LMFDB - Embedded newform 912.2.cc.d.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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([0, 0, 9, 17]))

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

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

chi := DirichletCharacter("912.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not 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} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			641.2
Root			$1.69944 - 0.334495i$ of defining polynomial
Character	$\chi$	$=$	912.641
Dual form			912.2.cc.d.737.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.560041 - 1.63901i) q^{3} +(-0.343148 + 0.408948i) q^{5} +(0.716507 + 1.24103i) q^{7} +(-2.37271 + 1.83583i) q^{9} +O(q^{10})$	\(q+(-0.560041 - 1.63901i) q^{3} +(-0.343148 + 0.408948i) q^{5} +(0.716507 + 1.24103i) q^{7} +(-2.37271 + 1.83583i) q^{9} +(1.25645 + 0.725411i) q^{11} +(2.94737 - 0.519701i) q^{13} +(0.862447 + 0.333396i) q^{15} +(-1.89590 - 5.20894i) q^{17} +(4.35653 - 0.143752i) q^{19} +(1.63278 - 1.86939i) q^{21} +(0.396438 + 0.472456i) q^{23} +(0.818753 + 4.64338i) q^{25} +(4.33775 + 2.86075i) q^{27} +(4.97822 + 1.81193i) q^{29} +(4.28601 - 2.47453i) q^{31} +(0.485293 - 2.46559i) q^{33} +(-0.753384 - 0.132842i) q^{35} +6.41883i q^{37} +(-2.50245 - 4.53972i) q^{39} +(1.37347 - 7.78933i) q^{41} +(-4.88757 - 4.10116i) q^{43} +(0.0634325 - 1.60027i) q^{45} +(4.37381 - 12.0169i) q^{47} +(2.47323 - 4.28377i) q^{49} +(-7.47572 + 6.02462i) q^{51} +(1.41439 - 1.18682i) q^{53} +(-0.727804 + 0.264899i) q^{55} +(-2.67545 - 7.05989i) q^{57} +(-1.75650 + 0.639313i) q^{59} +(9.02625 - 7.57392i) q^{61} +(-3.97837 - 1.62921i) q^{63} +(-0.798855 + 1.38366i) q^{65} +(-3.17216 + 8.71543i) q^{67} +(0.552339 - 0.914360i) q^{69} +(-9.59384 - 8.05019i) q^{71} +(-2.80621 + 15.9148i) q^{73} +(7.15201 - 3.94243i) q^{75} +2.07905i q^{77} +(7.87896 + 1.38927i) q^{79} +(2.25948 - 8.71176i) q^{81} +(4.29627 - 2.48045i) q^{83} +(2.78076 + 1.01211i) q^{85} +(0.181753 - 9.17411i) q^{87} +(0.832120 + 4.71919i) q^{89} +(2.75678 + 3.28540i) q^{91} +(-6.45612 - 5.63897i) q^{93} +(-1.43615 + 1.83092i) q^{95} +(-2.83601 - 7.79188i) q^{97} +(-4.31291 + 0.585434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$	$-1$	$1$

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
$3$	−0.560041	−	1.63901i	−0.323340	−	0.946283i
$3$	−0.560041	−	1.63901i	−0.323340	−	0.946283i
$4$		0			0
$5$	−0.343148	+	0.408948i	−0.153461	+	0.182887i	−0.837297	−	0.546748i	$-0.815866\pi$
$5$	−0.343148	+	0.408948i	−0.153461	+	0.182887i	0.683837	+	0.729635i	$0.260310\pi$
$6$		0			0
$7$	0.716507	+	1.24103i	0.270814	+	0.469064i	0.969071	−	0.246784i	$-0.0793737\pi$
$7$	0.716507	+	1.24103i	0.270814	+	0.469064i	−0.698256	+	0.715848i	$0.746040\pi$
$8$		0			0
$9$	−2.37271	+	1.83583i	−0.790902	+	0.611942i
$10$		0			0
$11$	1.25645	+	0.725411i	0.378834	+	0.218720i	0.677311	−	0.735697i	$-0.263145\pi$
$11$	1.25645	+	0.725411i	0.378834	+	0.218720i	−0.298477	+	0.954417i	$0.596479\pi$
$12$		0			0
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.250741	−	0.968054i	$-0.419326\pi$
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.566713	+	0.823915i	$0.308215\pi$
$14$		0			0
$15$	0.862447	+	0.333396i	0.222683	+	0.0860824i
$16$		0			0
$17$	−1.89590	−	5.20894i	−0.459823	−	1.26335i	−0.925618	−	0.378460i	$-0.876454\pi$
$17$	−1.89590	−	5.20894i	−0.459823	−	1.26335i	0.465795	−	0.884893i	$-0.345768\pi$
$18$		0			0
$19$	4.35653	−	0.143752i	0.999456	−	0.0329790i
$19$	4.35653	−	0.143752i	0.999456	−	0.0329790i
$20$		0			0
$21$	1.63278	−	1.86939i	0.356302	−	0.407934i
$22$		0			0
$23$	0.396438	+	0.472456i	0.0826630	+	0.0985139i	0.805791	−	0.592200i	$-0.201741\pi$
$23$	0.396438	+	0.472456i	0.0826630	+	0.0985139i	−0.723128	+	0.690714i	$0.757296\pi$
$24$		0			0
$25$	0.818753	+	4.64338i	0.163751	+	0.928676i
$26$		0			0
$27$	4.33775	+	2.86075i	0.834801	+	0.550552i
$28$		0			0
$29$	4.97822	+	1.81193i	0.924433	+	0.336466i	0.760001	−	0.649922i	$-0.225199\pi$
$29$	4.97822	+	1.81193i	0.924433	+	0.336466i	0.164432	+	0.986388i	$0.447421\pi$
$30$		0			0
$31$	4.28601	−	2.47453i	0.769790	−	0.444439i	−0.0630096	−	0.998013i	$-0.520070\pi$
$31$	4.28601	−	2.47453i	0.769790	−	0.444439i	0.832800	+	0.553574i	$0.186737\pi$
$32$		0			0
$33$	0.485293	−	2.46559i	0.0844786	−	0.429204i
$34$		0			0
$35$	−0.753384	−	0.132842i	−0.127345	−	0.0224544i
$36$		0			0
$37$			6.41883i			1.05525i	0.849478	+	0.527625i	$0.176917\pi$
$37$			6.41883i			1.05525i	−0.849478	+	0.527625i	$0.823083\pi$
$38$		0			0
$39$	−2.50245	−	4.53972i	−0.400712	−	0.726937i
$40$		0			0
$41$	1.37347	−	7.78933i	0.214500	−	1.21649i	−0.667273	−	0.744814i	$-0.732538\pi$
$41$	1.37347	−	7.78933i	0.214500	−	1.21649i	0.881772	−	0.471675i	$-0.156350\pi$
$42$		0			0
$43$	−4.88757	−	4.10116i	−0.745348	−	0.625421i	0.188920	−	0.981992i	$-0.439501\pi$
$43$	−4.88757	−	4.10116i	−0.745348	−	0.625421i	−0.934268	+	0.356571i	$0.883946\pi$
$44$		0			0
$45$	0.0634325	−	1.60027i	0.00945596	−	0.238555i
$46$		0			0
$47$	4.37381	−	12.0169i	0.637985	−	1.75285i	−0.0199780	−	0.999800i	$-0.506360\pi$
$47$	4.37381	−	12.0169i	0.637985	−	1.75285i	0.657963	−	0.753050i	$-0.271418\pi$
$48$		0			0
$49$	2.47323	−	4.28377i	0.353319	−	0.611967i
$50$		0			0
$51$	−7.47572	+	6.02462i	−1.04681	+	0.843615i
$52$		0			0
$53$	1.41439	−	1.18682i	0.194282	−	0.163022i	−0.540458	−	0.841371i	$-0.681749\pi$
$53$	1.41439	−	1.18682i	0.194282	−	0.163022i	0.734739	+	0.678349i	$0.237304\pi$
$54$		0			0
$55$	−0.727804	+	0.264899i	−0.0981370	+	0.0357190i
$56$		0			0
$57$	−2.67545	−	7.05989i	−0.354372	−	0.935105i
$58$		0			0
$59$	−1.75650	+	0.639313i	−0.228676	+	0.0832314i	−0.453817	−	0.891095i	$-0.649938\pi$
$59$	−1.75650	+	0.639313i	−0.228676	+	0.0832314i	0.225141	+	0.974326i	$0.427716\pi$
$60$		0			0
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.155856	−	0.987780i	$-0.450186\pi$
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.999837	+	0.0180382i	$0.00574206\pi$
$62$		0			0
$63$	−3.97837	−	1.62921i	−0.501228	−	0.205261i
$64$		0			0
$65$	−0.798855	+	1.38366i	−0.0990857	+	0.171622i
$66$		0			0
$67$	−3.17216	+	8.71543i	−0.387541	+	1.06476i	0.580564	+	0.814215i	$0.302832\pi$
$67$	−3.17216	+	8.71543i	−0.387541	+	1.06476i	−0.968105	+	0.250545i	$0.919390\pi$
$68$		0			0
$69$	0.552339	−	0.914360i	0.0664938	−	0.110076i
$70$		0			0
$71$	−9.59384	−	8.05019i	−1.13858	−	0.955382i	−0.139188	−	0.990266i	$-0.544449\pi$
$71$	−9.59384	−	8.05019i	−1.13858	−	0.955382i	−0.999391	+	0.0348843i	$0.988894\pi$
$72$		0			0
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	0.155852	+	0.987780i	$0.450188\pi$
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	−0.484294	+	0.874905i	$0.660923\pi$
$74$		0			0
$75$	7.15201	−	3.94243i	0.825843	−	0.455232i
$76$		0			0
$77$			2.07905i			0.236930i
$78$		0			0
$79$	7.87896	+	1.38927i	0.886452	+	0.156305i	0.598293	−	0.801277i	$-0.295846\pi$
$79$	7.87896	+	1.38927i	0.886452	+	0.156305i	0.288159	+	0.957583i	$0.406957\pi$
$80$		0			0
$81$	2.25948	−	8.71176i	0.251053	−	0.967973i
$82$		0			0
$83$	4.29627	−	2.48045i	0.471577	−	0.272265i	−0.245323	−	0.969442i	$-0.578894\pi$
$83$	4.29627	−	2.48045i	0.471577	−	0.272265i	0.716900	+	0.697176i	$0.245561\pi$
$84$		0			0
$85$	2.78076	+	1.01211i	0.301616	+	0.109779i
$86$		0			0
$87$	0.181753	−	9.17411i	0.0194859	−	0.983568i
$88$		0			0
$89$	0.832120	+	4.71919i	0.0882046	+	0.500233i	0.996619	+	0.0821621i	$0.0261825\pi$
$89$	0.832120	+	4.71919i	0.0882046	+	0.500233i	−0.908414	+	0.418071i	$0.862706\pi$
$90$		0			0
$91$	2.75678	+	3.28540i	0.288989	+	0.344403i
$92$		0			0
$93$	−6.45612	−	5.63897i	−0.669468	−	0.584734i
$94$		0			0
$95$	−1.43615	+	1.83092i	−0.147346	+	0.187849i
$96$		0			0
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	−0.996352	−	0.0853335i	$-0.972804\pi$
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	0.708399	−	0.705812i	$-0.249418\pi$
$98$		0			0
$99$	−4.31291	+	0.585434i	−0.433464	+	0.0588383i
$100$		0			0
$101$	−3.10192	+	0.546953i	−0.308653	+	0.0544238i	−0.325829	−	0.945429i	$-0.605643\pi$
$101$	−3.10192	+	0.546953i	−0.308653	+	0.0544238i	0.0171763	+	0.999852i	$0.494532\pi$
$102$		0			0
$103$	8.85438	+	5.11208i	0.872448	+	0.503708i	0.868161	−	0.496282i	$-0.165302\pi$
$103$	8.85438	+	5.11208i	0.872448	+	0.503708i	0.00428731	+	0.999991i	$0.498635\pi$
$104$		0			0
$105$	0.204197	+	1.30920i	0.0199276	+	0.127765i
$106$		0			0
$107$	5.80970	+	10.0627i	0.561645	+	0.972798i	0.997353	+	0.0727101i	$0.0231648\pi$
$107$	5.80970	+	10.0627i	0.561645	+	0.972798i	−0.435708	+	0.900088i	$0.643502\pi$
$108$		0			0
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	−0.767026	−	0.641616i	$-0.778264\pi$
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	0.765061	+	0.643958i	$0.222709\pi$
$110$		0			0
$111$	10.5205	−	3.59481i	0.998565	−	0.341204i
$112$		0			0
$113$	−10.3475			−0.973413			−0.486706	−	0.873566i	$-0.661802\pi$
$113$	−10.3475			−0.973413			−0.486706	+	0.873566i	$0.661802\pi$
$114$		0			0
$115$	−0.329247			−0.0307024
$116$		0			0
$117$	−6.03917	+	6.64396i	−0.558321	+	0.614235i
$118$		0			0
$119$	5.10601	−	6.08510i	0.468067	−	0.557820i
$120$		0			0
$121$	−4.44756	−	7.70340i	−0.404323	−	0.700309i
$122$		0			0
$123$	−13.5360	+	2.11122i	−1.22050	+	0.190362i
$124$		0			0
$125$	−4.49147	−	2.59315i	−0.401729	−	0.231938i
$126$		0			0
$127$	0.772141	−	0.136149i	0.0685165	−	0.0120813i	−0.139285	−	0.990252i	$-0.544480\pi$
$127$	0.772141	−	0.136149i	0.0685165	−	0.0120813i	0.207801	+	0.978171i	$0.433369\pi$
$128$		0			0
$129$	−3.98460	+	10.3076i	−0.350825	+	0.907534i
$130$		0			0
$131$	3.93973	+	10.8243i	0.344216	+	0.945726i	0.984157	+	0.177301i	$0.0567367\pi$
$131$	3.93973	+	10.8243i	0.344216	+	0.945726i	−0.639941	+	0.768424i	$0.721041\pi$
$132$		0			0
$133$	3.29988	+	5.30357i	0.286136	+	0.459878i
$134$		0			0
$135$	−2.65839	+	0.792254i	−0.228798	+	0.0681863i
$136$		0			0
$137$	8.70595	+	10.3754i	0.743800	+	0.886426i	0.996709	−	0.0810638i	$-0.0258318\pi$
$137$	8.70595	+	10.3754i	0.743800	+	0.886426i	−0.252909	+	0.967490i	$0.581387\pi$
$138$		0			0
$139$	1.25656	+	7.12628i	0.106580	+	0.604444i	0.990578	+	0.136953i	$0.0437308\pi$
$139$	1.25656	+	7.12628i	0.106580	+	0.604444i	−0.883998	+	0.467491i	$0.845158\pi$
$140$		0			0
$141$	−22.1454	−	0.438733i	−1.86498	−	0.0369480i
$142$		0			0
$143$	4.08022	+	1.48508i	0.341205	+	0.124188i
$144$		0			0
$145$	−2.44925	+	1.41408i	−0.203399	+	0.117433i
$146$		0			0
$147$	−8.40625	−	1.65457i	−0.693336	−	0.136467i
$148$		0			0
$149$	19.4195	+	3.42419i	1.59091	+	0.280520i	0.897831	−	0.440341i	$-0.145142\pi$
$149$	19.4195	+	3.42419i	1.59091	+	0.280520i	0.693079	+	0.720861i	$0.256254\pi$
$150$		0			0
$151$			4.23079i			0.344297i	0.985071	+	0.172148i	$0.0550709\pi$
$151$			4.23079i			0.344297i	−0.985071	+	0.172148i	$0.944929\pi$
$152$		0			0
$153$	14.0611	+	8.87874i	1.13677	+	0.717804i
$154$		0			0
$155$	−0.458783	+	2.60189i	−0.0368503	+	0.208989i
$156$		0			0
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	0.898211	−	0.439565i	$-0.144867\pi$
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	−0.276914	+	0.960895i	$0.589312\pi$
$158$		0			0
$159$	−2.73732	−	1.65354i	−0.217084	−	0.131134i
$160$		0			0
$161$	−0.302280	+	0.830508i	−0.0238230	+	0.0654532i
$162$		0			0
$163$	5.20216	−	9.01041i	0.407465	−	0.705750i	−0.587140	−	0.809485i	$-0.699746\pi$
$163$	5.20216	−	9.01041i	0.407465	−	0.705750i	0.994605	+	0.103735i	$0.0330795\pi$
$164$		0			0
$165$	0.841772	+	1.04452i	0.0655319	+	0.0813160i
$166$		0			0
$167$	−18.2265	+	15.2939i	−1.41041	+	1.18347i	−0.454162	+	0.890919i	$0.650061\pi$
$167$	−18.2265	+	15.2939i	−1.41041	+	1.18347i	−0.956249	+	0.292555i	$0.905494\pi$
$168$		0			0
$169$	−3.79909	+	1.38276i	−0.292238	+	0.106366i
$170$		0			0
$171$	−10.0729	+	8.33891i	−0.770291	+	0.637692i
$172$		0			0
$173$	−23.5435	+	8.56912i	−1.78998	+	0.651498i	−0.790752	+	0.612137i	$0.790310\pi$
$173$	−23.5435	+	8.56912i	−1.78998	+	0.651498i	−0.999225	+	0.0393612i	$0.987468\pi$
$174$		0			0
$175$	−5.17592	+	4.34311i	−0.391263	+	0.328308i
$176$		0			0
$177$	2.03155	+	2.52088i	0.152701	+	0.189481i
$178$		0			0
$179$	−7.77173	+	13.4610i	−0.580886	+	1.00612i	0.414488	+	0.910055i	$0.363961\pi$
$179$	−7.77173	+	13.4610i	−0.580886	+	1.00612i	−0.995375	+	0.0960699i	$0.969373\pi$
$180$		0			0
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	−0.322506	−	0.946567i	$-0.604525\pi$
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	0.855496	−	0.517810i	$-0.173252\pi$
$182$		0			0
$183$	−17.4688	−	10.5524i	−1.29133	−	0.780056i
$184$		0			0
$185$	−2.62497	−	2.20261i	−0.192992	−	0.161939i
$186$		0			0
$187$	1.39652	−	7.92007i	0.102124	−	0.579173i
$188$		0			0
$189$	−0.442240	+	7.43302i	−0.0321682	+	0.540673i
$190$		0			0
$191$		−	1.59398i		−	0.115336i	−0.998336	−	0.0576682i	$-0.981633\pi$
$191$		−	1.59398i		−	0.115336i	0.998336	−	0.0576682i	$-0.0183665\pi$
$192$		0			0
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	0.325898	−	0.945405i	$-0.394333\pi$
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	−0.0171035	+	0.999854i	$0.505444\pi$
$194$		0			0
$195$	2.71522	+	0.534426i	0.194441	+	0.0382710i
$196$		0			0
$197$	5.69700	−	3.28916i	0.405894	−	0.234343i	−0.283130	−	0.959082i	$-0.591373\pi$
$197$	5.69700	−	3.28916i	0.405894	−	0.234343i	0.689024	+	0.724738i	$0.258039\pi$
$198$		0			0
$199$	−10.2412	−	3.72750i	−0.725981	−	0.264235i	−0.0475182	−	0.998870i	$-0.515131\pi$
$199$	−10.2412	−	3.72750i	−0.725981	−	0.264235i	−0.678463	+	0.734635i	$0.737353\pi$
$200$		0			0
$201$	16.0612	+	0.318196i	1.13287	+	0.0224438i
$202$		0			0
$203$	1.31829	+	7.47637i	0.0925255	+	0.524738i
$204$		0			0
$205$	2.71413	+	3.23457i	0.189563	+	0.225912i
$206$		0			0
$207$	−1.80798	−	0.393209i	−0.125663	−	0.0273299i
$208$		0			0
$209$	5.57803	+	2.97966i	0.385841	+	0.206107i
$210$		0			0
$211$	2.58901	+	7.11324i	0.178235	+	0.489695i	0.996350	−	0.0853581i	$-0.0272034\pi$
$211$	2.58901	+	7.11324i	0.178235	+	0.489695i	−0.818116	+	0.575054i	$0.804981\pi$
$212$		0			0
$213$	−7.82139	+	20.2328i	−0.535913	+	1.38633i
$214$		0			0
$215$	3.35432	−	0.591458i	0.228763	−	0.0403371i
$216$		0			0
$217$	6.14192	+	3.54604i	0.416940	+	0.240721i
$218$		0			0
$219$	27.6561	−	4.31354i	1.86883	−	0.291482i
$220$		0			0
$221$	−8.29501	−	14.3674i	−0.557983	−	0.966454i
$222$		0			0
$223$	7.40150	−	8.82076i	0.495641	−	0.590682i	−0.459002	−	0.888435i	$-0.651793\pi$
$223$	7.40150	−	8.82076i	0.495641	−	0.590682i	0.954643	+	0.297753i	$0.0962373\pi$
$224$		0			0
$225$	−10.4671	−	9.51429i	−0.697807	−	0.634286i
$226$		0			0
$227$	1.54291			0.102407			0.0512033	−	0.998688i	$-0.483694\pi$
$227$	1.54291			0.102407			0.0512033	+	0.998688i	$0.483694\pi$
$228$		0			0
$229$	−8.17334			−0.540110			−0.270055	−	0.962845i	$-0.587042\pi$
$229$	−8.17334			−0.540110			−0.270055	+	0.962845i	$0.587042\pi$
$230$		0			0
$231$	3.40758	−	1.16435i	0.224202	−	0.0766088i
$232$		0			0
$233$	−5.39612	+	6.43084i	−0.353511	+	0.421298i	−0.913268	−	0.407358i	$-0.866450\pi$
$233$	−5.39612	+	6.43084i	−0.353511	+	0.421298i	0.559757	+	0.828657i	$0.310894\pi$
$234$		0			0
$235$	3.41344	+	5.91225i	0.222668	+	0.385673i
$236$		0			0
$237$	−2.13551	−	13.6917i	−0.138716	−	0.889375i
$238$		0			0
$239$	−7.60840	−	4.39271i	−0.492147	−	0.284141i	0.233318	−	0.972401i	$-0.425042\pi$
$239$	−7.60840	−	4.39271i	−0.492147	−	0.284141i	−0.725465	+	0.688260i	$0.758375\pi$
$240$		0			0
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.582806	−	0.812611i	$-0.698045\pi$
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.269730	+	0.962936i	$0.586934\pi$
$242$		0			0
$243$	−15.5441	+	1.17563i	−0.997152	+	0.0754169i
$244$		0			0
$245$	0.903153	+	2.48139i	0.0577003	+	0.158530i
$246$		0			0
$247$	12.7656	−	2.68778i	0.812256	−	0.171020i
$248$		0			0
$249$	−6.47158	−	5.65248i	−0.410120	−	0.358211i
$250$		0			0
$251$	5.05003	+	6.01839i	0.318755	+	0.379877i	0.901501	−	0.432777i	$-0.142466\pi$
$251$	5.05003	+	6.01839i	0.318755	+	0.379877i	−0.582746	+	0.812654i	$0.698022\pi$
$252$		0			0
$253$	0.155379	+	0.881197i	0.00976858	+	0.0554004i
$254$		0			0
$255$	0.101524	−	5.12452i	0.00635769	−	0.320910i
$256$		0			0
$257$	11.5445	+	4.20184i	0.720123	+	0.262103i	0.675978	−	0.736922i	$-0.263721\pi$
$257$	11.5445	+	4.20184i	0.720123	+	0.262103i	0.0441451	+	0.999025i	$0.485944\pi$
$258$		0			0
$259$	−7.96595	+	4.59914i	−0.494980	+	0.285777i
$260$		0			0
$261$	−15.1382	+	4.83999i	−0.937034	+	0.299588i
$262$		0			0
$263$	−23.4707	−	4.13852i	−1.44727	−	0.255192i	−0.605849	−	0.795579i	$-0.707167\pi$
$263$	−23.4707	−	4.13852i	−1.44727	−	0.255192i	−0.841416	+	0.540387i	$0.818278\pi$
$264$		0			0
$265$			0.985668i			0.0605491i
$266$		0			0
$267$	7.26877	−	4.00679i	0.444842	−	0.245212i
$268$		0			0
$269$	3.30229	−	18.7282i	0.201344	−	1.14188i	−0.701745	−	0.712428i	$-0.747596\pi$
$269$	3.30229	−	18.7282i	0.201344	−	1.14188i	0.903090	−	0.429452i	$-0.141293\pi$
$270$		0			0
$271$	−4.13554	−	3.47013i	−0.251216	−	0.210795i	0.508480	−	0.861074i	$-0.330208\pi$
$271$	−4.13554	−	3.47013i	−0.251216	−	0.210795i	−0.759696	+	0.650279i	$0.774652\pi$
$272$		0			0
$273$	3.84089	−	6.35834i	0.232461	−	0.384825i
$274$		0			0
$275$	−2.33964	+	6.42810i	−0.141085	+	0.387629i
$276$		0			0
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	−0.864619	−	0.502428i	$-0.832440\pi$
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	0.867425	+	0.497568i	$0.165774\pi$
$278$		0			0
$279$	−5.62664	+	13.7397i	−0.336858	+	0.822575i
$280$		0			0
$281$	−7.81505	+	6.55760i	−0.466207	+	0.391194i	−0.845409	−	0.534120i	$-0.820643\pi$
$281$	−7.81505	+	6.55760i	−0.466207	+	0.391194i	0.379202	+	0.925314i	$0.376199\pi$
$282$		0			0
$283$	−18.1732	+	6.61449i	−1.08028	+	0.393190i	−0.820013	−	0.572346i	$-0.806034\pi$
$283$	−18.1732	+	6.61449i	−1.08028	+	0.393190i	−0.260269	+	0.965536i	$0.583811\pi$
$284$		0			0
$285$	3.80520	+	1.32847i	0.225401	+	0.0786917i
$286$		0			0
$287$	10.6509	−	3.87660i	0.628701	−	0.228828i
$288$		0			0
$289$	−10.5158	+	8.82384i	−0.618579	+	0.519049i
$290$		0			0
$291$	−11.1827	+	9.01203i	−0.655541	+	0.528295i
$292$		0			0
$293$	−8.09268	+	14.0169i	−0.472780	+	0.818878i	−0.999515	−	0.0311512i	$-0.990083\pi$
$293$	−8.09268	+	14.0169i	−0.472780	+	0.818878i	0.526735	+	0.850030i	$0.323416\pi$
$294$		0			0
$295$	0.341293	−	0.937695i	0.0198709	−	0.0545947i
$296$		0			0
$297$	3.37494	+	6.74104i	0.195834	+	0.391155i
$298$		0			0
$299$	1.41399	+	1.18647i	0.0817729	+	0.0686156i
$300$		0			0
$301$	1.58767	−	9.00413i	0.0915118	−	0.518989i
$302$		0			0
$303$	2.63367	+	4.77777i	0.151300	+	0.274476i
$304$		0			0
$305$			6.29025i			0.360179i
$306$		0			0
$307$	−17.5661	−	3.09738i	−1.00255	−	0.176777i	−0.351806	−	0.936073i	$-0.614432\pi$
$307$	−17.5661	−	3.09738i	−1.00255	−	0.176777i	−0.650745	+	0.759296i	$0.725543\pi$
$308$		0			0
$309$	3.41993	−	17.3754i	0.194553	−	0.988452i
$310$		0			0
$311$	28.3493	−	16.3675i	1.60754	−	0.928114i	0.617622	−	0.786475i	$-0.288096\pi$
$311$	28.3493	−	16.3675i	1.60754	−	0.928114i	0.989918	−	0.141639i	$-0.0452373\pi$
$312$		0			0
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.474208	−	0.880413i	$-0.657265\pi$
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.929183	+	0.369621i	$0.879488\pi$
$314$		0			0
$315$	2.03143	−	1.06789i	0.114458	−	0.0601686i
$316$		0			0
$317$	2.32840	+	13.2050i	0.130776	+	0.741669i	0.977708	+	0.209968i	$0.0673359\pi$
$317$	2.32840	+	13.2050i	0.130776	+	0.741669i	−0.846932	+	0.531701i	$0.821553\pi$
$318$		0			0
$319$	4.94049	+	5.88785i	0.276614	+	0.329656i
$320$		0			0
$321$	13.2392	−	15.1577i	0.738940	−	0.846020i
$322$		0			0
$323$	−9.00833	−	22.4203i	−0.501237	−	1.24750i
$324$		0			0
$325$	4.82634	+	13.2603i	0.267717	+	0.735547i
$326$		0			0
$327$	0.0515616	+	0.0199321i	0.00285136	+	0.00110225i
$328$		0			0
$329$	18.0472	−	3.18221i	0.994975	−	0.175441i
$330$		0			0
$331$	−21.6450	−	12.4967i	−1.18971	−	0.686882i	−0.231473	−	0.972841i	$-0.574355\pi$
$331$	−21.6450	−	12.4967i	−1.18971	−	0.686882i	−0.958242	+	0.285959i	$0.907688\pi$
$332$		0			0
$333$	−11.7839	−	15.2300i	−0.645752	−	0.834600i
$334$		0			0
$335$	−2.47564	−	4.28793i	−0.135259	−	0.234275i
$336$		0			0
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	−0.390589	−	0.920565i	$-0.627729\pi$
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	0.974405	+	0.224801i	$0.0721732\pi$
$338$		0			0
$339$	5.79504	+	16.9597i	0.314743	+	0.921124i
$340$		0			0
$341$	7.18020			0.388830
$342$		0			0
$343$	17.1195			0.924364
$344$		0			0
$345$	0.184392	+	0.539639i	0.00992733	+	0.0290532i
$346$		0			0
$347$	23.0175	−	27.4312i	1.23564	−	1.47258i	0.406399	−	0.913696i	$-0.366784\pi$
$347$	23.0175	−	27.4312i	1.23564	−	1.47258i	0.829244	−	0.558886i	$-0.188771\pi$
$348$		0			0
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	0.999627	+	0.0273031i	$0.00869193\pi$
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	−0.476168	+	0.879354i	$0.657975\pi$
$350$		0			0
$351$	14.2717	+	6.17737i	0.761767	+	0.329723i
$352$		0			0
$353$	−27.9356	−	16.1286i	−1.48686	−	0.858441i	−0.486976	−	0.873416i	$-0.661900\pi$
$353$	−27.9356	−	16.1286i	−1.48686	−	0.858441i	−0.999888	+	0.0149745i	$0.995233\pi$
$354$		0			0
$355$	6.58422	−	1.16098i	0.349454	−	0.0616182i
$356$		0			0
$357$	−12.8331	−	4.96089i	−0.679201	−	0.262558i
$358$		0			0
$359$	−5.99057	−	16.4590i	−0.316170	−	0.868671i	−0.991377	−	0.131042i	$-0.958168\pi$
$359$	−5.99057	−	16.4590i	−0.316170	−	0.868671i	0.675206	−	0.737629i	$-0.264055\pi$
$360$		0			0
$361$	18.9587	−	1.25252i	0.997825	−	0.0659220i
$362$		0			0
$363$	−10.1351	+	11.6038i	−0.531956	+	0.609042i
$364$		0			0
$365$	−5.54538	−	6.60873i	−0.290258	−	0.345917i
$366$		0			0
$367$	−3.59236	−	20.3733i	−0.187520	−	1.06348i	−0.922675	−	0.385578i	$-0.874002\pi$
$367$	−3.59236	−	20.3733i	−0.187520	−	1.06348i	0.735155	−	0.677899i	$-0.237109\pi$
$368$		0			0
$369$	11.0410	+	21.0032i	0.574772	+	1.09339i
$370$		0			0
$371$	2.48630	+	0.904938i	0.129082	+	0.0469820i
$372$		0			0
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	−0.434738	−	0.900557i	$-0.643159\pi$
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	0.562536	+	0.826773i	$0.309826\pi$
$374$		0			0
$375$	−1.73479	+	8.81383i	−0.0895842	+	0.455144i
$376$		0			0
$377$	15.6143	+	2.75323i	0.804179	+	0.141798i
$378$		0			0
$379$			15.1648i			0.778963i	0.921034	+	0.389482i	$0.127346\pi$
$379$			15.1648i			0.778963i	−0.921034	+	0.389482i	$0.872654\pi$
$380$		0			0
$381$	−0.655581	−	1.18930i	−0.0335864	−	0.0609296i
$382$		0			0
$383$	0.366876	−	2.08066i	0.0187465	−	0.106317i	−0.973999	−	0.226553i	$-0.927254\pi$
$383$	0.366876	−	2.08066i	0.0187465	−	0.106317i	0.992745	+	0.120237i	$0.0383653\pi$
$384$		0			0
$385$	−0.850223	−	0.713422i	−0.0433314	−	0.0363594i
$386$		0			0
$387$	19.1258	+	0.758118i	0.972219	+	0.0385373i
$388$		0			0
$389$	−1.43738	+	3.94918i	−0.0728783	+	0.200231i	−0.970783	−	0.239958i	$-0.922866\pi$
$389$	−1.43738	+	3.94918i	−0.0728783	+	0.200231i	0.897905	+	0.440189i	$0.145089\pi$
$390$		0			0
$391$	1.70939	−	2.96075i	0.0864475	−	0.149731i
$392$		0			0
$393$	15.5348	−	12.5193i	0.783625	−	0.631517i
$394$		0			0
$395$	−3.27179	+	2.74536i	−0.164622	+	0.138134i
$396$		0			0
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	−0.334860	−	0.942268i	$-0.608689\pi$
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	0.349161	+	0.937063i	$0.386467\pi$
$398$		0			0
$399$	6.84453	−	8.37876i	0.342655	−	0.419463i
$400$		0			0
$401$	−11.8640	+	4.31814i	−0.592460	+	0.215638i	−0.620811	−	0.783960i	$-0.713197\pi$
$401$	−11.8640	+	4.31814i	−0.592460	+	0.215638i	0.0283512	+	0.999598i	$0.490974\pi$
$402$		0			0
$403$	11.3464	−	9.52080i	0.565207	−	0.474265i
$404$		0			0
$405$	2.78732	+	3.91344i	0.138503	+	0.194460i
$406$		0			0
$407$	−4.65629	+	8.06493i	−0.230804	+	0.399764i
$408$		0			0
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	0.660515	+	0.750813i	$0.270338\pi$
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	−0.988597	+	0.150585i	$0.951884\pi$
$410$		0			0
$411$	12.1296	−	20.0798i	0.598310	−	0.990462i
$412$		0			0
$413$	−2.05195	−	1.72179i	−0.100970	−	0.0847237i
$414$		0			0
$415$	−0.459881	+	2.60812i	−0.0225747	+	0.128027i
$416$		0			0
$417$	10.9763	−	6.05052i	0.537513	−	0.296295i
$418$		0			0
$419$			15.4879i			0.756633i	0.925676	+	0.378316i	$0.123497\pi$
$419$			15.4879i			0.756633i	−0.925676	+	0.378316i	$0.876503\pi$
$420$		0			0
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.498962	−	0.866624i	$-0.333715\pi$
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.172468	+	0.985015i	$0.444826\pi$
$422$		0			0
$423$	11.6832	+	36.5422i	0.568059	+	1.77674i
$424$		0			0
$425$	22.6348	−	13.0682i	1.09795	−	0.633901i
$426$		0			0
$427$	15.8668	+	5.77505i	0.767849	+	0.279474i
$428$		0			0
$429$	0.148967	−	7.51922i	0.00719219	−	0.363032i
$430$		0			0
$431$	4.86245	+	27.5763i	0.234216	+	1.32831i	0.844258	+	0.535936i	$0.180041\pi$
$431$	4.86245	+	27.5763i	0.234216	+	1.32831i	−0.610042	+	0.792369i	$0.708848\pi$
$432$		0			0
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	0.667488	−	0.744621i	$-0.267370\pi$
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	−0.849216	+	0.528045i	$0.822925\pi$
$434$		0			0
$435$	3.68937	+	3.22241i	0.176892	+	0.154503i
$436$		0			0
$437$	1.79501	+	2.00128i	0.0858669	+	0.0957342i
$438$		0			0
$439$	−7.65568	−	21.0338i	−0.365386	−	1.00389i	−0.977094	−	0.212806i	$-0.931740\pi$
$439$	−7.65568	−	21.0338i	−0.365386	−	1.00389i	0.611709	−	0.791083i	$-0.290482\pi$
$440$		0			0
$441$	1.99599	+	14.7046i	0.0950473	+	0.700217i
$442$		0			0
$443$	−14.6859	+	2.58952i	−0.697748	+	0.123032i	−0.511261	−	0.859426i	$-0.670821\pi$
$443$	−14.6859	+	2.58952i	−0.697748	+	0.123032i	−0.186487	+	0.982457i	$0.559710\pi$
$444$		0			0
$445$	−2.21544	−	1.27909i	−0.105022	−	0.0606345i
$446$		0			0
$447$	−5.26346	−	33.7465i	−0.248953	−	1.59615i
$448$		0			0
$449$	−2.44541	−	4.23557i	−0.115406	−	0.199889i	0.802536	−	0.596604i	$-0.203484\pi$
$449$	−2.44541	−	4.23557i	−0.115406	−	0.199889i	−0.917942	+	0.396715i	$0.870150\pi$
$450$		0			0
$451$	7.37616	−	8.79056i	0.347330	−	0.413931i
$452$		0			0
$453$	6.93431	−	2.36942i	0.325802	−	0.111325i
$454$		0			0
$455$	−2.28954			−0.107335
$456$		0			0
$457$	−30.3578			−1.42008			−0.710039	−	0.704162i	$-0.751323\pi$
$457$	−30.3578			−1.42008			−0.710039	+	0.704162i	$0.751323\pi$
$458$		0			0
$459$	6.67754	−	28.0188i	0.311681	−	1.30780i
$460$		0			0
$461$	16.0576	−	19.1367i	0.747879	−	0.891287i	−0.249138	−	0.968468i	$-0.580147\pi$
$461$	16.0576	−	19.1367i	0.747879	−	0.891287i	0.997017	+	0.0771808i	$0.0245919\pi$
$462$		0			0
$463$	2.94958	+	5.10883i	0.137079	+	0.237427i	0.926390	−	0.376566i	$-0.122895\pi$
$463$	2.94958	+	5.10883i	0.137079	+	0.237427i	−0.789311	+	0.613994i	$0.789562\pi$
$464$		0			0
$465$	4.52145	−	0.705214i	0.209677	−	0.0327035i
$466$		0			0
$467$	−4.76849	−	2.75309i	−0.220659	−	0.127398i	0.385596	−	0.922668i	$-0.373996\pi$
$467$	−4.76849	−	2.75309i	−0.220659	−	0.127398i	−0.606256	+	0.795270i	$0.707329\pi$
$468$		0			0
$469$	−13.0890	+	2.30794i	−0.604392	+	0.106571i
$470$		0			0
$471$	6.34659	−	16.4177i	0.292435	−	0.756489i
$472$		0			0
$473$	−3.16596	−	8.69840i	−0.145571	−	0.399953i
$474$		0			0
$475$	4.23442	+	20.1113i	0.194288	+	0.922770i
$476$		0			0
$477$	−1.17715	+	5.41255i	−0.0538981	+	0.247824i
$478$		0			0
$479$	21.4896	+	25.6103i	0.981884	+	1.17016i	0.985415	+	0.170170i	$0.0544317\pi$
$479$	21.4896	+	25.6103i	0.981884	+	1.17016i	−0.00353081	+	0.999994i	$0.501124\pi$
$480$		0			0
$481$	3.33588	+	18.9187i	0.152103	+	0.862618i
$482$		0			0
$483$	1.53050	+	0.0303215i	0.0696402	+	0.00137967i
$484$		0			0
$485$	4.15965	+	1.51399i	0.188880	+	0.0687467i
$486$		0			0
$487$	−21.9456	+	12.6703i	−0.994448	+	0.574145i	−0.906601	−	0.421989i	$-0.861332\pi$
$487$	−21.9456	+	12.6703i	−0.994448	+	0.574145i	−0.0878470	+	0.996134i	$0.527999\pi$
$488$		0			0
$489$	−17.6816	−	3.48020i	−0.799589	−	0.157380i
$490$		0			0
$491$	−7.76474	−	1.36913i	−0.350418	−	0.0617881i	−0.00433112	−	0.999991i	$-0.501379\pi$
$491$	−7.76474	−	1.36913i	−0.350418	−	0.0617881i	−0.346087	+	0.938202i	$0.612490\pi$
$492$		0			0
$493$		−	29.3665i		−	1.32260i
$494$		0			0
$495$	1.24056	−	1.96465i	0.0557589	−	0.0883044i
$496$		0			0
$497$	3.11645	−	17.6742i	0.139792	−	0.792798i
$498$		0			0
$499$	9.89069	+	8.29927i	0.442768	+	0.371526i	0.836744	−	0.547594i	$-0.184456\pi$
$499$	9.89069	+	8.29927i	0.442768	+	0.371526i	−0.393976	+	0.919121i	$0.628901\pi$
$500$		0			0
$501$	35.2744	+	21.3082i	1.57594	+	0.951982i
$502$		0			0
$503$	2.85952	−	7.85647i	0.127500	−	0.350303i	−0.859475	−	0.511178i	$-0.829209\pi$
$503$	2.85952	−	7.85647i	0.127500	−	0.350303i	0.986975	+	0.160875i	$0.0514316\pi$
$504$		0			0
$505$	0.840744	−	1.45621i	0.0374126	−	0.0648006i
$506$		0			0
$507$	4.39400	+	5.45235i	0.195144	+	0.242147i
$508$		0			0
$509$	−5.11088	+	4.28853i	−0.226536	+	0.190086i	−0.748990	−	0.662581i	$-0.769461\pi$
$509$	−5.11088	+	4.28853i	−0.226536	+	0.190086i	0.522454	+	0.852667i	$0.325016\pi$
$510$		0			0
$511$	−21.7614	+	7.92049i	−0.962666	+	0.350382i
$512$		0			0
$513$	19.3088	+	11.8394i	0.852503	+	0.522722i
$514$		0			0
$515$	−5.12894	+	1.86678i	−0.226008	+	0.0822603i
$516$		0			0
$517$	14.2127	−	11.9259i	0.625073	−	0.524499i
$518$		0			0
$519$	27.2302	+	33.7889i	1.19527	+	1.48317i
$520$		0			0
$521$	−7.75609	+	13.4339i	−0.339800	+	0.588552i	−0.984395	−	0.175973i	$-0.943693\pi$
$521$	−7.75609	+	13.4339i	−0.339800	+	0.588552i	0.644595	+	0.764525i	$0.277026\pi$
$522$		0			0
$523$	7.60779	−	20.9022i	0.332666	−	0.913991i	−0.654750	−	0.755845i	$-0.727226\pi$
$523$	7.60779	−	20.9022i	0.332666	−	0.913991i	0.987416	−	0.158146i	$-0.0505516\pi$
$524$		0			0
$525$	10.0171	+	6.05106i	0.437183	+	0.264090i
$526$		0			0
$527$	−21.0155	−	17.6341i	−0.915450	−	0.768154i
$528$		0			0
$529$	3.92786	−	22.2760i	0.170776	−	0.968521i
$530$		0			0
$531$	2.99399	−	4.74153i	0.129928	−	0.205765i
$532$		0			0
$533$		−	23.6718i		−	1.02534i
$534$		0			0
$535$	−6.10871	−	1.07713i	−0.264103	−	0.0465684i
$536$		0			0
$537$	26.4152	+	5.19921i	1.13990	+	0.224362i
$538$		0			0
$539$	6.21498	−	3.58822i	0.267698	−	0.154556i
$540$		0			0
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	0.493008	−	0.870025i	$-0.335897\pi$
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	−0.181575	+	0.983377i	$0.558119\pi$
$542$		0			0
$543$	−36.3063	−	0.719281i	−1.55805	−	0.0308673i
$544$		0			0
$545$	−0.00295864	−	0.0167793i	−0.000126734	−	0.000718746i
$546$		0			0
$547$	−18.1301	−	21.6066i	−0.775188	−	0.923833i	0.223518	−	0.974700i	$-0.428246\pi$
$547$	−18.1301	−	21.6066i	−0.775188	−	0.923833i	−0.998705	+	0.0508673i	$0.983801\pi$
$548$		0			0
$549$	−7.51224	+	34.5413i	−0.320615	+	1.47419i
$550$		0			0
$551$	21.9482	+	7.17807i	0.935026	+	0.305796i
$552$		0			0
$553$	3.92121	+	10.7734i	0.166747	+	0.458133i
$554$		0			0
$555$	−2.14001	+	5.53590i	−0.0908384	+	0.234986i
$556$		0			0
$557$	−30.7949	+	5.42997i	−1.30482	+	0.230075i	−0.782487	−	0.622666i	$-0.786049\pi$
$557$	−30.7949	+	5.42997i	−1.30482	+	0.230075i	−0.522333	+	0.852741i	$0.674938\pi$
$558$		0			0
$559$	−16.5369	−	9.54757i	−0.699435	−	0.403819i
$560$		0			0
$561$	−13.7632	+	2.14665i	−0.581082	+	0.0906317i
$562$		0			0
$563$	−4.37942	−	7.58538i	−0.184571	−	0.319686i	0.758861	−	0.651252i	$-0.225756\pi$
$563$	−4.37942	−	7.58538i	−0.184571	−	0.319686i	−0.943432	+	0.331567i	$0.892423\pi$
$564$		0			0
$565$	3.55073	−	4.23160i	0.149380	−	0.178025i
$566$		0			0
$567$	12.4305	−	3.43796i	0.522030	−	0.144381i
$568$		0			0
$569$	39.4950			1.65572			0.827859	−	0.560936i	$-0.189559\pi$
$569$	39.4950			1.65572			0.827859	+	0.560936i	$0.189559\pi$
$570$		0			0
$571$	1.49689			0.0626431			0.0313215	−	0.999509i	$-0.490028\pi$
$571$	1.49689			0.0626431			0.0313215	+	0.999509i	$0.490028\pi$
$572$		0			0
$573$	−2.61255	+	0.892695i	−0.109141	+	0.0372929i
$574$		0			0
$575$	−1.86921	+	2.22764i	−0.0779514	+	0.0928988i
$576$		0			0
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	0.733551	−	0.679634i	$-0.237861\pi$
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	−0.955356	+	0.295457i	$0.904528\pi$
$578$		0			0
$579$	−1.16274	−	7.45484i	−0.0483217	−	0.309813i
$580$		0			0
$581$	6.15662	+	3.55453i	0.255420	+	0.147467i
$582$		0			0
$583$	2.63804	−	0.465158i	0.109257	−	0.0192649i
$584$		0			0
$585$	−0.644706	−	4.74957i	−0.0266553	−	0.196371i
$586$		0			0
$587$	0.0214414	+	0.0589098i	0.000884983	+	0.00243147i	0.940134	−	0.340804i	$-0.110699\pi$
$587$	0.0214414	+	0.0589098i	0.000884983	+	0.00243147i	−0.939249	+	0.343236i	$0.888477\pi$
$588$		0			0
$589$	18.3164	−	11.3965i	0.754714	−	0.469584i
$590$		0			0
$591$	−8.58152	−	7.49537i	−0.352997	−	0.308318i
$592$		0			0
$593$	−10.0616	−	11.9910i	−0.413181	−	0.492409i	0.518811	−	0.854889i	$-0.326375\pi$
$593$	−10.0616	−	11.9910i	−0.413181	−	0.492409i	−0.931992	+	0.362479i	$0.881930\pi$
$594$		0			0
$595$	0.736374	+	4.17618i	0.0301884	+	0.171207i
$596$		0			0
$597$	−0.373902	+	18.8730i	−0.0153028	+	0.772421i
$598$		0			0
$599$	−2.10138	−	0.764839i	−0.0858600	−	0.0312505i	0.298733	−	0.954337i	$-0.403436\pi$
$599$	−2.10138	−	0.764839i	−0.0858600	−	0.0312505i	−0.384593	+	0.923086i	$0.625658\pi$
$600$		0			0
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	−0.792197	−	0.610266i	$-0.791063\pi$
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	0.132407	+	0.991195i	$0.457729\pi$
$602$		0			0
$603$	−8.47342	−	26.5027i	−0.345064	−	1.07927i
$604$		0			0
$605$	4.67646	+	0.824586i	0.190125	+	0.0335242i
$606$		0			0
$607$			43.2872i			1.75697i	0.477766	+	0.878487i	$0.341447\pi$
$607$			43.2872i			1.75697i	−0.477766	+	0.878487i	$0.658553\pi$
$608$		0			0
$609$	11.5155	−	6.34776i	0.466634	−	0.257224i
$610$		0			0
$611$	6.64602	−	37.6915i	0.268869	−	1.52483i
$612$		0			0
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	0.493902	−	0.869518i	$-0.335570\pi$
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	−0.770542	+	0.637389i	$0.780015\pi$
$614$		0			0
$615$	3.78147	−	6.25998i	0.152484	−	0.252427i
$616$		0			0
$617$	−8.89796	+	24.4469i	−0.358218	+	0.984197i	0.621429	+	0.783470i	$0.286552\pi$
$617$	−8.89796	+	24.4469i	−0.358218	+	0.984197i	−0.979647	+	0.200726i	$0.935670\pi$
$618$		0			0
$619$	9.72654	−	16.8469i	0.390943	−	0.677133i	−0.601631	−	0.798774i	$-0.705482\pi$
$619$	9.72654	−	16.8469i	0.390943	−	0.677133i	0.992574	+	0.121641i	$0.0388157\pi$
$620$		0			0
$621$	0.368069	+	3.18351i	0.0147701	+	0.127750i
$622$		0			0
$623$	−5.26042	+	4.41402i	−0.210754	+	0.176844i
$624$		0			0
$625$	−19.5516	+	7.11620i	−0.782064	+	0.284648i
$626$		0			0
$627$	1.75976	−	10.8112i	0.0702779	−	0.431757i
$628$		0			0
$629$	33.4353	−	12.1695i	1.33315	−	0.485228i
$630$		0			0
$631$	11.6007	−	9.73414i	0.461816	−	0.387510i	−0.381982	−	0.924170i	$-0.624759\pi$
$631$	11.6007	−	9.73414i	0.461816	−	0.387510i	0.843799	+	0.536660i	$0.180314\pi$
$632$		0			0
$633$	10.2087	−	8.22711i	0.405760	−	0.326998i
$634$		0			0
$635$	−0.209281	+	0.362485i	−0.00830506	+	0.0143848i
$636$		0			0
$637$	5.06326	−	13.9112i	0.200614	−	0.551182i
$638$		0			0
$639$	37.5421	+	1.48811i	1.48514	+	0.0588688i
$640$		0			0
$641$	−28.6682	−	24.0555i	−1.13233	−	0.950135i	−0.133166	−	0.991094i	$-0.542514\pi$
$641$	−28.6682	−	24.0555i	−1.13233	−	0.950135i	−0.999161	+	0.0409586i	$0.986959\pi$
$642$		0			0
$643$	−1.81700	+	10.3047i	−0.0716554	+	0.406378i	0.927791	+	0.373101i	$0.121705\pi$
$643$	−1.81700	+	10.3047i	−0.0716554	+	0.406378i	−0.999446	+	0.0332769i	$0.989406\pi$
$644$		0			0
$645$	−2.84797	−	5.16653i	−0.112139	−	0.203432i
$646$		0			0
$647$			15.2706i			0.600348i	0.953884	+	0.300174i	$0.0970448\pi$
$647$			15.2706i			0.600348i	−0.953884	+	0.300174i	$0.902955\pi$
$648$		0			0
$649$	−2.67071	−	0.470919i	−0.104835	−	0.0184852i
$650$		0			0
$651$	2.37226	−	12.0526i	0.0929763	−	0.472378i
$652$		0			0
$653$	−2.32583	+	1.34282i	−0.0910168	+	0.0525486i	−0.544818	−	0.838555i	$-0.683401\pi$
$653$	−2.32583	+	1.34282i	−0.0910168	+	0.0525486i	0.453801	+	0.891103i	$0.350068\pi$
$654$		0			0
$655$	−5.77850	−	2.10320i	−0.225785	−	0.0821789i
$656$		0			0
$657$	−22.5585	−	42.9129i	−0.880091	−	1.67419i
$658$		0			0
$659$	−5.97002	−	33.8577i	−0.232559	−	1.31891i	−0.847694	−	0.530486i	$-0.822009\pi$
$659$	−5.97002	−	33.8577i	−0.232559	−	1.31891i	0.615134	−	0.788422i	$-0.289102\pi$
$660$		0			0
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	0.938799	−	0.344465i	$-0.111940\pi$
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	−0.502253	+	0.864721i	$0.667495\pi$
$662$		0			0
$663$	−18.9027	+	21.6419i	−0.734121	+	0.840503i
$664$		0			0
$665$	−3.30123	−	0.470429i	−0.128016	−	0.0182425i
$666$		0			0
$667$	1.11750	+	3.07031i	0.0432698	+	0.118883i
$668$		0			0
$669$	−18.6025	−	7.19114i	−0.719213	−	0.278025i
$670$		0			0
$671$	16.8352	−	2.96851i	0.649917	−	0.114598i
$672$		0			0
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.474863	−	0.880060i	$-0.657502\pi$
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.999586	+	0.0287864i	$0.990836\pi$
$674$		0			0
$675$	−9.73201	+	22.4841i	−0.374585	+	0.865413i
$676$		0			0
$677$	−9.28464	−	16.0815i	−0.356838	−	0.618061i	0.630593	−	0.776114i	$-0.282812\pi$
$677$	−9.28464	−	16.0815i	−0.356838	−	0.618061i	−0.987431	+	0.158053i	$0.949478\pi$
$678$		0			0
$679$	7.63791	−	9.10251i	0.293116	−	0.349322i
$680$		0			0
$681$	−0.864093	−	2.52884i	−0.0331121	−	0.0969055i
$682$		0			0
$683$	18.9873			0.726527			0.363264	−	0.931686i	$-0.381662\pi$
$683$	18.9873			0.726527			0.363264	+	0.931686i	$0.381662\pi$
$684$		0			0
$685$	−7.23041			−0.276260
$686$		0			0
$687$	4.57741	+	13.3962i	0.174639	+	0.511096i
$688$		0			0
$689$	3.55195	−	4.23305i	0.135319	−	0.161266i
$690$		0			0
$691$	−7.53839	−	13.0569i	−0.286774	−	0.496707i	0.686264	−	0.727352i	$-0.259249\pi$
$691$	−7.53839	−	13.0569i	−0.286774	−	0.496707i	−0.973038	+	0.230646i	$0.925916\pi$
$692$		0			0
$693$	−3.81677	−	4.93298i	−0.144987	−	0.187388i
$694$		0			0
$695$	−3.34547	−	1.93151i	−0.126901	−	0.0732662i
$696$		0			0
$697$	−43.1781	+	7.61346i	−1.63549	+	0.288380i
$698$		0			0
$699$	13.5623	+	5.24275i	0.512972	+	0.198299i
$700$		0			0
$701$	4.16179	+	11.4344i	0.157189	+	0.431872i	0.993140	−	0.116931i	$-0.0373057\pi$
$701$	4.16179	+	11.4344i	0.157189	+	0.431872i	−0.835951	+	0.548804i	$0.815083\pi$
$702$		0			0
$703$	0.922720	+	27.9638i	0.0348010	+	1.05468i
$704$		0			0
$705$	7.77857	−	8.90577i	0.292958	−	0.335411i
$706$		0			0
$707$	−2.90133	−	3.45768i	−0.109116	−	0.130039i
$708$		0			0
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	−0.803369	−	0.595481i	$-0.796961\pi$
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	0.551253	−	0.834338i	$-0.314150\pi$
$710$		0			0
$711$	−21.2449	+	11.1681i	−0.796747	+	0.418835i
$712$		0			0
$713$	2.86824	+	1.04395i	0.107417	+	0.0390964i
$714$		0			0
$715$	−2.00744	+	1.15900i	−0.0750740	+	0.0433440i
$716$		0			0
$717$	−2.93868	+	14.9303i	−0.109747	+	0.557584i
$718$		0			0
$719$	26.0696	+	4.59678i	0.972233	+	0.171431i	0.637135	−	0.770752i	$-0.280119\pi$
$719$	26.0696	+	4.59678i	0.972233	+	0.171431i	0.335098	+	0.942183i	$0.391231\pi$
$720$		0			0
$721$			14.6514i			0.545646i
$722$		0			0
$723$	11.2370	+	20.3852i	0.417909	+	0.758134i
$724$		0			0
$725$	−4.33752	+	24.5993i	−0.161091	+	0.913595i
$726$		0			0
$727$	−23.0429	−	19.3353i	−0.854614	−	0.717107i	0.106187	−	0.994346i	$-0.466136\pi$
$727$	−23.0429	−	19.3353i	−0.854614	−	0.717107i	−0.960801	+	0.277240i	$0.910580\pi$
$728$		0			0
$729$	10.6322	+	24.8185i	0.393785	+	0.919203i
$730$		0			0
$731$	−12.0964	+	33.2345i	−0.447400	+	1.22922i
$732$		0			0
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	−0.762339	−	0.647178i	$-0.775949\pi$
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	0.941642	+	0.336616i	$0.109282\pi$
$734$		0			0
$735$	3.56122	−	2.86996i	0.131358	−	0.105860i
$736$		0			0
$737$	−10.3079	+	8.64938i	−0.379697	+	0.318604i
$738$		0			0
$739$	46.3353	−	16.8647i	1.70447	−	0.620377i	0.708150	−	0.706062i	$-0.249530\pi$
$739$	46.3353	−	16.8647i	1.70447	−	0.620377i	0.996322	+	0.0856846i	$0.0273078\pi$
$740$		0			0
$741$	−11.5546	−	19.4177i	−0.424468	−	0.713326i
$742$		0			0
$743$	−6.36036	+	2.31498i	−0.233339	+	0.0849285i	−0.456043	−	0.889958i	$-0.650734\pi$
$743$	−6.36036	+	2.31498i	−0.233339	+	0.0849285i	0.222704	+	0.974886i	$0.428512\pi$
$744$		0			0
$745$	−8.06409	+	6.76658i	−0.295445	+	0.247908i
$746$		0			0
$747$	−5.64011	+	13.7726i	−0.206361	+	0.503913i
$748$		0			0
$749$	−8.32539	+	14.4200i	−0.304203	+	0.526895i
$750$		0			0
$751$	−7.71871	+	21.2070i	−0.281660	+	0.773853i	0.715505	+	0.698607i	$0.246196\pi$
$751$	−7.71871	+	21.2070i	−0.281660	+	0.773853i	−0.997165	+	0.0752462i	$0.976026\pi$
$752$		0			0
$753$	7.03597	−	11.6476i	0.256405	−	0.424462i
$754$		0			0
$755$	−1.73017	−	1.45179i	−0.0629675	−	0.0528360i
$756$		0			0
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	0.142523	+	0.989791i	$0.454478\pi$
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	−0.472457	+	0.881354i	$0.656633\pi$
$758$		0			0
$759$	1.35727	−	0.748174i	0.0492659	−	0.0271570i
$760$		0			0
$761$			16.8329i			0.610193i	0.952321	+	0.305097i	$0.0986888\pi$
$761$			16.8329i			0.610193i	−0.952321	+	0.305097i	$0.901311\pi$
$762$		0			0
$763$	−0.0450412	−	0.00794198i	−0.00163060	−	0.000287519i
$764$		0			0
$765$	−8.45599	+	2.70354i	−0.305727	+	0.0977468i
$766$		0			0
$767$	−4.84480	+	2.79715i	−0.174936	+	0.100999i
$768$		0			0
$769$	2.83204	+	1.03078i	0.102126	+	0.0371708i	0.392578	−	0.919719i	$-0.371583\pi$
$769$	2.83204	+	1.03078i	0.102126	+	0.0371708i	−0.290452	+	0.956890i	$0.593806\pi$
$770$		0			0
$771$	0.421482	−	21.2747i	0.0151793	−	0.766189i
$772$		0			0
$773$	8.98386	+	50.9500i	0.323127	+	1.83254i	0.522523	+	0.852625i	$0.324991\pi$
$773$	8.98386	+	50.9500i	0.323127	+	1.83254i	−0.199396	+	0.979919i	$0.563898\pi$
$774$		0			0
$775$	14.9994	+	17.8755i	0.538793	+	0.642108i
$776$		0			0
$777$	11.9993	+	10.4806i	0.430472	+	0.375988i
$778$		0			0
$779$	4.86382	−	34.1319i	0.174265	−	1.22290i
$780$		0			0
$781$	−6.21447	−	17.0741i	−0.222371	−	0.610960i
$782$		0			0
$783$	16.4108	+	22.1011i	0.586475	+	0.789831i
$784$		0			0
$785$	−5.34270	+	0.942061i	−0.190689	+	0.0336236i
$786$		0			0
$787$	−14.8092	−	8.55010i	−0.527891	−	0.304778i	0.212266	−	0.977212i	$-0.431916\pi$
$787$	−14.8092	−	8.55010i	−0.527891	−	0.304778i	−0.740157	+	0.672434i	$0.765249\pi$
$788$		0			0
$789$	6.36149	+	40.7865i	0.226475	+	1.45204i
$790$		0			0
$791$	−7.41407	−	12.8416i	−0.263614	−	0.456593i
$792$		0			0
$793$	22.6675	−	27.0141i	0.804948	−	0.959300i
$794$		0			0
$795$	1.61552	−	0.552015i	0.0572966	−	0.0195779i
$796$		0			0
$797$	−7.92776			−0.280816			−0.140408	−	0.990094i	$-0.544841\pi$
$797$	−7.92776			−0.280816			−0.140408	+	0.990094i	$0.544841\pi$
$798$		0			0
$799$	−70.8878			−2.50783
$800$		0			0
$801$	−10.6380	−	9.66962i	−0.375875	−	0.341659i
$802$		0			0
$803$	−15.0706	+	17.9605i	−0.531831	+	0.633811i
$804$		0			0
$805$	−0.235908	−	0.408604i	−0.00831466	−	0.0144014i
$806$		0			0
$807$	−32.5452	+	5.07609i	−1.14564	+	0.178687i
$808$		0			0
$809$	−3.32547	−	1.91996i	−0.116917	−	0.0675022i	0.440401	−	0.897801i	$-0.354836\pi$
$809$	−3.32547	−	1.91996i	−0.116917	−	0.0675022i	−0.557318	+	0.830299i	$0.688170\pi$
$810$		0			0
$811$	−27.5374	+	4.85558i	−0.966968	+	0.170503i	−0.634765	−	0.772705i	$-0.718903\pi$
$811$	−27.5374	+	4.85558i	−0.966968	+	0.170503i	−0.332203	+	0.943208i	$0.607792\pi$
$812$		0			0
$813$	−3.37151	+	8.72161i	−0.118244	+	0.305880i
$814$		0			0
$815$	1.89968	+	5.21932i	0.0665428	+	0.182825i
$816$		0			0
$817$	−21.8824	−	17.1642i	−0.765568	−	0.600500i
$818$		0			0
$819$	−12.5724	−	2.73433i	−0.439317	−	0.0955451i
$820$		0			0
$821$	31.0592	+	37.0149i	1.08397	+	1.29183i	0.953834	+	0.300333i	$0.0970979\pi$
$821$	31.0592	+	37.0149i	1.08397	+	1.29183i	0.130139	+	0.991496i	$0.458458\pi$
$822$		0			0
$823$	−7.99935	−	45.3666i	−0.278840	−	1.58138i	−0.726494	−	0.687173i	$-0.758851\pi$
$823$	−7.99935	−	45.3666i	−0.278840	−	1.58138i	0.447654	−	0.894207i	$-0.352260\pi$
$824$		0			0
$825$	11.8460	+	0.234687i	0.412425	+	0.00817075i
$826$		0			0
$827$	−26.1088	−	9.50281i	−0.907891	−	0.330445i	−0.154480	−	0.987996i	$-0.549370\pi$
$827$	−26.1088	−	9.50281i	−0.907891	−	0.330445i	−0.753410	+	0.657551i	$0.771593\pi$
$828$		0			0
$829$	18.4501	−	10.6521i	0.640797	−	0.369964i	−0.144125	−	0.989560i	$-0.546037\pi$
$829$	18.4501	−	10.6521i	0.640797	−	0.369964i	0.784921	+	0.619595i	$0.212703\pi$
$830$		0			0
$831$	−0.158713	−	0.0312389i	−0.00550570	−	0.00108366i
$832$		0			0
$833$	−27.0029	−	4.76134i	−0.935594	−	0.164970i
$834$		0			0
$835$		−	12.7018i		−	0.439563i
$836$		0			0
$837$	25.6707	+	1.52732i	0.887308	+	0.0527919i
$838$		0			0
$839$	−6.05886	+	34.3615i	−0.209175	+	1.18629i	0.681558	+	0.731765i	$0.261303\pi$
$839$	−6.05886	+	34.3615i	−0.209175	+	1.18629i	−0.890733	+	0.454527i	$0.849808\pi$
$840$		0			0
$841$	−0.715656	−	0.600507i	−0.0246778	−	0.0207071i
$842$		0			0
$843$	15.1247	+	9.13641i	0.520923	+	0.314675i
$844$		0			0
$845$	0.738176	−	2.02812i	0.0253940	−	0.0697695i
$846$		0			0
$847$	6.37342	−	11.0391i	0.218993	−	0.379307i
$848$		0			0
$849$	21.0189	+	26.0816i	0.721368	+	0.895118i
$850$		0			0
$851$	−3.03262	+	2.54467i	−0.103957	+	0.0872301i
$852$		0			0
$853$	−0.565541	+	0.205840i	−0.0193638	+	0.00704783i	−0.351684	−	0.936119i	$-0.614391\pi$
$853$	−0.565541	+	0.205840i	−0.0193638	+	0.00704783i	0.332320	+	0.943167i	$0.392169\pi$
$854$		0			0
$855$	0.0463028	−	6.98076i	0.00158352	−	0.238737i
$856$		0			0
$857$	−4.78193	+	1.74048i	−0.163348	+	0.0594537i	−0.422400	−	0.906410i	$-0.638812\pi$
$857$	−4.78193	+	1.74048i	−0.163348	+	0.0594537i	0.259052	+	0.965863i	$0.416590\pi$
$858$		0			0
$859$	−23.1806	+	19.4509i	−0.790913	+	0.663655i	−0.945971	−	0.324250i	$-0.894888\pi$
$859$	−23.1806	+	19.4509i	−0.790913	+	0.663655i	0.155058	+	0.987905i	$0.450444\pi$
$860$		0			0
$861$	−12.3187	−	15.2858i	−0.419821	−	0.520940i
$862$		0			0
$863$	−20.1792	+	34.9514i	−0.686908	+	1.18976i	0.285925	+	0.958252i	$0.407699\pi$
$863$	−20.1792	+	34.9514i	−0.686908	+	1.18976i	−0.972833	+	0.231508i	$0.925634\pi$
$864$		0			0
$865$	4.57457	−	12.5685i	0.155540	−	0.427343i
$866$		0			0
$867$	20.3517	+	12.2939i	0.691179	+	0.417521i
$868$		0			0
$869$	8.89172	+	7.46104i	0.301631	+	0.253098i
$870$		0			0
$871$	−4.82011	+	27.3362i	−0.163323	+	0.926252i
$872$		0			0
$873$	21.0336	+	13.2814i	0.711879	+	0.449508i
$874$		0			0
$875$		−	7.43204i		−	0.251249i
$876$		0			0
$877$	34.2610	+	6.04114i	1.15691	+	0.203995i	0.718992	−	0.695019i	$-0.244604\pi$
$877$	34.2610	+	6.04114i	1.15691	+	0.203995i	0.437921	+	0.899014i	$0.355715\pi$
$878$		0			0
$879$	27.5061	+	5.41392i	0.927759	+	0.182607i
$880$		0			0
$881$	−9.93336	+	5.73503i	−0.334663	+	0.193218i	−0.657910	−	0.753097i	$-0.728559\pi$
$881$	−9.93336	+	5.73503i	−0.334663	+	0.193218i	0.323246	+	0.946315i	$0.395226\pi$
$882$		0			0
$883$	−4.25598	−	1.54905i	−0.143225	−	0.0521297i	0.269413	−	0.963025i	$-0.413170\pi$
$883$	−4.25598	−	1.54905i	−0.143225	−	0.0521297i	−0.412638	+	0.910895i	$0.635393\pi$
$884$		0			0
$885$	−1.72803	−	0.0342348i	−0.0580871	−	0.00115079i
$886$		0			0
$887$	9.37732	+	53.1814i	0.314859	+	1.78566i	0.573006	+	0.819551i	$0.305777\pi$
$887$	9.37732	+	53.1814i	0.314859	+	1.78566i	−0.258147	+	0.966106i	$0.583112\pi$
$888$		0			0
$889$	0.722210	+	0.860696i	0.0242221	+	0.0288668i
$890$		0			0
$891$	9.15853	−	9.30683i	0.306822	−	0.311790i
$892$		0			0
$893$	17.3272	−	52.9809i	0.579831	−	1.77294i
$894$		0			0
$895$	−2.83801	−	7.79736i	−0.0948641	−	0.260637i
$896$		0			0
$897$	1.15275	−	2.98201i	0.0384893	−	0.0995665i
$898$		0			0
$899$	25.8204	−	4.55283i	0.861158	−	0.151845i
$900$		0			0
$901$	−8.86360	−	5.11740i	−0.295289	−	0.170485i
$902$		0			0
$903$	−15.6470	+	2.44047i	−0.520700	+	0.0812139i
$904$		0			0
$905$	5.59617	+	9.69284i	0.186023	+	0.322201i
$906$		0			0
$907$	−4.49918	+	5.36192i	−0.149393	+	0.178039i	−0.835551	−	0.549413i	$-0.814851\pi$
$907$	−4.49918	+	5.36192i	−0.149393	+	0.178039i	0.686158	+	0.727452i	$0.259296\pi$
$908$		0			0
$909$	6.35585	−	6.99235i	0.210810	−	0.231922i
$910$		0			0
$911$	−13.0438			−0.432160			−0.216080	−	0.976376i	$-0.569327\pi$
$911$	−13.0438			−0.432160			−0.216080	+	0.976376i	$0.569327\pi$
$912$		0			0
$913$	7.19739			0.238199
$914$		0			0
$915$	10.3098	−	3.52280i	0.340831	−	0.116460i
$916$		0			0
$917$	−10.6104	+	12.6450i	−0.350387	+	0.417575i
$918$		0			0
$919$	3.44700	+	5.97038i	0.113706	+	0.196945i	0.917262	−	0.398285i	$-0.130394\pi$
$919$	3.44700	+	5.97038i	0.113706	+	0.196945i	−0.803556	+	0.595229i	$0.797061\pi$
$920$		0			0
$921$	4.76111	+	30.5257i	0.156884	+	1.00586i
$922$		0			0
$923$	−32.4603	−	18.7410i	−1.06844	−	0.616867i
$924$		0			0
$925$	−29.8051	+	5.25544i	−0.979985	+	0.172798i
$926$		0			0
$927$	−30.3938	+	4.12564i	−0.998262	+	0.135504i
$928$		0			0
$929$	13.7442	+	37.7618i	0.450931	+	1.23892i	0.932070	+	0.362279i	$0.118001\pi$
$929$	13.7442	+	37.7618i	0.450931	+	1.23892i	−0.481139	+	0.876645i	$0.659777\pi$
$930$		0			0
$931$	10.1589	−	19.0179i	0.332945	−	0.623286i
$932$		0			0
$933$	−42.7032	−	37.2983i	−1.39804	−	1.22109i
$934$		0			0
$935$	2.75968	+	3.28886i	0.0902513	+	0.107557i
$936$		0			0
$937$	3.70352	+	21.0037i	0.120989	+	0.686161i	0.983610	+	0.180310i	$0.0577101\pi$
$937$	3.70352	+	21.0037i	0.120989	+	0.686161i	−0.862621	+	0.505850i	$0.831179\pi$
$938$		0			0
$939$	−0.906477	+	45.7552i	−0.0295818	+	1.49316i
$940$		0			0
$941$	−33.1057	−	12.0495i	−1.07922	−	0.392802i	−0.259600	−	0.965716i	$-0.583591\pi$
$941$	−33.1057	−	12.0495i	−1.07922	−	0.392802i	−0.819616	+	0.572914i	$0.805813\pi$
$942$		0			0
$943$	4.22461	−	2.43908i	0.137572	−	0.0794274i
$944$		0			0
$945$	−2.88797	−	2.73148i	−0.0939455	−	0.0888551i
$946$		0			0
$947$	26.6972	+	4.70744i	0.867542	+	0.152971i	0.589667	−	0.807646i	$-0.299259\pi$
$947$	26.6972	+	4.70744i	0.867542	+	0.152971i	0.277875	+	0.960617i	$0.410370\pi$
$948$		0			0
$949$			48.3652i			1.57000i
$950$		0			0
$951$	20.3392	−	11.2116i	0.659543	−	0.363562i
$952$		0			0
$953$	1.20982	−	6.86124i	0.0391900	−	0.222258i	−0.958923	−	0.283668i	$-0.908449\pi$
$953$	1.20982	−	6.86124i	0.0391900	−	0.222258i	0.998113	+	0.0614103i	$0.0195598\pi$
$954$		0			0
$955$	0.651855	+	0.546972i	0.0210935	+	0.0176996i
$956$		0			0
$957$	6.88336	−	11.3950i	0.222508	−	0.368347i
$958$		0			0
$959$	−6.63821	+	18.2383i	−0.214359	+	0.588947i
$960$		0			0
$961$	−3.25341	+	5.63508i	−0.104949	+	0.181777i
$962$		0			0
$963$	−32.2581	−	13.2102i	−1.03950	−	0.425694i
$964$		0			0
$965$	−1.78142	+	1.49479i	−0.0573458	+	0.0481188i
$966$		0			0
$967$	37.2609	−	13.5619i	1.19823	−	0.436120i	0.335623	−	0.941996i	$-0.391053\pi$
$967$	37.2609	−	13.5619i	1.19823	−	0.436120i	0.862606	+	0.505876i	$0.168831\pi$
$968$		0			0
$969$	−31.7021	+	27.3211i	−1.01842	+	0.877679i
$970$		0			0
$971$	−48.3722	+	17.6060i	−1.55234	+	0.565004i	−0.968964	−	0.247201i	$-0.920489\pi$
$971$	−48.3722	+	17.6060i	−1.55234	+	0.565004i	−0.583372	+	0.812205i	$0.698267\pi$
$972$		0			0
$973$	−7.94358	+	6.66546i	−0.254660	+	0.213685i
$974$		0			0
$975$	19.0307	−	15.3367i	0.609472	−	0.491168i
$976$		0			0
$977$	29.8636	−	51.7252i	0.955421	−	1.65484i	0.222018	−	0.975042i	$-0.428736\pi$
$977$	29.8636	−	51.7252i	0.955421	−	1.65484i	0.733402	−	0.679795i	$-0.237931\pi$
$978$		0			0
$979$	−2.37783	+	6.53305i	−0.0759959	+	0.208797i
$980$		0			0
$981$	0.00379232	−	0.0956727i	0.000121080	−	0.00305459i
$982$		0			0
$983$	27.8849	+	23.3982i	0.889391	+	0.746288i	0.968088	−	0.250611i	$-0.0806315\pi$
$983$	27.8849	+	23.3982i	0.889391	+	0.746288i	−0.0786969	+	0.996899i	$0.525076\pi$
$984$		0			0
$985$	−0.609817	+	3.45845i	−0.0194304	+	0.110195i
$986$		0			0
$987$	−15.3229	−	27.7974i	−0.487732	−	0.884801i
$988$		0			0
$989$		−	3.93502i		−	0.125126i
$990$		0			0
$991$	45.8935	+	8.09227i	1.45786	+	0.257059i	0.845692	−	0.533671i	$-0.179188\pi$
$991$	45.8935	+	8.09227i	1.45786	+	0.257059i	0.612164	+	0.790730i	$0.290299\pi$
$992$		0			0
$993$	−8.36018	+	42.4750i	−0.265302	+	1.34790i
$994$		0			0
$995$	5.03861	−	2.90904i	0.159735	−	0.0922229i
$996$		0			0
$997$	6.98731	+	2.54317i	0.221290	+	0.0805430i	0.450286	−	0.892884i	$-0.351322\pi$
$997$	6.98731	+	2.54317i	0.221290	+	0.0805430i	−0.228996	+	0.973427i	$0.573544\pi$
$998$		0			0
$999$	−18.3627	+	27.8433i	−0.580970	+	0.880923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.d.641.2		18
3.2	odd	2		912.2.cc.c.641.1		18
4.3	odd	2		114.2.l.a.71.2	yes	18
12.11	even	2		114.2.l.b.71.3	yes	18
19.15	odd	18		912.2.cc.c.737.1		18
57.53	even	18	inner	912.2.cc.d.737.2		18
76.15	even	18		114.2.l.b.53.3	yes	18
228.167	odd	18		114.2.l.a.53.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.2	✓	18	228.167	odd	18
114.2.l.a.71.2	yes	18	4.3	odd	2
114.2.l.b.53.3	yes	18	76.15	even	18
114.2.l.b.71.3	yes	18	12.11	even	2
912.2.cc.c.641.1		18	3.2	odd	2
912.2.cc.c.737.1		18	19.15	odd	18
912.2.cc.d.641.2		18	1.1	even	1	trivial
912.2.cc.d.737.2		18	57.53	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.560041 - 1.63901i) q^{3} +(-0.343148 + 0.408948i) q^{5} +(0.716507 + 1.24103i) q^{7} +(-2.37271 + 1.83583i) q^{9} +O(q^{10})\)	\(q+(-0.560041 - 1.63901i) q^{3} +(-0.343148 + 0.408948i) q^{5} +(0.716507 + 1.24103i) q^{7} +(-2.37271 + 1.83583i) q^{9} +(1.25645 + 0.725411i) q^{11} +(2.94737 - 0.519701i) q^{13} +(0.862447 + 0.333396i) q^{15} +(-1.89590 - 5.20894i) q^{17} +(4.35653 - 0.143752i) q^{19} +(1.63278 - 1.86939i) q^{21} +(0.396438 + 0.472456i) q^{23} +(0.818753 + 4.64338i) q^{25} +(4.33775 + 2.86075i) q^{27} +(4.97822 + 1.81193i) q^{29} +(4.28601 - 2.47453i) q^{31} +(0.485293 - 2.46559i) q^{33} +(-0.753384 - 0.132842i) q^{35} +6.41883i q^{37} +(-2.50245 - 4.53972i) q^{39} +(1.37347 - 7.78933i) q^{41} +(-4.88757 - 4.10116i) q^{43} +(0.0634325 - 1.60027i) q^{45} +(4.37381 - 12.0169i) q^{47} +(2.47323 - 4.28377i) q^{49} +(-7.47572 + 6.02462i) q^{51} +(1.41439 - 1.18682i) q^{53} +(-0.727804 + 0.264899i) q^{55} +(-2.67545 - 7.05989i) q^{57} +(-1.75650 + 0.639313i) q^{59} +(9.02625 - 7.57392i) q^{61} +(-3.97837 - 1.62921i) q^{63} +(-0.798855 + 1.38366i) q^{65} +(-3.17216 + 8.71543i) q^{67} +(0.552339 - 0.914360i) q^{69} +(-9.59384 - 8.05019i) q^{71} +(-2.80621 + 15.9148i) q^{73} +(7.15201 - 3.94243i) q^{75} +2.07905i q^{77} +(7.87896 + 1.38927i) q^{79} +(2.25948 - 8.71176i) q^{81} +(4.29627 - 2.48045i) q^{83} +(2.78076 + 1.01211i) q^{85} +(0.181753 - 9.17411i) q^{87} +(0.832120 + 4.71919i) q^{89} +(2.75678 + 3.28540i) q^{91} +(-6.45612 - 5.63897i) q^{93} +(-1.43615 + 1.83092i) q^{95} +(-2.83601 - 7.79188i) q^{97} +(-4.31291 + 0.585434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53} - 30 q^{55} + 12 q^{57} + 3 q^{59} + 54 q^{61} - 84 q^{63} - 24 q^{65} + 15 q^{67} + 24 q^{69} + 36 q^{71} - 42 q^{73} + 6 q^{79} + 36 q^{83} + 54 q^{87} + 60 q^{89} + 18 q^{91} - 84 q^{93} + 6 q^{95} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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