LMFDB - Embedded newform 45.2.j.a.34.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(4,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.j (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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			34.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	45.34
Dual form			45.2.j.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67303 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-2.09077 - 0.792893i) q^{5} +(-2.36603 - 2.36603i) q^{6} +(0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(1.67303 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-2.09077 - 0.792893i) q^{5} +(-2.36603 - 2.36603i) q^{6} +(0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 + 1.50000i) q^{9} +(-2.73205 - 3.34607i) q^{10} +(-2.36603 + 4.09808i) q^{11} +(-0.776457 - 2.89778i) q^{12} +(2.12132 - 1.22474i) q^{13} +(0.866025 + 1.50000i) q^{14} +(3.14248 + 2.26380i) q^{15} +(2.23205 - 3.86603i) q^{16} -0.378937i q^{17} +(2.89778 + 5.01910i) q^{18} -2.73205 q^{19} +(-0.621320 - 3.82282i) q^{20} +(-1.09808 - 1.09808i) q^{21} +(-7.91688 + 4.57081i) q^{22} +(-1.67303 + 0.965926i) q^{23} +(-0.232051 + 0.866025i) q^{24} +(3.74264 + 3.31552i) q^{25} +4.73205 q^{26} +(-3.67423 - 3.67423i) q^{27} +1.55291i q^{28} +(3.23205 - 5.59808i) q^{29} +(3.07081 + 6.82282i) q^{30} +(1.36603 + 2.36603i) q^{31} +(6.57201 - 3.79435i) q^{32} +(5.79555 - 5.79555i) q^{33} +(0.366025 - 0.633975i) q^{34} +(-1.26795 - 1.55291i) q^{35} +5.19615i q^{36} +4.24264i q^{37} +(-4.57081 - 2.63896i) q^{38} +(-4.09808 + 1.09808i) q^{39} +(-0.410432 + 1.08226i) q^{40} +(-2.13397 - 3.69615i) q^{41} +(-0.776457 - 2.89778i) q^{42} +(-7.91688 - 4.57081i) q^{43} -8.19615 q^{44} +(-4.24264 - 5.19615i) q^{45} -3.73205 q^{46} +(3.79435 + 2.19067i) q^{47} +(-5.46739 + 5.46739i) q^{48} +(-3.09808 - 5.36603i) q^{49} +(3.05902 + 9.16208i) q^{50} +(-0.169873 + 0.633975i) q^{51} +(3.67423 + 2.12132i) q^{52} +3.86370i q^{53} +(-2.59808 - 9.69615i) q^{54} +(8.19615 - 6.69213i) q^{55} +(0.232051 - 0.401924i) q^{56} +(4.57081 + 1.22474i) q^{57} +(10.8147 - 6.24384i) q^{58} +(1.26795 + 2.19615i) q^{59} +(-0.674235 + 6.67423i) q^{60} +(-5.33013 + 9.23205i) q^{61} +5.27792i q^{62} +(1.34486 + 2.32937i) q^{63} +5.73205 q^{64} +(-5.40629 + 0.878680i) q^{65} +(15.2942 - 4.09808i) q^{66} +(4.45069 - 2.56961i) q^{67} +(0.568406 - 0.328169i) q^{68} +(3.23205 - 0.866025i) q^{69} +(-0.621320 - 3.82282i) q^{70} +3.80385 q^{71} +(0.776457 - 1.34486i) q^{72} +8.48528i q^{73} +(-4.09808 + 7.09808i) q^{74} +(-4.77526 - 7.22474i) q^{75} +(-2.36603 - 4.09808i) q^{76} +(-3.67423 + 2.12132i) q^{77} +(-7.91688 - 2.12132i) q^{78} +(0.267949 - 0.464102i) q^{79} +(-7.73205 + 6.31319i) q^{80} +(4.50000 + 7.79423i) q^{81} -8.24504i q^{82} +(9.02150 + 5.20857i) q^{83} +(0.696152 - 2.59808i) q^{84} +(-0.300457 + 0.792271i) q^{85} +(-8.83013 - 15.2942i) q^{86} +(-7.91688 + 7.91688i) q^{87} +(2.12132 + 1.22474i) q^{88} +7.39230 q^{89} +(-2.07898 - 12.7914i) q^{90} +2.19615 q^{91} +(-2.89778 - 1.67303i) q^{92} +(-1.22474 - 4.57081i) q^{93} +(4.23205 + 7.33013i) q^{94} +(5.71209 + 2.16622i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(-8.90138 - 5.13922i) q^{97} -11.9700i q^{98} +(-12.2942 + 7.09808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{6}+O(q^{10}) $ 8 * q - 12 * q^6	$ 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40} - 24 q^{41} - 24 q^{44} - 16 q^{46} - 4 q^{49} + 24 q^{50} - 36 q^{51} + 24 q^{55} - 12 q^{56} + 24 q^{59} + 24 q^{60} - 8 q^{61} + 32 q^{64} + 60 q^{66} + 12 q^{69} + 12 q^{70} + 72 q^{71} - 12 q^{74} - 48 q^{75} - 12 q^{76} + 16 q^{79} - 48 q^{80} + 36 q^{81} - 36 q^{84} + 16 q^{85} - 36 q^{86} - 24 q^{89} - 36 q^{90} - 24 q^{91} + 20 q^{94} + 12 q^{95} - 60 q^{96} - 36 q^{99}+O(q^{100}) $ 8 * q - 12 * q^6 - 8 * q^10 - 12 * q^11 + 12 * q^15 + 4 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^21 + 12 * q^24 - 4 * q^25 + 24 * q^26 + 12 * q^29 - 12 * q^30 + 4 * q^31 - 4 * q^34 - 24 * q^35 - 12 * q^39 - 4 * q^40 - 24 * q^41 - 24 * q^44 - 16 * q^46 - 4 * q^49 + 24 * q^50 - 36 * q^51 + 24 * q^55 - 12 * q^56 + 24 * q^59 + 24 * q^60 - 8 * q^61 + 32 * q^64 + 60 * q^66 + 12 * q^69 + 12 * q^70 + 72 * q^71 - 12 * q^74 - 48 * q^75 - 12 * q^76 + 16 * q^79 - 48 * q^80 + 36 * q^81 - 36 * q^84 + 16 * q^85 - 36 * q^86 - 24 * q^89 - 36 * q^90 - 24 * q^91 + 20 * q^94 + 12 * q^95 - 60 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.67303	+	0.965926i	1.18301	+	0.683013i	0.956710	−	0.291044i	$-0.0940027\pi$
$2$	1.67303	+	0.965926i	1.18301	+	0.683013i	0.226303	+	0.974057i	$0.427336\pi$
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$	0.866025	+	1.50000i	0.433013	+	0.750000i
$5$	−2.09077	−	0.792893i	−0.935021	−	0.354593i
$5$	−2.09077	−	0.792893i	−0.935021	−	0.354593i
$6$	−2.36603	−	2.36603i	−0.965926	−	0.965926i
$7$	0.776457	+	0.448288i	0.293473	+	0.169437i	0.639507	−	0.768785i	$-0.279138\pi$
$7$	0.776457	+	0.448288i	0.293473	+	0.169437i	−0.346034	+	0.938222i	$0.612472\pi$
$8$		−	0.517638i		−	0.183013i
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−2.73205	−	3.34607i	−0.863950	−	1.05812i
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	0.250196	+	0.968195i	$0.419505\pi$
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	−0.963580	+	0.267421i	$0.913828\pi$
$12$	−0.776457	−	2.89778i	−0.224144	−	0.836516i
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$	0.866025	+	1.50000i	0.231455	+	0.400892i
$15$	3.14248	+	2.26380i	0.811386	+	0.584511i
$16$	2.23205	−	3.86603i	0.558013	−	0.966506i
$17$		−	0.378937i		−	0.0919058i	−0.998944	−	0.0459529i	$-0.985368\pi$
$17$		−	0.378937i		−	0.0919058i	0.998944	−	0.0459529i	$-0.0146324\pi$
$18$	2.89778	+	5.01910i	0.683013	+	1.18301i
$19$	−2.73205			−0.626775			−0.313388	−	0.949625i	$-0.601464\pi$
$19$	−2.73205			−0.626775			−0.313388	+	0.949625i	$0.601464\pi$
$20$	−0.621320	−	3.82282i	−0.138931	−	0.854809i
$21$	−1.09808	−	1.09808i	−0.239620	−	0.239620i
$22$	−7.91688	+	4.57081i	−1.68788	+	0.974500i
$23$	−1.67303	+	0.965926i	−0.348851	+	0.201409i	−0.664179	−	0.747573i	$-0.731219\pi$
$23$	−1.67303	+	0.965926i	−0.348851	+	0.201409i	0.315328	+	0.948983i	$0.397886\pi$
$24$	−0.232051	+	0.866025i	−0.0473672	+	0.176777i
$25$	3.74264	+	3.31552i	0.748528	+	0.663103i
$26$	4.73205			0.928032
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$			1.55291i			0.293473i
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	−0.392617	−	0.919702i	$-0.628430\pi$
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	0.992794	−	0.119835i	$-0.0382364\pi$
$30$	3.07081	+	6.82282i	0.560651	+	1.24567i
$31$	1.36603	+	2.36603i	0.245345	+	0.424951i	0.962229	−	0.272243i	$-0.0877653\pi$
$31$	1.36603	+	2.36603i	0.245345	+	0.424951i	−0.716883	+	0.697193i	$0.754432\pi$
$32$	6.57201	−	3.79435i	1.16178	−	0.670753i
$33$	5.79555	−	5.79555i	1.00888	−	1.00888i
$34$	0.366025	−	0.633975i	0.0627728	−	0.108726i
$35$	−1.26795	−	1.55291i	−0.214323	−	0.262490i
$36$			5.19615i			0.866025i
$37$			4.24264i			0.697486i	0.937218	+	0.348743i	$0.113391\pi$
$37$			4.24264i			0.697486i	−0.937218	+	0.348743i	$0.886609\pi$
$38$	−4.57081	−	2.63896i	−0.741483	−	0.428096i
$39$	−4.09808	+	1.09808i	−0.656217	+	0.175833i
$40$	−0.410432	+	1.08226i	−0.0648950	+	0.171121i
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	0.649880	−	0.760037i	$-0.274819\pi$
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	−0.983151	+	0.182795i	$0.941486\pi$
$42$	−0.776457	−	2.89778i	−0.119810	−	0.447137i
$43$	−7.91688	−	4.57081i	−1.20731	−	0.697042i	−0.245141	−	0.969487i	$-0.578834\pi$
$43$	−7.91688	−	4.57081i	−1.20731	−	0.697042i	−0.962171	+	0.272445i	$0.912168\pi$
$44$	−8.19615			−1.23562
$45$	−4.24264	−	5.19615i	−0.632456	−	0.774597i
$46$	−3.73205			−0.550261
$47$	3.79435	+	2.19067i	0.553463	+	0.319542i	0.750518	−	0.660850i	$-0.229804\pi$
$47$	3.79435	+	2.19067i	0.553463	+	0.319542i	−0.197054	+	0.980393i	$0.563138\pi$
$48$	−5.46739	+	5.46739i	−0.789149	+	0.789149i
$49$	−3.09808	−	5.36603i	−0.442582	−	0.766575i
$50$	3.05902	+	9.16208i	0.432611	+	1.29571i
$51$	−0.169873	+	0.633975i	−0.0237870	+	0.0887742i
$52$	3.67423	+	2.12132i	0.509525	+	0.294174i
$53$			3.86370i			0.530720i	0.964149	+	0.265360i	$0.0854909\pi$
$53$			3.86370i			0.530720i	−0.964149	+	0.265360i	$0.914509\pi$
$54$	−2.59808	−	9.69615i	−0.353553	−	1.31948i
$55$	8.19615	−	6.69213i	1.10517	−	0.902367i
$56$	0.232051	−	0.401924i	0.0310091	−	0.0537093i
$57$	4.57081	+	1.22474i	0.605419	+	0.162221i
$58$	10.8147	−	6.24384i	1.42003	−	0.819857i
$59$	1.26795	+	2.19615i	0.165073	+	0.285915i	0.936681	−	0.350183i	$-0.113881\pi$
$59$	1.26795	+	2.19615i	0.165073	+	0.285915i	−0.771608	+	0.636098i	$0.780547\pi$
$60$	−0.674235	+	6.67423i	−0.0870433	+	0.861640i
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	0.291777	+	0.956486i	$0.405753\pi$
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	−0.974230	+	0.225557i	$0.927580\pi$
$62$			5.27792i			0.670296i
$63$	1.34486	+	2.32937i	0.169437	+	0.293473i
$64$	5.73205			0.716506
$65$	−5.40629	+	0.878680i	−0.670567	+	0.108987i
$66$	15.2942	−	4.09808i	1.88259	−	0.504438i
$67$	4.45069	−	2.56961i	0.543739	−	0.313928i	−0.202854	−	0.979209i	$-0.565022\pi$
$67$	4.45069	−	2.56961i	0.543739	−	0.313928i	0.746593	+	0.665281i	$0.231688\pi$
$68$	0.568406	−	0.328169i	0.0689294	−	0.0397964i
$69$	3.23205	−	0.866025i	0.389093	−	0.104257i
$70$	−0.621320	−	3.82282i	−0.0742620	−	0.456915i
$71$	3.80385			0.451434			0.225717	−	0.974193i	$-0.427528\pi$
$71$	3.80385			0.451434			0.225717	+	0.974193i	$0.427528\pi$
$72$	0.776457	−	1.34486i	0.0915064	−	0.158494i
$73$			8.48528i			0.993127i	0.868000	+	0.496564i	$0.165405\pi$
$73$			8.48528i			0.993127i	−0.868000	+	0.496564i	$0.834595\pi$
$74$	−4.09808	+	7.09808i	−0.476392	+	0.825135i
$75$	−4.77526	−	7.22474i	−0.551399	−	0.834242i
$76$	−2.36603	−	4.09808i	−0.271402	−	0.470082i
$77$	−3.67423	+	2.12132i	−0.418718	+	0.241747i
$78$	−7.91688	−	2.12132i	−0.896410	−	0.240192i
$79$	0.267949	−	0.464102i	0.0301466	−	0.0522155i	−0.850558	−	0.525880i	$-0.823736\pi$
$79$	0.267949	−	0.464102i	0.0301466	−	0.0522155i	0.880705	+	0.473665i	$0.157069\pi$
$80$	−7.73205	+	6.31319i	−0.864470	+	0.705836i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		−	8.24504i		−	0.910513i
$83$	9.02150	+	5.20857i	0.990238	+	0.571714i	0.905346	−	0.424676i	$-0.139612\pi$
$83$	9.02150	+	5.20857i	0.990238	+	0.571714i	0.0848929	+	0.996390i	$0.472945\pi$
$84$	0.696152	−	2.59808i	0.0759565	−	0.283473i
$85$	−0.300457	+	0.792271i	−0.0325891	+	0.0859339i
$86$	−8.83013	−	15.2942i	−0.952177	−	1.64922i
$87$	−7.91688	+	7.91688i	−0.848778	+	0.848778i
$88$	2.12132	+	1.22474i	0.226134	+	0.130558i
$89$	7.39230			0.783583			0.391791	−	0.920054i	$-0.371856\pi$
$89$	7.39230			0.783583			0.391791	+	0.920054i	$0.371856\pi$
$90$	−2.07898	−	12.7914i	−0.219144	−	1.34833i
$91$	2.19615			0.230219
$92$	−2.89778	−	1.67303i	−0.302114	−	0.174426i
$93$	−1.22474	−	4.57081i	−0.127000	−	0.473971i
$94$	4.23205	+	7.33013i	0.436503	+	0.756045i
$95$	5.71209	+	2.16622i	0.586048	+	0.222250i
$96$	−12.6962	+	3.40192i	−1.29580	+	0.347207i
$97$	−8.90138	−	5.13922i	−0.903799	−	0.521808i	−0.0253679	−	0.999678i	$-0.508076\pi$
$97$	−8.90138	−	5.13922i	−0.903799	−	0.521808i	−0.878431	+	0.477870i	$0.841409\pi$
$98$		−	11.9700i		−	1.20916i
$99$	−12.2942	+	7.09808i	−1.23562	+	0.713384i
$100$	−1.73205	+	8.48528i	−0.173205	+	0.848528i
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	−0.922188	−	0.386742i	$-0.873600\pi$
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	0.796022	+	0.605267i	$0.206934\pi$
$102$	−0.896575	+	0.896575i	−0.0887742	+	0.0887742i
$103$	−7.91688	+	4.57081i	−0.780073	+	0.450375i	−0.836456	−	0.548034i	$-0.815376\pi$
$103$	−7.91688	+	4.57081i	−0.780073	+	0.450375i	0.0563832	+	0.998409i	$0.482043\pi$
$104$	−0.633975	−	1.09808i	−0.0621663	−	0.107675i
$105$	1.42517	+	3.16648i	0.139082	+	0.309017i
$106$	−3.73205	+	6.46410i	−0.362489	+	0.627849i
$107$		−	11.7298i		−	1.13396i	−0.823730	−	0.566982i	$-0.808111\pi$
$107$		−	11.7298i		−	1.13396i	0.823730	−	0.566982i	$-0.191889\pi$
$108$	2.32937	−	8.69333i	0.224144	−	0.836516i
$109$	4.66025			0.446371			0.223186	−	0.974776i	$-0.428354\pi$
$109$	4.66025			0.446371			0.223186	+	0.974776i	$0.428354\pi$
$110$	20.1765	−	3.27928i	1.92376	−	0.312667i
$111$	1.90192	−	7.09808i	0.180523	−	0.673720i
$112$	3.46618	−	2.00120i	0.327524	−	0.189096i
$113$	2.20925	−	1.27551i	0.207829	−	0.119990i	−0.392473	−	0.919764i	$-0.628380\pi$
$113$	2.20925	−	1.27551i	0.207829	−	0.119990i	0.600302	+	0.799773i	$0.295047\pi$
$114$	6.46410	+	6.46410i	0.605419	+	0.605419i
$115$	4.26380	−	0.692993i	0.397602	−	0.0646219i
$116$	11.1962			1.03954
$117$	7.34847			0.679366
$118$			4.89898i			0.450988i
$119$	0.169873	−	0.294229i	0.0155722	−	0.0269719i
$120$	1.17183	−	1.62667i	0.106973	−	0.148494i
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$	−17.8350	+	10.2970i	−1.61470	+	0.932248i
$123$	1.91327	+	7.14042i	0.172514	+	0.643830i
$124$	−2.36603	+	4.09808i	−0.212475	+	0.368018i
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$			5.19615i			0.462910i
$127$			4.65874i			0.413397i	0.978405	+	0.206698i	$0.0662719\pi$
$127$			4.65874i			0.413397i	−0.978405	+	0.206698i	$0.933728\pi$
$128$	−3.55412	−	2.05197i	−0.314142	−	0.181370i
$129$	11.1962	+	11.1962i	0.985766	+	0.985766i
$130$	−9.89363	−	3.75201i	−0.867729	−	0.329073i
$131$	0.464102	+	0.803848i	0.0405487	+	0.0702325i	0.885588	−	0.464473i	$-0.153756\pi$
$131$	0.464102	+	0.803848i	0.0405487	+	0.0702325i	−0.845039	+	0.534705i	$0.820423\pi$
$132$	13.7124	+	3.67423i	1.19351	+	0.319801i
$133$	−2.12132	−	1.22474i	−0.183942	−	0.106199i
$134$	9.92820			0.857666
$135$	4.76870	+	10.5953i	0.410425	+	0.911894i
$136$	−0.196152			−0.0168199
$137$	−16.0740	−	9.28032i	−1.37329	−	0.792871i	−0.381952	−	0.924182i	$-0.624748\pi$
$137$	−16.0740	−	9.28032i	−1.37329	−	0.792871i	−0.991341	+	0.131311i	$0.958081\pi$
$138$	6.24384	+	1.67303i	0.531511	+	0.142418i
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	0.645021	−	0.764165i	$-0.276849\pi$
$139$	−4.00000	−	6.92820i	−0.339276	−	0.587643i	−0.984297	+	0.176522i	$0.943515\pi$
$140$	1.23130	−	3.24679i	0.104063	−	0.274404i
$141$	−5.36603	−	5.36603i	−0.451901	−	0.451901i
$142$	6.36396	+	3.67423i	0.534052	+	0.308335i
$143$			11.5911i			0.969297i
$144$	11.5981	−	6.69615i	0.966506	−	0.558013i
$145$	−11.1962	+	9.14162i	−0.929790	+	0.759170i
$146$	−8.19615	+	14.1962i	−0.678318	+	1.17488i
$147$	2.77766	+	10.3664i	0.229097	+	0.855003i
$148$	−6.36396	+	3.67423i	−0.523114	+	0.302020i
$149$	3.86603	+	6.69615i	0.316717	+	0.548570i	0.979801	−	0.199975i	$-0.0640861\pi$
$149$	3.86603	+	6.69615i	0.316717	+	0.548570i	−0.663084	+	0.748545i	$0.730753\pi$
$150$	−1.01059	−	16.6998i	−0.0825143	−	1.36353i
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.118343	−	0.992973i	$-0.462242\pi$
$151$	11.2942	−	19.5622i	0.919111	−	1.59195i	0.800768	−	0.598975i	$-0.204425\pi$
$152$			1.41421i			0.114708i
$153$	0.568406	−	0.984508i	0.0459529	−	0.0795928i
$154$	−8.19615			−0.660465
$155$	−0.980040	−	6.02993i	−0.0787187	−	0.484335i
$156$	−5.19615	−	5.19615i	−0.416025	−	0.416025i
$157$	18.5235	−	10.6945i	1.47833	−	0.853517i	0.478635	−	0.878014i	$-0.341132\pi$
$157$	18.5235	−	10.6945i	1.47833	−	0.853517i	0.999700	+	0.0244975i	$0.00779857\pi$
$158$	0.896575	−	0.517638i	0.0713277	−	0.0411811i
$159$	1.73205	−	6.46410i	0.137361	−	0.512637i
$160$	−16.7491	+	2.72222i	−1.32413	+	0.215210i
$161$	−1.73205			−0.136505
$162$			17.3867i			1.36603i
$163$		−	18.9396i		−	1.48346i	−0.670697	−	0.741731i	$-0.734005\pi$
$163$		−	18.9396i		−	1.48346i	0.670697	−	0.741731i	$-0.265995\pi$
$164$	3.69615	−	6.40192i	0.288621	−	0.499906i
$165$	−16.7124	+	7.52192i	−1.30106	+	0.585581i
$166$	10.0622	+	17.4282i	0.780976	+	1.35269i
$167$	14.7291	−	8.50386i	1.13977	−	0.658049i	0.193399	−	0.981120i	$-0.438049\pi$
$167$	14.7291	−	8.50386i	1.13977	−	0.658049i	0.946375	+	0.323071i	$0.104715\pi$
$168$	−0.568406	+	0.568406i	−0.0438535	+	0.0438535i
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$	−1.26795	+	1.03528i	−0.0972473	+	0.0794021i
$171$	−7.09808	−	4.09808i	−0.542803	−	0.313388i
$172$		−	15.8338i		−	1.20731i
$173$	−0.656339	−	0.378937i	−0.0499005	−	0.0288101i	0.474842	−	0.880071i	$-0.342505\pi$
$173$	−0.656339	−	0.378937i	−0.0499005	−	0.0288101i	−0.524743	+	0.851261i	$0.675838\pi$
$174$	−20.8923	+	5.59808i	−1.58384	+	0.424389i
$175$	1.41970	+	4.25214i	0.107319	+	0.321431i
$176$	10.5622	+	18.2942i	0.796154	+	1.37898i
$177$	−1.13681	−	4.24264i	−0.0854480	−	0.318896i
$178$	12.3676	+	7.14042i	0.926988	+	0.535197i
$179$	−24.5885			−1.83783			−0.918914	−	0.394458i	$-0.870932\pi$
$179$	−24.5885			−1.83783			−0.918914	+	0.394458i	$0.870932\pi$
$180$	4.11999	−	10.8640i	0.307086	−	0.809752i
$181$	8.46410			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$181$	8.46410			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$182$	3.67423	+	2.12132i	0.272352	+	0.157243i
$183$	13.0561	−	13.0561i	0.965134	−	0.965134i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	3.36396	−	8.87039i	0.247323	−	0.652164i
$186$	2.36603	−	8.83013i	0.173485	−	0.647456i
$187$	1.55291	+	0.896575i	0.113560	+	0.0655641i
$188$			7.58871i			0.553463i
$189$	−1.20577	−	4.50000i	−0.0877070	−	0.327327i
$190$	7.46410	+	9.14162i	0.541503	+	0.663203i
$191$	−0.169873	+	0.294229i	−0.0122916	+	0.0212896i	−0.872106	−	0.489317i	$-0.837246\pi$
$191$	−0.169873	+	0.294229i	−0.0122916	+	0.0212896i	0.859814	+	0.510607i	$0.170579\pi$
$192$	−9.58991	−	2.56961i	−0.692092	−	0.185445i
$193$	−17.9551	+	10.3664i	−1.29243	+	0.746187i	−0.979085	−	0.203451i	$-0.934784\pi$
$193$	−17.9551	+	10.3664i	−1.29243	+	0.746187i	−0.313349	+	0.949638i	$0.601451\pi$
$194$	−9.92820	−	17.1962i	−0.712803	−	1.23461i
$195$	9.43879	+	0.953512i	0.675926	+	0.0682824i
$196$	5.36603	−	9.29423i	0.383288	−	0.663873i
$197$			20.8343i			1.48438i	0.670190	+	0.742190i	$0.266213\pi$
$197$			20.8343i			1.48438i	−0.670190	+	0.742190i	$0.733787\pi$
$198$	−27.4249			−1.94900
$199$	−4.58846			−0.325267			−0.162634	−	0.986687i	$-0.551999\pi$
$199$	−4.58846			−0.325267			−0.162634	+	0.986687i	$0.551999\pi$
$200$	1.71624	−	1.93733i	0.121356	−	0.136990i
$201$	−8.59808	+	2.30385i	−0.606462	+	0.162501i
$202$	−4.24264	+	2.44949i	−0.298511	+	0.172345i
$203$	5.01910	−	2.89778i	0.352272	−	0.203384i
$204$	−1.09808	+	0.294229i	−0.0768807	+	0.0206001i
$205$	1.53100	+	9.41982i	0.106929	+	0.657909i
$206$	−17.6603			−1.23045
$207$	−5.79555			−0.402819
$208$		−	10.9348i		−	0.758190i
$209$	6.46410	−	11.1962i	0.447131	−	0.774454i
$210$	−0.674235	+	6.67423i	−0.0465266	+	0.460566i
$211$	6.56218	+	11.3660i	0.451759	+	0.782469i	0.998495	−	0.0548353i	$-0.0174634\pi$
$211$	6.56218	+	11.3660i	0.451759	+	0.782469i	−0.546736	+	0.837305i	$0.684130\pi$
$212$	−5.79555	+	3.34607i	−0.398040	+	0.229809i
$213$	−6.36396	−	1.70522i	−0.436051	−	0.116840i
$214$	11.3301	−	19.6244i	0.774512	−	1.34149i
$215$	12.9282	+	15.8338i	0.881696	+	1.07985i
$216$	−1.90192	+	1.90192i	−0.129410	+	0.129410i
$217$			2.44949i			0.166282i
$218$	7.79676	+	4.50146i	0.528063	+	0.304877i
$219$	3.80385	−	14.1962i	0.257040	−	0.959287i
$220$	17.1363	+	6.49867i	1.15533	+	0.438140i
$221$	−0.464102	−	0.803848i	−0.0312189	−	0.0540726i
$222$	10.0382	−	10.0382i	0.673720	−	0.673720i
$223$	14.4889	+	8.36516i	0.970248	+	0.560173i	0.899312	−	0.437308i	$-0.144068\pi$
$223$	14.4889	+	8.36516i	0.970248	+	0.560173i	0.0709359	+	0.997481i	$0.477401\pi$
$224$	6.80385			0.454601
$225$	4.75039	+	14.2279i	0.316693	+	0.948528i
$226$	4.92820			0.327819
$227$	−1.64085	−	0.947343i	−0.108907	−	0.0628774i	0.444557	−	0.895750i	$-0.353361\pi$
$227$	−1.64085	−	0.947343i	−0.108907	−	0.0628774i	−0.553464	+	0.832873i	$0.686694\pi$
$228$	2.12132	+	7.91688i	0.140488	+	0.524308i
$229$	9.96410	+	17.2583i	0.658446	+	1.14046i	0.981018	+	0.193917i	$0.0621194\pi$
$229$	9.96410	+	17.2583i	0.658446	+	1.14046i	−0.322571	+	0.946545i	$0.604547\pi$
$230$	7.80286	+	2.95912i	0.514505	+	0.195118i
$231$	7.09808	−	1.90192i	0.467019	−	0.125137i
$232$	−2.89778	−	1.67303i	−0.190248	−	0.109840i
$233$		−	7.07107i		−	0.463241i	−0.972806	−	0.231621i	$-0.925597\pi$
$233$		−	7.07107i		−	0.463241i	0.972806	−	0.231621i	$-0.0744028\pi$
$234$	12.2942	+	7.09808i	0.803699	+	0.464016i
$235$	−6.19615	−	7.58871i	−0.404192	−	0.495033i
$236$	−2.19615	+	3.80385i	−0.142957	+	0.247609i
$237$	−0.656339	+	0.656339i	−0.0426338	+	0.0426338i
$238$	0.568406	−	0.328169i	0.0368443	−	0.0212721i
$239$	6.46410	+	11.1962i	0.418128	+	0.724219i	0.995751	−	0.0920846i	$-0.0293530\pi$
$239$	6.46410	+	11.1962i	0.418128	+	0.724219i	−0.577623	+	0.816304i	$0.696020\pi$
$240$	15.7661	−	7.09599i	1.01770	−	0.458044i
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	−0.949133	−	0.314875i	$-0.898037\pi$
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	0.747256	+	0.664536i	$0.231371\pi$
$242$		−	22.0082i		−	1.41474i
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$	−18.4641			−1.18204
$245$	2.22268	+	13.6756i	0.142002	+	0.873700i
$246$	−3.69615	+	13.7942i	−0.235658	+	0.879488i
$247$	−5.79555	+	3.34607i	−0.368762	+	0.212905i
$248$	1.22474	−	0.707107i	0.0777714	−	0.0449013i
$249$	−12.7583	−	12.7583i	−0.808526	−	0.808526i
$250$	0.868845	−	21.5813i	0.0549506	−	1.36492i
$251$	18.5885			1.17329			0.586647	−	0.809843i	$-0.300448\pi$
$251$	18.5885			1.17329			0.586647	+	0.809843i	$0.300448\pi$
$252$	−2.32937	+	4.03459i	−0.146737	+	0.254155i
$253$		−	9.14162i		−	0.574729i
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$	0.857840	−	1.19080i	0.0537200	−	0.0745710i
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	−19.4201	+	11.2122i	−1.21139	+	0.699396i	−0.963062	−	0.269280i	$-0.913214\pi$
$257$	−19.4201	+	11.2122i	−1.21139	+	0.699396i	−0.248328	+	0.968676i	$0.579881\pi$
$258$	7.91688	+	29.5462i	0.492883	+	1.83946i
$259$	−1.90192	+	3.29423i	−0.118180	+	0.204693i
$260$	−6.00000	−	7.34847i	−0.372104	−	0.455733i
$261$	16.7942	−	9.69615i	1.03954	−	0.600177i
$262$			1.79315i			0.110781i
$263$	−6.60420	−	3.81294i	−0.407232	−	0.235116i	0.282368	−	0.959306i	$-0.408880\pi$
$263$	−6.60420	−	3.81294i	−0.407232	−	0.235116i	−0.689600	+	0.724191i	$0.742214\pi$
$264$	−3.00000	−	3.00000i	−0.184637	−	0.184637i
$265$	3.06350	−	8.07812i	0.188190	−	0.496235i
$266$	−2.36603	−	4.09808i	−0.145070	−	0.251269i
$267$	−12.3676	−	3.31388i	−0.756883	−	0.202806i
$268$	7.70882	+	4.45069i	0.470891	+	0.271869i
$269$	−17.1962			−1.04847			−0.524234	−	0.851574i	$-0.675648\pi$
$269$	−17.1962			−1.04847			−0.524234	+	0.851574i	$0.675648\pi$
$270$	−2.25603	+	22.3324i	−0.137298	+	1.35911i
$271$	−23.5167			−1.42854			−0.714268	−	0.699873i	$-0.753240\pi$
$271$	−23.5167			−1.42854			−0.714268	+	0.699873i	$0.753240\pi$
$272$	−1.46498	−	0.845807i	−0.0888276	−	0.0512846i
$273$	−3.67423	−	0.984508i	−0.222375	−	0.0595851i
$274$	−17.9282	−	31.0526i	−1.08308	−	1.87595i
$275$	−22.4424	+	7.49303i	−1.35333	+	0.451847i
$276$	4.09808	+	4.09808i	0.246675	+	0.246675i
$277$	−10.6066	−	6.12372i	−0.637289	−	0.367939i	0.146281	−	0.989243i	$-0.453270\pi$
$277$	−10.6066	−	6.12372i	−0.637289	−	0.367939i	−0.783569	+	0.621304i	$0.786603\pi$
$278$		−	15.4548i		−	0.926918i
$279$			8.19615i			0.490691i
$280$	−0.803848	+	0.656339i	−0.0480391	+	0.0392237i
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	−0.514624	−	0.857416i	$-0.672068\pi$
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	0.999856	+	0.0169692i	$0.00540173\pi$
$282$	−3.79435	−	14.1607i	−0.225950	−	0.843258i
$283$	−3.88229	+	2.24144i	−0.230778	+	0.133240i	−0.610931	−	0.791684i	$-0.709205\pi$
$283$	−3.88229	+	2.24144i	−0.230778	+	0.133240i	0.380153	+	0.924924i	$0.375871\pi$
$284$	3.29423	+	5.70577i	0.195477	+	0.338575i
$285$	−8.58542	−	6.18482i	−0.508557	−	0.366357i
$286$	−11.1962	+	19.3923i	−0.662042	+	1.14669i
$287$		−	3.82654i		−	0.225873i
$288$	22.7661			1.34151
$289$	16.8564			0.991553
$290$	−27.5617	+	4.47958i	−1.61848	+	0.263050i
$291$	12.5885	+	12.5885i	0.737948	+	0.737948i
$292$	−12.7279	+	7.34847i	−0.744845	+	0.430037i
$293$	−7.67664	+	4.43211i	−0.448474	+	0.258927i	−0.707186	−	0.707028i	$-0.750035\pi$
$293$	−7.67664	+	4.43211i	−0.448474	+	0.258927i	0.258711	+	0.965955i	$0.416702\pi$
$294$	−5.36603	+	20.0263i	−0.312953	+	1.16796i
$295$	−0.909676	−	5.59700i	−0.0529634	−	0.325870i
$296$	2.19615			0.127649
$297$	23.7506	−	6.36396i	1.37815	−	0.369274i
$298$			14.9372i			0.865287i
$299$	−2.36603	+	4.09808i	−0.136831	+	0.236998i
$300$	6.70163	−	13.4197i	0.386919	−	0.774786i
$301$	−4.09808	−	7.09808i	−0.236209	−	0.409126i
$302$	37.7912	−	21.8188i	2.17464	−	1.25553i
$303$	3.10583	−	3.10583i	0.178425	−	0.178425i
$304$	−6.09808	+	10.5622i	−0.349749	+	0.605782i
$305$	18.4641	−	15.0759i	1.05725	−	0.863242i
$306$	1.90192	−	1.09808i	0.108726	−	0.0627728i
$307$			25.8719i			1.47659i	0.674478	+	0.738295i	$0.264369\pi$
$307$			25.8719i			1.47659i	−0.674478	+	0.738295i	$0.735631\pi$
$308$	−6.36396	−	3.67423i	−0.362620	−	0.209359i
$309$	15.2942	−	4.09808i	0.870058	−	0.233131i
$310$	4.18482	−	11.0349i	0.237682	−	0.626741i
$311$	−14.0263	−	24.2942i	−0.795357	−	1.37760i	−0.922612	−	0.385729i	$-0.873950\pi$
$311$	−14.0263	−	24.2942i	−0.795357	−	1.37760i	0.127255	−	0.991870i	$-0.459383\pi$
$312$	0.568406	+	2.12132i	0.0321797	+	0.120096i
$313$	4.81105	+	2.77766i	0.271936	+	0.157003i	0.629767	−	0.776784i	$-0.283150\pi$
$313$	4.81105	+	2.77766i	0.271936	+	0.157003i	−0.357831	+	0.933786i	$0.616484\pi$
$314$	41.3205			2.33185
$315$	−0.964857	−	5.93651i	−0.0543635	−	0.334485i
$316$	0.928203			0.0522155
$317$	30.4428	+	17.5761i	1.70984	+	0.987174i	0.934742	+	0.355328i	$0.115631\pi$
$317$	30.4428	+	17.5761i	1.70984	+	0.987174i	0.775094	+	0.631846i	$0.217703\pi$
$318$	9.14162	−	9.14162i	0.512637	−	0.512637i
$319$	15.2942	+	26.4904i	0.856312	+	1.48318i
$320$	−11.9844	−	4.54490i	−0.669948	−	0.254068i
$321$	−5.25833	+	19.6244i	−0.293491	+	1.09532i
$322$	−2.89778	−	1.67303i	−0.161487	−	0.0932345i
$323$			1.03528i			0.0576043i
$324$	−7.79423	+	13.5000i	−0.433013	+	0.750000i
$325$	12.0000	+	2.44949i	0.665640	+	0.135873i
$326$	18.2942	−	31.6865i	1.01322	−	1.75495i
$327$	−7.79676	−	2.08913i	−0.431162	−	0.115529i
$328$	−1.91327	+	1.10463i	−0.105643	+	0.0609928i
$329$	1.96410	+	3.40192i	0.108284	+	0.187554i
$330$	−35.2261	−	3.55855i	−1.93913	−	0.195892i
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	−0.984539	−	0.175166i	$-0.943954\pi$
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	0.643968	+	0.765053i	$0.277287\pi$
$332$			18.0430i			0.990238i
$333$	−6.36396	+	11.0227i	−0.348743	+	0.604040i
$334$	32.8564			1.79782
$335$	−11.3428	+	1.84354i	−0.619723	+	0.100723i
$336$	−6.69615	+	1.79423i	−0.365305	+	0.0978832i
$337$	−1.55291	+	0.896575i	−0.0845926	+	0.0488396i	−0.541700	−	0.840572i	$-0.682219\pi$
$337$	−1.55291	+	0.896575i	−0.0845926	+	0.0488396i	0.457107	+	0.889412i	$0.348886\pi$
$338$	−11.7112	+	6.76148i	−0.637007	+	0.367776i
$339$	−4.26795	+	1.14359i	−0.231803	+	0.0621115i
$340$	−1.44861	+	0.235442i	−0.0785619	+	0.0127686i
$341$	−12.9282			−0.700101
$342$	−7.91688	−	13.7124i	−0.428096	−	0.741483i
$343$		−	11.8313i		−	0.638833i
$344$	−2.36603	+	4.09808i	−0.127568	+	0.220953i
$345$	−7.44414	−	0.752011i	−0.400779	−	0.0404869i
$346$	−0.732051	−	1.26795i	−0.0393553	−	0.0681654i
$347$	8.57321	−	4.94975i	0.460234	−	0.265716i	−0.251909	−	0.967751i	$-0.581058\pi$
$347$	8.57321	−	4.94975i	0.460234	−	0.265716i	0.712143	+	0.702035i	$0.247725\pi$
$348$	−18.7315	−	5.01910i	−1.00412	−	0.269052i
$349$	10.7679	−	18.6506i	0.576395	−	0.998346i	−0.419493	−	0.907758i	$-0.637792\pi$
$349$	10.7679	−	18.6506i	0.576395	−	0.998346i	0.995889	−	0.0905872i	$-0.0288744\pi$
$350$	−1.73205	+	8.48528i	−0.0925820	+	0.453557i
$351$	−12.2942	−	3.29423i	−0.656217	−	0.175833i
$352$			35.9101i			1.91402i
$353$	7.82894	+	4.52004i	0.416693	+	0.240578i	0.693661	−	0.720301i	$-0.255996\pi$
$353$	7.82894	+	4.52004i	0.416693	+	0.240578i	−0.276969	+	0.960879i	$0.589330\pi$
$354$	2.19615	−	8.19615i	0.116724	−	0.435621i
$355$	−7.95297	−	3.01604i	−0.422100	−	0.160075i
$356$	6.40192	+	11.0885i	0.339301	+	0.587687i
$357$	−0.416102	+	0.416102i	−0.0220225	+	0.0220225i
$358$	−41.1373	−	23.7506i	−2.17417	−	1.25526i
$359$	−9.80385			−0.517427			−0.258714	−	0.965954i	$-0.583299\pi$
$359$	−9.80385			−0.517427			−0.258714	+	0.965954i	$0.583299\pi$
$360$	−2.68973	+	2.19615i	−0.141761	+	0.115747i
$361$	−11.5359			−0.607153
$362$	14.1607	+	8.17569i	0.744271	+	0.429705i
$363$	5.10703	+	19.0597i	0.268050	+	1.00037i
$364$	1.90192	+	3.29423i	0.0996879	+	0.172664i
$365$	6.72792	−	17.7408i	0.352156	−	0.928595i
$366$	34.4545	−	9.23205i	1.80096	−	0.482567i
$367$	21.4770	+	12.3998i	1.12109	+	0.647262i	0.941679	−	0.336512i	$-0.109247\pi$
$367$	21.4770	+	12.3998i	1.12109	+	0.647262i	0.179411	+	0.983774i	$0.442581\pi$
$368$			8.62398i			0.449556i
$369$		−	12.8038i		−	0.666542i
$370$	14.1962	−	11.5911i	0.738023	−	0.602593i
$371$	−1.73205	+	3.00000i	−0.0899236	+	0.155752i
$372$	5.79555	−	5.79555i	0.300486	−	0.300486i
$373$	27.8410	−	16.0740i	1.44155	−	0.832280i	0.443597	−	0.896226i	$-0.353702\pi$
$373$	27.8410	−	16.0740i	1.44155	−	0.832280i	0.997953	+	0.0639468i	$0.0203688\pi$
$374$	1.73205	+	3.00000i	0.0895622	+	0.155126i
$375$	4.25551	+	18.8915i	0.219754	+	0.975555i
$376$	1.13397	−	1.96410i	0.0584803	−	0.101291i
$377$		−	15.8338i		−	0.815480i
$378$	2.32937	−	8.69333i	0.119810	−	0.447137i
$379$	−12.5359			−0.643926			−0.321963	−	0.946752i	$-0.604343\pi$
$379$	−12.5359			−0.643926			−0.321963	+	0.946752i	$0.604343\pi$
$380$	1.69748	+	10.4441i	0.0870788	+	0.535773i
$381$	2.08846	−	7.79423i	0.106995	−	0.399310i
$382$	−0.568406	+	0.328169i	−0.0290822	+	0.0167906i
$383$	−17.7148	+	10.2277i	−0.905186	+	0.522609i	−0.878879	−	0.477045i	$-0.841708\pi$
$383$	−17.7148	+	10.2277i	−0.905186	+	0.522609i	−0.0263067	+	0.999654i	$0.508375\pi$
$384$	5.02628	+	5.02628i	0.256496	+	0.256496i
$385$	9.36396	−	1.52192i	0.477232	−	0.0775641i
$386$	−40.0526			−2.03862
$387$	−13.7124	−	23.7506i	−0.697042	−	1.20731i
$388$		−	17.8028i		−	0.903799i
$389$	−12.0622	+	20.8923i	−0.611577	+	1.05928i	0.379398	+	0.925234i	$0.376131\pi$
$389$	−12.0622	+	20.8923i	−0.611577	+	1.05928i	−0.990975	+	0.134048i	$0.957202\pi$
$390$	14.8704	+	10.7124i	0.752991	+	0.542445i
$391$	0.366025	+	0.633975i	0.0185107	+	0.0320615i
$392$	−2.77766	+	1.60368i	−0.140293	+	0.0809982i
$393$	−0.416102	−	1.55291i	−0.0209896	−	0.0783342i
$394$	−20.1244	+	34.8564i	−1.01385	+	1.75604i
$395$	−0.928203	+	0.757875i	−0.0467030	+	0.0381328i
$396$	−21.2942	−	12.2942i	−1.07008	−	0.617808i
$397$		−	29.3939i		−	1.47524i	−0.675218	−	0.737618i	$-0.735950\pi$
$397$		−	29.3939i		−	1.47524i	0.675218	−	0.737618i	$-0.264050\pi$
$398$	−7.67664	−	4.43211i	−0.384795	−	0.222162i
$399$	3.00000	+	3.00000i	0.150188	+	0.150188i
$400$	21.1716	−	7.06875i	1.05858	−	0.353437i
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	0.936333	+	0.351115i	$0.114197\pi$
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	−0.164092	+	0.986445i	$0.552469\pi$
$402$	−16.6102	−	4.45069i	−0.828442	−	0.221980i
$403$	5.79555	+	3.34607i	0.288697	+	0.166679i
$404$	−4.39230			−0.218525
$405$	−3.22848	−	19.8640i	−0.160424	−	0.987048i
$406$	11.1962			0.555656
$407$	−17.3867	−	10.0382i	−0.861825	−	0.497575i
$408$	0.328169	+	0.0879327i	0.0162468	+	0.00435332i
$409$	−11.7321	−	20.3205i	−0.580113	−	1.00478i	−0.995465	−	0.0951241i	$-0.969675\pi$
$409$	−11.7321	−	20.3205i	−0.580113	−	1.00478i	0.415353	−	0.909660i	$-0.363658\pi$
$410$	−6.53744	+	17.2385i	−0.322861	+	0.851349i
$411$	22.7321	+	22.7321i	1.12129	+	1.12129i
$412$	−13.7124	−	7.91688i	−0.675563	−	0.390036i
$413$			2.27362i			0.111878i
$414$	−9.69615	−	5.59808i	−0.476540	−	0.275130i
$415$	−14.7321	−	18.0430i	−0.723168	−	0.885696i
$416$	9.29423	−	16.0981i	0.455687	−	0.789273i
$417$	3.58630	+	13.3843i	0.175622	+	0.655430i
$418$	21.6293	−	12.4877i	1.05792	−	0.610793i
$419$	−8.02628	−	13.9019i	−0.392109	−	0.679153i	0.600618	−	0.799536i	$-0.294921\pi$
$419$	−8.02628	−	13.9019i	−0.392109	−	0.679153i	−0.992728	+	0.120383i	$0.961588\pi$
$420$	−3.51549	+	4.88001i	−0.171538	+	0.238120i
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	−0.671887	−	0.740653i	$-0.734516\pi$
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	0.977368	+	0.211545i	$0.0678494\pi$
$422$			25.3543i			1.23423i
$423$	6.57201	+	11.3831i	0.319542	+	0.553463i
$424$	2.00000			0.0971286
$425$	1.25637	−	1.41823i	0.0609430	−	0.0687941i
$426$	−9.00000	−	9.00000i	−0.436051	−	0.436051i
$427$	−8.27723	+	4.77886i	−0.400563	+	0.231265i
$428$	17.5947	−	10.1583i	0.850473	−	0.491021i
$429$	5.19615	−	19.3923i	0.250873	−	0.936269i
$430$	6.33508	+	38.9781i	0.305505	+	1.87969i
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$	−22.4058	+	6.00361i	−1.07800	+	0.288849i
$433$			30.5307i			1.46721i	0.679575	+	0.733606i	$0.262164\pi$
$433$			30.5307i			1.46721i	−0.679575	+	0.733606i	$0.737836\pi$
$434$	−2.36603	+	4.09808i	−0.113573	+	0.196714i
$435$	22.8296	−	10.2751i	1.09460	−	0.492655i
$436$	4.03590	+	6.99038i	0.193284	+	0.334779i
$437$	4.57081	−	2.63896i	0.218651	−	0.126239i
$438$	20.0764	−	20.0764i	0.959287	−	0.959287i
$439$	4.66025	−	8.07180i	0.222422	−	0.385246i	−0.733121	−	0.680098i	$-0.761937\pi$
$439$	4.66025	−	8.07180i	0.222422	−	0.385246i	0.955543	+	0.294852i	$0.0952705\pi$
$440$	−3.46410	−	4.24264i	−0.165145	−	0.202260i
$441$		−	18.5885i		−	0.885165i
$442$		−	1.79315i		−	0.0852915i
$443$	−12.0394	−	6.95095i	−0.572009	−	0.330250i	0.185942	−	0.982561i	$-0.440466\pi$
$443$	−12.0394	−	6.95095i	−0.572009	−	0.330250i	−0.757951	+	0.652311i	$0.773800\pi$
$444$	12.2942	−	3.29423i	0.583458	−	0.156337i
$445$	−15.4556	−	5.86131i	−0.732666	−	0.277853i
$446$	16.1603	+	27.9904i	0.765210	+	1.32538i
$447$	−3.46618	−	12.9360i	−0.163945	−	0.611851i
$448$	4.45069	+	2.56961i	0.210275	+	0.121403i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$	−5.79555	+	28.3923i	−0.273205	+	1.33843i
$451$	20.1962			0.951000
$452$	3.82654	+	2.20925i	0.179985	+	0.103915i
$453$	−27.6651	+	27.6651i	−1.29982	+	1.29982i
$454$	−1.83013	−	3.16987i	−0.0858921	−	0.148770i
$455$	−4.59165	−	1.74131i	−0.215260	−	0.0816341i
$456$	0.633975	−	2.36603i	0.0296886	−	0.110799i
$457$	−29.9623	−	17.2987i	−1.40158	−	0.809201i	−0.407022	−	0.913418i	$-0.633433\pi$
$457$	−29.9623	−	17.2987i	−1.40158	−	0.809201i	−0.994554	+	0.104218i	$0.966766\pi$
$458$			38.4983i			1.79891i
$459$	−1.39230	+	1.39230i	−0.0649872	+	0.0649872i
$460$	4.73205	+	5.79555i	0.220633	+	0.270219i
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	−0.997358	−	0.0726397i	$-0.976858\pi$
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	0.561587	+	0.827418i	$0.310191\pi$
$462$	13.7124	+	3.67423i	0.637960	+	0.170941i
$463$	0.152304	−	0.0879327i	0.00707816	−	0.00408658i	−0.496457	−	0.868061i	$-0.665366\pi$
$463$	0.152304	−	0.0879327i	0.00707816	−	0.00408658i	0.503535	+	0.863975i	$0.332033\pi$
$464$	−14.4282	−	24.9904i	−0.669813	−	1.16015i
$465$	−1.06350	+	10.5276i	−0.0493188	+	0.488206i
$466$	6.83013	−	11.8301i	0.316400	−	0.548020i
$467$		−	5.75839i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$467$		−	5.75839i		−	0.266467i	0.991085	−	0.133233i	$-0.0425359\pi$
$468$	6.36396	+	11.0227i	0.294174	+	0.509525i
$469$	4.60770			0.212764
$470$	−3.03624	−	18.6812i	−0.140051	−	0.861698i
$471$	−35.7846	+	9.58846i	−1.64887	+	0.441813i
$472$	1.13681	−	0.656339i	0.0523260	−	0.0302104i
$473$	37.4631	−	21.6293i	1.72255	−	0.994517i
$474$	−1.73205	+	0.464102i	−0.0795557	+	0.0213169i
$475$	−10.2251	−	9.05816i	−0.469159	−	0.415617i
$476$	0.588457			0.0269719
$477$	−5.79555	+	10.0382i	−0.265360	+	0.459617i
$478$			24.9754i			1.14235i
$479$	15.9282	−	27.5885i	0.727778	−	1.26055i	−0.230042	−	0.973181i	$-0.573886\pi$
$479$	15.9282	−	27.5885i	0.727778	−	1.26055i	0.957820	−	0.287368i	$-0.0927803\pi$
$480$	29.2421	+	2.95405i	1.33471	+	0.134833i
$481$	5.19615	+	9.00000i	0.236924	+	0.410365i
$482$	−10.4865	+	6.05437i	−0.477646	+	0.275769i
$483$	2.89778	+	0.776457i	0.131853	+	0.0353300i
$484$	9.86603	−	17.0885i	0.448456	−	0.776748i
$485$	14.5359	+	17.8028i	0.660041	+	0.808382i
$486$	7.79423	−	29.0885i	0.353553	−	1.31948i
$487$		−	1.13681i		−	0.0515139i	−0.999668	−	0.0257569i	$-0.991800\pi$
$487$		−	1.13681i		−	0.0515139i	0.999668	−	0.0257569i	$-0.00819959\pi$
$488$	4.77886	+	2.75908i	0.216329	+	0.124898i
$489$	−8.49038	+	31.6865i	−0.383948	+	1.43291i
$490$	−9.49097	+	25.0266i	−0.428758	+	1.13059i
$491$	10.8564	+	18.8038i	0.489943	+	0.848606i	0.999933	−	0.0115744i	$-0.00368433\pi$
$491$	10.8564	+	18.8038i	0.489943	+	0.848606i	−0.509990	+	0.860180i	$0.670351\pi$
$492$	−9.05369	+	9.05369i	−0.408172	+	0.408172i
$493$	−2.12132	−	1.22474i	−0.0955395	−	0.0551597i
$494$	−12.9282			−0.581667
$495$	31.3324	−	5.09244i	1.40829	−	0.228888i
$496$	12.1962			0.547623
$497$	2.95352	+	1.70522i	0.132484	+	0.0764895i
$498$	−9.02150	−	33.6687i	−0.404263	−	1.50873i
$499$	−1.92820	−	3.33975i	−0.0863182	−	0.149508i	0.819634	−	0.572888i	$-0.194177\pi$
$499$	−1.92820	−	3.33975i	−0.0863182	−	0.149508i	−0.905952	+	0.423380i	$0.860844\pi$
$500$	10.3492	−	16.3674i	0.462832	−	0.731974i
$501$	−28.4545	+	7.62436i	−1.27125	+	0.340631i
$502$	31.0991	+	17.9551i	1.38802	+	0.801374i
$503$		−	29.3567i		−	1.30895i	−0.756083	−	0.654476i	$-0.772889\pi$
$503$		−	29.3567i		−	1.30895i	0.756083	−	0.654476i	$-0.227111\pi$
$504$	1.20577	−	0.696152i	0.0537093	−	0.0310091i
$505$	4.39230	−	3.58630i	0.195455	−	0.159588i
$506$	8.83013	−	15.2942i	0.392547	−	0.679911i
$507$	8.57321	−	8.57321i	0.380750	−	0.380750i
$508$	−6.98811	+	4.03459i	−0.310047	+	0.179006i
$509$	−5.42820	−	9.40192i	−0.240601	−	0.416733i	0.720285	−	0.693679i	$-0.244011\pi$
$509$	−5.42820	−	9.40192i	−0.240601	−	0.416733i	−0.960886	+	0.276946i	$0.910678\pi$
$510$	2.58542	−	1.16364i	0.114484	−	0.0515271i
$511$	−3.80385	+	6.58846i	−0.168272	+	0.291456i
$512$		−	29.2552i		−	1.29291i
$513$	10.0382	+	10.0382i	0.443197	+	0.443197i
$514$	−43.3205			−1.91079
$515$	20.1765	−	3.27928i	0.889084	−	0.144502i
$516$	−7.09808	+	26.4904i	−0.312475	+	1.16617i
$517$	−17.9551	+	10.3664i	−0.789663	+	0.455912i
$518$	−6.36396	+	3.67423i	−0.279616	+	0.161437i
$519$	0.928203	+	0.928203i	0.0407436	+	0.0407436i
$520$	0.454838	+	2.79850i	0.0199460	+	0.122722i
$521$	1.39230			0.0609980			0.0304990	−	0.999535i	$-0.490290\pi$
$521$	1.39230			0.0609980			0.0304990	+	0.999535i	$0.490290\pi$
$522$	37.4631			1.63971
$523$			30.9468i			1.35321i	0.736347	+	0.676604i	$0.236549\pi$
$523$			30.9468i			1.35321i	−0.736347	+	0.676604i	$0.763451\pi$
$524$	−0.803848	+	1.39230i	−0.0351162	+	0.0608231i
$525$	−0.469016	−	7.75039i	−0.0204696	−	0.338255i
$526$	−7.36603	−	12.7583i	−0.321174	−	0.556290i
$527$	0.896575	−	0.517638i	0.0390554	−	0.0225487i
$528$	−9.46979	−	35.3417i	−0.412120	−	1.53805i
$529$	−9.63397	+	16.6865i	−0.418868	+	0.725501i
$530$	12.9282	−	10.5558i	0.561565	−	0.458516i
$531$			7.60770i			0.330146i
$532$		−	4.24264i		−	0.183942i
$533$	−9.05369	−	5.22715i	−0.392159	−	0.226413i
$534$	−17.4904	−	17.4904i	−0.756883	−	0.756883i
$535$	−9.30049	+	24.5243i	−0.402095	+	1.06028i
$536$	−1.33013	−	2.30385i	−0.0574527	−	0.0995111i
$537$	41.1373	+	11.0227i	1.77521	+	0.475665i
$538$	−28.7697	−	16.6102i	−1.24035	−	0.716117i
$539$	29.3205			1.26292
$540$	−11.7631	+	16.3288i	−0.506202	+	0.702680i
$541$	21.3923			0.919727			0.459864	−	0.887990i	$-0.347898\pi$
$541$	21.3923			0.919727			0.459864	+	0.887990i	$0.347898\pi$
$542$	−39.3441	−	22.7153i	−1.68998	−	0.975708i
$543$	−14.1607	−	3.79435i	−0.607695	−	0.162831i
$544$	−1.43782	−	2.49038i	−0.0616461	−	0.106774i
$545$	−9.74352	−	3.69508i	−0.417367	−	0.158280i
$546$	−5.19615	−	5.19615i	−0.222375	−	0.222375i
$547$	26.2323	+	15.1452i	1.12161	+	0.647563i	0.941812	−	0.336140i	$-0.109122\pi$
$547$	26.2323	+	15.1452i	1.12161	+	0.647563i	0.179800	+	0.983703i	$0.442455\pi$
$548$		−	32.1480i		−	1.37329i
$549$	−27.6962	+	15.9904i	−1.18204	+	0.682453i
$550$	−44.7846	−	9.14162i	−1.90962	−	0.389800i
$551$	−8.83013	+	15.2942i	−0.376176	+	0.651556i
$552$	−0.448288	−	1.67303i	−0.0190804	−	0.0712090i
$553$	0.416102	−	0.240237i	0.0176945	−	0.0102159i
$554$	−11.8301	−	20.4904i	−0.502614	−	0.870553i
$555$	−9.60450	+	13.3324i	−0.407688	+	0.565930i
$556$	6.92820	−	12.0000i	0.293821	−	0.508913i
$557$			31.1127i			1.31829i	0.752017	+	0.659144i	$0.229081\pi$
$557$			31.1127i			1.31829i	−0.752017	+	0.659144i	$0.770919\pi$
$558$	−7.91688	+	13.7124i	−0.335148	+	0.580493i
$559$	−22.3923			−0.947094
$560$	−8.83373	+	1.43574i	−0.373293	+	0.0606711i
$561$	−2.19615	−	2.19615i	−0.0927216	−	0.0927216i
$562$	27.2168	−	15.7136i	1.14807	−	0.662840i
$563$	−23.8707	+	13.7818i	−1.00603	+	0.580833i	−0.910027	−	0.414548i	$-0.863940\pi$
$563$	−23.8707	+	13.7818i	−1.00603	+	0.580833i	−0.0960045	+	0.995381i	$0.530606\pi$
$564$	3.40192	−	12.6962i	0.143247	−	0.534604i
$565$	−5.63039	+	0.915103i	−0.236872	+	0.0384987i
$566$	−8.66025			−0.364018
$567$			8.06918i			0.338874i
$568$		−	1.96902i		−	0.0826181i
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	−0.916385	−	0.400299i	$-0.868906\pi$
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	0.804861	+	0.593463i	$0.202240\pi$
$570$	−8.38961	−	18.6403i	−0.351402	−	0.780756i
$571$	−2.73205	−	4.73205i	−0.114333	−	0.198030i	0.803180	−	0.595736i	$-0.203140\pi$
$571$	−2.73205	−	4.73205i	−0.114333	−	0.198030i	−0.917513	+	0.397706i	$0.869806\pi$
$572$	−17.3867	+	10.0382i	−0.726973	+	0.419718i
$573$	0.416102	−	0.416102i	0.0173829	−	0.0173829i
$574$	3.69615	−	6.40192i	0.154274	−	0.267211i
$575$	−9.46410	−	1.93185i	−0.394680	−	0.0805638i
$576$	14.8923	+	8.59808i	0.620513	+	0.358253i
$577$		−	28.5617i		−	1.18904i	−0.804082	−	0.594519i	$-0.797343\pi$
$577$		−	28.5617i		−	1.18904i	0.804082	−	0.594519i	$-0.202657\pi$
$578$	28.2013	+	16.2820i	1.17302	+	0.677244i
$579$	34.6865	−	9.29423i	1.44152	−	0.386255i
$580$	−23.4086	−	8.87735i	−0.971988	−	0.368612i
$581$	4.66987	+	8.08846i	0.193739	+	0.335566i
$582$	8.90138	+	33.2204i	0.368974	+	1.37703i
$583$	−15.8338	−	9.14162i	−0.655767	−	0.378607i
$584$	4.39230			0.181755
$585$	−15.3640	−	5.82655i	−0.635222	−	0.240898i
$586$	−17.1244			−0.707401
$587$	19.0597	+	11.0041i	0.786678	+	0.454189i	0.838792	−	0.544452i	$-0.183263\pi$
$587$	19.0597	+	11.0041i	0.786678	+	0.454189i	−0.0521138	+	0.998641i	$0.516596\pi$
$588$	−13.1440	+	13.1440i	−0.542050	+	0.542050i
$589$	−3.73205	−	6.46410i	−0.153776	−	0.266349i
$590$	3.88437	−	10.2426i	0.159917	−	0.421683i
$591$	9.33975	−	34.8564i	0.384186	−	1.43380i
$592$	16.4022	+	9.46979i	0.674124	+	0.389206i
$593$		−	28.9406i		−	1.18845i	−0.804299	−	0.594224i	$-0.797459\pi$
$593$		−	28.9406i		−	1.18845i	0.804299	−	0.594224i	$-0.202541\pi$
$594$	45.8827	+	12.2942i	1.88259	+	0.504438i
$595$	−0.588457	+	0.480473i	−0.0241244	+	0.0196975i
$596$	−6.69615	+	11.5981i	−0.274285	+	0.475076i
$597$	7.67664	+	2.05695i	0.314184	+	0.0841853i
$598$	−7.91688	+	4.57081i	−0.323745	+	0.186914i
$599$	16.8564	+	29.1962i	0.688734	+	1.19292i	0.972248	+	0.233954i	$0.0751666\pi$
$599$	16.8564	+	29.1962i	0.688734	+	1.19292i	−0.283514	+	0.958968i	$0.591500\pi$
$600$	−3.73980	+	2.47185i	−0.152677	+	0.100913i
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	−0.640143	−	0.768256i	$-0.721125\pi$
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	0.985401	+	0.170252i	$0.0544581\pi$
$602$		−	15.8338i		−	0.645335i
$603$	15.4176			0.627855
$604$	39.1244			1.59195
$605$	4.08664	+	25.1440i	0.166146	+	1.02225i
$606$	8.19615	−	2.19615i	0.332946	−	0.0892126i
$607$	−7.55652	+	4.36276i	−0.306710	+	0.177079i	−0.645453	−	0.763800i	$-0.723331\pi$
$607$	−7.55652	+	4.36276i	−0.306710	+	0.177079i	0.338743	+	0.940879i	$0.389998\pi$
$608$	−17.9551	+	10.3664i	−0.728174	+	0.420412i
$609$	−9.69615	+	2.59808i	−0.392908	+	0.105279i
$610$	45.4532	−	7.38748i	1.84035	−	0.299110i
$611$	10.7321			0.434172
$612$	1.96902			0.0795928
$613$		−	24.3190i		−	0.982236i	−0.871093	−	0.491118i	$-0.836588\pi$
$613$		−	24.3190i		−	0.982236i	0.871093	−	0.491118i	$-0.163412\pi$
$614$	−24.9904	+	43.2846i	−1.00853	+	1.74682i
$615$	1.66138	−	16.4460i	0.0669934	−	0.663166i
$616$	1.09808	+	1.90192i	0.0442428	+	0.0766307i
$617$	−11.3509	+	6.55343i	−0.456969	+	0.263831i	−0.710769	−	0.703426i	$-0.751653\pi$
$617$	−11.3509	+	6.55343i	−0.456969	+	0.263831i	0.253800	+	0.967257i	$0.418320\pi$
$618$	29.5462	+	7.91688i	1.18852	+	0.318463i
$619$	9.90192	−	17.1506i	0.397992	−	0.689342i	−0.595486	−	0.803366i	$-0.703041\pi$
$619$	9.90192	−	17.1506i	0.397992	−	0.689342i	0.993478	+	0.114023i	$0.0363739\pi$
$620$	8.19615	−	6.69213i	0.329165	−	0.268762i
$621$	9.69615	+	2.59808i	0.389093	+	0.104257i
$622$		−	54.1934i		−	2.17296i
$623$	5.73981	+	3.31388i	0.229961	+	0.132768i
$624$	−4.90192	+	18.2942i	−0.196234	+	0.732355i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	5.36603	+	9.29423i	0.214470	+	0.371472i
$627$	−15.8338	+	15.8338i	−0.632339	+	0.632339i
$628$	32.0836	+	18.5235i	1.28028	+	0.739167i
$629$	1.60770			0.0641030
$630$	4.11999	−	10.8640i	0.164144	−	0.432831i
$631$	−33.3205			−1.32647			−0.663234	−	0.748412i	$-0.730817\pi$
$631$	−33.3205			−1.32647			−0.663234	+	0.748412i	$0.730817\pi$
$632$	−0.240237	−	0.138701i	−0.00955610	−	0.00551722i
$633$	−5.88349	−	21.9575i	−0.233848	−	0.872731i
$634$	33.9545	+	58.8109i	1.34850	+	2.33568i
$635$	3.69389	−	9.74036i	0.146587	−	0.386534i
$636$	11.1962	−	3.00000i	0.443956	−	0.118958i
$637$	−13.1440	−	7.58871i	−0.520785	−	0.300675i
$638$			59.0924i			2.33949i
$639$	9.88269	+	5.70577i	0.390953	+	0.225717i
$640$	5.80385	+	7.10823i	0.229417	+	0.280978i
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	−0.505223	−	0.862989i	$-0.668590\pi$
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	0.999982	+	0.00604207i	$0.00192326\pi$
$642$	−27.7530	+	27.7530i	−1.09532	+	1.09532i
$643$	21.8374	−	12.6078i	0.861181	−	0.497203i	−0.00322641	−	0.999995i	$-0.501027\pi$
$643$	21.8374	−	12.6078i	0.861181	−	0.497203i	0.864408	+	0.502792i	$0.167694\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$	−14.5312	−	32.2859i	−0.572167	−	1.27126i
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$		−	12.3861i		−	0.486950i	−0.969907	−	0.243475i	$-0.921713\pi$
$647$		−	12.3861i		−	0.486950i	0.969907	−	0.243475i	$-0.0782873\pi$
$648$	4.03459	−	2.32937i	0.158494	−	0.0915064i
$649$	−12.0000			−0.471041
$650$	17.7104	+	15.6892i	0.694658	+	0.615381i
$651$	1.09808	−	4.09808i	0.0430370	−	0.160616i
$652$	28.4094	−	16.4022i	1.11260	−	0.642358i
$653$	0.392541	−	0.226633i	0.0153613	−	0.00886885i	−0.492300	−	0.870426i	$-0.663844\pi$
$653$	0.392541	−	0.226633i	0.0153613	−	0.00886885i	0.507661	+	0.861557i	$0.330510\pi$
$654$	−11.0263	−	11.0263i	−0.431162	−	0.431162i
$655$	−0.332965	−	2.04864i	−0.0130100	−	0.0800471i
$656$	−19.0526			−0.743877
$657$	−12.7279	+	22.0454i	−0.496564	+	0.860073i
$658$			7.58871i			0.295839i
$659$	18.1244	−	31.3923i	0.706025	−	1.22287i	−0.260296	−	0.965529i	$-0.583820\pi$
$659$	18.1244	−	31.3923i	0.706025	−	1.22287i	0.966320	−	0.257342i	$-0.0828466\pi$
$660$	−25.7563	−	18.5545i	−1.00256	−	0.722232i
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	0.993015	+	0.117992i	$0.0376457\pi$
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	−0.394323	+	0.918972i	$0.629021\pi$
$662$	−20.7327	+	11.9700i	−0.805800	+	0.465229i
$663$	0.416102	+	1.55291i	0.0161601	+	0.0603102i
$664$	2.69615	−	4.66987i	0.104631	−	0.181226i
$665$	3.46410	+	4.24264i	0.134332	+	0.164523i
$666$	−21.2942	+	12.2942i	−0.825135	+	0.476392i
$667$			12.4877i			0.483525i
$668$	25.5116	+	14.7291i	0.987073	+	0.569887i
$669$	−20.4904	−	20.4904i	−0.792204	−	0.792204i
$670$	−20.7576	−	7.87201i	−0.801936	−	0.304122i
$671$	−25.2224	−	43.6865i	−0.973701	−	1.68650i
$672$	−11.3831	−	3.05008i	−0.439111	−	0.117659i
$673$	1.40061	+	0.808643i	0.0539896	+	0.0311709i	0.526752	−	0.850019i	$-0.323410\pi$
$673$	1.40061	+	0.808643i	0.0539896	+	0.0311709i	−0.472762	+	0.881190i	$0.656743\pi$
$674$	−3.46410			−0.133432
$675$	−1.56936	−	25.9333i	−0.0604047	−	0.998174i
$676$	−12.1244			−0.466321
$677$	−28.6496	−	16.5409i	−1.10109	−	0.635717i	−0.164586	−	0.986363i	$-0.552629\pi$
$677$	−28.6496	−	16.5409i	−1.10109	−	0.635717i	−0.936508	+	0.350646i	$0.885962\pi$
$678$	−8.24504	−	2.20925i	−0.316649	−	0.0848459i
$679$	−4.60770	−	7.98076i	−0.176827	−	0.306274i
$680$	0.410110	+	0.155528i	0.0157270	+	0.00596422i
$681$	2.32051	+	2.32051i	0.0889221	+	0.0889221i
$682$	−21.6293	−	12.4877i	−0.828229	−	0.478178i
$683$			19.6975i			0.753702i	0.926274	+	0.376851i	$0.122993\pi$
$683$			19.6975i			0.753702i	−0.926274	+	0.376851i	$0.877007\pi$
$684$		−	14.1962i		−	0.542803i
$685$	26.2487	+	32.1480i	1.00291	+	1.22831i
$686$	11.4282	−	19.7942i	0.436331	−	0.755747i
$687$	−8.93357	−	33.3405i	−0.340837	−	1.27202i
$688$	−35.3417	+	20.4046i	−1.34739	+	0.777917i
$689$	4.73205	+	8.19615i	0.180277	+	0.312249i
$690$	−11.7279	−	8.44863i	−0.446474	−	0.321634i
$691$	−10.1244	+	17.5359i	−0.385149	+	0.667097i	−0.991790	−	0.127879i	$-0.959183\pi$
$691$	−10.1244	+	17.5359i	−0.385149	+	0.667097i	0.606641	+	0.794976i	$0.292516\pi$
$692$		−	1.31268i		−	0.0499005i
$693$	−12.7279			−0.483494
$694$	19.1244			0.725951
$695$	2.86976	+	17.6569i	0.108856	+	0.669763i
$696$	4.09808	+	4.09808i	0.155337	+	0.155337i
$697$	−1.40061	+	0.808643i	−0.0530519	+	0.0306295i
$698$	36.0303	−	20.8021i	1.36377	−	0.787370i
$699$	−3.16987	+	11.8301i	−0.119896	+	0.447456i
$700$	−5.14871	+	5.81200i	−0.194603	+	0.219673i
$701$	−23.1962			−0.876107			−0.438053	−	0.898949i	$-0.644332\pi$
$701$	−23.1962			−0.876107			−0.438053	+	0.898949i	$0.644332\pi$
$702$	−17.3867	−	17.3867i	−0.656217	−	0.656217i
$703$		−	11.5911i		−	0.437167i
$704$	−13.5622	+	23.4904i	−0.511144	+	0.885327i
$705$	6.96444	+	15.4738i	0.262296	+	0.582777i
$706$	8.73205	+	15.1244i	0.328635	+	0.569213i
$707$	−1.96902	+	1.13681i	−0.0740525	+	0.0427542i
$708$	5.37945	−	5.37945i	0.202172	−	0.202172i
$709$	−15.8923	+	27.5263i	−0.596848	+	1.03377i	0.396435	+	0.918063i	$0.370247\pi$
$709$	−15.8923	+	27.5263i	−0.596848	+	1.03377i	−0.993283	+	0.115708i	$0.963086\pi$
$710$	−10.3923	−	12.7279i	−0.390016	−	0.477670i
$711$	1.39230	−	0.803848i	0.0522155	−	0.0301466i
$712$		−	3.82654i		−	0.143406i
$713$	−4.57081	−	2.63896i	−0.171178	−	0.0988298i
$714$	−1.09808	+	0.294229i	−0.0410945	+	0.0110112i
$715$	9.19051	−	24.2343i	0.343706	−	0.906313i
$716$	−21.2942	−	36.8827i	−0.795803	−	1.37837i
$717$	−5.79555	−	21.6293i	−0.216439	−	0.807761i
$718$	−16.4022	−	9.46979i	−0.612123	−	0.353409i
$719$	−19.6077			−0.731244			−0.365622	−	0.930763i	$-0.619144\pi$
$719$	−19.6077			−0.731244			−0.365622	+	0.930763i	$0.619144\pi$
$720$	−29.5582	+	4.80408i	−1.10157	+	0.179038i
$721$	−8.19615			−0.305241
$722$	−19.2999	−	11.1428i	−0.718269	−	0.414693i
$723$	7.67664	−	7.67664i	0.285497	−	0.285497i
$724$	7.33013	+	12.6962i	0.272422	+	0.471849i
$725$	30.6569	−	10.2357i	1.13857	−	0.380143i
$726$	−9.86603	+	36.8205i	−0.366163	+	1.36654i
$727$	24.5271	+	14.1607i	0.909659	+	0.525192i	0.880321	−	0.474378i	$-0.157327\pi$
$727$	24.5271	+	14.1607i	0.909659	+	0.525192i	0.0293377	+	0.999570i	$0.490660\pi$
$728$		−	1.13681i		−	0.0421331i
$729$			27.0000i			1.00000i
$730$	28.3923	−	23.1822i	1.05085	−	0.858012i
$731$	−1.73205	+	3.00000i	−0.0640622	+	0.110959i
$732$	30.8910	+	8.27723i	1.14177	+	0.305935i
$733$	35.9101	−	20.7327i	1.32637	−	0.765781i	0.341635	−	0.939833i	$-0.389019\pi$
$733$	35.9101	−	20.7327i	1.32637	−	0.765781i	0.984736	+	0.174052i	$0.0556861\pi$
$734$	23.9545	+	41.4904i	0.884176	+	1.53144i
$735$	2.41197	−	23.8761i	0.0889670	−	0.880682i
$736$	−7.33013	+	12.6962i	−0.270192	+	0.467986i
$737$			24.3190i			0.895803i
$738$	12.3676	−	21.4213i	0.455256	−	0.788527i
$739$	45.8564			1.68686			0.843428	−	0.537243i	$-0.180534\pi$
$739$	45.8564			1.68686			0.843428	+	0.537243i	$0.180534\pi$
$740$	16.2189	−	2.63604i	0.596217	−	0.0969027i
$741$	11.1962	−	3.00000i	0.411301	−	0.110208i
$742$	−5.79555	+	3.34607i	−0.212762	+	0.122838i
$743$	21.9253	−	12.6586i	0.804361	−	0.464398i	−0.0406329	−	0.999174i	$-0.512937\pi$
$743$	21.9253	−	12.6586i	0.804361	−	0.464398i	0.844994	+	0.534776i	$0.179604\pi$
$744$	−2.36603	+	0.633975i	−0.0867427	+	0.0232426i
$745$	−2.77364	−	17.0655i	−0.101618	−	0.625230i
$746$	62.1051			2.27383
$747$	15.6257	+	27.0645i	0.571714	+	0.990238i
$748$			3.10583i			0.113560i
$749$	5.25833	−	9.10770i	0.192135	−	0.332788i
$750$	−11.1282	+	35.7167i	−0.406345	+	1.30419i
$751$	−17.2224	−	29.8301i	−0.628455	−	1.08852i	−0.987862	−	0.155336i	$-0.950354\pi$
$751$	−17.2224	−	29.8301i	−0.628455	−	1.08852i	0.359406	−	0.933181i	$-0.382979\pi$
$752$	16.9384	−	9.77938i	0.617679	−	0.356617i
$753$	−31.0991	−	8.33298i	−1.13331	−	0.303671i
$754$	15.2942	−	26.4904i	0.556983	−	0.964723i
$755$	−39.1244	+	31.9449i	−1.42388	+	1.16259i
$756$	5.70577	−	5.70577i	0.207517	−	0.207517i
$757$		−	7.34847i		−	0.267085i	−0.991043	−	0.133542i	$-0.957365\pi$
$757$		−	7.34847i		−	0.267085i	0.991043	−	0.133542i	$-0.0426352\pi$
$758$	−20.9730	−	12.1087i	−0.761772	−	0.439810i
$759$	−4.09808	+	15.2942i	−0.148751	+	0.555145i
$760$	1.12132	−	2.95680i	0.0406746	−	0.107254i
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	0.846639	−	0.532168i	$-0.178622\pi$
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	−0.884190	+	0.467127i	$0.845289\pi$
$762$	11.0227	−	11.0227i	0.399310	−	0.399310i
$763$	3.61849	+	2.08913i	0.130998	+	0.0756318i
$764$	−0.588457			−0.0212896
$765$	−1.96902	+	1.60770i	−0.0711899	+	0.0581263i
$766$	−39.5167			−1.42779
$767$	5.37945	+	3.10583i	0.194241	+	0.112145i

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67303 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-2.09077 - 0.792893i) q^{5} +(-2.36603 - 2.36603i) q^{6} +(0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(1.67303 + 0.965926i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-2.09077 - 0.792893i) q^{5} +(-2.36603 - 2.36603i) q^{6} +(0.776457 + 0.448288i) q^{7} -0.517638i q^{8} +(2.59808 + 1.50000i) q^{9} +(-2.73205 - 3.34607i) q^{10} +(-2.36603 + 4.09808i) q^{11} +(-0.776457 - 2.89778i) q^{12} +(2.12132 - 1.22474i) q^{13} +(0.866025 + 1.50000i) q^{14} +(3.14248 + 2.26380i) q^{15} +(2.23205 - 3.86603i) q^{16} -0.378937i q^{17} +(2.89778 + 5.01910i) q^{18} -2.73205 q^{19} +(-0.621320 - 3.82282i) q^{20} +(-1.09808 - 1.09808i) q^{21} +(-7.91688 + 4.57081i) q^{22} +(-1.67303 + 0.965926i) q^{23} +(-0.232051 + 0.866025i) q^{24} +(3.74264 + 3.31552i) q^{25} +4.73205 q^{26} +(-3.67423 - 3.67423i) q^{27} +1.55291i q^{28} +(3.23205 - 5.59808i) q^{29} +(3.07081 + 6.82282i) q^{30} +(1.36603 + 2.36603i) q^{31} +(6.57201 - 3.79435i) q^{32} +(5.79555 - 5.79555i) q^{33} +(0.366025 - 0.633975i) q^{34} +(-1.26795 - 1.55291i) q^{35} +5.19615i q^{36} +4.24264i q^{37} +(-4.57081 - 2.63896i) q^{38} +(-4.09808 + 1.09808i) q^{39} +(-0.410432 + 1.08226i) q^{40} +(-2.13397 - 3.69615i) q^{41} +(-0.776457 - 2.89778i) q^{42} +(-7.91688 - 4.57081i) q^{43} -8.19615 q^{44} +(-4.24264 - 5.19615i) q^{45} -3.73205 q^{46} +(3.79435 + 2.19067i) q^{47} +(-5.46739 + 5.46739i) q^{48} +(-3.09808 - 5.36603i) q^{49} +(3.05902 + 9.16208i) q^{50} +(-0.169873 + 0.633975i) q^{51} +(3.67423 + 2.12132i) q^{52} +3.86370i q^{53} +(-2.59808 - 9.69615i) q^{54} +(8.19615 - 6.69213i) q^{55} +(0.232051 - 0.401924i) q^{56} +(4.57081 + 1.22474i) q^{57} +(10.8147 - 6.24384i) q^{58} +(1.26795 + 2.19615i) q^{59} +(-0.674235 + 6.67423i) q^{60} +(-5.33013 + 9.23205i) q^{61} +5.27792i q^{62} +(1.34486 + 2.32937i) q^{63} +5.73205 q^{64} +(-5.40629 + 0.878680i) q^{65} +(15.2942 - 4.09808i) q^{66} +(4.45069 - 2.56961i) q^{67} +(0.568406 - 0.328169i) q^{68} +(3.23205 - 0.866025i) q^{69} +(-0.621320 - 3.82282i) q^{70} +3.80385 q^{71} +(0.776457 - 1.34486i) q^{72} +8.48528i q^{73} +(-4.09808 + 7.09808i) q^{74} +(-4.77526 - 7.22474i) q^{75} +(-2.36603 - 4.09808i) q^{76} +(-3.67423 + 2.12132i) q^{77} +(-7.91688 - 2.12132i) q^{78} +(0.267949 - 0.464102i) q^{79} +(-7.73205 + 6.31319i) q^{80} +(4.50000 + 7.79423i) q^{81} -8.24504i q^{82} +(9.02150 + 5.20857i) q^{83} +(0.696152 - 2.59808i) q^{84} +(-0.300457 + 0.792271i) q^{85} +(-8.83013 - 15.2942i) q^{86} +(-7.91688 + 7.91688i) q^{87} +(2.12132 + 1.22474i) q^{88} +7.39230 q^{89} +(-2.07898 - 12.7914i) q^{90} +2.19615 q^{91} +(-2.89778 - 1.67303i) q^{92} +(-1.22474 - 4.57081i) q^{93} +(4.23205 + 7.33013i) q^{94} +(5.71209 + 2.16622i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(-8.90138 - 5.13922i) q^{97} -11.9700i q^{98} +(-12.2942 + 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{6}+O(q^{10}) \) 8 * q - 12 * q^6	\( 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40} - 24 q^{41} - 24 q^{44} - 16 q^{46} - 4 q^{49} + 24 q^{50} - 36 q^{51} + 24 q^{55} - 12 q^{56} + 24 q^{59} + 24 q^{60} - 8 q^{61} + 32 q^{64} + 60 q^{66} + 12 q^{69} + 12 q^{70} + 72 q^{71} - 12 q^{74} - 48 q^{75} - 12 q^{76} + 16 q^{79} - 48 q^{80} + 36 q^{81} - 36 q^{84} + 16 q^{85} - 36 q^{86} - 24 q^{89} - 36 q^{90} - 24 q^{91} + 20 q^{94} + 12 q^{95} - 60 q^{96} - 36 q^{99}+O(q^{100}) \) 8 * q - 12 * q^6 - 8 * q^10 - 12 * q^11 + 12 * q^15 + 4 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^21 + 12 * q^24 - 4 * q^25 + 24 * q^26 + 12 * q^29 - 12 * q^30 + 4 * q^31 - 4 * q^34 - 24 * q^35 - 12 * q^39 - 4 * q^40 - 24 * q^41 - 24 * q^44 - 16 * q^46 - 4 * q^49 + 24 * q^50 - 36 * q^51 + 24 * q^55 - 12 * q^56 + 24 * q^59 + 24 * q^60 - 8 * q^61 + 32 * q^64 + 60 * q^66 + 12 * q^69 + 12 * q^70 + 72 * q^71 - 12 * q^74 - 48 * q^75 - 12 * q^76 + 16 * q^79 - 48 * q^80 + 36 * q^81 - 36 * q^84 + 16 * q^85 - 36 * q^86 - 24 * q^89 - 36 * q^90 - 24 * q^91 + 20 * q^94 + 12 * q^95 - 60 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more