LMFDB - Embedded newform 234.3.bb.f.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,3,Mod(19,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,-6,0,-2,16,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.612074651904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 2067x^{4} - 25778x^{2} + 121801 $ x^8 - 74x^6 + 2067x^4 - 25778*x^2 + 121801
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$3.90972 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.19
Dual form			234.3.bb.f.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.79174 + 4.79174i) q^{5} +(1.13983 - 4.25390i) q^{7} +(2.00000 + 2.00000i) q^{8} +(8.29953 + 4.79174i) q^{10} +(13.8758 - 3.71800i) q^{11} +(1.84809 - 12.8680i) q^{13} -6.22814 q^{14} +(2.00000 - 3.46410i) q^{16} +(20.9957 - 12.1219i) q^{17} +(25.4592 + 6.82178i) q^{19} +(3.50779 - 13.0913i) q^{20} +(-10.1578 - 17.5938i) q^{22} +(5.44507 + 3.14371i) q^{23} -20.9215i q^{25} +(-18.2544 + 2.18546i) q^{26} +(2.27966 + 8.50779i) q^{28} +(-11.1112 + 19.2451i) q^{29} +(-8.59518 + 8.59518i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-24.2437 - 24.2437i) q^{34} +(14.9218 + 25.8453i) q^{35} +(-6.13936 + 1.64504i) q^{37} -37.2749i q^{38} -19.1669 q^{40} +(-18.8845 - 70.4778i) q^{41} +(26.9695 - 15.5708i) q^{43} +(-20.3155 + 20.3155i) q^{44} +(2.30136 - 8.58878i) q^{46} +(-7.65637 - 7.65637i) q^{47} +(25.6388 + 14.8026i) q^{49} +(-28.5793 + 7.65779i) q^{50} +(9.66698 + 24.1361i) q^{52} +33.7616 q^{53} +(-48.6733 + 84.3047i) q^{55} +(10.7875 - 6.22814i) q^{56} +(30.3563 + 8.13394i) q^{58} +(-9.77592 + 36.4842i) q^{59} +(11.5359 + 19.9807i) q^{61} +(14.8873 + 8.59518i) q^{62} +8.00000i q^{64} +(52.8043 + 70.5155i) q^{65} +(-27.8544 - 103.954i) q^{67} +(-24.2437 + 41.9914i) q^{68} +(29.8436 - 29.8436i) q^{70} +(-2.20861 - 0.591796i) q^{71} +(38.1773 + 38.1773i) q^{73} +(4.49432 + 7.78440i) q^{74} +(-50.9185 + 13.6436i) q^{76} -63.2639i q^{77} -19.1299 q^{79} +(7.01559 + 26.1825i) q^{80} +(-89.3622 + 51.5933i) q^{82} +(-34.7720 + 34.7720i) q^{83} +(-42.5210 + 158.691i) q^{85} +(-31.1417 - 31.1417i) q^{86} +(35.1875 + 20.3155i) q^{88} +(-3.47190 + 0.930292i) q^{89} +(-52.6325 - 22.5289i) q^{91} -12.5748 q^{92} +(-7.65637 + 13.2612i) q^{94} +(-154.682 + 89.3058i) q^{95} +(-24.3107 - 6.51404i) q^{97} +(10.8362 - 40.4414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} - 18 q^{10} + 18 q^{11} + 36 q^{13} - 20 q^{14} + 16 q^{16} + 42 q^{17} + 46 q^{19} - 24 q^{20} - 42 q^{22} + 36 q^{23} - 40 q^{26} - 4 q^{28} + 6 q^{29} + 32 q^{31}+ \cdots + 250 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 - 18 * q^10 + 18 * q^11 + 36 * q^13 - 20 * q^14 + 16 * q^16 + 42 * q^17 + 46 * q^19 - 24 * q^20 - 42 * q^22 + 36 * q^23 - 40 * q^26 - 4 * q^28 + 6 * q^29 + 32 * q^31 - 16 * q^32 - 60 * q^34 + 78 * q^35 - 106 * q^37 - 24 * q^40 - 132 * q^41 - 108 * q^43 - 84 * q^44 + 90 * q^46 - 60 * q^47 + 258 * q^49 - 194 * q^50 + 32 * q^52 + 132 * q^53 - 162 * q^55 + 12 * q^56 - 24 * q^58 - 18 * q^59 + 36 * q^61 + 12 * q^62 + 300 * q^65 - 74 * q^67 - 60 * q^68 + 156 * q^70 + 174 * q^71 + 166 * q^73 + 32 * q^74 - 92 * q^76 - 96 * q^79 - 48 * q^80 - 252 * q^82 + 240 * q^83 - 24 * q^85 - 132 * q^86 - 12 * q^88 - 294 * q^89 + 298 * q^91 + 216 * q^92 - 60 * q^94 - 714 * q^95 - 58 * q^97 + 250 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−4.79174	+	4.79174i	−0.958347	+	0.958347i	−0.999167	−	0.0408192i	$-0.987003\pi$
$5$	−4.79174	+	4.79174i	−0.958347	+	0.958347i	0.0408192	+	0.999167i	$0.487003\pi$
$6$		0			0
$7$	1.13983	−	4.25390i	0.162833	−	0.607700i	−0.835474	−	0.549530i	$-0.814807\pi$
$7$	1.13983	−	4.25390i	0.162833	−	0.607700i	0.998307	−	0.0581698i	$-0.0185265\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	8.29953	+	4.79174i	0.829953	+	0.479174i
$11$	13.8758	−	3.71800i	1.26143	−	0.338000i	0.434690	−	0.900580i	$-0.356858\pi$
$11$	13.8758	−	3.71800i	1.26143	−	0.338000i	0.826743	+	0.562580i	$0.190191\pi$
$12$		0			0
$13$	1.84809	−	12.8680i	0.142161	−	0.989844i
$13$	1.84809	−	12.8680i	0.142161	−	0.989844i
$14$	−6.22814			−0.444867
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	20.9957	−	12.1219i	1.23504	−	0.713051i	0.266964	−	0.963707i	$-0.413980\pi$
$17$	20.9957	−	12.1219i	1.23504	−	0.713051i	0.968076	+	0.250656i	$0.0806462\pi$
$18$		0			0
$19$	25.4592	+	6.82178i	1.33996	+	0.359041i	0.856419	−	0.516281i	$-0.172684\pi$
$19$	25.4592	+	6.82178i	1.33996	+	0.359041i	0.483540	+	0.875322i	$0.339351\pi$
$20$	3.50779	−	13.0913i	0.175390	−	0.654563i
$21$		0			0
$22$	−10.1578	−	17.5938i	−0.461716	−	0.799716i
$23$	5.44507	+	3.14371i	0.236742	+	0.136683i	0.613678	−	0.789556i	$-0.289689\pi$
$23$	5.44507	+	3.14371i	0.236742	+	0.136683i	−0.376936	+	0.926239i	$0.623022\pi$
$24$		0			0
$25$		−	20.9215i		−	0.836859i
$26$	−18.2544	+	2.18546i	−0.702093	+	0.0840562i
$27$		0			0
$28$	2.27966	+	8.50779i	0.0814163	+	0.303850i
$29$	−11.1112	+	19.2451i	−0.383144	+	0.663625i	−0.991510	−	0.130032i	$-0.958492\pi$
$29$	−11.1112	+	19.2451i	−0.383144	+	0.663625i	0.608366	+	0.793657i	$0.291825\pi$
$30$		0			0
$31$	−8.59518	+	8.59518i	−0.277264	+	0.277264i	−0.832016	−	0.554752i	$-0.812813\pi$
$31$	−8.59518	+	8.59518i	−0.277264	+	0.277264i	0.554752	+	0.832016i	$0.312813\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$		0			0
$34$	−24.2437	−	24.2437i	−0.713051	−	0.713051i
$35$	14.9218	+	25.8453i	0.426337	+	0.738438i
$36$		0			0
$37$	−6.13936	+	1.64504i	−0.165929	+	0.0444605i	−0.340827	−	0.940126i	$-0.610707\pi$
$37$	−6.13936	+	1.64504i	−0.165929	+	0.0444605i	0.174898	+	0.984587i	$0.444040\pi$
$38$		−	37.2749i		−	0.980919i
$39$		0			0
$40$	−19.1669			−0.479174
$41$	−18.8845	−	70.4778i	−0.460596	−	1.71897i	−0.671091	−	0.741375i	$-0.734174\pi$
$41$	−18.8845	−	70.4778i	−0.460596	−	1.71897i	0.210495	−	0.977595i	$-0.432492\pi$
$42$		0			0
$43$	26.9695	−	15.5708i	0.627197	−	0.362113i	−0.152468	−	0.988308i	$-0.548722\pi$
$43$	26.9695	−	15.5708i	0.627197	−	0.362113i	0.779666	+	0.626196i	$0.215389\pi$
$44$	−20.3155	+	20.3155i	−0.461716	+	0.461716i
$45$		0			0
$46$	2.30136	−	8.58878i	0.0500295	−	0.186713i
$47$	−7.65637	−	7.65637i	−0.162902	−	0.162902i	0.620949	−	0.783851i	$-0.286747\pi$
$47$	−7.65637	−	7.65637i	−0.162902	−	0.162902i	−0.783851	+	0.620949i	$0.786747\pi$
$48$		0			0
$49$	25.6388	+	14.8026i	0.523241	+	0.302093i
$50$	−28.5793	+	7.65779i	−0.571585	+	0.153156i
$51$		0			0
$52$	9.66698	+	24.1361i	0.185903	+	0.464155i
$53$	33.7616			0.637010			0.318505	−	0.947921i	$-0.396819\pi$
$53$	33.7616			0.637010			0.318505	+	0.947921i	$0.396819\pi$
$54$		0			0
$55$	−48.6733	+	84.3047i	−0.884969	+	1.53281i
$56$	10.7875	−	6.22814i	0.192633	−	0.111217i
$57$		0			0
$58$	30.3563	+	8.13394i	0.523384	+	0.140240i
$59$	−9.77592	+	36.4842i	−0.165694	+	0.618377i	0.832257	+	0.554390i	$0.187048\pi$
$59$	−9.77592	+	36.4842i	−0.165694	+	0.618377i	−0.997951	+	0.0639871i	$0.979618\pi$
$60$		0			0
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	0.944955	−	0.327201i	$-0.106106\pi$
$61$	11.5359	+	19.9807i	0.189113	+	0.327553i	−0.755842	+	0.654754i	$0.772772\pi$
$62$	14.8873	+	8.59518i	0.240118	+	0.138632i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	52.8043	+	70.5155i	0.812374	+	1.08485i
$66$		0			0
$67$	−27.8544	−	103.954i	−0.415737	−	1.55155i	−0.783355	−	0.621575i	$-0.786493\pi$
$67$	−27.8544	−	103.954i	−0.415737	−	1.55155i	0.367618	−	0.929977i	$-0.380173\pi$
$68$	−24.2437	+	41.9914i	−0.356525	+	0.617520i
$69$		0			0
$70$	29.8436	−	29.8436i	0.426337	−	0.426337i
$71$	−2.20861	−	0.591796i	−0.0311072	−	0.00833516i	0.243232	−	0.969968i	$-0.421792\pi$
$71$	−2.20861	−	0.591796i	−0.0311072	−	0.00833516i	−0.274339	+	0.961633i	$0.588459\pi$
$72$		0			0
$73$	38.1773	+	38.1773i	0.522977	+	0.522977i	0.918469	−	0.395492i	$-0.129426\pi$
$73$	38.1773	+	38.1773i	0.522977	+	0.522977i	−0.395492	+	0.918469i	$0.629426\pi$
$74$	4.49432	+	7.78440i	0.0607341	+	0.105195i
$75$		0			0
$76$	−50.9185	+	13.6436i	−0.669980	+	0.179521i
$77$		−	63.2639i		−	0.821610i
$78$		0			0
$79$	−19.1299			−0.242150			−0.121075	−	0.992643i	$-0.538634\pi$
$79$	−19.1299			−0.242150			−0.121075	+	0.992643i	$0.538634\pi$
$80$	7.01559	+	26.1825i	0.0876949	+	0.327282i
$81$		0			0
$82$	−89.3622	+	51.5933i	−1.08978	+	0.629187i
$83$	−34.7720	+	34.7720i	−0.418940	+	0.418940i	−0.884838	−	0.465898i	$-0.845731\pi$
$83$	−34.7720	+	34.7720i	−0.418940	+	0.418940i	0.465898	+	0.884838i	$0.345731\pi$
$84$		0			0
$85$	−42.5210	+	158.691i	−0.500247	+	1.86695i
$86$	−31.1417	−	31.1417i	−0.362113	−	0.362113i
$87$		0			0
$88$	35.1875	+	20.3155i	0.399858	+	0.230858i
$89$	−3.47190	+	0.930292i	−0.0390101	+	0.0104527i	−0.278271	−	0.960503i	$-0.589761\pi$
$89$	−3.47190	+	0.930292i	−0.0390101	+	0.0104527i	0.239261	+	0.970955i	$0.423095\pi$
$90$		0			0
$91$	−52.6325	−	22.5289i	−0.578379	−	0.247570i
$92$	−12.5748			−0.136683
$93$		0			0
$94$	−7.65637	+	13.2612i	−0.0814508	+	0.141077i
$95$	−154.682	+	89.3058i	−1.62823	+	0.940061i
$96$		0			0
$97$	−24.3107	−	6.51404i	−0.250626	−	0.0671551i	0.131319	−	0.991340i	$-0.458079\pi$
$97$	−24.3107	−	6.51404i	−0.250626	−	0.0671551i	−0.381945	+	0.924185i	$0.624746\pi$
$98$	10.8362	−	40.4414i	0.110574	−	0.412667i
$99$		0			0
$100$	20.9215	+	36.2371i	0.209215	+	0.362371i
$101$	131.473	+	75.9060i	1.30171	+	0.751545i	0.980698	−	0.195529i	$-0.0626425\pi$
$101$	131.473	+	75.9060i	1.30171	+	0.751545i	0.321016	+	0.947074i	$0.395976\pi$
$102$		0			0
$103$			17.3672i			0.168614i	0.996440	+	0.0843069i	$0.0268676\pi$
$103$			17.3672i			0.168614i	−0.996440	+	0.0843069i	$0.973132\pi$
$104$	29.4321	−	22.0397i	0.283001	−	0.211921i
$105$		0			0
$106$	−12.3576	−	46.1191i	−0.116581	−	0.435086i
$107$	26.5964	−	46.0662i	0.248564	−	0.430526i	−0.714564	−	0.699571i	$-0.753375\pi$
$107$	26.5964	−	46.0662i	0.248564	−	0.430526i	0.963128	+	0.269045i	$0.0867080\pi$
$108$		0			0
$109$	53.3779	−	53.3779i	0.489705	−	0.489705i	−0.418508	−	0.908213i	$-0.637447\pi$
$109$	53.3779	−	53.3779i	0.489705	−	0.489705i	0.908213	+	0.418508i	$0.137447\pi$
$110$	132.978	+	35.6313i	1.20889	+	0.323921i
$111$		0			0
$112$	−12.4563	−	12.4563i	−0.111217	−	0.111217i
$113$	18.1133	+	31.3732i	0.160295	+	0.277639i	0.934974	−	0.354715i	$-0.115422\pi$
$113$	18.1133	+	31.3732i	0.160295	+	0.277639i	−0.774680	+	0.632354i	$0.782089\pi$
$114$		0			0
$115$	−41.1552	+	11.0275i	−0.357871	+	0.0958912i
$116$		−	44.4447i		−	0.383144i
$117$		0			0
$118$	53.4166			0.452683
$119$	−27.6337	−	103.130i	−0.232216	−	0.866641i
$120$		0			0
$121$	73.9242	−	42.6801i	0.610943	−	0.352728i
$122$	23.0717	−	23.0717i	0.189113	−	0.189113i
$123$		0			0
$124$	6.29211	−	23.4825i	0.0507428	−	0.189375i
$125$	−19.5432	−	19.5432i	−0.156346	−	0.156346i
$126$		0			0
$127$	−115.255	−	66.5425i	−0.907520	−	0.523957i	−0.0278874	−	0.999611i	$-0.508878\pi$
$127$	−115.255	−	66.5425i	−0.907520	−	0.523957i	−0.879632	+	0.475654i	$0.842211\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$		0			0
$130$	76.9982	−	97.9425i	0.592294	−	0.753404i
$131$	−38.2739			−0.292167			−0.146083	−	0.989272i	$-0.546667\pi$
$131$	−38.2739			−0.292167			−0.146083	+	0.989272i	$0.546667\pi$
$132$		0			0
$133$	58.0383	−	100.525i	0.436378	−	0.755829i
$134$	−131.808	+	76.0996i	−0.983644	+	0.567907i
$135$		0			0
$136$	66.2351	+	17.7476i	0.487023	+	0.130497i
$137$	−2.07966	+	7.76140i	−0.0151800	+	0.0566525i	−0.973100	−	0.230381i	$-0.926003\pi$
$137$	−2.07966	+	7.76140i	−0.0151800	+	0.0566525i	0.957920	+	0.287034i	$0.0926693\pi$
$138$		0			0
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.854012	+	0.520253i	$0.174162\pi$
$139$	121.981	+	211.277i	0.877558	+	1.51998i	0.0235463	+	0.999723i	$0.492504\pi$
$140$	−51.6906	−	29.8436i	−0.369219	−	0.213169i
$141$		0			0
$142$			3.23364i			0.0227721i
$143$	−22.1994	−	185.424i	−0.155241	−	1.29667i
$144$		0			0
$145$	−38.9757	−	145.459i	−0.268798	−	1.00317i
$146$	38.1773	−	66.1251i	0.261488	−	0.452911i
$147$		0			0
$148$	8.98865	−	8.98865i	0.0607341	−	0.0607341i
$149$	−182.687	−	48.9509i	−1.22609	−	0.328529i	−0.413033	−	0.910716i	$-0.635531\pi$
$149$	−182.687	−	48.9509i	−1.22609	−	0.328529i	−0.813055	+	0.582187i	$0.802197\pi$
$150$		0			0
$151$	−70.5995	−	70.5995i	−0.467546	−	0.467546i	0.433573	−	0.901119i	$-0.357253\pi$
$151$	−70.5995	−	70.5995i	−0.467546	−	0.467546i	−0.901119	+	0.433573i	$0.857253\pi$
$152$	37.2749	+	64.5620i	0.245230	+	0.424750i
$153$		0			0
$154$	−86.4202	+	23.1562i	−0.561170	+	0.150365i
$155$		−	82.3717i		−	0.531430i
$156$		0			0
$157$	176.794			1.12608			0.563038	−	0.826431i	$-0.309632\pi$
$157$	176.794			1.12608			0.563038	+	0.826431i	$0.309632\pi$
$158$	7.00202	+	26.1319i	0.0443166	+	0.165392i
$159$		0			0
$160$	33.1981	−	19.1669i	0.207488	−	0.119793i
$161$	19.5795	−	19.5795i	0.121612	−	0.121612i
$162$		0			0
$163$	31.3812	−	117.116i	0.192523	−	0.718504i	−0.800372	−	0.599504i	$-0.795365\pi$
$163$	31.3812	−	117.116i	0.192523	−	0.718504i	0.992894	−	0.119000i	$-0.0379688\pi$
$164$	103.187	+	103.187i	0.629187	+	0.629187i
$165$		0			0
$166$	60.2269	+	34.7720i	0.362813	+	0.209470i
$167$	−286.599	+	76.7939i	−1.71616	+	0.459844i	−0.976921	−	0.213601i	$-0.931481\pi$
$167$	−286.599	+	76.7939i	−1.71616	+	0.459844i	−0.739238	+	0.673444i	$0.764814\pi$
$168$		0			0
$169$	−162.169	−	47.5624i	−0.959581	−	0.281434i
$170$	232.339			1.36670
$171$		0			0
$172$	−31.1417	+	53.9390i	−0.181056	+	0.313599i
$173$	241.179	−	139.245i	1.39410	−	0.804884i	0.400334	−	0.916369i	$-0.368894\pi$
$173$	241.179	−	139.245i	1.39410	−	0.804884i	0.993766	+	0.111485i	$0.0355608\pi$
$174$		0			0
$175$	−88.9978	−	23.8469i	−0.508559	−	0.136268i
$176$	14.8720	−	55.5030i	0.0845000	−	0.315358i
$177$		0			0
$178$	2.54160	+	4.40219i	0.0142787	+	0.0247314i
$179$	−68.2036	−	39.3774i	−0.381026	−	0.219985i	0.297239	−	0.954803i	$-0.403934\pi$
$179$	−68.2036	−	39.3774i	−0.381026	−	0.219985i	−0.678264	+	0.734818i	$0.737268\pi$
$180$		0			0
$181$		−	200.758i		−	1.10916i	−0.832130	−	0.554581i	$-0.812879\pi$
$181$		−	200.758i		−	1.10916i	0.832130	−	0.554581i	$-0.187121\pi$
$182$	−11.5102	+	80.1435i	−0.0632427	+	0.440349i
$183$		0			0
$184$	4.60271	+	17.1776i	0.0250147	+	0.0933563i
$185$	21.5356	−	37.3008i	0.116409	−	0.201626i
$186$		0			0
$187$	246.262	−	246.262i	1.31691	−	1.31691i
$188$	20.9176	+	5.60485i	0.111264	+	0.0298131i
$189$		0			0
$190$	178.612	+	178.612i	0.940061	+	0.940061i
$191$	20.2650	+	35.1001i	0.106100	+	0.183770i	0.914187	−	0.405293i	$-0.132830\pi$
$191$	20.2650	+	35.1001i	0.106100	+	0.183770i	−0.808087	+	0.589063i	$0.799497\pi$
$192$		0			0
$193$	−140.149	+	37.5529i	−0.726163	+	0.194575i	−0.602920	−	0.797802i	$-0.705996\pi$
$193$	−140.149	+	37.5529i	−0.726163	+	0.194575i	−0.123243	+	0.992377i	$0.539329\pi$
$194$			35.5934i			0.183471i
$195$		0			0
$196$	−59.2103			−0.302093
$197$	40.0731	+	149.555i	0.203417	+	0.759161i	0.989926	+	0.141583i	$0.0452193\pi$
$197$	40.0731	+	149.555i	0.203417	+	0.759161i	−0.786510	+	0.617578i	$0.788114\pi$
$198$		0			0
$199$	−225.470	+	130.175i	−1.13302	+	0.654147i	−0.944691	−	0.327960i	$-0.893639\pi$
$199$	−225.470	+	130.175i	−1.13302	+	0.654147i	−0.188324	+	0.982107i	$0.560305\pi$
$200$	41.8430	−	41.8430i	0.209215	−	0.209215i
$201$		0			0
$202$	55.5671	−	207.379i	0.275084	−	1.02663i
$203$	69.2019	+	69.2019i	0.340896	+	0.340896i
$204$		0			0
$205$	428.200	+	247.221i	2.08878	+	1.20596i
$206$	23.7241	−	6.35684i	0.115165	−	0.0308585i
$207$		0			0
$208$	−40.8798	−	32.1379i	−0.196537	−	0.154509i
$209$	378.630			1.81162
$210$		0			0
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.352831	+	0.935687i	$0.614781\pi$
$211$	−208.203	+	360.618i	−0.986744	+	1.70909i	−0.633913	+	0.773404i	$0.718552\pi$
$212$	−58.4767	+	33.7616i	−0.275834	+	0.159253i
$213$		0			0
$214$	−72.6626	−	19.4699i	−0.339545	−	0.0909808i
$215$	−54.6193	+	203.842i	−0.254043	+	0.948103i
$216$		0			0
$217$	26.7660	+	46.3600i	0.123346	+	0.213641i
$218$	−92.4532	−	53.3779i	−0.424097	−	0.244853i
$219$		0			0
$220$		−	194.693i		−	0.884969i
$221$	−117.182	−	292.574i	−0.530234	−	1.32386i
$222$		0			0
$223$	52.8772	+	197.340i	0.237118	+	0.884935i	0.977183	+	0.212400i	$0.0681279\pi$
$223$	52.8772	+	197.340i	0.237118	+	0.884935i	−0.740065	+	0.672535i	$0.765205\pi$
$224$	−12.4563	+	21.5749i	−0.0556084	+	0.0963165i
$225$		0			0
$226$	36.2266	−	36.2266i	0.160295	−	0.160295i
$227$	107.452	+	28.7917i	0.473358	+	0.126836i	0.487608	−	0.873063i	$-0.337870\pi$
$227$	107.452	+	28.7917i	0.473358	+	0.126836i	−0.0142503	+	0.999898i	$0.504536\pi$
$228$		0			0
$229$	−212.309	−	212.309i	−0.927114	−	0.927114i	0.0704045	−	0.997519i	$-0.477571\pi$
$229$	−212.309	−	212.309i	−0.927114	−	0.927114i	−0.997519	+	0.0704045i	$0.977571\pi$
$230$	30.1277	+	52.1826i	0.130990	+	0.226881i
$231$		0			0
$232$	−60.7126	+	16.2679i	−0.261692	+	0.0701202i
$233$			46.5826i			0.199925i	0.994991	+	0.0999627i	$0.0318723\pi$
$233$			46.5826i			0.199925i	−0.994991	+	0.0999627i	$0.968128\pi$
$234$		0			0
$235$	73.3746			0.312233
$236$	−19.5518	−	72.9685i	−0.0828468	−	0.309188i
$237$		0			0
$238$	−130.764	+	75.4966i	−0.549429	+	0.317213i
$239$	−138.309	+	138.309i	−0.578698	+	0.578698i	−0.934544	−	0.355847i	$-0.884192\pi$
$239$	−138.309	+	138.309i	−0.578698	+	0.578698i	0.355847	+	0.934544i	$0.384192\pi$
$240$		0			0
$241$	−58.1972	+	217.195i	−0.241482	+	0.901223i	0.733637	+	0.679541i	$0.237821\pi$
$241$	−58.1972	+	217.195i	−0.241482	+	0.901223i	−0.975119	+	0.221682i	$0.928845\pi$
$242$	−85.3603	−	85.3603i	−0.352728	−	0.352728i
$243$		0			0
$244$	−39.9614	−	23.0717i	−0.163776	−	0.0945563i
$245$	−193.784	+	51.9244i	−0.790957	+	0.211936i
$246$		0			0
$247$	134.833	−	315.001i	0.545884	−	1.27531i
$248$	−34.3807			−0.138632
$249$		0			0
$250$	−19.5432	+	33.8498i	−0.0781728	+	0.135399i
$251$	−3.02255	+	1.74507i	−0.0120420	+	0.00695247i	−0.506009	−	0.862528i	$-0.668880\pi$
$251$	−3.02255	+	1.74507i	−0.0120420	+	0.00695247i	0.493967	+	0.869481i	$0.335546\pi$
$252$		0			0
$253$	87.2427	+	23.3766i	0.344833	+	0.0923977i
$254$	−48.7125	+	181.798i	−0.191781	+	0.715738i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	160.572	+	92.7065i	0.624795	+	0.360726i	0.778734	−	0.627355i	$-0.215862\pi$
$257$	160.572	+	92.7065i	0.624795	+	0.360726i	−0.153938	+	0.988080i	$0.549196\pi$
$258$		0			0
$259$			27.9913i			0.108074i
$260$	−161.975	−	69.3320i	−0.622982	−	0.266662i
$261$		0			0
$262$	14.0092	+	52.2831i	0.0534703	+	0.199554i
$263$	−93.6758	+	162.251i	−0.356182	+	0.616925i	−0.987319	−	0.158746i	$-0.949255\pi$
$263$	−93.6758	+	162.251i	−0.356182	+	0.616925i	0.631138	+	0.775671i	$0.282588\pi$
$264$		0			0
$265$	−161.776	+	161.776i	−0.610477	+	0.610477i
$266$	−158.564	−	42.4870i	−0.596104	−	0.159726i
$267$		0			0
$268$	152.199	+	152.199i	0.567907	+	0.567907i
$269$	172.006	+	297.923i	0.639427	+	1.10752i	0.985559	+	0.169334i	$0.0541617\pi$
$269$	172.006	+	297.923i	0.639427	+	1.10752i	−0.346132	+	0.938186i	$0.612505\pi$
$270$		0			0
$271$	23.4296	−	6.27795i	0.0864562	−	0.0231659i	−0.215332	−	0.976541i	$-0.569083\pi$
$271$	23.4296	−	6.27795i	0.0864562	−	0.0231659i	0.301788	+	0.953375i	$0.402417\pi$
$272$		−	96.9749i		−	0.356525i
$273$		0			0
$274$	11.3635			0.0414725
$275$	−77.7860	−	290.301i	−0.282858	−	1.05564i
$276$		0			0
$277$	−428.588	+	247.446i	−1.54725	+	0.893306i	−0.548901	+	0.835888i	$0.684953\pi$
$277$	−428.588	+	247.446i	−1.54725	+	0.893306i	−0.998350	+	0.0574180i	$0.981713\pi$
$278$	243.961	−	243.961i	0.877558	−	0.877558i
$279$		0			0
$280$	−21.8470	+	81.5342i	−0.0780251	+	0.291194i
$281$	−145.653	−	145.653i	−0.518337	−	0.518337i	0.398731	−	0.917068i	$-0.369451\pi$
$281$	−145.653	−	145.653i	−0.518337	−	0.518337i	−0.917068	+	0.398731i	$0.869451\pi$
$282$		0			0
$283$	372.577	+	215.107i	1.31653	+	0.760096i	0.983168	−	0.182704i	$-0.0584851\pi$
$283$	372.577	+	215.107i	1.31653	+	0.760096i	0.333357	+	0.942801i	$0.391818\pi$
$284$	4.41723	−	1.18359i	0.0155536	−	0.00416758i
$285$		0			0
$286$	−245.168	+	98.1949i	−0.857232	+	0.343339i
$287$	−321.330			−1.11962
$288$		0			0
$289$	149.379	−	258.732i	0.516883	−	0.895267i
$290$	−184.435	+	106.484i	−0.635983	+	0.367185i
$291$		0			0
$292$	−104.302	−	27.9477i	−0.357200	−	0.0957114i
$293$	−24.5565	+	91.6460i	−0.0838105	+	0.312785i	−0.995086	−	0.0990115i	$-0.968432\pi$
$293$	−24.5565	+	91.6460i	−0.0838105	+	0.312785i	0.911276	+	0.411797i	$0.135099\pi$
$294$		0			0
$295$	−127.979	−	221.667i	−0.433828	−	0.751412i
$296$	−15.5688	−	8.98865i	−0.0525973	−	0.0303671i
$297$		0			0
$298$			267.473i			0.897559i
$299$	50.5161	−	64.2571i	0.168950	−	0.214907i
$300$		0			0
$301$	−35.4962	−	132.474i	−0.117927	−	0.440111i
$302$	−70.5995	+	122.282i	−0.233773	+	0.404907i
$303$		0			0
$304$	74.5498	−	74.5498i	0.245230	−	0.245230i
$305$	−151.019	−	40.4655i	−0.495145	−	0.132674i
$306$		0			0
$307$	210.306	+	210.306i	0.685035	+	0.685035i	0.961130	−	0.276095i	$-0.0890406\pi$
$307$	210.306	+	210.306i	0.685035	+	0.685035i	−0.276095	+	0.961130i	$0.589041\pi$
$308$	63.2639	+	109.576i	0.205402	+	0.355767i
$309$		0			0
$310$	−112.522	+	30.1501i	−0.362974	+	0.0972585i
$311$			246.623i			0.793001i	0.918035	+	0.396500i	$0.129775\pi$
$311$			246.623i			0.793001i	−0.918035	+	0.396500i	$0.870225\pi$
$312$		0			0
$313$	−118.526			−0.378679			−0.189339	−	0.981912i	$-0.560635\pi$
$313$	−118.526			−0.378679			−0.189339	+	0.981912i	$0.560635\pi$
$314$	−64.7111	−	241.505i	−0.206086	−	0.769125i
$315$		0			0
$316$	33.1339	−	19.1299i	0.104854	−	0.0605376i
$317$	284.814	−	284.814i	0.898466	−	0.898466i	−0.0968348	−	0.995300i	$-0.530872\pi$
$317$	284.814	−	284.814i	0.898466	−	0.898466i	0.995300	+	0.0968348i	$0.0308718\pi$
$318$		0			0
$319$	−82.6227	+	308.352i	−0.259005	+	0.966621i
$320$	−38.3339	−	38.3339i	−0.119793	−	0.119793i
$321$		0			0
$322$	−33.9126	−	19.5795i	−0.105319	−	0.0608058i
$323$	617.227	−	165.385i	1.91092	−	0.512029i
$324$		0			0
$325$	−269.217	−	38.6648i	−0.828360	−	0.118969i
$326$	−171.470			−0.525981
$327$		0			0
$328$	103.187	−	178.724i	0.314593	−	0.544892i
$329$	−41.2964	+	23.8425i	−0.125521	+	0.0724695i
$330$		0			0
$331$	−433.118	−	116.054i	−1.30851	−	0.350615i	−0.463850	−	0.885914i	$-0.653532\pi$
$331$	−433.118	−	116.054i	−1.30851	−	0.350615i	−0.844663	+	0.535299i	$0.820199\pi$
$332$	25.4549	−	94.9990i	0.0766714	−	0.286141i
$333$		0			0
$334$	209.805	+	363.392i	0.628158	+	1.08800i
$335$	631.591	+	364.649i	1.88535	+	1.08850i
$336$		0			0
$337$		−	474.455i		−	1.40788i	−0.710260	−	0.703939i	$-0.751423\pi$
$337$		−	474.455i		−	1.40788i	0.710260	−	0.703939i	$-0.248577\pi$
$338$	−5.61338	+	238.936i	−0.0166076	+	0.706912i
$339$		0			0
$340$	−85.0420	−	317.381i	−0.250124	−	0.933474i
$341$	−87.3078	+	151.222i	−0.256035	+	0.443465i
$342$		0			0
$343$	244.782	−	244.782i	0.713650	−	0.713650i
$344$	85.0807	+	22.7973i	0.247328	+	0.0662712i
$345$		0			0
$346$	−278.490	−	278.490i	−0.804884	−	0.804884i
$347$	−266.818	−	462.142i	−0.768927	−	1.33182i	−0.938145	−	0.346242i	$-0.887457\pi$
$347$	−266.818	−	462.142i	−0.768927	−	1.33182i	0.169218	−	0.985579i	$-0.445876\pi$
$348$		0			0
$349$	260.973	−	69.9275i	0.747774	−	0.200365i	0.135244	−	0.990812i	$-0.456818\pi$
$349$	260.973	−	69.9275i	0.747774	−	0.200365i	0.612531	+	0.790447i	$0.290152\pi$
$350$			130.302i			0.372291i
$351$		0			0
$352$	−81.2621			−0.230858
$353$	91.3587	+	340.955i	0.258806	+	0.965879i	0.965933	+	0.258792i	$0.0833243\pi$
$353$	91.3587	+	340.955i	0.258806	+	0.965879i	−0.707127	+	0.707087i	$0.750009\pi$
$354$		0			0
$355$	13.4188	−	7.74736i	0.0377995	−	0.0218236i
$356$	5.08321	−	5.08321i	0.0142787	−	0.0142787i
$357$		0			0
$358$	−28.8262	+	107.581i	−0.0805202	+	0.300505i
$359$	−116.092	−	116.092i	−0.323375	−	0.323375i	0.526685	−	0.850060i	$-0.323435\pi$
$359$	−116.092	−	116.092i	−0.323375	−	0.323375i	−0.850060	+	0.526685i	$0.823435\pi$
$360$		0			0
$361$	289.001	+	166.855i	0.800556	+	0.462201i
$362$	−274.241	+	73.4826i	−0.757572	+	0.202991i
$363$		0			0
$364$	113.691	−	13.6114i	0.312338	−	0.0373938i
$365$	−365.871			−1.00239
$366$		0			0
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.160497	+	0.987036i	$0.551310\pi$
$367$	−343.162	+	594.375i	−0.935047	+	1.61955i	−0.774550	+	0.632513i	$0.782024\pi$
$368$	21.7803	−	12.5748i	0.0591855	−	0.0341708i
$369$		0			0
$370$	−58.8364	−	15.7652i	−0.159017	−	0.0426086i
$371$	38.4824	−	143.618i	0.103726	−	0.387111i
$372$		0			0
$373$	308.636	+	534.572i	0.827441	+	1.43317i	0.900039	+	0.435809i	$0.143538\pi$
$373$	308.636	+	534.572i	0.827441	+	1.43317i	−0.0725981	+	0.997361i	$0.523129\pi$
$374$	−426.538	−	246.262i	−1.14048	−	0.658455i
$375$		0			0
$376$		−	30.6255i		−	0.0814508i
$377$	227.111	+	178.545i	0.602417	+	0.473594i
$378$		0			0
$379$	−138.900	−	518.382i	−0.366491	−	1.36776i	−0.865389	−	0.501101i	$-0.832928\pi$
$379$	−138.900	−	518.382i	−0.366491	−	1.36776i	0.498898	−	0.866661i	$-0.333738\pi$
$380$	178.612	−	309.364i	0.470030	−	0.814116i
$381$		0			0
$382$	40.5301	−	40.5301i	0.106100	−	0.106100i
$383$	253.061	+	67.8074i	0.660732	+	0.177043i	0.573577	−	0.819152i	$-0.305556\pi$
$383$	253.061	+	67.8074i	0.660732	+	0.177043i	0.0871559	+	0.996195i	$0.472222\pi$
$384$		0			0
$385$	303.144	+	303.144i	0.787387	+	0.787387i
$386$	102.596	+	177.702i	0.265794	+	0.460369i
$387$		0			0
$388$	48.6215	−	13.0281i	0.125313	−	0.0335775i
$389$		−	184.591i		−	0.474527i	−0.971445	−	0.237264i	$-0.923749\pi$
$389$		−	184.591i		−	0.474527i	0.971445	−	0.237264i	$-0.0762505\pi$
$390$		0			0
$391$	152.431			0.389848
$392$	21.6725	+	80.8828i	0.0552869	+	0.206334i
$393$		0			0
$394$	189.628	−	109.482i	0.481289	−	0.277872i
$395$	91.6653	−	91.6653i	0.232064	−	0.232064i
$396$		0			0
$397$	65.7046	−	245.213i	0.165503	−	0.617664i	−0.832473	−	0.554066i	$-0.813076\pi$
$397$	65.7046	−	245.213i	0.165503	−	0.617664i	0.997976	−	0.0635986i	$-0.0202578\pi$
$398$	260.350	+	260.350i	0.654147	+	0.654147i
$399$		0			0
$400$	−72.4741	−	41.8430i	−0.181185	−	0.104607i
$401$	261.805	−	70.1504i	0.652880	−	0.174939i	0.0828492	−	0.996562i	$-0.473598\pi$
$401$	261.805	−	70.1504i	0.652880	−	0.174939i	0.570031	+	0.821623i	$0.306931\pi$
$402$		0			0
$403$	94.7178	+	126.487i	0.235032	+	0.313864i
$404$	−303.624			−0.751545
$405$		0			0
$406$	69.2019	−	119.861i	0.170448	−	0.295225i
$407$	−79.0721	+	45.6523i	−0.194280	+	0.112168i
$408$		0			0
$409$	152.496	+	40.8612i	0.372851	+	0.0999051i	0.440378	−	0.897812i	$-0.354844\pi$
$409$	152.496	+	40.8612i	0.372851	+	0.0999051i	−0.0675274	+	0.997717i	$0.521511\pi$
$410$	180.979	−	675.422i	0.441411	−	1.64737i
$411$		0			0
$412$	−17.3672	−	30.0809i	−0.0421534	−	0.0730119i
$413$	144.057	+	83.1715i	0.348807	+	0.201384i
$414$		0			0
$415$		−	333.237i		−	0.802980i
$416$	−28.9382	+	67.6061i	−0.0695629	+	0.162515i
$417$		0			0
$418$	−138.588	−	517.218i	−0.331550	−	1.23736i
$419$	−326.238	+	565.061i	−0.778611	+	1.34859i	0.154132	+	0.988050i	$0.450742\pi$
$419$	−326.238	+	565.061i	−0.778611	+	1.34859i	−0.932743	+	0.360543i	$0.882591\pi$
$420$		0			0
$421$	294.576	−	294.576i	0.699704	−	0.699704i	−0.264642	−	0.964347i	$-0.585254\pi$
$421$	294.576	−	294.576i	0.699704	−	0.699704i	0.964347	+	0.264642i	$0.0852538\pi$
$422$	568.821	+	152.415i	1.34792	+	0.361173i
$423$		0			0
$424$	67.5231	+	67.5231i	0.159253	+	0.159253i
$425$	−253.607	−	439.261i	−0.596723	−	1.03355i
$426$		0			0
$427$	98.1448	−	26.2978i	0.229847	−	0.0615874i
$428$			106.385i			0.248564i
$429$		0			0
$430$	298.445			0.694059
$431$	−18.2792	−	68.2190i	−0.0424112	−	0.158281i	0.941473	−	0.337089i	$-0.109442\pi$
$431$	−18.2792	−	68.2190i	−0.0424112	−	0.158281i	−0.983884	+	0.178808i	$0.942776\pi$
$432$		0			0
$433$	404.363	−	233.459i	0.933864	−	0.539167i	0.0458326	−	0.998949i	$-0.485406\pi$
$433$	404.363	−	233.459i	0.933864	−	0.539167i	0.888032	+	0.459782i	$0.152073\pi$
$434$	53.5320	−	53.5320i	0.123346	−	0.123346i
$435$		0			0
$436$	−39.0753	+	145.831i	−0.0896223	+	0.334475i
$437$	117.182	+	117.182i	0.268150	+	0.268150i
$438$		0			0
$439$	103.577	+	59.8002i	0.235938	+	0.136219i	0.613309	−	0.789843i	$-0.289838\pi$
$439$	103.577	+	59.8002i	0.235938	+	0.136219i	−0.377370	+	0.926063i	$0.623172\pi$
$440$	−265.956	+	71.2627i	−0.604445	+	0.161961i
$441$		0			0
$442$	−356.772	+	267.163i	−0.807177	+	0.604441i
$443$	56.7213			0.128039			0.0640195	−	0.997949i	$-0.479608\pi$
$443$	56.7213			0.128039			0.0640195	+	0.997949i	$0.479608\pi$
$444$		0			0
$445$	12.1787	−	21.0941i	0.0273679	−	0.0474025i
$446$	250.218	−	144.463i	0.561026	−	0.323909i
$447$		0			0
$448$	34.0312	+	9.11863i	0.0759625	+	0.0203541i
$449$	−47.8299	+	178.504i	−0.106525	+	0.397558i	−0.998514	−	0.0545000i	$-0.982643\pi$
$449$	−47.8299	+	178.504i	−0.106525	+	0.397558i	0.891988	+	0.452058i	$0.149310\pi$
$450$		0			0
$451$	−524.072	−	907.720i	−1.16202	−	2.01268i
$452$	−62.7464	−	36.2266i	−0.138819	−	0.0801474i
$453$		0			0
$454$		−	157.321i		−	0.346522i
$455$	360.153	−	144.249i	0.791546	−	0.317030i
$456$		0			0
$457$	76.6418	+	286.031i	0.167706	+	0.625889i	0.997680	+	0.0680852i	$0.0216890\pi$
$457$	76.6418	+	286.031i	0.167706	+	0.625889i	−0.829973	+	0.557803i	$0.811644\pi$
$458$	−212.309	+	367.730i	−0.463557	+	0.802904i
$459$		0			0
$460$	60.2553	−	60.2553i	0.130990	−	0.130990i
$461$	−596.206	−	159.753i	−1.29329	−	0.346535i	−0.454379	−	0.890808i	$-0.650139\pi$
$461$	−596.206	−	159.753i	−1.29329	−	0.346535i	−0.838908	+	0.544273i	$0.816806\pi$
$462$		0			0
$463$	198.699	+	198.699i	0.429156	+	0.429156i	0.888341	−	0.459185i	$-0.151858\pi$
$463$	198.699	+	198.699i	0.429156	+	0.429156i	−0.459185	+	0.888341i	$0.651858\pi$
$464$	44.4447	+	76.9805i	0.0957860	+	0.165906i
$465$		0			0
$466$	63.6330	−	17.0504i	0.136552	−	0.0365889i
$467$		−	522.015i		−	1.11781i	−0.829233	−	0.558903i	$-0.811223\pi$
$467$		−	522.015i		−	1.11781i	0.829233	−	0.558903i	$-0.188777\pi$
$468$		0			0
$469$	−473.959			−1.01057
$470$	−26.8570	−	100.232i	−0.0571425	−	0.213259i
$471$		0			0
$472$	−92.5203	+	53.4166i	−0.196018	+	0.113171i
$473$	316.330	−	316.330i	0.668773	−	0.668773i
$474$		0			0
$475$	142.722	−	532.645i	0.300467	−	1.12136i
$476$	150.993	+	150.993i	0.317213	+	0.317213i
$477$		0			0
$478$	239.558	+	138.309i	0.501167	+	0.289349i
$479$	−327.970	+	87.8794i	−0.684698	+	0.183464i	−0.584367	−	0.811490i	$-0.698657\pi$
$479$	−327.970	+	87.8794i	−0.684698	+	0.183464i	−0.100331	+	0.994954i	$0.531990\pi$
$480$		0			0
$481$	9.82218	+	82.0413i	0.0204203	+	0.170564i
$482$	317.995			0.659741
$483$		0			0
$484$	−85.3603	+	147.848i	−0.176364	+	0.305472i
$485$	147.704	−	85.2771i	0.304545	−	0.175829i
$486$		0			0
$487$	208.431	+	55.8489i	0.427990	+	0.114679i	0.466382	−	0.884583i	$-0.345557\pi$
$487$	208.431	+	55.8489i	0.427990	+	0.114679i	−0.0383927	+	0.999263i	$0.512224\pi$
$488$	−16.8897	+	63.0332i	−0.0346100	+	0.129166i
$489$		0			0
$490$	141.860	+	245.709i	0.289510	+	0.501447i
$491$	480.847	+	277.617i	0.979322	+	0.565412i	0.902065	−	0.431600i	$-0.142051\pi$
$491$	480.847	+	277.617i	0.979322	+	0.565412i	0.0772564	+	0.997011i	$0.475384\pi$
$492$		0			0
$493$			538.753i			1.09280i
$494$	−479.652	−	68.8874i	−0.970956	−	0.139448i
$495$		0			0
$496$	12.5842	+	46.9649i	0.0253714	+	0.0946874i
$497$	−5.03488	+	8.72067i	−0.0101305	+	0.0175466i
$498$		0			0
$499$	−401.619	+	401.619i	−0.804847	+	0.804847i	−0.983849	−	0.179002i	$-0.942713\pi$
$499$	−401.619	+	401.619i	−0.804847	+	0.804847i	0.179002	+	0.983849i	$0.442713\pi$
$500$	53.3930	+	14.3066i	0.106786	+	0.0286132i
$501$		0			0
$502$	3.49014	+	3.49014i	0.00695247	+	0.00695247i
$503$	−196.833	−	340.925i	−0.391319	−	0.677784i	0.601305	−	0.799020i	$-0.294648\pi$
$503$	−196.833	−	340.925i	−0.391319	−	0.677784i	−0.992624	+	0.121236i	$0.961314\pi$
$504$		0			0
$505$	−993.706	+	266.263i	−1.96773	+	0.527253i
$506$		−	127.732i		−	0.252435i
$507$		0			0
$508$	266.170			0.523957
$509$	−113.097	−	422.083i	−0.222194	−	0.829239i	−0.983509	−	0.180858i	$-0.942113\pi$
$509$	−113.097	−	422.083i	−0.222194	−	0.829239i	0.761315	−	0.648382i	$-0.224554\pi$
$510$		0			0
$511$	205.918	−	118.887i	0.402971	−	0.232655i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	67.8659	−	253.279i	0.132035	−	0.492761i
$515$	−83.2191	−	83.2191i	−0.161591	−	0.161591i
$516$		0			0
$517$	−134.704	−	77.7716i	−0.260550	−	0.150429i
$518$	38.2368	−	10.2455i	0.0738162	−	0.0197790i
$519$		0			0
$520$	−35.4223	+	246.640i	−0.0681198	+	0.474307i
$521$	−947.876			−1.81934			−0.909669	−	0.415333i	$-0.863665\pi$
$521$	−947.876			−1.81934			−0.909669	+	0.415333i	$0.863665\pi$
$522$		0			0
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	−0.793258	−	0.608886i	$-0.791617\pi$
$523$	68.3466	−	118.380i	0.130682	−	0.226348i	0.923940	+	0.382538i	$0.124950\pi$
$524$	66.2923	−	38.2739i	0.126512	−	0.0730417i
$525$		0			0
$526$	255.927	+	68.5754i	0.486553	+	0.130372i
$527$	−76.2721	+	284.651i	−0.144729	+	0.540135i
$528$		0			0
$529$	−244.734	−	423.892i	−0.462635	−	0.801308i
$530$	280.205	+	161.776i	0.528689	+	0.305239i
$531$		0			0
$532$			232.153i			0.436378i
$533$	−941.806	+	112.755i	−1.76699	+	0.211548i
$534$		0			0
$535$	93.2946	+	348.180i	0.174382	+	0.650804i
$536$	152.199	−	263.617i	0.283954	−	0.491822i
$537$		0			0
$538$	344.012	−	344.012i	0.639427	−	0.639427i
$539$	410.794	+	110.072i	0.762141	+	0.204215i
$540$		0			0
$541$	−394.763	−	394.763i	−0.729691	−	0.729691i	0.240867	−	0.970558i	$-0.422568\pi$
$541$	−394.763	−	394.763i	−0.729691	−	0.729691i	−0.970558	+	0.240867i	$0.922568\pi$
$542$	−17.1517	−	29.7076i	−0.0316452	−	0.0548110i
$543$		0			0
$544$	−132.470	+	35.4953i	−0.243511	+	0.0652487i
$545$			511.545i			0.938616i
$546$		0			0
$547$	−716.303			−1.30951			−0.654756	−	0.755840i	$-0.727229\pi$
$547$	−716.303			−1.30951			−0.654756	+	0.755840i	$0.727229\pi$
$548$	−4.15932	−	15.5228i	−0.00759000	−	0.0283263i
$549$		0			0
$550$	−368.087	+	212.515i	−0.669250	+	0.386392i
$551$	−414.168	+	414.168i	−0.751666	+	0.751666i
$552$		0			0
$553$	−21.8048	+	81.3765i	−0.0394300	+	0.147155i
$554$	494.891	+	494.891i	0.893306	+	0.893306i
$555$		0			0
$556$	−422.553	−	243.961i	−0.759988	−	0.438779i
$557$	58.2268	−	15.6018i	0.104536	−	0.0280104i	−0.206172	−	0.978516i	$-0.566101\pi$
$557$	58.2268	−	15.6018i	0.104536	−	0.0280104i	0.310708	+	0.950505i	$0.399434\pi$
$558$		0			0
$559$	−150.523	−	375.819i	−0.269272	−	0.672306i
$560$	119.374			0.213169
$561$		0			0
$562$	−145.653	+	252.278i	−0.259168	+	0.448893i
$563$	233.194	−	134.635i	0.414199	−	0.239138i	−0.278393	−	0.960467i	$-0.589802\pi$
$563$	233.194	−	134.635i	0.414199	−	0.239138i	0.692592	+	0.721329i	$0.256469\pi$
$564$		0			0
$565$	−237.126	−	63.5378i	−0.419693	−	0.112456i
$566$	157.469	−	587.684i	0.278215	−	1.03831i
$567$		0			0
$568$	−3.23364	−	5.60082i	−0.00569302	−	0.00986060i
$569$	−232.943	−	134.490i	−0.409390	−	0.236361i	0.281138	−	0.959667i	$-0.409288\pi$
$569$	−232.943	−	134.490i	−0.409390	−	0.236361i	−0.690528	+	0.723306i	$0.742622\pi$
$570$		0			0
$571$		−	328.719i		−	0.575689i	−0.957677	−	0.287845i	$-0.907061\pi$
$571$		−	328.719i		−	0.575689i	0.957677	−	0.287845i	$-0.0929387\pi$
$572$	223.875	+	298.964i	0.391389	+	0.522665i
$573$		0			0
$574$	117.615	+	438.945i	0.204904	+	0.764713i
$575$	65.7711	−	113.919i	0.114384	−	0.198120i
$576$		0			0
$577$	−18.1490	+	18.1490i	−0.0314540	+	0.0314540i	−0.722659	−	0.691205i	$-0.757080\pi$
$577$	−18.1490	+	18.1490i	−0.0314540	+	0.0314540i	0.691205	+	0.722659i	$0.257080\pi$
$578$	−408.111	−	109.353i	−0.706075	−	0.189192i
$579$		0			0
$580$	212.967	+	212.967i	0.367185	+	0.367185i
$581$	108.283	+	187.551i	0.186373	+	0.322807i
$582$		0			0
$583$	468.467	−	125.525i	0.803546	−	0.215309i
$584$			152.709i			0.261488i
$585$		0			0
$586$	134.179			0.228975
$587$	30.1430	+	112.495i	0.0513509	+	0.191644i	0.986837	−	0.161720i	$-0.0517042\pi$
$587$	30.1430	+	112.495i	0.0513509	+	0.191644i	−0.935486	+	0.353364i	$0.885038\pi$
$588$		0			0
$589$	−277.461	+	160.192i	−0.471072	+	0.271973i
$590$	−255.958	+	255.958i	−0.433828	+	0.433828i
$591$		0			0
$592$	−6.58015	+	24.5574i	−0.0111151	+	0.0414822i
$593$	−215.404	−	215.404i	−0.363244	−	0.363244i	0.501762	−	0.865006i	$-0.332685\pi$
$593$	−215.404	−	215.404i	−0.363244	−	0.363244i	−0.865006	+	0.501762i	$0.832685\pi$
$594$		0			0
$595$	626.587	+	361.760i	1.05309	+	0.608000i
$596$	365.374	−	97.9017i	0.613044	−	0.164265i
$597$		0			0
$598$	−106.267	−	45.4866i	−0.177704	−	0.0760646i
$599$	657.704			1.09800			0.549002	−	0.835821i	$-0.315008\pi$
$599$	657.704			1.09800			0.549002	+	0.835821i	$0.315008\pi$
$600$		0			0
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	−0.963211	−	0.268747i	$-0.913390\pi$
$601$	−149.567	+	259.057i	−0.248863	+	0.431044i	0.714347	+	0.699791i	$0.246724\pi$
$602$	−167.970	+	96.9774i	−0.279019	+	0.161092i
$603$		0			0
$604$	192.881	+	51.6824i	0.319340	+	0.0855669i
$605$	−149.713	+	558.737i	−0.247460	+	0.923532i
$606$		0			0
$607$	355.980	+	616.576i	0.586459	+	1.01578i	0.994692	+	0.102898i	$0.0328116\pi$
$607$	355.980	+	616.576i	0.586459	+	1.01578i	−0.408233	+	0.912878i	$0.633855\pi$
$608$	−129.124	−	74.5498i	−0.212375	−	0.122615i
$609$		0			0
$610$			221.107i			0.362471i
$611$	−112.672	+	84.3723i	−0.184405	+	0.138089i
$612$		0			0
$613$	189.142	+	705.887i	0.308551	+	1.15153i	0.929845	+	0.367951i	$0.119941\pi$
$613$	189.142	+	705.887i	0.308551	+	1.15153i	−0.621294	+	0.783578i	$0.713393\pi$
$614$	210.306	−	364.260i	0.342517	−	0.593257i
$615$		0			0
$616$	126.528	−	126.528i	0.205402	−	0.205402i
$617$	−338.746	−	90.7668i	−0.549021	−	0.147110i	−0.0263636	−	0.999652i	$-0.508393\pi$
$617$	−338.746	−	90.7668i	−0.549021	−	0.147110i	−0.522658	+	0.852543i	$0.675059\pi$
$618$		0			0
$619$	283.795	+	283.795i	0.458474	+	0.458474i	0.898154	−	0.439680i	$-0.144908\pi$
$619$	283.795	+	283.795i	0.458474	+	0.458474i	−0.439680	+	0.898154i	$0.644908\pi$
$620$	82.3717	+	142.672i	0.132858	+	0.230116i
$621$		0			0
$622$	336.894	−	90.2704i	0.541630	−	0.145129i
$623$			15.8295i			0.0254084i
$624$		0			0
$625$	710.329			1.13653
$626$	43.3837	+	161.910i	0.0693030	+	0.258642i
$627$		0			0
$628$	−306.216	+	176.794i	−0.487606	+	0.281519i
$629$	−108.959	+	108.959i	−0.173226	+	0.173226i
$630$		0			0
$631$	−298.859	+	1115.36i	−0.473627	+	1.76760i	0.152944	+	0.988235i	$0.451125\pi$
$631$	−298.859	+	1115.36i	−0.473627	+	1.76760i	−0.626570	+	0.779365i	$0.715542\pi$
$632$	−38.2597	−	38.2597i	−0.0605376	−	0.0605376i
$633$		0			0
$634$	−493.312	−	284.814i	−0.778094	−	0.449233i
$635$	871.126	−	233.417i	1.37185	−	0.367587i
$636$		0			0
$637$	237.862	−	302.563i	0.373410	−	0.474981i
$638$	451.459			0.707615
$639$		0			0
$640$	−38.3339	+	66.3963i	−0.0598967	+	0.103744i
$641$	−225.174	+	130.005i	−0.351286	+	0.202815i	−0.665252	−	0.746619i	$-0.731676\pi$
$641$	−225.174	+	130.005i	−0.351286	+	0.202815i	0.313965	+	0.949434i	$0.398342\pi$
$642$		0			0
$643$	11.9154	+	3.19272i	0.0185309	+	0.00496535i	0.268073	−	0.963399i	$-0.413613\pi$
$643$	11.9154	+	3.19272i	0.0185309	+	0.00496535i	−0.249542	+	0.968364i	$0.580280\pi$
$644$	−14.3332	+	53.4921i	−0.0222565	+	0.0830622i
$645$		0			0
$646$	−451.841	−	782.612i	−0.699445	−	1.21147i
$647$	−822.864	−	475.081i	−1.27182	−	0.734283i	−0.296486	−	0.955037i	$-0.595815\pi$
$647$	−822.864	−	475.081i	−1.27182	−	0.734283i	−0.975329	+	0.220755i	$0.929148\pi$
$648$		0			0
$649$			542.593i			0.836045i
$650$	45.7231	+	381.909i	0.0703432	+	0.587553i
$651$		0			0
$652$	62.7624	+	234.232i	0.0962613	+	0.359252i
$653$	282.884	−	489.970i	0.433207	−	0.750336i	−0.563941	−	0.825815i	$-0.690715\pi$
$653$	282.884	−	489.970i	0.433207	−	0.750336i	0.997147	+	0.0754792i	$0.0240486\pi$
$654$		0			0
$655$	183.398	−	183.398i	0.279997	−	0.279997i
$656$	−281.911	−	75.5378i	−0.429742	−	0.115149i
$657$		0			0
$658$	47.6849	+	47.6849i	0.0724695	+	0.0724695i
$659$	190.174	+	329.390i	0.288579	+	0.499833i	0.973471	−	0.228811i	$-0.0734839\pi$
$659$	190.174	+	329.390i	0.288579	+	0.499833i	−0.684892	+	0.728645i	$0.740151\pi$
$660$		0			0
$661$	−960.224	+	257.291i	−1.45268	+	0.389245i	−0.896956	−	0.442119i	$-0.854227\pi$
$661$	−960.224	+	257.291i	−1.45268	+	0.389245i	−0.555728	+	0.831364i	$0.687560\pi$
$662$			634.128i			0.957898i
$663$		0			0
$664$	−139.088			−0.209470
$665$	203.586	+	759.795i	0.306145	+	1.14255i
$666$		0			0
$667$	−121.002	+	69.8606i	−0.181413	+	0.104739i
$668$	419.609	−	419.609i	0.628158	−	0.628158i
$669$		0			0
$670$	266.942	−	996.240i	0.398420	−	1.48693i
$671$	234.357	+	234.357i	0.349266	+	0.349266i
$672$		0			0
$673$	−548.632	−	316.753i	−0.815204	−	0.470658i	0.0335560	−	0.999437i	$-0.489317\pi$
$673$	−548.632	−	316.753i	−0.815204	−	0.470658i	−0.848760	+	0.528779i	$0.822650\pi$
$674$	−648.117	+	173.663i	−0.961599	+	0.257660i
$675$		0			0
$676$	328.448	−	79.7887i	0.485869	−	0.118031i
$677$	221.745			0.327540			0.163770	−	0.986499i	$-0.447634\pi$
$677$	221.745			0.327540			0.163770	+	0.986499i	$0.447634\pi$
$678$		0			0
$679$	−55.4201	+	95.9905i	−0.0816202	+	0.141370i
$680$	−402.423	+	232.339i	−0.591799	+	0.341675i
$681$		0			0
$682$	238.529	+	63.9137i	0.349750	+	0.0937152i
$683$	−173.007	+	645.671i	−0.253304	+	0.945345i	0.715722	+	0.698386i	$0.246098\pi$
$683$	−173.007	+	645.671i	−0.253304	+	0.945345i	−0.969026	+	0.246959i	$0.920569\pi$
$684$		0			0
$685$	−27.2254	−	47.1558i	−0.0397451	−	0.0688405i
$686$	−423.975	−	244.782i	−0.618039	−	0.356825i
$687$		0			0
$688$		−	124.567i		−	0.181056i
$689$	62.3944	−	434.443i	0.0905580	−	0.630541i
$690$		0			0
$691$	−146.869	−	548.121i	−0.212545	−	0.793229i	−0.987016	−	0.160620i	$-0.948651\pi$
$691$	−146.869	−	548.121i	−0.212545	−	0.793229i	0.774471	−	0.632609i	$-0.218016\pi$
$692$	−278.490	+	482.359i	−0.402442	+	0.697050i
$693$		0			0
$694$	−533.636	+	533.636i	−0.768927	+	0.768927i
$695$	−1596.88	−	427.883i	−2.29767	−	0.615659i
$696$		0			0
$697$	−1250.81	−	1250.81i	−1.79457	−	1.79457i
$698$	−191.046	−	330.901i	−0.273704	−	0.474070i
$699$		0			0
$700$	177.996	−	47.6938i	0.254280	−	0.0681340i
$701$			597.453i			0.852287i	0.904656	+	0.426143i	$0.140128\pi$
$701$			597.453i			0.852287i	−0.904656	+	0.426143i	$0.859872\pi$
$702$		0			0
$703$	−167.526			−0.238301
$704$	29.7440	+	111.006i	0.0422500	+	0.157679i
$705$		0			0
$706$	432.314	−	249.596i	0.612342	−	0.353536i
$707$	472.753	−	472.753i	0.668675	−	0.668675i
$708$		0			0
$709$	−10.2632	+	38.3029i	−0.0144757	+	0.0540239i	−0.972786	−	0.231706i	$-0.925569\pi$
$709$	−10.2632	+	38.3029i	−0.0144757	+	0.0540239i	0.958310	+	0.285730i	$0.0922360\pi$
$710$	−15.4947	−	15.4947i	−0.0218236	−	0.0218236i
$711$		0			0
$712$	−8.80437	−	5.08321i	−0.0123657	−	0.00713934i
$713$	−73.8221	+	19.7806i	−0.103537	+	0.0277427i
$714$		0			0
$715$	994.877	+	782.129i	1.39144	+	1.09389i
$716$	157.509			0.219985
$717$		0			0
$718$	−116.092	+	201.077i	−0.161688	+	0.280051i
$719$	864.778	−	499.280i	1.20275	−	0.694409i	0.241585	−	0.970380i	$-0.422333\pi$
$719$	864.778	−	499.280i	1.20275	−	0.694409i	0.961166	+	0.275971i	$0.0889993\pi$
$720$		0			0
$721$	73.8783	+	19.7956i	0.102466	+	0.0274558i
$722$	122.146	−	455.855i	0.169177	−	0.631379i
$723$		0			0
$724$	200.758	+	347.724i	0.277290	+	0.480281i
$725$	402.636	+	232.462i	0.555360	+	0.320638i
$726$		0			0
$727$			685.178i			0.942473i	0.882007	+	0.471237i	$0.156192\pi$
$727$			685.178i			0.942473i	−0.882007	+	0.471237i	$0.843808\pi$
$728$	−60.2073	−	150.323i	−0.0827023	−	0.206487i
$729$		0			0
$730$	133.918	+	499.789i	0.183450	+	0.684643i
$731$	377.495	−	653.841i	0.516409	−	0.894447i
$732$		0			0
$733$	176.253	−	176.253i	0.240454	−	0.240454i	−0.576584	−	0.817038i	$-0.695615\pi$
$733$	176.253	−	176.253i	0.240454	−	0.240454i	0.817038	+	0.576584i	$0.195615\pi$
$734$	937.537	+	251.212i	1.27730	+	0.342251i
$735$		0			0
$736$	−25.1497	−	25.1497i	−0.0341708	−	0.0341708i
$737$	−773.001	−	1338.88i	−1.04885	−	1.81666i
$738$		0			0
$739$	1337.69	−	358.434i	1.81014	−	0.485026i	0.814655	−	0.579946i	$-0.196926\pi$
$739$	1337.69	−	358.434i	1.81014	−	0.485026i	0.995485	+	0.0949200i	$0.0302595\pi$
$740$			86.1425i			0.116409i
$741$		0			0
$742$	−210.272			−0.283385
$743$	150.945	+	563.335i	0.203156	+	0.758190i	0.990004	+	0.141042i	$0.0450452\pi$
$743$	150.945	+	563.335i	0.203156	+	0.758190i	−0.786847	+	0.617148i	$0.788288\pi$
$744$		0			0
$745$	1109.95	−	640.829i	1.48986	−	0.860173i
$746$	617.271	−	617.271i	0.827441	−	0.827441i
$747$		0			0
$748$	−180.276	+	672.800i	−0.241011	+	0.899466i
$749$	−165.646	−	165.646i	−0.221156	−	0.221156i
$750$		0			0
$751$	−1012.32	−	584.461i	−1.34796	−	0.778244i	−0.359998	−	0.932953i	$-0.617223\pi$
$751$	−1012.32	−	584.461i	−1.34796	−	0.778244i	−0.987960	+	0.154709i	$0.950556\pi$
$752$	−41.8352	+	11.2097i	−0.0556319	+	0.0149065i
$753$		0			0
$754$	160.769	−	375.591i	0.213221	−	0.498132i
$755$	676.588			0.896143
$756$		0			0
$757$	561.343	−	972.275i	0.741537	−	1.28438i	−0.210259	−	0.977646i	$-0.567431\pi$
$757$	561.343	−	972.275i	0.741537	−	1.28438i	0.951796	−	0.306733i	$-0.0992360\pi$
$758$	−657.282	+	379.482i	−0.867126	+	0.500636i
$759$		0			0
$760$	−487.976	−	130.753i	−0.642073	−	0.172043i
$761$	−246.221	+	918.907i	−0.323549	+	1.20750i	0.592214	+	0.805781i	$0.298254\pi$
$761$	−246.221	+	918.907i	−0.323549	+	1.20750i	−0.915763	+	0.401719i	$0.868413\pi$
$762$		0			0
$763$	−166.222	−	287.906i	−0.217854	−	0.377334i
$764$	−70.2001	−	40.5301i	−0.0918850	−	0.0530498i
$765$		0			0
$766$		−	370.506i		−	0.483690i
$767$	451.411	+	193.222i	0.588541	+	0.251920i
$768$		0			0
$769$	−53.4110	−	199.332i	−0.0694551	−	0.259210i	0.922464	−	0.386084i	$-0.126172\pi$
$769$	−53.4110	−	199.332i	−0.0694551	−	0.259210i	−0.991919	+	0.126874i	$0.959506\pi$
$770$	303.144	−	525.061i	0.393694	−	0.681898i
$771$		0			0
$772$	205.193	−	205.193i	0.265794	−	0.265794i
$773$	431.675	+	115.667i	0.558441	+	0.149634i	0.526990	−	0.849871i	$-0.323320\pi$
$773$	431.675	+	115.667i	0.558441	+	0.149634i	0.0314512	+	0.999505i	$0.489987\pi$
$774$		0			0
$775$	179.824	+	179.824i	0.232031	+	0.232031i
$776$	−35.5934	−	61.6496i	−0.0458678	−	0.0794453i
$777$		0			0
$778$	−252.156	+	67.5651i	−0.324108	+	0.0868445i
$779$		−	1923.14i		−	2.46872i
$780$		0			0
$781$	−32.8465			−0.0420570
$782$	−55.7934	−	208.224i	−0.0713471	−	0.266271i
$783$		0			0
$784$	102.555	−	59.2103i	0.130810	−	0.0755233i
$785$	−847.151	+	847.151i	−1.07917	+	1.07917i
$786$		0			0
$787$	173.642	−	648.040i	0.220638	−	0.823431i	−0.763468	−	0.645846i	$-0.776505\pi$
$787$	173.642	−	648.040i	0.220638	−	0.823431i	0.984105	−	0.177585i	$-0.0568284\pi$
$788$	−218.963	−	218.963i	−0.277872	−	0.277872i
$789$		0			0
$790$	−158.769	−	91.6653i	−0.200973	−	0.116032i
$791$	154.104	−	41.2921i	0.194822	−	0.0522025i
$792$		0			0
$793$	278.430	−	111.517i	0.351110	−	0.140627i
$794$	−359.016			−0.452162
$795$		0			0
$796$	260.350	−	450.940i	0.327073	−	0.566508i
$797$	207.230	−	119.644i	0.260013	−	0.150118i	−0.364328	−	0.931271i	$-0.618701\pi$
$797$	207.230	−	119.644i	0.260013	−	0.150118i	0.624340	+	0.781152i	$0.285368\pi$
$798$		0			0
$799$	−253.560	−	67.9413i	−0.317347	−	0.0850329i
$800$	−30.6312	+	114.317i	−0.0382890	+	0.142896i
$801$		0			0
$802$	−191.654	−	331.955i	−0.238971	−	0.413909i
$803$	671.683	+	387.796i	0.836466	+	0.482934i
$804$		0			0
$805$			187.639i			0.233092i
$806$	138.116	−	175.684i	0.171359	−	0.217971i
$807$		0			0
$808$	111.134	+	414.758i	0.137542	+	0.513315i
$809$	234.046	−	405.380i	0.289303	−	0.501088i	−0.684340	−	0.729163i	$-0.739910\pi$
$809$	234.046	−	405.380i	0.289303	−	0.501088i	0.973644	+	0.228075i	$0.0732431\pi$
$810$		0			0
$811$	−680.928	+	680.928i	−0.839615	+	0.839615i	−0.988808	−	0.149193i	$-0.952332\pi$
$811$	−680.928	+	680.928i	−0.839615	+	0.839615i	0.149193	+	0.988808i	$0.452332\pi$
$812$	−189.063	−	50.6593i	−0.232836	−	0.0623883i
$813$		0			0
$814$	91.3046	+	91.3046i	0.112168	+	0.112168i
$815$	410.819	+	711.560i	0.504073	+	0.873080i
$816$		0			0
$817$	792.843	−	212.442i	0.970433	−	0.260027i
$818$		−	223.270i		−	0.272946i
$819$		0			0
$820$	−988.886			−1.20596
$821$	326.171	+	1217.29i	0.397285	+	1.48269i	0.817854	+	0.575426i	$0.195164\pi$
$821$	326.171	+	1217.29i	0.397285	+	1.48269i	−0.420569	+	0.907260i	$0.638170\pi$
$822$		0			0
$823$	499.204	−	288.216i	0.606566	−	0.350201i	−0.165054	−	0.986285i	$-0.552780\pi$
$823$	499.204	−	288.216i	0.606566	−	0.350201i	0.771620	+	0.636083i	$0.219447\pi$
$824$	−34.7344	+	34.7344i	−0.0421534	+	0.0421534i
$825$		0			0
$826$	60.8858	−	227.229i	0.0737116	−	0.275095i
$827$	−434.651	−	434.651i	−0.525575	−	0.525575i	0.393675	−	0.919250i	$-0.371204\pi$
$827$	−434.651	−	434.651i	−0.525575	−	0.525575i	−0.919250	+	0.393675i	$0.871204\pi$
$828$		0			0
$829$	−109.340	−	63.1272i	−0.131893	−	0.0761486i	0.432602	−	0.901585i	$-0.357596\pi$
$829$	−109.340	−	63.1272i	−0.131893	−	0.0761486i	−0.564495	+	0.825437i	$0.690929\pi$
$830$	−455.210	+	121.973i	−0.548446	+	0.146956i
$831$		0			0
$832$	102.944	+	14.7847i	0.123730	+	0.0177701i
$833$	717.739			0.861632
$834$		0			0
$835$	1005.33	−	1741.28i	1.20399	−	2.08537i
$836$	−655.806	+	378.630i	−0.784457	+	0.452906i
$837$		0			0
$838$	891.299	+	238.823i	1.06360	+	0.284991i
$839$	329.574	−	1229.99i	0.392817	−	1.46601i	−0.432649	−	0.901562i	$-0.642421\pi$
$839$	329.574	−	1229.99i	0.392817	−	1.46601i	0.825466	−	0.564451i	$-0.190912\pi$
$840$		0			0
$841$	173.584	+	300.656i	0.206401	+	0.357498i
$842$	−510.220	−	294.576i	−0.605962	−	0.349852i
$843$		0			0
$844$		−	832.812i		−	0.986744i
$845$	1004.98	−	549.165i	1.18932	−	0.649900i
$846$		0			0
$847$	−97.2960	−	363.114i	−0.114871	−	0.428706i
$848$	67.5231	−	116.953i	0.0796263	−	0.137917i
$849$		0			0
$850$	−507.215	+	507.215i	−0.596723	+	0.596723i
$851$	−38.6007	−	10.3430i	−0.0453593	−	0.0121540i
$852$		0			0
$853$	162.871	+	162.871i	0.190939	+	0.190939i	0.796102	−	0.605163i	$-0.206892\pi$
$853$	162.871	+	162.871i	0.190939	+	0.190939i	−0.605163	+	0.796102i	$0.706892\pi$
$854$	−71.8470	−	124.443i	−0.0841299	−	0.145717i
$855$		0			0
$856$	145.325	−	38.9398i	0.169772	−	0.0454904i
$857$		−	1077.67i		−	1.25750i	−0.777609	−	0.628748i	$-0.783568\pi$
$857$		−	1077.67i		−	1.25750i	0.777609	−	0.628748i	$-0.216432\pi$
$858$		0			0
$859$	654.044			0.761402			0.380701	−	0.924698i	$-0.375683\pi$
$859$	654.044			0.761402			0.380701	+	0.924698i	$0.375683\pi$
$860$	−109.239	−	407.684i	−0.127022	−	0.474051i
$861$		0			0
$862$	−86.4982	+	49.9398i	−0.100346	+	0.0579348i
$863$	−916.358	+	916.358i	−1.06183	+	1.06183i	−0.0638705	+	0.997958i	$0.520344\pi$
$863$	−916.358	+	916.358i	−1.06183	+	1.06183i	−0.997958	+	0.0638705i	$0.979656\pi$
$864$		0			0
$865$	−488.443	+	1822.89i	−0.564674	+	2.10739i
$866$	−466.918	−	466.918i	−0.539167	−	0.539167i
$867$		0			0
$868$	−92.7201	−	53.5320i	−0.106820	−	0.0616728i
$869$	−265.441	+	71.1248i	−0.305456	+	0.0818468i
$870$		0			0
$871$	−1389.15	+	166.313i	−1.59490	+	0.190945i
$872$	213.512			0.244853
$873$		0			0
$874$	117.182	−	202.964i	0.134075	−	0.232225i
$875$	−105.411	+	60.8589i	−0.120469	+	0.0695530i
$876$		0			0
$877$	−886.252	−	237.471i	−1.01055	−	0.270776i	−0.284691	−	0.958619i	$-0.591891\pi$
$877$	−886.252	−	237.471i	−1.01055	−	0.270776i	−0.725859	+	0.687843i	$0.758558\pi$
$878$	43.7768	−	163.377i	0.0498597	−	0.186079i
$879$		0			0
$880$	194.693	+	337.219i	0.221242	+	0.383203i
$881$	−837.311	−	483.422i	−0.950410	−	0.548719i	−0.0572017	−	0.998363i	$-0.518218\pi$
$881$	−837.311	−	483.422i	−0.950410	−	0.548719i	−0.893208	+	0.449643i	$0.851551\pi$
$882$		0			0
$883$			1129.48i			1.27914i	0.768731	+	0.639572i	$0.220888\pi$
$883$			1129.48i			1.27914i	−0.768731	+	0.639572i	$0.779112\pi$
$884$	495.539	+	389.571i	0.560564	+	0.440692i
$885$		0			0
$886$	−20.7614	−	77.4827i	−0.0234328	−	0.0874523i
$887$	−827.477	+	1433.23i	−0.932894	+	1.61582i	−0.154547	+	0.987985i	$0.549392\pi$
$887$	−827.477	+	1433.23i	−0.932894	+	1.61582i	−0.778347	+	0.627834i	$0.783942\pi$
$888$		0			0
$889$	−414.436	+	414.436i	−0.466182	+	0.466182i
$890$	−33.2728	−	8.91542i	−0.0373852	−	0.0100173i
$891$		0			0
$892$	−288.926	−	288.926i	−0.323909	−	0.323909i
$893$	−142.695	−	247.155i	−0.159793	−	0.276770i
$894$		0			0
$895$	515.500	−	138.128i	0.575977	−	0.154333i
$896$		−	49.8251i		−	0.0556084i
$897$		0			0
$898$	261.348			0.291033
$899$	−69.9127	−	260.918i	−0.0777672	−	0.290231i
$900$		0			0
$901$	708.847	−	409.253i	0.786733	−	0.454221i
$902$	−1048.14	+	1048.14i	−1.16202	+	1.16202i
$903$		0			0
$904$	−26.5197	+	98.9730i	−0.0293360	+	0.109483i
$905$	961.981	+	961.981i	1.06296	+	1.06296i
$906$		0			0
$907$	386.408	+	223.093i	0.426029	+	0.245968i	0.697653	−	0.716435i	$-0.254228\pi$
$907$	386.408	+	223.093i	0.426029	+	0.245968i	−0.271625	+	0.962403i	$0.587561\pi$
$908$	−214.904	+	57.5835i	−0.236679	+	0.0634179i
$909$		0			0
$910$	−328.873	−	439.180i	−0.361399	−	0.482615i
$911$	−1639.85			−1.80005			−0.900025	−	0.435838i	$-0.856452\pi$
$911$	−1639.85			−1.80005			−0.900025	+	0.435838i	$0.856452\pi$
$912$		0			0
$913$	−353.206	+	611.771i	−0.386863	+	0.670067i
$914$	362.673	−	209.389i	0.396797	−	0.229091i
$915$		0			0
$916$	580.039	+	155.421i	0.633231	+	0.169674i
$917$	−43.6256	+	162.813i	−0.0475743	+	0.177550i
$918$		0			0
$919$	−595.311	−	1031.11i	−0.647782	−	1.12199i	−0.983652	−	0.180082i	$-0.942364\pi$
$919$	−595.311	−	1031.11i	−0.647782	−	1.12199i	0.335870	−	0.941908i	$-0.390970\pi$
$920$	−104.365	−	60.2553i	−0.113441	−	0.0654949i
$921$		0			0
$922$			872.906i			0.946752i
$923$	−11.6969	+	27.3267i	−0.0126727	+	0.0296064i
$924$		0			0
$925$	34.4166	+	128.445i	0.0372071	+	0.138859i
$926$	198.699	−	344.157i	0.214578	−	0.371660i
$927$		0			0
$928$	88.8894	−	88.8894i	0.0957860	−	0.0957860i
$929$	770.131	+	206.356i	0.828990	+	0.222127i	0.648273	−	0.761408i	$-0.275492\pi$
$929$	770.131	+	206.356i	0.828990	+	0.222127i	0.180717	+	0.983535i	$0.442158\pi$
$930$		0			0
$931$	551.765	+	551.765i	0.592658	+	0.592658i
$932$	−46.5826	−	80.6834i	−0.0499813	−	0.0865702i
$933$		0			0
$934$	−713.086	+	191.071i	−0.763475	+	0.204573i
$935$			2360.05i			2.52411i
$936$		0			0
$937$	406.611			0.433950			0.216975	−	0.976177i	$-0.430381\pi$
$937$	406.611			0.433950			0.216975	+	0.976177i	$0.430381\pi$
$938$	173.481	+	647.440i	0.184948	+	0.690234i
$939$		0			0
$940$	−127.089	+	73.3746i	−0.135201	+	0.0780581i
$941$	67.4219	−	67.4219i	0.0716492	−	0.0716492i	−0.670374	−	0.742023i	$-0.733866\pi$
$941$	67.4219	−	67.4219i	0.0716492	−	0.0716492i	0.742023	+	0.670374i	$0.233866\pi$
$942$		0			0
$943$	118.735	−	443.123i	0.125911	−	0.469908i
$944$	106.833	+	106.833i	0.113171	+	0.113171i
$945$		0			0
$946$	−547.899	−	316.330i	−0.579175	−	0.334387i
$947$	1589.57	−	425.925i	1.67853	−	0.449762i	0.711143	−	0.703047i	$-0.248178\pi$
$947$	1589.57	−	425.925i	1.67853	−	0.449762i	0.967392	+	0.253285i	$0.0815112\pi$
$948$		0			0
$949$	561.820	−	420.709i	0.592012	−	0.443318i
$950$	−779.846			−0.820891
$951$		0			0
$952$	150.993	−	261.528i	0.158606	−	0.274714i
$953$	807.423	−	466.166i	0.847243	−	0.489156i	−0.0124765	−	0.999922i	$-0.503971\pi$
$953$	807.423	−	466.166i	0.847243	−	0.489156i	0.859720	+	0.510766i	$0.170638\pi$
$954$		0			0
$955$	−265.295	−	71.0856i	−0.277796	−	0.0744351i
$956$	101.249	−	377.866i	0.105909	−	0.395258i
$957$		0			0
$958$	240.091	+	415.850i	0.250617	+	0.434081i
$959$	30.6457	+	17.6933i	0.0319559	+	0.0184498i
$960$		0			0
$961$			813.246i			0.846249i
$962$	108.475	−	43.4465i	0.112760	−	0.0451627i
$963$		0			0
$964$	−116.394	−	434.389i	−0.120741	−	0.450611i
$965$	491.615	−	851.503i	0.509446	−	0.882386i
$966$		0			0
$967$	−540.669	+	540.669i	−0.559120	+	0.559120i	−0.929057	−	0.369937i	$-0.879379\pi$
$967$	−540.669	+	540.669i	−0.559120	+	0.559120i	0.369937	+	0.929057i	$0.379379\pi$
$968$	233.209	+	62.4880i	0.240918	+	0.0645538i
$969$		0			0
$970$	−170.554	−	170.554i	−0.175829	−	0.175829i
$971$	848.378	+	1469.43i	0.873716	+	1.51332i	0.858124	+	0.513442i	$0.171630\pi$
$971$	848.378	+	1469.43i	0.873716	+	1.51332i	0.0155919	+	0.999878i	$0.495037\pi$
$972$		0			0
$973$	1037.79	−	278.074i	1.06658	−	0.285790i
$974$		−	305.164i		−	0.313310i
$975$		0			0
$976$	92.2869			0.0945563
$977$	−73.8571	−	275.638i	−0.0755958	−	0.282127i	0.917772	−	0.397108i	$-0.129986\pi$
$977$	−73.8571	−	275.638i	−0.0755958	−	0.282127i	−0.993368	+	0.114981i	$0.963319\pi$
$978$		0			0
$979$	−44.7164	+	25.8170i	−0.0456756	+	0.0263708i
$980$	283.720	−	283.720i	0.289510	−	0.289510i
$981$		0			0
$982$	203.230	−	758.464i	0.206955	−	0.772367i
$983$	41.0192	+	41.0192i	0.0417286	+	0.0417286i	0.727663	−	0.685935i	$-0.240606\pi$
$983$	41.0192	+	41.0192i	0.0417286	+	0.0417286i	−0.685935	+	0.727663i	$0.740606\pi$
$984$		0			0
$985$	−908.647	−	524.607i	−0.922484	−	0.532596i
$986$	735.950	−	197.197i	0.746399	−	0.199997i
$987$		0			0
$988$	81.4629	+	680.432i	0.0824523	+	0.688696i
$989$	195.801			0.197979
$990$		0			0
$991$	−188.074	+	325.754i	−0.189782	+	0.328712i	−0.945178	−	0.326557i	$-0.894111\pi$
$991$	−188.074	+	325.754i	−0.189782	+	0.328712i	0.755395	+	0.655269i	$0.227445\pi$
$992$	59.5492	−	34.3807i	0.0600294	−	0.0346580i
$993$		0			0
$994$	13.7556	+	3.68579i	0.0138386	+	0.00370804i
$995$	456.628	−	1704.16i	0.458922	−	1.71272i
$996$		0			0
$997$	722.549	+	1251.49i	0.724724	+	1.25526i	0.959088	+	0.283109i	$0.0913659\pi$
$997$	722.549	+	1251.49i	0.724724	+	1.25526i	−0.234364	+	0.972149i	$0.575301\pi$
$998$	695.624	+	401.619i	0.697018	+	0.402424i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.bb.f.19.1		8
3.2	odd	2		26.3.f.b.19.1	yes	8
12.11	even	2		208.3.bd.f.97.2		8
13.11	odd	12	inner	234.3.bb.f.37.1		8
39.2	even	12		338.3.f.i.89.1		8
39.5	even	4		338.3.f.j.319.1		8
39.8	even	4		338.3.f.h.319.1		8
39.11	even	12		26.3.f.b.11.1	✓	8
39.17	odd	6		338.3.d.f.239.3		8
39.20	even	12		338.3.d.g.99.3		8
39.23	odd	6		338.3.f.j.249.1		8
39.29	odd	6		338.3.f.h.249.1		8
39.32	even	12		338.3.d.f.99.3		8
39.35	odd	6		338.3.d.g.239.3		8
39.38	odd	2		338.3.f.i.19.1		8
156.11	odd	12		208.3.bd.f.193.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.1	✓	8	39.11	even	12
26.3.f.b.19.1	yes	8	3.2	odd	2
208.3.bd.f.97.2		8	12.11	even	2
208.3.bd.f.193.2		8	156.11	odd	12
234.3.bb.f.19.1		8	1.1	even	1	trivial
234.3.bb.f.37.1		8	13.11	odd	12	inner
338.3.d.f.99.3		8	39.32	even	12
338.3.d.f.239.3		8	39.17	odd	6
338.3.d.g.99.3		8	39.20	even	12
338.3.d.g.239.3		8	39.35	odd	6
338.3.f.h.249.1		8	39.29	odd	6
338.3.f.h.319.1		8	39.8	even	4
338.3.f.i.19.1		8	39.38	odd	2
338.3.f.i.89.1		8	39.2	even	12
338.3.f.j.249.1		8	39.23	odd	6
338.3.f.j.319.1		8	39.5	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.79174 + 4.79174i) q^{5} +(1.13983 - 4.25390i) q^{7} +(2.00000 + 2.00000i) q^{8} +(8.29953 + 4.79174i) q^{10} +(13.8758 - 3.71800i) q^{11} +(1.84809 - 12.8680i) q^{13} -6.22814 q^{14} +(2.00000 - 3.46410i) q^{16} +(20.9957 - 12.1219i) q^{17} +(25.4592 + 6.82178i) q^{19} +(3.50779 - 13.0913i) q^{20} +(-10.1578 - 17.5938i) q^{22} +(5.44507 + 3.14371i) q^{23} -20.9215i q^{25} +(-18.2544 + 2.18546i) q^{26} +(2.27966 + 8.50779i) q^{28} +(-11.1112 + 19.2451i) q^{29} +(-8.59518 + 8.59518i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-24.2437 - 24.2437i) q^{34} +(14.9218 + 25.8453i) q^{35} +(-6.13936 + 1.64504i) q^{37} -37.2749i q^{38} -19.1669 q^{40} +(-18.8845 - 70.4778i) q^{41} +(26.9695 - 15.5708i) q^{43} +(-20.3155 + 20.3155i) q^{44} +(2.30136 - 8.58878i) q^{46} +(-7.65637 - 7.65637i) q^{47} +(25.6388 + 14.8026i) q^{49} +(-28.5793 + 7.65779i) q^{50} +(9.66698 + 24.1361i) q^{52} +33.7616 q^{53} +(-48.6733 + 84.3047i) q^{55} +(10.7875 - 6.22814i) q^{56} +(30.3563 + 8.13394i) q^{58} +(-9.77592 + 36.4842i) q^{59} +(11.5359 + 19.9807i) q^{61} +(14.8873 + 8.59518i) q^{62} +8.00000i q^{64} +(52.8043 + 70.5155i) q^{65} +(-27.8544 - 103.954i) q^{67} +(-24.2437 + 41.9914i) q^{68} +(29.8436 - 29.8436i) q^{70} +(-2.20861 - 0.591796i) q^{71} +(38.1773 + 38.1773i) q^{73} +(4.49432 + 7.78440i) q^{74} +(-50.9185 + 13.6436i) q^{76} -63.2639i q^{77} -19.1299 q^{79} +(7.01559 + 26.1825i) q^{80} +(-89.3622 + 51.5933i) q^{82} +(-34.7720 + 34.7720i) q^{83} +(-42.5210 + 158.691i) q^{85} +(-31.1417 - 31.1417i) q^{86} +(35.1875 + 20.3155i) q^{88} +(-3.47190 + 0.930292i) q^{89} +(-52.6325 - 22.5289i) q^{91} -12.5748 q^{92} +(-7.65637 + 13.2612i) q^{94} +(-154.682 + 89.3058i) q^{95} +(-24.3107 - 6.51404i) q^{97} +(10.8362 - 40.4414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} - 18 q^{10} + 18 q^{11} + 36 q^{13} - 20 q^{14} + 16 q^{16} + 42 q^{17} + 46 q^{19} - 24 q^{20} - 42 q^{22} + 36 q^{23} - 40 q^{26} - 4 q^{28} + 6 q^{29} + 32 q^{31}+ \cdots + 250 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^5 - 2 * q^7 + 16 * q^8 - 18 * q^10 + 18 * q^11 + 36 * q^13 - 20 * q^14 + 16 * q^16 + 42 * q^17 + 46 * q^19 - 24 * q^20 - 42 * q^22 + 36 * q^23 - 40 * q^26 - 4 * q^28 + 6 * q^29 + 32 * q^31 - 16 * q^32 - 60 * q^34 + 78 * q^35 - 106 * q^37 - 24 * q^40 - 132 * q^41 - 108 * q^43 - 84 * q^44 + 90 * q^46 - 60 * q^47 + 258 * q^49 - 194 * q^50 + 32 * q^52 + 132 * q^53 - 162 * q^55 + 12 * q^56 - 24 * q^58 - 18 * q^59 + 36 * q^61 + 12 * q^62 + 300 * q^65 - 74 * q^67 - 60 * q^68 + 156 * q^70 + 174 * q^71 + 166 * q^73 + 32 * q^74 - 92 * q^76 - 96 * q^79 - 48 * q^80 - 252 * q^82 + 240 * q^83 - 24 * q^85 - 132 * q^86 - 12 * q^88 - 294 * q^89 + 298 * q^91 + 216 * q^92 - 60 * q^94 - 714 * q^95 - 58 * q^97 + 250 * q^98

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