LMFDB - Embedded newform 76.2.i.a.73.1

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			73.1
Root			$-1.25236 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	76.73
Dual form			76.2.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +O(q^{10})$	\(q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +(-0.350493 + 0.607072i) q^{11} +(-1.47751 - 0.537771i) q^{13} +(-1.98826 - 11.2760i) q^{15} +(2.88131 + 2.41771i) q^{17} +(4.28653 + 0.790990i) q^{19} +(0.321454 + 0.269732i) q^{21} +(1.02690 + 5.82385i) q^{23} +(-8.82337 - 3.21144i) q^{25} +(-4.69482 + 8.13166i) q^{27} +(5.28209 - 4.43220i) q^{29} +(1.43886 + 2.49217i) q^{31} +(0.367416 - 2.08372i) q^{33} +(0.495562 - 0.180370i) q^{35} -6.33018 q^{37} +4.74596 q^{39} +(-4.40018 + 1.60154i) q^{41} +(0.935226 - 5.30393i) q^{43} +(11.5902 + 20.0749i) q^{45} +(-1.42658 + 1.19704i) q^{47} +(3.49034 - 6.04544i) q^{49} +(-10.6684 - 3.88299i) q^{51} +(0.551093 + 3.12541i) q^{53} +(-2.03699 - 1.70923i) q^{55} +(-12.9748 + 2.18168i) q^{57} +(1.81608 + 1.52387i) q^{59} +(0.587398 + 3.33130i) q^{61} +(-0.798308 - 0.290560i) q^{63} +(2.98223 - 5.16537i) q^{65} +(7.61119 - 6.38655i) q^{67} +(-8.92496 - 15.4585i) q^{69} +(0.375070 - 2.12713i) q^{71} +(10.6967 - 3.89330i) q^{73} +28.3417 q^{75} +0.0974533 q^{77} +(7.36033 - 2.67894i) q^{79} +(1.73811 - 9.85732i) q^{81} +(-5.12849 - 8.88280i) q^{83} +(-10.9299 + 9.17125i) q^{85} +(-10.4064 + 18.0244i) q^{87} +(-12.2044 - 4.44204i) q^{89} +(0.0379580 + 0.215271i) q^{91} +(-6.65395 - 5.58333i) q^{93} +(-5.77852 + 15.4923i) q^{95} +(-0.581665 - 0.488075i) q^{97} +(0.743835 + 4.21850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−2.83638	+	1.03236i	−1.63758	+	0.596031i	−0.986614	−	0.163073i	$-0.947859\pi$
$3$	−2.83638	+	1.03236i	−1.63758	+	0.596031i	−0.650969	+	0.759105i	$0.725637\pi$
$4$		0			0
$5$	−0.658711	+	3.73574i	−0.294585	+	1.67067i	0.374301	+	0.927307i	$0.377883\pi$
$5$	−0.658711	+	3.73574i	−0.294585	+	1.67067i	−0.668886	+	0.743365i	$0.733228\pi$
$6$		0			0
$7$	−0.0695116	−	0.120398i	−0.0262729	−	0.0455060i	0.852590	−	0.522580i	$-0.175031\pi$
$7$	−0.0695116	−	0.120398i	−0.0262729	−	0.0455060i	−0.878863	+	0.477074i	$0.841697\pi$
$8$		0			0
$9$	4.68114	−	3.92794i	1.56038	−	1.30931i
$10$		0			0
$11$	−0.350493	+	0.607072i	−0.105678	+	0.183039i	−0.914015	−	0.405681i	$-0.867034\pi$
$11$	−0.350493	+	0.607072i	−0.105678	+	0.183039i	0.808337	+	0.588720i	$0.200368\pi$
$12$		0			0
$13$	−1.47751	−	0.537771i	−0.409789	−	0.149151i	0.128896	−	0.991658i	$-0.458857\pi$
$13$	−1.47751	−	0.537771i	−0.409789	−	0.149151i	−0.538685	+	0.842507i	$0.681079\pi$
$14$		0			0
$15$	−1.98826	−	11.2760i	−0.513366	−	2.91145i
$16$		0			0
$17$	2.88131	+	2.41771i	0.698820	+	0.586380i	0.921438	−	0.388526i	$-0.127016\pi$
$17$	2.88131	+	2.41771i	0.698820	+	0.586380i	−0.222617	+	0.974906i	$0.571460\pi$
$18$		0			0
$19$	4.28653	+	0.790990i	0.983397	+	0.181466i
$19$	4.28653	+	0.790990i	0.983397	+	0.181466i
$20$		0			0
$21$	0.321454	+	0.269732i	0.0701471	+	0.0588604i
$22$		0			0
$23$	1.02690	+	5.82385i	0.214124	+	1.21436i	0.882421	+	0.470461i	$0.155912\pi$
$23$	1.02690	+	5.82385i	0.214124	+	1.21436i	−0.668297	+	0.743895i	$0.732976\pi$
$24$		0			0
$25$	−8.82337	−	3.21144i	−1.76467	−	0.642289i
$26$		0			0
$27$	−4.69482	+	8.13166i	−0.903518	+	1.56494i
$28$		0			0
$29$	5.28209	−	4.43220i	0.980860	−	0.823039i	−0.00335912	−	0.999994i	$-0.501069\pi$
$29$	5.28209	−	4.43220i	0.980860	−	0.823039i	0.984219	+	0.176955i	$0.0566248\pi$
$30$		0			0
$31$	1.43886	+	2.49217i	0.258426	+	0.447608i	0.965821	−	0.259212i	$-0.0834627\pi$
$31$	1.43886	+	2.49217i	0.258426	+	0.447608i	−0.707394	+	0.706819i	$0.750129\pi$
$32$		0			0
$33$	0.367416	−	2.08372i	0.0639588	−	0.362729i
$34$		0			0
$35$	0.495562	−	0.180370i	0.0837653	−	0.0304881i
$36$		0			0
$37$	−6.33018			−1.04067			−0.520337	−	0.853961i	$-0.674194\pi$
$37$	−6.33018			−1.04067			−0.520337	+	0.853961i	$0.674194\pi$
$38$		0			0
$39$	4.74596			0.759961
$40$		0			0
$41$	−4.40018	+	1.60154i	−0.687193	+	0.250118i	−0.661933	−	0.749563i	$-0.730264\pi$
$41$	−4.40018	+	1.60154i	−0.687193	+	0.250118i	−0.0252602	+	0.999681i	$0.508041\pi$
$42$		0			0
$43$	0.935226	−	5.30393i	0.142621	−	0.808842i	−0.826626	−	0.562751i	$-0.809743\pi$
$43$	0.935226	−	5.30393i	0.142621	−	0.808842i	0.969247	−	0.246091i	$-0.0791461\pi$
$44$		0			0
$45$	11.5902	+	20.0749i	1.72777	+	2.99259i
$46$		0			0
$47$	−1.42658	+	1.19704i	−0.208088	+	0.174607i	−0.740875	−	0.671643i	$-0.765589\pi$
$47$	−1.42658	+	1.19704i	−0.208088	+	0.174607i	0.532787	+	0.846249i	$0.321145\pi$
$48$		0			0
$49$	3.49034	−	6.04544i	0.498619	−	0.863634i
$50$		0			0
$51$	−10.6684	−	3.88299i	−1.49388	−	0.543727i
$52$		0			0
$53$	0.551093	+	3.12541i	0.0756985	+	0.429307i	0.998979	+	0.0451806i	$0.0143863\pi$
$53$	0.551093	+	3.12541i	0.0756985	+	0.429307i	−0.923280	+	0.384127i	$0.874503\pi$
$54$		0			0
$55$	−2.03699	−	1.70923i	−0.274667	−	0.230473i
$56$		0			0
$57$	−12.9748	+	2.18168i	−1.71855	+	0.288971i
$58$		0			0
$59$	1.81608	+	1.52387i	0.236433	+	0.198391i	0.753304	−	0.657672i	$-0.228459\pi$
$59$	1.81608	+	1.52387i	0.236433	+	0.198391i	−0.516871	+	0.856063i	$0.672903\pi$
$60$		0			0
$61$	0.587398	+	3.33130i	0.0752086	+	0.426529i	0.999043	+	0.0437370i	$0.0139264\pi$
$61$	0.587398	+	3.33130i	0.0752086	+	0.426529i	−0.923834	+	0.382792i	$0.874963\pi$
$62$		0			0
$63$	−0.798308	−	0.290560i	−0.100577	−	0.0366072i
$64$		0			0
$65$	2.98223	−	5.16537i	0.369900	−	0.640685i
$66$		0			0
$67$	7.61119	−	6.38655i	0.929855	−	0.780241i	−0.0459367	−	0.998944i	$-0.514627\pi$
$67$	7.61119	−	6.38655i	0.929855	−	0.780241i	0.975791	+	0.218704i	$0.0701828\pi$
$68$		0			0
$69$	−8.92496	−	15.4585i	−1.07444	−	1.86098i
$70$		0			0
$71$	0.375070	−	2.12713i	0.0445127	−	0.252444i	−0.954429	−	0.298438i	$-0.903534\pi$
$71$	0.375070	−	2.12713i	0.0445127	−	0.252444i	0.998942	+	0.0459940i	$0.0146455\pi$
$72$		0			0
$73$	10.6967	−	3.89330i	1.25196	−	0.455676i	0.370896	−	0.928674i	$-0.379051\pi$
$73$	10.6967	−	3.89330i	1.25196	−	0.455676i	0.881063	+	0.472998i	$0.156828\pi$
$74$		0			0
$75$	28.3417			3.27262
$76$		0			0
$77$	0.0974533			0.0111058
$78$		0			0
$79$	7.36033	−	2.67894i	0.828102	−	0.301404i	0.107022	−	0.994257i	$-0.465868\pi$
$79$	7.36033	−	2.67894i	0.828102	−	0.301404i	0.721079	+	0.692852i	$0.243646\pi$
$80$		0			0
$81$	1.73811	−	9.85732i	0.193123	−	1.09526i
$82$		0			0
$83$	−5.12849	−	8.88280i	−0.562925	−	0.975014i	−0.997239	−	0.0742528i	$-0.976343\pi$
$83$	−5.12849	−	8.88280i	−0.562925	−	0.975014i	0.434315	−	0.900761i	$-0.356991\pi$
$84$		0			0
$85$	−10.9299	+	9.17125i	−1.18551	+	0.994761i
$86$		0			0
$87$	−10.4064	+	18.0244i	−1.11568	+	1.93242i
$88$		0			0
$89$	−12.2044	−	4.44204i	−1.29366	−	0.470856i	−0.398737	−	0.917066i	$-0.630551\pi$
$89$	−12.2044	−	4.44204i	−1.29366	−	0.470856i	−0.894928	+	0.446210i	$0.852773\pi$
$90$		0			0
$91$	0.0379580	+	0.215271i	0.00397908	+	0.0225665i
$92$		0			0
$93$	−6.65395	−	5.58333i	−0.689983	−	0.578964i
$94$		0			0
$95$	−5.77852	+	15.4923i	−0.592863	+	1.58948i
$96$		0			0
$97$	−0.581665	−	0.488075i	−0.0590591	−	0.0495565i	0.612780	−	0.790253i	$-0.290051\pi$
$97$	−0.581665	−	0.488075i	−0.0590591	−	0.0495565i	−0.671839	+	0.740697i	$0.734496\pi$
$98$		0			0
$99$	0.743835	+	4.21850i	0.0747583	+	0.423975i
$100$		0			0
$101$	11.7847	+	4.28927i	1.17262	+	0.426798i	0.853589	−	0.520947i	$-0.174421\pi$
$101$	11.7847	+	4.28927i	1.17262	+	0.426798i	0.319029	+	0.947745i	$0.396643\pi$
$102$		0			0
$103$	−4.32365	+	7.48879i	−0.426022	+	0.737892i	−0.996515	−	0.0834102i	$-0.973419\pi$
$103$	−4.32365	+	7.48879i	−0.426022	+	0.737892i	0.570493	+	0.821302i	$0.306752\pi$
$104$		0			0
$105$	−1.21939	+	1.02319i	−0.119001	+	0.0998534i
$106$		0			0
$107$	0.492451	+	0.852950i	0.0476070	+	0.0824578i	0.888847	−	0.458204i	$-0.151507\pi$
$107$	0.492451	+	0.852950i	0.0476070	+	0.0824578i	−0.841240	+	0.540662i	$0.818174\pi$
$108$		0			0
$109$	−2.47482	+	14.0354i	−0.237044	+	1.34435i	0.601221	+	0.799083i	$0.294681\pi$
$109$	−2.47482	+	14.0354i	−0.237044	+	1.34435i	−0.838265	+	0.545263i	$0.816430\pi$
$110$		0			0
$111$	17.9548	−	6.53500i	1.70419	−	0.620275i
$112$		0			0
$113$	2.86600			0.269611			0.134805	−	0.990872i	$-0.456959\pi$
$113$	2.86600			0.269611			0.134805	+	0.990872i	$0.456959\pi$
$114$		0			0
$115$	−22.4328			−2.09187
$116$		0			0
$117$	−9.02878	+	3.28621i	−0.834711	+	0.303810i
$118$		0			0
$119$	0.0908016	−	0.514962i	0.00832377	−	0.0472065i
$120$		0			0
$121$	5.25431	+	9.10073i	0.477664	+	0.827339i
$122$		0			0
$123$	10.8272	−	9.08512i	0.976258	−	0.819177i
$124$		0			0
$125$	8.32575	−	14.4206i	0.744677	−	1.28982i
$126$		0			0
$127$	19.8223	+	7.21472i	1.75894	+	0.640203i	0.999941	−	0.0108860i	$-0.00346520\pi$
$127$	19.8223	+	7.21472i	1.75894	+	0.640203i	0.759002	+	0.651089i	$0.225687\pi$
$128$		0			0
$129$	2.82289	+	16.0094i	0.248542	+	1.40955i
$130$		0			0
$131$	−7.87172	−	6.60516i	−0.687756	−	0.577096i	0.230505	−	0.973071i	$-0.425962\pi$
$131$	−7.87172	−	6.60516i	−0.687756	−	0.577096i	−0.918261	+	0.395975i	$0.870407\pi$
$132$		0			0
$133$	−0.202730	−	0.571071i	−0.0175789	−	0.0495181i
$134$		0			0
$135$	−27.2852	−	22.8950i	−2.34834	−	1.97049i
$136$		0			0
$137$	−2.08375	−	11.8175i	−0.178027	−	1.00964i	−0.934592	−	0.355722i	$-0.884235\pi$
$137$	−2.08375	−	11.8175i	−0.178027	−	1.00964i	0.756565	−	0.653919i	$-0.226876\pi$
$138$		0			0
$139$	−9.67258	−	3.52053i	−0.820417	−	0.298607i	−0.102497	−	0.994733i	$-0.532683\pi$
$139$	−9.67258	−	3.52053i	−0.820417	−	0.298607i	−0.717920	+	0.696126i	$0.754906\pi$
$140$		0			0
$141$	2.81054	−	4.86800i	0.236690	−	0.409960i
$142$		0			0
$143$	0.844324	−	0.708472i	0.0706059	−	0.0592454i
$144$		0			0
$145$	13.0782	+	22.6520i	1.08608	+	1.88115i
$146$		0			0
$147$	−3.65886	+	20.7504i	−0.301777	+	1.71147i
$148$		0			0
$149$	3.52238	−	1.28204i	0.288565	−	0.105029i	−0.193682	−	0.981064i	$-0.562043\pi$
$149$	3.52238	−	1.28204i	0.288565	−	0.105029i	0.482247	+	0.876035i	$0.339821\pi$
$150$		0			0
$151$	−13.3866			−1.08939			−0.544693	−	0.838636i	$-0.683354\pi$
$151$	−13.3866			−1.08939			−0.544693	+	0.838636i	$0.683354\pi$
$152$		0			0
$153$	22.9844			1.85818
$154$		0			0
$155$	−10.2579	+	3.73357i	−0.823934	+	0.299888i
$156$		0			0
$157$	1.40711	−	7.98010i	0.112299	−	0.636881i	−0.875753	−	0.482760i	$-0.839634\pi$
$157$	1.40711	−	7.98010i	0.112299	−	0.636881i	0.988052	−	0.154121i	$-0.0492546\pi$
$158$		0			0
$159$	−4.78964	−	8.29590i	−0.379843	−	0.657908i
$160$		0			0
$161$	0.629796	−	0.528461i	0.0496349	−	0.0416486i
$162$		0			0
$163$	4.12600	−	7.14644i	0.323173	−	0.559753i	−0.657968	−	0.753046i	$-0.728584\pi$
$163$	4.12600	−	7.14644i	0.323173	−	0.559753i	0.981141	+	0.193294i	$0.0619170\pi$
$164$		0			0
$165$	7.54220	+	2.74514i	0.587159	+	0.213709i
$166$		0			0
$167$	−2.04523	−	11.5991i	−0.158264	−	0.897562i	−0.955740	−	0.294211i	$-0.904943\pi$
$167$	−2.04523	−	11.5991i	−0.158264	−	0.897562i	0.797476	−	0.603351i	$-0.206168\pi$
$168$		0			0
$169$	−8.06473	−	6.76711i	−0.620364	−	0.520547i
$170$		0			0
$171$	23.1728	−	13.1345i	1.77207	−	1.00442i
$172$		0			0
$173$	7.17235	+	6.01832i	0.545304	+	0.457564i	0.873347	−	0.487098i	$-0.161945\pi$
$173$	7.17235	+	6.01832i	0.545304	+	0.457564i	−0.328043	+	0.944663i	$0.606389\pi$
$174$		0			0
$175$	0.226676	+	1.28555i	0.0171351	+	0.0971781i
$176$		0			0
$177$	−6.72425	−	2.44743i	−0.505426	−	0.183960i
$178$		0			0
$179$	−4.64499	+	8.04536i	−0.347183	+	0.601339i	−0.985748	−	0.168229i	$-0.946195\pi$
$179$	−4.64499	+	8.04536i	−0.347183	+	0.601339i	0.638565	+	0.769568i	$0.279528\pi$
$180$		0			0
$181$	−2.07659	+	1.74246i	−0.154351	+	0.129516i	−0.716693	−	0.697389i	$-0.754345\pi$
$181$	−2.07659	+	1.74246i	−0.154351	+	0.129516i	0.562342	+	0.826905i	$0.309901\pi$
$182$		0			0
$183$	−5.10517	−	8.84242i	−0.377385	−	0.653650i
$184$		0			0
$185$	4.16976	−	23.6479i	0.306567	−	1.73863i
$186$		0			0
$187$	−2.47760	+	0.901773i	−0.181180	+	0.0659441i
$188$		0			0
$189$	1.30538			0.0949522
$190$		0			0
$191$	−18.8935			−1.36709			−0.683544	−	0.729910i	$-0.739562\pi$
$191$	−18.8935			−1.36709			−0.683544	+	0.729910i	$0.739562\pi$
$192$		0			0
$193$	20.0362	−	7.29258i	1.44224	−	0.524931i	0.501825	−	0.864969i	$-0.332662\pi$
$193$	20.0362	−	7.29258i	1.44224	−	0.524931i	0.940412	+	0.340037i	$0.110440\pi$
$194$		0			0
$195$	−3.12622	+	17.7297i	−0.223873	+	1.26965i
$196$		0			0
$197$	−8.29055	−	14.3597i	−0.590677	−	1.02308i	−0.994141	−	0.108088i	$-0.965527\pi$
$197$	−8.29055	−	14.3597i	−0.590677	−	1.02308i	0.403464	−	0.914996i	$-0.367806\pi$
$198$		0			0
$199$	12.3943	−	10.4001i	0.878610	−	0.737241i	−0.0872832	−	0.996184i	$-0.527819\pi$
$199$	12.3943	−	10.4001i	0.878610	−	0.737241i	0.965893	+	0.258943i	$0.0833741\pi$
$200$		0			0
$201$	−14.9950	+	25.9721i	−1.05767	+	1.83193i
$202$		0			0
$203$	−0.900793	−	0.327862i	−0.0632233	−	0.0230114i
$204$		0			0
$205$	−3.08447	−	17.4929i	−0.215428	−	1.22176i
$206$		0			0
$207$	27.6828	+	23.2286i	1.92409	+	1.61450i
$208$		0			0
$209$	−1.98259	+	2.32499i	−0.137138	+	0.160823i
$210$		0			0
$211$	20.1088	+	16.8733i	1.38434	+	1.16160i	0.967573	+	0.252592i	$0.0812831\pi$
$211$	20.1088	+	16.8733i	1.38434	+	1.16160i	0.416772	+	0.909011i	$0.363161\pi$
$212$		0			0
$213$	1.13212	+	6.42055i	0.0775713	+	0.439929i
$214$		0			0
$215$	19.1981	+	6.98752i	1.30930	+	0.476545i
$216$		0			0
$217$	0.200035	−	0.346470i	0.0135792	−	0.0235199i
$218$		0			0
$219$	−26.3207	+	22.0857i	−1.77859	+	1.49241i
$220$		0			0
$221$	−2.95700	−	5.12168i	−0.198910	−	0.344522i
$222$		0			0
$223$	0.397301	−	2.25321i	0.0266053	−	0.150886i	−0.968611	−	0.248581i	$-0.920036\pi$
$223$	0.397301	−	2.25321i	0.0266053	−	0.150886i	0.995216	+	0.0976949i	$0.0311469\pi$
$224$		0			0
$225$	−53.9178	+	19.6245i	−3.59452	+	1.30830i
$226$		0			0
$227$	−17.4671			−1.15934			−0.579668	−	0.814853i	$-0.696818\pi$
$227$	−17.4671			−1.15934			−0.579668	+	0.814853i	$0.696818\pi$
$228$		0			0
$229$	8.14952			0.538536			0.269268	−	0.963065i	$-0.413218\pi$
$229$	8.14952			0.538536			0.269268	+	0.963065i	$0.413218\pi$
$230$		0			0
$231$	−0.276414	+	0.100607i	−0.0181867	+	0.00661943i
$232$		0			0
$233$	−3.69185	+	20.9375i	−0.241861	+	1.37166i	0.585810	+	0.810449i	$0.300777\pi$
$233$	−3.69185	+	20.9375i	−0.241861	+	1.37166i	−0.827671	+	0.561214i	$0.810335\pi$
$234$		0			0
$235$	−3.53213	−	6.11783i	−0.230411	−	0.399083i
$236$		0			0
$237$	−18.1110	+	15.1970i	−1.17644	+	0.987149i
$238$		0			0
$239$	10.3725	−	17.9657i	0.670941	−	1.16210i	−0.306697	−	0.951807i	$-0.599224\pi$
$239$	10.3725	−	17.9657i	0.670941	−	1.16210i	0.977638	−	0.210296i	$-0.0674429\pi$
$240$		0			0
$241$	−18.7960	−	6.84119i	−1.21076	−	0.440680i	−0.343791	−	0.939046i	$-0.611711\pi$
$241$	−18.7960	−	6.84119i	−1.21076	−	0.440680i	−0.866966	+	0.498367i	$0.833933\pi$
$242$		0			0
$243$	0.354850	+	2.01245i	0.0227636	+	0.129099i
$244$		0			0
$245$	20.2851	+	17.0212i	1.29596	+	1.08744i
$246$		0			0
$247$	−5.90804	−	3.47387i	−0.375919	−	0.221037i
$248$		0			0
$249$	23.7165	+	19.9005i	1.50297	+	1.26115i
$250$		0			0
$251$	−1.27528	−	7.23245i	−0.0804948	−	0.456508i	−0.998238	−	0.0593346i	$-0.981102\pi$
$251$	−1.27528	−	7.23245i	−0.0804948	−	0.456508i	0.917743	−	0.397174i	$-0.130009\pi$
$252$		0			0
$253$	−3.89541	−	1.41781i	−0.244903	−	0.0891372i
$254$		0			0
$255$	21.5332	−	37.2966i	1.34846	−	2.33561i
$256$		0			0
$257$	20.7914	−	17.4460i	1.29693	−	1.08825i	0.306265	−	0.951946i	$-0.400921\pi$
$257$	20.7914	−	17.4460i	1.29693	−	1.08825i	0.990666	−	0.136308i	$-0.0435238\pi$
$258$		0			0
$259$	0.440021	+	0.762139i	0.0273416	+	0.0473570i
$260$		0			0
$261$	7.31677	−	41.4955i	0.452897	−	2.56851i
$262$		0			0
$263$	−20.3152	+	7.39413i	−1.25269	+	0.455941i	−0.881309	−	0.472540i	$-0.843337\pi$
$263$	−20.3152	+	7.39413i	−1.25269	+	0.455941i	−0.371379	+	0.928481i	$0.621115\pi$
$264$		0			0
$265$	−12.0387			−0.739532
$266$		0			0
$267$	39.2021			2.39913
$268$		0			0
$269$	−5.63396	+	2.05060i	−0.343509	+	0.125027i	−0.508013	−	0.861349i	$-0.669620\pi$
$269$	−5.63396	+	2.05060i	−0.343509	+	0.125027i	0.164504	+	0.986376i	$0.447398\pi$
$270$		0			0
$271$	−4.11091	+	23.3141i	−0.249720	+	1.41623i	0.559551	+	0.828796i	$0.310974\pi$
$271$	−4.11091	+	23.3141i	−0.249720	+	1.41623i	−0.809271	+	0.587436i	$0.800137\pi$
$272$		0			0
$273$	−0.329899	−	0.571402i	−0.0199664	−	0.0345828i
$274$		0			0
$275$	5.04211	−	4.23083i	0.304050	−	0.255129i
$276$		0			0
$277$	4.74294	−	8.21502i	0.284976	−	0.493593i	−0.687628	−	0.726064i	$-0.741348\pi$
$277$	4.74294	−	8.21502i	0.284976	−	0.493593i	0.972603	+	0.232471i	$0.0746811\pi$
$278$		0			0
$279$	16.5246	+	6.01446i	0.989302	+	0.360076i
$280$		0			0
$281$	4.22110	+	23.9391i	0.251810	+	1.42808i	0.804131	+	0.594453i	$0.202631\pi$
$281$	4.22110	+	23.9391i	0.251810	+	1.42808i	−0.552321	+	0.833632i	$0.686258\pi$
$282$		0			0
$283$	−8.94917	−	7.50925i	−0.531973	−	0.446378i	0.336809	−	0.941573i	$-0.390652\pi$
$283$	−8.94917	−	7.50925i	−0.531973	−	0.446378i	−0.868782	+	0.495195i	$0.835097\pi$
$284$		0			0
$285$	0.396453	−	49.9075i	0.0234839	−	2.95627i
$286$		0			0
$287$	0.498685	+	0.418446i	0.0294364	+	0.0247001i
$288$		0			0
$289$	−0.495374	−	2.80941i	−0.0291397	−	0.165259i
$290$		0			0
$291$	2.15369	+	0.783879i	0.126251	+	0.0459518i
$292$		0			0
$293$	−7.01571	+	12.1516i	−0.409862	+	0.709902i	−0.994874	−	0.101122i	$-0.967757\pi$
$293$	−7.01571	+	12.1516i	−0.409862	+	0.709902i	0.585012	+	0.811025i	$0.301090\pi$
$294$		0			0
$295$	−6.88905	+	5.78060i	−0.401096	+	0.336559i
$296$		0			0
$297$	−3.29100	−	5.70018i	−0.190963	−	0.330758i
$298$		0			0
$299$	1.61464	−	9.15705i	0.0933768	−	0.529566i
$300$		0			0
$301$	−0.703590	+	0.256086i	−0.0405543	+	0.0147605i
$302$		0			0
$303$	−37.8538			−2.17464
$304$		0			0
$305$	−12.8318			−0.734746
$306$		0			0
$307$	0.522125	−	0.190038i	0.0297993	−	0.0108460i	−0.327078	−	0.944998i	$-0.606064\pi$
$307$	0.522125	−	0.190038i	0.0297993	−	0.0108460i	0.356877	+	0.934151i	$0.383842\pi$
$308$		0			0
$309$	4.53241	−	25.7046i	0.257840	−	1.46228i
$310$		0			0
$311$	7.89478	+	13.6742i	0.447672	+	0.775390i	0.998234	−	0.0594037i	$-0.0189199\pi$
$311$	7.89478	+	13.6742i	0.447672	+	0.775390i	−0.550562	+	0.834794i	$0.685587\pi$
$312$		0			0
$313$	−17.4399	+	14.6338i	−0.985763	+	0.827153i	−0.984949	−	0.172846i	$-0.944704\pi$
$313$	−17.4399	+	14.6338i	−0.985763	+	0.827153i	−0.000814014		1.00000i	$0.500259\pi$
$314$		0			0
$315$	1.61131	−	2.79087i	0.0907871	−	0.157248i
$316$		0			0
$317$	17.8284	+	6.48900i	1.00134	+	0.364458i	0.790102	−	0.612976i	$-0.210028\pi$
$317$	17.8284	+	6.48900i	1.00134	+	0.364458i	0.211240	+	0.977434i	$0.432250\pi$
$318$		0			0
$319$	0.839328	+	4.76006i	0.0469933	+	0.266512i
$320$		0			0
$321$	−2.27733	−	1.91090i	−0.127108	−	0.106656i
$322$		0			0
$323$	10.4384	+	12.6427i	0.580810	+	0.703456i
$324$		0			0
$325$	11.3096	+	9.48991i	0.627345	+	0.526405i
$326$		0			0
$327$	−7.47001	−	42.3645i	−0.413092	−	2.34276i
$328$		0			0
$329$	0.243285	+	0.0885485i	0.0134127	+	0.00488184i
$330$		0			0
$331$	7.38160	−	12.7853i	0.405729	−	0.702744i	−0.588677	−	0.808368i	$-0.700351\pi$
$331$	7.38160	−	12.7853i	0.405729	−	0.702744i	0.994406	+	0.105625i	$0.0336843\pi$
$332$		0			0
$333$	−29.6324	+	24.8646i	−1.62385	+	1.36257i
$334$		0			0
$335$	18.8449	+	32.6403i	1.02961	+	1.78333i
$336$		0			0
$337$	−1.43116	+	8.11649i	−0.0779601	+	0.442134i	0.920695	+	0.390283i	$0.127623\pi$
$337$	−1.43116	+	8.11649i	−0.0779601	+	0.442134i	−0.998655	+	0.0518502i	$0.983488\pi$
$338$		0			0
$339$	−8.12906	+	2.95874i	−0.441510	+	0.160697i
$340$		0			0
$341$	−2.01724			−0.109240
$342$		0			0
$343$	−1.94364			−0.104947
$344$		0			0
$345$	63.6278	−	23.1586i	3.42561	−	1.24682i
$346$		0			0
$347$	3.39699	−	19.2653i	0.182360	−	1.03421i	−0.746941	−	0.664891i	$-0.768478\pi$
$347$	3.39699	−	19.2653i	0.182360	−	1.03421i	0.929301	−	0.369324i	$-0.120411\pi$
$348$		0			0
$349$	−12.8829	−	22.3139i	−0.689607	−	1.19443i	−0.971965	−	0.235126i	$-0.924450\pi$
$349$	−12.8829	−	22.3139i	−0.689607	−	1.19443i	0.282358	−	0.959309i	$-0.408884\pi$
$350$		0			0
$351$	11.3096	−	9.48991i	0.603663	−	0.506534i
$352$		0			0
$353$	0.712979	−	1.23492i	0.0379480	−	0.0657279i	−0.846428	−	0.532504i	$-0.821251\pi$
$353$	0.712979	−	1.23492i	0.0379480	−	0.0657279i	0.884376	+	0.466776i	$0.154585\pi$
$354$		0			0
$355$	7.69934	+	2.80233i	0.408638	+	0.148732i
$356$		0			0
$357$	0.274076	+	1.55436i	0.0145057	+	0.0822657i
$358$		0			0
$359$	7.55106	+	6.33609i	0.398530	+	0.334406i	0.819925	−	0.572471i	$-0.194015\pi$
$359$	7.55106	+	6.33609i	0.398530	+	0.334406i	−0.421395	+	0.906877i	$0.638460\pi$
$360$		0			0
$361$	17.7487	+	6.78120i	0.934141	+	0.356905i
$362$		0			0
$363$	−24.2984	−	20.3888i	−1.27534	−	1.07013i
$364$		0			0
$365$	7.49827	+	42.5248i	0.392477	+	2.22585i
$366$		0			0
$367$	−10.7351	−	3.90726i	−0.560368	−	0.203957i	0.0462791	−	0.998929i	$-0.485264\pi$
$367$	−10.7351	−	3.90726i	−0.560368	−	0.203957i	−0.606647	+	0.794971i	$0.707486\pi$
$368$		0			0
$369$	−14.3071	+	24.7807i	−0.744799	+	1.29003i
$370$		0			0
$371$	0.337984	−	0.283602i	0.0175473	−	0.0147239i
$372$		0			0
$373$	−13.3194	−	23.0699i	−0.689653	−	1.19451i	−0.971950	−	0.235187i	$-0.924430\pi$
$373$	−13.3194	−	23.0699i	−0.689653	−	1.19451i	0.282297	−	0.959327i	$-0.408903\pi$
$374$		0			0
$375$	−8.72773	+	49.4974i	−0.450698	+	2.55604i
$376$		0			0
$377$	−10.1879	+	3.70808i	−0.524702	+	0.190976i
$378$		0			0
$379$	19.8016			1.01714			0.508569	−	0.861021i	$-0.330174\pi$
$379$	19.8016			1.01714			0.508569	+	0.861021i	$0.330174\pi$
$380$		0			0
$381$	−63.6716			−3.26199
$382$		0			0
$383$	−16.8435	+	6.13052i	−0.860661	+	0.313255i	−0.734379	−	0.678739i	$-0.762527\pi$
$383$	−16.8435	+	6.13052i	−0.860661	+	0.313255i	−0.126282	+	0.991994i	$0.540304\pi$
$384$		0			0
$385$	−0.0641936	+	0.364060i	−0.00327161	+	0.0185542i
$386$		0			0
$387$	−16.4556	−	28.5019i	−0.836485	−	1.44884i
$388$		0			0
$389$	−16.4626	+	13.8137i	−0.834685	+	0.700384i	−0.956362	−	0.292186i	$-0.905617\pi$
$389$	−16.4626	+	13.8137i	−0.834685	+	0.700384i	0.121676	+	0.992570i	$0.461173\pi$
$390$		0			0
$391$	−11.1215	+	19.2631i	−0.562440	+	0.974175i
$392$		0			0
$393$	29.1461	+	10.6083i	1.47022	+	0.535118i
$394$		0			0
$395$	5.15949	+	29.2609i	0.259602	+	1.47228i
$396$		0			0
$397$	4.26129	+	3.57565i	0.213868	+	0.179457i	0.743428	−	0.668816i	$-0.233199\pi$
$397$	4.26129	+	3.57565i	0.213868	+	0.179457i	−0.529560	+	0.848272i	$0.677643\pi$
$398$		0			0
$399$	1.16457	+	1.41048i	0.0583013	+	0.0706124i
$400$		0			0
$401$	−27.9884	−	23.4850i	−1.39767	−	1.17279i	−0.962121	−	0.272621i	$-0.912109\pi$
$401$	−27.9884	−	23.4850i	−1.39767	−	1.17279i	−0.435550	−	0.900164i	$-0.643446\pi$
$402$		0			0
$403$	−0.785713	−	4.45600i	−0.0391391	−	0.221969i
$404$		0			0
$405$	35.6794	+	12.9863i	1.77293	+	0.645292i
$406$		0			0
$407$	2.21868	−	3.84287i	0.109976	−	0.190484i
$408$		0			0
$409$	−0.581665	+	0.488075i	−0.0287615	+	0.0241338i	−0.657055	−	0.753843i	$-0.728198\pi$
$409$	−0.581665	+	0.488075i	−0.0287615	+	0.0241338i	0.628294	+	0.777976i	$0.283754\pi$
$410$		0			0
$411$	18.1102	+	31.3678i	0.893311	+	1.54726i
$412$		0			0
$413$	0.0572319	−	0.324578i	0.00281620	−	0.0159714i
$414$		0			0
$415$	36.5620	−	13.3075i	1.79476	−	0.653238i
$416$		0			0
$417$	31.0695			1.52148
$418$		0			0
$419$	16.2619			0.794446			0.397223	−	0.917722i	$-0.369974\pi$
$419$	16.2619			0.794446			0.397223	+	0.917722i	$0.369974\pi$
$420$		0			0
$421$	−14.1059	+	5.13414i	−0.687481	+	0.250223i	−0.662056	−	0.749454i	$-0.730316\pi$
$421$	−14.1059	+	5.13414i	−0.687481	+	0.250223i	−0.0254245	+	0.999677i	$0.508094\pi$
$422$		0			0
$423$	−1.97610	+	11.2070i	−0.0960814	+	0.544905i
$424$		0			0
$425$	−17.6585	−	30.5855i	−0.856565	−	1.48361i
$426$		0			0
$427$	0.360250	−	0.302285i	0.0174337	−	0.0146286i
$428$		0			0
$429$	−1.66342	+	2.88114i	−0.0803109	+	0.139103i
$430$		0			0
$431$	−9.41358	−	3.42626i	−0.453436	−	0.165037i	0.105198	−	0.994451i	$-0.466452\pi$
$431$	−9.41358	−	3.42626i	−0.453436	−	0.165037i	−0.558634	+	0.829414i	$0.688674\pi$
$432$		0			0
$433$	0.711701	+	4.03626i	0.0342022	+	0.193970i	0.997122	−	0.0758190i	$-0.0241571\pi$
$433$	0.711701	+	4.03626i	0.0342022	+	0.193970i	−0.962919	+	0.269789i	$0.913046\pi$
$434$		0			0
$435$	−60.4796	−	50.7484i	−2.89977	−	2.43320i
$436$		0			0
$437$	−0.204761	+	25.7764i	−0.00979506	+	1.23305i
$438$		0			0
$439$	−4.00981	−	3.36463i	−0.191378	−	0.160585i	0.542064	−	0.840337i	$-0.317643\pi$
$439$	−4.00981	−	3.36463i	−0.191378	−	0.160585i	−0.733442	+	0.679752i	$0.762087\pi$
$440$		0			0
$441$	−7.40738	−	42.0094i	−0.352733	−	2.00045i
$442$		0			0
$443$	31.8347	+	11.5869i	1.51251	+	0.550509i	0.959265	−	0.282508i	$-0.0911665\pi$
$443$	31.8347	+	11.5869i	1.51251	+	0.550509i	0.553247	+	0.833017i	$0.313389\pi$
$444$		0			0
$445$	24.6335	−	42.6664i	1.16774	−	2.02258i
$446$		0			0
$447$	−8.66727	+	7.27271i	−0.409948	+	0.343987i
$448$		0			0
$449$	0.545695	+	0.945172i	0.0257530	+	0.0446054i	0.878615	−	0.477531i	$-0.158468\pi$
$449$	0.545695	+	0.945172i	0.0257530	+	0.0446054i	−0.852862	+	0.522137i	$0.825135\pi$
$450$		0			0
$451$	0.569986	−	3.23255i	0.0268396	−	0.152215i
$452$		0			0
$453$	37.9694	−	13.8197i	1.78396	−	0.649308i
$454$		0			0
$455$	−0.829198			−0.0388734
$456$		0			0
$457$	16.9280			0.791858			0.395929	−	0.918281i	$-0.370423\pi$
$457$	16.9280			0.791858			0.395929	+	0.918281i	$0.370423\pi$
$458$		0			0
$459$	−33.1872	+	12.0792i	−1.54905	+	0.563806i
$460$		0			0
$461$	1.62318	−	9.20551i	0.0755991	−	0.428744i	−0.923393	−	0.383856i	$-0.874596\pi$
$461$	1.62318	−	9.20551i	0.0755991	−	0.428744i	0.998992	−	0.0448876i	$-0.0142930\pi$
$462$		0			0
$463$	−3.80227	−	6.58572i	−0.176706	−	0.306064i	0.764044	−	0.645164i	$-0.223211\pi$
$463$	−3.80227	−	6.58572i	−0.176706	−	0.306064i	−0.940750	+	0.339100i	$0.889878\pi$
$464$		0			0
$465$	25.2409	−	21.1796i	1.17052	−	0.982181i
$466$		0			0
$467$	17.7403	−	30.7272i	0.820925	−	1.42188i	−0.0840686	−	0.996460i	$-0.526792\pi$
$467$	17.7403	−	30.7272i	0.820925	−	1.42188i	0.904994	−	0.425424i	$-0.139875\pi$
$468$		0			0
$469$	−1.29799	−	0.472430i	−0.0599357	−	0.0218148i
$470$		0			0
$471$	4.24722	+	24.0872i	0.195702	+	1.10988i
$472$		0			0
$473$	2.89208	+	2.42674i	0.132978	+	0.111582i
$474$		0			0
$475$	−35.2814	−	20.7451i	−1.61882	−	0.951853i
$476$		0			0
$477$	14.8561	+	12.4658i	0.680216	+	0.570769i
$478$		0			0
$479$	−4.87224	−	27.6318i	−0.222618	−	1.26253i	−0.867186	−	0.497984i	$-0.834074\pi$
$479$	−4.87224	−	27.6318i	−0.222618	−	1.26253i	0.644568	−	0.764547i	$-0.277037\pi$
$480$		0			0
$481$	9.35293	+	3.40419i	0.426457	+	0.155218i
$482$		0			0
$483$	−1.24078	+	2.14909i	−0.0564573	+	0.0977870i
$484$		0			0
$485$	2.20647	−	1.85145i	0.100191	−	0.0840699i
$486$		0			0
$487$	−21.5368	−	37.3029i	−0.975926	−	1.69035i	−0.676844	−	0.736126i	$-0.736653\pi$
$487$	−21.5368	−	37.3029i	−0.975926	−	1.69035i	−0.299082	−	0.954228i	$-0.596680\pi$
$488$		0			0
$489$	−4.32521	+	24.5295i	−0.195593	+	1.10926i
$490$		0			0
$491$	17.4166	−	6.33912i	0.786000	−	0.286080i	0.0823275	−	0.996605i	$-0.473765\pi$
$491$	17.4166	−	6.33912i	0.786000	−	0.286080i	0.703672	+	0.710525i	$0.251542\pi$
$492$		0			0
$493$	25.9351			1.16806
$494$		0			0
$495$	−16.2492			−0.730346
$496$		0			0
$497$	−0.282173	+	0.102703i	−0.0126572	+	0.00460684i
$498$		0			0
$499$	−7.54046	+	42.7641i	−0.337557	+	1.91438i	0.0628031	+	0.998026i	$0.479996\pi$
$499$	−7.54046	+	42.7641i	−0.337557	+	1.91438i	−0.400361	+	0.916358i	$0.631115\pi$
$500$		0			0
$501$	17.7754	+	30.7879i	0.794146	+	1.37550i
$502$		0			0
$503$	−0.819590	+	0.687718i	−0.0365437	+	0.0306638i	−0.660877	−	0.750495i	$-0.729815\pi$
$503$	−0.819590	+	0.687718i	−0.0365437	+	0.0306638i	0.624333	+	0.781158i	$0.285371\pi$
$504$		0			0
$505$	−23.7863	+	41.1990i	−1.05847	+	1.83333i
$506$		0			0
$507$	29.8607	+	10.8684i	1.32616	+	0.482682i
$508$		0			0
$509$	1.01402	+	5.75077i	0.0449455	+	0.254899i	0.998999	−	0.0447386i	$-0.0142455\pi$
$509$	1.01402	+	5.75077i	0.0449455	+	0.254899i	−0.954053	+	0.299637i	$0.903134\pi$
$510$		0			0
$511$	−1.21229	−	1.01723i	−0.0536286	−	0.0449998i
$512$		0			0
$513$	−26.5565	+	31.1431i	−1.17250	+	1.37500i
$514$		0			0
$515$	−25.1281	−	21.0850i	−1.10728	−	0.929116i
$516$		0			0
$517$	−0.226684	−	1.28559i	−0.00996957	−	0.0565402i
$518$		0			0
$519$	−26.5565	−	9.66579i	−1.16570	−	0.424281i
$520$		0			0
$521$	5.78321	−	10.0168i	0.253367	−	0.438844i	−0.711084	−	0.703107i	$-0.751795\pi$
$521$	5.78321	−	10.0168i	0.253367	−	0.438844i	0.964451	+	0.264263i	$0.0851287\pi$
$522$		0			0
$523$	2.87535	−	2.41270i	0.125730	−	0.105500i	−0.577754	−	0.816211i	$-0.696071\pi$
$523$	2.87535	−	2.41270i	0.125730	−	0.105500i	0.703485	+	0.710710i	$0.251626\pi$
$524$		0			0
$525$	−1.97008	−	3.41228i	−0.0859814	−	0.148924i
$526$		0			0
$527$	−1.87955	+	10.6595i	−0.0818745	+	0.464333i
$528$		0			0
$529$	−11.2497	+	4.09457i	−0.489119	+	0.178025i
$530$		0			0
$531$	14.4870			0.628681
$532$		0			0
$533$	7.36259			0.318909
$534$		0			0
$535$	−3.51078	+	1.27782i	−0.151784	+	0.0552450i
$536$		0			0
$537$	4.86926	−	27.6150i	0.210124	−	1.19167i
$538$		0			0
$539$	2.44668	+	4.23777i	0.105386	+	0.182534i
$540$		0			0
$541$	−11.2927	+	9.47568i	−0.485510	+	0.407391i	−0.852414	−	0.522867i	$-0.824862\pi$
$541$	−11.2927	+	9.47568i	−0.485510	+	0.407391i	0.366904	+	0.930259i	$0.380418\pi$
$542$		0			0
$543$	4.09114	−	7.08606i	0.175568	−	0.304092i
$544$		0			0
$545$	−50.8023	−	18.4905i	−2.17613	−	0.792047i
$546$		0			0
$547$	−1.35734	−	7.69785i	−0.0580356	−	0.329136i	0.941942	−	0.335775i	$-0.108998\pi$
$547$	−1.35734	−	7.69785i	−0.0580356	−	0.329136i	−0.999978	+	0.00663836i	$0.997887\pi$
$548$		0			0
$549$	15.8348	+	13.2870i	0.675814	+	0.567076i
$550$		0			0
$551$	26.1477	−	14.8207i	1.11393	−	0.631382i
$552$		0			0
$553$	−0.834166	−	0.699949i	−0.0354724	−	0.0297648i
$554$		0			0
$555$	12.5860	+	71.3790i	0.534248	+	3.02987i
$556$		0			0
$557$	−0.775402	−	0.282223i	−0.0328549	−	0.0119582i	0.325540	−	0.945528i	$-0.394454\pi$
$557$	−0.775402	−	0.282223i	−0.0328549	−	0.0119582i	−0.358395	+	0.933570i	$0.616676\pi$
$558$		0			0
$559$	−4.23411	+	7.33370i	−0.179084	+	0.310182i
$560$		0			0
$561$	6.09645	−	5.11553i	0.257393	−	0.215978i
$562$		0			0
$563$	2.41715	+	4.18662i	0.101871	+	0.176445i	0.912455	−	0.409176i	$-0.134184\pi$
$563$	2.41715	+	4.18662i	0.101871	+	0.176445i	−0.810585	+	0.585621i	$0.800851\pi$
$564$		0			0
$565$	−1.88787	+	10.7066i	−0.0794232	+	0.450431i
$566$		0			0
$567$	−1.30762	+	0.475933i	−0.0549147	+	0.0199873i
$568$		0			0
$569$	−20.7045			−0.867977			−0.433989	−	0.900918i	$-0.642894\pi$
$569$	−20.7045			−0.867977			−0.433989	+	0.900918i	$0.642894\pi$
$570$		0			0
$571$	−8.15233			−0.341164			−0.170582	−	0.985343i	$-0.554565\pi$
$571$	−8.15233			−0.341164			−0.170582	+	0.985343i	$0.554565\pi$
$572$		0			0
$573$	53.5891	−	19.5048i	2.23872	−	0.814827i
$574$		0			0
$575$	9.64223	−	54.6838i	0.402109	−	2.28047i
$576$		0			0
$577$	2.61121	+	4.52275i	0.108706	+	0.188285i	0.915246	−	0.402895i	$-0.131996\pi$
$577$	2.61121	+	4.52275i	0.108706	+	0.188285i	−0.806540	+	0.591179i	$0.798663\pi$
$578$		0			0
$579$	−49.3017	+	41.3690i	−2.04891	+	1.71924i
$580$		0			0
$581$	−0.712979	+	1.23492i	−0.0295793	+	0.0512329i
$582$		0			0
$583$	−2.09050	−	0.760879i	−0.0865796	−	0.0315124i
$584$		0			0
$585$	−6.32905	−	35.8938i	−0.261674	−	1.48403i
$586$		0			0
$587$	4.74153	+	3.97861i	0.195704	+	0.164215i	0.735374	−	0.677662i	$-0.237007\pi$
$587$	4.74153	+	3.97861i	0.195704	+	0.164215i	−0.539670	+	0.841877i	$0.681451\pi$
$588$		0			0
$589$	4.19642	+	11.8209i	0.172910	+	0.487072i
$590$		0			0
$591$	38.3394	+	32.1706i	1.57707	+	1.32332i
$592$		0			0
$593$	2.92199	+	16.5715i	0.119992	+	0.680508i	0.984157	+	0.177300i	$0.0567361\pi$
$593$	2.92199	+	16.5715i	0.119992	+	0.680508i	−0.864165	+	0.503209i	$0.832153\pi$
$594$		0			0
$595$	1.86395	+	0.678422i	0.0764145	+	0.0278126i
$596$		0			0
$597$	−24.4184	+	42.2938i	−0.999377	+	1.73097i
$598$		0			0
$599$	26.5345	−	22.2651i	1.08417	−	0.909726i	0.0879086	−	0.996129i	$-0.471982\pi$
$599$	26.5345	−	22.2651i	1.08417	−	0.909726i	0.996260	+	0.0864028i	$0.0275372\pi$
$600$		0			0
$601$	10.0714	+	17.4442i	0.410822	+	0.711564i	0.994980	−	0.100076i	$-0.0319085\pi$
$601$	10.0714	+	17.4442i	0.410822	+	0.711564i	−0.584158	+	0.811640i	$0.698575\pi$
$602$		0			0
$603$	10.5430	−	59.7926i	0.429346	−	2.43494i
$604$		0			0
$605$	−37.4590	+	13.6340i	−1.52293	+	0.554300i
$606$		0			0
$607$	30.9282			1.25534			0.627668	−	0.778481i	$-0.284010\pi$
$607$	30.9282			1.25534			0.627668	+	0.778481i	$0.284010\pi$
$608$		0			0
$609$	2.89346			0.117249
$610$		0			0
$611$	2.75153	−	1.00147i	0.111315	−	0.0405153i
$612$		0			0
$613$	1.55289	−	8.80687i	0.0627206	−	0.355706i	−0.937254	−	0.348646i	$-0.886642\pi$
$613$	1.55289	−	8.80687i	0.0627206	−	0.355706i	0.999975	−	0.00706025i	$-0.00224737\pi$
$614$		0			0
$615$	26.8076	+	46.4321i	1.08099	+	1.87232i
$616$		0			0
$617$	16.4246	−	13.7819i	0.661230	−	0.554838i	−0.249225	−	0.968446i	$-0.580176\pi$
$617$	16.4246	−	13.7819i	0.661230	−	0.554838i	0.910455	+	0.413607i	$0.135731\pi$
$618$		0			0
$619$	−12.7984	+	22.1675i	−0.514413	+	0.890989i	0.485448	+	0.874266i	$0.338657\pi$
$619$	−12.7984	+	22.1675i	−0.514413	+	0.890989i	−0.999860	+	0.0167229i	$0.994677\pi$
$620$		0			0
$621$	−52.1787	−	18.9915i	−2.09386	−	0.762102i
$622$		0			0
$623$	0.313537	+	1.77816i	0.0125616	+	0.0712403i
$624$		0			0
$625$	12.4230	+	10.4241i	0.496919	+	0.416965i
$626$		0			0
$627$	3.22314	−	8.64129i	0.128720	−	0.345100i
$628$		0			0
$629$	−18.2392	−	15.3045i	−0.727245	−	0.610231i
$630$		0			0
$631$	−0.493858	−	2.80081i	−0.0196602	−	0.111498i	0.973398	−	0.229119i	$-0.0735845\pi$
$631$	−0.493858	−	2.80081i	−0.0196602	−	0.111498i	−0.993059	+	0.117621i	$0.962473\pi$
$632$		0			0
$633$	−74.4553	−	27.0995i	−2.95933	−	1.07711i
$634$		0			0
$635$	−40.0094	+	69.2984i	−1.58773	+	2.75002i
$636$		0			0
$637$	−8.40808	+	7.05522i	−0.333140	+	0.279538i
$638$		0			0
$639$	−6.59948	−	11.4306i	−0.261072	−	0.452189i
$640$		0			0
$641$	8.07050	−	45.7701i	0.318765	−	1.80781i	−0.231518	−	0.972831i	$-0.574369\pi$
$641$	8.07050	−	45.7701i	0.318765	−	1.80781i	0.550283	−	0.834978i	$-0.314520\pi$
$642$		0			0
$643$	−8.80807	+	3.20587i	−0.347356	+	0.126427i	−0.509806	−	0.860290i	$-0.670283\pi$
$643$	−8.80807	+	3.20587i	−0.347356	+	0.126427i	0.162450	+	0.986717i	$0.448061\pi$
$644$		0			0
$645$	−61.6665			−2.42812
$646$		0			0
$647$	−5.27319			−0.207311			−0.103655	−	0.994613i	$-0.533054\pi$
$647$	−5.27319			−0.207311			−0.103655	+	0.994613i	$0.533054\pi$
$648$		0			0
$649$	−1.56162	+	0.568383i	−0.0612990	+	0.0223110i
$650$		0			0
$651$	−0.209693	+	1.18923i	−0.00821851	+	0.0466095i
$652$		0			0
$653$	21.0269	+	36.4197i	0.822848	+	1.42521i	0.903553	+	0.428476i	$0.140949\pi$
$653$	21.0269	+	36.4197i	0.822848	+	1.42521i	−0.0807056	+	0.996738i	$0.525717\pi$
$654$		0			0
$655$	29.8603	−	25.0558i	1.16674	−	0.979011i
$656$		0			0
$657$	34.7803	−	60.2412i	1.35691	−	2.35023i
$658$		0			0
$659$	31.5671	+	11.4895i	1.22968	+	0.447567i	0.873488	−	0.486846i	$-0.161853\pi$
$659$	31.5671	+	11.4895i	1.22968	+	0.447567i	0.356192	+	0.934413i	$0.384075\pi$
$660$		0			0
$661$	−3.70331	−	21.0025i	−0.144042	−	0.816903i	−0.968131	−	0.250443i	$-0.919424\pi$
$661$	−3.70331	−	21.0025i	−0.144042	−	0.816903i	0.824089	−	0.566460i	$-0.191687\pi$
$662$		0			0
$663$	13.6746	+	11.4743i	0.531077	+	0.445626i
$664$		0			0
$665$	2.26691	−	0.381176i	0.0879071	−	0.0147814i
$666$		0			0
$667$	31.2366	+	26.2107i	1.20949	+	1.01488i
$668$		0			0
$669$	1.19922	+	6.80110i	0.0463644	+	0.262946i
$670$		0			0
$671$	−2.22822	−	0.811004i	−0.0860193	−	0.0313085i
$672$		0			0
$673$	16.8335	−	29.1564i	0.648882	−	1.12390i	−0.334508	−	0.942393i	$-0.608570\pi$
$673$	16.8335	−	29.1564i	0.648882	−	1.12390i	0.983390	−	0.181504i	$-0.0580964\pi$
$674$		0			0
$675$	67.5385	−	56.6715i	2.59956	−	2.18129i
$676$		0			0
$677$	−16.2965	−	28.2264i	−0.626327	−	1.08483i	−0.988283	−	0.152635i	$-0.951224\pi$
$677$	−16.2965	−	28.2264i	−0.626327	−	1.08483i	0.361956	−	0.932195i	$-0.382109\pi$
$678$		0			0
$679$	−0.0183306	+	0.103958i	−0.000703464	+	0.00398954i
$680$		0			0
$681$	49.5434	−	18.0323i	1.89851	−	0.691000i
$682$		0			0
$683$	−29.1071			−1.11375			−0.556875	−	0.830596i	$-0.688000\pi$
$683$	−29.1071			−1.11375			−0.556875	+	0.830596i	$0.688000\pi$
$684$		0			0
$685$	45.5198			1.73922
$686$		0			0
$687$	−23.1151	+	8.41321i	−0.881897	+	0.320984i
$688$		0			0
$689$	0.866505	−	4.91419i	0.0330112	−	0.187216i
$690$		0			0
$691$	17.4572	+	30.2367i	0.664102	+	1.15026i	0.979528	+	0.201309i	$0.0645195\pi$
$691$	17.4572	+	30.2367i	0.664102	+	1.15026i	−0.315425	+	0.948950i	$0.602147\pi$
$692$		0			0
$693$	0.456192	−	0.382791i	0.0173293	−	0.0145410i
$694$		0			0
$695$	19.5232	−	33.8152i	0.740558	−	1.28268i
$696$		0			0
$697$	−16.5503	−	6.02383i	−0.626889	−	0.228169i
$698$		0			0
$699$	−11.1435	−	63.1980i	−0.421486	−	2.39037i
$700$		0			0
$701$	1.84929	+	1.55174i	0.0698467	+	0.0586084i	0.677043	−	0.735944i	$-0.263261\pi$
$701$	1.84929	+	1.55174i	0.0698467	+	0.0586084i	−0.607196	+	0.794552i	$0.707706\pi$
$702$		0			0
$703$	−27.1345	−	5.00711i	−1.02340	−	0.188847i
$704$		0			0
$705$	16.3342	+	13.7061i	0.615183	+	0.516200i
$706$		0			0
$707$	−0.302753	−	1.71700i	−0.0113862	−	0.0645744i
$708$		0			0
$709$	−4.00623	−	1.45815i	−0.150457	−	0.0547619i	0.265694	−	0.964057i	$-0.414399\pi$
$709$	−4.00623	−	1.45815i	−0.150457	−	0.0547619i	−0.416151	+	0.909296i	$0.636621\pi$
$710$		0			0
$711$	23.9320	−	41.4514i	0.897519	−	1.55455i
$712$		0			0
$713$	−13.0365	+	10.9389i	−0.488220	+	0.409665i
$714$		0			0
$715$	2.09050	+	3.62085i	0.0781802	+	0.135412i
$716$		0			0
$717$	−10.8733	+	61.6656i	−0.406071	+	2.30294i
$718$		0			0
$719$	−27.5194	+	10.0162i	−1.02630	+	0.373543i	−0.799671	−	0.600438i	$-0.794993\pi$
$719$	−27.5194	+	10.0162i	−1.02630	+	0.373543i	−0.226630	+	0.973981i	$0.572771\pi$
$720$		0			0
$721$	1.20218			0.0447714
$722$		0			0
$723$	60.3751			2.24537
$724$		0			0
$725$	−60.8396	+	22.1438i	−2.25953	+	0.822400i
$726$		0			0
$727$	−7.25564	+	41.1488i	−0.269097	+	1.52612i	0.488013	+	0.872836i	$0.337722\pi$
$727$	−7.25564	+	41.1488i	−0.269097	+	1.52612i	−0.757110	+	0.653287i	$0.773389\pi$
$728$		0			0
$729$	11.9300	+	20.6634i	0.441852	+	0.765311i
$730$		0			0
$731$	15.5180	−	13.0212i	0.573955	−	0.481605i
$732$		0			0
$733$	−1.63173	+	2.82624i	−0.0602693	+	0.104390i	−0.894586	−	0.446896i	$-0.852529\pi$
$733$	−1.63173	+	2.82624i	−0.0602693	+	0.104390i	0.834316	+	0.551286i	$0.185863\pi$
$734$		0			0
$735$	−75.1080	−	27.3371i	−2.77040	−	1.00834i
$736$		0			0
$737$	1.20942	+	6.85898i	0.0445496	+	0.252654i
$738$		0			0
$739$	3.24786	+	2.72528i	0.119474	+	0.100251i	0.700567	−	0.713586i	$-0.252930\pi$
$739$	3.24786	+	2.72528i	0.119474	+	0.100251i	−0.581093	+	0.813837i	$0.697375\pi$
$740$		0			0
$741$	20.3437	+	3.75400i	0.747344	+	0.137907i
$742$		0			0
$743$	−12.3449	−	10.3586i	−0.452889	−	0.380019i	0.387618	−	0.921820i	$-0.373298\pi$
$743$	−12.3449	−	10.3586i	−0.452889	−	0.380019i	−0.840507	+	0.541801i	$0.817742\pi$
$744$		0			0
$745$	2.46914	+	14.0032i	0.0904623	+	0.513037i
$746$		0			0
$747$	−58.8982	−	21.4372i	−2.15497	−	0.784346i
$748$		0			0
$749$	0.0684621	−	0.118580i	0.00250155	−	0.00433281i
$750$		0			0
$751$	−26.4072	+	22.1583i	−0.963614	+	0.808568i	−0.981537	−	0.191271i	$-0.938739\pi$
$751$	−26.4072	+	22.1583i	−0.963614	+	0.808568i	0.0179232	+	0.999839i	$0.494295\pi$
$752$		0			0
$753$	11.0836	+	19.1974i	0.403910	+	0.699593i
$754$		0			0
$755$	8.81790	−	50.0088i	0.320916	−	1.82001i
$756$		0			0
$757$	−23.7846	+	8.65689i	−0.864466	+	0.314640i	−0.735924	−	0.677064i	$-0.763252\pi$
$757$	−23.7846	+	8.65689i	−0.864466	+	0.314640i	−0.128542	+	0.991704i	$0.541030\pi$
$758$		0			0
$759$	12.5125			0.454177
$760$		0			0
$761$	−13.6889			−0.496223			−0.248111	−	0.968731i	$-0.579810\pi$
$761$	−13.6889			−0.496223			−0.248111	+	0.968731i	$0.579810\pi$
$762$		0			0
$763$	1.86186	−	0.677660i	0.0674037	−	0.0245329i
$764$		0			0
$765$	−15.1401	+	85.8637i	−0.547391	+	3.10441i
$766$		0			0
$767$	−1.86379	−	3.22817i	−0.0672974	−	0.116563i
$768$		0			0
$769$	26.4169	−	22.1664i	0.952616	−	0.799340i	−0.0271198	−	0.999632i	$-0.508634\pi$
$769$	26.4169	−	22.1664i	0.952616	−	0.799340i	0.979736	+	0.200292i	$0.0641891\pi$
$770$		0			0
$771$	−40.9617	+	70.9477i	−1.47520	+	2.55512i
$772$		0			0
$773$	45.5996	+	16.5969i	1.64010	+	0.596948i	0.987057	−	0.160371i	$-0.0512689\pi$
$773$	45.5996	+	16.5969i	1.64010	+	0.596948i	0.653045	+	0.757319i	$0.273491\pi$
$774$		0			0
$775$	−4.69209	−	26.6102i	−0.168545	−	0.955866i
$776$		0			0
$777$	−2.03486	−	1.70745i	−0.0730003	−	0.0612545i
$778$		0			0
$779$	−20.1283	+	3.38453i	−0.721172	+	0.121263i
$780$		0			0
$781$	1.15986	+	0.973239i	0.0415031	+	0.0348252i
$782$		0			0
$783$	11.2427	+	63.7606i	0.401782	+	2.27862i
$784$		0			0
$785$	28.8847	+	10.5132i	1.03094	+	0.375231i
$786$		0			0
$787$	−23.4705	+	40.6521i	−0.836633	+	1.44909i	0.0560615	+	0.998427i	$0.482146\pi$
$787$	−23.4705	+	40.6521i	−0.836633	+	1.44909i	−0.892694	+	0.450663i	$0.851188\pi$
$788$		0			0
$789$	49.9882	−	41.9451i	1.77963	−	1.49328i
$790$		0			0
$791$	−0.199220	−	0.345060i	−0.00708346	−	0.0122689i
$792$		0			0
$793$	0.923588	−	5.23793i	0.0327976	−	0.186004i
$794$		0			0
$795$	34.1463	−	12.4282i	1.21104	−	0.440784i
$796$		0			0
$797$	45.6388			1.61661			0.808305	−	0.588764i	$-0.200385\pi$
$797$	45.6388			1.61661			0.808305	+	0.588764i	$0.200385\pi$
$798$		0			0
$799$	−7.00452			−0.247802
$800$		0			0
$801$	−74.5786	+	27.1444i	−2.63510	+	0.959100i
$802$		0			0
$803$	−1.38562	+	7.85826i	−0.0488976	+	0.277312i
$804$		0			0
$805$	1.55934	+	2.70086i	0.0549595	+	0.0951926i
$806$		0			0
$807$	13.8631	−	11.6325i	0.488004	−	0.409484i
$808$		0			0
$809$	−15.7365	+	27.2565i	−0.553267	+	0.958286i	0.444769	+	0.895645i	$0.353286\pi$
$809$	−15.7365	+	27.2565i	−0.553267	+	0.958286i	−0.998036	+	0.0626411i	$0.980048\pi$
$810$		0			0
$811$	−39.7312	−	14.4610i	−1.39515	−	0.507793i	−0.468415	−	0.883509i	$-0.655175\pi$
$811$	−39.7312	−	14.4610i	−1.39515	−	0.507793i	−0.926735	+	0.375716i	$0.877397\pi$
$812$		0			0
$813$	−12.4084	−	70.3715i	−0.435182	−	2.46804i
$814$		0			0
$815$	23.9794	+	20.1211i	0.839962	+	0.704811i
$816$		0			0
$817$	8.20423	−	21.9957i	0.287030	−	0.769532i
$818$		0			0
$819$	1.02326	+	0.858614i	0.0357555	+	0.0300024i
$820$		0			0
$821$	−3.33917	−	18.9374i	−0.116538	−	0.660919i	−0.985977	−	0.166879i	$-0.946631\pi$
$821$	−3.33917	−	18.9374i	−0.116538	−	0.660919i	0.869440	−	0.494039i	$-0.164480\pi$
$822$		0			0
$823$	24.9230	+	9.07122i	0.868760	+	0.316203i	0.737665	−	0.675167i	$-0.235928\pi$
$823$	24.9230	+	9.07122i	0.868760	+	0.316203i	0.131095	+	0.991370i	$0.458151\pi$
$824$		0			0
$825$	−9.93358	+	17.2055i	−0.345843	+	0.599018i
$826$		0			0
$827$	−13.3929	+	11.2380i	−0.465718	+	0.390784i	−0.845230	−	0.534403i	$-0.820536\pi$
$827$	−13.3929	+	11.2380i	−0.465718	+	0.390784i	0.379512	+	0.925187i	$0.376092\pi$
$828$		0			0
$829$	−12.9372	−	22.4079i	−0.449328	−	0.778259i	0.549014	−	0.835813i	$-0.315003\pi$
$829$	−12.9372	−	22.4079i	−0.449328	−	0.778259i	−0.998342	+	0.0575537i	$0.981670\pi$
$830$		0			0
$831$	−4.97194	+	28.1973i	−0.172475	+	0.978153i
$832$		0			0
$833$	24.6728	−	8.98018i	0.854863	−	0.311145i
$834$		0			0
$835$	44.6782			1.54615
$836$		0			0
$837$	−27.0207			−0.933972
$838$		0			0
$839$	37.2066	−	13.5421i	1.28451	−	0.467524i	0.392591	−	0.919713i	$-0.371579\pi$
$839$	37.2066	−	13.5421i	1.28451	−	0.467524i	0.891922	+	0.452189i	$0.149357\pi$
$840$		0			0
$841$	3.22029	−	18.2632i	0.111044	−	0.629764i
$842$		0			0
$843$	−36.6863	−	63.5425i	−1.26354	−	2.18852i
$844$		0			0
$845$	30.5925	−	25.6701i	1.05241	−	0.883079i
$846$		0			0
$847$	0.730471	−	1.26521i	0.0250993	−	0.0434732i
$848$		0			0
$849$	33.1354	+	12.0603i	1.13720	+	0.413909i
$850$		0			0
$851$	−6.50047	−	36.8660i	−0.222833	−	1.26375i
$852$		0			0
$853$	−23.9929	−	20.1325i	−0.821502	−	0.689322i	0.131821	−	0.991274i	$-0.457918\pi$
$853$	−23.9929	−	20.1325i	−0.821502	−	0.689322i	−0.953323	+	0.301951i	$0.902362\pi$
$854$		0			0
$855$	33.8029	+	95.2193i	1.15603	+	3.25643i
$856$		0			0
$857$	−12.5482	−	10.5292i	−0.428637	−	0.359669i	0.402800	−	0.915288i	$-0.368037\pi$
$857$	−12.5482	−	10.5292i	−0.428637	−	0.359669i	−0.831437	+	0.555619i	$0.812481\pi$
$858$		0			0
$859$	−6.23449	−	35.3576i	−0.212718	−	1.20638i	−0.884823	−	0.465928i	$-0.845721\pi$
$859$	−6.23449	−	35.3576i	−0.212718	−	1.20638i	0.672105	−	0.740456i	$-0.265391\pi$
$860$		0			0
$861$	−1.84644	−	0.672051i	−0.0629266	−	0.0229034i
$862$		0			0
$863$	−19.3886	+	33.5820i	−0.659995	+	1.14314i	0.320621	+	0.947207i	$0.396108\pi$
$863$	−19.3886	+	33.5820i	−0.659995	+	1.14314i	−0.980616	+	0.195938i	$0.937225\pi$
$864$		0			0
$865$	−27.2074	+	22.8297i	−0.925078	+	0.776233i
$866$		0			0
$867$	4.30538	+	7.45713i	0.146218	+	0.253258i
$868$		0			0
$869$	−0.953434	+	5.40720i	−0.0323430	+	0.183427i
$870$		0			0
$871$	−14.6801	+	5.34313i	−0.497418	+	0.181045i
$872$		0			0
$873$	−4.63998			−0.157040
$874$		0			0
$875$	−2.31494			−0.0782594
$876$		0			0
$877$	−12.6819	+	4.61584i	−0.428238	+	0.155866i	−0.547142	−	0.837040i	$-0.684284\pi$
$877$	−12.6819	+	4.61584i	−0.428238	+	0.155866i	0.118904	+	0.992906i	$0.462062\pi$
$878$		0			0
$879$	7.35445	−	41.7091i	0.248059	−	1.40681i
$880$		0			0
$881$	3.03251	+	5.25246i	0.102168	+	0.176960i	0.912578	−	0.408904i	$-0.134089\pi$
$881$	3.03251	+	5.25246i	0.102168	+	0.176960i	−0.810410	+	0.585864i	$0.800755\pi$
$882$		0			0
$883$	−5.42261	+	4.55011i	−0.182485	+	0.153123i	−0.729454	−	0.684029i	$-0.760226\pi$
$883$	−5.42261	+	4.55011i	−0.182485	+	0.153123i	0.546969	+	0.837153i	$0.315782\pi$
$884$		0			0
$885$	13.5723	−	23.5079i	0.456228	−	0.790209i
$886$		0			0
$887$	−42.7141	−	15.5466i	−1.43420	−	0.522005i	−0.496066	−	0.868285i	$-0.665223\pi$
$887$	−42.7141	−	15.5466i	−1.43420	−	0.522005i	−0.938132	+	0.346279i	$0.887445\pi$
$888$		0			0
$889$	−0.509243	−	2.88806i	−0.0170795	−	0.0968625i
$890$		0			0
$891$	5.37490	+	4.51008i	0.180066	+	0.151093i
$892$		0			0
$893$	−7.06192	+	4.00275i	−0.236318	+	0.133947i
$894$		0			0
$895$	−26.9957	−	22.6520i	−0.902365	−	0.757174i
$896$		0			0
$897$	4.87363	+	27.6397i	0.162726	+	0.922864i
$898$		0			0
$899$	18.6460	+	6.78659i	0.621879	+	0.226345i
$900$		0			0
$901$	−5.96844	+	10.3376i	−0.198838	+	0.344397i
$902$		0			0
$903$	1.73127	−	1.45271i	0.0576132	−	0.0483432i
$904$		0			0
$905$	−5.14151	−	8.90536i	−0.170910	−	0.296024i
$906$		0			0
$907$	−6.82814	+	38.7243i	−0.226725	+	1.28582i	0.632636	+	0.774450i	$0.281973\pi$
$907$	−6.82814	+	38.7243i	−0.226725	+	1.28582i	−0.859360	+	0.511370i	$0.829138\pi$
$908$		0			0
$909$	72.0136	−	26.2108i	2.38854	−	0.869357i
$910$		0			0
$911$	−9.52856			−0.315695			−0.157848	−	0.987463i	$-0.550455\pi$
$911$	−9.52856			−0.315695			−0.157848	+	0.987463i	$0.550455\pi$
$912$		0			0
$913$	7.18999			0.237954
$914$		0			0
$915$	36.3958	−	13.2470i	1.20321	−	0.437932i
$916$		0			0
$917$	−0.248070	+	1.40687i	−0.00819198	+	0.0464590i
$918$		0			0
$919$	8.36681	+	14.4917i	0.275996	+	0.478039i	0.970386	−	0.241560i	$-0.0776591\pi$
$919$	8.36681	+	14.4917i	0.275996	+	0.478039i	−0.694390	+	0.719599i	$0.744326\pi$
$920$		0			0
$921$	−1.28476	+	1.07804i	−0.0423342	+	0.0355226i
$922$		0			0
$923$	−1.69808	+	2.94116i	−0.0558930	+	0.0968096i
$924$		0			0
$925$	55.8535	+	20.3290i	1.83645	+	0.668414i
$926$		0			0
$927$	9.17590	+	52.0391i	0.301376	+	1.70919i
$928$		0			0
$929$	5.66832	+	4.75629i	0.185972	+	0.156049i	0.731020	−	0.682356i	$-0.239044\pi$
$929$	5.66832	+	4.75629i	0.185972	+	0.156049i	−0.545049	+	0.838404i	$0.683489\pi$
$930$		0			0
$931$	19.7433	−	23.1531i	0.647061	−	0.758813i
$932$		0			0
$933$	−36.5092	−	30.6348i	−1.19526	−	1.00294i
$934$		0			0
$935$	−1.73676	−	9.84967i	−0.0567982	−	0.322119i
$936$		0			0
$937$	−26.4994	−	9.64498i	−0.865697	−	0.315088i	−0.129273	−	0.991609i	$-0.541265\pi$
$937$	−26.4994	−	9.64498i	−0.865697	−	0.315088i	−0.736423	+	0.676521i	$0.763487\pi$
$938$		0			0
$939$	34.3589	−	59.5113i	1.12126	−	1.94208i
$940$		0			0
$941$	39.9787	−	33.5461i	1.30327	−	1.09357i	0.313698	−	0.949523i	$-0.398432\pi$
$941$	39.9787	−	33.5461i	1.30327	−	1.09357i	0.989570	−	0.144050i	$-0.0460125\pi$
$942$		0			0
$943$	−13.8457	−	23.9814i	−0.450877	−	0.780941i
$944$		0			0
$945$	−0.859867	+	4.87655i	−0.0279715	+	0.158634i
$946$		0			0
$947$	−22.1023	+	8.04458i	−0.718228	+	0.261414i	−0.675174	−	0.737659i	$-0.735931\pi$
$947$	−22.1023	+	8.04458i	−0.718228	+	0.261414i	−0.0430549	+	0.999073i	$0.513709\pi$
$948$		0			0
$949$	−17.8983			−0.581003
$950$		0			0
$951$	−57.2669			−1.85701
$952$		0			0
$953$	−35.1886	+	12.8076i	−1.13987	+	0.414879i	−0.841867	−	0.539686i	$-0.818543\pi$
$953$	−35.1886	+	12.8076i	−1.13987	+	0.414879i	−0.298004	+	0.954565i	$0.596321\pi$
$954$		0			0
$955$	12.4454	−	70.5812i	0.402723	−	2.28395i
$956$		0			0
$957$	−7.29473	−	12.6348i	−0.235805	−	0.408426i
$958$		0			0
$959$	−1.27796	+	1.07234i	−0.0412675	+	0.0346275i
$960$		0			0
$961$	11.3594	−	19.6750i	0.366432	−	0.634678i
$962$		0			0
$963$	5.65557	+	2.05846i	0.182248	+	0.0663329i
$964$		0			0
$965$	14.0451	+	79.6537i	0.452128	+	2.56414i
$966$		0			0
$967$	−25.3924	−	21.3068i	−0.816565	−	0.685179i	0.135600	−	0.990764i	$-0.456704\pi$
$967$	−25.3924	−	21.3068i	−0.816565	−	0.685179i	−0.952165	+	0.305585i	$0.901148\pi$
$968$		0			0
$969$	−42.6591	−	25.0831i	−1.37041	−	0.805787i
$970$		0			0
$971$	−12.1983	−	10.2356i	−0.391462	−	0.328476i	0.425720	−	0.904855i	$-0.360021\pi$
$971$	−12.1983	−	10.2356i	−0.391462	−	0.328476i	−0.817182	+	0.576379i	$0.804465\pi$
$972$		0			0
$973$	0.248493	+	1.40927i	0.00796632	+	0.0451792i
$974$		0			0
$975$	−41.8753	−	15.2414i	−1.34108	−	0.488115i
$976$		0			0
$977$	−0.950197	+	1.64579i	−0.0303995	+	0.0526535i	−0.880825	−	0.473442i	$-0.843011\pi$
$977$	−0.950197	+	1.64579i	−0.0303995	+	0.0526535i	0.850425	+	0.526096i	$0.176345\pi$
$978$		0			0
$979$	6.97420	−	5.85205i	0.222896	−	0.187032i
$980$		0			0
$981$	43.5452	+	75.4225i	1.39029	+	2.40805i
$982$		0			0
$983$	−2.74254	+	15.5537i	−0.0874733	+	0.496086i	0.909322	+	0.416093i	$0.136601\pi$
$983$	−2.74254	+	15.5537i	−0.0874733	+	0.496086i	−0.996795	+	0.0799929i	$0.974510\pi$
$984$		0			0
$985$	59.1050	−	21.5125i	1.88324	−	0.685444i
$986$		0			0
$987$	−0.781461			−0.0248742
$988$		0			0
$989$	31.8497			1.01276
$990$		0			0
$991$	36.1131	−	13.1441i	1.14717	−	0.417536i	0.302672	−	0.953095i	$-0.402121\pi$
$991$	36.1131	−	13.1441i	1.14717	−	0.417536i	0.844498	+	0.535559i	$0.179899\pi$
$992$		0			0
$993$	−7.73800	+	43.8844i	−0.245558	+	1.39263i
$994$		0			0
$995$	30.6876	+	53.1525i	0.972863	+	1.68505i
$996$		0			0
$997$	6.30982	−	5.29457i	0.199834	−	0.167681i	−0.537379	−	0.843341i	$-0.680586\pi$
$997$	6.30982	−	5.29457i	0.199834	−	0.167681i	0.737213	+	0.675660i	$0.236141\pi$
$998$		0			0
$999$	29.7190	−	51.4749i	0.940268	−	1.62859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.i.a.73.1	yes	12
3.2	odd	2		684.2.bo.c.73.2		12
4.3	odd	2		304.2.u.e.225.2		12
19.2	odd	18		1444.2.e.h.653.6		12
19.3	odd	18		1444.2.e.h.429.6		12
19.5	even	9		1444.2.a.h.1.6		6
19.6	even	9	inner	76.2.i.a.25.1	✓	12
19.14	odd	18		1444.2.a.g.1.1		6
19.16	even	9		1444.2.e.g.429.1		12
19.17	even	9		1444.2.e.g.653.1		12
57.44	odd	18		684.2.bo.c.253.2		12
76.43	odd	18		5776.2.a.bw.1.1		6
76.63	odd	18		304.2.u.e.177.2		12
76.71	even	18		5776.2.a.by.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.25.1	✓	12	19.6	even	9	inner
76.2.i.a.73.1	yes	12	1.1	even	1	trivial
304.2.u.e.177.2		12	76.63	odd	18
304.2.u.e.225.2		12	4.3	odd	2
684.2.bo.c.73.2		12	3.2	odd	2
684.2.bo.c.253.2		12	57.44	odd	18
1444.2.a.g.1.1		6	19.14	odd	18
1444.2.a.h.1.6		6	19.5	even	9
1444.2.e.g.429.1		12	19.16	even	9
1444.2.e.g.653.1		12	19.17	even	9
1444.2.e.h.429.6		12	19.3	odd	18
1444.2.e.h.653.6		12	19.2	odd	18
5776.2.a.bw.1.1		6	76.43	odd	18
5776.2.a.by.1.6		6	76.71	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)

\(f(q)\)	\(=\)	\(q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +O(q^{10})\)	\(q+(-2.83638 + 1.03236i) q^{3} +(-0.658711 + 3.73574i) q^{5} +(-0.0695116 - 0.120398i) q^{7} +(4.68114 - 3.92794i) q^{9} +(-0.350493 + 0.607072i) q^{11} +(-1.47751 - 0.537771i) q^{13} +(-1.98826 - 11.2760i) q^{15} +(2.88131 + 2.41771i) q^{17} +(4.28653 + 0.790990i) q^{19} +(0.321454 + 0.269732i) q^{21} +(1.02690 + 5.82385i) q^{23} +(-8.82337 - 3.21144i) q^{25} +(-4.69482 + 8.13166i) q^{27} +(5.28209 - 4.43220i) q^{29} +(1.43886 + 2.49217i) q^{31} +(0.367416 - 2.08372i) q^{33} +(0.495562 - 0.180370i) q^{35} -6.33018 q^{37} +4.74596 q^{39} +(-4.40018 + 1.60154i) q^{41} +(0.935226 - 5.30393i) q^{43} +(11.5902 + 20.0749i) q^{45} +(-1.42658 + 1.19704i) q^{47} +(3.49034 - 6.04544i) q^{49} +(-10.6684 - 3.88299i) q^{51} +(0.551093 + 3.12541i) q^{53} +(-2.03699 - 1.70923i) q^{55} +(-12.9748 + 2.18168i) q^{57} +(1.81608 + 1.52387i) q^{59} +(0.587398 + 3.33130i) q^{61} +(-0.798308 - 0.290560i) q^{63} +(2.98223 - 5.16537i) q^{65} +(7.61119 - 6.38655i) q^{67} +(-8.92496 - 15.4585i) q^{69} +(0.375070 - 2.12713i) q^{71} +(10.6967 - 3.89330i) q^{73} +28.3417 q^{75} +0.0974533 q^{77} +(7.36033 - 2.67894i) q^{79} +(1.73811 - 9.85732i) q^{81} +(-5.12849 - 8.88280i) q^{83} +(-10.9299 + 9.17125i) q^{85} +(-10.4064 + 18.0244i) q^{87} +(-12.2044 - 4.44204i) q^{89} +(0.0379580 + 0.215271i) q^{91} +(-6.65395 - 5.58333i) q^{93} +(-5.77852 + 15.4923i) q^{95} +(-0.581665 - 0.488075i) q^{97} +(0.743835 + 4.21850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 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

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Database

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