−0.907194	+	0.420712i	$0.861780\pi$
$128$	−114.474	−	57.2692i	−0.894326	−	0.447415i
$129$		0			0
$130$	26.4983	−	88.5819i	0.203833	−	0.681399i
$131$	153.198	−	153.198i	1.16945	−	1.16945i	0.187116	−	0.982338i	$-0.440086\pi$
$131$	153.198	−	153.198i	1.16945	−	1.16945i	0.982338	−	0.187116i	$-0.0599139\pi$
$132$		0			0
$133$	−130.644	+	130.644i	−0.982287	+	0.982287i
$134$	−30.7786	−	57.0523i	−0.229691	−	0.425764i
$135$		0			0
$136$	−41.5653	+	34.9244i	−0.305627	+	0.256797i
$137$			75.1700i			0.548686i	0.961632	+	0.274343i	$0.0884604\pi$
$137$			75.1700i			0.548686i	−0.961632	+	0.274343i	$0.911540\pi$
$138$		0			0
$139$	−107.425	−	107.425i	−0.772843	−	0.772843i	0.205760	−	0.978603i	$-0.434034\pi$
$139$	−107.425	−	107.425i	−0.772843	−	0.772843i	−0.978603	+	0.205760i	$0.934034\pi$
$140$	−197.325	+	40.8353i	−1.40946	+	0.291681i
$141$		0			0
$142$	29.5789	−	98.8801i	0.208302	−	0.696339i
$143$			69.2109i			0.483992i
$144$		0			0
$145$	35.8026			0.246915
$146$	150.420	+	44.9967i	1.03028	+	0.308196i
$147$		0			0
$148$	100.739	−	20.8474i	0.680668	−	0.140861i
$149$	146.031	−	146.031i	0.980074	−	0.980074i	−0.0197310	−	0.999805i	$-0.506281\pi$
$149$	146.031	−	146.031i	0.980074	−	0.980074i	0.999805	+	0.0197310i	$0.00628097\pi$
$150$		0			0
$151$	220.513			1.46035			0.730175	−	0.683260i	$-0.239439\pi$
$151$	220.513			1.46035			0.730175	+	0.683260i	$0.239439\pi$
$152$	−13.2285	+	152.366i	−0.0870294	+	1.00241i
$153$		0			0
$154$	132.751	−	71.6165i	0.862019	−	0.465042i
$155$	19.3751	+	19.3751i	0.125000	+	0.125000i
$156$		0			0
$157$	−109.561	−	109.561i	−0.697839	−	0.697839i	0.266105	−	0.963944i	$-0.414263\pi$
$157$	−109.561	−	109.561i	−0.697839	−	0.697839i	−0.963944	+	0.266105i	$0.914263\pi$
$158$	207.921	+	62.1974i	1.31596	+	0.393654i
$159$		0			0
$160$	−103.312	+	130.957i	−0.645700	+	0.818479i
$161$	165.058			1.02521
$162$		0			0
$163$	56.7781	−	56.7781i	0.348332	−	0.348332i	−0.511156	−	0.859488i	$-0.670783\pi$
$163$	56.7781	−	56.7781i	0.348332	−	0.348332i	0.859488	+	0.511156i	$0.170783\pi$
$164$	105.940	−	161.230i	0.645978	−	0.983108i
$165$		0			0
$166$	76.9727	+	142.679i	0.463691	+	0.859514i
$167$	−106.677			−0.638781			−0.319391	−	0.947623i	$-0.603478\pi$
$167$	−106.677			−0.638781			−0.319391	+	0.947623i	$0.603478\pi$
$168$		0			0
$169$		−	90.3414i		−	0.534564i
$170$	33.5905	+	62.2646i	0.197591	+	0.366262i
$171$		0			0
$172$	62.4899	+	301.964i	0.363313	+	1.75561i
$173$	−178.360	−	178.360i	−1.03098	−	1.03098i	−0.999504	−	0.0314805i	$-0.989978\pi$
$173$	−178.360	−	178.360i	−1.03098	−	1.03098i	−0.0314805	−	0.999504i	$-0.510022\pi$
$174$		0			0
$175$			20.9807i			0.119890i
$176$	45.9962	−	116.079i	0.261342	−	0.659537i
$177$		0			0
$178$	−84.5532	−	25.2932i	−0.475018	−	0.142097i
$179$	−60.4622	+	60.4622i	−0.337778	+	0.337778i	−0.855530	−	0.517753i	$-0.826769\pi$
$179$	−60.4622	+	60.4622i	−0.337778	+	0.337778i	0.517753	+	0.855530i	$0.326769\pi$
$180$		0			0
$181$	147.113	−	147.113i	0.812779	−	0.812779i	−0.172271	−	0.985050i	$-0.555110\pi$
$181$	147.113	−	147.113i	0.812779	−	0.812779i	0.985050	+	0.172271i	$0.0551105\pi$
$182$	150.872	−	81.3927i	0.828968	−	0.447212i
$183$		0			0
$184$	104.608	−	87.8946i	0.568520	−	0.477688i
$185$		−	134.059i		−	0.724642i
$186$		0			0
$187$	−37.4468	−	37.4468i	−0.200250	−	0.200250i
$188$	−88.7443	+	135.059i	−0.472044	+	0.718400i
$189$		0			0
$190$	190.942	+	57.1182i	1.00496	+	0.300622i
$191$			106.861i			0.559481i	0.960076	+	0.279741i	$0.0902485\pi$
$191$			106.861i			0.559481i	−0.960076	+	0.279741i	$0.909752\pi$
$192$		0			0
$193$	68.1873			0.353302			0.176651	−	0.984274i	$-0.443474\pi$
$193$	68.1873			0.353302			0.176651	+	0.984274i	$0.443474\pi$
$194$	64.5975	−	215.944i	0.332977	−	1.11312i
$195$		0			0
$196$	−148.429	−	97.5295i	−0.757293	−	0.497600i
$197$	61.8529	−	61.8529i	0.313974	−	0.313974i	−0.532473	−	0.846447i	$-0.678737\pi$
$197$	61.8529	−	61.8529i	0.313974	−	0.313974i	0.846447	+	0.532473i	$0.178737\pi$
$198$		0			0
$199$	−158.466			−0.796310			−0.398155	−	0.917318i	$-0.630349\pi$
$199$	−158.466			−0.796310			−0.398155	+	0.917318i	$0.630349\pi$
$200$	11.1724	+	13.2968i	0.0558618	+	0.0664839i
$201$		0			0
$202$	130.782	+	242.422i	0.647435	+	1.20011i
$203$	46.9379	+	46.9379i	0.231221	+	0.231221i
$204$		0			0
$205$	−177.769	−	177.769i	−0.867166	−	0.867166i
$206$	−79.4991	+	265.759i	−0.385918	+	1.29009i
$207$		0			0
$208$	52.2750	−	131.924i	0.251322	−	0.634250i
$209$	−149.187			−0.713813
$210$		0			0
$211$	−197.031	+	197.031i	−0.933798	+	0.933798i	−0.997941	−	0.0641430i	$-0.979569\pi$
$211$	−197.031	+	197.031i	−0.933798	+	0.933798i	0.0641430	+	0.997941i	$0.479569\pi$
$212$	60.3782	−	12.4949i	0.284803	−	0.0589384i
$213$		0			0
$214$	79.0064	−	42.6224i	0.369189	−	0.199170i
$215$	401.841			1.86903
$216$		0			0
$217$			50.8022i			0.234111i
$218$	1.77314	−	0.956574i	0.00813366	−	0.00438796i
$219$		0			0
$220$	−135.982	−	89.3503i	−0.618098	−	0.406138i
$221$	−42.5585	−	42.5585i	−0.192573	−	0.192573i
$222$		0			0
$223$			15.7698i			0.0707168i	0.999375	+	0.0353584i	$0.0112573\pi$
$223$			15.7698i			0.0707168i	−0.999375	+	0.0353584i	$0.988743\pi$
$224$	−307.131	+	36.2427i	−1.37112	+	0.161798i
$225$		0			0
$226$	−8.53398	+	28.5284i	−0.0377610	+	0.126232i
$227$	−199.289	+	199.289i	−0.877927	+	0.877927i	−0.993320	−	0.115393i	$-0.963187\pi$
$227$	−199.289	+	199.289i	−0.877927	+	0.877927i	0.115393	+	0.993320i	$0.463187\pi$
$228$		0			0
$229$	230.522	−	230.522i	1.00664	−	1.00664i	0.00666715	−	0.999978i	$-0.497878\pi$
$229$	230.522	−	230.522i	1.00664	−	1.00664i	0.999978	−	0.00666715i	$-0.00212224\pi$
$230$	−84.5376	−	156.702i	−0.367555	−	0.681312i
$231$		0			0
$232$	54.7422	+	4.75272i	0.235958	+	0.0204859i
$233$		−	344.791i		−	1.47979i	−0.672722	−	0.739895i	$-0.734875\pi$
$233$		−	344.791i		−	1.47979i	0.672722	−	0.739895i	$-0.265125\pi$
$234$		0			0
$235$	148.914	+	148.914i	0.633676	+	0.633676i
$236$	58.3383	+	281.903i	0.247196	+	1.19450i
$237$		0			0
$238$	−37.5922	+	125.668i	−0.157950	+	0.528016i
$239$			77.1978i			0.323004i	0.986872	+	0.161502i	$0.0516337\pi$
$239$			77.1978i			0.323004i	−0.986872	+	0.161502i	$0.948366\pi$
$240$		0			0
$241$	−293.483			−1.21777			−0.608885	−	0.793259i	$-0.708383\pi$
$241$	−293.483			−1.21777			−0.608885	+	0.793259i	$0.708383\pi$
$242$	−115.162	−	34.4495i	−0.475876	−	0.142353i
$243$		0			0
$244$	19.5051	+	94.2526i	0.0799388	+	0.386281i
$245$	−163.656	+	163.656i	−0.667982	+	0.667982i
$246$		0			0
$247$	−169.552			−0.686445
$248$	27.0525	+	32.1965i	0.109083	+	0.129824i
$249$		0			0
$250$	−209.460	+	113.000i	−0.837839	+	0.451998i
$251$	−79.6322	−	79.6322i	−0.317260	−	0.317260i	0.530454	−	0.847714i	$-0.322021\pi$
$251$	−79.6322	−	79.6322i	−0.317260	−	0.317260i	−0.847714	+	0.530454i	$0.822021\pi$
$252$		0			0
$253$	94.2427	+	94.2427i	0.372501	+	0.372501i
$254$	204.757	+	61.2508i	0.806129	+	0.241145i
$255$		0			0
$256$	−175.348	+	186.518i	−0.684954	+	0.728587i
$257$	−221.860			−0.863270			−0.431635	−	0.902048i	$-0.642063\pi$
$257$	−221.860			−0.863270			−0.431635	+	0.902048i	$0.642063\pi$
$258$		0			0
$259$	175.753	−	175.753i	0.678585	−	0.678585i
$260$	−154.544	−	101.547i	−0.594399	−	0.390566i
$261$		0			0
$262$	−205.734	−	381.355i	−0.785243	−	1.45555i
$263$	−374.223			−1.42290			−0.711451	−	0.702736i	$-0.751961\pi$
$263$	−374.223			−1.42290			−0.711451	+	0.702736i	$0.751961\pi$
$264$		0			0
$265$		−	80.3486i		−	0.303202i
$266$	175.445	+	325.211i	0.659568	+	1.22260i
$267$		0			0
$268$	−126.960	+	26.2737i	−0.473732	+	0.0980362i
$269$	357.970	+	357.970i	1.33075	+	1.33075i	0.904704	+	0.426042i	$0.140092\pi$
$269$	357.970	+	357.970i	1.33075	+	1.33075i	0.426042	+	0.904704i	$0.359908\pi$
$270$		0			0
$271$		−	359.030i		−	1.32484i	−0.749135	−	0.662418i	$-0.769530\pi$
$271$		−	359.030i		−	1.32484i	0.749135	−	0.662418i	$-0.230470\pi$
$272$	43.0944	+	99.6615i	0.158435	+	0.366403i
$273$		0			0
$274$	144.034	+	43.0862i	0.525670	+	0.157249i
$275$	−11.9793	+	11.9793i	−0.0435610	+	0.0435610i
$276$		0			0
$277$	−351.765	+	351.765i	−1.26991	+	1.26991i	−0.323775	+	0.946134i	$0.604952\pi$
$277$	−351.765	+	351.765i	−1.26991	+	1.26991i	−0.946134	+	0.323775i	$0.895048\pi$
$278$	−267.412	+	144.264i	−0.961915	+	0.518934i
$279$		0			0
$280$	−34.8585	+	401.502i	−0.124495	+	1.43393i
$281$			191.390i			0.681103i	0.940226	+	0.340552i	$0.110614\pi$
$281$			191.390i			0.681103i	−0.940226	+	0.340552i	$0.889386\pi$
$282$		0			0
$283$	−31.3119	−	31.3119i	−0.110643	−	0.110643i	0.649618	−	0.760261i	$-0.274929\pi$
$283$	−31.3119	−	31.3119i	−0.110643	−	0.110643i	−0.760261	+	0.649618i	$0.774929\pi$
$284$	−172.511	−	113.353i	−0.607432	−	0.399129i
$285$		0			0
$286$	132.615	+	39.6705i	0.463690	+	0.138708i
$287$		−	466.117i		−	1.62410i
$288$		0			0
$289$	−242.947			−0.840647
$290$	20.5214	−	68.6016i	0.0707636	−	0.236557i
$291$		0			0
$292$	172.437	−	262.430i	0.590537	−	0.898733i
$293$	92.0889	−	92.0889i	0.314297	−	0.314297i	−0.532275	−	0.846572i	$-0.678663\pi$
$293$	92.0889	−	92.0889i	0.314297	−	0.314297i	0.846572	+	0.532275i	$0.178663\pi$
$294$		0			0
$295$	375.144			1.27167
$296$	17.7960	−	204.976i	0.0601217	−	0.692485i
$297$		0			0
$298$	−196.109	−	363.513i	−0.658082	−	1.21984i
$299$	107.107	+	107.107i	0.358219	+	0.358219i
$300$		0			0
$301$	526.821	+	526.821i	1.75023	+	1.75023i
$302$	126.394	−	422.526i	0.418524	−	1.39909i
$303$		0			0
$304$	284.367	+	112.681i	0.935419	+	0.370661i
$305$	125.427			0.411236
$306$		0			0
$307$	−257.566	+	257.566i	−0.838978	+	0.838978i	−0.988724	−	0.149746i	$-0.952154\pi$
$307$	−257.566	+	257.566i	−0.838978	+	0.838978i	0.149746	+	0.988724i	$0.452154\pi$
$308$	−61.1343	−	295.414i	−0.198488	−	0.959137i
$309$		0			0
$310$	48.2302	−	26.0192i	0.155581	−	0.0839330i
$311$	130.914			0.420946			0.210473	−	0.977600i	$-0.432500\pi$
$311$	130.914			0.420946			0.210473	+	0.977600i	$0.432500\pi$
$312$		0			0
$313$		−	51.8354i		−	0.165608i	−0.996566	−	0.0828041i	$-0.973612\pi$
$313$		−	51.8354i		−	0.165608i	0.996566	−	0.0828041i	$-0.0263876\pi$
$314$	−272.728	+	147.132i	−0.868561	+	0.468572i
$315$		0			0
$316$	238.354	−	362.748i	0.754283	−	1.14794i
$317$	109.636	+	109.636i	0.345856	+	0.345856i	0.858563	−	0.512707i	$-0.171357\pi$
$317$	109.636	+	109.636i	0.345856	+	0.345856i	−0.512707	+	0.858563i	$0.671357\pi$
$318$		0			0
$319$			53.5999i			0.168025i
$320$	191.710	+	273.019i	0.599094	+	0.853184i
$321$		0			0
$322$	94.6086	−	316.269i	0.293815	−	0.982202i
$323$	91.7367	−	91.7367i	0.284014	−	0.284014i
$324$		0			0
$325$	−13.6145	+	13.6145i	−0.0418909	+	0.0418909i
$326$	−76.2486	−	141.337i	−0.233891	−	0.433549i
$327$		0			0
$328$	−248.210	−	295.407i	−0.756738	−	0.900631i
$329$			390.458i			1.18680i
$330$		0			0
$331$	323.226	+	323.226i	0.976515	+	0.976515i	0.999730	−	0.0232157i	$-0.00739046\pi$
$331$	323.226	+	323.226i	0.976515	+	0.976515i	−0.0232157	+	0.999730i	$0.507390\pi$
$332$	317.508	−	65.7066i	0.956349	−	0.197911i
$333$		0			0
$334$	−61.1451	+	204.403i	−0.183069	+	0.611986i
$335$			168.953i			0.504337i
$336$		0			0
$337$	315.159			0.935191			0.467596	−	0.883943i	$-0.345120\pi$
$337$	315.159			0.935191			0.467596	+	0.883943i	$0.345120\pi$
$338$	−173.104	−	51.7821i	−0.512141	−	0.153202i
$339$		0			0
$340$	138.559	−	28.6740i	0.407527	−	0.0843354i
$341$	−29.0063	+	29.0063i	−0.0850625	+	0.0850625i
$342$		0			0
$343$	44.4459			0.129580
$344$	614.414	+	53.3435i	1.78609	+	0.155068i
$345$		0			0
$346$	−443.990	+	239.524i	−1.28321	+	0.692267i
$347$	307.568	+	307.568i	0.886363	+	0.886363i	0.994172	−	0.107809i	$-0.0343835\pi$
$347$	307.568	+	307.568i	0.886363	+	0.886363i	−0.107809	+	0.994172i	$0.534384\pi$
$348$		0			0
$349$	170.461	+	170.461i	0.488427	+	0.488427i	0.907810	−	0.419382i	$-0.137753\pi$
$349$	170.461	+	170.461i	0.488427	+	0.488427i	−0.419382	+	0.907810i	$0.637753\pi$
$350$	40.2013	+	12.0258i	0.114861	+	0.0343594i
$351$		0			0
$352$	−196.054	−	154.668i	−0.556973	−	0.439397i
$353$	−238.136			−0.674606			−0.337303	−	0.941396i	$-0.609515\pi$
$353$	−238.136			−0.674606			−0.337303	+	0.941396i	$0.609515\pi$
$354$		0			0
$355$	−190.207	+	190.207i	−0.535795	+	0.535795i
$356$	−96.9289	+	147.515i	−0.272272	+	0.414369i
$357$		0			0
$358$	81.1961	+	150.508i	0.226805	+	0.420413i
$359$	−33.6470			−0.0937241			−0.0468620	−	0.998901i	$-0.514922\pi$
$359$	−33.6470			−0.0937241			−0.0468620	+	0.998901i	$0.514922\pi$
$360$		0			0
$361$		−	4.47577i		−	0.0123983i
$362$	−197.561	−	366.207i	−0.545750	−	1.01162i
$363$		0			0
$364$	−69.4796	−	335.740i	−0.190878	−	0.922363i
$365$	−289.351	−	289.351i	−0.792741	−	0.792741i
$366$		0			0
$367$		−	240.758i		−	0.656016i	−0.944675	−	0.328008i	$-0.893623\pi$
$367$		−	240.758i		−	0.656016i	0.944675	−	0.328008i	$-0.106377\pi$
$368$	−108.456	−	250.819i	−0.294717	−	0.681573i
$369$		0			0
$370$	−256.871	−	76.8402i	−0.694245	−	0.207676i
$371$	105.339	−	105.339i	0.283931	−	0.283931i
$372$		0			0
$373$	432.504	−	432.504i	1.15953	−	1.15953i	0.174951	−	0.984577i	$-0.444023\pi$
$373$	432.504	−	432.504i	1.15953	−	1.15953i	0.984577	−	0.174951i	$-0.0559766\pi$
$374$	−93.2159	+	50.2882i	−0.249240	+	0.134460i
$375$		0			0
$376$	207.921	+	247.457i	0.552982	+	0.658131i
$377$			60.9166i			0.161583i
$378$		0			0
$379$	−174.716	−	174.716i	−0.460993	−	0.460993i	0.437988	−	0.898981i	$-0.355691\pi$
$379$	−174.716	−	174.716i	−0.460993	−	0.460993i	−0.898981	+	0.437988i	$0.855691\pi$
$380$	218.889	−	333.126i	0.576024	−	0.876646i
$381$		0			0
$382$	204.757	+	61.2508i	0.536013	+	0.160343i
$383$		−	673.381i		−	1.75817i	−0.476661	−	0.879087i	$-0.658153\pi$
$383$		−	673.381i		−	1.75817i	0.476661	−	0.879087i	$-0.341847\pi$
$384$		0			0
$385$	−393.124			−1.02110
$386$	39.0838	−	130.654i	0.101253	−	0.338482i
$387$		0			0
$388$	−376.746	−	247.551i	−0.970995	−	0.638019i
$389$	274.646	−	274.646i	0.706031	−	0.706031i	−0.259667	−	0.965698i	$-0.583613\pi$
$389$	274.646	−	274.646i	0.706031	−	0.706031i	0.965698	+	0.259667i	$0.0836129\pi$
$390$		0			0
$391$	−115.902			−0.296424
$392$	−271.954	+	228.504i	−0.693760	+	0.582919i
$393$		0			0
$394$	−83.0637	−	153.970i	−0.210822	−	0.390786i
$395$	−399.960	−	399.960i	−1.01256	−	1.01256i
$396$		0			0
$397$	−271.254	−	271.254i	−0.683259	−	0.683259i	0.277474	−	0.960733i	$-0.410503\pi$
$397$	−271.254	−	271.254i	−0.683259	−	0.683259i	−0.960733	+	0.277474i	$0.910503\pi$
$398$	−90.8298	+	303.637i	−0.228216	+	0.762907i
$399$		0			0
$400$	31.8819	−	13.7860i	0.0797046	−	0.0344649i
$401$	415.193			1.03539			0.517697	−	0.855564i	$-0.326790\pi$
$401$	415.193			1.03539			0.517697	+	0.855564i	$0.326790\pi$
$402$		0			0
$403$	−32.9659	+	32.9659i	−0.0818011	+	0.0818011i
$404$	539.467	−	111.640i	1.33532	−	0.276336i
$405$		0			0
$406$	116.842	−	63.0340i	0.287788	−	0.155256i
$407$	200.699			0.493117
$408$		0			0
$409$			634.686i			1.55180i	0.630856	+	0.775900i	$0.282704\pi$
$409$			634.686i			1.55180i	−0.630856	+	0.775900i	$0.717296\pi$
$410$	−442.518	+	238.730i	−1.07931	+	0.582268i
$411$		0			0
$412$	463.656	+	304.657i	1.12538	+	0.739460i
$413$	491.820	+	491.820i	1.19085	+	1.19085i
$414$		0			0
$415$		−	422.525i		−	1.01813i
$416$	−222.817	−	175.781i	−0.535618	−	0.422550i
$417$		0			0
$418$	−85.5113	+	285.858i	−0.204573	+	0.683870i
$419$	−19.2687	+	19.2687i	−0.0459873	+	0.0459873i	−0.729726	−	0.683739i	$-0.760353\pi$
$419$	−19.2687	+	19.2687i	−0.0459873	+	0.0459873i	0.683739	+	0.729726i	$0.260353\pi$
$420$		0			0
$421$	244.505	−	244.505i	0.580773	−	0.580773i	−0.354343	−	0.935116i	$-0.615295\pi$
$421$	244.505	−	244.505i	0.580773	−	0.580773i	0.935116	+	0.354343i	$0.115295\pi$
$422$	264.598	+	490.468i	0.627009	+	1.16225i
$423$		0			0
$424$	10.6661	−	122.853i	0.0251559	−	0.289747i
$425$		−	14.7324i		−	0.0346644i
$426$		0			0
$427$	164.437	+	164.437i	0.385099	+	0.385099i
$428$	−36.3840	−	175.815i	−0.0850093	−	0.410783i
$429$		0			0
$430$	230.328	−	769.969i	0.535647	−	1.79063i
$431$			337.331i			0.782670i	0.920248	+	0.391335i	$0.127987\pi$
$431$			337.331i			0.782670i	−0.920248	+	0.391335i	$0.872013\pi$
$432$		0			0
$433$	−424.560			−0.980508			−0.490254	−	0.871580i	$-0.663096\pi$
$433$	−424.560			−0.980508			−0.490254	+	0.871580i	$0.663096\pi$
$434$	97.3423	+	29.1189i	0.224291	+	0.0670943i
$435$		0			0
$436$	−0.816565	−	3.94581i	−0.00187285	−	0.00905003i
$437$	−230.874	+	230.874i	−0.528317	+	0.528317i
$438$		0			0
$439$	−162.004			−0.369029			−0.184514	−	0.982830i	$-0.559071\pi$
$439$	−162.004			−0.369029			−0.184514	+	0.982830i	$0.559071\pi$
$440$	−249.147	+	209.341i	−0.566243	+	0.475775i
$441$		0			0
$442$	−105.940	+	57.1528i	−0.239684	+	0.129305i
$443$	−492.189	−	492.189i	−1.11104	−	1.11104i	−0.993010	−	0.118026i	$-0.962343\pi$
$443$	−492.189	−	492.189i	−1.11104	−	1.11104i	−0.118026	−	0.993010i	$-0.537657\pi$
$444$		0			0
$445$	162.648	+	162.648i	0.365500	+	0.365500i
$446$	30.2167	+	9.03900i	0.0677504	+	0.0202668i
$447$		0			0
$448$	−106.597	+	609.268i	−0.237940	+	1.35997i
$449$	−195.434			−0.435266			−0.217633	−	0.976031i	$-0.569834\pi$
$449$	−195.434			−0.435266			−0.217633	+	0.976031i	$0.569834\pi$
$450$		0			0
$451$	266.137	−	266.137i	0.590104	−	0.590104i
$452$	49.7720	+	32.7040i	0.110115	+	0.0723540i
$453$		0			0
$454$	267.630	+	496.089i	0.589494	+	1.09271i
$455$	−446.788			−0.981951
$456$		0			0
$457$			386.874i			0.846552i	0.906001	+	0.423276i	$0.139120\pi$
$457$			386.874i			0.846552i	−0.906001	+	0.423276i	$0.860880\pi$
$458$	−309.573	−	573.835i	−0.675923	−	1.25291i
$459$		0			0
$460$	−348.713	+	72.1642i	−0.758071	+	0.156879i
$461$	174.401	+	174.401i	0.378310	+	0.378310i	0.870492	−	0.492182i	$-0.163801\pi$
$461$	174.401	+	174.401i	0.378310	+	0.378310i	−0.492182	+	0.870492i	$0.663801\pi$
$462$		0			0
$463$			60.5295i			0.130733i	0.997861	+	0.0653666i	$0.0208217\pi$
$463$			60.5295i			0.130733i	−0.997861	+	0.0653666i	$0.979178\pi$
$464$	40.4840	−	102.168i	0.0872500	−	0.220189i
$465$		0			0
$466$	−660.656	−	197.628i	−1.41772	−	0.424095i
$467$	−306.482	+	306.482i	−0.656279	+	0.656279i	−0.954497	−	0.298219i	$-0.903607\pi$
$467$	−306.482	+	306.482i	−0.656279	+	0.656279i	0.298219	+	0.954497i	$0.403607\pi$
$468$		0			0
$469$	−221.500	+	221.500i	−0.472282	+	0.472282i
$470$	370.690	−	199.980i	0.788701	−	0.425489i
$471$		0			0
$472$	573.594	+	49.7995i	1.21524	+	0.105508i
$473$			601.593i			1.27187i
$474$		0			0
$475$	−29.3467	−	29.3467i	−0.0617825	−	0.0617825i
$476$	219.246	+	144.061i	0.460600	+	0.302650i
$477$		0			0
$478$	147.919	+	44.2485i	0.309454	+	0.0925700i
$479$		−	376.452i		−	0.785912i	−0.919557	−	0.392956i	$-0.871453\pi$
$479$		−	376.452i		−	0.785912i	0.919557	−	0.392956i	$-0.128547\pi$
$480$		0			0
$481$	228.095			0.474210
$482$	−168.219	+	562.344i	−0.349002	+	1.16669i
$483$		0			0
$484$	−132.018	+	200.917i	−0.272764	+	0.415117i
$485$	−415.393	+	415.393i	−0.856481	+	0.856481i
$486$		0			0
$487$	77.2033			0.158528			0.0792641	−	0.996854i	$-0.474743\pi$
$487$	77.2033			0.158528			0.0792641	+	0.996854i	$0.474743\pi$
$488$	191.778	+	16.6502i	0.392987	+	0.0341192i
$489$		0			0
$490$	219.777	+	407.386i	0.448524	+	0.831400i
$491$	581.438	+	581.438i	1.18419	+	1.18419i	0.978648	+	0.205543i	$0.0658960\pi$
$491$	581.438	+	581.438i	1.18419	+	1.18419i	0.205543	+	0.978648i	$0.434104\pi$
$492$		0			0
$493$	−32.9592	−	32.9592i	−0.0668543	−	0.0668543i
$494$	−97.1842	+	324.879i	−0.196729	+	0.657650i
$495$		0			0
$496$	77.1978	−	33.3809i	0.155641	−	0.0673002i
$497$	−498.730			−1.00348
$498$		0			0
$499$	−174.006	+	174.006i	−0.348709	+	0.348709i	−0.859629	−	0.510920i	$-0.829305\pi$
$499$	−174.006	+	174.006i	−0.348709	+	0.348709i	0.510920	+	0.859629i	$0.329305\pi$
$500$	96.4603	+	466.117i	0.192921	+	0.932233i
$501$		0			0
$502$	−198.228	+	106.940i	−0.394876	+	0.213028i
$503$	355.262			0.706286			0.353143	−	0.935569i	$-0.385113\pi$
$503$	355.262			0.706286			0.353143	+	0.935569i	$0.385113\pi$
$504$		0			0
$505$		−	717.899i		−	1.42158i
$506$	234.597	−	126.561i	0.463631	−	0.250120i
$507$		0			0
$508$	234.726	−	357.228i	0.462059	−	0.703204i
$509$	−279.667	−	279.667i	−0.549444	−	0.549444i	0.376836	−	0.926280i	$-0.377012\pi$
$509$	−279.667	−	279.667i	−0.549444	−	0.549444i	−0.926280	+	0.376836i	$0.877012\pi$
$510$		0			0
$511$		−	758.688i		−	1.48471i
$512$	256.882	+	442.895i	0.501723	+	0.865029i
$513$		0			0
$514$	−127.167	+	425.108i	−0.247406	+	0.827059i
$515$	511.218	−	511.218i	0.992657	−	0.992657i
$516$		0			0
$517$	−222.938	+	222.938i	−0.431215	+	0.431215i
$518$	−236.023	−	437.501i	−0.455644	−	0.844597i
$519$		0			0
$520$	−283.157	+	237.917i	−0.544533	+	0.457533i
$521$		−	705.745i		−	1.35460i	−0.735708	−	0.677299i	$-0.763151\pi$
$521$		−	705.745i		−	1.35460i	0.735708	−	0.677299i	$-0.236849\pi$
$522$		0			0
$523$	−186.762	−	186.762i	−0.357098	−	0.357098i	0.505644	−	0.862742i	$-0.331255\pi$
$523$	−186.762	−	186.762i	−0.357098	−	0.357098i	−0.862742	+	0.505644i	$0.831255\pi$
$524$	−848.640	+	175.621i	−1.61954	+	0.335155i
$525$		0			0
$526$	−214.498	+	717.051i	−0.407791	+	1.36321i
$527$		−	35.6726i		−	0.0676899i
$528$		0			0
$529$	−237.309			−0.448599
$530$	−153.956	−	46.0544i	−0.290484	−	0.0868952i
$531$		0			0
$532$	723.701	−	149.766i	1.36034	−	0.281515i
$533$	302.466	−	302.466i	0.567479	−	0.567479i
$534$		0			0
$535$	−233.967			−0.437321
$536$	−22.4281	+	258.329i	−0.0418435	+	0.481956i
$537$		0			0
$538$	891.092	−	480.727i	1.65630	−	0.893544i
$539$	−245.008	−	245.008i	−0.454560	−	0.454560i
$540$		0			0
$541$	119.274	+	119.274i	0.220470	+	0.220470i	0.808696	−	0.588226i	$-0.200174\pi$
$541$	119.274	+	119.274i	0.220470	+	0.220470i	−0.588226	+	0.808696i	$0.700174\pi$
$542$	−687.940	−	205.790i	−1.26926	−	0.379686i
$543$		0			0
$544$	215.663	−	25.4491i	0.396439	−	0.0467815i
$545$	−5.25091			−0.00963470
$546$		0			0
$547$	−141.472	+	141.472i	−0.258632	+	0.258632i	−0.824498	−	0.565865i	$-0.808542\pi$
$547$	−141.472	+	141.472i	−0.258632	+	0.258632i	0.565865	+	0.824498i	$0.308542\pi$
$548$	165.115	−	251.288i	0.301305	−	0.458554i
$549$		0			0
$550$	16.0873	+	29.8199i	0.0292496	+	0.0542180i
$551$	−131.308			−0.238309
$552$		0			0
$553$		−	1048.71i		−	1.89640i
$554$	472.393	+	875.644i	0.852695	+	1.58059i
$555$		0			0
$556$	123.149	+	595.080i	0.221490	+	1.07029i
$557$	−375.881	−	375.881i	−0.674831	−	0.674831i	0.283995	−	0.958826i	$-0.408340\pi$
$557$	−375.881	−	375.881i	−0.674831	−	0.674831i	−0.958826	+	0.283995i	$0.908340\pi$
$558$		0			0
$559$			683.715i			1.22310i
$560$	749.340	+	296.926i	1.33811	+	0.530226i
$561$		0			0
$562$	366.724	+	109.701i	0.652533	+	0.195198i
$563$	−305.349	+	305.349i	−0.542360	+	0.542360i	−0.924220	−	0.381860i	$-0.875284\pi$
$563$	−305.349	+	305.349i	−0.542360	+	0.542360i	0.381860	+	0.924220i	$0.375284\pi$
$564$		0			0
$565$	54.8777	−	54.8777i	0.0971287	−	0.0971287i
$566$	−77.9444	+	42.0495i	−0.137711	+	0.0742924i
$567$		0			0
$568$	−316.076	+	265.577i	−0.556472	+	0.467565i
$569$		−	296.778i		−	0.521578i	−0.965396	−	0.260789i	$-0.916017\pi$
$569$		−	296.778i		−	0.521578i	0.965396	−	0.260789i	$-0.0839827\pi$
$570$		0			0
$571$	−347.717	−	347.717i	−0.608961	−	0.608961i	0.333714	−	0.942674i	$-0.391698\pi$
$571$	−347.717	−	347.717i	−0.608961	−	0.608961i	−0.942674	+	0.333714i	$0.891698\pi$
$572$	152.026	−	231.367i	0.265779	−	0.404487i
$573$		0			0
$574$	−893.129	−	267.170i	−1.55597	−	0.465453i
$575$			37.0771i			0.0644820i
$576$		0			0
$577$	−189.382			−0.328218			−0.164109	−	0.986442i	$-0.552475\pi$
$577$	−189.382			−0.328218			−0.164109	+	0.986442i	$0.552475\pi$
$578$	−139.253	+	465.512i	−0.240922	+	0.805385i
$579$		0			0
$580$	−119.685	−	78.6425i	−0.206354	−	0.135591i
$581$	553.939	−	553.939i	0.953423	−	0.953423i
$582$		0			0
$583$	120.289			0.206328
$584$	−404.006	−	480.827i	−0.691791	−	0.823334i
$585$		0			0
$586$	−123.668	−	229.236i	−0.211038	−	0.391188i
$587$	641.187	+	641.187i	1.09231	+	1.09231i	0.995281	+	0.0970301i	$0.0309343\pi$
$587$	641.187	+	641.187i	1.09231	+	1.09231i	0.0970301	+	0.995281i	$0.469066\pi$
$588$		0			0
$589$	−71.0592	−	71.0592i	−0.120644	−	0.120644i
$590$	215.026	−	718.815i	0.364451	−	1.21833i
$591$		0			0
$592$	−382.555	−	151.588i	−0.646207	−	0.256060i
$593$	127.909			0.215697			0.107849	−	0.994167i	$-0.465604\pi$
$593$	127.909			0.215697			0.107849	+	0.994167i	$0.465604\pi$
$594$		0			0
$595$	241.736	−	241.736i	0.406279	−	0.406279i
$596$	−808.936	+	167.405i	−1.35728	+	0.280881i
$597$		0			0
$598$	266.621	−	143.837i	0.445855	−	0.240530i
$599$	−794.804			−1.32688			−0.663442	−	0.748227i	$-0.730905\pi$
$599$	−794.804			−1.32688			−0.663442	+	0.748227i	$0.730905\pi$
$600$		0			0
$601$		−	89.2746i		−	0.148543i	−0.997238	−	0.0742717i	$-0.976337\pi$
$601$		−	89.2746i		−	0.148543i	0.997238	−	0.0742717i	$-0.0236632\pi$
$602$	1311.41	−	707.479i	2.17842	−	1.17522i
$603$		0			0
$604$	−737.157	−	484.369i	−1.22046	−	0.801936i
$605$	221.527	+	221.527i	0.366160	+	0.366160i
$606$		0			0
$607$		−	316.002i		−	0.520596i	−0.965528	−	0.260298i	$-0.916179\pi$
$607$		−	316.002i		−	0.520596i	0.965528	−	0.260298i	$-0.0838208\pi$
$608$	378.903	−	480.291i	0.623195	−	0.789953i
$609$		0			0
$610$	71.8926	−	240.332i	0.117857	−	0.393986i
$611$	−253.370	+	253.370i	−0.414682	+	0.414682i
$612$		0			0
$613$	−192.003	+	192.003i	−0.313219	+	0.313219i	−0.846155	−	0.532936i	$-0.821089\pi$
$613$	−192.003	+	192.003i	−0.313219	+	0.313219i	0.532936	+	0.846155i	$0.321089\pi$
$614$	345.892	+	641.157i	0.563341	+	1.04423i
$615$		0			0
$616$	−601.086	−	52.1864i	−0.975789	−	0.0847182i
$617$			105.762i			0.171413i	0.996320	+	0.0857066i	$0.0273148\pi$
$617$			105.762i			0.171413i	−0.996320	+	0.0857066i	$0.972685\pi$
$618$		0			0
$619$	553.819	+	553.819i	0.894699	+	0.894699i	0.994961	−	0.100262i	$-0.0319681\pi$
$619$	553.819	+	553.819i	0.894699	+	0.894699i	−0.100262	+	0.994961i	$0.531968\pi$
$620$	−22.2109	−	107.328i	−0.0358241	−	0.173109i
$621$		0			0
$622$	75.0378	−	250.846i	0.120640	−	0.403289i
$623$			426.468i			0.684539i
$624$		0			0
$625$	674.560			1.07930
$626$	−99.3221	−	29.7111i	−0.158661	−	0.0474619i
$627$		0			0
$628$	125.597	+	606.909i	0.199995	+	0.966416i
$629$	−123.412	+	123.412i	−0.196203	+	0.196203i
$630$		0			0
$631$	762.907			1.20904			0.604522	−	0.796589i	$-0.293364\pi$
$631$	762.907			1.20904			0.604522	+	0.796589i	$0.293364\pi$
$632$	−558.444	−	664.632i	−0.883614	−	1.05163i
$633$		0			0
$634$	272.916	−	147.233i	0.430468	−	0.232229i
$635$	−393.873	−	393.873i	−0.620272	−	0.620272i
$636$		0			0
$637$	−278.453	−	278.453i	−0.437132	−	0.437132i
$638$	102.703	+	30.7225i	0.160977	+	0.0481544i
$639$		0			0
$640$	633.018	−	210.847i	0.989091	−	0.329449i
$641$	412.834			0.644046			0.322023	−	0.946732i	$-0.395637\pi$
$641$	412.834			0.644046			0.322023	+	0.946732i	$0.395637\pi$
$642$		0			0
$643$	−372.515	+	372.515i	−0.579339	+	0.579339i	−0.934721	−	0.355382i	$-0.884351\pi$
$643$	−372.515	+	372.515i	−0.579339	+	0.579339i	0.355382	+	0.934721i	$0.384351\pi$
$644$	−551.777	−	362.560i	−0.856797	−	0.562982i
$645$		0			0
$646$	−123.195	−	228.359i	−0.190705	−	0.353497i
$647$	1170.94			1.80980			0.904899	−	0.425627i	$-0.139946\pi$
$647$	1170.94			1.80980			0.904899	+	0.425627i	$0.139946\pi$
$648$		0			0
$649$			561.625i			0.865370i
$650$	18.2833	+	33.8905i	0.0281281	+	0.0521392i
$651$		0			0
$652$	−314.521	+	65.0884i	−0.482394	+	0.0998288i
$653$	−13.7523	−	13.7523i	−0.0210602	−	0.0210602i	0.696498	−	0.717558i	$-0.254740\pi$
$653$	−13.7523	−	13.7523i	−0.0210602	−	0.0210602i	−0.717558	+	0.696498i	$0.754740\pi$
$654$		0			0
$655$			1129.33i			1.72417i
$656$	−708.301	+	306.274i	−1.07973	+	0.466882i
$657$		0			0
$658$	748.158	+	223.804i	1.13702	+	0.340127i
$659$	−283.149	+	283.149i	−0.429664	+	0.429664i	−0.888514	−	0.458850i	$-0.848262\pi$
$659$	−283.149	+	283.149i	−0.429664	+	0.429664i	0.458850	+	0.888514i	$0.348262\pi$
$660$		0			0
$661$	287.535	−	287.535i	0.435000	−	0.435000i	−0.455325	−	0.890325i	$-0.650477\pi$
$661$	287.535	−	287.535i	0.435000	−	0.435000i	0.890325	+	0.455325i	$0.150477\pi$
$662$	804.604	−	434.068i	1.21541	−	0.655692i
$663$		0			0
$664$	56.0894	−	646.041i	0.0844720	−	0.972953i
$665$		−	963.069i		−	1.44822i
$666$		0			0
$667$	82.9486	+	82.9486i	0.124361	+	0.124361i
$668$	356.611	+	234.321i	0.533849	+	0.350780i
$669$		0			0
$670$	323.731	+	96.8408i	0.483181	+	0.144539i
$671$			187.776i			0.279845i
$672$		0			0
$673$	−45.5265			−0.0676471			−0.0338236	−	0.999428i	$-0.510768\pi$
$673$	−45.5265			−0.0676471			−0.0338236	+	0.999428i	$0.510768\pi$
$674$	180.644	−	603.879i	0.268018	−	0.895962i
$675$		0			0
$676$	−198.440	+	302.004i	−0.293550	+	0.446752i
$677$	−208.341	+	208.341i	−0.307742	+	0.307742i	−0.844033	−	0.536291i	$-0.819825\pi$
$677$	−208.341	+	208.341i	−0.307742	+	0.307742i	0.536291	+	0.844033i	$0.319825\pi$
$678$		0			0
$679$	−1089.18			−1.60409
$680$	24.4772	−	281.929i	0.0359958	−	0.414602i
$681$		0			0
$682$	38.9532	+	72.2051i	0.0571162	+	0.105873i
$683$	219.645	+	219.645i	0.321589	+	0.321589i	0.849377	−	0.527787i	$-0.176978\pi$
$683$	219.645	+	219.645i	0.321589	+	0.321589i	−0.527787	+	0.849377i	$0.676978\pi$
$684$		0			0
$685$	−277.065	−	277.065i	−0.404475	−	0.404475i
$686$	25.4756	−	85.1631i	0.0371365	−	0.124144i
$687$		0			0
$688$	454.383	−	1146.71i	0.660441	−	1.66672i
$689$	136.710			0.198418
$690$		0			0
$691$	692.991	−	692.991i	1.00288	−	1.00288i	0.00288571	−	0.999996i	$-0.499081\pi$
$691$	692.991	−	692.991i	1.00288	−	1.00288i	0.999996	−	0.00288571i	$-0.000918553\pi$
$692$	204.466	+	988.024i	0.295471	+	1.42778i
$693$		0			0
$694$	765.625	−	413.040i	1.10321	−	0.595158i
$695$	791.905			1.13943
$696$		0			0
$697$			327.301i			0.469585i
$698$	424.327	−	228.916i	0.607918	−	0.327960i
$699$		0			0
$700$	46.0854	−	70.1370i	0.0658363	−	0.100196i
$701$	−195.377	−	195.377i	−0.278712	−	0.278712i	0.553883	−	0.832595i	$-0.313146\pi$
$701$	−195.377	−	195.377i	−0.278712	−	0.278712i	−0.832595	+	0.553883i	$0.813146\pi$
$702$		0			0
$703$			491.668i			0.699386i
$704$	−408.735	+	287.008i	−0.580589	+	0.407682i
$705$		0			0
$706$	−136.495	+	456.294i	−0.193336	+	0.646308i
$707$	941.179	−	941.179i	1.33123	−	1.33123i
$708$		0			0
$709$	318.083	−	318.083i	0.448636	−	0.448636i	−0.446265	−	0.894901i	$-0.647246\pi$
$709$	318.083	−	318.083i	0.448636	−	0.448636i	0.894901	+	0.446265i	$0.147246\pi$
$710$	255.434	+	473.480i	0.359766	+	0.666874i
$711$		0			0
$712$	227.097	+	270.279i	0.318956	+	0.379606i
$713$			89.7775i			0.125915i
$714$		0			0
$715$	−255.101	−	255.101i	−0.356784	−	0.356784i
$716$	334.929	−	69.3118i	0.467778	−	0.0968042i
$717$		0			0
$718$	−19.2859	+	64.4711i	−0.0268605	+	0.0897926i
$719$			1122.38i			1.56103i	0.625139	+	0.780514i	$0.285042\pi$
$719$			1122.38i			1.56103i	−0.625139	+	0.780514i	$0.714958\pi$
$720$		0			0
$721$	1340.43			1.85913
$722$	−8.57606	−	2.56544i	−0.0118782	−	0.00355324i
$723$		0			0
$724$	−814.929	+	168.645i	−1.12559	+	0.232935i
$725$	−10.5437	+	10.5437i	−0.0145430	+	0.0145430i
$726$		0			0
$727$	529.192			0.727911			0.363956	−	0.931416i	$-0.381426\pi$
$727$	529.192			0.727911			0.363956	+	0.931416i	$0.381426\pi$
$728$	−683.138	−	59.3102i	−0.938376	−	0.0814700i
$729$		0			0
$730$	−720.277	+	388.576i	−0.986681	+	0.532295i
$731$	−369.926	−	369.926i	−0.506055	−	0.506055i
$732$		0			0
$733$	−263.121	−	263.121i	−0.358965	−	0.358965i	0.504466	−	0.863431i	$-0.331689\pi$
$733$	−263.121	−	263.121i	−0.358965	−	0.358965i	−0.863431	+	0.504466i	$0.831689\pi$
$734$	−461.317	−	137.998i	−0.628498	−	0.188008i
$735$		0			0
$736$	−542.761	+	64.0481i	−0.737447	+	0.0870218i
$737$	−252.938			−0.343200
$738$		0			0
$739$	−44.5459	+	44.5459i	−0.0602787	+	0.0602787i	−0.736603	−	0.676325i	$-0.763572\pi$
$739$	−44.5459	+	44.5459i	−0.0602787	+	0.0602787i	0.676325	+	0.736603i	$0.263572\pi$
$740$	−294.468	+	448.148i	−0.397929	+	0.605606i
$741$		0			0
$742$	−141.462	−	262.218i	−0.190649	−	0.353393i
$743$	−762.894			−1.02678			−0.513388	−	0.858157i	$-0.671610\pi$
$743$	−762.894			−1.02678			−0.513388	+	0.858157i	$0.671610\pi$
$744$		0			0
$745$			1076.50i			1.44496i
$746$	−580.820	−	1076.63i	−0.778578	−	1.44320i
$747$		0			0
$748$	42.9277	+	207.436i	0.0573900	+	0.277321i
$749$	−306.735	−	306.735i	−0.409526	−	0.409526i
$750$		0			0
$751$			1342.93i			1.78819i	0.447876	+	0.894095i	$0.352180\pi$
$751$			1342.93i			1.78819i	−0.447876	+	0.894095i	$0.647820\pi$
$752$	593.331	−	256.561i	0.789004	−	0.341171i
$753$		0			0
$754$	116.723	+	34.9163i	0.154805	+	0.0463082i
$755$	−812.776	+	812.776i	−1.07652	+	1.07652i
$756$		0			0
$757$	−394.830	+	394.830i	−0.521573	+	0.521573i	−0.918046	−	0.396474i	$-0.870234\pi$
$757$	−394.830	+	394.830i	−0.521573	+	0.521573i	0.396474	+	0.918046i	$0.370234\pi$
$758$	−434.920	+	234.631i	−0.573772	+	0.309539i
$759$		0			0
$760$	−512.840	−	610.356i	−0.674790	−	0.803101i
$761$			480.213i			0.631029i	0.948921	+	0.315514i	$0.102177\pi$
$761$			480.213i			0.631029i	−0.948921	+	0.315514i	$0.897823\pi$
$762$		0			0
$763$	−6.88404	−	6.88404i	−0.00902233	−	0.00902233i
$764$	234.726	−	357.228i	0.307233	−	0.467576i
$765$		0			0
$766$	−1290.27	−	385.970i	−1.68442	−	0.503878i
$767$			638.291i			0.832191i
$768$		0			0
$769$	472.763			0.614777			0.307388	−	0.951584i	$-0.400545\pi$
$769$	472.763			0.614777			0.307388	+	0.951584i	$0.400545\pi$
$770$	−225.332	+	753.267i	−0.292639	+	0.978269i
$771$		0			0
$772$	−227.945	−	149.777i	−0.295265	−	0.194012i
$773$	−857.735	+	857.735i	−1.10962	+	1.10962i	−0.116418	+	0.993200i	$0.537141\pi$
$773$	−857.735	+	857.735i	−1.10962	+	1.10962i	−0.993200	+	0.116418i	$0.962859\pi$
$774$		0			0
$775$	−11.4117			−0.0147248
$776$	−690.279	+	579.993i	−0.889534	+	0.747414i
$777$		0			0
$778$	−368.828	−	683.673i	−0.474072	−	0.878757i
$779$	651.978	+	651.978i	0.836942	+	0.836942i
$780$		0			0
$781$	−284.758	−	284.758i	−0.364607	−	0.364607i
$782$	−66.4329	+	222.080i	−0.0849525	+	0.283990i
$783$		0			0
$784$	281.959	+	652.067i	0.359641	+	0.831719i
$785$	807.648			1.02885
$786$		0			0
$787$	170.355	−	170.355i	0.216462	−	0.216462i	−0.590544	−	0.807006i	$-0.701087\pi$
$787$	170.355	−	170.355i	0.216462	−	0.216462i	0.807006	+	0.590544i	$0.201087\pi$
$788$	−342.633	+	70.9061i	−0.434814	+	0.0899823i
$789$		0			0
$790$	−995.615	+	537.115i	−1.26027	+	0.679893i
$791$	143.891			0.181911
$792$		0			0
$793$			213.409i			0.269116i
$794$	−675.229	+	364.273i	−0.850415	+	0.458782i
$795$		0			0
$796$	529.739	+	348.079i	0.665501	+	0.437285i
$797$	−835.571	−	835.571i	−1.04840	−	1.04840i	−0.998768	−	0.0496277i	$-0.984197\pi$
$797$	−835.571	−	835.571i	−1.04840	−	1.04840i	−0.0496277	−	0.998768i	$-0.515803\pi$
$798$		0			0
$799$		−	274.174i		−	0.343147i
$800$	−8.14121	−	68.9909i	−0.0101765	−	0.0862386i
$801$		0			0
$802$	237.981	−	795.553i	0.296735	−	0.991962i
$803$	433.185	−	433.185i	0.539458	−	0.539458i
$804$		0			0
$805$	−608.380	+	608.380i	−0.755751	+	0.755751i
$806$	44.2706	+	82.0615i	0.0549263	+	0.101813i
$807$		0			0
$808$	95.2996	−	1097.67i	0.117945	−	1.35850i
$809$			371.926i			0.459735i	0.973222	+	0.229868i	$0.0738293\pi$
$809$			371.926i			0.459735i	−0.973222	+	0.229868i	$0.926171\pi$
$810$		0			0
$811$	−275.629	−	275.629i	−0.339863	−	0.339863i	0.516453	−	0.856316i	$-0.327252\pi$
$811$	−275.629	−	275.629i	−0.339863	−	0.339863i	−0.856316	+	0.516453i	$0.827252\pi$
$812$	−53.8080	−	260.011i	−0.0662660	−	0.320211i
$813$		0			0
$814$	115.037	−	384.560i	0.141323	−	0.472432i
$815$			418.550i			0.513559i
$816$		0			0
$817$	−1473.77			−1.80389
$818$	1216.13	+	363.791i	1.48671	+	0.444732i
$819$		0			0
$820$	203.788	+	984.748i	0.248522	+	1.20091i
$821$	904.923	−	904.923i	1.10222	−	1.10222i	0.108079	−	0.994142i	$-0.465530\pi$
$821$	904.923	−	904.923i	1.10222	−	1.10222i	0.994142	−	0.108079i	$-0.0344699\pi$
$822$		0			0
$823$	523.237			0.635768			0.317884	−	0.948130i	$-0.397028\pi$
$823$	523.237			0.635768			0.317884	+	0.948130i	$0.397028\pi$
$824$	849.515	−	713.789i	1.03096	−	0.866249i
$825$		0			0
$826$	1224.28	−	660.477i	1.48218	−	0.799608i
$827$	−722.805	−	722.805i	−0.874008	−	0.874008i	0.118898	−	0.992906i	$-0.462064\pi$
$827$	−722.805	−	722.805i	−0.874008	−	0.874008i	−0.992906	+	0.118898i	$0.962064\pi$
$828$		0			0
$829$	−286.380	−	286.380i	−0.345453	−	0.345453i	0.512960	−	0.858413i	$-0.328549\pi$
$829$	−286.380	−	286.380i	−0.345453	−	0.345453i	−0.858413	+	0.512960i	$0.828549\pi$
$830$	−809.603	−	242.184i	−0.975426	−	0.291788i
$831$		0			0
$832$	−464.530	+	326.187i	−0.558329	+	0.392051i
$833$	301.316			0.361724
$834$		0			0
$835$	393.193	−	393.193i	0.470890	−	0.470890i
$836$	498.720	+	327.698i	0.596555	+	0.391983i
$837$		0			0
$838$	25.8763	+	47.9653i	0.0308787	+	0.0572378i
$839$	−1353.58			−1.61333			−0.806666	−	0.591008i	$-0.798730\pi$
$839$	−1353.58			−1.61333			−0.806666	+	0.591008i	$0.798730\pi$
$840$		0			0
$841$		−	793.824i		−	0.943904i
$842$	−328.352	−	608.645i	−0.389967	−	0.722856i
$843$		0			0
$844$	1091.45	−	225.870i	1.29319	−	0.267618i
$845$	332.984	+	332.984i	0.394064	+	0.394064i
$846$		0			0
$847$			580.852i			0.685776i
$848$	−229.286	−	90.8546i	−0.270384	−	0.107140i
$849$		0			0
$850$	−28.2288	−	8.44435i	−0.0332104	−	0.00993453i
$851$	310.591	−	310.591i	0.364972	−	0.364972i
$852$		0			0
$853$	−668.253	+	668.253i	−0.783415	+	0.783415i	−0.980405	−	0.196990i	$-0.936883\pi$
$853$	−668.253	+	668.253i	−0.783415	+	0.783415i	0.196990	+	0.980405i	$0.436883\pi$
$854$	409.332	−	220.827i	0.479311	−	0.258579i
$855$		0			0
$856$	−357.735	−	31.0586i	−0.417915	−	0.0362834i
$857$			488.688i			0.570230i	0.958493	+	0.285115i	$0.0920319\pi$
$857$			488.688i			0.570230i	−0.958493	+	0.285115i	$0.907968\pi$
$858$		0			0
$859$	−268.818	−	268.818i	−0.312943	−	0.312943i	0.533106	−	0.846048i	$-0.321025\pi$
$859$	−268.818	−	268.818i	−0.312943	−	0.312943i	−0.846048	+	0.533106i	$0.821025\pi$
$860$	−1343.32	−	882.666i	−1.56200	−	1.02636i
$861$		0			0
$862$	646.361	+	193.352i	0.749839	+	0.224306i
$863$		−	152.667i		−	0.176903i	−0.996080	−	0.0884514i	$-0.971808\pi$
$863$		−	152.667i		−	0.176903i	0.996080	−	0.0884514i	$-0.0281918\pi$
$864$		0			0
$865$	1314.82			1.52002
$866$	−243.351	+	813.502i	−0.281005	+	0.939379i
$867$		0			0
$868$	111.590	−	169.828i	0.128560	−	0.195654i
$869$	598.777	−	598.777i	0.689042	−	0.689042i
$870$		0			0
$871$	−287.466			−0.330041
$872$	−8.02864	−	0.697048i	−0.00920715	−	0.000799367i
$873$		0			0
$874$	310.047	+	574.713i	0.354744	+	0.657566i
$875$	813.208	+	813.208i	0.929380	+	0.929380i
$876$		0			0
$877$	162.637	+	162.637i	0.185447	+	0.185447i	0.793725	−	0.608277i	$-0.208139\pi$
$877$	162.637	+	162.637i	0.185447	+	0.185447i	−0.608277	+	0.793725i	$0.708139\pi$
$878$	−92.8576	+	310.416i	−0.105760	+	0.353549i
$879$		0			0
$880$	258.313	+	597.382i	0.293537	+	0.678844i
$881$	−873.243			−0.991196			−0.495598	−	0.868552i	$-0.665051\pi$
$881$	−873.243			−0.991196			−0.495598	+	0.868552i	$0.665051\pi$
$882$		0			0
$883$	−230.025	+	230.025i	−0.260504	+	0.260504i	−0.825259	−	0.564755i	$-0.808971\pi$
$883$	−230.025	+	230.025i	−0.260504	+	0.260504i	0.564755	+	0.825259i	$0.308971\pi$
$884$	48.7876	+	235.752i	0.0551896	+	0.266688i
$885$		0			0
$886$	−1225.20	+	660.972i	−1.38285	+	0.746018i
$887$	−430.685			−0.485552			−0.242776	−	0.970082i	$-0.578058\pi$
$887$	−430.685			−0.485552			−0.242776	+	0.970082i	$0.578058\pi$
$888$		0			0
$889$		−	1032.75i		−	1.16170i
$890$	404.877	−	218.423i	0.454918	−	0.245419i
$891$		0			0
$892$	34.6394	−	52.7174i	0.0388334	−	0.0591002i
$893$	−546.150	−	546.150i	−0.611590	−	0.611590i
$894$		0			0
$895$		−	445.709i		−	0.497999i
$896$	1106.32	+	553.473i	1.23474	+	0.617716i
$897$		0			0
$898$	−112.020	+	374.473i	−0.124743	+	0.417008i
$899$	−25.5302	+	25.5302i	−0.0283984	+	0.0283984i
$900$		0			0
$901$	−73.9673	+	73.9673i	−0.0820947	+	0.0820947i
$902$	−357.401	−	662.491i	−0.396232	−	0.734469i
$903$		0			0
$904$	91.1928	−	76.6230i	0.100877	−	0.0847600i
$905$			1084.47i			1.19831i
$906$		0			0
$907$	22.2262	+	22.2262i	0.0245052	+	0.0245052i	0.719253	−	0.694748i	$-0.244484\pi$
$907$	22.2262	+	22.2262i	0.0245052	+	0.0245052i	−0.694748	+	0.719253i	$0.744484\pi$
$908$	1103.96	−	228.459i	1.21582	−	0.251606i
$909$		0			0
$910$	−256.091	+	856.093i	−0.281419	+	0.940761i
$911$		−	1399.85i		−	1.53661i	−0.640083	−	0.768306i	$-0.721100\pi$
$911$		−	1399.85i		−	1.53661i	0.640083	−	0.768306i	$-0.278900\pi$
$912$		0			0
$913$	632.560			0.692837
$914$	741.292	+	221.750i	0.811042	+	0.242615i
$915$		0			0
$916$	−1276.97	+	264.262i	−1.39407	+	0.288496i
$917$	−1480.57	+	1480.57i	−1.61458	+	1.61458i
$918$		0			0
$919$	−806.944			−0.878068			−0.439034	−	0.898470i	$-0.644679\pi$
$919$	−806.944			−0.878068			−0.439034	+	0.898470i	$0.644679\pi$
$920$	−61.6018	+	709.534i	−0.0669585	+	0.771232i
$921$		0			0
$922$	434.134	−	234.207i	0.470861	−	0.254020i
$923$	−323.629	−	323.629i	−0.350628	−	0.350628i
$924$		0			0
$925$	39.4796	+	39.4796i	0.0426806	+	0.0426806i
$926$	115.981	+	34.6945i	0.125249	+	0.0374670i
$927$		0			0
$928$	−172.559	−	136.132i	−0.185947	−	0.146694i
$929$	1620.69			1.74455			0.872276	−	0.489013i	$-0.162643\pi$
$929$	1620.69			1.74455			0.872276	+	0.489013i	$0.162643\pi$
$930$		0			0
$931$	600.216	−	600.216i	0.644701	−	0.644701i
$932$	−757.354	+	1152.61i	−0.812611	+	1.23671i
$933$		0			0
$934$	411.582	+	762.922i	0.440666	+	0.816833i
$935$	276.046			0.295237
$936$		0			0
$937$		−	598.181i		−	0.638400i	−0.947687	−	0.319200i	$-0.896586\pi$
$937$		−	598.181i		−	0.638400i	0.947687	−	0.319200i	$-0.103414\pi$
$938$	297.458	+	551.378i	0.317119	+	0.587823i
$939$		0			0
$940$	−170.710	−	824.905i	−0.181606	−	0.877559i
$941$	977.842	+	977.842i	1.03915	+	1.03915i	0.999202	+	0.0399498i	$0.0127198\pi$
$941$	977.842	+	977.842i	1.03915	+	1.03915i	0.0399498	+	0.999202i	$0.487280\pi$
$942$		0			0
$943$		−	823.721i		−	0.873511i
$944$	424.195	−	1070.52i	0.449360	−	1.13403i
$945$		0			0
$946$	1152.72	+	344.823i	1.21852	+	0.364506i
$947$	827.881	−	827.881i	0.874215	−	0.874215i	−0.118714	−	0.992929i	$-0.537877\pi$
$947$	827.881	−	827.881i	0.874215	−	0.874215i	0.992929	+	0.118714i	$0.0378771\pi$
$948$		0			0
$949$	492.317	−	492.317i	0.518775	−	0.518775i
$950$	−73.0523	+	39.4103i	−0.0768972	+	0.0414846i
$951$		0			0
$952$	401.704	−	337.524i	0.421958	−	0.354542i
$953$		−	1846.78i		−	1.93786i	−0.247333	−	0.968930i	$-0.579554\pi$
$953$		−	1846.78i		−	1.93786i	0.247333	−	0.968930i	$-0.420446\pi$
$954$		0			0
$955$	−393.873	−	393.873i	−0.412432	−	0.412432i
$956$	169.570	−	258.066i	0.177374	−	0.269944i
$957$		0			0
$958$	−721.321	−	215.776i	−0.752945	−	0.225236i
$959$		−	726.475i		−	0.757534i
$960$		0			0
$961$	933.368			0.971247
$962$	130.740	−	437.055i	0.135905	−	0.454319i
$963$		0			0
$964$	981.090	+	644.651i	1.01773	+	0.668725i
$965$	−251.328	+	251.328i	−0.260443	+	0.260443i
$966$		0			0
$967$	−363.922			−0.376341			−0.188170	−	0.982136i	$-0.560256\pi$
$967$	−363.922			−0.376341			−0.188170	+	0.982136i	$0.560256\pi$
$968$	309.307	+	368.122i	0.319532	+	0.380291i
$969$		0			0
$970$	557.841	+	1034.03i	0.575094	+	1.06601i
$971$	−1161.30	−	1161.30i	−1.19598	−	1.19598i	−0.975360	−	0.220619i	$-0.929192\pi$
$971$	−1161.30	−	1161.30i	−1.19598	−	1.19598i	−0.220619	−	0.975360i	$-0.570808\pi$
$972$		0			0
$973$	1038.20	+	1038.20i	1.06701	+	1.06701i
$974$	44.2516	−	147.930i	0.0454328	−	0.151878i
$975$		0			0
$976$	141.827	−	357.923i	0.145315	−	0.366724i
$977$	−1159.63			−1.18693			−0.593467	−	0.804858i	$-0.702241\pi$
$977$	−1159.63			−1.18693			−0.593467	+	0.804858i	$0.702241\pi$
$978$		0			0
$979$	−243.499	+	243.499i	−0.248722	+	0.248722i
$980$	906.567	−	187.609i	0.925068	−	0.191438i
$981$		0			0
$982$	1447.37	−	780.826i	1.47390	−	0.795139i
$983$	1780.51			1.81131			0.905653	−	0.424020i	$-0.139382\pi$
$983$	1780.51			1.81131			0.905653	+	0.424020i	$0.139382\pi$
$984$		0			0
$985$			455.961i			0.462904i
$986$	−82.0449	+	44.2616i	−0.0832098	+	0.0448901i
$987$		0			0
$988$	566.799	+	372.430i	0.573683	+	0.376954i
$989$	930.997	+	930.997i	0.941352	+	0.941352i
$990$		0			0
$991$			675.783i			0.681920i	0.940078	+	0.340960i	$0.110752\pi$
$991$			675.783i			0.681920i	−0.940078	+	0.340960i	$0.889248\pi$
$992$	−19.7129	−	167.053i	−0.0198719	−	0.168400i
$993$		0			0
$994$	−285.863	+	955.619i	−0.287589	+	0.961388i
$995$	584.080	−	584.080i	0.587015	−	0.587015i
$996$		0			0
$997$	9.44963	−	9.44963i	0.00947806	−	0.00947806i	−0.702352	−	0.711830i	$-0.747867\pi$
$997$	9.44963	−	9.44963i	0.00947806	−	0.00947806i	0.711830	+	0.702352i	$0.247867\pi$
$998$	233.676	+	433.151i	0.234145	+	0.434019i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.a.19.2		6
3.2	odd	2		16.3.f.a.3.2	✓	6
4.3	odd	2		576.3.m.a.559.1		6
8.3	odd	2		1152.3.m.b.991.3		6
8.5	even	2		1152.3.m.a.991.3		6
12.11	even	2		64.3.f.a.47.2		6
15.2	even	4		400.3.k.d.99.1		6
15.8	even	4		400.3.k.c.99.3		6
15.14	odd	2		400.3.r.c.51.2		6
16.3	odd	4		1152.3.m.a.415.3		6
16.5	even	4		576.3.m.a.271.1		6
16.11	odd	4	inner	144.3.m.a.91.2		6
16.13	even	4		1152.3.m.b.415.3		6
24.5	odd	2		128.3.f.b.95.2		6
24.11	even	2		128.3.f.a.95.2		6
48.5	odd	4		64.3.f.a.15.2		6
48.11	even	4		16.3.f.a.11.2	yes	6
48.29	odd	4		128.3.f.a.31.2		6
48.35	even	4		128.3.f.b.31.2		6
96.5	odd	8		1024.3.c.j.1023.8		12
96.11	even	8		1024.3.c.j.1023.7		12
96.29	odd	8		1024.3.d.k.511.8		12
96.35	even	8		1024.3.d.k.511.6		12
96.53	odd	8		1024.3.c.j.1023.5		12
96.59	even	8		1024.3.c.j.1023.6		12
96.77	odd	8		1024.3.d.k.511.5		12
96.83	even	8		1024.3.d.k.511.7		12
240.59	even	4		400.3.r.c.251.2		6
240.107	odd	4		400.3.k.c.299.3		6
240.203	odd	4		400.3.k.d.299.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.2	✓	6	3.2	odd	2
16.3.f.a.11.2	yes	6	48.11	even	4
64.3.f.a.15.2		6	48.5	odd	4
64.3.f.a.47.2		6	12.11	even	2
128.3.f.a.31.2		6	48.29	odd	4
128.3.f.a.95.2		6	24.11	even	2
128.3.f.b.31.2		6	48.35	even	4
128.3.f.b.95.2		6	24.5	odd	2
144.3.m.a.19.2		6	1.1	even	1	trivial
144.3.m.a.91.2		6	16.11	odd	4	inner
400.3.k.c.99.3		6	15.8	even	4
400.3.k.c.299.3		6	240.107	odd	4
400.3.k.d.99.1		6	15.2	even	4
400.3.k.d.299.1		6	240.203	odd	4
400.3.r.c.51.2		6	15.14	odd	2
400.3.r.c.251.2		6	240.59	even	4
576.3.m.a.271.1		6	16.5	even	4
576.3.m.a.559.1		6	4.3	odd	2
1024.3.c.j.1023.5		12	96.53	odd	8
1024.3.c.j.1023.6		12	96.59	even	8
1024.3.c.j.1023.7		12	96.11	even	8
1024.3.c.j.1023.8		12	96.5	odd	8
1024.3.d.k.511.5		12	96.77	odd	8
1024.3.d.k.511.6		12	96.35	even	8
1024.3.d.k.511.7		12	96.83	even	8
1024.3.d.k.511.8		12	96.29	odd	8
1152.3.m.a.415.3		6	16.3	odd	4
1152.3.m.a.991.3		6	8.5	even	2
1152.3.m.b.415.3		6	16.13	even	4
1152.3.m.b.991.3		6	8.3	odd	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573183 - 1.91611i) q^{2} +(-3.34292 - 2.19656i) q^{4} +(-3.68585 + 3.68585i) q^{5} -9.66442 q^{7} +(-6.12494 + 5.14637i) q^{8} +O(q^{10})\)	\(q+(0.573183 - 1.91611i) q^{2} +(-3.34292 - 2.19656i) q^{4} +(-3.68585 + 3.68585i) q^{5} -9.66442 q^{7} +(-6.12494 + 5.14637i) q^{8} +(4.94981 + 9.17513i) q^{10} +(-5.51806 - 5.51806i) q^{11} +(-6.27131 - 6.27131i) q^{13} +(-5.53948 + 18.5181i) q^{14} +(6.35027 + 14.6858i) q^{16} +6.78623 q^{17} +(13.5181 - 13.5181i) q^{19} +(20.4177 - 4.22533i) q^{20} +(-13.7360 + 7.41033i) q^{22} -17.0790 q^{23} -2.17092i q^{25} +(-15.6111 + 8.42188i) q^{26} +(32.3074 + 21.2285i) q^{28} +(-4.85677 - 4.85677i) q^{29} -5.25662i q^{31} +(31.7795 - 3.75011i) q^{32} +(3.88975 - 13.0031i) q^{34} +(35.6216 - 35.6216i) q^{35} +(-18.1856 + 18.1856i) q^{37} +(-18.1537 - 33.6503i) q^{38} +(3.60688 - 41.5443i) q^{40} +48.2302i q^{41} +(-54.5113 - 54.5113i) q^{43} +(6.32571 + 30.5672i) q^{44} +(-9.78937 + 32.7251i) q^{46} -40.4015i q^{47} +44.4011 q^{49} +(-4.15972 - 1.24434i) q^{50} +(7.18921 + 34.7398i) q^{52} +(-10.8996 + 10.8996i) q^{53} +40.6774 q^{55} +(59.1940 - 49.7367i) q^{56} +(-12.0899 + 6.52227i) q^{58} +(-50.8898 - 50.8898i) q^{59} +(-17.0147 - 17.0147i) q^{61} +(-10.0722 - 3.01300i) q^{62} +(11.0298 - 63.0424i) q^{64} +46.2302 q^{65} +(22.9191 - 22.9191i) q^{67} +(-22.6858 - 14.9063i) q^{68} +(-47.8370 - 88.6724i) q^{70} +51.6047 q^{71} +78.5032i q^{73} +(24.4219 + 45.2692i) q^{74} +(-74.8830 + 15.4966i) q^{76} +(53.3288 + 53.3288i) q^{77} +108.512i q^{79} +(-77.5359 - 30.7237i) q^{80} +(92.4141 + 27.6447i) q^{82} +(-57.3173 + 57.3173i) q^{83} +(-25.0130 + 25.0130i) q^{85} +(-135.694 + 73.2045i) q^{86} +(62.1957 + 5.39985i) q^{88} -44.1276i q^{89} +(60.6086 + 60.6086i) q^{91} +(57.0937 + 37.5149i) q^{92} +(-77.4136 - 23.1575i) q^{94} +99.6510i q^{95} +112.700 q^{97} +(25.4499 - 85.0772i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8	\( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} + 36 q^{10} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 40 q^{16} + 4 q^{17} + 30 q^{19} + 84 q^{20} - 52 q^{22} - 60 q^{23} - 96 q^{26} + 56 q^{28} + 18 q^{29} - 8 q^{32} - 76 q^{34} + 100 q^{35} + 46 q^{37} - 40 q^{38} + 40 q^{40} - 114 q^{43} - 20 q^{44} + 28 q^{46} - 46 q^{49} - 46 q^{50} + 100 q^{52} - 78 q^{53} + 252 q^{55} + 168 q^{56} - 176 q^{58} - 206 q^{59} + 30 q^{61} + 144 q^{62} + 64 q^{64} - 12 q^{65} - 226 q^{67} - 112 q^{68} - 16 q^{70} + 260 q^{71} + 92 q^{74} - 188 q^{76} + 212 q^{77} - 232 q^{80} + 304 q^{82} - 318 q^{83} - 212 q^{85} - 268 q^{86} - 8 q^{88} + 188 q^{91} + 168 q^{92} + 48 q^{94} - 4 q^{97} - 10 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 + 36 * q^10 + 18 * q^11 - 2 * q^13 - 12 * q^14 - 40 * q^16 + 4 * q^17 + 30 * q^19 + 84 * q^20 - 52 * q^22 - 60 * q^23 - 96 * q^26 + 56 * q^28 + 18 * q^29 - 8 * q^32 - 76 * q^34 + 100 * q^35 + 46 * q^37 - 40 * q^38 + 40 * q^40 - 114 * q^43 - 20 * q^44 + 28 * q^46 - 46 * q^49 - 46 * q^50 + 100 * q^52 - 78 * q^53 + 252 * q^55 + 168 * q^56 - 176 * q^58 - 206 * q^59 + 30 * q^61 + 144 * q^62 + 64 * q^64 - 12 * q^65 - 226 * q^67 - 112 * q^68 - 16 * q^70 + 260 * q^71 + 92 * q^74 - 188 * q^76 + 212 * q^77 - 232 * q^80 + 304 * q^82 - 318 * q^83 - 212 * q^85 - 268 * q^86 - 8 * q^88 + 188 * q^91 + 168 * q^92 + 48 * q^94 - 4 * q^97 - 10 * q^98

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