LMFDB - Embedded newform 45.2.j.a.4.1

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			4.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	45.4
Dual form			45.2.j.a.34.1

$q$-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} +(0.358719 + 2.20711i) 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} +(1.58957 + 3.53175i) q^{15} +(2.23205 + 3.86603i) q^{16} -0.378937i q^{17} +(-2.89778 + 5.01910i) q^{18} -2.73205 q^{19} +(3.62132 + 1.37333i) 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} +(-4.74264 + 1.58346i) q^{25} +4.73205 q^{26} +(3.67423 - 3.67423i) q^{27} +1.55291i q^{28} +(3.23205 + 5.59808i) q^{29} +(-6.07081 - 4.37333i) 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} +(1.14248 - 0.185687i) 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} +(6.40508 - 7.23023i) 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} +(6.67423 + 0.674235i) q^{60} +(-5.33013 - 9.23205i) q^{61} +5.27792i q^{62} +(-1.34486 + 2.32937i) q^{63} +5.73205 q^{64} +(1.94218 - 5.12132i) 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} +(3.62132 + 1.37333i) q^{70} +3.80385 q^{71} +(-0.776457 - 1.34486i) q^{72} +8.48528i q^{73} +(-4.09808 - 7.09808i) q^{74} +(-7.22474 + 4.77526i) 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} +(0.836355 - 0.135932i) q^{85} +(-8.83013 + 15.2942i) q^{86} +(7.91688 + 7.91688i) q^{87} +(-2.12132 + 1.22474i) q^{88} +7.39230 q^{89} +(-12.1172 - 4.59526i) q^{90} +2.19615 q^{91} +(2.89778 - 1.67303i) q^{92} +(1.22474 - 4.57081i) q^{93} +(4.23205 - 7.33013i) q^{94} +(-0.980040 - 6.02993i) 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} - 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}+ \cdots - 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

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	−0.956710	−	0.291044i	$-0.905997\pi$
$2$	−1.67303	+	0.965926i	−1.18301	+	0.683013i	−0.226303	+	0.974057i	$0.572664\pi$
$3$	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
$5$	0.358719	+	2.20711i	0.160424	+	0.987048i
$5$	0.358719	+	2.20711i	0.160424	+	0.987048i
$6$	−2.36603	+	2.36603i	−0.965926	+	0.965926i
$7$	−0.776457	+	0.448288i	−0.293473	+	0.169437i	−0.639507	−	0.768785i	$-0.720862\pi$
$7$	−0.776457	+	0.448288i	−0.293473	+	0.169437i	0.346034	+	0.938222i	$0.387528\pi$
$8$		−	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	0.176096	−	0.984373i	$-0.443653\pi$
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	−0.764444	+	0.644690i	$0.776986\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$	1.58957	+	3.53175i	0.410425	+	0.911894i
$16$	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	$0.601464\pi$
$20$	3.62132	+	1.37333i	0.809752	+	0.307086i
$21$	−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	$-0.268781\pi$
$23$	1.67303	+	0.965926i	0.348851	+	0.201409i	−0.315328	+	0.948983i	$0.602114\pi$
$24$	−0.232051	−	0.866025i	−0.0473672	−	0.176777i
$25$	−4.74264	+	1.58346i	−0.948528	+	0.316693i
$26$	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	$0.628430\pi$
$30$	−6.07081	−	4.37333i	−1.10837	−	0.798457i
$31$	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	$0.113391\pi$
$37$			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
$40$	1.14248	−	0.185687i	0.180642	−	0.0293597i
$41$	−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	0.245141	−	0.969487i	$-0.421166\pi$
$43$	7.91688	−	4.57081i	1.20731	−	0.697042i	0.962171	+	0.272445i	$0.0878324\pi$
$44$	−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	$-0.770196\pi$
$47$	−3.79435	+	2.19067i	−0.553463	+	0.319542i	0.197054	+	0.980393i	$0.436862\pi$
$48$	5.46739	+	5.46739i	0.789149	+	0.789149i
$49$	−3.09808	+	5.36603i	−0.442582	+	0.766575i
$50$	6.40508	−	7.23023i	0.905816	−	1.02251i
$51$	−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	−0.771608	−	0.636098i	$-0.780547\pi$
$59$	1.26795	−	2.19615i	0.165073	−	0.285915i	0.936681	+	0.350183i	$0.113881\pi$
$60$	6.67423	+	0.674235i	0.861640	+	0.0870433i
$61$	−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
$65$	1.94218	−	5.12132i	0.240898	−	0.635222i
$66$	15.2942	+	4.09808i	1.88259	+	0.504438i
$67$	−4.45069	−	2.56961i	−0.543739	−	0.313928i	0.202854	−	0.979209i	$-0.434978\pi$
$67$	−4.45069	−	2.56961i	−0.543739	−	0.313928i	−0.746593	+	0.665281i	$0.768312\pi$
$68$	−0.568406	−	0.328169i	−0.0689294	−	0.0397964i
$69$	3.23205	+	0.866025i	0.389093	+	0.104257i
$70$	3.62132	+	1.37333i	0.432831	+	0.164144i
$71$	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
$75$	−7.22474	+	4.77526i	−0.834242	+	0.551399i
$76$	−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	−0.905346	−	0.424676i	$-0.860388\pi$
$83$	−9.02150	+	5.20857i	−0.990238	+	0.571714i	−0.0848929	+	0.996390i	$0.527055\pi$
$84$	0.696152	+	2.59808i	0.0759565	+	0.283473i
$85$	0.836355	−	0.135932i	0.0907155	−	0.0147439i
$86$	−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	$0.371856\pi$
$90$	−12.1172	−	4.59526i	−1.27726	−	0.484383i
$91$	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
$95$	−0.980040	−	6.02993i	−0.100550	−	0.618658i
$96$	−12.6962	−	3.40192i	−1.29580	−	0.347207i
$97$	8.90138	−	5.13922i	0.903799	−	0.521808i	0.0253679	−	0.999678i	$-0.491924\pi$
$97$	8.90138	−	5.13922i	0.903799	−	0.521808i	0.878431	+	0.477870i	$0.158591\pi$
$98$		−	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	0.836456	−	0.548034i	$-0.184624\pi$
$103$	7.91688	+	4.57081i	0.780073	+	0.450375i	−0.0563832	+	0.998409i	$0.517957\pi$
$104$	−0.633975	+	1.09808i	−0.0621663	+	0.107675i
$105$	−2.81747	−	2.02967i	−0.274957	−	0.198076i
$106$	−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	$0.428354\pi$
$110$	−7.24833	+	19.1130i	−0.691101	+	1.82236i
$111$	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	$-0.371620\pi$
$113$	−2.20925	−	1.27551i	−0.207829	−	0.119990i	−0.600302	+	0.799773i	$0.704953\pi$
$114$	6.46410	−	6.46410i	0.605419	−	0.605419i
$115$	−1.53175	+	4.03906i	−0.142837	+	0.376644i
$116$	11.1962			1.03954
$117$	−7.34847			−0.679366
$118$			4.89898i			0.450988i
$119$	0.169873	+	0.294229i	0.0155722	+	0.0269719i
$120$	1.82817	−	0.822821i	0.166888	−	0.0751129i
$121$	−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
$130$	1.69748	+	10.4441i	0.148879	+	0.916012i
$131$	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
$135$	9.42745	+	6.79141i	0.811386	+	0.584511i
$136$	−0.196152			−0.0168199
$137$	16.0740	−	9.28032i	1.37329	−	0.792871i	0.381952	−	0.924182i	$-0.375252\pi$
$137$	16.0740	−	9.28032i	1.37329	−	0.792871i	0.991341	+	0.131311i	$0.0419186\pi$
$138$	−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	$0.276849\pi$
$140$	−3.42745	+	0.557061i	−0.289672	+	0.0470802i
$141$	−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	$0.0640861\pi$
$150$	7.47469	−	14.9677i	0.610306	−	1.22211i
$151$	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
$155$	5.71209	+	2.16622i	0.458806	+	0.173995i
$156$	−5.19615	+	5.19615i	−0.416025	+	0.416025i
$157$	−18.5235	−	10.6945i	−1.47833	−	0.853517i	−0.478635	−	0.878014i	$-0.658868\pi$
$157$	−18.5235	−	10.6945i	−1.47833	−	0.853517i	−0.999700	+	0.0244975i	$0.992201\pi$
$158$	−0.896575	−	0.517638i	−0.0713277	−	0.0411811i
$159$	1.73205	+	6.46410i	0.137361	+	0.512637i
$160$	6.01703	−	15.8662i	0.475688	−	1.25434i
$161$	−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
$165$	10.7124	−	14.8704i	0.833962	−	1.15766i
$166$	10.0622	−	17.4282i	0.780976	−	1.35269i
$167$	−14.7291	−	8.50386i	−1.13977	−	0.658049i	−0.193399	−	0.981120i	$-0.561951\pi$
$167$	−14.7291	−	8.50386i	−1.13977	−	0.658049i	−0.946375	+	0.323071i	$0.895285\pi$
$168$	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	$-0.657495\pi$
$173$	0.656339	−	0.378937i	0.0499005	−	0.0288101i	0.524743	+	0.851261i	$0.324162\pi$
$174$	−20.8923	−	5.59808i	−1.58384	−	0.424389i
$175$	2.97261	−	3.35556i	0.224708	−	0.253656i
$176$	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	$0.870932\pi$
$180$	11.4685	−	1.86396i	0.854809	−	0.138931i
$181$	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
$185$	−9.36396	+	1.52192i	−0.688452	+	0.111894i
$186$	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	0.979085	−	0.203451i	$-0.0652157\pi$
$193$	17.9551	+	10.3664i	1.29243	+	0.746187i	0.313349	+	0.949638i	$0.398549\pi$
$194$	−9.92820	+	17.1962i	−0.712803	+	1.23461i
$195$	0.953512	−	9.43879i	0.0682824	−	0.675926i
$196$	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	$0.551999\pi$
$200$	0.819661	+	2.45497i	0.0579588	+	0.173593i
$201$	−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
$205$	−8.92330	−	3.38403i	−0.623230	−	0.236351i
$206$	−17.6603			−1.23045
$207$	5.79555			0.402819
$208$		−	10.9348i		−	0.758190i
$209$	6.46410	+	11.1962i	0.447131	+	0.774454i
$210$	6.67423	+	0.674235i	0.460566	+	0.0465266i
$211$	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
$220$	−2.94012	−	18.0898i	−0.198223	−	1.21961i
$221$	−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	$-0.855932\pi$
$223$	−14.4889	+	8.36516i	−0.970248	+	0.560173i	−0.0709359	+	0.997481i	$0.522599\pi$
$224$	6.80385			0.454601
$225$	−9.94655	+	11.2279i	−0.663103	+	0.748528i
$226$	4.92820			0.327819
$227$	1.64085	−	0.947343i	0.108907	−	0.0628774i	−0.444557	−	0.895750i	$-0.646639\pi$
$227$	1.64085	−	0.947343i	0.108907	−	0.0628774i	0.553464	+	0.832873i	$0.313306\pi$
$228$	−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	$-0.0621194\pi$
$230$	−1.33876	−	8.23703i	−0.0882752	−	0.543134i
$231$	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	−0.577623	−	0.816304i	$-0.696020\pi$
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	0.995751	+	0.0920846i	$0.0293530\pi$
$240$	−10.1058	+	14.0284i	−0.652330	+	0.905527i
$241$	−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
$245$	−12.9547	−	4.91289i	−0.827647	−	0.313873i
$246$	−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
$250$	18.2555	+	11.5431i	1.15458	+	0.730048i
$251$	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
$255$	1.33831	−	0.602347i	0.0838084	−	0.0377204i
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	19.4201	+	11.2122i	1.21139	+	0.699396i	0.963062	−	0.269280i	$-0.0867857\pi$
$257$	19.4201	+	11.2122i	1.21139	+	0.699396i	0.248328	+	0.968676i	$0.420119\pi$
$258$	−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	$-0.591120\pi$
$263$	6.60420	−	3.81294i	0.407232	−	0.235116i	0.689600	+	0.724191i	$0.257786\pi$
$264$	−3.00000	+	3.00000i	−0.184637	+	0.184637i
$265$	−8.52761	+	1.38599i	−0.523847	+	0.0851404i
$266$	−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	$0.675648\pi$
$270$	−22.3324	−	2.25603i	−1.35911	−	0.137298i
$271$	−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
$275$	17.7104	+	15.6892i	1.06798	+	0.946094i
$276$	4.09808	−	4.09808i	0.246675	−	0.246675i
$277$	10.6066	−	6.12372i	0.637289	−	0.367939i	−0.146281	−	0.989243i	$-0.546730\pi$
$277$	10.6066	−	6.12372i	0.637289	−	0.367939i	0.783569	+	0.621304i	$0.213397\pi$
$278$		−	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	0.610931	−	0.791684i	$-0.290795\pi$
$283$	3.88229	+	2.24144i	0.230778	+	0.133240i	−0.380153	+	0.924924i	$0.624129\pi$
$284$	3.29423	−	5.70577i	0.195477	−	0.338575i
$285$	−4.34278	−	9.64893i	−0.257244	−	0.571553i
$286$	−11.1962	−	19.3923i	−0.662042	−	1.14669i
$287$		−	3.82654i		−	0.225873i
$288$	−22.7661			−1.34151
$289$	16.8564			0.991553
$290$	9.90140	−	26.1089i	0.581430	−	1.53317i
$291$	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	$-0.249965\pi$
$293$	7.67664	+	4.43211i	0.448474	+	0.258927i	−0.258711	+	0.965955i	$0.583298\pi$
$294$	−5.36603	−	20.0263i	−0.312953	−	1.16796i
$295$	5.30198	+	2.01070i	0.308693	+	0.117067i
$296$	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
$300$	0.906070	+	14.9726i	0.0523120	+	0.864444i
$301$	−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
$310$	−11.6489	+	1.89329i	−0.661615	+	0.107532i
$311$	−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	−0.629767	−	0.776784i	$-0.716850\pi$
$313$	−4.81105	+	2.77766i	−0.271936	+	0.157003i	0.357831	+	0.933786i	$0.383516\pi$
$314$	41.3205			2.33185
$315$	−5.62360	−	2.13267i	−0.316854	−	0.120162i
$316$	0.928203			0.0522155
$317$	−30.4428	+	17.5761i	−1.70984	+	0.987174i	−0.775094	+	0.631846i	$0.782297\pi$
$317$	−30.4428	+	17.5761i	−1.70984	+	0.987174i	−0.934742	+	0.355328i	$0.884369\pi$
$318$	−9.14162	−	9.14162i	−0.512637	−	0.512637i
$319$	15.2942	−	26.4904i	0.856312	−	1.48318i
$320$	2.05620	+	12.6512i	0.114945	+	0.707226i
$321$	−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
$330$	−3.55855	+	35.2261i	−0.195892	+	1.93913i
$331$	−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
$335$	4.07485	−	10.7449i	0.222633	−	0.587058i
$336$	−6.69615	−	1.79423i	−0.365305	−	0.0978832i
$337$	1.55291	+	0.896575i	0.0845926	+	0.0488396i	0.541700	−	0.840572i	$-0.317781\pi$
$337$	1.55291	+	0.896575i	0.0845926	+	0.0488396i	−0.457107	+	0.889412i	$0.651114\pi$
$338$	11.7112	+	6.76148i	0.637007	+	0.367776i
$339$	−4.26795	−	1.14359i	−0.231803	−	0.0621115i
$340$	0.520407	−	1.37225i	0.0282230	−	0.0744209i
$341$	−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
$345$	−0.752011	+	7.44414i	−0.0404869	+	0.400779i
$346$	−0.732051	+	1.26795i	−0.0393553	+	0.0681654i
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	0.251909	−	0.967751i	$-0.418942\pi$
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	−0.712143	+	0.702035i	$0.752275\pi$
$348$	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	−0.693661	−	0.720301i	$-0.744004\pi$
$353$	−7.82894	+	4.52004i	−0.416693	+	0.240578i	0.276969	+	0.960879i	$0.410670\pi$
$354$	2.19615	+	8.19615i	0.116724	+	0.435621i
$355$	1.36451	+	8.39550i	0.0724209	+	0.445587i
$356$	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
$365$	−18.7279	+	3.04384i	−0.980264	+	0.159322i
$366$	34.4545	+	9.23205i	1.80096	+	0.482567i
$367$	−21.4770	+	12.3998i	−1.12109	+	0.647262i	−0.941679	−	0.336512i	$-0.890753\pi$
$367$	−21.4770	+	12.3998i	−1.12109	+	0.647262i	−0.179411	+	0.983774i	$0.557419\pi$
$368$			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	$-0.646298\pi$
$373$	−27.8410	−	16.0740i	−1.44155	−	0.832280i	−0.997953	+	0.0639468i	$0.979631\pi$
$374$	1.73205	−	3.00000i	0.0895622	−	0.155126i
$375$	−13.1312	−	14.2328i	−0.678090	−	0.734979i
$376$	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	$0.604343\pi$
$380$	−9.89363	−	3.75201i	−0.507533	−	0.192474i
$381$	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	$-0.158292\pi$
$383$	17.7148	+	10.2277i	0.905186	+	0.522609i	0.0263067	+	0.999654i	$0.491625\pi$
$384$	5.02628	−	5.02628i	0.256496	−	0.256496i
$385$	−3.36396	+	8.87039i	−0.171443	+	0.452077i
$386$	−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	$-0.376131\pi$
$390$	7.52192	+	16.7124i	0.380887	+	0.846267i
$391$	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
$400$	−16.7075	−	14.8008i	−0.835376	−	0.740040i
$401$	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
$405$	18.8169	+	7.13604i	0.935021	+	0.354593i
$406$	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	$0.969675\pi$
$410$	18.1977	−	2.95766i	0.898720	−	0.146068i
$411$	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	$0.294921\pi$
$420$	−5.48451	+	2.46846i	−0.267617	+	0.120449i
$421$	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
$425$	0.600034	+	1.79716i	0.0291059	+	0.0871753i
$426$	−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
$430$	−36.9235	−	14.0027i	−1.78061	−	0.675270i
$431$	−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
$435$	−14.6335	+	20.3133i	−0.701620	+	0.973949i
$436$	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	−0.185942	−	0.982561i	$-0.559534\pi$
$443$	12.0394	−	6.95095i	0.572009	−	0.330250i	0.757951	+	0.652311i	$0.226200\pi$
$444$	12.2942	+	3.29423i	0.583458	+	0.156337i
$445$	2.65176	+	16.3156i	0.125706	+	0.773434i
$446$	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
$455$	0.787803	+	4.84714i	0.0369328	+	0.227238i
$456$	0.633975	+	2.36603i	0.0296886	+	0.110799i
$457$	29.9623	−	17.2987i	1.40158	−	0.809201i	0.407022	−	0.913418i	$-0.366567\pi$
$457$	29.9623	−	17.2987i	1.40158	−	0.809201i	0.994554	+	0.104218i	$0.0332339\pi$
$458$			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	0.496457	−	0.868061i	$-0.334634\pi$
$463$	−0.152304	−	0.0879327i	−0.00707816	−	0.00408658i	−0.503535	+	0.863975i	$0.667967\pi$
$464$	−14.4282	+	24.9904i	−0.669813	+	1.16015i
$465$	10.5276	+	1.06350i	0.488206	+	0.0493188i
$466$	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
$470$	17.6965	+	6.71113i	0.816278	+	0.309561i
$471$	−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
$475$	12.9571	−	4.32611i	0.594514	−	0.198495i
$476$	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	$0.573886\pi$
$480$	2.95405	−	29.2421i	0.134833	−	1.33471i
$481$	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
$490$	26.4192	−	4.29389i	1.19350	−	0.193978i
$491$	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
$495$	11.2560	−	29.6809i	0.505921	−	1.33406i
$496$	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	$0.194177\pi$
$500$	−19.3492	−	0.778985i	−0.865324	−	0.0348373i
$501$	−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	−0.960886	−	0.276946i	$-0.910678\pi$
$509$	−5.42820	+	9.40192i	−0.240601	+	0.416733i	0.720285	+	0.693679i	$0.244011\pi$
$510$	−1.65722	+	2.30046i	−0.0733829	+	0.101866i
$511$	−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
$515$	−7.24833	+	19.1130i	−0.319400	+	0.842221i
$516$	−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
$520$	−2.65099	−	1.00535i	−0.116254	−	0.0440874i
$521$	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
$525$	3.46902	−	6.94655i	0.151400	−	0.303172i
$526$	−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
$535$	25.8889	−	4.20771i	1.11928	−	0.181915i
$536$	−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
$540$	18.3515	−	8.25964i	0.789724	−	0.355438i
$541$	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
$545$	1.67172	+	10.2857i	0.0716088	+	0.440590i
$546$	−5.19615	+	5.19615i	−0.222375	+	0.222375i
$547$	−26.2323	+	15.1452i	−1.12161	+	0.647563i	−0.941812	−	0.336140i	$-0.890878\pi$
$547$	−26.2323	+	15.1452i	−1.12161	+	0.647563i	−0.179800	+	0.983703i	$0.557545\pi$
$548$		−	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
$555$	−14.9840	+	6.74397i	−0.636033	+	0.286265i
$556$	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
$560$	3.17348	−	8.36811i	0.134104	−	0.353617i
$561$	−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	$-0.136060\pi$
$563$	23.8707	+	13.7818i	1.00603	+	0.580833i	0.0960045	+	0.995381i	$0.469394\pi$
$564$	3.40192	+	12.6962i	0.143247	+	0.534604i
$565$	2.02269	−	5.33361i	0.0850952	−	0.224387i
$566$	−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	$0.868906\pi$
$570$	16.5858	+	11.9482i	0.694701	+	0.500453i
$571$	−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	$-0.797343\pi$
$577$		−	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
$580$	4.01628	+	24.7111i	0.166767	+	1.02607i
$581$	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
$585$	−2.63604	−	16.2189i	−0.108987	−	0.670567i
$586$	−17.1244			−0.707401
$587$	−19.0597	+	11.0041i	−0.786678	+	0.454189i	−0.838792	−	0.544452i	$-0.816737\pi$
$587$	−19.0597	+	11.0041i	−0.786678	+	0.454189i	0.0521138	+	0.998641i	$0.483404\pi$
$588$	13.1440	+	13.1440i	0.542050	+	0.542050i
$589$	−3.73205	+	6.46410i	−0.153776	+	0.266349i
$590$	−10.8126	+	1.75736i	−0.445146	+	0.0723493i
$591$	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	−0.283514	−	0.958968i	$-0.591500\pi$
$599$	16.8564	−	29.1962i	0.688734	−	1.19292i	0.972248	−	0.233954i	$-0.0751666\pi$
$600$	2.47185	+	3.73980i	0.100913	+	0.152677i
$601$	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
$605$	−23.8187	−	9.03288i	−0.968368	−	0.367239i
$606$	8.19615	+	2.19615i	0.332946	+	0.0892126i
$607$	7.55652	+	4.36276i	0.306710	+	0.177079i	0.645453	−	0.763800i	$-0.276669\pi$
$607$	7.55652	+	4.36276i	0.306710	+	0.177079i	−0.338743	+	0.940879i	$0.610002\pi$
$608$	17.9551	+	10.3664i	0.728174	+	0.420412i
$609$	−9.69615	−	2.59808i	−0.392908	−	0.105279i
$610$	−16.3289	+	43.0574i	−0.661136	+	1.74334i
$611$	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
$615$	−16.4460	−	1.66138i	−0.663166	−	0.0669934i
$616$	1.09808	−	1.90192i	0.0442428	−	0.0766307i
$617$	11.3509	+	6.55343i	0.456969	+	0.263831i	0.710769	−	0.703426i	$-0.248347\pi$
$617$	11.3509	+	6.55343i	0.456969	+	0.263831i	−0.253800	+	0.967257i	$0.581680\pi$
$618$	−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
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	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
$630$	11.4685	−	1.86396i	0.456915	−	0.0742620i
$631$	−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
$635$	−10.2823	+	1.67118i	−0.408042	+	0.0663188i
$636$	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	0.00322641	−	0.999995i	$-0.498973\pi$
$643$	−21.8374	−	12.6078i	−0.861181	−	0.497203i	−0.864408	+	0.502792i	$0.832306\pi$
$644$	−1.50000	+	2.59808i	−0.0591083	+	0.102379i
$645$	28.7274	+	20.6948i	1.13114	+	0.814858i
$646$	−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
$650$	−22.4424	+	7.49303i	−0.880264	+	0.293901i
$651$	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	$-0.336156\pi$
$653$	−0.392541	−	0.226633i	−0.0153613	−	0.00886885i	−0.507661	+	0.861557i	$0.669490\pi$
$654$	−11.0263	+	11.0263i	−0.431162	+	0.431162i
$655$	1.94066	+	0.735966i	0.0758279	+	0.0287566i
$656$	−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	$0.583820\pi$
$660$	−13.0283	−	28.9468i	−0.507128	−	1.12675i
$661$	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
$670$	3.56144	+	21.9126i	0.137590	+	0.846558i
$671$	−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	$-0.676590\pi$
$673$	−1.40061	+	0.808643i	−0.0539896	+	0.0311709i	0.472762	+	0.881190i	$0.343257\pi$
$674$	−3.46410			−0.133432
$675$	−11.6076	+	23.2436i	−0.446775	+	0.894646i
$676$	−12.1244			−0.466321
$677$	28.6496	−	16.5409i	1.10109	−	0.635717i	0.164586	−	0.986363i	$-0.447371\pi$
$677$	28.6496	−	16.5409i	1.10109	−	0.635717i	0.936508	+	0.350646i	$0.114038\pi$
$678$	8.24504	−	2.20925i	0.316649	−	0.0848459i
$679$	−4.60770	+	7.98076i	−0.176827	+	0.306274i
$680$	−0.0703637	−	0.432929i	−0.00269832	−	0.0166021i
$681$	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
$690$	−5.93235	−	13.1807i	−0.225841	−	0.501780i
$691$	−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
$695$	−16.7262	−	6.34315i	−0.634459	−	0.240609i
$696$	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
$700$	−2.45898	−	7.36491i	−0.0929409	−	0.278368i
$701$	−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
$705$	−13.7683	−	9.91849i	−0.518544	−	0.373552i
$706$	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
$715$	−25.5828	+	4.15796i	−0.956743	+	0.155499i
$716$	−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	$0.619144\pi$
$720$	−10.6187	+	28.0002i	−0.395734	+	1.04351i
$721$	−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
$725$	−24.1928	−	21.4318i	−0.898498	−	0.795958i
$726$	−9.86603	−	36.8205i	−0.366163	−	1.36654i
$727$	−24.5271	+	14.1607i	−0.909659	+	0.525192i	−0.880321	−	0.474378i	$-0.842673\pi$
$727$	−24.5271	+	14.1607i	−0.909659	+	0.525192i	−0.0293377	+	0.999570i	$0.509340\pi$
$728$		−	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	$-0.610981\pi$
$733$	−35.9101	−	20.7327i	−1.32637	−	0.765781i	−0.984736	+	0.174052i	$0.944314\pi$
$734$	23.9545	−	41.4904i	0.884176	−	1.53144i
$735$	−23.8761	−	2.41197i	−0.880682	−	0.0889670i
$736$	−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	$0.180534\pi$
$740$	−5.82655	+	15.3640i	−0.214188	+	0.564790i
$741$	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	$-0.487063\pi$
$743$	−21.9253	−	12.6586i	−0.804361	−	0.464398i	−0.844994	+	0.534776i	$0.820396\pi$
$744$	−2.36603	−	0.633975i	−0.0867427	−	0.0232426i
$745$	16.1659	+	6.13069i	0.592274	+	0.224611i
$746$	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
$750$	35.7167	+	11.1282i	1.30419	+	0.406345i
$751$	−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	$-0.957365\pi$
$757$		−	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
$760$	−3.12132	+	0.507306i	−0.113222	+	0.0184019i
$761$	−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	$0.332738\pi$
$770$	−2.94012	−	18.0898i	−0.105955	−	0.651911i
$771$	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	$-0.955622\pi$
$773$		−	7.72741i		−	0.277935i	0.990297	−	0.138968i	$-0.0443784\pi$
$774$			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
$780$	−13.3324	−	9.60450i	−0.477377	−	0.343896i
$781$	−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
$785$	16.9592	−	44.7196i	0.605302	−	1.59611i
$786$	0.803848	+	3.00000i	0.0286723	+	0.107006i
$787$	−14.1285	−	8.15711i	−0.503628	−	0.290770i	0.226583	−	0.973992i	$-0.427245\pi$
$787$	−14.1285	−	8.15711i	−0.503628	−	0.290770i	−0.730210	+	0.683222i	$0.760578\pi$
$788$	31.2514	+	18.0430i	1.11328	+	0.642755i
$789$	9.33975	−	9.33975i	0.332504	−	0.332504i
$790$	0.820863	−	2.16452i	0.0292050	−	0.0770103i
$791$	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
$795$	−13.6456	+	6.14162i	−0.483961	+	0.217821i
$796$	−3.97372	+	6.88269i	−0.140845	+	0.243950i
$797$	13.7768	+	7.95404i	0.487999	+	0.281747i	0.723744	−	0.690068i	$-0.242420\pi$
$797$	13.7768	+	7.95404i	0.487999	+	0.281747i	−0.235745	+	0.971815i	$0.575753\pi$
$798$	−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
$805$	−0.621320	−	3.82282i	−0.0218987	−	0.134737i
$806$	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	$0.726715\pi$
$810$	−38.3742	+	6.23694i	−1.34833	+	0.219144i
$811$	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
$815$	41.8017	−	6.79400i	1.46425	−	0.237983i
$816$	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	0.468994	−	0.883201i	$-0.344617\pi$
$823$	−1.76097	−	1.01669i	−0.0613834	−	0.0354397i	−0.530378	+	0.847762i	$0.677950\pi$
$824$	2.36603	−	4.09808i	0.0824244	−	0.142763i
$825$	36.6633	+	18.3092i	1.27645	+	0.637444i
$826$	−2.19615	−	3.80385i	−0.0764139	−	0.132353i
$827$		−	11.5539i		−	0.401770i	−0.979615	−	0.200885i	$-0.935618\pi$
$827$		−	11.5539i		−	0.401770i	0.979615	−	0.200885i	$-0.0643818\pi$
$828$	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	$0.684822\pi$
$830$	42.0754	+	15.9565i	1.46046	+	0.553857i
$831$	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
$835$	13.4853	−	35.5593i	0.466678	−	1.23058i
$836$	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	$0.826366\pi$
$840$	−1.05063	+	1.45843i	−0.0362503	+	0.0503207i
$841$	−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
$850$	−2.73980	−	2.42713i	−0.0939745	−	0.0832497i
$851$	−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	−0.918788	−	0.394750i	$-0.870831\pi$
$853$	−30.2669	+	17.4746i	−1.03632	+	0.598319i	−0.117530	+	0.993069i	$0.537498\pi$
$854$	−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	−0.625351	−	0.780344i	$-0.715044\pi$
$857$	−7.67664	+	4.43211i	−0.262229	+	0.151398i	0.363122	+	0.931742i	$0.381711\pi$
$858$	−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	$0.291743\pi$
$860$	34.9468	−	5.67987i	1.19168	−	0.193682i
$861$	−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	$0.0714050\pi$
$863$			13.0697i			0.444898i	−0.974944	+	0.222449i	$0.928595\pi$
$864$	−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
$870$	4.86108	−	48.1197i	0.164806	−	1.63141i
$871$	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
$875$	8.47241	+	5.35716i	0.286420	+	0.181105i
$876$	24.5885	+	6.58846i	0.830767	+	0.222603i
$877$	−4.09034	−	2.36156i	−0.138121	−	0.0797441i	0.429347	−	0.903139i	$-0.358744\pi$
$877$	−4.09034	−	2.36156i	−0.138121	−	0.0797441i	−0.567468	+	0.823395i	$0.692077\pi$
$878$	−15.5935	−	9.00292i	−0.526256	−	0.303834i
$879$	14.8301	+	3.97372i	0.500208	+	0.134030i
$880$	44.1662	+	16.7494i	1.48884	+	0.564621i
$881$	−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	$0.0962126\pi$
$883$			17.6913i			0.595359i	−0.954666	+	0.297679i	$0.903787\pi$
$884$	0.803848	+	1.39230i	0.0270363	+	0.0468283i
$885$	9.77176	+	0.987148i	0.328474	+	0.0331826i
$886$	−13.4282	+	23.2583i	−0.451129	+	0.781379i
$887$	−24.4070	−	14.0914i	−0.819506	−	0.473142i	0.0307403	−	0.999527i	$-0.490214\pi$
$887$	−24.4070	−	14.0914i	−0.819506	−	0.473142i	−0.850246	+	0.526386i	$0.823547\pi$
$888$	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
$895$	−8.82036	−	54.2694i	−0.294832	−	1.81402i
$896$	−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
$900$	8.22792	+	24.6435i	0.274264	+	0.821449i
$901$	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
$905$	3.03624	+	18.6812i	0.100928	+	0.620983i
$906$	−73.0070	−	19.5622i	−2.42550	−	0.649910i
$907$	43.0506	−	24.8553i	1.42947	−	0.825305i	0.432392	−	0.901686i	$-0.357670\pi$
$907$	43.0506	−	24.8553i	1.42947	−	0.825305i	0.997079	+	0.0763808i	$0.0243365\pi$
$908$		−	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
$915$	24.1327	−	33.4997i	0.797803	−	1.10746i
$916$	−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	$0.419464\pi$
$920$	2.09077	+	0.792893i	0.0689307	+	0.0261409i
$921$	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
$925$	−6.71807	−	20.1213i	−0.220889	−	0.661585i
$926$	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	$0.815235\pi$
$930$	−18.6403	+	8.38961i	−0.611239	+	0.275106i
$931$	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	$0.0727187\pi$
$937$			13.8647i			0.452941i	−0.974018	+	0.226471i	$0.927281\pi$
$938$	−7.70882	+	4.45069i	−0.251702	+	0.145320i
$939$	−6.80385	+	6.80385i	−0.222035	+	0.222035i
$940$	−16.7491	+	2.72222i	−0.546295	+	0.0887889i
$941$	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
$945$	−10.3645	−	1.04703i	−0.337158	−	0.0340598i
$946$	83.5692			2.71707
$947$	2.00120	−	1.15539i	0.0650303	−	0.0375453i	−0.467132	−	0.884187i	$-0.654713\pi$
$947$	2.00120	−	1.15539i	0.0650303	−	0.0375453i	0.532163	+	0.846642i	$0.321379\pi$
$948$	1.55291	−	0.416102i	0.0504363	−	0.0135144i
$949$	10.3923	−	18.0000i	0.337348	−	0.584305i
$950$	−17.4990	+	19.7533i	−0.567743	+	0.640883i
$951$	−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	$0.204671\pi$
$953$			37.0197i			1.19919i	−0.800305	+	0.599594i	$0.795329\pi$
$954$	−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
$960$	9.11149	+	20.2442i	0.294072	+	0.653378i
$961$	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
$965$	−16.4388	+	43.3474i	−0.529185	+	1.39540i
$966$	4.09808	−	4.09808i	0.131853	−	0.131853i
$967$	30.0588	+	17.3545i	0.966627	+	0.558082i	0.898206	−	0.439574i	$-0.144871\pi$
$967$	30.0588	+	17.3545i	0.966627	+	0.558082i	0.0684208	+	0.997657i	$0.478204\pi$
$968$	5.10703	+	2.94855i	0.164146	+	0.0947698i
$969$	0.464102	+	1.73205i	0.0149091	+	0.0556415i
$970$	−41.5152	−	15.7440i	−1.33297	−	0.505510i
$971$	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
$975$	21.1745	−	1.28138i	0.678126	−	0.0410369i
$976$	23.7942	−	41.2128i	0.761635	−	1.31919i
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	0.699778	−	0.714360i	$-0.253282\pi$
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	−0.268765	+	0.963206i	$0.586615\pi$
$978$	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	−0.905537	−	0.424266i	$-0.860532\pi$
$983$	−31.0669	+	17.9365i	−0.990881	+	0.572085i	−0.0853431	+	0.996352i	$0.527199\pi$
$984$	3.69615	+	0.990381i	0.117829	+	0.0315722i
$985$	−45.9834	+	7.47366i	−1.46515	+	0.238131i
$986$	−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
$990$	9.83783	+	60.5296i	0.312667	+	1.92376i
$991$	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
$995$	−1.64597	−	10.1272i	−0.0521807	−	0.321054i
$996$	8.08846	+	30.1865i	0.256293	+	0.956497i
$997$	−13.1440	+	7.58871i	−0.416275	+	0.240337i	−0.693483	−	0.720473i	$-0.743925\pi$
$997$	−13.1440	+	7.58871i	−0.416275	+	0.240337i	0.277207	+	0.960810i	$0.410591\pi$
$998$		−	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.4.1	✓	8
3.2	odd	2		135.2.j.a.64.4		8
4.3	odd	2		720.2.by.d.49.1		8
5.2	odd	4		225.2.e.d.76.1		8
5.3	odd	4		225.2.e.d.76.4		8
5.4	even	2	inner	45.2.j.a.4.4	yes	8
9.2	odd	6		135.2.j.a.19.1		8
9.4	even	3		405.2.b.d.244.1		4
9.5	odd	6		405.2.b.c.244.4		4
9.7	even	3	inner	45.2.j.a.34.4	yes	8
12.11	even	2		2160.2.by.c.1009.2		8
15.2	even	4		675.2.e.d.226.4		8
15.8	even	4		675.2.e.d.226.1		8
15.14	odd	2		135.2.j.a.64.1		8
20.19	odd	2		720.2.by.d.49.4		8
36.7	odd	6		720.2.by.d.529.4		8
36.11	even	6		2160.2.by.c.289.4		8
45.2	even	12		675.2.e.d.451.4		8
45.4	even	6		405.2.b.d.244.4		4
45.7	odd	12		225.2.e.d.151.1		8
45.13	odd	12		2025.2.a.t.1.1		4
45.14	odd	6		405.2.b.c.244.1		4
45.22	odd	12		2025.2.a.t.1.4		4
45.23	even	12		2025.2.a.r.1.4		4
45.29	odd	6		135.2.j.a.19.4		8
45.32	even	12		2025.2.a.r.1.1		4
45.34	even	6	inner	45.2.j.a.34.1	yes	8
45.38	even	12		675.2.e.d.451.1		8
45.43	odd	12		225.2.e.d.151.4		8
60.59	even	2		2160.2.by.c.1009.4		8
180.79	odd	6		720.2.by.d.529.1		8
180.119	even	6		2160.2.by.c.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	1.1	even	1	trivial
45.2.j.a.4.4	yes	8	5.4	even	2	inner
45.2.j.a.34.1	yes	8	45.34	even	6	inner
45.2.j.a.34.4	yes	8	9.7	even	3	inner
135.2.j.a.19.1		8	9.2	odd	6
135.2.j.a.19.4		8	45.29	odd	6
135.2.j.a.64.1		8	15.14	odd	2
135.2.j.a.64.4		8	3.2	odd	2
225.2.e.d.76.1		8	5.2	odd	4
225.2.e.d.76.4		8	5.3	odd	4
225.2.e.d.151.1		8	45.7	odd	12
225.2.e.d.151.4		8	45.43	odd	12
405.2.b.c.244.1		4	45.14	odd	6
405.2.b.c.244.4		4	9.5	odd	6
405.2.b.d.244.1		4	9.4	even	3
405.2.b.d.244.4		4	45.4	even	6
675.2.e.d.226.1		8	15.8	even	4
675.2.e.d.226.4		8	15.2	even	4
675.2.e.d.451.1		8	45.38	even	12
675.2.e.d.451.4		8	45.2	even	12
720.2.by.d.49.1		8	4.3	odd	2
720.2.by.d.49.4		8	20.19	odd	2
720.2.by.d.529.1		8	180.79	odd	6
720.2.by.d.529.4		8	36.7	odd	6
2025.2.a.r.1.1		4	45.32	even	12
2025.2.a.r.1.4		4	45.23	even	12
2025.2.a.t.1.1		4	45.13	odd	12
2025.2.a.t.1.4		4	45.22	odd	12
2160.2.by.c.289.2		8	180.119	even	6
2160.2.by.c.289.4		8	36.11	even	6
2160.2.by.c.1009.2		8	12.11	even	2
2160.2.by.c.1009.4		8	60.59	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} +(0.358719 + 2.20711i) 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} +(1.58957 + 3.53175i) q^{15} +(2.23205 + 3.86603i) q^{16} -0.378937i q^{17} +(-2.89778 + 5.01910i) q^{18} -2.73205 q^{19} +(3.62132 + 1.37333i) 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} +(-4.74264 + 1.58346i) q^{25} +4.73205 q^{26} +(3.67423 - 3.67423i) q^{27} +1.55291i q^{28} +(3.23205 + 5.59808i) q^{29} +(-6.07081 - 4.37333i) 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} +(1.14248 - 0.185687i) 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} +(6.40508 - 7.23023i) 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} +(6.67423 + 0.674235i) q^{60} +(-5.33013 - 9.23205i) q^{61} +5.27792i q^{62} +(-1.34486 + 2.32937i) q^{63} +5.73205 q^{64} +(1.94218 - 5.12132i) 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} +(3.62132 + 1.37333i) q^{70} +3.80385 q^{71} +(-0.776457 - 1.34486i) q^{72} +8.48528i q^{73} +(-4.09808 - 7.09808i) q^{74} +(-7.22474 + 4.77526i) 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} +(0.836355 - 0.135932i) q^{85} +(-8.83013 + 15.2942i) q^{86} +(7.91688 + 7.91688i) q^{87} +(-2.12132 + 1.22474i) q^{88} +7.39230 q^{89} +(-12.1172 - 4.59526i) q^{90} +2.19615 q^{91} +(2.89778 - 1.67303i) q^{92} +(1.22474 - 4.57081i) q^{93} +(4.23205 - 7.33013i) q^{94} +(-0.980040 - 6.02993i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40}+ \cdots - 36 q^{99}+O(q^{100}) \) 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

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