LMFDB - Embedded newform 441.2.g.f.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.5
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.f.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19343 - 2.06709i) q^{2} +(-0.266999 - 1.71135i) q^{3} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 + 0.913855i) q^{9} +O(q^{10})$	\(q+(1.19343 - 2.06709i) q^{2} +(-0.266999 - 1.71135i) q^{3} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 + 0.913855i) q^{9} +(3.48586 - 6.03769i) q^{10} -1.35371 q^{11} +(-4.98586 + 4.01843i) q^{12} +(0.733001 - 1.26960i) q^{13} +(-0.779867 - 4.99862i) q^{15} +(-1.13729 + 1.96984i) q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.52113 + 6.99717i) q^{18} +(1.10329 + 1.91096i) q^{19} +(-5.39943 - 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} +2.62830 q^{23} +(1.08157 + 6.93243i) q^{24} +3.53146 q^{25} +(-1.74958 - 3.03036i) q^{26} +(2.32685 + 4.64605i) q^{27} +(0.521720 + 0.903646i) q^{29} +(-11.2633 - 4.35347i) q^{30} +(1.63729 + 2.83587i) q^{31} +(-1.33629 - 2.31453i) q^{32} +(0.361440 + 2.31668i) q^{33} +(3.95060 + 6.84263i) q^{34} +(8.20815 + 7.45963i) q^{36} +(5.43773 + 9.41842i) q^{37} +5.26683 q^{38} +(-2.36843 - 0.915440i) q^{39} -11.8320 q^{40} +(0.904289 - 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(2.50244 + 4.33435i) q^{44} +(-8.34615 + 2.66925i) q^{45} +(3.13670 - 5.43292i) q^{46} +(1.98957 - 3.44604i) q^{47} +(3.67474 + 1.42035i) q^{48} +(4.21456 - 7.29984i) q^{50} +(5.34798 + 2.06709i) q^{51} -5.42002 q^{52} +(-3.22743 + 5.59008i) q^{53} +(12.3807 + 0.734945i) q^{54} -3.95402 q^{55} +(2.97574 - 2.39834i) q^{57} +2.49056 q^{58} +(-6.10700 - 10.5776i) q^{59} +(-14.5630 + 11.7373i) q^{60} +(0.279867 - 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 - 3.70832i) q^{65} +(5.22013 + 2.01767i) q^{66} +(-6.40588 - 11.0953i) q^{67} +12.2386 q^{68} +(-0.701751 - 4.49793i) q^{69} +12.9177 q^{71} +(11.5750 - 3.70190i) q^{72} +(-5.22772 + 9.05467i) q^{73} +25.9583 q^{74} +(-0.942894 - 6.04355i) q^{75} +(4.07903 - 7.06509i) q^{76} +(-4.71886 + 3.80324i) q^{78} +(-0.383838 + 0.664827i) q^{79} +(-3.32187 + 5.75365i) q^{80} +(7.32974 - 5.22254i) q^{81} +(-2.15842 - 3.73849i) q^{82} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} -10.3652 q^{86} +(1.40715 - 1.13412i) q^{87} +5.48371 q^{88} +(-3.20356 - 5.54872i) q^{89} +(-4.44301 + 20.4378i) q^{90} +(-4.85859 - 8.41533i) q^{92} +(4.41601 - 3.55915i) q^{93} +(-4.74884 - 8.22524i) q^{94} +(3.22257 + 5.58166i) q^{95} +(-3.60418 + 2.90484i) q^{96} +(4.14143 + 7.17316i) q^{97} +(3.86814 - 1.23710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.19343	−	2.06709i	0.843886	−	1.46165i	−0.0426999	−	0.999088i	$-0.513596\pi$
$2$	1.19343	−	2.06709i	0.843886	−	1.46165i	0.886585	−	0.462565i	$-0.153071\pi$
$3$	−0.266999	−	1.71135i	−0.154152	−	0.988047i
$3$	−0.266999	−	1.71135i	−0.154152	−	0.988047i
$4$	−1.84857	−	3.20182i	−0.924286	−	1.60091i
$5$	2.92087			1.30625			0.653125	−	0.757250i	$-0.273457\pi$
$5$	2.92087			1.30625			0.653125	+	0.757250i	$0.273457\pi$
$6$	−3.85615	−	1.49047i	−1.57427	−	0.608483i
$7$		0			0
$7$		0			0
$8$	−4.05086			−1.43219
$9$	−2.85742	+	0.913855i	−0.952475	+	0.304618i
$10$	3.48586	−	6.03769i	1.10233	−	1.90929i
$11$	−1.35371			−0.408160			−0.204080	−	0.978954i	$-0.565420\pi$
$11$	−1.35371			−0.408160			−0.204080	+	0.978954i	$0.565420\pi$
$12$	−4.98586	+	4.01843i	−1.43929	+	1.16002i
$13$	0.733001	−	1.26960i	0.203298	−	0.352123i	−0.746291	−	0.665620i	$-0.768167\pi$
$13$	0.733001	−	1.26960i	0.203298	−	0.352123i	0.949589	+	0.313497i	$0.101501\pi$
$14$		0			0
$15$	−0.779867	−	4.99862i	−0.201361	−	1.29064i
$16$	−1.13729	+	1.96984i	−0.284323	+	0.492461i
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	−0.993899	−	0.110297i	$-0.964820\pi$
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	0.592469	+	0.805593i	$0.298153\pi$
$18$	−1.52113	+	6.99717i	−0.358533	+	1.64925i
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	0.964381	−	0.264516i	$-0.0852123\pi$
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	−0.711268	+	0.702921i	$0.751879\pi$
$20$	−5.39943	−	9.35209i	−1.20735	−	2.09119i
$21$		0			0
$22$	−1.61557	+	2.79825i	−0.344441	+	0.596589i
$23$	2.62830			0.548038			0.274019	−	0.961724i	$-0.411647\pi$
$23$	2.62830			0.548038			0.274019	+	0.961724i	$0.411647\pi$
$24$	1.08157	+	6.93243i	0.220775	+	1.41508i
$25$	3.53146			0.706292
$26$	−1.74958	−	3.03036i	−0.343121	−	0.594302i
$27$	2.32685	+	4.64605i	0.447803	+	0.894132i
$28$		0			0
$29$	0.521720	+	0.903646i	0.0968810	+	0.167803i	0.910392	−	0.413747i	$-0.135780\pi$
$29$	0.521720	+	0.903646i	0.0968810	+	0.167803i	−0.813511	+	0.581549i	$0.802447\pi$
$30$	−11.2633	−	4.35347i	−2.05639	−	0.794831i
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	0.974767	−	0.223224i	$-0.0716581\pi$
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	−0.680701	+	0.732561i	$0.738325\pi$
$32$	−1.33629	−	2.31453i	−0.236226	−	0.409155i
$33$	0.361440	+	2.31668i	0.0629186	+	0.403282i
$34$	3.95060	+	6.84263i	0.677521	+	1.17350i
$35$		0			0
$36$	8.20815	+	7.45963i	1.36803	+	1.24327i
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$	5.26683			0.854393
$39$	−2.36843	−	0.915440i	−0.379252	−	0.146588i
$40$	−11.8320			−1.87081
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	−0.786732	−	0.617294i	$-0.788229\pi$
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	0.927959	+	0.372683i	$0.121562\pi$
$42$		0			0
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	0.651613	−	0.758551i	$-0.274093\pi$
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	−0.982731	+	0.185038i	$0.940759\pi$
$44$	2.50244	+	4.33435i	0.377257	+	0.653428i
$45$	−8.34615	+	2.66925i	−1.24417	+	0.397908i
$46$	3.13670	−	5.43292i	0.462481	−	0.801041i
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	−0.683650	−	0.729810i	$-0.739609\pi$
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	0.973859	+	0.227154i	$0.0729419\pi$
$48$	3.67474	+	1.42035i	0.530404	+	0.205010i
$49$		0			0
$50$	4.21456	−	7.29984i	0.596029	−	1.03235i
$51$	5.34798	+	2.06709i	0.748867	+	0.289450i
$52$	−5.42002			−0.751622
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	−0.997934	−	0.0642533i	$-0.979533\pi$
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	0.554612	+	0.832109i	$0.312867\pi$
$54$	12.3807	+	0.734945i	1.68481	+	0.100013i
$55$	−3.95402			−0.533160
$56$		0			0
$57$	2.97574	−	2.39834i	0.394146	−	0.317668i
$58$	2.49056			0.327026
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	−0.922799	−	0.385283i	$-0.874104\pi$
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	0.127735	−	0.991808i	$-0.459229\pi$
$60$	−14.5630	+	11.7373i	−1.88008	+	1.51528i
$61$	0.279867	−	0.484744i	0.0358333	−	0.0620651i	−0.847553	−	0.530711i	$-0.821925\pi$
$61$	0.279867	−	0.484744i	0.0358333	−	0.0620651i	0.883386	+	0.468646i	$0.155258\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	2.14100	−	3.70832i	0.265558	−	0.459960i
$66$	5.22013	+	2.01767i	0.642554	+	0.248359i
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	−0.930420	−	0.366494i	$-0.880558\pi$
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	0.147817	−	0.989015i	$-0.452775\pi$
$68$	12.2386			1.48414
$69$	−0.701751	−	4.49793i	−0.0844809	−	0.541487i
$70$		0			0
$71$	12.9177			1.53305			0.766525	−	0.642214i	$-0.221984\pi$
$71$	12.9177			1.53305			0.766525	+	0.642214i	$0.221984\pi$
$72$	11.5750	−	3.70190i	1.36413	−	0.436273i
$73$	−5.22772	+	9.05467i	−0.611858	+	1.05977i	0.379069	+	0.925368i	$0.376244\pi$
$73$	−5.22772	+	9.05467i	−0.611858	+	1.05977i	−0.990927	+	0.134401i	$0.957089\pi$
$74$	25.9583			3.01759
$75$	−0.942894	−	6.04355i	−0.108876	−	0.697849i
$76$	4.07903	−	7.06509i	0.467897	−	0.810422i
$77$		0			0
$78$	−4.71886	+	3.80324i	−0.534306	+	0.430632i
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	−0.886810	−	0.462134i	$-0.847084\pi$
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	0.843625	+	0.536933i	$0.180417\pi$
$80$	−3.32187	+	5.75365i	−0.371397	+	0.643278i
$81$	7.32974	−	5.22254i	0.814415	−	0.580282i
$82$	−2.15842	−	3.73849i	−0.238358	−	0.412847i
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	0.914950	−	0.403567i	$-0.132230\pi$
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	−0.806974	+	0.590587i	$0.798896\pi$
$84$		0			0
$85$	−4.83443	+	8.37348i	−0.524368	+	0.908232i
$86$	−10.3652			−1.11770
$87$	1.40715	−	1.13412i	0.150863	−	0.121590i
$88$	5.48371			0.584565
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	0.644777	−	0.764371i	$-0.276950\pi$
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	−0.984353	+	0.176208i	$0.943617\pi$
$90$	−4.44301	+	20.4378i	−0.468335	+	2.15433i
$91$		0			0
$92$	−4.85859	−	8.41533i	−0.506543	−	0.877359i
$93$	4.41601	−	3.55915i	0.457919	−	0.369066i
$94$	−4.74884	−	8.22524i	−0.489806	−	0.848369i
$95$	3.22257	+	5.58166i	0.330629	+	0.572666i
$96$	−3.60418	+	2.90484i	−0.367850	+	0.296474i
$97$	4.14143	+	7.17316i	0.420498	+	0.728324i	0.995988	−	0.0894847i	$-0.0285220\pi$
$97$	4.14143	+	7.17316i	0.420498	+	0.728324i	−0.575490	+	0.817809i	$0.695189\pi$
$98$		0			0
$99$	3.86814	−	1.23710i	0.388762	−	0.124333i
$100$	−6.52815	−	11.3071i	−0.652815	−	1.13071i
$101$	16.2266			1.61461			0.807305	−	0.590134i	$-0.200925\pi$
$101$	16.2266			1.61461			0.807305	+	0.590134i	$0.200925\pi$
$102$	10.6553	−	8.58782i	1.05503	−	0.850320i
$103$	2.22683			0.219416			0.109708	−	0.993964i	$-0.465008\pi$
$103$	2.22683			0.219416			0.109708	+	0.993964i	$0.465008\pi$
$104$	−2.96929	+	5.14295i	−0.291162	+	0.504308i
$105$		0			0
$106$	7.70346	+	13.3428i	0.748226	+	1.29597i
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	−0.884501	−	0.466537i	$-0.845501\pi$
$107$	−8.75403	−	15.1624i	−0.846284	−	1.46581i	0.0382175	−	0.999269i	$-0.487832\pi$
$108$	10.5745	−	16.0387i	1.01753	−	1.54333i
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$	−4.71886	+	8.17331i	−0.449926	+	0.779295i
$111$	14.6663	−	11.8205i	1.39207	−	1.12196i
$112$		0			0
$113$	−0.844555	+	1.46281i	−0.0794491	+	0.137610i	−0.903012	−	0.429615i	$-0.858649\pi$
$113$	−0.844555	+	1.46281i	−0.0794491	+	0.137610i	0.823563	+	0.567224i	$0.191983\pi$
$114$	−1.40624	−	9.01338i	−0.131706	−	0.844181i
$115$	7.67690			0.715875
$116$	1.92887	−	3.34091i	0.179092	−	0.310196i
$117$	−0.934270	+	4.29763i	−0.0863733	+	0.397316i
$118$	−29.1532			−2.68377
$119$		0			0
$120$	3.15913	+	20.2487i	0.288388	+	1.84844i
$121$	−9.16746			−0.833405
$122$	−0.668005	−	1.15702i	−0.0604784	−	0.104752i
$123$	−2.92188	−	1.12936i	−0.263457	−	0.101831i
$124$	6.05330	−	10.4846i	0.543602	−	0.941546i
$125$	−4.28942			−0.383657
$126$		0			0
$127$	−3.96918			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$127$	−3.96918			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$128$	−10.3696	+	17.9607i	−0.916552	+	1.58751i
$129$	−5.85627	+	4.71995i	−0.515616	+	0.415569i
$130$	−5.11028	−	8.85127i	−0.448202	−	0.776308i
$131$	−5.32863			−0.465565			−0.232782	−	0.972529i	$-0.574783\pi$
$131$	−5.32863			−0.465565			−0.232782	+	0.972529i	$0.574783\pi$
$132$	6.74944	−	5.43981i	0.587463	−	0.473475i
$133$		0			0
$134$	−30.5800			−2.64171
$135$	6.79642	+	13.5705i	0.584943	+	1.16796i
$136$	6.70473	−	11.6129i	0.574925	−	0.995800i
$137$	−7.49543			−0.640378			−0.320189	−	0.947354i	$-0.603746\pi$
$137$	−7.49543			−0.640378			−0.320189	+	0.947354i	$0.603746\pi$
$138$	−10.1351	−	3.91740i	−0.862758	−	0.333471i
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	0.396812	+	0.917900i	$0.370116\pi$
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	−0.993331	+	0.115300i	$0.963217\pi$
$140$		0			0
$141$	−6.42858	−	2.48476i	−0.541384	−	0.209255i
$142$	15.4164	−	26.7021i	1.29372	−	2.24079i
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$	1.44957	−	6.66800i	0.120797	−	0.555667i
$145$	1.52388	+	2.63943i	0.126551	+	0.219193i
$146$	12.4779	+	21.6123i	1.03268	+	1.78865i
$147$		0			0
$148$	20.1041	−	34.8212i	1.65254	−	2.86229i
$149$	2.17971			0.178569			0.0892846	−	0.996006i	$-0.471542\pi$
$149$	2.17971			0.178569			0.0892846	+	0.996006i	$0.471542\pi$
$150$	−13.6178	−	5.26354i	−1.11189	−	0.429766i
$151$	14.0277			1.14156			0.570781	−	0.821102i	$-0.306641\pi$
$151$	14.0277			1.14156			0.570781	+	0.821102i	$0.306641\pi$
$152$	−4.46929	−	7.74103i	−0.362507	−	0.627880i
$153$	2.10961	−	9.70416i	0.170552	−	0.784535i
$154$		0			0
$155$	4.78231	+	8.28320i	0.384124	+	0.665322i
$156$	1.44714	+	9.27554i	0.115864	+	0.742638i
$157$	1.48312	+	2.56883i	0.118365	+	0.205015i	0.919120	−	0.393978i	$-0.128901\pi$
$157$	1.48312	+	2.56883i	0.118365	+	0.205015i	−0.800755	+	0.598993i	$0.795568\pi$
$158$	0.916172	+	1.58686i	0.0728867	+	0.126243i
$159$	10.4283	+	4.03072i	0.827017	+	0.319657i
$160$	−3.90314	−	6.76043i	−0.308570	−	0.534459i
$161$		0			0
$162$	−2.04789	−	21.3840i	−0.160898	−	1.68008i
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	0.858317	−	0.513120i	$-0.171511\pi$
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	−0.873534	+	0.486764i	$0.838177\pi$
$164$	−6.68657			−0.522133
$165$	1.05572	+	6.76670i	0.0821875	+	0.526787i
$166$	4.69596			0.364477
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	−0.971965	−	0.235124i	$-0.924450\pi$
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	0.689606	+	0.724185i	$0.257784\pi$
$168$		0			0
$169$	5.42542	+	9.39710i	0.417340	+	0.722854i
$170$	11.5392	+	19.9864i	0.885013	+	1.53289i
$171$	−4.89892	−	4.45217i	−0.374630	−	0.340466i
$172$	−8.02756	+	13.9041i	−0.612096	+	1.06018i
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	−0.932750	−	0.360525i	$-0.882598\pi$
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	0.778598	+	0.627522i	$0.215931\pi$
$174$	−0.664975	−	4.26221i	−0.0504116	−	0.323117i
$175$		0			0
$176$	1.53957	−	2.66661i	0.116049	−	0.201003i
$177$	−16.4715	+	13.2754i	−1.23807	+	0.997842i
$178$	−15.2929			−1.14625
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	−0.597600	−	0.801795i	$-0.703879\pi$
$179$	5.29243	−	9.16675i	0.395575	−	0.685155i	0.993174	+	0.116639i	$0.0372121\pi$
$180$	23.9749	+	21.7886i	1.78698	+	1.62402i
$181$	19.6312			1.45917			0.729586	−	0.683889i	$-0.239713\pi$
$181$	19.6312			1.45917			0.729586	+	0.683889i	$0.239713\pi$
$182$		0			0
$183$	−0.904289	−	0.349524i	−0.0668470	−	0.0258375i
$184$	−10.6469			−0.784896
$185$	15.8829	+	27.5099i	1.16773	+	2.02257i
$186$	−2.08686	−	13.3759i	−0.153016	−	0.980768i
$187$	2.24058	−	3.88081i	0.163848	−	0.283793i
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	−0.976094	−	0.217348i	$-0.930259\pi$
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	0.676276	+	0.736648i	$0.263593\pi$
$192$	2.91784	+	18.7021i	0.210577	+	1.34971i
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$	19.7701			1.41941
$195$	−6.91787	−	2.67388i	−0.495399	−	0.191480i
$196$		0			0
$197$	5.99634			0.427222			0.213611	−	0.976919i	$-0.431478\pi$
$197$	5.99634			0.427222			0.213611	+	0.976919i	$0.431478\pi$
$198$	2.05917	−	9.47218i	0.146339	−	0.673159i
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	0.489221	+	0.872160i	$0.337281\pi$
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	−0.999923	+	0.0124022i	$0.996052\pi$
$200$	−14.3054			−1.01155
$201$	−17.2776	+	13.9251i	−1.21867	+	0.982203i
$202$	19.3654	−	33.5419i	1.36255	−	2.36000i
$203$		0			0
$204$	−3.26768	−	20.9444i	−0.228783	−	1.46640i
$205$	2.64131	−	4.57488i	0.184477	−	0.319523i
$206$	2.65758	−	4.60306i	0.185162	−	0.320710i
$207$	−7.51015	+	2.40188i	−0.521992	+	0.166942i
$208$	1.66727	+	2.88780i	0.115604	+	0.200233i
$209$	−1.49354	−	2.58690i	−0.103311	−	0.178939i
$210$		0			0
$211$	−6.92418	+	11.9930i	−0.476680	+	0.825634i	−0.999643	−	0.0267212i	$-0.991493\pi$
$211$	−6.92418	+	11.9930i	−0.476680	+	0.825634i	0.522963	+	0.852356i	$0.324827\pi$
$212$	23.8646			1.63902
$213$	−3.44901	−	22.1067i	−0.236322	−	1.51473i
$214$	−41.7894			−2.85667
$215$	−6.34204	−	10.9847i	−0.432523	−	0.749153i
$216$	−9.42574	−	18.8205i	−0.641341	−	1.28057i
$217$		0			0
$218$	18.6156	+	32.2431i	1.26081	+	2.18378i
$219$	16.8915	+	6.52886i	1.14142	+	0.441179i
$220$	7.30929	+	12.6601i	0.492792	+	0.853541i
$221$	2.42644	+	4.20271i	0.163220	+	0.282705i
$222$	−6.93082	−	44.4237i	−0.465166	−	2.98152i
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	0.777082	−	0.629399i	$-0.216699\pi$
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	−0.933617	+	0.358273i	$0.883366\pi$
$224$		0			0
$225$	−10.0909	+	3.22724i	−0.672725	+	0.215149i
$226$	2.01584	+	3.49154i	0.134092	+	0.232254i
$227$	−19.7126			−1.30837			−0.654187	−	0.756333i	$-0.726989\pi$
$227$	−19.7126			−1.30837			−0.654187	+	0.756333i	$0.726989\pi$
$228$	−13.1799	−	5.09428i	−0.872862	−	0.337377i
$229$	−28.0728			−1.85510			−0.927552	−	0.373694i	$-0.878091\pi$
$229$	−28.0728			−1.85510			−0.927552	+	0.373694i	$0.878091\pi$
$230$	9.16188	−	15.8688i	0.604116	−	1.04636i
$231$		0			0
$232$	−2.11342	−	3.66054i	−0.138753	−	0.240326i
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	0.546409	−	0.837518i	$-0.315994\pi$
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	−0.998517	+	0.0544448i	$0.982661\pi$
$234$	7.76859	+	7.06016i	0.507849	+	0.461537i
$235$	5.81127	−	10.0654i	0.379085	−	0.656595i
$236$	−22.5785	+	39.1070i	−1.46973	+	2.54565i
$237$	1.24024	+	0.479373i	0.0805619	+	0.0311386i
$238$		0			0
$239$	5.53069	−	9.57944i	0.357751	−	0.619642i	−0.629834	−	0.776730i	$-0.716877\pi$
$239$	5.53069	−	9.57944i	0.357751	−	0.619642i	0.987585	+	0.157087i	$0.0502104\pi$
$240$	10.7334	+	4.14866i	0.692840	+	0.267795i
$241$	23.1697			1.49249			0.746247	−	0.665669i	$-0.231854\pi$
$241$	23.1697			1.49249			0.746247	+	0.665669i	$0.231854\pi$
$242$	−10.9408	+	18.9499i	−0.703299	+	1.21815i
$243$	−10.8946	−	11.1493i	−0.698890	−	0.715229i
$244$	−2.06942			−0.132481
$245$		0			0
$246$	−5.82157	+	4.69198i	−0.371169	+	0.299150i
$247$	3.23486			0.205829
$248$	−6.63243	−	11.4877i	−0.421160	−	0.729470i
$249$	2.65320	−	2.13839i	0.168140	−	0.135515i
$250$	−5.11914	+	8.86660i	−0.323763	+	0.560773i
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$	−4.73696	+	8.20466i	−0.297223	+	0.514806i
$255$	15.6207	+	6.03769i	0.978208	+	0.378095i
$256$	13.8226	+	23.9414i	0.863912	+	1.49634i
$257$	−10.3760			−0.647235			−0.323618	−	0.946188i	$-0.604899\pi$
$257$	−10.3760			−0.647235			−0.323618	+	0.946188i	$0.604899\pi$
$258$	2.76748	+	17.7384i	0.172296	+	1.10434i
$259$		0			0
$260$	−15.8312			−0.981807
$261$	−2.31658	−	2.10532i	−0.143393	−	0.130316i
$262$	−6.35937	+	11.0148i	−0.392883	+	0.680494i
$263$	−19.1331			−1.17980			−0.589898	−	0.807478i	$-0.700832\pi$
$263$	−19.1331			−1.17980			−0.589898	+	0.807478i	$0.700832\pi$
$264$	−1.46414	−	9.38453i	−0.0901117	−	0.577578i
$265$	−9.42689	+	16.3279i	−0.579090	+	1.00301i
$266$		0			0
$267$	−8.64045	+	6.96390i	−0.528787	+	0.426184i
$268$	−23.6835	+	41.0210i	−1.44670	+	2.50576i
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	−0.699311	−	0.714818i	$-0.746510\pi$
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	0.968706	+	0.248212i	$0.0798430\pi$
$270$	36.1625	+	2.14668i	2.20078	+	0.130643i
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	0.997744	+	0.0671321i	$0.0213849\pi$
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	−0.440734	+	0.897638i	$0.645282\pi$
$272$	−3.76474	−	6.52073i	−0.228271	−	0.395377i
$273$		0			0
$274$	−8.94531	+	15.4937i	−0.540406	+	0.936010i
$275$	−4.78059			−0.288280
$276$	−13.1043	+	10.5616i	−0.788787	+	0.635735i
$277$	5.10482			0.306719			0.153360	−	0.988170i	$-0.450991\pi$
$277$	5.10482			0.306719			0.153360	+	0.988170i	$0.450991\pi$
$278$	16.7865	+	29.0750i	1.00679	+	1.74381i
$279$	−7.27001	−	6.60704i	−0.435244	−	0.395553i
$280$		0			0
$281$	−0.853180	−	1.47775i	−0.0508964	−	0.0881552i	0.839455	−	0.543430i	$-0.182875\pi$
$281$	−0.853180	−	1.47775i	−0.0508964	−	0.0881552i	−0.890351	+	0.455274i	$0.849541\pi$
$282$	−12.8083	+	10.3231i	−0.762724	+	0.614729i
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	0.618571	−	0.785729i	$-0.287712\pi$
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	−0.989747	+	0.142833i	$0.954379\pi$
$284$	−23.8793	−	41.3602i	−1.41698	−	2.45428i
$285$	8.69174	−	7.00524i	0.514854	−	0.414954i
$286$	2.36843	+	4.10224i	0.140048	+	0.242571i
$287$		0			0
$288$	5.93351	+	5.39242i	0.349635	+	0.317751i
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$	7.27458			0.427178
$291$	11.1700	−	9.00264i	0.654798	−	0.527744i
$292$	38.6552			2.26213
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	−0.779955	−	0.625835i	$-0.784758\pi$
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	0.931967	+	0.362543i	$0.118091\pi$
$294$		0			0
$295$	−17.8377	−	30.8959i	−1.03855	−	1.79883i
$296$	−22.0275	−	38.1527i	−1.28032	−	2.21758i
$297$	−3.14989	−	6.28942i	−0.182775	−	0.364949i
$298$	2.60135	−	4.50566i	0.150692	−	0.261006i
$299$	1.92654	−	3.33687i	0.111415	−	0.192976i
$300$	−17.6074	+	14.1909i	−1.01656	+	0.819313i
$301$		0			0
$302$	16.7412	−	28.9966i	0.963347	−	1.66857i
$303$	−4.33249	−	27.7694i	−0.248895	−	1.59531i
$304$	−5.01906			−0.287863
$305$	0.817453	−	1.41587i	0.0468072	−	0.0810725i
$306$	−17.5417	−	15.9420i	−1.00279	−	0.911345i
$307$	−5.00136			−0.285442			−0.142721	−	0.989763i	$-0.545585\pi$
$307$	−5.00136			−0.285442			−0.142721	+	0.989763i	$0.545585\pi$
$308$		0			0
$309$	−0.594560	−	3.81088i	−0.0338234	−	0.216793i
$310$	22.8295			1.29663
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.801652	−	0.597791i	$-0.796045\pi$
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.116876	−	0.993146i	$-0.537288\pi$
$312$	9.59418	+	3.70832i	0.543163	+	0.209942i
$313$	0.759535	−	1.31555i	0.0429315	−	0.0743595i	−0.843761	−	0.536719i	$-0.819664\pi$
$313$	0.759535	−	1.31555i	0.0429315	−	0.0743595i	0.886693	+	0.462359i	$0.152997\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	−0.388175	−	0.921586i	$-0.626894\pi$
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	0.992204	−	0.124623i	$-0.0397723\pi$
$318$	20.7773	−	16.7458i	1.16513	−	0.939058i
$319$	−0.706261	−	1.22328i	−0.0395430	−	0.0684905i
$320$	−31.9200			−1.78439
$321$	−23.6109	+	19.0295i	−1.31783	+	1.06213i
$322$		0			0
$323$	−7.30441			−0.406428
$324$	−30.2712	−	13.8143i	−1.68173	−	0.767459i
$325$	2.58856	−	4.48352i	0.143588	−	0.248701i
$326$	−0.927430			−0.0513656
$327$	25.2002	+	9.74032i	1.39357	+	0.538641i
$328$	−3.66315	+	6.34476i	−0.202263	+	0.350330i
$329$		0			0
$330$	15.2473	+	5.89336i	0.839337	+	0.324419i
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	0.463844	+	0.885917i	$0.346470\pi$
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	−0.999149	+	0.0412580i	$0.986863\pi$
$332$	3.63691	−	6.29931i	0.199601	−	0.345719i
$333$	−24.1450	−	21.9431i	−1.32314	−	1.20248i
$334$	8.70942	+	15.0852i	0.476558	+	0.825423i
$335$	−18.7107	−	32.4079i	−1.02228	−	1.77063i
$336$		0			0
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	−0.703260	−	0.710933i	$-0.748273\pi$
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	0.967316	+	0.253575i	$0.0816063\pi$
$338$	25.8995			1.40875
$339$	2.72888	+	1.05476i	0.148212	+	0.0572867i
$340$	35.7472			1.93866
$341$	−2.21642	−	3.83896i	−0.120026	−	0.207891i
$342$	−15.0496	+	4.81312i	−0.813788	+	0.260264i
$343$		0			0
$344$	8.79558	+	15.2344i	0.474226	+	0.821383i
$345$	−2.04972	−	13.1378i	−0.110353	−	0.707318i
$346$	4.83948	+	8.38222i	0.260172	+	0.450631i
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	0.837553	−	0.546356i	$-0.183985\pi$
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	−0.891935	+	0.452164i	$0.850652\pi$
$348$	−6.23246	−	2.40896i	−0.334095	−	0.129134i
$349$	−8.14577	−	14.1089i	−0.436033	−	0.755231i	0.561346	−	0.827581i	$-0.310284\pi$
$349$	−8.14577	−	14.1089i	−0.436033	−	0.755231i	−0.997379	+	0.0723497i	$0.976950\pi$
$350$		0			0
$351$	7.60419	+	0.451400i	0.405882	+	0.0240939i
$352$	1.80896	+	3.13321i	0.0964180	+	0.167001i
$353$	−17.0614			−0.908089			−0.454045	−	0.890979i	$-0.650019\pi$
$353$	−17.0614			−0.908089			−0.454045	+	0.890979i	$0.650019\pi$
$354$	7.78387	+	49.8913i	0.413708	+	2.65169i
$355$	37.7309			2.00255
$356$	−11.8440	+	20.5144i	−0.627731	+	1.08726i
$357$		0			0
$358$	−12.6323	−	21.8798i	−0.667639	−	1.15639i
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	0.902518	−	0.430652i	$-0.141717\pi$
$359$	1.48363	+	2.56972i	0.0783030	+	0.135625i	−0.824215	+	0.566277i	$0.808383\pi$
$360$	33.8091	−	10.8127i	1.78189	−	0.569881i
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$	23.4285	−	40.5794i	1.23137	−	2.13280i
$363$	2.44770	+	15.6887i	0.128471	+	0.823444i
$364$		0			0
$365$	−15.2695	+	26.4475i	−0.799240	+	1.38432i
$366$	−1.80171	+	1.45211i	−0.0941767	+	0.0759031i
$367$	10.1575			0.530216			0.265108	−	0.964219i	$-0.414592\pi$
$367$	10.1575			0.530216			0.265108	+	0.964219i	$0.414592\pi$
$368$	−2.98914	+	5.17733i	−0.155819	+	0.269887i
$369$	−1.15259	+	5.30190i	−0.0600014	+	0.276006i
$370$	75.8207			3.94173
$371$		0			0
$372$	−19.5591	−	7.55992i	−1.01409	−	0.391964i
$373$	−25.4846			−1.31954			−0.659771	−	0.751467i	$-0.729347\pi$
$373$	−25.4846			−1.31954			−0.659771	+	0.751467i	$0.729347\pi$
$374$	−5.34798	−	9.26297i	−0.276537	−	0.478977i
$375$	1.14527	+	7.34068i	0.0591414	+	0.379071i
$376$	−8.05947	+	13.9594i	−0.415635	+	0.719902i
$377$	1.52969			0.0787829
$378$		0			0
$379$	9.85497			0.506216			0.253108	−	0.967438i	$-0.418547\pi$
$379$	9.85497			0.506216			0.253108	+	0.967438i	$0.418547\pi$
$380$	11.9143	−	20.6362i	0.611191	−	1.05861i
$381$	1.05977	+	6.79266i	0.0542935	+	0.347998i
$382$	9.89016	+	17.1303i	0.506025	+	0.876460i
$383$	27.3127			1.39561			0.697806	−	0.716286i	$-0.254160\pi$
$383$	27.3127			1.39561			0.697806	+	0.716286i	$0.254160\pi$
$384$	33.5056	+	12.9505i	1.70983	+	0.660878i
$385$		0			0
$386$	44.8370			2.28214
$387$	9.64109	+	8.76190i	0.490084	+	0.445392i
$388$	15.3114	−	26.5202i	0.777321	−	1.34636i
$389$	4.18446			0.212161			0.106080	−	0.994358i	$-0.466170\pi$
$389$	4.18446			0.212161			0.106080	+	0.994358i	$0.466170\pi$
$390$	−13.7832	+	11.1088i	−0.697938	+	0.562513i
$391$	−4.35019	+	7.53475i	−0.219999	+	0.381049i
$392$		0			0
$393$	1.42274	+	9.11914i	0.0717676	+	0.460000i
$394$	7.15624	−	12.3950i	0.360526	−	0.624450i
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$	−11.1115	−	10.0982i	−0.558374	−	0.507454i
$397$	−15.3354	−	26.5618i	−0.769664	−	1.33310i	−0.937745	−	0.347323i	$-0.887091\pi$
$397$	−15.3354	−	26.5618i	−0.769664	−	1.33310i	0.168082	−	0.985773i	$-0.446243\pi$
$398$	17.1958	+	29.7840i	0.861948	+	1.49294i
$399$		0			0
$400$	−4.01629	+	6.95642i	−0.200815	+	0.347821i
$401$	−6.84803			−0.341974			−0.170987	−	0.985273i	$-0.554696\pi$
$401$	−6.84803			−0.341974			−0.170987	+	0.985273i	$0.554696\pi$
$402$	8.16482	+	52.3330i	0.407224	+	2.61014i
$403$	4.80055			0.239132
$404$	−29.9961	−	51.9547i	−1.49236	−	2.58485i
$405$	21.4092	−	15.2543i	1.06383	−	0.757994i
$406$		0			0
$407$	−7.36113	−	12.7499i	−0.364878	−	0.631987i
$408$	−21.6639	−	8.37348i	−1.07252	−	0.414549i
$409$	−9.13490	−	15.8221i	−0.451692	−	0.782353i	0.546799	−	0.837264i	$-0.315846\pi$
$409$	−9.13490	−	15.8221i	−0.451692	−	0.782353i	−0.998491	+	0.0549104i	$0.982513\pi$
$410$	−6.30445	−	10.9196i	−0.311355	−	0.539282i
$411$	2.00127	+	12.8273i	0.0987154	+	0.632724i
$412$	−4.11646	−	7.12991i	−0.202803	−	0.351265i
$413$		0			0
$414$	−3.99798	+	18.3906i	−0.196490	+	0.903851i
$415$	2.87328	+	4.97666i	0.141044	+	0.244295i
$416$	−3.91802			−0.192097
$417$	22.7241	+	8.78327i	1.11280	+	0.430119i
$418$	−7.12979			−0.348729
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	0.449698	+	0.893181i	$0.351532\pi$
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	−0.998366	+	0.0571410i	$0.981802\pi$
$420$		0			0
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	0.999960	+	0.00894684i	$0.00284791\pi$
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	−0.492232	+	0.870464i	$0.663819\pi$
$422$	16.5271	+	28.6258i	0.804527	+	1.39348i
$423$	−2.53587	+	11.6650i	−0.123298	+	0.567170i
$424$	13.0739	−	22.6446i	0.634923	−	1.09972i
$425$	−5.84505	+	10.1239i	−0.283526	+	0.491082i
$426$	−49.8127	−	19.2535i	−2.41343	−	0.932834i
$427$		0			0
$428$	−32.3649	+	56.0577i	−1.56442	+	2.70965i
$429$	3.20618	+	1.23925i	0.154796	+	0.0598313i
$430$	−30.2752			−1.46000
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	−0.999897	−	0.0143427i	$-0.995434\pi$
$431$	−10.1213	+	17.5307i	−0.487527	+	0.844422i	0.512370	+	0.858765i	$0.328768\pi$
$432$	−11.7983	−	0.700370i	−0.567646	−	0.0336966i
$433$	21.6764			1.04170			0.520851	−	0.853648i	$-0.325615\pi$
$433$	21.6764			1.04170			0.520851	+	0.853648i	$0.325615\pi$
$434$		0			0
$435$	4.11011	−	3.31260i	0.197065	−	0.158827i
$436$	57.6693			2.76186
$437$	2.89978	+	5.02257i	0.138715	+	0.240262i
$438$	33.6546	−	27.1244i	1.60808	−	1.29606i
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	0.0375520	+	0.999295i	$0.488044\pi$
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	−0.884191	+	0.467126i	$0.845289\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	−0.542501	−	0.840055i	$-0.682523\pi$
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	0.998760	+	0.0497923i	$0.0158559\pi$
$444$	−64.9590	−	25.1078i	−3.08282	−	1.19156i
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$	−11.1589			−0.528390
$447$	−0.581980	−	3.73025i	−0.0275267	−	0.176435i
$448$		0			0
$449$	−29.6082			−1.39730			−0.698648	−	0.715465i	$-0.746215\pi$
$449$	−29.6082			−1.39730			−0.698648	+	0.715465i	$0.746215\pi$
$450$	−5.37180	+	24.7102i	−0.253229	+	1.16485i
$451$	−1.22415	+	2.12029i	−0.0576429	+	0.0998405i
$452$	6.24488			0.293735
$453$	−3.74539	−	24.0064i	−0.175974	−	1.12792i
$454$	−23.5257	+	40.7478i	−1.10412	+	1.91239i
$455$		0			0
$456$	−12.0543	+	9.71534i	−0.564494	+	0.454963i
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$	−33.5031	+	58.0290i	−1.56550	+	2.71152i
$459$	−17.1705	−	1.01927i	−0.801449	−	0.0475756i
$460$	−14.1913	−	24.5800i	−0.661673	−	1.14605i
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	−0.999951	−	0.00988416i	$-0.996854\pi$
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	0.491416	−	0.870925i	$-0.336480\pi$
$462$		0			0
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	−0.384010	−	0.923329i	$-0.625457\pi$
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	0.991631	−	0.129102i	$-0.0412094\pi$
$464$	−2.37339			−0.110182
$465$	12.8986	−	10.3958i	0.598157	−	0.482093i
$466$	−32.9442			−1.52611
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	0.913758	+	0.406258i	$0.133167\pi$
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	−0.105049	+	0.994467i	$0.533500\pi$
$468$	15.4873	−	4.95311i	0.715901	−	0.228958i
$469$		0			0
$470$	−13.8707	−	24.0248i	−0.639809	−	1.10818i
$471$	4.00017	−	3.22400i	0.184318	−	0.148554i
$472$	24.7386	+	42.8485i	1.13869	+	1.97226i
$473$	2.93930	+	5.09102i	0.135149	+	0.234086i
$474$	2.47105	−	1.99158i	0.113499	−	0.0914761i
$475$	3.89623	+	6.74848i	0.178771	+	0.309641i
$476$		0			0
$477$	4.11362	−	18.9226i	0.188350	−	0.866407i
$478$	−13.2010	−	22.8649i	−0.603801	−	1.04581i
$479$	29.8109			1.36209			0.681047	−	0.732240i	$-0.261525\pi$
$479$	29.8109			1.36209			0.681047	+	0.732240i	$0.261525\pi$
$480$	−10.5273	+	8.48465i	−0.480504	+	0.387270i
$481$	15.9434			0.726959
$482$	27.6516	−	47.8939i	1.25949	−	2.18151i
$483$		0			0
$484$	16.9467	+	29.3525i	0.770304	+	1.33421i
$485$	12.0965	+	20.9518i	0.549276	+	0.951374i
$486$	−36.0487	+	9.21415i	−1.63520	+	0.417962i
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	0.491283	+	0.871000i	$0.336528\pi$
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	−0.999950	+	0.0100365i	$0.996805\pi$
$488$	−1.13370	+	1.96363i	−0.0513202	+	0.0888892i
$489$	−0.523994	+	0.422321i	−0.0236958	+	0.0190980i
$490$		0			0
$491$	17.5222	−	30.3494i	0.790767	−	1.36965i	−0.134726	−	0.990883i	$-0.543016\pi$
$491$	17.5222	−	30.3494i	0.790767	−	1.36965i	0.925493	−	0.378765i	$-0.123651\pi$
$492$	1.78530	+	11.4430i	0.0804877	+	0.515893i
$493$	−3.45407			−0.155564
$494$	3.86060	−	6.68675i	0.173696	−	0.300851i
$495$	11.2983	−	3.61340i	0.507821	−	0.162410i
$496$	−7.44830			−0.334438
$497$		0			0
$498$	−1.25381	−	8.03642i	−0.0561848	−	0.360121i
$499$	−8.93520			−0.399994			−0.199997	−	0.979796i	$-0.564093\pi$
$499$	−8.93520			−0.399994			−0.199997	+	0.979796i	$0.564093\pi$
$500$	7.92929	+	13.7339i	0.354609	+	0.614200i
$501$	11.7901	+	4.55707i	0.526742	+	0.203595i
$502$	9.28972	−	16.0903i	0.414621	−	0.718144i
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$	−4.24620	+	7.35463i	−0.188766	+	0.326953i
$507$	14.6331	−	11.7938i	0.649880	−	0.523781i
$508$	7.33732	+	12.7086i	0.325541	+	0.563854i
$509$	28.1110			1.24600			0.623000	−	0.782222i	$-0.285914\pi$
$509$	28.1110			1.24600			0.623000	+	0.782222i	$0.285914\pi$
$510$	31.1228	−	25.0839i	1.37814	−	1.11073i
$511$		0			0
$512$	24.5070			1.08307
$513$	−6.31121	+	9.57247i	−0.278647	+	0.422635i
$514$	−12.3830	+	21.4480i	−0.546192	+	0.946033i
$515$	6.50427			0.286613
$516$	25.9382	+	10.0256i	1.14186	+	0.441351i
$517$	−2.69331	+	4.66495i	−0.118452	+	0.205164i
$518$		0			0
$519$	6.55127	+	2.53218i	0.287569	+	0.111150i
$520$	−8.67288	+	15.0219i	−0.380331	+	0.658753i
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	−0.943797	−	0.330524i	$-0.892774\pi$
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	0.758141	+	0.652090i	$0.226108\pi$
$522$	−7.11657	+	2.27601i	−0.311484	+	0.0996181i
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	−0.956339	−	0.292259i	$-0.905593\pi$
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	0.225066	−	0.974344i	$-0.427740\pi$
$524$	9.85035	+	17.0613i	0.430315	+	0.745327i
$525$		0			0
$526$	−22.8341	+	39.5498i	−0.995613	+	1.72445i
$527$	−10.8398			−0.472187
$528$	−4.97456	−	1.92275i	−0.216490	−	0.0836771i
$529$	−16.0921			−0.699655
$530$	22.5008	+	38.9725i	0.977371	+	1.69286i
$531$	27.1167	+	24.6439i	1.17677	+	1.06945i
$532$		0			0
$533$	−1.32569	−	2.29616i	−0.0574220	−	0.0994579i
$534$	4.08319	+	26.1715i	0.176697	+	1.13255i
$535$	−25.5693	−	44.2874i	−1.10546	−	1.91471i
$536$	25.9493	+	44.9456i	1.12084	+	1.94135i
$537$	−17.1006	−	6.60968i	−0.737944	−	0.285229i
$538$	−10.5461	−	18.2665i	−0.454677	−	0.787523i
$539$		0			0
$540$	30.8866	−	46.8469i	1.32915	−	2.01597i
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$	43.7730			1.88021
$543$	−5.24149	−	33.5957i	−0.224934	−	1.44173i
$544$	8.84701			0.379312
$545$	−22.7803	+	39.4567i	−0.975802	+	1.69014i
$546$		0			0
$547$	−2.88599	−	4.99869i	−0.123396	−	0.213728i	0.797709	−	0.603043i	$-0.206045\pi$
$547$	−2.88599	−	4.99869i	−0.123396	−	0.213728i	−0.921105	+	0.389315i	$0.872712\pi$
$548$	13.8558	+	23.9990i	0.591892	+	1.02519i
$549$	−0.356713	+	1.64088i	−0.0152241	+	0.0700309i
$550$	−5.70532	+	9.88190i	−0.243276	+	0.421366i
$551$	−1.15122	+	1.99397i	−0.0490437	+	0.0849461i
$552$	2.84269	+	18.2205i	0.120993	+	0.775515i
$553$		0			0
$554$	6.09227	−	10.5521i	0.258836	−	0.448317i
$555$	42.8384	−	34.5262i	1.81839	−	1.46556i
$556$	52.0029			2.20541
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	−0.258661	−	0.965968i	$-0.583281\pi$
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	0.965883	−	0.258977i	$-0.0833855\pi$
$558$	−22.3336	+	7.14268i	−0.945457	+	0.302374i
$559$	−6.36623			−0.269263
$560$		0			0
$561$	−7.23964	−	2.79825i	−0.305658	−	0.118142i
$562$	−4.07286			−0.171803
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	0.888190	−	0.459477i	$-0.151963\pi$
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	−0.842013	+	0.539457i	$0.818630\pi$
$564$	3.92794	+	25.1764i	0.165396	+	1.06012i
$565$	−2.46683	+	4.27268i	−0.103780	+	0.179753i
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	−0.993475	−	0.114049i	$-0.963618\pi$
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	0.595507	+	0.803350i	$0.296951\pi$
$570$	−4.10743	−	26.3269i	−0.172041	−	1.10271i
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	0.998680	−	0.0513674i	$-0.0163580\pi$
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	−0.543825	+	0.839198i	$0.683025\pi$
$572$	7.33717			0.306782
$573$	13.3885	+	5.17488i	0.559311	+	0.216184i
$574$		0			0
$575$	9.28172			0.387074
$576$	31.2267	−	9.98686i	1.30111	−	0.416119i
$577$	15.4516	−	26.7629i	0.643258	−	1.11416i	−0.341443	−	0.939903i	$-0.610916\pi$
$577$	15.4516	−	26.7629i	0.643258	−	1.11416i	0.984701	−	0.174253i	$-0.0557511\pi$
$578$	14.4217			0.599862
$579$	25.3327	−	20.4173i	1.05279	−	0.848513i
$580$	5.63398	−	9.75835i	0.233938	−	0.405193i
$581$		0			0
$582$	−5.27858	−	33.8335i	−0.218804	−	1.40244i
$583$	4.36902	−	7.56737i	0.180946	−	0.313408i
$584$	21.1767	−	36.6792i	0.876299	−	1.51780i
$585$	−2.72888	+	12.5528i	−0.112825	+	0.518994i
$586$	−6.21069	−	10.7572i	−0.256561	−	0.444377i
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	0.990922	−	0.134436i	$-0.0429222\pi$
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	−0.611886	+	0.790946i	$0.709589\pi$
$588$		0			0
$589$	−3.61282	+	6.25759i	−0.148864	+	0.257840i
$590$	−85.1527			−3.50568
$591$	−1.60101	−	10.2618i	−0.0658569	−	0.422115i
$592$	−24.7371			−1.01669
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	−0.996577	−	0.0826662i	$-0.973656\pi$
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$594$	−16.7600	−	0.994906i	−0.687671	−	0.0408215i
$595$		0			0
$596$	−4.02936	−	6.97905i	−0.165049	−	0.285873i
$597$	23.2782	+	8.99745i	0.952715	+	0.368241i
$598$	−4.59841	−	7.96468i	−0.188043	−	0.325700i
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	0.861881	−	0.507110i	$-0.169286\pi$
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	−0.870111	+	0.492856i	$0.835953\pi$
$600$	3.81953	+	24.4816i	0.155932	+	0.999456i
$601$	−12.3733	−	21.4312i	−0.504717	−	0.874196i	−0.999985	−	0.00545577i	$-0.998263\pi$
$601$	−12.3733	−	21.4312i	−0.504717	−	0.874196i	0.495268	−	0.868740i	$-0.335070\pi$
$602$		0			0
$603$	28.4438	+	25.8500i	1.15832	+	1.05269i
$604$	−25.9313	−	44.9143i	−1.05513	−	1.82754i
$605$	−26.7769			−1.08864
$606$	−62.5724	−	24.1853i	−2.54183	−	0.982462i
$607$	−24.0697			−0.976957			−0.488479	−	0.872576i	$-0.662448\pi$
$607$	−24.0697			−0.976957			−0.488479	+	0.872576i	$0.662448\pi$
$608$	2.94865	−	5.10721i	0.119584	−	0.207125i
$609$		0			0
$610$	−1.95115	−	3.37950i	−0.0789999	−	0.136832i
$611$	−2.91672	−	5.05190i	−0.117998	−	0.204378i
$612$	−34.9707	+	11.1843i	−1.41361	+	0.452097i
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$	−5.96879	+	10.3382i	−0.240881	+	0.417218i
$615$	−8.53443	−	3.29871i	−0.344142	−	0.133017i
$616$		0			0
$617$	−20.9315	+	36.2544i	−0.842669	+	1.45955i	0.0449604	+	0.998989i	$0.485684\pi$
$617$	−20.9315	+	36.2544i	−0.842669	+	1.45955i	−0.887630	+	0.460558i	$0.847650\pi$
$618$	−8.58700	−	3.31903i	−0.345420	−	0.133511i
$619$	−14.8219			−0.595743			−0.297871	−	0.954606i	$-0.596277\pi$
$619$	−14.8219			−0.595743			−0.297871	+	0.954606i	$0.596277\pi$
$620$	17.6809	−	30.6242i	0.710081	−	1.22990i
$621$	6.11565	+	12.2112i	0.245413	+	0.490018i
$622$	−77.3270			−3.10053
$623$		0			0
$624$	4.49687	−	3.62432i	0.180019	−	0.145089i
$625$	−30.1861			−1.20744
$626$	−1.81291	−	3.14005i	−0.0724585	−	0.125502i
$627$	−4.02830	+	3.24667i	−0.160875	+	0.129660i
$628$	5.48329	−	9.49734i	0.218807	−	0.378985i
$629$	−36.0007			−1.43544
$630$		0			0
$631$	−21.0294			−0.837169			−0.418585	−	0.908178i	$-0.637474\pi$
$631$	−21.0294			−0.837169			−0.418585	+	0.908178i	$0.637474\pi$
$632$	1.55487	−	2.69312i	0.0618496	−	0.107127i
$633$	22.3730	+	8.64756i	0.889247	+	0.343710i
$634$	−25.6694	−	44.4607i	−1.01946	−	1.76576i
$635$	−11.5935			−0.460072
$636$	−6.37180	−	40.8406i	−0.252658	−	1.61943i
$637$		0			0
$638$	−3.37150			−0.133479
$639$	−36.9114	+	11.8049i	−1.46019	+	0.466995i
$640$	−30.2882	+	52.4607i	−1.19725	+	2.07369i
$641$	11.9318			0.471279			0.235640	−	0.971840i	$-0.424281\pi$
$641$	11.9318			0.471279			0.235640	+	0.971840i	$0.424281\pi$
$642$	11.1577	+	71.5163i	0.440360	+	2.82252i
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	−0.140072	−	0.990141i	$-0.544733\pi$
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	0.927524	−	0.373765i	$-0.121933\pi$
$644$		0			0
$645$	−17.1054	+	13.7863i	−0.673524	+	0.542837i
$646$	−8.71733	+	15.0989i	−0.342979	+	0.594057i
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	−0.875582	−	0.483070i	$-0.839522\pi$
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	0.856142	+	0.516741i	$0.172855\pi$
$648$	−29.6917	+	21.1558i	−1.16640	+	0.831077i
$649$	8.26714	+	14.3191i	0.324514	+	0.562074i
$650$	−6.17856	−	10.7016i	−0.242343	−	0.419751i
$651$		0			0
$652$	−0.718272	+	1.24408i	−0.0281297	+	0.0487221i
$653$	22.7147			0.888894			0.444447	−	0.895805i	$-0.353400\pi$
$653$	22.7147			0.888894			0.444447	+	0.895805i	$0.353400\pi$
$654$	50.2089	−	40.4666i	1.96332	−	1.58237i
$655$	−15.5642			−0.608144
$656$	2.05688	+	3.56262i	0.0803076	+	0.139097i
$657$	6.66315	−	30.6504i	0.259954	−	1.19579i
$658$		0			0
$659$	−19.1943	−	33.2454i	−0.747702	−	1.29506i	−0.948922	−	0.315512i	$-0.897824\pi$
$659$	−19.1943	−	33.2454i	−0.747702	−	1.29506i	0.201220	−	0.979546i	$-0.435509\pi$
$660$	19.7142	−	15.8890i	0.767374	−	0.618477i
$661$	16.9629	+	29.3806i	0.659780	+	1.14277i	0.980672	+	0.195657i	$0.0626839\pi$
$661$	16.9629	+	29.3806i	0.659780	+	1.14277i	−0.320892	+	0.947116i	$0.603983\pi$
$662$	23.2458	+	40.2628i	0.903472	+	1.56486i
$663$	6.54444	−	5.27459i	0.254165	−	0.204848i
$664$	−3.98486	−	6.90198i	−0.154642	−	0.267849i
$665$		0			0
$666$	−74.1738	+	23.7221i	−2.87418	+	0.919213i
$667$	1.37124	+	2.37505i	0.0530944	+	0.0919623i
$668$	26.9809			1.04392
$669$	−6.30475	+	5.08140i	−0.243756	+	0.196458i
$670$	−89.3201			−3.45074
$671$	−0.378860	+	0.656205i	−0.0146257	+	0.0253325i
$672$		0			0
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	−0.989351	−	0.145549i	$-0.953505\pi$
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	0.368626	−	0.929578i	$-0.379828\pi$
$674$	−11.5702	−	20.0401i	−0.445666	−	0.771916i
$675$	8.21718	+	16.4073i	0.316279	+	0.631518i
$676$	20.0585	−	34.7424i	0.771483	−	1.33625i
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	0.227421	+	0.973797i	$0.426971\pi$
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	−0.957043	+	0.289946i	$0.906363\pi$
$678$	5.43702	−	4.38204i	0.208807	−	0.168291i
$679$		0			0
$680$	19.5836	−	33.9198i	0.750997	−	1.30076i
$681$	5.26324	+	33.7352i	0.201688	+	1.29273i
$682$	−10.5806			−0.405153
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	−0.683382	−	0.730061i	$-0.739492\pi$
$683$	7.59357	−	13.1525i	0.290560	−	0.503265i	0.973942	+	0.226796i	$0.0728251\pi$
$684$	−5.19906	+	23.9156i	−0.198791	+	0.914436i
$685$	−21.8932			−0.836495
$686$		0			0
$687$	7.49540	+	48.0424i	0.285967	+	1.83293i
$688$	9.87754			0.376578
$689$	4.73142	+	8.19507i	0.180253	+	0.312207i
$690$	−29.6033	−	11.4422i	−1.12698	−	0.435597i
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	−0.839293	−	0.543680i	$-0.817031\pi$
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	0.890487	+	0.455009i	$0.150364\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	−20.5420	+	35.5798i	−0.779203	+	1.34962i
$696$	−5.70018	+	4.59415i	−0.216065	+	0.174141i
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$	−38.8858			−1.47185
$699$	−18.6133	+	15.0017i	−0.704021	+	0.567416i
$700$		0			0
$701$	−11.8515			−0.447625			−0.223813	−	0.974632i	$-0.571850\pi$
$701$	−11.8515			−0.447625			−0.223813	+	0.974632i	$0.571850\pi$
$702$	10.0082	−	15.1798i	0.377735	−	0.572925i
$703$	−11.9988	+	20.7826i	−0.452544	+	0.783829i
$704$	14.7938			0.557562
$705$	−18.7770	−	7.25765i	−0.707184	−	0.273339i
$706$	−20.3617	+	35.2675i	−0.766323	+	1.32731i
$707$		0			0
$708$	72.9542	+	28.1981i	2.74179	+	1.05975i
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$	45.0294	−	77.9931i	1.68992	−	2.92703i
$711$	0.489233	−	2.25047i	0.0183477	−	0.0843991i
$712$	12.9772	+	22.4771i	0.486339	+	0.842364i
$713$	4.30328	+	7.45351i	0.161159	+	0.279136i
$714$		0			0
$715$	−2.89830	+	5.02001i	−0.108390	+	0.187738i
$716$	−39.1337			−1.46250
$717$	−17.8704	−	6.90724i	−0.667384	−	0.257956i
$718$	7.08246			0.264315
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	0.602516	−	0.798107i	$-0.294165\pi$
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	−0.992439	+	0.122741i	$0.960832\pi$
$720$	4.23400	−	19.4763i	0.157792	−	0.725840i
$721$		0			0
$722$	−16.8644	−	29.2100i	−0.627628	−	1.08708i
$723$	−6.18629	−	39.6515i	−0.230071	−	1.47466i
$724$	−36.2896	−	62.8554i	−1.34869	−	2.33600i
$725$	1.84243	+	3.19119i	0.0684263	+	0.118518i
$726$	35.3511	+	13.6638i	1.31200	+	0.507112i
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	0.840476	−	0.541849i	$-0.182276\pi$
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	−0.889493	+	0.456949i	$0.848942\pi$
$728$		0			0
$729$	−16.1715	+	21.6213i	−0.598945	+	0.800790i
$730$	36.4462	+	63.1267i	1.34893	+	2.33642i
$731$	14.3751			0.531683
$732$	0.552531	+	3.54149i	0.0204221	+	0.130897i
$733$	−14.1489			−0.522602			−0.261301	−	0.965257i	$-0.584152\pi$
$733$	−14.1489			−0.522602			−0.261301	+	0.965257i	$0.584152\pi$
$734$	12.1223	−	20.9964i	0.447442	−	0.774992i
$735$		0			0
$736$	−3.51218	−	6.08327i	−0.129461	−	0.224232i
$737$	8.67174	+	15.0199i	0.319428	+	0.553265i
$738$	9.58396	+	8.70997i	0.352790	+	0.320619i
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	−0.973595	−	0.228282i	$-0.926689\pi$
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	0.684495	+	0.729017i	$0.260023\pi$
$740$	58.7212	−	101.708i	2.15864	−	3.73887i
$741$	−0.863704	−	5.53598i	−0.0317289	−	0.203369i
$742$		0			0
$743$	10.5496	−	18.2724i	0.387026	−	0.670348i	−0.605022	−	0.796208i	$-0.706836\pi$
$743$	10.5496	−	18.2724i	0.387026	−	0.670348i	0.992048	+	0.125861i	$0.0401692\pi$
$744$	−17.8886	+	14.4176i	−0.655828	+	0.528575i
$745$	6.36665			0.233256
$746$	−30.4142	+	52.6789i	−1.11354	+	1.92871i
$747$	−4.36792	−	3.96960i	−0.159814	−	0.145240i
$748$	−16.5675			−0.605768
$749$		0			0
$750$	16.5406	+	6.39325i	0.603979	+	0.233449i
$751$	13.0370			0.475725			0.237863	−	0.971299i	$-0.423553\pi$
$751$	13.0370			0.475725			0.237863	+	0.971299i	$0.423553\pi$
$752$	4.52544	+	7.83829i	0.165026	+	0.285833i
$753$	−2.07832	−	13.3212i	−0.0757383	−	0.485451i
$754$	1.82558	−	3.16200i	0.0664838	−	0.115153i
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$	11.7613	−	20.3711i	0.427188	−	0.739912i
$759$	0.949971	+	6.08891i	0.0344818	+	0.221014i
$760$	−13.0542	−	22.6105i	−0.473525	−	0.820169i
$761$	6.04077			0.218978			0.109489	−	0.993988i	$-0.465079\pi$
$761$	6.04077			0.218978			0.109489	+	0.993988i	$0.465079\pi$
$762$	15.3058	+	5.91596i	0.554470	+	0.214313i
$763$		0			0
$764$	30.6388			1.10847
$765$	6.16188	−	28.3446i	0.222783	−	1.02480i
$766$	32.5959	−	56.4577i	1.17774	−	2.03990i
$767$	−17.9058			−0.646540
$768$	37.2815	−	30.0476i	1.34528	−	1.08425i
$769$	−0.108129	+	0.187285i	−0.00389924	+	0.00675368i	−0.867968	−	0.496619i	$-0.834575\pi$
$769$	−0.108129	+	0.187285i	−0.00389924	+	0.00675368i	0.864069	+	0.503373i	$0.167908\pi$
$770$		0			0
$771$	2.77037	+	17.7569i	0.0997724	+	0.639499i
$772$	34.7251	−	60.1457i	1.24979	−	2.16469i
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	0.299316	+	0.954154i	$0.403241\pi$
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	−0.975980	+	0.217861i	$0.930092\pi$
$774$	29.6176	−	9.47225i	1.06458	−	0.340473i
$775$	5.78202	+	10.0148i	0.207696	+	0.359741i
$776$	−16.7763	−	29.0575i	−0.602235	−	1.04310i
$777$		0			0
$778$	4.99388	−	8.64965i	0.179039	−	0.310105i
$779$	3.99078			0.142985
$780$	4.22690	+	27.0926i	0.151347	+	0.970072i
$781$	−17.4869			−0.625730
$782$	10.3833	+	17.9845i	0.371307	+	0.643123i
$783$	−2.98442	+	4.52659i	−0.106654	+	0.161767i
$784$		0			0
$785$	4.33198	+	7.50321i	0.154615	+	0.267801i
$786$	20.5480	+	7.94217i	0.732924	+	0.283288i
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	0.998330	+	0.0577648i	$0.0183973\pi$
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	−0.449139	+	0.893462i	$0.648269\pi$
$788$	−11.0847	−	19.1992i	−0.394875	−	0.683943i
$789$	5.10850	+	32.7433i	0.181867	+	1.16569i
$790$	2.67601	+	4.63499i	0.0952083	+	0.164906i
$791$		0			0
$792$	−15.6693	+	5.01131i	−0.556783	+	0.178069i
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$	−73.2074			−2.59803
$795$	30.4596	+	11.7732i	1.08029	+	0.417552i
$796$	53.2710			1.88814
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	−0.349264	−	0.937024i	$-0.613569\pi$
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	0.986119	−	0.166040i	$-0.0530981\pi$
$798$		0			0
$799$	6.58602	+	11.4073i	0.232997	+	0.403562i
$800$	−4.71907	−	8.17367i	−0.166844	−	0.288983i
$801$	14.2246	+	12.9275i	0.502603	+	0.456770i
$802$	−8.17268	+	14.1555i	−0.288587	+	0.499848i
$803$	7.07684	−	12.2574i	0.249736	−	0.432556i
$804$	76.5246	+	29.5781i	2.69882	+	1.04314i
$805$		0			0
$806$	5.72914	−	9.92315i	0.201800	−	0.349528i
$807$	−14.2765	−	5.51811i	−0.502556	−	0.194247i
$808$	−65.7318			−2.31244
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	0.288511	+	0.957477i	$0.406840\pi$
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	−0.973455	+	0.228880i	$0.926494\pi$
$810$	−5.98162	−	62.4597i	−0.210173	−	2.19461i
$811$	28.2811			0.993082			0.496541	−	0.868013i	$-0.334603\pi$
$811$	28.2811			0.993082			0.496541	+	0.868013i	$0.334603\pi$
$812$		0			0
$813$	24.7316	−	19.9328i	0.867374	−	0.699073i
$814$	−35.1401			−1.23166
$815$	−0.567459	−	0.982867i	−0.0198772	−	0.0344283i
$816$	−10.1541	+	8.18381i	−0.355463	+	0.286491i
$817$	4.79113	−	8.29849i	0.167621	−	0.290327i
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	0.233077	+	0.972458i	$0.425121\pi$
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	−0.958712	+	0.284378i	$0.908213\pi$
$822$	28.9035	+	11.1717i	1.00813	+	0.389659i
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	0.782835	−	0.622229i	$-0.213773\pi$
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	−0.930284	+	0.366841i	$0.880439\pi$
$824$	−9.02057			−0.314247
$825$	1.27641	+	8.18125i	0.0444389	+	0.284834i
$826$		0			0
$827$	44.2823			1.53985			0.769923	−	0.638137i	$-0.220294\pi$
$827$	44.2823			1.53985			0.769923	+	0.638137i	$0.220294\pi$
$828$	21.5734	+	19.6061i	0.749729	+	0.681360i
$829$	8.31637	−	14.4044i	0.288839	−	0.500284i	−0.684694	−	0.728831i	$-0.740064\pi$
$829$	8.31637	−	14.4044i	0.288839	−	0.500284i	0.973533	+	0.228547i	$0.0733973\pi$
$830$	13.7163			0.476099
$831$	−1.36298	−	8.73613i	−0.0472813	−	0.303053i
$832$	−8.01045	+	13.8745i	−0.277712	+	0.481012i
$833$		0			0
$834$	45.2755	−	36.4905i	1.56776	−	1.26356i
$835$	−10.6579	+	18.4601i	−0.368832	+	0.638836i
$836$	−5.52185	+	9.56412i	−0.190977	+	0.330782i
$837$	−9.36586	+	14.2056i	−0.323731	+	0.491017i
$838$	26.8068	+	46.4308i	0.926027	+	1.60393i
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	−0.999919	−	0.0127182i	$-0.995952\pi$
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	0.488945	−	0.872314i	$-0.337382\pi$
$840$		0			0
$841$	13.9556	−	24.1718i	0.481228	−	0.833512i
$842$	49.7314			1.71386
$843$	−2.30115	+	1.85464i	−0.0792557	+	0.0638773i
$844$	51.1994			1.76236
$845$	15.8469	+	27.4477i	0.545151	+	0.944228i
$846$	21.0861	+	19.1632i	0.724956	+	0.658846i
$847$		0			0
$848$	−7.34105	−	12.7151i	−0.252093	−	0.436638i
$849$	−16.8414	+	13.5736i	−0.577994	+	0.465843i
$850$	13.9514	+	24.1645i	0.478528	+	0.828834i
$851$	14.2920	+	24.7544i	0.489922	+	0.848570i
$852$	−64.4059	+	51.9089i	−2.20651	+	1.77837i
$853$	15.0619	+	26.0880i	0.515710	+	0.893236i	0.999834	+	0.0182366i	$0.00580520\pi$
$853$	15.0619	+	26.0880i	0.515710	+	0.893236i	−0.484124	+	0.875000i	$0.660861\pi$
$854$		0			0
$855$	−14.3091	−	13.0042i	−0.489360	−	0.444734i
$856$	35.4613	+	61.4208i	1.21204	+	2.09932i
$857$	−37.0894			−1.26695			−0.633475	−	0.773763i	$-0.718372\pi$
$857$	−37.0894			−1.26695			−0.633475	+	0.773763i	$0.718372\pi$
$858$	6.38800	−	5.14850i	0.218083	−	0.175767i
$859$	3.78333			0.129085			0.0645427	−	0.997915i	$-0.479441\pi$
$859$	3.78333			0.129085			0.0645427	+	0.997915i	$0.479441\pi$
$860$	−23.4474	+	40.6121i	−0.799551	+	1.38486i
$861$		0			0
$862$	24.1583	+	41.8434i	0.822835	+	1.42519i
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	0.869637	−	0.493691i	$-0.164353\pi$
$863$	0.213559	+	0.369895i	0.00726963	+	0.0125914i	−0.862368	+	0.506282i	$0.831019\pi$
$864$	7.64406	−	11.5941i	0.260056	−	0.394438i
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$	25.8694	−	44.8071i	0.879077	−	1.52261i
$867$	8.14818	−	6.56715i	0.276727	−	0.223032i
$868$		0			0
$869$	0.519608	−	0.899987i	0.0176265	−	0.0305300i
$870$	−1.94230	−	12.4493i	−0.0658502	−	0.422072i
$871$	−18.7821			−0.636407
$872$	31.5933	−	54.7212i	1.06988	−	1.85309i
$873$	−18.3890	−	16.7121i	−0.622374	−	0.565619i
$874$	13.8428			0.468240
$875$		0			0
$876$	−10.3209	−	66.1525i	−0.348710	−	2.23509i
$877$	11.2608			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$877$	11.2608			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$878$	42.3408	+	73.3364i	1.42893	+	2.47498i
$879$	−8.40750	−	3.24965i	−0.283578	−	0.109608i
$880$	4.49687	−	7.78881i	0.151589	−	0.262561i
$881$	35.4810			1.19538			0.597692	−	0.801726i	$-0.296084\pi$
$881$	35.4810			1.19538			0.597692	+	0.801726i	$0.296084\pi$
$882$		0			0
$883$	−5.30092			−0.178390			−0.0891952	−	0.996014i	$-0.528429\pi$
$883$	−5.30092			−0.178390			−0.0891952	+	0.996014i	$0.528429\pi$
$884$	8.97088	−	15.5380i	0.301723	−	0.522600i
$885$	−48.1109	+	38.7757i	−1.61723	+	1.30343i
$886$	−22.9214	−	39.7010i	−0.770060	−	1.33378i
$887$	−57.5664			−1.93289			−0.966446	−	0.256870i	$-0.917309\pi$
$887$	−57.5664			−1.93289			−0.966446	+	0.256870i	$0.917309\pi$
$888$	−59.4112	+	47.8834i	−1.99371	+	1.60686i
$889$		0			0
$890$	−44.6686			−1.49730
$891$	−9.92238	+	7.06983i	−0.332412	+	0.236848i
$892$	−8.64231	+	14.9689i	−0.289366	+	0.501197i
$893$	8.78032			0.293822
$894$	−8.40531	−	3.24880i	−0.281116	−	0.108656i
$895$	15.4585	−	26.7749i	0.516720	−	0.894985i
$896$		0			0
$897$	−6.22494	−	2.40605i	−0.207845	−	0.0803356i
$898$	−35.3354	+	61.2027i	−1.17916	+	2.04236i
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$	28.9867	+	26.3434i	0.966224	+	0.878112i
$901$	−10.6837	−	18.5047i	−0.355925	−	0.616480i
$902$	2.92188	+	5.06085i	0.0972881	+	0.168508i
$903$		0			0
$904$	3.42117	−	5.92565i	0.113787	−	0.197084i
$905$	57.3400			1.90605
$906$	−54.0931	−	20.9080i	−1.79712	−	0.694620i
$907$	20.8972			0.693879			0.346939	−	0.937888i	$-0.387221\pi$
$907$	20.8972			0.693879			0.346939	+	0.937888i	$0.387221\pi$
$908$	36.4402	+	63.1163i	1.20931	+	2.09459i
$909$	−46.3664	+	14.8288i	−1.53787	+	0.491840i
$910$		0			0
$911$	11.3819	+	19.7141i	0.377101	+	0.653157i	0.990639	−	0.136508i	$-0.0435878\pi$
$911$	11.3819	+	19.7141i	0.377101	+	0.653157i	−0.613539	+	0.789665i	$0.710254\pi$
$912$	1.34008	+	8.58936i	0.0443745	+	0.284422i
$913$	−1.33166	−	2.30650i	−0.0440715	−	0.0763340i
$914$	−11.4116	−	19.7654i	−0.377461	−	0.653782i
$915$	−2.64131	−	1.02091i	−0.0873189	−	0.0337503i
$916$	51.8946	+	89.8841i	1.71465	+	2.96986i
$917$		0			0
$918$	−22.5987	+	34.2764i	−0.745870	+	1.13129i
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	0.990339	+	0.138664i	$0.0442809\pi$
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	−0.375083	+	0.926991i	$0.622386\pi$
$920$	−31.0980			−1.02527
$921$	1.33535	+	8.55906i	0.0440014	+	0.282031i
$922$	−52.1231			−1.71658
$923$	9.46870	−	16.4003i	0.311666	−	0.539822i
$924$		0			0
$925$	19.2031	+	33.2607i	0.631394	+	1.09361i
$926$	−31.2070	−	54.0521i	−1.02553	−	1.77626i
$927$	−6.36300	+	2.03500i	−0.208988	+	0.0668381i
$928$	1.39434	−	2.41508i	0.0457716	−	0.0792787i
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	−0.815791	−	0.578347i	$-0.803698\pi$
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	0.908759	+	0.417322i	$0.137031\pi$
$930$	−6.09544	−	39.0692i	−0.199877	−	1.28113i
$931$		0			0
$932$	−25.5145	+	44.1923i	−0.835754	+	1.44757i
$933$	−43.6895	+	35.2122i	−1.43033	+	1.15279i
$934$	83.4275			2.72983
$935$	6.54444	−	11.3353i	0.214026	−	0.370704i
$936$	3.78459	−	17.4091i	0.123703	−	0.569034i
$937$	7.64754			0.249834			0.124917	−	0.992167i	$-0.460134\pi$
$937$	7.64754			0.249834			0.124917	+	0.992167i	$0.460134\pi$
$938$		0			0
$939$	−2.45416	−	0.948578i	−0.0800886	−	0.0309557i
$940$	−42.9702			−1.40153
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	0.983178	−	0.182650i	$-0.0584674\pi$
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	−0.649768	+	0.760132i	$0.725134\pi$
$942$	−1.89035	−	12.1164i	−0.0615909	−	0.394772i
$943$	2.37674	−	4.11663i	0.0773973	−	0.134056i
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	−0.824698	−	0.565573i	$-0.808655\pi$
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	0.902150	+	0.431423i	$0.141988\pi$
$948$	−0.757798	−	4.85716i	−0.0246121	−	0.157753i
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$	18.5996			0.603451
$951$	−34.7491	−	13.4311i	−1.12682	−	0.435534i
$952$		0			0
$953$	−48.9412			−1.58536			−0.792680	−	0.609638i	$-0.791315\pi$
$953$	−48.9412			−1.58536			−0.792680	+	0.609638i	$0.791315\pi$
$954$	−34.2054	−	31.0861i	−1.10744	−	1.00645i
$955$	−12.1028	+	20.9627i	−0.391638	+	0.678337i
$956$	−40.8955			−1.32266
$957$	−1.90489	+	1.53527i	−0.0615762	+	0.0496283i
$958$	35.5773	−	61.6217i	1.14945	−	1.99091i
$959$		0			0
$960$	8.52261	+	54.6263i	0.275066	+	1.76306i
$961$	10.1386	−	17.5605i	0.327050	−	0.566468i
$962$	19.0275	−	32.9565i	0.613470	−	1.06256i
$963$	38.8702	+	35.3256i	1.25258	+	1.13835i
$964$	−42.8309	−	74.1854i	−1.37949	−	2.38935i
$965$	27.4340	+	47.5171i	0.883132	+	1.52963i
$966$		0			0
$967$	−2.95856	+	5.12438i	−0.0951409	+	0.164789i	−0.909667	−	0.415337i	$-0.863664\pi$
$967$	−2.95856	+	5.12438i	−0.0951409	+	0.164789i	0.814526	+	0.580126i	$0.196997\pi$
$968$	37.1361			1.19360
$969$	1.95027	+	12.5004i	0.0626516	+	0.401570i
$970$	57.7458			1.85410
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	−0.999200	+	0.0399914i	$0.987267\pi$
$972$	−15.5587	+	55.4929i	−0.499044	+	1.77994i
$973$		0			0
$974$	26.7933	+	46.4074i	0.858513	+	1.48699i
$975$	−8.36401	−	3.23284i	−0.267863	−	0.103534i
$976$	0.636580	+	1.10259i	0.0203764	+	0.0352930i
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	0.623401	−	0.781902i	$-0.285750\pi$
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	−0.988848	+	0.148930i	$0.952417\pi$
$978$	0.247622	+	1.58716i	0.00791809	+	0.0507516i
$979$	4.33670	+	7.51139i	0.138602	+	0.240065i
$980$		0			0
$981$	9.94067	−	45.7270i	0.317381	−	1.45995i
$982$	−41.8232	−	72.4400i	−1.33463	−	2.31165i
$983$	31.2703			0.997367			0.498684	−	0.866784i	$-0.333817\pi$
$983$	31.2703			0.997367			0.498684	+	0.866784i	$0.333817\pi$
$984$	11.8361	+	4.57488i	0.377322	+	0.145842i
$985$	17.5145			0.558059
$986$	−4.12221	+	7.13988i	−0.131278	+	0.227380i
$987$		0			0
$988$	−5.97988	−	10.3574i	−0.190245	−	0.329514i
$989$	−5.70679	−	9.88444i	−0.181465	−	0.314307i
$990$	6.01457	−	27.6670i	0.191156	−	0.879314i
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	−0.804927	−	0.593374i	$-0.797796\pi$
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	0.916340	+	0.400400i	$0.131129\pi$
$992$	4.37581	−	7.57912i	0.138932	−	0.240637i
$993$	31.4681	+	12.1630i	0.998611	+	0.385981i
$994$		0			0
$995$	−21.0429	+	36.4474i	−0.667105	+	1.15546i
$996$	−11.7514	−	4.54211i	−0.372356	−	0.143922i
$997$	21.2878			0.674191			0.337095	−	0.941470i	$-0.390555\pi$
$997$	21.2878			0.674191			0.337095	+	0.941470i	$0.390555\pi$
$998$	−10.6636	+	18.4698i	−0.337549	+	0.584653i
$999$	−31.1056	+	47.1792i	−0.984139	+	1.49268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.f.67.5		10
3.2	odd	2		1323.2.g.f.361.1		10
7.2	even	3		441.2.h.f.373.1		10
7.3	odd	6		441.2.f.e.148.5		10
7.4	even	3		441.2.f.f.148.5		10
7.5	odd	6		63.2.h.b.58.1	yes	10
7.6	odd	2		63.2.g.b.4.5	✓	10
9.2	odd	6		1323.2.h.f.802.5		10
9.7	even	3		441.2.h.f.214.1		10
21.2	odd	6		1323.2.h.f.226.5		10
21.5	even	6		189.2.h.b.37.5		10
21.11	odd	6		1323.2.f.f.442.1		10
21.17	even	6		1323.2.f.e.442.1		10
21.20	even	2		189.2.g.b.172.1		10
28.19	even	6		1008.2.q.i.625.4		10
28.27	even	2		1008.2.t.i.193.3		10
63.2	odd	6		1323.2.g.f.667.1		10
63.4	even	3		3969.2.a.ba.1.1		5
63.5	even	6		567.2.e.e.163.1		10
63.11	odd	6		1323.2.f.f.883.1		10
63.13	odd	6		567.2.e.f.487.5		10
63.16	even	3	inner	441.2.g.f.79.5		10
63.20	even	6		189.2.h.b.46.5		10
63.25	even	3		441.2.f.f.295.5		10
63.31	odd	6		3969.2.a.z.1.1		5
63.32	odd	6		3969.2.a.bb.1.5		5
63.34	odd	6		63.2.h.b.25.1	yes	10
63.38	even	6		1323.2.f.e.883.1		10
63.40	odd	6		567.2.e.f.163.5		10
63.41	even	6		567.2.e.e.487.1		10
63.47	even	6		189.2.g.b.100.1		10
63.52	odd	6		441.2.f.e.295.5		10
63.59	even	6		3969.2.a.bc.1.5		5
63.61	odd	6		63.2.g.b.16.5	yes	10
84.47	odd	6		3024.2.q.i.2305.2		10
84.83	odd	2		3024.2.t.i.1873.4		10
252.47	odd	6		3024.2.t.i.289.4		10
252.83	odd	6		3024.2.q.i.2881.2		10
252.187	even	6		1008.2.t.i.961.3		10
252.223	even	6		1008.2.q.i.529.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	7.6	odd	2
63.2.g.b.16.5	yes	10	63.61	odd	6
63.2.h.b.25.1	yes	10	63.34	odd	6
63.2.h.b.58.1	yes	10	7.5	odd	6
189.2.g.b.100.1		10	63.47	even	6
189.2.g.b.172.1		10	21.20	even	2
189.2.h.b.37.5		10	21.5	even	6
189.2.h.b.46.5		10	63.20	even	6
441.2.f.e.148.5		10	7.3	odd	6
441.2.f.e.295.5		10	63.52	odd	6
441.2.f.f.148.5		10	7.4	even	3
441.2.f.f.295.5		10	63.25	even	3
441.2.g.f.67.5		10	1.1	even	1	trivial
441.2.g.f.79.5		10	63.16	even	3	inner
441.2.h.f.214.1		10	9.7	even	3
441.2.h.f.373.1		10	7.2	even	3
567.2.e.e.163.1		10	63.5	even	6
567.2.e.e.487.1		10	63.41	even	6
567.2.e.f.163.5		10	63.40	odd	6
567.2.e.f.487.5		10	63.13	odd	6
1008.2.q.i.529.4		10	252.223	even	6
1008.2.q.i.625.4		10	28.19	even	6
1008.2.t.i.193.3		10	28.27	even	2
1008.2.t.i.961.3		10	252.187	even	6
1323.2.f.e.442.1		10	21.17	even	6
1323.2.f.e.883.1		10	63.38	even	6
1323.2.f.f.442.1		10	21.11	odd	6
1323.2.f.f.883.1		10	63.11	odd	6
1323.2.g.f.361.1		10	3.2	odd	2
1323.2.g.f.667.1		10	63.2	odd	6
1323.2.h.f.226.5		10	21.2	odd	6
1323.2.h.f.802.5		10	9.2	odd	6
3024.2.q.i.2305.2		10	84.47	odd	6
3024.2.q.i.2881.2		10	252.83	odd	6
3024.2.t.i.289.4		10	252.47	odd	6
3024.2.t.i.1873.4		10	84.83	odd	2
3969.2.a.z.1.1		5	63.31	odd	6
3969.2.a.ba.1.1		5	63.4	even	3
3969.2.a.bb.1.5		5	63.32	odd	6
3969.2.a.bc.1.5		5	63.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19343 - 2.06709i) q^{2} +(-0.266999 - 1.71135i) q^{3} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 + 0.913855i) q^{9} +O(q^{10})\)	\(q+(1.19343 - 2.06709i) q^{2} +(-0.266999 - 1.71135i) q^{3} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(-2.85742 + 0.913855i) q^{9} +(3.48586 - 6.03769i) q^{10} -1.35371 q^{11} +(-4.98586 + 4.01843i) q^{12} +(0.733001 - 1.26960i) q^{13} +(-0.779867 - 4.99862i) q^{15} +(-1.13729 + 1.96984i) q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.52113 + 6.99717i) q^{18} +(1.10329 + 1.91096i) q^{19} +(-5.39943 - 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} +2.62830 q^{23} +(1.08157 + 6.93243i) q^{24} +3.53146 q^{25} +(-1.74958 - 3.03036i) q^{26} +(2.32685 + 4.64605i) q^{27} +(0.521720 + 0.903646i) q^{29} +(-11.2633 - 4.35347i) q^{30} +(1.63729 + 2.83587i) q^{31} +(-1.33629 - 2.31453i) q^{32} +(0.361440 + 2.31668i) q^{33} +(3.95060 + 6.84263i) q^{34} +(8.20815 + 7.45963i) q^{36} +(5.43773 + 9.41842i) q^{37} +5.26683 q^{38} +(-2.36843 - 0.915440i) q^{39} -11.8320 q^{40} +(0.904289 - 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(2.50244 + 4.33435i) q^{44} +(-8.34615 + 2.66925i) q^{45} +(3.13670 - 5.43292i) q^{46} +(1.98957 - 3.44604i) q^{47} +(3.67474 + 1.42035i) q^{48} +(4.21456 - 7.29984i) q^{50} +(5.34798 + 2.06709i) q^{51} -5.42002 q^{52} +(-3.22743 + 5.59008i) q^{53} +(12.3807 + 0.734945i) q^{54} -3.95402 q^{55} +(2.97574 - 2.39834i) q^{57} +2.49056 q^{58} +(-6.10700 - 10.5776i) q^{59} +(-14.5630 + 11.7373i) q^{60} +(0.279867 - 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 - 3.70832i) q^{65} +(5.22013 + 2.01767i) q^{66} +(-6.40588 - 11.0953i) q^{67} +12.2386 q^{68} +(-0.701751 - 4.49793i) q^{69} +12.9177 q^{71} +(11.5750 - 3.70190i) q^{72} +(-5.22772 + 9.05467i) q^{73} +25.9583 q^{74} +(-0.942894 - 6.04355i) q^{75} +(4.07903 - 7.06509i) q^{76} +(-4.71886 + 3.80324i) q^{78} +(-0.383838 + 0.664827i) q^{79} +(-3.32187 + 5.75365i) q^{80} +(7.32974 - 5.22254i) q^{81} +(-2.15842 - 3.73849i) q^{82} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} -10.3652 q^{86} +(1.40715 - 1.13412i) q^{87} +5.48371 q^{88} +(-3.20356 - 5.54872i) q^{89} +(-4.44301 + 20.4378i) q^{90} +(-4.85859 - 8.41533i) q^{92} +(4.41601 - 3.55915i) q^{93} +(-4.74884 - 8.22524i) q^{94} +(3.22257 + 5.58166i) q^{95} +(-3.60418 + 2.90484i) q^{96} +(4.14143 + 7.17316i) q^{97} +(3.86814 - 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

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