LMFDB - Embedded newform 912.2.bo.h.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 12 x^{10} - 16 x^{9} - 6 x^{8} + 27 x^{7} + 5 x^{6} - 27 x^{5} - 6 x^{4} + 16 x^{3} + \cdots + 1 $ x^12 - 3x^11 + 12x^10 - 16x^9 - 6x^8 + 27x^7 + 5x^6 - 27x^5 - 6x^4 + 16x^3 + 12x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$1.05581 - 0.885927i$ of defining polynomial
Character	$\chi$	$=$	912.289
Dual form			912.2.bo.h.385.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{3} +(-1.05581 + 0.885927i) q^{5} +(0.112213 - 0.194359i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-0.735431 - 1.27380i) q^{11} +(-0.821851 + 4.66095i) q^{13} +(1.05581 + 0.885927i) q^{15} +(-3.95753 - 1.44042i) q^{17} +(-1.63007 - 4.04263i) q^{19} +(-0.210892 - 0.0767582i) q^{21} +(-0.242193 - 0.203224i) q^{23} +(-0.538380 + 3.05330i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-7.31385 + 2.66202i) q^{29} +(-1.24150 + 2.15035i) q^{31} +(-1.12675 + 0.945452i) q^{33} +(0.0537123 + 0.304618i) q^{35} -0.191209 q^{37} +4.73285 q^{39} +(-0.144260 - 0.818139i) q^{41} +(-9.37929 + 7.87016i) q^{43} +(0.689129 - 1.19361i) q^{45} +(2.93341 - 1.06767i) q^{47} +(3.47482 + 6.01856i) q^{49} +(-0.731322 + 4.14753i) q^{51} +(-0.453098 - 0.380194i) q^{53} +(1.90497 + 0.693352i) q^{55} +(-3.69815 + 2.30731i) q^{57} +(-10.8224 - 3.93902i) q^{59} +(4.81237 + 4.03806i) q^{61} +(-0.0389712 + 0.221017i) q^{63} +(-3.26154 - 5.64916i) q^{65} +(-3.53896 + 1.28807i) q^{67} +(-0.158080 + 0.273803i) q^{69} +(-0.237470 + 0.199261i) q^{71} +(-0.975891 - 5.53455i) q^{73} +3.10041 q^{75} -0.330100 q^{77} +(0.0118758 + 0.0673508i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-4.33891 + 7.51521i) q^{83} +(5.45449 - 1.98527i) q^{85} +(3.89162 + 6.74048i) q^{87} +(1.06141 - 6.01955i) q^{89} +(0.813673 + 0.682753i) q^{91} +(2.33327 + 0.849239i) q^{93} +(5.30252 + 2.82411i) q^{95} +(10.7305 + 3.90559i) q^{97} +(1.12675 + 0.945452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{11} + 9 q^{13} + 3 q^{15} - 9 q^{17} - 6 q^{19} + 12 q^{21} - 24 q^{23} - 15 q^{25} + 6 q^{27} - 3 q^{29} - 3 q^{31} - 24 q^{35} - 30 q^{37} - 6 q^{39} + 15 q^{41} - 27 q^{43} + 3 q^{45}+ \cdots + 39 q^{97}+O(q^{100}) $ 12 * q - 3 * q^5 + 3 * q^11 + 9 * q^13 + 3 * q^15 - 9 * q^17 - 6 * q^19 + 12 * q^21 - 24 * q^23 - 15 * q^25 + 6 * q^27 - 3 * q^29 - 3 * q^31 - 24 * q^35 - 30 * q^37 - 6 * q^39 + 15 * q^41 - 27 * q^43 + 3 * q^45 + 30 * q^47 - 12 * q^49 + 6 * q^53 + 12 * q^55 + 3 * q^57 + 3 * q^59 - 6 * q^61 + 6 * q^63 - 9 * q^65 + 45 * q^67 + 12 * q^69 - 27 * q^71 + 21 * q^73 + 30 * q^75 - 30 * q^77 + 3 * q^79 - 6 * q^83 + 51 * q^85 + 3 * q^87 - 3 * q^89 + 42 * q^91 - 9 * q^93 - 24 * q^95 + 39 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$		0			0
$5$	−1.05581	+	0.885927i	−0.472171	+	0.396199i	−0.847586	−	0.530658i	$-0.821945\pi$
$5$	−1.05581	+	0.885927i	−0.472171	+	0.396199i	0.375415	+	0.926857i	$0.377500\pi$
$6$		0			0
$7$	0.112213	−	0.194359i	0.0424125	−	0.0734607i	−0.844040	−	0.536280i	$-0.819829\pi$
$7$	0.112213	−	0.194359i	0.0424125	−	0.0734607i	0.886452	+	0.462820i	$0.153162\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	−0.735431	−	1.27380i	−0.221741	−	0.384066i	0.733596	−	0.679586i	$-0.237841\pi$
$11$	−0.735431	−	1.27380i	−0.221741	−	0.384066i	−0.955337	+	0.295520i	$0.904507\pi$
$12$		0			0
$13$	−0.821851	+	4.66095i	−0.227940	+	1.29271i	0.629043	+	0.777371i	$0.283447\pi$
$13$	−0.821851	+	4.66095i	−0.227940	+	1.29271i	−0.856983	+	0.515344i	$0.827664\pi$
$14$		0			0
$15$	1.05581	+	0.885927i	0.272608	+	0.228745i
$16$		0			0
$17$	−3.95753	−	1.44042i	−0.959842	−	0.349354i	−0.185870	−	0.982574i	$-0.559510\pi$
$17$	−3.95753	−	1.44042i	−0.959842	−	0.349354i	−0.773972	+	0.633220i	$0.781733\pi$
$18$		0			0
$19$	−1.63007	−	4.04263i	−0.373965	−	0.927443i
$19$	−1.63007	−	4.04263i	−0.373965	−	0.927443i
$20$		0			0
$21$	−0.210892	−	0.0767582i	−0.0460203	−	0.0167500i
$22$		0			0
$23$	−0.242193	−	0.203224i	−0.0505006	−	0.0423751i	0.617188	−	0.786816i	$-0.288272\pi$
$23$	−0.242193	−	0.203224i	−0.0505006	−	0.0423751i	−0.667689	+	0.744441i	$0.732716\pi$
$24$		0			0
$25$	−0.538380	+	3.05330i	−0.107676	+	0.610661i
$26$		0			0
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$		0			0
$29$	−7.31385	+	2.66202i	−1.35815	+	0.494325i	−0.915481	−	0.402361i	$-0.868190\pi$
$29$	−7.31385	+	2.66202i	−1.35815	+	0.494325i	−0.442667	+	0.896686i	$0.645968\pi$
$30$		0			0
$31$	−1.24150	+	2.15035i	−0.222981	+	0.386214i	−0.955712	−	0.294304i	$-0.904912\pi$
$31$	−1.24150	+	2.15035i	−0.222981	+	0.386214i	0.732731	+	0.680519i	$0.238245\pi$
$32$		0			0
$33$	−1.12675	+	0.945452i	−0.196141	+	0.164582i
$34$		0			0
$35$	0.0537123	+	0.304618i	0.00907904	+	0.0514898i
$36$		0			0
$37$	−0.191209			−0.0314346			−0.0157173	−	0.999876i	$-0.505003\pi$
$37$	−0.191209			−0.0314346			−0.0157173	+	0.999876i	$0.505003\pi$
$38$		0			0
$39$	4.73285			0.757863
$40$		0			0
$41$	−0.144260	−	0.818139i	−0.0225296	−	0.127772i	0.971469	−	0.237168i	$-0.0762193\pi$
$41$	−0.144260	−	0.818139i	−0.0225296	−	0.127772i	−0.993998	+	0.109396i	$0.965108\pi$
$42$		0			0
$43$	−9.37929	+	7.87016i	−1.43033	+	1.20019i	−0.484809	+	0.874620i	$0.661111\pi$
$43$	−9.37929	+	7.87016i	−1.43033	+	1.20019i	−0.945519	+	0.325568i	$0.894445\pi$
$44$		0			0
$45$	0.689129	−	1.19361i	0.102729	−	0.177932i
$46$		0			0
$47$	2.93341	−	1.06767i	0.427882	−	0.155736i	−0.119097	−	0.992883i	$-0.538000\pi$
$47$	2.93341	−	1.06767i	0.427882	−	0.155736i	0.546979	+	0.837146i	$0.315778\pi$
$48$		0			0
$49$	3.47482	+	6.01856i	0.496402	+	0.859794i
$50$		0			0
$51$	−0.731322	+	4.14753i	−0.102406	+	0.580771i
$52$		0			0
$53$	−0.453098	−	0.380194i	−0.0622377	−	0.0522237i	0.611138	−	0.791524i	$-0.290712\pi$
$53$	−0.453098	−	0.380194i	−0.0622377	−	0.0522237i	−0.673376	+	0.739300i	$0.735156\pi$
$54$		0			0
$55$	1.90497	+	0.693352i	0.256866	+	0.0934916i
$56$		0			0
$57$	−3.69815	+	2.30731i	−0.489832	+	0.305610i
$58$		0			0
$59$	−10.8224	−	3.93902i	−1.40895	−	0.512817i	−0.478130	−	0.878289i	$-0.658685\pi$
$59$	−10.8224	−	3.93902i	−1.40895	−	0.512817i	−0.930822	+	0.365472i	$0.880907\pi$
$60$		0			0
$61$	4.81237	+	4.03806i	0.616161	+	0.517021i	0.896594	−	0.442853i	$-0.146034\pi$
$61$	4.81237	+	4.03806i	0.616161	+	0.517021i	−0.280433	+	0.959874i	$0.590478\pi$
$62$		0			0
$63$	−0.0389712	+	0.221017i	−0.00490991	+	0.0278455i
$64$		0			0
$65$	−3.26154	−	5.64916i	−0.404545	−	0.700692i
$66$		0			0
$67$	−3.53896	+	1.28807i	−0.432352	+	0.157363i	−0.549023	−	0.835807i	$-0.685000\pi$
$67$	−3.53896	+	1.28807i	−0.432352	+	0.157363i	0.116671	+	0.993171i	$0.462778\pi$
$68$		0			0
$69$	−0.158080	+	0.273803i	−0.0190306	+	0.0329620i
$70$		0			0
$71$	−0.237470	+	0.199261i	−0.0281825	+	0.0236479i	−0.656770	−	0.754091i	$-0.728078\pi$
$71$	−0.237470	+	0.199261i	−0.0281825	+	0.0236479i	0.628588	+	0.777739i	$0.283633\pi$
$72$		0			0
$73$	−0.975891	−	5.53455i	−0.114219	−	0.647770i	−0.987134	−	0.159897i	$-0.948884\pi$
$73$	−0.975891	−	5.53455i	−0.114219	−	0.647770i	0.872914	−	0.487873i	$-0.162227\pi$
$74$		0			0
$75$	3.10041			0.358004
$76$		0			0
$77$	−0.330100			−0.0376184
$78$		0			0
$79$	0.0118758	+	0.0673508i	0.00133613	+	0.00757756i	0.985469	−	0.169858i	$-0.0543309\pi$
$79$	0.0118758	+	0.0673508i	0.00133613	+	0.00757756i	−0.984132	+	0.177436i	$0.943220\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−4.33891	+	7.51521i	−0.476257	+	0.824901i	−0.999630	−	0.0272024i	$-0.991340\pi$
$83$	−4.33891	+	7.51521i	−0.476257	+	0.824901i	0.523373	+	0.852104i	$0.324673\pi$
$84$		0			0
$85$	5.45449	−	1.98527i	0.591623	−	0.215333i
$86$		0			0
$87$	3.89162	+	6.74048i	0.417225	+	0.722655i
$88$		0			0
$89$	1.06141	−	6.01955i	0.112509	−	0.638071i	−0.875444	−	0.483319i	$-0.839431\pi$
$89$	1.06141	−	6.01955i	0.112509	−	0.638071i	0.987953	−	0.154752i	$-0.0494579\pi$
$90$		0			0
$91$	0.813673	+	0.682753i	0.0852961	+	0.0715720i
$92$		0			0
$93$	2.33327	+	0.849239i	0.241948	+	0.0880620i
$94$		0			0
$95$	5.30252	+	2.82411i	0.544027	+	0.289747i
$96$		0			0
$97$	10.7305	+	3.90559i	1.08952	+	0.396553i	0.823443	−	0.567399i	$-0.192050\pi$
$97$	10.7305	+	3.90559i	1.08952	+	0.396553i	0.266077	+	0.963952i	$0.414272\pi$
$98$		0			0
$99$	1.12675	+	0.945452i	0.113242	+	0.0950215i
$100$		0			0
$101$	−1.39373	+	7.90423i	−0.138681	+	0.786500i	0.833544	+	0.552453i	$0.186308\pi$
$101$	−1.39373	+	7.90423i	−0.138681	+	0.786500i	−0.972225	+	0.234047i	$0.924803\pi$
$102$		0			0
$103$	−1.83438	−	3.17723i	−0.180746	−	0.313062i	0.761389	−	0.648296i	$-0.224518\pi$
$103$	−1.83438	−	3.17723i	−0.180746	−	0.313062i	−0.942135	+	0.335234i	$0.891185\pi$
$104$		0			0
$105$	0.290663	−	0.105793i	0.0283658	−	0.0103243i
$106$		0			0
$107$	−1.70295	+	2.94960i	−0.164630	+	0.285148i	−0.936524	−	0.350604i	$-0.885976\pi$
$107$	−1.70295	+	2.94960i	−0.164630	+	0.285148i	0.771894	+	0.635752i	$0.219310\pi$
$108$		0			0
$109$	2.34018	−	1.96364i	0.224148	−	0.188083i	−0.523797	−	0.851843i	$-0.675485\pi$
$109$	2.34018	−	1.96364i	0.224148	−	0.188083i	0.747945	+	0.663760i	$0.231040\pi$
$110$		0			0
$111$	0.0332032	+	0.188305i	0.00315151	+	0.0178731i
$112$		0			0
$113$	2.46657			0.232036			0.116018	−	0.993247i	$-0.462987\pi$
$113$	2.46657			0.232036			0.116018	+	0.993247i	$0.462987\pi$
$114$		0			0
$115$	0.435750			0.0406339
$116$		0			0
$117$	−0.821851	−	4.66095i	−0.0759801	−	0.430905i
$118$		0			0
$119$	−0.724045	+	0.607546i	−0.0663731	+	0.0556936i
$120$		0			0
$121$	4.41828	−	7.65269i	0.401662	−	0.695699i
$122$		0			0
$123$	−0.780659	+	0.284137i	−0.0703897	+	0.0256197i
$124$		0			0
$125$	−5.58222	−	9.66869i	−0.499289	−	0.864794i
$126$		0			0
$127$	−0.855404	+	4.85124i	−0.0759048	+	0.430478i	0.923046	+	0.384689i	$0.125691\pi$
$127$	−0.855404	+	4.85124i	−0.0759048	+	0.430478i	−0.998951	+	0.0457888i	$0.985420\pi$
$128$		0			0
$129$	9.37929	+	7.87016i	0.825800	+	0.692929i
$130$		0			0
$131$	−9.47605	−	3.44900i	−0.827926	−	0.301341i	−0.106919	−	0.994268i	$-0.534099\pi$
$131$	−9.47605	−	3.44900i	−0.827926	−	0.301341i	−0.721008	+	0.692927i	$0.756321\pi$
$132$		0			0
$133$	−0.968636	−	0.136817i	−0.0839914	−	0.0118635i
$134$		0			0
$135$	−1.29514	−	0.471392i	−0.111468	−	0.0405709i
$136$		0			0
$137$	−17.3300	−	14.5416i	−1.48060	−	1.24237i	−0.905538	−	0.424265i	$-0.860532\pi$
$137$	−17.3300	−	14.5416i	−1.48060	−	1.24237i	−0.575065	−	0.818108i	$-0.695023\pi$
$138$		0			0
$139$	1.01571	−	5.76038i	0.0861514	−	0.488589i	−0.910951	−	0.412515i	$-0.864650\pi$
$139$	1.01571	−	5.76038i	0.0861514	−	0.488589i	0.997102	−	0.0760740i	$-0.0242385\pi$
$140$		0			0
$141$	−1.56084	−	2.70345i	−0.131446	−	0.227671i
$142$		0			0
$143$	6.54155	−	2.38093i	0.547032	−	0.199103i
$144$		0			0
$145$	5.36365	−	9.29012i	0.445427	−	0.771502i
$146$		0			0
$147$	5.32373	−	4.46714i	0.439094	−	0.368443i
$148$		0			0
$149$	−1.90290	−	10.7919i	−0.155892	−	0.884107i	−0.957966	−	0.286882i	$-0.907381\pi$
$149$	−1.90290	−	10.7919i	−0.155892	−	0.884107i	0.802074	−	0.597225i	$-0.203730\pi$
$150$		0			0
$151$	14.7687			1.20186			0.600931	−	0.799301i	$-0.294797\pi$
$151$	14.7687			1.20186			0.600931	+	0.799301i	$0.294797\pi$
$152$		0			0
$153$	4.21151			0.340481
$154$		0			0
$155$	−0.594263	−	3.37024i	−0.0477324	−	0.270704i
$156$		0			0
$157$	5.99269	−	5.02846i	0.478269	−	0.401315i	−0.371531	−	0.928420i	$-0.621167\pi$
$157$	5.99269	−	5.02846i	0.478269	−	0.401315i	0.849800	+	0.527105i	$0.176723\pi$
$158$		0			0
$159$	−0.295738	+	0.512234i	−0.0234536	+	0.0406228i
$160$		0			0
$161$	−0.0666755	+	0.0242679i	−0.00525476	+	0.00191258i
$162$		0			0
$163$	−4.83995	−	8.38304i	−0.379094	−	0.656610i	0.611837	−	0.790984i	$-0.290431\pi$
$163$	−4.83995	−	8.38304i	−0.379094	−	0.656610i	−0.990931	+	0.134374i	$0.957098\pi$
$164$		0			0
$165$	0.352024	−	1.99643i	0.0274050	−	0.155422i
$166$		0			0
$167$	−6.20310	−	5.20502i	−0.480010	−	0.402776i	0.370420	−	0.928864i	$-0.379214\pi$
$167$	−6.20310	−	5.20502i	−0.480010	−	0.402776i	−0.850430	+	0.526088i	$0.823658\pi$
$168$		0			0
$169$	−8.83300	−	3.21495i	−0.679461	−	0.247304i
$170$		0			0
$171$	2.91443	+	3.24131i	0.222872	+	0.247869i
$172$		0			0
$173$	24.1487	+	8.78940i	1.83599	+	0.668246i	0.991068	+	0.133356i	$0.0425754\pi$
$173$	24.1487	+	8.78940i	1.83599	+	0.668246i	0.844922	+	0.534890i	$0.179647\pi$
$174$		0			0
$175$	0.533023	+	0.447259i	0.0402927	+	0.0338096i
$176$		0			0
$177$	−1.99989	+	11.3420i	−0.150321	+	0.852513i
$178$		0			0
$179$	−7.86954	−	13.6304i	−0.588197	−	1.01879i	−0.994469	−	0.105035i	$-0.966505\pi$
$179$	−7.86954	−	13.6304i	−0.588197	−	1.01879i	0.406271	−	0.913752i	$-0.366829\pi$
$180$		0			0
$181$	−21.5144	+	7.83061i	−1.59915	+	0.582045i	−0.979254	−	0.202636i	$-0.935049\pi$
$181$	−21.5144	+	7.83061i	−1.59915	+	0.582045i	−0.619900	+	0.784681i	$0.712827\pi$
$182$		0			0
$183$	3.14105	−	5.44047i	0.232193	−	0.402171i
$184$		0			0
$185$	0.201880	−	0.169398i	0.0148425	−	0.0124544i
$186$		0			0
$187$	1.07567	+	6.10045i	0.0786610	+	0.446109i
$188$		0			0
$189$	0.224426			0.0163246
$190$		0			0
$191$	13.5678			0.981733			0.490866	−	0.871235i	$-0.336680\pi$
$191$	13.5678			0.981733			0.490866	+	0.871235i	$0.336680\pi$
$192$		0			0
$193$	1.34685	+	7.63838i	0.0969486	+	0.549823i	0.994133	+	0.108166i	$0.0344979\pi$
$193$	1.34685	+	7.63838i	0.0969486	+	0.549823i	−0.897184	+	0.441656i	$0.854391\pi$
$194$		0			0
$195$	−4.99697	+	4.19296i	−0.357841	+	0.300264i
$196$		0			0
$197$	−2.94072	+	5.09347i	−0.209517	+	0.362895i	−0.951563	−	0.307455i	$-0.900523\pi$
$197$	−2.94072	+	5.09347i	−0.209517	+	0.362895i	0.742045	+	0.670350i	$0.233856\pi$
$198$		0			0
$199$	15.7834	−	5.74469i	1.11886	−	0.407231i	0.284622	−	0.958640i	$-0.408132\pi$
$199$	15.7834	−	5.74469i	1.11886	−	0.407231i	0.834235	+	0.551409i	$0.185910\pi$
$200$		0			0
$201$	1.88304	+	3.26152i	0.132819	+	0.230050i
$202$		0			0
$203$	−0.303322	+	1.72022i	−0.0212890	+	0.120736i
$204$		0			0
$205$	0.877122	+	0.735993i	0.0612609	+	0.0514040i
$206$		0			0
$207$	0.297093	+	0.108133i	0.0206494	+	0.00751577i
$208$		0			0
$209$	−3.95071	+	5.04947i	−0.273276	+	0.349279i
$210$		0			0
$211$	−1.03279	−	0.375905i	−0.0711002	−	0.0258784i	0.306225	−	0.951959i	$-0.400934\pi$
$211$	−1.03279	−	0.375905i	−0.0711002	−	0.0258784i	−0.377325	+	0.926081i	$0.623156\pi$
$212$		0			0
$213$	0.237470	+	0.199261i	0.0162712	+	0.0136531i
$214$		0			0
$215$	2.93033	−	16.6187i	0.199847	−	1.13339i
$216$		0			0
$217$	0.278626	+	0.482595i	0.0189144	+	0.0327606i
$218$		0			0
$219$	−5.28101	+	1.92213i	−0.356857	+	0.129885i
$220$		0			0
$221$	9.96624	−	17.2620i	0.670402	−	1.16117i
$222$		0			0
$223$	12.2051	−	10.2413i	0.817311	−	0.685805i	−0.135030	−	0.990842i	$-0.543113\pi$
$223$	12.2051	−	10.2413i	0.817311	−	0.685805i	0.952341	+	0.305036i	$0.0986686\pi$
$224$		0			0
$225$	−0.538380	−	3.05330i	−0.0358920	−	0.203554i
$226$		0			0
$227$	25.1660			1.67032			0.835162	−	0.550005i	$-0.185374\pi$
$227$	25.1660			1.67032			0.835162	+	0.550005i	$0.185374\pi$
$228$		0			0
$229$	9.22078			0.609327			0.304663	−	0.952460i	$-0.401456\pi$
$229$	9.22078			0.609327			0.304663	+	0.952460i	$0.401456\pi$
$230$		0			0
$231$	0.0573212	+	0.325085i	0.00377146	+	0.0213890i
$232$		0			0
$233$	−2.72490	+	2.28647i	−0.178514	+	0.149791i	−0.727667	−	0.685931i	$-0.759395\pi$
$233$	−2.72490	+	2.28647i	−0.178514	+	0.149791i	0.549152	+	0.835722i	$0.314951\pi$
$234$		0			0
$235$	−2.15123	+	3.72604i	−0.140331	+	0.243060i
$236$		0			0
$237$	0.0642654	−	0.0233907i	0.00417449	−	0.00151939i
$238$		0			0
$239$	−11.9844	−	20.7575i	−0.775204	−	1.34269i	−0.934680	−	0.355491i	$-0.884314\pi$
$239$	−11.9844	−	20.7575i	−0.775204	−	1.34269i	0.159476	−	0.987202i	$-0.449020\pi$
$240$		0			0
$241$	−4.59396	+	26.0536i	−0.295923	+	1.67826i	0.367505	+	0.930021i	$0.380212\pi$
$241$	−4.59396	+	26.0536i	−0.295923	+	1.67826i	−0.663428	+	0.748240i	$0.730899\pi$
$242$		0			0
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$		0			0
$245$	−9.00074	−	3.27600i	−0.575036	−	0.209296i
$246$		0			0
$247$	20.1822	−	4.27526i	1.28416	−	0.272028i
$248$		0			0
$249$	8.15448	+	2.96799i	0.516769	+	0.188089i
$250$		0			0
$251$	−19.3059	−	16.1996i	−1.21858	−	1.02251i	−0.998898	−	0.0469385i	$-0.985054\pi$
$251$	−19.3059	−	16.1996i	−1.21858	−	1.02251i	−0.219682	−	0.975571i	$-0.570502\pi$
$252$		0			0
$253$	−0.0807512	+	0.457963i	−0.00507679	+	0.0287919i
$254$		0			0
$255$	−2.90228	−	5.02689i	−0.181748	−	0.314796i
$256$		0			0
$257$	19.2995	−	7.02444i	1.20387	−	0.438173i	0.339296	−	0.940680i	$-0.389811\pi$
$257$	19.2995	−	7.02444i	1.20387	−	0.438173i	0.864573	+	0.502507i	$0.167589\pi$
$258$		0			0
$259$	−0.0214562	+	0.0371632i	−0.00133322	+	0.00230921i
$260$		0			0
$261$	5.96231	−	5.00297i	0.369057	−	0.309676i
$262$		0			0
$263$	1.33866	+	7.59191i	0.0825452	+	0.468137i	0.997859	+	0.0653964i	$0.0208312\pi$
$263$	1.33866	+	7.59191i	0.0825452	+	0.468137i	−0.915314	+	0.402741i	$0.868058\pi$
$264$		0			0
$265$	0.815207			0.0500778
$266$		0			0
$267$	−6.11242			−0.374074
$268$		0			0
$269$	4.00428	+	22.7094i	0.244145	+	1.38462i	0.822469	+	0.568809i	$0.192596\pi$
$269$	4.00428	+	22.7094i	0.244145	+	1.38462i	−0.578324	+	0.815807i	$0.696293\pi$
$270$		0			0
$271$	−17.8276	+	14.9591i	−1.08295	+	0.908702i	−0.996162	−	0.0875245i	$-0.972104\pi$
$271$	−17.8276	+	14.9591i	−1.08295	+	0.908702i	−0.0867870	+	0.996227i	$0.527660\pi$
$272$		0			0
$273$	0.531088	−	0.919871i	0.0321429	−	0.0556731i
$274$		0			0
$275$	4.28525	−	1.55970i	0.258410	−	0.0940537i
$276$		0			0
$277$	−15.8172	−	27.3961i	−0.950361	−	1.64607i	−0.744644	−	0.667462i	$-0.767381\pi$
$277$	−15.8172	−	27.3961i	−0.950361	−	1.64607i	−0.205717	−	0.978611i	$-0.565953\pi$
$278$		0			0
$279$	0.431170	−	2.44529i	0.0258135	−	0.146396i
$280$		0			0
$281$	−2.62785	−	2.20503i	−0.156764	−	0.131541i	0.561032	−	0.827794i	$-0.310405\pi$
$281$	−2.62785	−	2.20503i	−0.156764	−	0.131541i	−0.717796	+	0.696253i	$0.754849\pi$
$282$		0			0
$283$	31.2163	+	11.3618i	1.85562	+	0.675389i	0.982032	+	0.188716i	$0.0604326\pi$
$283$	31.2163	+	11.3618i	1.85562	+	0.675389i	0.873584	+	0.486673i	$0.161790\pi$
$284$		0			0
$285$	1.86043	−	5.71236i	0.110202	−	0.338371i
$286$		0			0
$287$	−0.175200	−	0.0637677i	−0.0103417	−	0.00376409i
$288$		0			0
$289$	0.564464	+	0.473642i	0.0332038	+	0.0278613i
$290$		0			0
$291$	1.98292	−	11.2457i	0.116241	−	0.659235i
$292$		0			0
$293$	11.6213	+	20.1286i	0.678921	+	1.17593i	0.975306	+	0.220857i	$0.0708853\pi$
$293$	11.6213	+	20.1286i	0.678921	+	1.17593i	−0.296386	+	0.955068i	$0.595781\pi$
$294$		0			0
$295$	14.9160	−	5.42898i	0.868444	−	0.316088i
$296$		0			0
$297$	0.735431	−	1.27380i	0.0426740	−	0.0739136i
$298$		0			0
$299$	1.14626	−	0.961828i	0.0662900	−	0.0556239i
$300$		0			0
$301$	0.477155	+	2.70608i	0.0275028	+	0.155976i
$302$		0			0
$303$	8.02616			0.461091
$304$		0			0
$305$	−8.65836			−0.495776
$306$		0			0
$307$	1.36160	+	7.72200i	0.0777104	+	0.440718i	0.998693	+	0.0511135i	$0.0162770\pi$
$307$	1.36160	+	7.72200i	0.0777104	+	0.440718i	−0.920982	+	0.389604i	$0.872612\pi$
$308$		0			0
$309$	−2.81043	+	2.35823i	−0.159880	+	0.134155i
$310$		0			0
$311$	−11.9284	+	20.6606i	−0.676399	+	1.17156i	0.299659	+	0.954046i	$0.403127\pi$
$311$	−11.9284	+	20.6606i	−0.676399	+	1.17156i	−0.976058	+	0.217510i	$0.930206\pi$
$312$		0			0
$313$	7.14722	−	2.60137i	0.403985	−	0.147038i	−0.132033	−	0.991245i	$-0.542150\pi$
$313$	7.14722	−	2.60137i	0.403985	−	0.147038i	0.536017	+	0.844207i	$0.319928\pi$
$314$		0			0
$315$	−0.154658	−	0.267876i	−0.00871402	−	0.0150931i
$316$		0			0
$317$	−3.30017	+	18.7162i	−0.185356	+	1.05121i	0.740141	+	0.672452i	$0.234759\pi$
$317$	−3.30017	+	18.7162i	−0.185356	+	1.05121i	−0.925497	+	0.378755i	$0.876352\pi$
$318$		0			0
$319$	8.76973	+	7.35868i	0.491011	+	0.412007i
$320$		0			0
$321$	3.20050	+	1.16489i	0.178634	+	0.0650176i
$322$		0			0
$323$	0.627973	+	18.3468i	0.0349414	+	1.02084i
$324$		0			0
$325$	−13.7888	−	5.01872i	−0.764866	−	0.278389i
$326$		0			0
$327$	−2.34018	−	1.96364i	−0.129412	−	0.108590i
$328$		0			0
$329$	0.121655	−	0.689941i	0.00670707	−	0.0380377i
$330$		0			0
$331$	−8.33615	−	14.4386i	−0.458196	−	0.793619i	0.540670	−	0.841235i	$-0.318171\pi$
$331$	−8.33615	−	14.4386i	−0.458196	−	0.793619i	−0.998866	+	0.0476162i	$0.984838\pi$
$332$		0			0
$333$	0.179678	−	0.0653975i	0.00984630	−	0.00358376i
$334$		0			0
$335$	2.59531	−	4.49521i	0.141797	−	0.245600i
$336$		0			0
$337$	−16.7123	+	14.0233i	−0.910380	+	0.763899i	−0.972191	−	0.234189i	$-0.924757\pi$
$337$	−16.7123	+	14.0233i	−0.910380	+	0.763899i	0.0618115	+	0.998088i	$0.480312\pi$
$338$		0			0
$339$	−0.428316	−	2.42910i	−0.0232629	−	0.131931i
$340$		0			0
$341$	3.65217			0.197776
$342$		0			0
$343$	3.13066			0.169040
$344$		0			0
$345$	−0.0756672	−	0.429130i	−0.00407378	−	0.0231036i
$346$		0			0
$347$	−14.0886	+	11.8217i	−0.756315	+	0.634623i	−0.937165	−	0.348887i	$-0.886560\pi$
$347$	−14.0886	+	11.8217i	−0.756315	+	0.634623i	0.180850	+	0.983511i	$0.442115\pi$
$348$		0			0
$349$	8.93506	−	15.4760i	0.478283	−	0.828410i	−0.521407	−	0.853308i	$-0.674593\pi$
$349$	8.93506	−	15.4760i	0.478283	−	0.828410i	0.999690	+	0.0248977i	$0.00792599\pi$
$350$		0			0
$351$	−4.44743	+	1.61873i	−0.237386	+	0.0864014i
$352$		0			0
$353$	−2.39710	−	4.15190i	−0.127585	−	0.220983i	0.795156	−	0.606406i	$-0.207389\pi$
$353$	−2.39710	−	4.15190i	−0.127585	−	0.220983i	−0.922740	+	0.385422i	$0.874056\pi$
$354$		0			0
$355$	0.0741917	−	0.420762i	0.00393768	−	0.0223317i
$356$		0			0
$357$	0.724045	+	0.607546i	0.0383205	+	0.0321547i
$358$		0			0
$359$	13.3149	+	4.84621i	0.702732	+	0.255773i	0.668577	−	0.743643i	$-0.266904\pi$
$359$	13.3149	+	4.84621i	0.702732	+	0.255773i	0.0341549	+	0.999417i	$0.489126\pi$
$360$		0			0
$361$	−13.6857	+	13.1796i	−0.720301	+	0.693662i
$362$		0			0
$363$	−8.30365	−	3.02228i	−0.435829	−	0.158629i
$364$		0			0
$365$	5.93356	+	4.97885i	0.310577	+	0.260605i
$366$		0			0
$367$	−4.76500	+	27.0236i	−0.248731	+	1.41062i	0.562936	+	0.826501i	$0.309672\pi$
$367$	−4.76500	+	27.0236i	−0.248731	+	1.41062i	−0.811666	+	0.584121i	$0.801439\pi$
$368$		0			0
$369$	0.415380	+	0.719459i	0.0216238	+	0.0374536i
$370$		0			0
$371$	−0.124737	+	0.0454007i	−0.00647605	+	0.00235709i
$372$		0			0
$373$	14.8768	−	25.7675i	0.770294	−	1.33419i	−0.167108	−	0.985939i	$-0.553443\pi$
$373$	14.8768	−	25.7675i	0.770294	−	1.33419i	0.937402	−	0.348250i	$-0.113224\pi$
$374$		0			0
$375$	−8.55246	+	7.17637i	−0.441647	+	0.370586i
$376$		0			0
$377$	−6.39666	−	36.2773i	−0.329445	−	1.86837i
$378$		0			0
$379$	−28.1970			−1.44838			−0.724192	−	0.689599i	$-0.757787\pi$
$379$	−28.1970			−1.44838			−0.724192	+	0.689599i	$0.757787\pi$
$380$		0			0
$381$	4.92607			0.252370
$382$		0			0
$383$	1.23470	+	7.00233i	0.0630902	+	0.357802i	0.999967	+	0.00814234i	$0.00259181\pi$
$383$	1.23470	+	7.00233i	0.0630902	+	0.357802i	−0.936877	+	0.349660i	$0.886297\pi$
$384$		0			0
$385$	0.348522	−	0.292444i	0.0177623	−	0.0149043i
$386$		0			0
$387$	6.12190	−	10.6034i	0.311193	−	0.539003i
$388$		0			0
$389$	−13.0258	+	4.74100i	−0.660434	+	0.240378i	−0.650424	−	0.759572i	$-0.725409\pi$
$389$	−13.0258	+	4.74100i	−0.660434	+	0.240378i	−0.0100102	+	0.999950i	$0.503186\pi$
$390$		0			0
$391$	0.665756	+	1.15312i	0.0336687	+	0.0583160i
$392$		0			0
$393$	−1.75110	+	9.93100i	−0.0883315	+	0.500953i
$394$		0			0
$395$	−0.0722064	−	0.0605884i	−0.00363310	−	0.00304853i
$396$		0			0
$397$	−28.8104	−	10.4861i	−1.44595	−	0.526284i	−0.504495	−	0.863415i	$-0.668321\pi$
$397$	−28.8104	−	10.4861i	−1.44595	−	0.526284i	−0.941458	+	0.337131i	$0.890543\pi$
$398$		0			0
$399$	0.0334639	+	0.977678i	0.00167529	+	0.0489451i
$400$		0			0
$401$	22.6613	+	8.24804i	1.13165	+	0.411887i	0.838892	−	0.544299i	$-0.183204\pi$
$401$	22.6613	+	8.24804i	1.13165	+	0.411887i	0.292760	+	0.956186i	$0.405426\pi$
$402$		0			0
$403$	−9.00234	−	7.55386i	−0.448438	−	0.376284i
$404$		0			0
$405$	−0.239332	+	1.35732i	−0.0118925	+	0.0674457i
$406$		0			0
$407$	0.140621	+	0.243563i	0.00697034	+	0.0120730i
$408$		0			0
$409$	−19.6088	+	7.13703i	−0.969594	+	0.352903i	−0.777786	−	0.628529i	$-0.783657\pi$
$409$	−19.6088	+	7.13703i	−0.969594	+	0.352903i	−0.191808	+	0.981432i	$0.561435\pi$
$410$		0			0
$411$	−11.3114	+	19.5919i	−0.557948	+	0.966395i
$412$		0			0
$413$	−1.97999	+	1.66141i	−0.0974291	+	0.0817527i
$414$		0			0
$415$	−2.07688	−	11.7786i	−0.101950	−	0.578187i
$416$		0			0
$417$	−5.84924			−0.286439
$418$		0			0
$419$	−21.7857			−1.06430			−0.532152	−	0.846649i	$-0.678616\pi$
$419$	−21.7857			−1.06430			−0.532152	+	0.846649i	$0.678616\pi$
$420$		0			0
$421$	−0.533134	−	3.02355i	−0.0259834	−	0.147359i	0.969056	−	0.246841i	$-0.0793925\pi$
$421$	−0.533134	−	3.02355i	−0.0259834	−	0.147359i	−0.995039	+	0.0994820i	$0.968281\pi$
$422$		0			0
$423$	−2.39134	+	2.00657i	−0.116271	+	0.0975628i
$424$		0			0
$425$	6.52870	−	11.3080i	0.316689	−	0.548521i
$426$		0			0
$427$	1.32484	−	0.482204i	0.0641137	−	0.0233355i
$428$		0			0
$429$	−3.48069	−	6.02872i	−0.168049	−	0.291070i
$430$		0			0
$431$	−5.13545	+	29.1246i	−0.247366	+	1.40288i	0.567567	+	0.823327i	$0.307885\pi$
$431$	−5.13545	+	29.1246i	−0.247366	+	1.40288i	−0.814933	+	0.579555i	$0.803226\pi$
$432$		0			0
$433$	14.2430	+	11.9513i	0.684475	+	0.574342i	0.917310	−	0.398174i	$-0.130356\pi$
$433$	14.2430	+	11.9513i	0.684475	+	0.574342i	−0.232835	+	0.972516i	$0.574800\pi$
$434$		0			0
$435$	−10.0804	−	3.66895i	−0.483317	−	0.175913i
$436$		0			0
$437$	−0.426766	+	1.31036i	−0.0204150	+	0.0626833i
$438$		0			0
$439$	−29.1860	−	10.6228i	−1.39297	−	0.507001i	−0.466888	−	0.884316i	$-0.654625\pi$
$439$	−29.1860	−	10.6228i	−1.39297	−	0.507001i	−0.926085	+	0.377315i	$0.876847\pi$
$440$		0			0
$441$	−5.32373	−	4.46714i	−0.253511	−	0.212721i
$442$		0			0
$443$	2.05326	−	11.6446i	0.0975532	−	0.553252i	−0.896382	−	0.443283i	$-0.853814\pi$
$443$	2.05326	−	11.6446i	0.0975532	−	0.553252i	0.993935	−	0.109969i	$-0.0350751\pi$
$444$		0			0
$445$	4.21224	+	7.29582i	0.199679	+	0.345855i
$446$		0			0
$447$	−10.2975	+	3.74799i	−0.487056	+	0.177274i
$448$		0			0
$449$	11.4036	−	19.7516i	0.538169	−	0.932135i	−0.460834	−	0.887486i	$-0.652450\pi$
$449$	11.4036	−	19.7516i	0.538169	−	0.932135i	0.999003	−	0.0446491i	$-0.0142170\pi$
$450$		0			0
$451$	−0.936055	+	0.785444i	−0.0440771	+	0.0369851i
$452$		0			0
$453$	−2.56456	−	14.5444i	−0.120494	−	0.683353i
$454$		0			0
$455$	−1.46395			−0.0686311
$456$		0			0
$457$	−8.80077			−0.411683			−0.205841	−	0.978585i	$-0.565993\pi$
$457$	−8.80077			−0.411683			−0.205841	+	0.978585i	$0.565993\pi$
$458$		0			0
$459$	−0.731322	−	4.14753i	−0.0341352	−	0.193590i
$460$		0			0
$461$	−12.9396	+	10.8576i	−0.602657	+	0.505689i	−0.892298	−	0.451446i	$-0.850908\pi$
$461$	−12.9396	+	10.8576i	−0.602657	+	0.505689i	0.289642	+	0.957135i	$0.406464\pi$
$462$		0			0
$463$	−10.4535	+	18.1060i	−0.485816	+	0.841457i	−0.999867	−	0.0163021i	$-0.994811\pi$
$463$	−10.4535	+	18.1060i	−0.485816	+	0.841457i	0.514052	+	0.857759i	$0.328144\pi$
$464$		0			0
$465$	−3.21584	+	1.17047i	−0.149131	+	0.0542793i
$466$		0			0
$467$	8.67007	+	15.0170i	0.401203	+	0.694904i	0.993871	−	0.110543i	$-0.0352589\pi$
$467$	8.67007	+	15.0170i	0.401203	+	0.694904i	−0.592669	+	0.805446i	$0.701926\pi$
$468$		0			0
$469$	−0.146768	+	0.832365i	−0.00677714	+	0.0384351i
$470$		0			0
$471$	−5.99269	−	5.02846i	−0.276128	−	0.231699i
$472$		0			0
$473$	16.9229	+	6.15942i	0.778114	+	0.283210i
$474$		0			0
$475$	13.2210	−	2.80064i	0.606620	−	0.128502i
$476$		0			0
$477$	0.555806	+	0.202297i	0.0254486	+	0.00926254i
$478$		0			0
$479$	−6.59338	−	5.53250i	−0.301259	−	0.252787i	0.479609	−	0.877482i	$-0.340779\pi$
$479$	−6.59338	−	5.53250i	−0.301259	−	0.252787i	−0.780868	+	0.624696i	$0.785223\pi$
$480$		0			0
$481$	0.157146	−	0.891217i	0.00716522	−	0.0406360i
$482$		0			0
$483$	0.0354773	+	0.0614484i	0.00161427	+	0.00279600i
$484$		0			0
$485$	−14.7894	+	5.38291i	−0.671553	+	0.244425i
$486$		0			0
$487$	−9.91739	+	17.1774i	−0.449400	+	0.778383i	−0.998347	−	0.0574739i	$-0.981695\pi$
$487$	−9.91739	+	17.1774i	−0.449400	+	0.778383i	0.548947	+	0.835857i	$0.315029\pi$
$488$		0			0
$489$	−7.41523	+	6.22212i	−0.335328	+	0.281374i
$490$		0			0
$491$	3.46859	+	19.6714i	0.156535	+	0.887756i	0.957369	+	0.288869i	$0.0932791\pi$
$491$	3.46859	+	19.6714i	0.156535	+	0.887756i	−0.800833	+	0.598887i	$0.795610\pi$
$492$		0			0
$493$	32.7792			1.47630
$494$		0			0
$495$	−2.02723			−0.0911171
$496$		0			0
$497$	0.0120809	+	0.0685140i	0.000541901	+	0.00307327i
$498$		0			0
$499$	−12.2806	+	10.3046i	−0.549755	+	0.461299i	−0.874858	−	0.484379i	$-0.839045\pi$
$499$	−12.2806	+	10.3046i	−0.549755	+	0.461299i	0.325103	+	0.945679i	$0.394601\pi$
$500$		0			0
$501$	−4.04878	+	7.01270i	−0.180886	+	0.313304i
$502$		0			0
$503$	−3.53158	+	1.28539i	−0.157465	+	0.0573126i	−0.419550	−	0.907732i	$-0.637812\pi$
$503$	−3.53158	+	1.28539i	−0.157465	+	0.0573126i	0.262085	+	0.965045i	$0.415590\pi$
$504$		0			0
$505$	−5.53106	−	9.58007i	−0.246129	−	0.426308i
$506$		0			0
$507$	−1.63227	+	9.25707i	−0.0724917	+	0.411121i
$508$		0			0
$509$	26.0513	+	21.8597i	1.15470	+	0.968912i	0.999819	−	0.0190199i	$-0.00605459\pi$
$509$	26.0513	+	21.8597i	1.15470	+	0.968912i	0.154886	+	0.987932i	$0.450499\pi$
$510$		0			0
$511$	−1.18520	−	0.431376i	−0.0524300	−	0.0190829i
$512$		0			0
$513$	2.68598	−	3.43300i	0.118589	−	0.151571i
$514$		0			0
$515$	4.75154	+	1.72942i	0.209378	+	0.0762073i
$516$		0			0
$517$	−3.51733	−	2.95139i	−0.154692	−	0.129802i
$518$		0			0
$519$	4.46250	−	25.3081i	0.195882	−	1.11090i
$520$		0			0
$521$	−2.01219	−	3.48522i	−0.0881558	−	0.152690i	0.818576	−	0.574399i	$-0.194764\pi$
$521$	−2.01219	−	3.48522i	−0.0881558	−	0.152690i	−0.906732	+	0.421708i	$0.861431\pi$
$522$		0			0
$523$	−13.8668	+	5.04710i	−0.606352	+	0.220694i	−0.626906	−	0.779095i	$-0.715679\pi$
$523$	−13.8668	+	5.04710i	−0.606352	+	0.220694i	0.0205541	+	0.999789i	$0.493457\pi$
$524$		0			0
$525$	0.347906	−	0.602591i	0.0151839	−	0.0262992i
$526$		0			0
$527$	8.01070	−	6.72178i	0.348952	−	0.292805i
$528$		0			0
$529$	−3.97655	−	22.5521i	−0.172894	−	0.980528i
$530$		0			0
$531$	11.5169			0.499792
$532$		0			0
$533$	3.93186			0.170308
$534$		0			0
$535$	−0.815141	−	4.62289i	−0.0352416	−	0.199865i
$536$		0			0
$537$	−12.0568	+	10.1169i	−0.520291	+	0.436576i
$538$		0			0
$539$	5.11098	−	8.85247i	0.220145	−	0.381303i
$540$		0			0
$541$	−17.0568	+	6.20816i	−0.733328	+	0.266910i	−0.681573	−	0.731750i	$-0.738704\pi$
$541$	−17.0568	+	6.20816i	−0.733328	+	0.266910i	−0.0517554	+	0.998660i	$0.516482\pi$
$542$		0			0
$543$	11.4476	+	19.8278i	0.491263	+	0.850892i
$544$		0			0
$545$	−0.731132	+	4.14645i	−0.0313182	+	0.177615i
$546$		0			0
$547$	19.8921	+	16.6914i	0.850524	+	0.713674i	0.959905	−	0.280326i	$-0.0904425\pi$
$547$	19.8921	+	16.6914i	0.850524	+	0.713674i	−0.109381	+	0.994000i	$0.534887\pi$
$548$		0			0
$549$	−5.90325	−	2.14861i	−0.251945	−	0.0917004i
$550$		0			0
$551$	22.6837	+	25.2279i	0.966358	+	1.07474i
$552$		0			0
$553$	0.0144228	+	0.00524948i	0.000613321	+	0.000223231i
$554$		0			0
$555$	−0.201880	−	0.169398i	−0.00856934	−	0.00719053i
$556$		0			0
$557$	−6.85624	+	38.8837i	−0.290508	+	1.64755i	0.394410	+	0.918934i	$0.370949\pi$
$557$	−6.85624	+	38.8837i	−0.290508	+	1.64755i	−0.684918	+	0.728620i	$0.740162\pi$
$558$		0			0
$559$	−28.9740	−	50.1845i	−1.22547	−	2.12258i
$560$		0			0
$561$	5.82098	−	2.11866i	0.245762	−	0.0894500i
$562$		0			0
$563$	10.9754	−	19.0099i	0.462557	−	0.801172i	−0.536531	−	0.843881i	$-0.680265\pi$
$563$	10.9754	−	19.0099i	0.462557	−	0.801172i	0.999088	+	0.0427089i	$0.0135988\pi$
$564$		0			0
$565$	−2.60422	+	2.18520i	−0.109560	+	0.0919322i
$566$		0			0
$567$	−0.0389712	−	0.221017i	−0.00163664	−	0.00928182i
$568$		0			0
$569$	−27.7545			−1.16353			−0.581765	−	0.813357i	$-0.697637\pi$
$569$	−27.7545			−1.16353			−0.581765	+	0.813357i	$0.697637\pi$
$570$		0			0
$571$	27.6610			1.15758			0.578789	−	0.815477i	$-0.303525\pi$
$571$	27.6610			1.15758			0.578789	+	0.815477i	$0.303525\pi$
$572$		0			0
$573$	−2.35603	−	13.3617i	−0.0984244	−	0.558193i
$574$		0			0
$575$	0.750895	−	0.630076i	0.0313145	−	0.0262760i
$576$		0			0
$577$	10.3297	−	17.8915i	0.430029	−	0.744833i	−0.566846	−	0.823824i	$-0.691837\pi$
$577$	10.3297	−	17.8915i	0.430029	−	0.744833i	0.996875	+	0.0789911i	$0.0251699\pi$
$578$		0			0
$579$	7.28846	−	2.65278i	0.302898	−	0.110246i
$580$		0			0
$581$	0.973764	+	1.68661i	0.0403985	+	0.0699723i
$582$		0			0
$583$	−0.151071	+	0.856764i	−0.00625671	+	0.0354835i
$584$		0			0
$585$	4.99697	+	4.19296i	0.206599	+	0.173358i
$586$		0			0
$587$	36.8394	+	13.4084i	1.52053	+	0.553426i	0.961279	−	0.275576i	$-0.0888686\pi$
$587$	36.8394	+	13.4084i	1.52053	+	0.553426i	0.559246	+	0.829002i	$0.311091\pi$
$588$		0			0
$589$	10.7168	+	1.51371i	0.441579	+	0.0623715i
$590$		0			0
$591$	5.52674	+	2.01157i	0.227340	+	0.0827449i
$592$		0			0
$593$	4.13801	+	3.47220i	0.169928	+	0.142586i	0.723785	−	0.690025i	$-0.242401\pi$
$593$	4.13801	+	3.47220i	0.169928	+	0.142586i	−0.553858	+	0.832611i	$0.686845\pi$
$594$		0			0
$595$	0.226210	−	1.28290i	0.00927371	−	0.0525938i
$596$		0			0
$597$	−8.39818	−	14.5461i	−0.343715	−	0.595331i
$598$		0			0
$599$	−36.1226	+	13.1475i	−1.47593	+	0.537194i	−0.949703	−	0.313151i	$-0.898615\pi$
$599$	−36.1226	+	13.1475i	−1.47593	+	0.537194i	−0.526226	+	0.850345i	$0.676393\pi$
$600$		0			0
$601$	−4.98002	+	8.62565i	−0.203139	+	0.351848i	−0.949538	−	0.313651i	$-0.898448\pi$
$601$	−4.98002	+	8.62565i	−0.203139	+	0.351848i	0.746399	+	0.665499i	$0.231781\pi$
$602$		0			0
$603$	2.88498	−	2.42079i	0.117486	−	0.0985821i
$604$		0			0
$605$	2.11487	+	11.9940i	0.0859818	+	0.487627i
$606$		0			0
$607$	−23.5654			−0.956490			−0.478245	−	0.878226i	$-0.658727\pi$
$607$	−23.5654			−0.956490			−0.478245	+	0.878226i	$0.658727\pi$
$608$		0			0
$609$	1.74676			0.0707823
$610$		0			0
$611$	2.56555	+	14.5499i	0.103791	+	0.588628i
$612$		0			0
$613$	−13.6777	+	11.4770i	−0.552439	+	0.463551i	−0.875766	−	0.482736i	$-0.839643\pi$
$613$	−13.6777	+	11.4770i	−0.552439	+	0.463551i	0.323327	+	0.946287i	$0.395199\pi$
$614$		0			0
$615$	0.572501	−	0.991600i	0.0230855	−	0.0399852i
$616$		0			0
$617$	0.507249	−	0.184624i	0.0204211	−	0.00743266i	−0.331789	−	0.943353i	$-0.607652\pi$
$617$	0.507249	−	0.184624i	0.0204211	−	0.00743266i	0.352210	+	0.935921i	$0.385430\pi$
$618$		0			0
$619$	−6.44901	−	11.1700i	−0.259208	−	0.448961i	0.706822	−	0.707391i	$-0.250128\pi$
$619$	−6.44901	−	11.1700i	−0.259208	−	0.448961i	−0.966030	+	0.258430i	$0.916795\pi$
$620$		0			0
$621$	0.0549006	−	0.311357i	0.00220309	−	0.0124943i
$622$		0			0
$623$	−1.05085	−	0.881767i	−0.0421014	−	0.0353272i
$624$		0			0
$625$	−0.107643	−	0.0391787i	−0.00430571	−	0.00156715i
$626$		0			0
$627$	5.65879	+	3.01386i	0.225990	+	0.120362i
$628$		0			0
$629$	0.756717	+	0.275422i	0.0301723	+	0.0109818i
$630$		0			0
$631$	−33.1594	−	27.8240i	−1.32005	−	1.10766i	−0.986294	−	0.164998i	$-0.947238\pi$
$631$	−33.1594	−	27.8240i	−1.32005	−	1.10766i	−0.333759	−	0.942658i	$-0.608317\pi$
$632$		0			0
$633$	−0.190852	+	1.08238i	−0.00758568	+	0.0430206i
$634$		0			0
$635$	−3.39470	−	5.87979i	−0.134715	−	0.233332i
$636$		0			0
$637$	−30.9080	+	11.2496i	−1.22462	+	0.445725i
$638$		0			0
$639$	0.154997	−	0.268463i	0.00613160	−	0.0106202i
$640$		0			0
$641$	−7.64561	+	6.41543i	−0.301984	+	0.253394i	−0.781169	−	0.624319i	$-0.785376\pi$
$641$	−7.64561	+	6.41543i	−0.301984	+	0.253394i	0.479186	+	0.877714i	$0.340932\pi$
$642$		0			0
$643$	−2.57514	−	14.6044i	−0.101554	−	0.575939i	−0.992541	−	0.121911i	$-0.961098\pi$
$643$	−2.57514	−	14.6044i	−0.101554	−	0.575939i	0.890987	−	0.454028i	$-0.150013\pi$
$644$		0			0
$645$	−16.8751			−0.664456
$646$		0			0
$647$	12.2996			0.483548			0.241774	−	0.970333i	$-0.422271\pi$
$647$	12.2996			0.483548			0.241774	+	0.970333i	$0.422271\pi$
$648$		0			0
$649$	2.94157	+	16.6825i	0.115467	+	0.654843i
$650$		0			0
$651$	0.426880	−	0.358195i	0.0167307	−	0.0140388i
$652$		0			0
$653$	−17.2787	+	29.9276i	−0.676169	+	1.17116i	0.299957	+	0.953953i	$0.403028\pi$
$653$	−17.2787	+	29.9276i	−0.676169	+	1.17116i	−0.976126	+	0.217206i	$0.930306\pi$
$654$		0			0
$655$	13.0604	−	4.75361i	0.510314	−	0.185739i
$656$		0			0
$657$	2.80997	+	4.86700i	0.109627	+	0.189880i
$658$		0			0
$659$	−4.05724	+	23.0098i	−0.158048	+	0.896333i	0.797899	+	0.602792i	$0.205945\pi$
$659$	−4.05724	+	23.0098i	−0.158048	+	0.896333i	−0.955946	+	0.293541i	$0.905166\pi$
$660$		0			0
$661$	8.82765	+	7.40728i	0.343356	+	0.288110i	0.798116	−	0.602504i	$-0.205830\pi$
$661$	8.82765	+	7.40728i	0.343356	+	0.288110i	−0.454760	+	0.890614i	$0.650275\pi$
$662$		0			0
$663$	−18.7304	−	6.81731i	−0.727428	−	0.264762i
$664$		0			0
$665$	1.14390	−	0.713689i	0.0443586	−	0.0276757i
$666$		0			0
$667$	2.31235	+	0.841625i	0.0895344	+	0.0325879i
$668$		0			0
$669$	−12.2051	−	10.2413i	−0.471875	−	0.395950i
$670$		0			0
$671$	1.60453	−	9.09974i	0.0619422	−	0.351292i
$672$		0			0
$673$	8.55688	+	14.8210i	0.329844	+	0.571306i	0.982481	−	0.186365i	$-0.0596707\pi$
$673$	8.55688	+	14.8210i	0.329844	+	0.571306i	−0.652637	+	0.757671i	$0.726337\pi$
$674$		0			0
$675$	−2.91343	+	1.06040i	−0.112138	+	0.0408149i
$676$		0			0
$677$	12.3694	−	21.4245i	0.475396	−	0.823411i	−0.524207	−	0.851591i	$-0.675638\pi$
$677$	12.3694	−	21.4245i	0.475396	−	0.823411i	0.999603	+	0.0281806i	$0.00897136\pi$
$678$		0			0
$679$	1.96319	−	1.64731i	0.0753403	−	0.0632181i
$680$		0			0
$681$	−4.37002	−	24.7836i	−0.167460	−	0.949711i
$682$		0			0
$683$	49.4101			1.89062			0.945312	−	0.326169i	$-0.105758\pi$
$683$	49.4101			1.89062			0.945312	+	0.326169i	$0.105758\pi$
$684$		0			0
$685$	31.1799			1.19132
$686$		0			0
$687$	−1.60117	−	9.08070i	−0.0610885	−	0.346450i
$688$		0			0
$689$	2.14444	−	1.79940i	0.0816968	−	0.0685517i
$690$		0			0
$691$	15.7808	−	27.3332i	0.600331	−	1.03980i	−0.392440	−	0.919778i	$-0.628369\pi$
$691$	15.7808	−	27.3332i	0.600331	−	1.03980i	0.992771	−	0.120026i	$-0.0382977\pi$
$692$		0			0
$693$	0.310192	−	0.112901i	0.0117832	−	0.00428875i
$694$		0			0
$695$	4.03088	+	6.98169i	0.152900	+	0.264831i
$696$		0			0
$697$	−0.607553	+	3.44560i	−0.0230127	+	0.130512i
$698$		0			0
$699$	2.72490	+	2.28647i	0.103065	+	0.0864821i
$700$		0			0
$701$	41.1334	+	14.9713i	1.55359	+	0.565459i	0.969256	−	0.246056i	$-0.0791347\pi$
$701$	41.1334	+	14.9713i	1.55359	+	0.565459i	0.584331	+	0.811515i	$0.301357\pi$
$702$		0			0
$703$	0.311686	+	0.772989i	0.0117554	+	0.0291538i
$704$		0			0
$705$	4.04299	+	1.47153i	0.152268	+	0.0554210i
$706$		0			0
$707$	1.37986	+	1.15784i	0.0518950	+	0.0435451i
$708$		0			0
$709$	3.01509	−	17.0994i	0.113234	−	0.642182i	−0.874375	−	0.485250i	$-0.838729\pi$
$709$	3.01509	−	17.0994i	0.113234	−	0.642182i	0.987609	−	0.156932i	$-0.0501603\pi$
$710$		0			0
$711$	−0.0341949	−	0.0592273i	−0.00128241	−	0.00222120i
$712$		0			0
$713$	0.737685	−	0.268495i	0.0276265	−	0.0100552i
$714$		0			0
$715$	−4.79728	+	8.30913i	−0.179408	+	0.310744i
$716$		0			0
$717$	−18.3611	+	15.4068i	−0.685708	+	0.575377i
$718$		0			0
$719$	−4.75813	−	26.9847i	−0.177448	−	1.00636i	−0.935280	−	0.353910i	$-0.884852\pi$
$719$	−4.75813	−	26.9847i	−0.177448	−	1.00636i	0.757831	−	0.652451i	$-0.226259\pi$
$720$		0			0
$721$	−0.823363			−0.0306637
$722$		0			0
$723$	26.4555			0.983892
$724$		0			0
$725$	−4.19034	−	23.7646i	−0.155625	−	0.882595i
$726$		0			0
$727$	−30.8238	+	25.8642i	−1.14319	+	0.959250i	−0.999538	−	0.0303782i	$-0.990329\pi$
$727$	−30.8238	+	25.8642i	−1.14319	+	0.959250i	−0.143651	+	0.989628i	$0.545884\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	48.4552	−	17.6362i	1.79218	−	0.652300i
$732$		0			0
$733$	24.4834	+	42.4065i	0.904315	+	1.56632i	0.821835	+	0.569726i	$0.192951\pi$
$733$	24.4834	+	42.4065i	0.904315	+	1.56632i	0.0824802	+	0.996593i	$0.473716\pi$
$734$		0			0
$735$	−1.66327	+	9.43287i	−0.0613506	+	0.347937i
$736$		0			0
$737$	4.24341	+	3.56065i	0.156308	+	0.131158i
$738$		0			0
$739$	−0.871374	−	0.317154i	−0.0320540	−	0.0116667i	0.325943	−	0.945389i	$-0.394318\pi$
$739$	−0.871374	−	0.317154i	−0.0320540	−	0.0116667i	−0.357997	+	0.933723i	$0.616540\pi$
$740$		0			0
$741$	−7.71490	−	19.1332i	−0.283414	−	0.702874i
$742$		0			0
$743$	−25.3808	−	9.23787i	−0.931132	−	0.338904i	−0.168474	−	0.985706i	$-0.553884\pi$
$743$	−25.3808	−	9.23787i	−0.931132	−	0.338904i	−0.762658	+	0.646802i	$0.776106\pi$
$744$		0			0
$745$	11.5699	+	9.70833i	0.423890	+	0.355686i
$746$		0			0
$747$	1.50689	−	8.54598i	0.0551341	−	0.312681i
$748$		0			0
$749$	0.382186	+	0.661966i	0.0139648	+	0.0241877i
$750$		0			0
$751$	11.3437	−	4.12877i	0.413938	−	0.150661i	−0.126652	−	0.991947i	$-0.540423\pi$
$751$	11.3437	−	4.12877i	0.413938	−	0.150661i	0.540590	+	0.841286i	$0.318201\pi$
$752$		0			0
$753$	−12.6011	+	21.8257i	−0.459208	+	0.795372i
$754$		0			0
$755$	−15.5929	+	13.0840i	−0.567484	+	0.476176i
$756$		0			0
$757$	−5.26975	−	29.8862i	−0.191532	−	1.08623i	−0.917271	−	0.398263i	$-0.869613\pi$
$757$	−5.26975	−	29.8862i	−0.191532	−	1.08623i	0.725739	−	0.687970i	$-0.241498\pi$
$758$		0			0
$759$	0.465028			0.0168794
$760$		0			0
$761$	−18.8427			−0.683049			−0.341525	−	0.939873i	$-0.610943\pi$
$761$	−18.8427			−0.683049			−0.341525	+	0.939873i	$0.610943\pi$
$762$		0			0
$763$	−0.119053	−	0.675180i	−0.00430999	−	0.0244432i
$764$		0			0
$765$	−4.44654	+	3.73109i	−0.160765	+	0.134898i
$766$		0			0
$767$	27.2539	−	47.2052i	0.984083	−	1.70448i
$768$		0			0
$769$	33.0309	−	12.0223i	1.19113	−	0.433534i	0.331007	−	0.943628i	$-0.392612\pi$
$769$	33.0309	−	12.0223i	1.19113	−	0.433534i	0.860119	+	0.510094i	$0.170389\pi$
$770$		0			0
$771$	−10.2690	−	17.7865i	−0.369831	−	0.640565i
$772$		0			0
$773$	−5.49606	+	31.1697i	−0.197680	+	1.12110i	0.710871	+	0.703322i	$0.248301\pi$
$773$	−5.49606	+	31.1697i	−0.197680	+	1.12110i	−0.908551	+	0.417774i	$0.862810\pi$
$774$		0			0
$775$	−5.89727	−	4.94840i	−0.211836	−	0.177752i
$776$		0			0
$777$	0.0403244	+	0.0146769i	0.00144663	+	0.000526531i
$778$		0			0
$779$	−3.07228	+	1.91682i	−0.110076	+	0.0686771i
$780$		0			0
$781$	0.428462	+	0.155947i	0.0153316	+	0.00558024i
$782$		0			0
$783$	−5.96231	−	5.00297i	−0.213075	−	0.178792i
$784$		0			0
$785$	−1.87227	+	10.6182i	−0.0668241	+	0.378979i
$786$		0			0
$787$	13.4218	+	23.2472i	0.478435	+	0.828675i	0.999694	−	0.0247241i	$-0.00787072\pi$
$787$	13.4218	+	23.2472i	0.478435	+	0.828675i	−0.521259	+	0.853399i	$0.674537\pi$
$788$		0			0
$789$	7.24411	−	2.63664i	0.257897	−	0.0938669i
$790$		0			0
$791$	0.276782	−	0.479400i	0.00984122	−	0.0170455i
$792$		0			0
$793$	−22.7763	+	19.1115i	−0.808808	+	0.678671i
$794$		0			0
$795$	−0.141559	−	0.802823i	−0.00502059	−	0.0284732i
$796$		0			0
$797$	32.0162			1.13407			0.567037	−	0.823693i	$-0.308090\pi$
$797$	32.0162			1.13407			0.567037	+	0.823693i	$0.308090\pi$
$798$		0			0
$799$	−13.1470			−0.465106
$800$		0			0
$801$	1.06141	+	6.01955i	0.0375031	+	0.212690i
$802$		0			0
$803$	−6.33223	+	5.31337i	−0.223460	+	0.187505i
$804$		0			0
$805$	0.0488968	−	0.0846918i	0.00172339	−	0.00298499i
$806$		0			0
$807$	21.6691	−	7.88689i	0.762787	−	0.277632i
$808$		0			0
$809$	−19.1646	−	33.1941i	−0.673793	−	1.16704i	−0.976820	−	0.214061i	$-0.931331\pi$
$809$	−19.1646	−	33.1941i	−0.673793	−	1.16704i	0.303028	−	0.952982i	$-0.402003\pi$
$810$		0			0
$811$	9.58364	−	54.3515i	0.336527	−	1.90854i	−0.0750780	−	0.997178i	$-0.523921\pi$
$811$	9.58364	−	54.3515i	0.336527	−	1.90854i	0.411605	−	0.911362i	$-0.364968\pi$
$812$		0			0
$813$	17.8276	+	14.9591i	0.625241	+	0.524640i
$814$		0			0
$815$	12.5368	+	4.56302i	0.439145	+	0.159836i
$816$		0			0
$817$	47.1051	+	25.0880i	1.64800	+	0.877719i
$818$		0			0
$819$	−0.998118	−	0.363285i	−0.0348771	−	0.0126942i
$820$		0			0
$821$	−27.8861	−	23.3992i	−0.973231	−	0.816638i	0.00982319	−	0.999952i	$-0.496873\pi$
$821$	−27.8861	−	23.3992i	−0.973231	−	0.816638i	−0.983054	+	0.183314i	$0.941318\pi$
$822$		0			0
$823$	−0.443577	+	2.51565i	−0.0154621	+	0.0876900i	−0.991562	−	0.129631i	$-0.958621\pi$
$823$	−0.443577	+	2.51565i	−0.0154621	+	0.0876900i	0.976100	+	0.217321i	$0.0697318\pi$
$824$		0			0
$825$	−2.28014	−	3.94931i	−0.0793841	−	0.137497i
$826$		0			0
$827$	43.7731	−	15.9321i	1.52214	−	0.554014i	0.560458	−	0.828183i	$-0.310625\pi$
$827$	43.7731	−	15.9321i	1.52214	−	0.554014i	0.961682	+	0.274169i	$0.0884028\pi$
$828$		0			0
$829$	21.2834	−	36.8640i	0.739204	−	1.28034i	−0.213650	−	0.976910i	$-0.568535\pi$
$829$	21.2834	−	36.8640i	0.739204	−	1.28034i	0.952854	−	0.303429i	$-0.0981314\pi$
$830$		0			0
$831$	−24.2333	+	20.3341i	−0.840644	+	0.705384i
$832$		0			0
$833$	−5.08242	−	28.8238i	−0.176095	−	0.998686i
$834$		0			0
$835$	11.1605			0.386226
$836$		0			0
$837$	−2.48301			−0.0858254
$838$		0			0
$839$	2.55595	+	14.4955i	0.0882413	+	0.500442i	0.996610	+	0.0822712i	$0.0262174\pi$
$839$	2.55595	+	14.4955i	0.0882413	+	0.500442i	−0.908369	+	0.418170i	$0.862672\pi$
$840$		0			0
$841$	24.1907	−	20.2984i	0.834164	−	0.699946i
$842$		0			0
$843$	−1.71521	+	2.97083i	−0.0590749	+	0.102321i
$844$		0			0
$845$	12.1741	−	4.43103i	0.418803	−	0.152432i
$846$		0			0
$847$	−0.991578	−	1.71746i	−0.0340710	−	0.0590127i
$848$		0			0
$849$	5.76854	−	32.7150i	0.197976	−	1.12278i
$850$		0			0
$851$	0.0463095	+	0.0388583i	0.00158747	+	0.00133205i
$852$		0			0
$853$	−42.1943	−	15.3575i	−1.44471	−	0.525830i	−0.503598	−	0.863938i	$-0.667991\pi$
$853$	−42.1943	−	15.3575i	−1.44471	−	0.525830i	−0.941107	+	0.338108i	$0.890213\pi$
$854$		0			0
$855$	−5.94864	−	0.840225i	−0.203439	−	0.0287351i
$856$		0			0
$857$	−10.6057	−	3.86015i	−0.362283	−	0.131860i	0.154464	−	0.987998i	$-0.450635\pi$
$857$	−10.6057	−	3.86015i	−0.362283	−	0.131860i	−0.516747	+	0.856138i	$0.672857\pi$
$858$		0			0
$859$	−11.6862	−	9.80589i	−0.398728	−	0.334573i	0.421274	−	0.906934i	$-0.361583\pi$
$859$	−11.6862	−	9.80589i	−0.398728	−	0.334573i	−0.820002	+	0.572361i	$0.806028\pi$
$860$		0			0
$861$	−0.0323757	+	0.183612i	−0.00110336	+	0.00625747i
$862$		0			0
$863$	14.2681	+	24.7130i	0.485691	+	0.841241i	0.999865	−	0.0164450i	$-0.00523484\pi$
$863$	14.2681	+	24.7130i	0.485691	+	0.841241i	−0.514174	+	0.857686i	$0.671902\pi$
$864$		0			0
$865$	−33.2831	+	12.1141i	−1.13166	+	0.411890i
$866$		0			0
$867$	0.368428	−	0.638136i	0.0125125	−	0.0216722i
$868$		0			0
$869$	0.0770579	−	0.0646593i	0.00261401	−	0.00219342i
$870$		0			0
$871$	−3.09515	−	17.5535i	−0.104875	−	0.594777i
$872$		0			0
$873$	−11.4192			−0.386481
$874$		0			0
$875$	−2.50559			−0.0847045
$876$		0			0
$877$	0.681808	+	3.86673i	0.0230230	+	0.130570i	0.994153	−	0.107981i	$-0.0344386\pi$
$877$	0.681808	+	3.86673i	0.0230230	+	0.130570i	−0.971130	+	0.238551i	$0.923328\pi$
$878$		0			0
$879$	17.8048	−	14.9400i	0.600541	−	0.503913i
$880$		0			0
$881$	13.5005	−	23.3836i	0.454843	−	0.787812i	−0.543836	−	0.839192i	$-0.683029\pi$
$881$	13.5005	−	23.3836i	0.454843	−	0.787812i	0.998679	+	0.0513797i	$0.0163619\pi$
$882$		0			0
$883$	−9.53744	+	3.47134i	−0.320960	+	0.116820i	−0.497476	−	0.867478i	$-0.665740\pi$
$883$	−9.53744	+	3.47134i	−0.320960	+	0.116820i	0.176515	+	0.984298i	$0.443517\pi$
$884$		0			0
$885$	−7.93664	−	13.7467i	−0.266787	−	0.462089i
$886$		0			0
$887$	−4.63248	+	26.2721i	−0.155543	+	0.882130i	0.802744	+	0.596324i	$0.203372\pi$
$887$	−4.63248	+	26.2721i	−0.155543	+	0.882130i	−0.958287	+	0.285806i	$0.907739\pi$
$888$		0			0
$889$	0.846892	+	0.710627i	0.0284039	+	0.0238337i
$890$		0			0
$891$	−1.38216	−	0.503064i	−0.0463040	−	0.0168533i
$892$		0			0
$893$	−9.09789	−	10.1183i	−0.304449	−	0.338596i
$894$		0			0
$895$	20.3843	+	7.41927i	0.681372	+	0.247999i
$896$		0			0
$897$	−1.14626	−	0.961828i	−0.0382726	−	0.0321145i
$898$		0			0
$899$	3.35590	−	19.0323i	0.111926	−	0.634761i
$900$		0			0
$901$	1.24551	+	2.15728i	0.0414938	+	0.0718695i
$902$		0			0
$903$	2.58211	−	0.939812i	0.0859273	−	0.0312750i
$904$		0			0
$905$	15.7777	−	27.3278i	0.524469	−	0.908407i
$906$		0			0
$907$	−17.5958	+	14.7646i	−0.584260	+	0.490252i	−0.886343	−	0.463030i	$-0.846762\pi$
$907$	−17.5958	+	14.7646i	−0.584260	+	0.490252i	0.302083	+	0.953282i	$0.402318\pi$
$908$		0			0
$909$	−1.39373	−	7.90423i	−0.0462270	−	0.262167i
$910$		0			0
$911$	−47.3993			−1.57041			−0.785205	−	0.619236i	$-0.787443\pi$
$911$	−47.3993			−1.57041			−0.785205	+	0.619236i	$0.787443\pi$
$912$		0			0
$913$	12.7639			0.422422
$914$		0			0
$915$	1.50351	+	8.52682i	0.0497045	+	0.281888i
$916$		0			0
$917$	−1.73368	+	1.45473i	−0.0572511	+	0.0480394i
$918$		0			0
$919$	−5.27984	+	9.14494i	−0.174166	+	0.301664i	−0.939872	−	0.341526i	$-0.889056\pi$
$919$	−5.27984	+	9.14494i	−0.174166	+	0.301664i	0.765707	+	0.643190i	$0.222390\pi$
$920$		0			0
$921$	7.36824	−	2.68182i	0.242792	−	0.0883690i
$922$		0			0
$923$	−0.733580	−	1.27060i	−0.0241461	−	0.0418222i
$924$		0			0
$925$	0.102943	−	0.583821i	0.00338476	−	0.0191959i
$926$		0			0
$927$	2.81043	+	2.35823i	0.0923065	+	0.0774544i
$928$		0			0
$929$	32.3423	+	11.7716i	1.06112	+	0.386215i	0.812848	−	0.582476i	$-0.197916\pi$
$929$	32.3423	+	11.7716i	1.06112	+	0.386215i	0.248269	+	0.968691i	$0.420138\pi$
$930$		0			0
$931$	18.6666	−	23.8581i	0.611773	−	0.781918i
$932$		0			0
$933$	22.4181	+	8.15952i	0.733935	+	0.267131i
$934$		0			0
$935$	−6.54025	−	5.48792i	−0.213889	−	0.179474i
$936$		0			0
$937$	9.88978	−	56.0877i	0.323085	−	1.83231i	−0.199719	−	0.979853i	$-0.564003\pi$
$937$	9.88978	−	56.0877i	0.323085	−	1.83231i	0.522804	−	0.852453i	$-0.324886\pi$
$938$		0			0
$939$	−3.80296	−	6.58691i	−0.124105	−	0.214956i
$940$		0			0
$941$	39.2466	−	14.2846i	1.27940	−	0.465664i	0.389167	−	0.921167i	$-0.372763\pi$
$941$	39.2466	−	14.2846i	1.27940	−	0.465664i	0.890234	+	0.455503i	$0.150541\pi$
$942$		0			0
$943$	−0.131327	+	0.227464i	−0.00427658	+	0.00740726i
$944$		0			0
$945$	−0.236951	+	0.198825i	−0.00770800	+	0.00646778i
$946$		0			0
$947$	0.135809	+	0.770213i	0.00441321	+	0.0250286i	0.986935	−	0.161120i	$-0.0515106\pi$
$947$	0.135809	+	0.770213i	0.00441321	+	0.0250286i	−0.982522	+	0.186148i	$0.940399\pi$
$948$		0			0
$949$	26.5983			0.863417
$950$		0			0
$951$	19.0049			0.616278
$952$		0			0
$953$	3.90927	+	22.1706i	0.126634	+	0.718175i	0.980324	+	0.197394i	$0.0632479\pi$
$953$	3.90927	+	22.1706i	0.126634	+	0.718175i	−0.853691	+	0.520781i	$0.825641\pi$
$954$		0			0
$955$	−14.3250	+	12.0201i	−0.463546	+	0.388961i
$956$		0			0
$957$	5.72403	−	9.91432i	0.185032	−	0.320484i
$958$		0			0
$959$	−4.77094	+	1.73648i	−0.154062	+	0.0560739i
$960$		0			0
$961$	12.4173	+	21.5074i	0.400559	+	0.693789i
$962$		0			0
$963$	0.591429	−	3.35416i	0.0190585	−	0.108086i
$964$		0			0
$965$	−8.18906	−	6.87144i	−0.263615	−	0.221199i
$966$		0			0
$967$	24.8352	+	9.03928i	0.798646	+	0.290684i	0.708925	−	0.705283i	$-0.249180\pi$
$967$	24.8352	+	9.03928i	0.798646	+	0.290684i	0.0897210	+	0.995967i	$0.471402\pi$
$968$		0			0
$969$	17.9590	−	3.80433i	0.576928	−	0.122213i
$970$		0			0
$971$	3.52810	+	1.28412i	0.113222	+	0.0412094i	0.398010	−	0.917381i	$-0.369701\pi$
$971$	3.52810	+	1.28412i	0.113222	+	0.0412094i	−0.284788	+	0.958591i	$0.591923\pi$
$972$		0			0
$973$	−1.00560	−	0.843802i	−0.0322382	−	0.0270511i
$974$		0			0
$975$	−2.54807	+	14.4508i	−0.0816036	+	0.462797i
$976$		0			0
$977$	4.78572	+	8.28911i	0.153109	+	0.265192i	0.932369	−	0.361509i	$-0.117738\pi$
$977$	4.78572	+	8.28911i	0.153109	+	0.265192i	−0.779260	+	0.626701i	$0.784405\pi$
$978$		0			0
$979$	−8.44833	+	3.07494i	−0.270010	+	0.0982755i
$980$		0			0
$981$	−1.52744	+	2.64561i	−0.0487675	+	0.0844678i
$982$		0			0
$983$	−1.23898	+	1.03963i	−0.0395173	+	0.0331589i	−0.662332	−	0.749210i	$-0.730433\pi$
$983$	−1.23898	+	1.03963i	−0.0395173	+	0.0331589i	0.622815	+	0.782369i	$0.285989\pi$
$984$		0			0
$985$	−1.40762	−	7.98298i	−0.0448504	−	0.254359i
$986$		0			0
$987$	−0.700584			−0.0222998
$988$		0			0
$989$	3.87100			0.123091
$990$		0			0
$991$	3.71896	+	21.0913i	0.118137	+	0.669986i	0.985149	+	0.171700i	$0.0549259\pi$
$991$	3.71896	+	21.0913i	0.118137	+	0.669986i	−0.867013	+	0.498286i	$0.833963\pi$
$992$		0			0
$993$	−12.7717	+	10.7167i	−0.405298	+	0.340086i
$994$		0			0
$995$	−11.5749	+	20.0482i	−0.366948	+	0.635572i
$996$		0			0
$997$	3.26498	−	1.18836i	0.103403	−	0.0376356i	−0.289801	−	0.957087i	$-0.593589\pi$
$997$	3.26498	−	1.18836i	0.103403	−	0.0376356i	0.393204	+	0.919451i	$0.371367\pi$
$998$		0			0
$999$	−0.0956047	−	0.165592i	−0.00302480	−	0.00523911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.h.289.1		12
4.3	odd	2		456.2.bg.a.289.1	✓	12
19.5	even	9	inner	912.2.bo.h.385.1		12
76.43	odd	18		456.2.bg.a.385.1	yes	12
76.47	odd	18		8664.2.a.bi.1.2		6
76.67	even	18		8664.2.a.bf.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bg.a.289.1	✓	12	4.3	odd	2
456.2.bg.a.385.1	yes	12	76.43	odd	18
912.2.bo.h.289.1		12	1.1	even	1	trivial
912.2.bo.h.385.1		12	19.5	even	9	inner
8664.2.a.bf.1.2		6	76.67	even	18
8664.2.a.bi.1.2		6	76.47	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{3} +(-1.05581 + 0.885927i) q^{5} +(0.112213 - 0.194359i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(-0.735431 - 1.27380i) q^{11} +(-0.821851 + 4.66095i) q^{13} +(1.05581 + 0.885927i) q^{15} +(-3.95753 - 1.44042i) q^{17} +(-1.63007 - 4.04263i) q^{19} +(-0.210892 - 0.0767582i) q^{21} +(-0.242193 - 0.203224i) q^{23} +(-0.538380 + 3.05330i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-7.31385 + 2.66202i) q^{29} +(-1.24150 + 2.15035i) q^{31} +(-1.12675 + 0.945452i) q^{33} +(0.0537123 + 0.304618i) q^{35} -0.191209 q^{37} +4.73285 q^{39} +(-0.144260 - 0.818139i) q^{41} +(-9.37929 + 7.87016i) q^{43} +(0.689129 - 1.19361i) q^{45} +(2.93341 - 1.06767i) q^{47} +(3.47482 + 6.01856i) q^{49} +(-0.731322 + 4.14753i) q^{51} +(-0.453098 - 0.380194i) q^{53} +(1.90497 + 0.693352i) q^{55} +(-3.69815 + 2.30731i) q^{57} +(-10.8224 - 3.93902i) q^{59} +(4.81237 + 4.03806i) q^{61} +(-0.0389712 + 0.221017i) q^{63} +(-3.26154 - 5.64916i) q^{65} +(-3.53896 + 1.28807i) q^{67} +(-0.158080 + 0.273803i) q^{69} +(-0.237470 + 0.199261i) q^{71} +(-0.975891 - 5.53455i) q^{73} +3.10041 q^{75} -0.330100 q^{77} +(0.0118758 + 0.0673508i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-4.33891 + 7.51521i) q^{83} +(5.45449 - 1.98527i) q^{85} +(3.89162 + 6.74048i) q^{87} +(1.06141 - 6.01955i) q^{89} +(0.813673 + 0.682753i) q^{91} +(2.33327 + 0.849239i) q^{93} +(5.30252 + 2.82411i) q^{95} +(10.7305 + 3.90559i) q^{97} +(1.12675 + 0.945452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{11} + 9 q^{13} + 3 q^{15} - 9 q^{17} - 6 q^{19} + 12 q^{21} - 24 q^{23} - 15 q^{25} + 6 q^{27} - 3 q^{29} - 3 q^{31} - 24 q^{35} - 30 q^{37} - 6 q^{39} + 15 q^{41} - 27 q^{43} + 3 q^{45}+ \cdots + 39 q^{97}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^11 + 9 * q^13 + 3 * q^15 - 9 * q^17 - 6 * q^19 + 12 * q^21 - 24 * q^23 - 15 * q^25 + 6 * q^27 - 3 * q^29 - 3 * q^31 - 24 * q^35 - 30 * q^37 - 6 * q^39 + 15 * q^41 - 27 * q^43 + 3 * q^45 + 30 * q^47 - 12 * q^49 + 6 * q^53 + 12 * q^55 + 3 * q^57 + 3 * q^59 - 6 * q^61 + 6 * q^63 - 9 * q^65 + 45 * q^67 + 12 * q^69 - 27 * q^71 + 21 * q^73 + 30 * q^75 - 30 * q^77 + 3 * q^79 - 6 * q^83 + 51 * q^85 + 3 * q^87 - 3 * q^89 + 42 * q^91 - 9 * q^93 - 24 * q^95 + 39 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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