LMFDB - Embedded newform 208.3.bd.b.145.1

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 = [4,0,-4,0,6,0,-16] 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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.145
Dual form			208.3.bd.b.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.732051 + 1.26795i) q^{3} +(-1.09808 + 1.09808i) q^{5} +(-10.9282 + 2.92820i) q^{7} +(3.42820 - 5.93782i) q^{9} +(-4.92820 + 18.3923i) q^{11} +(-11.2583 + 6.50000i) q^{13} +(-2.19615 - 0.588457i) q^{15} +(0.866025 + 0.500000i) q^{17} +(-5.80385 - 21.6603i) q^{19} +(-11.7128 - 11.7128i) q^{21} +(-11.6603 + 6.73205i) q^{23} +22.5885i q^{25} +23.2154 q^{27} +(7.66987 + 13.2846i) q^{29} +(-0.928203 + 0.928203i) q^{31} +(-26.9282 + 7.21539i) q^{33} +(8.78461 - 15.2154i) q^{35} +(-6.50000 + 24.2583i) q^{37} +(-16.4833 - 9.51666i) q^{39} +(-64.5070 - 17.2846i) q^{41} +(35.0718 + 20.2487i) q^{43} +(2.75575 + 10.2846i) q^{45} +(-9.60770 - 9.60770i) q^{47} +(68.4160 - 39.5000i) q^{49} +1.46410i q^{51} +80.7128 q^{53} +(-14.7846 - 25.6077i) q^{55} +(23.2154 - 23.2154i) q^{57} +(93.9615 - 25.1769i) q^{59} +(-8.35641 + 14.4737i) q^{61} +(-20.0770 + 74.9282i) q^{63} +(5.22501 - 19.5000i) q^{65} +(12.3397 + 3.30642i) q^{67} +(-17.0718 - 9.85641i) q^{69} +(-13.2679 - 49.5167i) q^{71} +(86.0596 + 86.0596i) q^{73} +(-28.6410 + 16.5359i) q^{75} -215.426i q^{77} -73.2820 q^{79} +(-13.8590 - 24.0045i) q^{81} +(-24.3923 + 24.3923i) q^{83} +(-1.50000 + 0.401924i) q^{85} +(-11.2295 + 19.4500i) q^{87} +(13.9878 - 52.2032i) q^{89} +(104.000 - 104.000i) q^{91} +(-1.85641 - 0.497423i) q^{93} +(30.1577 + 17.4115i) q^{95} +(35.5814 + 132.792i) q^{97} +(92.3154 + 92.3154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{5} - 16 q^{7} - 14 q^{9} + 8 q^{11} + 12 q^{15} - 44 q^{19} + 64 q^{21} - 12 q^{23} + 176 q^{27} + 48 q^{29} + 24 q^{31} - 80 q^{33} - 48 q^{35} - 26 q^{37} - 156 q^{39} - 116 q^{41}+ \cdots - 88 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 6 * q^5 - 16 * q^7 - 14 * q^9 + 8 * q^11 + 12 * q^15 - 44 * q^19 + 64 * q^21 - 12 * q^23 + 176 * q^27 + 48 * q^29 + 24 * q^31 - 80 * q^33 - 48 * q^35 - 26 * q^37 - 156 * q^39 - 116 * q^41 + 168 * q^43 - 228 * q^45 - 80 * q^47 + 212 * q^53 + 24 * q^55 + 176 * q^57 + 168 * q^59 + 22 * q^61 - 496 * q^63 + 156 * q^65 + 84 * q^67 - 96 * q^69 - 60 * q^71 + 126 * q^73 + 24 * q^75 - 16 * q^79 - 194 * q^81 - 56 * q^83 - 6 * q^85 + 156 * q^87 - 190 * q^89 + 416 * q^91 + 48 * q^93 - 108 * q^95 + 222 * q^97 - 88 * q^99

Character values

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

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

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
$3$	0.732051	+	1.26795i	0.244017	+	0.422650i	0.961855	−	0.273561i	$-0.0882014\pi$
$3$	0.732051	+	1.26795i	0.244017	+	0.422650i	−0.717838	+	0.696210i	$0.754868\pi$
$4$		0			0
$5$	−1.09808	+	1.09808i	−0.219615	+	0.219615i	−0.808336	−	0.588721i	$-0.799632\pi$
$5$	−1.09808	+	1.09808i	−0.219615	+	0.219615i	0.588721	+	0.808336i	$0.299632\pi$
$6$		0			0
$7$	−10.9282	+	2.92820i	−1.56117	+	0.418315i	−0.933034	−	0.359788i	$-0.882849\pi$
$7$	−10.9282	+	2.92820i	−1.56117	+	0.418315i	−0.628138	+	0.778102i	$0.716183\pi$
$8$		0			0
$9$	3.42820	−	5.93782i	0.380911	−	0.659758i
$10$		0			0
$11$	−4.92820	+	18.3923i	−0.448018	+	1.67203i	0.259823	+	0.965656i	$0.416336\pi$
$11$	−4.92820	+	18.3923i	−0.448018	+	1.67203i	−0.707841	+	0.706371i	$0.750331\pi$
$12$		0			0
$13$	−11.2583	+	6.50000i	−0.866025	+	0.500000i
$13$	−11.2583	+	6.50000i	−0.866025	+	0.500000i
$14$		0			0
$15$	−2.19615	−	0.588457i	−0.146410	−	0.0392305i
$16$		0			0
$17$	0.866025	+	0.500000i	0.0509427	+	0.0294118i	0.525255	−	0.850945i	$-0.323970\pi$
$17$	0.866025	+	0.500000i	0.0509427	+	0.0294118i	−0.474312	+	0.880357i	$0.657303\pi$
$18$		0			0
$19$	−5.80385	−	21.6603i	−0.305466	−	1.14001i	−0.932544	−	0.361057i	$-0.882416\pi$
$19$	−5.80385	−	21.6603i	−0.305466	−	1.14001i	0.627078	−	0.778956i	$-0.284251\pi$
$20$		0			0
$21$	−11.7128	−	11.7128i	−0.557753	−	0.557753i
$22$		0			0
$23$	−11.6603	+	6.73205i	−0.506968	+	0.292698i	−0.731586	−	0.681749i	$-0.761220\pi$
$23$	−11.6603	+	6.73205i	−0.506968	+	0.292698i	0.224619	+	0.974447i	$0.427886\pi$
$24$		0			0
$25$			22.5885i			0.903538i
$26$		0			0
$27$	23.2154			0.859829
$28$		0			0
$29$	7.66987	+	13.2846i	0.264478	+	0.458090i	0.967427	−	0.253151i	$-0.0814669\pi$
$29$	7.66987	+	13.2846i	0.264478	+	0.458090i	−0.702948	+	0.711241i	$0.748134\pi$
$30$		0			0
$31$	−0.928203	+	0.928203i	−0.0299420	+	0.0299420i	−0.721919	−	0.691977i	$-0.756740\pi$
$31$	−0.928203	+	0.928203i	−0.0299420	+	0.0299420i	0.691977	+	0.721919i	$0.256740\pi$
$32$		0			0
$33$	−26.9282	+	7.21539i	−0.816006	+	0.218648i
$34$		0			0
$35$	8.78461	−	15.2154i	0.250989	−	0.434725i
$36$		0			0
$37$	−6.50000	+	24.2583i	−0.175676	+	0.655631i	0.820760	+	0.571273i	$0.193550\pi$
$37$	−6.50000	+	24.2583i	−0.175676	+	0.655631i	−0.996436	+	0.0843572i	$0.973116\pi$
$38$		0			0
$39$	−16.4833	−	9.51666i	−0.422650	−	0.244017i
$40$		0			0
$41$	−64.5070	−	17.2846i	−1.57334	−	0.421576i	−0.636486	−	0.771289i	$-0.719613\pi$
$41$	−64.5070	−	17.2846i	−1.57334	−	0.421576i	−0.936857	+	0.349713i	$0.886279\pi$
$42$		0			0
$43$	35.0718	+	20.2487i	0.815623	+	0.470900i	0.848905	−	0.528546i	$-0.177262\pi$
$43$	35.0718	+	20.2487i	0.815623	+	0.470900i	−0.0332816	+	0.999446i	$0.510596\pi$
$44$		0			0
$45$	2.75575	+	10.2846i	0.0612390	+	0.228547i
$46$		0			0
$47$	−9.60770	−	9.60770i	−0.204419	−	0.204419i	0.597471	−	0.801890i	$-0.296172\pi$
$47$	−9.60770	−	9.60770i	−0.204419	−	0.204419i	−0.801890	+	0.597471i	$0.796172\pi$
$48$		0			0
$49$	68.4160	−	39.5000i	1.39625	−	0.806122i
$50$		0			0
$51$			1.46410i			0.0287079i
$52$		0			0
$53$	80.7128			1.52288			0.761442	−	0.648233i	$-0.224492\pi$
$53$	80.7128			1.52288			0.761442	+	0.648233i	$0.224492\pi$
$54$		0			0
$55$	−14.7846	−	25.6077i	−0.268811	−	0.465594i
$56$		0			0
$57$	23.2154	−	23.2154i	0.407288	−	0.407288i
$58$		0			0
$59$	93.9615	−	25.1769i	1.59257	−	0.426727i	0.649781	−	0.760122i	$-0.274861\pi$
$59$	93.9615	−	25.1769i	1.59257	−	0.426727i	0.942787	+	0.333394i	$0.108194\pi$
$60$		0			0
$61$	−8.35641	+	14.4737i	−0.136990	+	0.237274i	−0.926356	−	0.376649i	$-0.877076\pi$
$61$	−8.35641	+	14.4737i	−0.136990	+	0.237274i	0.789366	+	0.613923i	$0.210410\pi$
$62$		0			0
$63$	−20.0770	+	74.9282i	−0.318682	+	1.18934i
$64$		0			0
$65$	5.22501	−	19.5000i	0.0803848	−	0.300000i
$66$		0			0
$67$	12.3397	+	3.30642i	0.184175	+	0.0493496i	0.349728	−	0.936851i	$-0.386274\pi$
$67$	12.3397	+	3.30642i	0.184175	+	0.0493496i	−0.165553	+	0.986201i	$0.552941\pi$
$68$		0			0
$69$	−17.0718	−	9.85641i	−0.247417	−	0.142846i
$70$		0			0
$71$	−13.2679	−	49.5167i	−0.186873	−	0.697418i	−0.994222	−	0.107344i	$-0.965765\pi$
$71$	−13.2679	−	49.5167i	−0.186873	−	0.697418i	0.807349	−	0.590074i	$-0.200901\pi$
$72$		0			0
$73$	86.0596	+	86.0596i	1.17890	+	1.17890i	0.980025	+	0.198873i	$0.0637283\pi$
$73$	86.0596	+	86.0596i	1.17890	+	1.17890i	0.198873	+	0.980025i	$0.436272\pi$
$74$		0			0
$75$	−28.6410	+	16.5359i	−0.381880	+	0.220479i
$76$		0			0
$77$		−	215.426i		−	2.79774i
$78$		0			0
$79$	−73.2820			−0.927621			−0.463810	−	0.885935i	$-0.653518\pi$
$79$	−73.2820			−0.927621			−0.463810	+	0.885935i	$0.653518\pi$
$80$		0			0
$81$	−13.8590	−	24.0045i	−0.171099	−	0.296351i
$82$		0			0
$83$	−24.3923	+	24.3923i	−0.293883	+	0.293883i	−0.838612	−	0.544729i	$-0.816633\pi$
$83$	−24.3923	+	24.3923i	−0.293883	+	0.293883i	0.544729	+	0.838612i	$0.316633\pi$
$84$		0			0
$85$	−1.50000	+	0.401924i	−0.0176471	+	0.00472852i
$86$		0			0
$87$	−11.2295	+	19.4500i	−0.129074	+	0.223563i
$88$		0			0
$89$	13.9878	−	52.2032i	0.157166	−	0.586553i	−0.841744	−	0.539877i	$-0.818471\pi$
$89$	13.9878	−	52.2032i	0.157166	−	0.586553i	0.998910	−	0.0466755i	$-0.0148627\pi$
$90$		0			0
$91$	104.000	−	104.000i	1.14286	−	1.14286i
$92$		0			0
$93$	−1.85641	−	0.497423i	−0.0199614	−	0.00534863i
$94$		0			0
$95$	30.1577	+	17.4115i	0.317449	+	0.183279i
$96$		0			0
$97$	35.5814	+	132.792i	0.366819	+	1.36899i	0.864939	+	0.501878i	$0.167357\pi$
$97$	35.5814	+	132.792i	0.366819	+	1.36899i	−0.498120	+	0.867108i	$0.665976\pi$
$98$		0			0
$99$	92.3154	+	92.3154i	0.932478	+	0.932478i
$100$		0			0
$101$	37.5666	−	21.6891i	0.371947	−	0.214744i	−0.302362	−	0.953193i	$-0.597775\pi$
$101$	37.5666	−	21.6891i	0.371947	−	0.214744i	0.674309	+	0.738450i	$0.264442\pi$
$102$		0			0
$103$		−	76.8897i		−	0.746502i	−0.927730	−	0.373251i	$-0.878243\pi$
$103$		−	76.8897i		−	0.746502i	0.927730	−	0.373251i	$-0.121757\pi$
$104$		0			0
$105$	25.7231			0.244982
$106$		0			0
$107$	−4.83717	−	8.37822i	−0.0452072	−	0.0783011i	0.842536	−	0.538639i	$-0.181061\pi$
$107$	−4.83717	−	8.37822i	−0.0452072	−	0.0783011i	−0.887744	+	0.460338i	$0.847728\pi$
$108$		0			0
$109$	−123.785	+	123.785i	−1.13564	+	1.13564i	−0.146415	+	0.989223i	$0.546774\pi$
$109$	−123.785	+	123.785i	−1.13564	+	1.13564i	−0.989223	+	0.146415i	$0.953226\pi$
$110$		0			0
$111$	−35.5167	+	9.51666i	−0.319970	+	0.0857357i
$112$		0			0
$113$	−30.3494	+	52.5666i	−0.268578	+	0.465192i	−0.968495	−	0.249033i	$-0.919887\pi$
$113$	−30.3494	+	52.5666i	−0.268578	+	0.465192i	0.699917	+	0.714225i	$0.253221\pi$
$114$		0			0
$115$	5.41154	−	20.1962i	0.0470569	−	0.175619i
$116$		0			0
$117$			89.1333i			0.761823i
$118$		0			0
$119$	−10.9282	−	2.92820i	−0.0918336	−	0.0246067i
$120$		0			0
$121$	−209.201	−	120.782i	−1.72893	−	0.998199i
$122$		0			0
$123$	−25.3064	−	94.4449i	−0.205743	−	0.767844i
$124$		0			0
$125$	−52.2558	−	52.2558i	−0.418046	−	0.418046i
$126$		0			0
$127$	−147.804	+	85.3346i	−1.16381	+	0.671926i	−0.952214	−	0.305431i	$-0.901199\pi$
$127$	−147.804	+	85.3346i	−1.16381	+	0.671926i	−0.211596	+	0.977357i	$0.567866\pi$
$128$		0			0
$129$			59.2923i			0.459631i
$130$		0			0
$131$	30.4589			0.232511			0.116256	−	0.993219i	$-0.462911\pi$
$131$	30.4589			0.232511			0.116256	+	0.993219i	$0.462911\pi$
$132$		0			0
$133$	126.851	+	219.713i	0.953769	+	1.65198i
$134$		0			0
$135$	−25.4923	+	25.4923i	−0.188832	+	0.188832i
$136$		0			0
$137$	−244.136	+	65.4160i	−1.78201	+	0.477489i	−0.990948	−	0.134243i	$-0.957140\pi$
$137$	−244.136	+	65.4160i	−1.78201	+	0.477489i	−0.791065	+	0.611732i	$0.790473\pi$
$138$		0			0
$139$	−68.4589	+	118.574i	−0.492510	+	0.853053i	−0.999963	−	0.00862675i	$-0.997254\pi$
$139$	−68.4589	+	118.574i	−0.492510	+	0.853053i	0.507452	+	0.861680i	$0.330587\pi$
$140$		0			0
$141$	5.14875	−	19.2154i	0.0365159	−	0.136279i
$142$		0			0
$143$	−64.0666	−	239.100i	−0.448018	−	1.67203i
$144$		0			0
$145$	−23.0096	−	6.16541i	−0.158687	−	0.0425201i
$146$		0			0
$147$	100.168	+	57.8320i	0.681415	+	0.393415i
$148$		0			0
$149$	−1.71539	−	6.40192i	−0.0115127	−	0.0429659i	0.959931	−	0.280238i	$-0.0904134\pi$
$149$	−1.71539	−	6.40192i	−0.0115127	−	0.0429659i	−0.971443	+	0.237272i	$0.923747\pi$
$150$		0			0
$151$	183.569	+	183.569i	1.21569	+	1.21569i	0.969127	+	0.246564i	$0.0793014\pi$
$151$	183.569	+	183.569i	1.21569	+	1.21569i	0.246564	+	0.969127i	$0.420699\pi$
$152$		0			0
$153$	5.93782	−	3.42820i	0.0388093	−	0.0224066i
$154$		0			0
$155$		−	2.03848i		−	0.0131515i
$156$		0			0
$157$	4.37307			0.0278539			0.0139270	−	0.999903i	$-0.495567\pi$
$157$	4.37307			0.0278539			0.0139270	+	0.999903i	$0.495567\pi$
$158$		0			0
$159$	59.0859	+	102.340i	0.371609	+	0.643646i
$160$		0			0
$161$	107.713	−	107.713i	0.669024	−	0.669024i
$162$		0			0
$163$	−188.354	+	50.4693i	−1.15554	+	0.309627i	−0.785185	−	0.619261i	$-0.787432\pi$
$163$	−188.354	+	50.4693i	−1.15554	+	0.309627i	−0.370360	+	0.928888i	$0.620766\pi$
$164$		0			0
$165$	21.6462	−	37.4923i	0.131189	−	0.227226i
$166$		0			0
$167$	−20.2487	+	75.5692i	−0.121250	+	0.452510i	−0.999678	−	0.0253635i	$-0.991926\pi$
$167$	−20.2487	+	75.5692i	−0.121250	+	0.452510i	0.878429	+	0.477874i	$0.158592\pi$
$168$		0			0
$169$	84.5000	−	146.358i	0.500000	−	0.866025i
$170$		0			0
$171$	−148.512	−	39.7935i	−0.868488	−	0.232711i
$172$		0			0
$173$	52.5744	+	30.3538i	0.303898	+	0.175456i	0.644193	−	0.764863i	$-0.277193\pi$
$173$	52.5744	+	30.3538i	0.303898	+	0.175456i	−0.340295	+	0.940319i	$0.610527\pi$
$174$		0			0
$175$	−66.1436	−	246.851i	−0.377963	−	1.41058i
$176$		0			0
$177$	100.708	+	100.708i	0.568970	+	0.568970i
$178$		0			0
$179$	−53.0718	+	30.6410i	−0.296490	+	0.171179i	−0.640865	−	0.767653i	$-0.721424\pi$
$179$	−53.0718	+	30.6410i	−0.296490	+	0.171179i	0.344375	+	0.938832i	$0.388091\pi$
$180$		0			0
$181$		−	230.559i		−	1.27381i	−0.770944	−	0.636903i	$-0.780215\pi$
$181$		−	230.559i		−	1.27381i	0.770944	−	0.636903i	$-0.219785\pi$
$182$		0			0
$183$	−24.4693			−0.133712
$184$		0			0
$185$	−19.5000	−	33.7750i	−0.105405	−	0.182568i
$186$		0			0
$187$	−13.4641	+	13.4641i	−0.0720005	+	0.0720005i
$188$		0			0
$189$	−253.703	+	67.9794i	−1.34234	+	0.359679i
$190$		0			0
$191$	−48.6936	+	84.3397i	−0.254940	+	0.441569i	−0.964879	−	0.262694i	$-0.915389\pi$
$191$	−48.6936	+	84.3397i	−0.254940	+	0.441569i	0.709939	+	0.704263i	$0.248722\pi$
$192$		0			0
$193$	−11.7891	+	43.9974i	−0.0610833	+	0.227966i	−0.989719	−	0.143028i	$-0.954316\pi$
$193$	−11.7891	+	43.9974i	−0.0610833	+	0.227966i	0.928635	+	0.370994i	$0.120983\pi$
$194$		0			0
$195$	28.5500	−	7.64994i	0.146410	−	0.0392305i
$196$		0			0
$197$	−164.806	−	44.1596i	−0.836577	−	0.224160i	−0.184996	−	0.982739i	$-0.559227\pi$
$197$	−164.806	−	44.1596i	−0.836577	−	0.224160i	−0.651581	+	0.758579i	$0.725894\pi$
$198$		0			0
$199$	105.191	+	60.7321i	0.528598	+	0.305186i	0.740445	−	0.672117i	$-0.234615\pi$
$199$	105.191	+	60.7321i	0.528598	+	0.305186i	−0.211847	+	0.977303i	$0.567948\pi$
$200$		0			0
$201$	4.84094	+	18.0666i	0.0240843	+	0.0898838i
$202$		0			0
$203$	−122.718	−	122.718i	−0.604522	−	0.604522i
$204$		0			0
$205$	89.8135	−	51.8538i	0.438114	−	0.252946i
$206$		0			0
$207$			92.3154i			0.445968i
$208$		0			0
$209$	426.985			2.04299
$210$		0			0
$211$	−12.0526	−	20.8756i	−0.0571211	−	0.0989367i	0.836051	−	0.548652i	$-0.184859\pi$
$211$	−12.0526	−	20.8756i	−0.0571211	−	0.0989367i	−0.893172	+	0.449715i	$0.851525\pi$
$212$		0			0
$213$	53.0718	−	53.0718i	0.249163	−	0.249163i
$214$		0			0
$215$	−60.7461	+	16.2769i	−0.282540	+	0.0757064i
$216$		0			0
$217$	7.42563	−	12.8616i	0.0342195	−	0.0592699i
$218$		0			0
$219$	−46.1192	+	172.119i	−0.210590	+	0.785932i
$220$		0			0
$221$	−13.0000			−0.0588235
$222$		0			0
$223$	274.617	+	73.5833i	1.23146	+	0.329970i	0.815150	−	0.579250i	$-0.196655\pi$
$223$	274.617	+	73.5833i	1.23146	+	0.329970i	0.416315	+	0.909220i	$0.363321\pi$
$224$		0			0
$225$	134.126	+	77.4378i	0.596117	+	0.344168i
$226$		0			0
$227$	1.26795	+	4.73205i	0.00558568	+	0.0208460i	0.968662	−	0.248381i	$-0.0798985\pi$
$227$	1.26795	+	4.73205i	0.00558568	+	0.0208460i	−0.963077	+	0.269227i	$0.913232\pi$
$228$		0			0
$229$	217.641	+	217.641i	0.950397	+	0.950397i	0.998827	−	0.0484292i	$-0.0154215\pi$
$229$	217.641	+	217.641i	0.950397	+	0.950397i	−0.0484292	+	0.998827i	$0.515422\pi$
$230$		0			0
$231$	273.149	−	157.703i	1.18246	−	0.682695i
$232$		0			0
$233$		−	260.862i		−	1.11958i	−0.828635	−	0.559789i	$-0.810882\pi$
$233$		−	260.862i		−	1.11958i	0.828635	−	0.559789i	$-0.189118\pi$
$234$		0			0
$235$	21.1000			0.0897871
$236$		0			0
$237$	−53.6462	−	92.9179i	−0.226355	−	0.392059i
$238$		0			0
$239$	294.277	−	294.277i	1.23128	−	1.23128i	0.267813	−	0.963471i	$-0.413699\pi$
$239$	294.277	−	294.277i	1.23128	−	1.23128i	0.963471	−	0.267813i	$-0.0863010\pi$
$240$		0			0
$241$	−170.926	+	45.7994i	−0.709235	+	0.190039i	−0.595363	−	0.803457i	$-0.702992\pi$
$241$	−170.926	+	45.7994i	−0.709235	+	0.190039i	−0.113872	+	0.993495i	$0.536325\pi$
$242$		0			0
$243$	124.760	−	216.091i	0.513417	−	0.889264i
$244$		0			0
$245$	−31.7520	+	118.500i	−0.129600	+	0.483673i
$246$		0			0
$247$	206.133	+	206.133i	0.834548	+	0.834548i
$248$		0			0
$249$	−48.7846	−	13.0718i	−0.195922	−	0.0524972i
$250$		0			0
$251$	66.2910	+	38.2731i	0.264107	+	0.152482i	0.626207	−	0.779657i	$-0.284607\pi$
$251$	66.2910	+	38.2731i	0.264107	+	0.152482i	−0.362099	+	0.932139i	$0.617940\pi$
$252$		0			0
$253$	−66.3538	−	247.636i	−0.262268	−	0.978798i
$254$		0			0
$255$	−1.60770	−	1.60770i	−0.00630469	−	0.00630469i
$256$		0			0
$257$	−86.4948	+	49.9378i	−0.336556	+	0.194311i	−0.658748	−	0.752364i	$-0.728914\pi$
$257$	−86.4948	+	49.9378i	−0.336556	+	0.194311i	0.322192	+	0.946674i	$0.395580\pi$
$258$		0			0
$259$		−	284.133i		−	1.09704i
$260$		0			0
$261$	105.176			0.402971
$262$		0			0
$263$	−170.890	−	295.990i	−0.649771	−	1.12544i	−0.983177	−	0.182653i	$-0.941532\pi$
$263$	−170.890	−	295.990i	−0.649771	−	1.12544i	0.333407	−	0.942783i	$-0.391802\pi$
$264$		0			0
$265$	−88.6288	+	88.6288i	−0.334448	+	0.334448i
$266$		0			0
$267$	76.4308	−	20.4796i	0.286258	−	0.0767025i
$268$		0			0
$269$	−189.779	+	328.708i	−0.705500	+	1.22196i	0.261011	+	0.965336i	$0.415944\pi$
$269$	−189.779	+	328.708i	−0.705500	+	1.22196i	−0.966511	+	0.256626i	$0.917389\pi$
$270$		0			0
$271$	−19.4256	+	72.4974i	−0.0716813	+	0.267518i	−0.992460	−	0.122566i	$-0.960888\pi$
$271$	−19.4256	+	72.4974i	−0.0716813	+	0.267518i	0.920779	+	0.390085i	$0.127554\pi$
$272$		0			0
$273$	208.000	+	55.7334i	0.761905	+	0.204152i
$274$		0			0
$275$	−415.454	−	111.321i	−1.51074	−	0.404802i
$276$		0			0
$277$	388.500	+	224.301i	1.40253	+	0.809749i	0.994651	−	0.103288i	$-0.0329364\pi$
$277$	388.500	+	224.301i	1.40253	+	0.809749i	0.407876	+	0.913038i	$0.366270\pi$
$278$		0			0
$279$	2.32944	+	8.69358i	0.00834923	+	0.0311598i
$280$		0			0
$281$	−230.275	−	230.275i	−0.819484	−	0.819484i	0.166549	−	0.986033i	$-0.446738\pi$
$281$	−230.275	−	230.275i	−0.819484	−	0.819484i	−0.986033	+	0.166549i	$0.946738\pi$
$282$		0			0
$283$	−251.321	+	145.100i	−0.888058	+	0.512721i	−0.873307	−	0.487170i	$-0.838029\pi$
$283$	−251.321	+	145.100i	−0.888058	+	0.512721i	−0.0147514	+	0.999891i	$0.504696\pi$
$284$		0			0
$285$			50.9845i			0.178893i
$286$		0			0
$287$	755.559			2.63261
$288$		0			0
$289$	−144.000	−	249.415i	−0.498270	−	0.863029i
$290$		0			0
$291$	−142.326	+	142.326i	−0.489092	+	0.489092i
$292$		0			0
$293$	273.731	−	73.3461i	0.934237	−	0.250328i	0.240576	−	0.970630i	$-0.422664\pi$
$293$	273.731	−	73.3461i	0.934237	−	0.250328i	0.693660	+	0.720302i	$0.255997\pi$
$294$		0			0
$295$	−75.5307	+	130.823i	−0.256036	+	0.443468i
$296$		0			0
$297$	−114.410	+	426.985i	−0.385219	+	1.43766i
$298$		0			0
$299$	87.5167	−	151.583i	0.292698	−	0.506968i
$300$		0			0
$301$	−442.564	−	118.585i	−1.47031	−	0.393969i
$302$		0			0
$303$	55.0014	+	31.7551i	0.181523	+	0.104802i
$304$		0			0
$305$	−6.71728	−	25.0692i	−0.0220239	−	0.0821942i
$306$		0			0
$307$	125.503	+	125.503i	0.408803	+	0.408803i	0.881321	−	0.472518i	$-0.156655\pi$
$307$	125.503	+	125.503i	0.408803	+	0.408803i	−0.472518	+	0.881321i	$0.656655\pi$
$308$		0			0
$309$	97.4923	−	56.2872i	0.315509	−	0.182159i
$310$		0			0
$311$		−	490.592i		−	1.57747i	−0.614735	−	0.788733i	$-0.710737\pi$
$311$		−	490.592i		−	1.57747i	0.614735	−	0.788733i	$-0.289263\pi$
$312$		0			0
$313$	−198.123			−0.632981			−0.316490	−	0.948596i	$-0.602504\pi$
$313$	−198.123			−0.632981			−0.316490	+	0.948596i	$0.602504\pi$
$314$		0			0
$315$	−60.2309	−	104.323i	−0.191209	−	0.331184i
$316$		0			0
$317$	314.011	−	314.011i	0.990570	−	0.990570i	−0.00938556	−	0.999956i	$-0.502988\pi$
$317$	314.011	−	314.011i	0.990570	−	0.990570i	0.999956	+	0.00938556i	$0.00298756\pi$
$318$		0			0
$319$	−282.133	+	75.5974i	−0.884430	+	0.236982i
$320$		0			0
$321$	7.08211	−	12.2666i	0.0220626	−	0.0382136i
$322$		0			0
$323$	5.80385	−	21.6603i	0.0179686	−	0.0670596i
$324$		0			0
$325$	−146.825	−	254.308i	−0.451769	−	0.782487i
$326$		0			0
$327$	−247.569	−	66.3360i	−0.757092	−	0.202862i
$328$		0			0
$329$	133.128	+	76.8616i	0.404645	+	0.233622i
$330$		0			0
$331$	140.603	+	524.736i	0.424781	+	1.58530i	0.764401	+	0.644742i	$0.223035\pi$
$331$	140.603	+	524.736i	0.424781	+	1.58530i	−0.339619	+	0.940563i	$0.610298\pi$
$332$		0			0
$333$	121.758	+	121.758i	0.365641	+	0.365641i
$334$		0			0
$335$	−17.1807	+	9.91927i	−0.0512856	+	0.0296098i
$336$		0			0
$337$			15.4205i			0.0457581i	0.999738	+	0.0228790i	$0.00728326\pi$
$337$			15.4205i			0.0457581i	−0.999738	+	0.0228790i	$0.992717\pi$
$338$		0			0
$339$	−88.8691			−0.262151
$340$		0			0
$341$	−12.4974	−	21.6462i	−0.0366493	−	0.0634785i
$342$		0			0
$343$	−240.000	+	240.000i	−0.699708	+	0.699708i
$344$		0			0
$345$	29.5692	−	7.92305i	0.0857079	−	0.0229654i
$346$		0			0
$347$	−232.970	+	403.517i	−0.671385	+	1.16287i	0.306127	+	0.951991i	$0.400967\pi$
$347$	−232.970	+	403.517i	−0.671385	+	1.16287i	−0.977512	+	0.210882i	$0.932367\pi$
$348$		0			0
$349$	106.538	−	397.604i	0.305266	−	1.13927i	−0.627450	−	0.778657i	$-0.715901\pi$
$349$	106.538	−	397.604i	0.305266	−	1.13927i	0.932716	−	0.360611i	$-0.117432\pi$
$350$		0			0
$351$	−261.367	+	150.900i	−0.744634	+	0.429915i
$352$		0			0
$353$	467.556	+	125.281i	1.32452	+	0.354905i	0.850670	−	0.525700i	$-0.176196\pi$
$353$	467.556	+	125.281i	1.32452	+	0.354905i	0.473852	+	0.880604i	$0.342863\pi$
$354$		0			0
$355$	68.9423	+	39.8038i	0.194204	+	0.112124i
$356$		0			0
$357$	−4.28719	−	16.0000i	−0.0120089	−	0.0448179i
$358$		0			0
$359$	254.985	+	254.985i	0.710263	+	0.710263i	0.966590	−	0.256327i	$-0.0825123\pi$
$359$	254.985	+	254.985i	0.710263	+	0.710263i	−0.256327	+	0.966590i	$0.582512\pi$
$360$		0			0
$361$	−122.847	+	70.9256i	−0.340296	+	0.196470i
$362$		0			0
$363$		−	353.674i		−	0.974309i
$364$		0			0
$365$	−189.000			−0.517808
$366$		0			0
$367$	206.435	+	357.555i	0.562492	+	0.974265i	0.997278	+	0.0737310i	$0.0234906\pi$
$367$	206.435	+	357.555i	0.562492	+	0.974265i	−0.434786	+	0.900534i	$0.643176\pi$
$368$		0			0
$369$	−323.776	+	323.776i	−0.877442	+	0.877442i
$370$		0			0
$371$	−882.046	+	236.344i	−2.37748	+	0.637045i
$372$		0			0
$373$	−121.325	+	210.141i	−0.325268	+	0.563381i	−0.981567	−	0.191121i	$-0.938788\pi$
$373$	−121.325	+	210.141i	−0.325268	+	0.563381i	0.656299	+	0.754501i	$0.272121\pi$
$374$		0			0
$375$	28.0038	−	104.512i	0.0746767	−	0.278697i
$376$		0			0
$377$	−172.700	−	99.7083i	−0.458090	−	0.264478i
$378$		0			0
$379$	−186.981	−	50.1013i	−0.493353	−	0.132194i	0.00356045	−	0.999994i	$-0.498867\pi$
$379$	−186.981	−	50.1013i	−0.493353	−	0.132194i	−0.496913	+	0.867800i	$0.665533\pi$
$380$		0			0
$381$	−216.400	−	124.939i	−0.567979	−	0.327923i
$382$		0			0
$383$	−23.9230	−	89.2820i	−0.0624623	−	0.233112i	0.927637	−	0.373484i	$-0.121837\pi$
$383$	−23.9230	−	89.2820i	−0.0624623	−	0.233112i	−0.990099	+	0.140372i	$0.955170\pi$
$384$		0			0
$385$	236.554	+	236.554i	0.614425	+	0.614425i
$386$		0			0
$387$	240.466	−	138.833i	0.621360	−	0.358743i
$388$		0			0
$389$			493.256i			1.26801i	0.773329	+	0.634005i	$0.218590\pi$
$389$			493.256i			1.26801i	−0.773329	+	0.634005i	$0.781410\pi$
$390$		0			0
$391$	−13.4641			−0.0344350
$392$		0			0
$393$	22.2975	+	38.6204i	0.0567366	+	0.0982707i
$394$		0			0
$395$	80.4693	−	80.4693i	0.203720	−	0.203720i
$396$		0			0
$397$	−94.1647	+	25.2314i	−0.237191	+	0.0635551i	−0.375456	−	0.926840i	$-0.622514\pi$
$397$	−94.1647	+	25.2314i	−0.237191	+	0.0635551i	0.138265	+	0.990395i	$0.455847\pi$
$398$		0			0
$399$	−185.723	+	321.682i	−0.465471	+	0.806220i
$400$		0			0
$401$	46.2795	−	172.717i	0.115410	−	0.430716i	−0.883907	−	0.467662i	$-0.845096\pi$
$401$	46.2795	−	172.717i	0.115410	−	0.430716i	0.999317	+	0.0369460i	$0.0117630\pi$
$402$		0			0
$403$	4.41670	−	16.4833i	0.0109595	−	0.0409016i
$404$		0			0
$405$	41.5770	+	11.1405i	0.102659	+	0.0275074i
$406$		0			0
$407$	−414.133	−	239.100i	−1.01753	−	0.587469i
$408$		0			0
$409$	−159.635	−	595.767i	−0.390306	−	1.45664i	−0.829630	−	0.558313i	$-0.811449\pi$
$409$	−159.635	−	595.767i	−0.390306	−	1.45664i	0.439324	−	0.898329i	$-0.355218\pi$
$410$		0			0
$411$	−261.664	−	261.664i	−0.636652	−	0.636652i
$412$		0			0
$413$	−953.108	+	550.277i	−2.30777	+	1.33239i
$414$		0			0
$415$		−	53.5692i		−	0.129082i
$416$		0			0
$417$	−200.462			−0.480724
$418$		0			0
$419$	327.727	+	567.640i	0.782164	+	1.35475i	0.930678	+	0.365838i	$0.119218\pi$
$419$	327.727	+	567.640i	0.782164	+	1.35475i	−0.148514	+	0.988910i	$0.547449\pi$
$420$		0			0
$421$	101.107	−	101.107i	0.240159	−	0.240159i	−0.576757	−	0.816916i	$-0.695682\pi$
$421$	101.107	−	101.107i	0.240159	−	0.240159i	0.816916	+	0.576757i	$0.195682\pi$
$422$		0			0
$423$	−89.9859	+	24.1117i	−0.212733	+	0.0570015i
$424$		0			0
$425$	−11.2942	+	19.5622i	−0.0265747	+	0.0460287i
$426$		0			0
$427$	48.9385	−	182.641i	0.114610	−	0.427731i
$428$		0			0
$429$	256.267	−	256.267i	0.597358	−	0.597358i
$430$		0			0
$431$	413.387	+	110.767i	0.959135	+	0.256999i	0.704234	−	0.709968i	$-0.251291\pi$
$431$	413.387	+	110.767i	0.959135	+	0.256999i	0.254901	+	0.966967i	$0.417957\pi$
$432$		0			0
$433$	671.264	+	387.554i	1.55026	+	0.895045i	0.998120	+	0.0612959i	$0.0195233\pi$
$433$	671.264	+	387.554i	1.55026	+	0.895045i	0.552144	+	0.833749i	$0.313810\pi$
$434$		0			0
$435$	−9.02679	−	33.6884i	−0.0207512	−	0.0774446i
$436$		0			0
$437$	213.492	+	213.492i	0.488541	+	0.488541i
$438$		0			0
$439$	445.741	−	257.349i	1.01536	−	0.586216i	0.102600	−	0.994723i	$-0.467284\pi$
$439$	445.741	−	257.349i	1.01536	−	0.586216i	0.912755	+	0.408507i	$0.133950\pi$
$440$		0			0
$441$		−	541.656i		−	1.22825i
$442$		0			0
$443$	39.4256			0.0889969			0.0444984	−	0.999009i	$-0.485831\pi$
$443$	39.4256			0.0889969			0.0444984	+	0.999009i	$0.485831\pi$
$444$		0			0
$445$	41.9634	+	72.6828i	0.0942998	+	0.163332i
$446$		0			0
$447$	6.86156	−	6.86156i	0.0153502	−	0.0153502i
$448$		0			0
$449$	−55.1314	+	14.7724i	−0.122787	+	0.0329007i	−0.319689	−	0.947522i	$-0.603579\pi$
$449$	−55.1314	+	14.7724i	−0.122787	+	0.0329007i	0.196902	+	0.980423i	$0.436912\pi$
$450$		0			0
$451$	635.808	−	1101.25i	1.40977	−	2.44180i
$452$		0			0
$453$	−98.3744	+	367.138i	−0.217162	+	0.810460i
$454$		0			0
$455$			228.400i			0.501978i
$456$		0			0
$457$	183.435	+	49.1513i	0.401390	+	0.107552i	0.453866	−	0.891070i	$-0.350045\pi$
$457$	183.435	+	49.1513i	0.401390	+	0.107552i	−0.0524757	+	0.998622i	$0.516711\pi$
$458$		0			0
$459$	20.1051	+	11.6077i	0.0438020	+	0.0252891i
$460$		0			0
$461$	−30.0538	−	112.162i	−0.0651925	−	0.243302i	0.925638	−	0.378409i	$-0.123529\pi$
$461$	−30.0538	−	112.162i	−0.0651925	−	0.243302i	−0.990831	+	0.135107i	$0.956862\pi$
$462$		0			0
$463$	−23.3205	−	23.3205i	−0.0503683	−	0.0503683i	0.681474	−	0.731842i	$-0.261339\pi$
$463$	−23.3205	−	23.3205i	−0.0503683	−	0.0503683i	−0.731842	+	0.681474i	$0.761339\pi$
$464$		0			0
$465$	2.58468	−	1.49227i	0.00555846	−	0.00320918i
$466$		0			0
$467$			427.482i			0.915379i	0.889112	+	0.457689i	$0.151323\pi$
$467$			427.482i			0.915379i	−0.889112	+	0.457689i	$0.848677\pi$
$468$		0			0
$469$	−144.533			−0.308173
$470$		0			0
$471$	3.20131	+	5.54483i	0.00679683	+	0.0117725i
$472$		0			0
$473$	−545.261	+	545.261i	−1.15277	+	1.15277i
$474$		0			0
$475$	489.272	−	131.100i	1.03005	−	0.276000i
$476$		0			0
$477$	276.700	−	479.258i	0.580084	−	1.00473i
$478$		0			0
$479$	190.483	−	710.894i	0.397669	−	1.48412i	−0.419518	−	0.907747i	$-0.637801\pi$
$479$	190.483	−	710.894i	0.397669	−	1.48412i	0.817187	−	0.576373i	$-0.195532\pi$
$480$		0			0
$481$	−84.5000	−	315.358i	−0.175676	−	0.655631i
$482$		0			0
$483$	215.426	+	57.7231i	0.446016	+	0.119510i
$484$		0			0
$485$	−184.886	−	106.744i	−0.381209	−	0.220091i
$486$		0			0
$487$	−55.3308	−	206.497i	−0.113616	−	0.424019i	0.885564	−	0.464517i	$-0.153772\pi$
$487$	−55.3308	−	206.497i	−0.113616	−	0.424019i	−0.999180	+	0.0404981i	$0.987106\pi$
$488$		0			0
$489$	−201.877	−	201.877i	−0.412836	−	0.412836i
$490$		0			0
$491$	143.885	−	83.0718i	0.293044	−	0.169189i	−0.346270	−	0.938135i	$-0.612552\pi$
$491$	143.885	−	83.0718i	0.293044	−	0.169189i	0.639314	+	0.768946i	$0.279219\pi$
$492$		0			0
$493$			15.3397i			0.0311151i
$494$		0			0
$495$	−202.739			−0.409573
$496$		0			0
$497$	289.990	+	502.277i	0.583480	+	1.01062i
$498$		0			0
$499$	−53.6359	+	53.6359i	−0.107487	+	0.107487i	−0.758805	−	0.651318i	$-0.774216\pi$
$499$	−53.6359	+	53.6359i	−0.107487	+	0.107487i	0.651318	+	0.758805i	$0.274216\pi$
$500$		0			0
$501$	−110.641	+	29.6462i	−0.220840	+	0.0591740i
$502$		0			0
$503$	−334.669	+	579.664i	−0.665346	+	1.15241i	0.313845	+	0.949474i	$0.398383\pi$
$503$	−334.669	+	579.664i	−0.665346	+	1.15241i	−0.979191	+	0.202939i	$0.934951\pi$
$504$		0			0
$505$	−17.4347	+	65.0673i	−0.0345242	+	0.128846i
$506$		0			0
$507$	247.433			0.488034
$508$		0			0
$509$	450.535	+	120.721i	0.885138	+	0.237172i	0.672623	−	0.739986i	$-0.265168\pi$
$509$	450.535	+	120.721i	0.885138	+	0.237172i	0.212515	+	0.977158i	$0.431834\pi$
$510$		0			0
$511$	−1192.48	−	688.477i	−2.33361	−	1.34731i
$512$		0			0
$513$	−134.739	−	502.851i	−0.262648	−	0.980217i
$514$		0			0
$515$	84.4308	+	84.4308i	0.163943	+	0.163943i
$516$		0			0
$517$	224.056	−	129.359i	0.433378	−	0.250211i
$518$		0			0
$519$			88.8822i			0.171257i
$520$		0			0
$521$	187.283			0.359469			0.179735	−	0.983715i	$-0.442476\pi$
$521$	187.283			0.359469			0.179735	+	0.983715i	$0.442476\pi$
$522$		0			0
$523$	−5.75129	−	9.96152i	−0.0109967	−	0.0190469i	0.860475	−	0.509493i	$-0.170167\pi$
$523$	−5.75129	−	9.96152i	−0.0109967	−	0.0190469i	−0.871471	+	0.490446i	$0.836834\pi$
$524$		0			0
$525$	264.574	−	264.574i	0.503951	−	0.503951i
$526$		0			0
$527$	−1.26795	+	0.339746i	−0.00240598	+	0.000644679i
$528$		0			0
$529$	−173.859	+	301.133i	−0.328656	+	0.569249i
$530$		0			0
$531$	172.623	−	644.238i	0.325091	−	1.21325i
$532$		0			0
$533$	838.592	−	224.700i	1.57334	−	0.421576i
$534$		0			0
$535$	14.5115	+	3.88835i	0.0271243	+	0.00726794i
$536$		0			0
$537$	−77.7025	−	44.8616i	−0.144697	−	0.0835411i
$538$		0			0
$539$	389.328	+	1452.99i	0.722316	+	2.69572i
$540$		0			0
$541$	−99.4519	−	99.4519i	−0.183830	−	0.183830i	0.609193	−	0.793022i	$-0.291494\pi$
$541$	−99.4519	−	99.4519i	−0.183830	−	0.183830i	−0.793022	+	0.609193i	$0.791494\pi$
$542$		0			0
$543$	292.337	−	168.781i	0.538374	−	0.310830i
$544$		0			0
$545$		−	271.850i		−	0.498807i
$546$		0			0
$547$	554.438			1.01360			0.506799	−	0.862064i	$-0.330829\pi$
$547$	554.438			1.01360			0.506799	+	0.862064i	$0.330829\pi$
$548$		0			0
$549$	57.2949	+	99.2377i	0.104362	+	0.180761i
$550$		0			0
$551$	243.233	−	243.233i	0.441440	−	0.441440i
$552$		0			0
$553$	800.841	−	214.585i	1.44818	−	0.388037i
$554$		0			0
$555$	28.5500	−	49.4500i	0.0514414	−	0.0890991i
$556$		0			0
$557$	−140.766	+	525.346i	−0.252722	+	0.943171i	0.716622	+	0.697462i	$0.245687\pi$
$557$	−140.766	+	525.346i	−0.252722	+	0.943171i	−0.969344	+	0.245709i	$0.920979\pi$
$558$		0			0
$559$	−526.466			−0.941801
$560$		0			0
$561$	−26.9282	−	7.21539i	−0.0480004	−	0.0128617i
$562$		0			0
$563$	595.510	+	343.818i	1.05774	+	0.610689i	0.924807	−	0.380435i	$-0.124226\pi$
$563$	595.510	+	343.818i	1.05774	+	0.610689i	0.132937	+	0.991124i	$0.457559\pi$
$564$		0			0
$565$	−24.3963	−	91.0481i	−0.0431792	−	0.161147i
$566$		0			0
$567$	221.744	+	221.744i	0.391082	+	0.391082i
$568$		0			0
$569$	411.482	−	237.569i	0.723167	−	0.417521i	−0.0927503	−	0.995689i	$-0.529566\pi$
$569$	411.482	−	237.569i	0.723167	−	0.417521i	0.815917	+	0.578169i	$0.196232\pi$
$570$		0			0
$571$		−	444.728i		−	0.778859i	−0.921056	−	0.389429i	$-0.872672\pi$
$571$		−	444.728i		−	0.778859i	0.921056	−	0.389429i	$-0.127328\pi$
$572$		0			0
$573$	−142.585			−0.248839
$574$		0			0
$575$	−152.067	−	263.387i	−0.264464	−	0.458065i
$576$		0			0
$577$	374.542	−	374.542i	0.649119	−	0.649119i	−0.303661	−	0.952780i	$-0.598209\pi$
$577$	374.542	−	374.542i	0.649119	−	0.649119i	0.952780	+	0.303661i	$0.0982091\pi$
$578$		0			0
$579$	−64.4167	+	17.2604i	−0.111255	+	0.0298107i
$580$		0			0
$581$	195.138	−	337.990i	0.335867	−	0.581738i
$582$		0			0
$583$	−397.769	+	1484.49i	−0.682280	+	2.54630i
$584$		0			0
$585$	−97.8751	−	97.8751i	−0.167308	−	0.167308i
$586$		0			0
$587$	−710.582	−	190.400i	−1.21053	−	0.324361i	−0.403561	−	0.914953i	$-0.632228\pi$
$587$	−710.582	−	190.400i	−1.21053	−	0.324361i	−0.806970	+	0.590592i	$0.798894\pi$
$588$		0			0
$589$	25.4923	+	14.7180i	0.0432806	+	0.0249881i
$590$		0			0
$591$	−64.6541	−	241.292i	−0.109398	−	0.408278i
$592$		0			0
$593$	−278.901	−	278.901i	−0.470321	−	0.470321i	0.431697	−	0.902019i	$-0.357915\pi$
$593$	−278.901	−	278.901i	−0.470321	−	0.470321i	−0.902019	+	0.431697i	$0.857915\pi$
$594$		0			0
$595$	15.2154	−	8.78461i	0.0255721	−	0.0147640i
$596$		0			0
$597$			177.836i			0.297882i
$598$		0			0
$599$	−741.059			−1.23716			−0.618580	−	0.785722i	$-0.712292\pi$
$599$	−741.059			−1.23716			−0.618580	+	0.785722i	$0.712292\pi$
$600$		0			0
$601$	−320.339	−	554.844i	−0.533010	−	0.923201i	−0.999257	−	0.0385458i	$-0.987727\pi$
$601$	−320.339	−	554.844i	−0.533010	−	0.923201i	0.466247	−	0.884655i	$-0.345606\pi$
$602$		0			0
$603$	61.9361	−	61.9361i	0.102713	−	0.102713i
$604$		0			0
$605$	362.346	−	97.0903i	0.598919	−	0.160480i
$606$		0			0
$607$	−0.549981	+	0.952596i	−0.000906065	+	0.00156935i	−0.866478	−	0.499215i	$-0.833622\pi$
$607$	−0.549981	+	0.952596i	−0.000906065	+	0.00156935i	0.865572	+	0.500784i	$0.166955\pi$
$608$		0			0
$609$	65.7644	−	245.436i	0.107987	−	0.403015i
$610$		0			0
$611$	170.617	+	45.7166i	0.279242	+	0.0748226i
$612$		0			0
$613$	−84.9256	−	22.7558i	−0.138541	−	0.0371219i	0.188882	−	0.982000i	$-0.439514\pi$
$613$	−84.9256	−	22.7558i	−0.138541	−	0.0371219i	−0.327423	+	0.944878i	$0.606180\pi$
$614$		0			0
$615$	131.496	+	75.9193i	0.213815	+	0.123446i
$616$		0			0
$617$	188.859	+	704.831i	0.306092	+	1.14235i	0.932001	+	0.362456i	$0.118062\pi$
$617$	188.859	+	704.831i	0.306092	+	1.14235i	−0.625909	+	0.779896i	$0.715272\pi$
$618$		0			0
$619$	−359.138	−	359.138i	−0.580191	−	0.580191i	0.354764	−	0.934956i	$-0.384561\pi$
$619$	−359.138	−	359.138i	−0.580191	−	0.580191i	−0.934956	+	0.354764i	$0.884561\pi$
$620$		0			0
$621$	−270.697	+	156.287i	−0.435906	+	0.251670i
$622$		0			0
$623$			611.446i			0.981455i
$624$		0			0
$625$	−449.950			−0.719920
$626$		0			0
$627$	312.574	+	541.395i	0.498524	+	0.863468i
$628$		0			0
$629$	−17.7583	+	17.7583i	−0.0282326	+	0.0282326i
$630$		0			0
$631$	408.918	−	109.569i	0.648047	−	0.173644i	0.0802015	−	0.996779i	$-0.474444\pi$
$631$	408.918	−	109.569i	0.648047	−	0.173644i	0.567846	+	0.823135i	$0.307777\pi$
$632$		0			0
$633$	17.6462	−	30.5641i	0.0278770	−	0.0482845i
$634$		0			0
$635$	68.5960	−	256.004i	0.108025	−	0.403156i
$636$		0			0
$637$	−513.500	+	889.408i	−0.806122	+	1.39625i
$638$		0			0
$639$	−339.506	−	90.9705i	−0.531309	−	0.142364i
$640$		0			0
$641$	−11.6046	−	6.69993i	−0.0181039	−	0.0104523i	0.490921	−	0.871204i	$-0.336660\pi$
$641$	−11.6046	−	6.69993i	−0.0181039	−	0.0104523i	−0.509025	+	0.860752i	$0.669994\pi$
$642$		0			0
$643$	−114.161	−	426.056i	−0.177545	−	0.662607i	−0.996104	−	0.0881847i	$-0.971893\pi$
$643$	−114.161	−	426.056i	−0.177545	−	0.662607i	0.818559	−	0.574422i	$-0.194773\pi$
$644$		0			0
$645$	−65.1075	−	65.1075i	−0.100942	−	0.100942i
$646$		0			0
$647$	173.976	−	100.445i	0.268896	−	0.155247i	−0.359490	−	0.933149i	$-0.617049\pi$
$647$	173.976	−	100.445i	0.268896	−	0.155247i	0.628386	+	0.777902i	$0.283716\pi$
$648$		0			0
$649$			1852.25i			2.85400i
$650$		0			0
$651$	21.7437			0.0334005
$652$		0			0
$653$	−600.400	−	1039.92i	−0.919448	−	1.59253i	−0.800255	−	0.599660i	$-0.795302\pi$
$653$	−600.400	−	1039.92i	−0.919448	−	1.59253i	−0.119194	−	0.992871i	$-0.538031\pi$
$654$		0			0
$655$	−33.4462	+	33.4462i	−0.0510630	+	0.0510630i
$656$		0			0
$657$	806.036	−	215.977i	1.22684	−	0.328732i
$658$		0			0
$659$	94.3538	−	163.426i	0.143177	−	0.247990i	−0.785514	−	0.618844i	$-0.787601\pi$
$659$	94.3538	−	163.426i	0.143177	−	0.247990i	0.928691	+	0.370853i	$0.120935\pi$
$660$		0			0
$661$	−58.7820	+	219.378i	−0.0889289	+	0.331887i	−0.996029	−	0.0890273i	$-0.971624\pi$
$661$	−58.7820	+	219.378i	−0.0889289	+	0.331887i	0.907100	+	0.420915i	$0.138291\pi$
$662$		0			0
$663$	−9.51666	−	16.4833i	−0.0143539	−	0.0248617i
$664$		0			0
$665$	−380.554	−	101.969i	−0.572261	−	0.153337i
$666$		0			0
$667$	−178.865	−	103.268i	−0.268164	−	0.154825i
$668$		0			0
$669$	107.733	+	402.067i	0.161037	+	0.600996i
$670$		0			0
$671$	−225.023	−	225.023i	−0.335355	−	0.335355i
$672$		0			0
$673$	−68.7891	+	39.7154i	−0.102213	+	0.0590125i	−0.550235	−	0.835010i	$-0.685462\pi$
$673$	−68.7891	+	39.7154i	−0.102213	+	0.0590125i	0.448022	+	0.894022i	$0.352129\pi$
$674$		0			0
$675$			524.400i			0.776889i
$676$		0			0
$677$	−310.554			−0.458720			−0.229360	−	0.973342i	$-0.573663\pi$
$677$	−310.554			−0.458720			−0.229360	+	0.973342i	$0.573663\pi$
$678$		0			0
$679$	−777.682	−	1346.98i	−1.14533	−	1.98378i
$680$		0			0
$681$	−5.07180	+	5.07180i	−0.00744757	+	0.00744757i
$682$		0			0
$683$	627.678	−	168.186i	0.919002	−	0.246246i	0.231843	−	0.972753i	$-0.425524\pi$
$683$	627.678	−	168.186i	0.919002	−	0.246246i	0.687159	+	0.726507i	$0.258858\pi$
$684$		0			0
$685$	196.248	−	339.912i	0.286493	−	0.496221i
$686$		0			0
$687$	−116.633	+	435.282i	−0.169772	+	0.633598i
$688$		0			0
$689$	−908.692	+	524.633i	−1.31886	+	0.761442i
$690$		0			0
$691$	−294.603	−	78.9385i	−0.426342	−	0.114238i	0.0392664	−	0.999229i	$-0.487498\pi$
$691$	−294.603	−	78.9385i	−0.426342	−	0.114238i	−0.465609	+	0.884991i	$0.654165\pi$
$692$		0			0
$693$	−1279.16	−	738.523i	−1.84583	−	1.06569i
$694$		0			0
$695$	−55.0306	−	205.377i	−0.0791807	−	0.295506i
$696$		0			0
$697$	−47.2224	−	47.2224i	−0.0677510	−	0.0677510i
$698$		0			0
$699$	330.759	−	190.964i	0.473189	−	0.273196i
$700$		0			0
$701$		−	173.692i		−	0.247778i	−0.992296	−	0.123889i	$-0.960463\pi$
$701$		−	173.692i		−	0.247778i	0.992296	−	0.123889i	$-0.0395366\pi$
$702$		0			0
$703$	563.167			0.801090
$704$		0			0
$705$	15.4462	+	26.7537i	0.0219096	+	0.0379485i
$706$		0			0
$707$	−347.026	+	347.026i	−0.490843	+	0.490843i
$708$		0			0
$709$	75.2795	−	20.1711i	0.106177	−	0.0284500i	−0.205339	−	0.978691i	$-0.565830\pi$
$709$	75.2795	−	20.1711i	0.106177	−	0.0284500i	0.311516	+	0.950241i	$0.399163\pi$
$710$		0			0
$711$	−251.226	+	435.136i	−0.353341	+	0.612005i
$712$		0			0
$713$	4.57437	−	17.0718i	0.00641567	−	0.0239436i
$714$		0			0
$715$	332.900	+	192.200i	0.465594	+	0.268811i
$716$		0			0
$717$	588.554	+	157.703i	0.820856	+	0.219948i
$718$		0			0
$719$	280.077	+	161.703i	0.389537	+	0.224899i	0.681959	−	0.731390i	$-0.261128\pi$
$719$	280.077	+	161.703i	0.389537	+	0.224899i	−0.292423	+	0.956289i	$0.594461\pi$
$720$		0			0
$721$	225.149	+	840.267i	0.312273	+	1.16542i
$722$		0			0
$723$	−183.198	−	183.198i	−0.253385	−	0.253385i
$724$		0			0
$725$	−300.079	+	173.251i	−0.413902	+	0.238966i
$726$		0			0
$727$		−	642.221i		−	0.883385i	−0.897167	−	0.441692i	$-0.854378\pi$
$727$		−	642.221i		−	0.883385i	0.897167	−	0.441692i	$-0.145622\pi$
$728$		0			0
$729$	115.862			0.158932
$730$		0			0
$731$	20.2487	+	35.0718i	0.0277000	+	0.0479778i
$732$		0			0
$733$	−389.122	+	389.122i	−0.530863	+	0.530863i	−0.920829	−	0.389966i	$-0.872487\pi$
$733$	−389.122	+	389.122i	−0.530863	+	0.530863i	0.389966	+	0.920829i	$0.372487\pi$
$734$		0			0
$735$	−173.496	+	46.4881i	−0.236049	+	0.0632491i
$736$		0			0
$737$	−121.626	+	210.662i	−0.165028	+	0.285837i
$738$		0			0
$739$	−168.610	+	629.261i	−0.228160	+	0.851504i	0.752954	+	0.658073i	$0.228628\pi$
$739$	−168.610	+	629.261i	−0.228160	+	0.851504i	−0.981114	+	0.193431i	$0.938038\pi$
$740$		0			0
$741$	−110.466	+	412.267i	−0.149078	+	0.556365i
$742$		0			0
$743$	1049.62	+	281.244i	1.41267	+	0.378524i	0.882878	−	0.469602i	$-0.155603\pi$
$743$	1049.62	+	281.244i	1.41267	+	0.378524i	0.529794	+	0.848126i	$0.322269\pi$
$744$		0			0
$745$	8.91343	+	5.14617i	0.0119643	+	0.00690761i
$746$		0			0
$747$	61.2154	+	228.459i	0.0819483	+	0.305835i
$748$		0			0
$749$	77.3947	+	77.3947i	0.103331	+	0.103331i
$750$		0			0
$751$	−989.587	+	571.338i	−1.31769	+	0.760770i	−0.983357	−	0.181684i	$-0.941845\pi$
$751$	−989.587	+	571.338i	−1.31769	+	0.760770i	−0.334336	+	0.942454i	$0.608512\pi$
$752$		0			0
$753$			112.071i			0.148833i
$754$		0			0
$755$	−403.146			−0.533968
$756$		0			0
$757$	86.6462	+	150.076i	0.114460	+	0.198250i	0.917564	−	0.397589i	$-0.130153\pi$
$757$	86.6462	+	150.076i	0.114460	+	0.198250i	−0.803104	+	0.595839i	$0.796820\pi$
$758$		0			0
$759$	265.415	−	265.415i	0.349691	−	0.349691i
$760$		0			0
$761$	−780.638	+	209.171i	−1.02581	+	0.274864i	−0.732219	−	0.681069i	$-0.761515\pi$
$761$	−780.638	+	209.171i	−1.02581	+	0.274864i	−0.293586	+	0.955933i	$0.594849\pi$
$762$		0			0
$763$	990.277	−	1715.21i	1.29787	−	2.24798i
$764$		0			0
$765$	−2.75575	+	10.2846i	−0.00360229	+	0.0134439i
$766$		0			0
$767$	−894.200	+	894.200i	−1.16584	+	1.16584i
$768$		0			0
$769$	−1341.89	−	359.557i	−1.74497	−	0.467564i	−0.761432	−	0.648245i	$-0.775503\pi$
$769$	−1341.89	−	359.557i	−1.74497	−	0.467564i	−0.983542	+	0.180680i	$0.942170\pi$
$770$		0			0
$771$	−126.637	−	73.1140i	−0.164251	−	0.0948302i
$772$		0			0
$773$	−66.4007	−	247.811i	−0.0859000	−	0.320583i	0.909583	−	0.415522i	$-0.136401\pi$
$773$	−66.4007	−	247.811i	−0.0859000	−	0.320583i	−0.995483	+	0.0949388i	$0.969734\pi$
$774$		0			0
$775$	−20.9667	−	20.9667i	−0.0270538	−	0.0270538i
$776$		0			0
$777$	360.267	−	208.000i	0.463664	−	0.267696i
$778$		0			0
$779$			1497.56i			1.92241i
$780$		0			0
$781$	976.113			1.24982
$782$		0			0
$783$	178.059	+	308.407i	0.227406	+	0.393879i
$784$		0			0
$785$	−4.80196	+	4.80196i	−0.00611715	+	0.00611715i
$786$		0			0
$787$	406.750	−	108.988i	0.516836	−	0.138486i	0.00903330	−	0.999959i	$-0.497125\pi$
$787$	406.750	−	108.988i	0.516836	−	0.138486i	0.507803	+	0.861473i	$0.330458\pi$
$788$		0			0
$789$	250.200	−	433.359i	0.317110	−	0.549251i
$790$		0			0
$791$	177.738	−	663.328i	0.224701	−	0.838594i
$792$		0			0
$793$		−	217.267i		−	0.273981i
$794$		0			0
$795$	−177.258	−	47.4960i	−0.222966	−	0.0597434i
$796$		0			0
$797$	502.996	+	290.405i	0.631112	+	0.364373i	0.781183	−	0.624303i	$-0.214617\pi$
$797$	502.996	+	290.405i	0.631112	+	0.364373i	−0.150071	+	0.988675i	$0.547950\pi$
$798$		0			0
$799$	−3.51666	−	13.1244i	−0.00440133	−	0.0164260i
$800$		0			0
$801$	−262.020	−	262.020i	−0.327116	−	0.327116i
$802$		0			0
$803$	−2006.95	+	1158.72i	−2.49932	+	1.44298i
$804$		0			0
$805$			236.554i			0.293856i
$806$		0			0
$807$	−555.713			−0.688616
$808$		0			0
$809$	584.845	+	1012.98i	0.722924	+	1.25214i	0.959823	+	0.280607i	$0.0905356\pi$
$809$	584.845	+	1012.98i	0.722924	+	1.25214i	−0.236899	+	0.971534i	$0.576131\pi$
$810$		0			0
$811$	−559.177	+	559.177i	−0.689491	+	0.689491i	−0.962119	−	0.272629i	$-0.912107\pi$
$811$	−559.177	+	559.177i	−0.689491	+	0.689491i	0.272629	+	0.962119i	$0.412107\pi$
$812$		0			0
$813$	−106.144	+	28.4411i	−0.130558	+	0.0349829i
$814$		0			0
$815$	151.408	−	262.246i	0.185776	−	0.321774i
$816$		0			0
$817$	235.041	−	877.184i	0.287688	−	1.07367i
$818$		0			0
$819$	−261.000	−	974.067i	−0.318682	−	1.18934i
$820$		0			0
$821$	657.570	+	176.195i	0.800938	+	0.214611i	0.635996	−	0.771693i	$-0.280590\pi$
$821$	657.570	+	176.195i	0.800938	+	0.214611i	0.164942	+	0.986303i	$0.447256\pi$
$822$		0			0
$823$	−386.718	−	223.272i	−0.469888	−	0.271290i	0.246305	−	0.969192i	$-0.420784\pi$
$823$	−386.718	−	223.272i	−0.469888	−	0.271290i	−0.716193	+	0.697902i	$0.754117\pi$
$824$		0			0
$825$	−162.985	−	608.267i	−0.197557	−	0.737293i
$826$		0			0
$827$	−364.833	−	364.833i	−0.441153	−	0.441153i	0.451247	−	0.892399i	$-0.350980\pi$
$827$	−364.833	−	364.833i	−0.441153	−	0.441153i	−0.892399	+	0.451247i	$0.850980\pi$
$828$		0			0
$829$	1060.17	−	612.090i	1.27886	−	0.738348i	0.302218	−	0.953239i	$-0.402273\pi$
$829$	1060.17	−	612.090i	1.27886	−	0.738348i	0.976638	+	0.214891i	$0.0689396\pi$
$830$		0			0
$831$			656.798i			0.790370i
$832$		0			0
$833$	79.0000			0.0948379
$834$		0			0
$835$	−60.7461	−	105.215i	−0.0727499	−	0.126006i
$836$		0			0
$837$	−21.5486	+	21.5486i	−0.0257450	+	0.0257450i
$838$		0			0
$839$	1283.45	−	343.899i	1.52973	−	0.409891i	0.606802	−	0.794853i	$-0.292452\pi$
$839$	1283.45	−	343.899i	1.52973	−	0.409891i	0.922932	+	0.384962i	$0.125785\pi$
$840$		0			0
$841$	302.846	−	524.545i	0.360102	−	0.623716i
$842$		0			0
$843$	123.404	−	460.550i	0.146387	−	0.546323i
$844$		0			0
$845$	67.9251	+	253.500i	0.0803848	+	0.300000i
$846$		0			0
$847$	2639.86	+	707.349i	3.11672	+	0.835122i
$848$		0			0
$849$	−367.959	−	212.441i	−0.433403	−	0.250225i
$850$		0			0
$851$	−87.5167	−	326.617i	−0.102840	−	0.383803i
$852$		0			0
$853$	−787.174	−	787.174i	−0.922830	−	0.922830i	0.0743990	−	0.997229i	$-0.476296\pi$
$853$	−787.174	−	787.174i	−0.922830	−	0.922830i	−0.997229	+	0.0743990i	$0.976296\pi$
$854$		0			0
$855$	206.773	−	119.381i	0.241840	−	0.139626i
$856$		0			0
$857$		−	673.732i		−	0.786152i	−0.919506	−	0.393076i	$-0.871411\pi$
$857$		−	673.732i		−	0.786152i	0.919506	−	0.393076i	$-0.128589\pi$
$858$		0			0
$859$	−487.167			−0.567132			−0.283566	−	0.958953i	$-0.591518\pi$
$859$	−487.167			−0.567132			−0.283566	+	0.958953i	$0.591518\pi$
$860$		0			0
$861$	553.108	+	958.010i	0.642401	+	1.11267i
$862$		0			0
$863$	499.061	−	499.061i	0.578287	−	0.578287i	−0.356144	−	0.934431i	$-0.615909\pi$
$863$	499.061	−	499.061i	0.578287	−	0.578287i	0.934431	+	0.356144i	$0.115909\pi$
$864$		0			0
$865$	−91.0615	+	24.3999i	−0.105273	+	0.0282079i
$866$		0			0
$867$	210.831	−	365.169i	0.243173	−	0.421187i
$868$		0			0
$869$	361.149	−	1347.83i	0.415591	−	1.55101i
$870$		0			0
$871$	−160.417	+	42.9835i	−0.184175	+	0.0493496i
$872$		0			0
$873$	910.474	+	243.961i	1.04293	+	0.279451i
$874$		0			0
$875$	724.077	+	418.046i	0.827517	+	0.477767i
$876$		0			0
$877$	243.962	+	910.479i	0.278178	+	1.03817i	0.953682	+	0.300818i	$0.0972597\pi$
$877$	243.962	+	910.479i	0.278178	+	1.03817i	−0.675503	+	0.737357i	$0.736074\pi$
$878$		0			0
$879$	293.384	+	293.384i	0.333771	+	0.333771i
$880$		0			0
$881$	405.459	−	234.092i	0.460226	−	0.265711i	−0.251914	−	0.967750i	$-0.581060\pi$
$881$	405.459	−	234.092i	0.460226	−	0.265711i	0.712139	+	0.702038i	$0.247727\pi$
$882$		0			0
$883$			782.536i			0.886224i	0.896466	+	0.443112i	$0.146126\pi$
$883$			782.536i			0.886224i	−0.896466	+	0.443112i	$0.853874\pi$
$884$		0			0
$885$	−221.169			−0.249909
$886$		0			0
$887$	−60.4102	−	104.633i	−0.0681062	−	0.117963i	0.829961	−	0.557821i	$-0.188362\pi$
$887$	−60.4102	−	104.633i	−0.0681062	−	0.117963i	−0.898068	+	0.439857i	$0.855029\pi$
$888$		0			0
$889$	1365.35	−	1365.35i	1.53583	−	1.53583i
$890$		0			0
$891$	509.797	−	136.600i	0.572163	−	0.153311i
$892$		0			0
$893$	−152.344	+	263.867i	−0.170597	+	0.295483i
$894$		0			0
$895$	24.6307	−	91.9230i	0.0275203	−	0.102707i
$896$		0			0
$897$	256.267			0.285693
$898$		0			0
$899$	−19.4500	−	5.21162i	−0.0216352	−	0.00579713i
$900$		0			0
$901$	69.8993	+	40.3564i	0.0775797	+	0.0447907i
$902$		0			0
$903$	−173.620	−	647.959i	−0.192270	−	0.717562i
$904$		0			0
$905$	253.171	+	253.171i	0.279747	+	0.279747i
$906$		0			0
$907$	−761.867	+	439.864i	−0.839985	+	0.484966i	−0.857259	−	0.514885i	$-0.827835\pi$
$907$	−761.867	+	439.864i	−0.839985	+	0.484966i	0.0172739	+	0.999851i	$0.494501\pi$
$908$		0			0
$909$		−	297.419i		−	0.327193i
$910$		0			0
$911$	−1522.73			−1.67150			−0.835748	−	0.549113i	$-0.814966\pi$
$911$	−1522.73			−1.67150			−0.835748	+	0.549113i	$0.814966\pi$
$912$		0			0
$913$	−328.420	−	568.841i	−0.359716	−	0.623046i
$914$		0			0
$915$	26.8691	−	26.8691i	0.0293651	−	0.0293651i
$916$		0			0
$917$	−332.862	+	89.1900i	−0.362990	+	0.0972628i
$918$		0			0
$919$	−648.196	+	1122.71i	−0.705328	+	1.22166i	0.261245	+	0.965272i	$0.415867\pi$
$919$	−648.196	+	1122.71i	−0.705328	+	1.22166i	−0.966573	+	0.256391i	$0.917467\pi$
$920$		0			0
$921$	−67.2566	+	251.005i	−0.0730257	+	0.272535i
$922$		0			0
$923$	471.233	+	471.233i	0.510545	+	0.510545i
$924$		0			0
$925$	−547.958	−	146.825i	−0.592387	−	0.158730i
$926$		0			0
$927$	−456.558	−	263.594i	−0.492511	−	0.284351i
$928$		0			0
$929$	188.056	+	701.833i	0.202428	+	0.755472i	0.990218	+	0.139528i	$0.0445585\pi$
$929$	188.056	+	701.833i	0.202428	+	0.755472i	−0.787790	+	0.615944i	$0.788775\pi$
$930$		0			0
$931$	−1252.66	−	1252.66i	−1.34550	−	1.34550i
$932$		0			0
$933$	622.046	−	359.138i	0.666716	−	0.384929i
$934$		0			0
$935$		−	29.5692i		−	0.0316248i
$936$		0			0
$937$	−388.015			−0.414104			−0.207052	−	0.978330i	$-0.566387\pi$
$937$	−388.015			−0.414104			−0.207052	+	0.978330i	$0.566387\pi$
$938$		0			0
$939$	−145.036	−	251.210i	−0.154458	−	0.267529i
$940$		0			0
$941$	−698.815	+	698.815i	−0.742630	+	0.742630i	−0.973083	−	0.230453i	$-0.925979\pi$
$941$	−698.815	+	698.815i	−0.742630	+	0.742630i	0.230453	+	0.973083i	$0.425979\pi$
$942$		0			0
$943$	868.529	−	232.722i	0.921028	−	0.246789i
$944$		0			0
$945$	203.938	−	353.231i	0.215808	−	0.373790i
$946$		0			0
$947$	345.135	−	1288.06i	0.364451	−	1.36015i	−0.503714	−	0.863871i	$-0.668033\pi$
$947$	345.135	−	1288.06i	0.364451	−	1.36015i	0.868164	−	0.496277i	$-0.165300\pi$
$948$		0			0
$949$	−1528.27	−	409.500i	−1.61041	−	0.431507i
$950$		0			0
$951$	628.022	+	168.278i	0.660380	+	0.176948i
$952$		0			0
$953$	−929.569	−	536.687i	−0.975414	−	0.563155i	−0.0745313	−	0.997219i	$-0.523746\pi$
$953$	−929.569	−	536.687i	−0.975414	−	0.563155i	−0.900882	+	0.434063i	$0.857079\pi$
$954$		0			0
$955$	−39.1422	−	146.081i	−0.0409866	−	0.152964i
$956$		0			0
$957$	−302.390	−	302.390i	−0.315977	−	0.315977i
$958$		0			0
$959$	2476.41	−	1429.76i	2.58229	−	1.49089i
$960$		0			0
$961$			959.277i			0.998207i
$962$		0			0
$963$	−66.3312			−0.0688797
$964$		0			0
$965$	−35.3672	−	61.2578i	−0.0366500	−	0.0634796i
$966$		0			0
$967$	640.508	−	640.508i	0.662366	−	0.662366i	−0.293571	−	0.955937i	$-0.594844\pi$
$967$	640.508	−	640.508i	0.662366	−	0.662366i	0.955937	+	0.293571i	$0.0948438\pi$
$968$		0			0
$969$	31.7128	−	8.49742i	0.0327274	−	0.00876927i
$970$		0			0
$971$	23.6781	−	41.0117i	0.0243853	−	0.0422366i	−0.853575	−	0.520970i	$-0.825570\pi$
$971$	23.6781	−	41.0117i	0.0243853	−	0.0422366i	0.877961	+	0.478733i	$0.158904\pi$
$972$		0			0
$973$	400.923	−	1496.27i	0.412049	−	1.53779i
$974$		0			0
$975$	214.967	−	372.333i	0.220479	−	0.381880i
$976$		0			0
$977$	827.625	+	221.761i	0.847108	+	0.226982i	0.656163	−	0.754619i	$-0.272178\pi$
$977$	827.625	+	221.761i	0.847108	+	0.226982i	0.190945	+	0.981601i	$0.438845\pi$
$978$		0			0
$979$	891.202	+	514.536i	0.910319	+	0.525573i
$980$		0			0
$981$	310.652	+	1159.37i	0.316669	+	1.18182i
$982$		0			0
$983$	303.513	+	303.513i	0.308762	+	0.308762i	0.844429	−	0.535667i	$-0.179940\pi$
$983$	303.513	+	303.513i	0.308762	+	0.308762i	−0.535667	+	0.844429i	$0.679940\pi$
$984$		0			0
$985$	229.460	−	132.479i	0.232954	−	0.134496i
$986$		0			0
$987$			225.066i			0.228031i
$988$		0			0
$989$	−545.261			−0.551326
$990$		0			0
$991$	413.373	+	715.983i	0.417127	+	0.722486i	0.995649	−	0.0931813i	$-0.0297036\pi$
$991$	413.373	+	715.983i	0.417127	+	0.722486i	−0.578522	+	0.815667i	$0.696370\pi$
$992$		0			0
$993$	−562.410	+	562.410i	−0.566375	+	0.566375i
$994$		0			0
$995$	−182.196	+	48.8193i	−0.183112	+	0.0490646i
$996$		0			0
$997$	−666.761	+	1154.86i	−0.668768	+	1.15834i	0.309481	+	0.950906i	$0.399845\pi$
$997$	−666.761	+	1154.86i	−0.668768	+	1.15834i	−0.978249	+	0.207434i	$0.933489\pi$
$998$		0			0
$999$	−150.900	+	563.167i	−0.151051	+	0.563730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.b.145.1		4
4.3	odd	2		104.3.v.b.41.1	yes	4
13.7	odd	12	inner	208.3.bd.b.33.1		4
52.7	even	12		104.3.v.b.33.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.3.v.b.33.1	✓	4	52.7	even	12
104.3.v.b.41.1	yes	4	4.3	odd	2
208.3.bd.b.33.1		4	13.7	odd	12	inner
208.3.bd.b.145.1		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.732051 + 1.26795i) q^{3} +(-1.09808 + 1.09808i) q^{5} +(-10.9282 + 2.92820i) q^{7} +(3.42820 - 5.93782i) q^{9} +(-4.92820 + 18.3923i) q^{11} +(-11.2583 + 6.50000i) q^{13} +(-2.19615 - 0.588457i) q^{15} +(0.866025 + 0.500000i) q^{17} +(-5.80385 - 21.6603i) q^{19} +(-11.7128 - 11.7128i) q^{21} +(-11.6603 + 6.73205i) q^{23} +22.5885i q^{25} +23.2154 q^{27} +(7.66987 + 13.2846i) q^{29} +(-0.928203 + 0.928203i) q^{31} +(-26.9282 + 7.21539i) q^{33} +(8.78461 - 15.2154i) q^{35} +(-6.50000 + 24.2583i) q^{37} +(-16.4833 - 9.51666i) q^{39} +(-64.5070 - 17.2846i) q^{41} +(35.0718 + 20.2487i) q^{43} +(2.75575 + 10.2846i) q^{45} +(-9.60770 - 9.60770i) q^{47} +(68.4160 - 39.5000i) q^{49} +1.46410i q^{51} +80.7128 q^{53} +(-14.7846 - 25.6077i) q^{55} +(23.2154 - 23.2154i) q^{57} +(93.9615 - 25.1769i) q^{59} +(-8.35641 + 14.4737i) q^{61} +(-20.0770 + 74.9282i) q^{63} +(5.22501 - 19.5000i) q^{65} +(12.3397 + 3.30642i) q^{67} +(-17.0718 - 9.85641i) q^{69} +(-13.2679 - 49.5167i) q^{71} +(86.0596 + 86.0596i) q^{73} +(-28.6410 + 16.5359i) q^{75} -215.426i q^{77} -73.2820 q^{79} +(-13.8590 - 24.0045i) q^{81} +(-24.3923 + 24.3923i) q^{83} +(-1.50000 + 0.401924i) q^{85} +(-11.2295 + 19.4500i) q^{87} +(13.9878 - 52.2032i) q^{89} +(104.000 - 104.000i) q^{91} +(-1.85641 - 0.497423i) q^{93} +(30.1577 + 17.4115i) q^{95} +(35.5814 + 132.792i) q^{97} +(92.3154 + 92.3154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{5} - 16 q^{7} - 14 q^{9} + 8 q^{11} + 12 q^{15} - 44 q^{19} + 64 q^{21} - 12 q^{23} + 176 q^{27} + 48 q^{29} + 24 q^{31} - 80 q^{33} - 48 q^{35} - 26 q^{37} - 156 q^{39} - 116 q^{41}+ \cdots - 88 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^5 - 16 * q^7 - 14 * q^9 + 8 * q^11 + 12 * q^15 - 44 * q^19 + 64 * q^21 - 12 * q^23 + 176 * q^27 + 48 * q^29 + 24 * q^31 - 80 * q^33 - 48 * q^35 - 26 * q^37 - 156 * q^39 - 116 * q^41 + 168 * q^43 - 228 * q^45 - 80 * q^47 + 212 * q^53 + 24 * q^55 + 176 * q^57 + 168 * q^59 + 22 * q^61 - 496 * q^63 + 156 * q^65 + 84 * q^67 - 96 * q^69 - 60 * q^71 + 126 * q^73 + 24 * q^75 - 16 * q^79 - 194 * q^81 - 56 * q^83 - 6 * q^85 + 156 * q^87 - 190 * q^89 + 416 * q^91 + 48 * q^93 - 108 * q^95 + 222 * q^97 - 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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