LMFDB - Embedded newform 605.2.b.e.364.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (of order $2$, degree $1$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.2
Root			$-0.517638i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.e.364.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.517638i q^{2} +1.93185i q^{3} +1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} +1.00000 q^{6} +3.34607i q^{7} -1.93185i q^{8} -0.732051 q^{9} +O(q^{10})$	\(q-0.517638i q^{2} +1.93185i q^{3} +1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} +1.00000 q^{6} +3.34607i q^{7} -1.93185i q^{8} -0.732051 q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +4.24264i q^{13} +1.73205 q^{14} +(2.73205 + 3.34607i) q^{15} +2.46410 q^{16} -3.86370i q^{17} +0.378937i q^{18} -4.19615 q^{19} +(3.00000 - 2.44949i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +3.73205 q^{24} +(1.00000 - 4.89898i) q^{25} +2.19615 q^{26} +4.38134i q^{27} +5.79555i q^{28} +6.92820 q^{29} +(1.73205 - 1.41421i) q^{30} -8.73205 q^{31} -5.13922i q^{32} -2.00000 q^{34} +(4.73205 + 5.79555i) q^{35} -1.26795 q^{36} +1.79315i q^{37} +2.17209i q^{38} -8.19615 q^{39} +(-2.73205 - 3.34607i) q^{40} -1.73205 q^{41} +3.34607i q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} -1.80385 q^{46} +11.4524i q^{47} +4.76028i q^{48} -4.19615 q^{49} +(-2.53590 - 0.517638i) q^{50} +7.46410 q^{51} +7.34847i q^{52} -2.17209i q^{53} +2.26795 q^{54} +6.46410 q^{56} -8.10634i q^{57} -3.58630i q^{58} +1.26795 q^{59} +(4.73205 + 5.79555i) q^{60} +11.7321 q^{61} +4.52004i q^{62} -2.44949i q^{63} +2.26795 q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} -6.69213i q^{68} +6.73205 q^{69} +(3.00000 - 2.44949i) q^{70} -8.19615 q^{71} +1.41421i q^{72} -4.89898i q^{73} +0.928203 q^{74} +(9.46410 + 1.93185i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +1.46410 q^{79} +(4.26795 - 3.48477i) q^{80} -10.6603 q^{81} +0.896575i q^{82} -9.89949i q^{83} -11.1962 q^{84} +(-5.46410 - 6.69213i) q^{85} -3.33975 q^{86} +13.3843i q^{87} -0.464102 q^{89} +(0.535898 + 0.656339i) q^{90} -14.1962 q^{91} -6.03579i q^{92} -16.8690i q^{93} +5.92820 q^{94} +(-7.26795 + 5.93426i) q^{95} +9.92820 q^{96} -9.14162i q^{97} +2.17209i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^6 + 4 * q^9	$ 4 q + 4 q^{6} + 4 q^{9} + 4 q^{10} + 4 q^{15} - 4 q^{16} + 4 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{24} + 4 q^{25} - 12 q^{26} - 28 q^{31} - 8 q^{34} + 12 q^{35} - 12 q^{36} - 12 q^{39} - 4 q^{40} - 12 q^{45} - 28 q^{46} + 4 q^{49} - 24 q^{50} + 16 q^{51} + 16 q^{54} + 12 q^{56} + 12 q^{59} + 12 q^{60} + 40 q^{61} + 16 q^{64} + 24 q^{65} + 20 q^{69} + 12 q^{70} - 12 q^{71} - 24 q^{74} + 24 q^{75} - 36 q^{76} - 8 q^{79} + 24 q^{80} - 8 q^{81} - 24 q^{84} - 8 q^{85} - 48 q^{86} + 12 q^{89} + 16 q^{90} - 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) $ 4 * q + 4 * q^6 + 4 * q^9 + 4 * q^10 + 4 * q^15 - 4 * q^16 + 4 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^24 + 4 * q^25 - 12 * q^26 - 28 * q^31 - 8 * q^34 + 12 * q^35 - 12 * q^36 - 12 * q^39 - 4 * q^40 - 12 * q^45 - 28 * q^46 + 4 * q^49 - 24 * q^50 + 16 * q^51 + 16 * q^54 + 12 * q^56 + 12 * q^59 + 12 * q^60 + 40 * q^61 + 16 * q^64 + 24 * q^65 + 20 * q^69 + 12 * q^70 - 12 * q^71 - 24 * q^74 + 24 * q^75 - 36 * q^76 - 8 * q^79 + 24 * q^80 - 8 * q^81 - 24 * q^84 - 8 * q^85 - 48 * q^86 + 12 * q^89 + 16 * q^90 - 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.517638i		−	0.366025i	−0.983111	−	0.183013i	$-0.941415\pi$
$2$		−	0.517638i		−	0.366025i	0.983111	−	0.183013i	$-0.0585849\pi$
$3$			1.93185i			1.11536i	0.830058	+	0.557678i	$0.188307\pi$
$3$			1.93185i			1.11536i	−0.830058	+	0.557678i	$0.811693\pi$
$4$	1.73205			0.866025
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$6$	1.00000			0.408248
$7$			3.34607i			1.26469i	0.774685	+	0.632347i	$0.217908\pi$
$7$			3.34607i			1.26469i	−0.774685	+	0.632347i	$0.782092\pi$
$8$		−	1.93185i		−	0.683013i
$9$	−0.732051			−0.244017
$10$	−0.732051	−	0.896575i	−0.231495	−	0.283522i
$11$		0			0
$11$		0			0
$12$			3.34607i			0.965926i
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$	1.73205			0.462910
$15$	2.73205	+	3.34607i	0.705412	+	0.863950i
$16$	2.46410			0.616025
$17$		−	3.86370i		−	0.937086i	−0.883441	−	0.468543i	$-0.844779\pi$
$17$		−	3.86370i		−	0.937086i	0.883441	−	0.468543i	$-0.155221\pi$
$18$			0.378937i			0.0893164i
$19$	−4.19615			−0.962663			−0.481332	−	0.876539i	$-0.659847\pi$
$19$	−4.19615			−0.962663			−0.481332	+	0.876539i	$0.659847\pi$
$20$	3.00000	−	2.44949i	0.670820	−	0.547723i
$21$	−6.46410			−1.41058
$22$		0			0
$23$		−	3.48477i		−	0.726624i	−0.931668	−	0.363312i	$-0.881646\pi$
$23$		−	3.48477i		−	0.726624i	0.931668	−	0.363312i	$-0.118354\pi$
$24$	3.73205			0.761802
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$	2.19615			0.430701
$27$			4.38134i			0.843190i
$28$			5.79555i			1.09526i
$29$	6.92820			1.28654			0.643268	−	0.765641i	$-0.277578\pi$
$29$	6.92820			1.28654			0.643268	+	0.765641i	$0.277578\pi$
$30$	1.73205	−	1.41421i	0.316228	−	0.258199i
$31$	−8.73205			−1.56832			−0.784161	−	0.620557i	$-0.786907\pi$
$31$	−8.73205			−1.56832			−0.784161	+	0.620557i	$0.786907\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	4.73205	+	5.79555i	0.799863	+	0.979628i
$36$	−1.26795			−0.211325
$37$			1.79315i			0.294792i	0.989078	+	0.147396i	$0.0470892\pi$
$37$			1.79315i			0.294792i	−0.989078	+	0.147396i	$0.952911\pi$
$38$			2.17209i			0.352359i
$39$	−8.19615			−1.31243
$40$	−2.73205	−	3.34607i	−0.431975	−	0.529059i
$41$	−1.73205			−0.270501			−0.135250	−	0.990811i	$-0.543184\pi$
$41$	−1.73205			−0.270501			−0.135250	+	0.990811i	$0.543184\pi$
$42$			3.34607i			0.516309i
$43$		−	6.45189i		−	0.983905i	−0.870622	−	0.491952i	$-0.836283\pi$
$43$		−	6.45189i		−	0.983905i	0.870622	−	0.491952i	$-0.163717\pi$
$44$		0			0
$45$	−1.26795	+	1.03528i	−0.189015	+	0.154330i
$46$	−1.80385			−0.265963
$47$			11.4524i			1.67051i	0.549866	+	0.835253i	$0.314679\pi$
$47$			11.4524i			1.67051i	−0.549866	+	0.835253i	$0.685321\pi$
$48$			4.76028i			0.687087i
$49$	−4.19615			−0.599450
$50$	−2.53590	−	0.517638i	−0.358630	−	0.0732051i
$51$	7.46410			1.04518
$52$			7.34847i			1.01905i
$53$		−	2.17209i		−	0.298359i	−0.988810	−	0.149180i	$-0.952337\pi$
$53$		−	2.17209i		−	0.298359i	0.988810	−	0.149180i	$-0.0476633\pi$
$54$	2.26795			0.308629
$55$		0			0
$56$	6.46410			0.863802
$57$		−	8.10634i		−	1.07371i
$58$		−	3.58630i		−	0.470905i
$59$	1.26795			0.165073			0.0825365	−	0.996588i	$-0.473698\pi$
$59$	1.26795			0.165073			0.0825365	+	0.996588i	$0.473698\pi$
$60$	4.73205	+	5.79555i	0.610905	+	0.748203i
$61$	11.7321			1.50214			0.751068	−	0.660225i	$-0.229539\pi$
$61$	11.7321			1.50214			0.751068	+	0.660225i	$0.229539\pi$
$62$			4.52004i			0.574046i
$63$		−	2.44949i		−	0.308607i
$64$	2.26795			0.283494
$65$	6.00000	+	7.34847i	0.744208	+	0.911465i
$66$		0			0
$67$			2.20925i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$67$			2.20925i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$68$		−	6.69213i		−	0.811540i
$69$	6.73205			0.810444
$70$	3.00000	−	2.44949i	0.358569	−	0.292770i
$71$	−8.19615			−0.972704			−0.486352	−	0.873763i	$-0.661673\pi$
$71$	−8.19615			−0.972704			−0.486352	+	0.873763i	$0.661673\pi$
$72$			1.41421i			0.166667i
$73$		−	4.89898i		−	0.573382i	−0.958023	−	0.286691i	$-0.907445\pi$
$73$		−	4.89898i		−	0.573382i	0.958023	−	0.286691i	$-0.0925553\pi$
$74$	0.928203			0.107901
$75$	9.46410	+	1.93185i	1.09282	+	0.223071i
$76$	−7.26795			−0.833691
$77$		0			0
$78$			4.24264i			0.480384i
$79$	1.46410			0.164724			0.0823622	−	0.996602i	$-0.473754\pi$
$79$	1.46410			0.164724			0.0823622	+	0.996602i	$0.473754\pi$
$80$	4.26795	−	3.48477i	0.477171	−	0.389609i
$81$	−10.6603			−1.18447
$82$			0.896575i			0.0990102i
$83$		−	9.89949i		−	1.08661i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$		−	9.89949i		−	1.08661i	0.839535	−	0.543305i	$-0.182827\pi$
$84$	−11.1962			−1.22160
$85$	−5.46410	−	6.69213i	−0.592665	−	0.725863i
$86$	−3.33975			−0.360134
$87$			13.3843i			1.43494i
$88$		0			0
$89$	−0.464102			−0.0491947			−0.0245973	−	0.999697i	$-0.507830\pi$
$89$	−0.464102			−0.0491947			−0.0245973	+	0.999697i	$0.507830\pi$
$90$	0.535898	+	0.656339i	0.0564886	+	0.0691842i
$91$	−14.1962			−1.48816
$92$		−	6.03579i		−	0.629275i
$93$		−	16.8690i		−	1.74924i
$94$	5.92820			0.611447
$95$	−7.26795	+	5.93426i	−0.745676	+	0.608842i
$96$	9.92820			1.01329
$97$		−	9.14162i		−	0.928191i	−0.885785	−	0.464095i	$-0.846379\pi$
$97$		−	9.14162i		−	0.928191i	0.885785	−	0.464095i	$-0.153621\pi$
$98$			2.17209i			0.219414i
$99$		0			0
$100$	1.73205	−	8.48528i	0.173205	−	0.848528i
$101$	−19.3923			−1.92961			−0.964803	−	0.262973i	$-0.915297\pi$
$101$	−19.3923			−1.92961			−0.964803	+	0.262973i	$0.915297\pi$
$102$		−	3.86370i		−	0.382564i
$103$		−	4.24264i		−	0.418040i	−0.977911	−	0.209020i	$-0.932973\pi$
$103$		−	4.24264i		−	0.418040i	0.977911	−	0.209020i	$-0.0670273\pi$
$104$	8.19615			0.803699
$105$	−11.1962	+	9.14162i	−1.09263	+	0.892131i
$106$	−1.12436			−0.109207
$107$		−	2.96713i		−	0.286843i	−0.989662	−	0.143422i	$-0.954190\pi$
$107$		−	2.96713i		−	0.286843i	0.989662	−	0.143422i	$-0.0458105\pi$
$108$			7.58871i			0.730224i
$109$	9.19615			0.880832			0.440416	−	0.897794i	$-0.354831\pi$
$109$	9.19615			0.880832			0.440416	+	0.897794i	$0.354831\pi$
$110$		0			0
$111$	−3.46410			−0.328798
$112$			8.24504i			0.779083i
$113$		−	2.82843i		−	0.266076i	−0.991111	−	0.133038i	$-0.957527\pi$
$113$		−	2.82843i		−	0.266076i	0.991111	−	0.133038i	$-0.0424732\pi$
$114$	−4.19615			−0.393006
$115$	−4.92820	−	6.03579i	−0.459557	−	0.562840i
$116$	12.0000			1.11417
$117$		−	3.10583i		−	0.287134i
$118$		−	0.656339i		−	0.0604209i
$119$	12.9282			1.18513
$120$	6.46410	−	5.27792i	0.590089	−	0.481806i
$121$		0			0
$122$		−	6.07296i		−	0.549820i
$123$		−	3.34607i		−	0.301705i
$124$	−15.1244			−1.35821
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$	−1.26795			−0.112958
$127$			0.896575i			0.0795582i	0.999208	+	0.0397791i	$0.0126654\pi$
$127$			0.896575i			0.0795582i	−0.999208	+	0.0397791i	$0.987335\pi$
$128$		−	11.4524i		−	1.01226i
$129$	12.4641			1.09740
$130$	3.80385	−	3.10583i	0.333620	−	0.272399i
$131$	3.12436			0.272976			0.136488	−	0.990642i	$-0.456418\pi$
$131$	3.12436			0.272976			0.136488	+	0.990642i	$0.456418\pi$
$132$		0			0
$133$		−	14.0406i		−	1.21747i
$134$	1.14359			0.0987914
$135$	6.19615	+	7.58871i	0.533280	+	0.653132i
$136$	−7.46410			−0.640041
$137$		−	8.86422i		−	0.757321i	−0.925536	−	0.378661i	$-0.876385\pi$
$137$		−	8.86422i		−	0.757321i	0.925536	−	0.378661i	$-0.123615\pi$
$138$		−	3.48477i		−	0.296643i
$139$	−14.5885			−1.23738			−0.618688	−	0.785636i	$-0.712336\pi$
$139$	−14.5885			−1.23738			−0.618688	+	0.785636i	$0.712336\pi$
$140$	8.19615	+	10.0382i	0.692701	+	0.848382i
$141$	−22.1244			−1.86321
$142$			4.24264i			0.356034i
$143$		0			0
$144$	−1.80385			−0.150321
$145$	12.0000	−	9.79796i	0.996546	−	0.813676i
$146$	−2.53590			−0.209872
$147$		−	8.10634i		−	0.668600i
$148$			3.10583i			0.255298i
$149$	−10.2679			−0.841183			−0.420592	−	0.907250i	$-0.638177\pi$
$149$	−10.2679			−0.841183			−0.420592	+	0.907250i	$0.638177\pi$
$150$	1.00000	−	4.89898i	0.0816497	−	0.400000i
$151$	−4.19615			−0.341478			−0.170739	−	0.985316i	$-0.554616\pi$
$151$	−4.19615			−0.341478			−0.170739	+	0.985316i	$0.554616\pi$
$152$			8.10634i			0.657511i
$153$			2.82843i			0.228665i
$154$		0			0
$155$	−15.1244	+	12.3490i	−1.21482	+	0.991894i
$156$	−14.1962			−1.13660
$157$		−	21.8695i		−	1.74538i	−0.488275	−	0.872690i	$-0.662374\pi$
$157$		−	21.8695i		−	1.74538i	0.488275	−	0.872690i	$-0.337626\pi$
$158$		−	0.757875i		−	0.0602933i
$159$	4.19615			0.332777
$160$	−7.26795	−	8.90138i	−0.574582	−	0.703716i
$161$	11.6603			0.918957
$162$			5.51815i			0.433547i
$163$			5.13922i			0.402534i	0.979536	+	0.201267i	$0.0645060\pi$
$163$			5.13922i			0.402534i	−0.979536	+	0.201267i	$0.935494\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	−5.12436			−0.397727
$167$		−	0.517638i		−	0.0400560i	−0.999799	−	0.0200280i	$-0.993624\pi$
$167$		−	0.517638i		−	0.0400560i	0.999799	−	0.0200280i	$-0.00637554\pi$
$168$			12.4877i			0.963446i
$169$	−5.00000			−0.384615
$170$	−3.46410	+	2.82843i	−0.265684	+	0.216930i
$171$	3.07180			0.234906
$172$		−	11.1750i		−	0.852086i
$173$			21.7680i			1.65499i	0.561472	+	0.827495i	$0.310235\pi$
$173$			21.7680i			1.65499i	−0.561472	+	0.827495i	$0.689765\pi$
$174$	6.92820			0.525226
$175$	16.3923	+	3.34607i	1.23914	+	0.252939i
$176$		0			0
$177$			2.44949i			0.184115i
$178$			0.240237i			0.0180065i
$179$	15.4641			1.15584			0.577921	−	0.816093i	$-0.303864\pi$
$179$	15.4641			1.15584			0.577921	+	0.816093i	$0.303864\pi$
$180$	−2.19615	+	1.79315i	−0.163692	+	0.133654i
$181$	−17.3923			−1.29276			−0.646380	−	0.763016i	$-0.723718\pi$
$181$	−17.3923			−1.29276			−0.646380	+	0.763016i	$0.723718\pi$
$182$			7.34847i			0.544705i
$183$			22.6646i			1.67541i
$184$	−6.73205			−0.496293
$185$	2.53590	+	3.10583i	0.186443	+	0.228345i
$186$	−8.73205			−0.640265
$187$		0			0
$188$			19.8362i			1.44670i
$189$	−14.6603			−1.06638
$190$	3.07180	+	3.76217i	0.222852	+	0.272936i
$191$	−7.26795			−0.525890			−0.262945	−	0.964811i	$-0.584694\pi$
$191$	−7.26795			−0.525890			−0.262945	+	0.964811i	$0.584694\pi$
$192$			4.38134i			0.316196i
$193$			15.1774i			1.09249i	0.837624	+	0.546247i	$0.183944\pi$
$193$			15.1774i			1.09249i	−0.837624	+	0.546247i	$0.816056\pi$
$194$	−4.73205			−0.339741
$195$	−14.1962	+	11.5911i	−1.01661	+	0.830057i
$196$	−7.26795			−0.519139
$197$		−	17.2480i		−	1.22887i	−0.788969	−	0.614433i	$-0.789385\pi$
$197$		−	17.2480i		−	1.22887i	0.788969	−	0.614433i	$-0.210615\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	−9.46410	−	1.93185i	−0.669213	−	0.136603i
$201$	−4.26795			−0.301038
$202$			10.0382i			0.706285i
$203$			23.1822i			1.62707i
$204$	12.9282			0.905155
$205$	−3.00000	+	2.44949i	−0.209529	+	0.171080i
$206$	−2.19615			−0.153013
$207$			2.55103i			0.177309i
$208$			10.4543i			0.724875i
$209$		0			0
$210$	4.73205	+	5.79555i	0.326543	+	0.399931i
$211$	13.1244			0.903518			0.451759	−	0.892140i	$-0.350797\pi$
$211$	13.1244			0.903518			0.451759	+	0.892140i	$0.350797\pi$
$212$		−	3.76217i		−	0.258387i
$213$		−	15.8338i		−	1.08491i
$214$	−1.53590			−0.104992
$215$	−9.12436	−	11.1750i	−0.622276	−	0.762129i
$216$	8.46410			0.575909
$217$		−	29.2180i		−	1.98345i
$218$		−	4.76028i		−	0.322407i
$219$	9.46410			0.639525
$220$		0			0
$221$	16.3923			1.10267
$222$			1.79315i			0.120348i
$223$		−	1.55291i		−	0.103991i	−0.998647	−	0.0519954i	$-0.983442\pi$
$223$		−	1.55291i		−	0.103991i	0.998647	−	0.0519954i	$-0.0165581\pi$
$224$	17.1962			1.14897
$225$	−0.732051	+	3.58630i	−0.0488034	+	0.239087i
$226$	−1.46410			−0.0973906
$227$		−	20.1136i		−	1.33498i	−0.744617	−	0.667492i	$-0.767368\pi$
$227$		−	20.1136i		−	1.33498i	0.744617	−	0.667492i	$-0.232632\pi$
$228$		−	14.0406i		−	0.929861i
$229$	4.07180			0.269072			0.134536	−	0.990909i	$-0.457046\pi$
$229$	4.07180			0.269072			0.134536	+	0.990909i	$0.457046\pi$
$230$	−3.12436	+	2.55103i	−0.206014	+	0.168210i
$231$		0			0
$232$		−	13.3843i		−	0.878720i
$233$			1.69161i			0.110821i	0.998464	+	0.0554107i	$0.0176468\pi$
$233$			1.69161i			0.110821i	−0.998464	+	0.0554107i	$0.982353\pi$
$234$	−1.60770			−0.105098
$235$	16.1962	+	19.8362i	1.05652	+	1.29397i
$236$	2.19615			0.142957
$237$			2.82843i			0.183726i
$238$		−	6.69213i		−	0.433786i
$239$	5.66025			0.366131			0.183066	−	0.983101i	$-0.441398\pi$
$239$	5.66025			0.366131			0.183066	+	0.983101i	$0.441398\pi$
$240$	6.73205	+	8.24504i	0.434552	+	0.532215i
$241$	−14.1244			−0.909830			−0.454915	−	0.890535i	$-0.650330\pi$
$241$	−14.1244			−0.909830			−0.454915	+	0.890535i	$0.650330\pi$
$242$		0			0
$243$		−	7.45001i		−	0.477918i
$244$	20.3205			1.30089
$245$	−7.26795	+	5.93426i	−0.464332	+	0.379126i
$246$	−1.73205			−0.110432
$247$		−	17.8028i		−	1.13276i
$248$			16.8690i			1.07118i
$249$	19.1244			1.21196
$250$	−5.12436	+	2.68973i	−0.324093	+	0.170113i
$251$	−3.80385			−0.240097			−0.120048	−	0.992768i	$-0.538305\pi$
$251$	−3.80385			−0.240097			−0.120048	+	0.992768i	$0.538305\pi$
$252$		−	4.24264i		−	0.267261i
$253$		0			0
$254$	0.464102			0.0291203
$255$	12.9282	−	10.5558i	0.809595	−	0.661032i
$256$	−1.39230			−0.0870191
$257$			14.7985i			0.923103i	0.887113	+	0.461552i	$0.152707\pi$
$257$			14.7985i			0.923103i	−0.887113	+	0.461552i	$0.847293\pi$
$258$		−	6.45189i		−	0.401677i
$259$	−6.00000			−0.372822
$260$	10.3923	+	12.7279i	0.644503	+	0.789352i
$261$	−5.07180			−0.313936
$262$		−	1.61729i		−	0.0999162i
$263$		−	6.79367i		−	0.418915i	−0.977818	−	0.209458i	$-0.932830\pi$
$263$		−	6.79367i		−	0.418915i	0.977818	−	0.209458i	$-0.0671699\pi$
$264$		0			0
$265$	−3.07180	−	3.76217i	−0.188699	−	0.231108i
$266$	−7.26795			−0.445627
$267$		−	0.896575i		−	0.0548695i
$268$			3.82654i			0.233743i
$269$	16.2679			0.991874			0.495937	−	0.868358i	$-0.334825\pi$
$269$	16.2679			0.991874			0.495937	+	0.868358i	$0.334825\pi$
$270$	3.92820	−	3.20736i	0.239063	−	0.195194i
$271$	−11.4641			−0.696395			−0.348197	−	0.937421i	$-0.613206\pi$
$271$	−11.4641			−0.696395			−0.348197	+	0.937421i	$0.613206\pi$
$272$		−	9.52056i		−	0.577269i
$273$		−	27.4249i		−	1.65983i
$274$	−4.58846			−0.277199
$275$		0			0
$276$	11.6603			0.701865
$277$			31.1870i			1.87385i	0.349535	+	0.936923i	$0.386340\pi$
$277$			31.1870i			1.87385i	−0.349535	+	0.936923i	$0.613660\pi$
$278$			7.55154i			0.452911i
$279$	6.39230			0.382697
$280$	11.1962	−	9.14162i	0.669098	−	0.546316i
$281$	17.3205			1.03325			0.516627	−	0.856210i	$-0.327187\pi$
$281$	17.3205			1.03325			0.516627	+	0.856210i	$0.327187\pi$
$282$			11.4524i			0.681981i
$283$		−	8.06918i		−	0.479663i	−0.970815	−	0.239831i	$-0.922908\pi$
$283$		−	8.06918i		−	0.479663i	0.970815	−	0.239831i	$-0.0770922\pi$
$284$	−14.1962			−0.842387
$285$	−11.4641	−	14.0406i	−0.679075	−	0.831693i
$286$		0			0
$287$		−	5.79555i		−	0.342101i
$288$			3.76217i			0.221688i
$289$	2.07180			0.121870
$290$	−5.07180	−	6.21166i	−0.297826	−	0.364761i
$291$	17.6603			1.03526
$292$		−	8.48528i		−	0.496564i
$293$			15.0759i			0.880742i	0.897816	+	0.440371i	$0.145153\pi$
$293$			15.0759i			0.880742i	−0.897816	+	0.440371i	$0.854847\pi$
$294$	−4.19615			−0.244725
$295$	2.19615	−	1.79315i	0.127865	−	0.104401i
$296$	3.46410			0.201347
$297$		0			0
$298$			5.31508i			0.307894i
$299$	14.7846			0.855016
$300$	16.3923	+	3.34607i	0.946410	+	0.193185i
$301$	21.5885			1.24434
$302$			2.17209i			0.124990i
$303$		−	37.4631i		−	2.15220i
$304$	−10.3397			−0.593025
$305$	20.3205	−	16.5916i	1.16355	−	0.950034i
$306$	1.46410			0.0836971
$307$			7.82894i			0.446821i	0.974724	+	0.223411i	$0.0717191\pi$
$307$			7.82894i			0.446821i	−0.974724	+	0.223411i	$0.928281\pi$
$308$		0			0
$309$	8.19615			0.466263
$310$	6.39230	+	7.82894i	0.363059	+	0.444654i
$311$	10.0526			0.570028			0.285014	−	0.958523i	$-0.408002\pi$
$311$	10.0526			0.570028			0.285014	+	0.958523i	$0.408002\pi$
$312$			15.8338i			0.896410i
$313$			17.1464i			0.969173i	0.874743	+	0.484587i	$0.161030\pi$
$313$			17.1464i			0.969173i	−0.874743	+	0.484587i	$0.838970\pi$
$314$	−11.3205			−0.638853
$315$	−3.46410	−	4.24264i	−0.195180	−	0.239046i
$316$	2.53590			0.142655
$317$		−	12.6264i		−	0.709168i	−0.935024	−	0.354584i	$-0.884622\pi$
$317$		−	12.6264i		−	0.709168i	0.935024	−	0.354584i	$-0.115378\pi$
$318$		−	2.17209i		−	0.121805i
$319$		0			0
$320$	3.92820	−	3.20736i	0.219593	−	0.179297i
$321$	5.73205			0.319932
$322$		−	6.03579i		−	0.336362i
$323$			16.2127i			0.902098i
$324$	−18.4641			−1.02578
$325$	20.7846	+	4.24264i	1.15292	+	0.235339i
$326$	2.66025			0.147338
$327$			17.7656i			0.982440i
$328$			3.34607i			0.184756i
$329$	−38.3205			−2.11268
$330$		0			0
$331$	−18.1962			−1.00015			−0.500075	−	0.865982i	$-0.666694\pi$
$331$	−18.1962			−1.00015			−0.500075	+	0.865982i	$0.666694\pi$
$332$		−	17.1464i		−	0.941033i
$333$		−	1.31268i		−	0.0719343i
$334$	−0.267949			−0.0146615
$335$	3.12436	+	3.82654i	0.170702	+	0.209066i
$336$	−15.9282			−0.868955
$337$			17.6269i			0.960199i	0.877214	+	0.480099i	$0.159399\pi$
$337$			17.6269i			0.960199i	−0.877214	+	0.480099i	$0.840601\pi$
$338$			2.58819i			0.140779i
$339$	5.46410			0.296769
$340$	−9.46410	−	11.5911i	−0.513263	−	0.628616i
$341$		0			0
$342$		−	1.59008i		−	0.0859816i
$343$			9.38186i			0.506573i
$344$	−12.4641			−0.672019
$345$	11.6603	−	9.52056i	0.627767	−	0.512570i
$346$	11.2679			0.605769
$347$			4.38134i			0.235203i	0.993061	+	0.117601i	$0.0375205\pi$
$347$			4.38134i			0.235203i	−0.993061	+	0.117601i	$0.962479\pi$
$348$			23.1822i			1.24270i
$349$	−7.32051			−0.391858			−0.195929	−	0.980618i	$-0.562772\pi$
$349$	−7.32051			−0.391858			−0.195929	+	0.980618i	$0.562772\pi$
$350$	1.73205	−	8.48528i	0.0925820	−	0.453557i
$351$	−18.5885			−0.992178
$352$		0			0
$353$			13.0053i			0.692204i	0.938197	+	0.346102i	$0.112495\pi$
$353$			13.0053i			0.692204i	−0.938197	+	0.346102i	$0.887505\pi$
$354$	1.26795			0.0673907
$355$	−14.1962	+	11.5911i	−0.753454	+	0.615192i
$356$	−0.803848			−0.0426038
$357$			24.9754i			1.32184i
$358$		−	8.00481i		−	0.423067i
$359$	35.6603			1.88208			0.941038	−	0.338301i	$-0.109852\pi$
$359$	35.6603			1.88208			0.941038	+	0.338301i	$0.109852\pi$
$360$	2.00000	+	2.44949i	0.105409	+	0.129099i
$361$	−1.39230			−0.0732792
$362$			9.00292i			0.473183i
$363$		0			0
$364$	−24.5885			−1.28879
$365$	−6.92820	−	8.48528i	−0.362639	−	0.444140i
$366$	11.7321			0.613244
$367$		−	16.9062i		−	0.882496i	−0.897385	−	0.441248i	$-0.854536\pi$
$367$		−	16.9062i		−	0.882496i	0.897385	−	0.441248i	$-0.145464\pi$
$368$		−	8.58682i		−	0.447619i
$369$	1.26795			0.0660068
$370$	1.60770	−	1.31268i	0.0835801	−	0.0682429i
$371$	7.26795			0.377333
$372$		−	29.2180i		−	1.51488i
$373$			0.175865i			0.00910597i	0.999990	+	0.00455298i	$0.00144926\pi$
$373$			0.175865i			0.00910597i	−0.999990	+	0.00455298i	$0.998551\pi$
$374$		0			0
$375$	19.1244	−	10.0382i	0.987577	−	0.518370i
$376$	22.1244			1.14098
$377$			29.3939i			1.51386i
$378$			7.58871i			0.390321i
$379$	−1.46410			−0.0752058			−0.0376029	−	0.999293i	$-0.511972\pi$
$379$	−1.46410			−0.0752058			−0.0376029	+	0.999293i	$0.511972\pi$
$380$	−12.5885	+	10.2784i	−0.645774	+	0.527272i
$381$	−1.73205			−0.0887357
$382$			3.76217i			0.192489i
$383$			38.4612i			1.96527i	0.185539	+	0.982637i	$0.440597\pi$
$383$			38.4612i			1.96527i	−0.185539	+	0.982637i	$0.559403\pi$
$384$	22.1244			1.12903
$385$		0			0
$386$	7.85641			0.399881
$387$			4.72311i			0.240089i
$388$		−	15.8338i		−	0.803837i
$389$	−6.12436			−0.310517			−0.155259	−	0.987874i	$-0.549621\pi$
$389$	−6.12436			−0.310517			−0.155259	+	0.987874i	$0.549621\pi$
$390$	6.00000	+	7.34847i	0.303822	+	0.372104i
$391$	−13.4641			−0.680909
$392$			8.10634i			0.409432i
$393$			6.03579i			0.304465i
$394$	−8.92820			−0.449796
$395$	2.53590	−	2.07055i	0.127595	−	0.104181i
$396$		0			0
$397$			32.9802i			1.65523i	0.561298	+	0.827614i	$0.310302\pi$
$397$			32.9802i			1.65523i	−0.561298	+	0.827614i	$0.689698\pi$
$398$		−	1.03528i		−	0.0518937i
$399$	27.1244			1.35792
$400$	2.46410	−	12.0716i	0.123205	−	0.603579i
$401$	2.32051			0.115881			0.0579403	−	0.998320i	$-0.481547\pi$
$401$	2.32051			0.115881			0.0579403	+	0.998320i	$0.481547\pi$
$402$			2.20925i			0.110188i
$403$		−	37.0470i		−	1.84544i
$404$	−33.5885			−1.67109
$405$	−18.4641	+	15.0759i	−0.917489	+	0.749126i
$406$	12.0000			0.595550
$407$		0			0
$408$		−	14.4195i		−	0.713873i
$409$	−26.1244			−1.29177			−0.645883	−	0.763436i	$-0.723511\pi$
$409$	−26.1244			−1.29177			−0.645883	+	0.763436i	$0.723511\pi$
$410$	1.26795	+	1.55291i	0.0626195	+	0.0766930i
$411$	17.1244			0.844682
$412$		−	7.34847i		−	0.362033i
$413$			4.24264i			0.208767i
$414$	1.32051			0.0648994
$415$	−14.0000	−	17.1464i	−0.687233	−	0.841685i
$416$	21.8038			1.06902
$417$		−	28.1827i		−	1.38011i
$418$		0			0
$419$	12.3397			0.602836			0.301418	−	0.953492i	$-0.402540\pi$
$419$	12.3397			0.602836			0.301418	+	0.953492i	$0.402540\pi$
$420$	−19.3923	+	15.8338i	−0.946248	+	0.772608i
$421$	−17.0526			−0.831091			−0.415545	−	0.909572i	$-0.636409\pi$
$421$	−17.0526			−0.831091			−0.415545	+	0.909572i	$0.636409\pi$
$422$		−	6.79367i		−	0.330711i
$423$		−	8.38375i		−	0.407632i
$424$	−4.19615			−0.203783
$425$	−18.9282	−	3.86370i	−0.918153	−	0.187417i
$426$	−8.19615			−0.397105
$427$			39.2562i			1.89974i
$428$		−	5.13922i		−	0.248413i
$429$		0			0
$430$	−5.78461	+	4.72311i	−0.278959	+	0.227769i
$431$	5.07180			0.244300			0.122150	−	0.992512i	$-0.461021\pi$
$431$	5.07180			0.244300			0.122150	+	0.992512i	$0.461021\pi$
$432$			10.7961i			0.519426i
$433$			28.7375i			1.38104i	0.723314	+	0.690519i	$0.242618\pi$
$433$			28.7375i			1.38104i	−0.723314	+	0.690519i	$0.757382\pi$
$434$	−15.1244			−0.725992
$435$	18.9282	+	23.1822i	0.907538	+	1.11150i
$436$	15.9282			0.762823
$437$			14.6226i			0.699494i
$438$		−	4.89898i		−	0.234082i
$439$	28.2487			1.34824			0.674119	−	0.738623i	$-0.264524\pi$
$439$	28.2487			1.34824			0.674119	+	0.738623i	$0.264524\pi$
$440$		0			0
$441$	3.07180			0.146276
$442$		−	8.48528i		−	0.403604i
$443$		−	27.5636i		−	1.30958i	−0.755809	−	0.654792i	$-0.772756\pi$
$443$		−	27.5636i		−	1.30958i	0.755809	−	0.654792i	$-0.227244\pi$
$444$	−6.00000			−0.284747
$445$	−0.803848	+	0.656339i	−0.0381060	+	0.0311134i
$446$	−0.803848			−0.0380633
$447$		−	19.8362i		−	0.938218i
$448$			7.58871i			0.358533i
$449$	−34.5167			−1.62894			−0.814471	−	0.580204i	$-0.802973\pi$
$449$	−34.5167			−1.62894			−0.814471	+	0.580204i	$0.802973\pi$
$450$	1.85641	+	0.378937i	0.0875118	+	0.0178633i
$451$		0			0
$452$		−	4.89898i		−	0.230429i
$453$		−	8.10634i		−	0.380869i
$454$	−10.4115			−0.488638
$455$	−24.5885	+	20.0764i	−1.15272	+	0.941196i
$456$	−15.6603			−0.733359
$457$			21.2132i			0.992312i	0.868233	+	0.496156i	$0.165256\pi$
$457$			21.2132i			0.992312i	−0.868233	+	0.496156i	$0.834744\pi$
$458$		−	2.10772i		−	0.0984872i
$459$	16.9282			0.790141
$460$	−8.53590	−	10.4543i	−0.397988	−	0.487434i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$			20.3166i			0.944194i	0.881547	+	0.472097i	$0.156503\pi$
$463$			20.3166i			0.944194i	−0.881547	+	0.472097i	$0.843497\pi$
$464$	17.0718			0.792538
$465$	−23.8564	−	29.2180i	−1.10631	−	1.35495i
$466$	0.875644			0.0405634
$467$		−	0.619174i		−	0.0286520i	−0.999897	−	0.0143260i	$-0.995440\pi$
$467$		−	0.619174i		−	0.0286520i	0.999897	−	0.0143260i	$-0.00456026\pi$
$468$		−	5.37945i		−	0.248665i
$469$	−7.39230			−0.341345
$470$	10.2679	−	8.38375i	0.473625	−	0.386713i
$471$	42.2487			1.94672
$472$		−	2.44949i		−	0.112747i
$473$		0			0
$474$	1.46410			0.0672484
$475$	−4.19615	+	20.5569i	−0.192533	+	0.943214i
$476$	22.3923			1.02635
$477$			1.59008i			0.0728047i
$478$		−	2.92996i		−	0.134013i
$479$	2.53590			0.115868			0.0579341	−	0.998320i	$-0.481549\pi$
$479$	2.53590			0.115868			0.0579341	+	0.998320i	$0.481549\pi$
$480$	17.1962	−	14.0406i	0.784893	−	0.640863i
$481$	−7.60770			−0.346881
$482$			7.31130i			0.333021i
$483$			22.5259i			1.02496i
$484$		0			0
$485$	−12.9282	−	15.8338i	−0.587039	−	0.718974i
$486$	−3.85641			−0.174930
$487$			12.7279i			0.576757i	0.957516	+	0.288379i	$0.0931162\pi$
$487$			12.7279i			0.576757i	−0.957516	+	0.288379i	$0.906884\pi$
$488$		−	22.6646i		−	1.02598i
$489$	−9.92820			−0.448969
$490$	3.07180	+	3.76217i	0.138770	+	0.169957i
$491$	−39.7128			−1.79221			−0.896107	−	0.443838i	$-0.853617\pi$
$491$	−39.7128			−1.79221			−0.896107	+	0.443838i	$0.853617\pi$
$492$		−	5.79555i		−	0.261284i
$493$		−	26.7685i		−	1.20559i
$494$	−9.21539			−0.414620
$495$		0			0
$496$	−21.5167			−0.966127
$497$		−	27.4249i		−	1.23017i
$498$		−	9.89949i		−	0.443607i
$499$	−17.6077			−0.788229			−0.394114	−	0.919061i	$-0.628949\pi$
$499$	−17.6077			−0.788229			−0.394114	+	0.919061i	$0.628949\pi$
$500$	−9.00000	−	17.1464i	−0.402492	−	0.766812i
$501$	1.00000			0.0446767
$502$			1.96902i			0.0878815i
$503$		−	7.38563i		−	0.329309i	−0.986351	−	0.164655i	$-0.947349\pi$
$503$		−	7.38563i		−	0.329309i	0.986351	−	0.164655i	$-0.0526509\pi$
$504$	−4.73205			−0.210782
$505$	−33.5885	+	27.4249i	−1.49467	+	1.22039i
$506$		0			0
$507$		−	9.65926i		−	0.428983i
$508$			1.55291i			0.0688994i
$509$	8.07180			0.357776			0.178888	−	0.983869i	$-0.442750\pi$
$509$	8.07180			0.357776			0.178888	+	0.983869i	$0.442750\pi$
$510$	−5.46410	−	6.69213i	−0.241954	−	0.296333i
$511$	16.3923			0.725153
$512$		−	22.1841i		−	0.980408i
$513$		−	18.3848i		−	0.811708i
$514$	7.66025			0.337879
$515$	−6.00000	−	7.34847i	−0.264392	−	0.323812i
$516$	21.5885			0.950379
$517$		0			0
$518$			3.10583i			0.136462i
$519$	−42.0526			−1.84590
$520$	14.1962	−	11.5911i	0.622542	−	0.508304i
$521$	−9.24871			−0.405193			−0.202597	−	0.979262i	$-0.564938\pi$
$521$	−9.24871			−0.405193			−0.202597	+	0.979262i	$0.564938\pi$
$522$			2.62536i			0.114909i
$523$			25.6317i			1.12080i	0.828223	+	0.560398i	$0.189352\pi$
$523$			25.6317i			1.12080i	−0.828223	+	0.560398i	$0.810648\pi$
$524$	5.41154			0.236404
$525$	−6.46410	+	31.6675i	−0.282117	+	1.38208i
$526$	−3.51666			−0.153334
$527$			33.7381i			1.46965i
$528$		0			0
$529$	10.8564			0.472018
$530$	−1.94744	+	1.59008i	−0.0845914	+	0.0690686i
$531$	−0.928203			−0.0402806
$532$		−	24.3190i		−	1.05436i
$533$		−	7.34847i		−	0.318298i
$534$	−0.464102			−0.0200836
$535$	−4.19615	−	5.13922i	−0.181415	−	0.222188i
$536$	4.26795			0.184347
$537$			29.8744i			1.28917i
$538$		−	8.42091i		−	0.363051i
$539$		0			0
$540$	10.7321	+	13.1440i	0.461834	+	0.565629i
$541$	2.60770			0.112114			0.0560568	−	0.998428i	$-0.482147\pi$
$541$	2.60770			0.112114			0.0560568	+	0.998428i	$0.482147\pi$
$542$			5.93426i			0.254898i
$543$		−	33.5994i		−	1.44189i
$544$	−19.8564			−0.851336
$545$	15.9282	−	13.0053i	0.682289	−	0.557087i
$546$	−14.1962			−0.607539
$547$			28.7375i			1.22873i	0.789023	+	0.614364i	$0.210587\pi$
$547$			28.7375i			1.22873i	−0.789023	+	0.614364i	$0.789413\pi$
$548$		−	15.3533i		−	0.655859i
$549$	−8.58846			−0.366546
$550$		0			0
$551$	−29.0718			−1.23850
$552$		−	13.0053i		−	0.553543i
$553$			4.89898i			0.208326i
$554$	16.1436			0.685876
$555$	−6.00000	+	4.89898i	−0.254686	+	0.207950i
$556$	−25.2679			−1.07160
$557$			37.6018i			1.59324i	0.604482	+	0.796619i	$0.293380\pi$
$557$			37.6018i			1.59324i	−0.604482	+	0.796619i	$0.706620\pi$
$558$		−	3.30890i		−	0.140077i
$559$	27.3731			1.15776
$560$	11.6603	+	14.2808i	0.492736	+	0.603475i
$561$		0			0
$562$		−	8.96575i		−	0.378198i
$563$			15.9725i			0.673159i	0.941655	+	0.336579i	$0.109270\pi$
$563$			15.9725i			0.673159i	−0.941655	+	0.336579i	$0.890730\pi$
$564$	−38.3205			−1.61358
$565$	−4.00000	−	4.89898i	−0.168281	−	0.206102i
$566$	−4.17691			−0.175569
$567$		−	35.6699i		−	1.49800i
$568$			15.8338i			0.664369i
$569$	30.1244			1.26288			0.631439	−	0.775425i	$-0.282464\pi$
$569$	30.1244			1.26288			0.631439	+	0.775425i	$0.282464\pi$
$570$	−7.26795	+	5.93426i	−0.304421	+	0.248559i
$571$	19.7128			0.824956			0.412478	−	0.910968i	$-0.364663\pi$
$571$	19.7128			0.824956			0.412478	+	0.910968i	$0.364663\pi$
$572$		0			0
$573$		−	14.0406i		−	0.586554i
$574$	−3.00000			−0.125218
$575$	−17.0718	−	3.48477i	−0.711943	−	0.145325i
$576$	−1.66025			−0.0691773
$577$		−	3.76217i		−	0.156621i	−0.996929	−	0.0783105i	$-0.975047\pi$
$577$		−	3.76217i		−	0.156621i	0.996929	−	0.0783105i	$-0.0249526\pi$
$578$		−	1.07244i		−	0.0446077i
$579$	−29.3205			−1.21852
$580$	20.7846	−	16.9706i	0.863034	−	0.704664i
$581$	33.1244			1.37423
$582$		−	9.14162i		−	0.378932i
$583$		0			0
$584$	−9.46410			−0.391627
$585$	−4.39230	−	5.37945i	−0.181599	−	0.222413i
$586$	7.80385			0.322374
$587$		−	20.3910i		−	0.841625i	−0.907148	−	0.420812i	$-0.861745\pi$
$587$		−	20.3910i		−	0.841625i	0.907148	−	0.420812i	$-0.138255\pi$
$588$		−	14.0406i		−	0.579025i
$589$	36.6410			1.50977
$590$	−0.928203	−	1.13681i	−0.0382135	−	0.0468018i
$591$	33.3205			1.37062
$592$			4.41851i			0.181599i
$593$			0.859411i			0.0352918i	0.999844	+	0.0176459i	$0.00561715\pi$
$593$			0.859411i			0.0352918i	−0.999844	+	0.0176459i	$0.994383\pi$
$594$		0			0
$595$	22.3923	−	18.2832i	0.917995	−	0.749540i
$596$	−17.7846			−0.728486
$597$			3.86370i			0.158131i
$598$		−	7.65308i		−	0.312958i
$599$	38.4449			1.57081			0.785407	−	0.618979i	$-0.212454\pi$
$599$	38.4449			1.57081			0.785407	+	0.618979i	$0.212454\pi$
$600$	3.73205	−	18.2832i	0.152360	−	0.746410i
$601$	−20.0000			−0.815817			−0.407909	−	0.913023i	$-0.633742\pi$
$601$	−20.0000			−0.815817			−0.407909	+	0.913023i	$0.633742\pi$
$602$		−	11.1750i		−	0.455459i
$603$		−	1.61729i		−	0.0658610i
$604$	−7.26795			−0.295729
$605$		0			0
$606$	−19.3923			−0.787759
$607$		−	36.3906i		−	1.47705i	−0.674226	−	0.738525i	$-0.735523\pi$
$607$		−	36.3906i		−	1.47705i	0.674226	−	0.738525i	$-0.264477\pi$
$608$			21.5649i			0.874574i
$609$	−44.7846			−1.81476
$610$	−8.58846	−	10.5187i	−0.347736	−	0.425888i
$611$	−48.5885			−1.96568
$612$			4.89898i			0.198030i
$613$			1.79315i			0.0724247i	0.999344	+	0.0362123i	$0.0115293\pi$
$613$			1.79315i			0.0724247i	−0.999344	+	0.0362123i	$0.988471\pi$
$614$	4.05256			0.163548
$615$	−4.73205	−	5.79555i	−0.190815	−	0.233699i
$616$		0			0
$617$			13.0053i			0.523575i	0.965126	+	0.261787i	$0.0843119\pi$
$617$			13.0053i			0.523575i	−0.965126	+	0.261787i	$0.915688\pi$
$618$		−	4.24264i		−	0.170664i
$619$	−12.7846			−0.513857			−0.256928	−	0.966430i	$-0.582710\pi$
$619$	−12.7846			−0.513857			−0.256928	+	0.966430i	$0.582710\pi$
$620$	−26.1962	+	21.3891i	−1.05206	+	0.859006i
$621$	15.2679			0.612682
$622$		−	5.20359i		−	0.208645i
$623$		−	1.55291i		−	0.0622162i
$624$	−20.1962			−0.808493
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	8.87564			0.354742
$627$		0			0
$628$		−	37.8792i		−	1.51154i
$629$	6.92820			0.276246
$630$	−2.19615	+	1.79315i	−0.0874968	+	0.0714408i
$631$	−15.3205			−0.609900			−0.304950	−	0.952368i	$-0.598640\pi$
$631$	−15.3205			−0.609900			−0.304950	+	0.952368i	$0.598640\pi$
$632$		−	2.82843i		−	0.112509i
$633$			25.3543i			1.00774i
$634$	−6.53590			−0.259574
$635$	1.26795	+	1.55291i	0.0503170	+	0.0616255i
$636$	7.26795			0.288193
$637$		−	17.8028i		−	0.705371i
$638$		0			0
$639$	6.00000			0.237356
$640$	−16.1962	−	19.8362i	−0.640209	−	0.784093i
$641$	−7.85641			−0.310309			−0.155155	−	0.987890i	$-0.549588\pi$
$641$	−7.85641			−0.310309			−0.155155	+	0.987890i	$0.549588\pi$
$642$		−	2.96713i		−	0.117103i
$643$			10.5187i			0.414816i	0.978255	+	0.207408i	$0.0665027\pi$
$643$			10.5187i			0.414816i	−0.978255	+	0.207408i	$0.933497\pi$
$644$	20.1962			0.795840
$645$	21.5885	−	17.6269i	0.850045	−	0.694059i
$646$	8.39230			0.330191
$647$		−	37.3615i		−	1.46883i	−0.678699	−	0.734416i	$-0.737456\pi$
$647$		−	37.3615i		−	1.46883i	0.678699	−	0.734416i	$-0.262544\pi$
$648$			20.5940i			0.809010i
$649$		0			0
$650$	2.19615	−	10.7589i	0.0861402	−	0.421999i
$651$	56.4449			2.21225
$652$			8.90138i			0.348605i
$653$		−	12.1459i		−	0.475306i	−0.971350	−	0.237653i	$-0.923622\pi$
$653$		−	12.1459i		−	0.475306i	0.971350	−	0.237653i	$-0.0763782\pi$
$654$	9.19615			0.359598
$655$	5.41154	−	4.41851i	0.211446	−	0.172645i
$656$	−4.26795			−0.166635
$657$			3.58630i			0.139915i
$658$			19.8362i			0.773294i
$659$	−23.3205			−0.908438			−0.454219	−	0.890890i	$-0.650082\pi$
$659$	−23.3205			−0.908438			−0.454219	+	0.890890i	$0.650082\pi$
$660$		0			0
$661$	29.5885			1.15086			0.575429	−	0.817852i	$-0.304835\pi$
$661$	29.5885			1.15086			0.575429	+	0.817852i	$0.304835\pi$
$662$			9.41902i			0.366081i
$663$			31.6675i			1.22986i
$664$	−19.1244			−0.742169
$665$	−19.8564	−	24.3190i	−0.769998	−	0.943052i
$666$	−0.679492			−0.0263298
$667$		−	24.1432i		−	0.934827i
$668$		−	0.896575i		−	0.0346895i
$669$	3.00000			0.115987
$670$	1.98076	−	1.61729i	0.0765235	−	0.0624812i
$671$		0			0
$672$			33.2204i			1.28151i
$673$		−	40.8091i		−	1.57308i	−0.617542	−	0.786538i	$-0.711871\pi$
$673$		−	40.8091i		−	1.57308i	0.617542	−	0.786538i	$-0.288129\pi$
$674$	9.12436			0.351457
$675$	21.4641	+	4.38134i	0.826154	+	0.168638i
$676$	−8.66025			−0.333087
$677$		−	20.3538i		−	0.782260i	−0.920335	−	0.391130i	$-0.872084\pi$
$677$		−	20.3538i		−	0.782260i	0.920335	−	0.391130i	$-0.127916\pi$
$678$		−	2.82843i		−	0.108625i
$679$	30.5885			1.17388
$680$	−12.9282	+	10.5558i	−0.495774	+	0.404798i
$681$	38.8564			1.48898
$682$		0			0
$683$		−	29.8372i		−	1.14169i	−0.821058	−	0.570844i	$-0.806616\pi$
$683$		−	29.8372i		−	1.14169i	0.821058	−	0.570844i	$-0.193384\pi$
$684$	5.32051			0.203435
$685$	−12.5359	−	15.3533i	−0.478972	−	0.586619i
$686$	4.85641			0.185418
$687$			7.86611i			0.300111i
$688$		−	15.8981i		−	0.606110i
$689$	9.21539			0.351078
$690$	−4.92820	−	6.03579i	−0.187613	−	0.229779i
$691$	37.9090			1.44213			0.721063	−	0.692870i	$-0.243654\pi$
$691$	37.9090			1.44213			0.721063	+	0.692870i	$0.243654\pi$
$692$			37.7033i			1.43326i
$693$		0			0
$694$	2.26795			0.0860902
$695$	−25.2679	+	20.6312i	−0.958468	+	0.782586i
$696$	25.8564			0.980085
$697$			6.69213i			0.253483i
$698$			3.78937i			0.143430i
$699$	−3.26795			−0.123605
$700$	28.3923	+	5.79555i	1.07313	+	0.219051i
$701$	−37.8564			−1.42982			−0.714908	−	0.699218i	$-0.753532\pi$
$701$	−37.8564			−1.42982			−0.714908	+	0.699218i	$0.753532\pi$
$702$			9.62209i			0.363163i
$703$		−	7.52433i		−	0.283786i
$704$		0			0
$705$	−38.3205	+	31.2886i	−1.44323	+	1.17840i
$706$	6.73205			0.253364
$707$		−	64.8879i		−	2.44036i
$708$			4.24264i			0.159448i
$709$	−2.60770			−0.0979340			−0.0489670	−	0.998800i	$-0.515593\pi$
$709$	−2.60770			−0.0979340			−0.0489670	+	0.998800i	$0.515593\pi$
$710$	6.00000	+	7.34847i	0.225176	+	0.275783i
$711$	−1.07180			−0.0401955
$712$			0.896575i			0.0336006i
$713$			30.4292i			1.13958i
$714$	12.9282			0.483826
$715$		0			0
$716$	26.7846			1.00099
$717$			10.9348i			0.408367i
$718$		−	18.4591i		−	0.688888i
$719$	50.1962			1.87200			0.936000	−	0.351999i	$-0.114498\pi$
$719$	50.1962			1.87200			0.936000	+	0.351999i	$0.114498\pi$
$720$	−3.12436	+	2.55103i	−0.116438	+	0.0950711i
$721$	14.1962			0.528692
$722$			0.720710i			0.0268220i
$723$		−	27.2862i		−	1.01478i
$724$	−30.1244			−1.11956
$725$	6.92820	−	33.9411i	0.257307	−	1.26054i
$726$		0			0
$727$		−	8.24504i		−	0.305792i	−0.988242	−	0.152896i	$-0.951140\pi$
$727$		−	8.24504i		−	0.305792i	0.988242	−	0.152896i	$-0.0488599\pi$
$728$			27.4249i			1.01643i
$729$	−17.5885			−0.651424
$730$	−4.39230	+	3.58630i	−0.162566	+	0.132735i
$731$	−24.9282			−0.922003
$732$			39.2562i			1.45095i
$733$		−	9.31749i		−	0.344149i	−0.985084	−	0.172075i	$-0.944953\pi$
$733$		−	9.31749i		−	0.344149i	0.985084	−	0.172075i	$-0.0550470\pi$
$734$	−8.75129			−0.323016
$735$	−11.4641	−	14.0406i	−0.422860	−	0.517895i
$736$	−17.9090			−0.660133
$737$		0			0
$738$		−	0.656339i		−	0.0241602i
$739$	−38.9282			−1.43200			−0.715999	−	0.698102i	$-0.754028\pi$
$739$	−38.9282			−1.43200			−0.715999	+	0.698102i	$0.754028\pi$
$740$	4.39230	+	5.37945i	0.161464	+	0.197753i
$741$	34.3923			1.26343
$742$		−	3.76217i		−	0.138114i
$743$			43.3973i			1.59209i	0.605235	+	0.796046i	$0.293079\pi$
$743$			43.3973i			1.59209i	−0.605235	+	0.796046i	$0.706921\pi$
$744$	−32.5885			−1.19475
$745$	−17.7846	+	14.5211i	−0.651578	+	0.532011i
$746$	0.0910347			0.00333302
$747$			7.24693i			0.265151i
$748$		0			0
$749$	9.92820			0.362769
$750$	−5.19615	−	9.89949i	−0.189737	−	0.361478i
$751$	48.6410			1.77494			0.887468	−	0.460869i	$-0.152462\pi$
$751$	48.6410			1.77494			0.887468	+	0.460869i	$0.152462\pi$
$752$			28.2199i			1.02907i
$753$		−	7.34847i		−	0.267793i
$754$	15.2154			0.554112
$755$	−7.26795	+	5.93426i	−0.264508	+	0.215970i
$756$	−25.3923			−0.923509
$757$		−	49.7749i		−	1.80910i	−0.426369	−	0.904549i	$-0.640207\pi$
$757$		−	49.7749i		−	1.80910i	0.426369	−	0.904549i	$-0.359793\pi$
$758$			0.757875i			0.0275273i
$759$		0			0
$760$	11.4641	+	14.0406i	0.415847	+	0.509306i
$761$	19.8564			0.719794			0.359897	−	0.932992i	$-0.382812\pi$
$761$	19.8564			0.719794			0.359897	+	0.932992i	$0.382812\pi$
$762$			0.896575i			0.0324795i
$763$			30.7709i			1.11398i
$764$	−12.5885			−0.455434
$765$	4.00000	+	4.89898i	0.144620	+	0.177123i
$766$	19.9090			0.719340
$767$			5.37945i			0.194241i
$768$		−	2.68973i		−	0.0970571i
$769$	−9.85641			−0.355431			−0.177716	−	0.984082i	$-0.556871\pi$
$769$	−9.85641			−0.355431			−0.177716	+	0.984082i	$0.556871\pi$
$770$		0			0
$771$	−28.5885			−1.02959
$772$			26.2880i			0.946128i
$773$			12.0444i			0.433206i	0.976260	+	0.216603i	$0.0694977\pi$
$773$			12.0444i			0.433206i	−0.976260	+	0.216603i	$0.930502\pi$
$774$	2.44486			0.0878788
$775$	−8.73205	+	42.7781i	−0.313665	+	1.53664i
$776$	−17.6603			−0.633966
$777$		−	11.5911i		−	0.415829i
$778$			3.17020i			0.113657i
$779$	7.26795			0.260401
$780$	−24.5885	+	20.0764i	−0.880408	+	0.718850i
$781$		0			0
$782$			6.96953i			0.249230i
$783$			30.3548i			1.08479i
$784$	−10.3397			−0.369277
$785$	−30.9282	−	37.8792i	−1.10387	−	1.35197i
$786$	3.12436			0.111442
$787$			17.3867i			0.619768i	0.950774	+	0.309884i	$0.100290\pi$
$787$			17.3867i			0.619768i	−0.950774	+	0.309884i	$0.899710\pi$
$788$		−	29.8744i		−	1.06423i
$789$	13.1244			0.467239
$790$	−1.07180	−	1.31268i	−0.0381328	−	0.0467030i
$791$	9.46410			0.336505
$792$		0			0
$793$			49.7749i			1.76756i
$794$	17.0718			0.605855
$795$	7.26795	−	5.93426i	0.257768	−	0.210466i
$796$	3.46410			0.122782
$797$			36.1875i			1.28183i	0.767612	+	0.640914i	$0.221445\pi$
$797$			36.1875i			1.28183i	−0.767612	+	0.640914i	$0.778555\pi$
$798$		−	14.0406i		−	0.497032i
$799$	44.2487			1.56541
$800$	−25.1769	−	5.13922i	−0.890138	−	0.181699i
$801$	0.339746			0.0120043
$802$		−	1.20118i		−	0.0424153i
$803$		0			0
$804$	−7.39230			−0.260706
$805$	20.1962	−	16.4901i	0.711821	−	0.581199i
$806$	−19.1769			−0.675478
$807$			31.4273i			1.10629i
$808$			37.4631i			1.31795i
$809$	−14.5359			−0.511055			−0.255527	−	0.966802i	$-0.582249\pi$
$809$	−14.5359			−0.511055			−0.255527	+	0.966802i	$0.582249\pi$
$810$	7.80385	+	9.55772i	0.274199	+	0.335824i
$811$	−18.9808			−0.666505			−0.333252	−	0.942838i	$-0.608146\pi$
$811$	−18.9808			−0.666505			−0.333252	+	0.942838i	$0.608146\pi$
$812$			40.1528i			1.40909i
$813$		−	22.1469i		−	0.776727i
$814$		0			0
$815$	7.26795	+	8.90138i	0.254585	+	0.311802i
$816$	18.3923			0.643859
$817$			27.0731i			0.947169i
$818$			13.5230i			0.472819i
$819$	10.3923			0.363137
$820$	−5.19615	+	4.24264i	−0.181458	+	0.148159i
$821$	−29.1962			−1.01895			−0.509476	−	0.860485i	$-0.670161\pi$
$821$	−29.1962			−1.01895			−0.509476	+	0.860485i	$0.670161\pi$
$822$		−	8.86422i		−	0.309175i
$823$			6.75650i			0.235517i	0.993042	+	0.117758i	$0.0375708\pi$
$823$			6.75650i			0.235517i	−0.993042	+	0.117758i	$0.962429\pi$
$824$	−8.19615			−0.285526
$825$		0			0
$826$	2.19615			0.0764139
$827$			34.0798i			1.18507i	0.805544	+	0.592536i	$0.201873\pi$
$827$			34.0798i			1.18507i	−0.805544	+	0.592536i	$0.798127\pi$
$828$			4.41851i			0.153554i
$829$	9.98076			0.346646			0.173323	−	0.984865i	$-0.444550\pi$
$829$	9.98076			0.346646			0.173323	+	0.984865i	$0.444550\pi$
$830$	−8.87564	+	7.24693i	−0.308078	+	0.251545i
$831$	−60.2487			−2.09000
$832$			9.62209i			0.333586i
$833$			16.2127i			0.561736i
$834$	−14.5885			−0.505157
$835$	−0.732051	−	0.896575i	−0.0253337	−	0.0310273i
$836$		0			0
$837$		−	38.2581i		−	1.32239i
$838$		−	6.38752i		−	0.220653i
$839$	38.7846			1.33899			0.669497	−	0.742815i	$-0.266510\pi$
$839$	38.7846			1.33899			0.669497	+	0.742815i	$0.266510\pi$
$840$	17.6603	+	21.6293i	0.609337	+	0.746282i
$841$	19.0000			0.655172
$842$			8.82705i			0.304200i
$843$			33.4607i			1.15245i
$844$	22.7321			0.782469
$845$	−8.66025	+	7.07107i	−0.297922	+	0.243252i
$846$	−4.33975			−0.149204
$847$		0			0
$848$		−	5.35225i		−	0.183797i
$849$	15.5885			0.534994
$850$	−2.00000	+	9.79796i	−0.0685994	+	0.336067i
$851$	6.24871			0.214203
$852$		−	27.4249i		−	0.939560i
$853$		−	46.3644i		−	1.58749i	−0.608252	−	0.793744i	$-0.708129\pi$
$853$		−	46.3644i		−	1.58749i	0.608252	−	0.793744i	$-0.291871\pi$
$854$	20.3205			0.695353
$855$	5.32051	−	4.34418i	0.181958	−	0.148568i
$856$	−5.73205			−0.195917
$857$		−	29.3195i		−	1.00154i	−0.865581	−	0.500768i	$-0.833051\pi$
$857$		−	29.3195i		−	1.00154i	0.865581	−	0.500768i	$-0.166949\pi$
$858$		0			0
$859$	22.1962			0.757323			0.378661	−	0.925535i	$-0.376384\pi$
$859$	22.1962			0.757323			0.378661	+	0.925535i	$0.376384\pi$
$860$	−15.8038	−	19.3557i	−0.538907	−	0.660023i
$861$	11.1962			0.381564
$862$		−	2.62536i		−	0.0894200i
$863$		−	17.1093i		−	0.582406i	−0.956661	−	0.291203i	$-0.905944\pi$
$863$		−	17.1093i		−	0.582406i	0.956661	−	0.291203i	$-0.0940555\pi$
$864$	22.5167			0.766032
$865$	30.7846	+	37.7033i	1.04671	+	1.28195i
$866$	14.8756			0.505495
$867$			4.00240i			0.135929i
$868$		−	50.6071i		−	1.71772i
$869$		0			0
$870$	12.0000	−	9.79796i	0.406838	−	0.332182i
$871$	−9.37307			−0.317594
$872$		−	17.7656i		−	0.601619i
$873$			6.69213i			0.226494i
$874$	7.56922			0.256033
$875$	33.1244	−	17.3867i	1.11981	−	0.587777i
$876$	16.3923			0.553845
$877$		−	11.8957i		−	0.401690i	−0.979623	−	0.200845i	$-0.935631\pi$
$877$		−	11.8957i		−	0.401690i	0.979623	−	0.200845i	$-0.0643687\pi$
$878$		−	14.6226i		−	0.493489i
$879$	−29.1244			−0.982340
$880$		0			0
$881$	−26.9090			−0.906586			−0.453293	−	0.891362i	$-0.649751\pi$
$881$	−26.9090			−0.906586			−0.453293	+	0.891362i	$0.649751\pi$
$882$		−	1.59008i		−	0.0535407i
$883$			21.5649i			0.725718i	0.931844	+	0.362859i	$0.118199\pi$
$883$			21.5649i			0.725718i	−0.931844	+	0.362859i	$0.881801\pi$
$884$	28.3923			0.954937
$885$	3.46410	+	4.24264i	0.116445	+	0.142615i
$886$	−14.2679			−0.479341
$887$		−	15.6950i		−	0.526988i	−0.964661	−	0.263494i	$-0.915125\pi$
$887$		−	15.6950i		−	0.526988i	0.964661	−	0.263494i	$-0.0848750\pi$
$888$			6.69213i			0.224573i
$889$	−3.00000			−0.100617
$890$	0.339746	+	0.416102i	0.0113883	+	0.0139478i
$891$		0			0
$892$		−	2.68973i		−	0.0900587i
$893$		−	48.0561i		−	1.60813i
$894$	−10.2679			−0.343412
$895$	26.7846	−	21.8695i	0.895311	−	0.731018i
$896$	38.3205			1.28020
$897$			28.5617i			0.953646i
$898$			17.8671i			0.596234i
$899$	−60.4974			−2.01770
$900$	−1.26795	+	6.21166i	−0.0422650	+	0.207055i
$901$	−8.39230			−0.279588
$902$		0			0
$903$			41.7057i			1.38788i
$904$	−5.46410			−0.181733
$905$	−30.1244	+	24.5964i	−1.00137	+	0.817613i
$906$	−4.19615			−0.139408
$907$		−	30.1146i		−	0.999938i	−0.866043	−	0.499969i	$-0.833345\pi$
$907$		−	30.1146i		−	0.999938i	0.866043	−	0.499969i	$-0.166655\pi$
$908$		−	34.8377i		−	1.15613i
$909$	14.1962			0.470857
$910$	10.3923	+	12.7279i	0.344502	+	0.421927i
$911$	−30.2487			−1.00218			−0.501092	−	0.865394i	$-0.667068\pi$
$911$	−30.2487			−1.00218			−0.501092	+	0.865394i	$0.667068\pi$
$912$		−	19.9749i		−	0.661434i
$913$		0			0
$914$	10.9808			0.363211
$915$	32.0526	+	39.2562i	1.05962	+	1.29777i
$916$	7.05256			0.233023
$917$			10.4543i			0.345231i
$918$		−	8.76268i		−	0.289212i
$919$	−18.9808			−0.626118			−0.313059	−	0.949734i	$-0.601354\pi$
$919$	−18.9808			−0.626118			−0.313059	+	0.949734i	$0.601354\pi$
$920$	−11.6603	+	9.52056i	−0.384427	+	0.313883i
$921$	−15.1244			−0.498364
$922$		−	17.0821i		−	0.562568i
$923$		−	34.7733i		−	1.14458i
$924$		0			0
$925$	8.78461	+	1.79315i	0.288836	+	0.0589584i
$926$	10.5167			0.345599
$927$			3.10583i			0.102009i
$928$		−	35.6055i		−	1.16881i
$929$	43.8564			1.43888			0.719441	−	0.694554i	$-0.244398\pi$
$929$	43.8564			1.43888			0.719441	+	0.694554i	$0.244398\pi$
$930$	−15.1244	+	12.3490i	−0.495947	+	0.404939i
$931$	17.6077			0.577069
$932$			2.92996i			0.0959741i
$933$			19.4201i			0.635784i
$934$	−0.320508			−0.0104873
$935$		0			0
$936$	−6.00000			−0.196116
$937$			31.1870i			1.01884i	0.860519	+	0.509418i	$0.170139\pi$
$937$			31.1870i			1.01884i	−0.860519	+	0.509418i	$0.829861\pi$
$938$			3.82654i			0.124941i
$939$	−33.1244			−1.08097
$940$	28.0526	+	34.3572i	0.914974	+	1.12061i
$941$	27.0000			0.880175			0.440087	−	0.897955i	$-0.354947\pi$
$941$	27.0000			0.880175			0.440087	+	0.897955i	$0.354947\pi$
$942$		−	21.8695i		−	0.712548i
$943$			6.03579i			0.196552i
$944$	3.12436			0.101689
$945$	−25.3923	+	20.7327i	−0.826012	+	0.674436i
$946$		0			0
$947$		−	19.9749i		−	0.649096i	−0.945869	−	0.324548i	$-0.894788\pi$
$947$		−	19.9749i		−	0.649096i	0.945869	−	0.324548i	$-0.105212\pi$
$948$			4.89898i			0.159111i
$949$	20.7846			0.674697
$950$	10.6410	+	2.17209i	0.345240	+	0.0704719i
$951$	24.3923			0.790975
$952$		−	24.9754i		−	0.809456i
$953$			16.6932i			0.540745i	0.962756	+	0.270372i	$0.0871468\pi$
$953$			16.6932i			0.540745i	−0.962756	+	0.270372i	$0.912853\pi$
$954$	0.823085			0.0266484
$955$	−12.5885	+	10.2784i	−0.407353	+	0.332602i
$956$	9.80385			0.317079
$957$		0			0
$958$		−	1.31268i		−	0.0424107i
$959$	29.6603			0.957780
$960$	6.19615	+	7.58871i	0.199980	+	0.244924i
$961$	45.2487			1.45964
$962$			3.93803i			0.126967i
$963$			2.17209i			0.0699946i
$964$	−24.4641			−0.787936
$965$	21.4641	+	26.2880i	0.690954	+	0.846242i
$966$	11.6603			0.375163
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		0			0
$969$	−31.3205			−1.00616
$970$	−8.19615	+	6.69213i	−0.263163	+	0.214871i
$971$	−24.9282			−0.799984			−0.399992	−	0.916519i	$-0.630987\pi$
$971$	−24.9282			−0.799984			−0.399992	+	0.916519i	$0.630987\pi$
$972$		−	12.9038i		−	0.413889i
$973$		−	48.8139i		−	1.56490i
$974$	6.58846			0.211108
$975$	−8.19615	+	40.1528i	−0.262487	+	1.28592i
$976$	28.9090			0.925353
$977$		−	29.1165i		−	0.931519i	−0.884911	−	0.465759i	$-0.845781\pi$
$977$		−	29.1165i		−	0.931519i	0.884911	−	0.465759i	$-0.154219\pi$
$978$			5.13922i			0.164334i
$979$		0			0
$980$	−12.5885	+	10.2784i	−0.402124	+	0.328332i
$981$	−6.73205			−0.214938
$982$			20.5569i			0.655996i
$983$			56.0237i			1.78688i	0.449184	+	0.893439i	$0.351715\pi$
$983$			56.0237i			1.78688i	−0.449184	+	0.893439i	$0.648285\pi$
$984$	−6.46410			−0.206068
$985$	−24.3923	−	29.8744i	−0.777203	−	0.951876i
$986$	−13.8564			−0.441278
$987$		−	74.0295i		−	2.35639i
$988$		−	30.8353i		−	0.981001i
$989$	−22.4833			−0.714929
$990$		0			0
$991$	19.9090			0.632429			0.316215	−	0.948688i	$-0.397588\pi$
$991$	19.9090			0.632429			0.316215	+	0.948688i	$0.397588\pi$
$992$			44.8759i			1.42481i
$993$		−	35.1523i		−	1.11552i
$994$	−14.1962			−0.450275
$995$	3.46410	−	2.82843i	0.109819	−	0.0896672i
$996$	33.1244			1.04959
$997$			34.1170i			1.08050i	0.841506	+	0.540248i	$0.181670\pi$
$997$			34.1170i			1.08050i	−0.841506	+	0.540248i	$0.818330\pi$
$998$			9.11441i			0.288512i
$999$	−7.85641			−0.248566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.e.364.2	yes	4
5.2	odd	4		3025.2.a.z.1.3		4
5.3	odd	4		3025.2.a.z.1.2		4
5.4	even	2	inner	605.2.b.e.364.3	yes	4
11.2	odd	10		605.2.j.f.444.3		16
11.3	even	5		605.2.j.e.9.2		16
11.4	even	5		605.2.j.e.269.3		16
11.5	even	5		605.2.j.e.124.3		16
11.6	odd	10		605.2.j.f.124.2		16
11.7	odd	10		605.2.j.f.269.2		16
11.8	odd	10		605.2.j.f.9.3		16
11.9	even	5		605.2.j.e.444.2		16
11.10	odd	2		605.2.b.d.364.3	yes	4
55.4	even	10		605.2.j.e.269.2		16
55.9	even	10		605.2.j.e.444.3		16
55.14	even	10		605.2.j.e.9.3		16
55.19	odd	10		605.2.j.f.9.2		16
55.24	odd	10		605.2.j.f.444.2		16
55.29	odd	10		605.2.j.f.269.3		16
55.32	even	4		3025.2.a.y.1.2		4
55.39	odd	10		605.2.j.f.124.3		16
55.43	even	4		3025.2.a.y.1.3		4
55.49	even	10		605.2.j.e.124.2		16
55.54	odd	2		605.2.b.d.364.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.2	✓	4	55.54	odd	2
605.2.b.d.364.3	yes	4	11.10	odd	2
605.2.b.e.364.2	yes	4	1.1	even	1	trivial
605.2.b.e.364.3	yes	4	5.4	even	2	inner
605.2.j.e.9.2		16	11.3	even	5
605.2.j.e.9.3		16	55.14	even	10
605.2.j.e.124.2		16	55.49	even	10
605.2.j.e.124.3		16	11.5	even	5
605.2.j.e.269.2		16	55.4	even	10
605.2.j.e.269.3		16	11.4	even	5
605.2.j.e.444.2		16	11.9	even	5
605.2.j.e.444.3		16	55.9	even	10
605.2.j.f.9.2		16	55.19	odd	10
605.2.j.f.9.3		16	11.8	odd	10
605.2.j.f.124.2		16	11.6	odd	10
605.2.j.f.124.3		16	55.39	odd	10
605.2.j.f.269.2		16	11.7	odd	10
605.2.j.f.269.3		16	55.29	odd	10
605.2.j.f.444.2		16	55.24	odd	10
605.2.j.f.444.3		16	11.2	odd	10
3025.2.a.y.1.2		4	55.32	even	4
3025.2.a.y.1.3		4	55.43	even	4
3025.2.a.z.1.2		4	5.3	odd	4
3025.2.a.z.1.3		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.517638i q^{2} +1.93185i q^{3} +1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} +1.00000 q^{6} +3.34607i q^{7} -1.93185i q^{8} -0.732051 q^{9} +O(q^{10})\)	\(q-0.517638i q^{2} +1.93185i q^{3} +1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} +1.00000 q^{6} +3.34607i q^{7} -1.93185i q^{8} -0.732051 q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +4.24264i q^{13} +1.73205 q^{14} +(2.73205 + 3.34607i) q^{15} +2.46410 q^{16} -3.86370i q^{17} +0.378937i q^{18} -4.19615 q^{19} +(3.00000 - 2.44949i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +3.73205 q^{24} +(1.00000 - 4.89898i) q^{25} +2.19615 q^{26} +4.38134i q^{27} +5.79555i q^{28} +6.92820 q^{29} +(1.73205 - 1.41421i) q^{30} -8.73205 q^{31} -5.13922i q^{32} -2.00000 q^{34} +(4.73205 + 5.79555i) q^{35} -1.26795 q^{36} +1.79315i q^{37} +2.17209i q^{38} -8.19615 q^{39} +(-2.73205 - 3.34607i) q^{40} -1.73205 q^{41} +3.34607i q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} -1.80385 q^{46} +11.4524i q^{47} +4.76028i q^{48} -4.19615 q^{49} +(-2.53590 - 0.517638i) q^{50} +7.46410 q^{51} +7.34847i q^{52} -2.17209i q^{53} +2.26795 q^{54} +6.46410 q^{56} -8.10634i q^{57} -3.58630i q^{58} +1.26795 q^{59} +(4.73205 + 5.79555i) q^{60} +11.7321 q^{61} +4.52004i q^{62} -2.44949i q^{63} +2.26795 q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} -6.69213i q^{68} +6.73205 q^{69} +(3.00000 - 2.44949i) q^{70} -8.19615 q^{71} +1.41421i q^{72} -4.89898i q^{73} +0.928203 q^{74} +(9.46410 + 1.93185i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +1.46410 q^{79} +(4.26795 - 3.48477i) q^{80} -10.6603 q^{81} +0.896575i q^{82} -9.89949i q^{83} -11.1962 q^{84} +(-5.46410 - 6.69213i) q^{85} -3.33975 q^{86} +13.3843i q^{87} -0.464102 q^{89} +(0.535898 + 0.656339i) q^{90} -14.1962 q^{91} -6.03579i q^{92} -16.8690i q^{93} +5.92820 q^{94} +(-7.26795 + 5.93426i) q^{95} +9.92820 q^{96} -9.14162i q^{97} +2.17209i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^6 + 4 * q^9	\( 4 q + 4 q^{6} + 4 q^{9} + 4 q^{10} + 4 q^{15} - 4 q^{16} + 4 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{24} + 4 q^{25} - 12 q^{26} - 28 q^{31} - 8 q^{34} + 12 q^{35} - 12 q^{36} - 12 q^{39} - 4 q^{40} - 12 q^{45} - 28 q^{46} + 4 q^{49} - 24 q^{50} + 16 q^{51} + 16 q^{54} + 12 q^{56} + 12 q^{59} + 12 q^{60} + 40 q^{61} + 16 q^{64} + 24 q^{65} + 20 q^{69} + 12 q^{70} - 12 q^{71} - 24 q^{74} + 24 q^{75} - 36 q^{76} - 8 q^{79} + 24 q^{80} - 8 q^{81} - 24 q^{84} - 8 q^{85} - 48 q^{86} + 12 q^{89} + 16 q^{90} - 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) \) 4 * q + 4 * q^6 + 4 * q^9 + 4 * q^10 + 4 * q^15 - 4 * q^16 + 4 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^24 + 4 * q^25 - 12 * q^26 - 28 * q^31 - 8 * q^34 + 12 * q^35 - 12 * q^36 - 12 * q^39 - 4 * q^40 - 12 * q^45 - 28 * q^46 + 4 * q^49 - 24 * q^50 + 16 * q^51 + 16 * q^54 + 12 * q^56 + 12 * q^59 + 12 * q^60 + 40 * q^61 + 16 * q^64 + 24 * q^65 + 20 * q^69 + 12 * q^70 - 12 * q^71 - 24 * q^74 + 24 * q^75 - 36 * q^76 - 8 * q^79 + 24 * q^80 - 8 * q^81 - 24 * q^84 - 8 * q^85 - 48 * q^86 + 12 * q^89 + 16 * q^90 - 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more