LMFDB - Embedded newform 912.2.ci.c.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.101559956668416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{6} + 64 $ x^12 - 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.1
Root			$-1.39273 - 0.245576i$ of defining polynomial
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.c.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{3} +(0.0469641 - 0.0394076i) q^{5} +(1.48976 + 0.860113i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{3} +(0.0469641 - 0.0394076i) q^{5} +(1.48976 + 0.860113i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.740119 - 0.427308i) q^{11} +(0.588264 + 0.103727i) q^{13} +(-0.0469641 - 0.0394076i) q^{15} +(6.35893 + 2.31446i) q^{17} +(-3.13472 - 3.02878i) q^{19} +(0.588352 - 1.61648i) q^{21} +(3.05978 - 3.64650i) q^{23} +(-0.867588 + 4.92034i) q^{25} +(0.500000 + 0.866025i) q^{27} +(2.64493 + 7.26688i) q^{29} +(4.95699 - 8.58577i) q^{31} +(-0.549336 - 0.654673i) q^{33} +(0.103860 - 0.0183134i) q^{35} -4.26546i q^{37} -0.597339i q^{39} +(2.43866 - 0.430002i) q^{41} +(-0.605916 - 0.722102i) q^{43} +(-0.0306537 + 0.0530937i) q^{45} +(1.40086 + 3.84883i) q^{47} +(-2.02041 - 3.49946i) q^{49} +(1.17508 - 6.66423i) q^{51} +(4.83391 - 5.76083i) q^{53} +(0.0179199 - 0.0492344i) q^{55} +(-2.43843 + 3.61304i) q^{57} +(-0.268742 - 0.0978140i) q^{59} +(-3.13938 - 2.63425i) q^{61} +(-1.69409 - 0.298714i) q^{63} +(0.0317149 - 0.0183106i) q^{65} +(10.1697 - 3.70148i) q^{67} +(-4.12242 - 2.38008i) q^{69} +(1.45471 - 1.22064i) q^{71} +(1.65676 + 9.39595i) q^{73} +4.99624 q^{75} +1.47013 q^{77} +(-0.354603 - 2.01105i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-10.0086 - 5.77844i) q^{83} +(0.389849 - 0.141894i) q^{85} +(6.69719 - 3.86663i) q^{87} +(10.3830 + 1.83080i) q^{89} +(0.787154 + 0.660501i) q^{91} +(-9.31610 - 3.39078i) q^{93} +(-0.266577 - 0.0187124i) q^{95} +(1.48052 - 4.06769i) q^{97} +(-0.549336 + 0.654673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) $ 12 * q + 6 * q^5 - 18 * q^7	$ 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$	$-1$

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
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$		0			0
$5$	0.0469641	−	0.0394076i	0.0210030	−	0.0176236i	−0.632226	−	0.774784i	$-0.717858\pi$
$5$	0.0469641	−	0.0394076i	0.0210030	−	0.0176236i	0.653229	+	0.757161i	$0.273414\pi$
$6$		0			0
$7$	1.48976	+	0.860113i	0.563076	+	0.325092i	0.754379	−	0.656439i	$-0.227938\pi$
$7$	1.48976	+	0.860113i	0.563076	+	0.325092i	−0.191303	+	0.981531i	$0.561271\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	0.740119	−	0.427308i	0.223154	−	0.128838i	−0.384256	−	0.923227i	$-0.625542\pi$
$11$	0.740119	−	0.427308i	0.223154	−	0.128838i	0.607410	+	0.794389i	$0.292209\pi$
$12$		0			0
$13$	0.588264	+	0.103727i	0.163155	+	0.0287686i	0.254629	−	0.967039i	$-0.418047\pi$
$13$	0.588264	+	0.103727i	0.163155	+	0.0287686i	−0.0914739	+	0.995807i	$0.529158\pi$
$14$		0			0
$15$	−0.0469641	−	0.0394076i	−0.0121261	−	0.0101750i
$16$		0			0
$17$	6.35893	+	2.31446i	1.54227	+	0.561340i	0.966588	−	0.256335i	$-0.0825152\pi$
$17$	6.35893	+	2.31446i	1.54227	+	0.561340i	0.575680	+	0.817675i	$0.304737\pi$
$18$		0			0
$19$	−3.13472	−	3.02878i	−0.719154	−	0.694850i
$19$	−3.13472	−	3.02878i	−0.719154	−	0.694850i
$20$		0			0
$21$	0.588352	−	1.61648i	0.128389	−	0.352746i
$22$		0			0
$23$	3.05978	−	3.64650i	0.638007	−	0.760347i	−0.346047	−	0.938217i	$-0.612476\pi$
$23$	3.05978	−	3.64650i	0.638007	−	0.760347i	0.984054	+	0.177870i	$0.0569206\pi$
$24$		0			0
$25$	−0.867588	+	4.92034i	−0.173518	+	0.984067i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	2.64493	+	7.26688i	0.491151	+	1.34943i	0.899628	+	0.436657i	$0.143838\pi$
$29$	2.64493	+	7.26688i	0.491151	+	1.34943i	−0.408477	+	0.912769i	$0.633940\pi$
$30$		0			0
$31$	4.95699	−	8.58577i	0.890302	−	1.54205i	0.0507895	−	0.998709i	$-0.483826\pi$
$31$	4.95699	−	8.58577i	0.890302	−	1.54205i	0.839513	−	0.543340i	$-0.182840\pi$
$32$		0			0
$33$	−0.549336	−	0.654673i	−0.0956271	−	0.113964i
$34$		0			0
$35$	0.103860	−	0.0183134i	0.0175556	−	0.00309552i
$36$		0			0
$37$		−	4.26546i		−	0.701237i	−0.936518	−	0.350619i	$-0.885971\pi$
$37$		−	4.26546i		−	0.701237i	0.936518	−	0.350619i	$-0.114029\pi$
$38$		0			0
$39$		−	0.597339i		−	0.0956507i
$40$		0			0
$41$	2.43866	−	0.430002i	0.380855	−	0.0671550i	0.0200566	−	0.999799i	$-0.493615\pi$
$41$	2.43866	−	0.430002i	0.380855	−	0.0671550i	0.360798	+	0.932644i	$0.382504\pi$
$42$		0			0
$43$	−0.605916	−	0.722102i	−0.0924013	−	0.110120i	0.717863	−	0.696185i	$-0.245121\pi$
$43$	−0.605916	−	0.722102i	−0.0924013	−	0.110120i	−0.810264	+	0.586065i	$0.800676\pi$
$44$		0			0
$45$	−0.0306537	+	0.0530937i	−0.00456958	+	0.00791474i
$46$		0			0
$47$	1.40086	+	3.84883i	0.204336	+	0.561409i	0.998955	−	0.0456992i	$-0.0145516\pi$
$47$	1.40086	+	3.84883i	0.204336	+	0.561409i	−0.794619	+	0.607108i	$0.792329\pi$
$48$		0			0
$49$	−2.02041	−	3.49946i	−0.288630	−	0.499922i
$50$		0			0
$51$	1.17508	−	6.66423i	0.164545	−	0.933179i
$52$		0			0
$53$	4.83391	−	5.76083i	0.663989	−	0.791311i	−0.323963	−	0.946070i	$-0.605015\pi$
$53$	4.83391	−	5.76083i	0.663989	−	0.791311i	0.987952	+	0.154758i	$0.0494599\pi$
$54$		0			0
$55$	0.0179199	−	0.0492344i	0.00241631	−	0.00663877i
$56$		0			0
$57$	−2.43843	+	3.61304i	−0.322978	+	0.478559i
$58$		0			0
$59$	−0.268742	−	0.0978140i	−0.0349872	−	0.0127343i	0.324467	−	0.945897i	$-0.394815\pi$
$59$	−0.268742	−	0.0978140i	−0.0349872	−	0.0127343i	−0.359454	+	0.933163i	$0.617037\pi$
$60$		0			0
$61$	−3.13938	−	2.63425i	−0.401956	−	0.337281i	0.419293	−	0.907851i	$-0.362278\pi$
$61$	−3.13938	−	2.63425i	−0.401956	−	0.337281i	−0.821249	+	0.570570i	$0.806722\pi$
$62$		0			0
$63$	−1.69409	−	0.298714i	−0.213435	−	0.0376344i
$64$		0			0
$65$	0.0317149	−	0.0183106i	0.00393375	−	0.00227115i
$66$		0			0
$67$	10.1697	−	3.70148i	1.24243	−	0.452208i	0.364594	−	0.931167i	$-0.381208\pi$
$67$	10.1697	−	3.70148i	1.24243	−	0.452208i	0.877837	+	0.478959i	$0.158986\pi$
$68$		0			0
$69$	−4.12242	−	2.38008i	−0.496282	−	0.286528i
$70$		0			0
$71$	1.45471	−	1.22064i	0.172642	−	0.144864i	−0.552373	−	0.833597i	$-0.686277\pi$
$71$	1.45471	−	1.22064i	0.172642	−	0.144864i	0.725015	+	0.688733i	$0.241833\pi$
$72$		0			0
$73$	1.65676	+	9.39595i	0.193909	+	1.09971i	0.913964	+	0.405795i	$0.133005\pi$
$73$	1.65676	+	9.39595i	0.193909	+	1.09971i	−0.720055	+	0.693917i	$0.755883\pi$
$74$		0			0
$75$	4.99624			0.576916
$76$		0			0
$77$	1.47013			0.167537
$78$		0			0
$79$	−0.354603	−	2.01105i	−0.0398959	−	0.226261i	0.958340	−	0.285629i	$-0.0922026\pi$
$79$	−0.354603	−	2.01105i	−0.0398959	−	0.226261i	−0.998236	+	0.0593680i	$0.981091\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−10.0086	−	5.77844i	−1.09858	−	0.634266i	−0.162733	−	0.986670i	$-0.552031\pi$
$83$	−10.0086	−	5.77844i	−1.09858	−	0.634266i	−0.935848	+	0.352404i	$0.885364\pi$
$84$		0			0
$85$	0.389849	−	0.141894i	0.0422851	−	0.0153905i
$86$		0			0
$87$	6.69719	−	3.86663i	0.718014	−	0.414546i
$88$		0			0
$89$	10.3830	+	1.83080i	1.10060	+	0.194065i	0.694306	−	0.719680i	$-0.255711\pi$
$89$	10.3830	+	1.83080i	1.10060	+	0.194065i	0.406289	+	0.913745i	$0.366823\pi$
$90$		0			0
$91$	0.787154	+	0.660501i	0.0825162	+	0.0692393i
$92$		0			0
$93$	−9.31610	−	3.39078i	−0.966035	−	0.351608i
$94$		0			0
$95$	−0.266577	−	0.0187124i	−0.0273502	−	0.00191985i
$96$		0			0
$97$	1.48052	−	4.06769i	0.150324	−	0.413011i	−0.841559	−	0.540165i	$-0.818362\pi$
$97$	1.48052	−	4.06769i	0.150324	−	0.413011i	0.991883	+	0.127153i	$0.0405841\pi$
$98$		0			0
$99$	−0.549336	+	0.654673i	−0.0552104	+	0.0657971i
$100$		0			0
$101$	1.03298	−	5.85835i	0.102786	−	0.582927i	−0.889296	−	0.457332i	$-0.848805\pi$
$101$	1.03298	−	5.85835i	0.102786	−	0.582927i	0.992082	−	0.125595i	$-0.0400839\pi$
$102$		0			0
$103$	−2.45808	−	4.25752i	−0.242202	−	0.419506i	0.719139	−	0.694866i	$-0.244536\pi$
$103$	−2.45808	−	4.25752i	−0.242202	−	0.419506i	−0.961341	+	0.275360i	$0.911203\pi$
$104$		0			0
$105$	−0.0360703	−	0.0991023i	−0.00352010	−	0.00967139i
$106$		0			0
$107$	−6.66346	+	11.5415i	−0.644181	+	1.11575i	0.340309	+	0.940314i	$0.389468\pi$
$107$	−6.66346	+	11.5415i	−0.644181	+	1.11575i	−0.984490	+	0.175441i	$0.943865\pi$
$108$		0			0
$109$	−7.21154	−	8.59438i	−0.690740	−	0.823192i	0.300705	−	0.953717i	$-0.402778\pi$
$109$	−7.21154	−	8.59438i	−0.690740	−	0.823192i	−0.991445	+	0.130525i	$0.958334\pi$
$110$		0			0
$111$	−4.20066	+	0.740690i	−0.398709	+	0.0703031i
$112$		0			0
$113$			14.9166i			1.40323i	0.712554	+	0.701617i	$0.247538\pi$
$113$			14.9166i			1.40323i	−0.712554	+	0.701617i	$0.752462\pi$
$114$		0			0
$115$		−	0.291833i		−	0.0272136i
$116$		0			0
$117$	−0.588264	+	0.103727i	−0.0543850	+	0.00958954i
$118$		0			0
$119$	7.48258	+	8.91739i	0.685927	+	0.817456i
$120$		0			0
$121$	−5.13482	+	8.89376i	−0.466801	+	0.808524i
$122$		0			0
$123$	−0.846938	−	2.32694i	−0.0763659	−	0.209814i
$124$		0			0
$125$	0.306421	+	0.530738i	0.0274072	+	0.0474706i
$126$		0			0
$127$	−1.63950	+	9.29807i	−0.145482	+	0.825070i	0.821497	+	0.570213i	$0.193140\pi$
$127$	−1.63950	+	9.29807i	−0.145482	+	0.825070i	−0.966979	+	0.254857i	$0.917972\pi$
$128$		0			0
$129$	−0.605916	+	0.722102i	−0.0533479	+	0.0635776i
$130$		0			0
$131$	−6.85666	+	18.8385i	−0.599069	+	1.64593i	0.154065	+	0.988061i	$0.450764\pi$
$131$	−6.85666	+	18.8385i	−0.599069	+	1.64593i	−0.753134	+	0.657868i	$0.771459\pi$
$132$		0			0
$133$	−2.06488	−	7.20837i	−0.179048	−	0.625045i
$134$		0			0
$135$	0.0576100	+	0.0209683i	0.00495828	+	0.00180467i
$136$		0			0
$137$	12.3608	+	10.3719i	1.05605	+	0.886135i	0.993717	−	0.111920i	$-0.0357002\pi$
$137$	12.3608	+	10.3719i	1.05605	+	0.886135i	0.0623371	+	0.998055i	$0.480145\pi$
$138$		0			0
$139$	2.13627	+	0.376683i	0.181196	+	0.0319498i	0.263510	−	0.964657i	$-0.415120\pi$
$139$	2.13627	+	0.376683i	0.181196	+	0.0319498i	−0.0823136	+	0.996606i	$0.526231\pi$
$140$		0			0
$141$	3.54710	−	2.04792i	0.298720	−	0.172466i
$142$		0			0
$143$	0.479708	−	0.174599i	0.0401152	−	0.0146007i
$144$		0			0
$145$	0.410587	+	0.237053i	0.0340974	+	0.0196861i
$146$		0			0
$147$	−3.09545	+	2.59739i	−0.255309	+	0.214229i
$148$		0			0
$149$	−0.0364292	−	0.206600i	−0.00298440	−	0.0169254i	0.983279	−	0.182104i	$-0.0582909\pi$
$149$	−0.0364292	−	0.206600i	−0.00298440	−	0.0169254i	−0.986264	+	0.165179i	$0.947180\pi$
$150$		0			0
$151$	−16.7893			−1.36629			−0.683147	−	0.730281i	$-0.739389\pi$
$151$	−16.7893			−1.36629			−0.683147	+	0.730281i	$0.739389\pi$
$152$		0			0
$153$	−6.76704			−0.547082
$154$		0			0
$155$	−0.105543	−	0.598566i	−0.00847745	−	0.0480780i
$156$		0			0
$157$	−6.45287	+	5.41460i	−0.514995	+	0.432132i	−0.862883	−	0.505404i	$-0.831343\pi$
$157$	−6.45287	+	5.41460i	−0.514995	+	0.432132i	0.347888	+	0.937536i	$0.386899\pi$
$158$		0			0
$159$	−6.51271	−	3.76012i	−0.516492	−	0.298197i
$160$		0			0
$161$	7.69473	−	2.80065i	0.606429	−	0.220722i
$162$		0			0
$163$	2.04368	−	1.17992i	0.160073	−	0.0924184i	−0.417823	−	0.908528i	$-0.637207\pi$
$163$	2.04368	−	1.17992i	0.160073	−	0.0924184i	0.577897	+	0.816110i	$0.303874\pi$
$164$		0			0
$165$	−0.0515982	−	0.00909815i	−0.00401691	−	0.000708290i
$166$		0			0
$167$	−9.55564	−	8.01814i	−0.739438	−	0.620462i	0.193249	−	0.981150i	$-0.438098\pi$
$167$	−9.55564	−	8.01814i	−0.739438	−	0.620462i	−0.932687	+	0.360688i	$0.882542\pi$
$168$		0			0
$169$	−11.8807	−	4.32422i	−0.913901	−	0.332633i
$170$		0			0
$171$	3.98158	+	1.77399i	0.304479	+	0.135660i
$172$		0			0
$173$	5.62834	−	15.4637i	0.427915	−	1.17569i	−0.519162	−	0.854676i	$-0.673756\pi$
$173$	5.62834	−	15.4637i	0.427915	−	1.17569i	0.947076	−	0.321009i	$-0.104022\pi$
$174$		0			0
$175$	−5.52454	+	6.58389i	−0.417616	+	0.497695i
$176$		0			0
$177$	−0.0496615	+	0.281644i	−0.00373278	+	0.0211697i
$178$		0			0
$179$	6.24335	+	10.8138i	0.466650	+	0.808261i	0.999274	−	0.0380904i	$-0.0121275\pi$
$179$	6.24335	+	10.8138i	0.466650	+	0.808261i	−0.532624	+	0.846352i	$0.678794\pi$
$180$		0			0
$181$	−2.05015	−	5.63274i	−0.152386	−	0.418678i	0.839885	−	0.542764i	$-0.182622\pi$
$181$	−2.05015	−	5.63274i	−0.152386	−	0.418678i	−0.992271	+	0.124086i	$0.960400\pi$
$182$		0			0
$183$	−2.04908	+	3.54912i	−0.151473	+	0.262358i
$184$		0			0
$185$	−0.168092	−	0.200324i	−0.0123583	−	0.0147281i
$186$		0			0
$187$	5.69535	−	1.00424i	0.416485	−	0.0734376i
$188$		0			0
$189$			1.72023i			0.125128i
$190$		0			0
$191$			7.97484i			0.577039i	0.957474	+	0.288520i	$0.0931630\pi$
$191$			7.97484i			0.577039i	−0.957474	+	0.288520i	$0.906837\pi$
$192$		0			0
$193$	−13.7836	+	2.43042i	−0.992163	+	0.174945i	−0.646089	−	0.763262i	$-0.723597\pi$
$193$	−13.7836	+	2.43042i	−0.992163	+	0.174945i	−0.346074	+	0.938207i	$0.612485\pi$
$194$		0			0
$195$	−0.0235397	−	0.0280535i	−0.00168571	−	0.00200895i
$196$		0			0
$197$	−2.10270	+	3.64198i	−0.149811	+	0.259481i	−0.931158	−	0.364617i	$-0.881200\pi$
$197$	−2.10270	+	3.64198i	−0.149811	+	0.259481i	0.781346	+	0.624098i	$0.214533\pi$
$198$		0			0
$199$	8.27760	+	22.7425i	0.586784	+	1.61218i	0.776346	+	0.630307i	$0.217071\pi$
$199$	8.27760	+	22.7425i	0.586784	+	1.61218i	−0.189563	+	0.981869i	$0.560707\pi$
$200$		0			0
$201$	−5.41120	−	9.37248i	−0.381677	−	0.661084i
$202$		0			0
$203$	−2.31003	+	13.1008i	−0.162132	+	0.919498i
$204$		0			0
$205$	0.0975843	−	0.116296i	0.00681559	−	0.00812250i
$206$		0			0
$207$	−1.62807	+	4.47309i	−0.113159	+	0.310901i
$208$		0			0
$209$	−3.61429	−	0.902168i	−0.250005	−	0.0624043i
$210$		0			0
$211$	−11.0257	−	4.01302i	−0.759040	−	0.276268i	−0.0666352	−	0.997777i	$-0.521226\pi$
$211$	−11.0257	−	4.01302i	−0.759040	−	0.276268i	−0.692404	+	0.721510i	$0.743449\pi$
$212$		0			0
$213$	−1.45471	−	1.22064i	−0.0996749	−	0.0836372i
$214$		0			0
$215$	−0.0569126	−	0.0100352i	−0.00388141	−	0.000684397i
$216$		0			0
$217$	14.7695	−	8.52715i	1.00262	−	0.578860i
$218$		0			0
$219$	8.96551	−	3.26318i	0.605833	−	0.220505i
$220$		0			0
$221$	3.50066	+	2.02111i	0.235480	+	0.135954i
$222$		0			0
$223$	−6.29269	+	5.28020i	−0.421390	+	0.353588i	−0.828691	−	0.559706i	$-0.810914\pi$
$223$	−6.29269	+	5.28020i	−0.421390	+	0.353588i	0.407302	+	0.913294i	$0.366470\pi$
$224$		0			0
$225$	−0.867588	−	4.92034i	−0.0578392	−	0.328022i
$226$		0			0
$227$	−11.5648			−0.767584			−0.383792	−	0.923420i	$-0.625382\pi$
$227$	−11.5648			−0.767584			−0.383792	+	0.923420i	$0.625382\pi$
$228$		0			0
$229$	−7.76289			−0.512986			−0.256493	−	0.966546i	$-0.582567\pi$
$229$	−7.76289			−0.512986			−0.256493	+	0.966546i	$0.582567\pi$
$230$		0			0
$231$	−0.255286	−	1.44780i	−0.0167966	−	0.0952580i
$232$		0			0
$233$	−13.1250	+	11.0132i	−0.859850	+	0.721500i	−0.961936	−	0.273276i	$-0.911893\pi$
$233$	−13.1250	+	11.0132i	−0.859850	+	0.721500i	0.102086	+	0.994776i	$0.467448\pi$
$234$		0			0
$235$	0.217463	+	0.125552i	0.0141857	+	0.00819014i
$236$		0			0
$237$	−1.91892	+	0.698431i	−0.124648	+	0.0453680i
$238$		0			0
$239$	11.0765	−	6.39503i	0.716480	−	0.413660i	−0.0969758	−	0.995287i	$-0.530917\pi$
$239$	11.0765	−	6.39503i	0.716480	−	0.413660i	0.813456	+	0.581627i	$0.197584\pi$
$240$		0			0
$241$	14.9141	+	2.62976i	0.960701	+	0.169398i	0.631941	−	0.775016i	$-0.282258\pi$
$241$	14.9141	+	2.62976i	0.960701	+	0.169398i	0.328760	+	0.944414i	$0.393369\pi$
$242$		0			0
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$		0			0
$245$	−0.232792	−	0.0847294i	−0.0148725	−	0.00541316i
$246$		0			0
$247$	−1.52988	−	2.10688i	−0.0973437	−	0.134057i
$248$		0			0
$249$	−3.95269	+	10.8599i	−0.250491	+	0.688219i
$250$		0			0
$251$	−5.71021	+	6.80516i	−0.360425	+	0.429538i	−0.915534	−	0.402239i	$-0.868232\pi$
$251$	−5.71021	+	6.80516i	−0.360425	+	0.429538i	0.555109	+	0.831777i	$0.312676\pi$
$252$		0			0
$253$	0.706420	−	4.00631i	0.0444122	−	0.251874i
$254$		0			0
$255$	−0.207434	−	0.359287i	−0.0129900	−	0.0224994i
$256$		0			0
$257$	−1.69810	−	4.66549i	−0.105925	−	0.291025i	0.875396	−	0.483407i	$-0.160601\pi$
$257$	−1.69810	−	4.66549i	−0.105925	−	0.291025i	−0.981320	+	0.192382i	$0.938379\pi$
$258$		0			0
$259$	3.66878	−	6.35451i	0.227967	−	0.394850i
$260$		0			0
$261$	−4.97084	−	5.92402i	−0.307687	−	0.366687i
$262$		0			0
$263$	−5.87311	+	1.03559i	−0.362152	+	0.0638571i	−0.351763	−	0.936089i	$-0.614418\pi$
$263$	−5.87311	+	1.03559i	−0.362152	+	0.0638571i	−0.0103882	+	0.999946i	$0.503307\pi$
$264$		0			0
$265$		−	0.461046i		−	0.0283218i
$266$		0			0
$267$		−	10.5432i		−	0.645231i
$268$		0			0
$269$	−29.5070	+	5.20288i	−1.79907	+	0.317225i	−0.970217	−	0.242237i	$-0.922119\pi$
$269$	−29.5070	+	5.20288i	−1.79907	+	0.317225i	−0.828856	+	0.559462i	$0.811008\pi$
$270$		0			0
$271$	−7.11688	−	8.48156i	−0.432319	−	0.515218i	0.505271	−	0.862961i	$-0.331393\pi$
$271$	−7.11688	−	8.48156i	−0.432319	−	0.515218i	−0.937590	+	0.347743i	$0.886948\pi$
$272$		0			0
$273$	0.513779	−	0.889890i	0.0310953	−	0.0538586i
$274$		0			0
$275$	1.46038	+	4.01236i	0.0880642	+	0.241954i
$276$		0			0
$277$	−13.5969	−	23.5506i	−0.816961	−	1.41502i	−0.907911	−	0.419162i	$-0.862324\pi$
$277$	−13.5969	−	23.5506i	−0.816961	−	1.41502i	0.0909508	−	0.995855i	$-0.471009\pi$
$278$		0			0
$279$	−1.72155	+	9.76337i	−0.103066	+	0.584518i
$280$		0			0
$281$	1.94437	−	2.31720i	0.115991	−	0.138233i	−0.704925	−	0.709282i	$-0.749019\pi$
$281$	1.94437	−	2.31720i	0.115991	−	0.138233i	0.820916	+	0.571050i	$0.193464\pi$
$282$		0			0
$283$	0.563343	−	1.54777i	0.0334873	−	0.0920056i	−0.921822	−	0.387613i	$-0.873300\pi$
$283$	0.563343	−	1.54777i	0.0334873	−	0.0920056i	0.955310	+	0.295607i	$0.0955220\pi$
$284$		0			0
$285$	0.0278624	+	0.265776i	0.00165043	+	0.0157432i
$286$		0			0
$287$	4.00287	+	1.45692i	0.236282	+	0.0859996i
$288$		0			0
$289$	22.0565	+	18.5076i	1.29744	+	1.08868i
$290$		0			0
$291$	−4.26298	−	0.751679i	−0.249901	−	0.0440642i
$292$		0			0
$293$	22.1436	−	12.7846i	1.29364	−	0.746883i	0.314343	−	0.949310i	$-0.398216\pi$
$293$	22.1436	−	12.7846i	1.29364	−	0.746883i	0.979298	+	0.202426i	$0.0648826\pi$
$294$		0			0
$295$	−0.0164758	+	0.00599672i	−0.000959261	+	0.000349142i
$296$		0			0
$297$	0.740119	+	0.427308i	0.0429460	+	0.0247949i
$298$		0			0
$299$	2.17819	−	1.82772i	0.125968	−	0.105700i
$300$		0			0
$301$	−0.281579	−	1.59691i	−0.0162299	−	0.0920446i
$302$		0			0
$303$	−5.94872			−0.341745
$304$		0			0
$305$	−0.251248			−0.0143864
$306$		0			0
$307$	1.91791	+	10.8770i	0.109461	+	0.620784i	0.989344	+	0.145594i	$0.0465095\pi$
$307$	1.91791	+	10.8770i	0.109461	+	0.620784i	−0.879883	+	0.475190i	$0.842379\pi$
$308$		0			0
$309$	−3.76600	+	3.16005i	−0.214240	+	0.179769i
$310$		0			0
$311$	21.4149	+	12.3639i	1.21433	+	0.701092i	0.963699	−	0.266991i	$-0.0860293\pi$
$311$	21.4149	+	12.3639i	1.21433	+	0.701092i	0.250629	+	0.968083i	$0.419363\pi$
$312$		0			0
$313$	−18.3989	+	6.69665i	−1.03997	+	0.378517i	−0.804868	−	0.593454i	$-0.797764\pi$
$313$	−18.3989	+	6.69665i	−1.03997	+	0.378517i	−0.235100	+	0.971971i	$0.575542\pi$
$314$		0			0
$315$	−0.0913331	+	0.0527312i	−0.00514604	+	0.00297107i
$316$		0			0
$317$	−2.58943	−	0.456586i	−0.145437	−	0.0256444i	0.100456	−	0.994942i	$-0.467970\pi$
$317$	−2.58943	−	0.456586i	−0.145437	−	0.0256444i	−0.245893	+	0.969297i	$0.579081\pi$
$318$		0			0
$319$	5.06275	+	4.24816i	0.283460	+	0.237851i
$320$		0			0
$321$	12.5232	+	4.55808i	0.698977	+	0.254407i
$322$		0			0
$323$	−12.9235	−	26.5150i	−0.719081	−	1.47534i
$324$		0			0
$325$	−1.02074	+	2.80446i	−0.0566205	+	0.155564i
$326$		0			0
$327$	−7.21154	+	8.59438i	−0.398799	+	0.475270i
$328$		0			0
$329$	−1.22348	+	6.93872i	−0.0674528	+	0.382544i
$330$		0			0
$331$	6.94548	+	12.0299i	0.381758	+	0.661224i	0.991314	−	0.131519i	$-0.0419854\pi$
$331$	6.94548	+	12.0299i	0.381758	+	0.661224i	−0.609556	+	0.792743i	$0.708652\pi$
$332$		0			0
$333$	1.45887	+	4.00822i	0.0799458	+	0.219649i
$334$		0			0
$335$	0.331746	−	0.574602i	0.0181252	−	0.0313938i
$336$		0			0
$337$	−16.4841	−	19.6450i	−0.897946	−	1.07013i	−0.997179	−	0.0750664i	$-0.976083\pi$
$337$	−16.4841	−	19.6450i	−0.897946	−	1.07013i	0.0992323	−	0.995064i	$-0.468361\pi$
$338$		0			0
$339$	14.6900	−	2.59024i	0.797849	−	0.140682i
$340$		0			0
$341$		−	8.47265i		−	0.458820i
$342$		0			0
$343$		−	18.9927i		−	1.02551i
$344$		0			0
$345$	−0.287399	+	0.0506763i	−0.0154731	+	0.00272832i
$346$		0			0
$347$	−12.9723	−	15.4598i	−0.696389	−	0.829924i	0.295724	−	0.955274i	$-0.404439\pi$
$347$	−12.9723	−	15.4598i	−0.696389	−	0.829924i	−0.992113	+	0.125349i	$0.959995\pi$
$348$		0			0
$349$	−10.2297	+	17.7183i	−0.547581	+	0.948439i	0.450858	+	0.892596i	$0.351118\pi$
$349$	−10.2297	+	17.7183i	−0.547581	+	0.948439i	−0.998440	+	0.0558430i	$0.982215\pi$
$350$		0			0
$351$	0.204302	+	0.561315i	0.0109048	+	0.0299608i
$352$		0			0
$353$	−4.60671	−	7.97906i	−0.245191	−	0.424682i	0.716995	−	0.697079i	$-0.245517\pi$
$353$	−4.60671	−	7.97906i	−0.245191	−	0.424682i	−0.962185	+	0.272396i	$0.912184\pi$
$354$		0			0
$355$	0.0202164	−	0.114653i	0.00107298	−	0.00608515i
$356$		0			0
$357$	7.48258	−	8.91739i	0.396020	−	0.471958i
$358$		0			0
$359$	1.91506	−	5.26160i	0.101073	−	0.277696i	−0.878841	−	0.477114i	$-0.841683\pi$
$359$	1.91506	−	5.26160i	0.101073	−	0.277696i	0.979915	+	0.199418i	$0.0639051\pi$
$360$		0			0
$361$	0.652946	+	18.9888i	0.0343656	+	0.999409i
$362$		0			0
$363$	9.65030	+	3.51242i	0.506509	+	0.184354i
$364$		0			0
$365$	0.448080	+	0.375984i	0.0234536	+	0.0196799i
$366$		0			0
$367$	−20.1473	−	3.55251i	−1.05168	−	0.185439i	−0.379017	−	0.925390i	$-0.623738\pi$
$367$	−20.1473	−	3.55251i	−1.05168	−	0.185439i	−0.672662	+	0.739950i	$0.734849\pi$
$368$		0			0
$369$	−2.14452	+	1.23814i	−0.111639	+	0.0644551i
$370$		0			0
$371$	12.1563	−	4.42454i	0.631125	−	0.229711i
$372$		0			0
$373$	−3.19857	−	1.84669i	−0.165615	−	0.0956181i	0.414901	−	0.909866i	$-0.363816\pi$
$373$	−3.19857	−	1.84669i	−0.165615	−	0.0956181i	−0.580517	+	0.814248i	$0.697149\pi$
$374$		0			0
$375$	0.469465	−	0.393928i	0.0242431	−	0.0203423i
$376$		0			0
$377$	0.802145	+	4.54919i	0.0413126	+	0.234295i
$378$		0			0
$379$	11.0548			0.567846			0.283923	−	0.958847i	$-0.408364\pi$
$379$	11.0548			0.567846			0.283923	+	0.958847i	$0.408364\pi$
$380$		0			0
$381$	9.44151			0.483703
$382$		0			0
$383$	−2.83784	−	16.0942i	−0.145007	−	0.822375i	−0.967362	−	0.253400i	$-0.918451\pi$
$383$	−2.83784	−	16.0942i	−0.145007	−	0.822375i	0.822355	−	0.568975i	$-0.192660\pi$
$384$		0			0
$385$	0.0690434	−	0.0579343i	0.00351878	−	0.00295261i
$386$		0			0
$387$	0.816348	+	0.471319i	0.0414973	+	0.0239585i
$388$		0			0
$389$	22.1383	−	8.05769i	1.12246	−	0.408541i	0.286909	−	0.957958i	$-0.407372\pi$
$389$	22.1383	−	8.05769i	1.12246	−	0.408541i	0.835548	+	0.549417i	$0.185150\pi$
$390$		0			0
$391$	27.8966	−	16.1061i	1.41079	−	0.814521i
$392$		0			0
$393$	19.7430	+	3.48122i	0.995900	+	0.175604i
$394$		0			0
$395$	−0.0959044	−	0.0804733i	−0.00482547	−	0.00404905i
$396$		0			0
$397$	35.1592	+	12.7969i	1.76459	+	0.642259i	0.999997	−	0.00225438i	$-0.000717591\pi$
$397$	35.1592	+	12.7969i	1.76459	+	0.642259i	0.764593	+	0.644513i	$0.222940\pi$
$398$		0			0
$399$	−6.74029	+	3.28523i	−0.337437	+	0.164467i
$400$		0			0
$401$	8.61414	−	23.6671i	0.430170	−	1.18188i	−0.515539	−	0.856866i	$-0.672408\pi$
$401$	8.61414	−	23.6671i	0.430170	−	1.18188i	0.945709	−	0.325015i	$-0.105369\pi$
$402$		0			0
$403$	3.80659	−	4.53652i	0.189620	−	0.225980i
$404$		0			0
$405$	0.0106459	−	0.0603759i	0.000528999	−	0.00300010i
$406$		0			0
$407$	−1.82266	−	3.15695i	−0.0903461	−	0.156484i
$408$		0			0
$409$	4.24779	+	11.6707i	0.210039	+	0.577079i	0.999317	−	0.0369581i	$-0.0117668\pi$
$409$	4.24779	+	11.6707i	0.210039	+	0.577079i	−0.789277	+	0.614037i	$0.789545\pi$
$410$		0			0
$411$	8.06794	−	13.9741i	0.397962	−	0.689290i
$412$		0			0
$413$	−0.316229	−	0.376867i	−0.0155606	−	0.0185444i
$414$		0			0
$415$	−0.697757	+	0.123033i	−0.0342516	+	0.00603947i
$416$		0			0
$417$		−	2.16923i		−	0.106228i
$418$		0			0
$419$			20.5325i			1.00308i	0.865135	+	0.501539i	$0.167233\pi$
$419$			20.5325i			1.00308i	−0.865135	+	0.501539i	$0.832767\pi$
$420$		0			0
$421$	21.5395	−	3.79800i	1.04977	−	0.185103i	0.377958	−	0.925823i	$-0.376626\pi$
$421$	21.5395	−	3.79800i	1.04977	−	0.185103i	0.671815	+	0.740719i	$0.265515\pi$
$422$		0			0
$423$	−2.63275	−	3.13759i	−0.128009	−	0.152555i
$424$		0			0
$425$	−16.9049	+	29.2801i	−0.820007	+	1.42029i
$426$		0			0
$427$	−2.41116	−	6.62461i	−0.116684	−	0.320588i
$428$		0			0
$429$	−0.255247	−	0.442101i	−0.0123235	−	0.0213449i
$430$		0			0
$431$	3.69094	−	20.9323i	0.177786	−	1.00828i	−0.757093	−	0.653308i	$-0.773381\pi$
$431$	3.69094	−	20.9323i	0.177786	−	1.00828i	0.934879	−	0.354967i	$-0.115508\pi$
$432$		0			0
$433$	24.6844	−	29.4177i	1.18626	−	1.41372i	0.297882	−	0.954603i	$-0.403720\pi$
$433$	24.6844	−	29.4177i	1.18626	−	1.41372i	0.888374	−	0.459121i	$-0.151836\pi$
$434$		0			0
$435$	0.162153	−	0.445513i	0.00777466	−	0.0213607i
$436$		0			0
$437$	−20.6360	+	2.16336i	−0.987153	+	0.103487i
$438$		0			0
$439$	25.7827	+	9.38415i	1.23054	+	0.447881i	0.873784	−	0.486315i	$-0.161659\pi$
$439$	25.7827	+	9.38415i	1.23054	+	0.447881i	0.356760	+	0.934196i	$0.383881\pi$
$440$		0			0
$441$	3.09545	+	2.59739i	0.147402	+	0.123685i
$442$		0			0
$443$	−0.581789	−	0.102585i	−0.0276416	−	0.00487396i	0.159810	−	0.987148i	$-0.448912\pi$
$443$	−0.581789	−	0.102585i	−0.0276416	−	0.00487396i	−0.187452	+	0.982274i	$0.560023\pi$
$444$		0			0
$445$	0.559776	−	0.323187i	0.0265359	−	0.0153205i
$446$		0			0
$447$	−0.197136	+	0.0717516i	−0.00932420	+	0.00339373i
$448$		0			0
$449$	−15.5460	−	8.97548i	−0.733661	−	0.423579i	0.0860992	−	0.996287i	$-0.472560\pi$
$449$	−15.5460	−	8.97548i	−0.733661	−	0.423579i	−0.819760	+	0.572707i	$0.805893\pi$
$450$		0			0
$451$	1.62116	−	1.36031i	0.0763373	−	0.0640546i
$452$		0			0
$453$	2.91543	+	16.5342i	0.136979	+	0.776846i
$454$		0			0
$455$	0.0629968			0.00295333
$456$		0			0
$457$	17.7152			0.828684			0.414342	−	0.910121i	$-0.364012\pi$
$457$	17.7152			0.828684			0.414342	+	0.910121i	$0.364012\pi$
$458$		0			0
$459$	1.17508	+	6.66423i	0.0548482	+	0.311060i
$460$		0			0
$461$	−30.7626	+	25.8129i	−1.43276	+	1.20223i	−0.488697	+	0.872453i	$0.662528\pi$
$461$	−30.7626	+	25.8129i	−1.43276	+	1.20223i	−0.944060	+	0.329773i	$0.893028\pi$
$462$		0			0
$463$	−31.2993	−	18.0707i	−1.45460	−	0.839815i	−0.455864	−	0.890049i	$-0.650670\pi$
$463$	−31.2993	−	18.0707i	−1.45460	−	0.839815i	−0.998737	+	0.0502345i	$0.984003\pi$
$464$		0			0
$465$	−0.571145	+	0.207880i	−0.0264862	+	0.00964020i
$466$		0			0
$467$	17.9165	−	10.3441i	0.829075	−	0.478667i	−0.0244606	−	0.999701i	$-0.507787\pi$
$467$	17.9165	−	10.3441i	0.829075	−	0.478667i	0.853536	+	0.521034i	$0.174453\pi$
$468$		0			0
$469$	18.3341	+	3.23280i	0.846592	+	0.149277i
$470$		0			0
$471$	6.45287	+	5.41460i	0.297333	+	0.249492i
$472$		0			0
$473$	−0.757009	−	0.275529i	−0.0348073	−	0.0126688i
$474$		0			0
$475$	17.6223	−	12.7961i	0.808566	−	0.587127i
$476$		0			0
$477$	−2.57207	+	7.06671i	−0.117767	+	0.323562i
$478$		0			0
$479$	11.0212	−	13.1345i	0.503571	−	0.600133i	−0.453044	−	0.891488i	$-0.649662\pi$
$479$	11.0212	−	13.1345i	0.503571	−	0.600133i	0.956615	+	0.291356i	$0.0941063\pi$
$480$		0			0
$481$	0.442442	−	2.50922i	0.0201736	−	0.114410i
$482$		0			0
$483$	−4.09428	−	7.09150i	−0.186296	−	0.322674i
$484$		0			0
$485$	−0.0907666	−	0.249379i	−0.00412150	−	0.0113237i
$486$		0			0
$487$	−15.9246	+	27.5823i	−0.721614	+	1.24987i	0.238739	+	0.971084i	$0.423266\pi$
$487$	−15.9246	+	27.5823i	−0.721614	+	1.24987i	−0.960353	+	0.278788i	$0.910067\pi$
$488$		0			0
$489$	−1.51688	−	1.80774i	−0.0685955	−	0.0817489i
$490$		0			0
$491$	−34.8498	+	6.14496i	−1.57275	+	0.277318i	−0.890908	−	0.454183i	$-0.849931\pi$
$491$	−34.8498	+	6.14496i	−1.57275	+	0.277318i	−0.681840	+	0.731501i	$0.738820\pi$
$492$		0			0
$493$			52.3312i			2.35688i
$494$		0			0
$495$			0.0523942i			0.00235494i
$496$		0			0
$497$	3.21705	−	0.567254i	0.144305	−	0.0254448i
$498$		0			0
$499$	1.95409	+	2.32880i	0.0874773	+	0.104251i	0.808008	−	0.589172i	$-0.200546\pi$
$499$	1.95409	+	2.32880i	0.0874773	+	0.104251i	−0.720530	+	0.693423i	$0.756102\pi$
$500$		0			0
$501$	−6.23700	+	10.8028i	−0.278649	+	0.482634i
$502$		0			0
$503$	−3.95660	−	10.8707i	−0.176416	−	0.484700i	0.819695	−	0.572800i	$-0.194143\pi$
$503$	−3.95660	−	10.8707i	−0.176416	−	0.484700i	−0.996112	+	0.0881001i	$0.971920\pi$
$504$		0			0
$505$	−0.182350	−	0.315840i	−0.00811447	−	0.0140547i
$506$		0			0
$507$	−2.19547	+	12.4511i	−0.0975041	+	0.552973i
$508$		0			0
$509$	11.4312	−	13.6231i	0.506678	−	0.603835i	−0.450700	−	0.892676i	$-0.648825\pi$
$509$	11.4312	−	13.6231i	0.506678	−	0.603835i	0.957377	+	0.288841i	$0.0932699\pi$
$510$		0			0
$511$	−5.61340	+	15.4227i	−0.248322	+	0.682260i
$512$		0			0
$513$	1.05564	−	4.22914i	0.0466078	−	0.186721i
$514$		0			0
$515$	−0.283220	−	0.103084i	−0.0124802	−	0.00454241i
$516$		0			0
$517$	2.68144	+	2.24999i	0.117929	+	0.0989545i
$518$		0			0
$519$	−16.2061	−	2.85758i	−0.711371	−	0.125434i
$520$		0			0
$521$	6.61449	−	3.81888i	0.289786	−	0.167308i	−0.348059	−	0.937473i	$-0.613159\pi$
$521$	6.61449	−	3.81888i	0.289786	−	0.167308i	0.637845	+	0.770164i	$0.279826\pi$
$522$		0			0
$523$	−4.37217	+	1.59134i	−0.191182	+	0.0695845i	−0.435837	−	0.900026i	$-0.643548\pi$
$523$	−4.37217	+	1.59134i	−0.191182	+	0.0695845i	0.244655	+	0.969610i	$0.421325\pi$
$524$		0			0
$525$	7.44319	+	4.29733i	0.324848	+	0.187551i
$526$		0			0
$527$	51.3926	−	43.1235i	2.23870	−	1.87849i
$528$		0			0
$529$	0.0591838	+	0.335648i	0.00257321	+	0.0145934i
$530$		0			0
$531$	0.285989			0.0124109
$532$		0			0
$533$	1.47918			0.0640704
$534$		0			0
$535$	0.141877	+	0.804625i	0.00613388	+	0.0347870i
$536$		0			0
$537$	9.56537	−	8.02630i	0.412776	−	0.346360i
$538$		0			0
$539$	−2.99069	−	1.72668i	−0.128818	−	0.0743732i
$540$		0			0
$541$	41.2390	−	15.0098i	1.77300	−	0.645320i	0.773063	−	0.634330i	$-0.218724\pi$
$541$	41.2390	−	15.0098i	1.77300	−	0.645320i	0.999940	−	0.0109905i	$-0.00349845\pi$
$542$		0			0
$543$	−5.19116	+	2.99712i	−0.222774	+	0.128619i
$544$		0			0
$545$	−0.677367	−	0.119438i	−0.0290152	−	0.00511617i
$546$		0			0
$547$	−11.4231	−	9.58514i	−0.488417	−	0.409831i	0.365041	−	0.930991i	$-0.381055\pi$
$547$	−11.4231	−	9.58514i	−0.488417	−	0.409831i	−0.853459	+	0.521160i	$0.825499\pi$
$548$		0			0
$549$	3.85102	+	1.40166i	0.164357	+	0.0598212i
$550$		0			0
$551$	13.7187	−	30.7906i	0.584436	−	1.31172i
$552$		0			0
$553$	1.20146	−	3.30098i	0.0510912	−	0.140372i
$554$		0			0
$555$	−0.168092	+	0.200324i	−0.00713509	+	0.00850327i
$556$		0			0
$557$	−3.48688	+	19.7751i	−0.147744	+	0.837896i	0.817379	+	0.576100i	$0.195426\pi$
$557$	−3.48688	+	19.7751i	−0.147744	+	0.837896i	−0.965123	+	0.261796i	$0.915685\pi$
$558$		0			0
$559$	−0.281537	−	0.487636i	−0.0119077	−	0.0206248i
$560$		0			0
$561$	−1.97798	−	5.43444i	−0.0835102	−	0.229442i
$562$		0			0
$563$	8.86419	−	15.3532i	0.373581	−	0.647061i	−0.616533	−	0.787329i	$-0.711463\pi$
$563$	8.86419	−	15.3532i	0.373581	−	0.647061i	0.990114	+	0.140268i	$0.0447965\pi$
$564$		0			0
$565$	0.587827	+	0.700544i	0.0247300	+	0.0294721i
$566$		0			0
$567$	1.69409	−	0.298714i	0.0711451	−	0.0125448i
$568$		0			0
$569$			5.96784i			0.250185i	0.992145	+	0.125092i	$0.0399228\pi$
$569$			5.96784i			0.250185i	−0.992145	+	0.125092i	$0.960077\pi$
$570$		0			0
$571$		−	22.0999i		−	0.924851i	−0.886658	−	0.462425i	$-0.846979\pi$
$571$		−	22.0999i		−	0.924851i	0.886658	−	0.462425i	$-0.153021\pi$
$572$		0			0
$573$	7.85368	−	1.38482i	0.328092	−	0.0578515i
$574$		0			0
$575$	15.2874	+	18.2188i	0.637528	+	0.759776i
$576$		0			0
$577$	−7.31476	+	12.6695i	−0.304517	+	0.527440i	−0.977154	−	0.212534i	$-0.931829\pi$
$577$	−7.31476	+	12.6695i	−0.304517	+	0.527440i	0.672636	+	0.739973i	$0.265162\pi$
$578$		0			0
$579$	4.78698	+	13.1521i	0.198940	+	0.546584i
$580$		0			0
$581$	−9.94022	−	17.2170i	−0.412390	−	0.714280i
$582$		0			0
$583$	1.11602	−	6.32927i	0.0462209	−	0.262132i
$584$		0			0
$585$	−0.0235397	+	0.0280535i	−0.000973246	+	0.00115987i
$586$		0			0
$587$	5.99339	−	16.4667i	0.247374	−	0.679653i	−0.752407	−	0.658699i	$-0.771107\pi$
$587$	5.99339	−	16.4667i	0.247374	−	0.679653i	0.999780	−	0.0209546i	$-0.00667055\pi$
$588$		0			0
$589$	−41.5432	+	11.9003i	−1.71176	+	0.490344i
$590$		0			0
$591$	3.95178	+	1.43833i	0.162555	+	0.0591651i
$592$		0			0
$593$	−8.14675	−	6.83594i	−0.334547	−	0.280718i	0.460003	−	0.887918i	$-0.347848\pi$
$593$	−8.14675	−	6.83594i	−0.334547	−	0.280718i	−0.794550	+	0.607199i	$0.792293\pi$
$594$		0			0
$595$	0.702826	+	0.123927i	0.0288130	+	0.00508052i
$596$		0			0
$597$	20.9596	−	12.1010i	0.857821	−	0.495263i
$598$		0			0
$599$	−0.371756	+	0.135308i	−0.0151895	+	0.00552854i	−0.349604	−	0.936898i	$-0.613684\pi$
$599$	−0.371756	+	0.135308i	−0.0151895	+	0.00552854i	0.334414	+	0.942426i	$0.391462\pi$
$600$		0			0
$601$	−21.8148	−	12.5948i	−0.889843	−	0.513751i	−0.0159517	−	0.999873i	$-0.505078\pi$
$601$	−21.8148	−	12.5948i	−0.889843	−	0.513751i	−0.873891	+	0.486122i	$0.838411\pi$
$602$		0			0
$603$	−8.29045	+	6.95651i	−0.337613	+	0.283291i
$604$		0			0
$605$	0.109330	+	0.620039i	0.00444488	+	0.0252082i
$606$		0			0
$607$	18.0511			0.732672			0.366336	−	0.930483i	$-0.380612\pi$
$607$	18.0511			0.732672			0.366336	+	0.930483i	$0.380612\pi$
$608$		0			0
$609$	13.3029			0.539062
$610$		0			0
$611$	0.424848	+	2.40943i	0.0171875	+	0.0974752i
$612$		0			0
$613$	14.3334	−	12.0271i	0.578920	−	0.485771i	−0.305673	−	0.952137i	$-0.598881\pi$
$613$	14.3334	−	12.0271i	0.578920	−	0.485771i	0.884592	+	0.466366i	$0.154437\pi$
$614$		0			0
$615$	−0.131475	−	0.0759071i	−0.00530158	−	0.00306087i
$616$		0			0
$617$	−12.5692	+	4.57482i	−0.506018	+	0.184175i	−0.582399	−	0.812903i	$-0.697886\pi$
$617$	−12.5692	+	4.57482i	−0.506018	+	0.184175i	0.0763810	+	0.997079i	$0.475663\pi$
$618$		0			0
$619$	19.2502	−	11.1141i	0.773731	−	0.446714i	−0.0604727	−	0.998170i	$-0.519261\pi$
$619$	19.2502	−	11.1141i	0.773731	−	0.446714i	0.834204	+	0.551456i	$0.185927\pi$
$620$		0			0
$621$	4.68785	+	0.826594i	0.188117	+	0.0331701i
$622$		0			0
$623$	13.8935	+	11.6580i	0.556630	+	0.467068i
$624$		0			0
$625$	−23.4394	−	8.53123i	−0.937574	−	0.341249i
$626$		0			0
$627$	−0.260848	+	3.71604i	−0.0104173	+	0.148404i
$628$		0			0
$629$	9.87225	−	27.1238i	0.393632	−	1.08150i
$630$		0			0
$631$	−21.7280	+	25.8945i	−0.864980	+	1.03084i	0.134224	+	0.990951i	$0.457146\pi$
$631$	−21.7280	+	25.8945i	−0.864980	+	1.03084i	−0.999204	+	0.0398918i	$0.987299\pi$
$632$		0			0
$633$	−2.03746	+	11.5550i	−0.0809820	+	0.459271i
$634$		0			0
$635$	0.289417	+	0.501285i	0.0114852	+	0.0198929i
$636$		0			0
$637$	−0.825548	−	2.26817i	−0.0327094	−	0.0898683i
$638$		0			0
$639$	−0.949493	+	1.64457i	−0.0375614	+	0.0650582i
$640$		0			0
$641$	−23.4798	−	27.9821i	−0.927395	−	1.10523i	−0.994209	−	0.107461i	$-0.965728\pi$
$641$	−23.4798	−	27.9821i	−0.927395	−	1.10523i	0.0668143	−	0.997765i	$-0.478717\pi$
$642$		0			0
$643$	−15.7675	+	2.78023i	−0.621809	+	0.109642i	−0.475672	−	0.879623i	$-0.657795\pi$
$643$	−15.7675	+	2.78023i	−0.621809	+	0.109642i	−0.146137	+	0.989264i	$0.546684\pi$
$644$		0			0
$645$			0.0577906i			0.00227550i
$646$		0			0
$647$		−	13.2977i		−	0.522785i	−0.965233	−	0.261393i	$-0.915818\pi$
$647$		−	13.2977i		−	0.522785i	0.965233	−	0.261393i	$-0.0841817\pi$
$648$		0			0
$649$	−0.240697	+	0.0424415i	−0.00944820	+	0.00166597i
$650$		0			0
$651$	−10.9623	−	13.0643i	−0.429646	−	0.512032i
$652$		0			0
$653$	−23.9813	+	41.5368i	−0.938459	+	1.62546i	−0.170113	+	0.985425i	$0.554413\pi$
$653$	−23.9813	+	41.5368i	−0.938459	+	1.62546i	−0.768346	+	0.640034i	$0.778920\pi$
$654$		0			0
$655$	0.420363	+	1.15494i	0.0164250	+	0.0451272i
$656$		0			0
$657$	−4.77045	−	8.26266i	−0.186113	−	0.322357i
$658$		0			0
$659$	−8.59496	+	48.7444i	−0.334812	+	1.89881i	0.0942670	+	0.995547i	$0.469949\pi$
$659$	−8.59496	+	48.7444i	−0.334812	+	1.89881i	−0.429079	+	0.903267i	$0.641162\pi$
$660$		0			0
$661$	−3.93555	+	4.69020i	−0.153075	+	0.182428i	−0.837132	−	0.547001i	$-0.815769\pi$
$661$	−3.93555	+	4.69020i	−0.153075	+	0.182428i	0.684057	+	0.729429i	$0.260214\pi$
$662$		0			0
$663$	1.38252	−	3.79844i	0.0536925	−	0.147519i
$664$		0			0
$665$	−0.381040	−	0.257163i	−0.0147761	−	0.00997235i
$666$		0			0
$667$	34.5916	+	12.5903i	1.33939	+	0.487498i
$668$		0			0
$669$	6.29269	+	5.28020i	0.243290	+	0.204144i
$670$		0			0
$671$	−3.44915	−	0.608178i	−0.133153	−	0.0234784i
$672$		0			0
$673$	37.1100	−	21.4254i	1.43048	−	0.825890i	0.433326	−	0.901237i	$-0.357340\pi$
$673$	37.1100	−	21.4254i	1.43048	−	0.825890i	0.997157	+	0.0753469i	$0.0240064\pi$
$674$		0			0
$675$	−4.69493	+	1.70882i	−0.180708	+	0.0657723i
$676$		0			0
$677$	−21.0883	−	12.1753i	−0.810490	−	0.467936i	0.0366363	−	0.999329i	$-0.488336\pi$
$677$	−21.0883	−	12.1753i	−0.810490	−	0.467936i	−0.847126	+	0.531392i	$0.821669\pi$
$678$		0			0
$679$	5.70429	−	4.78647i	0.218911	−	0.183688i
$680$		0			0
$681$	2.00821	+	11.3891i	0.0769548	+	0.436432i
$682$		0			0
$683$	−41.7484			−1.59746			−0.798730	−	0.601690i	$-0.794494\pi$
$683$	−41.7484			−1.59746			−0.798730	+	0.601690i	$0.794494\pi$
$684$		0			0
$685$	0.989248			0.0377972
$686$		0			0
$687$	1.34801	+	7.64496i	0.0514299	+	0.291673i
$688$		0			0
$689$	3.44117	−	2.88748i	0.131098	−	0.110004i
$690$		0			0
$691$	−20.8632	−	12.0454i	−0.793675	−	0.458228i	0.0475800	−	0.998867i	$-0.484849\pi$
$691$	−20.8632	−	12.0454i	−0.793675	−	0.458228i	−0.841255	+	0.540639i	$0.818182\pi$
$692$		0			0
$693$	−1.38147	+	0.502814i	−0.0524777	+	0.0191003i
$694$		0			0
$695$	0.115172	−	0.0664949i	0.00436874	−	0.00252229i
$696$		0			0
$697$	16.5025	+	2.90984i	0.625077	+	0.110218i
$698$		0			0
$699$	13.1250	+	11.0132i	0.496435	+	0.416558i
$700$		0			0
$701$	22.5606	+	8.21139i	0.852103	+	0.310140i	0.730897	−	0.682487i	$-0.239102\pi$
$701$	22.5606	+	8.21139i	0.852103	+	0.310140i	0.121205	+	0.992627i	$0.461324\pi$
$702$		0			0
$703$	−12.9192	+	13.3710i	−0.487255	+	0.504298i
$704$		0			0
$705$	0.0858829	−	0.235961i	0.00323454	−	0.00888682i
$706$		0			0
$707$	6.57774	−	7.83904i	0.247381	−	0.294817i
$708$		0			0
$709$	−2.54803	+	14.4506i	−0.0956934	+	0.542704i	0.898839	+	0.438278i	$0.144412\pi$
$709$	−2.54803	+	14.4506i	−0.0956934	+	0.542704i	−0.994533	+	0.104426i	$0.966700\pi$
$710$		0			0
$711$	1.02104	+	1.76849i	0.0382919	+	0.0663236i
$712$		0			0
$713$	−16.1407	−	44.3462i	−0.604474	−	1.66078i
$714$		0			0
$715$	0.0156485	−	0.0271041i	0.000585222	−	0.00101363i
$716$		0			0
$717$	−8.22129	−	9.79775i	−0.307030	−	0.365904i
$718$		0			0
$719$	36.6046	−	6.45438i	1.36512	−	0.240708i	0.557387	−	0.830253i	$-0.311804\pi$
$719$	36.6046	−	6.45438i	1.36512	−	0.240708i	0.807735	+	0.589545i	$0.200693\pi$
$720$		0			0
$721$		−	8.45690i		−	0.314952i
$722$		0			0
$723$		−	15.1442i		−	0.563218i
$724$		0			0
$725$	−38.0502	+	6.70928i	−1.41315	+	0.249176i
$726$		0			0
$727$	−12.3532	−	14.7220i	−0.458156	−	0.546009i	0.486668	−	0.873587i	$-0.338212\pi$
$727$	−12.3532	−	14.7220i	−0.458156	−	0.546009i	−0.944824	+	0.327578i	$0.893768\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−2.18170	−	5.99417i	−0.0806931	−	0.221702i
$732$		0			0
$733$	−11.6109	−	20.1107i	−0.428860	−	0.742807i	0.567912	−	0.823089i	$-0.307751\pi$
$733$	−11.6109	−	20.1107i	−0.428860	−	0.742807i	−0.996772	+	0.0802818i	$0.974418\pi$
$734$		0			0
$735$	−0.0430182	+	0.243969i	−0.00158675	+	0.00899892i
$736$		0			0
$737$	5.94514	−	7.08514i	0.218992	−	0.260985i
$738$		0			0
$739$	−12.6525	+	34.7624i	−0.465429	+	1.27876i	0.455921	+	0.890020i	$0.349310\pi$
$739$	−12.6525	+	34.7624i	−0.465429	+	1.27876i	−0.921350	+	0.388735i	$0.872912\pi$
$740$		0			0
$741$	−1.80921	+	1.87249i	−0.0664630	+	0.0687876i
$742$		0			0
$743$	−39.2801	−	14.2968i	−1.44105	−	0.524498i	−0.500970	−	0.865464i	$-0.667023\pi$
$743$	−39.2801	−	14.2968i	−1.44105	−	0.524498i	−0.940075	+	0.340967i	$0.889246\pi$
$744$		0			0
$745$	−0.00985249	−	0.00826722i	−0.000360967	−	0.000302888i
$746$		0			0
$747$	11.3813	+	2.00683i	0.416420	+	0.0734261i
$748$		0			0
$749$	−19.8539	+	11.4627i	−0.725446	+	0.418836i
$750$		0			0
$751$	5.83203	−	2.12268i	0.212814	−	0.0774579i	−0.233413	−	0.972378i	$-0.574990\pi$
$751$	5.83203	−	2.12268i	0.212814	−	0.0774579i	0.446227	+	0.894920i	$0.352767\pi$
$752$		0			0
$753$	7.69334	+	4.44175i	0.280361	+	0.161866i
$754$		0			0
$755$	−0.788495	+	0.661626i	−0.0286963	+	0.0240790i
$756$		0			0
$757$	4.07578	+	23.1149i	0.148137	+	0.840126i	0.964795	+	0.263004i	$0.0847131\pi$
$757$	4.07578	+	23.1149i	0.148137	+	0.840126i	−0.816658	+	0.577122i	$0.804176\pi$
$758$		0			0
$759$	−4.06811			−0.147663
$760$		0			0
$761$	−44.5771			−1.61592			−0.807960	−	0.589237i	$-0.799428\pi$
$761$	−44.5771			−1.61592			−0.807960	+	0.589237i	$0.799428\pi$
$762$		0			0
$763$	−3.35132	−	19.0063i	−0.121326	−	0.688074i
$764$		0			0
$765$	−0.317808	+	0.266673i	−0.0114904	+	0.00964157i
$766$		0			0
$767$	−0.147945	−	0.0854161i	−0.00534199	−	0.00308420i
$768$		0			0
$769$	6.57444	−	2.39290i	0.237080	−	0.0862902i	−0.220748	−	0.975331i	$-0.570850\pi$
$769$	6.57444	−	2.39290i	0.237080	−	0.0862902i	0.457828	+	0.889041i	$0.348628\pi$
$770$		0			0
$771$	−4.29974	+	2.48246i	−0.154851	+	0.0894035i
$772$		0			0
$773$	29.0281	+	5.11843i	1.04407	+	0.184097i	0.669278	−	0.743012i	$-0.266604\pi$
$773$	29.0281	+	5.11843i	1.04407	+	0.184097i	0.374790	+	0.927110i	$0.377715\pi$
$774$		0			0
$775$	37.9442	+	31.8390i	1.36300	+	1.14369i
$776$		0			0
$777$	−6.89505	−	2.50959i	−0.247358	−	0.0900311i
$778$		0			0
$779$	−8.94691	−	6.03824i	−0.320556	−	0.216342i
$780$		0			0
$781$	0.555065	−	1.52503i	0.0198618	−	0.0545698i
$782$		0			0
$783$	−4.97084	+	5.92402i	−0.177643	+	0.211707i
$784$		0			0
$785$	−0.0896771	+	0.508584i	−0.00320071	+	0.0181521i
$786$		0			0
$787$	5.18290	+	8.97705i	0.184750	+	0.319997i	0.943492	−	0.331394i	$-0.107519\pi$
$787$	5.18290	+	8.97705i	0.184750	+	0.319997i	−0.758742	+	0.651391i	$0.774186\pi$
$788$		0			0
$789$	2.03971	+	5.60406i	0.0726156	+	0.199510i
$790$		0			0
$791$	−12.8299	+	22.2221i	−0.456180	+	0.790127i
$792$		0			0
$793$	−1.57354	−	1.87527i	−0.0558780	−	0.0665928i
$794$		0			0
$795$	−0.454041	+	0.0800597i	−0.0161032	+	0.00283943i
$796$		0			0
$797$			16.0350i			0.567987i	0.958826	+	0.283994i	$0.0916595\pi$
$797$			16.0350i			0.567987i	−0.958826	+	0.283994i	$0.908341\pi$
$798$		0			0
$799$			27.7167i			0.980545i
$800$		0			0
$801$	−10.3830	+	1.83080i	−0.366865	+	0.0646882i
$802$		0			0
$803$	5.24116	+	6.24617i	0.184956	+	0.220423i
$804$		0			0
$805$	0.251009	−	0.434761i	0.00884691	−	0.0153233i
$806$		0			0
$807$	10.2477	+	28.1552i	0.360735	+	0.991111i
$808$		0			0
$809$	−27.4192	−	47.4914i	−0.964006	−	1.66971i	−0.712261	−	0.701915i	$-0.752329\pi$
$809$	−27.4192	−	47.4914i	−0.964006	−	1.66971i	−0.251745	−	0.967793i	$-0.581005\pi$
$810$		0			0
$811$	−5.84400	+	33.1430i	−0.205211	+	1.16381i	0.691897	+	0.721996i	$0.256775\pi$
$811$	−5.84400	+	33.1430i	−0.205211	+	1.16381i	−0.897108	+	0.441812i	$0.854336\pi$
$812$		0			0
$813$	−7.11688	+	8.48156i	−0.249600	+	0.297461i
$814$		0			0
$815$	0.0494819	−	0.135950i	0.00173328	−	0.00476214i
$816$		0			0
$817$	−0.287714	+	4.09878i	−0.0100659	+	0.143398i
$818$		0			0
$819$	−0.965588	−	0.351445i	−0.0337404	−	0.0122805i
$820$		0			0
$821$	27.5558	+	23.1221i	0.961705	+	0.806966i	0.981230	−	0.192843i	$-0.0617709\pi$
$821$	27.5558	+	23.1221i	0.961705	+	0.806966i	−0.0195250	+	0.999809i	$0.506215\pi$
$822$		0			0
$823$	−44.9351	−	7.92327i	−1.56634	−	0.276188i	−0.677889	−	0.735164i	$-0.737105\pi$
$823$	−44.9351	−	7.92327i	−1.56634	−	0.276188i	−0.888449	+	0.458976i	$0.848216\pi$
$824$		0			0
$825$	3.69781	−	2.13493i	0.128741	−	0.0743288i
$826$		0			0
$827$	−47.8871	+	17.4295i	−1.66520	+	0.606082i	−0.991167	−	0.132621i	$-0.957661\pi$
$827$	−47.8871	+	17.4295i	−1.66520	+	0.606082i	−0.674030	+	0.738704i	$0.735438\pi$
$828$		0			0
$829$	34.4920	+	19.9140i	1.19796	+	0.691641i	0.960099	−	0.279659i	$-0.0902213\pi$
$829$	34.4920	+	19.9140i	1.19796	+	0.691641i	0.237858	+	0.971300i	$0.423555\pi$
$830$		0			0
$831$	−20.8317	+	17.4799i	−0.722644	+	0.606370i
$832$		0			0
$833$	−4.74831	−	26.9290i	−0.164519	−	0.933034i
$834$		0			0
$835$	−0.764748			−0.0264652
$836$		0			0
$837$	9.91399			0.342678
$838$		0			0
$839$	−3.43575	−	19.4851i	−0.118615	−	0.672700i	−0.984897	−	0.173144i	$-0.944607\pi$
$839$	−3.43575	−	19.4851i	−0.118615	−	0.672700i	0.866281	−	0.499556i	$-0.166504\pi$
$840$		0			0
$841$	−23.5966	+	19.7999i	−0.813676	+	0.682756i
$842$		0			0
$843$	−2.61964	−	1.51245i	−0.0902251	−	0.0520915i
$844$		0			0
$845$	−0.728375	+	0.265107i	−0.0250568	+	0.00911995i
$846$		0			0
$847$	−15.2993	+	8.83304i	−0.525689	+	0.303507i
$848$		0			0
$849$	−1.62208	−	0.286017i	−0.0556697	−	0.00981607i
$850$		0			0
$851$	−15.5540	−	13.0514i	−0.533184	−	0.447395i
$852$		0			0
$853$	−4.64863	−	1.69196i	−0.159166	−	0.0579316i	0.261208	−	0.965282i	$-0.415879\pi$
$853$	−4.64863	−	1.69196i	−0.159166	−	0.0579316i	−0.420374	+	0.907351i	$0.638101\pi$
$854$		0			0
$855$	0.256900	−	0.0735906i	0.00878579	−	0.00251675i
$856$		0			0
$857$	1.01002	−	2.77500i	0.0345016	−	0.0947923i	−0.921246	−	0.388981i	$-0.872827\pi$
$857$	1.01002	−	2.77500i	0.0345016	−	0.0947923i	0.955747	+	0.294189i	$0.0950494\pi$
$858$		0			0
$859$	−24.3581	+	29.0288i	−0.831087	+	0.990451i	0.168901	+	0.985633i	$0.445978\pi$
$859$	−24.3581	+	29.0288i	−0.831087	+	0.990451i	−0.999988	+	0.00481818i	$0.998466\pi$
$860$		0			0
$861$	0.739700	−	4.19505i	0.0252089	−	0.142967i
$862$		0			0
$863$	25.0758	+	43.4326i	0.853590	+	1.47846i	0.877947	+	0.478758i	$0.158913\pi$
$863$	25.0758	+	43.4326i	0.853590	+	1.47846i	−0.0243566	+	0.999703i	$0.507754\pi$
$864$		0			0
$865$	−0.345058	−	0.948040i	−0.0117323	−	0.0322343i
$866$		0			0
$867$	14.3964	−	24.9353i	0.488927	−	0.846846i
$868$		0			0
$869$	−1.12179	−	1.33689i	−0.0380540	−	0.0453510i
$870$		0			0
$871$	6.36643	−	1.12257i	0.215718	−	0.0380369i
$872$		0			0
$873$			4.32875i			0.146506i
$874$		0			0
$875$			1.05423i			0.0356394i
$876$		0			0
$877$	−56.3362	+	9.93360i	−1.90234	+	0.335434i	−0.996167	−	0.0874734i	$-0.972121\pi$
$877$	−56.3362	+	9.93360i	−1.90234	+	0.335434i	−0.906173	+	0.422907i	$0.861010\pi$
$878$		0			0
$879$	−16.4355	−	19.5871i	−0.554357	−	0.660657i
$880$		0			0
$881$	2.73034	−	4.72908i	0.0919873	−	0.159327i	−0.816360	−	0.577543i	$-0.804011\pi$
$881$	2.73034	−	4.72908i	0.0919873	−	0.159327i	0.908347	+	0.418217i	$0.137345\pi$
$882$		0			0
$883$	−2.55834	−	7.02897i	−0.0860948	−	0.236544i	0.889173	−	0.457572i	$-0.151281\pi$
$883$	−2.55834	−	7.02897i	−0.0860948	−	0.236544i	−0.975267	+	0.221028i	$0.929059\pi$
$884$		0			0
$885$	0.00876661	+	0.0151842i	0.000294686	+	0.000510412i
$886$		0			0
$887$	−7.12063	+	40.3831i	−0.239087	+	1.35593i	0.594745	+	0.803914i	$0.297253\pi$
$887$	−7.12063	+	40.3831i	−0.239087	+	1.35593i	−0.833833	+	0.552017i	$0.813858\pi$
$888$		0			0
$889$	−10.4399	+	12.4417i	−0.350141	+	0.417282i
$890$		0			0
$891$	0.292296	−	0.803076i	0.00979227	−	0.0269040i
$892$		0			0
$893$	7.26596	−	16.3079i	0.243146	−	0.545723i
$894$		0			0
$895$	0.719359	+	0.261825i	0.0240455	+	0.00875186i
$896$		0			0
$897$	−2.17819	−	1.82772i	−0.0727278	−	0.0610259i
$898$		0			0
$899$	75.5026	+	13.3132i	2.51815	+	0.444018i
$900$		0			0
$901$	44.0718	−	25.4448i	1.46824	−	0.847691i
$902$		0			0
$903$	−1.52376	+	0.554602i	−0.0507075	+	0.0184560i
$904$		0			0
$905$	−0.318256	−	0.183745i	−0.0105792	−	0.00610790i
$906$		0			0
$907$	−0.558708	+	0.468812i	−0.0185516	+	0.0155666i	−0.652016	−	0.758205i	$-0.726077\pi$
$907$	−0.558708	+	0.468812i	−0.0185516	+	0.0155666i	0.633465	+	0.773772i	$0.281632\pi$
$908$		0			0
$909$	1.03298	+	5.85835i	0.0342619	+	0.194309i
$910$		0			0
$911$	−30.4933			−1.01029			−0.505144	−	0.863035i	$-0.668560\pi$
$911$	−30.4933			−1.01029			−0.505144	+	0.863035i	$0.668560\pi$
$912$		0			0
$913$	−9.87669			−0.326871
$914$		0			0
$915$	0.0436287	+	0.247431i	0.00144232	+	0.00817980i
$916$		0			0
$917$	−26.4180	+	22.1673i	−0.872399	+	0.732030i
$918$		0			0
$919$	14.0893	+	8.13446i	0.464763	+	0.268331i	0.714045	−	0.700100i	$-0.246861\pi$
$919$	14.0893	+	8.13446i	0.464763	+	0.268331i	−0.249282	+	0.968431i	$0.580195\pi$
$920$		0			0
$921$	10.3787	−	3.77755i	0.341991	−	0.124474i
$922$		0			0
$923$	0.982365	−	0.567169i	0.0323349	−	0.0186686i
$924$		0			0
$925$	20.9875	+	3.70066i	0.690065	+	0.121677i
$926$		0			0
$927$	3.76600	+	3.16005i	0.123692	+	0.103790i
$928$		0			0
$929$	25.0876	+	9.13114i	0.823097	+	0.299583i	0.719023	−	0.694987i	$-0.244590\pi$
$929$	25.0876	+	9.13114i	0.823097	+	0.299583i	0.104075	+	0.994569i	$0.466812\pi$
$930$		0			0
$931$	−4.26567	+	17.0892i	−0.139802	+	0.560076i
$932$		0			0
$933$	8.45741	−	23.2365i	0.276883	−	0.760730i
$934$		0			0
$935$	0.227902	−	0.271604i	0.00745321	−	0.00888239i
$936$		0			0
$937$	2.68860	−	15.2478i	0.0878326	−	0.498123i	−0.908877	−	0.417065i	$-0.863059\pi$
$937$	2.68860	−	15.2478i	0.0878326	−	0.498123i	0.996709	−	0.0810586i	$-0.0258301\pi$
$938$		0			0
$939$	9.78985	+	16.9565i	0.319480	+	0.553355i
$940$		0			0
$941$	10.6903	+	29.3713i	0.348494	+	0.957478i	0.982845	+	0.184434i	$0.0590450\pi$
$941$	10.6903	+	29.3713i	0.348494	+	0.957478i	−0.634351	+	0.773045i	$0.718733\pi$
$942$		0			0
$943$	5.89376	−	10.2083i	0.191927	−	0.332428i
$944$		0			0
$945$	0.0677899	+	0.0807889i	0.00220521	+	0.00262806i
$946$		0			0
$947$	−41.8843	+	7.38533i	−1.36106	+	0.239991i	−0.806046	−	0.591852i	$-0.798397\pi$
$947$	−41.8843	+	7.38533i	−1.36106	+	0.239991i	−0.555011	+	0.831843i	$0.687286\pi$
$948$		0			0
$949$			5.69914i			0.185002i
$950$		0			0
$951$			2.62937i			0.0852633i
$952$		0			0
$953$	−3.50644	+	0.618280i	−0.113585	+	0.0200281i	−0.230152	−	0.973155i	$-0.573922\pi$
$953$	−3.50644	+	0.618280i	−0.113585	+	0.0200281i	0.116567	+	0.993183i	$0.462811\pi$
$954$		0			0
$955$	0.314269	+	0.374531i	0.0101695	+	0.0121196i
$956$		0			0
$957$	3.30448	−	5.72352i	0.106819	−	0.185015i
$958$		0			0
$959$	9.49357	+	26.0834i	0.306563	+	0.842276i
$960$		0			0
$961$	−33.6436	−	58.2724i	−1.08528	−	1.87975i
$962$		0			0
$963$	2.31420	−	13.1245i	0.0745739	−	0.422930i
$964$		0			0
$965$	−0.551557	+	0.657320i	−0.0177552	+	0.0211599i
$966$		0			0
$967$	9.17254	−	25.2013i	0.294969	−	0.810420i	−0.700352	−	0.713797i	$-0.746974\pi$
$967$	9.17254	−	25.2013i	0.294969	−	0.810420i	0.995321	−	0.0966228i	$-0.0308041\pi$
$968$		0			0
$969$	−23.8681	+	17.3314i	−0.766753	+	0.556766i
$970$		0			0
$971$	−19.0983	−	6.95120i	−0.612892	−	0.223074i	0.0168761	−	0.999858i	$-0.494628\pi$
$971$	−19.0983	−	6.95120i	−0.612892	−	0.223074i	−0.629768	+	0.776783i	$0.716850\pi$
$972$		0			0
$973$	2.85854	+	2.39860i	0.0916407	+	0.0768957i
$974$		0			0
$975$	2.93911	+	0.518244i	0.0941268	+	0.0165971i
$976$		0			0
$977$	5.92441	−	3.42046i	0.189539	−	0.109430i	−0.402228	−	0.915540i	$-0.631764\pi$
$977$	5.92441	−	3.42046i	0.189539	−	0.109430i	0.591767	+	0.806109i	$0.298431\pi$
$978$		0			0
$979$	8.46696	−	3.08172i	0.270605	−	0.0984923i
$980$		0			0
$981$	9.71608	+	5.60958i	0.310211	+	0.179100i
$982$		0			0
$983$	38.1823	−	32.0388i	1.21783	−	1.02188i	0.218891	−	0.975749i	$-0.429756\pi$
$983$	38.1823	−	32.0388i	1.21783	−	1.02188i	0.998936	−	0.0461285i	$-0.0146884\pi$
$984$		0			0
$985$	0.0447703	+	0.253905i	0.00142650	+	0.00809009i
$986$		0			0
$987$	7.04576			0.224269
$988$		0			0
$989$	−4.48711			−0.142682
$990$		0			0
$991$	−3.37260	−	19.1270i	−0.107134	−	0.607588i	−0.990346	−	0.138614i	$-0.955735\pi$
$991$	−3.37260	−	19.1270i	−0.107134	−	0.607588i	0.883212	−	0.468973i	$-0.155376\pi$
$992$		0			0
$993$	10.6411	−	8.92894i	0.337685	−	0.283351i
$994$		0			0
$995$	1.28498	+	0.741883i	0.0407366	+	0.0235193i
$996$		0			0
$997$	0.365260	−	0.132944i	0.0115679	−	0.00421037i	−0.336230	−	0.941780i	$-0.609152\pi$
$997$	0.365260	−	0.132944i	0.0115679	−	0.00421037i	0.347798	+	0.937570i	$0.386930\pi$
$998$		0			0
$999$	3.69400	−	2.13273i	0.116873	−	0.0674766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.c.319.1	yes	12
4.3	odd	2		912.2.ci.d.319.1	yes	12
19.14	odd	18		912.2.ci.d.223.1	yes	12
76.71	even	18	inner	912.2.ci.c.223.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.c.223.1	✓	12	76.71	even	18	inner
912.2.ci.c.319.1	yes	12	1.1	even	1	trivial
912.2.ci.d.223.1	yes	12	19.14	odd	18
912.2.ci.d.319.1	yes	12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{3} +(0.0469641 - 0.0394076i) q^{5} +(1.48976 + 0.860113i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{3} +(0.0469641 - 0.0394076i) q^{5} +(1.48976 + 0.860113i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.740119 - 0.427308i) q^{11} +(0.588264 + 0.103727i) q^{13} +(-0.0469641 - 0.0394076i) q^{15} +(6.35893 + 2.31446i) q^{17} +(-3.13472 - 3.02878i) q^{19} +(0.588352 - 1.61648i) q^{21} +(3.05978 - 3.64650i) q^{23} +(-0.867588 + 4.92034i) q^{25} +(0.500000 + 0.866025i) q^{27} +(2.64493 + 7.26688i) q^{29} +(4.95699 - 8.58577i) q^{31} +(-0.549336 - 0.654673i) q^{33} +(0.103860 - 0.0183134i) q^{35} -4.26546i q^{37} -0.597339i q^{39} +(2.43866 - 0.430002i) q^{41} +(-0.605916 - 0.722102i) q^{43} +(-0.0306537 + 0.0530937i) q^{45} +(1.40086 + 3.84883i) q^{47} +(-2.02041 - 3.49946i) q^{49} +(1.17508 - 6.66423i) q^{51} +(4.83391 - 5.76083i) q^{53} +(0.0179199 - 0.0492344i) q^{55} +(-2.43843 + 3.61304i) q^{57} +(-0.268742 - 0.0978140i) q^{59} +(-3.13938 - 2.63425i) q^{61} +(-1.69409 - 0.298714i) q^{63} +(0.0317149 - 0.0183106i) q^{65} +(10.1697 - 3.70148i) q^{67} +(-4.12242 - 2.38008i) q^{69} +(1.45471 - 1.22064i) q^{71} +(1.65676 + 9.39595i) q^{73} +4.99624 q^{75} +1.47013 q^{77} +(-0.354603 - 2.01105i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-10.0086 - 5.77844i) q^{83} +(0.389849 - 0.141894i) q^{85} +(6.69719 - 3.86663i) q^{87} +(10.3830 + 1.83080i) q^{89} +(0.787154 + 0.660501i) q^{91} +(-9.31610 - 3.39078i) q^{93} +(-0.266577 - 0.0187124i) q^{95} +(1.48052 - 4.06769i) q^{97} +(-0.549336 + 0.654673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) \) 12 * q + 6 * q^5 - 18 * q^7	\( 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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