LMFDB - Embedded newform 234.3.bb.f.37.1

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			37.1
Root			$3.90972 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.37
Dual form			234.3.bb.f.19.1

$q$-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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$

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	0.0408192	−	0.999167i	$-0.487003\pi$
$5$	−4.79174	−	4.79174i	−0.958347	−	0.958347i	−0.999167	+	0.0408192i	$0.987003\pi$
$6$		0			0
$7$	1.13983	+	4.25390i	0.162833	+	0.607700i	0.998307	+	0.0581698i	$0.0185265\pi$
$7$	1.13983	+	4.25390i	0.162833	+	0.607700i	−0.835474	+	0.549530i	$0.814807\pi$
$8$	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	0.826743	−	0.562580i	$-0.190191\pi$
$11$	13.8758	+	3.71800i	1.26143	+	0.338000i	0.434690	+	0.900580i	$0.356858\pi$
$12$		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	0.968076	−	0.250656i	$-0.0806462\pi$
$17$	20.9957	+	12.1219i	1.23504	+	0.713051i	0.266964	+	0.963707i	$0.413980\pi$
$18$		0			0
$19$	25.4592	−	6.82178i	1.33996	−	0.359041i	0.483540	−	0.875322i	$-0.339351\pi$
$19$	25.4592	−	6.82178i	1.33996	−	0.359041i	0.856419	+	0.516281i	$0.172684\pi$
$20$	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	−0.376936	−	0.926239i	$-0.623022\pi$
$23$	5.44507	−	3.14371i	0.236742	−	0.136683i	0.613678	+	0.789556i	$0.289689\pi$
$24$		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	0.608366	−	0.793657i	$-0.291825\pi$
$29$	−11.1112	−	19.2451i	−0.383144	−	0.663625i	−0.991510	+	0.130032i	$0.958492\pi$
$30$		0			0
$31$	−8.59518	−	8.59518i	−0.277264	−	0.277264i	0.554752	−	0.832016i	$-0.312813\pi$
$31$	−8.59518	−	8.59518i	−0.277264	−	0.277264i	−0.832016	+	0.554752i	$0.812813\pi$
$32$	−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	0.174898	−	0.984587i	$-0.444040\pi$
$37$	−6.13936	−	1.64504i	−0.165929	−	0.0444605i	−0.340827	+	0.940126i	$0.610707\pi$
$38$			37.2749i			0.980919i
$39$		0			0
$40$	−19.1669			−0.479174
$41$	−18.8845	+	70.4778i	−0.460596	+	1.71897i	0.210495	+	0.977595i	$0.432492\pi$
$41$	−18.8845	+	70.4778i	−0.460596	+	1.71897i	−0.671091	+	0.741375i	$0.734174\pi$
$42$		0			0
$43$	26.9695	+	15.5708i	0.627197	+	0.362113i	0.779666	−	0.626196i	$-0.215389\pi$
$43$	26.9695	+	15.5708i	0.627197	+	0.362113i	−0.152468	+	0.988308i	$0.548722\pi$
$44$	−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	−0.783851	−	0.620949i	$-0.786747\pi$
$47$	−7.65637	+	7.65637i	−0.162902	+	0.162902i	0.620949	+	0.783851i	$0.286747\pi$
$48$		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	−0.997951	−	0.0639871i	$-0.979618\pi$
$59$	−9.77592	−	36.4842i	−0.165694	−	0.618377i	0.832257	−	0.554390i	$-0.187048\pi$
$60$		0			0
$61$	11.5359	−	19.9807i	0.189113	−	0.327553i	−0.755842	−	0.654754i	$-0.772772\pi$
$61$	11.5359	−	19.9807i	0.189113	−	0.327553i	0.944955	+	0.327201i	$0.106106\pi$
$62$	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	0.367618	+	0.929977i	$0.380173\pi$
$67$	−27.8544	+	103.954i	−0.415737	+	1.55155i	−0.783355	+	0.621575i	$0.786493\pi$
$68$	−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	−0.274339	−	0.961633i	$-0.588459\pi$
$71$	−2.20861	+	0.591796i	−0.0311072	+	0.00833516i	0.243232	+	0.969968i	$0.421792\pi$
$72$		0			0
$73$	38.1773	−	38.1773i	0.522977	−	0.522977i	−0.395492	−	0.918469i	$-0.629426\pi$
$73$	38.1773	−	38.1773i	0.522977	−	0.522977i	0.918469	+	0.395492i	$0.129426\pi$
$74$	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	0.465898	−	0.884838i	$-0.345731\pi$
$83$	−34.7720	−	34.7720i	−0.418940	−	0.418940i	−0.884838	+	0.465898i	$0.845731\pi$
$84$		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	0.239261	−	0.970955i	$-0.423095\pi$
$89$	−3.47190	−	0.930292i	−0.0390101	−	0.0104527i	−0.278271	+	0.960503i	$0.589761\pi$
$90$		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	−0.381945	−	0.924185i	$-0.624746\pi$
$97$	−24.3107	+	6.51404i	−0.250626	+	0.0671551i	0.131319	+	0.991340i	$0.458079\pi$
$98$	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	0.321016	−	0.947074i	$-0.395976\pi$
$101$	131.473	−	75.9060i	1.30171	−	0.751545i	0.980698	+	0.195529i	$0.0626425\pi$
$102$		0			0
$103$		−	17.3672i		−	0.168614i	−0.996440	−	0.0843069i	$-0.973132\pi$
$103$		−	17.3672i		−	0.168614i	0.996440	−	0.0843069i	$-0.0268676\pi$
$104$	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	0.963128	−	0.269045i	$-0.0867080\pi$
$107$	26.5964	+	46.0662i	0.248564	+	0.430526i	−0.714564	+	0.699571i	$0.753375\pi$
$108$		0			0
$109$	53.3779	+	53.3779i	0.489705	+	0.489705i	0.908213	−	0.418508i	$-0.137447\pi$
$109$	53.3779	+	53.3779i	0.489705	+	0.489705i	−0.418508	+	0.908213i	$0.637447\pi$
$110$	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	−0.774680	−	0.632354i	$-0.782089\pi$
$113$	18.1133	−	31.3732i	0.160295	−	0.277639i	0.934974	+	0.354715i	$0.115422\pi$
$114$		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	−0.879632	−	0.475654i	$-0.842211\pi$
$127$	−115.255	+	66.5425i	−0.907520	+	0.523957i	−0.0278874	+	0.999611i	$0.508878\pi$
$128$	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	0.957920	−	0.287034i	$-0.0926693\pi$
$137$	−2.07966	−	7.76140i	−0.0151800	−	0.0566525i	−0.973100	+	0.230381i	$0.926003\pi$
$138$		0			0
$139$	121.981	−	211.277i	0.877558	−	1.51998i	0.0235463	−	0.999723i	$-0.492504\pi$
$139$	121.981	−	211.277i	0.877558	−	1.51998i	0.854012	−	0.520253i	$-0.174162\pi$
$140$	−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	−0.813055	−	0.582187i	$-0.802197\pi$
$149$	−182.687	+	48.9509i	−1.22609	+	0.328529i	−0.413033	+	0.910716i	$0.635531\pi$
$150$		0			0
$151$	−70.5995	+	70.5995i	−0.467546	+	0.467546i	−0.901119	−	0.433573i	$-0.857253\pi$
$151$	−70.5995	+	70.5995i	−0.467546	+	0.467546i	0.433573	+	0.901119i	$0.357253\pi$
$152$	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	0.992894	+	0.119000i	$0.0379688\pi$
$163$	31.3812	+	117.116i	0.192523	+	0.718504i	−0.800372	+	0.599504i	$0.795365\pi$
$164$	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	−0.739238	−	0.673444i	$-0.764814\pi$
$167$	−286.599	−	76.7939i	−1.71616	−	0.459844i	−0.976921	+	0.213601i	$0.931481\pi$
$168$		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	0.993766	−	0.111485i	$-0.0355608\pi$
$173$	241.179	+	139.245i	1.39410	+	0.804884i	0.400334	+	0.916369i	$0.368894\pi$
$174$		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	−0.678264	−	0.734818i	$-0.737268\pi$
$179$	−68.2036	+	39.3774i	−0.381026	+	0.219985i	0.297239	+	0.954803i	$0.403934\pi$
$180$		0			0
$181$			200.758i			1.10916i	0.832130	+	0.554581i	$0.187121\pi$
$181$			200.758i			1.10916i	−0.832130	+	0.554581i	$0.812879\pi$
$182$	−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	−0.808087	−	0.589063i	$-0.799497\pi$
$191$	20.2650	−	35.1001i	0.106100	−	0.183770i	0.914187	+	0.405293i	$0.132830\pi$
$192$		0			0
$193$	−140.149	−	37.5529i	−0.726163	−	0.194575i	−0.123243	−	0.992377i	$-0.539329\pi$
$193$	−140.149	−	37.5529i	−0.726163	−	0.194575i	−0.602920	+	0.797802i	$0.705996\pi$
$194$		−	35.5934i		−	0.183471i
$195$		0			0
$196$	−59.2103			−0.302093
$197$	40.0731	−	149.555i	0.203417	−	0.759161i	−0.786510	−	0.617578i	$-0.788114\pi$
$197$	40.0731	−	149.555i	0.203417	−	0.759161i	0.989926	−	0.141583i	$-0.0452193\pi$
$198$		0			0
$199$	−225.470	−	130.175i	−1.13302	−	0.654147i	−0.188324	−	0.982107i	$-0.560305\pi$
$199$	−225.470	−	130.175i	−1.13302	−	0.654147i	−0.944691	+	0.327960i	$0.893639\pi$
$200$	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	−0.633913	−	0.773404i	$-0.718552\pi$
$211$	−208.203	−	360.618i	−0.986744	−	1.70909i	−0.352831	−	0.935687i	$-0.614781\pi$
$212$	−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	−0.740065	−	0.672535i	$-0.765205\pi$
$223$	52.8772	−	197.340i	0.237118	−	0.884935i	0.977183	−	0.212400i	$-0.0681279\pi$
$224$	−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	−0.0142503	−	0.999898i	$-0.504536\pi$
$227$	107.452	−	28.7917i	0.473358	−	0.126836i	0.487608	+	0.873063i	$0.337870\pi$
$228$		0			0
$229$	−212.309	+	212.309i	−0.927114	+	0.927114i	−0.997519	−	0.0704045i	$-0.977571\pi$
$229$	−212.309	+	212.309i	−0.927114	+	0.927114i	0.0704045	+	0.997519i	$0.477571\pi$
$230$	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	$-0.968128\pi$
$233$		−	46.5826i		−	0.199925i	0.994991	−	0.0999627i	$-0.0318723\pi$
$234$		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	0.355847	−	0.934544i	$-0.384192\pi$
$239$	−138.309	−	138.309i	−0.578698	−	0.578698i	−0.934544	+	0.355847i	$0.884192\pi$
$240$		0			0
$241$	−58.1972	−	217.195i	−0.241482	−	0.901223i	−0.975119	−	0.221682i	$-0.928845\pi$
$241$	−58.1972	−	217.195i	−0.241482	−	0.901223i	0.733637	−	0.679541i	$-0.237821\pi$
$242$	−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	0.493967	−	0.869481i	$-0.335546\pi$
$251$	−3.02255	−	1.74507i	−0.0120420	−	0.00695247i	−0.506009	+	0.862528i	$0.668880\pi$
$252$		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	−0.153938	−	0.988080i	$-0.549196\pi$
$257$	160.572	−	92.7065i	0.624795	−	0.360726i	0.778734	+	0.627355i	$0.215862\pi$
$258$		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	0.631138	−	0.775671i	$-0.282588\pi$
$263$	−93.6758	−	162.251i	−0.356182	−	0.616925i	−0.987319	+	0.158746i	$0.949255\pi$
$264$		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	−0.346132	−	0.938186i	$-0.612505\pi$
$269$	172.006	−	297.923i	0.639427	−	1.10752i	0.985559	−	0.169334i	$-0.0541617\pi$
$270$		0			0
$271$	23.4296	+	6.27795i	0.0864562	+	0.0231659i	0.301788	−	0.953375i	$-0.402417\pi$
$271$	23.4296	+	6.27795i	0.0864562	+	0.0231659i	−0.215332	+	0.976541i	$0.569083\pi$
$272$			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	−0.998350	−	0.0574180i	$-0.981713\pi$
$277$	−428.588	−	247.446i	−1.54725	−	0.893306i	−0.548901	−	0.835888i	$-0.684953\pi$
$278$	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	−0.917068	−	0.398731i	$-0.869451\pi$
$281$	−145.653	+	145.653i	−0.518337	+	0.518337i	0.398731	+	0.917068i	$0.369451\pi$
$282$		0			0
$283$	372.577	−	215.107i	1.31653	−	0.760096i	0.333357	−	0.942801i	$-0.391818\pi$
$283$	372.577	−	215.107i	1.31653	−	0.760096i	0.983168	+	0.182704i	$0.0584851\pi$
$284$	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	0.911276	−	0.411797i	$-0.135099\pi$
$293$	−24.5565	−	91.6460i	−0.0838105	−	0.312785i	−0.995086	+	0.0990115i	$0.968432\pi$
$294$		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	−0.276095	−	0.961130i	$-0.589041\pi$
$307$	210.306	−	210.306i	0.685035	−	0.685035i	0.961130	+	0.276095i	$0.0890406\pi$
$308$	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	$-0.870225\pi$
$311$		−	246.623i		−	0.793001i	0.918035	−	0.396500i	$-0.129775\pi$
$312$		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	0.995300	−	0.0968348i	$-0.0308718\pi$
$317$	284.814	+	284.814i	0.898466	+	0.898466i	−0.0968348	+	0.995300i	$0.530872\pi$
$318$		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	−0.844663	−	0.535299i	$-0.820199\pi$
$331$	−433.118	+	116.054i	−1.30851	+	0.350615i	−0.463850	+	0.885914i	$0.653532\pi$
$332$	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	$0.248577\pi$
$337$			474.455i			1.40788i	−0.710260	+	0.703939i	$0.751423\pi$
$338$	−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	0.169218	+	0.985579i	$0.445876\pi$
$347$	−266.818	+	462.142i	−0.768927	+	1.33182i	−0.938145	+	0.346242i	$0.887457\pi$
$348$		0			0
$349$	260.973	+	69.9275i	0.747774	+	0.200365i	0.612531	−	0.790447i	$-0.290152\pi$
$349$	260.973	+	69.9275i	0.747774	+	0.200365i	0.135244	+	0.990812i	$0.456818\pi$
$350$		−	130.302i		−	0.372291i
$351$		0			0
$352$	−81.2621			−0.230858
$353$	91.3587	−	340.955i	0.258806	−	0.965879i	−0.707127	−	0.707087i	$-0.750009\pi$
$353$	91.3587	−	340.955i	0.258806	−	0.965879i	0.965933	−	0.258792i	$-0.0833243\pi$
$354$		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	−0.850060	−	0.526685i	$-0.823435\pi$
$359$	−116.092	+	116.092i	−0.323375	+	0.323375i	0.526685	+	0.850060i	$0.323435\pi$
$360$		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	−0.774550	−	0.632513i	$-0.782024\pi$
$367$	−343.162	−	594.375i	−0.935047	−	1.61955i	−0.160497	−	0.987036i	$-0.551310\pi$
$368$	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	−0.0725981	−	0.997361i	$-0.523129\pi$
$373$	308.636	−	534.572i	0.827441	−	1.43317i	0.900039	−	0.435809i	$-0.143538\pi$
$374$	−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	0.498898	+	0.866661i	$0.333738\pi$
$379$	−138.900	+	518.382i	−0.366491	+	1.36776i	−0.865389	+	0.501101i	$0.832928\pi$
$380$	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	0.0871559	−	0.996195i	$-0.472222\pi$
$383$	253.061	−	67.8074i	0.660732	−	0.177043i	0.573577	+	0.819152i	$0.305556\pi$
$384$		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	$0.0762505\pi$
$389$			184.591i			0.474527i	−0.971445	+	0.237264i	$0.923749\pi$
$390$		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	0.997976	+	0.0635986i	$0.0202578\pi$
$397$	65.7046	+	245.213i	0.165503	+	0.617664i	−0.832473	+	0.554066i	$0.813076\pi$
$398$	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	0.570031	−	0.821623i	$-0.306931\pi$
$401$	261.805	+	70.1504i	0.652880	+	0.174939i	0.0828492	+	0.996562i	$0.473598\pi$
$402$		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	−0.0675274	−	0.997717i	$-0.521511\pi$
$409$	152.496	−	40.8612i	0.372851	−	0.0999051i	0.440378	+	0.897812i	$0.354844\pi$
$410$	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	−0.932743	−	0.360543i	$-0.882591\pi$
$419$	−326.238	−	565.061i	−0.778611	−	1.34859i	0.154132	−	0.988050i	$-0.450742\pi$
$420$		0			0
$421$	294.576	+	294.576i	0.699704	+	0.699704i	0.964347	−	0.264642i	$-0.0852538\pi$
$421$	294.576	+	294.576i	0.699704	+	0.699704i	−0.264642	+	0.964347i	$0.585254\pi$
$422$	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	−0.983884	−	0.178808i	$-0.942776\pi$
$431$	−18.2792	+	68.2190i	−0.0424112	+	0.158281i	0.941473	+	0.337089i	$0.109442\pi$
$432$		0			0
$433$	404.363	+	233.459i	0.933864	+	0.539167i	0.888032	−	0.459782i	$-0.152073\pi$
$433$	404.363	+	233.459i	0.933864	+	0.539167i	0.0458326	+	0.998949i	$0.485406\pi$
$434$	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	−0.377370	−	0.926063i	$-0.623172\pi$
$439$	103.577	−	59.8002i	0.235938	−	0.136219i	0.613309	+	0.789843i	$0.289838\pi$
$440$	−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	0.891988	−	0.452058i	$-0.149310\pi$
$449$	−47.8299	−	178.504i	−0.106525	−	0.397558i	−0.998514	+	0.0545000i	$0.982643\pi$
$450$		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	−0.829973	−	0.557803i	$-0.811644\pi$
$457$	76.6418	−	286.031i	0.167706	−	0.625889i	0.997680	−	0.0680852i	$-0.0216890\pi$
$458$	−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	−0.838908	−	0.544273i	$-0.816806\pi$
$461$	−596.206	+	159.753i	−1.29329	+	0.346535i	−0.454379	+	0.890808i	$0.650139\pi$
$462$		0			0
$463$	198.699	−	198.699i	0.429156	−	0.429156i	−0.459185	−	0.888341i	$-0.651858\pi$
$463$	198.699	−	198.699i	0.429156	−	0.429156i	0.888341	+	0.459185i	$0.151858\pi$
$464$	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	$0.188777\pi$
$467$			522.015i			1.11781i	−0.829233	+	0.558903i	$0.811223\pi$
$468$		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	−0.100331	−	0.994954i	$-0.531990\pi$
$479$	−327.970	−	87.8794i	−0.684698	−	0.183464i	−0.584367	+	0.811490i	$0.698657\pi$
$480$		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	−0.0383927	−	0.999263i	$-0.512224\pi$
$487$	208.431	−	55.8489i	0.427990	−	0.114679i	0.466382	+	0.884583i	$0.345557\pi$
$488$	−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	0.0772564	−	0.997011i	$-0.475384\pi$
$491$	480.847	−	277.617i	0.979322	−	0.565412i	0.902065	+	0.431600i	$0.142051\pi$
$492$		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	0.179002	−	0.983849i	$-0.442713\pi$
$499$	−401.619	−	401.619i	−0.804847	−	0.804847i	−0.983849	+	0.179002i	$0.942713\pi$
$500$	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	−0.992624	−	0.121236i	$-0.961314\pi$
$503$	−196.833	+	340.925i	−0.391319	+	0.677784i	0.601305	+	0.799020i	$0.294648\pi$
$504$		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	0.761315	+	0.648382i	$0.224554\pi$
$509$	−113.097	+	422.083i	−0.222194	+	0.829239i	−0.983509	+	0.180858i	$0.942113\pi$
$510$		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	0.923940	−	0.382538i	$-0.124950\pi$
$523$	68.3466	+	118.380i	0.130682	+	0.226348i	−0.793258	+	0.608886i	$0.791617\pi$
$524$	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	−0.970558	−	0.240867i	$-0.922568\pi$
$541$	−394.763	+	394.763i	−0.729691	+	0.729691i	0.240867	+	0.970558i	$0.422568\pi$
$542$	−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	0.310708	−	0.950505i	$-0.399434\pi$
$557$	58.2268	+	15.6018i	0.104536	+	0.0280104i	−0.206172	+	0.978516i	$0.566101\pi$
$558$		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	0.692592	−	0.721329i	$-0.256469\pi$
$563$	233.194	+	134.635i	0.414199	+	0.239138i	−0.278393	+	0.960467i	$0.589802\pi$
$564$		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	−0.690528	−	0.723306i	$-0.742622\pi$
$569$	−232.943	+	134.490i	−0.409390	+	0.236361i	0.281138	+	0.959667i	$0.409288\pi$
$570$		0			0
$571$			328.719i			0.575689i	0.957677	+	0.287845i	$0.0929387\pi$
$571$			328.719i			0.575689i	−0.957677	+	0.287845i	$0.907061\pi$
$572$	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	0.691205	−	0.722659i	$-0.257080\pi$
$577$	−18.1490	−	18.1490i	−0.0314540	−	0.0314540i	−0.722659	+	0.691205i	$0.757080\pi$
$578$	−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	−0.935486	−	0.353364i	$-0.885038\pi$
$587$	30.1430	−	112.495i	0.0513509	−	0.191644i	0.986837	+	0.161720i	$0.0517042\pi$
$588$		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	−0.865006	−	0.501762i	$-0.832685\pi$
$593$	−215.404	+	215.404i	−0.363244	+	0.363244i	0.501762	+	0.865006i	$0.332685\pi$
$594$		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	0.714347	−	0.699791i	$-0.246724\pi$
$601$	−149.567	−	259.057i	−0.248863	−	0.431044i	−0.963211	+	0.268747i	$0.913390\pi$
$602$	−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	−0.408233	−	0.912878i	$-0.633855\pi$
$607$	355.980	−	616.576i	0.586459	−	1.01578i	0.994692	−	0.102898i	$-0.0328116\pi$
$608$	−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	−0.621294	−	0.783578i	$-0.713393\pi$
$613$	189.142	−	705.887i	0.308551	−	1.15153i	0.929845	−	0.367951i	$-0.119941\pi$
$614$	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	−0.522658	−	0.852543i	$-0.675059\pi$
$617$	−338.746	+	90.7668i	−0.549021	+	0.147110i	−0.0263636	+	0.999652i	$0.508393\pi$
$618$		0			0
$619$	283.795	−	283.795i	0.458474	−	0.458474i	−0.439680	−	0.898154i	$-0.644908\pi$
$619$	283.795	−	283.795i	0.458474	−	0.458474i	0.898154	+	0.439680i	$0.144908\pi$
$620$	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	−0.626570	−	0.779365i	$-0.715542\pi$
$631$	−298.859	−	1115.36i	−0.473627	−	1.76760i	0.152944	−	0.988235i	$-0.451125\pi$
$632$	−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	0.313965	−	0.949434i	$-0.398342\pi$
$641$	−225.174	−	130.005i	−0.351286	−	0.202815i	−0.665252	+	0.746619i	$0.731676\pi$
$642$		0			0
$643$	11.9154	−	3.19272i	0.0185309	−	0.00496535i	−0.249542	−	0.968364i	$-0.580280\pi$
$643$	11.9154	−	3.19272i	0.0185309	−	0.00496535i	0.268073	+	0.963399i	$0.413613\pi$
$644$	−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	−0.975329	−	0.220755i	$-0.929148\pi$
$647$	−822.864	+	475.081i	−1.27182	+	0.734283i	−0.296486	+	0.955037i	$0.595815\pi$
$648$		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	0.997147	−	0.0754792i	$-0.0240486\pi$
$653$	282.884	+	489.970i	0.433207	+	0.750336i	−0.563941	+	0.825815i	$0.690715\pi$
$654$		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	−0.684892	−	0.728645i	$-0.740151\pi$
$659$	190.174	−	329.390i	0.288579	−	0.499833i	0.973471	+	0.228811i	$0.0734839\pi$
$660$		0			0
$661$	−960.224	−	257.291i	−1.45268	−	0.389245i	−0.555728	−	0.831364i	$-0.687560\pi$
$661$	−960.224	−	257.291i	−1.45268	−	0.389245i	−0.896956	+	0.442119i	$0.854227\pi$
$662$		−	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	−0.848760	−	0.528779i	$-0.822650\pi$
$673$	−548.632	+	316.753i	−0.815204	+	0.470658i	0.0335560	+	0.999437i	$0.489317\pi$
$674$	−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	−0.969026	−	0.246959i	$-0.920569\pi$
$683$	−173.007	−	645.671i	−0.253304	−	0.945345i	0.715722	−	0.698386i	$-0.246098\pi$
$684$		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	0.774471	+	0.632609i	$0.218016\pi$
$691$	−146.869	+	548.121i	−0.212545	+	0.793229i	−0.987016	+	0.160620i	$0.948651\pi$
$692$	−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	$-0.859872\pi$
$701$		−	597.453i		−	0.852287i	0.904656	−	0.426143i	$-0.140128\pi$
$702$		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	0.958310	−	0.285730i	$-0.0922360\pi$
$709$	−10.2632	−	38.3029i	−0.0144757	−	0.0540239i	−0.972786	+	0.231706i	$0.925569\pi$
$710$	−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	0.961166	−	0.275971i	$-0.0889993\pi$
$719$	864.778	+	499.280i	1.20275	+	0.694409i	0.241585	+	0.970380i	$0.422333\pi$
$720$		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	$-0.843808\pi$
$727$		−	685.178i		−	0.942473i	0.882007	−	0.471237i	$-0.156192\pi$
$728$	−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	0.817038	−	0.576584i	$-0.195615\pi$
$733$	176.253	+	176.253i	0.240454	+	0.240454i	−0.576584	+	0.817038i	$0.695615\pi$
$734$	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	0.995485	−	0.0949200i	$-0.0302595\pi$
$739$	1337.69	+	358.434i	1.81014	+	0.485026i	0.814655	+	0.579946i	$0.196926\pi$
$740$		−	86.1425i		−	0.116409i
$741$		0			0
$742$	−210.272			−0.283385
$743$	150.945	−	563.335i	0.203156	−	0.758190i	−0.786847	−	0.617148i	$-0.788288\pi$
$743$	150.945	−	563.335i	0.203156	−	0.758190i	0.990004	−	0.141042i	$-0.0450452\pi$
$744$		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	−0.987960	−	0.154709i	$-0.950556\pi$
$751$	−1012.32	+	584.461i	−1.34796	+	0.778244i	−0.359998	+	0.932953i	$0.617223\pi$
$752$	−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	0.951796	+	0.306733i	$0.0992360\pi$
$757$	561.343	+	972.275i	0.741537	+	1.28438i	−0.210259	+	0.977646i	$0.567431\pi$
$758$	−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	−0.915763	−	0.401719i	$-0.868413\pi$
$761$	−246.221	−	918.907i	−0.323549	−	1.20750i	0.592214	−	0.805781i	$-0.298254\pi$
$762$		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	−0.991919	−	0.126874i	$-0.959506\pi$
$769$	−53.4110	+	199.332i	−0.0694551	+	0.259210i	0.922464	+	0.386084i	$0.126172\pi$
$770$	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	0.0314512	−	0.999505i	$-0.489987\pi$
$773$	431.675	−	115.667i	0.558441	−	0.149634i	0.526990	+	0.849871i	$0.323320\pi$
$774$		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	0.984105	+	0.177585i	$0.0568284\pi$
$787$	173.642	+	648.040i	0.220638	+	0.823431i	−0.763468	+	0.645846i	$0.776505\pi$
$788$	−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	0.624340	−	0.781152i	$-0.285368\pi$
$797$	207.230	+	119.644i	0.260013	+	0.150118i	−0.364328	+	0.931271i	$0.618701\pi$
$798$		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	0.973644	−	0.228075i	$-0.0732431\pi$
$809$	234.046	+	405.380i	0.289303	+	0.501088i	−0.684340	+	0.729163i	$0.739910\pi$
$810$		0			0
$811$	−680.928	−	680.928i	−0.839615	−	0.839615i	0.149193	−	0.988808i	$-0.452332\pi$
$811$	−680.928	−	680.928i	−0.839615	−	0.839615i	−0.988808	+	0.149193i	$0.952332\pi$
$812$	−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	−0.420569	−	0.907260i	$-0.638170\pi$
$821$	326.171	−	1217.29i	0.397285	−	1.48269i	0.817854	−	0.575426i	$-0.195164\pi$
$822$		0			0
$823$	499.204	+	288.216i	0.606566	+	0.350201i	0.771620	−	0.636083i	$-0.219447\pi$
$823$	499.204	+	288.216i	0.606566	+	0.350201i	−0.165054	+	0.986285i	$0.552780\pi$
$824$	−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	−0.919250	−	0.393675i	$-0.871204\pi$
$827$	−434.651	+	434.651i	−0.525575	+	0.525575i	0.393675	+	0.919250i	$0.371204\pi$
$828$		0			0
$829$	−109.340	+	63.1272i	−0.131893	+	0.0761486i	−0.564495	−	0.825437i	$-0.690929\pi$
$829$	−109.340	+	63.1272i	−0.131893	+	0.0761486i	0.432602	+	0.901585i	$0.357596\pi$
$830$	−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	0.825466	+	0.564451i	$0.190912\pi$
$839$	329.574	+	1229.99i	0.392817	+	1.46601i	−0.432649	+	0.901562i	$0.642421\pi$
$840$		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	−0.605163	−	0.796102i	$-0.706892\pi$
$853$	162.871	−	162.871i	0.190939	−	0.190939i	0.796102	+	0.605163i	$0.206892\pi$
$854$	−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	$0.216432\pi$
$857$			1077.67i			1.25750i	−0.777609	+	0.628748i	$0.783568\pi$
$858$		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	−0.997958	−	0.0638705i	$-0.979656\pi$
$863$	−916.358	−	916.358i	−1.06183	−	1.06183i	−0.0638705	−	0.997958i	$-0.520344\pi$
$864$		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	−0.725859	−	0.687843i	$-0.758558\pi$
$877$	−886.252	+	237.471i	−1.01055	+	0.270776i	−0.284691	+	0.958619i	$0.591891\pi$
$878$	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	−0.893208	−	0.449643i	$-0.851551\pi$
$881$	−837.311	+	483.422i	−0.950410	+	0.548719i	−0.0572017	+	0.998363i	$0.518218\pi$
$882$		0			0
$883$		−	1129.48i		−	1.27914i	−0.768731	−	0.639572i	$-0.779112\pi$
$883$		−	1129.48i		−	1.27914i	0.768731	−	0.639572i	$-0.220888\pi$
$884$	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	−0.778347	−	0.627834i	$-0.783942\pi$
$887$	−827.477	−	1433.23i	−0.932894	−	1.61582i	−0.154547	−	0.987985i	$-0.549392\pi$
$888$		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	−0.271625	−	0.962403i	$-0.587561\pi$
$907$	386.408	−	223.093i	0.426029	−	0.245968i	0.697653	+	0.716435i	$0.254228\pi$
$908$	−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	0.335870	+	0.941908i	$0.390970\pi$
$919$	−595.311	+	1031.11i	−0.647782	+	1.12199i	−0.983652	+	0.180082i	$0.942364\pi$
$920$	−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	0.180717	−	0.983535i	$-0.442158\pi$
$929$	770.131	−	206.356i	0.828990	−	0.222127i	0.648273	+	0.761408i	$0.275492\pi$
$930$		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	0.742023	−	0.670374i	$-0.233866\pi$
$941$	67.4219	+	67.4219i	0.0716492	+	0.0716492i	−0.670374	+	0.742023i	$0.733866\pi$
$942$		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	0.967392	−	0.253285i	$-0.0815112\pi$
$947$	1589.57	+	425.925i	1.67853	+	0.449762i	0.711143	+	0.703047i	$0.248178\pi$
$948$		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	0.859720	−	0.510766i	$-0.170638\pi$
$953$	807.423	+	466.166i	0.847243	+	0.489156i	−0.0124765	+	0.999922i	$0.503971\pi$
$954$		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	0.369937	−	0.929057i	$-0.379379\pi$
$967$	−540.669	−	540.669i	−0.559120	−	0.559120i	−0.929057	+	0.369937i	$0.879379\pi$
$968$	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	0.0155919	−	0.999878i	$-0.495037\pi$
$971$	848.378	−	1469.43i	0.873716	−	1.51332i	0.858124	−	0.513442i	$-0.171630\pi$
$972$		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	−0.993368	−	0.114981i	$-0.963319\pi$
$977$	−73.8571	+	275.638i	−0.0755958	+	0.282127i	0.917772	+	0.397108i	$0.129986\pi$
$978$		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	−0.685935	−	0.727663i	$-0.740606\pi$
$983$	41.0192	−	41.0192i	0.0417286	−	0.0417286i	0.727663	+	0.685935i	$0.240606\pi$
$984$		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	0.755395	−	0.655269i	$-0.227445\pi$
$991$	−188.074	−	325.754i	−0.189782	−	0.328712i	−0.945178	+	0.326557i	$0.894111\pi$
$992$	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	−0.234364	−	0.972149i	$-0.575301\pi$
$997$	722.549	−	1251.49i	0.724724	−	1.25526i	0.959088	−	0.283109i	$-0.0913659\pi$
$998$	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.37.1		8
3.2	odd	2		26.3.f.b.11.1	✓	8
12.11	even	2		208.3.bd.f.193.2		8
13.6	odd	12	inner	234.3.bb.f.19.1		8
39.2	even	12		338.3.d.g.239.3		8
39.5	even	4		338.3.f.h.249.1		8
39.8	even	4		338.3.f.j.249.1		8
39.11	even	12		338.3.d.f.239.3		8
39.17	odd	6		338.3.f.j.319.1		8
39.20	even	12		338.3.f.i.19.1		8
39.23	odd	6		338.3.d.f.99.3		8
39.29	odd	6		338.3.d.g.99.3		8
39.32	even	12		26.3.f.b.19.1	yes	8
39.35	odd	6		338.3.f.h.319.1		8
39.38	odd	2		338.3.f.i.89.1		8
156.71	odd	12		208.3.bd.f.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.1	✓	8	3.2	odd	2
26.3.f.b.19.1	yes	8	39.32	even	12
208.3.bd.f.97.2		8	156.71	odd	12
208.3.bd.f.193.2		8	12.11	even	2
234.3.bb.f.19.1		8	13.6	odd	12	inner
234.3.bb.f.37.1		8	1.1	even	1	trivial
338.3.d.f.99.3		8	39.23	odd	6
338.3.d.f.239.3		8	39.11	even	12
338.3.d.g.99.3		8	39.29	odd	6
338.3.d.g.239.3		8	39.2	even	12
338.3.f.h.249.1		8	39.5	even	4
338.3.f.h.319.1		8	39.35	odd	6
338.3.f.i.19.1		8	39.20	even	12
338.3.f.i.89.1		8	39.38	odd	2
338.3.f.j.249.1		8	39.8	even	4
338.3.f.j.319.1		8	39.17	odd	6

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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