LMFDB - Embedded newform 666.2.be.c.341.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.be (of order $12$, degree $4$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			341.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	666.341
Dual form			666.2.be.c.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.448288 + 1.67303i) q^{5} +(0.633975 - 1.09808i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.448288 + 1.67303i) q^{5} +(0.633975 - 1.09808i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.73205 q^{10} +2.44949 q^{11} +(0.366025 - 0.0980762i) q^{13} +(-0.896575 - 0.896575i) q^{14} +(0.500000 + 0.866025i) q^{16} +(6.24384 + 1.67303i) q^{17} +(-5.09808 + 1.36603i) q^{19} +(0.448288 - 1.67303i) q^{20} +(0.633975 - 2.36603i) q^{22} +(2.44949 - 2.44949i) q^{23} +(1.73205 - 1.00000i) q^{25} -0.378937i q^{26} +(-1.09808 + 0.633975i) q^{28} +(6.12372 + 6.12372i) q^{29} +(5.73205 - 5.73205i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.23205 - 5.59808i) q^{34} +(2.12132 + 0.568406i) q^{35} +(-4.69615 - 3.86603i) q^{37} +5.27792i q^{38} +(-1.50000 - 0.866025i) q^{40} +(2.89778 - 5.01910i) q^{41} +(0.267949 + 0.267949i) q^{43} +(-2.12132 - 1.22474i) q^{44} +(-1.73205 - 3.00000i) q^{46} +4.24264i q^{47} +(2.69615 + 4.66987i) q^{49} +(-0.517638 - 1.93185i) q^{50} +(-0.366025 - 0.0980762i) q^{52} +(-5.22715 + 3.01790i) q^{53} +(1.09808 + 4.09808i) q^{55} +(0.328169 + 1.22474i) q^{56} +(7.50000 - 4.33013i) q^{58} +(-5.79555 - 1.55291i) q^{59} +(-2.86603 - 10.6962i) q^{61} +(-4.05317 - 7.02030i) q^{62} -1.00000i q^{64} +(0.328169 + 0.568406i) q^{65} +(-3.63397 - 2.09808i) q^{67} +(-4.57081 - 4.57081i) q^{68} +(1.09808 - 1.90192i) q^{70} +(2.12132 + 1.22474i) q^{71} +6.39230i q^{73} +(-4.94975 + 3.53553i) q^{74} +(5.09808 + 1.36603i) q^{76} +(1.55291 - 2.68973i) q^{77} +(-3.36603 + 0.901924i) q^{79} +(-1.22474 + 1.22474i) q^{80} +(-4.09808 - 4.09808i) q^{82} +(-3.10583 + 1.79315i) q^{83} +11.1962i q^{85} +(0.328169 - 0.189469i) q^{86} +(-1.73205 + 1.73205i) q^{88} +(-1.10463 + 4.12252i) q^{89} +(0.124356 - 0.464102i) q^{91} +(-3.34607 + 0.896575i) q^{92} +(4.09808 + 1.09808i) q^{94} +(-4.57081 - 7.91688i) q^{95} +(0.366025 + 0.366025i) q^{97} +(5.20857 - 1.39563i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{7}+O(q^{10}) $ 8 * q + 12 * q^7	$ 8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100}) $ 8 * q + 12 * q^7 - 4 * q^13 + 4 * q^16 - 20 * q^19 + 12 * q^22 + 12 * q^28 + 32 * q^31 + 12 * q^34 + 4 * q^37 - 12 * q^40 + 16 * q^43 - 20 * q^49 + 4 * q^52 - 12 * q^55 + 60 * q^58 - 16 * q^61 - 36 * q^67 - 12 * q^70 + 20 * q^76 - 20 * q^79 - 12 * q^82 - 96 * q^91 + 12 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.448288	+	1.67303i	0.200480	+	0.748203i	0.990780	+	0.135482i	$0.0432583\pi$
$5$	0.448288	+	1.67303i	0.200480	+	0.748203i	−0.790299	+	0.612721i	$0.790075\pi$
$6$		0			0
$7$	0.633975	−	1.09808i	0.239620	−	0.415034i	−0.720985	−	0.692950i	$-0.756311\pi$
$7$	0.633975	−	1.09808i	0.239620	−	0.415034i	0.960605	+	0.277916i	$0.0896439\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.73205			0.547723
$11$	2.44949			0.738549			0.369274	−	0.929320i	$-0.379606\pi$
$11$	2.44949			0.738549			0.369274	+	0.929320i	$0.379606\pi$
$12$		0			0
$13$	0.366025	−	0.0980762i	0.101517	−	0.0272014i	−0.207703	−	0.978192i	$-0.566599\pi$
$13$	0.366025	−	0.0980762i	0.101517	−	0.0272014i	0.309220	+	0.950991i	$0.399932\pi$
$14$	−0.896575	−	0.896575i	−0.239620	−	0.239620i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	6.24384	+	1.67303i	1.51435	+	0.405770i	0.917879	−	0.396861i	$-0.129901\pi$
$17$	6.24384	+	1.67303i	1.51435	+	0.405770i	0.596476	+	0.802631i	$0.296567\pi$
$18$		0			0
$19$	−5.09808	+	1.36603i	−1.16958	+	0.313388i	−0.790785	−	0.612093i	$-0.790328\pi$
$19$	−5.09808	+	1.36603i	−1.16958	+	0.313388i	−0.378793	+	0.925481i	$0.623661\pi$
$20$	0.448288	−	1.67303i	0.100240	−	0.374101i
$21$		0			0
$22$	0.633975	−	2.36603i	0.135164	−	0.504438i
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	−0.404004	−	0.914757i	$-0.632382\pi$
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	0.914757	+	0.404004i	$0.132382\pi$
$24$		0			0
$25$	1.73205	−	1.00000i	0.346410	−	0.200000i
$26$		−	0.378937i		−	0.0743157i
$27$		0			0
$28$	−1.09808	+	0.633975i	−0.207517	+	0.119810i
$29$	6.12372	+	6.12372i	1.13715	+	1.13715i	0.988959	+	0.148188i	$0.0473440\pi$
$29$	6.12372	+	6.12372i	1.13715	+	1.13715i	0.148188	+	0.988959i	$0.452656\pi$
$30$		0			0
$31$	5.73205	−	5.73205i	1.02951	−	1.02951i	0.0299555	−	0.999551i	$-0.490463\pi$
$31$	5.73205	−	5.73205i	1.02951	−	1.02951i	0.999551	−	0.0299555i	$-0.00953655\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	3.23205	−	5.59808i	0.554292	−	0.960062i
$35$	2.12132	+	0.568406i	0.358569	+	0.0960782i
$36$		0			0
$37$	−4.69615	−	3.86603i	−0.772043	−	0.635571i
$37$	−4.69615	−	3.86603i	−0.772043	−	0.635571i
$38$			5.27792i			0.856191i
$39$		0			0
$40$	−1.50000	−	0.866025i	−0.237171	−	0.136931i
$41$	2.89778	−	5.01910i	0.452557	−	0.783851i	−0.545987	−	0.837793i	$-0.683845\pi$
$41$	2.89778	−	5.01910i	0.452557	−	0.783851i	0.998544	+	0.0539421i	$0.0171786\pi$
$42$		0			0
$43$	0.267949	+	0.267949i	0.0408619	+	0.0408619i	0.727242	−	0.686381i	$-0.240802\pi$
$43$	0.267949	+	0.267949i	0.0408619	+	0.0408619i	−0.686381	+	0.727242i	$0.740802\pi$
$44$	−2.12132	−	1.22474i	−0.319801	−	0.184637i
$45$		0			0
$46$	−1.73205	−	3.00000i	−0.255377	−	0.442326i
$47$			4.24264i			0.618853i	0.950923	+	0.309426i	$0.100137\pi$
$47$			4.24264i			0.618853i	−0.950923	+	0.309426i	$0.899863\pi$
$48$		0			0
$49$	2.69615	+	4.66987i	0.385165	+	0.667125i
$50$	−0.517638	−	1.93185i	−0.0732051	−	0.273205i
$51$		0			0
$52$	−0.366025	−	0.0980762i	−0.0507586	−	0.0136007i
$53$	−5.22715	+	3.01790i	−0.718004	+	0.414540i	−0.814018	−	0.580840i	$-0.802724\pi$
$53$	−5.22715	+	3.01790i	−0.718004	+	0.414540i	0.0960135	+	0.995380i	$0.469391\pi$
$54$		0			0
$55$	1.09808	+	4.09808i	0.148065	+	0.552584i
$56$	0.328169	+	1.22474i	0.0438535	+	0.163663i
$57$		0			0
$58$	7.50000	−	4.33013i	0.984798	−	0.568574i
$59$	−5.79555	−	1.55291i	−0.754517	−	0.202172i	−0.138996	−	0.990293i	$-0.544388\pi$
$59$	−5.79555	−	1.55291i	−0.754517	−	0.202172i	−0.615521	+	0.788121i	$0.711054\pi$
$60$		0			0
$61$	−2.86603	−	10.6962i	−0.366957	−	1.36950i	−0.864748	−	0.502205i	$-0.832522\pi$
$61$	−2.86603	−	10.6962i	−0.366957	−	1.36950i	0.497792	−	0.867297i	$-0.334144\pi$
$62$	−4.05317	−	7.02030i	−0.514753	−	0.891579i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.328169	+	0.568406i	0.0407044	+	0.0705021i
$66$		0			0
$67$	−3.63397	−	2.09808i	−0.443961	−	0.256321i	0.261316	−	0.965253i	$-0.415844\pi$
$67$	−3.63397	−	2.09808i	−0.443961	−	0.256321i	−0.705276	+	0.708933i	$0.749177\pi$
$68$	−4.57081	−	4.57081i	−0.554292	−	0.554292i
$69$		0			0
$70$	1.09808	−	1.90192i	0.131245	−	0.227323i
$71$	2.12132	+	1.22474i	0.251754	+	0.145350i	0.620567	−	0.784153i	$-0.286902\pi$
$71$	2.12132	+	1.22474i	0.251754	+	0.145350i	−0.368813	+	0.929504i	$0.620236\pi$
$72$		0			0
$73$			6.39230i			0.748163i	0.927396	+	0.374081i	$0.122042\pi$
$73$			6.39230i			0.748163i	−0.927396	+	0.374081i	$0.877958\pi$
$74$	−4.94975	+	3.53553i	−0.575396	+	0.410997i
$75$		0			0
$76$	5.09808	+	1.36603i	0.584789	+	0.156694i
$77$	1.55291	−	2.68973i	0.176971	−	0.306523i
$78$		0			0
$79$	−3.36603	+	0.901924i	−0.378707	+	0.101474i	−0.443151	−	0.896447i	$-0.646139\pi$
$79$	−3.36603	+	0.901924i	−0.378707	+	0.101474i	0.0644435	+	0.997921i	$0.479473\pi$
$80$	−1.22474	+	1.22474i	−0.136931	+	0.136931i
$81$		0			0
$82$	−4.09808	−	4.09808i	−0.452557	−	0.452557i
$83$	−3.10583	+	1.79315i	−0.340909	+	0.196824i	−0.660674	−	0.750673i	$-0.729729\pi$
$83$	−3.10583	+	1.79315i	−0.340909	+	0.196824i	0.319765	+	0.947497i	$0.396396\pi$
$84$		0			0
$85$			11.1962i			1.21439i
$86$	0.328169	−	0.189469i	0.0353874	−	0.0204309i
$87$		0			0
$88$	−1.73205	+	1.73205i	−0.184637	+	0.184637i
$89$	−1.10463	+	4.12252i	−0.117090	+	0.436986i	−0.999435	−	0.0336174i	$-0.989297\pi$
$89$	−1.10463	+	4.12252i	−0.117090	+	0.436986i	0.882345	+	0.470604i	$0.155964\pi$
$90$		0			0
$91$	0.124356	−	0.464102i	0.0130360	−	0.0486511i
$92$	−3.34607	+	0.896575i	−0.348851	+	0.0934745i
$93$		0			0
$94$	4.09808	+	1.09808i	0.422684	+	0.113258i
$95$	−4.57081	−	7.91688i	−0.468955	−	0.812254i
$96$		0			0
$97$	0.366025	+	0.366025i	0.0371642	+	0.0371642i	0.725445	−	0.688280i	$-0.241634\pi$
$97$	0.366025	+	0.366025i	0.0371642	+	0.0371642i	−0.688280	+	0.725445i	$0.741634\pi$
$98$	5.20857	−	1.39563i	0.526145	−	0.140980i
$99$		0			0
$100$	−2.00000			−0.200000
$101$	−2.20925			−0.219829			−0.109914	−	0.993941i	$-0.535058\pi$
$101$	−2.20925			−0.219829			−0.109914	+	0.993941i	$0.535058\pi$
$102$		0			0
$103$	−3.73205	+	3.73205i	−0.367730	+	0.367730i	−0.866649	−	0.498919i	$-0.833731\pi$
$103$	−3.73205	+	3.73205i	−0.367730	+	0.367730i	0.498919	+	0.866649i	$0.333731\pi$
$104$	−0.189469	+	0.328169i	−0.0185789	+	0.0321797i
$105$		0			0
$106$	1.56218	+	5.83013i	0.151732	+	0.566272i
$107$	−9.46979	−	5.46739i	−0.915479	−	0.528552i	−0.0332891	−	0.999446i	$-0.510598\pi$
$107$	−9.46979	−	5.46739i	−0.915479	−	0.528552i	−0.882190	+	0.470894i	$0.843932\pi$
$108$		0			0
$109$	−0.794229	+	2.96410i	−0.0760733	+	0.283909i	−0.993475	−	0.114054i	$-0.963616\pi$
$109$	−0.794229	+	2.96410i	−0.0760733	+	0.283909i	0.917401	+	0.397964i	$0.130283\pi$
$110$	4.24264			0.404520
$111$		0			0
$112$	1.26795			0.119810
$113$	−2.03339	+	7.58871i	−0.191285	+	0.713885i	0.801912	+	0.597442i	$0.203816\pi$
$113$	−2.03339	+	7.58871i	−0.191285	+	0.713885i	−0.993197	+	0.116444i	$0.962851\pi$
$114$		0			0
$115$	5.19615	+	3.00000i	0.484544	+	0.279751i
$116$	−2.24144	−	8.36516i	−0.208112	−	0.776686i
$117$		0			0
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	5.79555	−	5.79555i	0.531278	−	0.531278i
$120$		0			0
$121$	−5.00000			−0.454545
$122$	−11.0735			−1.00255
$123$		0			0
$124$	−7.83013	+	2.09808i	−0.703166	+	0.188413i
$125$	8.57321	+	8.57321i	0.766812	+	0.766812i
$126$		0			0
$127$	−1.19615	−	2.07180i	−0.106141	−	0.183842i	0.808063	−	0.589097i	$-0.200516\pi$
$127$	−1.19615	−	2.07180i	−0.106141	−	0.183842i	−0.914204	+	0.405254i	$0.867183\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	0.633975	−	0.169873i	0.0556033	−	0.0148988i
$131$	2.03339	−	7.58871i	0.177658	−	0.663028i	−0.818426	−	0.574612i	$-0.805153\pi$
$131$	2.03339	−	7.58871i	0.177658	−	0.663028i	0.996084	−	0.0884160i	$-0.0281805\pi$
$132$		0			0
$133$	−1.73205	+	6.46410i	−0.150188	+	0.560509i
$134$	−2.96713	+	2.96713i	−0.256321	+	0.256321i
$135$		0			0
$136$	−5.59808	+	3.23205i	−0.480031	+	0.277146i
$137$			16.0740i			1.37329i	0.726991	+	0.686647i	$0.240918\pi$
$137$			16.0740i			1.37329i	−0.726991	+	0.686647i	$0.759082\pi$
$138$		0			0
$139$	0.339746	−	0.196152i	0.0288169	−	0.0166374i	−0.485522	−	0.874224i	$-0.661371\pi$
$139$	0.339746	−	0.196152i	0.0288169	−	0.0166374i	0.514339	+	0.857587i	$0.328037\pi$
$140$	−1.55291	−	1.55291i	−0.131245	−	0.131245i
$141$		0			0
$142$	1.73205	−	1.73205i	0.145350	−	0.145350i
$143$	0.896575	−	0.240237i	0.0749754	−	0.0200896i
$144$		0			0
$145$	−7.50000	+	12.9904i	−0.622841	+	1.07879i
$146$	6.17449	+	1.65445i	0.511005	+	0.136923i
$147$		0			0
$148$	2.13397	+	5.69615i	0.175412	+	0.468221i
$149$			15.5935i			1.27747i	0.769427	+	0.638735i	$0.220542\pi$
$149$			15.5935i			1.27747i	−0.769427	+	0.638735i	$0.779458\pi$
$150$		0			0
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.965064	−	0.262016i	$-0.0843873\pi$
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.255619	+	0.966778i	$0.417721\pi$
$152$	2.63896	−	4.57081i	0.214048	−	0.370742i
$153$		0			0
$154$	−2.19615	−	2.19615i	−0.176971	−	0.176971i
$155$	12.1595	+	7.02030i	0.976676	+	0.563884i
$156$		0			0
$157$	−3.06218	−	5.30385i	−0.244388	−	0.423293i	0.717571	−	0.696485i	$-0.245254\pi$
$157$	−3.06218	−	5.30385i	−0.244388	−	0.423293i	−0.961959	+	0.273192i	$0.911921\pi$
$158$			3.48477i			0.277233i
$159$		0			0
$160$	0.866025	+	1.50000i	0.0684653	+	0.118585i
$161$	−1.13681	−	4.24264i	−0.0895933	−	0.334367i
$162$		0			0
$163$	−0.366025	−	0.0980762i	−0.0286693	−	0.00768192i	0.244456	−	0.969660i	$-0.421391\pi$
$163$	−0.366025	−	0.0980762i	−0.0286693	−	0.00768192i	−0.273125	+	0.961978i	$0.588057\pi$
$164$	−5.01910	+	2.89778i	−0.391926	+	0.226278i
$165$		0			0
$166$	0.928203	+	3.46410i	0.0720425	+	0.268866i
$167$	−6.45189	−	24.0788i	−0.499263	−	1.86327i	−0.504712	−	0.863288i	$-0.668401\pi$
$167$	−6.45189	−	24.0788i	−0.499263	−	1.86327i	0.00544916	−	0.999985i	$-0.498265\pi$
$168$		0			0
$169$	−11.1340	+	6.42820i	−0.856460	+	0.494477i
$170$	10.8147	+	2.89778i	0.829446	+	0.222249i
$171$		0			0
$172$	−0.0980762	−	0.366025i	−0.00747824	−	0.0279092i
$173$	−8.03699	−	13.9205i	−0.611041	−	1.05835i	−0.991065	−	0.133378i	$-0.957418\pi$
$173$	−8.03699	−	13.9205i	−0.611041	−	1.05835i	0.380024	−	0.924977i	$-0.375916\pi$
$174$		0			0
$175$		−	2.53590i		−	0.191696i
$176$	1.22474	+	2.12132i	0.0923186	+	0.159901i
$177$		0			0
$178$	3.69615	+	2.13397i	0.277038	+	0.159948i
$179$	−15.8338	−	15.8338i	−1.18347	−	1.18347i	−0.978839	−	0.204631i	$-0.934401\pi$
$179$	−15.8338	−	15.8338i	−1.18347	−	1.18347i	−0.204631	−	0.978839i	$-0.565599\pi$
$180$		0			0
$181$	−8.59808	+	14.8923i	−0.639090	+	1.10694i	0.346543	+	0.938034i	$0.387356\pi$
$181$	−8.59808	+	14.8923i	−0.639090	+	1.10694i	−0.985633	+	0.168902i	$0.945978\pi$
$182$	−0.416102	−	0.240237i	−0.0308435	−	0.0178075i
$183$		0			0
$184$			3.46410i			0.255377i
$185$	4.36276	−	9.58991i	0.320756	−	0.705064i
$186$		0			0
$187$	15.2942	+	4.09808i	1.11842	+	0.299681i
$188$	2.12132	−	3.67423i	0.154713	−	0.267971i
$189$		0			0
$190$	−8.83013	+	2.36603i	−0.640605	+	0.171650i
$191$	−9.14162	+	9.14162i	−0.661464	+	0.661464i	−0.955725	−	0.294261i	$-0.904927\pi$
$191$	−9.14162	+	9.14162i	−0.661464	+	0.661464i	0.294261	+	0.955725i	$0.404927\pi$
$192$		0			0
$193$	−2.90192	−	2.90192i	−0.208885	−	0.208885i	0.594908	−	0.803793i	$-0.297188\pi$
$193$	−2.90192	−	2.90192i	−0.208885	−	0.208885i	−0.803793	+	0.594908i	$0.797188\pi$
$194$	0.448288	−	0.258819i	0.0321852	−	0.0185821i
$195$		0			0
$196$		−	5.39230i		−	0.385165i
$197$	9.67784	−	5.58750i	0.689518	−	0.398093i	−0.113914	−	0.993491i	$-0.536339\pi$
$197$	9.67784	−	5.58750i	0.689518	−	0.398093i	0.803431	+	0.595397i	$0.203005\pi$
$198$		0			0
$199$	19.5885	−	19.5885i	1.38859	−	1.38859i	0.560297	−	0.828291i	$-0.310687\pi$
$199$	19.5885	−	19.5885i	1.38859	−	1.38859i	0.828291	−	0.560297i	$-0.189313\pi$
$200$	−0.517638	+	1.93185i	−0.0366025	+	0.136603i
$201$		0			0
$202$	−0.571797	+	2.13397i	−0.0402315	+	0.150146i
$203$	10.6066	−	2.84203i	0.744438	−	0.199471i
$204$		0			0
$205$	9.69615	+	2.59808i	0.677209	+	0.181458i
$206$	2.63896	+	4.57081i	0.183865	+	0.318463i
$207$		0			0
$208$	0.267949	+	0.267949i	0.0185789	+	0.0185789i
$209$	−12.4877	+	3.34607i	−0.863791	+	0.231452i
$210$		0			0
$211$	−17.8038			−1.22567			−0.612834	−	0.790212i	$-0.709970\pi$
$211$	−17.8038			−1.22567			−0.612834	+	0.790212i	$0.709970\pi$
$212$	6.03579			0.414540
$213$		0			0
$214$	−7.73205	+	7.73205i	−0.528552	+	0.528552i
$215$	−0.328169	+	0.568406i	−0.0223810	+	0.0387650i
$216$		0			0
$217$	−2.66025	−	9.92820i	−0.180590	−	0.673970i
$218$	2.65754	+	1.53433i	0.179991	+	0.103918i
$219$		0			0
$220$	1.09808	−	4.09808i	0.0740323	−	0.276292i
$221$	2.44949			0.164771
$222$		0			0
$223$	18.3923			1.23164			0.615820	−	0.787887i	$-0.288825\pi$
$223$	18.3923			1.23164			0.615820	+	0.787887i	$0.288825\pi$
$224$	0.328169	−	1.22474i	0.0219267	−	0.0818317i
$225$		0			0
$226$	6.80385	+	3.92820i	0.452585	+	0.261300i
$227$	5.22715	+	19.5080i	0.346938	+	1.29479i	0.890332	+	0.455312i	$0.150472\pi$
$227$	5.22715	+	19.5080i	0.346938	+	1.29479i	−0.543394	+	0.839478i	$0.682861\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$	4.24264	−	4.24264i	0.279751	−	0.279751i
$231$		0			0
$232$	−8.66025			−0.568574
$233$	−9.38186			−0.614626			−0.307313	−	0.951609i	$-0.599430\pi$
$233$	−9.38186			−0.614626			−0.307313	+	0.951609i	$0.599430\pi$
$234$		0			0
$235$	−7.09808	+	1.90192i	−0.463027	+	0.124068i
$236$	4.24264	+	4.24264i	0.276172	+	0.276172i
$237$		0			0
$238$	−4.09808	−	7.09808i	−0.265639	−	0.460100i
$239$	−22.8541	−	6.12372i	−1.47831	−	0.396111i	−0.572535	−	0.819880i	$-0.694040\pi$
$239$	−22.8541	−	6.12372i	−1.47831	−	0.396111i	−0.905770	+	0.423769i	$0.860707\pi$
$240$		0			0
$241$	−13.2942	+	3.56218i	−0.856357	+	0.229460i	−0.660179	−	0.751108i	$-0.729520\pi$
$241$	−13.2942	+	3.56218i	−0.856357	+	0.229460i	−0.196178	+	0.980568i	$0.562853\pi$
$242$	−1.29410	+	4.82963i	−0.0831876	+	0.310460i
$243$		0			0
$244$	−2.86603	+	10.6962i	−0.183478	+	0.684751i
$245$	−6.60420	+	6.60420i	−0.421927	+	0.421927i
$246$		0			0
$247$	−1.73205	+	1.00000i	−0.110208	+	0.0636285i
$248$			8.10634i			0.514753i
$249$		0			0
$250$	10.5000	−	6.06218i	0.664078	−	0.383406i
$251$	−5.13922	−	5.13922i	−0.324384	−	0.324384i	0.526062	−	0.850446i	$-0.323668\pi$
$251$	−5.13922	−	5.13922i	−0.324384	−	0.324384i	−0.850446	+	0.526062i	$0.823668\pi$
$252$		0			0
$253$	6.00000	−	6.00000i	0.377217	−	0.377217i
$254$	−2.31079	+	0.619174i	−0.144992	+	0.0388504i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.91567	−	1.58510i	−0.369010	−	0.0988758i	0.0695487	−	0.997579i	$-0.477844\pi$
$257$	−5.91567	−	1.58510i	−0.369010	−	0.0988758i	−0.438558	+	0.898703i	$0.644511\pi$
$258$		0			0
$259$	−7.22243	+	2.70577i	−0.448780	+	0.168128i
$260$		−	0.656339i		−	0.0407044i
$261$		0			0
$262$	−6.80385	−	3.92820i	−0.420343	−	0.242685i
$263$	−2.20925	+	3.82654i	−0.136228	+	0.235954i	−0.926066	−	0.377361i	$-0.876831\pi$
$263$	−2.20925	+	3.82654i	−0.136228	+	0.235954i	0.789838	+	0.613316i	$0.210165\pi$
$264$		0			0
$265$	−7.39230	−	7.39230i	−0.454106	−	0.454106i
$266$	5.79555	+	3.34607i	0.355348	+	0.205160i
$267$		0			0
$268$	2.09808	+	3.63397i	0.128160	+	0.221980i
$269$		−	4.24264i		−	0.258678i	−0.991600	−	0.129339i	$-0.958714\pi$
$269$		−	4.24264i		−	0.258678i	0.991600	−	0.129339i	$-0.0412856\pi$
$270$		0			0
$271$	13.5622	+	23.4904i	0.823844	+	1.42694i	0.902800	+	0.430061i	$0.141508\pi$
$271$	13.5622	+	23.4904i	0.823844	+	1.42694i	−0.0789562	+	0.996878i	$0.525159\pi$
$272$	1.67303	+	6.24384i	0.101443	+	0.378589i
$273$		0			0
$274$	15.5263	+	4.16025i	0.937977	+	0.251330i
$275$	4.24264	−	2.44949i	0.255841	−	0.147710i
$276$		0			0
$277$	−7.06218	−	26.3564i	−0.424325	−	1.58360i	−0.765392	−	0.643564i	$-0.777455\pi$
$277$	−7.06218	−	26.3564i	−0.424325	−	1.58360i	0.341067	−	0.940039i	$-0.389212\pi$
$278$	−0.101536	−	0.378937i	−0.00608972	−	0.0227272i
$279$		0			0
$280$	−1.90192	+	1.09808i	−0.113662	+	0.0656226i
$281$	27.5450	+	7.38065i	1.64320	+	0.440293i	0.957696	−	0.287780i	$-0.0929173\pi$
$281$	27.5450	+	7.38065i	1.64320	+	0.440293i	0.685499	+	0.728073i	$0.259584\pi$
$282$		0			0
$283$	−5.22243	−	19.4904i	−0.310441	−	1.15858i	−0.928159	−	0.372183i	$-0.878609\pi$
$283$	−5.22243	−	19.4904i	−0.310441	−	1.15858i	0.617718	−	0.786400i	$-0.288057\pi$
$284$	−1.22474	−	2.12132i	−0.0726752	−	0.125877i
$285$		0			0
$286$		−	0.928203i		−	0.0548858i
$287$	−3.67423	−	6.36396i	−0.216883	−	0.375653i
$288$		0			0
$289$	21.4641	+	12.3923i	1.26259	+	0.728959i
$290$	10.6066	+	10.6066i	0.622841	+	0.622841i
$291$		0			0
$292$	3.19615	−	5.53590i	0.187041	−	0.323964i
$293$	−10.2462	−	5.91567i	−0.598592	−	0.345597i	0.169895	−	0.985462i	$-0.445657\pi$
$293$	−10.2462	−	5.91567i	−0.598592	−	0.345597i	−0.768488	+	0.639865i	$0.778990\pi$
$294$		0			0
$295$		−	10.3923i		−	0.605063i
$296$	6.05437	−	0.586988i	0.351903	−	0.0341180i
$297$		0			0
$298$	15.0622	+	4.03590i	0.872529	+	0.233793i
$299$	0.656339	−	1.13681i	0.0379571	−	0.0657435i
$300$		0			0
$301$	0.464102	−	0.124356i	0.0267504	−	0.00716774i
$302$	12.2474	−	12.2474i	0.704761	−	0.704761i
$303$		0			0
$304$	−3.73205	−	3.73205i	−0.214048	−	0.214048i
$305$	16.6102	−	9.58991i	0.951098	−	0.549117i
$306$		0			0
$307$		−	33.1244i		−	1.89051i	−0.326337	−	0.945253i	$-0.605814\pi$
$307$		−	33.1244i		−	1.89051i	0.326337	−	0.945253i	$-0.394186\pi$
$308$	−2.68973	+	1.55291i	−0.153261	+	0.0884855i
$309$		0			0
$310$	9.92820	−	9.92820i	0.563884	−	0.563884i
$311$	0.744272	−	2.77766i	0.0422038	−	0.157507i	−0.941608	−	0.336711i	$-0.890686\pi$
$311$	0.744272	−	2.77766i	0.0422038	−	0.157507i	0.983812	+	0.179204i	$0.0573522\pi$
$312$		0			0
$313$	4.52628	−	16.8923i	0.255840	−	0.954810i	−0.711781	−	0.702402i	$-0.752111\pi$
$313$	4.52628	−	16.8923i	0.255840	−	0.954810i	0.967621	−	0.252408i	$-0.0812224\pi$
$314$	−5.91567	+	1.58510i	−0.333841	+	0.0894524i
$315$		0			0
$316$	3.36603	+	0.901924i	0.189354	+	0.0507372i
$317$	7.70882	+	13.3521i	0.432971	+	0.749927i	0.997128	−	0.0757404i	$-0.0241320\pi$
$317$	7.70882	+	13.3521i	0.432971	+	0.749927i	−0.564157	+	0.825668i	$0.690799\pi$
$318$		0			0
$319$	15.0000	+	15.0000i	0.839839	+	0.839839i
$320$	1.67303	−	0.448288i	0.0935254	−	0.0250600i
$321$		0			0
$322$	−4.39230			−0.244774
$323$	−34.1170			−1.89832
$324$		0			0
$325$	0.535898	−	0.535898i	0.0297263	−	0.0297263i
$326$	−0.189469	+	0.328169i	−0.0104937	+	0.0181756i
$327$		0			0
$328$	1.50000	+	5.59808i	0.0828236	+	0.309102i
$329$	4.65874	+	2.68973i	0.256845	+	0.148289i
$330$		0			0
$331$	5.85641	−	21.8564i	0.321897	−	1.20134i	−0.595497	−	0.803357i	$-0.703045\pi$
$331$	5.85641	−	21.8564i	0.321897	−	1.20134i	0.917394	−	0.397979i	$-0.130288\pi$
$332$	3.58630			0.196824
$333$		0			0
$334$	−24.9282			−1.36401
$335$	1.88108	−	7.02030i	0.102775	−	0.383560i
$336$		0			0
$337$	−31.2846	−	18.0622i	−1.70418	−	0.983910i	−0.941424	−	0.337224i	$-0.890512\pi$
$337$	−31.2846	−	18.0622i	−1.70418	−	0.983910i	−0.762757	−	0.646685i	$-0.776155\pi$
$338$	3.32748	+	12.4183i	0.180991	+	0.675468i
$339$		0			0
$340$	5.59808	−	9.69615i	0.303598	−	0.525848i
$341$	14.0406	−	14.0406i	0.760341	−	0.760341i
$342$		0			0
$343$	15.7128			0.848412
$344$	−0.378937			−0.0204309
$345$		0			0
$346$	−15.5263	+	4.16025i	−0.834698	+	0.223657i
$347$	13.3843	+	13.3843i	0.718505	+	0.718505i	0.968299	−	0.249794i	$-0.0803630\pi$
$347$	13.3843	+	13.3843i	0.718505	+	0.718505i	−0.249794	+	0.968299i	$0.580363\pi$
$348$		0			0
$349$	−2.76795	−	4.79423i	−0.148165	−	0.256629i	0.782384	−	0.622796i	$-0.214003\pi$
$349$	−2.76795	−	4.79423i	−0.148165	−	0.256629i	−0.930549	+	0.366167i	$0.880670\pi$
$350$	−2.44949	−	0.656339i	−0.130931	−	0.0350828i
$351$		0			0
$352$	2.36603	−	0.633975i	0.126110	−	0.0337910i
$353$	−6.48408	+	24.1989i	−0.345113	+	1.28798i	0.547368	+	0.836892i	$0.315630\pi$
$353$	−6.48408	+	24.1989i	−0.345113	+	1.28798i	−0.892480	+	0.451086i	$0.851037\pi$
$354$		0			0
$355$	−1.09808	+	4.09808i	−0.0582798	+	0.217503i
$356$	3.01790	−	3.01790i	0.159948	−	0.159948i
$357$		0			0
$358$	−19.3923	+	11.1962i	−1.02492	+	0.591735i
$359$		−	3.10583i		−	0.163919i	−0.996636	−	0.0819597i	$-0.973882\pi$
$359$		−	3.10583i		−	0.163919i	0.996636	−	0.0819597i	$-0.0261179\pi$
$360$		0			0
$361$	7.66987	−	4.42820i	0.403678	−	0.233063i
$362$	12.1595	+	12.1595i	0.639090	+	0.639090i
$363$		0			0
$364$	−0.339746	+	0.339746i	−0.0178075	+	0.0178075i
$365$	−10.6945	+	2.86559i	−0.559778	+	0.149992i
$366$		0			0
$367$	14.5885	−	25.2679i	0.761511	−	1.31898i	−0.180560	−	0.983564i	$-0.557791\pi$
$367$	14.5885	−	25.2679i	0.761511	−	1.31898i	0.942071	−	0.335412i	$-0.108876\pi$
$368$	3.34607	+	0.896575i	0.174426	+	0.0467372i
$369$		0			0
$370$	−8.13397	−	6.69615i	−0.422865	−	0.348116i
$371$			7.65308i			0.397328i
$372$		0			0
$373$	−6.06218	−	3.50000i	−0.313888	−	0.181223i	0.334777	−	0.942297i	$-0.391339\pi$
$373$	−6.06218	−	3.50000i	−0.313888	−	0.181223i	−0.648665	+	0.761074i	$0.724672\pi$
$374$	7.91688	−	13.7124i	0.409372	−	0.709053i
$375$		0			0
$376$	−3.00000	−	3.00000i	−0.154713	−	0.154713i
$377$	2.84203	+	1.64085i	0.146372	+	0.0845079i
$378$		0			0
$379$	−4.56218	−	7.90192i	−0.234343	−	0.405895i	0.724738	−	0.689024i	$-0.241961\pi$
$379$	−4.56218	−	7.90192i	−0.234343	−	0.405895i	−0.959082	+	0.283130i	$0.908627\pi$
$380$			9.14162i			0.468955i
$381$		0			0
$382$	6.46410	+	11.1962i	0.330732	+	0.572845i
$383$	−4.81105	−	17.9551i	−0.245833	−	0.917461i	−0.972963	−	0.230961i	$-0.925813\pi$
$383$	−4.81105	−	17.9551i	−0.245833	−	0.917461i	0.727130	−	0.686500i	$-0.240854\pi$
$384$		0			0
$385$	5.19615	+	1.39230i	0.264820	+	0.0709584i
$386$	−3.55412	+	2.05197i	−0.180900	+	0.104443i
$387$		0			0
$388$	−0.133975	−	0.500000i	−0.00680153	−	0.0253837i
$389$	0.536220	+	2.00120i	0.0271875	+	0.101465i	0.978186	−	0.207729i	$-0.0666073\pi$
$389$	0.536220	+	2.00120i	0.0271875	+	0.101465i	−0.950999	+	0.309194i	$0.899941\pi$
$390$		0			0
$391$	19.3923	−	11.1962i	0.980711	−	0.566214i
$392$	−5.20857	−	1.39563i	−0.263072	−	0.0704900i
$393$		0			0
$394$	−2.89230	−	10.7942i	−0.145712	−	0.543805i
$395$	−3.01790	−	5.22715i	−0.151847	−	0.263006i
$396$		0			0
$397$		−	7.58846i		−	0.380854i	−0.981701	−	0.190427i	$-0.939013\pi$
$397$		−	7.58846i		−	0.380854i	0.981701	−	0.190427i	$-0.0609872\pi$
$398$	−13.8511	−	23.9909i	−0.694294	−	1.20255i
$399$		0			0
$400$	1.73205	+	1.00000i	0.0866025	+	0.0500000i
$401$	−12.0716	−	12.0716i	−0.602826	−	0.602826i	0.338235	−	0.941062i	$-0.390170\pi$
$401$	−12.0716	−	12.0716i	−0.602826	−	0.602826i	−0.941062	+	0.338235i	$0.890170\pi$
$402$		0			0
$403$	1.53590	−	2.66025i	0.0765085	−	0.132517i
$404$	1.91327	+	1.10463i	0.0951887	+	0.0549572i
$405$		0			0
$406$		−	10.9808i		−	0.544966i
$407$	−11.5032	−	9.46979i	−0.570191	−	0.469400i
$408$		0			0
$409$	27.2583	+	7.30385i	1.34784	+	0.361152i	0.859336	−	0.511411i	$-0.170877\pi$
$409$	27.2583	+	7.30385i	1.34784	+	0.361152i	0.488501	+	0.872563i	$0.337544\pi$
$410$	5.01910	−	8.69333i	0.247876	−	0.429333i
$411$		0			0
$412$	5.09808	−	1.36603i	0.251164	−	0.0672992i
$413$	−5.37945	+	5.37945i	−0.264706	+	0.264706i
$414$		0			0
$415$	−4.39230	−	4.39230i	−0.215610	−	0.215610i
$416$	0.328169	−	0.189469i	0.0160898	−	0.00928947i
$417$		0			0
$418$			12.9282i			0.632339i
$419$	17.5390	−	10.1261i	0.856835	−	0.494694i	−0.00611634	−	0.999981i	$-0.501947\pi$
$419$	17.5390	−	10.1261i	0.856835	−	0.494694i	0.862951	+	0.505288i	$0.168614\pi$
$420$		0			0
$421$	−10.8301	+	10.8301i	−0.527828	+	0.527828i	−0.919924	−	0.392096i	$-0.871750\pi$
$421$	−10.8301	+	10.8301i	−0.527828	+	0.527828i	0.392096	+	0.919924i	$0.371750\pi$
$422$	−4.60797	+	17.1972i	−0.224313	+	0.837146i
$423$		0			0
$424$	1.56218	−	5.83013i	0.0758661	−	0.283136i
$425$	12.4877	−	3.34607i	0.605742	−	0.162308i
$426$		0			0
$427$	−13.5622	−	3.63397i	−0.656320	−	0.175860i
$428$	5.46739	+	9.46979i	0.264276	+	0.457740i
$429$		0			0
$430$	0.464102	+	0.464102i	0.0223810	+	0.0223810i
$431$	19.5080	−	5.22715i	0.939667	−	0.251783i	0.243695	−	0.969852i	$-0.421640\pi$
$431$	19.5080	−	5.22715i	0.939667	−	0.251783i	0.695972	+	0.718069i	$0.254974\pi$
$432$		0			0
$433$	18.8038			0.903655			0.451828	−	0.892105i	$-0.350772\pi$
$433$	18.8038			0.903655			0.451828	+	0.892105i	$0.350772\pi$
$434$	−10.2784			−0.493381
$435$		0			0
$436$	2.16987	−	2.16987i	0.103918	−	0.103918i
$437$	−9.14162	+	15.8338i	−0.437303	+	0.757431i
$438$		0			0
$439$	7.66025	+	28.5885i	0.365604	+	1.36445i	0.866600	+	0.499003i	$0.166300\pi$
$439$	7.66025	+	28.5885i	0.365604	+	1.36445i	−0.500996	+	0.865449i	$0.667033\pi$
$440$	−3.67423	−	2.12132i	−0.175162	−	0.101130i
$441$		0			0
$442$	0.633975	−	2.36603i	0.0301551	−	0.112540i
$443$	23.6627			1.12425			0.562124	−	0.827053i	$-0.309984\pi$
$443$	23.6627			1.12425			0.562124	+	0.827053i	$0.309984\pi$
$444$		0			0
$445$	−7.39230			−0.350429
$446$	4.76028	−	17.7656i	0.225406	−	0.841226i
$447$		0			0
$448$	−1.09808	−	0.633975i	−0.0518792	−	0.0299525i
$449$	4.00240	+	14.9372i	0.188885	+	0.704929i	0.993765	+	0.111492i	$0.0355628\pi$
$449$	4.00240	+	14.9372i	0.188885	+	0.704929i	−0.804880	+	0.593437i	$0.797771\pi$
$450$		0			0
$451$	7.09808	−	12.2942i	0.334235	−	0.578913i
$452$	5.55532	−	5.55532i	0.261300	−	0.261300i
$453$		0			0
$454$	20.1962			0.947852
$455$	0.832204			0.0390143
$456$		0			0
$457$	0.669873	−	0.179492i	0.0313353	−	0.00839628i	−0.243117	−	0.969997i	$-0.578170\pi$
$457$	0.669873	−	0.179492i	0.0313353	−	0.00839628i	0.274453	+	0.961601i	$0.411503\pi$
$458$	0.707107	+	0.707107i	0.0330409	+	0.0330409i
$459$		0			0
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	9.14162	+	2.44949i	0.425768	+	0.114084i	0.465339	−	0.885133i	$-0.345932\pi$
$461$	9.14162	+	2.44949i	0.425768	+	0.114084i	−0.0395711	+	0.999217i	$0.512599\pi$
$462$		0			0
$463$	−40.9545	+	10.9737i	−1.90332	+	0.509992i	−0.907337	+	0.420403i	$0.861889\pi$
$463$	−40.9545	+	10.9737i	−1.90332	+	0.509992i	−0.995979	+	0.0895888i	$0.971445\pi$
$464$	−2.24144	+	8.36516i	−0.104056	+	0.388343i
$465$		0			0
$466$	−2.42820	+	9.06218i	−0.112484	+	0.419797i
$467$	−3.76217	+	3.76217i	−0.174092	+	0.174092i	−0.788775	−	0.614682i	$-0.789284\pi$
$467$	−3.76217	+	3.76217i	−0.174092	+	0.174092i	0.614682	+	0.788775i	$0.289284\pi$
$468$		0			0
$469$	−4.60770	+	2.66025i	−0.212764	+	0.122839i
$470$			7.34847i			0.338960i
$471$		0			0
$472$	5.19615	−	3.00000i	0.239172	−	0.138086i
$473$	0.656339	+	0.656339i	0.0301785	+	0.0301785i
$474$		0			0
$475$	−7.46410	+	7.46410i	−0.342476	+	0.342476i
$476$	−7.91688	+	2.12132i	−0.362869	+	0.0972306i
$477$		0			0
$478$	−11.8301	+	20.4904i	−0.541097	+	0.937208i
$479$	−2.68973	−	0.720710i	−0.122897	−	0.0329301i	0.196846	−	0.980434i	$-0.436930\pi$
$479$	−2.68973	−	0.720710i	−0.122897	−	0.0329301i	−0.319743	+	0.947504i	$0.603597\pi$
$480$		0			0
$481$	−2.09808	−	0.954483i	−0.0956640	−	0.0435207i
$482$			13.7632i			0.626897i
$483$		0			0
$484$	4.33013	+	2.50000i	0.196824	+	0.113636i
$485$	−0.448288	+	0.776457i	−0.0203557	+	0.0352571i
$486$		0			0
$487$	−9.26795	−	9.26795i	−0.419971	−	0.419971i	0.465223	−	0.885194i	$-0.345974\pi$
$487$	−9.26795	−	9.26795i	−0.419971	−	0.419971i	−0.885194	+	0.465223i	$0.845974\pi$
$488$	9.58991	+	5.53674i	0.434115	+	0.250636i
$489$		0			0
$490$	4.66987	+	8.08846i	0.210963	+	0.365399i
$491$			22.5259i			1.01658i	0.861186	+	0.508289i	$0.169722\pi$
$491$			22.5259i			1.01658i	−0.861186	+	0.508289i	$0.830278\pi$
$492$		0			0
$493$	27.9904	+	48.4808i	1.26062	+	2.18346i
$494$	0.517638	+	1.93185i	0.0232896	+	0.0869181i
$495$		0			0
$496$	7.83013	+	2.09808i	0.351583	+	0.0942064i
$497$	2.68973	−	1.55291i	0.120651	−	0.0696577i
$498$		0			0
$499$	0.366025	+	1.36603i	0.0163855	+	0.0611517i	0.973635	−	0.228113i	$-0.0732557\pi$
$499$	0.366025	+	1.36603i	0.0163855	+	0.0611517i	−0.957249	+	0.289265i	$0.906589\pi$
$500$	−3.13801	−	11.7112i	−0.140336	−	0.523742i
$501$		0			0
$502$	−6.29423	+	3.63397i	−0.280925	+	0.162192i
$503$	−3.67423	−	0.984508i	−0.163826	−	0.0438971i	0.175974	−	0.984395i	$-0.443693\pi$
$503$	−3.67423	−	0.984508i	−0.163826	−	0.0438971i	−0.339800	+	0.940498i	$0.610359\pi$
$504$		0			0
$505$	−0.990381	−	3.69615i	−0.0440714	−	0.164477i
$506$	−4.24264	−	7.34847i	−0.188608	−	0.326679i
$507$		0			0
$508$			2.39230i			0.106141i
$509$	3.46618	+	6.00361i	0.153636	+	0.266105i	0.932561	−	0.361011i	$-0.117568\pi$
$509$	3.46618	+	6.00361i	0.153636	+	0.266105i	−0.778926	+	0.627116i	$0.784235\pi$
$510$		0			0
$511$	7.01924	+	4.05256i	0.310513	+	0.179275i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−3.06218	+	5.30385i	−0.135067	+	0.233943i
$515$	−7.91688	−	4.57081i	−0.348859	−	0.201414i
$516$		0			0
$517$			10.3923i			0.457053i
$518$	0.744272	+	7.67664i	0.0327014	+	0.337292i
$519$		0			0
$520$	−0.633975	−	0.169873i	−0.0278016	−	0.00744942i
$521$	13.9527	−	24.1667i	0.611277	−	1.05876i	−0.379748	−	0.925090i	$-0.623989\pi$
$521$	13.9527	−	24.1667i	0.611277	−	1.05876i	0.991025	−	0.133674i	$-0.0426774\pi$
$522$		0			0
$523$	−31.5885	+	8.46410i	−1.38127	+	0.370109i	−0.871581	−	0.490251i	$-0.836905\pi$
$523$	−31.5885	+	8.46410i	−1.38127	+	0.370109i	−0.509686	+	0.860361i	$0.670238\pi$
$524$	−5.55532	+	5.55532i	−0.242685	+	0.242685i
$525$		0			0
$526$	3.12436	+	3.12436i	0.136228	+	0.136228i
$527$	45.3799	−	26.2001i	1.97678	−	1.14129i
$528$		0			0
$529$			11.0000i			0.478261i
$530$	−9.05369	+	5.22715i	−0.393267	+	0.227053i
$531$		0			0
$532$	4.73205	−	4.73205i	0.205160	−	0.205160i
$533$	0.568406	−	2.12132i	0.0246204	−	0.0918846i
$534$		0			0
$535$	4.90192	−	18.2942i	0.211929	−	0.790928i
$536$	4.05317	−	1.08604i	0.175070	−	0.0469100i
$537$		0			0
$538$	−4.09808	−	1.09808i	−0.176681	−	0.0473414i
$539$	6.60420	+	11.4388i	0.284463	+	0.492704i
$540$		0			0
$541$	19.4186	+	19.4186i	0.834870	+	0.834870i	0.988178	−	0.153308i	$-0.0489927\pi$
$541$	19.4186	+	19.4186i	0.834870	+	0.834870i	−0.153308	+	0.988178i	$0.548993\pi$
$542$	26.2001	−	7.02030i	1.12539	−	0.301548i
$543$		0			0
$544$	6.46410			0.277146
$545$	−5.31508			−0.227673
$546$		0			0
$547$	−28.3205	+	28.3205i	−1.21090	+	1.21090i	−0.240166	+	0.970732i	$0.577202\pi$
$547$	−28.3205	+	28.3205i	−1.21090	+	1.21090i	−0.970732	+	0.240166i	$0.922798\pi$
$548$	8.03699	−	13.9205i	0.343323	−	0.594653i
$549$		0			0
$550$	−1.26795	−	4.73205i	−0.0540655	−	0.201775i
$551$	−39.5844	−	22.8541i	−1.68635	−	0.973615i
$552$		0			0
$553$	−1.14359	+	4.26795i	−0.0486305	+	0.181492i
$554$	−27.2862			−1.15928
$555$		0			0
$556$	−0.392305			−0.0166374
$557$	−4.53862	+	16.9384i	−0.192308	+	0.717702i	0.800640	+	0.599146i	$0.204493\pi$
$557$	−4.53862	+	16.9384i	−0.192308	+	0.717702i	−0.992947	+	0.118556i	$0.962174\pi$
$558$		0			0
$559$	0.124356	+	0.0717968i	0.00525968	+	0.00303668i
$560$	0.568406	+	2.12132i	0.0240195	+	0.0896421i
$561$		0			0
$562$	14.2583	−	24.6962i	0.601451	−	1.04174i
$563$	−28.7375	+	28.7375i	−1.21114	+	1.21114i	−0.240492	+	0.970651i	$0.577309\pi$
$563$	−28.7375	+	28.7375i	−1.21114	+	1.21114i	−0.970651	+	0.240492i	$0.922691\pi$
$564$		0			0
$565$	−13.6077			−0.572480
$566$	−20.1779			−0.848142
$567$		0			0
$568$	−2.36603	+	0.633975i	−0.0992762	+	0.0266010i
$569$	17.7148	+	17.7148i	0.742644	+	0.742644i	0.973086	−	0.230442i	$-0.0740171\pi$
$569$	17.7148	+	17.7148i	0.742644	+	0.742644i	−0.230442	+	0.973086i	$0.574017\pi$
$570$		0			0
$571$	12.9282	+	22.3923i	0.541028	+	0.937089i	0.998845	+	0.0480423i	$0.0152982\pi$
$571$	12.9282	+	22.3923i	0.541028	+	0.937089i	−0.457817	+	0.889047i	$0.651368\pi$
$572$	−0.896575	−	0.240237i	−0.0374877	−	0.0100448i
$573$		0			0
$574$	−7.09808	+	1.90192i	−0.296268	+	0.0793848i
$575$	1.79315	−	6.69213i	0.0747796	−	0.279081i
$576$		0			0
$577$	−3.70577	+	13.8301i	−0.154273	+	0.575756i	0.844893	+	0.534935i	$0.179664\pi$
$577$	−3.70577	+	13.8301i	−0.154273	+	0.575756i	−0.999166	+	0.0408207i	$0.987003\pi$
$578$	17.5254	−	17.5254i	0.728959	−	0.728959i
$579$		0			0
$580$	12.9904	−	7.50000i	0.539396	−	0.311421i
$581$			4.54725i			0.188652i
$582$		0			0
$583$	−12.8038	+	7.39230i	−0.530281	+	0.306158i
$584$	−4.52004	−	4.52004i	−0.187041	−	0.187041i
$585$		0			0
$586$	−8.36603	+	8.36603i	−0.345597	+	0.345597i
$587$	−12.4877	+	3.34607i	−0.515422	+	0.138107i	−0.507148	−	0.861859i	$-0.669300\pi$
$587$	−12.4877	+	3.34607i	−0.515422	+	0.138107i	−0.00827376	+	0.999966i	$0.502634\pi$
$588$		0			0
$589$	−21.3923	+	37.0526i	−0.881455	+	1.52672i
$590$	−10.0382	−	2.68973i	−0.413266	−	0.110734i
$591$		0			0
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$			21.1488i			0.868478i	0.900798	+	0.434239i	$0.142983\pi$
$593$			21.1488i			0.868478i	−0.900798	+	0.434239i	$0.857017\pi$
$594$		0			0
$595$	12.2942	+	7.09808i	0.504014	+	0.290993i
$596$	7.79676	−	13.5044i	0.319368	−	0.553161i
$597$		0			0
$598$	−0.928203	−	0.928203i	−0.0379571	−	0.0379571i
$599$	14.4331	+	8.33298i	0.589722	+	0.340476i	0.764988	−	0.644045i	$-0.222745\pi$
$599$	14.4331	+	8.33298i	0.589722	+	0.340476i	−0.175266	+	0.984521i	$0.556078\pi$
$600$		0			0
$601$	−12.2321	−	21.1865i	−0.498956	−	0.864217i	0.501044	−	0.865422i	$-0.332950\pi$
$601$	−12.2321	−	21.1865i	−0.498956	−	0.864217i	−0.999999	+	0.00120537i	$0.999616\pi$
$602$		−	0.480473i		−	0.0195826i
$603$		0			0
$604$	−8.66025	−	15.0000i	−0.352381	−	0.610341i
$605$	−2.24144	−	8.36516i	−0.0911274	−	0.340092i
$606$		0			0
$607$	−37.4904	−	10.0455i	−1.52169	−	0.407735i	−0.601391	−	0.798955i	$-0.705386\pi$
$607$	−37.4904	−	10.0455i	−1.52169	−	0.407735i	−0.920297	+	0.391220i	$0.872053\pi$
$608$	−4.57081	+	2.63896i	−0.185371	+	0.107024i
$609$		0			0
$610$	−4.96410	−	18.5263i	−0.200991	−	0.750107i
$611$	0.416102	+	1.55291i	0.0168337	+	0.0628242i
$612$		0			0
$613$	26.0885	−	15.0622i	1.05370	−	0.608356i	0.130019	−	0.991511i	$-0.458496\pi$
$613$	26.0885	−	15.0622i	1.05370	−	0.608356i	0.923684	+	0.383156i	$0.125163\pi$
$614$	−31.9957	−	8.57321i	−1.29124	−	0.345987i
$615$		0			0
$616$	0.803848	+	3.00000i	0.0323879	+	0.120873i
$617$	−17.4746	−	30.2669i	−0.703501	−	1.21850i	−0.967230	−	0.253902i	$-0.918286\pi$
$617$	−17.4746	−	30.2669i	−0.703501	−	1.21850i	0.263729	−	0.964597i	$-0.415048\pi$
$618$		0			0
$619$			44.1962i			1.77639i	0.459463	+	0.888197i	$0.348042\pi$
$619$			44.1962i			1.77639i	−0.459463	+	0.888197i	$0.651958\pi$
$620$	−7.02030	−	12.1595i	−0.281942	−	0.488338i
$621$		0			0
$622$	−2.49038	−	1.43782i	−0.0998552	−	0.0576514i
$623$	3.82654	+	3.82654i	0.153307	+	0.153307i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−15.1452	−	8.74410i	−0.605325	−	0.349485i
$627$		0			0
$628$			6.12436i			0.244388i
$629$	−22.8541	−	31.9957i	−0.911251	−	1.27575i
$630$		0			0
$631$	10.6603	+	2.85641i	0.424378	+	0.113712i	0.464686	−	0.885476i	$-0.346167\pi$
$631$	10.6603	+	2.85641i	0.424378	+	0.113712i	−0.0403079	+	0.999187i	$0.512834\pi$
$632$	1.74238	−	3.01790i	0.0693083	−	0.120045i
$633$		0			0
$634$	14.8923	−	3.99038i	0.591449	−	0.158478i
$635$	2.92996	−	2.92996i	0.116272	−	0.116272i
$636$		0			0
$637$	1.44486	+	1.44486i	0.0572476	+	0.0572476i
$638$	18.3712	−	10.6066i	0.727322	−	0.419919i
$639$		0			0
$640$		−	1.73205i		−	0.0684653i
$641$	−42.3299	+	24.4392i	−1.67193	+	0.965288i	−0.705371	+	0.708838i	$0.749220\pi$
$641$	−42.3299	+	24.4392i	−1.67193	+	0.965288i	−0.966557	+	0.256450i	$0.917447\pi$
$642$		0			0
$643$	−13.3397	+	13.3397i	−0.526068	+	0.526068i	−0.919398	−	0.393329i	$-0.871323\pi$
$643$	−13.3397	+	13.3397i	−0.526068	+	0.526068i	0.393329	+	0.919398i	$0.371323\pi$
$644$	−1.13681	+	4.24264i	−0.0447967	+	0.167183i
$645$		0			0
$646$	−8.83013	+	32.9545i	−0.347417	+	1.29658i
$647$	26.8565	−	7.19617i	1.05584	−	0.282910i	0.311175	−	0.950353i	$-0.399278\pi$
$647$	26.8565	−	7.19617i	1.05584	−	0.282910i	0.744662	+	0.667442i	$0.232611\pi$
$648$		0			0
$649$	−14.1962	−	3.80385i	−0.557248	−	0.149314i
$650$	−0.378937	−	0.656339i	−0.0148631	−	0.0257437i
$651$		0			0
$652$	0.267949	+	0.267949i	0.0104937	+	0.0104937i
$653$	13.5923	−	3.64205i	0.531908	−	0.142524i	0.0171389	−	0.999853i	$-0.494544\pi$
$653$	13.5923	−	3.64205i	0.531908	−	0.142524i	0.514769	+	0.857329i	$0.327878\pi$
$654$		0			0
$655$	13.6077			0.531697
$656$	5.79555			0.226278
$657$		0			0
$658$	3.80385	−	3.80385i	0.148289	−	0.148289i
$659$	−17.8671	+	30.9468i	−0.696005	+	1.20552i	0.273836	+	0.961776i	$0.411707\pi$
$659$	−17.8671	+	30.9468i	−0.696005	+	1.20552i	−0.969841	+	0.243739i	$0.921626\pi$
$660$		0			0
$661$	−7.55256	−	28.1865i	−0.293760	−	1.09633i	−0.942197	−	0.335060i	$-0.891243\pi$
$661$	−7.55256	−	28.1865i	−0.293760	−	1.09633i	0.648436	−	0.761269i	$-0.275423\pi$
$662$	−19.5959	−	11.3137i	−0.761617	−	0.439720i
$663$		0			0
$664$	0.928203	−	3.46410i	0.0360213	−	0.134433i
$665$	−11.5911			−0.449484
$666$		0			0
$667$	30.0000			1.16160
$668$	−6.45189	+	24.0788i	−0.249631	+	0.931637i
$669$		0			0
$670$	−6.29423	−	3.63397i	−0.243167	−	0.140393i
$671$	−7.02030	−	26.2001i	−0.271016	−	1.01144i
$672$		0			0
$673$	11.6603	−	20.1962i	0.449470	−	0.778504i	−0.548882	−	0.835900i	$-0.684946\pi$
$673$	11.6603	−	20.1962i	0.449470	−	0.778504i	0.998352	+	0.0573955i	$0.0182796\pi$
$674$	−25.5438	+	25.5438i	−0.983910	+	0.983910i
$675$		0			0
$676$	12.8564			0.494477
$677$	20.3166			0.780831			0.390416	−	0.920639i	$-0.372331\pi$
$677$	20.3166			0.780831			0.390416	+	0.920639i	$0.372331\pi$
$678$		0			0
$679$	0.633975	−	0.169873i	0.0243297	−	0.00651913i
$680$	−7.91688	−	7.91688i	−0.303598	−	0.303598i
$681$		0			0
$682$	−9.92820	−	17.1962i	−0.380171	−	0.658475i
$683$	−14.3688	−	3.85010i	−0.549806	−	0.147320i	−0.0267869	−	0.999641i	$-0.508528\pi$
$683$	−14.3688	−	3.85010i	−0.549806	−	0.147320i	−0.523019	+	0.852321i	$0.675194\pi$
$684$		0			0
$685$	−26.8923	+	7.20577i	−1.02750	+	0.275318i
$686$	4.06678	−	15.1774i	0.155270	−	0.579476i
$687$		0			0
$688$	−0.0980762	+	0.366025i	−0.00373912	+	0.0139546i
$689$	−1.61729	+	1.61729i	−0.0616137	+	0.0616137i
$690$		0			0
$691$	−19.5622	+	11.2942i	−0.744180	+	0.429653i	−0.823587	−	0.567190i	$-0.808031\pi$
$691$	−19.5622	+	11.2942i	−0.744180	+	0.429653i	0.0794069	+	0.996842i	$0.474697\pi$
$692$			16.0740i			0.611041i
$693$		0			0
$694$	16.3923	−	9.46410i	0.622243	−	0.359252i
$695$	0.480473	+	0.480473i	0.0182254	+	0.0182254i
$696$		0			0
$697$	26.4904	−	26.4904i	1.00339	−	1.00339i
$698$	−5.34727	+	1.43280i	−0.202397	+	0.0542321i
$699$		0			0
$700$	−1.26795	+	2.19615i	−0.0479240	+	0.0830068i
$701$	15.8338	+	4.24264i	0.598033	+	0.160242i	0.545122	−	0.838357i	$-0.316483\pi$
$701$	15.8338	+	4.24264i	0.598033	+	0.160242i	0.0529108	+	0.998599i	$0.483150\pi$
$702$		0			0
$703$	29.2224	+	13.2942i	1.10214	+	0.501401i
$704$		−	2.44949i		−	0.0923186i
$705$		0			0
$706$	21.6962	+	12.5263i	0.816545	+	0.471433i
$707$	−1.40061	+	2.42593i	−0.0526754	+	0.0912364i
$708$		0			0
$709$	−25.9282	−	25.9282i	−0.973754	−	0.973754i	0.0259102	−	0.999664i	$-0.491752\pi$
$709$	−25.9282	−	25.9282i	−0.973754	−	0.973754i	−0.999664	+	0.0259102i	$0.991752\pi$
$710$	3.67423	+	2.12132i	0.137892	+	0.0796117i
$711$		0			0
$712$	−2.13397	−	3.69615i	−0.0799741	−	0.138519i
$713$		−	28.0812i		−	1.05165i
$714$		0			0
$715$	0.803848	+	1.39230i	0.0300622	+	0.0520692i
$716$	5.79555	+	21.6293i	0.216590	+	0.808325i
$717$		0			0
$718$	−3.00000	−	0.803848i	−0.111959	−	0.0299993i
$719$	10.8704	−	6.27603i	0.405398	−	0.234056i	−0.283413	−	0.958998i	$-0.591467\pi$
$719$	10.8704	−	6.27603i	0.405398	−	0.234056i	0.688810	+	0.724942i	$0.258133\pi$
$720$		0			0
$721$	1.73205	+	6.46410i	0.0645049	+	0.240736i
$722$	−2.29221	−	8.55463i	−0.0853071	−	0.318370i
$723$		0			0
$724$	14.8923	−	8.59808i	0.553468	−	0.319545i
$725$	16.7303	+	4.48288i	0.621349	+	0.166490i
$726$		0			0
$727$	−11.4641	−	42.7846i	−0.425180	−	1.58679i	−0.763530	−	0.645773i	$-0.776535\pi$
$727$	−11.4641	−	42.7846i	−0.425180	−	1.58679i	0.338350	−	0.941020i	$-0.390131\pi$
$728$	0.240237	+	0.416102i	0.00890376	+	0.0154218i
$729$		0			0
$730$			11.0718i			0.409786i
$731$	1.22474	+	2.12132i	0.0452988	+	0.0784599i
$732$		0			0
$733$	6.00000	+	3.46410i	0.221615	+	0.127950i	0.606698	−	0.794933i	$-0.292494\pi$
$733$	6.00000	+	3.46410i	0.221615	+	0.127950i	−0.385083	+	0.922882i	$0.625827\pi$
$734$	−20.6312	−	20.6312i	−0.761511	−	0.761511i
$735$		0			0
$736$	1.73205	−	3.00000i	0.0638442	−	0.110581i
$737$	−8.90138	−	5.13922i	−0.327887	−	0.189305i
$738$		0			0
$739$			28.3923i			1.04443i	0.852815	+	0.522214i	$0.174894\pi$
$739$			28.3923i			1.04443i	−0.852815	+	0.522214i	$0.825106\pi$
$740$	−8.57321	+	6.12372i	−0.315158	+	0.225113i
$741$		0			0
$742$	7.39230	+	1.98076i	0.271380	+	0.0727161i
$743$	2.12132	−	3.67423i	0.0778237	−	0.134795i	−0.824487	−	0.565881i	$-0.808536\pi$
$743$	2.12132	−	3.67423i	0.0778237	−	0.134795i	0.902311	+	0.431086i	$0.141870\pi$
$744$		0			0
$745$	−26.0885	+	6.99038i	−0.955807	+	0.256108i
$746$	−4.94975	+	4.94975i	−0.181223	+	0.181223i
$747$		0			0
$748$	−11.1962	−	11.1962i	−0.409372	−	0.409372i
$749$	−12.0072	+	6.93237i	−0.438734	+	0.253303i
$750$		0			0
$751$			50.5885i			1.84600i	0.384801	+	0.923000i	$0.374270\pi$
$751$			50.5885i			1.84600i	−0.384801	+	0.923000i	$0.625730\pi$
$752$	−3.67423	+	2.12132i	−0.133986	+	0.0773566i
$753$		0			0
$754$	2.32051	−	2.32051i	0.0845079	−	0.0845079i
$755$	−7.76457	+	28.9778i	−0.282582	+	1.05461i
$756$		0			0
$757$	9.91858	−	37.0167i	0.360497	−	1.34539i	−0.512927	−	0.858432i	$-0.671439\pi$
$757$	9.91858	−	37.0167i	0.360497	−	1.34539i	0.873424	−	0.486961i	$-0.161895\pi$
$758$	−8.81345	+	2.36156i	−0.320119	+	0.0857756i
$759$		0			0
$760$	8.83013	+	2.36603i	0.320302	+	0.0858248i
$761$	−0.776457	−	1.34486i	−0.0281465	−	0.0487513i	0.851609	−	0.524178i	$-0.175627\pi$
$761$	−0.776457	−	1.34486i	−0.0281465	−	0.0487513i	−0.879756	+	0.475426i	$0.842294\pi$
$762$		0			0
$763$	2.75129	+	2.75129i	0.0996033	+	0.0996033i
$764$	12.4877	−	3.34607i	0.451789	−	0.121056i
$765$		0			0
$766$	−18.5885			−0.671628
$767$	−2.27362			−0.0820958
$768$		0			0
$769$	−27.1962	+	27.1962i	−0.980718	+	0.980718i	−0.999818	−	0.0190993i	$-0.993920\pi$
$769$	−27.1962	+	27.1962i	−0.980718	+	0.980718i	0.0190993	+	0.999818i	$0.493920\pi$
$770$	2.68973	−	4.65874i	0.0969310	−	0.167889i
$771$		0			0
$772$	1.06218	+	3.96410i	0.0382286	+	0.142671i
$773$	−14.0728	−	8.12493i	−0.506163	−	0.292233i	0.225092	−	0.974337i	$-0.427732\pi$
$773$	−14.0728	−	8.12493i	−0.506163	−	0.292233i	−0.731255	+	0.682104i	$0.761065\pi$
$774$		0			0
$775$	4.19615	−	15.6603i	0.150730	−	0.562533i
$776$	−0.517638			−0.0185821
$777$		0			0
$778$	2.07180			0.0742775
$779$	−7.91688	+	29.5462i	−0.283651	+	1.05860i
$780$		0			0
$781$	5.19615	+	3.00000i	0.185933	+	0.107348i
$782$	−5.79555	−	21.6293i	−0.207249	−	0.773462i
$783$		0			0
$784$	−2.69615	+	4.66987i	−0.0962912	+	0.166781i
$785$	7.50077	−	7.50077i	0.267714	−	0.267714i
$786$		0			0
$787$	8.00000			0.285169			0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000			0.285169			0.142585	+	0.989783i	$0.454459\pi$
$788$	−11.1750			−0.398093
$789$		0			0
$790$	−5.83013	+	1.56218i	−0.207427	+	0.0555798i
$791$	7.04386	+	7.04386i	0.250451	+	0.250451i
$792$		0			0
$793$	−2.09808	−	3.63397i	−0.0745049	−	0.129046i
$794$	−7.32989	−	1.96404i	−0.260128	−	0.0697011i
$795$		0			0
$796$	−26.7583	+	7.16987i	−0.948424	+	0.254129i
$797$	3.52193	−	13.1440i	0.124753	−	0.465585i	−0.875078	−	0.483983i	$-0.839190\pi$
$797$	3.52193	−	13.1440i	0.124753	−	0.465585i	0.999831	+	0.0183975i	$0.00585643\pi$
$798$		0			0
$799$	−7.09808	+	26.4904i	−0.251112	+	0.937162i
$800$	1.41421	−	1.41421i	0.0500000	−	0.0500000i
$801$		0			0
$802$	−14.7846	+	8.53590i	−0.522063	+	0.301413i
$803$			15.6579i			0.552555i
$804$		0			0
$805$	6.58846	−	3.80385i	0.232213	−	0.134068i
$806$	−2.17209	−	2.17209i	−0.0765085	−	0.0765085i
$807$		0			0
$808$	1.56218	−	1.56218i	0.0549572	−	0.0549572i
$809$	6.69213	−	1.79315i	0.235283	−	0.0630438i	−0.139251	−	0.990257i	$-0.544469\pi$
$809$	6.69213	−	1.79315i	0.235283	−	0.0630438i	0.374534	+	0.927213i	$0.377803\pi$
$810$		0			0
$811$	−15.0000	+	25.9808i	−0.526721	+	0.912308i	0.472794	+	0.881173i	$0.343245\pi$
$811$	−15.0000	+	25.9808i	−0.526721	+	0.912308i	−0.999515	+	0.0311349i	$0.990088\pi$
$812$	−10.6066	−	2.84203i	−0.372219	−	0.0997357i
$813$		0			0
$814$	−12.1244	+	8.66025i	−0.424958	+	0.303542i
$815$		−	0.656339i		−	0.0229905i
$816$		0			0
$817$	−1.73205	−	1.00000i	−0.0605968	−	0.0349856i
$818$	14.1100	−	24.4392i	0.493343	−	0.854495i
$819$		0			0
$820$	−7.09808	−	7.09808i	−0.247876	−	0.247876i
$821$	44.6592	+	25.7840i	1.55862	+	0.899868i	0.997390	+	0.0722070i	$0.0230042\pi$
$821$	44.6592	+	25.7840i	1.55862	+	0.899868i	0.561228	+	0.827661i	$0.310329\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$		−	5.27792i		−	0.183865i
$825$		0			0
$826$	3.80385	+	6.58846i	0.132353	+	0.229242i
$827$	10.7589	+	40.1528i	0.374124	+	1.39625i	0.854621	+	0.519253i	$0.173790\pi$
$827$	10.7589	+	40.1528i	0.374124	+	1.39625i	−0.480497	+	0.876996i	$0.659544\pi$
$828$		0			0
$829$	46.4186	+	12.4378i	1.61218	+	0.431983i	0.948692	−	0.316200i	$-0.102407\pi$
$829$	46.4186	+	12.4378i	1.61218	+	0.431983i	0.663492	+	0.748184i	$0.269074\pi$
$830$	−5.37945	+	3.10583i	−0.186724	+	0.107805i
$831$		0			0
$832$	−0.0980762	−	0.366025i	−0.00340018	−	0.0126896i
$833$	9.02150	+	33.6687i	0.312577	+	1.16655i
$834$		0			0
$835$	37.3923	−	21.5885i	1.29401	−	0.747099i
$836$	12.4877	+	3.34607i	0.431896	+	0.115726i
$837$		0			0
$838$	−5.24167	−	19.5622i	−0.181070	−	0.675764i
$839$	−12.9038	−	22.3500i	−0.445488	−	0.771608i	0.552598	−	0.833448i	$-0.313637\pi$
$839$	−12.9038	−	22.3500i	−0.445488	−	0.771608i	−0.998086	+	0.0618398i	$0.980303\pi$
$840$		0			0
$841$			46.0000i			1.58621i
$842$	7.65806	+	13.2641i	0.263914	+	0.457113i
$843$		0			0
$844$	15.4186	+	8.90192i	0.530730	+	0.306417i
$845$	−15.7458	−	15.7458i	−0.541673	−	0.541673i
$846$		0			0
$847$	−3.16987	+	5.49038i	−0.108918	+	0.188652i
$848$	−5.22715	−	3.01790i	−0.179501	−	0.103635i
$849$		0			0
$850$		−	12.9282i		−	0.443434i
$851$	−20.9730	+	2.03339i	−0.718944	+	0.0697036i
$852$		0			0
$853$	0.0358984	+	0.00961894i	0.00122914	+	0.000329346i	0.259434	−	0.965761i	$-0.416464\pi$
$853$	0.0358984	+	0.00961894i	0.00122914	+	0.000329346i	−0.258204	+	0.966090i	$0.583131\pi$
$854$	−7.02030	+	12.1595i	−0.240230	+	0.416090i
$855$		0			0
$856$	10.5622	−	2.83013i	0.361008	−	0.0967318i
$857$	20.6448	−	20.6448i	0.705213	−	0.705213i	−0.260312	−	0.965525i	$-0.583825\pi$
$857$	20.6448	−	20.6448i	0.705213	−	0.705213i	0.965525	+	0.260312i	$0.0838253\pi$
$858$		0			0
$859$	−29.0000	−	29.0000i	−0.989467	−	0.989467i	0.0104779	−	0.999945i	$-0.496665\pi$
$859$	−29.0000	−	29.0000i	−0.989467	−	0.989467i	−0.999945	+	0.0104779i	$0.996665\pi$
$860$	0.568406	−	0.328169i	0.0193825	−	0.0111905i
$861$		0			0
$862$		−	20.1962i		−	0.687884i
$863$	8.18067	−	4.72311i	0.278473	−	0.160777i	−0.354259	−	0.935147i	$-0.615267\pi$
$863$	8.18067	−	4.72311i	0.278473	−	0.160777i	0.632732	+	0.774371i	$0.281933\pi$
$864$		0			0
$865$	19.6865	−	19.6865i	0.669362	−	0.669362i
$866$	4.86679	−	18.1631i	0.165380	−	0.617208i
$867$		0			0
$868$	−2.66025	+	9.92820i	−0.0902949	+	0.336985i
$869$	−8.24504	+	2.20925i	−0.279694	+	0.0749438i
$870$		0			0
$871$	−1.53590	−	0.411543i	−0.0520419	−	0.0139446i
$872$	−1.53433	−	2.65754i	−0.0519590	−	0.0899957i
$873$		0			0
$874$	12.9282	+	12.9282i	0.437303	+	0.437303i
$875$	14.8492	−	3.97884i	0.501996	−	0.134509i
$876$		0			0
$877$	55.7321			1.88194			0.940969	−	0.338493i	$-0.109917\pi$
$877$	55.7321			1.88194			0.940969	+	0.338493i	$0.109917\pi$
$878$	29.5969			0.998849
$879$		0			0
$880$	−3.00000	+	3.00000i	−0.101130	+	0.101130i
$881$	−10.0060	+	17.3309i	−0.337111	+	0.583893i	−0.983888	−	0.178786i	$-0.942783\pi$
$881$	−10.0060	+	17.3309i	−0.337111	+	0.583893i	0.646777	+	0.762679i	$0.276116\pi$
$882$		0			0
$883$	−6.53590	−	24.3923i	−0.219950	−	0.820866i	−0.984365	−	0.176141i	$-0.943638\pi$
$883$	−6.53590	−	24.3923i	−0.219950	−	0.820866i	0.764414	−	0.644725i	$-0.223028\pi$
$884$	−2.12132	−	1.22474i	−0.0713477	−	0.0411926i
$885$		0			0
$886$	6.12436	−	22.8564i	0.205752	−	0.767876i
$887$	31.1870			1.04716			0.523579	−	0.851977i	$-0.324597\pi$
$887$	31.1870			1.04716			0.523579	+	0.851977i	$0.324597\pi$
$888$		0			0
$889$	−3.03332			−0.101734
$890$	−1.91327	+	7.14042i	−0.0641329	+	0.239347i
$891$		0			0
$892$	−15.9282	−	9.19615i	−0.533316	−	0.307910i
$893$	−5.79555	−	21.6293i	−0.193941	−	0.723797i
$894$		0			0
$895$	19.3923	−	33.5885i	0.648213	−	1.12274i
$896$	−0.896575	+	0.896575i	−0.0299525	+	0.0299525i
$897$		0			0
$898$	15.4641			0.516044
$899$	70.2030			2.34140
$900$		0			0
$901$	−37.6865	+	10.0981i	−1.25552	+	0.336416i
$902$	−10.0382	−	10.0382i	−0.334235	−	0.334235i
$903$		0			0
$904$	−3.92820	−	6.80385i	−0.130650	−	0.226293i
$905$	−28.7697	−	7.70882i	−0.956338	−	0.256250i
$906$		0			0
$907$	3.56218	−	0.954483i	0.118280	−	0.0316931i	−0.199193	−	0.979960i	$-0.563832\pi$
$907$	3.56218	−	0.954483i	0.118280	−	0.0316931i	0.317474	+	0.948267i	$0.397166\pi$
$908$	5.22715	−	19.5080i	0.173469	−	0.647395i
$909$		0			0
$910$	0.215390	−	0.803848i	0.00714012	−	0.0266473i
$911$	12.7279	−	12.7279i	0.421695	−	0.421695i	−0.464092	−	0.885787i	$-0.653619\pi$
$911$	12.7279	−	12.7279i	0.421695	−	0.421695i	0.885787	+	0.464092i	$0.153619\pi$
$912$		0			0
$913$	−7.60770	+	4.39230i	−0.251778	+	0.145364i
$914$		−	0.693504i		−	0.0229391i
$915$		0			0
$916$	0.866025	−	0.500000i	0.0286143	−	0.0165205i
$917$	−7.04386	−	7.04386i	−0.232609	−	0.232609i
$918$		0			0
$919$	−11.1244	+	11.1244i	−0.366959	+	0.366959i	−0.866367	−	0.499408i	$-0.833551\pi$
$919$	−11.1244	+	11.1244i	−0.366959	+	0.366959i	0.499408	+	0.866367i	$0.333551\pi$
$920$	−5.79555	+	1.55291i	−0.191074	+	0.0511981i
$921$		0			0
$922$	4.73205	−	8.19615i	0.155842	−	0.269926i
$923$	0.896575	+	0.240237i	0.0295111	+	0.00790749i
$924$		0			0
$925$	−12.0000	−	2.00000i	−0.394558	−	0.0657596i
$926$			42.3992i			1.39332i
$927$		0			0
$928$	7.50000	+	4.33013i	0.246200	+	0.142143i
$929$	7.55652	−	13.0883i	0.247921	−	0.429412i	−0.715028	−	0.699096i	$-0.753586\pi$
$929$	7.55652	−	13.0883i	0.247921	−	0.429412i	0.962949	+	0.269684i	$0.0869192\pi$
$930$		0			0
$931$	−20.1244	−	20.1244i	−0.659549	−	0.659549i
$932$	8.12493	+	4.69093i	0.266141	+	0.153656i
$933$		0			0
$934$	2.66025	+	4.60770i	0.0870462	+	0.150768i
$935$			27.4249i			0.896889i
$936$		0			0
$937$	7.59808	+	13.1603i	0.248218	+	0.429927i	0.963032	−	0.269389i	$-0.0868216\pi$
$937$	7.59808	+	13.1603i	0.248218	+	0.429927i	−0.714813	+	0.699315i	$0.753488\pi$
$938$	1.37705	+	5.13922i	0.0449622	+	0.167801i
$939$		0			0
$940$	7.09808	+	1.90192i	0.231514	+	0.0620339i
$941$	−13.1998	+	7.62089i	−0.430300	+	0.248434i	−0.699475	−	0.714658i	$-0.746583\pi$
$941$	−13.1998	+	7.62089i	−0.430300	+	0.248434i	0.269174	+	0.963091i	$0.413249\pi$
$942$		0			0
$943$	−5.19615	−	19.3923i	−0.169210	−	0.631500i
$944$	−1.55291	−	5.79555i	−0.0505431	−	0.188629i
$945$		0			0
$946$	0.803848	−	0.464102i	0.0261353	−	0.0150892i
$947$	27.6651	+	7.41284i	0.898995	+	0.240885i	0.678585	−	0.734522i	$-0.262594\pi$
$947$	27.6651	+	7.41284i	0.898995	+	0.240885i	0.220410	+	0.975407i	$0.429260\pi$
$948$		0			0
$949$	0.626933	+	2.33975i	0.0203511	+	0.0759514i
$950$	5.27792	+	9.14162i	0.171238	+	0.296593i
$951$		0			0
$952$			8.19615i			0.265639i
$953$	−7.26054	−	12.5756i	−0.235192	−	0.407364i	0.724137	−	0.689657i	$-0.242239\pi$
$953$	−7.26054	−	12.5756i	−0.235192	−	0.407364i	−0.959328	+	0.282292i	$0.908905\pi$
$954$		0			0
$955$	−19.3923	−	11.1962i	−0.627520	−	0.362299i
$956$	16.7303	+	16.7303i	0.541097	+	0.541097i
$957$		0			0
$958$	−1.39230	+	2.41154i	−0.0449833	+	0.0779134i
$959$	17.6505	+	10.1905i	0.569963	+	0.329068i
$960$		0			0
$961$		−	34.7128i		−	1.11977i
$962$	−1.46498	+	1.77955i	−0.0472329	+	0.0573749i
$963$		0			0
$964$	13.2942	+	3.56218i	0.428178	+	0.114730i
$965$	3.55412	−	6.15591i	0.114411	−	0.198166i
$966$		0			0
$967$	−12.2679	+	3.28719i	−0.394511	+	0.105709i	−0.450620	−	0.892716i	$-0.648797\pi$
$967$	−12.2679	+	3.28719i	−0.394511	+	0.105709i	0.0561095	+	0.998425i	$0.482130\pi$
$968$	3.53553	−	3.53553i	0.113636	−	0.113636i
$969$		0			0
$970$	0.633975	+	0.633975i	0.0203557	+	0.0203557i
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$		0			0
$973$		−	0.497423i		−	0.0159466i
$974$	−11.3509	+	6.55343i	−0.363705	+	0.209985i
$975$		0			0
$976$	7.83013	−	7.83013i	0.250636	−	0.250636i
$977$	−13.5601	+	50.6071i	−0.433827	+	1.61906i	0.310031	+	0.950726i	$0.399660\pi$
$977$	−13.5601	+	50.6071i	−0.433827	+	1.61906i	−0.743858	+	0.668338i	$0.767006\pi$
$978$		0			0
$979$	−2.70577	+	10.0981i	−0.0864768	+	0.322736i
$980$	9.02150	−	2.41730i	0.288181	−	0.0772179i
$981$		0			0
$982$	21.7583	+	5.83013i	0.694336	+	0.186047i
$983$	−12.1595	−	21.0609i	−0.387828	−	0.671738i	0.604329	−	0.796735i	$-0.293441\pi$
$983$	−12.1595	−	21.0609i	−0.387828	−	0.671738i	−0.992157	+	0.124997i	$0.960108\pi$
$984$		0			0
$985$	13.6865	+	13.6865i	0.436089	+	0.436089i
$986$	54.0733	−	14.4889i	1.72204	−	0.461420i
$987$		0			0
$988$	2.00000			0.0636285
$989$	1.31268			0.0417407
$990$		0			0
$991$	34.6603	−	34.6603i	1.10102	−	1.10102i	0.106731	−	0.994288i	$-0.465962\pi$
$991$	34.6603	−	34.6603i	1.10102	−	1.10102i	0.994288	−	0.106731i	$-0.0340385\pi$
$992$	4.05317	−	7.02030i	0.128688	−	0.222895i
$993$		0			0
$994$	−0.803848	−	3.00000i	−0.0254965	−	0.0951542i
$995$	41.5534	+	23.9909i	1.31733	+	0.760561i
$996$		0			0
$997$	8.04552	−	30.0263i	0.254804	−	0.950942i	−0.713395	−	0.700762i	$-0.752844\pi$
$997$	8.04552	−	30.0263i	0.254804	−	0.950942i	0.968199	−	0.250180i	$-0.0804898\pi$
$998$	1.41421			0.0447661
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.be.c.341.2	yes	8
3.2	odd	2	inner	666.2.be.c.341.1	yes	8
37.14	odd	12	inner	666.2.be.c.125.1	✓	8
111.14	even	12	inner	666.2.be.c.125.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.be.c.125.1	✓	8	37.14	odd	12	inner
666.2.be.c.125.2	yes	8	111.14	even	12	inner
666.2.be.c.341.1	yes	8	3.2	odd	2	inner
666.2.be.c.341.2	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.448288 + 1.67303i) q^{5} +(0.633975 - 1.09808i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.448288 + 1.67303i) q^{5} +(0.633975 - 1.09808i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.73205 q^{10} +2.44949 q^{11} +(0.366025 - 0.0980762i) q^{13} +(-0.896575 - 0.896575i) q^{14} +(0.500000 + 0.866025i) q^{16} +(6.24384 + 1.67303i) q^{17} +(-5.09808 + 1.36603i) q^{19} +(0.448288 - 1.67303i) q^{20} +(0.633975 - 2.36603i) q^{22} +(2.44949 - 2.44949i) q^{23} +(1.73205 - 1.00000i) q^{25} -0.378937i q^{26} +(-1.09808 + 0.633975i) q^{28} +(6.12372 + 6.12372i) q^{29} +(5.73205 - 5.73205i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.23205 - 5.59808i) q^{34} +(2.12132 + 0.568406i) q^{35} +(-4.69615 - 3.86603i) q^{37} +5.27792i q^{38} +(-1.50000 - 0.866025i) q^{40} +(2.89778 - 5.01910i) q^{41} +(0.267949 + 0.267949i) q^{43} +(-2.12132 - 1.22474i) q^{44} +(-1.73205 - 3.00000i) q^{46} +4.24264i q^{47} +(2.69615 + 4.66987i) q^{49} +(-0.517638 - 1.93185i) q^{50} +(-0.366025 - 0.0980762i) q^{52} +(-5.22715 + 3.01790i) q^{53} +(1.09808 + 4.09808i) q^{55} +(0.328169 + 1.22474i) q^{56} +(7.50000 - 4.33013i) q^{58} +(-5.79555 - 1.55291i) q^{59} +(-2.86603 - 10.6962i) q^{61} +(-4.05317 - 7.02030i) q^{62} -1.00000i q^{64} +(0.328169 + 0.568406i) q^{65} +(-3.63397 - 2.09808i) q^{67} +(-4.57081 - 4.57081i) q^{68} +(1.09808 - 1.90192i) q^{70} +(2.12132 + 1.22474i) q^{71} +6.39230i q^{73} +(-4.94975 + 3.53553i) q^{74} +(5.09808 + 1.36603i) q^{76} +(1.55291 - 2.68973i) q^{77} +(-3.36603 + 0.901924i) q^{79} +(-1.22474 + 1.22474i) q^{80} +(-4.09808 - 4.09808i) q^{82} +(-3.10583 + 1.79315i) q^{83} +11.1962i q^{85} +(0.328169 - 0.189469i) q^{86} +(-1.73205 + 1.73205i) q^{88} +(-1.10463 + 4.12252i) q^{89} +(0.124356 - 0.464102i) q^{91} +(-3.34607 + 0.896575i) q^{92} +(4.09808 + 1.09808i) q^{94} +(-4.57081 - 7.91688i) q^{95} +(0.366025 + 0.366025i) q^{97} +(5.20857 - 1.39563i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7}+O(q^{10}) \) 8 * q + 12 * q^7	\( 8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100}) \) 8 * q + 12 * q^7 - 4 * q^13 + 4 * q^16 - 20 * q^19 + 12 * q^22 + 12 * q^28 + 32 * q^31 + 12 * q^34 + 4 * q^37 - 12 * q^40 + 16 * q^43 - 20 * q^49 + 4 * q^52 - 12 * q^55 + 60 * q^58 - 16 * q^61 - 36 * q^67 - 12 * q^70 + 20 * q^76 - 20 * q^79 - 12 * q^82 - 96 * q^91 + 12 * q^94 - 4 * q^97

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