LMFDB - Embedded newform 208.3.bd.b.33.1

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			33.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.33
Dual form			208.3.bd.b.145.1

$q$-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 $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{12}\right)$

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	−0.717838	−	0.696210i	$-0.754868\pi$
$3$	0.732051	−	1.26795i	0.244017	−	0.422650i	0.961855	+	0.273561i	$0.0882014\pi$
$4$		0			0
$5$	−1.09808	−	1.09808i	−0.219615	−	0.219615i	0.588721	−	0.808336i	$-0.299632\pi$
$5$	−1.09808	−	1.09808i	−0.219615	−	0.219615i	−0.808336	+	0.588721i	$0.799632\pi$
$6$		0			0
$7$	−10.9282	−	2.92820i	−1.56117	−	0.418315i	−0.628138	−	0.778102i	$-0.716183\pi$
$7$	−10.9282	−	2.92820i	−1.56117	−	0.418315i	−0.933034	+	0.359788i	$0.882849\pi$
$8$		0			0
$9$	3.42820	+	5.93782i	0.380911	+	0.659758i
$10$		0			0
$11$	−4.92820	−	18.3923i	−0.448018	−	1.67203i	−0.707841	−	0.706371i	$-0.750331\pi$
$11$	−4.92820	−	18.3923i	−0.448018	−	1.67203i	0.259823	−	0.965656i	$-0.416336\pi$
$12$		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	−0.474312	−	0.880357i	$-0.657303\pi$
$17$	0.866025	−	0.500000i	0.0509427	−	0.0294118i	0.525255	+	0.850945i	$0.323970\pi$
$18$		0			0
$19$	−5.80385	+	21.6603i	−0.305466	+	1.14001i	0.627078	+	0.778956i	$0.284251\pi$
$19$	−5.80385	+	21.6603i	−0.305466	+	1.14001i	−0.932544	+	0.361057i	$0.882416\pi$
$20$		0			0
$21$	−11.7128	+	11.7128i	−0.557753	+	0.557753i
$22$		0			0
$23$	−11.6603	−	6.73205i	−0.506968	−	0.292698i	0.224619	−	0.974447i	$-0.427886\pi$
$23$	−11.6603	−	6.73205i	−0.506968	−	0.292698i	−0.731586	+	0.681749i	$0.761220\pi$
$24$		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	−0.702948	−	0.711241i	$-0.748134\pi$
$29$	7.66987	−	13.2846i	0.264478	−	0.458090i	0.967427	+	0.253151i	$0.0814669\pi$
$30$		0			0
$31$	−0.928203	−	0.928203i	−0.0299420	−	0.0299420i	0.691977	−	0.721919i	$-0.256740\pi$
$31$	−0.928203	−	0.928203i	−0.0299420	−	0.0299420i	−0.721919	+	0.691977i	$0.756740\pi$
$32$		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	−0.996436	−	0.0843572i	$-0.973116\pi$
$37$	−6.50000	−	24.2583i	−0.175676	−	0.655631i	0.820760	−	0.571273i	$-0.193550\pi$
$38$		0			0
$39$	−16.4833	+	9.51666i	−0.422650	+	0.244017i
$40$		0			0
$41$	−64.5070	+	17.2846i	−1.57334	+	0.421576i	−0.936857	−	0.349713i	$-0.886279\pi$
$41$	−64.5070	+	17.2846i	−1.57334	+	0.421576i	−0.636486	+	0.771289i	$0.719613\pi$
$42$		0			0
$43$	35.0718	−	20.2487i	0.815623	−	0.470900i	−0.0332816	−	0.999446i	$-0.510596\pi$
$43$	35.0718	−	20.2487i	0.815623	−	0.470900i	0.848905	+	0.528546i	$0.177262\pi$
$44$		0			0
$45$	2.75575	−	10.2846i	0.0612390	−	0.228547i
$46$		0			0
$47$	−9.60770	+	9.60770i	−0.204419	+	0.204419i	−0.801890	−	0.597471i	$-0.796172\pi$
$47$	−9.60770	+	9.60770i	−0.204419	+	0.204419i	0.597471	+	0.801890i	$0.296172\pi$
$48$		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	0.942787	−	0.333394i	$-0.108194\pi$
$59$	93.9615	+	25.1769i	1.59257	+	0.426727i	0.649781	+	0.760122i	$0.274861\pi$
$60$		0			0
$61$	−8.35641	−	14.4737i	−0.136990	−	0.237274i	0.789366	−	0.613923i	$-0.210410\pi$
$61$	−8.35641	−	14.4737i	−0.136990	−	0.237274i	−0.926356	+	0.376649i	$0.877076\pi$
$62$		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	−0.165553	−	0.986201i	$-0.552941\pi$
$67$	12.3397	−	3.30642i	0.184175	−	0.0493496i	0.349728	+	0.936851i	$0.386274\pi$
$68$		0			0
$69$	−17.0718	+	9.85641i	−0.247417	+	0.142846i
$70$		0			0
$71$	−13.2679	+	49.5167i	−0.186873	+	0.697418i	0.807349	+	0.590074i	$0.200901\pi$
$71$	−13.2679	+	49.5167i	−0.186873	+	0.697418i	−0.994222	+	0.107344i	$0.965765\pi$
$72$		0			0
$73$	86.0596	−	86.0596i	1.17890	−	1.17890i	0.198873	−	0.980025i	$-0.436272\pi$
$73$	86.0596	−	86.0596i	1.17890	−	1.17890i	0.980025	−	0.198873i	$-0.0637283\pi$
$74$		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	0.544729	−	0.838612i	$-0.316633\pi$
$83$	−24.3923	−	24.3923i	−0.293883	−	0.293883i	−0.838612	+	0.544729i	$0.816633\pi$
$84$		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	0.998910	+	0.0466755i	$0.0148627\pi$
$89$	13.9878	+	52.2032i	0.157166	+	0.586553i	−0.841744	+	0.539877i	$0.818471\pi$
$90$		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	−0.498120	−	0.867108i	$-0.665976\pi$
$97$	35.5814	−	132.792i	0.366819	−	1.36899i	0.864939	−	0.501878i	$-0.167357\pi$
$98$		0			0
$99$	92.3154	−	92.3154i	0.932478	−	0.932478i
$100$		0			0
$101$	37.5666	+	21.6891i	0.371947	+	0.214744i	0.674309	−	0.738450i	$-0.264442\pi$
$101$	37.5666	+	21.6891i	0.371947	+	0.214744i	−0.302362	+	0.953193i	$0.597775\pi$
$102$		0			0
$103$			76.8897i			0.746502i	0.927730	+	0.373251i	$0.121757\pi$
$103$			76.8897i			0.746502i	−0.927730	+	0.373251i	$0.878243\pi$
$104$		0			0
$105$	25.7231			0.244982
$106$		0			0
$107$	−4.83717	+	8.37822i	−0.0452072	+	0.0783011i	−0.887744	−	0.460338i	$-0.847728\pi$
$107$	−4.83717	+	8.37822i	−0.0452072	+	0.0783011i	0.842536	+	0.538639i	$0.181061\pi$
$108$		0			0
$109$	−123.785	−	123.785i	−1.13564	−	1.13564i	−0.989223	−	0.146415i	$-0.953226\pi$
$109$	−123.785	−	123.785i	−1.13564	−	1.13564i	−0.146415	−	0.989223i	$-0.546774\pi$
$110$		0			0
$111$	−35.5167	−	9.51666i	−0.319970	−	0.0857357i
$112$		0			0
$113$	−30.3494	−	52.5666i	−0.268578	−	0.465192i	0.699917	−	0.714225i	$-0.253221\pi$
$113$	−30.3494	−	52.5666i	−0.268578	−	0.465192i	−0.968495	+	0.249033i	$0.919887\pi$
$114$		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	−0.211596	−	0.977357i	$-0.567866\pi$
$127$	−147.804	−	85.3346i	−1.16381	−	0.671926i	−0.952214	+	0.305431i	$0.901199\pi$
$128$		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	−0.791065	−	0.611732i	$-0.790473\pi$
$137$	−244.136	−	65.4160i	−1.78201	−	0.477489i	−0.990948	+	0.134243i	$0.957140\pi$
$138$		0			0
$139$	−68.4589	−	118.574i	−0.492510	−	0.853053i	0.507452	−	0.861680i	$-0.330587\pi$
$139$	−68.4589	−	118.574i	−0.492510	−	0.853053i	−0.999963	+	0.00862675i	$0.997254\pi$
$140$		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	−0.971443	−	0.237272i	$-0.923747\pi$
$149$	−1.71539	+	6.40192i	−0.0115127	+	0.0429659i	0.959931	+	0.280238i	$0.0904134\pi$
$150$		0			0
$151$	183.569	−	183.569i	1.21569	−	1.21569i	0.246564	−	0.969127i	$-0.420699\pi$
$151$	183.569	−	183.569i	1.21569	−	1.21569i	0.969127	−	0.246564i	$-0.0793014\pi$
$152$		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	−0.370360	−	0.928888i	$-0.620766\pi$
$163$	−188.354	−	50.4693i	−1.15554	−	0.309627i	−0.785185	+	0.619261i	$0.787432\pi$
$164$		0			0
$165$	21.6462	+	37.4923i	0.131189	+	0.227226i
$166$		0			0
$167$	−20.2487	−	75.5692i	−0.121250	−	0.452510i	0.878429	−	0.477874i	$-0.158592\pi$
$167$	−20.2487	−	75.5692i	−0.121250	−	0.452510i	−0.999678	+	0.0253635i	$0.991926\pi$
$168$		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	−0.340295	−	0.940319i	$-0.610527\pi$
$173$	52.5744	−	30.3538i	0.303898	−	0.175456i	0.644193	+	0.764863i	$0.277193\pi$
$174$		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	0.344375	−	0.938832i	$-0.388091\pi$
$179$	−53.0718	−	30.6410i	−0.296490	−	0.171179i	−0.640865	+	0.767653i	$0.721424\pi$
$180$		0			0
$181$			230.559i			1.27381i	0.770944	+	0.636903i	$0.219785\pi$
$181$			230.559i			1.27381i	−0.770944	+	0.636903i	$0.780215\pi$
$182$		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	0.709939	−	0.704263i	$-0.248722\pi$
$191$	−48.6936	−	84.3397i	−0.254940	−	0.441569i	−0.964879	+	0.262694i	$0.915389\pi$
$192$		0			0
$193$	−11.7891	−	43.9974i	−0.0610833	−	0.227966i	0.928635	−	0.370994i	$-0.120983\pi$
$193$	−11.7891	−	43.9974i	−0.0610833	−	0.227966i	−0.989719	+	0.143028i	$0.954316\pi$
$194$		0			0
$195$	28.5500	+	7.64994i	0.146410	+	0.0392305i
$196$		0			0
$197$	−164.806	+	44.1596i	−0.836577	+	0.224160i	−0.651581	−	0.758579i	$-0.725894\pi$
$197$	−164.806	+	44.1596i	−0.836577	+	0.224160i	−0.184996	+	0.982739i	$0.559227\pi$
$198$		0			0
$199$	105.191	−	60.7321i	0.528598	−	0.305186i	−0.211847	−	0.977303i	$-0.567948\pi$
$199$	105.191	−	60.7321i	0.528598	−	0.305186i	0.740445	+	0.672117i	$0.234615\pi$
$200$		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	−0.893172	−	0.449715i	$-0.851525\pi$
$211$	−12.0526	+	20.8756i	−0.0571211	+	0.0989367i	0.836051	+	0.548652i	$0.184859\pi$
$212$		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	0.416315	−	0.909220i	$-0.363321\pi$
$223$	274.617	−	73.5833i	1.23146	−	0.329970i	0.815150	+	0.579250i	$0.196655\pi$
$224$		0			0
$225$	134.126	−	77.4378i	0.596117	−	0.344168i
$226$		0			0
$227$	1.26795	−	4.73205i	0.00558568	−	0.0208460i	−0.963077	−	0.269227i	$-0.913232\pi$
$227$	1.26795	−	4.73205i	0.00558568	−	0.0208460i	0.968662	+	0.248381i	$0.0798985\pi$
$228$		0			0
$229$	217.641	−	217.641i	0.950397	−	0.950397i	−0.0484292	−	0.998827i	$-0.515422\pi$
$229$	217.641	−	217.641i	0.950397	−	0.950397i	0.998827	+	0.0484292i	$0.0154215\pi$
$230$		0			0
$231$	273.149	+	157.703i	1.18246	+	0.682695i
$232$		0			0
$233$			260.862i			1.11958i	0.828635	+	0.559789i	$0.189118\pi$
$233$			260.862i			1.11958i	−0.828635	+	0.559789i	$0.810882\pi$
$234$		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	0.963471	+	0.267813i	$0.0863010\pi$
$239$	294.277	+	294.277i	1.23128	+	1.23128i	0.267813	+	0.963471i	$0.413699\pi$
$240$		0			0
$241$	−170.926	−	45.7994i	−0.709235	−	0.190039i	−0.113872	−	0.993495i	$-0.536325\pi$
$241$	−170.926	−	45.7994i	−0.709235	−	0.190039i	−0.595363	+	0.803457i	$0.702992\pi$
$242$		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	−0.362099	−	0.932139i	$-0.617940\pi$
$251$	66.2910	−	38.2731i	0.264107	−	0.152482i	0.626207	+	0.779657i	$0.284607\pi$
$252$		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	0.322192	−	0.946674i	$-0.395580\pi$
$257$	−86.4948	−	49.9378i	−0.336556	−	0.194311i	−0.658748	+	0.752364i	$0.728914\pi$
$258$		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	0.333407	+	0.942783i	$0.391802\pi$
$263$	−170.890	+	295.990i	−0.649771	+	1.12544i	−0.983177	+	0.182653i	$0.941532\pi$
$264$		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	−0.966511	−	0.256626i	$-0.917389\pi$
$269$	−189.779	−	328.708i	−0.705500	−	1.22196i	0.261011	−	0.965336i	$-0.415944\pi$
$270$		0			0
$271$	−19.4256	−	72.4974i	−0.0716813	−	0.267518i	0.920779	−	0.390085i	$-0.127554\pi$
$271$	−19.4256	−	72.4974i	−0.0716813	−	0.267518i	−0.992460	+	0.122566i	$0.960888\pi$
$272$		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	0.407876	−	0.913038i	$-0.366270\pi$
$277$	388.500	−	224.301i	1.40253	−	0.809749i	0.994651	+	0.103288i	$0.0329364\pi$
$278$		0			0
$279$	2.32944	−	8.69358i	0.00834923	−	0.0311598i
$280$		0			0
$281$	−230.275	+	230.275i	−0.819484	+	0.819484i	−0.986033	−	0.166549i	$-0.946738\pi$
$281$	−230.275	+	230.275i	−0.819484	+	0.819484i	0.166549	+	0.986033i	$0.446738\pi$
$282$		0			0
$283$	−251.321	−	145.100i	−0.888058	−	0.512721i	−0.0147514	−	0.999891i	$-0.504696\pi$
$283$	−251.321	−	145.100i	−0.888058	−	0.512721i	−0.873307	+	0.487170i	$0.838029\pi$
$284$		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	0.693660	−	0.720302i	$-0.255997\pi$
$293$	273.731	+	73.3461i	0.934237	+	0.250328i	0.240576	+	0.970630i	$0.422664\pi$
$294$		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	−0.472518	−	0.881321i	$-0.656655\pi$
$307$	125.503	−	125.503i	0.408803	−	0.408803i	0.881321	+	0.472518i	$0.156655\pi$
$308$		0			0
$309$	97.4923	+	56.2872i	0.315509	+	0.182159i
$310$		0			0
$311$			490.592i			1.57747i	0.614735	+	0.788733i	$0.289263\pi$
$311$			490.592i			1.57747i	−0.614735	+	0.788733i	$0.710737\pi$
$312$		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	0.999956	−	0.00938556i	$-0.00298756\pi$
$317$	314.011	+	314.011i	0.990570	+	0.990570i	−0.00938556	+	0.999956i	$0.502988\pi$
$318$		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	−0.339619	−	0.940563i	$-0.610298\pi$
$331$	140.603	−	524.736i	0.424781	−	1.58530i	0.764401	−	0.644742i	$-0.223035\pi$
$332$		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	$-0.992717\pi$
$337$		−	15.4205i		−	0.0457581i	0.999738	−	0.0228790i	$-0.00728326\pi$
$338$		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	−0.977512	−	0.210882i	$-0.932367\pi$
$347$	−232.970	−	403.517i	−0.671385	−	1.16287i	0.306127	−	0.951991i	$-0.400967\pi$
$348$		0			0
$349$	106.538	+	397.604i	0.305266	+	1.13927i	0.932716	+	0.360611i	$0.117432\pi$
$349$	106.538	+	397.604i	0.305266	+	1.13927i	−0.627450	+	0.778657i	$0.715901\pi$
$350$		0			0
$351$	−261.367	−	150.900i	−0.744634	−	0.429915i
$352$		0			0
$353$	467.556	−	125.281i	1.32452	−	0.354905i	0.473852	−	0.880604i	$-0.342863\pi$
$353$	467.556	−	125.281i	1.32452	−	0.354905i	0.850670	+	0.525700i	$0.176196\pi$
$354$		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	−0.256327	−	0.966590i	$-0.582512\pi$
$359$	254.985	−	254.985i	0.710263	−	0.710263i	0.966590	+	0.256327i	$0.0825123\pi$
$360$		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	−0.434786	−	0.900534i	$-0.643176\pi$
$367$	206.435	−	357.555i	0.562492	−	0.974265i	0.997278	−	0.0737310i	$-0.0234906\pi$
$368$		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	0.656299	−	0.754501i	$-0.272121\pi$
$373$	−121.325	−	210.141i	−0.325268	−	0.563381i	−0.981567	+	0.191121i	$0.938788\pi$
$374$		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	−0.496913	−	0.867800i	$-0.665533\pi$
$379$	−186.981	+	50.1013i	−0.493353	+	0.132194i	0.00356045	+	0.999994i	$0.498867\pi$
$380$		0			0
$381$	−216.400	+	124.939i	−0.567979	+	0.327923i
$382$		0			0
$383$	−23.9230	+	89.2820i	−0.0624623	+	0.233112i	−0.990099	−	0.140372i	$-0.955170\pi$
$383$	−23.9230	+	89.2820i	−0.0624623	+	0.233112i	0.927637	+	0.373484i	$0.121837\pi$
$384$		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	$-0.781410\pi$
$389$		−	493.256i		−	1.26801i	0.773329	−	0.634005i	$-0.218590\pi$
$390$		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	0.138265	−	0.990395i	$-0.455847\pi$
$397$	−94.1647	−	25.2314i	−0.237191	−	0.0635551i	−0.375456	+	0.926840i	$0.622514\pi$
$398$		0			0
$399$	−185.723	−	321.682i	−0.465471	−	0.806220i
$400$		0			0
$401$	46.2795	+	172.717i	0.115410	+	0.430716i	0.999317	−	0.0369460i	$-0.0117630\pi$
$401$	46.2795	+	172.717i	0.115410	+	0.430716i	−0.883907	+	0.467662i	$0.845096\pi$
$402$		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	0.439324	+	0.898329i	$0.355218\pi$
$409$	−159.635	+	595.767i	−0.390306	+	1.45664i	−0.829630	+	0.558313i	$0.811449\pi$
$410$		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	−0.148514	−	0.988910i	$-0.547449\pi$
$419$	327.727	−	567.640i	0.782164	−	1.35475i	0.930678	−	0.365838i	$-0.119218\pi$
$420$		0			0
$421$	101.107	+	101.107i	0.240159	+	0.240159i	0.816916	−	0.576757i	$-0.195682\pi$
$421$	101.107	+	101.107i	0.240159	+	0.240159i	−0.576757	+	0.816916i	$0.695682\pi$
$422$		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	0.254901	−	0.966967i	$-0.417957\pi$
$431$	413.387	−	110.767i	0.959135	−	0.256999i	0.704234	+	0.709968i	$0.251291\pi$
$432$		0			0
$433$	671.264	−	387.554i	1.55026	−	0.895045i	0.552144	−	0.833749i	$-0.313810\pi$
$433$	671.264	−	387.554i	1.55026	−	0.895045i	0.998120	−	0.0612959i	$-0.0195233\pi$
$434$		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	0.912755	−	0.408507i	$-0.133950\pi$
$439$	445.741	+	257.349i	1.01536	+	0.586216i	0.102600	+	0.994723i	$0.467284\pi$
$440$		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	0.196902	−	0.980423i	$-0.436912\pi$
$449$	−55.1314	−	14.7724i	−0.122787	−	0.0329007i	−0.319689	+	0.947522i	$0.603579\pi$
$450$		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	−0.0524757	−	0.998622i	$-0.516711\pi$
$457$	183.435	−	49.1513i	0.401390	−	0.107552i	0.453866	+	0.891070i	$0.350045\pi$
$458$		0			0
$459$	20.1051	−	11.6077i	0.0438020	−	0.0252891i
$460$		0			0
$461$	−30.0538	+	112.162i	−0.0651925	+	0.243302i	−0.990831	−	0.135107i	$-0.956862\pi$
$461$	−30.0538	+	112.162i	−0.0651925	+	0.243302i	0.925638	+	0.378409i	$0.123529\pi$
$462$		0			0
$463$	−23.3205	+	23.3205i	−0.0503683	+	0.0503683i	−0.731842	−	0.681474i	$-0.761339\pi$
$463$	−23.3205	+	23.3205i	−0.0503683	+	0.0503683i	0.681474	+	0.731842i	$0.261339\pi$
$464$		0			0
$465$	2.58468	+	1.49227i	0.00555846	+	0.00320918i
$466$		0			0
$467$		−	427.482i		−	0.915379i	−0.889112	−	0.457689i	$-0.848677\pi$
$467$		−	427.482i		−	0.915379i	0.889112	−	0.457689i	$-0.151323\pi$
$468$		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	0.817187	+	0.576373i	$0.195532\pi$
$479$	190.483	+	710.894i	0.397669	+	1.48412i	−0.419518	+	0.907747i	$0.637801\pi$
$480$		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	−0.999180	−	0.0404981i	$-0.987106\pi$
$487$	−55.3308	+	206.497i	−0.113616	+	0.424019i	0.885564	+	0.464517i	$0.153772\pi$
$488$		0			0
$489$	−201.877	+	201.877i	−0.412836	+	0.412836i
$490$		0			0
$491$	143.885	+	83.0718i	0.293044	+	0.169189i	0.639314	−	0.768946i	$-0.279219\pi$
$491$	143.885	+	83.0718i	0.293044	+	0.169189i	−0.346270	+	0.938135i	$0.612552\pi$
$492$		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	0.651318	−	0.758805i	$-0.274216\pi$
$499$	−53.6359	−	53.6359i	−0.107487	−	0.107487i	−0.758805	+	0.651318i	$0.774216\pi$
$500$		0			0
$501$	−110.641	−	29.6462i	−0.220840	−	0.0591740i
$502$		0			0
$503$	−334.669	−	579.664i	−0.665346	−	1.15241i	−0.979191	−	0.202939i	$-0.934951\pi$
$503$	−334.669	−	579.664i	−0.665346	−	1.15241i	0.313845	−	0.949474i	$-0.398383\pi$
$504$		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	0.212515	−	0.977158i	$-0.431834\pi$
$509$	450.535	−	120.721i	0.885138	−	0.237172i	0.672623	+	0.739986i	$0.265168\pi$
$510$		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	−0.871471	−	0.490446i	$-0.836834\pi$
$523$	−5.75129	+	9.96152i	−0.0109967	+	0.0190469i	0.860475	+	0.509493i	$0.170167\pi$
$524$		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	−0.793022	−	0.609193i	$-0.791494\pi$
$541$	−99.4519	+	99.4519i	−0.183830	+	0.183830i	0.609193	+	0.793022i	$0.291494\pi$
$542$		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	−0.969344	−	0.245709i	$-0.920979\pi$
$557$	−140.766	−	525.346i	−0.252722	−	0.943171i	0.716622	−	0.697462i	$-0.245687\pi$
$558$		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	0.132937	−	0.991124i	$-0.457559\pi$
$563$	595.510	−	343.818i	1.05774	−	0.610689i	0.924807	+	0.380435i	$0.124226\pi$
$564$		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	0.815917	−	0.578169i	$-0.196232\pi$
$569$	411.482	+	237.569i	0.723167	+	0.417521i	−0.0927503	+	0.995689i	$0.529566\pi$
$570$		0			0
$571$			444.728i			0.778859i	0.921056	+	0.389429i	$0.127328\pi$
$571$			444.728i			0.778859i	−0.921056	+	0.389429i	$0.872672\pi$
$572$		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	0.952780	−	0.303661i	$-0.0982091\pi$
$577$	374.542	+	374.542i	0.649119	+	0.649119i	−0.303661	+	0.952780i	$0.598209\pi$
$578$		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	−0.806970	−	0.590592i	$-0.798894\pi$
$587$	−710.582	+	190.400i	−1.21053	+	0.324361i	−0.403561	+	0.914953i	$0.632228\pi$
$588$		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	−0.902019	−	0.431697i	$-0.857915\pi$
$593$	−278.901	+	278.901i	−0.470321	+	0.470321i	0.431697	+	0.902019i	$0.357915\pi$
$594$		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	0.466247	+	0.884655i	$0.345606\pi$
$601$	−320.339	+	554.844i	−0.533010	+	0.923201i	−0.999257	+	0.0385458i	$0.987727\pi$
$602$		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	0.865572	−	0.500784i	$-0.166955\pi$
$607$	−0.549981	−	0.952596i	−0.000906065	−	0.00156935i	−0.866478	+	0.499215i	$0.833622\pi$
$608$		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	−0.327423	−	0.944878i	$-0.606180\pi$
$613$	−84.9256	+	22.7558i	−0.138541	+	0.0371219i	0.188882	+	0.982000i	$0.439514\pi$
$614$		0			0
$615$	131.496	−	75.9193i	0.213815	−	0.123446i
$616$		0			0
$617$	188.859	−	704.831i	0.306092	−	1.14235i	−0.625909	−	0.779896i	$-0.715272\pi$
$617$	188.859	−	704.831i	0.306092	−	1.14235i	0.932001	−	0.362456i	$-0.118062\pi$
$618$		0			0
$619$	−359.138	+	359.138i	−0.580191	+	0.580191i	−0.934956	−	0.354764i	$-0.884561\pi$
$619$	−359.138	+	359.138i	−0.580191	+	0.580191i	0.354764	+	0.934956i	$0.384561\pi$
$620$		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	0.567846	−	0.823135i	$-0.307777\pi$
$631$	408.918	+	109.569i	0.648047	+	0.173644i	0.0802015	+	0.996779i	$0.474444\pi$
$632$		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	−0.509025	−	0.860752i	$-0.669994\pi$
$641$	−11.6046	+	6.69993i	−0.0181039	+	0.0104523i	0.490921	+	0.871204i	$0.336660\pi$
$642$		0			0
$643$	−114.161	+	426.056i	−0.177545	+	0.662607i	0.818559	+	0.574422i	$0.194773\pi$
$643$	−114.161	+	426.056i	−0.177545	+	0.662607i	−0.996104	+	0.0881847i	$0.971893\pi$
$644$		0			0
$645$	−65.1075	+	65.1075i	−0.100942	+	0.100942i
$646$		0			0
$647$	173.976	+	100.445i	0.268896	+	0.155247i	0.628386	−	0.777902i	$-0.283716\pi$
$647$	173.976	+	100.445i	0.268896	+	0.155247i	−0.359490	+	0.933149i	$0.617049\pi$
$648$		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	−0.119194	+	0.992871i	$0.538031\pi$
$653$	−600.400	+	1039.92i	−0.919448	+	1.59253i	−0.800255	+	0.599660i	$0.795302\pi$
$654$		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	0.928691	−	0.370853i	$-0.120935\pi$
$659$	94.3538	+	163.426i	0.143177	+	0.247990i	−0.785514	+	0.618844i	$0.787601\pi$
$660$		0			0
$661$	−58.7820	−	219.378i	−0.0889289	−	0.331887i	0.907100	−	0.420915i	$-0.138291\pi$
$661$	−58.7820	−	219.378i	−0.0889289	−	0.331887i	−0.996029	+	0.0890273i	$0.971624\pi$
$662$		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	0.448022	−	0.894022i	$-0.352129\pi$
$673$	−68.7891	−	39.7154i	−0.102213	−	0.0590125i	−0.550235	+	0.835010i	$0.685462\pi$
$674$		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	0.687159	−	0.726507i	$-0.258858\pi$
$683$	627.678	+	168.186i	0.919002	+	0.246246i	0.231843	+	0.972753i	$0.425524\pi$
$684$		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	−0.465609	−	0.884991i	$-0.654165\pi$
$691$	−294.603	+	78.9385i	−0.426342	+	0.114238i	0.0392664	+	0.999229i	$0.487498\pi$
$692$		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	$0.0395366\pi$
$701$			173.692i			0.247778i	−0.992296	+	0.123889i	$0.960463\pi$
$702$		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	0.311516	−	0.950241i	$-0.399163\pi$
$709$	75.2795	+	20.1711i	0.106177	+	0.0284500i	−0.205339	+	0.978691i	$0.565830\pi$
$710$		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	−0.292423	−	0.956289i	$-0.594461\pi$
$719$	280.077	−	161.703i	0.389537	−	0.224899i	0.681959	+	0.731390i	$0.261128\pi$
$720$		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	$0.145622\pi$
$727$			642.221i			0.883385i	−0.897167	+	0.441692i	$0.854378\pi$
$728$		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	0.389966	−	0.920829i	$-0.372487\pi$
$733$	−389.122	−	389.122i	−0.530863	−	0.530863i	−0.920829	+	0.389966i	$0.872487\pi$
$734$		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	−0.981114	−	0.193431i	$-0.938038\pi$
$739$	−168.610	−	629.261i	−0.228160	−	0.851504i	0.752954	−	0.658073i	$-0.228628\pi$
$740$		0			0
$741$	−110.466	−	412.267i	−0.149078	−	0.556365i
$742$		0			0
$743$	1049.62	−	281.244i	1.41267	−	0.378524i	0.529794	−	0.848126i	$-0.322269\pi$
$743$	1049.62	−	281.244i	1.41267	−	0.378524i	0.882878	+	0.469602i	$0.155603\pi$
$744$		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	−0.334336	−	0.942454i	$-0.608512\pi$
$751$	−989.587	−	571.338i	−1.31769	−	0.760770i	−0.983357	+	0.181684i	$0.941845\pi$
$752$		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	−0.803104	−	0.595839i	$-0.796820\pi$
$757$	86.6462	−	150.076i	0.114460	−	0.198250i	0.917564	+	0.397589i	$0.130153\pi$
$758$		0			0
$759$	265.415	+	265.415i	0.349691	+	0.349691i
$760$		0			0
$761$	−780.638	−	209.171i	−1.02581	−	0.274864i	−0.293586	−	0.955933i	$-0.594849\pi$
$761$	−780.638	−	209.171i	−1.02581	−	0.274864i	−0.732219	+	0.681069i	$0.761515\pi$
$762$		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	−0.983542	−	0.180680i	$-0.942170\pi$
$769$	−1341.89	+	359.557i	−1.74497	+	0.467564i	−0.761432	+	0.648245i	$0.775503\pi$
$770$		0			0
$771$	−126.637	+	73.1140i	−0.164251	+	0.0948302i
$772$		0			0
$773$	−66.4007	+	247.811i	−0.0859000	+	0.320583i	−0.995483	−	0.0949388i	$-0.969734\pi$
$773$	−66.4007	+	247.811i	−0.0859000	+	0.320583i	0.909583	+	0.415522i	$0.136401\pi$
$774$		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	0.507803	−	0.861473i	$-0.330458\pi$
$787$	406.750	+	108.988i	0.516836	+	0.138486i	0.00903330	+	0.999959i	$0.497125\pi$
$788$		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	−0.150071	−	0.988675i	$-0.547950\pi$
$797$	502.996	−	290.405i	0.631112	−	0.364373i	0.781183	+	0.624303i	$0.214617\pi$
$798$		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	−0.236899	−	0.971534i	$-0.576131\pi$
$809$	584.845	−	1012.98i	0.722924	−	1.25214i	0.959823	−	0.280607i	$-0.0905356\pi$
$810$		0			0
$811$	−559.177	−	559.177i	−0.689491	−	0.689491i	0.272629	−	0.962119i	$-0.412107\pi$
$811$	−559.177	−	559.177i	−0.689491	−	0.689491i	−0.962119	+	0.272629i	$0.912107\pi$
$812$		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	0.164942	−	0.986303i	$-0.447256\pi$
$821$	657.570	−	176.195i	0.800938	−	0.214611i	0.635996	+	0.771693i	$0.280590\pi$
$822$		0			0
$823$	−386.718	+	223.272i	−0.469888	+	0.271290i	−0.716193	−	0.697902i	$-0.754117\pi$
$823$	−386.718	+	223.272i	−0.469888	+	0.271290i	0.246305	+	0.969192i	$0.420784\pi$
$824$		0			0
$825$	−162.985	+	608.267i	−0.197557	+	0.737293i
$826$		0			0
$827$	−364.833	+	364.833i	−0.441153	+	0.441153i	−0.892399	−	0.451247i	$-0.850980\pi$
$827$	−364.833	+	364.833i	−0.441153	+	0.441153i	0.451247	+	0.892399i	$0.350980\pi$
$828$		0			0
$829$	1060.17	+	612.090i	1.27886	+	0.738348i	0.976638	−	0.214891i	$-0.0689396\pi$
$829$	1060.17	+	612.090i	1.27886	+	0.738348i	0.302218	+	0.953239i	$0.402273\pi$
$830$		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	0.922932	−	0.384962i	$-0.125785\pi$
$839$	1283.45	+	343.899i	1.52973	+	0.409891i	0.606802	+	0.794853i	$0.292452\pi$
$840$		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	−0.997229	−	0.0743990i	$-0.976296\pi$
$853$	−787.174	+	787.174i	−0.922830	+	0.922830i	0.0743990	+	0.997229i	$0.476296\pi$
$854$		0			0
$855$	206.773	+	119.381i	0.241840	+	0.139626i
$856$		0			0
$857$			673.732i			0.786152i	0.919506	+	0.393076i	$0.128589\pi$
$857$			673.732i			0.786152i	−0.919506	+	0.393076i	$0.871411\pi$
$858$		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	0.934431	−	0.356144i	$-0.115909\pi$
$863$	499.061	+	499.061i	0.578287	+	0.578287i	−0.356144	+	0.934431i	$0.615909\pi$
$864$		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	−0.675503	−	0.737357i	$-0.736074\pi$
$877$	243.962	−	910.479i	0.278178	−	1.03817i	0.953682	−	0.300818i	$-0.0972597\pi$
$878$		0			0
$879$	293.384	−	293.384i	0.333771	−	0.333771i
$880$		0			0
$881$	405.459	+	234.092i	0.460226	+	0.265711i	0.712139	−	0.702038i	$-0.247727\pi$
$881$	405.459	+	234.092i	0.460226	+	0.265711i	−0.251914	+	0.967750i	$0.581060\pi$
$882$		0			0
$883$		−	782.536i		−	0.886224i	−0.896466	−	0.443112i	$-0.853874\pi$
$883$		−	782.536i		−	0.886224i	0.896466	−	0.443112i	$-0.146126\pi$
$884$		0			0
$885$	−221.169			−0.249909
$886$		0			0
$887$	−60.4102	+	104.633i	−0.0681062	+	0.117963i	−0.898068	−	0.439857i	$-0.855029\pi$
$887$	−60.4102	+	104.633i	−0.0681062	+	0.117963i	0.829961	+	0.557821i	$0.188362\pi$
$888$		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	0.0172739	−	0.999851i	$-0.494501\pi$
$907$	−761.867	−	439.864i	−0.839985	−	0.484966i	−0.857259	+	0.514885i	$0.827835\pi$
$908$		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	−0.966573	−	0.256391i	$-0.917467\pi$
$919$	−648.196	−	1122.71i	−0.705328	−	1.22166i	0.261245	−	0.965272i	$-0.415867\pi$
$920$		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	−0.787790	−	0.615944i	$-0.788775\pi$
$929$	188.056	−	701.833i	0.202428	−	0.755472i	0.990218	−	0.139528i	$-0.0445585\pi$
$930$		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	0.230453	−	0.973083i	$-0.425979\pi$
$941$	−698.815	−	698.815i	−0.742630	−	0.742630i	−0.973083	+	0.230453i	$0.925979\pi$
$942$		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	0.868164	+	0.496277i	$0.165300\pi$
$947$	345.135	+	1288.06i	0.364451	+	1.36015i	−0.503714	+	0.863871i	$0.668033\pi$
$948$		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	−0.900882	−	0.434063i	$-0.857079\pi$
$953$	−929.569	+	536.687i	−0.975414	+	0.563155i	−0.0745313	+	0.997219i	$0.523746\pi$
$954$		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	0.955937	−	0.293571i	$-0.0948438\pi$
$967$	640.508	+	640.508i	0.662366	+	0.662366i	−0.293571	+	0.955937i	$0.594844\pi$
$968$		0			0
$969$	31.7128	+	8.49742i	0.0327274	+	0.00876927i
$970$		0			0
$971$	23.6781	+	41.0117i	0.0243853	+	0.0422366i	0.877961	−	0.478733i	$-0.158904\pi$
$971$	23.6781	+	41.0117i	0.0243853	+	0.0422366i	−0.853575	+	0.520970i	$0.825570\pi$
$972$		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	0.190945	−	0.981601i	$-0.438845\pi$
$977$	827.625	−	221.761i	0.847108	−	0.226982i	0.656163	+	0.754619i	$0.272178\pi$
$978$		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	−0.535667	−	0.844429i	$-0.679940\pi$
$983$	303.513	−	303.513i	0.308762	−	0.308762i	0.844429	+	0.535667i	$0.179940\pi$
$984$		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	−0.578522	−	0.815667i	$-0.696370\pi$
$991$	413.373	−	715.983i	0.417127	−	0.722486i	0.995649	+	0.0931813i	$0.0297036\pi$
$992$		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	−0.978249	−	0.207434i	$-0.933489\pi$
$997$	−666.761	−	1154.86i	−0.668768	−	1.15834i	0.309481	−	0.950906i	$-0.399845\pi$
$998$		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.33.1		4
4.3	odd	2		104.3.v.b.33.1	✓	4
13.2	odd	12	inner	208.3.bd.b.145.1		4
52.15	even	12		104.3.v.b.41.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.3.v.b.33.1	✓	4	4.3	odd	2
104.3.v.b.41.1	yes	4	52.15	even	12
208.3.bd.b.33.1		4	1.1	even	1	trivial
208.3.bd.b.145.1		4	13.2	odd	12	inner

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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