LMFDB - Embedded newform 192.2.j.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(49,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("192.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.j (of order $4$, degree $2$, not 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 + 0.691860i$ of defining polynomial
Character	$\chi$	$=$	192.49
Dual form			192.2.j.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-2.68554 - 2.68554i) q^{5} -2.15894i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.68554 - 2.68554i) q^{5} -2.15894i q^{7} -1.00000i q^{9} +(-1.79793 - 1.79793i) q^{11} +(1.38372 - 1.38372i) q^{13} +3.79793 q^{15} -0.224777 q^{17} +(-0.158942 + 0.158942i) q^{19} +(1.52660 + 1.52660i) q^{21} -2.82843i q^{23} +9.42429i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.85712 + 1.85712i) q^{29} -1.84106 q^{31} +2.54266 q^{33} +(-5.79793 + 5.79793i) q^{35} +(-3.66949 - 3.66949i) q^{37} +1.95687i q^{39} -5.88163i q^{41} +(7.75481 + 7.75481i) q^{43} +(-2.68554 + 2.68554i) q^{45} +2.82843 q^{47} +2.33897 q^{49} +(0.158942 - 0.158942i) q^{51} +(7.51397 + 7.51397i) q^{53} +9.65685i q^{55} -0.224777i q^{57} +(-4.00000 - 4.00000i) q^{59} +(5.98737 - 5.98737i) q^{61} -2.15894 q^{63} -7.43208 q^{65} +(10.4243 - 10.4243i) q^{67} +(2.00000 + 2.00000i) q^{69} +4.31788i q^{71} -5.97474i q^{73} +(-6.66398 - 6.66398i) q^{75} +(-3.88163 + 3.88163i) q^{77} -15.0075 q^{79} -1.00000 q^{81} +(10.1158 - 10.1158i) q^{83} +(0.603650 + 0.603650i) q^{85} -2.62636i q^{87} -1.42847i q^{89} +(-2.98737 - 2.98737i) q^{91} +(1.30182 - 1.30182i) q^{93} +0.853690 q^{95} -16.3990 q^{97} +(-1.79793 + 1.79793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{43} - 8 q^{49} - 8 q^{51} + 16 q^{53} - 32 q^{59} + 16 q^{61} - 8 q^{63} - 16 q^{65} + 16 q^{67} + 16 q^{69} - 16 q^{75} + 16 q^{77} + 24 q^{79} - 8 q^{81} + 40 q^{83} - 16 q^{85} + 8 q^{91} + 48 q^{95} + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^43 - 8 * q^49 - 8 * q^51 + 16 * q^53 - 32 * q^59 + 16 * q^61 - 8 * q^63 - 16 * q^65 + 16 * q^67 + 16 * q^69 - 16 * q^75 + 16 * q^77 + 24 * q^79 - 8 * q^81 + 40 * q^83 - 16 * q^85 + 8 * q^91 + 48 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−2.68554	−	2.68554i	−1.20101	−	1.20101i	−0.973859	−	0.227153i	$-0.927058\pi$
$5$	−2.68554	−	2.68554i	−1.20101	−	1.20101i	−0.227153	−	0.973859i	$-0.572942\pi$
$6$		0			0
$7$		−	2.15894i		−	0.816003i	−0.912981	−	0.408002i	$-0.866226\pi$
$7$		−	2.15894i		−	0.816003i	0.912981	−	0.408002i	$-0.133774\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.79793	−	1.79793i	−0.542097	−	0.542097i	0.382046	−	0.924143i	$-0.375220\pi$
$11$	−1.79793	−	1.79793i	−0.542097	−	0.542097i	−0.924143	+	0.382046i	$0.875220\pi$
$12$		0			0
$13$	1.38372	−	1.38372i	0.383775	−	0.383775i	−0.488685	−	0.872460i	$-0.662523\pi$
$13$	1.38372	−	1.38372i	0.383775	−	0.383775i	0.872460	+	0.488685i	$0.162523\pi$
$14$		0			0
$15$	3.79793			0.980622
$16$		0			0
$17$	−0.224777			−0.0545165			−0.0272583	−	0.999628i	$-0.508678\pi$
$17$	−0.224777			−0.0545165			−0.0272583	+	0.999628i	$0.508678\pi$
$18$		0			0
$19$	−0.158942	+	0.158942i	−0.0364637	+	0.0364637i	−0.725104	−	0.688640i	$-0.758208\pi$
$19$	−0.158942	+	0.158942i	−0.0364637	+	0.0364637i	0.688640	+	0.725104i	$0.258208\pi$
$20$		0			0
$21$	1.52660	+	1.52660i	0.333132	+	0.333132i
$22$		0			0
$23$		−	2.82843i		−	0.589768i	−0.955533	−	0.294884i	$-0.904719\pi$
$23$		−	2.82843i		−	0.589768i	0.955533	−	0.294884i	$-0.0952810\pi$
$24$		0			0
$25$			9.42429i			1.88486i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−1.85712	+	1.85712i	−0.344858	+	0.344858i	−0.858190	−	0.513332i	$-0.828411\pi$
$29$	−1.85712	+	1.85712i	−0.344858	+	0.344858i	0.513332	+	0.858190i	$0.328411\pi$
$30$		0			0
$31$	−1.84106			−0.330664			−0.165332	−	0.986238i	$-0.552870\pi$
$31$	−1.84106			−0.330664			−0.165332	+	0.986238i	$0.552870\pi$
$32$		0			0
$33$	2.54266			0.442620
$34$		0			0
$35$	−5.79793	+	5.79793i	−0.980029	+	0.980029i
$36$		0			0
$37$	−3.66949	−	3.66949i	−0.603260	−	0.603260i	0.337916	−	0.941176i	$-0.390278\pi$
$37$	−3.66949	−	3.66949i	−0.603260	−	0.603260i	−0.941176	+	0.337916i	$0.890278\pi$
$38$		0			0
$39$			1.95687i			0.313351i
$40$		0			0
$41$		−	5.88163i		−	0.918557i	−0.888292	−	0.459278i	$-0.848108\pi$
$41$		−	5.88163i		−	0.918557i	0.888292	−	0.459278i	$-0.151892\pi$
$42$		0			0
$43$	7.75481	+	7.75481i	1.18260	+	1.18260i	0.979069	+	0.203528i	$0.0652407\pi$
$43$	7.75481	+	7.75481i	1.18260	+	1.18260i	0.203528	+	0.979069i	$0.434759\pi$
$44$		0			0
$45$	−2.68554	+	2.68554i	−0.400337	+	0.400337i
$46$		0			0
$47$	2.82843			0.412568			0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843			0.412568			0.206284	+	0.978492i	$0.433863\pi$
$48$		0			0
$49$	2.33897			0.334139
$50$		0			0
$51$	0.158942	−	0.158942i	0.0222563	−	0.0222563i
$52$		0			0
$53$	7.51397	+	7.51397i	1.03212	+	1.03212i	0.999467	+	0.0326567i	$0.0103968\pi$
$53$	7.51397	+	7.51397i	1.03212	+	1.03212i	0.0326567	+	0.999467i	$0.489603\pi$
$54$		0			0
$55$			9.65685i			1.30213i
$56$		0			0
$57$		−	0.224777i		−	0.0297725i
$58$		0			0
$59$	−4.00000	−	4.00000i	−0.520756	−	0.520756i	0.397044	−	0.917800i	$-0.370036\pi$
$59$	−4.00000	−	4.00000i	−0.520756	−	0.520756i	−0.917800	+	0.397044i	$0.870036\pi$
$60$		0			0
$61$	5.98737	−	5.98737i	0.766604	−	0.766604i	−0.210903	−	0.977507i	$-0.567640\pi$
$61$	5.98737	−	5.98737i	0.766604	−	0.766604i	0.977507	+	0.210903i	$0.0676404\pi$
$62$		0			0
$63$	−2.15894			−0.272001
$64$		0			0
$65$	−7.43208			−0.921836
$66$		0			0
$67$	10.4243	−	10.4243i	1.27353	−	1.27353i	0.329307	−	0.944223i	$-0.393185\pi$
$67$	10.4243	−	10.4243i	1.27353	−	1.27353i	0.944223	−	0.329307i	$-0.106815\pi$
$68$		0			0
$69$	2.00000	+	2.00000i	0.240772	+	0.240772i
$70$		0			0
$71$			4.31788i			0.512438i	0.966619	+	0.256219i	$0.0824769\pi$
$71$			4.31788i			0.512438i	−0.966619	+	0.256219i	$0.917523\pi$
$72$		0			0
$73$		−	5.97474i		−	0.699290i	−0.936882	−	0.349645i	$-0.886302\pi$
$73$		−	5.97474i		−	0.699290i	0.936882	−	0.349645i	$-0.113698\pi$
$74$		0			0
$75$	−6.66398	−	6.66398i	−0.769490	−	0.769490i
$76$		0			0
$77$	−3.88163	+	3.88163i	−0.442353	+	0.442353i
$78$		0			0
$79$	−15.0075			−1.68848			−0.844239	−	0.535966i	$-0.819947\pi$
$79$	−15.0075			−1.68848			−0.844239	+	0.535966i	$0.819947\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	10.1158	−	10.1158i	1.11036	−	1.11036i	0.117253	−	0.993102i	$-0.462591\pi$
$83$	10.1158	−	10.1158i	1.11036	−	1.11036i	0.993102	−	0.117253i	$-0.0374088\pi$
$84$		0			0
$85$	0.603650	+	0.603650i	0.0654750	+	0.0654750i
$86$		0			0
$87$		−	2.62636i		−	0.281575i
$88$		0			0
$89$		−	1.42847i		−	0.151417i	−0.997130	−	0.0757086i	$-0.975878\pi$
$89$		−	1.42847i		−	0.151417i	0.997130	−	0.0757086i	$-0.0241219\pi$
$90$		0			0
$91$	−2.98737	−	2.98737i	−0.313161	−	0.313161i
$92$		0			0
$93$	1.30182	−	1.30182i	0.134993	−	0.134993i
$94$		0			0
$95$	0.853690			0.0875867
$96$		0			0
$97$	−16.3990			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$97$	−16.3990			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$98$		0			0
$99$	−1.79793	+	1.79793i	−0.180699	+	0.180699i
$100$		0			0
$101$	0.0818942	+	0.0818942i	0.00814878	+	0.00814878i	0.711169	−	0.703021i	$-0.248166\pi$
$101$	0.0818942	+	0.0818942i	0.00814878	+	0.00814878i	−0.703021	+	0.711169i	$0.748166\pi$
$102$		0			0
$103$		−	13.3507i		−	1.31548i	−0.753245	−	0.657740i	$-0.771512\pi$
$103$		−	13.3507i		−	1.31548i	0.753245	−	0.657740i	$-0.228488\pi$
$104$		0			0
$105$		−	8.19951i		−	0.800191i
$106$		0			0
$107$	7.27798	+	7.27798i	0.703589	+	0.703589i	0.965179	−	0.261590i	$-0.0842468\pi$
$107$	7.27798	+	7.27798i	0.703589	+	0.703589i	−0.261590	+	0.965179i	$0.584247\pi$
$108$		0			0
$109$	−7.04057	+	7.04057i	−0.674365	+	0.674365i	−0.958719	−	0.284355i	$-0.908221\pi$
$109$	−7.04057	+	7.04057i	−0.674365	+	0.674365i	0.284355	+	0.958719i	$0.408221\pi$
$110$		0			0
$111$	5.18944			0.492559
$112$		0			0
$113$	18.8486			1.77313			0.886563	−	0.462608i	$-0.153086\pi$
$113$	18.8486			1.77313			0.886563	+	0.462608i	$0.153086\pi$
$114$		0			0
$115$	−7.59587	+	7.59587i	−0.708318	+	0.708318i
$116$		0			0
$117$	−1.38372	−	1.38372i	−0.127925	−	0.127925i
$118$		0			0
$119$			0.485281i			0.0444857i
$120$		0			0
$121$		−	4.53488i		−	0.412261i
$122$		0			0
$123$	4.15894	+	4.15894i	0.374999	+	0.374999i
$124$		0			0
$125$	11.8816	−	11.8816i	1.06273	−	1.06273i
$126$		0			0
$127$	3.81580			0.338597			0.169299	−	0.985565i	$-0.445850\pi$
$127$	3.81580			0.338597			0.169299	+	0.985565i	$0.445850\pi$
$128$		0			0
$129$	−10.9670			−0.965586
$130$		0			0
$131$	0.767438	−	0.767438i	0.0670514	−	0.0670514i	−0.672786	−	0.739837i	$-0.734902\pi$
$131$	0.767438	−	0.767438i	0.0670514	−	0.0670514i	0.739837	+	0.672786i	$0.234902\pi$
$132$		0			0
$133$	0.343146	+	0.343146i	0.0297545	+	0.0297545i
$134$		0			0
$135$		−	3.79793i		−	0.326874i
$136$		0			0
$137$			5.31010i			0.453672i	0.973933	+	0.226836i	$0.0728382\pi$
$137$			5.31010i			0.453672i	−0.973933	+	0.226836i	$0.927162\pi$
$138$		0			0
$139$	−8.76744	−	8.76744i	−0.743644	−	0.743644i	0.229633	−	0.973277i	$-0.426247\pi$
$139$	−8.76744	−	8.76744i	−0.743644	−	0.743644i	−0.973277	+	0.229633i	$0.926247\pi$
$140$		0			0
$141$	−2.00000	+	2.00000i	−0.168430	+	0.168430i
$142$		0			0
$143$	−4.97567			−0.416086
$144$		0			0
$145$	9.97474			0.828357
$146$		0			0
$147$	−1.65390	+	1.65390i	−0.136412	+	0.136412i
$148$		0			0
$149$	−1.02869	−	1.02869i	−0.0842735	−	0.0842735i	0.663713	−	0.747987i	$-0.268979\pi$
$149$	−1.02869	−	1.02869i	−0.0842735	−	0.0842735i	−0.747987	+	0.663713i	$0.768979\pi$
$150$		0			0
$151$			2.03696i			0.165766i	0.996559	+	0.0828829i	$0.0264127\pi$
$151$			2.03696i			0.165766i	−0.996559	+	0.0828829i	$0.973587\pi$
$152$		0			0
$153$			0.224777i			0.0181722i
$154$		0			0
$155$	4.94424	+	4.94424i	0.397131	+	0.397131i
$156$		0			0
$157$	6.09378	−	6.09378i	0.486336	−	0.486336i	−0.420812	−	0.907148i	$-0.638255\pi$
$157$	6.09378	−	6.09378i	0.486336	−	0.486336i	0.907148	+	0.420812i	$0.138255\pi$
$158$		0			0
$159$	−10.6264			−0.842725
$160$		0			0
$161$	−6.10641			−0.481252
$162$		0			0
$163$	−3.43692	+	3.43692i	−0.269201	+	0.269201i	−0.828778	−	0.559577i	$-0.810963\pi$
$163$	−3.43692	+	3.43692i	−0.269201	+	0.269201i	0.559577	+	0.828778i	$0.310963\pi$
$164$		0			0
$165$	−6.82843	−	6.82843i	−0.531592	−	0.531592i
$166$		0			0
$167$			21.7023i			1.67937i	0.543072	+	0.839686i	$0.317261\pi$
$167$			21.7023i			1.67937i	−0.543072	+	0.839686i	$0.682739\pi$
$168$		0			0
$169$			9.17064i			0.705434i
$170$		0			0
$171$	0.158942	+	0.158942i	0.0121546	+	0.0121546i
$172$		0			0
$173$	−8.74653	+	8.74653i	−0.664987	+	0.664987i	−0.956551	−	0.291565i	$-0.905824\pi$
$173$	−8.74653	+	8.74653i	−0.664987	+	0.664987i	0.291565	+	0.956551i	$0.405824\pi$
$174$		0			0
$175$	20.3465			1.53805
$176$		0			0
$177$	5.65685			0.425195
$178$		0			0
$179$	−8.23163	+	8.23163i	−0.615261	+	0.615261i	−0.944312	−	0.329051i	$-0.893271\pi$
$179$	−8.23163	+	8.23163i	−0.615261	+	0.615261i	0.329051	+	0.944312i	$0.393271\pi$
$180$		0			0
$181$	6.72269	+	6.72269i	0.499694	+	0.499694i	0.911343	−	0.411649i	$-0.135047\pi$
$181$	6.72269	+	6.72269i	0.499694	+	0.499694i	−0.411649	+	0.911343i	$0.635047\pi$
$182$		0			0
$183$			8.46742i			0.625930i
$184$		0			0
$185$			19.7091i			1.44904i
$186$		0			0
$187$	0.404135	+	0.404135i	0.0295533	+	0.0295533i
$188$		0			0
$189$	1.52660	−	1.52660i	0.111044	−	0.111044i
$190$		0			0
$191$	20.8032			1.50526			0.752632	−	0.658441i	$-0.228784\pi$
$191$	20.8032			1.50526			0.752632	+	0.658441i	$0.228784\pi$
$192$		0			0
$193$	14.1454			1.01821			0.509103	−	0.860705i	$-0.329977\pi$
$193$	14.1454			1.01821			0.509103	+	0.860705i	$0.329977\pi$
$194$		0			0
$195$	5.25527	−	5.25527i	0.376338	−	0.376338i
$196$		0			0
$197$	−2.42865	−	2.42865i	−0.173034	−	0.173034i	0.615277	−	0.788311i	$-0.289044\pi$
$197$	−2.42865	−	2.42865i	−0.173034	−	0.173034i	−0.788311	+	0.615277i	$0.789044\pi$
$198$		0			0
$199$		−	0.306182i		−	0.0217047i	−0.999941	−	0.0108523i	$-0.996546\pi$
$199$		−	0.306182i		−	0.0217047i	0.999941	−	0.0108523i	$-0.00345447\pi$
$200$		0			0
$201$			14.7422i			1.03983i
$202$		0			0
$203$	4.00941	+	4.00941i	0.281405	+	0.281405i
$204$		0			0
$205$	−15.7954	+	15.7954i	−1.10320	+	1.10320i
$206$		0			0
$207$	−2.82843			−0.196589
$208$		0			0
$209$	0.571533			0.0395337
$210$		0			0
$211$	−7.23256	+	7.23256i	−0.497910	+	0.497910i	−0.910787	−	0.412877i	$-0.864524\pi$
$211$	−7.23256	+	7.23256i	−0.497910	+	0.497910i	0.412877	+	0.910787i	$0.364524\pi$
$212$		0			0
$213$	−3.05320	−	3.05320i	−0.209202	−	0.209202i
$214$		0			0
$215$		−	41.6517i		−	2.84063i
$216$		0			0
$217$			3.97474i			0.269823i
$218$		0			0
$219$	4.22478	+	4.22478i	0.285484	+	0.285484i
$220$		0			0
$221$	−0.311029	+	0.311029i	−0.0209221	+	0.0209221i
$222$		0			0
$223$	1.71908			0.115118			0.0575591	−	0.998342i	$-0.481668\pi$
$223$	1.71908			0.115118			0.0575591	+	0.998342i	$0.481668\pi$
$224$		0			0
$225$	9.42429			0.628286
$226$		0			0
$227$	−10.1158	+	10.1158i	−0.671410	+	0.671410i	−0.958041	−	0.286631i	$-0.907465\pi$
$227$	−10.1158	+	10.1158i	−0.671410	+	0.671410i	0.286631	+	0.958041i	$0.407465\pi$
$228$		0			0
$229$	−12.0195	−	12.0195i	−0.794270	−	0.794270i	0.187915	−	0.982185i	$-0.439827\pi$
$229$	−12.0195	−	12.0195i	−0.794270	−	0.794270i	−0.982185	+	0.187915i	$0.939827\pi$
$230$		0			0
$231$		−	5.48946i		−	0.361180i
$232$		0			0
$233$		−	13.3779i		−	0.876418i	−0.898873	−	0.438209i	$-0.855613\pi$
$233$		−	13.3779i		−	0.876418i	0.898873	−	0.438209i	$-0.144387\pi$
$234$		0			0
$235$	−7.59587	−	7.59587i	−0.495500	−	0.495500i
$236$		0			0
$237$	10.6119	−	10.6119i	0.689319	−	0.689319i
$238$		0			0
$239$	−13.3675			−0.864670			−0.432335	−	0.901713i	$-0.642310\pi$
$239$	−13.3675			−0.864670			−0.432335	+	0.901713i	$0.642310\pi$
$240$		0			0
$241$	0.211474			0.0136222			0.00681112	−	0.999977i	$-0.497832\pi$
$241$	0.211474			0.0136222			0.00681112	+	0.999977i	$0.497832\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−6.28141	−	6.28141i	−0.401305	−	0.401305i
$246$		0			0
$247$			0.439861i			0.0279877i
$248$		0			0
$249$			14.3059i			0.906601i
$250$		0			0
$251$	−10.4337	−	10.4337i	−0.658569	−	0.658569i	0.296472	−	0.955041i	$-0.404190\pi$
$251$	−10.4337	−	10.4337i	−0.658569	−	0.658569i	−0.955041	+	0.296472i	$0.904190\pi$
$252$		0			0
$253$	−5.08532	+	5.08532i	−0.319711	+	0.319711i
$254$		0			0
$255$	−0.853690			−0.0534601
$256$		0			0
$257$	−0.742176			−0.0462957			−0.0231478	−	0.999732i	$-0.507369\pi$
$257$	−0.742176			−0.0462957			−0.0231478	+	0.999732i	$0.507369\pi$
$258$		0			0
$259$	−7.92221	+	7.92221i	−0.492262	+	0.492262i
$260$		0			0
$261$	1.85712	+	1.85712i	0.114953	+	0.114953i
$262$		0			0
$263$		−	5.48435i		−	0.338180i	−0.985601	−	0.169090i	$-0.945917\pi$
$263$		−	5.48435i		−	0.338180i	0.985601	−	0.169090i	$-0.0540828\pi$
$264$		0			0
$265$		−	40.3582i		−	2.47918i
$266$		0			0
$267$	1.01008	+	1.01008i	0.0618158	+	0.0618158i
$268$		0			0
$269$	14.4741	−	14.4741i	0.882500	−	0.882500i	−0.111289	−	0.993788i	$-0.535498\pi$
$269$	14.4741	−	14.4741i	0.882500	−	0.882500i	0.993788	+	0.111289i	$0.0354978\pi$
$270$		0			0
$271$	14.0370			0.852685			0.426342	−	0.904562i	$-0.359802\pi$
$271$	14.0370			0.852685			0.426342	+	0.904562i	$0.359802\pi$
$272$		0			0
$273$	4.22478			0.255695
$274$		0			0
$275$	16.9442	−	16.9442i	1.02178	−	1.02178i
$276$		0			0
$277$	9.49013	+	9.49013i	0.570207	+	0.570207i	0.932186	−	0.361980i	$-0.117899\pi$
$277$	9.49013	+	9.49013i	0.570207	+	0.570207i	−0.361980	+	0.932186i	$0.617899\pi$
$278$		0			0
$279$			1.84106i			0.110221i
$280$		0			0
$281$			3.89359i			0.232272i	0.993233	+	0.116136i	$0.0370509\pi$
$281$			3.89359i			0.232272i	−0.993233	+	0.116136i	$0.962949\pi$
$282$		0			0
$283$	12.4853	+	12.4853i	0.742173	+	0.742173i	0.972996	−	0.230823i	$-0.0741418\pi$
$283$	12.4853	+	12.4853i	0.742173	+	0.742173i	−0.230823	+	0.972996i	$0.574142\pi$
$284$		0			0
$285$	−0.603650	+	0.603650i	−0.0357571	+	0.0357571i
$286$		0			0
$287$	−12.6981			−0.749545
$288$		0			0
$289$	−16.9495			−0.997028
$290$		0			0
$291$	11.5959	−	11.5959i	0.679762	−	0.679762i
$292$		0			0
$293$	−11.1553	−	11.1553i	−0.651697	−	0.651697i	0.301704	−	0.953402i	$-0.402444\pi$
$293$	−11.1553	−	11.1553i	−0.651697	−	0.651697i	−0.953402	+	0.301704i	$0.902444\pi$
$294$		0			0
$295$			21.4844i			1.25087i
$296$		0			0
$297$		−	2.54266i		−	0.147540i
$298$		0			0
$299$	−3.91375	−	3.91375i	−0.226338	−	0.226338i
$300$		0			0
$301$	16.7422	−	16.7422i	0.965003	−	0.965003i
$302$		0			0
$303$	−0.115816			−0.00665345
$304$		0			0
$305$	−32.1587			−1.84140
$306$		0			0
$307$	5.40320	−	5.40320i	0.308377	−	0.308377i	−0.535903	−	0.844280i	$-0.680029\pi$
$307$	5.40320	−	5.40320i	0.308377	−	0.308377i	0.844280	+	0.535903i	$0.180029\pi$
$308$		0			0
$309$	9.44035	+	9.44035i	0.537043	+	0.537043i
$310$		0			0
$311$			24.1623i			1.37012i	0.728488	+	0.685059i	$0.240224\pi$
$311$			24.1623i			1.37012i	−0.728488	+	0.685059i	$0.759776\pi$
$312$		0			0
$313$		−	16.6105i		−	0.938881i	−0.882964	−	0.469441i	$-0.844456\pi$
$313$		−	16.6105i		−	0.938881i	0.882964	−	0.469441i	$-0.155544\pi$
$314$		0			0
$315$	5.79793	+	5.79793i	0.326676	+	0.326676i
$316$		0			0
$317$	1.81170	−	1.81170i	0.101755	−	0.101755i	−0.654397	−	0.756152i	$-0.727077\pi$
$317$	1.81170	−	1.81170i	0.101755	−	0.101755i	0.756152	+	0.654397i	$0.227077\pi$
$318$		0			0
$319$	6.67794			0.373893
$320$		0			0
$321$	−10.2926			−0.574478
$322$		0			0
$323$	0.0357265	−	0.0357265i	0.00198788	−	0.00198788i
$324$		0			0
$325$	13.0406	+	13.0406i	0.723361	+	0.723361i
$326$		0			0
$327$		−	9.95687i		−	0.550616i
$328$		0			0
$329$		−	6.10641i		−	0.336657i
$330$		0			0
$331$	−13.5252	−	13.5252i	−0.743411	−	0.743411i	0.229822	−	0.973233i	$-0.426186\pi$
$331$	−13.5252	−	13.5252i	−0.743411	−	0.743411i	−0.973233	+	0.229822i	$0.926186\pi$
$332$		0			0
$333$	−3.66949	+	3.66949i	−0.201087	+	0.201087i
$334$		0			0
$335$	−55.9898			−3.05905
$336$		0			0
$337$	−1.12615			−0.0613454			−0.0306727	−	0.999529i	$-0.509765\pi$
$337$	−1.12615			−0.0613454			−0.0306727	+	0.999529i	$0.509765\pi$
$338$		0			0
$339$	−13.3280	+	13.3280i	−0.723876	+	0.723876i
$340$		0			0
$341$	3.31010	+	3.31010i	0.179252	+	0.179252i
$342$		0			0
$343$		−	20.1623i		−	1.08866i
$344$		0			0
$345$		−	10.7422i		−	0.578339i
$346$		0			0
$347$	−20.7938	−	20.7938i	−1.11627	−	1.11627i	−0.992284	−	0.123983i	$-0.960433\pi$
$347$	−20.7938	−	20.7938i	−1.11627	−	1.11627i	−0.123983	−	0.992284i	$-0.539567\pi$
$348$		0			0
$349$	−19.2855	+	19.2855i	−1.03233	+	1.03233i	−0.0328700	+	0.999460i	$0.510465\pi$
$349$	−19.2855	+	19.2855i	−1.03233	+	1.03233i	−0.999460	+	0.0328700i	$0.989535\pi$
$350$		0			0
$351$	1.95687			0.104450
$352$		0			0
$353$	25.5908			1.36206			0.681029	−	0.732256i	$-0.261533\pi$
$353$	25.5908			1.36206			0.681029	+	0.732256i	$0.261533\pi$
$354$		0			0
$355$	11.5959	−	11.5959i	0.615445	−	0.615445i
$356$		0			0
$357$	−0.343146	−	0.343146i	−0.0181612	−	0.0181612i
$358$		0			0
$359$		−	3.77296i		−	0.199129i	−0.995031	−	0.0995645i	$-0.968255\pi$
$359$		−	3.77296i		−	0.199129i	0.995031	−	0.0995645i	$-0.0317450\pi$
$360$		0			0
$361$			18.9495i			0.997341i
$362$		0			0
$363$	3.20664	+	3.20664i	0.168305	+	0.168305i
$364$		0			0
$365$	−16.0454	+	16.0454i	−0.839856	+	0.839856i
$366$		0			0
$367$	27.4474			1.43274			0.716371	−	0.697720i	$-0.245802\pi$
$367$	27.4474			1.43274			0.716371	+	0.697720i	$0.245802\pi$
$368$		0			0
$369$	−5.88163			−0.306186
$370$		0			0
$371$	16.2222	−	16.2222i	0.842216	−	0.842216i
$372$		0			0
$373$	12.6231	+	12.6231i	0.653601	+	0.653601i	0.953858	−	0.300257i	$-0.0970725\pi$
$373$	12.6231	+	12.6231i	0.653601	+	0.653601i	−0.300257	+	0.953858i	$0.597072\pi$
$374$		0			0
$375$			16.8032i			0.867712i
$376$		0			0
$377$			5.13946i			0.264695i
$378$		0			0
$379$	11.6686	+	11.6686i	0.599373	+	0.599373i	0.940146	−	0.340772i	$-0.110689\pi$
$379$	11.6686	+	11.6686i	0.599373	+	0.599373i	−0.340772	+	0.940146i	$0.610689\pi$
$380$		0			0
$381$	−2.69818	+	2.69818i	−0.138232	+	0.138232i
$382$		0			0
$383$	17.1885			0.878291			0.439145	−	0.898416i	$-0.355281\pi$
$383$	17.1885			0.878291			0.439145	+	0.898416i	$0.355281\pi$
$384$		0			0
$385$	20.8486			1.06254
$386$		0			0
$387$	7.75481	−	7.75481i	0.394199	−	0.394199i
$388$		0			0
$389$	−1.88238	−	1.88238i	−0.0954404	−	0.0954404i	0.657774	−	0.753215i	$-0.271498\pi$
$389$	−1.88238	−	1.88238i	−0.0954404	−	0.0954404i	−0.753215	+	0.657774i	$0.771498\pi$
$390$		0			0
$391$			0.635767i			0.0321521i
$392$		0			0
$393$			1.08532i			0.0547472i
$394$		0			0
$395$	40.3034	+	40.3034i	2.02788	+	2.02788i
$396$		0			0
$397$	8.41166	−	8.41166i	0.422169	−	0.422169i	−0.463781	−	0.885950i	$-0.653507\pi$
$397$	8.41166	−	8.41166i	0.422169	−	0.422169i	0.885950	+	0.463781i	$0.153507\pi$
$398$		0			0
$399$	−0.485281			−0.0242945
$400$		0			0
$401$	1.12389			0.0561242			0.0280621	−	0.999606i	$-0.491066\pi$
$401$	1.12389			0.0561242			0.0280621	+	0.999606i	$0.491066\pi$
$402$		0			0
$403$	−2.54751	+	2.54751i	−0.126900	+	0.126900i
$404$		0			0
$405$	2.68554	+	2.68554i	0.133446	+	0.133446i
$406$		0			0
$407$			13.1950i			0.654051i
$408$		0			0
$409$			13.7211i			0.678464i	0.940703	+	0.339232i	$0.110167\pi$
$409$			13.7211i			0.678464i	−0.940703	+	0.339232i	$0.889833\pi$
$410$		0			0
$411$	−3.75481	−	3.75481i	−0.185211	−	0.185211i
$412$		0			0
$413$	−8.63577	+	8.63577i	−0.424938	+	0.424938i
$414$		0			0
$415$	−54.3329			−2.66710
$416$		0			0
$417$	12.3990			0.607183
$418$		0			0
$419$	9.30755	−	9.30755i	0.454703	−	0.454703i	−0.442209	−	0.896912i	$-0.645805\pi$
$419$	9.30755	−	9.30755i	0.454703	−	0.454703i	0.896912	+	0.442209i	$0.145805\pi$
$420$		0			0
$421$	8.44378	+	8.44378i	0.411525	+	0.411525i	0.882269	−	0.470745i	$-0.156015\pi$
$421$	8.44378	+	8.44378i	0.411525	+	0.411525i	−0.470745	+	0.882269i	$0.656015\pi$
$422$		0			0
$423$		−	2.82843i		−	0.137523i
$424$		0			0
$425$		−	2.11837i		−	0.102756i
$426$		0			0
$427$	−12.9264	−	12.9264i	−0.625551	−	0.625551i
$428$		0			0
$429$	3.51833	−	3.51833i	0.169866	−	0.169866i
$430$		0			0
$431$	30.6054			1.47421			0.737105	−	0.675778i	$-0.236192\pi$
$431$	30.6054			1.47421			0.737105	+	0.675778i	$0.236192\pi$
$432$		0			0
$433$	−15.3137			−0.735930			−0.367965	−	0.929840i	$-0.619945\pi$
$433$	−15.3137			−0.735930			−0.367965	+	0.929840i	$0.619945\pi$
$434$		0			0
$435$	−7.05320	+	7.05320i	−0.338175	+	0.338175i
$436$		0			0
$437$	0.449555	+	0.449555i	0.0215051	+	0.0215051i
$438$		0			0
$439$			33.3676i			1.59255i	0.604936	+	0.796274i	$0.293199\pi$
$439$			33.3676i			1.59255i	−0.604936	+	0.796274i	$0.706801\pi$
$440$		0			0
$441$		−	2.33897i		−	0.111380i
$442$		0			0
$443$	−2.28832	−	2.28832i	−0.108721	−	0.108721i	0.650653	−	0.759375i	$-0.274495\pi$
$443$	−2.28832	−	2.28832i	−0.108721	−	0.108721i	−0.759375	+	0.650653i	$0.774495\pi$
$444$		0			0
$445$	−3.83621	+	3.83621i	−0.181854	+	0.181854i
$446$		0			0
$447$	1.45479			0.0688091
$448$		0			0
$449$	−27.4165			−1.29387			−0.646933	−	0.762547i	$-0.723948\pi$
$449$	−27.4165			−1.29387			−0.646933	+	0.762547i	$0.723948\pi$
$450$		0			0
$451$	−10.5748	+	10.5748i	−0.497947	+	0.497947i
$452$		0			0
$453$	−1.44035	−	1.44035i	−0.0676736	−	0.0676736i
$454$		0			0
$455$			16.0454i			0.752221i
$456$		0			0
$457$			10.9147i			0.510567i	0.966866	+	0.255284i	$0.0821688\pi$
$457$			10.9147i			0.510567i	−0.966866	+	0.255284i	$0.917831\pi$
$458$		0			0
$459$	−0.158942	−	0.158942i	−0.00741876	−	0.00741876i
$460$		0			0
$461$	17.8319	−	17.8319i	0.830512	−	0.830512i	−0.157075	−	0.987587i	$-0.550206\pi$
$461$	17.8319	−	17.8319i	0.830512	−	0.830512i	0.987587	+	0.157075i	$0.0502063\pi$
$462$		0			0
$463$	−22.4937			−1.04537			−0.522686	−	0.852525i	$-0.675070\pi$
$463$	−22.4937			−1.04537			−0.522686	+	0.852525i	$0.675070\pi$
$464$		0			0
$465$	−6.99222			−0.324256
$466$		0			0
$467$	−24.2171	+	24.2171i	−1.12063	+	1.12063i	−0.128989	+	0.991646i	$0.541173\pi$
$467$	−24.2171	+	24.2171i	−1.12063	+	1.12063i	−0.991646	+	0.128989i	$0.958827\pi$
$468$		0			0
$469$	−22.5054	−	22.5054i	−1.03920	−	1.03920i
$470$		0			0
$471$			8.61790i			0.397092i
$472$		0			0
$473$		−	27.8852i		−	1.28216i
$474$		0			0
$475$	−1.49791	−	1.49791i	−0.0687289	−	0.0687289i
$476$		0			0
$477$	7.51397	−	7.51397i	0.344041	−	0.344041i
$478$		0			0
$479$	36.2362			1.65568			0.827838	−	0.560968i	$-0.189571\pi$
$479$	36.2362			1.65568			0.827838	+	0.560968i	$0.189571\pi$
$480$		0			0
$481$	−10.1551			−0.463032
$482$		0			0
$483$	4.31788	−	4.31788i	0.196470	−	0.196470i
$484$		0			0
$485$	44.0403	+	44.0403i	1.99977	+	1.99977i
$486$		0			0
$487$		−	16.8200i		−	0.762186i	−0.924537	−	0.381093i	$-0.875548\pi$
$487$		−	16.8200i		−	0.762186i	0.924537	−	0.381093i	$-0.124452\pi$
$488$		0			0
$489$		−	4.86054i		−	0.219801i
$490$		0			0
$491$	−6.10641	−	6.10641i	−0.275578	−	0.275578i	0.555763	−	0.831341i	$-0.312426\pi$
$491$	−6.10641	−	6.10641i	−0.275578	−	0.275578i	−0.831341	+	0.555763i	$0.812426\pi$
$492$		0			0
$493$	0.417438	−	0.417438i	0.0188005	−	0.0188005i
$494$		0			0
$495$	9.65685			0.434043
$496$		0			0
$497$	9.32206			0.418151
$498$		0			0
$499$	19.6770	−	19.6770i	0.880864	−	0.880864i	−0.112758	−	0.993622i	$-0.535969\pi$
$499$	19.6770	−	19.6770i	0.880864	−	0.880864i	0.993622	+	0.112758i	$0.0359686\pi$
$500$		0			0
$501$	−15.3458	−	15.3458i	−0.685601	−	0.685601i
$502$		0			0
$503$		−	25.7308i		−	1.14728i	−0.819108	−	0.573639i	$-0.805531\pi$
$503$		−	25.7308i		−	1.14728i	0.819108	−	0.573639i	$-0.194469\pi$
$504$		0			0
$505$		−	0.439861i		−	0.0195736i
$506$		0			0
$507$	−6.48462	−	6.48462i	−0.287992	−	0.287992i
$508$		0			0
$509$	1.73514	−	1.73514i	0.0769087	−	0.0769087i	−0.667606	−	0.744515i	$-0.732681\pi$
$509$	1.73514	−	1.73514i	0.0769087	−	0.0769087i	0.744515	+	0.667606i	$0.232681\pi$
$510$		0			0
$511$	−12.8991			−0.570623
$512$		0			0
$513$	−0.224777			−0.00992417
$514$		0			0
$515$	−35.8538	+	35.8538i	−1.57991	+	1.57991i
$516$		0			0
$517$	−5.08532	−	5.08532i	−0.223652	−	0.223652i
$518$		0			0
$519$		−	12.3695i		−	0.542959i
$520$		0			0
$521$			33.5944i			1.47180i	0.677092	+	0.735898i	$0.263240\pi$
$521$			33.5944i			1.47180i	−0.677092	+	0.735898i	$0.736760\pi$
$522$		0			0
$523$	21.8158	+	21.8158i	0.953938	+	0.953938i	0.998985	−	0.0450467i	$-0.0143437\pi$
$523$	21.8158	+	21.8158i	0.953938	+	0.953938i	−0.0450467	+	0.998985i	$0.514344\pi$
$524$		0			0
$525$	−14.3871	+	14.3871i	−0.627907	+	0.627907i
$526$		0			0
$527$	0.413828			0.0180266
$528$		0			0
$529$	15.0000			0.652174
$530$		0			0
$531$	−4.00000	+	4.00000i	−0.173585	+	0.173585i
$532$		0			0
$533$	−8.13853	−	8.13853i	−0.352519	−	0.352519i
$534$		0			0
$535$		−	39.0907i		−	1.69004i
$536$		0			0
$537$		−	11.6413i		−	0.502359i
$538$		0			0
$539$	−4.20531	−	4.20531i	−0.181136	−	0.181136i
$540$		0			0
$541$	27.2112	−	27.2112i	1.16990	−	1.16990i	0.187669	−	0.982232i	$-0.439907\pi$
$541$	27.2112	−	27.2112i	1.16990	−	1.16990i	0.982232	−	0.187669i	$-0.0600933\pi$
$542$		0			0
$543$	−9.50732			−0.407998
$544$		0			0
$545$	37.8155			1.61984
$546$		0			0
$547$	6.80116	−	6.80116i	0.290796	−	0.290796i	−0.546598	−	0.837395i	$-0.684078\pi$
$547$	6.80116	−	6.80116i	0.290796	−	0.290796i	0.837395	+	0.546598i	$0.184078\pi$
$548$		0			0
$549$	−5.98737	−	5.98737i	−0.255535	−	0.255535i
$550$		0			0
$551$		−	0.590346i		−	0.0251496i
$552$		0			0
$553$			32.4004i			1.37780i
$554$		0			0
$555$	−13.9365	−	13.9365i	−0.591570	−	0.591570i
$556$		0			0
$557$	−4.29337	+	4.29337i	−0.181916	+	0.181916i	−0.792190	−	0.610274i	$-0.791059\pi$
$557$	−4.29337	+	4.29337i	−0.181916	+	0.181916i	0.610274	+	0.792190i	$0.291059\pi$
$558$		0			0
$559$	21.4609			0.907701
$560$		0			0
$561$	−0.571533			−0.0241301
$562$		0			0
$563$	10.0801	−	10.0801i	0.424825	−	0.424825i	−0.462036	−	0.886861i	$-0.652881\pi$
$563$	10.0801	−	10.0801i	0.424825	−	0.424825i	0.886861	+	0.462036i	$0.152881\pi$
$564$		0			0
$565$	−50.6187	−	50.6187i	−2.12954	−	2.12954i
$566$		0			0
$567$			2.15894i			0.0906670i
$568$		0			0
$569$		−	32.5018i		−	1.36255i	−0.732029	−	0.681274i	$-0.761426\pi$
$569$		−	32.5018i		−	1.36255i	0.732029	−	0.681274i	$-0.238574\pi$
$570$		0			0
$571$	9.17157	+	9.17157i	0.383818	+	0.383818i	0.872476	−	0.488657i	$-0.162513\pi$
$571$	9.17157	+	9.17157i	0.383818	+	0.383818i	−0.488657	+	0.872476i	$0.662513\pi$
$572$		0			0
$573$	−14.7101	+	14.7101i	−0.614522	+	0.614522i
$574$		0			0
$575$	26.6559			1.11163
$576$		0			0
$577$	11.7536			0.489308			0.244654	−	0.969611i	$-0.421326\pi$
$577$	11.7536			0.489308			0.244654	+	0.969611i	$0.421326\pi$
$578$		0			0
$579$	−10.0023	+	10.0023i	−0.415681	+	0.415681i
$580$		0			0
$581$	−21.8395	−	21.8395i	−0.906053	−	0.906053i
$582$		0			0
$583$		−	27.0192i		−	1.11902i
$584$		0			0
$585$			7.43208i			0.307279i
$586$		0			0
$587$	−6.46002	−	6.46002i	−0.266634	−	0.266634i	0.561109	−	0.827742i	$-0.310375\pi$
$587$	−6.46002	−	6.46002i	−0.266634	−	0.266634i	−0.827742	+	0.561109i	$0.810375\pi$
$588$		0			0
$589$	0.292621	−	0.292621i	0.0120572	−	0.0120572i
$590$		0			0
$591$	3.43463			0.141282
$592$		0			0
$593$	5.49270			0.225558			0.112779	−	0.993620i	$-0.464025\pi$
$593$	5.49270			0.225558			0.112779	+	0.993620i	$0.464025\pi$
$594$		0			0
$595$	1.30324	−	1.30324i	0.0534278	−	0.0534278i
$596$		0			0
$597$	0.216503	+	0.216503i	0.00886089	+	0.00886089i
$598$		0			0
$599$		−	36.4348i		−	1.48868i	−0.667799	−	0.744342i	$-0.732763\pi$
$599$		−	36.4348i		−	1.48868i	0.667799	−	0.744342i	$-0.267237\pi$
$600$		0			0
$601$		−	9.97474i		−	0.406878i	−0.979088	−	0.203439i	$-0.934788\pi$
$601$		−	9.97474i		−	0.406878i	0.979088	−	0.203439i	$-0.0652119\pi$
$602$		0			0
$603$	−10.4243	−	10.4243i	−0.424510	−	0.424510i
$604$		0			0
$605$	−12.1786	+	12.1786i	−0.495131	+	0.495131i
$606$		0			0
$607$	−4.51900			−0.183421			−0.0917103	−	0.995786i	$-0.529233\pi$
$607$	−4.51900			−0.183421			−0.0917103	+	0.995786i	$0.529233\pi$
$608$		0			0
$609$	−5.67016			−0.229766
$610$		0			0
$611$	3.91375	−	3.91375i	0.158333	−	0.158333i
$612$		0			0
$613$	−8.43692	−	8.43692i	−0.340764	−	0.340764i	0.515890	−	0.856655i	$-0.327461\pi$
$613$	−8.43692	−	8.43692i	−0.340764	−	0.340764i	−0.856655	+	0.515890i	$0.827461\pi$
$614$		0			0
$615$		−	22.3380i		−	0.900757i
$616$		0			0
$617$			32.1201i			1.29311i	0.762869	+	0.646554i	$0.223790\pi$
$617$			32.1201i			1.29311i	−0.762869	+	0.646554i	$0.776210\pi$
$618$		0			0
$619$	−15.0412	−	15.0412i	−0.604559	−	0.604559i	0.336960	−	0.941519i	$-0.390601\pi$
$619$	−15.0412	−	15.0412i	−0.604559	−	0.604559i	−0.941519	+	0.336960i	$0.890601\pi$
$620$		0			0
$621$	2.00000	−	2.00000i	0.0802572	−	0.0802572i
$622$		0			0
$623$	−3.08398			−0.123557
$624$		0			0
$625$	−16.6958			−0.667833
$626$		0			0
$627$	−0.404135	+	0.404135i	−0.0161396	+	0.0161396i
$628$		0			0
$629$	0.824818	+	0.824818i	0.0328876	+	0.0328876i
$630$		0			0
$631$			36.4685i			1.45179i	0.687807	+	0.725894i	$0.258574\pi$
$631$			36.4685i			1.45179i	−0.687807	+	0.725894i	$0.741426\pi$
$632$		0			0
$633$		−	10.2284i		−	0.406542i
$634$		0			0
$635$	−10.2475	−	10.2475i	−0.406659	−	0.406659i
$636$		0			0
$637$	3.23648	−	3.23648i	0.128234	−	0.128234i
$638$		0			0
$639$	4.31788			0.170813
$640$		0			0
$641$	14.0036			0.553109			0.276555	−	0.960998i	$-0.410807\pi$
$641$	14.0036			0.553109			0.276555	+	0.960998i	$0.410807\pi$
$642$		0			0
$643$	−16.6034	+	16.6034i	−0.654774	+	0.654774i	−0.954139	−	0.299365i	$-0.903225\pi$
$643$	−16.6034	+	16.6034i	−0.654774	+	0.654774i	0.299365	+	0.954139i	$0.403225\pi$
$644$		0			0
$645$	29.4522	+	29.4522i	1.15968	+	1.15968i
$646$		0			0
$647$			12.1908i			0.479270i	0.970863	+	0.239635i	$0.0770277\pi$
$647$			12.1908i			0.479270i	−0.970863	+	0.239635i	$0.922972\pi$
$648$		0			0
$649$			14.3835i			0.564600i
$650$		0			0
$651$	−2.81056	−	2.81056i	−0.110155	−	0.110155i
$652$		0			0
$653$	0.983270	−	0.983270i	0.0384783	−	0.0384783i	−0.687606	−	0.726084i	$-0.741338\pi$
$653$	0.983270	−	0.983270i	0.0384783	−	0.0384783i	0.726084	+	0.687606i	$0.241338\pi$
$654$		0			0
$655$	−4.12198			−0.161059
$656$		0			0
$657$	−5.97474			−0.233097
$658$		0			0
$659$	18.0559	−	18.0559i	0.703357	−	0.703357i	−0.261772	−	0.965130i	$-0.584307\pi$
$659$	18.0559	−	18.0559i	0.703357	−	0.703357i	0.965130	+	0.261772i	$0.0843069\pi$
$660$		0			0
$661$	−4.55890	−	4.55890i	−0.177321	−	0.177321i	0.612866	−	0.790187i	$-0.290017\pi$
$661$	−4.55890	−	4.55890i	−0.177321	−	0.177321i	−0.790187	+	0.612866i	$0.790017\pi$
$662$		0			0
$663$		−	0.439861i		−	0.0170828i
$664$		0			0
$665$		−	1.84307i		−	0.0714710i
$666$		0			0
$667$	5.25272	+	5.25272i	0.203386	+	0.203386i
$668$		0			0
$669$	−1.21557	+	1.21557i	−0.0469968	+	0.0469968i
$670$		0			0
$671$	−21.5298			−0.831148
$672$		0			0
$673$	−10.8569			−0.418504			−0.209252	−	0.977862i	$-0.567103\pi$
$673$	−10.8569			−0.418504			−0.209252	+	0.977862i	$0.567103\pi$
$674$		0			0
$675$	−6.66398	+	6.66398i	−0.256497	+	0.256497i
$676$		0			0
$677$	23.7066	+	23.7066i	0.911120	+	0.911120i	0.996360	−	0.0852405i	$-0.0271659\pi$
$677$	23.7066	+	23.7066i	0.911120	+	0.911120i	−0.0852405	+	0.996360i	$0.527166\pi$
$678$		0			0
$679$			35.4045i			1.35870i
$680$		0			0
$681$		−	14.3059i		−	0.548204i
$682$		0			0
$683$	17.8337	+	17.8337i	0.682386	+	0.682386i	0.960537	−	0.278151i	$-0.0897217\pi$
$683$	17.8337	+	17.8337i	0.682386	+	0.682386i	−0.278151	+	0.960537i	$0.589722\pi$
$684$		0			0
$685$	14.2605	−	14.2605i	0.544866	−	0.544866i
$686$		0			0
$687$	16.9981			0.648519
$688$		0			0
$689$	20.7945			0.792205
$690$		0			0
$691$	−10.8557	+	10.8557i	−0.412970	+	0.412970i	−0.882772	−	0.469802i	$-0.844325\pi$
$691$	−10.8557	+	10.8557i	−0.412970	+	0.412970i	0.469802	+	0.882772i	$0.344325\pi$
$692$		0			0
$693$	3.88163	+	3.88163i	0.147451	+	0.147451i
$694$		0			0
$695$			47.0907i			1.78625i
$696$		0			0
$697$			1.32206i			0.0500765i
$698$		0			0
$699$	9.45963	+	9.45963i	0.357796	+	0.357796i
$700$		0			0
$701$	−6.08875	+	6.08875i	−0.229969	+	0.229969i	−0.812680	−	0.582711i	$-0.801992\pi$
$701$	−6.08875	+	6.08875i	−0.229969	+	0.229969i	0.582711	+	0.812680i	$0.301992\pi$
$702$		0			0
$703$	1.16647			0.0439942
$704$		0			0
$705$	10.7422			0.404574
$706$		0			0
$707$	0.176805	−	0.176805i	0.00664943	−	0.00664943i
$708$		0			0
$709$	22.8836	+	22.8836i	0.859413	+	0.859413i	0.991269	−	0.131856i	$-0.0420936\pi$
$709$	22.8836	+	22.8836i	0.859413	+	0.859413i	−0.131856	+	0.991269i	$0.542094\pi$
$710$		0			0
$711$			15.0075i			0.562826i
$712$		0			0
$713$			5.20730i			0.195015i
$714$		0			0
$715$	13.3624	+	13.3624i	0.499724	+	0.499724i
$716$		0			0
$717$	9.45223	−	9.45223i	0.353000	−	0.353000i
$718$		0			0
$719$	1.46744			0.0547262			0.0273631	−	0.999626i	$-0.491289\pi$
$719$	1.46744			0.0547262			0.0273631	+	0.999626i	$0.491289\pi$
$720$		0			0
$721$	−28.8233			−1.07344
$722$		0			0
$723$	−0.149535	+	0.149535i	−0.00556126	+	0.00556126i
$724$		0			0
$725$	−17.5020	−	17.5020i	−0.650008	−	0.650008i
$726$		0			0
$727$		−	15.3928i		−	0.570889i	−0.958395	−	0.285445i	$-0.907859\pi$
$727$		−	15.3928i		−	0.570889i	0.958395	−	0.285445i	$-0.0921412\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−1.74311	−	1.74311i	−0.0644711	−	0.0644711i
$732$		0			0
$733$	−12.4185	+	12.4185i	−0.458688	+	0.458688i	−0.898225	−	0.439536i	$-0.855143\pi$
$733$	−12.4185	+	12.4185i	−0.458688	+	0.458688i	0.439536	+	0.898225i	$0.355143\pi$
$734$		0			0
$735$	8.88325			0.327664
$736$		0			0
$737$	−37.4844			−1.38075
$738$		0			0
$739$	14.6559	−	14.6559i	0.539127	−	0.539127i	−0.384146	−	0.923273i	$-0.625504\pi$
$739$	14.6559	−	14.6559i	0.539127	−	0.539127i	0.923273	+	0.384146i	$0.125504\pi$
$740$		0			0
$741$	−0.311029	−	0.311029i	−0.0114259	−	0.0114259i
$742$		0			0
$743$			31.7821i			1.16597i	0.812482	+	0.582986i	$0.198116\pi$
$743$			31.7821i			1.16597i	−0.812482	+	0.582986i	$0.801884\pi$
$744$		0			0
$745$			5.52518i			0.202427i
$746$		0			0
$747$	−10.1158	−	10.1158i	−0.370118	−	0.370118i
$748$		0			0
$749$	15.7127	−	15.7127i	0.574131	−	0.574131i
$750$		0			0
$751$	−29.7594			−1.08594			−0.542968	−	0.839753i	$-0.682699\pi$
$751$	−29.7594			−1.08594			−0.542968	+	0.839753i	$0.682699\pi$
$752$		0			0
$753$	14.7555			0.537720
$754$		0			0
$755$	5.47036	−	5.47036i	0.199087	−	0.199087i
$756$		0			0
$757$	15.6355	+	15.6355i	0.568282	+	0.568282i	0.931647	−	0.363365i	$-0.118372\pi$
$757$	15.6355	+	15.6355i	0.568282	+	0.568282i	−0.363365	+	0.931647i	$0.618372\pi$
$758$		0			0
$759$		−	7.19173i		−	0.261043i
$760$		0			0
$761$		−	4.55957i		−	0.165284i	−0.996579	−	0.0826422i	$-0.973664\pi$
$761$		−	4.55957i		−	0.165284i	0.996579	−	0.0826422i	$-0.0263359\pi$
$762$		0			0
$763$	15.2002	+	15.2002i	0.550284	+	0.550284i
$764$		0			0
$765$	0.603650	−	0.603650i	0.0218250	−	0.0218250i
$766$		0			0
$767$	−11.0698			−0.399706
$768$		0			0
$769$	36.5794			1.31909			0.659543	−	0.751667i	$-0.270750\pi$
$769$	36.5794			1.31909			0.659543	+	0.751667i	$0.270750\pi$
$770$		0			0
$771$	0.524797	−	0.524797i	0.0189001	−	0.0189001i
$772$		0			0
$773$	−18.7108	−	18.7108i	−0.672981	−	0.672981i	0.285421	−	0.958402i	$-0.407867\pi$
$773$	−18.7108	−	18.7108i	−0.672981	−	0.672981i	−0.958402	+	0.285421i	$0.907867\pi$
$774$		0			0
$775$		−	17.3507i		−	0.623255i
$776$		0			0
$777$		−	11.2037i		−	0.401930i
$778$		0			0
$779$	0.934836	+	0.934836i	0.0334940	+	0.0334940i
$780$		0			0
$781$	7.76326	−	7.76326i	0.277791	−	0.277791i
$782$		0			0
$783$	−2.62636			−0.0938584
$784$		0			0
$785$	−32.7302			−1.16819
$786$		0			0
$787$	−13.3759	+	13.3759i	−0.476801	+	0.476801i	−0.904107	−	0.427306i	$-0.859463\pi$
$787$	−13.3759	+	13.3759i	−0.476801	+	0.476801i	0.427306	+	0.904107i	$0.359463\pi$
$788$		0			0
$789$	3.87802	+	3.87802i	0.138061	+	0.138061i
$790$		0			0
$791$		−	40.6930i		−	1.44688i
$792$		0			0
$793$		−	16.5697i		−	0.588406i
$794$		0			0
$795$	28.5376	+	28.5376i	1.01212	+	1.01212i
$796$		0			0
$797$	−33.8043	+	33.8043i	−1.19741	+	1.19741i	−0.222471	+	0.974939i	$0.571412\pi$
$797$	−33.8043	+	33.8043i	−1.19741	+	1.19741i	−0.974939	+	0.222471i	$0.928588\pi$
$798$		0			0
$799$	−0.635767			−0.0224918
$800$		0			0
$801$	−1.42847			−0.0504724
$802$		0			0
$803$	−10.7422	+	10.7422i	−0.379083	+	0.379083i
$804$		0			0
$805$	16.3990	+	16.3990i	0.577990	+	0.577990i
$806$		0			0
$807$			20.4694i			0.720558i
$808$		0			0
$809$		−	29.9862i		−	1.05426i	−0.849785	−	0.527129i	$-0.823268\pi$
$809$		−	29.9862i		−	1.05426i	0.849785	−	0.527129i	$-0.176732\pi$
$810$		0			0
$811$	8.05388	+	8.05388i	0.282810	+	0.282810i	0.834229	−	0.551419i	$-0.185913\pi$
$811$	8.05388	+	8.05388i	0.282810	+	0.282810i	−0.551419	+	0.834229i	$0.685913\pi$
$812$		0			0
$813$	−9.92563	+	9.92563i	−0.348107	+	0.348107i
$814$		0			0
$815$	18.4600			0.646626
$816$		0			0
$817$	−2.46512			−0.0862438
$818$		0			0
$819$	−2.98737	+	2.98737i	−0.104387	+	0.104387i
$820$		0			0
$821$	13.9250	+	13.9250i	0.485984	+	0.485984i	0.907036	−	0.421052i	$-0.138339\pi$
$821$	13.9250	+	13.9250i	0.485984	+	0.485984i	−0.421052	+	0.907036i	$0.638339\pi$
$822$		0			0
$823$			22.4666i			0.783137i	0.920149	+	0.391568i	$0.128067\pi$
$823$			22.4666i			0.783137i	−0.920149	+	0.391568i	$0.871933\pi$
$824$		0			0
$825$			23.9628i			0.834277i
$826$		0			0
$827$	−7.63159	−	7.63159i	−0.265376	−	0.265376i	0.561858	−	0.827234i	$-0.310087\pi$
$827$	−7.63159	−	7.63159i	−0.265376	−	0.265376i	−0.827234	+	0.561858i	$0.810087\pi$
$828$		0			0
$829$	−32.4860	+	32.4860i	−1.12828	+	1.12828i	−0.137828	+	0.990456i	$0.544012\pi$
$829$	−32.4860	+	32.4860i	−1.12828	+	1.12828i	−0.990456	+	0.137828i	$0.955988\pi$
$830$		0			0
$831$	−13.4211			−0.465572
$832$		0			0
$833$	−0.525748			−0.0182161
$834$		0			0
$835$	58.2824	−	58.2824i	2.01695	−	2.01695i
$836$		0			0
$837$	−1.30182	−	1.30182i	−0.0449976	−	0.0449976i
$838$		0			0
$839$		−	22.9142i		−	0.791085i	−0.918448	−	0.395542i	$-0.870557\pi$
$839$		−	22.9142i		−	0.791085i	0.918448	−	0.395542i	$-0.129443\pi$
$840$		0			0
$841$			22.1022i			0.762146i
$842$		0			0
$843$	−2.75318	−	2.75318i	−0.0948247	−	0.0948247i
$844$		0			0
$845$	24.6282	−	24.6282i	0.847235	−	0.847235i
$846$		0			0
$847$	−9.79053			−0.336407
$848$		0			0
$849$	−17.6569			−0.605982
$850$		0			0
$851$	−10.3789	+	10.3789i	−0.355783	+	0.355783i
$852$		0			0
$853$	38.9424	+	38.9424i	1.33336	+	1.33336i	0.902344	+	0.431018i	$0.141845\pi$
$853$	38.9424	+	38.9424i	1.33336	+	1.33336i	0.431018	+	0.902344i	$0.358155\pi$
$854$		0			0
$855$		−	0.853690i		−	0.0291956i
$856$		0			0
$857$		−	1.79079i		−	0.0611723i	−0.999532	−	0.0305861i	$-0.990263\pi$
$857$		−	1.79079i		−	0.0611723i	0.999532	−	0.0305861i	$-0.00973739\pi$
$858$		0			0
$859$	−18.0643	−	18.0643i	−0.616347	−	0.616347i	0.328245	−	0.944593i	$-0.393543\pi$
$859$	−18.0643	−	18.0643i	−0.616347	−	0.616347i	−0.944593	+	0.328245i	$0.893543\pi$
$860$		0			0
$861$	8.97891	−	8.97891i	0.306001	−	0.306001i
$862$		0			0
$863$	−42.1150			−1.43361			−0.716806	−	0.697273i	$-0.754397\pi$
$863$	−42.1150			−1.43361			−0.716806	+	0.697273i	$0.754397\pi$
$864$		0			0
$865$	46.9784			1.59731
$866$		0			0
$867$	11.9851	−	11.9851i	0.407035	−	0.407035i
$868$		0			0
$869$	26.9825	+	26.9825i	0.915319	+	0.915319i
$870$		0			0
$871$		−	28.8486i		−	0.977497i
$872$		0			0
$873$			16.3990i			0.555023i
$874$		0			0
$875$	−25.6517	−	25.6517i	−0.867187	−	0.867187i
$876$		0			0
$877$	0.714491	−	0.714491i	0.0241267	−	0.0241267i	−0.694941	−	0.719067i	$-0.744569\pi$
$877$	0.714491	−	0.714491i	0.0241267	−	0.0241267i	0.719067	+	0.694941i	$0.244569\pi$
$878$		0			0
$879$	15.7759			0.532108
$880$		0			0
$881$	−44.3972			−1.49578			−0.747889	−	0.663823i	$-0.768933\pi$
$881$	−44.3972			−1.49578			−0.747889	+	0.663823i	$0.768933\pi$
$882$		0			0
$883$	−1.28968	+	1.28968i	−0.0434013	+	0.0434013i	−0.728474	−	0.685073i	$-0.759770\pi$
$883$	−1.28968	+	1.28968i	−0.0434013	+	0.0434013i	0.685073	+	0.728474i	$0.259770\pi$
$884$		0			0
$885$	−15.1917	−	15.1917i	−0.510664	−	0.510664i
$886$		0			0
$887$			4.38532i			0.147245i	0.997286	+	0.0736223i	$0.0234559\pi$
$887$			4.38532i			0.147245i	−0.997286	+	0.0736223i	$0.976544\pi$
$888$		0			0
$889$		−	8.23808i		−	0.276296i
$890$		0			0
$891$	1.79793	+	1.79793i	0.0602330	+	0.0602330i
$892$		0			0
$893$	−0.449555	+	0.449555i	−0.0150438	+	0.0150438i
$894$		0			0
$895$	44.2128			1.47787
$896$		0			0
$897$	5.53488			0.184804
$898$		0			0
$899$	3.41906	−	3.41906i	0.114032	−	0.114032i
$900$		0			0
$901$	−1.68897	−	1.68897i	−0.0562678	−	0.0562678i
$902$		0			0
$903$			23.6770i			0.787922i
$904$		0			0
$905$		−	36.1082i		−	1.20028i
$906$		0			0
$907$	2.87261	+	2.87261i	0.0953835	+	0.0953835i	0.753188	−	0.657805i	$-0.228515\pi$
$907$	2.87261	+	2.87261i	0.0953835	+	0.0953835i	−0.657805	+	0.753188i	$0.728515\pi$
$908$		0			0
$909$	0.0818942	−	0.0818942i	0.00271626	−	0.00271626i
$910$		0			0
$911$	−42.3784			−1.40406			−0.702029	−	0.712149i	$-0.747722\pi$
$911$	−42.3784			−1.40406			−0.702029	+	0.712149i	$0.747722\pi$
$912$		0			0
$913$	−36.3751			−1.20384
$914$		0			0
$915$	22.7396	−	22.7396i	0.751749	−	0.751749i
$916$		0			0
$917$	−1.65685	−	1.65685i	−0.0547141	−	0.0547141i
$918$		0			0
$919$			44.8603i			1.47980i	0.672715	+	0.739902i	$0.265128\pi$
$919$			44.8603i			1.47980i	−0.672715	+	0.739902i	$0.734872\pi$
$920$		0			0
$921$			7.64129i			0.251789i
$922$		0			0
$923$	5.97474	+	5.97474i	0.196661	+	0.196661i
$924$		0			0
$925$	34.5823	−	34.5823i	1.13706	−	1.13706i
$926$		0			0
$927$	−13.3507			−0.438494
$928$		0			0
$929$	−2.96695			−0.0973426			−0.0486713	−	0.998815i	$-0.515499\pi$
$929$	−2.96695			−0.0973426			−0.0486713	+	0.998815i	$0.515499\pi$
$930$		0			0
$931$	−0.371760	+	0.371760i	−0.0121839	+	0.0121839i
$932$		0			0
$933$	−17.0853	−	17.0853i	−0.559348	−	0.559348i
$934$		0			0
$935$		−	2.17064i		−	0.0709876i
$936$		0			0
$937$		−	54.7669i		−	1.78916i	−0.446910	−	0.894579i	$-0.647476\pi$
$937$		−	54.7669i		−	1.78916i	0.446910	−	0.894579i	$-0.352524\pi$
$938$		0			0
$939$	11.7454	+	11.7454i	0.383297	+	0.383297i
$940$		0			0
$941$	−6.29012	+	6.29012i	−0.205052	+	0.205052i	−0.802161	−	0.597108i	$-0.796316\pi$
$941$	−6.29012	+	6.29012i	−0.205052	+	0.205052i	0.597108	+	0.802161i	$0.296316\pi$
$942$		0			0
$943$	−16.6358			−0.541735
$944$		0			0
$945$	−8.19951			−0.266730
$946$		0			0
$947$	11.2105	−	11.2105i	0.364294	−	0.364294i	−0.501097	−	0.865391i	$-0.667070\pi$
$947$	11.2105	−	11.2105i	0.364294	−	0.364294i	0.865391	+	0.501097i	$0.167070\pi$
$948$		0			0
$949$	−8.26736	−	8.26736i	−0.268370	−	0.268370i
$950$		0			0
$951$			2.56213i			0.0830826i
$952$		0			0
$953$		−	30.2807i		−	0.980887i	−0.871473	−	0.490443i	$-0.836835\pi$
$953$		−	30.2807i		−	0.980887i	0.871473	−	0.490443i	$-0.163165\pi$
$954$		0			0
$955$	−55.8678	−	55.8678i	−1.80784	−	1.80784i
$956$		0			0
$957$	−4.72202	+	4.72202i	−0.152641	+	0.152641i
$958$		0			0
$959$	11.4642			0.370198
$960$		0			0
$961$	−27.6105			−0.890661
$962$		0			0
$963$	7.27798	−	7.27798i	0.234530	−	0.234530i
$964$		0			0
$965$	−37.9880	−	37.9880i	−1.22288	−	1.22288i
$966$		0			0
$967$			10.5273i			0.338537i	0.985570	+	0.169268i	$0.0541405\pi$
$967$			10.5273i			0.338537i	−0.985570	+	0.169268i	$0.945860\pi$
$968$		0			0
$969$			0.0505249i			0.00162309i
$970$		0			0
$971$	−27.3685	−	27.3685i	−0.878298	−	0.878298i	0.115060	−	0.993358i	$-0.463294\pi$
$971$	−27.3685	−	27.3685i	−0.878298	−	0.878298i	−0.993358	+	0.115060i	$0.963294\pi$
$972$		0			0
$973$	−18.9284	+	18.9284i	−0.606816	+	0.606816i
$974$		0			0
$975$	−18.4422			−0.590622
$976$		0			0
$977$	−16.9009			−0.540706			−0.270353	−	0.962761i	$-0.587140\pi$
$977$	−16.9009			−0.540706			−0.270353	+	0.962761i	$0.587140\pi$
$978$		0			0
$979$	−2.56829	+	2.56829i	−0.0820828	+	0.0820828i
$980$		0			0
$981$	7.04057	+	7.04057i	0.224788	+	0.224788i
$982$		0			0
$983$		−	10.0798i		−	0.321496i	−0.986995	−	0.160748i	$-0.948609\pi$
$983$		−	10.0798i		−	0.321496i	0.986995	−	0.160748i	$-0.0513906\pi$
$984$		0			0
$985$			13.0445i			0.415632i
$986$		0			0
$987$	4.31788	+	4.31788i	0.137440	+	0.137440i
$988$		0			0
$989$	21.9339	−	21.9339i	0.697458	−	0.697458i
$990$		0			0
$991$	42.3446			1.34512			0.672561	−	0.740042i	$-0.265194\pi$
$991$	42.3446			1.34512			0.672561	+	0.740042i	$0.265194\pi$
$992$		0			0
$993$	19.1275			0.606993
$994$		0			0
$995$	−0.822265	+	0.822265i	−0.0260676	+	0.0260676i
$996$		0			0
$997$	−33.6676	−	33.6676i	−1.06626	−	1.06626i	−0.997643	−	0.0686216i	$-0.978140\pi$
$997$	−33.6676	−	33.6676i	−1.06626	−	1.06626i	−0.0686216	−	0.997643i	$-0.521860\pi$
$998$		0			0
$999$		−	5.18944i		−	0.164186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.j.a.49.1		8
3.2	odd	2		576.2.k.b.433.4		8
4.3	odd	2		48.2.j.a.37.3	yes	8
8.3	odd	2		384.2.j.b.97.2		8
8.5	even	2		384.2.j.a.97.4		8
12.11	even	2		144.2.k.b.37.2		8
16.3	odd	4		48.2.j.a.13.3	✓	8
16.5	even	4		384.2.j.a.289.4		8
16.11	odd	4		384.2.j.b.289.2		8
16.13	even	4	inner	192.2.j.a.145.1		8
24.5	odd	2		1152.2.k.f.865.1		8
24.11	even	2		1152.2.k.c.865.1		8
32.3	odd	8		3072.2.a.t.1.4		4
32.5	even	8		3072.2.d.i.1537.1		8
32.11	odd	8		3072.2.d.f.1537.4		8
32.13	even	8		3072.2.a.o.1.1		4
32.19	odd	8		3072.2.a.i.1.1		4
32.21	even	8		3072.2.d.i.1537.8		8
32.27	odd	8		3072.2.d.f.1537.5		8
32.29	even	8		3072.2.a.n.1.4		4
48.5	odd	4		1152.2.k.f.289.1		8
48.11	even	4		1152.2.k.c.289.1		8
48.29	odd	4		576.2.k.b.145.4		8
48.35	even	4		144.2.k.b.109.2		8
96.29	odd	8		9216.2.a.x.1.1		4
96.35	even	8		9216.2.a.y.1.1		4
96.77	odd	8		9216.2.a.bn.1.4		4
96.83	even	8		9216.2.a.bo.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.3	✓	8	16.3	odd	4
48.2.j.a.37.3	yes	8	4.3	odd	2
144.2.k.b.37.2		8	12.11	even	2
144.2.k.b.109.2		8	48.35	even	4
192.2.j.a.49.1		8	1.1	even	1	trivial
192.2.j.a.145.1		8	16.13	even	4	inner
384.2.j.a.97.4		8	8.5	even	2
384.2.j.a.289.4		8	16.5	even	4
384.2.j.b.97.2		8	8.3	odd	2
384.2.j.b.289.2		8	16.11	odd	4
576.2.k.b.145.4		8	48.29	odd	4
576.2.k.b.433.4		8	3.2	odd	2
1152.2.k.c.289.1		8	48.11	even	4
1152.2.k.c.865.1		8	24.11	even	2
1152.2.k.f.289.1		8	48.5	odd	4
1152.2.k.f.865.1		8	24.5	odd	2
3072.2.a.i.1.1		4	32.19	odd	8
3072.2.a.n.1.4		4	32.29	even	8
3072.2.a.o.1.1		4	32.13	even	8
3072.2.a.t.1.4		4	32.3	odd	8
3072.2.d.f.1537.4		8	32.11	odd	8
3072.2.d.f.1537.5		8	32.27	odd	8
3072.2.d.i.1537.1		8	32.5	even	8
3072.2.d.i.1537.8		8	32.21	even	8
9216.2.a.x.1.1		4	96.29	odd	8
9216.2.a.y.1.1		4	96.35	even	8
9216.2.a.bn.1.4		4	96.77	odd	8
9216.2.a.bo.1.4		4	96.83	even	8

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.68554 - 2.68554i) q^{5} -2.15894i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.68554 - 2.68554i) q^{5} -2.15894i q^{7} -1.00000i q^{9} +(-1.79793 - 1.79793i) q^{11} +(1.38372 - 1.38372i) q^{13} +3.79793 q^{15} -0.224777 q^{17} +(-0.158942 + 0.158942i) q^{19} +(1.52660 + 1.52660i) q^{21} -2.82843i q^{23} +9.42429i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.85712 + 1.85712i) q^{29} -1.84106 q^{31} +2.54266 q^{33} +(-5.79793 + 5.79793i) q^{35} +(-3.66949 - 3.66949i) q^{37} +1.95687i q^{39} -5.88163i q^{41} +(7.75481 + 7.75481i) q^{43} +(-2.68554 + 2.68554i) q^{45} +2.82843 q^{47} +2.33897 q^{49} +(0.158942 - 0.158942i) q^{51} +(7.51397 + 7.51397i) q^{53} +9.65685i q^{55} -0.224777i q^{57} +(-4.00000 - 4.00000i) q^{59} +(5.98737 - 5.98737i) q^{61} -2.15894 q^{63} -7.43208 q^{65} +(10.4243 - 10.4243i) q^{67} +(2.00000 + 2.00000i) q^{69} +4.31788i q^{71} -5.97474i q^{73} +(-6.66398 - 6.66398i) q^{75} +(-3.88163 + 3.88163i) q^{77} -15.0075 q^{79} -1.00000 q^{81} +(10.1158 - 10.1158i) q^{83} +(0.603650 + 0.603650i) q^{85} -2.62636i q^{87} -1.42847i q^{89} +(-2.98737 - 2.98737i) q^{91} +(1.30182 - 1.30182i) q^{93} +0.853690 q^{95} -16.3990 q^{97} +(-1.79793 + 1.79793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{11} + 8 q^{15} + 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{43} - 8 q^{49} - 8 q^{51} + 16 q^{53} - 32 q^{59} + 16 q^{61} - 8 q^{63} - 16 q^{65} + 16 q^{67} + 16 q^{69} - 16 q^{75} + 16 q^{77} + 24 q^{79} - 8 q^{81} + 40 q^{83} - 16 q^{85} + 8 q^{91} + 48 q^{95} + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^11 + 8 * q^15 + 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^43 - 8 * q^49 - 8 * q^51 + 16 * q^53 - 32 * q^59 + 16 * q^61 - 8 * q^63 - 16 * q^65 + 16 * q^67 + 16 * q^69 - 16 * q^75 + 16 * q^77 + 24 * q^79 - 8 * q^81 + 40 * q^83 - 16 * q^85 + 8 * q^91 + 48 * q^95 + 8 * q^99

Introduction

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