LMFDB - Embedded newform 140.2.q.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(9,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("140.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.q (of order $6$, degree $2$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	140.109
Dual form			140.2.q.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(2.13746 + 0.656712i) q^{5} +(1.13746 - 2.38876i) q^{7} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(2.13746 + 0.656712i) q^{5} +(1.13746 - 2.38876i) q^{7} +(2.63746 - 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 - 2.83616i) q^{15} +(0.362541 + 0.209313i) q^{17} +(1.63746 + 2.83616i) q^{19} +(-3.77492 + 2.59808i) q^{21} +(-6.77492 + 3.91150i) q^{23} +(4.13746 + 2.80739i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(-7.91238 + 4.56821i) q^{33} +(4.00000 - 4.35890i) q^{35} +(8.63746 - 4.98684i) q^{37} +(2.27492 - 3.94027i) q^{39} -3.72508 q^{41} -2.15068i q^{43} +(-5.63746 + 3.25479i) q^{47} +(-4.41238 - 5.43424i) q^{49} +(-0.362541 - 0.627940i) q^{51} +(4.91238 + 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} -5.67232i q^{57} +(-1.63746 + 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-1.72508 + 5.61478i) q^{65} +(3.04983 + 1.76082i) q^{67} +13.5498 q^{69} -4.54983 q^{71} +(-5.63746 - 3.25479i) q^{73} +(-3.77492 - 7.79423i) q^{75} +(-7.91238 - 11.4964i) q^{77} +(3.63746 + 6.30026i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(6.41238 + 3.70219i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(4.91238 - 2.83616i) q^{93} +(1.63746 + 7.13752i) q^{95} +6.92820i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + q^{5} - 3 q^{7}+O(q^{10}) $ 4 * q - 6 * q^3 + q^5 - 3 * q^7	$ 4 q - 6 q^{3} + q^{5} - 3 q^{7} + 3 q^{11} - 3 q^{15} + 9 q^{17} - q^{19} - 12 q^{23} + 9 q^{25} - 2 q^{29} + q^{31} - 9 q^{33} + 16 q^{35} + 27 q^{37} - 6 q^{39} - 30 q^{41} - 15 q^{47} + 5 q^{49} - 9 q^{51} - 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} - 22 q^{65} - 18 q^{67} + 24 q^{69} + 12 q^{71} - 15 q^{73} - 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} + 3 q^{87} - 14 q^{89} + 10 q^{91} - 3 q^{93} - q^{95}+O(q^{100}) $ 4 * q - 6 * q^3 + q^5 - 3 * q^7 + 3 * q^11 - 3 * q^15 + 9 * q^17 - q^19 - 12 * q^23 + 9 * q^25 - 2 * q^29 + q^31 - 9 * q^33 + 16 * q^35 + 27 * q^37 - 6 * q^39 - 30 * q^41 - 15 * q^47 + 5 * q^49 - 9 * q^51 - 3 * q^53 + 27 * q^55 + q^59 + 12 * q^61 - 22 * q^65 - 18 * q^67 + 24 * q^69 + 12 * q^71 - 15 * q^73 - 9 * q^77 + 7 * q^79 + 18 * q^81 - 5 * q^85 + 3 * q^87 - 14 * q^89 + 10 * q^91 - 3 * q^93 - q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	2.13746	+	0.656712i	0.955901	+	0.293691i
$5$	2.13746	+	0.656712i	0.955901	+	0.293691i
$6$		0			0
$7$	1.13746	−	2.38876i	0.429919	−	0.902867i
$7$	1.13746	−	2.38876i	0.429919	−	0.902867i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	−0.127473	−	0.991842i	$-0.540687\pi$
$11$	2.63746	−	4.56821i	0.795224	−	1.37737i	0.922697	−	0.385526i	$-0.125980\pi$
$12$		0			0
$13$			2.62685i			0.728557i	0.931290	+	0.364278i	$0.118684\pi$
$13$			2.62685i			0.728557i	−0.931290	+	0.364278i	$0.881316\pi$
$14$		0			0
$15$	−2.63746	−	2.83616i	−0.680989	−	0.732294i
$16$		0			0
$17$	0.362541	+	0.209313i	0.0879292	+	0.0507659i	0.543320	−	0.839526i	$-0.317167\pi$
$17$	0.362541	+	0.209313i	0.0879292	+	0.0507659i	−0.455391	+	0.890292i	$0.650500\pi$
$18$		0			0
$19$	1.63746	+	2.83616i	0.375659	+	0.650660i	0.990425	−	0.138049i	$-0.0440831\pi$
$19$	1.63746	+	2.83616i	0.375659	+	0.650660i	−0.614767	+	0.788709i	$0.710750\pi$
$20$		0			0
$21$	−3.77492	+	2.59808i	−0.823754	+	0.566947i
$22$		0			0
$23$	−6.77492	+	3.91150i	−1.41267	+	0.815604i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−6.77492	+	3.91150i	−1.41267	+	0.815604i	−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	4.13746	+	2.80739i	0.827492	+	0.561478i
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.27492			−0.793832			−0.396916	−	0.917855i	$-0.629920\pi$
$29$	−4.27492			−0.793832			−0.396916	+	0.917855i	$0.629920\pi$
$30$		0			0
$31$	−1.63746	+	2.83616i	−0.294096	+	0.509390i	−0.974774	−	0.223193i	$-0.928352\pi$
$31$	−1.63746	+	2.83616i	−0.294096	+	0.509390i	0.680678	+	0.732583i	$0.261685\pi$
$32$		0			0
$33$	−7.91238	+	4.56821i	−1.37737	+	0.795224i
$34$		0			0
$35$	4.00000	−	4.35890i	0.676123	−	0.736788i
$36$		0			0
$37$	8.63746	−	4.98684i	1.41999	−	0.819831i	0.423692	−	0.905806i	$-0.360734\pi$
$37$	8.63746	−	4.98684i	1.41999	−	0.819831i	0.996297	+	0.0859750i	$0.0274005\pi$
$38$		0			0
$39$	2.27492	−	3.94027i	0.364278	−	0.630949i
$40$		0			0
$41$	−3.72508			−0.581760			−0.290880	−	0.956760i	$-0.593948\pi$
$41$	−3.72508			−0.581760			−0.290880	+	0.956760i	$0.593948\pi$
$42$		0			0
$43$		−	2.15068i		−	0.327975i	−0.986462	−	0.163988i	$-0.947564\pi$
$43$		−	2.15068i		−	0.327975i	0.986462	−	0.163988i	$-0.0524357\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.63746	+	3.25479i	−0.822308	+	0.474760i	−0.851212	−	0.524823i	$-0.824132\pi$
$47$	−5.63746	+	3.25479i	−0.822308	+	0.474760i	0.0289038	+	0.999582i	$0.490798\pi$
$48$		0			0
$49$	−4.41238	−	5.43424i	−0.630339	−	0.776320i
$50$		0			0
$51$	−0.362541	−	0.627940i	−0.0507659	−	0.0879292i
$52$		0			0
$53$	4.91238	+	2.83616i	0.674767	+	0.389577i	0.797880	−	0.602816i	$-0.205955\pi$
$53$	4.91238	+	2.83616i	0.674767	+	0.389577i	−0.123114	+	0.992393i	$0.539288\pi$
$54$		0			0
$55$	8.63746	−	8.03231i	1.16467	−	1.08308i
$56$		0			0
$57$		−	5.67232i		−	0.751318i
$58$		0			0
$59$	−1.63746	+	2.83616i	−0.213179	+	0.369237i	−0.952708	−	0.303888i	$-0.901715\pi$
$59$	−1.63746	+	2.83616i	−0.213179	+	0.369237i	0.739529	+	0.673125i	$0.235048\pi$
$60$		0			0
$61$	6.77492	+	11.7345i	0.867439	+	1.50245i	0.864605	+	0.502453i	$0.167569\pi$
$61$	6.77492	+	11.7345i	0.867439	+	1.50245i	0.00283468	+	0.999996i	$0.499098\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.72508	+	5.61478i	−0.213970	+	0.696428i
$66$		0			0
$67$	3.04983	+	1.76082i	0.372597	+	0.215119i	0.674592	−	0.738191i	$-0.264319\pi$
$67$	3.04983	+	1.76082i	0.372597	+	0.215119i	−0.301996	+	0.953309i	$0.597653\pi$
$68$		0			0
$69$	13.5498			1.63121
$70$		0			0
$71$	−4.54983			−0.539966			−0.269983	−	0.962865i	$-0.587018\pi$
$71$	−4.54983			−0.539966			−0.269983	+	0.962865i	$0.587018\pi$
$72$		0			0
$73$	−5.63746	−	3.25479i	−0.659815	−	0.380944i	0.132392	−	0.991197i	$-0.457734\pi$
$73$	−5.63746	−	3.25479i	−0.659815	−	0.380944i	−0.792206	+	0.610253i	$0.791068\pi$
$74$		0			0
$75$	−3.77492	−	7.79423i	−0.435890	−	0.900000i
$76$		0			0
$77$	−7.91238	−	11.4964i	−0.901699	−	1.31014i
$78$		0			0
$79$	3.63746	+	6.30026i	0.409246	+	0.708835i	0.994805	−	0.101795i	$-0.0324584\pi$
$79$	3.63746	+	6.30026i	0.409246	+	0.708835i	−0.585559	+	0.810630i	$0.699125\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$		−	7.40437i		−	0.812736i	−0.913710	−	0.406368i	$-0.866795\pi$
$83$		−	7.40437i		−	0.812736i	0.913710	−	0.406368i	$-0.133205\pi$
$84$		0			0
$85$	0.637459	+	0.685484i	0.0691421	+	0.0743512i
$86$		0			0
$87$	6.41238	+	3.70219i	0.687479	+	0.396916i
$88$		0			0
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	0.618720	−	0.785611i	$-0.287651\pi$
$89$	−3.50000	−	6.06218i	−0.370999	−	0.642590i	−0.989720	+	0.143022i	$0.954318\pi$
$90$		0			0
$91$	6.27492	+	2.98793i	0.657790	+	0.313220i
$92$		0			0
$93$	4.91238	−	2.83616i	0.509390	−	0.294096i
$94$		0			0
$95$	1.63746	+	7.13752i	0.168000	+	0.732294i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.77492	−	11.7345i	0.674129	−	1.16763i	−0.302593	−	0.953120i	$-0.597852\pi$
$101$	6.77492	−	11.7345i	0.674129	−	1.16763i	0.976723	−	0.214507i	$-0.0688144\pi$
$102$		0			0
$103$	9.77492	−	5.64355i	0.963151	−	0.556076i	0.0660098	−	0.997819i	$-0.478973\pi$
$103$	9.77492	−	5.64355i	0.963151	−	0.556076i	0.897141	+	0.441743i	$0.145640\pi$
$104$		0			0
$105$	−9.77492	+	3.07425i	−0.953934	+	0.300016i
$106$		0			0
$107$	−3.04983	+	1.76082i	−0.294839	+	0.170225i	−0.640122	−	0.768273i	$-0.721116\pi$
$107$	−3.04983	+	1.76082i	−0.294839	+	0.170225i	0.345283	+	0.938499i	$0.387783\pi$
$108$		0			0
$109$	−5.77492	+	10.0025i	−0.553137	+	0.958061i	0.444909	+	0.895576i	$0.353236\pi$
$109$	−5.77492	+	10.0025i	−0.553137	+	0.958061i	−0.998046	+	0.0624852i	$0.980097\pi$
$110$		0			0
$111$	−17.2749			−1.63966
$112$		0			0
$113$			4.30136i			0.404637i	0.979320	+	0.202319i	$0.0648477\pi$
$113$			4.30136i			0.404637i	−0.979320	+	0.202319i	$0.935152\pi$
$114$		0			0
$115$	−17.0498	+	3.91150i	−1.58991	+	0.364749i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.912376	−	0.627940i	0.0836374	−	0.0575632i
$120$		0			0
$121$	−8.41238	−	14.5707i	−0.764761	−	1.32461i
$122$		0			0
$123$	5.58762	+	3.22602i	0.503819	+	0.290880i
$124$		0			0
$125$	7.00000	+	8.71780i	0.626099	+	0.779744i
$126$		0			0
$127$			15.6460i			1.38836i	0.719802	+	0.694179i	$0.244232\pi$
$127$			15.6460i			1.38836i	−0.719802	+	0.694179i	$0.755768\pi$
$128$		0			0
$129$	−1.86254	+	3.22602i	−0.163988	+	0.284035i
$130$		0			0
$131$	5.36254	+	9.28819i	0.468527	+	0.811513i	0.999353	−	0.0359678i	$-0.0114514\pi$
$131$	5.36254	+	9.28819i	0.468527	+	0.811513i	−0.530826	+	0.847481i	$0.678118\pi$
$132$		0			0
$133$	8.63746	−	0.685484i	0.748963	−	0.0594390i
$134$		0			0
$135$	−3.41238	+	11.1066i	−0.293691	+	0.955901i
$136$		0			0
$137$	−18.4622	−	10.6592i	−1.57733	−	0.910674i	−0.995230	−	0.0975588i	$-0.968897\pi$
$137$	−18.4622	−	10.6592i	−1.57733	−	0.910674i	−0.582103	−	0.813115i	$-0.697770\pi$
$138$		0			0
$139$	−13.0997			−1.11110			−0.555550	−	0.831483i	$-0.687492\pi$
$139$	−13.0997			−1.11110			−0.555550	+	0.831483i	$0.687492\pi$
$140$		0			0
$141$	11.2749			0.949519
$142$		0			0
$143$	12.0000	+	6.92820i	1.00349	+	0.579365i
$144$		0			0
$145$	−9.13746	−	2.80739i	−0.758825	−	0.233141i
$146$		0			0
$147$	1.91238	+	11.9726i	0.157730	+	0.987482i
$148$		0			0
$149$	−3.77492	−	6.53835i	−0.309253	−	0.535642i	0.668946	−	0.743311i	$-0.266746\pi$
$149$	−3.77492	−	6.53835i	−0.309253	−	0.535642i	−0.978199	+	0.207669i	$0.933412\pi$
$150$		0			0
$151$	6.36254	−	11.0202i	0.517776	−	0.896815i	−0.482011	−	0.876165i	$-0.660093\pi$
$151$	6.36254	−	11.0202i	0.517776	−	0.896815i	0.999787	−	0.0206494i	$-0.00657337\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.36254	+	4.98684i	−0.430730	+	0.400553i
$156$		0			0
$157$	−1.91238	−	1.10411i	−0.152624	−	0.0881176i	0.421743	−	0.906715i	$-0.361418\pi$
$157$	−1.91238	−	1.10411i	−0.152624	−	0.0881176i	−0.574367	+	0.818598i	$0.694752\pi$
$158$		0			0
$159$	−4.91238	−	8.50848i	−0.389577	−	0.674767i
$160$		0			0
$161$	1.63746	+	20.6328i	0.129050	+	1.62610i
$162$		0			0
$163$	4.91238	−	2.83616i	0.384767	−	0.222145i	−0.295123	−	0.955459i	$-0.595361\pi$
$163$	4.91238	−	2.83616i	0.384767	−	0.222145i	0.679890	+	0.733314i	$0.262027\pi$
$164$		0			0
$165$	−19.9124	+	4.56821i	−1.55018	+	0.355635i
$166$		0			0
$167$			0.476171i			0.0368472i	0.999830	+	0.0184236i	$0.00586474\pi$
$167$			0.476171i			0.0368472i	−0.999830	+	0.0184236i	$0.994135\pi$
$168$		0			0
$169$	6.09967			0.469205
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.7371	−	10.2405i	1.34853	−	0.778573i	0.360488	−	0.932764i	$-0.382610\pi$
$173$	17.7371	−	10.2405i	1.34853	−	0.778573i	0.988041	+	0.154190i	$0.0492769\pi$
$174$		0			0
$175$	11.4124	−	6.69012i	0.862695	−	0.505725i
$176$		0			0
$177$	4.91238	−	2.83616i	0.369237	−	0.213179i
$178$		0			0
$179$	−3.63746	+	6.30026i	−0.271876	+	0.470904i	−0.969342	−	0.245714i	$-0.920978\pi$
$179$	−3.63746	+	6.30026i	−0.271876	+	0.470904i	0.697466	+	0.716618i	$0.254311\pi$
$180$		0			0
$181$	−24.2749			−1.80434			−0.902170	−	0.431380i	$-0.858027\pi$
$181$	−24.2749			−1.80434			−0.902170	+	0.431380i	$0.858027\pi$
$182$		0			0
$183$		−	23.4690i		−	1.73488i
$184$		0			0
$185$	21.7371	−	4.98684i	1.59815	−	0.366640i
$186$		0			0
$187$	1.91238	−	1.10411i	0.139847	−	0.0807406i
$188$		0			0
$189$	12.4124	+	5.91041i	0.902867	+	0.429919i
$190$		0			0
$191$	−0.0876242	−	0.151770i	−0.00634026	−	0.0109817i	0.862838	−	0.505481i	$-0.168685\pi$
$191$	−0.0876242	−	0.151770i	−0.00634026	−	0.0109817i	−0.869178	+	0.494499i	$0.835352\pi$
$192$		0			0
$193$	−18.4622	−	10.6592i	−1.32894	−	0.767263i	−0.343803	−	0.939042i	$-0.611715\pi$
$193$	−18.4622	−	10.6592i	−1.32894	−	0.767263i	−0.985136	+	0.171778i	$0.945049\pi$
$194$		0			0
$195$	7.45017	−	6.92820i	0.533517	−	0.496139i
$196$		0			0
$197$		−	8.60271i		−	0.612918i	−0.951884	−	0.306459i	$-0.900856\pi$
$197$		−	8.60271i		−	0.612918i	0.951884	−	0.306459i	$-0.0991442\pi$
$198$		0			0
$199$	8.63746	−	14.9605i	0.612293	−	1.06052i	−0.378560	−	0.925577i	$-0.623581\pi$
$199$	8.63746	−	14.9605i	0.612293	−	1.06052i	0.990853	−	0.134946i	$-0.0430861\pi$
$200$		0			0
$201$	−3.04983	−	5.28247i	−0.215119	−	0.372597i
$202$		0			0
$203$	−4.86254	+	10.2118i	−0.341284	+	0.716725i
$204$		0			0
$205$	−7.96221	−	2.44631i	−0.556105	−	0.170857i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	17.2749			1.19493
$210$		0			0
$211$	25.6495			1.76578			0.882892	−	0.469576i	$-0.155593\pi$
$211$	25.6495			1.76578			0.882892	+	0.469576i	$0.155593\pi$
$212$		0			0
$213$	6.82475	+	3.94027i	0.467624	+	0.269983i
$214$		0			0
$215$	1.41238	−	4.59698i	0.0963232	−	0.313512i
$216$		0			0
$217$	4.91238	+	7.13752i	0.333474	+	0.484526i
$218$		0			0
$219$	5.63746	+	9.76436i	0.380944	+	0.659815i
$220$		0			0
$221$	−0.549834	+	0.952341i	−0.0369859	+	0.0640614i
$222$		0			0
$223$		−	8.71780i		−	0.583787i	−0.956451	−	0.291893i	$-0.905715\pi$
$223$		−	8.71780i		−	0.583787i	0.956451	−	0.291893i	$-0.0942853\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.9124	−	9.76436i	−1.12251	−	0.648084i	−0.180472	−	0.983580i	$-0.557763\pi$
$227$	−16.9124	−	9.76436i	−1.12251	−	0.648084i	−0.942041	+	0.335496i	$0.891096\pi$
$228$		0			0
$229$	1.63746	+	2.83616i	0.108206	+	0.187419i	0.915044	−	0.403355i	$-0.132156\pi$
$229$	1.63746	+	2.83616i	0.108206	+	0.187419i	−0.806837	+	0.590774i	$0.798823\pi$
$230$		0			0
$231$	1.91238	+	24.0969i	0.125825	+	1.58546i
$232$		0			0
$233$	12.3625	−	7.13752i	0.809897	−	0.467594i	−0.0370231	−	0.999314i	$-0.511788\pi$
$233$	12.3625	−	7.13752i	0.809897	−	0.467594i	0.846920	+	0.531720i	$0.178454\pi$
$234$		0			0
$235$	−14.1873	+	3.25479i	−0.925477	+	0.212319i
$236$		0			0
$237$		−	12.6005i		−	0.818492i
$238$		0			0
$239$	−0.549834			−0.0355658			−0.0177829	−	0.999842i	$-0.505661\pi$
$239$	−0.549834			−0.0355658			−0.0177829	+	0.999842i	$0.505661\pi$
$240$		0			0
$241$	−4.91238	+	8.50848i	−0.316434	+	0.548080i	−0.979741	−	0.200267i	$-0.935819\pi$
$241$	−4.91238	+	8.50848i	−0.316434	+	0.548080i	0.663307	+	0.748347i	$0.269152\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.86254	−	14.5131i	−0.374544	−	0.927209i
$246$		0			0
$247$	−7.45017	+	4.30136i	−0.474043	+	0.273689i
$248$		0			0
$249$	−6.41238	+	11.1066i	−0.406368	+	0.703850i
$250$		0			0
$251$	−20.5498			−1.29709			−0.648547	−	0.761175i	$-0.724623\pi$
$251$	−20.5498			−1.29709			−0.648547	+	0.761175i	$0.724623\pi$
$252$		0			0
$253$			41.2657i			2.59435i
$254$		0			0
$255$	−0.362541	−	1.58028i	−0.0227032	−	0.0989611i
$256$		0			0
$257$	10.0876	−	5.82409i	0.629249	−	0.363297i	−0.151212	−	0.988501i	$-0.548318\pi$
$257$	10.0876	−	5.82409i	0.629249	−	0.363297i	0.780461	+	0.625204i	$0.214984\pi$
$258$		0			0
$259$	−2.08762	−	26.3052i	−0.129719	−	1.63452i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.675248	−	0.389855i	−0.0416376	−	0.0240395i	0.479037	−	0.877795i	$-0.340986\pi$
$263$	−0.675248	−	0.389855i	−0.0416376	−	0.0240395i	−0.520674	+	0.853755i	$0.674319\pi$
$264$		0			0
$265$	8.63746	+	9.28819i	0.530595	+	0.570569i
$266$		0			0
$267$			12.1244i			0.741999i
$268$		0			0
$269$	−7.22508	+	12.5142i	−0.440521	+	0.763005i	−0.997728	−	0.0673687i	$-0.978540\pi$
$269$	−7.22508	+	12.5142i	−0.440521	+	0.763005i	0.557207	+	0.830374i	$0.311873\pi$
$270$		0			0
$271$	−4.91238	−	8.50848i	−0.298406	−	0.516854i	0.677366	−	0.735646i	$-0.263121\pi$
$271$	−4.91238	−	8.50848i	−0.298406	−	0.516854i	−0.975771	+	0.218793i	$0.929788\pi$
$272$		0			0
$273$	−6.82475	−	9.91613i	−0.413053	−	0.600152i
$274$		0			0
$275$	23.7371	−	11.4964i	1.43140	−	0.693260i
$276$		0			0
$277$	12.3625	+	7.13752i	0.742793	+	0.428852i	0.823084	−	0.567920i	$-0.192252\pi$
$277$	12.3625	+	7.13752i	0.742793	+	0.428852i	−0.0802909	+	0.996771i	$0.525585\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−9.46221	−	5.46301i	−0.562470	−	0.324742i	0.191666	−	0.981460i	$-0.438611\pi$
$283$	−9.46221	−	5.46301i	−0.562470	−	0.324742i	−0.754136	+	0.656718i	$0.771944\pi$
$284$		0			0
$285$	3.72508	−	12.1244i	0.220655	−	0.718185i
$286$		0			0
$287$	−4.23713	+	8.89834i	−0.250110	+	0.525252i
$288$		0			0
$289$	−8.41238	−	14.5707i	−0.494846	−	0.857098i
$290$		0			0
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$		0			0
$293$			6.92820i			0.404750i	0.979308	+	0.202375i	$0.0648660\pi$
$293$			6.92820i			0.404750i	−0.979308	+	0.202375i	$0.935134\pi$
$294$		0			0
$295$	−5.36254	+	4.98684i	−0.312219	+	0.290345i
$296$		0			0
$297$	23.7371	+	13.7046i	1.37737	+	0.795224i
$298$		0			0
$299$	−10.2749	−	17.7967i	−0.594214	−	1.02921i
$300$		0			0
$301$	−5.13746	−	2.44631i	−0.296118	−	0.141003i
$302$		0			0
$303$	−20.3248	+	11.7345i	−1.16763	+	0.674129i
$304$		0			0
$305$	6.77492	+	29.5312i	0.387931	+	1.69095i
$306$		0			0
$307$		−	26.5145i		−	1.51326i	−0.653843	−	0.756631i	$-0.726844\pi$
$307$		−	26.5145i		−	1.51326i	0.653843	−	0.756631i	$-0.273156\pi$
$308$		0			0
$309$	−19.5498			−1.11215
$310$		0			0
$311$	4.91238	−	8.50848i	0.278555	−	0.482472i	−0.692471	−	0.721446i	$-0.743478\pi$
$311$	4.91238	−	8.50848i	0.278555	−	0.482472i	0.971026	+	0.238974i	$0.0768111\pi$
$312$		0			0
$313$	−29.0120	+	16.7501i	−1.63986	+	0.946772i	−0.658977	+	0.752163i	$0.729010\pi$
$313$	−29.0120	+	16.7501i	−1.63986	+	0.946772i	−0.980881	+	0.194609i	$0.937656\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.1873	+	12.8098i	−1.24616	+	0.719472i	−0.970342	−	0.241737i	$-0.922283\pi$
$317$	−22.1873	+	12.8098i	−1.24616	+	0.719472i	−0.275821	+	0.961209i	$0.588950\pi$
$318$		0			0
$319$	−11.2749	+	19.5287i	−0.631274	+	1.09340i
$320$		0			0
$321$	6.09967			0.340450
$322$		0			0
$323$			1.37097i			0.0762827i
$324$		0			0
$325$	−7.37459	+	10.8685i	−0.409068	+	0.602875i
$326$		0			0
$327$	17.3248	−	10.0025i	0.958061	−	0.553137i
$328$		0			0
$329$	1.36254	+	17.1687i	0.0751193	+	0.946543i
$330$		0			0
$331$	−8.91238	−	15.4367i	−0.489868	−	0.848477i	0.510064	−	0.860137i	$-0.329622\pi$
$331$	−8.91238	−	15.4367i	−0.489868	−	0.848477i	−0.999932	+	0.0116596i	$0.996289\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.36254	+	5.76655i	0.292987	+	0.315060i
$336$		0			0
$337$			4.30136i			0.234310i	0.993114	+	0.117155i	$0.0373774\pi$
$337$			4.30136i			0.234310i	−0.993114	+	0.117155i	$0.962623\pi$
$338$		0			0
$339$	3.72508	−	6.45203i	0.202319	−	0.350426i
$340$		0			0
$341$	8.63746	+	14.9605i	0.467745	+	0.810157i
$342$		0			0
$343$	−18.0000	+	4.35890i	−0.971909	+	0.235358i
$344$		0			0
$345$	28.9622	+	8.89834i	1.55927	+	0.479070i
$346$		0			0
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	0.754617	−	0.656165i	$-0.227823\pi$
$347$	10.5000	+	6.06218i	0.563670	+	0.325435i	−0.190947	+	0.981600i	$0.561156\pi$
$348$		0			0
$349$	3.72508			0.199399			0.0996996	−	0.995018i	$-0.468212\pi$
$349$	3.72508			0.199399			0.0996996	+	0.995018i	$0.468212\pi$
$350$		0			0
$351$	−13.6495			−0.728557
$352$		0			0
$353$	−7.08762	−	4.09204i	−0.377236	−	0.217797i	0.299379	−	0.954134i	$-0.403221\pi$
$353$	−7.08762	−	4.09204i	−0.377236	−	0.217797i	−0.676615	+	0.736337i	$0.736554\pi$
$354$		0			0
$355$	−9.72508	−	2.98793i	−0.516154	−	0.158583i
$356$		0			0
$357$	−1.91238	+	0.151770i	−0.101214	+	0.00803249i
$358$		0			0
$359$	18.1873	+	31.5013i	0.959889	+	1.66258i	0.722762	+	0.691097i	$0.242872\pi$
$359$	18.1873	+	31.5013i	0.959889	+	1.66258i	0.237127	+	0.971479i	$0.423794\pi$
$360$		0			0
$361$	4.13746	−	7.16629i	0.217761	−	0.377173i
$362$		0			0
$363$			29.1413i			1.52952i
$364$		0			0
$365$	−9.91238	−	10.6592i	−0.518837	−	0.557926i
$366$		0			0
$367$	−5.22508	−	3.01670i	−0.272747	−	0.157471i	0.357388	−	0.933956i	$-0.383667\pi$
$367$	−5.22508	−	3.01670i	−0.272747	−	0.157471i	−0.630135	+	0.776485i	$0.717001\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.3625	−	8.50848i	0.641831	−	0.441739i
$372$		0			0
$373$	8.63746	−	4.98684i	0.447231	−	0.258209i	−0.259429	−	0.965762i	$-0.583534\pi$
$373$	8.63746	−	4.98684i	0.447231	−	0.258209i	0.706660	+	0.707553i	$0.250201\pi$
$374$		0			0
$375$	−2.95017	−	19.1389i	−0.152346	−	0.988327i
$376$		0			0
$377$		−	11.2296i		−	0.578352i
$378$		0			0
$379$	21.6495			1.11206			0.556030	−	0.831162i	$-0.312324\pi$
$379$	21.6495			1.11206			0.556030	+	0.831162i	$0.312324\pi$
$380$		0			0
$381$	13.5498	−	23.4690i	0.694179	−	1.20235i
$382$		0			0
$383$	−5.32475	+	3.07425i	−0.272082	+	0.157087i	−0.629833	−	0.776730i	$-0.716877\pi$
$383$	−5.32475	+	3.07425i	−0.272082	+	0.157087i	0.357751	+	0.933817i	$0.383544\pi$
$384$		0			0
$385$	−9.36254	−	29.7693i	−0.477159	−	1.51718i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.1873	−	28.0372i	0.820728	−	1.42154i	−0.0844123	−	0.996431i	$-0.526901\pi$
$389$	16.1873	−	28.0372i	0.820728	−	1.42154i	0.905141	−	0.425112i	$-0.139765\pi$
$390$		0			0
$391$	−3.27492			−0.165620
$392$		0			0
$393$		−	18.5764i		−	0.937055i
$394$		0			0
$395$	3.63746	+	15.8553i	0.183020	+	0.797767i
$396$		0			0
$397$	−9.36254	+	5.40547i	−0.469892	+	0.271293i	−0.716195	−	0.697901i	$-0.754118\pi$
$397$	−9.36254	+	5.40547i	−0.469892	+	0.271293i	0.246302	+	0.969193i	$0.420784\pi$
$398$		0			0
$399$	−13.5498	−	6.45203i	−0.678340	−	0.323006i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−7.45017	−	4.30136i	−0.371119	−	0.214266i
$404$		0			0
$405$	14.7371	−	13.7046i	0.732294	−	0.680989i
$406$		0			0
$407$		−	52.6103i		−	2.60780i
$408$		0			0
$409$	−10.0498	+	17.4068i	−0.496932	+	0.860712i	−0.999994	−	0.00353862i	$-0.998874\pi$
$409$	−10.0498	+	17.4068i	−0.496932	+	0.860712i	0.503061	+	0.864251i	$0.332207\pi$
$410$		0			0
$411$	18.4622	+	31.9775i	0.910674	+	1.57733i
$412$		0			0
$413$	4.91238	+	7.13752i	0.241722	+	0.351214i
$414$		0			0
$415$	4.86254	−	15.8265i	0.238693	−	0.776894i
$416$		0			0
$417$	19.6495	+	11.3446i	0.962240	+	0.555550i
$418$		0			0
$419$	13.0997			0.639961			0.319980	−	0.947424i	$-0.396324\pi$
$419$	13.0997			0.639961			0.319980	+	0.947424i	$0.396324\pi$
$420$		0			0
$421$	−4.27492			−0.208347			−0.104173	−	0.994559i	$-0.533220\pi$
$421$	−4.27492			−0.208347			−0.104173	+	0.994559i	$0.533220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.912376	+	1.88382i	0.0442567	+	0.0913787i
$426$		0			0
$427$	35.7371	−	2.83616i	1.72944	−	0.137251i
$428$		0			0
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$		0			0
$431$	9.18729	−	15.9129i	0.442536	−	0.766495i	−0.555341	−	0.831623i	$-0.687412\pi$
$431$	9.18729	−	15.9129i	0.442536	−	0.766495i	0.997877	+	0.0651276i	$0.0207454\pi$
$432$		0			0
$433$		−	18.1578i		−	0.872606i	−0.899800	−	0.436303i	$-0.856288\pi$
$433$		−	18.1578i		−	0.872606i	0.899800	−	0.436303i	$-0.143712\pi$
$434$		0			0
$435$	11.2749	+	12.1244i	0.540591	+	0.581318i
$436$		0			0
$437$	−22.1873	−	12.8098i	−1.06136	−	0.612778i
$438$		0			0
$439$	11.9124	+	20.6328i	0.568547	+	0.984752i	0.996710	+	0.0810504i	$0.0258275\pi$
$439$	11.9124	+	20.6328i	0.568547	+	0.984752i	−0.428163	+	0.903701i	$0.640839\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	−0.728247	−	0.685315i	$-0.759665\pi$
$443$	−10.5000	+	6.06218i	−0.498870	+	0.288023i	0.229377	+	0.973338i	$0.426331\pi$
$444$		0			0
$445$	−3.50000	−	15.2561i	−0.165916	−	0.723211i
$446$		0			0
$447$			13.0767i			0.618507i
$448$		0			0
$449$	3.17525			0.149849			0.0749246	−	0.997189i	$-0.476128\pi$
$449$	3.17525			0.149849			0.0749246	+	0.997189i	$0.476128\pi$
$450$		0			0
$451$	−9.82475	+	17.0170i	−0.462629	+	0.801298i
$452$		0			0
$453$	−19.0876	+	11.0202i	−0.896815	+	0.517776i
$454$		0			0
$455$	11.4502	+	10.5074i	0.536792	+	0.492594i
$456$		0			0
$457$	1.18729	−	0.685484i	0.0555392	−	0.0320656i	−0.471973	−	0.881613i	$-0.656458\pi$
$457$	1.18729	−	0.685484i	0.0555392	−	0.0320656i	0.527512	+	0.849547i	$0.323125\pi$
$458$		0			0
$459$	−1.08762	+	1.88382i	−0.0507659	+	0.0879292i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$			2.15068i			0.0999505i	0.998750	+	0.0499752i	$0.0159142\pi$
$463$			2.15068i			0.0999505i	−0.998750	+	0.0499752i	$0.984086\pi$
$464$		0			0
$465$	12.3625	−	2.83616i	0.573299	−	0.131524i
$466$		0			0
$467$	−13.5997	+	7.85177i	−0.629318	+	0.363337i	−0.780488	−	0.625171i	$-0.785029\pi$
$467$	−13.5997	+	7.85177i	−0.629318	+	0.363337i	0.151170	+	0.988508i	$0.451696\pi$
$468$		0			0
$469$	7.67525	−	5.28247i	0.354410	−	0.243922i
$470$		0			0
$471$	1.91238	+	3.31233i	0.0881176	+	0.152624i
$472$		0			0
$473$	−9.82475	−	5.67232i	−0.451743	−	0.260814i
$474$		0			0
$475$	−1.18729	+	16.3315i	−0.0544767	+	0.749340i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.91238	−	8.50848i	0.224452	−	0.388763i	−0.731703	−	0.681624i	$-0.761274\pi$
$479$	4.91238	−	8.50848i	0.224452	−	0.388763i	0.956155	+	0.292861i	$0.0946074\pi$
$480$		0			0
$481$	13.0997	+	22.6893i	0.597293	+	1.03454i
$482$		0			0
$483$	15.4124	−	32.3673i	0.701287	−	1.47277i
$484$		0			0
$485$	−4.54983	+	14.8087i	−0.206597	+	0.672431i
$486$		0			0
$487$	2.53779	+	1.46519i	0.114998	+	0.0663943i	0.556396	−	0.830917i	$-0.312184\pi$
$487$	2.53779	+	1.46519i	0.114998	+	0.0663943i	−0.441398	+	0.897312i	$0.645517\pi$
$488$		0			0
$489$	−9.82475			−0.444291
$490$		0			0
$491$	−28.5498			−1.28844			−0.644218	−	0.764842i	$-0.722817\pi$
$491$	−28.5498			−1.28844			−0.644218	+	0.764842i	$0.722817\pi$
$492$		0			0
$493$	−1.54983	−	0.894797i	−0.0698010	−	0.0402996i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.17525	+	10.8685i	−0.232142	+	0.487518i
$498$		0			0
$499$	0.812707	+	1.40765i	0.0363818	+	0.0630151i	0.883643	−	0.468161i	$-0.155083\pi$
$499$	0.812707	+	1.40765i	0.0363818	+	0.0630151i	−0.847261	+	0.531177i	$0.821750\pi$
$500$		0			0
$501$	0.412376	−	0.714256i	0.0184236	−	0.0319106i
$502$		0			0
$503$			31.7682i			1.41647i	0.705975	+	0.708236i	$0.250509\pi$
$503$			31.7682i			1.41647i	−0.705975	+	0.708236i	$0.749491\pi$
$504$		0			0
$505$	22.1873	−	20.6328i	0.987322	−	0.918149i
$506$		0			0
$507$	−9.14950	−	5.28247i	−0.406344	−	0.234603i
$508$		0			0
$509$	−7.22508	−	12.5142i	−0.320246	−	0.554683i	0.660293	−	0.751008i	$-0.270432\pi$
$509$	−7.22508	−	12.5142i	−0.320246	−	0.554683i	−0.980539	+	0.196326i	$0.937099\pi$
$510$		0			0
$511$	−14.1873	+	9.76436i	−0.627609	+	0.431950i
$512$		0			0
$513$	−14.7371	+	8.50848i	−0.650660	+	0.375659i
$514$		0			0
$515$	24.5997	−	5.64355i	1.08399	−	0.248685i
$516$		0			0
$517$			34.3375i			1.51016i
$518$		0			0
$519$	−35.4743			−1.55715
$520$		0			0
$521$	−4.91238	+	8.50848i	−0.215215	+	0.372763i	−0.953339	−	0.301902i	$-0.902379\pi$
$521$	−4.91238	+	8.50848i	−0.215215	+	0.372763i	0.738124	+	0.674665i	$0.235712\pi$
$522$		0			0
$523$	6.36254	−	3.67341i	0.278215	−	0.160627i	−0.354400	−	0.935094i	$-0.615315\pi$
$523$	6.36254	−	3.67341i	0.278215	−	0.160627i	0.632615	+	0.774467i	$0.281982\pi$
$524$		0			0
$525$	−22.9124	+	0.151770i	−0.999978	+	0.00662376i
$526$		0			0
$527$	−1.18729	+	0.685484i	−0.0517193	+	0.0298602i
$528$		0			0
$529$	19.0997	−	33.0816i	0.830420	−	1.43833i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	9.78523i		−	0.423845i
$534$		0			0
$535$	−7.67525	+	1.76082i	−0.331830	+	0.0761270i
$536$		0			0
$537$	10.9124	−	6.30026i	0.470904	−	0.271876i
$538$		0			0
$539$	−36.4622	+	5.82409i	−1.57054	+	0.250861i
$540$		0			0
$541$	8.77492	+	15.1986i	0.377263	+	0.653439i	0.990663	−	0.136334i	$-0.0435319\pi$
$541$	8.77492	+	15.1986i	0.377263	+	0.653439i	−0.613400	+	0.789773i	$0.710199\pi$
$542$		0			0
$543$	36.4124	+	21.0227i	1.56260	+	0.902170i
$544$		0			0
$545$	−18.9124	+	17.5874i	−0.810117	+	0.753360i
$546$		0			0
$547$			20.5386i			0.878168i	0.898446	+	0.439084i	$0.144697\pi$
$547$			20.5386i			0.878168i	−0.898446	+	0.439084i	$0.855303\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.00000	−	12.1244i	−0.298210	−	0.516515i
$552$		0			0
$553$	19.1873	−	1.52274i	0.815927	−	0.0647534i
$554$		0			0
$555$	−36.9244	−	11.3446i	−1.56735	−	0.481553i
$556$		0			0
$557$	8.63746	+	4.98684i	0.365981	+	0.211299i	0.671701	−	0.740822i	$-0.265564\pi$
$557$	8.63746	+	4.98684i	0.365981	+	0.211299i	−0.305720	+	0.952121i	$0.598897\pi$
$558$		0			0
$559$	5.64950			0.238949
$560$		0			0
$561$	−3.82475			−0.161481
$562$		0			0
$563$	19.5997	+	11.3159i	0.826028	+	0.476907i	0.852491	−	0.522743i	$-0.175091\pi$
$563$	19.5997	+	11.3159i	0.826028	+	0.476907i	−0.0264630	+	0.999650i	$0.508424\pi$
$564$		0			0
$565$	−2.82475	+	9.19397i	−0.118838	+	0.386793i
$566$		0			0
$567$	−13.5000	−	19.6150i	−0.566947	−	0.823754i
$568$		0			0
$569$	4.18729	+	7.25260i	0.175540	+	0.304045i	0.940348	−	0.340214i	$-0.110499\pi$
$569$	4.18729	+	7.25260i	0.175540	+	0.304045i	−0.764808	+	0.644259i	$0.777166\pi$
$570$		0			0
$571$	−3.63746	+	6.30026i	−0.152223	+	0.263658i	−0.932044	−	0.362344i	$-0.881976\pi$
$571$	−3.63746	+	6.30026i	−0.152223	+	0.263658i	0.779821	+	0.626002i	$0.215310\pi$
$572$		0			0
$573$			0.303539i			0.0126805i
$574$		0			0
$575$	−39.0120	−	2.83616i	−1.62691	−	0.118276i
$576$		0			0
$577$	−3.36254	−	1.94136i	−0.139984	−	0.0808200i	0.428372	−	0.903602i	$-0.359087\pi$
$577$	−3.36254	−	1.94136i	−0.139984	−	0.0808200i	−0.568357	+	0.822782i	$0.692421\pi$
$578$		0			0
$579$	18.4622	+	31.9775i	0.767263	+	1.32894i
$580$		0			0
$581$	−17.6873	−	8.42217i	−0.733793	−	0.349410i
$582$		0			0
$583$	25.9124	−	14.9605i	1.07318	−	0.619601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	20.8997i		−	0.862623i	−0.902203	−	0.431311i	$-0.858051\pi$
$587$		−	20.8997i		−	0.862623i	0.902203	−	0.431311i	$-0.141949\pi$
$588$		0			0
$589$	−10.7251			−0.441919
$590$		0			0
$591$	−7.45017	+	12.9041i	−0.306459	+	0.530802i
$592$		0			0
$593$	28.9124	−	16.6926i	1.18729	−	0.685482i	0.229600	−	0.973285i	$-0.426258\pi$
$593$	28.9124	−	16.6926i	1.18729	−	0.685482i	0.957689	+	0.287804i	$0.0929250\pi$
$594$		0			0
$595$	2.36254	−	0.743028i	0.0968548	−	0.0304612i
$596$		0			0
$597$	−25.9124	+	14.9605i	−1.06052	+	0.612293i
$598$		0			0
$599$	2.63746	−	4.56821i	0.107764	−	0.186652i	−0.807100	−	0.590414i	$-0.798964\pi$
$599$	2.63746	−	4.56821i	0.107764	−	0.186652i	0.914864	+	0.403762i	$0.132298\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.41238	−	36.6687i	−0.342012	−	1.49079i
$606$		0			0
$607$	−9.87459	+	5.70109i	−0.400797	+	0.231400i	−0.686828	−	0.726820i	$-0.740997\pi$
$607$	−9.87459	+	5.70109i	−0.400797	+	0.231400i	0.286031	+	0.958220i	$0.407664\pi$
$608$		0			0
$609$	16.1375	−	11.1066i	0.653923	−	0.450061i
$610$		0			0
$611$	−8.54983	−	14.8087i	−0.345889	−	0.599098i
$612$		0			0
$613$	24.5619	+	14.1808i	0.992045	+	0.572757i	0.905885	−	0.423524i	$-0.139207\pi$
$613$	24.5619	+	14.1808i	0.992045	+	0.572757i	0.0861600	+	0.996281i	$0.472540\pi$
$614$		0			0
$615$	9.82475	+	10.5649i	0.396172	+	0.426019i
$616$		0			0
$617$			31.2920i			1.25977i	0.776689	+	0.629884i	$0.216898\pi$
$617$			31.2920i			1.25977i	−0.776689	+	0.629884i	$0.783102\pi$
$618$		0			0
$619$	−4.46221	+	7.72877i	−0.179351	+	0.310646i	−0.941659	−	0.336570i	$-0.890733\pi$
$619$	−4.46221	+	7.72877i	−0.179351	+	0.310646i	0.762307	+	0.647215i	$0.224067\pi$
$620$		0			0
$621$	−20.3248	−	35.2035i	−0.815604	−	1.41267i
$622$		0			0
$623$	−18.4622	+	1.46519i	−0.739673	+	0.0587017i
$624$		0			0
$625$	9.23713	+	23.2309i	0.369485	+	0.929237i
$626$		0			0
$627$	−25.9124	−	14.9605i	−1.03484	−	0.597466i
$628$		0			0
$629$	4.17525			0.166478
$630$		0			0
$631$	33.0997			1.31768			0.658839	−	0.752284i	$-0.271048\pi$
$631$	33.0997			1.31768			0.658839	+	0.752284i	$0.271048\pi$
$632$		0			0
$633$	−38.4743	−	22.2131i	−1.52921	−	0.882892i
$634$		0			0
$635$	−10.2749	+	33.4427i	−0.407748	+	1.32713i
$636$		0			0
$637$	14.2749	−	11.5906i	0.565593	−	0.459238i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.04983	−	1.81837i	0.0414660	−	0.0718212i	−0.844548	−	0.535481i	$-0.820131\pi$
$641$	1.04983	−	1.81837i	0.0414660	−	0.0718212i	0.886014	+	0.463659i	$0.153464\pi$
$642$		0			0
$643$		−	31.4071i		−	1.23857i	−0.785164	−	0.619287i	$-0.787422\pi$
$643$		−	31.4071i		−	1.23857i	0.785164	−	0.619287i	$-0.212578\pi$
$644$		0			0
$645$	−6.09967	+	5.67232i	−0.240174	+	0.223348i
$646$		0			0
$647$	23.3248	+	13.4666i	0.916991	+	0.529425i	0.882674	−	0.469986i	$-0.155741\pi$
$647$	23.3248	+	13.4666i	0.916991	+	0.529425i	0.0343169	+	0.999411i	$0.489074\pi$
$648$		0			0
$649$	8.63746	+	14.9605i	0.339050	+	0.587252i
$650$		0			0
$651$	−1.18729	−	14.9605i	−0.0465337	−	0.586349i
$652$		0			0
$653$	24.5619	−	14.1808i	0.961181	−	0.554938i	0.0646444	−	0.997908i	$-0.479409\pi$
$653$	24.5619	−	14.1808i	0.961181	−	0.554938i	0.896536	+	0.442970i	$0.146075\pi$
$654$		0			0
$655$	5.36254	+	23.3748i	0.209532	+	0.913328i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	40.5498			1.57960			0.789799	−	0.613366i	$-0.210185\pi$
$659$	40.5498			1.57960			0.789799	+	0.613366i	$0.210185\pi$
$660$		0			0
$661$	0.225083	−	0.389855i	0.00875471	−	0.0151636i	−0.861615	−	0.507563i	$-0.830547\pi$
$661$	0.225083	−	0.389855i	0.00875471	−	0.0151636i	0.870370	+	0.492399i	$0.163880\pi$
$662$		0			0
$663$	1.64950	−	0.952341i	0.0640614	−	0.0369859i
$664$		0			0
$665$	18.9124	+	4.20713i	0.733390	+	0.163145i
$666$		0			0
$667$	28.9622	−	16.7213i	1.12142	−	0.647453i
$668$		0			0
$669$	−7.54983	+	13.0767i	−0.291893	+	0.505574i
$670$		0			0
$671$	71.4743			2.75923
$672$		0			0
$673$		−	31.2920i		−	1.20622i	−0.797659	−	0.603109i	$-0.793928\pi$
$673$		−	31.2920i		−	1.20622i	0.797659	−	0.603109i	$-0.206072\pi$
$674$		0			0
$675$	−14.5876	+	21.4989i	−0.561478	+	0.827492i
$676$		0			0
$677$	−40.1873	+	23.2021i	−1.54452	+	0.891731i	−0.545979	+	0.837799i	$0.683842\pi$
$677$	−40.1873	+	23.2021i	−1.54452	+	0.891731i	−0.998545	+	0.0539317i	$0.982825\pi$
$678$		0			0
$679$	16.5498	+	7.88054i	0.635124	+	0.302428i
$680$		0			0
$681$	16.9124	+	29.2931i	0.648084	+	1.12251i
$682$		0			0
$683$	−16.5997	−	9.58382i	−0.635169	−	0.366715i	0.147582	−	0.989050i	$-0.452851\pi$
$683$	−16.5997	−	9.58382i	−0.635169	−	0.366715i	−0.782751	+	0.622335i	$0.786184\pi$
$684$		0			0
$685$	−32.4622	−	34.9079i	−1.24032	−	1.33376i
$686$		0			0
$687$		−	5.67232i		−	0.216413i
$688$		0			0
$689$	−7.45017	+	12.9041i	−0.283829	+	0.491606i
$690$		0			0
$691$	−15.1873	−	26.3052i	−0.577752	−	1.00070i	−0.995737	−	0.0922416i	$-0.970597\pi$
$691$	−15.1873	−	26.3052i	−0.577752	−	1.00070i	0.417985	−	0.908454i	$-0.362737\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.0000	−	8.60271i	−1.06210	−	0.326319i
$696$		0			0
$697$	−1.35050	−	0.779710i	−0.0511537	−	0.0295336i
$698$		0			0
$699$	−24.7251			−0.935189
$700$		0			0
$701$	8.82475			0.333306			0.166653	−	0.986016i	$-0.446704\pi$
$701$	8.82475			0.333306			0.166653	+	0.986016i	$0.446704\pi$
$702$		0			0
$703$	28.2870	+	16.3315i	1.06686	+	0.615954i
$704$		0			0
$705$	24.0997	+	7.40437i	0.907646	+	0.278865i
$706$		0			0
$707$	−20.3248	−	29.5312i	−0.764391	−	1.11063i
$708$		0			0
$709$	−5.22508	−	9.05011i	−0.196232	−	0.339884i	0.751072	−	0.660221i	$-0.229537\pi$
$709$	−5.22508	−	9.05011i	−0.196232	−	0.339884i	−0.947304	+	0.320337i	$0.896204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	25.6197i		−	0.959465i
$714$		0			0
$715$	21.0997	+	22.6893i	0.789083	+	0.848531i
$716$		0			0
$717$	0.824752	+	0.476171i	0.0308009	+	0.0177829i
$718$		0			0
$719$	−15.1873	−	26.3052i	−0.566390	−	0.981017i	−0.996919	−	0.0784400i	$-0.975006\pi$
$719$	−15.1873	−	26.3052i	−0.566390	−	0.981017i	0.430528	−	0.902577i	$-0.358327\pi$
$720$		0			0
$721$	−2.36254	−	29.7693i	−0.0879856	−	1.10867i
$722$		0			0
$723$	14.7371	−	8.50848i	0.548080	−	0.316434i
$724$		0			0
$725$	−17.6873	−	12.0014i	−0.656890	−	0.445719i
$726$		0			0
$727$		−	3.10302i		−	0.115085i	−0.998343	−	0.0575423i	$-0.981674\pi$
$727$		−	3.10302i		−	0.115085i	0.998343	−	0.0575423i	$-0.0183264\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	0.450166	−	0.779710i	0.0166500	−	0.0288386i
$732$		0			0
$733$	32.6375	−	18.8432i	1.20549	−	0.695991i	0.243721	−	0.969845i	$-0.421632\pi$
$733$	32.6375	−	18.8432i	1.20549	−	0.695991i	0.961771	+	0.273854i	$0.0882986\pi$
$734$		0			0
$735$	−3.77492	+	26.8468i	−0.139240	+	0.990259i
$736$		0			0
$737$	16.0876	−	9.28819i	0.592595	−	0.342135i
$738$		0			0
$739$	−10.4622	+	18.1211i	−0.384859	+	0.666595i	−0.991750	−	0.128190i	$-0.959083\pi$
$739$	−10.4622	+	18.1211i	−0.384859	+	0.666595i	0.606891	+	0.794785i	$0.292416\pi$
$740$		0			0
$741$	14.9003			0.547377
$742$		0			0
$743$		−	6.45203i		−	0.236702i	−0.992972	−	0.118351i	$-0.962239\pi$
$743$		−	6.45203i		−	0.236702i	0.992972	−	0.118351i	$-0.0377608\pi$
$744$		0			0
$745$	−3.77492	−	16.4545i	−0.138302	−	0.602846i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.737127	+	9.28819i	0.0269341	+	0.339383i
$750$		0			0
$751$	7.36254	+	12.7523i	0.268663	+	0.465338i	0.968517	−	0.248948i	$-0.0800849\pi$
$751$	7.36254	+	12.7523i	0.268663	+	0.465338i	−0.699854	+	0.714286i	$0.746752\pi$
$752$		0			0
$753$	30.8248	+	17.7967i	1.12332	+	0.648547i
$754$		0			0
$755$	20.8368	−	19.3770i	0.758329	−	0.705200i
$756$		0			0
$757$		−	35.5934i		−	1.29366i	−0.762633	−	0.646831i	$-0.776094\pi$
$757$		−	35.5934i		−	1.29366i	0.762633	−	0.646831i	$-0.223906\pi$
$758$		0			0
$759$	35.7371	−	61.8985i	1.29718	−	2.24677i
$760$		0			0
$761$	−11.4622	−	19.8531i	−0.415505	−	0.719675i	0.579977	−	0.814633i	$-0.303062\pi$
$761$	−11.4622	−	19.8531i	−0.415505	−	0.719675i	−0.995481	+	0.0949578i	$0.969728\pi$
$762$		0			0
$763$	17.3248	+	25.1723i	0.627198	+	0.911298i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.45017	−	4.30136i	−0.269010	−	0.155313i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	−20.1752			−0.726594
$772$		0			0
$773$	34.9124	+	20.1567i	1.25571	+	0.724985i	0.972238	−	0.233995i	$-0.0751800\pi$
$773$	34.9124	+	20.1567i	1.25571	+	0.724985i	0.283473	+	0.958980i	$0.408513\pi$
$774$		0			0
$775$	−14.7371	+	7.13752i	−0.529373	+	0.256387i
$776$		0			0
$777$	−19.6495	+	41.2657i	−0.704922	+	1.48040i
$778$		0			0
$779$	−6.09967	−	10.5649i	−0.218543	−	0.378528i
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$		0			0
$783$		−	22.2131i		−	0.793832i
$784$		0			0
$785$	−3.36254	−	3.61587i	−0.120014	−	0.129056i
$786$		0			0
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	0.473027	−	0.881048i	$-0.343161\pi$
$787$	−1.50000	−	0.866025i	−0.0534692	−	0.0308705i	−0.526496	+	0.850177i	$0.676495\pi$
$788$		0			0
$789$	0.675248	+	1.16956i	0.0240395	+	0.0416376i
$790$		0			0
$791$	10.2749	+	4.89261i	0.365334	+	0.173961i
$792$		0			0
$793$	−30.8248	+	17.7967i	−1.09462	+	0.631979i
$794$		0			0
$795$	−4.91238	−	21.4125i	−0.174224	−	0.759425i
$796$		0			0
$797$			46.8229i			1.65855i	0.558839	+	0.829276i	$0.311247\pi$
$797$			46.8229i			1.65855i	−0.558839	+	0.829276i	$0.688753\pi$
$798$		0			0
$799$	−2.72508			−0.0964065
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−29.7371	+	17.1687i	−1.04940	+	0.605872i
$804$		0			0
$805$	−10.0498	+	45.1772i	−0.354210	+	1.59229i
$806$		0			0
$807$	21.6752	−	12.5142i	0.763005	−	0.440521i
$808$		0			0
$809$	−8.59967	+	14.8951i	−0.302348	+	0.523683i	−0.976667	−	0.214757i	$-0.931104\pi$
$809$	−8.59967	+	14.8951i	−0.302348	+	0.523683i	0.674319	+	0.738440i	$0.264437\pi$
$810$		0			0
$811$	7.45017			0.261611			0.130805	−	0.991408i	$-0.458244\pi$
$811$	7.45017			0.261611			0.130805	+	0.991408i	$0.458244\pi$
$812$		0			0
$813$			17.0170i			0.596811i
$814$		0			0
$815$	12.3625	−	2.83616i	0.433041	−	0.0993464i
$816$		0			0
$817$	6.09967	−	3.52165i	0.213400	−	0.123207i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.1873	+	17.6449i	0.355539	+	0.615812i	0.987210	−	0.159425i	$-0.0509640\pi$
$821$	10.1873	+	17.6449i	0.355539	+	0.615812i	−0.631671	+	0.775237i	$0.717631\pi$
$822$		0			0
$823$	−39.9743	−	23.0791i	−1.39341	−	0.804488i	−0.399723	−	0.916636i	$-0.630894\pi$
$823$	−39.9743	−	23.0791i	−1.39341	−	0.804488i	−0.993692	+	0.112147i	$0.964227\pi$
$824$		0			0
$825$	−45.5619	−	3.31233i	−1.58626	−	0.115321i
$826$		0			0
$827$			15.0547i			0.523505i	0.965135	+	0.261752i	$0.0843004\pi$
$827$			15.0547i			0.523505i	−0.965135	+	0.261752i	$0.915700\pi$
$828$		0			0
$829$	−25.4622	+	44.1018i	−0.884339	+	1.53172i	−0.0378699	+	0.999283i	$0.512057\pi$
$829$	−25.4622	+	44.1018i	−0.884339	+	1.53172i	−0.846469	+	0.532438i	$0.821276\pi$
$830$		0			0
$831$	−12.3625	−	21.4125i	−0.428852	−	0.742793i
$832$		0			0
$833$	−0.462210	−	2.89371i	−0.0160146	−	0.100261i
$834$		0			0
$835$	−0.312707	+	1.01779i	−0.0108217	+	0.0352222i
$836$		0			0
$837$	−14.7371	−	8.50848i	−0.509390	−	0.294096i
$838$		0			0
$839$	−41.0997			−1.41892			−0.709459	−	0.704747i	$-0.751061\pi$
$839$	−41.0997			−1.41892			−0.709459	+	0.704747i	$0.751061\pi$
$840$		0			0
$841$	−10.7251			−0.369830
$842$		0			0
$843$	−9.00000	−	5.19615i	−0.309976	−	0.178965i
$844$		0			0
$845$	13.0378	+	4.00573i	0.448514	+	0.137801i
$846$		0			0
$847$	−44.3746	+	3.52165i	−1.52473	+	0.121005i
$848$		0			0
$849$	9.46221	+	16.3890i	0.324742	+	0.562470i
$850$		0			0
$851$	−39.0120	+	67.5708i	−1.33732	+	2.31630i
$852$		0			0
$853$			13.1342i			0.449708i	0.974392	+	0.224854i	$0.0721905\pi$
$853$			13.1342i			0.449708i	−0.974392	+	0.224854i	$0.927810\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	32.6375	+	18.8432i	1.11487	+	0.643673i	0.940087	−	0.340933i	$-0.110743\pi$
$857$	32.6375	+	18.8432i	1.11487	+	0.643673i	0.174787	+	0.984606i	$0.444076\pi$
$858$		0			0
$859$	−1.18729	−	2.05645i	−0.0405099	−	0.0701652i	0.845060	−	0.534672i	$-0.179565\pi$
$859$	−1.18729	−	2.05645i	−0.0405099	−	0.0701652i	−0.885569	+	0.464507i	$0.846232\pi$
$860$		0			0
$861$	14.0619	−	9.67805i	0.479228	−	0.329827i
$862$		0			0
$863$	−14.2251	+	8.21286i	−0.484227	+	0.279569i	−0.722177	−	0.691709i	$-0.756858\pi$
$863$	−14.2251	+	8.21286i	−0.484227	+	0.279569i	0.237949	+	0.971278i	$0.423525\pi$
$864$		0			0
$865$	44.6375	−	10.2405i	1.51772	−	0.348189i
$866$		0			0
$867$			29.1413i			0.989691i
$868$		0			0
$869$	38.3746			1.30177
$870$		0			0
$871$	−4.62541	+	8.01145i	−0.156726	+	0.271458i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.7870	−	6.80521i	0.973177	−	0.230058i
$876$		0			0
$877$	19.8127	−	11.4389i	0.669028	−	0.386263i	−0.126681	−	0.991944i	$-0.540432\pi$
$877$	19.8127	−	11.4389i	0.669028	−	0.386263i	0.795708	+	0.605680i	$0.207099\pi$
$878$		0			0
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$		0			0
$881$	−43.0241			−1.44952			−0.724759	−	0.689002i	$-0.758049\pi$
$881$	−43.0241			−1.44952			−0.724759	+	0.689002i	$0.758049\pi$
$882$		0			0
$883$			55.5407i			1.86909i	0.355840	+	0.934547i	$0.384195\pi$
$883$			55.5407i			1.86909i	−0.355840	+	0.934547i	$0.615805\pi$
$884$		0			0
$885$	12.3625	−	2.83616i	0.415562	−	0.0953365i
$886$		0			0
$887$	33.9743	−	19.6150i	1.14074	−	0.658609i	0.194129	−	0.980976i	$-0.437812\pi$
$887$	33.9743	−	19.6150i	1.14074	−	0.658609i	0.946615	+	0.322367i	$0.104479\pi$
$888$		0			0
$889$	37.3746	+	17.7967i	1.25350	+	0.596881i
$890$		0			0
$891$	−23.7371	−	41.1139i	−0.795224	−	1.37737i
$892$		0			0
$893$	−18.4622	−	10.6592i	−0.617814	−	0.356695i
$894$		0			0
$895$	−11.9124	+	11.0778i	−0.398187	+	0.370290i
$896$		0			0
$897$			35.5934i			1.18843i
$898$		0			0
$899$	7.00000	−	12.1244i	0.233463	−	0.404370i
$900$		0			0
$901$	1.18729	+	2.05645i	0.0395545	+	0.0685103i
$902$		0			0
$903$	5.58762	+	8.11863i	0.185944	+	0.270171i
$904$		0			0
$905$	−51.8866	−	15.9416i	−1.72477	−	0.529918i
$906$		0			0
$907$	−36.2492	−	20.9285i	−1.20363	−	0.694918i	−0.242273	−	0.970208i	$-0.577893\pi$
$907$	−36.2492	−	20.9285i	−1.20363	−	0.694918i	−0.961361	+	0.275290i	$0.911226\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.0997			−0.831589			−0.415795	−	0.909459i	$-0.636496\pi$
$911$	−25.0997			−0.831589			−0.415795	+	0.909459i	$0.636496\pi$
$912$		0			0
$913$	−33.8248	−	19.5287i	−1.11944	−	0.646307i
$914$		0			0
$915$	15.4124	−	50.1640i	0.509517	−	1.65837i
$916$		0			0
$917$	28.2870	−	2.24490i	0.934118	−	0.0741332i
$918$		0			0
$919$	−23.4622	−	40.6377i	−0.773947	−	1.34052i	−0.935384	−	0.353632i	$-0.884946\pi$
$919$	−23.4622	−	40.6377i	−0.773947	−	1.34052i	0.161438	−	0.986883i	$-0.448387\pi$
$920$		0			0
$921$	−22.9622	+	39.7717i	−0.756631	+	1.31052i
$922$		0			0
$923$		−	11.9517i		−	0.393396i
$924$		0			0
$925$	49.7371	+	3.61587i	1.63535	+	0.118889i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.0498	−	41.6555i	−0.789049	−	1.36667i	−0.926550	−	0.376172i	$-0.877240\pi$
$929$	−24.0498	−	41.6555i	−0.789049	−	1.36667i	0.137500	−	0.990502i	$-0.456093\pi$
$930$		0			0
$931$	8.18729	−	21.4125i	0.268328	−	0.701768i
$932$		0			0
$933$	−14.7371	+	8.50848i	−0.482472	+	0.278555i
$934$		0			0
$935$	4.81271	−	1.10411i	0.157392	−	0.0361083i
$936$		0			0
$937$		−	24.3638i		−	0.795931i	−0.917400	−	0.397965i	$-0.869716\pi$
$937$		−	24.3638i		−	0.795931i	0.917400	−	0.397965i	$-0.130284\pi$
$938$		0			0
$939$	58.0241			1.89354
$940$		0			0
$941$	1.63746	−	2.83616i	0.0533796	−	0.0924562i	−0.838101	−	0.545515i	$-0.816334\pi$
$941$	1.63746	−	2.83616i	0.0533796	−	0.0924562i	0.891481	+	0.453059i	$0.149667\pi$
$942$		0			0
$943$	25.2371	−	14.5707i	0.821834	−	0.474486i
$944$		0			0
$945$	22.6495	+	20.7846i	0.736788	+	0.676123i
$946$		0			0
$947$	9.14950	−	5.28247i	0.297319	−	0.171657i	−0.343919	−	0.938999i	$-0.611755\pi$
$947$	9.14950	−	5.28247i	0.297319	−	0.171657i	0.641238	+	0.767342i	$0.278421\pi$
$948$		0			0
$949$	8.54983	−	14.8087i	0.277539	−	0.480712i
$950$		0			0
$951$	44.3746			1.43894
$952$		0			0
$953$			22.6893i			0.734978i	0.930028	+	0.367489i	$0.119782\pi$
$953$			22.6893i			0.734978i	−0.930028	+	0.367489i	$0.880218\pi$
$954$		0			0
$955$	−0.0876242	−	0.381945i	−0.00283545	−	0.0123594i
$956$		0			0
$957$	33.8248	−	19.5287i	1.09340	−	0.631274i
$958$		0			0
$959$	−46.4622	+	31.9775i	−1.50034	+	1.03261i
$960$		0			0
$961$	10.1375	+	17.5586i	0.327015	+	0.566406i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.4622	−	34.9079i	−1.04500	−	1.12372i
$966$		0			0
$967$			2.15068i			0.0691611i	0.999402	+	0.0345806i	$0.0110095\pi$
$967$			2.15068i			0.0691611i	−0.999402	+	0.0345806i	$0.988990\pi$
$968$		0			0
$969$	1.18729	−	2.05645i	0.0381413	−	0.0660628i
$970$		0			0
$971$	18.4622	+	31.9775i	0.592481	+	1.02621i	0.993897	+	0.110311i	$0.0351846\pi$
$971$	18.4622	+	31.9775i	0.592481	+	1.02621i	−0.401417	+	0.915896i	$0.631482\pi$
$972$		0			0
$973$	−14.9003	+	31.2920i	−0.477683	+	1.00318i
$974$		0			0
$975$	20.4743	−	9.91613i	0.655701	−	0.317570i
$976$		0			0
$977$	−25.9124	−	14.9605i	−0.829010	−	0.478629i	0.0245034	−	0.999700i	$-0.492200\pi$
$977$	−25.9124	−	14.9605i	−0.829010	−	0.478629i	−0.853514	+	0.521070i	$0.825533\pi$
$978$		0			0
$979$	−36.9244			−1.18011
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.7749	−	22.9641i	−1.26862	−	0.732440i	−0.293895	−	0.955838i	$-0.594952\pi$
$983$	−39.7749	−	22.9641i	−1.26862	−	0.732440i	−0.974727	+	0.223398i	$0.928285\pi$
$984$		0			0
$985$	5.64950	−	18.3879i	0.180008	−	0.585888i
$986$		0			0
$987$	12.8248	−	26.9331i	0.408216	−	0.857290i
$988$		0			0
$989$	8.41238	+	14.5707i	0.267498	+	0.463320i
$990$		0			0
$991$	−16.7371	+	28.9896i	−0.531672	+	0.920884i	0.467644	+	0.883917i	$0.345103\pi$
$991$	−16.7371	+	28.9896i	−0.531672	+	0.920884i	−0.999316	+	0.0369667i	$0.988230\pi$
$992$		0			0
$993$			30.8734i			0.979737i
$994$		0			0
$995$	28.2870	−	26.3052i	0.896757	−	0.833930i
$996$		0			0
$997$	0.362541	+	0.209313i	0.0114818	+	0.00662902i	0.505730	−	0.862692i	$-0.331223\pi$
$997$	0.362541	+	0.209313i	0.0114818	+	0.00662902i	−0.494248	+	0.869321i	$0.664557\pi$
$998$		0			0
$999$	25.9124	+	44.8816i	0.819831	+	1.41999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.q.a.109.2	yes	4
3.2	odd	2		1260.2.bm.a.109.1		4
4.3	odd	2		560.2.bw.e.529.2		4
5.2	odd	4		700.2.i.f.501.2		8
5.3	odd	4		700.2.i.f.501.3		8
5.4	even	2		140.2.q.b.109.2	yes	4
7.2	even	3		140.2.q.b.9.1	yes	4
7.3	odd	6		980.2.e.c.589.2		4
7.4	even	3		980.2.e.f.589.3		4
7.5	odd	6		980.2.q.b.569.2		4
7.6	odd	2		980.2.q.g.949.1		4
15.14	odd	2		1260.2.bm.b.109.1		4
20.19	odd	2		560.2.bw.a.529.2		4
21.2	odd	6		1260.2.bm.b.289.2		4
28.23	odd	6		560.2.bw.a.289.1		4
35.2	odd	12		700.2.i.f.401.2		8
35.3	even	12		4900.2.a.bf.1.3		4
35.4	even	6		980.2.e.f.589.1		4
35.9	even	6	inner	140.2.q.a.9.2	✓	4
35.17	even	12		4900.2.a.bf.1.1		4
35.18	odd	12		4900.2.a.be.1.1		4
35.19	odd	6		980.2.q.g.569.1		4
35.23	odd	12		700.2.i.f.401.3		8
35.24	odd	6		980.2.e.c.589.4		4
35.32	odd	12		4900.2.a.be.1.3		4
35.34	odd	2		980.2.q.b.949.1		4
105.44	odd	6		1260.2.bm.a.289.1		4
140.79	odd	6		560.2.bw.e.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.2	✓	4	35.9	even	6	inner
140.2.q.a.109.2	yes	4	1.1	even	1	trivial
140.2.q.b.9.1	yes	4	7.2	even	3
140.2.q.b.109.2	yes	4	5.4	even	2
560.2.bw.a.289.1		4	28.23	odd	6
560.2.bw.a.529.2		4	20.19	odd	2
560.2.bw.e.289.2		4	140.79	odd	6
560.2.bw.e.529.2		4	4.3	odd	2
700.2.i.f.401.2		8	35.2	odd	12
700.2.i.f.401.3		8	35.23	odd	12
700.2.i.f.501.2		8	5.2	odd	4
700.2.i.f.501.3		8	5.3	odd	4
980.2.e.c.589.2		4	7.3	odd	6
980.2.e.c.589.4		4	35.24	odd	6
980.2.e.f.589.1		4	35.4	even	6
980.2.e.f.589.3		4	7.4	even	3
980.2.q.b.569.2		4	7.5	odd	6
980.2.q.b.949.1		4	35.34	odd	2
980.2.q.g.569.1		4	35.19	odd	6
980.2.q.g.949.1		4	7.6	odd	2
1260.2.bm.a.109.1		4	3.2	odd	2
1260.2.bm.a.289.1		4	105.44	odd	6
1260.2.bm.b.109.1		4	15.14	odd	2
1260.2.bm.b.289.2		4	21.2	odd	6
4900.2.a.be.1.1		4	35.18	odd	12
4900.2.a.be.1.3		4	35.32	odd	12
4900.2.a.bf.1.1		4	35.17	even	12
4900.2.a.bf.1.3		4	35.3	even	12

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(2.13746 + 0.656712i) q^{5} +(1.13746 - 2.38876i) q^{7} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(2.13746 + 0.656712i) q^{5} +(1.13746 - 2.38876i) q^{7} +(2.63746 - 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 - 2.83616i) q^{15} +(0.362541 + 0.209313i) q^{17} +(1.63746 + 2.83616i) q^{19} +(-3.77492 + 2.59808i) q^{21} +(-6.77492 + 3.91150i) q^{23} +(4.13746 + 2.80739i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(-7.91238 + 4.56821i) q^{33} +(4.00000 - 4.35890i) q^{35} +(8.63746 - 4.98684i) q^{37} +(2.27492 - 3.94027i) q^{39} -3.72508 q^{41} -2.15068i q^{43} +(-5.63746 + 3.25479i) q^{47} +(-4.41238 - 5.43424i) q^{49} +(-0.362541 - 0.627940i) q^{51} +(4.91238 + 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} -5.67232i q^{57} +(-1.63746 + 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-1.72508 + 5.61478i) q^{65} +(3.04983 + 1.76082i) q^{67} +13.5498 q^{69} -4.54983 q^{71} +(-5.63746 - 3.25479i) q^{73} +(-3.77492 - 7.79423i) q^{75} +(-7.91238 - 11.4964i) q^{77} +(3.63746 + 6.30026i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(6.41238 + 3.70219i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(4.91238 - 2.83616i) q^{93} +(1.63746 + 7.13752i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + q^{5} - 3 q^{7}+O(q^{10}) \) 4 * q - 6 * q^3 + q^5 - 3 * q^7	\( 4 q - 6 q^{3} + q^{5} - 3 q^{7} + 3 q^{11} - 3 q^{15} + 9 q^{17} - q^{19} - 12 q^{23} + 9 q^{25} - 2 q^{29} + q^{31} - 9 q^{33} + 16 q^{35} + 27 q^{37} - 6 q^{39} - 30 q^{41} - 15 q^{47} + 5 q^{49} - 9 q^{51} - 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} - 22 q^{65} - 18 q^{67} + 24 q^{69} + 12 q^{71} - 15 q^{73} - 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} + 3 q^{87} - 14 q^{89} + 10 q^{91} - 3 q^{93} - q^{95}+O(q^{100}) \) 4 * q - 6 * q^3 + q^5 - 3 * q^7 + 3 * q^11 - 3 * q^15 + 9 * q^17 - q^19 - 12 * q^23 + 9 * q^25 - 2 * q^29 + q^31 - 9 * q^33 + 16 * q^35 + 27 * q^37 - 6 * q^39 - 30 * q^41 - 15 * q^47 + 5 * q^49 - 9 * q^51 - 3 * q^53 + 27 * q^55 + q^59 + 12 * q^61 - 22 * q^65 - 18 * q^67 + 24 * q^69 + 12 * q^71 - 15 * q^73 - 9 * q^77 + 7 * q^79 + 18 * q^81 - 5 * q^85 + 3 * q^87 - 14 * q^89 + 10 * q^91 - 3 * q^93 - q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more