LMFDB - Embedded newform 441.2.g.f.79.5

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			79.5
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.f.67.5

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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	0.886585	+	0.462565i	$0.153071\pi$
$2$	1.19343	+	2.06709i	0.843886	+	1.46165i	−0.0426999	+	0.999088i	$0.513596\pi$
$3$	−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	0.949589	−	0.313497i	$-0.101501\pi$
$13$	0.733001	+	1.26960i	0.203298	+	0.352123i	−0.746291	+	0.665620i	$0.768167\pi$
$14$		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	0.592469	−	0.805593i	$-0.298153\pi$
$17$	−1.65514	−	2.86678i	−0.401430	−	0.695297i	−0.993899	+	0.110297i	$0.964820\pi$
$18$	−1.52113	−	6.99717i	−0.358533	−	1.64925i
$19$	1.10329	−	1.91096i	0.253113	−	0.438404i	−0.711268	−	0.702921i	$-0.751879\pi$
$19$	1.10329	−	1.91096i	0.253113	−	0.438404i	0.964381	+	0.264516i	$0.0852123\pi$
$20$	−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	−0.813511	−	0.581549i	$-0.802447\pi$
$29$	0.521720	−	0.903646i	0.0968810	−	0.167803i	0.910392	+	0.413747i	$0.135780\pi$
$30$	−11.2633	+	4.35347i	−2.05639	+	0.794831i
$31$	1.63729	−	2.83587i	0.294066	−	0.509337i	−0.680701	−	0.732561i	$-0.738325\pi$
$31$	1.63729	−	2.83587i	0.294066	−	0.509337i	0.974767	+	0.223224i	$0.0716581\pi$
$32$	−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	0.0588664	−	0.998266i	$-0.481251\pi$
$37$	5.43773	−	9.41842i	0.893957	−	1.54838i	0.835090	−	0.550113i	$-0.185415\pi$
$38$	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	0.927959	−	0.372683i	$-0.121562\pi$
$41$	0.904289	+	1.56627i	0.141226	+	0.244611i	−0.786732	+	0.617294i	$0.788229\pi$
$42$		0			0
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	−0.982731	−	0.185038i	$-0.940759\pi$
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	0.651613	+	0.758551i	$0.274093\pi$
$44$	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	0.973859	−	0.227154i	$-0.0729419\pi$
$47$	1.98957	+	3.44604i	0.290209	+	0.502656i	−0.683650	+	0.729810i	$0.739609\pi$
$48$	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	0.554612	−	0.832109i	$-0.312867\pi$
$53$	−3.22743	−	5.59008i	−0.443322	−	0.767856i	−0.997934	+	0.0642533i	$0.979533\pi$
$54$	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	0.127735	+	0.991808i	$0.459229\pi$
$59$	−6.10700	+	10.5776i	−0.795064	+	1.37709i	−0.922799	+	0.385283i	$0.874104\pi$
$60$	−14.5630	−	11.7373i	−1.88008	−	1.51528i
$61$	0.279867	+	0.484744i	0.0358333	+	0.0620651i	0.883386	−	0.468646i	$-0.155258\pi$
$61$	0.279867	+	0.484744i	0.0358333	+	0.0620651i	−0.847553	+	0.530711i	$0.821925\pi$
$62$	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	0.147817	+	0.989015i	$0.452775\pi$
$67$	−6.40588	+	11.0953i	−0.782603	+	1.35551i	−0.930420	+	0.366494i	$0.880558\pi$
$68$	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	−0.990927	−	0.134401i	$-0.957089\pi$
$73$	−5.22772	−	9.05467i	−0.611858	−	1.05977i	0.379069	−	0.925368i	$-0.376244\pi$
$74$	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	0.843625	−	0.536933i	$-0.180417\pi$
$79$	−0.383838	−	0.664827i	−0.0431852	−	0.0747989i	−0.886810	+	0.462134i	$0.847084\pi$
$80$	−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	−0.806974	−	0.590587i	$-0.798896\pi$
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	0.914950	+	0.403567i	$0.132230\pi$
$84$		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	−0.984353	−	0.176208i	$-0.943617\pi$
$89$	−3.20356	+	5.54872i	−0.339576	+	0.588163i	0.644777	+	0.764371i	$0.276950\pi$
$90$	−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	−0.575490	−	0.817809i	$-0.695189\pi$
$97$	4.14143	−	7.17316i	0.420498	−	0.728324i	0.995988	+	0.0894847i	$0.0285220\pi$
$98$		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	0.0382175	+	0.999269i	$0.487832\pi$
$107$	−8.75403	+	15.1624i	−0.846284	+	1.46581i	−0.884501	+	0.466537i	$0.845501\pi$
$108$	10.5745	+	16.0387i	1.01753	+	1.54333i
$109$	−7.79917	−	13.5086i	−0.747025	−	1.29388i	−0.949243	−	0.314544i	$-0.898148\pi$
$109$	−7.79917	−	13.5086i	−0.747025	−	1.29388i	0.202218	−	0.979341i	$-0.435185\pi$
$110$	−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	0.823563	−	0.567224i	$-0.191983\pi$
$113$	−0.844555	−	1.46281i	−0.0794491	−	0.137610i	−0.903012	+	0.429615i	$0.858649\pi$
$114$	−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	−0.993331	−	0.115300i	$-0.963217\pi$
$139$	−7.03285	−	12.1812i	−0.596518	−	1.03320i	0.396812	−	0.917900i	$-0.370116\pi$
$140$		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	−0.800755	−	0.598993i	$-0.795568\pi$
$157$	1.48312	−	2.56883i	0.118365	−	0.205015i	0.919120	+	0.393978i	$0.128901\pi$
$158$	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	−0.873534	−	0.486764i	$-0.838177\pi$
$163$	−0.194278	+	0.336499i	−0.0152170	+	0.0263566i	0.858317	+	0.513120i	$0.171511\pi$
$164$	−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	0.689606	−	0.724185i	$-0.257784\pi$
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	−0.971965	+	0.235124i	$0.924450\pi$
$168$		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	0.778598	−	0.627522i	$-0.215931\pi$
$173$	−2.02754	−	3.51181i	−0.154151	−	0.266998i	−0.932750	+	0.360525i	$0.882598\pi$
$174$	−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	0.993174	−	0.116639i	$-0.0372121\pi$
$179$	5.29243	+	9.16675i	0.395575	+	0.685155i	−0.597600	+	0.801795i	$0.703879\pi$
$180$	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	0.676276	−	0.736648i	$-0.263593\pi$
$191$	−4.14357	−	7.17688i	−0.299818	−	0.519301i	−0.976094	+	0.217348i	$0.930259\pi$
$192$	2.91784	−	18.7021i	0.210577	−	1.34971i
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	−0.300070	−	0.953917i	$-0.597010\pi$
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	0.976152	−	0.217090i	$-0.0696566\pi$
$194$	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	−0.999923	−	0.0124022i	$-0.996052\pi$
$199$	−7.20434	−	12.4783i	−0.510702	−	0.884562i	0.489221	−	0.872160i	$-0.337281\pi$
$200$	−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	0.522963	−	0.852356i	$-0.324827\pi$
$211$	−6.92418	−	11.9930i	−0.476680	−	0.825634i	−0.999643	+	0.0267212i	$0.991493\pi$
$212$	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	−0.933617	−	0.358273i	$-0.883366\pi$
$223$	−2.33756	+	4.04878i	−0.156535	+	0.271126i	0.777082	+	0.629399i	$0.216699\pi$
$224$		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	−0.998517	−	0.0544448i	$-0.982661\pi$
$233$	−6.90113	+	11.9531i	−0.452108	+	0.783074i	0.546409	+	0.837518i	$0.315994\pi$
$234$	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	0.987585	−	0.157087i	$-0.0502104\pi$
$239$	5.53069	+	9.57944i	0.357751	+	0.619642i	−0.629834	+	0.776730i	$0.716877\pi$
$240$	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	0.968706	−	0.248212i	$-0.0798430\pi$
$269$	4.41840	+	7.65290i	0.269395	+	0.466605i	−0.699311	+	0.714818i	$0.746510\pi$
$270$	36.1625	−	2.14668i	2.20078	−	0.130643i
$271$	9.16955	−	15.8821i	0.557010	−	0.964770i	−0.440734	−	0.897638i	$-0.645282\pi$
$271$	9.16955	−	15.8821i	0.557010	−	0.964770i	0.997744	−	0.0671321i	$-0.0213849\pi$
$272$	−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	−0.890351	−	0.455274i	$-0.849541\pi$
$281$	−0.853180	+	1.47775i	−0.0508964	+	0.0881552i	0.839455	+	0.543430i	$0.182875\pi$
$282$	−12.8083	−	10.3231i	−0.762724	−	0.614729i
$283$	−6.24415	+	10.8152i	−0.371176	+	0.642896i	−0.989747	−	0.142833i	$-0.954379\pi$
$283$	−6.24415	+	10.8152i	−0.371176	+	0.642896i	0.618571	+	0.785729i	$0.287712\pi$
$284$	−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	0.931967	−	0.362543i	$-0.118091\pi$
$293$	2.60202	+	4.50684i	0.152012	+	0.263292i	−0.779955	+	0.625835i	$0.784758\pi$
$294$		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	−0.116876	+	0.993146i	$0.537288\pi$
$311$	−16.1984	+	28.0565i	−0.918528	+	1.59094i	−0.801652	+	0.597791i	$0.796045\pi$
$312$	9.59418	−	3.70832i	0.543163	−	0.209942i
$313$	0.759535	+	1.31555i	0.0429315	+	0.0743595i	0.886693	−	0.462359i	$-0.152997\pi$
$313$	0.759535	+	1.31555i	0.0429315	+	0.0743595i	−0.843761	+	0.536719i	$0.819664\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	10.7544	+	18.6272i	0.604029	+	1.04621i	0.992204	+	0.124623i	$0.0397723\pi$
$317$	10.7544	+	18.6272i	0.604029	+	1.04621i	−0.388175	+	0.921586i	$0.626894\pi$
$318$	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	−0.999149	−	0.0412580i	$-0.986863\pi$
$331$	−9.73902	−	16.8685i	−0.535305	−	0.927175i	0.463844	−	0.885917i	$-0.346470\pi$
$332$	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	0.967316	−	0.253575i	$-0.0816063\pi$
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	−0.703260	+	0.710933i	$0.748273\pi$
$338$	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	−0.891935	−	0.452164i	$-0.850652\pi$
$347$	−1.01302	+	1.75460i	−0.0543817	+	0.0941919i	0.837553	+	0.546356i	$0.183985\pi$
$348$	−6.23246	+	2.40896i	−0.334095	+	0.129134i
$349$	−8.14577	+	14.1089i	−0.436033	+	0.755231i	−0.997379	−	0.0723497i	$-0.976950\pi$
$349$	−8.14577	+	14.1089i	−0.436033	+	0.755231i	0.561346	+	0.827581i	$0.310284\pi$
$350$		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	−0.824215	−	0.566277i	$-0.808383\pi$
$359$	1.48363	−	2.56972i	0.0783030	−	0.135625i	0.902518	+	0.430652i	$0.141717\pi$
$360$	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	0.168082	+	0.985773i	$0.446243\pi$
$397$	−15.3354	+	26.5618i	−0.769664	+	1.33310i	−0.937745	+	0.347323i	$0.887091\pi$
$398$	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	−0.998491	−	0.0549104i	$-0.982513\pi$
$409$	−9.13490	+	15.8221i	−0.451692	+	0.782353i	0.546799	+	0.837264i	$0.315846\pi$
$410$	−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	−0.998366	−	0.0571410i	$-0.981802\pi$
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	0.449698	−	0.893181i	$-0.351532\pi$
$420$		0			0
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	−0.492232	−	0.870464i	$-0.663819\pi$
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	0.999960	−	0.00894684i	$-0.00284791\pi$
$422$	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	0.512370	−	0.858765i	$-0.328768\pi$
$431$	−10.1213	−	17.5307i	−0.487527	−	0.844422i	−0.999897	+	0.0143427i	$0.995434\pi$
$432$	−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	−0.884191	−	0.467126i	$-0.845289\pi$
$439$	−17.7390	−	30.7249i	−0.846639	−	1.46642i	0.0375520	−	0.999295i	$-0.488044\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	9.60313	+	16.6331i	0.456258	+	0.790263i	0.998760	−	0.0497923i	$-0.0158559\pi$
$443$	9.60313	+	16.6331i	0.456258	+	0.790263i	−0.542501	+	0.840055i	$0.682523\pi$
$444$	−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	0.955912	−	0.293653i	$-0.0948711\pi$
$457$	4.78098	+	8.28090i	0.223645	+	0.387364i	−0.732267	+	0.681017i	$0.761538\pi$
$458$	−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	0.491416	+	0.870925i	$0.336480\pi$
$461$	−10.9187	+	18.9118i	−0.508536	+	0.880809i	−0.999951	+	0.00988416i	$0.996854\pi$
$462$		0			0
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	0.991631	+	0.129102i	$0.0412094\pi$
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	−0.384010	+	0.923329i	$0.625457\pi$
$464$	−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	−0.105049	−	0.994467i	$-0.533500\pi$
$467$	17.4764	−	30.2699i	0.808709	−	1.40073i	0.913758	−	0.406258i	$-0.133167\pi$
$468$	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	−0.999950	−	0.0100365i	$-0.996805\pi$
$487$	−11.2253	−	19.4428i	−0.508667	−	0.881037i	0.491283	−	0.871000i	$-0.336528\pi$
$488$	−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	0.925493	+	0.378765i	$0.123651\pi$
$491$	17.5222	+	30.3494i	0.790767	+	1.36965i	−0.134726	+	0.990883i	$0.543016\pi$
$492$	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	0.758141	−	0.652090i	$-0.226108\pi$
$521$	−4.23768	−	7.33988i	−0.185656	−	0.321566i	−0.943797	+	0.330524i	$0.892774\pi$
$522$	−7.11657	−	2.27601i	−0.311484	−	0.0996181i
$523$	−16.7236	+	28.9662i	−0.731273	+	1.26660i	0.225066	+	0.974344i	$0.427740\pi$
$523$	−16.7236	+	28.9662i	−0.731273	+	1.26660i	−0.956339	+	0.292259i	$0.905593\pi$
$524$	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	−0.992778	−	0.119962i	$-0.961723\pi$
$541$	−9.12929	+	15.8124i	−0.392499	+	0.679828i	0.600280	+	0.799790i	$0.295056\pi$
$542$	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	−0.921105	−	0.389315i	$-0.872712\pi$
$547$	−2.88599	+	4.99869i	−0.123396	+	0.213728i	0.797709	+	0.603043i	$0.206045\pi$
$548$	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	0.965883	+	0.258977i	$0.0833855\pi$
$557$	16.6911	+	28.9098i	0.707223	+	1.22495i	−0.258661	+	0.965968i	$0.583281\pi$
$558$	−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	−0.842013	−	0.539457i	$-0.818630\pi$
$563$	1.09566	−	1.89773i	0.0461764	−	0.0799799i	0.888190	+	0.459477i	$0.151963\pi$
$564$	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	0.595507	−	0.803350i	$-0.296951\pi$
$569$	−9.49302	−	16.4424i	−0.397968	−	0.689301i	−0.993475	+	0.114049i	$0.963618\pi$
$570$	−4.10743	+	26.3269i	−0.172041	+	1.10271i
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	−0.543825	−	0.839198i	$-0.683025\pi$
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	0.998680	+	0.0513674i	$0.0163580\pi$
$572$	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	0.984701	+	0.174253i	$0.0557511\pi$
$577$	15.4516	+	26.7629i	0.643258	+	1.11416i	−0.341443	+	0.939903i	$0.610916\pi$
$578$	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	−0.611886	−	0.790946i	$-0.709589\pi$
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	0.990922	+	0.134436i	$0.0429222\pi$
$588$		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	0.426698	+	0.904394i	$0.359677\pi$
$593$	−13.8775	+	24.0365i	−0.569880	+	0.987061i	−0.996577	+	0.0826662i	$0.973656\pi$
$594$	−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	−0.870111	−	0.492856i	$-0.835953\pi$
$599$	−0.201412	+	0.348855i	−0.00822945	+	0.0142538i	0.861881	+	0.507110i	$0.169286\pi$
$600$	3.81953	−	24.4816i	0.155932	−	0.999456i
$601$	−12.3733	+	21.4312i	−0.504717	+	0.874196i	0.495268	+	0.868740i	$0.335070\pi$
$601$	−12.3733	+	21.4312i	−0.504717	+	0.874196i	−0.999985	+	0.00545577i	$0.998263\pi$
$602$		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	0.995065	−	0.0992261i	$-0.0316367\pi$
$613$	10.1907	+	17.6509i	0.411600	+	0.712912i	−0.583465	+	0.812138i	$0.698303\pi$
$614$	−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	−0.887630	−	0.460558i	$-0.847650\pi$
$617$	−20.9315	−	36.2544i	−0.842669	−	1.45955i	0.0449604	−	0.998989i	$-0.485684\pi$
$618$	−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	0.927524	+	0.373765i	$0.121933\pi$
$643$	19.9678	+	34.5852i	0.787452	+	1.36391i	−0.140072	+	0.990141i	$0.544733\pi$
$644$		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	0.856142	−	0.516741i	$-0.172855\pi$
$647$	−0.494477	−	0.856459i	−0.0194399	−	0.0336709i	−0.875582	+	0.483070i	$0.839522\pi$
$648$	−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	0.201220	+	0.979546i	$0.435509\pi$
$659$	−19.1943	+	33.2454i	−0.747702	+	1.29506i	−0.948922	+	0.315512i	$0.897824\pi$
$660$	19.7142	+	15.8890i	0.767374	+	0.618477i
$661$	16.9629	−	29.3806i	0.659780	−	1.14277i	−0.320892	−	0.947116i	$-0.603983\pi$
$661$	16.9629	−	29.3806i	0.659780	−	1.14277i	0.980672	−	0.195657i	$-0.0626839\pi$
$662$	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	0.368626	+	0.929578i	$0.379828\pi$
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	−0.989351	+	0.145549i	$0.953505\pi$
$674$	−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	−0.957043	−	0.289946i	$-0.906363\pi$
$677$	−18.9842	−	32.8816i	−0.729622	−	1.26374i	0.227421	−	0.973797i	$-0.426971\pi$
$678$	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	0.973942	−	0.226796i	$-0.0728251\pi$
$683$	7.59357	+	13.1525i	0.290560	+	0.503265i	−0.683382	+	0.730061i	$0.739492\pi$
$684$	−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	0.890487	−	0.455009i	$-0.150364\pi$
$691$	1.34574	+	2.33089i	0.0511943	+	0.0886711i	−0.839293	+	0.543680i	$0.817031\pi$
$692$	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	0.937278	+	0.348582i	$0.113337\pi$
$709$	20.5167	+	35.5359i	0.770520	+	1.33458i	−0.166759	+	0.985998i	$0.553330\pi$
$710$	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	−0.992439	−	0.122741i	$-0.960832\pi$
$719$	−10.4555	+	18.1094i	−0.389923	+	0.675366i	0.602516	+	0.798107i	$0.294165\pi$
$720$	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	−0.889493	−	0.456949i	$-0.848942\pi$
$727$	−1.32165	+	2.28917i	−0.0490173	+	0.0849005i	0.840476	+	0.541849i	$0.182276\pi$
$728$		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	0.684495	−	0.729017i	$-0.260023\pi$
$739$	−7.85905	−	13.6123i	−0.289100	−	0.500736i	−0.973595	+	0.228282i	$0.926689\pi$
$740$	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	0.992048	−	0.125861i	$-0.0401692\pi$
$743$	10.5496	+	18.2724i	0.387026	+	0.670348i	−0.605022	+	0.796208i	$0.706836\pi$
$744$	−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	0.864069	−	0.503373i	$-0.167908\pi$
$769$	−0.108129	−	0.187285i	−0.00389924	−	0.00675368i	−0.867968	+	0.496619i	$0.834575\pi$
$770$		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	−0.975980	−	0.217861i	$-0.930092\pi$
$773$	−18.8132	−	32.5854i	−0.676663	−	1.17202i	0.299316	−	0.954154i	$-0.403241\pi$
$774$	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	−0.449139	−	0.893462i	$-0.648269\pi$
$787$	15.4067	−	26.6853i	0.549191	−	0.951226i	0.998330	−	0.0577648i	$-0.0183973\pi$
$788$	−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	0.986119	+	0.166040i	$0.0530981\pi$
$797$	17.9792	+	31.1408i	0.636855	+	1.10306i	−0.349264	+	0.937024i	$0.613569\pi$
$798$		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	−0.973455	−	0.228880i	$-0.926494\pi$
$809$	−19.4818	−	33.7435i	−0.684943	−	1.18636i	0.288511	−	0.957477i	$-0.406840\pi$
$810$	−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	−0.958712	−	0.284378i	$-0.908213\pi$
$821$	−20.7917	−	36.0123i	−0.725635	−	1.25684i	0.233077	−	0.972458i	$-0.425121\pi$
$822$	28.9035	−	11.1717i	1.00813	−	0.389659i
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	−0.930284	−	0.366841i	$-0.880439\pi$
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	0.782835	+	0.622229i	$0.213773\pi$
$824$	−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	0.973533	−	0.228547i	$-0.0733973\pi$
$829$	8.31637	+	14.4044i	0.288839	+	0.500284i	−0.684694	+	0.728831i	$0.740064\pi$
$830$	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	0.488945	+	0.872314i	$0.337382\pi$
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	−0.999919	+	0.0127182i	$0.995952\pi$
$840$		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	−0.484124	−	0.875000i	$-0.660861\pi$
$853$	15.0619	−	26.0880i	0.515710	−	0.893236i	0.999834	−	0.0182366i	$-0.00580520\pi$
$854$		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	−0.862368	−	0.506282i	$-0.831019\pi$
$863$	0.213559	−	0.369895i	0.00726963	−	0.0125914i	0.869637	+	0.493691i	$0.164353\pi$
$864$	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	−0.613539	−	0.789665i	$-0.710254\pi$
$911$	11.3819	−	19.7141i	0.377101	−	0.653157i	0.990639	+	0.136508i	$0.0435878\pi$
$912$	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	−0.375083	−	0.926991i	$-0.622386\pi$
$919$	18.6515	−	32.3054i	0.615257	−	1.06566i	0.990339	−	0.138664i	$-0.0442809\pi$
$920$	−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	0.908759	−	0.417322i	$-0.137031\pi$
$929$	2.83363	+	4.90799i	0.0929683	+	0.161026i	−0.815791	+	0.578347i	$0.803698\pi$
$930$	−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	−0.649768	−	0.760132i	$-0.725134\pi$
$941$	10.2276	−	17.7147i	0.333410	−	0.577483i	0.983178	+	0.182650i	$0.0584674\pi$
$942$	−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	0.902150	−	0.431423i	$-0.141988\pi$
$947$	2.38343	+	4.12823i	0.0774512	+	0.134149i	−0.824698	+	0.565573i	$0.808655\pi$
$948$	−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	0.814526	−	0.580126i	$-0.196997\pi$
$967$	−2.95856	−	5.12438i	−0.0951409	−	0.164789i	−0.909667	+	0.415337i	$0.863664\pi$
$968$	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	−0.999200	−	0.0399914i	$-0.987267\pi$
$971$	−14.4888	+	25.0953i	−0.464966	+	0.805345i	0.534234	+	0.845337i	$0.320600\pi$
$972$	−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	−0.988848	−	0.148930i	$-0.952417\pi$
$977$	−11.4228	+	19.7848i	−0.365447	+	0.632972i	0.623401	+	0.781902i	$0.285750\pi$
$978$	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	0.916340	−	0.400400i	$-0.131129\pi$
$991$	3.50732	+	6.07485i	0.111414	+	0.192974i	−0.804927	+	0.593374i	$0.797796\pi$
$992$	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.79.5		10
3.2	odd	2		1323.2.g.f.667.1		10
7.2	even	3		441.2.f.f.295.5		10
7.3	odd	6		63.2.h.b.25.1	yes	10
7.4	even	3		441.2.h.f.214.1		10
7.5	odd	6		441.2.f.e.295.5		10
7.6	odd	2		63.2.g.b.16.5	yes	10
9.4	even	3		441.2.h.f.373.1		10
9.5	odd	6		1323.2.h.f.226.5		10
21.2	odd	6		1323.2.f.f.883.1		10
21.5	even	6		1323.2.f.e.883.1		10
21.11	odd	6		1323.2.h.f.802.5		10
21.17	even	6		189.2.h.b.46.5		10
21.20	even	2		189.2.g.b.100.1		10
28.3	even	6		1008.2.q.i.529.4		10
28.27	even	2		1008.2.t.i.961.3		10
63.2	odd	6		3969.2.a.bb.1.5		5
63.4	even	3	inner	441.2.g.f.67.5		10
63.5	even	6		1323.2.f.e.442.1		10
63.13	odd	6		63.2.h.b.58.1	yes	10
63.16	even	3		3969.2.a.ba.1.1		5
63.20	even	6		567.2.e.e.163.1		10
63.23	odd	6		1323.2.f.f.442.1		10
63.31	odd	6		63.2.g.b.4.5	✓	10
63.32	odd	6		1323.2.g.f.361.1		10
63.34	odd	6		567.2.e.f.163.5		10
63.38	even	6		567.2.e.e.487.1		10
63.40	odd	6		441.2.f.e.148.5		10
63.41	even	6		189.2.h.b.37.5		10
63.47	even	6		3969.2.a.bc.1.5		5
63.52	odd	6		567.2.e.f.487.5		10
63.58	even	3		441.2.f.f.148.5		10
63.59	even	6		189.2.g.b.172.1		10
63.61	odd	6		3969.2.a.z.1.1		5
84.59	odd	6		3024.2.q.i.2881.2		10
84.83	odd	2		3024.2.t.i.289.4		10
252.31	even	6		1008.2.t.i.193.3		10
252.59	odd	6		3024.2.t.i.1873.4		10
252.139	even	6		1008.2.q.i.625.4		10
252.167	odd	6		3024.2.q.i.2305.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	63.31	odd	6
63.2.g.b.16.5	yes	10	7.6	odd	2
63.2.h.b.25.1	yes	10	7.3	odd	6
63.2.h.b.58.1	yes	10	63.13	odd	6
189.2.g.b.100.1		10	21.20	even	2
189.2.g.b.172.1		10	63.59	even	6
189.2.h.b.37.5		10	63.41	even	6
189.2.h.b.46.5		10	21.17	even	6
441.2.f.e.148.5		10	63.40	odd	6
441.2.f.e.295.5		10	7.5	odd	6
441.2.f.f.148.5		10	63.58	even	3
441.2.f.f.295.5		10	7.2	even	3
441.2.g.f.67.5		10	63.4	even	3	inner
441.2.g.f.79.5		10	1.1	even	1	trivial
441.2.h.f.214.1		10	7.4	even	3
441.2.h.f.373.1		10	9.4	even	3
567.2.e.e.163.1		10	63.20	even	6
567.2.e.e.487.1		10	63.38	even	6
567.2.e.f.163.5		10	63.34	odd	6
567.2.e.f.487.5		10	63.52	odd	6
1008.2.q.i.529.4		10	28.3	even	6
1008.2.q.i.625.4		10	252.139	even	6
1008.2.t.i.193.3		10	252.31	even	6
1008.2.t.i.961.3		10	28.27	even	2
1323.2.f.e.442.1		10	63.5	even	6
1323.2.f.e.883.1		10	21.5	even	6
1323.2.f.f.442.1		10	63.23	odd	6
1323.2.f.f.883.1		10	21.2	odd	6
1323.2.g.f.361.1		10	63.32	odd	6
1323.2.g.f.667.1		10	3.2	odd	2
1323.2.h.f.226.5		10	9.5	odd	6
1323.2.h.f.802.5		10	21.11	odd	6
3024.2.q.i.2305.2		10	252.167	odd	6
3024.2.q.i.2881.2		10	84.59	odd	6
3024.2.t.i.289.4		10	84.83	odd	2
3024.2.t.i.1873.4		10	252.59	odd	6
3969.2.a.z.1.1		5	63.61	odd	6
3969.2.a.ba.1.1		5	63.16	even	3
3969.2.a.bb.1.5		5	63.2	odd	6
3969.2.a.bc.1.5		5	63.47	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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