LMFDB - Embedded newform 1520.2.q.j.881.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, 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:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			881.3
Root			$1.14257 + 1.97899i$ of defining polynomial
Character	$\chi$	$=$	1520.881
Dual form			1520.2.q.j.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14257 + 1.97899i) q^{3} +(0.500000 + 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 + 1.92420i) q^{9} +O(q^{10})$	\(q+(1.14257 + 1.97899i) q^{3} +(0.500000 + 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 + 1.92420i) q^{9} -0.285142 q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.14257 + 1.97899i) q^{15} +(3.11796 + 5.40046i) q^{17} +(-2.92771 + 3.22932i) q^{19} +(1.46837 + 2.54329i) q^{21} +(-2.61796 + 4.53443i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.77812 q^{27} +(-0.642571 + 1.11297i) q^{29} +1.22188 q^{31} +(-0.325796 - 0.564295i) q^{33} +(0.642571 + 1.11297i) q^{35} +10.8695 q^{37} +11.4257 q^{39} +(0.420695 + 0.728665i) q^{41} +(-2.47539 - 4.28749i) q^{43} -2.22188 q^{45} +(2.86445 - 4.96137i) q^{47} -5.34841 q^{49} +(-7.12498 + 12.3408i) q^{51} +(-6.18122 + 10.7062i) q^{53} +(-0.142571 - 0.246941i) q^{55} +(-9.73591 - 2.10419i) q^{57} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-1.42771 + 2.47287i) q^{63} +5.00000 q^{65} +(-0.492981 + 0.853869i) q^{67} -11.9648 q^{69} +(-1.46135 - 2.53113i) q^{71} +(0.382043 + 0.661718i) q^{73} -2.28514 q^{75} -0.366449 q^{77} +(-7.72889 - 13.3868i) q^{79} +(5.36445 + 9.29150i) q^{81} -1.66563 q^{83} +(-3.11796 + 5.40046i) q^{85} -2.93673 q^{87} +(8.01404 - 13.8807i) q^{89} +(3.21286 - 5.56483i) q^{91} +(1.39608 + 2.41808i) q^{93} +(-4.26053 - 0.920816i) q^{95} +(-5.87147 - 10.1697i) q^{97} +(0.316776 - 0.548672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q + q^3 + 3 * q^5 - 4 * q^7 - 4 * q^9	$ 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9} + 10 q^{11} + 15 q^{13} - q^{15} - q^{17} + 12 q^{21} + 4 q^{23} - 3 q^{25} + 16 q^{27} + 2 q^{29} + 2 q^{31} - 11 q^{33} - 2 q^{35} - 4 q^{37} + 10 q^{39} + 2 q^{41} - q^{43} - 8 q^{45} + 6 q^{47} - 14 q^{49} - 6 q^{51} - 11 q^{53} + 5 q^{55} - 19 q^{57} + 6 q^{59} + 9 q^{61} + 9 q^{63} + 30 q^{65} - 20 q^{67} - 10 q^{69} - 29 q^{71} + 22 q^{73} - 2 q^{75} - 32 q^{77} - 24 q^{79} + 21 q^{81} + 6 q^{83} + q^{85} - 24 q^{87} + 14 q^{89} - 10 q^{91} - 6 q^{93} - 7 q^{97} - 13 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 - 4 * q^7 - 4 * q^9 + 10 * q^11 + 15 * q^13 - q^15 - q^17 + 12 * q^21 + 4 * q^23 - 3 * q^25 + 16 * q^27 + 2 * q^29 + 2 * q^31 - 11 * q^33 - 2 * q^35 - 4 * q^37 + 10 * q^39 + 2 * q^41 - q^43 - 8 * q^45 + 6 * q^47 - 14 * q^49 - 6 * q^51 - 11 * q^53 + 5 * q^55 - 19 * q^57 + 6 * q^59 + 9 * q^61 + 9 * q^63 + 30 * q^65 - 20 * q^67 - 10 * q^69 - 29 * q^71 + 22 * q^73 - 2 * q^75 - 32 * q^77 - 24 * q^79 + 21 * q^81 + 6 * q^83 + q^85 - 24 * q^87 + 14 * q^89 - 10 * q^91 - 6 * q^93 - 7 * q^97 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	1.14257	+	1.97899i	0.659664	+	1.14257i	0.980703	+	0.195505i	$0.0626347\pi$
$3$	1.14257	+	1.97899i	0.659664	+	1.14257i	−0.321039	+	0.947066i	$0.604032\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.28514			0.485738			0.242869	−	0.970059i	$-0.421911\pi$
$7$	1.28514			0.485738			0.242869	+	0.970059i	$0.421911\pi$
$8$		0			0
$9$	−1.11094	+	1.92420i	−0.370313	+	0.641400i
$10$		0			0
$11$	−0.285142			−0.0859737			−0.0429868	−	0.999076i	$-0.513687\pi$
$11$	−0.285142			−0.0859737			−0.0429868	+	0.999076i	$0.513687\pi$
$12$		0			0
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$	−1.14257	+	1.97899i	−0.295011	+	0.510973i
$16$		0			0
$17$	3.11796	+	5.40046i	0.756216	+	1.30980i	0.944768	+	0.327741i	$0.106287\pi$
$17$	3.11796	+	5.40046i	0.756216	+	1.30980i	−0.188552	+	0.982063i	$0.560379\pi$
$18$		0			0
$19$	−2.92771	+	3.22932i	−0.671664	+	0.740856i
$19$	−2.92771	+	3.22932i	−0.671664	+	0.740856i
$20$		0			0
$21$	1.46837	+	2.54329i	0.320424	+	0.554990i
$22$		0			0
$23$	−2.61796	+	4.53443i	−0.545882	+	0.945495i	0.452669	+	0.891679i	$0.350472\pi$
$23$	−2.61796	+	4.53443i	−0.545882	+	0.945495i	−0.998551	+	0.0538163i	$0.982861\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.77812			0.342200
$28$		0			0
$29$	−0.642571	+	1.11297i	−0.119322	+	0.206673i	−0.919499	−	0.393091i	$-0.871406\pi$
$29$	−0.642571	+	1.11297i	−0.119322	+	0.206673i	0.800177	+	0.599764i	$0.204739\pi$
$30$		0			0
$31$	1.22188			0.219455			0.109728	−	0.993962i	$-0.465002\pi$
$31$	1.22188			0.219455			0.109728	+	0.993962i	$0.465002\pi$
$32$		0			0
$33$	−0.325796	−	0.564295i	−0.0567137	−	0.0982311i
$34$		0			0
$35$	0.642571	+	1.11297i	0.108614	+	0.188126i
$36$		0			0
$37$	10.8695			1.78693			0.893464	−	0.449134i	$-0.148267\pi$
$37$	10.8695			1.78693			0.893464	+	0.449134i	$0.148267\pi$
$38$		0			0
$39$	11.4257			1.82958
$40$		0			0
$41$	0.420695	+	0.728665i	0.0657015	+	0.113798i	0.897005	−	0.442020i	$-0.145738\pi$
$41$	0.420695	+	0.728665i	0.0657015	+	0.113798i	−0.831303	+	0.555819i	$0.812405\pi$
$42$		0			0
$43$	−2.47539	−	4.28749i	−0.377493	−	0.653837i	0.613204	−	0.789925i	$-0.289880\pi$
$43$	−2.47539	−	4.28749i	−0.377493	−	0.653837i	−0.990697	+	0.136088i	$0.956547\pi$
$44$		0			0
$45$	−2.22188			−0.331218
$46$		0			0
$47$	2.86445	−	4.96137i	0.417823	−	0.723690i	−0.577898	−	0.816109i	$-0.696127\pi$
$47$	2.86445	−	4.96137i	0.417823	−	0.723690i	0.995720	+	0.0924193i	$0.0294600\pi$
$48$		0			0
$49$	−5.34841			−0.764058
$50$		0			0
$51$	−7.12498	+	12.3408i	−0.997696	+	1.72806i
$52$		0			0
$53$	−6.18122	+	10.7062i	−0.849056	+	1.47061i	0.0329952	+	0.999456i	$0.489495\pi$
$53$	−6.18122	+	10.7062i	−0.849056	+	1.47061i	−0.882051	+	0.471153i	$0.843838\pi$
$54$		0			0
$55$	−0.142571	−	0.246941i	−0.0192243	−	0.0332975i
$56$		0			0
$57$	−9.73591	−	2.10419i	−1.28955	−	0.278707i
$58$		0			0
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	0.990013	−	0.140974i	$-0.0450235\pi$
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	−0.617094	+	0.786889i	$0.711690\pi$
$60$		0			0
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	−0.972701	−	0.232060i	$-0.925453\pi$
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	0.687321	+	0.726354i	$0.258787\pi$
$62$		0			0
$63$	−1.42771	+	2.47287i	−0.179875	+	0.311553i
$64$		0			0
$65$	5.00000			0.620174
$66$		0			0
$67$	−0.492981	+	0.853869i	−0.0602273	+	0.104317i	−0.894567	−	0.446934i	$-0.852516\pi$
$67$	−0.492981	+	0.853869i	−0.0602273	+	0.104317i	0.834340	+	0.551251i	$0.185849\pi$
$68$		0			0
$69$	−11.9648			−1.44039
$70$		0			0
$71$	−1.46135	−	2.53113i	−0.173430	−	0.300390i	0.766187	−	0.642618i	$-0.222152\pi$
$71$	−1.46135	−	2.53113i	−0.173430	−	0.300390i	−0.939617	+	0.342228i	$0.888818\pi$
$72$		0			0
$73$	0.382043	+	0.661718i	0.0447148	+	0.0774483i	0.887517	−	0.460776i	$-0.152429\pi$
$73$	0.382043	+	0.661718i	0.0447148	+	0.0774483i	−0.842802	+	0.538224i	$0.819095\pi$
$74$		0			0
$75$	−2.28514			−0.263866
$76$		0			0
$77$	−0.366449			−0.0417607
$78$		0			0
$79$	−7.72889	−	13.3868i	−0.869569	−	1.50614i	−0.862438	−	0.506162i	$-0.831064\pi$
$79$	−7.72889	−	13.3868i	−0.869569	−	1.50614i	−0.00713043	−	0.999975i	$-0.502270\pi$
$80$		0			0
$81$	5.36445	+	9.29150i	0.596050	+	1.03239i
$82$		0			0
$83$	−1.66563			−0.182826			−0.0914132	−	0.995813i	$-0.529138\pi$
$83$	−1.66563			−0.182826			−0.0914132	+	0.995813i	$0.529138\pi$
$84$		0			0
$85$	−3.11796	+	5.40046i	−0.338190	+	0.585762i
$86$		0			0
$87$	−2.93673			−0.314851
$88$		0			0
$89$	8.01404	−	13.8807i	0.849486	−	1.47135i	−0.0321812	−	0.999482i	$-0.510245\pi$
$89$	8.01404	−	13.8807i	0.849486	−	1.47135i	0.881667	−	0.471871i	$-0.156421\pi$
$90$		0			0
$91$	3.21286	−	5.56483i	0.336799	−	0.583353i
$92$		0			0
$93$	1.39608	+	2.41808i	0.144767	+	0.250743i
$94$		0			0
$95$	−4.26053	−	0.920816i	−0.437121	−	0.0944737i
$96$		0			0
$97$	−5.87147	−	10.1697i	−0.596157	−	1.03257i	−0.993382	−	0.114853i	$-0.963360\pi$
$97$	−5.87147	−	10.1697i	−0.596157	−	1.03257i	0.397225	−	0.917721i	$-0.369973\pi$
$98$		0			0
$99$	0.316776	−	0.548672i	0.0318371	−	0.0551436i
$100$		0			0
$101$	3.95935	−	6.85779i	0.393970	−	0.682376i	−0.598999	−	0.800750i	$-0.704435\pi$
$101$	3.95935	−	6.85779i	0.393970	−	0.682376i	0.992969	+	0.118374i	$0.0377681\pi$
$102$		0			0
$103$	12.8202			1.26322			0.631608	−	0.775288i	$-0.282395\pi$
$103$	12.8202			1.26322			0.631608	+	0.775288i	$0.282395\pi$
$104$		0			0
$105$	−1.46837	+	2.54329i	−0.143298	+	0.248199i
$106$		0			0
$107$	−13.8062			−1.33470			−0.667348	−	0.744746i	$-0.732571\pi$
$107$	−13.8062			−1.33470			−0.667348	+	0.744746i	$0.732571\pi$
$108$		0			0
$109$	4.60192	+	7.97076i	0.440784	+	0.763460i	0.997748	−	0.0670767i	$-0.0213672\pi$
$109$	4.60192	+	7.97076i	0.440784	+	0.763460i	−0.556964	+	0.830537i	$0.688034\pi$
$110$		0			0
$111$	12.4191	+	21.5106i	1.17877	+	2.04169i
$112$		0			0
$113$	−17.3273			−1.63001			−0.815005	−	0.579453i	$-0.803266\pi$
$113$	−17.3273			−1.63001			−0.815005	+	0.579453i	$0.803266\pi$
$114$		0			0
$115$	−5.23591			−0.488251
$116$		0			0
$117$	5.55469	+	9.62101i	0.513531	+	0.889462i
$118$		0			0
$119$	4.00702	+	6.94036i	0.367323	+	0.636222i
$120$		0			0
$121$	−10.9187			−0.992609
$122$		0			0
$123$	−0.961348	+	1.66510i	−0.0866818	+	0.150137i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.66563	−	8.08111i	0.414008	−	0.717082i	−0.581316	−	0.813678i	$-0.697462\pi$
$127$	4.66563	−	8.08111i	0.414008	−	0.717082i	0.995324	+	0.0965956i	$0.0307954\pi$
$128$		0			0
$129$	5.65661	−	9.79753i	0.498037	−	0.862625i
$130$		0			0
$131$	6.21286	+	10.7610i	0.542820	+	0.940191i	0.998741	+	0.0501711i	$0.0159767\pi$
$131$	6.21286	+	10.7610i	0.542820	+	0.940191i	−0.455921	+	0.890020i	$0.650690\pi$
$132$		0			0
$133$	−3.76253	+	4.15013i	−0.326253	+	0.359862i
$134$		0			0
$135$	0.889062	+	1.53990i	0.0765183	+	0.132534i
$136$		0			0
$137$	9.26755	−	16.0519i	0.791780	−	1.37140i	−0.133084	−	0.991105i	$-0.542488\pi$
$137$	9.26755	−	16.0519i	0.791780	−	1.37140i	0.924864	−	0.380298i	$-0.124179\pi$
$138$		0			0
$139$	−3.00702	+	5.20831i	−0.255052	+	0.441763i	−0.964910	−	0.262582i	$-0.915426\pi$
$139$	−3.00702	+	5.20831i	−0.255052	+	0.441763i	0.709858	+	0.704345i	$0.248759\pi$
$140$		0			0
$141$	13.0913			1.10249
$142$		0			0
$143$	−0.712856	+	1.23470i	−0.0596120	+	0.103251i
$144$		0			0
$145$	−1.28514			−0.106725
$146$		0			0
$147$	−6.11094	−	10.5845i	−0.504022	−	0.872991i
$148$		0			0
$149$	3.39608	+	5.88218i	0.278218	+	0.481887i	0.970942	−	0.239315i	$-0.0769230\pi$
$149$	3.39608	+	5.88218i	0.278218	+	0.481887i	−0.692724	+	0.721203i	$0.743590\pi$
$150$		0			0
$151$	15.8875			1.29291			0.646453	−	0.762953i	$-0.276251\pi$
$151$	15.8875			1.29291			0.646453	+	0.762953i	$0.276251\pi$
$152$		0			0
$153$	−13.8554			−1.12014
$154$		0			0
$155$	0.610938	+	1.05818i	0.0490717	+	0.0849947i
$156$		0			0
$157$	−3.75351	−	6.50127i	−0.299563	−	0.518858i	0.676473	−	0.736467i	$-0.263507\pi$
$157$	−3.75351	−	6.50127i	−0.299563	−	0.518858i	−0.976036	+	0.217609i	$0.930174\pi$
$158$		0			0
$159$	−28.2500			−2.24037
$160$		0			0
$161$	−3.36445	+	5.82739i	−0.265156	+	0.459263i
$162$		0			0
$163$	−21.8202			−1.70909			−0.854546	−	0.519375i	$-0.826165\pi$
$163$	−21.8202			−1.70909			−0.854546	+	0.519375i	$0.826165\pi$
$164$		0			0
$165$	0.325796	−	0.564295i	0.0253632	−	0.0439303i
$166$		0			0
$167$	5.64257	−	9.77322i	0.436635	−	0.756274i	−0.560792	−	0.827957i	$-0.689503\pi$
$167$	5.64257	−	9.77322i	0.436635	−	0.756274i	0.997428	+	0.0716821i	$0.0228367\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	−2.96135	−	9.22108i	−0.226460	−	0.705154i
$172$		0			0
$173$	2.92771	+	5.07095i	0.222590	+	0.385537i	0.955594	−	0.294688i	$-0.0952156\pi$
$173$	2.92771	+	5.07095i	0.222590	+	0.385537i	−0.733004	+	0.680225i	$0.761882\pi$
$174$		0			0
$175$	−0.642571	+	1.11297i	−0.0485738	+	0.0841323i
$176$		0			0
$177$	−6.54567	+	11.3374i	−0.492003	+	0.852174i
$178$		0			0
$179$	18.7922			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$179$	18.7922			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$180$		0			0
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	−0.999989	−	0.00464265i	$-0.998522\pi$
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	0.504015	+	0.863695i	$0.331856\pi$
$182$		0			0
$183$	−10.1867			−0.753021
$184$		0			0
$185$	5.43473	+	9.41323i	0.399569	+	0.692075i
$186$		0			0
$187$	−0.889062	−	1.53990i	−0.0650146	−	0.112609i
$188$		0			0
$189$	2.28514			0.166220
$190$		0			0
$191$	0.668743			0.0483885			0.0241943	−	0.999707i	$-0.492298\pi$
$191$	0.668743			0.0483885			0.0241943	+	0.999707i	$0.492298\pi$
$192$		0			0
$193$	1.88204	+	3.25979i	0.135472	+	0.234645i	0.925778	−	0.378068i	$-0.123411\pi$
$193$	1.88204	+	3.25979i	0.135472	+	0.234645i	−0.790305	+	0.612713i	$0.790078\pi$
$194$		0			0
$195$	5.71286	+	9.89496i	0.409106	+	0.708593i
$196$		0			0
$197$	14.6164			1.04138			0.520688	−	0.853747i	$-0.325676\pi$
$197$	14.6164			1.04138			0.520688	+	0.853747i	$0.325676\pi$
$198$		0			0
$199$	5.76053	−	9.97753i	0.408353	−	0.707288i	−0.586352	−	0.810056i	$-0.699437\pi$
$199$	5.76053	−	9.97753i	0.408353	−	0.707288i	0.994705	+	0.102768i	$0.0327699\pi$
$200$		0			0
$201$	−2.25307			−0.158919
$202$		0			0
$203$	−0.825796	+	1.43032i	−0.0579595	+	0.100389i
$204$		0			0
$205$	−0.420695	+	0.728665i	−0.0293826	+	0.0508922i
$206$		0			0
$207$	−5.81678	−	10.0750i	−0.404294	−	0.700257i
$208$		0			0
$209$	0.834816	−	0.920816i	0.0577454	−	0.0636941i
$210$		0			0
$211$	−8.57028	−	14.8442i	−0.590003	−	1.02191i	−0.994231	−	0.107257i	$-0.965793\pi$
$211$	−8.57028	−	14.8442i	−0.590003	−	1.02191i	0.404229	−	0.914658i	$-0.367540\pi$
$212$		0			0
$213$	3.33939	−	5.78399i	0.228811	−	0.396313i
$214$		0			0
$215$	2.47539	−	4.28749i	0.168820	−	0.292405i
$216$		0			0
$217$	1.57028			0.106598
$218$		0			0
$219$	−0.873023	+	1.51212i	−0.0589934	+	0.102180i
$220$		0			0
$221$	31.1796			2.09736
$222$		0			0
$223$	0.762085	+	1.31997i	0.0510330	+	0.0883918i	0.890413	−	0.455153i	$-0.150415\pi$
$223$	0.762085	+	1.31997i	0.0510330	+	0.0883918i	−0.839380	+	0.543544i	$0.817082\pi$
$224$		0			0
$225$	−1.11094	−	1.92420i	−0.0740625	−	0.128280i
$226$		0			0
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$		0			0
$229$	18.4397			1.21853			0.609266	−	0.792966i	$-0.291464\pi$
$229$	18.4397			1.21853			0.609266	+	0.792966i	$0.291464\pi$
$230$		0			0
$231$	−0.418694	−	0.725199i	−0.0275480	−	0.0477146i
$232$		0			0
$233$	−6.35587	−	11.0087i	−0.416387	−	0.721203i	0.579186	−	0.815195i	$-0.303371\pi$
$233$	−6.35587	−	11.0087i	−0.416387	−	0.721203i	−0.995573	+	0.0939920i	$0.970037\pi$
$234$		0			0
$235$	5.72889			0.373712
$236$		0			0
$237$	17.6616	−	30.5908i	1.14725	−	1.98709i
$238$		0			0
$239$	10.8343			0.700811			0.350405	−	0.936598i	$-0.386044\pi$
$239$	10.8343			0.700811			0.350405	+	0.936598i	$0.386044\pi$
$240$		0			0
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	−0.662068	−	0.749444i	$-0.730321\pi$
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	0.980071	+	0.198646i	$0.0636545\pi$
$242$		0			0
$243$	−9.59134	+	16.6127i	−0.615285	+	1.06570i
$244$		0			0
$245$	−2.67420	−	4.63186i	−0.170849	−	0.295919i
$246$		0			0
$247$	6.66407	+	20.7507i	0.424025	+	1.32033i
$248$		0			0
$249$	−1.90310	−	3.29626i	−0.120604	−	0.208892i
$250$		0			0
$251$	8.88550	−	15.3901i	0.560848	−	0.971417i	−0.436575	−	0.899668i	$-0.643809\pi$
$251$	8.88550	−	15.3901i	0.560848	−	0.971417i	0.997423	−	0.0717492i	$-0.0228581\pi$
$252$		0			0
$253$	0.746491	−	1.29296i	0.0469315	−	0.0812877i
$254$		0			0
$255$	−14.2500			−0.892367
$256$		0			0
$257$	−4.07930	+	7.06556i	−0.254460	+	0.440738i	−0.964749	−	0.263173i	$-0.915231\pi$
$257$	−4.07930	+	7.06556i	−0.254460	+	0.440738i	0.710289	+	0.703911i	$0.248564\pi$
$258$		0			0
$259$	13.9688			0.867980
$260$		0			0
$261$	−1.42771	−	2.47287i	−0.0883733	−	0.153067i
$262$		0			0
$263$	3.15861	+	5.47087i	0.194768	+	0.337348i	0.946825	−	0.321750i	$-0.104271\pi$
$263$	3.15861	+	5.47087i	0.194768	+	0.337348i	−0.752056	+	0.659099i	$0.770938\pi$
$264$		0			0
$265$	−12.3624			−0.759419
$266$		0			0
$267$	36.6264			2.24150
$268$		0			0
$269$	−4.11951	−	7.13521i	−0.251171	−	0.435041i	0.712677	−	0.701492i	$-0.247482\pi$
$269$	−4.11951	−	7.13521i	−0.251171	−	0.435041i	−0.963849	+	0.266451i	$0.914149\pi$
$270$		0			0
$271$	−2.11094	−	3.65625i	−0.128230	−	0.222101i	0.794761	−	0.606923i	$-0.207596\pi$
$271$	−2.11094	−	3.65625i	−0.128230	−	0.222101i	−0.922991	+	0.384821i	$0.874263\pi$
$272$		0			0
$273$	14.6837			0.888696
$274$		0			0
$275$	0.142571	−	0.246941i	0.00859737	−	0.0148911i
$276$		0			0
$277$	−9.83739			−0.591071			−0.295536	−	0.955332i	$-0.595498\pi$
$277$	−9.83739			−0.591071			−0.295536	+	0.955332i	$0.595498\pi$
$278$		0			0
$279$	−1.35743	+	2.35114i	−0.0812671	+	0.140759i
$280$		0			0
$281$	−2.69024	+	4.65964i	−0.160486	+	0.277971i	−0.935043	−	0.354534i	$-0.884640\pi$
$281$	−2.69024	+	4.65964i	−0.160486	+	0.277971i	0.774557	+	0.632504i	$0.217973\pi$
$282$		0			0
$283$	−2.48240	−	4.29965i	−0.147564	−	0.255588i	0.782763	−	0.622320i	$-0.213810\pi$
$283$	−2.48240	−	4.29965i	−0.147564	−	0.255588i	−0.930326	+	0.366732i	$0.880476\pi$
$284$		0			0
$285$	−3.04567	−	9.48365i	−0.180410	−	0.561763i
$286$		0			0
$287$	0.540653	+	0.936439i	0.0319137	+	0.0552762i
$288$		0			0
$289$	−10.9433	+	18.9544i	−0.643724	+	1.11496i
$290$		0			0
$291$	13.4171	−	23.2392i	0.786526	−	1.36230i
$292$		0			0
$293$	−3.80620			−0.222360			−0.111180	−	0.993800i	$-0.535463\pi$
$293$	−3.80620			−0.222360			−0.111180	+	0.993800i	$0.535463\pi$
$294$		0			0
$295$	−2.86445	+	4.96137i	−0.166775	+	0.288862i
$296$		0			0
$297$	−0.507019			−0.0294202
$298$		0			0
$299$	13.0898	+	22.6722i	0.757002	+	1.31117i
$300$		0			0
$301$	−3.18122	−	5.51004i	−0.183363	−	0.317593i
$302$		0			0
$303$	18.0953			1.03955
$304$		0			0
$305$	−4.45779			−0.255252
$306$		0			0
$307$	0.287144	+	0.497348i	0.0163882	+	0.0283851i	0.874103	−	0.485740i	$-0.161450\pi$
$307$	0.287144	+	0.497348i	0.0163882	+	0.0283851i	−0.857715	+	0.514125i	$0.828117\pi$
$308$		0			0
$309$	14.6480	+	25.3711i	0.833297	+	1.44331i
$310$		0			0
$311$	8.61640			0.488591			0.244296	−	0.969701i	$-0.421443\pi$
$311$	8.61640			0.488591			0.244296	+	0.969701i	$0.421443\pi$
$312$		0			0
$313$	17.0617	−	29.5517i	0.964385	−	1.67036i	0.253126	−	0.967433i	$-0.418541\pi$
$313$	17.0617	−	29.5517i	0.964385	−	1.67036i	0.711259	−	0.702930i	$-0.248125\pi$
$314$		0			0
$315$	−2.85543			−0.160885
$316$		0			0
$317$	5.53865	−	9.59323i	0.311082	−	0.538809i	−0.667515	−	0.744596i	$-0.732642\pi$
$317$	5.53865	−	9.59323i	0.311082	−	0.538809i	0.978597	+	0.205787i	$0.0659754\pi$
$318$		0			0
$319$	0.183224	−	0.317354i	0.0102586	−	0.0177684i
$320$		0			0
$321$	−15.7746	−	27.3223i	−0.880450	−	1.52498i
$322$		0			0
$323$	−26.5683	−	5.74213i	−1.47830	−	0.319500i
$324$		0			0
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$		0			0
$327$	−10.5160	+	18.2143i	−0.581538	+	1.00725i
$328$		0			0
$329$	3.68122	−	6.37607i	0.202952	−	0.351524i
$330$		0			0
$331$	−6.41168			−0.352418			−0.176209	−	0.984353i	$-0.556383\pi$
$331$	−6.41168			−0.352418			−0.176209	+	0.984353i	$0.556383\pi$
$332$		0			0
$333$	−12.0753	+	20.9150i	−0.661722	+	1.14614i
$334$		0			0
$335$	−0.985963			−0.0538689
$336$		0			0
$337$	12.6336	+	21.8820i	0.688193	+	1.19199i	0.972422	+	0.233229i	$0.0749293\pi$
$337$	12.6336	+	21.8820i	0.688193	+	1.19199i	−0.284228	+	0.958757i	$0.591737\pi$
$338$		0			0
$339$	−19.7976	−	34.2905i	−1.07526	−	1.86240i
$340$		0			0
$341$	−0.348409			−0.0188674
$342$		0			0
$343$	−15.8695			−0.856871
$344$		0			0
$345$	−5.98240	−	10.3618i	−0.322082	−	0.557862i
$346$		0			0
$347$	6.20428	+	10.7461i	0.333063	+	0.576882i	0.983111	−	0.183011i	$-0.0585844\pi$
$347$	6.20428	+	10.7461i	0.333063	+	0.576882i	−0.650048	+	0.759893i	$0.725251\pi$
$348$		0			0
$349$	6.20384			0.332084			0.166042	−	0.986119i	$-0.446901\pi$
$349$	6.20384			0.332084			0.166042	+	0.986119i	$0.446901\pi$
$350$		0			0
$351$	4.44531	−	7.69950i	0.237273	−	0.410969i
$352$		0			0
$353$	−23.3484			−1.24271			−0.621355	−	0.783529i	$-0.713418\pi$
$353$	−23.3484			−1.24271			−0.621355	+	0.783529i	$0.713418\pi$
$354$		0			0
$355$	1.46135	−	2.53113i	0.0775603	−	0.134338i
$356$		0			0
$357$	−9.15661	+	15.8597i	−0.484619	+	0.839385i
$358$		0			0
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.580333	−	0.814379i	$-0.697078\pi$
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.415107	−	0.909773i	$-0.636256\pi$
$360$		0			0
$361$	−1.85698	−	18.9090i	−0.0977360	−	0.995212i
$362$		0			0
$363$	−12.4754	−	21.6080i	−0.654788	−	1.13413i
$364$		0			0
$365$	−0.382043	+	0.661718i	−0.0199971	+	0.0346359i
$366$		0			0
$367$	14.7038	−	25.4678i	0.767534	−	1.32941i	−0.171362	−	0.985208i	$-0.554817\pi$
$367$	14.7038	−	25.4678i	0.767534	−	1.32941i	0.938896	−	0.344200i	$-0.111850\pi$
$368$		0			0
$369$	−1.86946			−0.0973204
$370$		0			0
$371$	−7.94375	+	13.7590i	−0.412419	+	0.714331i
$372$		0			0
$373$	−21.5491			−1.11577			−0.557886	−	0.829918i	$-0.688387\pi$
$373$	−21.5491			−1.11577			−0.557886	+	0.829918i	$0.688387\pi$
$374$		0			0
$375$	−1.14257	−	1.97899i	−0.0590021	−	0.102195i
$376$		0			0
$377$	3.21286	+	5.56483i	0.165471	+	0.286603i
$378$		0			0
$379$	19.3945			0.996230			0.498115	−	0.867111i	$-0.334026\pi$
$379$	19.3945			0.996230			0.498115	+	0.867111i	$0.334026\pi$
$380$		0			0
$381$	21.3233			1.09242
$382$		0			0
$383$	9.44331	+	16.3563i	0.482531	+	0.835767i	0.999799	−	0.0200559i	$-0.00638442\pi$
$383$	9.44331	+	16.3563i	0.482531	+	0.835767i	−0.517268	+	0.855823i	$0.673051\pi$
$384$		0			0
$385$	−0.183224	−	0.317354i	−0.00933798	−	0.0161739i
$386$		0			0
$387$	11.0000			0.559161
$388$		0			0
$389$	4.54021	−	7.86387i	0.230198	−	0.398714i	−0.727668	−	0.685929i	$-0.759396\pi$
$389$	4.54021	−	7.86387i	0.230198	−	0.398714i	0.957866	+	0.287215i	$0.0927294\pi$
$390$		0			0
$391$	−32.6507			−1.65122
$392$		0			0
$393$	−14.1973	+	24.5904i	−0.716157	+	1.24042i
$394$		0			0
$395$	7.72889	−	13.3868i	0.388883	−	0.673565i
$396$		0			0
$397$	−8.49800	−	14.7190i	−0.426502	−	0.738724i	0.570057	−	0.821605i	$-0.306921\pi$
$397$	−8.49800	−	14.7190i	−0.426502	−	0.738724i	−0.996559	+	0.0828814i	$0.973588\pi$
$398$		0			0
$399$	−12.5120	−	2.70419i	−0.626385	−	0.135379i
$400$		0			0
$401$	−0.795720	−	1.37823i	−0.0397363	−	0.0688254i	0.845473	−	0.534018i	$-0.179318\pi$
$401$	−0.795720	−	1.37823i	−0.0397363	−	0.0688254i	−0.885210	+	0.465192i	$0.845985\pi$
$402$		0			0
$403$	3.05469	−	5.29088i	0.152165	−	0.263557i
$404$		0			0
$405$	−5.36445	+	9.29150i	−0.266562	+	0.461698i
$406$		0			0
$407$	−3.09935			−0.153629
$408$		0			0
$409$	0.998443	−	1.72935i	0.0493698	−	0.0855110i	−0.840284	−	0.542146i	$-0.817612\pi$
$409$	0.998443	−	1.72935i	0.0493698	−	0.0855110i	0.889654	+	0.456635i	$0.150945\pi$
$410$		0			0
$411$	42.3553			2.08923
$412$		0			0
$413$	3.68122	+	6.37607i	0.181141	+	0.313746i
$414$		0			0
$415$	−0.832814	−	1.44248i	−0.0408812	−	0.0708084i
$416$		0			0
$417$	−13.7429			−0.672994
$418$		0			0
$419$	22.7781			1.11278			0.556392	−	0.830920i	$-0.312185\pi$
$419$	22.7781			1.11278			0.556392	+	0.830920i	$0.312185\pi$
$420$		0			0
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	0.983923	−	0.178594i	$-0.0571550\pi$
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	−0.646629	+	0.762805i	$0.723822\pi$
$422$		0			0
$423$	6.36445	+	11.0235i	0.309450	+	0.535983i
$424$		0			0
$425$	−6.23591			−0.302486
$426$		0			0
$427$	−2.86445	+	4.96137i	−0.138620	+	0.240097i
$428$		0			0
$429$	−3.25796			−0.157296
$430$		0			0
$431$	1.71987	−	2.97891i	0.0828435	−	0.143489i	−0.821627	−	0.570026i	$-0.806933\pi$
$431$	1.71987	−	2.97891i	0.0828435	−	0.143489i	0.904470	+	0.426537i	$0.140267\pi$
$432$		0			0
$433$	4.60036	−	7.96806i	0.221079	−	0.382920i	−0.734057	−	0.679088i	$-0.762375\pi$
$433$	4.60036	−	7.96806i	0.221079	−	0.382920i	0.955136	+	0.296168i	$0.0957087\pi$
$434$		0			0
$435$	−1.46837	−	2.54329i	−0.0704028	−	0.121941i
$436$		0			0
$437$	−6.97850	−	21.7297i	−0.333827	−	1.03947i
$438$		0			0
$439$	−18.7550	−	32.4846i	−0.895126	−	1.55040i	−0.833649	−	0.552295i	$-0.813752\pi$
$439$	−18.7550	−	32.4846i	−0.895126	−	1.55040i	−0.0614769	−	0.998109i	$-0.519581\pi$
$440$		0			0
$441$	5.94175	−	10.2914i	0.282941	−	0.490067i
$442$		0			0
$443$	7.33939	−	12.7122i	0.348705	−	0.603975i	−0.637315	−	0.770604i	$-0.719955\pi$
$443$	7.33939	−	12.7122i	0.348705	−	0.603975i	0.986020	+	0.166629i	$0.0532882\pi$
$444$		0			0
$445$	16.0281			0.759804
$446$		0			0
$447$	−7.76053	+	13.4416i	−0.367060	+	0.635767i
$448$		0			0
$449$	−7.39052			−0.348780			−0.174390	−	0.984677i	$-0.555795\pi$
$449$	−7.39052			−0.348780			−0.174390	+	0.984677i	$0.555795\pi$
$450$		0			0
$451$	−0.119958	−	0.207773i	−0.00564860	−	0.00978367i
$452$		0			0
$453$	18.1526	+	31.4412i	0.852884	+	1.47724i
$454$		0			0
$455$	6.42571			0.301242
$456$		0			0
$457$	2.30007			0.107593			0.0537963	−	0.998552i	$-0.482868\pi$
$457$	2.30007			0.107593			0.0537963	+	0.998552i	$0.482868\pi$
$458$		0			0
$459$	5.54411	+	9.60269i	0.258777	+	0.448215i
$460$		0			0
$461$	−9.87848	−	17.1100i	−0.460087	−	0.796894i	0.538878	−	0.842384i	$-0.318848\pi$
$461$	−9.87848	−	17.1100i	−0.460087	−	0.796894i	−0.998965	+	0.0454900i	$0.985515\pi$
$462$		0			0
$463$	−28.9468			−1.34527			−0.672635	−	0.739974i	$-0.734838\pi$
$463$	−28.9468			−1.34527			−0.672635	+	0.739974i	$0.734838\pi$
$464$		0			0
$465$	−1.39608	+	2.41808i	−0.0647417	+	0.112136i
$466$		0			0
$467$	3.31722			0.153503			0.0767513	−	0.997050i	$-0.475545\pi$
$467$	3.31722			0.153503			0.0767513	+	0.997050i	$0.475545\pi$
$468$		0			0
$469$	−0.633551	+	1.09734i	−0.0292547	+	0.0506706i
$470$		0			0
$471$	8.57730	−	14.8563i	0.395221	−	0.684543i
$472$		0			0
$473$	0.705838	+	1.22255i	0.0324544	+	0.0562127i
$474$		0			0
$475$	−1.33281	−	4.15013i	−0.0611537	−	0.190421i
$476$		0			0
$477$	−13.7339	−	23.7878i	−0.628833	−	1.08917i
$478$		0			0
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.0784026	+	0.996922i	$0.524982\pi$
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.824158	+	0.566360i	$0.808351\pi$
$480$		0			0
$481$	27.1737	−	47.0662i	1.23901	−	2.14603i
$482$		0			0
$483$	−15.3765			−0.699654
$484$		0			0
$485$	5.87147	−	10.1697i	0.266610	−	0.461781i
$486$		0			0
$487$	24.7781			1.12280			0.561402	−	0.827543i	$-0.310262\pi$
$487$	24.7781			1.12280			0.561402	+	0.827543i	$0.310262\pi$
$488$		0			0
$489$	−24.9312	−	43.1821i	−1.12743	−	1.95276i
$490$		0			0
$491$	−6.81176	−	11.7983i	−0.307410	−	0.532450i	0.670385	−	0.742014i	$-0.266129\pi$
$491$	−6.81176	−	11.7983i	−0.307410	−	0.532450i	−0.977795	+	0.209563i	$0.932796\pi$
$492$		0			0
$493$	−8.01404			−0.360934
$494$		0			0
$495$	0.633551			0.0284760
$496$		0			0
$497$	−1.87804	−	3.25286i	−0.0842416	−	0.145911i
$498$		0			0
$499$	4.09490	+	7.09257i	0.183313	+	0.317507i	0.943007	−	0.332774i	$-0.107985\pi$
$499$	4.09490	+	7.09257i	0.183313	+	0.317507i	−0.759694	+	0.650281i	$0.774651\pi$
$500$		0			0
$501$	25.7882			1.15213
$502$		0			0
$503$	9.14257	−	15.8354i	0.407647	−	0.706065i	−0.586978	−	0.809603i	$-0.699683\pi$
$503$	9.14257	−	15.8354i	0.407647	−	0.706065i	0.994626	+	0.103537i	$0.0330160\pi$
$504$		0			0
$505$	7.91869			0.352377
$506$		0			0
$507$	13.7109	−	23.7479i	0.608920	−	1.05468i
$508$		0			0
$509$	−5.94220	+	10.2922i	−0.263383	+	0.456193i	−0.967139	−	0.254249i	$-0.918172\pi$
$509$	−5.94220	+	10.2922i	−0.263383	+	0.456193i	0.703756	+	0.710442i	$0.251505\pi$
$510$		0			0
$511$	0.490980	+	0.850402i	0.0217197	+	0.0376196i
$512$		0			0
$513$	−5.20584	+	5.74213i	−0.229843	+	0.253521i
$514$		0			0
$515$	6.41012	+	11.1026i	0.282464	+	0.489241i
$516$		0			0
$517$	−0.816776	+	1.41470i	−0.0359218	+	0.0622183i
$518$		0			0
$519$	−6.69024	+	11.5878i	−0.293669	+	0.508650i
$520$		0			0
$521$	21.3725			0.936345			0.468173	−	0.883637i	$-0.344913\pi$
$521$	21.3725			0.936345			0.468173	+	0.883637i	$0.344913\pi$
$522$		0			0
$523$	−2.88862	+	5.00323i	−0.126310	+	0.218776i	−0.922244	−	0.386607i	$-0.873647\pi$
$523$	−2.88862	+	5.00323i	−0.126310	+	0.218776i	0.795934	+	0.605383i	$0.206980\pi$
$524$		0			0
$525$	−2.93673			−0.128170
$526$		0			0
$527$	3.80976	+	6.59869i	0.165956	+	0.287444i
$528$		0			0
$529$	−2.20739	−	3.82332i	−0.0959737	−	0.166231i
$530$		0			0
$531$	−12.7289			−0.552387
$532$		0			0
$533$	4.20695			0.182223
$534$		0			0
$535$	−6.90310	−	11.9565i	−0.298447	−	0.516925i
$536$		0			0
$537$	21.4714	+	37.1895i	0.926559	+	1.60485i
$538$		0			0
$539$	1.52506			0.0656889
$540$		0			0
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	−0.892943	−	0.450170i	$-0.851363\pi$
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	0.836330	+	0.548226i	$0.184697\pi$
$542$		0			0
$543$	−30.4959			−1.30870
$544$		0			0
$545$	−4.60192	+	7.97076i	−0.197125	+	0.341430i
$546$		0			0
$547$	−18.1812	+	31.4908i	−0.777373	+	1.34645i	0.156078	+	0.987745i	$0.450115\pi$
$547$	−18.1812	+	31.4908i	−0.777373	+	1.34645i	−0.933451	+	0.358705i	$0.883218\pi$
$548$		0			0
$549$	−4.95233	−	8.57768i	−0.211360	−	0.366087i
$550$		0			0
$551$	−1.71286	−	5.33351i	−0.0729701	−	0.227215i
$552$		0			0
$553$	−9.93273	−	17.2040i	−0.422383	−	0.731588i
$554$		0			0
$555$	−12.4191	+	21.5106i	−0.527163	+	0.913073i
$556$		0			0
$557$	−11.9824	+	20.7541i	−0.507711	+	0.879381i	0.492249	+	0.870454i	$0.336175\pi$
$557$	−11.9824	+	20.7541i	−0.507711	+	0.879381i	−0.999960	+	0.00892662i	$0.997159\pi$
$558$		0			0
$559$	−24.7539			−1.04698
$560$		0			0
$561$	2.03163	−	3.51889i	0.0857756	−	0.148568i
$562$		0			0
$563$	8.52017			0.359082			0.179541	−	0.983750i	$-0.442539\pi$
$563$	8.52017			0.359082			0.179541	+	0.983750i	$0.442539\pi$
$564$		0			0
$565$	−8.66363	−	15.0058i	−0.364482	−	0.631301i
$566$		0			0
$567$	6.89408	+	11.9409i	0.289524	+	0.501470i
$568$		0			0
$569$	16.3734			0.686407			0.343204	−	0.939261i	$-0.388488\pi$
$569$	16.3734			0.686407			0.343204	+	0.939261i	$0.388488\pi$
$570$		0			0
$571$	5.21876			0.218398			0.109199	−	0.994020i	$-0.465171\pi$
$571$	5.21876			0.218398			0.109199	+	0.994020i	$0.465171\pi$
$572$		0			0
$573$	0.764087	+	1.32344i	0.0319202	+	0.0552874i
$574$		0			0
$575$	−2.61796	−	4.53443i	−0.109176	−	0.189099i
$576$		0			0
$577$	−32.0390			−1.33380			−0.666900	−	0.745147i	$-0.732379\pi$
$577$	−32.0390			−1.33380			−0.666900	+	0.745147i	$0.732379\pi$
$578$		0			0
$579$	−4.30074	+	7.44910i	−0.178733	+	0.309574i
$580$		0			0
$581$	−2.14057			−0.0888058
$582$		0			0
$583$	1.76253	−	3.05279i	0.0729965	−	0.126434i
$584$		0			0
$585$	−5.55469	+	9.62101i	−0.229658	+	0.397780i
$586$		0			0
$587$	−1.67220	−	2.89634i	−0.0690192	−	0.119545i	0.829451	−	0.558580i	$-0.188654\pi$
$587$	−1.67220	−	2.89634i	−0.0690192	−	0.119545i	−0.898470	+	0.439035i	$0.855320\pi$
$588$		0			0
$589$	−3.57730	+	3.94583i	−0.147400	+	0.162585i
$590$		0			0
$591$	16.7003	+	28.9257i	0.686958	+	1.18985i
$592$		0			0
$593$	−21.1054	+	36.5556i	−0.866694	+	1.50116i	−0.00133875	+	0.999999i	$0.500426\pi$
$593$	−21.1054	+	36.5556i	−0.866694	+	1.50116i	−0.865355	+	0.501159i	$0.832907\pi$
$594$		0			0
$595$	−4.00702	+	6.94036i	−0.164272	+	0.284527i
$596$		0			0
$597$	26.3273			1.07750
$598$		0			0
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	−0.914397	−	0.404818i	$-0.867335\pi$
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	0.807781	+	0.589483i	$0.200668\pi$
$600$		0			0
$601$	−10.1546			−0.414215			−0.207108	−	0.978318i	$-0.566405\pi$
$601$	−10.1546			−0.414215			−0.207108	+	0.978318i	$0.566405\pi$
$602$		0			0
$603$	−1.09534	−	1.89719i	−0.0446058	−	0.0772596i
$604$		0			0
$605$	−5.45935	−	9.45587i	−0.221954	−	0.384436i
$606$		0			0
$607$	−42.8764			−1.74030			−0.870149	−	0.492788i	$-0.835978\pi$
$607$	−42.8764			−1.74030			−0.870149	+	0.492788i	$0.835978\pi$
$608$		0			0
$609$	−3.77412			−0.152935
$610$		0			0
$611$	−14.3222	−	24.8068i	−0.579416	−	1.00358i
$612$		0			0
$613$	−12.5367	−	21.7141i	−0.506351	−	0.877025i	−0.999973	−	0.00734857i	$-0.997661\pi$
$613$	−12.5367	−	21.7141i	−0.506351	−	0.877025i	0.493622	−	0.869676i	$-0.335672\pi$
$614$		0			0
$615$	−1.92270			−0.0775306
$616$		0			0
$617$	2.74849	−	4.76053i	0.110650	−	0.191652i	−0.805382	−	0.592756i	$-0.798040\pi$
$617$	2.74849	−	4.76053i	0.110650	−	0.191652i	0.916033	+	0.401104i	$0.131373\pi$
$618$		0			0
$619$	−15.4899			−0.622590			−0.311295	−	0.950313i	$-0.600763\pi$
$619$	−15.4899			−0.622590			−0.311295	+	0.950313i	$0.600763\pi$
$620$		0			0
$621$	−4.65505	+	8.06279i	−0.186801	+	0.323548i
$622$		0			0
$623$	10.2992	−	17.8387i	0.412628	−	0.714693i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	2.77612	+	0.599995i	0.110868	+	0.0239615i
$628$		0			0
$629$	33.8905	+	58.7001i	1.35130	+	2.34053i
$630$		0			0
$631$	20.6616	−	35.7870i	0.822526	−	1.42466i	−0.0812689	−	0.996692i	$-0.525897\pi$
$631$	20.6616	−	35.7870i	0.822526	−	1.42466i	0.903795	−	0.427965i	$-0.140769\pi$
$632$		0			0
$633$	19.5843	−	33.9210i	0.778407	−	1.34824i
$634$		0			0
$635$	9.33126			0.370300
$636$		0			0
$637$	−13.3710	+	23.1593i	−0.529779	+	0.917604i
$638$		0			0
$639$	6.49387			0.256894
$640$		0			0
$641$	15.3358	+	26.5624i	0.605729	+	1.04915i	0.991936	+	0.126741i	$0.0404517\pi$
$641$	15.3358	+	26.5624i	0.605729	+	1.04915i	−0.386207	+	0.922412i	$0.626215\pi$
$642$		0			0
$643$	−4.00902	−	6.94383i	−0.158100	−	0.273838i	0.776083	−	0.630630i	$-0.217204\pi$
$643$	−4.00902	−	6.94383i	−0.158100	−	0.273838i	−0.934184	+	0.356793i	$0.883870\pi$
$644$		0			0
$645$	11.3132			0.445457
$646$		0			0
$647$	−10.0272			−0.394209			−0.197105	−	0.980382i	$-0.563154\pi$
$647$	−10.0272			−0.394209			−0.197105	+	0.980382i	$0.563154\pi$
$648$		0			0
$649$	−0.816776	−	1.41470i	−0.0320612	−	0.0555317i
$650$		0			0
$651$	1.79416	+	3.10758i	0.0703188	+	0.121796i
$652$		0			0
$653$	20.4117			0.798771			0.399385	−	0.916783i	$-0.369224\pi$
$653$	20.4117			0.798771			0.399385	+	0.916783i	$0.369224\pi$
$654$		0			0
$655$	−6.21286	+	10.7610i	−0.242756	+	0.420466i
$656$		0			0
$657$	−1.69771			−0.0662338
$658$		0			0
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	0.240765	+	0.970584i	$0.422602\pi$
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	−0.960932	+	0.276783i	$0.910732\pi$
$660$		0			0
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	−0.895402	−	0.445259i	$-0.853112\pi$
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	0.833307	+	0.552811i	$0.186445\pi$
$662$		0			0
$663$	35.6249	+	61.7041i	1.38356	+	2.39639i
$664$		0			0
$665$	−5.47539	−	1.18338i	−0.212326	−	0.0458895i
$666$		0			0
$667$	−3.36445	−	5.82739i	−0.130272	−	0.225638i
$668$		0			0
$669$	−1.74147	+	3.01632i	−0.0673292	+	0.116618i
$670$		0			0
$671$	0.635553	−	1.10081i	0.0245352	−	0.0424963i
$672$		0			0
$673$	−15.0742			−0.581067			−0.290534	−	0.956865i	$-0.593833\pi$
$673$	−15.0742			−0.581067			−0.290534	+	0.956865i	$0.593833\pi$
$674$		0			0
$675$	−0.889062	+	1.53990i	−0.0342200	+	0.0592708i
$676$		0			0
$677$	17.9648			0.690444			0.345222	−	0.938521i	$-0.387804\pi$
$677$	17.9648			0.690444			0.345222	+	0.938521i	$0.387804\pi$
$678$		0			0
$679$	−7.54567	−	13.0695i	−0.289576	−	0.501561i
$680$		0			0
$681$	−4.57028	−	7.91597i	−0.175134	−	0.303340i
$682$		0			0
$683$	3.78524			0.144838			0.0724191	−	0.997374i	$-0.476928\pi$
$683$	3.78524			0.144838			0.0724191	+	0.997374i	$0.476928\pi$
$684$		0			0
$685$	18.5351			0.708190
$686$		0			0
$687$	21.0687	+	36.4921i	0.803822	+	1.39226i
$688$		0			0
$689$	30.9061	+	53.5310i	1.17743	+	2.03937i
$690$		0			0
$691$	10.3335			0.393104			0.196552	−	0.980493i	$-0.437026\pi$
$691$	10.3335			0.393104			0.196552	+	0.980493i	$0.437026\pi$
$692$		0			0
$693$	0.407102	−	0.705121i	0.0154645	−	0.0267853i
$694$		0			0
$695$	−6.01404			−0.228125
$696$		0			0
$697$	−2.62342	+	4.54389i	−0.0993690	+	0.172112i
$698$		0			0
$699$	14.5241	−	25.1564i	0.549351	−	0.951504i
$700$		0			0
$701$	−17.9980	−	31.1734i	−0.679775	−	1.17740i	−0.975048	−	0.221992i	$-0.928744\pi$
$701$	−17.9980	−	31.1734i	−0.679775	−	1.17740i	0.295273	−	0.955413i	$-0.404589\pi$
$702$		0			0
$703$	−31.8227	+	35.1010i	−1.20022	+	1.32386i
$704$		0			0
$705$	6.54567	+	11.3374i	0.246524	+	0.426992i
$706$		0			0
$707$	5.08832	−	8.81324i	0.191366	−	0.331456i
$708$		0			0
$709$	−4.40266	+	7.62562i	−0.165345	+	0.286386i	−0.936778	−	0.349925i	$-0.886207\pi$
$709$	−4.40266	+	7.62562i	−0.165345	+	0.286386i	0.771433	+	0.636311i	$0.219540\pi$
$710$		0			0
$711$	34.3453			1.28805
$712$		0			0
$713$	−3.19882	+	5.54052i	−0.119797	+	0.207494i
$714$		0			0
$715$	−1.42571			−0.0533186
$716$		0			0
$717$	12.3789	+	21.4409i	0.462300	+	0.800726i
$718$		0			0
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	0.986971	−	0.160901i	$-0.0514400\pi$
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	−0.632830	+	0.774291i	$0.718107\pi$
$720$		0			0
$721$	16.4758			0.613592
$722$		0			0
$723$	22.5623			0.839100
$724$		0			0
$725$	−0.642571	−	1.11297i	−0.0238645	−	0.0413345i
$726$		0			0
$727$	2.04567	+	3.54321i	0.0758697	+	0.131410i	0.901464	−	0.432854i	$-0.142493\pi$
$727$	2.04567	+	3.54321i	0.0758697	+	0.131410i	−0.825594	+	0.564264i	$0.809160\pi$
$728$		0			0
$729$	−11.6485			−0.431425
$730$		0			0
$731$	15.4363	−	26.7364i	0.570932	−	0.988883i
$732$		0			0
$733$	−50.4678			−1.86407			−0.932036	−	0.362366i	$-0.881969\pi$
$733$	−50.4678			−1.86407			−0.932036	+	0.362366i	$0.881969\pi$
$734$		0			0
$735$	6.11094	−	10.5845i	0.225405	−	0.390414i
$736$		0			0
$737$	0.140570	−	0.243474i	0.00517796	−	0.00896849i
$738$		0			0
$739$	17.1148	+	29.6438i	0.629580	+	1.09046i	0.987636	+	0.156764i	$0.0501062\pi$
$739$	17.1148	+	29.6438i	0.629580	+	1.09046i	−0.358056	+	0.933700i	$0.616560\pi$
$740$		0			0
$741$	−33.4512	+	36.8973i	−1.22886	+	1.35545i
$742$		0			0
$743$	11.2996	+	19.5715i	0.414543	+	0.718010i	0.995380	−	0.0960101i	$-0.0306081\pi$
$743$	11.2996	+	19.5715i	0.414543	+	0.718010i	−0.580837	+	0.814020i	$0.697275\pi$
$744$		0			0
$745$	−3.39608	+	5.88218i	−0.124423	+	0.215507i
$746$		0			0
$747$	1.85041	−	3.20500i	0.0677030	−	0.117265i
$748$		0			0
$749$	−17.7429			−0.648313
$750$		0			0
$751$	−12.7199	+	22.0315i	−0.464155	+	0.803940i	−0.999163	−	0.0409072i	$-0.986975\pi$
$751$	−12.7199	+	22.0315i	−0.464155	+	0.803940i	0.535008	+	0.844847i	$0.320309\pi$
$752$		0			0
$753$	40.6093			1.47988
$754$		0			0
$755$	7.94375	+	13.7590i	0.289103	+	0.500741i
$756$		0			0
$757$	−21.4015	−	37.0686i	−0.777852	−	1.34728i	−0.933177	−	0.359416i	$-0.882976\pi$
$757$	−21.4015	−	37.0686i	−0.777852	−	1.34728i	0.155325	−	0.987863i	$-0.450357\pi$
$758$		0			0
$759$	3.41168			0.123836
$760$		0			0
$761$	−29.8944			−1.08367			−0.541836	−	0.840484i	$-0.682271\pi$
$761$	−29.8944			−1.08367			−0.541836	+	0.840484i	$0.682271\pi$
$762$		0			0
$763$	5.91412	+	10.2436i	0.214106	+	0.370842i
$764$		0			0
$765$	−6.92771	−	11.9992i	−0.250472	−	0.433830i
$766$		0			0
$767$	28.6445			1.03429
$768$		0			0
$769$	8.32179	−	14.4138i	0.300092	−	0.519774i	−0.676065	−	0.736842i	$-0.736316\pi$
$769$	8.32179	−	14.4138i	0.300092	−	0.519774i	0.976156	+	0.217068i	$0.0696494\pi$
$770$		0			0
$771$	−18.6436			−0.671432
$772$		0			0
$773$	−3.05669	+	5.29435i	−0.109942	+	0.190424i	−0.915746	−	0.401757i	$-0.868400\pi$
$773$	−3.05669	+	5.29435i	−0.109942	+	0.190424i	0.805805	+	0.592181i	$0.201733\pi$
$774$		0			0
$775$	−0.610938	+	1.05818i	−0.0219455	+	0.0380108i
$776$		0			0
$777$	15.9604	+	27.6442i	0.572575	+	0.991729i
$778$		0			0
$779$	−3.58477	−	0.774765i	−0.128438	−	0.0277588i
$780$		0			0
$781$	0.416692	+	0.721732i	0.0149104	+	0.0258256i
$782$		0			0
$783$	−1.14257	+	1.97899i	−0.0408322	+	0.0707234i
$784$		0			0
$785$	3.75351	−	6.50127i	0.133968	−	0.232040i
$786$		0			0
$787$	18.7781			0.669368			0.334684	−	0.942330i	$-0.391370\pi$
$787$	18.7781			0.669368			0.334684	+	0.942330i	$0.391370\pi$
$788$		0			0
$789$	−7.21787	+	12.5017i	−0.256963	+	0.445073i
$790$		0			0
$791$	−22.2680			−0.791759
$792$		0			0
$793$	11.1445	+	19.3028i	0.395752	+	0.685462i
$794$		0			0
$795$	−14.1250	−	24.4652i	−0.500961	−	0.867690i
$796$		0			0
$797$	30.2851			1.07275			0.536377	−	0.843978i	$-0.319792\pi$
$797$	30.2851			1.07275			0.536377	+	0.843978i	$0.319792\pi$
$798$		0			0
$799$	35.7249			1.26386
$800$		0			0
$801$	17.8062	+	30.8412i	0.629151	+	1.08972i
$802$		0			0
$803$	−0.108937	−	0.188684i	−0.00384430	−	0.00665851i
$804$		0			0
$805$	−6.72889			−0.237162
$806$		0			0
$807$	9.41368	−	16.3050i	0.331377	−	0.573962i
$808$		0			0
$809$	13.6015			0.478202			0.239101	−	0.970995i	$-0.423147\pi$
$809$	13.6015			0.478202			0.239101	+	0.970995i	$0.423147\pi$
$810$		0			0
$811$	0.799180	−	1.38422i	0.0280630	−	0.0486065i	−0.851653	−	0.524106i	$-0.824399\pi$
$811$	0.799180	−	1.38422i	0.0280630	−	0.0486065i	0.879716	+	0.475500i	$0.157733\pi$
$812$		0			0
$813$	4.82379	−	8.35506i	0.169178	−	0.293025i
$814$		0			0
$815$	−10.9101	−	18.8969i	−0.382165	−	0.661929i
$816$		0			0
$817$	21.0929	+	4.55875i	0.737947	+	0.159490i
$818$		0			0
$819$	7.13857	+	12.3644i	0.249442	+	0.432046i
$820$		0			0
$821$	9.40110	−	16.2832i	0.328101	−	0.568287i	−0.654034	−	0.756465i	$-0.726925\pi$
$821$	9.40110	−	16.2832i	0.328101	−	0.568287i	0.982135	+	0.188178i	$0.0602582\pi$
$822$		0			0
$823$	26.5984	−	46.0697i	0.927161	−	1.60589i	0.139111	−	0.990277i	$-0.455575\pi$
$823$	26.5984	−	46.0697i	0.927161	−	1.60589i	0.788049	−	0.615612i	$-0.211091\pi$
$824$		0			0
$825$	0.651591			0.0226855
$826$		0			0
$827$	−12.5371	+	21.7149i	−0.435957	+	0.755101i	−0.997373	−	0.0724334i	$-0.976924\pi$
$827$	−12.5371	+	21.7149i	−0.435957	+	0.755101i	0.561416	+	0.827534i	$0.310257\pi$
$828$		0			0
$829$	−28.2740			−0.981997			−0.490999	−	0.871160i	$-0.663368\pi$
$829$	−28.2740			−0.981997			−0.490999	+	0.871160i	$0.663368\pi$
$830$		0			0
$831$	−11.2399	−	19.4681i	−0.389908	−	0.675341i
$832$		0			0
$833$	−16.6761	−	28.8839i	−0.577793	−	1.00077i
$834$		0			0
$835$	11.2851			0.390538
$836$		0			0
$837$	2.17265			0.0750977
$838$		0			0
$839$	7.33983	+	12.7130i	0.253399	+	0.438900i	0.964459	−	0.264231i	$-0.0851181\pi$
$839$	7.33983	+	12.7130i	0.253399	+	0.438900i	−0.711060	+	0.703131i	$0.751785\pi$
$840$		0			0
$841$	13.6742	+	23.6844i	0.471524	+	0.816704i
$842$		0			0
$843$	−12.2952			−0.423468
$844$		0			0
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$	−14.0321			−0.482148
$848$		0			0
$849$	5.67265	−	9.82531i	0.194685	−	0.337204i
$850$		0			0
$851$	−28.4558	+	49.2869i	−0.975452	+	1.68953i
$852$		0			0
$853$	12.9523	+	22.4341i	0.443479	+	0.768129i	0.997945	−	0.0640780i	$-0.0204106\pi$
$853$	12.9523	+	22.4341i	0.443479	+	0.768129i	−0.554466	+	0.832207i	$0.687077\pi$
$854$		0			0
$855$	6.50502	−	7.17514i	0.222467	−	0.245385i
$856$		0			0
$857$	6.45277	+	11.1765i	0.220423	+	0.381783i	0.954936	−	0.296811i	$-0.0959231\pi$
$857$	6.45277	+	11.1765i	0.220423	+	0.381783i	−0.734514	+	0.678594i	$0.762590\pi$
$858$		0			0
$859$	−14.3589	+	24.8703i	−0.489919	+	0.848564i	−0.999933	−	0.0116018i	$-0.996307\pi$
$859$	−14.3589	+	24.8703i	−0.489919	+	0.848564i	0.510014	+	0.860166i	$0.329640\pi$
$860$		0			0
$861$	−1.23547	+	2.13990i	−0.0421047	+	0.0729275i
$862$		0			0
$863$	3.04300			0.103585			0.0517925	−	0.998658i	$-0.483507\pi$
$863$	3.04300			0.103585			0.0517925	+	0.998658i	$0.483507\pi$
$864$		0			0
$865$	−2.92771	+	5.07095i	−0.0995453	+	0.172417i
$866$		0			0
$867$	−50.0140			−1.69857
$868$		0			0
$869$	2.20384	+	3.81716i	0.0747600	+	0.129488i
$870$		0			0
$871$	2.46491	+	4.26934i	0.0835202	+	0.144661i
$872$		0			0
$873$	26.0913			0.883058
$874$		0			0
$875$	−1.28514			−0.0434457
$876$		0			0
$877$	−5.68468	−	9.84616i	−0.191958	−	0.332481i	0.753941	−	0.656942i	$-0.228150\pi$
$877$	−5.68468	−	9.84616i	−0.191958	−	0.332481i	−0.945899	+	0.324461i	$0.894817\pi$
$878$		0			0
$879$	−4.34885	−	7.53243i	−0.146683	−	0.254063i
$880$		0			0
$881$	36.4014			1.22640			0.613198	−	0.789929i	$-0.289883\pi$
$881$	36.4014			1.22640			0.613198	+	0.789929i	$0.289883\pi$
$882$		0			0
$883$	−24.8839	+	43.1003i	−0.837411	+	1.45044i	0.0546404	+	0.998506i	$0.482599\pi$
$883$	−24.8839	+	43.1003i	−0.837411	+	1.45044i	−0.892052	+	0.451933i	$0.850735\pi$
$884$		0			0
$885$	−13.0913			−0.440061
$886$		0			0
$887$	−7.84885	+	13.5946i	−0.263539	+	0.456462i	−0.967180	−	0.254093i	$-0.918223\pi$
$887$	−7.84885	+	13.5946i	−0.263539	+	0.456462i	0.703641	+	0.710556i	$0.251556\pi$
$888$		0			0
$889$	5.99600	−	10.3854i	0.201099	−	0.348314i
$890$		0			0
$891$	−1.52963	−	2.64940i	−0.0512446	−	0.0887582i
$892$		0			0
$893$	7.63555	+	23.7757i	0.255514	+	0.795623i
$894$		0			0
$895$	9.39608	+	16.2745i	0.314076	+	0.543996i
$896$		0			0
$897$	−29.9120	+	51.8091i	−0.998733	+	1.72986i
$898$		0			0
$899$	−0.785142	+	1.35991i	−0.0261860	+	0.0453554i
$900$		0			0
$901$	−77.0911			−2.56828
$902$		0			0
$903$	7.26955	−	12.5912i	0.241915	−	0.419010i
$904$		0			0
$905$	−13.3453			−0.443613
$906$		0			0
$907$	−16.4578	−	28.5057i	−0.546472	−	0.946517i	−0.998513	−	0.0545199i	$-0.982637\pi$
$907$	−16.4578	−	28.5057i	−0.546472	−	0.946517i	0.452041	−	0.891997i	$-0.350696\pi$
$908$		0			0
$909$	8.79718	+	15.2372i	0.291784	+	0.505385i
$910$		0			0
$911$	18.7109			0.619918			0.309959	−	0.950750i	$-0.399685\pi$
$911$	18.7109			0.619918			0.309959	+	0.950750i	$0.399685\pi$
$912$		0			0
$913$	0.474941			0.0157183
$914$		0			0
$915$	−5.09334	−	8.82193i	−0.168381	−	0.291644i
$916$		0			0
$917$	7.98441	+	13.8294i	0.263668	+	0.456687i
$918$		0			0
$919$	50.9506			1.68070			0.840352	−	0.542041i	$-0.182348\pi$
$919$	50.9506			1.68070			0.840352	+	0.542041i	$0.182348\pi$
$920$		0			0
$921$	−0.656164	+	1.13651i	−0.0216214	+	0.0374493i
$922$		0			0
$923$	−14.6135			−0.481009
$924$		0			0
$925$	−5.43473	+	9.41323i	−0.178693	+	0.309505i
$926$		0			0
$927$	−14.2425	+	24.6687i	−0.467785	+	0.810227i
$928$		0			0
$929$	−5.74249	−	9.94628i	−0.188405	−	0.326327i	0.756314	−	0.654209i	$-0.226998\pi$
$929$	−5.74249	−	9.94628i	−0.188405	−	0.326327i	−0.944719	+	0.327882i	$0.893665\pi$
$930$		0			0
$931$	15.6586	−	17.2717i	0.513190	−	0.566057i
$932$		0			0
$933$	9.84485	+	17.0518i	0.322306	+	0.558250i
$934$		0			0
$935$	0.889062	−	1.53990i	0.0290754	−	0.0503601i
$936$		0			0
$937$	−8.08477	+	14.0032i	−0.264118	+	0.457465i	−0.967332	−	0.253512i	$-0.918414\pi$
$937$	−8.08477	+	14.0032i	−0.264118	+	0.457465i	0.703214	+	0.710978i	$0.251747\pi$
$938$		0			0
$939$	77.9769			2.54468
$940$		0			0
$941$	12.6937	−	21.9861i	0.413803	−	0.716728i	−0.581499	−	0.813547i	$-0.697534\pi$
$941$	12.6937	−	21.9861i	0.413803	−	0.716728i	0.995302	+	0.0968194i	$0.0308669\pi$
$942$		0			0
$943$	−4.40545			−0.143461
$944$		0			0
$945$	1.14257	+	1.97899i	0.0371678	+	0.0643766i
$946$		0			0
$947$	11.6902	+	20.2481i	0.379882	+	0.657975i	0.991045	−	0.133530i	$-0.0426313\pi$
$947$	11.6902	+	20.2481i	0.379882	+	0.657975i	−0.611163	+	0.791505i	$0.709298\pi$
$948$		0			0
$949$	3.82043			0.124016
$950$		0			0
$951$	25.3132			0.820837
$952$		0			0
$953$	11.0893	+	19.2073i	0.359219	+	0.622185i	0.987831	−	0.155534i	$-0.0497098\pi$
$953$	11.0893	+	19.2073i	0.359219	+	0.622185i	−0.628612	+	0.777719i	$0.716376\pi$
$954$		0			0
$955$	0.334372	+	0.579148i	0.0108200	+	0.0187408i
$956$		0			0
$957$	0.837388			0.0270689
$958$		0			0
$959$	11.9101	−	20.6289i	0.384598	−	0.666143i
$960$		0			0
$961$	−29.5070			−0.951839
$962$		0			0
$963$	15.3378	−	26.5659i	0.494255	−	0.856074i
$964$		0			0
$965$	−1.88204	+	3.25979i	−0.0605851	+	0.104937i
$966$		0			0
$967$	−20.4297	−	35.3853i	−0.656975	−	1.13791i	−0.981395	−	0.192001i	$-0.938502\pi$
$967$	−20.4297	−	35.3853i	−0.656975	−	1.13791i	0.324419	−	0.945913i	$-0.394831\pi$
$968$		0			0
$969$	−18.9925	−	59.1392i	−0.610128	−	1.89982i
$970$		0			0
$971$	12.3238	+	21.3454i	0.395489	+	0.685008i	0.993164	−	0.116731i	$-0.0372417\pi$
$971$	12.3238	+	21.3454i	0.395489	+	0.685008i	−0.597674	+	0.801739i	$0.703908\pi$
$972$		0			0
$973$	−3.86445	+	6.69342i	−0.123888	+	0.214581i
$974$		0			0
$975$	−5.71286	+	9.89496i	−0.182958	+	0.316892i
$976$		0			0
$977$	−13.7077			−0.438549			−0.219275	−	0.975663i	$-0.570369\pi$
$977$	−13.7077			−0.438549			−0.219275	+	0.975663i	$0.570369\pi$
$978$		0			0
$979$	−2.28514	+	3.95798i	−0.0730335	+	0.126498i
$980$		0			0
$981$	−20.4498			−0.652911
$982$		0			0
$983$	0.141014	+	0.244243i	0.00449765	+	0.00779015i	0.868265	−	0.496100i	$-0.165235\pi$
$983$	0.141014	+	0.244243i	0.00449765	+	0.00779015i	−0.863768	+	0.503890i	$0.831902\pi$
$984$		0			0
$985$	7.30820	+	12.6582i	0.232859	+	0.403323i
$986$		0			0
$987$	16.8242			0.535521
$988$		0			0
$989$	25.9218			0.824266
$990$		0			0
$991$	12.2992	+	21.3028i	0.390696	+	0.676706i	0.992542	−	0.121907i	$-0.0389009\pi$
$991$	12.2992	+	21.3028i	0.390696	+	0.676706i	−0.601845	+	0.798613i	$0.705568\pi$
$992$		0			0
$993$	−7.32580	−	12.6887i	−0.232477	−	0.402662i
$994$		0			0
$995$	11.5211			0.365242
$996$		0			0
$997$	11.5913	−	20.0768i	0.367101	−	0.635838i	−0.622010	−	0.783010i	$-0.713684\pi$
$997$	11.5913	−	20.0768i	0.367101	−	0.635838i	0.989111	+	0.147171i	$0.0470169\pi$
$998$		0			0
$999$	19.3273			0.611487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.j.881.3		6
4.3	odd	2		95.2.e.b.26.2	yes	6
12.11	even	2		855.2.k.g.406.2		6
19.11	even	3	inner	1520.2.q.j.961.3		6
20.3	even	4		475.2.j.b.349.3		12
20.7	even	4		475.2.j.b.349.4		12
20.19	odd	2		475.2.e.d.26.2		6
76.7	odd	6		1805.2.a.h.1.2		3
76.11	odd	6		95.2.e.b.11.2	✓	6
76.31	even	6		1805.2.a.g.1.2		3
228.11	even	6		855.2.k.g.676.2		6
380.87	even	12		475.2.j.b.49.3		12
380.159	odd	6		9025.2.a.z.1.2		3
380.163	even	12		475.2.j.b.49.4		12
380.239	odd	6		475.2.e.d.201.2		6
380.259	even	6		9025.2.a.ba.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.2	✓	6	76.11	odd	6
95.2.e.b.26.2	yes	6	4.3	odd	2
475.2.e.d.26.2		6	20.19	odd	2
475.2.e.d.201.2		6	380.239	odd	6
475.2.j.b.49.3		12	380.87	even	12
475.2.j.b.49.4		12	380.163	even	12
475.2.j.b.349.3		12	20.3	even	4
475.2.j.b.349.4		12	20.7	even	4
855.2.k.g.406.2		6	12.11	even	2
855.2.k.g.676.2		6	228.11	even	6
1520.2.q.j.881.3		6	1.1	even	1	trivial
1520.2.q.j.961.3		6	19.11	even	3	inner
1805.2.a.g.1.2		3	76.31	even	6
1805.2.a.h.1.2		3	76.7	odd	6
9025.2.a.z.1.2		3	380.159	odd	6
9025.2.a.ba.1.2		3	380.259	even	6

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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14257 + 1.97899i) q^{3} +(0.500000 + 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 + 1.92420i) q^{9} +O(q^{10})\)	\(q+(1.14257 + 1.97899i) q^{3} +(0.500000 + 0.866025i) q^{5} +1.28514 q^{7} +(-1.11094 + 1.92420i) q^{9} -0.285142 q^{11} +(2.50000 - 4.33013i) q^{13} +(-1.14257 + 1.97899i) q^{15} +(3.11796 + 5.40046i) q^{17} +(-2.92771 + 3.22932i) q^{19} +(1.46837 + 2.54329i) q^{21} +(-2.61796 + 4.53443i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.77812 q^{27} +(-0.642571 + 1.11297i) q^{29} +1.22188 q^{31} +(-0.325796 - 0.564295i) q^{33} +(0.642571 + 1.11297i) q^{35} +10.8695 q^{37} +11.4257 q^{39} +(0.420695 + 0.728665i) q^{41} +(-2.47539 - 4.28749i) q^{43} -2.22188 q^{45} +(2.86445 - 4.96137i) q^{47} -5.34841 q^{49} +(-7.12498 + 12.3408i) q^{51} +(-6.18122 + 10.7062i) q^{53} +(-0.142571 - 0.246941i) q^{55} +(-9.73591 - 2.10419i) q^{57} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-1.42771 + 2.47287i) q^{63} +5.00000 q^{65} +(-0.492981 + 0.853869i) q^{67} -11.9648 q^{69} +(-1.46135 - 2.53113i) q^{71} +(0.382043 + 0.661718i) q^{73} -2.28514 q^{75} -0.366449 q^{77} +(-7.72889 - 13.3868i) q^{79} +(5.36445 + 9.29150i) q^{81} -1.66563 q^{83} +(-3.11796 + 5.40046i) q^{85} -2.93673 q^{87} +(8.01404 - 13.8807i) q^{89} +(3.21286 - 5.56483i) q^{91} +(1.39608 + 2.41808i) q^{93} +(-4.26053 - 0.920816i) q^{95} +(-5.87147 - 10.1697i) q^{97} +(0.316776 - 0.548672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q + q^3 + 3 * q^5 - 4 * q^7 - 4 * q^9	\( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9} + 10 q^{11} + 15 q^{13} - q^{15} - q^{17} + 12 q^{21} + 4 q^{23} - 3 q^{25} + 16 q^{27} + 2 q^{29} + 2 q^{31} - 11 q^{33} - 2 q^{35} - 4 q^{37} + 10 q^{39} + 2 q^{41} - q^{43} - 8 q^{45} + 6 q^{47} - 14 q^{49} - 6 q^{51} - 11 q^{53} + 5 q^{55} - 19 q^{57} + 6 q^{59} + 9 q^{61} + 9 q^{63} + 30 q^{65} - 20 q^{67} - 10 q^{69} - 29 q^{71} + 22 q^{73} - 2 q^{75} - 32 q^{77} - 24 q^{79} + 21 q^{81} + 6 q^{83} + q^{85} - 24 q^{87} + 14 q^{89} - 10 q^{91} - 6 q^{93} - 7 q^{97} - 13 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 - 4 * q^7 - 4 * q^9 + 10 * q^11 + 15 * q^13 - q^15 - q^17 + 12 * q^21 + 4 * q^23 - 3 * q^25 + 16 * q^27 + 2 * q^29 + 2 * q^31 - 11 * q^33 - 2 * q^35 - 4 * q^37 + 10 * q^39 + 2 * q^41 - q^43 - 8 * q^45 + 6 * q^47 - 14 * q^49 - 6 * q^51 - 11 * q^53 + 5 * q^55 - 19 * q^57 + 6 * q^59 + 9 * q^61 + 9 * q^63 + 30 * q^65 - 20 * q^67 - 10 * q^69 - 29 * q^71 + 22 * q^73 - 2 * q^75 - 32 * q^77 - 24 * q^79 + 21 * q^81 + 6 * q^83 + q^85 - 24 * q^87 + 14 * q^89 - 10 * q^91 - 6 * q^93 - 7 * q^97 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more