LMFDB - Embedded newform 76.2.i.a.25.1

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			25.1
Root			$-1.25236 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	76.25
Dual form			76.2.i.a.73.1

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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	−0.650969	−	0.759105i	$-0.725637\pi$
$3$	−2.83638	−	1.03236i	−1.63758	−	0.596031i	−0.986614	+	0.163073i	$0.947859\pi$
$4$		0			0
$5$	−0.658711	−	3.73574i	−0.294585	−	1.67067i	−0.668886	−	0.743365i	$-0.733228\pi$
$5$	−0.658711	−	3.73574i	−0.294585	−	1.67067i	0.374301	−	0.927307i	$-0.377883\pi$
$6$		0			0
$7$	−0.0695116	+	0.120398i	−0.0262729	+	0.0455060i	−0.878863	−	0.477074i	$-0.841697\pi$
$7$	−0.0695116	+	0.120398i	−0.0262729	+	0.0455060i	0.852590	+	0.522580i	$0.175031\pi$
$8$		0			0
$9$	4.68114	+	3.92794i	1.56038	+	1.30931i
$10$		0			0
$11$	−0.350493	−	0.607072i	−0.105678	−	0.183039i	0.808337	−	0.588720i	$-0.200368\pi$
$11$	−0.350493	−	0.607072i	−0.105678	−	0.183039i	−0.914015	+	0.405681i	$0.867034\pi$
$12$		0			0
$13$	−1.47751	+	0.537771i	−0.409789	+	0.149151i	−0.538685	−	0.842507i	$-0.681079\pi$
$13$	−1.47751	+	0.537771i	−0.409789	+	0.149151i	0.128896	+	0.991658i	$0.458857\pi$
$14$		0			0
$15$	−1.98826	+	11.2760i	−0.513366	+	2.91145i
$16$		0			0
$17$	2.88131	−	2.41771i	0.698820	−	0.586380i	−0.222617	−	0.974906i	$-0.571460\pi$
$17$	2.88131	−	2.41771i	0.698820	−	0.586380i	0.921438	+	0.388526i	$0.127016\pi$
$18$		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	−0.668297	−	0.743895i	$-0.732976\pi$
$23$	1.02690	−	5.82385i	0.214124	−	1.21436i	0.882421	−	0.470461i	$-0.155912\pi$
$24$		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	0.984219	−	0.176955i	$-0.0566248\pi$
$29$	5.28209	+	4.43220i	0.980860	+	0.823039i	−0.00335912	+	0.999994i	$0.501069\pi$
$30$		0			0
$31$	1.43886	−	2.49217i	0.258426	−	0.447608i	−0.707394	−	0.706819i	$-0.750129\pi$
$31$	1.43886	−	2.49217i	0.258426	−	0.447608i	0.965821	+	0.259212i	$0.0834627\pi$
$32$		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	−0.0252602	−	0.999681i	$-0.508041\pi$
$41$	−4.40018	−	1.60154i	−0.687193	−	0.250118i	−0.661933	+	0.749563i	$0.730264\pi$
$42$		0			0
$43$	0.935226	+	5.30393i	0.142621	+	0.808842i	0.969247	+	0.246091i	$0.0791461\pi$
$43$	0.935226	+	5.30393i	0.142621	+	0.808842i	−0.826626	+	0.562751i	$0.809743\pi$
$44$		0			0
$45$	11.5902	−	20.0749i	1.72777	−	2.99259i
$46$		0			0
$47$	−1.42658	−	1.19704i	−0.208088	−	0.174607i	0.532787	−	0.846249i	$-0.321145\pi$
$47$	−1.42658	−	1.19704i	−0.208088	−	0.174607i	−0.740875	+	0.671643i	$0.765589\pi$
$48$		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	−0.923280	−	0.384127i	$-0.874503\pi$
$53$	0.551093	−	3.12541i	0.0756985	−	0.429307i	0.998979	−	0.0451806i	$-0.0143863\pi$
$54$		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	−0.516871	−	0.856063i	$-0.672903\pi$
$59$	1.81608	−	1.52387i	0.236433	−	0.198391i	0.753304	+	0.657672i	$0.228459\pi$
$60$		0			0
$61$	0.587398	−	3.33130i	0.0752086	−	0.426529i	−0.923834	−	0.382792i	$-0.874963\pi$
$61$	0.587398	−	3.33130i	0.0752086	−	0.426529i	0.999043	−	0.0437370i	$-0.0139264\pi$
$62$		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	0.975791	−	0.218704i	$-0.0701828\pi$
$67$	7.61119	+	6.38655i	0.929855	+	0.780241i	−0.0459367	+	0.998944i	$0.514627\pi$
$68$		0			0
$69$	−8.92496	+	15.4585i	−1.07444	+	1.86098i
$70$		0			0
$71$	0.375070	+	2.12713i	0.0445127	+	0.252444i	0.998942	−	0.0459940i	$-0.0146455\pi$
$71$	0.375070	+	2.12713i	0.0445127	+	0.252444i	−0.954429	+	0.298438i	$0.903534\pi$
$72$		0			0
$73$	10.6967	+	3.89330i	1.25196	+	0.455676i	0.881063	−	0.472998i	$-0.156828\pi$
$73$	10.6967	+	3.89330i	1.25196	+	0.455676i	0.370896	+	0.928674i	$0.379051\pi$
$74$		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	0.721079	−	0.692852i	$-0.243646\pi$
$79$	7.36033	+	2.67894i	0.828102	+	0.301404i	0.107022	+	0.994257i	$0.465868\pi$
$80$		0			0
$81$	1.73811	+	9.85732i	0.193123	+	1.09526i
$82$		0			0
$83$	−5.12849	+	8.88280i	−0.562925	+	0.975014i	0.434315	+	0.900761i	$0.356991\pi$
$83$	−5.12849	+	8.88280i	−0.562925	+	0.975014i	−0.997239	+	0.0742528i	$0.976343\pi$
$84$		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	−0.894928	−	0.446210i	$-0.852773\pi$
$89$	−12.2044	+	4.44204i	−1.29366	+	0.470856i	−0.398737	+	0.917066i	$0.630551\pi$
$90$		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	−0.671839	−	0.740697i	$-0.734496\pi$
$97$	−0.581665	+	0.488075i	−0.0590591	+	0.0495565i	0.612780	+	0.790253i	$0.290051\pi$
$98$		0			0
$99$	0.743835	−	4.21850i	0.0747583	−	0.423975i
$100$		0			0
$101$	11.7847	−	4.28927i	1.17262	−	0.426798i	0.319029	−	0.947745i	$-0.396643\pi$
$101$	11.7847	−	4.28927i	1.17262	−	0.426798i	0.853589	+	0.520947i	$0.174421\pi$
$102$		0			0
$103$	−4.32365	−	7.48879i	−0.426022	−	0.737892i	0.570493	−	0.821302i	$-0.306752\pi$
$103$	−4.32365	−	7.48879i	−0.426022	−	0.737892i	−0.996515	+	0.0834102i	$0.973419\pi$
$104$		0			0
$105$	−1.21939	−	1.02319i	−0.119001	−	0.0998534i
$106$		0			0
$107$	0.492451	−	0.852950i	0.0476070	−	0.0824578i	−0.841240	−	0.540662i	$-0.818174\pi$
$107$	0.492451	−	0.852950i	0.0476070	−	0.0824578i	0.888847	+	0.458204i	$0.151507\pi$
$108$		0			0
$109$	−2.47482	−	14.0354i	−0.237044	−	1.34435i	−0.838265	−	0.545263i	$-0.816430\pi$
$109$	−2.47482	−	14.0354i	−0.237044	−	1.34435i	0.601221	−	0.799083i	$-0.294681\pi$
$110$		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	0.759002	−	0.651089i	$-0.225687\pi$
$127$	19.8223	−	7.21472i	1.75894	−	0.640203i	0.999941	+	0.0108860i	$0.00346520\pi$
$128$		0			0
$129$	2.82289	−	16.0094i	0.248542	−	1.40955i
$130$		0			0
$131$	−7.87172	+	6.60516i	−0.687756	+	0.577096i	−0.918261	−	0.395975i	$-0.870407\pi$
$131$	−7.87172	+	6.60516i	−0.687756	+	0.577096i	0.230505	+	0.973071i	$0.425962\pi$
$132$		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	0.756565	+	0.653919i	$0.226876\pi$
$137$	−2.08375	+	11.8175i	−0.178027	+	1.00964i	−0.934592	+	0.355722i	$0.884235\pi$
$138$		0			0
$139$	−9.67258	+	3.52053i	−0.820417	+	0.298607i	−0.717920	−	0.696126i	$-0.754906\pi$
$139$	−9.67258	+	3.52053i	−0.820417	+	0.298607i	−0.102497	+	0.994733i	$0.532683\pi$
$140$		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	0.482247	−	0.876035i	$-0.339821\pi$
$149$	3.52238	+	1.28204i	0.288565	+	0.105029i	−0.193682	+	0.981064i	$0.562043\pi$
$150$		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	0.988052	+	0.154121i	$0.0492546\pi$
$157$	1.40711	+	7.98010i	0.112299	+	0.636881i	−0.875753	+	0.482760i	$0.839634\pi$
$158$		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	0.981141	−	0.193294i	$-0.0619170\pi$
$163$	4.12600	+	7.14644i	0.323173	+	0.559753i	−0.657968	+	0.753046i	$0.728584\pi$
$164$		0			0
$165$	7.54220	−	2.74514i	0.587159	−	0.213709i
$166$		0			0
$167$	−2.04523	+	11.5991i	−0.158264	+	0.897562i	0.797476	+	0.603351i	$0.206168\pi$
$167$	−2.04523	+	11.5991i	−0.158264	+	0.897562i	−0.955740	+	0.294211i	$0.904943\pi$
$168$		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	−0.328043	−	0.944663i	$-0.606389\pi$
$173$	7.17235	−	6.01832i	0.545304	−	0.457564i	0.873347	+	0.487098i	$0.161945\pi$
$174$		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	0.638565	−	0.769568i	$-0.279528\pi$
$179$	−4.64499	−	8.04536i	−0.347183	−	0.601339i	−0.985748	+	0.168229i	$0.946195\pi$
$180$		0			0
$181$	−2.07659	−	1.74246i	−0.154351	−	0.129516i	0.562342	−	0.826905i	$-0.309901\pi$
$181$	−2.07659	−	1.74246i	−0.154351	−	0.129516i	−0.716693	+	0.697389i	$0.754345\pi$
$182$		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	0.940412	−	0.340037i	$-0.110440\pi$
$193$	20.0362	+	7.29258i	1.44224	+	0.524931i	0.501825	+	0.864969i	$0.332662\pi$
$194$		0			0
$195$	−3.12622	−	17.7297i	−0.223873	−	1.26965i
$196$		0			0
$197$	−8.29055	+	14.3597i	−0.590677	+	1.02308i	0.403464	+	0.914996i	$0.367806\pi$
$197$	−8.29055	+	14.3597i	−0.590677	+	1.02308i	−0.994141	+	0.108088i	$0.965527\pi$
$198$		0			0
$199$	12.3943	+	10.4001i	0.878610	+	0.737241i	0.965893	−	0.258943i	$-0.0833741\pi$
$199$	12.3943	+	10.4001i	0.878610	+	0.737241i	−0.0872832	+	0.996184i	$0.527819\pi$
$200$		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	0.416772	−	0.909011i	$-0.363161\pi$
$211$	20.1088	−	16.8733i	1.38434	−	1.16160i	0.967573	−	0.252592i	$-0.0812831\pi$
$212$		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	0.995216	−	0.0976949i	$-0.0311469\pi$
$223$	0.397301	+	2.25321i	0.0266053	+	0.150886i	−0.968611	+	0.248581i	$0.920036\pi$
$224$		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	−0.827671	−	0.561214i	$-0.810335\pi$
$233$	−3.69185	−	20.9375i	−0.241861	−	1.37166i	0.585810	−	0.810449i	$-0.300777\pi$
$234$		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	0.977638	+	0.210296i	$0.0674429\pi$
$239$	10.3725	+	17.9657i	0.670941	+	1.16210i	−0.306697	+	0.951807i	$0.599224\pi$
$240$		0			0
$241$	−18.7960	+	6.84119i	−1.21076	+	0.440680i	−0.866966	−	0.498367i	$-0.833933\pi$
$241$	−18.7960	+	6.84119i	−1.21076	+	0.440680i	−0.343791	+	0.939046i	$0.611711\pi$
$242$		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	0.917743	+	0.397174i	$0.130009\pi$
$251$	−1.27528	+	7.23245i	−0.0804948	+	0.456508i	−0.998238	+	0.0593346i	$0.981102\pi$
$252$		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	0.990666	+	0.136308i	$0.0435238\pi$
$257$	20.7914	+	17.4460i	1.29693	+	1.08825i	0.306265	+	0.951946i	$0.400921\pi$
$258$		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	−0.371379	−	0.928481i	$-0.621115\pi$
$263$	−20.3152	−	7.39413i	−1.25269	−	0.455941i	−0.881309	+	0.472540i	$0.843337\pi$
$264$		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	0.164504	−	0.986376i	$-0.447398\pi$
$269$	−5.63396	−	2.05060i	−0.343509	−	0.125027i	−0.508013	+	0.861349i	$0.669620\pi$
$270$		0			0
$271$	−4.11091	−	23.3141i	−0.249720	−	1.41623i	−0.809271	−	0.587436i	$-0.800137\pi$
$271$	−4.11091	−	23.3141i	−0.249720	−	1.41623i	0.559551	−	0.828796i	$-0.310974\pi$
$272$		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	0.972603	−	0.232471i	$-0.0746811\pi$
$277$	4.74294	+	8.21502i	0.284976	+	0.493593i	−0.687628	+	0.726064i	$0.741348\pi$
$278$		0			0
$279$	16.5246	−	6.01446i	0.989302	−	0.360076i
$280$		0			0
$281$	4.22110	−	23.9391i	0.251810	−	1.42808i	−0.552321	−	0.833632i	$-0.686258\pi$
$281$	4.22110	−	23.9391i	0.251810	−	1.42808i	0.804131	−	0.594453i	$-0.202631\pi$
$282$		0			0
$283$	−8.94917	+	7.50925i	−0.531973	+	0.446378i	−0.868782	−	0.495195i	$-0.835097\pi$
$283$	−8.94917	+	7.50925i	−0.531973	+	0.446378i	0.336809	+	0.941573i	$0.390652\pi$
$284$		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	0.585012	−	0.811025i	$-0.301090\pi$
$293$	−7.01571	−	12.1516i	−0.409862	−	0.709902i	−0.994874	+	0.101122i	$0.967757\pi$
$294$		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	0.356877	−	0.934151i	$-0.383842\pi$
$307$	0.522125	+	0.190038i	0.0297993	+	0.0108460i	−0.327078	+	0.944998i	$0.606064\pi$
$308$		0			0
$309$	4.53241	+	25.7046i	0.257840	+	1.46228i
$310$		0			0
$311$	7.89478	−	13.6742i	0.447672	−	0.775390i	−0.550562	−	0.834794i	$-0.685587\pi$
$311$	7.89478	−	13.6742i	0.447672	−	0.775390i	0.998234	+	0.0594037i	$0.0189199\pi$
$312$		0			0
$313$	−17.4399	−	14.6338i	−0.985763	−	0.827153i	−0.000814014	−	1.00000i	$-0.500259\pi$
$313$	−17.4399	−	14.6338i	−0.985763	−	0.827153i	−0.984949	+	0.172846i	$0.944704\pi$
$314$		0			0
$315$	1.61131	+	2.79087i	0.0907871	+	0.157248i
$316$		0			0
$317$	17.8284	−	6.48900i	1.00134	−	0.364458i	0.211240	−	0.977434i	$-0.432250\pi$
$317$	17.8284	−	6.48900i	1.00134	−	0.364458i	0.790102	+	0.612976i	$0.210028\pi$
$318$		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	0.994406	−	0.105625i	$-0.0336843\pi$
$331$	7.38160	+	12.7853i	0.405729	+	0.702744i	−0.588677	+	0.808368i	$0.700351\pi$
$332$		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	−0.998655	−	0.0518502i	$-0.983488\pi$
$337$	−1.43116	−	8.11649i	−0.0779601	−	0.442134i	0.920695	−	0.390283i	$-0.127623\pi$
$338$		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	0.929301	+	0.369324i	$0.120411\pi$
$347$	3.39699	+	19.2653i	0.182360	+	1.03421i	−0.746941	+	0.664891i	$0.768478\pi$
$348$		0			0
$349$	−12.8829	+	22.3139i	−0.689607	+	1.19443i	0.282358	+	0.959309i	$0.408884\pi$
$349$	−12.8829	+	22.3139i	−0.689607	+	1.19443i	−0.971965	+	0.235126i	$0.924450\pi$
$350$		0			0
$351$	11.3096	+	9.48991i	0.603663	+	0.506534i
$352$		0			0
$353$	0.712979	+	1.23492i	0.0379480	+	0.0657279i	0.884376	−	0.466776i	$-0.154585\pi$
$353$	0.712979	+	1.23492i	0.0379480	+	0.0657279i	−0.846428	+	0.532504i	$0.821251\pi$
$354$		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	−0.421395	−	0.906877i	$-0.638460\pi$
$359$	7.55106	−	6.33609i	0.398530	−	0.334406i	0.819925	+	0.572471i	$0.194015\pi$
$360$		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	−0.606647	−	0.794971i	$-0.707486\pi$
$367$	−10.7351	+	3.90726i	−0.560368	+	0.203957i	0.0462791	+	0.998929i	$0.485264\pi$
$368$		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	0.282297	+	0.959327i	$0.408903\pi$
$373$	−13.3194	+	23.0699i	−0.689653	+	1.19451i	−0.971950	+	0.235187i	$0.924430\pi$
$374$		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	−0.126282	−	0.991994i	$-0.540304\pi$
$383$	−16.8435	−	6.13052i	−0.860661	−	0.313255i	−0.734379	+	0.678739i	$0.762527\pi$
$384$		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	0.121676	−	0.992570i	$-0.461173\pi$
$389$	−16.4626	−	13.8137i	−0.834685	−	0.700384i	−0.956362	+	0.292186i	$0.905617\pi$
$390$		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	−0.529560	−	0.848272i	$-0.677643\pi$
$397$	4.26129	−	3.57565i	0.213868	−	0.179457i	0.743428	+	0.668816i	$0.233199\pi$
$398$		0			0
$399$	1.16457	−	1.41048i	0.0583013	−	0.0706124i
$400$		0			0
$401$	−27.9884	+	23.4850i	−1.39767	+	1.17279i	−0.435550	+	0.900164i	$0.643446\pi$
$401$	−27.9884	+	23.4850i	−1.39767	+	1.17279i	−0.962121	+	0.272621i	$0.912109\pi$
$402$		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	0.628294	−	0.777976i	$-0.283754\pi$
$409$	−0.581665	−	0.488075i	−0.0287615	−	0.0241338i	−0.657055	+	0.753843i	$0.728198\pi$
$410$		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	−0.0254245	−	0.999677i	$-0.508094\pi$
$421$	−14.1059	−	5.13414i	−0.687481	−	0.250223i	−0.662056	+	0.749454i	$0.730316\pi$
$422$		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	−0.558634	−	0.829414i	$-0.688674\pi$
$431$	−9.41358	+	3.42626i	−0.453436	+	0.165037i	0.105198	+	0.994451i	$0.466452\pi$
$432$		0			0
$433$	0.711701	−	4.03626i	0.0342022	−	0.193970i	−0.962919	−	0.269789i	$-0.913046\pi$
$433$	0.711701	−	4.03626i	0.0342022	−	0.193970i	0.997122	+	0.0758190i	$0.0241571\pi$
$434$		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	−0.733442	−	0.679752i	$-0.762087\pi$
$439$	−4.00981	+	3.36463i	−0.191378	+	0.160585i	0.542064	+	0.840337i	$0.317643\pi$
$440$		0			0
$441$	−7.40738	+	42.0094i	−0.352733	+	2.00045i
$442$		0			0
$443$	31.8347	−	11.5869i	1.51251	−	0.550509i	0.553247	−	0.833017i	$-0.313389\pi$
$443$	31.8347	−	11.5869i	1.51251	−	0.550509i	0.959265	+	0.282508i	$0.0911665\pi$
$444$		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	−0.852862	−	0.522137i	$-0.825135\pi$
$449$	0.545695	−	0.945172i	0.0257530	−	0.0446054i	0.878615	+	0.477531i	$0.158468\pi$
$450$		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	0.998992	+	0.0448876i	$0.0142930\pi$
$461$	1.62318	+	9.20551i	0.0755991	+	0.428744i	−0.923393	+	0.383856i	$0.874596\pi$
$462$		0			0
$463$	−3.80227	+	6.58572i	−0.176706	+	0.306064i	−0.940750	−	0.339100i	$-0.889878\pi$
$463$	−3.80227	+	6.58572i	−0.176706	+	0.306064i	0.764044	+	0.645164i	$0.223211\pi$
$464$		0			0
$465$	25.2409	+	21.1796i	1.17052	+	0.982181i
$466$		0			0
$467$	17.7403	+	30.7272i	0.820925	+	1.42188i	0.904994	+	0.425424i	$0.139875\pi$
$467$	17.7403	+	30.7272i	0.820925	+	1.42188i	−0.0840686	+	0.996460i	$0.526792\pi$
$468$		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	0.644568	+	0.764547i	$0.277037\pi$
$479$	−4.87224	+	27.6318i	−0.222618	+	1.26253i	−0.867186	+	0.497984i	$0.834074\pi$
$480$		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	−0.299082	+	0.954228i	$0.596680\pi$
$487$	−21.5368	+	37.3029i	−0.975926	+	1.69035i	−0.676844	+	0.736126i	$0.736653\pi$
$488$		0			0
$489$	−4.32521	−	24.5295i	−0.195593	−	1.10926i
$490$		0			0
$491$	17.4166	+	6.33912i	0.786000	+	0.286080i	0.703672	−	0.710525i	$-0.251542\pi$
$491$	17.4166	+	6.33912i	0.786000	+	0.286080i	0.0823275	+	0.996605i	$0.473765\pi$
$492$		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	−0.400361	−	0.916358i	$-0.631115\pi$
$499$	−7.54046	−	42.7641i	−0.337557	−	1.91438i	0.0628031	−	0.998026i	$-0.479996\pi$
$500$		0			0
$501$	17.7754	−	30.7879i	0.794146	−	1.37550i
$502$		0			0
$503$	−0.819590	−	0.687718i	−0.0365437	−	0.0306638i	0.624333	−	0.781158i	$-0.285371\pi$
$503$	−0.819590	−	0.687718i	−0.0365437	−	0.0306638i	−0.660877	+	0.750495i	$0.729815\pi$
$504$		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	−0.954053	−	0.299637i	$-0.903134\pi$
$509$	1.01402	−	5.75077i	0.0449455	−	0.254899i	0.998999	+	0.0447386i	$0.0142455\pi$
$510$		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	0.964451	−	0.264263i	$-0.0851287\pi$
$521$	5.78321	+	10.0168i	0.253367	+	0.438844i	−0.711084	+	0.703107i	$0.751795\pi$
$522$		0			0
$523$	2.87535	+	2.41270i	0.125730	+	0.105500i	0.703485	−	0.710710i	$-0.251626\pi$
$523$	2.87535	+	2.41270i	0.125730	+	0.105500i	−0.577754	+	0.816211i	$0.696071\pi$
$524$		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	0.366904	−	0.930259i	$-0.380418\pi$
$541$	−11.2927	−	9.47568i	−0.485510	−	0.407391i	−0.852414	+	0.522867i	$0.824862\pi$
$542$		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	−0.999978	−	0.00663836i	$-0.997887\pi$
$547$	−1.35734	+	7.69785i	−0.0580356	+	0.329136i	0.941942	+	0.335775i	$0.108998\pi$
$548$		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	−0.358395	−	0.933570i	$-0.616676\pi$
$557$	−0.775402	+	0.282223i	−0.0328549	+	0.0119582i	0.325540	+	0.945528i	$0.394454\pi$
$558$		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	−0.810585	−	0.585621i	$-0.800851\pi$
$563$	2.41715	−	4.18662i	0.101871	−	0.176445i	0.912455	+	0.409176i	$0.134184\pi$
$564$		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	−0.806540	−	0.591179i	$-0.798663\pi$
$577$	2.61121	−	4.52275i	0.108706	−	0.188285i	0.915246	+	0.402895i	$0.131996\pi$
$578$		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	−0.539670	−	0.841877i	$-0.681451\pi$
$587$	4.74153	−	3.97861i	0.195704	−	0.164215i	0.735374	+	0.677662i	$0.237007\pi$
$588$		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	−0.864165	−	0.503209i	$-0.832153\pi$
$593$	2.92199	−	16.5715i	0.119992	−	0.680508i	0.984157	−	0.177300i	$-0.0567361\pi$
$594$		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	0.996260	−	0.0864028i	$-0.0275372\pi$
$599$	26.5345	+	22.2651i	1.08417	+	0.909726i	0.0879086	+	0.996129i	$0.471982\pi$
$600$		0			0
$601$	10.0714	−	17.4442i	0.410822	−	0.711564i	−0.584158	−	0.811640i	$-0.698575\pi$
$601$	10.0714	−	17.4442i	0.410822	−	0.711564i	0.994980	+	0.100076i	$0.0319085\pi$
$602$		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	0.999975	+	0.00706025i	$0.00224737\pi$
$613$	1.55289	+	8.80687i	0.0627206	+	0.355706i	−0.937254	+	0.348646i	$0.886642\pi$
$614$		0			0
$615$	26.8076	−	46.4321i	1.08099	−	1.87232i
$616$		0			0
$617$	16.4246	+	13.7819i	0.661230	+	0.554838i	0.910455	−	0.413607i	$-0.135731\pi$
$617$	16.4246	+	13.7819i	0.661230	+	0.554838i	−0.249225	+	0.968446i	$0.580176\pi$
$618$		0			0
$619$	−12.7984	−	22.1675i	−0.514413	−	0.890989i	−0.999860	−	0.0167229i	$-0.994677\pi$
$619$	−12.7984	−	22.1675i	−0.514413	−	0.890989i	0.485448	−	0.874266i	$-0.338657\pi$
$620$		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	−0.993059	−	0.117621i	$-0.962473\pi$
$631$	−0.493858	+	2.80081i	−0.0196602	+	0.111498i	0.973398	+	0.229119i	$0.0735845\pi$
$632$		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	0.550283	+	0.834978i	$0.314520\pi$
$641$	8.07050	+	45.7701i	0.318765	+	1.80781i	−0.231518	+	0.972831i	$0.574369\pi$
$642$		0			0
$643$	−8.80807	−	3.20587i	−0.347356	−	0.126427i	0.162450	−	0.986717i	$-0.448061\pi$
$643$	−8.80807	−	3.20587i	−0.347356	−	0.126427i	−0.509806	+	0.860290i	$0.670283\pi$
$644$		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	−0.0807056	−	0.996738i	$-0.525717\pi$
$653$	21.0269	−	36.4197i	0.822848	−	1.42521i	0.903553	−	0.428476i	$-0.140949\pi$
$654$		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	0.356192	−	0.934413i	$-0.384075\pi$
$659$	31.5671	−	11.4895i	1.22968	−	0.447567i	0.873488	+	0.486846i	$0.161853\pi$
$660$		0			0
$661$	−3.70331	+	21.0025i	−0.144042	+	0.816903i	0.824089	+	0.566460i	$0.191687\pi$
$661$	−3.70331	+	21.0025i	−0.144042	+	0.816903i	−0.968131	+	0.250443i	$0.919424\pi$
$662$		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	0.983390	+	0.181504i	$0.0580964\pi$
$673$	16.8335	+	29.1564i	0.648882	+	1.12390i	−0.334508	+	0.942393i	$0.608570\pi$
$674$		0			0
$675$	67.5385	+	56.6715i	2.59956	+	2.18129i
$676$		0			0
$677$	−16.2965	+	28.2264i	−0.626327	+	1.08483i	0.361956	+	0.932195i	$0.382109\pi$
$677$	−16.2965	+	28.2264i	−0.626327	+	1.08483i	−0.988283	+	0.152635i	$0.951224\pi$
$678$		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	−0.315425	−	0.948950i	$-0.602147\pi$
$691$	17.4572	−	30.2367i	0.664102	−	1.15026i	0.979528	−	0.201309i	$-0.0645195\pi$
$692$		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	−0.607196	−	0.794552i	$-0.707706\pi$
$701$	1.84929	−	1.55174i	0.0698467	−	0.0586084i	0.677043	+	0.735944i	$0.263261\pi$
$702$		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	−0.416151	−	0.909296i	$-0.636621\pi$
$709$	−4.00623	+	1.45815i	−0.150457	+	0.0547619i	0.265694	+	0.964057i	$0.414399\pi$
$710$		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	−0.226630	−	0.973981i	$-0.572771\pi$
$719$	−27.5194	−	10.0162i	−1.02630	−	0.373543i	−0.799671	+	0.600438i	$0.794993\pi$
$720$		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	−0.757110	−	0.653287i	$-0.773389\pi$
$727$	−7.25564	−	41.1488i	−0.269097	−	1.52612i	0.488013	−	0.872836i	$-0.337722\pi$
$728$		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	0.834316	−	0.551286i	$-0.185863\pi$
$733$	−1.63173	−	2.82624i	−0.0602693	−	0.104390i	−0.894586	+	0.446896i	$0.852529\pi$
$734$		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	−0.581093	−	0.813837i	$-0.697375\pi$
$739$	3.24786	−	2.72528i	0.119474	−	0.100251i	0.700567	+	0.713586i	$0.252930\pi$
$740$		0			0
$741$	20.3437	−	3.75400i	0.747344	−	0.137907i
$742$		0			0
$743$	−12.3449	+	10.3586i	−0.452889	+	0.380019i	−0.840507	−	0.541801i	$-0.817742\pi$
$743$	−12.3449	+	10.3586i	−0.452889	+	0.380019i	0.387618	+	0.921820i	$0.373298\pi$
$744$		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	0.0179232	−	0.999839i	$-0.494295\pi$
$751$	−26.4072	−	22.1583i	−0.963614	−	0.808568i	−0.981537	+	0.191271i	$0.938739\pi$
$752$		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	−0.128542	−	0.991704i	$-0.541030\pi$
$757$	−23.7846	−	8.65689i	−0.864466	−	0.314640i	−0.735924	+	0.677064i	$0.763252\pi$
$758$		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	0.979736	−	0.200292i	$-0.0641891\pi$
$769$	26.4169	+	22.1664i	0.952616	+	0.799340i	−0.0271198	+	0.999632i	$0.508634\pi$
$770$		0			0
$771$	−40.9617	−	70.9477i	−1.47520	−	2.55512i
$772$		0			0
$773$	45.5996	−	16.5969i	1.64010	−	0.596948i	0.653045	−	0.757319i	$-0.273491\pi$
$773$	45.5996	−	16.5969i	1.64010	−	0.596948i	0.987057	+	0.160371i	$0.0512689\pi$
$774$		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	−0.892694	−	0.450663i	$-0.851188\pi$
$787$	−23.4705	−	40.6521i	−0.836633	−	1.44909i	0.0560615	−	0.998427i	$-0.482146\pi$
$788$		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	−0.998036	−	0.0626411i	$-0.980048\pi$
$809$	−15.7365	−	27.2565i	−0.553267	−	0.958286i	0.444769	−	0.895645i	$-0.353286\pi$
$810$		0			0
$811$	−39.7312	+	14.4610i	−1.39515	+	0.507793i	−0.926735	−	0.375716i	$-0.877397\pi$
$811$	−39.7312	+	14.4610i	−1.39515	+	0.507793i	−0.468415	+	0.883509i	$0.655175\pi$
$812$		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	0.869440	+	0.494039i	$0.164480\pi$
$821$	−3.33917	+	18.9374i	−0.116538	+	0.660919i	−0.985977	+	0.166879i	$0.946631\pi$
$822$		0			0
$823$	24.9230	−	9.07122i	0.868760	−	0.316203i	0.131095	−	0.991370i	$-0.458151\pi$
$823$	24.9230	−	9.07122i	0.868760	−	0.316203i	0.737665	+	0.675167i	$0.235928\pi$
$824$		0			0
$825$	−9.93358	−	17.2055i	−0.345843	−	0.599018i
$826$		0			0
$827$	−13.3929	−	11.2380i	−0.465718	−	0.390784i	0.379512	−	0.925187i	$-0.376092\pi$
$827$	−13.3929	−	11.2380i	−0.465718	−	0.390784i	−0.845230	+	0.534403i	$0.820536\pi$
$828$		0			0
$829$	−12.9372	+	22.4079i	−0.449328	+	0.778259i	−0.998342	−	0.0575537i	$-0.981670\pi$
$829$	−12.9372	+	22.4079i	−0.449328	+	0.778259i	0.549014	+	0.835813i	$0.315003\pi$
$830$		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	0.891922	−	0.452189i	$-0.149357\pi$
$839$	37.2066	+	13.5421i	1.28451	+	0.467524i	0.392591	+	0.919713i	$0.371579\pi$
$840$		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	−0.953323	−	0.301951i	$-0.902362\pi$
$853$	−23.9929	+	20.1325i	−0.821502	+	0.689322i	0.131821	+	0.991274i	$0.457918\pi$
$854$		0			0
$855$	33.8029	−	95.2193i	1.15603	−	3.25643i
$856$		0			0
$857$	−12.5482	+	10.5292i	−0.428637	+	0.359669i	−0.831437	−	0.555619i	$-0.812481\pi$
$857$	−12.5482	+	10.5292i	−0.428637	+	0.359669i	0.402800	+	0.915288i	$0.368037\pi$
$858$		0			0
$859$	−6.23449	+	35.3576i	−0.212718	+	1.20638i	0.672105	+	0.740456i	$0.265391\pi$
$859$	−6.23449	+	35.3576i	−0.212718	+	1.20638i	−0.884823	+	0.465928i	$0.845721\pi$
$860$		0			0
$861$	−1.84644	+	0.672051i	−0.0629266	+	0.0229034i
$862$		0			0
$863$	−19.3886	−	33.5820i	−0.659995	−	1.14314i	−0.980616	−	0.195938i	$-0.937225\pi$
$863$	−19.3886	−	33.5820i	−0.659995	−	1.14314i	0.320621	−	0.947207i	$-0.396108\pi$
$864$		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	0.118904	−	0.992906i	$-0.462062\pi$
$877$	−12.6819	−	4.61584i	−0.428238	−	0.155866i	−0.547142	+	0.837040i	$0.684284\pi$
$878$		0			0
$879$	7.35445	+	41.7091i	0.248059	+	1.40681i
$880$		0			0
$881$	3.03251	−	5.25246i	0.102168	−	0.176960i	−0.810410	−	0.585864i	$-0.800755\pi$
$881$	3.03251	−	5.25246i	0.102168	−	0.176960i	0.912578	+	0.408904i	$0.134089\pi$
$882$		0			0
$883$	−5.42261	−	4.55011i	−0.182485	−	0.153123i	0.546969	−	0.837153i	$-0.315782\pi$
$883$	−5.42261	−	4.55011i	−0.182485	−	0.153123i	−0.729454	+	0.684029i	$0.760226\pi$
$884$		0			0
$885$	13.5723	+	23.5079i	0.456228	+	0.790209i
$886$		0			0
$887$	−42.7141	+	15.5466i	−1.43420	+	0.522005i	−0.938132	−	0.346279i	$-0.887445\pi$
$887$	−42.7141	+	15.5466i	−1.43420	+	0.522005i	−0.496066	+	0.868285i	$0.665223\pi$
$888$		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	−0.859360	−	0.511370i	$-0.829138\pi$
$907$	−6.82814	−	38.7243i	−0.226725	−	1.28582i	0.632636	−	0.774450i	$-0.281973\pi$
$908$		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	−0.694390	−	0.719599i	$-0.744326\pi$
$919$	8.36681	−	14.4917i	0.275996	−	0.478039i	0.970386	+	0.241560i	$0.0776591\pi$
$920$		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	−0.545049	−	0.838404i	$-0.683489\pi$
$929$	5.66832	−	4.75629i	0.185972	−	0.156049i	0.731020	+	0.682356i	$0.239044\pi$
$930$		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	−0.736423	−	0.676521i	$-0.763487\pi$
$937$	−26.4994	+	9.64498i	−0.865697	+	0.315088i	−0.129273	+	0.991609i	$0.541265\pi$
$938$		0			0
$939$	34.3589	+	59.5113i	1.12126	+	1.94208i
$940$		0			0
$941$	39.9787	+	33.5461i	1.30327	+	1.09357i	0.989570	+	0.144050i	$0.0460125\pi$
$941$	39.9787	+	33.5461i	1.30327	+	1.09357i	0.313698	+	0.949523i	$0.398432\pi$
$942$		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	−0.0430549	−	0.999073i	$-0.513709\pi$
$947$	−22.1023	−	8.04458i	−0.718228	−	0.261414i	−0.675174	+	0.737659i	$0.735931\pi$
$948$		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	−0.298004	−	0.954565i	$-0.596321\pi$
$953$	−35.1886	−	12.8076i	−1.13987	−	0.414879i	−0.841867	+	0.539686i	$0.818543\pi$
$954$		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	−0.952165	−	0.305585i	$-0.901148\pi$
$967$	−25.3924	+	21.3068i	−0.816565	+	0.685179i	0.135600	+	0.990764i	$0.456704\pi$
$968$		0			0
$969$	−42.6591	+	25.0831i	−1.37041	+	0.805787i
$970$		0			0
$971$	−12.1983	+	10.2356i	−0.391462	+	0.328476i	−0.817182	−	0.576379i	$-0.804465\pi$
$971$	−12.1983	+	10.2356i	−0.391462	+	0.328476i	0.425720	+	0.904855i	$0.360021\pi$
$972$		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	0.850425	−	0.526096i	$-0.176345\pi$
$977$	−0.950197	−	1.64579i	−0.0303995	−	0.0526535i	−0.880825	+	0.473442i	$0.843011\pi$
$978$		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	−0.996795	−	0.0799929i	$-0.974510\pi$
$983$	−2.74254	−	15.5537i	−0.0874733	−	0.496086i	0.909322	−	0.416093i	$-0.136601\pi$
$984$		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	0.844498	−	0.535559i	$-0.179899\pi$
$991$	36.1131	+	13.1441i	1.14717	+	0.417536i	0.302672	+	0.953095i	$0.402121\pi$
$992$		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	0.737213	−	0.675660i	$-0.236141\pi$
$997$	6.30982	+	5.29457i	0.199834	+	0.167681i	−0.537379	+	0.843341i	$0.680586\pi$
$998$		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.25.1	✓	12
3.2	odd	2		684.2.bo.c.253.2		12
4.3	odd	2		304.2.u.e.177.2		12
19.4	even	9		1444.2.a.h.1.6		6
19.6	even	9		1444.2.e.g.653.1		12
19.9	even	9		1444.2.e.g.429.1		12
19.10	odd	18		1444.2.e.h.429.6		12
19.13	odd	18		1444.2.e.h.653.6		12
19.15	odd	18		1444.2.a.g.1.1		6
19.16	even	9	inner	76.2.i.a.73.1	yes	12
57.35	odd	18		684.2.bo.c.73.2		12
76.15	even	18		5776.2.a.by.1.6		6
76.23	odd	18		5776.2.a.bw.1.1		6
76.35	odd	18		304.2.u.e.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.i.a.25.1	✓	12	1.1	even	1	trivial
76.2.i.a.73.1	yes	12	19.16	even	9	inner
304.2.u.e.177.2		12	4.3	odd	2
304.2.u.e.225.2		12	76.35	odd	18
684.2.bo.c.73.2		12	57.35	odd	18
684.2.bo.c.253.2		12	3.2	odd	2
1444.2.a.g.1.1		6	19.15	odd	18
1444.2.a.h.1.6		6	19.4	even	9
1444.2.e.g.429.1		12	19.9	even	9
1444.2.e.g.653.1		12	19.6	even	9
1444.2.e.h.429.6		12	19.10	odd	18
1444.2.e.h.653.6		12	19.13	odd	18
5776.2.a.bw.1.1		6	76.23	odd	18
5776.2.a.by.1.6		6	76.15	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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