LMFDB - Embedded newform 441.2.h.f.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.1
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.f.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38687 q^{2} +(1.61557 - 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 - 2.01767i) q^{9} +O(q^{10})$	\(q-2.38687 q^{2} +(1.61557 - 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 - 2.01767i) q^{9} +(3.48586 - 6.03769i) q^{10} +(0.676857 + 1.17235i) q^{11} +(5.97299 - 2.30867i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +2.27458 q^{16} +(-1.65514 + 2.86678i) q^{17} +(-5.29917 + 4.81592i) q^{18} +(1.10329 + 1.91096i) q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(-1.31415 + 2.27617i) q^{23} +(-6.54444 + 2.52954i) q^{24} +(-1.76573 - 3.05833i) q^{25} +(-1.74958 - 3.03036i) q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(1.86144 - 11.9310i) q^{30} -3.27458 q^{31} +2.67259 q^{32} +(1.82558 + 1.47135i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} +(5.43773 + 9.41842i) q^{37} +(-2.63342 - 4.56121i) q^{38} +(1.97701 + 1.59340i) q^{39} +(5.91601 - 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +(2.50244 + 4.33435i) q^{44} +(1.86144 + 8.56260i) q^{45} +(3.13670 - 5.43292i) q^{46} -3.97914 q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(-0.883838 + 5.66503i) q^{51} +(2.71001 + 4.69388i) q^{52} +(-3.22743 + 5.59008i) q^{53} +(-5.55389 + 11.0895i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +(-1.24528 + 2.15688i) q^{58} +12.2140 q^{59} +(-2.88328 + 18.4806i) q^{60} -0.559734 q^{61} +7.81600 q^{62} -10.9283 q^{64} -4.28200 q^{65} +(-4.35742 - 3.51193i) q^{66} +12.8118 q^{67} +(-6.11928 + 10.5989i) q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(-8.99344 + 8.17331i) q^{72} +(-5.22772 + 9.05467i) q^{73} +(-12.9791 - 22.4805i) q^{74} +(-4.76242 - 3.83835i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +0.767677 q^{79} +(-3.32187 + 5.75365i) q^{80} +(0.857983 - 8.95901i) q^{81} +(-2.15842 - 3.73849i) q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(5.18258 - 8.97649i) q^{86} +(0.278597 - 1.78569i) q^{87} +(-2.74185 - 4.74903i) q^{88} +(-3.20356 - 5.54872i) q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(-5.29031 + 2.04480i) q^{93} +9.49769 q^{94} -6.44514 q^{95} +(4.31776 - 1.66889i) q^{96} +(4.14143 - 7.17316i) q^{97} +(3.86814 + 1.23710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.38687			−1.68777			−0.843886	−	0.536523i	$-0.819737\pi$
$2$	−2.38687			−1.68777			−0.843886	+	0.536523i	$0.819737\pi$
$3$	1.61557	−	0.624446i	0.932750	−	0.360524i
$3$	1.61557	−	0.624446i	0.932750	−	0.360524i
$4$	3.69714			1.84857
$5$	−1.46043	+	2.52954i	−0.653125	+	1.13125i	0.329235	+	0.944248i	$0.393209\pi$
$5$	−1.46043	+	2.52954i	−0.653125	+	1.13125i	−0.982360	+	0.186998i	$0.940124\pi$
$6$	−3.85615	+	1.49047i	−1.57427	+	0.608483i
$7$		0			0
$7$		0			0
$8$	−4.05086			−1.43219
$9$	2.22013	−	2.01767i	0.740044	−	0.672558i
$10$	3.48586	−	6.03769i	1.10233	−	1.90929i
$11$	0.676857	+	1.17235i	0.204080	+	0.353477i	0.949839	−	0.312738i	$-0.101246\pi$
$11$	0.676857	+	1.17235i	0.204080	+	0.353477i	−0.745759	+	0.666216i	$0.767913\pi$
$12$	5.97299	−	2.30867i	1.72425	−	0.666455i
$13$	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
$16$	2.27458			0.568645
$17$	−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	$0.298153\pi$
$18$	−5.29917	+	4.81592i	−1.24903	+	1.13512i
$19$	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
$23$	−1.31415	+	2.27617i	−0.274019	+	0.474614i	−0.969887	−	0.243555i	$-0.921686\pi$
$23$	−1.31415	+	2.27617i	−0.274019	+	0.474614i	0.695868	+	0.718169i	$0.255020\pi$
$24$	−6.54444	+	2.52954i	−1.33588	+	0.516341i
$25$	−1.76573	−	3.05833i	−0.353146	−	0.611666i
$26$	−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	$0.135780\pi$
$30$	1.86144	−	11.9310i	0.339851	−	2.17830i
$31$	−3.27458			−0.588132			−0.294066	−	0.955785i	$-0.595009\pi$
$31$	−3.27458			−0.588132			−0.294066	+	0.955785i	$0.595009\pi$
$32$	2.67259			0.472452
$33$	1.82558	+	1.47135i	0.317793	+	0.256130i
$34$	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	$0.481251\pi$
$38$	−2.63342	−	4.56121i	−0.427197	−	0.739926i
$39$	1.97701	+	1.59340i	0.316575	+	0.255148i
$40$	5.91601	−	10.2468i	0.935403	−	1.62017i
$41$	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
$45$	1.86144	+	8.56260i	0.277487	+	1.27644i
$46$	3.13670	−	5.43292i	0.462481	−	0.801041i
$47$	−3.97914			−0.580417			−0.290209	−	0.956963i	$-0.593725\pi$
$47$	−3.97914			−0.580417			−0.290209	+	0.956963i	$0.593725\pi$
$48$	3.67474	−	1.42035i	0.530404	−	0.205010i
$49$		0			0
$50$	4.21456	+	7.29984i	0.596029	+	1.03235i
$51$	−0.883838	+	5.66503i	−0.123762	+	0.793263i
$52$	2.71001	+	4.69388i	0.375811	+	0.650924i
$53$	−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	$0.312867\pi$
$54$	−5.55389	+	11.0895i	−0.755789	+	1.50909i
$55$	−3.95402			−0.533160
$56$		0			0
$57$	2.97574	+	2.39834i	0.394146	+	0.317668i
$58$	−1.24528	+	2.15688i	−0.163513	+	0.283213i
$59$	12.2140			1.59013			0.795064	−	0.606526i	$-0.207437\pi$
$59$	12.2140			1.59013			0.795064	+	0.606526i	$0.207437\pi$
$60$	−2.88328	+	18.4806i	−0.372230	+	2.38584i
$61$	−0.559734			−0.0716666			−0.0358333	−	0.999358i	$-0.511409\pi$
$61$	−0.559734			−0.0716666			−0.0358333	+	0.999358i	$0.511409\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	−4.28200			−0.531117
$66$	−4.35742	−	3.51193i	−0.536362	−	0.432289i
$67$	12.8118			1.56521			0.782603	−	0.622521i	$-0.213891\pi$
$67$	12.8118			1.56521			0.782603	+	0.622521i	$0.213891\pi$
$68$	−6.11928	+	10.5989i	−0.742072	+	1.28531i
$69$	−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	$0.221984\pi$
$72$	−8.99344	+	8.17331i	−1.05989	+	0.963234i
$73$	−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	$0.957089\pi$
$74$	−12.9791	−	22.4805i	−1.50879	−	2.61331i
$75$	−4.76242	−	3.83835i	−0.549917	−	0.443214i
$76$	4.07903	+	7.06509i	0.467897	+	0.810422i
$77$		0			0
$78$	−4.71886	−	3.80324i	−0.534306	−	0.430632i
$79$	0.767677			0.0863704			0.0431852	−	0.999067i	$-0.486249\pi$
$79$	0.767677			0.0863704			0.0431852	+	0.999067i	$0.486249\pi$
$80$	−3.32187	+	5.75365i	−0.371397	+	0.643278i
$81$	0.857983	−	8.95901i	0.0953314	−	0.995446i
$82$	−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
$86$	5.18258	−	8.97649i	0.558852	−	0.967960i
$87$	0.278597	−	1.78569i	0.0298687	−	0.191446i
$88$	−2.74185	−	4.74903i	−0.292283	−	0.506248i
$89$	−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
$93$	−5.29031	+	2.04480i	−0.548580	+	0.212036i
$94$	9.49769			0.979612
$95$	−6.44514			−0.661258
$96$	4.31776	−	1.66889i	0.440679	−	0.170330i
$97$	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
$101$	−8.11331	−	14.0527i	−0.807305	−	1.39829i	−0.914724	−	0.404079i	$-0.867592\pi$
$101$	−8.11331	−	14.0527i	−0.807305	−	1.39829i	0.107419	−	0.994214i	$-0.465741\pi$
$102$	2.10961	−	13.5217i	0.208882	−	1.33885i
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	−0.915652	−	0.401972i	$-0.868325\pi$
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	0.805944	+	0.591992i	$0.201658\pi$
$104$	−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	$-0.487832\pi$
$108$	8.60270	−	17.1771i	0.827795	−	1.65287i
$109$	−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	$0.898148\pi$
$110$	9.43773			0.899852
$111$	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	$0.858649\pi$
$114$	−7.10270	−	5.72453i	−0.665229	−	0.536151i
$115$	−3.83845	−	6.64839i	−0.357937	−	0.619966i
$116$	1.92887	−	3.34091i	0.179092	−	0.310196i
$117$	4.18899	+	1.33971i	0.387272	+	0.123857i
$118$	−29.1532			−2.68377
$119$		0			0
$120$	3.15913	−	20.2487i	0.288388	−	1.84844i
$121$	4.58373	−	7.93925i	0.416703	−	0.721750i
$122$	1.33601			0.120957
$123$	2.43900	+	1.96575i	0.219917	+	0.177245i
$124$	−12.1066			−1.08720
$125$	−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	$0.556350\pi$
$128$	20.7392			1.83310
$129$	−1.15946	+	7.43166i	−0.102085	+	0.654321i
$130$	10.2206			0.896403
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	−0.725844	−	0.687860i	$-0.758550\pi$
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	0.958626	+	0.284669i	$0.0918837\pi$
$132$	6.74944	+	5.43981i	0.587463	+	0.473475i
$133$		0			0
$134$	−30.5800			−2.64171
$135$	8.35417	+	12.6711i	0.719013	+	1.09056i
$136$	6.70473	−	11.6129i	0.574925	−	0.995800i
$137$	3.74772	+	6.49124i	0.320189	+	0.554584i	0.980527	−	0.196385i	$-0.0629202\pi$
$137$	3.74772	+	6.49124i	0.320189	+	0.554584i	−0.660338	+	0.750969i	$0.729587\pi$
$138$	1.67499	−	10.7360i	0.142584	−	0.913906i
$139$	−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
$142$	−30.8329			−2.58744
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$	5.04987	−	4.58936i	0.420823	−	0.382447i
$145$	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
$149$	−1.08986	+	1.88769i	−0.0892846	+	0.154645i	−0.907209	−	0.420680i	$-0.861791\pi$
$149$	−1.08986	+	1.88769i	−0.0892846	+	0.154645i	0.817924	+	0.575326i	$0.195125\pi$
$150$	11.3673	+	9.16163i	0.928135	+	0.748044i
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	−0.996486	−	0.0837595i	$-0.973307\pi$
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	0.425705	−	0.904862i	$-0.360026\pi$
$152$	−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
$156$	7.30929	+	5.89103i	0.585211	+	0.471660i
$157$	−2.96623			−0.236731			−0.118365	−	0.992970i	$-0.537765\pi$
$157$	−2.96623			−0.236731			−0.118365	+	0.992970i	$0.537765\pi$
$158$	−1.83234			−0.145773
$159$	−1.72344	+	11.0465i	−0.136678	+	0.876046i
$160$	−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	$0.838177\pi$
$164$	3.34329	+	5.79074i	0.261067	+	0.452181i
$165$	−6.38800	+	2.46907i	−0.497305	+	0.192217i
$166$	−2.34798	+	4.06682i	−0.182239	+	0.315646i
$167$	−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
$171$	6.30515	+	2.01650i	0.482167	+	0.154206i
$172$	−8.02756	+	13.9041i	−0.612096	+	1.06018i
$173$	4.05508			0.308302			0.154151	−	0.988047i	$-0.450736\pi$
$173$	4.05508			0.308302			0.154151	+	0.988047i	$0.450736\pi$
$174$	−0.664975	+	4.26221i	−0.0504116	+	0.323117i
$175$		0			0
$176$	1.53957	+	2.66661i	0.116049	+	0.201003i
$177$	19.7326	−	7.62699i	1.48319	−	0.573280i
$178$	7.64647	+	13.2441i	0.573127	+	0.992685i
$179$	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	$0.0372121\pi$
$180$	6.88201	+	31.6572i	0.512955	+	2.35959i
$181$	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
$184$	5.32343	−	9.22045i	0.392448	−	0.679740i
$185$	−31.7657			−2.33546
$186$	12.6273	−	4.88067i	0.925878	−	0.357868i
$187$	−4.48117			−0.327695
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	8.28714			0.599637			0.299818	−	0.953996i	$-0.403074\pi$
$191$	8.28714			0.599637			0.299818	+	0.953996i	$0.403074\pi$
$192$	−17.6554	+	6.82413i	−1.27417	+	0.492489i
$193$	−18.7848			−1.35216			−0.676082	−	0.736827i	$-0.736323\pi$
$193$	−18.7848			−1.35216			−0.676082	+	0.736827i	$0.736323\pi$
$194$	−9.88504	+	17.1214i	−0.709705	+	1.22924i
$195$	−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	$0.431478\pi$
$198$	−9.23274	−	2.95279i	−0.656142	−	0.209846i
$199$	−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	$0.996052\pi$
$200$	7.15272	+	12.3889i	0.505773	+	0.876025i
$201$	20.6983	−	8.00026i	1.45995	−	0.564295i
$202$	19.3654	+	33.5419i	1.36255	+	2.36000i
$203$		0			0
$204$	−3.26768	+	20.9444i	−0.228783	+	1.46640i
$205$	−5.28261			−0.368954
$206$	2.65758	−	4.60306i	0.185162	−	0.320710i
$207$	1.67499	+	7.70492i	0.116420	+	0.535529i
$208$	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	$0.991493\pi$
$212$	−11.9323	+	20.6673i	−0.819512	+	1.41944i
$213$	20.8695	−	8.06642i	1.42995	−	0.552702i
$214$	20.8947	+	36.1907i	1.42833	+	2.47395i
$215$	−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
$219$	−2.79158	+	17.8929i	−0.188638	+	1.20909i
$220$	−14.6186			−0.985584
$221$	−4.85287			−0.326439
$222$	−35.0066	−	28.2141i	−2.34949	−	1.89361i
$223$	−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
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	0.982097	+	0.188376i	$0.0603222\pi$
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	−0.327910	+	0.944709i	$0.606344\pi$
$228$	11.0017	+	8.86702i	0.728608	+	0.587232i
$229$	14.0364	−	24.3118i	0.927552	−	1.60657i	0.140148	−	0.990131i	$-0.455242\pi$
$229$	14.0364	−	24.3118i	0.927552	−	1.60657i	0.787404	−	0.616437i	$-0.211425\pi$
$230$	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	$0.982661\pi$
$234$	−9.99857	−	3.19772i	−0.653627	−	0.209042i
$235$	5.81127	−	10.0654i	0.379085	−	0.656595i
$236$	45.1569			2.93947
$237$	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	$0.716877\pi$
$240$	−1.77387	+	11.3698i	−0.114503	+	0.733915i
$241$	−11.5849	−	20.0656i	−0.746247	−	1.29254i	−0.949610	−	0.313435i	$-0.898520\pi$
$241$	−11.5849	−	20.0656i	−0.746247	−	1.29254i	0.203362	−	0.979104i	$-0.434813\pi$
$242$	−10.9408	+	18.9499i	−0.703299	+	1.21815i
$243$	−4.20829	−	15.0097i	−0.269962	−	0.962871i
$244$	−2.06942			−0.132481
$245$		0			0
$246$	−5.82157	−	4.69198i	−0.371169	−	0.299150i
$247$	−1.61743	+	2.80147i	−0.102915	+	0.178253i
$248$	13.2649			0.842320
$249$	0.525297	−	3.36693i	0.0332893	−	0.213371i
$250$	10.2383			0.647525
$251$	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
$254$	9.47392			0.594447
$255$	−13.0392	−	10.5091i	−0.816544	−	0.658106i
$256$	−27.6452			−1.72782
$257$	5.18798	−	8.98585i	0.323618	−	0.560522i	−0.657614	−	0.753355i	$-0.728434\pi$
$257$	5.18798	−	8.98585i	0.323618	−	0.560522i	0.981232	+	0.192833i	$0.0617676\pi$
$258$	2.76748	−	17.7384i	0.172296	−	1.10434i
$259$		0			0
$260$	−15.8312			−0.981807
$261$	−0.664975	−	3.05888i	−0.0411609	−	0.189340i
$262$	−6.35937	+	11.0148i	−0.392883	+	0.680494i
$263$	9.56654	+	16.5697i	0.589898	+	1.02173i	0.994245	+	0.107128i	$0.0341653\pi$
$263$	9.56654	+	16.5697i	0.589898	+	1.02173i	−0.404347	+	0.914605i	$0.632501\pi$
$264$	−7.39517	−	5.96025i	−0.455141	−	0.366828i
$265$	−9.42689	−	16.3279i	−0.579090	−	1.00301i
$266$		0			0
$267$	−8.64045	−	6.96390i	−0.528787	−	0.426184i
$268$	47.3669			2.89340
$269$	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	$0.0798430\pi$
$270$	−19.9403	−	30.2443i	−1.21353	−	1.84061i
$271$	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
$275$	2.39029	−	4.14011i	0.144140	−	0.249658i
$276$	−2.59447	+	16.6295i	−0.156169	+	1.00098i
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	0.779101	−	0.626899i	$-0.215676\pi$
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	−0.932460	+	0.361272i	$0.882343\pi$
$278$	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	$0.182875\pi$
$282$	15.3442	−	5.93080i	0.913733	−	0.353174i
$283$	12.4883			0.742352			0.371176	−	0.928562i	$-0.378955\pi$
$283$	12.4883			0.742352			0.371176	+	0.928562i	$0.378955\pi$
$284$	47.7586			2.83395
$285$	−10.4126	+	4.02465i	−0.616788	+	0.238400i
$286$	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
$290$	−3.63729	−	6.29997i	−0.213589	−	0.369947i
$291$	2.21151	−	14.1748i	0.129641	−	0.830944i
$292$	−19.3276	+	33.4764i	−1.13106	+	1.95906i
$293$	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
$297$	7.02175	−	0.416825i	0.407443	−	0.0241866i
$298$	2.60135	−	4.50566i	0.150692	−	0.261006i
$299$	−3.85309			−0.222830
$300$	−17.6074	−	14.1909i	−1.01656	−	0.819313i
$301$		0			0
$302$	16.7412	+	28.9966i	0.963347	+	1.66857i
$303$	−21.8828	−	17.6367i	−1.25713	−	1.01320i
$304$	2.50953	+	4.34663i	0.143931	+	0.249297i
$305$	0.817453	−	1.41587i	0.0468072	−	0.0810725i
$306$	−5.03535	−	23.1626i	−0.287852	−	1.32412i
$307$	−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
$310$	−11.4147	+	19.7709i	−0.648313	+	1.12291i
$311$	32.3968			1.83706			0.918528	−	0.395355i	$-0.129379\pi$
$311$	32.3968			1.83706			0.918528	+	0.395355i	$0.129379\pi$
$312$	−8.00859	−	6.45464i	−0.453397	−	0.365422i
$313$	−1.51907			−0.0858629			−0.0429315	−	0.999078i	$-0.513670\pi$
$313$	−1.51907			−0.0858629			−0.0429315	+	0.999078i	$0.513670\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	−21.5089			−1.20806			−0.604029	−	0.796962i	$-0.706439\pi$
$317$	−21.5089			−1.20806			−0.604029	+	0.796962i	$0.706439\pi$
$318$	4.11362	−	26.3666i	0.230680	−	1.47856i
$319$	1.41252			0.0790860
$320$	15.9600	−	27.6436i	0.892193	−	1.54532i
$321$	−23.6109	−	19.0295i	−1.31783	−	1.06213i
$322$		0			0
$323$	−7.30441			−0.406428
$324$	3.17208	−	33.1227i	0.176227	−	1.84015i
$325$	2.58856	−	4.48352i	0.143588	−	0.248701i
$326$	0.463715	+	0.803178i	0.0256828	+	0.0444839i
$327$	−4.16473	+	26.6942i	−0.230310	+	1.47619i
$328$	−3.66315	−	6.34476i	−0.202263	−	0.350330i
$329$		0			0
$330$	15.2473	−	5.89336i	0.839337	−	0.324419i
$331$	19.4780			1.07061			0.535305	−	0.844659i	$-0.320197\pi$
$331$	19.4780			1.07061			0.535305	+	0.844659i	$0.320197\pi$
$332$	3.63691	−	6.29931i	0.199601	−	0.345719i
$333$	31.0758	+	9.93858i	1.70294	+	0.544631i
$334$	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	$0.748273\pi$
$338$	−12.9498	+	22.4296i	−0.704374	+	1.22001i
$339$	−2.27789	−	1.83590i	−0.123718	−	0.0997122i
$340$	−17.8736	−	30.9580i	−0.969332	−	1.67893i
$341$	−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
$345$	−10.3528	−	8.34403i	−0.557379	−	0.449228i
$346$	−9.67895			−0.520344
$347$	2.02604			0.108763			0.0543817	−	0.998520i	$-0.482681\pi$
$347$	2.02604			0.108763			0.0543817	+	0.998520i	$0.482681\pi$
$348$	1.03001	−	6.60195i	0.0552145	−	0.353902i
$349$	−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
$353$	8.53072	+	14.7756i	0.454045	+	0.786428i	0.998633	−	0.0522753i	$-0.0166473\pi$
$353$	8.53072	+	14.7756i	0.454045	+	0.786428i	−0.544588	+	0.838704i	$0.683314\pi$
$354$	−47.0991	+	18.2046i	−2.50329	+	0.967565i
$355$	−18.8655	+	32.6759i	−1.00127	+	1.73426i
$356$	−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	$0.808383\pi$
$360$	−7.54043	−	34.6859i	−0.397415	−	1.82811i
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$	−46.8570			−2.46275
$363$	2.44770	−	15.6887i	0.128471	−	0.823444i
$364$		0			0
$365$	−15.2695	−	26.4475i	−0.799240	−	1.38432i
$366$	2.15842	−	0.834267i	0.112822	−	0.0436078i
$367$	−5.07874	−	8.79664i	−0.265108	−	0.459181i	0.702484	−	0.711700i	$-0.252074\pi$
$367$	−5.07874	−	8.79664i	−0.265108	−	0.459181i	−0.967592	+	0.252519i	$0.918741\pi$
$368$	−2.98914	+	5.17733i	−0.155819	+	0.269887i
$369$	5.16787	+	1.65278i	0.269029	+	0.0860402i
$370$	75.8207			3.94173
$371$		0			0
$372$	−19.5591	+	7.55992i	−1.01409	+	0.391964i
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	−0.320904	−	0.947112i	$-0.603987\pi$
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	0.980675	−	0.195645i	$-0.0626799\pi$
$374$	10.6960			0.553075
$375$	−6.92985	+	2.67851i	−0.357856	+	0.138318i
$376$	16.1189			0.831271
$377$	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	$0.418547\pi$
$380$	−23.8286			−1.22238
$381$	−6.41250	+	2.47854i	−0.328522	+	0.126980i
$382$	−19.7803			−1.01205
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	0.271419	+	0.962461i	$0.412507\pi$
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	−0.969225	+	0.246175i	$0.920826\pi$
$384$	33.5056	−	12.9505i	1.70983	−	0.660878i
$385$		0			0
$386$	44.8370			2.28214
$387$	2.76748	+	12.7304i	0.140679	+	0.647122i
$388$	15.3114	−	26.5202i	0.777321	−	1.34636i
$389$	−2.09223	−	3.62385i	−0.106080	−	0.183736i	0.808099	−	0.589047i	$-0.200497\pi$
$389$	−2.09223	−	3.62385i	−0.106080	−	0.183736i	−0.914179	+	0.405311i	$0.867163\pi$
$390$	16.5120	−	6.38220i	0.836120	−	0.323175i
$391$	−4.35019	−	7.53475i	−0.219999	−	0.381049i
$392$		0			0
$393$	1.42274	−	9.11914i	0.0717676	−	0.460000i
$394$	−14.3125			−0.721053
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$	14.3011	+	4.57373i	0.718655	+	0.229839i
$397$	−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
$401$	3.42402	−	5.93057i	0.170987	−	0.296158i	−0.767778	−	0.640716i	$-0.778638\pi$
$401$	3.42402	−	5.93057i	0.170987	−	0.296158i	0.938765	+	0.344557i	$0.111971\pi$
$402$	−49.4042	+	19.0956i	−2.46406	+	0.952401i
$403$	−2.40027	−	4.15739i	−0.119566	−	0.207095i
$404$	−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
$408$	3.58030	−	22.9482i	0.177251	−	1.13611i
$409$	18.2698			0.903384			0.451692	−	0.892174i	$-0.350821\pi$
$409$	18.2698			0.903384			0.451692	+	0.892174i	$0.350821\pi$
$410$	12.6089			0.622709
$411$	10.1081	+	8.14680i	0.498597	+	0.401852i
$412$	−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
$416$	1.95901	+	3.39311i	0.0960485	+	0.166361i
$417$	−18.9686	−	15.2880i	−0.928896	−	0.748658i
$418$	3.56490	−	6.17458i	0.174365	−	0.302009i
$419$	−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
$423$	−8.83422	+	8.02861i	−0.429535	+	0.390364i
$424$	13.0739	−	22.6446i	0.634923	−	1.09972i
$425$	11.6901			0.567053
$426$	−49.8127	+	19.2535i	−2.41343	+	0.932834i
$427$		0			0
$428$	−32.3649	−	56.0577i	−1.56442	−	2.70965i
$429$	−0.529872	+	3.39626i	−0.0255825	+	0.163973i
$430$	15.1376	+	26.2191i	0.730001	+	1.26440i
$431$	−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	$0.328768\pi$
$432$	5.29261	−	10.5678i	0.254641	−	0.508444i
$433$	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
$436$	−28.8346	+	49.9431i	−1.38093	+	2.39184i
$437$	−5.79956			−0.277431
$438$	6.66315	−	42.7080i	0.318377	−	2.04067i
$439$	35.4781			1.69328			0.846639	−	0.532168i	$-0.178623\pi$
$439$	35.4781			1.69328			0.846639	+	0.532168i	$0.178623\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	−19.2063			−0.912517			−0.456258	−	0.889847i	$-0.650811\pi$
$443$	−19.2063			−0.912517			−0.456258	+	0.889847i	$0.650811\pi$
$444$	54.2235	+	43.7023i	2.57333	+	2.07402i
$445$	18.7143			0.887144
$446$	5.57946	−	9.66391i	0.264195	−	0.457599i
$447$	−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	$0.746215\pi$
$450$	24.0856	+	7.70300i	1.13541	+	0.363123i
$451$	−1.22415	+	2.12029i	−0.0576429	+	0.0998405i
$452$	−3.12244	−	5.40823i	−0.146867	−	0.254382i
$453$	−18.9174	−	15.2468i	−0.888818	−	0.716356i
$454$	−23.5257	−	40.7478i	−1.10412	−	1.91239i
$455$		0			0
$456$	−12.0543	−	9.71534i	−0.564494	−	0.454963i
$457$	−9.56196			−0.447290			−0.223645	−	0.974671i	$-0.571796\pi$
$457$	−9.56196			−0.447290			−0.223645	+	0.974671i	$0.571796\pi$
$458$	−33.5031	+	58.0290i	−1.56550	+	2.71152i
$459$	9.46795	+	14.3604i	0.441926	+	0.670287i
$460$	−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	$0.625457\pi$
$464$	1.18670	−	2.05542i	0.0550909	−	0.0954203i
$465$	2.55374	−	16.3684i	0.118427	−	0.759065i
$466$	16.4721	+	28.5305i	0.763054	+	1.32165i
$467$	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
$471$	−4.79215	+	1.85225i	−0.220811	+	0.0853473i
$472$	−49.4772			−2.27737
$473$	−5.87861			−0.270299
$474$	−2.96028	+	1.14420i	−0.135970	+	0.0525549i
$475$	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
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	−0.974662	−	0.223684i	$-0.928192\pi$
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	0.293615	−	0.955924i	$-0.405142\pi$
$480$	−2.08426	+	13.3593i	−0.0951332	+	0.609764i
$481$	−7.97172	+	13.8074i	−0.363479	+	0.629565i
$482$	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
$486$	10.0446	+	35.8261i	0.455634	+	1.62511i
$487$	−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	$0.996805\pi$
$488$	2.26740			0.102640
$489$	−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	$0.543016\pi$
$492$	9.01732	+	7.26764i	0.406532	+	0.327651i
$493$	1.72704	+	2.99132i	0.0777819	+	0.134722i
$494$	3.86060	−	6.68675i	0.173696	−	0.300851i
$495$	−8.77845	+	7.97792i	−0.394562	+	0.358581i
$496$	−7.44830			−0.334438
$497$		0			0
$498$	−1.25381	+	8.03642i	−0.0561848	+	0.360121i
$499$	4.46760	−	7.73811i	0.199997	−	0.346405i	−0.748530	−	0.663101i	$-0.769240\pi$
$499$	4.46760	−	7.73811i	0.199997	−	0.346405i	0.948527	+	0.316696i	$0.102573\pi$
$500$	−15.8586			−0.709217
$501$	−9.84158	−	7.93197i	−0.439689	−	0.354374i
$502$	−18.5794			−0.829241
$503$	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
$506$	8.49239			0.377533
$507$	2.89716	−	18.5696i	0.128667	−	0.824703i
$508$	−14.6746			−0.651082
$509$	−14.0555	+	24.3449i	−0.623000	+	1.07907i	0.365924	+	0.930645i	$0.380753\pi$
$509$	−14.0555	+	24.3449i	−0.623000	+	1.07907i	−0.988924	+	0.148423i	$0.952580\pi$
$510$	31.1228	+	25.0839i	1.37814	+	1.11073i
$511$		0			0
$512$	24.5070			1.08307
$513$	11.4456	−	0.679434i	0.505336	−	0.0299978i
$514$	−12.3830	+	21.4480i	−0.546192	+	0.946033i
$515$	−3.25214	−	5.63287i	−0.143306	−	0.248214i
$516$	−4.28669	+	27.4759i	−0.188711	+	1.20956i
$517$	−2.69331	−	4.66495i	−0.118452	−	0.205164i
$518$		0			0
$519$	6.55127	−	2.53218i	0.287569	−	0.111150i
$520$	17.3458			0.760662
$521$	−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	$0.226108\pi$
$522$	1.58721	+	7.30114i	0.0694702	+	0.319562i
$523$	−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
$527$	5.41988	−	9.38751i	0.236094	−	0.408926i
$528$	4.15243	+	3.34672i	0.180711	+	0.145647i
$529$	8.04603	+	13.9361i	0.349827	+	0.605919i
$530$	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
$534$	20.6236	+	16.6219i	0.892471	+	0.719301i
$535$	51.1387			2.21092
$536$	−51.8987			−2.24168
$537$	2.82614	−	18.1144i	0.121957	−	0.781693i
$538$	−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	$0.961723\pi$
$542$	−21.8865	−	37.9085i	−0.940106	−	1.62831i
$543$	31.7155	−	12.2586i	1.36104	−	0.526067i
$544$	−4.42350	+	7.66173i	−0.189656	+	0.328494i
$545$	−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
$549$	−1.24268	+	1.12936i	−0.0530364	+	0.0481999i
$550$	−5.70532	+	9.88190i	−0.243276	+	0.421366i
$551$	2.30244			0.0980874
$552$	2.84269	−	18.2205i	0.120993	−	0.775515i
$553$		0			0
$554$	6.09227	+	10.5521i	0.258836	+	0.448317i
$555$	−51.3198	+	19.8360i	−2.17840	+	0.841992i
$556$	−26.0014	−	45.0358i	−1.10271	−	1.90994i
$557$	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	$-0.0833855\pi$
$558$	17.3526	−	15.7701i	0.734592	−	0.667603i
$559$	−6.36623			−0.269263
$560$		0			0
$561$	−7.23964	+	2.79825i	−0.305658	+	0.118142i
$562$	2.03643	−	3.52720i	0.0859015	−	0.148786i
$563$	−2.19131			−0.0923528			−0.0461764	−	0.998933i	$-0.514704\pi$
$563$	−2.19131			−0.0923528			−0.0461764	+	0.998933i	$0.514704\pi$
$564$	−23.7674	+	9.18652i	−1.00079	+	0.386822i
$565$	4.93367			0.207561
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	18.9860			0.795936			0.397968	−	0.917399i	$-0.369716\pi$
$569$	18.9860			0.795936			0.397968	+	0.917399i	$0.369716\pi$
$570$	24.8535	−	9.60631i	1.04100	−	0.402364i
$571$	−21.7380			−0.909709			−0.454854	−	0.890566i	$-0.650309\pi$
$571$	−21.7380			−0.909709			−0.454854	+	0.890566i	$0.650309\pi$
$572$	−3.66858	+	6.35417i	−0.153391	+	0.265681i
$573$	13.3885	−	5.17488i	0.559311	−	0.216184i
$574$		0			0
$575$	9.28172			0.387074
$576$	−24.2622	+	22.0497i	−1.01093	+	0.918738i
$577$	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	$-0.0557511\pi$
$578$	−7.21083	−	12.4895i	−0.299931	−	0.519496i
$579$	−30.3482	+	11.7301i	−1.26123	+	0.487488i
$580$	5.63398	+	9.75835i	0.233938	+	0.405193i
$581$		0			0
$582$	−5.27858	+	33.8335i	−0.218804	+	1.40244i
$583$	−8.73804			−0.361893
$584$	21.1767	−	36.6792i	0.876299	−	1.51780i
$585$	−9.50661	+	8.63968i	−0.393050	+	0.357207i
$586$	−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
$590$	42.5763	−	73.7444i	1.75284	−	3.03601i
$591$	9.68751	−	3.74440i	0.398491	−	0.154024i
$592$	12.3685	+	21.4230i	0.508344	+	0.880478i
$593$	−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
$597$	−3.84710	+	24.6583i	−0.157451	+	1.00920i
$598$	9.19682			0.376086
$599$	0.402823			0.0164589			0.00822945	−	0.999966i	$-0.497380\pi$
$599$	0.402823			0.0164589			0.00822945	+	0.999966i	$0.497380\pi$
$600$	19.2919	+	15.5486i	0.787589	+	0.634769i
$601$	−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
$605$	13.3885	+	23.1895i	0.544318	+	0.942787i
$606$	52.2313	+	42.0966i	2.12175	+	1.71006i
$607$	12.0348	−	20.8449i	0.488479	−	0.846070i	−0.511434	−	0.859323i	$-0.670885\pi$
$607$	12.0348	−	20.8449i	0.488479	−	0.846070i	0.999912	+	0.0132531i	$0.00421872\pi$
$608$	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
$612$	7.79952	+	35.8777i	0.315277	+	1.45027i
$613$	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	$0.0316367\pi$
$614$	11.9376			0.481762
$615$	−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	$-0.485684\pi$
$618$	1.41914	−	9.09607i	0.0570861	−	0.365898i
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	0.975649	−	0.219339i	$-0.0703900\pi$
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	−0.677777	+	0.735267i	$0.737057\pi$
$620$	17.6809	−	30.6242i	0.710081	−	1.22990i
$621$	7.51737	+	11.4019i	0.301662	+	0.457543i
$622$	−77.3270			−3.10053
$623$		0			0
$624$	4.49687	+	3.62432i	0.180019	+	0.145089i
$625$	15.0930	−	26.1419i	0.603722	−	1.04568i
$626$	3.62582			0.144917
$627$	−0.797548	+	5.11195i	−0.0318510	+	0.204152i
$628$	−10.9666			−0.437614
$629$	−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	$0.637474\pi$
$632$	−3.10975			−0.123699
$633$	−18.6755	−	15.0518i	−0.742285	−	0.598255i
$634$	51.3388			2.03893
$635$	5.79673	−	10.0402i	0.230036	−	0.398434i
$636$	−6.37180	+	40.8406i	−0.252658	+	1.61943i
$637$		0			0
$638$	−3.37150			−0.133479
$639$	28.6790	−	26.0637i	1.13453	−	1.03107i
$640$	−30.2882	+	52.4607i	−1.19725	+	2.07369i
$641$	−5.96592	−	10.3333i	−0.235640	−	0.408140i	0.723819	−	0.689990i	$-0.242385\pi$
$641$	−5.96592	−	10.3333i	−0.235640	−	0.408140i	−0.959458	+	0.281850i	$0.909052\pi$
$642$	56.3561	+	45.4210i	2.22420	+	1.79262i
$643$	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
$646$	17.4347			0.685958
$647$	−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	$0.172855\pi$
$648$	−3.47557	+	36.2917i	−0.136533	+	1.42567i
$649$	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
$653$	−11.3573	+	19.6715i	−0.444447	+	0.769804i	−0.998014	−	0.0630004i	$-0.979933\pi$
$653$	−11.3573	+	19.6715i	−0.444447	+	0.769804i	0.553567	+	0.832805i	$0.313266\pi$
$654$	9.94067	−	63.7155i	0.388711	−	2.49147i
$655$	7.78211	+	13.4790i	0.304072	+	0.526668i
$656$	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	$0.897824\pi$
$660$	−23.6173	+	9.12852i	−0.919304	+	0.355327i
$661$	−33.9258			−1.31956			−0.659780	−	0.751459i	$-0.729351\pi$
$661$	−33.9258			−1.31956			−0.659780	+	0.751459i	$0.729351\pi$
$662$	−46.4915			−1.80694
$663$	−7.84015	+	3.03036i	−0.304486	+	0.117689i
$664$	−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
$668$	−13.4905	−	23.3662i	−0.521962	−	0.904064i
$669$	−1.24825	+	8.00077i	−0.0482602	+	0.309328i
$670$	44.6601	−	77.3535i	1.72537	−	2.98843i
$671$	−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
$675$	−18.3177	+	1.08738i	−0.705050	+	0.0418532i
$676$	20.0585	−	34.7424i	0.771483	−	1.33625i
$677$	37.9684			1.45924			0.729622	−	0.683850i	$-0.239696\pi$
$677$	37.9684			1.45924			0.729622	+	0.683850i	$0.239696\pi$
$678$	5.43702	+	4.38204i	0.208807	+	0.168291i
$679$		0			0
$680$	19.5836	+	33.9198i	0.750997	+	1.30076i
$681$	26.5839	+	21.4257i	1.01870	+	0.821034i
$682$	5.29031	+	9.16309i	0.202577	+	0.350873i
$683$	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	$0.0728251\pi$
$684$	23.3111	+	7.45529i	0.891320	+	0.285060i
$685$	−21.8932			−0.836495
$686$		0			0
$687$	7.49540	−	48.0424i	0.285967	−	1.83293i
$688$	−4.93877	+	8.55420i	−0.188289	+	0.326126i
$689$	−9.46285			−0.360506
$690$	24.7109	+	19.9161i	0.940728	+	0.758193i
$691$	−2.69148			−0.102389			−0.0511943	−	0.998689i	$-0.516303\pi$
$691$	−2.69148			−0.102389			−0.0511943	+	0.998689i	$0.516303\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	41.0840			1.55841
$696$	−1.12856	+	7.23358i	−0.0427779	+	0.274188i
$697$	−5.98689			−0.226770
$698$	19.4429	−	33.6761i	0.735924	−	1.27466i
$699$	−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	$0.571850\pi$
$702$	−18.1502	+	1.07743i	−0.685035	+	0.0406650i
$703$	−11.9988	+	20.7826i	−0.452544	+	0.783829i
$704$	−7.39689	−	12.8118i	−0.278781	−	0.482862i
$705$	3.10320	−	19.8902i	0.116873	−	0.749109i
$706$	−20.3617	−	35.2675i	−0.766323	−	1.32731i
$707$		0			0
$708$	72.9542	−	28.1981i	2.74179	−	1.05975i
$709$	−41.0333			−1.54104			−0.770520	−	0.637416i	$-0.780003\pi$
$709$	−41.0333			−1.54104			−0.770520	+	0.637416i	$0.780003\pi$
$710$	45.0294	−	77.9931i	1.68992	−	2.92703i
$711$	1.70434	−	1.54892i	0.0639179	−	0.0580891i
$712$	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
$716$	19.5669	−	33.8908i	0.731248	−	1.26656i
$717$	14.9171	+	12.0226i	0.557088	+	0.448993i
$718$	−3.54123	−	6.13359i	−0.132158	−	0.228904i
$719$	−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
$723$	−31.2461	−	25.1832i	−1.16205	−	0.936574i
$724$	72.5792			2.69738
$725$	−3.68487			−0.136853
$726$	−5.84233	+	37.4469i	−0.216829	+	1.38978i
$727$	−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
$731$	−7.18756	−	12.4492i	−0.265841	−	0.460451i
$732$	−3.34329	+	1.29224i	−0.123571	+	0.0477625i
$733$	7.07446	−	12.2533i	0.261301	−	0.452587i	−0.705287	−	0.708922i	$-0.749182\pi$
$733$	7.07446	−	12.2533i	0.261301	−	0.452587i	0.966588	+	0.256335i	$0.0825151\pi$
$734$	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
$738$	−12.3350	−	3.94496i	−0.454059	−	0.145216i
$739$	−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	$0.260023\pi$
$740$	−117.442			−4.31727
$741$	−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	$0.706836\pi$
$744$	21.4303	−	8.28320i	0.785673	−	0.303677i
$745$	−3.18333	−	5.51368i	−0.116628	−	0.202006i
$746$	−30.4142	+	52.6789i	−1.11354	+	1.92871i
$747$	−1.25381	−	5.76753i	−0.0458747	−	0.211023i
$748$	−16.5675			−0.605768
$749$		0			0
$750$	16.5406	−	6.39325i	0.603979	−	0.233449i
$751$	−6.51848	+	11.2903i	−0.237863	+	0.411990i	−0.960101	−	0.279654i	$-0.909780\pi$
$751$	−6.51848	+	11.2903i	−0.237863	+	0.411990i	0.722238	+	0.691644i	$0.243113\pi$
$752$	−9.05088			−0.330052
$753$	12.5756	−	4.86071i	0.458282	−	0.177134i
$754$	−3.65116			−0.132968
$755$	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	$0.574047\pi$
$758$	−23.5225			−0.854377
$759$	−5.74814	+	2.22176i	−0.208644	+	0.0806447i
$760$	26.1084			0.947050
$761$	−3.02038	+	5.23146i	−0.109489	+	0.189640i	−0.915563	−	0.402174i	$-0.868255\pi$
$761$	−3.02038	+	5.23146i	−0.109489	+	0.189640i	0.806074	+	0.591814i	$0.201588\pi$
$762$	15.3058	−	5.91596i	0.554470	−	0.214313i
$763$		0			0
$764$	30.6388			1.10847
$765$	−27.6280	−	8.83594i	−0.998894	−	0.319464i
$766$	32.5959	−	56.4577i	1.17774	−	2.03990i
$767$	8.95288	+	15.5068i	0.323270	+	0.559920i
$768$	−44.6627	+	17.2629i	−1.61163	+	0.622923i
$769$	−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
$772$	−69.4503			−2.49957
$773$	−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	$0.930092\pi$
$774$	−6.60562	−	30.3858i	−0.237434	−	1.09219i
$775$	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
$779$	−1.99539	+	3.45612i	−0.0714923	+	0.123828i
$780$	−25.5763	+	9.88571i	−0.915780	+	0.353965i
$781$	8.74345	+	15.1441i	0.312865	+	0.541898i
$782$	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
$786$	−3.39589	+	21.7662i	−0.121127	+	0.776374i
$787$	−30.8135			−1.09838			−0.549191	−	0.835697i	$-0.685064\pi$
$787$	−30.8135			−1.09838			−0.549191	+	0.835697i	$0.685064\pi$
$788$	22.1693			0.789750
$789$	25.8023	+	20.7958i	0.918587	+	0.740349i
$790$	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
$794$	36.6037	+	63.3994i	1.29902	+	2.24996i
$795$	−25.4257	−	20.4922i	−0.901756	−	0.726784i
$796$	−26.6355	+	46.1340i	−0.944070	+	1.63518i
$797$	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
$801$	−18.3078	−	5.85517i	−0.646876	−	0.206882i
$802$	−8.17268	+	14.1555i	−0.288587	+	0.499848i
$803$	−14.1537			−0.499472
$804$	76.5246	−	29.5781i	2.69882	−	1.04314i
$805$		0			0
$806$	5.72914	+	9.92315i	0.201800	+	0.349528i
$807$	2.35941	−	15.1229i	0.0830553	−	0.532350i
$808$	32.8659	+	56.9254i	1.15622	+	2.00263i
$809$	−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	$0.926494\pi$
$810$	−51.1009	−	36.4101i	−1.79550	−	1.27932i
$811$	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
$814$	17.5701	−	30.4322i	0.615830	−	1.06665i
$815$	1.13492			0.0397544
$816$	−2.01036	+	12.8856i	−0.0703767	+	0.451085i
$817$	−9.58227			−0.335241
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	41.5834			1.45127			0.725635	−	0.688080i	$-0.241546\pi$
$821$	41.5834			1.45127			0.725635	+	0.688080i	$0.241546\pi$
$822$	−24.1268	−	19.4453i	−0.841518	−	0.678234i
$823$	8.45998			0.294896			0.147448	−	0.989070i	$-0.452894\pi$
$823$	8.45998			0.294896			0.147448	+	0.989070i	$0.452894\pi$
$824$	4.51029	−	7.81205i	0.157123	−	0.272146i
$825$	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	$0.220294\pi$
$828$	6.19267	+	28.4862i	0.215210	+	0.989964i
$829$	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	$0.0733973\pi$
$830$	−6.85813	−	11.8786i	−0.238049	−	0.412314i
$831$	−6.88422	−	5.54844i	−0.238811	−	0.192473i
$832$	−8.01045	−	13.8745i	−0.277712	−	0.481012i
$833$		0			0
$834$	45.2755	+	36.4905i	1.56776	+	1.26356i
$835$	21.3158			0.737665
$836$	−5.52185	+	9.56412i	−0.190977	+	0.330782i
$837$	−7.61946	+	15.2139i	−0.263367	+	0.525868i
$838$	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
$842$	−24.8657	+	43.0687i	−0.856929	+	1.48424i
$843$	−0.455595	+	2.92017i	−0.0156915	+	0.100576i
$844$	−25.5997	−	44.3400i	−0.881178	−	1.52624i
$845$	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
$849$	20.1757	−	7.79827i	0.692429	−	0.267636i
$850$	−27.9027			−0.957055
$851$	−28.5839			−0.979844
$852$	77.1574	−	29.8227i	2.64337	−	1.02171i
$853$	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
$857$	18.5447	+	32.1204i	0.633475	+	1.09721i	0.986836	+	0.161724i	$0.0517053\pi$
$857$	18.5447	+	32.1204i	0.633475	+	1.09721i	−0.353361	+	0.935487i	$0.614961\pi$
$858$	1.26473	−	8.10642i	0.0431773	−	0.276749i
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	−0.896491	−	0.443062i	$-0.853892\pi$
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	0.831948	+	0.554853i	$0.187226\pi$
$860$	−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	$0.831019\pi$
$864$	6.21872	−	12.4170i	0.211565	−	0.422434i
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$	−51.7388			−1.75815
$867$	8.14818	+	6.56715i	0.276727	+	0.223032i
$868$		0			0
$869$	0.519608	+	0.899987i	0.0176265	+	0.0305300i
$870$	−9.81029	−	7.90675i	−0.332600	−	0.268064i
$871$	9.39105	+	16.2658i	0.318203	+	0.551145i
$872$	31.5933	−	54.7212i	1.06988	−	1.85309i
$873$	−5.27858	−	24.2814i	−0.178653	−	0.821801i
$874$	13.8428			0.468240
$875$		0			0
$876$	−10.3209	+	66.1525i	−0.348710	+	2.23509i
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	−0.945291	−	0.326228i	$-0.894222\pi$
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	0.755167	+	0.655532i	$0.227556\pi$
$878$	−84.6816			−2.85786
$879$	7.01803	+	5.65629i	0.236712	+	0.190782i
$880$	−8.99374			−0.303179
$881$	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	$0.528429\pi$
$884$	−17.9418			−0.603447
$885$	−9.52530	+	61.0531i	−0.320189	+	2.05228i
$886$	45.8428			1.54012
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.260767	−	0.965402i	$-0.416025\pi$
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.705679	−	0.708532i	$-0.250642\pi$
$888$	−59.4112	−	47.8834i	−1.99371	−	1.60686i
$889$		0			0
$890$	−44.6686			−1.49730
$891$	11.0838	−	5.05812i	0.371323	−	0.169453i
$892$	−8.64231	+	14.9689i	−0.289366	+	0.501197i
$893$	−4.39016	−	7.60398i	−0.146911	−	0.254458i
$894$	1.38911	−	8.90362i	0.0464588	−	0.297781i
$895$	15.4585	+	26.7749i	0.516720	+	0.894985i
$896$		0			0
$897$	−6.22494	+	2.40605i	−0.207845	+	0.0803356i
$898$	70.6708			2.35832
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$	−37.3074	−	11.9316i	−1.24358	−	0.397719i
$901$	−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
$905$	−28.6700	+	49.6579i	−0.953023	+	1.65068i
$906$	45.1534	+	36.3921i	1.50012	+	1.20905i
$907$	−10.4486	−	18.0975i	−0.346939	−	0.600917i	0.638765	−	0.769402i	$-0.279446\pi$
$907$	−10.4486	−	18.0975i	−0.346939	−	0.600917i	−0.985704	+	0.168485i	$0.946112\pi$
$908$	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	$0.0435878\pi$
$912$	6.76856	+	5.45522i	0.224129	+	0.180641i
$913$	2.66332			0.0881430
$914$	22.8231			0.754923
$915$	0.436518	−	2.79789i	0.0144308	−	0.0924955i
$916$	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	$0.622386\pi$
$920$	15.5490	+	26.9317i	0.512636	+	0.887911i
$921$	−8.08004	+	3.12308i	−0.266246	+	0.102909i
$922$	26.0616	−	45.1399i	0.858292	−	1.48660i
$923$	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
$927$	1.41914	+	6.52802i	0.0466106	+	0.214408i
$928$	1.39434	−	2.41508i	0.0457716	−	0.0792787i
$929$	−5.66725			−0.185937			−0.0929683	−	0.995669i	$-0.529636\pi$
$929$	−5.66725			−0.185937			−0.0929683	+	0.995669i	$0.529636\pi$
$930$	−6.09544	+	39.0692i	−0.199877	+	1.28113i
$931$		0			0
$932$	−25.5145	−	44.1923i	−0.835754	−	1.44757i
$933$	52.3394	−	20.2301i	1.71351	−	0.662304i
$934$	−41.7138	−	72.2503i	−1.36492	−	2.36410i
$935$	6.54444	−	11.3353i	0.214026	−	0.370704i
$936$	−16.9690	−	5.42699i	−0.554649	−	0.177387i
$937$	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
$940$	21.4851	−	37.2133i	0.700766	−	1.21376i
$941$	−20.4552			−0.666819			−0.333410	−	0.942782i	$-0.608199\pi$
$941$	−20.4552			−0.666819			−0.333410	+	0.942782i	$0.608199\pi$
$942$	11.4382	−	4.42108i	0.372678	−	0.144047i
$943$	−4.75348			−0.154795
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	−4.76687			−0.154902			−0.0774512	−	0.996996i	$-0.524678\pi$
$947$	−4.76687			−0.154902			−0.0774512	+	0.996996i	$0.524678\pi$
$948$	4.58533	−	1.77231i	0.148924	−	0.0575620i
$949$	−15.3277			−0.497558
$950$	−9.29980	+	16.1077i	−0.301725	+	0.522604i
$951$	−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	$0.791315\pi$
$954$	−9.81868	−	45.1658i	−0.317891	−	1.46230i
$955$	−12.1028	+	20.9627i	−0.391638	+	0.678337i
$956$	20.4478	+	35.4166i	0.661328	+	1.14545i
$957$	2.28203	−	0.882044i	0.0737675	−	0.0285124i
$958$	35.5773	+	61.6217i	1.14945	+	1.99091i
$959$		0			0
$960$	8.52261	−	54.6263i	0.275066	−	1.76306i
$961$	−20.2771			−0.654101
$962$	19.0275	−	32.9565i	0.613470	−	1.06256i
$963$	−50.0279	−	15.9998i	−1.61213	−	0.515587i
$964$	−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	$0.863664\pi$
$968$	−18.5680	+	32.1608i	−0.596799	+	1.03369i
$969$	−11.8008	+	4.56121i	−0.379096	+	0.146527i
$970$	−28.8729	−	50.0093i	−0.927052	−	1.60570i
$971$	−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
$975$	1.38229	−	8.85987i	0.0442686	−	0.283743i
$976$	−1.27316			−0.0407528
$977$	22.8455			0.730893			0.365447	−	0.930832i	$-0.380916\pi$
$977$	22.8455			0.730893			0.365447	+	0.930832i	$0.380916\pi$
$978$	1.25071	+	1.00802i	0.0399932	+	0.0322331i
$979$	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
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	0.501315	−	0.865265i	$-0.332850\pi$
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	−0.999999	+	0.00151933i	$0.999516\pi$
$984$	−9.88003	−	7.96296i	−0.314964	−	0.253850i
$985$	−8.75726	+	15.1680i	−0.279029	+	0.483293i
$986$	−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
$990$	20.9530	−	19.0423i	0.665930	−	0.605203i
$991$	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	$0.131129\pi$
$992$	−8.75161			−0.277864
$993$	31.4681	−	12.1630i	0.998611	−	0.385981i
$994$		0			0
$995$	−21.0429	−	36.4474i	−0.667105	−	1.15546i
$996$	1.94210	−	12.4480i	0.0615377	−	0.394431i
$997$	−10.6439	−	18.4358i	−0.337095	−	0.583866i	0.646790	−	0.762668i	$-0.276111\pi$
$997$	−10.6439	−	18.4358i	−0.337095	−	0.583866i	−0.983885	+	0.178802i	$0.942778\pi$
$998$	−10.6636	+	18.4698i	−0.337549	+	0.584653i
$999$	56.4112	−	3.34868i	1.78477	−	0.105948i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	63.13	odd	6
63.2.g.b.16.5	yes	10	7.5	odd	6
63.2.h.b.25.1	yes	10	7.6	odd	2
63.2.h.b.58.1	yes	10	63.40	odd	6
189.2.g.b.100.1		10	21.5	even	6
189.2.g.b.172.1		10	63.41	even	6
189.2.h.b.37.5		10	63.5	even	6
189.2.h.b.46.5		10	21.20	even	2
441.2.f.e.148.5		10	63.31	odd	6
441.2.f.e.295.5		10	7.3	odd	6
441.2.f.f.148.5		10	63.4	even	3
441.2.f.f.295.5		10	7.4	even	3
441.2.g.f.67.5		10	9.4	even	3
441.2.g.f.79.5		10	7.2	even	3
441.2.h.f.214.1		10	1.1	even	1	trivial
441.2.h.f.373.1		10	63.58	even	3	inner
567.2.e.e.163.1		10	63.47	even	6
567.2.e.e.487.1		10	63.20	even	6
567.2.e.f.163.5		10	63.61	odd	6
567.2.e.f.487.5		10	63.34	odd	6
1008.2.q.i.529.4		10	28.27	even	2
1008.2.q.i.625.4		10	252.103	even	6
1008.2.t.i.193.3		10	252.139	even	6
1008.2.t.i.961.3		10	28.19	even	6
1323.2.f.e.442.1		10	63.59	even	6
1323.2.f.e.883.1		10	21.17	even	6
1323.2.f.f.442.1		10	63.32	odd	6
1323.2.f.f.883.1		10	21.11	odd	6
1323.2.g.f.361.1		10	9.5	odd	6
1323.2.g.f.667.1		10	21.2	odd	6
1323.2.h.f.226.5		10	63.23	odd	6
1323.2.h.f.802.5		10	3.2	odd	2
3024.2.q.i.2305.2		10	252.131	odd	6
3024.2.q.i.2881.2		10	84.83	odd	2
3024.2.t.i.289.4		10	84.47	odd	6
3024.2.t.i.1873.4		10	252.167	odd	6
3969.2.a.z.1.1		5	63.52	odd	6
3969.2.a.ba.1.1		5	63.25	even	3
3969.2.a.bb.1.5		5	63.11	odd	6
3969.2.a.bc.1.5		5	63.38	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.38687 q^{2} +(1.61557 - 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 - 2.01767i) q^{9} +O(q^{10})\)	\(q-2.38687 q^{2} +(1.61557 - 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 + 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 - 2.01767i) q^{9} +(3.48586 - 6.03769i) q^{10} +(0.676857 + 1.17235i) q^{11} +(5.97299 - 2.30867i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +2.27458 q^{16} +(-1.65514 + 2.86678i) q^{17} +(-5.29917 + 4.81592i) q^{18} +(1.10329 + 1.91096i) q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(-1.31415 + 2.27617i) q^{23} +(-6.54444 + 2.52954i) q^{24} +(-1.76573 - 3.05833i) q^{25} +(-1.74958 - 3.03036i) q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(1.86144 - 11.9310i) q^{30} -3.27458 q^{31} +2.67259 q^{32} +(1.82558 + 1.47135i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} +(5.43773 + 9.41842i) q^{37} +(-2.63342 - 4.56121i) q^{38} +(1.97701 + 1.59340i) q^{39} +(5.91601 - 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +(2.50244 + 4.33435i) q^{44} +(1.86144 + 8.56260i) q^{45} +(3.13670 - 5.43292i) q^{46} -3.97914 q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(-0.883838 + 5.66503i) q^{51} +(2.71001 + 4.69388i) q^{52} +(-3.22743 + 5.59008i) q^{53} +(-5.55389 + 11.0895i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +(-1.24528 + 2.15688i) q^{58} +12.2140 q^{59} +(-2.88328 + 18.4806i) q^{60} -0.559734 q^{61} +7.81600 q^{62} -10.9283 q^{64} -4.28200 q^{65} +(-4.35742 - 3.51193i) q^{66} +12.8118 q^{67} +(-6.11928 + 10.5989i) q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(-8.99344 + 8.17331i) q^{72} +(-5.22772 + 9.05467i) q^{73} +(-12.9791 - 22.4805i) q^{74} +(-4.76242 - 3.83835i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +0.767677 q^{79} +(-3.32187 + 5.75365i) q^{80} +(0.857983 - 8.95901i) q^{81} +(-2.15842 - 3.73849i) q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(5.18258 - 8.97649i) q^{86} +(0.278597 - 1.78569i) q^{87} +(-2.74185 - 4.74903i) q^{88} +(-3.20356 - 5.54872i) q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(-5.29031 + 2.04480i) q^{93} +9.49769 q^{94} -6.44514 q^{95} +(4.31776 - 1.66889i) q^{96} +(4.14143 - 7.17316i) q^{97} +(3.86814 + 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

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