LMFDB - Embedded newform 275.2.h.a.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(26,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("275.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.a.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09676 - 0.796845i) q^{2} +(-0.177837 - 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +O(q^{10})$	\(q+(1.09676 - 0.796845i) q^{2} +(-0.177837 - 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +(0.490303 - 3.28018i) q^{11} +0.0933146 q^{12} +(-2.29029 + 1.66399i) q^{13} +(-1.52884 - 4.70527i) q^{14} +(2.95244 + 2.14507i) q^{16} +(2.98685 + 2.17008i) q^{17} +(1.11803 - 3.44095i) q^{18} +(-0.0293950 - 0.0904686i) q^{19} -2.10021 q^{21} +(-2.07605 - 3.98828i) q^{22} -1.16215 q^{23} +(1.36470 - 0.991515i) q^{24} +(-1.18596 + 3.65001i) q^{26} +(-2.63930 - 1.91757i) q^{27} +(0.478730 + 0.347817i) q^{28} +(-2.08707 + 6.42333i) q^{29} +(-5.48382 + 3.98423i) q^{31} -0.914918 q^{32} +(-1.88253 + 0.314983i) q^{33} +5.00509 q^{34} +(0.133724 + 0.411560i) q^{36} +(-3.04066 + 9.35820i) q^{37} +(-0.104329 - 0.0757994i) q^{38} +(1.31805 + 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +(-2.30344 + 1.67354i) q^{42} +2.96862 q^{43} +(0.481274 + 0.239968i) q^{44} +(-1.27460 + 0.926052i) q^{46} +(0.687534 + 2.11601i) q^{47} +(0.649001 - 1.99742i) q^{48} +(-5.11155 - 3.71376i) q^{49} +(0.656567 - 2.02070i) q^{51} +(-0.141849 - 0.436565i) q^{52} +(2.42214 - 1.75979i) q^{53} -4.42270 q^{54} +10.6970 q^{56} +(-0.0442883 + 0.0321774i) q^{57} +(2.82938 + 8.70794i) q^{58} +(-2.62930 + 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(-2.83964 + 8.73951i) q^{62} +(-3.00970 - 9.26289i) q^{63} +(-6.90832 + 5.01919i) q^{64} +(-1.81369 + 1.84554i) q^{66} +13.4153 q^{67} +(-0.484310 + 0.351872i) q^{68} +(0.206673 + 0.636074i) q^{69} +(-6.71734 - 4.88043i) q^{71} +(6.32872 + 4.59808i) q^{72} +(0.407912 - 1.25542i) q^{73} +(4.12215 + 12.6867i) q^{74} +0.0154241 q^{76} +(-10.8319 - 5.40091i) q^{77} +2.20866 q^{78} +(11.2179 - 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-9.12312 - 6.62834i) q^{82} +(-8.61155 - 6.25666i) q^{83} +(0.105234 - 0.323876i) q^{84} +(3.25587 - 2.36553i) q^{86} +3.88682 q^{87} +(9.58829 - 1.60431i) q^{88} -12.1612 q^{89} +(3.19256 + 9.82567i) q^{91} +(0.0582308 - 0.179216i) q^{92} +(3.15590 + 2.29290i) q^{93} +(2.44020 + 1.77291i) q^{94} +(0.162706 + 0.500759i) q^{96} +(-3.50412 + 2.54589i) q^{97} -8.56545 q^{98} +(-4.08696 - 7.85141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.09676	−	0.796845i	0.775529	−	0.563455i	−0.128105	−	0.991761i	$-0.540889\pi$
$2$	1.09676	−	0.796845i	0.775529	−	0.563455i	0.903634	+	0.428306i	$0.140889\pi$
$3$	−0.177837	−	0.547326i	−0.102674	−	0.315999i	0.886503	−	0.462722i	$-0.153127\pi$
$3$	−0.177837	−	0.547326i	−0.102674	−	0.315999i	−0.989178	+	0.146723i	$0.953127\pi$
$4$	−0.0501062	+	0.154211i	−0.0250531	+	0.0771056i
$5$		0			0
$5$		0			0
$6$	−0.631180	−	0.458579i	−0.257678	−	0.187214i
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	−0.475558	−	0.879685i	$-0.657754\pi$
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	0.901800	−	0.432154i	$-0.142246\pi$
$8$	0.905781	+	2.78771i	0.320242	+	0.985603i
$9$	2.15911	−	1.56869i	0.719704	−	0.522895i
$10$		0			0
$11$	0.490303	−	3.28018i	0.147832	−	0.989012i
$11$	0.490303	−	3.28018i	0.147832	−	0.989012i
$12$	0.0933146			0.0269376
$13$	−2.29029	+	1.66399i	−0.635212	+	0.461509i	−0.858202	−	0.513312i	$-0.828418\pi$
$13$	−2.29029	+	1.66399i	−0.635212	+	0.461509i	0.222990	+	0.974821i	$0.428418\pi$
$14$	−1.52884	−	4.70527i	−0.408599	−	1.25754i
$15$		0			0
$16$	2.95244	+	2.14507i	0.738109	+	0.536268i
$17$	2.98685	+	2.17008i	0.724419	+	0.526321i	0.887793	−	0.460243i	$-0.152238\pi$
$17$	2.98685	+	2.17008i	0.724419	+	0.526321i	−0.163374	+	0.986564i	$0.552238\pi$
$18$	1.11803	−	3.44095i	0.263523	−	0.811041i
$19$	−0.0293950	−	0.0904686i	−0.00674368	−	0.0207549i	0.947628	−	0.319376i	$-0.103473\pi$
$19$	−0.0293950	−	0.0904686i	−0.00674368	−	0.0207549i	−0.954372	+	0.298621i	$0.903473\pi$
$20$		0			0
$21$	−2.10021			−0.458304
$22$	−2.07605	−	3.98828i	−0.442616	−	0.850304i
$23$	−1.16215			−0.242324			−0.121162	−	0.992633i	$-0.538662\pi$
$23$	−1.16215			−0.242324			−0.121162	+	0.992633i	$0.538662\pi$
$24$	1.36470	−	0.991515i	0.278569	−	0.202392i
$25$		0			0
$26$	−1.18596	+	3.65001i	−0.232586	+	0.715827i
$27$	−2.63930	−	1.91757i	−0.507934	−	0.369036i
$28$	0.478730	+	0.347817i	0.0904714	+	0.0657313i
$29$	−2.08707	+	6.42333i	−0.387559	+	1.19278i	0.547049	+	0.837101i	$0.315751\pi$
$29$	−2.08707	+	6.42333i	−0.387559	+	1.19278i	−0.934607	+	0.355682i	$0.884249\pi$
$30$		0			0
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.958803	−	0.284071i	$-0.908315\pi$
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.0261194	+	0.999659i	$0.508315\pi$
$32$	−0.914918			−0.161736
$33$	−1.88253	+	0.314983i	−0.327706	+	0.0548314i
$34$	5.00509			0.858366
$35$		0			0
$36$	0.133724	+	0.411560i	0.0222873	+	0.0685933i
$37$	−3.04066	+	9.35820i	−0.499882	+	1.53848i	0.309326	+	0.950956i	$0.399897\pi$
$37$	−3.04066	+	9.35820i	−0.499882	+	1.53848i	−0.809208	+	0.587523i	$0.800103\pi$
$38$	−0.104329	−	0.0757994i	−0.0169244	−	0.0122963i
$39$	1.31805	+	0.957617i	0.211056	+	0.153341i
$40$		0			0
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	−0.923831	−	0.382800i	$-0.874960\pi$
$41$	−2.57047	−	7.91110i	−0.401440	−	1.23551i	0.522391	−	0.852706i	$-0.325040\pi$
$42$	−2.30344	+	1.67354i	−0.355428	+	0.258234i
$43$	2.96862			0.452710			0.226355	−	0.974045i	$-0.427319\pi$
$43$	2.96862			0.452710			0.226355	+	0.974045i	$0.427319\pi$
$44$	0.481274	+	0.239968i	0.0725547	+	0.0361765i
$45$		0			0
$46$	−1.27460	+	0.926052i	−0.187930	+	0.136539i
$47$	0.687534	+	2.11601i	0.100287	+	0.308652i	0.988595	−	0.150595i	$-0.0481191\pi$
$47$	0.687534	+	2.11601i	0.100287	+	0.308652i	−0.888308	+	0.459248i	$0.848119\pi$
$48$	0.649001	−	1.99742i	0.0936753	−	0.288303i
$49$	−5.11155	−	3.71376i	−0.730221	−	0.530537i
$50$		0			0
$51$	0.656567	−	2.02070i	0.0919377	−	0.282955i
$52$	−0.141849	−	0.436565i	−0.0196708	−	0.0605407i
$53$	2.42214	−	1.75979i	0.332706	−	0.241725i	−0.408872	−	0.912592i	$-0.634078\pi$
$53$	2.42214	−	1.75979i	0.332706	−	0.241725i	0.741578	+	0.670867i	$0.234078\pi$
$54$	−4.42270			−0.601853
$55$		0			0
$56$	10.6970			1.42945
$57$	−0.0442883	+	0.0321774i	−0.00586613	+	0.00426200i
$58$	2.82938	+	8.70794i	0.371516	+	1.14341i
$59$	−2.62930	+	8.09216i	−0.342306	+	1.05351i	0.620704	+	0.784045i	$0.286847\pi$
$59$	−2.62930	+	8.09216i	−0.342306	+	1.05351i	−0.963010	+	0.269465i	$0.913153\pi$
$60$		0			0
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	0.932836	−	0.360302i	$-0.117326\pi$
$61$	6.86076	+	4.98464i	0.878431	+	0.638217i	−0.0544052	+	0.998519i	$0.517326\pi$
$62$	−2.83964	+	8.73951i	−0.360634	+	1.10992i
$63$	−3.00970	−	9.26289i	−0.379186	−	1.16702i
$64$	−6.90832	+	5.01919i	−0.863541	+	0.627399i
$65$		0			0
$66$	−1.81369	+	1.84554i	−0.223250	+	0.227171i
$67$	13.4153			1.63894			0.819469	−	0.573123i	$-0.194268\pi$
$67$	13.4153			1.63894			0.819469	+	0.573123i	$0.194268\pi$
$68$	−0.484310	+	0.351872i	−0.0587312	+	0.0426707i
$69$	0.206673	+	0.636074i	0.0248805	+	0.0765743i
$70$		0			0
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	0.112890	−	0.993607i	$-0.463989\pi$
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	−0.910092	+	0.414406i	$0.863989\pi$
$72$	6.32872	+	4.59808i	0.745846	+	0.541889i
$73$	0.407912	−	1.25542i	0.0477425	−	0.146936i	−0.924343	−	0.381562i	$-0.875386\pi$
$73$	0.407912	−	1.25542i	0.0477425	−	0.146936i	0.972086	+	0.234625i	$0.0753864\pi$
$74$	4.12215	+	12.6867i	0.479190	+	1.47480i
$75$		0			0
$76$	0.0154241			0.00176927
$77$	−10.8319	−	5.40091i	−1.23441	−	0.615491i
$78$	2.20866			0.250081
$79$	11.2179	−	8.15028i	1.26211	−	0.916978i	0.263253	−	0.964727i	$-0.415205\pi$
$79$	11.2179	−	8.15028i	1.26211	−	0.916978i	0.998859	+	0.0477484i	$0.0152046\pi$
$80$		0			0
$81$	1.89395	−	5.82899i	0.210439	−	0.647665i
$82$	−9.12312	−	6.62834i	−1.00748	−	0.731977i
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	0.00443607	−	0.999990i	$-0.498588\pi$
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	−0.949676	+	0.313233i	$0.898588\pi$
$84$	0.105234	−	0.323876i	0.0114819	−	0.0353378i
$85$		0			0
$86$	3.25587	−	2.36553i	0.351090	−	0.255082i
$87$	3.88682			0.416710
$88$	9.58829	−	1.60431i	1.02212	−	0.171020i
$89$	−12.1612			−1.28908			−0.644540	−	0.764570i	$-0.722951\pi$
$89$	−12.1612			−1.28908			−0.644540	+	0.764570i	$0.722951\pi$
$90$		0			0
$91$	3.19256	+	9.82567i	0.334671	+	1.03001i
$92$	0.0582308	−	0.179216i	0.00607098	−	0.0186846i
$93$	3.15590	+	2.29290i	0.327252	+	0.237762i
$94$	2.44020	+	1.77291i	0.251687	+	0.182861i
$95$		0			0
$96$	0.162706	+	0.500759i	0.0166062	+	0.0511085i
$97$	−3.50412	+	2.54589i	−0.355789	+	0.258496i	−0.751294	−	0.659968i	$-0.770570\pi$
$97$	−3.50412	+	2.54589i	−0.355789	+	0.258496i	0.395504	+	0.918464i	$0.370570\pi$
$98$	−8.56545			−0.865241
$99$	−4.08696	−	7.85141i	−0.410755	−	0.789096i
$100$		0			0
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	−0.910153	−	0.414271i	$-0.864036\pi$
$101$	−8.01388	+	5.82242i	−0.797411	+	0.579353i	0.112743	+	0.993624i	$0.464036\pi$
$102$	−0.890091	−	2.73942i	−0.0881321	−	0.271243i
$103$	−1.25643	+	3.86690i	−0.123800	+	0.381017i	−0.993681	−	0.112245i	$-0.964196\pi$
$103$	−1.25643	+	3.86690i	−0.123800	+	0.381017i	0.869880	+	0.493263i	$0.164196\pi$
$104$	−6.71323	−	4.87744i	−0.658286	−	0.478273i
$105$		0			0
$106$	1.25424	−	3.86014i	0.121822	−	0.374930i
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	0.917916	−	0.396776i	$-0.129871\pi$
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	−0.975828	+	0.218539i	$0.929871\pi$
$108$	0.427956	−	0.310928i	0.0411801	−	0.0299191i
$109$	6.12664			0.586825			0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664			0.586825			0.293413	+	0.955986i	$0.405209\pi$
$110$		0			0
$111$	5.66273			0.537483
$112$	10.7747	−	7.82825i	1.01811	−	0.739700i
$113$	−1.78775	−	5.50212i	−0.168177	−	0.517596i	0.831079	−	0.556154i	$-0.187724\pi$
$113$	−1.78775	−	5.50212i	−0.168177	−	0.517596i	−0.999256	+	0.0385582i	$0.987724\pi$
$114$	−0.0229335	+	0.0705819i	−0.00214791	+	0.00661060i
$115$		0			0
$116$	−0.885974	−	0.643698i	−0.0822606	−	0.0597659i
$117$	−2.33471	+	7.18549i	−0.215844	+	0.664299i
$118$	3.56448	+	10.9703i	0.328137	+	1.00990i
$119$	10.9003	−	7.91951i	0.999226	−	0.725980i
$120$		0			0
$121$	−10.5192	−	3.21657i	−0.956291	−	0.292415i
$122$	11.4966			1.04085
$123$	−3.87283	+	2.81377i	−0.349201	+	0.253710i
$124$	−0.339639	−	1.04530i	−0.0305005	−	0.0938708i
$125$		0			0
$126$	−10.6820	−	7.76094i	−0.951630	−	0.691400i
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	0.671841	−	0.740695i	$-0.265504\pi$
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	−0.496833	+	0.867846i	$0.665504\pi$
$128$	−3.01183	+	9.26945i	−0.266211	+	0.819312i
$129$	−0.527931	−	1.62480i	−0.0464817	−	0.143056i
$130$		0			0
$131$	7.04156			0.615224			0.307612	−	0.951512i	$-0.400470\pi$
$131$	7.04156			0.615224			0.307612	+	0.951512i	$0.400470\pi$
$132$	0.0457524	−	0.306089i	0.00398224	−	0.0266416i
$133$	−0.347148			−0.0301016
$134$	14.7134	−	10.6899i	1.27104	−	0.923468i
$135$		0			0
$136$	−3.34410	+	10.2921i	−0.286754	+	0.882539i
$137$	−7.74461	−	5.62678i	−0.661666	−	0.480729i	0.205559	−	0.978645i	$-0.434099\pi$
$137$	−7.74461	−	5.62678i	−0.661666	−	0.480729i	−0.867225	+	0.497916i	$0.834099\pi$
$138$	0.733524	+	0.532936i	0.0624417	+	0.0453666i
$139$	0.159299	−	0.490271i	0.0135116	−	0.0415843i	−0.944073	−	0.329735i	$-0.893041\pi$
$139$	0.159299	−	0.490271i	0.0135116	−	0.0415843i	0.957585	+	0.288151i	$0.0930405\pi$
$140$		0			0
$141$	1.03588	−	0.752611i	0.0872369	−	0.0633813i
$142$	−11.2563			−0.944607
$143$	4.33527	+	8.32843i	0.362533	+	0.696459i
$144$	9.73958			0.811632
$145$		0			0
$146$	−0.552996	−	1.70195i	−0.0457663	−	0.140854i
$147$	−1.12361	+	3.45813i	−0.0926742	+	0.285222i
$148$	−1.29078	−	0.937809i	−0.106102	−	0.0770874i
$149$	6.60144	+	4.79623i	0.540811	+	0.392922i	0.824386	−	0.566028i	$-0.191521\pi$
$149$	6.60144	+	4.79623i	0.540811	+	0.392922i	−0.283575	+	0.958950i	$0.591521\pi$
$150$		0			0
$151$	0.599563	+	1.84526i	0.0487917	+	0.150165i	0.972484	−	0.232970i	$-0.0748443\pi$
$151$	0.599563	+	1.84526i	0.0487917	+	0.150165i	−0.923692	+	0.383135i	$0.874844\pi$
$152$	0.225574	−	0.163889i	0.0182965	−	0.0132932i
$153$	9.85312			0.796577
$154$	−16.1838	+	2.70785i	−1.30412	+	0.218205i
$155$		0			0
$156$	−0.213718	+	0.155275i	−0.0171111	+	0.0124319i
$157$	−6.57418	−	20.2332i	−0.524676	−	1.61479i	−0.764955	−	0.644084i	$-0.777239\pi$
$157$	−6.57418	−	20.2332i	−0.524676	−	1.61479i	0.240279	−	0.970704i	$-0.422761\pi$
$158$	5.80887	−	17.8779i	0.462129	−	1.42229i
$159$	−1.39392	−	1.01274i	−0.110545	−	0.0803159i
$160$		0			0
$161$	−1.31059	+	4.03358i	−0.103289	+	0.317891i
$162$	−2.56758	−	7.90221i	−0.201728	−	0.620856i
$163$	−12.9289	+	9.39337i	−1.01267	+	0.735746i	−0.964767	−	0.263107i	$-0.915253\pi$
$163$	−12.9289	+	9.39337i	−1.01267	+	0.735746i	−0.0479001	+	0.998852i	$0.515253\pi$
$164$	1.34878			0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.126199	−	0.992005i	$-0.459722\pi$
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.982450	+	0.186524i	$0.0597223\pi$
$168$	−1.90233	−	5.85477i	−0.146768	−	0.451706i
$169$	−1.54066	+	4.74168i	−0.118513	+	0.364744i
$170$		0			0
$171$	−0.205384	−	0.149220i	−0.0157061	−	0.0114112i
$172$	−0.148746	+	0.457794i	−0.0113418	+	0.0349065i
$173$	−4.90888	−	15.1080i	−0.373216	−	1.14864i	−0.944675	−	0.328009i	$-0.893622\pi$
$173$	−4.90888	−	15.1080i	−0.373216	−	1.14864i	0.571459	−	0.820631i	$-0.306378\pi$
$174$	4.26292	−	3.09719i	0.323171	−	0.234798i
$175$		0			0
$176$	8.48382	−	8.63280i	0.639492	−	0.650722i
$177$	4.89664			0.368054
$178$	−13.3379	+	9.69057i	−0.999719	+	0.726339i
$179$	−5.21653	−	16.0548i	−0.389902	−	1.19999i	−0.932862	−	0.360235i	$-0.882696\pi$
$179$	−5.21653	−	16.0548i	−0.389902	−	1.19999i	0.542960	−	0.839759i	$-0.317304\pi$
$180$		0			0
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.986187	+	0.165636i	$0.0529676\pi$
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.462277	+	0.886735i	$0.347032\pi$
$182$	11.3310	+	8.23247i	0.839911	+	0.610231i
$183$	1.50812	−	4.64153i	0.111484	−	0.343112i
$184$	−1.05265	−	3.23972i	−0.0776024	−	0.238836i
$185$		0			0
$186$	5.28836			0.387761
$187$	8.58271	−	8.73343i	0.627630	−	0.638652i
$188$	−0.360762			−0.0263113
$189$	−9.63191	+	6.99800i	−0.700619	+	0.509029i
$190$		0			0
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	−0.872669	−	0.488312i	$-0.837613\pi$
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	0.993027	+	0.117890i	$0.0376129\pi$
$192$	3.97569	+	2.88851i	0.286921	+	0.208460i
$193$	14.7921	+	10.7471i	1.06476	+	0.773593i	0.974963	−	0.222367i	$-0.0713785\pi$
$193$	14.7921	+	10.7471i	1.06476	+	0.773593i	0.0897961	+	0.995960i	$0.471378\pi$
$194$	−1.81451	+	5.58448i	−0.130274	+	0.400942i
$195$		0			0
$196$	0.828823	−	0.602175i	0.0592017	−	0.0430125i
$197$	−2.64566			−0.188496			−0.0942478	−	0.995549i	$-0.530045\pi$
$197$	−2.64566			−0.188496			−0.0942478	+	0.995549i	$0.530045\pi$
$198$	−10.7388	−	5.35447i	−0.763172	−	0.380525i
$199$	6.52800			0.462757			0.231379	−	0.972864i	$-0.425676\pi$
$199$	6.52800			0.462757			0.231379	+	0.972864i	$0.425676\pi$
$200$		0			0
$201$	−2.38574	−	7.34254i	−0.168277	−	0.517903i
$202$	−4.14976	+	12.7716i	−0.291976	+	0.898610i
$203$	19.9404	+	14.4876i	1.39954	+	1.01683i
$204$	0.278717	+	0.202500i	0.0195141	+	0.0141778i
$205$		0			0
$206$	1.70331	+	5.24226i	0.118676	+	0.365246i
$207$	−2.50920	+	1.82304i	−0.174402	+	0.126710i
$208$	−10.3313			−0.716349
$209$	−0.311166	+	0.0520641i	−0.0215238	+	0.00360135i
$210$		0			0
$211$	22.2057	−	16.1334i	1.52871	−	1.11067i	0.571752	−	0.820426i	$-0.306264\pi$
$211$	22.2057	−	16.1334i	1.52871	−	1.11067i	0.956953	−	0.290243i	$-0.0937362\pi$
$212$	0.150014	+	0.461697i	0.0103030	+	0.0317095i
$213$	−1.47660	+	4.54450i	−0.101175	+	0.311384i
$214$	−2.12616	−	1.54474i	−0.145341	−	0.105597i
$215$		0			0
$216$	2.95498	−	9.09450i	0.201061	−	0.618802i
$217$	7.64418	+	23.5264i	0.518921	+	1.59707i
$218$	6.71947	−	4.88198i	0.455100	−	0.330650i
$219$	−0.759669			−0.0513337
$220$		0			0
$221$	−10.4518			−0.703061
$222$	6.21068	−	4.51232i	0.416834	−	0.302847i
$223$	1.57040	+	4.83321i	0.105162	+	0.323656i	0.989768	−	0.142683i	$-0.0455729\pi$
$223$	1.57040	+	4.83321i	0.105162	+	0.323656i	−0.884606	+	0.466338i	$0.845573\pi$
$224$	−1.03178	+	3.17550i	−0.0689388	+	0.212172i
$225$		0			0
$226$	−6.34507	−	4.60997i	−0.422068	−	0.306650i
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	−0.982055	−	0.188593i	$-0.939607\pi$
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	0.905351	+	0.424663i	$0.139607\pi$
$228$	−0.00274299	−	0.00844204i	−0.000181659	−	0.000559088i
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.451232	+	0.892407i	$0.649015\pi$
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.988168	+	0.153378i	$0.950985\pi$
$230$		0			0
$231$	−1.02974	+	6.88908i	−0.0677520	+	0.453268i
$232$	−19.7968			−1.29972
$233$	14.8185	−	10.7663i	0.970794	−	0.705323i	0.0151615	−	0.999885i	$-0.495174\pi$
$233$	14.8185	−	10.7663i	0.970794	−	0.705323i	0.955632	+	0.294562i	$0.0951737\pi$
$234$	3.16510	+	9.74119i	0.206909	+	0.636801i
$235$		0			0
$236$	−1.11616	−	0.810936i	−0.0726557	−	0.0527874i
$237$	−6.45582	−	4.69043i	−0.419351	−	0.304676i
$238$	5.64439	−	17.3717i	0.365872	−	1.12604i
$239$	−3.38555	−	10.4196i	−0.218993	−	0.673991i	−0.998846	−	0.0480283i	$-0.984706\pi$
$239$	−3.38555	−	10.4196i	−0.218993	−	0.673991i	0.779853	−	0.625963i	$-0.215294\pi$
$240$		0			0
$241$	−9.99444			−0.643798			−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444			−0.643798			−0.321899	+	0.946774i	$0.604321\pi$
$242$	−14.1002	+	4.85437i	−0.906394	+	0.312050i
$243$	−13.3143			−0.854110
$244$	−1.11245	+	0.808245i	−0.0712175	+	0.0517426i
$245$		0			0
$246$	−2.00543	+	6.17209i	−0.127862	+	0.393518i
$247$	0.217862	+	0.158286i	0.0138622	+	0.0100715i
$248$	−16.0740	−	11.6784i	−1.02070	−	0.741581i
$249$	−1.89298	+	5.82599i	−0.119963	+	0.369207i
$250$		0			0
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	−0.806396	−	0.591376i	$-0.798585\pi$
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	0.313242	+	0.949673i	$0.398585\pi$
$252$	1.57925			0.0994832
$253$	−0.569804	+	3.81206i	−0.0358233	+	0.239662i
$254$	3.30490			0.207368
$255$		0			0
$256$	−1.19443	−	3.67608i	−0.0746520	−	0.229755i
$257$	−3.22230	+	9.91721i	−0.201001	+	0.618618i	0.798853	+	0.601527i	$0.205441\pi$
$257$	−3.22230	+	9.91721i	−0.201001	+	0.618618i	−0.999854	+	0.0170916i	$0.994559\pi$
$258$	−1.87373	−	1.36135i	−0.116654	−	0.0847538i
$259$	29.0514	+	21.1071i	1.80517	+	1.31153i
$260$		0			0
$261$	5.56998	+	17.1426i	0.344773	+	1.06110i
$262$	7.72292	−	5.61103i	0.477124	−	0.346651i
$263$	10.9619			0.675937			0.337968	−	0.941157i	$-0.390260\pi$
$263$	10.9619			0.675937			0.337968	+	0.941157i	$0.390260\pi$
$264$	−2.58323	−	4.96262i	−0.158987	−	0.305428i
$265$		0			0
$266$	−0.380739	+	0.276623i	−0.0233446	+	0.0169609i
$267$	2.16271	+	6.65613i	0.132355	+	0.407348i
$268$	−0.672190	+	2.06879i	−0.0410605	+	0.126371i
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	0.589987	−	0.807413i	$-0.299133\pi$
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	−0.585580	+	0.810615i	$0.699133\pi$
$270$		0			0
$271$	−4.14069	+	12.7437i	−0.251529	+	0.774126i	0.742965	+	0.669330i	$0.233419\pi$
$271$	−4.14069	+	12.7437i	−0.251529	+	0.774126i	−0.994494	+	0.104796i	$0.966581\pi$
$272$	4.16353	+	12.8140i	0.252451	+	0.776965i
$273$	4.81010	−	3.49474i	0.291120	−	0.211511i
$274$	−12.9777			−0.784010
$275$		0			0
$276$	−0.108445			−0.00652764
$277$	−3.16057	+	2.29629i	−0.189901	+	0.137971i	−0.678673	−	0.734440i	$-0.737445\pi$
$277$	−3.16057	+	2.29629i	−0.189901	+	0.137971i	0.488773	+	0.872411i	$0.337445\pi$
$278$	−0.215957	−	0.664648i	−0.0129523	−	0.0398630i
$279$	−5.59017	+	17.2048i	−0.334675	+	1.03002i
$280$		0			0
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	0.624267	−	0.781211i	$-0.285398\pi$
$281$	1.24381	+	0.903680i	0.0741994	+	0.0539090i	−0.550067	+	0.835120i	$0.685398\pi$
$282$	0.536401	−	1.65087i	0.0319422	−	0.0983081i
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	0.988377	−	0.152020i	$-0.0485778\pi$
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	−0.888969	+	0.457967i	$0.848578\pi$
$284$	1.08920	−	0.791349i	0.0646320	−	0.0469579i
$285$		0			0
$286$	11.3912	+	5.67979i	0.673578	+	0.335853i
$287$	−30.3566			−1.79190
$288$	−1.97541	+	1.43522i	−0.116402	+	0.0845711i
$289$	−1.04122	−	3.20456i	−0.0612484	−	0.188503i
$290$		0			0
$291$	2.01659	+	1.46514i	0.118215	+	0.0858881i
$292$	0.173162	+	0.125809i	0.0101335	+	0.00736243i
$293$	−3.52789	+	10.8577i	−0.206102	+	0.634315i	0.793565	+	0.608486i	$0.208223\pi$
$293$	−3.52789	+	10.8577i	−0.206102	+	0.634315i	−0.999666	+	0.0258295i	$0.991777\pi$
$294$	1.52326	+	4.68810i	0.0888381	+	0.273415i
$295$		0			0
$296$	−28.8421			−1.67641
$297$	−7.58403	+	7.71721i	−0.440070	+	0.447798i
$298$	11.0621			0.640808
$299$	2.66165	−	1.93381i	0.153927	−	0.111835i
$300$		0			0
$301$	3.34780	−	10.3035i	0.192964	−	0.593883i
$302$	2.12797	+	1.54606i	0.122451	+	0.0889657i
$303$	4.61193	+	3.35077i	0.264949	+	0.192496i
$304$	0.107275	−	0.330157i	0.00615262	−	0.0189358i
$305$		0			0
$306$	10.8065	−	7.85141i	0.617769	−	0.448835i
$307$	4.25008			0.242565			0.121282	−	0.992618i	$-0.461299\pi$
$307$	4.25008			0.242565			0.121282	+	0.992618i	$0.461299\pi$
$308$	1.37563	−	1.39978i	0.0783836	−	0.0797601i
$309$	2.33990			0.133112
$310$		0			0
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	−0.984465	−	0.175579i	$-0.943820\pi$
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	0.693247	−	0.720700i	$-0.256180\pi$
$312$	−1.47569	+	4.54172i	−0.0835447	+	0.257124i
$313$	−21.5012	−	15.6215i	−1.21532	−	0.882982i	−0.219617	−	0.975586i	$-0.570481\pi$
$313$	−21.5012	−	15.6215i	−1.21532	−	0.882982i	−0.995703	+	0.0926041i	$0.970481\pi$
$314$	−23.3331	−	16.9525i	−1.31676	−	0.956683i
$315$		0			0
$316$	0.694778	+	2.13831i	0.0390843	+	0.120289i
$317$	4.68982	−	3.40736i	0.263407	−	0.191376i	−0.448241	−	0.893913i	$-0.647949\pi$
$317$	4.68982	−	3.40736i	0.263407	−	0.191376i	0.711648	+	0.702537i	$0.247949\pi$
$318$	−2.33581			−0.130985
$319$	20.0464	+	9.99534i	1.12238	+	0.559632i
$320$		0			0
$321$	−0.902569	+	0.655755i	−0.0503765	+	0.0366007i
$322$	1.77673	+	5.46822i	0.0990134	+	0.304732i
$323$	0.108525	−	0.334006i	0.00603850	−	0.0185846i
$324$	0.803996	+	0.584137i	0.0446664	+	0.0324521i
$325$		0			0
$326$	−6.69484	+	20.6046i	−0.370793	+	1.14118i
$327$	−1.08954	−	3.35327i	−0.0602519	−	0.185436i
$328$	19.7255	−	14.3314i	1.08916	−	0.791321i
$329$	8.11961			0.447648
$330$		0			0
$331$	−12.9230			−0.710311			−0.355155	−	0.934807i	$-0.615572\pi$
$331$	−12.9230			−0.710311			−0.355155	+	0.934807i	$0.615572\pi$
$332$	1.39634	−	1.01450i	0.0766340	−	0.0556779i
$333$	8.11495	+	24.9752i	0.444696	+	1.36863i
$334$	7.41878	−	22.8327i	0.405938	−	1.24935i
$335$		0			0
$336$	−6.20075	−	4.50511i	−0.338278	−	0.245774i
$337$	−4.13631	+	12.7303i	−0.225319	+	0.693461i	0.772940	+	0.634479i	$0.218785\pi$
$337$	−4.13631	+	12.7303i	−0.225319	+	0.693461i	−0.998259	+	0.0589818i	$0.981215\pi$
$338$	2.08864	+	6.42817i	0.113607	+	0.349646i
$339$	−2.69353	+	1.95696i	−0.146292	+	0.106288i
$340$		0			0
$341$	10.3803	+	19.9414i	0.562123	+	1.07989i
$342$	−0.344163			−0.0186102
$343$	2.01291	−	1.46246i	0.108687	−	0.0789656i
$344$	2.68892	+	8.27564i	0.144977	+	0.446193i
$345$		0			0
$346$	−17.4226	−	12.6583i	−0.936646	−	0.680513i
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	0.389000	−	0.921238i	$-0.372821\pi$
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	−0.755942	+	0.654639i	$0.772821\pi$
$348$	−0.194754	+	0.599391i	−0.0104399	+	0.0321307i
$349$	−3.21341	−	9.88987i	−0.172010	−	0.529393i	0.827474	−	0.561504i	$-0.189777\pi$
$349$	−3.21341	−	9.88987i	−0.172010	−	0.529393i	−0.999484	+	0.0321111i	$0.989777\pi$
$350$		0			0
$351$	9.23559			0.492959
$352$	−0.448587	+	3.00110i	−0.0239098	+	0.159959i
$353$	−19.1073			−1.01698			−0.508489	−	0.861069i	$-0.669796\pi$
$353$	−19.1073			−1.01698			−0.508489	+	0.861069i	$0.669796\pi$
$354$	5.37046	−	3.90187i	0.285437	−	0.207382i
$355$		0			0
$356$	0.609350	−	1.87539i	0.0322955	−	0.0993953i
$357$	−6.27303	−	4.55762i	−0.332004	−	0.241215i
$358$	−18.5145	−	13.4516i	−0.978522	−	0.710938i
$359$	−1.36405	+	4.19813i	−0.0719920	+	0.221569i	−0.980578	−	0.196129i	$-0.937163\pi$
$359$	−1.36405	+	4.19813i	−0.0719920	+	0.221569i	0.908586	+	0.417698i	$0.137163\pi$
$360$		0			0
$361$	15.3640	−	11.1626i	0.808632	−	0.587505i
$362$	32.6546			1.71629
$363$	0.110193	+	6.32946i	0.00578362	+	0.332211i
$364$	−1.67520			−0.0878041
$365$		0			0
$366$	−2.04453	−	6.29240i	−0.106869	−	0.328909i
$367$	9.07327	−	27.9247i	0.473621	−	1.45766i	−0.374188	−	0.927353i	$-0.622078\pi$
$367$	9.07327	−	27.9247i	0.473621	−	1.45766i	0.847809	−	0.530302i	$-0.177922\pi$
$368$	−3.43117	−	2.49289i	−0.178862	−	0.129951i
$369$	−17.9600	−	13.0487i	−0.934958	−	0.679287i
$370$		0			0
$371$	−3.37634	−	10.3913i	−0.175291	−	0.539490i
$372$	−0.511720	+	0.371787i	−0.0265315	+	0.0192762i
$373$	4.96478			0.257067			0.128533	−	0.991705i	$-0.458973\pi$
$373$	4.96478			0.257067			0.128533	+	0.991705i	$0.458973\pi$
$374$	2.45401	−	16.4176i	0.126894	−	0.848934i
$375$		0			0
$376$	−5.27606	+	3.83329i	−0.272092	+	0.197687i
$377$	−5.90839	−	18.1842i	−0.304298	−	0.936532i
$378$	−4.98761	+	15.3503i	−0.256535	+	0.789534i
$379$	−6.40996	−	4.65711i	−0.329258	−	0.239220i	0.410858	−	0.911699i	$-0.365229\pi$
$379$	−6.40996	−	4.65711i	−0.329258	−	0.239220i	−0.740116	+	0.672480i	$0.765229\pi$
$380$		0			0
$381$	0.433536	−	1.33429i	0.0222107	−	0.0683576i
$382$	−2.25499	−	6.94016i	−0.115375	−	0.355089i
$383$	−19.8335	+	14.4099i	−1.01344	+	0.736309i	−0.964928	−	0.262514i	$-0.915449\pi$
$383$	−19.8335	+	14.4099i	−1.01344	+	0.736309i	−0.0485140	+	0.998823i	$0.515449\pi$
$384$	5.60903			0.286235
$385$		0			0
$386$	24.7872			1.26164
$387$	6.40958	−	4.65683i	0.325817	−	0.236720i
$388$	−0.217026	−	0.667939i	−0.0110179	−	0.0339095i
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	−0.899118	−	0.437706i	$-0.855791\pi$
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	0.984679	+	0.174377i	$0.0557911\pi$
$390$		0			0
$391$	−3.47116	−	2.52195i	−0.175544	−	0.127540i
$392$	5.72292	−	17.6133i	0.289051	−	0.889608i
$393$	−1.25225	−	3.85403i	−0.0631677	−	0.194410i
$394$	−2.90166	+	2.10818i	−0.146184	+	0.106209i
$395$		0			0
$396$	1.41556	−	0.236850i	0.0711344	−	0.0119022i
$397$	6.43455			0.322941			0.161470	−	0.986878i	$-0.448376\pi$
$397$	6.43455			0.322941			0.161470	+	0.986878i	$0.448376\pi$
$398$	7.15967	−	5.20180i	0.358882	−	0.260743i
$399$	0.0617358	+	0.190003i	0.00309066	+	0.00951206i
$400$		0			0
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	0.843741	−	0.536751i	$-0.180348\pi$
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	−0.249750	+	0.968310i	$0.580348\pi$
$402$	−8.46746	−	6.15197i	−0.422319	−	0.306832i
$403$	5.92981	−	18.2501i	0.295385	−	0.909101i
$404$	−0.496337	−	1.52757i	−0.0246937	−	0.0759994i
$405$		0			0
$406$	33.4143			1.65832
$407$	29.2058	+	14.5623i	1.44768	+	0.721826i
$408$	6.22784			0.308324
$409$	−3.55625	+	2.58376i	−0.175845	+	0.127759i	−0.672226	−	0.740346i	$-0.734662\pi$
$409$	−3.55625	+	2.58376i	−0.175845	+	0.127759i	0.496381	+	0.868105i	$0.334662\pi$
$410$		0			0
$411$	−1.70241	+	5.23948i	−0.0839737	+	0.258444i
$412$	−0.533365	−	0.387512i	−0.0262770	−	0.0190914i
$413$	25.1211	+	18.2516i	1.23613	+	0.898101i
$414$	−1.29932	+	3.99890i	−0.0638581	+	0.196535i
$415$		0			0
$416$	2.09543	−	1.52242i	0.102737	−	0.0746427i
$417$	−0.296668			−0.0145279
$418$	−0.299789	+	0.305053i	−0.0146631	+	0.0149206i
$419$	17.8526			0.872159			0.436079	−	0.899908i	$-0.356367\pi$
$419$	17.8526			0.872159			0.436079	+	0.899908i	$0.356367\pi$
$420$		0			0
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	0.908090	−	0.418776i	$-0.137541\pi$
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	−0.980810	+	0.194965i	$0.937541\pi$
$422$	11.4986	−	35.3891i	0.559743	−	1.72271i
$423$	4.80382	+	3.49018i	0.233570	+	0.169698i
$424$	7.09969	+	5.15823i	0.344792	+	0.250506i
$425$		0			0
$426$	2.00179	+	6.16086i	0.0969868	+	0.298495i
$427$	25.0378	−	18.1910i	1.21166	−	0.880324i
$428$	0.314335			0.0151939
$429$	3.78740	−	3.85391i	0.182857	−	0.186069i
$430$		0			0
$431$	20.1234	−	14.6205i	0.969312	−	0.704247i	0.0140175	−	0.999902i	$-0.495538\pi$
$431$	20.1234	−	14.6205i	0.969312	−	0.704247i	0.955295	+	0.295655i	$0.0955380\pi$
$432$	−3.67906	−	11.3230i	−0.177009	−	0.544778i
$433$	6.56669	−	20.2102i	0.315575	−	0.971240i	−0.659942	−	0.751316i	$-0.729419\pi$
$433$	6.56669	−	20.2102i	0.315575	−	0.971240i	0.975517	−	0.219923i	$-0.0705807\pi$
$434$	27.1307	+	19.7116i	1.30232	+	0.946188i
$435$		0			0
$436$	−0.306983	+	0.944796i	−0.0147018	+	0.0452475i
$437$	0.0341614	+	0.105138i	0.00163416	+	0.00502943i
$438$	−0.833177	+	0.605339i	−0.0398107	+	0.0289242i
$439$	−15.9119			−0.759434			−0.379717	−	0.925103i	$-0.623979\pi$
$439$	−15.9119			−0.759434			−0.379717	+	0.925103i	$0.623979\pi$
$440$		0			0
$441$	−16.8621			−0.802958
$442$	−11.4631	+	8.32843i	−0.545244	+	0.396143i
$443$	−8.12332	−	25.0010i	−0.385951	−	1.18783i	−0.935788	−	0.352562i	$-0.885310\pi$
$443$	−8.12332	−	25.0010i	−0.385951	−	1.18783i	0.549838	−	0.835272i	$-0.314690\pi$
$444$	−0.283738	+	0.873257i	−0.0134656	+	0.0414429i
$445$		0			0
$446$	5.57368	+	4.04952i	0.263922	+	0.191750i
$447$	1.45112	−	4.46609i	0.0686356	−	0.211239i
$448$	9.62987	+	29.6377i	0.454969	+	1.40025i
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	−0.420366	−	0.907354i	$-0.638098\pi$
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	0.733045	+	0.680180i	$0.238098\pi$
$450$		0			0
$451$	−27.2102	+	4.55278i	−1.28128	+	0.214382i
$452$	0.938065			0.0441229
$453$	0.903337	−	0.656313i	0.0424425	−	0.0308363i
$454$	1.56670	+	4.82181i	0.0735289	+	0.226299i
$455$		0			0
$456$	−0.129817	−	0.0943172i	−0.00607922	−	0.00441681i
$457$	9.64056	+	7.00428i	0.450966	+	0.327646i	0.789977	−	0.613136i	$-0.210092\pi$
$457$	9.64056	+	7.00428i	0.450966	+	0.327646i	−0.339011	+	0.940782i	$0.610092\pi$
$458$	−11.2792	+	34.7139i	−0.527043	+	1.62207i
$459$	−3.72195	−	11.4550i	−0.173726	−	0.534673i
$460$		0			0
$461$	6.96172			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$462$	4.36015	+	8.37624i	0.202853	+	0.389698i
$463$	−12.4762			−0.579817			−0.289909	−	0.957054i	$-0.593625\pi$
$463$	−12.4762			−0.579817			−0.289909	+	0.957054i	$0.593625\pi$
$464$	−19.9404	+	14.4876i	−0.925712	+	0.672569i
$465$		0			0
$466$	7.67335	−	23.6161i	0.355461	−	1.09400i
$467$	−4.97235	−	3.61263i	−0.230093	−	0.167172i	0.466765	−	0.884381i	$-0.345419\pi$
$467$	−4.97235	−	3.61263i	−0.230093	−	0.167172i	−0.696858	+	0.717209i	$0.745419\pi$
$468$	−0.991100	−	0.720076i	−0.0458136	−	0.0332855i
$469$	15.1288	−	46.5618i	0.698585	−	2.15002i
$470$		0			0
$471$	−9.90505	+	7.19644i	−0.456401	+	0.331594i
$472$	−24.9401			−1.14796
$473$	1.45552	−	9.73762i	0.0669250	−	0.447736i
$474$	−10.8181			−0.496890
$475$		0			0
$476$	0.675105	+	2.07776i	0.0309434	+	0.0952340i
$477$	2.46911	−	7.59915i	0.113053	−	0.347941i
$478$	−12.0160	−	8.73013i	−0.549599	−	0.399307i
$479$	−17.9555	−	13.0454i	−0.820406	−	0.596060i	0.0964228	−	0.995340i	$-0.469260\pi$
$479$	−17.9555	−	13.0454i	−0.820406	−	0.596060i	−0.916829	+	0.399281i	$0.869260\pi$
$480$		0			0
$481$	−8.60798	−	26.4926i	−0.392490	−	1.20796i
$482$	−10.9615	+	7.96402i	−0.499284	+	0.362751i
$483$	2.44076			0.111058
$484$	1.02311	−	1.46101i	0.0465049	−	0.0664095i
$485$		0			0
$486$	−14.6026	+	10.6094i	−0.662387	+	0.481252i
$487$	10.5778	+	32.5553i	0.479328	+	1.47522i	0.840030	+	0.542539i	$0.182537\pi$
$487$	10.5778	+	32.5553i	0.479328	+	1.47522i	−0.360702	+	0.932681i	$0.617463\pi$
$488$	−7.68135	+	23.6408i	−0.347719	+	1.07017i
$489$	7.44047	+	5.40582i	0.336470	+	0.244460i
$490$		0			0
$491$	−5.25197	+	16.1639i	−0.237018	+	0.729467i	0.759829	+	0.650123i	$0.225283\pi$
$491$	−5.25197	+	16.1639i	−0.237018	+	0.729467i	−0.996847	+	0.0793441i	$0.974717\pi$
$492$	−0.239863	−	0.738221i	−0.0108138	−	0.0332816i
$493$	−20.1729	+	14.6565i	−0.908541	+	0.660094i
$494$	0.365073			0.0164254
$495$		0			0
$496$	−24.7371			−1.11073
$497$	−24.5144	+	17.8107i	−1.09962	+	0.798920i
$498$	2.56626	+	7.89815i	0.114997	+	0.353925i
$499$	1.61599	−	4.97352i	0.0723418	−	0.222645i	−0.908348	−	0.418215i	$-0.862656\pi$
$499$	1.61599	−	4.97352i	0.0723418	−	0.222645i	0.980690	+	0.195570i	$0.0626558\pi$
$500$		0			0
$501$	−8.24504	−	5.99037i	−0.368361	−	0.267630i
$502$	−4.04575	+	12.4515i	−0.180571	+	0.555740i
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	−0.625973	−	0.779845i	$-0.715298\pi$
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	0.0480416	−	0.998845i	$-0.484702\pi$
$504$	23.0961	−	16.7803i	1.02878	−	0.747454i
$505$		0			0
$506$	2.41268	+	4.63497i	0.107257	+	0.206050i
$507$	2.86923			0.127427
$508$	−0.319794	+	0.232344i	−0.0141886	+	0.0103086i
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	0.988140	+	0.153557i	$0.0490728\pi$
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	−0.709163	+	0.705044i	$0.750927\pi$
$510$		0			0
$511$	−3.89731	−	2.83156i	−0.172407	−	0.125261i
$512$	−20.0094	−	14.5377i	−0.884300	−	0.642481i
$513$	−0.0958972	+	0.295141i	−0.00423396	+	0.0130308i
$514$	4.36838	+	13.4445i	0.192681	+	0.593012i
$515$		0			0
$516$	0.277016			0.0121949
$517$	7.27801	−	1.21775i	0.320086	−	0.0535566i
$518$	48.6816			2.13895
$519$	−7.39602	+	5.37352i	−0.324649	+	0.235872i
$520$		0			0
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	−0.803958	−	0.594686i	$-0.797276\pi$
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	0.999963	−	0.00855656i	$-0.00272367\pi$
$522$	19.7690	+	14.3630i	0.865265	+	0.628652i
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	0.767419	−	0.641146i	$-0.221541\pi$
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	−0.372620	+	0.927984i	$0.621541\pi$
$524$	−0.352826	+	1.08589i	−0.0154133	+	0.0474372i
$525$		0			0
$526$	12.0226	−	8.73490i	0.524209	−	0.380860i
$527$	−25.0254			−1.09013
$528$	−6.23370	−	3.10818i	−0.271287	−	0.135266i
$529$	−21.6494			−0.941279
$530$		0			0
$531$	7.01710	+	21.5964i	0.304516	+	0.937205i
$532$	0.0173943	−	0.0535341i	0.000754138	−	0.00232100i
$533$	19.0511	+	13.8415i	0.825197	+	0.599540i
$534$	7.67588	+	5.57685i	0.332168	+	0.241334i
$535$		0			0
$536$	12.1513	+	37.3979i	0.524857	+	1.61534i
$537$	−7.85954	+	5.71029i	−0.339164	+	0.246417i
$538$	0.121123			0.00522197
$539$	−14.6880	+	14.9459i	−0.632658	+	0.643768i
$540$		0			0
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	−0.757834	−	0.652447i	$-0.773742\pi$
$541$	−8.64094	+	6.27801i	−0.371503	+	0.269913i	0.386331	+	0.922360i	$0.373742\pi$
$542$	5.61343	+	17.2763i	0.241117	+	0.742083i
$543$	4.28363	−	13.1837i	0.183828	−	0.565765i
$544$	−2.73273	−	1.98544i	−0.117165	−	0.0851251i
$545$		0			0
$546$	2.49077	−	7.66581i	0.106595	−	0.328066i
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	0.938847	−	0.344334i	$-0.111895\pi$
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	−0.961938	+	0.273269i	$0.911895\pi$
$548$	1.25577	−	0.912367i	0.0536437	−	0.0389744i
$549$	22.6325			0.965930
$550$		0			0
$551$	0.642459			0.0273697
$552$	−1.58599	+	1.15229i	−0.0675041	+	0.0490446i
$553$	−15.6372	−	48.1264i	−0.664962	−	2.04654i
$554$	−1.63661	+	5.03698i	−0.0695331	+	0.214001i
$555$		0			0
$556$	0.0676235	+	0.0491313i	0.00286787	+	0.00208363i
$557$	6.02100	−	18.5307i	0.255118	−	0.785173i	−0.738688	−	0.674047i	$-0.764554\pi$
$557$	6.02100	−	18.5307i	0.255118	−	0.785173i	0.993806	−	0.111126i	$-0.0354456\pi$
$558$	7.57845	+	23.3241i	0.320821	+	0.987387i
$559$	−6.79900	+	4.93976i	−0.287567	+	0.208930i
$560$		0			0
$561$	−6.30636	−	3.14442i	−0.266255	−	0.132757i
$562$	2.08426			0.0879191
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	−0.809338	−	0.587343i	$-0.800174\pi$
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	0.308497	+	0.951225i	$0.400174\pi$
$564$	0.0641570	+	0.197455i	0.00270150	+	0.00831435i
$565$		0			0
$566$	5.93535	+	4.31228i	0.249481	+	0.181259i
$567$	−18.0954	−	13.1471i	−0.759934	−	0.552124i
$568$	7.52078	−	23.1466i	0.315565	−	0.971209i
$569$	6.15980	+	18.9579i	0.258232	+	0.794758i	0.993176	+	0.116629i	$0.0372088\pi$
$569$	6.15980	+	18.9579i	0.258232	+	0.794758i	−0.734943	+	0.678129i	$0.762791\pi$
$570$		0			0
$571$	5.24422			0.219464			0.109732	−	0.993961i	$-0.465001\pi$
$571$	5.24422			0.219464			0.109732	+	0.993961i	$0.465001\pi$
$572$	−1.50156	+	0.251240i	−0.0627834	+	0.0105049i
$573$	−3.09776			−0.129411
$574$	−33.2940	+	24.1895i	−1.38967	+	1.00965i
$575$		0			0
$576$	−7.04230	+	21.6740i	−0.293429	+	0.903083i
$577$	30.4194	+	22.1010i	1.26637	+	0.920075i	0.999052	−	0.0435320i	$-0.0138610\pi$
$577$	30.4194	+	22.1010i	1.26637	+	0.920075i	0.267323	+	0.963607i	$0.413861\pi$
$578$	−3.69551	−	2.68495i	−0.153713	−	0.111679i
$579$	3.25158	−	10.0073i	0.135131	−	0.415891i
$580$		0			0
$581$	−31.4271	+	22.8331i	−1.30382	+	0.947278i
$582$	3.37922			0.140073
$583$	−4.58484	−	8.80789i	−0.189885	−	0.364785i
$584$	3.86923			0.160110
$585$		0			0
$586$	4.78267	+	14.7195i	0.197570	+	0.608059i
$587$	−7.90191	+	24.3196i	−0.326147	+	1.00378i	0.644774	+	0.764373i	$0.276952\pi$
$587$	−7.90191	+	24.3196i	−0.326147	+	1.00378i	−0.970920	+	0.239403i	$0.923048\pi$
$588$	−0.476982	−	0.346548i	−0.0196704	−	0.0142914i
$589$	0.521644	+	0.378997i	0.0214940	+	0.0156163i
$590$		0			0
$591$	0.470497	+	1.44804i	0.0193536	+	0.0595644i
$592$	−29.0514	+	21.1071i	−1.19400	+	0.867495i
$593$	−40.2260			−1.65188			−0.825942	−	0.563754i	$-0.809356\pi$
$593$	−40.2260			−1.65188			−0.825942	+	0.563754i	$0.809356\pi$
$594$	−2.16846	+	14.5073i	−0.0889731	+	0.595240i
$595$		0			0
$596$	−1.07040	+	0.777695i	−0.0438455	+	0.0318556i
$597$	−1.16092	−	3.57295i	−0.0475133	−	0.146231i
$598$	1.37826	−	4.24185i	0.0563613	−	0.173462i
$599$	−3.98843	−	2.89776i	−0.162963	−	0.118399i	0.503315	−	0.864103i	$-0.332114\pi$
$599$	−3.98843	−	2.89776i	−0.162963	−	0.118399i	−0.666278	+	0.745704i	$0.732114\pi$
$600$		0			0
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	−0.0339497	−	0.999424i	$-0.510809\pi$
$601$	14.2425	−	43.8338i	0.580963	−	1.78802i	0.614912	−	0.788596i	$-0.289191\pi$
$602$	−4.53853	−	13.9682i	−0.184977	−	0.569300i
$603$	28.9651	−	21.0444i	1.17955	−	0.856993i
$604$	−0.314602			−0.0128010
$605$		0			0
$606$	7.72824			0.313938
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.505288	+	0.862951i	$0.668614\pi$
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.976857	+	0.213891i	$0.931386\pi$
$608$	0.0268941	+	0.0827714i	0.00109070	+	0.00335682i
$609$	4.38328	−	13.4904i	0.177620	−	0.546657i
$610$		0			0
$611$	−5.09568	−	3.70223i	−0.206149	−	0.149776i
$612$	−0.493703	+	1.51946i	−0.0199567	+	0.0614206i
$613$	−1.46294	−	4.50247i	−0.0590877	−	0.181853i	0.917156	−	0.398528i	$-0.130479\pi$
$613$	−1.46294	−	4.50247i	−0.0590877	−	0.181853i	−0.976244	+	0.216675i	$0.930479\pi$
$614$	4.66133	−	3.38666i	0.188116	−	0.136674i
$615$		0			0
$616$	5.24479	−	35.0883i	0.211319	−	1.41375i
$617$	−17.8468			−0.718486			−0.359243	−	0.933244i	$-0.616965\pi$
$617$	−17.8468			−0.718486			−0.359243	+	0.933244i	$0.616965\pi$
$618$	2.56632	−	1.86454i	0.103232	−	0.0750027i
$619$	0.110304	+	0.339482i	0.00443351	+	0.0136449i	0.953249	−	0.302187i	$-0.0977166\pi$
$619$	0.110304	+	0.339482i	0.00443351	+	0.0136449i	−0.948815	+	0.315832i	$0.897717\pi$
$620$		0			0
$621$	3.06726	+	2.22850i	0.123085	+	0.0894264i
$622$	−18.2276	−	13.2431i	−0.730861	−	0.531002i
$623$	−13.7145	+	42.2089i	−0.549461	+	1.69107i
$624$	1.83729	+	5.65461i	0.0735506	+	0.226365i
$625$		0			0
$626$	−36.0297			−1.44004
$627$	0.0838329	+	0.161051i	0.00334796	+	0.00643174i
$628$	3.44960			0.137654
$629$	−29.3900	+	21.3531i	−1.17186	+	0.851404i
$630$		0			0
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	0.536516	+	0.843890i	$0.319740\pi$
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	−0.930077	+	0.367366i	$0.880260\pi$
$632$	32.8815	+	23.8898i	1.30796	+	0.950287i
$633$	−12.7792	−	9.28466i	−0.507929	−	0.369032i
$634$	2.42849	−	7.47413i	0.0964477	−	0.296836i
$635$		0			0
$636$	0.226021	−	0.164214i	0.00896231	−	0.00651150i
$637$	17.8866			0.708693
$638$	29.9509	−	5.01136i	1.18577	−	0.198402i
$639$	−22.1594			−0.876610
$640$		0			0
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	0.957047	−	0.289932i	$-0.0936326\pi$
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	−0.944685	+	0.327979i	$0.893633\pi$
$642$	−0.467370	+	1.43842i	−0.0184456	+	0.0567697i
$643$	−12.1130	−	8.80057i	−0.477688	−	0.347061i	0.322742	−	0.946487i	$-0.395395\pi$
$643$	−12.1130	−	8.80057i	−0.477688	−	0.347061i	−0.800430	+	0.599426i	$0.795395\pi$
$644$	−0.556354	−	0.404215i	−0.0219234	−	0.0159283i
$645$		0			0
$646$	−0.147125	−	0.452803i	−0.00578855	−	0.0178153i
$647$	14.4712	−	10.5139i	0.568920	−	0.413345i	−0.265793	−	0.964030i	$-0.585634\pi$
$647$	14.4712	−	10.5139i	0.568920	−	0.413345i	0.834713	+	0.550686i	$0.185634\pi$
$648$	17.9650			0.705732
$649$	25.2546	+	12.5922i	0.991331	+	0.494287i
$650$		0			0
$651$	11.5172	−	8.36772i	0.451394	−	0.327957i
$652$	−0.800746	−	2.46444i	−0.0313596	−	0.0965150i
$653$	−14.1419	+	43.5244i	−0.553416	+	1.70324i	0.146673	+	0.989185i	$0.453144\pi$
$653$	−14.1419	+	43.5244i	−0.553416	+	1.70324i	−0.700089	+	0.714055i	$0.746856\pi$
$654$	−3.86701	−	2.80955i	−0.151212	−	0.109862i
$655$		0			0
$656$	9.38072	−	28.8709i	0.366255	−	1.12722i
$657$	−1.08864	−	3.35049i	−0.0424719	−	0.130715i
$658$	8.90529	−	6.47007i	0.347164	−	0.252230i
$659$	−9.54036			−0.371640			−0.185820	−	0.982584i	$-0.559494\pi$
$659$	−9.54036			−0.371640			−0.185820	+	0.982584i	$0.559494\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$	−14.1734	+	10.2976i	−0.550866	+	0.400228i
$663$	1.85871	+	5.72052i	0.0721863	+	0.222167i
$664$	9.64154	−	29.6736i	0.374164	−	1.15156i
$665$		0			0
$666$	28.8016	+	20.9256i	1.11604	+	0.810850i
$667$	2.42548	−	7.46486i	0.0939149	−	0.289040i
$668$	0.887333	+	2.73093i	0.0343319	+	0.105663i
$669$	2.36607	−	1.71905i	0.0914774	−	0.0664622i
$670$		0			0
$671$	19.7144	−	20.0606i	0.761065	−	0.774430i
$672$	1.92152			0.0741243
$673$	38.2690	−	27.8041i	1.47516	−	1.07177i	0.496086	−	0.868273i	$-0.334770\pi$
$673$	38.2690	−	27.8041i	1.47516	−	1.07177i	0.979076	−	0.203494i	$-0.0652299\pi$
$674$	5.60749	+	17.2581i	0.215992	+	0.664756i
$675$		0			0
$676$	−0.654023	−	0.475175i	−0.0251547	−	0.0182760i
$677$	22.2828	+	16.1894i	0.856399	+	0.622210i	0.926903	−	0.375301i	$-0.122461\pi$
$677$	22.2828	+	16.1894i	0.856399	+	0.622210i	−0.0705039	+	0.997512i	$0.522461\pi$
$678$	−1.39477	+	4.29265i	−0.0535657	+	0.164858i
$679$	4.88457	+	15.0332i	0.187453	+	0.576920i
$680$		0			0
$681$	2.15223			0.0824736
$682$	27.2749	+	13.5995i	1.04441	+	0.520753i
$683$	27.1617			1.03931			0.519656	−	0.854375i	$-0.326060\pi$
$683$	27.1617			1.03931			0.519656	+	0.854375i	$0.326060\pi$
$684$	0.0333024	−	0.0241956i	0.00127335	−	0.000925143i
$685$		0			0
$686$	1.04233	−	3.20795i	0.0397962	−	0.122480i
$687$	12.5354	+	9.10752i	0.478256	+	0.347474i
$688$	8.76467	+	6.36790i	0.334150	+	0.242774i
$689$	−2.61913	+	8.06084i	−0.0997808	+	0.307094i
$690$		0			0
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	−0.465906	−	0.884834i	$-0.654272\pi$
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	0.697554	+	0.716532i	$0.254272\pi$
$692$	2.57579			0.0979167
$693$	−31.8597	+	5.33073i	−1.21025	+	0.202498i
$694$	−11.4541			−0.434791
$695$		0			0
$696$	3.52060	+	10.8353i	0.133448	+	0.410711i
$697$	9.49007	−	29.2074i	0.359462	−	1.10631i
$698$	−11.4051	−	8.28625i	−0.431688	−	0.313639i
$699$	−8.52796	−	6.19593i	−0.322557	−	0.234351i
$700$		0			0
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	−0.945880	−	0.324516i	$-0.894799\pi$
$701$	−9.83315	−	30.2633i	−0.371393	−	1.14303i	0.574487	−	0.818513i	$-0.305201\pi$
$702$	10.1293	−	7.35934i	0.382304	−	0.277760i
$703$	0.936004			0.0353021
$704$	13.0767	+	25.1215i	0.492847	+	0.946802i
$705$		0			0
$706$	−20.9562	+	15.2255i	−0.788696	+	0.573021i
$707$	11.1710	+	34.3807i	0.420127	+	1.29302i
$708$	−0.245352	+	0.755117i	−0.00922091	+	0.0283790i
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	0.785109	−	0.619357i	$-0.212607\pi$
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	−0.346432	+	0.938075i	$0.612607\pi$
$710$		0			0
$711$	11.4355	−	35.1947i	0.428863	−	1.31991i
$712$	−11.0153	−	33.9017i	−0.412817	−	1.27052i
$713$	6.37300	−	4.63026i	0.238671	−	0.173405i
$714$	−10.5117			−0.393392
$715$		0			0
$716$	2.73721			0.102294
$717$	−5.10087	+	3.70600i	−0.190496	+	0.138403i
$718$	1.84921	+	5.69129i	0.0690120	+	0.212397i
$719$	1.67179	−	5.14526i	0.0623474	−	0.191886i	−0.915031	−	0.403383i	$-0.867834\pi$
$719$	1.67179	−	5.14526i	0.0623474	−	0.191886i	0.977378	+	0.211498i	$0.0678341\pi$
$720$		0			0
$721$	12.0043	+	8.72166i	0.447065	+	0.324811i
$722$	7.95581	−	24.4855i	0.296085	−	0.911255i
$723$	1.77738	+	5.47022i	0.0661016	+	0.203440i
$724$	−3.15978	+	2.29571i	−0.117432	+	0.0853195i
$725$		0			0
$726$	5.16446	+	6.85412i	0.191671	+	0.254380i
$727$	16.7753			0.622161			0.311080	−	0.950384i	$-0.399309\pi$
$727$	16.7753			0.622161			0.311080	+	0.950384i	$0.399309\pi$
$728$	−24.4993	+	17.7998i	−0.908006	+	0.659705i
$729$	−3.31409	−	10.1997i	−0.122744	−	0.377767i
$730$		0			0
$731$	8.86684	+	6.44213i	0.327952	+	0.238271i
$732$	0.640209	+	0.465139i	0.0236628	+	0.0171920i
$733$	4.35252	−	13.3957i	0.160764	−	0.494781i	−0.837935	−	0.545770i	$-0.816237\pi$
$733$	4.35252	−	13.3957i	0.160764	−	0.494781i	0.998699	+	0.0509889i	$0.0162373\pi$
$734$	−12.3004	−	37.8567i	−0.454016	−	1.39732i
$735$		0			0
$736$	1.06327			0.0391926
$737$	6.57756	−	44.0046i	0.242287	−	1.62093i
$738$	−30.0956			−1.10783
$739$	29.4043	−	21.3635i	1.08165	−	0.785868i	0.103683	−	0.994610i	$-0.466937\pi$
$739$	29.4043	−	21.3635i	1.08165	−	0.785868i	0.977971	+	0.208743i	$0.0669371\pi$
$740$		0			0
$741$	0.0478902	−	0.147391i	0.00175929	−	0.00541454i
$742$	−11.9833	−	8.70640i	−0.439922	−	0.319622i
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	0.558362	−	0.829597i	$-0.311430\pi$
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	−0.616451	+	0.787394i	$0.711430\pi$
$744$	−3.53336	+	10.8746i	−0.129539	+	0.398681i
$745$		0			0
$746$	5.44519	−	3.95617i	0.199363	−	0.144846i
$747$	−28.4080			−1.03939
$748$	0.916745	+	1.76115i	0.0335195	+	0.0643940i
$749$	−7.07466			−0.258503
$750$		0			0
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	0.999414	+	0.0342181i	$0.0108941\pi$
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	−0.788430	+	0.615124i	$0.789106\pi$
$752$	−2.50910	+	7.72220i	−0.0914973	+	0.281600i
$753$	4.49634	+	3.26678i	0.163856	+	0.119048i
$754$	−20.9701	−	15.2356i	−0.763685	−	0.554850i
$755$		0			0
$756$	−0.596550	−	1.83599i	−0.0216963	−	0.0667744i
$757$	−11.7688	+	8.55054i	−0.427744	+	0.310775i	−0.780746	−	0.624848i	$-0.785161\pi$
$757$	−11.7688	+	8.55054i	−0.427744	+	0.310775i	0.353002	+	0.935623i	$0.385161\pi$
$758$	−10.7412			−0.390138
$759$	2.18777	−	0.366056i	0.0794111	−	0.0132870i
$760$		0			0
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	−0.763556	−	0.645741i	$-0.776548\pi$
$761$	−10.6309	+	7.72383i	−0.385371	+	0.279989i	0.378185	+	0.925730i	$0.376548\pi$
$762$	−0.587734	−	1.80886i	−0.0212914	−	0.0655281i
$763$	6.90920	−	21.2643i	0.250130	−	0.769820i
$764$	0.706114	+	0.513022i	0.0255463	+	0.0185605i
$765$		0			0
$766$	−10.2702	+	31.6084i	−0.371077	+	1.14206i
$767$	−7.44344	−	22.9085i	−0.268767	−	0.827180i
$768$	−1.79960	+	1.30749i	−0.0649376	+	0.0471799i
$769$	38.9767			1.40554			0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767			1.40554			0.702768	+	0.711419i	$0.251947\pi$
$770$		0			0
$771$	6.00099			0.216121
$772$	−2.39850	+	1.74261i	−0.0863239	+	0.0627179i
$773$	11.9756	+	36.8571i	0.430733	+	1.32566i	0.897397	+	0.441225i	$0.145456\pi$
$773$	11.9756	+	36.8571i	0.430733	+	1.32566i	−0.466664	+	0.884435i	$0.654544\pi$
$774$	3.31902	−	10.2149i	0.119300	−	0.367167i
$775$		0			0
$776$	−10.2712	−	7.46243i	−0.368713	−	0.267886i
$777$	6.38604	−	19.6542i	0.229098	−	0.705091i
$778$	−2.28773	−	7.04091i	−0.0820192	−	0.252429i
$779$	−0.640147	+	0.465094i	−0.0229356	+	0.0166637i
$780$		0			0
$781$	−19.3023	+	19.6412i	−0.690689	+	0.702818i
$782$	−5.81665			−0.208003
$783$	17.8256	−	12.9510i	0.637034	−	0.462832i
$784$	−7.12525	−	21.9293i	−0.254473	−	0.783188i
$785$		0			0
$786$	−4.44449	−	3.22911i	−0.158530	−	0.115179i
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	0.235077	−	0.971977i	$-0.424466\pi$
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	−0.851762	+	0.523929i	$0.824466\pi$
$788$	0.132564	−	0.407990i	0.00472240	−	0.0145341i
$789$	−1.94943	−	5.99971i	−0.0694014	−	0.213595i
$790$		0			0
$791$	−21.1128			−0.750686
$792$	18.1855	−	18.5049i	0.646195	−	0.657543i
$793$	−24.0075			−0.852533
$794$	7.05718	−	5.12734i	0.250450	−	0.181963i
$795$		0			0
$796$	−0.327093	+	1.00669i	−0.0115935	+	0.0356812i
$797$	−1.79970	−	1.30756i	−0.0637488	−	0.0463162i	0.555454	−	0.831547i	$-0.312544\pi$
$797$	−1.79970	−	1.30756i	−0.0637488	−	0.0463162i	−0.619203	+	0.785231i	$0.712544\pi$
$798$	0.219113	+	0.159195i	0.00775651	+	0.00563543i
$799$	−2.53834	+	7.81222i	−0.0898002	+	0.276377i
$800$		0			0
$801$	−26.2573	+	19.0770i	−0.927756	+	0.674054i
$802$	19.9319			0.703821
$803$	−3.91802	−	1.95356i	−0.138264	−	0.0689398i
$804$	1.25184			0.0441491
$805$		0			0
$806$	−8.03889	−	24.7412i	−0.283158	−	0.871470i
$807$	0.0158888	−	0.0489008i	0.000559314	−	0.00172139i
$808$	−23.4900	−	17.0665i	−0.826376	−	0.600397i
$809$	−17.1254	−	12.4424i	−0.602098	−	0.437450i	0.244525	−	0.969643i	$-0.421368\pi$
$809$	−17.1254	−	12.4424i	−0.602098	−	0.437450i	−0.846623	+	0.532193i	$0.821368\pi$
$810$		0			0
$811$	−11.3462	−	34.9201i	−0.398420	−	1.22621i	−0.926266	−	0.376871i	$-0.877000\pi$
$811$	−11.3462	−	34.9201i	−0.398420	−	1.22621i	0.527845	−	0.849341i	$-0.323000\pi$
$812$	−3.23329	+	2.34912i	−0.113466	+	0.0824380i
$813$	7.71135			0.270449
$814$	43.6357	−	7.30109i	1.52943	−	0.255903i
$815$		0			0
$816$	6.27303	−	4.55762i	0.219600	−	0.159549i
$817$	−0.0872627	−	0.268567i	−0.00305294	−	0.00939597i
$818$	−1.84150	+	5.66756i	−0.0643866	+	0.198161i
$819$	22.3065	+	16.2066i	0.779451	+	0.566305i
$820$		0			0
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	0.472439	+	0.881363i	$0.343374\pi$
$821$	−12.2585	+	37.7278i	−0.427825	+	1.31671i	−0.900264	+	0.435345i	$0.856626\pi$
$822$	2.30791	+	7.10303i	0.0804977	+	0.247747i
$823$	−37.1568	+	26.9960i	−1.29520	+	0.941021i	−0.999897	−	0.0143810i	$-0.995422\pi$
$823$	−37.1568	+	26.9960i	−1.29520	+	0.941021i	−0.295308	+	0.955402i	$0.595422\pi$
$824$	−11.9178			−0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.983707	−	0.179779i	$-0.942462\pi$
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.133002	+	0.991116i	$0.542462\pi$
$828$	−0.155407	−	0.478293i	−0.00540076	−	0.0166218i
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	−0.901530	−	0.432716i	$-0.857555\pi$
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	0.983697	+	0.179832i	$0.0575553\pi$
$830$		0			0
$831$	1.81889	+	1.32150i	0.0630966	+	0.0458423i
$832$	7.47017	−	22.9908i	0.258982	−	0.797063i
$833$	−7.20831	−	22.1849i	−0.249753	−	0.768661i
$834$	−0.325374	+	0.236398i	−0.0112668	+	0.00818580i
$835$		0			0
$836$	0.00756251	−	0.0505940i	0.000261555	−	0.00174983i
$837$	22.1135			0.764354
$838$	19.5801	−	14.2258i	0.676384	−	0.491422i
$839$	8.52536	+	26.2383i	0.294328	+	0.905848i	0.983446	+	0.181200i	$0.0579980\pi$
$839$	8.52536	+	26.2383i	0.294328	+	0.905848i	−0.689118	+	0.724649i	$0.742002\pi$
$840$		0			0
$841$	−13.4418	−	9.76607i	−0.463512	−	0.336761i
$842$	−5.29576	−	3.84760i	−0.182504	−	0.132597i
$843$	0.273412	−	0.841477i	0.00941683	−	0.0289820i
$844$	1.37531	+	4.23276i	0.0473400	+	0.145697i
$845$		0			0
$846$	8.04979			0.276757
$847$	−23.0269	+	32.8826i	−0.791213	+	1.12986i
$848$	10.9261			0.375203
$849$	2.51960	−	1.83059i	0.0864724	−	0.0628258i
$850$		0			0
$851$	3.53370	−	10.8756i	0.121134	−	0.372811i
$852$	−0.626826	−	0.455416i	−0.0214747	−	0.0156023i
$853$	34.0998	+	24.7749i	1.16755	+	0.848277i	0.990714	−	0.135962i	$-0.0434126\pi$
$853$	34.0998	+	24.7749i	1.16755	+	0.848277i	0.176840	+	0.984240i	$0.443413\pi$
$854$	12.9651	−	39.9024i	0.443656	−	1.36543i
$855$		0			0
$856$	4.59707	−	3.33997i	0.157125	−	0.114158i
$857$	45.0850			1.54008			0.770038	−	0.637998i	$-0.220237\pi$
$857$	45.0850			1.54008			0.770038	+	0.637998i	$0.220237\pi$
$858$	1.08291	−	7.24480i	0.0369700	−	0.247333i
$859$	−11.8257			−0.403488			−0.201744	−	0.979438i	$-0.564661\pi$
$859$	−11.8257			−0.403488			−0.201744	+	0.979438i	$0.564661\pi$
$860$		0			0
$861$	5.39854	+	16.6150i	0.183982	+	0.566237i
$862$	10.4204	−	32.0705i	0.354919	−	1.09233i
$863$	22.5484	+	16.3823i	0.767555	+	0.557662i	0.901218	−	0.433365i	$-0.142674\pi$
$863$	22.5484	+	16.3823i	0.767555	+	0.557662i	−0.133663	+	0.991027i	$0.542674\pi$
$864$	2.41475	+	1.75442i	0.0821514	+	0.0596865i
$865$		0			0
$866$	−8.90229	−	27.3984i	−0.302512	−	0.931037i
$867$	−1.56877	+	1.13978i	−0.0532782	+	0.0387089i
$868$	−4.01105			−0.136144
$869$	−21.2342	−	40.7929i	−0.720323	−	1.38380i
$870$		0			0
$871$	−30.7249	+	22.3230i	−1.04107	+	0.756384i
$872$	5.54939	+	17.0793i	0.187926	+	0.578377i
$873$	−3.57207	+	10.9937i	−0.120896	+	0.372081i
$874$	0.121246	+	0.0880900i	0.00410119	+	0.00297969i
$875$		0			0
$876$	0.0380642	−	0.117149i	0.00128607	−	0.00395811i
$877$	3.53736	+	10.8869i	0.119448	+	0.367624i	0.992849	−	0.119379i	$-0.0380902\pi$
$877$	3.53736	+	10.8869i	0.119448	+	0.367624i	−0.873401	+	0.487003i	$0.838090\pi$
$878$	−17.4516	+	12.6793i	−0.588963	+	0.427907i
$879$	6.57011			0.221604
$880$		0			0
$881$	47.0037			1.58360			0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037			1.58360			0.791798	+	0.610783i	$0.209145\pi$
$882$	−18.4938	+	13.4365i	−0.622717	+	0.452431i
$883$	14.4974	+	44.6185i	0.487877	+	1.50153i	0.827770	+	0.561067i	$0.189609\pi$
$883$	14.4974	+	44.6185i	0.487877	+	1.50153i	−0.339894	+	0.940464i	$0.610391\pi$
$884$	0.523698	−	1.61178i	0.0176139	−	0.0542099i
$885$		0			0
$886$	−28.8313	−	20.9472i	−0.968607	−	0.703734i
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	−0.696316	−	0.717735i	$-0.745179\pi$
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	0.985206	−	0.171375i	$-0.0548210\pi$
$888$	5.12920	+	15.7860i	0.172125	+	0.529745i
$889$	7.19754	−	5.22932i	0.241398	−	0.175386i
$890$		0			0
$891$	−18.1915	−	9.07048i	−0.609439	−	0.303872i
$892$	−0.824022			−0.0275903
$893$	0.171223	−	0.124401i	0.00572975	−	0.00416290i
$894$	−1.96725	−	6.05456i	−0.0657946	−	0.202495i
$895$		0			0
$896$	28.7759	+	20.9069i	0.961335	+	0.698451i
$897$	−1.53176	−	1.11289i	−0.0511441	−	0.0371584i
$898$	3.43085	−	10.5591i	0.114489	−	0.352360i
$899$	−14.1469	−	43.5397i	−0.471826	−	1.45213i
$900$		0			0
$901$	11.0534			0.368244
$902$	−26.2153	+	26.6756i	−0.872872	+	0.888201i
$903$	−6.23473			−0.207479
$904$	13.7190	−	9.96742i	0.456287	−	0.331512i
$905$		0			0
$906$	0.467767	−	1.43964i	0.0155405	−	0.0478288i
$907$	−23.1567	−	16.8243i	−0.768907	−	0.558643i	0.132723	−	0.991153i	$-0.457628\pi$
$907$	−23.1567	−	16.8243i	−0.768907	−	0.558643i	−0.901629	+	0.432510i	$0.857628\pi$
$908$	−0.490586	−	0.356432i	−0.0162807	−	0.0118286i
$909$	−8.16930	+	25.1425i	−0.270959	+	0.833925i
$910$		0			0
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	−0.654389	−	0.756158i	$-0.727074\pi$
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	0.516932	+	0.856026i	$0.327074\pi$
$912$	−0.199781			−0.00661542
$913$	−24.7452	+	25.1798i	−0.818948	+	0.833330i
$914$	16.1547			0.534351
$915$		0			0
$916$	−1.34907	−	4.15200i	−0.0445744	−	0.137186i
$917$	7.94098	−	24.4398i	0.262234	−	0.807074i
$918$	−13.2100	−	9.59759i	−0.435993	−	0.316768i
$919$	−28.5429	−	20.7376i	−0.941544	−	0.684072i	0.00724799	−	0.999974i	$-0.497693\pi$
$919$	−28.5429	−	20.7376i	−0.941544	−	0.684072i	−0.948792	+	0.315902i	$0.897693\pi$
$920$		0			0
$921$	−0.755822	−	2.32618i	−0.0249052	−	0.0766503i
$922$	7.63536	−	5.54742i	0.251457	−	0.182694i
$923$	23.5057			0.773699
$924$	−1.01078	−	0.503984i	−0.0332521	−	0.0165798i
$925$		0			0
$926$	−13.6834	+	9.94159i	−0.449665	+	0.326701i
$927$	3.35318	+	10.3200i	0.110133	+	0.338954i
$928$	1.90950	−	5.87682i	0.0626823	−	0.192916i
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.927325	+	0.374256i	$0.122102\pi$
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.642498	+	0.766287i	$0.277898\pi$
$930$		0			0
$931$	−0.185724	+	0.571601i	−0.00608687	+	0.0187335i
$932$	0.917781	+	2.82464i	0.0300629	+	0.0925242i
$933$	−7.73775	+	5.62181i	−0.253323	+	0.184050i
$934$	−8.33220			−0.272638
$935$		0			0
$936$	−22.1458			−0.723857
$937$	11.6843	−	8.48911i	0.381708	−	0.277327i	−0.380341	−	0.924846i	$-0.624193\pi$
$937$	11.6843	−	8.48911i	0.381708	−	0.277327i	0.762049	+	0.647519i	$0.224193\pi$
$938$	−20.5098	−	63.1226i	−0.669668	−	2.06103i
$939$	−4.72637	+	14.5463i	−0.154239	+	0.474700i
$940$		0			0
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	0.805991	−	0.591927i	$-0.201633\pi$
$941$	15.0955	+	10.9675i	0.492100	+	0.357532i	−0.313891	+	0.949459i	$0.601633\pi$
$942$	−5.12905	+	15.7856i	−0.167113	+	0.514322i
$943$	2.98727	+	9.19386i	0.0972788	+	0.299393i
$944$	−25.1211	+	18.2516i	−0.817623	+	0.594038i
$945$		0			0
$946$	−6.16301	−	11.8397i	−0.200377	−	0.384942i
$947$	0.991391			0.0322159			0.0161079	−	0.999870i	$-0.494872\pi$
$947$	0.991391			0.0322159			0.0161079	+	0.999870i	$0.494872\pi$
$948$	1.04679	−	0.760540i	0.0339983	−	0.0247012i
$949$	1.15478	+	3.55405i	0.0374858	+	0.115369i
$950$		0			0
$951$	−2.69896	−	1.96091i	−0.0875198	−	0.0635869i
$952$	31.9505	+	23.2134i	1.03552	+	0.752351i
$953$	2.55373	−	7.85957i	0.0827234	−	0.254597i	−0.901137	−	0.433535i	$-0.857266\pi$
$953$	2.55373	−	7.85957i	0.0827234	−	0.254597i	0.983860	+	0.178938i	$0.0572662\pi$
$954$	−3.34731	−	10.3020i	−0.108373	−	0.333539i
$955$		0			0
$956$	1.77646			0.0574549
$957$	1.90572	−	12.7495i	0.0616031	−	0.412132i
$958$	−30.0881			−0.972101
$959$	−28.2633	+	20.5345i	−0.912669	+	0.663093i
$960$		0			0
$961$	4.61867	−	14.2148i	0.148989	−	0.458542i
$962$	−30.5515	−	22.1969i	−0.985019	−	0.715658i
$963$	−4.18560	−	3.04102i	−0.134879	−	0.0979954i
$964$	0.500784	−	1.54125i	0.0161292	−	0.0496404i
$965$		0			0
$966$	2.67693	−	1.94491i	0.0861289	−	0.0625763i
$967$	−7.36029			−0.236691			−0.118345	−	0.992972i	$-0.537759\pi$
$967$	−7.36029			−0.236691			−0.118345	+	0.992972i	$0.537759\pi$
$968$	−0.561246	−	32.2380i	−0.0180391	−	1.03617i
$969$	−0.202110			−0.00649271
$970$		0			0
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	0.923339	−	0.383986i	$-0.125449\pi$
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	−0.972698	+	0.232074i	$0.925449\pi$
$972$	0.667127	−	2.05321i	0.0213981	−	0.0658566i
$973$	−1.52199	−	1.10579i	−0.0487927	−	0.0354500i
$974$	37.5429	+	27.2765i	1.20295	+	0.873996i
$975$		0			0
$976$	9.56357	+	29.4337i	0.306123	+	0.942148i
$977$	8.36266	−	6.07583i	0.267545	−	0.194383i	−0.445922	−	0.895072i	$-0.647124\pi$
$977$	8.36266	−	6.07583i	0.267545	−	0.194383i	0.713467	+	0.700689i	$0.247124\pi$
$978$	12.4680			0.398684
$979$	−5.96266	+	39.8908i	−0.190567	+	1.27492i
$980$		0			0
$981$	13.2281	−	9.61077i	0.422340	−	0.306848i
$982$	7.11996	+	21.9130i	0.227207	+	0.699272i
$983$	8.98045	−	27.6390i	0.286432	−	0.881547i	−0.699534	−	0.714599i	$-0.746609\pi$
$983$	8.98045	−	27.6390i	0.286432	−	0.881547i	0.985966	−	0.166947i	$-0.0533910\pi$
$984$	−11.3519	−	8.24764i	−0.361886	−	0.262925i
$985$		0			0
$986$	−10.4460	+	32.1493i	−0.332667	+	1.02384i
$987$	−1.44397	−	4.44408i	−0.0459620	−	0.141456i
$988$	−0.0353258	+	0.0256657i	−0.00112386	+	0.000816534i
$989$	−3.44997			−0.109703
$990$		0			0
$991$	7.70381			0.244719			0.122360	−	0.992486i	$-0.460954\pi$
$991$	7.70381			0.244719			0.122360	+	0.992486i	$0.460954\pi$
$992$	5.01724	−	3.64524i	0.159298	−	0.115737i
$993$	2.29818	+	7.07308i	0.0729307	+	0.224458i
$994$	−12.6941	+	39.0683i	−0.402631	+	1.23917i
$995$		0			0
$996$	−0.803583	−	0.583837i	−0.0254625	−	0.0184996i
$997$	0.885080	−	2.72400i	0.0280308	−	0.0862698i	−0.936062	−	0.351834i	$-0.885558\pi$
$997$	0.885080	−	2.72400i	0.0280308	−	0.0862698i	0.964093	+	0.265564i	$0.0855582\pi$
$998$	−2.19076	−	6.74247i	−0.0693473	−	0.213429i
$999$	25.9702	−	18.8685i	0.821661	−	0.596972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.a.201.2		8
5.2	odd	4		275.2.z.a.124.4		16
5.3	odd	4		275.2.z.a.124.1		16
5.4	even	2		55.2.g.b.36.1	yes	8
11.2	odd	10		3025.2.a.w.1.4		4
11.4	even	5	inner	275.2.h.a.26.2		8
11.9	even	5		3025.2.a.bd.1.1		4
15.14	odd	2		495.2.n.e.91.2		8
20.19	odd	2		880.2.bo.h.641.1		8
55.4	even	10		55.2.g.b.26.1	✓	8
55.9	even	10		605.2.a.j.1.4		4
55.14	even	10		605.2.g.m.511.2		8
55.19	odd	10		605.2.g.e.511.1		8
55.24	odd	10		605.2.a.k.1.1		4
55.29	odd	10		605.2.g.k.81.2		8
55.37	odd	20		275.2.z.a.224.1		16
55.39	odd	10		605.2.g.e.251.1		8
55.48	odd	20		275.2.z.a.224.4		16
55.49	even	10		605.2.g.m.251.2		8
55.54	odd	2		605.2.g.k.366.2		8
165.59	odd	10		495.2.n.e.136.2		8
165.119	odd	10		5445.2.a.bp.1.1		4
165.134	even	10		5445.2.a.bi.1.4		4
220.59	odd	10		880.2.bo.h.81.1		8
220.79	even	10		9680.2.a.cm.1.2		4
220.119	odd	10		9680.2.a.cn.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	55.4	even	10
55.2.g.b.36.1	yes	8	5.4	even	2
275.2.h.a.26.2		8	11.4	even	5	inner
275.2.h.a.201.2		8	1.1	even	1	trivial
275.2.z.a.124.1		16	5.3	odd	4
275.2.z.a.124.4		16	5.2	odd	4
275.2.z.a.224.1		16	55.37	odd	20
275.2.z.a.224.4		16	55.48	odd	20
495.2.n.e.91.2		8	15.14	odd	2
495.2.n.e.136.2		8	165.59	odd	10
605.2.a.j.1.4		4	55.9	even	10
605.2.a.k.1.1		4	55.24	odd	10
605.2.g.e.251.1		8	55.39	odd	10
605.2.g.e.511.1		8	55.19	odd	10
605.2.g.k.81.2		8	55.29	odd	10
605.2.g.k.366.2		8	55.54	odd	2
605.2.g.m.251.2		8	55.49	even	10
605.2.g.m.511.2		8	55.14	even	10
880.2.bo.h.81.1		8	220.59	odd	10
880.2.bo.h.641.1		8	20.19	odd	2
3025.2.a.w.1.4		4	11.2	odd	10
3025.2.a.bd.1.1		4	11.9	even	5
5445.2.a.bi.1.4		4	165.134	even	10
5445.2.a.bp.1.1		4	165.119	odd	10
9680.2.a.cm.1.2		4	220.79	even	10
9680.2.a.cn.1.2		4	220.119	odd	10

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09676 - 0.796845i) q^{2} +(-0.177837 - 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +O(q^{10})\)	\(q+(1.09676 - 0.796845i) q^{2} +(-0.177837 - 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(-0.631180 - 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +(0.490303 - 3.28018i) q^{11} +0.0933146 q^{12} +(-2.29029 + 1.66399i) q^{13} +(-1.52884 - 4.70527i) q^{14} +(2.95244 + 2.14507i) q^{16} +(2.98685 + 2.17008i) q^{17} +(1.11803 - 3.44095i) q^{18} +(-0.0293950 - 0.0904686i) q^{19} -2.10021 q^{21} +(-2.07605 - 3.98828i) q^{22} -1.16215 q^{23} +(1.36470 - 0.991515i) q^{24} +(-1.18596 + 3.65001i) q^{26} +(-2.63930 - 1.91757i) q^{27} +(0.478730 + 0.347817i) q^{28} +(-2.08707 + 6.42333i) q^{29} +(-5.48382 + 3.98423i) q^{31} -0.914918 q^{32} +(-1.88253 + 0.314983i) q^{33} +5.00509 q^{34} +(0.133724 + 0.411560i) q^{36} +(-3.04066 + 9.35820i) q^{37} +(-0.104329 - 0.0757994i) q^{38} +(1.31805 + 0.957617i) q^{39} +(-2.57047 - 7.91110i) q^{41} +(-2.30344 + 1.67354i) q^{42} +2.96862 q^{43} +(0.481274 + 0.239968i) q^{44} +(-1.27460 + 0.926052i) q^{46} +(0.687534 + 2.11601i) q^{47} +(0.649001 - 1.99742i) q^{48} +(-5.11155 - 3.71376i) q^{49} +(0.656567 - 2.02070i) q^{51} +(-0.141849 - 0.436565i) q^{52} +(2.42214 - 1.75979i) q^{53} -4.42270 q^{54} +10.6970 q^{56} +(-0.0442883 + 0.0321774i) q^{57} +(2.82938 + 8.70794i) q^{58} +(-2.62930 + 8.09216i) q^{59} +(6.86076 + 4.98464i) q^{61} +(-2.83964 + 8.73951i) q^{62} +(-3.00970 - 9.26289i) q^{63} +(-6.90832 + 5.01919i) q^{64} +(-1.81369 + 1.84554i) q^{66} +13.4153 q^{67} +(-0.484310 + 0.351872i) q^{68} +(0.206673 + 0.636074i) q^{69} +(-6.71734 - 4.88043i) q^{71} +(6.32872 + 4.59808i) q^{72} +(0.407912 - 1.25542i) q^{73} +(4.12215 + 12.6867i) q^{74} +0.0154241 q^{76} +(-10.8319 - 5.40091i) q^{77} +2.20866 q^{78} +(11.2179 - 8.15028i) q^{79} +(1.89395 - 5.82899i) q^{81} +(-9.12312 - 6.62834i) q^{82} +(-8.61155 - 6.25666i) q^{83} +(0.105234 - 0.323876i) q^{84} +(3.25587 - 2.36553i) q^{86} +3.88682 q^{87} +(9.58829 - 1.60431i) q^{88} -12.1612 q^{89} +(3.19256 + 9.82567i) q^{91} +(0.0582308 - 0.179216i) q^{92} +(3.15590 + 2.29290i) q^{93} +(2.44020 + 1.77291i) q^{94} +(0.162706 + 0.500759i) q^{96} +(-3.50412 + 2.54589i) q^{97} -8.56545 q^{98} +(-4.08696 - 7.85141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} + 5 q^{3} - 2 q^{4} - 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} + 3 q^{11} - 16 q^{12} + 2 q^{13} - 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} - 20 q^{21} + 7 q^{22} - 10 q^{23} + 13 q^{24} + 10 q^{26} - 10 q^{27} + 6 q^{28} - 9 q^{29} - 10 q^{31} - 16 q^{32} - 5 q^{33} + 4 q^{34} - 15 q^{36} - 24 q^{37} + 21 q^{39} + 8 q^{41} - 9 q^{42} + 38 q^{43} - 12 q^{44} + 3 q^{46} - 5 q^{48} + q^{49} + q^{51} + 28 q^{52} - 13 q^{53} + 16 q^{54} + 22 q^{56} + 45 q^{57} - 12 q^{58} - 27 q^{59} + 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} + 13 q^{66} + 38 q^{67} - 11 q^{68} - q^{69} - 20 q^{71} + 30 q^{72} - 13 q^{73} + 20 q^{74} - 34 q^{77} + 16 q^{78} + 37 q^{79} + 8 q^{81} - 28 q^{82} - 27 q^{83} + 28 q^{84} - 3 q^{86} - 38 q^{87} + 36 q^{88} - 16 q^{89} + 44 q^{91} - 11 q^{92} + 35 q^{93} + 17 q^{94} - 17 q^{96} - 24 q^{97} - 16 q^{98} - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 5 * q^3 - 2 * q^4 - 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 + 3 * q^11 - 16 * q^12 + 2 * q^13 - 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 - 20 * q^21 + 7 * q^22 - 10 * q^23 + 13 * q^24 + 10 * q^26 - 10 * q^27 + 6 * q^28 - 9 * q^29 - 10 * q^31 - 16 * q^32 - 5 * q^33 + 4 * q^34 - 15 * q^36 - 24 * q^37 + 21 * q^39 + 8 * q^41 - 9 * q^42 + 38 * q^43 - 12 * q^44 + 3 * q^46 - 5 * q^48 + q^49 + q^51 + 28 * q^52 - 13 * q^53 + 16 * q^54 + 22 * q^56 + 45 * q^57 - 12 * q^58 - 27 * q^59 + 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 + 13 * q^66 + 38 * q^67 - 11 * q^68 - q^69 - 20 * q^71 + 30 * q^72 - 13 * q^73 + 20 * q^74 - 34 * q^77 + 16 * q^78 + 37 * q^79 + 8 * q^81 - 28 * q^82 - 27 * q^83 + 28 * q^84 - 3 * q^86 - 38 * q^87 + 36 * q^88 - 16 * q^89 + 44 * q^91 - 11 * q^92 + 35 * q^93 + 17 * q^94 - 17 * q^96 - 24 * q^97 - 16 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more