LMFDB - Embedded newform 136.2.n.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			9.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	136.9
Dual form			136.2.n.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 0.414214i) q^{3} +(-1.29289 + 3.12132i) q^{5} +(1.00000 + 2.41421i) q^{7} +(-1.29289 - 1.29289i) q^{9} +O(q^{10})$	\(q+(1.00000 + 0.414214i) q^{3} +(-1.29289 + 3.12132i) q^{5} +(1.00000 + 2.41421i) q^{7} +(-1.29289 - 1.29289i) q^{9} +(4.41421 - 1.82843i) q^{11} -5.41421i q^{13} +(-2.58579 + 2.58579i) q^{15} +(-2.82843 + 3.00000i) q^{17} +(2.58579 - 2.58579i) q^{19} +2.82843i q^{21} +(-0.414214 + 0.171573i) q^{23} +(-4.53553 - 4.53553i) q^{25} +(-2.00000 - 4.82843i) q^{27} +(-0.878680 + 2.12132i) q^{29} +(2.41421 + 1.00000i) q^{31} +5.17157 q^{33} -8.82843 q^{35} +(0.121320 + 0.0502525i) q^{37} +(2.24264 - 5.41421i) q^{39} +(-1.46447 - 3.53553i) q^{41} +(-8.24264 - 8.24264i) q^{43} +(5.70711 - 2.36396i) q^{45} +6.82843i q^{47} +(0.121320 - 0.121320i) q^{49} +(-4.07107 + 1.82843i) q^{51} +(0.171573 - 0.171573i) q^{53} +16.1421i q^{55} +(3.65685 - 1.51472i) q^{57} +(9.07107 + 9.07107i) q^{59} +(-0.121320 - 0.292893i) q^{61} +(1.82843 - 4.41421i) q^{63} +(16.8995 + 7.00000i) q^{65} +2.82843 q^{67} -0.485281 q^{69} +(-13.4853 - 5.58579i) q^{71} +(-5.36396 + 12.9497i) q^{73} +(-2.65685 - 6.41421i) q^{75} +(8.82843 + 8.82843i) q^{77} +(4.41421 - 1.82843i) q^{79} -0.171573i q^{81} +(5.07107 - 5.07107i) q^{83} +(-5.70711 - 12.7071i) q^{85} +(-1.75736 + 1.75736i) q^{87} +4.24264i q^{89} +(13.0711 - 5.41421i) q^{91} +(2.00000 + 2.00000i) q^{93} +(4.72792 + 11.4142i) q^{95} +(0.121320 - 0.292893i) q^{97} +(-8.07107 - 3.34315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9	$ 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9} + 12 q^{11} - 16 q^{15} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 32 q^{33} - 24 q^{35} - 8 q^{37} - 8 q^{39} - 20 q^{41} - 16 q^{43} + 20 q^{45} - 8 q^{49} + 12 q^{51} + 12 q^{53} - 8 q^{57} + 8 q^{59} + 8 q^{61} - 4 q^{63} + 28 q^{65} + 32 q^{69} - 20 q^{71} + 4 q^{73} + 12 q^{75} + 24 q^{77} + 12 q^{79} - 8 q^{83} - 20 q^{85} - 24 q^{87} + 24 q^{91} + 8 q^{93} - 32 q^{95} - 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9 + 12 * q^11 - 16 * q^15 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 32 * q^33 - 24 * q^35 - 8 * q^37 - 8 * q^39 - 20 * q^41 - 16 * q^43 + 20 * q^45 - 8 * q^49 + 12 * q^51 + 12 * q^53 - 8 * q^57 + 8 * q^59 + 8 * q^61 - 4 * q^63 + 28 * q^65 + 32 * q^69 - 20 * q^71 + 4 * q^73 + 12 * q^75 + 24 * q^77 + 12 * q^79 - 8 * q^83 - 20 * q^85 - 24 * q^87 + 24 * q^91 + 8 * q^93 - 32 * q^95 - 8 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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
$3$	1.00000	+	0.414214i	0.577350	+	0.239146i	0.652198	−	0.758049i	$-0.273847\pi$
$3$	1.00000	+	0.414214i	0.577350	+	0.239146i	−0.0748477	+	0.997195i	$0.523847\pi$
$4$		0			0
$5$	−1.29289	+	3.12132i	−0.578199	+	1.39590i	0.316228	+	0.948683i	$0.397584\pi$
$5$	−1.29289	+	3.12132i	−0.578199	+	1.39590i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	1.00000	+	2.41421i	0.377964	+	0.912487i	0.992347	+	0.123479i	$0.0394051\pi$
$7$	1.00000	+	2.41421i	0.377964	+	0.912487i	−0.614383	+	0.789008i	$0.710595\pi$
$8$		0			0
$9$	−1.29289	−	1.29289i	−0.430964	−	0.430964i
$10$		0			0
$11$	4.41421	−	1.82843i	1.33094	−	0.551292i	0.400013	−	0.916509i	$-0.369005\pi$
$11$	4.41421	−	1.82843i	1.33094	−	0.551292i	0.930922	+	0.365218i	$0.119005\pi$
$12$		0			0
$13$		−	5.41421i		−	1.50163i	−0.660511	−	0.750816i	$-0.729660\pi$
$13$		−	5.41421i		−	1.50163i	0.660511	−	0.750816i	$-0.270340\pi$
$14$		0			0
$15$	−2.58579	+	2.58579i	−0.667647	+	0.667647i
$16$		0			0
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$17$	−2.82843	+	3.00000i	−0.685994	+	0.727607i
$18$		0			0
$19$	2.58579	−	2.58579i	0.593220	−	0.593220i	−0.345280	−	0.938500i	$-0.612216\pi$
$19$	2.58579	−	2.58579i	0.593220	−	0.593220i	0.938500	+	0.345280i	$0.112216\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$		0			0
$23$	−0.414214	+	0.171573i	−0.0863695	+	0.0357754i	−0.425450	−	0.904982i	$-0.639884\pi$
$23$	−0.414214	+	0.171573i	−0.0863695	+	0.0357754i	0.339080	+	0.940757i	$0.389884\pi$
$24$		0			0
$25$	−4.53553	−	4.53553i	−0.907107	−	0.907107i
$26$		0			0
$27$	−2.00000	−	4.82843i	−0.384900	−	0.929231i
$28$		0			0
$29$	−0.878680	+	2.12132i	−0.163167	+	0.393919i	−0.984224	−	0.176926i	$-0.943385\pi$
$29$	−0.878680	+	2.12132i	−0.163167	+	0.393919i	0.821057	+	0.570846i	$0.193385\pi$
$30$		0			0
$31$	2.41421	+	1.00000i	0.433606	+	0.179605i	0.588800	−	0.808279i	$-0.299600\pi$
$31$	2.41421	+	1.00000i	0.433606	+	0.179605i	−0.155195	+	0.987884i	$0.549600\pi$
$32$		0			0
$33$	5.17157			0.900255
$34$		0			0
$35$	−8.82843			−1.49228
$36$		0			0
$37$	0.121320	+	0.0502525i	0.0199449	+	0.00826147i	0.392634	−	0.919695i	$-0.371564\pi$
$37$	0.121320	+	0.0502525i	0.0199449	+	0.00826147i	−0.372689	+	0.927956i	$0.621564\pi$
$38$		0			0
$39$	2.24264	−	5.41421i	0.359110	−	0.866968i
$40$		0			0
$41$	−1.46447	−	3.53553i	−0.228711	−	0.552158i	0.767310	−	0.641277i	$-0.221595\pi$
$41$	−1.46447	−	3.53553i	−0.228711	−	0.552158i	−0.996021	+	0.0891190i	$0.971595\pi$
$42$		0			0
$43$	−8.24264	−	8.24264i	−1.25699	−	1.25699i	−0.952522	−	0.304469i	$-0.901521\pi$
$43$	−8.24264	−	8.24264i	−1.25699	−	1.25699i	−0.304469	−	0.952522i	$-0.598479\pi$
$44$		0			0
$45$	5.70711	−	2.36396i	0.850765	−	0.352399i
$46$		0			0
$47$			6.82843i			0.996028i	0.867169	+	0.498014i	$0.165937\pi$
$47$			6.82843i			0.996028i	−0.867169	+	0.498014i	$0.834063\pi$
$48$		0			0
$49$	0.121320	−	0.121320i	0.0173315	−	0.0173315i
$50$		0			0
$51$	−4.07107	+	1.82843i	−0.570064	+	0.256031i
$52$		0			0
$53$	0.171573	−	0.171573i	0.0235673	−	0.0235673i	−0.695225	−	0.718792i	$-0.744695\pi$
$53$	0.171573	−	0.171573i	0.0235673	−	0.0235673i	0.718792	+	0.695225i	$0.244695\pi$
$54$		0			0
$55$			16.1421i			2.17661i
$56$		0			0
$57$	3.65685	−	1.51472i	0.484362	−	0.200629i
$58$		0			0
$59$	9.07107	+	9.07107i	1.18095	+	1.18095i	0.979498	+	0.201455i	$0.0645668\pi$
$59$	9.07107	+	9.07107i	1.18095	+	1.18095i	0.201455	+	0.979498i	$0.435433\pi$
$60$		0			0
$61$	−0.121320	−	0.292893i	−0.0155335	−	0.0375011i	0.915922	−	0.401355i	$-0.131461\pi$
$61$	−0.121320	−	0.292893i	−0.0155335	−	0.0375011i	−0.931456	+	0.363854i	$0.881461\pi$
$62$		0			0
$63$	1.82843	−	4.41421i	0.230360	−	0.556139i
$64$		0			0
$65$	16.8995	+	7.00000i	2.09612	+	0.868243i
$66$		0			0
$67$	2.82843			0.345547			0.172774	−	0.984962i	$-0.444727\pi$
$67$	2.82843			0.345547			0.172774	+	0.984962i	$0.444727\pi$
$68$		0			0
$69$	−0.485281			−0.0584210
$70$		0			0
$71$	−13.4853	−	5.58579i	−1.60041	−	0.662911i	−0.608935	−	0.793220i	$-0.708403\pi$
$71$	−13.4853	−	5.58579i	−1.60041	−	0.662911i	−0.991473	+	0.130309i	$0.958403\pi$
$72$		0			0
$73$	−5.36396	+	12.9497i	−0.627804	+	1.51565i	0.214541	+	0.976715i	$0.431174\pi$
$73$	−5.36396	+	12.9497i	−0.627804	+	1.51565i	−0.842345	+	0.538938i	$0.818826\pi$
$74$		0			0
$75$	−2.65685	−	6.41421i	−0.306787	−	0.740650i
$76$		0			0
$77$	8.82843	+	8.82843i	1.00609	+	1.00609i
$78$		0			0
$79$	4.41421	−	1.82843i	0.496638	−	0.205714i	−0.120283	−	0.992740i	$-0.538380\pi$
$79$	4.41421	−	1.82843i	0.496638	−	0.205714i	0.616920	+	0.787026i	$0.288380\pi$
$80$		0			0
$81$		−	0.171573i		−	0.0190637i
$82$		0			0
$83$	5.07107	−	5.07107i	0.556622	−	0.556622i	−0.371722	−	0.928344i	$-0.621233\pi$
$83$	5.07107	−	5.07107i	0.556622	−	0.556622i	0.928344	+	0.371722i	$0.121233\pi$
$84$		0			0
$85$	−5.70711	−	12.7071i	−0.619023	−	1.37828i
$86$		0			0
$87$	−1.75736	+	1.75736i	−0.188409	+	0.188409i
$88$		0			0
$89$			4.24264i			0.449719i	0.974391	+	0.224860i	$0.0721923\pi$
$89$			4.24264i			0.449719i	−0.974391	+	0.224860i	$0.927808\pi$
$90$		0			0
$91$	13.0711	−	5.41421i	1.37022	−	0.567564i
$92$		0			0
$93$	2.00000	+	2.00000i	0.207390	+	0.207390i
$94$		0			0
$95$	4.72792	+	11.4142i	0.485075	+	1.17107i
$96$		0			0
$97$	0.121320	−	0.292893i	0.0123182	−	0.0297388i	−0.917601	−	0.397503i	$-0.869877\pi$
$97$	0.121320	−	0.292893i	0.0123182	−	0.0297388i	0.929919	+	0.367764i	$0.119877\pi$
$98$		0			0
$99$	−8.07107	−	3.34315i	−0.811173	−	0.335999i
$100$		0			0
$101$	−9.41421			−0.936749			−0.468375	−	0.883530i	$-0.655160\pi$
$101$	−9.41421			−0.936749			−0.468375	+	0.883530i	$0.655160\pi$
$102$		0			0
$103$	−2.82843			−0.278693			−0.139347	−	0.990244i	$-0.544500\pi$
$103$	−2.82843			−0.278693			−0.139347	+	0.990244i	$0.544500\pi$
$104$		0			0
$105$	−8.82843	−	3.65685i	−0.861566	−	0.356872i
$106$		0			0
$107$	−4.65685	+	11.2426i	−0.450195	+	1.08687i	0.522053	+	0.852913i	$0.325166\pi$
$107$	−4.65685	+	11.2426i	−0.450195	+	1.08687i	−0.972248	+	0.233954i	$0.924834\pi$
$108$		0			0
$109$	−6.70711	−	16.1924i	−0.642424	−	1.55095i	−0.823400	−	0.567462i	$-0.807925\pi$
$109$	−6.70711	−	16.1924i	−0.642424	−	1.55095i	0.180975	−	0.983488i	$-0.442075\pi$
$110$		0			0
$111$	0.100505	+	0.100505i	0.00953952	+	0.00953952i
$112$		0			0
$113$	−2.70711	+	1.12132i	−0.254663	+	0.105485i	−0.506363	−	0.862320i	$-0.669010\pi$
$113$	−2.70711	+	1.12132i	−0.254663	+	0.105485i	0.251700	+	0.967805i	$0.419010\pi$
$114$		0			0
$115$		−	1.51472i		−	0.141248i
$116$		0			0
$117$	−7.00000	+	7.00000i	−0.647150	+	0.647150i
$118$		0			0
$119$	−10.0711	−	3.82843i	−0.923213	−	0.350951i
$120$		0			0
$121$	8.36396	−	8.36396i	0.760360	−	0.760360i
$122$		0			0
$123$		−	4.14214i		−	0.373484i
$124$		0			0
$125$	4.41421	−	1.82843i	0.394819	−	0.163539i
$126$		0			0
$127$	3.41421	+	3.41421i	0.302962	+	0.302962i	0.842172	−	0.539209i	$-0.181277\pi$
$127$	3.41421	+	3.41421i	0.302962	+	0.302962i	−0.539209	+	0.842172i	$0.681277\pi$
$128$		0			0
$129$	−4.82843	−	11.6569i	−0.425119	−	1.02633i
$130$		0			0
$131$	3.00000	−	7.24264i	0.262111	−	0.632792i	−0.736958	−	0.675939i	$-0.763738\pi$
$131$	3.00000	−	7.24264i	0.262111	−	0.632792i	0.999069	+	0.0431466i	$0.0137383\pi$
$132$		0			0
$133$	8.82843	+	3.65685i	0.765522	+	0.317089i
$134$		0			0
$135$	17.6569			1.51966
$136$		0			0
$137$	−16.2426			−1.38770			−0.693851	−	0.720118i	$-0.744087\pi$
$137$	−16.2426			−1.38770			−0.693851	+	0.720118i	$0.744087\pi$
$138$		0			0
$139$	16.0711	+	6.65685i	1.36313	+	0.564627i	0.939917	−	0.341403i	$-0.110902\pi$
$139$	16.0711	+	6.65685i	1.36313	+	0.564627i	0.423213	+	0.906030i	$0.360902\pi$
$140$		0			0
$141$	−2.82843	+	6.82843i	−0.238197	+	0.575057i
$142$		0			0
$143$	−9.89949	−	23.8995i	−0.827837	−	1.99858i
$144$		0			0
$145$	−5.48528	−	5.48528i	−0.455528	−	0.455528i
$146$		0			0
$147$	0.171573	−	0.0710678i	0.0141511	−	0.00586157i
$148$		0			0
$149$		−	19.3137i		−	1.58224i	−0.611661	−	0.791120i	$-0.709498\pi$
$149$		−	19.3137i		−	1.58224i	0.611661	−	0.791120i	$-0.290502\pi$
$150$		0			0
$151$	−8.24264	+	8.24264i	−0.670777	+	0.670777i	−0.957895	−	0.287118i	$-0.907303\pi$
$151$	−8.24264	+	8.24264i	−0.670777	+	0.670777i	0.287118	+	0.957895i	$0.407303\pi$
$152$		0			0
$153$	7.53553	−	0.221825i	0.609212	−	0.0179335i
$154$		0			0
$155$	−6.24264	+	6.24264i	−0.501421	+	0.501421i
$156$		0			0
$157$			20.0000i			1.59617i	0.602542	+	0.798087i	$0.294154\pi$
$157$			20.0000i			1.59617i	−0.602542	+	0.798087i	$0.705846\pi$
$158$		0			0
$159$	0.242641	−	0.100505i	0.0192427	−	0.00797057i
$160$		0			0
$161$	−0.828427	−	0.828427i	−0.0652892	−	0.0652892i
$162$		0			0
$163$	−0.757359	−	1.82843i	−0.0593210	−	0.143213i	0.891440	−	0.453139i	$-0.149696\pi$
$163$	−0.757359	−	1.82843i	−0.0593210	−	0.143213i	−0.950761	+	0.309926i	$0.899696\pi$
$164$		0			0
$165$	−6.68629	+	16.1421i	−0.520527	+	1.25666i
$166$		0			0
$167$	8.65685	+	3.58579i	0.669887	+	0.277476i	0.691592	−	0.722288i	$-0.256909\pi$
$167$	8.65685	+	3.58579i	0.669887	+	0.277476i	−0.0217050	+	0.999764i	$0.506909\pi$
$168$		0			0
$169$	−16.3137			−1.25490
$170$		0			0
$171$	−6.68629			−0.511313
$172$		0			0
$173$	9.70711	+	4.02082i	0.738018	+	0.305697i	0.719842	−	0.694138i	$-0.244214\pi$
$173$	9.70711	+	4.02082i	0.738018	+	0.305697i	0.0181756	+	0.999835i	$0.494214\pi$
$174$		0			0
$175$	6.41421	−	15.4853i	0.484869	−	1.17058i
$176$		0			0
$177$	5.31371	+	12.8284i	0.399403	+	0.964244i
$178$		0			0
$179$	4.58579	+	4.58579i	0.342758	+	0.342758i	0.857403	−	0.514645i	$-0.172076\pi$
$179$	4.58579	+	4.58579i	0.342758	+	0.342758i	−0.514645	+	0.857403i	$0.672076\pi$
$180$		0			0
$181$	−13.5355	+	5.60660i	−1.00609	+	0.416735i	−0.824026	−	0.566552i	$-0.808277\pi$
$181$	−13.5355	+	5.60660i	−1.00609	+	0.416735i	−0.182062	+	0.983287i	$0.558277\pi$
$182$		0			0
$183$		−	0.343146i		−	0.0253661i
$184$		0			0
$185$	−0.313708	+	0.313708i	−0.0230643	+	0.0230643i
$186$		0			0
$187$	−7.00000	+	18.4142i	−0.511891	+	1.34658i
$188$		0			0
$189$	9.65685	−	9.65685i	0.702433	−	0.702433i
$190$		0			0
$191$		−	6.34315i		−	0.458974i	−0.973312	−	0.229487i	$-0.926295\pi$
$191$		−	6.34315i		−	0.458974i	0.973312	−	0.229487i	$-0.0737048\pi$
$192$		0			0
$193$	14.7782	−	6.12132i	1.06376	−	0.440622i	0.218973	−	0.975731i	$-0.429729\pi$
$193$	14.7782	−	6.12132i	1.06376	−	0.440622i	0.844783	+	0.535109i	$0.179729\pi$
$194$		0			0
$195$	14.0000	+	14.0000i	1.00256	+	1.00256i
$196$		0			0
$197$	−3.22183	−	7.77817i	−0.229546	−	0.554172i	0.766577	−	0.642153i	$-0.221959\pi$
$197$	−3.22183	−	7.77817i	−0.229546	−	0.554172i	−0.996122	+	0.0879809i	$0.971959\pi$
$198$		0			0
$199$	4.75736	−	11.4853i	0.337240	−	0.814170i	−0.660738	−	0.750616i	$-0.729757\pi$
$199$	4.75736	−	11.4853i	0.337240	−	0.814170i	0.997978	−	0.0635535i	$-0.0202434\pi$
$200$		0			0
$201$	2.82843	+	1.17157i	0.199502	+	0.0826364i
$202$		0			0
$203$	−6.00000			−0.421117
$204$		0			0
$205$	12.9289			0.902996
$206$		0			0
$207$	0.757359	+	0.313708i	0.0526401	+	0.0218042i
$208$		0			0
$209$	6.68629	−	16.1421i	0.462500	−	1.11657i
$210$		0			0
$211$	7.97056	+	19.2426i	0.548716	+	1.32472i	0.918434	+	0.395574i	$0.129454\pi$
$211$	7.97056	+	19.2426i	0.548716	+	1.32472i	−0.369718	+	0.929144i	$0.620546\pi$
$212$		0			0
$213$	−11.1716	−	11.1716i	−0.765464	−	0.765464i
$214$		0			0
$215$	36.3848	−	15.0711i	2.48142	−	1.02784i
$216$		0			0
$217$			6.82843i			0.463544i
$218$		0			0
$219$	−10.7279	+	10.7279i	−0.724926	+	0.724926i
$220$		0			0
$221$	16.2426	+	15.3137i	1.09260	+	1.03011i
$222$		0			0
$223$	−17.8995	+	17.8995i	−1.19864	+	1.19864i	−0.224065	+	0.974574i	$0.571933\pi$
$223$	−17.8995	+	17.8995i	−1.19864	+	1.19864i	−0.974574	+	0.224065i	$0.928067\pi$
$224$		0			0
$225$			11.7279i			0.781861i
$226$		0			0
$227$	−4.41421	+	1.82843i	−0.292982	+	0.121357i	−0.524333	−	0.851513i	$-0.675685\pi$
$227$	−4.41421	+	1.82843i	−0.292982	+	0.121357i	0.231351	+	0.972870i	$0.425685\pi$
$228$		0			0
$229$	−3.17157	−	3.17157i	−0.209583	−	0.209583i	0.594507	−	0.804090i	$-0.297347\pi$
$229$	−3.17157	−	3.17157i	−0.209583	−	0.209583i	−0.804090	+	0.594507i	$0.797347\pi$
$230$		0			0
$231$	5.17157	+	12.4853i	0.340265	+	0.821471i
$232$		0			0
$233$	−8.12132	+	19.6066i	−0.532045	+	1.28447i	0.398121	+	0.917333i	$0.369662\pi$
$233$	−8.12132	+	19.6066i	−0.532045	+	1.28447i	−0.930166	+	0.367138i	$0.880338\pi$
$234$		0			0
$235$	−21.3137	−	8.82843i	−1.39035	−	0.575903i
$236$		0			0
$237$	5.17157			0.335930
$238$		0			0
$239$	−0.485281			−0.0313902			−0.0156951	−	0.999877i	$-0.504996\pi$
$239$	−0.485281			−0.0313902			−0.0156951	+	0.999877i	$0.504996\pi$
$240$		0			0
$241$	7.36396	+	3.05025i	0.474354	+	0.196484i	0.607035	−	0.794675i	$-0.292359\pi$
$241$	7.36396	+	3.05025i	0.474354	+	0.196484i	−0.132681	+	0.991159i	$0.542359\pi$
$242$		0			0
$243$	−5.92893	+	14.3137i	−0.380341	+	0.918225i
$244$		0			0
$245$	0.221825	+	0.535534i	0.0141719	+	0.0342140i
$246$		0			0
$247$	−14.0000	−	14.0000i	−0.890799	−	0.890799i
$248$		0			0
$249$	7.17157	−	2.97056i	0.454480	−	0.188252i
$250$		0			0
$251$		−	24.4853i		−	1.54550i	−0.634712	−	0.772749i	$-0.718881\pi$
$251$		−	24.4853i		−	1.54550i	0.634712	−	0.772749i	$-0.281119\pi$
$252$		0			0
$253$	−1.51472	+	1.51472i	−0.0952295	+	0.0952295i
$254$		0			0
$255$	−0.443651	−	15.0711i	−0.0277825	−	0.943787i
$256$		0			0
$257$	10.0000	−	10.0000i	0.623783	−	0.623783i	−0.322714	−	0.946497i	$-0.604595\pi$
$257$	10.0000	−	10.0000i	0.623783	−	0.623783i	0.946497	+	0.322714i	$0.104595\pi$
$258$		0			0
$259$			0.343146i			0.0213220i
$260$		0			0
$261$	3.87868	−	1.60660i	0.240084	−	0.0994461i
$262$		0			0
$263$	−11.0711	−	11.0711i	−0.682671	−	0.682671i	0.277930	−	0.960601i	$-0.410352\pi$
$263$	−11.0711	−	11.0711i	−0.682671	−	0.682671i	−0.960601	+	0.277930i	$0.910352\pi$
$264$		0			0
$265$	0.313708	+	0.757359i	0.0192710	+	0.0465242i
$266$		0			0
$267$	−1.75736	+	4.24264i	−0.107549	+	0.259645i
$268$		0			0
$269$	−4.12132	−	1.70711i	−0.251281	−	0.104084i	0.253488	−	0.967339i	$-0.418422\pi$
$269$	−4.12132	−	1.70711i	−0.251281	−	0.104084i	−0.504769	+	0.863255i	$0.668422\pi$
$270$		0			0
$271$	−2.14214			−0.130125			−0.0650627	−	0.997881i	$-0.520725\pi$
$271$	−2.14214			−0.130125			−0.0650627	+	0.997881i	$0.520725\pi$
$272$		0			0
$273$	15.3137			0.926828
$274$		0			0
$275$	−28.3137	−	11.7279i	−1.70738	−	0.707220i
$276$		0			0
$277$	−3.02082	+	7.29289i	−0.181503	+	0.438187i	−0.988277	−	0.152673i	$-0.951212\pi$
$277$	−3.02082	+	7.29289i	−0.181503	+	0.438187i	0.806774	+	0.590861i	$0.201212\pi$
$278$		0			0
$279$	−1.82843	−	4.41421i	−0.109465	−	0.264272i
$280$		0			0
$281$	−1.34315	−	1.34315i	−0.0801254	−	0.0801254i	0.665908	−	0.746034i	$-0.268044\pi$
$281$	−1.34315	−	1.34315i	−0.0801254	−	0.0801254i	−0.746034	+	0.665908i	$0.768044\pi$
$282$		0			0
$283$	8.89949	−	3.68629i	0.529020	−	0.219127i	−0.102154	−	0.994769i	$-0.532573\pi$
$283$	8.89949	−	3.68629i	0.529020	−	0.219127i	0.631174	+	0.775641i	$0.282573\pi$
$284$		0			0
$285$			13.3726i			0.792123i
$286$		0			0
$287$	7.07107	−	7.07107i	0.417392	−	0.417392i
$288$		0			0
$289$	−1.00000	−	16.9706i	−0.0588235	−	0.998268i
$290$		0			0
$291$	0.242641	−	0.242641i	0.0142238	−	0.0142238i
$292$		0			0
$293$		−	22.9706i		−	1.34195i	−0.741478	−	0.670977i	$-0.765875\pi$
$293$		−	22.9706i		−	1.34195i	0.741478	−	0.670977i	$-0.234125\pi$
$294$		0			0
$295$	−40.0416	+	16.5858i	−2.33131	+	0.965662i
$296$		0			0
$297$	−17.6569	−	17.6569i	−1.02455	−	1.02455i
$298$		0			0
$299$	0.928932	+	2.24264i	0.0537215	+	0.129695i
$300$		0			0
$301$	11.6569	−	28.1421i	0.671890	−	1.62209i
$302$		0			0
$303$	−9.41421	−	3.89949i	−0.540832	−	0.224020i
$304$		0			0
$305$	1.07107			0.0613292
$306$		0			0
$307$	14.1421			0.807134			0.403567	−	0.914950i	$-0.367770\pi$
$307$	14.1421			0.807134			0.403567	+	0.914950i	$0.367770\pi$
$308$		0			0
$309$	−2.82843	−	1.17157i	−0.160904	−	0.0666485i
$310$		0			0
$311$	7.14214	−	17.2426i	0.404993	−	0.977740i	−0.581442	−	0.813588i	$-0.697511\pi$
$311$	7.14214	−	17.2426i	0.404993	−	0.977740i	0.986435	−	0.164152i	$-0.0524889\pi$
$312$		0			0
$313$	1.46447	+	3.53553i	0.0827765	+	0.199840i	0.959849	−	0.280519i	$-0.0905064\pi$
$313$	1.46447	+	3.53553i	0.0827765	+	0.199840i	−0.877072	+	0.480359i	$0.840506\pi$
$314$		0			0
$315$	11.4142	+	11.4142i	0.643118	+	0.643118i
$316$		0			0
$317$	−2.87868	+	1.19239i	−0.161683	+	0.0669712i	−0.462057	−	0.886850i	$-0.652888\pi$
$317$	−2.87868	+	1.19239i	−0.161683	+	0.0669712i	0.300374	+	0.953821i	$0.402888\pi$
$318$		0			0
$319$			10.9706i			0.614234i
$320$		0			0
$321$	−9.31371	+	9.31371i	−0.519841	+	0.519841i
$322$		0			0
$323$	0.443651	+	15.0711i	0.0246854	+	0.838577i
$324$		0			0
$325$	−24.5563	+	24.5563i	−1.36214	+	1.36214i
$326$		0			0
$327$		−	18.9706i		−	1.04907i
$328$		0			0
$329$	−16.4853	+	6.82843i	−0.908863	+	0.376463i
$330$		0			0
$331$	10.5858	+	10.5858i	0.581847	+	0.581847i	0.935411	−	0.353563i	$-0.115030\pi$
$331$	10.5858	+	10.5858i	0.581847	+	0.581847i	−0.353563	+	0.935411i	$0.615030\pi$
$332$		0			0
$333$	−0.0918831	−	0.221825i	−0.00503516	−	0.0121560i
$334$		0			0
$335$	−3.65685	+	8.82843i	−0.199795	+	0.482349i
$336$		0			0
$337$	9.12132	+	3.77817i	0.496870	+	0.205810i	0.617023	−	0.786945i	$-0.288339\pi$
$337$	9.12132	+	3.77817i	0.496870	+	0.205810i	−0.120153	+	0.992755i	$0.538339\pi$
$338$		0			0
$339$	−3.17157			−0.172256
$340$		0			0
$341$	12.4853			0.676116
$342$		0			0
$343$	17.3137	+	7.17157i	0.934852	+	0.387229i
$344$		0			0
$345$	0.627417	−	1.51472i	0.0337790	−	0.0815497i
$346$		0			0
$347$	3.92893	+	9.48528i	0.210916	+	0.509197i	0.993565	−	0.113267i	$-0.0361317\pi$
$347$	3.92893	+	9.48528i	0.210916	+	0.509197i	−0.782648	+	0.622464i	$0.786132\pi$
$348$		0			0
$349$	15.4853	+	15.4853i	0.828908	+	0.828908i	0.987366	−	0.158458i	$-0.0506521\pi$
$349$	15.4853	+	15.4853i	0.828908	+	0.828908i	−0.158458	+	0.987366i	$0.550652\pi$
$350$		0			0
$351$	−26.1421	+	10.8284i	−1.39536	+	0.577979i
$352$		0			0
$353$		−	1.31371i		−	0.0699216i	−0.999389	−	0.0349608i	$-0.988869\pi$
$353$		−	1.31371i		−	0.0699216i	0.999389	−	0.0349608i	$-0.0111306\pi$
$354$		0			0
$355$	34.8701	−	34.8701i	1.85071	−	1.85071i
$356$		0			0
$357$	−8.48528	−	8.00000i	−0.449089	−	0.423405i
$358$		0			0
$359$	12.2426	−	12.2426i	0.646142	−	0.646142i	−0.305916	−	0.952058i	$-0.598963\pi$
$359$	12.2426	−	12.2426i	0.646142	−	0.646142i	0.952058	+	0.305916i	$0.0989628\pi$
$360$		0			0
$361$			5.62742i			0.296180i
$362$		0			0
$363$	11.8284	−	4.89949i	0.620831	−	0.257157i
$364$		0			0
$365$	−33.4853	−	33.4853i	−1.75270	−	1.75270i
$366$		0			0
$367$	1.68629	+	4.07107i	0.0880237	+	0.212508i	0.961761	−	0.273890i	$-0.0883105\pi$
$367$	1.68629	+	4.07107i	0.0880237	+	0.212508i	−0.873737	+	0.486398i	$0.838310\pi$
$368$		0			0
$369$	−2.67767	+	6.46447i	−0.139394	+	0.336527i
$370$		0			0
$371$	0.585786	+	0.242641i	0.0304125	+	0.0125973i
$372$		0			0
$373$	29.6985			1.53773			0.768865	−	0.639412i	$-0.220822\pi$
$373$	29.6985			1.53773			0.768865	+	0.639412i	$0.220822\pi$
$374$		0			0
$375$	5.17157			0.267059
$376$		0			0
$377$	11.4853	+	4.75736i	0.591522	+	0.245016i
$378$		0			0
$379$	7.14214	−	17.2426i	0.366867	−	0.885695i	−0.627393	−	0.778703i	$-0.715878\pi$
$379$	7.14214	−	17.2426i	0.366867	−	0.885695i	0.994260	−	0.106992i	$-0.0341220\pi$
$380$		0			0
$381$	2.00000	+	4.82843i	0.102463	+	0.247368i
$382$		0			0
$383$	15.0711	+	15.0711i	0.770096	+	0.770096i	0.978123	−	0.208027i	$-0.0667043\pi$
$383$	15.0711	+	15.0711i	0.770096	+	0.770096i	−0.208027	+	0.978123i	$0.566704\pi$
$384$		0			0
$385$	−38.9706	+	16.1421i	−1.98612	+	0.822679i
$386$		0			0
$387$			21.3137i			1.08344i
$388$		0			0
$389$	0.585786	−	0.585786i	0.0297006	−	0.0297006i	−0.692101	−	0.721801i	$-0.743315\pi$
$389$	0.585786	−	0.585786i	0.0297006	−	0.0297006i	0.721801	+	0.692101i	$0.243315\pi$
$390$		0			0
$391$	0.656854	−	1.72792i	0.0332185	−	0.0873848i
$392$		0			0
$393$	6.00000	−	6.00000i	0.302660	−	0.302660i
$394$		0			0
$395$			16.1421i			0.812199i
$396$		0			0
$397$	−0.121320	+	0.0502525i	−0.00608889	+	0.00252210i	−0.385726	−	0.922613i	$-0.626049\pi$
$397$	−0.121320	+	0.0502525i	−0.00608889	+	0.00252210i	0.379637	+	0.925136i	$0.376049\pi$
$398$		0			0
$399$	7.31371	+	7.31371i	0.366143	+	0.366143i
$400$		0			0
$401$	−3.12132	−	7.53553i	−0.155871	−	0.376307i	0.826582	−	0.562817i	$-0.190282\pi$
$401$	−3.12132	−	7.53553i	−0.155871	−	0.376307i	−0.982453	+	0.186510i	$0.940282\pi$
$402$		0			0
$403$	5.41421	−	13.0711i	0.269701	−	0.651116i
$404$		0			0
$405$	0.535534	+	0.221825i	0.0266109	+	0.0110226i
$406$		0			0
$407$	0.627417			0.0310999
$408$		0			0
$409$	−24.0000			−1.18672			−0.593362	−	0.804936i	$-0.702200\pi$
$409$	−24.0000			−1.18672			−0.593362	+	0.804936i	$0.702200\pi$
$410$		0			0
$411$	−16.2426	−	6.72792i	−0.801190	−	0.331864i
$412$		0			0
$413$	−12.8284	+	30.9706i	−0.631246	+	1.52396i
$414$		0			0
$415$	9.27208	+	22.3848i	0.455148	+	1.09883i
$416$		0			0
$417$	13.3137	+	13.3137i	0.651975	+	0.651975i
$418$		0			0
$419$	−24.3137	+	10.0711i	−1.18780	+	0.492004i	−0.887039	−	0.461695i	$-0.847242\pi$
$419$	−24.3137	+	10.0711i	−1.18780	+	0.492004i	−0.300764	+	0.953699i	$0.597242\pi$
$420$		0			0
$421$			12.0416i			0.586873i	0.955979	+	0.293437i	$0.0947990\pi$
$421$			12.0416i			0.586873i	−0.955979	+	0.293437i	$0.905201\pi$
$422$		0			0
$423$	8.82843	−	8.82843i	0.429253	−	0.429253i
$424$		0			0
$425$	26.4350	−	0.778175i	1.28229	−	0.0377470i
$426$		0			0
$427$	0.585786	−	0.585786i	0.0283482	−	0.0283482i
$428$		0			0
$429$		−	28.0000i		−	1.35185i
$430$		0			0
$431$	2.07107	−	0.857864i	0.0997598	−	0.0413219i	−0.332245	−	0.943193i	$-0.607806\pi$
$431$	2.07107	−	0.857864i	0.0997598	−	0.0413219i	0.432005	+	0.901871i	$0.357806\pi$
$432$		0			0
$433$	27.2132	+	27.2132i	1.30778	+	1.30778i	0.923012	+	0.384771i	$0.125720\pi$
$433$	27.2132	+	27.2132i	1.30778	+	1.30778i	0.384771	+	0.923012i	$0.374280\pi$
$434$		0			0
$435$	−3.21320	−	7.75736i	−0.154061	−	0.371937i
$436$		0			0
$437$	−0.627417	+	1.51472i	−0.0300134	+	0.0724588i
$438$		0			0
$439$	20.3137	+	8.41421i	0.969520	+	0.401589i	0.810534	−	0.585692i	$-0.199177\pi$
$439$	20.3137	+	8.41421i	0.969520	+	0.401589i	0.158987	+	0.987281i	$0.449177\pi$
$440$		0			0
$441$	−0.313708			−0.0149385
$442$		0			0
$443$	−6.14214			−0.291822			−0.145911	−	0.989298i	$-0.546611\pi$
$443$	−6.14214			−0.291822			−0.145911	+	0.989298i	$0.546611\pi$
$444$		0			0
$445$	−13.2426	−	5.48528i	−0.627761	−	0.260027i
$446$		0			0
$447$	8.00000	−	19.3137i	0.378387	−	0.913507i
$448$		0			0
$449$	5.09188	+	12.2929i	0.240301	+	0.580137i	0.997313	−	0.0732637i	$-0.0233415\pi$
$449$	5.09188	+	12.2929i	0.240301	+	0.580137i	−0.757012	+	0.653401i	$0.773341\pi$
$450$		0			0
$451$	−12.9289	−	12.9289i	−0.608800	−	0.608800i
$452$		0			0
$453$	−11.6569	+	4.82843i	−0.547687	+	0.226859i
$454$		0			0
$455$			47.7990i			2.24085i
$456$		0			0
$457$	23.6569	−	23.6569i	1.10662	−	1.10662i	0.113029	−	0.993592i	$-0.463945\pi$
$457$	23.6569	−	23.6569i	1.10662	−	1.10662i	0.993592	−	0.113029i	$-0.0360554\pi$
$458$		0			0
$459$	20.1421	+	7.65685i	0.940154	+	0.357391i
$460$		0			0
$461$	11.1421	−	11.1421i	0.518941	−	0.518941i	−0.398310	−	0.917251i	$-0.630403\pi$
$461$	11.1421	−	11.1421i	0.518941	−	0.518941i	0.917251	+	0.398310i	$0.130403\pi$
$462$		0			0
$463$		−	38.6274i		−	1.79517i	−0.440843	−	0.897584i	$-0.645321\pi$
$463$		−	38.6274i		−	1.79517i	0.440843	−	0.897584i	$-0.354679\pi$
$464$		0			0
$465$	−8.82843	+	3.65685i	−0.409409	+	0.169583i
$466$		0			0
$467$	2.24264	+	2.24264i	0.103777	+	0.103777i	0.757089	−	0.653312i	$-0.226621\pi$
$467$	2.24264	+	2.24264i	0.103777	+	0.103777i	−0.653312	+	0.757089i	$0.726621\pi$
$468$		0			0
$469$	2.82843	+	6.82843i	0.130605	+	0.315307i
$470$		0			0
$471$	−8.28427	+	20.0000i	−0.381719	+	0.921551i
$472$		0			0
$473$	−51.4558	−	21.3137i	−2.36594	−	0.980005i
$474$		0			0
$475$	−23.4558			−1.07623
$476$		0			0
$477$	−0.443651			−0.0203134
$478$		0			0
$479$	35.3848	+	14.6569i	1.61677	+	0.669689i	0.993658	−	0.112443i	$-0.0358675\pi$
$479$	35.3848	+	14.6569i	1.61677	+	0.669689i	0.623113	+	0.782131i	$0.285867\pi$
$480$		0			0
$481$	0.272078	−	0.656854i	0.0124057	−	0.0299500i
$482$		0			0
$483$	−0.485281	−	1.17157i	−0.0220811	−	0.0533084i
$484$		0			0
$485$	0.757359	+	0.757359i	0.0343899	+	0.0343899i
$486$		0			0
$487$	−17.1421	+	7.10051i	−0.776784	+	0.321755i	−0.735617	−	0.677398i	$-0.763108\pi$
$487$	−17.1421	+	7.10051i	−0.776784	+	0.321755i	−0.0411673	+	0.999152i	$0.513108\pi$
$488$		0			0
$489$		−	2.14214i		−	0.0968707i
$490$		0			0
$491$	12.2426	−	12.2426i	0.552503	−	0.552503i	−0.374660	−	0.927162i	$-0.622240\pi$
$491$	12.2426	−	12.2426i	0.552503	−	0.552503i	0.927162	+	0.374660i	$0.122240\pi$
$492$		0			0
$493$	−3.87868	−	8.63604i	−0.174687	−	0.388948i
$494$		0			0
$495$	20.8701	−	20.8701i	0.938039	−	0.938039i
$496$		0			0
$497$		−	38.1421i		−	1.71091i
$498$		0			0
$499$	−1.48528	+	0.615224i	−0.0664903	+	0.0275412i	−0.415681	−	0.909511i	$-0.636457\pi$
$499$	−1.48528	+	0.615224i	−0.0664903	+	0.0275412i	0.349190	+	0.937052i	$0.386457\pi$
$500$		0			0
$501$	7.17157	+	7.17157i	0.320402	+	0.320402i
$502$		0			0
$503$	4.17157	+	10.0711i	0.186001	+	0.449047i	0.989183	−	0.146687i	$-0.0468612\pi$
$503$	4.17157	+	10.0711i	0.186001	+	0.449047i	−0.803182	+	0.595734i	$0.796861\pi$
$504$		0			0
$505$	12.1716	−	29.3848i	0.541628	−	1.30761i
$506$		0			0
$507$	−16.3137	−	6.75736i	−0.724517	−	0.300105i
$508$		0			0
$509$	−20.0000			−0.886484			−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000			−0.886484			−0.443242	+	0.896402i	$0.646172\pi$
$510$		0			0
$511$	−36.6274			−1.62030
$512$		0			0
$513$	−17.6569	−	7.31371i	−0.779569	−	0.322908i
$514$		0			0
$515$	3.65685	−	8.82843i	0.161140	−	0.389027i
$516$		0			0
$517$	12.4853	+	30.1421i	0.549102	+	1.32565i
$518$		0			0
$519$	8.04163	+	8.04163i	0.352988	+	0.352988i
$520$		0			0
$521$	4.53553	−	1.87868i	0.198705	−	0.0823065i	−0.281112	−	0.959675i	$-0.590703\pi$
$521$	4.53553	−	1.87868i	0.198705	−	0.0823065i	0.479817	+	0.877369i	$0.340703\pi$
$522$		0			0
$523$		−	23.1127i		−	1.01065i	−0.862930	−	0.505324i	$-0.831373\pi$
$523$		−	23.1127i		−	1.01065i	0.862930	−	0.505324i	$-0.168627\pi$
$524$		0			0
$525$	12.8284	−	12.8284i	0.559878	−	0.559878i
$526$		0			0
$527$	−9.82843	+	4.41421i	−0.428133	+	0.192286i
$528$		0			0
$529$	−16.1213	+	16.1213i	−0.700927	+	0.700927i
$530$		0			0
$531$		−	23.4558i		−	1.01790i
$532$		0			0
$533$	−19.1421	+	7.92893i	−0.829138	+	0.343440i
$534$		0			0
$535$	−29.0711	−	29.0711i	−1.25685	−	1.25685i
$536$		0			0
$537$	2.68629	+	6.48528i	0.115922	+	0.279861i
$538$		0			0
$539$	0.313708	−	0.757359i	0.0135124	−	0.0326218i
$540$		0			0
$541$	−6.94975	−	2.87868i	−0.298793	−	0.123764i	0.228250	−	0.973602i	$-0.426699\pi$
$541$	−6.94975	−	2.87868i	−0.298793	−	0.123764i	−0.527043	+	0.849838i	$0.676699\pi$
$542$		0			0
$543$	−15.8579			−0.680526
$544$		0			0
$545$	59.2132			2.53641
$546$		0			0
$547$	−15.8284	−	6.55635i	−0.676775	−	0.280329i	0.0177032	−	0.999843i	$-0.494365\pi$
$547$	−15.8284	−	6.55635i	−0.676775	−	0.280329i	−0.694478	+	0.719514i	$0.744365\pi$
$548$		0			0
$549$	−0.221825	+	0.535534i	−0.00946728	+	0.0228560i
$550$		0			0
$551$	3.21320	+	7.75736i	0.136887	+	0.330475i
$552$		0			0
$553$	8.82843	+	8.82843i	0.375423	+	0.375423i
$554$		0			0
$555$	−0.443651	+	0.183766i	−0.0188319	+	0.00780044i
$556$		0			0
$557$		−	0.242641i		−	0.0102810i	−0.999987	−	0.00514051i	$-0.998364\pi$
$557$		−	0.242641i		−	0.0102810i	0.999987	−	0.00514051i	$-0.00163628\pi$
$558$		0			0
$559$	−44.6274	+	44.6274i	−1.88754	+	1.88754i
$560$		0			0
$561$	−14.6274	+	15.5147i	−0.617570	+	0.655032i
$562$		0			0
$563$	−14.3848	+	14.3848i	−0.606246	+	0.606246i	−0.941963	−	0.335717i	$-0.891021\pi$
$563$	−14.3848	+	14.3848i	−0.606246	+	0.606246i	0.335717	+	0.941963i	$0.391021\pi$
$564$		0			0
$565$		−	9.89949i		−	0.416475i
$566$		0			0
$567$	0.414214	−	0.171573i	0.0173953	−	0.00720538i
$568$		0			0
$569$	6.17157	+	6.17157i	0.258726	+	0.258726i	0.824536	−	0.565810i	$-0.191436\pi$
$569$	6.17157	+	6.17157i	0.258726	+	0.258726i	−0.565810	+	0.824536i	$0.691436\pi$
$570$		0			0
$571$	−8.51472	−	20.5563i	−0.356330	−	0.860256i	−0.995810	−	0.0914486i	$-0.970850\pi$
$571$	−8.51472	−	20.5563i	−0.356330	−	0.860256i	0.639480	−	0.768808i	$-0.279150\pi$
$572$		0			0
$573$	2.62742	−	6.34315i	0.109762	−	0.264989i
$574$		0			0
$575$	2.65685	+	1.10051i	0.110798	+	0.0458942i
$576$		0			0
$577$	−25.2132			−1.04964			−0.524820	−	0.851213i	$-0.675867\pi$
$577$	−25.2132			−1.04964			−0.524820	+	0.851213i	$0.675867\pi$
$578$		0			0
$579$	17.3137			0.719533
$580$		0			0
$581$	17.3137	+	7.17157i	0.718294	+	0.297527i
$582$		0			0
$583$	0.443651	−	1.07107i	0.0183741	−	0.0443591i
$584$		0			0
$585$	−12.7990	−	30.8995i	−0.529173	−	1.27754i
$586$		0			0
$587$	−18.0416	−	18.0416i	−0.744658	−	0.744658i	0.228813	−	0.973470i	$-0.426516\pi$
$587$	−18.0416	−	18.0416i	−0.744658	−	0.744658i	−0.973470	+	0.228813i	$0.926516\pi$
$588$		0			0
$589$	8.82843	−	3.65685i	0.363769	−	0.150678i
$590$		0			0
$591$		−	9.11270i		−	0.374846i
$592$		0			0
$593$	−13.4853	+	13.4853i	−0.553774	+	0.553774i	−0.927528	−	0.373754i	$-0.878070\pi$
$593$	−13.4853	+	13.4853i	−0.553774	+	0.553774i	0.373754	+	0.927528i	$0.378070\pi$
$594$		0			0
$595$	24.9706	−	26.4853i	1.02369	−	1.08579i
$596$		0			0
$597$	9.51472	−	9.51472i	0.389412	−	0.389412i
$598$		0			0
$599$		−	1.65685i		−	0.0676972i	−0.999427	−	0.0338486i	$-0.989224\pi$
$599$		−	1.65685i		−	0.0676972i	0.999427	−	0.0338486i	$-0.0107764\pi$
$600$		0			0
$601$	−5.12132	+	2.12132i	−0.208903	+	0.0865305i	−0.484681	−	0.874691i	$-0.661064\pi$
$601$	−5.12132	+	2.12132i	−0.208903	+	0.0865305i	0.275778	+	0.961221i	$0.411064\pi$
$602$		0			0
$603$	−3.65685	−	3.65685i	−0.148919	−	0.148919i
$604$		0			0
$605$	15.2929	+	36.9203i	0.621745	+	1.50102i
$606$		0			0
$607$	10.8995	−	26.3137i	0.442397	−	1.06804i	−0.532709	−	0.846299i	$-0.678826\pi$
$607$	10.8995	−	26.3137i	0.442397	−	1.06804i	0.975105	−	0.221742i	$-0.0711742\pi$
$608$		0			0
$609$	−6.00000	−	2.48528i	−0.243132	−	0.100709i
$610$		0			0
$611$	36.9706			1.49567
$612$		0			0
$613$	21.3137			0.860853			0.430426	−	0.902626i	$-0.358363\pi$
$613$	21.3137			0.860853			0.430426	+	0.902626i	$0.358363\pi$
$614$		0			0
$615$	12.9289	+	5.35534i	0.521345	+	0.215948i
$616$		0			0
$617$	8.36396	−	20.1924i	0.336720	−	0.812915i	−0.661306	−	0.750116i	$-0.729997\pi$
$617$	8.36396	−	20.1924i	0.336720	−	0.812915i	0.998026	−	0.0627985i	$-0.0200026\pi$
$618$		0			0
$619$	8.41421	+	20.3137i	0.338196	+	0.816477i	0.997889	+	0.0649419i	$0.0206862\pi$
$619$	8.41421	+	20.3137i	0.338196	+	0.816477i	−0.659693	+	0.751535i	$0.729314\pi$
$620$		0			0
$621$	1.65685	+	1.65685i	0.0664873	+	0.0664873i
$622$		0			0
$623$	−10.2426	+	4.24264i	−0.410363	+	0.169978i
$624$		0			0
$625$		−	15.9289i		−	0.637157i
$626$		0			0
$627$	13.3726	−	13.3726i	0.534050	−	0.534050i
$628$		0			0
$629$	−0.493903	+	0.221825i	−0.0196932	+	0.00884476i
$630$		0			0
$631$	−27.2132	+	27.2132i	−1.08334	+	1.08334i	−0.0871449	+	0.996196i	$0.527774\pi$
$631$	−27.2132	+	27.2132i	−1.08334	+	1.08334i	−0.996196	+	0.0871449i	$0.972226\pi$
$632$		0			0
$633$			22.5442i			0.896050i
$634$		0			0
$635$	−15.0711	+	6.24264i	−0.598077	+	0.247732i
$636$		0			0
$637$	−0.656854	−	0.656854i	−0.0260255	−	0.0260255i
$638$		0			0
$639$	10.2132	+	24.6569i	0.404028	+	0.975410i
$640$		0			0
$641$	−9.05025	+	21.8492i	−0.357463	+	0.862993i	0.638192	+	0.769877i	$0.279683\pi$
$641$	−9.05025	+	21.8492i	−0.357463	+	0.862993i	−0.995655	+	0.0931158i	$0.970317\pi$
$642$		0			0
$643$	−6.31371	−	2.61522i	−0.248988	−	0.103134i	0.254699	−	0.967020i	$-0.418024\pi$
$643$	−6.31371	−	2.61522i	−0.248988	−	0.103134i	−0.503687	+	0.863886i	$0.668024\pi$
$644$		0			0
$645$	42.6274			1.67845
$646$		0			0
$647$	−1.17157			−0.0460593			−0.0230296	−	0.999735i	$-0.507331\pi$
$647$	−1.17157			−0.0460593			−0.0230296	+	0.999735i	$0.507331\pi$
$648$		0			0
$649$	56.6274	+	23.4558i	2.22282	+	0.920722i
$650$		0			0
$651$	−2.82843	+	6.82843i	−0.110855	+	0.267627i
$652$		0			0
$653$	8.39340	+	20.2635i	0.328459	+	0.792970i	0.998707	+	0.0508332i	$0.0161877\pi$
$653$	8.39340	+	20.2635i	0.328459	+	0.792970i	−0.670248	+	0.742137i	$0.733812\pi$
$654$		0			0
$655$	18.7279	+	18.7279i	0.731760	+	0.731760i
$656$		0			0
$657$	23.6777	−	9.80761i	0.923754	−	0.382631i
$658$		0			0
$659$			18.1421i			0.706717i	0.935488	+	0.353359i	$0.114960\pi$
$659$			18.1421i			0.706717i	−0.935488	+	0.353359i	$0.885040\pi$
$660$		0			0
$661$	21.3431	−	21.3431i	0.830152	−	0.830152i	−0.157385	−	0.987537i	$-0.550306\pi$
$661$	21.3431	−	21.3431i	0.830152	−	0.830152i	0.987537	+	0.157385i	$0.0503064\pi$
$662$		0			0
$663$	9.89949	+	22.0416i	0.384465	+	0.856026i
$664$		0			0
$665$	−22.8284	+	22.8284i	−0.885248	+	0.885248i
$666$		0			0
$667$		−	1.02944i		−	0.0398600i
$668$		0			0
$669$	−25.3137	+	10.4853i	−0.978685	+	0.405384i
$670$		0			0
$671$	−1.07107	−	1.07107i	−0.0413481	−	0.0413481i
$672$		0			0
$673$	−5.77817	−	13.9497i	−0.222732	−	0.537723i	0.772527	−	0.634982i	$-0.218993\pi$
$673$	−5.77817	−	13.9497i	−0.222732	−	0.537723i	−0.995259	+	0.0972588i	$0.968993\pi$
$674$		0			0
$675$	−12.8284	+	30.9706i	−0.493766	+	1.19206i
$676$		0			0
$677$	−39.8492	−	16.5061i	−1.53153	−	0.634381i	−0.551670	−	0.834062i	$-0.686009\pi$
$677$	−39.8492	−	16.5061i	−1.53153	−	0.634381i	−0.979861	+	0.199682i	$0.936009\pi$
$678$		0			0
$679$	0.828427			0.0317921
$680$		0			0
$681$	−5.17157			−0.198175
$682$		0			0
$683$	−20.3137	−	8.41421i	−0.777282	−	0.321961i	−0.0414642	−	0.999140i	$-0.513202\pi$
$683$	−20.3137	−	8.41421i	−0.777282	−	0.321961i	−0.735818	+	0.677179i	$0.763202\pi$
$684$		0			0
$685$	21.0000	−	50.6985i	0.802369	−	1.93709i
$686$		0			0
$687$	−1.85786	−	4.48528i	−0.0708819	−	0.171124i
$688$		0			0
$689$	−0.928932	−	0.928932i	−0.0353895	−	0.0353895i
$690$		0			0
$691$	6.07107	−	2.51472i	0.230954	−	0.0956644i	−0.264205	−	0.964466i	$-0.585110\pi$
$691$	6.07107	−	2.51472i	0.230954	−	0.0956644i	0.495160	+	0.868802i	$0.335110\pi$
$692$		0			0
$693$		−	22.8284i		−	0.867180i
$694$		0			0
$695$	−41.5563	+	41.5563i	−1.57632	+	1.57632i
$696$		0			0
$697$	14.7487	+	5.60660i	0.558648	+	0.212365i
$698$		0			0
$699$	−16.2426	+	16.2426i	−0.614353	+	0.614353i
$700$		0			0
$701$			31.7574i			1.19946i	0.800203	+	0.599729i	$0.204725\pi$
$701$			31.7574i			1.19946i	−0.800203	+	0.599729i	$0.795275\pi$
$702$		0			0
$703$	0.443651	−	0.183766i	0.0167326	−	0.00693087i
$704$		0			0
$705$	−17.6569	−	17.6569i	−0.664996	−	0.664996i
$706$		0			0
$707$	−9.41421	−	22.7279i	−0.354058	−	0.854771i
$708$		0			0
$709$	−18.9203	+	45.6777i	−0.710567	+	1.71546i	−0.0119880	+	0.999928i	$0.503816\pi$
$709$	−18.9203	+	45.6777i	−0.710567	+	1.71546i	−0.698579	+	0.715533i	$0.746184\pi$
$710$		0			0
$711$	−8.07107	−	3.34315i	−0.302689	−	0.125378i
$712$		0			0
$713$	−1.17157			−0.0438757
$714$		0			0
$715$	87.3970			3.26846
$716$		0			0
$717$	−0.485281	−	0.201010i	−0.0181232	−	0.00750686i
$718$		0			0
$719$	−8.65685	+	20.8995i	−0.322846	+	0.779420i	0.676240	+	0.736681i	$0.263608\pi$
$719$	−8.65685	+	20.8995i	−0.322846	+	0.779420i	−0.999086	+	0.0427384i	$0.986392\pi$
$720$		0			0
$721$	−2.82843	−	6.82843i	−0.105336	−	0.254304i
$722$		0			0
$723$	6.10051	+	6.10051i	0.226880	+	0.226880i
$724$		0			0
$725$	13.6066	−	5.63604i	0.505337	−	0.209317i
$726$		0			0
$727$		−	48.4853i		−	1.79822i	−0.437723	−	0.899110i	$-0.644215\pi$
$727$		−	48.4853i		−	1.79822i	0.437723	−	0.899110i	$-0.355785\pi$
$728$		0			0
$729$	−12.2218	+	12.2218i	−0.452660	+	0.452660i
$730$		0			0
$731$	48.0416	−	1.41421i	1.77688	−	0.0523066i
$732$		0			0
$733$	−15.3431	+	15.3431i	−0.566712	+	0.566712i	−0.931206	−	0.364494i	$-0.881242\pi$
$733$	−15.3431	+	15.3431i	−0.566712	+	0.566712i	0.364494	+	0.931206i	$0.381242\pi$
$734$		0			0
$735$			0.627417i			0.0231426i
$736$		0			0
$737$	12.4853	−	5.17157i	0.459901	−	0.190497i
$738$		0			0
$739$	−29.0711	−	29.0711i	−1.06940	−	1.06940i	−0.997405	−	0.0719913i	$-0.977065\pi$
$739$	−29.0711	−	29.0711i	−1.06940	−	1.06940i	−0.0719913	−	0.997405i	$-0.522935\pi$
$740$		0			0
$741$	−8.20101	−	19.7990i	−0.301272	−	0.727334i
$742$		0			0
$743$	1.24264	−	3.00000i	0.0455881	−	0.110059i	−0.899445	−	0.437034i	$-0.856029\pi$
$743$	1.24264	−	3.00000i	0.0455881	−	0.110059i	0.945033	+	0.326974i	$0.106029\pi$
$744$		0			0
$745$	60.2843	+	24.9706i	2.20864	+	0.914851i
$746$		0			0
$747$	−13.1127			−0.479769
$748$		0			0
$749$	−31.7990			−1.16191
$750$		0			0
$751$	29.1421	+	12.0711i	1.06341	+	0.440480i	0.844661	−	0.535301i	$-0.179802\pi$
$751$	29.1421	+	12.0711i	1.06341	+	0.440480i	0.218750	+	0.975781i	$0.429802\pi$
$752$		0			0
$753$	10.1421	−	24.4853i	0.369600	−	0.892293i
$754$		0			0
$755$	−15.0711	−	36.3848i	−0.548492	−	1.32418i
$756$		0			0
$757$	−20.1421	−	20.1421i	−0.732078	−	0.732078i	0.238953	−	0.971031i	$-0.423196\pi$
$757$	−20.1421	−	20.1421i	−0.732078	−	0.732078i	−0.971031	+	0.238953i	$0.923196\pi$
$758$		0			0
$759$	−2.14214	+	0.887302i	−0.0777546	+	0.0322070i
$760$		0			0
$761$			40.5269i			1.46910i	0.678555	+	0.734550i	$0.262607\pi$
$761$			40.5269i			1.46910i	−0.678555	+	0.734550i	$0.737393\pi$
$762$		0			0
$763$	32.3848	−	32.3848i	1.17241	−	1.17241i
$764$		0			0
$765$	−9.05025	+	23.8076i	−0.327213	+	0.860766i
$766$		0			0
$767$	49.1127	−	49.1127i	1.77336	−	1.77336i
$768$		0			0
$769$		−	20.2426i		−	0.729968i	−0.931014	−	0.364984i	$-0.881074\pi$
$769$		−	20.2426i		−	0.729968i	0.931014	−	0.364984i	$-0.118926\pi$
$770$		0			0
$771$	14.1421	−	5.85786i	0.509317	−	0.210966i
$772$		0			0
$773$	24.5858	+	24.5858i	0.884289	+	0.884289i	0.993967	−	0.109678i	$-0.0349819\pi$
$773$	24.5858	+	24.5858i	0.884289	+	0.884289i	−0.109678	+	0.993967i	$0.534982\pi$
$774$		0			0
$775$	−6.41421	−	15.4853i	−0.230405	−	0.556248i
$776$		0			0
$777$	−0.142136	+	0.343146i	−0.00509909	+	0.0123103i
$778$		0			0
$779$	−12.9289	−	5.35534i	−0.463227	−	0.191875i
$780$		0			0
$781$	−69.7401			−2.49550
$782$		0			0
$783$	12.0000			0.428845
$784$		0			0
$785$	−62.4264	−	25.8579i	−2.22809	−	0.922907i
$786$		0			0
$787$	−15.0416	+	36.3137i	−0.536176	+	1.29444i	0.391197	+	0.920307i	$0.372061\pi$
$787$	−15.0416	+	36.3137i	−0.536176	+	1.29444i	−0.927373	+	0.374137i	$0.877939\pi$
$788$		0			0
$789$	−6.48528	−	15.6569i	−0.230882	−	0.557399i
$790$		0			0
$791$	−5.41421	−	5.41421i	−0.192507	−	0.192507i
$792$		0			0
$793$	−1.58579	+	0.656854i	−0.0563129	+	0.0233256i
$794$		0			0
$795$			0.887302i			0.0314693i
$796$		0			0
$797$	−11.9706	+	11.9706i	−0.424019	+	0.424019i	−0.886585	−	0.462566i	$-0.846929\pi$
$797$	−11.9706	+	11.9706i	−0.424019	+	0.424019i	0.462566	+	0.886585i	$0.346929\pi$
$798$		0			0
$799$	−20.4853	−	19.3137i	−0.724717	−	0.683270i
$800$		0			0
$801$	5.48528	−	5.48528i	0.193813	−	0.193813i
$802$		0			0
$803$			66.9706i			2.36334i
$804$		0			0
$805$	3.65685	−	1.51472i	0.128887	−	0.0533868i
$806$		0			0
$807$	−3.41421	−	3.41421i	−0.120186	−	0.120186i
$808$		0			0
$809$	17.2929	+	41.7487i	0.607986	+	1.46781i	0.865187	+	0.501450i	$0.167200\pi$
$809$	17.2929	+	41.7487i	0.607986	+	1.46781i	−0.257201	+	0.966358i	$0.582800\pi$
$810$		0			0
$811$	−9.24264	+	22.3137i	−0.324553	+	0.783540i	0.674425	+	0.738343i	$0.264392\pi$
$811$	−9.24264	+	22.3137i	−0.324553	+	0.783540i	−0.998978	+	0.0451970i	$0.985608\pi$
$812$		0			0
$813$	−2.14214	−	0.887302i	−0.0751280	−	0.0311190i
$814$		0			0
$815$	6.68629			0.234211
$816$		0			0
$817$	−42.6274			−1.49134
$818$		0			0
$819$	−23.8995	−	9.89949i	−0.835116	−	0.345916i
$820$		0			0
$821$	14.9203	−	36.0208i	0.520722	−	1.25714i	−0.416733	−	0.909029i	$-0.636825\pi$
$821$	14.9203	−	36.0208i	0.520722	−	1.25714i	0.937455	−	0.348106i	$-0.113175\pi$
$822$		0			0
$823$	13.0416	+	31.4853i	0.454603	+	1.09751i	0.970553	+	0.240889i	$0.0774390\pi$
$823$	13.0416	+	31.4853i	0.454603	+	1.09751i	−0.515950	+	0.856619i	$0.672561\pi$
$824$		0			0
$825$	−23.4558	−	23.4558i	−0.816628	−	0.816628i
$826$		0			0
$827$	−0.656854	+	0.272078i	−0.0228411	+	0.00946108i	−0.394075	−	0.919078i	$-0.628935\pi$
$827$	−0.656854	+	0.272078i	−0.0228411	+	0.00946108i	0.371234	+	0.928539i	$0.378935\pi$
$828$		0			0
$829$			4.97056i			0.172635i	0.996268	+	0.0863174i	$0.0275099\pi$
$829$			4.97056i			0.172635i	−0.996268	+	0.0863174i	$0.972490\pi$
$830$		0			0
$831$	−6.04163	+	6.04163i	−0.209582	+	0.209582i
$832$		0			0
$833$	0.0208153	+	0.707107i	0.000721207	+	0.0244998i
$834$		0			0
$835$	−22.3848	+	22.3848i	−0.774657	+	0.774657i
$836$		0			0
$837$		−	13.6569i		−	0.472050i
$838$		0			0
$839$	41.2843	−	17.1005i	1.42529	−	0.590375i	0.469107	−	0.883141i	$-0.344576\pi$
$839$	41.2843	−	17.1005i	1.42529	−	0.590375i	0.956184	+	0.292766i	$0.0945758\pi$
$840$		0			0
$841$	16.7782	+	16.7782i	0.578558	+	0.578558i
$842$		0			0
$843$	−0.786797	−	1.89949i	−0.0270987	−	0.0654221i
$844$		0			0
$845$	21.0919	−	50.9203i	0.725583	−	1.75171i
$846$		0			0
$847$	28.5563	+	11.8284i	0.981208	+	0.406430i
$848$		0			0
$849$	10.4264			0.357833
$850$		0			0
$851$	−0.0588745			−0.00201819
$852$		0			0
$853$	−22.9497	−	9.50610i	−0.785784	−	0.325483i	−0.0465370	−	0.998917i	$-0.514819\pi$
$853$	−22.9497	−	9.50610i	−0.785784	−	0.325483i	−0.739247	+	0.673434i	$0.764819\pi$
$854$		0			0
$855$	8.64466	−	20.8701i	0.295641	−	0.713741i
$856$		0			0
$857$	−3.12132	−	7.53553i	−0.106622	−	0.257409i	0.861560	−	0.507656i	$-0.169488\pi$
$857$	−3.12132	−	7.53553i	−0.106622	−	0.257409i	−0.968182	+	0.250247i	$0.919488\pi$
$858$		0			0
$859$	−10.7279	−	10.7279i	−0.366032	−	0.366032i	0.499996	−	0.866028i	$-0.333335\pi$
$859$	−10.7279	−	10.7279i	−0.366032	−	0.366032i	−0.866028	+	0.499996i	$0.833335\pi$
$860$		0			0
$861$	10.0000	−	4.14214i	0.340799	−	0.141164i
$862$		0			0
$863$		−	17.6569i		−	0.601046i	−0.953775	−	0.300523i	$-0.902839\pi$
$863$		−	17.6569i		−	0.601046i	0.953775	−	0.300523i	$-0.0971613\pi$
$864$		0			0
$865$	−25.1005	+	25.1005i	−0.853443	+	0.853443i
$866$		0			0
$867$	6.02944	−	17.3848i	0.204770	−	0.590418i
$868$		0			0
$869$	16.1421	−	16.1421i	0.547584	−	0.547584i
$870$		0			0
$871$		−	15.3137i		−	0.518885i
$872$		0			0
$873$	−0.535534	+	0.221825i	−0.0181251	+	0.00750765i
$874$		0			0
$875$	8.82843	+	8.82843i	0.298455	+	0.298455i
$876$		0			0
$877$	−14.4645	−	34.9203i	−0.488430	−	1.17918i	−0.955510	−	0.294960i	$-0.904694\pi$
$877$	−14.4645	−	34.9203i	−0.488430	−	1.17918i	0.467079	−	0.884215i	$-0.345306\pi$
$878$		0			0
$879$	9.51472	−	22.9706i	0.320923	−	0.774778i
$880$		0			0
$881$	−31.8492	−	13.1924i	−1.07303	−	0.444463i	−0.224970	−	0.974366i	$-0.572228\pi$
$881$	−31.8492	−	13.1924i	−1.07303	−	0.444463i	−0.848058	+	0.529903i	$0.822228\pi$
$882$		0			0
$883$	−37.6569			−1.26725			−0.633627	−	0.773639i	$-0.718435\pi$
$883$	−37.6569			−1.26725			−0.633627	+	0.773639i	$0.718435\pi$
$884$		0			0
$885$	−46.9117			−1.57692
$886$		0			0
$887$	33.3848	+	13.8284i	1.12095	+	0.464313i	0.864696	−	0.502296i	$-0.167511\pi$
$887$	33.3848	+	13.8284i	1.12095	+	0.464313i	0.256255	+	0.966609i	$0.417511\pi$
$888$		0			0
$889$	−4.82843	+	11.6569i	−0.161940	+	0.390958i
$890$		0			0
$891$	−0.313708	−	0.757359i	−0.0105096	−	0.0253725i
$892$		0			0
$893$	17.6569	+	17.6569i	0.590864	+	0.590864i
$894$		0			0
$895$	−20.2426	+	8.38478i	−0.676637	+	0.280272i
$896$		0			0
$897$			2.62742i			0.0877269i
$898$		0			0
$899$	−4.24264	+	4.24264i	−0.141500	+	0.141500i
$900$		0			0
$901$	0.0294373	+	1.00000i	0.000980697	+	0.0333148i
$902$		0			0
$903$	23.3137	−	23.3137i	0.775832	−	0.775832i
$904$		0			0
$905$		−	49.4975i		−	1.64535i
$906$		0			0
$907$	3.24264	−	1.34315i	0.107670	−	0.0445984i	−0.328198	−	0.944609i	$-0.606441\pi$
$907$	3.24264	−	1.34315i	0.107670	−	0.0445984i	0.435868	+	0.900010i	$0.356441\pi$
$908$		0			0
$909$	12.1716	+	12.1716i	0.403706	+	0.403706i
$910$		0			0
$911$	−1.48528	−	3.58579i	−0.0492096	−	0.118802i	0.897363	−	0.441293i	$-0.145480\pi$
$911$	−1.48528	−	3.58579i	−0.0492096	−	0.118802i	−0.946573	+	0.322490i	$0.895480\pi$
$912$		0			0
$913$	13.1127	−	31.6569i	0.433967	−	1.04769i
$914$		0			0
$915$	1.07107	+	0.443651i	0.0354084	+	0.0146666i
$916$		0			0
$917$	20.4853			0.676484
$918$		0			0
$919$	−3.31371			−0.109309			−0.0546546	−	0.998505i	$-0.517406\pi$
$919$	−3.31371			−0.109309			−0.0546546	+	0.998505i	$0.517406\pi$
$920$		0			0
$921$	14.1421	+	5.85786i	0.465999	+	0.193023i
$922$		0			0
$923$	−30.2426	+	73.0122i	−0.995449	+	2.40323i
$924$		0			0
$925$	−0.322330	−	0.778175i	−0.0105982	−	0.0255862i
$926$		0			0
$927$	3.65685	+	3.65685i	0.120107	+	0.120107i
$928$		0			0
$929$	−19.9497	+	8.26346i	−0.654530	+	0.271115i	−0.685135	−	0.728416i	$-0.740257\pi$
$929$	−19.9497	+	8.26346i	−0.654530	+	0.271115i	0.0306047	+	0.999532i	$0.490257\pi$
$930$		0			0
$931$		−	0.627417i		−	0.0205628i
$932$		0			0
$933$	14.2843	−	14.2843i	0.467646	−	0.467646i
$934$		0			0
$935$	−48.4264	−	45.6569i	−1.58371	−	1.49314i
$936$		0			0
$937$	−19.1421	+	19.1421i	−0.625346	+	0.625346i	−0.946894	−	0.321547i	$-0.895797\pi$
$937$	−19.1421	+	19.1421i	−0.625346	+	0.625346i	0.321547	+	0.946894i	$0.395797\pi$
$938$		0			0
$939$			4.14214i			0.135173i
$940$		0			0
$941$	8.43503	−	3.49390i	0.274974	−	0.113898i	−0.240935	−	0.970541i	$-0.577454\pi$
$941$	8.43503	−	3.49390i	0.274974	−	0.113898i	0.515909	+	0.856643i	$0.327454\pi$
$942$		0			0
$943$	1.21320	+	1.21320i	0.0395073	+	0.0395073i
$944$		0			0
$945$	17.6569	+	42.6274i	0.574378	+	1.38667i
$946$		0			0
$947$	−11.4437	+	27.6274i	−0.371869	+	0.897770i	0.621565	+	0.783362i	$0.286497\pi$
$947$	−11.4437	+	27.6274i	−0.371869	+	0.897770i	−0.993434	+	0.114408i	$0.963503\pi$
$948$		0			0
$949$	70.1127	+	29.0416i	2.27595	+	0.942731i
$950$		0			0
$951$	−3.37258			−0.109363
$952$		0			0
$953$	−0.727922			−0.0235797			−0.0117899	−	0.999930i	$-0.503753\pi$
$953$	−0.727922			−0.0235797			−0.0117899	+	0.999930i	$0.503753\pi$
$954$		0			0
$955$	19.7990	+	8.20101i	0.640680	+	0.265378i
$956$		0			0
$957$	−4.54416	+	10.9706i	−0.146892	+	0.354628i
$958$		0			0
$959$	−16.2426	−	39.2132i	−0.524502	−	1.26626i
$960$		0			0
$961$	−17.0919	−	17.0919i	−0.551351	−	0.551351i
$962$		0			0
$963$	20.5563	−	8.51472i	0.662419	−	0.274383i
$964$		0			0
$965$			54.0416i			1.73966i
$966$		0			0
$967$	−5.07107	+	5.07107i	−0.163075	+	0.163075i	−0.783927	−	0.620853i	$-0.786787\pi$
$967$	−5.07107	+	5.07107i	−0.163075	+	0.163075i	0.620853	+	0.783927i	$0.286787\pi$
$968$		0			0
$969$	−5.79899	+	15.2548i	−0.186290	+	0.490056i
$970$		0			0
$971$	27.7574	−	27.7574i	0.890776	−	0.890776i	−0.103820	−	0.994596i	$-0.533107\pi$
$971$	27.7574	−	27.7574i	0.890776	−	0.890776i	0.994596	+	0.103820i	$0.0331066\pi$
$972$		0			0
$973$			45.4558i			1.45725i
$974$		0			0
$975$	−34.7279	+	14.3848i	−1.11218	+	0.460682i
$976$		0			0
$977$	26.5147	+	26.5147i	0.848281	+	0.848281i	0.989919	−	0.141638i	$-0.0452368\pi$
$977$	26.5147	+	26.5147i	0.848281	+	0.848281i	−0.141638	+	0.989919i	$0.545237\pi$
$978$		0			0
$979$	7.75736	+	18.7279i	0.247926	+	0.598547i
$980$		0			0
$981$	−12.2635	+	29.6066i	−0.391542	+	0.945266i
$982$		0			0
$983$	−18.7990	−	7.78680i	−0.599595	−	0.248360i	0.0621777	−	0.998065i	$-0.480195\pi$
$983$	−18.7990	−	7.78680i	−0.599595	−	0.248360i	−0.661772	+	0.749705i	$0.730195\pi$
$984$		0			0
$985$	28.4437			0.906290
$986$		0			0
$987$	−19.3137			−0.614762
$988$		0			0
$989$	4.82843	+	2.00000i	0.153535	+	0.0635963i
$990$		0			0
$991$	−12.3137	+	29.7279i	−0.391158	+	0.944339i	0.598530	+	0.801100i	$0.295752\pi$
$991$	−12.3137	+	29.7279i	−0.391158	+	0.944339i	−0.989688	+	0.143238i	$0.954248\pi$
$992$		0			0
$993$	6.20101	+	14.9706i	0.196783	+	0.475076i
$994$		0			0
$995$	29.6985	+	29.6985i	0.941505	+	0.941505i
$996$		0			0
$997$	23.3640	−	9.67767i	0.739944	−	0.306495i	0.0193129	−	0.999813i	$-0.493852\pi$
$997$	23.3640	−	9.67767i	0.739944	−	0.306495i	0.720631	+	0.693319i	$0.243852\pi$
$998$		0			0
$999$		−	0.686292i		−	0.0217133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.b.9.1	✓	4
3.2	odd	2		1224.2.bq.b.145.1		4
4.3	odd	2		272.2.v.a.145.1		4
17.2	even	8	inner	136.2.n.b.121.1	yes	4
17.6	odd	16		2312.2.a.t.1.3		4
17.7	odd	16		2312.2.b.i.577.2		4
17.10	odd	16		2312.2.b.i.577.3		4
17.11	odd	16		2312.2.a.t.1.2		4
51.2	odd	8		1224.2.bq.b.937.1		4
68.11	even	16		4624.2.a.bo.1.3		4
68.19	odd	8		272.2.v.a.257.1		4
68.23	even	16		4624.2.a.bo.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.b.9.1	✓	4	1.1	even	1	trivial
136.2.n.b.121.1	yes	4	17.2	even	8	inner
272.2.v.a.145.1		4	4.3	odd	2
272.2.v.a.257.1		4	68.19	odd	8
1224.2.bq.b.145.1		4	3.2	odd	2
1224.2.bq.b.937.1		4	51.2	odd	8
2312.2.a.t.1.2		4	17.11	odd	16
2312.2.a.t.1.3		4	17.6	odd	16
2312.2.b.i.577.2		4	17.7	odd	16
2312.2.b.i.577.3		4	17.10	odd	16
4624.2.a.bo.1.2		4	68.23	even	16
4624.2.a.bo.1.3		4	68.11	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 0.414214i) q^{3} +(-1.29289 + 3.12132i) q^{5} +(1.00000 + 2.41421i) q^{7} +(-1.29289 - 1.29289i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 0.414214i) q^{3} +(-1.29289 + 3.12132i) q^{5} +(1.00000 + 2.41421i) q^{7} +(-1.29289 - 1.29289i) q^{9} +(4.41421 - 1.82843i) q^{11} -5.41421i q^{13} +(-2.58579 + 2.58579i) q^{15} +(-2.82843 + 3.00000i) q^{17} +(2.58579 - 2.58579i) q^{19} +2.82843i q^{21} +(-0.414214 + 0.171573i) q^{23} +(-4.53553 - 4.53553i) q^{25} +(-2.00000 - 4.82843i) q^{27} +(-0.878680 + 2.12132i) q^{29} +(2.41421 + 1.00000i) q^{31} +5.17157 q^{33} -8.82843 q^{35} +(0.121320 + 0.0502525i) q^{37} +(2.24264 - 5.41421i) q^{39} +(-1.46447 - 3.53553i) q^{41} +(-8.24264 - 8.24264i) q^{43} +(5.70711 - 2.36396i) q^{45} +6.82843i q^{47} +(0.121320 - 0.121320i) q^{49} +(-4.07107 + 1.82843i) q^{51} +(0.171573 - 0.171573i) q^{53} +16.1421i q^{55} +(3.65685 - 1.51472i) q^{57} +(9.07107 + 9.07107i) q^{59} +(-0.121320 - 0.292893i) q^{61} +(1.82843 - 4.41421i) q^{63} +(16.8995 + 7.00000i) q^{65} +2.82843 q^{67} -0.485281 q^{69} +(-13.4853 - 5.58579i) q^{71} +(-5.36396 + 12.9497i) q^{73} +(-2.65685 - 6.41421i) q^{75} +(8.82843 + 8.82843i) q^{77} +(4.41421 - 1.82843i) q^{79} -0.171573i q^{81} +(5.07107 - 5.07107i) q^{83} +(-5.70711 - 12.7071i) q^{85} +(-1.75736 + 1.75736i) q^{87} +4.24264i q^{89} +(13.0711 - 5.41421i) q^{91} +(2.00000 + 2.00000i) q^{93} +(4.72792 + 11.4142i) q^{95} +(0.121320 - 0.292893i) q^{97} +(-8.07107 - 3.34315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9	\( 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9} + 12 q^{11} - 16 q^{15} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 32 q^{33} - 24 q^{35} - 8 q^{37} - 8 q^{39} - 20 q^{41} - 16 q^{43} + 20 q^{45} - 8 q^{49} + 12 q^{51} + 12 q^{53} - 8 q^{57} + 8 q^{59} + 8 q^{61} - 4 q^{63} + 28 q^{65} + 32 q^{69} - 20 q^{71} + 4 q^{73} + 12 q^{75} + 24 q^{77} + 12 q^{79} - 8 q^{83} - 20 q^{85} - 24 q^{87} + 24 q^{91} + 8 q^{93} - 32 q^{95} - 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9 + 12 * q^11 - 16 * q^15 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 32 * q^33 - 24 * q^35 - 8 * q^37 - 8 * q^39 - 20 * q^41 - 16 * q^43 + 20 * q^45 - 8 * q^49 + 12 * q^51 + 12 * q^53 - 8 * q^57 + 8 * q^59 + 8 * q^61 - 4 * q^63 + 28 * q^65 + 32 * q^69 - 20 * q^71 + 4 * q^73 + 12 * q^75 + 24 * q^77 + 12 * q^79 - 8 * q^83 - 20 * q^85 - 24 * q^87 + 24 * q^91 + 8 * q^93 - 32 * q^95 - 8 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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