LMFDB - Embedded newform 45.2.j.a.4.4

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			4.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	45.4
Dual form			45.2.j.a.34.4

$q$-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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

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	0.226303	−	0.974057i	$-0.427336\pi$
$2$	1.67303	−	0.965926i	1.18301	−	0.683013i	0.956710	+	0.291044i	$0.0940027\pi$
$3$	−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	−0.346034	−	0.938222i	$-0.612472\pi$
$7$	0.776457	−	0.448288i	0.293473	−	0.169437i	0.639507	+	0.768785i	$0.279138\pi$
$8$			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	−0.963580	−	0.267421i	$-0.913828\pi$
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	0.250196	−	0.968195i	$-0.419505\pi$
$12$	−0.776457	+	2.89778i	−0.224144	+	0.836516i
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	0.764444	−	0.644690i	$-0.223014\pi$
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	−0.176096	+	0.984373i	$0.556347\pi$
$14$	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	$0.0146324\pi$
$17$			0.378937i			0.0919058i	−0.998944	+	0.0459529i	$0.985368\pi$
$18$	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	0.315328	−	0.948983i	$-0.397886\pi$
$23$	−1.67303	−	0.965926i	−0.348851	−	0.201409i	−0.664179	+	0.747573i	$0.731219\pi$
$24$	−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	0.992794	+	0.119835i	$0.0382364\pi$
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	−0.392617	+	0.919702i	$0.628430\pi$
$30$	3.07081	−	6.82282i	0.560651	−	1.24567i
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	−0.716883	−	0.697193i	$-0.754432\pi$
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	0.962229	+	0.272243i	$0.0877653\pi$
$32$	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	$-0.886609\pi$
$37$		−	4.24264i		−	0.697486i	0.937218	−	0.348743i	$-0.113391\pi$
$38$	−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	−0.983151	−	0.182795i	$-0.941486\pi$
$41$	−2.13397	+	3.69615i	−0.333271	+	0.577242i	0.649880	+	0.760037i	$0.274819\pi$
$42$	−0.776457	+	2.89778i	−0.119810	+	0.447137i
$43$	−7.91688	+	4.57081i	−1.20731	+	0.697042i	−0.962171	−	0.272445i	$-0.912168\pi$
$43$	−7.91688	+	4.57081i	−1.20731	+	0.697042i	−0.245141	+	0.969487i	$0.578834\pi$
$44$	−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	−0.197054	−	0.980393i	$-0.563138\pi$
$47$	3.79435	−	2.19067i	0.553463	−	0.319542i	0.750518	+	0.660850i	$0.229804\pi$
$48$	−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	$-0.914509\pi$
$53$		−	3.86370i		−	0.530720i	0.964149	−	0.265360i	$-0.0854909\pi$
$54$	−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	−0.771608	−	0.636098i	$-0.780547\pi$
$59$	1.26795	−	2.19615i	0.165073	−	0.285915i	0.936681	+	0.350183i	$0.113881\pi$
$60$	−0.674235	−	6.67423i	−0.0870433	−	0.861640i
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	−0.974230	−	0.225557i	$-0.927580\pi$
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	0.291777	−	0.956486i	$-0.405753\pi$
$62$		−	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	0.746593	−	0.665281i	$-0.231688\pi$
$67$	4.45069	+	2.56961i	0.543739	+	0.313928i	−0.202854	+	0.979209i	$0.565022\pi$
$68$	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	$-0.834595\pi$
$73$		−	8.48528i		−	0.993127i	0.868000	−	0.496564i	$-0.165405\pi$
$74$	−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	0.880705	−	0.473665i	$-0.157069\pi$
$79$	0.267949	+	0.464102i	0.0301466	+	0.0522155i	−0.850558	+	0.525880i	$0.823736\pi$
$80$	−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	0.0848929	−	0.996390i	$-0.472945\pi$
$83$	9.02150	−	5.20857i	0.990238	−	0.571714i	0.905346	+	0.424676i	$0.139612\pi$
$84$	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	−0.878431	−	0.477870i	$-0.841409\pi$
$97$	−8.90138	+	5.13922i	−0.903799	+	0.521808i	−0.0253679	+	0.999678i	$0.508076\pi$
$98$			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	0.796022	−	0.605267i	$-0.206934\pi$
$101$	−1.26795	−	2.19615i	−0.126166	−	0.218525i	−0.922188	+	0.386742i	$0.873600\pi$
$102$	−0.896575	−	0.896575i	−0.0887742	−	0.0887742i
$103$	−7.91688	−	4.57081i	−0.780073	−	0.450375i	0.0563832	−	0.998409i	$-0.482043\pi$
$103$	−7.91688	−	4.57081i	−0.780073	−	0.450375i	−0.836456	+	0.548034i	$0.815376\pi$
$104$	−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	$0.191889\pi$
$107$			11.7298i			1.13396i	−0.823730	+	0.566982i	$0.808111\pi$
$108$	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	0.600302	−	0.799773i	$-0.295047\pi$
$113$	2.20925	+	1.27551i	0.207829	+	0.119990i	−0.392473	+	0.919764i	$0.628380\pi$
$114$	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	$-0.933728\pi$
$127$		−	4.65874i		−	0.413397i	0.978405	−	0.206698i	$-0.0662719\pi$
$128$	−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	−0.845039	−	0.534705i	$-0.820423\pi$
$131$	0.464102	−	0.803848i	0.0405487	−	0.0702325i	0.885588	+	0.464473i	$0.153756\pi$
$132$	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	−0.991341	−	0.131311i	$-0.958081\pi$
$137$	−16.0740	+	9.28032i	−1.37329	+	0.792871i	−0.381952	+	0.924182i	$0.624748\pi$
$138$	6.24384	−	1.67303i	0.531511	−	0.142418i
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	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	−0.663084	−	0.748545i	$-0.730753\pi$
$149$	3.86603	−	6.69615i	0.316717	−	0.548570i	0.979801	+	0.199975i	$0.0640861\pi$
$150$	−1.01059	+	16.6998i	−0.0825143	+	1.36353i
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.800768	+	0.598975i	$0.204425\pi$
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.118343	+	0.992973i	$0.462242\pi$
$152$		−	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	0.999700	−	0.0244975i	$-0.00779857\pi$
$157$	18.5235	+	10.6945i	1.47833	+	0.853517i	0.478635	+	0.878014i	$0.341132\pi$
$158$	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	$0.265995\pi$
$163$			18.9396i			1.48346i	−0.670697	+	0.741731i	$0.734005\pi$
$164$	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	0.946375	−	0.323071i	$-0.104715\pi$
$167$	14.7291	+	8.50386i	1.13977	+	0.658049i	0.193399	+	0.981120i	$0.438049\pi$
$168$	−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	−0.524743	−	0.851261i	$-0.675838\pi$
$173$	−0.656339	+	0.378937i	−0.0499005	+	0.0288101i	0.474842	+	0.880071i	$0.342505\pi$
$174$	−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	0.859814	−	0.510607i	$-0.170579\pi$
$191$	−0.169873	−	0.294229i	−0.0122916	−	0.0212896i	−0.872106	+	0.489317i	$0.837246\pi$
$192$	−9.58991	+	2.56961i	−0.692092	+	0.185445i
$193$	−17.9551	−	10.3664i	−1.29243	−	0.746187i	−0.313349	−	0.949638i	$-0.601451\pi$
$193$	−17.9551	−	10.3664i	−1.29243	−	0.746187i	−0.979085	+	0.203451i	$0.934784\pi$
$194$	−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	$-0.733787\pi$
$197$		−	20.8343i		−	1.48438i	0.670190	−	0.742190i	$-0.266213\pi$
$198$	−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	−0.546736	−	0.837305i	$-0.684130\pi$
$211$	6.56218	−	11.3660i	0.451759	−	0.782469i	0.998495	+	0.0548353i	$0.0174634\pi$
$212$	−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	0.0709359	−	0.997481i	$-0.477401\pi$
$223$	14.4889	−	8.36516i	0.970248	−	0.560173i	0.899312	+	0.437308i	$0.144068\pi$
$224$	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	−0.553464	−	0.832873i	$-0.686694\pi$
$227$	−1.64085	+	0.947343i	−0.108907	+	0.0628774i	0.444557	+	0.895750i	$0.353361\pi$
$228$	2.12132	−	7.91688i	0.140488	−	0.524308i
$229$	9.96410	−	17.2583i	0.658446	−	1.14046i	−0.322571	−	0.946545i	$-0.604547\pi$
$229$	9.96410	−	17.2583i	0.658446	−	1.14046i	0.981018	−	0.193917i	$-0.0621194\pi$
$230$	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	$0.0744028\pi$
$233$			7.07107i			0.463241i	−0.972806	+	0.231621i	$0.925597\pi$
$234$	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	−0.577623	−	0.816304i	$-0.696020\pi$
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	0.995751	+	0.0920846i	$0.0293530\pi$
$240$	15.7661	+	7.09599i	1.01770	+	0.458044i
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	0.747256	−	0.664536i	$-0.231371\pi$
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	−0.949133	+	0.314875i	$0.898037\pi$
$242$			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	−0.248328	−	0.968676i	$-0.579881\pi$
$257$	−19.4201	−	11.2122i	−1.21139	−	0.699396i	−0.963062	+	0.269280i	$0.913214\pi$
$258$	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	−0.689600	−	0.724191i	$-0.742214\pi$
$263$	−6.60420	+	3.81294i	−0.407232	+	0.235116i	0.282368	+	0.959306i	$0.408880\pi$
$264$	−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	−0.783569	−	0.621304i	$-0.786603\pi$
$277$	−10.6066	+	6.12372i	−0.637289	+	0.367939i	0.146281	+	0.989243i	$0.453270\pi$
$278$			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	0.999856	−	0.0169692i	$-0.00540173\pi$
$281$	8.13397	+	14.0885i	0.485232	+	0.840447i	−0.514624	+	0.857416i	$0.672068\pi$
$282$	−3.79435	+	14.1607i	−0.225950	+	0.843258i
$283$	−3.88229	−	2.24144i	−0.230778	−	0.133240i	0.380153	−	0.924924i	$-0.375871\pi$
$283$	−3.88229	−	2.24144i	−0.230778	−	0.133240i	−0.610931	+	0.791684i	$0.709205\pi$
$284$	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	0.258711	−	0.965955i	$-0.416702\pi$
$293$	−7.67664	−	4.43211i	−0.448474	−	0.258927i	−0.707186	+	0.707028i	$0.750035\pi$
$294$	−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	$-0.735631\pi$
$307$		−	25.8719i		−	1.47659i	0.674478	−	0.738295i	$-0.264369\pi$
$308$	−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	0.127255	+	0.991870i	$0.459383\pi$
$311$	−14.0263	+	24.2942i	−0.795357	+	1.37760i	−0.922612	+	0.385729i	$0.873950\pi$
$312$	0.568406	−	2.12132i	0.0321797	−	0.120096i
$313$	4.81105	−	2.77766i	0.271936	−	0.157003i	−0.357831	−	0.933786i	$-0.616484\pi$
$313$	4.81105	−	2.77766i	0.271936	−	0.157003i	0.629767	+	0.776784i	$0.283150\pi$
$314$	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	0.775094	−	0.631846i	$-0.217703\pi$
$317$	30.4428	−	17.5761i	1.70984	−	0.987174i	0.934742	−	0.355328i	$-0.115631\pi$
$318$	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	0.643968	−	0.765053i	$-0.277287\pi$
$331$	−6.19615	−	10.7321i	−0.340571	−	0.589887i	−0.984539	+	0.175166i	$0.943954\pi$
$332$		−	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	0.457107	−	0.889412i	$-0.348886\pi$
$337$	−1.55291	−	0.896575i	−0.0845926	−	0.0488396i	−0.541700	+	0.840572i	$0.682219\pi$
$338$	−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	0.712143	−	0.702035i	$-0.247725\pi$
$347$	8.57321	+	4.94975i	0.460234	+	0.265716i	−0.251909	+	0.967751i	$0.581058\pi$
$348$	−18.7315	+	5.01910i	−1.00412	+	0.269052i
$349$	10.7679	+	18.6506i	0.576395	+	0.998346i	0.995889	+	0.0905872i	$0.0288744\pi$
$349$	10.7679	+	18.6506i	0.576395	+	0.998346i	−0.419493	+	0.907758i	$0.637792\pi$
$350$	−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	−0.276969	−	0.960879i	$-0.589330\pi$
$353$	7.82894	−	4.52004i	0.416693	−	0.240578i	0.693661	+	0.720301i	$0.255996\pi$
$354$	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	0.179411	−	0.983774i	$-0.442581\pi$
$367$	21.4770	−	12.3998i	1.12109	−	0.647262i	0.941679	+	0.336512i	$0.109247\pi$
$368$		−	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	0.997953	−	0.0639468i	$-0.0203688\pi$
$373$	27.8410	+	16.0740i	1.44155	+	0.832280i	0.443597	+	0.896226i	$0.353702\pi$
$374$	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	−0.0263067	−	0.999654i	$-0.508375\pi$
$383$	−17.7148	−	10.2277i	−0.905186	−	0.522609i	−0.878879	+	0.477045i	$0.841708\pi$
$384$	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	−0.990975	−	0.134048i	$-0.957202\pi$
$389$	−12.0622	−	20.8923i	−0.611577	−	1.05928i	0.379398	−	0.925234i	$-0.376131\pi$
$390$	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	$0.264050\pi$
$397$			29.3939i			1.47524i	−0.675218	+	0.737618i	$0.735950\pi$
$398$	−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	−0.164092	−	0.986445i	$-0.552469\pi$
$401$	15.4641	−	26.7846i	0.772240	−	1.33756i	0.936333	−	0.351115i	$-0.114197\pi$
$402$	−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	0.415353	+	0.909660i	$0.363658\pi$
$409$	−11.7321	+	20.3205i	−0.580113	+	1.00478i	−0.995465	+	0.0951241i	$0.969675\pi$
$410$	−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	−0.992728	−	0.120383i	$-0.961588\pi$
$419$	−8.02628	+	13.9019i	−0.392109	+	0.679153i	0.600618	+	0.799536i	$0.294921\pi$
$420$	−3.51549	−	4.88001i	−0.171538	−	0.238120i
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	0.977368	−	0.211545i	$-0.0678494\pi$
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	−0.671887	+	0.740653i	$0.734516\pi$
$422$		−	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	$-0.737836\pi$
$433$		−	30.5307i		−	1.46721i	0.679575	−	0.733606i	$-0.262164\pi$
$434$	−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	0.955543	−	0.294852i	$-0.0952705\pi$
$439$	4.66025	+	8.07180i	0.222422	+	0.385246i	−0.733121	+	0.680098i	$0.761937\pi$
$440$	−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	−0.757951	−	0.652311i	$-0.773800\pi$
$443$	−12.0394	+	6.95095i	−0.572009	+	0.330250i	0.185942	+	0.982561i	$0.440466\pi$
$444$	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	−0.994554	−	0.104218i	$-0.966766\pi$
$457$	−29.9623	+	17.2987i	−1.40158	+	0.809201i	−0.407022	+	0.913418i	$0.633433\pi$
$458$		−	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	0.561587	−	0.827418i	$-0.310191\pi$
$461$	−9.35641	−	16.2058i	−0.435771	−	0.754778i	−0.997358	+	0.0726397i	$0.976858\pi$
$462$	13.7124	−	3.67423i	0.637960	−	0.170941i
$463$	0.152304	+	0.0879327i	0.00707816	+	0.00408658i	0.503535	−	0.863975i	$-0.332033\pi$
$463$	0.152304	+	0.0879327i	0.00707816	+	0.00408658i	−0.496457	+	0.868061i	$0.665366\pi$
$464$	−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	$0.0425359\pi$
$467$			5.75839i			0.266467i	−0.991085	+	0.133233i	$0.957464\pi$
$468$	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	0.957820	+	0.287368i	$0.0927803\pi$
$479$	15.9282	+	27.5885i	0.727778	+	1.26055i	−0.230042	+	0.973181i	$0.573886\pi$
$480$	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	$0.00819959\pi$
$487$			1.13681i			0.0515139i	−0.999668	+	0.0257569i	$0.991800\pi$
$488$	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	−0.509990	−	0.860180i	$-0.670351\pi$
$491$	10.8564	−	18.8038i	0.489943	−	0.848606i	0.999933	+	0.0115744i	$0.00368433\pi$
$492$	−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	−0.905952	−	0.423380i	$-0.860844\pi$
$499$	−1.92820	+	3.33975i	−0.0863182	+	0.149508i	0.819634	+	0.572888i	$0.194177\pi$
$500$	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	$0.227111\pi$
$503$			29.3567i			1.30895i	−0.756083	+	0.654476i	$0.772889\pi$
$504$	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	−0.960886	−	0.276946i	$-0.910678\pi$
$509$	−5.42820	+	9.40192i	−0.240601	+	0.416733i	0.720285	+	0.693679i	$0.244011\pi$
$510$	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	$-0.763451\pi$
$523$		−	30.9468i		−	1.35321i	0.736347	−	0.676604i	$-0.236549\pi$
$524$	−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	0.179800	−	0.983703i	$-0.442455\pi$
$547$	26.2323	−	15.1452i	1.12161	−	0.647563i	0.941812	+	0.336140i	$0.109122\pi$
$548$			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	$-0.770919\pi$
$557$		−	31.1127i		−	1.31829i	0.752017	−	0.659144i	$-0.229081\pi$
$558$	−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	−0.0960045	−	0.995381i	$-0.530606\pi$
$563$	−23.8707	−	13.7818i	−1.00603	−	0.580833i	−0.910027	+	0.414548i	$0.863940\pi$
$564$	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	0.804861	−	0.593463i	$-0.202240\pi$
$569$	−2.66025	−	4.60770i	−0.111524	−	0.193165i	−0.916385	+	0.400299i	$0.868906\pi$
$570$	−8.38961	+	18.6403i	−0.351402	+	0.780756i
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	−0.917513	−	0.397706i	$-0.869806\pi$
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	0.803180	+	0.595736i	$0.203140\pi$
$572$	−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	$0.202657\pi$
$577$			28.5617i			1.18904i	−0.804082	+	0.594519i	$0.797343\pi$
$578$	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	−0.0521138	−	0.998641i	$-0.516596\pi$
$587$	19.0597	−	11.0041i	0.786678	−	0.454189i	0.838792	+	0.544452i	$0.183263\pi$
$588$	−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	$0.202541\pi$
$593$			28.9406i			1.18845i	−0.804299	+	0.594224i	$0.797459\pi$
$594$	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	−0.283514	−	0.958968i	$-0.591500\pi$
$599$	16.8564	−	29.1962i	0.688734	−	1.19292i	0.972248	−	0.233954i	$-0.0751666\pi$
$600$	−3.73980	−	2.47185i	−0.152677	−	0.100913i
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	0.985401	−	0.170252i	$-0.0544581\pi$
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	−0.640143	+	0.768256i	$0.721125\pi$
$602$			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	0.338743	−	0.940879i	$-0.389998\pi$
$607$	−7.55652	−	4.36276i	−0.306710	−	0.177079i	−0.645453	+	0.763800i	$0.723331\pi$
$608$	−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	$0.163412\pi$
$613$			24.3190i			0.982236i	−0.871093	+	0.491118i	$0.836588\pi$
$614$	−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	0.253800	−	0.967257i	$-0.418320\pi$
$617$	−11.3509	−	6.55343i	−0.456969	−	0.263831i	−0.710769	+	0.703426i	$0.751653\pi$
$618$	29.5462	−	7.91688i	1.18852	−	0.318463i
$619$	9.90192	+	17.1506i	0.397992	+	0.689342i	0.993478	−	0.114023i	$-0.0363739\pi$
$619$	9.90192	+	17.1506i	0.397992	+	0.689342i	−0.595486	+	0.803366i	$0.703041\pi$
$620$	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	0.999982	−	0.00604207i	$-0.00192326\pi$
$641$	12.5263	+	21.6962i	0.494758	+	0.856946i	−0.505223	+	0.862989i	$0.668590\pi$
$642$	−27.7530	−	27.7530i	−1.09532	−	1.09532i
$643$	21.8374	+	12.6078i	0.861181	+	0.497203i	0.864408	−	0.502792i	$-0.167694\pi$
$643$	21.8374	+	12.6078i	0.861181	+	0.497203i	−0.00322641	+	0.999995i	$0.501027\pi$
$644$	−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	$0.0782873\pi$
$647$			12.3861i			0.486950i	−0.969907	+	0.243475i	$0.921713\pi$
$648$	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	0.507661	−	0.861557i	$-0.330510\pi$
$653$	0.392541	+	0.226633i	0.0153613	+	0.00886885i	−0.492300	+	0.870426i	$0.663844\pi$
$654$	−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	0.966320	+	0.257342i	$0.0828466\pi$
$659$	18.1244	+	31.3923i	0.706025	+	1.22287i	−0.260296	+	0.965529i	$0.583820\pi$
$660$	−25.7563	+	18.5545i	−1.00256	+	0.722232i
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	−0.394323	−	0.918972i	$-0.629021\pi$
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	0.993015	−	0.117992i	$-0.0376457\pi$
$662$	−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	−0.472762	−	0.881190i	$-0.656743\pi$
$673$	1.40061	−	0.808643i	0.0539896	−	0.0311709i	0.526752	+	0.850019i	$0.323410\pi$
$674$	−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	−0.936508	−	0.350646i	$-0.885962\pi$
$677$	−28.6496	+	16.5409i	−1.10109	+	0.635717i	−0.164586	+	0.986363i	$0.552629\pi$
$678$	−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	$-0.877007\pi$
$683$		−	19.6975i		−	0.753702i	0.926274	−	0.376851i	$-0.122993\pi$
$684$			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	0.606641	−	0.794976i	$-0.292516\pi$
$691$	−10.1244	−	17.5359i	−0.385149	−	0.667097i	−0.991790	+	0.127879i	$0.959183\pi$
$692$			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	−0.993283	−	0.115708i	$-0.963086\pi$
$709$	−15.8923	−	27.5263i	−0.596848	−	1.03377i	0.396435	−	0.918063i	$-0.370247\pi$
$710$	−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	0.0293377	−	0.999570i	$-0.490660\pi$
$727$	24.5271	−	14.1607i	0.909659	−	0.525192i	0.880321	+	0.474378i	$0.157327\pi$
$728$			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	0.984736	−	0.174052i	$-0.0556861\pi$
$733$	35.9101	+	20.7327i	1.32637	+	0.765781i	0.341635	+	0.939833i	$0.389019\pi$
$734$	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	0.844994	−	0.534776i	$-0.179604\pi$
$743$	21.9253	+	12.6586i	0.804361	+	0.464398i	−0.0406329	+	0.999174i	$0.512937\pi$
$744$	−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	0.359406	+	0.933181i	$0.382979\pi$
$751$	−17.2224	+	29.8301i	−0.628455	+	1.08852i	−0.987862	+	0.155336i	$0.950354\pi$
$752$	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	$0.0426352\pi$
$757$			7.34847i			0.267085i	−0.991043	+	0.133542i	$0.957365\pi$
$758$	−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	−0.884190	−	0.467127i	$-0.845289\pi$
$761$	−1.03590	+	1.79423i	−0.0375513	+	0.0650407i	0.846639	+	0.532168i	$0.178622\pi$
$762$	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
$768$	8.69333	−	32.4440i	0.313694	−	1.17072i
$769$	−13.8205	+	23.9378i	−0.498380	+	0.863220i	−0.999998	−	0.00186930i	$-0.999405\pi$
$769$	−13.8205	+	23.9378i	−0.498380	+	0.863220i	0.501618	+	0.865089i	$0.332738\pi$
$770$	17.1363	−	6.49867i	0.617548	−	0.234196i
$771$	37.5167	+	10.0526i	1.35113	+	0.362034i
$772$	−31.0991	+	17.9551i	−1.11928	+	0.646217i
$773$			7.72741i			0.277935i	0.990297	+	0.138968i	$0.0443784\pi$
$773$			7.72741i			0.277935i	−0.990297	+	0.138968i	$0.955622\pi$
$774$			52.9808i			1.90435i
$775$	−2.73205	−	13.3843i	−0.0981382	−	0.480777i
$776$	−2.66025	−	4.60770i	−0.0954976	−	0.165407i
$777$	4.65874	+	4.65874i	0.167131	+	0.167131i
$778$	−40.3608	−	23.3023i	−1.44701	−	0.835429i
$779$	5.83013	−	10.0981i	0.208886	−	0.361801i
$780$	6.74397	−	14.9840i	0.241473	−	0.536512i
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$		−	1.41421i		−	0.0505722i
$783$	−32.4440	−	8.69333i	−1.15945	−	0.310674i
$784$	−27.6603			−0.987866
$785$	−47.2080	−	7.67268i	−1.68492	−	0.273850i
$786$	0.803848	+	3.00000i	0.0286723	+	0.107006i
$787$	14.1285	+	8.15711i	0.503628	+	0.290770i	0.730210	−	0.683222i	$-0.239422\pi$
$787$	14.1285	+	8.15711i	0.503628	+	0.290770i	−0.226583	+	0.973992i	$0.572755\pi$
$788$	−31.2514	−	18.0430i	−1.11328	−	0.642755i
$789$	9.33975	−	9.33975i	0.332504	−	0.332504i
$790$	−2.28497	−	0.371374i	−0.0812954	−	0.0132129i
$791$	2.28719			0.0813230
$792$	3.67423	−	6.36396i	0.130558	−	0.226134i
$793$		−	26.1122i		−	0.927271i
$794$	28.3923	+	49.1769i	1.00761	+	1.74522i
$795$	−8.74666	−	12.1416i	−0.310212	−	0.430619i
$796$	−3.97372	+	6.88269i	−0.140845	+	0.243950i
$797$	−13.7768	−	7.95404i	−0.487999	−	0.281747i	0.235745	−	0.971815i	$-0.424247\pi$
$797$	−13.7768	−	7.95404i	−0.487999	−	0.281747i	−0.723744	+	0.690068i	$0.757580\pi$
$798$	2.12132	−	7.91688i	0.0750939	−	0.280254i
$799$	0.830127	+	1.43782i	0.0293678	+	0.0508665i
$800$	37.1769	−	7.58871i	1.31440	−	0.268301i
$801$	19.2058	−	11.0885i	0.678603	−	0.391791i
$802$		−	59.7487i		−	2.10980i
$803$	−34.7733	+	20.0764i	−1.22712	+	0.708480i
$804$	−10.9019	+	10.9019i	−0.384481	+	0.384481i
$805$	3.62132	−	1.37333i	0.127635	−	0.0484036i
$806$	6.46410	−	11.1962i	0.227688	−	0.394368i
$807$	28.7697	−	7.70882i	1.01274	−	0.271363i
$808$	1.13681	−	0.656339i	0.0399929	−	0.0230899i
$809$	−37.1769			−1.30707			−0.653535	−	0.756896i	$-0.726715\pi$
$809$	−37.1769			−1.30707			−0.653535	+	0.756896i	$0.726715\pi$
$810$	13.7858	+	36.3515i	0.484383	+	1.27726i
$811$	43.5692			1.52992			0.764961	−	0.644076i	$-0.222758\pi$
$811$	43.5692			1.52992			0.764961	+	0.644076i	$0.222758\pi$
$812$	8.69333	−	5.01910i	0.305076	−	0.176136i
$813$	39.3441	−	10.5422i	1.37986	−	0.369732i
$814$	−19.3923	+	33.5885i	−0.679700	+	1.17727i
$815$	−15.0171	−	39.5983i	−0.526025	−	1.38707i
$816$	2.07180	−	2.07180i	0.0725274	−	0.0725274i
$817$	21.6293	−	12.4877i	0.756714	−	0.436889i
$818$			45.3292i			1.58490i
$819$	5.70577	−	3.29423i	0.199376	−	0.115110i
$820$	−12.8038	−	10.4543i	−0.447130	−	0.365080i
$821$	14.7224	+	25.5000i	0.513816	+	0.889956i	0.999872	+	0.0160280i	$0.00510208\pi$
$821$	14.7224	+	25.5000i	0.513816	+	0.889956i	−0.486055	+	0.873928i	$0.661565\pi$
$822$	16.0740	−	59.9889i	0.560645	−	2.09235i
$823$	1.76097	+	1.01669i	0.0613834	+	0.0354397i	0.530378	−	0.847762i	$-0.322050\pi$
$823$	1.76097	+	1.01669i	0.0613834	+	0.0354397i	−0.468994	+	0.883201i	$0.655383\pi$
$824$	2.36603	−	4.09808i	0.0824244	−	0.142763i
$825$	40.9059	+	2.47543i	1.42416	+	0.0861834i
$826$	−2.19615	−	3.80385i	−0.0764139	−	0.132353i
$827$			11.5539i			0.401770i	0.979615	+	0.200885i	$0.0643818\pi$
$827$			11.5539i			0.401770i	−0.979615	+	0.200885i	$0.935618\pi$
$828$	−5.01910	+	8.69333i	−0.174426	+	0.302114i
$829$	−31.5885			−1.09711			−0.548556	−	0.836114i	$-0.684822\pi$
$829$	−31.5885			−1.09711			−0.548556	+	0.836114i	$0.684822\pi$
$830$	−7.21900	+	44.4166i	−0.250575	+	1.54172i
$831$	15.0000	−	15.0000i	0.520344	−	0.520344i
$832$	12.1595	+	7.02030i	0.421555	+	0.243385i
$833$	−2.03339	−	1.17398i	−0.0704527	−	0.0406759i
$834$	−6.92820	−	25.8564i	−0.239904	−	0.895334i
$835$	−37.5379	−	6.10100i	−1.29905	−	0.211134i
$836$	22.3923			0.774454
$837$	3.67423	+	13.7124i	0.127000	+	0.473971i
$838$			31.0112i			1.07126i
$839$	0.633975	+	1.09808i	0.0218872	+	0.0379098i	0.876762	−	0.480925i	$-0.159699\pi$
$839$	0.633975	+	1.09808i	0.0218872	+	0.0379098i	−0.854874	+	0.518835i	$0.826366\pi$
$840$	1.63909	+	0.737721i	0.0565540	+	0.0254538i
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	20.9730	+	12.1087i	0.722776	+	0.417295i
$843$	−19.9241	−	19.9241i	−0.686222	−	0.686222i
$844$	−11.3660	−	19.6865i	−0.391235	−	0.677638i
$845$	12.1244	+	9.89949i	0.417091	+	0.340553i
$846$		−	25.3923i		−	0.873005i
$847$			10.2141i			0.350959i
$848$	14.9372	−	8.62398i	0.512945	−	0.296149i
$849$	7.50000	+	2.00962i	0.257399	+	0.0689699i
$850$	3.47185	+	1.15918i	0.119084	+	0.0397594i
$851$	−4.09808	+	7.09808i	−0.140480	+	0.243319i
$852$	−2.95352	+	11.0227i	−0.101186	+	0.377632i
$853$	30.2669	−	17.4746i	1.03632	−	0.598319i	0.117530	−	0.993069i	$-0.462502\pi$
$853$	30.2669	−	17.4746i	1.03632	−	0.598319i	0.918788	+	0.394750i	$0.129169\pi$
$854$	−18.4641			−0.631829
$855$	11.5911	−	14.1962i	0.396408	−	0.485498i
$856$	−6.07180			−0.207530
$857$	7.67664	−	4.43211i	0.262229	−	0.151398i	−0.363122	−	0.931742i	$-0.618289\pi$
$857$	7.67664	−	4.43211i	0.262229	−	0.151398i	0.625351	+	0.780344i	$0.284956\pi$
$858$	27.4249	+	27.4249i	0.936269	+	0.936269i
$859$	−11.2224	+	19.4378i	−0.382904	+	0.663210i	−0.991476	−	0.130289i	$-0.958409\pi$
$859$	−11.2224	+	19.4378i	−0.382904	+	0.663210i	0.608572	+	0.793499i	$0.291743\pi$
$860$	−12.5545	−	33.1047i	−0.428104	−	1.12886i
$861$	−1.71539	−	6.40192i	−0.0584603	−	0.218177i
$862$	−10.0382	+	5.79555i	−0.341902	+	0.197397i
$863$		−	13.0697i		−	0.444898i	−0.974944	−	0.222449i	$-0.928595\pi$
$863$		−	13.0697i		−	0.444898i	0.974944	−	0.222449i	$-0.0714050\pi$
$864$	−38.0885	+	10.2058i	−1.29580	+	0.347207i
$865$	1.07180	−	1.31268i	0.0364422	−	0.0446324i
$866$	−29.4904	−	51.0788i	−1.00212	−	1.73573i
$867$	−28.2013	+	7.55652i	−0.957767	+	0.256633i
$868$	−3.67423	−	2.12132i	−0.124712	−	0.0720023i
$869$	1.26795	−	2.19615i	0.0430122	−	0.0744994i
$870$	48.1197	−	4.86108i	1.63141	−	0.164806i
$871$	6.29423	+	10.9019i	0.213272	+	0.369398i
$872$			2.41233i			0.0816916i
$873$	−15.4176	+	26.7042i	−0.521808	+	0.903799i
$874$	10.1962			0.344890
$875$	0.403233	+	10.0159i	0.0136317	+	0.338599i
$876$	24.5885	+	6.58846i	0.830767	+	0.222603i
$877$	4.09034	+	2.36156i	0.138121	+	0.0797441i	0.567468	−	0.823395i	$-0.307923\pi$
$877$	4.09034	+	2.36156i	0.138121	+	0.0797441i	−0.429347	+	0.903139i	$0.641256\pi$
$878$	15.5935	+	9.00292i	0.526256	+	0.303834i
$879$	14.8301	+	3.97372i	0.500208	+	0.134030i
$880$	−7.57772	+	46.6237i	−0.255445	+	1.57168i
$881$	−8.41154			−0.283392			−0.141696	−	0.989910i	$-0.545256\pi$
$881$	−8.41154			−0.283392			−0.141696	+	0.989910i	$0.545256\pi$
$882$	17.9551	+	31.0991i	0.604579	+	1.04716i
$883$		−	17.6913i		−	0.595359i	−0.954666	−	0.297679i	$-0.903787\pi$
$883$		−	17.6913i		−	0.595359i	0.954666	−	0.297679i	$-0.0962126\pi$
$884$	0.803848	+	1.39230i	0.0270363	+	0.0468283i
$885$	−0.987148	−	9.77176i	−0.0331826	−	0.328474i
$886$	−13.4282	+	23.2583i	−0.451129	+	0.781379i
$887$	24.4070	+	14.0914i	0.819506	+	0.473142i	0.850246	−	0.526386i	$-0.176453\pi$
$887$	24.4070	+	14.0914i	0.819506	+	0.473142i	−0.0307403	+	0.999527i	$0.509786\pi$
$888$	−3.67423	+	0.984508i	−0.123299	+	0.0330379i
$889$	−2.08846	−	3.61731i	−0.0700446	−	0.121321i
$890$	−20.1962	+	24.7351i	−0.676977	+	0.829124i
$891$	−42.5885			−1.42677
$892$		−	28.9778i		−	0.970248i
$893$	−10.3664	+	5.98502i	−0.346897	+	0.200281i
$894$	6.69615	+	24.9904i	0.223953	+	0.835803i
$895$	51.4088	−	19.4960i	1.71841	−	0.651680i
$896$	−1.83975	+	3.18653i	−0.0614616	+	0.106455i
$897$	5.79555	+	5.79555i	0.193508	+	0.193508i
$898$	20.0764	−	11.5911i	0.669958	−	0.386800i
$899$	17.6603			0.589002
$900$	−17.2279	−	19.4473i	−0.574264	−	0.648244i
$901$	1.46410			0.0487763
$902$	33.7888	−	19.5080i	1.12504	−	0.649545i
$903$	3.67423	−	13.7124i	0.122271	−	0.456321i
$904$	−0.660254	+	1.14359i	−0.0219597	+	0.0380354i
$905$	−17.6965	+	6.71113i	−0.588251	+	0.223085i
$906$	−73.0070	−	19.5622i	−2.42550	−	0.649910i
$907$	−43.0506	+	24.8553i	−1.42947	+	0.825305i	−0.997079	−	0.0763808i	$-0.975664\pi$
$907$	−43.0506	+	24.8553i	−1.42947	+	0.825305i	−0.432392	+	0.901686i	$0.642330\pi$
$908$			3.28169i			0.108907i
$909$	−6.58846	−	3.80385i	−0.218525	−	0.126166i
$910$	−6.00000	+	7.34847i	−0.198898	+	0.243599i
$911$	−11.0718	−	19.1769i	−0.366825	−	0.635360i	0.622242	−	0.782825i	$-0.286222\pi$
$911$	−11.0718	−	19.1769i	−0.366825	−	0.635360i	−0.989067	+	0.147465i	$0.952889\pi$
$912$	14.9372	+	14.9372i	0.494619	+	0.494619i
$913$	−42.6902	−	24.6472i	−1.41284	−	0.815703i
$914$	−33.4186	+	57.8827i	−1.10539	+	1.91459i
$915$	−37.6494	−	16.9452i	−1.24465	−	0.560191i
$916$	−17.2583	−	29.8923i	−0.570231	−	0.987670i
$917$		−	0.832204i		−	0.0274818i
$918$	−3.67423	−	0.984508i	−0.121268	−	0.0324936i
$919$	15.1769			0.500640			0.250320	−	0.968163i	$-0.419464\pi$
$919$	15.1769			0.500640			0.250320	+	0.968163i	$0.419464\pi$
$920$	−0.358719	+	2.20711i	−0.0118266	+	0.0727662i
$921$	11.5981	+	43.2846i	0.382170	+	1.42628i
$922$	−31.3071	−	18.0752i	−1.03105	−	0.595275i
$923$	8.06918	+	4.65874i	0.265600	+	0.153344i
$924$	9.00000	−	9.00000i	0.296078	−	0.296078i
$925$	−14.0665	−	15.8787i	−0.462505	−	0.522088i
$926$	0.339746			0.0111647
$927$	−27.4249			−0.900751
$928$			49.0542i			1.61028i
$929$	1.73205	+	3.00000i	0.0568267	+	0.0984268i	0.893039	−	0.449979i	$-0.148568\pi$
$929$	1.73205	+	3.00000i	0.0568267	+	0.0984268i	−0.836213	+	0.548405i	$0.815235\pi$
$930$	−11.9482	−	16.5858i	−0.391796	−	0.543869i
$931$	8.46410	−	14.6603i	0.277400	−	0.480470i
$932$	10.6066	+	6.12372i	0.347431	+	0.200589i
$933$	12.5756	−	46.9328i	0.411707	−	1.53651i
$934$	5.56218	+	9.63397i	0.182000	+	0.315233i
$935$	−2.53590	+	3.10583i	−0.0829327	+	0.101571i
$936$			3.80385i			0.124333i
$937$		−	13.8647i		−	0.452941i	−0.974018	−	0.226471i	$-0.927281\pi$
$937$		−	13.8647i		−	0.452941i	0.974018	−	0.226471i	$-0.0727187\pi$
$938$	7.70882	−	4.45069i	0.251702	−	0.145320i
$939$	−6.80385	+	6.80385i	−0.222035	+	0.222035i
$940$	6.01703	+	15.8662i	0.196254	+	0.517500i
$941$	4.16025	−	7.20577i	0.135620	−	0.234901i	−0.790214	−	0.612831i	$-0.790031\pi$
$941$	4.16025	−	7.20577i	0.135620	−	0.234901i	0.925834	+	0.377930i	$0.123364\pi$
$942$	−69.1306	+	18.5235i	−2.25240	+	0.603527i
$943$	7.14042	−	4.12252i	0.232524	−	0.134248i
$944$	11.3205			0.368451
$945$	−1.04703	−	10.3645i	−0.0340598	−	0.337158i
$946$	83.5692			2.71707
$947$	−2.00120	+	1.15539i	−0.0650303	+	0.0375453i	−0.532163	−	0.846642i	$-0.678621\pi$
$947$	−2.00120	+	1.15539i	−0.0650303	+	0.0375453i	0.467132	+	0.884187i	$0.345287\pi$
$948$	−1.55291	+	0.416102i	−0.0504363	+	0.0135144i
$949$	10.3923	−	18.0000i	0.337348	−	0.584305i
$950$	−8.35739	+	25.0313i	−0.271150	+	0.812121i
$951$	−43.0526	+	43.0526i	−1.39607	+	1.39607i
$952$	−0.152304	+	0.0879327i	−0.00493620	+	0.00284992i
$953$		−	37.0197i		−	1.19919i	−0.800305	−	0.599594i	$-0.795329\pi$
$953$		−	37.0197i		−	1.19919i	0.800305	−	0.599594i	$-0.204671\pi$
$954$	−19.3923	−	11.1962i	−0.627849	−	0.362489i
$955$	0.588457	+	0.480473i	0.0190420	+	0.0155478i
$956$	−11.1962	−	19.3923i	−0.362109	−	0.627192i
$957$	−13.7124	+	51.1755i	−0.443260	+	1.65427i
$958$	53.2968	+	30.7709i	1.72194	+	0.994163i
$959$	−8.32051	+	14.4115i	−0.268683	+	0.465373i
$960$	18.0129	−	12.9762i	0.581363	−	0.418806i
$961$	11.7679	+	20.3827i	0.379611	+	0.657506i
$962$		−	20.0764i		−	0.647289i
$963$	17.5947	+	30.4749i	0.566982	+	0.982041i
$964$	−10.8564			−0.349661
$965$	45.7593	+	7.43723i	1.47305	+	0.239413i
$966$	4.09808	−	4.09808i	0.131853	−	0.131853i
$967$	−30.0588	−	17.3545i	−0.966627	−	0.558082i	−0.0684208	−	0.997657i	$-0.521796\pi$
$967$	−30.0588	−	17.3545i	−0.966627	−	0.558082i	−0.898206	+	0.439574i	$0.855129\pi$
$968$	−5.10703	−	2.94855i	−0.164146	−	0.0947698i
$969$	0.464102	+	1.73205i	0.0149091	+	0.0556415i
$970$	7.12288	−	43.8252i	0.228702	−	1.40714i
$971$	27.8038			0.892268			0.446134	−	0.894966i	$-0.352800\pi$
$971$	27.8038			0.892268			0.446134	+	0.894966i	$0.352800\pi$
$972$	19.0919	+	19.0919i	0.612372	+	0.612372i
$973$			7.17260i			0.229943i
$974$	1.09808	+	1.90192i	0.0351846	+	0.0609416i
$975$	−18.9783	+	9.47753i	−0.607793	+	0.303524i
$976$	23.7942	−	41.2128i	0.761635	−	1.31919i
$977$	−13.4722	−	7.77817i	−0.431014	−	0.248846i	0.268765	−	0.963206i	$-0.413385\pi$
$977$	−13.4722	−	7.77817i	−0.431014	−	0.248846i	−0.699778	+	0.714360i	$0.746718\pi$
$978$	−44.8115	−	44.8115i	−1.43291	−	1.43291i
$979$	−17.4904	−	30.2942i	−0.558995	−	0.968208i
$980$	−18.5885	−	15.1774i	−0.593786	−	0.484825i
$981$	12.1077	−	6.99038i	0.386569	−	0.223186i
$982$		−	41.9459i		−	1.33855i
$983$	31.0669	−	17.9365i	0.990881	−	0.572085i	0.0853431	−	0.996352i	$-0.472801\pi$
$983$	31.0669	−	17.9365i	0.990881	−	0.572085i	0.905537	+	0.424266i	$0.139468\pi$
$984$	3.69615	+	0.990381i	0.117829	+	0.0315722i
$985$	16.5193	+	43.5597i	0.526350	+	1.38793i
$986$	−2.36603	+	4.09808i	−0.0753496	+	0.130509i
$987$	−1.76097	+	6.57201i	−0.0560521	+	0.209189i
$988$	−10.0382	+	5.79555i	−0.319358	+	0.184381i
$989$	17.6603			0.561563
$990$	57.3391	−	21.7450i	1.82236	−	0.691101i
$991$	25.0718			0.796432			0.398216	−	0.917292i	$-0.369629\pi$
$991$	25.0718			0.796432			0.398216	+	0.917292i	$0.369629\pi$
$992$	17.9551	−	10.3664i	0.570074	−	0.329132i
$993$	15.1774	+	15.1774i	0.481641	+	0.481641i
$994$	3.29423	−	5.70577i	0.104487	−	0.180976i
$995$	9.59341	−	3.63816i	0.304132	−	0.115337i
$996$	8.08846	+	30.1865i	0.256293	+	0.956497i
$997$	13.1440	−	7.58871i	0.416275	−	0.240337i	−0.277207	−	0.960810i	$-0.589409\pi$
$997$	13.1440	−	7.58871i	0.416275	−	0.240337i	0.693483	+	0.720473i	$0.256075\pi$
$998$			7.45001i			0.235826i
$999$	15.5885	+	15.5885i	0.493197	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.j.a.4.4	yes	8
3.2	odd	2		135.2.j.a.64.1		8
4.3	odd	2		720.2.by.d.49.4		8
5.2	odd	4		225.2.e.d.76.4		8
5.3	odd	4		225.2.e.d.76.1		8
5.4	even	2	inner	45.2.j.a.4.1	✓	8
9.2	odd	6		135.2.j.a.19.4		8
9.4	even	3		405.2.b.d.244.4		4
9.5	odd	6		405.2.b.c.244.1		4
9.7	even	3	inner	45.2.j.a.34.1	yes	8
12.11	even	2		2160.2.by.c.1009.4		8
15.2	even	4		675.2.e.d.226.1		8
15.8	even	4		675.2.e.d.226.4		8
15.14	odd	2		135.2.j.a.64.4		8
20.19	odd	2		720.2.by.d.49.1		8
36.7	odd	6		720.2.by.d.529.1		8
36.11	even	6		2160.2.by.c.289.2		8
45.2	even	12		675.2.e.d.451.1		8
45.4	even	6		405.2.b.d.244.1		4
45.7	odd	12		225.2.e.d.151.4		8
45.13	odd	12		2025.2.a.t.1.4		4
45.14	odd	6		405.2.b.c.244.4		4
45.22	odd	12		2025.2.a.t.1.1		4
45.23	even	12		2025.2.a.r.1.1		4
45.29	odd	6		135.2.j.a.19.1		8
45.32	even	12		2025.2.a.r.1.4		4
45.34	even	6	inner	45.2.j.a.34.4	yes	8
45.38	even	12		675.2.e.d.451.4		8
45.43	odd	12		225.2.e.d.151.1		8
60.59	even	2		2160.2.by.c.1009.2		8
180.79	odd	6		720.2.by.d.529.4		8
180.119	even	6		2160.2.by.c.289.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	5.4	even	2	inner
45.2.j.a.4.4	yes	8	1.1	even	1	trivial
45.2.j.a.34.1	yes	8	9.7	even	3	inner
45.2.j.a.34.4	yes	8	45.34	even	6	inner
135.2.j.a.19.1		8	45.29	odd	6
135.2.j.a.19.4		8	9.2	odd	6
135.2.j.a.64.1		8	3.2	odd	2
135.2.j.a.64.4		8	15.14	odd	2
225.2.e.d.76.1		8	5.3	odd	4
225.2.e.d.76.4		8	5.2	odd	4
225.2.e.d.151.1		8	45.43	odd	12
225.2.e.d.151.4		8	45.7	odd	12
405.2.b.c.244.1		4	9.5	odd	6
405.2.b.c.244.4		4	45.14	odd	6
405.2.b.d.244.1		4	45.4	even	6
405.2.b.d.244.4		4	9.4	even	3
675.2.e.d.226.1		8	15.2	even	4
675.2.e.d.226.4		8	15.8	even	4
675.2.e.d.451.1		8	45.2	even	12
675.2.e.d.451.4		8	45.38	even	12
720.2.by.d.49.1		8	20.19	odd	2
720.2.by.d.49.4		8	4.3	odd	2
720.2.by.d.529.1		8	36.7	odd	6
720.2.by.d.529.4		8	180.79	odd	6
2025.2.a.r.1.1		4	45.23	even	12
2025.2.a.r.1.4		4	45.32	even	12
2025.2.a.t.1.1		4	45.22	odd	12
2025.2.a.t.1.4		4	45.13	odd	12
2160.2.by.c.289.2		8	36.11	even	6
2160.2.by.c.289.4		8	180.119	even	6
2160.2.by.c.1009.2		8	60.59	even	2
2160.2.by.c.1009.4		8	12.11	even	2

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

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