LMFDB - Embedded newform 1344.2.s.c.239.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.12
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0806676 - 1.73017i) q^{3} +(-1.66193 - 1.66193i) q^{5} +1.00000 q^{7} +(-2.98699 - 0.279137i) q^{9} +O(q^{10})$	\(q+(0.0806676 - 1.73017i) q^{3} +(-1.66193 - 1.66193i) q^{5} +1.00000 q^{7} +(-2.98699 - 0.279137i) q^{9} +(-3.32524 + 3.32524i) q^{11} +(-0.938005 - 0.938005i) q^{13} +(-3.00950 + 2.74137i) q^{15} -0.811469i q^{17} +(-0.974336 + 0.974336i) q^{19} +(0.0806676 - 1.73017i) q^{21} +7.19240i q^{23} +0.524053i q^{25} +(-0.723909 + 5.14548i) q^{27} +(2.21393 - 2.21393i) q^{29} +6.74878i q^{31} +(5.48500 + 6.02148i) q^{33} +(-1.66193 - 1.66193i) q^{35} +(-3.62622 + 3.62622i) q^{37} +(-1.69858 + 1.54724i) q^{39} -6.63194 q^{41} +(-8.58019 - 8.58019i) q^{43} +(4.50027 + 5.42808i) q^{45} +11.4602 q^{47} +1.00000 q^{49} +(-1.40398 - 0.0654593i) q^{51} +(-5.01755 - 5.01755i) q^{53} +11.0527 q^{55} +(1.60717 + 1.76437i) q^{57} +(3.36018 - 3.36018i) q^{59} +(9.07854 + 9.07854i) q^{61} +(-2.98699 - 0.279137i) q^{63} +3.11781i q^{65} +(-2.30161 + 2.30161i) q^{67} +(12.4441 + 0.580193i) q^{69} +1.63685i q^{71} +1.89680i q^{73} +(0.906702 + 0.0422741i) q^{75} +(-3.32524 + 3.32524i) q^{77} +13.3142i q^{79} +(8.84416 + 1.66756i) q^{81} +(-5.35833 - 5.35833i) q^{83} +(-1.34861 + 1.34861i) q^{85} +(-3.65188 - 4.00907i) q^{87} +7.32588 q^{89} +(-0.938005 - 0.938005i) q^{91} +(11.6766 + 0.544408i) q^{93} +3.23857 q^{95} -19.2019 q^{97} +(10.8606 - 9.00425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.0806676	−	1.73017i	0.0465734	−	0.998915i
$3$	0.0806676	−	1.73017i	0.0465734	−	0.998915i
$4$		0			0
$5$	−1.66193	−	1.66193i	−0.743240	−	0.743240i	0.229960	−	0.973200i	$-0.426140\pi$
$5$	−1.66193	−	1.66193i	−0.743240	−	0.743240i	−0.973200	+	0.229960i	$0.926140\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	−2.98699	−	0.279137i	−0.995662	−	0.0930458i
$10$		0			0
$11$	−3.32524	+	3.32524i	−1.00260	+	1.00260i	−0.00260141	+	0.999997i	$0.500828\pi$
$11$	−3.32524	+	3.32524i	−1.00260	+	1.00260i	−0.999997	+	0.00260141i	$0.999172\pi$
$12$		0			0
$13$	−0.938005	−	0.938005i	−0.260156	−	0.260156i	0.564961	−	0.825117i	$-0.308891\pi$
$13$	−0.938005	−	0.938005i	−0.260156	−	0.260156i	−0.825117	+	0.564961i	$0.808891\pi$
$14$		0			0
$15$	−3.00950	+	2.74137i	−0.777048	+	0.707818i
$16$		0			0
$17$		−	0.811469i		−	0.196810i	−0.995146	−	0.0984051i	$-0.968626\pi$
$17$		−	0.811469i		−	0.196810i	0.995146	−	0.0984051i	$-0.0313741\pi$
$18$		0			0
$19$	−0.974336	+	0.974336i	−0.223528	+	0.223528i	−0.809982	−	0.586454i	$-0.800523\pi$
$19$	−0.974336	+	0.974336i	−0.223528	+	0.223528i	0.586454	+	0.809982i	$0.300523\pi$
$20$		0			0
$21$	0.0806676	−	1.73017i	0.0176031	−	0.377554i
$22$		0			0
$23$			7.19240i			1.49972i	0.661598	+	0.749859i	$0.269879\pi$
$23$			7.19240i			1.49972i	−0.661598	+	0.749859i	$0.730121\pi$
$24$		0			0
$25$			0.524053i			0.104811i
$26$		0			0
$27$	−0.723909	+	5.14548i	−0.139316	+	0.990248i
$28$		0			0
$29$	2.21393	−	2.21393i	0.411116	−	0.411116i	−0.471011	−	0.882127i	$-0.656111\pi$
$29$	2.21393	−	2.21393i	0.411116	−	0.411116i	0.882127	+	0.471011i	$0.156111\pi$
$30$		0			0
$31$			6.74878i			1.21212i	0.795420	+	0.606059i	$0.207250\pi$
$31$			6.74878i			1.21212i	−0.795420	+	0.606059i	$0.792750\pi$
$32$		0			0
$33$	5.48500	+	6.02148i	0.954816	+	1.04820i
$34$		0			0
$35$	−1.66193	−	1.66193i	−0.280918	−	0.280918i
$36$		0			0
$37$	−3.62622	+	3.62622i	−0.596146	+	0.596146i	−0.939285	−	0.343138i	$-0.888510\pi$
$37$	−3.62622	+	3.62622i	−0.596146	+	0.596146i	0.343138	+	0.939285i	$0.388510\pi$
$38$		0			0
$39$	−1.69858	+	1.54724i	−0.271990	+	0.247757i
$40$		0			0
$41$	−6.63194			−1.03574			−0.517868	−	0.855461i	$-0.673274\pi$
$41$	−6.63194			−1.03574			−0.517868	+	0.855461i	$0.673274\pi$
$42$		0			0
$43$	−8.58019	−	8.58019i	−1.30847	−	1.30847i	−0.922522	−	0.385944i	$-0.873876\pi$
$43$	−8.58019	−	8.58019i	−1.30847	−	1.30847i	−0.385944	−	0.922522i	$-0.626124\pi$
$44$		0			0
$45$	4.50027	+	5.42808i	0.670860	+	0.809171i
$46$		0			0
$47$	11.4602			1.67164			0.835819	−	0.549005i	$-0.184993\pi$
$47$	11.4602			1.67164			0.835819	+	0.549005i	$0.184993\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−1.40398	−	0.0654593i	−0.196597	−	0.00916613i
$52$		0			0
$53$	−5.01755	−	5.01755i	−0.689214	−	0.689214i	0.272845	−	0.962058i	$-0.412036\pi$
$53$	−5.01755	−	5.01755i	−0.689214	−	0.689214i	−0.962058	+	0.272845i	$0.912036\pi$
$54$		0			0
$55$	11.0527			1.49034
$56$		0			0
$57$	1.60717	+	1.76437i	0.212875	+	0.233696i
$58$		0			0
$59$	3.36018	−	3.36018i	0.437459	−	0.437459i	−0.453697	−	0.891156i	$-0.649895\pi$
$59$	3.36018	−	3.36018i	0.437459	−	0.437459i	0.891156	+	0.453697i	$0.149895\pi$
$60$		0			0
$61$	9.07854	+	9.07854i	1.16239	+	1.16239i	0.983951	+	0.178437i	$0.0571041\pi$
$61$	9.07854	+	9.07854i	1.16239	+	1.16239i	0.178437	+	0.983951i	$0.442896\pi$
$62$		0			0
$63$	−2.98699	−	0.279137i	−0.376325	−	0.0351680i
$64$		0			0
$65$			3.11781i			0.386716i
$66$		0			0
$67$	−2.30161	+	2.30161i	−0.281186	+	0.281186i	−0.833582	−	0.552396i	$-0.813714\pi$
$67$	−2.30161	+	2.30161i	−0.281186	+	0.281186i	0.552396	+	0.833582i	$0.313714\pi$
$68$		0			0
$69$	12.4441	+	0.580193i	1.49809	+	0.0698471i
$70$		0			0
$71$			1.63685i			0.194259i	0.995272	+	0.0971293i	$0.0309660\pi$
$71$			1.63685i			0.194259i	−0.995272	+	0.0971293i	$0.969034\pi$
$72$		0			0
$73$			1.89680i			0.222003i	0.993820	+	0.111002i	$0.0354059\pi$
$73$			1.89680i			0.222003i	−0.993820	+	0.111002i	$0.964594\pi$
$74$		0			0
$75$	0.906702	+	0.0422741i	0.104697	+	0.00488139i
$76$		0			0
$77$	−3.32524	+	3.32524i	−0.378946	+	0.378946i
$78$		0			0
$79$			13.3142i			1.49797i	0.662588	+	0.748984i	$0.269458\pi$
$79$			13.3142i			1.49797i	−0.662588	+	0.748984i	$0.730542\pi$
$80$		0			0
$81$	8.84416	+	1.66756i	0.982685	+	0.185284i
$82$		0			0
$83$	−5.35833	−	5.35833i	−0.588153	−	0.588153i	0.348978	−	0.937131i	$-0.386529\pi$
$83$	−5.35833	−	5.35833i	−0.588153	−	0.588153i	−0.937131	+	0.348978i	$0.886529\pi$
$84$		0			0
$85$	−1.34861	+	1.34861i	−0.146277	+	0.146277i
$86$		0			0
$87$	−3.65188	−	4.00907i	−0.391523	−	0.429817i
$88$		0			0
$89$	7.32588			0.776542			0.388271	−	0.921545i	$-0.373072\pi$
$89$	7.32588			0.776542			0.388271	+	0.921545i	$0.373072\pi$
$90$		0			0
$91$	−0.938005	−	0.938005i	−0.0983296	−	0.0983296i
$92$		0			0
$93$	11.6766	+	0.544408i	1.21080	+	0.0564525i
$94$		0			0
$95$	3.23857			0.332270
$96$		0			0
$97$	−19.2019			−1.94966			−0.974830	−	0.222947i	$-0.928432\pi$
$97$	−19.2019			−1.94966			−0.974830	+	0.222947i	$0.928432\pi$
$98$		0			0
$99$	10.8606	−	9.00425i	1.09154	−	0.904961i
$100$		0			0
$101$	0.206592	+	0.206592i	0.0205567	+	0.0205567i	0.717310	−	0.696754i	$-0.245373\pi$
$101$	0.206592	+	0.206592i	0.0205567	+	0.0205567i	−0.696754	+	0.717310i	$0.745373\pi$
$102$		0			0
$103$	−7.36936			−0.726125			−0.363062	−	0.931765i	$-0.618269\pi$
$103$	−7.36936			−0.726125			−0.363062	+	0.931765i	$0.618269\pi$
$104$		0			0
$105$	−3.00950	+	2.74137i	−0.293697	+	0.267530i
$106$		0			0
$107$	−11.7713	+	11.7713i	−1.13798	+	1.13798i	−0.149165	+	0.988812i	$0.547659\pi$
$107$	−11.7713	+	11.7713i	−1.13798	+	1.13798i	−0.988812	+	0.149165i	$0.952341\pi$
$108$		0			0
$109$	−2.16723	−	2.16723i	−0.207583	−	0.207583i	0.595656	−	0.803240i	$-0.296892\pi$
$109$	−2.16723	−	2.16723i	−0.207583	−	0.207583i	−0.803240	+	0.595656i	$0.796892\pi$
$110$		0			0
$111$	5.98146	+	6.56650i	0.567735	+	0.623264i
$112$		0			0
$113$			7.11741i			0.669550i	0.942298	+	0.334775i	$0.108660\pi$
$113$			7.11741i			0.669550i	−0.942298	+	0.334775i	$0.891340\pi$
$114$		0			0
$115$	11.9533	−	11.9533i	1.11465	−	1.11465i
$116$		0			0
$117$	2.53997	+	3.06364i	0.234821	+	0.283234i
$118$		0			0
$119$		−	0.811469i		−	0.0743873i
$120$		0			0
$121$		−	11.1145i		−	1.01041i
$122$		0			0
$123$	−0.534983	+	11.4744i	−0.0482378	+	1.03461i
$124$		0			0
$125$	−7.43873	+	7.43873i	−0.665340	+	0.665340i
$126$		0			0
$127$		−	6.85451i		−	0.608239i	−0.952634	−	0.304120i	$-0.901638\pi$
$127$		−	6.85451i		−	0.608239i	0.952634	−	0.304120i	$-0.0983623\pi$
$128$		0			0
$129$	−15.5373	+	14.1531i	−1.36799	+	1.24611i
$130$		0			0
$131$	5.31306	+	5.31306i	0.464204	+	0.464204i	0.900031	−	0.435827i	$-0.143544\pi$
$131$	5.31306	+	5.31306i	0.464204	+	0.464204i	−0.435827	+	0.900031i	$0.643544\pi$
$132$		0			0
$133$	−0.974336	+	0.974336i	−0.0844857	+	0.0844857i
$134$		0			0
$135$	9.75454	−	7.34836i	0.839537	−	0.632446i
$136$		0			0
$137$	−4.22774			−0.361200			−0.180600	−	0.983557i	$-0.557804\pi$
$137$	−4.22774			−0.361200			−0.180600	+	0.983557i	$0.557804\pi$
$138$		0			0
$139$	9.07286	+	9.07286i	0.769550	+	0.769550i	0.978027	−	0.208477i	$-0.0668507\pi$
$139$	9.07286	+	9.07286i	0.769550	+	0.769550i	−0.208477	+	0.978027i	$0.566851\pi$
$140$		0			0
$141$	0.924464	−	19.8281i	0.0778539	−	1.66982i
$142$		0			0
$143$	6.23819			0.521663
$144$		0			0
$145$	−7.35880			−0.611115
$146$		0			0
$147$	0.0806676	−	1.73017i	0.00665335	−	0.142702i
$148$		0			0
$149$	−4.96193	−	4.96193i	−0.406497	−	0.406497i	0.474018	−	0.880515i	$-0.342803\pi$
$149$	−4.96193	−	4.96193i	−0.406497	−	0.406497i	−0.880515	+	0.474018i	$0.842803\pi$
$150$		0			0
$151$	−14.7086			−1.19697			−0.598485	−	0.801134i	$-0.704230\pi$
$151$	−14.7086			−1.19697			−0.598485	+	0.801134i	$0.704230\pi$
$152$		0			0
$153$	−0.226512	+	2.42385i	−0.0183124	+	0.195956i
$154$		0			0
$155$	11.2160	−	11.2160i	0.900894	−	0.900894i
$156$		0			0
$157$	0.0695589	+	0.0695589i	0.00555141	+	0.00555141i	0.709877	−	0.704326i	$-0.248750\pi$
$157$	0.0695589	+	0.0695589i	0.00555141	+	0.00555141i	−0.704326	+	0.709877i	$0.748750\pi$
$158$		0			0
$159$	−9.08598	+	8.27647i	−0.720565	+	0.656367i
$160$		0			0
$161$			7.19240i			0.566840i
$162$		0			0
$163$	4.97500	−	4.97500i	0.389672	−	0.389672i	−0.484899	−	0.874570i	$-0.661143\pi$
$163$	4.97500	−	4.97500i	0.389672	−	0.389672i	0.874570	+	0.484899i	$0.161143\pi$
$164$		0			0
$165$	0.891592	−	19.1230i	0.0694103	−	1.48872i
$166$		0			0
$167$		−	2.85361i		−	0.220819i	−0.993886	−	0.110410i	$-0.964784\pi$
$167$		−	2.85361i		−	0.220819i	0.993886	−	0.110410i	$-0.0352163\pi$
$168$		0			0
$169$		−	11.2403i		−	0.864638i
$170$		0			0
$171$	3.18230	−	2.63835i	0.243357	−	0.201760i
$172$		0			0
$173$	1.31058	−	1.31058i	0.0996414	−	0.0996414i	−0.655529	−	0.755170i	$-0.727554\pi$
$173$	1.31058	−	1.31058i	0.0996414	−	0.0996414i	0.755170	+	0.655529i	$0.227554\pi$
$174$		0			0
$175$			0.524053i			0.0396147i
$176$		0			0
$177$	−5.54263	−	6.08475i	−0.416610	−	0.457358i
$178$		0			0
$179$	−10.5923	−	10.5923i	−0.791706	−	0.791706i	0.190066	−	0.981771i	$-0.439130\pi$
$179$	−10.5923	−	10.5923i	−0.791706	−	0.791706i	−0.981771	+	0.190066i	$0.939130\pi$
$180$		0			0
$181$	−4.42164	+	4.42164i	−0.328658	+	0.328658i	−0.852076	−	0.523418i	$-0.824657\pi$
$181$	−4.42164	+	4.42164i	−0.328658	+	0.328658i	0.523418	+	0.852076i	$0.324657\pi$
$182$		0			0
$183$	16.4398	−	14.9751i	1.21526	−	1.10699i
$184$		0			0
$185$	12.0531			0.886160
$186$		0			0
$187$	2.69833	+	2.69833i	0.197322	+	0.197322i
$188$		0			0
$189$	−0.723909	+	5.14548i	−0.0526566	+	0.374279i
$190$		0			0
$191$	−8.08539			−0.585038			−0.292519	−	0.956260i	$-0.594494\pi$
$191$	−8.08539			−0.585038			−0.292519	+	0.956260i	$0.594494\pi$
$192$		0			0
$193$	−6.54682			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$193$	−6.54682			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$194$		0			0
$195$	5.39434	+	0.251506i	0.386297	+	0.0180107i
$196$		0			0
$197$	−2.94137	−	2.94137i	−0.209564	−	0.209564i	0.594518	−	0.804082i	$-0.297343\pi$
$197$	−2.94137	−	2.94137i	−0.209564	−	0.209564i	−0.804082	+	0.594518i	$0.797343\pi$
$198$		0			0
$199$	−26.0086			−1.84370			−0.921849	−	0.387549i	$-0.873322\pi$
$199$	−26.0086			−1.84370			−0.921849	+	0.387549i	$0.873322\pi$
$200$		0			0
$201$	3.79651	+	4.16784i	0.267785	+	0.293977i
$202$		0			0
$203$	2.21393	−	2.21393i	0.155387	−	0.155387i
$204$		0			0
$205$	11.0219	+	11.0219i	0.769800	+	0.769800i
$206$		0			0
$207$	2.00767	−	21.4836i	0.139543	−	1.49321i
$208$		0			0
$209$		−	6.47981i		−	0.448218i
$210$		0			0
$211$	−18.2987	+	18.2987i	−1.25974	+	1.25974i	−0.308518	+	0.951219i	$0.599833\pi$
$211$	−18.2987	+	18.2987i	−1.25974	+	1.25974i	−0.951219	+	0.308518i	$0.900167\pi$
$212$		0			0
$213$	2.83203	+	0.132041i	0.194048	+	0.00904729i
$214$		0			0
$215$			28.5194i			1.94501i
$216$		0			0
$217$			6.74878i			0.458137i
$218$		0			0
$219$	3.28178	+	0.153010i	0.221762	+	0.0103395i
$220$		0			0
$221$	−0.761162	+	0.761162i	−0.0512013	+	0.0512013i
$222$		0			0
$223$		−	19.6776i		−	1.31771i	−0.752271	−	0.658854i	$-0.771041\pi$
$223$		−	19.6776i		−	1.31771i	0.752271	−	0.658854i	$-0.228959\pi$
$224$		0			0
$225$	0.146283	−	1.56534i	0.00975219	−	0.104356i
$226$		0			0
$227$	−18.0340	−	18.0340i	−1.19696	−	1.19696i	−0.975072	−	0.221889i	$-0.928778\pi$
$227$	−18.0340	−	18.0340i	−1.19696	−	1.19696i	−0.221889	−	0.975072i	$-0.571222\pi$
$228$		0			0
$229$	11.9505	−	11.9505i	0.789714	−	0.789714i	−0.191733	−	0.981447i	$-0.561411\pi$
$229$	11.9505	−	11.9505i	0.789714	−	0.789714i	0.981447	+	0.191733i	$0.0614107\pi$
$230$		0			0
$231$	5.48500	+	6.02148i	0.360886	+	0.396184i
$232$		0			0
$233$	−10.0806			−0.660405			−0.330202	−	0.943910i	$-0.607117\pi$
$233$	−10.0806			−0.660405			−0.330202	+	0.943910i	$0.607117\pi$
$234$		0			0
$235$	−19.0461	−	19.0461i	−1.24243	−	1.24243i
$236$		0			0
$237$	23.0359	+	1.07403i	1.49634	+	0.0697655i
$238$		0			0
$239$	25.9167			1.67641			0.838206	−	0.545354i	$-0.183605\pi$
$239$	25.9167			1.67641			0.838206	+	0.545354i	$0.183605\pi$
$240$		0			0
$241$	−13.0822			−0.842697			−0.421349	−	0.906899i	$-0.638443\pi$
$241$	−13.0822			−0.842697			−0.421349	+	0.906899i	$0.638443\pi$
$242$		0			0
$243$	3.59860	−	15.1674i	0.230850	−	0.972989i
$244$		0			0
$245$	−1.66193	−	1.66193i	−0.106177	−	0.106177i
$246$		0			0
$247$	1.82786			0.116304
$248$		0			0
$249$	−9.70307	+	8.83858i	−0.614907	+	0.560122i
$250$		0			0
$251$	−13.7635	+	13.7635i	−0.868744	+	0.868744i	−0.992333	−	0.123589i	$-0.960559\pi$
$251$	−13.7635	+	13.7635i	−0.868744	+	0.868744i	0.123589	+	0.992333i	$0.460559\pi$
$252$		0			0
$253$	−23.9165	−	23.9165i	−1.50361	−	1.50361i
$254$		0			0
$255$	2.22454	+	2.44211i	0.139306	+	0.152931i
$256$		0			0
$257$		−	2.96212i		−	0.184772i	−0.995723	−	0.0923861i	$-0.970551\pi$
$257$		−	2.96212i		−	0.184772i	0.995723	−	0.0923861i	$-0.0294494\pi$
$258$		0			0
$259$	−3.62622	+	3.62622i	−0.225322	+	0.225322i
$260$		0			0
$261$	−7.23096	+	5.99498i	−0.447585	+	0.371080i
$262$		0			0
$263$			7.31268i			0.450919i	0.974253	+	0.225460i	$0.0723884\pi$
$263$			7.31268i			0.450919i	−0.974253	+	0.225460i	$0.927612\pi$
$264$		0			0
$265$			16.6777i			1.02450i
$266$		0			0
$267$	0.590961	−	12.6750i	0.0361662	−	0.775699i
$268$		0			0
$269$	4.77804	−	4.77804i	0.291322	−	0.291322i	−0.546280	−	0.837603i	$-0.683957\pi$
$269$	4.77804	−	4.77804i	0.291322	−	0.291322i	0.837603	+	0.546280i	$0.183957\pi$
$270$		0			0
$271$			5.38998i			0.327418i	0.986509	+	0.163709i	$0.0523458\pi$
$271$			5.38998i			0.327418i	−0.986509	+	0.163709i	$0.947654\pi$
$272$		0			0
$273$	−1.69858	+	1.54724i	−0.102802	+	0.0936434i
$274$		0			0
$275$	−1.74260	−	1.74260i	−0.105083	−	0.105083i
$276$		0			0
$277$	13.2792	−	13.2792i	0.797869	−	0.797869i	−0.184891	−	0.982759i	$-0.559193\pi$
$277$	13.2792	−	13.2792i	0.797869	−	0.797869i	0.982759	+	0.184891i	$0.0591931\pi$
$278$		0			0
$279$	1.88384	−	20.1585i	0.112782	−	1.20686i
$280$		0			0
$281$	21.5222			1.28390			0.641952	−	0.766744i	$-0.278125\pi$
$281$	21.5222			1.28390			0.641952	+	0.766744i	$0.278125\pi$
$282$		0			0
$283$	8.95185	+	8.95185i	0.532132	+	0.532132i	0.921206	−	0.389074i	$-0.127205\pi$
$283$	8.95185	+	8.95185i	0.532132	+	0.532132i	−0.389074	+	0.921206i	$0.627205\pi$
$284$		0			0
$285$	0.261247	−	5.60327i	0.0154750	−	0.331909i
$286$		0			0
$287$	−6.63194			−0.391471
$288$		0			0
$289$	16.3415			0.961266
$290$		0			0
$291$	−1.54897	+	33.2226i	−0.0908024	+	1.94755i
$292$		0			0
$293$	17.7011	+	17.7011i	1.03411	+	1.03411i	0.999397	+	0.0347134i	$0.0110518\pi$
$293$	17.7011	+	17.7011i	1.03411	+	1.03411i	0.0347134	+	0.999397i	$0.488948\pi$
$294$		0			0
$295$	−11.1688			−0.650273
$296$		0			0
$297$	−14.7028	−	19.5171i	−0.853142	−	1.13250i
$298$		0			0
$299$	6.74650	−	6.74650i	0.390160	−	0.390160i
$300$		0			0
$301$	−8.58019	−	8.58019i	−0.494554	−	0.494554i
$302$		0			0
$303$	0.374105	−	0.340775i	0.0214918	−	0.0195770i
$304$		0			0
$305$		−	30.1759i		−	1.72787i
$306$		0			0
$307$	−11.3441	+	11.3441i	−0.647441	+	0.647441i	−0.952374	−	0.304933i	$-0.901366\pi$
$307$	−11.3441	+	11.3441i	−0.647441	+	0.647441i	0.304933	+	0.952374i	$0.401366\pi$
$308$		0			0
$309$	−0.594469	+	12.7503i	−0.0338181	+	0.725337i
$310$		0			0
$311$			9.26895i			0.525594i	0.964851	+	0.262797i	$0.0846450\pi$
$311$			9.26895i			0.525594i	−0.964851	+	0.262797i	$0.915355\pi$
$312$		0			0
$313$			4.67743i			0.264384i	0.991224	+	0.132192i	$0.0422015\pi$
$313$			4.67743i			0.264384i	−0.991224	+	0.132192i	$0.957798\pi$
$314$		0			0
$315$	4.50027	+	5.42808i	0.253561	+	0.305838i
$316$		0			0
$317$	−3.28355	+	3.28355i	−0.184423	+	0.184423i	−0.793280	−	0.608857i	$-0.791628\pi$
$317$	−3.28355	+	3.28355i	−0.184423	+	0.184423i	0.608857	+	0.793280i	$0.291628\pi$
$318$		0			0
$319$			14.7237i			0.824368i
$320$		0			0
$321$	19.4169	+	21.3160i	1.08374	+	1.18974i
$322$		0			0
$323$	0.790644	+	0.790644i	0.0439926	+	0.0439926i
$324$		0			0
$325$	0.491565	−	0.491565i	0.0272671	−	0.0272671i
$326$		0			0
$327$	−3.92451	+	3.57486i	−0.217026	+	0.197690i
$328$		0			0
$329$	11.4602			0.631820
$330$		0			0
$331$	−20.5621	−	20.5621i	−1.13019	−	1.13019i	−0.990145	−	0.140049i	$-0.955274\pi$
$331$	−20.5621	−	20.5621i	−1.13019	−	1.13019i	−0.140049	−	0.990145i	$-0.544726\pi$
$332$		0			0
$333$	11.8437	−	9.81925i	0.649029	−	0.538091i
$334$		0			0
$335$	7.65025			0.417978
$336$		0			0
$337$	−24.4137			−1.32990			−0.664948	−	0.746889i	$-0.731546\pi$
$337$	−24.4137			−1.32990			−0.664948	+	0.746889i	$0.731546\pi$
$338$		0			0
$339$	12.3143	+	0.574144i	0.668823	+	0.0311832i
$340$		0			0
$341$	−22.4413	−	22.4413i	−1.21527	−	1.21527i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−19.7170	−	21.6455i	−1.06153	−	1.16535i
$346$		0			0
$347$	21.7785	−	21.7785i	1.16913	−	1.16913i	0.186717	−	0.982414i	$-0.440215\pi$
$347$	21.7785	−	21.7785i	1.16913	−	1.16913i	0.982414	−	0.186717i	$-0.0597848\pi$
$348$		0			0
$349$	−8.31266	−	8.31266i	−0.444966	−	0.444966i	0.448711	−	0.893677i	$-0.351883\pi$
$349$	−8.31266	−	8.31266i	−0.444966	−	0.444966i	−0.893677	+	0.448711i	$0.851883\pi$
$350$		0			0
$351$	5.50552	−	4.14746i	0.293863	−	0.221375i
$352$		0			0
$353$		−	10.1998i		−	0.542882i	−0.962455	−	0.271441i	$-0.912500\pi$
$353$		−	10.1998i		−	0.542882i	0.962455	−	0.271441i	$-0.0875002\pi$
$354$		0			0
$355$	2.72034	−	2.72034i	0.144381	−	0.144381i
$356$		0			0
$357$	−1.40398	−	0.0654593i	−0.0743066	−	0.00346447i
$358$		0			0
$359$		−	24.0022i		−	1.26679i	−0.773829	−	0.633394i	$-0.781661\pi$
$359$		−	24.0022i		−	1.26679i	0.773829	−	0.633394i	$-0.218339\pi$
$360$		0			0
$361$			17.1013i			0.900070i
$362$		0			0
$363$	−19.2299	−	0.896577i	−1.00931	−	0.0470581i
$364$		0			0
$365$	3.15235	−	3.15235i	0.165002	−	0.165002i
$366$		0			0
$367$		−	26.9781i		−	1.40825i	−0.710078	−	0.704123i	$-0.751340\pi$
$367$		−	26.9781i		−	1.40825i	0.710078	−	0.704123i	$-0.248660\pi$
$368$		0			0
$369$	19.8095	+	1.85122i	1.03124	+	0.0963708i
$370$		0			0
$371$	−5.01755	−	5.01755i	−0.260498	−	0.260498i
$372$		0			0
$373$	−6.62243	+	6.62243i	−0.342896	+	0.342896i	−0.857455	−	0.514559i	$-0.827956\pi$
$373$	−6.62243	+	6.62243i	−0.342896	+	0.342896i	0.514559	+	0.857455i	$0.327956\pi$
$374$		0			0
$375$	12.2702	+	13.4703i	0.633631	+	0.695606i
$376$		0			0
$377$	−4.15335			−0.213908
$378$		0			0
$379$	−8.92425	−	8.92425i	−0.458408	−	0.458408i	0.439725	−	0.898133i	$-0.355076\pi$
$379$	−8.92425	−	8.92425i	−0.458408	−	0.458408i	−0.898133	+	0.439725i	$0.855076\pi$
$380$		0			0
$381$	−11.8595	−	0.552937i	−0.607579	−	0.0283278i
$382$		0			0
$383$	−3.53428			−0.180593			−0.0902965	−	0.995915i	$-0.528781\pi$
$383$	−3.53428			−0.180593			−0.0902965	+	0.995915i	$0.528781\pi$
$384$		0			0
$385$	11.0527			0.563296
$386$		0			0
$387$	23.2338	+	28.0239i	1.18104	+	1.42454i
$388$		0			0
$389$	16.0582	+	16.0582i	0.814181	+	0.814181i	0.985258	−	0.171076i	$-0.0547245\pi$
$389$	16.0582	+	16.0582i	0.814181	+	0.814181i	−0.171076	+	0.985258i	$0.554725\pi$
$390$		0			0
$391$	5.83641			0.295160
$392$		0			0
$393$	9.62109	−	8.76391i	0.485320	−	0.442081i
$394$		0			0
$395$	22.1274	−	22.1274i	1.11335	−	1.11335i
$396$		0			0
$397$	2.84454	+	2.84454i	0.142763	+	0.142763i	0.774876	−	0.632113i	$-0.217812\pi$
$397$	2.84454	+	2.84454i	0.142763	+	0.142763i	−0.632113	+	0.774876i	$0.717812\pi$
$398$		0			0
$399$	1.60717	+	1.76437i	0.0804592	+	0.0883288i
$400$		0			0
$401$			14.8620i			0.742171i	0.928599	+	0.371085i	$0.121014\pi$
$401$			14.8620i			0.742171i	−0.928599	+	0.371085i	$0.878986\pi$
$402$		0			0
$403$	6.33039	−	6.33039i	0.315339	−	0.315339i
$404$		0			0
$405$	−11.9270	−	17.4698i	−0.592660	−	0.868081i
$406$		0			0
$407$		−	24.1161i		−	1.19539i
$408$		0			0
$409$		−	21.3384i		−	1.05512i	−0.849519	−	0.527559i	$-0.823107\pi$
$409$		−	21.3384i		−	1.05512i	0.849519	−	0.527559i	$-0.176893\pi$
$410$		0			0
$411$	−0.341041	+	7.31471i	−0.0168223	+	0.360808i
$412$		0			0
$413$	3.36018	−	3.36018i	0.165344	−	0.165344i
$414$		0			0
$415$			17.8104i			0.874277i
$416$		0			0
$417$	16.4295	−	14.9657i	0.804556	−	0.732874i
$418$		0			0
$419$	7.71515	+	7.71515i	0.376910	+	0.376910i	0.869986	−	0.493076i	$-0.164128\pi$
$419$	7.71515	+	7.71515i	0.376910	+	0.376910i	−0.493076	+	0.869986i	$0.664128\pi$
$420$		0			0
$421$	−3.87124	+	3.87124i	−0.188673	+	0.188673i	−0.795122	−	0.606449i	$-0.792593\pi$
$421$	−3.87124	+	3.87124i	−0.188673	+	0.188673i	0.606449	+	0.795122i	$0.292593\pi$
$422$		0			0
$423$	−34.2314	−	3.19896i	−1.66439	−	0.155539i
$424$		0			0
$425$	0.425253			0.0206278
$426$		0			0
$427$	9.07854	+	9.07854i	0.439342	+	0.439342i
$428$		0			0
$429$	0.503219	−	10.7931i	0.0242957	−	0.521097i
$430$		0			0
$431$	−12.8133			−0.617193			−0.308596	−	0.951193i	$-0.599859\pi$
$431$	−12.8133			−0.617193			−0.308596	+	0.951193i	$0.599859\pi$
$432$		0			0
$433$	38.6393			1.85688			0.928442	−	0.371476i	$-0.121148\pi$
$433$	38.6393			1.85688			0.928442	+	0.371476i	$0.121148\pi$
$434$		0			0
$435$	−0.593617	+	12.7320i	−0.0284618	+	0.610452i
$436$		0			0
$437$	−7.00781	−	7.00781i	−0.335229	−	0.335229i
$438$		0			0
$439$	2.53256			0.120873			0.0604363	−	0.998172i	$-0.480751\pi$
$439$	2.53256			0.120873			0.0604363	+	0.998172i	$0.480751\pi$
$440$		0			0
$441$	−2.98699	−	0.279137i	−0.142237	−	0.0132923i
$442$		0			0
$443$	−24.9057	+	24.9057i	−1.18330	+	1.18330i	−0.204420	+	0.978883i	$0.565531\pi$
$443$	−24.9057	+	24.9057i	−1.18330	+	1.18330i	−0.978883	+	0.204420i	$0.934469\pi$
$444$		0			0
$445$	−12.1751	−	12.1751i	−0.577157	−	0.577157i
$446$		0			0
$447$	−8.98526	+	8.18473i	−0.424988	+	0.387124i
$448$		0			0
$449$		−	39.0818i		−	1.84438i	−0.386733	−	0.922192i	$-0.626396\pi$
$449$		−	39.0818i		−	1.84438i	0.386733	−	0.922192i	$-0.373604\pi$
$450$		0			0
$451$	22.0528	−	22.0528i	1.03843	−	1.03843i
$452$		0			0
$453$	−1.18651	+	25.4484i	−0.0557470	+	1.19567i
$454$		0			0
$455$			3.11781i			0.146165i
$456$		0			0
$457$		−	16.6974i		−	0.781072i	−0.920588	−	0.390536i	$-0.872290\pi$
$457$		−	16.6974i		−	0.781072i	0.920588	−	0.390536i	$-0.127710\pi$
$458$		0			0
$459$	4.17540	+	0.587430i	0.194891	+	0.0274189i
$460$		0			0
$461$	−16.2110	+	16.2110i	−0.755020	+	0.755020i	−0.975411	−	0.220392i	$-0.929267\pi$
$461$	−16.2110	+	16.2110i	−0.755020	+	0.755020i	0.220392	+	0.975411i	$0.429267\pi$
$462$		0			0
$463$		−	32.6428i		−	1.51704i	−0.651650	−	0.758520i	$-0.725923\pi$
$463$		−	32.6428i		−	1.51704i	0.651650	−	0.758520i	$-0.274077\pi$
$464$		0			0
$465$	−18.5009	−	20.3104i	−0.857959	−	0.941874i
$466$		0			0
$467$	−6.41993	−	6.41993i	−0.297079	−	0.297079i	0.542790	−	0.839869i	$-0.317368\pi$
$467$	−6.41993	−	6.41993i	−0.297079	−	0.297079i	−0.839869	+	0.542790i	$0.817368\pi$
$468$		0			0
$469$	−2.30161	+	2.30161i	−0.106278	+	0.106278i
$470$		0			0
$471$	0.125960	−	0.114738i	0.00580393	−	0.00528683i
$472$		0			0
$473$	57.0624			2.62373
$474$		0			0
$475$	−0.510604	−	0.510604i	−0.0234281	−	0.0234281i
$476$		0			0
$477$	13.5868	+	16.3879i	0.622095	+	0.750352i
$478$		0			0
$479$	−8.55974			−0.391104			−0.195552	−	0.980693i	$-0.562650\pi$
$479$	−8.55974			−0.391104			−0.195552	+	0.980693i	$0.562650\pi$
$480$		0			0
$481$	6.80282			0.310182
$482$		0			0
$483$	12.4441	+	0.580193i	0.566225	+	0.0263997i
$484$		0			0
$485$	31.9124	+	31.9124i	1.44907	+	1.44907i
$486$		0			0
$487$	−6.28627			−0.284858			−0.142429	−	0.989805i	$-0.545491\pi$
$487$	−6.28627			−0.284858			−0.142429	+	0.989805i	$0.545491\pi$
$488$		0			0
$489$	−8.20628	−	9.00892i	−0.371101	−	0.407397i
$490$		0			0
$491$	−3.59762	+	3.59762i	−0.162358	+	0.162358i	−0.783611	−	0.621252i	$-0.786624\pi$
$491$	−3.59762	+	3.59762i	−0.162358	+	0.162358i	0.621252	+	0.783611i	$0.286624\pi$
$492$		0			0
$493$	−1.79653	−	1.79653i	−0.0809118	−	0.0809118i
$494$		0			0
$495$	−33.0142	−	3.08521i	−1.48388	−	0.138670i
$496$		0			0
$497$			1.63685i			0.0734229i
$498$		0			0
$499$	−12.3424	+	12.3424i	−0.552521	+	0.552521i	−0.927168	−	0.374646i	$-0.877764\pi$
$499$	−12.3424	+	12.3424i	−0.552521	+	0.552521i	0.374646	+	0.927168i	$0.377764\pi$
$500$		0			0
$501$	−4.93724	−	0.230194i	−0.220580	−	0.0102843i
$502$		0			0
$503$			13.0160i			0.580354i	0.956973	+	0.290177i	$0.0937141\pi$
$503$			13.0160i			0.580354i	−0.956973	+	0.290177i	$0.906286\pi$
$504$		0			0
$505$		−	0.686685i		−	0.0305571i
$506$		0			0
$507$	−19.4476	−	0.906727i	−0.863700	−	0.0402692i
$508$		0			0
$509$	−29.2938	+	29.2938i	−1.29843	+	1.29843i	−0.368996	+	0.929431i	$0.620298\pi$
$509$	−29.2938	+	29.2938i	−1.29843	+	1.29843i	−0.929431	+	0.368996i	$0.879702\pi$
$510$		0			0
$511$			1.89680i			0.0839093i
$512$		0			0
$513$	−4.30810	−	5.71876i	−0.190207	−	0.252489i
$514$		0			0
$515$	12.2474	+	12.2474i	0.539685	+	0.539685i
$516$		0			0
$517$	−38.1078	+	38.1078i	−1.67598	+	1.67598i
$518$		0			0
$519$	−2.16180	−	2.37324i	−0.0948926	−	0.104174i
$520$		0			0
$521$	40.6889			1.78261			0.891306	−	0.453402i	$-0.149790\pi$
$521$	40.6889			1.78261			0.891306	+	0.453402i	$0.149790\pi$
$522$		0			0
$523$	21.7560	+	21.7560i	0.951325	+	0.951325i	0.998869	−	0.0475446i	$-0.0151396\pi$
$523$	21.7560	+	21.7560i	0.951325	+	0.951325i	−0.0475446	+	0.998869i	$0.515140\pi$
$524$		0			0
$525$	0.906702	+	0.0422741i	0.0395717	+	0.00184499i
$526$		0			0
$527$	5.47643			0.238557
$528$		0			0
$529$	−28.7306			−1.24915
$530$		0			0
$531$	−10.9748	+	9.09886i	−0.476264	+	0.394857i
$532$		0			0
$533$	6.22079	+	6.22079i	0.269453	+	0.269453i
$534$		0			0
$535$	39.1264			1.69158
$536$		0			0
$537$	−19.1809	+	17.4720i	−0.827719	+	0.753974i
$538$		0			0
$539$	−3.32524	+	3.32524i	−0.143228	+	0.143228i
$540$		0			0
$541$	20.7435	+	20.7435i	0.891834	+	0.891834i	0.994696	−	0.102862i	$-0.0327999\pi$
$541$	20.7435	+	20.7435i	0.891834	+	0.891834i	−0.102862	+	0.994696i	$0.532800\pi$
$542$		0			0
$543$	7.29352	+	8.00688i	0.312995	+	0.343608i
$544$		0			0
$545$			7.20360i			0.308568i
$546$		0			0
$547$	−6.35975	+	6.35975i	−0.271923	+	0.271923i	−0.829874	−	0.557951i	$-0.811588\pi$
$547$	−6.35975	+	6.35975i	−0.271923	+	0.271923i	0.557951	+	0.829874i	$0.311588\pi$
$548$		0			0
$549$	−24.5833	−	29.6516i	−1.04919	−	1.26550i
$550$		0			0
$551$			4.31422i			0.183792i
$552$		0			0
$553$			13.3142i			0.566179i
$554$		0			0
$555$	0.972292	−	20.8539i	0.0412715	−	0.885198i
$556$		0			0
$557$	−0.541034	+	0.541034i	−0.0229244	+	0.0229244i	−0.718476	−	0.695552i	$-0.755160\pi$
$557$	−0.541034	+	0.541034i	−0.0229244	+	0.0229244i	0.695552	+	0.718476i	$0.255160\pi$
$558$		0			0
$559$			16.0965i			0.680810i
$560$		0			0
$561$	4.88624	−	4.45091i	0.206297	−	0.187917i
$562$		0			0
$563$	−1.99456	−	1.99456i	−0.0840608	−	0.0840608i	0.663826	−	0.747887i	$-0.268931\pi$
$563$	−1.99456	−	1.99456i	−0.0840608	−	0.0840608i	−0.747887	+	0.663826i	$0.768931\pi$
$564$		0			0
$565$	11.8287	−	11.8287i	0.497636	−	0.497636i
$566$		0			0
$567$	8.84416	+	1.66756i	0.371420	+	0.0700309i
$568$		0			0
$569$	−23.0030			−0.964334			−0.482167	−	0.876079i	$-0.660150\pi$
$569$	−23.0030			−0.964334			−0.482167	+	0.876079i	$0.660150\pi$
$570$		0			0
$571$	14.4124	+	14.4124i	0.603140	+	0.603140i	0.941145	−	0.338004i	$-0.109752\pi$
$571$	14.4124	+	14.4124i	0.603140	+	0.603140i	−0.338004	+	0.941145i	$0.609752\pi$
$572$		0			0
$573$	−0.652229	+	13.9891i	−0.0272473	+	0.584404i
$574$		0			0
$575$	−3.76920			−0.157186
$576$		0			0
$577$	26.1743			1.08965			0.544824	−	0.838550i	$-0.316596\pi$
$577$	26.1743			1.08965			0.544824	+	0.838550i	$0.316596\pi$
$578$		0			0
$579$	−0.528116	+	11.3271i	−0.0219478	+	0.470739i
$580$		0			0
$581$	−5.35833	−	5.35833i	−0.222301	−	0.222301i
$582$		0			0
$583$	33.3691			1.38201
$584$		0			0
$585$	0.870296	−	9.31284i	0.0359823	−	0.385039i
$586$		0			0
$587$	24.3921	−	24.3921i	1.00677	−	1.00677i	0.00679153	−	0.999977i	$-0.497838\pi$
$587$	24.3921	−	24.3921i	1.00677	−	1.00677i	0.999977	−	0.00679153i	$-0.00216183\pi$
$588$		0			0
$589$	−6.57559	−	6.57559i	−0.270942	−	0.270942i
$590$		0			0
$591$	−5.32634	+	4.85179i	−0.219096	+	0.199576i
$592$		0			0
$593$		−	6.18685i		−	0.254064i	−0.991899	−	0.127032i	$-0.959455\pi$
$593$		−	6.18685i		−	0.254064i	0.991899	−	0.127032i	$-0.0405450\pi$
$594$		0			0
$595$	−1.34861	+	1.34861i	−0.0552876	+	0.0552876i
$596$		0			0
$597$	−2.09805	+	44.9993i	−0.0858674	+	1.84170i
$598$		0			0
$599$			23.6940i			0.968111i	0.875037	+	0.484056i	$0.160837\pi$
$599$			23.6940i			0.968111i	−0.875037	+	0.484056i	$0.839163\pi$
$600$		0			0
$601$		−	6.54817i		−	0.267106i	−0.991042	−	0.133553i	$-0.957361\pi$
$601$		−	6.54817i		−	0.267106i	0.991042	−	0.133553i	$-0.0426386\pi$
$602$		0			0
$603$	7.51734	−	6.23241i	0.306130	−	0.253803i
$604$		0			0
$605$	−18.4715	+	18.4715i	−0.750974	+	0.750974i
$606$		0			0
$607$			27.5295i			1.11739i	0.829373	+	0.558695i	$0.188698\pi$
$607$			27.5295i			1.11739i	−0.829373	+	0.558695i	$0.811302\pi$
$608$		0			0
$609$	−3.65188	−	4.00907i	−0.147982	−	0.162456i
$610$		0			0
$611$	−10.7497	−	10.7497i	−0.434886	−	0.434886i
$612$		0			0
$613$	−15.1690	+	15.1690i	−0.612670	+	0.612670i	−0.943641	−	0.330971i	$-0.892624\pi$
$613$	−15.1690	+	15.1690i	−0.612670	+	0.612670i	0.330971	+	0.943641i	$0.392624\pi$
$614$		0			0
$615$	19.9588	−	18.1806i	0.804817	−	0.733112i
$616$		0			0
$617$	−24.4155			−0.982932			−0.491466	−	0.870897i	$-0.663539\pi$
$617$	−24.4155			−0.982932			−0.491466	+	0.870897i	$0.663539\pi$
$618$		0			0
$619$	26.0744	+	26.0744i	1.04802	+	1.04802i	0.998787	+	0.0492326i	$0.0156775\pi$
$619$	26.0744	+	26.0744i	1.04802	+	1.04802i	0.0492326	+	0.998787i	$0.484322\pi$
$620$		0			0
$621$	−37.0083	−	5.20664i	−1.48509	−	0.208935i
$622$		0			0
$623$	7.32588			0.293505
$624$		0			0
$625$	27.3456			1.09383
$626$		0			0
$627$	−11.2112	−	0.522710i	−0.447731	−	0.0208750i
$628$		0			0
$629$	2.94256	+	2.94256i	0.117328	+	0.117328i
$630$		0			0
$631$	−0.142420			−0.00566964			−0.00283482	−	0.999996i	$-0.500902\pi$
$631$	−0.142420			−0.00566964			−0.00283482	+	0.999996i	$0.500902\pi$
$632$		0			0
$633$	30.1838	+	33.1361i	1.19970	+	1.31704i
$634$		0			0
$635$	−11.3917	+	11.3917i	−0.452068	+	0.452068i
$636$		0			0
$637$	−0.938005	−	0.938005i	−0.0371651	−	0.0371651i
$638$		0			0
$639$	0.456907	−	4.88925i	0.0180750	−	0.193416i
$640$		0			0
$641$			34.9890i			1.38198i	0.722863	+	0.690991i	$0.242826\pi$
$641$			34.9890i			1.38198i	−0.722863	+	0.690991i	$0.757174\pi$
$642$		0			0
$643$	0.780208	−	0.780208i	0.0307684	−	0.0307684i	−0.691555	−	0.722324i	$-0.743074\pi$
$643$	0.780208	−	0.780208i	0.0307684	−	0.0307684i	0.722324	+	0.691555i	$0.243074\pi$
$644$		0			0
$645$	49.3435	+	2.30059i	1.94290	+	0.0905857i
$646$		0			0
$647$			1.17164i			0.0460618i	0.999735	+	0.0230309i	$0.00733161\pi$
$647$			1.17164i			0.0460618i	−0.999735	+	0.0230309i	$0.992668\pi$
$648$		0			0
$649$			22.3468i			0.877190i
$650$		0			0
$651$	11.6766	+	0.544408i	0.457640	+	0.0213370i
$652$		0			0
$653$	−14.2218	+	14.2218i	−0.556544	+	0.556544i	−0.928322	−	0.371778i	$-0.878748\pi$
$653$	−14.2218	+	14.2218i	−0.556544	+	0.556544i	0.371778	+	0.928322i	$0.378748\pi$
$654$		0			0
$655$		−	17.6599i		−	0.690029i
$656$		0			0
$657$	0.529467	−	5.66570i	0.0206565	−	0.221040i
$658$		0			0
$659$	−13.1135	−	13.1135i	−0.510828	−	0.510828i	0.403952	−	0.914780i	$-0.367636\pi$
$659$	−13.1135	−	13.1135i	−0.510828	−	0.510828i	−0.914780	+	0.403952i	$0.867636\pi$
$660$		0			0
$661$	12.0228	−	12.0228i	0.467631	−	0.467631i	−0.433515	−	0.901146i	$-0.642727\pi$
$661$	12.0228	−	12.0228i	0.467631	−	0.467631i	0.901146	+	0.433515i	$0.142727\pi$
$662$		0			0
$663$	1.25554	+	1.37834i	0.0487611	+	0.0535304i
$664$		0			0
$665$	3.23857			0.125586
$666$		0			0
$667$	15.9234	+	15.9234i	0.616558	+	0.616558i
$668$		0			0
$669$	−34.0456	−	1.58734i	−1.31628	−	0.0613702i
$670$		0			0
$671$	−60.3767			−2.33082
$672$		0			0
$673$	22.2730			0.858560			0.429280	−	0.903171i	$-0.358767\pi$
$673$	22.2730			0.858560			0.429280	+	0.903171i	$0.358767\pi$
$674$		0			0
$675$	−2.69651	−	0.379367i	−0.103789	−	0.0146018i
$676$		0			0
$677$	−26.1377	−	26.1377i	−1.00455	−	1.00455i	−0.999990	−	0.00456227i	$-0.998548\pi$
$677$	−26.1377	−	26.1377i	−1.00455	−	1.00455i	−0.00456227	−	0.999990i	$-0.501452\pi$
$678$		0			0
$679$	−19.2019			−0.736903
$680$		0			0
$681$	−32.6567	+	29.7472i	−1.25141	+	1.13992i
$682$		0			0
$683$	−1.51612	+	1.51612i	−0.0580129	+	0.0580129i	−0.735518	−	0.677505i	$-0.763061\pi$
$683$	−1.51612	+	1.51612i	−0.0580129	+	0.0580129i	0.677505	+	0.735518i	$0.263061\pi$
$684$		0			0
$685$	7.02622	+	7.02622i	0.268458	+	0.268458i
$686$		0			0
$687$	−19.7125	−	21.6405i	−0.752078	−	0.825637i
$688$		0			0
$689$			9.41297i			0.358606i
$690$		0			0
$691$	13.1379	−	13.1379i	0.499788	−	0.499788i	−0.411584	−	0.911372i	$-0.635024\pi$
$691$	13.1379	−	13.1379i	0.499788	−	0.499788i	0.911372	+	0.411584i	$0.135024\pi$
$692$		0			0
$693$	10.8606	−	9.00425i	0.412562	−	0.342043i
$694$		0			0
$695$		−	30.1570i		−	1.14392i
$696$		0			0
$697$			5.38162i			0.203843i
$698$		0			0
$699$	−0.813181	+	17.4412i	−0.0307573	+	0.659688i
$700$		0			0
$701$	3.26007	−	3.26007i	0.123131	−	0.123131i	−0.642856	−	0.765987i	$-0.722251\pi$
$701$	3.26007	−	3.26007i	0.123131	−	0.123131i	0.765987	+	0.642856i	$0.222251\pi$
$702$		0			0
$703$		−	7.06631i		−	0.266511i
$704$		0			0
$705$	−34.4893	+	31.4165i	−1.29894	+	1.18322i
$706$		0			0
$707$	0.206592	+	0.206592i	0.00776970	+	0.00776970i
$708$		0			0
$709$	10.0423	−	10.0423i	0.377148	−	0.377148i	−0.492924	−	0.870072i	$-0.664072\pi$
$709$	10.0423	−	10.0423i	0.377148	−	0.377148i	0.870072	+	0.492924i	$0.164072\pi$
$710$		0			0
$711$	3.71650	−	39.7694i	0.139380	−	1.49147i
$712$		0			0
$713$	−48.5399			−1.81783
$714$		0			0
$715$	−10.3675	−	10.3675i	−0.387721	−	0.387721i
$716$		0			0
$717$	2.09064	−	44.8403i	0.0780763	−	1.67459i
$718$		0			0
$719$	−25.3964			−0.947126			−0.473563	−	0.880760i	$-0.657032\pi$
$719$	−25.3964			−0.947126			−0.473563	+	0.880760i	$0.657032\pi$
$720$		0			0
$721$	−7.36936			−0.274449
$722$		0			0
$723$	−1.05531	+	22.6344i	−0.0392473	+	0.841783i
$724$		0			0
$725$	1.16022	+	1.16022i	0.0430893	+	0.0430893i
$726$		0			0
$727$	33.7960			1.25342			0.626712	−	0.779251i	$-0.284400\pi$
$727$	33.7960			1.25342			0.626712	+	0.779251i	$0.284400\pi$
$728$		0			0
$729$	−25.9519	−	7.44971i	−0.961182	−	0.275915i
$730$		0			0
$731$	−6.96256	+	6.96256i	−0.257520	+	0.257520i
$732$		0			0
$733$	16.9845	+	16.9845i	0.627337	+	0.627337i	0.947397	−	0.320060i	$-0.103703\pi$
$733$	16.9845	+	16.9845i	0.627337	+	0.627337i	−0.320060	+	0.947397i	$0.603703\pi$
$734$		0			0
$735$	−3.00950	+	2.74137i	−0.111007	+	0.101117i
$736$		0			0
$737$		−	15.3068i		−	0.563834i
$738$		0			0
$739$	14.0004	−	14.0004i	0.515012	−	0.515012i	−0.401046	−	0.916058i	$-0.631353\pi$
$739$	14.0004	−	14.0004i	0.515012	−	0.515012i	0.916058	+	0.401046i	$0.131353\pi$
$740$		0			0
$741$	0.147449	−	3.16252i	0.00541669	−	0.116178i
$742$		0			0
$743$		−	0.453653i		−	0.0166429i	−0.999965	−	0.00832145i	$-0.997351\pi$
$743$		−	0.453653i		−	0.0166429i	0.999965	−	0.00832145i	$-0.00264883\pi$
$744$		0			0
$745$			16.4928i			0.604250i
$746$		0			0
$747$	14.5095	+	17.5010i	0.530876	+	0.640326i
$748$		0			0
$749$	−11.7713	+	11.7713i	−0.430115	+	0.430115i
$750$		0			0
$751$		−	27.8490i		−	1.01622i	−0.861291	−	0.508111i	$-0.830344\pi$
$751$		−	27.8490i		−	1.01622i	0.861291	−	0.508111i	$-0.169656\pi$
$752$		0			0
$753$	22.7029	+	24.9235i	0.827341	+	0.908262i
$754$		0			0
$755$	24.4447	+	24.4447i	0.889635	+	0.889635i
$756$		0			0
$757$	−16.8016	+	16.8016i	−0.610666	+	0.610666i	−0.943120	−	0.332454i	$-0.892124\pi$
$757$	−16.8016	+	16.8016i	−0.610666	+	0.610666i	0.332454	+	0.943120i	$0.392124\pi$
$758$		0			0
$759$	−43.3088	+	39.4503i	−1.57201	+	1.43195i
$760$		0			0
$761$	−27.5910			−1.00017			−0.500087	−	0.865975i	$-0.666698\pi$
$761$	−27.5910			−1.00017			−0.500087	+	0.865975i	$0.666698\pi$
$762$		0			0
$763$	−2.16723	−	2.16723i	−0.0784591	−	0.0784591i
$764$		0			0
$765$	4.40472	−	3.65183i	0.159253	−	0.132032i
$766$		0			0
$767$	−6.30374			−0.227615
$768$		0			0
$769$	11.9979			0.432656			0.216328	−	0.976321i	$-0.430592\pi$
$769$	11.9979			0.432656			0.216328	+	0.976321i	$0.430592\pi$
$770$		0			0
$771$	−5.12498	−	0.238947i	−0.184572	−	0.00860548i
$772$		0			0
$773$	18.0551	+	18.0551i	0.649397	+	0.649397i	0.952847	−	0.303450i	$-0.0981385\pi$
$773$	18.0551	+	18.0551i	0.649397	+	0.649397i	−0.303450	+	0.952847i	$0.598139\pi$
$774$		0			0
$775$	−3.53672			−0.127043
$776$		0			0
$777$	5.98146	+	6.56650i	0.214584	+	0.235572i
$778$		0			0
$779$	6.46174	−	6.46174i	0.231516	−	0.231516i
$780$		0			0
$781$	−5.44293	−	5.44293i	−0.194763	−	0.194763i
$782$		0			0
$783$	9.78904	+	12.9944i	0.349832	+	0.464382i
$784$		0			0
$785$		−	0.231205i		−	0.00825205i
$786$		0			0
$787$	−31.9058	+	31.9058i	−1.13732	+	1.13732i	−0.148390	+	0.988929i	$0.547409\pi$
$787$	−31.9058	+	31.9058i	−1.13732	+	1.13732i	−0.988929	+	0.148390i	$0.952591\pi$
$788$		0			0
$789$	12.6522	+	0.589896i	0.450430	+	0.0210009i
$790$		0			0
$791$			7.11741i			0.253066i
$792$		0			0
$793$		−	17.0314i		−	0.604804i
$794$		0			0
$795$	28.8552	+	1.34535i	1.02339	+	0.0477146i
$796$		0			0
$797$	13.6958	−	13.6958i	0.485130	−	0.485130i	−0.421635	−	0.906765i	$-0.638544\pi$
$797$	13.6958	−	13.6958i	0.485130	−	0.485130i	0.906765	+	0.421635i	$0.138544\pi$
$798$		0			0
$799$		−	9.29958i		−	0.328995i
$800$		0			0
$801$	−21.8823	−	2.04493i	−0.773173	−	0.0722540i
$802$		0			0
$803$	−6.30731	−	6.30731i	−0.222580	−	0.222580i
$804$		0			0
$805$	11.9533	−	11.9533i	0.421298	−	0.421298i
$806$		0			0
$807$	−7.88140	−	8.65226i	−0.277438	−	0.304574i
$808$		0			0
$809$	3.13855			0.110346			0.0551728	−	0.998477i	$-0.482429\pi$
$809$	3.13855			0.110346			0.0551728	+	0.998477i	$0.482429\pi$
$810$		0			0
$811$	−20.9034	−	20.9034i	−0.734018	−	0.734018i	0.237395	−	0.971413i	$-0.423706\pi$
$811$	−20.9034	−	20.9034i	−0.734018	−	0.734018i	−0.971413	+	0.237395i	$0.923706\pi$
$812$		0			0
$813$	9.32559	+	0.434797i	0.327063	+	0.0152490i
$814$		0			0
$815$	−16.5362			−0.579239
$816$		0			0
$817$	16.7200			0.584958
$818$		0			0
$819$	2.53997	+	3.06364i	0.0887539	+	0.107052i
$820$		0			0
$821$	12.4649	+	12.4649i	0.435027	+	0.435027i	0.890334	−	0.455308i	$-0.150471\pi$
$821$	12.4649	+	12.4649i	0.435027	+	0.435027i	−0.455308	+	0.890334i	$0.650471\pi$
$822$		0			0
$823$	3.04888			0.106277			0.0531387	−	0.998587i	$-0.483077\pi$
$823$	3.04888			0.106277			0.0531387	+	0.998587i	$0.483077\pi$
$824$		0			0
$825$	−3.15557	+	2.87443i	−0.109863	+	0.100075i
$826$		0			0
$827$	−30.0425	+	30.0425i	−1.04468	+	1.04468i	−0.0457277	+	0.998954i	$0.514561\pi$
$827$	−30.0425	+	30.0425i	−1.04468	+	1.04468i	−0.998954	+	0.0457277i	$0.985439\pi$
$828$		0			0
$829$	−3.28132	−	3.28132i	−0.113965	−	0.113965i	0.647825	−	0.761790i	$-0.275679\pi$
$829$	−3.28132	−	3.28132i	−0.113965	−	0.113965i	−0.761790	+	0.647825i	$0.775679\pi$
$830$		0			0
$831$	−21.9041	−	24.0465i	−0.759843	−	0.834162i
$832$		0			0
$833$		−	0.811469i		−	0.0281157i
$834$		0			0
$835$	−4.74252	+	4.74252i	−0.164122	+	0.164122i
$836$		0			0
$837$	−34.7257	−	4.88550i	−1.20030	−	0.168868i
$838$		0			0
$839$			28.0314i			0.967750i	0.875137	+	0.483875i	$0.160771\pi$
$839$			28.0314i			0.967750i	−0.875137	+	0.483875i	$0.839229\pi$
$840$		0			0
$841$			19.1971i			0.661967i
$842$		0			0
$843$	1.73614	−	37.2370i	0.0597959	−	1.28251i
$844$		0			0
$845$	−18.6806	+	18.6806i	−0.642633	+	0.642633i
$846$		0			0
$847$		−	11.1145i		−	0.381897i
$848$		0			0
$849$	16.2104	−	14.7661i	0.556338	−	0.506772i
$850$		0			0
$851$	−26.0812	−	26.0812i	−0.894052	−	0.894052i
$852$		0			0
$853$	27.9482	−	27.9482i	0.956927	−	0.956927i	−0.0421831	−	0.999110i	$-0.513431\pi$
$853$	27.9482	−	27.9482i	0.956927	−	0.956927i	0.999110	+	0.0421831i	$0.0134313\pi$
$854$		0			0
$855$	−9.67355	−	0.904005i	−0.330828	−	0.0309163i
$856$		0			0
$857$	1.73008			0.0590983			0.0295491	−	0.999563i	$-0.490593\pi$
$857$	1.73008			0.0590983			0.0295491	+	0.999563i	$0.490593\pi$
$858$		0			0
$859$	23.9580	+	23.9580i	0.817436	+	0.817436i	0.985736	−	0.168300i	$-0.0538277\pi$
$859$	23.9580	+	23.9580i	0.817436	+	0.817436i	−0.168300	+	0.985736i	$0.553828\pi$
$860$		0			0
$861$	−0.534983	+	11.4744i	−0.0182322	+	0.391046i
$862$		0			0
$863$	36.5495			1.24416			0.622079	−	0.782954i	$-0.286288\pi$
$863$	36.5495			1.24416			0.622079	+	0.782954i	$0.286288\pi$
$864$		0			0
$865$	−4.35619			−0.148115
$866$		0			0
$867$	1.31823	−	28.2736i	0.0447695	−	0.960223i
$868$		0			0
$869$	−44.2730	−	44.2730i	−1.50186	−	1.50186i
$870$		0			0
$871$	4.31784			0.146305
$872$		0			0
$873$	57.3559	+	5.35998i	1.94120	+	0.181408i
$874$		0			0
$875$	−7.43873	+	7.43873i	−0.251475	+	0.251475i
$876$		0			0
$877$	39.3736	+	39.3736i	1.32955	+	1.32955i	0.905758	+	0.423795i	$0.139302\pi$
$877$	39.3736	+	39.3736i	1.32955	+	1.32955i	0.423795	+	0.905758i	$0.360698\pi$
$878$		0			0
$879$	32.0539	−	29.1981i	1.08115	−	0.984826i
$880$		0			0
$881$		−	38.8112i		−	1.30758i	−0.756675	−	0.653791i	$-0.773178\pi$
$881$		−	38.8112i		−	1.30758i	0.756675	−	0.653791i	$-0.226822\pi$
$882$		0			0
$883$	−5.01750	+	5.01750i	−0.168852	+	0.168852i	−0.786475	−	0.617622i	$-0.788096\pi$
$883$	−5.01750	+	5.01750i	−0.168852	+	0.168852i	0.617622	+	0.786475i	$0.288096\pi$
$884$		0			0
$885$	−0.900961	+	19.3240i	−0.0302855	+	0.649567i
$886$		0			0
$887$			27.7806i			0.932781i	0.884579	+	0.466390i	$0.154446\pi$
$887$			27.7806i			0.932781i	−0.884579	+	0.466390i	$0.845554\pi$
$888$		0			0
$889$		−	6.85451i		−	0.229893i
$890$		0			0
$891$	−34.9540	+	23.8639i	−1.17100	+	0.799472i
$892$		0			0
$893$	−11.1661	+	11.1661i	−0.373658	+	0.373658i
$894$		0			0
$895$			35.2074i			1.17685i
$896$		0			0
$897$	−11.1284	−	12.2168i	−0.371566	−	0.407908i
$898$		0			0
$899$	14.9413	+	14.9413i	0.498321	+	0.498321i
$900$		0			0
$901$	−4.07159	+	4.07159i	−0.135644	+	0.135644i
$902$		0			0
$903$	−15.5373	+	14.1531i	−0.517050	+	0.470984i
$904$		0			0
$905$	14.6970			0.488544
$906$		0			0
$907$	10.0949	+	10.0949i	0.335196	+	0.335196i	0.854556	−	0.519360i	$-0.173830\pi$
$907$	10.0949	+	10.0949i	0.335196	+	0.335196i	−0.519360	+	0.854556i	$0.673830\pi$
$908$		0			0
$909$	−0.559420	−	0.674756i	−0.0185548	−	0.0223802i
$910$		0			0
$911$	44.3527			1.46947			0.734736	−	0.678353i	$-0.237306\pi$
$911$	44.3527			1.46947			0.734736	+	0.678353i	$0.237306\pi$
$912$		0			0
$913$	35.6355			1.17936
$914$		0			0
$915$	−52.2095	−	2.43422i	−1.72599	−	0.0804727i
$916$		0			0
$917$	5.31306	+	5.31306i	0.175453	+	0.175453i
$918$		0			0
$919$	42.3965			1.39853			0.699265	−	0.714862i	$-0.253511\pi$
$919$	42.3965			1.39853			0.699265	+	0.714862i	$0.253511\pi$
$920$		0			0
$921$	18.7121	+	20.5423i	0.616585	+	0.676892i
$922$		0			0
$923$	1.53538	−	1.53538i	0.0505375	−	0.0505375i
$924$		0			0
$925$	−1.90033	−	1.90033i	−0.0624825	−	0.0624825i
$926$		0			0
$927$	22.0122	+	2.05707i	0.722975	+	0.0675629i
$928$		0			0
$929$		−	5.59975i		−	0.183722i	−0.995772	−	0.0918609i	$-0.970718\pi$
$929$		−	5.59975i		−	0.183722i	0.995772	−	0.0918609i	$-0.0292815\pi$
$930$		0			0
$931$	−0.974336	+	0.974336i	−0.0319326	+	0.0319326i
$932$		0			0
$933$	16.0369	+	0.747704i	0.525024	+	0.0244787i
$934$		0			0
$935$		−	8.96890i		−	0.293314i
$936$		0			0
$937$		−	46.2381i		−	1.51053i	−0.655417	−	0.755267i	$-0.727507\pi$
$937$		−	46.2381i		−	1.51053i	0.655417	−	0.755267i	$-0.272493\pi$
$938$		0			0
$939$	8.09276	+	0.377317i	0.264097	+	0.0123133i
$940$		0			0
$941$	−2.78308	+	2.78308i	−0.0907258	+	0.0907258i	−0.751013	−	0.660287i	$-0.770435\pi$
$941$	−2.78308	+	2.78308i	−0.0907258	+	0.0907258i	0.660287	+	0.751013i	$0.270435\pi$
$942$		0			0
$943$		−	47.6996i		−	1.55331i
$944$		0			0
$945$	9.75454	−	7.34836i	0.317315	−	0.239042i
$946$		0			0
$947$	21.9819	+	21.9819i	0.714315	+	0.714315i	0.967435	−	0.253120i	$-0.0814567\pi$
$947$	21.9819	+	21.9819i	0.714315	+	0.714315i	−0.253120	+	0.967435i	$0.581457\pi$
$948$		0			0
$949$	1.77920	−	1.77920i	0.0577554	−	0.0577554i
$950$		0			0
$951$	5.41623	+	5.94599i	0.175633	+	0.192812i
$952$		0			0
$953$	7.09802			0.229927			0.114964	−	0.993370i	$-0.463325\pi$
$953$	7.09802			0.229927			0.114964	+	0.993370i	$0.463325\pi$
$954$		0			0
$955$	13.4374	+	13.4374i	0.434824	+	0.434824i
$956$		0			0
$957$	25.4745	+	1.18772i	0.823474	+	0.0383937i
$958$		0			0
$959$	−4.22774			−0.136521
$960$		0			0
$961$	−14.5461			−0.469229
$962$		0			0
$963$	38.4466	−	31.8750i	1.23892	−	1.02716i
$964$		0			0
$965$	10.8804	+	10.8804i	0.350252	+	0.350252i
$966$		0			0
$967$	−18.2659			−0.587392			−0.293696	−	0.955899i	$-0.594885\pi$
$967$	−18.2659			−0.587392			−0.293696	+	0.955899i	$0.594885\pi$
$968$		0			0
$969$	1.43173	−	1.30417i	0.0459938	−	0.0418960i
$970$		0			0
$971$	−12.0505	+	12.0505i	−0.386720	+	0.386720i	−0.873516	−	0.486796i	$-0.838166\pi$
$971$	−12.0505	+	12.0505i	−0.386720	+	0.386720i	0.486796	+	0.873516i	$0.338166\pi$
$972$		0			0
$973$	9.07286	+	9.07286i	0.290863	+	0.290863i
$974$		0			0
$975$	−0.810838	−	0.890144i	−0.0259676	−	0.0285074i
$976$		0			0
$977$			7.20150i			0.230396i	0.993343	+	0.115198i	$0.0367503\pi$
$977$			7.20150i			0.230396i	−0.993343	+	0.115198i	$0.963250\pi$
$978$		0			0
$979$	−24.3603	+	24.3603i	−0.778559	+	0.778559i
$980$		0			0
$981$	5.86854	+	7.07845i	0.187368	+	0.225998i
$982$		0			0
$983$			45.8466i			1.46228i	0.682228	+	0.731140i	$0.261011\pi$
$983$			45.8466i			1.46228i	−0.682228	+	0.731140i	$0.738989\pi$
$984$		0			0
$985$			9.77672i			0.311512i
$986$		0			0
$987$	0.924464	−	19.8281i	0.0294260	−	0.631134i
$988$		0			0
$989$	61.7121	−	61.7121i	1.96233	−	1.96233i
$990$		0			0
$991$			13.5100i			0.429159i	0.976706	+	0.214580i	$0.0688382\pi$
$991$			13.5100i			0.429159i	−0.976706	+	0.214580i	$0.931162\pi$
$992$		0			0
$993$	−37.2346	+	33.9172i	−1.18160	+	1.07633i
$994$		0			0
$995$	43.2245	+	43.2245i	1.37031	+	1.37031i
$996$		0			0
$997$	28.3395	−	28.3395i	0.897520	−	0.897520i	−0.0976959	−	0.995216i	$-0.531147\pi$
$997$	28.3395	−	28.3395i	0.897520	−	0.897520i	0.995216	+	0.0976959i	$0.0311473\pi$
$998$		0			0
$999$	−16.0336	−	21.2837i	−0.507280	−	0.673386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.12		40
3.2	odd	2	inner	1344.2.s.c.239.20		40
4.3	odd	2		336.2.s.c.323.6	yes	40
12.11	even	2		336.2.s.c.323.15	yes	40
16.5	even	4		336.2.s.c.155.15	yes	40
16.11	odd	4	inner	1344.2.s.c.911.20		40
48.5	odd	4		336.2.s.c.155.6	✓	40
48.11	even	4	inner	1344.2.s.c.911.12		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.6	✓	40	48.5	odd	4
336.2.s.c.155.15	yes	40	16.5	even	4
336.2.s.c.323.6	yes	40	4.3	odd	2
336.2.s.c.323.15	yes	40	12.11	even	2
1344.2.s.c.239.12		40	1.1	even	1	trivial
1344.2.s.c.239.20		40	3.2	odd	2	inner
1344.2.s.c.911.12		40	48.11	even	4	inner
1344.2.s.c.911.20		40	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0806676 - 1.73017i) q^{3} +(-1.66193 - 1.66193i) q^{5} +1.00000 q^{7} +(-2.98699 - 0.279137i) q^{9} +O(q^{10})\)	\(q+(0.0806676 - 1.73017i) q^{3} +(-1.66193 - 1.66193i) q^{5} +1.00000 q^{7} +(-2.98699 - 0.279137i) q^{9} +(-3.32524 + 3.32524i) q^{11} +(-0.938005 - 0.938005i) q^{13} +(-3.00950 + 2.74137i) q^{15} -0.811469i q^{17} +(-0.974336 + 0.974336i) q^{19} +(0.0806676 - 1.73017i) q^{21} +7.19240i q^{23} +0.524053i q^{25} +(-0.723909 + 5.14548i) q^{27} +(2.21393 - 2.21393i) q^{29} +6.74878i q^{31} +(5.48500 + 6.02148i) q^{33} +(-1.66193 - 1.66193i) q^{35} +(-3.62622 + 3.62622i) q^{37} +(-1.69858 + 1.54724i) q^{39} -6.63194 q^{41} +(-8.58019 - 8.58019i) q^{43} +(4.50027 + 5.42808i) q^{45} +11.4602 q^{47} +1.00000 q^{49} +(-1.40398 - 0.0654593i) q^{51} +(-5.01755 - 5.01755i) q^{53} +11.0527 q^{55} +(1.60717 + 1.76437i) q^{57} +(3.36018 - 3.36018i) q^{59} +(9.07854 + 9.07854i) q^{61} +(-2.98699 - 0.279137i) q^{63} +3.11781i q^{65} +(-2.30161 + 2.30161i) q^{67} +(12.4441 + 0.580193i) q^{69} +1.63685i q^{71} +1.89680i q^{73} +(0.906702 + 0.0422741i) q^{75} +(-3.32524 + 3.32524i) q^{77} +13.3142i q^{79} +(8.84416 + 1.66756i) q^{81} +(-5.35833 - 5.35833i) q^{83} +(-1.34861 + 1.34861i) q^{85} +(-3.65188 - 4.00907i) q^{87} +7.32588 q^{89} +(-0.938005 - 0.938005i) q^{91} +(11.6766 + 0.544408i) q^{93} +3.23857 q^{95} -19.2019 q^{97} +(10.8606 - 9.00425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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