LMFDB - Embedded newform 912.2.bo.b.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(289,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			625.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	912.625
Dual form			912.2.bo.b.769.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 + 0.642788i) q^{3} +(-0.826352 + 0.300767i) q^{5} +(-1.43969 - 2.49362i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-0.918748 + 1.59132i) q^{11} +(-2.11334 + 1.77330i) q^{13} +(-0.826352 - 0.300767i) q^{15} +(-1.23396 + 6.99811i) q^{17} +(-3.93969 + 1.86516i) q^{19} +(0.500000 - 2.83564i) q^{21} +(6.19846 + 2.25606i) q^{23} +(-3.23783 + 2.71686i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.543233 - 3.08083i) q^{29} +(3.82635 + 6.62744i) q^{31} +(-1.72668 + 0.628461i) q^{33} +(1.93969 + 1.62760i) q^{35} +2.83750 q^{37} -2.75877 q^{39} +(3.05303 + 2.56180i) q^{41} +(-10.7626 + 3.91728i) q^{43} +(-0.439693 - 0.761570i) q^{45} +(-0.383256 - 2.17355i) q^{47} +(-0.645430 + 1.11792i) q^{49} +(-5.44356 + 4.56769i) q^{51} +(-2.53936 - 0.924252i) q^{53} +(0.280592 - 1.59132i) q^{55} +(-4.21688 - 1.10359i) q^{57} +(1.46064 - 8.28368i) q^{59} +(-0.578726 - 0.210639i) q^{61} +(2.20574 - 1.85083i) q^{63} +(1.21301 - 2.10100i) q^{65} +(0.638156 + 3.61916i) q^{67} +(3.29813 + 5.71253i) q^{69} +(-7.00387 + 2.54920i) q^{71} +(-7.66637 - 6.43285i) q^{73} -4.22668 q^{75} +5.29086 q^{77} +(-1.23396 - 1.03541i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(0.492726 + 0.853427i) q^{83} +(-1.08512 - 6.15403i) q^{85} +(1.56418 - 2.70924i) q^{87} +(13.0667 - 10.9643i) q^{89} +(7.46451 + 2.71686i) q^{91} +(-1.32888 + 7.53644i) q^{93} +(2.69459 - 2.72621i) q^{95} +(-1.02481 + 5.81201i) q^{97} +(-1.72668 - 0.628461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} - 3 q^{7} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{27} + 12 q^{29} + 24 q^{31} + 3 q^{33} + 6 q^{35} + 12 q^{37} + 6 q^{39} + 6 q^{41} - 18 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 + 9 * q^23 - 3 * q^27 + 12 * q^29 + 24 * q^31 + 3 * q^33 + 6 * q^35 + 12 * q^37 + 6 * q^39 + 6 * q^41 - 18 * q^43 + 3 * q^45 + 33 * q^47 + 12 * q^49 - 3 * q^51 - 24 * q^53 + 33 * q^55 - 9 * q^57 - 21 * q^61 + 3 * q^63 + 15 * q^65 - 30 * q^67 + 6 * q^69 - 18 * q^71 - 27 * q^73 - 12 * q^75 - 12 * q^79 - 15 * q^83 + 15 * q^85 - 9 * q^87 + 45 * q^89 + 12 * q^91 + 6 * q^93 + 12 * q^95 + 21 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$		0			0
$5$	−0.826352	+	0.300767i	−0.369556	+	0.134507i	−0.520121	−	0.854093i	$-0.674113\pi$
$5$	−0.826352	+	0.300767i	−0.369556	+	0.134507i	0.150565	+	0.988600i	$0.451891\pi$
$6$		0			0
$7$	−1.43969	−	2.49362i	−0.544153	−	0.942500i	−0.998660	−	0.0517569i	$-0.983518\pi$
$7$	−1.43969	−	2.49362i	−0.544153	−	0.942500i	0.454507	−	0.890743i	$-0.349815\pi$
$8$		0			0
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$		0			0
$11$	−0.918748	+	1.59132i	−0.277013	+	0.479801i	−0.970641	−	0.240533i	$-0.922678\pi$
$11$	−0.918748	+	1.59132i	−0.277013	+	0.479801i	0.693628	+	0.720333i	$0.256011\pi$
$12$		0			0
$13$	−2.11334	+	1.77330i	−0.586135	+	0.491826i	−0.886955	−	0.461855i	$-0.847184\pi$
$13$	−2.11334	+	1.77330i	−0.586135	+	0.491826i	0.300820	+	0.953681i	$0.402740\pi$
$14$		0			0
$15$	−0.826352	−	0.300767i	−0.213363	−	0.0776578i
$16$		0			0
$17$	−1.23396	+	6.99811i	−0.299278	+	1.69729i	0.350008	+	0.936747i	$0.386179\pi$
$17$	−1.23396	+	6.99811i	−0.299278	+	1.69729i	−0.649286	+	0.760544i	$0.724932\pi$
$18$		0			0
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$20$		0			0
$21$	0.500000	−	2.83564i	0.109109	−	0.618788i
$22$		0			0
$23$	6.19846	+	2.25606i	1.29247	+	0.470420i	0.894537	−	0.446995i	$-0.147506\pi$
$23$	6.19846	+	2.25606i	1.29247	+	0.470420i	0.397932	+	0.917415i	$0.369728\pi$
$24$		0			0
$25$	−3.23783	+	2.71686i	−0.647565	+	0.543372i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−0.543233	−	3.08083i	−0.100876	−	0.572096i	−0.992788	−	0.119886i	$-0.961747\pi$
$29$	−0.543233	−	3.08083i	−0.100876	−	0.572096i	0.891912	−	0.452209i	$-0.149364\pi$
$30$		0			0
$31$	3.82635	+	6.62744i	0.687233	+	1.19032i	0.972729	+	0.231943i	$0.0745082\pi$
$31$	3.82635	+	6.62744i	0.687233	+	1.19032i	−0.285496	+	0.958380i	$0.592158\pi$
$32$		0			0
$33$	−1.72668	+	0.628461i	−0.300577	+	0.109401i
$34$		0			0
$35$	1.93969	+	1.62760i	0.327868	+	0.275114i
$36$		0			0
$37$	2.83750			0.466481			0.233241	−	0.972419i	$-0.425067\pi$
$37$	2.83750			0.466481			0.233241	+	0.972419i	$0.425067\pi$
$38$		0			0
$39$	−2.75877			−0.441757
$40$		0			0
$41$	3.05303	+	2.56180i	0.476804	+	0.400086i	0.849269	−	0.527960i	$-0.177043\pi$
$41$	3.05303	+	2.56180i	0.476804	+	0.400086i	−0.372465	+	0.928046i	$0.621487\pi$
$42$		0			0
$43$	−10.7626	+	3.91728i	−1.64129	+	0.597380i	−0.987263	−	0.159094i	$-0.949143\pi$
$43$	−10.7626	+	3.91728i	−1.64129	+	0.597380i	−0.654024	+	0.756474i	$0.726920\pi$
$44$		0			0
$45$	−0.439693	−	0.761570i	−0.0655455	−	0.113528i
$46$		0			0
$47$	−0.383256	−	2.17355i	−0.0559036	−	0.317045i	0.944014	−	0.329906i	$-0.107017\pi$
$47$	−0.383256	−	2.17355i	−0.0559036	−	0.317045i	−0.999917	+	0.0128613i	$0.995906\pi$
$48$		0			0
$49$	−0.645430	+	1.11792i	−0.0922042	+	0.159702i
$50$		0			0
$51$	−5.44356	+	4.56769i	−0.762251	+	0.639605i
$52$		0			0
$53$	−2.53936	−	0.924252i	−0.348808	−	0.126956i	0.161674	−	0.986844i	$-0.448311\pi$
$53$	−2.53936	−	0.924252i	−0.348808	−	0.126956i	−0.510482	+	0.859888i	$0.670533\pi$
$54$		0			0
$55$	0.280592	−	1.59132i	0.0378351	−	0.214573i
$56$		0			0
$57$	−4.21688	−	1.10359i	−0.558540	−	0.146174i
$58$		0			0
$59$	1.46064	−	8.28368i	0.190159	−	1.07844i	−0.728987	−	0.684527i	$-0.760009\pi$
$59$	1.46064	−	8.28368i	0.190159	−	1.07844i	0.919146	−	0.393917i	$-0.128880\pi$
$60$		0			0
$61$	−0.578726	−	0.210639i	−0.0740982	−	0.0269696i	0.304705	−	0.952447i	$-0.401442\pi$
$61$	−0.578726	−	0.210639i	−0.0740982	−	0.0269696i	−0.378803	+	0.925477i	$0.623664\pi$
$62$		0			0
$63$	2.20574	−	1.85083i	0.277897	−	0.233183i
$64$		0			0
$65$	1.21301	−	2.10100i	0.150456	−	0.260597i
$66$		0			0
$67$	0.638156	+	3.61916i	0.0779631	+	0.442151i	0.998654	+	0.0518592i	$0.0165147\pi$
$67$	0.638156	+	3.61916i	0.0779631	+	0.442151i	−0.920691	+	0.390292i	$0.872374\pi$
$68$		0			0
$69$	3.29813	+	5.71253i	0.397049	+	0.687708i
$70$		0			0
$71$	−7.00387	+	2.54920i	−0.831206	+	0.302534i	−0.722354	−	0.691523i	$-0.756940\pi$
$71$	−7.00387	+	2.54920i	−0.831206	+	0.302534i	−0.108853	+	0.994058i	$0.534718\pi$
$72$		0			0
$73$	−7.66637	−	6.43285i	−0.897281	−	0.752908i	0.0723759	−	0.997377i	$-0.476942\pi$
$73$	−7.66637	−	6.43285i	−0.897281	−	0.752908i	−0.969657	+	0.244469i	$0.921386\pi$
$74$		0			0
$75$	−4.22668			−0.488055
$76$		0			0
$77$	5.29086			0.602949
$78$		0			0
$79$	−1.23396	−	1.03541i	−0.138831	−	0.116493i	0.570728	−	0.821139i	$-0.306661\pi$
$79$	−1.23396	−	1.03541i	−0.138831	−	0.116493i	−0.709559	+	0.704646i	$0.751106\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$		0			0
$83$	0.492726	+	0.853427i	0.0540837	+	0.0936757i	0.891800	−	0.452430i	$-0.149443\pi$
$83$	0.492726	+	0.853427i	0.0540837	+	0.0936757i	−0.837716	+	0.546106i	$0.816110\pi$
$84$		0			0
$85$	−1.08512	−	6.15403i	−0.117698	−	0.667499i
$86$		0			0
$87$	1.56418	−	2.70924i	0.167697	−	0.290461i
$88$		0			0
$89$	13.0667	−	10.9643i	1.38507	−	1.16221i	0.417774	−	0.908551i	$-0.362810\pi$
$89$	13.0667	−	10.9643i	1.38507	−	1.16221i	0.967294	−	0.253659i	$-0.0816341\pi$
$90$		0			0
$91$	7.46451	+	2.71686i	0.782493	+	0.284804i
$92$		0			0
$93$	−1.32888	+	7.53644i	−0.137798	+	0.781493i
$94$		0			0
$95$	2.69459	−	2.72621i	0.276459	−	0.279703i
$96$		0			0
$97$	−1.02481	+	5.81201i	−0.104054	+	0.590121i	0.887540	+	0.460731i	$0.152413\pi$
$97$	−1.02481	+	5.81201i	−0.104054	+	0.590121i	−0.991594	+	0.129389i	$0.958698\pi$
$98$		0			0
$99$	−1.72668	−	0.628461i	−0.173538	−	0.0631627i
$100$		0			0
$101$	−3.29813	+	2.76746i	−0.328177	+	0.275373i	−0.791956	−	0.610578i	$-0.790937\pi$
$101$	−3.29813	+	2.76746i	−0.328177	+	0.275373i	0.463780	+	0.885950i	$0.346493\pi$
$102$		0			0
$103$	8.90420	−	15.4225i	0.877357	−	1.51963i	0.0231262	−	0.999733i	$-0.492638\pi$
$103$	8.90420	−	15.4225i	0.877357	−	1.51963i	0.854231	−	0.519894i	$-0.174029\pi$
$104$		0			0
$105$	0.439693	+	2.49362i	0.0429096	+	0.243352i
$106$		0			0
$107$	2.94356	+	5.09840i	0.284565	+	0.492881i	0.972504	−	0.232888i	$-0.0748175\pi$
$107$	2.94356	+	5.09840i	0.284565	+	0.492881i	−0.687939	+	0.725769i	$0.741484\pi$
$108$		0			0
$109$	−14.2023	+	5.16923i	−1.36034	+	0.495122i	−0.916158	−	0.400816i	$-0.868727\pi$
$109$	−14.2023	+	5.16923i	−1.36034	+	0.495122i	−0.444178	+	0.895938i	$0.646504\pi$
$110$		0			0
$111$	2.17365	+	1.82391i	0.206314	+	0.173118i
$112$		0			0
$113$	−6.08378			−0.572314			−0.286157	−	0.958183i	$-0.592378\pi$
$113$	−6.08378			−0.572314			−0.286157	+	0.958183i	$0.592378\pi$
$114$		0			0
$115$	−5.80066			−0.540914
$116$		0			0
$117$	−2.11334	−	1.77330i	−0.195378	−	0.163942i
$118$		0			0
$119$	19.2271	−	6.99811i	1.76255	−	0.641516i
$120$		0			0
$121$	3.81180	+	6.60224i	0.346528	+	0.600203i
$122$		0			0
$123$	0.692066	+	3.92490i	0.0624015	+	0.353897i
$124$		0			0
$125$	4.05690	−	7.02676i	0.362861	−	0.628493i
$126$		0			0
$127$	−9.13223	+	7.66285i	−0.810354	+	0.679968i	−0.950692	−	0.310136i	$-0.899625\pi$
$127$	−9.13223	+	7.66285i	−0.810354	+	0.679968i	0.140338	+	0.990104i	$0.455181\pi$
$128$		0			0
$129$	−10.7626	−	3.91728i	−0.947598	−	0.344897i
$130$		0			0
$131$	0.415345	−	2.35554i	0.0362888	−	0.205804i	−0.961272	−	0.275600i	$-0.911124\pi$
$131$	0.415345	−	2.35554i	0.0362888	−	0.205804i	0.997561	+	0.0697956i	$0.0222347\pi$
$132$		0			0
$133$	10.3229	+	7.13884i	0.895113	+	0.619016i
$134$		0			0
$135$	0.152704	−	0.866025i	0.0131426	−	0.0745356i
$136$		0			0
$137$	20.5069	+	7.46389i	1.75202	+	0.637683i	0.999775	−	0.0212013i	$-0.00674907\pi$
$137$	20.5069	+	7.46389i	1.75202	+	0.637683i	0.752244	+	0.658884i	$0.228971\pi$
$138$		0			0
$139$	−6.33409	+	5.31493i	−0.537251	+	0.450807i	−0.870596	−	0.491998i	$-0.836267\pi$
$139$	−6.33409	+	5.31493i	−0.537251	+	0.450807i	0.333346	+	0.942805i	$0.391822\pi$
$140$		0			0
$141$	1.10354	−	1.91139i	0.0929349	−	0.160968i
$142$		0			0
$143$	−0.880263	−	4.99222i	−0.0736113	−	0.417470i
$144$		0			0
$145$	1.37551	+	2.38246i	0.114230	+	0.197853i
$146$		0			0
$147$	−1.21301	+	0.441500i	−0.100047	+	0.0364143i
$148$		0			0
$149$	5.88532	+	4.93837i	0.482144	+	0.404567i	0.851201	−	0.524840i	$-0.175875\pi$
$149$	5.88532	+	4.93837i	0.482144	+	0.404567i	−0.369057	+	0.929407i	$0.620319\pi$
$150$		0			0
$151$	5.94356			0.483680			0.241840	−	0.970316i	$-0.422249\pi$
$151$	5.94356			0.483680			0.241840	+	0.970316i	$0.422249\pi$
$152$		0			0
$153$	−7.10607			−0.574491
$154$		0			0
$155$	−5.15523	−	4.32575i	−0.414078	−	0.347453i
$156$		0			0
$157$	9.76991	−	3.55596i	0.779724	−	0.283796i	0.0786665	−	0.996901i	$-0.474934\pi$
$157$	9.76991	−	3.55596i	0.779724	−	0.283796i	0.701058	+	0.713105i	$0.252712\pi$
$158$		0			0
$159$	−1.35117	−	2.34029i	−0.107154	−	0.185597i
$160$		0			0
$161$	−3.29813	−	18.7046i	−0.259929	−	1.47413i
$162$		0			0
$163$	5.03596	−	8.72254i	0.394447	−	0.683202i	−0.598584	−	0.801060i	$-0.704270\pi$
$163$	5.03596	−	8.72254i	0.394447	−	0.683202i	0.993030	+	0.117858i	$0.0376029\pi$
$164$		0			0
$165$	1.23783	−	1.03866i	0.0963646	−	0.0808595i
$166$		0			0
$167$	7.63816	+	2.78006i	0.591058	+	0.215128i	0.620195	−	0.784448i	$-0.287054\pi$
$167$	7.63816	+	2.78006i	0.591058	+	0.215128i	−0.0291366	+	0.999575i	$0.509276\pi$
$168$		0			0
$169$	−0.935822	+	5.30731i	−0.0719863	+	0.408255i
$170$		0			0
$171$	−2.52094	−	3.55596i	−0.192781	−	0.271931i
$172$		0			0
$173$	−0.922618	+	5.23243i	−0.0701454	+	0.397814i	0.929439	+	0.368977i	$0.120292\pi$
$173$	−0.922618	+	5.23243i	−0.0701454	+	0.397814i	−0.999584	+	0.0288377i	$0.990819\pi$
$174$		0			0
$175$	11.4363	+	4.16247i	0.864502	+	0.314653i
$176$		0			0
$177$	6.44356	−	5.40679i	0.484328	−	0.406399i
$178$		0			0
$179$	−8.51367	+	14.7461i	−0.636342	+	1.10218i	0.349888	+	0.936792i	$0.386220\pi$
$179$	−8.51367	+	14.7461i	−0.636342	+	1.10218i	−0.986229	+	0.165384i	$0.947114\pi$
$180$		0			0
$181$	−2.96404	−	16.8099i	−0.220315	−	1.24947i	−0.871441	−	0.490501i	$-0.836814\pi$
$181$	−2.96404	−	16.8099i	−0.220315	−	1.24947i	0.651125	−	0.758970i	$-0.274297\pi$
$182$		0			0
$183$	−0.307934	−	0.533356i	−0.0227631	−	0.0394268i
$184$		0			0
$185$	−2.34477	+	0.853427i	−0.172391	+	0.0627452i
$186$		0			0
$187$	−10.0025	−	8.39312i	−0.731457	−	0.613765i
$188$		0			0
$189$	2.87939			0.209444
$190$		0			0
$191$	−3.62361			−0.262195			−0.131098	−	0.991369i	$-0.541850\pi$
$191$	−3.62361			−0.262195			−0.131098	+	0.991369i	$0.541850\pi$
$192$		0			0
$193$	−3.92468	−	3.29320i	−0.282504	−	0.237049i	0.490513	−	0.871434i	$-0.336809\pi$
$193$	−3.92468	−	3.29320i	−0.282504	−	0.237049i	−0.773018	+	0.634384i	$0.781254\pi$
$194$		0			0
$195$	2.27972	−	0.829748i	0.163254	−	0.0594195i
$196$		0			0
$197$	4.56418	+	7.90539i	0.325184	+	0.563236i	0.981550	−	0.191208i	$-0.0612404\pi$
$197$	4.56418	+	7.90539i	0.325184	+	0.563236i	−0.656365	+	0.754443i	$0.727907\pi$
$198$		0			0
$199$	−3.83497	−	21.7492i	−0.271854	−	1.54176i	−0.748781	−	0.662817i	$-0.769361\pi$
$199$	−3.83497	−	21.7492i	−0.271854	−	1.54176i	0.476928	−	0.878943i	$-0.341750\pi$
$200$		0			0
$201$	−1.83750	+	3.18264i	−0.129607	+	0.224486i
$202$		0			0
$203$	−6.90033	+	5.79006i	−0.484308	+	0.406383i
$204$		0			0
$205$	−3.29339	−	1.19869i	−0.230020	−	0.0837204i
$206$		0			0
$207$	−1.14543	+	6.49605i	−0.0796129	+	0.451507i
$208$		0			0
$209$	0.651522	−	7.98292i	0.0450667	−	0.552190i
$210$		0			0
$211$	−1.16756	+	6.62154i	−0.0803779	+	0.455846i	0.917881	+	0.396856i	$0.129899\pi$
$211$	−1.16756	+	6.62154i	−0.0803779	+	0.455846i	−0.998259	+	0.0589893i	$0.981212\pi$
$212$		0			0
$213$	−7.00387	−	2.54920i	−0.479897	−	0.174668i
$214$		0			0
$215$	7.71554	−	6.47410i	0.526195	−	0.441530i
$216$		0			0
$217$	11.0175	−	19.0829i	0.747919	−	1.29543i
$218$		0			0
$219$	−1.73783	−	9.85570i	−0.117431	−	0.665987i
$220$		0			0
$221$	−9.80200	−	16.9776i	−0.659354	−	1.14203i
$222$		0			0
$223$	−4.30066	+	1.56531i	−0.287993	+	0.104821i	−0.481977	−	0.876184i	$-0.660081\pi$
$223$	−4.30066	+	1.56531i	−0.287993	+	0.104821i	0.193984	+	0.981005i	$0.437859\pi$
$224$		0			0
$225$	−3.23783	−	2.71686i	−0.215855	−	0.181124i
$226$		0			0
$227$	15.8425			1.05151			0.525753	−	0.850637i	$-0.323783\pi$
$227$	15.8425			1.05151			0.525753	+	0.850637i	$0.323783\pi$
$228$		0			0
$229$	3.86753			0.255573			0.127787	−	0.991802i	$-0.459213\pi$
$229$	3.86753			0.255573			0.127787	+	0.991802i	$0.459213\pi$
$230$		0			0
$231$	4.05303	+	3.40090i	0.266670	+	0.223763i
$232$		0			0
$233$	22.2939	−	8.11430i	1.46052	−	0.531585i	0.515011	−	0.857184i	$-0.327788\pi$
$233$	22.2939	−	8.11430i	1.46052	−	0.531585i	0.945508	+	0.325598i	$0.105566\pi$
$234$		0			0
$235$	0.970437	+	1.68085i	0.0633044	+	0.109646i
$236$		0			0
$237$	−0.279715	−	1.58634i	−0.0181694	−	0.103044i
$238$		0			0
$239$	2.27332	−	3.93750i	0.147049	−	0.254696i	−0.783087	−	0.621913i	$-0.786356\pi$
$239$	2.27332	−	3.93750i	0.147049	−	0.254696i	0.930135	+	0.367217i	$0.119689\pi$
$240$		0			0
$241$	−0.837496	+	0.702743i	−0.0539479	+	0.0452676i	−0.669363	−	0.742936i	$-0.733433\pi$
$241$	−0.837496	+	0.702743i	−0.0539479	+	0.0452676i	0.615415	+	0.788203i	$0.288988\pi$
$242$		0			0
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$		0			0
$245$	0.197119	−	1.11792i	0.0125935	−	0.0714211i
$246$		0			0
$247$	5.01842	−	10.9280i	0.319314	−	0.695331i
$248$		0			0
$249$	−0.171122	+	0.970481i	−0.0108444	+	0.0615017i
$250$		0			0
$251$	12.9427	+	4.71075i	0.816935	+	0.297340i	0.716485	−	0.697602i	$-0.245750\pi$
$251$	12.9427	+	4.71075i	0.816935	+	0.297340i	0.100450	+	0.994942i	$0.467972\pi$
$252$		0			0
$253$	−9.28493	+	7.79098i	−0.583739	+	0.489815i
$254$		0			0
$255$	3.12449	−	5.41177i	0.195663	−	0.338898i
$256$		0			0
$257$	2.23442	+	12.6720i	0.139379	+	0.790460i	0.971709	+	0.236180i	$0.0758954\pi$
$257$	2.23442	+	12.6720i	0.139379	+	0.790460i	−0.832330	+	0.554280i	$0.812994\pi$
$258$		0			0
$259$	−4.08512	−	7.07564i	−0.253837	−	0.439659i
$260$		0			0
$261$	2.93969	−	1.06996i	0.181962	−	0.0662289i
$262$		0			0
$263$	10.6040	+	8.89782i	0.653871	+	0.548663i	0.908243	−	0.418444i	$-0.137424\pi$
$263$	10.6040	+	8.89782i	0.653871	+	0.548663i	−0.254372	+	0.967107i	$0.581869\pi$
$264$		0			0
$265$	2.37639			0.145981
$266$		0			0
$267$	17.0574			1.04389
$268$		0			0
$269$	−10.6382	−	8.92647i	−0.648620	−	0.544257i	0.258032	−	0.966136i	$-0.416926\pi$
$269$	−10.6382	−	8.92647i	−0.648620	−	0.544257i	−0.906652	+	0.421880i	$0.861370\pi$
$270$		0			0
$271$	5.53849	−	2.01584i	0.336439	−	0.122454i	−0.168276	−	0.985740i	$-0.553820\pi$
$271$	5.53849	−	2.01584i	0.336439	−	0.122454i	0.504715	+	0.863286i	$0.331598\pi$
$272$		0			0
$273$	3.97178	+	6.87933i	0.240383	+	0.416356i
$274$		0			0
$275$	−1.34864	−	7.64852i	−0.0813261	−	0.461223i
$276$		0			0
$277$	2.26945	−	3.93080i	0.136358	−	0.236179i	−0.789757	−	0.613419i	$-0.789794\pi$
$277$	2.26945	−	3.93080i	0.136358	−	0.236179i	0.926115	+	0.377240i	$0.123127\pi$
$278$		0			0
$279$	−5.86231	+	4.91906i	−0.350967	+	0.294497i
$280$		0			0
$281$	16.0052	+	5.82542i	0.954791	+	0.347516i	0.771990	−	0.635634i	$-0.219261\pi$
$281$	16.0052	+	5.82542i	0.954791	+	0.347516i	0.182801	+	0.983150i	$0.441484\pi$
$282$		0			0
$283$	−3.95290	+	22.4180i	−0.234975	+	1.33261i	0.607690	+	0.794174i	$0.292096\pi$
$283$	−3.95290	+	22.4180i	−0.234975	+	1.33261i	−0.842666	+	0.538437i	$0.819015\pi$
$284$		0			0
$285$	3.81655	−	0.356347i	0.226073	−	0.0211082i
$286$		0			0
$287$	1.99273	−	11.3013i	0.117627	−	0.667095i
$288$		0			0
$289$	−31.4761	−	11.4564i	−1.85154	−	0.673904i
$290$		0			0
$291$	−4.52094	+	3.79352i	−0.265022	+	0.222380i
$292$		0			0
$293$	2.77972	−	4.81461i	0.162393	−	0.281272i	−0.773334	−	0.633999i	$-0.781412\pi$
$293$	2.77972	−	4.81461i	0.162393	−	0.281272i	0.935726	+	0.352727i	$0.114746\pi$
$294$		0			0
$295$	1.28446	+	7.28455i	0.0747843	+	0.424123i
$296$		0			0
$297$	−0.918748	−	1.59132i	−0.0533112	−	0.0923377i
$298$		0			0
$299$	−17.1001	+	6.22394i	−0.988926	+	0.359940i
$300$		0			0
$301$	25.2631	+	21.1983i	1.45614	+	1.22185i
$302$		0			0
$303$	−4.30541			−0.247339
$304$		0			0
$305$	0.541584			0.0310110
$306$		0			0
$307$	9.06283	+	7.60462i	0.517243	+	0.434019i	0.863669	−	0.504059i	$-0.168160\pi$
$307$	9.06283	+	7.60462i	0.517243	+	0.434019i	−0.346426	+	0.938077i	$0.612605\pi$
$308$		0			0
$309$	16.7344	−	6.09083i	0.951988	−	0.346495i
$310$		0			0
$311$	−9.02141	−	15.6255i	−0.511557	−	0.886043i	−0.999910	−	0.0133970i	$-0.995735\pi$
$311$	−9.02141	−	15.6255i	−0.511557	−	0.886043i	0.488353	−	0.872646i	$-0.337598\pi$
$312$		0			0
$313$	1.19712	+	6.78920i	0.0676652	+	0.383748i	0.999768	+	0.0215537i	$0.00686128\pi$
$313$	1.19712	+	6.78920i	0.0676652	+	0.383748i	−0.932103	+	0.362195i	$0.882028\pi$
$314$		0			0
$315$	−1.26604	+	2.19285i	−0.0713335	+	0.123553i
$316$		0			0
$317$	−25.5292	+	21.4215i	−1.43386	+	1.20315i	−0.490473	+	0.871456i	$0.663176\pi$
$317$	−25.5292	+	21.4215i	−1.43386	+	1.20315i	−0.943387	+	0.331695i	$0.892379\pi$
$318$		0			0
$319$	5.40167	+	1.96605i	0.302436	+	0.110078i
$320$		0			0
$321$	−1.02229	+	5.79769i	−0.0570586	+	0.323595i
$322$		0			0
$323$	−8.19119	−	29.8719i	−0.455770	−	1.66212i
$324$		0			0
$325$	2.02481	−	11.4833i	0.112317	−	0.636979i
$326$		0			0
$327$	−14.2023	−	5.16923i	−0.785391	−	0.285859i
$328$		0			0
$329$	−4.86824	+	4.08494i	−0.268395	+	0.225210i
$330$		0			0
$331$	2.47178	−	4.28125i	0.135861	−	0.235319i	−0.790065	−	0.613023i	$-0.789953\pi$
$331$	2.47178	−	4.28125i	0.135861	−	0.235319i	0.925926	+	0.377705i	$0.123286\pi$
$332$		0			0
$333$	0.492726	+	2.79439i	0.0270012	+	0.153132i
$334$		0			0
$335$	−1.61587	−	2.79876i	−0.0882842	−	0.152913i
$336$		0			0
$337$	−8.85117	+	3.22156i	−0.482154	+	0.175490i	−0.571650	−	0.820498i	$-0.693697\pi$
$337$	−8.85117	+	3.22156i	−0.482154	+	0.175490i	0.0894963	+	0.995987i	$0.471474\pi$
$338$		0			0
$339$	−4.66044	−	3.91058i	−0.253121	−	0.212393i
$340$		0			0
$341$	−14.0618			−0.761490
$342$		0			0
$343$	−16.4388			−0.887613
$344$		0			0
$345$	−4.44356	−	3.72859i	−0.239233	−	0.200741i
$346$		0			0
$347$	−11.1493	+	4.05801i	−0.598526	+	0.217846i	−0.623475	−	0.781843i	$-0.714280\pi$
$347$	−11.1493	+	4.05801i	−0.598526	+	0.217846i	0.0249494	+	0.999689i	$0.492058\pi$
$348$		0			0
$349$	−10.9709	−	19.0022i	−0.587259	−	1.01716i	−0.994590	−	0.103882i	$-0.966874\pi$
$349$	−10.9709	−	19.0022i	−0.587259	−	1.01716i	0.407331	−	0.913281i	$-0.366460\pi$
$350$		0			0
$351$	−0.479055	−	2.71686i	−0.0255701	−	0.145015i
$352$		0			0
$353$	−1.94697	+	3.37225i	−0.103627	+	0.179486i	−0.913176	−	0.407565i	$-0.866378\pi$
$353$	−1.94697	+	3.37225i	−0.103627	+	0.179486i	0.809550	+	0.587051i	$0.199711\pi$
$354$		0			0
$355$	5.02094	−	4.21307i	0.266484	−	0.223607i
$356$		0			0
$357$	19.2271	+	6.99811i	1.01761	+	0.370379i
$358$		0			0
$359$	2.08466	−	11.8227i	0.110024	−	0.623977i	−0.879070	−	0.476692i	$-0.841836\pi$
$359$	2.08466	−	11.8227i	0.110024	−	0.623977i	0.989094	−	0.147284i	$-0.0470533\pi$
$360$		0			0
$361$	12.0424	−	14.6963i	0.633808	−	0.773490i
$362$		0			0
$363$	−1.32383	+	7.50779i	−0.0694828	+	0.394057i
$364$		0			0
$365$	8.26991	+	3.01000i	0.432867	+	0.157551i
$366$		0			0
$367$	20.5326	−	17.2289i	1.07179	−	0.899339i	0.0765772	−	0.997064i	$-0.475601\pi$
$367$	20.5326	−	17.2289i	1.07179	−	0.899339i	0.995214	+	0.0977245i	$0.0311564\pi$
$368$		0			0
$369$	−1.99273	+	3.45150i	−0.103737	+	0.179678i
$370$		0			0
$371$	1.35117	+	7.66285i	0.0701491	+	0.397835i
$372$		0			0
$373$	14.2909	+	24.7525i	0.739953	+	1.28164i	0.952516	+	0.304488i	$0.0984855\pi$
$373$	14.2909	+	24.7525i	0.739953	+	1.28164i	−0.212563	+	0.977147i	$0.568181\pi$
$374$		0			0
$375$	7.62449	−	2.77509i	0.393727	−	0.143305i
$376$		0			0
$377$	6.61128	+	5.54752i	0.340498	+	0.285712i
$378$		0			0
$379$	3.09833			0.159150			0.0795752	−	0.996829i	$-0.474644\pi$
$379$	3.09833			0.159150			0.0795752	+	0.996829i	$0.474644\pi$
$380$		0			0
$381$	−11.9213			−0.610745
$382$		0			0
$383$	21.9270	+	18.3989i	1.12042	+	0.940140i	0.998625	−	0.0524160i	$-0.0166922\pi$
$383$	21.9270	+	18.3989i	1.12042	+	0.940140i	0.121790	+	0.992556i	$0.461137\pi$
$384$		0			0
$385$	−4.37211	+	1.59132i	−0.222823	+	0.0811011i
$386$		0			0
$387$	−5.72668	−	9.91890i	−0.291104	−	0.504206i
$388$		0			0
$389$	−3.89218	−	22.0736i	−0.197341	−	1.11918i	−0.909045	−	0.416698i	$-0.863187\pi$
$389$	−3.89218	−	22.0736i	−0.197341	−	1.11918i	0.711704	−	0.702480i	$-0.247924\pi$
$390$		0			0
$391$	−23.4368	+	40.5937i	−1.18525	+	2.05291i
$392$		0			0
$393$	1.83228	−	1.53747i	0.0924264	−	0.0775549i
$394$		0			0
$395$	1.33110	+	0.484481i	0.0669749	+	0.0243769i
$396$		0			0
$397$	−2.38444	+	13.5228i	−0.119671	+	0.678691i	0.864659	+	0.502359i	$0.167534\pi$
$397$	−2.38444	+	13.5228i	−0.119671	+	0.678691i	−0.984331	+	0.176332i	$0.943577\pi$
$398$		0			0
$399$	3.31908	+	12.1041i	0.166162	+	0.605965i
$400$		0			0
$401$	−5.08559	+	28.8418i	−0.253962	+	1.44029i	0.544760	+	0.838592i	$0.316621\pi$
$401$	−5.08559	+	28.8418i	−0.253962	+	1.44029i	−0.798723	+	0.601699i	$0.794491\pi$
$402$		0			0
$403$	−19.8388	−	7.22075i	−0.988243	−	0.359691i
$404$		0			0
$405$	0.673648	−	0.565258i	0.0334738	−	0.0280879i
$406$		0			0
$407$	−2.60694	+	4.51536i	−0.129221	+	0.223818i
$408$		0			0
$409$	−0.405544	−	2.29996i	−0.0200529	−	0.113726i	0.973138	−	0.230221i	$-0.0739450\pi$
$409$	−0.405544	−	2.29996i	−0.0200529	−	0.113726i	−0.993191	+	0.116496i	$0.962834\pi$
$410$		0			0
$411$	10.9115	+	18.8992i	0.538223	+	0.932230i
$412$		0			0
$413$	−22.7592	+	8.28368i	−1.11991	+	0.407613i
$414$		0			0
$415$	−0.663848	−	0.557035i	−0.0325870	−	0.0273438i
$416$		0			0
$417$	−8.26857			−0.404914
$418$		0			0
$419$	−2.27362			−0.111074			−0.0555369	−	0.998457i	$-0.517687\pi$
$419$	−2.27362			−0.111074			−0.0555369	+	0.998457i	$0.517687\pi$
$420$		0			0
$421$	14.5688	+	12.2246i	0.710038	+	0.595793i	0.924610	−	0.380916i	$-0.124391\pi$
$421$	14.5688	+	12.2246i	0.710038	+	0.595793i	−0.214572	+	0.976708i	$0.568836\pi$
$422$		0			0
$423$	2.07398	−	0.754866i	0.100840	−	0.0367029i
$424$		0			0
$425$	−15.0175	−	26.0111i	−0.728458	−	1.26173i
$426$		0			0
$427$	0.307934	+	1.74638i	0.0149019	+	0.0845131i
$428$		0			0
$429$	2.53462	−	4.39008i	0.122372	−	0.211955i
$430$		0			0
$431$	9.80066	−	8.22373i	0.472081	−	0.396123i	−0.375472	−	0.926834i	$-0.622519\pi$
$431$	9.80066	−	8.22373i	0.472081	−	0.396123i	0.847553	+	0.530711i	$0.178075\pi$
$432$		0			0
$433$	−13.6959	−	4.98491i	−0.658185	−	0.239560i	−0.00873229	−	0.999962i	$-0.502780\pi$
$433$	−13.6959	−	4.98491i	−0.658185	−	0.239560i	−0.649452	+	0.760402i	$0.725002\pi$
$434$		0			0
$435$	−0.477711	+	2.70924i	−0.0229045	+	0.129898i
$436$		0			0
$437$	−28.6279	+	2.67296i	−1.36946	+	0.127865i
$438$		0			0
$439$	−4.27513	+	24.2455i	−0.204041	+	1.15717i	0.694901	+	0.719105i	$0.255448\pi$
$439$	−4.27513	+	24.2455i	−0.204041	+	1.15717i	−0.898942	+	0.438068i	$0.855663\pi$
$440$		0			0
$441$	−1.21301	−	0.441500i	−0.0577624	−	0.0210238i
$442$		0			0
$443$	−29.5198	+	24.7701i	−1.40253	+	1.17686i	−0.442565	+	0.896736i	$0.645932\pi$
$443$	−29.5198	+	24.7701i	−1.40253	+	1.17686i	−0.959963	+	0.280125i	$0.909624\pi$
$444$		0			0
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$		0			0
$447$	1.33409	+	7.56602i	0.0631004	+	0.357860i
$448$		0			0
$449$	17.5903	+	30.4674i	0.830139	+	1.43784i	0.897927	+	0.440144i	$0.145073\pi$
$449$	17.5903	+	30.4674i	0.830139	+	1.43784i	−0.0677880	+	0.997700i	$0.521594\pi$
$450$		0			0
$451$	−6.88161	+	2.50470i	−0.324042	+	0.117942i
$452$		0			0
$453$	4.55303	+	3.82045i	0.213920	+	0.179500i
$454$		0			0
$455$	−6.98545			−0.327483
$456$		0			0
$457$	−13.7983			−0.645457			−0.322729	−	0.946492i	$-0.604600\pi$
$457$	−13.7983			−0.645457			−0.322729	+	0.946492i	$0.604600\pi$
$458$		0			0
$459$	−5.44356	−	4.56769i	−0.254084	−	0.213202i
$460$		0			0
$461$	−22.8084	+	8.30158i	−1.06229	+	0.386643i	−0.813289	−	0.581859i	$-0.802325\pi$
$461$	−22.8084	+	8.30158i	−1.06229	+	0.386643i	−0.249004	+	0.968503i	$0.580103\pi$
$462$		0			0
$463$	−5.64543	−	9.77817i	−0.262365	−	0.454430i	0.704505	−	0.709699i	$-0.251169\pi$
$463$	−5.64543	−	9.77817i	−0.262365	−	0.454430i	−0.966870	+	0.255269i	$0.917836\pi$
$464$		0			0
$465$	−1.16860	−	6.62744i	−0.0541923	−	0.307340i
$466$		0			0
$467$	−2.39393	+	4.14641i	−0.110778	+	0.191873i	−0.916084	−	0.400986i	$-0.868668\pi$
$467$	−2.39393	+	4.14641i	−0.110778	+	0.191873i	0.805306	+	0.592859i	$0.202001\pi$
$468$		0			0
$469$	8.10607	−	6.80180i	0.374303	−	0.314078i
$470$		0			0
$471$	9.76991	+	3.55596i	0.450174	+	0.163850i
$472$		0			0
$473$	3.65451	−	20.7258i	0.168035	−	0.952972i
$474$		0			0
$475$	7.68866	−	16.7427i	0.352780	−	0.768206i
$476$		0			0
$477$	0.469255	−	2.66128i	0.0214857	−	0.121852i
$478$		0			0
$479$	−15.8897	−	5.78336i	−0.726017	−	0.264248i	−0.0475389	−	0.998869i	$-0.515138\pi$
$479$	−15.8897	−	5.78336i	−0.726017	−	0.264248i	−0.678478	+	0.734621i	$0.737360\pi$
$480$		0			0
$481$	−5.99660	+	5.03174i	−0.273421	+	0.229428i
$482$		0			0
$483$	9.49660	−	16.4486i	0.432110	−	0.748437i
$484$		0			0
$485$	−0.901207	−	5.11100i	−0.0409217	−	0.232079i
$486$		0			0
$487$	3.88191	+	6.72367i	0.175906	+	0.304678i	0.940475	−	0.339864i	$-0.110381\pi$
$487$	3.88191	+	6.72367i	0.175906	+	0.304678i	−0.764568	+	0.644543i	$0.777048\pi$
$488$		0			0
$489$	9.46451	−	3.44480i	0.428000	−	0.155779i
$490$		0			0
$491$	11.1270	+	9.33667i	0.502155	+	0.421358i	0.858359	−	0.513050i	$-0.171485\pi$
$491$	11.1270	+	9.33667i	0.502155	+	0.421358i	−0.356204	+	0.934408i	$0.615929\pi$
$492$		0			0
$493$	22.2303			1.00120
$494$		0			0
$495$	1.61587			0.0726278
$496$		0			0
$497$	16.4402	+	13.7949i	0.737442	+	0.618787i
$498$		0			0
$499$	26.5646	−	9.66874i	1.18920	−	0.432832i	0.329755	−	0.944066i	$-0.393034\pi$
$499$	26.5646	−	9.66874i	1.18920	−	0.432832i	0.859441	+	0.511234i	$0.170812\pi$
$500$		0			0
$501$	4.06418	+	7.03936i	0.181574	+	0.314496i
$502$		0			0
$503$	6.60947	+	37.4842i	0.294702	+	1.67134i	0.668412	+	0.743791i	$0.266974\pi$
$503$	6.60947	+	37.4842i	0.294702	+	1.67134i	−0.373710	+	0.927545i	$0.621915\pi$
$504$		0			0
$505$	1.89306	−	3.27887i	0.0842399	−	0.145908i
$506$		0			0
$507$	−4.12836	+	3.46410i	−0.183347	+	0.153846i
$508$		0			0
$509$	12.9226	+	4.70345i	0.572785	+	0.208477i	0.612141	−	0.790749i	$-0.290308\pi$
$509$	12.9226	+	4.70345i	0.572785	+	0.208477i	−0.0393561	+	0.999225i	$0.512531\pi$
$510$		0			0
$511$	−5.00387	+	28.3784i	−0.221358	+	1.25538i
$512$		0			0
$513$	0.354570	−	4.34445i	0.0156547	−	0.191812i
$514$		0			0
$515$	−2.71941	+	15.4225i	−0.119831	+	0.679598i
$516$		0			0
$517$	3.81093	+	1.38706i	0.167604	+	0.0610030i
$518$		0			0
$519$	−4.07011	+	3.41523i	−0.178658	+	0.149912i
$520$		0			0
$521$	−7.69712	+	13.3318i	−0.337217	+	0.584077i	−0.983908	−	0.178675i	$-0.942819\pi$
$521$	−7.69712	+	13.3318i	−0.337217	+	0.584077i	0.646691	+	0.762752i	$0.276152\pi$
$522$		0			0
$523$	−0.0452926	−	0.256867i	−0.00198051	−	0.0112320i	0.983801	−	0.179261i	$-0.0573708\pi$
$523$	−0.0452926	−	0.256867i	−0.00198051	−	0.0112320i	−0.985782	+	0.168029i	$0.946260\pi$
$524$		0			0
$525$	6.08512	+	10.5397i	0.265577	+	0.459992i
$526$		0			0
$527$	−51.1011	+	18.5993i	−2.22600	+	0.810197i
$528$		0			0
$529$	15.7121	+	13.1840i	0.683136	+	0.573219i
$530$		0			0
$531$	8.41147			0.365027
$532$		0			0
$533$	−10.9949			−0.476244
$534$		0			0
$535$	−3.96585	−	3.32774i	−0.171459	−	0.143871i
$536$		0			0
$537$	−16.0005	+	5.82369i	−0.690471	+	0.251311i
$538$		0			0
$539$	−1.18597	−	2.05417i	−0.0510835	−	0.0884793i
$540$		0			0
$541$	0.202333	+	1.14749i	0.00869900	+	0.0493345i	0.988848	−	0.148926i	$-0.0475818\pi$
$541$	0.202333	+	1.14749i	0.00869900	+	0.0493345i	−0.980149	+	0.198261i	$0.936471\pi$
$542$		0			0
$543$	8.53462	−	14.7824i	0.366255	−	0.634373i
$544$		0			0
$545$	10.1814	−	8.54320i	0.436123	−	0.365950i
$546$		0			0
$547$	5.18954	+	1.88884i	0.221889	+	0.0807609i	0.450572	−	0.892740i	$-0.351220\pi$
$547$	5.18954	+	1.88884i	0.221889	+	0.0807609i	−0.228684	+	0.973501i	$0.573442\pi$
$548$		0			0
$549$	0.106944	−	0.606511i	0.00456427	−	0.0258852i
$550$		0			0
$551$	7.88641	+	11.1243i	0.335972	+	0.473911i
$552$		0			0
$553$	−0.805407	+	4.56769i	−0.0342494	+	0.194238i
$554$		0			0
$555$	−2.34477	−	0.853427i	−0.0995299	−	0.0362259i
$556$		0			0
$557$	−22.7178	+	19.0625i	−0.962585	+	0.807704i	−0.981372	−	0.192119i	$-0.938464\pi$
$557$	−22.7178	+	19.0625i	−0.962585	+	0.807704i	0.0187869	+	0.999824i	$0.494020\pi$
$558$		0			0
$559$	15.7986	−	27.3640i	0.668210	−	1.15737i
$560$		0			0
$561$	−2.26739	−	12.8590i	−0.0957292	−	0.542907i
$562$		0			0
$563$	6.15389	+	10.6588i	0.259355	+	0.449217i	0.966069	−	0.258283i	$-0.0831566\pi$
$563$	6.15389	+	10.6588i	0.259355	+	0.449217i	−0.706714	+	0.707499i	$0.749823\pi$
$564$		0			0
$565$	5.02734	−	1.82980i	0.211502	−	0.0769804i
$566$		0			0
$567$	2.20574	+	1.85083i	0.0926322	+	0.0777277i
$568$		0			0
$569$	24.3054			1.01894			0.509468	−	0.860490i	$-0.329842\pi$
$569$	24.3054			1.01894			0.509468	+	0.860490i	$0.329842\pi$
$570$		0			0
$571$	7.99731			0.334677			0.167339	−	0.985899i	$-0.446483\pi$
$571$	7.99731			0.334677			0.167339	+	0.985899i	$0.446483\pi$
$572$		0			0
$573$	−2.77584	−	2.32921i	−0.115963	−	0.0973042i
$574$		0			0
$575$	−26.1989	+	9.53563i	−1.09257	+	0.397663i
$576$		0			0
$577$	5.84848	+	10.1299i	0.243475	+	0.421712i	0.961702	−	0.274098i	$-0.0883792\pi$
$577$	5.84848	+	10.1299i	0.243475	+	0.421712i	−0.718227	+	0.695809i	$0.755046\pi$
$578$		0			0
$579$	−0.889652	−	5.04547i	−0.0369727	−	0.209683i
$580$		0			0
$581$	1.41875	−	2.45734i	0.0588596	−	0.101948i
$582$		0			0
$583$	3.80381	−	3.19178i	0.157538	−	0.132190i
$584$		0			0
$585$	2.27972	+	0.829748i	0.0942546	+	0.0343059i
$586$		0			0
$587$	−1.12748	+	6.39425i	−0.0465360	+	0.263919i	−0.999195	−	0.0401228i	$-0.987225\pi$
$587$	−1.12748	+	6.39425i	−0.0465360	+	0.263919i	0.952659	+	0.304042i	$0.0983362\pi$
$588$		0			0
$589$	−27.4359	−	18.9733i	−1.13048	−	0.781781i
$590$		0			0
$591$	−1.58512	+	8.98968i	−0.0652032	+	0.369786i
$592$		0			0
$593$	−21.5021	−	7.82613i	−0.882986	−	0.321381i	−0.139572	−	0.990212i	$-0.544573\pi$
$593$	−21.5021	−	7.82613i	−0.882986	−	0.321381i	−0.743414	+	0.668831i	$0.766795\pi$
$594$		0			0
$595$	−13.7836	+	11.5658i	−0.565072	+	0.474152i
$596$		0			0
$597$	11.0424	−	19.1259i	0.451934	−	0.782772i
$598$		0			0
$599$	−4.79339	−	27.1846i	−0.195852	−	1.11073i	−0.911200	−	0.411965i	$-0.864843\pi$
$599$	−4.79339	−	27.1846i	−0.195852	−	1.11073i	0.715347	−	0.698769i	$-0.246269\pi$
$600$		0			0
$601$	7.06552	+	12.2378i	0.288209	+	0.499192i	0.973382	−	0.229188i	$-0.0736070\pi$
$601$	7.06552	+	12.2378i	0.288209	+	0.499192i	−0.685174	+	0.728380i	$0.740274\pi$
$602$		0			0
$603$	−3.45336	+	1.25692i	−0.140632	+	0.0511858i
$604$		0			0
$605$	−5.13563	−	4.30930i	−0.208793	−	0.175198i
$606$		0			0
$607$	−9.50980			−0.385991			−0.192995	−	0.981200i	$-0.561820\pi$
$607$	−9.50980			−0.385991			−0.192995	+	0.981200i	$0.561820\pi$
$608$		0			0
$609$	−9.00774			−0.365012
$610$		0			0
$611$	4.66431	+	3.91382i	0.188698	+	0.158336i
$612$		0			0
$613$	39.5766	−	14.4047i	1.59848	−	0.581800i	0.619366	−	0.785102i	$-0.287390\pi$
$613$	39.5766	−	14.4047i	1.59848	−	0.581800i	0.979116	+	0.203302i	$0.0651674\pi$
$614$		0			0
$615$	−1.75237	−	3.03520i	−0.0706625	−	0.122391i
$616$		0			0
$617$	−5.02915	−	28.5217i	−0.202466	−	1.14824i	−0.901378	−	0.433034i	$-0.857443\pi$
$617$	−5.02915	−	28.5217i	−0.202466	−	1.14824i	0.698912	−	0.715208i	$-0.253668\pi$
$618$		0			0
$619$	15.4598	−	26.7771i	0.621380	−	1.07626i	−0.367849	−	0.929886i	$-0.619906\pi$
$619$	15.4598	−	26.7771i	0.621380	−	1.07626i	0.989229	−	0.146376i	$-0.0467611\pi$
$620$		0			0
$621$	−5.05303	+	4.24000i	−0.202771	+	0.170145i
$622$		0			0
$623$	−46.1528	−	16.7982i	−1.84907	−	0.673007i
$624$		0			0
$625$	2.43077	−	13.7856i	0.0972308	−	0.551423i
$626$		0			0
$627$	5.63041	−	5.69648i	0.224857	−	0.227495i
$628$		0			0
$629$	−3.50134	+	19.8571i	−0.139608	+	0.791755i
$630$		0			0
$631$	−8.05778	−	2.93279i	−0.320775	−	0.116753i	0.176614	−	0.984280i	$-0.443486\pi$
$631$	−8.05778	−	2.93279i	−0.320775	−	0.116753i	−0.497389	+	0.867528i	$0.665708\pi$
$632$		0			0
$633$	−5.15064	+	4.32190i	−0.204720	+	0.171780i
$634$		0			0
$635$	5.24170	−	9.07888i	0.208010	−	0.360285i
$636$		0			0
$637$	−0.618393	−	3.50708i	−0.0245016	−	0.138956i
$638$		0			0
$639$	−3.72668	−	6.45480i	−0.147425	−	0.255348i
$640$		0			0
$641$	−24.9234	+	9.07137i	−0.984415	+	0.358298i	−0.783555	−	0.621322i	$-0.786596\pi$
$641$	−24.9234	+	9.07137i	−0.984415	+	0.358298i	−0.200860	+	0.979620i	$0.564374\pi$
$642$		0			0
$643$	16.0974	+	13.5074i	0.634821	+	0.532678i	0.902423	−	0.430851i	$-0.141787\pi$
$643$	16.0974	+	13.5074i	0.634821	+	0.532678i	−0.267602	+	0.963530i	$0.586231\pi$
$644$		0			0
$645$	10.0719			0.396581
$646$		0			0
$647$	−38.0273			−1.49501			−0.747505	−	0.664257i	$-0.768748\pi$
$647$	−38.0273			−1.49501			−0.747505	+	0.664257i	$0.768748\pi$
$648$		0			0
$649$	11.8400	+	9.93496i	0.464762	+	0.389981i
$650$		0			0
$651$	20.7062	−	7.53644i	0.811540	−	0.295376i
$652$		0			0
$653$	−16.5959	−	28.7449i	−0.649446	−	1.12487i	−0.983255	−	0.182233i	$-0.941668\pi$
$653$	−16.5959	−	28.7449i	−0.649446	−	1.12487i	0.333809	−	0.942641i	$-0.391666\pi$
$654$		0			0
$655$	0.365248	+	2.07142i	0.0142714	+	0.0809372i
$656$		0			0
$657$	5.00387	−	8.66696i	0.195220	−	0.338130i
$658$		0			0
$659$	30.1976	−	25.3388i	1.17633	−	0.987059i	0.176335	−	0.984330i	$-0.443576\pi$
$659$	30.1976	−	25.3388i	1.17633	−	0.987059i	0.999996	−	0.00272857i	$-0.000868533\pi$
$660$		0			0
$661$	1.81180	+	0.659443i	0.0704710	+	0.0256493i	0.377015	−	0.926207i	$-0.376950\pi$
$661$	1.81180	+	0.659443i	0.0704710	+	0.0256493i	−0.306544	+	0.951856i	$0.599173\pi$
$662$		0			0
$663$	3.40420	−	19.3062i	0.132208	−	0.749790i
$664$		0			0
$665$	−10.6775	−	2.79439i	−0.414056	−	0.108362i
$666$		0			0
$667$	3.58331	−	20.3220i	0.138746	−	0.786870i
$668$		0			0
$669$	−4.30066	−	1.56531i	−0.166273	−	0.0605185i
$670$		0			0
$671$	0.866897	−	0.727413i	0.0334662	−	0.0280815i
$672$		0			0
$673$	−6.69325	+	11.5930i	−0.258006	+	0.446879i	−0.965708	−	0.259632i	$-0.916399\pi$
$673$	−6.69325	+	11.5930i	−0.258006	+	0.446879i	0.707702	+	0.706511i	$0.249732\pi$
$674$		0			0
$675$	−0.733956	−	4.16247i	−0.0282500	−	0.160213i
$676$		0			0
$677$	−5.52094	−	9.56256i	−0.212187	−	0.367519i	0.740212	−	0.672374i	$-0.234725\pi$
$677$	−5.52094	−	9.56256i	−0.212187	−	0.367519i	−0.952399	+	0.304855i	$0.901392\pi$
$678$		0			0
$679$	15.9684	−	5.81201i	0.612810	−	0.223045i
$680$		0			0
$681$	12.1361	+	10.1834i	0.465056	+	0.390229i
$682$		0			0
$683$	9.16014			0.350503			0.175252	−	0.984524i	$-0.443926\pi$
$683$	9.16014			0.350503			0.175252	+	0.984524i	$0.443926\pi$
$684$		0			0
$685$	−19.1908			−0.733242
$686$		0			0
$687$	2.96270	+	2.48600i	0.113034	+	0.0948467i
$688$		0			0
$689$	7.00552	−	2.54980i	0.266889	−	0.0971397i
$690$		0			0
$691$	−4.89693	−	8.48172i	−0.186288	−	0.322660i	0.757722	−	0.652578i	$-0.226312\pi$
$691$	−4.89693	−	8.48172i	−0.186288	−	0.322660i	−0.944010	+	0.329918i	$0.892979\pi$
$692$		0			0
$693$	0.918748	+	5.21048i	0.0349004	+	0.197930i
$694$		0			0
$695$	3.63563	−	6.29710i	0.137907	−	0.238862i
$696$		0			0
$697$	−21.6951	+	18.2043i	−0.821759	+	0.689538i
$698$		0			0
$699$	22.2939	+	8.11430i	0.843231	+	0.306911i
$700$		0			0
$701$	−3.16163	+	17.9305i	−0.119413	+	0.677225i	0.865057	+	0.501673i	$0.167282\pi$
$701$	−3.16163	+	17.9305i	−0.119413	+	0.677225i	−0.984470	+	0.175552i	$0.943829\pi$
$702$		0			0
$703$	−11.1789	+	5.29238i	−0.421619	+	0.199606i
$704$		0			0
$705$	−0.337029	+	1.91139i	−0.0126933	+	0.0719871i
$706$		0			0
$707$	11.6493	+	4.24000i	0.438117	+	0.159462i
$708$		0			0
$709$	32.3109	−	27.1121i	1.21346	−	1.01822i	0.214322	−	0.976763i	$-0.431246\pi$
$709$	32.3109	−	27.1121i	1.21346	−	1.01822i	0.999140	−	0.0414527i	$-0.0131986\pi$
$710$		0			0
$711$	0.805407	−	1.39501i	0.0302051	−	0.0523168i
$712$		0			0
$713$	8.76563	+	49.7124i	0.328276	+	1.86174i
$714$		0			0
$715$	2.22890	+	3.86057i	0.0833563	+	0.144377i
$716$		0			0
$717$	4.27244	−	1.55504i	0.159557	−	0.0580741i
$718$		0			0
$719$	3.46451	+	2.90707i	0.129204	+	0.108415i	0.705100	−	0.709108i	$-0.250902\pi$
$719$	3.46451	+	2.90707i	0.129204	+	0.108415i	−0.575896	+	0.817523i	$0.695347\pi$
$720$		0			0
$721$	−51.2772			−1.90966
$722$		0			0
$723$	−1.09327			−0.0406593
$724$		0			0
$725$	10.1291	+	8.49930i	0.376184	+	0.315656i
$726$		0			0
$727$	25.0834	−	9.12960i	0.930291	−	0.338598i	0.167966	−	0.985793i	$-0.446280\pi$
$727$	25.0834	−	9.12960i	0.930291	−	0.338598i	0.762325	+	0.647195i	$0.224058\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−14.1329	−	80.1519i	−0.522726	−	2.96452i
$732$		0			0
$733$	2.52481	−	4.37311i	0.0932562	−	0.161524i	−0.815623	−	0.578583i	$-0.803606\pi$
$733$	2.52481	−	4.37311i	0.0932562	−	0.161524i	0.908879	+	0.417059i	$0.136939\pi$
$734$		0			0
$735$	0.869585	−	0.729669i	0.0320751	−	0.0269142i
$736$		0			0
$737$	−6.34554	−	2.30959i	−0.233741	−	0.0850748i
$738$		0			0
$739$	1.46286	−	8.29628i	0.0538121	−	0.305184i	−0.946008	−	0.324143i	$-0.894924\pi$
$739$	1.46286	−	8.29628i	0.0538121	−	0.305184i	0.999820	+	0.0189592i	$0.00603525\pi$
$740$		0			0
$741$	10.8687	−	5.14555i	0.399272	−	0.189026i
$742$		0			0
$743$	−9.20068	+	52.1797i	−0.337540	+	1.91429i	0.0630120	+	0.998013i	$0.479929\pi$
$743$	−9.20068	+	52.1797i	−0.337540	+	1.91429i	−0.400552	+	0.916274i	$0.631182\pi$
$744$		0			0
$745$	−6.34864	−	2.31072i	−0.232596	−	0.0846581i
$746$		0			0
$747$	−0.754900	+	0.633436i	−0.0276203	+	0.0231762i
$748$		0			0
$749$	8.47565	−	14.6803i	0.309694	−	0.536405i
$750$		0			0
$751$	2.06939	+	11.7361i	0.0755132	+	0.428257i	0.999003	+	0.0446346i	$0.0142123\pi$
$751$	2.06939	+	11.7361i	0.0755132	+	0.428257i	−0.923490	+	0.383622i	$0.874677\pi$
$752$		0			0
$753$	6.88666	+	11.9280i	0.250964	+	0.434682i
$754$		0			0
$755$	−4.91147	+	1.78763i	−0.178747	+	0.0650585i
$756$		0			0
$757$	−23.6138	−	19.8143i	−0.858258	−	0.720164i	0.103334	−	0.994647i	$-0.467049\pi$
$757$	−23.6138	−	19.8143i	−0.858258	−	0.720164i	−0.961592	+	0.274482i	$0.911493\pi$
$758$		0			0
$759$	−12.1206			−0.439950
$760$		0			0
$761$	43.9053			1.59157			0.795783	−	0.605582i	$-0.207060\pi$
$761$	43.9053			1.59157			0.795783	+	0.605582i	$0.207060\pi$
$762$		0			0
$763$	33.3371	+	27.9731i	1.20688	+	1.01270i
$764$		0			0
$765$	5.87211	−	2.13727i	0.212307	−	0.0772733i
$766$		0			0
$767$	11.6027	+	20.0964i	0.418948	+	0.725639i
$768$		0			0
$769$	−1.53895	−	8.72783i	−0.0554960	−	0.314734i	0.944405	−	0.328784i	$-0.106639\pi$
$769$	−1.53895	−	8.72783i	−0.0554960	−	0.314734i	−0.999901	+	0.0140500i	$0.995528\pi$
$770$		0			0
$771$	−6.43376	+	11.1436i	−0.231706	+	0.401327i
$772$		0			0
$773$	34.1987	−	28.6961i	1.23004	−	1.03213i	0.231805	−	0.972762i	$-0.425537\pi$
$773$	34.1987	−	28.6961i	1.23004	−	1.03213i	0.998236	−	0.0593647i	$-0.0189075\pi$
$774$		0			0
$775$	−30.3949	−	11.0628i	−1.09182	−	0.397388i
$776$		0			0
$777$	1.41875	−	8.04612i	0.0508973	−	0.288653i
$778$		0			0
$779$	−16.8062	−	4.39831i	−0.602144	−	0.157586i
$780$		0			0
$781$	2.37820	−	13.4875i	0.0850988	−	0.482619i
$782$		0			0
$783$	2.93969	+	1.06996i	0.105056	+	0.0382373i
$784$		0			0
$785$	−7.00387	+	5.87695i	−0.249979	+	0.209757i
$786$		0			0
$787$	−9.25268	+	16.0261i	−0.329822	+	0.571269i	−0.982476	−	0.186387i	$-0.940322\pi$
$787$	−9.25268	+	16.0261i	−0.329822	+	0.571269i	0.652654	+	0.757656i	$0.273656\pi$
$788$		0			0
$789$	2.40373	+	13.6322i	0.0855752	+	0.485321i
$790$		0			0
$791$	8.75877	+	15.1706i	0.311426	+	0.539406i
$792$		0			0
$793$	1.59657	−	0.581104i	0.0566959	−	0.0206356i
$794$		0			0
$795$	1.82042	+	1.52752i	0.0645637	+	0.0541754i
$796$		0			0
$797$	−15.3209			−0.542694			−0.271347	−	0.962482i	$-0.587469\pi$
$797$	−15.3209			−0.542694			−0.271347	+	0.962482i	$0.587469\pi$
$798$		0			0
$799$	15.6837			0.554848
$800$		0			0
$801$	13.0667	+	10.9643i	0.461689	+	0.387403i
$802$		0			0
$803$	17.2802	−	6.28947i	0.609804	−	0.221951i
$804$		0			0
$805$	8.35117	+	14.4646i	0.294340	+	0.509812i
$806$		0			0
$807$	−2.41147	−	13.6761i	−0.0848879	−	0.481423i
$808$		0			0
$809$	7.04798	−	12.2075i	0.247794	−	0.429191i	−0.715120	−	0.699002i	$-0.753628\pi$
$809$	7.04798	−	12.2075i	0.247794	−	0.429191i	0.962913	+	0.269811i	$0.0869611\pi$
$810$		0			0
$811$	33.4996	−	28.1095i	1.17633	−	0.987058i	0.176333	−	0.984330i	$-0.443576\pi$
$811$	33.4996	−	28.1095i	1.17633	−	0.987058i	0.999996	−	0.00272731i	$-0.000868131\pi$
$812$		0			0
$813$	5.53849	+	2.01584i	0.194243	+	0.0706987i
$814$		0			0
$815$	−1.53802	+	8.72254i	−0.0538744	+	0.305537i
$816$		0			0
$817$	35.0951	−	35.5069i	1.22782	−	1.24223i
$818$		0			0
$819$	−1.37939	+	7.82288i	−0.0481996	+	0.273354i
$820$		0			0
$821$	12.1189	+	4.41090i	0.422951	+	0.153942i	0.544722	−	0.838617i	$-0.316635\pi$
$821$	12.1189	+	4.41090i	0.422951	+	0.153942i	−0.121771	+	0.992558i	$0.538857\pi$
$822$		0			0
$823$	−23.7802	+	19.9539i	−0.828925	+	0.695551i	−0.955044	−	0.296464i	$-0.904192\pi$
$823$	−23.7802	+	19.9539i	−0.828925	+	0.695551i	0.126119	+	0.992015i	$0.459748\pi$
$824$		0			0
$825$	3.88326	−	6.72600i	0.135198	−	0.234169i
$826$		0			0
$827$	−4.61990	−	26.2008i	−0.160650	−	0.911089i	−0.953437	−	0.301591i	$-0.902482\pi$
$827$	−4.61990	−	26.2008i	−0.160650	−	0.911089i	0.792788	−	0.609498i	$-0.208629\pi$
$828$		0			0
$829$	−24.1832	−	41.8865i	−0.839917	−	1.45478i	−0.889963	−	0.456032i	$-0.849270\pi$
$829$	−24.1832	−	41.8865i	−0.839917	−	1.45478i	0.0500459	−	0.998747i	$-0.484063\pi$
$830$		0			0
$831$	4.26517	−	1.55239i	0.147957	−	0.0538519i
$832$		0			0
$833$	−7.02687	−	5.89625i	−0.243467	−	0.204293i
$834$		0			0
$835$	−7.14796			−0.247365
$836$		0			0
$837$	−7.65270			−0.264516
$838$		0			0
$839$	13.4003	+	11.2442i	0.462631	+	0.388193i	0.844098	−	0.536189i	$-0.180137\pi$
$839$	13.4003	+	11.2442i	0.462631	+	0.388193i	−0.381467	+	0.924382i	$0.624581\pi$
$840$		0			0
$841$	18.0547	−	6.57137i	0.622575	−	0.226599i
$842$		0			0
$843$	8.51620	+	14.7505i	0.293313	+	0.508034i
$844$		0			0
$845$	−0.822948	−	4.66717i	−0.0283103	−	0.160556i
$846$		0			0
$847$	10.9757	−	19.0104i	0.377128	−	0.653205i
$848$		0			0
$849$	−17.4381	+	14.6323i	−0.598474	+	0.502179i
$850$		0			0
$851$	17.5881	+	6.40155i	0.602913	+	0.219442i
$852$		0			0
$853$	−9.83884	+	55.7988i	−0.336875	+	1.91052i	0.0709964	+	0.997477i	$0.477382\pi$
$853$	−9.83884	+	55.7988i	−0.336875	+	1.91052i	−0.407872	+	0.913039i	$0.633729\pi$
$854$		0			0
$855$	3.15270	+	2.18025i	0.107820	+	0.0745631i
$856$		0			0
$857$	5.05927	−	28.6925i	0.172821	−	0.980118i	−0.767807	−	0.640681i	$-0.778652\pi$
$857$	5.05927	−	28.6925i	0.172821	−	0.980118i	0.940629	−	0.339437i	$-0.110237\pi$
$858$		0			0
$859$	−16.8332	−	6.12679i	−0.574342	−	0.209043i	0.0384868	−	0.999259i	$-0.487746\pi$
$859$	−16.8332	−	6.12679i	−0.574342	−	0.209043i	−0.612829	+	0.790216i	$0.709968\pi$
$860$		0			0
$861$	8.79086	−	7.37641i	0.299592	−	0.251387i
$862$		0			0
$863$	−11.6373	+	20.1564i	−0.396138	+	0.686130i	−0.993246	−	0.116030i	$-0.962983\pi$
$863$	−11.6373	+	20.1564i	−0.396138	+	0.686130i	0.597108	+	0.802161i	$0.296316\pi$
$864$		0			0
$865$	−0.811337	−	4.60132i	−0.0275863	−	0.156450i
$866$		0			0
$867$	−16.7481	−	29.0085i	−0.568795	−	0.985182i
$868$		0			0
$869$	2.78136	−	1.01233i	0.0943513	−	0.0343411i
$870$		0			0
$871$	−7.76651	−	6.51688i	−0.263158	−	0.220816i
$872$		0			0
$873$	−5.90167			−0.199741
$874$		0			0
$875$	−23.3628			−0.789806
$876$		0			0
$877$	21.1713	+	17.7649i	0.714905	+	0.599877i	0.925971	−	0.377595i	$-0.123249\pi$
$877$	21.1713	+	17.7649i	0.714905	+	0.599877i	−0.211065	+	0.977472i	$0.567693\pi$
$878$		0			0
$879$	5.22416	−	1.90144i	0.176206	−	0.0641339i
$880$		0			0
$881$	−7.70187	−	13.3400i	−0.259482	−	0.449437i	0.706621	−	0.707592i	$-0.250219\pi$
$881$	−7.70187	−	13.3400i	−0.259482	−	0.449437i	−0.966103	+	0.258155i	$0.916885\pi$
$882$		0			0
$883$	−3.94727	−	22.3861i	−0.132836	−	0.753352i	−0.976342	−	0.216232i	$-0.930623\pi$
$883$	−3.94727	−	22.3861i	−0.132836	−	0.753352i	0.843506	−	0.537120i	$-0.180488\pi$
$884$		0			0
$885$	−3.69846	+	6.40593i	−0.124322	+	0.215333i
$886$		0			0
$887$	9.23577	−	7.74973i	0.310107	−	0.260210i	−0.474429	−	0.880294i	$-0.657346\pi$
$887$	9.23577	−	7.74973i	0.310107	−	0.260210i	0.784536	+	0.620083i	$0.212901\pi$
$888$		0			0
$889$	32.2558	+	11.7402i	1.08183	+	0.393752i
$890$		0			0
$891$	0.319078	−	1.80958i	0.0106895	−	0.0606232i
$892$		0			0
$893$	5.56393	+	7.84829i	0.186190	+	0.262633i
$894$		0			0
$895$	2.60014	−	14.7461i	0.0869130	−	0.492908i
$896$		0			0
$897$	−17.1001	−	6.22394i	−0.570957	−	0.207811i
$898$		0			0
$899$	18.3394	−	15.3886i	0.611653	−	0.513238i
$900$		0			0
$901$	9.60148	−	16.6303i	0.319872	−	0.554034i
$902$		0			0
$903$	5.72668	+	32.4776i	0.190572	+	1.08079i
$904$		0			0
$905$	7.50521	+	12.9994i	0.249482	+	0.432115i
$906$		0			0
$907$	−33.4320	+	12.1683i	−1.11009	+	0.404040i	−0.831027	−	0.556232i	$-0.812247\pi$
$907$	−33.4320	+	12.1683i	−1.11009	+	0.404040i	−0.279065	+	0.960272i	$0.590024\pi$
$908$		0			0
$909$	−3.29813	−	2.76746i	−0.109392	−	0.0917909i
$910$		0			0
$911$	−7.00505			−0.232088			−0.116044	−	0.993244i	$-0.537021\pi$
$911$	−7.00505			−0.232088			−0.116044	+	0.993244i	$0.537021\pi$
$912$		0			0
$913$	−1.81076			−0.0599276
$914$		0			0
$915$	0.414878	+	0.348124i	0.0137154	+	0.0115086i
$916$		0			0
$917$	−6.47178	+	2.35554i	−0.213717	+	0.0777866i
$918$		0			0
$919$	−4.18227	−	7.24390i	−0.137960	−	0.238954i	0.788764	−	0.614696i	$-0.210721\pi$
$919$	−4.18227	−	7.24390i	−0.137960	−	0.238954i	−0.926724	+	0.375742i	$0.877388\pi$
$920$		0			0
$921$	2.05438	+	11.6510i	0.0676940	+	0.383912i
$922$		0			0
$923$	10.2811	−	17.8073i	0.338405	−	0.586135i
$924$		0			0
$925$	−9.18732	+	7.70908i	−0.302077	+	0.253473i
$926$		0			0
$927$	16.7344	+	6.09083i	0.549631	+	0.200049i
$928$		0			0
$929$	8.83322	−	50.0957i	0.289808	−	1.64359i	−0.397777	−	0.917482i	$-0.630218\pi$
$929$	8.83322	−	50.0957i	0.289808	−	1.64359i	0.687586	−	0.726103i	$-0.258671\pi$
$930$		0			0
$931$	0.457700	−	5.60808i	0.0150005	−	0.183797i
$932$		0			0
$933$	3.13310	−	17.7687i	0.102573	−	0.581722i
$934$		0			0
$935$	10.7900	+	3.92723i	0.352870	+	0.128434i
$936$		0			0
$937$	18.0646	−	15.1580i	0.590146	−	0.495191i	−0.298115	−	0.954530i	$-0.596358\pi$
$937$	18.0646	−	15.1580i	0.590146	−	0.495191i	0.888261	+	0.459338i	$0.151913\pi$
$938$		0			0
$939$	−3.44697	+	5.97032i	−0.112488	+	0.194834i
$940$		0			0
$941$	−7.76036	−	44.0112i	−0.252981	−	1.43472i	−0.801203	−	0.598392i	$-0.795807\pi$
$941$	−7.76036	−	44.0112i	−0.252981	−	1.43472i	0.548223	−	0.836332i	$-0.315305\pi$
$942$		0			0
$943$	13.1446	+	22.7670i	0.428046	+	0.741397i
$944$		0			0
$945$	−2.37939	+	0.866025i	−0.0774014	+	0.0281718i
$946$		0			0
$947$	32.3107	+	27.1119i	1.04996	+	0.881018i	0.993089	−	0.117364i	$-0.0374445\pi$
$947$	32.3107	+	27.1119i	1.04996	+	0.881018i	0.0568670	+	0.998382i	$0.481889\pi$
$948$		0			0
$949$	27.6091			0.896228
$950$		0			0
$951$	−33.3259			−1.08067
$952$		0			0
$953$	39.6430	+	33.2644i	1.28416	+	1.07754i	0.992656	+	0.120970i	$0.0386005\pi$
$953$	39.6430	+	33.2644i	1.28416	+	1.07754i	0.291505	+	0.956569i	$0.405844\pi$
$954$		0			0
$955$	2.99437	−	1.08986i	0.0968957	−	0.0352671i
$956$		0			0
$957$	2.87417	+	4.97821i	0.0929087	+	0.160923i
$958$		0			0
$959$	−10.9115	−	61.8820i	−0.352350	−	1.99828i
$960$		0			0
$961$	−13.7819	+	23.8710i	−0.444579	+	0.770033i
$962$		0			0
$963$	−4.50980	+	3.78417i	−0.145326	+	0.121943i
$964$		0			0
$965$	4.23365	+	1.54092i	0.136286	+	0.0496041i
$966$		0			0
$967$	−3.10039	+	17.5832i	−0.0997017	+	0.565436i	0.893503	+	0.449057i	$0.148240\pi$
$967$	−3.10039	+	17.5832i	−0.0997017	+	0.565436i	−0.993205	+	0.116379i	$0.962871\pi$
$968$		0			0
$969$	12.9265	−	28.1484i	0.415259	−	0.904257i
$970$		0			0
$971$	7.21419	−	40.9137i	0.231514	−	1.31298i	−0.618317	−	0.785929i	$-0.712185\pi$
$971$	7.21419	−	40.9137i	0.231514	−	1.31298i	0.849831	−	0.527055i	$-0.176704\pi$
$972$		0			0
$973$	22.3726	+	8.14295i	0.717232	+	0.261051i
$974$		0			0
$975$	8.93242	−	7.49519i	0.286066	−	0.240038i
$976$		0			0
$977$	−6.17634	+	10.6977i	−0.197599	+	0.342251i	−0.947749	−	0.319016i	$-0.896648\pi$
$977$	−6.17634	+	10.6977i	−0.197599	+	0.342251i	0.750151	+	0.661267i	$0.229981\pi$
$978$		0			0
$979$	5.44263	+	30.8667i	0.173947	+	0.986504i
$980$		0			0
$981$	−7.55690	−	13.0889i	−0.241273	−	0.417898i
$982$		0			0
$983$	15.2875	−	5.56418i	0.487594	−	0.177470i	−0.0865117	−	0.996251i	$-0.527572\pi$
$983$	15.2875	−	5.56418i	0.487594	−	0.177470i	0.574106	+	0.818781i	$0.305350\pi$
$984$		0			0
$985$	−6.14930	−	5.15988i	−0.195933	−	0.164407i
$986$		0			0
$987$	−6.35504			−0.202283
$988$		0			0
$989$	−75.5494			−2.40233
$990$		0			0
$991$	−8.50253	−	7.13447i	−0.270092	−	0.226634i	0.497675	−	0.867364i	$-0.334187\pi$
$991$	−8.50253	−	7.13447i	−0.270092	−	0.226634i	−0.767766	+	0.640730i	$0.778632\pi$
$992$		0			0
$993$	4.64543	−	1.69080i	0.147418	−	0.0536559i
$994$		0			0
$995$	9.71048	+	16.8191i	0.307843	+	0.533200i
$996$		0			0
$997$	−2.71688	−	15.4082i	−0.0860445	−	0.487983i	−0.997126	−	0.0757570i	$-0.975863\pi$
$997$	−2.71688	−	15.4082i	−0.0860445	−	0.487983i	0.911082	−	0.412226i	$-0.135248\pi$
$998$		0			0
$999$	−1.41875	+	2.45734i	−0.0448872	+	0.0777469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.b.625.1		6
4.3	odd	2		57.2.i.a.55.1	yes	6
12.11	even	2		171.2.u.a.55.1		6
19.9	even	9	inner	912.2.bo.b.769.1		6
76.3	even	18		1083.2.a.n.1.1		3
76.35	odd	18		1083.2.a.m.1.3		3
76.47	odd	18		57.2.i.a.28.1	✓	6
228.35	even	18		3249.2.a.w.1.1		3
228.47	even	18		171.2.u.a.28.1		6
228.155	odd	18		3249.2.a.x.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.28.1	✓	6	76.47	odd	18
57.2.i.a.55.1	yes	6	4.3	odd	2
171.2.u.a.28.1		6	228.47	even	18
171.2.u.a.55.1		6	12.11	even	2
912.2.bo.b.625.1		6	1.1	even	1	trivial
912.2.bo.b.769.1		6	19.9	even	9	inner
1083.2.a.m.1.3		3	76.35	odd	18
1083.2.a.n.1.1		3	76.3	even	18
3249.2.a.w.1.1		3	228.35	even	18
3249.2.a.x.1.3		3	228.155	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{3} +(-0.826352 + 0.300767i) q^{5} +(-1.43969 - 2.49362i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-0.918748 + 1.59132i) q^{11} +(-2.11334 + 1.77330i) q^{13} +(-0.826352 - 0.300767i) q^{15} +(-1.23396 + 6.99811i) q^{17} +(-3.93969 + 1.86516i) q^{19} +(0.500000 - 2.83564i) q^{21} +(6.19846 + 2.25606i) q^{23} +(-3.23783 + 2.71686i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.543233 - 3.08083i) q^{29} +(3.82635 + 6.62744i) q^{31} +(-1.72668 + 0.628461i) q^{33} +(1.93969 + 1.62760i) q^{35} +2.83750 q^{37} -2.75877 q^{39} +(3.05303 + 2.56180i) q^{41} +(-10.7626 + 3.91728i) q^{43} +(-0.439693 - 0.761570i) q^{45} +(-0.383256 - 2.17355i) q^{47} +(-0.645430 + 1.11792i) q^{49} +(-5.44356 + 4.56769i) q^{51} +(-2.53936 - 0.924252i) q^{53} +(0.280592 - 1.59132i) q^{55} +(-4.21688 - 1.10359i) q^{57} +(1.46064 - 8.28368i) q^{59} +(-0.578726 - 0.210639i) q^{61} +(2.20574 - 1.85083i) q^{63} +(1.21301 - 2.10100i) q^{65} +(0.638156 + 3.61916i) q^{67} +(3.29813 + 5.71253i) q^{69} +(-7.00387 + 2.54920i) q^{71} +(-7.66637 - 6.43285i) q^{73} -4.22668 q^{75} +5.29086 q^{77} +(-1.23396 - 1.03541i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(0.492726 + 0.853427i) q^{83} +(-1.08512 - 6.15403i) q^{85} +(1.56418 - 2.70924i) q^{87} +(13.0667 - 10.9643i) q^{89} +(7.46451 + 2.71686i) q^{91} +(-1.32888 + 7.53644i) q^{93} +(2.69459 - 2.72621i) q^{95} +(-1.02481 + 5.81201i) q^{97} +(-1.72668 - 0.628461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 3 q^{7} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{27} + 12 q^{29} + 24 q^{31} + 3 q^{33} + 6 q^{35} + 12 q^{37} + 6 q^{39} + 6 q^{41} - 18 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 + 9 * q^23 - 3 * q^27 + 12 * q^29 + 24 * q^31 + 3 * q^33 + 6 * q^35 + 12 * q^37 + 6 * q^39 + 6 * q^41 - 18 * q^43 + 3 * q^45 + 33 * q^47 + 12 * q^49 - 3 * q^51 - 24 * q^53 + 33 * q^55 - 9 * q^57 - 21 * q^61 + 3 * q^63 + 15 * q^65 - 30 * q^67 + 6 * q^69 - 18 * q^71 - 27 * q^73 - 12 * q^75 - 12 * q^79 - 15 * q^83 + 15 * q^85 - 9 * q^87 + 45 * q^89 + 12 * q^91 + 6 * q^93 + 12 * q^95 + 21 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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