LMFDB - Embedded newform 208.3.bd.f.97.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,3,Mod(33,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.33"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,6,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.66758949869$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.2
Root			$3.90972 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.97
Dual form			208.3.bd.f.193.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52185 - 2.63592i) q^{3} +(4.79174 - 4.79174i) q^{5} +(-1.13983 + 4.25390i) q^{7} +(-0.132034 - 0.228689i) q^{9} +(13.8758 - 3.71800i) q^{11} +(1.84809 - 12.8680i) q^{13} +(-5.33833 - 19.9229i) q^{15} +(-20.9957 + 12.1219i) q^{17} +(-25.4592 - 6.82178i) q^{19} +(9.47827 + 9.47827i) q^{21} +(5.44507 + 3.14371i) q^{23} -20.9215i q^{25} +26.5895 q^{27} +(11.1112 - 19.2451i) q^{29} +(8.59518 - 8.59518i) q^{31} +(11.3164 - 42.2336i) q^{33} +(14.9218 + 25.8453i) q^{35} +(-6.13936 + 1.64504i) q^{37} +(-31.1064 - 24.4545i) q^{39} +(18.8845 + 70.4778i) q^{41} +(-26.9695 + 15.5708i) q^{43} +(-1.72849 - 0.463147i) q^{45} +(-7.65637 - 7.65637i) q^{47} +(25.6388 + 14.8026i) q^{49} +73.7905i q^{51} -33.7616 q^{53} +(48.6733 - 84.3047i) q^{55} +(-56.7267 + 56.7267i) q^{57} +(-9.77592 + 36.4842i) q^{59} +(11.5359 + 19.9807i) q^{61} +(1.12332 - 0.300991i) q^{63} +(-52.8043 - 70.5155i) q^{65} +(27.8544 + 103.954i) q^{67} +(16.5731 - 9.56849i) q^{69} +(-2.20861 - 0.591796i) q^{71} +(38.1773 + 38.1773i) q^{73} +(-55.1473 - 31.8393i) q^{75} +63.2639i q^{77} +19.1299 q^{79} +(41.6534 - 72.1459i) q^{81} +(-34.7720 + 34.7720i) q^{83} +(-42.5210 + 158.691i) q^{85} +(-33.8190 - 58.5762i) q^{87} +(3.47190 - 0.930292i) q^{89} +(52.6325 + 22.5289i) q^{91} +(-9.57562 - 35.7367i) q^{93} +(-154.682 + 89.3058i) q^{95} +(-24.3107 - 6.51404i) q^{97} +(-2.68233 - 2.68233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} + 2 q^{7} - 42 q^{9} + 18 q^{11} + 36 q^{13} - 66 q^{15} - 42 q^{17} - 46 q^{19} - 102 q^{21} + 36 q^{23} - 72 q^{27} - 6 q^{29} - 32 q^{31} + 42 q^{33} + 78 q^{35} - 106 q^{37} - 12 q^{39}+ \cdots - 252 q^{99}+O(q^{100}) $ 8 * q + 6 * q^5 + 2 * q^7 - 42 * q^9 + 18 * q^11 + 36 * q^13 - 66 * q^15 - 42 * q^17 - 46 * q^19 - 102 * q^21 + 36 * q^23 - 72 * q^27 - 6 * q^29 - 32 * q^31 + 42 * q^33 + 78 * q^35 - 106 * q^37 - 12 * q^39 + 132 * q^41 + 108 * q^43 + 240 * q^45 - 60 * q^47 + 258 * q^49 - 132 * q^53 + 162 * q^55 - 294 * q^57 - 18 * q^59 + 36 * q^61 + 72 * q^63 - 300 * q^65 + 74 * q^67 + 258 * q^69 + 174 * q^71 + 166 * q^73 - 6 * q^75 + 96 * q^79 - 12 * q^81 + 240 * q^83 - 24 * q^85 - 360 * q^87 + 294 * q^89 - 298 * q^91 + 270 * q^93 - 714 * q^95 - 58 * q^97 - 252 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.52185	−	2.63592i	0.507282	−	0.878639i	−0.492682	−	0.870209i	$-0.663984\pi$
$3$	1.52185	−	2.63592i	0.507282	−	0.878639i	0.999964	−	0.00842924i	$-0.00268314\pi$
$4$		0			0
$5$	4.79174	−	4.79174i	0.958347	−	0.958347i	−0.0408192	−	0.999167i	$-0.512997\pi$
$5$	4.79174	−	4.79174i	0.958347	−	0.958347i	0.999167	+	0.0408192i	$0.0129968\pi$
$6$		0			0
$7$	−1.13983	+	4.25390i	−0.162833	+	0.607700i	0.835474	+	0.549530i	$0.185193\pi$
$7$	−1.13983	+	4.25390i	−0.162833	+	0.607700i	−0.998307	+	0.0581698i	$0.981474\pi$
$8$		0			0
$9$	−0.132034	−	0.228689i	−0.0146704	−	0.0254099i
$10$		0			0
$11$	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
$14$		0			0
$15$	−5.33833	−	19.9229i	−0.355888	−	1.32819i
$16$		0			0
$17$	−20.9957	+	12.1219i	−1.23504	+	0.713051i	−0.968076	−	0.250656i	$-0.919354\pi$
$17$	−20.9957	+	12.1219i	−1.23504	+	0.713051i	−0.266964	+	0.963707i	$0.586020\pi$
$18$		0			0
$19$	−25.4592	−	6.82178i	−1.33996	−	0.359041i	−0.483540	−	0.875322i	$-0.660649\pi$
$19$	−25.4592	−	6.82178i	−1.33996	−	0.359041i	−0.856419	+	0.516281i	$0.827316\pi$
$20$		0			0
$21$	9.47827	+	9.47827i	0.451346	+	0.451346i
$22$		0			0
$23$	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
$26$		0			0
$27$	26.5895			0.984796
$28$		0			0
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	−0.608366	−	0.793657i	$-0.708175\pi$
$29$	11.1112	−	19.2451i	0.383144	−	0.663625i	0.991510	+	0.130032i	$0.0415080\pi$
$30$		0			0
$31$	8.59518	−	8.59518i	0.277264	−	0.277264i	−0.554752	−	0.832016i	$-0.687187\pi$
$31$	8.59518	−	8.59518i	0.277264	−	0.277264i	0.832016	+	0.554752i	$0.187187\pi$
$32$		0			0
$33$	11.3164	−	42.2336i	0.342923	−	1.27980i
$34$		0			0
$35$	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	$0.444040\pi$
$38$		0			0
$39$	−31.1064	−	24.4545i	−0.797599	−	0.627038i
$40$		0			0
$41$	18.8845	+	70.4778i	0.460596	+	1.71897i	0.671091	+	0.741375i	$0.265826\pi$
$41$	18.8845	+	70.4778i	0.460596	+	1.71897i	−0.210495	+	0.977595i	$0.567508\pi$
$42$		0			0
$43$	−26.9695	+	15.5708i	−0.627197	+	0.362113i	−0.779666	−	0.626196i	$-0.784611\pi$
$43$	−26.9695	+	15.5708i	−0.627197	+	0.362113i	0.152468	+	0.988308i	$0.451278\pi$
$44$		0			0
$45$	−1.72849	−	0.463147i	−0.0384109	−	0.0102922i
$46$		0			0
$47$	−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
$50$		0			0
$51$			73.7905i			1.44687i
$52$		0			0
$53$	−33.7616			−0.637010			−0.318505	−	0.947921i	$-0.603181\pi$
$53$	−33.7616			−0.637010			−0.318505	+	0.947921i	$0.603181\pi$
$54$		0			0
$55$	48.6733	−	84.3047i	0.884969	−	1.53281i
$56$		0			0
$57$	−56.7267	+	56.7267i	−0.995205	+	0.995205i
$58$		0			0
$59$	−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	$0.772772\pi$
$62$		0			0
$63$	1.12332	−	0.300991i	0.0178304	−	0.00477764i
$64$		0			0
$65$	−52.8043	−	70.5155i	−0.812374	−	1.08485i
$66$		0			0
$67$	27.8544	+	103.954i	0.415737	+	1.55155i	0.783355	+	0.621575i	$0.213507\pi$
$67$	27.8544	+	103.954i	0.415737	+	1.55155i	−0.367618	+	0.929977i	$0.619827\pi$
$68$		0			0
$69$	16.5731	−	9.56849i	0.240190	−	0.138674i
$70$		0			0
$71$	−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	$0.629426\pi$
$74$		0			0
$75$	−55.1473	−	31.8393i	−0.735297	−	0.424524i
$76$		0			0
$77$			63.2639i			0.821610i
$78$		0			0
$79$	19.1299			0.242150			0.121075	−	0.992643i	$-0.461366\pi$
$79$	19.1299			0.242150			0.121075	+	0.992643i	$0.461366\pi$
$80$		0			0
$81$	41.6534	−	72.1459i	0.514240	−	0.890690i
$82$		0			0
$83$	−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
$86$		0			0
$87$	−33.8190	−	58.5762i	−0.388724	−	0.673290i
$88$		0			0
$89$	3.47190	−	0.930292i	0.0390101	−	0.0104527i	−0.239261	−	0.970955i	$-0.576905\pi$
$89$	3.47190	−	0.930292i	0.0390101	−	0.0104527i	0.278271	+	0.960503i	$0.410239\pi$
$90$		0			0
$91$	52.6325	+	22.5289i	0.578379	+	0.247570i
$92$		0			0
$93$	−9.57562	−	35.7367i	−0.102964	−	0.384266i
$94$		0			0
$95$	−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	$0.624746\pi$
$98$		0			0
$99$	−2.68233	−	2.68233i	−0.0270943	−	0.0270943i
$100$		0			0
$101$	−131.473	−	75.9060i	−1.30171	−	0.751545i	−0.321016	−	0.947074i	$-0.604024\pi$
$101$	−131.473	−	75.9060i	−1.30171	−	0.751545i	−0.980698	+	0.195529i	$0.937358\pi$
$102$		0			0
$103$		−	17.3672i		−	0.168614i	−0.996440	−	0.0843069i	$-0.973132\pi$
$103$		−	17.3672i		−	0.168614i	0.996440	−	0.0843069i	$-0.0268676\pi$
$104$		0			0
$105$	90.8347			0.865093
$106$		0			0
$107$	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	$0.137447\pi$
$110$		0			0
$111$	−5.00699	+	18.6863i	−0.0451080	+	0.168345i
$112$		0			0
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	0.774680	−	0.632354i	$-0.217911\pi$
$113$	−18.1133	−	31.3732i	−0.160295	−	0.277639i	−0.934974	+	0.354715i	$0.884578\pi$
$114$		0			0
$115$	41.1552	−	11.0275i	0.357871	−	0.0958912i
$116$		0			0
$117$	−3.18677	+	1.27637i	−0.0272374	+	0.0109091i
$118$		0			0
$119$	−27.6337	−	103.130i	−0.232216	−	0.866641i
$120$		0			0
$121$	73.9242	−	42.6801i	0.610943	−	0.352728i
$122$		0			0
$123$	214.513	+	57.4785i	1.74401	+	0.467305i
$124$		0			0
$125$	19.5432	+	19.5432i	0.156346	+	0.156346i
$126$		0			0
$127$	115.255	+	66.5425i	0.907520	+	0.523957i	0.879632	−	0.475654i	$-0.157789\pi$
$127$	115.255	+	66.5425i	0.907520	+	0.523957i	0.0278874	+	0.999611i	$0.491122\pi$
$128$		0			0
$129$			94.7857i			0.734773i
$130$		0			0
$131$	−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
$134$		0			0
$135$	127.410	−	127.410i	0.943777	−	0.943777i
$136$		0			0
$137$	2.07966	−	7.76140i	0.0151800	−	0.0566525i	−0.957920	−	0.287034i	$-0.907331\pi$
$137$	2.07966	−	7.76140i	0.0151800	−	0.0566525i	0.973100	+	0.230381i	$0.0739974\pi$
$138$		0			0
$139$	−121.981	−	211.277i	−0.877558	−	1.51998i	−0.854012	−	0.520253i	$-0.825838\pi$
$139$	−121.981	−	211.277i	−0.877558	−	1.51998i	−0.0235463	−	0.999723i	$-0.507496\pi$
$140$		0			0
$141$	−31.8334	+	8.52973i	−0.225769	+	0.0604945i
$142$		0			0
$143$	−22.1994	−	185.424i	−0.155241	−	1.29667i
$144$		0			0
$145$	−38.9757	−	145.459i	−0.268798	−	1.00317i
$146$		0			0
$147$	78.0367	−	45.0545i	0.530862	−	0.306493i
$148$		0			0
$149$	182.687	+	48.9509i	1.22609	+	0.328529i	0.813055	−	0.582187i	$-0.197803\pi$
$149$	182.687	+	48.9509i	1.22609	+	0.328529i	0.413033	+	0.910716i	$0.364469\pi$
$150$		0			0
$151$	70.5995	+	70.5995i	0.467546	+	0.467546i	0.901119	−	0.433573i	$-0.142747\pi$
$151$	70.5995	+	70.5995i	0.467546	+	0.467546i	−0.433573	+	0.901119i	$0.642747\pi$
$152$		0			0
$153$	5.54428	+	3.20099i	0.0362371	+	0.0209215i
$154$		0			0
$155$		−	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	$0.309632\pi$
$158$		0			0
$159$	−51.3799	+	88.9926i	−0.323144	+	0.559702i
$160$		0			0
$161$	−19.5795	+	19.5795i	−0.121612	+	0.121612i
$162$		0			0
$163$	−31.3812	+	117.116i	−0.192523	+	0.718504i	0.800372	+	0.599504i	$0.204635\pi$
$163$	−31.3812	+	117.116i	−0.192523	+	0.718504i	−0.992894	+	0.119000i	$0.962031\pi$
$164$		0			0
$165$	−148.147	−	256.598i	−0.897858	−	1.55514i
$166$		0			0
$167$	−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
$170$		0			0
$171$	1.80141	+	6.72295i	0.0105346	+	0.0393155i
$172$		0			0
$173$	−241.179	+	139.245i	−1.39410	+	0.804884i	−0.993766	−	0.111485i	$-0.964439\pi$
$173$	−241.179	+	139.245i	−1.39410	+	0.804884i	−0.400334	+	0.916369i	$0.631106\pi$
$174$		0			0
$175$	88.9978	+	23.8469i	0.508559	+	0.136268i
$176$		0			0
$177$	81.2919	+	81.2919i	0.459276	+	0.459276i
$178$		0			0
$179$	−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	$-0.187121\pi$
$182$		0			0
$183$	70.2233			0.383734
$184$		0			0
$185$	−21.5356	+	37.3008i	−0.116409	+	0.201626i
$186$		0			0
$187$	−246.262	+	246.262i	−1.31691	+	1.31691i
$188$		0			0
$189$	−30.3075	+	113.109i	−0.160357	+	0.598460i
$190$		0			0
$191$	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	$0.539329\pi$
$194$		0			0
$195$	−266.233	+	31.8740i	−1.36530	+	0.163457i
$196$		0			0
$197$	−40.0731	−	149.555i	−0.203417	−	0.759161i	−0.989926	−	0.141583i	$-0.954781\pi$
$197$	−40.0731	−	149.555i	−0.203417	−	0.759161i	0.786510	−	0.617578i	$-0.211886\pi$
$198$		0			0
$199$	225.470	−	130.175i	1.13302	−	0.654147i	0.188324	−	0.982107i	$-0.439695\pi$
$199$	225.470	−	130.175i	1.13302	−	0.654147i	0.944691	+	0.327960i	$0.106361\pi$
$200$		0			0
$201$	316.404	+	84.7802i	1.57415	+	0.421792i
$202$		0			0
$203$	69.2019	+	69.2019i	0.340896	+	0.340896i
$204$		0			0
$205$	428.200	+	247.221i	2.08878	+	1.20596i
$206$		0			0
$207$		−	1.66030i		−	0.00802079i
$208$		0			0
$209$	−378.630			−1.81162
$210$		0			0
$211$	208.203	−	360.618i	0.986744	−	1.70909i	0.352831	−	0.935687i	$-0.385219\pi$
$211$	208.203	−	360.618i	0.986744	−	1.70909i	0.633913	−	0.773404i	$-0.281448\pi$
$212$		0			0
$213$	−4.92110	+	4.92110i	−0.0231037	+	0.0231037i
$214$		0			0
$215$	−54.6193	+	203.842i	−0.254043	+	0.948103i
$216$		0			0
$217$	26.7660	+	46.3600i	0.123346	+	0.213641i
$218$		0			0
$219$	158.732	−	42.5322i	0.724805	−	0.194211i
$220$		0			0
$221$	117.182	+	292.574i	0.530234	+	1.32386i
$222$		0			0
$223$	−52.8772	−	197.340i	−0.237118	−	0.884935i	−0.977183	−	0.212400i	$-0.931872\pi$
$223$	−52.8772	−	197.340i	−0.237118	−	0.884935i	0.740065	−	0.672535i	$-0.234795\pi$
$224$		0			0
$225$	−4.78451	+	2.76234i	−0.0212645	+	0.0122771i
$226$		0			0
$227$	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	$0.977571\pi$
$230$		0			0
$231$	166.758	+	96.2780i	0.721898	+	0.416788i
$232$		0			0
$233$		−	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
$236$		0			0
$237$	29.1127	−	50.4247i	0.122839	−	0.212763i
$238$		0			0
$239$	−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	$0.928845\pi$
$242$		0			0
$243$	−7.12754	−	12.3453i	−0.0293314	−	0.0508035i
$244$		0			0
$245$	193.784	−	51.9244i	0.790957	−	0.211936i
$246$		0			0
$247$	−134.833	+	315.001i	−0.545884	+	1.27531i
$248$		0			0
$249$	38.7384	+	144.574i	0.155576	+	0.580618i
$250$		0			0
$251$	−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
$254$		0			0
$255$	353.584	+	353.584i	1.38661	+	1.38661i
$256$		0			0
$257$	−160.572	−	92.7065i	−0.624795	−	0.360726i	0.153938	−	0.988080i	$-0.450804\pi$
$257$	−160.572	−	92.7065i	−0.624795	−	0.360726i	−0.778734	+	0.627355i	$0.784138\pi$
$258$		0			0
$259$		−	27.9913i		−	0.108074i
$260$		0			0
$261$	−5.86820			−0.0224835
$262$		0			0
$263$	−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
$266$		0			0
$267$	2.83152	−	10.5674i	0.0106050	−	0.0395782i
$268$		0			0
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	−0.985559	−	0.169334i	$-0.945838\pi$
$269$	−172.006	−	297.923i	−0.639427	−	1.10752i	0.346132	−	0.938186i	$-0.387495\pi$
$270$		0			0
$271$	−23.4296	+	6.27795i	−0.0864562	+	0.0231659i	−0.301788	−	0.953375i	$-0.597583\pi$
$271$	−23.4296	+	6.27795i	−0.0864562	+	0.0231659i	0.215332	+	0.976541i	$0.430917\pi$
$272$		0			0
$273$	139.483	−	104.449i	0.510926	−	0.382598i
$274$		0			0
$275$	−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	$0.981713\pi$
$278$		0			0
$279$	−3.10048	−	0.830770i	−0.0111128	−	0.00297767i
$280$		0			0
$281$	145.653	+	145.653i	0.518337	+	0.518337i	0.917068	−	0.398731i	$-0.130549\pi$
$281$	145.653	+	145.653i	0.518337	+	0.518337i	−0.398731	+	0.917068i	$0.630549\pi$
$282$		0			0
$283$	−372.577	−	215.107i	−1.31653	−	0.760096i	−0.333357	−	0.942801i	$-0.608182\pi$
$283$	−372.577	−	215.107i	−1.31653	−	0.760096i	−0.983168	+	0.182704i	$0.941515\pi$
$284$		0			0
$285$			543.639i			1.90750i
$286$		0			0
$287$	−321.330			−1.11962
$288$		0			0
$289$	149.379	−	258.732i	0.516883	−	0.895267i
$290$		0			0
$291$	−54.1677	+	54.1677i	−0.186143	+	0.186143i
$292$		0			0
$293$	24.5565	−	91.6460i	0.0838105	−	0.312785i	−0.911276	−	0.411797i	$-0.864901\pi$
$293$	24.5565	−	91.6460i	0.0838105	−	0.312785i	0.995086	+	0.0990115i	$0.0315681\pi$
$294$		0			0
$295$	127.979	+	221.667i	0.433828	+	0.751412i
$296$		0			0
$297$	368.950	−	98.8597i	1.24225	−	0.332861i
$298$		0			0
$299$	50.5161	−	64.2571i	0.168950	−	0.214907i
$300$		0			0
$301$	−35.4962	−	132.474i	−0.117927	−	0.440111i
$302$		0			0
$303$	−400.164	+	231.035i	−1.32067	+	0.762490i
$304$		0			0
$305$	151.019	+	40.4655i	0.495145	+	0.132674i
$306$		0			0
$307$	−210.306	−	210.306i	−0.685035	−	0.685035i	0.276095	−	0.961130i	$-0.410959\pi$
$307$	−210.306	−	210.306i	−0.685035	−	0.685035i	−0.961130	+	0.276095i	$0.910959\pi$
$308$		0			0
$309$	−45.7785	−	26.4302i	−0.148151	−	0.0855347i
$310$		0			0
$311$			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	$0.560635\pi$
$314$		0			0
$315$	3.94036	−	6.82490i	0.0125091	−	0.0216664i
$316$		0			0
$317$	−284.814	+	284.814i	−0.898466	+	0.898466i	−0.995300	−	0.0968348i	$-0.969128\pi$
$317$	−284.814	+	284.814i	−0.898466	+	0.898466i	0.0968348	+	0.995300i	$0.469128\pi$
$318$		0			0
$319$	82.6227	−	308.352i	0.259005	−	0.966621i
$320$		0			0
$321$	−80.9512	−	140.212i	−0.252184	−	0.436796i
$322$		0			0
$323$	617.227	−	165.385i	1.91092	−	0.512029i
$324$		0			0
$325$	−269.217	−	38.6648i	−0.828360	−	0.118969i
$326$		0			0
$327$	−59.4666	−	221.933i	−0.181855	−	0.678693i
$328$		0			0
$329$	41.2964	−	23.8425i	0.125521	−	0.0724695i
$330$		0			0
$331$	433.118	+	116.054i	1.30851	+	0.350615i	0.844663	−	0.535299i	$-0.179801\pi$
$331$	433.118	+	116.054i	1.30851	+	0.350615i	0.463850	+	0.885914i	$0.346468\pi$
$332$		0			0
$333$	1.18680	+	1.18680i	0.00356398	+	0.00356398i
$334$		0			0
$335$	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	$-0.248577\pi$
$338$		0			0
$339$	−110.263			−0.325259
$340$		0			0
$341$	87.3078	−	151.222i	0.256035	−	0.443465i
$342$		0			0
$343$	−244.782	+	244.782i	−0.713650	+	0.713650i
$344$		0			0
$345$	33.5643	−	125.264i	0.0972878	−	0.363083i
$346$		0			0
$347$	−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	$0.290152\pi$
$350$		0			0
$351$	49.1398	−	342.153i	0.140000	−	0.974794i
$352$		0			0
$353$	−91.3587	−	340.955i	−0.258806	−	0.965879i	−0.965933	−	0.258792i	$-0.916676\pi$
$353$	−91.3587	−	340.955i	−0.258806	−	0.965879i	0.707127	−	0.707087i	$-0.249991\pi$
$354$		0			0
$355$	−13.4188	+	7.74736i	−0.0377995	+	0.0218236i
$356$		0			0
$357$	−313.897	−	84.1085i	−0.879263	−	0.235598i
$358$		0			0
$359$	−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
$362$		0			0
$363$		−	259.810i		−	0.715731i
$364$		0			0
$365$	365.871			1.00239
$366$		0			0
$367$	343.162	−	594.375i	0.935047	−	1.61955i	0.160497	−	0.987036i	$-0.448690\pi$
$367$	343.162	−	594.375i	0.935047	−	1.61955i	0.774550	−	0.632513i	$-0.217976\pi$
$368$		0			0
$369$	13.6241	−	13.6241i	0.0369217	−	0.0369217i
$370$		0			0
$371$	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	$0.523129\pi$
$374$		0			0
$375$	81.2560	−	21.7725i	0.216683	−	0.0580599i
$376$		0			0
$377$	−227.111	−	178.545i	−0.602417	−	0.473594i
$378$		0			0
$379$	138.900	+	518.382i	0.366491	+	1.36776i	0.865389	+	0.501101i	$0.167072\pi$
$379$	138.900	+	518.382i	0.366491	+	1.36776i	−0.498898	+	0.866661i	$0.666262\pi$
$380$		0			0
$381$	350.801	−	202.535i	0.920737	−	0.531588i
$382$		0			0
$383$	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
$386$		0			0
$387$	7.12176	+	4.11175i	0.0184025	+	0.0106247i
$388$		0			0
$389$			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
$392$		0			0
$393$	−58.2469	+	100.887i	−0.148211	+	0.256709i
$394$		0			0
$395$	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	$-0.0202578\pi$
$398$		0			0
$399$	−176.651	−	305.968i	−0.442734	−	0.766838i
$400$		0			0
$401$	−261.805	+	70.1504i	−0.652880	+	0.174939i	−0.570031	−	0.821623i	$-0.693069\pi$
$401$	−261.805	+	70.1504i	−0.652880	+	0.174939i	−0.0828492	+	0.996562i	$0.526402\pi$
$402$		0			0
$403$	−94.7178	−	126.487i	−0.235032	−	0.313864i
$404$		0			0
$405$	−146.112	−	545.296i	−0.360770	−	1.34641i
$406$		0			0
$407$	−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	$0.521511\pi$
$410$		0			0
$411$	−17.2935	−	17.2935i	−0.0420766	−	0.0420766i
$412$		0			0
$413$	−144.057	−	83.1715i	−0.348807	−	0.201384i
$414$		0			0
$415$			333.237i			0.802980i
$416$		0			0
$417$	−742.543			−1.78068
$418$		0			0
$419$	−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	$0.0852538\pi$
$422$		0			0
$423$	−0.740029	+	2.76183i	−0.00174948	+	0.00652914i
$424$		0			0
$425$	253.607	+	439.261i	0.596723	+	1.03355i
$426$		0			0
$427$	−98.1448	+	26.2978i	−0.229847	+	0.0615874i
$428$		0			0
$429$	−522.546	−	223.671i	−1.21806	−	0.521378i
$430$		0			0
$431$	−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	$0.152073\pi$
$434$		0			0
$435$	−442.734	−	118.630i	−1.01778	−	0.272713i
$436$		0			0
$437$	−117.182	−	117.182i	−0.268150	−	0.268150i
$438$		0			0
$439$	−103.577	−	59.8002i	−0.235938	−	0.136219i	0.377370	−	0.926063i	$-0.376828\pi$
$439$	−103.577	−	59.8002i	−0.235938	−	0.136219i	−0.613309	+	0.789843i	$0.710162\pi$
$440$		0			0
$441$		−	7.81775i		−	0.0177273i
$442$		0			0
$443$	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
$446$		0			0
$447$	407.052	−	407.052i	0.910631	−	0.910631i
$448$		0			0
$449$	47.8299	−	178.504i	0.106525	−	0.397558i	−0.891988	−	0.452058i	$-0.850690\pi$
$449$	47.8299	−	178.504i	0.106525	−	0.397558i	0.998514	+	0.0545000i	$0.0173565\pi$
$450$		0			0
$451$	524.072	+	907.720i	1.16202	+	2.01268i
$452$		0			0
$453$	293.536	−	78.6527i	0.647982	−	0.173626i
$454$		0			0
$455$	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	$0.811644\pi$
$458$		0			0
$459$	−558.265	+	322.314i	−1.21626	+	0.702210i
$460$		0			0
$461$	596.206	+	159.753i	1.29329	+	0.346535i	0.838908	−	0.544273i	$-0.183194\pi$
$461$	596.206	+	159.753i	1.29329	+	0.346535i	0.454379	+	0.890808i	$0.349861\pi$
$462$		0			0
$463$	−198.699	−	198.699i	−0.429156	−	0.429156i	0.459185	−	0.888341i	$-0.348142\pi$
$463$	−198.699	−	198.699i	−0.429156	−	0.429156i	−0.888341	+	0.459185i	$0.848142\pi$
$464$		0			0
$465$	−217.125	−	125.357i	−0.466935	−	0.269585i
$466$		0			0
$467$		−	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
$470$		0			0
$471$	269.053	−	466.014i	0.571239	−	0.989414i
$472$		0			0
$473$	−316.330	+	316.330i	−0.668773	+	0.668773i
$474$		0			0
$475$	−142.722	+	532.645i	−0.300467	+	1.12136i
$476$		0			0
$477$	4.45766	+	7.72090i	0.00934520	+	0.0161864i
$478$		0			0
$479$	−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
$482$		0			0
$483$	21.8129	+	81.4067i	0.0451612	+	0.168544i
$484$		0			0
$485$	−147.704	+	85.2771i	−0.304545	+	0.175829i
$486$		0			0
$487$	−208.431	−	55.8489i	−0.427990	−	0.114679i	0.0383927	−	0.999263i	$-0.487776\pi$
$487$	−208.431	−	55.8489i	−0.427990	−	0.114679i	−0.466382	+	0.884583i	$0.654443\pi$
$488$		0			0
$489$	260.951	+	260.951i	0.533642	+	0.533642i
$490$		0			0
$491$	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
$494$		0			0
$495$	−25.7061			−0.0519315
$496$		0			0
$497$	5.03488	−	8.72067i	0.0101305	−	0.0175466i
$498$		0			0
$499$	401.619	−	401.619i	0.804847	−	0.804847i	−0.179002	−	0.983849i	$-0.557287\pi$
$499$	401.619	−	401.619i	0.804847	−	0.804847i	0.983849	+	0.179002i	$0.0572868\pi$
$500$		0			0
$501$	−233.737	+	872.318i	−0.466541	+	1.74115i
$502$		0			0
$503$	−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
$506$		0			0
$507$	−372.167	+	355.081i	−0.734057	+	0.700358i
$508$		0			0
$509$	113.097	+	422.083i	0.222194	+	0.829239i	0.983509	+	0.180858i	$0.0578873\pi$
$509$	113.097	+	422.083i	0.222194	+	0.829239i	−0.761315	+	0.648382i	$0.775446\pi$
$510$		0			0
$511$	−205.918	+	118.887i	−0.402971	+	0.232655i
$512$		0			0
$513$	−676.948	−	181.388i	−1.31959	−	0.353582i
$514$		0			0
$515$	−83.2191	−	83.2191i	−0.161591	−	0.161591i
$516$		0			0
$517$	−134.704	−	77.7716i	−0.260550	−	0.150429i
$518$		0			0
$519$			847.638i			1.63321i
$520$		0			0
$521$	947.876			1.81934			0.909669	−	0.415333i	$-0.136335\pi$
$521$	947.876			1.81934			0.909669	+	0.415333i	$0.136335\pi$
$522$		0			0
$523$	−68.3466	+	118.380i	−0.130682	+	0.226348i	−0.923940	−	0.382538i	$-0.875050\pi$
$523$	−68.3466	+	118.380i	−0.130682	+	0.226348i	0.793258	+	0.608886i	$0.208383\pi$
$524$		0			0
$525$	198.299	−	198.299i	0.377713	−	0.377713i
$526$		0			0
$527$	−76.2721	+	284.651i	−0.144729	+	0.540135i
$528$		0			0
$529$	−244.734	−	423.892i	−0.462635	−	0.801308i
$530$		0			0
$531$	9.63430	−	2.58150i	0.0181437	−	0.00486159i
$532$		0			0
$533$	941.806	−	112.755i	1.76699	−	0.211548i
$534$		0			0
$535$	−93.2946	−	348.180i	−0.174382	−	0.650804i
$536$		0			0
$537$	−207.591	+	119.853i	−0.386575	+	0.223189i
$538$		0			0
$539$	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	$0.922568\pi$
$542$		0			0
$543$	−529.182	−	305.523i	−0.974552	−	0.562658i
$544$		0			0
$545$		−	511.545i		−	0.938616i
$546$		0			0
$547$	716.303			1.30951			0.654756	−	0.755840i	$-0.272771\pi$
$547$	716.303			1.30951			0.654756	+	0.755840i	$0.272771\pi$
$548$		0			0
$549$	3.04625	−	5.27625i	0.00554872	−	0.00961066i
$550$		0			0
$551$	−414.168	+	414.168i	−0.751666	+	0.751666i
$552$		0			0
$553$	−21.8048	+	81.3765i	−0.0394300	+	0.147155i
$554$		0			0
$555$	65.5478	+	113.532i	0.118104	+	0.204562i
$556$		0			0
$557$	−58.2268	+	15.6018i	−0.104536	+	0.0280104i	−0.310708	−	0.950505i	$-0.600566\pi$
$557$	−58.2268	+	15.6018i	−0.104536	+	0.0280104i	0.206172	+	0.978516i	$0.433899\pi$
$558$		0			0
$559$	150.523	+	375.819i	0.269272	+	0.672306i
$560$		0			0
$561$	274.353	+	1023.90i	0.489043	+	1.82513i
$562$		0			0
$563$	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
$566$		0			0
$567$	259.423	+	259.423i	0.457537	+	0.457537i
$568$		0			0
$569$	232.943	+	134.490i	0.409390	+	0.236361i	0.690528	−	0.723306i	$-0.257378\pi$
$569$	232.943	+	134.490i	0.409390	+	0.236361i	−0.281138	+	0.959667i	$0.590712\pi$
$570$		0			0
$571$			328.719i			0.575689i	0.957677	+	0.287845i	$0.0929387\pi$
$571$			328.719i			0.575689i	−0.957677	+	0.287845i	$0.907061\pi$
$572$		0			0
$573$	123.361			0.215290
$574$		0			0
$575$	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	$0.257080\pi$
$578$		0			0
$579$	−114.300	+	426.572i	−0.197409	+	0.736739i
$580$		0			0
$581$	−108.283	−	187.551i	−0.186373	−	0.322807i
$582$		0			0
$583$	−468.467	+	125.525i	−0.803546	+	0.215309i
$584$		0			0
$585$	−9.15417	+	21.3862i	−0.0156481	+	0.0365576i
$586$		0			0
$587$	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
$590$		0			0
$591$	−455.199	−	121.970i	−0.770218	−	0.206379i
$592$		0			0
$593$	215.404	+	215.404i	0.363244	+	0.363244i	0.865006	−	0.501762i	$-0.167315\pi$
$593$	215.404	+	215.404i	0.363244	+	0.363244i	−0.501762	+	0.865006i	$0.667315\pi$
$594$		0			0
$595$	−626.587	−	361.760i	−1.05309	−	0.608000i
$596$		0			0
$597$		−	792.427i		−	1.32735i
$598$		0			0
$599$	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	$0.246724\pi$
$602$		0			0
$603$	20.0954	−	20.0954i	0.0333257	−	0.0333257i
$604$		0			0
$605$	149.713	−	558.737i	0.247460	−	0.923532i
$606$		0			0
$607$	−355.980	−	616.576i	−0.586459	−	1.01578i	−0.994692	−	0.102898i	$-0.967188\pi$
$607$	−355.980	−	616.576i	−0.586459	−	1.01578i	0.408233	−	0.912878i	$-0.366145\pi$
$608$		0			0
$609$	287.725	−	77.0957i	0.472455	−	0.126594i
$610$		0			0
$611$	−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	$0.713393\pi$
$614$		0			0
$615$	1303.31	−	752.466i	2.11920	−	1.22352i
$616$		0			0
$617$	338.746	+	90.7668i	0.549021	+	0.147110i	0.522658	−	0.852543i	$-0.324941\pi$
$617$	338.746	+	90.7668i	0.549021	+	0.147110i	0.0263636	+	0.999652i	$0.491607\pi$
$618$		0			0
$619$	−283.795	−	283.795i	−0.458474	−	0.458474i	0.439680	−	0.898154i	$-0.355092\pi$
$619$	−283.795	−	283.795i	−0.458474	−	0.458474i	−0.898154	+	0.439680i	$0.855092\pi$
$620$		0			0
$621$	144.782	+	83.5897i	0.233143	+	0.134605i
$622$		0			0
$623$			15.8295i			0.0254084i
$624$		0			0
$625$	710.329			1.13653
$626$		0			0
$627$	−576.216	+	998.036i	−0.919005	+	1.59176i
$628$		0			0
$629$	108.959	−	108.959i	0.173226	−	0.173226i
$630$		0			0
$631$	298.859	−	1115.36i	0.473627	−	1.76760i	−0.152944	−	0.988235i	$-0.548875\pi$
$631$	298.859	−	1115.36i	0.473627	−	1.76760i	0.626570	−	0.779365i	$-0.284458\pi$
$632$		0			0
$633$	−633.706	−	1097.61i	−1.00112	−	1.73398i
$634$		0			0
$635$	871.126	−	233.417i	1.37185	−	0.367587i
$636$		0			0
$637$	237.862	−	302.563i	0.373410	−	0.474981i
$638$		0			0
$639$	0.156274	+	0.583223i	0.000244560	+	0.000912712i
$640$		0			0
$641$	225.174	−	130.005i	0.351286	−	0.202815i	−0.313965	−	0.949434i	$-0.601658\pi$
$641$	225.174	−	130.005i	0.351286	−	0.202815i	0.665252	+	0.746619i	$0.268324\pi$
$642$		0			0
$643$	−11.9154	−	3.19272i	−0.0185309	−	0.00496535i	0.249542	−	0.968364i	$-0.419720\pi$
$643$	−11.9154	−	3.19272i	−0.0185309	−	0.00496535i	−0.268073	+	0.963399i	$0.586387\pi$
$644$		0			0
$645$	454.188	+	454.188i	0.704168	+	0.704168i
$646$		0			0
$647$	−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
$650$		0			0
$651$	162.935			0.250284
$652$		0			0
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	−0.997147	−	0.0754792i	$-0.975951\pi$
$653$	−282.884	+	489.970i	−0.433207	+	0.750336i	0.563941	+	0.825815i	$0.309285\pi$
$654$		0			0
$655$	−183.398	+	183.398i	−0.279997	+	0.279997i
$656$		0			0
$657$	3.69004	−	13.7714i	0.00561650	−	0.0209611i
$658$		0			0
$659$	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	$0.687560\pi$
$662$		0			0
$663$	949.533	+	136.372i	1.43218	+	0.205689i
$664$		0			0
$665$	−203.586	−	759.795i	−0.306145	−	1.14255i
$666$		0			0
$667$	121.002	−	69.8606i	0.181413	−	0.104739i
$668$		0			0
$669$	−600.644	−	160.942i	−0.897823	−	0.240571i
$670$		0			0
$671$	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	$0.822650\pi$
$674$		0			0
$675$		−	556.292i		−	0.824136i
$676$		0			0
$677$	−221.745			−0.327540			−0.163770	−	0.986499i	$-0.552366\pi$
$677$	−221.745			−0.327540			−0.163770	+	0.986499i	$0.552366\pi$
$678$		0			0
$679$	55.4201	−	95.9905i	0.0816202	−	0.141370i
$680$		0			0
$681$	239.418	−	239.418i	0.351569	−	0.351569i
$682$		0			0
$683$	−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
$686$		0			0
$687$	−882.731	+	236.527i	−1.28491	+	0.344290i
$688$		0			0
$689$	−62.3944	+	434.443i	−0.0905580	+	0.630541i
$690$		0			0
$691$	146.869	+	548.121i	0.212545	+	0.793229i	0.987016	+	0.160620i	$0.0513494\pi$
$691$	146.869	+	548.121i	0.212545	+	0.793229i	−0.774471	+	0.632609i	$0.781984\pi$
$692$		0			0
$693$	14.4678	−	8.35297i	0.0208770	−	0.0120534i
$694$		0			0
$695$	−1596.88	−	427.883i	−2.29767	−	0.615659i
$696$		0			0
$697$	−1250.81	−	1250.81i	−1.79457	−	1.79457i
$698$		0			0
$699$	−122.788	−	70.8916i	−0.175662	−	0.101419i
$700$		0			0
$701$		−	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
$704$		0			0
$705$	−111.665	+	193.409i	−0.158390	+	0.274339i
$706$		0			0
$707$	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	$0.0922360\pi$
$710$		0			0
$711$	−2.52579	−	4.37479i	−0.00355244	−	0.00615301i
$712$		0			0
$713$	73.8221	−	19.7806i	0.103537	−	0.0277427i
$714$		0			0
$715$	−994.877	−	782.129i	−1.39144	−	1.09389i
$716$		0			0
$717$	154.085	+	575.055i	0.214903	+	0.802029i
$718$		0			0
$719$	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
$722$		0			0
$723$	483.940	+	483.940i	0.669350	+	0.669350i
$724$		0			0
$725$	−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	$-0.156192\pi$
$728$		0			0
$729$	706.374			0.968963
$730$		0			0
$731$	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	$0.195615\pi$
$734$		0			0
$735$	158.042	−	589.820i	0.215023	−	0.802477i
$736$		0			0
$737$	773.001	+	1338.88i	1.04885	+	1.81666i
$738$		0			0
$739$	−1337.69	+	358.434i	−1.81014	+	0.485026i	−0.995485	−	0.0949200i	$-0.969740\pi$
$739$	−1337.69	+	358.434i	−1.81014	+	0.485026i	−0.814655	+	0.579946i	$0.803074\pi$
$740$		0			0
$741$	625.121	+	834.793i	0.843618	+	1.12658i
$742$		0			0
$743$	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
$746$		0			0
$747$	12.5431	+	3.36090i	0.0167912	+	0.00449920i
$748$		0			0
$749$	165.646	+	165.646i	0.221156	+	0.221156i
$750$		0			0
$751$	1012.32	+	584.461i	1.34796	+	0.778244i	0.987960	−	0.154709i	$-0.0494441\pi$
$751$	1012.32	+	584.461i	1.34796	+	0.778244i	0.359998	+	0.932953i	$0.382777\pi$
$752$		0			0
$753$			10.6229i			0.0141075i
$754$		0			0
$755$	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	$-0.0992360\pi$
$758$		0			0
$759$	194.389	−	194.389i	0.256112	−	0.256112i
$760$		0			0
$761$	246.221	−	918.907i	0.323549	−	1.20750i	−0.592214	−	0.805781i	$-0.701746\pi$
$761$	246.221	−	918.907i	0.323549	−	1.20750i	0.915763	−	0.401719i	$-0.131587\pi$
$762$		0			0
$763$	166.222	+	287.906i	0.217854	+	0.377334i
$764$		0			0
$765$	41.9050	−	11.2284i	0.0547778	−	0.0146777i
$766$		0			0
$767$	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	$0.959506\pi$
$770$		0			0
$771$	−488.733	+	282.170i	−0.633895	+	0.365979i
$772$		0			0
$773$	−431.675	−	115.667i	−0.558441	−	0.149634i	−0.0314512	−	0.999505i	$-0.510013\pi$
$773$	−431.675	−	115.667i	−0.558441	−	0.149634i	−0.526990	+	0.849871i	$0.676680\pi$
$774$		0			0
$775$	−179.824	−	179.824i	−0.232031	−	0.232031i
$776$		0			0
$777$	−73.7826	−	42.5984i	−0.0949583	−	0.0548242i
$778$		0			0
$779$		−	1923.14i		−	2.46872i
$780$		0			0
$781$	−32.8465			−0.0420570
$782$		0			0
$783$	295.441	−	511.718i	0.377319	−	0.653535i
$784$		0			0
$785$	847.151	−	847.151i	1.07917	−	1.07917i
$786$		0			0
$787$	−173.642	+	648.040i	−0.220638	+	0.823431i	0.763468	+	0.645846i	$0.223495\pi$
$787$	−173.642	+	648.040i	−0.220638	+	0.823431i	−0.984105	+	0.177585i	$0.943172\pi$
$788$		0			0
$789$	285.120	+	493.843i	0.361369	+	0.625910i
$790$		0			0
$791$	154.104	−	41.2921i	0.194822	−	0.0522025i
$792$		0			0
$793$	278.430	−	111.517i	0.351110	−	0.140627i
$794$		0			0
$795$	180.230	+	672.628i	0.226705	+	0.846073i
$796$		0			0
$797$	−207.230	+	119.644i	−0.260013	+	0.150118i	−0.624340	−	0.781152i	$-0.714632\pi$
$797$	−207.230	+	119.644i	−0.260013	+	0.150118i	0.364328	+	0.931271i	$0.381299\pi$
$798$		0			0
$799$	253.560	+	67.9413i	0.317347	+	0.0850329i
$800$		0			0
$801$	−0.671155	−	0.671155i	−0.000837896	−	0.000837896i
$802$		0			0
$803$	671.683	+	387.796i	0.836466	+	0.482934i
$804$		0			0
$805$			187.639i			0.233092i
$806$		0			0
$807$	−1047.07			−1.29748
$808$		0			0
$809$	−234.046	+	405.380i	−0.289303	+	0.501088i	−0.973644	−	0.228075i	$-0.926757\pi$
$809$	−234.046	+	405.380i	−0.289303	+	0.501088i	0.684340	+	0.729163i	$0.260090\pi$
$810$		0			0
$811$	680.928	−	680.928i	0.839615	−	0.839615i	−0.149193	−	0.988808i	$-0.547668\pi$
$811$	680.928	−	680.928i	0.839615	−	0.839615i	0.988808	+	0.149193i	$0.0476675\pi$
$812$		0			0
$813$	−19.1082	+	71.3126i	−0.0235033	+	0.0877154i
$814$		0			0
$815$	410.819	+	711.560i	0.504073	+	0.873080i
$816$		0			0
$817$	792.843	−	212.442i	0.970433	−	0.260027i
$818$		0			0
$819$	−1.79716	−	15.0110i	−0.00219433	−	0.0183285i
$820$		0			0
$821$	−326.171	−	1217.29i	−0.397285	−	1.48269i	−0.817854	−	0.575426i	$-0.804836\pi$
$821$	−326.171	−	1217.29i	−0.397285	−	1.48269i	0.420569	−	0.907260i	$-0.361830\pi$
$822$		0			0
$823$	−499.204	+	288.216i	−0.606566	+	0.350201i	−0.771620	−	0.636083i	$-0.780553\pi$
$823$	−499.204	+	288.216i	−0.606566	+	0.350201i	0.165054	+	0.986285i	$0.447220\pi$
$824$		0			0
$825$	−883.589	−	236.757i	−1.07102	−	0.286978i
$826$		0			0
$827$	−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	$0.690929\pi$
$830$		0			0
$831$			1506.30i			1.81263i
$832$		0			0
$833$	−717.739			−0.861632
$834$		0			0
$835$	−1005.33	+	1741.28i	−1.20399	+	2.08537i
$836$		0			0
$837$	228.542	−	228.542i	0.273048	−	0.273048i
$838$		0			0
$839$	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
$842$		0			0
$843$	605.589	−	162.267i	0.718374	−	0.192488i
$844$		0			0
$845$	−1004.98	+	549.165i	−1.18932	+	0.649900i
$846$		0			0
$847$	97.2960	+	363.114i	0.114871	+	0.428706i
$848$		0			0
$849$	−1134.01	+	654.720i	−1.33570	+	0.771166i
$850$		0			0
$851$	−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	$0.706892\pi$
$854$		0			0
$855$	40.8465	+	23.5827i	0.0477737	+	0.0275822i
$856$		0			0
$857$			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	$-0.624317\pi$
$859$	−654.044			−0.761402			−0.380701	+	0.924698i	$0.624317\pi$
$860$		0			0
$861$	−489.015	+	846.999i	−0.567962	+	0.983739i
$862$		0			0
$863$	−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
$866$		0			0
$867$	−454.664	−	787.502i	−0.524411	−	0.908306i
$868$		0			0
$869$	265.441	−	71.1248i	0.305456	−	0.0818468i
$870$		0			0
$871$	1389.15	−	166.313i	1.59490	−	0.190945i
$872$		0			0
$873$	1.72015	+	6.41967i	0.00197039	+	0.00735358i
$874$		0			0
$875$	−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	$0.758558\pi$
$878$		0			0
$879$	−204.200	−	204.200i	−0.232309	−	0.232309i
$880$		0			0
$881$	837.311	+	483.422i	0.950410	+	0.548719i	0.893208	−	0.449643i	$-0.148449\pi$
$881$	837.311	+	483.422i	0.950410	+	0.548719i	0.0572017	+	0.998363i	$0.481782\pi$
$882$		0			0
$883$		−	1129.48i		−	1.27914i	−0.768731	−	0.639572i	$-0.779112\pi$
$883$		−	1129.48i		−	1.27914i	0.768731	−	0.639572i	$-0.220888\pi$
$884$		0			0
$885$	779.059			0.880293
$886$		0			0
$887$	−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
$890$		0			0
$891$	309.735	−	1155.95i	0.347626	−	1.29736i
$892$		0			0
$893$	142.695	+	247.155i	0.159793	+	0.276770i
$894$		0			0
$895$	−515.500	+	138.128i	−0.575977	+	0.154333i
$896$		0			0
$897$	−92.4984	−	230.946i	−0.103120	−	0.257464i
$898$		0			0
$899$	−69.9127	−	260.918i	−0.0777672	−	0.290231i
$900$		0			0
$901$	708.847	−	409.253i	0.786733	−	0.454221i
$902$		0			0
$903$	−403.209	−	108.039i	−0.446521	−	0.119645i
$904$		0			0
$905$	−961.981	−	961.981i	−1.06296	−	1.06296i
$906$		0			0
$907$	−386.408	−	223.093i	−0.426029	−	0.245968i	0.271625	−	0.962403i	$-0.412439\pi$
$907$	−386.408	−	223.093i	−0.426029	−	0.245968i	−0.697653	+	0.716435i	$0.745772\pi$
$908$		0			0
$909$			40.0886i			0.0441019i
$910$		0			0
$911$	−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
$914$		0			0
$915$	336.491	−	336.491i	0.367750	−	0.367750i
$916$		0			0
$917$	43.6256	−	162.813i	0.0475743	−	0.177550i
$918$		0			0
$919$	595.311	+	1031.11i	0.647782	+	1.12199i	0.983652	+	0.180082i	$0.0576364\pi$
$919$	595.311	+	1031.11i	0.647782	+	1.12199i	−0.335870	+	0.941908i	$0.609030\pi$
$920$		0			0
$921$	−874.401	+	234.295i	−0.949404	+	0.254392i
$922$		0			0
$923$	−11.6969	+	27.3267i	−0.0126727	+	0.0296064i
$924$		0			0
$925$	34.4166	+	128.445i	0.0372071	+	0.138859i
$926$		0			0
$927$	−3.97169	+	2.29306i	−0.00428446	+	0.00247363i
$928$		0			0
$929$	−770.131	−	206.356i	−0.828990	−	0.222127i	−0.180717	−	0.983535i	$-0.557842\pi$
$929$	−770.131	−	206.356i	−0.828990	−	0.222127i	−0.648273	+	0.761408i	$0.724508\pi$
$930$		0			0
$931$	−551.765	−	551.765i	−0.592658	−	0.592658i
$932$		0			0
$933$	650.078	+	375.323i	0.696761	+	0.402275i
$934$		0			0
$935$			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	$0.430381\pi$
$938$		0			0
$939$	−180.379	+	312.426i	−0.192097	+	0.332722i
$940$		0			0
$941$	−67.4219	+	67.4219i	−0.0716492	+	0.0716492i	−0.742023	−	0.670374i	$-0.766134\pi$
$941$	−67.4219	+	67.4219i	−0.0716492	+	0.0716492i	0.670374	+	0.742023i	$0.266134\pi$
$942$		0			0
$943$	−118.735	+	443.123i	−0.125911	+	0.469908i
$944$		0			0
$945$	396.763	+	687.214i	0.419855	+	0.727210i
$946$		0			0
$947$	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
$950$		0			0
$951$	317.302	+	1184.19i	0.333651	+	1.24520i
$952$		0			0
$953$	−807.423	+	466.166i	−0.847243	+	0.489156i	−0.859720	−	0.510766i	$-0.829362\pi$
$953$	−807.423	+	466.166i	−0.847243	+	0.489156i	0.0124765	+	0.999922i	$0.496029\pi$
$954$		0			0
$955$	265.295	+	71.0856i	0.277796	+	0.0744351i
$956$		0			0
$957$	−687.051	−	687.051i	−0.717921	−	0.717921i
$958$		0			0
$959$	30.6457	+	17.6933i	0.0319559	+	0.0184498i
$960$		0			0
$961$			813.246i			0.846249i
$962$		0			0
$963$	−14.0465			−0.0145862
$964$		0			0
$965$	−491.615	+	851.503i	−0.509446	+	0.882386i
$966$		0			0
$967$	540.669	−	540.669i	0.559120	−	0.559120i	−0.369937	−	0.929057i	$-0.620621\pi$
$967$	540.669	−	540.669i	0.559120	−	0.559120i	0.929057	+	0.369937i	$0.120621\pi$
$968$		0			0
$969$	503.382	−	1878.65i	0.519486	−	1.93875i
$970$		0			0
$971$	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
$974$		0			0
$975$	−511.624	+	650.791i	−0.524743	+	0.667478i
$976$		0			0
$977$	73.8571	+	275.638i	0.0755958	+	0.282127i	0.993368	−	0.114981i	$-0.0366806\pi$
$977$	73.8571	+	275.638i	0.0755958	+	0.282127i	−0.917772	+	0.397108i	$0.870014\pi$
$978$		0			0
$979$	44.7164	−	25.8170i	0.0456756	−	0.0263708i
$980$		0			0
$981$	−19.2546	−	5.15926i	−0.0196275	−	0.00525918i
$982$		0			0
$983$	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
$986$		0			0
$987$		−	145.138i		−	0.147050i
$988$		0			0
$989$	−195.801			−0.197979
$990$		0			0
$991$	188.074	−	325.754i	0.189782	−	0.328712i	−0.755395	−	0.655269i	$-0.772555\pi$
$991$	188.074	−	325.754i	0.189782	−	0.328712i	0.945178	+	0.326557i	$0.105889\pi$
$992$		0			0
$993$	965.046	−	965.046i	0.971849	−	0.971849i
$994$		0			0
$995$	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	$0.575301\pi$
$998$		0			0
$999$	−163.243	+	43.7407i	−0.163406	+	0.0437845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.f.97.2		8
4.3	odd	2		26.3.f.b.19.1	yes	8
12.11	even	2		234.3.bb.f.19.1		8
13.11	odd	12	inner	208.3.bd.f.193.2		8
52.3	odd	6		338.3.f.h.249.1		8
52.7	even	12		338.3.d.g.99.3		8
52.11	even	12		26.3.f.b.11.1	✓	8
52.15	even	12		338.3.f.i.89.1		8
52.19	even	12		338.3.d.f.99.3		8
52.23	odd	6		338.3.f.j.249.1		8
52.31	even	4		338.3.f.j.319.1		8
52.35	odd	6		338.3.d.g.239.3		8
52.43	odd	6		338.3.d.f.239.3		8
52.47	even	4		338.3.f.h.319.1		8
52.51	odd	2		338.3.f.i.19.1		8
156.11	odd	12		234.3.bb.f.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.b.11.1	✓	8	52.11	even	12
26.3.f.b.19.1	yes	8	4.3	odd	2
208.3.bd.f.97.2		8	1.1	even	1	trivial
208.3.bd.f.193.2		8	13.11	odd	12	inner
234.3.bb.f.19.1		8	12.11	even	2
234.3.bb.f.37.1		8	156.11	odd	12
338.3.d.f.99.3		8	52.19	even	12
338.3.d.f.239.3		8	52.43	odd	6
338.3.d.g.99.3		8	52.7	even	12
338.3.d.g.239.3		8	52.35	odd	6
338.3.f.h.249.1		8	52.3	odd	6
338.3.f.h.319.1		8	52.47	even	4
338.3.f.i.19.1		8	52.51	odd	2
338.3.f.i.89.1		8	52.15	even	12
338.3.f.j.249.1		8	52.23	odd	6
338.3.f.j.319.1		8	52.31	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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52185 - 2.63592i) q^{3} +(4.79174 - 4.79174i) q^{5} +(-1.13983 + 4.25390i) q^{7} +(-0.132034 - 0.228689i) q^{9} +(13.8758 - 3.71800i) q^{11} +(1.84809 - 12.8680i) q^{13} +(-5.33833 - 19.9229i) q^{15} +(-20.9957 + 12.1219i) q^{17} +(-25.4592 - 6.82178i) q^{19} +(9.47827 + 9.47827i) q^{21} +(5.44507 + 3.14371i) q^{23} -20.9215i q^{25} +26.5895 q^{27} +(11.1112 - 19.2451i) q^{29} +(8.59518 - 8.59518i) q^{31} +(11.3164 - 42.2336i) q^{33} +(14.9218 + 25.8453i) q^{35} +(-6.13936 + 1.64504i) q^{37} +(-31.1064 - 24.4545i) q^{39} +(18.8845 + 70.4778i) q^{41} +(-26.9695 + 15.5708i) q^{43} +(-1.72849 - 0.463147i) q^{45} +(-7.65637 - 7.65637i) q^{47} +(25.6388 + 14.8026i) q^{49} +73.7905i q^{51} -33.7616 q^{53} +(48.6733 - 84.3047i) q^{55} +(-56.7267 + 56.7267i) q^{57} +(-9.77592 + 36.4842i) q^{59} +(11.5359 + 19.9807i) q^{61} +(1.12332 - 0.300991i) q^{63} +(-52.8043 - 70.5155i) q^{65} +(27.8544 + 103.954i) q^{67} +(16.5731 - 9.56849i) q^{69} +(-2.20861 - 0.591796i) q^{71} +(38.1773 + 38.1773i) q^{73} +(-55.1473 - 31.8393i) q^{75} +63.2639i q^{77} +19.1299 q^{79} +(41.6534 - 72.1459i) q^{81} +(-34.7720 + 34.7720i) q^{83} +(-42.5210 + 158.691i) q^{85} +(-33.8190 - 58.5762i) q^{87} +(3.47190 - 0.930292i) q^{89} +(52.6325 + 22.5289i) q^{91} +(-9.57562 - 35.7367i) q^{93} +(-154.682 + 89.3058i) q^{95} +(-24.3107 - 6.51404i) q^{97} +(-2.68233 - 2.68233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} + 2 q^{7} - 42 q^{9} + 18 q^{11} + 36 q^{13} - 66 q^{15} - 42 q^{17} - 46 q^{19} - 102 q^{21} + 36 q^{23} - 72 q^{27} - 6 q^{29} - 32 q^{31} + 42 q^{33} + 78 q^{35} - 106 q^{37} - 12 q^{39}+ \cdots - 252 q^{99}+O(q^{100}) \) 8 * q + 6 * q^5 + 2 * q^7 - 42 * q^9 + 18 * q^11 + 36 * q^13 - 66 * q^15 - 42 * q^17 - 46 * q^19 - 102 * q^21 + 36 * q^23 - 72 * q^27 - 6 * q^29 - 32 * q^31 + 42 * q^33 + 78 * q^35 - 106 * q^37 - 12 * q^39 + 132 * q^41 + 108 * q^43 + 240 * q^45 - 60 * q^47 + 258 * q^49 - 132 * q^53 + 162 * q^55 - 294 * q^57 - 18 * q^59 + 36 * q^61 + 72 * q^63 - 300 * q^65 + 74 * q^67 + 258 * q^69 + 174 * q^71 + 166 * q^73 - 6 * q^75 + 96 * q^79 - 12 * q^81 + 240 * q^83 - 24 * q^85 - 360 * q^87 + 294 * q^89 - 298 * q^91 + 270 * q^93 - 714 * q^95 - 58 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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