LMFDB - Embedded newform 441.2.f.f.295.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, 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			295.5
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	441.295
Dual form			441.2.f.f.148.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} +O(q^{10})$	\(q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} -6.97172 q^{10} +(0.676857 - 1.17235i) q^{11} +(-0.987132 + 6.32710i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +(-1.13729 + 1.96984i) q^{16} +3.31027 q^{17} +(6.82030 + 2.18125i) q^{18} -2.20659 q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(-1.31415 - 2.27617i) q^{23} +(5.46287 + 4.40288i) q^{24} +(-1.76573 + 3.05833i) q^{25} +3.49916 q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(9.40187 + 7.57758i) q^{30} +(1.63729 + 2.83587i) q^{31} +(-1.33629 - 2.31453i) q^{32} +(-2.18702 + 0.845323i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} -10.8755 q^{37} +(-2.63342 + 4.56121i) q^{38} +(0.391421 - 2.50884i) q^{39} +(5.91601 + 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} -5.00488 q^{44} +(6.48471 - 5.89336i) q^{45} -6.27340 q^{46} +(1.98957 - 3.44604i) q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(-4.46414 - 3.59794i) q^{51} +(2.71001 - 4.69388i) q^{52} +6.45486 q^{53} +(-6.82685 - 10.3546i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +(-1.24528 - 2.15688i) q^{58} +(-6.10700 - 10.5776i) q^{59} +(17.4463 - 6.74331i) q^{60} +(0.279867 - 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 - 3.70832i) q^{65} +(-0.862710 + 5.52960i) q^{66} +(-6.40588 - 11.0953i) q^{67} +(-6.11928 - 10.5989i) q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(-2.58157 - 11.8752i) q^{72} +10.4554 q^{73} +(-12.9791 + 22.4805i) q^{74} +(5.70532 - 2.20521i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +(-0.383838 + 0.664827i) q^{79} +6.64375 q^{80} +(-8.18772 + 3.73647i) q^{81} +4.31684 q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(5.18258 + 8.97649i) q^{86} +(-1.68575 + 0.651573i) q^{87} +(-2.74185 + 4.74903i) q^{88} +6.40711 q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(0.874308 - 5.60395i) q^{93} +(-4.74884 - 8.22524i) q^{94} +(3.22257 + 5.58166i) q^{95} +(-0.713577 + 4.57373i) 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} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	$ 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.0426999	−	0.999088i	$-0.513596\pi$
$2$	1.19343	−	2.06709i	0.843886	−	1.46165i	0.886585	−	0.462565i	$-0.153071\pi$
$3$	−1.34857	−	1.08690i	−0.778598	−	0.627523i
$3$	−1.34857	−	1.08690i	−0.778598	−	0.627523i
$4$	−1.84857	−	3.20182i	−0.924286	−	1.60091i
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	−0.982360	−	0.186998i	$-0.940124\pi$
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	0.329235	−	0.944248i	$-0.393209\pi$
$6$	−3.85615	+	1.49047i	−1.57427	+	0.608483i
$7$		0			0
$7$		0			0
$8$	−4.05086			−1.43219
$9$	0.637290	+	2.93153i	0.212430	+	0.977176i
$10$	−6.97172			−2.20465
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	−0.745759	−	0.666216i	$-0.767913\pi$
$11$	0.676857	−	1.17235i	0.204080	−	0.353477i	0.949839	+	0.312738i	$0.101246\pi$
$12$	−0.987132	+	6.32710i	−0.284960	+	1.82648i
$13$	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
$17$	3.31027			0.802859			0.401430	−	0.915890i	$-0.368513\pi$
$17$	3.31027			0.802859			0.401430	+	0.915890i	$0.368513\pi$
$18$	6.82030	+	2.18125i	1.60756	+	0.514126i
$19$	−2.20659			−0.506226			−0.253113	−	0.967437i	$-0.581454\pi$
$19$	−2.20659			−0.506226			−0.253113	+	0.967437i	$0.581454\pi$
$20$	−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	0.695868	−	0.718169i	$-0.255020\pi$
$23$	−1.31415	−	2.27617i	−0.274019	−	0.474614i	−0.969887	+	0.243555i	$0.921686\pi$
$24$	5.46287	+	4.40288i	1.11510	+	0.898735i
$25$	−1.76573	+	3.05833i	−0.353146	+	0.611666i
$26$	3.49916			0.686241
$27$	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	$0.135780\pi$
$30$	9.40187	+	7.57758i	1.71654	+	1.38347i
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	0.974767	−	0.223224i	$-0.0716581\pi$
$31$	1.63729	+	2.83587i	0.294066	+	0.509337i	−0.680701	+	0.732561i	$0.738325\pi$
$32$	−1.33629	−	2.31453i	−0.236226	−	0.409155i
$33$	−2.18702	+	0.845323i	−0.380712	+	0.147152i
$34$	3.95060	−	6.84263i	0.677521	−	1.17350i
$35$		0			0
$36$	8.20815	−	7.45963i	1.36803	−	1.24327i
$37$	−10.8755			−1.78791			−0.893957	−	0.448153i	$-0.852082\pi$
$37$	−10.8755			−1.78791			−0.893957	+	0.448153i	$0.852082\pi$
$38$	−2.63342	+	4.56121i	−0.427197	+	0.739926i
$39$	0.391421	−	2.50884i	0.0626775	−	0.401736i
$40$	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	$0.274093\pi$
$44$	−5.00488			−0.754514
$45$	6.48471	−	5.89336i	0.966684	−	0.878530i
$46$	−6.27340			−0.924962
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	−0.683650	−	0.729810i	$-0.739609\pi$
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	0.973859	+	0.227154i	$0.0729419\pi$
$48$	3.67474	−	1.42035i	0.530404	−	0.205010i
$49$		0			0
$50$	4.21456	+	7.29984i	0.596029	+	1.03235i
$51$	−4.46414	−	3.59794i	−0.625105	−	0.503813i
$52$	2.71001	−	4.69388i	0.375811	−	0.650924i
$53$	6.45486			0.886644			0.443322	−	0.896363i	$-0.353800\pi$
$53$	6.45486			0.886644			0.443322	+	0.896363i	$0.353800\pi$
$54$	−6.82685	−	10.3546i	−0.929017	−	1.40908i
$55$	−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
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	−0.922799	−	0.385283i	$-0.874104\pi$
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	0.127735	−	0.991808i	$-0.459229\pi$
$60$	17.4463	−	6.74331i	2.25231	−	0.870558i
$61$	0.279867	−	0.484744i	0.0358333	−	0.0620651i	−0.847553	−	0.530711i	$-0.821925\pi$
$61$	0.279867	−	0.484744i	0.0358333	−	0.0620651i	0.883386	+	0.468646i	$0.155258\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	2.14100	−	3.70832i	0.265558	−	0.459960i
$66$	−0.862710	+	5.52960i	−0.106192	+	0.680647i
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	−0.930420	−	0.366494i	$-0.880558\pi$
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	0.147817	−	0.989015i	$-0.452775\pi$
$68$	−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	$0.221984\pi$
$72$	−2.58157	−	11.8752i	−0.304241	−	1.39951i
$73$	10.4554			1.22372			0.611858	−	0.790968i	$-0.290422\pi$
$73$	10.4554			1.22372			0.611858	+	0.790968i	$0.290422\pi$
$74$	−12.9791	+	22.4805i	−1.50879	+	2.61331i
$75$	5.70532	−	2.20521i	0.658793	−	0.254635i
$76$	4.07903	+	7.06509i	0.467897	+	0.810422i
$77$		0			0
$78$	−4.71886	−	3.80324i	−0.534306	−	0.430632i
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	−0.886810	−	0.462134i	$-0.847084\pi$
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	0.843625	+	0.536933i	$0.180417\pi$
$80$	6.64375			0.742793
$81$	−8.18772	+	3.73647i	−0.909747	+	0.415163i
$82$	4.31684			0.476715
$83$	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
$87$	−1.68575	+	0.651573i	−0.180732	+	0.0698559i
$88$	−2.74185	+	4.74903i	−0.292283	+	0.506248i
$89$	6.40711			0.679153			0.339576	−	0.940579i	$-0.389716\pi$
$89$	6.40711			0.679153			0.339576	+	0.940579i	$0.389716\pi$
$90$	−4.44301	−	20.4378i	−0.468335	−	2.15433i
$91$		0			0
$92$	−4.85859	+	8.41533i	−0.506543	+	0.877359i
$93$	0.874308	−	5.60395i	0.0906615	−	0.581102i
$94$	−4.74884	−	8.22524i	−0.489806	−	0.848369i
$95$	3.22257	+	5.58166i	0.330629	+	0.572666i
$96$	−0.713577	+	4.57373i	−0.0728292	+	0.466804i
$97$	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
$100$	13.0563			1.30563
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	0.107419	+	0.994214i	$0.465741\pi$
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	−0.914724	+	0.404079i	$0.867592\pi$
$102$	−12.7649	+	4.93387i	−1.26392	+	0.488526i
$103$	−1.11342	−	1.92849i	−0.109708	−	0.190020i	0.805944	−	0.591992i	$-0.201658\pi$
$103$	−1.11342	−	1.92849i	−0.109708	−	0.190020i	−0.915652	+	0.401972i	$0.868325\pi$
$104$	−2.96929	−	5.14295i	−0.291162	−	0.504308i
$105$		0			0
$106$	7.70346	−	13.3428i	0.748226	−	1.29597i
$107$	17.5081			1.69257			0.846284	−	0.532732i	$-0.178835\pi$
$107$	17.5081			1.69257			0.846284	+	0.532732i	$0.178835\pi$
$108$	−19.1772	+	1.13839i	−1.84532	+	0.109542i
$109$	15.5983			1.49405			0.747025	−	0.664796i	$-0.231482\pi$
$109$	15.5983			1.49405			0.747025	+	0.664796i	$0.231482\pi$
$110$	−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	$0.858649\pi$
$114$	8.50894	−	3.28886i	0.796935	−	0.308030i
$115$	−3.83845	+	6.64839i	−0.357937	+	0.619966i
$116$	−3.85775			−0.358183
$117$	−3.25472	+	2.95792i	−0.300899	+	0.273459i
$118$	−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
$122$	−0.668005	−	1.15702i	−0.0604784	−	0.104752i
$123$	0.482888	−	3.09511i	0.0435405	−	0.279076i
$124$	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
$129$	7.01573	−	2.71171i	0.617701	−	0.238752i
$130$	−5.11028	−	8.85127i	−0.448202	−	0.776308i
$131$	2.66432	+	4.61473i	0.232782	+	0.403191i	0.958626	−	0.284669i	$-0.0918837\pi$
$131$	2.66432	+	4.61473i	0.232782	+	0.403191i	−0.725844	+	0.687860i	$0.758550\pi$
$132$	6.74944	+	5.43981i	0.587463	+	0.473475i
$133$		0			0
$134$	−30.5800			−2.64171
$135$	−15.1506	+	0.899369i	−1.30396	+	0.0774054i
$136$	−13.4095			−1.14985
$137$	3.74772	−	6.49124i	0.320189	−	0.554584i	−0.660338	−	0.750969i	$-0.729587\pi$
$137$	3.74772	−	6.49124i	0.320189	−	0.554584i	0.980527	+	0.196385i	$0.0629202\pi$
$138$	8.46013	+	6.81856i	0.720174	+	0.580435i
$139$	−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
$143$	1.98455			0.165956
$144$	−6.49944	−	2.07864i	−0.541620	−	0.173220i
$145$	−3.04775			−0.253102
$146$	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	0.817924	−	0.575326i	$-0.195125\pi$
$149$	−1.08986	−	1.88769i	−0.0892846	−	0.154645i	−0.907209	+	0.420680i	$0.861791\pi$
$150$	2.25056	−	14.4252i	0.183758	−	1.17781i
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	0.425705	+	0.904862i	$0.360026\pi$
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	−0.996486	+	0.0837595i	$0.973307\pi$
$152$	8.93857			0.725014
$153$	2.10961	+	9.70416i	0.170552	+	0.784535i
$154$		0			0
$155$	4.78231	−	8.28320i	0.384124	−	0.665322i
$156$	−8.75643	+	3.38451i	−0.701075	+	0.270978i
$157$	1.48312	+	2.56883i	0.118365	+	0.205015i	0.919120	−	0.393978i	$-0.128901\pi$
$157$	1.48312	+	2.56883i	0.118365	+	0.205015i	−0.800755	+	0.598993i	$0.795568\pi$
$158$	0.916172	+	1.58686i	0.0728867	+	0.126243i
$159$	−8.70484	−	7.01580i	−0.690339	−	0.556389i
$160$	−3.90314	+	6.76043i	−0.308570	+	0.534459i
$161$		0			0
$162$	−2.04789	+	21.3840i	−0.160898	+	1.68008i
$163$	0.388555			0.0304340			0.0152170	−	0.999884i	$-0.495156\pi$
$163$	0.388555			0.0304340			0.0152170	+	0.999884i	$0.495156\pi$
$164$	3.34329	−	5.79074i	0.261067	−	0.452181i
$165$	5.33228	+	4.29763i	0.415117	+	0.334570i
$166$	−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
$170$	−23.0783			−1.77003
$171$	−1.40624	−	6.46867i	−0.107538	−	0.494672i
$172$	16.0551			1.22419
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	−0.932750	−	0.360525i	$-0.882598\pi$
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	0.778598	+	0.627522i	$0.215931\pi$
$174$	−0.664975	+	4.26221i	−0.0504116	+	0.323117i
$175$		0			0
$176$	1.53957	+	2.66661i	0.116049	+	0.201003i
$177$	−3.26112	+	20.9024i	−0.245121	+	1.57112i
$178$	7.64647	−	13.2441i	0.573127	−	0.992685i
$179$	−10.5849			−0.791149			−0.395575	−	0.918434i	$-0.629455\pi$
$179$	−10.5849			−0.791149			−0.395575	+	0.918434i	$0.629455\pi$
$180$	−30.8569	−	9.86859i	−2.29994	−	0.735561i
$181$	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
$185$	15.8829	+	27.5099i	1.16773	+	2.02257i
$186$	−10.5404	−	8.49522i	−0.772862	−	0.622899i
$187$	2.24058	−	3.88081i	0.163848	−	0.283793i
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	−0.976094	−	0.217348i	$-0.930259\pi$
$191$	−4.14357	+	7.17688i	−0.299818	+	0.519301i	0.676276	+	0.736648i	$0.263593\pi$
$192$	14.7376	+	11.8780i	1.06359	+	0.857218i
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$	−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	$0.431478\pi$
$198$	7.17356	−	6.51939i	0.509803	−	0.463313i
$199$	14.4087			1.02140			0.510702	−	0.859758i	$-0.329385\pi$
$199$	14.4087			1.02140			0.510702	+	0.859758i	$0.329385\pi$
$200$	7.15272	−	12.3889i	0.505773	−	0.876025i
$201$	−3.42072	+	21.9254i	−0.241279	+	1.54650i
$202$	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
$206$	−5.31515			−0.370324
$207$	5.83517	−	5.30304i	0.405572	−	0.368587i
$208$	−3.33454			−0.231209
$209$	−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
$213$	−17.4205	−	14.0403i	−1.19363	−	0.962024i
$214$	20.8947	−	36.1907i	1.42833	−	2.47395i
$215$	12.6841			0.865047
$216$	−9.42574	+	18.8205i	−0.641341	+	1.28057i
$217$		0			0
$218$	18.6156	−	32.2431i	1.26081	−	2.18378i
$219$	−14.0999	−	11.3640i	−0.952783	−	0.767910i
$220$	7.30929	+	12.6601i	0.492792	+	0.853541i
$221$	2.42644	+	4.20271i	0.163220	+	0.282705i
$222$	41.9374	−	16.2096i	2.81466	−	1.08791i
$223$	−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
$226$	−4.03169			−0.268184
$227$	9.85631	−	17.0716i	0.654187	−	1.13308i	−0.327910	−	0.944709i	$-0.606344\pi$
$227$	9.85631	−	17.0716i	0.654187	−	1.13308i	0.982097	−	0.188376i	$-0.0603222\pi$
$228$	2.17819	−	13.9613i	0.144254	−	0.924609i
$229$	14.0364	+	24.3118i	0.927552	+	1.60657i	0.787404	+	0.616437i	$0.211425\pi$
$229$	14.0364	+	24.3118i	0.927552	+	1.60657i	0.140148	+	0.990131i	$0.455242\pi$
$230$	9.16188	+	15.8688i	0.604116	+	1.04636i
$231$		0			0
$232$	−2.11342	+	3.66054i	−0.138753	+	0.240326i
$233$	13.8023			0.904216			0.452108	−	0.891963i	$-0.350672\pi$
$233$	13.8023			0.904216			0.452108	+	0.891963i	$0.350672\pi$
$234$	2.22998	+	10.2579i	0.145778	+	0.670579i
$235$	−11.6225			−0.758171
$236$	−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	$0.716877\pi$
$240$	−8.95957	−	7.22110i	−0.578338	−	0.466120i
$241$	−11.5849	+	20.0656i	−0.746247	+	1.29254i	0.203362	+	0.979104i	$0.434813\pi$
$241$	−11.5849	+	20.0656i	−0.746247	+	1.29254i	−0.949610	+	0.313435i	$0.898520\pi$
$242$	21.8815			1.40660
$243$	15.1029	+	3.86035i	0.968852	+	0.247642i
$244$	−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
$248$	−6.63243	−	11.4877i	−0.421160	−	0.729470i
$249$	−3.17850	+	1.22854i	−0.201429	+	0.0778559i
$250$	−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
$255$	−2.58157	+	16.5468i	−0.161664	+	1.03620i
$256$	13.8226	+	23.9414i	0.863912	+	1.49634i
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	0.981232	−	0.192833i	$-0.0617676\pi$
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	−0.657614	+	0.753355i	$0.728434\pi$
$258$	2.76748	−	17.7384i	0.172296	−	1.10434i
$259$		0			0
$260$	−15.8312			−0.981807
$261$	2.98155	+	0.953553i	0.184553	+	0.0590235i
$262$	12.7187			0.785767
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	−0.404347	−	0.914605i	$-0.632501\pi$
$263$	9.56654	−	16.5697i	0.589898	−	1.02173i	0.994245	−	0.107128i	$-0.0341653\pi$
$264$	8.85931	−	3.42428i	0.545253	−	0.210750i
$265$	−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
$269$	−8.83681			−0.538790			−0.269395	−	0.963030i	$-0.586824\pi$
$269$	−8.83681			−0.538790			−0.269395	+	0.963030i	$0.586824\pi$
$270$	−16.2222	+	32.3910i	−0.987249	+	1.97125i
$271$	−18.3391			−1.11402			−0.557010	−	0.830506i	$-0.688052\pi$
$271$	−18.3391			−1.11402			−0.557010	+	0.830506i	$0.688052\pi$
$272$	−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
$276$	15.6988	−	6.06786i	0.944956	−	0.365242i
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	−0.932460	−	0.361272i	$-0.882343\pi$
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	0.779101	+	0.626899i	$0.215676\pi$
$278$	−33.5730			−2.01357
$279$	−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	$0.182875\pi$
$282$	−2.53587	+	16.2538i	−0.151009	+	0.967903i
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	0.618571	−	0.785729i	$-0.287712\pi$
$283$	−6.24415	−	10.8152i	−0.371176	−	0.642896i	−0.989747	+	0.142833i	$0.954379\pi$
$284$	−23.8793	−	41.3602i	−1.41698	−	2.45428i
$285$	1.72084	−	11.0299i	0.101934	−	0.653354i
$286$	2.36843	−	4.10224i	0.140048	−	0.242571i
$287$		0			0
$288$	5.93351	−	5.39242i	0.349635	−	0.317751i
$289$	−6.04208			−0.355417
$290$	−3.63729	+	6.29997i	−0.213589	+	0.369947i
$291$	−13.3815	+	5.17220i	−0.784439	+	0.303200i
$292$	−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
$296$	44.0549			2.56064
$297$	−3.87186	−	5.87260i	−0.224668	−	0.340763i
$298$	−5.20269			−0.301384
$299$	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
$303$	26.2153	−	10.1327i	1.50603	−	0.582106i
$304$	2.50953	−	4.34663i	0.143931	−	0.249297i
$305$	−1.63491			−0.0936145
$306$	22.5770	+	7.22054i	1.29064	+	0.412771i
$307$	−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
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.801652	−	0.597791i	$-0.796045\pi$
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.116876	−	0.993146i	$-0.537288\pi$
$312$	−1.58559	+	10.1630i	−0.0897663	+	0.575364i
$313$	0.759535	−	1.31555i	0.0429315	−	0.0743595i	−0.843761	−	0.536719i	$-0.819664\pi$
$313$	0.759535	−	1.31555i	0.0429315	−	0.0743595i	0.886693	+	0.462359i	$0.152997\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	−0.388175	−	0.921586i	$-0.626894\pi$
$317$	10.7544	−	18.6272i	0.604029	−	1.04621i	0.992204	−	0.124623i	$-0.0397723\pi$
$318$	−24.8909	+	9.62079i	−1.39581	+	0.539507i
$319$	−0.706261	−	1.22328i	−0.0395430	−	0.0684905i
$320$	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
$324$	27.0991	+	19.3085i	1.50551	+	1.07269i
$325$	−5.17713			−0.287175
$326$	0.463715	−	0.803178i	0.0256828	−	0.0444839i
$327$	−21.0355	−	16.9539i	−1.16326	−	0.937550i
$328$	−3.66315	−	6.34476i	−0.202263	−	0.350330i
$329$		0			0
$330$	15.2473	−	5.89336i	0.839337	−	0.324419i
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	0.463844	+	0.885917i	$0.346470\pi$
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	−0.999149	+	0.0412580i	$0.986863\pi$
$332$	−7.27381			−0.399202
$333$	−6.93082	−	31.8817i	−0.379807	−	1.74711i
$334$	−17.4188			−0.953116
$335$	−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
$339$	−0.450990	+	2.89066i	−0.0244944	+	0.156999i
$340$	−17.8736	+	30.9580i	−0.969332	+	1.67893i
$341$	4.43285			0.240052
$342$	−15.0496	−	4.81312i	−0.813788	−	0.260264i
$343$		0			0
$344$	8.79558	−	15.2344i	0.474226	−	0.821383i
$345$	12.4026	−	4.79381i	0.667732	−	0.258090i
$346$	4.83948	+	8.38222i	0.260172	+	0.450631i
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	0.837553	−	0.546356i	$-0.183985\pi$
$347$	−1.01302	−	1.75460i	−0.0543817	−	0.0941919i	−0.891935	+	0.452164i	$0.850652\pi$
$348$	5.20245	+	4.19299i	0.278881	+	0.224768i
$349$	−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
$352$	−3.61792			−0.192836
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	−0.544588	−	0.838704i	$-0.683314\pi$
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	0.998633	+	0.0522753i	$0.0166473\pi$
$354$	39.3152	+	31.6867i	2.08958	+	1.68413i
$355$	−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
$359$	−2.96726			−0.156606			−0.0783030	−	0.996930i	$-0.524950\pi$
$359$	−2.96726			−0.156606			−0.0783030	+	0.996930i	$0.524950\pi$
$360$	−26.2686	+	23.8731i	−1.38448	+	1.25823i
$361$	−14.1310			−0.743736
$362$	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
$366$	−0.356713	+	2.28638i	−0.0186457	+	0.119511i
$367$	−5.07874	+	8.79664i	−0.265108	+	0.459181i	−0.967592	−	0.252519i	$-0.918741\pi$
$367$	−5.07874	+	8.79664i	−0.265108	+	0.459181i	0.702484	+	0.711700i	$0.252074\pi$
$368$	5.97827			0.311639
$369$	−4.01528	+	3.64912i	−0.209027	+	0.189966i
$370$	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	0.980675	+	0.195645i	$0.0626799\pi$
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	−0.320904	+	0.947112i	$0.603987\pi$
$374$	−5.34798	−	9.26297i	−0.276537	−	0.478977i
$375$	5.78458	+	4.66217i	0.298715	+	0.240754i
$376$	−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
$381$	5.35273	+	4.31411i	0.274229	+	0.221019i
$382$	9.89016	+	17.1303i	0.506025	+	0.876460i
$383$	−13.6563	−	23.6535i	−0.697806	−	1.20864i	−0.969225	−	0.246175i	$-0.920826\pi$
$383$	−13.6563	−	23.6535i	−0.697806	−	1.20864i	0.271419	−	0.962461i	$-0.412507\pi$
$384$	33.5056	−	12.9505i	1.70983	−	0.660878i
$385$		0			0
$386$	44.8370			2.28214
$387$	−12.4086	−	3.96848i	−0.630763	−	0.201729i
$388$	−30.6229			−1.55464
$389$	−2.09223	+	3.62385i	−0.106080	+	0.183736i	−0.914179	−	0.405311i	$-0.867163\pi$
$389$	−2.09223	+	3.62385i	−0.106080	+	0.183736i	0.808099	+	0.589047i	$0.200497\pi$
$390$	−2.72888	+	17.4909i	−0.138182	+	0.885689i
$391$	−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
$395$	2.24228			0.112821
$396$	−3.18956	−	14.6719i	−0.160281	−	0.737293i
$397$	30.6709			1.53933			0.769664	−	0.638450i	$-0.220424\pi$
$397$	30.6709			1.53933			0.769664	+	0.638450i	$0.220424\pi$
$398$	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	0.938765	−	0.344557i	$-0.111971\pi$
$401$	3.42402	+	5.93057i	0.170987	+	0.296158i	−0.767778	+	0.640716i	$0.778638\pi$
$402$	41.2393	+	33.2375i	2.05683	+	1.65773i
$403$	−2.40027	+	4.15739i	−0.119566	+	0.207095i
$404$	59.9922			2.98472
$405$	21.4092	+	15.2543i	1.06383	+	0.757994i
$406$		0			0
$407$	−7.36113	+	12.7499i	−0.364878	+	0.631987i
$408$	18.0836	+	14.5748i	0.895272	+	0.721558i
$409$	−9.13490	−	15.8221i	−0.451692	−	0.782353i	0.546799	−	0.837264i	$-0.315846\pi$
$409$	−9.13490	−	15.8221i	−0.451692	−	0.782353i	−0.998491	+	0.0549104i	$0.982513\pi$
$410$	−6.30445	−	10.9196i	−0.311355	−	0.539282i
$411$	−12.1094	+	4.68050i	−0.597313	+	0.230872i
$412$	−4.11646	+	7.12991i	−0.202803	+	0.351265i
$413$		0			0
$414$	−3.99798	−	18.3906i	−0.196490	−	0.903851i
$415$	−5.74655			−0.282087
$416$	1.95901	−	3.39311i	0.0960485	−	0.166361i
$417$	−3.75552	+	24.0713i	−0.183909	+	1.17878i
$418$	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	$-0.00284791\pi$
$422$	−33.0542			−1.60905
$423$	11.3701	+	3.63636i	0.552833	+	0.176806i
$424$	−26.1477			−1.26985
$425$	−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
$429$	−2.67631	−	2.15701i	−0.129213	−	0.104141i
$430$	15.1376	−	26.2191i	0.730001	−	1.26440i
$431$	20.2427			0.975055			0.487527	−	0.873108i	$-0.337899\pi$
$431$	20.2427			0.975055			0.487527	+	0.873108i	$0.337899\pi$
$432$	6.50569	+	9.86744i	0.313005	+	0.474748i
$433$	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
$437$	2.89978	+	5.02257i	0.138715	+	0.240262i
$438$	−40.3178	+	15.5835i	−1.92646	+	0.744610i
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	0.0375520	+	0.999295i	$0.488044\pi$
$439$	−17.7390	+	30.7249i	−0.846639	+	1.46642i	−0.884191	+	0.467126i	$0.845289\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	−0.542501	−	0.840055i	$-0.682523\pi$
$443$	9.60313	−	16.6331i	0.456258	−	0.790263i	0.998760	+	0.0497923i	$0.0158559\pi$
$444$	10.7355	−	68.8101i	0.509485	−	3.26558i
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$	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	$0.746215\pi$
$450$	−18.7138	+	17.0072i	−0.882176	+	0.801728i
$451$	2.44830			0.115286
$452$	−3.12244	+	5.40823i	−0.146867	+	0.254382i
$453$	22.6628	−	8.75958i	1.06479	−	0.411561i
$454$	−23.5257	−	40.7478i	−1.10412	−	1.91239i
$455$		0			0
$456$	−12.0543	−	9.71534i	−0.564494	−	0.454963i
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$	67.0062			3.13099
$459$	7.70252	−	15.3797i	0.359523	−	0.717863i
$460$	28.3826			1.32335
$461$	−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
$465$	−15.4523	+	5.97259i	−0.716583	+	0.276972i
$466$	16.4721	−	28.5305i	0.763054	−	1.32165i
$467$	−34.9527			−1.61742			−0.808709	−	0.588209i	$-0.799833\pi$
$467$	−34.9527			−1.61742			−0.808709	+	0.588209i	$0.799833\pi$
$468$	15.4873	+	4.95311i	0.715901	+	0.228958i
$469$		0			0
$470$	−13.8707	+	24.0248i	−0.639809	+	1.10818i
$471$	0.791979	−	5.07625i	0.0364925	−	0.233901i
$472$	24.7386	+	42.8485i	1.13869	+	1.97226i
$473$	2.93930	+	5.09102i	0.135149	+	0.234086i
$474$	0.489233	−	3.13578i	0.0224712	−	0.144031i
$475$	3.89623	−	6.74848i	0.178771	−	0.309641i
$476$		0			0
$477$	4.11362	+	18.9226i	0.188350	+	0.866407i
$478$	26.4021			1.20760
$479$	−14.9054	+	25.8170i	−0.681047	+	1.17961i	0.293615	+	0.955924i	$0.405142\pi$
$479$	−14.9054	+	25.8170i	−0.681047	+	1.17961i	−0.974662	+	0.223684i	$0.928192\pi$
$480$	12.6116	−	4.87460i	0.575638	−	0.222494i
$481$	−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
$485$	−24.1931			−1.09855
$486$	26.0040	−	26.6120i	1.17957	−	1.20714i
$487$	22.4506			1.01733			0.508667	−	0.860964i	$-0.330139\pi$
$487$	22.4506			1.01733			0.508667	+	0.860964i	$0.330139\pi$
$488$	−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	$0.543016\pi$
$492$	−10.8026	+	4.17541i	−0.487020	+	0.188242i
$493$	1.72704	−	2.99132i	0.0777819	−	0.134722i
$494$	−7.72119			−0.347393
$495$	−2.51986	−	11.5913i	−0.113259	−	0.520991i
$496$	−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	0.948527	−	0.316696i	$-0.102573\pi$
$499$	4.46760	+	7.73811i	0.199997	+	0.346405i	−0.748530	+	0.663101i	$0.769240\pi$
$500$	7.92929	+	13.7339i	0.354609	+	0.614200i
$501$	−1.94850	+	12.4890i	−0.0870524	+	0.557969i
$502$	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
$507$	−17.5303	+	6.77577i	−0.778547	+	0.300922i
$508$	7.33732	+	12.7086i	0.325541	+	0.563854i
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	−0.988924	−	0.148423i	$-0.952580\pi$
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	0.365924	−	0.930645i	$-0.380753\pi$
$510$	31.1228	+	25.0839i	1.37814	+	1.11073i
$511$		0			0
$512$	24.5070			1.08307
$513$	−5.13440	+	10.2519i	−0.226689	+	0.452633i
$514$	24.7661			1.09238
$515$	−3.25214	+	5.63287i	−0.143306	+	0.248214i
$516$	−21.6515	−	17.4503i	−0.953153	−	0.768208i
$517$	−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
$521$	8.47536			0.371312			0.185656	−	0.982615i	$-0.440559\pi$
$521$	8.47536			0.371312			0.185656	+	0.982615i	$0.440559\pi$
$522$	5.52937	−	5.02513i	0.242014	−	0.219944i
$523$	33.4473			1.46255			0.731273	−	0.682085i	$-0.238926\pi$
$523$	33.4473			1.46255			0.731273	+	0.682085i	$0.238926\pi$
$524$	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
$528$	0.822124	−	5.26947i	0.0357784	−	0.229324i
$529$	8.04603	−	13.9361i	0.349827	−	0.605919i
$530$	−45.0015			−1.95474
$531$	27.1167	−	24.6439i	1.17677	−	1.06945i
$532$		0			0
$533$	−1.32569	+	2.29616i	−0.0574220	+	0.0994579i
$534$	−24.7068	+	9.54962i	−1.06917	+	0.413253i
$535$	−25.5693	−	44.2874i	−1.10546	−	1.91471i
$536$	25.9493	+	44.9456i	1.12084	+	1.94135i
$537$	14.2744	+	11.5047i	0.615987	+	0.496464i
$538$	−10.5461	+	18.2665i	−0.454677	+	0.787523i
$539$		0			0
$540$	30.8866	+	46.8469i	1.32915	+	2.01597i
$541$	18.2586			0.784998			0.392499	−	0.919752i	$-0.371611\pi$
$541$	18.2586			0.784998			0.392499	+	0.919752i	$0.371611\pi$
$542$	−21.8865	+	37.9085i	−0.940106	+	1.62831i
$543$	−26.4740	−	21.3371i	−1.13611	−	0.915664i
$544$	−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	$0.206045\pi$
$548$	−27.7117			−1.18378
$549$	1.59940	+	0.511515i	0.0682606	+	0.0218309i
$550$	11.4106			0.486551
$551$	−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
$555$	8.48141	−	54.3622i	0.360016	−	2.30755i
$556$	−26.0014	+	45.0358i	−1.10271	+	1.90994i
$557$	−33.3821			−1.41445			−0.707223	−	0.706991i	$-0.750052\pi$
$557$	−33.3821			−1.41445			−0.707223	+	0.706991i	$0.750052\pi$
$558$	4.98106	+	22.9128i	0.210865	+	0.969977i
$559$	−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
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	0.888190	−	0.459477i	$-0.151963\pi$
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	−0.842013	+	0.539457i	$0.818630\pi$
$564$	19.8394	+	15.9899i	0.835392	+	0.673296i
$565$	−2.46683	+	4.27268i	−0.103780	+	0.179753i
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	−0.993475	−	0.114049i	$-0.963618\pi$
$569$	−9.49302	+	16.4424i	−0.397968	+	0.689301i	0.595507	+	0.803350i	$0.296951\pi$
$570$	−20.7460	−	16.7206i	−0.868956	−	0.700348i
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	0.998680	−	0.0513674i	$-0.0163580\pi$
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	−0.543825	+	0.839198i	$0.683025\pi$
$572$	−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
$576$	−6.96449	−	32.0366i	−0.290187	−	1.33486i
$577$	−30.9032			−1.28652			−0.643258	−	0.765649i	$-0.722418\pi$
$577$	−30.9032			−1.28652			−0.643258	+	0.765649i	$0.722418\pi$
$578$	−7.21083	+	12.4895i	−0.299931	+	0.519496i
$579$	5.01553	−	32.1474i	0.208438	−	1.33600i
$580$	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
$584$	−42.3535			−1.75260
$585$	12.2355	+	3.91312i	0.505875	+	0.161788i
$586$	12.4214			0.513122
$587$	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
$591$	−8.08650	−	6.51743i	−0.332634	−	0.268091i
$592$	12.3685	−	21.4230i	0.508344	−	0.880478i
$593$	27.7550			1.13976			0.569880	−	0.821728i	$-0.306990\pi$
$593$	27.7550			1.13976			0.569880	+	0.821728i	$0.306990\pi$
$594$	−16.7600	+	0.994906i	−0.687671	+	0.0408215i
$595$		0			0
$596$	−4.02936	+	6.97905i	−0.165049	+	0.285873i
$597$	−19.4311	−	15.6608i	−0.795264	−	0.640955i
$598$	−4.59841	−	7.96468i	−0.188043	−	0.325700i
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	0.861881	−	0.507110i	$-0.169286\pi$
$599$	−0.201412	−	0.348855i	−0.00822945	−	0.0142538i	−0.870111	+	0.492856i	$0.835953\pi$
$600$	−23.1114	+	8.93298i	−0.943520	+	0.364687i
$601$	−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
$604$	51.8626			2.11026
$605$	13.3885	−	23.1895i	0.544318	−	0.942787i
$606$	10.3411	−	66.2819i	0.420077	−	2.69252i
$607$	12.0348	+	20.8449i	0.488479	+	0.846070i	0.999912	−	0.0132531i	$-0.00421872\pi$
$607$	12.0348	+	20.8449i	0.488479	+	0.846070i	−0.511434	+	0.859323i	$0.670885\pi$
$608$	2.94865	+	5.10721i	0.119584	+	0.207125i
$609$		0			0
$610$	−1.95115	+	3.37950i	−0.0789999	+	0.136832i
$611$	5.83343			0.235995
$612$	27.1712	−	24.6934i	1.09833	−	0.998172i
$613$	−20.3815			−0.823200			−0.411600	−	0.911365i	$-0.635030\pi$
$613$	−20.3815			−0.823200			−0.411600	+	0.911365i	$0.635030\pi$
$614$	−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	$-0.485684\pi$
$618$	7.16786	+	5.77705i	0.288334	+	0.232387i
$619$	7.41095	−	12.8361i	0.297871	−	0.515928i	−0.677777	−	0.735267i	$-0.737057\pi$
$619$	7.41095	−	12.8361i	0.297871	−	0.515928i	0.975649	+	0.219339i	$0.0703900\pi$
$620$	−35.3617			−1.42016
$621$	−13.6330	+	0.809283i	−0.547075	+	0.0324754i
$622$	−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
$626$	−1.81291	−	3.14005i	−0.0724585	−	0.125502i
$627$	4.82585	−	1.86528i	0.192726	−	0.0744920i
$628$	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
$633$	−3.69749	+	23.6994i	−0.146962	+	0.941965i
$634$	−25.6694	−	44.4607i	−1.01946	−	1.76576i
$635$	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
$639$	8.23233	+	37.8686i	0.325666	+	1.49806i
$640$	60.5764			2.39449
$641$	−5.96592	+	10.3333i	−0.235640	+	0.408140i	−0.959458	−	0.281850i	$-0.909052\pi$
$641$	−5.96592	+	10.3333i	−0.235640	+	0.408140i	0.723819	+	0.689990i	$0.242385\pi$
$642$	−67.5138	+	26.0953i	−2.66456	+	1.02990i
$643$	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
$647$	0.988954			0.0388798			0.0194399	−	0.999811i	$-0.493812\pi$
$647$	0.988954			0.0388798			0.0194399	+	0.999811i	$0.493812\pi$
$648$	33.1673	−	15.1359i	1.30293	−	0.594595i
$649$	−16.5343			−0.649027
$650$	−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	0.553567	−	0.832805i	$-0.313266\pi$
$653$	−11.3573	−	19.6715i	−0.444447	−	0.769804i	−0.998014	+	0.0630004i	$0.979933\pi$
$654$	−60.1496	+	23.2489i	−2.35203	+	0.909103i
$655$	7.78211	−	13.4790i	0.304072	−	0.526668i
$656$	−4.11376			−0.160615
$657$	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	$0.897824\pi$
$660$	3.90314	−	25.0175i	0.151929	−	0.973804i
$661$	16.9629	+	29.3806i	0.659780	+	1.14277i	0.980672	+	0.195657i	$0.0626839\pi$
$661$	16.9629	+	29.3806i	0.659780	+	1.14277i	−0.320892	+	0.947116i	$0.603983\pi$
$662$	23.2458	+	40.2628i	0.903472	+	1.56486i
$663$	1.29571	−	8.30495i	0.0503212	−	0.322538i
$664$	−3.98486	+	6.90198i	−0.154642	+	0.267849i
$665$		0			0
$666$	−74.1738	−	23.7221i	−2.87418	−	0.919213i
$667$	−2.74247			−0.106189
$668$	−13.4905	+	23.3662i	−0.521962	+	0.904064i
$669$	7.55300	−	2.91937i	0.292016	−	0.112869i
$670$	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	$0.953505\pi$
$674$	23.1403			0.891332
$675$	10.1006	+	15.3199i	0.388771	+	0.589665i
$676$	−40.1171			−1.54297
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	0.227421	+	0.973797i	$0.426971\pi$
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	−0.957043	+	0.289946i	$0.906363\pi$
$678$	5.43702	+	4.38204i	0.208807	+	0.168291i
$679$		0			0
$680$	19.5836	+	33.9198i	0.750997	+	1.30076i
$681$	−31.8471	+	12.3095i	−1.22038	+	0.471700i
$682$	5.29031	−	9.16309i	0.202577	−	0.350873i
$683$	−15.1871			−0.581120			−0.290560	−	0.956857i	$-0.593842\pi$
$683$	−15.1871			−0.581120			−0.290560	+	0.956857i	$0.593842\pi$
$684$	−18.1120	+	16.4603i	−0.692529	+	0.629376i
$685$	−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
$689$	4.73142	+	8.19507i	0.180253	+	0.312207i
$690$	4.89241	−	31.3583i	0.186251	−	1.19379i
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	−0.839293	−	0.543680i	$-0.817031\pi$
$691$	1.34574	−	2.33089i	0.0511943	−	0.0886711i	0.890487	+	0.455009i	$0.150364\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	−20.5420	+	35.5798i	−0.779203	+	1.34962i
$696$	6.82874	−	2.63943i	0.258843	−	0.100047i
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$	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	$0.571850\pi$
$702$	8.14202	−	16.2573i	0.307301	−	0.613590i
$703$	23.9976			0.905088
$704$	−7.39689	+	12.8118i	−0.278781	+	0.482862i
$705$	15.6738	+	12.6326i	0.590310	+	0.475769i
$706$	−20.3617	−	35.2675i	−0.766323	−	1.32731i
$707$		0			0
$708$	72.9542	−	28.1981i	2.74179	−	1.05975i
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$	−90.0587			−3.37984
$711$	−2.19358	−	0.701545i	−0.0822656	−	0.0263100i
$712$	−25.9543			−0.972679
$713$	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
$717$	2.95337	−	18.9299i	0.110296	−	0.706949i
$718$	−3.54123	+	6.13359i	−0.132158	+	0.228904i
$719$	20.9109			0.779845			0.389923	−	0.920848i	$-0.372502\pi$
$719$	20.9109			0.779845			0.389923	+	0.920848i	$0.372502\pi$
$720$	4.23400	+	19.4763i	0.157792	+	0.725840i
$721$		0			0
$722$	−16.8644	+	29.2100i	−0.627628	+	1.08708i
$723$	37.4323	−	14.4683i	1.39212	−	0.538081i
$724$	−36.2896	−	62.8554i	−1.34869	−	2.33600i
$725$	1.84243	+	3.19119i	0.0684263	+	0.118518i
$726$	−29.5088	−	23.7831i	−1.09517	−	0.882672i
$727$	−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
$730$	−72.8924			−2.69787
$731$	−7.18756	+	12.4492i	−0.265841	+	0.460451i
$732$	2.79075	+	2.24925i	0.103149	+	0.0831347i
$733$	7.07446	+	12.2533i	0.261301	+	0.452587i	0.966588	−	0.256335i	$-0.0825151\pi$
$733$	7.07446	+	12.2533i	0.261301	+	0.452587i	−0.705287	+	0.708922i	$0.749182\pi$
$734$	12.1223	+	20.9964i	0.447442	+	0.774992i
$735$		0			0
$736$	−3.51218	+	6.08327i	−0.129461	+	0.224232i
$737$	−17.3435			−0.638855
$738$	2.75108	+	12.6549i	0.101269	+	0.465835i
$739$	15.7181			0.578200			0.289100	−	0.957299i	$-0.406644\pi$
$739$	15.7181			0.578200			0.289100	+	0.957299i	$0.406644\pi$
$740$	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	$0.706836\pi$
$744$	−3.54170	+	22.7008i	−0.129845	+	0.832252i
$745$	−3.18333	+	5.51368i	−0.116628	+	0.202006i
$746$	60.8283			2.22708
$747$	5.62174	+	1.79793i	0.205689	+	0.0657828i
$748$	−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	0.722238	−	0.691644i	$-0.243113\pi$
$751$	−6.51848	−	11.2903i	−0.237863	−	0.411990i	−0.960101	+	0.279654i	$0.909780\pi$
$752$	4.52544	+	7.83829i	0.165026	+	0.285833i
$753$	−10.4973	−	8.46047i	−0.382543	−	0.308317i
$754$	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
$759$	4.79817	+	3.86716i	0.174162	+	0.140369i
$760$	−13.0542	−	22.6105i	−0.473525	−	0.820169i
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	0.806074	−	0.591814i	$-0.201588\pi$
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	−0.915563	+	0.402174i	$0.868255\pi$
$762$	15.3058	−	5.91596i	0.554470	−	0.214313i
$763$		0			0
$764$	30.6388			1.10847
$765$	21.4662	−	19.5086i	0.776111	−	0.705336i
$766$	−65.1918			−2.35547
$767$	8.95288	−	15.5068i	0.323270	−	0.559920i
$768$	7.38122	−	47.3105i	0.266347	−	1.70717i
$769$	−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
$773$	37.6264			1.35333			0.676663	−	0.736293i	$-0.263425\pi$
$773$	37.6264			1.35333			0.676663	+	0.736293i	$0.263425\pi$
$774$	−23.0120	+	20.9135i	−0.827150	+	0.751721i
$775$	−11.5640			−0.415393
$776$	−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
$780$	21.3495	+	17.2069i	0.764433	+	0.616106i
$781$	8.74345	−	15.1441i	0.312865	−	0.541898i
$782$	−20.7667			−0.742614
$783$	−2.98442	−	4.52659i	−0.106654	−	0.161767i
$784$		0			0
$785$	4.33198	−	7.50321i	0.154615	−	0.267801i
$786$	−17.1521	−	13.8240i	−0.611796	−	0.493086i
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	0.998330	+	0.0577648i	$0.0183973\pi$
$787$	15.4067	+	26.6853i	0.549191	+	0.951226i	−0.449139	+	0.893462i	$0.648269\pi$
$788$	−11.0847	−	19.1992i	−0.394875	−	0.683943i
$789$	−30.9108	+	11.9476i	−1.10045	+	0.425345i
$790$	2.67601	−	4.63499i	0.0952083	−	0.164906i
$791$		0			0
$792$	−15.6693	−	5.01131i	−0.556783	−	0.178069i
$793$	0.820571			0.0291393
$794$	36.6037	−	63.3994i	1.29902	−	2.24996i
$795$	−5.03393	+	32.2654i	−0.178535	+	1.14434i
$796$	−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
$800$	9.43814			0.333689
$801$	4.08319	+	18.7826i	0.144272	+	0.663652i
$802$	16.3454			0.577174
$803$	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
$807$	11.9171	+	9.60474i	0.419501	+	0.338103i
$808$	32.8659	−	56.9254i	1.15622	−	2.00263i
$809$	38.9636			1.36989			0.684943	−	0.728596i	$-0.259827\pi$
$809$	38.9636			1.36989			0.684943	+	0.728596i	$0.259827\pi$
$810$	57.0825	−	26.0496i	2.00568	−	0.915291i
$811$	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
$815$	−0.567459	−	0.982867i	−0.0198772	−	0.0344283i
$816$	12.1644	−	4.70176i	0.425840	−	0.164595i
$817$	4.79113	−	8.29849i	0.167621	−	0.290327i
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	0.233077	+	0.972458i	$0.425121\pi$
$821$	−20.7917	+	36.0123i	−0.725635	+	1.25684i	−0.958712	+	0.284378i	$0.908213\pi$
$822$	−4.77677	+	30.6171i	−0.166609	+	1.06789i
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	0.782835	−	0.622229i	$-0.213773\pi$
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	−0.930284	+	0.366841i	$0.880439\pi$
$824$	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	$0.220294\pi$
$828$	−27.7661	−	8.88010i	−0.964939	−	0.308605i
$829$	−16.6327			−0.577679			−0.288839	−	0.957378i	$-0.593269\pi$
$829$	−16.6327			−0.577679			−0.288839	+	0.957378i	$0.593269\pi$
$830$	−6.85813	+	11.8786i	−0.238049	+	0.412314i
$831$	8.24720	−	3.18769i	0.286092	−	0.110580i
$832$	−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
$836$	11.0437			0.381954
$837$	16.9853	−	1.00828i	0.587099	−	0.0348513i
$838$	−53.6137			−1.85205
$839$	−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
$843$	2.75674	−	1.06553i	0.0949473	−	0.0366988i
$844$	−25.5997	+	44.3400i	−0.881178	+	1.52624i
$845$	−31.6938			−1.09030
$846$	21.0861	−	19.1632i	0.724956	−	0.658846i
$847$		0			0
$848$	−7.34105	+	12.7151i	−0.252093	+	0.436638i
$849$	−3.33436	+	21.3718i	−0.114435	+	0.733479i
$850$	13.9514	+	24.1645i	0.478528	+	0.828834i
$851$	14.2920	+	24.7544i	0.489922	+	0.848570i
$852$	−12.7515	+	81.7316i	−0.436859	+	2.80008i
$853$	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
$856$	−70.9227			−2.42409
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	−0.353361	−	0.935487i	$-0.614961\pi$
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	0.986836	−	0.161724i	$-0.0517053\pi$
$858$	−7.65273	+	2.95792i	−0.261260	+	0.100982i
$859$	−1.89166	−	3.27646i	−0.0645427	−	0.111791i	0.831948	−	0.554853i	$-0.187226\pi$
$859$	−1.89166	−	3.27646i	−0.0645427	−	0.111791i	−0.896491	+	0.443062i	$0.853892\pi$
$860$	−23.4474	−	40.6121i	−0.799551	−	1.38486i
$861$		0			0
$862$	24.1583	−	41.8434i	0.822835	−	1.42519i
$863$	−0.427118			−0.0145393			−0.00726963	−	0.999974i	$-0.502314\pi$
$863$	−0.427118			−0.0145393			−0.00726963	+	0.999974i	$0.502314\pi$
$864$	−13.8628	+	0.822922i	−0.471621	+	0.0279964i
$865$	11.8444			0.402720
$866$	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
$870$	11.7526	−	4.54259i	0.398450	−	0.154008i
$871$	9.39105	−	16.2658i	0.318203	−	0.551145i
$872$	−63.1866			−2.13977
$873$	23.6676	+	7.56932i	0.801027	+	0.256183i
$874$	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	0.755167	−	0.655532i	$-0.227556\pi$
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	−0.945291	+	0.326228i	$0.894222\pi$
$878$	42.3408	+	73.3364i	1.42893	+	2.47498i
$879$	1.38947	−	8.90594i	0.0468658	−	0.300390i
$880$	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
$885$	57.6362	−	22.2774i	1.93742	−	0.748847i
$886$	−22.9214	−	39.7010i	−0.770060	−	1.33378i
$887$	28.7832	+	49.8540i	0.966446	+	1.67393i	0.705679	+	0.708532i	$0.250642\pi$
$887$	28.7832	+	49.8540i	0.966446	+	1.67393i	0.260767	+	0.965402i	$0.416025\pi$
$888$	−59.4112	−	47.8834i	−1.99371	−	1.60686i
$889$		0			0
$890$	−44.6686			−1.49730
$891$	−1.16146	+	12.1279i	−0.0389105	+	0.406301i
$892$	17.2846			0.578732
$893$	−4.39016	+	7.60398i	−0.146911	+	0.254458i
$894$	7.01620	+	5.65481i	0.234657	+	0.189125i
$895$	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
$899$	3.41683			0.113958
$900$	8.32066	+	38.2749i	0.277355	+	1.27583i
$901$	21.3674			0.711850
$902$	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
$906$	8.93975	−	57.3000i	0.297003	−	1.90367i
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	−0.985704	−	0.168485i	$-0.946112\pi$
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	0.638765	+	0.769402i	$0.279446\pi$
$908$	−72.8804			−2.41862
$909$	−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	$0.0435878\pi$
$912$	−8.10864	+	3.13413i	−0.268504	+	0.103782i
$913$	−1.33166	−	2.30650i	−0.0440715	−	0.0763340i
$914$	−11.4116	−	19.7654i	−0.377461	−	0.653782i
$915$	2.20479	+	1.77698i	0.0728881	+	0.0587452i
$916$	51.8946	−	89.8841i	1.71465	−	2.96986i
$917$		0			0
$918$	−22.5987	−	34.2764i	−0.745870	−	1.13129i
$919$	−37.3030			−1.23051			−0.615257	−	0.788327i	$-0.710948\pi$
$919$	−37.3030			−1.23051			−0.615257	+	0.788327i	$0.710948\pi$
$920$	15.5490	−	26.9317i	0.512636	−	0.887911i
$921$	6.74469	+	5.43598i	0.222245	+	0.179122i
$922$	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
$926$	62.4140			2.05105
$927$	4.94386	−	4.49302i	0.162378	−	0.147570i
$928$	−2.78869			−0.0915432
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	−0.815791	−	0.578347i	$-0.803698\pi$
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	0.908759	+	0.417322i	$0.137031\pi$
$930$	−6.09544	+	39.0692i	−0.199877	+	1.28113i
$931$		0			0
$932$	−25.5145	−	44.1923i	−0.835754	−	1.44757i
$933$	−8.64991	+	55.4423i	−0.283185	+	1.81510i
$934$	−41.7138	+	72.2503i	−1.36492	+	2.36410i
$935$	−13.0889			−0.428052
$936$	13.1844	−	11.9821i	0.430946	−	0.391647i
$937$	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
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	0.983178	−	0.182650i	$-0.0584674\pi$
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	−0.649768	+	0.760132i	$0.725134\pi$
$942$	−9.54789	−	7.69527i	−0.311087	−	0.250725i
$943$	2.37674	−	4.11663i	0.0773973	−	0.134056i
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	−0.824698	−	0.565573i	$-0.808655\pi$
$947$	2.38343	−	4.12823i	0.0774512	−	0.134149i	0.902150	+	0.431423i	$0.141988\pi$
$948$	−3.82753	−	3.08485i	−0.124312	−	0.100191i
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$	−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	$0.791315\pi$
$954$	44.0241	+	14.0797i	1.42533	+	0.455846i
$955$	24.2056			0.783276
$956$	20.4478	−	35.4166i	0.661328	−	1.14545i
$957$	−0.377141	+	2.41732i	−0.0121912	+	0.0781407i
$958$	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
$962$	−38.0549			−1.22694
$963$	11.1577	+	51.3254i	0.359552	+	1.65394i
$964$	85.6619			2.75898
$965$	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
$969$	9.85052	+	7.93917i	0.316444	+	0.255043i
$970$	−28.8729	+	50.0093i	−0.927052	+	1.60570i
$971$	28.9775			0.929933			0.464966	−	0.885328i	$-0.346066\pi$
$971$	28.9775			0.929933			0.464966	+	0.885328i	$0.346066\pi$
$972$	−15.5587	−	55.4929i	−0.499044	−	1.77994i
$973$		0			0
$974$	26.7933	−	46.4074i	0.858513	−	1.48699i
$975$	6.98173	+	5.62703i	0.223594	+	0.180209i
$976$	0.636580	+	1.10259i	0.0203764	+	0.0352930i
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	0.623401	−	0.781902i	$-0.285750\pi$
$977$	−11.4228	−	19.7848i	−0.365447	−	0.632972i	−0.988848	+	0.148930i	$0.952417\pi$
$978$	−1.49833	+	0.579130i	−0.0479112	+	0.0185185i
$979$	4.33670	−	7.51139i	0.138602	−	0.240065i
$980$		0			0
$981$	9.94067	+	45.7270i	0.317381	+	1.45995i
$982$	83.6465			2.66927
$983$	−15.6351	+	27.0809i	−0.498684	+	0.863745i	−0.999999	−	0.00151933i	$-0.999516\pi$
$983$	−15.6351	+	27.0809i	−0.498684	+	0.863745i	0.501315	+	0.865265i	$0.332850\pi$
$984$	−1.95611	+	12.5378i	−0.0623585	+	0.399692i
$985$	−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
$989$	11.4136			0.362930
$990$	−26.9676	−	8.62471i	−0.857086	−	0.274111i
$991$	−7.01463			−0.222827			−0.111414	−	0.993774i	$-0.535538\pi$
$991$	−7.01463			−0.222827			−0.111414	+	0.993774i	$0.535538\pi$
$992$	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
$996$	9.80926	+	7.90592i	0.310818	+	0.250509i
$997$	−10.6439	+	18.4358i	−0.337095	+	0.583866i	−0.983885	−	0.178802i	$-0.942778\pi$
$997$	−10.6439	+	18.4358i	−0.337095	+	0.583866i	0.646790	+	0.762668i	$0.276111\pi$
$998$	21.3271			0.675099
$999$	−25.3056	+	50.5279i	−0.800633	+	1.59863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.f.295.5		10
3.2	odd	2		1323.2.f.f.883.1		10
7.2	even	3		441.2.h.f.214.1		10
7.3	odd	6		63.2.g.b.16.5	yes	10
7.4	even	3		441.2.g.f.79.5		10
7.5	odd	6		63.2.h.b.25.1	yes	10
7.6	odd	2		441.2.f.e.295.5		10
9.2	odd	6		3969.2.a.bb.1.5		5
9.4	even	3	inner	441.2.f.f.148.5		10
9.5	odd	6		1323.2.f.f.442.1		10
9.7	even	3		3969.2.a.ba.1.1		5
21.2	odd	6		1323.2.h.f.802.5		10
21.5	even	6		189.2.h.b.46.5		10
21.11	odd	6		1323.2.g.f.667.1		10
21.17	even	6		189.2.g.b.100.1		10
21.20	even	2		1323.2.f.e.883.1		10
28.3	even	6		1008.2.t.i.961.3		10
28.19	even	6		1008.2.q.i.529.4		10
63.4	even	3		441.2.h.f.373.1		10
63.5	even	6		189.2.g.b.172.1		10
63.13	odd	6		441.2.f.e.148.5		10
63.20	even	6		3969.2.a.bc.1.5		5
63.23	odd	6		1323.2.g.f.361.1		10
63.31	odd	6		63.2.h.b.58.1	yes	10
63.32	odd	6		1323.2.h.f.226.5		10
63.34	odd	6		3969.2.a.z.1.1		5
63.38	even	6		567.2.e.e.163.1		10
63.40	odd	6		63.2.g.b.4.5	✓	10
63.41	even	6		1323.2.f.e.442.1		10
63.47	even	6		567.2.e.e.487.1		10
63.52	odd	6		567.2.e.f.163.5		10
63.58	even	3		441.2.g.f.67.5		10
63.59	even	6		189.2.h.b.37.5		10
63.61	odd	6		567.2.e.f.487.5		10
84.47	odd	6		3024.2.q.i.2881.2		10
84.59	odd	6		3024.2.t.i.289.4		10
252.31	even	6		1008.2.q.i.625.4		10
252.59	odd	6		3024.2.q.i.2305.2		10
252.103	even	6		1008.2.t.i.193.3		10
252.131	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	63.40	odd	6
63.2.g.b.16.5	yes	10	7.3	odd	6
63.2.h.b.25.1	yes	10	7.5	odd	6
63.2.h.b.58.1	yes	10	63.31	odd	6
189.2.g.b.100.1		10	21.17	even	6
189.2.g.b.172.1		10	63.5	even	6
189.2.h.b.37.5		10	63.59	even	6
189.2.h.b.46.5		10	21.5	even	6
441.2.f.e.148.5		10	63.13	odd	6
441.2.f.e.295.5		10	7.6	odd	2
441.2.f.f.148.5		10	9.4	even	3	inner
441.2.f.f.295.5		10	1.1	even	1	trivial
441.2.g.f.67.5		10	63.58	even	3
441.2.g.f.79.5		10	7.4	even	3
441.2.h.f.214.1		10	7.2	even	3
441.2.h.f.373.1		10	63.4	even	3
567.2.e.e.163.1		10	63.38	even	6
567.2.e.e.487.1		10	63.47	even	6
567.2.e.f.163.5		10	63.52	odd	6
567.2.e.f.487.5		10	63.61	odd	6
1008.2.q.i.529.4		10	28.19	even	6
1008.2.q.i.625.4		10	252.31	even	6
1008.2.t.i.193.3		10	252.103	even	6
1008.2.t.i.961.3		10	28.3	even	6
1323.2.f.e.442.1		10	63.41	even	6
1323.2.f.e.883.1		10	21.20	even	2
1323.2.f.f.442.1		10	9.5	odd	6
1323.2.f.f.883.1		10	3.2	odd	2
1323.2.g.f.361.1		10	63.23	odd	6
1323.2.g.f.667.1		10	21.11	odd	6
1323.2.h.f.226.5		10	63.32	odd	6
1323.2.h.f.802.5		10	21.2	odd	6
3024.2.q.i.2305.2		10	252.59	odd	6
3024.2.q.i.2881.2		10	84.47	odd	6
3024.2.t.i.289.4		10	84.59	odd	6
3024.2.t.i.1873.4		10	252.131	odd	6
3969.2.a.z.1.1		5	63.34	odd	6
3969.2.a.ba.1.1		5	9.7	even	3
3969.2.a.bb.1.5		5	9.2	odd	6
3969.2.a.bc.1.5		5	63.20	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} +O(q^{10})\)	\(q+(1.19343 - 2.06709i) q^{2} +(-1.34857 - 1.08690i) q^{3} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 + 1.49047i) q^{6} -4.05086 q^{8} +(0.637290 + 2.93153i) q^{9} -6.97172 q^{10} +(0.676857 - 1.17235i) q^{11} +(-0.987132 + 6.32710i) q^{12} +(0.733001 + 1.26960i) q^{13} +(-0.779867 + 4.99862i) q^{15} +(-1.13729 + 1.96984i) q^{16} +3.31027 q^{17} +(6.82030 + 2.18125i) q^{18} -2.20659 q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(-1.31415 - 2.27617i) q^{23} +(5.46287 + 4.40288i) q^{24} +(-1.76573 + 3.05833i) q^{25} +3.49916 q^{26} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} +(9.40187 + 7.57758i) q^{30} +(1.63729 + 2.83587i) q^{31} +(-1.33629 - 2.31453i) q^{32} +(-2.18702 + 0.845323i) q^{33} +(3.95060 - 6.84263i) q^{34} +(8.20815 - 7.45963i) q^{36} -10.8755 q^{37} +(-2.63342 + 4.56121i) q^{38} +(0.391421 - 2.50884i) q^{39} +(5.91601 + 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} -5.00488 q^{44} +(6.48471 - 5.89336i) q^{45} -6.27340 q^{46} +(1.98957 - 3.44604i) q^{47} +(3.67474 - 1.42035i) q^{48} +(4.21456 + 7.29984i) q^{50} +(-4.46414 - 3.59794i) q^{51} +(2.71001 - 4.69388i) q^{52} +6.45486 q^{53} +(-6.82685 - 10.3546i) q^{54} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +(-1.24528 - 2.15688i) q^{58} +(-6.10700 - 10.5776i) q^{59} +(17.4463 - 6.74331i) q^{60} +(0.279867 - 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(2.14100 - 3.70832i) q^{65} +(-0.862710 + 5.52960i) q^{66} +(-6.40588 - 11.0953i) q^{67} +(-6.11928 - 10.5989i) q^{68} +(-0.701751 + 4.49793i) q^{69} +12.9177 q^{71} +(-2.58157 - 11.8752i) q^{72} +10.4554 q^{73} +(-12.9791 + 22.4805i) q^{74} +(5.70532 - 2.20521i) q^{75} +(4.07903 + 7.06509i) q^{76} +(-4.71886 - 3.80324i) q^{78} +(-0.383838 + 0.664827i) q^{79} +6.64375 q^{80} +(-8.18772 + 3.73647i) q^{81} +4.31684 q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(5.18258 + 8.97649i) q^{86} +(-1.68575 + 0.651573i) q^{87} +(-2.74185 + 4.74903i) q^{88} +6.40711 q^{89} +(-4.44301 - 20.4378i) q^{90} +(-4.85859 + 8.41533i) q^{92} +(0.874308 - 5.60395i) q^{93} +(-4.74884 - 8.22524i) q^{94} +(3.22257 + 5.58166i) q^{95} +(-0.713577 + 4.57373i) q^{96} +(4.14143 - 7.17316i) q^{97} +(3.86814 + 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * q^99

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