LMFDB - Embedded newform 228.2.q.a.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(25,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("228.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.q (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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			157.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	228.157
Dual form			228.2.q.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{3} +(1.93969 + 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{3} +(1.93969 + 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(-1.05303 - 5.97205i) q^{13} +(1.93969 - 1.62760i) q^{15} +(5.58512 - 2.03282i) q^{17} +(4.34002 + 0.405223i) q^{19} +(3.03209 - 1.10359i) q^{21} +(-5.14543 + 4.31753i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-6.69846 - 2.43804i) q^{29} +(-3.81908 - 6.61484i) q^{31} +(2.37939 + 1.99654i) q^{33} +(-1.41875 + 8.04612i) q^{35} +2.10607 q^{37} -6.06418 q^{39} +(-1.22281 + 6.93491i) q^{41} +(-7.17752 - 6.02265i) q^{43} +(-1.26604 - 2.19285i) q^{45} +(4.37211 + 1.59132i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(-1.03209 - 5.85327i) q^{51} +(-4.86824 + 4.08494i) q^{53} +(-7.39053 + 2.68993i) q^{55} +(1.15270 - 4.20372i) q^{57} +(0.252374 - 0.0918566i) q^{59} +(1.21688 - 1.02108i) q^{61} +(-0.560307 - 3.17766i) q^{63} +(7.67752 - 13.2979i) q^{65} +(1.22668 + 0.446476i) q^{67} +(3.35844 + 5.81699i) q^{69} +(-6.34002 - 5.31991i) q^{71} +(0.159978 - 0.907278i) q^{73} +1.41147 q^{75} -10.0223 q^{77} +(-2.09492 + 11.8809i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-0.0432332 - 0.0748822i) q^{83} +(14.1420 + 5.14728i) q^{85} +(-3.56418 + 6.17334i) q^{87} +(-1.22803 - 6.96448i) q^{89} +(14.9893 - 12.5775i) q^{91} +(-7.17752 + 2.61240i) q^{93} +(7.75877 + 7.84981i) q^{95} +(-3.12701 + 1.13814i) q^{97} +(2.37939 - 1.99654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 6 * q^5 + 3 * q^7	$ 6 q + 6 q^{5} + 3 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 12 q^{17} + 6 q^{19} + 9 q^{21} - 15 q^{23} - 3 q^{27} - 12 q^{29} - 6 q^{31} + 3 q^{33} - 6 q^{35} - 12 q^{37} - 18 q^{39} - 18 q^{41} - 18 q^{43} - 3 q^{45} - 3 q^{47} + 3 q^{51} - 24 q^{53} - 27 q^{55} + 9 q^{57} + 18 q^{59} - 9 q^{61} - 9 q^{63} + 21 q^{65} - 6 q^{67} + 12 q^{69} - 18 q^{71} + 21 q^{73} - 12 q^{75} - 48 q^{77} + 6 q^{79} + 15 q^{83} + 27 q^{85} - 3 q^{87} + 15 q^{89} + 30 q^{91} - 18 q^{93} + 24 q^{95} + 9 q^{97} + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^5 + 3 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 12 * q^17 + 6 * q^19 + 9 * q^21 - 15 * q^23 - 3 * q^27 - 12 * q^29 - 6 * q^31 + 3 * q^33 - 6 * q^35 - 12 * q^37 - 18 * q^39 - 18 * q^41 - 18 * q^43 - 3 * q^45 - 3 * q^47 + 3 * q^51 - 24 * q^53 - 27 * q^55 + 9 * q^57 + 18 * q^59 - 9 * q^61 - 9 * q^63 + 21 * q^65 - 6 * q^67 + 12 * q^69 - 18 * q^71 + 21 * q^73 - 12 * q^75 - 48 * q^77 + 6 * q^79 + 15 * q^83 + 27 * q^85 - 3 * q^87 + 15 * q^89 + 30 * q^91 - 18 * q^93 + 24 * q^95 + 9 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$		0			0
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	0.963561	−	0.267489i	$-0.0861937\pi$
$5$	1.93969	+	1.62760i	0.867457	+	0.727883i	−0.0961041	+	0.995371i	$0.530638\pi$
$6$		0			0
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	0.991275	+	0.131806i	$0.0420778\pi$
$7$	1.61334	+	2.79439i	0.609786	+	1.05618i	−0.381490	+	0.924373i	$0.624589\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	−0.999342	−	0.0362735i	$-0.988451\pi$
$11$	−1.55303	+	2.68993i	−0.468257	+	0.811045i	0.531085	+	0.847319i	$0.321785\pi$
$12$		0			0
$13$	−1.05303	−	5.97205i	−0.292059	−	1.65635i	−0.678921	−	0.734211i	$-0.737552\pi$
$13$	−1.05303	−	5.97205i	−0.292059	−	1.65635i	0.386862	−	0.922137i	$-0.373559\pi$
$14$		0			0
$15$	1.93969	−	1.62760i	0.500826	−	0.420243i
$16$		0			0
$17$	5.58512	−	2.03282i	1.35459	−	0.493031i	0.440213	−	0.897893i	$-0.354903\pi$
$17$	5.58512	−	2.03282i	1.35459	−	0.493031i	0.914378	+	0.404862i	$0.132681\pi$
$18$		0			0
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$19$	4.34002	+	0.405223i	0.995669	+	0.0929645i
$20$		0			0
$21$	3.03209	−	1.10359i	0.661656	−	0.240823i
$22$		0			0
$23$	−5.14543	+	4.31753i	−1.07290	+	0.900267i	−0.995312	−	0.0967189i	$-0.969165\pi$
$23$	−5.14543	+	4.31753i	−1.07290	+	0.900267i	−0.0775845	+	0.996986i	$0.524721\pi$
$24$		0			0
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−6.69846	−	2.43804i	−1.24387	−	0.452733i	−0.365546	−	0.930793i	$-0.619118\pi$
$29$	−6.69846	−	2.43804i	−1.24387	−	0.452733i	−0.878327	+	0.478060i	$0.841340\pi$
$30$		0			0
$31$	−3.81908	−	6.61484i	−0.685927	−	1.18806i	−0.973145	−	0.230195i	$-0.926064\pi$
$31$	−3.81908	−	6.61484i	−0.685927	−	1.18806i	0.287218	−	0.957865i	$-0.407270\pi$
$32$		0			0
$33$	2.37939	+	1.99654i	0.414198	+	0.347553i
$34$		0			0
$35$	−1.41875	+	8.04612i	−0.239812	+	1.36004i
$36$		0			0
$37$	2.10607			0.346235			0.173118	−	0.984901i	$-0.444616\pi$
$37$	2.10607			0.346235			0.173118	+	0.984901i	$0.444616\pi$
$38$		0			0
$39$	−6.06418			−0.971046
$40$		0			0
$41$	−1.22281	+	6.93491i	−0.190971	+	1.08305i	0.727069	+	0.686564i	$0.240882\pi$
$41$	−1.22281	+	6.93491i	−0.190971	+	1.08305i	−0.918041	+	0.396487i	$0.870229\pi$
$42$		0			0
$43$	−7.17752	−	6.02265i	−1.09456	−	0.918446i	−0.0975139	−	0.995234i	$-0.531089\pi$
$43$	−7.17752	−	6.02265i	−1.09456	−	0.918446i	−0.997047	+	0.0767882i	$0.975533\pi$
$44$		0			0
$45$	−1.26604	−	2.19285i	−0.188731	−	0.326891i
$46$		0			0
$47$	4.37211	+	1.59132i	0.637738	+	0.232118i	0.640596	−	0.767878i	$-0.278687\pi$
$47$	4.37211	+	1.59132i	0.637738	+	0.232118i	−0.00285780	+	0.999996i	$0.500910\pi$
$48$		0			0
$49$	−1.70574	+	2.95442i	−0.243677	+	0.422060i
$50$		0			0
$51$	−1.03209	−	5.85327i	−0.144521	−	0.819621i
$52$		0			0
$53$	−4.86824	+	4.08494i	−0.668704	+	0.561110i	−0.912682	−	0.408671i	$-0.865992\pi$
$53$	−4.86824	+	4.08494i	−0.668704	+	0.561110i	0.243977	+	0.969781i	$0.421548\pi$
$54$		0			0
$55$	−7.39053	+	2.68993i	−0.996539	+	0.362710i
$56$		0			0
$57$	1.15270	−	4.20372i	0.152679	−	0.556797i
$58$		0			0
$59$	0.252374	−	0.0918566i	0.0328563	−	0.0119587i	−0.325540	−	0.945528i	$-0.605546\pi$
$59$	0.252374	−	0.0918566i	0.0328563	−	0.0119587i	0.358396	+	0.933570i	$0.383324\pi$
$60$		0			0
$61$	1.21688	−	1.02108i	0.155806	−	0.130737i	−0.561552	−	0.827441i	$-0.689796\pi$
$61$	1.21688	−	1.02108i	0.155806	−	0.130737i	0.717358	+	0.696705i	$0.245351\pi$
$62$		0			0
$63$	−0.560307	−	3.17766i	−0.0705921	−	0.400348i
$64$		0			0
$65$	7.67752	−	13.2979i	0.952279	−	1.64940i
$66$		0			0
$67$	1.22668	+	0.446476i	0.149863	+	0.0545457i	0.415863	−	0.909427i	$-0.363480\pi$
$67$	1.22668	+	0.446476i	0.149863	+	0.0545457i	−0.266000	+	0.963973i	$0.585702\pi$
$68$		0			0
$69$	3.35844	+	5.81699i	0.404309	+	0.700283i
$70$		0			0
$71$	−6.34002	−	5.31991i	−0.752422	−	0.631357i	0.183720	−	0.982979i	$-0.441186\pi$
$71$	−6.34002	−	5.31991i	−0.752422	−	0.631357i	−0.936142	+	0.351621i	$0.885630\pi$
$72$		0			0
$73$	0.159978	−	0.907278i	0.0187240	−	0.106189i	−0.974013	−	0.226490i	$-0.927275\pi$
$73$	0.159978	−	0.907278i	0.0187240	−	0.106189i	0.992737	+	0.120301i	$0.0383860\pi$
$74$		0			0
$75$	1.41147			0.162983
$76$		0			0
$77$	−10.0223			−1.14215
$78$		0			0
$79$	−2.09492	+	11.8809i	−0.235697	+	1.33671i	0.605443	+	0.795888i	$0.292996\pi$
$79$	−2.09492	+	11.8809i	−0.235697	+	1.33671i	−0.841140	+	0.540817i	$0.818115\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−0.0432332	−	0.0748822i	−0.00474546	−	0.00821939i	0.863643	−	0.504104i	$-0.168177\pi$
$83$	−0.0432332	−	0.0748822i	−0.00474546	−	0.00821939i	−0.868388	+	0.495885i	$0.834844\pi$
$84$		0			0
$85$	14.1420	+	5.14728i	1.53392	+	0.558301i
$86$		0			0
$87$	−3.56418	+	6.17334i	−0.382120	+	0.661851i
$88$		0			0
$89$	−1.22803	−	6.96448i	−0.130170	−	0.738233i	−0.978102	−	0.208127i	$-0.933263\pi$
$89$	−1.22803	−	6.96448i	−0.130170	−	0.738233i	0.847931	−	0.530106i	$-0.177848\pi$
$90$		0			0
$91$	14.9893	−	12.5775i	1.57131	−	1.31848i
$92$		0			0
$93$	−7.17752	+	2.61240i	−0.744274	+	0.270894i
$94$		0			0
$95$	7.75877	+	7.84981i	0.796033	+	0.805373i
$96$		0			0
$97$	−3.12701	+	1.13814i	−0.317500	+	0.115561i	−0.495854	−	0.868406i	$-0.665145\pi$
$97$	−3.12701	+	1.13814i	−0.317500	+	0.115561i	0.178354	+	0.983966i	$0.442923\pi$
$98$		0			0
$99$	2.37939	−	1.99654i	0.239137	−	0.200660i
$100$		0			0
$101$	−1.86824	−	10.5953i	−0.185897	−	1.05427i	−0.924798	−	0.380459i	$-0.875766\pi$
$101$	−1.86824	−	10.5953i	−0.185897	−	1.05427i	0.738901	−	0.673814i	$-0.235345\pi$
$102$		0			0
$103$	−2.96451	+	5.13468i	−0.292102	+	0.505935i	−0.974306	−	0.225226i	$-0.927688\pi$
$103$	−2.96451	+	5.13468i	−0.292102	+	0.505935i	0.682205	+	0.731161i	$0.261021\pi$
$104$		0			0
$105$	7.67752	+	2.79439i	0.749249	+	0.272704i
$106$		0			0
$107$	−1.29086	−	2.23583i	−0.124792	−	0.216146i	0.796860	−	0.604165i	$-0.206493\pi$
$107$	−1.29086	−	2.23583i	−0.124792	−	0.216146i	−0.921652	+	0.388018i	$0.873160\pi$
$108$		0			0
$109$	3.66250	+	3.07321i	0.350804	+	0.294360i	0.801113	−	0.598513i	$-0.204242\pi$
$109$	3.66250	+	3.07321i	0.350804	+	0.294360i	−0.450309	+	0.892873i	$0.648686\pi$
$110$		0			0
$111$	0.365715	−	2.07407i	0.0347121	−	0.196862i
$112$		0			0
$113$	16.6655			1.56776			0.783879	−	0.620914i	$-0.213238\pi$
$113$	16.6655			1.56776			0.783879	+	0.620914i	$0.213238\pi$
$114$		0			0
$115$	−17.0077			−1.58598
$116$		0			0
$117$	−1.05303	+	5.97205i	−0.0973530	+	0.552116i
$118$		0			0
$119$	14.6912	+	12.3274i	1.34674	+	1.13005i
$120$		0			0
$121$	0.676174	+	1.17117i	0.0614704	+	0.106470i
$122$		0			0
$123$	6.61721	+	2.40847i	0.596654	+	0.217164i
$124$		0			0
$125$	4.54323	−	7.86911i	0.406359	−	0.703835i
$126$		0			0
$127$	0.906260	+	5.13965i	0.0804175	+	0.456070i	0.998252	+	0.0591064i	$0.0188251\pi$
$127$	0.906260	+	5.13965i	0.0804175	+	0.456070i	−0.917834	+	0.396964i	$0.870064\pi$
$128$		0			0
$129$	−7.17752	+	6.02265i	−0.631945	+	0.530265i
$130$		0			0
$131$	8.13563	−	2.96113i	0.710813	−	0.258715i	0.0387926	−	0.999247i	$-0.487649\pi$
$131$	8.13563	−	2.96113i	0.710813	−	0.258715i	0.672021	+	0.740532i	$0.265427\pi$
$132$		0			0
$133$	5.86959	+	12.7815i	0.508958	+	1.10829i
$134$		0			0
$135$	−2.37939	+	0.866025i	−0.204785	+	0.0745356i
$136$		0			0
$137$	−10.4684	+	8.78401i	−0.894374	+	0.750469i	−0.969083	−	0.246737i	$-0.920642\pi$
$137$	−10.4684	+	8.78401i	−0.894374	+	0.750469i	0.0747087	+	0.997205i	$0.476197\pi$
$138$		0			0
$139$	−2.37551	−	13.4722i	−0.201489	−	1.14270i	−0.902870	−	0.429913i	$-0.858544\pi$
$139$	−2.37551	−	13.4722i	−0.201489	−	1.14270i	0.701382	−	0.712786i	$-0.252567\pi$
$140$		0			0
$141$	2.32635	−	4.02936i	0.195914	−	0.339333i
$142$		0			0
$143$	17.6998	+	6.44220i	1.48013	+	0.538724i
$144$		0			0
$145$	−9.02481	−	15.6314i	−0.749470	−	1.29812i
$146$		0			0
$147$	2.61334	+	2.19285i	0.215545	+	0.180863i
$148$		0			0
$149$	4.12314	−	23.3835i	0.337781	−	1.91565i	−0.0600574	−	0.998195i	$-0.519128\pi$
$149$	4.12314	−	23.3835i	0.337781	−	1.91565i	0.397838	−	0.917456i	$-0.369761\pi$
$150$		0			0
$151$	8.33544			0.678328			0.339164	−	0.940727i	$-0.389856\pi$
$151$	8.33544			0.678328			0.339164	+	0.940727i	$0.389856\pi$
$152$		0			0
$153$	−5.94356			−0.480509
$154$		0			0
$155$	3.35844	−	19.0467i	0.269756	−	1.52986i
$156$		0			0
$157$	16.6197	+	13.9456i	1.32640	+	1.11298i	0.984905	+	0.173098i	$0.0553776\pi$
$157$	16.6197	+	13.9456i	1.32640	+	1.11298i	0.341495	+	0.939884i	$0.389067\pi$
$158$		0			0
$159$	3.17752	+	5.50362i	0.251994	+	0.436466i
$160$		0			0
$161$	−20.3662	−	7.41268i	−1.60508	−	0.584201i
$162$		0			0
$163$	11.4927	−	19.9060i	0.900180	−	1.55916i	0.0729198	−	0.997338i	$-0.476768\pi$
$163$	11.4927	−	19.9060i	0.900180	−	1.55916i	0.827260	−	0.561819i	$-0.189898\pi$
$164$		0			0
$165$	1.36571	+	7.74535i	0.106321	+	0.602975i
$166$		0			0
$167$	−5.85710	+	4.91469i	−0.453236	+	0.380310i	−0.840635	−	0.541602i	$-0.817818\pi$
$167$	−5.85710	+	4.91469i	−0.453236	+	0.380310i	0.387399	+	0.921912i	$0.373374\pi$
$168$		0			0
$169$	−22.3405	+	8.13127i	−1.71850	+	0.625483i
$170$		0			0
$171$	−3.93969	−	1.86516i	−0.301276	−	0.142632i
$172$		0			0
$173$	−11.0360	+	4.01676i	−0.839048	+	0.305389i	−0.725567	−	0.688151i	$-0.758422\pi$
$173$	−11.0360	+	4.01676i	−0.839048	+	0.305389i	−0.113481	+	0.993540i	$0.536200\pi$
$174$		0			0
$175$	−3.48886	+	2.92750i	−0.263733	+	0.221298i
$176$		0			0
$177$	−0.0466368	−	0.264490i	−0.00350544	−	0.0198803i
$178$		0			0
$179$	2.09879	−	3.63522i	0.156871	−	0.271709i	−0.776868	−	0.629664i	$-0.783193\pi$
$179$	2.09879	−	3.63522i	0.156871	−	0.271709i	0.933739	+	0.357955i	$0.116526\pi$
$180$		0			0
$181$	−11.5842	−	4.21632i	−0.861050	−	0.313397i	−0.126513	−	0.991965i	$-0.540379\pi$
$181$	−11.5842	−	4.21632i	−0.861050	−	0.313397i	−0.734537	+	0.678568i	$0.762601\pi$
$182$		0			0
$183$	−0.794263	−	1.37570i	−0.0587136	−	0.101695i
$184$		0			0
$185$	4.08512	+	3.42782i	0.300344	+	0.252019i
$186$		0			0
$187$	−3.20574	+	18.1806i	−0.234427	+	1.32950i
$188$		0			0
$189$	−3.22668			−0.234707
$190$		0			0
$191$	−10.2044			−0.738364			−0.369182	−	0.929357i	$-0.620362\pi$
$191$	−10.2044			−0.738364			−0.369182	+	0.929357i	$0.620362\pi$
$192$		0			0
$193$	−3.76945	+	21.3776i	−0.271331	+	1.53879i	0.479050	+	0.877788i	$0.340981\pi$
$193$	−3.76945	+	21.3776i	−0.271331	+	1.53879i	−0.750381	+	0.661006i	$0.770130\pi$
$194$		0			0
$195$	−11.7626	−	9.87003i	−0.842340	−	0.706807i
$196$		0			0
$197$	8.34255	+	14.4497i	0.594382	+	1.02950i	0.993634	+	0.112658i	$0.0359366\pi$
$197$	8.34255	+	14.4497i	0.594382	+	1.02950i	−0.399252	+	0.916841i	$0.630730\pi$
$198$		0			0
$199$	2.31180	+	0.841428i	0.163879	+	0.0596472i	0.422657	−	0.906290i	$-0.361097\pi$
$199$	2.31180	+	0.841428i	0.163879	+	0.0596472i	−0.258778	+	0.965937i	$0.583320\pi$
$200$		0			0
$201$	0.652704	−	1.13052i	0.0460382	−	0.0797404i
$202$		0			0
$203$	−3.99407	−	22.6515i	−0.280329	−	1.58982i
$204$		0			0
$205$	−13.6591	+	11.4613i	−0.953993	+	0.800495i
$206$		0			0
$207$	6.31180	−	2.29731i	0.438701	−	0.159674i
$208$		0			0
$209$	−7.83022	+	11.0450i	−0.541628	+	0.764002i
$210$		0			0
$211$	1.15745	−	0.421278i	0.0796822	−	0.0290020i	−0.301871	−	0.953349i	$-0.597611\pi$
$211$	1.15745	−	0.421278i	0.0796822	−	0.0290020i	0.381554	+	0.924347i	$0.375389\pi$
$212$		0			0
$213$	−6.34002	+	5.31991i	−0.434411	+	0.364514i
$214$		0			0
$215$	−4.11974	−	23.3642i	−0.280964	−	1.59342i
$216$		0			0
$217$	12.3229	−	21.3440i	0.836536	−	1.44892i
$218$		0			0
$219$	−0.865715	−	0.315094i	−0.0584996	−	0.0212921i
$220$		0			0
$221$	−18.0214	−	31.2140i	−1.21225	−	2.09968i
$222$		0			0
$223$	5.03983	+	4.22892i	0.337492	+	0.283189i	0.795744	−	0.605633i	$-0.207080\pi$
$223$	5.03983	+	4.22892i	0.337492	+	0.283189i	−0.458252	+	0.888822i	$0.651524\pi$
$224$		0			0
$225$	0.245100	−	1.39003i	0.0163400	−	0.0926687i
$226$		0			0
$227$	9.72967			0.645781			0.322891	−	0.946436i	$-0.395345\pi$
$227$	9.72967			0.645781			0.322891	+	0.946436i	$0.395345\pi$
$228$		0			0
$229$	−9.86753			−0.652064			−0.326032	−	0.945359i	$-0.605712\pi$
$229$	−9.86753			−0.652064			−0.326032	+	0.945359i	$0.605712\pi$
$230$		0			0
$231$	−1.74035	+	9.87003i	−0.114507	+	0.649400i
$232$		0			0
$233$	16.7121	+	14.0231i	1.09485	+	0.918687i	0.997068	−	0.0765212i	$-0.0243813\pi$
$233$	16.7121	+	14.0231i	1.09485	+	0.918687i	0.0977803	+	0.995208i	$0.468826\pi$
$234$		0			0
$235$	5.89053	+	10.2027i	0.384256	+	0.665551i
$236$		0			0
$237$	11.3366	+	4.12619i	0.736393	+	0.268025i
$238$		0			0
$239$	−10.6557	+	18.4562i	−0.689260	+	1.19383i	0.282818	+	0.959174i	$0.408731\pi$
$239$	−10.6557	+	18.4562i	−0.689260	+	1.19383i	−0.972078	+	0.234659i	$0.924603\pi$
$240$		0			0
$241$	2.71688	+	15.4082i	0.175010	+	0.992529i	0.938133	+	0.346276i	$0.112554\pi$
$241$	2.71688	+	15.4082i	0.175010	+	0.992529i	−0.763123	+	0.646253i	$0.776335\pi$
$242$		0			0
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$		0			0
$245$	−8.11721	+	2.95442i	−0.518590	+	0.188751i
$246$		0			0
$247$	−2.15018	−	26.3455i	−0.136813	−	1.67633i
$248$		0			0
$249$	−0.0812519	+	0.0295733i	−0.00514913	+	0.00187413i
$250$		0			0
$251$	−7.75356	+	6.50601i	−0.489400	+	0.410655i	−0.853811	−	0.520583i	$-0.825715\pi$
$251$	−7.75356	+	6.50601i	−0.489400	+	0.410655i	0.364411	+	0.931238i	$0.381270\pi$
$252$		0			0
$253$	−3.62284	−	20.5461i	−0.227766	−	1.29172i
$254$		0			0
$255$	7.52481	−	13.0334i	0.471222	−	0.816181i
$256$		0			0
$257$	4.49020	+	1.63430i	0.280091	+	0.101945i	0.478246	−	0.878226i	$-0.341273\pi$
$257$	4.49020	+	1.63430i	0.280091	+	0.101945i	−0.198155	+	0.980171i	$0.563495\pi$
$258$		0			0
$259$	3.39780	+	5.88517i	0.211129	+	0.365687i
$260$		0			0
$261$	5.46064	+	4.58202i	0.338005	+	0.283620i
$262$		0			0
$263$	−3.76651	+	21.3609i	−0.232253	+	1.31717i	0.616069	+	0.787692i	$0.288724\pi$
$263$	−3.76651	+	21.3609i	−0.232253	+	1.31717i	−0.848322	+	0.529480i	$0.822387\pi$
$264$		0			0
$265$	−16.0915			−0.988494
$266$		0			0
$267$	−7.07192			−0.432794
$268$		0			0
$269$	−0.561185	+	3.18264i	−0.0342160	+	0.194049i	−0.997125	−	0.0757790i	$-0.975856\pi$
$269$	−0.561185	+	3.18264i	−0.0342160	+	0.194049i	0.962909	+	0.269828i	$0.0869668\pi$
$270$		0			0
$271$	−8.97952	−	7.53471i	−0.545467	−	0.457701i	0.327935	−	0.944700i	$-0.393647\pi$
$271$	−8.97952	−	7.53471i	−0.545467	−	0.457701i	−0.873403	+	0.486999i	$0.838092\pi$
$272$		0			0
$273$	−9.78359	−	16.9457i	−0.592130	−	1.02560i
$274$		0			0
$275$	−4.11974	−	1.49946i	−0.248430	−	0.0904209i
$276$		0			0
$277$	−4.38666	+	7.59792i	−0.263569	+	0.456515i	−0.967188	−	0.254063i	$-0.918233\pi$
$277$	−4.38666	+	7.59792i	−0.263569	+	0.456515i	0.703619	+	0.710578i	$0.251566\pi$
$278$		0			0
$279$	1.32635	+	7.52211i	0.0794066	+	0.450337i
$280$		0			0
$281$	19.4702	−	16.3374i	1.16149	−	0.974609i	0.161569	−	0.986861i	$-0.448345\pi$
$281$	19.4702	−	16.3374i	1.16149	−	0.974609i	0.999925	+	0.0122521i	$0.00390007\pi$
$282$		0			0
$283$	2.51114	−	0.913982i	0.149272	−	0.0543306i	−0.266304	−	0.963889i	$-0.585802\pi$
$283$	2.51114	−	0.913982i	0.149272	−	0.0543306i	0.415576	+	0.909559i	$0.363580\pi$
$284$		0			0
$285$	9.07785	−	6.27779i	0.537725	−	0.371864i
$286$		0			0
$287$	−21.3516	+	7.77136i	−1.26035	+	0.458729i
$288$		0			0
$289$	14.0385	−	11.7797i	0.825793	−	0.692923i
$290$		0			0
$291$	0.577848	+	3.27714i	0.0338741	+	0.192109i
$292$		0			0
$293$	−9.97683	+	17.2804i	−0.582853	+	1.00953i	0.412287	+	0.911054i	$0.364730\pi$
$293$	−9.97683	+	17.2804i	−0.582853	+	1.00953i	−0.995139	+	0.0984765i	$0.968603\pi$
$294$		0			0
$295$	0.639033	+	0.232589i	0.0372059	+	0.0135419i
$296$		0			0
$297$	−1.55303	−	2.68993i	−0.0901161	−	0.156086i
$298$		0			0
$299$	31.2028	+	26.1823i	1.80450	+	1.51416i
$300$		0			0
$301$	5.24985	−	29.7734i	0.302596	−	1.71611i
$302$		0			0
$303$	−10.7588			−0.618075
$304$		0			0
$305$	4.02229			0.230316
$306$		0			0
$307$	−4.16431	+	23.6170i	−0.237670	+	1.34789i	0.599247	+	0.800564i	$0.295467\pi$
$307$	−4.16431	+	23.6170i	−0.237670	+	1.34789i	−0.836917	+	0.547330i	$0.815644\pi$
$308$		0			0
$309$	4.54189	+	3.81110i	0.258379	+	0.216806i
$310$		0			0
$311$	0.0812519	+	0.140732i	0.00460737	+	0.00798020i	0.868320	−	0.496005i	$-0.165200\pi$
$311$	0.0812519	+	0.140732i	0.00460737	+	0.00798020i	−0.863713	+	0.503985i	$0.831867\pi$
$312$		0			0
$313$	−6.31655	−	2.29904i	−0.357033	−	0.129949i	0.157275	−	0.987555i	$-0.449729\pi$
$313$	−6.31655	−	2.29904i	−0.357033	−	0.129949i	−0.514308	+	0.857606i	$0.671951\pi$
$314$		0			0
$315$	4.08512	−	7.07564i	0.230171	−	0.398667i
$316$		0			0
$317$	2.48024	+	14.0661i	0.139304	+	0.790032i	0.971765	+	0.235949i	$0.0758199\pi$
$317$	2.48024	+	14.0661i	0.139304	+	0.790032i	−0.832461	+	0.554083i	$0.813069\pi$
$318$		0			0
$319$	16.9611	−	14.2321i	0.949640	−	0.796842i
$320$		0			0
$321$	−2.42602	+	0.883000i	−0.135407	+	0.0492842i
$322$		0			0
$323$	25.0633	−	6.55926i	1.39456	−	0.364967i
$324$		0			0
$325$	8.04323	−	2.92750i	0.446158	−	0.162388i
$326$		0			0
$327$	3.66250	−	3.07321i	0.202537	−	0.169949i
$328$		0			0
$329$	2.60694	+	14.7847i	0.143725	+	0.815108i
$330$		0			0
$331$	16.6532	−	28.8441i	0.915341	−	1.58542i	0.108940	−	0.994048i	$-0.465254\pi$
$331$	16.6532	−	28.8441i	0.915341	−	1.58542i	0.806401	−	0.591369i	$-0.201412\pi$
$332$		0			0
$333$	−1.97906	−	0.720317i	−0.108452	−	0.0394731i
$334$		0			0
$335$	1.65270	+	2.86257i	0.0902968	+	0.156399i
$336$		0			0
$337$	−1.41669	−	1.18874i	−0.0771720	−	0.0647550i	0.603386	−	0.797450i	$-0.293818\pi$
$337$	−1.41669	−	1.18874i	−0.0771720	−	0.0647550i	−0.680558	+	0.732695i	$0.738262\pi$
$338$		0			0
$339$	2.89393	−	16.4123i	0.157177	−	0.891394i
$340$		0			0
$341$	23.7246			1.28476
$342$		0			0
$343$	11.5790			0.625209
$344$		0			0
$345$	−2.95336	+	16.7494i	−0.159004	+	0.901755i
$346$		0			0
$347$	−5.28493	−	4.43458i	−0.283710	−	0.238061i	0.489816	−	0.871826i	$-0.337064\pi$
$347$	−5.28493	−	4.43458i	−0.283710	−	0.238061i	−0.773525	+	0.633765i	$0.781509\pi$
$348$		0			0
$349$	5.61081	+	9.71822i	0.300340	+	0.520204i	0.976213	−	0.216814i	$-0.0695665\pi$
$349$	5.61081	+	9.71822i	0.300340	+	0.520204i	−0.675873	+	0.737018i	$0.736233\pi$
$350$		0			0
$351$	5.69846	+	2.07407i	0.304161	+	0.110706i
$352$		0			0
$353$	0.954241	−	1.65279i	0.0507891	−	0.0879693i	−0.839513	−	0.543339i	$-0.817160\pi$
$353$	0.954241	−	1.65279i	0.0507891	−	0.0879693i	0.890302	+	0.455370i	$0.150493\pi$
$354$		0			0
$355$	−3.63903	−	20.6380i	−0.193140	−	1.09535i
$356$		0			0
$357$	14.6912	−	12.3274i	0.777540	−	0.652434i
$358$		0			0
$359$	−8.95558	+	3.25957i	−0.472658	+	0.172033i	−0.567356	−	0.823473i	$-0.692034\pi$
$359$	−8.95558	+	3.25957i	−0.472658	+	0.172033i	0.0946982	+	0.995506i	$0.469811\pi$
$360$		0			0
$361$	18.6716	+	3.51735i	0.982715	+	0.185124i
$362$		0			0
$363$	1.27079	−	0.462531i	0.0666993	−	0.0242766i
$364$		0			0
$365$	1.78699	−	1.49946i	0.0935353	−	0.0784854i
$366$		0			0
$367$	3.11216	+	17.6499i	0.162453	+	0.921319i	0.951651	+	0.307180i	$0.0993854\pi$
$367$	3.11216	+	17.6499i	0.162453	+	0.921319i	−0.789198	+	0.614139i	$0.789504\pi$
$368$		0			0
$369$	3.52094	−	6.09845i	0.183293	−	0.317473i
$370$		0			0
$371$	−19.2690	−	7.01336i	−1.00040	−	0.364115i
$372$		0			0
$373$	15.2344	+	26.3868i	0.788808	+	1.36626i	0.926697	+	0.375809i	$0.122635\pi$
$373$	15.2344	+	26.3868i	0.788808	+	1.36626i	−0.137889	+	0.990448i	$0.544032\pi$
$374$		0			0
$375$	−6.96064	−	5.84067i	−0.359446	−	0.301611i
$376$		0			0
$377$	−7.50640	+	42.5709i	−0.386599	+	2.19251i
$378$		0			0
$379$	6.57903			0.337942			0.168971	−	0.985621i	$-0.445956\pi$
$379$	6.57903			0.337942			0.168971	+	0.985621i	$0.445956\pi$
$380$		0			0
$381$	5.21894			0.267374
$382$		0			0
$383$	3.99525	−	22.6582i	0.204148	−	1.15778i	−0.694627	−	0.719370i	$-0.744431\pi$
$383$	3.99525	−	22.6582i	0.204148	−	1.15778i	0.898775	−	0.438410i	$-0.144458\pi$
$384$		0			0
$385$	−19.4402	−	16.3122i	−0.990762	−	0.831348i
$386$		0			0
$387$	4.68479	+	8.11430i	0.238141	+	0.412473i
$388$		0			0
$389$	−25.6587	−	9.33900i	−1.30095	−	0.473506i	−0.403642	−	0.914917i	$-0.632256\pi$
$389$	−25.6587	−	9.33900i	−1.30095	−	0.473506i	−0.897305	+	0.441411i	$0.854478\pi$
$390$		0			0
$391$	−19.9611	+	34.5736i	−1.00948	+	1.74846i
$392$		0			0
$393$	−1.50340	−	8.52623i	−0.0758367	−	0.430091i
$394$		0			0
$395$	−23.4008	+	19.6356i	−1.17742	+	0.987974i
$396$		0			0
$397$	5.52734	−	2.01179i	0.277409	−	0.100969i	−0.199569	−	0.979884i	$-0.563954\pi$
$397$	5.52734	−	2.01179i	0.277409	−	0.100969i	0.476978	+	0.878915i	$0.341732\pi$
$398$		0			0
$399$	13.6065	−	3.56093i	0.681179	−	0.178270i
$400$		0			0
$401$	4.02987	−	1.46675i	0.201242	−	0.0732461i	−0.239433	−	0.970913i	$-0.576961\pi$
$401$	4.02987	−	1.46675i	0.201242	−	0.0732461i	0.440675	+	0.897667i	$0.354739\pi$
$402$		0			0
$403$	−35.4825	+	29.7734i	−1.76751	+	1.48312i
$404$		0			0
$405$	0.439693	+	2.49362i	0.0218485	+	0.123909i
$406$		0			0
$407$	−3.27079	+	5.66518i	−0.162127	+	0.280812i
$408$		0			0
$409$	30.4714	+	11.0907i	1.50671	+	0.548398i	0.957788	−	0.287474i	$-0.0928155\pi$
$409$	30.4714	+	11.0907i	1.50671	+	0.548398i	0.548924	+	0.835872i	$0.315038\pi$
$410$		0			0
$411$	6.83275	+	11.8347i	0.337035	+	0.583761i
$412$		0			0
$413$	0.663848	+	0.557035i	0.0326658	+	0.0274099i
$414$		0			0
$415$	0.0380187	−	0.215615i	0.00186626	−	0.0105841i
$416$		0			0
$417$	−13.6800			−0.669915
$418$		0			0
$419$	9.86577			0.481974			0.240987	−	0.970528i	$-0.422529\pi$
$419$	9.86577			0.481974			0.240987	+	0.970528i	$0.422529\pi$
$420$		0			0
$421$	3.83884	−	21.7711i	0.187094	−	1.06106i	−0.736142	−	0.676827i	$-0.763355\pi$
$421$	3.83884	−	21.7711i	0.187094	−	1.06106i	0.923236	−	0.384234i	$-0.125534\pi$
$422$		0			0
$423$	−3.56418	−	2.99070i	−0.173296	−	0.145413i
$424$		0			0
$425$	4.19459	+	7.26525i	0.203468	+	0.352416i
$426$		0			0
$427$	4.81655	+	1.75308i	0.233089	+	0.0848376i
$428$		0			0
$429$	9.41787	−	16.3122i	0.454699	−	0.787562i
$430$		0			0
$431$	−4.39693	−	24.9362i	−0.211792	−	1.20113i	−0.886387	−	0.462946i	$-0.846792\pi$
$431$	−4.39693	−	24.9362i	−0.211792	−	1.20113i	0.674594	−	0.738189i	$-0.264319\pi$
$432$		0			0
$433$	9.81702	−	8.23746i	0.471776	−	0.395867i	−0.375666	−	0.926755i	$-0.622586\pi$
$433$	9.81702	−	8.23746i	0.471776	−	0.395867i	0.847442	+	0.530888i	$0.178142\pi$
$434$		0			0
$435$	−16.9611	+	6.17334i	−0.813223	+	0.295989i
$436$		0			0
$437$	−24.0808	+	16.6531i	−1.15194	+	0.796627i
$438$		0			0
$439$	4.90895	−	1.78671i	0.234291	−	0.0852751i	−0.222206	−	0.975000i	$-0.571326\pi$
$439$	4.90895	−	1.78671i	0.234291	−	0.0852751i	0.456498	+	0.889725i	$0.349104\pi$
$440$		0			0
$441$	2.61334	−	2.19285i	0.124445	−	0.104422i
$442$		0			0
$443$	−3.02141	−	17.1353i	−0.143552	−	0.814121i	−0.968519	−	0.248941i	$-0.919918\pi$
$443$	−3.02141	−	17.1353i	−0.143552	−	0.814121i	0.824967	−	0.565181i	$-0.191194\pi$
$444$		0			0
$445$	8.95336	−	15.5077i	0.424430	−	0.735135i
$446$		0			0
$447$	−22.3123	−	8.12100i	−1.05533	−	0.384110i
$448$		0			0
$449$	−11.8255	−	20.4823i	−0.558079	−	0.966621i	−0.997657	−	0.0684163i	$-0.978205\pi$
$449$	−11.8255	−	20.4823i	−0.558079	−	0.966621i	0.439578	−	0.898204i	$-0.355128\pi$
$450$		0			0
$451$	−16.7554	−	14.0594i	−0.788979	−	0.662032i
$452$		0			0
$453$	1.44743	−	8.20880i	0.0680064	−	0.385683i
$454$		0			0
$455$	49.5458			2.32274
$456$		0			0
$457$	−24.2695			−1.13528			−0.567640	−	0.823277i	$-0.692143\pi$
$457$	−24.2695			−1.13528			−0.567640	+	0.823277i	$0.692143\pi$
$458$		0			0
$459$	−1.03209	+	5.85327i	−0.0481738	+	0.273207i
$460$		0			0
$461$	5.34318	+	4.48346i	0.248857	+	0.208815i	0.758680	−	0.651464i	$-0.225845\pi$
$461$	5.34318	+	4.48346i	0.248857	+	0.208815i	−0.509823	+	0.860279i	$0.670289\pi$
$462$		0			0
$463$	−14.0385	−	24.3154i	−0.652424	−	1.13003i	−0.982533	−	0.186088i	$-0.940419\pi$
$463$	−14.0385	−	24.3154i	−0.652424	−	1.13003i	0.330109	−	0.943943i	$-0.392914\pi$
$464$		0			0
$465$	−18.1741	−	6.61484i	−0.842804	−	0.306756i
$466$		0			0
$467$	−1.91147	+	3.31077i	−0.0884525	+	0.153204i	−0.906857	−	0.421438i	$-0.861525\pi$
$467$	−1.91147	+	3.31077i	−0.0884525	+	0.153204i	0.818405	+	0.574642i	$0.194859\pi$
$468$		0			0
$469$	0.731429	+	4.14814i	0.0337743	+	0.191543i
$470$		0			0
$471$	16.6197	−	13.9456i	0.765797	−	0.642580i
$472$		0			0
$473$	27.3475	−	9.95366i	1.25744	−	0.457670i
$474$		0			0
$475$	0.500467	+	6.13208i	0.0229630	+	0.281359i
$476$		0			0
$477$	5.97178	−	2.17355i	0.273429	−	0.0995201i
$478$		0			0
$479$	−23.7010	+	19.8875i	−1.08293	+	0.908683i	−0.996160	−	0.0875461i	$-0.972097\pi$
$479$	−23.7010	+	19.8875i	−1.08293	+	0.908683i	−0.0867654	+	0.996229i	$0.527653\pi$
$480$		0			0
$481$	−2.21776	−	12.5775i	−0.101121	−	0.573486i
$482$		0			0
$483$	−10.8366	+	18.7696i	−0.493083	+	0.854045i
$484$		0			0
$485$	−7.91787	−	2.88187i	−0.359532	−	0.130859i
$486$		0			0
$487$	1.43242	+	2.48102i	0.0649091	+	0.112426i	0.896654	−	0.442733i	$-0.145991\pi$
$487$	1.43242	+	2.48102i	0.0649091	+	0.112426i	−0.831745	+	0.555159i	$0.812658\pi$
$488$		0			0
$489$	−17.6079	−	14.7748i	−0.796256	−	0.668138i
$490$		0			0
$491$	−7.24985	+	41.1159i	−0.327181	+	1.85554i	0.166702	+	0.986007i	$0.446688\pi$
$491$	−7.24985	+	41.1159i	−0.327181	+	1.85554i	−0.493883	+	0.869529i	$0.664423\pi$
$492$		0			0
$493$	−42.3678			−1.90815
$494$		0			0
$495$	7.86484			0.353498
$496$		0			0
$497$	4.63728	−	26.2993i	0.208010	−	1.17969i
$498$		0			0
$499$	7.26991	+	6.10018i	0.325446	+	0.273082i	0.790841	−	0.612021i	$-0.209643\pi$
$499$	7.26991	+	6.10018i	0.325446	+	0.273082i	−0.465395	+	0.885103i	$0.654088\pi$
$500$		0			0
$501$	3.82295	+	6.62154i	0.170797	+	0.295829i
$502$		0			0
$503$	11.8785	+	4.32342i	0.529636	+	0.192772i	0.592976	−	0.805220i	$-0.297953\pi$
$503$	11.8785	+	4.32342i	0.529636	+	0.192772i	−0.0633395	+	0.997992i	$0.520175\pi$
$504$		0			0
$505$	13.6211	−	23.5924i	0.606130	−	1.04985i
$506$		0			0
$507$	4.12836	+	23.4131i	0.183347	+	1.03981i
$508$		0			0
$509$	−14.9349	+	12.5319i	−0.661980	+	0.555467i	−0.910679	−	0.413114i	$-0.864441\pi$
$509$	−14.9349	+	12.5319i	−0.661980	+	0.555467i	0.248700	+	0.968581i	$0.419997\pi$
$510$		0			0
$511$	2.79339	−	1.01671i	0.123572	−	0.0449766i
$512$		0			0
$513$	−2.52094	+	3.55596i	−0.111302	+	0.156999i
$514$		0			0
$515$	−14.1074	+	5.13468i	−0.621647	+	0.226261i
$516$		0			0
$517$	−11.0706	+	9.28931i	−0.486883	+	0.408544i
$518$		0			0
$519$	2.03936	+	11.5658i	0.0895181	+	0.507682i
$520$		0			0
$521$	−10.1416	+	17.5657i	−0.444310	+	0.769567i	−0.998004	−	0.0631531i	$-0.979884\pi$
$521$	−10.1416	+	17.5657i	−0.444310	+	0.769567i	0.553694	+	0.832720i	$0.313218\pi$
$522$		0			0
$523$	−14.3461	−	5.22156i	−0.627312	−	0.228323i	0.00874906	−	0.999962i	$-0.497215\pi$
$523$	−14.3461	−	5.22156i	−0.627312	−	0.228323i	−0.636061	+	0.771639i	$0.719437\pi$
$524$		0			0
$525$	2.27719	+	3.94421i	0.0993847	+	0.172139i
$526$		0			0
$527$	−34.7768	−	29.1812i	−1.51490	−	1.27115i
$528$		0			0
$529$	3.84049	−	21.7805i	0.166978	−	0.946978i
$530$		0			0
$531$	−0.268571			−0.0116550
$532$		0			0
$533$	42.7033			1.84968
$534$		0			0
$535$	1.13516	−	6.43783i	0.0490774	−	0.278332i
$536$		0			0
$537$	−3.21554	−	2.69816i	−0.138761	−	0.116434i
$538$		0			0
$539$	−5.29813	−	9.17664i	−0.228207	−	0.395266i
$540$		0			0
$541$	19.3726	+	7.05104i	0.832892	+	0.303148i	0.723045	−	0.690801i	$-0.242742\pi$
$541$	19.3726	+	7.05104i	0.832892	+	0.303148i	0.109847	+	0.993949i	$0.464964\pi$
$542$		0			0
$543$	−6.16385	+	10.6761i	−0.264516	+	0.458155i
$544$		0			0
$545$	2.10220	+	11.9221i	0.0900482	+	0.510689i
$546$		0			0
$547$	−21.7645	+	18.2625i	−0.930581	+	0.780850i	−0.975922	−	0.218122i	$-0.930007\pi$
$547$	−21.7645	+	18.2625i	−0.930581	+	0.780850i	0.0453408	+	0.998972i	$0.485563\pi$
$548$		0			0
$549$	−1.49273	+	0.543308i	−0.0637080	+	0.0231878i
$550$		0			0
$551$	−28.0835	−	13.2955i	−1.19640	−	0.566408i
$552$		0			0
$553$	−36.5797	+	13.3139i	−1.55553	+	0.566165i
$554$		0			0
$555$	4.08512	−	3.42782i	0.173404	−	0.145503i
$556$		0			0
$557$	−6.56717	−	37.2443i	−0.278260	−	1.57809i	−0.728412	−	0.685139i	$-0.759741\pi$
$557$	−6.56717	−	37.2443i	−0.278260	−	1.57809i	0.450152	−	0.892952i	$-0.351370\pi$
$558$		0			0
$559$	−28.4094	+	49.2065i	−1.20159	+	2.08122i
$560$		0			0
$561$	17.3478	+	6.31407i	0.732423	+	0.266580i
$562$		0			0
$563$	−4.82042	−	8.34922i	−0.203157	−	0.351877i	0.746387	−	0.665512i	$-0.231787\pi$
$563$	−4.82042	−	8.34922i	−0.203157	−	0.351877i	−0.949544	+	0.313634i	$0.898453\pi$
$564$		0			0
$565$	32.3259	+	27.1247i	1.35996	+	1.14114i
$566$		0			0
$567$	−0.560307	+	3.17766i	−0.0235307	+	0.133449i
$568$		0			0
$569$	21.1129			0.885098			0.442549	−	0.896744i	$-0.354074\pi$
$569$	21.1129			0.885098			0.442549	+	0.896744i	$0.354074\pi$
$570$		0			0
$571$	−2.11112			−0.0883476			−0.0441738	−	0.999024i	$-0.514066\pi$
$571$	−2.11112			−0.0883476			−0.0441738	+	0.999024i	$0.514066\pi$
$572$		0			0
$573$	−1.77197	+	10.0494i	−0.0740253	+	0.419818i
$574$		0			0
$575$	−7.26264	−	6.09408i	−0.302873	−	0.254141i
$576$		0			0
$577$	−11.5715	−	20.0423i	−0.481726	−	0.834374i	0.518054	−	0.855348i	$-0.326657\pi$
$577$	−11.5715	−	20.0423i	−0.481726	−	0.834374i	−0.999780	+	0.0209742i	$0.993323\pi$
$578$		0			0
$579$	20.3983	+	7.42436i	0.847723	+	0.308546i
$580$		0			0
$581$	0.139500	−	0.241621i	0.00578743	−	0.0100241i
$582$		0			0
$583$	−3.42767	−	19.4393i	−0.141960	−	0.805093i
$584$		0			0
$585$	−11.7626	+	9.87003i	−0.486325	+	0.408075i
$586$		0			0
$587$	18.0052	−	6.55336i	0.743155	−	0.270486i	0.0574324	−	0.998349i	$-0.481709\pi$
$587$	18.0052	−	6.55336i	0.743155	−	0.270486i	0.685722	+	0.727863i	$0.259486\pi$
$588$		0			0
$589$	−13.8944	−	30.2561i	−0.572509	−	1.24668i
$590$		0			0
$591$	15.6789	−	5.70664i	0.644942	−	0.234740i
$592$		0			0
$593$	28.4978	−	23.9125i	1.17026	−	0.981968i	0.170269	−	0.985398i	$-0.445536\pi$
$593$	28.4978	−	23.9125i	1.17026	−	0.981968i	0.999994	+	0.00342988i	$0.00109177\pi$
$594$		0			0
$595$	8.43242	+	47.8226i	0.345695	+	1.96054i
$596$		0			0
$597$	1.23009	−	2.13057i	0.0503440	−	0.0871984i
$598$		0			0
$599$	−29.0412	−	10.5701i	−1.18659	−	0.431884i	−0.328065	−	0.944655i	$-0.606397\pi$
$599$	−29.0412	−	10.5701i	−1.18659	−	0.431884i	−0.858525	+	0.512772i	$0.828619\pi$
$600$		0			0
$601$	21.7802	+	37.7244i	0.888432	+	1.53881i	0.841729	+	0.539901i	$0.181538\pi$
$601$	21.7802	+	37.7244i	0.888432	+	1.53881i	0.0467035	+	0.998909i	$0.485128\pi$
$602$		0			0
$603$	−1.00000	−	0.839100i	−0.0407231	−	0.0341708i
$604$		0			0
$605$	−0.594618	+	3.37225i	−0.0241747	+	0.137101i
$606$		0			0
$607$	20.9659			0.850978			0.425489	−	0.904964i	$-0.360102\pi$
$607$	20.9659			0.850978			0.425489	+	0.904964i	$0.360102\pi$
$608$		0			0
$609$	−23.0009			−0.932045
$610$		0			0
$611$	4.89945	−	27.7862i	0.198211	−	1.12411i
$612$		0			0
$613$	4.82951	+	4.05244i	0.195062	+	0.163676i	0.735088	−	0.677972i	$-0.237141\pi$
$613$	4.82951	+	4.05244i	0.195062	+	0.163676i	−0.540026	+	0.841649i	$0.681585\pi$
$614$		0			0
$615$	8.91534	+	15.4418i	0.359501	+	0.622675i
$616$		0			0
$617$	36.1241	+	13.1481i	1.45430	+	0.529322i	0.943789	−	0.330549i	$-0.107234\pi$
$617$	36.1241	+	13.1481i	1.45430	+	0.529322i	0.510512	+	0.859871i	$0.329456\pi$
$618$		0			0
$619$	9.31908	−	16.1411i	0.374565	−	0.648766i	−0.615697	−	0.787983i	$-0.711125\pi$
$619$	9.31908	−	16.1411i	0.374565	−	0.648766i	0.990262	+	0.139217i	$0.0444586\pi$
$620$		0			0
$621$	−1.16637	−	6.61484i	−0.0468050	−	0.265444i
$622$		0			0
$623$	17.4802	−	14.6677i	0.700331	−	0.587647i
$624$		0			0
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$		0			0
$627$	9.51754	+	9.62922i	0.380094	+	0.384554i
$628$		0			0
$629$	11.7626	−	4.28125i	0.469007	−	0.170705i
$630$		0			0
$631$	11.8407	−	9.93556i	0.471372	−	0.395528i	−0.375923	−	0.926651i	$-0.622674\pi$
$631$	11.8407	−	9.93556i	0.471372	−	0.395528i	0.847295	+	0.531123i	$0.178230\pi$
$632$		0			0
$633$	−0.213888	−	1.21302i	−0.00850130	−	0.0482133i
$634$		0			0
$635$	−6.60741	+	11.4444i	−0.262207	+	0.454156i
$636$		0			0
$637$	19.4402	+	7.07564i	0.770247	+	0.280347i
$638$		0			0
$639$	4.13816	+	7.16750i	0.163703	+	0.283542i
$640$		0			0
$641$	−19.1630	−	16.0796i	−0.756892	−	0.635108i	0.180424	−	0.983589i	$-0.442253\pi$
$641$	−19.1630	−	16.0796i	−0.756892	−	0.635108i	−0.937316	+	0.348481i	$0.886697\pi$
$642$		0			0
$643$	3.96333	−	22.4771i	0.156298	−	0.886412i	−0.801291	−	0.598275i	$-0.795853\pi$
$643$	3.96333	−	22.4771i	0.156298	−	0.886412i	0.957589	−	0.288137i	$-0.0930358\pi$
$644$		0			0
$645$	−23.7246			−0.934156
$646$		0			0
$647$	46.1252			1.81337			0.906684	−	0.421811i	$-0.138605\pi$
$647$	46.1252			1.81337			0.906684	+	0.421811i	$0.138605\pi$
$648$		0			0
$649$	−0.144857	+	0.821525i	−0.00568614	+	0.0322477i
$650$		0			0
$651$	−18.8799	−	15.8421i	−0.739960	−	0.620900i
$652$		0			0
$653$	7.33868	+	12.7110i	0.287185	+	0.497418i	0.973137	−	0.230228i	$-0.0739473\pi$
$653$	7.33868	+	12.7110i	0.287185	+	0.497418i	−0.685952	+	0.727647i	$0.740614\pi$
$654$		0			0
$655$	20.6001	+	7.49784i	0.804914	+	0.292965i
$656$		0			0
$657$	−0.460637	+	0.797847i	−0.0179712	+	0.0311270i
$658$		0			0
$659$	−3.73648	−	21.1906i	−0.145553	−	0.825470i	−0.966922	−	0.255073i	$-0.917900\pi$
$659$	−3.73648	−	21.1906i	−0.145553	−	0.825470i	0.821369	−	0.570397i	$-0.193211\pi$
$660$		0			0
$661$	−24.0494	+	20.1798i	−0.935413	+	0.784904i	−0.976781	−	0.214240i	$-0.931273\pi$
$661$	−24.0494	+	20.1798i	−0.935413	+	0.784904i	0.0413686	+	0.999144i	$0.486828\pi$
$662$		0			0
$663$	−33.8692	+	12.3274i	−1.31537	+	0.478755i
$664$		0			0
$665$	−9.41787	+	34.3454i	−0.365209	+	1.33186i
$666$		0			0
$667$	44.9928	−	16.3760i	1.74213	−	0.634083i
$668$		0			0
$669$	5.03983	−	4.22892i	0.194851	−	0.163499i
$670$		0			0
$671$	0.856792	+	4.85911i	0.0330761	+	0.187584i
$672$		0			0
$673$	−5.83662	+	10.1093i	−0.224985	+	0.389686i	−0.956315	−	0.292338i	$-0.905567\pi$
$673$	−5.83662	+	10.1093i	−0.224985	+	0.389686i	0.731330	+	0.682024i	$0.238900\pi$
$674$		0			0
$675$	−1.32635	−	0.482753i	−0.0510513	−	0.0185812i
$676$		0			0
$677$	−20.6866	−	35.8302i	−0.795051	−	1.37707i	−0.922807	−	0.385263i	$-0.874111\pi$
$677$	−20.6866	−	35.8302i	−0.795051	−	1.37707i	0.127756	−	0.991806i	$-0.459223\pi$
$678$		0			0
$679$	−8.22534	−	6.90188i	−0.315659	−	0.264870i
$680$		0			0
$681$	1.68954	−	9.58186i	0.0647433	−	0.367178i
$682$		0			0
$683$	−29.5117			−1.12923			−0.564616	−	0.825354i	$-0.690976\pi$
$683$	−29.5117			−1.12923			−0.564616	+	0.825354i	$0.690976\pi$
$684$		0			0
$685$	−34.6023			−1.32208
$686$		0			0
$687$	−1.71348	+	9.71762i	−0.0653733	+	0.370750i
$688$		0			0
$689$	29.5219	+	24.7718i	1.12469	+	0.943730i
$690$		0			0
$691$	2.23917	+	3.87836i	0.0851820	+	0.147540i	0.905469	−	0.424413i	$-0.139519\pi$
$691$	2.23917	+	3.87836i	0.0851820	+	0.147540i	−0.820287	+	0.571953i	$0.806186\pi$
$692$		0			0
$693$	9.41787	+	3.42782i	0.357755	+	0.130212i
$694$		0			0
$695$	17.3195	−	29.9983i	0.656968	−	1.13790i
$696$		0			0
$697$	7.26786	+	41.2181i	0.275290	+	1.56125i
$698$		0			0
$699$	16.7121	−	14.0231i	0.632111	−	0.530404i
$700$		0			0
$701$	−5.55690	+	2.02255i	−0.209881	+	0.0763906i	−0.444821	−	0.895619i	$-0.646733\pi$
$701$	−5.55690	+	2.02255i	−0.209881	+	0.0763906i	0.234940	+	0.972010i	$0.424511\pi$
$702$		0			0
$703$	9.14038	+	0.853427i	0.344736	+	0.0321876i
$704$		0			0
$705$	11.0706	−	4.02936i	0.416942	−	0.151754i
$706$		0			0
$707$	26.5933	−	22.3145i	1.00015	−	0.839221i
$708$		0			0
$709$	5.19830	+	29.4810i	0.195226	+	1.10718i	0.912096	+	0.409976i	$0.134463\pi$
$709$	5.19830	+	29.4810i	0.195226	+	1.10718i	−0.716870	+	0.697207i	$0.754426\pi$
$710$		0			0
$711$	6.03209	−	10.4479i	0.226221	−	0.391826i
$712$		0			0
$713$	48.2105	+	17.5472i	1.80550	+	0.657148i
$714$		0			0
$715$	23.8469	+	41.3040i	0.891823	+	1.54468i
$716$		0			0
$717$	16.3255	+	13.6987i	0.609686	+	0.511587i
$718$		0			0
$719$	8.29709	−	47.0552i	0.309429	−	1.75486i	−0.292456	−	0.956279i	$-0.594473\pi$
$719$	8.29709	−	47.0552i	0.309429	−	1.75486i	0.601886	−	0.798582i	$-0.294416\pi$
$720$		0			0
$721$	−19.1310			−0.712477
$722$		0			0
$723$	15.6459			0.581877
$724$		0			0
$725$	1.74716	−	9.90863i	0.0648879	−	0.367997i
$726$		0			0
$727$	−32.0933	−	26.9295i	−1.19028	−	0.998760i	−0.999855	−	0.0170574i	$-0.994570\pi$
$727$	−32.0933	−	26.9295i	−1.19028	−	0.998760i	−0.190421	−	0.981702i	$-0.560985\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−52.3303	−	19.0467i	−1.93551	−	0.704466i
$732$		0			0
$733$	−10.8068	+	18.7178i	−0.399156	+	0.691359i	−0.993622	−	0.112762i	$-0.964030\pi$
$733$	−10.8068	+	18.7178i	−0.399156	+	0.691359i	0.594466	+	0.804121i	$0.297364\pi$
$734$		0			0
$735$	1.50000	+	8.50692i	0.0553283	+	0.313783i
$736$		0			0
$737$	−3.10607	+	2.60630i	−0.114413	+	0.0960043i
$738$		0			0
$739$	−30.4688	+	11.0898i	−1.12081	+	0.407943i	−0.834949	−	0.550327i	$-0.814503\pi$
$739$	−30.4688	+	11.0898i	−1.12081	+	0.407943i	−0.285865	+	0.958270i	$0.592281\pi$
$740$		0			0
$741$	−26.3187	−	2.45734i	−0.966840	−	0.0902728i
$742$		0			0
$743$	25.2754	−	9.19951i	0.927266	−	0.337497i	0.166141	−	0.986102i	$-0.446869\pi$
$743$	25.2754	−	9.19951i	0.927266	−	0.337497i	0.761125	+	0.648605i	$0.224647\pi$
$744$		0			0
$745$	46.0565	−	38.6460i	1.68738	−	1.41588i
$746$		0			0
$747$	0.0150147	+	0.0851529i	0.000549361	+	0.00311558i
$748$		0			0
$749$	4.16519	−	7.21432i	0.152193	−	0.263606i
$750$		0			0
$751$	5.38103	+	1.95854i	0.196357	+	0.0714680i	0.438327	−	0.898816i	$-0.355571\pi$
$751$	5.38103	+	1.95854i	0.196357	+	0.0714680i	−0.241970	+	0.970284i	$0.577794\pi$
$752$		0			0
$753$	5.06077	+	8.76552i	0.184425	+	0.319433i
$754$		0			0
$755$	16.1682	+	13.5667i	0.588421	+	0.493743i
$756$		0			0
$757$	1.50269	−	8.52217i	0.0546161	−	0.309744i	−0.945246	−	0.326359i	$-0.894178\pi$
$757$	1.50269	−	8.52217i	0.0546161	−	0.309744i	0.999862	+	0.0166157i	$0.00528920\pi$
$758$		0			0
$759$	−20.8631			−0.757282
$760$		0			0
$761$	−37.7279			−1.36764			−0.683818	−	0.729653i	$-0.739682\pi$
$761$	−37.7279			−1.36764			−0.683818	+	0.729653i	$0.739682\pi$
$762$		0			0
$763$	−2.67886	+	15.1926i	−0.0969813	+	0.550009i
$764$		0			0
$765$	−11.5287	−	9.67372i	−0.416820	−	0.349754i
$766$		0			0
$767$	−0.814330	−	1.41046i	−0.0294038	−	0.0509288i
$768$		0			0
$769$	−34.5724	−	12.5833i	−1.24671	−	0.453766i	−0.367423	−	0.930054i	$-0.619760\pi$
$769$	−34.5724	−	12.5833i	−1.24671	−	0.453766i	−0.879289	+	0.476288i	$0.841982\pi$
$770$		0			0
$771$	2.38919	−	4.13819i	0.0860444	−	0.149033i
$772$		0			0
$773$	3.46750	+	19.6652i	0.124717	+	0.707307i	0.981475	+	0.191588i	$0.0613639\pi$
$773$	3.46750	+	19.6652i	0.124717	+	0.707307i	−0.856758	+	0.515719i	$0.827525\pi$
$774$		0			0
$775$	8.25877	−	6.92993i	0.296664	−	0.248930i
$776$		0			0
$777$	6.38578	−	2.32423i	0.229089	−	0.0833814i
$778$		0			0
$779$	−8.11721	+	29.6021i	−0.290829	+	1.06061i
$780$		0			0
$781$	24.1565	−	8.79224i	0.864386	−	0.314611i
$782$		0			0
$783$	5.46064	−	4.58202i	0.195147	−	0.163748i
$784$		0			0
$785$	9.53936	+	54.1004i	0.340474	+	1.93093i
$786$		0			0
$787$	−4.18392	+	7.24675i	−0.149140	+	0.258319i	−0.930910	−	0.365249i	$-0.880984\pi$
$787$	−4.18392	+	7.24675i	−0.149140	+	0.258319i	0.781770	+	0.623567i	$0.214317\pi$
$788$		0			0
$789$	20.3824	+	7.41858i	0.725632	+	0.264108i
$790$		0			0
$791$	26.8871	+	46.5699i	0.955996	+	1.65583i
$792$		0			0
$793$	−7.37939	−	6.19204i	−0.262050	−	0.219886i
$794$		0			0
$795$	−2.79426	+	15.8471i	−0.0991023	+	0.562037i
$796$		0			0
$797$	−42.1729			−1.49384			−0.746921	−	0.664913i	$-0.768469\pi$
$797$	−42.1729			−1.49384			−0.746921	+	0.664913i	$0.768469\pi$
$798$		0			0
$799$	27.6536			0.978315
$800$		0			0
$801$	−1.22803	+	6.96448i	−0.0433902	+	0.246078i
$802$		0			0
$803$	2.19207	+	1.83936i	0.0773563	+	0.0649097i
$804$		0			0
$805$	−27.4393	−	47.5262i	−0.967108	−	1.67508i
$806$		0			0
$807$	3.03684	+	1.10532i	0.106902	+	0.0389090i
$808$		0			0
$809$	3.03121	−	5.25021i	0.106572	−	0.184588i	−0.807808	−	0.589446i	$-0.799346\pi$
$809$	3.03121	−	5.25021i	0.106572	−	0.184588i	0.914379	+	0.404859i	$0.132679\pi$
$810$		0			0
$811$	4.46168	+	25.3034i	0.156671	+	0.888523i	0.957243	+	0.289287i	$0.0934181\pi$
$811$	4.46168	+	25.3034i	0.156671	+	0.888523i	−0.800572	+	0.599237i	$0.795471\pi$
$812$		0			0
$813$	−8.97952	+	7.53471i	−0.314926	+	0.264254i
$814$		0			0
$815$	54.6912	−	19.9060i	1.91575	−	0.697276i
$816$		0			0
$817$	−28.7101	−	29.0469i	−1.00444	−	1.01622i
$818$		0			0
$819$	−18.3871	+	6.69237i	−0.642498	+	0.233850i
$820$		0			0
$821$	−0.192533	+	0.161555i	−0.00671946	+	0.00563830i	−0.646141	−	0.763218i	$-0.723618\pi$
$821$	−0.192533	+	0.161555i	−0.00671946	+	0.00563830i	0.639422	+	0.768856i	$0.279174\pi$
$822$		0			0
$823$	2.83497	+	16.0779i	0.0988208	+	0.560441i	0.993509	+	0.113750i	$0.0362864\pi$
$823$	2.83497	+	16.0779i	0.0988208	+	0.560441i	−0.894689	+	0.446691i	$0.852603\pi$
$824$		0			0
$825$	−2.19207	+	3.79677i	−0.0763180	+	0.132187i
$826$		0			0
$827$	−24.9008	−	9.06315i	−0.865886	−	0.315157i	−0.129386	−	0.991594i	$-0.541301\pi$
$827$	−24.9008	−	9.06315i	−0.865886	−	0.315157i	−0.736500	+	0.676438i	$0.763523\pi$
$828$		0			0
$829$	−20.8148	−	36.0523i	−0.722928	−	1.25215i	−0.959821	−	0.280612i	$-0.909463\pi$
$829$	−20.8148	−	36.0523i	−0.722928	−	1.25215i	0.236894	−	0.971536i	$-0.423871\pi$
$830$		0			0
$831$	6.72075	+	5.63938i	0.233140	+	0.195628i
$832$		0			0
$833$	−3.52094	+	19.9683i	−0.121993	+	0.691860i
$834$		0			0
$835$	−19.3601			−0.669984
$836$		0			0
$837$	7.63816			0.264013
$838$		0			0
$839$	4.93289	−	27.9758i	0.170302	−	0.965831i	−0.773126	−	0.634253i	$-0.781308\pi$
$839$	4.93289	−	27.9758i	0.170302	−	0.965831i	0.943428	−	0.331578i	$-0.107581\pi$
$840$		0			0
$841$	16.7101	+	14.0214i	0.576209	+	0.483497i
$842$		0			0
$843$	−12.7083	−	22.0114i	−0.437696	−	0.758111i
$844$		0			0
$845$	−56.5681	−	20.5891i	−1.94600	−	0.708287i
$846$		0			0
$847$	−2.18180	+	3.77899i	−0.0749675	+	0.129848i
$848$		0			0
$849$	−0.464041	−	2.63171i	−0.0159258	−	0.0903199i
$850$		0			0
$851$	−10.8366	+	9.09300i	−0.371475	+	0.311704i
$852$		0			0
$853$	25.5535	−	9.30071i	0.874935	−	0.318450i	0.134771	−	0.990877i	$-0.456970\pi$
$853$	25.5535	−	9.30071i	0.874935	−	0.318450i	0.740164	+	0.672426i	$0.234748\pi$
$854$		0			0
$855$	−4.60607	−	10.0301i	−0.157524	−	0.343021i
$856$		0			0
$857$	−39.4381	+	14.3543i	−1.34718	+	0.490333i	−0.912066	−	0.410042i	$-0.865514\pi$
$857$	−39.4381	+	14.3543i	−1.34718	+	0.490333i	−0.435113	+	0.900376i	$0.643292\pi$
$858$		0			0
$859$	27.0519	−	22.6992i	0.922999	−	0.774488i	−0.0515481	−	0.998671i	$-0.516416\pi$
$859$	27.0519	−	22.6992i	0.922999	−	0.774488i	0.974547	+	0.224182i	$0.0719711\pi$
$860$		0			0
$861$	3.94562	+	22.3767i	0.134466	+	0.762597i
$862$		0			0
$863$	−6.00521	+	10.4013i	−0.204420	+	0.354066i	−0.949948	−	0.312409i	$-0.898864\pi$
$863$	−6.00521	+	10.4013i	−0.204420	+	0.354066i	0.745528	+	0.666474i	$0.232197\pi$
$864$		0			0
$865$	−27.9440	−	10.1708i	−0.950126	−	0.345817i
$866$		0			0
$867$	−9.16297	−	15.8707i	−0.311191	−	0.538998i
$868$		0			0
$869$	−28.7053	−	24.0866i	−0.973762	−	0.817083i
$870$		0			0
$871$	1.37464	−	7.79596i	0.0465778	−	0.264156i
$872$		0			0
$873$	3.32770			0.112625
$874$		0			0
$875$	29.3191			0.991168
$876$		0			0
$877$	−3.13145	+	17.7594i	−0.105742	+	0.599691i	0.885180	+	0.465249i	$0.154035\pi$
$877$	−3.13145	+	17.7594i	−0.105742	+	0.599691i	−0.990921	+	0.134442i	$0.957076\pi$
$878$		0			0
$879$	15.2854	+	12.8260i	0.515564	+	0.432609i
$880$		0			0
$881$	−11.9101	−	20.6290i	−0.401262	−	0.695007i	0.592616	−	0.805485i	$-0.298095\pi$
$881$	−11.9101	−	20.6290i	−0.401262	−	0.695007i	−0.993879	+	0.110478i	$0.964762\pi$
$882$		0			0
$883$	−11.1197	−	4.04725i	−0.374209	−	0.136201i	0.148067	−	0.988977i	$-0.452695\pi$
$883$	−11.1197	−	4.04725i	−0.374209	−	0.136201i	−0.522276	+	0.852776i	$0.674917\pi$
$884$		0			0
$885$	0.340022	−	0.588936i	0.0114297	−	0.0197969i
$886$		0			0
$887$	−6.37283	−	36.1421i	−0.213979	−	1.21353i	−0.882670	−	0.469993i	$-0.844256\pi$
$887$	−6.37283	−	36.1421i	−0.213979	−	1.21353i	0.668692	−	0.743540i	$-0.266855\pi$
$888$		0			0
$889$	−12.9001	+	10.8245i	−0.432655	+	0.363041i
$890$		0			0
$891$	−2.91875	+	1.06234i	−0.0977817	+	0.0355896i
$892$		0			0
$893$	18.3302	+	8.67804i	0.613397	+	0.290399i
$894$		0			0
$895$	9.98767	−	3.63522i	0.333851	−	0.121512i
$896$		0			0
$897$	31.2028	−	26.1823i	1.04183	−	0.874200i
$898$		0			0
$899$	9.45471	+	53.6203i	0.315332	+	1.78834i
$900$		0			0
$901$	−18.8858	+	32.7111i	−0.629177	+	1.08977i
$902$		0			0
$903$	−28.4094	−	10.3402i	−0.945406	−	0.344100i
$904$		0			0
$905$	−15.6074	−	27.0328i	−0.518808	−	0.898602i
$906$		0			0
$907$	−22.3746	−	18.7746i	−0.742938	−	0.623399i	0.190687	−	0.981651i	$-0.438928\pi$
$907$	−22.3746	−	18.7746i	−0.742938	−	0.623399i	−0.933625	+	0.358252i	$0.883373\pi$
$908$		0			0
$909$	−1.86824	+	10.5953i	−0.0619656	+	0.351425i
$910$		0			0
$911$	3.12567			0.103558			0.0517790	−	0.998659i	$-0.483511\pi$
$911$	3.12567			0.103558			0.0517790	+	0.998659i	$0.483511\pi$
$912$		0			0
$913$	0.268571			0.00888839
$914$		0			0
$915$	0.698463	−	3.96118i	0.0230905	−	0.130953i
$916$		0			0
$917$	21.4001	+	17.9568i	0.706693	+	0.592986i
$918$		0			0
$919$	4.39322	+	7.60928i	0.144919	+	0.251007i	0.929343	−	0.369218i	$-0.120375\pi$
$919$	4.39322	+	7.60928i	0.144919	+	0.251007i	−0.784424	+	0.620225i	$0.787041\pi$
$920$		0			0
$921$	22.5351	+	8.20210i	0.742556	+	0.270268i
$922$		0			0
$923$	−25.0945	+	43.4650i	−0.825996	+	1.43067i
$924$		0			0
$925$	0.516197	+	2.92750i	0.0169724	+	0.0962555i
$926$		0			0
$927$	4.54189	−	3.81110i	0.149175	−	0.125173i
$928$		0			0
$929$	−23.6377	+	8.60344i	−0.775529	+	0.282270i	−0.699307	−	0.714821i	$-0.746508\pi$
$929$	−23.6377	+	8.60344i	−0.775529	+	0.282270i	−0.0762221	+	0.997091i	$0.524286\pi$
$930$		0			0
$931$	−8.60014	+	12.1311i	−0.281858	+	0.397579i
$932$		0			0
$933$	0.152704	−	0.0555796i	0.00499929	−	0.00181959i
$934$		0			0
$935$	−35.8089	+	30.0472i	−1.17108	+	0.982649i
$936$		0			0
$937$	−4.59698	−	26.0708i	−0.150177	−	0.851695i	−0.963064	−	0.269274i	$-0.913216\pi$
$937$	−4.59698	−	26.0708i	−0.150177	−	0.851695i	0.812887	−	0.582422i	$-0.197895\pi$
$938$		0			0
$939$	−3.36097	+	5.82137i	−0.109681	+	0.189973i
$940$		0			0
$941$	−4.95171	−	1.80228i	−0.161421	−	0.0587525i	0.260046	−	0.965596i	$-0.416262\pi$
$941$	−4.95171	−	1.80228i	−0.161421	−	0.0587525i	−0.421467	+	0.906844i	$0.638485\pi$
$942$		0			0
$943$	−23.6498	−	40.9626i	−0.770142	−	1.33393i
$944$		0			0
$945$	−6.25877	−	5.25173i	−0.203598	−	0.170839i
$946$		0			0
$947$	4.23324	−	24.0079i	0.137562	−	0.780152i	−0.835480	−	0.549521i	$-0.814810\pi$
$947$	4.23324	−	24.0079i	0.137562	−	0.780152i	0.973041	−	0.230630i	$-0.0740788\pi$
$948$		0			0
$949$	−5.58677			−0.181354
$950$		0			0
$951$	14.2831			0.463162
$952$		0			0
$953$	8.61633	−	48.8657i	0.279110	−	1.58291i	−0.446484	−	0.894792i	$-0.647324\pi$
$953$	8.61633	−	48.8657i	0.279110	−	1.58291i	0.725595	−	0.688122i	$-0.241565\pi$
$954$		0			0
$955$	−19.7934	−	16.6086i	−0.640499	−	0.537442i
$956$		0			0
$957$	−11.0706	−	19.1748i	−0.357861	−	0.619833i
$958$		0			0
$959$	−41.4350	−	15.0811i	−1.33801	−	0.486994i
$960$		0			0
$961$	−13.6707	+	23.6784i	−0.440991	+	0.763818i
$962$		0			0
$963$	0.448311	+	2.54250i	0.0144466	+	0.0819308i
$964$		0			0
$965$	−42.1057	+	35.3308i	−1.35543	+	1.13734i
$966$		0			0
$967$	24.3307	−	8.85565i	0.782422	−	0.284778i	0.0802399	−	0.996776i	$-0.474431\pi$
$967$	24.3307	−	8.85565i	0.782422	−	0.284778i	0.702182	+	0.711997i	$0.252209\pi$
$968$		0			0
$969$	−2.10741	−	25.8215i	−0.0676998	−	0.829507i
$970$		0			0
$971$	−11.8645	+	4.31834i	−0.380751	+	0.138582i	−0.525303	−	0.850915i	$-0.676048\pi$
$971$	−11.8645	+	4.31834i	−0.380751	+	0.138582i	0.144552	+	0.989497i	$0.453826\pi$
$972$		0			0
$973$	33.8141	−	28.3734i	1.08403	−	0.909609i
$974$		0			0
$975$	−1.48633	−	8.42939i	−0.0476006	−	0.269957i
$976$		0			0
$977$	−1.69072	+	2.92842i	−0.0540910	+	0.0936884i	−0.891803	−	0.452424i	$-0.850559\pi$
$977$	−1.69072	+	2.92842i	−0.0540910	+	0.0936884i	0.837712	+	0.546112i	$0.183893\pi$
$978$		0			0
$979$	20.6411	+	7.51276i	0.659694	+	0.240109i
$980$		0			0
$981$	−2.39053	−	4.14052i	−0.0763237	−	0.132197i
$982$		0			0
$983$	−0.170493	−	0.143061i	−0.00543788	−	0.00456293i	0.640065	−	0.768321i	$-0.278908\pi$
$983$	−0.170493	−	0.143061i	−0.00543788	−	0.00456293i	−0.645503	+	0.763758i	$0.723352\pi$
$984$		0			0
$985$	−7.33631	+	41.6063i	−0.233754	+	1.32569i
$986$		0			0
$987$	15.0128			0.477862
$988$		0			0
$989$	62.9344			2.00120
$990$		0			0
$991$	−0.838536	+	4.75557i	−0.0266370	+	0.151066i	−0.995225	−	0.0976038i	$-0.968882\pi$
$991$	−0.838536	+	4.75557i	−0.0266370	+	0.151066i	0.968588	+	0.248670i	$0.0799933\pi$
$992$		0			0
$993$	−25.5141	−	21.4089i	−0.809667	−	0.679391i
$994$		0			0
$995$	3.11468	+	5.39479i	0.0987422	+	0.171026i
$996$		0			0
$997$	11.8794	+	4.32374i	0.376224	+	0.136934i	0.523209	−	0.852204i	$-0.324735\pi$
$997$	11.8794	+	4.32374i	0.376224	+	0.136934i	−0.146985	+	0.989139i	$0.546957\pi$
$998$		0			0
$999$	−1.05303	+	1.82391i	−0.0333165	+	0.0577059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.q.a.157.1	yes	6
3.2	odd	2		684.2.bo.a.613.1		6
4.3	odd	2		912.2.bo.e.385.1		6
19.2	odd	18		4332.2.a.n.1.3		3
19.4	even	9	inner	228.2.q.a.61.1	✓	6
19.17	even	9		4332.2.a.o.1.3		3
57.23	odd	18		684.2.bo.a.289.1		6
76.23	odd	18		912.2.bo.e.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.a.61.1	✓	6	19.4	even	9	inner
228.2.q.a.157.1	yes	6	1.1	even	1	trivial
684.2.bo.a.289.1		6	57.23	odd	18
684.2.bo.a.613.1		6	3.2	odd	2
912.2.bo.e.289.1		6	76.23	odd	18
912.2.bo.e.385.1		6	4.3	odd	2
4332.2.a.n.1.3		3	19.2	odd	18
4332.2.a.o.1.3		3	19.17	even	9

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{3} +(1.93969 + 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{3} +(1.93969 + 1.62760i) q^{5} +(1.61334 + 2.79439i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-1.55303 + 2.68993i) q^{11} +(-1.05303 - 5.97205i) q^{13} +(1.93969 - 1.62760i) q^{15} +(5.58512 - 2.03282i) q^{17} +(4.34002 + 0.405223i) q^{19} +(3.03209 - 1.10359i) q^{21} +(-5.14543 + 4.31753i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-6.69846 - 2.43804i) q^{29} +(-3.81908 - 6.61484i) q^{31} +(2.37939 + 1.99654i) q^{33} +(-1.41875 + 8.04612i) q^{35} +2.10607 q^{37} -6.06418 q^{39} +(-1.22281 + 6.93491i) q^{41} +(-7.17752 - 6.02265i) q^{43} +(-1.26604 - 2.19285i) q^{45} +(4.37211 + 1.59132i) q^{47} +(-1.70574 + 2.95442i) q^{49} +(-1.03209 - 5.85327i) q^{51} +(-4.86824 + 4.08494i) q^{53} +(-7.39053 + 2.68993i) q^{55} +(1.15270 - 4.20372i) q^{57} +(0.252374 - 0.0918566i) q^{59} +(1.21688 - 1.02108i) q^{61} +(-0.560307 - 3.17766i) q^{63} +(7.67752 - 13.2979i) q^{65} +(1.22668 + 0.446476i) q^{67} +(3.35844 + 5.81699i) q^{69} +(-6.34002 - 5.31991i) q^{71} +(0.159978 - 0.907278i) q^{73} +1.41147 q^{75} -10.0223 q^{77} +(-2.09492 + 11.8809i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-0.0432332 - 0.0748822i) q^{83} +(14.1420 + 5.14728i) q^{85} +(-3.56418 + 6.17334i) q^{87} +(-1.22803 - 6.96448i) q^{89} +(14.9893 - 12.5775i) q^{91} +(-7.17752 + 2.61240i) q^{93} +(7.75877 + 7.84981i) q^{95} +(-3.12701 + 1.13814i) q^{97} +(2.37939 - 1.99654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 6 * q^5 + 3 * q^7	\( 6 q + 6 q^{5} + 3 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 12 q^{17} + 6 q^{19} + 9 q^{21} - 15 q^{23} - 3 q^{27} - 12 q^{29} - 6 q^{31} + 3 q^{33} - 6 q^{35} - 12 q^{37} - 18 q^{39} - 18 q^{41} - 18 q^{43} - 3 q^{45} - 3 q^{47} + 3 q^{51} - 24 q^{53} - 27 q^{55} + 9 q^{57} + 18 q^{59} - 9 q^{61} - 9 q^{63} + 21 q^{65} - 6 q^{67} + 12 q^{69} - 18 q^{71} + 21 q^{73} - 12 q^{75} - 48 q^{77} + 6 q^{79} + 15 q^{83} + 27 q^{85} - 3 q^{87} + 15 q^{89} + 30 q^{91} - 18 q^{93} + 24 q^{95} + 9 q^{97} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^5 + 3 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 12 * q^17 + 6 * q^19 + 9 * q^21 - 15 * q^23 - 3 * q^27 - 12 * q^29 - 6 * q^31 + 3 * q^33 - 6 * q^35 - 12 * q^37 - 18 * q^39 - 18 * q^41 - 18 * q^43 - 3 * q^45 - 3 * q^47 + 3 * q^51 - 24 * q^53 - 27 * q^55 + 9 * q^57 + 18 * q^59 - 9 * q^61 - 9 * q^63 + 21 * q^65 - 6 * q^67 + 12 * q^69 - 18 * q^71 + 21 * q^73 - 12 * q^75 - 48 * q^77 + 6 * q^79 + 15 * q^83 + 27 * q^85 - 3 * q^87 + 15 * q^89 + 30 * q^91 - 18 * q^93 + 24 * q^95 + 9 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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