LMFDB - Embedded newform 912.2.ci.f.319.2

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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} + \cdots + 1367631 $ x^18 - 6x^17 - 3x^16 + 100x^15 - 171x^14 - 471x^13 + 1537x^12 + 321x^11 - 3936x^10 - 1317x^9 + 4941x^8 + 21078x^7 - 14829x^6 - 68589x^5 - 45711x^4 + 421452x^3 - 61938x^2 - 1219779*x + 1367631
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			319.2
Root			$-2.61262 + 0.231530i$ of defining polynomial
Character	$\chi$	$=$	912.319
Dual form			912.2.ci.f.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(-0.345737 + 0.290108i) q^{5} +(-0.993418 - 0.573550i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(-0.345737 + 0.290108i) q^{5} +(-0.993418 - 0.573550i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.09134 - 0.630083i) q^{11} +(-6.39019 - 1.12676i) q^{13} +(-0.345737 - 0.290108i) q^{15} +(-4.00915 - 1.45921i) q^{17} +(2.14602 + 3.79402i) q^{19} +(0.392332 - 1.07792i) q^{21} +(-5.76755 + 6.87349i) q^{23} +(-0.832869 + 4.72344i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.29392 - 6.30249i) q^{29} +(2.64248 - 4.57690i) q^{31} +(0.810019 + 0.965343i) q^{33} +(0.509853 - 0.0899008i) q^{35} -3.13949i q^{37} -6.48877i q^{39} +(-3.40942 + 0.601174i) q^{41} +(-6.46550 - 7.70528i) q^{43} +(0.225664 - 0.390861i) q^{45} +(3.37128 + 9.26251i) q^{47} +(-2.84208 - 4.92263i) q^{49} +(0.740861 - 4.20163i) q^{51} +(-7.68029 + 9.15302i) q^{53} +(-0.194523 + 0.534448i) q^{55} +(-3.36373 + 2.77224i) q^{57} +(10.0337 + 3.65196i) q^{59} +(-5.87608 - 4.93062i) q^{61} +(1.12967 + 0.199192i) q^{63} +(2.53621 - 1.46428i) q^{65} +(6.07297 - 2.21038i) q^{67} +(-7.77059 - 4.48635i) q^{69} +(-6.08682 + 5.10745i) q^{71} +(0.463830 + 2.63051i) q^{73} -4.79630 q^{75} -1.44554 q^{77} +(-2.29356 - 13.0074i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-3.21005 - 1.85332i) q^{83} +(1.80944 - 0.658583i) q^{85} +(5.80840 - 3.35348i) q^{87} +(9.48811 + 1.67301i) q^{89} +(5.70188 + 4.78444i) q^{91} +(4.96623 + 1.80756i) q^{93} +(-1.84263 - 0.689157i) q^{95} +(-0.447536 + 1.22960i) q^{97} +(-0.810019 + 0.965343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) $ 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * 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
$5$	−0.345737	+	0.290108i	−0.154618	+	0.129740i	−0.716815	−	0.697263i	$-0.754401\pi$
$5$	−0.345737	+	0.290108i	−0.154618	+	0.129740i	0.562197	+	0.827004i	$0.309956\pi$
$6$		0			0
$7$	−0.993418	−	0.573550i	−0.375477	−	0.216782i	0.300372	−	0.953822i	$-0.402889\pi$
$7$	−0.993418	−	0.573550i	−0.375477	−	0.216782i	−0.675848	+	0.737041i	$0.736223\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	1.09134	−	0.630083i	0.329050	−	0.189977i	−0.326369	−	0.945242i	$-0.605825\pi$
$11$	1.09134	−	0.630083i	0.329050	−	0.189977i	0.655419	+	0.755265i	$0.272492\pi$
$12$		0			0
$13$	−6.39019	−	1.12676i	−1.77232	−	0.312508i	−0.810408	−	0.585866i	$-0.800754\pi$
$13$	−6.39019	−	1.12676i	−1.77232	−	0.312508i	−0.961912	+	0.273358i	$0.911866\pi$
$14$		0			0
$15$	−0.345737	−	0.290108i	−0.0892689	−	0.0749055i
$16$		0			0
$17$	−4.00915	−	1.45921i	−0.972362	−	0.353911i	−0.193496	−	0.981101i	$-0.561983\pi$
$17$	−4.00915	−	1.45921i	−0.972362	−	0.353911i	−0.778866	+	0.627190i	$0.784205\pi$
$18$		0			0
$19$	2.14602	+	3.79402i	0.492331	+	0.870408i
$19$	2.14602	+	3.79402i	0.492331	+	0.870408i
$20$		0			0
$21$	0.392332	−	1.07792i	0.0856138	−	0.235222i
$22$		0			0
$23$	−5.76755	+	6.87349i	−1.20262	+	1.43322i	−0.330583	+	0.943777i	$0.607245\pi$
$23$	−5.76755	+	6.87349i	−1.20262	+	1.43322i	−0.872034	+	0.489445i	$0.837199\pi$
$24$		0			0
$25$	−0.832869	+	4.72344i	−0.166574	+	0.944687i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−2.29392	−	6.30249i	−0.425970	−	1.17034i	−0.948238	−	0.317561i	$-0.897136\pi$
$29$	−2.29392	−	6.30249i	−0.425970	−	1.17034i	0.522268	−	0.852781i	$-0.325086\pi$
$30$		0			0
$31$	2.64248	−	4.57690i	0.474603	−	0.822036i	−0.524974	−	0.851118i	$-0.675925\pi$
$31$	2.64248	−	4.57690i	0.474603	−	0.822036i	0.999577	+	0.0290819i	$0.00925835\pi$
$32$		0			0
$33$	0.810019	+	0.965343i	0.141006	+	0.168045i
$34$		0			0
$35$	0.509853	−	0.0899008i	0.0861809	−	0.0151960i
$36$		0			0
$37$		−	3.13949i		−	0.516130i	−0.966128	−	0.258065i	$-0.916915\pi$
$37$		−	3.13949i		−	0.516130i	0.966128	−	0.258065i	$-0.0830848\pi$
$38$		0			0
$39$		−	6.48877i		−	1.03903i
$40$		0			0
$41$	−3.40942	+	0.601174i	−0.532463	+	0.0938875i	−0.433414	−	0.901195i	$-0.642691\pi$
$41$	−3.40942	+	0.601174i	−0.532463	+	0.0938875i	−0.0990489	+	0.995083i	$0.531580\pi$
$42$		0			0
$43$	−6.46550	−	7.70528i	−0.985979	−	1.17504i	−0.984560	−	0.175045i	$-0.943993\pi$
$43$	−6.46550	−	7.70528i	−0.985979	−	1.17504i	−0.00141867	−	0.999999i	$-0.500452\pi$
$44$		0			0
$45$	0.225664	−	0.390861i	0.0336400	−	0.0582662i
$46$		0			0
$47$	3.37128	+	9.26251i	0.491751	+	1.35108i	0.899076	+	0.437792i	$0.144239\pi$
$47$	3.37128	+	9.26251i	0.491751	+	1.35108i	−0.407325	+	0.913283i	$0.633538\pi$
$48$		0			0
$49$	−2.84208	−	4.92263i	−0.406011	−	0.703232i
$50$		0			0
$51$	0.740861	−	4.20163i	0.103741	−	0.588346i
$52$		0			0
$53$	−7.68029	+	9.15302i	−1.05497	+	1.25726i	−0.0897105	+	0.995968i	$0.528594\pi$
$53$	−7.68029	+	9.15302i	−1.05497	+	1.25726i	−0.965259	+	0.261296i	$0.915850\pi$
$54$		0			0
$55$	−0.194523	+	0.534448i	−0.0262295	+	0.0720650i
$56$		0			0
$57$	−3.36373	+	2.77224i	−0.445537	+	0.367192i
$58$		0			0
$59$	10.0337	+	3.65196i	1.30627	+	0.475445i	0.899035	−	0.437877i	$-0.144269\pi$
$59$	10.0337	+	3.65196i	1.30627	+	0.475445i	0.407239	+	0.913322i	$0.366492\pi$
$60$		0			0
$61$	−5.87608	−	4.93062i	−0.752355	−	0.631301i	0.183770	−	0.982969i	$-0.441170\pi$
$61$	−5.87608	−	4.93062i	−0.752355	−	0.631301i	−0.936125	+	0.351669i	$0.885614\pi$
$62$		0			0
$63$	1.12967	+	0.199192i	0.142325	+	0.0250958i
$64$		0			0
$65$	2.53621	−	1.46428i	0.314578	−	0.181622i
$66$		0			0
$67$	6.07297	−	2.21038i	0.741931	−	0.270041i	0.0567248	−	0.998390i	$-0.481934\pi$
$67$	6.07297	−	2.21038i	0.741931	−	0.270041i	0.685206	+	0.728349i	$0.259712\pi$
$68$		0			0
$69$	−7.77059	−	4.48635i	−0.935470	−	0.540094i
$70$		0			0
$71$	−6.08682	+	5.10745i	−0.722373	+	0.606143i	−0.928041	−	0.372479i	$-0.878508\pi$
$71$	−6.08682	+	5.10745i	−0.722373	+	0.606143i	0.205668	+	0.978622i	$0.434063\pi$
$72$		0			0
$73$	0.463830	+	2.63051i	0.0542872	+	0.307878i	0.999846	−	0.0175745i	$-0.00559443\pi$
$73$	0.463830	+	2.63051i	0.0542872	+	0.307878i	−0.945558	+	0.325453i	$0.894483\pi$
$74$		0			0
$75$	−4.79630			−0.553829
$76$		0			0
$77$	−1.44554			−0.164734
$78$		0			0
$79$	−2.29356	−	13.0074i	−0.258046	−	1.46345i	−0.788132	−	0.615506i	$-0.788951\pi$
$79$	−2.29356	−	13.0074i	−0.258046	−	1.46345i	0.530086	−	0.847944i	$-0.322160\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−3.21005	−	1.85332i	−0.352348	−	0.203428i	0.313371	−	0.949631i	$-0.398542\pi$
$83$	−3.21005	−	1.85332i	−0.352348	−	0.203428i	−0.665719	+	0.746202i	$0.731875\pi$
$84$		0			0
$85$	1.80944	−	0.658583i	0.196261	−	0.0714333i
$86$		0			0
$87$	5.80840	−	3.35348i	0.622726	−	0.359531i
$88$		0			0
$89$	9.48811	+	1.67301i	1.00574	+	0.177339i	0.652172	−	0.758071i	$-0.273858\pi$
$89$	9.48811	+	1.67301i	1.00574	+	0.177339i	0.353566	+	0.935410i	$0.384969\pi$
$90$		0			0
$91$	5.70188	+	4.78444i	0.597719	+	0.501546i
$92$		0			0
$93$	4.96623	+	1.80756i	0.514974	+	0.187435i
$94$		0			0
$95$	−1.84263	−	0.689157i	−0.189050	−	0.0707060i
$96$		0			0
$97$	−0.447536	+	1.22960i	−0.0454404	+	0.124847i	−0.960337	−	0.278841i	$-0.910050\pi$
$97$	−0.447536	+	1.22960i	−0.0454404	+	0.124847i	0.914897	+	0.403688i	$0.132272\pi$
$98$		0			0
$99$	−0.810019	+	0.965343i	−0.0814100	+	0.0970206i
$100$		0			0
$101$	2.08089	−	11.8013i	0.207056	−	1.17427i	−0.687115	−	0.726549i	$-0.741123\pi$
$101$	2.08089	−	11.8013i	0.207056	−	1.17427i	0.894171	−	0.447725i	$-0.147766\pi$
$102$		0			0
$103$	−0.863454	−	1.49555i	−0.0850786	−	0.147361i	0.820346	−	0.571867i	$-0.193781\pi$
$103$	−0.863454	−	1.49555i	−0.0850786	−	0.147361i	−0.905425	+	0.424507i	$0.860447\pi$
$104$		0			0
$105$	0.177070	+	0.486496i	0.0172803	+	0.0474772i
$106$		0			0
$107$	−2.29100	+	3.96813i	−0.221479	+	0.383614i	−0.955257	−	0.295776i	$-0.904422\pi$
$107$	−2.29100	+	3.96813i	−0.221479	+	0.383614i	0.733778	+	0.679389i	$0.237755\pi$
$108$		0			0
$109$	4.13325	+	4.92582i	0.395894	+	0.471808i	0.926763	−	0.375646i	$-0.122579\pi$
$109$	4.13325	+	4.92582i	0.395894	+	0.471808i	−0.530870	+	0.847453i	$0.678135\pi$
$110$		0			0
$111$	3.09180	−	0.545167i	0.293460	−	0.0517450i
$112$		0			0
$113$			14.5994i			1.37340i	0.726942	+	0.686698i	$0.240941\pi$
$113$			14.5994i			1.37340i	−0.726942	+	0.686698i	$0.759059\pi$
$114$		0			0
$115$		−	4.04963i		−	0.377630i
$116$		0			0
$117$	6.39019	−	1.12676i	0.590773	−	0.104169i
$118$		0			0
$119$	3.14583	+	3.74906i	0.288378	+	0.343676i
$120$		0			0
$121$	−4.70599	+	8.15102i	−0.427817	+	0.741001i
$122$		0			0
$123$	−1.18408	−	3.25324i	−0.106765	−	0.293334i
$124$		0			0
$125$	−2.21067	−	3.82900i	−0.197728	−	0.342476i
$126$		0			0
$127$	−3.08507	+	17.4963i	−0.273755	+	1.55254i	0.469133	+	0.883128i	$0.344567\pi$
$127$	−3.08507	+	17.4963i	−0.273755	+	1.55254i	−0.742888	+	0.669416i	$0.766544\pi$
$128$		0			0
$129$	6.46550	−	7.70528i	0.569255	−	0.678412i
$130$		0			0
$131$	−2.49975	+	6.86800i	−0.218404	+	0.600060i	−0.999710	−	0.0240885i	$-0.992332\pi$
$131$	−2.49975	+	6.86800i	−0.218404	+	0.600060i	0.781306	+	0.624148i	$0.214554\pi$
$132$		0			0
$133$	0.0441677	−	4.99990i	0.00382983	−	0.433546i
$134$		0			0
$135$	0.424109	+	0.154363i	0.0365015	+	0.0132855i
$136$		0			0
$137$	8.23744	+	6.91203i	0.703772	+	0.590535i	0.922844	−	0.385174i	$-0.125859\pi$
$137$	8.23744	+	6.91203i	0.703772	+	0.590535i	−0.219072	+	0.975709i	$0.570303\pi$
$138$		0			0
$139$	−18.9469	−	3.34084i	−1.60705	−	0.283367i	−0.703129	−	0.711062i	$-0.748214\pi$
$139$	−18.9469	−	3.34084i	−1.60705	−	0.283367i	−0.903923	+	0.427696i	$0.859326\pi$
$140$		0			0
$141$	−8.53637	+	4.92848i	−0.718892	+	0.415053i
$142$		0			0
$143$	−7.68380	+	2.79667i	−0.642551	+	0.233870i
$144$		0			0
$145$	2.62149	+	1.51352i	0.217703	+	0.125691i
$146$		0			0
$147$	4.35432	−	3.65371i	0.359138	−	0.301353i
$148$		0			0
$149$	−2.86619	−	16.2549i	−0.234807	−	1.33166i	−0.843020	−	0.537883i	$-0.819224\pi$
$149$	−2.86619	−	16.2549i	−0.234807	−	1.33166i	0.608213	−	0.793774i	$-0.291887\pi$
$150$		0			0
$151$	2.24853			0.182983			0.0914916	−	0.995806i	$-0.470837\pi$
$151$	2.24853			0.182983			0.0914916	+	0.995806i	$0.470837\pi$
$152$		0			0
$153$	4.26645			0.344922
$154$		0			0
$155$	0.414194	+	2.34901i	0.0332688	+	0.188677i
$156$		0			0
$157$	4.97845	−	4.17742i	0.397324	−	0.333394i	−0.422134	−	0.906533i	$-0.638719\pi$
$157$	4.97845	−	4.17742i	0.397324	−	0.333394i	0.819458	+	0.573139i	$0.194275\pi$
$158$		0			0
$159$	−10.3476	−	5.97421i	−0.820620	−	0.473785i
$160$		0			0
$161$	9.67188	−	3.52028i	0.762251	−	0.277437i
$162$		0			0
$163$	13.7890	−	7.96109i	1.08004	−	0.623561i	0.149132	−	0.988817i	$-0.452352\pi$
$163$	13.7890	−	7.96109i	1.08004	−	0.623561i	0.930907	+	0.365257i	$0.119019\pi$
$164$		0			0
$165$	−0.560107	−	0.0987620i	−0.0436043	−	0.00768861i
$166$		0			0
$167$	7.57630	+	6.35727i	0.586272	+	0.491941i	0.887000	−	0.461769i	$-0.152785\pi$
$167$	7.57630	+	6.35727i	0.586272	+	0.491941i	−0.300728	+	0.953710i	$0.597230\pi$
$168$		0			0
$169$	27.3489	+	9.95420i	2.10376	+	0.765708i
$170$		0			0
$171$	−3.31423	−	2.83123i	−0.253446	−	0.216510i
$172$		0			0
$173$	−7.19786	+	19.7760i	−0.547244	+	1.50354i	0.290173	+	0.956974i	$0.406287\pi$
$173$	−7.19786	+	19.7760i	−0.547244	+	1.50354i	−0.837417	+	0.546565i	$0.815935\pi$
$174$		0			0
$175$	3.53652	−	4.21466i	0.267335	−	0.318598i
$176$		0			0
$177$	−1.85415	+	10.5154i	−0.139366	+	0.790386i
$178$		0			0
$179$	10.1500	+	17.5802i	0.758644	+	1.31401i	0.943542	+	0.331252i	$0.107471\pi$
$179$	10.1500	+	17.5802i	0.758644	+	1.31401i	−0.184899	+	0.982758i	$0.559196\pi$
$180$		0			0
$181$	−2.32528	−	6.38864i	−0.172836	−	0.474864i	0.822784	−	0.568355i	$-0.192420\pi$
$181$	−2.32528	−	6.38864i	−0.172836	−	0.474864i	−0.995620	+	0.0934904i	$0.970198\pi$
$182$		0			0
$183$	3.83534	−	6.64300i	0.283516	−	0.491065i
$184$		0			0
$185$	0.910792	+	1.08544i	0.0669628	+	0.0798031i
$186$		0			0
$187$	−5.29476	+	0.933608i	−0.387191	+	0.0682722i
$188$		0			0
$189$			1.14710i			0.0834393i
$190$		0			0
$191$			12.4753i			0.902681i	0.892352	+	0.451341i	$0.149054\pi$
$191$			12.4753i			0.902681i	−0.892352	+	0.451341i	$0.850946\pi$
$192$		0			0
$193$	15.0298	−	2.65017i	1.08187	−	0.190763i	0.395829	−	0.918324i	$-0.370457\pi$
$193$	15.0298	−	2.65017i	1.08187	−	0.190763i	0.686043	+	0.727561i	$0.259346\pi$
$194$		0			0
$195$	1.88244	+	2.24341i	0.134805	+	0.160654i
$196$		0			0
$197$	9.19899	−	15.9331i	0.655401	−	1.13519i	−0.326392	−	0.945234i	$-0.605833\pi$
$197$	9.19899	−	15.9331i	0.655401	−	1.13519i	0.981793	−	0.189953i	$-0.0608336\pi$
$198$		0			0
$199$	0.670160	+	1.84125i	0.0475064	+	0.130523i	0.961177	−	0.275933i	$-0.0889868\pi$
$199$	0.670160	+	1.84125i	0.0475064	+	0.130523i	−0.913671	+	0.406456i	$0.866765\pi$
$200$		0			0
$201$	3.23136	+	5.59688i	0.227922	+	0.394773i
$202$		0			0
$203$	−1.33597	+	7.57668i	−0.0937670	+	0.531779i
$204$		0			0
$205$	1.00436	−	1.19695i	0.0701475	−	0.0835985i
$206$		0			0
$207$	3.06885	−	8.43159i	0.213300	−	0.586036i
$208$		0			0
$209$	4.73258	+	2.78838i	0.327359	+	0.192876i
$210$		0			0
$211$	−1.44093	−	0.524454i	−0.0991975	−	0.0361049i	0.291945	−	0.956435i	$-0.405698\pi$
$211$	−1.44093	−	0.524454i	−0.0991975	−	0.0361049i	−0.391142	+	0.920330i	$0.627920\pi$
$212$		0			0
$213$	−6.08682	−	5.10745i	−0.417062	−	0.349957i
$214$		0			0
$215$	4.47072	+	0.788309i	0.304901	+	0.0537623i
$216$		0			0
$217$	−5.25017	+	3.03119i	−0.356405	+	0.205770i
$218$		0			0
$219$	−2.51001	+	0.913567i	−0.169610	+	0.0617332i
$220$		0			0
$221$	23.9751	+	13.8420i	1.61274	+	0.931114i
$222$		0			0
$223$	15.5124	−	13.0165i	1.03879	−	0.871647i	0.0469175	−	0.998899i	$-0.485060\pi$
$223$	15.5124	−	13.0165i	1.03879	−	0.871647i	0.991870	+	0.127252i	$0.0406158\pi$
$224$		0			0
$225$	−0.832869	−	4.72344i	−0.0555246	−	0.314896i
$226$		0			0
$227$	−25.6706			−1.70382			−0.851908	−	0.523691i	$-0.824555\pi$
$227$	−25.6706			−1.70382			−0.851908	+	0.523691i	$0.824555\pi$
$228$		0			0
$229$	−2.90313			−0.191844			−0.0959221	−	0.995389i	$-0.530580\pi$
$229$	−2.90313			−0.191844			−0.0959221	+	0.995389i	$0.530580\pi$
$230$		0			0
$231$	−0.251015	−	1.42358i	−0.0165156	−	0.0936644i
$232$		0			0
$233$	7.20495	−	6.04567i	0.472012	−	0.396065i	−0.375516	−	0.926816i	$-0.622534\pi$
$233$	7.20495	−	6.04567i	0.472012	−	0.396065i	0.847528	+	0.530751i	$0.178090\pi$
$234$		0			0
$235$	−3.85270	−	2.22436i	−0.251323	−	0.145101i
$236$		0			0
$237$	12.4115	−	4.51743i	0.806217	−	0.293439i
$238$		0			0
$239$	5.53002	−	3.19276i	0.357707	−	0.206522i	−0.310367	−	0.950617i	$-0.600452\pi$
$239$	5.53002	−	3.19276i	0.357707	−	0.206522i	0.668075	+	0.744094i	$0.267119\pi$
$240$		0			0
$241$	2.91521	+	0.514030i	0.187785	+	0.0331116i	0.266750	−	0.963766i	$-0.414050\pi$
$241$	2.91521	+	0.514030i	0.187785	+	0.0331116i	−0.0789646	+	0.996877i	$0.525161\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	2.41071	+	0.877425i	0.154014	+	0.0560566i
$246$		0			0
$247$	−9.43851	−	26.6626i	−0.600558	−	1.69650i
$248$		0			0
$249$	1.26775	−	3.48310i	0.0803402	−	0.220733i
$250$		0			0
$251$	5.50822	−	6.56444i	0.347676	−	0.414344i	−0.563661	−	0.826007i	$-0.690607\pi$
$251$	5.50822	−	6.56444i	0.347676	−	0.414344i	0.911336	+	0.411663i	$0.135052\pi$
$252$		0			0
$253$	−1.96346	+	11.1353i	−0.123442	+	0.700072i
$254$		0			0
$255$	0.962784	+	1.66759i	0.0602919	+	0.104429i
$256$		0			0
$257$	−2.52809	−	6.94588i	−0.157698	−	0.433272i	0.835531	−	0.549443i	$-0.185160\pi$
$257$	−2.52809	−	6.94588i	−0.157698	−	0.433272i	−0.993229	+	0.116171i	$0.962938\pi$
$258$		0			0
$259$	−1.80066	+	3.11883i	−0.111887	+	0.193795i
$260$		0			0
$261$	4.31115	+	5.13783i	0.266854	+	0.318024i
$262$		0			0
$263$	−16.2693	+	2.86872i	−1.00321	+	0.176893i	−0.651040	−	0.759043i	$-0.725667\pi$
$263$	−16.2693	+	2.86872i	−1.00321	+	0.176893i	−0.352169	+	0.935936i	$0.614556\pi$
$264$		0			0
$265$		−	5.39265i		−	0.331268i
$266$		0			0
$267$			9.63448i			0.589621i
$268$		0			0
$269$	−13.7156	+	2.41842i	−0.836252	+	0.147454i	−0.575346	−	0.817910i	$-0.695132\pi$
$269$	−13.7156	+	2.41842i	−0.836252	+	0.147454i	−0.260906	+	0.965364i	$0.584021\pi$
$270$		0			0
$271$	5.90186	+	7.03357i	0.358513	+	0.427259i	0.914910	−	0.403657i	$-0.132261\pi$
$271$	5.90186	+	7.03357i	0.358513	+	0.427259i	−0.556397	+	0.830916i	$0.687817\pi$
$272$		0			0
$273$	−3.72164	+	6.44606i	−0.225244	+	0.390133i
$274$		0			0
$275$	2.06722	+	5.67963i	0.124658	+	0.342495i
$276$		0			0
$277$	2.27533	+	3.94099i	0.136712	+	0.236791i	0.926250	−	0.376910i	$-0.123013\pi$
$277$	2.27533	+	3.94099i	0.136712	+	0.236791i	−0.789538	+	0.613701i	$0.789680\pi$
$278$		0			0
$279$	−0.917723	+	5.20466i	−0.0549426	+	0.311595i
$280$		0			0
$281$	−14.4117	+	17.1751i	−0.859727	+	1.02458i	0.139681	+	0.990197i	$0.455392\pi$
$281$	−14.4117	+	17.1751i	−0.859727	+	1.02458i	−0.999409	+	0.0343866i	$0.989052\pi$
$282$		0			0
$283$	−1.87946	+	5.16379i	−0.111723	+	0.306955i	−0.982936	−	0.183950i	$-0.941112\pi$
$283$	−1.87946	+	5.16379i	−0.111723	+	0.306955i	0.871213	+	0.490905i	$0.163334\pi$
$284$		0			0
$285$	0.358717	−	1.93431i	0.0212486	−	0.114579i
$286$		0			0
$287$	3.73179	+	1.35826i	0.220280	+	0.0801755i
$288$		0			0
$289$	0.921241	+	0.773013i	0.0541907	+	0.0454714i
$290$		0			0
$291$	−1.28863	−	0.227220i	−0.0755408	−	0.0133199i
$292$		0			0
$293$	8.15482	−	4.70819i	0.476410	−	0.275055i	−0.242509	−	0.970149i	$-0.577971\pi$
$293$	8.15482	−	4.70819i	0.476410	−	0.275055i	0.718919	+	0.695094i	$0.244637\pi$
$294$		0			0
$295$	−4.52848	+	1.64823i	−0.263658	+	0.0959637i
$296$		0			0
$297$	−1.09134	−	0.630083i	−0.0633257	−	0.0365611i
$298$		0			0
$299$	44.6005	−	37.4243i	2.57931	−	2.16430i
$300$		0			0
$301$	2.00358	+	11.3629i	0.115484	+	0.654944i
$302$		0			0
$303$	11.9834			0.688426
$304$		0			0
$305$	3.46199			0.198233
$306$		0			0
$307$	0.946832	+	5.36975i	0.0540385	+	0.306468i	0.999833	−	0.0182993i	$-0.00582518\pi$
$307$	0.946832	+	5.36975i	0.0540385	+	0.306468i	−0.945794	+	0.324767i	$0.894714\pi$
$308$		0			0
$309$	1.32289	−	1.11003i	0.0752565	−	0.0631477i
$310$		0			0
$311$	−16.7417	−	9.66584i	−0.949336	−	0.548099i	−0.0564612	−	0.998405i	$-0.517982\pi$
$311$	−16.7417	−	9.66584i	−0.949336	−	0.548099i	−0.892875	+	0.450306i	$0.851315\pi$
$312$		0			0
$313$	−3.98062	+	1.44883i	−0.224998	+	0.0818926i	−0.452059	−	0.891988i	$-0.649310\pi$
$313$	−3.98062	+	1.44883i	−0.224998	+	0.0818926i	0.227061	+	0.973880i	$0.427088\pi$
$314$		0			0
$315$	−0.448357	+	0.258859i	−0.0252621	+	0.0145851i
$316$		0			0
$317$	−7.68959	−	1.35588i	−0.431890	−	0.0761539i	−0.0465231	−	0.998917i	$-0.514814\pi$
$317$	−7.68959	−	1.35588i	−0.431890	−	0.0761539i	−0.385367	+	0.922763i	$0.625925\pi$
$318$		0			0
$319$	−6.47452	−	5.43277i	−0.362504	−	0.304177i
$320$		0			0
$321$	−4.30567	−	1.56714i	−0.240319	−	0.0874690i
$322$		0			0
$323$	−3.06743	−	18.3423i	−0.170677	−	1.02059i
$324$		0			0
$325$	10.6444	−	29.2452i	0.590444	−	1.62223i
$326$		0			0
$327$	−4.13325	+	4.92582i	−0.228569	+	0.272398i
$328$		0			0
$329$	1.96343	−	11.1351i	0.108247	−	0.613900i
$330$		0			0
$331$	12.4730	+	21.6039i	0.685578	+	1.18746i	0.973255	+	0.229728i	$0.0737838\pi$
$331$	12.4730	+	21.6039i	0.685578	+	1.18746i	−0.287677	+	0.957728i	$0.592883\pi$
$332$		0			0
$333$	1.07377	+	2.95016i	0.0588422	+	0.161668i
$334$		0			0
$335$	−1.45840	+	2.52603i	−0.0796810	+	0.138012i
$336$		0			0
$337$	2.59966	+	3.09815i	0.141612	+	0.168767i	0.832189	−	0.554492i	$-0.187088\pi$
$337$	2.59966	+	3.09815i	0.141612	+	0.168767i	−0.690576	+	0.723259i	$0.742643\pi$
$338$		0			0
$339$	−14.3776	+	2.53516i	−0.780885	+	0.137691i
$340$		0			0
$341$		−	6.65992i		−	0.360655i
$342$		0			0
$343$			14.5500i			0.785627i
$344$		0			0
$345$	3.98811	−	0.703211i	0.214713	−	0.0378596i
$346$		0			0
$347$	−16.0011	−	19.0694i	−0.858984	−	1.02370i	−0.999435	−	0.0336098i	$-0.989300\pi$
$347$	−16.0011	−	19.0694i	−0.858984	−	1.02370i	0.140451	−	0.990088i	$-0.455145\pi$
$348$		0			0
$349$	0.667220	−	1.15566i	0.0357155	−	0.0618610i	−0.847615	−	0.530612i	$-0.821962\pi$
$349$	0.667220	−	1.15566i	0.0357155	−	0.0618610i	0.883331	+	0.468750i	$0.155296\pi$
$350$		0			0
$351$	2.21929	+	6.09745i	0.118457	+	0.325458i
$352$		0			0
$353$	−8.57112	−	14.8456i	−0.456195	−	0.790153i	0.542561	−	0.840016i	$-0.317455\pi$
$353$	−8.57112	−	14.8456i	−0.456195	−	0.790153i	−0.998756	+	0.0498637i	$0.984121\pi$
$354$		0			0
$355$	0.622729	−	3.53167i	0.0330510	−	0.187442i
$356$		0			0
$357$	−3.14583	+	3.74906i	−0.166495	+	0.198421i
$358$		0			0
$359$	−7.88443	+	21.6623i	−0.416124	+	1.14329i	0.537755	+	0.843101i	$0.319273\pi$
$359$	−7.88443	+	21.6623i	−0.416124	+	1.14329i	−0.953879	+	0.300191i	$0.902950\pi$
$360$		0			0
$361$	−9.78920	+	16.2841i	−0.515221	+	0.857057i
$362$		0			0
$363$	−8.84437	−	3.21909i	−0.464209	−	0.168958i
$364$		0			0
$365$	−0.923496	−	0.774905i	−0.0483380	−	0.0405604i
$366$		0			0
$367$	19.1452	+	3.37582i	0.999372	+	0.176216i	0.649321	−	0.760514i	$-0.275053\pi$
$367$	19.1452	+	3.37582i	0.999372	+	0.176216i	0.350051	+	0.936731i	$0.386164\pi$
$368$		0			0
$369$	2.99820	−	1.73101i	0.156080	−	0.0901128i
$370$		0			0
$371$	12.8795	−	4.68774i	0.668668	−	0.243375i
$372$		0			0
$373$	−10.5154	−	6.07109i	−0.544468	−	0.314349i	0.202420	−	0.979299i	$-0.435120\pi$
$373$	−10.5154	−	6.07109i	−0.544468	−	0.314349i	−0.746888	+	0.664950i	$0.768453\pi$
$374$		0			0
$375$	3.38695	−	2.84198i	0.174901	−	0.146759i
$376$		0			0
$377$	7.55716	+	42.8588i	0.389214	+	2.20734i
$378$		0			0
$379$	−20.1216			−1.03358			−0.516788	−	0.856114i	$-0.672872\pi$
$379$	−20.1216			−1.03358			−0.516788	+	0.856114i	$0.672872\pi$
$380$		0			0
$381$	−17.7662			−0.910189
$382$		0			0
$383$	−3.10309	−	17.5985i	−0.158560	−	0.899241i	−0.955458	−	0.295127i	$-0.904638\pi$
$383$	−3.10309	−	17.5985i	−0.158560	−	0.899241i	0.796898	−	0.604114i	$-0.206473\pi$
$384$		0			0
$385$	0.499776	−	0.419362i	0.0254709	−	0.0213727i
$386$		0			0
$387$	8.71094	+	5.02926i	0.442802	+	0.255652i
$388$		0			0
$389$	−2.36299	+	0.860058i	−0.119808	+	0.0436067i	−0.401229	−	0.915978i	$-0.631417\pi$
$389$	−2.36299	+	0.860058i	−0.119808	+	0.0436067i	0.281420	+	0.959585i	$0.409195\pi$
$390$		0			0
$391$	33.1528	−	19.1408i	1.67661	−	0.967992i
$392$		0			0
$393$	−7.19773	−	1.26915i	−0.363078	−	0.0640204i
$394$		0			0
$395$	4.56653	+	3.83177i	0.229767	+	0.192797i
$396$		0			0
$397$	−20.0849	−	7.31032i	−1.00803	−	0.366895i	−0.215357	−	0.976535i	$-0.569091\pi$
$397$	−20.0849	−	7.31032i	−1.00803	−	0.366895i	−0.792678	+	0.609641i	$0.791314\pi$
$398$		0			0
$399$	4.93161	−	0.824727i	0.246889	−	0.0412880i
$400$		0			0
$401$	−4.61950	+	12.6920i	−0.230687	+	0.633807i	−0.999987	−	0.00508032i	$-0.998383\pi$
$401$	−4.61950	+	12.6920i	−0.230687	+	0.633807i	0.769300	+	0.638888i	$0.220605\pi$
$402$		0			0
$403$	−22.0430	+	26.2698i	−1.09804	+	1.30859i
$404$		0			0
$405$	−0.0783722	+	0.444471i	−0.00389435	+	0.0220859i
$406$		0			0
$407$	−1.97814	−	3.42624i	−0.0980528	−	0.169833i
$408$		0			0
$409$	−10.3009	−	28.3014i	−0.509346	−	1.39942i	−0.881914	−	0.471411i	$-0.843745\pi$
$409$	−10.3009	−	28.3014i	−0.509346	−	1.39942i	0.372568	−	0.928005i	$-0.378477\pi$
$410$		0			0
$411$	−5.37661	+	9.31255i	−0.265208	+	0.459354i
$412$		0			0
$413$	−7.87306	−	9.38275i	−0.387408	−	0.461695i
$414$		0			0
$415$	1.64750	−	0.290498i	0.0808724	−	0.0142600i
$416$		0			0
$417$		−	19.2391i		−	0.942145i
$418$		0			0
$419$		−	10.4841i		−	0.512184i	−0.966652	−	0.256092i	$-0.917565\pi$
$419$		−	10.4841i		−	0.512184i	0.966652	−	0.256092i	$-0.0824350\pi$
$420$		0			0
$421$	−12.8629	+	2.26807i	−0.626898	+	0.110539i	−0.478067	−	0.878324i	$-0.658662\pi$
$421$	−12.8629	+	2.26807i	−0.626898	+	0.110539i	−0.148831	+	0.988863i	$0.547551\pi$
$422$		0			0
$423$	−6.33593	−	7.55086i	−0.308063	−	0.367136i
$424$		0			0
$425$	10.2316	−	17.7216i	0.496305	−	0.859626i
$426$		0			0
$427$	3.00945	+	8.26839i	0.145637	+	0.400135i
$428$		0			0
$429$	−4.08846	−	7.08143i	−0.197393	−	0.341895i
$430$		0			0
$431$	−5.85069	+	33.1809i	−0.281818	+	1.59827i	0.434617	+	0.900616i	$0.356884\pi$
$431$	−5.85069	+	33.1809i	−0.281818	+	1.59827i	−0.716435	+	0.697654i	$0.754227\pi$
$432$		0			0
$433$	−2.21020	+	2.63401i	−0.106215	+	0.126583i	−0.816533	−	0.577299i	$-0.804107\pi$
$433$	−2.21020	+	2.63401i	−0.106215	+	0.126583i	0.710318	+	0.703881i	$0.248551\pi$
$434$		0			0
$435$	−1.03531	+	2.84449i	−0.0496393	+	0.136383i
$436$		0			0
$437$	−38.4555	−	7.13155i	−1.83957	−	0.341148i
$438$		0			0
$439$	3.64682	+	1.32734i	0.174053	+	0.0633503i	0.427577	−	0.903979i	$-0.359367\pi$
$439$	3.64682	+	1.32734i	0.174053	+	0.0633503i	−0.253524	+	0.967329i	$0.581590\pi$
$440$		0			0
$441$	4.35432	+	3.65371i	0.207349	+	0.173986i
$442$		0			0
$443$	−7.36498	−	1.29864i	−0.349921	−	0.0617005i	−0.00407456	−	0.999992i	$-0.501297\pi$
$443$	−7.36498	−	1.29864i	−0.349921	−	0.0617005i	−0.345846	+	0.938291i	$0.612408\pi$
$444$		0			0
$445$	−3.76575	+	2.17415i	−0.178514	+	0.103065i
$446$		0			0
$447$	15.5103	−	5.64528i	0.733612	−	0.267013i
$448$		0			0
$449$	−13.8206	−	7.97934i	−0.652235	−	0.376568i	0.137077	−	0.990560i	$-0.456229\pi$
$449$	−13.8206	−	7.97934i	−0.652235	−	0.376568i	−0.789312	+	0.613992i	$0.789563\pi$
$450$		0			0
$451$	−3.34204	+	2.80430i	−0.157370	+	0.132049i
$452$		0			0
$453$	0.390454	+	2.21437i	0.0183451	+	0.104040i
$454$		0			0
$455$	−3.35936			−0.157489
$456$		0			0
$457$	−31.2832			−1.46337			−0.731684	−	0.681645i	$-0.761265\pi$
$457$	−31.2832			−1.46337			−0.731684	+	0.681645i	$0.761265\pi$
$458$		0			0
$459$	0.740861	+	4.20163i	0.0345804	+	0.196115i
$460$		0			0
$461$	−4.97429	+	4.17392i	−0.231676	+	0.194399i	−0.751234	−	0.660036i	$-0.770541\pi$
$461$	−4.97429	+	4.17392i	−0.231676	+	0.194399i	0.519558	+	0.854435i	$0.326097\pi$
$462$		0			0
$463$	−29.7320	−	17.1658i	−1.38176	−	0.797761i	−0.389394	−	0.921071i	$-0.627316\pi$
$463$	−29.7320	−	17.1658i	−1.38176	−	0.797761i	−0.992368	+	0.123310i	$0.960649\pi$
$464$		0			0
$465$	−2.24140	+	0.815802i	−0.103942	+	0.0378319i
$466$		0			0
$467$	33.3097	−	19.2313i	1.54139	−	0.889920i	0.542635	−	0.839968i	$-0.317427\pi$
$467$	33.3097	−	19.2313i	1.54139	−	0.889920i	0.998752	−	0.0499518i	$-0.0159068\pi$
$468$		0			0
$469$	−7.30076	−	1.28732i	−0.337118	−	0.0594430i
$470$		0			0
$471$	4.97845	+	4.17742i	0.229395	+	0.192485i
$472$		0			0
$473$	−11.9110	−	4.33525i	−0.547668	−	0.199335i
$474$		0			0
$475$	−19.7082	+	6.97666i	−0.904273	+	0.320111i
$476$		0			0
$477$	4.08660	−	11.2278i	0.187112	−	0.514087i
$478$		0			0
$479$	−12.4800	+	14.8731i	−0.570225	+	0.679567i	−0.971677	−	0.236313i	$-0.924061\pi$
$479$	−12.4800	+	14.8731i	−0.570225	+	0.679567i	0.401453	+	0.915880i	$0.368505\pi$
$480$		0			0
$481$	−3.53747	+	20.0620i	−0.161295	+	0.914747i
$482$		0			0
$483$	5.14630	+	8.91365i	0.234165	+	0.405585i
$484$		0			0
$485$	−0.201985	−	0.554951i	−0.00917169	−	0.0251990i
$486$		0			0
$487$	−0.921131	+	1.59545i	−0.0417404	+	0.0722965i	−0.886141	−	0.463416i	$-0.846624\pi$
$487$	−0.921131	+	1.59545i	−0.0417404	+	0.0722965i	0.844400	+	0.535713i	$0.179957\pi$
$488$		0			0
$489$	10.2346	+	12.1971i	0.462824	+	0.551572i
$490$		0			0
$491$	14.1909	−	2.50225i	0.640428	−	0.112925i	0.156002	−	0.987757i	$-0.450139\pi$
$491$	14.1909	−	2.50225i	0.640428	−	0.112925i	0.484427	+	0.874832i	$0.339028\pi$
$492$		0			0
$493$			28.6149i			1.28875i
$494$		0			0
$495$		−	0.568748i		−	0.0255633i
$496$		0			0
$497$	8.97614	−	1.58273i	0.402635	−	0.0709954i
$498$		0			0
$499$	−6.73938	−	8.03168i	−0.301696	−	0.359547i	0.593803	−	0.804610i	$-0.297626\pi$
$499$	−6.73938	−	8.03168i	−0.301696	−	0.359547i	−0.895499	+	0.445063i	$0.853181\pi$
$500$		0			0
$501$	−4.94508	+	8.56513i	−0.220930	+	0.382662i
$502$		0			0
$503$	−4.14166	−	11.3791i	−0.184668	−	0.507370i	0.812468	−	0.583006i	$-0.198124\pi$
$503$	−4.14166	−	11.3791i	−0.184668	−	0.507370i	−0.997136	+	0.0756357i	$0.975901\pi$
$504$		0			0
$505$	2.70421	+	4.68383i	0.120336	+	0.208428i
$506$		0			0
$507$	−5.05388	+	28.6620i	−0.224451	+	1.27292i
$508$		0			0
$509$	8.30624	−	9.89899i	0.368168	−	0.438765i	−0.549875	−	0.835247i	$-0.685325\pi$
$509$	8.30624	−	9.89899i	0.368168	−	0.438765i	0.918043	+	0.396482i	$0.129769\pi$
$510$		0			0
$511$	1.04795	−	2.87923i	0.0463587	−	0.127370i
$512$		0			0
$513$	2.21271	−	3.75552i	0.0976935	−	0.165810i
$514$		0			0
$515$	0.732398	+	0.266571i	0.0322733	+	0.0117465i
$516$		0			0
$517$	9.51534	+	7.98432i	0.418484	+	0.351150i
$518$		0			0
$519$	−20.7254	−	3.65445i	−0.909745	−	0.160413i
$520$		0			0
$521$	−14.9330	+	8.62156i	−0.654226	+	0.377717i	−0.790073	−	0.613012i	$-0.789958\pi$
$521$	−14.9330	+	8.62156i	−0.654226	+	0.377717i	0.135848	+	0.990730i	$0.456624\pi$
$522$		0			0
$523$	−12.8077	+	4.66163i	−0.560043	+	0.203839i	−0.606503	−	0.795081i	$-0.707428\pi$
$523$	−12.8077	+	4.66163i	−0.560043	+	0.203839i	0.0464600	+	0.998920i	$0.485206\pi$
$524$		0			0
$525$	4.76474	+	2.75092i	0.207950	+	0.120060i
$526$		0			0
$527$	−17.2728	+	14.4936i	−0.752413	+	0.631350i
$528$		0			0
$529$	−9.98642	−	56.6358i	−0.434192	−	2.46243i
$530$		0			0
$531$	−10.6776			−0.463369
$532$		0			0
$533$	22.4643			0.973035
$534$		0			0
$535$	−0.359102	−	2.03657i	−0.0155253	−	0.0880485i
$536$		0			0
$537$	−15.5506	+	13.0485i	−0.671060	+	0.563086i
$538$		0			0
$539$	−6.20333	−	3.58149i	−0.267196	−	0.154266i
$540$		0			0
$541$	21.2817	−	7.74590i	0.914971	−	0.333022i	0.158735	−	0.987321i	$-0.449258\pi$
$541$	21.2817	−	7.74590i	0.914971	−	0.333022i	0.756236	+	0.654299i	$0.227036\pi$
$542$		0			0
$543$	5.88781	−	3.39933i	0.252670	−	0.145879i
$544$		0			0
$545$	−2.85804	−	0.503949i	−0.122425	−	0.0215868i
$546$		0			0
$547$	33.2694	+	27.9163i	1.42250	+	1.19362i	0.949987	+	0.312291i	$0.101096\pi$
$547$	33.2694	+	27.9163i	1.42250	+	1.19362i	0.472510	+	0.881325i	$0.343348\pi$
$548$		0			0
$549$	7.20808	+	2.62353i	0.307633	+	0.111969i
$550$		0			0
$551$	18.9890	−	22.2284i	0.808958	−	0.946963i
$552$		0			0
$553$	−5.18195	+	14.2373i	−0.220359	+	0.605431i
$554$		0			0
$555$	−0.910792	+	1.08544i	−0.0386610	+	0.0460743i
$556$		0			0
$557$	−2.73039	+	15.4848i	−0.115690	+	0.656112i	0.870716	+	0.491786i	$0.163656\pi$
$557$	−2.73039	+	15.4848i	−0.115690	+	0.656112i	−0.986406	+	0.164325i	$0.947455\pi$
$558$		0			0
$559$	32.6337	+	56.5233i	1.38026	+	2.39068i
$560$		0			0
$561$	−1.83885	−	5.05220i	−0.0776363	−	0.213304i
$562$		0			0
$563$	12.1940	−	21.1207i	0.513917	−	0.890129i	−0.485953	−	0.873985i	$-0.661527\pi$
$563$	12.1940	−	21.1207i	0.513917	−	0.890129i	0.999870	−	0.0161446i	$-0.00513922\pi$
$564$		0			0
$565$	−4.23540	−	5.04756i	−0.178185	−	0.212352i
$566$		0			0
$567$	−1.12967	+	0.199192i	−0.0474418	+	0.00836527i
$568$		0			0
$569$		−	9.40585i		−	0.394314i	−0.980372	−	0.197157i	$-0.936829\pi$
$569$		−	9.40585i		−	0.394314i	0.980372	−	0.197157i	$-0.0631708\pi$
$570$		0			0
$571$		−	27.7817i		−	1.16263i	−0.813679	−	0.581314i	$-0.802539\pi$
$571$		−	27.7817i		−	1.16263i	0.813679	−	0.581314i	$-0.197461\pi$
$572$		0			0
$573$	−12.2858	+	2.16631i	−0.513246	+	0.0904990i
$574$		0			0
$575$	−27.6629	−	32.9674i	−1.15362	−	1.37483i
$576$		0			0
$577$	17.2279	−	29.8396i	0.717207	−	1.24224i	−0.244895	−	0.969550i	$-0.578753\pi$
$577$	17.2279	−	29.8396i	0.717207	−	1.24224i	0.962102	−	0.272690i	$-0.0879132\pi$
$578$		0			0
$579$	5.21981	+	14.3413i	0.216928	+	0.596005i
$580$		0			0
$581$	2.12595	+	3.68225i	0.0881991	+	0.152765i
$582$		0			0
$583$	−2.61462	+	14.8282i	−0.108286	+	0.614123i
$584$		0			0
$585$	−1.88244	+	2.24341i	−0.0778295	+	0.0927535i
$586$		0			0
$587$	8.38030	−	23.0247i	0.345892	−	0.950330i	−0.637758	−	0.770237i	$-0.720138\pi$
$587$	8.38030	−	23.0247i	0.345892	−	0.950330i	0.983650	−	0.180093i	$-0.0576399\pi$
$588$		0			0
$589$	23.0357	+	0.203491i	0.949169	+	0.00838469i
$590$		0			0
$591$	17.2884	+	6.29248i	0.711151	+	0.258838i
$592$		0			0
$593$	−32.9668	−	27.6624i	−1.35379	−	1.13596i	−0.977848	−	0.209315i	$-0.932877\pi$
$593$	−32.9668	−	27.6624i	−1.35379	−	1.13596i	−0.375937	−	0.926645i	$-0.622679\pi$
$594$		0			0
$595$	−2.17526	−	0.383557i	−0.0891771	−	0.0157243i
$596$		0			0
$597$	−1.69690	+	0.979708i	−0.0694497	+	0.0400968i
$598$		0			0
$599$	21.2010	−	7.71653i	0.866249	−	0.315289i	0.129602	−	0.991566i	$-0.458630\pi$
$599$	21.2010	−	7.71653i	0.866249	−	0.315289i	0.736647	+	0.676277i	$0.236408\pi$
$600$		0			0
$601$	−0.197687	−	0.114135i	−0.00806382	−	0.00465565i	0.495963	−	0.868344i	$-0.334815\pi$
$601$	−0.197687	−	0.114135i	−0.00806382	−	0.00465565i	−0.504026	+	0.863688i	$0.668149\pi$
$602$		0			0
$603$	−4.95073	+	4.15416i	−0.201609	+	0.169170i
$604$		0			0
$605$	−0.737638	−	4.18335i	−0.0299893	−	0.170078i
$606$		0			0
$607$	−22.5108			−0.913684			−0.456842	−	0.889548i	$-0.651020\pi$
$607$	−22.5108			−0.913684			−0.456842	+	0.889548i	$0.651020\pi$
$608$		0			0
$609$	−7.69356			−0.311759
$610$		0			0
$611$	−11.1065	−	62.9878i	−0.449319	−	2.54821i
$612$		0			0
$613$	−27.2545	+	22.8693i	−1.10080	+	0.923681i	−0.997479	−	0.0709674i	$-0.977391\pi$
$613$	−27.2545	+	22.8693i	−1.10080	+	0.923681i	−0.103321	+	0.994648i	$0.532947\pi$
$614$		0			0
$615$	1.35317	+	0.781253i	0.0545651	+	0.0315032i
$616$		0			0
$617$	−33.0077	+	12.0138i	−1.32884	+	0.483658i	−0.906280	−	0.422677i	$-0.861090\pi$
$617$	−33.0077	+	12.0138i	−1.32884	+	0.483658i	−0.422560	+	0.906335i	$0.638868\pi$
$618$		0			0
$619$	9.19055	−	5.30616i	0.369399	−	0.213273i	−0.303797	−	0.952737i	$-0.598254\pi$
$619$	9.19055	−	5.30616i	0.369399	−	0.213273i	0.673196	+	0.739464i	$0.264921\pi$
$620$		0			0
$621$	8.83639	+	1.55809i	0.354592	+	0.0625242i
$622$		0			0
$623$	−8.46611	−	7.10391i	−0.339188	−	0.284612i
$624$		0			0
$625$	−20.6601	−	7.51967i	−0.826405	−	0.300787i
$626$		0			0
$627$	−1.92422	+	5.14488i	−0.0768458	+	0.205467i
$628$		0			0
$629$	−4.58119	+	12.5867i	−0.182664	+	0.501865i
$630$		0			0
$631$	−23.2744	+	27.7373i	−0.926538	+	1.10421i	0.0677741	+	0.997701i	$0.478410\pi$
$631$	−23.2744	+	27.7373i	−0.926538	+	1.10421i	−0.994312	+	0.106504i	$0.966034\pi$
$632$		0			0
$633$	0.266272	−	1.51011i	0.0105834	−	0.0600213i
$634$		0			0
$635$	−4.00919	−	6.94411i	−0.159100	−	0.275569i
$636$		0			0
$637$	12.6148	+	34.6589i	0.499817	+	1.37323i
$638$		0			0
$639$	3.97289	−	6.88125i	0.157165	−	0.272218i
$640$		0			0
$641$	−31.4346	−	37.4623i	−1.24159	−	1.47967i	−0.819456	−	0.573142i	$-0.805725\pi$
$641$	−31.4346	−	37.4623i	−1.24159	−	1.47967i	−0.422137	−	0.906532i	$-0.638720\pi$
$642$		0			0
$643$	5.69253	−	1.00375i	0.224491	−	0.0395839i	−0.0602709	−	0.998182i	$-0.519196\pi$
$643$	5.69253	−	1.00375i	0.224491	−	0.0395839i	0.284762	+	0.958598i	$0.408085\pi$
$644$		0			0
$645$			4.53969i			0.178750i
$646$		0			0
$647$		−	20.6857i		−	0.813240i	−0.913597	−	0.406620i	$-0.866707\pi$
$647$		−	20.6857i		−	0.813240i	0.913597	−	0.406620i	$-0.133293\pi$
$648$		0			0
$649$	13.2512	−	2.33654i	0.520153	−	0.0917171i
$650$		0			0
$651$	−3.89682	−	4.64405i	−0.152728	−	0.182015i
$652$		0			0
$653$	−16.0648	+	27.8250i	−0.628663	+	1.08888i	0.359157	+	0.933277i	$0.383064\pi$
$653$	−16.0648	+	27.8250i	−0.628663	+	1.08888i	−0.987820	+	0.155600i	$0.950269\pi$
$654$		0			0
$655$	−1.12821	−	3.09972i	−0.0440826	−	0.121116i
$656$		0			0
$657$	−1.33555	−	2.31323i	−0.0521046	−	0.0902478i
$658$		0			0
$659$	1.89652	−	10.7557i	0.0738780	−	0.418983i	−0.925329	−	0.379165i	$-0.876211\pi$
$659$	1.89652	−	10.7557i	0.0738780	−	0.418983i	0.999207	−	0.0398176i	$-0.0126777\pi$
$660$		0			0
$661$	3.14723	−	3.75072i	0.122413	−	0.145886i	−0.701357	−	0.712810i	$-0.747422\pi$
$661$	3.14723	−	3.75072i	0.122413	−	0.145886i	0.823770	+	0.566924i	$0.191867\pi$
$662$		0			0
$663$	−9.46849	+	26.0145i	−0.367726	+	1.01032i
$664$		0			0
$665$	1.43524	+	1.74146i	0.0556562	+	0.0675311i
$666$		0			0
$667$	56.5504	+	20.5827i	2.18964	+	0.796964i
$668$		0			0
$669$	15.5124	+	13.0165i	0.599744	+	0.503245i
$670$		0			0
$671$	−9.51947	−	1.67854i	−0.367495	−	0.0647993i
$672$		0			0
$673$	−20.8068	+	12.0128i	−0.802042	+	0.463059i	−0.844185	−	0.536053i	$-0.819915\pi$
$673$	−20.8068	+	12.0128i	−0.802042	+	0.463059i	0.0421428	+	0.999112i	$0.486582\pi$
$674$		0			0
$675$	4.50705	−	1.64043i	0.173476	−	0.0631403i
$676$		0			0
$677$	24.6225	+	14.2158i	0.946319	+	0.546357i	0.891935	−	0.452163i	$-0.149347\pi$
$677$	24.6225	+	14.2158i	0.946319	+	0.546357i	0.0543833	+	0.998520i	$0.482681\pi$
$678$		0			0
$679$	1.14983	−	0.964818i	0.0441263	−	0.0370263i
$680$		0			0
$681$	−4.45765	−	25.2806i	−0.170818	−	0.968754i
$682$		0			0
$683$	13.9631			0.534282			0.267141	−	0.963657i	$-0.413921\pi$
$683$	13.9631			0.534282			0.267141	+	0.963657i	$0.413921\pi$
$684$		0			0
$685$	−4.85322			−0.185432
$686$		0			0
$687$	−0.504123	−	2.85902i	−0.0192335	−	0.109079i
$688$		0			0
$689$	59.3918	−	49.8357i	2.26265	−	1.89859i
$690$		0			0
$691$	−35.6029	−	20.5553i	−1.35440	−	0.781962i	−0.365536	−	0.930797i	$-0.619114\pi$
$691$	−35.6029	−	20.5553i	−1.35440	−	0.781962i	−0.988862	+	0.148835i	$0.952448\pi$
$692$		0			0
$693$	1.35836	−	0.494403i	0.0515999	−	0.0187808i
$694$		0			0
$695$	7.51984	−	4.34158i	0.285244	−	0.164686i
$696$		0			0
$697$	14.5461	+	2.56488i	0.550974	+	0.0971516i
$698$		0			0
$699$	7.20495	+	6.04567i	0.272516	+	0.228668i
$700$		0			0
$701$	30.5935	+	11.1351i	1.15550	+	0.420568i	0.847488	−	0.530814i	$-0.178114\pi$
$701$	30.5935	+	11.1351i	1.15550	+	0.420568i	0.308013	+	0.951382i	$0.400336\pi$
$702$		0			0
$703$	11.9113	−	6.73741i	0.449243	−	0.254106i
$704$		0			0
$705$	1.52155	−	4.18043i	0.0573049	−	0.157444i
$706$		0			0
$707$	−8.83584	+	10.5301i	−0.332306	+	0.396027i
$708$		0			0
$709$	7.88409	−	44.7129i	0.296093	−	1.67923i	−0.366632	−	0.930366i	$-0.619489\pi$
$709$	7.88409	−	44.7129i	0.296093	−	1.67923i	0.662725	−	0.748863i	$-0.269400\pi$
$710$		0			0
$711$	6.60405	+	11.4385i	0.247671	+	0.428979i
$712$		0			0
$713$	16.2187	+	44.5606i	0.607396	+	1.66881i
$714$		0			0
$715$	1.84524	−	3.19604i	0.0690080	−	0.119525i
$716$		0			0
$717$	4.10453	+	4.89159i	0.153287	+	0.182680i
$718$		0			0
$719$	4.27096	−	0.753085i	0.159280	−	0.0280853i	−0.0934395	−	0.995625i	$-0.529786\pi$
$719$	4.27096	−	0.753085i	0.159280	−	0.0280853i	0.252719	+	0.967540i	$0.418675\pi$
$720$		0			0
$721$			1.98094i			0.0737739i
$722$		0			0
$723$			2.96018i			0.110090i
$724$		0			0
$725$	31.6799	−	5.58603i	1.17656	−	0.207460i
$726$		0			0
$727$	−13.9656	−	16.6436i	−0.517956	−	0.617276i	0.442140	−	0.896946i	$-0.354219\pi$
$727$	−13.9656	−	16.6436i	−0.517956	−	0.617276i	−0.960096	+	0.279670i	$0.909775\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	14.6775	+	40.3262i	0.542868	+	1.49152i
$732$		0			0
$733$	−0.286737	−	0.496644i	−0.0105909	−	0.0183439i	0.860681	−	0.509144i	$-0.170038\pi$
$733$	−0.286737	−	0.496644i	−0.0105909	−	0.0183439i	−0.871272	+	0.490800i	$0.836705\pi$
$734$		0			0
$735$	−0.445480	+	2.52644i	−0.0164318	+	0.0931893i
$736$		0			0
$737$	5.23493	−	6.23874i	0.192831	−	0.229807i
$738$		0			0
$739$	−9.67878	+	26.5922i	−0.356040	+	0.978211i	0.624351	+	0.781144i	$0.285364\pi$
$739$	−9.67878	+	26.5922i	−0.356040	+	0.978211i	−0.980390	+	0.197066i	$0.936859\pi$
$740$		0			0
$741$	24.6185	−	13.9250i	0.904384	−	0.511549i
$742$		0			0
$743$	37.7541	+	13.7414i	1.38507	+	0.504122i	0.923710	−	0.383093i	$-0.125141\pi$
$743$	37.7541	+	13.7414i	1.38507	+	0.504122i	0.461355	+	0.887215i	$0.347363\pi$
$744$		0			0
$745$	5.70663	+	4.78844i	0.209075	+	0.175435i
$746$		0			0
$747$	3.65033	+	0.643652i	0.133559	+	0.0235500i
$748$		0			0
$749$	4.55184	−	2.62801i	0.166321	−	0.0960253i
$750$		0			0
$751$	14.3464	−	5.22168i	0.523509	−	0.190542i	−0.0667288	−	0.997771i	$-0.521256\pi$
$751$	14.3464	−	5.22168i	0.523509	−	0.190542i	0.590238	+	0.807230i	$0.299034\pi$
$752$		0			0
$753$	7.42120	+	4.28463i	0.270444	+	0.156141i
$754$		0			0
$755$	−0.777402	+	0.652317i	−0.0282925	+	0.0237403i
$756$		0			0
$757$	5.95117	+	33.7507i	0.216299	+	1.22669i	0.878638	+	0.477488i	$0.158453\pi$
$757$	5.95117	+	33.7507i	0.216299	+	1.22669i	−0.662339	+	0.749204i	$0.730436\pi$
$758$		0			0
$759$	−11.3071			−0.410422
$760$		0			0
$761$	15.4377			0.559615			0.279808	−	0.960056i	$-0.409729\pi$
$761$	15.4377			0.559615			0.279808	+	0.960056i	$0.409729\pi$
$762$		0			0
$763$	−1.28084	−	7.26402i	−0.0463696	−	0.262975i
$764$		0			0
$765$	−1.47507	+	1.23773i	−0.0533313	+	0.0447503i
$766$		0			0
$767$	−60.0022	−	34.6423i	−2.16656	−	1.25086i
$768$		0			0
$769$	2.42227	−	0.881633i	0.0873492	−	0.0317925i	−0.297976	−	0.954573i	$-0.596312\pi$
$769$	2.42227	−	0.881633i	0.0873492	−	0.0317925i	0.385325	+	0.922781i	$0.374089\pi$
$770$		0			0
$771$	6.40136	−	3.69583i	0.230539	−	0.133102i
$772$		0			0
$773$	28.2934	+	4.98889i	1.01764	+	0.179438i	0.657496	−	0.753458i	$-0.271616\pi$
$773$	28.2934	+	4.98889i	1.01764	+	0.179438i	0.360146	+	0.932896i	$0.382727\pi$
$774$		0			0
$775$	19.4179	+	16.2935i	0.697511	+	0.585281i
$776$		0			0
$777$	−3.38413	−	1.23172i	−0.121405	−	0.0441878i
$778$		0			0
$779$	−9.59756	−	11.6453i	−0.343868	−	0.417236i
$780$		0			0
$781$	−3.42465	+	9.40914i	−0.122544	+	0.336686i
$782$		0			0
$783$	−4.31115	+	5.13783i	−0.154068	+	0.183611i
$784$		0			0
$785$	−0.509334	+	2.88858i	−0.0181789	+	0.103098i
$786$		0			0
$787$	−21.5771	−	37.3726i	−0.769140	−	1.33219i	−0.938030	−	0.346554i	$-0.887352\pi$
$787$	−21.5771	−	37.3726i	−0.769140	−	1.33219i	0.168890	−	0.985635i	$-0.445982\pi$
$788$		0			0
$789$	−5.65028	−	15.5240i	−0.201155	−	0.552669i
$790$		0			0
$791$	8.37350	−	14.5033i	0.297727	−	0.515679i
$792$		0			0
$793$	31.9936	+	38.1285i	1.13613	+	1.35398i
$794$		0			0
$795$	5.31072	−	0.936424i	0.188352	−	0.0332115i
$796$		0			0
$797$			13.8710i			0.491337i	0.969354	+	0.245669i	$0.0790075\pi$
$797$			13.8710i			0.491337i	−0.969354	+	0.245669i	$0.920993\pi$
$798$		0			0
$799$		−	42.0542i		−	1.48777i
$800$		0			0
$801$	−9.48811	+	1.67301i	−0.335246	+	0.0591129i
$802$		0			0
$803$	2.16364	+	2.57852i	0.0763530	+	0.0909940i
$804$		0			0
$805$	−2.32267	+	4.02298i	−0.0818633	+	0.141791i
$806$		0			0
$807$	−4.76336	−	13.0872i	−0.167678	−	0.460692i
$808$		0			0
$809$	−0.180910	−	0.313345i	−0.00636045	−	0.0110166i	0.862828	−	0.505498i	$-0.168691\pi$
$809$	−0.180910	−	0.313345i	−0.00636045	−	0.0110166i	−0.869188	+	0.494482i	$0.835358\pi$
$810$		0			0
$811$	−6.82369	+	38.6991i	−0.239612	+	1.35891i	0.593067	+	0.805153i	$0.297917\pi$
$811$	−6.82369	+	38.6991i	−0.239612	+	1.35891i	−0.832680	+	0.553755i	$0.813194\pi$
$812$		0			0
$813$	−5.90186	+	7.03357i	−0.206987	+	0.246678i
$814$		0			0
$815$	−2.45780	+	6.75275i	−0.0860929	+	0.236538i
$816$		0			0
$817$	15.3589	−	41.0659i	0.537341	−	1.43671i
$818$		0			0
$819$	−6.99439	−	2.54575i	−0.244404	−	0.0889557i
$820$		0			0
$821$	−18.5564	−	15.5707i	−0.647624	−	0.543421i	0.258725	−	0.965951i	$-0.416698\pi$
$821$	−18.5564	−	15.5707i	−0.647624	−	0.543421i	−0.906349	+	0.422530i	$0.861142\pi$
$822$		0			0
$823$	−4.68599	−	0.826267i	−0.163343	−	0.0288019i	0.0913783	−	0.995816i	$-0.470873\pi$
$823$	−4.68599	−	0.826267i	−0.163343	−	0.0288019i	−0.254722	+	0.967014i	$0.581984\pi$
$824$		0			0
$825$	−5.23438	+	3.02207i	−0.182238	+	0.105215i
$826$		0			0
$827$	−11.4868	+	4.18086i	−0.399436	+	0.145383i	−0.533924	−	0.845532i	$-0.679283\pi$
$827$	−11.4868	+	4.18086i	−0.399436	+	0.145383i	0.134488	+	0.990915i	$0.457061\pi$
$828$		0			0
$829$	−15.7311	−	9.08236i	−0.546364	−	0.315443i	0.201290	−	0.979532i	$-0.435487\pi$
$829$	−15.7311	−	9.08236i	−0.546364	−	0.315443i	−0.747654	+	0.664088i	$0.768820\pi$
$830$		0			0
$831$	−3.48601	+	2.92511i	−0.120928	+	0.101471i
$832$		0			0
$833$	4.21117	+	23.8828i	0.145909	+	0.827488i
$834$		0			0
$835$	−4.46370			−0.154473
$836$		0			0
$837$	−5.28495			−0.182675
$838$		0			0
$839$	6.02590	+	34.1746i	0.208037	+	1.17984i	0.892588	+	0.450872i	$0.148887\pi$
$839$	6.02590	+	34.1746i	0.208037	+	1.17984i	−0.684551	+	0.728965i	$0.740002\pi$
$840$		0			0
$841$	−12.2440	+	10.2739i	−0.422207	+	0.354273i
$842$		0			0
$843$	−19.4168	−	11.2103i	−0.668749	−	0.386103i
$844$		0			0
$845$	−12.3433	+	4.49261i	−0.424624	+	0.154550i
$846$		0			0
$847$	9.35003	−	5.39824i	0.321271	−	0.185486i
$848$		0			0
$849$	−5.41170	−	0.954229i	−0.185729	−	0.0327491i
$850$		0			0
$851$	21.5793	+	18.1072i	0.739729	+	0.620706i
$852$		0			0
$853$	48.5240	+	17.6613i	1.66143	+	0.604711i	0.990587	−	0.136887i	$-0.0437098\pi$
$853$	48.5240	+	17.6613i	1.66143	+	0.604711i	0.670844	+	0.741599i	$0.265932\pi$
$854$		0			0
$855$	1.96722	+	0.0173778i	0.0672773	+	0.000594309i
$856$		0			0
$857$	5.79546	−	15.9229i	0.197969	−	0.543916i	−0.800494	−	0.599341i	$-0.795429\pi$
$857$	5.79546	−	15.9229i	0.197969	−	0.543916i	0.998463	+	0.0554253i	$0.0176515\pi$
$858$		0			0
$859$	−9.19470	+	10.9578i	−0.313719	+	0.373876i	−0.899745	−	0.436417i	$-0.856247\pi$
$859$	−9.19470	+	10.9578i	−0.313719	+	0.373876i	0.586026	+	0.810293i	$0.300692\pi$
$860$		0			0
$861$	−0.689607	+	3.91095i	−0.0235017	+	0.133285i
$862$		0			0
$863$	24.6380	+	42.6743i	0.838688	+	1.45265i	0.890992	+	0.454019i	$0.150010\pi$
$863$	24.6380	+	42.6743i	0.838688	+	1.45265i	−0.0523045	+	0.998631i	$0.516657\pi$
$864$		0			0
$865$	−3.24860	−	8.92544i	−0.110456	−	0.303474i
$866$		0			0
$867$	−0.601298	+	1.04148i	−0.0204211	+	0.0353704i
$868$		0			0
$869$	−10.6988	−	12.7503i	−0.362932	−	0.432526i
$870$		0			0
$871$	−41.2980	+	7.28195i	−1.39933	+	0.246740i
$872$		0			0
$873$		−	1.30851i		−	0.0442863i
$874$		0			0
$875$			5.07173i			0.171456i
$876$		0			0
$877$	1.53804	−	0.271199i	0.0519361	−	0.00915773i	−0.147620	−	0.989044i	$-0.547161\pi$
$877$	1.53804	−	0.271199i	0.0519361	−	0.00915773i	0.199556	+	0.979886i	$0.436050\pi$
$878$		0			0
$879$	6.05273	+	7.21336i	0.204153	+	0.243301i
$880$		0			0
$881$	1.22902	−	2.12873i	0.0414069	−	0.0717188i	−0.844579	−	0.535431i	$-0.820149\pi$
$881$	1.22902	−	2.12873i	0.0414069	−	0.0717188i	0.885986	+	0.463712i	$0.153483\pi$
$882$		0			0
$883$	18.9395	+	52.0359i	0.637365	+	1.75115i	0.659847	+	0.751400i	$0.270621\pi$
$883$	18.9395	+	52.0359i	0.637365	+	1.75115i	−0.0224821	+	0.999747i	$0.507157\pi$
$884$		0			0
$885$	−2.40955	−	4.17347i	−0.0809962	−	0.140290i
$886$		0			0
$887$	−3.67671	+	20.8517i	−0.123452	+	0.700130i	0.858763	+	0.512372i	$0.171233\pi$
$887$	−3.67671	+	20.8517i	−0.123452	+	0.700130i	−0.982215	+	0.187758i	$0.939878\pi$
$888$		0			0
$889$	13.0998	−	15.6117i	0.439352	−	0.523599i
$890$		0			0
$891$	0.431002	−	1.18417i	0.0144391	−	0.0396711i
$892$		0			0
$893$	−27.9073	+	32.6682i	−0.933883	+	1.09320i
$894$		0			0
$895$	−8.60939	−	3.13356i	−0.287780	−	0.104743i
$896$		0			0
$897$	44.6005	+	37.4243i	1.48917	+	1.24956i
$898$		0			0
$899$	−34.9075	−	6.15513i	−1.16423	−	0.205285i
$900$		0			0
$901$	44.1476	−	25.4887i	1.47077	−	0.849150i
$902$		0			0
$903$	−10.8423	+	3.94628i	−0.360809	+	0.131324i
$904$		0			0
$905$	2.65733	+	1.53421i	0.0883326	+	0.0509989i
$906$		0			0
$907$	32.0549	−	26.8973i	1.06437	−	0.893109i	0.0698362	−	0.997558i	$-0.477752\pi$
$907$	32.0549	−	26.8973i	1.06437	−	0.893109i	0.994530	+	0.104449i	$0.0333079\pi$
$908$		0			0
$909$	2.08089	+	11.8013i	0.0690187	+	0.391425i
$910$		0			0
$911$	−22.0644			−0.731027			−0.365513	−	0.930806i	$-0.619107\pi$
$911$	−22.0644			−0.731027			−0.365513	+	0.930806i	$0.619107\pi$
$912$		0			0
$913$	−4.67098			−0.154587
$914$		0			0
$915$	0.601168	+	3.40939i	0.0198740	+	0.112711i
$916$		0			0
$917$	6.42244	−	5.38906i	0.212088	−	0.177963i
$918$		0			0
$919$	7.25325	+	4.18767i	0.239263	+	0.138138i	0.614838	−	0.788654i	$-0.289221\pi$
$919$	7.25325	+	4.18767i	0.239263	+	0.138138i	−0.375575	+	0.926792i	$0.622555\pi$
$920$		0			0
$921$	−5.12376	+	1.86489i	−0.168833	+	0.0614504i
$922$		0			0
$923$	44.6508	−	25.7792i	1.46970	−	0.848532i
$924$		0			0
$925$	14.8292	+	2.61479i	0.487581	+	0.0859737i
$926$		0			0
$927$	1.32289	+	1.11003i	0.0434493	+	0.0364583i
$928$		0			0
$929$	6.94216	+	2.52674i	0.227765	+	0.0828996i	0.453382	−	0.891317i	$-0.350217\pi$
$929$	6.94216	+	2.52674i	0.227765	+	0.0828996i	−0.225617	+	0.974216i	$0.572440\pi$
$930$		0			0
$931$	12.5774	−	21.3470i	0.412208	−	0.699619i
$932$		0			0
$933$	6.61182	−	18.1658i	0.216461	−	0.594723i
$934$		0			0
$935$	1.55975	−	1.85883i	0.0510092	−	0.0607903i
$936$		0			0
$937$	0.270086	−	1.53173i	0.00882332	−	0.0500395i	−0.980078	−	0.198612i	$-0.936357\pi$
$937$	0.270086	−	1.53173i	0.00882332	−	0.0500395i	0.988902	+	0.148572i	$0.0474678\pi$
$938$		0			0
$939$	−2.11804	−	3.66856i	−0.0691198	−	0.119719i
$940$		0			0
$941$	11.9064	+	32.7127i	0.388139	+	1.06640i	0.967838	+	0.251573i	$0.0809477\pi$
$941$	11.9064	+	32.7127i	0.388139	+	1.06640i	−0.579699	+	0.814830i	$0.696830\pi$
$942$		0			0
$943$	15.5319	−	26.9020i	0.505787	−	0.876048i
$944$		0			0
$945$	−0.332783	−	0.396595i	−0.0108254	−	0.0129012i
$946$		0			0
$947$	−39.1043	+	6.89514i	−1.27072	+	0.224062i	−0.768034	−	0.640409i	$-0.778765\pi$
$947$	−39.1043	+	6.89514i	−1.27072	+	0.224062i	−0.502684	+	0.864471i	$0.667654\pi$
$948$		0			0
$949$		−	17.3321i		−	0.562624i
$950$		0			0
$951$		−	7.80821i		−	0.253199i
$952$		0			0
$953$	−2.11544	+	0.373010i	−0.0685259	+	0.0120830i	−0.207806	−	0.978170i	$-0.566632\pi$
$953$	−2.11544	+	0.373010i	−0.0685259	+	0.0120830i	0.139280	+	0.990253i	$0.455521\pi$
$954$		0			0
$955$	−3.61918	−	4.31318i	−0.117114	−	0.139571i
$956$		0			0
$957$	4.22595	−	7.31955i	0.136605	−	0.236608i
$958$		0			0
$959$	−4.21882	−	11.5911i	−0.136233	−	0.374297i
$960$		0			0
$961$	1.53463	+	2.65806i	0.0495042	+	0.0857438i
$962$		0			0
$963$	0.795656	−	4.51239i	0.0256397	−	0.145410i
$964$		0			0
$965$	−4.42754	+	5.27654i	−0.142528	+	0.169858i
$966$		0			0
$967$	−3.78041	+	10.3866i	−0.121570	+	0.334011i	−0.985518	−	0.169570i	$-0.945762\pi$
$967$	−3.78041	+	10.3866i	−0.121570	+	0.334011i	0.863948	+	0.503581i	$0.167984\pi$
$968$		0			0
$969$	17.5310	−	6.20594i	0.563177	−	0.199364i
$970$		0			0
$971$	9.94831	+	3.62089i	0.319256	+	0.116200i	0.496677	−	0.867935i	$-0.334553\pi$
$971$	9.94831	+	3.62089i	0.319256	+	0.116200i	−0.177421	+	0.984135i	$0.556775\pi$
$972$		0			0
$973$	16.9060	+	14.1858i	0.541982	+	0.454777i
$974$		0			0
$975$	30.6493	+	5.40430i	0.981563	+	0.173076i
$976$		0			0
$977$	30.1721	−	17.4198i	0.965290	−	0.557310i	0.0674927	−	0.997720i	$-0.478500\pi$
$977$	30.1721	−	17.4198i	0.965290	−	0.557310i	0.897797	+	0.440410i	$0.145167\pi$
$978$		0			0
$979$	11.4089	−	4.15248i	0.364629	−	0.132714i
$980$		0			0
$981$	−5.56871	−	3.21510i	−0.177795	−	0.102650i
$982$		0			0
$983$	30.4994	−	25.5921i	0.972781	−	0.816260i	−0.0102039	−	0.999948i	$-0.503248\pi$
$983$	30.4994	−	25.5921i	0.972781	−	0.816260i	0.982985	+	0.183688i	$0.0588036\pi$
$984$		0			0
$985$	1.44189	+	8.17737i	0.0459425	+	0.260553i
$986$		0			0
$987$	11.3069			0.359903
$988$		0			0
$989$	90.2522			2.86985
$990$		0			0
$991$	7.24648	+	41.0968i	0.230192	+	1.30548i	0.852507	+	0.522716i	$0.175081\pi$
$991$	7.24648	+	41.0968i	0.230192	+	1.30548i	−0.622315	+	0.782767i	$0.713808\pi$
$992$		0			0
$993$	−19.1097	+	16.0350i	−0.606429	+	0.508855i
$994$		0			0
$995$	−0.765860	−	0.442169i	−0.0242794	−	0.0140177i
$996$		0			0
$997$	5.37230	−	1.95536i	0.170142	−	0.0619267i	−0.255545	−	0.966797i	$-0.582255\pi$
$997$	5.37230	−	1.95536i	0.170142	−	0.0619267i	0.425687	+	0.904871i	$0.360033\pi$
$998$		0			0
$999$	−2.71888	+	1.56975i	−0.0860216	+	0.0496646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.f.319.2	yes	18
4.3	odd	2		912.2.ci.e.319.2	yes	18
19.14	odd	18		912.2.ci.e.223.2	✓	18
76.71	even	18	inner	912.2.ci.f.223.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.e.223.2	✓	18	19.14	odd	18
912.2.ci.e.319.2	yes	18	4.3	odd	2
912.2.ci.f.223.2	yes	18	76.71	even	18	inner
912.2.ci.f.319.2	yes	18	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(-0.345737 + 0.290108i) q^{5} +(-0.993418 - 0.573550i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(-0.345737 + 0.290108i) q^{5} +(-0.993418 - 0.573550i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.09134 - 0.630083i) q^{11} +(-6.39019 - 1.12676i) q^{13} +(-0.345737 - 0.290108i) q^{15} +(-4.00915 - 1.45921i) q^{17} +(2.14602 + 3.79402i) q^{19} +(0.392332 - 1.07792i) q^{21} +(-5.76755 + 6.87349i) q^{23} +(-0.832869 + 4.72344i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.29392 - 6.30249i) q^{29} +(2.64248 - 4.57690i) q^{31} +(0.810019 + 0.965343i) q^{33} +(0.509853 - 0.0899008i) q^{35} -3.13949i q^{37} -6.48877i q^{39} +(-3.40942 + 0.601174i) q^{41} +(-6.46550 - 7.70528i) q^{43} +(0.225664 - 0.390861i) q^{45} +(3.37128 + 9.26251i) q^{47} +(-2.84208 - 4.92263i) q^{49} +(0.740861 - 4.20163i) q^{51} +(-7.68029 + 9.15302i) q^{53} +(-0.194523 + 0.534448i) q^{55} +(-3.36373 + 2.77224i) q^{57} +(10.0337 + 3.65196i) q^{59} +(-5.87608 - 4.93062i) q^{61} +(1.12967 + 0.199192i) q^{63} +(2.53621 - 1.46428i) q^{65} +(6.07297 - 2.21038i) q^{67} +(-7.77059 - 4.48635i) q^{69} +(-6.08682 + 5.10745i) q^{71} +(0.463830 + 2.63051i) q^{73} -4.79630 q^{75} -1.44554 q^{77} +(-2.29356 - 13.0074i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-3.21005 - 1.85332i) q^{83} +(1.80944 - 0.658583i) q^{85} +(5.80840 - 3.35348i) q^{87} +(9.48811 + 1.67301i) q^{89} +(5.70188 + 4.78444i) q^{91} +(4.96623 + 1.80756i) q^{93} +(-1.84263 - 0.689157i) q^{95} +(-0.447536 + 1.22960i) q^{97} +(-0.810019 + 0.965343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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