LMFDB - Embedded newform 896.2.ba.a.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(289,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-4,0,6,0,0,0,6,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			289.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.289
Dual form			896.2.ba.a.865.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.133975 + 0.500000i) q^{3} +(-0.232051 - 0.866025i) q^{5} +(1.73205 - 2.00000i) q^{7} +(2.36603 + 1.36603i) q^{9} +(2.86603 + 0.767949i) q^{11} +(-3.73205 - 3.73205i) q^{13} +0.464102 q^{15} +(-3.23205 - 5.59808i) q^{17} +(-2.86603 + 0.767949i) q^{19} +(0.767949 + 1.13397i) q^{21} +(3.86603 + 2.23205i) q^{23} +(3.63397 - 2.09808i) q^{25} +(-2.09808 + 2.09808i) q^{27} +(0.267949 + 0.267949i) q^{29} +(1.86603 + 3.23205i) q^{31} +(-0.767949 + 1.33013i) q^{33} +(-2.13397 - 1.03590i) q^{35} +(-0.303848 - 1.13397i) q^{37} +(2.36603 - 1.36603i) q^{39} -4.92820i q^{41} +(6.46410 - 6.46410i) q^{43} +(0.633975 - 2.36603i) q^{45} +(2.13397 - 3.69615i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(3.23205 - 0.866025i) q^{51} +(-3.96410 - 1.06218i) q^{53} -2.66025i q^{55} -1.53590i q^{57} +(11.3301 + 3.03590i) q^{59} +(6.96410 - 1.86603i) q^{61} +(6.83013 - 2.36603i) q^{63} +(-2.36603 + 4.09808i) q^{65} +(1.33013 - 4.96410i) q^{67} +(-1.63397 + 1.63397i) q^{69} -0.535898i q^{71} +(-6.23205 + 3.59808i) q^{73} +(0.562178 + 2.09808i) q^{75} +(6.50000 - 4.40192i) q^{77} +(-8.33013 + 14.4282i) q^{79} +(3.33013 + 5.76795i) q^{81} +(1.53590 + 1.53590i) q^{83} +(-4.09808 + 4.09808i) q^{85} +(-0.169873 + 0.0980762i) q^{87} +(4.50000 + 2.59808i) q^{89} +(-13.9282 + 1.00000i) q^{91} +(-1.86603 + 0.500000i) q^{93} +(1.33013 + 2.30385i) q^{95} -2.92820 q^{97} +(5.73205 + 5.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 6 q^{5} + 6 q^{9} + 8 q^{11} - 8 q^{13} - 12 q^{15} - 6 q^{17} - 8 q^{19} + 10 q^{21} + 12 q^{23} + 18 q^{25} + 2 q^{27} + 8 q^{29} + 4 q^{31} - 10 q^{33} - 12 q^{35} - 22 q^{37} + 6 q^{39}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 6 * q^5 + 6 * q^9 + 8 * q^11 - 8 * q^13 - 12 * q^15 - 6 * q^17 - 8 * q^19 + 10 * q^21 + 12 * q^23 + 18 * q^25 + 2 * q^27 + 8 * q^29 + 4 * q^31 - 10 * q^33 - 12 * q^35 - 22 * q^37 + 6 * q^39 + 12 * q^43 + 6 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 2 * q^53 + 28 * q^59 + 14 * q^61 + 10 * q^63 - 6 * q^65 - 12 * q^67 - 10 * q^69 - 18 * q^73 - 22 * q^75 + 26 * q^77 - 16 * q^79 - 4 * q^81 + 20 * q^83 - 6 * q^85 - 18 * q^87 + 18 * q^89 - 28 * q^91 - 4 * q^93 - 12 * q^95 + 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.133975	+	0.500000i	−0.0773503	+	0.288675i	−0.993756	−	0.111576i	$-0.964410\pi$
$3$	−0.133975	+	0.500000i	−0.0773503	+	0.288675i	0.916406	+	0.400251i	$0.131077\pi$
$4$		0			0
$5$	−0.232051	−	0.866025i	−0.103776	−	0.387298i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	−0.232051	−	0.866025i	−0.103776	−	0.387298i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$		0			0
$9$	2.36603	+	1.36603i	0.788675	+	0.455342i
$10$		0			0
$11$	2.86603	+	0.767949i	0.864139	+	0.231545i	0.663552	−	0.748130i	$-0.269048\pi$
$11$	2.86603	+	0.767949i	0.864139	+	0.231545i	0.200587	+	0.979676i	$0.435715\pi$
$12$		0			0
$13$	−3.73205	−	3.73205i	−1.03508	−	1.03508i	−0.999362	−	0.0357229i	$-0.988627\pi$
$13$	−3.73205	−	3.73205i	−1.03508	−	1.03508i	−0.0357229	−	0.999362i	$-0.511373\pi$
$14$		0			0
$15$	0.464102			0.119831
$16$		0			0
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	−0.929661	−	0.368415i	$-0.879901\pi$
$17$	−3.23205	−	5.59808i	−0.783887	−	1.35773i	0.145774	−	0.989318i	$-0.453433\pi$
$18$		0			0
$19$	−2.86603	+	0.767949i	−0.657511	+	0.176180i	−0.572123	−	0.820168i	$-0.693880\pi$
$19$	−2.86603	+	0.767949i	−0.657511	+	0.176180i	−0.0853887	+	0.996348i	$0.527213\pi$
$20$		0			0
$21$	0.767949	+	1.13397i	0.167580	+	0.247454i
$22$		0			0
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	0.845607	−	0.533805i	$-0.179239\pi$
$23$	3.86603	+	2.23205i	0.806122	+	0.465415i	−0.0394853	+	0.999220i	$0.512572\pi$
$24$		0			0
$25$	3.63397	−	2.09808i	0.726795	−	0.419615i
$26$		0			0
$27$	−2.09808	+	2.09808i	−0.403775	+	0.403775i
$28$		0			0
$29$	0.267949	+	0.267949i	0.0497569	+	0.0497569i	0.731547	−	0.681791i	$-0.238798\pi$
$29$	0.267949	+	0.267949i	0.0497569	+	0.0497569i	−0.681791	+	0.731547i	$0.738798\pi$
$30$		0			0
$31$	1.86603	+	3.23205i	0.335148	+	0.580493i	0.983513	−	0.180836i	$-0.0578803\pi$
$31$	1.86603	+	3.23205i	0.335148	+	0.580493i	−0.648365	+	0.761329i	$0.724547\pi$
$32$		0			0
$33$	−0.767949	+	1.33013i	−0.133683	+	0.231545i
$34$		0			0
$35$	−2.13397	−	1.03590i	−0.360708	−	0.175099i
$36$		0			0
$37$	−0.303848	−	1.13397i	−0.0499522	−	0.186424i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	−0.303848	−	1.13397i	−0.0499522	−	0.186424i	−0.986394	+	0.164399i	$0.947432\pi$
$38$		0			0
$39$	2.36603	−	1.36603i	0.378867	−	0.218739i
$40$		0			0
$41$		−	4.92820i		−	0.769656i	−0.922988	−	0.384828i	$-0.874261\pi$
$41$		−	4.92820i		−	0.769656i	0.922988	−	0.384828i	$-0.125739\pi$
$42$		0			0
$43$	6.46410	−	6.46410i	0.985766	−	0.985766i	−0.0141339	−	0.999900i	$-0.504499\pi$
$43$	6.46410	−	6.46410i	0.985766	−	0.985766i	0.999900	+	0.0141339i	$0.00449910\pi$
$44$		0			0
$45$	0.633975	−	2.36603i	0.0945074	−	0.352706i
$46$		0			0
$47$	2.13397	−	3.69615i	0.311272	−	0.539139i	−0.667366	−	0.744730i	$-0.732578\pi$
$47$	2.13397	−	3.69615i	0.311272	−	0.539139i	0.978638	+	0.205591i	$0.0659116\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	3.23205	−	0.866025i	0.452578	−	0.121268i
$52$		0			0
$53$	−3.96410	−	1.06218i	−0.544511	−	0.145901i	−0.0239302	−	0.999714i	$-0.507618\pi$
$53$	−3.96410	−	1.06218i	−0.544511	−	0.145901i	−0.520581	+	0.853812i	$0.674285\pi$
$54$		0			0
$55$		−	2.66025i		−	0.358709i
$56$		0			0
$57$		−	1.53590i		−	0.203435i
$58$		0			0
$59$	11.3301	+	3.03590i	1.47506	+	0.395240i	0.904662	−	0.426130i	$-0.140123\pi$
$59$	11.3301	+	3.03590i	1.47506	+	0.395240i	0.570395	+	0.821370i	$0.306790\pi$
$60$		0			0
$61$	6.96410	−	1.86603i	0.891662	−	0.238920i	0.216230	−	0.976342i	$-0.430624\pi$
$61$	6.96410	−	1.86603i	0.891662	−	0.238920i	0.675432	+	0.737422i	$0.263957\pi$
$62$		0			0
$63$	6.83013	−	2.36603i	0.860515	−	0.298091i
$64$		0			0
$65$	−2.36603	+	4.09808i	−0.293469	+	0.508304i
$66$		0			0
$67$	1.33013	−	4.96410i	0.162501	−	0.606462i	−0.835845	−	0.548966i	$-0.815022\pi$
$67$	1.33013	−	4.96410i	0.162501	−	0.606462i	0.998346	−	0.0574958i	$-0.0183116\pi$
$68$		0			0
$69$	−1.63397	+	1.63397i	−0.196707	+	0.196707i
$70$		0			0
$71$		−	0.535898i		−	0.0635994i	−0.999494	−	0.0317997i	$-0.989876\pi$
$71$		−	0.535898i		−	0.0635994i	0.999494	−	0.0317997i	$-0.0101239\pi$
$72$		0			0
$73$	−6.23205	+	3.59808i	−0.729406	+	0.421123i	−0.818205	−	0.574927i	$-0.805031\pi$
$73$	−6.23205	+	3.59808i	−0.729406	+	0.421123i	0.0887986	+	0.996050i	$0.471697\pi$
$74$		0			0
$75$	0.562178	+	2.09808i	0.0649147	+	0.242265i
$76$		0			0
$77$	6.50000	−	4.40192i	0.740744	−	0.501646i
$78$		0			0
$79$	−8.33013	+	14.4282i	−0.937213	+	1.62330i	−0.166572	+	0.986029i	$0.553270\pi$
$79$	−8.33013	+	14.4282i	−0.937213	+	1.62330i	−0.770640	+	0.637270i	$0.780063\pi$
$80$		0			0
$81$	3.33013	+	5.76795i	0.370014	+	0.640883i
$82$		0			0
$83$	1.53590	+	1.53590i	0.168587	+	0.168587i	0.786358	−	0.617771i	$-0.211964\pi$
$83$	1.53590	+	1.53590i	0.168587	+	0.168587i	−0.617771	+	0.786358i	$0.711964\pi$
$84$		0			0
$85$	−4.09808	+	4.09808i	−0.444499	+	0.444499i
$86$		0			0
$87$	−0.169873	+	0.0980762i	−0.0182123	+	0.0105149i
$88$		0			0
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	0.719165	−	0.694839i	$-0.244525\pi$
$89$	4.50000	+	2.59808i	0.476999	+	0.275396i	−0.242166	+	0.970235i	$0.577858\pi$
$90$		0			0
$91$	−13.9282	+	1.00000i	−1.46007	+	0.104828i
$92$		0			0
$93$	−1.86603	+	0.500000i	−0.193498	+	0.0518476i
$94$		0			0
$95$	1.33013	+	2.30385i	0.136468	+	0.236370i
$96$		0			0
$97$	−2.92820			−0.297314			−0.148657	−	0.988889i	$-0.547495\pi$
$97$	−2.92820			−0.297314			−0.148657	+	0.988889i	$0.547495\pi$
$98$		0			0
$99$	5.73205	+	5.73205i	0.576093	+	0.576093i
$100$		0			0
$101$	18.8923	+	5.06218i	1.87985	+	0.503706i	0.999572	+	0.0292559i	$0.00931376\pi$
$101$	18.8923	+	5.06218i	1.87985	+	0.503706i	0.880283	+	0.474450i	$0.157353\pi$
$102$		0			0
$103$	−5.59808	−	3.23205i	−0.551595	−	0.318463i	0.198170	−	0.980168i	$-0.436500\pi$
$103$	−5.59808	−	3.23205i	−0.551595	−	0.318463i	−0.749765	+	0.661704i	$0.769833\pi$
$104$		0			0
$105$	0.803848	−	0.928203i	0.0784475	−	0.0905834i
$106$		0			0
$107$	−0.866025	−	3.23205i	−0.0837218	−	0.312454i	0.911347	−	0.411638i	$-0.135043\pi$
$107$	−0.866025	−	3.23205i	−0.0837218	−	0.312454i	−0.995069	+	0.0991843i	$0.968377\pi$
$108$		0			0
$109$	−0.571797	+	2.13397i	−0.0547682	+	0.204398i	−0.987888	−	0.155167i	$-0.950408\pi$
$109$	−0.571797	+	2.13397i	−0.0547682	+	0.204398i	0.933120	+	0.359565i	$0.117075\pi$
$110$		0			0
$111$	0.607695			0.0576799
$112$		0			0
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$		0			0
$115$	1.03590	−	3.86603i	0.0965980	−	0.360509i
$116$		0			0
$117$	−3.73205	−	13.9282i	−0.345028	−	1.28766i
$118$		0			0
$119$	−16.7942	−	3.23205i	−1.53952	−	0.296282i
$120$		0			0
$121$	−1.90192	−	1.09808i	−0.172902	−	0.0998251i
$122$		0			0
$123$	2.46410	+	0.660254i	0.222181	+	0.0595331i
$124$		0			0
$125$	−5.83013	−	5.83013i	−0.521462	−	0.521462i
$126$		0			0
$127$	−9.46410			−0.839803			−0.419902	−	0.907570i	$-0.637935\pi$
$127$	−9.46410			−0.839803			−0.419902	+	0.907570i	$0.637935\pi$
$128$		0			0
$129$	2.36603	+	4.09808i	0.208317	+	0.360815i
$130$		0			0
$131$	7.59808	−	2.03590i	0.663847	−	0.177877i	0.0888654	−	0.996044i	$-0.471676\pi$
$131$	7.59808	−	2.03590i	0.663847	−	0.177877i	0.574982	+	0.818166i	$0.305009\pi$
$132$		0			0
$133$	−3.42820	+	7.06218i	−0.297263	+	0.612368i
$134$		0			0
$135$	2.30385	+	1.33013i	0.198284	+	0.114479i
$136$		0			0
$137$	−15.2321	+	8.79423i	−1.30136	+	0.751342i	−0.980638	−	0.195831i	$-0.937260\pi$
$137$	−15.2321	+	8.79423i	−1.30136	+	0.751342i	−0.320724	+	0.947173i	$0.603926\pi$
$138$		0			0
$139$	−11.9282	+	11.9282i	−1.01174	+	1.01174i	−0.0118067	+	0.999930i	$0.503758\pi$
$139$	−11.9282	+	11.9282i	−1.01174	+	1.01174i	−0.999930	+	0.0118067i	$0.996242\pi$
$140$		0			0
$141$	1.56218	+	1.56218i	0.131559	+	0.131559i
$142$		0			0
$143$	−7.83013	−	13.5622i	−0.654788	−	1.13413i
$144$		0			0
$145$	0.169873	−	0.294229i	0.0141072	−	0.0244344i
$146$		0			0
$147$	3.59808	+	0.428203i	0.296764	+	0.0353176i
$148$		0			0
$149$	−2.03590	−	7.59808i	−0.166787	−	0.622459i	−0.997805	−	0.0662134i	$-0.978908\pi$
$149$	−2.03590	−	7.59808i	−0.166787	−	0.622459i	0.831018	−	0.556245i	$-0.187758\pi$
$150$		0			0
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	−0.0415935	−	0.999135i	$-0.513243\pi$
$151$	9.86603	−	5.69615i	0.802886	−	0.463546i	0.844479	+	0.535588i	$0.179910\pi$
$152$		0			0
$153$		−	17.6603i		−	1.42775i
$154$		0			0
$155$	2.36603	−	2.36603i	0.190044	−	0.190044i
$156$		0			0
$157$	−4.89230	+	18.2583i	−0.390448	+	1.45717i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−4.89230	+	18.2583i	−0.390448	+	1.45717i	−0.829396	+	0.558661i	$0.811315\pi$
$158$		0			0
$159$	1.06218	−	1.83975i	0.0842362	−	0.145901i
$160$		0			0
$161$	11.1603	−	3.86603i	0.879551	−	0.304685i
$162$		0			0
$163$	−12.0622	+	3.23205i	−0.944783	+	0.253154i	−0.698147	−	0.715954i	$-0.745992\pi$
$163$	−12.0622	+	3.23205i	−0.944783	+	0.253154i	−0.246636	+	0.969108i	$0.579325\pi$
$164$		0			0
$165$	1.33013	+	0.356406i	0.103550	+	0.0277462i
$166$		0			0
$167$			21.8564i			1.69130i	0.533738	+	0.845650i	$0.320787\pi$
$167$			21.8564i			1.69130i	−0.533738	+	0.845650i	$0.679213\pi$
$168$		0			0
$169$			14.8564i			1.14280i
$170$		0			0
$171$	−7.83013	−	2.09808i	−0.598785	−	0.160444i
$172$		0			0
$173$	2.23205	−	0.598076i	0.169700	−	0.0454709i	−0.172969	−	0.984927i	$-0.555336\pi$
$173$	2.23205	−	0.598076i	0.169700	−	0.0454709i	0.342668	+	0.939456i	$0.388669\pi$
$174$		0			0
$175$	2.09808	−	10.9019i	0.158600	−	0.824108i
$176$		0			0
$177$	−3.03590	+	5.25833i	−0.228192	+	0.395240i
$178$		0			0
$179$	−2.40192	+	8.96410i	−0.179528	+	0.670008i	0.816208	+	0.577759i	$0.196072\pi$
$179$	−2.40192	+	8.96410i	−0.179528	+	0.670008i	−0.995736	+	0.0922498i	$0.970594\pi$
$180$		0			0
$181$	−13.3923	+	13.3923i	−0.995442	+	0.995442i	−0.999990	−	0.00454748i	$-0.998552\pi$
$181$	−13.3923	+	13.3923i	−0.995442	+	0.995442i	0.00454748	+	0.999990i	$0.498552\pi$
$182$		0			0
$183$			3.73205i			0.275881i
$184$		0			0
$185$	−0.911543	+	0.526279i	−0.0670180	+	0.0386928i
$186$		0			0
$187$	−4.96410	−	18.5263i	−0.363011	−	1.35478i
$188$		0			0
$189$	0.562178	+	7.83013i	0.0408924	+	0.569558i
$190$		0			0
$191$	4.33013	−	7.50000i	0.313317	−	0.542681i	−0.665761	−	0.746165i	$-0.731893\pi$
$191$	4.33013	−	7.50000i	0.313317	−	0.542681i	0.979078	+	0.203484i	$0.0652264\pi$
$192$		0			0
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$		0			0
$195$	−1.73205	−	1.73205i	−0.124035	−	0.124035i
$196$		0			0
$197$	16.6603	−	16.6603i	1.18699	−	1.18699i	0.209100	−	0.977894i	$-0.432947\pi$
$197$	16.6603	−	16.6603i	1.18699	−	1.18699i	0.977894	−	0.209100i	$-0.0670533\pi$
$198$		0			0
$199$	−10.3301	+	5.96410i	−0.732283	+	0.422784i	−0.819257	−	0.573427i	$-0.805614\pi$
$199$	−10.3301	+	5.96410i	−0.732283	+	0.422784i	0.0869736	+	0.996211i	$0.472280\pi$
$200$		0			0
$201$	2.30385	+	1.33013i	0.162501	+	0.0938199i
$202$		0			0
$203$	1.00000	−	0.0717968i	0.0701862	−	0.00503915i
$204$		0			0
$205$	−4.26795	+	1.14359i	−0.298087	+	0.0798720i
$206$		0			0
$207$	6.09808	+	10.5622i	0.423846	+	0.734122i
$208$		0			0
$209$	−8.80385			−0.608975
$210$		0			0
$211$	−15.9282	−	15.9282i	−1.09654	−	1.09654i	−0.994812	−	0.101731i	$-0.967562\pi$
$211$	−15.9282	−	15.9282i	−1.09654	−	1.09654i	−0.101731	−	0.994812i	$-0.532438\pi$
$212$		0			0
$213$	0.267949	+	0.0717968i	0.0183596	+	0.00491943i
$214$		0			0
$215$	−7.09808	−	4.09808i	−0.484085	−	0.279486i
$216$		0			0
$217$	9.69615	+	1.86603i	0.658218	+	0.126674i
$218$		0			0
$219$	−0.964102	−	3.59808i	−0.0651479	−	0.243135i
$220$		0			0
$221$	−8.83013	+	32.9545i	−0.593979	+	2.21676i
$222$		0			0
$223$	−9.85641			−0.660034			−0.330017	−	0.943975i	$-0.607054\pi$
$223$	−9.85641			−0.660034			−0.330017	+	0.943975i	$0.607054\pi$
$224$		0			0
$225$	11.4641			0.764273
$226$		0			0
$227$	−2.99038	+	11.1603i	−0.198479	+	0.740732i	0.792860	+	0.609403i	$0.208591\pi$
$227$	−2.99038	+	11.1603i	−0.198479	+	0.740732i	−0.991339	+	0.131329i	$0.958076\pi$
$228$		0			0
$229$	3.57180	+	13.3301i	0.236031	+	0.880880i	0.977681	+	0.210093i	$0.0673767\pi$
$229$	3.57180	+	13.3301i	0.236031	+	0.880880i	−0.741650	+	0.670787i	$0.765957\pi$
$230$		0			0
$231$	1.33013	+	3.83975i	0.0875159	+	0.252637i
$232$		0			0
$233$	−0.696152	−	0.401924i	−0.0456065	−	0.0263309i	0.477023	−	0.878891i	$-0.341716\pi$
$233$	−0.696152	−	0.401924i	−0.0456065	−	0.0263309i	−0.522630	+	0.852560i	$0.675049\pi$
$234$		0			0
$235$	−3.69615	−	0.990381i	−0.241110	−	0.0646053i
$236$		0			0
$237$	−6.09808	−	6.09808i	−0.396113	−	0.396113i
$238$		0			0
$239$	8.53590			0.552141			0.276071	−	0.961137i	$-0.410968\pi$
$239$	8.53590			0.552141			0.276071	+	0.961137i	$0.410968\pi$
$240$		0			0
$241$	−6.96410	−	12.0622i	−0.448597	−	0.776993i	0.549698	−	0.835364i	$-0.314743\pi$
$241$	−6.96410	−	12.0622i	−0.448597	−	0.776993i	−0.998295	+	0.0583704i	$0.981410\pi$
$242$		0			0
$243$	−11.9282	+	3.19615i	−0.765195	+	0.205033i
$244$		0			0
$245$	−5.76795	+	2.47372i	−0.368501	+	0.158040i
$246$		0			0
$247$	13.5622	+	7.83013i	0.862941	+	0.498219i
$248$		0			0
$249$	−0.973721	+	0.562178i	−0.0617070	+	0.0356266i
$250$		0			0
$251$	−17.5885	+	17.5885i	−1.11017	+	1.11017i	−0.117047	+	0.993126i	$0.537343\pi$
$251$	−17.5885	+	17.5885i	−1.11017	+	1.11017i	−0.993126	+	0.117047i	$0.962657\pi$
$252$		0			0
$253$	9.36603	+	9.36603i	0.588837	+	0.588837i
$254$		0			0
$255$	−1.50000	−	2.59808i	−0.0939336	−	0.162698i
$256$		0			0
$257$	9.69615	−	16.7942i	0.604829	−	1.04760i	−0.387249	−	0.921975i	$-0.626575\pi$
$257$	9.69615	−	16.7942i	0.604829	−	1.04760i	0.992078	−	0.125620i	$-0.0400920\pi$
$258$		0			0
$259$	−2.79423	−	1.35641i	−0.173625	−	0.0842830i
$260$		0			0
$261$	0.267949	+	1.00000i	0.0165856	+	0.0618984i
$262$		0			0
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	−0.371900	−	0.928273i	$-0.621294\pi$
$263$	3.99038	−	2.30385i	0.246057	−	0.142061i	0.617958	+	0.786211i	$0.287960\pi$
$264$		0			0
$265$			3.67949i			0.226029i
$266$		0			0
$267$	−1.90192	+	1.90192i	−0.116396	+	0.116396i
$268$		0			0
$269$	2.62436	−	9.79423i	0.160010	−	0.597165i	−0.838614	−	0.544726i	$-0.816634\pi$
$269$	2.62436	−	9.79423i	0.160010	−	0.597165i	0.998624	−	0.0524390i	$-0.0166995\pi$
$270$		0			0
$271$	6.06218	−	10.5000i	0.368251	−	0.637830i	−0.621041	−	0.783778i	$-0.713290\pi$
$271$	6.06218	−	10.5000i	0.368251	−	0.637830i	0.989292	+	0.145948i	$0.0466233\pi$
$272$		0			0
$273$	1.36603	−	7.09808i	0.0826756	−	0.429595i
$274$		0			0
$275$	12.0263	−	3.22243i	0.725212	−	0.194320i
$276$		0			0
$277$	−4.50000	−	1.20577i	−0.270379	−	0.0724478i	0.121082	−	0.992642i	$-0.461364\pi$
$277$	−4.50000	−	1.20577i	−0.270379	−	0.0724478i	−0.391461	+	0.920195i	$0.628030\pi$
$278$		0			0
$279$			10.1962i			0.610428i
$280$		0			0
$281$		−	0.928203i		−	0.0553720i	−0.999617	−	0.0276860i	$-0.991186\pi$
$281$		−	0.928203i		−	0.0553720i	0.999617	−	0.0276860i	$-0.00881385\pi$
$282$		0			0
$283$	14.5263	+	3.89230i	0.863498	+	0.231374i	0.663274	−	0.748377i	$-0.269166\pi$
$283$	14.5263	+	3.89230i	0.863498	+	0.231374i	0.200224	+	0.979750i	$0.435833\pi$
$284$		0			0
$285$	−1.33013	+	0.356406i	−0.0787899	+	0.0211117i
$286$		0			0
$287$	−9.85641	−	8.53590i	−0.581805	−	0.503858i
$288$		0			0
$289$	−12.3923	+	21.4641i	−0.728959	+	1.26259i
$290$		0			0
$291$	0.392305	−	1.46410i	0.0229973	−	0.0858272i
$292$		0			0
$293$	7.92820	−	7.92820i	0.463171	−	0.463171i	−0.436523	−	0.899693i	$-0.643790\pi$
$293$	7.92820	−	7.92820i	0.463171	−	0.463171i	0.899693	+	0.436523i	$0.143790\pi$
$294$		0			0
$295$		−	10.5167i		−	0.612304i
$296$		0			0
$297$	−7.62436	+	4.40192i	−0.442410	+	0.255426i
$298$		0			0
$299$	−6.09808	−	22.7583i	−0.352661	−	1.31615i
$300$		0			0
$301$	−1.73205	−	24.1244i	−0.0998337	−	1.39050i
$302$		0			0
$303$	−5.06218	+	8.76795i	−0.290815	+	0.503706i
$304$		0			0
$305$	−3.23205	−	5.59808i	−0.185067	−	0.320545i
$306$		0			0
$307$	9.00000	+	9.00000i	0.513657	+	0.513657i	0.915645	−	0.401988i	$-0.131681\pi$
$307$	9.00000	+	9.00000i	0.513657	+	0.513657i	−0.401988	+	0.915645i	$0.631681\pi$
$308$		0			0
$309$	2.36603	−	2.36603i	0.134598	−	0.134598i
$310$		0			0
$311$	5.59808	−	3.23205i	0.317438	−	0.183273i	−0.332812	−	0.942993i	$-0.607998\pi$
$311$	5.59808	−	3.23205i	0.317438	−	0.183273i	0.650250	+	0.759720i	$0.274664\pi$
$312$		0			0
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.924537	−	0.381093i	$-0.124452\pi$
$313$	18.6962	+	10.7942i	1.05677	+	0.610126i	0.132232	+	0.991219i	$0.457786\pi$
$314$		0			0
$315$	−3.63397	−	5.36603i	−0.204751	−	0.302341i
$316$		0			0
$317$	−14.1603	+	3.79423i	−0.795319	+	0.213105i	−0.633528	−	0.773720i	$-0.718394\pi$
$317$	−14.1603	+	3.79423i	−0.795319	+	0.213105i	−0.161791	+	0.986825i	$0.551727\pi$
$318$		0			0
$319$	0.562178	+	0.973721i	0.0314759	+	0.0545179i
$320$		0			0
$321$	1.73205			0.0966736
$322$		0			0
$323$	13.5622	+	13.5622i	0.754620	+	0.754620i
$324$		0			0
$325$	−21.3923	−	5.73205i	−1.18663	−	0.317957i
$326$		0			0
$327$	−0.990381	−	0.571797i	−0.0547682	−	0.0316204i
$328$		0			0
$329$	−3.69615	−	10.6699i	−0.203775	−	0.588249i
$330$		0			0
$331$	5.25833	+	19.6244i	0.289024	+	1.07865i	0.945848	+	0.324609i	$0.105233\pi$
$331$	5.25833	+	19.6244i	0.289024	+	1.07865i	−0.656824	+	0.754044i	$0.728101\pi$
$332$		0			0
$333$	0.830127	−	3.09808i	0.0454907	−	0.169774i
$334$		0			0
$335$	−4.60770			−0.251745
$336$		0			0
$337$	−6.14359			−0.334663			−0.167331	−	0.985901i	$-0.553515\pi$
$337$	−6.14359			−0.334663			−0.167331	+	0.985901i	$0.553515\pi$
$338$		0			0
$339$	0.196152	−	0.732051i	0.0106535	−	0.0397595i
$340$		0			0
$341$	2.86603	+	10.6962i	0.155204	+	0.579229i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$	1.79423	+	1.03590i	0.0965980	+	0.0557709i
$346$		0			0
$347$	23.5263	+	6.30385i	1.26296	+	0.338408i	0.827329	−	0.561718i	$-0.189860\pi$
$347$	23.5263	+	6.30385i	1.26296	+	0.338408i	0.435628	+	0.900127i	$0.356526\pi$
$348$		0			0
$349$	−6.12436	−	6.12436i	−0.327829	−	0.327829i	0.523931	−	0.851761i	$-0.324465\pi$
$349$	−6.12436	−	6.12436i	−0.327829	−	0.327829i	−0.851761	+	0.523931i	$0.824465\pi$
$350$		0			0
$351$	15.6603			0.835883
$352$		0			0
$353$	13.8923	+	24.0622i	0.739413	+	1.28070i	0.952760	+	0.303724i	$0.0982301\pi$
$353$	13.8923	+	24.0622i	0.739413	+	1.28070i	−0.213347	+	0.976976i	$0.568437\pi$
$354$		0			0
$355$	−0.464102	+	0.124356i	−0.0246320	+	0.00660011i
$356$		0			0
$357$	3.86603	−	7.96410i	0.204612	−	0.421505i
$358$		0			0
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	0.394498	−	0.918897i	$-0.370919\pi$
$359$	−3.86603	−	2.23205i	−0.204041	−	0.117803i	−0.598539	+	0.801094i	$0.704252\pi$
$360$		0			0
$361$	−8.83013	+	5.09808i	−0.464744	+	0.268320i
$362$		0			0
$363$	0.803848	−	0.803848i	0.0421911	−	0.0421911i
$364$		0			0
$365$	4.56218	+	4.56218i	0.238795	+	0.238795i
$366$		0			0
$367$	3.06218	+	5.30385i	0.159844	+	0.276859i	0.934812	−	0.355142i	$-0.115567\pi$
$367$	3.06218	+	5.30385i	0.159844	+	0.276859i	−0.774968	+	0.632000i	$0.782234\pi$
$368$		0			0
$369$	6.73205	−	11.6603i	0.350457	−	0.607009i
$370$		0			0
$371$	−8.99038	+	6.08846i	−0.466757	+	0.316097i
$372$		0			0
$373$	0.232051	+	0.866025i	0.0120151	+	0.0448411i	0.971673	−	0.236329i	$-0.0759442\pi$
$373$	0.232051	+	0.866025i	0.0120151	+	0.0448411i	−0.959658	+	0.281170i	$0.909278\pi$
$374$		0			0
$375$	3.69615	−	2.13397i	0.190868	−	0.110198i
$376$		0			0
$377$		−	2.00000i		−	0.103005i
$378$		0			0
$379$	0.124356	−	0.124356i	0.00638772	−	0.00638772i	−0.703906	−	0.710293i	$-0.748562\pi$
$379$	0.124356	−	0.124356i	0.00638772	−	0.00638772i	0.710293	+	0.703906i	$0.248562\pi$
$380$		0			0
$381$	1.26795	−	4.73205i	0.0649590	−	0.242430i
$382$		0			0
$383$	−12.5981	+	21.8205i	−0.643732	+	1.11498i	0.340861	+	0.940114i	$0.389281\pi$
$383$	−12.5981	+	21.8205i	−0.643732	+	1.11498i	−0.984593	+	0.174862i	$0.944052\pi$
$384$		0			0
$385$	−5.32051	−	4.60770i	−0.271158	−	0.234830i
$386$		0			0
$387$	24.1244	−	6.46410i	1.22631	−	0.328589i
$388$		0			0
$389$	22.3564	+	5.99038i	1.13351	+	0.303724i	0.776341	−	0.630313i	$-0.217074\pi$
$389$	22.3564	+	5.99038i	1.13351	+	0.303724i	0.357174	+	0.934038i	$0.383740\pi$
$390$		0			0
$391$		−	28.8564i		−	1.45933i
$392$		0			0
$393$			4.07180i			0.205395i
$394$		0			0
$395$	14.4282	+	3.86603i	0.725962	+	0.194521i
$396$		0			0
$397$	25.6244	−	6.86603i	1.28605	−	0.344596i	0.449891	−	0.893084i	$-0.351463\pi$
$397$	25.6244	−	6.86603i	1.28605	−	0.344596i	0.836159	+	0.548488i	$0.184796\pi$
$398$		0			0
$399$	−3.07180	−	2.66025i	−0.153782	−	0.133179i
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	5.09808	−	19.0263i	0.253953	−	0.947766i
$404$		0			0
$405$	4.22243	−	4.22243i	0.209814	−	0.209814i
$406$		0			0
$407$		−	3.48334i		−	0.172663i
$408$		0			0
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$		0			0
$411$	−2.35641	−	8.79423i	−0.116233	−	0.433787i
$412$		0			0
$413$	25.6962	−	17.4019i	1.26442	−	0.856293i
$414$		0			0
$415$	0.973721	−	1.68653i	0.0477981	−	0.0827887i
$416$		0			0
$417$	−4.36603	−	7.56218i	−0.213805	−	0.370321i
$418$		0			0
$419$	−19.0000	−	19.0000i	−0.928211	−	0.928211i	0.0693796	−	0.997590i	$-0.477898\pi$
$419$	−19.0000	−	19.0000i	−0.928211	−	0.928211i	−0.997590	+	0.0693796i	$0.977898\pi$
$420$		0			0
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	−0.885918	−	0.463843i	$-0.846470\pi$
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	0.463843	+	0.885918i	$0.346470\pi$
$422$		0			0
$423$	10.0981	−	5.83013i	0.490985	−	0.283470i
$424$		0			0
$425$	−23.4904	−	13.5622i	−1.13945	−	0.657862i
$426$		0			0
$427$	8.33013	−	17.1603i	0.403123	−	0.830443i
$428$		0			0
$429$	7.83013	−	2.09808i	0.378042	−	0.101296i
$430$		0			0
$431$	15.3301	+	26.5526i	0.738426	+	1.27899i	0.953204	+	0.302329i	$0.0977640\pi$
$431$	15.3301	+	26.5526i	0.738426	+	1.27899i	−0.214777	+	0.976663i	$0.568903\pi$
$432$		0			0
$433$	−33.1769			−1.59438			−0.797190	−	0.603728i	$-0.793681\pi$
$433$	−33.1769			−1.59438			−0.797190	+	0.603728i	$0.793681\pi$
$434$		0			0
$435$	0.124356	+	0.124356i	0.00596240	+	0.00596240i
$436$		0			0
$437$	−12.7942	−	3.42820i	−0.612031	−	0.163993i
$438$		0			0
$439$	6.52628	+	3.76795i	0.311482	+	0.179834i	0.647590	−	0.761989i	$-0.275777\pi$
$439$	6.52628	+	3.76795i	0.311482	+	0.179834i	−0.336107	+	0.941824i	$0.609110\pi$
$440$		0			0
$441$	7.09808	−	17.7583i	0.338004	−	0.845635i
$442$		0			0
$443$	2.79423	+	10.4282i	0.132758	+	0.495459i	0.999997	−	0.00243278i	$-0.000774379\pi$
$443$	2.79423	+	10.4282i	0.132758	+	0.495459i	−0.867239	+	0.497892i	$0.834108\pi$
$444$		0			0
$445$	1.20577	−	4.50000i	0.0571590	−	0.213320i
$446$		0			0
$447$	4.07180			0.192589
$448$		0			0
$449$	−23.3205			−1.10056			−0.550281	−	0.834979i	$-0.685480\pi$
$449$	−23.3205			−1.10056			−0.550281	+	0.834979i	$0.685480\pi$
$450$		0			0
$451$	3.78461	−	14.1244i	0.178210	−	0.665090i
$452$		0			0
$453$	1.52628	+	5.69615i	0.0717109	+	0.267629i
$454$		0			0
$455$	4.09808	+	11.8301i	0.192121	+	0.554605i
$456$		0			0
$457$	−16.2846	−	9.40192i	−0.761762	−	0.439803i	0.0681661	−	0.997674i	$-0.478285\pi$
$457$	−16.2846	−	9.40192i	−0.761762	−	0.439803i	−0.829928	+	0.557871i	$0.811619\pi$
$458$		0			0
$459$	18.5263	+	4.96410i	0.864733	+	0.231704i
$460$		0			0
$461$	−18.6603	−	18.6603i	−0.869095	−	0.869095i	0.123278	−	0.992372i	$-0.460659\pi$
$461$	−18.6603	−	18.6603i	−0.869095	−	0.869095i	−0.992372	+	0.123278i	$0.960659\pi$
$462$		0			0
$463$	−2.14359			−0.0996212			−0.0498106	−	0.998759i	$-0.515862\pi$
$463$	−2.14359			−0.0996212			−0.0498106	+	0.998759i	$0.515862\pi$
$464$		0			0
$465$	0.866025	+	1.50000i	0.0401610	+	0.0695608i
$466$		0			0
$467$	25.9904	−	6.96410i	1.20269	−	0.322260i	0.398801	−	0.917038i	$-0.369426\pi$
$467$	25.9904	−	6.96410i	1.20269	−	0.322260i	0.803890	+	0.594777i	$0.202760\pi$
$468$		0			0
$469$	−7.62436	−	11.2583i	−0.352060	−	0.519861i
$470$		0			0
$471$	−8.47372	−	4.89230i	−0.390448	−	0.225426i
$472$		0			0
$473$	23.4904	−	13.5622i	1.08009	−	0.623590i
$474$		0			0
$475$	−8.80385	+	8.80385i	−0.403948	+	0.403948i
$476$		0			0
$477$	−7.92820	−	7.92820i	−0.363007	−	0.363007i
$478$		0			0
$479$	7.79423	+	13.5000i	0.356127	+	0.616831i	0.987310	−	0.158803i	$-0.0507636\pi$
$479$	7.79423	+	13.5000i	0.356127	+	0.616831i	−0.631183	+	0.775634i	$0.717430\pi$
$480$		0			0
$481$	−3.09808	+	5.36603i	−0.141260	+	0.244670i
$482$		0			0
$483$	0.437822	+	6.09808i	0.0199216	+	0.277472i
$484$		0			0
$485$	0.679492	+	2.53590i	0.0308541	+	0.115149i
$486$		0			0
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	−0.238375	−	0.971173i	$-0.576615\pi$
$487$	10.6699	−	6.16025i	0.483498	−	0.279148i	0.721873	+	0.692025i	$0.243281\pi$
$488$		0			0
$489$		−	6.46410i		−	0.292317i
$490$		0			0
$491$	−3.58846	+	3.58846i	−0.161945	+	0.161945i	−0.783428	−	0.621483i	$-0.786531\pi$
$491$	−3.58846	+	3.58846i	−0.161945	+	0.161945i	0.621483	+	0.783428i	$0.286531\pi$
$492$		0			0
$493$	0.633975	−	2.36603i	0.0285528	−	0.106560i
$494$		0			0
$495$	3.63397	−	6.29423i	0.163335	−	0.282905i
$496$		0			0
$497$	−1.07180	−	0.928203i	−0.0480767	−	0.0416356i
$498$		0			0
$499$	−24.9904	+	6.69615i	−1.11872	+	0.299761i	−0.770367	−	0.637601i	$-0.779927\pi$
$499$	−24.9904	+	6.69615i	−1.11872	+	0.299761i	−0.348356	+	0.937362i	$0.613260\pi$
$500$		0			0
$501$	−10.9282	−	2.92820i	−0.488236	−	0.130822i
$502$		0			0
$503$			31.8564i			1.42041i	0.703996	+	0.710203i	$0.251397\pi$
$503$			31.8564i			1.42041i	−0.703996	+	0.710203i	$0.748603\pi$
$504$		0			0
$505$		−	17.5359i		−	0.780337i
$506$		0			0
$507$	−7.42820	−	1.99038i	−0.329898	−	0.0883959i
$508$		0			0
$509$	9.42820	−	2.52628i	0.417898	−	0.111975i	−0.0437420	−	0.999043i	$-0.513928\pi$
$509$	9.42820	−	2.52628i	0.417898	−	0.111975i	0.461640	+	0.887067i	$0.347261\pi$
$510$		0			0
$511$	−3.59808	+	18.6962i	−0.159170	+	0.827069i
$512$		0			0
$513$	4.40192	−	7.62436i	0.194350	−	0.336624i
$514$		0			0
$515$	−1.50000	+	5.59808i	−0.0660979	+	0.246681i
$516$		0			0
$517$	8.95448	−	8.95448i	0.393818	−	0.393818i
$518$		0			0
$519$			1.19615i			0.0525053i
$520$		0			0
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	−0.177516	−	0.984118i	$-0.556806\pi$
$521$	13.3756	−	7.72243i	0.585998	−	0.338326i	0.763513	+	0.645792i	$0.223473\pi$
$522$		0			0
$523$	8.65064	+	32.2846i	0.378266	+	1.41171i	0.848514	+	0.529173i	$0.177498\pi$
$523$	8.65064	+	32.2846i	0.378266	+	1.41171i	−0.470248	+	0.882534i	$0.655836\pi$
$524$		0			0
$525$	5.16987	+	2.50962i	0.225632	+	0.109529i
$526$		0			0
$527$	12.0622	−	20.8923i	0.525437	−	0.910083i
$528$		0			0
$529$	−1.53590	−	2.66025i	−0.0667782	−	0.115663i
$530$		0			0
$531$	22.6603	+	22.6603i	0.983371	+	0.983371i
$532$		0			0
$533$	−18.3923	+	18.3923i	−0.796659	+	0.796659i
$534$		0			0
$535$	−2.59808	+	1.50000i	−0.112325	+	0.0648507i
$536$		0			0
$537$	−4.16025	−	2.40192i	−0.179528	−	0.103651i
$538$		0			0
$539$	2.45448	−	20.6244i	0.105722	−	0.888354i
$540$		0			0
$541$	9.23205	−	2.47372i	0.396917	−	0.106354i	−0.0548389	−	0.998495i	$-0.517465\pi$
$541$	9.23205	−	2.47372i	0.396917	−	0.106354i	0.451756	+	0.892142i	$0.350798\pi$
$542$		0			0
$543$	−4.90192	−	8.49038i	−0.210362	−	0.364357i
$544$		0			0
$545$	1.98076			0.0848465
$546$		0			0
$547$	−23.0526	−	23.0526i	−0.985656	−	0.985656i	0.0142423	−	0.999899i	$-0.495466\pi$
$547$	−23.0526	−	23.0526i	−0.985656	−	0.985656i	−0.999899	+	0.0142423i	$0.995466\pi$
$548$		0			0
$549$	19.0263	+	5.09808i	0.812022	+	0.217581i
$550$		0			0
$551$	−0.973721	−	0.562178i	−0.0414819	−	0.0239496i
$552$		0			0
$553$	14.4282	+	41.6506i	0.613550	+	1.77117i
$554$		0			0
$555$	−0.141016	−	0.526279i	−0.00598580	−	0.0223393i
$556$		0			0
$557$	1.76795	−	6.59808i	0.0749104	−	0.279569i	−0.918303	−	0.395879i	$-0.870440\pi$
$557$	1.76795	−	6.59808i	0.0749104	−	0.279569i	0.993213	+	0.116310i	$0.0371065\pi$
$558$		0			0
$559$	−48.2487			−2.04070
$560$		0			0
$561$	9.92820			0.419169
$562$		0			0
$563$	0.650635	−	2.42820i	0.0274210	−	0.102337i	−0.950859	−	0.309624i	$-0.899797\pi$
$563$	0.650635	−	2.42820i	0.0274210	−	0.102337i	0.978280	+	0.207287i	$0.0664635\pi$
$564$		0			0
$565$	0.339746	+	1.26795i	0.0142932	+	0.0533430i
$566$		0			0
$567$	17.3038	+	3.33013i	0.726693	+	0.139852i
$568$		0			0
$569$	5.08846	+	2.93782i	0.213319	+	0.123160i	0.602853	−	0.797852i	$-0.294031\pi$
$569$	5.08846	+	2.93782i	0.213319	+	0.123160i	−0.389534	+	0.921012i	$0.627364\pi$
$570$		0			0
$571$	26.7224	+	7.16025i	1.11830	+	0.299647i	0.770195	−	0.637809i	$-0.220159\pi$
$571$	26.7224	+	7.16025i	1.11830	+	0.299647i	0.348104	+	0.937456i	$0.386826\pi$
$572$		0			0
$573$	3.16987	+	3.16987i	0.132423	+	0.132423i
$574$		0			0
$575$	18.7321			0.781181
$576$		0			0
$577$	−6.62436	−	11.4737i	−0.275776	−	0.477657i	0.694555	−	0.719440i	$-0.255601\pi$
$577$	−6.62436	−	11.4737i	−0.275776	−	0.477657i	−0.970330	+	0.241782i	$0.922268\pi$
$578$		0			0
$579$	−11.5000	+	3.08142i	−0.477924	+	0.128059i
$580$		0			0
$581$	5.73205	−	0.411543i	0.237806	−	0.0170737i
$582$		0			0
$583$	−10.5455	−	6.08846i	−0.436751	−	0.252158i
$584$		0			0
$585$	−11.1962	+	6.46410i	−0.462904	+	0.267258i
$586$		0			0
$587$	21.9282	−	21.9282i	0.905074	−	0.905074i	−0.0907957	−	0.995870i	$-0.528941\pi$
$587$	21.9282	−	21.9282i	0.905074	−	0.905074i	0.995870	+	0.0907957i	$0.0289410\pi$
$588$		0			0
$589$	−7.83013	−	7.83013i	−0.322635	−	0.322635i
$590$		0			0
$591$	6.09808	+	10.5622i	0.250841	+	0.434470i
$592$		0			0
$593$	5.69615	−	9.86603i	0.233913	−	0.405149i	−0.725043	−	0.688703i	$-0.758180\pi$
$593$	5.69615	−	9.86603i	0.233913	−	0.405149i	0.958956	+	0.283554i	$0.0915136\pi$
$594$		0			0
$595$	1.09808	+	15.2942i	0.0450167	+	0.627002i
$596$		0			0
$597$	−1.59808	−	5.96410i	−0.0654049	−	0.244094i
$598$		0			0
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	−0.119162	−	0.992875i	$-0.538021\pi$
$599$	16.6699	−	9.62436i	0.681113	−	0.393241i	0.800274	+	0.599634i	$0.204687\pi$
$600$		0			0
$601$			10.0000i			0.407909i	0.978980	+	0.203954i	$0.0653794\pi$
$601$			10.0000i			0.407909i	−0.978980	+	0.203954i	$0.934621\pi$
$602$		0			0
$603$	9.92820	−	9.92820i	0.404308	−	0.404308i
$604$		0			0
$605$	−0.509619	+	1.90192i	−0.0207190	+	0.0773242i
$606$		0			0
$607$	8.52628	−	14.7679i	0.346071	−	0.599413i	−0.639477	−	0.768810i	$-0.720849\pi$
$607$	8.52628	−	14.7679i	0.346071	−	0.599413i	0.985548	+	0.169398i	$0.0541823\pi$
$608$		0			0
$609$	−0.0980762	+	0.509619i	−0.00397425	+	0.0206508i
$610$		0			0
$611$	−21.7583	+	5.83013i	−0.880248	+	0.235862i
$612$		0			0
$613$	9.23205	+	2.47372i	0.372879	+	0.0999126i	0.440392	−	0.897806i	$-0.354840\pi$
$613$	9.23205	+	2.47372i	0.372879	+	0.0999126i	−0.0675126	+	0.997718i	$0.521506\pi$
$614$		0			0
$615$		−	2.28719i		−	0.0922283i
$616$		0			0
$617$			0.535898i			0.0215745i	0.999942	+	0.0107872i	$0.00343375\pi$
$617$			0.535898i			0.0215745i	−0.999942	+	0.0107872i	$0.996566\pi$
$618$		0			0
$619$	−19.0622	−	5.10770i	−0.766174	−	0.205296i	−0.145493	−	0.989359i	$-0.546477\pi$
$619$	−19.0622	−	5.10770i	−0.766174	−	0.205296i	−0.620680	+	0.784064i	$0.713144\pi$
$620$		0			0
$621$	−12.7942	+	3.42820i	−0.513415	+	0.137569i
$622$		0			0
$623$	12.9904	−	4.50000i	0.520449	−	0.180289i
$624$		0			0
$625$	6.79423	−	11.7679i	0.271769	−	0.470718i
$626$		0			0
$627$	1.17949	−	4.40192i	0.0471044	−	0.175796i
$628$		0			0
$629$	−5.36603	+	5.36603i	−0.213957	+	0.213957i
$630$		0			0
$631$		−	32.2487i		−	1.28380i	−0.766788	−	0.641900i	$-0.778146\pi$
$631$		−	32.2487i		−	1.28380i	0.766788	−	0.641900i	$-0.221854\pi$
$632$		0			0
$633$	10.0981	−	5.83013i	0.401362	−	0.231727i
$634$		0			0
$635$	2.19615	+	8.19615i	0.0871517	+	0.325254i
$636$		0			0
$637$	−22.1244	+	29.5885i	−0.876599	+	1.17234i
$638$		0			0
$639$	0.732051	−	1.26795i	0.0289595	−	0.0501593i
$640$		0			0
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	0.954830	−	0.297153i	$-0.0960372\pi$
$641$	5.57180	+	9.65064i	0.220073	+	0.381177i	−0.734757	+	0.678330i	$0.762704\pi$
$642$		0			0
$643$	−5.39230	−	5.39230i	−0.212652	−	0.212652i	0.592741	−	0.805393i	$-0.298046\pi$
$643$	−5.39230	−	5.39230i	−0.212652	−	0.212652i	−0.805393	+	0.592741i	$0.798046\pi$
$644$		0			0
$645$	3.00000	−	3.00000i	0.118125	−	0.118125i
$646$		0			0
$647$	30.8660	−	17.8205i	1.21347	−	0.700596i	0.249955	−	0.968257i	$-0.419584\pi$
$647$	30.8660	−	17.8205i	1.21347	−	0.700596i	0.963513	+	0.267661i	$0.0862507\pi$
$648$		0			0
$649$	30.1410	+	17.4019i	1.18314	+	0.683085i
$650$		0			0
$651$	−2.23205	+	4.59808i	−0.0874810	+	0.180213i
$652$		0			0
$653$	−32.5526	+	8.72243i	−1.27388	+	0.341335i	−0.831516	−	0.555501i	$-0.812527\pi$
$653$	−32.5526	+	8.72243i	−1.27388	+	0.341335i	−0.442364	+	0.896836i	$0.645860\pi$
$654$		0			0
$655$	−3.52628	−	6.10770i	−0.137783	−	0.238647i
$656$		0			0
$657$	−19.6603			−0.767020
$658$		0			0
$659$	18.8564	+	18.8564i	0.734541	+	0.734541i	0.971516	−	0.236975i	$-0.0761558\pi$
$659$	18.8564	+	18.8564i	0.734541	+	0.734541i	−0.236975	+	0.971516i	$0.576156\pi$
$660$		0			0
$661$	−22.1603	−	5.93782i	−0.861934	−	0.230955i	−0.199337	−	0.979931i	$-0.563879\pi$
$661$	−22.1603	−	5.93782i	−0.861934	−	0.230955i	−0.662597	+	0.748976i	$0.730546\pi$
$662$		0			0
$663$	−15.2942	−	8.83013i	−0.593979	−	0.342934i
$664$		0			0
$665$	6.91154	+	1.33013i	0.268018	+	0.0515801i
$666$		0			0
$667$	0.437822	+	1.63397i	0.0169525	+	0.0632677i
$668$		0			0
$669$	1.32051	−	4.92820i	0.0510538	−	0.190535i
$670$		0			0
$671$	21.3923			0.825841
$672$		0			0
$673$	40.7846			1.57213			0.786066	−	0.618143i	$-0.212115\pi$
$673$	40.7846			1.57213			0.786066	+	0.618143i	$0.212115\pi$
$674$		0			0
$675$	−3.22243	+	12.0263i	−0.124031	+	0.462892i
$676$		0			0
$677$	−11.4474	−	42.7224i	−0.439961	−	1.64196i	−0.728908	−	0.684611i	$-0.759972\pi$
$677$	−11.4474	−	42.7224i	−0.439961	−	1.64196i	0.288947	−	0.957345i	$-0.406695\pi$
$678$		0			0
$679$	−5.07180	+	5.85641i	−0.194638	+	0.224748i
$680$		0			0
$681$	−5.17949	−	2.99038i	−0.198479	−	0.114592i
$682$		0			0
$683$	−45.5788	−	12.2128i	−1.74403	−	0.467310i	−0.760691	−	0.649114i	$-0.775140\pi$
$683$	−45.5788	−	12.2128i	−1.74403	−	0.467310i	−0.983335	+	0.181804i	$0.941806\pi$
$684$		0			0
$685$	11.1506	+	11.1506i	0.426044	+	0.426044i
$686$		0			0
$687$	−7.14359			−0.272545
$688$		0			0
$689$	10.8301	+	18.7583i	0.412595	+	0.714635i
$690$		0			0
$691$	−22.9904	+	6.16025i	−0.874595	+	0.234347i	−0.668074	−	0.744095i	$-0.732881\pi$
$691$	−22.9904	+	6.16025i	−0.874595	+	0.234347i	−0.206521	+	0.978442i	$0.566214\pi$
$692$		0			0
$693$	21.3923	−	1.53590i	0.812626	−	0.0583440i
$694$		0			0
$695$	13.0981	+	7.56218i	0.496838	+	0.286850i
$696$		0			0
$697$	−27.5885	+	15.9282i	−1.04499	+	0.603324i
$698$		0			0
$699$	0.294229	−	0.294229i	0.0111287	−	0.0111287i
$700$		0			0
$701$	13.3923	+	13.3923i	0.505820	+	0.505820i	0.913241	−	0.407420i	$-0.133572\pi$
$701$	13.3923	+	13.3923i	0.505820	+	0.505820i	−0.407420	+	0.913241i	$0.633572\pi$
$702$		0			0
$703$	1.74167	+	3.01666i	0.0656883	+	0.113776i
$704$		0			0
$705$	0.990381	−	1.71539i	0.0372999	−	0.0646053i
$706$		0			0
$707$	42.8468	−	29.0167i	1.61142	−	1.09128i
$708$		0			0
$709$	12.2321	+	45.6506i	0.459384	+	1.71445i	0.674868	+	0.737938i	$0.264200\pi$
$709$	12.2321	+	45.6506i	0.459384	+	1.71445i	−0.215484	+	0.976507i	$0.569133\pi$
$710$		0			0
$711$	−39.4186	+	22.7583i	−1.47831	+	0.853504i
$712$		0			0
$713$			16.6603i			0.623931i
$714$		0			0
$715$	−9.92820	+	9.92820i	−0.371294	+	0.371294i
$716$		0			0
$717$	−1.14359	+	4.26795i	−0.0427083	+	0.159389i
$718$		0			0
$719$	0.205771	−	0.356406i	0.00767398	−	0.0132917i	−0.862163	−	0.506631i	$-0.830891\pi$
$719$	0.205771	−	0.356406i	0.00767398	−	0.0132917i	0.869837	+	0.493339i	$0.164224\pi$
$720$		0			0
$721$	−16.1603	+	5.59808i	−0.601839	+	0.208483i
$722$		0			0
$723$	6.96410	−	1.86603i	0.258998	−	0.0693982i
$724$		0			0
$725$	1.53590	+	0.411543i	0.0570418	+	0.0152843i
$726$		0			0
$727$			41.3205i			1.53249i	0.642547	+	0.766246i	$0.277878\pi$
$727$			41.3205i			1.53249i	−0.642547	+	0.766246i	$0.722122\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	−57.0788	−	15.2942i	−2.11114	−	0.565677i
$732$		0			0
$733$	−32.8923	+	8.81347i	−1.21490	+	0.325533i	−0.808685	−	0.588242i	$-0.799820\pi$
$733$	−32.8923	+	8.81347i	−1.21490	+	0.325533i	−0.406220	+	0.913775i	$0.633153\pi$
$734$		0			0
$735$	−0.464102	−	3.21539i	−0.0171186	−	0.118601i
$736$		0			0
$737$	7.62436	−	13.2058i	0.280847	−	0.486441i
$738$		0			0
$739$	−10.3109	+	38.4808i	−0.379292	+	1.41554i	0.467679	+	0.883899i	$0.345090\pi$
$739$	−10.3109	+	38.4808i	−0.379292	+	1.41554i	−0.846971	+	0.531639i	$0.821576\pi$
$740$		0			0
$741$	−5.73205	+	5.73205i	−0.210572	+	0.210572i
$742$		0			0
$743$			11.0718i			0.406185i	0.979160	+	0.203092i	$0.0650992\pi$
$743$			11.0718i			0.406185i	−0.979160	+	0.203092i	$0.934901\pi$
$744$		0			0
$745$	−6.10770	+	3.52628i	−0.223769	+	0.129193i
$746$		0			0
$747$	1.53590	+	5.73205i	0.0561956	+	0.209725i
$748$		0			0
$749$	−7.96410	−	3.86603i	−0.291002	−	0.141261i
$750$		0			0
$751$	6.52628	−	11.3038i	0.238147	−	0.412483i	−0.722035	−	0.691856i	$-0.756793\pi$
$751$	6.52628	−	11.3038i	0.238147	−	0.412483i	0.960183	+	0.279373i	$0.0901266\pi$
$752$		0			0
$753$	−6.43782	−	11.1506i	−0.234607	−	0.406352i
$754$		0			0
$755$	−7.22243	−	7.22243i	−0.262851	−	0.262851i
$756$		0			0
$757$	18.6603	−	18.6603i	0.678218	−	0.678218i	−0.281378	−	0.959597i	$-0.590792\pi$
$757$	18.6603	−	18.6603i	0.678218	−	0.678218i	0.959597	+	0.281378i	$0.0907916\pi$
$758$		0			0
$759$	−5.93782	+	3.42820i	−0.215529	+	0.124436i
$760$		0			0
$761$	−11.7679	−	6.79423i	−0.426588	−	0.246291i	0.271304	−	0.962494i	$-0.412545\pi$
$761$	−11.7679	−	6.79423i	−0.426588	−	0.246291i	−0.697892	+	0.716203i	$0.745878\pi$
$762$		0			0
$763$	3.27757	+	4.83975i	0.118656	+	0.175211i
$764$		0			0
$765$	−15.2942	+	4.09808i	−0.552964	+	0.148166i
$766$		0			0
$767$	−30.9545	−	53.6147i	−1.11770	−	1.93592i
$768$		0			0
$769$	9.85641			0.355431			0.177716	−	0.984082i	$-0.443129\pi$
$769$	9.85641			0.355431			0.177716	+	0.984082i	$0.443129\pi$
$770$		0			0
$771$	7.09808	+	7.09808i	0.255631	+	0.255631i
$772$		0			0
$773$	−10.9641	−	2.93782i	−0.394351	−	0.105666i	0.0561936	−	0.998420i	$-0.482104\pi$
$773$	−10.9641	−	2.93782i	−0.394351	−	0.105666i	−0.450545	+	0.892754i	$0.648770\pi$
$774$		0			0
$775$	13.5622	+	7.83013i	0.487168	+	0.281266i
$776$		0			0
$777$	1.05256	−	1.21539i	0.0377603	−	0.0436019i
$778$		0			0
$779$	3.78461	+	14.1244i	0.135598	+	0.506058i
$780$		0			0
$781$	0.411543	−	1.53590i	0.0147262	−	0.0549588i
$782$		0			0
$783$	−1.12436			−0.0401812
$784$		0			0
$785$	16.9474			0.604880
$786$		0			0
$787$	3.52628	−	13.1603i	0.125698	−	0.469112i	−0.874165	−	0.485628i	$-0.838591\pi$
$787$	3.52628	−	13.1603i	0.125698	−	0.469112i	0.999864	+	0.0165161i	$0.00525747\pi$
$788$		0			0
$789$	0.617314	+	2.30385i	0.0219770	+	0.0820191i
$790$		0			0
$791$	−2.53590	+	2.92820i	−0.0901662	+	0.104115i
$792$		0			0
$793$	−32.9545	−	19.0263i	−1.17025	−	0.675643i
$794$		0			0
$795$	−1.83975	−	0.492958i	−0.0652491	−	0.0174834i
$796$		0			0
$797$	13.3397	+	13.3397i	0.472518	+	0.472518i	0.902729	−	0.430211i	$-0.141561\pi$
$797$	13.3397	+	13.3397i	0.472518	+	0.472518i	−0.430211	+	0.902729i	$0.641561\pi$
$798$		0			0
$799$	−27.5885			−0.976009
$800$		0			0
$801$	7.09808	+	12.2942i	0.250798	+	0.434395i
$802$		0			0
$803$	−20.6244	+	5.52628i	−0.727818	+	0.195018i
$804$		0			0
$805$	−5.93782	−	8.76795i	−0.209281	−	0.309030i
$806$		0			0
$807$	4.54552	+	2.62436i	0.160010	+	0.0923817i
$808$		0			0
$809$	29.4282	−	16.9904i	1.03464	−	0.597350i	0.116330	−	0.993211i	$-0.462887\pi$
$809$	29.4282	−	16.9904i	1.03464	−	0.597350i	0.918311	+	0.395861i	$0.129554\pi$
$810$		0			0
$811$	24.3205	−	24.3205i	0.854009	−	0.854009i	−0.136616	−	0.990624i	$-0.543623\pi$
$811$	24.3205	−	24.3205i	0.854009	−	0.854009i	0.990624	+	0.136616i	$0.0436225\pi$
$812$		0			0
$813$	4.43782	+	4.43782i	0.155641	+	0.155641i
$814$		0			0
$815$	5.59808	+	9.69615i	0.196092	+	0.339641i
$816$		0			0
$817$	−13.5622	+	23.4904i	−0.474481	+	0.821824i
$818$		0			0
$819$	−34.3205	−	16.6603i	−1.19926	−	0.582156i
$820$		0			0
$821$	0.160254	+	0.598076i	0.00559290	+	0.0208730i	0.968666	−	0.248367i	$-0.0798940\pi$
$821$	0.160254	+	0.598076i	0.00559290	+	0.0208730i	−0.963073	+	0.269240i	$0.913227\pi$
$822$		0			0
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	−0.737221	−	0.675652i	$-0.763862\pi$
$823$	−14.9378	+	8.62436i	−0.520700	+	0.300626i	0.216521	+	0.976278i	$0.430529\pi$
$824$		0			0
$825$			6.44486i			0.224381i
$826$		0			0
$827$	−3.78461	+	3.78461i	−0.131604	+	0.131604i	−0.769840	−	0.638237i	$-0.779664\pi$
$827$	−3.78461	+	3.78461i	−0.131604	+	0.131604i	0.638237	+	0.769840i	$0.279664\pi$
$828$		0			0
$829$	−0.820508	+	3.06218i	−0.0284974	+	0.106354i	−0.978710	−	0.205250i	$-0.934199\pi$
$829$	−0.820508	+	3.06218i	−0.0284974	+	0.106354i	0.950212	+	0.311603i	$0.100866\pi$
$830$		0			0
$831$	1.20577	−	2.08846i	0.0418277	−	0.0724478i
$832$		0			0
$833$	−35.5526	+	27.9904i	−1.23182	+	0.969809i
$834$		0			0
$835$	18.9282	−	5.07180i	0.655037	−	0.175517i
$836$		0			0
$837$	−10.6962	−	2.86603i	−0.369713	−	0.0990643i
$838$		0			0
$839$		−	17.7128i		−	0.611514i	−0.952110	−	0.305757i	$-0.901090\pi$
$839$		−	17.7128i		−	0.611514i	0.952110	−	0.305757i	$-0.0989096\pi$
$840$		0			0
$841$		−	28.8564i		−	0.995048i
$842$		0			0
$843$	0.464102	+	0.124356i	0.0159845	+	0.00428304i
$844$		0			0
$845$	12.8660	−	3.44744i	0.442605	−	0.118596i
$846$		0			0
$847$	−5.49038	+	1.90192i	−0.188652	+	0.0653509i
$848$		0			0
$849$	−3.89230	+	6.74167i	−0.133584	+	0.231374i
$850$		0			0
$851$	1.35641	−	5.06218i	0.0464970	−	0.173529i
$852$		0			0
$853$	11.8756	−	11.8756i	0.406614	−	0.406614i	−0.473942	−	0.880556i	$-0.657169\pi$
$853$	11.8756	−	11.8756i	0.406614	−	0.406614i	0.880556	+	0.473942i	$0.157169\pi$
$854$		0			0
$855$			7.26795i			0.248559i
$856$		0			0
$857$	−11.8923	+	6.86603i	−0.406233	+	0.234539i	−0.689170	−	0.724600i	$-0.742025\pi$
$857$	−11.8923	+	6.86603i	−0.406233	+	0.234539i	0.282937	+	0.959139i	$0.408691\pi$
$858$		0			0
$859$	−3.65064	−	13.6244i	−0.124558	−	0.464857i	0.875265	−	0.483643i	$-0.160687\pi$
$859$	−3.65064	−	13.6244i	−0.124558	−	0.464857i	−0.999824	+	0.0187858i	$0.994020\pi$
$860$		0			0
$861$	5.58846	−	3.78461i	0.190454	−	0.128979i
$862$		0			0
$863$	−16.3301	+	28.2846i	−0.555884	+	0.962819i	0.441950	+	0.897040i	$0.354287\pi$
$863$	−16.3301	+	28.2846i	−0.555884	+	0.962819i	−0.997834	+	0.0657797i	$0.979047\pi$
$864$		0			0
$865$	−1.03590	−	1.79423i	−0.0352216	−	0.0610056i
$866$		0			0
$867$	−9.07180	−	9.07180i	−0.308094	−	0.308094i
$868$		0			0
$869$	−34.9545	+	34.9545i	−1.18575	+	1.18575i
$870$		0			0
$871$	−23.4904	+	13.5622i	−0.795941	+	0.459537i
$872$		0			0
$873$	−6.92820	−	4.00000i	−0.234484	−	0.135379i
$874$		0			0
$875$	−21.7583	+	1.56218i	−0.735566	+	0.0528112i
$876$		0			0
$877$	30.5526	−	8.18653i	1.03169	−	0.276440i	0.297022	−	0.954871i	$-0.404006\pi$
$877$	30.5526	−	8.18653i	1.03169	−	0.276440i	0.734664	+	0.678431i	$0.237340\pi$
$878$		0			0
$879$	2.90192	+	5.02628i	0.0978795	+	0.169532i
$880$		0			0
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$		0			0
$883$	−5.00000	−	5.00000i	−0.168263	−	0.168263i	0.617952	−	0.786216i	$-0.287963\pi$
$883$	−5.00000	−	5.00000i	−0.168263	−	0.168263i	−0.786216	+	0.617952i	$0.787963\pi$
$884$		0			0
$885$	5.25833	+	1.40897i	0.176757	+	0.0473619i
$886$		0			0
$887$	−39.7750	−	22.9641i	−1.33551	−	0.771059i	−0.349375	−	0.936983i	$-0.613606\pi$
$887$	−39.7750	−	22.9641i	−1.33551	−	0.771059i	−0.986139	+	0.165924i	$0.946939\pi$
$888$		0			0
$889$	−16.3923	+	18.9282i	−0.549780	+	0.634832i
$890$		0			0
$891$	5.11474	+	19.0885i	0.171350	+	0.639487i
$892$		0			0
$893$	−3.27757	+	12.2321i	−0.109680	+	0.409330i
$894$		0			0
$895$	8.32051			0.278124
$896$		0			0
$897$	12.1962			0.407218
$898$		0			0
$899$	−0.366025	+	1.36603i	−0.0122076	+	0.0455595i
$900$		0			0
$901$	6.86603	+	25.6244i	0.228740	+	0.853671i
$902$		0			0
$903$	12.2942	+	2.36603i	0.409126	+	0.0787364i
$904$		0			0
$905$	14.7058	+	8.49038i	0.488836	+	0.282230i
$906$		0			0
$907$	−26.7224	−	7.16025i	−0.887304	−	0.237752i	−0.213748	−	0.976889i	$-0.568567\pi$
$907$	−26.7224	−	7.16025i	−0.887304	−	0.237752i	−0.673556	+	0.739136i	$0.735234\pi$
$908$		0			0
$909$	37.7846	+	37.7846i	1.25324	+	1.25324i
$910$		0			0
$911$	−7.32051			−0.242539			−0.121270	−	0.992620i	$-0.538697\pi$
$911$	−7.32051			−0.242539			−0.121270	+	0.992620i	$0.538697\pi$
$912$		0			0
$913$	3.22243	+	5.58142i	0.106647	+	0.184718i
$914$		0			0
$915$	3.23205	−	0.866025i	0.106848	−	0.0286299i
$916$		0			0
$917$	9.08846	−	18.7224i	0.300127	−	0.618269i
$918$		0			0
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	0.214941	−	0.976627i	$-0.431044\pi$
$919$	−15.8660	−	9.16025i	−0.523372	−	0.302169i	−0.738313	+	0.674458i	$0.764377\pi$
$920$		0			0
$921$	−5.70577	+	3.29423i	−0.188012	+	0.108549i
$922$		0			0
$923$	−2.00000	+	2.00000i	−0.0658308	+	0.0658308i
$924$		0			0
$925$	−3.48334	−	3.48334i	−0.114531	−	0.114531i
$926$		0			0
$927$	−8.83013	−	15.2942i	−0.290019	−	0.502328i
$928$		0			0
$929$	−25.0167	+	43.3301i	−0.820770	+	1.42162i	0.0843396	+	0.996437i	$0.473122\pi$
$929$	−25.0167	+	43.3301i	−0.820770	+	1.42162i	−0.905110	+	0.425178i	$0.860211\pi$
$930$		0			0
$931$	8.18653	+	19.0885i	0.268303	+	0.625599i
$932$		0			0
$933$	0.866025	+	3.23205i	0.0283524	+	0.105813i
$934$		0			0
$935$	−14.8923	+	8.59808i	−0.487030	+	0.281187i
$936$		0			0
$937$		−	29.0718i		−	0.949734i	−0.880058	−	0.474867i	$-0.842496\pi$
$937$		−	29.0718i		−	0.949734i	0.880058	−	0.474867i	$-0.157504\pi$
$938$		0			0
$939$	−7.90192	+	7.90192i	−0.257870	+	0.257870i
$940$		0			0
$941$	−6.30385	+	23.5263i	−0.205500	+	0.766935i	0.783797	+	0.621017i	$0.213280\pi$
$941$	−6.30385	+	23.5263i	−0.205500	+	0.766935i	−0.989297	+	0.145918i	$0.953386\pi$
$942$		0			0
$943$	11.0000	−	19.0526i	0.358209	−	0.620437i
$944$		0			0
$945$	6.65064	−	2.30385i	0.216345	−	0.0749442i
$946$		0			0
$947$	5.40192	−	1.44744i	0.175539	−	0.0470355i	−0.169979	−	0.985448i	$-0.554370\pi$
$947$	5.40192	−	1.44744i	0.175539	−	0.0470355i	0.345518	+	0.938412i	$0.387703\pi$
$948$		0			0
$949$	36.6865	+	9.83013i	1.19090	+	0.319099i
$950$		0			0
$951$		−	7.58846i		−	0.246073i
$952$		0			0
$953$			16.5359i			0.535650i	0.963468	+	0.267825i	$0.0863050\pi$
$953$			16.5359i			0.535650i	−0.963468	+	0.267825i	$0.913695\pi$
$954$		0			0
$955$	−7.50000	−	2.00962i	−0.242694	−	0.0650297i
$956$		0			0
$957$	−0.562178	+	0.150635i	−0.0181726	+	0.00486934i
$958$		0			0
$959$	−8.79423	+	45.6962i	−0.283980	+	1.47561i
$960$		0			0
$961$	8.53590	−	14.7846i	0.275352	−	0.476923i
$962$		0			0
$963$	2.36603	−	8.83013i	0.0762441	−	0.284547i
$964$		0			0
$965$	14.5814	−	14.5814i	0.469392	−	0.469392i
$966$		0			0
$967$			60.2487i			1.93747i	0.248102	+	0.968734i	$0.420193\pi$
$967$			60.2487i			1.93747i	−0.248102	+	0.968734i	$0.579807\pi$
$968$		0			0
$969$	−8.59808	+	4.96410i	−0.276210	+	0.159470i
$970$		0			0
$971$	14.0429	+	52.4090i	0.450659	+	1.68188i	0.700545	+	0.713608i	$0.252940\pi$
$971$	14.0429	+	52.4090i	0.450659	+	1.68188i	−0.249885	+	0.968275i	$0.580393\pi$
$972$		0			0
$973$	3.19615	+	44.5167i	0.102464	+	1.42714i
$974$		0			0
$975$	5.73205	−	9.92820i	0.183573	−	0.317957i
$976$		0			0
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	0.969942	−	0.243336i	$-0.0782417\pi$
$977$	8.57180	+	14.8468i	0.274236	+	0.474991i	−0.695706	+	0.718327i	$0.744908\pi$
$978$		0			0
$979$	10.9019	+	10.9019i	0.348427	+	0.348427i
$980$		0			0
$981$	−4.26795	+	4.26795i	−0.136265	+	0.136265i
$982$		0			0
$983$	17.1340	−	9.89230i	0.546489	−	0.315516i	−0.201216	−	0.979547i	$-0.564489\pi$
$983$	17.1340	−	9.89230i	0.546489	−	0.315516i	0.747705	+	0.664031i	$0.231156\pi$
$984$		0			0
$985$	−18.2942	−	10.5622i	−0.582903	−	0.336539i
$986$		0			0
$987$	5.83013	−	0.418584i	0.185575	−	0.0133237i
$988$		0			0
$989$	39.4186	−	10.5622i	1.25344	−	0.335858i
$990$		0			0
$991$	−4.20577	−	7.28461i	−0.133601	−	0.231403i	0.791461	−	0.611219i	$-0.209321\pi$
$991$	−4.20577	−	7.28461i	−0.133601	−	0.231403i	−0.925062	+	0.379816i	$0.875987\pi$
$992$		0			0
$993$	−10.5167			−0.333736
$994$		0			0
$995$	7.56218	+	7.56218i	0.239737	+	0.239737i
$996$		0			0
$997$	1.50000	+	0.401924i	0.0475055	+	0.0127291i	0.282494	−	0.959269i	$-0.408838\pi$
$997$	1.50000	+	0.401924i	0.0475055	+	0.0127291i	−0.234988	+	0.971998i	$0.575505\pi$
$998$		0			0
$999$	3.01666	+	1.74167i	0.0954429	+	0.0551040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.ba.a.289.1		4
4.3	odd	2		896.2.ba.d.289.1		4
7.4	even	3		896.2.ba.c.417.1		4
8.3	odd	2		112.2.w.a.93.1	yes	4
8.5	even	2		448.2.ba.b.401.1		4
16.3	odd	4		112.2.w.b.37.1	yes	4
16.5	even	4		896.2.ba.c.737.1		4
16.11	odd	4		896.2.ba.b.737.1		4
16.13	even	4		448.2.ba.a.177.1		4
28.11	odd	6		896.2.ba.b.417.1		4
56.3	even	6		784.2.x.h.557.1		4
56.11	odd	6		112.2.w.b.109.1	yes	4
56.19	even	6		784.2.m.d.589.2		4
56.27	even	2		784.2.x.a.765.1		4
56.51	odd	6		784.2.m.e.589.2		4
56.53	even	6		448.2.ba.a.81.1		4
112.3	even	12		784.2.x.a.165.1		4
112.11	odd	12		896.2.ba.d.865.1		4
112.19	even	12		784.2.m.d.197.2		4
112.51	odd	12		784.2.m.e.197.2		4
112.53	even	12	inner	896.2.ba.a.865.1		4
112.67	odd	12		112.2.w.a.53.1	✓	4
112.83	even	4		784.2.x.h.373.1		4
112.109	even	12		448.2.ba.b.305.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.53.1	✓	4	112.67	odd	12
112.2.w.a.93.1	yes	4	8.3	odd	2
112.2.w.b.37.1	yes	4	16.3	odd	4
112.2.w.b.109.1	yes	4	56.11	odd	6
448.2.ba.a.81.1		4	56.53	even	6
448.2.ba.a.177.1		4	16.13	even	4
448.2.ba.b.305.1		4	112.109	even	12
448.2.ba.b.401.1		4	8.5	even	2
784.2.m.d.197.2		4	112.19	even	12
784.2.m.d.589.2		4	56.19	even	6
784.2.m.e.197.2		4	112.51	odd	12
784.2.m.e.589.2		4	56.51	odd	6
784.2.x.a.165.1		4	112.3	even	12
784.2.x.a.765.1		4	56.27	even	2
784.2.x.h.373.1		4	112.83	even	4
784.2.x.h.557.1		4	56.3	even	6
896.2.ba.a.289.1		4	1.1	even	1	trivial
896.2.ba.a.865.1		4	112.53	even	12	inner
896.2.ba.b.417.1		4	28.11	odd	6
896.2.ba.b.737.1		4	16.11	odd	4
896.2.ba.c.417.1		4	7.4	even	3
896.2.ba.c.737.1		4	16.5	even	4
896.2.ba.d.289.1		4	4.3	odd	2
896.2.ba.d.865.1		4	112.11	odd	12

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.133975 + 0.500000i) q^{3} +(-0.232051 - 0.866025i) q^{5} +(1.73205 - 2.00000i) q^{7} +(2.36603 + 1.36603i) q^{9} +(2.86603 + 0.767949i) q^{11} +(-3.73205 - 3.73205i) q^{13} +0.464102 q^{15} +(-3.23205 - 5.59808i) q^{17} +(-2.86603 + 0.767949i) q^{19} +(0.767949 + 1.13397i) q^{21} +(3.86603 + 2.23205i) q^{23} +(3.63397 - 2.09808i) q^{25} +(-2.09808 + 2.09808i) q^{27} +(0.267949 + 0.267949i) q^{29} +(1.86603 + 3.23205i) q^{31} +(-0.767949 + 1.33013i) q^{33} +(-2.13397 - 1.03590i) q^{35} +(-0.303848 - 1.13397i) q^{37} +(2.36603 - 1.36603i) q^{39} -4.92820i q^{41} +(6.46410 - 6.46410i) q^{43} +(0.633975 - 2.36603i) q^{45} +(2.13397 - 3.69615i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(3.23205 - 0.866025i) q^{51} +(-3.96410 - 1.06218i) q^{53} -2.66025i q^{55} -1.53590i q^{57} +(11.3301 + 3.03590i) q^{59} +(6.96410 - 1.86603i) q^{61} +(6.83013 - 2.36603i) q^{63} +(-2.36603 + 4.09808i) q^{65} +(1.33013 - 4.96410i) q^{67} +(-1.63397 + 1.63397i) q^{69} -0.535898i q^{71} +(-6.23205 + 3.59808i) q^{73} +(0.562178 + 2.09808i) q^{75} +(6.50000 - 4.40192i) q^{77} +(-8.33013 + 14.4282i) q^{79} +(3.33013 + 5.76795i) q^{81} +(1.53590 + 1.53590i) q^{83} +(-4.09808 + 4.09808i) q^{85} +(-0.169873 + 0.0980762i) q^{87} +(4.50000 + 2.59808i) q^{89} +(-13.9282 + 1.00000i) q^{91} +(-1.86603 + 0.500000i) q^{93} +(1.33013 + 2.30385i) q^{95} -2.92820 q^{97} +(5.73205 + 5.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 6 q^{5} + 6 q^{9} + 8 q^{11} - 8 q^{13} - 12 q^{15} - 6 q^{17} - 8 q^{19} + 10 q^{21} + 12 q^{23} + 18 q^{25} + 2 q^{27} + 8 q^{29} + 4 q^{31} - 10 q^{33} - 12 q^{35} - 22 q^{37} + 6 q^{39}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 6 * q^5 + 6 * q^9 + 8 * q^11 - 8 * q^13 - 12 * q^15 - 6 * q^17 - 8 * q^19 + 10 * q^21 + 12 * q^23 + 18 * q^25 + 2 * q^27 + 8 * q^29 + 4 * q^31 - 10 * q^33 - 12 * q^35 - 22 * q^37 + 6 * q^39 + 12 * q^43 + 6 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 2 * q^53 + 28 * q^59 + 14 * q^61 + 10 * q^63 - 6 * q^65 - 12 * q^67 - 10 * q^69 - 18 * q^73 - 22 * q^75 + 26 * q^77 - 16 * q^79 - 4 * q^81 + 20 * q^83 - 6 * q^85 - 18 * q^87 + 18 * q^89 - 28 * q^91 - 4 * q^93 - 12 * q^95 + 16 * q^97 + 16 * q^99

Introduction

L-functions

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