LMFDB - Embedded newform 1521.2.i.e.746.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1521,2,Mod(746,1521)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1521, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1521.746");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1521 = 3^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1521.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.1452461474$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			746.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1521.746
Dual form			1521.2.i.e.944.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(1.93185 + 1.93185i) q^{5} +(-0.366025 - 0.366025i) q^{7} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(1.93185 + 1.93185i) q^{5} +(-0.366025 - 0.366025i) q^{7} -5.46410i q^{10} +(2.96713 - 2.96713i) q^{11} +1.03528i q^{14} +4.00000 q^{16} +6.69213 q^{17} +(-4.46410 + 4.46410i) q^{19} +(-3.86370 + 3.86370i) q^{20} -8.39230 q^{22} +2.44949 q^{23} +2.46410i q^{25} +(0.732051 - 0.732051i) q^{28} -1.41421i q^{29} +(-4.63397 + 4.63397i) q^{31} +(-5.65685 - 5.65685i) q^{32} +(-9.46410 - 9.46410i) q^{34} -1.41421i q^{35} +(-2.26795 - 2.26795i) q^{37} +12.6264 q^{38} +(1.03528 + 1.03528i) q^{41} +7.73205i q^{43} +(5.93426 + 5.93426i) q^{44} +(-3.46410 - 3.46410i) q^{46} +(2.31079 - 2.31079i) q^{47} -6.73205i q^{49} +(3.48477 - 3.48477i) q^{50} +5.93426i q^{53} +11.4641 q^{55} +(-2.00000 + 2.00000i) q^{58} +(-0.138701 + 0.138701i) q^{59} +13.1962 q^{61} +13.1069 q^{62} +8.00000i q^{64} +(-5.56218 + 5.56218i) q^{67} +13.3843i q^{68} +(-2.00000 + 2.00000i) q^{70} +(11.0735 + 11.0735i) q^{71} +(-2.90192 - 2.90192i) q^{73} +6.41473i q^{74} +(-8.92820 - 8.92820i) q^{76} -2.17209 q^{77} +7.19615 q^{79} +(7.72741 + 7.72741i) q^{80} -2.92820i q^{82} +(5.27792 + 5.27792i) q^{83} +(12.9282 + 12.9282i) q^{85} +(10.9348 - 10.9348i) q^{86} +(3.20736 - 3.20736i) q^{89} +4.89898i q^{92} -6.53590 q^{94} -17.2480 q^{95} +(3.56218 - 3.56218i) q^{97} +(-9.52056 + 9.52056i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} + 32 q^{16} - 8 q^{19} + 16 q^{22} - 8 q^{28} - 44 q^{31} - 48 q^{34} - 32 q^{37} + 64 q^{55} - 16 q^{58} + 64 q^{61} + 4 q^{67} - 16 q^{70} - 44 q^{73} - 16 q^{76} + 16 q^{79} + 48 q^{85} - 80 q^{94} - 20 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 + 32 * q^16 - 8 * q^19 + 16 * q^22 - 8 * q^28 - 44 * q^31 - 48 * q^34 - 32 * q^37 + 64 * q^55 - 16 * q^58 + 64 * q^61 + 4 * q^67 - 16 * q^70 - 44 * q^73 - 16 * q^76 + 16 * q^79 + 48 * q^85 - 80 * q^94 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41421	−	1.41421i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$2$	−1.41421	−	1.41421i	−1.00000	−	1.00000i	−1.00000			$\pi$
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$	1.93185	+	1.93185i	0.863950	+	0.863950i	0.991794	−	0.127844i	$-0.0408057\pi$
$5$	1.93185	+	1.93185i	0.863950	+	0.863950i	−0.127844	+	0.991794i	$0.540806\pi$
$6$		0			0
$7$	−0.366025	−	0.366025i	−0.138345	−	0.138345i	0.634543	−	0.772888i	$-0.281188\pi$
$7$	−0.366025	−	0.366025i	−0.138345	−	0.138345i	−0.772888	+	0.634543i	$0.781188\pi$
$8$		0			0
$9$		0			0
$10$		−	5.46410i		−	1.72790i
$11$	2.96713	−	2.96713i	0.894623	−	0.894623i	−0.100331	−	0.994954i	$-0.531990\pi$
$11$	2.96713	−	2.96713i	0.894623	−	0.894623i	0.994954	+	0.100331i	$0.0319903\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$			1.03528i			0.276689i
$15$		0			0
$16$	4.00000			1.00000
$17$	6.69213			1.62308			0.811540	−	0.584297i	$-0.198630\pi$
$17$	6.69213			1.62308			0.811540	+	0.584297i	$0.198630\pi$
$18$		0			0
$19$	−4.46410	+	4.46410i	−1.02414	+	1.02414i	−0.0244337	+	0.999701i	$0.507778\pi$
$19$	−4.46410	+	4.46410i	−1.02414	+	1.02414i	−0.999701	+	0.0244337i	$0.992222\pi$
$20$	−3.86370	+	3.86370i	−0.863950	+	0.863950i
$21$		0			0
$22$	−8.39230			−1.78925
$23$	2.44949			0.510754			0.255377	−	0.966842i	$-0.417800\pi$
$23$	2.44949			0.510754			0.255377	+	0.966842i	$0.417800\pi$
$24$		0			0
$25$			2.46410i			0.492820i
$26$		0			0
$27$		0			0
$28$	0.732051	−	0.732051i	0.138345	−	0.138345i
$29$		−	1.41421i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$29$		−	1.41421i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$30$		0			0
$31$	−4.63397	+	4.63397i	−0.832286	+	0.832286i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−4.63397	+	4.63397i	−0.832286	+	0.832286i	0.155543	+	0.987829i	$0.450287\pi$
$32$	−5.65685	−	5.65685i	−1.00000	−	1.00000i
$33$		0			0
$34$	−9.46410	−	9.46410i	−1.62308	−	1.62308i
$35$		−	1.41421i		−	0.239046i
$36$		0			0
$37$	−2.26795	−	2.26795i	−0.372849	−	0.372849i	0.495665	−	0.868514i	$-0.334924\pi$
$37$	−2.26795	−	2.26795i	−0.372849	−	0.372849i	−0.868514	+	0.495665i	$0.834924\pi$
$38$	12.6264			2.04827
$39$		0			0
$40$		0			0
$41$	1.03528	+	1.03528i	0.161683	+	0.161683i	0.783312	−	0.621629i	$-0.213529\pi$
$41$	1.03528	+	1.03528i	0.161683	+	0.161683i	−0.621629	+	0.783312i	$0.713529\pi$
$42$		0			0
$43$			7.73205i			1.17913i	0.807722	+	0.589563i	$0.200700\pi$
$43$			7.73205i			1.17913i	−0.807722	+	0.589563i	$0.799300\pi$
$44$	5.93426	+	5.93426i	0.894623	+	0.894623i
$45$		0			0
$46$	−3.46410	−	3.46410i	−0.510754	−	0.510754i
$47$	2.31079	−	2.31079i	0.337063	−	0.337063i	−0.518198	−	0.855261i	$-0.673397\pi$
$47$	2.31079	−	2.31079i	0.337063	−	0.337063i	0.855261	+	0.518198i	$0.173397\pi$
$48$		0			0
$49$		−	6.73205i		−	0.961722i
$50$	3.48477	−	3.48477i	0.492820	−	0.492820i
$51$		0			0
$52$		0			0
$53$			5.93426i			0.815133i	0.913176	+	0.407566i	$0.133622\pi$
$53$			5.93426i			0.815133i	−0.913176	+	0.407566i	$0.866378\pi$
$54$		0			0
$55$	11.4641			1.54582
$56$		0			0
$57$		0			0
$58$	−2.00000	+	2.00000i	−0.262613	+	0.262613i
$59$	−0.138701	+	0.138701i	−0.0180573	+	0.0180573i	−0.716078	−	0.698020i	$-0.754064\pi$
$59$	−0.138701	+	0.138701i	−0.0180573	+	0.0180573i	0.698020	+	0.716078i	$0.254064\pi$
$60$		0			0
$61$	13.1962			1.68959			0.844797	−	0.535087i	$-0.179721\pi$
$61$	13.1962			1.68959			0.844797	+	0.535087i	$0.179721\pi$
$62$	13.1069			1.66457
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$		0			0
$67$	−5.56218	+	5.56218i	−0.679528	+	0.679528i	−0.959893	−	0.280365i	$-0.909544\pi$
$67$	−5.56218	+	5.56218i	−0.679528	+	0.679528i	0.280365	+	0.959893i	$0.409544\pi$
$68$			13.3843i			1.62308i
$69$		0			0
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$	11.0735	+	11.0735i	1.31418	+	1.31418i	0.918304	+	0.395875i	$0.129559\pi$
$71$	11.0735	+	11.0735i	1.31418	+	1.31418i	0.395875	+	0.918304i	$0.370441\pi$
$72$		0			0
$73$	−2.90192	−	2.90192i	−0.339644	−	0.339644i	0.516589	−	0.856233i	$-0.327202\pi$
$73$	−2.90192	−	2.90192i	−0.339644	−	0.339644i	−0.856233	+	0.516589i	$0.827202\pi$
$74$			6.41473i			0.745697i
$75$		0			0
$76$	−8.92820	−	8.92820i	−1.02414	−	1.02414i
$77$	−2.17209			−0.247532
$78$		0			0
$79$	7.19615			0.809630			0.404815	−	0.914399i	$-0.367336\pi$
$79$	7.19615			0.809630			0.404815	+	0.914399i	$0.367336\pi$
$80$	7.72741	+	7.72741i	0.863950	+	0.863950i
$81$		0			0
$82$		−	2.92820i		−	0.323366i
$83$	5.27792	+	5.27792i	0.579327	+	0.579327i	0.934718	−	0.355391i	$-0.115652\pi$
$83$	5.27792	+	5.27792i	0.579327	+	0.579327i	−0.355391	+	0.934718i	$0.615652\pi$
$84$		0			0
$85$	12.9282	+	12.9282i	1.40226	+	1.40226i
$86$	10.9348	−	10.9348i	1.17913	−	1.17913i
$87$		0			0
$88$		0			0
$89$	3.20736	−	3.20736i	0.339980	−	0.339980i	−0.516380	−	0.856360i	$-0.672721\pi$
$89$	3.20736	−	3.20736i	0.339980	−	0.339980i	0.856360	+	0.516380i	$0.172721\pi$
$90$		0			0
$91$		0			0
$92$			4.89898i			0.510754i
$93$		0			0
$94$	−6.53590			−0.674126
$95$	−17.2480			−1.76960
$96$		0			0
$97$	3.56218	−	3.56218i	0.361684	−	0.361684i	−0.502748	−	0.864433i	$-0.667678\pi$
$97$	3.56218	−	3.56218i	0.361684	−	0.361684i	0.864433	+	0.502748i	$0.167678\pi$
$98$	−9.52056	+	9.52056i	−0.961722	+	0.961722i
$99$		0			0
$100$	−4.92820			−0.492820
$101$	−1.13681			−0.113117			−0.0565585	−	0.998399i	$-0.518013\pi$
$101$	−1.13681			−0.113117			−0.0565585	+	0.998399i	$0.518013\pi$
$102$		0			0
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$		0			0
$105$		0			0
$106$	8.39230	−	8.39230i	0.815133	−	0.815133i
$107$			1.69161i			0.163535i	0.996651	+	0.0817673i	$0.0260564\pi$
$107$			1.69161i			0.163535i	−0.996651	+	0.0817673i	$0.973944\pi$
$108$		0			0
$109$	11.2942	−	11.2942i	1.08179	−	1.08179i	0.0854483	−	0.996343i	$-0.472768\pi$
$109$	11.2942	−	11.2942i	1.08179	−	1.08179i	0.996343	−	0.0854483i	$-0.0272322\pi$
$110$	−16.2127	−	16.2127i	−1.54582	−	1.54582i
$111$		0			0
$112$	−1.46410	−	1.46410i	−0.138345	−	0.138345i
$113$		−	4.52004i		−	0.425210i	−0.977138	−	0.212605i	$-0.931805\pi$
$113$		−	4.52004i		−	0.425210i	0.977138	−	0.212605i	$-0.0681947\pi$
$114$		0			0
$115$	4.73205	+	4.73205i	0.441266	+	0.441266i
$116$	2.82843			0.262613
$117$		0			0
$118$	0.392305			0.0361146
$119$	−2.44949	−	2.44949i	−0.224544	−	0.224544i
$120$		0			0
$121$		−	6.60770i		−	0.600700i
$122$	−18.6622	−	18.6622i	−1.68959	−	1.68959i
$123$		0			0
$124$	−9.26795	−	9.26795i	−0.832286	−	0.832286i
$125$	4.89898	−	4.89898i	0.438178	−	0.438178i
$126$		0			0
$127$			9.92820i			0.880986i	0.897756	+	0.440493i	$0.145196\pi$
$127$			9.92820i			0.880986i	−0.897756	+	0.440493i	$0.854804\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$			7.07107i			0.617802i	0.951094	+	0.308901i	$0.0999612\pi$
$131$			7.07107i			0.617802i	−0.951094	+	0.308901i	$0.900039\pi$
$132$		0			0
$133$	3.26795			0.283367
$134$	15.7322			1.35906
$135$		0			0
$136$		0			0
$137$	10.5558	−	10.5558i	0.901846	−	0.901846i	−0.0937500	−	0.995596i	$-0.529885\pi$
$137$	10.5558	−	10.5558i	0.901846	−	0.901846i	0.995596	+	0.0937500i	$0.0298854\pi$
$138$		0			0
$139$	3.39230			0.287732			0.143866	−	0.989597i	$-0.454047\pi$
$139$	3.39230			0.287732			0.143866	+	0.989597i	$0.454047\pi$
$140$	2.82843			0.239046
$141$		0			0
$142$		−	31.3205i		−	2.62836i
$143$		0			0
$144$		0			0
$145$	2.73205	−	2.73205i	0.226884	−	0.226884i
$146$			8.20788i			0.679289i
$147$		0			0
$148$	4.53590	−	4.53590i	0.372849	−	0.372849i
$149$	−4.52004	−	4.52004i	−0.370296	−	0.370296i	0.497289	−	0.867585i	$-0.334329\pi$
$149$	−4.52004	−	4.52004i	−0.370296	−	0.370296i	−0.867585	+	0.497289i	$0.834329\pi$
$150$		0			0
$151$	8.46410	+	8.46410i	0.688799	+	0.688799i	0.961966	−	0.273168i	$-0.0880714\pi$
$151$	8.46410	+	8.46410i	0.688799	+	0.688799i	−0.273168	+	0.961966i	$0.588071\pi$
$152$		0			0
$153$		0			0
$154$	3.07180	+	3.07180i	0.247532	+	0.247532i
$155$	−17.9043			−1.43811
$156$		0			0
$157$	−11.3923			−0.909205			−0.454602	−	0.890694i	$-0.650219\pi$
$157$	−11.3923			−0.909205			−0.454602	+	0.890694i	$0.650219\pi$
$158$	−10.1769	−	10.1769i	−0.809630	−	0.809630i
$159$		0			0
$160$		−	21.8564i		−	1.72790i
$161$	−0.896575	−	0.896575i	−0.0706600	−	0.0706600i
$162$		0			0
$163$	11.7583	+	11.7583i	0.920984	+	0.920984i	0.997099	−	0.0761155i	$-0.0242518\pi$
$163$	11.7583	+	11.7583i	0.920984	+	0.920984i	−0.0761155	+	0.997099i	$0.524252\pi$
$164$	−2.07055	+	2.07055i	−0.161683	+	0.161683i
$165$		0			0
$166$		−	14.9282i		−	1.15865i
$167$	3.86370	−	3.86370i	0.298982	−	0.298982i	−0.541633	−	0.840615i	$-0.682194\pi$
$167$	3.86370	−	3.86370i	0.298982	−	0.298982i	0.840615	+	0.541633i	$0.182194\pi$
$168$		0			0
$169$		0			0
$170$		−	36.5665i		−	2.80452i
$171$		0			0
$172$	−15.4641			−1.17913
$173$	−14.0406			−1.06749			−0.533744	−	0.845646i	$-0.679215\pi$
$173$	−14.0406			−1.06749			−0.533744	+	0.845646i	$0.679215\pi$
$174$		0			0
$175$	0.901924	−	0.901924i	0.0681790	−	0.0681790i
$176$	11.8685	−	11.8685i	0.894623	−	0.894623i
$177$		0			0
$178$	−9.07180			−0.679960
$179$	16.4901			1.23253			0.616264	−	0.787540i	$-0.288646\pi$
$179$	16.4901			1.23253			0.616264	+	0.787540i	$0.288646\pi$
$180$		0			0
$181$		−	6.00000i		−	0.445976i	−0.974821	−	0.222988i	$-0.928419\pi$
$181$		−	6.00000i		−	0.445976i	0.974821	−	0.222988i	$-0.0715812\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		−	8.76268i		−	0.644245i
$186$		0			0
$187$	19.8564	−	19.8564i	1.45204	−	1.45204i
$188$	4.62158	+	4.62158i	0.337063	+	0.337063i
$189$		0			0
$190$	24.3923	+	24.3923i	1.76960	+	1.76960i
$191$		−	13.0053i		−	0.941032i	−0.882391	−	0.470516i	$-0.844068\pi$
$191$		−	13.0053i		−	0.941032i	0.882391	−	0.470516i	$-0.155932\pi$
$192$		0			0
$193$	−0.830127	−	0.830127i	−0.0597539	−	0.0597539i	0.676598	−	0.736352i	$-0.263453\pi$
$193$	−0.830127	−	0.830127i	−0.0597539	−	0.0597539i	−0.736352	+	0.676598i	$0.763453\pi$
$194$	−10.0754			−0.723369
$195$		0			0
$196$	13.4641			0.961722
$197$	−5.00052	−	5.00052i	−0.356272	−	0.356272i	0.506165	−	0.862437i	$-0.331063\pi$
$197$	−5.00052	−	5.00052i	−0.356272	−	0.356272i	−0.862437	+	0.506165i	$0.831063\pi$
$198$		0			0
$199$			0.464102i			0.0328993i	0.999865	+	0.0164496i	$0.00523632\pi$
$199$			0.464102i			0.0328993i	−0.999865	+	0.0164496i	$0.994764\pi$
$200$		0			0
$201$		0			0
$202$	1.60770	+	1.60770i	0.113117	+	0.113117i
$203$	−0.517638	+	0.517638i	−0.0363311	+	0.0363311i
$204$		0			0
$205$			4.00000i			0.279372i
$206$	−12.2474	+	12.2474i	−0.853320	+	0.853320i
$207$		0			0
$208$		0			0
$209$			26.4911i			1.83243i
$210$		0			0
$211$	−15.1962			−1.04615			−0.523073	−	0.852288i	$-0.675215\pi$
$211$	−15.1962			−1.04615			−0.523073	+	0.852288i	$0.675215\pi$
$212$	−11.8685			−0.815133
$213$		0			0
$214$	2.39230	−	2.39230i	0.163535	−	0.163535i
$215$	−14.9372	+	14.9372i	−1.01871	+	1.01871i
$216$		0			0
$217$	3.39230			0.230285
$218$	−31.9449			−2.16358
$219$		0			0
$220$			22.9282i			1.54582i
$221$		0			0
$222$		0			0
$223$	−17.3923	+	17.3923i	−1.16467	+	1.16467i	−0.181235	+	0.983440i	$0.558009\pi$
$223$	−17.3923	+	17.3923i	−1.16467	+	1.16467i	−0.983440	+	0.181235i	$0.941991\pi$
$224$			4.14110i			0.276689i
$225$		0			0
$226$	−6.39230	+	6.39230i	−0.425210	+	0.425210i
$227$	4.62158	+	4.62158i	0.306745	+	0.306745i	0.843646	−	0.536901i	$-0.180405\pi$
$227$	4.62158	+	4.62158i	0.306745	+	0.306745i	−0.536901	+	0.843646i	$0.680405\pi$
$228$		0			0
$229$	3.73205	+	3.73205i	0.246621	+	0.246621i	0.819582	−	0.572961i	$-0.194206\pi$
$229$	3.73205	+	3.73205i	0.246621	+	0.246621i	−0.572961	+	0.819582i	$0.694206\pi$
$230$		−	13.3843i		−	0.882532i
$231$		0			0
$232$		0			0
$233$	−18.9396			−1.24077			−0.620387	−	0.784296i	$-0.713024\pi$
$233$	−18.9396			−1.24077			−0.620387	+	0.784296i	$0.713024\pi$
$234$		0			0
$235$	8.92820			0.582412
$236$	−0.277401	−	0.277401i	−0.0180573	−	0.0180573i
$237$		0			0
$238$			6.92820i			0.449089i
$239$	4.62158	+	4.62158i	0.298945	+	0.298945i	0.840601	−	0.541656i	$-0.182202\pi$
$239$	4.62158	+	4.62158i	0.298945	+	0.298945i	−0.541656	+	0.840601i	$0.682202\pi$
$240$		0			0
$241$	−8.26795	−	8.26795i	−0.532585	−	0.532585i	0.388756	−	0.921341i	$-0.372905\pi$
$241$	−8.26795	−	8.26795i	−0.532585	−	0.532585i	−0.921341	+	0.388756i	$0.872905\pi$
$242$	−9.34469	+	9.34469i	−0.600700	+	0.600700i
$243$		0			0
$244$			26.3923i			1.68959i
$245$	13.0053	−	13.0053i	0.830880	−	0.830880i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−13.8564			−0.876356
$251$	21.3891			1.35007			0.675033	−	0.737788i	$-0.264129\pi$
$251$	21.3891			1.35007			0.675033	+	0.737788i	$0.264129\pi$
$252$		0			0
$253$	7.26795	−	7.26795i	0.456932	−	0.456932i
$254$	14.0406	−	14.0406i	0.880986	−	0.880986i
$255$		0			0
$256$	16.0000			1.00000
$257$	1.31268			0.0818826			0.0409413	−	0.999162i	$-0.486964\pi$
$257$	1.31268			0.0818826			0.0409413	+	0.999162i	$0.486964\pi$
$258$		0			0
$259$			1.66025i			0.103163i
$260$		0			0
$261$		0			0
$262$	10.0000	−	10.0000i	0.617802	−	0.617802i
$263$		−	23.4596i		−	1.44658i	−0.690543	−	0.723291i	$-0.742628\pi$
$263$		−	23.4596i		−	1.44658i	0.690543	−	0.723291i	$-0.257372\pi$
$264$		0			0
$265$	−11.4641	+	11.4641i	−0.704234	+	0.704234i
$266$	−4.62158	−	4.62158i	−0.283367	−	0.283367i
$267$		0			0
$268$	−11.1244	−	11.1244i	−0.679528	−	0.679528i
$269$			20.6312i			1.25791i	0.777443	+	0.628953i	$0.216516\pi$
$269$			20.6312i			1.25791i	−0.777443	+	0.628953i	$0.783484\pi$
$270$		0			0
$271$	−7.16987	−	7.16987i	−0.435539	−	0.435539i	0.454969	−	0.890507i	$-0.349650\pi$
$271$	−7.16987	−	7.16987i	−0.435539	−	0.435539i	−0.890507	+	0.454969i	$0.849650\pi$
$272$	26.7685			1.62308
$273$		0			0
$274$	−29.8564			−1.80369
$275$	7.31130	+	7.31130i	0.440888	+	0.440888i
$276$		0			0
$277$		−	19.8564i		−	1.19306i	−0.802592	−	0.596528i	$-0.796546\pi$
$277$		−	19.8564i		−	1.19306i	0.802592	−	0.596528i	$-0.203454\pi$
$278$	−4.79744	−	4.79744i	−0.287732	−	0.287732i
$279$		0			0
$280$		0			0
$281$	−16.6288	+	16.6288i	−0.991990	+	0.991990i	−0.999968	−	0.00797773i	$-0.997461\pi$
$281$	−16.6288	+	16.6288i	−0.991990	+	0.991990i	0.00797773	+	0.999968i	$0.497461\pi$
$282$		0			0
$283$			22.8564i			1.35867i	0.733827	+	0.679336i	$0.237732\pi$
$283$			22.8564i			1.35867i	−0.733827	+	0.679336i	$0.762268\pi$
$284$	−22.1469	+	22.1469i	−1.31418	+	1.31418i
$285$		0			0
$286$		0			0
$287$		−	0.757875i		−	0.0447359i
$288$		0			0
$289$	27.7846			1.63439
$290$	−7.72741			−0.453769
$291$		0			0
$292$	5.80385	−	5.80385i	0.339644	−	0.339644i
$293$	8.34658	−	8.34658i	0.487612	−	0.487612i	−0.419940	−	0.907552i	$-0.637949\pi$
$293$	8.34658	−	8.34658i	0.487612	−	0.487612i	0.907552	+	0.419940i	$0.137949\pi$
$294$		0			0
$295$	−0.535898			−0.0312012
$296$		0			0
$297$		0			0
$298$			12.7846i			0.740593i
$299$		0			0
$300$		0			0
$301$	2.83013	−	2.83013i	0.163126	−	0.163126i
$302$		−	23.9401i		−	1.37760i
$303$		0			0
$304$	−17.8564	+	17.8564i	−1.02414	+	1.02414i
$305$	25.4930	+	25.4930i	1.45973	+	1.45973i
$306$		0			0
$307$	−19.2942	−	19.2942i	−1.10118	−	1.10118i	−0.994269	−	0.106911i	$-0.965904\pi$
$307$	−19.2942	−	19.2942i	−1.10118	−	1.10118i	−0.106911	−	0.994269i	$-0.534096\pi$
$308$		−	4.34418i		−	0.247532i
$309$		0			0
$310$	25.3205	+	25.3205i	1.43811	+	1.43811i
$311$	11.1106			0.630026			0.315013	−	0.949087i	$-0.397991\pi$
$311$	11.1106			0.630026			0.315013	+	0.949087i	$0.397991\pi$
$312$		0			0
$313$	−3.19615			−0.180657			−0.0903286	−	0.995912i	$-0.528792\pi$
$313$	−3.19615			−0.180657			−0.0903286	+	0.995912i	$0.528792\pi$
$314$	16.1112	+	16.1112i	0.909205	+	0.909205i
$315$		0			0
$316$			14.3923i			0.809630i
$317$	−10.5558	−	10.5558i	−0.592875	−	0.592875i	0.345532	−	0.938407i	$-0.387698\pi$
$317$	−10.5558	−	10.5558i	−0.592875	−	0.592875i	−0.938407	+	0.345532i	$0.887698\pi$
$318$		0			0
$319$	−4.19615	−	4.19615i	−0.234939	−	0.234939i
$320$	−15.4548	+	15.4548i	−0.863950	+	0.863950i
$321$		0			0
$322$			2.53590i			0.141320i
$323$	−29.8744	+	29.8744i	−1.66225	+	1.66225i
$324$		0			0
$325$		0			0
$326$		−	33.2576i		−	1.84197i
$327$		0			0
$328$		0			0
$329$	−1.69161			−0.0932618
$330$		0			0
$331$	−3.83013	+	3.83013i	−0.210523	+	0.210523i	−0.804490	−	0.593967i	$-0.797561\pi$
$331$	−3.83013	+	3.83013i	−0.210523	+	0.210523i	0.593967	+	0.804490i	$0.297561\pi$
$332$	−10.5558	+	10.5558i	−0.579327	+	0.579327i
$333$		0			0
$334$	−10.9282			−0.597965
$335$	−21.4906			−1.17416
$336$		0			0
$337$			27.9282i			1.52135i	0.649135	+	0.760673i	$0.275131\pi$
$337$			27.9282i			1.52135i	−0.649135	+	0.760673i	$0.724869\pi$
$338$		0			0
$339$		0			0
$340$	−25.8564	+	25.8564i	−1.40226	+	1.40226i
$341$			27.4992i			1.48916i
$342$		0			0
$343$	−5.02628	+	5.02628i	−0.271394	+	0.271394i
$344$		0			0
$345$		0			0
$346$	19.8564	+	19.8564i	1.06749	+	1.06749i
$347$			29.1165i			1.56305i	0.623871	+	0.781527i	$0.285559\pi$
$347$			29.1165i			1.56305i	−0.623871	+	0.781527i	$0.714441\pi$
$348$		0			0
$349$	1.49038	+	1.49038i	0.0797783	+	0.0797783i	0.745870	−	0.666092i	$-0.232034\pi$
$349$	1.49038	+	1.49038i	0.0797783	+	0.0797783i	−0.666092	+	0.745870i	$0.732034\pi$
$350$	−2.55103			−0.136358
$351$		0			0
$352$	−33.5692			−1.78925
$353$	1.27551	+	1.27551i	0.0678887	+	0.0678887i	0.740236	−	0.672347i	$-0.234714\pi$
$353$	1.27551	+	1.27551i	0.0678887	+	0.0678887i	−0.672347	+	0.740236i	$0.734714\pi$
$354$		0			0
$355$			42.7846i			2.27077i
$356$	6.41473	+	6.41473i	0.339980	+	0.339980i
$357$		0			0
$358$	−23.3205	−	23.3205i	−1.23253	−	1.23253i
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	−0.868640	−	0.495443i	$-0.835006\pi$
$359$	−7.07107	+	7.07107i	−0.373197	+	0.373197i	0.495443	+	0.868640i	$0.335006\pi$
$360$		0			0
$361$		−	20.8564i		−	1.09771i
$362$	−8.48528	+	8.48528i	−0.445976	+	0.445976i
$363$		0			0
$364$		0			0
$365$		−	11.2122i		−	0.586872i
$366$		0			0
$367$	−5.39230			−0.281476			−0.140738	−	0.990047i	$-0.544948\pi$
$367$	−5.39230			−0.281476			−0.140738	+	0.990047i	$0.544948\pi$
$368$	9.79796			0.510754
$369$		0			0
$370$	−12.3923	+	12.3923i	−0.644245	+	0.644245i
$371$	2.17209	−	2.17209i	0.112769	−	0.112769i
$372$		0			0
$373$	−7.58846			−0.392915			−0.196458	−	0.980512i	$-0.562944\pi$
$373$	−7.58846			−0.392915			−0.196458	+	0.980512i	$0.562944\pi$
$374$	−56.1624			−2.90409
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	16.3660	−	16.3660i	0.840666	−	0.840666i	−0.148279	−	0.988946i	$-0.547373\pi$
$379$	16.3660	−	16.3660i	0.840666	−	0.840666i	0.988946	+	0.148279i	$0.0473734\pi$
$380$		−	34.4959i		−	1.76960i
$381$		0			0
$382$	−18.3923	+	18.3923i	−0.941032	+	0.941032i
$383$	7.07107	+	7.07107i	0.361315	+	0.361315i	0.864297	−	0.502982i	$-0.167764\pi$
$383$	7.07107	+	7.07107i	0.361315	+	0.361315i	−0.502982	+	0.864297i	$0.667764\pi$
$384$		0			0
$385$	−4.19615	−	4.19615i	−0.213856	−	0.213856i
$386$			2.34795i			0.119508i
$387$		0			0
$388$	7.12436	+	7.12436i	0.361684	+	0.361684i
$389$	6.69213			0.339304			0.169652	−	0.985504i	$-0.445736\pi$
$389$	6.69213			0.339304			0.169652	+	0.985504i	$0.445736\pi$
$390$		0			0
$391$	16.3923			0.828994
$392$		0			0
$393$		0			0
$394$			14.1436i			0.712544i
$395$	13.9019	+	13.9019i	0.699480	+	0.699480i
$396$		0			0
$397$	−11.2224	−	11.2224i	−0.563238	−	0.563238i	0.366988	−	0.930226i	$-0.380389\pi$
$397$	−11.2224	−	11.2224i	−0.563238	−	0.563238i	−0.930226	+	0.366988i	$0.880389\pi$
$398$	0.656339	−	0.656339i	0.0328993	−	0.0328993i
$399$		0			0
$400$			9.85641i			0.492820i
$401$	28.1827	−	28.1827i	1.40738	−	1.40738i	0.634253	−	0.773125i	$-0.281308\pi$
$401$	28.1827	−	28.1827i	1.40738	−	1.40738i	0.773125	−	0.634253i	$-0.218692\pi$
$402$		0			0
$403$		0			0
$404$		−	2.27362i		−	0.113117i
$405$		0			0
$406$	1.46410			0.0726621
$407$	−13.4586			−0.667118
$408$		0			0
$409$	12.0981	−	12.0981i	0.598211	−	0.598211i	−0.341625	−	0.939836i	$-0.610977\pi$
$409$	12.0981	−	12.0981i	0.598211	−	0.598211i	0.939836	+	0.341625i	$0.110977\pi$
$410$	5.65685	−	5.65685i	0.279372	−	0.279372i
$411$		0			0
$412$	17.3205			0.853320
$413$	0.101536			0.00499626
$414$		0			0
$415$			20.3923i			1.00102i
$416$		0			0
$417$		0			0
$418$	37.4641	−	37.4641i	1.83243	−	1.83243i
$419$		−	3.38323i		−	0.165282i	−0.996579	−	0.0826408i	$-0.973665\pi$
$419$		−	3.38323i		−	0.165282i	0.996579	−	0.0826408i	$-0.0263354\pi$
$420$		0			0
$421$	−15.3660	+	15.3660i	−0.748894	+	0.748894i	−0.974272	−	0.225377i	$-0.927639\pi$
$421$	−15.3660	+	15.3660i	−0.748894	+	0.748894i	0.225377	+	0.974272i	$0.427639\pi$
$422$	21.4906	+	21.4906i	1.04615	+	1.04615i
$423$		0			0
$424$		0			0
$425$			16.4901i			0.799887i
$426$		0			0
$427$	−4.83013	−	4.83013i	−0.233746	−	0.233746i
$428$	−3.38323			−0.163535
$429$		0			0
$430$	42.2487			2.03741
$431$	−11.2122	−	11.2122i	−0.540071	−	0.540071i	0.383478	−	0.923550i	$-0.374726\pi$
$431$	−11.2122	−	11.2122i	−0.540071	−	0.540071i	−0.923550	+	0.383478i	$0.874726\pi$
$432$		0			0
$433$			18.4641i			0.887328i	0.896193	+	0.443664i	$0.146322\pi$
$433$			18.4641i			0.887328i	−0.896193	+	0.443664i	$0.853678\pi$
$434$	−4.79744	−	4.79744i	−0.230285	−	0.230285i
$435$		0			0
$436$	22.5885	+	22.5885i	1.08179	+	1.08179i
$437$	−10.9348	+	10.9348i	−0.523081	+	0.523081i
$438$		0			0
$439$		−	9.58846i		−	0.457632i	−0.973470	−	0.228816i	$-0.926515\pi$
$439$		−	9.58846i		−	0.457632i	0.973470	−	0.228816i	$-0.0734854\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			23.7370i			1.12778i	0.825850	+	0.563890i	$0.190696\pi$
$443$			23.7370i			1.12778i	−0.825850	+	0.563890i	$0.809304\pi$
$444$		0			0
$445$	12.3923			0.587452
$446$	49.1929			2.32935
$447$		0			0
$448$	2.92820	−	2.92820i	0.138345	−	0.138345i
$449$	−6.17449	+	6.17449i	−0.291392	+	0.291392i	−0.837630	−	0.546238i	$-0.816059\pi$
$449$	−6.17449	+	6.17449i	−0.291392	+	0.291392i	0.546238	+	0.837630i	$0.316059\pi$
$450$		0			0
$451$	6.14359			0.289291
$452$	9.04008			0.425210
$453$		0			0
$454$		−	13.0718i		−	0.613490i
$455$		0			0
$456$		0			0
$457$	−8.09808	+	8.09808i	−0.378812	+	0.378812i	−0.870673	−	0.491861i	$-0.836317\pi$
$457$	−8.09808	+	8.09808i	−0.378812	+	0.378812i	0.491861	+	0.870673i	$0.336317\pi$
$458$		−	10.5558i		−	0.493242i
$459$		0			0
$460$	−9.46410	+	9.46410i	−0.441266	+	0.441266i
$461$	−1.89469	−	1.89469i	−0.0882444	−	0.0882444i	0.661607	−	0.749851i	$-0.269875\pi$
$461$	−1.89469	−	1.89469i	−0.0882444	−	0.0882444i	−0.749851	+	0.661607i	$0.769875\pi$
$462$		0			0
$463$	4.83013	+	4.83013i	0.224475	+	0.224475i	0.810380	−	0.585905i	$-0.199261\pi$
$463$	4.83013	+	4.83013i	0.224475	+	0.224475i	−0.585905	+	0.810380i	$0.699261\pi$
$464$		−	5.65685i		−	0.262613i
$465$		0			0
$466$	26.7846	+	26.7846i	1.24077	+	1.24077i
$467$	−22.0454			−1.02014			−0.510070	−	0.860133i	$-0.670380\pi$
$467$	−22.0454			−1.02014			−0.510070	+	0.860133i	$0.670380\pi$
$468$		0			0
$469$	4.07180			0.188018
$470$	−12.6264	−	12.6264i	−0.582412	−	0.582412i
$471$		0			0
$472$		0			0
$473$	22.9420	+	22.9420i	1.05487	+	1.05487i
$474$		0			0
$475$	−11.0000	−	11.0000i	−0.504715	−	0.504715i
$476$	4.89898	−	4.89898i	0.224544	−	0.224544i
$477$		0			0
$478$		−	13.0718i		−	0.597890i
$479$	−2.82843	+	2.82843i	−0.129234	+	0.129234i	−0.768765	−	0.639531i	$-0.779129\pi$
$479$	−2.82843	+	2.82843i	−0.129234	+	0.129234i	0.639531	+	0.768765i	$0.279129\pi$
$480$		0			0
$481$		0			0
$482$			23.3853i			1.06517i
$483$		0			0
$484$	13.2154			0.600700
$485$	13.7632			0.624955
$486$		0			0
$487$	14.1244	−	14.1244i	0.640036	−	0.640036i	−0.310528	−	0.950564i	$-0.600506\pi$
$487$	14.1244	−	14.1244i	0.640036	−	0.640036i	0.950564	+	0.310528i	$0.100506\pi$
$488$		0			0
$489$		0			0
$490$	−36.7846			−1.66176
$491$	−26.1122			−1.17843			−0.589213	−	0.807978i	$-0.700562\pi$
$491$	−26.1122			−1.17843			−0.589213	+	0.807978i	$0.700562\pi$
$492$		0			0
$493$		−	9.46410i		−	0.426242i
$494$		0			0
$495$		0			0
$496$	−18.5359	+	18.5359i	−0.832286	+	0.832286i
$497$		−	8.10634i		−	0.363619i
$498$		0			0
$499$	24.2679	−	24.2679i	1.08638	−	1.08638i	0.0904848	−	0.995898i	$-0.471158\pi$
$499$	24.2679	−	24.2679i	1.08638	−	1.08638i	0.995898	−	0.0904848i	$-0.0288416\pi$
$500$	9.79796	+	9.79796i	0.438178	+	0.438178i
$501$		0			0
$502$	−30.2487	−	30.2487i	−1.35007	−	1.35007i
$503$		−	26.8701i		−	1.19808i	−0.800720	−	0.599038i	$-0.795550\pi$
$503$		−	26.8701i		−	1.19808i	0.800720	−	0.599038i	$-0.204450\pi$
$504$		0			0
$505$	−2.19615	−	2.19615i	−0.0977275	−	0.0977275i
$506$	−20.5569			−0.913864
$507$		0			0
$508$	−19.8564			−0.880986
$509$	−5.89709	−	5.89709i	−0.261384	−	0.261384i	0.564232	−	0.825616i	$-0.309172\pi$
$509$	−5.89709	−	5.89709i	−0.261384	−	0.261384i	−0.825616	+	0.564232i	$0.809172\pi$
$510$		0			0
$511$			2.12436i			0.0939760i
$512$	−22.6274	−	22.6274i	−1.00000	−	1.00000i
$513$		0			0
$514$	−1.85641	−	1.85641i	−0.0818826	−	0.0818826i
$515$	16.7303	−	16.7303i	0.737226	−	0.737226i
$516$		0			0
$517$		−	13.7128i		−	0.603089i
$518$	2.34795	−	2.34795i	0.103163	−	0.103163i
$519$		0			0
$520$		0			0
$521$		−	26.5654i		−	1.16385i	−0.813241	−	0.581927i	$-0.802299\pi$
$521$		−	26.5654i		−	1.16385i	0.813241	−	0.581927i	$-0.197701\pi$
$522$		0			0
$523$	−42.7846			−1.87084			−0.935420	−	0.353538i	$-0.884979\pi$
$523$	−42.7846			−1.87084			−0.935420	+	0.353538i	$0.884979\pi$
$524$	−14.1421			−0.617802
$525$		0			0
$526$	−33.1769	+	33.1769i	−1.44658	+	1.44658i
$527$	−31.0112	+	31.0112i	−1.35087	+	1.35087i
$528$		0			0
$529$	−17.0000			−0.739130
$530$	32.4254			1.40847
$531$		0			0
$532$			6.53590i			0.283367i
$533$		0			0
$534$		0			0
$535$	−3.26795	+	3.26795i	−0.141286	+	0.141286i
$536$		0			0
$537$		0			0
$538$	29.1769	−	29.1769i	1.25791	−	1.25791i
$539$	−19.9749	−	19.9749i	−0.860378	−	0.860378i
$540$		0			0
$541$	30.6865	+	30.6865i	1.31932	+	1.31932i	0.914316	+	0.405001i	$0.132729\pi$
$541$	30.6865	+	30.6865i	1.31932	+	1.31932i	0.405001	+	0.914316i	$0.367271\pi$
$542$			20.2795i			0.871078i
$543$		0			0
$544$	−37.8564	−	37.8564i	−1.62308	−	1.62308i
$545$	43.6375			1.86923
$546$		0			0
$547$	−17.3923			−0.743641			−0.371821	−	0.928305i	$-0.621266\pi$
$547$	−17.3923			−0.743641			−0.371821	+	0.928305i	$0.621266\pi$
$548$	21.1117	+	21.1117i	0.901846	+	0.901846i
$549$		0			0
$550$		−	20.6795i		−	0.881776i
$551$	6.31319	+	6.31319i	0.268951	+	0.268951i
$552$		0			0
$553$	−2.63397	−	2.63397i	−0.112008	−	0.112008i
$554$	−28.0812	+	28.0812i	−1.19306	+	1.19306i
$555$		0			0
$556$			6.78461i			0.287732i
$557$	3.20736	−	3.20736i	0.135900	−	0.135900i	−0.635884	−	0.771785i	$-0.719364\pi$
$557$	3.20736	−	3.20736i	0.135900	−	0.135900i	0.771785	+	0.635884i	$0.219364\pi$
$558$		0			0
$559$		0			0
$560$		−	5.65685i		−	0.239046i
$561$		0			0
$562$	47.0333			1.98398
$563$	−29.6985			−1.25164			−0.625821	−	0.779967i	$-0.715236\pi$
$563$	−29.6985			−1.25164			−0.625821	+	0.779967i	$0.715236\pi$
$564$		0			0
$565$	8.73205	−	8.73205i	0.367360	−	0.367360i
$566$	32.3238	−	32.3238i	1.35867	−	1.35867i
$567$		0			0
$568$		0			0
$569$	7.34847			0.308064			0.154032	−	0.988066i	$-0.450774\pi$
$569$	7.34847			0.308064			0.154032	+	0.988066i	$0.450774\pi$
$570$		0			0
$571$			21.7128i			0.908653i	0.890835	+	0.454326i	$0.150120\pi$
$571$			21.7128i			0.908653i	−0.890835	+	0.454326i	$0.849880\pi$
$572$		0			0
$573$		0			0
$574$	−1.07180	+	1.07180i	−0.0447359	+	0.0447359i
$575$			6.03579i			0.251710i
$576$		0			0
$577$	−9.19615	+	9.19615i	−0.382841	+	0.382841i	−0.872125	−	0.489284i	$-0.837258\pi$
$577$	−9.19615	+	9.19615i	−0.382841	+	0.382841i	0.489284	+	0.872125i	$0.337258\pi$
$578$	−39.2934	−	39.2934i	−1.63439	−	1.63439i
$579$		0			0
$580$	5.46410	+	5.46410i	0.226884	+	0.226884i
$581$		−	3.86370i		−	0.160293i
$582$		0			0
$583$	17.6077	+	17.6077i	0.729236	+	0.729236i
$584$		0			0
$585$		0			0
$586$	−23.6077			−0.975225
$587$	−27.2862	−	27.2862i	−1.12622	−	1.12622i	−0.990786	−	0.135434i	$-0.956757\pi$
$587$	−27.2862	−	27.2862i	−1.12622	−	1.12622i	−0.135434	−	0.990786i	$-0.543243\pi$
$588$		0			0
$589$		−	41.3731i		−	1.70475i
$590$	0.757875	+	0.757875i	0.0312012	+	0.0312012i
$591$		0			0
$592$	−9.07180	−	9.07180i	−0.372849	−	0.372849i
$593$	4.10394	−	4.10394i	0.168529	−	0.168529i	−0.617804	−	0.786332i	$-0.711977\pi$
$593$	4.10394	−	4.10394i	0.168529	−	0.168529i	0.786332	+	0.617804i	$0.211977\pi$
$594$		0			0
$595$		−	9.46410i		−	0.387990i
$596$	9.04008	−	9.04008i	0.370296	−	0.370296i
$597$		0			0
$598$		0			0
$599$		−	15.2789i		−	0.624281i	−0.950036	−	0.312140i	$-0.898954\pi$
$599$		−	15.2789i		−	0.624281i	0.950036	−	0.312140i	$-0.101046\pi$
$600$		0			0
$601$	−36.7846			−1.50048			−0.750238	−	0.661168i	$-0.770061\pi$
$601$	−36.7846			−1.50048			−0.750238	+	0.661168i	$0.770061\pi$
$602$	−8.00481			−0.326252
$603$		0			0
$604$	−16.9282	+	16.9282i	−0.688799	+	0.688799i
$605$	12.7651	−	12.7651i	0.518975	−	0.518975i
$606$		0			0
$607$	−38.3923			−1.55830			−0.779148	−	0.626840i	$-0.784348\pi$
$607$	−38.3923			−1.55830			−0.779148	+	0.626840i	$0.784348\pi$
$608$	50.5055			2.04827
$609$		0			0
$610$		−	72.1051i		−	2.91945i
$611$		0			0
$612$		0			0
$613$	−4.63397	+	4.63397i	−0.187164	+	0.187164i	−0.794469	−	0.607305i	$-0.792251\pi$
$613$	−4.63397	+	4.63397i	−0.187164	+	0.187164i	0.607305	+	0.794469i	$0.292251\pi$
$614$			54.5723i			2.20236i
$615$		0			0
$616$		0			0
$617$	−21.9067	−	21.9067i	−0.881931	−	0.881931i	0.111800	−	0.993731i	$-0.464338\pi$
$617$	−21.9067	−	21.9067i	−0.881931	−	0.881931i	−0.993731	+	0.111800i	$0.964338\pi$
$618$		0			0
$619$	−12.8301	−	12.8301i	−0.515686	−	0.515686i	0.400577	−	0.916263i	$-0.368810\pi$
$619$	−12.8301	−	12.8301i	−0.515686	−	0.515686i	−0.916263	+	0.400577i	$0.868810\pi$
$620$		−	35.8086i		−	1.43811i
$621$		0			0
$622$	−15.7128	−	15.7128i	−0.630026	−	0.630026i
$623$	−2.34795			−0.0940688
$624$		0			0
$625$	31.2487			1.24995
$626$	4.52004	+	4.52004i	0.180657	+	0.180657i
$627$		0			0
$628$		−	22.7846i		−	0.909205i
$629$	−15.1774	−	15.1774i	−0.605163	−	0.605163i
$630$		0			0
$631$	28.1506	+	28.1506i	1.12066	+	1.12066i	0.991642	+	0.129017i	$0.0411821\pi$
$631$	28.1506	+	28.1506i	1.12066	+	1.12066i	0.129017	+	0.991642i	$0.458818\pi$
$632$		0			0
$633$		0			0
$634$			29.8564i			1.18575i
$635$	−19.1798	+	19.1798i	−0.761128	+	0.761128i
$636$		0			0
$637$		0			0
$638$			11.8685i			0.469879i
$639$		0			0
$640$		0			0
$641$	26.9444			1.06424			0.532120	−	0.846669i	$-0.321396\pi$
$641$	26.9444			1.06424			0.532120	+	0.846669i	$0.321396\pi$
$642$		0			0
$643$	−16.2942	+	16.2942i	−0.642582	+	0.642582i	−0.951189	−	0.308608i	$-0.900137\pi$
$643$	−16.2942	+	16.2942i	−0.642582	+	0.642582i	0.308608	+	0.951189i	$0.400137\pi$
$644$	1.79315	−	1.79315i	0.0706600	−	0.0706600i
$645$		0			0
$646$	84.4974			3.32451
$647$	28.3858			1.11596			0.557981	−	0.829854i	$-0.311576\pi$
$647$	28.3858			1.11596			0.557981	+	0.829854i	$0.311576\pi$
$648$		0			0
$649$			0.823085i			0.0323089i
$650$		0			0
$651$		0			0
$652$	−23.5167	+	23.5167i	−0.920984	+	0.920984i
$653$			11.3137i			0.442740i	0.975190	+	0.221370i	$0.0710528\pi$
$653$			11.3137i			0.442740i	−0.975190	+	0.221370i	$0.928947\pi$
$654$		0			0
$655$	−13.6603	+	13.6603i	−0.533750	+	0.533750i
$656$	4.14110	+	4.14110i	0.161683	+	0.161683i
$657$		0			0
$658$	2.39230	+	2.39230i	0.0932618	+	0.0932618i
$659$		−	46.6418i		−	1.81691i	−0.417985	−	0.908454i	$-0.637263\pi$
$659$		−	46.6418i		−	1.81691i	0.417985	−	0.908454i	$-0.362737\pi$
$660$		0			0
$661$	−26.2224	−	26.2224i	−1.01993	−	1.01993i	−0.999797	−	0.0201372i	$-0.993590\pi$
$661$	−26.2224	−	26.2224i	−1.01993	−	1.01993i	−0.0201372	−	0.999797i	$-0.506410\pi$
$662$	10.8332			0.421046
$663$		0			0
$664$		0			0
$665$	6.31319	+	6.31319i	0.244815	+	0.244815i
$666$		0			0
$667$		−	3.46410i		−	0.134131i
$668$	7.72741	+	7.72741i	0.298982	+	0.298982i
$669$		0			0
$670$	30.3923	+	30.3923i	1.17416	+	1.17416i
$671$	39.1547	−	39.1547i	1.51155	−	1.51155i
$672$		0			0
$673$			8.41154i			0.324241i	0.986771	+	0.162121i	$0.0518334\pi$
$673$			8.41154i			0.324241i	−0.986771	+	0.162121i	$0.948167\pi$
$674$	39.4964	−	39.4964i	1.52135	−	1.52135i
$675$		0			0
$676$		0			0
$677$			13.5873i			0.522204i	0.965311	+	0.261102i	$0.0840858\pi$
$677$			13.5873i			0.522204i	−0.965311	+	0.261102i	$0.915914\pi$
$678$		0			0
$679$	−2.60770			−0.100074
$680$		0			0
$681$		0			0
$682$	38.8897	−	38.8897i	1.48916	−	1.48916i
$683$	−12.3861	+	12.3861i	−0.473943	+	0.473943i	−0.903188	−	0.429245i	$-0.858780\pi$
$683$	−12.3861	+	12.3861i	−0.473943	+	0.473943i	0.429245	+	0.903188i	$0.358780\pi$
$684$		0			0
$685$	40.7846			1.55830
$686$	14.2165			0.542787
$687$		0			0
$688$			30.9282i			1.17913i
$689$		0			0
$690$		0			0
$691$	17.8827	−	17.8827i	0.680289	−	0.680289i	−0.279776	−	0.960065i	$-0.590260\pi$
$691$	17.8827	−	17.8827i	0.680289	−	0.680289i	0.960065	+	0.279776i	$0.0902602\pi$
$692$		−	28.0812i		−	1.06749i
$693$		0			0
$694$	41.1769	−	41.1769i	1.56305	−	1.56305i
$695$	6.55343	+	6.55343i	0.248586	+	0.248586i
$696$		0			0
$697$	6.92820	+	6.92820i	0.262424	+	0.262424i
$698$		−	4.21543i		−	0.159557i
$699$		0			0
$700$	1.80385	+	1.80385i	0.0681790	+	0.0681790i
$701$	−23.1822			−0.875580			−0.437790	−	0.899077i	$-0.644239\pi$
$701$	−23.1822			−0.875580			−0.437790	+	0.899077i	$0.644239\pi$
$702$		0			0
$703$	20.2487			0.763695
$704$	23.7370	+	23.7370i	0.894623	+	0.894623i
$705$		0			0
$706$		−	3.60770i		−	0.135777i
$707$	0.416102	+	0.416102i	0.0156491	+	0.0156491i
$708$		0			0
$709$	−8.56218	−	8.56218i	−0.321559	−	0.321559i	0.527806	−	0.849365i	$-0.323015\pi$
$709$	−8.56218	−	8.56218i	−0.321559	−	0.321559i	−0.849365	+	0.527806i	$0.823015\pi$
$710$	60.5066	−	60.5066i	2.27077	−	2.27077i
$711$		0			0
$712$		0			0
$713$	−11.3509	+	11.3509i	−0.425094	+	0.425094i
$714$		0			0
$715$		0			0
$716$			32.9802i			1.23253i
$717$		0			0
$718$	20.0000			0.746393
$719$	−43.9149			−1.63775			−0.818876	−	0.573971i	$-0.805402\pi$
$719$	−43.9149			−1.63775			−0.818876	+	0.573971i	$0.805402\pi$
$720$		0			0
$721$	−3.16987	+	3.16987i	−0.118052	+	0.118052i
$722$	−29.4954	+	29.4954i	−1.09771	+	1.09771i
$723$		0			0
$724$	12.0000			0.445976
$725$	3.48477			0.129421
$726$		0			0
$727$		−	35.1051i		−	1.30198i	−0.759088	−	0.650988i	$-0.774355\pi$
$727$		−	35.1051i		−	1.30198i	0.759088	−	0.650988i	$-0.225645\pi$
$728$		0			0
$729$		0			0
$730$	−15.8564	+	15.8564i	−0.586872	+	0.586872i
$731$			51.7439i			1.91382i
$732$		0			0
$733$	32.7583	−	32.7583i	1.20996	−	1.20996i	0.238916	−	0.971040i	$-0.423208\pi$
$733$	32.7583	−	32.7583i	1.20996	−	1.20996i	0.971040	−	0.238916i	$-0.0767922\pi$
$734$	7.62587	+	7.62587i	0.281476	+	0.281476i
$735$		0			0
$736$	−13.8564	−	13.8564i	−0.510754	−	0.510754i
$737$			33.0074i			1.21584i
$738$		0			0
$739$	1.53590	+	1.53590i	0.0564989	+	0.0564989i	0.734792	−	0.678293i	$-0.237280\pi$
$739$	1.53590	+	1.53590i	0.0564989	+	0.0564989i	−0.678293	+	0.734792i	$0.737280\pi$
$740$	17.5254			0.644245
$741$		0			0
$742$	−6.14359			−0.225538
$743$	4.86181	+	4.86181i	0.178363	+	0.178363i	0.790642	−	0.612279i	$-0.209747\pi$
$743$	4.86181	+	4.86181i	0.178363	+	0.178363i	−0.612279	+	0.790642i	$0.709747\pi$
$744$		0			0
$745$		−	17.4641i		−	0.639835i
$746$	10.7317	+	10.7317i	0.392915	+	0.392915i
$747$		0			0
$748$	39.7128	+	39.7128i	1.45204	+	1.45204i
$749$	0.619174	−	0.619174i	0.0226241	−	0.0226241i
$750$		0			0
$751$		−	10.1436i		−	0.370145i	−0.982725	−	0.185072i	$-0.940748\pi$
$751$		−	10.1436i		−	0.370145i	0.982725	−	0.185072i	$-0.0592520\pi$
$752$	9.24316	−	9.24316i	0.337063	−	0.337063i
$753$		0			0
$754$		0			0
$755$			32.7028i			1.19018i
$756$		0			0
$757$	−29.6077			−1.07611			−0.538055	−	0.842910i	$-0.680841\pi$
$757$	−29.6077			−1.07611			−0.538055	+	0.842910i	$0.680841\pi$
$758$	−46.2901			−1.68133
$759$		0			0
$760$		0			0
$761$	−0.859411	+	0.859411i	−0.0311536	+	0.0311536i	−0.722512	−	0.691358i	$-0.757013\pi$
$761$	−0.859411	+	0.859411i	−0.0311536	+	0.0311536i	0.691358	+	0.722512i	$0.257013\pi$
$762$		0			0
$763$	−8.26795			−0.299320
$764$	26.0106			0.941032
$765$		0			0
$766$		−	20.0000i		−	0.722629i
$767$		0			0
$768$		0			0
$769$	24.5167	−	24.5167i	0.884093	−	0.884093i	−0.109854	−	0.993948i	$-0.535038\pi$
$769$	24.5167	−	24.5167i	0.884093	−	0.884093i	0.993948	+	0.109854i	$0.0350384\pi$
$770$			11.8685i			0.427711i
$771$		0			0
$772$	1.66025	−	1.66025i	0.0597539	−	0.0597539i
$773$	−2.79126	−	2.79126i	−0.100395	−	0.100395i	0.655125	−	0.755520i	$-0.272616\pi$
$773$	−2.79126	−	2.79126i	−0.100395	−	0.100395i	−0.755520	+	0.655125i	$0.772616\pi$
$774$		0			0
$775$	−11.4186	−	11.4186i	−0.410168	−	0.410168i
$776$		0			0
$777$		0			0
$778$	−9.46410	−	9.46410i	−0.339304	−	0.339304i
$779$	−9.24316			−0.331170
$780$		0			0
$781$	65.7128			2.35139
$782$	−23.1822	−	23.1822i	−0.828994	−	0.828994i
$783$		0			0
$784$		−	26.9282i		−	0.961722i
$785$	−22.0082	−	22.0082i	−0.785508	−	0.785508i
$786$		0			0
$787$	−8.90192	−	8.90192i	−0.317319	−	0.317319i	0.530417	−	0.847737i	$-0.322035\pi$
$787$	−8.90192	−	8.90192i	−0.317319	−	0.317319i	−0.847737	+	0.530417i	$0.822035\pi$
$788$	10.0010	−	10.0010i	0.356272	−	0.356272i
$789$		0			0
$790$		−	39.3205i		−	1.39896i
$791$	−1.65445	+	1.65445i	−0.0588255	+	0.0588255i
$792$		0			0
$793$		0			0
$794$			31.7418i			1.12648i
$795$		0			0
$796$	−0.928203			−0.0328993
$797$	28.5617			1.01171			0.505853	−	0.862620i	$-0.331178\pi$
$797$	28.5617			1.01171			0.505853	+	0.862620i	$0.331178\pi$
$798$		0			0
$799$	15.4641	−	15.4641i	0.547081	−	0.547081i
$800$	13.9391	−	13.9391i	0.492820	−	0.492820i
$801$		0			0
$802$	−79.7128			−2.81476
$803$	−17.2208			−0.607707
$804$		0			0
$805$		−	3.46410i		−	0.122094i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			48.3607i			1.70027i	0.526565	+	0.850135i	$0.323480\pi$
$809$			48.3607i			1.70027i	−0.526565	+	0.850135i	$0.676520\pi$
$810$		0			0
$811$	−8.09808	+	8.09808i	−0.284362	+	0.284362i	−0.834846	−	0.550484i	$-0.814443\pi$
$811$	−8.09808	+	8.09808i	−0.284362	+	0.284362i	0.550484	+	0.834846i	$0.314443\pi$
$812$	−1.03528	−	1.03528i	−0.0363311	−	0.0363311i
$813$		0			0
$814$	19.0333	+	19.0333i	0.667118	+	0.667118i
$815$			45.4307i			1.59137i
$816$		0			0
$817$	−34.5167	−	34.5167i	−1.20759	−	1.20759i
$818$	−34.2185			−1.19642
$819$		0			0
$820$	−8.00000			−0.279372
$821$	37.1857	+	37.1857i	1.29779	+	1.29779i	0.929850	+	0.367938i	$0.119936\pi$
$821$	37.1857	+	37.1857i	1.29779	+	1.29779i	0.367938	+	0.929850i	$0.380064\pi$
$822$		0			0
$823$		−	4.39230i		−	0.153106i	−0.997066	−	0.0765531i	$-0.975609\pi$
$823$		−	4.39230i		−	0.153106i	0.997066	−	0.0765531i	$-0.0243915\pi$
$824$		0			0
$825$		0			0
$826$	−0.143594	−	0.143594i	−0.00499626	−	0.00499626i
$827$	−17.5254	+	17.5254i	−0.609417	+	0.609417i	−0.942794	−	0.333377i	$-0.891812\pi$
$827$	−17.5254	+	17.5254i	−0.609417	+	0.609417i	0.333377	+	0.942794i	$0.391812\pi$
$828$		0			0
$829$			18.7128i			0.649923i	0.945727	+	0.324961i	$0.105351\pi$
$829$			18.7128i			0.649923i	−0.945727	+	0.324961i	$0.894649\pi$
$830$	28.8391	−	28.8391i	1.00102	−	1.00102i
$831$		0			0
$832$		0			0
$833$		−	45.0518i		−	1.56095i
$834$		0			0
$835$	14.9282			0.516612
$836$	−52.9822			−1.83243
$837$		0			0
$838$	−4.78461	+	4.78461i	−0.165282	+	0.165282i
$839$	10.1397	−	10.1397i	0.350062	−	0.350062i	−0.510070	−	0.860133i	$-0.670381\pi$
$839$	10.1397	−	10.1397i	0.350062	−	0.350062i	0.860133	+	0.510070i	$0.170381\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	43.4617			1.49779
$843$		0			0
$844$		−	30.3923i		−	1.04615i
$845$		0			0
$846$		0			0
$847$	−2.41858	+	2.41858i	−0.0831035	+	0.0831035i
$848$			23.7370i			0.815133i
$849$		0			0
$850$	23.3205	−	23.3205i	0.799887	−	0.799887i
$851$	−5.55532	−	5.55532i	−0.190434	−	0.190434i
$852$		0			0
$853$	−11.2224	−	11.2224i	−0.384249	−	0.384249i	0.488381	−	0.872630i	$-0.337587\pi$
$853$	−11.2224	−	11.2224i	−0.384249	−	0.384249i	−0.872630	+	0.488381i	$0.837587\pi$
$854$			13.6617i			0.467492i
$855$		0			0
$856$		0			0
$857$	3.28169			0.112101			0.0560503	−	0.998428i	$-0.482149\pi$
$857$	3.28169			0.112101			0.0560503	+	0.998428i	$0.482149\pi$
$858$		0			0
$859$	−51.1962			−1.74679			−0.873395	−	0.487012i	$-0.838087\pi$
$859$	−51.1962			−1.74679			−0.873395	+	0.487012i	$0.838087\pi$
$860$	−29.8744	−	29.8744i	−1.01871	−	1.01871i
$861$		0			0
$862$			31.7128i			1.08014i
$863$	−10.3156	−	10.3156i	−0.351147	−	0.351147i	0.509389	−	0.860536i	$-0.329871\pi$
$863$	−10.3156	−	10.3156i	−0.351147	−	0.351147i	−0.860536	+	0.509389i	$0.829871\pi$
$864$		0			0
$865$	−27.1244	−	27.1244i	−0.922256	−	0.922256i
$866$	26.1122	−	26.1122i	0.887328	−	0.887328i
$867$		0			0
$868$			6.78461i			0.230285i
$869$	21.3519	−	21.3519i	0.724314	−	0.724314i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	30.9282			1.04616
$875$	−3.58630			−0.121239
$876$		0			0
$877$	−16.8038	+	16.8038i	−0.567426	+	0.567426i	−0.931406	−	0.363981i	$-0.881417\pi$
$877$	−16.8038	+	16.8038i	−0.567426	+	0.567426i	0.363981	+	0.931406i	$0.381417\pi$
$878$	−13.5601	+	13.5601i	−0.457632	+	0.457632i
$879$		0			0
$880$	45.8564			1.54582
$881$	−0.480473			−0.0161876			−0.00809378	−	0.999967i	$-0.502576\pi$
$881$	−0.480473			−0.0161876			−0.00809378	+	0.999967i	$0.502576\pi$
$882$		0			0
$883$		−	23.7846i		−	0.800416i	−0.916424	−	0.400208i	$-0.868938\pi$
$883$		−	23.7846i		−	0.800416i	0.916424	−	0.400208i	$-0.131062\pi$
$884$		0			0
$885$		0			0
$886$	33.5692	−	33.5692i	1.12778	−	1.12778i
$887$		−	44.6728i		−	1.49997i	−0.661457	−	0.749983i	$-0.730061\pi$
$887$		−	44.6728i		−	1.49997i	0.661457	−	0.749983i	$-0.269939\pi$
$888$		0			0
$889$	3.63397	−	3.63397i	0.121880	−	0.121880i
$890$	−17.5254	−	17.5254i	−0.587452	−	0.587452i
$891$		0			0
$892$	−34.7846	−	34.7846i	−1.16467	−	1.16467i
$893$			20.6312i			0.690397i
$894$		0			0
$895$	31.8564	+	31.8564i	1.06484	+	1.06484i
$896$		0			0
$897$		0			0
$898$	17.4641			0.582785
$899$	6.55343	+	6.55343i	0.218569	+	0.218569i
$900$		0			0
$901$			39.7128i			1.32303i
$902$	−8.68835	−	8.68835i	−0.289291	−	0.289291i
$903$		0			0
$904$		0			0
$905$	11.5911	−	11.5911i	0.385302	−	0.385302i
$906$		0			0
$907$		−	18.0000i		−	0.597680i	−0.954303	−	0.298840i	$-0.903400\pi$
$907$		−	18.0000i		−	0.597680i	0.954303	−	0.298840i	$-0.0965997\pi$
$908$	−9.24316	+	9.24316i	−0.306745	+	0.306745i
$909$		0			0
$910$		0			0
$911$		−	52.0213i		−	1.72354i	−0.507297	−	0.861771i	$-0.669355\pi$
$911$		−	52.0213i		−	1.72354i	0.507297	−	0.861771i	$-0.330645\pi$
$912$		0			0
$913$	31.3205			1.03656
$914$	22.9048			0.757624
$915$		0			0
$916$	−7.46410	+	7.46410i	−0.246621	+	0.246621i
$917$	2.58819	−	2.58819i	0.0854696	−	0.0854696i
$918$		0			0
$919$	−29.1769			−0.962458			−0.481229	−	0.876595i	$-0.659809\pi$
$919$	−29.1769			−0.962458			−0.481229	+	0.876595i	$0.659809\pi$
$920$		0			0
$921$		0			0
$922$			5.35898i			0.176489i
$923$		0			0
$924$		0			0
$925$	5.58846	−	5.58846i	0.183747	−	0.183747i
$926$		−	13.6617i		−	0.448950i
$927$		0			0
$928$	−8.00000	+	8.00000i	−0.262613	+	0.262613i
$929$	−6.13733	−	6.13733i	−0.201359	−	0.201359i	0.599223	−	0.800582i	$-0.295476\pi$
$929$	−6.13733	−	6.13733i	−0.201359	−	0.201359i	−0.800582	+	0.599223i	$0.795476\pi$
$930$		0			0
$931$	30.0526	+	30.0526i	0.984933	+	0.984933i
$932$		−	37.8792i		−	1.24077i
$933$		0			0
$934$	31.1769	+	31.1769i	1.02014	+	1.02014i
$935$	76.7193			2.50899
$936$		0			0
$937$	−51.5692			−1.68469			−0.842346	−	0.538936i	$-0.818826\pi$
$937$	−51.5692			−1.68469			−0.842346	+	0.538936i	$0.818826\pi$
$938$	−5.75839	−	5.75839i	−0.188018	−	0.188018i
$939$		0			0
$940$			17.8564i			0.582412i
$941$	−6.55343	−	6.55343i	−0.213636	−	0.213636i	0.592174	−	0.805810i	$-0.298270\pi$
$941$	−6.55343	−	6.55343i	−0.213636	−	0.213636i	−0.805810	+	0.592174i	$0.798270\pi$
$942$		0			0
$943$	2.53590	+	2.53590i	0.0825802	+	0.0825802i
$944$	−0.554803	+	0.554803i	−0.0180573	+	0.0180573i
$945$		0			0
$946$		−	64.8897i		−	2.10975i
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	−0.751568	−	0.659656i	$-0.770702\pi$
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	0.659656	+	0.751568i	$0.270702\pi$
$948$		0			0
$949$		0			0
$950$			31.1127i			1.00943i
$951$		0			0
$952$		0			0
$953$	59.5728			1.92975			0.964877	−	0.262703i	$-0.0846140\pi$
$953$	59.5728			1.92975			0.964877	+	0.262703i	$0.0846140\pi$
$954$		0			0
$955$	25.1244	−	25.1244i	0.813005	−	0.813005i
$956$	−9.24316	+	9.24316i	−0.298945	+	0.298945i
$957$		0			0
$958$	8.00000			0.258468
$959$	−7.72741			−0.249531
$960$		0			0
$961$		−	11.9474i		−	0.385401i
$962$		0			0
$963$		0			0
$964$	16.5359	−	16.5359i	0.532585	−	0.532585i
$965$		−	3.20736i		−	0.103249i
$966$		0			0
$967$	−5.73205	+	5.73205i	−0.184330	+	0.184330i	−0.793240	−	0.608909i	$-0.791607\pi$
$967$	−5.73205	+	5.73205i	−0.184330	+	0.184330i	0.608909	+	0.793240i	$0.291607\pi$
$968$		0			0
$969$		0			0
$970$	−19.4641	−	19.4641i	−0.624955	−	0.624955i
$971$		−	52.0213i		−	1.66944i	−0.550673	−	0.834721i	$-0.685629\pi$
$971$		−	52.0213i		−	1.66944i	0.550673	−	0.834721i	$-0.314371\pi$
$972$		0			0
$973$	−1.24167	−	1.24167i	−0.0398061	−	0.0398061i
$974$	−39.9497			−1.28007
$975$		0			0
$976$	52.7846			1.68959
$977$	7.24693	+	7.24693i	0.231850	+	0.231850i	0.813465	−	0.581615i	$-0.197579\pi$
$977$	7.24693	+	7.24693i	0.231850	+	0.231850i	−0.581615	+	0.813465i	$0.697579\pi$
$978$		0			0
$979$		−	19.0333i		−	0.608308i
$980$	26.0106	+	26.0106i	0.830880	+	0.830880i
$981$		0			0
$982$	36.9282	+	36.9282i	1.17843	+	1.17843i
$983$	4.27981	−	4.27981i	0.136505	−	0.136505i	−0.635553	−	0.772057i	$-0.719228\pi$
$983$	4.27981	−	4.27981i	0.136505	−	0.136505i	0.772057	+	0.635553i	$0.219228\pi$
$984$		0			0
$985$		−	19.3205i		−	0.615603i
$986$	−13.3843	+	13.3843i	−0.426242	+	0.426242i
$987$		0			0
$988$		0			0
$989$			18.9396i			0.602244i
$990$		0			0
$991$	9.60770			0.305198			0.152599	−	0.988288i	$-0.451236\pi$
$991$	9.60770			0.305198			0.152599	+	0.988288i	$0.451236\pi$
$992$	52.4274			1.66457
$993$		0			0
$994$	−11.4641	+	11.4641i	−0.363619	+	0.363619i
$995$	−0.896575	+	0.896575i	−0.0284234	+	0.0284234i
$996$		0			0
$997$	−39.7846			−1.25999			−0.629996	−	0.776599i	$-0.716943\pi$
$997$	−39.7846			−1.25999			−0.629996	+	0.776599i	$0.716943\pi$
$998$	−68.6401			−2.17277
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1521.2.i.e.746.2		8
3.2	odd	2	inner	1521.2.i.e.746.3		8
13.2	odd	12		117.2.ba.a.98.1	yes	8
13.4	even	6		117.2.ba.a.80.2	yes	8
13.5	odd	4		1521.2.i.d.944.2		8
13.8	odd	4	inner	1521.2.i.e.944.3		8
13.12	even	2		1521.2.i.d.746.3		8
39.2	even	12		117.2.ba.a.98.2	yes	8
39.5	even	4		1521.2.i.d.944.3		8
39.8	even	4	inner	1521.2.i.e.944.2		8
39.17	odd	6		117.2.ba.a.80.1	✓	8
39.38	odd	2		1521.2.i.d.746.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.ba.a.80.1	✓	8	39.17	odd	6
117.2.ba.a.80.2	yes	8	13.4	even	6
117.2.ba.a.98.1	yes	8	13.2	odd	12
117.2.ba.a.98.2	yes	8	39.2	even	12
1521.2.i.d.746.2		8	39.38	odd	2
1521.2.i.d.746.3		8	13.12	even	2
1521.2.i.d.944.2		8	13.5	odd	4
1521.2.i.d.944.3		8	39.5	even	4
1521.2.i.e.746.2		8	1.1	even	1	trivial
1521.2.i.e.746.3		8	3.2	odd	2	inner
1521.2.i.e.944.2		8	39.8	even	4	inner
1521.2.i.e.944.3		8	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 1521 = 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1521.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(1.93185 + 1.93185i) q^{5} +(-0.366025 - 0.366025i) q^{7} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +2.00000i q^{4} +(1.93185 + 1.93185i) q^{5} +(-0.366025 - 0.366025i) q^{7} -5.46410i q^{10} +(2.96713 - 2.96713i) q^{11} +1.03528i q^{14} +4.00000 q^{16} +6.69213 q^{17} +(-4.46410 + 4.46410i) q^{19} +(-3.86370 + 3.86370i) q^{20} -8.39230 q^{22} +2.44949 q^{23} +2.46410i q^{25} +(0.732051 - 0.732051i) q^{28} -1.41421i q^{29} +(-4.63397 + 4.63397i) q^{31} +(-5.65685 - 5.65685i) q^{32} +(-9.46410 - 9.46410i) q^{34} -1.41421i q^{35} +(-2.26795 - 2.26795i) q^{37} +12.6264 q^{38} +(1.03528 + 1.03528i) q^{41} +7.73205i q^{43} +(5.93426 + 5.93426i) q^{44} +(-3.46410 - 3.46410i) q^{46} +(2.31079 - 2.31079i) q^{47} -6.73205i q^{49} +(3.48477 - 3.48477i) q^{50} +5.93426i q^{53} +11.4641 q^{55} +(-2.00000 + 2.00000i) q^{58} +(-0.138701 + 0.138701i) q^{59} +13.1962 q^{61} +13.1069 q^{62} +8.00000i q^{64} +(-5.56218 + 5.56218i) q^{67} +13.3843i q^{68} +(-2.00000 + 2.00000i) q^{70} +(11.0735 + 11.0735i) q^{71} +(-2.90192 - 2.90192i) q^{73} +6.41473i q^{74} +(-8.92820 - 8.92820i) q^{76} -2.17209 q^{77} +7.19615 q^{79} +(7.72741 + 7.72741i) q^{80} -2.92820i q^{82} +(5.27792 + 5.27792i) q^{83} +(12.9282 + 12.9282i) q^{85} +(10.9348 - 10.9348i) q^{86} +(3.20736 - 3.20736i) q^{89} +4.89898i q^{92} -6.53590 q^{94} -17.2480 q^{95} +(3.56218 - 3.56218i) q^{97} +(-9.52056 + 9.52056i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} + 32 q^{16} - 8 q^{19} + 16 q^{22} - 8 q^{28} - 44 q^{31} - 48 q^{34} - 32 q^{37} + 64 q^{55} - 16 q^{58} + 64 q^{61} + 4 q^{67} - 16 q^{70} - 44 q^{73} - 16 q^{76} + 16 q^{79} + 48 q^{85} - 80 q^{94} - 20 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 + 32 * q^16 - 8 * q^19 + 16 * q^22 - 8 * q^28 - 44 * q^31 - 48 * q^34 - 32 * q^37 + 64 * q^55 - 16 * q^58 + 64 * q^61 + 4 * q^67 - 16 * q^70 - 44 * q^73 - 16 * q^76 + 16 * q^79 + 48 * q^85 - 80 * q^94 - 20 * q^97

Introduction

L-functions

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