LMFDB - Embedded newform 136.2.n.a.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:	$\Z[a_1, a_2, a_3]$
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.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70711 - 0.707107i) q^{3} +(0.292893 - 0.707107i) q^{5} +(-1.70711 - 4.12132i) q^{7} +(0.292893 + 0.292893i) q^{9} +O(q^{10})$	\(q+(-1.70711 - 0.707107i) q^{3} +(0.292893 - 0.707107i) q^{5} +(-1.70711 - 4.12132i) q^{7} +(0.292893 + 0.292893i) q^{9} +(1.70711 - 0.707107i) q^{11} +(-1.00000 + 1.00000i) q^{15} +(1.00000 - 4.00000i) q^{17} +(-4.41421 + 4.41421i) q^{19} +8.24264i q^{21} +(4.53553 - 1.87868i) q^{23} +(3.12132 + 3.12132i) q^{25} +(1.82843 + 4.41421i) q^{27} +(-0.878680 + 2.12132i) q^{29} +(5.12132 + 2.12132i) q^{31} -3.41421 q^{33} -3.41421 q^{35} +(1.70711 + 0.707107i) q^{37} +(-3.70711 - 8.94975i) q^{41} +(-1.24264 - 1.24264i) q^{43} +(0.292893 - 0.121320i) q^{45} -7.17157i q^{47} +(-9.12132 + 9.12132i) q^{49} +(-4.53553 + 6.12132i) q^{51} +(7.82843 - 7.82843i) q^{53} -1.41421i q^{55} +(10.6569 - 4.41421i) q^{57} +(8.41421 + 8.41421i) q^{59} +(-4.87868 - 11.7782i) q^{61} +(0.707107 - 1.70711i) q^{63} -1.65685 q^{67} -9.07107 q^{69} +(2.29289 + 0.949747i) q^{71} +(-5.36396 + 12.9497i) q^{73} +(-3.12132 - 7.53553i) q^{75} +(-5.82843 - 5.82843i) q^{77} +(12.5355 - 5.19239i) q^{79} -10.0711i q^{81} +(1.24264 - 1.24264i) q^{83} +(-2.53553 - 1.87868i) q^{85} +(3.00000 - 3.00000i) q^{87} +9.65685i q^{89} +(-7.24264 - 7.24264i) q^{93} +(1.82843 + 4.41421i) q^{95} +(0.778175 - 1.87868i) q^{97} +(0.707107 + 0.292893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{17} - 12 q^{19} + 4 q^{23} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 12 q^{31} - 8 q^{33} - 8 q^{35} + 4 q^{37} - 12 q^{41} + 12 q^{43} + 4 q^{45} - 28 q^{49} - 4 q^{51} + 20 q^{53} + 20 q^{57} + 28 q^{59} - 28 q^{61} + 16 q^{67} - 8 q^{69} + 12 q^{71} + 4 q^{73} - 4 q^{75} - 12 q^{77} + 36 q^{79} - 12 q^{83} + 4 q^{85} + 12 q^{87} - 12 q^{93} - 4 q^{95} - 28 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 4 * q^9 + 4 * q^11 - 4 * q^15 + 4 * q^17 - 12 * q^19 + 4 * q^23 + 4 * q^25 - 4 * q^27 - 12 * q^29 + 12 * q^31 - 8 * q^33 - 8 * q^35 + 4 * q^37 - 12 * q^41 + 12 * q^43 + 4 * q^45 - 28 * q^49 - 4 * q^51 + 20 * q^53 + 20 * q^57 + 28 * q^59 - 28 * q^61 + 16 * q^67 - 8 * q^69 + 12 * q^71 + 4 * q^73 - 4 * q^75 - 12 * q^77 + 36 * q^79 - 12 * q^83 + 4 * q^85 + 12 * q^87 - 12 * q^93 - 4 * q^95 - 28 * q^97

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
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	−1.70711	−	0.707107i	−0.985599	−	0.408248i	−0.816497	+	0.577350i	$0.804087\pi$
$4$		0			0
$5$	0.292893	−	0.707107i	0.130986	−	0.316228i	−0.844756	−	0.535151i	$-0.820255\pi$
$5$	0.292893	−	0.707107i	0.130986	−	0.316228i	0.975742	+	0.218924i	$0.0702546\pi$
$6$		0			0
$7$	−1.70711	−	4.12132i	−0.645226	−	1.55771i	−0.819540	−	0.573023i	$-0.805771\pi$
$7$	−1.70711	−	4.12132i	−0.645226	−	1.55771i	0.174314	−	0.984690i	$-0.444229\pi$
$8$		0			0
$9$	0.292893	+	0.292893i	0.0976311	+	0.0976311i
$10$		0			0
$11$	1.70711	−	0.707107i	0.514712	−	0.213201i	−0.110180	−	0.993912i	$-0.535143\pi$
$11$	1.70711	−	0.707107i	0.514712	−	0.213201i	0.624892	+	0.780711i	$0.285143\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−1.00000	+	1.00000i	−0.258199	+	0.258199i
$16$		0			0
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$17$	1.00000	−	4.00000i	0.242536	−	0.970143i
$18$		0			0
$19$	−4.41421	+	4.41421i	−1.01269	+	1.01269i	−0.0127716	+	0.999918i	$0.504065\pi$
$19$	−4.41421	+	4.41421i	−1.01269	+	1.01269i	−0.999918	+	0.0127716i	$0.995935\pi$
$20$		0			0
$21$			8.24264i			1.79869i
$22$		0			0
$23$	4.53553	−	1.87868i	0.945724	−	0.391732i	0.144102	−	0.989563i	$-0.453971\pi$
$23$	4.53553	−	1.87868i	0.945724	−	0.391732i	0.801622	+	0.597831i	$0.203971\pi$
$24$		0			0
$25$	3.12132	+	3.12132i	0.624264	+	0.624264i
$26$		0			0
$27$	1.82843	+	4.41421i	0.351881	+	0.849516i
$28$		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
$31$	5.12132	+	2.12132i	0.919816	+	0.381000i	0.791806	−	0.610772i	$-0.209141\pi$
$31$	5.12132	+	2.12132i	0.919816	+	0.381000i	0.128010	+	0.991773i	$0.459141\pi$
$32$		0			0
$33$	−3.41421			−0.594338
$34$		0			0
$35$	−3.41421			−0.577107
$36$		0			0
$37$	1.70711	+	0.707107i	0.280647	+	0.116248i	0.518567	−	0.855037i	$-0.326466\pi$
$37$	1.70711	+	0.707107i	0.280647	+	0.116248i	−0.237920	+	0.971285i	$0.576466\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.70711	−	8.94975i	−0.578953	−	1.39772i	−0.893754	−	0.448558i	$-0.851938\pi$
$41$	−3.70711	−	8.94975i	−0.578953	−	1.39772i	0.314801	−	0.949158i	$-0.398062\pi$
$42$		0			0
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	0.605979	−	0.795480i	$-0.292781\pi$
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	−0.795480	+	0.605979i	$0.792781\pi$
$44$		0			0
$45$	0.292893	−	0.121320i	0.0436619	−	0.0180854i
$46$		0			0
$47$		−	7.17157i		−	1.04608i	−0.852308	−	0.523041i	$-0.824798\pi$
$47$		−	7.17157i		−	1.04608i	0.852308	−	0.523041i	$-0.175202\pi$
$48$		0			0
$49$	−9.12132	+	9.12132i	−1.30305	+	1.30305i
$50$		0			0
$51$	−4.53553	+	6.12132i	−0.635102	+	0.857156i
$52$		0			0
$53$	7.82843	−	7.82843i	1.07532	−	1.07532i	0.0783948	−	0.996922i	$-0.475021\pi$
$53$	7.82843	−	7.82843i	1.07532	−	1.07532i	0.996922	−	0.0783948i	$-0.0249795\pi$
$54$		0			0
$55$		−	1.41421i		−	0.190693i
$56$		0			0
$57$	10.6569	−	4.41421i	1.41153	−	0.584677i
$58$		0			0
$59$	8.41421	+	8.41421i	1.09544	+	1.09544i	0.994937	+	0.100500i	$0.0320443\pi$
$59$	8.41421	+	8.41421i	1.09544	+	1.09544i	0.100500	+	0.994937i	$0.467956\pi$
$60$		0			0
$61$	−4.87868	−	11.7782i	−0.624651	−	1.50804i	−0.846186	−	0.532888i	$-0.821107\pi$
$61$	−4.87868	−	11.7782i	−0.624651	−	1.50804i	0.221535	−	0.975152i	$-0.428893\pi$
$62$		0			0
$63$	0.707107	−	1.70711i	0.0890871	−	0.215075i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.65685			−0.202417			−0.101208	−	0.994865i	$-0.532271\pi$
$67$	−1.65685			−0.202417			−0.101208	+	0.994865i	$0.532271\pi$
$68$		0			0
$69$	−9.07107			−1.09203
$70$		0			0
$71$	2.29289	+	0.949747i	0.272116	+	0.112714i	0.514569	−	0.857449i	$-0.327952\pi$
$71$	2.29289	+	0.949747i	0.272116	+	0.112714i	−0.242453	+	0.970163i	$0.577952\pi$
$72$		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
$75$	−3.12132	−	7.53553i	−0.360419	−	0.870129i
$76$		0			0
$77$	−5.82843	−	5.82843i	−0.664211	−	0.664211i
$78$		0			0
$79$	12.5355	−	5.19239i	1.41036	−	0.584189i	0.457939	−	0.888983i	$-0.348588\pi$
$79$	12.5355	−	5.19239i	1.41036	−	0.584189i	0.952418	+	0.304794i	$0.0985876\pi$
$80$		0			0
$81$		−	10.0711i		−	1.11901i
$82$		0			0
$83$	1.24264	−	1.24264i	0.136398	−	0.136398i	−0.635612	−	0.772009i	$-0.719252\pi$
$83$	1.24264	−	1.24264i	0.136398	−	0.136398i	0.772009	+	0.635612i	$0.219252\pi$
$84$		0			0
$85$	−2.53553	−	1.87868i	−0.275017	−	0.203771i
$86$		0			0
$87$	3.00000	−	3.00000i	0.321634	−	0.321634i
$88$		0			0
$89$			9.65685i			1.02362i	0.859097	+	0.511812i	$0.171026\pi$
$89$			9.65685i			1.02362i	−0.859097	+	0.511812i	$0.828974\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.24264	−	7.24264i	−0.751027	−	0.751027i
$94$		0			0
$95$	1.82843	+	4.41421i	0.187593	+	0.452889i
$96$		0			0
$97$	0.778175	−	1.87868i	0.0790117	−	0.190751i	−0.879438	−	0.476014i	$-0.842081\pi$
$97$	0.778175	−	1.87868i	0.0790117	−	0.190751i	0.958449	+	0.285263i	$0.0920810\pi$
$98$		0			0
$99$	0.707107	+	0.292893i	0.0710669	+	0.0294369i
$100$		0			0
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$		0			0
$103$	−13.6569			−1.34565			−0.672825	−	0.739802i	$-0.734919\pi$
$103$	−13.6569			−1.34565			−0.672825	+	0.739802i	$0.734919\pi$
$104$		0			0
$105$	5.82843	+	2.41421i	0.568796	+	0.235603i
$106$		0			0
$107$	−0.636039	+	1.53553i	−0.0614882	+	0.148446i	−0.951637	−	0.307224i	$-0.900600\pi$
$107$	−0.636039	+	1.53553i	−0.0614882	+	0.148446i	0.890149	+	0.455669i	$0.150600\pi$
$108$		0			0
$109$	4.77817	+	11.5355i	0.457666	+	1.10490i	0.969340	+	0.245724i	$0.0790257\pi$
$109$	4.77817	+	11.5355i	0.457666	+	1.10490i	−0.511674	+	0.859180i	$0.670974\pi$
$110$		0			0
$111$	−2.41421	−	2.41421i	−0.229147	−	0.229147i
$112$		0			0
$113$	−1.12132	+	0.464466i	−0.105485	+	0.0436933i	−0.434802	−	0.900526i	$-0.643182\pi$
$113$	−1.12132	+	0.464466i	−0.105485	+	0.0436933i	0.329317	+	0.944219i	$0.393182\pi$
$114$		0			0
$115$		−	3.75736i		−	0.350376i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−18.1924	+	2.70711i	−1.66769	+	0.248160i
$120$		0			0
$121$	−5.36396	+	5.36396i	−0.487633	+	0.487633i
$122$		0			0
$123$			17.8995i			1.61394i
$124$		0			0
$125$	6.65685	−	2.75736i	0.595407	−	0.246626i
$126$		0			0
$127$	7.24264	+	7.24264i	0.642680	+	0.642680i	0.951214	−	0.308533i	$-0.0998381\pi$
$127$	7.24264	+	7.24264i	0.642680	+	0.642680i	−0.308533	+	0.951214i	$0.599838\pi$
$128$		0			0
$129$	1.24264	+	3.00000i	0.109408	+	0.264135i
$130$		0			0
$131$	−0.636039	+	1.53553i	−0.0555710	+	0.134160i	−0.949227	−	0.314593i	$-0.898132\pi$
$131$	−0.636039	+	1.53553i	−0.0555710	+	0.134160i	0.893656	+	0.448753i	$0.148132\pi$
$132$		0			0
$133$	25.7279	+	10.6569i	2.23089	+	0.924066i
$134$		0			0
$135$	3.65685			0.314732
$136$		0			0
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$		0			0
$139$	−18.1924	−	7.53553i	−1.54306	−	0.639156i	−0.561014	−	0.827806i	$-0.689589\pi$
$139$	−18.1924	−	7.53553i	−1.54306	−	0.639156i	−0.982044	+	0.188651i	$0.939589\pi$
$140$		0			0
$141$	−5.07107	+	12.2426i	−0.427061	+	1.03102i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	1.24264	+	1.24264i	0.103196	+	0.103196i
$146$		0			0
$147$	22.0208	−	9.12132i	1.81625	−	0.752314i
$148$		0			0
$149$			17.6569i			1.44651i	0.690583	+	0.723253i	$0.257354\pi$
$149$			17.6569i			1.44651i	−0.690583	+	0.723253i	$0.742646\pi$
$150$		0			0
$151$	0.0710678	−	0.0710678i	0.00578342	−	0.00578342i	−0.704209	−	0.709993i	$-0.748698\pi$
$151$	0.0710678	−	0.0710678i	0.00578342	−	0.00578342i	0.709993	+	0.704209i	$0.248698\pi$
$152$		0			0
$153$	1.46447	−	0.878680i	0.118395	−	0.0710370i
$154$		0			0
$155$	3.00000	−	3.00000i	0.240966	−	0.240966i
$156$		0			0
$157$			7.31371i			0.583697i	0.956464	+	0.291849i	$0.0942704\pi$
$157$			7.31371i			0.583697i	−0.956464	+	0.291849i	$0.905730\pi$
$158$		0			0
$159$	−18.8995	+	7.82843i	−1.49883	+	0.620835i
$160$		0			0
$161$	−15.4853	−	15.4853i	−1.22041	−	1.22041i
$162$		0			0
$163$	−5.70711	−	13.7782i	−0.447015	−	1.07919i	−0.973435	−	0.228965i	$-0.926466\pi$
$163$	−5.70711	−	13.7782i	−0.447015	−	1.07919i	0.526420	−	0.850225i	$-0.323534\pi$
$164$		0			0
$165$	−1.00000	+	2.41421i	−0.0778499	+	0.187946i
$166$		0			0
$167$	−1.70711	−	0.707107i	−0.132100	−	0.0547176i	0.315654	−	0.948874i	$-0.397776\pi$
$167$	−1.70711	−	0.707107i	−0.132100	−	0.0547176i	−0.447754	+	0.894157i	$0.647776\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−2.58579			−0.197740
$172$		0			0
$173$	−22.7782	−	9.43503i	−1.73179	−	0.717332i	−0.999333	−	0.0365215i	$-0.988372\pi$
$173$	−22.7782	−	9.43503i	−1.73179	−	0.717332i	−0.732460	−	0.680810i	$-0.761628\pi$
$174$		0			0
$175$	7.53553	−	18.1924i	0.569633	−	1.37522i
$176$		0			0
$177$	−8.41421	−	20.3137i	−0.632451	−	1.52687i
$178$		0			0
$179$	−6.89949	−	6.89949i	−0.515692	−	0.515692i	0.400573	−	0.916265i	$-0.368811\pi$
$179$	−6.89949	−	6.89949i	−0.515692	−	0.515692i	−0.916265	+	0.400573i	$0.868811\pi$
$180$		0			0
$181$	−1.12132	+	0.464466i	−0.0833471	+	0.0345235i	−0.423967	−	0.905677i	$-0.639363\pi$
$181$	−1.12132	+	0.464466i	−0.0833471	+	0.0345235i	0.340620	+	0.940201i	$0.389363\pi$
$182$		0			0
$183$			23.5563i			1.74134i
$184$		0			0
$185$	1.00000	−	1.00000i	0.0735215	−	0.0735215i
$186$		0			0
$187$	−1.12132	−	7.53553i	−0.0819991	−	0.551053i
$188$		0			0
$189$	15.0711	−	15.0711i	1.09626	−	1.09626i
$190$		0			0
$191$			3.17157i			0.229487i	0.993395	+	0.114743i	$0.0366046\pi$
$191$			3.17157i			0.229487i	−0.993395	+	0.114743i	$0.963395\pi$
$192$		0			0
$193$	1.70711	−	0.707107i	0.122880	−	0.0508987i	−0.320396	−	0.947284i	$-0.603816\pi$
$193$	1.70711	−	0.707107i	0.122880	−	0.0508987i	0.443276	+	0.896385i	$0.353816\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.36396	−	3.29289i	−0.0971782	−	0.234609i	0.867813	−	0.496891i	$-0.165525\pi$
$197$	−1.36396	−	3.29289i	−0.0971782	−	0.234609i	−0.964991	+	0.262282i	$0.915525\pi$
$198$		0			0
$199$	5.22183	−	12.6066i	0.370165	−	0.893658i	−0.623556	−	0.781778i	$-0.714313\pi$
$199$	5.22183	−	12.6066i	0.370165	−	0.893658i	0.993722	−	0.111880i	$-0.0356872\pi$
$200$		0			0
$201$	2.82843	+	1.17157i	0.199502	+	0.0826364i
$202$		0			0
$203$	10.2426			0.718892
$204$		0			0
$205$	−7.41421			−0.517831
$206$		0			0
$207$	1.87868	+	0.778175i	0.130577	+	0.0540869i
$208$		0			0
$209$	−4.41421	+	10.6569i	−0.305338	+	0.737150i
$210$		0			0
$211$	5.80761	+	14.0208i	0.399812	+	0.965233i	0.987710	+	0.156297i	$0.0499558\pi$
$211$	5.80761	+	14.0208i	0.399812	+	0.965233i	−0.587898	+	0.808935i	$0.700044\pi$
$212$		0			0
$213$	−3.24264	−	3.24264i	−0.222182	−	0.222182i
$214$		0			0
$215$	−1.24264	+	0.514719i	−0.0847474	+	0.0351035i
$216$		0			0
$217$		−	24.7279i		−	1.67864i
$218$		0			0
$219$	18.3137	−	18.3137i	1.23753	−	1.23753i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.58579	+	9.58579i	−0.641912	+	0.641912i	−0.951025	−	0.309113i	$-0.899968\pi$
$223$	−9.58579	+	9.58579i	−0.641912	+	0.641912i	0.309113	+	0.951025i	$0.399968\pi$
$224$		0			0
$225$			1.82843i			0.121895i
$226$		0			0
$227$	11.3640	−	4.70711i	0.754253	−	0.312422i	0.0277772	−	0.999614i	$-0.491157\pi$
$227$	11.3640	−	4.70711i	0.754253	−	0.312422i	0.726475	+	0.687192i	$0.241157\pi$
$228$		0			0
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	0.436925	−	0.899498i	$-0.356068\pi$
$229$	−7.00000	−	7.00000i	−0.462573	−	0.462573i	−0.899498	+	0.436925i	$0.856068\pi$
$230$		0			0
$231$	5.82843	+	14.0711i	0.383482	+	0.925808i
$232$		0			0
$233$	−6.53553	+	15.7782i	−0.428157	+	1.03366i	0.551714	+	0.834033i	$0.313974\pi$
$233$	−6.53553	+	15.7782i	−0.428157	+	1.03366i	−0.979871	+	0.199629i	$0.936026\pi$
$234$		0			0
$235$	−5.07107	−	2.10051i	−0.330800	−	0.137022i
$236$		0			0
$237$	−25.0711			−1.62854
$238$		0			0
$239$	−11.3137			−0.731823			−0.365911	−	0.930650i	$-0.619243\pi$
$239$	−11.3137			−0.731823			−0.365911	+	0.930650i	$0.619243\pi$
$240$		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
$243$	−1.63604	+	3.94975i	−0.104952	+	0.253376i
$244$		0			0
$245$	3.77817	+	9.12132i	0.241379	+	0.582740i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−3.00000	+	1.24264i	−0.190117	+	0.0787492i
$250$		0			0
$251$			4.82843i			0.304768i	0.988321	+	0.152384i	$0.0486950\pi$
$251$			4.82843i			0.304768i	−0.988321	+	0.152384i	$0.951305\pi$
$252$		0			0
$253$	6.41421	−	6.41421i	0.403258	−	0.403258i
$254$		0			0
$255$	3.00000	+	5.00000i	0.187867	+	0.313112i
$256$		0			0
$257$	−0.171573	+	0.171573i	−0.0107024	+	0.0107024i	−0.712438	−	0.701735i	$-0.752409\pi$
$257$	−0.171573	+	0.171573i	−0.0107024	+	0.0107024i	0.701735	+	0.712438i	$0.252409\pi$
$258$		0			0
$259$		−	8.24264i		−	0.512173i
$260$		0			0
$261$	−0.878680	+	0.363961i	−0.0543889	+	0.0225286i
$262$		0			0
$263$	11.2426	+	11.2426i	0.693251	+	0.693251i	0.962946	−	0.269695i	$-0.0869228\pi$
$263$	11.2426	+	11.2426i	0.693251	+	0.693251i	−0.269695	+	0.962946i	$0.586923\pi$
$264$		0			0
$265$	−3.24264	−	7.82843i	−0.199194	−	0.480896i
$266$		0			0
$267$	6.82843	−	16.4853i	0.417893	−	1.00888i
$268$		0			0
$269$	7.36396	+	3.05025i	0.448989	+	0.185977i	0.595708	−	0.803201i	$-0.296871\pi$
$269$	7.36396	+	3.05025i	0.448989	+	0.185977i	−0.146720	+	0.989178i	$0.546871\pi$
$270$		0			0
$271$	11.3137			0.687259			0.343629	−	0.939105i	$-0.388344\pi$
$271$	11.3137			0.687259			0.343629	+	0.939105i	$0.388344\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.53553	+	3.12132i	0.454410	+	0.188223i
$276$		0			0
$277$	1.46447	−	3.53553i	0.0879912	−	0.212430i	−0.873758	−	0.486361i	$-0.838324\pi$
$277$	1.46447	−	3.53553i	0.0879912	−	0.212430i	0.961749	+	0.273931i	$0.0883241\pi$
$278$		0			0
$279$	0.878680	+	2.12132i	0.0526052	+	0.127000i
$280$		0			0
$281$	20.3137	+	20.3137i	1.21181	+	1.21181i	0.970429	+	0.241385i	$0.0776016\pi$
$281$	20.3137	+	20.3137i	1.21181	+	1.21181i	0.241385	+	0.970429i	$0.422398\pi$
$282$		0			0
$283$	−19.9497	+	8.26346i	−1.18589	+	0.491211i	−0.886414	−	0.462893i	$-0.846812\pi$
$283$	−19.9497	+	8.26346i	−1.18589	+	0.491211i	−0.299475	+	0.954104i	$0.596812\pi$
$284$		0			0
$285$		−	8.82843i		−	0.522951i
$286$		0			0
$287$	−30.5563	+	30.5563i	−1.80368	+	1.80368i
$288$		0			0
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$		0			0
$291$	−2.65685	+	2.65685i	−0.155748	+	0.155748i
$292$		0			0
$293$		−	15.3137i		−	0.894636i	−0.894375	−	0.447318i	$-0.852379\pi$
$293$		−	15.3137i		−	0.894636i	0.894375	−	0.447318i	$-0.147621\pi$
$294$		0			0
$295$	8.41421	−	3.48528i	0.489894	−	0.202921i
$296$		0			0
$297$	6.24264	+	6.24264i	0.362235	+	0.362235i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−3.00000	+	7.24264i	−0.172917	+	0.417459i
$302$		0			0
$303$	−17.0711	−	7.07107i	−0.980707	−	0.406222i
$304$		0			0
$305$	−9.75736			−0.558705
$306$		0			0
$307$	18.6274			1.06312			0.531561	−	0.847020i	$-0.321605\pi$
$307$	18.6274			1.06312			0.531561	+	0.847020i	$0.321605\pi$
$308$		0			0
$309$	23.3137	+	9.65685i	1.32627	+	0.549359i
$310$		0			0
$311$	−2.29289	+	5.53553i	−0.130018	+	0.313891i	−0.975460	−	0.220176i	$-0.929337\pi$
$311$	−2.29289	+	5.53553i	−0.130018	+	0.313891i	0.845442	+	0.534067i	$0.179337\pi$
$312$		0			0
$313$	5.94975	+	14.3640i	0.336300	+	0.811899i	0.998064	+	0.0621876i	$0.0198077\pi$
$313$	5.94975	+	14.3640i	0.336300	+	0.811899i	−0.661765	+	0.749711i	$0.730192\pi$
$314$		0			0
$315$	−1.00000	−	1.00000i	−0.0563436	−	0.0563436i
$316$		0			0
$317$	−15.9497	+	6.60660i	−0.895827	+	0.371064i	−0.782614	−	0.622507i	$-0.786114\pi$
$317$	−15.9497	+	6.60660i	−0.895827	+	0.371064i	−0.113213	+	0.993571i	$0.536114\pi$
$318$		0			0
$319$			4.24264i			0.237542i
$320$		0			0
$321$	2.17157	−	2.17157i	0.121205	−	0.121205i
$322$		0			0
$323$	13.2426	+	22.0711i	0.736840	+	1.22807i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	23.0711i		−	1.27583i
$328$		0			0
$329$	−29.5563	+	12.2426i	−1.62949	+	0.674959i
$330$		0			0
$331$	15.7279	+	15.7279i	0.864485	+	0.864485i	0.991855	−	0.127370i	$-0.0406537\pi$
$331$	15.7279	+	15.7279i	0.864485	+	0.864485i	−0.127370	+	0.991855i	$0.540654\pi$
$332$		0			0
$333$	0.292893	+	0.707107i	0.0160504	+	0.0387492i
$334$		0			0
$335$	−0.485281	+	1.17157i	−0.0265138	+	0.0640099i
$336$		0			0
$337$	−3.94975	−	1.63604i	−0.215156	−	0.0891207i	0.272502	−	0.962155i	$-0.412149\pi$
$337$	−3.94975	−	1.63604i	−0.215156	−	0.0891207i	−0.487658	+	0.873034i	$0.662149\pi$
$338$		0			0
$339$	2.24264			0.121804
$340$		0			0
$341$	10.2426			0.554670
$342$		0			0
$343$	24.3137	+	10.0711i	1.31282	+	0.543787i
$344$		0			0
$345$	−2.65685	+	6.41421i	−0.143040	+	0.345330i
$346$		0			0
$347$	−7.36396	−	17.7782i	−0.395318	−	0.954382i	−0.988761	−	0.149506i	$-0.952232\pi$
$347$	−7.36396	−	17.7782i	−0.395318	−	0.954382i	0.593443	−	0.804876i	$-0.297768\pi$
$348$		0			0
$349$	1.48528	+	1.48528i	0.0795053	+	0.0795053i	0.745741	−	0.666236i	$-0.232096\pi$
$349$	1.48528	+	1.48528i	0.0795053	+	0.0795053i	−0.666236	+	0.745741i	$0.732096\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	8.97056i		−	0.477455i	−0.971087	−	0.238727i	$-0.923270\pi$
$353$		−	8.97056i		−	0.477455i	0.971087	−	0.238727i	$-0.0767302\pi$
$354$		0			0
$355$	1.34315	−	1.34315i	0.0712868	−	0.0712868i
$356$		0			0
$357$	32.9706	+	8.24264i	1.74499	+	0.436247i
$358$		0			0
$359$	9.72792	−	9.72792i	0.513420	−	0.513420i	−0.402153	−	0.915573i	$-0.631738\pi$
$359$	9.72792	−	9.72792i	0.513420	−	0.513420i	0.915573	+	0.402153i	$0.131738\pi$
$360$		0			0
$361$		−	19.9706i		−	1.05108i
$362$		0			0
$363$	12.9497	−	5.36396i	0.679685	−	0.281535i
$364$		0			0
$365$	7.58579	+	7.58579i	0.397058	+	0.397058i
$366$		0			0
$367$	7.94975	+	19.1924i	0.414973	+	1.00183i	0.983783	+	0.179365i	$0.0574043\pi$
$367$	7.94975	+	19.1924i	0.414973	+	1.00183i	−0.568809	+	0.822470i	$0.692596\pi$
$368$		0			0
$369$	1.53553	−	3.70711i	0.0799367	−	0.192984i
$370$		0			0
$371$	−45.6274	−	18.8995i	−2.36886	−	0.981213i
$372$		0			0
$373$	−31.9411			−1.65385			−0.826924	−	0.562313i	$-0.809912\pi$
$373$	−31.9411			−1.65385			−0.826924	+	0.562313i	$0.809912\pi$
$374$		0			0
$375$	−13.3137			−0.687517
$376$		0			0
$377$		0			0
$378$		0			0
$379$	4.05025	−	9.77817i	0.208047	−	0.502271i	−0.785068	−	0.619409i	$-0.787372\pi$
$379$	4.05025	−	9.77817i	0.208047	−	0.502271i	0.993116	+	0.117138i	$0.0373721\pi$
$380$		0			0
$381$	−7.24264	−	17.4853i	−0.371052	−	0.895798i
$382$		0			0
$383$	−10.4142	−	10.4142i	−0.532141	−	0.532141i	0.389068	−	0.921209i	$-0.372797\pi$
$383$	−10.4142	−	10.4142i	−0.532141	−	0.532141i	−0.921209	+	0.389068i	$0.872797\pi$
$384$		0			0
$385$	−5.82843	+	2.41421i	−0.297044	+	0.123040i
$386$		0			0
$387$		−	0.727922i		−	0.0370024i
$388$		0			0
$389$	−2.31371	+	2.31371i	−0.117310	+	0.117310i	−0.763325	−	0.646015i	$-0.776434\pi$
$389$	−2.31371	+	2.31371i	−0.117310	+	0.117310i	0.646015	+	0.763325i	$0.276434\pi$
$390$		0			0
$391$	−2.97918	−	20.0208i	−0.150664	−	1.01250i
$392$		0			0
$393$	2.17157	−	2.17157i	0.109541	−	0.109541i
$394$		0			0
$395$		−	10.3848i		−	0.522515i
$396$		0			0
$397$	6.87868	−	2.84924i	0.345231	−	0.142999i	−0.203329	−	0.979110i	$-0.565176\pi$
$397$	6.87868	−	2.84924i	0.345231	−	0.142999i	0.548560	+	0.836111i	$0.315176\pi$
$398$		0			0
$399$	−36.3848	−	36.3848i	−1.82152	−	1.82152i
$400$		0			0
$401$	0.979185	+	2.36396i	0.0488982	+	0.118051i	0.946441	−	0.322876i	$-0.104650\pi$
$401$	0.979185	+	2.36396i	0.0488982	+	0.118051i	−0.897543	+	0.440927i	$0.854650\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−7.12132	−	2.94975i	−0.353861	−	0.146574i
$406$		0			0
$407$	3.41421			0.169236
$408$		0			0
$409$	18.0000			0.890043			0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000			0.890043			0.445021	+	0.895520i	$0.353196\pi$
$410$		0			0
$411$	−23.8995	−	9.89949i	−1.17888	−	0.488306i
$412$		0			0
$413$	20.3137	−	49.0416i	0.999572	−	2.41318i
$414$		0			0
$415$	−0.514719	−	1.24264i	−0.0252665	−	0.0609988i
$416$		0			0
$417$	25.7279	+	25.7279i	1.25990	+	1.25990i
$418$		0			0
$419$	4.53553	−	1.87868i	0.221575	−	0.0917795i	−0.269134	−	0.963103i	$-0.586738\pi$
$419$	4.53553	−	1.87868i	0.221575	−	0.0917795i	0.490710	+	0.871323i	$0.336738\pi$
$420$		0			0
$421$		−	11.3137i		−	0.551396i	−0.961244	−	0.275698i	$-0.911091\pi$
$421$		−	11.3137i		−	0.551396i	0.961244	−	0.275698i	$-0.0889090\pi$
$422$		0			0
$423$	2.10051	−	2.10051i	0.102130	−	0.102130i
$424$		0			0
$425$	15.6066	−	9.36396i	0.757031	−	0.454219i
$426$		0			0
$427$	−40.2132	+	40.2132i	−1.94605	+	1.94605i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.12132	+	2.12132i	−0.246685	+	0.102180i	−0.502600	−	0.864519i	$-0.667623\pi$
$431$	−5.12132	+	2.12132i	−0.246685	+	0.102180i	0.255915	+	0.966699i	$0.417623\pi$
$432$		0			0
$433$	−1.82843	−	1.82843i	−0.0878686	−	0.0878686i	0.661806	−	0.749675i	$-0.269790\pi$
$433$	−1.82843	−	1.82843i	−0.0878686	−	0.0878686i	−0.749675	+	0.661806i	$0.769790\pi$
$434$		0			0
$435$	−1.24264	−	3.00000i	−0.0595801	−	0.143839i
$436$		0			0
$437$	−11.7279	+	28.3137i	−0.561023	+	1.35443i
$438$		0			0
$439$	17.6066	+	7.29289i	0.840317	+	0.348071i	0.760979	−	0.648777i	$-0.224719\pi$
$439$	17.6066	+	7.29289i	0.840317	+	0.348071i	0.0793386	+	0.996848i	$0.474719\pi$
$440$		0			0
$441$	−5.34315			−0.254436
$442$		0			0
$443$	16.2843			0.773689			0.386845	−	0.922145i	$-0.373565\pi$
$443$	16.2843			0.773689			0.386845	+	0.922145i	$0.373565\pi$
$444$		0			0
$445$	6.82843	+	2.82843i	0.323698	+	0.134080i
$446$		0			0
$447$	12.4853	−	30.1421i	0.590534	−	1.42567i
$448$		0			0
$449$	9.46447	+	22.8492i	0.446656	+	1.07832i	0.973567	+	0.228402i	$0.0733501\pi$
$449$	9.46447	+	22.8492i	0.446656	+	1.07832i	−0.526911	+	0.849920i	$0.676650\pi$
$450$		0			0
$451$	−12.6569	−	12.6569i	−0.595988	−	0.595988i
$452$		0			0
$453$	−0.171573	+	0.0710678i	−0.00806120	+	0.00333906i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.4853	−	13.4853i	0.630815	−	0.630815i	−0.317458	−	0.948272i	$-0.602829\pi$
$457$	13.4853	−	13.4853i	0.630815	−	0.630815i	0.948272	+	0.317458i	$0.102829\pi$
$458$		0			0
$459$	19.4853	−	2.89949i	0.909495	−	0.135337i
$460$		0			0
$461$	−19.4853	+	19.4853i	−0.907520	+	0.907520i	−0.996072	−	0.0885516i	$-0.971776\pi$
$461$	−19.4853	+	19.4853i	−0.907520	+	0.907520i	0.0885516	+	0.996072i	$0.471776\pi$
$462$		0			0
$463$			4.14214i			0.192501i	0.995357	+	0.0962507i	$0.0306850\pi$
$463$			4.14214i			0.192501i	−0.995357	+	0.0962507i	$0.969315\pi$
$464$		0			0
$465$	−7.24264	+	3.00000i	−0.335869	+	0.139122i
$466$		0			0
$467$	12.4142	+	12.4142i	0.574461	+	0.574461i	0.933372	−	0.358911i	$-0.116852\pi$
$467$	12.4142	+	12.4142i	0.574461	+	0.574461i	−0.358911	+	0.933372i	$0.616852\pi$
$468$		0			0
$469$	2.82843	+	6.82843i	0.130605	+	0.315307i
$470$		0			0
$471$	5.17157	−	12.4853i	0.238293	−	0.575291i
$472$		0			0
$473$	−3.00000	−	1.24264i	−0.137940	−	0.0571367i
$474$		0			0
$475$	−27.5563			−1.26437
$476$		0			0
$477$	4.58579			0.209969
$478$		0			0
$479$	7.46447	+	3.09188i	0.341060	+	0.141272i	0.546638	−	0.837369i	$-0.315907\pi$
$479$	7.46447	+	3.09188i	0.341060	+	0.141272i	−0.205578	+	0.978641i	$0.565907\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	15.4853	+	37.3848i	0.704605	+	1.70107i
$484$		0			0
$485$	−1.10051	−	1.10051i	−0.0499714	−	0.0499714i
$486$		0			0
$487$	−39.2635	+	16.2635i	−1.77920	+	0.736968i	−0.786321	+	0.617819i	$0.788017\pi$
$487$	−39.2635	+	16.2635i	−1.77920	+	0.736968i	−0.992876	+	0.119149i	$0.961983\pi$
$488$		0			0
$489$			27.5563i			1.24614i
$490$		0			0
$491$	11.5858	−	11.5858i	0.522859	−	0.522859i	−0.395575	−	0.918434i	$-0.629455\pi$
$491$	11.5858	−	11.5858i	0.522859	−	0.522859i	0.918434	+	0.395575i	$0.129455\pi$
$492$		0			0
$493$	7.60660	+	5.63604i	0.342584	+	0.253834i
$494$		0			0
$495$	0.414214	−	0.414214i	0.0186175	−	0.0186175i
$496$		0			0
$497$		−	11.0711i		−	0.496605i
$498$		0			0
$499$	−20.4350	+	8.46447i	−0.914798	+	0.378922i	−0.789891	−	0.613247i	$-0.789863\pi$
$499$	−20.4350	+	8.46447i	−0.914798	+	0.378922i	−0.124906	+	0.992169i	$0.539863\pi$
$500$		0			0
$501$	2.41421	+	2.41421i	0.107859	+	0.107859i
$502$		0			0
$503$	−1.70711	−	4.12132i	−0.0761161	−	0.183761i	0.881241	−	0.472667i	$-0.156708\pi$
$503$	−1.70711	−	4.12132i	−0.0761161	−	0.183761i	−0.957357	+	0.288906i	$0.906708\pi$
$504$		0			0
$505$	2.92893	−	7.07107i	0.130336	−	0.314658i
$506$		0			0
$507$	−22.1924	−	9.19239i	−0.985599	−	0.408248i
$508$		0			0
$509$	18.2843			0.810436			0.405218	−	0.914220i	$-0.367196\pi$
$509$	18.2843			0.810436			0.405218	+	0.914220i	$0.367196\pi$
$510$		0			0
$511$	62.5269			2.76603
$512$		0			0
$513$	−27.5563	−	11.4142i	−1.21664	−	0.503950i
$514$		0			0
$515$	−4.00000	+	9.65685i	−0.176261	+	0.425532i
$516$		0			0
$517$	−5.07107	−	12.2426i	−0.223025	−	0.538431i
$518$		0			0
$519$	32.2132	+	32.2132i	1.41400	+	1.41400i
$520$		0			0
$521$	9.02082	−	3.73654i	0.395209	−	0.163701i	−0.176223	−	0.984350i	$-0.556388\pi$
$521$	9.02082	−	3.73654i	0.395209	−	0.163701i	0.571432	+	0.820649i	$0.306388\pi$
$522$		0			0
$523$			24.1421i			1.05566i	0.849349	+	0.527831i	$0.176995\pi$
$523$			24.1421i			1.05566i	−0.849349	+	0.527831i	$0.823005\pi$
$524$		0			0
$525$	−25.7279	+	25.7279i	−1.12286	+	1.12286i
$526$		0			0
$527$	13.6066	−	18.3640i	0.592713	−	0.799947i
$528$		0			0
$529$	0.778175	−	0.778175i	0.0338337	−	0.0338337i
$530$		0			0
$531$			4.92893i			0.213897i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.899495	+	0.899495i	0.0388886	+	0.0388886i
$536$		0			0
$537$	6.89949	+	16.6569i	0.297735	+	0.718796i
$538$		0			0
$539$	−9.12132	+	22.0208i	−0.392883	+	0.948504i
$540$		0			0
$541$	0.0502525	+	0.0208153i	0.00216053	+	0.000894919i	0.383763	−	0.923431i	$-0.374628\pi$
$541$	0.0502525	+	0.0208153i	0.00216053	+	0.000894919i	−0.381603	+	0.924326i	$0.624628\pi$
$542$		0			0
$543$	2.24264			0.0962409
$544$		0			0
$545$	9.55635			0.409349
$546$		0			0
$547$	15.2635	+	6.32233i	0.652618	+	0.270323i	0.684329	−	0.729174i	$-0.260095\pi$
$547$	15.2635	+	6.32233i	0.652618	+	0.270323i	−0.0317103	+	0.999497i	$0.510095\pi$
$548$		0			0
$549$	2.02082	−	4.87868i	0.0862463	−	0.208217i
$550$		0			0
$551$	−5.48528	−	13.2426i	−0.233681	−	0.564155i
$552$		0			0
$553$	−42.7990	−	42.7990i	−1.82000	−	1.82000i
$554$		0			0
$555$	−2.41421	+	1.00000i	−0.102478	+	0.0424476i
$556$		0			0
$557$			16.0000i			0.677942i	0.940797	+	0.338971i	$0.110079\pi$
$557$			16.0000i			0.677942i	−0.940797	+	0.338971i	$0.889921\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.41421	+	13.6569i	−0.144148	+	0.576593i
$562$		0			0
$563$	15.5858	−	15.5858i	0.656863	−	0.656863i	−0.297774	−	0.954636i	$-0.596244\pi$
$563$	15.5858	−	15.5858i	0.656863	−	0.656863i	0.954636	+	0.297774i	$0.0962441\pi$
$564$		0			0
$565$			0.928932i			0.0390805i
$566$		0			0
$567$	−41.5061	+	17.1924i	−1.74309	+	0.722012i
$568$		0			0
$569$	−32.6569	−	32.6569i	−1.36905	−	1.36905i	−0.861802	−	0.507244i	$-0.830664\pi$
$569$	−32.6569	−	32.6569i	−1.36905	−	1.36905i	−0.507244	−	0.861802i	$-0.669336\pi$
$570$		0			0
$571$	0.150758	+	0.363961i	0.00630901	+	0.0152313i	0.927003	−	0.375055i	$-0.122376\pi$
$571$	0.150758	+	0.363961i	0.00630901	+	0.0152313i	−0.920694	+	0.390286i	$0.872376\pi$
$572$		0			0
$573$	2.24264	−	5.41421i	0.0936877	−	0.226182i
$574$		0			0
$575$	20.0208	+	8.29289i	0.834926	+	0.345838i
$576$		0			0
$577$	14.0000			0.582828			0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000			0.582828			0.291414	+	0.956597i	$0.405874\pi$
$578$		0			0
$579$	−3.41421			−0.141890
$580$		0			0
$581$	−7.24264	−	3.00000i	−0.300475	−	0.124461i
$582$		0			0
$583$	7.82843	−	18.8995i	0.324220	−	0.782737i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	31.7279	+	31.7279i	1.30955	+	1.30955i	0.921738	+	0.387814i	$0.126770\pi$
$587$	31.7279	+	31.7279i	1.30955	+	1.30955i	0.387814	+	0.921738i	$0.373230\pi$
$588$		0			0
$589$	−31.9706	+	13.2426i	−1.31732	+	0.545654i
$590$		0			0
$591$			6.58579i			0.270903i
$592$		0			0
$593$	26.6569	−	26.6569i	1.09467	−	1.09467i	0.0996425	−	0.995023i	$-0.468230\pi$
$593$	26.6569	−	26.6569i	1.09467	−	1.09467i	0.995023	−	0.0996425i	$-0.0317699\pi$
$594$		0			0
$595$	−3.41421	+	13.6569i	−0.139969	+	0.559876i
$596$		0			0
$597$	−17.8284	+	17.8284i	−0.729669	+	0.729669i
$598$		0			0
$599$		−	39.1716i		−	1.60051i	−0.599662	−	0.800254i	$-0.704698\pi$
$599$		−	39.1716i		−	1.60051i	0.599662	−	0.800254i	$-0.295302\pi$
$600$		0			0
$601$	−9.60660	+	3.97918i	−0.391861	+	0.162314i	−0.569910	−	0.821707i	$-0.693022\pi$
$601$	−9.60660	+	3.97918i	−0.391861	+	0.162314i	0.178048	+	0.984022i	$0.443022\pi$
$602$		0			0
$603$	−0.485281	−	0.485281i	−0.0197622	−	0.0197622i
$604$		0			0
$605$	2.22183	+	5.36396i	0.0903300	+	0.218076i
$606$		0			0
$607$	−2.09188	+	5.05025i	−0.0849069	+	0.204983i	−0.960630	−	0.277830i	$-0.910385\pi$
$607$	−2.09188	+	5.05025i	−0.0849069	+	0.204983i	0.875723	+	0.482813i	$0.160385\pi$
$608$		0			0
$609$	−17.4853	−	7.24264i	−0.708539	−	0.293487i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−6.68629			−0.270057			−0.135028	−	0.990842i	$-0.543113\pi$
$613$	−6.68629			−0.270057			−0.135028	+	0.990842i	$0.543113\pi$
$614$		0			0
$615$	12.6569	+	5.24264i	0.510374	+	0.211404i
$616$		0			0
$617$	−7.22183	+	17.4350i	−0.290740	+	0.701908i	−0.999995	−	0.00304356i	$-0.999031\pi$
$617$	−7.22183	+	17.4350i	−0.290740	+	0.701908i	0.709256	+	0.704951i	$0.249031\pi$
$618$		0			0
$619$	7.94975	+	19.1924i	0.319527	+	0.771407i	0.999279	+	0.0379649i	$0.0120875\pi$
$619$	7.94975	+	19.1924i	0.319527	+	0.771407i	−0.679752	+	0.733442i	$0.737912\pi$
$620$		0			0
$621$	16.5858	+	16.5858i	0.665565	+	0.665565i
$622$		0			0
$623$	39.7990	−	16.4853i	1.59451	−	0.660469i
$624$		0			0
$625$			16.5563i			0.662254i
$626$		0			0
$627$	15.0711	−	15.0711i	0.601880	−	0.601880i
$628$		0			0
$629$	4.53553	−	6.12132i	0.180844	−	0.244073i
$630$		0			0
$631$	19.3848	−	19.3848i	0.771696	−	0.771696i	−0.206707	−	0.978403i	$-0.566275\pi$
$631$	19.3848	−	19.3848i	0.771696	−	0.771696i	0.978403	+	0.206707i	$0.0662747\pi$
$632$		0			0
$633$		−	28.0416i		−	1.11455i
$634$		0			0
$635$	7.24264	−	3.00000i	0.287415	−	0.119051i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.393398	+	0.949747i	0.0155626	+	0.0375714i
$640$		0			0
$641$	15.1213	−	36.5061i	0.597256	−	1.44190i	−0.279110	−	0.960259i	$-0.590039\pi$
$641$	15.1213	−	36.5061i	0.597256	−	1.44190i	0.876366	−	0.481645i	$-0.159961\pi$
$642$		0			0
$643$	−9.02082	−	3.73654i	−0.355746	−	0.147355i	0.197651	−	0.980272i	$-0.436669\pi$
$643$	−9.02082	−	3.73654i	−0.355746	−	0.147355i	−0.553397	+	0.832918i	$0.686669\pi$
$644$		0			0
$645$	2.48528			0.0978579
$646$		0			0
$647$	−45.2548			−1.77915			−0.889576	−	0.456788i	$-0.849000\pi$
$647$	−45.2548			−1.77915			−0.889576	+	0.456788i	$0.849000\pi$
$648$		0			0
$649$	20.3137	+	8.41421i	0.797383	+	0.330287i
$650$		0			0
$651$	−17.4853	+	42.2132i	−0.685302	+	1.65447i
$652$		0			0
$653$	10.6360	+	25.6777i	0.416220	+	1.00484i	0.983433	+	0.181273i	$0.0580219\pi$
$653$	10.6360	+	25.6777i	0.416220	+	1.00484i	−0.567212	+	0.823572i	$0.691978\pi$
$654$		0			0
$655$	0.899495	+	0.899495i	0.0351462	+	0.0351462i
$656$		0			0
$657$	−5.36396	+	2.22183i	−0.209268	+	0.0866817i
$658$		0			0
$659$		−	50.7696i		−	1.97770i	−0.148912	−	0.988850i	$-0.547577\pi$
$659$		−	50.7696i		−	1.97770i	0.148912	−	0.988850i	$-0.452423\pi$
$660$		0			0
$661$	20.7990	−	20.7990i	0.808987	−	0.808987i	−0.175494	−	0.984481i	$-0.556152\pi$
$661$	20.7990	−	20.7990i	0.808987	−	0.808987i	0.984481	+	0.175494i	$0.0561521\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.0711	−	15.0711i	0.584431	−	0.584431i
$666$		0			0
$667$			11.2721i			0.436457i
$668$		0			0
$669$	23.1421	−	9.58579i	0.894727	−	0.370608i
$670$		0			0
$671$	−16.6569	−	16.6569i	−0.643031	−	0.643031i
$672$		0			0
$673$	−4.19239	−	10.1213i	−0.161605	−	0.390148i	0.822248	−	0.569130i	$-0.192720\pi$
$673$	−4.19239	−	10.1213i	−0.161605	−	0.390148i	−0.983852	+	0.178981i	$0.942720\pi$
$674$		0			0
$675$	−8.07107	+	19.4853i	−0.310656	+	0.749989i
$676$		0			0
$677$	−42.0919	−	17.4350i	−1.61772	−	0.670083i	−0.623945	−	0.781468i	$-0.714471\pi$
$677$	−42.0919	−	17.4350i	−1.61772	−	0.670083i	−0.993777	+	0.111385i	$0.964471\pi$
$678$		0			0
$679$	−9.07107			−0.348116
$680$		0			0
$681$	−22.7279			−0.870936
$682$		0			0
$683$	−37.0208	−	15.3345i	−1.41656	−	0.586759i	−0.462568	−	0.886584i	$-0.653072\pi$
$683$	−37.0208	−	15.3345i	−1.41656	−	0.586759i	−0.953994	+	0.299825i	$0.903072\pi$
$684$		0			0
$685$	4.10051	−	9.89949i	0.156672	−	0.378240i
$686$		0			0
$687$	7.00000	+	16.8995i	0.267067	+	0.644756i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−33.6066	+	13.9203i	−1.27846	+	0.529554i	−0.915524	−	0.402262i	$-0.868224\pi$
$691$	−33.6066	+	13.9203i	−1.27846	+	0.529554i	−0.362931	+	0.931816i	$0.618224\pi$
$692$		0			0
$693$		−	3.41421i		−	0.129695i
$694$		0			0
$695$	−10.6569	+	10.6569i	−0.404238	+	0.404238i
$696$		0			0
$697$	−39.5061	+	5.87868i	−1.49640	+	0.222671i
$698$		0			0
$699$	22.3137	−	22.3137i	0.843982	−	0.843982i
$700$		0			0
$701$		−	51.3137i		−	1.93809i	−0.246880	−	0.969046i	$-0.579405\pi$
$701$		−	51.3137i		−	1.93809i	0.246880	−	0.969046i	$-0.420595\pi$
$702$		0			0
$703$	−10.6569	+	4.41421i	−0.401931	+	0.166485i
$704$		0			0
$705$	7.17157	+	7.17157i	0.270097	+	0.270097i
$706$		0			0
$707$	−17.0711	−	41.2132i	−0.642024	−	1.54998i
$708$		0			0
$709$	15.8076	−	38.1630i	0.593667	−	1.43324i	−0.286270	−	0.958149i	$-0.592415\pi$
$709$	15.8076	−	38.1630i	0.593667	−	1.43324i	0.879937	−	0.475091i	$-0.157585\pi$
$710$		0			0
$711$	5.19239	+	2.15076i	0.194730	+	0.0806597i
$712$		0			0
$713$	27.2132			1.01914
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.3137	+	8.00000i	0.721284	+	0.298765i
$718$		0			0
$719$	8.05025	−	19.4350i	0.300224	−	0.724804i	−0.699722	−	0.714415i	$-0.746693\pi$
$719$	8.05025	−	19.4350i	0.300224	−	0.724804i	0.999946	−	0.0103893i	$-0.00330708\pi$
$720$		0			0
$721$	23.3137	+	56.2843i	0.868248	+	2.09614i
$722$		0			0
$723$	−10.4142	−	10.4142i	−0.387309	−	0.387309i
$724$		0			0
$725$	−9.36396	+	3.87868i	−0.347769	+	0.144051i
$726$		0			0
$727$		−	21.7990i		−	0.808480i	−0.914653	−	0.404240i	$-0.867536\pi$
$727$		−	21.7990i		−	0.808480i	0.914653	−	0.404240i	$-0.132464\pi$
$728$		0			0
$729$	−15.7782	+	15.7782i	−0.584377	+	0.584377i
$730$		0			0
$731$	−6.21320	+	3.72792i	−0.229804	+	0.137882i
$732$		0			0
$733$	0.514719	−	0.514719i	0.0190116	−	0.0190116i	−0.697537	−	0.716549i	$-0.745721\pi$
$733$	0.514719	−	0.514719i	0.0190116	−	0.0190116i	0.716549	+	0.697537i	$0.245721\pi$
$734$		0			0
$735$		−	18.2426i		−	0.672890i
$736$		0			0
$737$	−2.82843	+	1.17157i	−0.104186	+	0.0431554i
$738$		0			0
$739$	−3.58579	−	3.58579i	−0.131905	−	0.131905i	0.638072	−	0.769977i	$-0.279732\pi$
$739$	−3.58579	−	3.58579i	−0.131905	−	0.131905i	−0.769977	+	0.638072i	$0.779732\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.150758	+	0.363961i	−0.00553076	+	0.0133524i	−0.926621	−	0.375997i	$-0.877300\pi$
$743$	−0.150758	+	0.363961i	−0.00553076	+	0.0133524i	0.921090	+	0.389350i	$0.127300\pi$
$744$		0			0
$745$	12.4853	+	5.17157i	0.457425	+	0.189472i
$746$		0			0
$747$	0.727922			0.0266333
$748$		0			0
$749$	7.41421			0.270909
$750$		0			0
$751$	23.2635	+	9.63604i	0.848896	+	0.351624i	0.764355	−	0.644796i	$-0.223058\pi$
$751$	23.2635	+	9.63604i	0.848896	+	0.351624i	0.0845408	+	0.996420i	$0.473058\pi$
$752$		0			0
$753$	3.41421	−	8.24264i	0.124421	−	0.300379i
$754$		0			0
$755$	−0.0294373	−	0.0710678i	−0.00107133	−	0.00258642i
$756$		0			0
$757$	−23.9706	−	23.9706i	−0.871225	−	0.871225i	0.121381	−	0.992606i	$-0.461268\pi$
$757$	−23.9706	−	23.9706i	−0.871225	−	0.871225i	−0.992606	+	0.121381i	$0.961268\pi$
$758$		0			0
$759$	−15.4853	+	6.41421i	−0.562080	+	0.232821i
$760$		0			0
$761$			36.9706i			1.34018i	0.742279	+	0.670091i	$0.233745\pi$
$761$			36.9706i			1.34018i	−0.742279	+	0.670091i	$0.766255\pi$
$762$		0			0
$763$	39.3848	−	39.3848i	1.42582	−	1.42582i
$764$		0			0
$765$	−0.192388	−	1.29289i	−0.00695581	−	0.0467447i
$766$		0			0
$767$		0			0
$768$		0			0
$769$			35.5980i			1.28370i	0.766832	+	0.641848i	$0.221832\pi$
$769$			35.5980i			1.28370i	−0.766832	+	0.641848i	$0.778168\pi$
$770$		0			0
$771$	0.414214	−	0.171573i	0.0149175	−	0.00617905i
$772$		0			0
$773$	33.2843	+	33.2843i	1.19715	+	1.19715i	0.975016	+	0.222136i	$0.0713030\pi$
$773$	33.2843	+	33.2843i	1.19715	+	1.19715i	0.222136	+	0.975016i	$0.428697\pi$
$774$		0			0
$775$	9.36396	+	22.6066i	0.336363	+	0.812053i
$776$		0			0
$777$	−5.82843	+	14.0711i	−0.209094	+	0.504797i
$778$		0			0
$779$	55.8701	+	23.1421i	2.00175	+	0.829153i
$780$		0			0
$781$	4.58579			0.164092
$782$		0			0
$783$	−10.9706			−0.392056
$784$		0			0
$785$	5.17157	+	2.14214i	0.184581	+	0.0764561i
$786$		0			0
$787$	−16.4350	+	39.6777i	−0.585846	+	1.41436i	0.301596	+	0.953436i	$0.402481\pi$
$787$	−16.4350	+	39.6777i	−0.585846	+	1.41436i	−0.887442	+	0.460920i	$0.847519\pi$
$788$		0			0
$789$	−11.2426	−	27.1421i	−0.400249	−	0.966286i
$790$		0			0
$791$	3.82843	+	3.82843i	0.136123	+	0.136123i
$792$		0			0
$793$		0			0
$794$		0			0
$795$			15.6569i			0.555291i
$796$		0			0
$797$	−7.48528	+	7.48528i	−0.265142	+	0.265142i	−0.827139	−	0.561997i	$-0.810033\pi$
$797$	−7.48528	+	7.48528i	−0.265142	+	0.265142i	0.561997	+	0.827139i	$0.310033\pi$
$798$		0			0
$799$	−28.6863	−	7.17157i	−1.01485	−	0.253712i
$800$		0			0
$801$	−2.82843	+	2.82843i	−0.0999376	+	0.0999376i
$802$		0			0
$803$			25.8995i			0.913973i
$804$		0			0
$805$	−15.4853	+	6.41421i	−0.545784	+	0.226071i
$806$		0			0
$807$	−10.4142	−	10.4142i	−0.366598	−	0.366598i
$808$		0			0
$809$	0.778175	+	1.87868i	0.0273592	+	0.0660509i	0.936969	−	0.349413i	$-0.113619\pi$
$809$	0.778175	+	1.87868i	0.0273592	+	0.0660509i	−0.909609	+	0.415464i	$0.863619\pi$
$810$		0			0
$811$	1.50610	−	3.63604i	0.0528862	−	0.127679i	−0.895228	−	0.445608i	$-0.852988\pi$
$811$	1.50610	−	3.63604i	0.0528862	−	0.127679i	0.948114	+	0.317929i	$0.102988\pi$
$812$		0			0
$813$	−19.3137	−	8.00000i	−0.677361	−	0.280572i
$814$		0			0
$815$	−11.4142			−0.399822
$816$		0			0
$817$	10.9706			0.383811
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.5650	+	42.4056i	−0.613022	+	1.47997i	0.246643	+	0.969106i	$0.420673\pi$
$821$	−17.5650	+	42.4056i	−0.613022	+	1.47997i	−0.859665	+	0.510859i	$0.829327\pi$
$822$		0			0
$823$	6.77817	+	16.3640i	0.236272	+	0.570412i	0.996892	−	0.0787865i	$-0.0251045\pi$
$823$	6.77817	+	16.3640i	0.236272	+	0.570412i	−0.760619	+	0.649198i	$0.775105\pi$
$824$		0			0
$825$	−10.6569	−	10.6569i	−0.371024	−	0.371024i
$826$		0			0
$827$	−1.12132	+	0.464466i	−0.0389921	+	0.0161511i	−0.402094	−	0.915598i	$-0.631718\pi$
$827$	−1.12132	+	0.464466i	−0.0389921	+	0.0161511i	0.363102	+	0.931749i	$0.381718\pi$
$828$		0			0
$829$			13.9411i			0.484195i	0.970252	+	0.242098i	$0.0778354\pi$
$829$			13.9411i			0.484195i	−0.970252	+	0.242098i	$0.922165\pi$
$830$		0			0
$831$	−5.00000	+	5.00000i	−0.173448	+	0.173448i
$832$		0			0
$833$	27.3640	+	45.6066i	0.948105	+	1.58018i
$834$		0			0
$835$	−1.00000	+	1.00000i	−0.0346064	+	0.0346064i
$836$		0			0
$837$			26.4853i			0.915465i
$838$		0			0
$839$	−0.636039	+	0.263456i	−0.0219585	+	0.00909551i	−0.393636	−	0.919267i	$-0.628783\pi$
$839$	−0.636039	+	0.263456i	−0.0219585	+	0.00909551i	0.371677	+	0.928362i	$0.378783\pi$
$840$		0			0
$841$	16.7782	+	16.7782i	0.578558	+	0.578558i
$842$		0			0
$843$	−20.3137	−	49.0416i	−0.699641	−	1.68908i
$844$		0			0
$845$	3.80761	−	9.19239i	0.130986	−	0.316228i
$846$		0			0
$847$	31.2635	+	12.9497i	1.07423	+	0.444959i
$848$		0			0
$849$	39.8995			1.36935
$850$		0			0
$851$	9.07107			0.310952
$852$		0			0
$853$	−15.9497	−	6.60660i	−0.546109	−	0.226206i	0.0925332	−	0.995710i	$-0.470504\pi$
$853$	−15.9497	−	6.60660i	−0.546109	−	0.226206i	−0.638642	+	0.769504i	$0.720504\pi$
$854$		0			0
$855$	−0.757359	+	1.82843i	−0.0259011	+	0.0625309i
$856$		0			0
$857$	−5.36396	−	12.9497i	−0.183229	−	0.442355i	0.805399	−	0.592733i	$-0.201951\pi$
$857$	−5.36396	−	12.9497i	−0.183229	−	0.442355i	−0.988629	+	0.150378i	$0.951951\pi$
$858$		0			0
$859$	−4.27208	−	4.27208i	−0.145761	−	0.145761i	0.630460	−	0.776222i	$-0.282866\pi$
$859$	−4.27208	−	4.27208i	−0.145761	−	0.145761i	−0.776222	+	0.630460i	$0.782866\pi$
$860$		0			0
$861$	73.7696	−	30.5563i	2.51406	−	1.04136i
$862$		0			0
$863$			44.1421i			1.50262i	0.659952	+	0.751308i	$0.270577\pi$
$863$			44.1421i			1.50262i	−0.659952	+	0.751308i	$0.729423\pi$
$864$		0			0
$865$	−13.3431	+	13.3431i	−0.453681	+	0.453681i
$866$		0			0
$867$	19.9497	+	24.2635i	0.677529	+	0.824030i
$868$		0			0
$869$	17.7279	−	17.7279i	0.601379	−	0.601379i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.778175	−	0.322330i	0.0263372	−	0.0109092i
$874$		0			0
$875$	−22.7279	−	22.7279i	−0.768344	−	0.768344i
$876$		0			0
$877$	8.77817	+	21.1924i	0.296418	+	0.715616i	0.999988	+	0.00498980i	$0.00158831\pi$
$877$	8.77817	+	21.1924i	0.296418	+	0.715616i	−0.703570	+	0.710626i	$0.748412\pi$
$878$		0			0
$879$	−10.8284	+	26.1421i	−0.365234	+	0.881752i
$880$		0			0
$881$	−23.2635	−	9.63604i	−0.783766	−	0.324646i	−0.0453316	−	0.998972i	$-0.514434\pi$
$881$	−23.2635	−	9.63604i	−0.783766	−	0.324646i	−0.738434	+	0.674326i	$0.764434\pi$
$882$		0			0
$883$	−49.2548			−1.65756			−0.828779	−	0.559577i	$-0.810964\pi$
$883$	−49.2548			−1.65756			−0.828779	+	0.559577i	$0.810964\pi$
$884$		0			0
$885$	−16.8284			−0.565681
$886$		0			0
$887$	−23.8492	−	9.87868i	−0.800779	−	0.331694i	−0.0555107	−	0.998458i	$-0.517679\pi$
$887$	−23.8492	−	9.87868i	−0.800779	−	0.331694i	−0.745268	+	0.666764i	$0.767679\pi$
$888$		0			0
$889$	17.4853	−	42.2132i	0.586438	−	1.41579i
$890$		0			0
$891$	−7.12132	−	17.1924i	−0.238573	−	0.575967i
$892$		0			0
$893$	31.6569	+	31.6569i	1.05936	+	1.05936i
$894$		0			0
$895$	−6.89949	+	2.85786i	−0.230625	+	0.0955279i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.00000	+	9.00000i	−0.300167	+	0.300167i
$900$		0			0
$901$	−23.4853	−	39.1421i	−0.782408	−	1.30401i
$902$		0			0
$903$	10.2426	−	10.2426i	0.340854	−	0.340854i
$904$		0			0
$905$			0.928932i			0.0308788i
$906$		0			0
$907$	33.0208	−	13.6777i	1.09644	−	0.454160i	0.240191	−	0.970726i	$-0.422790\pi$
$907$	33.0208	−	13.6777i	1.09644	−	0.454160i	0.856247	+	0.516566i	$0.172790\pi$
$908$		0			0
$909$	2.92893	+	2.92893i	0.0971465	+	0.0971465i
$910$		0			0
$911$	16.9203	+	40.8492i	0.560595	+	1.35340i	0.909291	+	0.416160i	$0.136624\pi$
$911$	16.9203	+	40.8492i	0.560595	+	1.35340i	−0.348696	+	0.937236i	$0.613376\pi$
$912$		0			0
$913$	1.24264	−	3.00000i	0.0411254	−	0.0992855i
$914$		0			0
$915$	16.6569	+	6.89949i	0.550659	+	0.228090i
$916$		0			0
$917$	7.41421			0.244839
$918$		0			0
$919$	−12.2843			−0.405221			−0.202610	−	0.979259i	$-0.564942\pi$
$919$	−12.2843			−0.405221			−0.202610	+	0.979259i	$0.564942\pi$
$920$		0			0
$921$	−31.7990	−	13.1716i	−1.04781	−	0.434018i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	3.12132	+	7.53553i	0.102628	+	0.247767i
$926$		0			0
$927$	−4.00000	−	4.00000i	−0.131377	−	0.131377i
$928$		0			0
$929$	23.3640	−	9.67767i	0.766547	−	0.317514i	0.0350740	−	0.999385i	$-0.488833\pi$
$929$	23.3640	−	9.67767i	0.766547	−	0.317514i	0.731473	+	0.681871i	$0.238833\pi$
$930$		0			0
$931$		−	80.5269i		−	2.63916i
$932$		0			0
$933$	7.82843	−	7.82843i	0.256291	−	0.256291i
$934$		0			0
$935$	−5.65685	−	1.41421i	−0.184999	−	0.0462497i
$936$		0			0
$937$	−22.3137	+	22.3137i	−0.728957	+	0.728957i	−0.970412	−	0.241455i	$-0.922375\pi$
$937$	−22.3137	+	22.3137i	−0.728957	+	0.728957i	0.241455	+	0.970412i	$0.422375\pi$
$938$		0			0
$939$		−	28.7279i		−	0.937500i
$940$		0			0
$941$	−28.9203	+	11.9792i	−0.942775	+	0.390510i	−0.800511	−	0.599318i	$-0.795438\pi$
$941$	−28.9203	+	11.9792i	−0.942775	+	0.390510i	−0.142264	+	0.989829i	$0.545438\pi$
$942$		0			0
$943$	−33.6274	−	33.6274i	−1.09506	−	1.09506i
$944$		0			0
$945$	−6.24264	−	15.0711i	−0.203073	−	0.490262i
$946$		0			0
$947$	−6.49390	+	15.6777i	−0.211024	+	0.509456i	−0.993581	−	0.113122i	$-0.963915\pi$
$947$	−6.49390	+	15.6777i	−0.211024	+	0.509456i	0.782558	+	0.622578i	$0.213915\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	31.8995			1.03441
$952$		0			0
$953$	−50.0000			−1.61966			−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000			−1.61966			−0.809829	+	0.586665i	$0.800440\pi$
$954$		0			0
$955$	2.24264	+	0.928932i	0.0725701	+	0.0300595i
$956$		0			0
$957$	3.00000	−	7.24264i	0.0969762	−	0.234121i
$958$		0			0
$959$	−23.8995	−	57.6985i	−0.771755	−	1.86318i
$960$		0			0
$961$	−0.192388	−	0.192388i	−0.00620607	−	0.00620607i
$962$		0			0
$963$	−0.636039	+	0.263456i	−0.0204961	+	0.00848975i
$964$		0			0
$965$		−	1.41421i		−	0.0455251i
$966$		0			0
$967$	−21.5858	+	21.5858i	−0.694152	+	0.694152i	−0.963143	−	0.268991i	$-0.913310\pi$
$967$	−21.5858	+	21.5858i	−0.694152	+	0.694152i	0.268991	+	0.963143i	$0.413310\pi$
$968$		0			0
$969$	−7.00000	−	47.0416i	−0.224872	−	1.51119i
$970$		0			0
$971$	−20.6985	+	20.6985i	−0.664246	+	0.664246i	−0.956378	−	0.292132i	$-0.905635\pi$
$971$	−20.6985	+	20.6985i	−0.664246	+	0.664246i	0.292132	+	0.956378i	$0.405635\pi$
$972$		0			0
$973$			87.8406i			2.81604i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.68629	+	1.68629i	0.0539492	+	0.0539492i	0.733567	−	0.679617i	$-0.237854\pi$
$977$	1.68629	+	1.68629i	0.0539492	+	0.0539492i	−0.679617	+	0.733567i	$0.737854\pi$
$978$		0			0
$979$	6.82843	+	16.4853i	0.218237	+	0.526872i
$980$		0			0
$981$	−1.97918	+	4.77817i	−0.0631905	+	0.152555i
$982$		0			0
$983$	28.9203	+	11.9792i	0.922415	+	0.382077i	0.792796	−	0.609487i	$-0.208625\pi$
$983$	28.9203	+	11.9792i	0.922415	+	0.382077i	0.129619	+	0.991564i	$0.458625\pi$
$984$		0			0
$985$	−2.72792			−0.0869188
$986$		0			0
$987$	59.1127			1.88158
$988$		0			0
$989$	−7.97056	−	3.30152i	−0.253449	−	0.104982i
$990$		0			0
$991$	3.07969	−	7.43503i	0.0978296	−	0.236181i	−0.867386	−	0.497635i	$-0.834202\pi$
$991$	3.07969	−	7.43503i	0.0978296	−	0.236181i	0.965216	+	0.261454i	$0.0842019\pi$
$992$		0			0
$993$	−15.7279	−	37.9706i	−0.499111	−	1.20496i
$994$		0			0
$995$	−7.38478	−	7.38478i	−0.234113	−	0.234113i
$996$		0			0
$997$	38.6777	−	16.0208i	1.22493	−	0.507384i	0.325959	−	0.945384i	$-0.394313\pi$
$997$	38.6777	−	16.0208i	1.22493	−	0.507384i	0.898975	+	0.438000i	$0.144313\pi$
$998$		0			0
$999$			8.82843i			0.279319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.a.9.1	✓	4
3.2	odd	2		1224.2.bq.a.145.1		4
4.3	odd	2		272.2.v.e.145.1		4
17.2	even	8	inner	136.2.n.a.121.1	yes	4
17.6	odd	16		2312.2.a.s.1.1		4
17.7	odd	16		2312.2.b.j.577.4		4
17.10	odd	16		2312.2.b.j.577.1		4
17.11	odd	16		2312.2.a.s.1.4		4
51.2	odd	8		1224.2.bq.a.937.1		4
68.11	even	16		4624.2.a.bm.1.1		4
68.19	odd	8		272.2.v.e.257.1		4
68.23	even	16		4624.2.a.bm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.a.9.1	✓	4	1.1	even	1	trivial
136.2.n.a.121.1	yes	4	17.2	even	8	inner
272.2.v.e.145.1		4	4.3	odd	2
272.2.v.e.257.1		4	68.19	odd	8
1224.2.bq.a.145.1		4	3.2	odd	2
1224.2.bq.a.937.1		4	51.2	odd	8
2312.2.a.s.1.1		4	17.6	odd	16
2312.2.a.s.1.4		4	17.11	odd	16
2312.2.b.j.577.1		4	17.10	odd	16
2312.2.b.j.577.4		4	17.7	odd	16
4624.2.a.bm.1.1		4	68.11	even	16
4624.2.a.bm.1.4		4	68.23	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)

\(f(q)\)	\(=\)	\(q+(-1.70711 - 0.707107i) q^{3} +(0.292893 - 0.707107i) q^{5} +(-1.70711 - 4.12132i) q^{7} +(0.292893 + 0.292893i) q^{9} +O(q^{10})\)	\(q+(-1.70711 - 0.707107i) q^{3} +(0.292893 - 0.707107i) q^{5} +(-1.70711 - 4.12132i) q^{7} +(0.292893 + 0.292893i) q^{9} +(1.70711 - 0.707107i) q^{11} +(-1.00000 + 1.00000i) q^{15} +(1.00000 - 4.00000i) q^{17} +(-4.41421 + 4.41421i) q^{19} +8.24264i q^{21} +(4.53553 - 1.87868i) q^{23} +(3.12132 + 3.12132i) q^{25} +(1.82843 + 4.41421i) q^{27} +(-0.878680 + 2.12132i) q^{29} +(5.12132 + 2.12132i) q^{31} -3.41421 q^{33} -3.41421 q^{35} +(1.70711 + 0.707107i) q^{37} +(-3.70711 - 8.94975i) q^{41} +(-1.24264 - 1.24264i) q^{43} +(0.292893 - 0.121320i) q^{45} -7.17157i q^{47} +(-9.12132 + 9.12132i) q^{49} +(-4.53553 + 6.12132i) q^{51} +(7.82843 - 7.82843i) q^{53} -1.41421i q^{55} +(10.6569 - 4.41421i) q^{57} +(8.41421 + 8.41421i) q^{59} +(-4.87868 - 11.7782i) q^{61} +(0.707107 - 1.70711i) q^{63} -1.65685 q^{67} -9.07107 q^{69} +(2.29289 + 0.949747i) q^{71} +(-5.36396 + 12.9497i) q^{73} +(-3.12132 - 7.53553i) q^{75} +(-5.82843 - 5.82843i) q^{77} +(12.5355 - 5.19239i) q^{79} -10.0711i q^{81} +(1.24264 - 1.24264i) q^{83} +(-2.53553 - 1.87868i) q^{85} +(3.00000 - 3.00000i) q^{87} +9.65685i q^{89} +(-7.24264 - 7.24264i) q^{93} +(1.82843 + 4.41421i) q^{95} +(0.778175 - 1.87868i) q^{97} +(0.707107 + 0.292893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} + 4 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} - 4 q^{15} + 4 q^{17} - 12 q^{19} + 4 q^{23} + 4 q^{25} - 4 q^{27} - 12 q^{29} + 12 q^{31} - 8 q^{33} - 8 q^{35} + 4 q^{37} - 12 q^{41} + 12 q^{43} + 4 q^{45} - 28 q^{49} - 4 q^{51} + 20 q^{53} + 20 q^{57} + 28 q^{59} - 28 q^{61} + 16 q^{67} - 8 q^{69} + 12 q^{71} + 4 q^{73} - 4 q^{75} - 12 q^{77} + 36 q^{79} - 12 q^{83} + 4 q^{85} + 12 q^{87} - 12 q^{93} - 4 q^{95} - 28 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^5 - 4 * q^7 + 4 * q^9 + 4 * q^11 - 4 * q^15 + 4 * q^17 - 12 * q^19 + 4 * q^23 + 4 * q^25 - 4 * q^27 - 12 * q^29 + 12 * q^31 - 8 * q^33 - 8 * q^35 + 4 * q^37 - 12 * q^41 + 12 * q^43 + 4 * q^45 - 28 * q^49 - 4 * q^51 + 20 * q^53 + 20 * q^57 + 28 * q^59 - 28 * q^61 + 16 * q^67 - 8 * q^69 + 12 * q^71 + 4 * q^73 - 4 * q^75 - 12 * q^77 + 36 * q^79 - 12 * q^83 + 4 * q^85 + 12 * q^87 - 12 * q^93 - 4 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

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Database

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