LMFDB - Embedded newform 686.2.g.h.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			373.1
Character	$\chi$	$=$	686.373
Dual form			686.2.g.h.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826239 + 0.563320i) q^{2} +(-1.91561 + 1.77743i) q^{3} +(0.365341 - 0.930874i) q^{4} +(2.16774 + 0.668658i) q^{5} +(0.581491 - 2.54768i) q^{6} +(0.222521 + 0.974928i) q^{8} +(0.286126 - 3.81809i) q^{9} +O(q^{10})$	\(q+(-0.826239 + 0.563320i) q^{2} +(-1.91561 + 1.77743i) q^{3} +(0.365341 - 0.930874i) q^{4} +(2.16774 + 0.668658i) q^{5} +(0.581491 - 2.54768i) q^{6} +(0.222521 + 0.974928i) q^{8} +(0.286126 - 3.81809i) q^{9} +(-2.16774 + 0.668658i) q^{10} +(-0.169527 - 2.26218i) q^{11} +(0.954708 + 2.43256i) q^{12} +(5.56864 + 2.68171i) q^{13} +(-5.34103 + 2.57210i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(2.60688 + 0.392924i) q^{17} +(1.91440 + 3.31584i) q^{18} +(3.20757 - 5.55567i) q^{19} +(1.41440 - 1.77360i) q^{20} +(1.41440 + 1.77360i) q^{22} +(4.94226 - 0.744926i) q^{23} +(-2.15912 - 1.47207i) q^{24} +(0.120784 + 0.0823491i) q^{25} +(-6.11169 + 0.921189i) q^{26} +(1.35036 + 1.69330i) q^{27} +(2.53592 - 3.17994i) q^{29} +(2.96405 - 5.13388i) q^{30} +(2.91361 + 5.04652i) q^{31} +(0.988831 + 0.149042i) q^{32} +(4.34560 + 4.03213i) q^{33} +(-2.37524 + 1.14386i) q^{34} +(-3.44963 - 1.66125i) q^{36} +(-0.902727 - 2.30011i) q^{37} +(0.479404 + 6.39720i) q^{38} +(-15.4339 + 4.76072i) q^{39} +(-0.169527 + 2.26218i) q^{40} +(0.0937760 + 0.410859i) q^{41} +(-1.93075 + 8.45917i) q^{43} +(-2.16774 - 0.668658i) q^{44} +(3.17325 - 8.08530i) q^{45} +(-3.66386 + 3.39956i) q^{46} +(-7.30248 + 4.97875i) q^{47} +2.61320 q^{48} -0.146185 q^{50} +(-5.69215 + 3.88084i) q^{51} +(4.53079 - 4.20396i) q^{52} +(0.161911 - 0.412542i) q^{53} +(-2.06959 - 0.638385i) q^{54} +(1.14513 - 5.01716i) q^{55} +(3.73034 + 16.3437i) q^{57} +(-0.303950 + 4.05593i) q^{58} +(-3.42738 + 1.05721i) q^{59} +(0.443007 + 5.91151i) q^{60} +(3.43620 + 8.75529i) q^{61} +(-5.25014 - 2.52833i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(10.2782 + 9.53677i) q^{65} +(-5.86188 - 0.883536i) q^{66} +(-0.186127 - 0.322382i) q^{67} +(1.31816 - 2.28312i) q^{68} +(-8.14339 + 10.2115i) q^{69} +(-8.51015 - 10.6714i) q^{71} +(3.78603 - 0.570653i) q^{72} +(8.75312 + 5.96778i) q^{73} +(2.04157 + 1.39192i) q^{74} +(-0.377744 + 0.0569357i) q^{75} +(-3.99977 - 5.01555i) q^{76} +(10.0703 - 12.6277i) q^{78} +(-3.57698 + 6.19550i) q^{79} +(-1.13426 - 1.96460i) q^{80} +(5.76162 + 0.868424i) q^{81} +(-0.308927 - 0.286642i) q^{82} +(4.26774 - 2.05523i) q^{83} +(5.38829 + 2.59486i) q^{85} +(-3.16996 - 8.07693i) q^{86} +(0.794280 + 10.5989i) q^{87} +(2.16774 - 0.668658i) q^{88} +(0.190871 - 2.54699i) q^{89} +(1.93275 + 8.46794i) q^{90} +(1.11218 - 4.87277i) q^{92} +(-14.5511 - 4.48843i) q^{93} +(3.22897 - 8.22727i) q^{94} +(10.6680 - 9.89846i) q^{95} +(-2.15912 + 1.47207i) q^{96} +0.652366 q^{97} -8.68571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.826239	+	0.563320i	−0.584239	+	0.398327i
$2$	−0.826239	+	0.563320i	−0.584239	+	0.398327i
$3$	−1.91561	+	1.77743i	−1.10598	+	1.02620i	−0.106486	+	0.994314i	$0.533960\pi$
$3$	−1.91561	+	1.77743i	−1.10598	+	1.02620i	−0.999492	+	0.0318828i	$0.989850\pi$
$4$	0.365341	−	0.930874i	0.182671	−	0.465437i
$5$	2.16774	+	0.668658i	0.969441	+	0.299033i	0.738739	−	0.673991i	$-0.235422\pi$
$5$	2.16774	+	0.668658i	0.969441	+	0.299033i	0.230702	+	0.973024i	$0.425898\pi$
$6$	0.581491	−	2.54768i	0.237393	−	1.04009i
$7$		0			0
$7$		0			0
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	0.286126	−	3.81809i	0.0953755	−	1.27270i
$10$	−2.16774	+	0.668658i	−0.685498	+	0.211448i
$11$	−0.169527	−	2.26218i	−0.0511142	−	0.682072i	−0.962632	−	0.270812i	$-0.912708\pi$
$11$	−0.169527	−	2.26218i	−0.0511142	−	0.682072i	0.911518	−	0.411260i	$-0.134911\pi$
$12$	0.954708	+	2.43256i	0.275600	+	0.702219i
$13$	5.56864	+	2.68171i	1.54446	+	0.743774i	0.995738	−	0.0922296i	$-0.0293994\pi$
$13$	5.56864	+	2.68171i	1.54446	+	0.743774i	0.548724	+	0.836003i	$0.315114\pi$
$14$		0			0
$15$	−5.34103	+	2.57210i	−1.37905	+	0.664114i
$16$	−0.733052	−	0.680173i	−0.183263	−	0.170043i
$17$	2.60688	+	0.392924i	0.632261	+	0.0952980i	0.457351	−	0.889286i	$-0.348798\pi$
$17$	2.60688	+	0.392924i	0.632261	+	0.0952980i	0.174910	+	0.984584i	$0.444037\pi$
$18$	1.91440	+	3.31584i	0.451228	+	0.781550i
$19$	3.20757	−	5.55567i	0.735866	−	1.27456i	−0.218476	−	0.975842i	$-0.570108\pi$
$19$	3.20757	−	5.55567i	0.735866	−	1.27456i	0.954342	−	0.298716i	$-0.0965582\pi$
$20$	1.41440	−	1.77360i	0.316269	−	0.396589i
$21$		0			0
$22$	1.41440	+	1.77360i	0.301551	+	0.378133i
$23$	4.94226	−	0.744926i	1.03053	−	0.155328i	0.388058	−	0.921635i	$-0.373146\pi$
$23$	4.94226	−	0.744926i	1.03053	−	0.155328i	0.642474	+	0.766307i	$0.277908\pi$
$24$	−2.15912	−	1.47207i	−0.440729	−	0.300484i
$25$	0.120784	+	0.0823491i	0.0241568	+	0.0164698i
$26$	−6.11169	+	0.921189i	−1.19860	+	0.180660i
$27$	1.35036	+	1.69330i	0.259878	+	0.325876i
$28$		0			0
$29$	2.53592	−	3.17994i	0.470908	−	0.590501i	−0.488485	−	0.872572i	$-0.662450\pi$
$29$	2.53592	−	3.17994i	0.470908	−	0.590501i	0.959393	+	0.282072i	$0.0910217\pi$
$30$	2.96405	−	5.13388i	0.541158	−	0.937313i
$31$	2.91361	+	5.04652i	0.523299	+	0.906381i	0.999632	+	0.0271159i	$0.00863233\pi$
$31$	2.91361	+	5.04652i	0.523299	+	0.906381i	−0.476333	+	0.879265i	$0.658034\pi$
$32$	0.988831	+	0.149042i	0.174802	+	0.0263472i
$33$	4.34560	+	4.03213i	0.756472	+	0.701903i
$34$	−2.37524	+	1.14386i	−0.407351	+	0.196170i
$35$		0			0
$36$	−3.44963	−	1.66125i	−0.574938	−	0.276876i
$37$	−0.902727	−	2.30011i	−0.148407	−	0.378136i	0.837267	−	0.546794i	$-0.184152\pi$
$37$	−0.902727	−	2.30011i	−0.148407	−	0.378136i	−0.985675	+	0.168658i	$0.946057\pi$
$38$	0.479404	+	6.39720i	0.0777695	+	1.03776i
$39$	−15.4339	+	4.76072i	−2.47140	+	0.762326i
$40$	−0.169527	+	2.26218i	−0.0268045	+	0.357682i
$41$	0.0937760	+	0.410859i	0.0146453	+	0.0641654i	0.981723	−	0.190318i	$-0.0609518\pi$
$41$	0.0937760	+	0.410859i	0.0146453	+	0.0641654i	−0.967077	+	0.254483i	$0.918095\pi$
$42$		0			0
$43$	−1.93075	+	8.45917i	−0.294437	+	1.29001i	0.583844	+	0.811866i	$0.301548\pi$
$43$	−1.93075	+	8.45917i	−0.294437	+	1.29001i	−0.878280	+	0.478146i	$0.841309\pi$
$44$	−2.16774	−	0.668658i	−0.326799	−	0.100804i
$45$	3.17325	−	8.08530i	0.473040	−	1.20529i
$46$	−3.66386	+	3.39956i	−0.540206	+	0.501238i
$47$	−7.30248	+	4.97875i	−1.06518	+	0.726225i	−0.963261	−	0.268568i	$-0.913450\pi$
$47$	−7.30248	+	4.97875i	−1.06518	+	0.726225i	−0.101916	+	0.994793i	$0.532497\pi$
$48$	2.61320			0.377183
$49$		0			0
$50$	−0.146185			−0.0206737
$51$	−5.69215	+	3.88084i	−0.797060	+	0.543427i
$52$	4.53079	−	4.20396i	0.628307	−	0.582984i
$53$	0.161911	−	0.412542i	0.0222402	−	0.0566670i	−0.919322	−	0.393505i	$-0.871262\pi$
$53$	0.161911	−	0.412542i	0.0222402	−	0.0566670i	0.941563	+	0.336838i	$0.109358\pi$
$54$	−2.06959	−	0.638385i	−0.281636	−	0.0868732i
$55$	1.14513	−	5.01716i	0.154410	−	0.676514i
$56$		0			0
$57$	3.73034	+	16.3437i	0.494096	+	2.16478i
$58$	−0.303950	+	4.05593i	−0.0399105	+	0.532569i
$59$	−3.42738	+	1.05721i	−0.446207	+	0.137637i	−0.509712	−	0.860345i	$-0.670248\pi$
$59$	−3.42738	+	1.05721i	−0.446207	+	0.137637i	0.0635055	+	0.997981i	$0.479772\pi$
$60$	0.443007	+	5.91151i	0.0571919	+	0.763173i
$61$	3.43620	+	8.75529i	0.439960	+	1.12100i	0.963193	+	0.268810i	$0.0866305\pi$
$61$	3.43620	+	8.75529i	0.439960	+	1.12100i	−0.523233	+	0.852190i	$0.675274\pi$
$62$	−5.25014	−	2.52833i	−0.666768	−	0.321099i
$63$		0			0
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	10.2782	+	9.53677i	1.27485	+	1.18289i
$66$	−5.86188	−	0.883536i	−0.721547	−	0.108756i
$67$	−0.186127	−	0.322382i	−0.0227391	−	0.0393852i	0.854432	−	0.519563i	$-0.173905\pi$
$67$	−0.186127	−	0.322382i	−0.0227391	−	0.0393852i	−0.877171	+	0.480178i	$0.840572\pi$
$68$	1.31816	−	2.28312i	0.159851	−	0.276869i
$69$	−8.14339	+	10.2115i	−0.980349	+	1.22932i
$70$		0			0
$71$	−8.51015	−	10.6714i	−1.00997	−	1.26646i	−0.963547	−	0.267540i	$-0.913789\pi$
$71$	−8.51015	−	10.6714i	−1.00997	−	1.26646i	−0.0464226	−	0.998922i	$-0.514782\pi$
$72$	3.78603	−	0.570653i	0.446188	−	0.0672521i
$73$	8.75312	+	5.96778i	1.02448	+	0.698476i	0.954236	−	0.299054i	$-0.0966712\pi$
$73$	8.75312	+	5.96778i	1.02448	+	0.698476i	0.0702397	+	0.997530i	$0.477624\pi$
$74$	2.04157	+	1.39192i	0.237327	+	0.161807i
$75$	−0.377744	+	0.0569357i	−0.0436181	+	0.00657437i
$76$	−3.99977	−	5.01555i	−0.458805	−	0.575324i
$77$		0			0
$78$	10.0703	−	12.6277i	1.14023	−	1.42981i
$79$	−3.57698	+	6.19550i	−0.402441	+	0.697048i	−0.994020	−	0.109199i	$-0.965172\pi$
$79$	−3.57698	+	6.19550i	−0.402441	+	0.697048i	0.591579	+	0.806247i	$0.298505\pi$
$80$	−1.13426	−	1.96460i	−0.126814	−	0.219649i
$81$	5.76162	+	0.868424i	0.640180	+	0.0964916i
$82$	−0.308927	−	0.286642i	−0.0341152	−	0.0316543i
$83$	4.26774	−	2.05523i	0.468445	−	0.225591i	−0.184743	−	0.982787i	$-0.559145\pi$
$83$	4.26774	−	2.05523i	0.468445	−	0.225591i	0.653188	+	0.757196i	$0.273431\pi$
$84$		0			0
$85$	5.38829	+	2.59486i	0.584442	+	0.281453i
$86$	−3.16996	−	8.07693i	−0.341826	−	0.870958i
$87$	0.794280	+	10.5989i	0.0851558	+	1.13633i
$88$	2.16774	−	0.668658i	0.231081	−	0.0712792i
$89$	0.190871	−	2.54699i	0.0202322	−	0.269981i	−0.977909	−	0.209032i	$-0.932969\pi$
$89$	0.190871	−	2.54699i	0.0202322	−	0.269981i	0.998141	−	0.0609480i	$-0.0194124\pi$
$90$	1.93275	+	8.46794i	0.203730	+	0.892599i
$91$		0			0
$92$	1.11218	−	4.87277i	0.115953	−	0.508022i
$93$	−14.5511	−	4.48843i	−1.50888	−	0.465429i
$94$	3.22897	−	8.22727i	0.333042	−	0.848578i
$95$	10.6680	−	9.89846i	1.09451	−	1.01556i
$96$	−2.15912	+	1.47207i	−0.220365	+	0.150242i
$97$	0.652366			0.0662378			0.0331189	−	0.999451i	$-0.489456\pi$
$97$	0.652366			0.0662378			0.0331189	+	0.999451i	$0.489456\pi$
$98$		0			0
$99$	−8.68571			−0.872947
$100$	0.120784	−	0.0823491i	0.0120784	−	0.00823491i
$101$	−12.4500	+	11.5519i	−1.23882	+	1.14946i	−0.255654	+	0.966768i	$0.582291\pi$
$101$	−12.4500	+	11.5519i	−1.23882	+	1.14946i	−0.983170	+	0.182693i	$0.941519\pi$
$102$	2.51692	−	6.41300i	0.249212	−	0.634982i
$103$	−11.6052	−	3.57974i	−1.14350	−	0.352722i	−0.335576	−	0.942013i	$-0.608931\pi$
$103$	−11.6052	−	3.57974i	−1.14350	−	0.352722i	−0.807921	+	0.589291i	$0.799407\pi$
$104$	−1.37534	+	6.02576i	−0.134863	+	0.590874i
$105$		0			0
$106$	0.0986162	+	0.432066i	0.00957845	+	0.0419659i
$107$	0.0867115	−	1.15708i	0.00838272	−	0.111860i	−0.991443	−	0.130542i	$-0.958328\pi$
$107$	0.0867115	−	1.15708i	0.00838272	−	0.111860i	0.999825	+	0.0186827i	$0.00594723\pi$
$108$	2.06959	−	0.638385i	0.199147	−	0.0614286i
$109$	−0.251298	−	3.35334i	−0.0240700	−	0.321192i	−0.996222	−	0.0868413i	$-0.972323\pi$
$109$	−0.251298	−	3.35334i	−0.0240700	−	0.321192i	0.972152	−	0.234351i	$-0.0752964\pi$
$110$	1.88011	+	4.79045i	0.179262	+	0.456751i
$111$	5.81755	+	2.80158i	0.552177	+	0.265915i
$112$		0			0
$113$	5.57078	−	2.68275i	0.524055	−	0.252371i	−0.153102	−	0.988210i	$-0.548926\pi$
$113$	5.57078	−	2.68275i	0.524055	−	0.252371i	0.677157	+	0.735839i	$0.263212\pi$
$114$	−12.2889	−	11.4024i	−1.15096	−	1.06793i
$115$	11.2116	+	1.68988i	1.04549	+	0.157582i
$116$	−2.03365	−	3.52238i	−0.188820	−	0.327045i
$117$	11.8324	−	20.4943i	1.09390	−	1.89470i
$118$	2.23629	−	2.80422i	0.205867	−	0.258149i
$119$		0			0
$120$	−3.69610	−	4.63477i	−0.337407	−	0.423095i
$121$	5.78843	−	0.872466i	0.526221	−	0.0793151i
$122$	−7.77115	−	5.29828i	−0.703567	−	0.479684i
$123$	−0.909910	−	0.620366i	−0.0820438	−	0.0559365i
$124$	5.76213	−	0.868501i	0.517454	−	0.0779937i
$125$	−6.86523	−	8.60873i	−0.614045	−	0.769988i
$126$		0			0
$127$	12.0103	−	15.0604i	1.06574	−	1.33640i	0.126948	−	0.991909i	$-0.459482\pi$
$127$	12.0103	−	15.0604i	1.06574	−	1.33640i	0.938791	−	0.344486i	$-0.111947\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−11.3370	−	19.6362i	−0.998166	−	1.72887i
$130$	−13.8645	−	2.08974i	−1.21600	−	0.183282i
$131$	−4.18075	−	3.87916i	−0.365273	−	0.338924i	0.476087	−	0.879398i	$-0.342055\pi$
$131$	−4.18075	−	3.87916i	−0.365273	−	0.338924i	−0.841361	+	0.540474i	$0.818245\pi$
$132$	5.34103	−	2.57210i	0.464877	−	0.223873i
$133$		0			0
$134$	0.335390	+	0.161515i	0.0289733	+	0.0139528i
$135$	1.79499	+	4.57356i	0.154488	+	0.393630i
$136$	0.197013	+	2.62895i	0.0168937	+	0.225431i
$137$	18.3277	−	5.65334i	1.56584	−	0.482998i	0.613926	−	0.789364i	$-0.289589\pi$
$137$	18.3277	−	5.65334i	1.56584	−	0.482998i	0.951914	+	0.306366i	$0.0991132\pi$
$138$	0.976048	−	13.0245i	0.0830867	−	1.10872i
$139$	1.40588	+	6.15956i	0.119245	+	0.522447i	0.998902	+	0.0468392i	$0.0149149\pi$
$139$	1.40588	+	6.15956i	0.119245	+	0.522447i	−0.879657	+	0.475608i	$0.842228\pi$
$140$		0			0
$141$	5.13935	−	22.5170i	0.432811	−	1.89627i
$142$	13.0428	+	4.02318i	1.09453	+	0.337618i
$143$	5.12248	−	13.0519i	0.428363	−	1.09145i
$144$	−2.80671	+	2.60424i	−0.233892	+	0.217020i
$145$	7.62350	−	5.19761i	0.633097	−	0.431638i
$146$	−10.5939			−0.876761
$147$		0			0
$148$	−2.47092			−0.203108
$149$	−10.3985	+	7.08957i	−0.851878	+	0.580800i	−0.908637	−	0.417588i	$-0.862876\pi$
$149$	−10.3985	+	7.08957i	−0.851878	+	0.580800i	0.0567591	+	0.998388i	$0.481923\pi$
$150$	0.280034	−	0.259833i	0.0228647	−	0.0212153i
$151$	2.04293	−	5.20531i	0.166252	−	0.423602i	−0.823332	−	0.567560i	$-0.807888\pi$
$151$	2.04293	−	5.20531i	0.166252	−	0.423602i	0.989584	+	0.143957i	$0.0459828\pi$
$152$	6.13013	+	1.89089i	0.497219	+	0.153372i
$153$	2.24612	−	9.84087i	0.181588	−	0.795587i
$154$		0			0
$155$	2.94154	+	12.8877i	0.236270	+	1.03517i
$156$	−1.20700	+	16.1063i	−0.0966372	+	1.28953i
$157$	0.535685	−	0.165237i	0.0427524	−	0.0131874i	−0.273305	−	0.961927i	$-0.588117\pi$
$157$	0.535685	−	0.165237i	0.0427524	−	0.0131874i	0.316058	+	0.948740i	$0.397641\pi$
$158$	−0.534615	−	7.13395i	−0.0425317	−	0.567546i
$159$	0.423105	+	1.07805i	0.0335544	+	0.0854952i
$160$	2.04387	+	0.984274i	0.161582	+	0.0778137i
$161$		0			0
$162$	−5.24967	+	2.52811i	−0.412453	+	0.198627i
$163$	13.9597	+	12.9527i	1.09341	+	1.01454i	0.999821	+	0.0189252i	$0.00602445\pi$
$163$	13.9597	+	12.9527i	1.09341	+	1.01454i	0.0935890	+	0.995611i	$0.470166\pi$
$164$	0.416718	+	0.0628102i	0.0325402	+	0.00490465i
$165$	6.72400	+	11.6463i	0.523463	+	0.906664i
$166$	−2.36841	+	4.10221i	−0.183825	+	0.318394i
$167$	−3.23190	+	4.05267i	−0.250092	+	0.313605i	−0.890992	−	0.454019i	$-0.849990\pi$
$167$	−3.23190	+	4.05267i	−0.250092	+	0.313605i	0.640900	+	0.767624i	$0.278561\pi$
$168$		0			0
$169$	15.7128	+	19.7032i	1.20867	+	1.51563i
$170$	−5.91375	+	0.891355i	−0.453564	+	0.0683638i
$171$	−20.2943	−	13.8364i	−1.55194	−	1.05810i
$172$	7.16904	+	4.88777i	0.546634	+	0.372689i
$173$	−4.79895	+	0.723325i	−0.364857	+	0.0549934i	−0.328913	−	0.944360i	$-0.606682\pi$
$173$	−4.79895	+	0.723325i	−0.364857	+	0.0549934i	−0.0359448	+	0.999354i	$0.511444\pi$
$174$	−6.62686	−	8.30982i	−0.502381	−	0.629966i
$175$		0			0
$176$	−1.41440	+	1.77360i	−0.106614	+	0.133690i
$177$	4.68641	−	8.11710i	0.352252	−	0.610119i
$178$	1.27707	+	2.21194i	0.0957202	+	0.165792i
$179$	−13.2211	−	1.99276i	−0.988189	−	0.148946i	−0.364992	−	0.931011i	$-0.618928\pi$
$179$	−13.2211	−	1.99276i	−0.988189	−	0.148946i	−0.623197	+	0.782065i	$0.714166\pi$
$180$	−6.36707	−	5.90778i	−0.474574	−	0.440340i
$181$	12.0759	−	5.81545i	0.897595	−	0.432259i	0.0725754	−	0.997363i	$-0.476878\pi$
$181$	12.0759	−	5.81545i	0.897595	−	0.432259i	0.825020	+	0.565104i	$0.191164\pi$
$182$		0			0
$183$	−22.1443	−	10.6641i	−1.63695	−	0.788315i
$184$	1.82601	+	4.65259i	0.134615	+	0.342993i
$185$	−0.418886	−	5.58965i	−0.0307971	−	0.410959i
$186$	14.5511	−	4.48843i	1.06694	−	0.329108i
$187$	0.446927	−	5.96383i	0.0326826	−	0.436118i
$188$	1.96669	+	8.61663i	0.143436	+	0.628432i
$189$		0			0
$190$	−3.23832	+	14.1880i	−0.234932	+	1.02931i
$191$	13.1190	+	4.04668i	0.949259	+	0.292808i	0.730455	−	0.682961i	$-0.239308\pi$
$191$	13.1190	+	4.04668i	0.949259	+	0.292808i	0.218804	+	0.975769i	$0.429784\pi$
$192$	0.954708	−	2.43256i	0.0689001	−	0.175555i
$193$	−4.59294	+	4.26163i	−0.330607	+	0.306759i	−0.827957	−	0.560791i	$-0.810497\pi$
$193$	−4.59294	+	4.26163i	−0.330607	+	0.306759i	0.497350	+	0.867550i	$0.334307\pi$
$194$	−0.539010	+	0.367491i	−0.0386987	+	0.0263843i
$195$	−36.6399			−2.62384
$196$		0			0
$197$	−20.5511			−1.46421			−0.732104	−	0.681193i	$-0.761461\pi$
$197$	−20.5511			−1.46421			−0.732104	+	0.681193i	$0.761461\pi$
$198$	7.17647	−	4.89283i	0.510009	−	0.347719i
$199$	−2.52696	+	2.34468i	−0.179131	+	0.166210i	−0.764642	−	0.644455i	$-0.777084\pi$
$199$	−2.52696	+	2.34468i	−0.179131	+	0.166210i	0.585511	+	0.810664i	$0.300894\pi$
$200$	−0.0534075	+	0.136080i	−0.00377648	+	0.00962231i
$201$	0.929558	+	0.286731i	0.0655659	+	0.0202244i
$202$	3.77926	−	16.5580i	0.265908	−	1.16502i
$203$		0			0
$204$	1.53300	+	6.71650i	0.107331	+	0.470249i
$205$	−0.0714429	+	0.953339i	−0.00498979	+	0.0665841i
$206$	11.6052	−	3.57974i	0.808574	−	0.249412i
$207$	−1.43008	−	19.0831i	−0.0993977	−	1.32637i
$208$	−2.25807	−	5.75347i	−0.156569	−	0.398931i
$209$	−13.1117	−	6.31425i	−0.906954	−	0.436766i
$210$		0			0
$211$	9.64399	−	4.64430i	0.663920	−	0.319727i	−0.0713996	−	0.997448i	$-0.522747\pi$
$211$	9.64399	−	4.64430i	0.663920	−	0.319727i	0.735319	+	0.677721i	$0.237032\pi$
$212$	−0.324872	−	0.301437i	−0.0223123	−	0.0207028i
$213$	35.2697	+	5.31606i	2.41664	+	0.364250i
$214$	0.580164	+	1.00487i	0.0396592	+	0.0686918i
$215$	−9.84166	+	17.0462i	−0.671195	+	1.16254i
$216$	−1.35036	+	1.69330i	−0.0918806	+	0.115215i
$217$		0			0
$218$	2.09664	+	2.62910i	0.142002	+	0.178065i
$219$	−27.3748	+	4.12609i	−1.84982	+	0.278816i
$220$	−4.25198	−	2.89895i	−0.286668	−	0.195447i
$221$	13.4630	+	9.17895i	0.905622	+	0.617443i
$222$	−6.38487	+	0.962365i	−0.428525	+	0.0645897i
$223$	6.51578	+	8.17053i	0.436329	+	0.547139i	0.950572	−	0.310505i	$-0.100498\pi$
$223$	6.51578	+	8.17053i	0.436329	+	0.547139i	−0.514243	+	0.857645i	$0.671927\pi$
$224$		0			0
$225$	0.348976	−	0.437602i	0.0232651	−	0.0291735i
$226$	−3.09155	+	5.35472i	−0.205647	+	0.356191i
$227$	−5.33732	−	9.24451i	−0.354250	−	0.613580i	0.632739	−	0.774365i	$-0.281931\pi$
$227$	−5.33732	−	9.24451i	−0.354250	−	0.613580i	−0.986989	+	0.160785i	$0.948597\pi$
$228$	16.5768	+	2.49855i	1.09782	+	0.165470i
$229$	−5.92183	−	5.49465i	−0.391325	−	0.363097i	0.459833	−	0.888005i	$-0.347909\pi$
$229$	−5.92183	−	5.49465i	−0.391325	−	0.363097i	−0.851159	+	0.524908i	$0.824100\pi$
$230$	−10.2154	+	4.91949i	−0.673585	+	0.324381i
$231$		0			0
$232$	3.66451	+	1.76473i	0.240587	+	0.115861i
$233$	−0.946517	−	2.41169i	−0.0620084	−	0.157995i	0.896511	−	0.443020i	$-0.146093\pi$
$233$	−0.946517	−	2.41169i	−0.0620084	−	0.157995i	−0.958520	+	0.285026i	$0.907998\pi$
$234$	1.76847	+	23.5986i	0.115608	+	1.54269i
$235$	−19.1589	+	5.90975i	−1.24979	+	0.385510i
$236$	−0.268036	+	3.57670i	−0.0174477	+	0.232823i
$237$	−4.15996	−	18.2260i	−0.270218	−	1.18390i
$238$		0			0
$239$	−0.924979	+	4.05260i	−0.0598319	+	0.262141i	−0.995993	−	0.0894305i	$-0.971495\pi$
$239$	−0.924979	+	4.05260i	−0.0598319	+	0.262141i	0.936161	+	0.351571i	$0.114352\pi$
$240$	5.66472	+	1.74734i	0.365656	+	0.112790i
$241$	2.42109	−	6.16883i	0.155956	−	0.397370i	−0.831445	−	0.555607i	$-0.812486\pi$
$241$	2.42109	−	6.16883i	0.155956	−	0.397370i	0.987401	+	0.158237i	$0.0505811\pi$
$242$	−4.29115	+	3.98161i	−0.275846	+	0.255947i
$243$	−17.9490	+	12.2374i	−1.15143	+	0.785031i
$244$	9.40545			0.602122
$245$		0			0
$246$	1.10127			0.0702143
$247$	32.7605	−	22.3357i	2.08450	−	1.42119i
$248$	−4.27165	+	3.96351i	−0.271250	+	0.251683i
$249$	−4.52229	+	11.5226i	−0.286588	+	0.730215i
$250$	10.5218	+	3.24554i	0.665457	+	0.205266i
$251$	−5.53382	+	24.2453i	−0.349292	+	1.53035i	0.429501	+	0.903066i	$0.358689\pi$
$251$	−5.53382	+	24.2453i	−0.349292	+	1.53035i	−0.778793	+	0.627281i	$0.784168\pi$
$252$		0			0
$253$	−2.52300	−	11.0540i	−0.158620	−	0.694958i
$254$	−1.43953	+	19.2091i	−0.0903238	+	1.20529i
$255$	−14.9340	+	4.60654i	−0.935206	+	0.288473i
$256$	0.0747301	+	0.997204i	0.00467063	+	0.0623252i
$257$	−6.89346	−	17.5643i	−0.430002	−	1.09563i	−0.967614	−	0.252436i	$-0.918768\pi$
$257$	−6.89346	−	17.5643i	−0.430002	−	1.09563i	0.537611	−	0.843193i	$-0.319327\pi$
$258$	20.4285	+	9.83787i	1.27183	+	0.612479i
$259$		0			0
$260$	12.6326	−	6.08352i	0.783439	−	0.377284i
$261$	−11.4157	−	10.5922i	−0.706615	−	0.655643i
$262$	5.63950	+	0.850019i	0.348410	+	0.0525143i
$263$	3.89711	+	6.74999i	0.240306	+	0.416222i	0.960801	−	0.277238i	$-0.0894189\pi$
$263$	3.89711	+	6.74999i	0.240306	+	0.416222i	−0.720496	+	0.693460i	$0.756086\pi$
$264$	−2.96405	+	5.13388i	−0.182424	+	0.315968i
$265$	0.626829	−	0.786019i	0.0385058	−	0.0482848i
$266$		0			0
$267$	4.16145	+	5.21830i	0.254677	+	0.319355i
$268$	−0.368097	+	0.0554817i	−0.0224851	+	0.00338908i
$269$	1.02761	+	0.700611i	0.0626544	+	0.0427170i	0.594242	−	0.804286i	$-0.297452\pi$
$269$	1.02761	+	0.700611i	0.0626544	+	0.0427170i	−0.531588	+	0.847003i	$0.678404\pi$
$270$	−4.05947	−	2.76770i	−0.247052	−	0.168437i
$271$	20.5739	−	3.10101i	1.24977	−	0.188373i	0.509377	−	0.860544i	$-0.329876\pi$
$271$	20.5739	−	3.10101i	1.24977	−	0.188373i	0.740396	+	0.672171i	$0.234638\pi$
$272$	−1.64372	−	2.06116i	−0.0996652	−	0.124976i
$273$		0			0
$274$	−11.9584	+	14.9954i	−0.722433	+	0.905903i
$275$	0.165812	−	0.287195i	0.00999884	−	0.0173185i
$276$	6.53049	+	11.3111i	0.393089	+	0.680851i
$277$	−3.94869	−	0.595170i	−0.237254	−	0.0357603i	0.0293389	−	0.999570i	$-0.490660\pi$
$277$	−3.94869	−	0.595170i	−0.237254	−	0.0357603i	−0.266593	+	0.963809i	$0.585898\pi$
$278$	−4.63140	−	4.29731i	−0.277773	−	0.257736i
$279$	20.1017	−	9.68048i	1.20346	−	0.579555i
$280$		0			0
$281$	−22.9864	−	11.0697i	−1.37126	−	0.660362i	−0.404140	−	0.914697i	$-0.632429\pi$
$281$	−22.9864	−	11.0697i	−1.37126	−	0.660362i	−0.967116	+	0.254335i	$0.918143\pi$
$282$	8.43792	+	21.4995i	0.502471	+	1.28028i
$283$	−0.209183	−	2.79136i	−0.0124347	−	0.165929i	−0.999964	−	0.00849351i	$-0.997296\pi$
$283$	−0.209183	−	2.79136i	−0.0124347	−	0.165929i	0.987529	−	0.157436i	$-0.0503226\pi$
$284$	−13.0428	+	4.02318i	−0.773950	+	0.238732i
$285$	−2.84195	+	37.9232i	−0.168342	+	2.24637i
$286$	3.11999	+	13.6696i	0.184489	+	0.808298i
$287$		0			0
$288$	0.851988	−	3.73280i	0.0502039	−	0.219958i
$289$	−9.60332	−	2.96223i	−0.564901	−	0.174249i
$290$	−3.37091	+	8.58894i	−0.197947	+	0.504360i
$291$	−1.24968	+	1.15953i	−0.0732575	+	0.0679730i
$292$	8.75312	−	5.96778i	0.512238	−	0.349238i
$293$	1.32109			0.0771787			0.0385893	−	0.999255i	$-0.487714\pi$
$293$	1.32109			0.0771787			0.0385893	+	0.999255i	$0.487714\pi$
$294$		0			0
$295$	−8.13656			−0.473729
$296$	2.04157	−	1.39192i	0.118664	−	0.0809035i
$297$	3.60163	−	3.34182i	0.208988	−	0.193912i
$298$	4.59794	−	11.7154i	0.266351	−	0.678652i
$299$	29.5193	+	9.10551i	1.70715	+	0.526585i
$300$	−0.0850054	+	0.372433i	−0.00490779	+	0.0215024i
$301$		0			0
$302$	1.24431	+	5.45166i	0.0716017	+	0.313708i
$303$	3.31668	−	44.2580i	0.190538	−	2.54256i
$304$	−6.13013	+	1.89089i	−0.351587	+	0.108450i
$305$	1.59448	+	21.2768i	0.0912994	+	1.21831i
$306$	3.68773	+	9.39619i	0.210814	+	0.537145i
$307$	10.2045	+	4.91424i	0.582403	+	0.280471i	0.701798	−	0.712376i	$-0.252381\pi$
$307$	10.2045	+	4.91424i	0.582403	+	0.280471i	−0.119394	+	0.992847i	$0.538095\pi$
$308$		0			0
$309$	28.5938	−	13.7700i	1.62664	−	0.783350i
$310$	−9.69033	−	8.99131i	−0.550374	−	0.510672i
$311$	−8.55415	−	1.28933i	−0.485061	−	0.0731112i	−0.0980408	−	0.995182i	$-0.531258\pi$
$311$	−8.55415	−	1.28933i	−0.485061	−	0.0731112i	−0.387020	+	0.922071i	$0.626496\pi$
$312$	−8.07572	−	13.9876i	−0.457198	−	0.791890i
$313$	−2.36042	+	4.08837i	−0.133419	+	0.231088i	−0.924992	−	0.379986i	$-0.875929\pi$
$313$	−2.36042	+	4.08837i	−0.133419	+	0.231088i	0.791574	+	0.611074i	$0.209262\pi$
$314$	−0.349523	+	0.438288i	−0.0197247	+	0.0247340i
$315$		0			0
$316$	4.46041	+	5.59318i	0.250918	+	0.314641i
$317$	−15.5264	+	2.34022i	−0.872048	+	0.131440i	−0.569794	−	0.821787i	$-0.692977\pi$
$317$	−15.5264	+	2.34022i	−0.872048	+	0.131440i	−0.302254	+	0.953228i	$0.597739\pi$
$318$	−0.956875	−	0.652386i	−0.0536589	−	0.0365840i
$319$	−7.62350	−	5.19761i	−0.426834	−	0.291011i
$320$	−2.24318	+	0.338105i	−0.125398	+	0.0189007i
$321$	1.89053	+	2.37064i	0.105519	+	0.132316i
$322$		0			0
$323$	10.5447	−	13.2226i	0.586722	−	0.735726i
$324$	2.91335	−	5.04607i	0.161853	−	0.280337i
$325$	0.451765	+	0.782480i	0.0250594	+	0.0434042i
$326$	−18.8306	−	2.83826i	−1.04293	−	0.157196i
$327$	6.44170	+	5.97703i	0.356227	+	0.330530i
$328$	−0.379691	+	0.182850i	−0.0209649	+	0.0100962i
$329$		0			0
$330$	−12.1162	−	5.83487i	−0.666976	−	0.321199i
$331$	−7.22317	−	18.4043i	−0.397021	−	1.01159i	−0.979981	−	0.199093i	$-0.936201\pi$
$331$	−7.22317	−	18.4043i	−0.397021	−	1.01159i	0.582959	−	0.812501i	$-0.301895\pi$
$332$	−0.353984	−	4.72358i	−0.0194274	−	0.259240i
$333$	−9.04033	+	2.78857i	−0.495407	+	0.152813i
$334$	0.387368	−	5.16907i	0.0211958	−	0.282839i
$335$	−0.187912	−	0.823295i	−0.0102667	−	0.0449814i
$336$		0			0
$337$	−1.00188	+	4.38952i	−0.0545758	+	0.239112i	−0.994857	−	0.101285i	$-0.967705\pi$
$337$	−1.00188	+	4.38952i	−0.0545758	+	0.239112i	0.940282	+	0.340398i	$0.110562\pi$
$338$	−24.0817	−	7.42822i	−1.30987	−	0.404042i
$339$	−5.90305	+	15.0407i	−0.320610	+	0.816901i
$340$	4.38406	−	4.06781i	0.237759	−	0.220608i
$341$	10.9222	−	7.44661i	0.591469	−	0.403257i
$342$	24.5623			1.32817
$343$		0			0
$344$	−8.67672			−0.467817
$345$	−24.4807	+	16.6907i	−1.31800	+	0.898595i
$346$	3.55762	−	3.30098i	0.191259	−	0.177462i
$347$	0.952443	−	2.42678i	0.0511298	−	0.130277i	−0.903027	−	0.429584i	$-0.858660\pi$
$347$	0.952443	−	2.42678i	0.0511298	−	0.130277i	0.954157	+	0.299307i	$0.0967555\pi$
$348$	10.1565	+	3.13285i	0.544443	+	0.167938i
$349$	0.376110	−	1.64785i	0.0201327	−	0.0882072i	−0.963863	−	0.266397i	$-0.914167\pi$
$349$	0.376110	−	1.64785i	0.0201327	−	0.0882072i	0.983996	+	0.178190i	$0.0570240\pi$
$350$		0			0
$351$	2.97873	+	13.0507i	0.158993	+	0.696593i
$352$	0.169527	−	2.26218i	0.00903581	−	0.120574i
$353$	−23.4978	+	7.24811i	−1.25066	+	0.385778i	−0.848208	−	0.529663i	$-0.822318\pi$
$353$	−23.4978	+	7.24811i	−1.25066	+	0.385778i	−0.402453	+	0.915441i	$0.631842\pi$
$354$	0.700432	+	9.34662i	0.0372275	+	0.496767i
$355$	−11.3123	−	28.8232i	−0.600392	−	1.52977i
$356$	−2.30119	−	1.10820i	−0.121963	−	0.0587343i
$357$		0			0
$358$	12.0463	−	5.80120i	0.636668	−	0.306603i
$359$	−10.1971	−	9.46148i	−0.538180	−	0.499358i	0.363599	−	0.931556i	$-0.381548\pi$
$359$	−10.1971	−	9.46148i	−0.538180	−	0.499358i	−0.901779	+	0.432198i	$0.857738\pi$
$360$	8.58870	+	1.29454i	0.452664	+	0.0682281i
$361$	−11.0770	−	19.1859i	−0.582999	−	1.00978i
$362$	−6.70162	+	11.6076i	−0.352229	+	0.610079i
$363$	−9.53763	+	11.9598i	−0.500596	+	0.627727i
$364$		0			0
$365$	14.9841	+	18.7894i	0.784302	+	0.983483i
$366$	24.3038	−	3.66321i	1.27038	−	0.191479i
$367$	3.07454	+	2.09618i	0.160489	+	0.109420i	0.640902	−	0.767623i	$-0.278561\pi$
$367$	3.07454	+	2.09618i	0.160489	+	0.109420i	−0.480412	+	0.877043i	$0.659513\pi$
$368$	−4.12961	−	2.81552i	−0.215271	−	0.146769i
$369$	1.59553	−	0.240488i	0.0830600	−	0.0125193i
$370$	3.49486	+	4.38242i	0.181689	+	0.227831i
$371$		0			0
$372$	−9.49429	+	11.9055i	−0.492256	+	0.617269i
$373$	−7.99131	+	13.8414i	−0.413774	+	0.716678i	−0.995299	−	0.0968506i	$-0.969123\pi$
$373$	−7.99131	+	13.8414i	−0.413774	+	0.716678i	0.581525	+	0.813529i	$0.302456\pi$
$374$	2.99028	+	5.17931i	0.154624	+	0.267816i
$375$	28.4525	+	4.28852i	1.46928	+	0.221458i
$376$	−6.47888	−	6.01152i	−0.334122	−	0.310020i
$377$	22.6493	−	10.9073i	1.16650	−	0.561756i
$378$		0			0
$379$	8.48937	+	4.08827i	0.436070	+	0.210000i	0.639022	−	0.769189i	$-0.279339\pi$
$379$	8.48937	+	4.08827i	0.436070	+	0.210000i	−0.202952	+	0.979189i	$0.565054\pi$
$380$	−5.31676	−	13.5469i	−0.272744	−	0.694940i
$381$	3.76176	+	50.1972i	0.192721	+	2.57168i
$382$	−13.1190	+	4.04668i	−0.671227	+	0.207046i
$383$	−0.968473	+	12.9234i	−0.0494867	+	0.660354i	0.916213	+	0.400692i	$0.131230\pi$
$383$	−0.968473	+	12.9234i	−0.0494867	+	0.660354i	−0.965700	+	0.259662i	$0.916389\pi$
$384$	0.581491	+	2.54768i	0.0296741	+	0.130011i
$385$		0			0
$386$	1.39421	−	6.10842i	0.0709633	−	0.310910i
$387$	31.7455	+	9.79218i	1.61371	+	0.497765i
$388$	0.238336	−	0.607271i	0.0120997	−	0.0308295i
$389$	−18.9634	+	17.5955i	−0.961483	+	0.892126i	−0.994223	−	0.107338i	$-0.965767\pi$
$389$	−18.9634	+	17.5955i	−0.961483	+	0.892126i	0.0327393	+	0.999464i	$0.489577\pi$
$390$	30.2733	−	20.6400i	1.53295	−	1.04515i
$391$	13.1766			0.666368
$392$		0			0
$393$	14.9036			0.751787
$394$	16.9801	−	11.5769i	0.855447	−	0.583234i
$395$	−11.8966	+	11.0384i	−0.598584	+	0.555404i
$396$	−3.17325	+	8.08530i	−0.159462	+	0.406302i
$397$	−30.7883	−	9.49693i	−1.54522	−	0.476637i	−0.599161	−	0.800629i	$-0.704499\pi$
$397$	−30.7883	−	9.49693i	−1.54522	−	0.476637i	−0.946060	+	0.323991i	$0.894975\pi$
$398$	0.767069	−	3.36075i	0.0384497	−	0.168459i
$399$		0			0
$400$	−0.0325293	−	0.142520i	−0.00162646	−	0.00712600i
$401$	1.79081	−	23.8967i	0.0894287	−	1.19334i	−0.754284	−	0.656548i	$-0.772016\pi$
$401$	1.79081	−	23.8967i	0.0894287	−	1.19334i	0.843713	−	0.536795i	$-0.180365\pi$
$402$	−0.929558	+	0.286731i	−0.0463621	+	0.0143008i
$403$	2.69151	+	35.9157i	0.134074	+	1.78909i
$404$	6.20489	+	15.8098i	0.308705	+	0.786567i
$405$	11.9090	+	5.73507i	0.591762	+	0.284978i
$406$		0			0
$407$	−5.05022	+	2.43206i	−0.250330	+	0.120553i
$408$	−5.05016	−	4.68587i	−0.250020	−	0.231985i
$409$	20.9871	+	3.16329i	1.03774	+	0.156415i	0.645747	−	0.763552i	$-0.276546\pi$
$409$	20.9871	+	3.16329i	1.03774	+	0.156415i	0.391997	+	0.919966i	$0.371784\pi$
$410$	−0.478006	−	0.827931i	−0.0236070	−	0.0408886i
$411$	−25.0603	+	43.4057i	−1.23613	+	2.14104i
$412$	−7.57215	+	9.49517i	−0.373053	+	0.467793i
$413$		0			0
$414$	11.9315	+	14.9616i	0.586402	+	0.735325i
$415$	10.6256	−	1.60155i	0.521589	−	0.0786169i
$416$	5.10675	+	3.48172i	0.250379	+	0.170706i
$417$	−13.6413	−	9.30047i	−0.668017	−	0.455446i
$418$	14.3903	−	2.16899i	0.703854	−	0.106089i
$419$	−1.32580	−	1.66250i	−0.0647694	−	0.0812183i	0.748391	−	0.663257i	$-0.230827\pi$
$419$	−1.32580	−	1.66250i	−0.0647694	−	0.0812183i	−0.813161	+	0.582039i	$0.802255\pi$
$420$		0			0
$421$	−14.4305	+	18.0953i	−0.703302	+	0.881913i	−0.997265	−	0.0739040i	$-0.976454\pi$
$421$	−14.4305	+	18.0953i	−0.703302	+	0.881913i	0.293963	+	0.955817i	$0.405026\pi$
$422$	−5.35201	+	9.26995i	−0.260532	+	0.451254i
$423$	16.9199	+	29.3061i	0.822673	+	1.42491i
$424$	0.438227	+	0.0660521i	0.0212822	+	0.00320777i
$425$	0.282512	+	0.262133i	0.0137038	+	0.0127153i
$426$	−32.1359	+	15.4758i	−1.55699	+	0.749806i
$427$		0			0
$428$	−1.04542	−	0.503448i	−0.0505323	−	0.0243351i
$429$	13.3861	+	34.1071i	0.646285	+	1.64671i
$430$	−1.47094	−	19.6283i	−0.0709348	−	0.946559i
$431$	37.8307	−	11.6692i	1.82224	−	0.562087i	0.822267	−	0.569102i	$-0.192709\pi$
$431$	37.8307	−	11.6692i	1.82224	−	0.562087i	0.999975	+	0.00701529i	$0.00223305\pi$
$432$	0.161852	−	2.15976i	0.00778708	−	0.103911i
$433$	−3.01461	−	13.2079i	−0.144873	−	0.634730i	−0.994263	−	0.106964i	$-0.965887\pi$
$433$	−3.01461	−	13.2079i	−0.144873	−	0.634730i	0.849390	−	0.527766i	$-0.176970\pi$
$434$		0			0
$435$	−5.36527	+	23.5068i	−0.257245	+	1.12706i
$436$	−3.21335	−	0.991186i	−0.153891	−	0.0474692i
$437$	11.7141	−	29.8470i	0.560360	−	1.42777i
$438$	20.2938	−	18.8299i	0.969678	−	0.899729i
$439$	−31.6420	+	21.5731i	−1.51019	+	1.02963i	−0.526413	+	0.850229i	$0.676464\pi$
$439$	−31.6420	+	21.5731i	−1.51019	+	1.02963i	−0.983776	+	0.179401i	$0.942584\pi$
$440$	5.14619			0.245335
$441$		0			0
$442$	−16.2944			−0.775044
$443$	15.2209	−	10.3774i	0.723165	−	0.493046i	−0.144931	−	0.989442i	$-0.546296\pi$
$443$	15.2209	−	10.3774i	0.723165	−	0.493046i	0.868096	+	0.496396i	$0.165344\pi$
$444$	4.73331	−	4.39187i	0.224633	−	0.208429i
$445$	2.11682	−	5.39358i	0.100347	−	0.255680i
$446$	−9.98622	−	3.08034i	−0.472861	−	0.145858i
$447$	7.31826	−	32.0634i	0.346142	−	1.51655i
$448$		0			0
$449$	−6.09815	−	26.7178i	−0.287790	−	1.26089i	−0.887551	−	0.460710i	$-0.847595\pi$
$449$	−6.09815	−	26.7178i	−0.287790	−	1.26089i	0.599761	−	0.800179i	$-0.295262\pi$
$450$	−0.0418275	+	0.558149i	−0.00197177	+	0.0263114i
$451$	0.913539	−	0.281789i	0.0430169	−	0.0132689i
$452$	−0.462063	−	6.16581i	−0.0217336	−	0.290015i
$453$	5.33859	+	13.6025i	0.250829	+	0.639102i
$454$	9.61752	+	4.63155i	0.451373	+	0.217370i
$455$		0			0
$456$	−15.1039	+	7.27363i	−0.707303	+	0.340619i
$457$	4.79996	+	4.45371i	0.224533	+	0.208336i	0.784415	−	0.620236i	$-0.212963\pi$
$457$	4.79996	+	4.45371i	0.224533	+	0.208336i	−0.559882	+	0.828572i	$0.689154\pi$
$458$	7.98809	+	1.20401i	0.373259	+	0.0562598i
$459$	2.85489	+	4.94482i	0.133255	+	0.230804i
$460$	5.66913	−	9.81922i	0.264324	−	0.457823i
$461$	14.6775	−	18.4051i	0.683601	−	0.857209i	−0.312079	−	0.950056i	$-0.601025\pi$
$461$	14.6775	−	18.4051i	0.683601	−	0.857209i	0.995680	+	0.0928471i	$0.0295968\pi$
$462$		0			0
$463$	−1.95626	−	2.45307i	−0.0909149	−	0.114004i	0.734293	−	0.678832i	$-0.237514\pi$
$463$	−1.95626	−	2.45307i	−0.0909149	−	0.114004i	−0.825208	+	0.564829i	$0.808942\pi$
$464$	−4.02187	+	0.606199i	−0.186711	+	0.0281421i
$465$	−28.5418	−	19.4595i	−1.32359	−	0.902411i
$466$	2.14060	+	1.45944i	0.0991614	+	0.0676071i
$467$	33.3988	−	5.03406i	1.54551	−	0.232948i	0.679765	−	0.733430i	$-0.262082\pi$
$467$	33.3988	−	5.03406i	1.54551	−	0.232948i	0.865747	+	0.500482i	$0.166844\pi$
$468$	−14.7547	−	18.5018i	−0.682037	−	0.855248i
$469$		0			0
$470$	12.5008	−	15.6755i	0.576618	−	0.723056i
$471$	−0.732467	+	1.26867i	−0.0337503	+	0.0584573i
$472$	−1.79336	−	3.10620i	−0.0825463	−	0.142974i
$473$	19.4635	+	2.93365i	0.894931	+	0.134889i
$474$	13.7042	+	12.7156i	0.629453	+	0.584047i
$475$	0.844927	−	0.406895i	0.0387679	−	0.0186696i
$476$		0			0
$477$	−1.52880	−	0.736229i	−0.0699988	−	0.0337096i
$478$	−1.51866	−	3.86947i	−0.0694617	−	0.176985i
$479$	−2.18643	−	29.1758i	−0.0999004	−	1.33308i	−0.791665	−	0.610955i	$-0.790785\pi$
$479$	−2.18643	−	29.1758i	−0.0999004	−	1.33308i	0.691765	−	0.722123i	$-0.256834\pi$
$480$	−5.66472	+	1.74734i	−0.258558	+	0.0797546i
$481$	1.14128	−	15.2293i	0.0520379	−	0.694398i
$482$	1.47463	+	6.46078i	0.0671676	+	0.294280i
$483$		0			0
$484$	1.30260	−	5.70705i	0.0592089	−	0.259411i
$485$	1.41416	+	0.436210i	0.0642136	+	0.0198073i
$486$	7.93658	−	20.2221i	0.360010	−	0.917292i
$487$	−7.76879	+	7.20839i	−0.352038	+	0.326643i	−0.836292	−	0.548284i	$-0.815281\pi$
$487$	−7.76879	+	7.20839i	−0.352038	+	0.326643i	0.484255	+	0.874927i	$0.339091\pi$
$488$	−7.77115	+	5.29828i	−0.351783	+	0.239842i
$489$	−49.7639			−2.25040
$490$		0			0
$491$	−24.1721			−1.09087			−0.545437	−	0.838152i	$-0.683636\pi$
$491$	−24.1721			−1.09087			−0.545437	+	0.838152i	$0.683636\pi$
$492$	−0.909910	+	0.620366i	−0.0410219	+	0.0279683i
$493$	7.86031	−	7.29330i	0.354010	−	0.328474i
$494$	−14.4858	+	36.9093i	−0.651748	+	1.66063i
$495$	−18.8283	−	5.80777i	−0.846270	−	0.261040i
$496$	1.29668	−	5.68111i	0.0582225	−	0.255090i
$497$		0			0
$498$	−2.75442	−	12.0679i	−0.123429	−	0.540776i
$499$	−1.96910	+	26.2758i	−0.0881491	+	1.17627i	0.761229	+	0.648483i	$0.224596\pi$
$499$	−1.96910	+	26.2758i	−0.0881491	+	1.17627i	−0.849378	+	0.527785i	$0.823023\pi$
$500$	−10.5218	+	3.24554i	−0.470549	+	0.145145i
$501$	−1.01227	−	13.5078i	−0.0452249	−	0.603484i
$502$	−9.08559	−	23.1497i	−0.405510	−	1.03322i
$503$	7.03178	+	3.38632i	0.313531	+	0.150989i	0.584031	−	0.811731i	$-0.301475\pi$
$503$	7.03178	+	3.38632i	0.313531	+	0.150989i	−0.270500	+	0.962720i	$0.587189\pi$
$504$		0			0
$505$	−34.7127	+	16.7167i	−1.54469	+	0.743885i
$506$	8.31153	+	7.71197i	0.369493	+	0.342839i
$507$	−65.1204	−	9.81533i	−2.89210	−	0.435914i
$508$	−9.63150	−	16.6822i	−0.427328	−	0.740155i
$509$	4.05789	−	7.02848i	0.179863	−	0.311532i	−0.761970	−	0.647612i	$-0.775768\pi$
$509$	4.05789	−	7.02848i	0.179863	−	0.311532i	0.941833	+	0.336080i	$0.109101\pi$
$510$	9.74412	−	12.2187i	0.431477	−	0.541055i
$511$		0			0
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	13.7388	−	2.07079i	0.606583	−	0.0914277i
$514$	15.5899	+	10.6290i	0.687643	+	0.468827i
$515$	−22.7634	−	15.5199i	−1.00308	−	0.683886i
$516$	−22.4207	+	3.37938i	−0.987017	+	0.148769i
$517$	12.5008	+	15.6755i	0.549784	+	0.689407i
$518$		0			0
$519$	7.90726	−	9.91539i	0.347090	−	0.435237i
$520$	−7.01055	+	12.1426i	−0.307433	+	0.532489i
$521$	12.0225	+	20.8236i	0.526716	+	0.912299i	0.999515	+	0.0311285i	$0.00991012\pi$
$521$	12.0225	+	20.8236i	0.526716	+	0.912299i	−0.472800	+	0.881170i	$0.656757\pi$
$522$	15.3989	+	2.32102i	0.673993	+	0.101588i
$523$	10.8504	+	10.0677i	0.474455	+	0.440230i	0.880799	−	0.473490i	$-0.157006\pi$
$523$	10.8504	+	10.0677i	0.474455	+	0.440230i	−0.406344	+	0.913720i	$0.633197\pi$
$524$	−5.13841	+	2.47453i	−0.224472	+	0.108100i
$525$		0			0
$526$	−7.02234	−	3.38178i	−0.306189	−	0.147453i
$527$	5.61252	+	14.3005i	0.244485	+	0.622938i
$528$	−0.443007	−	5.91151i	−0.0192794	−	0.257266i
$529$	1.89285	−	0.583865i	0.0822976	−	0.0253855i
$530$	−0.0751304	+	1.00255i	−0.00326345	+	0.0435478i
$531$	3.05585	+	13.3885i	0.132613	+	0.581013i
$532$		0			0
$533$	−0.579603	+	2.53941i	−0.0251054	+	0.109994i
$534$	−6.37793	−	1.96733i	−0.276000	−	0.0851347i
$535$	0.961661	−	2.45027i	0.0415763	−	0.105935i
$536$	0.272882	−	0.253198i	0.0117867	−	0.0109365i
$537$	28.8684	−	19.6821i	1.24576	−	0.849346i
$538$	−1.24372			−0.0536205
$539$		0			0
$540$	4.91319			0.211430
$541$	−29.8647	+	20.3614i	−1.28398	+	0.875405i	−0.996598	−	0.0824107i	$-0.973738\pi$
$541$	−29.8647	+	20.3614i	−1.28398	+	0.875405i	−0.287384	+	0.957815i	$0.592786\pi$
$542$	−15.2521	+	14.1518i	−0.655132	+	0.607874i
$543$	−12.7962	+	32.6042i	−0.549137	+	1.39918i
$544$	2.51920	+	0.777070i	0.108010	+	0.0333166i
$545$	1.69749	−	7.43719i	0.0727125	−	0.318574i
$546$		0			0
$547$	2.82714	+	12.3865i	0.120880	+	0.529608i	0.998717	+	0.0506486i	$0.0161288\pi$
$547$	2.82714	+	12.3865i	0.120880	+	0.529608i	−0.877837	+	0.478960i	$0.841014\pi$
$548$	1.43331	−	19.1262i	0.0612279	−	0.817029i
$549$	34.4117	−	10.6146i	1.46866	−	0.453020i
$550$	0.0247823	+	0.330697i	0.00105672	+	0.0141010i
$551$	−9.53258	−	24.2886i	−0.406101	−	1.03473i
$552$	−11.7675	−	5.66695i	−0.500860	−	0.241201i
$553$		0			0
$554$	3.59783	−	1.73263i	0.152857	−	0.0736122i
$555$	10.7376	+	9.96305i	0.455786	+	0.422908i
$556$	6.24740	+	0.941644i	0.264949	+	0.0399346i
$557$	4.18062	+	7.24105i	0.177139	+	0.306813i	0.940899	−	0.338686i	$-0.109983\pi$
$557$	4.18062	+	7.24105i	0.177139	+	0.306813i	−0.763761	+	0.645499i	$0.776649\pi$
$558$	−11.1556	+	19.3221i	−0.472255	+	0.817969i
$559$	−33.4367	+	41.9284i	−1.41422	+	1.77338i
$560$		0			0
$561$	9.74412	+	12.2187i	0.411397	+	0.515876i
$562$	25.2281	−	3.80252i	1.06418	−	0.160400i
$563$	5.05481	+	3.44631i	0.213035	+	0.145245i	0.665137	−	0.746722i	$-0.268373\pi$
$563$	5.05481	+	3.44631i	0.213035	+	0.145245i	−0.452102	+	0.891966i	$0.649326\pi$
$564$	−19.0828	−	13.0104i	−0.803532	−	0.547839i
$565$	13.8698	−	2.09054i	0.583508	−	0.0879496i
$566$	1.74526	+	2.18849i	0.0733589	+	0.0919892i
$567$		0			0
$568$	8.51015	−	10.6714i	0.357078	−	0.447762i
$569$	19.2082	−	33.2697i	0.805251	−	1.39474i	−0.110870	−	0.993835i	$-0.535364\pi$
$569$	19.2082	−	33.2697i	0.805251	−	1.39474i	0.916121	−	0.400901i	$-0.131303\pi$
$570$	−19.0148	−	32.9345i	−0.796440	−	1.37948i
$571$	−13.0972	−	1.97409i	−0.548101	−	0.0826130i	−0.130847	−	0.991403i	$-0.541770\pi$
$571$	−13.0972	−	1.97409i	−0.548101	−	0.0826130i	−0.417255	+	0.908790i	$0.637008\pi$
$572$	−10.2782	−	9.53677i	−0.429753	−	0.398752i
$573$	−32.3236	+	15.5662i	−1.35034	+	0.650288i
$574$		0			0
$575$	0.658289	+	0.317015i	0.0274526	+	0.0132205i
$576$	1.39882	+	3.56413i	0.0582841	+	0.148505i
$577$	−0.917157	−	12.2386i	−0.0381818	−	0.509500i	−0.983206	−	0.182500i	$-0.941581\pi$
$577$	−0.917157	−	12.2386i	−0.0381818	−	0.509500i	0.945024	−	0.327000i	$-0.106038\pi$
$578$	9.60332	−	2.96223i	0.399445	−	0.123213i
$579$	1.22356	−	16.3272i	0.0508493	−	0.678537i
$580$	−2.05315	−	8.99542i	−0.0852522	−	0.373514i
$581$		0			0
$582$	0.379345	−	1.66202i	0.0157244	−	0.0688929i
$583$	−0.960691	−	0.296334i	−0.0397878	−	0.0122729i
$584$	−3.87040	+	9.86162i	−0.160158	+	0.408077i
$585$	39.3531	−	36.5144i	1.62705	−	1.50968i
$586$	−1.09153	+	0.744194i	−0.0450908	+	0.0307424i
$587$	1.62164			0.0669322			0.0334661	−	0.999440i	$-0.489345\pi$
$587$	1.62164			0.0669322			0.0334661	+	0.999440i	$0.489345\pi$
$588$		0			0
$589$	37.3824			1.54031
$590$	6.72274	−	4.58349i	0.276771	−	0.188699i
$591$	39.3679	−	36.5281i	1.61938	−	1.50257i
$592$	−0.902727	+	2.30011i	−0.0371019	+	0.0945340i
$593$	−21.0990	−	6.50817i	−0.866431	−	0.267259i	−0.170492	−	0.985359i	$-0.554536\pi$
$593$	−21.0990	−	6.50817i	−0.866431	−	0.267259i	−0.695939	+	0.718101i	$0.745012\pi$
$594$	−1.09329	+	4.79001i	−0.0448582	+	0.196537i
$595$		0			0
$596$	2.80050	+	12.2698i	0.114713	+	0.502590i
$597$	0.673180	−	8.98297i	0.0275514	−	0.367648i
$598$	−29.5193	+	9.10551i	−1.20714	+	0.372352i
$599$	−2.62912	−	35.0832i	−0.107423	−	1.43346i	−0.747046	−	0.664773i	$-0.768528\pi$
$599$	−2.62912	−	35.0832i	−0.107423	−	1.43346i	0.639623	−	0.768689i	$-0.279091\pi$
$600$	−0.139564	−	0.355604i	−0.00569768	−	0.0145175i
$601$	−40.3838	−	19.4478i	−1.64729	−	0.793293i	−0.999505	−	0.0314699i	$-0.989981\pi$
$601$	−40.3838	−	19.4478i	−1.64729	−	0.793293i	−0.647785	−	0.761823i	$-0.724305\pi$
$602$		0			0
$603$	−1.28414	+	0.618410i	−0.0522943	+	0.0251836i
$604$	−4.09912	−	3.80343i	−0.166791	−	0.154759i
$605$	13.1312	+	1.97921i	0.533858	+	0.0804662i
$606$	22.1910	+	38.4360i	0.901450	+	1.56136i
$607$	16.0138	−	27.7367i	0.649980	−	1.12580i	−0.333147	−	0.942875i	$-0.608110\pi$
$607$	16.0138	−	27.7367i	0.649980	−	1.12580i	0.983127	−	0.182924i	$-0.0585562\pi$
$608$	3.99977	−	5.01555i	0.162212	−	0.203408i
$609$		0			0
$610$	−13.3031	−	16.6815i	−0.538625	−	0.675415i
$611$	−54.0165	+	8.14167i	−2.18527	+	0.329377i
$612$	−8.34001	−	5.68612i	−0.337125	−	0.229848i
$613$	−11.9086	−	8.11918i	−0.480986	−	0.327930i	0.298437	−	0.954429i	$-0.403535\pi$
$613$	−11.9086	−	8.11918i	−0.480986	−	0.327930i	−0.779422	+	0.626499i	$0.784487\pi$
$614$	−11.1997	+	1.68808i	−0.451982	+	0.0681253i
$615$	−1.55763	−	1.95321i	−0.0628098	−	0.0787610i
$616$		0			0
$617$	−18.4529	+	23.1392i	−0.742886	+	0.931549i	−0.999388	−	0.0349946i	$-0.988859\pi$
$617$	−18.4529	+	23.1392i	−0.742886	+	0.931549i	0.256502	+	0.966544i	$0.417430\pi$
$618$	−15.8684	+	27.4848i	−0.638319	+	1.10560i
$619$	−5.47803	−	9.48823i	−0.220181	−	0.381364i	0.734682	−	0.678412i	$-0.237331\pi$
$619$	−5.47803	−	9.48823i	−0.220181	−	0.381364i	−0.954863	+	0.297048i	$0.903998\pi$
$620$	13.0715	+	1.97021i	0.524964	+	0.0791256i
$621$	7.93523	+	7.36282i	0.318430	+	0.295460i
$622$	7.79407	−	3.75343i	0.312514	−	0.150499i
$623$		0			0
$624$	14.5519	+	7.00785i	0.582544	+	0.280538i
$625$	−9.39276	−	23.9324i	−0.375710	−	0.957294i
$626$	−0.352789	−	4.70764i	−0.0141003	−	0.188155i
$627$	36.3400	−	11.2094i	1.45128	−	0.447660i
$628$	0.0418930	−	0.559023i	0.00167171	−	0.0223075i
$629$	−1.44953	−	6.35081i	−0.0577966	−	0.253223i
$630$		0			0
$631$	3.86535	−	16.9352i	0.153877	−	0.674180i	−0.837859	−	0.545887i	$-0.816193\pi$
$631$	3.86535	−	16.9352i	0.153877	−	0.674180i	0.991736	−	0.128293i	$-0.0409499\pi$
$632$	−6.83612	−	2.10866i	−0.271926	−	0.0838781i
$633$	−10.2192	+	26.0381i	−0.406177	+	1.03492i
$634$	11.5102	−	10.6799i	0.457128	−	0.424153i
$635$	36.1054	−	24.6162i	1.43280	−	0.976865i
$636$	1.15811			0.0459220
$637$		0			0
$638$	9.22675			0.365291
$639$	−43.1794	+	29.4392i	−1.70815	+	1.16460i
$640$	1.66294	−	1.54299i	0.0657336	−	0.0609919i
$641$	6.07429	−	15.4770i	0.239920	−	0.611307i	−0.759302	−	0.650738i	$-0.774460\pi$
$641$	6.07429	−	15.4770i	0.239920	−	0.611307i	0.999222	+	0.0394317i	$0.0125547\pi$
$642$	−2.89746	−	0.893747i	−0.114354	−	0.0352734i
$643$	0.609866	−	2.67200i	0.0240508	−	0.105373i	−0.961478	−	0.274882i	$-0.911361\pi$
$643$	0.609866	−	2.67200i	0.0240508	−	0.105373i	0.985529	+	0.169509i	$0.0542182\pi$
$644$		0			0
$645$	−11.4457	−	50.1468i	−0.450673	−	1.97453i
$646$	−1.26386	+	16.8651i	−0.0497260	+	0.663548i
$647$	16.8481	−	5.19694i	0.662366	−	0.204313i	0.0546969	−	0.998503i	$-0.482581\pi$
$647$	16.8481	−	5.19694i	0.662366	−	0.204313i	0.607669	+	0.794190i	$0.292105\pi$
$648$	0.435430	+	5.81040i	0.0171053	+	0.228254i
$649$	2.97262	+	7.57411i	0.116686	+	0.297310i
$650$	−0.814052	−	0.392027i	−0.0319298	−	0.0153766i
$651$		0			0
$652$	17.1574	−	8.26258i	0.671936	−	0.323587i
$653$	25.5084	+	23.6683i	0.998220	+	0.926212i	0.997274	−	0.0737872i	$-0.0235086\pi$
$653$	25.5084	+	23.6683i	0.998220	+	0.926212i	0.000945523		1.00000i	$0.499699\pi$
$654$	−8.68936	−	1.30971i	−0.339781	−	0.0512138i
$655$	−6.46892	−	11.2045i	−0.252762	−	0.437796i
$656$	0.210713	−	0.364965i	0.00822695	−	0.0142495i
$657$	25.2900	−	31.7127i	0.986658	−	1.23723i
$658$		0			0
$659$	−27.3299	−	34.2706i	−1.06462	−	1.33499i	−0.939383	−	0.342868i	$-0.888602\pi$
$659$	−27.3299	−	34.2706i	−1.06462	−	1.33499i	−0.125239	−	0.992127i	$-0.539970\pi$
$660$	13.2978	−	2.00432i	0.517616	−	0.0780180i
$661$	5.49139	+	3.74397i	0.213590	+	0.145623i	0.665390	−	0.746496i	$-0.268265\pi$
$661$	5.49139	+	3.74397i	0.213590	+	0.145623i	−0.451799	+	0.892120i	$0.649218\pi$
$662$	16.3356	+	11.1374i	0.634901	+	0.432868i
$663$	−42.1048	+	6.34628i	−1.63522	+	0.246469i
$664$	2.95336	+	3.70340i	0.114613	+	0.143720i
$665$		0			0
$666$	5.89861	−	7.39663i	0.228567	−	0.286613i
$667$	10.1644	−	17.6052i	0.393565	−	0.681675i
$668$	2.59178	+	4.48910i	0.100279	+	0.173688i
$669$	−27.0042	−	4.07023i	−1.04404	−	0.157364i
$670$	0.619039	+	0.574384i	0.0239155	+	0.0221904i
$671$	19.2235	−	9.25754i	0.742115	−	0.357384i
$672$		0			0
$673$	2.76926	+	1.33361i	0.106747	+	0.0514067i	0.486495	−	0.873683i	$-0.338275\pi$
$673$	2.76926	+	1.33361i	0.106747	+	0.0514067i	−0.379748	+	0.925090i	$0.623989\pi$
$674$	−1.64491	−	4.19117i	−0.0633597	−	0.161438i
$675$	0.0236603	+	0.315725i	0.000910685	+	0.0121523i
$676$	24.0817	−	7.42822i	0.926219	−	0.285701i
$677$	0.425509	−	5.67802i	0.0163536	−	0.218224i	−0.983040	−	0.183393i	$-0.941292\pi$
$677$	0.425509	−	5.67802i	0.0163536	−	0.218224i	0.999393	−	0.0348306i	$-0.0110892\pi$
$678$	−3.59542	−	15.7525i	−0.138081	−	0.604973i
$679$		0			0
$680$	−1.33080	+	5.83061i	−0.0510338	+	0.223594i
$681$	26.6557	+	8.22218i	1.02145	+	0.315075i
$682$	−4.82950	+	12.3054i	−0.184931	+	0.471197i
$683$	−13.4119	+	12.4445i	−0.513194	+	0.476174i	−0.893738	−	0.448588i	$-0.851927\pi$
$683$	−13.4119	+	12.4445i	−0.513194	+	0.476174i	0.380545	+	0.924762i	$0.375736\pi$
$684$	−20.2943	+	13.8364i	−0.775972	+	0.529049i
$685$	43.5097			1.66242
$686$		0			0
$687$	21.1102			0.805406
$688$	7.16904	−	4.88777i	0.273317	−	0.186344i
$689$	2.00794	−	1.86310i	0.0764965	−	0.0709784i
$690$	10.8247	−	27.5810i	0.412090	−	1.04999i
$691$	32.0196	+	9.87673i	1.21808	+	0.375729i	0.836170	−	0.548470i	$-0.184790\pi$
$691$	32.0196	+	9.87673i	1.21808	+	0.375729i	0.381912	+	0.924199i	$0.375266\pi$
$692$	−1.07993	+	4.73148i	−0.0410527	+	0.179864i
$693$		0			0
$694$	0.580111	+	2.54163i	0.0220207	+	0.0964791i
$695$	−1.07106	+	14.2924i	−0.0406278	+	0.542140i
$696$	−10.1565	+	3.13285i	−0.384979	+	0.118750i
$697$	0.0830261	+	1.10791i	0.00314484	+	0.0419650i
$698$	0.617508	+	1.57338i	0.0233730	+	0.0595535i
$699$	6.09975	+	2.93748i	0.230714	+	0.111106i
$700$		0			0
$701$	38.4598	−	18.5213i	1.45261	−	0.699538i	0.469561	−	0.882900i	$-0.344412\pi$
$701$	38.4598	−	18.5213i	1.45261	−	0.699538i	0.983045	+	0.183362i	$0.0586980\pi$
$702$	−9.81285	−	9.10499i	−0.370362	−	0.343646i
$703$	−15.6742	−	2.36251i	−0.591164	−	0.0891037i
$704$	1.13426	+	1.96460i	0.0427490	+	0.0740435i
$705$	26.1969	−	45.3744i	0.986632	−	1.70890i
$706$	15.3318	−	19.2254i	0.577019	−	0.723559i
$707$		0			0
$708$	−5.84386	−	7.32797i	−0.219626	−	0.275402i
$709$	12.0941	−	1.82289i	0.454203	−	0.0684600i	0.0820430	−	0.996629i	$-0.473856\pi$
$709$	12.0941	−	1.82289i	0.454203	−	0.0684600i	0.372160	+	0.928169i	$0.378617\pi$
$710$	25.5833	+	17.4424i	0.960124	+	0.654601i
$711$	22.6315	+	15.4299i	0.848749	+	0.578667i
$712$	2.52561	−	0.380674i	0.0946511	−	0.0142664i
$713$	18.1591	+	22.7708i	0.680063	+	0.852772i
$714$		0			0
$715$	19.8314	−	24.8678i	0.741653	−	0.930004i
$716$	−6.68520	+	11.5791i	−0.249838	+	0.432732i
$717$	−5.43129	−	9.40727i	−0.202835	−	0.351321i
$718$	13.7550	+	2.07324i	0.513334	+	0.0773726i
$719$	16.5726	+	15.3772i	0.618055	+	0.573472i	0.925808	−	0.377995i	$-0.123386\pi$
$719$	16.5726	+	15.3772i	0.618055	+	0.573472i	−0.307752	+	0.951467i	$0.599577\pi$
$720$	−7.82555	+	3.76859i	−0.291641	+	0.140447i
$721$		0			0
$722$	19.9600	+	9.61224i	0.742835	+	0.357731i
$723$	6.32678	+	16.1204i	0.235296	+	0.599523i
$724$	−1.00163	−	13.3658i	−0.0372251	−	0.496735i
$725$	0.568163	−	0.175255i	0.0211011	−	0.00650882i
$726$	1.14316	−	15.2544i	0.0424266	−	0.566144i
$727$	5.97800	+	26.1913i	0.221712	+	0.971382i	0.956189	+	0.292749i	$0.0945702\pi$
$727$	5.97800	+	26.1913i	0.221712	+	0.971382i	−0.734478	+	0.678633i	$0.762573\pi$
$728$		0			0
$729$	8.74248	−	38.3033i	0.323796	−	1.41864i
$730$	−22.9649	−	7.08372i	−0.849968	−	0.262180i
$731$	−8.35704	+	21.2934i	−0.309096	+	0.787565i
$732$	−18.0172	+	16.7175i	−0.665934	+	0.617896i
$733$	−22.8893	+	15.6057i	−0.845437	+	0.576409i	−0.906731	−	0.421710i	$-0.861430\pi$
$733$	−22.8893	+	15.6057i	−0.845437	+	0.576409i	0.0612933	+	0.998120i	$0.480477\pi$
$734$	−3.72112			−0.137349
$735$		0			0
$736$	4.99808			0.184232
$737$	−0.697732	+	0.475706i	−0.0257013	+	0.0175228i
$738$	−1.18282	+	1.09749i	−0.0435401	+	0.0403993i
$739$	11.4439	−	29.1585i	0.420969	−	1.07261i	−0.550371	−	0.834920i	$-0.685514\pi$
$739$	11.4439	−	29.1585i	0.420969	−	1.07261i	0.971340	−	0.237692i	$-0.0763910\pi$
$740$	−5.35630	−	1.65220i	−0.196901	−	0.0607360i
$741$	−23.0562	+	101.016i	−0.846991	+	3.71091i
$742$		0			0
$743$	10.0807	+	44.1664i	0.369825	+	1.62031i	0.727255	+	0.686368i	$0.240796\pi$
$743$	10.0807	+	44.1664i	0.369825	+	1.62031i	−0.357430	+	0.933940i	$0.616347\pi$
$744$	1.13796	−	15.1851i	0.0417198	−	0.556712i
$745$	−27.2817	+	8.41529i	−0.999524	+	0.308312i
$746$	−1.19438	−	15.9379i	−0.0437295	−	0.583529i
$747$	−6.62596	−	16.8827i	−0.242431	−	0.617704i
$748$	−5.38829	−	2.59486i	−0.197015	−	0.0948776i
$749$		0			0
$750$	−25.9243	+	12.4845i	−0.946623	+	0.455870i
$751$	−11.8201	−	10.9675i	−0.431322	−	0.400209i	0.434410	−	0.900715i	$-0.356957\pi$
$751$	−11.8201	−	10.9675i	−0.431322	−	0.400209i	−0.865733	+	0.500506i	$0.833147\pi$
$752$	8.73951	+	1.31727i	0.318697	+	0.0480358i
$753$	−32.4935	−	56.2804i	−1.18413	−	2.05097i
$754$	−12.5694	+	21.7709i	−0.457751	+	0.792849i
$755$	7.90912	−	9.91772i	0.287842	−	0.360943i
$756$		0			0
$757$	−22.6223	−	28.3675i	−0.822222	−	1.03103i	−0.998906	−	0.0467657i	$-0.985109\pi$
$757$	−22.6223	−	28.3675i	−0.822222	−	1.03103i	0.176684	−	0.984268i	$-0.443463\pi$
$758$	−9.31725	+	1.40435i	−0.338418	+	0.0510083i
$759$	24.4807	+	16.6907i	0.888594	+	0.605833i
$760$	12.0241	+	8.19792i	0.436161	+	0.297370i
$761$	−36.7657	+	5.54153i	−1.33275	+	0.200880i	−0.776493	−	0.630126i	$-0.783003\pi$
$761$	−36.7657	+	5.54153i	−1.33275	+	0.200880i	−0.556262	+	0.831007i	$0.687765\pi$
$762$	−31.3852	−	39.3558i	−1.13697	−	1.42571i
$763$		0			0
$764$	8.55987	−	10.7337i	0.309685	−	0.388333i
$765$	11.4492	−	19.8305i	0.413945	−	0.716975i
$766$	−6.47981	−	11.2234i	−0.234125	−	0.405516i
$767$	−21.9210	−	3.30405i	−0.791520	−	0.119302i
$768$	−1.91561	−	1.77743i	−0.0691236	−	0.0641373i
$769$	−8.29691	+	3.99558i	−0.299194	+	0.144084i	−0.577458	−	0.816420i	$-0.695955\pi$
$769$	−8.29691	+	3.99558i	−0.299194	+	0.144084i	0.278264	+	0.960505i	$0.410241\pi$
$770$		0			0
$771$	44.4243	+	21.3936i	1.59990	+	0.770473i
$772$	2.28905	+	5.83240i	0.0823846	+	0.209913i
$773$	−1.63943	−	21.8767i	−0.0589662	−	0.786849i	−0.945798	−	0.324756i	$-0.894718\pi$
$773$	−1.63943	−	21.8767i	−0.0589662	−	0.786849i	0.886832	−	0.462093i	$-0.152901\pi$
$774$	−31.7455	+	9.79218i	−1.14107	+	0.351973i
$775$	−0.0636590	+	0.849470i	−0.00228670	+	0.0305139i
$776$	0.145165	+	0.636010i	0.00521113	+	0.0228314i
$777$		0			0
$778$	5.75642	−	25.2205i	0.206378	−	0.904200i
$779$	2.58339	+	0.796871i	0.0925596	+	0.0285509i
$780$	−13.3861	+	34.1071i	−0.479297	+	1.22123i
$781$	−22.6979	+	21.0606i	−0.812194	+	0.753606i
$782$	−10.8870	+	7.42262i	−0.389318	+	0.265432i
$783$	8.80902			0.314809
$784$		0			0
$785$	1.27171			0.0453893
$786$	−12.3139	+	8.39550i	−0.439223	+	0.299457i
$787$	11.0316	−	10.2359i	0.393236	−	0.364869i	−0.458632	−	0.888626i	$-0.651660\pi$
$787$	11.0316	−	10.2359i	0.393236	−	0.364869i	0.851868	+	0.523757i	$0.175470\pi$
$788$	−7.50817	+	19.1305i	−0.267468	+	0.681496i
$789$	−19.4629	−	6.00352i	−0.692899	−	0.213731i
$790$	3.61127	−	15.8220i	0.128483	−	0.562921i
$791$		0			0
$792$	−1.93275	−	8.46794i	−0.0686774	−	0.300895i
$793$	−4.34425	+	57.9699i	−0.154269	+	2.05857i
$794$	30.7883	−	9.49693i	1.09264	−	0.337034i
$795$	0.196330	+	2.61985i	0.00696312	+	0.0929164i
$796$	1.25940	+	3.20889i	0.0446381	+	0.113736i
$797$	−20.3285	−	9.78967i	−0.720071	−	0.346768i	0.0376996	−	0.999289i	$-0.487997\pi$
$797$	−20.3285	−	9.78967i	−0.720071	−	0.346768i	−0.757770	+	0.652521i	$0.773711\pi$
$798$		0			0
$799$	−20.9929	+	10.1097i	−0.742677	+	0.357654i
$800$	0.107161	+	0.0994312i	0.00378873	+	0.00351542i
$801$	−9.67004	−	1.45752i	−0.341674	−	0.0514991i
$802$	11.9818	+	20.7532i	0.423094	+	0.732820i
$803$	12.0163	−	20.8128i	0.424046	−	0.734468i
$804$	0.606515	−	0.760546i	0.0213902	−	0.0268224i
$805$		0			0
$806$	−22.4558	−	28.1587i	−0.790974	−	0.991849i
$807$	−3.21378	+	0.484399i	−0.113130	+	0.0170517i
$808$	−14.0327	−	9.56733i	−0.493669	−	0.336578i
$809$	44.2259	+	30.1527i	1.55490	+	1.06011i	0.968159	+	0.250335i	$0.0805409\pi$
$809$	44.2259	+	30.1527i	1.55490	+	1.06011i	0.586739	+	0.809776i	$0.300411\pi$
$810$	−13.0703	+	1.97004i	−0.459245	+	0.0692201i
$811$	−30.3854	−	38.1021i	−1.06698	−	1.33795i	−0.938130	−	0.346282i	$-0.887444\pi$
$811$	−30.3854	−	38.1021i	−1.06698	−	1.33795i	−0.128847	−	0.991665i	$-0.541127\pi$
$812$		0			0
$813$	−33.8996	+	42.5088i	−1.18891	+	1.49085i
$814$	2.80266	−	4.85435i	0.0982333	−	0.170145i
$815$	21.6001	+	37.4124i	0.756617	+	1.31050i
$816$	6.81228	+	1.02679i	0.238478	+	0.0359447i
$817$	40.8034	+	37.8600i	1.42753	+	1.32455i
$818$	−19.1223	+	9.20880i	−0.668595	+	0.321978i
$819$		0			0
$820$	0.861337	+	0.414798i	0.0300792	+	0.0144854i
$821$	−17.3437	−	44.1910i	−0.605299	−	1.54228i	−0.824063	−	0.566498i	$-0.808298\pi$
$821$	−17.3437	−	44.1910i	−0.605299	−	1.54228i	0.218764	−	0.975778i	$-0.429797\pi$
$822$	−3.74551	−	49.9804i	−0.130640	−	1.74327i
$823$	−18.9470	+	5.84438i	−0.660452	+	0.203722i	−0.606821	−	0.794838i	$-0.707556\pi$
$823$	−18.9470	+	5.84438i	−0.660452	+	0.203722i	−0.0536307	+	0.998561i	$0.517079\pi$
$824$	0.907580	−	12.1108i	0.0316171	−	0.421900i
$825$	0.192836	+	0.844872i	0.00671370	+	0.0294147i
$826$		0			0
$827$	−6.93486	+	30.3836i	−0.241149	+	1.05654i	0.698825	+	0.715293i	$0.253707\pi$
$827$	−6.93486	+	30.3836i	−0.241149	+	1.05654i	−0.939973	+	0.341248i	$0.889150\pi$
$828$	−18.2865	−	5.64063i	−0.635499	−	0.196025i
$829$	−6.49095	+	16.5387i	−0.225440	+	0.574412i	−0.998180	−	0.0603113i	$-0.980791\pi$
$829$	−6.49095	+	16.5387i	−0.225440	+	0.574412i	0.772740	+	0.634723i	$0.218886\pi$
$830$	−7.87708	+	7.30886i	−0.273417	+	0.253694i
$831$	8.62202	−	5.87839i	0.299095	−	0.203919i
$832$	−6.18072			−0.214278
$833$		0			0
$834$	16.5101			0.571698
$835$	−9.71576	+	6.62409i	−0.336228	+	0.229236i
$836$	−10.6680	+	9.89846i	−0.368961	+	0.342345i
$837$	−4.61085	+	11.7482i	−0.159374	+	0.406079i
$838$	2.03194	+	0.626771i	0.0701923	+	0.0216515i
$839$	−6.45878	+	28.2978i	−0.222982	+	0.976947i	0.732238	+	0.681049i	$0.238476\pi$
$839$	−6.45878	+	28.2978i	−0.222982	+	0.976947i	−0.955219	+	0.295898i	$0.904381\pi$
$840$		0			0
$841$	2.77196	+	12.1448i	0.0955848	+	0.418785i
$842$	1.72961	−	23.0801i	0.0596064	−	0.795392i
$843$	63.7086	−	19.6515i	2.19424	−	0.676833i
$844$	−0.799912	−	10.6741i	−0.0275341	−	0.367417i
$845$	20.8864	+	53.2178i	0.718515	+	1.83075i
$846$	−30.4886	−	14.6825i	−1.04822	−	0.504796i
$847$		0			0
$848$	−0.399289	+	0.192287i	−0.0137116	+	0.00660317i
$849$	5.36215	+	4.97534i	0.184028	+	0.170753i
$850$	−0.381087	−	0.0574396i	−0.0130712	−	0.00197016i
$851$	−6.17492	−	10.6953i	−0.211674	−	0.366630i
$852$	17.8341	−	30.8895i	0.610985	−	1.05826i
$853$	−31.6955	+	39.7449i	−1.08523	+	1.36084i	−0.157532	+	0.987514i	$0.550354\pi$
$853$	−31.6955	+	39.7449i	−1.08523	+	1.36084i	−0.927701	+	0.373325i	$0.878218\pi$
$854$		0			0
$855$	−34.7408	−	43.5636i	−1.18811	−	1.48985i
$856$	1.14737	−	0.172938i	0.0392163	−	0.00591090i
$857$	−37.4968	−	25.5649i	−1.28086	−	0.873279i	−0.284517	−	0.958671i	$-0.591833\pi$
$857$	−37.4968	−	25.5649i	−1.28086	−	0.873279i	−0.996347	+	0.0853921i	$0.972786\pi$
$858$	−30.2733	−	20.6400i	−1.03351	−	0.704637i
$859$	−31.8587	+	4.80193i	−1.08701	+	0.163840i	−0.668013	−	0.744150i	$-0.732855\pi$
$859$	−31.8587	+	4.80193i	−1.08701	+	0.163840i	−0.418993	+	0.907989i	$0.637617\pi$
$860$	12.2723	+	15.3890i	0.418483	+	0.524762i
$861$		0			0
$862$	−24.6837	+	30.9524i	−0.840730	+	1.05424i
$863$	−16.1162	+	27.9141i	−0.548602	+	0.950206i	0.449769	+	0.893145i	$0.351506\pi$
$863$	−16.1162	+	27.9141i	−0.548602	+	0.950206i	−0.998371	+	0.0570609i	$0.981827\pi$
$864$	1.08291	+	1.87565i	0.0368413	+	0.0638109i
$865$	−10.8865	−	1.64088i	−0.370153	−	0.0557915i
$866$	9.93105	+	9.21467i	0.337471	+	0.313127i
$867$	23.6613	−	11.3947i	0.803581	−	0.386984i
$868$		0			0
$869$	14.6217	+	7.04145i	0.496008	+	0.238865i
$870$	−8.80885	−	22.4446i	−0.298648	−	0.760943i
$871$	−0.171939	−	2.29437i	−0.00582594	−	0.0777418i
$872$	3.21335	−	0.991186i	0.108818	−	0.0335658i
$873$	0.186659	−	2.49079i	0.00631746	−	0.0843006i
$874$	7.13477	+	31.2595i	0.241337	+	1.05737i
$875$		0			0
$876$	−6.16028	+	26.9900i	−0.208137	+	0.911906i
$877$	8.69191	+	2.68110i	0.293505	+	0.0905343i	0.438011	−	0.898970i	$-0.355683\pi$
$877$	8.69191	+	2.68110i	0.293505	+	0.0905343i	−0.144506	+	0.989504i	$0.546159\pi$
$878$	13.9913	−	35.6491i	0.472182	−	1.20310i
$879$	−2.53068	+	2.34813i	−0.0853578	+	0.0792005i
$880$	−4.25198	+	2.89895i	−0.143334	+	0.0977236i
$881$	10.2269			0.344554			0.172277	−	0.985049i	$-0.444888\pi$
$881$	10.2269			0.344554			0.172277	+	0.985049i	$0.444888\pi$
$882$		0			0
$883$	16.8330			0.566476			0.283238	−	0.959050i	$-0.408591\pi$
$883$	16.8330			0.566476			0.283238	+	0.959050i	$0.408591\pi$
$884$	13.4630	−	9.17895i	0.452811	−	0.308721i
$885$	15.5865	−	14.4621i	0.523934	−	0.486139i
$886$	−6.73027	+	17.1484i	−0.226108	+	0.576113i
$887$	4.62999	+	1.42816i	0.155460	+	0.0479530i	0.371508	−	0.928430i	$-0.378841\pi$
$887$	4.62999	+	1.42816i	0.155460	+	0.0479530i	−0.216049	+	0.976383i	$0.569317\pi$
$888$	−1.43682	+	6.29510i	−0.0482164	+	0.211250i
$889$		0			0
$890$	1.28931	+	5.64883i	0.0432177	+	0.189349i
$891$	0.987781	−	13.1810i	0.0330919	−	0.441581i
$892$	9.98622	−	3.08034i	0.334363	−	0.103137i
$893$	4.23708	+	56.5398i	0.141788	+	1.89203i
$894$	12.0153	+	30.6145i	0.401852	+	1.02390i
$895$	−27.3273	−	13.1601i	−0.913452	−	0.439895i
$896$		0			0
$897$	−72.7319	+	35.0258i	−2.42845	+	1.16948i
$898$	20.0892	+	18.6400i	0.670385	+	0.622026i
$899$	23.4363	+	3.53245i	0.781644	+	0.117814i
$900$	−0.279857	−	0.484726i	−0.00932856	−	0.0161575i
$901$	0.584179	−	1.01183i	0.0194618	−	0.0337089i
$902$	−0.596064	+	0.747440i	−0.0198468	+	0.0248870i
$903$		0			0
$904$	3.85510	+	4.83414i	0.128219	+	0.160781i
$905$	30.0659	−	4.53171i	0.999425	−	0.150639i
$906$	−12.0735	−	8.23158i	−0.401116	−	0.273476i
$907$	15.5611	+	10.6094i	0.516697	+	0.352278i	0.793423	−	0.608671i	$-0.208297\pi$
$907$	15.5611	+	10.6094i	0.516697	+	0.352278i	−0.276726	+	0.960949i	$0.589249\pi$
$908$	−10.5554	+	1.59097i	−0.350294	+	0.0527983i
$909$	40.5441	+	50.8407i	1.34476	+	1.68628i
$910$		0			0
$911$	−12.3583	+	15.4968i	−0.409447	+	0.513431i	−0.943207	−	0.332205i	$-0.892207\pi$
$911$	−12.3583	+	15.4968i	−0.409447	+	0.513431i	0.533760	+	0.845636i	$0.320779\pi$
$912$	8.38201	−	14.5181i	0.277556	−	0.480741i
$913$	−5.37280	−	9.30596i	−0.177814	−	0.307982i
$914$	−6.47478	−	0.975916i	−0.214167	−	0.0322804i
$915$	−40.8723	−	37.9240i	−1.35120	−	1.25373i
$916$	−7.27832	+	3.50505i	−0.240482	+	0.115810i
$917$		0			0
$918$	−5.14434	−	2.47738i	−0.169789	−	0.0817658i
$919$	−7.43276	−	18.9384i	−0.245184	−	0.624719i	0.754310	−	0.656518i	$-0.227971\pi$
$919$	−7.43276	−	18.9384i	−0.245184	−	0.624719i	−0.999494	+	0.0317994i	$0.989876\pi$
$920$	0.847309	+	11.3066i	0.0279350	+	0.372766i
$921$	−28.2826	+	8.72402i	−0.931943	+	0.287466i
$922$	−1.75922	+	23.4751i	−0.0579368	+	0.773112i
$923$	−18.7723	−	82.2469i	−0.617899	−	2.70719i
$924$		0			0
$925$	0.0803771	−	0.352155i	0.00264278	−	0.0115788i
$926$	2.99820	+	0.924821i	0.0985269	+	0.0303915i
$927$	−16.9883	+	43.2855i	−0.557970	+	1.42168i
$928$	2.98154	−	2.76647i	0.0978739	−	0.0908137i
$929$	−7.90826	+	5.39176i	−0.259462	+	0.176898i	−0.686064	−	0.727542i	$-0.740663\pi$
$929$	−7.90826	+	5.39176i	−0.259462	+	0.176898i	0.426602	+	0.904439i	$0.359710\pi$
$930$	34.5443			1.13275
$931$		0			0
$932$	−2.59078			−0.0848637
$933$	18.6781	−	12.7345i	0.611493	−	0.416909i
$934$	−24.7596	+	22.9735i	−0.810159	+	0.751717i
$935$	4.95658	−	12.6292i	0.162098	−	0.413018i
$936$	22.6134	+	6.97530i	0.739141	+	0.227995i
$937$	11.2692	−	49.3735i	0.368148	−	1.61296i	−0.363714	−	0.931511i	$-0.618491\pi$
$937$	11.2692	−	49.3735i	0.368148	−	1.61296i	0.731862	−	0.681453i	$-0.238651\pi$
$938$		0			0
$939$	−2.74513	−	12.0272i	−0.0895838	−	0.392492i
$940$	−1.49832	+	19.9936i	−0.0488697	+	0.652120i
$941$	−32.0381	+	9.88243i	−1.04441	+	0.322158i	−0.769054	−	0.639184i	$-0.779272\pi$
$941$	−32.0381	+	9.88243i	−1.04441	+	0.322158i	−0.275357	+	0.961342i	$0.588796\pi$
$942$	−0.109475	−	1.46084i	−0.00356688	−	0.0475967i
$943$	0.769525	+	1.96072i	0.0250592	+	0.0638497i
$944$	3.23153	+	1.55622i	0.105177	+	0.0506507i
$945$		0			0
$946$	−17.7341	+	8.54027i	−0.576584	+	0.277668i
$947$	28.0720	+	26.0470i	0.912216	+	0.846413i	0.988585	−	0.150667i	$-0.0481421\pi$
$947$	28.0720	+	26.0470i	0.912216	+	0.846413i	−0.0763686	+	0.997080i	$0.524333\pi$
$948$	−18.4859	−	2.78630i	−0.600393	−	0.0904947i
$949$	32.7391	+	56.7058i	1.06276	+	1.84075i
$950$	−0.468899	+	0.812157i	−0.0152131	+	0.0263498i
$951$	25.5829	−	32.0799i	0.829582	−	1.04026i
$952$		0			0
$953$	35.8905	+	45.0053i	1.16261	+	1.45786i	0.864003	+	0.503486i	$0.167950\pi$
$953$	35.8905	+	45.0053i	1.16261	+	1.45786i	0.298604	+	0.954377i	$0.403479\pi$
$954$	1.67788	−	0.252900i	0.0543235	−	0.00818795i
$955$	25.7327	+	17.5443i	0.832692	+	0.567720i
$956$	3.43452	+	2.34162i	0.111080	+	0.0757333i
$957$	23.8420	−	3.59361i	0.770703	−	0.116165i
$958$	18.2419	+	22.8746i	0.589367	+	0.739043i
$959$		0			0
$960$	3.69610	−	4.63477i	0.119291	−	0.149587i
$961$	−1.47821	+	2.56034i	−0.0476842	+	0.0825915i
$962$	7.63602	+	13.2260i	0.246195	+	0.426423i
$963$	−4.39304	−	0.662145i	−0.141564	−	0.0213373i
$964$	−4.85788	−	4.50746i	−0.156462	−	0.145175i
$965$	−12.8059	+	6.16698i	−0.412235	+	0.198522i
$966$		0			0
$967$	16.5206	+	7.95588i	0.531265	+	0.255844i	0.680230	−	0.732999i	$-0.261880\pi$
$967$	16.5206	+	7.95588i	0.531265	+	0.255844i	−0.148965	+	0.988842i	$0.547594\pi$
$968$	2.13864	+	5.44916i	0.0687385	+	0.175143i
$969$	3.30272	+	44.0718i	0.106099	+	1.41579i
$970$	−1.41416	+	0.436210i	−0.0454059	+	0.0140059i
$971$	−1.89087	+	25.2319i	−0.0606809	+	0.809730i	0.880977	+	0.473159i	$0.156886\pi$
$971$	−1.89087	+	25.2319i	−0.0606809	+	0.809730i	−0.941658	+	0.336571i	$0.890733\pi$
$972$	4.83399	+	21.1791i	0.155050	+	0.679320i
$973$		0			0
$974$	2.35825	−	10.3322i	0.0755632	−	0.331064i
$975$	−2.25620	−	0.695947i	−0.0722564	−	0.0222881i
$976$	3.43620	−	8.75529i	0.109990	−	0.280250i
$977$	24.5528	−	22.7817i	0.785514	−	0.728851i	−0.181550	−	0.983382i	$-0.558112\pi$
$977$	24.5528	−	22.7817i	0.785514	−	0.728851i	0.967065	+	0.254531i	$0.0819211\pi$
$978$	41.1169	−	28.0330i	1.31477	−	0.896396i
$979$	−5.79410			−0.185180
$980$		0			0
$981$	−12.8753			−0.411076
$982$	19.9720	−	13.6166i	0.637331	−	0.434525i
$983$	−1.16023	+	1.07653i	−0.0370055	+	0.0343361i	−0.698459	−	0.715650i	$-0.746130\pi$
$983$	−1.16023	+	1.07653i	−0.0370055	+	0.0343361i	0.661453	+	0.749986i	$0.269940\pi$
$984$	0.402338	−	1.02514i	0.0128261	−	0.0326803i
$985$	−44.5494	−	13.7417i	−1.41946	−	0.437846i
$986$	−2.38603	+	10.4539i	−0.0759866	+	0.332919i
$987$		0			0
$988$	−8.82299	−	38.6560i	−0.280697	−	1.22981i
$989$	−3.24082	+	43.2457i	−0.103052	+	1.37513i
$990$	18.8283	−	5.80777i	0.598404	−	0.184583i
$991$	−0.425961	−	5.68405i	−0.0135311	−	0.180560i	−0.999874	−	0.0158567i	$-0.994952\pi$
$991$	−0.425961	−	5.68405i	−0.0135311	−	0.180560i	0.986343	−	0.164703i	$-0.0526666\pi$
$992$	2.12892	+	5.42440i	0.0675933	+	0.172225i
$993$	46.5491	+	22.4169i	1.47719	+	0.711378i
$994$		0			0
$995$	−7.04557	+	3.39297i	−0.223360	+	0.107564i
$996$	9.07391	+	8.41936i	0.287518	+	0.266778i
$997$	−31.1850	−	4.70038i	−0.987639	−	0.148863i	−0.364693	−	0.931128i	$-0.618826\pi$
$997$	−31.1850	−	4.70038i	−0.987639	−	0.148863i	−0.622945	+	0.782265i	$0.714064\pi$
$998$	−13.1748	−	22.8193i	−0.417040	−	0.722334i
$999$	2.67577	−	4.63457i	0.0846577	−	0.146631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.h.373.1		36
7.2	even	3		98.2.e.b.29.1	✓	18
7.3	odd	6		686.2.g.g.459.1		36
7.4	even	3	inner	686.2.g.h.459.3		36
7.5	odd	6		686.2.e.b.197.3		18
7.6	odd	2		686.2.g.g.373.3		36
21.2	odd	6		882.2.u.g.127.2		18
28.23	odd	6		784.2.u.d.225.3		18
49.2	even	21		4802.2.a.d.1.9		9
49.4	even	21	inner	686.2.g.h.263.1		36
49.22	even	7	inner	686.2.g.h.275.3		36
49.23	even	21		98.2.e.b.71.1	yes	18
49.26	odd	42		686.2.e.b.491.3		18
49.27	odd	14		686.2.g.g.275.1		36
49.45	odd	42		686.2.g.g.263.3		36
49.47	odd	42		4802.2.a.c.1.1		9
147.23	odd	42		882.2.u.g.757.2		18
196.23	odd	42		784.2.u.d.561.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.29.1	✓	18	7.2	even	3
98.2.e.b.71.1	yes	18	49.23	even	21
686.2.e.b.197.3		18	7.5	odd	6
686.2.e.b.491.3		18	49.26	odd	42
686.2.g.g.263.3		36	49.45	odd	42
686.2.g.g.275.1		36	49.27	odd	14
686.2.g.g.373.3		36	7.6	odd	2
686.2.g.g.459.1		36	7.3	odd	6
686.2.g.h.263.1		36	49.4	even	21	inner
686.2.g.h.275.3		36	49.22	even	7	inner
686.2.g.h.373.1		36	1.1	even	1	trivial
686.2.g.h.459.3		36	7.4	even	3	inner
784.2.u.d.225.3		18	28.23	odd	6
784.2.u.d.561.3		18	196.23	odd	42
882.2.u.g.127.2		18	21.2	odd	6
882.2.u.g.757.2		18	147.23	odd	42
4802.2.a.c.1.1		9	49.47	odd	42
4802.2.a.d.1.9		9	49.2	even	21

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.826239 + 0.563320i) q^{2} +(-1.91561 + 1.77743i) q^{3} +(0.365341 - 0.930874i) q^{4} +(2.16774 + 0.668658i) q^{5} +(0.581491 - 2.54768i) q^{6} +(0.222521 + 0.974928i) q^{8} +(0.286126 - 3.81809i) q^{9} +O(q^{10})\)	\(q+(-0.826239 + 0.563320i) q^{2} +(-1.91561 + 1.77743i) q^{3} +(0.365341 - 0.930874i) q^{4} +(2.16774 + 0.668658i) q^{5} +(0.581491 - 2.54768i) q^{6} +(0.222521 + 0.974928i) q^{8} +(0.286126 - 3.81809i) q^{9} +(-2.16774 + 0.668658i) q^{10} +(-0.169527 - 2.26218i) q^{11} +(0.954708 + 2.43256i) q^{12} +(5.56864 + 2.68171i) q^{13} +(-5.34103 + 2.57210i) q^{15} +(-0.733052 - 0.680173i) q^{16} +(2.60688 + 0.392924i) q^{17} +(1.91440 + 3.31584i) q^{18} +(3.20757 - 5.55567i) q^{19} +(1.41440 - 1.77360i) q^{20} +(1.41440 + 1.77360i) q^{22} +(4.94226 - 0.744926i) q^{23} +(-2.15912 - 1.47207i) q^{24} +(0.120784 + 0.0823491i) q^{25} +(-6.11169 + 0.921189i) q^{26} +(1.35036 + 1.69330i) q^{27} +(2.53592 - 3.17994i) q^{29} +(2.96405 - 5.13388i) q^{30} +(2.91361 + 5.04652i) q^{31} +(0.988831 + 0.149042i) q^{32} +(4.34560 + 4.03213i) q^{33} +(-2.37524 + 1.14386i) q^{34} +(-3.44963 - 1.66125i) q^{36} +(-0.902727 - 2.30011i) q^{37} +(0.479404 + 6.39720i) q^{38} +(-15.4339 + 4.76072i) q^{39} +(-0.169527 + 2.26218i) q^{40} +(0.0937760 + 0.410859i) q^{41} +(-1.93075 + 8.45917i) q^{43} +(-2.16774 - 0.668658i) q^{44} +(3.17325 - 8.08530i) q^{45} +(-3.66386 + 3.39956i) q^{46} +(-7.30248 + 4.97875i) q^{47} +2.61320 q^{48} -0.146185 q^{50} +(-5.69215 + 3.88084i) q^{51} +(4.53079 - 4.20396i) q^{52} +(0.161911 - 0.412542i) q^{53} +(-2.06959 - 0.638385i) q^{54} +(1.14513 - 5.01716i) q^{55} +(3.73034 + 16.3437i) q^{57} +(-0.303950 + 4.05593i) q^{58} +(-3.42738 + 1.05721i) q^{59} +(0.443007 + 5.91151i) q^{60} +(3.43620 + 8.75529i) q^{61} +(-5.25014 - 2.52833i) q^{62} +(-0.900969 + 0.433884i) q^{64} +(10.2782 + 9.53677i) q^{65} +(-5.86188 - 0.883536i) q^{66} +(-0.186127 - 0.322382i) q^{67} +(1.31816 - 2.28312i) q^{68} +(-8.14339 + 10.2115i) q^{69} +(-8.51015 - 10.6714i) q^{71} +(3.78603 - 0.570653i) q^{72} +(8.75312 + 5.96778i) q^{73} +(2.04157 + 1.39192i) q^{74} +(-0.377744 + 0.0569357i) q^{75} +(-3.99977 - 5.01555i) q^{76} +(10.0703 - 12.6277i) q^{78} +(-3.57698 + 6.19550i) q^{79} +(-1.13426 - 1.96460i) q^{80} +(5.76162 + 0.868424i) q^{81} +(-0.308927 - 0.286642i) q^{82} +(4.26774 - 2.05523i) q^{83} +(5.38829 + 2.59486i) q^{85} +(-3.16996 - 8.07693i) q^{86} +(0.794280 + 10.5989i) q^{87} +(2.16774 - 0.668658i) q^{88} +(0.190871 - 2.54699i) q^{89} +(1.93275 + 8.46794i) q^{90} +(1.11218 - 4.87277i) q^{92} +(-14.5511 - 4.48843i) q^{93} +(3.22897 - 8.22727i) q^{94} +(10.6680 - 9.89846i) q^{95} +(-2.15912 + 1.47207i) q^{96} +0.652366 q^{97} -8.68571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

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