LMFDB - Embedded newform 275.2.h.a.26.2

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			26.2
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	275.26
Dual form			275.2.h.a.201.2

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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	0.903634	−	0.428306i	$-0.140889\pi$
$2$	1.09676	+	0.796845i	0.775529	+	0.563455i	−0.128105	+	0.991761i	$0.540889\pi$
$3$	−0.177837	+	0.547326i	−0.102674	+	0.315999i	−0.989178	−	0.146723i	$-0.953127\pi$
$3$	−0.177837	+	0.547326i	−0.102674	+	0.315999i	0.886503	+	0.462722i	$0.153127\pi$
$4$	−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	0.901800	+	0.432154i	$0.142246\pi$
$7$	1.12773	+	3.47080i	0.426242	+	1.31184i	−0.475558	+	0.879685i	$0.657754\pi$
$8$	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	0.222990	−	0.974821i	$-0.428418\pi$
$13$	−2.29029	−	1.66399i	−0.635212	−	0.461509i	−0.858202	+	0.513312i	$0.828418\pi$
$14$	−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	−0.163374	−	0.986564i	$-0.552238\pi$
$17$	2.98685	−	2.17008i	0.724419	−	0.526321i	0.887793	+	0.460243i	$0.152238\pi$
$18$	1.11803	+	3.44095i	0.263523	+	0.811041i
$19$	−0.0293950	+	0.0904686i	−0.00674368	+	0.0207549i	−0.954372	−	0.298621i	$-0.903473\pi$
$19$	−0.0293950	+	0.0904686i	−0.00674368	+	0.0207549i	0.947628	+	0.319376i	$0.103473\pi$
$20$		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	−0.934607	−	0.355682i	$-0.884249\pi$
$29$	−2.08707	−	6.42333i	−0.387559	−	1.19278i	0.547049	−	0.837101i	$-0.315751\pi$
$30$		0			0
$31$	−5.48382	−	3.98423i	−0.984923	−	0.715588i	−0.0261194	−	0.999659i	$-0.508315\pi$
$31$	−5.48382	−	3.98423i	−0.984923	−	0.715588i	−0.958803	+	0.284071i	$0.908315\pi$
$32$	−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	−0.809208	−	0.587523i	$-0.800103\pi$
$37$	−3.04066	−	9.35820i	−0.499882	−	1.53848i	0.309326	−	0.950956i	$-0.399897\pi$
$38$	−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	0.522391	+	0.852706i	$0.325040\pi$
$41$	−2.57047	+	7.91110i	−0.401440	+	1.23551i	−0.923831	+	0.382800i	$0.874960\pi$
$42$	−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	−0.888308	−	0.459248i	$-0.848119\pi$
$47$	0.687534	−	2.11601i	0.100287	−	0.308652i	0.988595	+	0.150595i	$0.0481191\pi$
$48$	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	0.741578	−	0.670867i	$-0.234078\pi$
$53$	2.42214	+	1.75979i	0.332706	+	0.241725i	−0.408872	+	0.912592i	$0.634078\pi$
$54$	−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	−0.963010	−	0.269465i	$-0.913153\pi$
$59$	−2.62930	−	8.09216i	−0.342306	−	1.05351i	0.620704	−	0.784045i	$-0.286847\pi$
$60$		0			0
$61$	6.86076	−	4.98464i	0.878431	−	0.638217i	−0.0544052	−	0.998519i	$-0.517326\pi$
$61$	6.86076	−	4.98464i	0.878431	−	0.638217i	0.932836	+	0.360302i	$0.117326\pi$
$62$	−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	−0.910092	−	0.414406i	$-0.863989\pi$
$71$	−6.71734	+	4.88043i	−0.797202	+	0.579201i	0.112890	+	0.993607i	$0.463989\pi$
$72$	6.32872	−	4.59808i	0.745846	−	0.541889i
$73$	0.407912	+	1.25542i	0.0477425	+	0.146936i	0.972086	−	0.234625i	$-0.0753864\pi$
$73$	0.407912	+	1.25542i	0.0477425	+	0.146936i	−0.924343	+	0.381562i	$0.875386\pi$
$74$	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	0.998859	−	0.0477484i	$-0.0152046\pi$
$79$	11.2179	+	8.15028i	1.26211	+	0.916978i	0.263253	+	0.964727i	$0.415205\pi$
$80$		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	−0.949676	−	0.313233i	$-0.898588\pi$
$83$	−8.61155	+	6.25666i	−0.945240	+	0.686757i	0.00443607	+	0.999990i	$0.498588\pi$
$84$	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	0.395504	−	0.918464i	$-0.370570\pi$
$97$	−3.50412	−	2.54589i	−0.355789	−	0.258496i	−0.751294	+	0.659968i	$0.770570\pi$
$98$	−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	0.112743	−	0.993624i	$-0.464036\pi$
$101$	−8.01388	−	5.82242i	−0.797411	−	0.579353i	−0.910153	+	0.414271i	$0.864036\pi$
$102$	−0.890091	+	2.73942i	−0.0881321	+	0.271243i
$103$	−1.25643	−	3.86690i	−0.123800	−	0.381017i	0.869880	−	0.493263i	$-0.164196\pi$
$103$	−1.25643	−	3.86690i	−0.123800	−	0.381017i	−0.993681	+	0.112245i	$0.964196\pi$
$104$	−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	−0.975828	−	0.218539i	$-0.929871\pi$
$107$	−0.599053	+	1.84369i	−0.0579126	+	0.178237i	0.917916	+	0.396776i	$0.129871\pi$
$108$	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	−0.999256	−	0.0385582i	$-0.987724\pi$
$113$	−1.78775	+	5.50212i	−0.168177	+	0.517596i	0.831079	+	0.556154i	$0.187724\pi$
$114$	−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	−0.496833	−	0.867846i	$-0.665504\pi$
$127$	1.97224	−	1.43292i	0.175008	−	0.127151i	0.671841	+	0.740695i	$0.265504\pi$
$128$	−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	−0.867225	−	0.497916i	$-0.834099\pi$
$137$	−7.74461	+	5.62678i	−0.661666	+	0.480729i	0.205559	+	0.978645i	$0.434099\pi$
$138$	0.733524	−	0.532936i	0.0624417	−	0.0453666i
$139$	0.159299	+	0.490271i	0.0135116	+	0.0415843i	0.957585	−	0.288151i	$-0.0930405\pi$
$139$	0.159299	+	0.490271i	0.0135116	+	0.0415843i	−0.944073	+	0.329735i	$0.893041\pi$
$140$		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	−0.283575	−	0.958950i	$-0.591521\pi$
$149$	6.60144	−	4.79623i	0.540811	−	0.392922i	0.824386	+	0.566028i	$0.191521\pi$
$150$		0			0
$151$	0.599563	−	1.84526i	0.0487917	−	0.150165i	−0.923692	−	0.383135i	$-0.874844\pi$
$151$	0.599563	−	1.84526i	0.0487917	−	0.150165i	0.972484	+	0.232970i	$0.0748443\pi$
$152$	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	0.240279	+	0.970704i	$0.422761\pi$
$157$	−6.57418	+	20.2332i	−0.524676	+	1.61479i	−0.764955	+	0.644084i	$0.777239\pi$
$158$	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	−0.0479001	−	0.998852i	$-0.515253\pi$
$163$	−12.9289	−	9.39337i	−1.01267	−	0.735746i	−0.964767	+	0.263107i	$0.915253\pi$
$164$	1.34878			0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	14.3269	+	10.4091i	1.10865	+	0.805481i	0.982450	−	0.186524i	$-0.0597223\pi$
$167$	14.3269	+	10.4091i	1.10865	+	0.805481i	0.126199	+	0.992005i	$0.459722\pi$
$168$	−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	0.571459	+	0.820631i	$0.306378\pi$
$173$	−4.90888	+	15.1080i	−0.373216	+	1.14864i	−0.944675	+	0.328009i	$0.893622\pi$
$174$	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	0.542960	+	0.839759i	$0.317304\pi$
$179$	−5.21653	+	16.0548i	−0.389902	+	1.19999i	−0.932862	+	0.360235i	$0.882696\pi$
$180$		0			0
$181$	19.4871	−	14.1582i	1.44846	−	1.05237i	0.462277	−	0.886735i	$-0.347032\pi$
$181$	19.4871	−	14.1582i	1.44846	−	1.05237i	0.986187	−	0.165636i	$-0.0529676\pi$
$182$	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	0.993027	−	0.117890i	$-0.0376129\pi$
$191$	1.66337	+	5.11934i	0.120358	+	0.370422i	−0.872669	+	0.488312i	$0.837613\pi$
$192$	3.97569	−	2.88851i	0.286921	−	0.208460i
$193$	14.7921	−	10.7471i	1.06476	−	0.773593i	0.0897961	−	0.995960i	$-0.471378\pi$
$193$	14.7921	−	10.7471i	1.06476	−	0.773593i	0.974963	+	0.222367i	$0.0713785\pi$
$194$	−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	0.956953	+	0.290243i	$0.0937362\pi$
$211$	22.2057	+	16.1334i	1.52871	+	1.11067i	0.571752	+	0.820426i	$0.306264\pi$
$212$	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	−0.884606	−	0.466338i	$-0.845573\pi$
$223$	1.57040	−	4.83321i	0.105162	−	0.323656i	0.989768	+	0.142683i	$0.0455729\pi$
$224$	−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	0.905351	−	0.424663i	$-0.139607\pi$
$227$	−1.15566	−	3.55676i	−0.0767040	−	0.236071i	−0.982055	+	0.188593i	$0.939607\pi$
$228$	−0.00274299	+	0.00844204i	−0.000181659	+	0.000559088i
$229$	−21.7821	−	15.8256i	−1.43940	−	1.04578i	−0.988168	−	0.153378i	$-0.950985\pi$
$229$	−21.7821	−	15.8256i	−1.43940	−	1.04578i	−0.451232	−	0.892407i	$-0.649015\pi$
$230$		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	0.955632	−	0.294562i	$-0.0951737\pi$
$233$	14.8185	+	10.7663i	0.970794	+	0.705323i	0.0151615	+	0.999885i	$0.495174\pi$
$234$	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	0.779853	+	0.625963i	$0.215294\pi$
$239$	−3.38555	+	10.4196i	−0.218993	+	0.673991i	−0.998846	+	0.0480283i	$0.984706\pi$
$240$		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	0.313242	−	0.949673i	$-0.398585\pi$
$251$	−7.81303	−	5.67650i	−0.493154	−	0.358297i	−0.806396	+	0.591376i	$0.798585\pi$
$252$	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	−0.999854	−	0.0170916i	$-0.994559\pi$
$257$	−3.22230	−	9.91721i	−0.201001	−	0.618618i	0.798853	−	0.601527i	$-0.205441\pi$
$258$	−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	−0.585580	−	0.810615i	$-0.699133\pi$
$269$	0.0722816	−	0.0525156i	0.00440708	−	0.00320193i	0.589987	+	0.807413i	$0.299133\pi$
$270$		0			0
$271$	−4.14069	−	12.7437i	−0.251529	−	0.774126i	−0.994494	−	0.104796i	$-0.966581\pi$
$271$	−4.14069	−	12.7437i	−0.251529	−	0.774126i	0.742965	−	0.669330i	$-0.233419\pi$
$272$	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	0.488773	−	0.872411i	$-0.337445\pi$
$277$	−3.16057	−	2.29629i	−0.189901	−	0.137971i	−0.678673	+	0.734440i	$0.737445\pi$
$278$	−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	−0.550067	−	0.835120i	$-0.685398\pi$
$281$	1.24381	−	0.903680i	0.0741994	−	0.0539090i	0.624267	+	0.781211i	$0.285398\pi$
$282$	0.536401	+	1.65087i	0.0319422	+	0.0983081i
$283$	1.67231	−	5.14683i	0.0994083	−	0.305947i	−0.888969	−	0.457967i	$-0.848578\pi$
$283$	1.67231	−	5.14683i	0.0994083	−	0.305947i	0.988377	+	0.152020i	$0.0485778\pi$
$284$	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	−0.999666	−	0.0258295i	$-0.991777\pi$
$293$	−3.52789	−	10.8577i	−0.206102	−	0.634315i	0.793565	−	0.608486i	$-0.208223\pi$
$294$	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	0.693247	+	0.720700i	$0.256180\pi$
$311$	−5.13570	+	15.8061i	−0.291219	+	0.896279i	−0.984465	+	0.175579i	$0.943820\pi$
$312$	−1.47569	−	4.54172i	−0.0835447	−	0.257124i
$313$	−21.5012	+	15.6215i	−1.21532	+	0.882982i	−0.995703	−	0.0926041i	$-0.970481\pi$
$313$	−21.5012	+	15.6215i	−1.21532	+	0.882982i	−0.219617	+	0.975586i	$0.570481\pi$
$314$	−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	0.711648	−	0.702537i	$-0.247949\pi$
$317$	4.68982	+	3.40736i	0.263407	+	0.191376i	−0.448241	+	0.893913i	$0.647949\pi$
$318$	−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	−0.998259	−	0.0589818i	$-0.981215\pi$
$337$	−4.13631	−	12.7303i	−0.225319	−	0.693461i	0.772940	−	0.634479i	$-0.218785\pi$
$338$	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	−0.755942	−	0.654639i	$-0.772821\pi$
$347$	−6.83538	+	4.96619i	−0.366942	+	0.266599i	0.389000	+	0.921238i	$0.372821\pi$
$348$	−0.194754	−	0.599391i	−0.0104399	−	0.0321307i
$349$	−3.21341	+	9.88987i	−0.172010	+	0.529393i	−0.999484	−	0.0321111i	$-0.989777\pi$
$349$	−3.21341	+	9.88987i	−0.172010	+	0.529393i	0.827474	+	0.561504i	$0.189777\pi$
$350$		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	0.908586	−	0.417698i	$-0.137163\pi$
$359$	−1.36405	−	4.19813i	−0.0719920	−	0.221569i	−0.980578	+	0.196129i	$0.937163\pi$
$360$		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	0.847809	+	0.530302i	$0.177922\pi$
$367$	9.07327	+	27.9247i	0.473621	+	1.45766i	−0.374188	+	0.927353i	$0.622078\pi$
$368$	−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	−0.740116	−	0.672480i	$-0.765229\pi$
$379$	−6.40996	+	4.65711i	−0.329258	+	0.239220i	0.410858	+	0.911699i	$0.365229\pi$
$380$		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	−0.0485140	−	0.998823i	$-0.515449\pi$
$383$	−19.8335	−	14.4099i	−1.01344	−	0.736309i	−0.964928	+	0.262514i	$0.915449\pi$
$384$	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	0.984679	−	0.174377i	$-0.0557911\pi$
$389$	1.68752	+	5.19366i	0.0855608	+	0.263329i	−0.899118	+	0.437706i	$0.855791\pi$
$390$		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	−0.249750	−	0.968310i	$-0.580348\pi$
$401$	11.8947	−	8.64197i	0.593991	−	0.431560i	0.843741	+	0.536751i	$0.180348\pi$
$402$	−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	0.496381	−	0.868105i	$-0.334662\pi$
$409$	−3.55625	−	2.58376i	−0.175845	−	0.127759i	−0.672226	+	0.740346i	$0.734662\pi$
$410$		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	−0.980810	−	0.194965i	$-0.937541\pi$
$421$	−1.49210	+	4.59221i	−0.0727205	+	0.223811i	0.908090	+	0.418776i	$0.137541\pi$
$422$	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	0.955295	−	0.295655i	$-0.0955380\pi$
$431$	20.1234	+	14.6205i	0.969312	+	0.704247i	0.0140175	+	0.999902i	$0.495538\pi$
$432$	−3.67906	+	11.3230i	−0.177009	+	0.544778i
$433$	6.56669	+	20.2102i	0.315575	+	0.971240i	0.975517	+	0.219923i	$0.0705807\pi$
$433$	6.56669	+	20.2102i	0.315575	+	0.971240i	−0.659942	+	0.751316i	$0.729419\pi$
$434$	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	0.549838	+	0.835272i	$0.314690\pi$
$443$	−8.12332	+	25.0010i	−0.385951	+	1.18783i	−0.935788	+	0.352562i	$0.885310\pi$
$444$	−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	0.733045	−	0.680180i	$-0.238098\pi$
$449$	6.62554	+	4.81373i	0.312678	+	0.227174i	−0.420366	+	0.907354i	$0.638098\pi$
$450$		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	−0.339011	−	0.940782i	$-0.610092\pi$
$457$	9.64056	−	7.00428i	0.450966	−	0.327646i	0.789977	+	0.613136i	$0.210092\pi$
$458$	−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	−0.696858	−	0.717209i	$-0.745419\pi$
$467$	−4.97235	+	3.61263i	−0.230093	+	0.167172i	0.466765	+	0.884381i	$0.345419\pi$
$468$	−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	−0.916829	−	0.399281i	$-0.869260\pi$
$479$	−17.9555	+	13.0454i	−0.820406	+	0.596060i	0.0964228	+	0.995340i	$0.469260\pi$
$480$		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	−0.360702	−	0.932681i	$-0.617463\pi$
$487$	10.5778	−	32.5553i	0.479328	−	1.47522i	0.840030	−	0.542539i	$-0.182537\pi$
$488$	−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	−0.996847	−	0.0793441i	$-0.974717\pi$
$491$	−5.25197	−	16.1639i	−0.237018	−	0.729467i	0.759829	−	0.650123i	$-0.225283\pi$
$492$	−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	0.980690	−	0.195570i	$-0.0626558\pi$
$499$	1.61599	+	4.97352i	0.0723418	+	0.222645i	−0.908348	+	0.418215i	$0.862656\pi$
$500$		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	0.0480416	+	0.998845i	$0.484702\pi$
$503$	−12.9617	+	39.8919i	−0.577931	+	1.77869i	−0.625973	+	0.779845i	$0.715298\pi$
$504$	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	−0.709163	−	0.705044i	$-0.750927\pi$
$509$	6.29399	−	19.3709i	0.278976	−	0.858601i	0.988140	−	0.153557i	$-0.0490728\pi$
$510$		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	0.999963	+	0.00855656i	$0.00272367\pi$
$521$	4.47391	+	13.7693i	0.196005	+	0.603243i	−0.803958	+	0.594686i	$0.797276\pi$
$522$	19.7690	−	14.3630i	0.865265	−	0.628652i
$523$	9.02873	−	6.55975i	0.394799	−	0.286838i	−0.372620	−	0.927984i	$-0.621541\pi$
$523$	9.02873	−	6.55975i	0.394799	−	0.286838i	0.767419	+	0.641146i	$0.221541\pi$
$524$	−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	0.386331	−	0.922360i	$-0.373742\pi$
$541$	−8.64094	−	6.27801i	−0.371503	−	0.269913i	−0.757834	+	0.652447i	$0.773742\pi$
$542$	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	−0.961938	−	0.273269i	$-0.911895\pi$
$547$	−0.540038	+	1.66207i	−0.0230904	+	0.0710648i	0.938847	+	0.344334i	$0.111895\pi$
$548$	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	0.993806	+	0.111126i	$0.0354456\pi$
$557$	6.02100	+	18.5307i	0.255118	+	0.785173i	−0.738688	+	0.674047i	$0.764554\pi$
$558$	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	0.308497	−	0.951225i	$-0.400174\pi$
$563$	−11.8838	−	8.63407i	−0.500842	−	0.363883i	−0.809338	+	0.587343i	$0.800174\pi$
$564$	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	−0.734943	−	0.678129i	$-0.762791\pi$
$569$	6.15980	−	18.9579i	0.258232	−	0.794758i	0.993176	−	0.116629i	$-0.0372088\pi$
$570$		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	0.267323	−	0.963607i	$-0.413861\pi$
$577$	30.4194	−	22.1010i	1.26637	−	0.920075i	0.999052	+	0.0435320i	$0.0138610\pi$
$578$	−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	−0.970920	−	0.239403i	$-0.923048\pi$
$587$	−7.90191	−	24.3196i	−0.326147	−	1.00378i	0.644774	−	0.764373i	$-0.276952\pi$
$588$	−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	−0.666278	−	0.745704i	$-0.732114\pi$
$599$	−3.98843	+	2.89776i	−0.162963	+	0.118399i	0.503315	+	0.864103i	$0.332114\pi$
$600$		0			0
$601$	14.2425	+	43.8338i	0.580963	+	1.78802i	0.614912	+	0.788596i	$0.289191\pi$
$601$	14.2425	+	43.8338i	0.580963	+	1.78802i	−0.0339497	+	0.999424i	$0.510809\pi$
$602$	−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	−0.976857	−	0.213891i	$-0.931386\pi$
$607$	−36.5162	−	26.5306i	−1.48215	−	1.07684i	−0.505288	−	0.862951i	$-0.668614\pi$
$608$	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	−0.976244	−	0.216675i	$-0.930479\pi$
$613$	−1.46294	+	4.50247i	−0.0590877	+	0.181853i	0.917156	+	0.398528i	$0.130479\pi$
$614$	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	−0.948815	−	0.315832i	$-0.897717\pi$
$619$	0.110304	−	0.339482i	0.00443351	−	0.0136449i	0.953249	+	0.302187i	$0.0977166\pi$
$620$		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	−0.930077	−	0.367366i	$-0.880260\pi$
$631$	−9.88614	−	30.4264i	−0.393561	−	1.21126i	0.536516	−	0.843890i	$-0.319740\pi$
$632$	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	−0.944685	−	0.327979i	$-0.893633\pi$
$641$	0.312987	−	0.963274i	0.0123622	−	0.0380470i	0.957047	+	0.289932i	$0.0936326\pi$
$642$	−0.467370	−	1.43842i	−0.0184456	−	0.0567697i
$643$	−12.1130	+	8.80057i	−0.477688	+	0.347061i	−0.800430	−	0.599426i	$-0.795395\pi$
$643$	−12.1130	+	8.80057i	−0.477688	+	0.347061i	0.322742	+	0.946487i	$0.395395\pi$
$644$	−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	0.834713	−	0.550686i	$-0.185634\pi$
$647$	14.4712	+	10.5139i	0.568920	+	0.413345i	−0.265793	+	0.964030i	$0.585634\pi$
$648$	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	−0.700089	−	0.714055i	$-0.746856\pi$
$653$	−14.1419	−	43.5244i	−0.553416	−	1.70324i	0.146673	−	0.989185i	$-0.453144\pi$
$654$	−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	0.979076	+	0.203494i	$0.0652299\pi$
$673$	38.2690	+	27.8041i	1.47516	+	1.07177i	0.496086	+	0.868273i	$0.334770\pi$
$674$	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	−0.0705039	−	0.997512i	$-0.522461\pi$
$677$	22.2828	−	16.1894i	0.856399	−	0.622210i	0.926903	+	0.375301i	$0.122461\pi$
$678$	−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	0.697554	−	0.716532i	$-0.254272\pi$
$691$	6.08931	+	4.42414i	0.231648	+	0.168302i	−0.465906	+	0.884834i	$0.654272\pi$
$692$	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	0.574487	+	0.818513i	$0.305201\pi$
$701$	−9.83315	+	30.2633i	−0.371393	+	1.14303i	−0.945880	+	0.324516i	$0.894799\pi$
$702$	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	−0.346432	−	0.938075i	$-0.612607\pi$
$709$	11.6807	−	8.48651i	0.438677	−	0.318718i	0.785109	+	0.619357i	$0.212607\pi$
$710$		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	0.977378	−	0.211498i	$-0.0678341\pi$
$719$	1.67179	+	5.14526i	0.0623474	+	0.191886i	−0.915031	+	0.403383i	$0.867834\pi$
$720$		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	0.998699	−	0.0509889i	$-0.0162373\pi$
$733$	4.35252	+	13.3957i	0.160764	+	0.494781i	−0.837935	+	0.545770i	$0.816237\pi$
$734$	−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	0.977971	−	0.208743i	$-0.0669371\pi$
$739$	29.4043	+	21.3635i	1.08165	+	0.785868i	0.103683	+	0.994610i	$0.466937\pi$
$740$		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	−0.616451	−	0.787394i	$-0.711430\pi$
$743$	−1.58338	+	1.15039i	−0.0580884	+	0.0422037i	0.558362	+	0.829597i	$0.311430\pi$
$744$	−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	−0.788430	−	0.615124i	$-0.789106\pi$
$751$	5.78189	−	17.7948i	0.210984	−	0.649342i	0.999414	−	0.0342181i	$-0.0108941\pi$
$752$	−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	0.353002	−	0.935623i	$-0.385161\pi$
$757$	−11.7688	−	8.55054i	−0.427744	−	0.310775i	−0.780746	+	0.624848i	$0.785161\pi$
$758$	−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	0.378185	−	0.925730i	$-0.376548\pi$
$761$	−10.6309	−	7.72383i	−0.385371	−	0.279989i	−0.763556	+	0.645741i	$0.776548\pi$
$762$	−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	−0.466664	−	0.884435i	$-0.654544\pi$
$773$	11.9756	−	36.8571i	0.430733	−	1.32566i	0.897397	−	0.441225i	$-0.145456\pi$
$774$	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	−0.851762	−	0.523929i	$-0.824466\pi$
$787$	−17.3002	+	12.5693i	−0.616685	+	0.448048i	0.235077	+	0.971977i	$0.424466\pi$
$788$	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	−0.619203	−	0.785231i	$-0.712544\pi$
$797$	−1.79970	+	1.30756i	−0.0637488	+	0.0463162i	0.555454	+	0.831547i	$0.312544\pi$
$798$	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	−0.846623	−	0.532193i	$-0.821368\pi$
$809$	−17.1254	+	12.4424i	−0.602098	+	0.437450i	0.244525	+	0.969643i	$0.421368\pi$
$810$		0			0
$811$	−11.3462	+	34.9201i	−0.398420	+	1.22621i	0.527845	+	0.849341i	$0.323000\pi$
$811$	−11.3462	+	34.9201i	−0.398420	+	1.22621i	−0.926266	+	0.376871i	$0.877000\pi$
$812$	−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	−0.900264	−	0.435345i	$-0.856626\pi$
$821$	−12.2585	−	37.7278i	−0.427825	−	1.31671i	0.472439	−	0.881363i	$-0.343374\pi$
$822$	2.30791	−	7.10303i	0.0804977	−	0.247747i
$823$	−37.1568	−	26.9960i	−1.29520	−	0.941021i	−0.295308	−	0.955402i	$-0.595422\pi$
$823$	−37.1568	−	26.9960i	−1.29520	−	0.941021i	−0.999897	+	0.0143810i	$0.995422\pi$
$824$	−11.9178			−0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	−32.1139	−	23.3321i	−1.11671	−	0.811337i	−0.133002	−	0.991116i	$-0.542462\pi$
$827$	−32.1139	−	23.3321i	−1.11671	−	0.811337i	−0.983707	+	0.179779i	$0.942462\pi$
$828$	−0.155407	+	0.478293i	−0.00540076	+	0.0166218i
$829$	2.36578	+	7.28113i	0.0821671	+	0.252884i	0.983697	−	0.179832i	$-0.0575553\pi$
$829$	2.36578	+	7.28113i	0.0821671	+	0.252884i	−0.901530	+	0.432716i	$0.857555\pi$
$830$		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	−0.689118	−	0.724649i	$-0.742002\pi$
$839$	8.52536	−	26.2383i	0.294328	−	0.905848i	0.983446	−	0.181200i	$-0.0579980\pi$
$840$		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	0.176840	−	0.984240i	$-0.443413\pi$
$853$	34.0998	−	24.7749i	1.16755	−	0.848277i	0.990714	+	0.135962i	$0.0434126\pi$
$854$	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	−0.133663	−	0.991027i	$-0.542674\pi$
$863$	22.5484	−	16.3823i	0.767555	−	0.557662i	0.901218	+	0.433365i	$0.142674\pi$
$864$	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	−0.873401	−	0.487003i	$-0.838090\pi$
$877$	3.53736	−	10.8869i	0.119448	−	0.367624i	0.992849	+	0.119379i	$0.0380902\pi$
$878$	−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	−0.339894	−	0.940464i	$-0.610391\pi$
$883$	14.4974	−	44.6185i	0.487877	−	1.50153i	0.827770	−	0.561067i	$-0.189609\pi$
$884$	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	0.985206	+	0.171375i	$0.0548210\pi$
$887$	8.60386	+	26.4800i	0.288889	+	0.889110i	−0.696316	+	0.717735i	$0.745179\pi$
$888$	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	−0.901629	−	0.432510i	$-0.857628\pi$
$907$	−23.1567	+	16.8243i	−0.768907	+	0.558643i	0.132723	+	0.991153i	$0.457628\pi$
$908$	−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	0.516932	−	0.856026i	$-0.327074\pi$
$911$	−4.14883	−	3.01430i	−0.137457	−	0.0998682i	−0.654389	+	0.756158i	$0.727074\pi$
$912$	−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	−0.948792	−	0.315902i	$-0.897693\pi$
$919$	−28.5429	+	20.7376i	−0.941544	+	0.684072i	0.00724799	+	0.999974i	$0.497693\pi$
$920$		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	0.642498	−	0.766287i	$-0.277898\pi$
$929$	47.8474	−	34.7632i	1.56982	−	1.14054i	0.927325	−	0.374256i	$-0.122102\pi$
$930$		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	0.762049	−	0.647519i	$-0.224193\pi$
$937$	11.6843	+	8.48911i	0.381708	+	0.277327i	−0.380341	+	0.924846i	$0.624193\pi$
$938$	−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	−0.313891	−	0.949459i	$-0.601633\pi$
$941$	15.0955	−	10.9675i	0.492100	−	0.357532i	0.805991	+	0.591927i	$0.201633\pi$
$942$	−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	0.983860	−	0.178938i	$-0.0572662\pi$
$953$	2.55373	+	7.85957i	0.0827234	+	0.254597i	−0.901137	+	0.433535i	$0.857266\pi$
$954$	−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	−0.972698	−	0.232074i	$-0.925449\pi$
$971$	−1.53808	+	4.73372i	−0.0493593	+	0.151912i	0.923339	+	0.383986i	$0.125449\pi$
$972$	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	0.713467	−	0.700689i	$-0.247124\pi$
$977$	8.36266	+	6.07583i	0.267545	+	0.194383i	−0.445922	+	0.895072i	$0.647124\pi$
$978$	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	0.985966	+	0.166947i	$0.0533910\pi$
$983$	8.98045	+	27.6390i	0.286432	+	0.881547i	−0.699534	+	0.714599i	$0.746609\pi$
$984$	−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	0.964093	−	0.265564i	$-0.0855582\pi$
$997$	0.885080	+	2.72400i	0.0280308	+	0.0862698i	−0.936062	+	0.351834i	$0.885558\pi$
$998$	−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.26.2		8
5.2	odd	4		275.2.z.a.224.1		16
5.3	odd	4		275.2.z.a.224.4		16
5.4	even	2		55.2.g.b.26.1	✓	8
11.3	even	5	inner	275.2.h.a.201.2		8
11.5	even	5		3025.2.a.bd.1.1		4
11.6	odd	10		3025.2.a.w.1.4		4
15.14	odd	2		495.2.n.e.136.2		8
20.19	odd	2		880.2.bo.h.81.1		8
55.3	odd	20		275.2.z.a.124.1		16
55.4	even	10		605.2.g.m.251.2		8
55.9	even	10		605.2.g.m.511.2		8
55.14	even	10		55.2.g.b.36.1	yes	8
55.19	odd	10		605.2.g.k.366.2		8
55.24	odd	10		605.2.g.e.511.1		8
55.29	odd	10		605.2.g.e.251.1		8
55.39	odd	10		605.2.a.k.1.1		4
55.47	odd	20		275.2.z.a.124.4		16
55.49	even	10		605.2.a.j.1.4		4
55.54	odd	2		605.2.g.k.81.2		8
165.14	odd	10		495.2.n.e.91.2		8
165.104	odd	10		5445.2.a.bp.1.1		4
165.149	even	10		5445.2.a.bi.1.4		4
220.39	even	10		9680.2.a.cm.1.2		4
220.159	odd	10		9680.2.a.cn.1.2		4
220.179	odd	10		880.2.bo.h.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	5.4	even	2
55.2.g.b.36.1	yes	8	55.14	even	10
275.2.h.a.26.2		8	1.1	even	1	trivial
275.2.h.a.201.2		8	11.3	even	5	inner
275.2.z.a.124.1		16	55.3	odd	20
275.2.z.a.124.4		16	55.47	odd	20
275.2.z.a.224.1		16	5.2	odd	4
275.2.z.a.224.4		16	5.3	odd	4
495.2.n.e.91.2		8	165.14	odd	10
495.2.n.e.136.2		8	15.14	odd	2
605.2.a.j.1.4		4	55.49	even	10
605.2.a.k.1.1		4	55.39	odd	10
605.2.g.e.251.1		8	55.29	odd	10
605.2.g.e.511.1		8	55.24	odd	10
605.2.g.k.81.2		8	55.54	odd	2
605.2.g.k.366.2		8	55.19	odd	10
605.2.g.m.251.2		8	55.4	even	10
605.2.g.m.511.2		8	55.9	even	10
880.2.bo.h.81.1		8	20.19	odd	2
880.2.bo.h.641.1		8	220.179	odd	10
3025.2.a.w.1.4		4	11.6	odd	10
3025.2.a.bd.1.1		4	11.5	even	5
5445.2.a.bi.1.4		4	165.149	even	10
5445.2.a.bp.1.1		4	165.104	odd	10
9680.2.a.cm.1.2		4	220.39	even	10
9680.2.a.cn.1.2		4	220.159	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

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