LMFDB - Embedded newform 76.2.i.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 $ x^12 - 6x^11 - 3x^10 + 70x^9 - 15x^8 - 426x^7 + 64x^6 + 1659x^5 + 267x^4 - 3969x^3 - 2088x^2 + 4446*x + 4161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.2
Root			$-1.75227 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	76.5
Dual form			76.2.i.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +O(q^{10})$	\(q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +(-0.622469 + 1.07815i) q^{11} +(0.977096 + 5.54139i) q^{13} +(0.391845 - 0.328797i) q^{15} +(-6.25251 + 2.27573i) q^{17} +(3.09208 - 3.07231i) q^{19} +(-1.97557 + 0.719049i) q^{21} +(-4.65029 + 3.90205i) q^{23} +(-0.854412 - 4.84561i) q^{25} +(2.46018 - 4.26116i) q^{27} +(3.64892 + 1.32810i) q^{29} +(-0.0400606 - 0.0693870i) q^{31} +(1.72862 + 1.45048i) q^{33} +(0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +10.1991 q^{39} +(1.11697 - 6.33464i) q^{41} +(0.189407 + 0.158931i) q^{43} +(-0.0402752 - 0.0697587i) q^{45} +(-10.8939 - 3.96505i) q^{47} +(2.82735 - 4.89711i) q^{49} +(2.09428 + 11.8773i) q^{51} +(3.50255 - 2.93899i) q^{53} +(-0.330140 + 0.120161i) q^{55} +(-4.51095 - 6.48649i) q^{57} +(-9.32947 + 3.39565i) q^{59} +(-4.27534 + 3.58744i) q^{61} +(0.0574889 + 0.326036i) q^{63} +(-0.793965 + 1.37519i) q^{65} +(-3.47734 - 1.26565i) q^{67} +(5.50164 + 9.52912i) q^{69} +(7.14016 + 5.99131i) q^{71} +(0.191208 - 1.08439i) q^{73} -8.91853 q^{75} +1.44397 q^{77} +(-1.50923 + 8.55928i) q^{79} +(-7.48795 - 6.28314i) q^{81} +(5.77114 + 9.99591i) q^{83} +(-1.76449 - 0.642221i) q^{85} +(3.51920 - 6.09544i) q^{87} +(-0.418534 - 2.37362i) q^{89} +(4.99955 - 4.19512i) q^{91} +(-0.136468 + 0.0496702i) q^{93} +(1.22576 - 0.103280i) q^{95} +(-13.4638 + 4.90042i) q^{97} +(0.272211 - 0.228412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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			0
$2$		0			0
$3$	0.314751	−	1.78504i	0.181721	−	1.03059i	−0.748375	−	0.663276i	$-0.769165\pi$
$3$	0.314751	−	1.78504i	0.181721	−	1.03059i	0.930096	−	0.367317i	$-0.119723\pi$
$4$		0			0
$5$	0.216181	+	0.181398i	0.0966793	+	0.0811235i	0.689846	−	0.723956i	$-0.257678\pi$
$5$	0.216181	+	0.181398i	0.0966793	+	0.0811235i	−0.593167	+	0.805079i	$0.702123\pi$
$6$		0			0
$7$	−0.579936	−	1.00448i	−0.219195	−	0.379657i	0.735367	−	0.677669i	$-0.237010\pi$
$7$	−0.579936	−	1.00448i	−0.219195	−	0.379657i	−0.954562	+	0.298012i	$0.903677\pi$
$8$		0			0
$9$	−0.268219	−	0.0976237i	−0.0894063	−	0.0325412i
$10$		0			0
$11$	−0.622469	+	1.07815i	−0.187682	+	0.325074i	−0.944477	−	0.328578i	$-0.893431\pi$
$11$	−0.622469	+	1.07815i	−0.187682	+	0.325074i	0.756795	+	0.653652i	$0.226764\pi$
$12$		0			0
$13$	0.977096	+	5.54139i	0.270998	+	1.53690i	0.751395	+	0.659853i	$0.229381\pi$
$13$	0.977096	+	5.54139i	0.270998	+	1.53690i	−0.480397	+	0.877051i	$0.659508\pi$
$14$		0			0
$15$	0.391845	−	0.328797i	0.101174	−	0.0848951i
$16$		0			0
$17$	−6.25251	+	2.27573i	−1.51646	+	0.551945i	−0.960260	−	0.279106i	$-0.909962\pi$
$17$	−6.25251	+	2.27573i	−1.51646	+	0.551945i	−0.556196	+	0.831051i	$0.687740\pi$
$18$		0			0
$19$	3.09208	−	3.07231i	0.709371	−	0.704835i
$19$	3.09208	−	3.07231i	0.709371	−	0.704835i
$20$		0			0
$21$	−1.97557	+	0.719049i	−0.431105	+	0.156909i
$22$		0			0
$23$	−4.65029	+	3.90205i	−0.969652	+	0.813635i	−0.982496	−	0.186283i	$-0.940356\pi$
$23$	−4.65029	+	3.90205i	−0.969652	+	0.813635i	0.0128443	+	0.999918i	$0.495911\pi$
$24$		0			0
$25$	−0.854412	−	4.84561i	−0.170882	−	0.969122i
$26$		0			0
$27$	2.46018	−	4.26116i	0.473462	−	0.820060i
$28$		0			0
$29$	3.64892	+	1.32810i	0.677587	+	0.246621i	0.657811	−	0.753183i	$-0.271483\pi$
$29$	3.64892	+	1.32810i	0.677587	+	0.246621i	0.0197756	+	0.999804i	$0.493705\pi$
$30$		0			0
$31$	−0.0400606	−	0.0693870i	−0.00719510	−	0.0124623i	0.862405	−	0.506218i	$-0.168957\pi$
$31$	−0.0400606	−	0.0693870i	−0.00719510	−	0.0124623i	−0.869601	+	0.493756i	$0.835624\pi$
$32$		0			0
$33$	1.72862	+	1.45048i	0.300913	+	0.252496i
$34$		0			0
$35$	0.0568388	−	0.322349i	0.00960751	−	0.0544869i
$36$		0			0
$37$	3.71365			0.610521			0.305260	−	0.952269i	$-0.401256\pi$
$37$	3.71365			0.610521			0.305260	+	0.952269i	$0.401256\pi$
$38$		0			0
$39$	10.1991			1.63317
$40$		0			0
$41$	1.11697	−	6.33464i	0.174441	−	0.989305i	−0.764346	−	0.644806i	$-0.776938\pi$
$41$	1.11697	−	6.33464i	0.174441	−	0.989305i	0.938787	−	0.344498i	$-0.111951\pi$
$42$		0			0
$43$	0.189407	+	0.158931i	0.0288842	+	0.0242368i	0.657115	−	0.753790i	$-0.271776\pi$
$43$	0.189407	+	0.158931i	0.0288842	+	0.0242368i	−0.628231	+	0.778027i	$0.716221\pi$
$44$		0			0
$45$	−0.0402752	−	0.0697587i	−0.00600387	−	0.0103990i
$46$		0			0
$47$	−10.8939	−	3.96505i	−1.58904	−	0.578362i	−0.611893	−	0.790940i	$-0.709592\pi$
$47$	−10.8939	−	3.96505i	−1.58904	−	0.578362i	−0.977144	+	0.212578i	$0.931814\pi$
$48$		0			0
$49$	2.82735	−	4.89711i	0.403907	−	0.699587i
$50$		0			0
$51$	2.09428	+	11.8773i	0.293258	+	1.66315i
$52$		0			0
$53$	3.50255	−	2.93899i	0.481113	−	0.403702i	−0.369716	−	0.929145i	$-0.620545\pi$
$53$	3.50255	−	2.93899i	0.481113	−	0.403702i	0.850829	+	0.525443i	$0.176100\pi$
$54$		0			0
$55$	−0.330140	+	0.120161i	−0.0445161	+	0.0162025i
$56$		0			0
$57$	−4.51095	−	6.48649i	−0.597490	−	0.859156i
$58$		0			0
$59$	−9.32947	+	3.39565i	−1.21459	+	0.442076i	−0.868295	−	0.496049i	$-0.834784\pi$
$59$	−9.32947	+	3.39565i	−1.21459	+	0.442076i	−0.346298	+	0.938124i	$0.612562\pi$
$60$		0			0
$61$	−4.27534	+	3.58744i	−0.547401	+	0.459324i	−0.874060	−	0.485818i	$-0.838522\pi$
$61$	−4.27534	+	3.58744i	−0.547401	+	0.459324i	0.326659	+	0.945142i	$0.394077\pi$
$62$		0			0
$63$	0.0574889	+	0.326036i	0.00724292	+	0.0410766i
$64$		0			0
$65$	−0.793965	+	1.37519i	−0.0984792	+	0.170571i
$66$		0			0
$67$	−3.47734	−	1.26565i	−0.424824	−	0.154623i	0.120756	−	0.992682i	$-0.461468\pi$
$67$	−3.47734	−	1.26565i	−0.424824	−	0.154623i	−0.545580	+	0.838059i	$0.683691\pi$
$68$		0			0
$69$	5.50164	+	9.52912i	0.662319	+	1.14717i
$70$		0			0
$71$	7.14016	+	5.99131i	0.847382	+	0.711038i	0.959211	−	0.282690i	$-0.0912267\pi$
$71$	7.14016	+	5.99131i	0.847382	+	0.711038i	−0.111830	+	0.993727i	$0.535671\pi$
$72$		0			0
$73$	0.191208	−	1.08439i	0.0223792	−	0.126919i	−0.971571	−	0.236747i	$-0.923919\pi$
$73$	0.191208	−	1.08439i	0.0223792	−	0.126919i	0.993951	+	0.109828i	$0.0350300\pi$
$74$		0			0
$75$	−8.91853			−1.02982
$76$		0			0
$77$	1.44397			0.164556
$78$		0			0
$79$	−1.50923	+	8.55928i	−0.169802	+	0.962994i	0.774172	+	0.632975i	$0.218166\pi$
$79$	−1.50923	+	8.55928i	−0.169802	+	0.962994i	−0.943974	+	0.330019i	$0.892945\pi$
$80$		0			0
$81$	−7.48795	−	6.28314i	−0.831995	−	0.698126i
$82$		0			0
$83$	5.77114	+	9.99591i	0.633465	+	1.09719i	0.986838	+	0.161711i	$0.0517014\pi$
$83$	5.77114	+	9.99591i	0.633465	+	1.09719i	−0.353373	+	0.935483i	$0.614965\pi$
$84$		0			0
$85$	−1.76449	−	0.642221i	−0.191386	−	0.0696587i
$86$		0			0
$87$	3.51920	−	6.09544i	0.377298	−	0.653500i
$88$		0			0
$89$	−0.418534	−	2.37362i	−0.0443645	−	0.251603i	0.954557	−	0.298027i	$-0.0963286\pi$
$89$	−0.418534	−	2.37362i	−0.0443645	−	0.251603i	−0.998922	+	0.0464239i	$0.985218\pi$
$90$		0			0
$91$	4.99955	−	4.19512i	0.524095	−	0.439768i
$92$		0			0
$93$	−0.136468	+	0.0496702i	−0.0141510	+	0.00515056i
$94$		0			0
$95$	1.22576	−	0.103280i	0.125760	−	0.0105963i
$96$		0			0
$97$	−13.4638	+	4.90042i	−1.36704	+	0.497562i	−0.918224	−	0.396062i	$-0.870376\pi$
$97$	−13.4638	+	4.90042i	−1.36704	+	0.497562i	−0.448816	+	0.893624i	$0.648154\pi$
$98$		0			0
$99$	0.272211	−	0.228412i	0.0273582	−	0.0229563i
$100$		0			0
$101$	−2.97288	−	16.8600i	−0.295813	−	1.67764i	−0.663881	−	0.747838i	$-0.731092\pi$
$101$	−2.97288	−	16.8600i	−0.295813	−	1.67764i	0.368068	−	0.929799i	$-0.380019\pi$
$102$		0			0
$103$	6.64081	−	11.5022i	0.654339	−	1.13335i	−0.327720	−	0.944775i	$-0.606280\pi$
$103$	6.64081	−	11.5022i	0.654339	−	1.13335i	0.982059	−	0.188573i	$-0.0603863\pi$
$104$		0			0
$105$	−0.557515	−	0.202919i	−0.0544079	−	0.0198029i
$106$		0			0
$107$	−0.494870	−	0.857140i	−0.0478409	−	0.0828628i	0.841113	−	0.540859i	$-0.181901\pi$
$107$	−0.494870	−	0.857140i	−0.0478409	−	0.0828628i	−0.888954	+	0.457996i	$0.848567\pi$
$108$		0			0
$109$	10.3519	+	8.68625i	0.991529	+	0.831991i	0.985788	−	0.167992i	$-0.0537283\pi$
$109$	10.3519	+	8.68625i	0.991529	+	0.831991i	0.00574045	+	0.999984i	$0.498173\pi$
$110$		0			0
$111$	1.16887	−	6.62902i	0.110945	−	0.629198i
$112$		0			0
$113$	16.5369			1.55566			0.777829	−	0.628476i	$-0.216321\pi$
$113$	16.5369			1.55566			0.777829	+	0.628476i	$0.216321\pi$
$114$		0			0
$115$	−1.71313			−0.159750
$116$		0			0
$117$	0.278895	−	1.58169i	0.0257838	−	0.146227i
$118$		0			0
$119$	5.91198	+	4.96074i	0.541950	+	0.454750i
$120$		0			0
$121$	4.72506	+	8.18405i	0.429551	+	0.744005i
$122$		0			0
$123$	−10.9560	−	3.98766i	−0.987871	−	0.359555i
$124$		0			0
$125$	1.39979	−	2.42450i	0.125201	−	0.216854i
$126$		0			0
$127$	−0.388935	−	2.20576i	−0.0345124	−	0.195729i	0.962677	−	0.270653i	$-0.0872397\pi$
$127$	−0.388935	−	2.20576i	−0.0345124	−	0.195729i	−0.997189	+	0.0749239i	$0.976129\pi$
$128$		0			0
$129$	0.343314	−	0.288075i	0.0302271	−	0.0253636i
$130$		0			0
$131$	16.5173	−	6.01181i	1.44313	−	0.525255i	0.502463	−	0.864599i	$-0.332427\pi$
$131$	16.5173	−	6.01181i	1.44313	−	0.525255i	0.940662	+	0.339344i	$0.110205\pi$
$132$		0			0
$133$	−4.87927	−	1.32418i	−0.423087	−	0.114821i
$134$		0			0
$135$	1.30481	−	0.474912i	0.112300	−	0.0408739i
$136$		0			0
$137$	4.36728	−	3.66458i	0.373122	−	0.313086i	−0.436873	−	0.899523i	$-0.643914\pi$
$137$	4.36728	−	3.66458i	0.373122	−	0.313086i	0.809995	+	0.586437i	$0.199470\pi$
$138$		0			0
$139$	0.891090	+	5.05362i	0.0755813	+	0.428643i	0.998994	+	0.0448352i	$0.0142763\pi$
$139$	0.891090	+	5.05362i	0.0755813	+	0.428643i	−0.923413	+	0.383808i	$0.874613\pi$
$140$		0			0
$141$	−10.5066	+	18.1980i	−0.884818	+	1.53255i
$142$		0			0
$143$	−6.58265	−	2.39589i	−0.550469	−	0.200354i
$144$		0			0
$145$	0.547914	+	0.949015i	0.0455018	+	0.0788114i
$146$		0			0
$147$	−7.85162	−	6.58829i	−0.647591	−	0.543393i
$148$		0			0
$149$	−2.06723	+	11.7238i	−0.169354	+	0.960454i	0.775107	+	0.631830i	$0.217696\pi$
$149$	−2.06723	+	11.7238i	−0.169354	+	0.960454i	−0.944461	+	0.328624i	$0.893415\pi$
$150$		0			0
$151$	−14.8628			−1.20952			−0.604759	−	0.796409i	$-0.706731\pi$
$151$	−14.8628			−1.20952			−0.604759	+	0.796409i	$0.706731\pi$
$152$		0			0
$153$	1.89921			0.153542
$154$		0			0
$155$	0.00392629	−	0.0222671i	0.000315367	−	0.00178854i
$156$		0			0
$157$	−8.45258	−	7.09255i	−0.674589	−	0.566047i	0.239831	−	0.970815i	$-0.422908\pi$
$157$	−8.45258	−	7.09255i	−0.674589	−	0.566047i	−0.914420	+	0.404767i	$0.867353\pi$
$158$		0			0
$159$	−4.14379	−	7.17725i	−0.328624	−	0.569193i
$160$		0			0
$161$	6.61640	+	2.40817i	0.521446	+	0.189791i
$162$		0			0
$163$	−1.99237	+	3.45089i	−0.156055	+	0.270295i	−0.933443	−	0.358727i	$-0.883211\pi$
$163$	−1.99237	+	3.45089i	−0.156055	+	0.270295i	0.777388	+	0.629021i	$0.216544\pi$
$164$		0			0
$165$	0.110581	+	0.627134i	0.00860869	+	0.0488223i
$166$		0			0
$167$	−6.19785	+	5.20061i	−0.479604	+	0.402436i	−0.850283	−	0.526325i	$-0.823569\pi$
$167$	−6.19785	+	5.20061i	−0.479604	+	0.402436i	0.370679	+	0.928761i	$0.379125\pi$
$168$		0			0
$169$	−17.5362	+	6.38267i	−1.34894	+	0.490974i
$170$		0			0
$171$	−1.12928	+	0.522190i	−0.0863584	+	0.0399329i
$172$		0			0
$173$	6.13327	−	2.23233i	0.466304	−	0.169721i	−0.0981735	−	0.995169i	$-0.531300\pi$
$173$	6.13327	−	2.23233i	0.466304	−	0.169721i	0.564477	+	0.825449i	$0.309078\pi$
$174$		0			0
$175$	−4.37181	+	3.66838i	−0.330478	+	0.277304i
$176$		0			0
$177$	3.12491	+	17.7222i	0.234883	+	1.33209i
$178$		0			0
$179$	4.91617	−	8.51506i	0.367452	−	0.636445i	−0.621715	−	0.783244i	$-0.713564\pi$
$179$	4.91617	−	8.51506i	0.367452	−	0.636445i	0.989166	+	0.146799i	$0.0468969\pi$
$180$		0			0
$181$	12.9463	+	4.71208i	0.962293	+	0.350246i	0.774932	−	0.632045i	$-0.217784\pi$
$181$	12.9463	+	4.71208i	0.962293	+	0.350246i	0.187361	+	0.982291i	$0.440007\pi$
$182$		0			0
$183$	5.05805	+	8.76080i	0.373902	+	0.647617i
$184$		0			0
$185$	0.802823	+	0.673648i	0.0590247	+	0.0495276i
$186$		0			0
$187$	1.43842	−	8.15771i	0.105188	−	0.596551i
$188$		0			0
$189$	−5.70699			−0.415123
$190$		0			0
$191$	1.03137			0.0746275			0.0373137	−	0.999304i	$-0.488120\pi$
$191$	1.03137			0.0746275			0.0373137	+	0.999304i	$0.488120\pi$
$192$		0			0
$193$	−0.407183	+	2.30925i	−0.0293097	+	0.166224i	−0.995949	−	0.0899169i	$-0.971340\pi$
$193$	−0.407183	+	2.30925i	−0.0293097	+	0.166224i	0.966640	+	0.256140i	$0.0824510\pi$
$194$		0			0
$195$	2.20486	+	1.85010i	0.157893	+	0.132488i
$196$		0			0
$197$	−7.78406	−	13.4824i	−0.554592	−	0.960581i	−0.997935	−	0.0642291i	$-0.979541\pi$
$197$	−7.78406	−	13.4824i	−0.554592	−	0.960581i	0.443344	−	0.896352i	$-0.353792\pi$
$198$		0			0
$199$	12.8701	+	4.68434i	0.912339	+	0.332064i	0.755186	−	0.655510i	$-0.227546\pi$
$199$	12.8701	+	4.68434i	0.912339	+	0.332064i	0.157153	+	0.987574i	$0.449769\pi$
$200$		0			0
$201$	−3.35372	+	5.80882i	−0.236553	+	0.409722i
$202$		0			0
$203$	−0.782093	−	4.43547i	−0.0548922	−	0.311309i
$204$		0			0
$205$	1.39056	−	1.16682i	0.0971207	−	0.0814940i
$206$		0			0
$207$	1.62823	−	0.592626i	0.113170	−	0.0411904i
$208$		0			0
$209$	1.38768	+	5.24614i	0.0959878	+	0.362883i
$210$		0			0
$211$	20.2595	−	7.37386i	1.39472	−	0.507638i	0.468116	−	0.883667i	$-0.344933\pi$
$211$	20.2595	−	7.37386i	1.39472	−	0.507638i	0.926608	+	0.376030i	$0.122711\pi$
$212$		0			0
$213$	12.9421	−	10.8597i	0.886778	−	0.744095i
$214$		0			0
$215$	0.0121165	+	0.0687159i	0.000826336	+	0.00468638i
$216$		0			0
$217$	−0.0464652	+	0.0804801i	−0.00315426	+	0.00546335i
$218$		0			0
$219$	−1.87550	−	0.682627i	−0.126735	−	0.0461276i
$220$		0			0
$221$	−18.7200	−	32.4240i	−1.25924	−	2.18107i
$222$		0			0
$223$	−19.9848	−	16.7693i	−1.33828	−	1.12295i	−0.982063	−	0.188551i	$-0.939621\pi$
$223$	−19.9848	−	16.7693i	−1.33828	−	1.12295i	−0.356220	−	0.934402i	$-0.615935\pi$
$224$		0			0
$225$	−0.243877	+	1.38309i	−0.0162585	+	0.0922063i
$226$		0			0
$227$	21.7357			1.44265			0.721325	−	0.692596i	$-0.243533\pi$
$227$	21.7357			1.44265			0.721325	+	0.692596i	$0.243533\pi$
$228$		0			0
$229$	−20.1255			−1.32993			−0.664964	−	0.746875i	$-0.731553\pi$
$229$	−20.1255			−1.32993			−0.664964	+	0.746875i	$0.731553\pi$
$230$		0			0
$231$	0.454491	−	2.57754i	0.0299033	−	0.169590i
$232$		0			0
$233$	16.8667	+	14.1529i	1.10498	+	0.927184i	0.997750	−	0.0670504i	$-0.0213588\pi$
$233$	16.8667	+	14.1529i	1.10498	+	0.927184i	0.107226	+	0.994235i	$0.465803\pi$
$234$		0			0
$235$	−1.63581	−	2.83330i	−0.106708	−	0.184824i
$236$		0			0
$237$	14.8036	+	5.38808i	0.961598	+	0.349993i
$238$		0			0
$239$	−2.18637	+	3.78691i	−0.141425	+	0.244955i	−0.928033	−	0.372497i	$-0.878502\pi$
$239$	−2.18637	+	3.78691i	−0.141425	+	0.244955i	0.786609	+	0.617452i	$0.211835\pi$
$240$		0			0
$241$	−2.60506	−	14.7740i	−0.167807	−	0.951679i	−0.946123	−	0.323807i	$-0.895037\pi$
$241$	−2.60506	−	14.7740i	−0.167807	−	0.951679i	0.778317	−	0.627872i	$-0.216074\pi$
$242$		0			0
$243$	−2.26484	+	1.90042i	−0.145289	+	0.121912i
$244$		0			0
$245$	1.49954	−	0.545790i	0.0958024	−	0.0348692i
$246$		0			0
$247$	20.0461	+	14.1325i	1.27550	+	0.899226i
$248$		0			0
$249$	19.6596	−	7.15550i	1.24587	−	0.453461i
$250$		0			0
$251$	−17.9754	+	15.0832i	−1.13460	+	0.952042i	−0.999249	−	0.0387556i	$-0.987661\pi$
$251$	−17.9754	+	15.0832i	−1.13460	+	0.952042i	−0.135351	+	0.990798i	$0.543216\pi$
$252$		0			0
$253$	−1.31233	−	7.44261i	−0.0825057	−	0.467913i
$254$		0			0
$255$	−1.70176	+	2.94754i	−0.106569	+	0.184582i
$256$		0			0
$257$	−0.0996901	−	0.0362842i	−0.00621850	−	0.00226335i	0.338909	−	0.940819i	$-0.389942\pi$
$257$	−0.0996901	−	0.0362842i	−0.00621850	−	0.00226335i	−0.345128	+	0.938556i	$0.612164\pi$
$258$		0			0
$259$	−2.15368	−	3.73029i	−0.133823	−	0.231789i
$260$		0			0
$261$	−0.849054	−	0.712441i	−0.0525551	−	0.0440990i
$262$		0			0
$263$	−2.70397	+	15.3350i	−0.166734	+	0.945594i	0.780525	+	0.625124i	$0.214952\pi$
$263$	−2.70397	+	15.3350i	−0.166734	+	0.945594i	−0.947259	+	0.320469i	$0.896159\pi$
$264$		0			0
$265$	1.29031			0.0792633
$266$		0			0
$267$	−4.36874			−0.267363
$268$		0			0
$269$	2.43886	−	13.8315i	0.148700	−	0.843321i	−0.815621	−	0.578586i	$-0.803605\pi$
$269$	2.43886	−	13.8315i	0.148700	−	0.843321i	0.964321	−	0.264734i	$-0.0852843\pi$
$270$		0			0
$271$	8.77391	+	7.36218i	0.532977	+	0.447221i	0.869128	−	0.494587i	$-0.164681\pi$
$271$	8.77391	+	7.36218i	0.532977	+	0.447221i	−0.336151	+	0.941808i	$0.609125\pi$
$272$		0			0
$273$	−5.91485	−	10.2448i	−0.357983	−	0.620044i
$274$		0			0
$275$	5.75613	+	2.09506i	0.347108	+	0.126337i
$276$		0			0
$277$	−12.8642	+	22.2814i	−0.772932	+	1.33876i	0.163017	+	0.986623i	$0.447878\pi$
$277$	−12.8642	+	22.2814i	−0.772932	+	1.33876i	−0.935949	+	0.352135i	$0.885456\pi$
$278$		0			0
$279$	0.00397120	+	0.0225218i	0.000237749	+	0.00134834i
$280$		0			0
$281$	−20.6252	+	17.3066i	−1.23039	+	1.03242i	−0.232181	+	0.972673i	$0.574586\pi$
$281$	−20.6252	+	17.3066i	−1.23039	+	1.03242i	−0.998213	+	0.0597510i	$0.980969\pi$
$282$		0			0
$283$	−2.78007	+	1.01186i	−0.165258	+	0.0601491i	−0.423324	−	0.905978i	$-0.639137\pi$
$283$	−2.78007	+	1.01186i	−0.165258	+	0.0601491i	0.258066	+	0.966127i	$0.416915\pi$
$284$		0			0
$285$	0.201450	−	2.22053i	0.0119329	−	0.131533i
$286$		0			0
$287$	−7.01078	+	2.55172i	−0.413834	+	0.150623i
$288$		0			0
$289$	20.8922	−	17.5306i	1.22895	−	1.03121i
$290$		0			0
$291$	4.50970	+	25.5758i	0.264363	+	1.49928i
$292$		0			0
$293$	−5.01204	+	8.68111i	−0.292807	+	0.507156i	−0.974472	−	0.224508i	$-0.927923\pi$
$293$	−5.01204	+	8.68111i	−0.292807	+	0.507156i	0.681666	+	0.731664i	$0.261256\pi$
$294$		0			0
$295$	−2.63282	−	0.958268i	−0.153289	−	0.0557925i
$296$		0			0
$297$	3.06277	+	5.30488i	0.177720	+	0.307820i
$298$		0			0
$299$	−26.1666	−	21.9564i	−1.51325	−	1.26977i
$300$		0			0
$301$	0.0497991	−	0.282425i	0.00287037	−	0.0162787i
$302$		0			0
$303$	−31.0316			−1.78272
$304$		0			0
$305$	−1.57500			−0.0901844
$306$		0			0
$307$	−2.87822	+	16.3232i	−0.164269	+	0.931614i	0.785547	+	0.618802i	$0.212382\pi$
$307$	−2.87822	+	16.3232i	−0.164269	+	0.931614i	−0.949815	+	0.312811i	$0.898729\pi$
$308$		0			0
$309$	−18.4417	−	15.4744i	−1.04911	−	0.880310i
$310$		0			0
$311$	−0.215620	−	0.373465i	−0.0122267	−	0.0211772i	0.859847	−	0.510551i	$-0.170559\pi$
$311$	−0.215620	−	0.373465i	−0.0122267	−	0.0211772i	−0.872074	+	0.489374i	$0.837225\pi$
$312$		0			0
$313$	13.0841	+	4.76223i	0.739557	+	0.269177i	0.684205	−	0.729290i	$-0.260149\pi$
$313$	13.0841	+	4.76223i	0.739557	+	0.269177i	0.0553527	+	0.998467i	$0.482372\pi$
$314$		0			0
$315$	−0.0467141	+	0.0809112i	−0.00263204	+	0.00455883i
$316$		0			0
$317$	−2.87712	−	16.3170i	−0.161595	−	0.916452i	−0.952506	−	0.304521i	$-0.901504\pi$
$317$	−2.87712	−	16.3170i	−0.161595	−	0.916452i	0.790911	−	0.611932i	$-0.209607\pi$
$318$		0			0
$319$	−3.70322	+	3.10737i	−0.207341	+	0.173980i
$320$		0			0
$321$	−1.68579	+	0.613577i	−0.0940915	+	0.0342465i
$322$		0			0
$323$	−12.3415	+	26.2463i	−0.686700	+	1.46039i
$324$		0			0
$325$	26.0165	−	9.46925i	1.44314	−	0.525259i
$326$		0			0
$327$	18.7635	−	15.7445i	1.03763	−	0.870672i
$328$		0			0
$329$	2.33495	+	13.2422i	0.128730	+	0.730064i
$330$		0			0
$331$	−4.74773	+	8.22332i	−0.260959	+	0.451994i	−0.966497	−	0.256678i	$-0.917372\pi$
$331$	−4.74773	+	8.22332i	−0.260959	+	0.451994i	0.705538	+	0.708672i	$0.250705\pi$
$332$		0			0
$333$	−0.996072	−	0.362540i	−0.0545844	−	0.0198671i
$334$		0			0
$335$	−0.522150	−	0.904390i	−0.0285281	−	0.0494121i
$336$		0			0
$337$	9.65934	+	8.10515i	0.526178	+	0.441515i	0.866779	−	0.498692i	$-0.166186\pi$
$337$	9.65934	+	8.10515i	0.526178	+	0.441515i	−0.340601	+	0.940208i	$0.610631\pi$
$338$		0			0
$339$	5.20499	−	29.5190i	0.282696	−	1.60325i
$340$		0			0
$341$	0.0997461			0.00540155
$342$		0			0
$343$	−14.6778			−0.792529
$344$		0			0
$345$	−0.539208	+	3.05800i	−0.0290300	+	0.164637i
$346$		0			0
$347$	8.36688	+	7.02065i	0.449158	+	0.376888i	0.839123	−	0.543941i	$-0.183069\pi$
$347$	8.36688	+	7.02065i	0.449158	+	0.376888i	−0.389965	+	0.920830i	$0.627513\pi$
$348$		0			0
$349$	−4.20032	−	7.27517i	−0.224838	−	0.389431i	0.731433	−	0.681913i	$-0.238852\pi$
$349$	−4.20032	−	7.27517i	−0.224838	−	0.389431i	−0.956271	+	0.292483i	$0.905519\pi$
$350$		0			0
$351$	26.0165	+	9.46925i	1.38866	+	0.505431i
$352$		0			0
$353$	−6.69379	+	11.5940i	−0.356274	+	0.617086i	−0.987335	−	0.158648i	$-0.949287\pi$
$353$	−6.69379	+	11.5940i	−0.356274	+	0.617086i	0.631061	+	0.775733i	$0.282620\pi$
$354$		0			0
$355$	0.456761	+	2.59042i	0.0242423	+	0.137485i
$356$		0			0
$357$	10.7159	−	8.99172i	0.567146	−	0.475892i
$358$		0			0
$359$	26.6099	−	9.68521i	1.40442	−	0.511166i	0.474931	−	0.880023i	$-0.342473\pi$
$359$	26.6099	−	9.68521i	1.40442	−	0.511166i	0.929486	+	0.368857i	$0.120251\pi$
$360$		0			0
$361$	0.121876	−	18.9996i	0.00641452	−	0.999979i
$362$		0			0
$363$	16.0961	−	5.85849i	0.844824	−	0.307491i
$364$		0			0
$365$	0.238042	−	0.199741i	0.0124597	−	0.0104549i
$366$		0			0
$367$	0.0720091	+	0.408384i	0.00375884	+	0.0213175i	0.986629	−	0.162979i	$-0.0521104\pi$
$367$	0.0720091	+	0.408384i	0.00375884	+	0.0213175i	−0.982871	+	0.184297i	$0.940999\pi$
$368$		0			0
$369$	−0.918003	+	1.59003i	−0.0477893	+	0.0827735i
$370$		0			0
$371$	−4.98342	−	1.81381i	−0.258726	−	0.0941686i
$372$		0			0
$373$	2.01032	+	3.48198i	0.104090	+	0.180290i	0.913366	−	0.407139i	$-0.133474\pi$
$373$	2.01032	+	3.48198i	0.104090	+	0.180290i	−0.809276	+	0.587429i	$0.800140\pi$
$374$		0			0
$375$	−3.88725	−	3.26179i	−0.200737	−	0.168438i
$376$		0			0
$377$	−3.79416	+	21.5177i	−0.195409	+	1.10822i
$378$		0			0
$379$	14.1791			0.728332			0.364166	−	0.931334i	$-0.381354\pi$
$379$	14.1791			0.728332			0.364166	+	0.931334i	$0.381354\pi$
$380$		0			0
$381$	−4.05978			−0.207989
$382$		0			0
$383$	1.88738	−	10.7039i	0.0964407	−	0.546943i	−0.897856	−	0.440290i	$-0.854876\pi$
$383$	1.88738	−	10.7039i	0.0964407	−	0.546943i	0.994296	−	0.106653i	$-0.0340133\pi$
$384$		0			0
$385$	0.312160	+	0.261933i	0.0159091	+	0.0133493i
$386$		0			0
$387$	−0.0352870	−	0.0611189i	−0.00179374	−	0.00310685i
$388$		0			0
$389$	−24.0167	−	8.74136i	−1.21769	−	0.443205i	−0.348328	−	0.937373i	$-0.613251\pi$
$389$	−24.0167	−	8.74136i	−1.21769	−	0.443205i	−0.869367	+	0.494168i	$0.835473\pi$
$390$		0			0
$391$	20.1960	−	34.9804i	1.02135	−	1.76904i
$392$		0			0
$393$	−5.53249	−	31.3763i	−0.279077	−	1.58272i
$394$		0			0
$395$	−1.87890	+	1.57659i	−0.0945378	+	0.0793267i
$396$		0			0
$397$	16.1594	−	5.88155i	0.811018	−	0.295186i	0.0969735	−	0.995287i	$-0.469084\pi$
$397$	16.1594	−	5.88155i	0.811018	−	0.295186i	0.714044	+	0.700101i	$0.246862\pi$
$398$		0			0
$399$	−3.89948	+	8.29291i	−0.195218	+	0.415165i
$400$		0			0
$401$	−14.4376	+	5.25485i	−0.720979	+	0.262415i	−0.676341	−	0.736588i	$-0.736436\pi$
$401$	−14.4376	+	5.25485i	−0.720979	+	0.262415i	−0.0446377	+	0.999003i	$0.514213\pi$
$402$		0			0
$403$	0.345357	−	0.289789i	0.0172035	−	0.0144354i
$404$		0			0
$405$	−0.479009	−	2.71659i	−0.0238021	−	0.134989i
$406$		0			0
$407$	−2.31164	+	4.00387i	−0.114584	+	0.198465i
$408$		0			0
$409$	−13.4638	−	4.90042i	−0.665741	−	0.242310i	−0.0130280	−	0.999915i	$-0.504147\pi$
$409$	−13.4638	−	4.90042i	−0.665741	−	0.242310i	−0.652713	+	0.757605i	$0.726369\pi$
$410$		0			0
$411$	−5.16682	−	8.94920i	−0.254860	−	0.441431i
$412$		0			0
$413$	8.82135	+	7.40200i	0.434070	+	0.364228i
$414$		0			0
$415$	−0.565622	+	3.20780i	−0.0277653	+	0.157465i
$416$		0			0
$417$	9.30139			0.455491
$418$		0			0
$419$	−17.2723			−0.843805			−0.421902	−	0.906641i	$-0.638637\pi$
$419$	−17.2723			−0.843805			−0.421902	+	0.906641i	$0.638637\pi$
$420$		0			0
$421$	−4.83458	+	27.4183i	−0.235623	+	1.33629i	0.605674	+	0.795713i	$0.292903\pi$
$421$	−4.83458	+	27.4183i	−0.235623	+	1.33629i	−0.841297	+	0.540573i	$0.818208\pi$
$422$		0			0
$423$	2.53486	+	2.12700i	0.123249	+	0.103418i
$424$		0			0
$425$	16.3695	+	28.3528i	0.794038	+	1.37531i
$426$		0			0
$427$	6.08293	+	2.21401i	0.294374	+	0.107143i
$428$		0			0
$429$	−6.34865	+	10.9962i	−0.306516	+	0.530901i
$430$		0			0
$431$	−6.57872	−	37.3098i	−0.316886	−	1.79715i	−0.561444	−	0.827515i	$-0.689754\pi$
$431$	−6.57872	−	37.3098i	−0.316886	−	1.79715i	0.244558	−	0.969635i	$-0.421357\pi$
$432$		0			0
$433$	5.76405	−	4.83661i	0.277003	−	0.232433i	−0.493693	−	0.869636i	$-0.664353\pi$
$433$	5.76405	−	4.83661i	0.277003	−	0.232433i	0.770696	+	0.637204i	$0.219909\pi$
$434$		0			0
$435$	1.86648	−	0.679345i	0.0894911	−	0.0325721i
$436$		0			0
$437$	−2.39074	+	26.3526i	−0.114365	+	1.26061i
$438$		0			0
$439$	−19.9813	+	7.27259i	−0.953655	+	0.347102i	−0.771544	−	0.636176i	$-0.780515\pi$
$439$	−19.9813	+	7.27259i	−0.953655	+	0.347102i	−0.182111	+	0.983278i	$0.558293\pi$
$440$		0			0
$441$	−1.23642	+	1.03748i	−0.0588772	+	0.0494039i
$442$		0			0
$443$	−2.59412	−	14.7120i	−0.123250	−	0.698988i	−0.982332	−	0.187149i	$-0.940075\pi$
$443$	−2.59412	−	14.7120i	−0.123250	−	0.698988i	0.859081	−	0.511839i	$-0.171036\pi$
$444$		0			0
$445$	0.340090	−	0.589054i	0.0161218	−	0.0279238i
$446$		0			0
$447$	20.2768	+	7.38017i	0.959062	+	0.349070i
$448$		0			0
$449$	−8.47286	−	14.6754i	−0.399859	−	0.692576i	0.593849	−	0.804576i	$-0.297608\pi$
$449$	−8.47286	−	14.6754i	−0.399859	−	0.692576i	−0.993708	+	0.112000i	$0.964274\pi$
$450$		0			0
$451$	6.13441	+	5.14738i	0.288858	+	0.242381i
$452$		0			0
$453$	−4.67808	+	26.5307i	−0.219795	+	1.24652i
$454$		0			0
$455$	1.84180			0.0863447
$456$		0			0
$457$	−10.2922			−0.481448			−0.240724	−	0.970594i	$-0.577385\pi$
$457$	−10.2922			−0.481448			−0.240724	+	0.970594i	$0.577385\pi$
$458$		0			0
$459$	−5.68507	+	32.2416i	−0.265356	+	1.50491i
$460$		0			0
$461$	4.59397	+	3.85480i	0.213962	+	0.179536i	0.743470	−	0.668770i	$-0.233179\pi$
$461$	4.59397	+	3.85480i	0.213962	+	0.179536i	−0.529507	+	0.848305i	$0.677623\pi$
$462$		0			0
$463$	−1.69033	−	2.92774i	−0.0785563	−	0.136063i	0.824071	−	0.566487i	$-0.191698\pi$
$463$	−1.69033	−	2.92774i	−0.0785563	−	0.136063i	−0.902627	+	0.430423i	$0.858364\pi$
$464$		0			0
$465$	−0.0385118	−	0.0140172i	−0.00178594	−	0.000650030i
$466$		0			0
$467$	−1.03045	+	1.78480i	−0.0476837	+	0.0825906i	−0.888882	−	0.458136i	$-0.848517\pi$
$467$	−1.03045	+	1.78480i	−0.0476837	+	0.0825906i	0.841198	+	0.540727i	$0.181851\pi$
$468$		0			0
$469$	0.745318	+	4.22691i	0.0344156	+	0.195180i
$470$		0			0
$471$	−15.3209	+	12.8558i	−0.705952	+	0.592364i
$472$		0			0
$473$	−0.289251	+	0.105279i	−0.0132998	+	0.00484073i
$474$		0			0
$475$	−17.5291	−	12.3580i	−0.804290	−	0.567023i
$476$		0			0
$477$	−1.22637	+	0.446361i	−0.0561515	+	0.0204375i
$478$		0			0
$479$	−4.53663	+	3.80668i	−0.207284	+	0.173932i	−0.740519	−	0.672035i	$-0.765420\pi$
$479$	−4.53663	+	3.80668i	−0.207284	+	0.173932i	0.533235	+	0.845967i	$0.320976\pi$
$480$		0			0
$481$	3.62860	+	20.5788i	0.165450	+	0.938312i
$482$		0			0
$483$	6.38120	−	11.0526i	0.290355	−	0.502909i
$484$		0			0
$485$	−3.79954	−	1.38292i	−0.172528	−	0.0627952i
$486$		0			0
$487$	13.3232	+	23.0764i	0.603731	+	1.04569i	0.992251	+	0.124252i	$0.0396532\pi$
$487$	13.3232	+	23.0764i	0.603731	+	1.04569i	−0.388520	+	0.921440i	$0.627013\pi$
$488$		0			0
$489$	5.53287	+	4.64263i	0.250205	+	0.209947i
$490$		0			0
$491$	6.15100	−	34.8841i	0.277591	−	1.57430i	−0.453019	−	0.891501i	$-0.649653\pi$
$491$	6.15100	−	34.8841i	0.277591	−	1.57430i	0.730610	−	0.682795i	$-0.239236\pi$
$492$		0			0
$493$	−25.8373			−1.16365
$494$		0			0
$495$	0.100280			0.00450727
$496$		0			0
$497$	1.87730	−	10.6467i	0.0842086	−	0.477571i
$498$		0			0
$499$	−26.5322	−	22.2631i	−1.18774	−	0.996634i	−0.999896	−	0.0144356i	$-0.995405\pi$
$499$	−26.5322	−	22.2631i	−1.18774	−	0.996634i	−0.187846	−	0.982198i	$-0.560151\pi$
$500$		0			0
$501$	7.33252	+	12.7003i	0.327593	+	0.567408i
$502$		0			0
$503$	−29.0173	−	10.5614i	−1.29382	−	0.470912i	−0.398840	−	0.917020i	$-0.630587\pi$
$503$	−29.0173	−	10.5614i	−1.29382	−	0.470912i	−0.894979	+	0.446109i	$0.852810\pi$
$504$		0			0
$505$	2.41569	−	4.18410i	0.107497	−	0.186190i
$506$		0			0
$507$	5.87377	+	33.3118i	0.260863	+	1.47943i
$508$		0			0
$509$	11.9255	−	10.0067i	0.528590	−	0.443540i	−0.339024	−	0.940778i	$-0.610097\pi$
$509$	11.9255	−	10.0067i	0.528590	−	0.443540i	0.867614	+	0.497238i	$0.165652\pi$
$510$		0			0
$511$	−1.20014	+	0.436815i	−0.0530910	+	0.0193235i
$512$		0			0
$513$	−5.48451	−	20.7343i	−0.242147	−	0.915440i
$514$		0			0
$515$	3.52210	−	1.28194i	0.155202	−	0.0564890i
$516$		0			0
$517$	11.0560	−	9.27711i	0.486244	−	0.408007i
$518$		0			0
$519$	−2.05434	−	11.6507i	−0.0901756	−	0.511411i
$520$		0			0
$521$	−11.1132	+	19.2486i	−0.486877	+	0.843295i	−0.999886	−	0.0150876i	$-0.995197\pi$
$521$	−11.1132	+	19.2486i	−0.486877	+	0.843295i	0.513009	+	0.858383i	$0.328531\pi$
$522$		0			0
$523$	−10.1135	−	3.68103i	−0.442234	−	0.160960i	0.111299	−	0.993787i	$-0.464499\pi$
$523$	−10.1135	−	3.68103i	−0.442234	−	0.160960i	−0.553534	+	0.832827i	$0.686721\pi$
$524$		0			0
$525$	5.17218	+	8.95848i	0.225732	+	0.390980i
$526$		0			0
$527$	0.408385	+	0.342676i	0.0177895	+	0.0149272i
$528$		0			0
$529$	2.40523	−	13.6408i	0.104575	−	0.593077i
$530$		0			0
$531$	2.83383			0.122978
$532$		0			0
$533$	36.1941			1.56774
$534$		0			0
$535$	0.0485015	−	0.275066i	0.00209690	−	0.0118921i
$536$		0			0
$537$	−13.6523	−	11.4557i	−0.589142	−	0.494349i
$538$		0			0
$539$	3.51988	+	6.09660i	0.151612	+	0.262599i
$540$		0			0
$541$	11.5235	+	4.19422i	0.495435	+	0.180323i	0.577639	−	0.816292i	$-0.303974\pi$
$541$	11.5235	+	4.19422i	0.495435	+	0.180323i	−0.0822049	+	0.996615i	$0.526196\pi$
$542$		0			0
$543$	12.4861	−	21.6266i	0.535830	−	0.928085i
$544$		0			0
$545$	0.662215	+	3.75561i	0.0283662	+	0.160873i
$546$		0			0
$547$	14.2562	−	11.9624i	0.609552	−	0.511475i	−0.284948	−	0.958543i	$-0.591976\pi$
$547$	14.2562	−	11.9624i	0.609552	−	0.511475i	0.894500	+	0.447068i	$0.147532\pi$
$548$		0			0
$549$	1.49695	−	0.544844i	0.0638881	−	0.0232534i
$550$		0			0
$551$	15.3630	−	7.10401i	0.654488	−	0.302641i
$552$		0			0
$553$	9.47288	−	3.44785i	0.402828	−	0.146617i
$554$		0			0
$555$	1.45518	−	1.22104i	0.0617688	−	0.0518302i
$556$		0			0
$557$	−0.706865	−	4.00883i	−0.0299508	−	0.169860i	0.966163	−	0.257931i	$-0.0830407\pi$
$557$	−0.706865	−	4.00883i	−0.0299508	−	0.169860i	−0.996114	+	0.0880715i	$0.971930\pi$
$558$		0			0
$559$	−0.695630	+	1.20487i	−0.0294220	+	0.0509604i
$560$		0			0
$561$	−14.1091	−	5.13529i	−0.595686	−	0.216812i
$562$		0			0
$563$	12.4377	+	21.5428i	0.524188	+	0.907920i	0.999603	+	0.0281586i	$0.00896435\pi$
$563$	12.4377	+	21.5428i	0.524188	+	0.907920i	−0.475416	+	0.879761i	$0.657702\pi$
$564$		0			0
$565$	3.57496	+	2.99975i	0.150400	+	0.126201i
$566$		0			0
$567$	−1.96875	+	11.1653i	−0.0826795	+	0.468899i
$568$		0			0
$569$	19.2420			0.806667			0.403334	−	0.915053i	$-0.367851\pi$
$569$	19.2420			0.806667			0.403334	+	0.915053i	$0.367851\pi$
$570$		0			0
$571$	13.5395			0.566612			0.283306	−	0.959030i	$-0.408569\pi$
$571$	13.5395			0.566612			0.283306	+	0.959030i	$0.408569\pi$
$572$		0			0
$573$	0.324625	−	1.84104i	0.0135614	−	0.0769106i
$574$		0			0
$575$	22.8811	+	19.1995i	0.954207	+	0.800675i
$576$		0			0
$577$	−12.8402	−	22.2398i	−0.534543	−	0.925855i	−0.999185	−	0.0403567i	$-0.987151\pi$
$577$	−12.8402	−	22.2398i	−0.534543	−	0.925855i	0.464643	−	0.885498i	$-0.346183\pi$
$578$		0			0
$579$	3.99394	+	1.45368i	0.165983	+	0.0604127i
$580$		0			0
$581$	6.69379	−	11.5940i	0.277705	−	0.481000i
$582$		0			0
$583$	0.988438	+	5.60571i	0.0409369	+	0.232165i
$584$		0			0
$585$	0.347207	−	0.291341i	0.0143552	−	0.0120455i
$586$		0			0
$587$	17.4378	−	6.34683i	0.719734	−	0.261962i	0.0439211	−	0.999035i	$-0.486015\pi$
$587$	17.4378	−	6.34683i	0.719734	−	0.261962i	0.675813	+	0.737073i	$0.263793\pi$
$588$		0			0
$589$	−0.337049	−	0.0914715i	−0.0138878	−	0.00376902i
$590$		0			0
$591$	−26.5166	+	9.65127i	−1.09075	+	0.397000i
$592$		0			0
$593$	2.75772	−	2.31400i	0.113246	−	0.0950248i	−0.584406	−	0.811461i	$-0.698673\pi$
$593$	2.75772	−	2.31400i	0.113246	−	0.0950248i	0.697652	+	0.716437i	$0.254228\pi$
$594$		0			0
$595$	0.378193	+	2.14484i	0.0155044	+	0.0879298i
$596$		0			0
$597$	12.4126	−	21.4993i	0.508014	−	0.879907i
$598$		0			0
$599$	12.3328	+	4.48878i	0.503905	+	0.183407i	0.581450	−	0.813582i	$-0.302486\pi$
$599$	12.3328	+	4.48878i	0.503905	+	0.183407i	−0.0775443	+	0.996989i	$0.524708\pi$
$600$		0			0
$601$	−6.78825	−	11.7576i	−0.276898	−	0.479602i	0.693714	−	0.720251i	$-0.255973\pi$
$601$	−6.78825	−	11.7576i	−0.276898	−	0.479602i	−0.970612	+	0.240649i	$0.922640\pi$
$602$		0			0
$603$	0.809130	+	0.678941i	0.0329503	+	0.0276486i
$604$		0			0
$605$	−0.463097	+	2.62635i	−0.0188276	+	0.106777i
$606$		0			0
$607$	−18.3633			−0.745343			−0.372672	−	0.927963i	$-0.621558\pi$
$607$	−18.3633			−0.745343			−0.372672	+	0.927963i	$0.621558\pi$
$608$		0			0
$609$	−8.16365			−0.330808
$610$		0			0
$611$	11.3275	−	64.2415i	0.458262	−	2.59893i
$612$		0			0
$613$	4.42518	+	3.71316i	0.178731	+	0.149973i	0.727764	−	0.685827i	$-0.240559\pi$
$613$	4.42518	+	3.71316i	0.178731	+	0.149973i	−0.549033	+	0.835801i	$0.685004\pi$
$614$		0			0
$615$	−1.64513	−	2.84945i	−0.0663382	−	0.114901i
$616$		0			0
$617$	−39.3443	−	14.3201i	−1.58394	−	0.576507i	−0.607885	−	0.794025i	$-0.707982\pi$
$617$	−39.3443	−	14.3201i	−1.58394	−	0.576507i	−0.976056	+	0.217518i	$0.930204\pi$
$618$		0			0
$619$	−18.0480	+	31.2601i	−0.725412	+	1.25645i	0.233392	+	0.972383i	$0.425017\pi$
$619$	−18.0480	+	31.2601i	−0.725412	+	1.25645i	−0.958804	+	0.284068i	$0.908316\pi$
$620$		0			0
$621$	5.18672	+	29.4154i	0.208136	+	1.18040i
$622$		0			0
$623$	−2.14153	+	1.79696i	−0.0857986	+	0.0719936i
$624$		0			0
$625$	−22.3757	+	8.14410i	−0.895029	+	0.325764i
$626$		0			0
$627$	9.80133	−	0.825838i	0.391427	−	0.0329808i
$628$		0			0
$629$	−23.2197	+	8.45126i	−0.925828	+	0.336974i
$630$		0			0
$631$	−29.6886	+	24.9117i	−1.18188	+	0.991717i	−0.181918	+	0.983314i	$0.558231\pi$
$631$	−29.6886	+	24.9117i	−1.18188	+	0.991717i	−0.999965	+	0.00840360i	$0.997325\pi$
$632$		0			0
$633$	−6.78594	−	38.4850i	−0.269717	−	1.52964i
$634$		0			0
$635$	0.316039	−	0.547396i	0.0125416	−	0.0217227i
$636$		0			0
$637$	29.8994	+	10.8825i	1.18466	+	0.431179i
$638$		0			0
$639$	−1.33023	−	2.30403i	−0.0526232	−	0.0911461i
$640$		0			0
$641$	5.24003	+	4.39691i	0.206969	+	0.173667i	0.740380	−	0.672189i	$-0.234646\pi$
$641$	5.24003	+	4.39691i	0.206969	+	0.173667i	−0.533411	+	0.845856i	$0.679090\pi$
$642$		0			0
$643$	−2.89363	+	16.4106i	−0.114114	+	0.647171i	0.873072	+	0.487592i	$0.162125\pi$
$643$	−2.89363	+	16.4106i	−0.114114	+	0.647171i	−0.987185	+	0.159579i	$0.948986\pi$
$644$		0			0
$645$	0.126474			0.00497992
$646$		0			0
$647$	36.1664			1.42185			0.710924	−	0.703269i	$-0.248277\pi$
$647$	36.1664			1.42185			0.710924	+	0.703269i	$0.248277\pi$
$648$		0			0
$649$	2.14629	−	12.1722i	0.0842494	−	0.477802i
$650$		0			0
$651$	0.129035	+	0.108273i	0.00505729	+	0.00424357i
$652$		0			0
$653$	4.83426	+	8.37319i	0.189179	+	0.327668i	0.944977	−	0.327137i	$-0.106084\pi$
$653$	4.83426	+	8.37319i	0.189179	+	0.327668i	−0.755798	+	0.654805i	$0.772751\pi$
$654$		0			0
$655$	4.66127	+	1.69656i	0.182131	+	0.0662902i
$656$		0			0
$657$	−0.157148	+	0.272188i	−0.00613093	+	0.0106191i
$658$		0			0
$659$	4.94409	+	28.0393i	0.192594	+	1.09226i	0.915803	+	0.401627i	$0.131555\pi$
$659$	4.94409	+	28.0393i	0.192594	+	1.09226i	−0.723209	+	0.690629i	$0.757334\pi$
$660$		0			0
$661$	−19.5360	+	16.3927i	−0.759863	+	0.637601i	−0.938091	−	0.346388i	$-0.887408\pi$
$661$	−19.5360	+	16.3927i	−0.759863	+	0.637601i	0.178228	+	0.983989i	$0.442964\pi$
$662$		0			0
$663$	−63.7702	+	23.2104i	−2.47663	+	0.901419i
$664$		0			0
$665$	−0.814604	−	1.17135i	−0.0315890	−	0.0454231i
$666$		0			0
$667$	−22.1508	+	8.06223i	−0.857683	+	0.312171i
$668$		0			0
$669$	−36.2240	+	30.3956i	−1.40050	+	1.17516i
$670$		0			0
$671$	−1.20652	−	6.84252i	−0.0465772	−	0.264153i
$672$		0			0
$673$	20.3192	−	35.1938i	0.783246	−	1.35662i	−0.146795	−	0.989167i	$-0.546896\pi$
$673$	20.3192	−	35.1938i	0.783246	−	1.35662i	0.930041	−	0.367456i	$-0.119771\pi$
$674$		0			0
$675$	−22.7499	−	8.28029i	−0.875644	−	0.318708i
$676$		0			0
$677$	−10.2220	−	17.7050i	−0.392862	−	0.680457i	0.599964	−	0.800027i	$-0.295182\pi$
$677$	−10.2220	−	17.7050i	−0.392862	−	0.680457i	−0.992826	+	0.119570i	$0.961848\pi$
$678$		0			0
$679$	12.7305	+	10.6822i	0.488552	+	0.409944i
$680$		0			0
$681$	6.84133	−	38.7991i	0.262160	−	1.48679i
$682$		0			0
$683$	39.8318			1.52412			0.762061	−	0.647505i	$-0.224187\pi$
$683$	39.8318			1.52412			0.762061	+	0.647505i	$0.224187\pi$
$684$		0			0
$685$	1.60887			0.0614718
$686$		0			0
$687$	−6.33450	+	35.9247i	−0.241676	+	1.37061i
$688$		0			0
$689$	19.7084	+	16.5373i	0.750831	+	0.630022i
$690$		0			0
$691$	14.0389	+	24.3160i	0.534064	+	0.925025i	0.999208	+	0.0397906i	$0.0126691\pi$
$691$	14.0389	+	24.3160i	0.534064	+	0.925025i	−0.465144	+	0.885235i	$0.653998\pi$
$692$		0			0
$693$	−0.387300	−	0.140966i	−0.0147123	−	0.00535484i
$694$		0			0
$695$	−0.724079	+	1.25414i	−0.0274659	+	0.0475723i
$696$		0			0
$697$	7.43206	+	42.1493i	0.281509	+	1.59652i
$698$		0			0
$699$	30.5722	−	25.6531i	1.15635	−	0.970290i
$700$		0			0
$701$	−4.02822	+	1.46615i	−0.152144	+	0.0553757i	−0.416969	−	0.908921i	$-0.636908\pi$
$701$	−4.02822	+	1.46615i	−0.152144	+	0.0553757i	0.264826	+	0.964296i	$0.414686\pi$
$702$		0			0
$703$	11.4829	−	11.4095i	0.433086	−	0.430317i
$704$		0			0
$705$	−5.57242	+	2.02819i	−0.209869	+	0.0763862i
$706$		0			0
$707$	−15.2115	+	12.7639i	−0.572087	+	0.480038i
$708$		0			0
$709$	−0.715927	−	4.06022i	−0.0268872	−	0.152485i	0.968408	−	0.249369i	$-0.0802234\pi$
$709$	−0.715927	−	4.06022i	−0.0268872	−	0.152485i	−0.995296	+	0.0968845i	$0.969112\pi$
$710$		0			0
$711$	1.24039	−	2.14842i	0.0465184	−	0.0805722i
$712$		0			0
$713$	0.457045	+	0.166351i	0.0171165	+	0.00622989i
$714$		0			0
$715$	−0.988438	−	1.71202i	−0.0369655	−	0.0640261i
$716$		0			0
$717$	6.07162	+	5.09469i	0.226749	+	0.190265i
$718$		0			0
$719$	−7.79796	+	44.2244i	−0.290815	+	1.64929i	0.392927	+	0.919570i	$0.371462\pi$
$719$	−7.79796	+	44.2244i	−0.290815	+	1.64929i	−0.683742	+	0.729724i	$0.739649\pi$
$720$		0			0
$721$	−15.4050			−0.573712
$722$		0			0
$723$	−27.1922			−1.01129
$724$		0			0
$725$	3.31776	−	18.8160i	0.123219	−	0.698807i
$726$		0			0
$727$	−26.7341	−	22.4326i	−0.991514	−	0.831979i	−0.00572754	−	0.999984i	$-0.501823\pi$
$727$	−26.7341	−	22.4326i	−0.991514	−	0.831979i	−0.985786	+	0.168005i	$0.946268\pi$
$728$		0			0
$729$	−11.9828	−	20.7548i	−0.443806	−	0.768695i
$730$		0			0
$731$	−1.54595	−	0.562680i	−0.0571791	−	0.0208115i
$732$		0			0
$733$	0.524006	−	0.907605i	0.0193546	−	0.0335232i	−0.856186	−	0.516668i	$-0.827172\pi$
$733$	0.524006	−	0.907605i	0.0193546	−	0.0335232i	0.875540	+	0.483145i	$0.160506\pi$
$734$		0			0
$735$	−0.502273	−	2.84853i	−0.0185266	−	0.105070i
$736$		0			0
$737$	3.52909	−	2.96126i	0.129996	−	0.109079i
$738$		0			0
$739$	−20.8426	+	7.58607i	−0.766706	+	0.279058i	−0.695618	−	0.718412i	$-0.744869\pi$
$739$	−20.8426	+	7.58607i	−0.766706	+	0.279058i	−0.0710882	+	0.997470i	$0.522647\pi$
$740$		0			0
$741$	31.5365	−	31.3348i	1.15852	−	1.15111i
$742$		0			0
$743$	35.7965	−	13.0288i	1.31325	−	0.477982i	0.411957	−	0.911203i	$-0.364845\pi$
$743$	35.7965	−	13.0288i	1.31325	−	0.477982i	0.901288	+	0.433221i	$0.142623\pi$
$744$		0			0
$745$	−2.57357	+	2.15948i	−0.0942884	+	0.0791174i
$746$		0			0
$747$	−0.572091	−	3.24449i	−0.0209317	−	0.118710i
$748$		0			0
$749$	−0.573986	+	0.994173i	−0.0209730	+	0.0363263i
$750$		0			0
$751$	11.9657	+	4.35515i	0.436634	+	0.158922i	0.550979	−	0.834519i	$-0.314255\pi$
$751$	11.9657	+	4.35515i	0.436634	+	0.158922i	−0.114345	+	0.993441i	$0.536477\pi$
$752$		0			0
$753$	21.2663	+	36.8343i	0.774987	+	1.34232i
$754$		0			0
$755$	−3.21306	−	2.69608i	−0.116935	−	0.0981203i
$756$		0			0
$757$	7.21125	−	40.8970i	0.262097	−	1.48643i	−0.515078	−	0.857143i	$-0.672237\pi$
$757$	7.21125	−	40.8970i	0.262097	−	1.48643i	0.777175	−	0.629284i	$-0.216652\pi$
$758$		0			0
$759$	−13.6984			−0.497221
$760$		0			0
$761$	36.4398			1.32094			0.660471	−	0.750851i	$-0.270357\pi$
$761$	36.4398			1.32094			0.660471	+	0.750851i	$0.270357\pi$
$762$		0			0
$763$	2.72173	−	15.4357i	0.0985333	−	0.558810i
$764$		0			0
$765$	0.410573	+	0.344512i	0.0148443	+	0.0124558i
$766$		0			0
$767$	−27.9324	−	48.3803i	−1.00858	−	1.74691i
$768$		0			0
$769$	−11.0091	−	4.00697i	−0.396997	−	0.144495i	0.135804	−	0.990736i	$-0.456638\pi$
$769$	−11.0091	−	4.00697i	−0.396997	−	0.144495i	−0.532801	+	0.846241i	$0.678860\pi$
$770$		0			0
$771$	−0.0961463	+	0.166530i	−0.00346263	+	0.00599744i
$772$		0			0
$773$	6.22310	+	35.2929i	0.223829	+	1.26940i	0.864911	+	0.501926i	$0.167375\pi$
$773$	6.22310	+	35.2929i	0.223829	+	1.26940i	−0.641081	+	0.767473i	$0.721514\pi$
$774$		0			0
$775$	−0.301994	+	0.253403i	−0.0108480	+	0.00910251i
$776$		0			0
$777$	−7.33658	+	2.67030i	−0.263198	+	0.0957964i
$778$		0			0
$779$	−16.0082	−	23.0189i	−0.573553	−	0.824736i
$780$		0			0
$781$	−10.9041	+	3.96875i	−0.390178	+	0.142013i
$782$		0			0
$783$	14.6362	−	12.2812i	0.523056	−	0.438896i
$784$		0			0
$785$	−0.540717	−	3.06656i	−0.0192990	−	0.109450i
$786$		0			0
$787$	−1.05573	+	1.82858i	−0.0376328	+	0.0651819i	−0.884228	−	0.467055i	$-0.845315\pi$
$787$	−1.05573	+	1.82858i	−0.0376328	+	0.0651819i	0.846596	+	0.532237i	$0.178648\pi$
$788$		0			0
$789$	26.5224	+	9.65337i	0.944223	+	0.343669i
$790$		0			0
$791$	−9.59033	−	16.6109i	−0.340993	−	0.590617i
$792$		0			0
$793$	−24.0568	−	20.1860i	−0.854282	−	0.716827i
$794$		0			0
$795$	0.406127	−	2.30326i	0.0144038	−	0.0816882i
$796$		0			0
$797$	14.9794			0.530596			0.265298	−	0.964166i	$-0.414530\pi$
$797$	14.9794			0.530596			0.265298	+	0.964166i	$0.414530\pi$
$798$		0			0
$799$	77.1376			2.72893
$800$		0			0
$801$	−0.119463	+	0.677509i	−0.00422102	+	0.0239386i
$802$		0			0
$803$	1.05012	+	0.881152i	0.0370578	+	0.0310952i
$804$		0			0
$805$	0.993506	+	1.72080i	0.0350165	+	0.0606503i
$806$		0			0
$807$	−23.9221	−	8.70694i	−0.842098	−	0.306499i
$808$		0			0
$809$	19.1248	−	33.1251i	0.672392	−	1.16462i	−0.304831	−	0.952406i	$-0.598600\pi$
$809$	19.1248	−	33.1251i	0.672392	−	1.16462i	0.977224	−	0.212211i	$-0.0680666\pi$
$810$		0			0
$811$	5.50463	+	31.2183i	0.193294	+	1.09622i	0.914828	+	0.403844i	$0.132326\pi$
$811$	5.50463	+	31.2183i	0.193294	+	1.09622i	−0.721534	+	0.692379i	$0.756563\pi$
$812$		0			0
$813$	15.9034	−	13.3445i	0.557756	−	0.468013i
$814$		0			0
$815$	−1.05670	+	0.384606i	−0.0370145	+	0.0134722i
$816$		0			0
$817$	1.07394	−	0.0904882i	0.0375726	−	0.00316578i
$818$		0			0
$819$	−1.75052	+	0.637136i	−0.0611680	+	0.0222633i
$820$		0			0
$821$	−10.7629	+	9.03111i	−0.375627	+	0.315188i	−0.810983	−	0.585070i	$-0.801067\pi$
$821$	−10.7629	+	9.03111i	−0.375627	+	0.315188i	0.435356	+	0.900258i	$0.356622\pi$
$822$		0			0
$823$	−3.19150	−	18.0999i	−0.111249	−	0.630923i	−0.988539	−	0.150963i	$-0.951762\pi$
$823$	−3.19150	−	18.0999i	−0.111249	−	0.630923i	0.877291	−	0.479960i	$-0.159349\pi$
$824$		0			0
$825$	5.55151	−	9.61550i	0.193279	−	0.334769i
$826$		0			0
$827$	5.23011	+	1.90360i	0.181869	+	0.0661948i	0.431349	−	0.902185i	$-0.358038\pi$
$827$	5.23011	+	1.90360i	0.181869	+	0.0661948i	−0.249481	+	0.968380i	$0.580260\pi$
$828$		0			0
$829$	21.0061	+	36.3837i	0.729573	+	1.26366i	0.957064	+	0.289878i	$0.0936146\pi$
$829$	21.0061	+	36.3837i	0.729573	+	1.26366i	−0.227490	+	0.973780i	$0.573052\pi$
$830$		0			0
$831$	35.7241	+	29.9761i	1.23926	+	1.03986i
$832$		0			0
$833$	−6.53353	+	37.0535i	−0.226373	+	1.28383i
$834$		0			0
$835$	−2.28324			−0.0790148
$836$		0			0
$837$	−0.394225			−0.0136264
$838$		0			0
$839$	5.46639	−	31.0014i	0.188721	−	1.07029i	−0.732360	−	0.680918i	$-0.761581\pi$
$839$	5.46639	−	31.0014i	0.188721	−	1.07029i	0.921081	−	0.389371i	$-0.127308\pi$
$840$		0			0
$841$	−10.6645	−	8.94862i	−0.367743	−	0.308573i
$842$		0			0
$843$	24.4011	+	42.2640i	0.840419	+	1.45565i
$844$		0			0
$845$	−4.94881	−	1.80122i	−0.170244	−	0.0619638i
$846$		0			0
$847$	5.48047	−	9.49246i	0.188311	−	0.326165i
$848$		0			0
$849$	0.931187	+	5.28103i	0.0319583	+	0.181244i
$850$		0			0
$851$	−17.2696	+	14.4909i	−0.591993	+	0.496741i
$852$		0			0
$853$	−10.6345	+	3.87065i	−0.364119	+	0.132529i	−0.517599	−	0.855623i	$-0.673174\pi$
$853$	−10.6345	+	3.87065i	−0.364119	+	0.132529i	0.153480	+	0.988152i	$0.450952\pi$
$854$		0			0
$855$	−0.338854	−	0.0919615i	−0.0115886	−	0.00314502i
$856$		0			0
$857$	−46.2117	+	16.8197i	−1.57856	+	0.574550i	−0.974891	−	0.222683i	$-0.928519\pi$
$857$	−46.2117	+	16.8197i	−1.57856	+	0.574550i	−0.603672	+	0.797233i	$0.706296\pi$
$858$		0			0
$859$	19.9118	−	16.7080i	0.679382	−	0.570069i	−0.236444	−	0.971645i	$-0.575982\pi$
$859$	19.9118	−	16.7080i	0.679382	−	0.570069i	0.915826	+	0.401576i	$0.131537\pi$
$860$		0			0
$861$	2.34827	+	13.3177i	0.0800287	+	0.453865i
$862$		0			0
$863$	0.199487	−	0.345522i	0.00679062	−	0.0117617i	−0.862610	−	0.505869i	$-0.831172\pi$
$863$	0.199487	−	0.345522i	0.00679062	−	0.0117617i	0.869401	+	0.494108i	$0.164505\pi$
$864$		0			0
$865$	1.73084	+	0.629973i	0.0588502	+	0.0214197i
$866$		0			0
$867$	−24.7170	−	42.8111i	−0.839434	−	1.45394i
$868$		0			0
$869$	−8.28873	−	6.95507i	−0.281176	−	0.235935i
$870$		0			0
$871$	3.61575	−	20.5059i	0.122515	−	0.694817i
$872$		0			0
$873$	4.08964			0.138413
$874$		0			0
$875$	−3.24715			−0.109774
$876$		0			0
$877$	1.98754	−	11.2719i	0.0671145	−	0.380625i	−0.932687	−	0.360687i	$-0.882542\pi$
$877$	1.98754	−	11.2719i	0.0671145	−	0.380625i	0.999801	−	0.0199377i	$-0.00634679\pi$
$878$		0			0
$879$	13.9186	+	11.6791i	0.469462	+	0.393925i
$880$		0			0
$881$	8.37742	+	14.5101i	0.282242	+	0.488858i	0.971937	−	0.235242i	$-0.0755884\pi$
$881$	8.37742	+	14.5101i	0.282242	+	0.488858i	−0.689694	+	0.724101i	$0.742255\pi$
$882$		0			0
$883$	−43.5805	−	15.8620i	−1.46660	−	0.533799i	−0.519425	−	0.854516i	$-0.673854\pi$
$883$	−43.5805	−	15.8620i	−1.46660	−	0.533799i	−0.947175	+	0.320718i	$0.896076\pi$
$884$		0			0
$885$	−2.53923	+	4.39807i	−0.0853552	+	0.147840i
$886$		0			0
$887$	−3.45930	−	19.6187i	−0.116152	−	0.658730i	−0.986173	−	0.165717i	$-0.947006\pi$
$887$	−3.45930	−	19.6187i	−0.116152	−	0.658730i	0.870022	−	0.493014i	$-0.164105\pi$
$888$		0			0
$889$	−1.99008	+	1.66988i	−0.0667452	+	0.0560059i
$890$		0			0
$891$	11.4352	−	4.16206i	0.383093	−	0.139434i
$892$		0			0
$893$	−45.8666	+	21.2091i	−1.53487	+	0.709736i
$894$		0			0
$895$	2.60740	−	0.949015i	0.0871557	−	0.0317221i
$896$		0			0
$897$	−47.4289	+	39.7976i	−1.58360	+	1.32880i
$898$		0			0
$899$	−0.0540251	−	0.306392i	−0.00180184	−	0.0102187i
$900$		0			0
$901$	−15.2114	+	26.3469i	−0.506766	+	0.877744i
$902$		0			0
$903$	−0.488465	−	0.177787i	−0.0162551	−	0.00591637i
$904$		0			0
$905$	1.94399	+	3.36710i	0.0646206	+	0.111926i
$906$		0			0
$907$	8.40693	+	7.05425i	0.279147	+	0.234232i	0.771602	−	0.636106i	$-0.219456\pi$
$907$	8.40693	+	7.05425i	0.279147	+	0.234232i	−0.492455	+	0.870338i	$0.663900\pi$
$908$		0			0
$909$	−0.848557	+	4.81240i	−0.0281449	+	0.159617i
$910$		0			0
$911$	−1.79760			−0.0595572			−0.0297786	−	0.999557i	$-0.509480\pi$
$911$	−1.79760			−0.0595572			−0.0297786	+	0.999557i	$0.509480\pi$
$912$		0			0
$913$	−14.3694			−0.475559
$914$		0			0
$915$	−0.495733	+	2.81144i	−0.0163884	+	0.0929433i
$916$		0			0
$917$	−15.6177	−	13.1048i	−0.515743	−	0.432760i
$918$		0			0
$919$	−2.62319	−	4.54349i	−0.0865309	−	0.149876i	0.819512	−	0.573063i	$-0.194245\pi$
$919$	−2.62319	−	4.54349i	−0.0865309	−	0.149876i	−0.906043	+	0.423187i	$0.860911\pi$
$920$		0			0
$921$	28.2316	+	10.2755i	0.930263	+	0.338588i
$922$		0			0
$923$	−26.2235	+	45.4205i	−0.863158	+	1.49503i
$924$		0			0
$925$	−3.17299	−	17.9949i	−0.104327	−	0.591669i
$926$		0			0
$927$	−2.90408	+	2.43681i	−0.0953825	+	0.0800354i
$928$		0			0
$929$	24.9915	−	9.09617i	0.819946	−	0.298436i	0.102220	−	0.994762i	$-0.467405\pi$
$929$	24.9915	−	9.09617i	0.819946	−	0.298436i	0.717726	+	0.696326i	$0.245183\pi$
$930$		0			0
$931$	−6.30304	−	23.8287i	−0.206574	−	0.780955i
$932$		0			0
$933$	−0.734516	+	0.267342i	−0.0240470	+	0.00875238i
$934$		0			0
$935$	1.79075	−	1.50262i	0.0585638	−	0.0491408i
$936$		0			0
$937$	1.97310	+	11.1900i	0.0644582	+	0.365561i	0.999926	+	0.0121492i	$0.00386732\pi$
$937$	1.97310	+	11.1900i	0.0644582	+	0.365561i	−0.935468	+	0.353411i	$0.885022\pi$
$938$		0			0
$939$	12.6190	−	21.8567i	0.411805	−	0.713267i
$940$		0			0
$941$	−46.0984	−	16.7785i	−1.50277	−	0.546962i	−0.545991	−	0.837791i	$-0.683847\pi$
$941$	−46.0984	−	16.7785i	−1.50277	−	0.546962i	−0.956775	+	0.290829i	$0.906069\pi$
$942$		0			0
$943$	19.5239	+	33.8164i	0.635785	+	1.10121i
$944$		0			0
$945$	−1.23375	−	1.03524i	−0.0401337	−	0.0336762i
$946$		0			0
$947$	−0.862194	+	4.88975i	−0.0280175	+	0.158895i	−0.995607	−	0.0936345i	$-0.970151\pi$
$947$	−0.862194	+	4.88975i	−0.0280175	+	0.158895i	0.967589	+	0.252530i	$0.0812626\pi$
$948$		0			0
$949$	6.19587			0.201126
$950$		0			0
$951$	−30.0320			−0.973854
$952$		0			0
$953$	−7.05030	+	39.9842i	−0.228382	+	1.29522i	0.627732	+	0.778429i	$0.283983\pi$
$953$	−7.05030	+	39.9842i	−0.228382	+	1.29522i	−0.856114	+	0.516787i	$0.827128\pi$
$954$		0			0
$955$	0.222964	+	0.187089i	0.00721493	+	0.00605405i
$956$		0			0
$957$	4.38119	+	7.58845i	0.141624	+	0.245300i
$958$		0			0
$959$	−6.21374	−	2.26162i	−0.200652	−	0.0730314i
$960$		0			0
$961$	15.4968	−	26.8412i	0.499896	−	0.865846i
$962$		0			0
$963$	0.0490563	+	0.278212i	0.00158082	+	0.00896526i
$964$		0			0
$965$	−0.506918	+	0.425355i	−0.0163183	+	0.0136927i
$966$		0			0
$967$	−4.40584	+	1.60359i	−0.141682	+	0.0515681i	−0.411888	−	0.911234i	$-0.635130\pi$
$967$	−4.40584	+	1.60359i	−0.141682	+	0.0515681i	0.270206	+	0.962803i	$0.412908\pi$
$968$		0			0
$969$	42.9663	+	30.2911i	1.38027	+	0.973091i
$970$		0			0
$971$	−31.9910	+	11.6438i	−1.02664	+	0.373666i	−0.799800	−	0.600266i	$-0.795061\pi$
$971$	−31.9910	+	11.6438i	−1.02664	+	0.373666i	−0.226839	+	0.973932i	$0.572839\pi$
$972$		0			0
$973$	4.55948	−	3.82586i	0.146170	−	0.122651i
$974$		0			0
$975$	−8.71426	−	49.4210i	−0.279080	−	1.58274i
$976$		0			0
$977$	−5.37934	+	9.31729i	−0.172100	+	0.298086i	−0.939154	−	0.343497i	$-0.888389\pi$
$977$	−5.37934	+	9.31729i	−0.172100	+	0.298086i	0.767054	+	0.641583i	$0.221722\pi$
$978$		0			0
$979$	2.81964	+	1.02627i	0.0901161	+	0.0327996i
$980$		0			0
$981$	−1.92858	−	3.34040i	−0.0615749	−	0.106651i
$982$		0			0
$983$	46.0661	+	38.6540i	1.46928	+	1.23287i	0.916800	+	0.399346i	$0.130763\pi$
$983$	46.0661	+	38.6540i	1.46928	+	1.23287i	0.552480	+	0.833526i	$0.313682\pi$
$984$		0			0
$985$	0.762906	−	4.32665i	0.0243082	−	0.137859i
$986$		0			0
$987$	24.3727			0.775792
$988$		0			0
$989$	−1.50095			−0.0477275
$990$		0			0
$991$	−6.88681	+	39.0571i	−0.218767	+	1.24069i	0.655482	+	0.755211i	$0.272465\pi$
$991$	−6.88681	+	39.0571i	−0.218767	+	1.24069i	−0.874249	+	0.485478i	$0.838646\pi$
$992$		0			0
$993$	13.1846	+	11.0632i	0.418400	+	0.351080i
$994$		0			0
$995$	1.93255	+	3.34728i	0.0612660	+	0.106116i
$996$		0			0
$997$	13.8021	+	5.02356i	0.437117	+	0.159098i	0.551199	−	0.834374i	$-0.314170\pi$
$997$	13.8021	+	5.02356i	0.437117	+	0.159098i	−0.114082	+	0.993471i	$0.536393\pi$
$998$		0			0
$999$	9.13626	−	15.8245i	0.289058	−	0.500664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.i.a.5.2	✓	12
3.2	odd	2		684.2.bo.c.613.1		12
4.3	odd	2		304.2.u.e.81.1		12
19.2	odd	18		1444.2.a.g.1.3		6
19.3	odd	18		1444.2.e.h.653.4		12
19.4	even	9	inner	76.2.i.a.61.2	yes	12
19.5	even	9		1444.2.e.g.429.3		12
19.14	odd	18		1444.2.e.h.429.4		12
19.16	even	9		1444.2.e.g.653.3		12
19.17	even	9		1444.2.a.h.1.4		6
57.23	odd	18		684.2.bo.c.289.1		12
76.23	odd	18		304.2.u.e.289.1		12
76.55	odd	18		5776.2.a.bw.1.3		6
76.59	even	18		5776.2.a.by.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.5.2	✓	12	1.1	even	1	trivial
76.2.i.a.61.2	yes	12	19.4	even	9	inner
304.2.u.e.81.1		12	4.3	odd	2
304.2.u.e.289.1		12	76.23	odd	18
684.2.bo.c.289.1		12	57.23	odd	18
684.2.bo.c.613.1		12	3.2	odd	2
1444.2.a.g.1.3		6	19.2	odd	18
1444.2.a.h.1.4		6	19.17	even	9
1444.2.e.g.429.3		12	19.5	even	9
1444.2.e.g.653.3		12	19.16	even	9
1444.2.e.h.429.4		12	19.14	odd	18
1444.2.e.h.653.4		12	19.3	odd	18
5776.2.a.bw.1.3		6	76.55	odd	18
5776.2.a.by.1.4		6	76.59	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +O(q^{10})\)	\(q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +(-0.622469 + 1.07815i) q^{11} +(0.977096 + 5.54139i) q^{13} +(0.391845 - 0.328797i) q^{15} +(-6.25251 + 2.27573i) q^{17} +(3.09208 - 3.07231i) q^{19} +(-1.97557 + 0.719049i) q^{21} +(-4.65029 + 3.90205i) q^{23} +(-0.854412 - 4.84561i) q^{25} +(2.46018 - 4.26116i) q^{27} +(3.64892 + 1.32810i) q^{29} +(-0.0400606 - 0.0693870i) q^{31} +(1.72862 + 1.45048i) q^{33} +(0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +10.1991 q^{39} +(1.11697 - 6.33464i) q^{41} +(0.189407 + 0.158931i) q^{43} +(-0.0402752 - 0.0697587i) q^{45} +(-10.8939 - 3.96505i) q^{47} +(2.82735 - 4.89711i) q^{49} +(2.09428 + 11.8773i) q^{51} +(3.50255 - 2.93899i) q^{53} +(-0.330140 + 0.120161i) q^{55} +(-4.51095 - 6.48649i) q^{57} +(-9.32947 + 3.39565i) q^{59} +(-4.27534 + 3.58744i) q^{61} +(0.0574889 + 0.326036i) q^{63} +(-0.793965 + 1.37519i) q^{65} +(-3.47734 - 1.26565i) q^{67} +(5.50164 + 9.52912i) q^{69} +(7.14016 + 5.99131i) q^{71} +(0.191208 - 1.08439i) q^{73} -8.91853 q^{75} +1.44397 q^{77} +(-1.50923 + 8.55928i) q^{79} +(-7.48795 - 6.28314i) q^{81} +(5.77114 + 9.99591i) q^{83} +(-1.76449 - 0.642221i) q^{85} +(3.51920 - 6.09544i) q^{87} +(-0.418534 - 2.37362i) q^{89} +(4.99955 - 4.19512i) q^{91} +(-0.136468 + 0.0496702i) q^{93} +(1.22576 - 0.103280i) q^{95} +(-13.4638 + 4.90042i) q^{97} +(0.272211 - 0.228412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9} + 3 q^{11} - 9 q^{13} - 15 q^{15} - 3 q^{17} - 12 q^{19} - 15 q^{21} - 12 q^{23} - 18 q^{25} - 9 q^{27} + 27 q^{29} + 6 q^{31} + 48 q^{33} + 33 q^{35} - 12 q^{37} + 60 q^{39} + 3 q^{41} + 27 q^{43} + 24 q^{45} - 15 q^{47} + 9 q^{49} - 33 q^{51} - 21 q^{53} - 27 q^{55} - 42 q^{57} - 48 q^{59} - 6 q^{61} - 9 q^{63} - 33 q^{65} + 24 q^{67} - 33 q^{69} + 30 q^{73} + 42 q^{75} + 24 q^{77} + 3 q^{79} + 3 q^{81} + 3 q^{83} - 42 q^{85} - 18 q^{87} - 18 q^{89} - 24 q^{91} - 78 q^{93} + 9 q^{95} + 12 q^{97} - 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 + 3 * q^11 - 9 * q^13 - 15 * q^15 - 3 * q^17 - 12 * q^19 - 15 * q^21 - 12 * q^23 - 18 * q^25 - 9 * q^27 + 27 * q^29 + 6 * q^31 + 48 * q^33 + 33 * q^35 - 12 * q^37 + 60 * q^39 + 3 * q^41 + 27 * q^43 + 24 * q^45 - 15 * q^47 + 9 * q^49 - 33 * q^51 - 21 * q^53 - 27 * q^55 - 42 * q^57 - 48 * q^59 - 6 * q^61 - 9 * q^63 - 33 * q^65 + 24 * q^67 - 33 * q^69 + 30 * q^73 + 42 * q^75 + 24 * q^77 + 3 * q^79 + 3 * q^81 + 3 * q^83 - 42 * q^85 - 18 * q^87 - 18 * q^89 - 24 * q^91 - 78 * q^93 + 9 * q^95 + 12 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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