LMFDB - Embedded newform 375.2.g.e.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, 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("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			226.3
Root			$-0.536547i$ of defining polynomial
Character	$\chi$	$=$	375.226
Dual form			375.2.g.e.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165802 - 0.510286i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.38513 + 1.00636i) q^{4} +(-0.434076 + 0.315374i) q^{6} +2.57318 q^{7} +(1.61134 - 1.17071i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.165802 - 0.510286i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.38513 + 1.00636i) q^{4} +(-0.434076 + 0.315374i) q^{6} +2.57318 q^{7} +(1.61134 - 1.17071i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.58949 + 4.89194i) q^{11} +(-0.529073 - 1.62832i) q^{12} +(-0.455776 - 1.40274i) q^{13} +(0.426639 - 1.31306i) q^{14} +(0.727915 + 2.24029i) q^{16} +(-0.556490 + 0.404314i) q^{17} +0.536547 q^{18} +(6.54709 - 4.75674i) q^{19} +(-2.08175 - 1.51248i) q^{21} +(2.23275 + 1.62219i) q^{22} +(0.115186 - 0.354506i) q^{23} -1.99173 q^{24} -0.791365 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.56419 + 2.58954i) q^{28} +(-0.0288595 - 0.0209676i) q^{29} +(3.63169 - 2.63858i) q^{31} +5.24733 q^{32} +(4.16133 - 3.02338i) q^{33} +(0.114049 + 0.351005i) q^{34} +(-0.529073 + 1.62832i) q^{36} +(0.590022 + 1.81590i) q^{37} +(-1.34178 - 4.12957i) q^{38} +(-0.455776 + 1.40274i) q^{39} +(-1.59739 - 4.91625i) q^{41} +(-1.11695 + 0.811515i) q^{42} -11.4506 q^{43} +(-7.12469 + 5.17639i) q^{44} +(-0.161802 - 0.117556i) q^{46} +(-6.89374 - 5.00860i) q^{47} +(0.727915 - 2.24029i) q^{48} -0.378747 q^{49} +0.687859 q^{51} +(0.780343 - 2.40165i) q^{52} +(7.38080 + 5.36247i) q^{53} +(-0.434076 - 0.315374i) q^{54} +(4.14627 - 3.01244i) q^{56} -8.09265 q^{57} +(-0.0154845 + 0.0112501i) q^{58} +(-0.0544457 - 0.167567i) q^{59} +(-1.98127 + 6.09772i) q^{61} +(-0.744289 - 2.29069i) q^{62} +(0.795156 + 2.44724i) q^{63} +(-0.585811 + 1.80294i) q^{64} +(-0.852834 - 2.62475i) q^{66} +(-0.0675025 + 0.0490435i) q^{67} -1.17770 q^{68} +(-0.301561 + 0.219097i) q^{69} +(-9.83589 - 7.14619i) q^{71} +(1.61134 + 1.17071i) q^{72} +(-3.72421 + 11.4619i) q^{73} +1.02446 q^{74} +13.8556 q^{76} +(-4.09004 + 12.5878i) q^{77} +(0.640228 + 0.465153i) q^{78} +(-4.01019 - 2.91357i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.77354 q^{82} +(-7.57501 + 5.50356i) q^{83} +(-1.36140 - 4.18996i) q^{84} +(-1.89853 + 5.84308i) q^{86} +(0.0110233 + 0.0339264i) q^{87} +(3.16582 + 9.74340i) q^{88} +(-0.00380677 + 0.0117160i) q^{89} +(-1.17279 - 3.60949i) q^{91} +(0.516308 - 0.375120i) q^{92} -4.48902 q^{93} +(-3.69882 + 2.68735i) q^{94} +(-4.24518 - 3.08430i) q^{96} +(6.16504 + 4.47917i) q^{97} +(-0.0627970 + 0.193269i) q^{98} -5.14369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.165802	−	0.510286i	0.117240	−	0.360827i	−0.875168	−	0.483820i	$-0.839249\pi$
$2$	0.165802	−	0.510286i	0.117240	−	0.360827i	0.992408	+	0.122993i	$0.0392491\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	1.38513	+	1.00636i	0.692566	+	0.503179i
$5$		0			0
$5$		0			0
$6$	−0.434076	+	0.315374i	−0.177211	+	0.128751i
$7$	2.57318			0.972570			0.486285	−	0.873800i	$-0.338352\pi$
$7$	2.57318			0.972570			0.486285	+	0.873800i	$0.338352\pi$
$8$	1.61134	−	1.17071i	0.569695	−	0.413907i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.58949	+	4.89194i	−0.479248	+	1.47497i	0.360893	+	0.932607i	$0.382472\pi$
$11$	−1.58949	+	4.89194i	−0.479248	+	1.47497i	−0.840141	+	0.542368i	$0.817528\pi$
$12$	−0.529073	−	1.62832i	−0.152730	−	0.470056i
$13$	−0.455776	−	1.40274i	−0.126410	−	0.389049i	0.867746	−	0.497009i	$-0.165568\pi$
$13$	−0.455776	−	1.40274i	−0.126410	−	0.389049i	−0.994155	+	0.107960i	$0.965568\pi$
$14$	0.426639	−	1.31306i	0.114024	−	0.350930i
$15$		0			0
$16$	0.727915	+	2.24029i	0.181979	+	0.560073i
$17$	−0.556490	+	0.404314i	−0.134969	+	0.0980605i	−0.653221	−	0.757167i	$-0.726583\pi$
$17$	−0.556490	+	0.404314i	−0.134969	+	0.0980605i	0.518252	+	0.855228i	$0.326583\pi$
$18$	0.536547			0.126465
$19$	6.54709	−	4.75674i	1.50201	−	1.09127i	0.532432	−	0.846473i	$-0.321278\pi$
$19$	6.54709	−	4.75674i	1.50201	−	1.09127i	0.969574	−	0.244799i	$-0.0787219\pi$
$20$		0			0
$21$	−2.08175	−	1.51248i	−0.454274	−	0.330050i
$22$	2.23275	+	1.62219i	0.476024	+	0.345852i
$23$	0.115186	−	0.354506i	0.0240180	−	0.0739197i	−0.938329	−	0.345743i	$-0.887627\pi$
$23$	0.115186	−	0.354506i	0.0240180	−	0.0739197i	0.962347	+	0.271824i	$0.0876268\pi$
$24$	−1.99173			−0.406559
$25$		0			0
$26$	−0.791365			−0.155200
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	3.56419	+	2.58954i	0.673569	+	0.489377i
$29$	−0.0288595	−	0.0209676i	−0.00535907	−	0.00389359i	0.585102	−	0.810959i	$-0.301054\pi$
$29$	−0.0288595	−	0.0209676i	−0.00535907	−	0.00389359i	−0.590462	+	0.807066i	$0.701054\pi$
$30$		0			0
$31$	3.63169	−	2.63858i	0.652272	−	0.473903i	−0.211773	−	0.977319i	$-0.567924\pi$
$31$	3.63169	−	2.63858i	0.652272	−	0.473903i	0.864044	+	0.503416i	$0.167924\pi$
$32$	5.24733			0.927606
$33$	4.16133	−	3.02338i	0.724395	−	0.526304i
$34$	0.114049	+	0.351005i	0.0195592	+	0.0601969i
$35$		0			0
$36$	−0.529073	+	1.62832i	−0.0881789	+	0.271387i
$37$	0.590022	+	1.81590i	0.0969991	+	0.298532i	0.987770	−	0.155921i	$-0.0498346\pi$
$37$	0.590022	+	1.81590i	0.0969991	+	0.298532i	−0.890770	+	0.454454i	$0.849835\pi$
$38$	−1.34178	−	4.12957i	−0.217665	−	0.669905i
$39$	−0.455776	+	1.40274i	−0.0729826	+	0.224617i
$40$		0			0
$41$	−1.59739	−	4.91625i	−0.249470	−	0.767789i	−0.994869	−	0.101171i	$-0.967741\pi$
$41$	−1.59739	−	4.91625i	−0.249470	−	0.767789i	0.745399	−	0.666618i	$-0.232259\pi$
$42$	−1.11695	+	0.811515i	−0.172350	+	0.125219i
$43$	−11.4506			−1.74620			−0.873099	−	0.487543i	$-0.837893\pi$
$43$	−11.4506			−1.74620			−0.873099	+	0.487543i	$0.837893\pi$
$44$	−7.12469	+	5.17639i	−1.07409	+	0.780370i
$45$		0			0
$46$	−0.161802	−	0.117556i	−0.0238564	−	0.0173327i
$47$	−6.89374	−	5.00860i	−1.00556	−	0.730579i	−0.0422836	−	0.999106i	$-0.513463\pi$
$47$	−6.89374	−	5.00860i	−1.00556	−	0.730579i	−0.963272	+	0.268527i	$0.913463\pi$
$48$	0.727915	−	2.24029i	0.105065	−	0.323358i
$49$	−0.378747			−0.0541067
$50$		0			0
$51$	0.687859			0.0963196
$52$	0.780343	−	2.40165i	0.108214	−	0.333049i
$53$	7.38080	+	5.36247i	1.01383	+	0.736592i	0.965009	−	0.262216i	$-0.0844533\pi$
$53$	7.38080	+	5.36247i	1.01383	+	0.736592i	0.0488220	+	0.998807i	$0.484453\pi$
$54$	−0.434076	−	0.315374i	−0.0590702	−	0.0429170i
$55$		0			0
$56$	4.14627	−	3.01244i	0.554068	−	0.402554i
$57$	−8.09265			−1.07190
$58$	−0.0154845	+	0.0112501i	−0.00203321	+	0.00147721i
$59$	−0.0544457	−	0.167567i	−0.00708822	−	0.0218153i	0.947450	−	0.319904i	$-0.103651\pi$
$59$	−0.0544457	−	0.167567i	−0.00708822	−	0.0218153i	−0.954538	+	0.298089i	$0.903651\pi$
$60$		0			0
$61$	−1.98127	+	6.09772i	−0.253676	+	0.780733i	0.740412	+	0.672153i	$0.234630\pi$
$61$	−1.98127	+	6.09772i	−0.253676	+	0.780733i	−0.994088	+	0.108580i	$0.965370\pi$
$62$	−0.744289	−	2.29069i	−0.0945248	−	0.290918i
$63$	0.795156	+	2.44724i	0.100180	+	0.308323i
$64$	−0.585811	+	1.80294i	−0.0732263	+	0.225367i
$65$		0			0
$66$	−0.852834	−	2.62475i	−0.104977	−	0.323085i
$67$	−0.0675025	+	0.0490435i	−0.00824675	+	0.00599161i	−0.591901	−	0.806011i	$-0.701622\pi$
$67$	−0.0675025	+	0.0490435i	−0.00824675	+	0.00599161i	0.583654	+	0.812002i	$0.301622\pi$
$68$	−1.17770			−0.142817
$69$	−0.301561	+	0.219097i	−0.0363037	+	0.0263762i
$70$		0			0
$71$	−9.83589	−	7.14619i	−1.16731	−	0.848097i	−0.176622	−	0.984279i	$-0.556517\pi$
$71$	−9.83589	−	7.14619i	−1.16731	−	0.848097i	−0.990684	+	0.136182i	$0.956517\pi$
$72$	1.61134	+	1.17071i	0.189898	+	0.137969i
$73$	−3.72421	+	11.4619i	−0.435886	+	1.34152i	0.456290	+	0.889831i	$0.349178\pi$
$73$	−3.72421	+	11.4619i	−0.435886	+	1.34152i	−0.892176	+	0.451688i	$0.850822\pi$
$74$	1.02446			0.119091
$75$		0			0
$76$	13.8556			1.58934
$77$	−4.09004	+	12.5878i	−0.466103	+	1.43452i
$78$	0.640228	+	0.465153i	0.0724916	+	0.0526682i
$79$	−4.01019	−	2.91357i	−0.451182	−	0.327803i	0.338881	−	0.940829i	$-0.389952\pi$
$79$	−4.01019	−	2.91357i	−0.451182	−	0.327803i	−0.790062	+	0.613027i	$0.789952\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.77354			−0.306287
$83$	−7.57501	+	5.50356i	−0.831465	+	0.604095i	−0.919973	−	0.391981i	$-0.871790\pi$
$83$	−7.57501	+	5.50356i	−0.831465	+	0.604095i	0.0885084	+	0.996075i	$0.471790\pi$
$84$	−1.36140	−	4.18996i	−0.148541	−	0.457162i
$85$		0			0
$86$	−1.89853	+	5.84308i	−0.204724	+	0.630075i
$87$	0.0110233	+	0.0339264i	0.00118183	+	0.00363729i
$88$	3.16582	+	9.74340i	0.337478	+	1.03865i
$89$	−0.00380677	+	0.0117160i	−0.000403517	+	0.00124190i	−0.951258	−	0.308396i	$-0.900208\pi$
$89$	−0.00380677	+	0.0117160i	−0.000403517	+	0.00124190i	0.950855	+	0.309638i	$0.100208\pi$
$90$		0			0
$91$	−1.17279	−	3.60949i	−0.122942	−	0.378377i
$92$	0.516308	−	0.375120i	0.0538288	−	0.0391089i
$93$	−4.48902			−0.465490
$94$	−3.69882	+	2.68735i	−0.381504	+	0.277179i
$95$		0			0
$96$	−4.24518	−	3.08430i	−0.433272	−	0.314790i
$97$	6.16504	+	4.47917i	0.625965	+	0.454790i	0.855000	−	0.518628i	$-0.173557\pi$
$97$	6.16504	+	4.47917i	0.625965	+	0.454790i	−0.229035	+	0.973418i	$0.573557\pi$
$98$	−0.0627970	+	0.193269i	−0.00634345	+	0.0195231i
$99$	−5.14369			−0.516960
$100$		0			0
$101$	8.27518			0.823411			0.411706	−	0.911317i	$-0.364933\pi$
$101$	8.27518			0.823411			0.411706	+	0.911317i	$0.364933\pi$
$102$	0.114049	−	0.351005i	0.0112925	−	0.0347547i
$103$	−8.40247	−	6.10475i	−0.827920	−	0.601519i	0.0910504	−	0.995846i	$-0.470978\pi$
$103$	−8.40247	−	6.10475i	−0.827920	−	0.601519i	−0.918970	+	0.394328i	$0.870978\pi$
$104$	−2.37660	−	1.72670i	−0.233045	−	0.169317i
$105$		0			0
$106$	3.96015	−	2.87722i	0.384643	−	0.279460i
$107$	−12.2737			−1.18655			−0.593274	−	0.805001i	$-0.702165\pi$
$107$	−12.2737			−1.18655			−0.593274	+	0.805001i	$0.702165\pi$
$108$	1.38513	−	1.00636i	0.133284	−	0.0968368i
$109$	−1.30684	−	4.02203i	−0.125172	−	0.385241i	0.868760	−	0.495233i	$-0.164917\pi$
$109$	−1.30684	−	4.02203i	−0.125172	−	0.385241i	−0.993932	+	0.109992i	$0.964917\pi$
$110$		0			0
$111$	0.590022	−	1.81590i	0.0560024	−	0.172358i
$112$	1.87305	+	5.76467i	0.176987	+	0.544710i
$113$	−5.67623	−	17.4696i	−0.533974	−	1.64340i	−0.745855	−	0.666109i	$-0.767959\pi$
$113$	−5.67623	−	17.4696i	−0.533974	−	1.64340i	0.211880	−	0.977296i	$-0.432041\pi$
$114$	−1.34178	+	4.12957i	−0.125669	+	0.386770i
$115$		0			0
$116$	−0.0188733	−	0.0580859i	−0.00175234	−	0.00539314i
$117$	1.19324	−	0.866938i	0.110315	−	0.0801485i
$118$	−0.0945341			−0.00870257
$119$	−1.43195	+	1.04037i	−0.131267	+	0.0953707i
$120$		0			0
$121$	−12.5054	−	9.08571i	−1.13685	−	0.825974i
$122$	2.78309	+	2.02203i	0.251969	+	0.183066i
$123$	−1.59739	+	4.91625i	−0.144031	+	0.443283i
$124$	7.68573			0.690199
$125$		0			0
$126$	1.38063			0.122996
$127$	0.106766	−	0.328591i	0.00947391	−	0.0291577i	−0.946208	−	0.323560i	$-0.895120\pi$
$127$	0.106766	−	0.328591i	0.00947391	−	0.0291577i	0.955682	+	0.294402i	$0.0951204\pi$
$128$	9.31325	+	6.76647i	0.823182	+	0.598077i
$129$	9.26372	+	6.73048i	0.815625	+	0.592586i
$130$		0			0
$131$	3.69438	−	2.68413i	0.322780	−	0.234513i	−0.414581	−	0.910012i	$-0.636072\pi$
$131$	3.69438	−	2.68413i	0.322780	−	0.234513i	0.737361	+	0.675499i	$0.236072\pi$
$132$	8.80660			0.766516
$133$	16.8468	−	12.2400i	1.46081	−	1.06134i
$134$	0.0138342	+	0.0425771i	0.00119509	+	0.00367810i
$135$		0			0
$136$	−0.423362	+	1.30297i	−0.0363030	+	0.111729i
$137$	−1.48870	−	4.58174i	−0.127188	−	0.391445i	0.867105	−	0.498125i	$-0.165978\pi$
$137$	−1.48870	−	4.58174i	−0.127188	−	0.391445i	−0.994293	+	0.106680i	$0.965978\pi$
$138$	0.0618027	+	0.190209i	0.00526100	+	0.0161917i
$139$	−1.15595	+	3.55766i	−0.0980468	+	0.301757i	−0.988036	−	0.154225i	$-0.950712\pi$
$139$	−1.15595	+	3.55766i	−0.0980468	+	0.301757i	0.889989	+	0.455982i	$0.150712\pi$
$140$		0			0
$141$	2.63318	+	8.10408i	0.221753	+	0.682487i
$142$	−5.27742	+	3.83427i	−0.442871	+	0.321765i
$143$	7.58655			0.634419
$144$	−1.90570	+	1.38458i	−0.158809	+	0.115381i
$145$		0			0
$146$	5.23139	+	3.80083i	0.432953	+	0.314559i
$147$	0.306412	+	0.222622i	0.0252725	+	0.0183615i
$148$	−1.01019	+	3.10904i	−0.0830369	+	0.255561i
$149$	8.64621			0.708325			0.354163	−	0.935184i	$-0.384766\pi$
$149$	8.64621			0.708325			0.354163	+	0.935184i	$0.384766\pi$
$150$		0			0
$151$	−1.24898			−0.101641			−0.0508205	−	0.998708i	$-0.516184\pi$
$151$	−1.24898			−0.101641			−0.0508205	+	0.998708i	$0.516184\pi$
$152$	4.98084	−	15.3295i	0.404000	−	1.24338i
$153$	−0.556490	−	0.404314i	−0.0449895	−	0.0326868i
$154$	5.74527	+	4.17418i	0.462967	+	0.336365i
$155$		0			0
$156$	−2.04296	+	1.48430i	−0.163568	+	0.118839i
$157$	3.86574			0.308520			0.154260	−	0.988030i	$-0.450701\pi$
$157$	3.86574			0.308520			0.154260	+	0.988030i	$0.450701\pi$
$158$	−2.15166	+	1.56327i	−0.171176	+	0.124367i
$159$	−2.81922	−	8.67665i	−0.223578	−	0.688103i
$160$		0			0
$161$	0.296394	−	0.912208i	0.0233592	−	0.0718921i
$162$	0.165802	+	0.510286i	0.0130266	+	0.0400919i
$163$	−2.15512	−	6.63277i	−0.168802	−	0.519519i	0.830494	−	0.557027i	$-0.188058\pi$
$163$	−2.15512	−	6.63277i	−0.168802	−	0.519519i	−0.999296	+	0.0375081i	$0.988058\pi$
$164$	2.73491	−	8.41719i	0.213561	−	0.657272i
$165$		0			0
$166$	1.55244	+	4.77793i	0.120493	+	0.370839i
$167$	12.9114	−	9.38069i	0.999115	−	0.725900i	0.0372169	−	0.999307i	$-0.488151\pi$
$167$	12.9114	−	9.38069i	0.999115	−	0.725900i	0.961898	+	0.273408i	$0.0881507\pi$
$168$	−5.12507			−0.395407
$169$	8.75729	−	6.36254i	0.673637	−	0.489426i
$170$		0			0
$171$	6.54709	+	4.75674i	0.500669	+	0.363757i
$172$	−15.8606	−	11.5234i	−1.20936	−	0.878649i
$173$	−2.37118	+	7.29774i	−0.180277	+	0.554837i	−0.999835	−	0.0181597i	$-0.994219\pi$
$173$	−2.37118	+	7.29774i	−0.180277	+	0.554837i	0.819558	+	0.572997i	$0.194219\pi$
$174$	0.0191399			0.00145099
$175$		0			0
$176$	−12.1164			−0.913306
$177$	−0.0544457	+	0.167567i	−0.00409239	+	0.0125951i
$178$	0.00534737	+	0.00388509i	0.000400802	+	0.000291200i
$179$	−8.58312	−	6.23600i	−0.641532	−	0.466100i	0.218844	−	0.975760i	$-0.429771\pi$
$179$	−8.58312	−	6.23600i	−0.641532	−	0.466100i	−0.860376	+	0.509659i	$0.829771\pi$
$180$		0			0
$181$	−12.2223	+	8.88005i	−0.908480	+	0.660049i	−0.940630	−	0.339434i	$-0.889764\pi$
$181$	−12.2223	+	8.88005i	−0.908480	+	0.660049i	0.0321503	+	0.999483i	$0.489764\pi$
$182$	−2.03633			−0.150942
$183$	5.18703	−	3.76860i	0.383436	−	0.278583i
$184$	−0.229419	−	0.706079i	−0.0169130	−	0.0520528i
$185$		0			0
$186$	−0.744289	+	2.29069i	−0.0545739	+	0.167961i
$187$	−1.09334	−	3.36497i	−0.0799532	−	0.246071i
$188$	−4.50831	−	13.8751i	−0.328802	−	1.01195i
$189$	0.795156	−	2.44724i	0.0578391	−	0.178010i
$190$		0			0
$191$	3.78359	+	11.6447i	0.273771	+	0.842580i	0.989542	+	0.144245i	$0.0460754\pi$
$191$	3.78359	+	11.6447i	0.273771	+	0.842580i	−0.715771	+	0.698335i	$0.753925\pi$
$192$	1.53367	−	1.11428i	0.110683	−	0.0804161i
$193$	14.2421			1.02517			0.512585	−	0.858637i	$-0.328688\pi$
$193$	14.2421			1.02517			0.512585	+	0.858637i	$0.328688\pi$
$194$	3.30783	−	2.40328i	0.237489	−	0.172546i
$195$		0			0
$196$	−0.524614	−	0.381154i	−0.0374724	−	0.0272253i
$197$	14.3591	+	10.4325i	1.02304	+	0.743286i	0.966905	−	0.255137i	$-0.0821207\pi$
$197$	14.3591	+	10.4325i	1.02304	+	0.743286i	0.0561399	+	0.998423i	$0.482121\pi$
$198$	−0.852834	+	2.62475i	−0.0606083	+	0.186533i
$199$	−18.9550			−1.34369			−0.671843	−	0.740693i	$-0.734497\pi$
$199$	−18.9550			−1.34369			−0.671843	+	0.740693i	$0.734497\pi$
$200$		0			0
$201$	0.0834377			0.00588524
$202$	1.37204	−	4.22271i	0.0965366	−	0.297109i
$203$	−0.0742606	−	0.0539535i	−0.00521207	−	0.00378679i
$204$	0.952776	+	0.692232i	0.0667077	+	0.0484660i
$205$		0			0
$206$	−4.50832	+	3.27548i	−0.314109	+	0.228214i
$207$	0.372750			0.0259079
$208$	2.81077	−	2.04214i	0.194892	−	0.141597i
$209$	12.8632	+	39.5888i	0.889764	+	2.73841i
$210$		0			0
$211$	−3.33022	+	10.2494i	−0.229262	+	0.705596i	0.768569	+	0.639767i	$0.220969\pi$
$211$	−3.33022	+	10.2494i	−0.229262	+	0.705596i	−0.997831	+	0.0658288i	$0.979031\pi$
$212$	4.82683	+	14.8555i	0.331508	+	1.02028i
$213$	3.75698	+	11.5628i	0.257424	+	0.792269i
$214$	−2.03501	+	6.26312i	−0.139111	+	0.428138i
$215$		0			0
$216$	−0.615477	−	1.89424i	−0.0418779	−	0.128887i
$217$	9.34500	−	6.78954i	0.634380	−	0.460904i
$218$	−2.26907			−0.153681
$219$	9.75012	−	7.08387i	0.658852	−	0.478684i
$220$		0			0
$221$	0.820780	+	0.596332i	0.0552116	+	0.0401136i
$222$	−0.828803	−	0.602161i	−0.0556256	−	0.0404144i
$223$	8.51983	−	26.2213i	0.570530	−	1.75591i	−0.0803900	−	0.996763i	$-0.525617\pi$
$223$	8.51983	−	26.2213i	0.570530	−	1.75591i	0.650920	−	0.759147i	$-0.274383\pi$
$224$	13.5023			0.902162
$225$		0			0
$226$	−9.85565			−0.655588
$227$	−1.23057	+	3.78731i	−0.0816758	+	0.251372i	−0.983553	−	0.180620i	$-0.942189\pi$
$227$	−1.23057	+	3.78731i	−0.0816758	+	0.251372i	0.901877	+	0.431993i	$0.142189\pi$
$228$	−11.2094	−	8.14410i	−0.742360	−	0.539356i
$229$	−9.68373	−	7.03564i	−0.639919	−	0.464928i	0.219903	−	0.975522i	$-0.429426\pi$
$229$	−9.68373	−	7.03564i	−0.639919	−	0.464928i	−0.859822	+	0.510593i	$0.829426\pi$
$230$		0			0
$231$	10.7079	−	7.77971i	0.704525	−	0.511867i
$232$	−0.0710494			−0.00466462
$233$	−17.0849	+	12.4129i	−1.11927	+	0.813197i	−0.984098	−	0.177625i	$-0.943159\pi$
$233$	−17.0849	+	12.4129i	−1.11927	+	0.813197i	−0.135172	+	0.990822i	$0.543159\pi$
$234$	−0.244545	−	0.752633i	−0.0159864	−	0.0492012i
$235$		0			0
$236$	0.0932174	−	0.286894i	0.00606793	−	0.0186752i
$237$	1.53176	+	4.71426i	0.0994983	+	0.306224i
$238$	0.293467	+	0.903200i	0.0190227	+	0.0585457i
$239$	8.09778	−	24.9224i	0.523802	−	1.61210i	−0.242871	−	0.970059i	$-0.578089\pi$
$239$	8.09778	−	24.9224i	0.523802	−	1.61210i	0.766673	−	0.642038i	$-0.221911\pi$
$240$		0			0
$241$	−2.52607	−	7.77443i	−0.162718	−	0.500795i	0.836143	−	0.548512i	$-0.184805\pi$
$241$	−2.52607	−	7.77443i	−0.162718	−	0.500795i	−0.998861	+	0.0477169i	$0.984805\pi$
$242$	−6.70974	+	4.87491i	−0.431318	+	0.313371i
$243$	1.00000			0.0641500
$244$	−8.88081	+	6.45228i	−0.568535	+	0.413065i
$245$		0			0
$246$	2.24384	+	1.63025i	0.143062	+	0.103941i
$247$	−9.65646	−	7.01583i	−0.614426	−	0.446406i
$248$	2.76289	−	8.50330i	0.175444	−	0.539960i
$249$	9.36322			0.593370
$250$		0			0
$251$	24.8145			1.56628			0.783139	−	0.621847i	$-0.213618\pi$
$251$	24.8145			1.56628			0.783139	+	0.621847i	$0.213618\pi$
$252$	−1.36140	+	4.18996i	−0.0857602	+	0.263943i
$253$	1.55114	+	1.12697i	0.0975191	+	0.0708518i
$254$	−0.149973	−	0.108962i	−0.00941017	−	0.00683689i
$255$		0			0
$256$	1.92965	−	1.40197i	0.120603	−	0.0876232i
$257$	24.2995			1.51576			0.757882	−	0.652392i	$-0.226234\pi$
$257$	24.2995			1.51576			0.757882	+	0.652392i	$0.226234\pi$
$258$	4.97042	−	3.61122i	0.309445	−	0.224825i
$259$	1.51823	+	4.67264i	0.0943384	+	0.290344i
$260$		0			0
$261$	0.0110233	−	0.0339264i	0.000682328	−	0.00209999i
$262$	−0.757137	−	2.33023i	−0.0467761	−	0.143962i
$263$	2.63366	+	8.10556i	0.162398	+	0.499810i	0.998835	−	0.0482528i	$-0.0153653\pi$
$263$	2.63366	+	8.10556i	0.162398	+	0.499810i	−0.836437	+	0.548063i	$0.815365\pi$
$264$	3.16582	−	9.74340i	0.194843	−	0.599665i
$265$		0			0
$266$	−3.45264	−	10.6261i	−0.211695	−	0.651530i
$267$	0.00996627	−	0.00724092i	0.000609926	−	0.000443137i
$268$	−0.142855			−0.00872627
$269$	−2.08979	+	1.51832i	−0.127417	+	0.0925737i	−0.649668	−	0.760218i	$-0.725092\pi$
$269$	−2.08979	+	1.51832i	−0.127417	+	0.0925737i	0.522252	+	0.852791i	$0.325092\pi$
$270$		0			0
$271$	10.9940	+	7.98759i	0.667837	+	0.485212i	0.869300	−	0.494284i	$-0.164570\pi$
$271$	10.9940	+	7.98759i	0.667837	+	0.485212i	−0.201464	+	0.979496i	$0.564570\pi$
$272$	−1.31086	−	0.952393i	−0.0794824	−	0.0577473i
$273$	−1.17279	+	3.60949i	−0.0709807	+	0.218456i
$274$	−2.58483			−0.156155
$275$		0			0
$276$	−0.638192			−0.0384146
$277$	2.82434	−	8.69242i	0.169698	−	0.522277i	−0.829654	−	0.558278i	$-0.811462\pi$
$277$	2.82434	−	8.69242i	0.169698	−	0.522277i	0.999352	+	0.0360015i	$0.0114621\pi$
$278$	1.62377	+	1.17974i	0.0973870	+	0.0707558i
$279$	3.63169	+	2.63858i	0.217424	+	0.157968i
$280$		0			0
$281$	−8.42195	+	6.11890i	−0.502411	+	0.365023i	−0.809937	−	0.586517i	$-0.800499\pi$
$281$	−8.42195	+	6.11890i	−0.502411	+	0.365023i	0.307526	+	0.951540i	$0.400499\pi$
$282$	4.57199			0.272258
$283$	−3.89611	+	2.83069i	−0.231600	+	0.168267i	−0.697533	−	0.716553i	$-0.745719\pi$
$283$	−3.89611	+	2.83069i	−0.231600	+	0.168267i	0.465933	+	0.884820i	$0.345719\pi$
$284$	−6.43238	−	19.7968i	−0.381692	−	1.17473i
$285$		0			0
$286$	1.25787	−	3.87131i	0.0743791	−	0.228915i
$287$	−4.11036	−	12.6504i	−0.242627	−	0.746729i
$288$	1.62151	+	4.99051i	0.0955486	+	0.294068i
$289$	−5.10708	+	15.7180i	−0.300416	+	0.924586i
$290$		0			0
$291$	−2.35484	−	7.24744i	−0.138043	−	0.424853i
$292$	−16.6933	+	12.1284i	−0.976904	+	0.709762i
$293$	24.4506			1.42842			0.714210	−	0.699932i	$-0.246786\pi$
$293$	24.4506			1.42842			0.714210	+	0.699932i	$0.246786\pi$
$294$	0.164405	−	0.119447i	0.00958827	−	0.00696629i
$295$		0			0
$296$	3.07661	+	2.23529i	0.178825	+	0.129924i
$297$	4.16133	+	3.02338i	0.241465	+	0.175435i
$298$	1.43356	−	4.41205i	0.0830439	−	0.255583i
$299$	−0.549778			−0.0317945
$300$		0			0
$301$	−29.4644			−1.69830
$302$	−0.207084	+	0.637340i	−0.0119164	+	0.0366748i
$303$	−6.69476	−	4.86403i	−0.384604	−	0.279431i
$304$	15.4222	+	11.2049i	0.884524	+	0.642645i
$305$		0			0
$306$	−0.298583	+	0.216933i	−0.0170689	+	0.0124012i
$307$	−9.51655			−0.543138			−0.271569	−	0.962419i	$-0.587543\pi$
$307$	−9.51655			−0.543138			−0.271569	+	0.962419i	$0.587543\pi$
$308$	−18.3331	+	13.3198i	−1.04463	+	0.758965i
$309$	3.20946	+	9.87769i	0.182580	+	0.561922i
$310$		0			0
$311$	7.71967	−	23.7587i	0.437742	−	1.34723i	−0.452508	−	0.891760i	$-0.649471\pi$
$311$	7.71967	−	23.7587i	0.437742	−	1.34723i	0.890250	−	0.455471i	$-0.150529\pi$
$312$	0.907781	+	2.79386i	0.0513930	+	0.158171i
$313$	3.05359	+	9.39797i	0.172599	+	0.531205i	0.999516	−	0.0311197i	$-0.00990729\pi$
$313$	3.05359	+	9.39797i	0.172599	+	0.531205i	−0.826917	+	0.562324i	$0.809907\pi$
$314$	0.640948	−	1.97264i	0.0361708	−	0.111322i
$315$		0			0
$316$	−2.62255	−	8.07137i	−0.147530	−	0.454050i
$317$	−20.0078	+	14.5365i	−1.12375	+	0.816453i	−0.984773	−	0.173842i	$-0.944382\pi$
$317$	−20.0078	+	14.5365i	−1.12375	+	0.816453i	−0.138978	+	0.990296i	$0.544382\pi$
$318$	−4.89501			−0.274499
$319$	0.148444	−	0.107851i	0.00831128	−	0.00603850i
$320$		0			0
$321$	9.92967	+	7.21433i	0.554220	+	0.402664i
$322$	−0.416345	−	0.302492i	−0.0232020	−	0.0168572i
$323$	−1.72018	+	5.29416i	−0.0957132	+	0.294575i
$324$	−1.71212			−0.0951176
$325$		0			0
$326$	−3.74194			−0.207247
$327$	−1.30684	+	4.02203i	−0.0722683	+	0.222419i
$328$	−8.32941	−	6.05167i	−0.459915	−	0.334148i
$329$	−17.7388	−	12.8880i	−0.977974	−	0.710540i
$330$		0			0
$331$	−0.872336	+	0.633789i	−0.0479479	+	0.0348362i	−0.611501	−	0.791244i	$-0.709434\pi$
$331$	−0.872336	+	0.633789i	−0.0479479	+	0.0348362i	0.563553	+	0.826080i	$0.309434\pi$
$332$	−16.0309			−0.879812
$333$	−1.54470	+	1.12229i	−0.0846490	+	0.0615011i
$334$	−2.64610	−	8.14386i	−0.144788	−	0.445612i
$335$		0			0
$336$	1.87305	−	5.76467i	0.102184	−	0.314489i
$337$	−4.34507	−	13.3727i	−0.236691	−	0.728460i	−0.996893	−	0.0787727i	$-0.974900\pi$
$337$	−4.34507	−	13.3727i	−0.236691	−	0.728460i	0.760202	−	0.649687i	$-0.225100\pi$
$338$	−1.79474	−	5.52365i	−0.0976211	−	0.300447i
$339$	−5.67623	+	17.4696i	−0.308290	+	0.948820i
$340$		0			0
$341$	7.13524	+	21.9600i	0.386395	+	1.18920i
$342$	3.51282	−	2.55222i	0.189952	−	0.138008i
$343$	−18.9868			−1.02519
$344$	−18.4508	+	13.4053i	−0.994799	+	0.722764i
$345$		0			0
$346$	3.33079	+	2.41996i	0.179064	+	0.130098i
$347$	4.60804	+	3.34793i	0.247372	+	0.179726i	0.704561	−	0.709643i	$-0.251144\pi$
$347$	4.60804	+	3.34793i	0.247372	+	0.179726i	−0.457189	+	0.889369i	$0.651144\pi$
$348$	−0.0188733	+	0.0580859i	−0.00101171	+	0.00311373i
$349$	−28.4950			−1.52530			−0.762651	−	0.646810i	$-0.776103\pi$
$349$	−28.4950			−1.52530			−0.762651	+	0.646810i	$0.776103\pi$
$350$		0			0
$351$	−1.47492			−0.0787256
$352$	−8.34056	+	25.6696i	−0.444554	+	1.36820i
$353$	10.3276	+	7.50341i	0.549681	+	0.399366i	0.827668	−	0.561218i	$-0.189667\pi$
$353$	10.3276	+	7.50341i	0.549681	+	0.399366i	−0.277987	+	0.960585i	$0.589667\pi$
$354$	0.0764797	+	0.0555658i	0.00406485	+	0.00295329i
$355$		0			0
$356$	−0.0170634	+	0.0123973i	−0.000904359	+	0.000657056i
$357$	1.76999			0.0936776
$358$	−4.60524	+	3.34591i	−0.243395	+	0.176837i
$359$	−1.39620	−	4.29707i	−0.0736888	−	0.226791i	0.907428	−	0.420208i	$-0.138043\pi$
$359$	−1.39620	−	4.29707i	−0.0736888	−	0.226791i	−0.981117	+	0.193417i	$0.938043\pi$
$360$		0			0
$361$	14.3665	−	44.2156i	0.756132	−	2.32714i
$362$	2.50488	+	7.70923i	0.131654	+	0.405188i
$363$	4.77664	+	14.7010i	0.250709	+	0.771602i
$364$	2.00796	−	6.17987i	0.105246	−	0.323913i
$365$		0			0
$366$	−1.06304	−	3.27171i	−0.0555662	−	0.171015i
$367$	2.45493	−	1.78361i	0.128146	−	0.0931039i	−0.521866	−	0.853028i	$-0.674764\pi$
$367$	2.45493	−	1.78361i	0.128146	−	0.0931039i	0.650012	+	0.759924i	$0.274764\pi$
$368$	0.878043			0.0457711
$369$	4.18201	−	3.03841i	0.217707	−	0.158173i
$370$		0			0
$371$	18.9921	+	13.7986i	0.986022	+	0.716387i
$372$	−6.21789	−	4.51756i	−0.322382	−	0.234225i
$373$	−4.74831	+	14.6138i	−0.245858	+	0.756674i	0.749636	+	0.661850i	$0.230229\pi$
$373$	−4.74831	+	14.6138i	−0.245858	+	0.756674i	−0.995494	+	0.0948232i	$0.969771\pi$
$374$	−1.89838			−0.0981626
$375$		0			0
$376$	−16.9718			−0.875252
$377$	−0.0162586	+	0.0500388i	−0.000837359	+	0.00257713i
$378$	−1.11695	−	0.811515i	−0.0574499	−	0.0417398i
$379$	−8.38117	−	6.08927i	−0.430512	−	0.312785i	0.351342	−	0.936247i	$-0.385725\pi$
$379$	−8.38117	−	6.08927i	−0.430512	−	0.312785i	−0.781853	+	0.623462i	$0.785725\pi$
$380$		0			0
$381$	−0.279516	+	0.203080i	−0.0143200	+	0.0104041i
$382$	6.56946			0.336123
$383$	−12.5289	+	9.10278i	−0.640197	+	0.465130i	−0.859918	−	0.510432i	$-0.829485\pi$
$383$	−12.5289	+	9.10278i	−0.640197	+	0.465130i	0.219721	+	0.975563i	$0.429485\pi$
$384$	−3.55734	−	10.9484i	−0.181535	−	0.558707i
$385$		0			0
$386$	2.36137	−	7.26756i	0.120191	−	0.369909i
$387$	−3.53843	−	10.8902i	−0.179868	−	0.553578i
$388$	4.03176	+	12.4085i	0.204681	+	0.629945i
$389$	−6.61139	+	20.3478i	−0.335211	+	1.03167i	0.631407	+	0.775451i	$0.282478\pi$
$389$	−6.61139	+	20.3478i	−0.335211	+	1.03167i	−0.966618	+	0.256221i	$0.917522\pi$
$390$		0			0
$391$	0.0792318	+	0.243850i	0.00400693	+	0.0123320i
$392$	−0.610289	+	0.443401i	−0.0308243	+	0.0223951i
$393$	−4.56651			−0.230350
$394$	7.70434	−	5.59753i	0.388139	−	0.282000i
$395$		0			0
$396$	−7.12469	−	5.17639i	−0.358029	−	0.260123i
$397$	10.1140	+	7.34827i	0.507608	+	0.368799i	0.811916	−	0.583775i	$-0.198425\pi$
$397$	10.1140	+	7.34827i	0.507608	+	0.368799i	−0.304307	+	0.952574i	$0.598425\pi$
$398$	−3.14278	+	9.67249i	−0.157534	+	0.484838i
$399$	−20.8238			−1.04250
$400$		0			0
$401$	−33.0478			−1.65033			−0.825164	−	0.564893i	$-0.808917\pi$
$401$	−33.0478			−1.65033			−0.825164	+	0.564893i	$0.808917\pi$
$402$	0.0138342	−	0.0425771i	0.000689985	−	0.00212355i
$403$	−5.35647	−	3.89170i	−0.266825	−	0.193860i
$404$	11.4622	+	8.32779i	0.570267	+	0.414323i
$405$		0			0
$406$	−0.0398443	+	0.0289486i	−0.00197744	+	0.00143669i
$407$	−9.82111			−0.486815
$408$	1.10837	−	0.805282i	0.0548727	−	0.0398674i
$409$	0.932426	+	2.86971i	0.0461055	+	0.141898i	0.971459	−	0.237207i	$-0.0762319\pi$
$409$	0.932426	+	2.86971i	0.0461055	+	0.141898i	−0.925354	+	0.379105i	$0.876232\pi$
$410$		0			0
$411$	−1.48870	+	4.58174i	−0.0734321	+	0.226001i
$412$	−5.49497	−	16.9118i	−0.270718	−	0.833183i
$413$	−0.140098	−	0.431179i	−0.00689379	−	0.0212169i
$414$	0.0618027	−	0.190209i	0.00303744	−	0.00934827i
$415$		0			0
$416$	−2.39161	−	7.36062i	−0.117258	−	0.360884i
$417$	3.02633	−	2.19876i	0.148200	−	0.107674i
$418$	22.3343			1.09241
$419$	−5.75511	+	4.18133i	−0.281156	+	0.204272i	−0.719421	−	0.694574i	$-0.755593\pi$
$419$	−5.75511	+	4.18133i	−0.281156	+	0.204272i	0.438266	+	0.898845i	$0.355593\pi$
$420$		0			0
$421$	17.6826	+	12.8472i	0.861798	+	0.626133i	0.928373	−	0.371649i	$-0.121207\pi$
$421$	17.6826	+	12.8472i	0.861798	+	0.626133i	−0.0665758	+	0.997781i	$0.521207\pi$
$422$	4.67796	+	3.39873i	0.227719	+	0.165448i
$423$	2.63318	−	8.10408i	0.128029	−	0.394034i
$424$	18.1709			0.882455
$425$		0			0
$426$	6.52325			0.316052
$427$	−5.09816	+	15.6905i	−0.246717	+	0.759318i
$428$	−17.0008	−	12.3518i	−0.821763	−	0.597045i
$429$	−6.13764	−	4.45926i	−0.296328	−	0.215295i
$430$		0			0
$431$	−3.23115	+	2.34757i	−0.155639	+	0.113078i	−0.662879	−	0.748726i	$-0.730666\pi$
$431$	−3.23115	+	2.34757i	−0.155639	+	0.113078i	0.507240	+	0.861805i	$0.330666\pi$
$432$	2.35558			0.113333
$433$	20.3802	−	14.8071i	0.979410	−	0.711583i	0.0218335	−	0.999762i	$-0.493050\pi$
$433$	20.3802	−	14.8071i	0.979410	−	0.711583i	0.957577	+	0.288178i	$0.0930496\pi$
$434$	−1.91519	−	5.89435i	−0.0919321	−	0.282938i
$435$		0			0
$436$	2.23746	−	6.88620i	0.107155	−	0.329789i
$437$	−0.932161	−	2.86890i	−0.0445913	−	0.137238i
$438$	−1.99822	−	6.14987i	−0.0954784	−	0.293852i
$439$	−0.529997	+	1.63116i	−0.0252954	+	0.0778511i	−0.962907	−	0.269833i	$-0.913032\pi$
$439$	−0.529997	+	1.63116i	−0.0252954	+	0.0778511i	0.937612	+	0.347684i	$0.113032\pi$
$440$		0			0
$441$	−0.117039	−	0.360209i	−0.00557329	−	0.0171528i
$442$	0.440387	−	0.319960i	0.0209471	−	0.0152189i
$443$	11.7475			0.558140			0.279070	−	0.960271i	$-0.409974\pi$
$443$	11.7475			0.558140			0.279070	+	0.960271i	$0.409974\pi$
$444$	2.64471	−	1.92149i	0.125512	−	0.0911899i
$445$		0			0
$446$	−11.9678	−	8.69510i	−0.566691	−	0.411725i
$447$	−6.99493	−	5.08212i	−0.330849	−	0.240376i
$448$	−1.50740	+	4.63929i	−0.0712178	+	0.219186i
$449$	12.8415			0.606030			0.303015	−	0.952986i	$-0.402007\pi$
$449$	12.8415			0.606030			0.303015	+	0.952986i	$0.402007\pi$
$450$		0			0
$451$	26.5890			1.25203
$452$	9.71837	−	29.9101i	0.457114	−	1.40685i
$453$	1.01045	+	0.734135i	0.0474751	+	0.0344927i
$454$	1.72858	+	1.25589i	0.0811263	+	0.0589417i
$455$		0			0
$456$	−13.0400	+	9.47412i	−0.610654	+	0.443666i
$457$	−13.6882			−0.640309			−0.320155	−	0.947365i	$-0.603735\pi$
$457$	−13.6882			−0.640309			−0.320155	+	0.947365i	$0.603735\pi$
$458$	−5.19577	+	3.77495i	−0.242783	+	0.176392i
$459$	0.212560	+	0.654193i	0.00992146	+	0.0305351i
$460$		0			0
$461$	3.00160	−	9.23799i	0.139799	−	0.430256i	−0.856507	−	0.516136i	$-0.827370\pi$
$461$	3.00160	−	9.23799i	0.139799	−	0.430256i	0.996306	+	0.0858796i	$0.0273700\pi$
$462$	−2.19450	−	6.75396i	−0.102097	−	0.314223i
$463$	6.57403	+	20.2328i	0.305521	+	0.940297i	0.979482	+	0.201531i	$0.0645915\pi$
$463$	6.57403	+	20.2328i	0.305521	+	0.940297i	−0.673961	+	0.738767i	$0.735408\pi$
$464$	0.0259664	−	0.0799163i	0.00120546	−	0.00371002i
$465$		0			0
$466$	3.50143	+	10.7763i	0.162201	+	0.499202i
$467$	11.2465	−	8.17106i	0.520426	−	0.378112i	−0.296338	−	0.955083i	$-0.595766\pi$
$467$	11.2465	−	8.17106i	0.520426	−	0.378112i	0.816764	+	0.576971i	$0.195766\pi$
$468$	2.52524			0.116729
$469$	−0.173696	+	0.126198i	−0.00802054	+	0.00582727i
$470$		0			0
$471$	−3.12745	−	2.27223i	−0.144105	−	0.104699i
$472$	−0.283902	−	0.206267i	−0.0130676	−	0.00949419i
$473$	18.2006	−	56.0156i	0.836862	−	2.57560i
$474$	2.65959			0.122159
$475$		0			0
$476$	−3.03042			−0.138899
$477$	−2.81922	+	8.67665i	−0.129083	+	0.397277i
$478$	−11.3749	−	8.26438i	−0.520278	−	0.378004i
$479$	10.0057	+	7.26958i	0.457173	+	0.332155i	0.792421	−	0.609974i	$-0.208820\pi$
$479$	10.0057	+	7.26958i	0.457173	+	0.332155i	−0.335249	+	0.942130i	$0.608820\pi$
$480$		0			0
$481$	2.27831	−	1.65529i	0.103882	−	0.0754747i
$482$	−4.38601			−0.199777
$483$	−0.775971	+	0.563776i	−0.0353079	+	0.0256527i
$484$	−8.17817	−	25.1698i	−0.371735	−	1.14408i
$485$		0			0
$486$	0.165802	−	0.510286i	0.00752094	−	0.0231471i
$487$	10.9170	+	33.5990i	0.494695	+	1.52251i	0.817432	+	0.576026i	$0.195397\pi$
$487$	10.9170	+	33.5990i	0.494695	+	1.52251i	−0.322737	+	0.946489i	$0.604603\pi$
$488$	3.94614	+	12.1450i	0.178634	+	0.549778i
$489$	−2.15512	+	6.63277i	−0.0974578	+	0.299944i
$490$		0			0
$491$	−6.70374	−	20.6320i	−0.302536	−	0.931109i	−0.980585	−	0.196093i	$-0.937175\pi$
$491$	−6.70374	−	20.6320i	−0.302536	−	0.931109i	0.678050	−	0.735016i	$-0.262825\pi$
$492$	−7.16009	+	5.20211i	−0.322802	+	0.234529i
$493$	0.0245375			0.00110511
$494$	−5.18114	+	3.76432i	−0.233111	+	0.169365i
$495$		0			0
$496$	8.55475	+	6.21539i	0.384120	+	0.279079i
$497$	−25.3095	−	18.3884i	−1.13529	−	0.824834i
$498$	1.55244	−	4.77793i	0.0695666	−	0.214104i
$499$	38.7869			1.73634			0.868171	−	0.496265i	$-0.165296\pi$
$499$	38.7869			1.73634			0.868171	+	0.496265i	$0.165296\pi$
$500$		0			0
$501$	−15.9594			−0.713013
$502$	4.11430	−	12.6625i	0.183630	−	0.565155i
$503$	5.19360	+	3.77337i	0.231571	+	0.168246i	0.697520	−	0.716565i	$-0.254287\pi$
$503$	5.19360	+	3.77337i	0.231571	+	0.168246i	−0.465949	+	0.884812i	$0.654287\pi$
$504$	4.14627	+	3.01244i	0.184689	+	0.134185i
$505$		0			0
$506$	0.832257	−	0.604670i	0.0369983	−	0.0268809i
$507$	−10.8246			−0.480737
$508$	0.478564	−	0.347697i	0.0212328	−	0.0154266i
$509$	−2.22343	−	6.84300i	−0.0985516	−	0.303311i	0.889611	−	0.456718i	$-0.150975\pi$
$509$	−2.22343	−	6.84300i	−0.0985516	−	0.303311i	−0.988163	+	0.153408i	$0.950975\pi$
$510$		0			0
$511$	−9.58307	+	29.4937i	−0.423930	+	1.30472i
$512$	6.71922	+	20.6796i	0.296950	+	0.913919i
$513$	−2.50077	−	7.69657i	−0.110412	−	0.339812i
$514$	4.02891	−	12.3997i	0.177708	−	0.546928i
$515$		0			0
$516$	6.05820	+	18.6452i	0.266697	+	0.820810i
$517$	35.4593	−	25.7627i	1.55950	−	1.13304i
$518$	2.63611			0.115824
$519$	6.20783	−	4.51025i	0.272493	−	0.197978i
$520$		0			0
$521$	8.51120	+	6.18375i	0.372882	+	0.270915i	0.758405	−	0.651783i	$-0.225979\pi$
$521$	8.51120	+	6.18375i	0.372882	+	0.270915i	−0.385523	+	0.922698i	$0.625979\pi$
$522$	−0.0154845	−	0.0112501i	−0.000677737	−	0.000492404i
$523$	3.49938	−	10.7700i	0.153017	−	0.470938i	−0.844938	−	0.534865i	$-0.820362\pi$
$523$	3.49938	−	10.7700i	0.153017	−	0.470938i	0.997955	+	0.0639269i	$0.0203625\pi$
$524$	7.81840			0.341548
$525$		0			0
$526$	4.57282			0.199385
$527$	−0.954188	+	2.93669i	−0.0415651	+	0.127924i
$528$	9.80235	+	7.12183i	0.426593	+	0.309938i
$529$	18.4950	+	13.4374i	0.804130	+	0.584234i
$530$		0			0
$531$	0.142541	−	0.103562i	0.00618573	−	0.00449420i
$532$	35.6529			1.54575
$533$	−6.16814	+	4.48142i	−0.267172	+	0.194112i
$534$	−0.00204251	−	0.00628621i	−8.83882e−5	−	0.000272031i
$535$		0			0
$536$	−0.0513540	+	0.158051i	−0.00221815	+	0.00682678i
$537$	3.27846	+	10.0901i	0.141476	+	0.435418i
$538$	0.428287	+	1.31813i	0.0184648	+	0.0568287i
$539$	0.602013	−	1.85281i	0.0259305	−	0.0798060i
$540$		0			0
$541$	5.22898	+	16.0931i	0.224811	+	0.691898i	0.998311	+	0.0581012i	$0.0185046\pi$
$541$	5.22898	+	16.0931i	0.224811	+	0.691898i	−0.773499	+	0.633797i	$0.781495\pi$
$542$	5.89879	−	4.28572i	0.253375	−	0.184087i
$543$	15.1076			0.648331
$544$	−2.92009	+	2.12157i	−0.125198	+	0.0909614i
$545$		0			0
$546$	1.64742	+	1.19692i	0.0705032	+	0.0512235i
$547$	35.7073	+	25.9429i	1.52674	+	1.10924i	0.958019	+	0.286705i	$0.0925600\pi$
$547$	35.7073	+	25.9429i	1.52674	+	1.10924i	0.568717	+	0.822533i	$0.307440\pi$
$548$	2.54883	−	7.84448i	0.108881	−	0.335100i
$549$	−6.41152			−0.273637
$550$		0			0
$551$	−0.288683			−0.0122983
$552$	−0.229419	+	0.706079i	−0.00976472	+	0.0300527i
$553$	−10.3189	−	7.49715i	−0.438806	−	0.318811i
$554$	−3.96734	−	2.88244i	−0.168556	−	0.122463i
$555$		0			0
$556$	−5.18143	+	3.76453i	−0.219741	+	0.159652i
$557$	17.8472			0.756210			0.378105	−	0.925763i	$-0.376576\pi$
$557$	17.8472			0.756210			0.378105	+	0.925763i	$0.376576\pi$
$558$	1.94857	−	1.41572i	0.0824897	−	0.0599323i
$559$	5.21891	+	16.0621i	0.220736	+	0.679356i
$560$		0			0
$561$	−1.09334	+	3.36497i	−0.0461610	+	0.142069i
$562$	1.72602	+	5.31213i	0.0728076	+	0.224079i
$563$	−6.61490	−	20.3586i	−0.278785	−	0.858012i	−0.988193	−	0.153214i	$-0.951038\pi$
$563$	−6.61490	−	20.3586i	−0.278785	−	0.858012i	0.709408	−	0.704798i	$-0.248962\pi$
$564$	−4.50831	+	13.8751i	−0.189834	+	0.584249i
$565$		0			0
$566$	0.798480	+	2.45747i	0.0335626	+	0.103295i
$567$	−2.08175	+	1.51248i	−0.0874251	+	0.0635181i
$568$	−24.2151			−1.01604
$569$	21.0929	−	15.3249i	0.884262	−	0.642454i	−0.0501135	−	0.998744i	$-0.515958\pi$
$569$	21.0929	−	15.3249i	0.884262	−	0.642454i	0.934376	+	0.356289i	$0.115958\pi$
$570$		0			0
$571$	7.71705	+	5.60676i	0.322948	+	0.234636i	0.737433	−	0.675421i	$-0.236038\pi$
$571$	7.71705	+	5.60676i	0.322948	+	0.234636i	−0.414484	+	0.910057i	$0.636038\pi$
$572$	10.5084	+	7.63478i	0.439377	+	0.319226i
$573$	3.78359	−	11.6447i	0.158062	−	0.486464i
$574$	−7.13683			−0.297885
$575$		0			0
$576$	−1.89572			−0.0789885
$577$	2.81361	−	8.65941i	0.117132	−	0.360496i	−0.875254	−	0.483664i	$-0.839306\pi$
$577$	2.81361	−	8.65941i	0.117132	−	0.360496i	0.992386	+	0.123169i	$0.0393056\pi$
$578$	7.17390	+	5.21214i	0.298395	+	0.216797i
$579$	−11.5221	−	8.37130i	−0.478843	−	0.347900i
$580$		0			0
$581$	−19.4919	+	14.1617i	−0.808658	+	0.587525i
$582$	−4.08871			−0.169482
$583$	−37.9646	+	27.5829i	−1.57233	+	1.14237i
$584$	7.41761	+	22.8291i	0.306943	+	0.944673i
$585$		0			0
$586$	4.05396	−	12.4768i	0.167468	−	0.515412i
$587$	−9.10008	−	28.0072i	−0.375600	−	1.15598i	−0.943073	−	0.332587i	$-0.892079\pi$
$587$	−9.10008	−	28.0072i	−0.375600	−	1.15598i	0.567472	−	0.823393i	$-0.307921\pi$
$588$	0.200385	+	0.616721i	0.00826373	+	0.0254331i
$589$	11.2260	−	34.5501i	0.462559	−	1.42361i
$590$		0			0
$591$	−5.48469	−	16.8802i	−0.225610	−	0.694357i
$592$	−3.63866	+	2.64364i	−0.149548	+	0.108653i
$593$	−33.7757			−1.38700			−0.693501	−	0.720456i	$-0.743933\pi$
$593$	−33.7757			−1.38700			−0.693501	+	0.720456i	$0.743933\pi$
$594$	2.23275	−	1.62219i	0.0916108	−	0.0665592i
$595$		0			0
$596$	11.9761	+	8.70118i	0.490562	+	0.356414i
$597$	15.3349	+	11.1415i	0.627617	+	0.455991i
$598$	−0.0911543	+	0.280544i	−0.00372758	+	0.0114723i
$599$	−12.0575			−0.492656			−0.246328	−	0.969187i	$-0.579224\pi$
$599$	−12.0575			−0.492656			−0.246328	+	0.969187i	$0.579224\pi$
$600$		0			0
$601$	0.0653240			0.00266462			0.00133231	−	0.999999i	$-0.499576\pi$
$601$	0.0653240			0.00266462			0.00133231	+	0.999999i	$0.499576\pi$
$602$	−4.88526	+	15.0353i	−0.199108	+	0.612793i
$603$	−0.0675025	−	0.0490435i	−0.00274892	−	0.00199720i
$604$	−1.73001	−	1.25692i	−0.0703930	−	0.0511435i
$605$		0			0
$606$	−3.59205	+	2.60978i	−0.145917	+	0.106015i
$607$	−25.9556			−1.05350			−0.526752	−	0.850019i	$-0.676590\pi$
$607$	−25.9556			−1.05350			−0.526752	+	0.850019i	$0.676590\pi$
$608$	34.3548	−	24.9602i	1.39327	−	1.01227i
$609$	0.0283650	+	0.0872986i	0.00114941	+	0.00353752i
$610$		0			0
$611$	−3.88373	+	11.9529i	−0.157119	+	0.483563i
$612$	−0.363928	−	1.12006i	−0.0147109	−	0.0452756i
$613$	3.88472	+	11.9559i	0.156902	+	0.482896i	0.998349	−	0.0574448i	$-0.0182953\pi$
$613$	3.88472	+	11.9559i	0.156902	+	0.482896i	−0.841446	+	0.540341i	$0.818295\pi$
$614$	−1.57786	+	4.85617i	−0.0636774	+	0.195979i
$615$		0			0
$616$	8.14623	+	25.0715i	0.328221	+	1.01016i
$617$	1.50253	−	1.09165i	0.0604896	−	0.0439483i	−0.557130	−	0.830426i	$-0.688097\pi$
$617$	1.50253	−	1.09165i	0.0604896	−	0.0439483i	0.617619	+	0.786477i	$0.288097\pi$
$618$	5.57259			0.224162
$619$	14.5814	−	10.5940i	0.586077	−	0.425810i	−0.254833	−	0.966985i	$-0.582020\pi$
$619$	14.5814	−	10.5940i	0.586077	−	0.425810i	0.840910	+	0.541175i	$0.182020\pi$
$620$		0			0
$621$	−0.301561	−	0.219097i	−0.0121012	−	0.00879206i
$622$	−10.8438	−	7.87848i	−0.434797	−	0.315898i
$623$	−0.00979552	+	0.0301475i	−0.000392449	+	0.00120783i
$624$	−3.47430			−0.139083
$625$		0			0
$626$	5.30195			0.211908
$627$	12.8632	−	39.5888i	0.513705	−	1.58102i
$628$	5.35456	+	3.89032i	0.213670	+	0.155241i
$629$	−1.06254	−	0.771977i	−0.0423661	−	0.0307807i
$630$		0			0
$631$	−17.3636	+	12.6154i	−0.691233	+	0.502210i	−0.877065	−	0.480371i	$-0.840502\pi$
$631$	−17.3636	+	12.6154i	−0.691233	+	0.502210i	0.185832	+	0.982582i	$0.440502\pi$
$632$	−9.87272			−0.392716
$633$	8.71864	−	6.33446i	0.346535	−	0.251772i
$634$	4.10046	+	12.6199i	0.162850	+	0.501201i
$635$		0			0
$636$	4.82683	−	14.8555i	0.191396	−	0.589057i
$637$	0.172624	+	0.531281i	0.00683960	+	0.0210501i
$638$	−0.0304225	−	0.0936310i	−0.00120444	−	0.00370689i
$639$	3.75698	−	11.5628i	0.148624	−	0.457417i
$640$		0			0
$641$	12.2648	+	37.7471i	0.484430	+	1.49092i	0.832805	+	0.553567i	$0.186734\pi$
$641$	12.2648	+	37.7471i	0.484430	+	1.49092i	−0.348374	+	0.937355i	$0.613266\pi$
$642$	5.32773	−	3.87082i	0.210269	−	0.152769i
$643$	−1.26211			−0.0497729			−0.0248864	−	0.999690i	$-0.507922\pi$
$643$	−1.26211			−0.0497729			−0.0248864	+	0.999690i	$0.507922\pi$
$644$	1.32855	−	0.965250i	0.0523523	−	0.0380362i
$645$		0			0
$646$	2.41633	+	1.75557i	0.0950692	+	0.0690718i
$647$	−23.4029	−	17.0032i	−0.920064	−	0.668466i	0.0234758	−	0.999724i	$-0.492527\pi$
$647$	−23.4029	−	17.0032i	−0.920064	−	0.668466i	−0.943540	+	0.331259i	$0.892527\pi$
$648$	−0.615477	+	1.89424i	−0.0241782	+	0.0744129i
$649$	0.906266			0.0355740
$650$		0			0
$651$	−11.5511			−0.452722
$652$	3.68982	−	11.3561i	0.144504	−	0.444739i
$653$	14.1413	+	10.2743i	0.553393	+	0.402063i	0.829035	−	0.559197i	$-0.188890\pi$
$653$	14.1413	+	10.2743i	0.553393	+	0.402063i	−0.275642	+	0.961260i	$0.588890\pi$
$654$	1.83571	+	1.33372i	0.0717821	+	0.0521527i
$655$		0			0
$656$	9.85106	−	7.15721i	0.384619	−	0.279442i
$657$	−12.0518			−0.470186
$658$	−9.51772	+	6.91503i	−0.371039	+	0.269576i
$659$	3.50406	+	10.7844i	0.136499	+	0.420100i	0.995820	−	0.0913359i	$-0.0291137\pi$
$659$	3.50406	+	10.7844i	0.136499	+	0.420100i	−0.859321	+	0.511436i	$0.829114\pi$
$660$		0			0
$661$	1.43350	−	4.41185i	0.0557565	−	0.171601i	−0.919300	−	0.393557i	$-0.871244\pi$
$661$	1.43350	−	4.41185i	0.0557565	−	0.171601i	0.975057	+	0.221956i	$0.0712443\pi$
$662$	0.178779	+	0.550225i	0.00694844	+	0.0213851i
$663$	−0.313510	−	0.964885i	−0.0121757	−	0.0374730i
$664$	−5.76285	+	17.7362i	−0.223642	+	0.688299i
$665$		0			0
$666$	0.316575	+	0.974317i	0.0122670	+	0.0377540i
$667$	−0.0107574	+	0.00781569i	−0.000416527	+	0.000302625i
$668$	27.3243			1.05721
$669$	−22.3052	+	16.2057i	−0.862369	+	0.626547i
$670$		0			0
$671$	−26.6805	−	19.3845i	−1.02999	−	0.748330i
$672$	−10.9236	−	7.93647i	−0.421387	−	0.306156i
$673$	−2.32741	+	7.16302i	−0.0897149	+	0.276114i	−0.985840	−	0.167687i	$-0.946370\pi$
$673$	−2.32741	+	7.16302i	−0.0897149	+	0.276114i	0.896125	+	0.443801i	$0.146370\pi$
$674$	−7.54435			−0.290598
$675$		0			0
$676$	18.5330			0.712807
$677$	−9.77055	+	30.0707i	−0.375513	+	1.15571i	0.567619	+	0.823291i	$0.307864\pi$
$677$	−9.77055	+	30.0707i	−0.375513	+	1.15571i	−0.943132	+	0.332418i	$0.892136\pi$
$678$	7.97338	+	5.79300i	0.306216	+	0.222479i
$679$	15.8638	+	11.5257i	0.608795	+	0.442316i
$680$		0			0
$681$	3.22167	−	2.34068i	0.123455	−	0.0896952i
$682$	12.3889			0.474397
$683$	24.8045	−	18.0215i	0.949118	−	0.689575i	−0.00148011	−	0.999999i	$-0.500471\pi$
$683$	24.8045	−	18.0215i	0.949118	−	0.689575i	0.950598	+	0.310424i	$0.100471\pi$
$684$	4.28161	+	13.1774i	0.163711	+	0.503852i
$685$		0			0
$686$	−3.14806	+	9.68873i	−0.120193	+	0.369917i
$687$	3.69886	+	11.3839i	0.141120	+	0.434323i
$688$	−8.33505	−	25.6526i	−0.317771	−	0.977998i
$689$	4.15813	−	12.7974i	0.158412	−	0.487542i
$690$		0			0
$691$	−10.7334	−	33.0341i	−0.408318	−	1.25667i	−0.918092	−	0.396366i	$-0.870271\pi$
$691$	−10.7334	−	33.0341i	−0.408318	−	1.25667i	0.509774	−	0.860308i	$-0.329729\pi$
$692$	−10.6285	+	7.72208i	−0.404036	+	0.293550i
$693$	−13.2356			−0.502780
$694$	2.47243	−	1.79632i	0.0938520	−	0.0681875i
$695$		0			0
$696$	0.0574802	+	0.0417618i	0.00217878	+	0.00158298i
$697$	2.87663	+	2.09000i	0.108960	+	0.0791643i
$698$	−4.72453	+	14.5406i	−0.178826	+	0.550370i
$699$	21.1181			0.798761
$700$		0			0
$701$	−19.5437			−0.738154			−0.369077	−	0.929399i	$-0.620326\pi$
$701$	−19.5437			−0.738154			−0.369077	+	0.929399i	$0.620326\pi$
$702$	−0.244545	+	0.752633i	−0.00922977	+	0.0284063i
$703$	12.5007	+	9.08230i	0.471473	+	0.342545i
$704$	−7.88873	−	5.73150i	−0.297318	−	0.216014i
$705$		0			0
$706$	5.54122	−	4.02593i	0.208547	−	0.151518i
$707$	21.2935			0.800825
$708$	−0.244046	+	0.177310i	−0.00917182	+	0.00666372i
$709$	−7.82140	−	24.0718i	−0.293739	−	0.904035i	−0.983642	−	0.180133i	$-0.942347\pi$
$709$	−7.82140	−	24.0718i	−0.293739	−	0.904035i	0.689904	−	0.723901i	$-0.257653\pi$
$710$		0			0
$711$	1.53176	−	4.71426i	0.0574453	−	0.176799i
$712$	0.00758205	+	0.0233351i	0.000284149	+	0.000874522i
$713$	−0.517073	−	1.59139i	−0.0193645	−	0.0595979i
$714$	0.293467	−	0.903200i	0.0109827	−	0.0338014i
$715$		0			0
$716$	−5.61311	−	17.2754i	−0.209772	−	0.645611i
$717$	−21.2003	+	15.4029i	−0.791738	+	0.575232i
$718$	−2.42423			−0.0904715
$719$	7.43539	−	5.40213i	0.277293	−	0.201465i	−0.440443	−	0.897781i	$-0.645178\pi$
$719$	7.43539	−	5.40213i	0.277293	−	0.201465i	0.717736	+	0.696315i	$0.245178\pi$
$720$		0			0
$721$	−21.6211	−	15.7086i	−0.805210	−	0.585019i
$722$	−20.1806	−	14.6621i	−0.751045	−	0.545666i
$723$	−2.52607	+	7.77443i	−0.0939454	+	0.289134i
$724$	−25.8661			−0.961305
$725$		0			0
$726$	8.29369			0.307808
$727$	4.03726	−	12.4254i	0.149734	−	0.460833i	−0.847856	−	0.530227i	$-0.822107\pi$
$727$	4.03726	−	12.4254i	0.149734	−	0.460833i	0.997589	+	0.0693942i	$0.0221066\pi$
$728$	−6.11542	−	4.44312i	−0.226653	−	0.164673i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	6.37213	−	4.62963i	0.235682	−	0.171233i
$732$	10.9773			0.405732
$733$	−7.83202	+	5.69030i	−0.289282	+	0.210176i	−0.722956	−	0.690894i	$-0.757217\pi$
$733$	−7.83202	+	5.69030i	−0.289282	+	0.210176i	0.433674	+	0.901070i	$0.357217\pi$
$734$	−0.503121	−	1.54845i	−0.0185705	−	0.0571542i
$735$		0			0
$736$	0.604419	−	1.86021i	0.0222792	−	0.0685683i
$737$	−0.132623	−	0.408172i	−0.00488524	−	0.0150352i
$738$	−0.857072	−	2.63780i	−0.0315493	−	0.0970986i
$739$	2.82260	−	8.68707i	0.103831	−	0.319559i	−0.885623	−	0.464404i	$-0.846268\pi$
$739$	2.82260	−	8.68707i	0.103831	−	0.319559i	0.989454	+	0.144845i	$0.0462684\pi$
$740$		0			0
$741$	3.68844	+	11.3518i	0.135498	+	0.417021i
$742$	10.1902	−	7.40359i	0.374093	−	0.271794i
$743$	6.35760			0.233238			0.116619	−	0.993177i	$-0.462794\pi$
$743$	6.35760			0.233238			0.116619	+	0.993177i	$0.462794\pi$
$744$	−7.23334	+	5.25533i	−0.265187	+	0.192670i
$745$		0			0
$746$	6.66994	+	4.84600i	0.244204	+	0.177425i
$747$	−7.57501	−	5.50356i	−0.277155	−	0.201365i
$748$	1.87193	−	5.76122i	0.0684446	−	0.210651i
$749$	−31.5825			−1.15400
$750$		0			0
$751$	35.0142			1.27768			0.638842	−	0.769338i	$-0.279414\pi$
$751$	35.0142			1.27768			0.638842	+	0.769338i	$0.279414\pi$
$752$	6.20266	−	19.0898i	0.226188	−	0.696134i
$753$	−20.0754	−	14.5856i	−0.731586	−	0.531529i
$754$	0.0228384	+	0.0165931i	0.000831725	+	0.000604284i
$755$		0			0
$756$	3.56419	−	2.58954i	0.129628	−	0.0941806i
$757$	−11.5175			−0.418609			−0.209305	−	0.977850i	$-0.567120\pi$
$757$	−11.5175			−0.418609			−0.209305	+	0.977850i	$0.567120\pi$
$758$	−4.49689	+	3.26718i	−0.163334	+	0.118669i
$759$	−0.592481	−	1.82347i	−0.0215057	−	0.0661878i
$760$		0			0
$761$	12.6925	−	39.0635i	0.460102	−	1.41605i	−0.404936	−	0.914345i	$-0.632706\pi$
$761$	12.6925	−	39.0635i	0.460102	−	1.41605i	0.865039	−	0.501705i	$-0.167294\pi$
$762$	0.0572847	+	0.176304i	0.00207521	+	0.00638683i
$763$	−3.36273	−	10.3494i	−0.121739	−	0.374674i
$764$	−6.47795	+	19.9371i	−0.234364	+	0.721298i
$765$		0			0
$766$	2.56771	+	7.90259i	0.0927750	+	0.285532i
$767$	−0.210236	+	0.152746i	−0.00759120	+	0.00551533i
$768$	−2.38518			−0.0860677
$769$	−14.5193	+	10.5489i	−0.523578	+	0.380402i	−0.817950	−	0.575289i	$-0.804889\pi$
$769$	−14.5193	+	10.5489i	−0.523578	+	0.380402i	0.294372	+	0.955691i	$0.404889\pi$
$770$		0			0
$771$	−19.6587	−	14.2829i	−0.707992	−	0.514386i
$772$	19.7272	+	14.3327i	0.709998	+	0.515844i
$773$	−16.0762	+	49.4776i	−0.578222	+	1.77958i	0.0467133	+	0.998908i	$0.485125\pi$
$773$	−16.0762	+	49.4776i	−0.578222	+	1.77958i	−0.624935	+	0.780676i	$0.714875\pi$
$774$	−6.14378			−0.220833
$775$		0			0
$776$	15.1778			0.544850
$777$	1.51823	−	4.67264i	0.0544663	−	0.167630i
$778$	9.28701	+	6.74741i	0.332955	+	0.241906i
$779$	−33.8435	−	24.5888i	−1.21257	−	0.880984i
$780$		0			0
$781$	50.5928	−	36.7578i	1.81035	−	1.31530i
$782$	0.137570			0.00491951
$783$	−0.0288595	+	0.0209676i	−0.00103135	+	0.000749322i
$784$	−0.275695	−	0.848502i	−0.00984626	−	0.0303037i
$785$		0			0
$786$	−0.757137	+	2.33023i	−0.0270062	+	0.0831165i
$787$	3.87021	+	11.9113i	0.137958	+	0.424592i	0.996038	−	0.0889240i	$-0.0283428\pi$
$787$	3.87021	+	11.9113i	0.137958	+	0.424592i	−0.858080	+	0.513516i	$0.828343\pi$
$788$	9.39044	+	28.9008i	0.334521	+	1.02955i
$789$	2.63366	−	8.10556i	0.0937607	−	0.288566i
$790$		0			0
$791$	−14.6060	−	44.9525i	−0.519328	−	1.59833i
$792$	−8.28823	+	6.02175i	−0.294509	+	0.213974i
$793$	9.45650			0.335810
$794$	5.42665	−	3.94269i	0.192585	−	0.139921i
$795$		0			0
$796$	−26.2552	−	19.0755i	−0.930591	−	0.676114i
$797$	20.3400	+	14.7779i	0.720481	+	0.523460i	0.886538	−	0.462656i	$-0.153104\pi$
$797$	20.3400	+	14.7779i	0.720481	+	0.523460i	−0.166057	+	0.986116i	$0.553104\pi$
$798$	−3.45264	+	10.6261i	−0.122222	+	0.376161i
$799$	5.86134			0.207359
$800$		0			0
$801$	−0.0123190			−0.000435270
$802$	−5.47939	+	16.8638i	−0.193484	+	0.595483i
$803$	−50.1516	−	36.4372i	−1.76981	−	1.28584i
$804$	0.115572	+	0.0839682i	0.00407592	+	0.00296133i
$805$		0			0
$806$	−2.87400	+	2.08808i	−0.101232	+	0.0735495i
$807$	2.58312			0.0909302
$808$	13.3341	−	9.68781i	0.469093	−	0.340816i
$809$	−1.49157	−	4.59059i	−0.0524409	−	0.161396i	0.921406	−	0.388601i	$-0.127041\pi$
$809$	−1.49157	−	4.59059i	−0.0524409	−	0.161396i	−0.973847	+	0.227204i	$0.927041\pi$
$810$		0			0
$811$	−11.3898	+	35.0543i	−0.399952	+	1.23092i	0.525086	+	0.851049i	$0.324033\pi$
$811$	−11.3898	+	35.0543i	−0.399952	+	1.23092i	−0.925038	+	0.379875i	$0.875967\pi$
$812$	−0.0485643	−	0.149465i	−0.00170427	−	0.00524521i
$813$	−4.19933	−	12.9242i	−0.147277	−	0.453271i
$814$	−1.62836	+	5.01158i	−0.0570740	+	0.175656i
$815$		0			0
$816$	0.500703	+	1.54100i	0.0175281	+	0.0539460i
$817$	−74.9680	+	54.4675i	−2.62280	+	1.90558i
$818$	1.61897			0.0566061
$819$	3.07042	−	2.23079i	0.107289	−	0.0779500i
$820$		0			0
$821$	−11.4772	−	8.33868i	−0.400557	−	0.291022i	0.369211	−	0.929346i	$-0.379628\pi$
$821$	−11.4772	−	8.33868i	−0.400557	−	0.291022i	−0.769768	+	0.638324i	$0.779628\pi$
$822$	2.09117	+	1.51933i	0.0729380	+	0.0529926i
$823$	−8.03241	+	24.7212i	−0.279992	+	0.861728i	0.707863	+	0.706350i	$0.249660\pi$
$823$	−8.03241	+	24.7212i	−0.279992	+	0.861728i	−0.987855	+	0.155378i	$0.950340\pi$
$824$	−20.6861			−0.720634
$825$		0			0
$826$	−0.243253			−0.00846386
$827$	−13.2673	+	40.8326i	−0.461350	+	1.41989i	0.402166	+	0.915567i	$0.368257\pi$
$827$	−13.2673	+	40.8326i	−0.461350	+	1.41989i	−0.863516	+	0.504322i	$0.831743\pi$
$828$	0.516308	+	0.375120i	0.0179429	+	0.0130363i
$829$	4.56100	+	3.31376i	0.158410	+	0.115092i	0.664167	−	0.747585i	$-0.268787\pi$
$829$	4.56100	+	3.31376i	0.158410	+	0.115092i	−0.505756	+	0.862676i	$0.668787\pi$
$830$		0			0
$831$	−7.39421	+	5.37221i	−0.256502	+	0.186360i
$832$	2.79605			0.0969355
$833$	0.210769	−	0.153132i	0.00730270	−	0.00530572i
$834$	−0.620224	−	1.90885i	−0.0214766	−	0.0660981i
$835$		0			0
$836$	−22.0233	+	67.7806i	−0.761690	+	2.34424i
$837$	−1.38718	−	4.26931i	−0.0479481	−	0.147569i
$838$	1.17947	+	3.63003i	0.0407441	+	0.125397i
$839$	−7.12687	+	21.9343i	−0.246047	+	0.757255i	0.749416	+	0.662100i	$0.230335\pi$
$839$	−7.12687	+	21.9343i	−0.246047	+	0.757255i	−0.995463	+	0.0951546i	$0.969665\pi$
$840$		0			0
$841$	−8.96110	−	27.5794i	−0.309003	−	0.951015i
$842$	9.48755	−	6.89311i	0.326963	−	0.237552i
$843$	10.4101			0.358543
$844$	−14.9273	+	10.8453i	−0.513820	+	0.373312i
$845$		0			0
$846$	−3.69882	−	2.68735i	−0.127168	−	0.0923929i
$847$	−32.1787	−	23.3792i	−1.10567	−	0.803317i
$848$	−6.64089	+	20.4386i	−0.228049	+	0.701863i
$849$	4.81586			0.165280
$850$		0			0
$851$	0.711711			0.0243971
$852$	−6.43238	+	19.7968i	−0.220370	+	0.678229i
$853$	31.5886	+	22.9504i	1.08157	+	0.785808i	0.977956	−	0.208809i	$-0.0669587\pi$
$853$	31.5886	+	22.9504i	1.08157	+	0.785808i	0.103616	+	0.994617i	$0.466959\pi$
$854$	7.16138	+	5.20305i	0.245057	+	0.178045i
$855$		0			0
$856$	−19.7772	+	14.3690i	−0.675970	+	0.491121i
$857$	−12.7315			−0.434899			−0.217450	−	0.976072i	$-0.569774\pi$
$857$	−12.7315			−0.434899			−0.217450	+	0.976072i	$0.569774\pi$
$858$	−3.29313	+	2.39260i	−0.112426	+	0.0816821i
$859$	4.50752	+	13.8727i	0.153795	+	0.473331i	0.998037	−	0.0626308i	$-0.0199491\pi$
$859$	4.50752	+	13.8727i	0.153795	+	0.473331i	−0.844242	+	0.535962i	$0.819949\pi$
$860$		0			0
$861$	−4.11036	+	12.6504i	−0.140081	+	0.431124i
$862$	0.662201	+	2.03805i	0.0225547	+	0.0694161i
$863$	5.41229	+	16.6573i	0.184236	+	0.567021i	0.999934	−	0.0114567i	$-0.00364687\pi$
$863$	5.41229	+	16.6573i	0.184236	+	0.567021i	−0.815698	+	0.578478i	$0.803647\pi$
$864$	1.62151	−	4.99051i	0.0551650	−	0.169781i
$865$		0			0
$866$	−4.17677	−	12.8548i	−0.141933	−	0.436824i
$867$	13.3705	−	9.71424i	0.454086	−	0.329913i
$868$	19.7768			0.671267
$869$	20.6272	−	14.9865i	0.699729	−	0.508383i
$870$		0			0
$871$	0.0995611	+	0.0723353i	0.00337350	+	0.00245099i
$872$	−6.81438	−	4.95094i	−0.230764	−	0.167660i
$873$	−2.35484	+	7.24744i	−0.0796992	+	0.245289i
$874$	−1.61851			−0.0547470
$875$		0			0
$876$	20.6341			0.697162
$877$	−2.81435	+	8.66169i	−0.0950340	+	0.292485i	−0.987263	−	0.159100i	$-0.949141\pi$
$877$	−2.81435	+	8.66169i	−0.0950340	+	0.292485i	0.892229	+	0.451584i	$0.149141\pi$
$878$	0.744485	+	0.540900i	0.0251252	+	0.0182545i
$879$	−19.7809	−	14.3717i	−0.667195	−	0.484745i
$880$		0			0
$881$	36.5744	−	26.5728i	1.23222	−	0.895261i	0.235167	−	0.971955i	$-0.424436\pi$
$881$	36.5744	−	26.5728i	1.23222	−	0.895261i	0.997055	+	0.0766939i	$0.0244364\pi$
$882$	−0.203215			−0.00684262
$883$	−3.43206	+	2.49354i	−0.115498	+	0.0839142i	−0.644035	−	0.764996i	$-0.722741\pi$
$883$	−3.43206	+	2.49354i	−0.115498	+	0.0839142i	0.528537	+	0.848910i	$0.322741\pi$
$884$	0.536766	+	1.65200i	0.0180534	+	0.0555626i
$885$		0			0
$886$	1.94776	−	5.99458i	0.0654362	−	0.201392i
$887$	3.95124	+	12.1607i	0.132670	+	0.408316i	0.995220	−	0.0976554i	$-0.0311343\pi$
$887$	3.95124	+	12.1607i	0.132670	+	0.408316i	−0.862551	+	0.505971i	$0.831134\pi$
$888$	−1.17516	−	3.61678i	−0.0394359	−	0.121371i
$889$	0.274727	−	0.845523i	0.00921405	−	0.0283579i
$890$		0			0
$891$	−1.58949	−	4.89194i	−0.0532498	−	0.163886i
$892$	38.1891	−	27.7460i	1.27867	−	0.929005i
$893$	−68.9586			−2.30761
$894$	−3.75311	+	2.72679i	−0.125523	+	0.0911976i
$895$		0			0
$896$	23.9647	+	17.4113i	0.800603	+	0.581672i
$897$	0.444779	+	0.323151i	0.0148508	+	0.0107897i
$898$	2.12916	−	6.55287i	0.0710508	−	0.218672i
$899$	−0.160134			−0.00534076
$900$		0			0
$901$	−6.27546			−0.209066
$902$	4.40851	−	13.5680i	0.146787	−	0.451765i
$903$	23.8372	+	17.3187i	0.793253	+	0.576332i
$904$	−29.5981	−	21.5043i	−0.984419	−	0.715223i
$905$		0			0
$906$	0.542154	−	0.393898i	0.0180118	−	0.0130864i
$907$	−9.51928			−0.316082			−0.158041	−	0.987433i	$-0.550518\pi$
$907$	−9.51928			−0.316082			−0.158041	+	0.987433i	$0.550518\pi$
$908$	−5.51589	+	4.00753i	−0.183051	+	0.132994i
$909$	2.55717	+	7.87016i	0.0848160	+	0.261037i
$910$		0			0
$911$	−12.8107	+	39.4274i	−0.424438	+	1.30629i	0.479093	+	0.877764i	$0.340966\pi$
$911$	−12.8107	+	39.4274i	−0.424438	+	1.30629i	−0.903531	+	0.428522i	$0.859034\pi$
$912$	−5.89076	−	18.1299i	−0.195063	−	0.600341i
$913$	−14.8827	−	45.8043i	−0.492546	−	1.51590i
$914$	−2.26954	+	6.98492i	−0.0750697	+	0.231041i
$915$		0			0
$916$	−6.33287	−	19.4906i	−0.209244	−	0.643987i
$917$	9.50631	−	6.90674i	0.313926	−	0.228081i
$918$	0.369069			0.0121811
$919$	−12.8372	+	9.32675i	−0.423459	+	0.307661i	−0.779028	−	0.626989i	$-0.784287\pi$
$919$	−12.8372	+	9.32675i	−0.423459	+	0.307661i	0.355569	+	0.934650i	$0.384287\pi$
$920$		0			0
$921$	7.69905	+	5.59369i	0.253692	+	0.184318i
$922$	−4.21635	−	3.06336i	−0.138858	−	0.100886i
$923$	−5.54125	+	17.0542i	−0.182393	+	0.561346i
$924$	22.6610			0.745491
$925$		0			0
$926$	11.4145			0.375104
$927$	3.20946	−	9.87769i	0.105412	−	0.324426i
$928$	−0.151435	−	0.110024i	−0.00497110	−	0.00361172i
$929$	23.7938	+	17.2872i	0.780650	+	0.567175i	0.905174	−	0.425041i	$-0.139740\pi$
$929$	23.7938	+	17.2872i	0.780650	+	0.567175i	−0.124524	+	0.992217i	$0.539740\pi$
$930$		0			0
$931$	−2.47969	+	1.80160i	−0.0812685	+	0.0590451i
$932$	−36.1567			−1.18435
$933$	−20.2103	+	14.6837i	−0.661657	+	0.480722i
$934$	−2.30489	−	7.09372i	−0.0754182	−	0.232114i
$935$		0			0
$936$	0.907781	−	2.79386i	0.0296718	−	0.0913203i
$937$	−17.9579	−	55.2688i	−0.586660	−	1.80555i	−0.592499	−	0.805571i	$-0.701859\pi$
$937$	−17.9579	−	55.2688i	−0.586660	−	1.80555i	0.00583887	−	0.999983i	$-0.498141\pi$
$938$	0.0355978	+	0.109559i	0.00116231	+	0.00357722i
$939$	3.05359	−	9.39797i	0.0996500	−	0.306691i
$940$		0			0
$941$	10.5779	+	32.5553i	0.344828	+	1.06127i	0.961676	+	0.274189i	$0.0884095\pi$
$941$	10.5779	+	32.5553i	0.344828	+	1.06127i	−0.616848	+	0.787083i	$0.711591\pi$
$942$	−1.67802	+	1.21916i	−0.0546730	+	0.0397222i
$943$	−1.92684			−0.0627464
$944$	0.335766	−	0.243948i	0.0109282	−	0.00793984i
$945$		0			0
$946$	−25.5663	−	18.5750i	−0.831232	−	0.603925i
$947$	30.7511	+	22.3420i	0.999275	+	0.726016i	0.961933	−	0.273286i	$-0.0881107\pi$
$947$	30.7511	+	22.3420i	0.999275	+	0.726016i	0.0373427	+	0.999303i	$0.488111\pi$
$948$	−2.62255	+	8.07137i	−0.0851764	+	0.262146i
$949$	17.7755			0.577017
$950$		0			0
$951$	24.7310			0.801958
$952$	−1.08939	+	3.35278i	−0.0353072	+	0.108664i
$953$	13.6845	+	9.94235i	0.443284	+	0.322064i	0.786938	−	0.617032i	$-0.211665\pi$
$953$	13.6845	+	9.94235i	0.443284	+	0.322064i	−0.343655	+	0.939096i	$0.611665\pi$
$954$	3.96015	+	2.87722i	0.128214	+	0.0931533i
$955$		0			0
$956$	36.2973	−	26.3716i	1.17394	−	0.852917i
$957$	−0.183487			−0.00593130
$958$	5.36853	−	3.90047i	0.173449	−	0.126018i
$959$	−3.83069	−	11.7897i	−0.123699	−	0.380708i
$960$		0			0
$961$	−3.35243	+	10.3177i	−0.108143	+	0.332829i
$962$	−0.466923	−	1.43704i	−0.0150542	−	0.0463321i
$963$	−3.79280	−	11.6730i	−0.122221	−	0.376158i
$964$	4.32492	−	13.3107i	0.139296	−	0.428710i
$965$		0			0
$966$	0.159030	+	0.489443i	0.00511669	+	0.0157476i
$967$	−18.4330	+	13.3924i	−0.592767	+	0.430670i	−0.843304	−	0.537437i	$-0.819393\pi$
$967$	−18.4330	+	13.3924i	−0.592767	+	0.430670i	0.250537	+	0.968107i	$0.419393\pi$
$968$	−30.7872			−0.989537
$969$	4.50348	−	3.27197i	0.144673	−	0.105111i
$970$		0			0
$971$	−35.5849	−	25.8539i	−1.14197	−	0.829692i	−0.154580	−	0.987980i	$-0.549402\pi$
$971$	−35.5849	−	25.8539i	−1.14197	−	0.829692i	−0.987393	+	0.158288i	$0.949402\pi$
$972$	1.38513	+	1.00636i	0.0444281	+	0.0322789i
$973$	−2.97448	+	9.15450i	−0.0953574	+	0.293480i
$974$	18.9552			0.607362
$975$		0			0
$976$	−15.1029			−0.483431
$977$	5.75794	−	17.7211i	0.184213	−	0.566948i	−0.815721	−	0.578445i	$-0.803660\pi$
$977$	5.75794	−	17.7211i	0.184213	−	0.566948i	0.999934	+	0.0114968i	$0.00365964\pi$
$978$	3.02729	+	2.19946i	0.0968021	+	0.0703308i
$979$	−0.0512634	−	0.0372450i	−0.00163838	−	0.00119036i
$980$		0			0
$981$	3.42135	−	2.48575i	0.109235	−	0.0793640i
$982$	−11.6397			−0.371438
$983$	44.0975	−	32.0387i	1.40649	−	1.02188i	0.412672	−	0.910880i	$-0.364595\pi$
$983$	44.0975	−	32.0387i	1.40649	−	1.02188i	0.993821	−	0.110998i	$-0.0354046\pi$
$984$	3.18155	+	9.79181i	0.101424	+	0.312152i
$985$		0			0
$986$	0.00406837	−	0.0125212i	0.000129563	−	0.000398755i
$987$	6.77563	+	20.8533i	0.215671	+	0.663767i
$988$	−6.31504	−	19.4357i	−0.200908	−	0.618332i
$989$	−1.31895	+	4.05930i	−0.0419401	+	0.129078i
$990$		0			0
$991$	11.1881	+	34.4335i	0.355403	+	1.09382i	0.955776	+	0.294097i	$0.0950188\pi$
$991$	11.1881	+	34.4335i	0.355403	+	1.09382i	−0.600373	+	0.799720i	$0.704981\pi$
$992$	19.0567	−	13.8455i	0.605051	−	0.439595i
$993$	1.07827			0.0342178
$994$	−13.5797	+	9.86626i	−0.430723	+	0.312939i
$995$		0			0
$996$	12.9693	+	9.42275i	0.410948	+	0.298571i
$997$	−5.81865	−	4.22750i	−0.184279	−	0.133886i	0.491821	−	0.870696i	$-0.336331\pi$
$997$	−5.81865	−	4.22750i	−0.184279	−	0.133886i	−0.676100	+	0.736810i	$0.736331\pi$
$998$	6.43096	−	19.7924i	0.203568	−	0.626519i
$999$	1.90935			0.0604092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.e.226.3		16
5.2	odd	4		375.2.i.c.274.3		16
5.3	odd	4		75.2.i.a.4.2	✓	16
5.4	even	2		375.2.g.d.226.2		16
15.8	even	4		225.2.m.b.154.3		16
25.6	even	5	inner	375.2.g.e.151.3		16
25.8	odd	20		375.2.i.c.349.3		16
25.9	even	10		1875.2.a.p.1.3		8
25.12	odd	20		1875.2.b.h.1249.10		16
25.13	odd	20		1875.2.b.h.1249.7		16
25.16	even	5		1875.2.a.m.1.6		8
25.17	odd	20		75.2.i.a.19.2	yes	16
25.19	even	10		375.2.g.d.151.2		16
75.17	even	20		225.2.m.b.19.3		16
75.41	odd	10		5625.2.a.bd.1.3		8
75.59	odd	10		5625.2.a.t.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.2	✓	16	5.3	odd	4
75.2.i.a.19.2	yes	16	25.17	odd	20
225.2.m.b.19.3		16	75.17	even	20
225.2.m.b.154.3		16	15.8	even	4
375.2.g.d.151.2		16	25.19	even	10
375.2.g.d.226.2		16	5.4	even	2
375.2.g.e.151.3		16	25.6	even	5	inner
375.2.g.e.226.3		16	1.1	even	1	trivial
375.2.i.c.274.3		16	5.2	odd	4
375.2.i.c.349.3		16	25.8	odd	20
1875.2.a.m.1.6		8	25.16	even	5
1875.2.a.p.1.3		8	25.9	even	10
1875.2.b.h.1249.7		16	25.13	odd	20
1875.2.b.h.1249.10		16	25.12	odd	20
5625.2.a.t.1.6		8	75.59	odd	10
5625.2.a.bd.1.3		8	75.41	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.165802 - 0.510286i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.38513 + 1.00636i) q^{4} +(-0.434076 + 0.315374i) q^{6} +2.57318 q^{7} +(1.61134 - 1.17071i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.165802 - 0.510286i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.38513 + 1.00636i) q^{4} +(-0.434076 + 0.315374i) q^{6} +2.57318 q^{7} +(1.61134 - 1.17071i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.58949 + 4.89194i) q^{11} +(-0.529073 - 1.62832i) q^{12} +(-0.455776 - 1.40274i) q^{13} +(0.426639 - 1.31306i) q^{14} +(0.727915 + 2.24029i) q^{16} +(-0.556490 + 0.404314i) q^{17} +0.536547 q^{18} +(6.54709 - 4.75674i) q^{19} +(-2.08175 - 1.51248i) q^{21} +(2.23275 + 1.62219i) q^{22} +(0.115186 - 0.354506i) q^{23} -1.99173 q^{24} -0.791365 q^{26} +(0.309017 - 0.951057i) q^{27} +(3.56419 + 2.58954i) q^{28} +(-0.0288595 - 0.0209676i) q^{29} +(3.63169 - 2.63858i) q^{31} +5.24733 q^{32} +(4.16133 - 3.02338i) q^{33} +(0.114049 + 0.351005i) q^{34} +(-0.529073 + 1.62832i) q^{36} +(0.590022 + 1.81590i) q^{37} +(-1.34178 - 4.12957i) q^{38} +(-0.455776 + 1.40274i) q^{39} +(-1.59739 - 4.91625i) q^{41} +(-1.11695 + 0.811515i) q^{42} -11.4506 q^{43} +(-7.12469 + 5.17639i) q^{44} +(-0.161802 - 0.117556i) q^{46} +(-6.89374 - 5.00860i) q^{47} +(0.727915 - 2.24029i) q^{48} -0.378747 q^{49} +0.687859 q^{51} +(0.780343 - 2.40165i) q^{52} +(7.38080 + 5.36247i) q^{53} +(-0.434076 - 0.315374i) q^{54} +(4.14627 - 3.01244i) q^{56} -8.09265 q^{57} +(-0.0154845 + 0.0112501i) q^{58} +(-0.0544457 - 0.167567i) q^{59} +(-1.98127 + 6.09772i) q^{61} +(-0.744289 - 2.29069i) q^{62} +(0.795156 + 2.44724i) q^{63} +(-0.585811 + 1.80294i) q^{64} +(-0.852834 - 2.62475i) q^{66} +(-0.0675025 + 0.0490435i) q^{67} -1.17770 q^{68} +(-0.301561 + 0.219097i) q^{69} +(-9.83589 - 7.14619i) q^{71} +(1.61134 + 1.17071i) q^{72} +(-3.72421 + 11.4619i) q^{73} +1.02446 q^{74} +13.8556 q^{76} +(-4.09004 + 12.5878i) q^{77} +(0.640228 + 0.465153i) q^{78} +(-4.01019 - 2.91357i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.77354 q^{82} +(-7.57501 + 5.50356i) q^{83} +(-1.36140 - 4.18996i) q^{84} +(-1.89853 + 5.84308i) q^{86} +(0.0110233 + 0.0339264i) q^{87} +(3.16582 + 9.74340i) q^{88} +(-0.00380677 + 0.0117160i) q^{89} +(-1.17279 - 3.60949i) q^{91} +(0.516308 - 0.375120i) q^{92} -4.48902 q^{93} +(-3.69882 + 2.68735i) q^{94} +(-4.24518 - 3.08430i) q^{96} +(6.16504 + 4.47917i) q^{97} +(-0.0627970 + 0.193269i) q^{98} -5.14369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

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