LMFDB - Embedded newform 432.3.bc.a.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.2
Character	$\chi$	$=$	432.257
Dual form			432.3.bc.a.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47633 + 2.61160i) q^{3} +(3.16671 - 3.77394i) q^{5} +(3.18911 + 1.16074i) q^{7} +(-4.64090 - 7.71116i) q^{9} +O(q^{10})$	\(q+(-1.47633 + 2.61160i) q^{3} +(3.16671 - 3.77394i) q^{5} +(3.18911 + 1.16074i) q^{7} +(-4.64090 - 7.71116i) q^{9} +(-10.2080 - 12.1655i) q^{11} +(-0.621316 + 3.52366i) q^{13} +(5.18090 + 13.8417i) q^{15} +(-9.99899 - 5.77292i) q^{17} +(-9.59953 - 16.6269i) q^{19} +(-7.73958 + 6.61505i) q^{21} +(-5.28374 - 14.5170i) q^{23} +(0.126652 + 0.718282i) q^{25} +(26.9900 - 0.735947i) q^{27} +(-11.0239 + 1.94382i) q^{29} +(-23.0339 + 8.38364i) q^{31} +(46.8417 - 8.69905i) q^{33} +(14.4796 - 8.35978i) q^{35} +(21.2827 - 36.8628i) q^{37} +(-8.28512 - 6.82471i) q^{39} +(6.57199 + 1.15882i) q^{41} +(36.6672 - 30.7674i) q^{43} +(-43.7978 - 6.90455i) q^{45} +(17.5573 - 48.2383i) q^{47} +(-28.7131 - 24.0931i) q^{49} +(29.8383 - 17.5906i) q^{51} -61.1404i q^{53} -78.2375 q^{55} +(57.5948 - 0.523372i) q^{57} +(28.8982 - 34.4395i) q^{59} +(4.52766 + 1.64793i) q^{61} +(-5.84968 - 29.9787i) q^{63} +(11.3305 + 13.5032i) q^{65} +(-2.06484 + 11.7103i) q^{67} +(45.7130 + 7.63281i) q^{69} +(76.5190 + 44.1783i) q^{71} +(21.5726 + 37.3649i) q^{73} +(-2.06284 - 0.729655i) q^{75} +(-18.4336 - 50.6459i) q^{77} +(25.8836 + 146.793i) q^{79} +(-37.9241 + 71.5735i) q^{81} +(-78.1129 + 13.7734i) q^{83} +(-53.4505 + 19.4544i) q^{85} +(11.1985 - 31.6598i) q^{87} +(69.3002 - 40.0105i) q^{89} +(-6.07151 + 10.5162i) q^{91} +(12.1109 - 72.5322i) q^{93} +(-93.1477 - 16.4244i) q^{95} +(-141.047 + 118.352i) q^{97} +(-46.4354 + 135.174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.47633	+	2.61160i	−0.492110	+	0.870533i
$3$	−1.47633	+	2.61160i	−0.492110	+	0.870533i
$4$		0			0
$5$	3.16671	−	3.77394i	0.633342	−	0.754787i	−0.349961	−	0.936764i	$-0.613805\pi$
$5$	3.16671	−	3.77394i	0.633342	−	0.754787i	0.983303	+	0.181977i	$0.0582496\pi$
$6$		0			0
$7$	3.18911	+	1.16074i	0.455588	+	0.165820i	0.559613	−	0.828754i	$-0.310950\pi$
$7$	3.18911	+	1.16074i	0.455588	+	0.165820i	−0.104025	+	0.994575i	$0.533172\pi$
$8$		0			0
$9$	−4.64090	−	7.71116i	−0.515656	−	0.856796i
$10$		0			0
$11$	−10.2080	−	12.1655i	−0.928002	−	1.10595i	−0.994136	−	0.108139i	$-0.965511\pi$
$11$	−10.2080	−	12.1655i	−0.928002	−	1.10595i	0.0661334	−	0.997811i	$-0.478934\pi$
$12$		0			0
$13$	−0.621316	+	3.52366i	−0.0477935	+	0.271051i	−0.999335	−	0.0364707i	$-0.988388\pi$
$13$	−0.621316	+	3.52366i	−0.0477935	+	0.271051i	0.951541	+	0.307521i	$0.0994995\pi$
$14$		0			0
$15$	5.18090	+	13.8417i	0.345393	+	0.922783i
$16$		0			0
$17$	−9.99899	−	5.77292i	−0.588176	−	0.339583i	0.176200	−	0.984354i	$-0.443619\pi$
$17$	−9.99899	−	5.77292i	−0.588176	−	0.339583i	−0.764376	+	0.644771i	$0.776953\pi$
$18$		0			0
$19$	−9.59953	−	16.6269i	−0.505238	−	0.875098i	−0.999982	−	0.00605928i	$-0.998071\pi$
$19$	−9.59953	−	16.6269i	−0.505238	−	0.875098i	0.494743	−	0.869039i	$-0.335262\pi$
$20$		0			0
$21$	−7.73958	+	6.61505i	−0.368551	+	0.315002i
$22$		0			0
$23$	−5.28374	−	14.5170i	−0.229728	−	0.631172i	0.770251	−	0.637741i	$-0.220131\pi$
$23$	−5.28374	−	14.5170i	−0.229728	−	0.631172i	−0.999978	+	0.00656926i	$0.997909\pi$
$24$		0			0
$25$	0.126652	+	0.718282i	0.00506610	+	0.0287313i
$26$		0			0
$27$	26.9900	−	0.735947i	0.999628	−	0.0272573i
$28$		0			0
$29$	−11.0239	+	1.94382i	−0.380136	+	0.0670282i	−0.360451	−	0.932778i	$-0.617377\pi$
$29$	−11.0239	+	1.94382i	−0.380136	+	0.0670282i	−0.0196846	+	0.999806i	$0.506266\pi$
$30$		0			0
$31$	−23.0339	+	8.38364i	−0.743027	+	0.270440i	−0.685669	−	0.727914i	$-0.740490\pi$
$31$	−23.0339	+	8.38364i	−0.743027	+	0.270440i	−0.0573588	+	0.998354i	$0.518268\pi$
$32$		0			0
$33$	46.8417	−	8.69905i	1.41945	−	0.263608i
$34$		0			0
$35$	14.4796	−	8.35978i	0.413702	−	0.238851i
$36$		0			0
$37$	21.2827	−	36.8628i	0.575209	−	0.996292i	−0.420810	−	0.907149i	$-0.638254\pi$
$37$	21.2827	−	36.8628i	0.575209	−	0.996292i	0.996019	−	0.0891427i	$-0.0284127\pi$
$38$		0			0
$39$	−8.28512	−	6.82471i	−0.212439	−	0.174993i
$40$		0			0
$41$	6.57199	+	1.15882i	0.160293	+	0.0282639i	0.253218	−	0.967409i	$-0.418511\pi$
$41$	6.57199	+	1.15882i	0.160293	+	0.0282639i	−0.0929259	+	0.995673i	$0.529622\pi$
$42$		0			0
$43$	36.6672	−	30.7674i	0.852725	−	0.715521i	−0.107663	−	0.994187i	$-0.534337\pi$
$43$	36.6672	−	30.7674i	0.852725	−	0.715521i	0.960388	+	0.278666i	$0.0898924\pi$
$44$		0			0
$45$	−43.7978	−	6.90455i	−0.973285	−	0.153434i
$46$		0			0
$47$	17.5573	−	48.2383i	0.373559	−	1.02635i	−0.600415	−	0.799688i	$-0.704998\pi$
$47$	17.5573	−	48.2383i	0.373559	−	1.02635i	0.973975	−	0.226657i	$-0.0727798\pi$
$48$		0			0
$49$	−28.7131	−	24.0931i	−0.585981	−	0.491696i
$50$		0			0
$51$	29.8383	−	17.5906i	0.585066	−	0.344914i
$52$		0			0
$53$		−	61.1404i		−	1.15359i	−0.816888	−	0.576797i	$-0.804303\pi$
$53$		−	61.1404i		−	1.15359i	0.816888	−	0.576797i	$-0.195697\pi$
$54$		0			0
$55$	−78.2375			−1.42250
$56$		0			0
$57$	57.5948	−	0.523372i	1.01043	−	0.00918196i
$58$		0			0
$59$	28.8982	−	34.4395i	0.489799	−	0.583720i	−0.463367	−	0.886166i	$-0.653359\pi$
$59$	28.8982	−	34.4395i	0.489799	−	0.583720i	0.953166	+	0.302446i	$0.0978033\pi$
$60$		0			0
$61$	4.52766	+	1.64793i	0.0742240	+	0.0270153i	0.378865	−	0.925452i	$-0.376314\pi$
$61$	4.52766	+	1.64793i	0.0742240	+	0.0270153i	−0.304641	+	0.952467i	$0.598537\pi$
$62$		0			0
$63$	−5.84968	−	29.9787i	−0.0928521	−	0.475852i
$64$		0			0
$65$	11.3305	+	13.5032i	0.174316	+	0.207742i
$66$		0			0
$67$	−2.06484	+	11.7103i	−0.0308185	+	0.174780i	−0.996332	−	0.0855729i	$-0.972728\pi$
$67$	−2.06484	+	11.7103i	−0.0308185	+	0.174780i	0.965513	+	0.260353i	$0.0838391\pi$
$68$		0			0
$69$	45.7130	+	7.63281i	0.662508	+	0.110620i
$70$		0			0
$71$	76.5190	+	44.1783i	1.07773	+	0.622229i	0.930284	−	0.366841i	$-0.119561\pi$
$71$	76.5190	+	44.1783i	1.07773	+	0.622229i	0.147448	+	0.989070i	$0.452894\pi$
$72$		0			0
$73$	21.5726	+	37.3649i	0.295516	+	0.511848i	0.975105	−	0.221745i	$-0.0711752\pi$
$73$	21.5726	+	37.3649i	0.295516	+	0.511848i	−0.679589	+	0.733593i	$0.737842\pi$
$74$		0			0
$75$	−2.06284	−	0.729655i	−0.0275046	−	0.00972874i
$76$		0			0
$77$	−18.4336	−	50.6459i	−0.239397	−	0.657739i
$78$		0			0
$79$	25.8836	+	146.793i	0.327641	+	1.85814i	0.490429	+	0.871481i	$0.336840\pi$
$79$	25.8836	+	146.793i	0.327641	+	1.85814i	−0.162789	+	0.986661i	$0.552049\pi$
$80$		0			0
$81$	−37.9241	+	71.5735i	−0.468199	+	0.883623i
$82$		0			0
$83$	−78.1129	+	13.7734i	−0.941119	+	0.165945i	−0.623102	−	0.782140i	$-0.714128\pi$
$83$	−78.1129	+	13.7734i	−0.941119	+	0.165945i	−0.318017	+	0.948085i	$0.603017\pi$
$84$		0			0
$85$	−53.4505	+	19.4544i	−0.628829	+	0.228875i
$86$		0			0
$87$	11.1985	−	31.6598i	0.128718	−	0.363906i
$88$		0			0
$89$	69.3002	−	40.0105i	0.778654	−	0.449556i	−0.0572990	−	0.998357i	$-0.518249\pi$
$89$	69.3002	−	40.0105i	0.778654	−	0.449556i	0.835953	+	0.548801i	$0.184916\pi$
$90$		0			0
$91$	−6.07151	+	10.5162i	−0.0667199	+	0.115562i
$92$		0			0
$93$	12.1109	−	72.5322i	0.130224	−	0.779916i
$94$		0			0
$95$	−93.1477	−	16.4244i	−0.980502	−	0.172889i
$96$		0			0
$97$	−141.047	+	118.352i	−1.45409	+	1.22012i	−0.524559	+	0.851374i	$0.675770\pi$
$97$	−141.047	+	118.352i	−1.45409	+	1.22012i	−0.929528	+	0.368751i	$0.879786\pi$
$98$		0			0
$99$	−46.4354	+	135.174i	−0.469044	+	1.36540i
$100$		0			0
$101$	34.9812	−	96.1100i	0.346348	−	0.951584i	−0.637162	−	0.770730i	$-0.719892\pi$
$101$	34.9812	−	96.1100i	0.346348	−	0.951584i	0.983510	−	0.180854i	$-0.0578861\pi$
$102$		0			0
$103$	−101.070	−	84.8077i	−0.981261	−	0.823376i	0.00301802	−	0.999995i	$-0.499039\pi$
$103$	−101.070	−	84.8077i	−0.981261	−	0.823376i	−0.984279	+	0.176620i	$0.943484\pi$
$104$		0			0
$105$	0.455780	+	50.1566i	0.00434076	+	0.477682i
$106$		0			0
$107$		−	21.6029i		−	0.201896i	−0.994892	−	0.100948i	$-0.967812\pi$
$107$		−	21.6029i		−	0.201896i	0.994892	−	0.100948i	$-0.0321876\pi$
$108$		0			0
$109$	−149.823			−1.37452			−0.687262	−	0.726410i	$-0.741187\pi$
$109$	−149.823			−1.37452			−0.687262	+	0.726410i	$0.741187\pi$
$110$		0			0
$111$	64.8505	+	110.004i	0.584239	+	0.991024i
$112$		0			0
$113$	−59.7192	+	71.1705i	−0.528488	+	0.629828i	−0.962566	−	0.271048i	$-0.912630\pi$
$113$	−59.7192	+	71.1705i	−0.528488	+	0.629828i	0.434078	+	0.900875i	$0.357074\pi$
$114$		0			0
$115$	−71.5181	−	26.0305i	−0.621897	−	0.226352i
$116$		0			0
$117$	30.0550	−	11.5619i	0.256880	−	0.0988194i
$118$		0			0
$119$	−25.1870	−	30.0167i	−0.211656	−	0.252242i
$120$		0			0
$121$	−22.7830	+	129.209i	−0.188289	+	1.06784i
$122$		0			0
$123$	−12.7288	+	15.4526i	−0.103486	+	0.125631i
$124$		0			0
$125$	109.774	+	63.3782i	0.878194	+	0.507025i
$126$		0			0
$127$	50.8221	+	88.0264i	0.400174	+	0.693122i	0.993747	−	0.111659i	$-0.0356164\pi$
$127$	50.8221	+	88.0264i	0.400174	+	0.693122i	−0.593573	+	0.804780i	$0.702283\pi$
$128$		0			0
$129$	26.2193	+	141.183i	0.203250	+	1.09444i
$130$		0			0
$131$	10.8158	+	29.7161i	0.0825631	+	0.226840i	0.974104	−	0.226099i	$-0.0725974\pi$
$131$	10.8158	+	29.7161i	0.0825631	+	0.226840i	−0.891541	+	0.452940i	$0.850375\pi$
$132$		0			0
$133$	−11.3145	−	64.1676i	−0.0850712	−	0.482463i
$134$		0			0
$135$	82.6919	−	104.189i	0.612533	−	0.771770i
$136$		0			0
$137$	27.4305	−	4.83673i	0.200222	−	0.0353046i	−0.0726374	−	0.997358i	$-0.523142\pi$
$137$	27.4305	−	4.83673i	0.200222	−	0.0353046i	0.272860	+	0.962054i	$0.412030\pi$
$138$		0			0
$139$	184.723	−	67.2338i	1.32895	−	0.483697i	0.422631	−	0.906302i	$-0.361106\pi$
$139$	184.723	−	67.2338i	1.32895	−	0.483697i	0.906314	+	0.422605i	$0.138884\pi$
$140$		0			0
$141$	100.059	+	117.068i	0.709636	+	0.830271i
$142$		0			0
$143$	49.2093	−	28.4110i	0.344121	−	0.198678i
$144$		0			0
$145$	−27.5738	+	47.7592i	−0.190164	+	0.329374i
$146$		0			0
$147$	105.311	−	39.4176i	0.716405	−	0.268147i
$148$		0			0
$149$	−134.050	−	23.6366i	−0.899664	−	0.158635i	−0.295357	−	0.955387i	$-0.595439\pi$
$149$	−134.050	−	23.6366i	−0.899664	−	0.158635i	−0.604307	+	0.796752i	$0.706550\pi$
$150$		0			0
$151$	−113.431	+	95.1799i	−0.751199	+	0.630331i	−0.935820	−	0.352479i	$-0.885339\pi$
$151$	−113.431	+	95.1799i	−0.751199	+	0.630331i	0.184621	+	0.982810i	$0.440894\pi$
$152$		0			0
$153$	1.88838	+	103.895i	0.0123423	+	0.679055i
$154$		0			0
$155$	−41.3022	+	113.477i	−0.266466	+	0.732109i
$156$		0			0
$157$	26.9427	+	22.6076i	0.171609	+	0.143997i	0.724547	−	0.689225i	$-0.242049\pi$
$157$	26.9427	+	22.6076i	0.171609	+	0.143997i	−0.552938	+	0.833222i	$0.686493\pi$
$158$		0			0
$159$	159.674	+	90.2635i	1.00424	+	0.567695i
$160$		0			0
$161$		−	52.4293i		−	0.325648i
$162$		0			0
$163$	−147.146			−0.902737			−0.451368	−	0.892338i	$-0.649064\pi$
$163$	−147.146			−0.902737			−0.451368	+	0.892338i	$0.649064\pi$
$164$		0			0
$165$	115.504	−	204.325i	0.700026	−	1.23833i
$166$		0			0
$167$	136.943	−	163.202i	0.820018	−	0.977259i	−0.179962	−	0.983674i	$-0.557597\pi$
$167$	136.943	−	163.202i	0.820018	−	0.977259i	0.999979	+	0.00641460i	$0.00204184\pi$
$168$		0			0
$169$	146.778	+	53.4228i	0.868508	+	0.316111i
$170$		0			0
$171$	−83.6621	+	151.187i	−0.489252	+	0.884135i
$172$		0			0
$173$	−34.0171	−	40.5400i	−0.196631	−	0.234335i	0.658716	−	0.752392i	$-0.271100\pi$
$173$	−34.0171	−	40.5400i	−0.196631	−	0.234335i	−0.855346	+	0.518057i	$0.826656\pi$
$174$		0			0
$175$	−0.429831	+	2.43769i	−0.00245618	+	0.0139297i
$176$		0			0
$177$	47.2789	+	126.314i	0.267112	+	0.713641i
$178$		0			0
$179$	−48.8286	−	28.1912i	−0.272786	−	0.157493i	0.357367	−	0.933964i	$-0.383674\pi$
$179$	−48.8286	−	28.1912i	−0.272786	−	0.157493i	−0.630153	+	0.776471i	$0.717008\pi$
$180$		0			0
$181$	−92.1392	−	159.590i	−0.509056	−	0.881712i	−0.999945	−	0.0104893i	$-0.996661\pi$
$181$	−92.1392	−	159.590i	−0.509056	−	0.881712i	0.490888	−	0.871222i	$-0.336672\pi$
$182$		0			0
$183$	−10.9881	+	9.39155i	−0.0600441	+	0.0513199i
$184$		0			0
$185$	−71.7216	−	197.053i	−0.387684	−	1.06515i
$186$		0			0
$187$	31.8398	+	180.572i	0.170266	+	0.965627i
$188$		0			0
$189$	86.9283	+	28.9814i	0.459938	+	0.153341i
$190$		0			0
$191$	−29.0406	+	5.12064i	−0.152045	+	0.0268096i	−0.249153	−	0.968464i	$-0.580152\pi$
$191$	−29.0406	+	5.12064i	−0.152045	+	0.0268096i	0.0971075	+	0.995274i	$0.469041\pi$
$192$		0			0
$193$	355.362	−	129.341i	1.84126	−	0.670162i	0.852083	−	0.523406i	$-0.175339\pi$
$193$	355.362	−	129.341i	1.84126	−	0.670162i	0.989173	−	0.146757i	$-0.0468834\pi$
$194$		0			0
$195$	−51.9926	+	9.65563i	−0.266629	+	0.0495160i
$196$		0			0
$197$	11.5940	−	6.69378i	0.0588526	−	0.0339786i	−0.470285	−	0.882515i	$-0.655849\pi$
$197$	11.5940	−	6.69378i	0.0588526	−	0.0339786i	0.529138	+	0.848536i	$0.322516\pi$
$198$		0			0
$199$	−38.0531	+	65.9099i	−0.191222	+	0.331205i	−0.945655	−	0.325171i	$-0.894578\pi$
$199$	−38.0531	+	65.9099i	−0.191222	+	0.331205i	0.754434	+	0.656376i	$0.227912\pi$
$200$		0			0
$201$	−27.5342	−	22.6808i	−0.136986	−	0.112840i
$202$		0			0
$203$	−37.4129	−	6.59690i	−0.184300	−	0.0324970i
$204$		0			0
$205$	25.1849	−	21.1326i	0.122853	−	0.103086i
$206$		0			0
$207$	−87.4213	+	108.116i	−0.422325	+	0.522297i
$208$		0			0
$209$	−104.281	+	286.510i	−0.498953	+	1.37086i
$210$		0			0
$211$	0.311814	+	0.261643i	0.00147779	+	0.00124001i	0.643526	−	0.765424i	$-0.277471\pi$
$211$	0.311814	+	0.261643i	0.00147779	+	0.00124001i	−0.642048	+	0.766664i	$0.721915\pi$
$212$		0			0
$213$	−228.343	+	134.615i	−1.07203	+	0.631996i
$214$		0			0
$215$		−	235.811i		−	1.09680i
$216$		0			0
$217$	−83.1888			−0.383359
$218$		0			0
$219$	−129.431	+	1.17615i	−0.591007	+	0.00537056i
$220$		0			0
$221$	26.5543	−	31.6462i	0.120155	−	0.143196i
$222$		0			0
$223$	−13.5814	−	4.94323i	−0.0609032	−	0.0221669i	0.311389	−	0.950283i	$-0.399206\pi$
$223$	−13.5814	−	4.94323i	−0.0609032	−	0.0221669i	−0.372292	+	0.928116i	$0.621428\pi$
$224$		0			0
$225$	4.95101	−	4.31011i	0.0220045	−	0.0191561i
$226$		0			0
$227$	223.465	+	266.315i	0.984427	+	1.17319i	0.984888	+	0.173195i	$0.0554090\pi$
$227$	223.465	+	266.315i	0.984427	+	1.17319i	−0.000460345		1.00000i	$0.500147\pi$
$228$		0			0
$229$	16.9908	−	96.3597i	0.0741957	−	0.420785i	−0.924974	−	0.380032i	$-0.875913\pi$
$229$	16.9908	−	96.3597i	0.0741957	−	0.420785i	0.999169	−	0.0407532i	$-0.0129757\pi$
$230$		0			0
$231$	159.481	+	26.6289i	0.690393	+	0.115277i
$232$		0			0
$233$	−59.9442	−	34.6088i	−0.257271	−	0.148536i	0.365818	−	0.930686i	$-0.380789\pi$
$233$	−59.9442	−	34.6088i	−0.257271	−	0.148536i	−0.623089	+	0.782151i	$0.714123\pi$
$234$		0			0
$235$	−126.449	−	219.017i	−0.538082	−	0.931985i
$236$		0			0
$237$	−421.578	−	149.118i	−1.77881	−	0.629188i
$238$		0			0
$239$	−105.758	−	290.567i	−0.442502	−	1.21576i	−0.937841	−	0.347064i	$-0.887179\pi$
$239$	−105.758	−	290.567i	−0.442502	−	1.21576i	0.495340	−	0.868699i	$-0.335044\pi$
$240$		0			0
$241$	34.5873	+	196.154i	0.143516	+	0.813917i	0.968547	+	0.248831i	$0.0800462\pi$
$241$	34.5873	+	196.154i	0.143516	+	0.813917i	−0.825031	+	0.565087i	$0.808843\pi$
$242$		0			0
$243$	−130.933	−	204.709i	−0.538818	−	0.842422i
$244$		0			0
$245$	−181.852	+	32.0654i	−0.742252	+	0.130879i
$246$		0			0
$247$	64.5518	−	23.4949i	0.261343	−	0.0951211i
$248$		0			0
$249$	79.3498	−	224.334i	0.318674	−	0.900938i
$250$		0			0
$251$	41.4853	−	23.9516i	0.165280	−	0.0954245i	−0.415078	−	0.909786i	$-0.636246\pi$
$251$	41.4853	−	23.9516i	0.165280	−	0.0954245i	0.580358	+	0.814361i	$0.302912\pi$
$252$		0			0
$253$	−122.669	+	212.469i	−0.484857	+	0.839797i
$254$		0			0
$255$	28.1035	−	168.312i	0.110210	−	0.660049i
$256$		0			0
$257$	311.030	+	54.8430i	1.21023	+	0.213397i	0.742118	−	0.670269i	$-0.233821\pi$
$257$	311.030	+	54.8430i	1.21023	+	0.213397i	0.468117	+	0.883667i	$0.344933\pi$
$258$		0			0
$259$	110.661	−	92.8559i	0.427264	−	0.358517i
$260$		0			0
$261$	66.1501	+	75.9864i	0.253449	+	0.291135i
$262$		0			0
$263$	−51.1774	+	140.609i	−0.194591	+	0.534634i	−0.998164	−	0.0605722i	$-0.980707\pi$
$263$	−51.1774	+	140.609i	−0.194591	+	0.534634i	0.803573	+	0.595206i	$0.202930\pi$
$264$		0			0
$265$	−230.740	−	193.614i	−0.870717	−	0.730619i
$266$		0			0
$267$	2.18139	+	240.053i	0.00817002	+	0.899075i
$268$		0			0
$269$			60.3653i			0.224406i	0.993685	+	0.112203i	$0.0357907\pi$
$269$			60.3653i			0.224406i	−0.993685	+	0.112203i	$0.964209\pi$
$270$		0			0
$271$	−127.511			−0.470522			−0.235261	−	0.971932i	$-0.575594\pi$
$271$	−127.511			−0.470522			−0.235261	+	0.971932i	$0.575594\pi$
$272$		0			0
$273$	−18.5004	−	31.3817i	−0.0677672	−	0.114951i
$274$		0			0
$275$	7.44535	−	8.87302i	0.0270740	−	0.0322655i
$276$		0			0
$277$	166.678	+	60.6658i	0.601726	+	0.219010i	0.624879	−	0.780722i	$-0.285148\pi$
$277$	166.678	+	60.6658i	0.601726	+	0.219010i	−0.0231533	+	0.999732i	$0.507371\pi$
$278$		0			0
$279$	171.545	+	138.710i	0.614858	+	0.497169i
$280$		0			0
$281$	325.897	+	388.389i	1.15977	+	1.38217i	0.910385	+	0.413763i	$0.135786\pi$
$281$	325.897	+	388.389i	1.15977	+	1.38217i	0.249390	+	0.968403i	$0.419770\pi$
$282$		0			0
$283$	15.9014	−	90.1813i	0.0561887	−	0.318662i	−0.943739	−	0.330691i	$-0.892718\pi$
$283$	15.9014	−	90.1813i	0.0561887	−	0.318662i	0.999928	+	0.0120294i	$0.00382918\pi$
$284$		0			0
$285$	180.411	−	219.016i	0.633020	−	0.768479i
$286$		0			0
$287$	19.6137	+	11.3240i	0.0683406	+	0.0394565i
$288$		0			0
$289$	−77.8468	−	134.835i	−0.269366	−	0.466556i
$290$		0			0
$291$	−100.857	−	543.084i	−0.346588	−	1.86627i
$292$		0			0
$293$	−163.781	−	449.986i	−0.558981	−	1.53579i	−0.821119	−	0.570757i	$-0.806650\pi$
$293$	−163.781	−	449.986i	−0.558981	−	1.53579i	0.262138	−	0.965030i	$-0.415572\pi$
$294$		0			0
$295$	−38.4604	−	218.120i	−0.130374	−	0.739389i
$296$		0			0
$297$	−284.467	−	320.833i	−0.957803	−	1.08024i
$298$		0			0
$299$	54.4357	−	9.59848i	0.182059	−	0.0321019i
$300$		0			0
$301$	152.649	−	55.5596i	0.507139	−	0.184583i
$302$		0			0
$303$	199.357	+	233.247i	0.657944	+	0.769792i
$304$		0			0
$305$	20.5570	−	11.8686i	0.0674000	−	0.0389134i
$306$		0			0
$307$	24.1538	−	41.8357i	0.0786770	−	0.136273i	−0.824002	−	0.566586i	$-0.808264\pi$
$307$	24.1538	−	41.8357i	0.0786770	−	0.136273i	0.902679	+	0.430314i	$0.141597\pi$
$308$		0			0
$309$	370.696	−	138.750i	1.19966	−	0.449029i
$310$		0			0
$311$	−423.676	−	74.7056i	−1.36230	−	0.240211i	−0.555739	−	0.831357i	$-0.687565\pi$
$311$	−423.676	−	74.7056i	−1.36230	−	0.240211i	−0.806565	+	0.591146i	$0.798676\pi$
$312$		0			0
$313$	−154.131	+	129.331i	−0.492431	+	0.413198i	−0.854896	−	0.518799i	$-0.826379\pi$
$313$	−154.131	+	129.331i	−0.492431	+	0.413198i	0.362466	+	0.931997i	$0.381935\pi$
$314$		0			0
$315$	−131.662	−	72.8574i	−0.417974	−	0.231293i
$316$		0			0
$317$	6.28319	−	17.2629i	0.0198208	−	0.0544571i	−0.929388	−	0.369105i	$-0.879664\pi$
$317$	6.28319	−	17.2629i	0.0198208	−	0.0544571i	0.949208	+	0.314648i	$0.101886\pi$
$318$		0			0
$319$	136.180	+	114.269i	0.426897	+	0.358209i
$320$		0			0
$321$	56.4181	+	31.8930i	0.175757	+	0.0993551i
$322$		0			0
$323$			221.669i			0.686282i
$324$		0			0
$325$	−2.60967			−0.00802976
$326$		0			0
$327$	221.188	−	391.278i	0.676417	−	1.19657i
$328$		0			0
$329$	111.984	−	133.458i	0.340378	−	0.405647i
$330$		0			0
$331$	142.866	+	51.9990i	0.431619	+	0.157097i	0.548688	−	0.836027i	$-0.315128\pi$
$331$	142.866	+	51.9990i	0.431619	+	0.157097i	−0.117069	+	0.993124i	$0.537350\pi$
$332$		0			0
$333$	−383.026	+	6.96180i	−1.15023	+	0.0209063i
$334$		0			0
$335$	37.6551	+	44.8757i	0.112403	+	0.133957i
$336$		0			0
$337$	83.2947	−	472.388i	0.247165	−	1.40174i	−0.568244	−	0.822860i	$-0.692377\pi$
$337$	83.2947	−	472.388i	0.247165	−	1.40174i	0.815409	−	0.578885i	$-0.196512\pi$
$338$		0			0
$339$	−97.7037	−	261.034i	−0.288211	−	0.770011i
$340$		0			0
$341$	337.121	+	194.637i	0.988624	+	0.570782i
$342$		0			0
$343$	−146.751	−	254.180i	−0.427846	−	0.741050i
$344$		0			0
$345$	173.566	−	148.347i	0.503089	−	0.429992i
$346$		0			0
$347$	140.030	+	384.729i	0.403545	+	1.10873i	0.960522	+	0.278203i	$0.0897387\pi$
$347$	140.030	+	384.729i	0.403545	+	1.10873i	−0.556978	+	0.830528i	$0.688039\pi$
$348$		0			0
$349$	18.5808	+	105.377i	0.0532400	+	0.301939i	0.999787	−	0.0206260i	$-0.00656593\pi$
$349$	18.5808	+	105.377i	0.0532400	+	0.301939i	−0.946547	+	0.322565i	$0.895455\pi$
$350$		0			0
$351$	−14.1761	+	95.5607i	−0.0403877	+	0.272253i
$352$		0			0
$353$	−549.853	+	96.9540i	−1.55766	+	0.274657i	−0.885105	−	0.465391i	$-0.845914\pi$
$353$	−549.853	+	96.9540i	−1.55766	+	0.274657i	−0.672554	+	0.740048i	$0.734803\pi$
$354$		0			0
$355$	409.039	−	148.878i	1.15222	−	0.419375i
$356$		0			0
$357$	115.576	−	21.4638i	0.323743	−	0.0601228i
$358$		0			0
$359$	191.972	−	110.835i	0.534740	−	0.308732i	−0.208205	−	0.978085i	$-0.566762\pi$
$359$	191.972	−	110.835i	0.534740	−	0.308732i	0.742944	+	0.669353i	$0.233429\pi$
$360$		0			0
$361$	−3.80187	+	6.58504i	−0.0105315	+	0.0182411i
$362$		0			0
$363$	−303.806	−	250.255i	−0.836932	−	0.689407i
$364$		0			0
$365$	209.327	+	36.9100i	0.573499	+	0.101123i
$366$		0			0
$367$	−131.786	+	110.582i	−0.359091	+	0.301313i	−0.804428	−	0.594050i	$-0.797528\pi$
$367$	−131.786	+	110.582i	−0.359091	+	0.301313i	0.445337	+	0.895363i	$0.353084\pi$
$368$		0			0
$369$	−21.5641	−	56.0557i	−0.0584393	−	0.151912i
$370$		0			0
$371$	70.9683	−	194.984i	0.191289	−	0.525563i
$372$		0			0
$373$	95.7777	+	80.3671i	0.256777	+	0.215461i	0.762084	−	0.647478i	$-0.224176\pi$
$373$	95.7777	+	80.3671i	0.256777	+	0.215461i	−0.505307	+	0.862940i	$0.668621\pi$
$374$		0			0
$375$	−327.581	+	193.119i	−0.873550	+	0.514984i
$376$		0			0
$377$		−	40.0523i		−	0.106240i
$378$		0			0
$379$	613.387			1.61843			0.809217	−	0.587510i	$-0.199892\pi$
$379$	613.387			1.61843			0.809217	+	0.587510i	$0.199892\pi$
$380$		0			0
$381$	−304.920	+	2.77085i	−0.800315	+	0.00727257i
$382$		0			0
$383$	−47.0489	+	56.0707i	−0.122843	+	0.146399i	−0.823961	−	0.566647i	$-0.808240\pi$
$383$	−47.0489	+	56.0707i	−0.122843	+	0.146399i	0.701118	+	0.713046i	$0.252685\pi$
$384$		0			0
$385$	−249.508	−	90.8136i	−0.648073	−	0.235879i
$386$		0			0
$387$	−407.421	−	139.958i	−1.05277	−	0.361649i
$388$		0			0
$389$	−11.0042	−	13.1143i	−0.0282885	−	0.0337129i	0.751715	−	0.659488i	$-0.229227\pi$
$389$	−11.0042	−	13.1143i	−0.0282885	−	0.0337129i	−0.780003	+	0.625776i	$0.784783\pi$
$390$		0			0
$391$	−30.9732	+	175.657i	−0.0792152	+	0.449252i
$392$		0			0
$393$	−93.5742	−	15.6243i	−0.238102	−	0.0397565i
$394$		0			0
$395$	635.954	+	367.168i	1.61001	+	0.929540i
$396$		0			0
$397$	82.5885	+	143.048i	0.208032	+	0.360321i	0.951094	−	0.308900i	$-0.0999610\pi$
$397$	82.5885	+	143.048i	0.208032	+	0.360321i	−0.743063	+	0.669222i	$0.766628\pi$
$398$		0			0
$399$	184.284	+	65.1836i	0.461864	+	0.163368i
$400$		0			0
$401$	−38.8116	−	106.634i	−0.0967870	−	0.265920i	0.881845	−	0.471539i	$-0.156301\pi$
$401$	−38.8116	−	106.634i	−0.0967870	−	0.265920i	−0.978632	+	0.205619i	$0.934079\pi$
$402$		0			0
$403$	−15.2298	−	86.3723i	−0.0377910	−	0.214323i
$404$		0			0
$405$	150.019	+	369.775i	0.370418	+	0.913026i
$406$		0			0
$407$	−665.707	+	117.382i	−1.63564	+	0.288408i
$408$		0			0
$409$	516.352	−	187.937i	1.26247	−	0.459503i	0.377875	−	0.925857i	$-0.376655\pi$
$409$	516.352	−	187.937i	1.26247	−	0.459503i	0.884598	+	0.466354i	$0.154433\pi$
$410$		0			0
$411$	−27.8648	+	78.7780i	−0.0677976	+	0.191674i
$412$		0			0
$413$	132.135	−	76.2881i	0.319939	−	0.184717i
$414$		0			0
$415$	−195.381	+	338.409i	−0.470797	+	0.815444i
$416$		0			0
$417$	−97.1249	+	581.683i	−0.232913	+	1.39492i
$418$		0			0
$419$	−356.561	−	62.8714i	−0.850982	−	0.150051i	−0.268887	−	0.963172i	$-0.586656\pi$
$419$	−356.561	−	62.8714i	−0.850982	−	0.150051i	−0.582095	+	0.813121i	$0.697767\pi$
$420$		0			0
$421$	490.256	−	411.374i	1.16450	−	0.977135i	0.164546	−	0.986369i	$-0.447384\pi$
$421$	490.256	−	411.374i	1.16450	−	0.977135i	0.999957	+	0.00923468i	$0.00293953\pi$
$422$		0			0
$423$	−453.455	+	88.4818i	−1.07200	+	0.209177i
$424$		0			0
$425$	2.88019	−	7.91324i	0.00677691	−	0.0186194i
$426$		0			0
$427$	12.5264	+	10.5109i	0.0293358	+	0.0246157i
$428$		0			0
$429$	1.54898	+	170.459i	0.00361069	+	0.397340i
$430$		0			0
$431$			140.062i			0.324969i	0.986711	+	0.162484i	$0.0519507\pi$
$431$			140.062i			0.324969i	−0.986711	+	0.162484i	$0.948049\pi$
$432$		0			0
$433$	28.4373			0.0656750			0.0328375	−	0.999461i	$-0.489546\pi$
$433$	28.4373			0.0656750			0.0328375	+	0.999461i	$0.489546\pi$
$434$		0			0
$435$	−84.0198	−	142.520i	−0.193149	−	0.327632i
$436$		0			0
$437$	−190.650	+	227.208i	−0.436270	+	0.519927i
$438$		0			0
$439$	613.293	+	223.221i	1.39702	+	0.508475i	0.927294	−	0.374335i	$-0.122129\pi$
$439$	613.293	+	223.221i	1.39702	+	0.508475i	0.469730	+	0.882810i	$0.344351\pi$
$440$		0			0
$441$	−52.5315	+	333.225i	−0.119119	+	0.755612i
$442$		0			0
$443$	431.525	+	514.271i	0.974097	+	1.16088i	0.986960	+	0.160966i	$0.0514611\pi$
$443$	431.525	+	514.271i	0.974097	+	1.16088i	−0.0128628	+	0.999917i	$0.504094\pi$
$444$		0			0
$445$	68.4565	−	388.236i	0.153835	−	0.872441i
$446$		0			0
$447$	259.631	−	315.189i	0.580831	−	0.705121i
$448$		0			0
$449$	−8.53167	−	4.92576i	−0.0190015	−	0.0109705i	0.490469	−	0.871459i	$-0.336825\pi$
$449$	−8.53167	−	4.92576i	−0.0190015	−	0.0109705i	−0.509471	+	0.860488i	$0.670159\pi$
$450$		0			0
$451$	−52.9895	−	91.7805i	−0.117493	−	0.203505i
$452$		0			0
$453$	−81.1102	−	436.753i	−0.179051	−	0.964136i
$454$		0			0
$455$	20.4606	+	56.2151i	0.0449684	+	0.123550i
$456$		0			0
$457$	133.817	+	758.914i	0.292816	+	1.66064i	0.675949	+	0.736949i	$0.263734\pi$
$457$	133.817	+	758.914i	0.292816	+	1.66064i	−0.383132	+	0.923693i	$0.625155\pi$
$458$		0			0
$459$	−274.121	−	148.452i	−0.597213	−	0.323425i
$460$		0			0
$461$	−430.700	+	75.9441i	−0.934274	+	0.164738i	−0.620007	−	0.784597i	$-0.712870\pi$
$461$	−430.700	+	75.9441i	−0.934274	+	0.164738i	−0.314268	+	0.949334i	$0.601759\pi$
$462$		0			0
$463$	197.228	−	71.7851i	0.425978	−	0.155043i	−0.120130	−	0.992758i	$-0.538331\pi$
$463$	197.228	−	71.7851i	0.425978	−	0.155043i	0.546108	+	0.837715i	$0.316109\pi$
$464$		0			0
$465$	−235.380	−	275.394i	−0.506194	−	0.592245i
$466$		0			0
$467$	155.371	−	89.7038i	0.332701	−	0.192085i	−0.324338	−	0.945941i	$-0.605142\pi$
$467$	155.371	−	89.7038i	0.332701	−	0.192085i	0.657040	+	0.753856i	$0.271808\pi$
$468$		0			0
$469$	−20.1776	+	34.9487i	−0.0430227	+	0.0745175i
$470$		0			0
$471$	−98.8182	+	36.9872i	−0.209805	+	0.0785290i
$472$		0			0
$473$	−748.599	−	131.998i	−1.58266	−	0.279066i
$474$		0			0
$475$	10.7270	−	9.00100i	0.0225831	−	0.0189495i
$476$		0			0
$477$	−471.464	+	283.747i	−0.988394	+	0.594857i
$478$		0			0
$479$	33.0001	−	90.6672i	0.0688938	−	0.189284i	−0.900468	−	0.434923i	$-0.856776\pi$
$479$	33.0001	−	90.6672i	0.0688938	−	0.189284i	0.969361	+	0.245639i	$0.0789978\pi$
$480$		0			0
$481$	116.669	+	97.8966i	0.242554	+	0.203527i
$482$		0			0
$483$	136.924	+	77.4030i	0.283487	+	0.160255i
$484$		0			0
$485$			907.087i			1.87028i
$486$		0			0
$487$	−392.647			−0.806257			−0.403128	−	0.915143i	$-0.632077\pi$
$487$	−392.647			−0.806257			−0.403128	+	0.915143i	$0.632077\pi$
$488$		0			0
$489$	217.236	−	384.287i	0.444246	−	0.785862i
$490$		0			0
$491$	−268.188	+	319.613i	−0.546207	+	0.650944i	−0.966567	−	0.256413i	$-0.917459\pi$
$491$	−268.188	+	319.613i	−0.546207	+	0.650944i	0.420360	+	0.907357i	$0.361904\pi$
$492$		0			0
$493$	121.450	+	44.2041i	0.246348	+	0.0896635i
$494$		0			0
$495$	363.092	+	603.302i	0.733520	+	1.21879i
$496$		0			0
$497$	192.748	+	229.708i	0.387823	+	0.462190i
$498$		0			0
$499$	141.491	−	802.435i	0.283549	−	1.60809i	−0.426874	−	0.904311i	$-0.640385\pi$
$499$	141.491	−	802.435i	0.283549	−	1.60809i	0.710423	−	0.703775i	$-0.248504\pi$
$500$		0			0
$501$	224.046	+	598.580i	0.447197	+	1.19477i
$502$		0			0
$503$	−507.223	−	292.845i	−1.00840	−	0.582197i	−0.0976739	−	0.995218i	$-0.531140\pi$
$503$	−507.223	−	292.845i	−1.00840	−	0.582197i	−0.910721	+	0.413021i	$0.864474\pi$
$504$		0			0
$505$	−251.938	−	436.369i	−0.498887	−	0.864097i
$506$		0			0
$507$	−356.212	+	304.455i	−0.702587	+	0.600504i
$508$		0			0
$509$	283.147	+	777.939i	0.556280	+	1.52837i	0.824990	+	0.565147i	$0.191181\pi$
$509$	283.147	+	777.939i	0.556280	+	1.52837i	−0.268710	+	0.963221i	$0.586597\pi$
$510$		0			0
$511$	25.4266	+	144.201i	0.0497585	+	0.282194i
$512$		0			0
$513$	−271.327	−	441.694i	−0.528903	−	0.861002i
$514$		0			0
$515$	−640.118	+	112.870i	−1.24295	+	0.219165i
$516$		0			0
$517$	−766.065	+	278.825i	−1.48175	+	0.539313i
$518$		0			0
$519$	156.095	−	28.9886i	0.300760	−	0.0558547i
$520$		0			0
$521$	568.718	−	328.350i	1.09159	−	0.630230i	0.157590	−	0.987505i	$-0.449627\pi$
$521$	568.718	−	328.350i	1.09159	−	0.630230i	0.933999	+	0.357275i	$0.116294\pi$
$522$		0			0
$523$	260.887	−	451.869i	0.498827	−	0.863995i	−0.501172	−	0.865348i	$-0.667097\pi$
$523$	260.887	−	451.869i	0.498827	−	0.863995i	0.999999	+	0.00135338i	$0.000430795\pi$
$524$		0			0
$525$	−5.73171	−	4.72139i	−0.0109175	−	0.00899312i
$526$		0			0
$527$	278.713	+	49.1447i	0.528868	+	0.0932536i
$528$		0			0
$529$	222.413	−	186.627i	0.420441	−	0.352792i
$530$		0			0
$531$	−399.682	−	63.0083i	−0.752697	−	0.118660i
$532$		0			0
$533$	−8.16657	+	22.4375i	−0.0153219	+	0.0420966i
$534$		0			0
$535$	−81.5279	−	68.4100i	−0.152389	−	0.127869i
$536$		0			0
$537$	145.711	−	85.9013i	0.271343	−	0.159965i
$538$		0			0
$539$			595.250i			1.10436i
$540$		0			0
$541$	−10.3822			−0.0191908			−0.00959538	−	0.999954i	$-0.503054\pi$
$541$	−10.3822			−0.0191908			−0.00959538	+	0.999954i	$0.503054\pi$
$542$		0			0
$543$	552.813	−	5.02348i	1.01807	−	0.00925135i
$544$		0			0
$545$	−474.446	+	565.423i	−0.870543	+	1.03747i
$546$		0			0
$547$	228.429	+	83.1412i	0.417602	+	0.151995i	0.542271	−	0.840204i	$-0.317565\pi$
$547$	228.429	+	83.1412i	0.417602	+	0.151995i	−0.124669	+	0.992198i	$0.539787\pi$
$548$		0			0
$549$	−8.30494	−	42.5615i	−0.0151274	−	0.0775254i
$550$		0			0
$551$	138.144	+	164.634i	0.250716	+	0.298791i
$552$		0			0
$553$	−87.8434	+	498.185i	−0.158849	+	0.900876i
$554$		0			0
$555$	620.509	+	103.608i	1.11803	+	0.186681i
$556$		0			0
$557$	420.452	+	242.748i	0.754851	+	0.435813i	0.827444	−	0.561548i	$-0.189794\pi$
$557$	420.452	+	242.748i	0.754851	+	0.435813i	−0.0725930	+	0.997362i	$0.523127\pi$
$558$		0			0
$559$	85.6319	+	148.319i	0.153188	+	0.265329i
$560$		0			0
$561$	−518.588	−	183.432i	−0.924400	−	0.326972i
$562$		0			0
$563$	−151.668	−	416.705i	−0.269393	−	0.740151i	−0.998448	−	0.0556959i	$-0.982262\pi$
$563$	−151.668	−	416.705i	−0.269393	−	0.740151i	0.729055	−	0.684455i	$-0.239960\pi$
$564$		0			0
$565$	79.4798	+	450.753i	0.140672	+	0.797792i
$566$		0			0
$567$	−204.023	+	184.236i	−0.359828	+	0.324931i
$568$		0			0
$569$	226.327	−	39.9075i	0.397762	−	0.0701362i	0.0288107	−	0.999585i	$-0.490828\pi$
$569$	226.327	−	39.9075i	0.397762	−	0.0701362i	0.368951	+	0.929449i	$0.379717\pi$
$570$		0			0
$571$	−280.598	+	102.129i	−0.491414	+	0.178860i	−0.575828	−	0.817571i	$-0.695320\pi$
$571$	−280.598	+	102.129i	−0.491414	+	0.178860i	0.0844140	+	0.996431i	$0.473098\pi$
$572$		0			0
$573$	29.5004	−	83.4022i	0.0514842	−	0.145554i
$574$		0			0
$575$	9.75807	−	5.63382i	0.0169706	−	0.00979795i
$576$		0			0
$577$	319.742	−	553.809i	0.554145	−	0.959808i	−0.443824	−	0.896114i	$-0.646379\pi$
$577$	319.742	−	553.809i	0.554145	−	0.959808i	0.997969	−	0.0636938i	$-0.0202881\pi$
$578$		0			0
$579$	−186.844	+	1119.01i	−0.322702	+	1.93267i
$580$		0			0
$581$	−265.098	−	46.7440i	−0.456279	−	0.0804543i
$582$		0			0
$583$	−743.801	+	624.123i	−1.27582	+	1.07054i
$584$		0			0
$585$	51.5416	−	150.039i	0.0881052	−	0.256476i
$586$		0			0
$587$	−218.698	+	600.869i	−0.372570	+	1.02363i	0.601795	+	0.798651i	$0.294453\pi$
$587$	−218.698	+	600.869i	−0.372570	+	1.02363i	−0.974364	+	0.224976i	$0.927770\pi$
$588$		0			0
$589$	360.508	+	302.502i	0.612067	+	0.513586i
$590$		0			0
$591$	0.364948	+	40.1610i	0.000617510	+	0.0679543i
$592$		0			0
$593$		−	576.408i		−	0.972021i	−0.873953	−	0.486010i	$-0.838452\pi$
$593$		−	576.408i		−	0.972021i	0.873953	−	0.486010i	$-0.161548\pi$
$594$		0			0
$595$	−193.041			−0.324439
$596$		0			0
$597$	−115.951	−	196.684i	−0.194223	−	0.329454i
$598$		0			0
$599$	403.522	−	480.899i	0.673660	−	0.802836i	−0.315618	−	0.948886i	$-0.602212\pi$
$599$	403.522	−	480.899i	0.673660	−	0.802836i	0.989277	+	0.146050i	$0.0466561\pi$
$600$		0			0
$601$	139.248	+	50.6819i	0.231693	+	0.0843294i	0.455258	−	0.890360i	$-0.349547\pi$
$601$	139.248	+	50.6819i	0.231693	+	0.0843294i	−0.223565	+	0.974689i	$0.571769\pi$
$602$		0			0
$603$	99.8827	−	38.4240i	0.165643	−	0.0637213i
$604$		0			0
$605$	415.478	+	495.148i	0.686741	+	0.818426i
$606$		0			0
$607$	−5.52421	+	31.3294i	−0.00910085	+	0.0516135i	−0.989020	−	0.147782i	$-0.952787\pi$
$607$	−5.52421	+	31.3294i	−0.00910085	+	0.0516135i	0.979919	+	0.199395i	$0.0638978\pi$
$608$		0			0
$609$	72.4622	−	87.9682i	0.118986	−	0.144447i
$610$		0			0
$611$	159.066	+	91.8371i	0.260338	+	0.150306i
$612$		0			0
$613$	45.0079	+	77.9560i	0.0734223	+	0.127171i	0.900399	−	0.435065i	$-0.143275\pi$
$613$	45.0079	+	77.9560i	0.0734223	+	0.127171i	−0.826977	+	0.562236i	$0.809941\pi$
$614$		0			0
$615$	18.0088	+	96.9716i	0.0292825	+	0.157677i
$616$		0			0
$617$	−176.000	−	483.557i	−0.285252	−	0.783722i	−0.996714	−	0.0809984i	$-0.974189\pi$
$617$	−176.000	−	483.557i	−0.285252	−	0.783722i	0.711463	−	0.702724i	$-0.248033\pi$
$618$		0			0
$619$	156.565	+	887.926i	0.252933	+	1.43445i	0.801324	+	0.598231i	$0.204129\pi$
$619$	156.565	+	887.926i	0.252933	+	1.43445i	−0.548391	+	0.836222i	$0.684759\pi$
$620$		0			0
$621$	−153.292	−	387.924i	−0.246847	−	0.624676i
$622$		0			0
$623$	267.448	−	47.1583i	0.429291	−	0.0756956i
$624$		0			0
$625$	569.674	−	207.344i	0.911478	−	0.331751i
$626$		0			0
$627$	−594.296	−	695.324i	−0.947841	−	1.10897i
$628$		0			0
$629$	−425.612	+	245.727i	−0.676648	+	0.390663i
$630$		0			0
$631$	79.0534	−	136.925i	0.125283	−	0.216996i	−0.796561	−	0.604559i	$-0.793350\pi$
$631$	79.0534	−	136.925i	0.125283	−	0.216996i	0.921843	+	0.387562i	$0.126683\pi$
$632$		0			0
$633$	−1.14365	+	0.428061i	−0.00180671	+	0.000676242i
$634$		0			0
$635$	493.145	+	86.9548i	0.776606	+	0.136937i
$636$		0			0
$637$	102.736	−	86.2055i	0.161281	−	0.135331i
$638$		0			0
$639$	−14.4511	−	795.077i	−0.0226152	−	1.24425i
$640$		0			0
$641$	263.469	−	723.876i	0.411029	−	1.12929i	−0.545616	−	0.838035i	$-0.683704\pi$
$641$	263.469	−	723.876i	0.411029	−	1.12929i	0.956645	−	0.291257i	$-0.0940734\pi$
$642$		0			0
$643$	−179.371	−	150.510i	−0.278959	−	0.234074i	0.492563	−	0.870277i	$-0.336060\pi$
$643$	−179.371	−	150.510i	−0.278959	−	0.234074i	−0.771522	+	0.636202i	$0.780504\pi$
$644$		0			0
$645$	615.844	+	348.135i	0.954796	+	0.539744i
$646$		0			0
$647$		−	1162.87i		−	1.79733i	−0.438638	−	0.898664i	$-0.644539\pi$
$647$		−	1162.87i		−	1.79733i	0.438638	−	0.898664i	$-0.355461\pi$
$648$		0			0
$649$	−713.965			−1.10010
$650$		0			0
$651$	122.814	−	217.256i	0.188655	−	0.333726i
$652$		0			0
$653$	576.994	−	687.635i	0.883605	−	1.05304i	−0.114615	−	0.993410i	$-0.536564\pi$
$653$	576.994	−	687.635i	0.883605	−	1.05304i	0.998221	−	0.0596298i	$-0.0189920\pi$
$654$		0			0
$655$	146.397	+	53.2842i	0.223507	+	0.0813499i
$656$		0			0
$657$	188.011	−	339.757i	0.286165	−	0.517134i
$658$		0			0
$659$	−131.158	−	156.308i	−0.199026	−	0.237190i	0.657296	−	0.753633i	$-0.271700\pi$
$659$	−131.158	−	156.308i	−0.199026	−	0.237190i	−0.856322	+	0.516443i	$0.827256\pi$
$660$		0			0
$661$	−112.430	+	637.624i	−0.170091	+	0.964636i	0.773567	+	0.633715i	$0.218471\pi$
$661$	−112.430	+	637.624i	−0.170091	+	0.964636i	−0.943658	+	0.330921i	$0.892641\pi$
$662$		0			0
$663$	43.4443	+	116.069i	0.0655268	+	0.175067i
$664$		0			0
$665$	−277.994	−	160.500i	−0.418036	−	0.241353i
$666$		0			0
$667$	86.4660	+	149.763i	0.129634	+	0.224533i
$668$		0			0
$669$	32.9604	−	28.1714i	0.0492681	−	0.0421096i
$670$		0			0
$671$	−26.1706	−	71.9032i	−0.0390024	−	0.107158i
$672$		0			0
$673$	−77.1241	−	437.392i	−0.114597	−	0.649914i	−0.986949	−	0.161035i	$-0.948517\pi$
$673$	−77.1241	−	437.392i	−0.114597	−	0.649914i	0.872351	−	0.488880i	$-0.162594\pi$
$674$		0			0
$675$	3.94696	+	19.2932i	0.00584735	+	0.0285825i
$676$		0			0
$677$	−269.098	+	47.4493i	−0.397487	+	0.0700876i	−0.368819	−	0.929501i	$-0.620238\pi$
$677$	−269.098	+	47.4493i	−0.397487	+	0.0700876i	−0.0286680	+	0.999589i	$0.509127\pi$
$678$		0			0
$679$	−587.190	+	213.720i	−0.864786	+	0.314756i
$680$		0			0
$681$	−1025.42	+	190.432i	−1.50575	+	0.279636i
$682$		0			0
$683$	207.206	−	119.631i	0.303377	−	0.175155i	−0.340582	−	0.940215i	$-0.610624\pi$
$683$	207.206	−	119.631i	0.303377	−	0.175155i	0.643959	+	0.765060i	$0.277291\pi$
$684$		0			0
$685$	68.6108	−	118.837i	0.100162	−	0.173485i
$686$		0			0
$687$	226.569	+	186.632i	0.329795	+	0.271662i
$688$		0			0
$689$	215.438	+	37.9875i	0.312682	+	0.0551343i
$690$		0			0
$691$	711.536	−	597.049i	1.02972	−	0.864037i	0.0389016	−	0.999243i	$-0.487614\pi$
$691$	711.536	−	597.049i	1.02972	−	0.864037i	0.990817	+	0.135206i	$0.0431697\pi$
$692$		0			0
$693$	−304.990	+	377.187i	−0.440102	+	0.544282i
$694$		0			0
$695$	331.229	−	910.044i	0.476589	−	1.30942i
$696$		0			0
$697$	−59.0235	−	49.5266i	−0.0846822	−	0.0710568i
$698$		0			0
$699$	178.882	−	105.456i	0.255911	−	0.150867i
$700$		0			0
$701$		−	211.750i		−	0.302068i	−0.988529	−	0.151034i	$-0.951740\pi$
$701$		−	211.750i		−	0.302068i	0.988529	−	0.151034i	$-0.0482604\pi$
$702$		0			0
$703$	−817.217			−1.16247
$704$		0			0
$705$	758.664	−	6.89409i	1.07612	−	0.00977885i
$706$		0			0
$707$	223.118	−	265.902i	0.315584	−	0.376098i
$708$		0			0
$709$	−105.372	−	38.3523i	−0.148621	−	0.0540935i	0.266639	−	0.963797i	$-0.414087\pi$
$709$	−105.372	−	38.3523i	−0.148621	−	0.0540935i	−0.415259	+	0.909703i	$0.636309\pi$
$710$		0			0
$711$	1011.82	−	880.845i	1.42310	−	1.23888i
$712$		0			0
$713$	243.410	+	290.085i	0.341388	+	0.406851i
$714$		0			0
$715$	48.6102	−	275.682i	0.0679863	−	0.385569i
$716$		0			0
$717$	914.979	+	152.776i	1.27612	+	0.213077i
$718$		0			0
$719$	590.067	+	340.675i	0.820677	+	0.473818i	0.850650	−	0.525733i	$-0.176209\pi$
$719$	590.067	+	340.675i	0.820677	+	0.473818i	−0.0299730	+	0.999551i	$0.509542\pi$
$720$		0			0
$721$	−223.884	−	387.778i	−0.310518	−	0.537833i
$722$		0			0
$723$	−563.338	−	199.260i	−0.779167	−	0.275602i
$724$		0			0
$725$	−2.79242	−	7.67211i	−0.00385161	−	0.0105822i
$726$		0			0
$727$	−71.1534	−	403.531i	−0.0978726	−	0.555063i	−0.993829	−	0.110922i	$-0.964620\pi$
$727$	−71.1534	−	403.531i	−0.0978726	−	0.555063i	0.895957	−	0.444142i	$-0.146491\pi$
$728$		0			0
$729$	727.917	−	39.7264i	0.998514	−	0.0544943i
$730$		0			0
$731$	−544.252	+	95.9663i	−0.744531	+	0.131281i
$732$		0			0
$733$	−756.221	+	275.242i	−1.03168	+	0.375501i	−0.801720	−	0.597700i	$-0.796082\pi$
$733$	−756.221	+	275.242i	−1.03168	+	0.375501i	−0.229959	+	0.973200i	$0.573859\pi$
$734$		0			0
$735$	184.731	−	522.263i	0.251335	−	0.710562i
$736$		0			0
$737$	163.539	−	94.4192i	0.221898	−	0.128113i
$738$		0			0
$739$	13.7790	−	23.8659i	0.0186455	−	0.0322949i	−0.856552	−	0.516061i	$-0.827398\pi$
$739$	13.7790	−	23.8659i	0.0186455	−	0.0322949i	0.875198	+	0.483766i	$0.160731\pi$
$740$		0			0
$741$	−33.9404	+	203.270i	−0.0458035	+	0.274318i
$742$		0			0
$743$	257.568	+	45.4162i	0.346660	+	0.0611255i	0.344267	−	0.938872i	$-0.388127\pi$
$743$	257.568	+	45.4162i	0.346660	+	0.0611255i	0.00239254	+	0.999997i	$0.499238\pi$
$744$		0			0
$745$	−513.700	+	431.046i	−0.689530	+	0.578585i
$746$		0			0
$747$	468.723	+	538.420i	0.627474	+	0.720777i
$748$		0			0
$749$	25.0754	−	68.8941i	0.0334785	−	0.0919814i
$750$		0			0
$751$	498.722	+	418.477i	0.664077	+	0.557227i	0.911306	−	0.411730i	$-0.135075\pi$
$751$	498.722	+	418.477i	0.664077	+	0.557227i	−0.247229	+	0.968957i	$0.579520\pi$
$752$		0			0
$753$	1.30585	+	143.703i	0.00173420	+	0.190841i
$754$		0			0
$755$			729.489i			0.966210i
$756$		0			0
$757$	636.818			0.841240			0.420620	−	0.907237i	$-0.361813\pi$
$757$	636.818			0.841240			0.420620	+	0.907237i	$0.361813\pi$
$758$		0			0
$759$	−373.783	−	634.035i	−0.492468	−	0.835356i
$760$		0			0
$761$	−567.900	+	676.797i	−0.746256	+	0.889353i	−0.996896	−	0.0787275i	$-0.974914\pi$
$761$	−567.900	+	676.797i	−0.746256	+	0.889353i	0.250641	+	0.968080i	$0.419359\pi$
$762$		0			0
$763$	−477.803	−	173.906i	−0.626216	−	0.227924i
$764$		0			0
$765$	398.074	+	321.880i	0.520359	+	0.420758i
$766$		0			0
$767$	103.398	+	123.225i	0.134808	+	0.160658i
$768$		0			0
$769$	94.4274	−	535.524i	0.122792	−	0.696391i	−0.859802	−	0.510627i	$-0.829413\pi$
$769$	94.4274	−	535.524i	0.122792	−	0.696391i	0.982595	−	0.185763i	$-0.0594757\pi$
$770$		0			0
$771$	−602.411	+	731.320i	−0.781338	+	0.948535i
$772$		0			0
$773$	−1004.48	−	579.936i	−1.29945	−	0.750241i	−0.319145	−	0.947706i	$-0.603396\pi$
$773$	−1004.48	−	579.936i	−1.29945	−	0.750241i	−0.980310	+	0.197465i	$0.936729\pi$
$774$		0			0
$775$	−8.93911	−	15.4830i	−0.0115343	−	0.0199780i
$776$		0			0
$777$	79.1297	+	426.089i	0.101840	+	0.548377i
$778$		0			0
$779$	−43.8205	−	120.396i	−0.0562522	−	0.154552i
$780$		0			0
$781$	−243.659	−	1381.86i	−0.311984	−	1.76935i
$782$		0			0
$783$	−296.105	+	60.5766i	−0.378168	+	0.0773648i
$784$		0			0
$785$	170.639	−	30.0883i	0.217375	−	0.0383290i
$786$		0			0
$787$	158.838	−	57.8123i	0.201827	−	0.0734590i	−0.239129	−	0.970988i	$-0.576862\pi$
$787$	158.838	−	57.8123i	0.201827	−	0.0734590i	0.440956	+	0.897529i	$0.354640\pi$
$788$		0			0
$789$	−291.659	−	341.240i	−0.369657	−	0.432497i
$790$		0			0
$791$	−273.062	+	157.652i	−0.345211	+	0.199308i
$792$		0			0
$793$	−8.61987	+	14.9300i	−0.0108699	+	0.0188273i
$794$		0			0
$795$	846.290	−	316.763i	1.06452	−	0.398443i
$796$		0			0
$797$	−7.27679	−	1.28309i	−0.00913022	−	0.00160990i	0.169081	−	0.985602i	$-0.445920\pi$
$797$	−7.27679	−	1.28309i	−0.00913022	−	0.00160990i	−0.178211	+	0.983992i	$0.557031\pi$
$798$		0			0
$799$	−454.031	+	380.977i	−0.568248	+	0.476817i
$800$		0			0
$801$	−630.143	−	348.701i	−0.786695	−	0.435332i
$802$		0			0
$803$	234.347	−	643.863i	0.291839	−	0.801822i
$804$		0			0
$805$	−197.865	−	166.028i	−0.245795	−	0.206246i
$806$		0			0
$807$	−157.650	−	89.1191i	−0.195353	−	0.110433i
$808$		0			0
$809$		−	1006.43i		−	1.24404i	−0.783001	−	0.622021i	$-0.786312\pi$
$809$		−	1006.43i		−	1.24404i	0.783001	−	0.622021i	$-0.213688\pi$
$810$		0			0
$811$	−662.217			−0.816543			−0.408272	−	0.912861i	$-0.633868\pi$
$811$	−662.217			−0.816543			−0.408272	+	0.912861i	$0.633868\pi$
$812$		0			0
$813$	188.249	−	333.008i	0.231548	−	0.409605i
$814$		0			0
$815$	−465.969	+	555.320i	−0.571741	+	0.681374i
$816$		0			0
$817$	−863.553	−	314.308i	−1.05698	−	0.384709i
$818$		0			0
$819$	109.269	−	1.98605i	0.133418	−	0.00242497i
$820$		0			0
$821$	−449.086	−	535.200i	−0.546999	−	0.651888i	0.419743	−	0.907643i	$-0.362120\pi$
$821$	−449.086	−	535.200i	−0.546999	−	0.651888i	−0.966742	+	0.255755i	$0.917676\pi$
$822$		0			0
$823$	82.8647	−	469.949i	0.100686	−	0.571020i	−0.892170	−	0.451700i	$-0.850818\pi$
$823$	82.8647	−	469.949i	0.100686	−	0.571020i	0.992856	−	0.119319i	$-0.0380712\pi$
$824$		0			0
$825$	12.1810	+	32.5438i	0.0147648	+	0.0394470i
$826$		0			0
$827$	−1393.63	−	804.614i	−1.68517	−	0.972931i	−0.958131	−	0.286330i	$-0.907565\pi$
$827$	−1393.63	−	804.614i	−1.68517	−	0.972931i	−0.727035	−	0.686601i	$-0.759102\pi$
$828$		0			0
$829$	712.510	+	1234.10i	0.859481	+	1.48867i	0.872424	+	0.488749i	$0.162547\pi$
$829$	712.510	+	1234.10i	0.859481	+	1.48867i	−0.0129428	+	0.999916i	$0.504120\pi$
$830$		0			0
$831$	−404.507	+	345.733i	−0.486771	+	0.416045i
$832$		0			0
$833$	148.014	+	406.665i	0.177688	+	0.488193i
$834$		0			0
$835$	−182.256	−	1033.63i	−0.218271	−	1.23788i
$836$		0			0
$837$	−615.513	+	243.226i	−0.735380	+	0.290592i
$838$		0			0
$839$	−592.994	+	104.561i	−0.706786	+	0.124626i	−0.515476	−	0.856904i	$-0.672385\pi$
$839$	−592.994	+	104.561i	−0.706786	+	0.124626i	−0.191311	+	0.981530i	$0.561274\pi$
$840$		0			0
$841$	−672.533	+	244.782i	−0.799682	+	0.291060i
$842$		0			0
$843$	−1495.45	+	277.722i	−1.77396	+	0.329445i
$844$		0			0
$845$	666.417	−	384.756i	0.788659	−	0.455333i
$846$		0			0
$847$	−222.636	+	385.616i	−0.262852	+	0.455273i
$848$		0			0
$849$	212.042	+	174.666i	0.249755	+	0.205731i
$850$		0			0
$851$	−647.588	−	114.187i	−0.760973	−	0.134180i
$852$		0			0
$853$	−1069.57	+	897.478i	−1.25389	+	1.05214i	−0.257590	+	0.966254i	$0.582928\pi$
$853$	−1069.57	+	897.478i	−1.25389	+	1.05214i	−0.996305	+	0.0858882i	$0.972627\pi$
$854$		0			0
$855$	305.637	+	794.501i	0.357471	+	0.929241i
$856$		0			0
$857$	288.440	−	792.482i	0.336569	−	0.924716i	−0.649791	−	0.760113i	$-0.725143\pi$
$857$	288.440	−	792.482i	0.336569	−	0.924716i	0.986360	−	0.164603i	$-0.0526343\pi$
$858$		0			0
$859$	508.470	+	426.657i	0.591933	+	0.496691i	0.888841	−	0.458215i	$-0.151511\pi$
$859$	508.470	+	426.657i	0.591933	+	0.496691i	−0.296908	+	0.954906i	$0.595956\pi$
$860$		0			0
$861$	−58.5301	+	34.5053i	−0.0679792	+	0.0400758i
$862$		0			0
$863$			437.898i			0.507414i	0.967281	+	0.253707i	$0.0816499\pi$
$863$			437.898i			0.507414i	−0.967281	+	0.253707i	$0.918350\pi$
$864$		0			0
$865$	−260.717			−0.301408
$866$		0			0
$867$	467.062	−	4.24425i	0.538710	−	0.00489533i
$868$		0			0
$869$	1521.59	−	1813.35i	1.75096	−	2.08671i
$870$		0			0
$871$	−39.9801	−	14.5516i	−0.0459014	−	0.0167068i
$872$		0			0
$873$	1567.21	+	538.373i	1.79521	+	0.616693i
$874$		0			0
$875$	276.517	+	329.540i	0.316019	+	0.376617i
$876$		0			0
$877$	257.401	−	1459.79i	0.293501	−	1.66453i	−0.379730	−	0.925098i	$-0.623983\pi$
$877$	257.401	−	1459.79i	0.293501	−	1.66453i	0.673231	−	0.739432i	$-0.264906\pi$
$878$		0			0
$879$	1416.98	+	236.596i	1.61203	+	0.269165i
$880$		0			0
$881$	311.715	+	179.969i	0.353820	+	0.204278i	0.666366	−	0.745625i	$-0.267849\pi$
$881$	311.715	+	179.969i	0.353820	+	0.204278i	−0.312547	+	0.949902i	$0.601182\pi$
$882$		0			0
$883$	262.307	+	454.329i	0.297064	+	0.514529i	0.975463	−	0.220164i	$-0.0706594\pi$
$883$	262.307	+	454.329i	0.297064	+	0.514529i	−0.678399	+	0.734693i	$0.737326\pi$
$884$		0			0
$885$	626.421	+	221.573i	0.707821	+	0.250365i
$886$		0			0
$887$	−413.187	−	1135.22i	−0.465825	−	1.27984i	−0.921042	−	0.389463i	$-0.872661\pi$
$887$	−413.187	−	1135.22i	−0.465825	−	1.27984i	0.455218	−	0.890380i	$-0.349562\pi$
$888$		0			0
$889$	59.9014	+	339.718i	0.0673807	+	0.382135i
$890$		0			0
$891$	1257.85	−	269.260i	1.41173	−	0.302200i
$892$		0			0
$893$	−970.593	+	171.142i	−1.08689	+	0.191648i
$894$		0			0
$895$	−261.018	+	95.0028i	−0.291640	+	0.106148i
$896$		0			0
$897$	−55.2976	+	156.335i	−0.0616473	+	0.174286i
$898$		0			0
$899$	237.628	−	137.194i	0.264324	−	0.152608i
$900$		0			0
$901$	−352.959	+	611.342i	−0.391741	+	0.678515i
$902$		0			0
$903$	−80.2606	+	480.682i	−0.0888821	+	0.532317i
$904$		0			0
$905$	−894.060	−	157.647i	−0.987911	−	0.174195i
$906$		0			0
$907$	1076.97	−	903.682i	1.18739	−	0.996342i	0.187493	−	0.982266i	$-0.439964\pi$
$907$	1076.97	−	903.682i	1.18739	−	0.996342i	0.999901	−	0.0140759i	$-0.00448066\pi$
$908$		0			0
$909$	−903.464	+	176.291i	−0.993910	+	0.193940i
$910$		0			0
$911$	531.891	−	1461.36i	0.583854	−	1.60412i	−0.197684	−	0.980266i	$-0.563342\pi$
$911$	531.891	−	1461.36i	0.583854	−	1.60412i	0.781537	−	0.623859i	$-0.214436\pi$
$912$		0			0
$913$	964.938	+	809.679i	1.05689	+	0.886834i
$914$		0			0
$915$	0.647082	+	71.2086i	0.000707193	+	0.0778236i
$916$		0			0
$917$			107.322i			0.117036i
$918$		0			0
$919$	1361.80			1.48183			0.740916	−	0.671597i	$-0.234391\pi$
$919$	1361.80			1.48183			0.740916	+	0.671597i	$0.234391\pi$
$920$		0			0
$921$	73.5990	+	124.843i	0.0799121	+	0.135552i
$922$		0			0
$923$	−203.212	+	242.178i	−0.220164	+	0.262381i
$924$		0			0
$925$	29.1734	+	10.6182i	0.0315388	+	0.0114792i
$926$		0			0
$927$	−184.911	+	1172.95i	−0.199472	+	1.26532i
$928$		0			0
$929$	997.475	+	1188.74i	1.07371	+	1.27960i	0.958141	+	0.286296i	$0.0924239\pi$
$929$	997.475	+	1188.74i	1.07371	+	1.27960i	0.115567	+	0.993300i	$0.463132\pi$
$930$		0			0
$931$	−124.961	+	708.691i	−0.134223	+	0.761214i
$932$		0			0
$933$	820.587	−	996.183i	0.879515	−	1.06772i
$934$		0			0
$935$	782.296	+	451.659i	0.836680	+	0.483057i
$936$		0			0
$937$	109.572	+	189.785i	0.116939	+	0.202545i	0.918553	−	0.395297i	$-0.129358\pi$
$937$	109.572	+	189.785i	0.116939	+	0.202545i	−0.801614	+	0.597842i	$0.796025\pi$
$938$		0			0
$939$	−110.213	−	593.463i	−0.117373	−	0.632016i
$940$		0			0
$941$	32.0317	+	88.0063i	0.0340400	+	0.0935242i	0.955548	−	0.294834i	$-0.0952644\pi$
$941$	32.0317	+	88.0063i	0.0340400	+	0.0935242i	−0.921508	+	0.388359i	$0.873042\pi$
$942$		0			0
$943$	−17.9022	−	101.528i	−0.0189843	−	0.107665i
$944$		0			0
$945$	384.651	−	236.286i	0.407038	−	0.250039i
$946$		0			0
$947$	492.768	−	86.8883i	0.520346	−	0.0917511i	0.0926944	−	0.995695i	$-0.470452\pi$
$947$	492.768	−	86.8883i	0.520346	−	0.0917511i	0.427652	+	0.903944i	$0.359341\pi$
$948$		0			0
$949$	−145.065	+	52.7992i	−0.152861	+	0.0556367i
$950$		0			0
$951$	35.8078	+	41.8949i	0.0376527	+	0.0440535i
$952$		0			0
$953$	−1162.81	+	671.350i	−1.22016	+	0.704459i	−0.964952	−	0.262427i	$-0.915477\pi$
$953$	−1162.81	+	671.350i	−1.22016	+	0.704459i	−0.255208	+	0.966886i	$0.582144\pi$
$954$		0			0
$955$	−72.6381	+	125.813i	−0.0760609	+	0.131741i
$956$		0			0
$957$	−499.471	+	186.950i	−0.521913	+	0.195350i
$958$		0			0
$959$	93.0931	+	16.4148i	0.0970731	+	0.0171166i
$960$		0			0
$961$	−275.896	+	231.504i	−0.287092	+	0.240899i
$962$		0			0
$963$	−166.583	+	100.257i	−0.172984	+	0.104109i
$964$		0			0
$965$	637.203	−	1750.70i	0.660314	−	1.81420i
$966$		0			0
$967$	−550.128	−	461.612i	−0.568902	−	0.477365i	0.312380	−	0.949957i	$-0.398874\pi$
$967$	−550.128	−	461.612i	−0.568902	−	0.477365i	−0.881281	+	0.472592i	$0.843318\pi$
$968$		0			0
$969$	−578.911	−	327.257i	−0.597431	−	0.337726i
$970$		0			0
$971$		−	1118.48i		−	1.15189i	−0.817489	−	0.575944i	$-0.804635\pi$
$971$		−	1118.48i		−	1.15189i	0.817489	−	0.575944i	$-0.195365\pi$
$972$		0			0
$973$	667.145			0.685658
$974$		0			0
$975$	3.85274	−	6.81541i	0.00395152	−	0.00699017i
$976$		0			0
$977$	413.760	−	493.100i	0.423501	−	0.504709i	−0.511535	−	0.859263i	$-0.670923\pi$
$977$	413.760	−	493.100i	0.423501	−	0.504709i	0.935036	+	0.354554i	$0.115367\pi$
$978$		0			0
$979$	−1194.16	−	434.640i	−1.21978	−	0.443963i
$980$		0			0
$981$	695.314	+	1155.31i	0.708780	+	1.17769i
$982$		0			0
$983$	−222.783	−	265.503i	−0.226636	−	0.270094i	0.640729	−	0.767767i	$-0.278632\pi$
$983$	−222.783	−	265.503i	−0.226636	−	0.270094i	−0.867365	+	0.497673i	$0.834188\pi$
$984$		0			0
$985$	11.4528	−	64.9521i	0.0116272	−	0.0659412i
$986$		0			0
$987$	183.212	+	489.486i	0.185625	+	0.495933i
$988$		0			0
$989$	−640.389	−	369.729i	−0.647512	−	0.373841i
$990$		0			0
$991$	204.099	+	353.510i	0.205953	+	0.356720i	0.950436	−	0.310921i	$-0.100637\pi$
$991$	204.099	+	353.510i	0.205953	+	0.356720i	−0.744483	+	0.667641i	$0.767304\pi$
$992$		0			0
$993$	−346.718	+	296.341i	−0.349162	+	0.298430i
$994$		0			0
$995$	128.237	+	352.327i	0.128881	+	0.354098i
$996$		0			0
$997$	−151.991	−	861.986i	−0.152449	−	0.864579i	−0.961081	−	0.276266i	$-0.910903\pi$
$997$	−151.991	−	861.986i	−0.152449	−	0.864579i	0.808633	−	0.588314i	$-0.200208\pi$
$998$		0			0
$999$	547.291	−	1010.59i	0.547839	−	1.01160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.257.2		30
4.3	odd	2		27.3.f.a.14.1	yes	30
12.11	even	2		81.3.f.a.71.5		30
27.2	odd	18	inner	432.3.bc.a.353.2		30
36.7	odd	6		243.3.f.d.134.5		30
36.11	even	6		243.3.f.a.134.1		30
36.23	even	6		243.3.f.b.53.1		30
36.31	odd	6		243.3.f.c.53.5		30
108.7	odd	18		243.3.f.a.107.1		30
108.11	even	18		243.3.f.c.188.5		30
108.43	odd	18		243.3.f.b.188.1		30
108.47	even	18		243.3.f.d.107.5		30
108.59	even	18		729.3.b.a.728.2		30
108.79	odd	18		81.3.f.a.8.5		30
108.83	even	18		27.3.f.a.2.1	✓	30
108.103	odd	18		729.3.b.a.728.29		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.1	✓	30	108.83	even	18
27.3.f.a.14.1	yes	30	4.3	odd	2
81.3.f.a.8.5		30	108.79	odd	18
81.3.f.a.71.5		30	12.11	even	2
243.3.f.a.107.1		30	108.7	odd	18
243.3.f.a.134.1		30	36.11	even	6
243.3.f.b.53.1		30	36.23	even	6
243.3.f.b.188.1		30	108.43	odd	18
243.3.f.c.53.5		30	36.31	odd	6
243.3.f.c.188.5		30	108.11	even	18
243.3.f.d.107.5		30	108.47	even	18
243.3.f.d.134.5		30	36.7	odd	6
432.3.bc.a.257.2		30	1.1	even	1	trivial
432.3.bc.a.353.2		30	27.2	odd	18	inner
729.3.b.a.728.2		30	108.59	even	18
729.3.b.a.728.29		30	108.103	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.47633 + 2.61160i) q^{3} +(3.16671 - 3.77394i) q^{5} +(3.18911 + 1.16074i) q^{7} +(-4.64090 - 7.71116i) q^{9} +O(q^{10})\)	\(q+(-1.47633 + 2.61160i) q^{3} +(3.16671 - 3.77394i) q^{5} +(3.18911 + 1.16074i) q^{7} +(-4.64090 - 7.71116i) q^{9} +(-10.2080 - 12.1655i) q^{11} +(-0.621316 + 3.52366i) q^{13} +(5.18090 + 13.8417i) q^{15} +(-9.99899 - 5.77292i) q^{17} +(-9.59953 - 16.6269i) q^{19} +(-7.73958 + 6.61505i) q^{21} +(-5.28374 - 14.5170i) q^{23} +(0.126652 + 0.718282i) q^{25} +(26.9900 - 0.735947i) q^{27} +(-11.0239 + 1.94382i) q^{29} +(-23.0339 + 8.38364i) q^{31} +(46.8417 - 8.69905i) q^{33} +(14.4796 - 8.35978i) q^{35} +(21.2827 - 36.8628i) q^{37} +(-8.28512 - 6.82471i) q^{39} +(6.57199 + 1.15882i) q^{41} +(36.6672 - 30.7674i) q^{43} +(-43.7978 - 6.90455i) q^{45} +(17.5573 - 48.2383i) q^{47} +(-28.7131 - 24.0931i) q^{49} +(29.8383 - 17.5906i) q^{51} -61.1404i q^{53} -78.2375 q^{55} +(57.5948 - 0.523372i) q^{57} +(28.8982 - 34.4395i) q^{59} +(4.52766 + 1.64793i) q^{61} +(-5.84968 - 29.9787i) q^{63} +(11.3305 + 13.5032i) q^{65} +(-2.06484 + 11.7103i) q^{67} +(45.7130 + 7.63281i) q^{69} +(76.5190 + 44.1783i) q^{71} +(21.5726 + 37.3649i) q^{73} +(-2.06284 - 0.729655i) q^{75} +(-18.4336 - 50.6459i) q^{77} +(25.8836 + 146.793i) q^{79} +(-37.9241 + 71.5735i) q^{81} +(-78.1129 + 13.7734i) q^{83} +(-53.4505 + 19.4544i) q^{85} +(11.1985 - 31.6598i) q^{87} +(69.3002 - 40.0105i) q^{89} +(-6.07151 + 10.5162i) q^{91} +(12.1109 - 72.5322i) q^{93} +(-93.1477 - 16.4244i) q^{95} +(-141.047 + 118.352i) q^{97} +(-46.4354 + 135.174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Introduction

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