LMFDB - Embedded newform 375.2.i.c.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, 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 $\Q(\zeta_{10})$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.3
Root			$0.536547i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.c.274.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.510286 - 0.165802i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(-0.434076 - 0.315374i) q^{6} -2.57318i q^{7} +(-1.17071 + 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.510286 - 0.165802i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(-0.434076 - 0.315374i) q^{6} -2.57318i q^{7} +(-1.17071 + 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.58949 - 4.89194i) q^{11} +(1.62832 + 0.529073i) q^{12} +(-1.40274 - 0.455776i) q^{13} +(-0.426639 - 1.31306i) q^{14} +(0.727915 - 2.24029i) q^{16} +(-0.404314 + 0.556490i) q^{17} +0.536547i q^{18} +(-6.54709 - 4.75674i) q^{19} +(-2.08175 + 1.51248i) q^{21} +(-1.62219 - 2.23275i) q^{22} +(-0.354506 + 0.115186i) q^{23} +1.99173 q^{24} -0.791365 q^{26} +(0.951057 - 0.309017i) q^{27} +(2.58954 + 3.56419i) q^{28} +(0.0288595 - 0.0209676i) q^{29} +(3.63169 + 2.63858i) q^{31} -5.24733i q^{32} +(-3.02338 + 4.16133i) q^{33} +(-0.114049 + 0.351005i) q^{34} +(-0.529073 - 1.62832i) q^{36} +(-1.81590 - 0.590022i) q^{37} +(-4.12957 - 1.34178i) q^{38} +(0.455776 + 1.40274i) q^{39} +(-1.59739 + 4.91625i) q^{41} +(-0.811515 + 1.11695i) q^{42} -11.4506i q^{43} +(7.12469 + 5.17639i) q^{44} +(-0.161802 + 0.117556i) q^{46} +(5.00860 + 6.89374i) q^{47} +(-2.24029 + 0.727915i) q^{48} +0.378747 q^{49} +0.687859 q^{51} +(2.40165 - 0.780343i) q^{52} +(5.36247 + 7.38080i) q^{53} +(0.434076 - 0.315374i) q^{54} +(4.14627 + 3.01244i) q^{56} +8.09265i q^{57} +(0.0112501 - 0.0154845i) q^{58} +(0.0544457 - 0.167567i) q^{59} +(-1.98127 - 6.09772i) q^{61} +(2.29069 + 0.744289i) q^{62} +(2.44724 + 0.795156i) q^{63} +(0.585811 + 1.80294i) q^{64} +(-0.852834 + 2.62475i) q^{66} +(-0.0490435 + 0.0675025i) q^{67} -1.17770i q^{68} +(0.301561 + 0.219097i) q^{69} +(-9.83589 + 7.14619i) q^{71} +(-1.17071 - 1.61134i) q^{72} +(11.4619 - 3.72421i) q^{73} -1.02446 q^{74} +13.8556 q^{76} +(-12.5878 + 4.09004i) q^{77} +(0.465153 + 0.640228i) q^{78} +(4.01019 - 2.91357i) q^{79} +(-0.809017 - 0.587785i) q^{81} +2.77354i q^{82} +(5.50356 - 7.57501i) q^{83} +(1.36140 - 4.18996i) q^{84} +(-1.89853 - 5.84308i) q^{86} +(-0.0339264 - 0.0110233i) q^{87} +(9.74340 + 3.16582i) q^{88} +(0.00380677 + 0.0117160i) q^{89} +(-1.17279 + 3.60949i) q^{91} +(0.375120 - 0.516308i) q^{92} -4.48902i q^{93} +(3.69882 + 2.68735i) q^{94} +(-4.24518 + 3.08430i) q^{96} +(-4.47917 - 6.16504i) q^{97} +(0.193269 - 0.0627970i) q^{98} +5.14369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	0.510286	−	0.165802i	0.360827	−	0.117240i	−0.122993	−	0.992408i	$-0.539249\pi$
$2$	0.510286	−	0.165802i	0.360827	−	0.117240i	0.483820	+	0.875168i	$0.339249\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−1.38513	+	1.00636i	−0.692566	+	0.503179i
$5$		0			0
$5$		0			0
$6$	−0.434076	−	0.315374i	−0.177211	−	0.128751i
$7$		−	2.57318i		−	0.972570i	−0.873800	−	0.486285i	$-0.838352\pi$
$7$		−	2.57318i		−	0.972570i	0.873800	−	0.486285i	$-0.161648\pi$
$8$	−1.17071	+	1.61134i	−0.413907	+	0.569695i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	−1.58949	−	4.89194i	−0.479248	−	1.47497i	−0.840141	−	0.542368i	$-0.817528\pi$
$11$	−1.58949	−	4.89194i	−0.479248	−	1.47497i	0.360893	−	0.932607i	$-0.382472\pi$
$12$	1.62832	+	0.529073i	0.470056	+	0.152730i
$13$	−1.40274	−	0.455776i	−0.389049	−	0.126410i	0.107960	−	0.994155i	$-0.465568\pi$
$13$	−1.40274	−	0.455776i	−0.389049	−	0.126410i	−0.497009	+	0.867746i	$0.665568\pi$
$14$	−0.426639	−	1.31306i	−0.114024	−	0.350930i
$15$		0			0
$16$	0.727915	−	2.24029i	0.181979	−	0.560073i
$17$	−0.404314	+	0.556490i	−0.0980605	+	0.134969i	−0.855228	−	0.518252i	$-0.826583\pi$
$17$	−0.404314	+	0.556490i	−0.0980605	+	0.134969i	0.757167	+	0.653221i	$0.226583\pi$
$18$			0.536547i			0.126465i
$19$	−6.54709	−	4.75674i	−1.50201	−	1.09127i	−0.969574	−	0.244799i	$-0.921278\pi$
$19$	−6.54709	−	4.75674i	−1.50201	−	1.09127i	−0.532432	−	0.846473i	$-0.678722\pi$
$20$		0			0
$21$	−2.08175	+	1.51248i	−0.454274	+	0.330050i
$22$	−1.62219	−	2.23275i	−0.345852	−	0.476024i
$23$	−0.354506	+	0.115186i	−0.0739197	+	0.0240180i	−0.345743	−	0.938329i	$-0.612373\pi$
$23$	−0.354506	+	0.115186i	−0.0739197	+	0.0240180i	0.271824	+	0.962347i	$0.412373\pi$
$24$	1.99173			0.406559
$25$		0			0
$26$	−0.791365			−0.155200
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	2.58954	+	3.56419i	0.489377	+	0.673569i
$29$	0.0288595	−	0.0209676i	0.00535907	−	0.00389359i	−0.585102	−	0.810959i	$-0.698946\pi$
$29$	0.0288595	−	0.0209676i	0.00535907	−	0.00389359i	0.590462	+	0.807066i	$0.298946\pi$
$30$		0			0
$31$	3.63169	+	2.63858i	0.652272	+	0.473903i	0.864044	−	0.503416i	$-0.167924\pi$
$31$	3.63169	+	2.63858i	0.652272	+	0.473903i	−0.211773	+	0.977319i	$0.567924\pi$
$32$		−	5.24733i		−	0.927606i
$33$	−3.02338	+	4.16133i	−0.526304	+	0.724395i
$34$	−0.114049	+	0.351005i	−0.0195592	+	0.0601969i
$35$		0			0
$36$	−0.529073	−	1.62832i	−0.0881789	−	0.271387i
$37$	−1.81590	−	0.590022i	−0.298532	−	0.0969991i	0.155921	−	0.987770i	$-0.450165\pi$
$37$	−1.81590	−	0.590022i	−0.298532	−	0.0969991i	−0.454454	+	0.890770i	$0.650165\pi$
$38$	−4.12957	−	1.34178i	−0.669905	−	0.217665i
$39$	0.455776	+	1.40274i	0.0729826	+	0.224617i
$40$		0			0
$41$	−1.59739	+	4.91625i	−0.249470	+	0.767789i	0.745399	+	0.666618i	$0.232259\pi$
$41$	−1.59739	+	4.91625i	−0.249470	+	0.767789i	−0.994869	+	0.101171i	$0.967741\pi$
$42$	−0.811515	+	1.11695i	−0.125219	+	0.172350i
$43$		−	11.4506i		−	1.74620i	−0.487543	−	0.873099i	$-0.662107\pi$
$43$		−	11.4506i		−	1.74620i	0.487543	−	0.873099i	$-0.337893\pi$
$44$	7.12469	+	5.17639i	1.07409	+	0.780370i
$45$		0			0
$46$	−0.161802	+	0.117556i	−0.0238564	+	0.0173327i
$47$	5.00860	+	6.89374i	0.730579	+	1.00556i	0.999106	+	0.0422836i	$0.0134633\pi$
$47$	5.00860	+	6.89374i	0.730579	+	1.00556i	−0.268527	+	0.963272i	$0.586537\pi$
$48$	−2.24029	+	0.727915i	−0.323358	+	0.105065i
$49$	0.378747			0.0541067
$50$		0			0
$51$	0.687859			0.0963196
$52$	2.40165	−	0.780343i	0.333049	−	0.108214i
$53$	5.36247	+	7.38080i	0.736592	+	1.01383i	0.998807	+	0.0488220i	$0.0155467\pi$
$53$	5.36247	+	7.38080i	0.736592	+	1.01383i	−0.262216	+	0.965009i	$0.584453\pi$
$54$	0.434076	−	0.315374i	0.0590702	−	0.0429170i
$55$		0			0
$56$	4.14627	+	3.01244i	0.554068	+	0.402554i
$57$			8.09265i			1.07190i
$58$	0.0112501	−	0.0154845i	0.00147721	−	0.00203321i
$59$	0.0544457	−	0.167567i	0.00708822	−	0.0218153i	−0.947450	−	0.319904i	$-0.896349\pi$
$59$	0.0544457	−	0.167567i	0.00708822	−	0.0218153i	0.954538	+	0.298089i	$0.0963492\pi$
$60$		0			0
$61$	−1.98127	−	6.09772i	−0.253676	−	0.780733i	−0.994088	−	0.108580i	$-0.965370\pi$
$61$	−1.98127	−	6.09772i	−0.253676	−	0.780733i	0.740412	−	0.672153i	$-0.234630\pi$
$62$	2.29069	+	0.744289i	0.290918	+	0.0945248i
$63$	2.44724	+	0.795156i	0.308323	+	0.100180i
$64$	0.585811	+	1.80294i	0.0732263	+	0.225367i
$65$		0			0
$66$	−0.852834	+	2.62475i	−0.104977	+	0.323085i
$67$	−0.0490435	+	0.0675025i	−0.00599161	+	0.00824675i	−0.812002	−	0.583654i	$-0.801622\pi$
$67$	−0.0490435	+	0.0675025i	−0.00599161	+	0.00824675i	0.806011	+	0.591901i	$0.201622\pi$
$68$		−	1.17770i		−	0.142817i
$69$	0.301561	+	0.219097i	0.0363037	+	0.0263762i
$70$		0			0
$71$	−9.83589	+	7.14619i	−1.16731	+	0.848097i	−0.990684	−	0.136182i	$-0.956517\pi$
$71$	−9.83589	+	7.14619i	−1.16731	+	0.848097i	−0.176622	+	0.984279i	$0.556517\pi$
$72$	−1.17071	−	1.61134i	−0.137969	−	0.189898i
$73$	11.4619	−	3.72421i	1.34152	−	0.435886i	0.451688	−	0.892176i	$-0.350822\pi$
$73$	11.4619	−	3.72421i	1.34152	−	0.435886i	0.889831	+	0.456290i	$0.150822\pi$
$74$	−1.02446			−0.119091
$75$		0			0
$76$	13.8556			1.58934
$77$	−12.5878	+	4.09004i	−1.43452	+	0.466103i
$78$	0.465153	+	0.640228i	0.0526682	+	0.0724916i
$79$	4.01019	−	2.91357i	0.451182	−	0.327803i	−0.338881	−	0.940829i	$-0.610048\pi$
$79$	4.01019	−	2.91357i	0.451182	−	0.327803i	0.790062	+	0.613027i	$0.210048\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			2.77354i			0.306287i
$83$	5.50356	−	7.57501i	0.604095	−	0.831465i	−0.391981	−	0.919973i	$-0.628210\pi$
$83$	5.50356	−	7.57501i	0.604095	−	0.831465i	0.996075	+	0.0885084i	$0.0282100\pi$
$84$	1.36140	−	4.18996i	0.148541	−	0.457162i
$85$		0			0
$86$	−1.89853	−	5.84308i	−0.204724	−	0.630075i
$87$	−0.0339264	−	0.0110233i	−0.00363729	−	0.00118183i
$88$	9.74340	+	3.16582i	1.03865	+	0.337478i
$89$	0.00380677	+	0.0117160i	0.000403517	+	0.00124190i	0.951258	−	0.308396i	$-0.0997922\pi$
$89$	0.00380677	+	0.0117160i	0.000403517	+	0.00124190i	−0.950855	+	0.309638i	$0.899792\pi$
$90$		0			0
$91$	−1.17279	+	3.60949i	−0.122942	+	0.378377i
$92$	0.375120	−	0.516308i	0.0391089	−	0.0538288i
$93$		−	4.48902i		−	0.465490i
$94$	3.69882	+	2.68735i	0.381504	+	0.277179i
$95$		0			0
$96$	−4.24518	+	3.08430i	−0.433272	+	0.314790i
$97$	−4.47917	−	6.16504i	−0.454790	−	0.625965i	0.518628	−	0.855000i	$-0.326443\pi$
$97$	−4.47917	−	6.16504i	−0.454790	−	0.625965i	−0.973418	+	0.229035i	$0.926443\pi$
$98$	0.193269	−	0.0627970i	0.0195231	−	0.00634345i
$99$	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	$0.364933\pi$
$102$	0.351005	−	0.114049i	0.0347547	−	0.0112925i
$103$	−6.10475	−	8.40247i	−0.601519	−	0.827920i	0.394328	−	0.918970i	$-0.370978\pi$
$103$	−6.10475	−	8.40247i	−0.601519	−	0.827920i	−0.995846	+	0.0910504i	$0.970978\pi$
$104$	2.37660	−	1.72670i	0.233045	−	0.169317i
$105$		0			0
$106$	3.96015	+	2.87722i	0.384643	+	0.279460i
$107$			12.2737i			1.18655i	0.805001	+	0.593274i	$0.202165\pi$
$107$			12.2737i			1.18655i	−0.805001	+	0.593274i	$0.797835\pi$
$108$	−1.00636	+	1.38513i	−0.0968368	+	0.133284i
$109$	1.30684	−	4.02203i	0.125172	−	0.385241i	−0.868760	−	0.495233i	$-0.835083\pi$
$109$	1.30684	−	4.02203i	0.125172	−	0.385241i	0.993932	+	0.109992i	$0.0350826\pi$
$110$		0			0
$111$	0.590022	+	1.81590i	0.0560024	+	0.172358i
$112$	−5.76467	−	1.87305i	−0.544710	−	0.176987i
$113$	−17.4696	−	5.67623i	−1.64340	−	0.533974i	−0.666109	−	0.745855i	$-0.732041\pi$
$113$	−17.4696	−	5.67623i	−1.64340	−	0.533974i	−0.977296	+	0.211880i	$0.932041\pi$
$114$	1.34178	+	4.12957i	0.125669	+	0.386770i
$115$		0			0
$116$	−0.0188733	+	0.0580859i	−0.00175234	+	0.00539314i
$117$	0.866938	−	1.19324i	0.0801485	−	0.110315i
$118$		−	0.0945341i		−	0.00870257i
$119$	1.43195	+	1.04037i	0.131267	+	0.0953707i
$120$		0			0
$121$	−12.5054	+	9.08571i	−1.13685	+	0.825974i
$122$	−2.02203	−	2.78309i	−0.183066	−	0.251969i
$123$	4.91625	−	1.59739i	0.443283	−	0.144031i
$124$	−7.68573			−0.690199
$125$		0			0
$126$	1.38063			0.122996
$127$	0.328591	−	0.106766i	0.0291577	−	0.00947391i	−0.294402	−	0.955682i	$-0.595120\pi$
$127$	0.328591	−	0.106766i	0.0291577	−	0.00947391i	0.323560	+	0.946208i	$0.395120\pi$
$128$	6.76647	+	9.31325i	0.598077	+	0.823182i
$129$	−9.26372	+	6.73048i	−0.815625	+	0.592586i
$130$		0			0
$131$	3.69438	+	2.68413i	0.322780	+	0.234513i	0.737361	−	0.675499i	$-0.236072\pi$
$131$	3.69438	+	2.68413i	0.322780	+	0.234513i	−0.414581	+	0.910012i	$0.636072\pi$
$132$		−	8.80660i		−	0.766516i
$133$	−12.2400	+	16.8468i	−1.06134	+	1.46081i
$134$	−0.0138342	+	0.0425771i	−0.00119509	+	0.00367810i
$135$		0			0
$136$	−0.423362	−	1.30297i	−0.0363030	−	0.111729i
$137$	4.58174	+	1.48870i	0.391445	+	0.127188i	0.498125	−	0.867105i	$-0.334022\pi$
$137$	4.58174	+	1.48870i	0.391445	+	0.127188i	−0.106680	+	0.994293i	$0.534022\pi$
$138$	0.190209	+	0.0618027i	0.0161917	+	0.00526100i
$139$	1.15595	+	3.55766i	0.0980468	+	0.301757i	0.988036	−	0.154225i	$-0.0492881\pi$
$139$	1.15595	+	3.55766i	0.0980468	+	0.301757i	−0.889989	+	0.455982i	$0.849288\pi$
$140$		0			0
$141$	2.63318	−	8.10408i	0.221753	−	0.682487i
$142$	−3.83427	+	5.27742i	−0.321765	+	0.442871i
$143$			7.58655i			0.634419i
$144$	1.90570	+	1.38458i	0.158809	+	0.115381i
$145$		0			0
$146$	5.23139	−	3.80083i	0.432953	−	0.314559i
$147$	−0.222622	−	0.306412i	−0.0183615	−	0.0252725i
$148$	3.10904	−	1.01019i	0.255561	−	0.0830369i
$149$	−8.64621			−0.708325			−0.354163	−	0.935184i	$-0.615234\pi$
$149$	−8.64621			−0.708325			−0.354163	+	0.935184i	$0.615234\pi$
$150$		0			0
$151$	−1.24898			−0.101641			−0.0508205	−	0.998708i	$-0.516184\pi$
$151$	−1.24898			−0.101641			−0.0508205	+	0.998708i	$0.516184\pi$
$152$	15.3295	−	4.98084i	1.24338	−	0.404000i
$153$	−0.404314	−	0.556490i	−0.0326868	−	0.0449895i
$154$	−5.74527	+	4.17418i	−0.462967	+	0.336365i
$155$		0			0
$156$	−2.04296	−	1.48430i	−0.163568	−	0.118839i
$157$		−	3.86574i		−	0.308520i	−0.988030	−	0.154260i	$-0.950701\pi$
$157$		−	3.86574i		−	0.308520i	0.988030	−	0.154260i	$-0.0492993\pi$
$158$	1.56327	−	2.15166i	0.124367	−	0.171176i
$159$	2.81922	−	8.67665i	0.223578	−	0.688103i
$160$		0			0
$161$	0.296394	+	0.912208i	0.0233592	+	0.0718921i
$162$	−0.510286	−	0.165802i	−0.0400919	−	0.0130266i
$163$	−6.63277	−	2.15512i	−0.519519	−	0.168802i	0.0375081	−	0.999296i	$-0.488058\pi$
$163$	−6.63277	−	2.15512i	−0.519519	−	0.168802i	−0.557027	+	0.830494i	$0.688058\pi$
$164$	−2.73491	−	8.41719i	−0.213561	−	0.657272i
$165$		0			0
$166$	1.55244	−	4.77793i	0.120493	−	0.370839i
$167$	9.38069	−	12.9114i	0.725900	−	0.999115i	−0.273408	−	0.961898i	$-0.588151\pi$
$167$	9.38069	−	12.9114i	0.725900	−	0.999115i	0.999307	−	0.0372169i	$-0.0118493\pi$
$168$		−	5.12507i		−	0.395407i
$169$	−8.75729	−	6.36254i	−0.673637	−	0.489426i
$170$		0			0
$171$	6.54709	−	4.75674i	0.500669	−	0.363757i
$172$	11.5234	+	15.8606i	0.878649	+	1.20936i
$173$	7.29774	−	2.37118i	0.554837	−	0.180277i	−0.0181597	−	0.999835i	$-0.505781\pi$
$173$	7.29774	−	2.37118i	0.554837	−	0.180277i	0.572997	+	0.819558i	$0.305781\pi$
$174$	−0.0191399			−0.00145099
$175$		0			0
$176$	−12.1164			−0.913306
$177$	−0.167567	+	0.0544457i	−0.0125951	+	0.00409239i
$178$	0.00388509	+	0.00534737i	0.000291200	+	0.000400802i
$179$	8.58312	−	6.23600i	0.641532	−	0.466100i	−0.218844	−	0.975760i	$-0.570229\pi$
$179$	8.58312	−	6.23600i	0.641532	−	0.466100i	0.860376	+	0.509659i	$0.170229\pi$
$180$		0			0
$181$	−12.2223	−	8.88005i	−0.908480	−	0.660049i	0.0321503	−	0.999483i	$-0.489764\pi$
$181$	−12.2223	−	8.88005i	−0.908480	−	0.660049i	−0.940630	+	0.339434i	$0.889764\pi$
$182$			2.03633i			0.150942i
$183$	−3.76860	+	5.18703i	−0.278583	+	0.383436i
$184$	0.229419	−	0.706079i	0.0169130	−	0.0520528i
$185$		0			0
$186$	−0.744289	−	2.29069i	−0.0545739	−	0.167961i
$187$	3.36497	+	1.09334i	0.246071	+	0.0799532i
$188$	−13.8751	−	4.50831i	−1.01195	−	0.328802i
$189$	−0.795156	−	2.44724i	−0.0578391	−	0.178010i
$190$		0			0
$191$	3.78359	−	11.6447i	0.273771	−	0.842580i	−0.715771	−	0.698335i	$-0.753925\pi$
$191$	3.78359	−	11.6447i	0.273771	−	0.842580i	0.989542	−	0.144245i	$-0.0460754\pi$
$192$	1.11428	−	1.53367i	0.0804161	−	0.110683i
$193$			14.2421i			1.02517i	0.858637	+	0.512585i	$0.171312\pi$
$193$			14.2421i			1.02517i	−0.858637	+	0.512585i	$0.828688\pi$
$194$	−3.30783	−	2.40328i	−0.237489	−	0.172546i
$195$		0			0
$196$	−0.524614	+	0.381154i	−0.0374724	+	0.0272253i
$197$	−10.4325	−	14.3591i	−0.743286	−	1.02304i	−0.998423	−	0.0561399i	$-0.982121\pi$
$197$	−10.4325	−	14.3591i	−0.743286	−	1.02304i	0.255137	−	0.966905i	$-0.417879\pi$
$198$	2.62475	−	0.852834i	0.186533	−	0.0606083i
$199$	18.9550			1.34369			0.671843	−	0.740693i	$-0.265503\pi$
$199$	18.9550			1.34369			0.671843	+	0.740693i	$0.265503\pi$
$200$		0			0
$201$	0.0834377			0.00588524
$202$	4.22271	−	1.37204i	0.297109	−	0.0965366i
$203$	−0.0539535	−	0.0742606i	−0.00378679	−	0.00521207i
$204$	−0.952776	+	0.692232i	−0.0667077	+	0.0484660i
$205$		0			0
$206$	−4.50832	−	3.27548i	−0.314109	−	0.228214i
$207$		−	0.372750i		−	0.0259079i
$208$	−2.04214	+	2.81077i	−0.141597	+	0.194892i
$209$	−12.8632	+	39.5888i	−0.889764	+	2.73841i
$210$		0			0
$211$	−3.33022	−	10.2494i	−0.229262	−	0.705596i	−0.997831	−	0.0658288i	$-0.979031\pi$
$211$	−3.33022	−	10.2494i	−0.229262	−	0.705596i	0.768569	−	0.639767i	$-0.220969\pi$
$212$	−14.8555	−	4.82683i	−1.02028	−	0.331508i
$213$	11.5628	+	3.75698i	0.792269	+	0.257424i
$214$	2.03501	+	6.26312i	0.139111	+	0.428138i
$215$		0			0
$216$	−0.615477	+	1.89424i	−0.0418779	+	0.128887i
$217$	6.78954	−	9.34500i	0.460904	−	0.634380i
$218$		−	2.26907i		−	0.153681i
$219$	−9.75012	−	7.08387i	−0.658852	−	0.478684i
$220$		0			0
$221$	0.820780	−	0.596332i	0.0552116	−	0.0401136i
$222$	0.602161	+	0.828803i	0.0404144	+	0.0556256i
$223$	−26.2213	+	8.51983i	−1.75591	+	0.570530i	−0.996763	−	0.0803900i	$-0.974383\pi$
$223$	−26.2213	+	8.51983i	−1.75591	+	0.570530i	−0.759147	+	0.650920i	$0.774383\pi$
$224$	−13.5023			−0.902162
$225$		0			0
$226$	−9.85565			−0.655588
$227$	−3.78731	+	1.23057i	−0.251372	+	0.0816758i	−0.431993	−	0.901877i	$-0.642189\pi$
$227$	−3.78731	+	1.23057i	−0.251372	+	0.0816758i	0.180620	+	0.983553i	$0.442189\pi$
$228$	−8.14410	−	11.2094i	−0.539356	−	0.742360i
$229$	9.68373	−	7.03564i	0.639919	−	0.464928i	−0.219903	−	0.975522i	$-0.570574\pi$
$229$	9.68373	−	7.03564i	0.639919	−	0.464928i	0.859822	+	0.510593i	$0.170574\pi$
$230$		0			0
$231$	10.7079	+	7.77971i	0.704525	+	0.511867i
$232$			0.0710494i			0.00466462i
$233$	12.4129	−	17.0849i	0.813197	−	1.11927i	−0.177625	−	0.984098i	$-0.556841\pi$
$233$	12.4129	−	17.0849i	0.813197	−	1.11927i	0.990822	−	0.135172i	$-0.0431587\pi$
$234$	0.244545	−	0.752633i	0.0159864	−	0.0492012i
$235$		0			0
$236$	0.0932174	+	0.286894i	0.00606793	+	0.0186752i
$237$	−4.71426	−	1.53176i	−0.306224	−	0.0994983i
$238$	0.903200	+	0.293467i	0.0585457	+	0.0190227i
$239$	−8.09778	−	24.9224i	−0.523802	−	1.61210i	−0.766673	−	0.642038i	$-0.778089\pi$
$239$	−8.09778	−	24.9224i	−0.523802	−	1.61210i	0.242871	−	0.970059i	$-0.421911\pi$
$240$		0			0
$241$	−2.52607	+	7.77443i	−0.162718	+	0.500795i	−0.998861	−	0.0477169i	$-0.984805\pi$
$241$	−2.52607	+	7.77443i	−0.162718	+	0.500795i	0.836143	+	0.548512i	$0.184805\pi$
$242$	−4.87491	+	6.70974i	−0.313371	+	0.431318i
$243$			1.00000i			0.0641500i
$244$	8.88081	+	6.45228i	0.568535	+	0.413065i
$245$		0			0
$246$	2.24384	−	1.63025i	0.143062	−	0.103941i
$247$	7.01583	+	9.65646i	0.446406	+	0.614426i
$248$	−8.50330	+	2.76289i	−0.539960	+	0.175444i
$249$	−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	$0.213618\pi$
$252$	−4.18996	+	1.36140i	−0.263943	+	0.0857602i
$253$	1.12697	+	1.55114i	0.0708518	+	0.0975191i
$254$	0.149973	−	0.108962i	0.00941017	−	0.00683689i
$255$		0			0
$256$	1.92965	+	1.40197i	0.120603	+	0.0876232i
$257$		−	24.2995i		−	1.51576i	−0.652392	−	0.757882i	$-0.726234\pi$
$257$		−	24.2995i		−	1.51576i	0.652392	−	0.757882i	$-0.273766\pi$
$258$	−3.61122	+	4.97042i	−0.224825	+	0.309445i
$259$	−1.51823	+	4.67264i	−0.0943384	+	0.290344i
$260$		0			0
$261$	0.0110233	+	0.0339264i	0.000682328	+	0.00209999i
$262$	2.33023	+	0.757137i	0.143962	+	0.0467761i
$263$	8.10556	+	2.63366i	0.499810	+	0.162398i	0.548063	−	0.836437i	$-0.315365\pi$
$263$	8.10556	+	2.63366i	0.499810	+	0.162398i	−0.0482528	+	0.998835i	$0.515365\pi$
$264$	−3.16582	−	9.74340i	−0.194843	−	0.599665i
$265$		0			0
$266$	−3.45264	+	10.6261i	−0.211695	+	0.651530i
$267$	0.00724092	−	0.00996627i	0.000443137	−	0.000609926i
$268$		−	0.142855i		−	0.00872627i
$269$	2.08979	+	1.51832i	0.127417	+	0.0925737i	0.649668	−	0.760218i	$-0.274908\pi$
$269$	2.08979	+	1.51832i	0.127417	+	0.0925737i	−0.522252	+	0.852791i	$0.674908\pi$
$270$		0			0
$271$	10.9940	−	7.98759i	0.667837	−	0.485212i	−0.201464	−	0.979496i	$-0.564570\pi$
$271$	10.9940	−	7.98759i	0.667837	−	0.485212i	0.869300	+	0.494284i	$0.164570\pi$
$272$	0.952393	+	1.31086i	0.0577473	+	0.0794824i
$273$	3.60949	−	1.17279i	0.218456	−	0.0709807i
$274$	2.58483			0.156155
$275$		0			0
$276$	−0.638192			−0.0384146
$277$	8.69242	−	2.82434i	0.522277	−	0.169698i	−0.0360015	−	0.999352i	$-0.511462\pi$
$277$	8.69242	−	2.82434i	0.522277	−	0.169698i	0.558278	+	0.829654i	$0.311462\pi$
$278$	1.17974	+	1.62377i	0.0707558	+	0.0973870i
$279$	−3.63169	+	2.63858i	−0.217424	+	0.157968i
$280$		0			0
$281$	−8.42195	−	6.11890i	−0.502411	−	0.365023i	0.307526	−	0.951540i	$-0.400499\pi$
$281$	−8.42195	−	6.11890i	−0.502411	−	0.365023i	−0.809937	+	0.586517i	$0.800499\pi$
$282$		−	4.57199i		−	0.272258i
$283$	2.83069	−	3.89611i	0.168267	−	0.231600i	−0.716553	−	0.697533i	$-0.754281\pi$
$283$	2.83069	−	3.89611i	0.168267	−	0.231600i	0.884820	+	0.465933i	$0.154281\pi$
$284$	6.43238	−	19.7968i	0.381692	−	1.17473i
$285$		0			0
$286$	1.25787	+	3.87131i	0.0743791	+	0.228915i
$287$	12.6504	+	4.11036i	0.746729	+	0.242627i
$288$	4.99051	+	1.62151i	0.294068	+	0.0955486i
$289$	5.10708	+	15.7180i	0.300416	+	0.924586i
$290$		0			0
$291$	−2.35484	+	7.24744i	−0.138043	+	0.424853i
$292$	−12.1284	+	16.6933i	−0.709762	+	0.976904i
$293$			24.4506i			1.42842i	0.699932	+	0.714210i	$0.253214\pi$
$293$			24.4506i			1.42842i	−0.699932	+	0.714210i	$0.746786\pi$
$294$	−0.164405	−	0.119447i	−0.00958827	−	0.00696629i
$295$		0			0
$296$	3.07661	−	2.23529i	0.178825	−	0.129924i
$297$	−3.02338	−	4.16133i	−0.175435	−	0.241465i
$298$	−4.41205	+	1.43356i	−0.255583	+	0.0830439i
$299$	0.549778			0.0317945
$300$		0			0
$301$	−29.4644			−1.69830
$302$	−0.637340	+	0.207084i	−0.0366748	+	0.0119164i
$303$	−4.86403	−	6.69476i	−0.279431	−	0.384604i
$304$	−15.4222	+	11.2049i	−0.884524	+	0.642645i
$305$		0			0
$306$	−0.298583	−	0.216933i	−0.0170689	−	0.0124012i
$307$			9.51655i			0.543138i	0.962419	+	0.271569i	$0.0875426\pi$
$307$			9.51655i			0.543138i	−0.962419	+	0.271569i	$0.912457\pi$
$308$	13.3198	−	18.3331i	0.758965	−	1.04463i
$309$	−3.20946	+	9.87769i	−0.182580	+	0.561922i
$310$		0			0
$311$	7.71967	+	23.7587i	0.437742	+	1.34723i	0.890250	+	0.455471i	$0.150529\pi$
$311$	7.71967	+	23.7587i	0.437742	+	1.34723i	−0.452508	+	0.891760i	$0.649471\pi$
$312$	−2.79386	−	0.907781i	−0.158171	−	0.0513930i
$313$	9.39797	+	3.05359i	0.531205	+	0.172599i	0.562324	−	0.826917i	$-0.309907\pi$
$313$	9.39797	+	3.05359i	0.531205	+	0.172599i	−0.0311197	+	0.999516i	$0.509907\pi$
$314$	−0.640948	−	1.97264i	−0.0361708	−	0.111322i
$315$		0			0
$316$	−2.62255	+	8.07137i	−0.147530	+	0.454050i
$317$	−14.5365	+	20.0078i	−0.816453	+	1.12375i	0.173842	+	0.984773i	$0.444382\pi$
$317$	−14.5365	+	20.0078i	−0.816453	+	1.12375i	−0.990296	+	0.138978i	$0.955618\pi$
$318$		−	4.89501i		−	0.274499i
$319$	−0.148444	−	0.107851i	−0.00831128	−	0.00603850i
$320$		0			0
$321$	9.92967	−	7.21433i	0.554220	−	0.402664i
$322$	0.302492	+	0.416345i	0.0168572	+	0.0232020i
$323$	5.29416	−	1.72018i	0.294575	−	0.0957132i
$324$	1.71212			0.0951176
$325$		0			0
$326$	−3.74194			−0.207247
$327$	−4.02203	+	1.30684i	−0.222419	+	0.0722683i
$328$	−6.05167	−	8.32941i	−0.334148	−	0.459915i
$329$	17.7388	−	12.8880i	0.977974	−	0.710540i
$330$		0			0
$331$	−0.872336	−	0.633789i	−0.0479479	−	0.0348362i	0.563553	−	0.826080i	$-0.309434\pi$
$331$	−0.872336	−	0.633789i	−0.0479479	−	0.0348362i	−0.611501	+	0.791244i	$0.709434\pi$
$332$			16.0309i			0.879812i
$333$	1.12229	−	1.54470i	0.0615011	−	0.0846490i
$334$	2.64610	−	8.14386i	0.144788	−	0.445612i
$335$		0			0
$336$	1.87305	+	5.76467i	0.102184	+	0.314489i
$337$	13.3727	+	4.34507i	0.728460	+	0.236691i	0.649687	−	0.760202i	$-0.274900\pi$
$337$	13.3727	+	4.34507i	0.728460	+	0.236691i	0.0787727	+	0.996893i	$0.474900\pi$
$338$	−5.52365	−	1.79474i	−0.300447	−	0.0976211i
$339$	5.67623	+	17.4696i	0.308290	+	0.948820i
$340$		0			0
$341$	7.13524	−	21.9600i	0.386395	−	1.18920i
$342$	2.55222	−	3.51282i	0.138008	−	0.189952i
$343$		−	18.9868i		−	1.02519i
$344$	18.4508	+	13.4053i	0.994799	+	0.722764i
$345$		0			0
$346$	3.33079	−	2.41996i	0.179064	−	0.130098i
$347$	−3.34793	−	4.60804i	−0.179726	−	0.247372i	0.709643	−	0.704561i	$-0.248856\pi$
$347$	−3.34793	−	4.60804i	−0.179726	−	0.247372i	−0.889369	+	0.457189i	$0.848856\pi$
$348$	0.0580859	−	0.0188733i	0.00311373	−	0.00101171i
$349$	28.4950			1.52530			0.762651	−	0.646810i	$-0.223897\pi$
$349$	28.4950			1.52530			0.762651	+	0.646810i	$0.223897\pi$
$350$		0			0
$351$	−1.47492			−0.0787256
$352$	−25.6696	+	8.34056i	−1.36820	+	0.444554i
$353$	7.50341	+	10.3276i	0.399366	+	0.549681i	0.960585	−	0.277987i	$-0.0896672\pi$
$353$	7.50341	+	10.3276i	0.399366	+	0.549681i	−0.561218	+	0.827668i	$0.689667\pi$
$354$	−0.0764797	+	0.0555658i	−0.00406485	+	0.00295329i
$355$		0			0
$356$	−0.0170634	−	0.0123973i	−0.000904359	−	0.000657056i
$357$		−	1.76999i		−	0.0936776i
$358$	3.34591	−	4.60524i	0.176837	−	0.243395i
$359$	1.39620	−	4.29707i	0.0736888	−	0.226791i	−0.907428	−	0.420208i	$-0.861957\pi$
$359$	1.39620	−	4.29707i	0.0736888	−	0.226791i	0.981117	+	0.193417i	$0.0619571\pi$
$360$		0			0
$361$	14.3665	+	44.2156i	0.756132	+	2.32714i
$362$	−7.70923	−	2.50488i	−0.405188	−	0.131654i
$363$	14.7010	+	4.77664i	0.771602	+	0.250709i
$364$	−2.00796	−	6.17987i	−0.105246	−	0.323913i
$365$		0			0
$366$	−1.06304	+	3.27171i	−0.0555662	+	0.171015i
$367$	1.78361	−	2.45493i	0.0931039	−	0.128146i	−0.759924	−	0.650012i	$-0.774764\pi$
$367$	1.78361	−	2.45493i	0.0931039	−	0.128146i	0.853028	+	0.521866i	$0.174764\pi$
$368$			0.878043i			0.0457711i
$369$	−4.18201	−	3.03841i	−0.217707	−	0.158173i
$370$		0			0
$371$	18.9921	−	13.7986i	0.986022	−	0.716387i
$372$	4.51756	+	6.21789i	0.234225	+	0.322382i
$373$	14.6138	−	4.74831i	0.756674	−	0.245858i	0.0948232	−	0.995494i	$-0.469771\pi$
$373$	14.6138	−	4.74831i	0.756674	−	0.245858i	0.661850	+	0.749636i	$0.269771\pi$
$374$	1.89838			0.0981626
$375$		0			0
$376$	−16.9718			−0.875252
$377$	−0.0500388	+	0.0162586i	−0.00257713	+	0.000837359i
$378$	−0.811515	−	1.11695i	−0.0417398	−	0.0574499i
$379$	8.38117	−	6.08927i	0.430512	−	0.312785i	−0.351342	−	0.936247i	$-0.614275\pi$
$379$	8.38117	−	6.08927i	0.430512	−	0.312785i	0.781853	+	0.623462i	$0.214275\pi$
$380$		0			0
$381$	−0.279516	−	0.203080i	−0.0143200	−	0.0104041i
$382$		−	6.56946i		−	0.336123i
$383$	9.10278	−	12.5289i	0.465130	−	0.640197i	−0.510432	−	0.859918i	$-0.670515\pi$
$383$	9.10278	−	12.5289i	0.465130	−	0.640197i	0.975563	+	0.219721i	$0.0705147\pi$
$384$	3.55734	−	10.9484i	0.181535	−	0.558707i
$385$		0			0
$386$	2.36137	+	7.26756i	0.120191	+	0.369909i
$387$	10.8902	+	3.53843i	0.553578	+	0.179868i
$388$	12.4085	+	4.03176i	0.629945	+	0.204681i
$389$	6.61139	+	20.3478i	0.335211	+	1.03167i	0.966618	+	0.256221i	$0.0824776\pi$
$389$	6.61139	+	20.3478i	0.335211	+	1.03167i	−0.631407	+	0.775451i	$0.717522\pi$
$390$		0			0
$391$	0.0792318	−	0.243850i	0.00400693	−	0.0123320i
$392$	−0.443401	+	0.610289i	−0.0223951	+	0.0308243i
$393$		−	4.56651i		−	0.230350i
$394$	−7.70434	−	5.59753i	−0.388139	−	0.282000i
$395$		0			0
$396$	−7.12469	+	5.17639i	−0.358029	+	0.260123i
$397$	−7.34827	−	10.1140i	−0.368799	−	0.507608i	0.583775	−	0.811916i	$-0.301575\pi$
$397$	−7.34827	−	10.1140i	−0.368799	−	0.507608i	−0.952574	+	0.304307i	$0.901575\pi$
$398$	9.67249	−	3.14278i	0.484838	−	0.157534i
$399$	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	$0.808917\pi$
$402$	0.0425771	−	0.0138342i	0.00212355	−	0.000689985i
$403$	−3.89170	−	5.35647i	−0.193860	−	0.266825i
$404$	−11.4622	+	8.32779i	−0.570267	+	0.414323i
$405$		0			0
$406$	−0.0398443	−	0.0289486i	−0.00197744	−	0.00143669i
$407$			9.82111i			0.486815i
$408$	−0.805282	+	1.10837i	−0.0398674	+	0.0548727i
$409$	−0.932426	+	2.86971i	−0.0461055	+	0.141898i	−0.971459	−	0.237207i	$-0.923768\pi$
$409$	−0.932426	+	2.86971i	−0.0461055	+	0.141898i	0.925354	+	0.379105i	$0.123768\pi$
$410$		0			0
$411$	−1.48870	−	4.58174i	−0.0734321	−	0.226001i
$412$	16.9118	+	5.49497i	0.833183	+	0.270718i
$413$	−0.431179	−	0.140098i	−0.0212169	−	0.00689379i
$414$	−0.0618027	−	0.190209i	−0.00303744	−	0.00934827i
$415$		0			0
$416$	−2.39161	+	7.36062i	−0.117258	+	0.360884i
$417$	2.19876	−	3.02633i	0.107674	−	0.148200i
$418$			22.3343i			1.09241i
$419$	5.75511	+	4.18133i	0.281156	+	0.204272i	0.719421	−	0.694574i	$-0.244407\pi$
$419$	5.75511	+	4.18133i	0.281156	+	0.204272i	−0.438266	+	0.898845i	$0.644407\pi$
$420$		0			0
$421$	17.6826	−	12.8472i	0.861798	−	0.626133i	−0.0665758	−	0.997781i	$-0.521207\pi$
$421$	17.6826	−	12.8472i	0.861798	−	0.626133i	0.928373	+	0.371649i	$0.121207\pi$
$422$	−3.39873	−	4.67796i	−0.165448	−	0.227719i
$423$	−8.10408	+	2.63318i	−0.394034	+	0.128029i
$424$	−18.1709			−0.882455
$425$		0			0
$426$	6.52325			0.316052
$427$	−15.6905	+	5.09816i	−0.759318	+	0.246717i
$428$	−12.3518	−	17.0008i	−0.597045	−	0.821763i
$429$	6.13764	−	4.45926i	0.296328	−	0.215295i
$430$		0			0
$431$	−3.23115	−	2.34757i	−0.155639	−	0.113078i	0.507240	−	0.861805i	$-0.330666\pi$
$431$	−3.23115	−	2.34757i	−0.155639	−	0.113078i	−0.662879	+	0.748726i	$0.730666\pi$
$432$		−	2.35558i		−	0.113333i
$433$	−14.8071	+	20.3802i	−0.711583	+	0.979410i	0.288178	+	0.957577i	$0.406950\pi$
$433$	−14.8071	+	20.3802i	−0.711583	+	0.979410i	−0.999762	+	0.0218335i	$0.993050\pi$
$434$	1.91519	−	5.89435i	0.0919321	−	0.282938i
$435$		0			0
$436$	2.23746	+	6.88620i	0.107155	+	0.329789i
$437$	2.86890	+	0.932161i	0.137238	+	0.0445913i
$438$	−6.14987	−	1.99822i	−0.293852	−	0.0954784i
$439$	0.529997	+	1.63116i	0.0252954	+	0.0778511i	0.962907	−	0.269833i	$-0.0869683\pi$
$439$	0.529997	+	1.63116i	0.0252954	+	0.0778511i	−0.937612	+	0.347684i	$0.886968\pi$
$440$		0			0
$441$	−0.117039	+	0.360209i	−0.00557329	+	0.0171528i
$442$	0.319960	−	0.440387i	0.0152189	−	0.0209471i
$443$			11.7475i			0.558140i	0.960271	+	0.279070i	$0.0900261\pi$
$443$			11.7475i			0.558140i	−0.960271	+	0.279070i	$0.909974\pi$
$444$	−2.64471	−	1.92149i	−0.125512	−	0.0911899i
$445$		0			0
$446$	−11.9678	+	8.69510i	−0.566691	+	0.411725i
$447$	5.08212	+	6.99493i	0.240376	+	0.330849i
$448$	4.63929	−	1.50740i	0.219186	−	0.0712178i
$449$	−12.8415			−0.606030			−0.303015	−	0.952986i	$-0.597993\pi$
$449$	−12.8415			−0.606030			−0.303015	+	0.952986i	$0.597993\pi$
$450$		0			0
$451$	26.5890			1.25203
$452$	29.9101	−	9.71837i	1.40685	−	0.457114i
$453$	0.734135	+	1.01045i	0.0344927	+	0.0474751i
$454$	−1.72858	+	1.25589i	−0.0811263	+	0.0589417i
$455$		0			0
$456$	−13.0400	−	9.47412i	−0.610654	−	0.443666i
$457$			13.6882i			0.640309i	0.947365	+	0.320155i	$0.103735\pi$
$457$			13.6882i			0.640309i	−0.947365	+	0.320155i	$0.896265\pi$
$458$	3.77495	−	5.19577i	0.176392	−	0.242783i
$459$	−0.212560	+	0.654193i	−0.00992146	+	0.0305351i
$460$		0			0
$461$	3.00160	+	9.23799i	0.139799	+	0.430256i	0.996306	−	0.0858796i	$-0.0273700\pi$
$461$	3.00160	+	9.23799i	0.139799	+	0.430256i	−0.856507	+	0.516136i	$0.827370\pi$
$462$	6.75396	+	2.19450i	0.314223	+	0.102097i
$463$	20.2328	+	6.57403i	0.940297	+	0.305521i	0.738767	−	0.673961i	$-0.235408\pi$
$463$	20.2328	+	6.57403i	0.940297	+	0.305521i	0.201531	+	0.979482i	$0.435408\pi$
$464$	−0.0259664	−	0.0799163i	−0.00120546	−	0.00371002i
$465$		0			0
$466$	3.50143	−	10.7763i	0.162201	−	0.499202i
$467$	8.17106	−	11.2465i	0.378112	−	0.520426i	−0.576971	−	0.816764i	$-0.695766\pi$
$467$	8.17106	−	11.2465i	0.378112	−	0.520426i	0.955083	+	0.296338i	$0.0957656\pi$
$468$			2.52524i			0.116729i
$469$	0.173696	+	0.126198i	0.00802054	+	0.00582727i
$470$		0			0
$471$	−3.12745	+	2.27223i	−0.144105	+	0.104699i
$472$	0.206267	+	0.283902i	0.00949419	+	0.0130676i
$473$	−56.0156	+	18.2006i	−2.57560	+	0.836862i
$474$	−2.65959			−0.122159
$475$		0			0
$476$	−3.03042			−0.138899
$477$	−8.67665	+	2.81922i	−0.397277	+	0.129083i
$478$	−8.26438	−	11.3749i	−0.378004	−	0.520278i
$479$	−10.0057	+	7.26958i	−0.457173	+	0.332155i	−0.792421	−	0.609974i	$-0.791180\pi$
$479$	−10.0057	+	7.26958i	−0.457173	+	0.332155i	0.335249	+	0.942130i	$0.391180\pi$
$480$		0			0
$481$	2.27831	+	1.65529i	0.103882	+	0.0754747i
$482$			4.38601i			0.199777i
$483$	0.563776	−	0.775971i	0.0256527	−	0.0353079i
$484$	8.17817	−	25.1698i	0.371735	−	1.14408i
$485$		0			0
$486$	0.165802	+	0.510286i	0.00752094	+	0.0231471i
$487$	−33.5990	−	10.9170i	−1.52251	−	0.494695i	−0.576026	−	0.817432i	$-0.695397\pi$
$487$	−33.5990	−	10.9170i	−1.52251	−	0.494695i	−0.946489	+	0.322737i	$0.895397\pi$
$488$	12.1450	+	3.94614i	0.549778	+	0.178634i
$489$	2.15512	+	6.63277i	0.0974578	+	0.299944i
$490$		0			0
$491$	−6.70374	+	20.6320i	−0.302536	+	0.931109i	0.678050	+	0.735016i	$0.262825\pi$
$491$	−6.70374	+	20.6320i	−0.302536	+	0.931109i	−0.980585	+	0.196093i	$0.937175\pi$
$492$	−5.20211	+	7.16009i	−0.234529	+	0.322802i
$493$			0.0245375i			0.00110511i
$494$	5.18114	+	3.76432i	0.233111	+	0.169365i
$495$		0			0
$496$	8.55475	−	6.21539i	0.384120	−	0.279079i
$497$	18.3884	+	25.3095i	0.824834	+	1.13529i
$498$	−4.77793	+	1.55244i	−0.214104	+	0.0695666i
$499$	−38.7869			−1.73634			−0.868171	−	0.496265i	$-0.834704\pi$
$499$	−38.7869			−1.73634			−0.868171	+	0.496265i	$0.834704\pi$
$500$		0			0
$501$	−15.9594			−0.713013
$502$	12.6625	−	4.11430i	0.565155	−	0.183630i
$503$	3.77337	+	5.19360i	0.168246	+	0.231571i	0.884812	−	0.465949i	$-0.154287\pi$
$503$	3.77337	+	5.19360i	0.168246	+	0.231571i	−0.716565	+	0.697520i	$0.754287\pi$
$504$	−4.14627	+	3.01244i	−0.184689	+	0.134185i
$505$		0			0
$506$	0.832257	+	0.604670i	0.0369983	+	0.0268809i
$507$			10.8246i			0.480737i
$508$	−0.347697	+	0.478564i	−0.0154266	+	0.0212328i
$509$	2.22343	−	6.84300i	0.0985516	−	0.303311i	−0.889611	−	0.456718i	$-0.849025\pi$
$509$	2.22343	−	6.84300i	0.0985516	−	0.303311i	0.988163	+	0.153408i	$0.0490247\pi$
$510$		0			0
$511$	−9.58307	−	29.4937i	−0.423930	−	1.30472i
$512$	−20.6796	−	6.71922i	−0.913919	−	0.296950i
$513$	−7.69657	−	2.50077i	−0.339812	−	0.110412i
$514$	−4.02891	−	12.3997i	−0.177708	−	0.546928i
$515$		0			0
$516$	6.05820	−	18.6452i	0.266697	−	0.820810i
$517$	25.7627	−	35.4593i	1.13304	−	1.55950i
$518$			2.63611i			0.115824i
$519$	−6.20783	−	4.51025i	−0.272493	−	0.197978i
$520$		0			0
$521$	8.51120	−	6.18375i	0.372882	−	0.270915i	−0.385523	−	0.922698i	$-0.625979\pi$
$521$	8.51120	−	6.18375i	0.372882	−	0.270915i	0.758405	+	0.651783i	$0.225979\pi$
$522$	0.0112501	+	0.0154845i	0.000492404	+	0.000677737i
$523$	−10.7700	+	3.49938i	−0.470938	+	0.153017i	−0.534865	−	0.844938i	$-0.679638\pi$
$523$	−10.7700	+	3.49938i	−0.470938	+	0.153017i	0.0639269	+	0.997955i	$0.479638\pi$
$524$	−7.81840			−0.341548
$525$		0			0
$526$	4.57282			0.199385
$527$	−2.93669	+	0.954188i	−0.127924	+	0.0415651i
$528$	7.12183	+	9.80235i	0.309938	+	0.426593i
$529$	−18.4950	+	13.4374i	−0.804130	+	0.584234i
$530$		0			0
$531$	0.142541	+	0.103562i	0.00618573	+	0.00449420i
$532$		−	35.6529i		−	1.54575i
$533$	4.48142	−	6.16814i	0.194112	−	0.267172i
$534$	0.00204251	−	0.00628621i	8.83882e−5	−	0.000272031i
$535$		0			0
$536$	−0.0513540	−	0.158051i	−0.00221815	−	0.00682678i
$537$	−10.0901	−	3.27846i	−0.435418	−	0.141476i
$538$	1.31813	+	0.428287i	0.0568287	+	0.0184648i
$539$	−0.602013	−	1.85281i	−0.0259305	−	0.0798060i
$540$		0			0
$541$	5.22898	−	16.0931i	0.224811	−	0.691898i	−0.773499	−	0.633797i	$-0.781495\pi$
$541$	5.22898	−	16.0931i	0.224811	−	0.691898i	0.998311	−	0.0581012i	$-0.0185046\pi$
$542$	4.28572	−	5.89879i	0.184087	−	0.253375i
$543$			15.1076i			0.648331i
$544$	2.92009	+	2.12157i	0.125198	+	0.0909614i
$545$		0			0
$546$	1.64742	−	1.19692i	0.0705032	−	0.0512235i
$547$	−25.9429	−	35.7073i	−1.10924	−	1.52674i	−0.822533	−	0.568717i	$-0.807440\pi$
$547$	−25.9429	−	35.7073i	−1.10924	−	1.52674i	−0.286705	−	0.958019i	$-0.592560\pi$
$548$	−7.84448	+	2.54883i	−0.335100	+	0.108881i
$549$	6.41152			0.273637
$550$		0			0
$551$	−0.288683			−0.0122983
$552$	−0.706079	+	0.229419i	−0.0300527	+	0.00976472i
$553$	−7.49715	−	10.3189i	−0.318811	−	0.438806i
$554$	3.96734	−	2.88244i	0.168556	−	0.122463i
$555$		0			0
$556$	−5.18143	−	3.76453i	−0.219741	−	0.159652i
$557$		−	17.8472i		−	0.756210i	−0.925763	−	0.378105i	$-0.876576\pi$
$557$		−	17.8472i		−	0.756210i	0.925763	−	0.378105i	$-0.123424\pi$
$558$	−1.41572	+	1.94857i	−0.0599323	+	0.0824897i
$559$	−5.21891	+	16.0621i	−0.220736	+	0.679356i
$560$		0			0
$561$	−1.09334	−	3.36497i	−0.0461610	−	0.142069i
$562$	−5.31213	−	1.72602i	−0.224079	−	0.0728076i
$563$	−20.3586	−	6.61490i	−0.858012	−	0.278785i	−0.153214	−	0.988193i	$-0.548962\pi$
$563$	−20.3586	−	6.61490i	−0.858012	−	0.278785i	−0.704798	+	0.709408i	$0.748962\pi$
$564$	4.50831	+	13.8751i	0.189834	+	0.584249i
$565$		0			0
$566$	0.798480	−	2.45747i	0.0335626	−	0.103295i
$567$	−1.51248	+	2.08175i	−0.0635181	+	0.0874251i
$568$		−	24.2151i		−	1.01604i
$569$	−21.0929	−	15.3249i	−0.884262	−	0.642454i	0.0501135	−	0.998744i	$-0.484042\pi$
$569$	−21.0929	−	15.3249i	−0.884262	−	0.642454i	−0.934376	+	0.356289i	$0.884042\pi$
$570$		0			0
$571$	7.71705	−	5.60676i	0.322948	−	0.234636i	−0.414484	−	0.910057i	$-0.636038\pi$
$571$	7.71705	−	5.60676i	0.322948	−	0.234636i	0.737433	+	0.675421i	$0.236038\pi$
$572$	−7.63478	−	10.5084i	−0.319226	−	0.439377i
$573$	−11.6447	+	3.78359i	−0.486464	+	0.158062i
$574$	7.13683			0.297885
$575$		0			0
$576$	−1.89572			−0.0789885
$577$	8.65941	−	2.81361i	0.360496	−	0.117132i	−0.123169	−	0.992386i	$-0.539306\pi$
$577$	8.65941	−	2.81361i	0.360496	−	0.117132i	0.483664	+	0.875254i	$0.339306\pi$
$578$	5.21214	+	7.17390i	0.216797	+	0.298395i
$579$	11.5221	−	8.37130i	0.478843	−	0.347900i
$580$		0			0
$581$	−19.4919	−	14.1617i	−0.808658	−	0.587525i
$582$			4.08871i			0.169482i
$583$	27.5829	−	37.9646i	1.14237	−	1.57233i
$584$	−7.41761	+	22.8291i	−0.306943	+	0.944673i
$585$		0			0
$586$	4.05396	+	12.4768i	0.167468	+	0.515412i
$587$	28.0072	+	9.10008i	1.15598	+	0.375600i	0.823393	−	0.567472i	$-0.192079\pi$
$587$	28.0072	+	9.10008i	1.15598	+	0.375600i	0.332587	+	0.943073i	$0.392079\pi$
$588$	0.616721	+	0.200385i	0.0254331	+	0.00826373i
$589$	−11.2260	−	34.5501i	−0.462559	−	1.42361i
$590$		0			0
$591$	−5.48469	+	16.8802i	−0.225610	+	0.694357i
$592$	−2.64364	+	3.63866i	−0.108653	+	0.149548i
$593$		−	33.7757i		−	1.38700i	−0.720456	−	0.693501i	$-0.756067\pi$
$593$		−	33.7757i		−	1.38700i	0.720456	−	0.693501i	$-0.243933\pi$
$594$	−2.23275	−	1.62219i	−0.0916108	−	0.0665592i
$595$		0			0
$596$	11.9761	−	8.70118i	0.490562	−	0.356414i
$597$	−11.1415	−	15.3349i	−0.455991	−	0.627617i
$598$	0.280544	−	0.0911543i	0.0114723	−	0.00372758i
$599$	12.0575			0.492656			0.246328	−	0.969187i	$-0.420776\pi$
$599$	12.0575			0.492656			0.246328	+	0.969187i	$0.420776\pi$
$600$		0			0
$601$	0.0653240			0.00266462			0.00133231	−	0.999999i	$-0.499576\pi$
$601$	0.0653240			0.00266462			0.00133231	+	0.999999i	$0.499576\pi$
$602$	−15.0353	+	4.88526i	−0.612793	+	0.199108i
$603$	−0.0490435	−	0.0675025i	−0.00199720	−	0.00274892i
$604$	1.73001	−	1.25692i	0.0703930	−	0.0511435i
$605$		0			0
$606$	−3.59205	−	2.60978i	−0.145917	−	0.106015i
$607$			25.9556i			1.05350i	0.850019	+	0.526752i	$0.176590\pi$
$607$			25.9556i			1.05350i	−0.850019	+	0.526752i	$0.823410\pi$
$608$	−24.9602	+	34.3548i	−1.01227	+	1.39327i
$609$	−0.0283650	+	0.0872986i	−0.00114941	+	0.00353752i
$610$		0			0
$611$	−3.88373	−	11.9529i	−0.157119	−	0.483563i
$612$	1.12006	+	0.363928i	0.0452756	+	0.0147109i
$613$	11.9559	+	3.88472i	0.482896	+	0.156902i	0.540341	−	0.841446i	$-0.318295\pi$
$613$	11.9559	+	3.88472i	0.482896	+	0.156902i	−0.0574448	+	0.998349i	$0.518295\pi$
$614$	1.57786	+	4.85617i	0.0636774	+	0.195979i
$615$		0			0
$616$	8.14623	−	25.0715i	0.328221	−	1.01016i
$617$	1.09165	−	1.50253i	0.0439483	−	0.0604896i	−0.786477	−	0.617619i	$-0.788097\pi$
$617$	1.09165	−	1.50253i	0.0439483	−	0.0604896i	0.830426	+	0.557130i	$0.188097\pi$
$618$			5.57259i			0.224162i
$619$	−14.5814	−	10.5940i	−0.586077	−	0.425810i	0.254833	−	0.966985i	$-0.417980\pi$
$619$	−14.5814	−	10.5940i	−0.586077	−	0.425810i	−0.840910	+	0.541175i	$0.817980\pi$
$620$		0			0
$621$	−0.301561	+	0.219097i	−0.0121012	+	0.00879206i
$622$	7.87848	+	10.8438i	0.315898	+	0.434797i
$623$	0.0301475	−	0.00979552i	0.00120783	−	0.000392449i
$624$	3.47430			0.139083
$625$		0			0
$626$	5.30195			0.211908
$627$	39.5888	−	12.8632i	1.58102	−	0.513705i
$628$	3.89032	+	5.35456i	0.155241	+	0.213670i
$629$	1.06254	−	0.771977i	0.0423661	−	0.0307807i
$630$		0			0
$631$	−17.3636	−	12.6154i	−0.691233	−	0.502210i	0.185832	−	0.982582i	$-0.440502\pi$
$631$	−17.3636	−	12.6154i	−0.691233	−	0.502210i	−0.877065	+	0.480371i	$0.840502\pi$
$632$			9.87272i			0.392716i
$633$	−6.33446	+	8.71864i	−0.251772	+	0.346535i
$634$	−4.10046	+	12.6199i	−0.162850	+	0.501201i
$635$		0			0
$636$	4.82683	+	14.8555i	0.191396	+	0.589057i
$637$	−0.531281	−	0.172624i	−0.0210501	−	0.00683960i
$638$	−0.0936310	−	0.0304225i	−0.00370689	−	0.00120444i
$639$	−3.75698	−	11.5628i	−0.148624	−	0.457417i
$640$		0			0
$641$	12.2648	−	37.7471i	0.484430	−	1.49092i	−0.348374	−	0.937355i	$-0.613266\pi$
$641$	12.2648	−	37.7471i	0.484430	−	1.49092i	0.832805	−	0.553567i	$-0.186734\pi$
$642$	3.87082	−	5.32773i	0.152769	−	0.210269i
$643$		−	1.26211i		−	0.0497729i	−0.999690	−	0.0248864i	$-0.992078\pi$
$643$		−	1.26211i		−	0.0497729i	0.999690	−	0.0248864i	$-0.00792242\pi$
$644$	−1.32855	−	0.965250i	−0.0523523	−	0.0380362i
$645$		0			0
$646$	2.41633	−	1.75557i	0.0950692	−	0.0690718i
$647$	17.0032	+	23.4029i	0.668466	+	0.920064i	0.999724	−	0.0234758i	$-0.00747326\pi$
$647$	17.0032	+	23.4029i	0.668466	+	0.920064i	−0.331259	+	0.943540i	$0.607473\pi$
$648$	1.89424	−	0.615477i	0.0744129	−	0.0241782i
$649$	−0.906266			−0.0355740
$650$		0			0
$651$	−11.5511			−0.452722
$652$	11.3561	−	3.68982i	0.444739	−	0.144504i
$653$	10.2743	+	14.1413i	0.402063	+	0.553393i	0.961260	−	0.275642i	$-0.0888904\pi$
$653$	10.2743	+	14.1413i	0.402063	+	0.553393i	−0.559197	+	0.829035i	$0.688890\pi$
$654$	−1.83571	+	1.33372i	−0.0717821	+	0.0521527i
$655$		0			0
$656$	9.85106	+	7.15721i	0.384619	+	0.279442i
$657$			12.0518i			0.470186i
$658$	6.91503	−	9.51772i	0.269576	−	0.371039i
$659$	−3.50406	+	10.7844i	−0.136499	+	0.420100i	−0.995820	−	0.0913359i	$-0.970886\pi$
$659$	−3.50406	+	10.7844i	−0.136499	+	0.420100i	0.859321	+	0.511436i	$0.170886\pi$
$660$		0			0
$661$	1.43350	+	4.41185i	0.0557565	+	0.171601i	0.975057	−	0.221956i	$-0.0712443\pi$
$661$	1.43350	+	4.41185i	0.0557565	+	0.171601i	−0.919300	+	0.393557i	$0.871244\pi$
$662$	−0.550225	−	0.178779i	−0.0213851	−	0.00694844i
$663$	−0.964885	−	0.313510i	−0.0374730	−	0.0121757i
$664$	5.76285	+	17.7362i	0.223642	+	0.688299i
$665$		0			0
$666$	0.316575	−	0.974317i	0.0122670	−	0.0377540i
$667$	−0.00781569	+	0.0107574i	−0.000302625	+	0.000416527i
$668$			27.3243i			1.05721i
$669$	22.3052	+	16.2057i	0.862369	+	0.626547i
$670$		0			0
$671$	−26.6805	+	19.3845i	−1.02999	+	0.748330i
$672$	7.93647	+	10.9236i	0.306156	+	0.421387i
$673$	7.16302	−	2.32741i	0.276114	−	0.0897149i	−0.167687	−	0.985840i	$-0.553630\pi$
$673$	7.16302	−	2.32741i	0.276114	−	0.0897149i	0.443801	+	0.896125i	$0.353630\pi$
$674$	7.54435			0.290598
$675$		0			0
$676$	18.5330			0.712807
$677$	−30.0707	+	9.77055i	−1.15571	+	0.375513i	−0.823291	−	0.567619i	$-0.807864\pi$
$677$	−30.0707	+	9.77055i	−1.15571	+	0.375513i	−0.332418	+	0.943132i	$0.607864\pi$
$678$	5.79300	+	7.97338i	0.222479	+	0.306216i
$679$	−15.8638	+	11.5257i	−0.608795	+	0.442316i
$680$		0			0
$681$	3.22167	+	2.34068i	0.123455	+	0.0896952i
$682$		−	12.3889i		−	0.474397i
$683$	−18.0215	+	24.8045i	−0.689575	+	0.949118i	−0.999999	−	0.00148011i	$-0.999529\pi$
$683$	−18.0215	+	24.8045i	−0.689575	+	0.949118i	0.310424	+	0.950598i	$0.399529\pi$
$684$	−4.28161	+	13.1774i	−0.163711	+	0.503852i
$685$		0			0
$686$	−3.14806	−	9.68873i	−0.120193	−	0.369917i
$687$	−11.3839	−	3.69886i	−0.434323	−	0.141120i
$688$	−25.6526	−	8.33505i	−0.977998	−	0.317771i
$689$	−4.15813	−	12.7974i	−0.158412	−	0.487542i
$690$		0			0
$691$	−10.7334	+	33.0341i	−0.408318	+	1.25667i	0.509774	+	0.860308i	$0.329729\pi$
$691$	−10.7334	+	33.0341i	−0.408318	+	1.25667i	−0.918092	+	0.396366i	$0.870271\pi$
$692$	−7.72208	+	10.6285i	−0.293550	+	0.404036i
$693$		−	13.2356i		−	0.502780i
$694$	−2.47243	−	1.79632i	−0.0938520	−	0.0681875i
$695$		0			0
$696$	0.0574802	−	0.0417618i	0.00217878	−	0.00158298i
$697$	−2.09000	−	2.87663i	−0.0791643	−	0.108960i
$698$	14.5406	−	4.72453i	0.550370	−	0.178826i
$699$	−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	$0.620326\pi$
$702$	−0.752633	+	0.244545i	−0.0284063	+	0.00922977i
$703$	9.08230	+	12.5007i	0.342545	+	0.471473i
$704$	7.88873	−	5.73150i	0.297318	−	0.216014i
$705$		0			0
$706$	5.54122	+	4.02593i	0.208547	+	0.151518i
$707$		−	21.2935i		−	0.800825i
$708$	0.177310	−	0.244046i	0.00666372	−	0.00917182i
$709$	7.82140	−	24.0718i	0.293739	−	0.904035i	−0.689904	−	0.723901i	$-0.742347\pi$
$709$	7.82140	−	24.0718i	0.293739	−	0.904035i	0.983642	−	0.180133i	$-0.0576529\pi$
$710$		0			0
$711$	1.53176	+	4.71426i	0.0574453	+	0.176799i
$712$	−0.0233351	−	0.00758205i	−0.000874522	−	0.000284149i
$713$	−1.59139	−	0.517073i	−0.0595979	−	0.0193645i
$714$	−0.293467	−	0.903200i	−0.0109827	−	0.0338014i
$715$		0			0
$716$	−5.61311	+	17.2754i	−0.209772	+	0.645611i
$717$	−15.4029	+	21.2003i	−0.575232	+	0.791738i
$718$		−	2.42423i		−	0.0904715i
$719$	−7.43539	−	5.40213i	−0.277293	−	0.201465i	0.440443	−	0.897781i	$-0.354822\pi$
$719$	−7.43539	−	5.40213i	−0.277293	−	0.201465i	−0.717736	+	0.696315i	$0.754822\pi$
$720$		0			0
$721$	−21.6211	+	15.7086i	−0.805210	+	0.585019i
$722$	14.6621	+	20.1806i	0.545666	+	0.751045i
$723$	7.77443	−	2.52607i	0.289134	−	0.0939454i
$724$	25.8661			0.961305
$725$		0			0
$726$	8.29369			0.307808
$727$	12.4254	−	4.03726i	0.460833	−	0.149734i	−0.0693942	−	0.997589i	$-0.522107\pi$
$727$	12.4254	−	4.03726i	0.460833	−	0.149734i	0.530227	+	0.847856i	$0.322107\pi$
$728$	−4.44312	−	6.11542i	−0.164673	−	0.226653i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	6.37213	+	4.62963i	0.235682	+	0.171233i
$732$		−	10.9773i		−	0.405732i
$733$	5.69030	−	7.83202i	0.210176	−	0.289282i	−0.690894	−	0.722956i	$-0.742783\pi$
$733$	5.69030	−	7.83202i	0.210176	−	0.289282i	0.901070	+	0.433674i	$0.142783\pi$
$734$	0.503121	−	1.54845i	0.0185705	−	0.0571542i
$735$		0			0
$736$	0.604419	+	1.86021i	0.0222792	+	0.0685683i
$737$	0.408172	+	0.132623i	0.0150352	+	0.00488524i
$738$	−2.63780	−	0.857072i	−0.0970986	−	0.0315493i
$739$	−2.82260	−	8.68707i	−0.103831	−	0.319559i	0.885623	−	0.464404i	$-0.153732\pi$
$739$	−2.82260	−	8.68707i	−0.103831	−	0.319559i	−0.989454	+	0.144845i	$0.953732\pi$
$740$		0			0
$741$	3.68844	−	11.3518i	0.135498	−	0.417021i
$742$	7.40359	−	10.1902i	0.271794	−	0.374093i
$743$			6.35760i			0.233238i	0.993177	+	0.116619i	$0.0372056\pi$
$743$			6.35760i			0.233238i	−0.993177	+	0.116619i	$0.962794\pi$
$744$	7.23334	+	5.25533i	0.265187	+	0.192670i
$745$		0			0
$746$	6.66994	−	4.84600i	0.244204	−	0.177425i
$747$	5.50356	+	7.57501i	0.201365	+	0.277155i
$748$	−5.76122	+	1.87193i	−0.210651	+	0.0684446i
$749$	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	$0.279414\pi$
$752$	19.0898	−	6.20266i	0.696134	−	0.226188i
$753$	−14.5856	−	20.0754i	−0.531529	−	0.731586i
$754$	−0.0228384	+	0.0165931i	−0.000831725	+	0.000604284i
$755$		0			0
$756$	3.56419	+	2.58954i	0.129628	+	0.0941806i
$757$			11.5175i			0.418609i	0.977850	+	0.209305i	$0.0671200\pi$
$757$			11.5175i			0.418609i	−0.977850	+	0.209305i	$0.932880\pi$
$758$	3.26718	−	4.49689i	0.118669	−	0.163334i
$759$	0.592481	−	1.82347i	0.0215057	−	0.0661878i
$760$		0			0
$761$	12.6925	+	39.0635i	0.460102	+	1.41605i	0.865039	+	0.501705i	$0.167294\pi$
$761$	12.6925	+	39.0635i	0.460102	+	1.41605i	−0.404936	+	0.914345i	$0.632706\pi$
$762$	−0.176304	−	0.0572847i	−0.00638683	−	0.00207521i
$763$	−10.3494	−	3.36273i	−0.374674	−	0.121739i
$764$	6.47795	+	19.9371i	0.234364	+	0.721298i
$765$		0			0
$766$	2.56771	−	7.90259i	0.0927750	−	0.285532i
$767$	−0.152746	+	0.210236i	−0.00551533	+	0.00759120i
$768$		−	2.38518i		−	0.0860677i
$769$	14.5193	+	10.5489i	0.523578	+	0.380402i	0.817950	−	0.575289i	$-0.195111\pi$
$769$	14.5193	+	10.5489i	0.523578	+	0.380402i	−0.294372	+	0.955691i	$0.595111\pi$
$770$		0			0
$771$	−19.6587	+	14.2829i	−0.707992	+	0.514386i
$772$	−14.3327	−	19.7272i	−0.515844	−	0.709998i
$773$	49.4776	−	16.0762i	1.77958	−	0.578222i	0.780676	−	0.624935i	$-0.214875\pi$
$773$	49.4776	−	16.0762i	1.77958	−	0.578222i	0.998908	+	0.0467133i	$0.0148747\pi$
$774$	6.14378			0.220833
$775$		0			0
$776$	15.1778			0.544850
$777$	4.67264	−	1.51823i	0.167630	−	0.0544663i
$778$	6.74741	+	9.28701i	0.241906	+	0.332955i
$779$	33.8435	−	24.5888i	1.21257	−	0.880984i
$780$		0			0
$781$	50.5928	+	36.7578i	1.81035	+	1.31530i
$782$		−	0.137570i		−	0.00491951i
$783$	0.0209676	−	0.0288595i	0.000749322	−	0.00103135i
$784$	0.275695	−	0.848502i	0.00984626	−	0.0303037i
$785$		0			0
$786$	−0.757137	−	2.33023i	−0.0270062	−	0.0831165i
$787$	−11.9113	−	3.87021i	−0.424592	−	0.137958i	0.0889240	−	0.996038i	$-0.471657\pi$
$787$	−11.9113	−	3.87021i	−0.424592	−	0.137958i	−0.513516	+	0.858080i	$0.671657\pi$
$788$	28.9008	+	9.39044i	1.02955	+	0.334521i
$789$	−2.63366	−	8.10556i	−0.0937607	−	0.288566i
$790$		0			0
$791$	−14.6060	+	44.9525i	−0.519328	+	1.59833i
$792$	−6.02175	+	8.28823i	−0.213974	+	0.294509i
$793$			9.45650i			0.335810i
$794$	−5.42665	−	3.94269i	−0.192585	−	0.139921i
$795$		0			0
$796$	−26.2552	+	19.0755i	−0.930591	+	0.676114i
$797$	−14.7779	−	20.3400i	−0.523460	−	0.720481i	0.462656	−	0.886538i	$-0.346896\pi$
$797$	−14.7779	−	20.3400i	−0.523460	−	0.720481i	−0.986116	+	0.166057i	$0.946896\pi$
$798$	10.6261	−	3.45264i	0.376161	−	0.122222i
$799$	−5.86134			−0.207359
$800$		0			0
$801$	−0.0123190			−0.000435270
$802$	−16.8638	+	5.47939i	−0.595483	+	0.193484i
$803$	−36.4372	−	50.1516i	−1.28584	−	1.76981i
$804$	−0.115572	+	0.0839682i	−0.00407592	+	0.00296133i
$805$		0			0
$806$	−2.87400	−	2.08808i	−0.101232	−	0.0735495i
$807$		−	2.58312i		−	0.0909302i
$808$	−9.68781	+	13.3341i	−0.340816	+	0.469093i
$809$	1.49157	−	4.59059i	0.0524409	−	0.161396i	−0.921406	−	0.388601i	$-0.872959\pi$
$809$	1.49157	−	4.59059i	0.0524409	−	0.161396i	0.973847	+	0.227204i	$0.0729585\pi$
$810$		0			0
$811$	−11.3898	−	35.0543i	−0.399952	−	1.23092i	−0.925038	−	0.379875i	$-0.875967\pi$
$811$	−11.3898	−	35.0543i	−0.399952	−	1.23092i	0.525086	−	0.851049i	$-0.324033\pi$
$812$	0.149465	+	0.0485643i	0.00524521	+	0.00170427i
$813$	−12.9242	−	4.19933i	−0.453271	−	0.147277i
$814$	1.62836	+	5.01158i	0.0570740	+	0.175656i
$815$		0			0
$816$	0.500703	−	1.54100i	0.0175281	−	0.0539460i
$817$	−54.4675	+	74.9680i	−1.90558	+	2.62280i
$818$			1.61897i			0.0566061i
$819$	−3.07042	−	2.23079i	−0.107289	−	0.0779500i
$820$		0			0
$821$	−11.4772	+	8.33868i	−0.400557	+	0.291022i	−0.769768	−	0.638324i	$-0.779628\pi$
$821$	−11.4772	+	8.33868i	−0.400557	+	0.291022i	0.369211	+	0.929346i	$0.379628\pi$
$822$	−1.51933	−	2.09117i	−0.0529926	−	0.0729380i
$823$	24.7212	−	8.03241i	0.861728	−	0.279992i	0.155378	−	0.987855i	$-0.450340\pi$
$823$	24.7212	−	8.03241i	0.861728	−	0.279992i	0.706350	+	0.707863i	$0.250340\pi$
$824$	20.6861			0.720634
$825$		0			0
$826$	−0.243253			−0.00846386
$827$	−40.8326	+	13.2673i	−1.41989	+	0.461350i	−0.915567	−	0.402166i	$-0.868257\pi$
$827$	−40.8326	+	13.2673i	−1.41989	+	0.461350i	−0.504322	+	0.863516i	$0.668257\pi$
$828$	0.375120	+	0.516308i	0.0130363	+	0.0179429i
$829$	−4.56100	+	3.31376i	−0.158410	+	0.115092i	−0.664167	−	0.747585i	$-0.731213\pi$
$829$	−4.56100	+	3.31376i	−0.158410	+	0.115092i	0.505756	+	0.862676i	$0.331213\pi$
$830$		0			0
$831$	−7.39421	−	5.37221i	−0.256502	−	0.186360i
$832$		−	2.79605i		−	0.0969355i
$833$	−0.153132	+	0.210769i	−0.00530572	+	0.00730270i
$834$	0.620224	−	1.90885i	0.0214766	−	0.0660981i
$835$		0			0
$836$	−22.0233	−	67.7806i	−0.761690	−	2.34424i
$837$	4.26931	+	1.38718i	0.147569	+	0.0479481i
$838$	3.63003	+	1.17947i	0.125397	+	0.0407441i
$839$	7.12687	+	21.9343i	0.246047	+	0.757255i	0.995463	+	0.0951546i	$0.0303346\pi$
$839$	7.12687	+	21.9343i	0.246047	+	0.757255i	−0.749416	+	0.662100i	$0.769665\pi$
$840$		0			0
$841$	−8.96110	+	27.5794i	−0.309003	+	0.951015i
$842$	6.89311	−	9.48755i	0.237552	−	0.326963i
$843$			10.4101i			0.358543i
$844$	14.9273	+	10.8453i	0.513820	+	0.373312i
$845$		0			0
$846$	−3.69882	+	2.68735i	−0.127168	+	0.0923929i
$847$	23.3792	+	32.1787i	0.803317	+	1.10567i
$848$	20.4386	−	6.64089i	0.701863	−	0.228049i
$849$	−4.81586			−0.165280
$850$		0			0
$851$	0.711711			0.0243971
$852$	−19.7968	+	6.43238i	−0.678229	+	0.220370i
$853$	22.9504	+	31.5886i	0.785808	+	1.08157i	0.994617	+	0.103616i	$0.0330413\pi$
$853$	22.9504	+	31.5886i	0.785808	+	1.08157i	−0.208809	+	0.977956i	$0.566959\pi$
$854$	−7.16138	+	5.20305i	−0.245057	+	0.178045i
$855$		0			0
$856$	−19.7772	−	14.3690i	−0.675970	−	0.491121i
$857$			12.7315i			0.434899i	0.976072	+	0.217450i	$0.0697738\pi$
$857$			12.7315i			0.434899i	−0.976072	+	0.217450i	$0.930226\pi$
$858$	2.39260	−	3.29313i	0.0816821	−	0.112426i
$859$	−4.50752	+	13.8727i	−0.153795	+	0.473331i	−0.998037	−	0.0626308i	$-0.980051\pi$
$859$	−4.50752	+	13.8727i	−0.153795	+	0.473331i	0.844242	+	0.535962i	$0.180051\pi$
$860$		0			0
$861$	−4.11036	−	12.6504i	−0.140081	−	0.431124i
$862$	−2.03805	−	0.662201i	−0.0694161	−	0.0225547i
$863$	16.6573	+	5.41229i	0.567021	+	0.184236i	0.578478	−	0.815698i	$-0.303647\pi$
$863$	16.6573	+	5.41229i	0.567021	+	0.184236i	−0.0114567	+	0.999934i	$0.503647\pi$
$864$	−1.62151	−	4.99051i	−0.0551650	−	0.169781i
$865$		0			0
$866$	−4.17677	+	12.8548i	−0.141933	+	0.436824i
$867$	9.71424	−	13.3705i	0.329913	−	0.454086i
$868$			19.7768i			0.671267i
$869$	−20.6272	−	14.9865i	−0.699729	−	0.508383i
$870$		0			0
$871$	0.0995611	−	0.0723353i	0.00337350	−	0.00245099i
$872$	4.95094	+	6.81438i	0.167660	+	0.230764i
$873$	7.24744	−	2.35484i	0.245289	−	0.0796992i
$874$	1.61851			0.0547470
$875$		0			0
$876$	20.6341			0.697162
$877$	−8.66169	+	2.81435i	−0.292485	+	0.0950340i	−0.451584	−	0.892229i	$-0.649141\pi$
$877$	−8.66169	+	2.81435i	−0.292485	+	0.0950340i	0.159100	+	0.987263i	$0.449141\pi$
$878$	0.540900	+	0.744485i	0.0182545	+	0.0251252i
$879$	19.7809	−	14.3717i	0.667195	−	0.484745i
$880$		0			0
$881$	36.5744	+	26.5728i	1.23222	+	0.895261i	0.997055	−	0.0766939i	$-0.0244364\pi$
$881$	36.5744	+	26.5728i	1.23222	+	0.895261i	0.235167	+	0.971955i	$0.424436\pi$
$882$			0.203215i			0.00684262i
$883$	2.49354	−	3.43206i	0.0839142	−	0.115498i	−0.764996	−	0.644035i	$-0.777259\pi$
$883$	2.49354	−	3.43206i	0.0839142	−	0.115498i	0.848910	+	0.528537i	$0.177259\pi$
$884$	−0.536766	+	1.65200i	−0.0180534	+	0.0555626i
$885$		0			0
$886$	1.94776	+	5.99458i	0.0654362	+	0.201392i
$887$	−12.1607	−	3.95124i	−0.408316	−	0.132670i	0.0976554	−	0.995220i	$-0.468866\pi$
$887$	−12.1607	−	3.95124i	−0.408316	−	0.132670i	−0.505971	+	0.862551i	$0.668866\pi$
$888$	−3.61678	−	1.17516i	−0.121371	−	0.0394359i
$889$	−0.274727	−	0.845523i	−0.00921405	−	0.0283579i
$890$		0			0
$891$	−1.58949	+	4.89194i	−0.0532498	+	0.163886i
$892$	27.7460	−	38.1891i	0.929005	−	1.27867i
$893$		−	68.9586i		−	2.30761i
$894$	3.75311	+	2.72679i	0.125523	+	0.0911976i
$895$		0			0
$896$	23.9647	−	17.4113i	0.800603	−	0.581672i
$897$	−0.323151	−	0.444779i	−0.0107897	−	0.0148508i
$898$	−6.55287	+	2.12916i	−0.218672	+	0.0710508i
$899$	0.160134			0.00534076
$900$		0			0
$901$	−6.27546			−0.209066
$902$	13.5680	−	4.40851i	0.451765	−	0.146787i
$903$	17.3187	+	23.8372i	0.576332	+	0.793253i
$904$	29.5981	−	21.5043i	0.984419	−	0.715223i
$905$		0			0
$906$	0.542154	+	0.393898i	0.0180118	+	0.0130864i
$907$			9.51928i			0.316082i	0.987433	+	0.158041i	$0.0505179\pi$
$907$			9.51928i			0.316082i	−0.987433	+	0.158041i	$0.949482\pi$
$908$	4.00753	−	5.51589i	0.132994	−	0.183051i
$909$	−2.55717	+	7.87016i	−0.0848160	+	0.261037i
$910$		0			0
$911$	−12.8107	−	39.4274i	−0.424438	−	1.30629i	−0.903531	−	0.428522i	$-0.859034\pi$
$911$	−12.8107	−	39.4274i	−0.424438	−	1.30629i	0.479093	−	0.877764i	$-0.340966\pi$
$912$	18.1299	+	5.89076i	0.600341	+	0.195063i
$913$	−45.8043	−	14.8827i	−1.51590	−	0.492546i
$914$	2.26954	+	6.98492i	0.0750697	+	0.231041i
$915$		0			0
$916$	−6.33287	+	19.4906i	−0.209244	+	0.643987i
$917$	6.90674	−	9.50631i	0.228081	−	0.313926i
$918$			0.369069i			0.0121811i
$919$	12.8372	+	9.32675i	0.423459	+	0.307661i	0.779028	−	0.626989i	$-0.215713\pi$
$919$	12.8372	+	9.32675i	0.423459	+	0.307661i	−0.355569	+	0.934650i	$0.615713\pi$
$920$		0			0
$921$	7.69905	−	5.59369i	0.253692	−	0.184318i
$922$	3.06336	+	4.21635i	0.100886	+	0.138858i
$923$	17.0542	−	5.54125i	0.561346	−	0.182393i
$924$	−22.6610			−0.745491
$925$		0			0
$926$	11.4145			0.375104
$927$	9.87769	−	3.20946i	0.324426	−	0.105412i
$928$	−0.110024	−	0.151435i	−0.00361172	−	0.00497110i
$929$	−23.7938	+	17.2872i	−0.780650	+	0.567175i	−0.905174	−	0.425041i	$-0.860260\pi$
$929$	−23.7938	+	17.2872i	−0.780650	+	0.567175i	0.124524	+	0.992217i	$0.460260\pi$
$930$		0			0
$931$	−2.47969	−	1.80160i	−0.0812685	−	0.0590451i
$932$			36.1567i			1.18435i
$933$	14.6837	−	20.2103i	0.480722	−	0.661657i
$934$	2.30489	−	7.09372i	0.0754182	−	0.232114i
$935$		0			0
$936$	0.907781	+	2.79386i	0.0296718	+	0.0913203i
$937$	55.2688	+	17.9579i	1.80555	+	0.586660i	0.999983	−	0.00583887i	$-0.00185858\pi$
$937$	55.2688	+	17.9579i	1.80555	+	0.586660i	0.805571	+	0.592499i	$0.201859\pi$
$938$	0.109559	+	0.0355978i	0.00357722	+	0.00116231i
$939$	−3.05359	−	9.39797i	−0.0996500	−	0.306691i
$940$		0			0
$941$	10.5779	−	32.5553i	0.344828	−	1.06127i	−0.616848	−	0.787083i	$-0.711591\pi$
$941$	10.5779	−	32.5553i	0.344828	−	1.06127i	0.961676	−	0.274189i	$-0.0884095\pi$
$942$	−1.21916	+	1.67802i	−0.0397222	+	0.0546730i
$943$		−	1.92684i		−	0.0627464i
$944$	−0.335766	−	0.243948i	−0.0109282	−	0.00793984i
$945$		0			0
$946$	−25.5663	+	18.5750i	−0.831232	+	0.603925i
$947$	−22.3420	−	30.7511i	−0.726016	−	0.999275i	−0.999303	−	0.0373427i	$-0.988111\pi$
$947$	−22.3420	−	30.7511i	−0.726016	−	0.999275i	0.273286	−	0.961933i	$-0.411889\pi$
$948$	8.07137	−	2.62255i	0.262146	−	0.0851764i
$949$	−17.7755			−0.577017
$950$		0			0
$951$	24.7310			0.801958
$952$	−3.35278	+	1.08939i	−0.108664	+	0.0353072i
$953$	9.94235	+	13.6845i	0.322064	+	0.443284i	0.939096	−	0.343655i	$-0.111665\pi$
$953$	9.94235	+	13.6845i	0.322064	+	0.443284i	−0.617032	+	0.786938i	$0.711665\pi$
$954$	−3.96015	+	2.87722i	−0.128214	+	0.0931533i
$955$		0			0
$956$	36.2973	+	26.3716i	1.17394	+	0.852917i
$957$			0.183487i			0.00593130i
$958$	−3.90047	+	5.36853i	−0.126018	+	0.173449i
$959$	3.83069	−	11.7897i	0.123699	−	0.380708i
$960$		0			0
$961$	−3.35243	−	10.3177i	−0.108143	−	0.332829i
$962$	1.43704	+	0.466923i	0.0463321	+	0.0150542i
$963$	−11.6730	−	3.79280i	−0.376158	−	0.122221i
$964$	−4.32492	−	13.3107i	−0.139296	−	0.428710i
$965$		0			0
$966$	0.159030	−	0.489443i	0.00511669	−	0.0157476i
$967$	−13.3924	+	18.4330i	−0.430670	+	0.592767i	−0.968107	−	0.250537i	$-0.919393\pi$
$967$	−13.3924	+	18.4330i	−0.430670	+	0.592767i	0.537437	+	0.843304i	$0.319393\pi$
$968$		−	30.7872i		−	0.989537i
$969$	−4.50348	−	3.27197i	−0.144673	−	0.105111i
$970$		0			0
$971$	−35.5849	+	25.8539i	−1.14197	+	0.829692i	−0.987393	−	0.158288i	$-0.949402\pi$
$971$	−35.5849	+	25.8539i	−1.14197	+	0.829692i	−0.154580	+	0.987980i	$0.549402\pi$
$972$	−1.00636	−	1.38513i	−0.0322789	−	0.0444281i
$973$	9.15450	−	2.97448i	0.293480	−	0.0953574i
$974$	−18.9552			−0.607362
$975$		0			0
$976$	−15.1029			−0.483431
$977$	17.7211	−	5.75794i	0.566948	−	0.184213i	−0.0114968	−	0.999934i	$-0.503660\pi$
$977$	17.7211	−	5.75794i	0.566948	−	0.184213i	0.578445	+	0.815721i	$0.303660\pi$
$978$	2.19946	+	3.02729i	0.0703308	+	0.0968021i
$979$	0.0512634	−	0.0372450i	0.00163838	−	0.00119036i
$980$		0			0
$981$	3.42135	+	2.48575i	0.109235	+	0.0793640i
$982$			11.6397i			0.371438i
$983$	−32.0387	+	44.0975i	−1.02188	+	1.40649i	−0.110998	+	0.993821i	$0.535405\pi$
$983$	−32.0387	+	44.0975i	−1.02188	+	1.40649i	−0.910880	+	0.412672i	$0.864595\pi$
$984$	−3.18155	+	9.79181i	−0.101424	+	0.312152i
$985$		0			0
$986$	0.00406837	+	0.0125212i	0.000129563	+	0.000398755i
$987$	−20.8533	−	6.77563i	−0.663767	−	0.215671i
$988$	−19.4357	−	6.31504i	−0.618332	−	0.200908i
$989$	1.31895	+	4.05930i	0.0419401	+	0.129078i
$990$		0			0
$991$	11.1881	−	34.4335i	0.355403	−	1.09382i	−0.600373	−	0.799720i	$-0.704981\pi$
$991$	11.1881	−	34.4335i	0.355403	−	1.09382i	0.955776	−	0.294097i	$-0.0950188\pi$
$992$	13.8455	−	19.0567i	0.439595	−	0.605051i
$993$			1.07827i			0.0342178i
$994$	13.5797	+	9.86626i	0.430723	+	0.312939i
$995$		0			0
$996$	12.9693	−	9.42275i	0.410948	−	0.298571i
$997$	4.22750	+	5.81865i	0.133886	+	0.184279i	0.870696	−	0.491821i	$-0.163669\pi$
$997$	4.22750	+	5.81865i	0.133886	+	0.184279i	−0.736810	+	0.676100i	$0.763669\pi$
$998$	−19.7924	+	6.43096i	−0.626519	+	0.203568i
$999$	−1.90935			−0.0604092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.349.3		16
5.2	odd	4		375.2.g.e.151.3		16
5.3	odd	4		375.2.g.d.151.2		16
5.4	even	2		75.2.i.a.19.2	yes	16
15.14	odd	2		225.2.m.b.19.3		16
25.2	odd	20		1875.2.a.m.1.6		8
25.3	odd	20		375.2.g.d.226.2		16
25.4	even	10	inner	375.2.i.c.274.3		16
25.11	even	5		1875.2.b.h.1249.7		16
25.14	even	10		1875.2.b.h.1249.10		16
25.21	even	5		75.2.i.a.4.2	✓	16
25.22	odd	20		375.2.g.e.226.3		16
25.23	odd	20		1875.2.a.p.1.3		8
75.2	even	20		5625.2.a.bd.1.3		8
75.23	even	20		5625.2.a.t.1.6		8
75.71	odd	10		225.2.m.b.154.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.2	✓	16	25.21	even	5
75.2.i.a.19.2	yes	16	5.4	even	2
225.2.m.b.19.3		16	15.14	odd	2
225.2.m.b.154.3		16	75.71	odd	10
375.2.g.d.151.2		16	5.3	odd	4
375.2.g.d.226.2		16	25.3	odd	20
375.2.g.e.151.3		16	5.2	odd	4
375.2.g.e.226.3		16	25.22	odd	20
375.2.i.c.274.3		16	25.4	even	10	inner
375.2.i.c.349.3		16	1.1	even	1	trivial
1875.2.a.m.1.6		8	25.2	odd	20
1875.2.a.p.1.3		8	25.23	odd	20
1875.2.b.h.1249.7		16	25.11	even	5
1875.2.b.h.1249.10		16	25.14	even	10
5625.2.a.t.1.6		8	75.23	even	20
5625.2.a.bd.1.3		8	75.2	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.510286 - 0.165802i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(-0.434076 - 0.315374i) q^{6} -2.57318i q^{7} +(-1.17071 + 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.510286 - 0.165802i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.38513 + 1.00636i) q^{4} +(-0.434076 - 0.315374i) q^{6} -2.57318i q^{7} +(-1.17071 + 1.61134i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-1.58949 - 4.89194i) q^{11} +(1.62832 + 0.529073i) q^{12} +(-1.40274 - 0.455776i) q^{13} +(-0.426639 - 1.31306i) q^{14} +(0.727915 - 2.24029i) q^{16} +(-0.404314 + 0.556490i) q^{17} +0.536547i q^{18} +(-6.54709 - 4.75674i) q^{19} +(-2.08175 + 1.51248i) q^{21} +(-1.62219 - 2.23275i) q^{22} +(-0.354506 + 0.115186i) q^{23} +1.99173 q^{24} -0.791365 q^{26} +(0.951057 - 0.309017i) q^{27} +(2.58954 + 3.56419i) q^{28} +(0.0288595 - 0.0209676i) q^{29} +(3.63169 + 2.63858i) q^{31} -5.24733i q^{32} +(-3.02338 + 4.16133i) q^{33} +(-0.114049 + 0.351005i) q^{34} +(-0.529073 - 1.62832i) q^{36} +(-1.81590 - 0.590022i) q^{37} +(-4.12957 - 1.34178i) q^{38} +(0.455776 + 1.40274i) q^{39} +(-1.59739 + 4.91625i) q^{41} +(-0.811515 + 1.11695i) q^{42} -11.4506i q^{43} +(7.12469 + 5.17639i) q^{44} +(-0.161802 + 0.117556i) q^{46} +(5.00860 + 6.89374i) q^{47} +(-2.24029 + 0.727915i) q^{48} +0.378747 q^{49} +0.687859 q^{51} +(2.40165 - 0.780343i) q^{52} +(5.36247 + 7.38080i) q^{53} +(0.434076 - 0.315374i) q^{54} +(4.14627 + 3.01244i) q^{56} +8.09265i q^{57} +(0.0112501 - 0.0154845i) q^{58} +(0.0544457 - 0.167567i) q^{59} +(-1.98127 - 6.09772i) q^{61} +(2.29069 + 0.744289i) q^{62} +(2.44724 + 0.795156i) q^{63} +(0.585811 + 1.80294i) q^{64} +(-0.852834 + 2.62475i) q^{66} +(-0.0490435 + 0.0675025i) q^{67} -1.17770i q^{68} +(0.301561 + 0.219097i) q^{69} +(-9.83589 + 7.14619i) q^{71} +(-1.17071 - 1.61134i) q^{72} +(11.4619 - 3.72421i) q^{73} -1.02446 q^{74} +13.8556 q^{76} +(-12.5878 + 4.09004i) q^{77} +(0.465153 + 0.640228i) q^{78} +(4.01019 - 2.91357i) q^{79} +(-0.809017 - 0.587785i) q^{81} +2.77354i q^{82} +(5.50356 - 7.57501i) q^{83} +(1.36140 - 4.18996i) q^{84} +(-1.89853 - 5.84308i) q^{86} +(-0.0339264 - 0.0110233i) q^{87} +(9.74340 + 3.16582i) q^{88} +(0.00380677 + 0.0117160i) q^{89} +(-1.17279 + 3.60949i) q^{91} +(0.375120 - 0.516308i) q^{92} -4.48902i q^{93} +(3.69882 + 2.68735i) q^{94} +(-4.24518 + 3.08430i) q^{96} +(-4.47917 - 6.16504i) q^{97} +(0.193269 - 0.0627970i) q^{98} +5.14369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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