LMFDB - Embedded newform 1170.2.m.e.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(73,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0,4,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.1
Root			$1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.73
Dual form			1170.2.m.e.577.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 - 1.65831i) q^{5} -3.00000i q^{7} +1.00000 q^{8} +(-1.50000 - 1.65831i) q^{10} +(-3.31662 + 3.31662i) q^{11} +(-2.00000 - 3.00000i) q^{13} -3.00000i q^{14} +1.00000 q^{16} +(-3.15831 - 3.15831i) q^{17} +(-2.00000 + 2.00000i) q^{19} +(-1.50000 - 1.65831i) q^{20} +(-3.31662 + 3.31662i) q^{22} +(-3.31662 + 3.31662i) q^{23} +(-0.500000 + 4.97494i) q^{25} +(-2.00000 - 3.00000i) q^{26} -3.00000i q^{28} -6.31662i q^{29} +(1.00000 + 1.00000i) q^{31} +1.00000 q^{32} +(-3.15831 - 3.15831i) q^{34} +(-4.97494 + 4.50000i) q^{35} -3.00000i q^{37} +(-2.00000 + 2.00000i) q^{38} +(-1.50000 - 1.65831i) q^{40} +(6.31662 + 6.31662i) q^{41} +(-2.47494 + 2.47494i) q^{43} +(-3.31662 + 3.31662i) q^{44} +(-3.31662 + 3.31662i) q^{46} -9.31662i q^{47} -2.00000 q^{49} +(-0.500000 + 4.97494i) q^{50} +(-2.00000 - 3.00000i) q^{52} +(-9.63325 - 9.63325i) q^{53} +(10.4749 + 0.525063i) q^{55} -3.00000i q^{56} -6.31662i q^{58} +(0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +(1.00000 + 1.00000i) q^{62} +1.00000 q^{64} +(-1.97494 + 7.81662i) q^{65} -4.94987 q^{67} +(-3.15831 - 3.15831i) q^{68} +(-4.97494 + 4.50000i) q^{70} +(2.84169 + 2.84169i) q^{71} -4.00000 q^{73} -3.00000i q^{74} +(-2.00000 + 2.00000i) q^{76} +(9.94987 + 9.94987i) q^{77} -12.9499i q^{79} +(-1.50000 - 1.65831i) q^{80} +(6.31662 + 6.31662i) q^{82} -6.31662i q^{83} +(-0.500000 + 9.97494i) q^{85} +(-2.47494 + 2.47494i) q^{86} +(-3.31662 + 3.31662i) q^{88} +(0.316625 + 0.316625i) q^{89} +(-9.00000 + 6.00000i) q^{91} +(-3.31662 + 3.31662i) q^{92} -9.31662i q^{94} +(6.31662 + 0.316625i) q^{95} +8.94987 q^{97} -2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 6 q^{10} - 8 q^{13} + 4 q^{16} - 6 q^{17} - 8 q^{19} - 6 q^{20} - 2 q^{25} - 8 q^{26} + 4 q^{31} + 4 q^{32} - 6 q^{34} - 8 q^{38} - 6 q^{40} + 12 q^{41} + 10 q^{43}+ \cdots - 8 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 6 * q^10 - 8 * q^13 + 4 * q^16 - 6 * q^17 - 8 * q^19 - 6 * q^20 - 2 * q^25 - 8 * q^26 + 4 * q^31 + 4 * q^32 - 6 * q^34 - 8 * q^38 - 6 * q^40 + 12 * q^41 + 10 * q^43 - 8 * q^49 - 2 * q^50 - 8 * q^52 - 12 * q^53 + 22 * q^55 - 12 * q^59 + 8 * q^61 + 4 * q^62 + 4 * q^64 + 12 * q^65 + 20 * q^67 - 6 * q^68 + 18 * q^71 - 16 * q^73 - 8 * q^76 - 6 * q^80 + 12 * q^82 - 2 * q^85 + 10 * q^86 - 12 * q^89 - 36 * q^91 + 12 * q^95 - 4 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$5$	−1.50000	−	1.65831i	−0.670820	−	0.741620i
$6$		0			0
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.50000	−	1.65831i	−0.474342	−	0.524404i
$11$	−3.31662	+	3.31662i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$11$	−3.31662	+	3.31662i	−1.00000	+	1.00000i	−1.00000			$\pi$
$12$		0			0
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$		−	3.00000i		−	0.801784i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.15831	−	3.15831i	−0.766003	−	0.766003i	0.211397	−	0.977400i	$-0.432199\pi$
$17$	−3.15831	−	3.15831i	−0.766003	−	0.766003i	−0.977400	+	0.211397i	$0.932199\pi$
$18$		0			0
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	−0.898272	−	0.439440i	$-0.855177\pi$
$19$	−2.00000	+	2.00000i	−0.458831	+	0.458831i	0.439440	+	0.898272i	$0.355177\pi$
$20$	−1.50000	−	1.65831i	−0.335410	−	0.370810i
$21$		0			0
$22$	−3.31662	+	3.31662i	−0.707107	+	0.707107i
$23$	−3.31662	+	3.31662i	−0.691564	+	0.691564i	−0.962576	−	0.271012i	$-0.912642\pi$
$23$	−3.31662	+	3.31662i	−0.691564	+	0.691564i	0.271012	+	0.962576i	$0.412642\pi$
$24$		0			0
$25$	−0.500000	+	4.97494i	−0.100000	+	0.994987i
$26$	−2.00000	−	3.00000i	−0.392232	−	0.588348i
$27$		0			0
$28$		−	3.00000i		−	0.566947i
$29$		−	6.31662i		−	1.17297i	−0.809961	−	0.586484i	$-0.800512\pi$
$29$		−	6.31662i		−	1.17297i	0.809961	−	0.586484i	$-0.199488\pi$
$30$		0			0
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−3.15831	−	3.15831i	−0.541646	−	0.541646i
$35$	−4.97494	+	4.50000i	−0.840918	+	0.760639i
$36$		0			0
$37$		−	3.00000i		−	0.493197i	−0.969118	−	0.246598i	$-0.920687\pi$
$37$		−	3.00000i		−	0.493197i	0.969118	−	0.246598i	$-0.0793129\pi$
$38$	−2.00000	+	2.00000i	−0.324443	+	0.324443i
$39$		0			0
$40$	−1.50000	−	1.65831i	−0.237171	−	0.262202i
$41$	6.31662	+	6.31662i	0.986491	+	0.986491i	0.999910	−	0.0134189i	$-0.00427150\pi$
$41$	6.31662	+	6.31662i	0.986491	+	0.986491i	−0.0134189	+	0.999910i	$0.504271\pi$
$42$		0			0
$43$	−2.47494	+	2.47494i	−0.377424	+	0.377424i	−0.870172	−	0.492748i	$-0.835993\pi$
$43$	−2.47494	+	2.47494i	−0.377424	+	0.377424i	0.492748	+	0.870172i	$0.335993\pi$
$44$	−3.31662	+	3.31662i	−0.500000	+	0.500000i
$45$		0			0
$46$	−3.31662	+	3.31662i	−0.489010	+	0.489010i
$47$		−	9.31662i		−	1.35897i	−0.733690	−	0.679485i	$-0.762203\pi$
$47$		−	9.31662i		−	1.35897i	0.733690	−	0.679485i	$-0.237797\pi$
$48$		0			0
$49$	−2.00000			−0.285714
$50$	−0.500000	+	4.97494i	−0.0707107	+	0.703562i
$51$		0			0
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	−9.63325	−	9.63325i	−1.32323	−	1.32323i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$	−9.63325	−	9.63325i	−1.32323	−	1.32323i	−0.412082	−	0.911147i	$-0.635198\pi$
$54$		0			0
$55$	10.4749	+	0.525063i	1.41244	+	0.0707995i
$56$		−	3.00000i		−	0.400892i
$57$		0			0
$58$		−	6.31662i		−	0.829413i
$59$	0.316625	+	0.316625i	0.0412210	+	0.0412210i	0.727417	−	0.686196i	$-0.240721\pi$
$59$	0.316625	+	0.316625i	0.0412210	+	0.0412210i	−0.686196	+	0.727417i	$0.740721\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	1.00000	+	1.00000i	0.127000	+	0.127000i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.97494	+	7.81662i	−0.244961	+	0.969533i
$66$		0			0
$67$	−4.94987			−0.604723			−0.302362	−	0.953193i	$-0.597775\pi$
$67$	−4.94987			−0.604723			−0.302362	+	0.953193i	$0.597775\pi$
$68$	−3.15831	−	3.15831i	−0.383002	−	0.383002i
$69$		0			0
$70$	−4.97494	+	4.50000i	−0.594619	+	0.537853i
$71$	2.84169	+	2.84169i	0.337246	+	0.337246i	0.855330	−	0.518084i	$-0.173354\pi$
$71$	2.84169	+	2.84169i	0.337246	+	0.337246i	−0.518084	+	0.855330i	$0.673354\pi$
$72$		0			0
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$		−	3.00000i		−	0.348743i
$75$		0			0
$76$	−2.00000	+	2.00000i	−0.229416	+	0.229416i
$77$	9.94987	+	9.94987i	1.13389	+	1.13389i
$78$		0			0
$79$		−	12.9499i		−	1.45697i	−0.685059	−	0.728487i	$-0.740224\pi$
$79$		−	12.9499i		−	1.45697i	0.685059	−	0.728487i	$-0.259776\pi$
$80$	−1.50000	−	1.65831i	−0.167705	−	0.185405i
$81$		0			0
$82$	6.31662	+	6.31662i	0.697555	+	0.697555i
$83$		−	6.31662i		−	0.693340i	−0.937987	−	0.346670i	$-0.887312\pi$
$83$		−	6.31662i		−	0.693340i	0.937987	−	0.346670i	$-0.112688\pi$
$84$		0			0
$85$	−0.500000	+	9.97494i	−0.0542326	+	1.08193i
$86$	−2.47494	+	2.47494i	−0.266879	+	0.266879i
$87$		0			0
$88$	−3.31662	+	3.31662i	−0.353553	+	0.353553i
$89$	0.316625	+	0.316625i	0.0335622	+	0.0335622i	0.723689	−	0.690127i	$-0.242445\pi$
$89$	0.316625	+	0.316625i	0.0335622	+	0.0335622i	−0.690127	+	0.723689i	$0.742445\pi$
$90$		0			0
$91$	−9.00000	+	6.00000i	−0.943456	+	0.628971i
$92$	−3.31662	+	3.31662i	−0.345782	+	0.345782i
$93$		0			0
$94$		−	9.31662i		−	0.960936i
$95$	6.31662	+	0.316625i	0.648072	+	0.0324850i
$96$		0			0
$97$	8.94987			0.908722			0.454361	−	0.890818i	$-0.349868\pi$
$97$	8.94987			0.908722			0.454361	+	0.890818i	$0.349868\pi$
$98$	−2.00000			−0.202031
$99$		0			0
$100$	−0.500000	+	4.97494i	−0.0500000	+	0.497494i
$101$		−	19.2665i		−	1.91709i	−0.284944	−	0.958544i	$-0.591975\pi$
$101$		−	19.2665i		−	1.91709i	0.284944	−	0.958544i	$-0.408025\pi$
$102$		0			0
$103$	7.94987	−	7.94987i	0.783324	−	0.783324i	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	7.94987	−	7.94987i	0.783324	−	0.783324i	0.980390	+	0.197066i	$0.0631413\pi$
$104$	−2.00000	−	3.00000i	−0.196116	−	0.294174i
$105$		0			0
$106$	−9.63325	−	9.63325i	−0.935664	−	0.935664i
$107$	9.63325	−	9.63325i	0.931281	−	0.931281i	−0.0665047	−	0.997786i	$-0.521185\pi$
$107$	9.63325	−	9.63325i	0.931281	−	0.931281i	0.997786	+	0.0665047i	$0.0211847\pi$
$108$		0			0
$109$	1.47494	−	1.47494i	0.141273	−	0.141273i	−0.632933	−	0.774206i	$-0.718149\pi$
$109$	1.47494	−	1.47494i	0.141273	−	0.141273i	0.774206	+	0.632933i	$0.218149\pi$
$110$	10.4749	+	0.525063i	0.998746	+	0.0500628i
$111$		0			0
$112$		−	3.00000i		−	0.283473i
$113$	−2.68338	−	2.68338i	−0.252431	−	0.252431i	0.569536	−	0.821967i	$-0.307123\pi$
$113$	−2.68338	−	2.68338i	−0.252431	−	0.252431i	−0.821967	+	0.569536i	$0.807123\pi$
$114$		0			0
$115$	10.4749	+	0.525063i	0.976793	+	0.0489624i
$116$		−	6.31662i		−	0.586484i
$117$		0			0
$118$	0.316625	+	0.316625i	0.0291477	+	0.0291477i
$119$	−9.47494	+	9.47494i	−0.868566	+	0.868566i
$120$		0			0
$121$		−	11.0000i		−	1.00000i
$122$	2.00000			0.181071
$123$		0			0
$124$	1.00000	+	1.00000i	0.0898027	+	0.0898027i
$125$	9.00000	−	6.63325i	0.804984	−	0.593296i
$126$		0			0
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	0.945825	−	0.324676i	$-0.105255\pi$
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	−0.324676	+	0.945825i	$0.605255\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.97494	+	7.81662i	−0.173213	+	0.685563i
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$	−4.94987			−0.427604
$135$		0			0
$136$	−3.15831	−	3.15831i	−0.270823	−	0.270823i
$137$			5.68338i			0.485564i	0.970081	+	0.242782i	$0.0780599\pi$
$137$			5.68338i			0.485564i	−0.970081	+	0.242782i	$0.921940\pi$
$138$		0			0
$139$			15.9499i			1.35285i	0.736511	+	0.676425i	$0.236472\pi$
$139$			15.9499i			1.35285i	−0.736511	+	0.676425i	$0.763528\pi$
$140$	−4.97494	+	4.50000i	−0.420459	+	0.380319i
$141$		0			0
$142$	2.84169	+	2.84169i	0.238469	+	0.238469i
$143$	16.5831	+	3.31662i	1.38675	+	0.277350i
$144$		0			0
$145$	−10.4749	+	9.47494i	−0.869896	+	0.786851i
$146$	−4.00000			−0.331042
$147$		0			0
$148$		−	3.00000i		−	0.246598i
$149$	−15.3166	+	15.3166i	−1.25479	+	1.25479i	−0.301238	+	0.953549i	$0.597400\pi$
$149$	−15.3166	+	15.3166i	−1.25479	+	1.25479i	−0.953549	+	0.301238i	$0.902600\pi$
$150$		0			0
$151$	4.47494	−	4.47494i	0.364165	−	0.364165i	−0.501179	−	0.865344i	$-0.667100\pi$
$151$	4.47494	−	4.47494i	0.364165	−	0.364165i	0.865344	+	0.501179i	$0.167100\pi$
$152$	−2.00000	+	2.00000i	−0.162221	+	0.162221i
$153$		0			0
$154$	9.94987	+	9.94987i	0.801784	+	0.801784i
$155$	0.158312	−	3.15831i	0.0127160	−	0.253682i
$156$		0			0
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	−0.184707	−	0.982794i	$-0.559134\pi$
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	0.982794	+	0.184707i	$0.0591335\pi$
$158$		−	12.9499i		−	1.03024i
$159$		0			0
$160$	−1.50000	−	1.65831i	−0.118585	−	0.131101i
$161$	9.94987	+	9.94987i	0.784160	+	0.784160i
$162$		0			0
$163$	2.94987			0.231052			0.115526	−	0.993304i	$-0.463145\pi$
$163$	2.94987			0.231052			0.115526	+	0.993304i	$0.463145\pi$
$164$	6.31662	+	6.31662i	0.493246	+	0.493246i
$165$		0			0
$166$		−	6.31662i		−	0.490265i
$167$			12.6332i			0.977590i	0.872399	+	0.488795i	$0.162563\pi$
$167$			12.6332i			0.977590i	−0.872399	+	0.488795i	$0.837437\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	−0.500000	+	9.97494i	−0.0383482	+	0.765043i
$171$		0			0
$172$	−2.47494	+	2.47494i	−0.188712	+	0.188712i
$173$	−3.31662	+	3.31662i	−0.252158	+	0.252158i	−0.821855	−	0.569697i	$-0.807061\pi$
$173$	−3.31662	+	3.31662i	−0.252158	+	0.252158i	0.569697	+	0.821855i	$0.307061\pi$
$174$		0			0
$175$	14.9248	+	1.50000i	1.12821	+	0.113389i
$176$	−3.31662	+	3.31662i	−0.250000	+	0.250000i
$177$		0			0
$178$	0.316625	+	0.316625i	0.0237320	+	0.0237320i
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		0			0
$181$			6.94987i			0.516580i	0.966067	+	0.258290i	$0.0831590\pi$
$181$			6.94987i			0.516580i	−0.966067	+	0.258290i	$0.916841\pi$
$182$	−9.00000	+	6.00000i	−0.667124	+	0.444750i
$183$		0			0
$184$	−3.31662	+	3.31662i	−0.244505	+	0.244505i
$185$	−4.97494	+	4.50000i	−0.365765	+	0.330847i
$186$		0			0
$187$	20.9499			1.53201
$188$		−	9.31662i		−	0.679485i
$189$		0			0
$190$	6.31662	+	0.316625i	0.458256	+	0.0229704i
$191$	−5.05013			−0.365414			−0.182707	−	0.983167i	$-0.558486\pi$
$191$	−5.05013			−0.365414			−0.182707	+	0.983167i	$0.558486\pi$
$192$		0			0
$193$	−10.9499			−0.788189			−0.394095	−	0.919070i	$-0.628942\pi$
$193$	−10.9499			−0.788189			−0.394095	+	0.919070i	$0.628942\pi$
$194$	8.94987			0.642564
$195$		0			0
$196$	−2.00000			−0.142857
$197$	−3.94987			−0.281417			−0.140708	−	0.990051i	$-0.544938\pi$
$197$	−3.94987			−0.281417			−0.140708	+	0.990051i	$0.544938\pi$
$198$		0			0
$199$	−16.9499			−1.20154			−0.600772	−	0.799420i	$-0.705140\pi$
$199$	−16.9499			−1.20154			−0.600772	+	0.799420i	$0.705140\pi$
$200$	−0.500000	+	4.97494i	−0.0353553	+	0.351781i
$201$		0			0
$202$		−	19.2665i		−	1.35559i
$203$	−18.9499			−1.33002
$204$		0			0
$205$	1.00000	−	19.9499i	0.0698430	−	1.39336i
$206$	7.94987	−	7.94987i	0.553894	−	0.553894i
$207$		0			0
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$		−	13.2665i		−	0.917663i
$210$		0			0
$211$	−19.9499			−1.37341			−0.686703	−	0.726938i	$-0.740943\pi$
$211$	−19.9499			−1.37341			−0.686703	+	0.726938i	$0.740943\pi$
$212$	−9.63325	−	9.63325i	−0.661614	−	0.661614i
$213$		0			0
$214$	9.63325	−	9.63325i	0.658515	−	0.658515i
$215$	7.81662	+	0.391813i	0.533089	+	0.0267214i
$216$		0			0
$217$	3.00000	−	3.00000i	0.203653	−	0.203653i
$218$	1.47494	−	1.47494i	0.0998954	−	0.0998954i
$219$		0			0
$220$	10.4749	+	0.525063i	0.706220	+	0.0353997i
$221$	−3.15831	+	15.7916i	−0.212451	+	1.06226i
$222$		0			0
$223$			15.9499i			1.06808i	0.845458	+	0.534041i	$0.179327\pi$
$223$			15.9499i			1.06808i	−0.845458	+	0.534041i	$0.820673\pi$
$224$		−	3.00000i		−	0.200446i
$225$		0			0
$226$	−2.68338	−	2.68338i	−0.178495	−	0.178495i
$227$	18.0000			1.19470			0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000			1.19470			0.597351	+	0.801980i	$0.296220\pi$
$228$		0			0
$229$	3.52506	+	3.52506i	0.232943	+	0.232943i	0.813920	−	0.580977i	$-0.197329\pi$
$229$	3.52506	+	3.52506i	0.232943	+	0.232943i	−0.580977	+	0.813920i	$0.697329\pi$
$230$	10.4749	+	0.525063i	0.690697	+	0.0346216i
$231$		0			0
$232$		−	6.31662i		−	0.414707i
$233$	−6.79156	+	6.79156i	−0.444930	+	0.444930i	−0.893665	−	0.448735i	$-0.851875\pi$
$233$	−6.79156	+	6.79156i	−0.444930	+	0.444930i	0.448735	+	0.893665i	$0.351875\pi$
$234$		0			0
$235$	−15.4499	+	13.9749i	−1.00784	+	0.911624i
$236$	0.316625	+	0.316625i	0.0206105	+	0.0206105i
$237$		0			0
$238$	−9.47494	+	9.47494i	−0.614169	+	0.614169i
$239$	−11.8417	+	11.8417i	−0.765975	+	0.765975i	−0.977395	−	0.211420i	$-0.932191\pi$
$239$	−11.8417	+	11.8417i	−0.765975	+	0.765975i	0.211420	+	0.977395i	$0.432191\pi$
$240$		0			0
$241$	16.0000	−	16.0000i	1.03065	−	1.03065i	0.0311354	−	0.999515i	$-0.490088\pi$
$241$	16.0000	−	16.0000i	1.03065	−	1.03065i	0.999515	−	0.0311354i	$-0.00991232\pi$
$242$		−	11.0000i		−	0.707107i
$243$		0			0
$244$	2.00000			0.128037
$245$	3.00000	+	3.31662i	0.191663	+	0.211891i
$246$		0			0
$247$	10.0000	+	2.00000i	0.636285	+	0.127257i
$248$	1.00000	+	1.00000i	0.0635001	+	0.0635001i
$249$		0			0
$250$	9.00000	−	6.63325i	0.569210	−	0.419524i
$251$		−	19.2665i		−	1.21609i	−0.793902	−	0.608045i	$-0.791954\pi$
$251$		−	19.2665i		−	1.21609i	0.793902	−	0.608045i	$-0.208046\pi$
$252$		0			0
$253$		−	22.0000i		−	1.38313i
$254$	7.00000	+	7.00000i	0.439219	+	0.439219i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.8417	+	11.8417i	0.738664	+	0.738664i	0.972319	−	0.233655i	$-0.0750687\pi$
$257$	11.8417	+	11.8417i	0.738664	+	0.738664i	−0.233655	+	0.972319i	$0.575069\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$	−1.97494	+	7.81662i	−0.122480	+	0.484766i
$261$		0			0
$262$	3.00000			0.185341
$263$	12.3166	+	12.3166i	0.759476	+	0.759476i	0.976227	−	0.216751i	$-0.0695461\pi$
$263$	12.3166	+	12.3166i	0.759476	+	0.759476i	−0.216751	+	0.976227i	$0.569546\pi$
$264$		0			0
$265$	−1.52506	+	30.4248i	−0.0936839	+	1.86898i
$266$	6.00000	+	6.00000i	0.367884	+	0.367884i
$267$		0			0
$268$	−4.94987			−0.302362
$269$		−	13.2665i		−	0.808873i	−0.914566	−	0.404436i	$-0.867468\pi$
$269$		−	13.2665i		−	0.808873i	0.914566	−	0.404436i	$-0.132532\pi$
$270$		0			0
$271$	−10.5251	+	10.5251i	−0.639352	+	0.639352i	−0.950396	−	0.311044i	$-0.899321\pi$
$271$	−10.5251	+	10.5251i	−0.639352	+	0.639352i	0.311044	+	0.950396i	$0.399321\pi$
$272$	−3.15831	−	3.15831i	−0.191501	−	0.191501i
$273$		0			0
$274$			5.68338i			0.343345i
$275$	−14.8417	−	18.1583i	−0.894987	−	1.09499i
$276$		0			0
$277$	−21.8997	−	21.8997i	−1.31583	−	1.31583i	−0.917045	−	0.398783i	$-0.869433\pi$
$277$	−21.8997	−	21.8997i	−1.31583	−	1.31583i	−0.398783	−	0.917045i	$-0.630567\pi$
$278$			15.9499i			0.956610i
$279$		0			0
$280$	−4.97494	+	4.50000i	−0.297309	+	0.268926i
$281$	11.6834	−	11.6834i	0.696972	−	0.696972i	−0.266784	−	0.963756i	$-0.585961\pi$
$281$	11.6834	−	11.6834i	0.696972	−	0.696972i	0.963756	+	0.266784i	$0.0859612\pi$
$282$		0			0
$283$	7.94987	−	7.94987i	0.472571	−	0.472571i	−0.430175	−	0.902746i	$-0.641548\pi$
$283$	7.94987	−	7.94987i	0.472571	−	0.472571i	0.902746	+	0.430175i	$0.141548\pi$
$284$	2.84169	+	2.84169i	0.168623	+	0.168623i
$285$		0			0
$286$	16.5831	+	3.31662i	0.980581	+	0.196116i
$287$	18.9499	−	18.9499i	1.11858	−	1.11858i
$288$		0			0
$289$			2.94987i			0.173522i
$290$	−10.4749	+	9.47494i	−0.615109	+	0.556387i
$291$		0			0
$292$	−4.00000			−0.234082
$293$	22.8997			1.33782			0.668909	−	0.743344i	$-0.266762\pi$
$293$	22.8997			1.33782			0.668909	+	0.743344i	$0.266762\pi$
$294$		0			0
$295$	0.0501256	−	1.00000i	0.00291843	−	0.0582223i
$296$		−	3.00000i		−	0.174371i
$297$		0			0
$298$	−15.3166	+	15.3166i	−0.887268	+	0.887268i
$299$	16.5831	+	3.31662i	0.959027	+	0.191805i
$300$		0			0
$301$	7.42481	+	7.42481i	0.427959	+	0.427959i
$302$	4.47494	−	4.47494i	0.257504	−	0.257504i
$303$		0			0
$304$	−2.00000	+	2.00000i	−0.114708	+	0.114708i
$305$	−3.00000	−	3.31662i	−0.171780	−	0.189909i
$306$		0			0
$307$			25.8997i			1.47818i	0.673608	+	0.739088i	$0.264743\pi$
$307$			25.8997i			1.47818i	−0.673608	+	0.739088i	$0.735257\pi$
$308$	9.94987	+	9.94987i	0.566947	+	0.566947i
$309$		0			0
$310$	0.158312	−	3.15831i	0.00899154	−	0.179380i
$311$		−	19.2665i		−	1.09250i	−0.837621	−	0.546251i	$-0.816054\pi$
$311$		−	19.2665i		−	1.09250i	0.837621	−	0.546251i	$-0.183946\pi$
$312$		0			0
$313$	−15.4248	−	15.4248i	−0.871862	−	0.871862i	0.120813	−	0.992675i	$-0.461450\pi$
$313$	−15.4248	−	15.4248i	−0.871862	−	0.871862i	−0.992675	+	0.120813i	$0.961450\pi$
$314$	10.0000	−	10.0000i	0.564333	−	0.564333i
$315$		0			0
$316$		−	12.9499i		−	0.728487i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$	20.9499	+	20.9499i	1.17297	+	1.17297i
$320$	−1.50000	−	1.65831i	−0.0838525	−	0.0927025i
$321$		0			0
$322$	9.94987	+	9.94987i	0.554485	+	0.554485i
$323$	12.6332			0.702933
$324$		0			0
$325$	15.9248	−	8.44987i	0.883350	−	0.468715i
$326$	2.94987			0.163378
$327$		0			0
$328$	6.31662	+	6.31662i	0.348777	+	0.348777i
$329$	−27.9499			−1.54093
$330$		0			0
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	0.734055	−	0.679090i	$-0.237625\pi$
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	−0.679090	+	0.734055i	$0.737625\pi$
$332$		−	6.31662i		−	0.346670i
$333$		0			0
$334$			12.6332i			0.691261i
$335$	7.42481	+	8.20844i	0.405661	+	0.448475i
$336$		0			0
$337$	3.52506	+	3.52506i	0.192022	+	0.192022i	0.796569	−	0.604547i	$-0.206646\pi$
$337$	3.52506	+	3.52506i	0.192022	+	0.192022i	−0.604547	+	0.796569i	$0.706646\pi$
$338$	−5.00000	+	12.0000i	−0.271964	+	0.652714i
$339$		0			0
$340$	−0.500000	+	9.97494i	−0.0271163	+	0.540967i
$341$	−6.63325			−0.359211
$342$		0			0
$343$		−	15.0000i		−	0.809924i
$344$	−2.47494	+	2.47494i	−0.133440	+	0.133440i
$345$		0			0
$346$	−3.31662	+	3.31662i	−0.178303	+	0.178303i
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	−0.728034	−	0.685541i	$-0.759566\pi$
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	0.685541	+	0.728034i	$0.259566\pi$
$348$		0			0
$349$	−18.4248	−	18.4248i	−0.986258	−	0.986258i	0.0136493	−	0.999907i	$-0.495655\pi$
$349$	−18.4248	−	18.4248i	−0.986258	−	0.986258i	−0.999907	+	0.0136493i	$0.995655\pi$
$350$	14.9248	+	1.50000i	0.797765	+	0.0801784i
$351$		0			0
$352$	−3.31662	+	3.31662i	−0.176777	+	0.176777i
$353$			7.58312i			0.403609i	0.979426	+	0.201804i	$0.0646806\pi$
$353$			7.58312i			0.403609i	−0.979426	+	0.201804i	$0.935319\pi$
$354$		0			0
$355$	0.449874	−	8.97494i	0.0238769	−	0.476340i
$356$	0.316625	+	0.316625i	0.0167811	+	0.0167811i
$357$		0			0
$358$	15.0000			0.792775
$359$	22.2665	+	22.2665i	1.17518	+	1.17518i	0.980957	+	0.194224i	$0.0622187\pi$
$359$	22.2665	+	22.2665i	1.17518	+	1.17518i	0.194224	+	0.980957i	$0.437781\pi$
$360$		0			0
$361$			11.0000i			0.578947i
$362$			6.94987i			0.365277i
$363$		0			0
$364$	−9.00000	+	6.00000i	−0.471728	+	0.314485i
$365$	6.00000	+	6.63325i	0.314054	+	0.347200i
$366$		0			0
$367$	1.94987	−	1.94987i	0.101783	−	0.101783i	−0.654382	−	0.756164i	$-0.727071\pi$
$367$	1.94987	−	1.94987i	0.101783	−	0.101783i	0.756164	+	0.654382i	$0.227071\pi$
$368$	−3.31662	+	3.31662i	−0.172891	+	0.172891i
$369$		0			0
$370$	−4.97494	+	4.50000i	−0.258635	+	0.233944i
$371$	−28.8997	+	28.8997i	−1.50040	+	1.50040i
$372$		0			0
$373$	−20.0000	−	20.0000i	−1.03556	−	1.03556i	−0.999344	−	0.0362168i	$-0.988469\pi$
$373$	−20.0000	−	20.0000i	−1.03556	−	1.03556i	−0.0362168	−	0.999344i	$-0.511531\pi$
$374$	20.9499			1.08329
$375$		0			0
$376$		−	9.31662i		−	0.480468i
$377$	−18.9499	+	12.6332i	−0.975968	+	0.650645i
$378$		0			0
$379$	13.0000	−	13.0000i	0.667765	−	0.667765i	−0.289433	−	0.957198i	$-0.593467\pi$
$379$	13.0000	−	13.0000i	0.667765	−	0.667765i	0.957198	+	0.289433i	$0.0934668\pi$
$380$	6.31662	+	0.316625i	0.324036	+	0.0162425i
$381$		0			0
$382$	−5.05013			−0.258387
$383$		−	14.3668i		−	0.734107i	−0.930200	−	0.367053i	$-0.880367\pi$
$383$		−	14.3668i		−	0.734107i	0.930200	−	0.367053i	$-0.119633\pi$
$384$		0			0
$385$	1.57519	−	31.4248i	0.0802790	−	1.60156i
$386$	−10.9499			−0.557334
$387$		0			0
$388$	8.94987			0.454361
$389$	−13.8997			−0.704745			−0.352373	−	0.935860i	$-0.614625\pi$
$389$	−13.8997			−0.704745			−0.352373	+	0.935860i	$0.614625\pi$
$390$		0			0
$391$	20.9499			1.05948
$392$	−2.00000			−0.101015
$393$		0			0
$394$	−3.94987			−0.198992
$395$	−21.4749	+	19.4248i	−1.08052	+	0.977368i
$396$		0			0
$397$		−	18.0000i		−	0.903394i	−0.892171	−	0.451697i	$-0.850819\pi$
$397$		−	18.0000i		−	0.903394i	0.892171	−	0.451697i	$-0.149181\pi$
$398$	−16.9499			−0.849620
$399$		0			0
$400$	−0.500000	+	4.97494i	−0.0250000	+	0.248747i
$401$	10.5831	−	10.5831i	0.528496	−	0.528496i	−0.391628	−	0.920124i	$-0.628088\pi$
$401$	10.5831	−	10.5831i	0.528496	−	0.528496i	0.920124	+	0.391628i	$0.128088\pi$
$402$		0			0
$403$	1.00000	−	5.00000i	0.0498135	−	0.249068i
$404$		−	19.2665i		−	0.958544i
$405$		0			0
$406$	−18.9499			−0.940466
$407$	9.94987	+	9.94987i	0.493197	+	0.493197i
$408$		0			0
$409$	−23.9499	+	23.9499i	−1.18425	+	1.18425i	−0.205611	+	0.978634i	$0.565918\pi$
$409$	−23.9499	+	23.9499i	−1.18425	+	1.18425i	−0.978634	+	0.205611i	$0.934082\pi$
$410$	1.00000	−	19.9499i	0.0493865	−	0.985254i
$411$		0			0
$412$	7.94987	−	7.94987i	0.391662	−	0.391662i
$413$	0.949874	−	0.949874i	0.0467403	−	0.0467403i
$414$		0			0
$415$	−10.4749	+	9.47494i	−0.514194	+	0.465106i
$416$	−2.00000	−	3.00000i	−0.0980581	−	0.147087i
$417$		0			0
$418$		−	13.2665i		−	0.648886i
$419$			8.68338i			0.424211i	0.977247	+	0.212105i	$0.0680320\pi$
$419$			8.68338i			0.424211i	−0.977247	+	0.212105i	$0.931968\pi$
$420$		0			0
$421$	−2.47494	−	2.47494i	−0.120621	−	0.120621i	0.644220	−	0.764841i	$-0.277182\pi$
$421$	−2.47494	−	2.47494i	−0.120621	−	0.120621i	−0.764841	+	0.644220i	$0.777182\pi$
$422$	−19.9499			−0.971145
$423$		0			0
$424$	−9.63325	−	9.63325i	−0.467832	−	0.467832i
$425$	17.2916	−	14.1332i	0.838764	−	0.685563i
$426$		0			0
$427$		−	6.00000i		−	0.290360i
$428$	9.63325	−	9.63325i	0.465641	−	0.465641i
$429$		0			0
$430$	7.81662	+	0.391813i	0.376951	+	0.0188949i
$431$	−12.1583	−	12.1583i	−0.585645	−	0.585645i	0.350804	−	0.936449i	$-0.385908\pi$
$431$	−12.1583	−	12.1583i	−0.585645	−	0.585645i	−0.936449	+	0.350804i	$0.885908\pi$
$432$		0			0
$433$	12.5251	−	12.5251i	0.601916	−	0.601916i	−0.338905	−	0.940821i	$-0.610056\pi$
$433$	12.5251	−	12.5251i	0.601916	−	0.601916i	0.940821	+	0.338905i	$0.110056\pi$
$434$	3.00000	−	3.00000i	0.144005	−	0.144005i
$435$		0			0
$436$	1.47494	−	1.47494i	0.0706367	−	0.0706367i
$437$		−	13.2665i		−	0.634623i
$438$		0			0
$439$	33.8997			1.61795			0.808973	−	0.587845i	$-0.200024\pi$
$439$	33.8997			1.61795			0.808973	+	0.587845i	$0.200024\pi$
$440$	10.4749	+	0.525063i	0.499373	+	0.0250314i
$441$		0			0
$442$	−3.15831	+	15.7916i	−0.150226	+	0.751128i
$443$	−20.0581	−	20.0581i	−0.952987	−	0.952987i	0.0459562	−	0.998943i	$-0.485367\pi$
$443$	−20.0581	−	20.0581i	−0.952987	−	0.952987i	−0.998943	+	0.0459562i	$0.985367\pi$
$444$		0			0
$445$	0.0501256	−	1.00000i	0.00237618	−	0.0474045i
$446$			15.9499i			0.755248i
$447$		0			0
$448$		−	3.00000i		−	0.141737i
$449$	−21.6332	−	21.6332i	−1.02094	−	1.02094i	−0.999776	−	0.0211601i	$-0.993264\pi$
$449$	−21.6332	−	21.6332i	−1.02094	−	1.02094i	−0.0211601	−	0.999776i	$-0.506736\pi$
$450$		0			0
$451$	−41.8997			−1.97298
$452$	−2.68338	−	2.68338i	−0.126215	−	0.126215i
$453$		0			0
$454$	18.0000			0.844782
$455$	23.4499	+	5.92481i	1.09935	+	0.277759i
$456$		0			0
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$	3.52506	+	3.52506i	0.164715	+	0.164715i
$459$		0			0
$460$	10.4749	+	0.525063i	0.488396	+	0.0244812i
$461$	−4.10819	−	4.10819i	−0.191337	−	0.191337i	0.604936	−	0.796274i	$-0.293199\pi$
$461$	−4.10819	−	4.10819i	−0.191337	−	0.191337i	−0.796274	+	0.604936i	$0.793199\pi$
$462$		0			0
$463$	9.89975			0.460080			0.230040	−	0.973181i	$-0.426114\pi$
$463$	9.89975			0.460080			0.230040	+	0.973181i	$0.426114\pi$
$464$		−	6.31662i		−	0.293242i
$465$		0			0
$466$	−6.79156	+	6.79156i	−0.314613	+	0.314613i
$467$	8.36675	+	8.36675i	0.387167	+	0.387167i	0.873676	−	0.486509i	$-0.161730\pi$
$467$	8.36675	+	8.36675i	0.387167	+	0.387167i	−0.486509	+	0.873676i	$0.661730\pi$
$468$		0			0
$469$			14.8496i			0.685692i
$470$	−15.4499	+	13.9749i	−0.712650	+	0.644616i
$471$		0			0
$472$	0.316625	+	0.316625i	0.0145738	+	0.0145738i
$473$		−	16.4169i		−	0.754849i
$474$		0			0
$475$	−8.94987	−	10.9499i	−0.410648	−	0.502415i
$476$	−9.47494	+	9.47494i	−0.434283	+	0.434283i
$477$		0			0
$478$	−11.8417	+	11.8417i	−0.541626	+	0.541626i
$479$	−3.15831	−	3.15831i	−0.144307	−	0.144307i	0.631262	−	0.775569i	$-0.282537\pi$
$479$	−3.15831	−	3.15831i	−0.144307	−	0.144307i	−0.775569	+	0.631262i	$0.782537\pi$
$480$		0			0
$481$	−9.00000	+	6.00000i	−0.410365	+	0.273576i
$482$	16.0000	−	16.0000i	0.728780	−	0.728780i
$483$		0			0
$484$		−	11.0000i		−	0.500000i
$485$	−13.4248	−	14.8417i	−0.609589	−	0.673926i
$486$		0			0
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	2.00000			0.0905357
$489$		0			0
$490$	3.00000	+	3.31662i	0.135526	+	0.149830i
$491$			32.6834i			1.47498i	0.675358	+	0.737490i	$0.263989\pi$
$491$			32.6834i			1.47498i	−0.675358	+	0.737490i	$0.736011\pi$
$492$		0			0
$493$	−19.9499	+	19.9499i	−0.898497	+	0.898497i
$494$	10.0000	+	2.00000i	0.449921	+	0.0899843i
$495$		0			0
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	8.52506	−	8.52506i	0.382401	−	0.382401i
$498$		0			0
$499$	−8.94987	+	8.94987i	−0.400651	+	0.400651i	−0.878463	−	0.477811i	$-0.841430\pi$
$499$	−8.94987	+	8.94987i	−0.400651	+	0.400651i	0.477811	+	0.878463i	$0.341430\pi$
$500$	9.00000	−	6.63325i	0.402492	−	0.296648i
$501$		0			0
$502$		−	19.2665i		−	0.859906i
$503$	−1.58312	−	1.58312i	−0.0705880	−	0.0705880i	0.670931	−	0.741519i	$-0.265894\pi$
$503$	−1.58312	−	1.58312i	−0.0705880	−	0.0705880i	−0.741519	+	0.670931i	$0.765894\pi$
$504$		0			0
$505$	−31.9499	+	28.8997i	−1.42175	+	1.28602i
$506$		−	22.0000i		−	0.978019i
$507$		0			0
$508$	7.00000	+	7.00000i	0.310575	+	0.310575i
$509$	−15.3166	+	15.3166i	−0.678897	+	0.678897i	−0.959751	−	0.280853i	$-0.909383\pi$
$509$	−15.3166	+	15.3166i	−0.678897	+	0.678897i	0.280853	+	0.959751i	$0.409383\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$	1.00000			0.0441942
$513$		0			0
$514$	11.8417	+	11.8417i	0.522314	+	0.522314i
$515$	−25.1082	−	1.25856i	−1.10640	−	0.0554589i
$516$		0			0
$517$	30.8997	+	30.8997i	1.35897	+	1.35897i
$518$	−9.00000			−0.395437
$519$		0			0
$520$	−1.97494	+	7.81662i	−0.0866067	+	0.342782i
$521$	−10.8997			−0.477527			−0.238763	−	0.971078i	$-0.576742\pi$
$521$	−10.8997			−0.477527			−0.238763	+	0.971078i	$0.576742\pi$
$522$		0			0
$523$	−5.00000	−	5.00000i	−0.218635	−	0.218635i	0.589288	−	0.807923i	$-0.299408\pi$
$523$	−5.00000	−	5.00000i	−0.218635	−	0.218635i	−0.807923	+	0.589288i	$0.799408\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$	12.3166	+	12.3166i	0.537030	+	0.537030i
$527$		−	6.31662i		−	0.275156i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−1.52506	+	30.4248i	−0.0662445	+	1.32157i
$531$		0			0
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	6.31662	−	31.5831i	0.273603	−	1.36802i
$534$		0			0
$535$	−30.4248	−	1.52506i	−1.31538	−	0.0659342i
$536$	−4.94987			−0.213802
$537$		0			0
$538$		−	13.2665i		−	0.571959i
$539$	6.63325	−	6.63325i	0.285714	−	0.285714i
$540$		0			0
$541$	4.47494	−	4.47494i	0.192393	−	0.192393i	−0.604337	−	0.796729i	$-0.706562\pi$
$541$	4.47494	−	4.47494i	0.192393	−	0.192393i	0.796729	+	0.604337i	$0.206562\pi$
$542$	−10.5251	+	10.5251i	−0.452090	+	0.452090i
$543$		0			0
$544$	−3.15831	−	3.15831i	−0.135412	−	0.135412i
$545$	−4.65831	−	0.233501i	−0.199540	−	0.0100021i
$546$		0			0
$547$	21.5251	−	21.5251i	0.920345	−	0.920345i	−0.0767083	−	0.997054i	$-0.524441\pi$
$547$	21.5251	−	21.5251i	0.920345	−	0.920345i	0.997054	+	0.0767083i	$0.0244410\pi$
$548$			5.68338i			0.242782i
$549$		0			0
$550$	−14.8417	−	18.1583i	−0.632852	−	0.774273i
$551$	12.6332	+	12.6332i	0.538195	+	0.538195i
$552$		0			0
$553$	−38.8496			−1.65205
$554$	−21.8997	−	21.8997i	−0.930431	−	0.930431i
$555$		0			0
$556$			15.9499i			0.676425i
$557$			4.58312i			0.194193i	0.995275	+	0.0970966i	$0.0309556\pi$
$557$			4.58312i			0.194193i	−0.995275	+	0.0970966i	$0.969044\pi$
$558$		0			0
$559$	12.3747	+	2.47494i	0.523393	+	0.104679i
$560$	−4.97494	+	4.50000i	−0.210229	+	0.190160i
$561$		0			0
$562$	11.6834	−	11.6834i	0.492833	−	0.492833i
$563$	−6.79156	+	6.79156i	−0.286230	+	0.286230i	−0.835588	−	0.549357i	$-0.814873\pi$
$563$	−6.79156	+	6.79156i	−0.286230	+	0.286230i	0.549357	+	0.835588i	$0.314873\pi$
$564$		0			0
$565$	−0.424812	+	8.47494i	−0.0178720	+	0.356543i
$566$	7.94987	−	7.94987i	0.334158	−	0.334158i
$567$		0			0
$568$	2.84169	+	2.84169i	0.119235	+	0.119235i
$569$	42.7995			1.79425			0.897124	−	0.441779i	$-0.145652\pi$
$569$	42.7995			1.79425			0.897124	+	0.441779i	$0.145652\pi$
$570$		0			0
$571$		−	28.8997i		−	1.20942i	−0.796447	−	0.604708i	$-0.793290\pi$
$571$		−	28.8997i		−	1.20942i	0.796447	−	0.604708i	$-0.206710\pi$
$572$	16.5831	+	3.31662i	0.693375	+	0.138675i
$573$		0			0
$574$	18.9499	−	18.9499i	0.790952	−	0.790952i
$575$	−14.8417	−	18.1583i	−0.618941	−	0.757254i
$576$		0			0
$577$	−41.8997			−1.74431			−0.872155	−	0.489230i	$-0.837278\pi$
$577$	−41.8997			−1.74431			−0.872155	+	0.489230i	$0.837278\pi$
$578$			2.94987i			0.122699i
$579$		0			0
$580$	−10.4749	+	9.47494i	−0.434948	+	0.393425i
$581$	−18.9499			−0.786173
$582$		0			0
$583$	63.8997			2.64646
$584$	−4.00000			−0.165521
$585$		0			0
$586$	22.8997			0.945980
$587$	24.9499			1.02979			0.514896	−	0.857253i	$-0.327831\pi$
$587$	24.9499			1.02979			0.514896	+	0.857253i	$0.327831\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$	0.0501256	−	1.00000i	0.00206364	−	0.0411693i
$591$		0			0
$592$		−	3.00000i		−	0.123299i
$593$	−12.9499			−0.531788			−0.265894	−	0.964002i	$-0.585667\pi$
$593$	−12.9499			−0.531788			−0.265894	+	0.964002i	$0.585667\pi$
$594$		0			0
$595$	29.9248	+	1.50000i	1.22680	+	0.0614940i
$596$	−15.3166	+	15.3166i	−0.627393	+	0.627393i
$597$		0			0
$598$	16.5831	+	3.31662i	0.678134	+	0.135627i
$599$		−	13.2665i		−	0.542054i	−0.962572	−	0.271027i	$-0.912637\pi$
$599$		−	13.2665i		−	0.542054i	0.962572	−	0.271027i	$-0.0873633\pi$
$600$		0			0
$601$	−6.05013			−0.246790			−0.123395	−	0.992358i	$-0.539378\pi$
$601$	−6.05013			−0.246790			−0.123395	+	0.992358i	$0.539378\pi$
$602$	7.42481	+	7.42481i	0.302613	+	0.302613i
$603$		0			0
$604$	4.47494	−	4.47494i	0.182083	−	0.182083i
$605$	−18.2414	+	16.5000i	−0.741620	+	0.670820i
$606$		0			0
$607$	3.05013	−	3.05013i	0.123801	−	0.123801i	−0.642492	−	0.766293i	$-0.722099\pi$
$607$	3.05013	−	3.05013i	0.123801	−	0.123801i	0.766293	+	0.642492i	$0.222099\pi$
$608$	−2.00000	+	2.00000i	−0.0811107	+	0.0811107i
$609$		0			0
$610$	−3.00000	−	3.31662i	−0.121466	−	0.134286i
$611$	−27.9499	+	18.6332i	−1.13073	+	0.753821i
$612$		0			0
$613$			24.0000i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$613$			24.0000i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$614$			25.8997i			1.04523i
$615$		0			0
$616$	9.94987	+	9.94987i	0.400892	+	0.400892i
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$		0			0
$619$	−21.8997	−	21.8997i	−0.880225	−	0.880225i	0.113332	−	0.993557i	$-0.463848\pi$
$619$	−21.8997	−	21.8997i	−0.880225	−	0.880225i	−0.993557	+	0.113332i	$0.963848\pi$
$620$	0.158312	−	3.15831i	0.00635798	−	0.126841i
$621$		0			0
$622$		−	19.2665i		−	0.772516i
$623$	0.949874	−	0.949874i	0.0380559	−	0.0380559i
$624$		0			0
$625$	−24.5000	−	4.97494i	−0.980000	−	0.198997i
$626$	−15.4248	−	15.4248i	−0.616499	−	0.616499i
$627$		0			0
$628$	10.0000	−	10.0000i	0.399043	−	0.399043i
$629$	−9.47494	+	9.47494i	−0.377790	+	0.377790i
$630$		0			0
$631$	4.47494	−	4.47494i	0.178144	−	0.178144i	−0.612402	−	0.790546i	$-0.709797\pi$
$631$	4.47494	−	4.47494i	0.178144	−	0.178144i	0.790546	+	0.612402i	$0.209797\pi$
$632$		−	12.9499i		−	0.515118i
$633$		0			0
$634$	−12.0000			−0.476581
$635$	1.10819	−	22.1082i	0.0439771	−	0.877337i
$636$		0			0
$637$	4.00000	+	6.00000i	0.158486	+	0.237729i
$638$	20.9499	+	20.9499i	0.829413	+	0.829413i
$639$		0			0
$640$	−1.50000	−	1.65831i	−0.0592927	−	0.0655506i
$641$		−	5.36675i		−	0.211974i	−0.994368	−	0.105987i	$-0.966200\pi$
$641$		−	5.36675i		−	0.211974i	0.994368	−	0.105987i	$-0.0338002\pi$
$642$		0			0
$643$		−	12.9499i		−	0.510693i	−0.966850	−	0.255347i	$-0.917810\pi$
$643$		−	12.9499i		−	0.510693i	0.966850	−	0.255347i	$-0.0821896\pi$
$644$	9.94987	+	9.94987i	0.392080	+	0.392080i
$645$		0			0
$646$	12.6332			0.497049
$647$	−6.63325	−	6.63325i	−0.260780	−	0.260780i	0.564591	−	0.825371i	$-0.309034\pi$
$647$	−6.63325	−	6.63325i	−0.260780	−	0.260780i	−0.825371	+	0.564591i	$0.809034\pi$
$648$		0			0
$649$	−2.10025			−0.0824421
$650$	15.9248	−	8.44987i	0.624622	−	0.331431i
$651$		0			0
$652$	2.94987			0.115526
$653$	−31.5831	−	31.5831i	−1.23594	−	1.23594i	−0.961645	−	0.274299i	$-0.911554\pi$
$653$	−31.5831	−	31.5831i	−1.23594	−	1.23594i	−0.274299	−	0.961645i	$-0.588446\pi$
$654$		0			0
$655$	−4.50000	−	4.97494i	−0.175830	−	0.194387i
$656$	6.31662	+	6.31662i	0.246623	+	0.246623i
$657$		0			0
$658$	−27.9499			−1.08960
$659$			0.633250i			0.0246679i	0.999924	+	0.0123340i	$0.00392612\pi$
$659$			0.633250i			0.0246679i	−0.999924	+	0.0123340i	$0.996074\pi$
$660$		0			0
$661$	−12.8997	+	12.8997i	−0.501742	+	0.501742i	−0.911979	−	0.410237i	$-0.865446\pi$
$661$	−12.8997	+	12.8997i	−0.501742	+	0.501742i	0.410237	+	0.911979i	$0.365446\pi$
$662$	1.00000	+	1.00000i	0.0388661	+	0.0388661i
$663$		0			0
$664$		−	6.31662i		−	0.245133i
$665$	0.949874	−	18.9499i	0.0368345	−	0.734845i
$666$		0			0
$667$	20.9499	+	20.9499i	0.811182	+	0.811182i
$668$			12.6332i			0.488795i
$669$		0			0
$670$	7.42481	+	8.20844i	0.286845	+	0.317120i
$671$	−6.63325	+	6.63325i	−0.256074	+	0.256074i
$672$		0			0
$673$	11.4248	−	11.4248i	0.440394	−	0.440394i	−0.451750	−	0.892144i	$-0.649200\pi$
$673$	11.4248	−	11.4248i	0.440394	−	0.440394i	0.892144	+	0.451750i	$0.149200\pi$
$674$	3.52506	+	3.52506i	0.135780	+	0.135780i
$675$		0			0
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	2.68338	−	2.68338i	0.103130	−	0.103130i	−0.653659	−	0.756789i	$-0.726767\pi$
$677$	2.68338	−	2.68338i	0.103130	−	0.103130i	0.756789	+	0.653659i	$0.226767\pi$
$678$		0			0
$679$		−	26.8496i		−	1.03039i
$680$	−0.500000	+	9.97494i	−0.0191741	+	0.382521i
$681$		0			0
$682$	−6.63325			−0.254000
$683$	30.9499			1.18426			0.592132	−	0.805841i	$-0.298286\pi$
$683$	30.9499			1.18426			0.592132	+	0.805841i	$0.298286\pi$
$684$		0			0
$685$	9.42481	−	8.52506i	0.360104	−	0.325726i
$686$		−	15.0000i		−	0.572703i
$687$		0			0
$688$	−2.47494	+	2.47494i	−0.0943561	+	0.0943561i
$689$	−9.63325	+	48.1662i	−0.366998	+	1.83499i
$690$		0			0
$691$	−14.0000	−	14.0000i	−0.532585	−	0.532585i	0.388756	−	0.921341i	$-0.372905\pi$
$691$	−14.0000	−	14.0000i	−0.532585	−	0.532585i	−0.921341	+	0.388756i	$0.872905\pi$
$692$	−3.31662	+	3.31662i	−0.126079	+	0.126079i
$693$		0			0
$694$	−0.791562	+	0.791562i	−0.0300473	+	0.0300473i
$695$	26.4499	−	23.9248i	1.00330	−	0.907520i
$696$		0			0
$697$		−	39.8997i		−	1.51131i
$698$	−18.4248	−	18.4248i	−0.697389	−	0.697389i
$699$		0			0
$700$	14.9248	+	1.50000i	0.564105	+	0.0566947i
$701$			45.4829i			1.71786i	0.512089	+	0.858932i	$0.328872\pi$
$701$			45.4829i			1.71786i	−0.512089	+	0.858932i	$0.671128\pi$
$702$		0			0
$703$	6.00000	+	6.00000i	0.226294	+	0.226294i
$704$	−3.31662	+	3.31662i	−0.125000	+	0.125000i
$705$		0			0
$706$			7.58312i			0.285395i
$707$	−57.7995			−2.17377
$708$		0			0
$709$	−29.9499	−	29.9499i	−1.12479	−	1.12479i	−0.991011	−	0.133780i	$-0.957288\pi$
$709$	−29.9499	−	29.9499i	−1.12479	−	1.12479i	−0.133780	−	0.991011i	$-0.542712\pi$
$710$	0.449874	−	8.97494i	0.0168835	−	0.336823i
$711$		0			0
$712$	0.316625	+	0.316625i	0.0118660	+	0.0118660i
$713$	−6.63325			−0.248417
$714$		0			0
$715$	−19.3747	−	32.4749i	−0.724572	−	1.21449i
$716$	15.0000			0.560576
$717$		0			0
$718$	22.2665	+	22.2665i	0.830978	+	0.830978i
$719$	−6.94987			−0.259187			−0.129593	−	0.991567i	$-0.541367\pi$
$719$	−6.94987			−0.259187			−0.129593	+	0.991567i	$0.541367\pi$
$720$		0			0
$721$	−23.8496	−	23.8496i	−0.888206	−	0.888206i
$722$			11.0000i			0.409378i
$723$		0			0
$724$			6.94987i			0.258290i
$725$	31.4248	+	3.15831i	1.16709	+	0.117297i
$726$		0			0
$727$	13.9499	+	13.9499i	0.517372	+	0.517372i	0.916775	−	0.399403i	$-0.130783\pi$
$727$	13.9499	+	13.9499i	0.517372	+	0.517372i	−0.399403	+	0.916775i	$0.630783\pi$
$728$	−9.00000	+	6.00000i	−0.333562	+	0.222375i
$729$		0			0
$730$	6.00000	+	6.63325i	0.222070	+	0.245508i
$731$	15.6332			0.578217
$732$		0			0
$733$			36.7995i			1.35922i	0.733573	+	0.679610i	$0.237851\pi$
$733$			36.7995i			1.35922i	−0.733573	+	0.679610i	$0.762149\pi$
$734$	1.94987	−	1.94987i	0.0719712	−	0.0719712i
$735$		0			0
$736$	−3.31662	+	3.31662i	−0.122252	+	0.122252i
$737$	16.4169	−	16.4169i	0.604723	−	0.604723i
$738$		0			0
$739$	35.8997	+	35.8997i	1.32059	+	1.32059i	0.913295	+	0.407299i	$0.133529\pi$
$739$	35.8997	+	35.8997i	1.32059	+	1.32059i	0.407299	+	0.913295i	$0.366471\pi$
$740$	−4.97494	+	4.50000i	−0.182882	+	0.165423i
$741$		0			0
$742$	−28.8997	+	28.8997i	−1.06094	+	1.06094i
$743$			15.6332i			0.573528i	0.958001	+	0.286764i	$0.0925796\pi$
$743$			15.6332i			0.573528i	−0.958001	+	0.286764i	$0.907420\pi$
$744$		0			0
$745$	48.3747	+	2.42481i	1.77231	+	0.0888382i
$746$	−20.0000	−	20.0000i	−0.732252	−	0.732252i
$747$		0			0
$748$	20.9499			0.766003
$749$	−28.8997	−	28.8997i	−1.05597	−	1.05597i
$750$		0			0
$751$		−	13.8997i		−	0.507209i	−0.967308	−	0.253605i	$-0.918384\pi$
$751$		−	13.8997i		−	0.507209i	0.967308	−	0.253605i	$-0.0816162\pi$
$752$		−	9.31662i		−	0.339742i
$753$		0			0
$754$	−18.9499	+	12.6332i	−0.690114	+	0.460076i
$755$	−14.1332	−	0.708438i	−0.514362	−	0.0257827i
$756$		0			0
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	−0.792108	−	0.610380i	$-0.791017\pi$
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	0.610380	+	0.792108i	$0.291017\pi$
$758$	13.0000	−	13.0000i	0.472181	−	0.472181i
$759$		0			0
$760$	6.31662	+	0.316625i	0.229128	+	0.0114852i
$761$	25.5831	−	25.5831i	0.927388	−	0.927388i	−0.0701490	−	0.997537i	$-0.522347\pi$
$761$	25.5831	−	25.5831i	0.927388	−	0.927388i	0.997537	+	0.0701490i	$0.0223475\pi$
$762$		0			0
$763$	−4.42481	−	4.42481i	−0.160189	−	0.160189i
$764$	−5.05013			−0.182707
$765$		0			0
$766$		−	14.3668i		−	0.519092i
$767$	0.316625	−	1.58312i	0.0114327	−	0.0571633i
$768$		0			0
$769$	4.94987	−	4.94987i	0.178497	−	0.178497i	−0.612203	−	0.790700i	$-0.709717\pi$
$769$	4.94987	−	4.94987i	0.178497	−	0.178497i	0.790700	+	0.612203i	$0.209717\pi$
$770$	1.57519	−	31.4248i	0.0567659	−	1.13247i
$771$		0			0
$772$	−10.9499			−0.394095
$773$			22.5831i			0.812259i	0.913816	+	0.406129i	$0.133122\pi$
$773$			22.5831i			0.812259i	−0.913816	+	0.406129i	$0.866878\pi$
$774$		0			0
$775$	−5.47494	+	4.47494i	−0.196666	+	0.160744i
$776$	8.94987			0.321282
$777$		0			0
$778$	−13.8997			−0.498330
$779$	−25.2665			−0.905266
$780$		0			0
$781$	−18.8496			−0.674493
$782$	20.9499			0.749166
$783$		0			0
$784$	−2.00000			−0.0714286
$785$	−31.5831	−	1.58312i	−1.12725	−	0.0565041i
$786$		0			0
$787$			25.8997i			0.923226i	0.887081	+	0.461613i	$0.152729\pi$
$787$			25.8997i			0.923226i	−0.887081	+	0.461613i	$0.847271\pi$
$788$	−3.94987			−0.140708
$789$		0			0
$790$	−21.4749	+	19.4248i	−0.764044	+	0.691104i
$791$	−8.05013	+	8.05013i	−0.286230	+	0.286230i
$792$		0			0
$793$	−4.00000	−	6.00000i	−0.142044	−	0.213066i
$794$		−	18.0000i		−	0.638796i
$795$		0			0
$796$	−16.9499			−0.600772
$797$	7.26650	+	7.26650i	0.257393	+	0.257393i	0.823993	−	0.566600i	$-0.191742\pi$
$797$	7.26650	+	7.26650i	0.257393	+	0.257393i	−0.566600	+	0.823993i	$0.691742\pi$
$798$		0			0
$799$	−29.4248	+	29.4248i	−1.04098	+	1.04098i
$800$	−0.500000	+	4.97494i	−0.0176777	+	0.175891i
$801$		0			0
$802$	10.5831	−	10.5831i	0.373703	−	0.373703i
$803$	13.2665	−	13.2665i	0.468165	−	0.468165i
$804$		0			0
$805$	1.57519	−	31.4248i	0.0555181	−	1.10758i
$806$	1.00000	−	5.00000i	0.0352235	−	0.176117i
$807$		0			0
$808$		−	19.2665i		−	0.677793i
$809$		−	14.3668i		−	0.505108i	−0.967583	−	0.252554i	$-0.918729\pi$
$809$		−	14.3668i		−	0.505108i	0.967583	−	0.252554i	$-0.0812705\pi$
$810$		0			0
$811$	22.9499	+	22.9499i	0.805879	+	0.805879i	0.984007	−	0.178128i	$-0.0570042\pi$
$811$	22.9499	+	22.9499i	0.805879	+	0.805879i	−0.178128	+	0.984007i	$0.557004\pi$
$812$	−18.9499			−0.665010
$813$		0			0
$814$	9.94987	+	9.94987i	0.348743	+	0.348743i
$815$	−4.42481	−	4.89181i	−0.154994	−	0.171353i
$816$		0			0
$817$		−	9.89975i		−	0.346348i
$818$	−23.9499	+	23.9499i	−0.837388	+	0.837388i
$819$		0			0
$820$	1.00000	−	19.9499i	0.0349215	−	0.696680i
$821$	24.7916	+	24.7916i	0.865231	+	0.865231i	0.991940	−	0.126709i	$-0.0404413\pi$
$821$	24.7916	+	24.7916i	0.865231	+	0.865231i	−0.126709	+	0.991940i	$0.540441\pi$
$822$		0			0
$823$	−27.8997	+	27.8997i	−0.972524	+	0.972524i	−0.999632	−	0.0271084i	$-0.991370\pi$
$823$	−27.8997	+	27.8997i	−0.972524	+	0.972524i	0.0271084	+	0.999632i	$0.491370\pi$
$824$	7.94987	−	7.94987i	0.276947	−	0.276947i
$825$		0			0
$826$	0.949874	−	0.949874i	0.0330504	−	0.0330504i
$827$		−	31.2665i		−	1.08724i	−0.839331	−	0.543621i	$-0.817053\pi$
$827$		−	31.2665i		−	1.08724i	0.839331	−	0.543621i	$-0.182947\pi$
$828$		0			0
$829$	−30.8496			−1.07145			−0.535726	−	0.844392i	$-0.679962\pi$
$829$	−30.8496			−1.07145			−0.535726	+	0.844392i	$0.679962\pi$
$830$	−10.4749	+	9.47494i	−0.363590	+	0.328880i
$831$		0			0
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$	6.31662	+	6.31662i	0.218858	+	0.218858i
$834$		0			0
$835$	20.9499	−	18.9499i	0.725000	−	0.655787i
$836$		−	13.2665i		−	0.458831i
$837$		0			0
$838$			8.68338i			0.299962i
$839$	−21.6332	−	21.6332i	−0.746863	−	0.746863i	0.227026	−	0.973889i	$-0.427100\pi$
$839$	−21.6332	−	21.6332i	−0.746863	−	0.746863i	−0.973889	+	0.227026i	$0.927100\pi$
$840$		0			0
$841$	−10.8997			−0.375853
$842$	−2.47494	−	2.47494i	−0.0852920	−	0.0852920i
$843$		0			0
$844$	−19.9499			−0.686703
$845$	27.3997	−	9.70844i	0.942580	−	0.333980i
$846$		0			0
$847$	−33.0000			−1.13389
$848$	−9.63325	−	9.63325i	−0.330807	−	0.330807i
$849$		0			0
$850$	17.2916	−	14.1332i	0.593096	−	0.484766i
$851$	9.94987	+	9.94987i	0.341077	+	0.341077i
$852$		0			0
$853$	4.05013			0.138674			0.0693368	−	0.997593i	$-0.477912\pi$
$853$	4.05013			0.138674			0.0693368	+	0.997593i	$0.477912\pi$
$854$		−	6.00000i		−	0.205316i
$855$		0			0
$856$	9.63325	−	9.63325i	0.329258	−	0.329258i
$857$	15.3166	+	15.3166i	0.523206	+	0.523206i	0.918538	−	0.395332i	$-0.129371\pi$
$857$	15.3166	+	15.3166i	0.523206	+	0.523206i	−0.395332	+	0.918538i	$0.629371\pi$
$858$		0			0
$859$		−	19.8997i		−	0.678971i	−0.940611	−	0.339485i	$-0.889747\pi$
$859$		−	19.8997i		−	0.678971i	0.940611	−	0.339485i	$-0.110253\pi$
$860$	7.81662	+	0.391813i	0.266545	+	0.0133607i
$861$		0			0
$862$	−12.1583	−	12.1583i	−0.414114	−	0.414114i
$863$			22.5831i			0.768738i	0.923179	+	0.384369i	$0.125581\pi$
$863$			22.5831i			0.768738i	−0.923179	+	0.384369i	$0.874419\pi$
$864$		0			0
$865$	10.4749	+	0.525063i	0.356159	+	0.0178527i
$866$	12.5251	−	12.5251i	0.425619	−	0.425619i
$867$		0			0
$868$	3.00000	−	3.00000i	0.101827	−	0.101827i
$869$	42.9499	+	42.9499i	1.45697	+	1.45697i
$870$		0			0
$871$	9.89975	+	14.8496i	0.335440	+	0.503160i
$872$	1.47494	−	1.47494i	0.0499477	−	0.0499477i
$873$		0			0
$874$		−	13.2665i		−	0.448746i
$875$	−19.8997	−	27.0000i	−0.672734	−	0.912767i
$876$		0			0
$877$	−6.05013			−0.204298			−0.102149	−	0.994769i	$-0.532572\pi$
$877$	−6.05013			−0.204298			−0.102149	+	0.994769i	$0.532572\pi$
$878$	33.8997			1.14406
$879$		0			0
$880$	10.4749	+	0.525063i	0.353110	+	0.0176999i
$881$			16.5831i			0.558700i	0.960189	+	0.279350i	$0.0901189\pi$
$881$			16.5831i			0.558700i	−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	−24.4248	+	24.4248i	−0.821960	+	0.821960i	−0.986389	−	0.164429i	$-0.947422\pi$
$883$	−24.4248	+	24.4248i	−0.821960	+	0.821960i	0.164429	+	0.986389i	$0.447422\pi$
$884$	−3.15831	+	15.7916i	−0.106226	+	0.531128i
$885$		0			0
$886$	−20.0581	−	20.0581i	−0.673864	−	0.673864i
$887$	−5.36675	+	5.36675i	−0.180198	+	0.180198i	−0.791442	−	0.611244i	$-0.790669\pi$
$887$	−5.36675	+	5.36675i	−0.180198	+	0.180198i	0.611244	+	0.791442i	$0.290669\pi$
$888$		0			0
$889$	21.0000	−	21.0000i	0.704317	−	0.704317i
$890$	0.0501256	−	1.00000i	0.00168021	−	0.0335201i
$891$		0			0
$892$			15.9499i			0.534041i
$893$	18.6332	+	18.6332i	0.623538	+	0.623538i
$894$		0			0
$895$	−22.5000	−	24.8747i	−0.752092	−	0.831469i
$896$		−	3.00000i		−	0.100223i
$897$		0			0
$898$	−21.6332	−	21.6332i	−0.721911	−	0.721911i
$899$	6.31662	−	6.31662i	0.210671	−	0.210671i
$900$		0			0
$901$			60.8496i			2.02719i
$902$	−41.8997			−1.39511
$903$		0			0
$904$	−2.68338	−	2.68338i	−0.0892477	−	0.0892477i
$905$	11.5251	−	10.4248i	0.383106	−	0.346532i
$906$		0			0
$907$	−32.3246	−	32.3246i	−1.07332	−	1.07332i	−0.997090	−	0.0762291i	$-0.975712\pi$
$907$	−32.3246	−	32.3246i	−1.07332	−	1.07332i	−0.0762291	−	0.997090i	$-0.524288\pi$
$908$	18.0000			0.597351
$909$		0			0
$910$	23.4499	+	5.92481i	0.777356	+	0.196406i
$911$	11.0501			0.366107			0.183053	−	0.983103i	$-0.441402\pi$
$911$	11.0501			0.366107			0.183053	+	0.983103i	$0.441402\pi$
$912$		0			0
$913$	20.9499	+	20.9499i	0.693340	+	0.693340i
$914$	2.00000			0.0661541
$915$		0			0
$916$	3.52506	+	3.52506i	0.116471	+	0.116471i
$917$		−	9.00000i		−	0.297206i
$918$		0			0
$919$			10.1003i			0.333177i	0.986027	+	0.166588i	$0.0532751\pi$
$919$			10.1003i			0.333177i	−0.986027	+	0.166588i	$0.946725\pi$
$920$	10.4749	+	0.525063i	0.345348	+	0.0173108i
$921$		0			0
$922$	−4.10819	−	4.10819i	−0.135296	−	0.135296i
$923$	2.84169	−	14.2084i	0.0935353	−	0.467676i
$924$		0			0
$925$	14.9248	+	1.50000i	0.490725	+	0.0493197i
$926$	9.89975			0.325326
$927$		0			0
$928$		−	6.31662i		−	0.207353i
$929$	13.5831	−	13.5831i	0.445648	−	0.445648i	−0.448257	−	0.893905i	$-0.647955\pi$
$929$	13.5831	−	13.5831i	0.445648	−	0.445648i	0.893905	+	0.448257i	$0.147955\pi$
$930$		0			0
$931$	4.00000	−	4.00000i	0.131095	−	0.131095i
$932$	−6.79156	+	6.79156i	−0.222465	+	0.222465i
$933$		0			0
$934$	8.36675	+	8.36675i	0.273768	+	0.273768i
$935$	−31.4248	−	34.7414i	−1.02770	−	1.13617i
$936$		0			0
$937$	1.94987	−	1.94987i	0.0636996	−	0.0636996i	−0.674539	−	0.738239i	$-0.735658\pi$
$937$	1.94987	−	1.94987i	0.0636996	−	0.0636996i	0.738239	+	0.674539i	$0.235658\pi$
$938$			14.8496i			0.484857i
$939$		0			0
$940$	−15.4499	+	13.9749i	−0.503919	+	0.455812i
$941$	1.74144	+	1.74144i	0.0567692	+	0.0567692i	0.734921	−	0.678152i	$-0.237219\pi$
$941$	1.74144	+	1.74144i	0.0567692	+	0.0567692i	−0.678152	+	0.734921i	$0.737219\pi$
$942$		0			0
$943$	−41.8997			−1.36444
$944$	0.316625	+	0.316625i	0.0103053	+	0.0103053i
$945$		0			0
$946$		−	16.4169i		−	0.533759i
$947$			5.68338i			0.184685i	0.995727	+	0.0923424i	$0.0294354\pi$
$947$			5.68338i			0.184685i	−0.995727	+	0.0923424i	$0.970565\pi$
$948$		0			0
$949$	8.00000	+	12.0000i	0.259691	+	0.389536i
$950$	−8.94987	−	10.9499i	−0.290372	−	0.355261i
$951$		0			0
$952$	−9.47494	+	9.47494i	−0.307084	+	0.307084i
$953$	21.0079	−	21.0079i	0.680514	−	0.680514i	−0.279602	−	0.960116i	$-0.590203\pi$
$953$	21.0079	−	21.0079i	0.680514	−	0.680514i	0.960116	+	0.279602i	$0.0902026\pi$
$954$		0			0
$955$	7.57519	+	8.37469i	0.245127	+	0.270998i
$956$	−11.8417	+	11.8417i	−0.382988	+	0.382988i
$957$		0			0
$958$	−3.15831	−	3.15831i	−0.102040	−	0.102040i
$959$	17.0501			0.550577
$960$		0			0
$961$		−	29.0000i		−	0.935484i
$962$	−9.00000	+	6.00000i	−0.290172	+	0.193448i
$963$		0			0
$964$	16.0000	−	16.0000i	0.515325	−	0.515325i
$965$	16.4248	+	18.1583i	0.528733	+	0.584537i
$966$		0			0
$967$	−36.0501			−1.15929			−0.579647	−	0.814868i	$-0.696810\pi$
$967$	−36.0501			−1.15929			−0.579647	+	0.814868i	$0.696810\pi$
$968$		−	11.0000i		−	0.353553i
$969$		0			0
$970$	−13.4248	−	14.8417i	−0.431045	−	0.476538i
$971$	−20.0501			−0.643439			−0.321720	−	0.946835i	$-0.604261\pi$
$971$	−20.0501			−0.643439			−0.321720	+	0.946835i	$0.604261\pi$
$972$		0			0
$973$	47.8496			1.53399
$974$	2.00000			0.0640841
$975$		0			0
$976$	2.00000			0.0640184
$977$	−35.0501			−1.12135			−0.560676	−	0.828035i	$-0.689459\pi$
$977$	−35.0501			−1.12135			−0.560676	+	0.828035i	$0.689459\pi$
$978$		0			0
$979$	−2.10025			−0.0671243
$980$	3.00000	+	3.31662i	0.0958315	+	0.105946i
$981$		0			0
$982$			32.6834i			1.04297i
$983$	2.05013			0.0653889			0.0326944	−	0.999465i	$-0.489591\pi$
$983$	2.05013			0.0653889			0.0326944	+	0.999465i	$0.489591\pi$
$984$		0			0
$985$	5.92481	+	6.55013i	0.188780	+	0.208704i
$986$	−19.9499	+	19.9499i	−0.635333	+	0.635333i
$987$		0			0
$988$	10.0000	+	2.00000i	0.318142	+	0.0636285i
$989$		−	16.4169i		−	0.522026i
$990$		0			0
$991$	59.7995			1.89959			0.949797	−	0.312867i	$-0.101290\pi$
$991$	59.7995			1.89959			0.949797	+	0.312867i	$0.101290\pi$
$992$	1.00000	+	1.00000i	0.0317500	+	0.0317500i
$993$		0			0
$994$	8.52506	−	8.52506i	0.270399	−	0.270399i
$995$	25.4248	+	28.1082i	0.806021	+	0.891089i
$996$		0			0
$997$	8.89975	−	8.89975i	0.281858	−	0.281858i	−0.551992	−	0.833850i	$-0.686132\pi$
$997$	8.89975	−	8.89975i	0.281858	−	0.281858i	0.833850	+	0.551992i	$0.186132\pi$
$998$	−8.94987	+	8.94987i	−0.283303	+	0.283303i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.m.e.73.1		4
3.2	odd	2		130.2.g.d.73.1	yes	4
5.2	odd	4		1170.2.w.e.307.1		4
12.11	even	2		1040.2.bg.k.593.2		4
13.5	odd	4		1170.2.w.e.343.1		4
15.2	even	4		130.2.j.d.47.1	yes	4
15.8	even	4		650.2.j.f.307.2		4
15.14	odd	2		650.2.g.g.593.2		4
39.5	even	4		130.2.j.d.83.1	yes	4
60.47	odd	4		1040.2.cd.i.177.2		4
65.57	even	4	inner	1170.2.m.e.577.2		4
156.83	odd	4		1040.2.cd.i.993.2		4
195.44	even	4		650.2.j.f.343.2		4
195.83	odd	4		650.2.g.g.57.2		4
195.122	odd	4		130.2.g.d.57.1	✓	4
780.707	even	4		1040.2.bg.k.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.d.57.1	✓	4	195.122	odd	4
130.2.g.d.73.1	yes	4	3.2	odd	2
130.2.j.d.47.1	yes	4	15.2	even	4
130.2.j.d.83.1	yes	4	39.5	even	4
650.2.g.g.57.2		4	195.83	odd	4
650.2.g.g.593.2		4	15.14	odd	2
650.2.j.f.307.2		4	15.8	even	4
650.2.j.f.343.2		4	195.44	even	4
1040.2.bg.k.577.2		4	780.707	even	4
1040.2.bg.k.593.2		4	12.11	even	2
1040.2.cd.i.177.2		4	60.47	odd	4
1040.2.cd.i.993.2		4	156.83	odd	4
1170.2.m.e.73.1		4	1.1	even	1	trivial
1170.2.m.e.577.2		4	65.57	even	4	inner
1170.2.w.e.307.1		4	5.2	odd	4
1170.2.w.e.343.1		4	13.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 - 1.65831i) q^{5} -3.00000i q^{7} +1.00000 q^{8} +(-1.50000 - 1.65831i) q^{10} +(-3.31662 + 3.31662i) q^{11} +(-2.00000 - 3.00000i) q^{13} -3.00000i q^{14} +1.00000 q^{16} +(-3.15831 - 3.15831i) q^{17} +(-2.00000 + 2.00000i) q^{19} +(-1.50000 - 1.65831i) q^{20} +(-3.31662 + 3.31662i) q^{22} +(-3.31662 + 3.31662i) q^{23} +(-0.500000 + 4.97494i) q^{25} +(-2.00000 - 3.00000i) q^{26} -3.00000i q^{28} -6.31662i q^{29} +(1.00000 + 1.00000i) q^{31} +1.00000 q^{32} +(-3.15831 - 3.15831i) q^{34} +(-4.97494 + 4.50000i) q^{35} -3.00000i q^{37} +(-2.00000 + 2.00000i) q^{38} +(-1.50000 - 1.65831i) q^{40} +(6.31662 + 6.31662i) q^{41} +(-2.47494 + 2.47494i) q^{43} +(-3.31662 + 3.31662i) q^{44} +(-3.31662 + 3.31662i) q^{46} -9.31662i q^{47} -2.00000 q^{49} +(-0.500000 + 4.97494i) q^{50} +(-2.00000 - 3.00000i) q^{52} +(-9.63325 - 9.63325i) q^{53} +(10.4749 + 0.525063i) q^{55} -3.00000i q^{56} -6.31662i q^{58} +(0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +(1.00000 + 1.00000i) q^{62} +1.00000 q^{64} +(-1.97494 + 7.81662i) q^{65} -4.94987 q^{67} +(-3.15831 - 3.15831i) q^{68} +(-4.97494 + 4.50000i) q^{70} +(2.84169 + 2.84169i) q^{71} -4.00000 q^{73} -3.00000i q^{74} +(-2.00000 + 2.00000i) q^{76} +(9.94987 + 9.94987i) q^{77} -12.9499i q^{79} +(-1.50000 - 1.65831i) q^{80} +(6.31662 + 6.31662i) q^{82} -6.31662i q^{83} +(-0.500000 + 9.97494i) q^{85} +(-2.47494 + 2.47494i) q^{86} +(-3.31662 + 3.31662i) q^{88} +(0.316625 + 0.316625i) q^{89} +(-9.00000 + 6.00000i) q^{91} +(-3.31662 + 3.31662i) q^{92} -9.31662i q^{94} +(6.31662 + 0.316625i) q^{95} +8.94987 q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 6 q^{10} - 8 q^{13} + 4 q^{16} - 6 q^{17} - 8 q^{19} - 6 q^{20} - 2 q^{25} - 8 q^{26} + 4 q^{31} + 4 q^{32} - 6 q^{34} - 8 q^{38} - 6 q^{40} + 12 q^{41} + 10 q^{43}+ \cdots - 8 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 6 * q^10 - 8 * q^13 + 4 * q^16 - 6 * q^17 - 8 * q^19 - 6 * q^20 - 2 * q^25 - 8 * q^26 + 4 * q^31 + 4 * q^32 - 6 * q^34 - 8 * q^38 - 6 * q^40 + 12 * q^41 + 10 * q^43 - 8 * q^49 - 2 * q^50 - 8 * q^52 - 12 * q^53 + 22 * q^55 - 12 * q^59 + 8 * q^61 + 4 * q^62 + 4 * q^64 + 12 * q^65 + 20 * q^67 - 6 * q^68 + 18 * q^71 - 16 * q^73 - 8 * q^76 - 6 * q^80 + 12 * q^82 - 2 * q^85 + 10 * q^86 - 12 * q^89 - 36 * q^91 + 12 * q^95 - 4 * q^97 - 8 * q^98

Introduction

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