LMFDB - Embedded newform 775.2.ck.a.324.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			324.4
Character	$\chi$	$=$	775.324
Dual form			775.2.ck.a.299.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.55849 + 0.831304i) q^{2} +(1.05464 + 0.949606i) q^{3} +(4.23677 + 3.07819i) q^{4} +(1.90889 + 3.30629i) q^{6} +(-1.71742 - 0.180508i) q^{7} +(5.11835 + 7.04481i) q^{8} +(-0.103062 - 0.980572i) q^{9} +(-1.22177 + 0.543967i) q^{11} +(1.54521 + 7.26966i) q^{12} +(0.763174 - 3.59045i) q^{13} +(-4.24394 - 1.88952i) q^{14} +(4.00227 + 12.3177i) q^{16} +(-1.12374 + 2.52396i) q^{17} +(0.551469 - 2.59446i) q^{18} +(-2.51157 + 0.533850i) q^{19} +(-1.63986 - 1.82124i) q^{21} +(-3.57808 + 0.376072i) q^{22} +(0.316969 + 0.436271i) q^{23} +(-1.29175 + 12.2902i) q^{24} +(4.93733 - 8.55171i) q^{26} +(3.32495 - 4.57641i) q^{27} +(-6.72067 - 6.05132i) q^{28} +(2.51258 - 7.73291i) q^{29} +(4.75081 - 2.90341i) q^{31} +17.4262i q^{32} +(-1.80509 - 0.586508i) q^{33} +(-4.97326 + 5.52336i) q^{34} +(2.58174 - 4.47170i) q^{36} +(-6.70735 + 3.87249i) q^{37} +(-6.86961 - 0.722025i) q^{38} +(4.21439 - 3.06194i) q^{39} +(-0.0696243 - 0.0773256i) q^{41} +(-2.68155 - 6.02285i) q^{42} +(0.624713 + 2.93904i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(0.448289 + 1.37969i) q^{46} +(-6.39584 + 2.07813i) q^{47} +(-7.47602 + 16.7914i) q^{48} +(-3.93009 - 0.835366i) q^{49} +(-3.58192 + 1.59477i) q^{51} +(14.2855 - 12.8627i) q^{52} +(2.78341 - 0.292549i) q^{53} +(12.3112 - 8.94464i) q^{54} +(-7.51871 - 13.0228i) q^{56} +(-3.15576 - 1.82198i) q^{57} +(12.8568 - 17.6959i) q^{58} +(-0.311970 + 0.346478i) q^{59} -5.11468 q^{61} +(14.5685 - 3.47898i) q^{62} +1.70266i q^{63} +(-6.48190 + 19.9492i) q^{64} +(-4.13073 - 3.00115i) q^{66} +(7.18668 + 4.14923i) q^{67} +(-12.5303 + 7.23436i) q^{68} +(-0.0799956 + 0.761107i) q^{69} +(-0.497420 - 4.73264i) q^{71} +(6.38043 - 5.74497i) q^{72} +(3.05304 + 6.85725i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-12.2842 - 5.46929i) q^{76} +(2.19648 - 0.713679i) q^{77} +(13.3279 - 4.33049i) q^{78} +(8.86044 + 3.94492i) q^{79} +(4.95915 - 1.05410i) q^{81} +(-0.113852 - 0.255716i) q^{82} +(12.3991 - 11.1642i) q^{83} +(-1.34155 - 12.7640i) q^{84} +(-0.844916 + 8.03884i) q^{86} +(9.99310 - 5.76952i) q^{87} +(-10.0856 - 5.82292i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.95880 + 6.02855i) q^{91} +2.82407i q^{92} +(7.76751 + 1.44933i) q^{93} -18.0912 q^{94} +(-16.5480 + 18.3784i) q^{96} +(0.751881 - 1.03488i) q^{97} +(-9.36065 - 5.40437i) q^{98} +(0.659316 + 1.14197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{11}{15}\right)$	$-1$

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 $

$2$	2.55849	+	0.831304i	1.80913	+	0.587821i	1.00000		0.000184800i	$5.88237e-5\pi$
$2$	2.55849	+	0.831304i	1.80913	+	0.587821i	0.809126	+	0.587636i	$0.199941\pi$
$3$	1.05464	+	0.949606i	0.608899	+	0.548255i	0.914851	−	0.403792i	$-0.132308\pi$
$3$	1.05464	+	0.949606i	0.608899	+	0.548255i	−0.305952	+	0.952047i	$0.598975\pi$
$4$	4.23677	+	3.07819i	2.11839	+	1.53910i
$5$		0			0
$5$		0			0
$6$	1.90889	+	3.30629i	0.779300	+	1.34979i
$7$	−1.71742	−	0.180508i	−0.649123	−	0.0682256i	−0.225756	−	0.974184i	$-0.572485\pi$
$7$	−1.71742	−	0.180508i	−0.649123	−	0.0682256i	−0.423367	+	0.905958i	$0.639152\pi$
$8$	5.11835	+	7.04481i	1.80961	+	2.49072i
$9$	−0.103062	−	0.980572i	−0.0343541	−	0.326857i
$10$		0			0
$11$	−1.22177	+	0.543967i	−0.368377	+	0.164012i	−0.582572	−	0.812779i	$-0.697954\pi$
$11$	−1.22177	+	0.543967i	−0.368377	+	0.164012i	0.214195	+	0.976791i	$0.431287\pi$
$12$	1.54521	+	7.26966i	0.446065	+	2.09857i
$13$	0.763174	−	3.59045i	0.211666	−	0.995812i	−0.736106	−	0.676866i	$-0.763338\pi$
$13$	0.763174	−	3.59045i	0.211666	−	0.995812i	0.947773	−	0.318946i	$-0.103329\pi$
$14$	−4.24394	−	1.88952i	−1.13424	−	0.504997i
$15$		0			0
$16$	4.00227	+	12.3177i	1.00057	+	3.07943i
$17$	−1.12374	+	2.52396i	−0.272547	+	0.612150i	−0.997019	−	0.0771534i	$-0.975417\pi$
$17$	−1.12374	+	2.52396i	−0.272547	+	0.612150i	0.724472	+	0.689304i	$0.242084\pi$
$18$	0.551469	−	2.59446i	0.129983	−	0.611520i
$19$	−2.51157	+	0.533850i	−0.576193	+	0.122474i	−0.486786	−	0.873522i	$-0.661831\pi$
$19$	−2.51157	+	0.533850i	−0.576193	+	0.122474i	−0.0894075	+	0.995995i	$0.528497\pi$
$20$		0			0
$21$	−1.63986	−	1.82124i	−0.357846	−	0.397428i
$22$	−3.57808	+	0.376072i	−0.762850	+	0.0801788i
$23$	0.316969	+	0.436271i	0.0660927	+	0.0909688i	0.840784	−	0.541371i	$-0.182095\pi$
$23$	0.316969	+	0.436271i	0.0660927	+	0.0909688i	−0.774691	+	0.632340i	$0.782095\pi$
$24$	−1.29175	+	12.2902i	−0.263678	+	2.50872i
$25$		0			0
$26$	4.93733	−	8.55171i	0.968290	−	1.67713i
$27$	3.32495	−	4.57641i	0.639888	−	0.880730i
$28$	−6.72067	−	6.05132i	−1.27009	−	1.14359i
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	−0.390419	−	0.920637i	$-0.627670\pi$
$29$	2.51258	−	7.73291i	0.466574	−	1.43597i	0.856993	−	0.515329i	$-0.172330\pi$
$30$		0			0
$31$	4.75081	−	2.90341i	0.853271	−	0.521468i
$31$	4.75081	−	2.90341i	0.853271	−	0.521468i
$32$			17.4262i			3.08054i
$33$	−1.80509	−	0.586508i	−0.314225	−	0.102098i
$34$	−4.97326	+	5.52336i	−0.852906	+	0.947248i
$35$		0			0
$36$	2.58174	−	4.47170i	0.430290	−	0.745284i
$37$	−6.70735	+	3.87249i	−1.10268	+	0.636633i	−0.936924	−	0.349533i	$-0.886340\pi$
$37$	−6.70735	+	3.87249i	−1.10268	+	0.636633i	−0.165757	+	0.986167i	$0.553007\pi$
$38$	−6.86961	−	0.722025i	−1.11440	−	0.117128i
$39$	4.21439	−	3.06194i	0.674843	−	0.490302i
$40$		0			0
$41$	−0.0696243	−	0.0773256i	−0.0108735	−	0.0120762i	0.737684	−	0.675147i	$-0.235920\pi$
$41$	−0.0696243	−	0.0773256i	−0.0108735	−	0.0120762i	−0.748557	+	0.663070i	$0.769253\pi$
$42$	−2.68155	−	6.02285i	−0.413772	−	0.929346i
$43$	0.624713	+	2.93904i	0.0952678	+	0.448200i	0.999764	+	0.0217184i	$0.00691373\pi$
$43$	0.624713	+	2.93904i	0.0952678	+	0.448200i	−0.904496	+	0.426481i	$0.859753\pi$
$44$	−6.85079	−	1.45618i	−1.03280	−	0.219527i
$45$		0			0
$46$	0.448289	+	1.37969i	0.0660967	+	0.203425i
$47$	−6.39584	+	2.07813i	−0.932929	+	0.303127i	−0.735760	−	0.677243i	$-0.763175\pi$
$47$	−6.39584	+	2.07813i	−0.932929	+	0.303127i	−0.197169	+	0.980370i	$0.563175\pi$
$48$	−7.47602	+	16.7914i	−1.07907	+	2.42363i
$49$	−3.93009	−	0.835366i	−0.561441	−	0.119338i
$50$		0			0
$51$	−3.58192	+	1.59477i	−0.501568	+	0.223313i
$52$	14.2855	−	12.8627i	1.98104	−	1.78374i
$53$	2.78341	−	0.292549i	0.382331	−	0.0401846i	0.0885864	−	0.996068i	$-0.471765\pi$
$53$	2.78341	−	0.292549i	0.382331	−	0.0401846i	0.293745	+	0.955884i	$0.405098\pi$
$54$	12.3112	−	8.94464i	1.67535	−	1.21721i
$55$		0			0
$56$	−7.51871	−	13.0228i	−1.00473	−	1.74024i
$57$	−3.15576	−	1.82198i	−0.417990	−	0.241327i
$58$	12.8568	−	17.6959i	1.68818	−	2.32358i
$59$	−0.311970	+	0.346478i	−0.0406151	+	0.0451076i	−0.763110	−	0.646269i	$-0.776329\pi$
$59$	−0.311970	+	0.346478i	−0.0406151	+	0.0451076i	0.722495	+	0.691376i	$0.242995\pi$
$60$		0			0
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$	14.5685	−	3.47898i	1.85020	−	0.441831i
$63$			1.70266i			0.214514i
$64$	−6.48190	+	19.9492i	−0.810238	+	2.49365i
$65$		0			0
$66$	−4.13073	−	3.00115i	−0.508457	−	0.369416i
$67$	7.18668	+	4.14923i	0.877993	+	0.506910i	0.869996	−	0.493058i	$-0.164121\pi$
$67$	7.18668	+	4.14923i	0.877993	+	0.506910i	0.00799701	+	0.999968i	$0.497454\pi$
$68$	−12.5303	+	7.23436i	−1.51952	+	0.877294i
$69$	−0.0799956	+	0.761107i	−0.00963034	+	0.0916265i
$70$		0			0
$71$	−0.497420	−	4.73264i	−0.0590329	−	0.561661i	−0.983565	−	0.180556i	$-0.942210\pi$
$71$	−0.497420	−	4.73264i	−0.0590329	−	0.561661i	0.924532	−	0.381105i	$-0.124456\pi$
$72$	6.38043	−	5.74497i	0.751941	−	0.677051i
$73$	3.05304	+	6.85725i	0.357332	+	0.802580i	0.999356	+	0.0358953i	$0.0114283\pi$
$73$	3.05304	+	6.85725i	0.357332	+	0.802580i	−0.642024	+	0.766685i	$0.721905\pi$
$74$	−20.3799	+	4.33188i	−2.36911	+	0.503571i
$75$		0			0
$76$	−12.2842	−	5.46929i	−1.40910	−	0.627371i
$77$	2.19648	−	0.713679i	0.250312	−	0.0813313i
$78$	13.3279	−	4.33049i	1.50909	−	0.490332i
$79$	8.86044	+	3.94492i	0.996877	+	0.443838i	0.839300	−	0.543668i	$-0.182965\pi$
$79$	8.86044	+	3.94492i	0.996877	+	0.443838i	0.157577	+	0.987507i	$0.449632\pi$
$80$		0			0
$81$	4.95915	−	1.05410i	0.551017	−	0.117122i
$82$	−0.113852	−	0.255716i	−0.0125728	−	0.0282391i
$83$	12.3991	−	11.1642i	1.36097	−	1.22543i	0.411567	−	0.911380i	$-0.364982\pi$
$83$	12.3991	−	11.1642i	1.36097	−	1.22543i	0.949407	−	0.314047i	$-0.101685\pi$
$84$	−1.34155	−	12.7640i	−0.146375	−	1.39266i
$85$		0			0
$86$	−0.844916	+	8.03884i	−0.0911096	+	0.866850i
$87$	9.99310	−	5.76952i	1.07137	−	0.618557i
$88$	−10.0856	−	5.82292i	−1.07513	−	0.620725i
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.999989	−	0.00468333i	$-0.998509\pi$
$89$	−12.3911	−	9.00268i	−1.31346	−	0.954282i	−0.313468	−	0.949599i	$-0.601491\pi$
$90$		0			0
$91$	−1.95880	+	6.02855i	−0.205338	+	0.631964i
$92$			2.82407i			0.294430i
$93$	7.76751	+	1.44933i	0.805454	+	0.150289i
$94$	−18.0912			−1.86597
$95$		0			0
$96$	−16.5480	+	18.3784i	−1.68892	+	1.87574i
$97$	0.751881	−	1.03488i	0.0763420	−	0.105076i	−0.769138	−	0.639082i	$-0.779314\pi$
$97$	0.751881	−	1.03488i	0.0763420	−	0.105076i	0.845480	+	0.534007i	$0.179314\pi$
$98$	−9.36065	−	5.40437i	−0.945568	−	0.545924i
$99$	0.659316	+	1.14197i	0.0662638	+	0.114772i
$100$		0			0
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	−0.864523	−	0.502593i	$-0.832379\pi$
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	0.210842	+	0.977520i	$0.432379\pi$
$102$	−10.4900	+	1.10255i	−1.03867	+	0.109168i
$103$	−11.2605	+	10.1390i	−1.10953	+	0.999026i	−0.109544	+	0.993982i	$0.534939\pi$
$103$	−11.2605	+	10.1390i	−1.10953	+	0.999026i	−0.999987	+	0.00504416i	$0.998394\pi$
$104$	29.2002	−	13.0008i	2.86332	−	1.27483i
$105$		0			0
$106$	7.36453	+	1.56538i	0.715307	+	0.152043i
$107$	−5.03362	+	11.3057i	−0.486618	+	1.09296i	0.488759	+	0.872419i	$0.337450\pi$
$107$	−5.03362	+	11.3057i	−0.486618	+	1.09296i	−0.975377	+	0.220543i	$0.929217\pi$
$108$	28.1741	−	9.15433i	2.71106	−	0.880876i
$109$	−2.22788	−	6.85672i	−0.213392	−	0.656755i	−0.999264	−	0.0383645i	$-0.987785\pi$
$109$	−2.22788	−	6.85672i	−0.213392	−	0.656755i	0.785871	−	0.618390i	$-0.212215\pi$
$110$		0			0
$111$	−10.7512	−	2.28524i	−1.02046	−	0.216905i
$112$	−4.65013	−	21.8772i	−0.439396	−	2.06720i
$113$	6.78103	+	15.2304i	0.637906	+	1.43276i	0.885844	+	0.463984i	$0.153580\pi$
$113$	6.78103	+	15.2304i	0.637906	+	1.43276i	−0.247938	+	0.968776i	$0.579753\pi$
$114$	−6.55936	−	7.28491i	−0.614340	−	0.682294i
$115$		0			0
$116$	34.4486	−	25.0284i	3.19847	−	2.32383i
$117$	−3.59935	−	0.378307i	−0.332760	−	0.0349745i
$118$	−1.08620	+	0.627119i	−0.0999930	+	0.0577310i
$119$	2.38553	−	4.13185i	0.218681	−	0.378767i
$120$		0			0
$121$	−6.16362	+	6.84539i	−0.560329	+	0.622308i
$122$	−13.0859	−	4.25185i	−1.18474	−	0.384944i
$123$		−	0.147667i		−	0.0133147i
$124$	29.0654	+	2.32284i	2.61015	+	0.208597i
$125$		0			0
$126$	−1.41542	+	4.35623i	−0.126096	+	0.388084i
$127$	9.59358	+	8.63810i	0.851293	+	0.766507i	0.974146	−	0.225918i	$-0.0725380\pi$
$127$	9.59358	+	8.63810i	0.851293	+	0.766507i	−0.122854	+	0.992425i	$0.539205\pi$
$128$	−12.6820	+	17.4553i	−1.12095	+	1.54285i
$129$	−2.13208	+	3.69288i	−0.187720	+	0.325140i
$130$		0			0
$131$	0.254818	−	2.42443i	0.0222635	−	0.211823i	−0.977735	−	0.209846i	$-0.932704\pi$
$131$	0.254818	−	2.42443i	0.0222635	−	0.211823i	0.999998	−	0.00197767i	$-0.000629511\pi$
$132$	−5.84235	−	8.04130i	−0.508511	−	0.699906i
$133$	4.40978	−	0.463486i	0.382376	−	0.0401894i
$134$	14.9378	+	16.5901i	1.29043	+	1.43317i
$135$		0			0
$136$	−23.5325	+	5.00199i	−2.01790	+	0.428917i
$137$	−1.69320	+	7.96586i	−0.144660	+	0.680570i	0.844719	+	0.535210i	$0.179767\pi$
$137$	−1.69320	+	7.96586i	−0.144660	+	0.680570i	−0.989379	+	0.145360i	$0.953566\pi$
$138$	−0.837379	+	1.88078i	−0.0712824	+	0.160103i
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	0.967225	−	0.253921i	$-0.0817204\pi$
$139$	0.418212	+	1.28712i	0.0354723	+	0.109172i	−0.931753	+	0.363094i	$0.881720\pi$
$140$		0			0
$141$	−8.71874	−	3.88183i	−0.734251	−	0.326909i
$142$	2.66162	−	12.5219i	0.223358	−	1.05082i
$143$	1.02066	+	4.80184i	0.0853522	+	0.401550i
$144$	11.6659	−	5.19401i	0.972161	−	0.432834i
$145$		0			0
$146$	2.11072	+	20.0822i	0.174685	+	1.66201i
$147$	−3.35158	−	4.61305i	−0.276433	−	0.380478i
$148$	−40.3378	−	4.23967i	−3.31574	−	0.348499i
$149$	−4.50192	−	7.79756i	−0.368812	−	0.638801i	0.620568	−	0.784153i	$-0.286902\pi$
$149$	−4.50192	−	7.79756i	−0.368812	−	0.638801i	−0.989380	+	0.145351i	$0.953569\pi$
$150$		0			0
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	0.688371	−	0.725359i	$-0.258326\pi$
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	−0.477139	+	0.878828i	$0.658326\pi$
$152$	−16.6160	−	14.9611i	−1.34773	−	1.21350i
$153$	2.59074	+	0.841782i	0.209449	+	0.0680541i
$154$	6.21295			0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	3.16395	+	1.02803i	0.252510	+	0.0820456i	0.432537	−	0.901616i	$-0.357618\pi$
$157$	3.16395	+	1.02803i	0.252510	+	0.0820456i	−0.180027	+	0.983662i	$0.557618\pi$
$158$	19.3899	+	17.4588i	1.54258	+	1.38894i
$159$	3.21332	+	2.33461i	0.254833	+	0.185147i
$160$		0			0
$161$	−0.465619	−	0.806476i	−0.0366959	−	0.0635592i
$162$	13.5642	+	1.42566i	1.06570	+	0.112010i
$163$	−1.02295	−	1.40797i	−0.0801236	−	0.110281i	0.767074	−	0.641559i	$-0.221712\pi$
$163$	−1.02295	−	1.40797i	−0.0801236	−	0.110281i	−0.847198	+	0.531278i	$0.821712\pi$
$164$	−0.0569589	−	0.541928i	−0.00444774	−	0.0423175i
$165$		0			0
$166$	41.0037	−	18.2560i	3.18250	−	1.41694i
$167$	−2.91419	−	13.7102i	−0.225507	−	1.06093i	−0.934570	−	0.355780i	$-0.884215\pi$
$167$	−2.91419	−	13.7102i	−0.225507	−	1.06093i	0.709063	−	0.705145i	$-0.249118\pi$
$168$	4.43696	−	20.8742i	0.342319	−	1.61048i
$169$	−0.432821	−	0.192704i	−0.0332939	−	0.0148234i
$170$		0			0
$171$	0.782326	+	2.40775i	0.0598260	+	0.184125i
$172$	−6.40018	+	14.3750i	−0.488009	+	1.09609i
$173$	−0.00249097	+	0.0117191i	−0.000189385	+	0.000890985i	−0.978242	−	0.207466i	$-0.933478\pi$
$173$	−0.00249097	+	0.0117191i	−0.000189385	+	0.000890985i	0.978053	+	0.208357i	$0.0668116\pi$
$174$	30.3635	−	6.45395i	2.30185	−	0.489273i
$175$		0			0
$176$	−11.5903	−	12.8723i	−0.873651	−	0.970288i
$177$	−0.658036	+	0.0691624i	−0.0494610	+	0.00519856i
$178$	−24.2186	−	33.3341i	−1.81526	−	2.49849i
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	0.883812	+	0.467842i	$0.154968\pi$
$179$	−1.04299	+	9.92334i	−0.0779564	+	0.741706i	−0.961769	+	0.273864i	$0.911698\pi$
$180$		0			0
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	−0.280004	−	0.959999i	$-0.590336\pi$
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	0.971385	−	0.237509i	$-0.0763308\pi$
$182$	−10.0231	+	13.7956i	−0.742963	+	1.02260i
$183$	−5.39417	−	4.85693i	−0.398748	−	0.359035i
$184$	−1.45108	+	4.46598i	−0.106975	+	0.329236i
$185$		0			0
$186$	18.6683	+	10.1653i	1.36882	+	0.745354i
$187$		−	3.69497i		−	0.270203i
$188$	−33.4946	−	10.8831i	−2.44284	−	0.793728i
$189$	−6.53642	+	7.25943i	−0.475454	+	0.528046i
$190$		0			0
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	−0.886885	−	0.461991i	$-0.847135\pi$
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	0.843538	+	0.537069i	$0.180469\pi$
$192$	−25.7800	+	14.8841i	−1.86051	+	1.07417i
$193$	−12.6568	−	1.33029i	−0.911059	−	0.0957562i	−0.362611	−	0.931941i	$-0.618115\pi$
$193$	−12.6568	−	1.33029i	−0.911059	−	0.0957562i	−0.548448	+	0.836184i	$0.684781\pi$
$194$	2.78398	−	2.02268i	0.199878	−	0.145220i
$195$		0			0
$196$	−14.0795	−	15.6368i	−1.00568	−	1.11692i
$197$	1.20744	+	2.71195i	0.0860263	+	0.193218i	0.951436	−	0.307847i	$-0.0996084\pi$
$197$	1.20744	+	2.71195i	0.0860263	+	0.193218i	−0.865410	+	0.501065i	$0.832942\pi$
$198$	0.737531	+	3.46981i	0.0524140	+	0.246589i
$199$	−12.8960	−	2.74112i	−0.914170	−	0.194313i	−0.273270	−	0.961937i	$-0.588105\pi$
$199$	−12.8960	−	2.74112i	−0.914170	−	0.194313i	−0.640900	+	0.767625i	$0.721439\pi$
$200$		0			0
$201$	3.63926	+	11.2005i	0.256694	+	0.790021i
$202$	−20.7755	+	6.75039i	−1.46176	+	0.474955i
$203$	−5.71100	+	12.8271i	−0.400834	+	0.900287i
$204$	−20.0848	−	4.26915i	−1.40622	−	0.298900i
$205$		0			0
$206$	−37.2385	+	16.5796i	−2.59453	+	1.15516i
$207$	0.395127	−	0.355774i	0.0274633	−	0.0247280i
$208$	47.2807	−	4.96940i	3.27832	−	0.344566i
$209$	2.77816	−	2.01845i	0.192169	−	0.139619i
$210$		0			0
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	−0.987343	−	0.158600i	$-0.949302\pi$
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	0.356320	−	0.934364i	$-0.384031\pi$
$212$	12.6932	+	7.32843i	0.871773	+	0.503318i
$213$	3.96954	−	5.46361i	0.271989	−	0.374360i
$214$	−22.2769	+	24.7410i	−1.52282	+	1.69126i
$215$		0			0
$216$	49.2582			3.35160
$217$	−8.68322	+	4.12881i	−0.589456	+	0.280282i
$218$		−	19.3949i		−	1.31359i
$219$	−3.29181	+	10.1311i	−0.222440	+	0.684599i
$220$		0			0
$221$	8.20455	+	5.96096i	0.551898	+	0.400977i
$222$	−25.6071	−	14.7843i	−1.71864	−	0.992256i
$223$	8.13718	−	4.69801i	0.544906	−	0.314602i	−0.202159	−	0.979353i	$-0.564796\pi$
$223$	8.13718	−	4.69801i	0.544906	−	0.314602i	0.747065	+	0.664751i	$0.231462\pi$
$224$	3.14557	−	29.9281i	0.210172	−	1.99965i
$225$		0			0
$226$	4.68807	+	44.6040i	0.311846	+	2.96702i
$227$	6.28658	−	5.66046i	0.417255	−	0.375698i	−0.433594	−	0.901108i	$-0.642755\pi$
$227$	6.28658	−	5.66046i	0.417255	−	0.375698i	0.850849	+	0.525410i	$0.176088\pi$
$228$	−7.76182	−	17.4333i	−0.514039	−	1.15455i
$229$	22.3443	−	4.74942i	1.47655	−	0.313850i	0.601887	−	0.798582i	$-0.294416\pi$
$229$	22.3443	−	4.74942i	1.47655	−	0.313850i	0.874663	+	0.484731i	$0.161083\pi$
$230$		0			0
$231$	2.99422	+	1.33311i	0.197005	+	0.0877123i
$232$	67.3372	−	21.8792i	4.42090	−	1.43644i
$233$	−15.4580	+	5.02260i	−1.01269	+	0.329042i	−0.767923	−	0.640542i	$-0.778710\pi$
$233$	−15.4580	+	5.02260i	−1.01269	+	0.329042i	−0.244762	+	0.969583i	$0.578710\pi$
$234$	−8.89441	−	3.96005i	−0.581446	−	0.258876i
$235$		0			0
$236$	−2.38828	+	0.507644i	−0.155463	+	0.0330448i
$237$	5.59849	+	12.5744i	0.363661	+	0.816796i
$238$	9.53817	−	8.58821i	0.618268	−	0.556691i
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	0.864035	+	0.503433i	$0.167930\pi$
$239$	1.91005	+	18.1729i	0.123551	+	1.17551i	−0.740484	+	0.672074i	$0.765404\pi$
$240$		0			0
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	−0.745222	−	0.666816i	$-0.767657\pi$
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	0.867576	−	0.497304i	$-0.165677\pi$
$242$	−21.4602	+	12.3900i	−1.37951	+	0.796461i
$243$	−8.46555	−	4.88759i	−0.543065	−	0.313539i
$244$	−21.6697	−	15.7440i	−1.38726	−	1.00790i
$245$		0			0
$246$	0.122756	−	0.377804i	0.00782663	−	0.0240879i
$247$			9.42508i			0.599704i
$248$	44.7703	+	18.6079i	2.84292	+	1.18160i
$249$	23.6782			1.50054
$250$		0			0
$251$	−15.3433	+	17.0405i	−0.968461	+	1.07558i	0.0286471	+	0.999590i	$0.490880\pi$
$251$	−15.3433	+	17.0405i	−0.968461	+	1.07558i	−0.997108	+	0.0759953i	$0.975787\pi$
$252$	−5.24111	+	7.21376i	−0.330159	+	0.454424i
$253$	−0.624580	−	0.360602i	−0.0392670	−	0.0226708i
$254$	17.3642	+	30.0757i	1.08953	+	1.88712i
$255$		0			0
$256$	−13.0179	+	9.45807i	−0.813620	+	0.591129i
$257$	−0.105611	+	0.0111002i	−0.00658785	+	0.000692411i	−0.107822	−	0.994170i	$-0.534388\pi$
$257$	−0.105611	+	0.0111002i	−0.00658785	+	0.000692411i	0.101234	+	0.994863i	$0.467721\pi$
$258$	−8.52482	+	7.67578i	−0.530732	+	0.477873i
$259$	12.2183	−	5.43996i	0.759211	−	0.338022i
$260$		0			0
$261$	−7.84163	−	1.66679i	−0.485385	−	0.103172i
$262$	2.66739	−	5.99105i	0.164792	−	0.370128i
$263$	6.94015	−	2.25499i	0.427948	−	0.139049i	−0.0871204	−	0.996198i	$-0.527766\pi$
$263$	6.94015	−	2.25499i	0.427948	−	0.139049i	0.515068	+	0.857149i	$0.327766\pi$
$264$	−5.10723	−	15.7184i	−0.314328	−	0.967403i
$265$		0			0
$266$	11.6677	+	2.48004i	0.715391	+	0.152061i
$267$	−4.51923	−	21.2613i	−0.276573	−	1.30117i
$268$	17.6762	+	39.7014i	1.07974	+	2.42515i
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	0.315088	−	0.949063i	$-0.397966\pi$
$269$	−10.8529	−	12.0533i	−0.661711	−	0.734905i	−0.976799	+	0.214158i	$0.931299\pi$
$270$		0			0
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	−0.454123	−	0.890939i	$-0.650047\pi$
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	0.707002	+	0.707212i	$0.250047\pi$
$272$	−35.5870	−	3.74034i	−2.15778	−	0.226792i
$273$	−7.79058	+	4.49790i	−0.471508	+	0.272225i
$274$	−10.9541	+	18.9730i	−0.661760	+	1.14620i
$275$		0			0
$276$	−2.68176	+	2.97839i	−0.161423	+	0.179278i
$277$	16.0946	+	5.22944i	0.967029	+	0.314207i	0.749616	−	0.661873i	$-0.230238\pi$
$277$	16.0946	+	5.22944i	0.967029	+	0.314207i	0.217413	+	0.976080i	$0.430238\pi$
$278$			3.64076i			0.218358i
$279$	−3.33663	−	4.35928i	−0.199759	−	0.260983i
$280$		0			0
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	−0.931943	−	0.362605i	$-0.881888\pi$
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	0.967091	+	0.254429i	$0.0818876\pi$
$282$	−19.0798	−	17.1796i	−1.13619	−	1.02303i
$283$	−8.99888	+	12.3859i	−0.534928	+	0.736265i	−0.987871	−	0.155274i	$-0.950374\pi$
$283$	−8.99888	+	12.3859i	−0.534928	+	0.736265i	0.452944	+	0.891539i	$0.350374\pi$
$284$	12.4605	−	21.5823i	0.739396	−	1.28067i
$285$		0			0
$286$	−1.38043	+	13.1339i	−0.0816268	+	0.776627i
$287$	0.105616	+	0.145368i	0.00623433	+	0.00858081i
$288$	17.0876	−	1.79598i	1.00690	−	0.105829i
$289$	6.26763	+	6.96091i	0.368684	+	0.409465i
$290$		0			0
$291$	1.77569	−	0.377435i	0.104093	−	0.0221256i
$292$	−8.17289	+	38.4504i	−0.478282	+	2.25014i
$293$	−10.8980	+	24.4772i	−0.636666	+	1.42998i	0.250313	+	0.968165i	$0.419467\pi$
$293$	−10.8980	+	24.4772i	−0.636666	+	1.42998i	−0.886979	+	0.461810i	$0.847200\pi$
$294$	−4.74013	−	14.5886i	−0.276450	−	0.850826i
$295$		0			0
$296$	−61.6115	−	27.4312i	−3.58110	−	1.59441i
$297$	−1.57291	+	7.39998i	−0.0912697	+	0.429390i
$298$	−5.03599	−	23.6924i	−0.291727	−	1.37247i
$299$	1.80831	−	0.805113i	0.104577	−	0.0465609i
$300$		0			0
$301$	−0.542373	−	5.16033i	−0.0312619	−	0.297437i
$302$	5.07324	+	6.98272i	0.291932	+	0.401810i
$303$	−11.4608	−	1.20458i	−0.658407	−	0.0692014i
$304$	−16.6278	−	28.8002i	−0.953670	−	1.65181i
$305$		0			0
$306$	5.92860	+	4.30738i	0.338916	+	0.246237i
$307$	−6.65208	−	5.98956i	−0.379654	−	0.341842i	0.457105	−	0.889413i	$-0.348886\pi$
$307$	−6.65208	−	5.98956i	−0.379654	−	0.341842i	−0.836760	+	0.547570i	$0.815553\pi$
$308$	11.5028	+	3.73749i	0.655434	+	0.212963i
$309$	−21.5039			−1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	43.1415	+	14.0175i	2.44241	+	0.793586i
$313$	0.335397	+	0.301993i	0.0189577	+	0.0170696i	0.678555	−	0.734550i	$-0.262606\pi$
$313$	0.335397	+	0.301993i	0.0189577	+	0.0170696i	−0.659597	+	0.751619i	$0.729273\pi$
$314$	7.24032	+	5.26040i	0.408595	+	0.296862i
$315$		0			0
$316$	25.3964	+	43.9879i	1.42866	+	2.47451i
$317$	−5.55027	−	0.583357i	−0.311734	−	0.0327646i	−0.0526304	−	0.998614i	$-0.516761\pi$
$317$	−5.55027	−	0.583357i	−0.311734	−	0.0327646i	−0.259104	+	0.965849i	$0.583427\pi$
$318$	6.28047	+	8.64432i	0.352191	+	0.484750i
$319$	1.13666	+	10.8146i	0.0636407	+	0.605501i
$320$		0			0
$321$	−16.0446	+	7.14353i	−0.895524	+	0.398713i
$322$	−0.520855	−	2.45043i	−0.0290261	−	0.136557i
$323$	1.47493	−	6.93901i	0.0820674	−	0.386097i
$324$	24.2555	+	10.7992i	1.34753	+	0.599958i
$325$		0			0
$326$	−1.44676	−	4.45266i	−0.0801284	−	0.246610i
$327$	4.16156	−	9.34701i	0.230135	−	0.516891i
$328$	0.188382	−	0.886270i	0.0104017	−	0.0489360i
$329$	11.3595	−	2.41453i	0.626267	−	0.133117i
$330$		0			0
$331$	16.1966	+	17.9882i	0.890246	+	0.988719i	0.999986	−	0.00524168i	$-0.00166849\pi$
$331$	16.1966	+	17.9882i	0.890246	+	0.988719i	−0.109740	+	0.993960i	$0.535002\pi$
$332$	86.8975	−	9.13329i	4.76912	−	0.501255i
$333$	4.48853	+	6.17793i	0.245970	+	0.338548i
$334$	3.94140	−	37.4999i	0.215664	−	2.05191i
$335$		0			0
$336$	15.8704	−	27.4884i	0.865804	−	1.49962i
$337$	−6.48679	+	8.92830i	−0.353358	+	0.486355i	−0.948283	−	0.317426i	$-0.897182\pi$
$337$	−6.48679	+	8.92830i	−0.353358	+	0.486355i	0.594925	+	0.803781i	$0.297182\pi$
$338$	−0.947173	−	0.852838i	−0.0515194	−	0.0463883i
$339$	−7.31135	+	22.5020i	−0.397098	+	1.22214i
$340$		0			0
$341$	−4.22504	+	6.13158i	−0.228799	+	0.332044i
$342$			6.81056i			0.368273i
$343$	18.0953	+	5.87953i	0.977056	+	0.317465i
$344$	−17.5075	+	19.4440i	−0.943941	+	1.04835i
$345$		0			0
$346$	−0.0161152	+	0.0279124i	−0.000866360	+	0.00150058i
$347$	16.0798	−	9.28369i	0.863210	−	0.498375i	−0.00187589	−	0.999998i	$-0.500597\pi$
$347$	16.0798	−	9.28369i	0.863210	−	0.498375i	0.865086	+	0.501624i	$0.167264\pi$
$348$	60.0982	+	6.31657i	3.22160	+	0.338604i
$349$	−26.0298	+	18.9118i	−1.39334	+	1.01232i	−0.397855	+	0.917448i	$0.630245\pi$
$349$	−26.0298	+	18.9118i	−1.39334	+	1.01232i	−0.995489	+	0.0948756i	$0.969755\pi$
$350$		0			0
$351$	−13.8939	−	15.4307i	−0.741599	−	0.823629i
$352$	−9.47926	−	21.2908i	−0.505246	−	1.13480i
$353$	−6.69754	−	31.5094i	−0.356474	−	1.67708i	−0.681849	−	0.731493i	$-0.738824\pi$
$353$	−6.69754	−	31.5094i	−0.356474	−	1.67708i	0.325375	−	0.945585i	$-0.394510\pi$
$354$	−1.74107	−	0.370077i	−0.0925370	−	0.0196693i
$355$		0			0
$356$	−24.7864	−	76.2846i	−1.31367	−	4.04307i
$357$	6.43952	−	2.09233i	0.340815	−	0.110738i
$358$	−10.9178	+	24.5217i	−0.577023	+	1.29601i
$359$	20.6998	+	4.39988i	1.09249	+	0.232217i	0.718718	−	0.695302i	$-0.244729\pi$
$359$	20.6998	+	4.39988i	1.09249	+	0.232217i	0.373777	+	0.927519i	$0.378063\pi$
$360$		0			0
$361$	−11.3344	+	5.04639i	−0.596547	+	0.265600i
$362$	37.1910	−	33.4869i	1.95472	−	1.76003i
$363$	−13.0009	+	1.36644i	−0.682368	+	0.0717197i
$364$	−26.8560	+	19.5120i	−1.40764	+	1.02271i
$365$		0			0
$366$	−9.76334	−	16.9106i	−0.510338	−	0.883931i
$367$	11.2552	+	6.49822i	0.587519	+	0.339204i	0.764116	−	0.645079i	$-0.223176\pi$
$367$	11.2552	+	6.49822i	0.587519	+	0.339204i	−0.176597	+	0.984283i	$0.556509\pi$
$368$	−4.10527	+	5.65042i	−0.214002	+	0.294549i
$369$	−0.0686477	+	0.0762409i	−0.00357365	+	0.00396894i
$370$		0			0
$371$	−4.83309			−0.250922
$372$	28.4478	+	30.0504i	1.47495	+	1.55804i
$373$		−	4.42592i		−	0.229166i	−0.993414	−	0.114583i	$-0.963447\pi$
$373$		−	4.42592i		−	0.229166i	0.993414	−	0.114583i	$-0.0365531\pi$
$374$	3.07165	−	9.45355i	0.158831	−	0.488832i
$375$		0			0
$376$	−47.3762	−	34.4208i	−2.44324	−	1.77512i
$377$	−25.8471	−	14.9228i	−1.33119	−	0.768566i
$378$	−22.7581	+	13.1394i	−1.17055	+	0.675819i
$379$	−1.56330	+	14.8738i	−0.0803013	+	0.764016i	0.878078	+	0.478518i	$0.158826\pi$
$379$	−1.56330	+	14.8738i	−0.0803013	+	0.764016i	−0.958379	+	0.285498i	$0.907841\pi$
$380$		0			0
$381$	1.91503	+	18.2202i	0.0981097	+	0.933452i
$382$	−2.39525	+	2.15669i	−0.122552	+	0.110346i
$383$	−4.73862	−	10.6431i	−0.242132	−	0.543838i	0.751072	−	0.660220i	$-0.229537\pi$
$383$	−4.73862	−	10.6431i	−0.242132	−	0.543838i	−0.993205	+	0.116382i	$0.962870\pi$
$384$	−29.9508	+	6.36623i	−1.52842	+	0.324875i
$385$		0			0
$386$	−31.2765	−	13.9252i	−1.59193	−	0.708774i
$387$	2.81756	−	0.915480i	0.143225	−	0.0465365i
$388$	6.37110	−	2.07009i	0.323443	−	0.105093i
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	0.0451198	−	0.998982i	$-0.485633\pi$
$389$	−13.1568	−	5.85779i	−0.667077	−	0.297002i	−0.712197	+	0.701980i	$0.752300\pi$
$390$		0			0
$391$	−1.45732	+	0.309763i	−0.0737000	+	0.0156654i
$392$	−14.2306	−	31.9624i	−0.718753	−	1.61435i
$393$	2.57100	−	2.31493i	0.129690	−	0.116773i
$394$	0.834763	+	7.94224i	0.0420547	+	0.400124i
$395$		0			0
$396$	−0.721831	+	6.86777i	−0.0362734	+	0.345118i
$397$	−13.6746	+	7.89506i	−0.686311	+	0.396242i	−0.802229	−	0.597017i	$-0.796352\pi$
$397$	−13.6746	+	7.89506i	−0.686311	+	0.396242i	0.115918	+	0.993259i	$0.463019\pi$
$398$	−30.7155	−	17.7336i	−1.53963	−	0.888904i
$399$	5.09088	+	3.69874i	0.254863	+	0.185169i
$400$		0			0
$401$	9.58670	−	29.5048i	0.478737	−	1.47340i	−0.362114	−	0.932134i	$-0.617945\pi$
$401$	9.58670	−	29.5048i	0.478737	−	1.47340i	0.840851	−	0.541267i	$-0.182055\pi$
$402$			31.6817i			1.58014i
$403$	−6.79886	−	19.2734i	−0.338675	−	0.960075i
$404$	−42.5252			−2.11571
$405$		0			0
$406$	−25.2748	+	28.0705i	−1.25437	+	1.39311i
$407$	6.08832	−	8.37986i	0.301787	−	0.415374i
$408$	−29.5684	−	17.0713i	−1.46385	−	0.845156i
$409$	3.29291	+	5.70349i	0.162824	+	0.282019i	0.935880	−	0.352318i	$-0.114606\pi$
$409$	3.29291	+	5.70349i	0.162824	+	0.282019i	−0.773056	+	0.634337i	$0.781273\pi$
$410$		0			0
$411$	−9.35015	+	6.79328i	−0.461209	+	0.335088i
$412$	−78.9180	+	8.29462i	−3.88801	+	0.408647i
$413$	0.598326	−	0.538735i	0.0294417	−	0.0265094i
$414$	1.30669	−	0.581774i	0.0642201	−	0.0285926i
$415$		0			0
$416$	62.5679	+	13.2992i	3.06764	+	0.652047i
$417$	−0.781196	+	1.75460i	−0.0382554	+	0.0859229i
$418$	8.78583	−	2.85469i	0.429729	−	0.139627i
$419$	4.53389	+	13.9539i	0.221495	+	0.681692i	0.998628	+	0.0523559i	$0.0166730\pi$
$419$	4.53389	+	13.9539i	0.221495	+	0.681692i	−0.777133	+	0.629336i	$0.783327\pi$
$420$		0			0
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.794616	−	0.607112i	$-0.207672\pi$
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.478983	+	0.877824i	$0.341006\pi$
$422$	−10.2535	−	48.2390i	−0.499133	−	2.34824i
$423$	2.69693	+	6.05740i	0.131129	+	0.294521i
$424$	16.3074	+	18.1113i	0.791959	+	0.879560i
$425$		0			0
$426$	14.6980	−	10.6787i	0.712118	−	0.517384i
$427$	8.78404	+	0.923240i	0.425090	+	0.0446787i
$428$	−56.1274	+	32.4052i	−2.71302	+	1.56636i
$429$	−3.48342	+	6.03347i	−0.168181	+	0.291299i
$430$		0			0
$431$	2.66850	−	2.96367i	0.128537	−	0.142755i	−0.675441	−	0.737414i	$-0.736046\pi$
$431$	2.66850	−	2.96367i	0.128537	−	0.142755i	0.803978	+	0.594660i	$0.202713\pi$
$432$	69.6783	+	22.6399i	3.35240	+	1.08926i
$433$			18.0766i			0.868704i	0.900743	+	0.434352i	$0.143023\pi$
$433$			18.0766i			0.868704i	−0.900743	+	0.434352i	$0.856977\pi$
$434$	−25.6482	+	3.34513i	−1.23115	+	0.160571i
$435$		0			0
$436$	11.6673	−	35.9082i	0.558762	−	1.71969i
$437$	−1.02899	−	0.926510i	−0.0492234	−	0.0443210i
$438$	−16.8441	+	23.1839i	−0.804843	+	1.10777i
$439$	11.4543	−	19.8394i	0.546684	−	0.946884i	−0.451815	−	0.892112i	$-0.649223\pi$
$439$	11.4543	−	19.8394i	0.546684	−	0.946884i	0.998499	−	0.0547723i	$-0.0174433\pi$
$440$		0			0
$441$	−0.414093	+	3.93983i	−0.0197187	+	0.187611i
$442$	16.0359	+	22.0715i	0.762750	+	1.04984i
$443$	−21.3736	+	2.24645i	−1.01549	+	0.106732i	−0.597624	−	0.801777i	$-0.703888\pi$
$443$	−21.3736	+	2.24645i	−1.01549	+	0.106732i	−0.417866	+	0.908509i	$0.637222\pi$
$444$	−38.5160	−	42.7763i	−1.82789	−	2.03008i
$445$		0			0
$446$	24.7244	−	5.25533i	1.17073	−	0.248847i
$447$	2.65668	−	12.4987i	0.125657	−	0.591169i
$448$	14.7331	−	33.0912i	0.696075	−	1.56341i
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	−0.989440	−	0.144945i	$-0.953700\pi$
$449$	−5.80940	−	17.8795i	−0.274163	−	0.843786i	0.715277	−	0.698841i	$-0.246300\pi$
$450$		0			0
$451$	0.127127	+	0.0566007i	0.00598619	+	0.00266522i
$452$	−18.1526	+	85.4012i	−0.853826	+	4.01694i
$453$	0.946676	+	4.45376i	0.0444787	+	0.209256i
$454$	20.7897	−	9.25617i	0.975709	−	0.434414i
$455$		0			0
$456$	−3.31680	−	31.5572i	−0.155323	−	1.47780i
$457$	2.41344	+	3.32182i	0.112896	+	0.155388i	0.861726	−	0.507374i	$-0.169384\pi$
$457$	2.41344	+	3.32182i	0.112896	+	0.155388i	−0.748830	+	0.662763i	$0.769384\pi$
$458$	61.1158	+	6.42352i	2.85575	+	0.300152i
$459$	7.81429	+	13.5347i	0.364740	+	0.631748i
$460$		0			0
$461$	18.5063	+	13.4456i	0.861924	+	0.626225i	0.928408	−	0.371563i	$-0.121178\pi$
$461$	18.5063	+	13.4456i	0.861924	+	0.626225i	−0.0664836	+	0.997788i	$0.521178\pi$
$462$	6.55246	+	5.89986i	0.304848	+	0.274486i
$463$	−15.7561	−	5.11947i	−0.732249	−	0.237922i	−0.0809233	−	0.996720i	$-0.525787\pi$
$463$	−15.7561	−	5.11947i	−0.732249	−	0.237922i	−0.651326	+	0.758798i	$0.725787\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	−36.2792	−	11.7878i	−1.67880	−	0.545476i	−0.694124	−	0.719855i	$-0.744208\pi$
$467$	−36.2792	−	11.7878i	−1.67880	−	0.545476i	−0.984679	+	0.174379i	$0.944208\pi$
$468$	−14.0851	−	12.6823i	−0.651085	−	0.586239i
$469$	−11.5936	−	8.42323i	−0.535342	−	0.388949i
$470$		0			0
$471$	2.36062	+	4.08871i	0.108771	+	0.188398i
$472$	−4.03765	−	0.424374i	−0.185848	−	0.0195334i
$473$	−2.36200	−	3.25101i	−0.108605	−	0.149482i
$474$	3.87052	+	36.8256i	0.177779	+	1.69145i
$475$		0			0
$476$	22.8256	−	10.1626i	1.04621	−	0.465802i
$477$	−0.573730	−	2.69919i	−0.0262693	−	0.123587i
$478$	−10.2204	+	48.0830i	−0.467468	+	2.19926i
$479$	30.7726	+	13.7008i	1.40603	+	0.626007i	0.962755	−	0.270377i	$-0.0871483\pi$
$479$	30.7726	+	13.7008i	1.40603	+	0.626007i	0.443279	+	0.896383i	$0.353815\pi$
$480$		0			0
$481$	8.78511	+	27.0378i	0.400567	+	1.23282i
$482$	19.8830	−	44.6580i	0.905647	−	2.03412i
$483$	0.274772	−	1.29270i	0.0125026	−	0.0588199i
$484$	−47.1853	+	10.0295i	−2.14479	+	0.455888i
$485$		0			0
$486$	−17.5960	−	19.5423i	−0.798169	−	0.886456i
$487$	20.5634	−	2.16130i	0.931817	−	0.0979379i	0.373560	−	0.927606i	$-0.378137\pi$
$487$	20.5634	−	2.16130i	0.931817	−	0.0979379i	0.558257	+	0.829668i	$0.311470\pi$
$488$	−26.1787	−	36.0319i	−1.18506	−	1.63109i
$489$	0.258168	−	2.45631i	0.0116748	−	0.111078i
$490$		0			0
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	0.439570	+	0.898209i	$0.355131\pi$
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	−0.997656	+	0.0684258i	$0.978202\pi$
$492$	0.454547	−	0.625630i	0.0204925	−	0.0282056i
$493$	16.6941	+	15.0314i	0.751864	+	0.676982i
$494$	−7.83511	+	24.1140i	−0.352518	+	1.08494i
$495$		0			0
$496$	54.7775	+	46.8990i	2.45958	+	2.10583i
$497$			8.21771i			0.368615i
$498$	60.5804	+	19.6838i	2.71467	+	0.882050i
$499$	16.4340	−	18.2518i	0.735685	−	0.817061i	−0.252937	−	0.967483i	$-0.581396\pi$
$499$	16.4340	−	18.2518i	0.735685	−	0.817061i	0.988622	+	0.150422i	$0.0480631\pi$
$500$		0			0
$501$	9.94584	−	17.2267i	0.444347	−	0.769632i
$502$	−53.4215	+	30.8429i	−2.38432	+	1.37659i
$503$	−14.6584	−	1.54066i	−0.653585	−	0.0686946i	−0.228068	−	0.973645i	$-0.573241\pi$
$503$	−14.6584	−	1.54066i	−0.653585	−	0.0686946i	−0.425517	+	0.904951i	$0.639908\pi$
$504$	−11.9949	+	8.71479i	−0.534295	+	0.388188i
$505$		0			0
$506$	−1.29821	−	1.44181i	−0.0577126	−	0.0640963i
$507$	−0.273479	−	0.614244i	−0.0121456	−	0.0272795i
$508$	14.0561	+	66.1285i	0.623637	+	2.93398i
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.531392	−	0.847126i	$-0.321669\pi$
$509$	15.1674	+	3.22394i	0.672285	+	0.142899i	0.140893	+	0.990025i	$0.455003\pi$
$510$		0			0
$511$	−4.00557	−	12.3279i	−0.177196	−	0.545353i
$512$	−0.128768	+	0.0418393i	−0.00569080	+	0.00184905i
$513$	−5.90773	+	13.2690i	−0.260833	+	0.585840i
$514$	−0.279433	−	0.0593953i	−0.0123253	−	0.00261982i
$515$		0			0
$516$	−20.4005	+	9.08291i	−0.898084	+	0.399853i
$517$	6.68380	−	6.01812i	0.293953	−	0.264677i
$518$	35.7828	−	3.76092i	1.57220	−	0.165245i
$519$	−0.0137556	+	0.00999402i	−0.000603803	+	0.000438689i
$520$		0			0
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	−0.984454	−	0.175642i	$-0.943800\pi$
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	0.340117	−	0.940383i	$-0.389533\pi$
$522$	−18.6771	−	10.7832i	−0.817475	−	0.471970i
$523$	26.4656	−	36.4268i	1.15726	−	1.59283i	0.436397	−	0.899754i	$-0.356254\pi$
$523$	26.4656	−	36.4268i	1.15726	−	1.59283i	0.720863	−	0.693078i	$-0.243746\pi$
$524$	8.54247	−	9.48737i	0.373180	−	0.414458i
$525$		0			0
$526$	19.6309			0.855947
$527$	1.98942	+	15.2535i	0.0866604	+	0.664455i
$528$		−	24.5819i		−	1.06979i
$529$	7.01753	−	21.5977i	0.305110	−	0.939032i
$530$		0			0
$531$	0.371899	+	0.270201i	0.0161391	+	0.0117257i
$532$	20.1099	+	11.6105i	0.871876	+	0.503378i
$533$	−0.330769	+	0.190970i	−0.0143272	+	0.00827182i
$534$	6.11220	−	58.1537i	0.264501	−	2.51656i
$535$		0			0
$536$	7.55343	+	71.8661i	0.326258	+	3.10414i
$537$	−10.5232	+	9.47518i	−0.454112	+	0.408884i
$538$	−17.7470	−	39.8604i	−0.765127	−	1.71850i
$539$	5.25607	−	1.11721i	0.226395	−	0.0481217i
$540$		0			0
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.979234	−	0.202731i	$-0.0649818\pi$
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.504577	+	0.863367i	$0.331648\pi$
$542$	13.1651	−	4.27759i	0.565488	−	0.183738i
$543$	25.1088	−	8.15834i	1.07752	−	0.350108i
$544$	−43.9830	−	19.5825i	−1.88576	−	0.839593i
$545$		0			0
$546$	−23.6712	+	5.03148i	−1.01304	+	0.215327i
$547$	7.40617	+	16.6345i	0.316665	+	0.711241i	0.999819	−	0.0190333i	$-0.00605885\pi$
$547$	7.40617	+	16.6345i	0.316665	+	0.711241i	−0.683154	+	0.730274i	$0.739392\pi$
$548$	−31.6942	+	28.5375i	−1.35391	+	1.21906i
$549$	0.527130	+	5.01531i	0.0224974	+	0.214048i
$550$		0			0
$551$	−2.18229	+	20.7631i	−0.0929686	+	0.884537i
$552$	−5.77130	+	3.33206i	−0.245643	+	0.141822i
$553$	−14.5050	−	8.37446i	−0.616815	−	0.356118i
$554$	36.8305	+	26.7590i	1.56478	+	1.13688i
$555$		0			0
$556$	−2.19015	+	6.74059i	−0.0928831	+	0.285865i
$557$			9.19760i			0.389715i	0.980832	+	0.194857i	$0.0624244\pi$
$557$			9.19760i			0.389715i	−0.980832	+	0.194857i	$0.937576\pi$
$558$	−4.91285	−	13.9269i	−0.207978	−	0.589574i
$559$	11.0293			0.466488
$560$		0			0
$561$	3.50877	−	3.89688i	0.148140	−	0.164527i
$562$	3.01489	−	4.14964i	0.127175	−	0.175042i
$563$	31.3170	+	18.0809i	1.31986	+	0.762019i	0.983705	−	0.179790i	$-0.0575417\pi$
$563$	31.3170	+	18.0809i	1.31986	+	0.762019i	0.336150	+	0.941808i	$0.390875\pi$
$564$	−24.9903	−	43.2844i	−1.05228	−	1.82260i
$565$		0			0
$566$	−33.3200	+	24.2084i	−1.40054	+	1.01755i
$567$	−8.70721	+	0.915165i	−0.365668	+	0.0384333i
$568$	30.7946	−	27.7276i	1.29211	−	1.16342i
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.995303	−	0.0968056i	$-0.969137\pi$
$569$	−37.9119	+	16.8795i	−1.58935	+	0.707624i	−0.594047	+	0.804430i	$0.702471\pi$
$570$		0			0
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.815859	−	0.578251i	$-0.196265\pi$
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.510128	+	0.860099i	$0.329598\pi$
$572$	−10.4567	+	23.4861i	−0.437216	+	0.982004i
$573$	−1.61711	+	0.525430i	−0.0675556	+	0.0219501i
$574$	0.149373	+	0.459722i	0.00623470	+	0.0191884i
$575$		0			0
$576$	20.2297	+	4.29995i	0.842904	+	0.179165i
$577$	8.52075	+	40.0870i	0.354723	+	1.66884i	0.687768	+	0.725931i	$0.258591\pi$
$577$	8.52075	+	40.0870i	0.354723	+	1.66884i	−0.333044	+	0.942911i	$0.608076\pi$
$578$	10.2490	+	23.0197i	0.426304	+	0.957494i
$579$	−12.0852	−	13.4220i	−0.502245	−	0.557799i
$580$		0			0
$581$	−23.3096	+	16.9354i	−0.967046	+	0.702600i
$582$	4.85685	+	0.510476i	0.201323	+	0.0211599i
$583$	−3.24155	+	1.87151i	−0.134251	+	0.0775100i
$584$	−32.6814	+	56.6059i	−1.35237	+	2.34237i
$585$		0			0
$586$	−48.2304	+	53.5652i	−1.99238	+	2.21276i
$587$	−24.2818	−	7.88963i	−1.00222	−	0.325640i	−0.238466	−	0.971151i	$-0.576644\pi$
$587$	−24.2818	−	7.88963i	−1.00222	−	0.325640i	−0.763751	+	0.645511i	$0.776644\pi$
$588$		−	29.8612i		−	1.23146i
$589$	−10.3820	+	9.82833i	−0.427783	+	0.404969i
$590$		0			0
$591$	−1.30187	+	4.00673i	−0.0535516	+	0.164815i
$592$	−74.5449	−	67.1206i	−3.06378	−	2.75864i
$593$	26.1751	−	36.0269i	1.07488	−	1.47945i	0.209850	−	0.977734i	$-0.432702\pi$
$593$	26.1751	−	36.0269i	1.07488	−	1.47945i	0.865033	−	0.501716i	$-0.167298\pi$
$594$	−10.1759	+	17.6252i	−0.417523	+	0.723170i
$595$		0			0
$596$	4.92879	−	46.8943i	0.201891	−	1.92086i
$597$	−10.9977	−	15.1370i	−0.450104	−	0.619515i
$598$	5.29584	−	0.556616i	0.216563	−	0.0227617i
$599$	−12.7001	−	14.1049i	−0.518911	−	0.576309i	0.425549	−	0.904935i	$-0.360081\pi$
$599$	−12.7001	−	14.1049i	−0.518911	−	0.576309i	−0.944460	+	0.328627i	$0.893414\pi$
$600$		0			0
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.0554947	−	0.998459i	$-0.482326\pi$
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.456807	+	0.889566i	$0.348993\pi$
$602$	2.90215	−	13.6535i	0.118283	−	0.556477i
$603$	3.32795	−	7.47469i	0.135524	−	0.304393i
$604$	5.19217	+	15.9799i	0.211267	+	0.650212i
$605$		0			0
$606$	−28.3210	−	12.6093i	−1.15046	−	0.512219i
$607$	7.92960	−	37.3059i	0.321853	−	1.51420i	−0.458407	−	0.888742i	$-0.651580\pi$
$607$	7.92960	−	37.3059i	0.321853	−	1.51420i	0.780260	−	0.625456i	$-0.215087\pi$
$608$	−9.30297	−	43.7670i	−0.377285	−	1.77499i
$609$	−18.2038	+	8.10485i	−0.737654	+	0.328425i
$610$		0			0
$611$	2.58030	+	24.5499i	0.104388	+	0.993184i
$612$	8.38520	+	11.5412i	0.338952	+	0.466527i
$613$	18.4408	+	1.93821i	0.744817	+	0.0782834i	0.469332	−	0.883022i	$-0.344495\pi$
$613$	18.4408	+	1.93821i	0.744817	+	0.0782834i	0.275485	+	0.961305i	$0.411162\pi$
$614$	−12.0401	−	20.8541i	−0.485901	−	0.841605i
$615$		0			0
$616$	16.2701	+	11.8209i	0.655541	+	0.476278i
$617$	−6.04589	−	5.44374i	−0.243398	−	0.219157i	0.538398	−	0.842691i	$-0.319030\pi$
$617$	−6.04589	−	5.44374i	−0.243398	−	0.219157i	−0.781796	+	0.623534i	$0.785696\pi$
$618$	−55.0175	−	17.8763i	−2.21313	−	0.719089i
$619$	5.36063			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	52.8472	+	17.1711i	2.11898	+	0.688499i
$623$	19.6557	+	17.6981i	0.787489	+	0.709058i
$624$	54.5833	+	39.6571i	2.18508	+	1.58755i
$625$		0			0
$626$	0.607062	+	1.05146i	0.0242631	+	0.0420249i
$627$	4.84670	+	0.509409i	0.193559	+	0.0203438i
$628$	10.2404	+	14.0948i	0.408638	+	0.562442i
$629$	−2.23670	−	21.2808i	−0.0891830	−	0.848519i
$630$		0			0
$631$	26.5358	−	11.8145i	1.05637	−	0.470327i	0.196324	−	0.980539i	$-0.437100\pi$
$631$	26.5358	−	11.8145i	1.05637	−	0.470327i	0.860049	+	0.510212i	$0.170433\pi$
$632$	17.5596	+	82.6116i	0.698485	+	3.28611i
$633$	5.40914	−	25.4480i	0.214994	−	1.01147i
$634$	−13.7154	−	6.10647i	−0.544707	−	0.242519i
$635$		0			0
$636$	6.42770	+	19.7824i	0.254875	+	0.784424i
$637$	−5.99868	+	13.4733i	−0.237677	+	0.533830i
$638$	−6.08208	+	28.6139i	−0.240792	+	1.13284i
$639$	−4.58943	+	0.975513i	−0.181555	+	0.0385907i
$640$		0			0
$641$	−18.4717	−	20.5149i	−0.729589	−	0.810290i	0.258200	−	0.966092i	$-0.416871\pi$
$641$	−18.4717	−	20.5149i	−0.729589	−	0.810290i	−0.987788	+	0.155801i	$0.950204\pi$
$642$	−46.9884	+	4.93868i	−1.85449	+	0.194914i
$643$	2.48577	+	3.42136i	0.0980291	+	0.134925i	0.855214	−	0.518275i	$-0.173426\pi$
$643$	2.48577	+	3.42136i	0.0980291	+	0.134925i	−0.757185	+	0.653201i	$0.773426\pi$
$644$	0.509768	−	4.85012i	0.0200877	−	0.191121i
$645$		0			0
$646$	9.54202	−	16.5273i	0.375426	−	0.650257i
$647$	15.4475	−	21.2617i	0.607304	−	0.835883i	−0.389048	−	0.921217i	$-0.627196\pi$
$647$	15.4475	−	21.2617i	0.607304	−	0.835883i	0.996352	+	0.0853349i	$0.0271960\pi$
$648$	32.8086	+	29.5410i	1.28884	+	1.16048i
$649$	0.192683	−	0.593018i	0.00756348	−	0.0232780i
$650$		0			0
$651$	−13.0785	−	3.89121i	−0.512585	−	0.152509i
$652$		−	9.11408i		−	0.356935i
$653$	−12.6983	−	4.12592i	−0.496922	−	0.161460i	0.0498246	−	0.998758i	$-0.484134\pi$
$653$	−12.6983	−	4.12592i	−0.496922	−	0.161460i	−0.546746	+	0.837298i	$0.684134\pi$
$654$	18.4175	−	20.4547i	0.720182	−	0.799843i
$655$		0			0
$656$	0.673821	−	1.16709i	0.0263083	−	0.0455673i
$657$	6.40937	−	3.70045i	0.250053	−	0.144368i
$658$	31.0702	+	3.26561i	1.21124	+	0.127307i
$659$	−12.4717	+	9.06119i	−0.485827	+	0.352974i	−0.803577	−	0.595200i	$-0.797073\pi$
$659$	−12.4717	+	9.06119i	−0.485827	+	0.352974i	0.317750	+	0.948174i	$0.397073\pi$
$660$		0			0
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	0.678542	−	0.734562i	$-0.262612\pi$
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	−0.801465	+	0.598042i	$0.795946\pi$
$662$	26.4852	+	59.4868i	1.02938	+	2.31202i
$663$	2.99233	+	14.0778i	0.116212	+	0.546736i
$664$	142.112	+	30.2069i	5.51502	+	1.17225i
$665$		0			0
$666$	6.34812	+	19.5375i	0.245984	+	0.757062i
$667$	4.17006	−	1.35493i	0.161465	−	0.0524632i
$668$	29.8558	−	67.0573i	1.15516	−	2.59453i
$669$	13.0431	+	2.77239i	0.504275	+	0.107187i
$670$		0			0
$671$	6.24895	−	2.78221i	0.241238	−	0.107406i
$672$	31.7373	−	28.5764i	1.22429	−	1.10236i
$673$	−30.9028	+	3.24801i	−1.19121	+	0.125202i	−0.679317	−	0.733845i	$-0.737724\pi$
$673$	−30.9028	+	3.24801i	−1.19121	+	0.125202i	−0.511898	+	0.859046i	$0.671057\pi$
$674$	−24.0185	+	17.4505i	−0.925158	+	0.672167i
$675$		0			0
$676$	−1.24058	−	2.14875i	−0.0477147	−	0.0826443i
$677$	−7.82883	−	4.51998i	−0.300886	−	0.173717i	0.341955	−	0.939716i	$-0.388911\pi$
$677$	−7.82883	−	4.51998i	−0.300886	−	0.173717i	−0.642841	+	0.766000i	$0.722244\pi$
$678$	−37.4120	+	51.4932i	−1.43680	+	1.97759i
$679$	−1.47810	+	1.64159i	−0.0567242	+	0.0629986i
$680$		0			0
$681$	12.0053			0.460044
$682$	−15.9069	+	12.1753i	−0.609107	+	0.466216i
$683$			7.13535i			0.273027i	0.990638	+	0.136513i	$0.0435897\pi$
$683$			7.13535i			0.273027i	−0.990638	+	0.136513i	$0.956410\pi$
$684$	−4.09699	+	12.6092i	−0.156652	+	0.482127i
$685$		0			0
$686$	41.4091	+	30.0854i	1.58101	+	1.14867i
$687$	28.0753	+	16.2093i	1.07114	+	0.618423i
$688$	−33.7021	+	19.4579i	−1.28488	+	0.741826i
$689$	1.07385	−	10.2170i	0.0409103	−	0.389236i
$690$		0			0
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	−0.788749	−	0.614716i	$-0.789271\pi$
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	0.643706	−	0.765273i	$-0.277396\pi$
$692$	−0.0466272	+	0.0419833i	−0.00177250	+	0.00159597i
$693$	−0.926188	−	2.08025i	−0.0351830	−	0.0790222i
$694$	48.8576	−	10.3850i	1.85461	−	0.394210i
$695$		0			0
$696$	91.7934	+	40.8690i	3.47942	+	1.54914i
$697$	0.273406	−	0.0888351i	0.0103560	−	0.00336487i
$698$	−82.3185	+	26.7469i	−3.11580	+	1.01238i
$699$	−21.0722	−	9.38193i	−0.797022	−	0.354857i
$700$		0			0
$701$	1.57916	−	0.335661i	0.0596441	−	0.0126777i	−0.177993	−	0.984032i	$-0.556960\pi$
$701$	1.57916	−	0.335661i	0.0596441	−	0.0126777i	0.237637	+	0.971354i	$0.423627\pi$
$702$	−22.7197	−	51.0293i	−0.857500	−	1.92598i
$703$	14.7786	−	13.3067i	0.557386	−	0.501873i
$704$	−2.93233	−	27.8993i	−0.110516	−	1.05149i
$705$		0			0
$706$	9.05833	−	86.1843i	0.340915	−	3.24359i
$707$	12.1440	−	7.01134i	0.456722	−	0.263688i
$708$	−3.00084	−	1.73254i	−0.112779	−	0.0651127i
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	0.748467	−	0.663172i	$-0.230790\pi$
$709$	9.29395	+	6.75245i	0.349042	+	0.253594i	−0.399425	+	0.916766i	$0.630790\pi$
$710$		0			0
$711$	2.95510	−	9.09487i	0.110825	−	0.341084i
$712$		−	133.372i		−	4.99833i
$713$	2.77254	+	1.15235i	0.103832	+	0.0431558i
$714$	18.2148			0.681672
$715$		0			0
$716$	−34.9649	+	38.8324i	−1.30670	+	1.45124i
$717$	−15.2427	+	20.9797i	−0.569248	+	0.783503i
$718$	49.3026	+	28.4649i	1.83996	+	1.06230i
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	0.703121	−	0.711070i	$-0.251789\pi$
$719$	−7.08549	−	12.2724i	−0.264244	−	0.457685i	−0.967365	+	0.253386i	$0.918456\pi$
$720$		0			0
$721$	21.1692	−	15.3803i	0.788382	−	0.572793i
$722$	−33.1940	+	3.48883i	−1.23535	+	0.129841i
$723$	19.1645	−	17.2558i	0.712736	−	0.641751i
$724$	89.0009	−	39.6258i	3.30769	−	1.47268i
$725$		0			0
$726$	−34.3985	−	7.31162i	−1.27665	−	0.271360i
$727$	−10.9606	+	24.6180i	−0.406507	+	0.913030i	0.588049	+	0.808826i	$0.299896\pi$
$727$	−10.9606	+	24.6180i	−0.406507	+	0.913030i	−0.994556	+	0.104205i	$0.966770\pi$
$728$	−52.4958	+	17.0569i	−1.94562	+	0.632172i
$729$	−8.98695	−	27.6590i	−0.332850	−	1.02441i
$730$		0			0
$731$	−8.12005	−	1.72597i	−0.300331	−	0.0638373i
$732$	−7.90328	−	37.1820i	−0.292113	−	1.37429i
$733$	−11.5609	−	25.9662i	−0.427011	−	0.959083i	−0.991069	−	0.133348i	$-0.957427\pi$
$733$	−11.5609	−	25.9662i	−0.427011	−	0.959083i	0.564058	−	0.825735i	$-0.309239\pi$
$734$	23.3944	+	25.9822i	0.863504	+	0.959019i
$735$		0			0
$736$	−7.60254	+	5.52357i	−0.280233	+	0.203601i
$737$	−11.0375	−	1.16009i	−0.406572	−	0.0427324i
$738$	−0.239014	+	0.137995i	−0.00879822	+	0.00507965i
$739$	−0.348653	+	0.603885i	−0.0128254	+	0.0222143i	−0.872367	−	0.488852i	$-0.837416\pi$
$739$	−0.348653	+	0.603885i	−0.0128254	+	0.0222143i	0.859541	+	0.511066i	$0.170749\pi$
$740$		0			0
$741$	−8.95012	+	9.94011i	−0.328791	+	0.365159i
$742$	−12.3654	−	4.01777i	−0.453949	−	0.147497i
$743$		−	18.1815i		−	0.667015i	−0.942747	−	0.333508i	$-0.891768\pi$
$743$		−	18.1815i		−	0.667015i	0.942747	−	0.333508i	$-0.108232\pi$
$744$	29.5466	+	62.1389i	1.08323	+	2.27812i
$745$		0			0
$746$	3.67929	−	11.3237i	0.134708	−	0.414589i
$747$	−12.2251	−	11.0076i	−0.447295	−	0.402746i
$748$	11.3738	−	15.6548i	0.415869	−	0.572395i
$749$	10.6856	−	18.5080i	0.390443	−	0.676267i
$750$		0			0
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	−0.661920	−	0.749574i	$-0.730258\pi$
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	0.803301	−	0.595573i	$-0.203075\pi$
$752$	−51.1958	−	70.4650i	−1.86692	−	2.56959i
$753$	−32.3635	+	3.40154i	−1.17939	+	0.123959i
$754$	−53.7242	−	59.6668i	−1.95652	−	2.17294i
$755$		0			0
$756$	−50.0392	+	10.6362i	−1.81991	+	0.386834i
$757$	−1.33105	+	6.26211i	−0.0483779	+	0.227600i	−0.995694	−	0.0926997i	$-0.970450\pi$
$757$	−1.33105	+	6.26211i	−0.0483779	+	0.227600i	0.947316	+	0.320300i	$0.103784\pi$
$758$	−16.3643	+	36.7549i	−0.594380	+	1.33500i
$759$	−0.316281	−	0.973412i	−0.0114803	−	0.0353326i
$760$		0			0
$761$	−19.4940	−	8.67928i	−0.706657	−	0.314624i	0.0217552	−	0.999763i	$-0.493075\pi$
$761$	−19.4940	−	8.67928i	−0.706657	−	0.314624i	−0.728412	+	0.685140i	$0.759741\pi$
$762$	−10.2470	+	48.2083i	−0.371209	+	1.74640i
$763$	2.58852	+	12.1780i	0.0937106	+	0.440874i
$764$	−5.73201	+	2.55206i	−0.207377	+	0.0923302i
$765$		0			0
$766$	−3.27605	−	31.1696i	−0.118369	−	1.12620i
$767$	1.00593	+	1.38454i	0.0363219	+	0.0499928i
$768$	−22.7107	−	2.38699i	−0.819502	−	0.0861332i
$769$	−6.12828	−	10.6145i	−0.220991	−	0.382768i	0.734118	−	0.679022i	$-0.237596\pi$
$769$	−6.12828	−	10.6145i	−0.220991	−	0.382768i	−0.955109	+	0.296254i	$0.904263\pi$
$770$		0			0
$771$	−0.121923	−	0.0885824i	−0.00439096	−	0.00319022i
$772$	−49.5292	−	44.5963i	−1.78260	−	1.60506i
$773$	−33.0050	−	10.7240i	−1.18711	−	0.385714i	−0.352104	−	0.935961i	$-0.614534\pi$
$773$	−33.0050	−	10.7240i	−1.18711	−	0.385714i	−0.835002	+	0.550247i	$0.814534\pi$
$774$	7.96974			0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	18.0518	+	5.86539i	0.647605	+	0.210420i
$778$	−28.7920	−	25.9244i	−1.03224	−	0.929435i
$779$	0.216146	+	0.157040i	0.00774425	+	0.00562652i
$780$		0			0
$781$	3.18213	+	5.51161i	0.113866	+	0.197221i
$782$	−3.98605	−	0.418951i	−0.142541	−	0.0149817i
$783$	−27.0348	−	37.2102i	−0.966144	−	1.32978i
$784$	−5.43948	−	51.7532i	−0.194267	−	1.84833i
$785$		0			0
$786$	8.50228	−	3.78546i	0.303266	−	0.135023i
$787$	−4.18281	−	19.6786i	−0.149101	−	0.701465i	−0.987655	−	0.156646i	$-0.949932\pi$
$787$	−4.18281	−	19.6786i	−0.149101	−	0.701465i	0.838554	−	0.544819i	$-0.183402\pi$
$788$	−3.23227	+	15.2066i	−0.115145	+	0.541714i
$789$	9.46075	+	4.21220i	0.336812	+	0.149958i
$790$		0			0
$791$	−8.89666	−	27.3811i	−0.316329	−	0.973559i
$792$	−4.67034	+	10.4898i	−0.165953	+	0.372737i
$793$	−3.90339	+	18.3640i	−0.138613	+	0.652125i
$794$	−41.5496	+	8.83165i	−1.47454	+	0.313423i
$795$		0			0
$796$	−46.1995	−	51.3097i	−1.63750	−	1.81863i
$797$	−26.0584	+	2.73885i	−0.923036	+	0.0970150i	−0.554110	−	0.832444i	$-0.686941\pi$
$797$	−26.0584	+	2.73885i	−0.923036	+	0.0970150i	−0.368926	+	0.929459i	$0.620275\pi$
$798$	9.95018	+	13.6953i	0.352233	+	0.484807i
$799$	1.94213	−	18.4781i	0.0687076	−	0.653709i
$800$		0			0
$801$	−7.55072	+	13.0782i	−0.266791	+	0.462096i
$802$	49.0549	−	67.5183i	1.73219	−	2.38416i
$803$	−7.46022	−	6.71722i	−0.263266	−	0.237045i
$804$	−19.0586	+	58.6562i	−0.672144	+	2.06865i
$805$		0			0
$806$	−1.37278	−	54.9626i	−0.0483543	−	1.93598i
$807$		−	23.0179i		−	0.810270i
$808$	−67.2491	−	21.8506i	−2.36582	−	0.768700i
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	−0.999295	−	0.0375423i	$-0.988047\pi$
$809$	−24.3899	+	27.0877i	−0.857504	+	0.952354i	0.141791	+	0.989897i	$0.454714\pi$
$810$		0			0
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	−0.648114	−	0.761543i	$-0.724442\pi$
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	0.983573	+	0.180511i	$0.0577753\pi$
$812$	−63.6805	+	36.7660i	−2.23475	+	1.29023i
$813$	7.26250	+	0.763320i	0.254707	+	0.0267708i
$814$	22.5431	−	16.3785i	0.790136	−	0.574067i
$815$		0			0
$816$	−33.9798	−	37.7384i	−1.18953	−	1.32111i
$817$	−3.13802	−	7.04810i	−0.109785	−	0.246582i
$818$	3.68355	+	17.3297i	0.128792	+	0.605920i
$819$	6.11330	+	1.29942i	0.213616	+	0.0454055i
$820$		0			0
$821$	12.1937	+	37.5285i	0.425565	+	1.30975i	0.902453	+	0.430789i	$0.141765\pi$
$821$	12.1937	+	37.5285i	0.425565	+	1.30975i	−0.476888	+	0.878964i	$0.658235\pi$
$822$	−29.5696	+	9.60773i	−1.03136	+	0.335108i
$823$	12.8480	−	28.8571i	0.447853	−	1.00589i	−0.538707	−	0.842493i	$-0.681087\pi$
$823$	12.8480	−	28.8571i	0.447853	−	1.00589i	0.986560	−	0.163401i	$-0.0522463\pi$
$824$	−129.063	−	27.4331i	−4.49611	−	0.955678i
$825$		0			0
$826$	1.97866	−	0.880958i	0.0688465	−	0.0306525i
$827$	14.7364	−	13.2688i	0.512436	−	0.461400i	−0.371885	−	0.928279i	$-0.621288\pi$
$827$	14.7364	−	13.2688i	0.512436	−	0.461400i	0.884321	+	0.466879i	$0.154622\pi$
$828$	2.76921	−	0.291055i	0.0962366	−	0.0101149i
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	−0.454122	−	0.890940i	$-0.650047\pi$
$829$	7.28104	−	5.28999i	0.252881	−	0.183729i	0.707003	+	0.707211i	$0.250047\pi$
$830$		0			0
$831$	12.0081	+	20.7987i	0.416558	+	0.721499i
$832$	66.6800	+	38.4977i	2.31171	+	1.33467i
$833$	6.52483	−	8.98066i	0.226072	−	0.311161i
$834$	−3.45729	+	3.83970i	−0.119716	+	0.132958i
$835$		0			0
$836$	17.9836			0.621976
$837$	2.50905	−	31.3954i	0.0867253	−	1.08518i
$838$			39.4699i			1.36347i
$839$	9.84070	−	30.2866i	0.339739	−	1.04561i	−0.624602	−	0.780944i	$-0.714739\pi$
$839$	9.84070	−	30.2866i	0.339739	−	1.04561i	0.964340	−	0.264665i	$-0.0852614\pi$
$840$		0			0
$841$	−30.0234	−	21.8133i	−1.03529	−	0.752183i
$842$	62.2411	+	35.9349i	2.14497	+	1.23840i
$843$	2.34336	−	1.35294i	0.0807095	−	0.0465976i
$844$	10.0353	−	95.4791i	0.345428	−	3.28652i
$845$		0			0
$846$	1.86452	+	17.7398i	0.0641037	+	0.609906i
$847$	11.8212	−	10.6438i	0.406180	−	0.365726i
$848$	14.7435	+	33.1145i	0.506295	+	1.13716i
$849$	−21.2523	+	4.51733i	−0.729379	+	0.155034i
$850$		0			0
$851$	−3.81548	−	1.69876i	−0.130793	−	0.0582328i
$852$	33.6361	−	10.9290i	1.15235	−	0.374422i
$853$	46.6890	−	15.1702i	1.59860	−	0.519417i	0.631839	−	0.775099i	$-0.282300\pi$
$853$	46.6890	−	15.1702i	1.59860	−	0.519417i	0.966761	+	0.255683i	$0.0823002\pi$
$854$	21.7064	+	9.66431i	0.742778	+	0.330706i
$855$		0			0
$856$	−105.410	+	22.4056i	−3.60285	+	0.765809i
$857$	−7.82580	−	17.5770i	−0.267324	−	0.600420i	0.729147	−	0.684357i	$-0.239917\pi$
$857$	−7.82580	−	17.5770i	−0.267324	−	0.600420i	−0.996471	+	0.0839371i	$0.973251\pi$
$858$	−13.9279	+	12.5408i	−0.475492	+	0.428135i
$859$	0.485236	+	4.61672i	0.0165561	+	0.157520i	0.999676	−	0.0254400i	$-0.00809867\pi$
$859$	0.485236	+	4.61672i	0.0165561	+	0.157520i	−0.983120	+	0.182960i	$0.941432\pi$
$860$		0			0
$861$	−0.0266550	+	0.253606i	−0.000908401	+	0.00864285i
$862$	9.29104	−	5.36418i	0.316454	−	0.182705i
$863$	33.3683	+	19.2652i	1.13587	+	0.655795i	0.945405	−	0.325899i	$-0.105667\pi$
$863$	33.3683	+	19.2652i	1.13587	+	0.655795i	0.190466	+	0.981694i	$0.439000\pi$
$864$	79.7493	+	57.9413i	2.71313	+	1.97120i
$865$		0			0
$866$	−15.0271	+	46.2487i	−0.510642	+	1.57159i
$867$			13.2931i			0.451456i
$868$	−49.4981	−	9.23582i	−1.68008	−	0.313484i
$869$	−12.9713			−0.440022
$870$		0			0
$871$	20.3823	−	22.6369i	0.690629	−	0.767021i
$872$	36.9012	−	50.7901i	1.24963	−	1.71997i
$873$	−1.09226	−	0.630617i	−0.0369674	−	0.0213431i
$874$	−1.86246	−	3.22587i	−0.0629986	−	0.109117i
$875$		0			0
$876$	−45.1323	+	32.7905i	−1.52488	+	1.10789i
$877$	9.20763	−	0.967760i	0.310919	−	0.0326789i	0.0522162	−	0.998636i	$-0.483372\pi$
$877$	9.20763	−	0.967760i	0.310919	−	0.0326789i	0.258703	+	0.965957i	$0.416705\pi$
$878$	45.7983	−	41.2370i	1.54562	−	1.39168i
$879$	−34.7372	+	15.4660i	−1.17166	+	0.521655i
$880$		0			0
$881$	17.4884	+	3.71727i	0.589198	+	0.125238i	0.492857	−	0.870110i	$-0.335953\pi$
$881$	17.4884	+	3.71727i	0.589198	+	0.125238i	0.0963414	+	0.995348i	$0.469286\pi$
$882$	−4.33465	+	9.73577i	−0.145955	+	0.327821i
$883$	45.9509	−	14.9303i	1.54637	−	0.502446i	0.593244	−	0.805022i	$-0.297847\pi$
$883$	45.9509	−	14.9303i	1.54637	−	0.502446i	0.953125	+	0.302577i	$0.0978468\pi$
$884$	16.4118	+	50.5104i	0.551990	+	1.69885i
$885$		0			0
$886$	−56.5516	−	12.0204i	−1.89989	−	0.403834i
$887$	4.88847	+	22.9984i	0.164139	+	0.772211i	0.980788	+	0.195077i	$0.0624957\pi$
$887$	4.88847	+	22.9984i	0.164139	+	0.772211i	−0.816649	+	0.577134i	$0.804171\pi$
$888$	−38.9294	−	87.4369i	−1.30639	−	2.93419i
$889$	−14.9170	−	16.5670i	−0.500298	−	0.555638i
$890$		0			0
$891$	−5.48554	+	3.98548i	−0.183772	+	0.133518i
$892$	48.9368	+	5.14346i	1.63852	+	0.172216i
$893$	14.9542	−	8.63379i	0.500422	−	0.288919i
$894$	17.1873	−	29.7693i	0.574830	−	0.995635i
$895$		0			0
$896$	24.9312	−	27.6889i	0.832894	−	0.925022i
$897$	2.67167	+	0.868078i	0.0892044	+	0.0289843i
$898$		−	50.5739i		−	1.68767i
$899$	−10.5150	−	44.0327i	−0.350696	−	1.46857i
$900$		0			0
$901$	−2.38945	+	7.35398i	−0.0796042	+	0.244996i
$902$	0.278202	+	0.250494i	0.00926310	+	0.00834053i
$903$	4.32827	−	5.95736i	0.144036	−	0.198249i
$904$	−72.5879	+	125.726i	−2.41424	+	4.18158i
$905$		0			0
$906$	−1.28037	+	12.1819i	−0.0425373	+	0.404716i
$907$	−7.39560	−	10.1792i	−0.245567	−	0.337994i	0.668386	−	0.743815i	$-0.266986\pi$
$907$	−7.39560	−	10.1792i	−0.245567	−	0.337994i	−0.913952	+	0.405821i	$0.866986\pi$
$908$	44.0588	−	4.63076i	1.46214	−	0.153677i
$909$	5.35728	+	5.94987i	0.177690	+	0.197345i
$910$		0			0
$911$	46.2512	−	9.83100i	1.53237	−	0.325715i	0.636939	−	0.770914i	$-0.280200\pi$
$911$	46.2512	−	9.83100i	1.53237	−	0.325715i	0.895432	+	0.445199i	$0.146867\pi$
$912$	9.81243	−	46.1639i	0.324922	−	1.52864i
$913$	−9.07586	+	20.3847i	−0.300367	+	0.674635i
$914$	3.41333	+	10.5051i	0.112903	+	0.347479i
$915$		0			0
$916$	109.287	+	48.6578i	3.61095	+	1.60770i
$917$	−0.875258	+	4.11776i	−0.0289036	+	0.135981i
$918$	8.74130	+	41.1246i	0.288506	+	1.35731i
$919$	21.1320	−	9.40858i	0.697081	−	0.310360i	−0.0274300	−	0.999624i	$-0.508732\pi$
$919$	21.1320	−	9.40858i	0.697081	−	0.310360i	0.724511	+	0.689263i	$0.242066\pi$
$920$		0			0
$921$	−1.32786	−	12.6337i	−0.0437544	−	0.416295i
$922$	36.1708	+	49.7848i	1.19122	+	1.63958i
$923$	−17.3719	−	1.82586i	−0.571804	−	0.0600990i
$924$	8.58224	+	14.8649i	0.282335	+	0.489019i
$925$		0			0
$926$	−36.0560	−	26.1962i	−1.18488	−	0.860862i
$927$	11.1026	+	9.99679i	0.364656	+	0.328338i
$928$	134.755	+	43.7846i	4.42355	+	1.43730i
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	−80.9524	−	26.3030i	−2.65169	−	0.861585i
$933$	21.7844	+	19.6147i	0.713188	+	0.642157i
$934$	−83.0208	−	60.3181i	−2.71652	−	1.97367i
$935$		0			0
$936$	−15.7576	−	27.2930i	−0.515055	−	0.892101i
$937$	19.6186	+	2.06200i	0.640911	+	0.0673625i	0.419409	−	0.907797i	$-0.362237\pi$
$937$	19.6186	+	2.06200i	0.640911	+	0.0673625i	0.221502	+	0.975160i	$0.428904\pi$
$938$	−22.6598	−	31.1885i	−0.739868	−	1.01834i
$939$	0.0669503	+	0.636990i	0.00218484	+	0.0207874i
$940$		0			0
$941$	−8.06045	+	3.58874i	−0.262763	+	0.116990i	−0.533890	−	0.845554i	$-0.679270\pi$
$941$	−8.06045	+	3.58874i	−0.262763	+	0.116990i	0.271127	+	0.962544i	$0.412604\pi$
$942$	2.64066	+	12.4233i	0.0860372	+	0.404773i
$943$	0.0116661	−	0.0548849i	0.000379902	−	0.00178730i
$944$	−5.51642	−	2.45607i	−0.179544	−	0.0799382i
$945$		0			0
$946$	−3.34057	−	10.2812i	−0.108611	−	0.334271i
$947$	6.32930	−	14.2158i	0.205675	−	0.461953i	−0.781026	−	0.624498i	$-0.785304\pi$
$947$	6.32930	−	14.2158i	0.205675	−	0.461953i	0.986701	+	0.162545i	$0.0519703\pi$
$948$	−14.9870	+	70.5082i	−0.486754	+	2.29000i
$949$	26.9506	−	5.72853i	0.874854	−	0.185956i
$950$		0			0
$951$	−5.29960	−	5.88581i	−0.171851	−	0.190860i
$952$	41.3181	−	4.34271i	1.33913	−	0.140748i
$953$	−5.67314	−	7.80840i	−0.183771	−	0.252939i	0.707185	−	0.707028i	$-0.249965\pi$
$953$	−5.67314	−	7.80840i	−0.183771	−	0.252939i	−0.890956	+	0.454089i	$0.849965\pi$
$954$	0.775962	−	7.38278i	0.0251227	−	0.239026i
$955$		0			0
$956$	−47.8473	+	82.8739i	−1.54749	+	2.68033i
$957$	−9.07083	+	12.4849i	−0.293218	+	0.403580i
$958$	67.3417	+	60.6348i	2.17571	+	1.95902i
$959$	4.34583	−	13.3751i	0.140334	−	0.431904i
$960$		0			0
$961$	14.1404	−	27.5871i	0.456143	−	0.889907i
$962$			76.4790i			2.46578i
$963$	11.6048	+	3.77063i	0.373960	+	0.121507i
$964$	63.6766	−	70.7201i	2.05089	−	2.27774i
$965$		0			0
$966$	1.77763	−	3.07894i	0.0571942	−	0.0990633i
$967$	−24.5930	+	14.1988i	−0.790858	+	0.456602i	−0.840264	−	0.542177i	$-0.817600\pi$
$967$	−24.5930	+	14.1988i	−0.790858	+	0.456602i	0.0494066	+	0.998779i	$0.484267\pi$
$968$	−79.7720	−	8.38438i	−2.56397	−	0.269484i
$969$	8.14485	−	5.91758i	0.261650	−	0.190100i
$970$		0			0
$971$	−14.8059	−	16.4436i	−0.475144	−	0.527701i	0.457156	−	0.889386i	$-0.348868\pi$
$971$	−14.8059	−	16.4436i	−0.475144	−	0.527701i	−0.932300	+	0.361686i	$0.882201\pi$
$972$	−20.8217	−	46.7662i	−0.667855	−	1.50003i
$973$	−0.485909	−	2.28602i	−0.0155775	−	0.0732865i
$974$	54.4080	+	11.5648i	1.74334	+	0.370559i
$975$		0			0
$976$	−20.4703	−	63.0012i	−0.655240	−	2.01662i
$977$	−18.9377	+	6.15324i	−0.605871	+	0.196859i	−0.595857	−	0.803090i	$-0.703188\pi$
$977$	−18.9377	+	6.15324i	−0.605871	+	0.196859i	−0.0100140	+	0.999950i	$0.503188\pi$
$978$	2.70246	−	6.06982i	0.0864151	−	0.194091i
$979$	20.0362	+	4.25884i	0.640361	+	0.136113i
$980$		0			0
$981$	−6.49389	+	2.89127i	−0.207334	+	0.0923111i
$982$	−49.4451	+	44.5206i	−1.57786	+	1.42071i
$983$	−24.7938	+	2.60593i	−0.790800	+	0.0831164i	−0.491312	−	0.870984i	$-0.663482\pi$
$983$	−24.7938	+	2.60593i	−0.790800	+	0.0831164i	−0.299488	+	0.954100i	$0.596816\pi$
$984$	1.04028	−	0.755810i	0.0331630	−	0.0240944i
$985$		0			0
$986$	30.2160	+	52.3356i	0.962273	+	1.66671i
$987$	14.2730	+	8.24054i	0.454316	+	0.262299i
$988$	−29.0122	+	39.9319i	−0.923002	+	1.27040i
$989$	−1.08420	+	1.20413i	−0.0344757	+	0.0382891i
$990$		0			0
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$	50.5953	+	82.7885i	1.60640	+	2.62854i
$993$			34.3515i			1.09011i
$994$	−6.83142	+	21.0249i	−0.216679	+	0.666871i
$995$		0			0
$996$	100.319	+	72.8860i	3.17873	+	2.30948i
$997$	12.5268	+	7.23233i	0.396727	+	0.229050i	0.685071	−	0.728477i	$-0.259771\pi$
$997$	12.5268	+	7.23233i	0.396727	+	0.229050i	−0.288344	+	0.957527i	$0.593105\pi$
$998$	57.2189	−	33.0353i	1.81123	−	1.04572i
$999$	−4.57954	+	43.5714i	−0.144890	+	1.37854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.a.324.4		32
5.2	odd	4		31.2.g.a.14.1	✓	16
5.3	odd	4		775.2.bl.a.76.2		16
5.4	even	2	inner	775.2.ck.a.324.1		32
15.2	even	4		279.2.y.c.262.2		16
20.7	even	4		496.2.bg.c.417.1		16
31.20	even	15	inner	775.2.ck.a.299.1		32
155.2	odd	20		961.2.c.j.521.1		16
155.7	odd	60		961.2.d.o.531.1		16
155.12	even	60		961.2.a.j.1.1		8
155.17	even	60		961.2.d.q.388.4		16
155.22	even	60		961.2.g.m.235.2		16
155.27	even	20		961.2.g.j.844.1		16
155.37	even	12		961.2.d.n.628.1		16
155.42	even	60		961.2.g.l.547.1		16
155.47	odd	20		961.2.g.s.732.2		16
155.52	even	60		961.2.c.i.439.1		16
155.57	even	12		961.2.g.j.846.1		16
155.67	odd	12		961.2.g.k.846.1		16
155.72	odd	60		961.2.c.j.439.1		16
155.77	even	20		961.2.g.m.732.2		16
155.82	odd	60		31.2.g.a.20.1	yes	16
155.87	odd	12		961.2.d.o.628.1		16
155.92	even	4		961.2.g.l.448.1		16
155.97	odd	20		961.2.g.k.844.1		16
155.102	odd	60		961.2.g.s.235.2		16
155.107	odd	60		961.2.d.p.388.4		16
155.112	odd	60		961.2.a.i.1.1		8
155.113	odd	60		775.2.bl.a.51.2		16
155.117	even	60		961.2.d.n.531.1		16
155.122	even	20		961.2.c.i.521.1		16
155.127	even	60		961.2.d.q.374.4		16
155.132	odd	20		961.2.g.t.338.2		16
155.137	even	60		961.2.g.n.816.2		16
155.142	odd	60		961.2.g.t.816.2		16
155.144	even	30	inner	775.2.ck.a.299.4		32
155.147	even	20		961.2.g.n.338.2		16
155.152	odd	60		961.2.d.p.374.4		16
465.167	odd	60		8649.2.a.be.1.8		8
465.392	even	60		279.2.y.c.82.2		16
465.422	even	60		8649.2.a.bf.1.8		8
620.547	even	60		496.2.bg.c.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	5.2	odd	4
31.2.g.a.20.1	yes	16	155.82	odd	60
279.2.y.c.82.2		16	465.392	even	60
279.2.y.c.262.2		16	15.2	even	4
496.2.bg.c.113.1		16	620.547	even	60
496.2.bg.c.417.1		16	20.7	even	4
775.2.bl.a.51.2		16	155.113	odd	60
775.2.bl.a.76.2		16	5.3	odd	4
775.2.ck.a.299.1		32	31.20	even	15	inner
775.2.ck.a.299.4		32	155.144	even	30	inner
775.2.ck.a.324.1		32	5.4	even	2	inner
775.2.ck.a.324.4		32	1.1	even	1	trivial
961.2.a.i.1.1		8	155.112	odd	60
961.2.a.j.1.1		8	155.12	even	60
961.2.c.i.439.1		16	155.52	even	60
961.2.c.i.521.1		16	155.122	even	20
961.2.c.j.439.1		16	155.72	odd	60
961.2.c.j.521.1		16	155.2	odd	20
961.2.d.n.531.1		16	155.117	even	60
961.2.d.n.628.1		16	155.37	even	12
961.2.d.o.531.1		16	155.7	odd	60
961.2.d.o.628.1		16	155.87	odd	12
961.2.d.p.374.4		16	155.152	odd	60
961.2.d.p.388.4		16	155.107	odd	60
961.2.d.q.374.4		16	155.127	even	60
961.2.d.q.388.4		16	155.17	even	60
961.2.g.j.844.1		16	155.27	even	20
961.2.g.j.846.1		16	155.57	even	12
961.2.g.k.844.1		16	155.97	odd	20
961.2.g.k.846.1		16	155.67	odd	12
961.2.g.l.448.1		16	155.92	even	4
961.2.g.l.547.1		16	155.42	even	60
961.2.g.m.235.2		16	155.22	even	60
961.2.g.m.732.2		16	155.77	even	20
961.2.g.n.338.2		16	155.147	even	20
961.2.g.n.816.2		16	155.137	even	60
961.2.g.s.235.2		16	155.102	odd	60
961.2.g.s.732.2		16	155.47	odd	20
961.2.g.t.338.2		16	155.132	odd	20
961.2.g.t.816.2		16	155.142	odd	60
8649.2.a.be.1.8		8	465.167	odd	60
8649.2.a.bf.1.8		8	465.422	even	60

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.55849 + 0.831304i) q^{2} +(1.05464 + 0.949606i) q^{3} +(4.23677 + 3.07819i) q^{4} +(1.90889 + 3.30629i) q^{6} +(-1.71742 - 0.180508i) q^{7} +(5.11835 + 7.04481i) q^{8} +(-0.103062 - 0.980572i) q^{9} +(-1.22177 + 0.543967i) q^{11} +(1.54521 + 7.26966i) q^{12} +(0.763174 - 3.59045i) q^{13} +(-4.24394 - 1.88952i) q^{14} +(4.00227 + 12.3177i) q^{16} +(-1.12374 + 2.52396i) q^{17} +(0.551469 - 2.59446i) q^{18} +(-2.51157 + 0.533850i) q^{19} +(-1.63986 - 1.82124i) q^{21} +(-3.57808 + 0.376072i) q^{22} +(0.316969 + 0.436271i) q^{23} +(-1.29175 + 12.2902i) q^{24} +(4.93733 - 8.55171i) q^{26} +(3.32495 - 4.57641i) q^{27} +(-6.72067 - 6.05132i) q^{28} +(2.51258 - 7.73291i) q^{29} +(4.75081 - 2.90341i) q^{31} +17.4262i q^{32} +(-1.80509 - 0.586508i) q^{33} +(-4.97326 + 5.52336i) q^{34} +(2.58174 - 4.47170i) q^{36} +(-6.70735 + 3.87249i) q^{37} +(-6.86961 - 0.722025i) q^{38} +(4.21439 - 3.06194i) q^{39} +(-0.0696243 - 0.0773256i) q^{41} +(-2.68155 - 6.02285i) q^{42} +(0.624713 + 2.93904i) q^{43} +(-6.85079 - 1.45618i) q^{44} +(0.448289 + 1.37969i) q^{46} +(-6.39584 + 2.07813i) q^{47} +(-7.47602 + 16.7914i) q^{48} +(-3.93009 - 0.835366i) q^{49} +(-3.58192 + 1.59477i) q^{51} +(14.2855 - 12.8627i) q^{52} +(2.78341 - 0.292549i) q^{53} +(12.3112 - 8.94464i) q^{54} +(-7.51871 - 13.0228i) q^{56} +(-3.15576 - 1.82198i) q^{57} +(12.8568 - 17.6959i) q^{58} +(-0.311970 + 0.346478i) q^{59} -5.11468 q^{61} +(14.5685 - 3.47898i) q^{62} +1.70266i q^{63} +(-6.48190 + 19.9492i) q^{64} +(-4.13073 - 3.00115i) q^{66} +(7.18668 + 4.14923i) q^{67} +(-12.5303 + 7.23436i) q^{68} +(-0.0799956 + 0.761107i) q^{69} +(-0.497420 - 4.73264i) q^{71} +(6.38043 - 5.74497i) q^{72} +(3.05304 + 6.85725i) q^{73} +(-20.3799 + 4.33188i) q^{74} +(-12.2842 - 5.46929i) q^{76} +(2.19648 - 0.713679i) q^{77} +(13.3279 - 4.33049i) q^{78} +(8.86044 + 3.94492i) q^{79} +(4.95915 - 1.05410i) q^{81} +(-0.113852 - 0.255716i) q^{82} +(12.3991 - 11.1642i) q^{83} +(-1.34155 - 12.7640i) q^{84} +(-0.844916 + 8.03884i) q^{86} +(9.99310 - 5.76952i) q^{87} +(-10.0856 - 5.82292i) q^{88} +(-12.3911 - 9.00268i) q^{89} +(-1.95880 + 6.02855i) q^{91} +2.82407i q^{92} +(7.76751 + 1.44933i) q^{93} -18.0912 q^{94} +(-16.5480 + 18.3784i) q^{96} +(0.751881 - 1.03488i) q^{97} +(-9.36065 - 5.40437i) q^{98} +(0.659316 + 1.14197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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