LMFDB - Embedded newform 912.2.bo.k.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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, 0, 2]))

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

//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);

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: 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 $\Q(\zeta_{9})$
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} - 3 x^{17} + 30 x^{16} - 51 x^{15} + 501 x^{14} - 768 x^{13} + 4499 x^{12} - 2946 x^{11} + \cdots + 64 $ x^18 - 3x^17 + 30x^16 - 51x^15 + 501x^14 - 768x^13 + 4499x^12 - 2946x^11 + 21141x^10 - 7991x^9 + 67482x^8 + 18777x^7 + 57847x^6 - 1446x^5 + 22860x^4 + 3088x^3 + 3312x^2 - 384*x + 64
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			625.2
Root			$0.323050 - 0.559539i$ of defining polynomial
Character	$\chi$	$=$	912.625
Dual form			912.2.bo.k.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{3} +(-0.607135 + 0.220979i) q^{5} +(1.81642 + 3.14613i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{3} +(-0.607135 + 0.220979i) q^{5} +(1.81642 + 3.14613i) q^{7} +(0.173648 + 0.984808i) q^{9} +(1.36297 - 2.36074i) q^{11} +(-2.44183 + 2.04894i) q^{13} +(-0.607135 - 0.220979i) q^{15} +(-0.277218 + 1.57218i) q^{17} +(4.22286 + 1.08051i) q^{19} +(-0.630836 + 3.57765i) q^{21} +(1.15085 + 0.418875i) q^{23} +(-3.51044 + 2.94561i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.245561 - 1.39265i) q^{29} +(2.01802 + 3.49531i) q^{31} +(2.56155 - 0.932330i) q^{33} +(-1.79804 - 1.50874i) q^{35} -9.34827 q^{37} -3.18758 q^{39} +(0.208072 + 0.174593i) q^{41} +(0.357087 - 0.129969i) q^{43} +(-0.323050 - 0.559539i) q^{45} +(1.47840 + 8.38443i) q^{47} +(-3.09876 + 5.36721i) q^{49} +(-1.22294 + 1.02617i) q^{51} +(10.0745 + 3.66683i) q^{53} +(-0.305835 + 1.73448i) q^{55} +(2.54036 + 3.54212i) q^{57} +(2.37272 - 13.4563i) q^{59} +(5.97110 + 2.17330i) q^{61} +(-2.78292 + 2.33514i) q^{63} +(1.02975 - 1.78357i) q^{65} +(1.34053 + 7.60255i) q^{67} +(0.612354 + 1.06063i) q^{69} +(-4.05161 + 1.47467i) q^{71} +(-6.11749 - 5.13319i) q^{73} -4.58256 q^{75} +9.90294 q^{77} +(1.34748 + 1.13067i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(5.57750 + 9.66051i) q^{83} +(-0.179111 - 1.01579i) q^{85} +(0.707066 - 1.22467i) q^{87} +(5.37716 - 4.51198i) q^{89} +(-10.8816 - 3.96058i) q^{91} +(-0.700851 + 3.97472i) q^{93} +(-2.80261 + 0.277149i) q^{95} +(3.31794 - 18.8170i) q^{97} +(2.56155 + 0.932330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{5}+O(q^{10}) $ 18 * q - 3 * q^5	$ 18 q - 3 q^{5} + 3 q^{11} + 18 q^{13} - 3 q^{15} - 3 q^{17} + 3 q^{19} - 3 q^{21} - 12 q^{23} - 3 q^{25} - 9 q^{27} + 3 q^{29} - 21 q^{31} + 6 q^{33} - 12 q^{35} - 30 q^{37} - 6 q^{39} + 33 q^{41} + 6 q^{43} - 3 q^{45} + 6 q^{47} - 21 q^{49} - 12 q^{51} + 30 q^{53} + 24 q^{55} - 21 q^{57} + 9 q^{59} + 48 q^{61} + 6 q^{63} - 9 q^{65} + 18 q^{67} - 6 q^{69} + 51 q^{71} + 12 q^{75} + 30 q^{77} + 39 q^{79} + 30 q^{83} - 87 q^{85} + 21 q^{87} + 45 q^{89} - 72 q^{91} - 27 q^{93} + 78 q^{95} + 39 q^{97} + 6 q^{99}+O(q^{100}) $ 18 * q - 3 * q^5 + 3 * q^11 + 18 * q^13 - 3 * q^15 - 3 * q^17 + 3 * q^19 - 3 * q^21 - 12 * q^23 - 3 * q^25 - 9 * q^27 + 3 * q^29 - 21 * q^31 + 6 * q^33 - 12 * q^35 - 30 * q^37 - 6 * q^39 + 33 * q^41 + 6 * q^43 - 3 * q^45 + 6 * q^47 - 21 * q^49 - 12 * q^51 + 30 * q^53 + 24 * q^55 - 21 * q^57 + 9 * q^59 + 48 * q^61 + 6 * q^63 - 9 * q^65 + 18 * q^67 - 6 * q^69 + 51 * q^71 + 12 * q^75 + 30 * q^77 + 39 * q^79 + 30 * q^83 - 87 * q^85 + 21 * q^87 + 45 * q^89 - 72 * q^91 - 27 * q^93 + 78 * q^95 + 39 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$		0			0
$5$	−0.607135	+	0.220979i	−0.271519	+	0.0988249i	−0.474191	−	0.880422i	$-0.657260\pi$
$5$	−0.607135	+	0.220979i	−0.271519	+	0.0988249i	0.202672	+	0.979247i	$0.435037\pi$
$6$		0			0
$7$	1.81642	+	3.14613i	0.686542	+	1.18913i	0.972949	+	0.231018i	$0.0742056\pi$
$7$	1.81642	+	3.14613i	0.686542	+	1.18913i	−0.286407	+	0.958108i	$0.592461\pi$
$8$		0			0
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$		0			0
$11$	1.36297	−	2.36074i	0.410952	−	0.711790i	−0.584042	−	0.811724i	$-0.698530\pi$
$11$	1.36297	−	2.36074i	0.410952	−	0.711790i	0.994994	+	0.0999332i	$0.0318629\pi$
$12$		0			0
$13$	−2.44183	+	2.04894i	−0.677241	+	0.568272i	−0.915199	−	0.403003i	$-0.867966\pi$
$13$	−2.44183	+	2.04894i	−0.677241	+	0.568272i	0.237958	+	0.971275i	$0.423522\pi$
$14$		0			0
$15$	−0.607135	−	0.220979i	−0.156762	−	0.0570566i
$16$		0			0
$17$	−0.277218	+	1.57218i	−0.0672353	+	0.381311i	0.932559	+	0.361018i	$0.117571\pi$
$17$	−0.277218	+	1.57218i	−0.0672353	+	0.381311i	−0.999794	+	0.0202923i	$0.993540\pi$
$18$		0			0
$19$	4.22286	+	1.08051i	0.968789	+	0.247885i
$19$	4.22286	+	1.08051i	0.968789	+	0.247885i
$20$		0			0
$21$	−0.630836	+	3.57765i	−0.137660	+	0.780707i
$22$		0			0
$23$	1.15085	+	0.418875i	0.239969	+	0.0873415i	0.459205	−	0.888330i	$-0.348134\pi$
$23$	1.15085	+	0.418875i	0.239969	+	0.0873415i	−0.219236	+	0.975672i	$0.570357\pi$
$24$		0			0
$25$	−3.51044	+	2.94561i	−0.702088	+	0.589122i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−0.245561	−	1.39265i	−0.0455996	−	0.258608i	0.953482	−	0.301449i	$-0.0974703\pi$
$29$	−0.245561	−	1.39265i	−0.0455996	−	0.258608i	−0.999082	+	0.0428407i	$0.986359\pi$
$30$		0			0
$31$	2.01802	+	3.49531i	0.362447	+	0.627776i	0.988363	−	0.152114i	$-0.0486081\pi$
$31$	2.01802	+	3.49531i	0.362447	+	0.627776i	−0.625916	+	0.779890i	$0.715275\pi$
$32$		0			0
$33$	2.56155	−	0.932330i	0.445909	−	0.162298i
$34$		0			0
$35$	−1.79804	−	1.50874i	−0.303925	−	0.255023i
$36$		0			0
$37$	−9.34827			−1.53685			−0.768423	−	0.639942i	$-0.778958\pi$
$37$	−9.34827			−1.53685			−0.768423	+	0.639942i	$0.778958\pi$
$38$		0			0
$39$	−3.18758			−0.510421
$40$		0			0
$41$	0.208072	+	0.174593i	0.0324954	+	0.0272669i	0.658891	−	0.752239i	$-0.271026\pi$
$41$	0.208072	+	0.174593i	0.0324954	+	0.0272669i	−0.626395	+	0.779506i	$0.715470\pi$
$42$		0			0
$43$	0.357087	−	0.129969i	0.0544552	−	0.0198201i	−0.314649	−	0.949208i	$-0.601887\pi$
$43$	0.357087	−	0.129969i	0.0544552	−	0.0198201i	0.369104	+	0.929388i	$0.379665\pi$
$44$		0			0
$45$	−0.323050	−	0.559539i	−0.0481574	−	0.0834111i
$46$		0			0
$47$	1.47840	+	8.38443i	0.215647	+	1.22300i	0.879780	+	0.475381i	$0.157690\pi$
$47$	1.47840	+	8.38443i	0.215647	+	1.22300i	−0.664133	+	0.747614i	$0.731199\pi$
$48$		0			0
$49$	−3.09876	+	5.36721i	−0.442680	+	0.766745i
$50$		0			0
$51$	−1.22294	+	1.02617i	−0.171246	+	0.143693i
$52$		0			0
$53$	10.0745	+	3.66683i	1.38384	+	0.503678i	0.923341	−	0.383981i	$-0.125447\pi$
$53$	10.0745	+	3.66683i	1.38384	+	0.503678i	0.460502	+	0.887658i	$0.347669\pi$
$54$		0			0
$55$	−0.305835	+	1.73448i	−0.0412388	+	0.233877i
$56$		0			0
$57$	2.54036	+	3.54212i	0.336479	+	0.469165i
$58$		0			0
$59$	2.37272	−	13.4563i	0.308901	−	1.75187i	−0.295646	−	0.955297i	$-0.595535\pi$
$59$	2.37272	−	13.4563i	0.308901	−	1.75187i	0.604548	−	0.796569i	$-0.293354\pi$
$60$		0			0
$61$	5.97110	+	2.17330i	0.764521	+	0.278263i	0.694703	−	0.719297i	$-0.255536\pi$
$61$	5.97110	+	2.17330i	0.764521	+	0.278263i	0.0698179	+	0.997560i	$0.477758\pi$
$62$		0			0
$63$	−2.78292	+	2.33514i	−0.350615	+	0.294201i
$64$		0			0
$65$	1.02975	−	1.78357i	0.127724	−	0.221225i
$66$		0			0
$67$	1.34053	+	7.60255i	0.163772	+	0.928799i	0.950321	+	0.311271i	$0.100755\pi$
$67$	1.34053	+	7.60255i	0.163772	+	0.928799i	−0.786549	+	0.617528i	$0.788134\pi$
$68$		0			0
$69$	0.612354	+	1.06063i	0.0737188	+	0.127685i
$70$		0			0
$71$	−4.05161	+	1.47467i	−0.480838	+	0.175011i	−0.571056	−	0.820911i	$-0.693466\pi$
$71$	−4.05161	+	1.47467i	−0.480838	+	0.175011i	0.0902177	+	0.995922i	$0.471244\pi$
$72$		0			0
$73$	−6.11749	−	5.13319i	−0.715999	−	0.600794i	0.210277	−	0.977642i	$-0.432564\pi$
$73$	−6.11749	−	5.13319i	−0.715999	−	0.600794i	−0.926275	+	0.376848i	$0.877008\pi$
$74$		0			0
$75$	−4.58256			−0.529148
$76$		0			0
$77$	9.90294			1.12854
$78$		0			0
$79$	1.34748	+	1.13067i	0.151604	+	0.127211i	0.715435	−	0.698679i	$-0.246229\pi$
$79$	1.34748	+	1.13067i	0.151604	+	0.127211i	−0.563831	+	0.825890i	$0.690673\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$		0			0
$83$	5.57750	+	9.66051i	0.612210	+	1.06038i	0.990867	+	0.134841i	$0.0430525\pi$
$83$	5.57750	+	9.66051i	0.612210	+	1.06038i	−0.378657	+	0.925537i	$0.623614\pi$
$84$		0			0
$85$	−0.179111	−	1.01579i	−0.0194273	−	0.110178i
$86$		0			0
$87$	0.707066	−	1.22467i	0.0758054	−	0.131299i
$88$		0			0
$89$	5.37716	−	4.51198i	0.569978	−	0.478269i	−0.311660	−	0.950194i	$-0.600885\pi$
$89$	5.37716	−	4.51198i	0.569978	−	0.478269i	0.881639	+	0.471925i	$0.156441\pi$
$90$		0			0
$91$	−10.8816	−	3.96058i	−1.14070	−	0.415181i
$92$		0			0
$93$	−0.700851	+	3.97472i	−0.0726748	+	0.412159i
$94$		0			0
$95$	−2.80261	+	0.277149i	−0.287542	+	0.0284349i
$96$		0			0
$97$	3.31794	−	18.8170i	0.336886	−	1.91058i	−0.0708698	−	0.997486i	$-0.522577\pi$
$97$	3.31794	−	18.8170i	0.336886	−	1.91058i	0.407756	−	0.913091i	$-0.366311\pi$
$98$		0			0
$99$	2.56155	+	0.932330i	0.257446	+	0.0937027i
$100$		0			0
$101$	2.18242	−	1.83127i	0.217159	−	0.182218i	−0.527718	−	0.849419i	$-0.676952\pi$
$101$	2.18242	−	1.83127i	0.217159	−	0.182218i	0.744878	+	0.667201i	$0.232508\pi$
$102$		0			0
$103$	−3.67168	+	6.35954i	−0.361782	+	0.626624i	−0.988254	−	0.152819i	$-0.951165\pi$
$103$	−3.67168	+	6.35954i	−0.361782	+	0.626624i	0.626472	+	0.779444i	$0.284498\pi$
$104$		0			0
$105$	−0.407583	−	2.31152i	−0.0397760	−	0.225581i
$106$		0			0
$107$	−6.26016	−	10.8429i	−0.605192	−	1.04822i	−0.992021	−	0.126072i	$-0.959763\pi$
$107$	−6.26016	−	10.8429i	−0.605192	−	1.04822i	0.386829	−	0.922151i	$-0.373570\pi$
$108$		0			0
$109$	4.59777	−	1.67345i	0.440387	−	0.160288i	−0.112304	−	0.993674i	$-0.535823\pi$
$109$	4.59777	−	1.67345i	0.440387	−	0.160288i	0.552691	+	0.833386i	$0.313601\pi$
$110$		0			0
$111$	−7.16119	−	6.00895i	−0.679710	−	0.570345i
$112$		0			0
$113$	−8.04618			−0.756920			−0.378460	−	0.925618i	$-0.623546\pi$
$113$	−8.04618			−0.756920			−0.378460	+	0.925618i	$0.623546\pi$
$114$		0			0
$115$	−0.791284			−0.0737876
$116$		0			0
$117$	−2.44183	−	2.04894i	−0.225747	−	0.189424i
$118$		0			0
$119$	−5.44984	+	1.98358i	−0.499586	+	0.181835i
$120$		0			0
$121$	1.78460	+	3.09102i	0.162236	+	0.281002i
$122$		0			0
$123$	0.0471662	+	0.267493i	0.00425283	+	0.0241190i
$124$		0			0
$125$	3.09564	−	5.36181i	0.276883	−	0.479575i
$126$		0			0
$127$	−8.38055	+	7.03211i	−0.743653	+	0.623999i	−0.933816	−	0.357753i	$-0.883543\pi$
$127$	−8.38055	+	7.03211i	−0.743653	+	0.623999i	0.190163	+	0.981753i	$0.439098\pi$
$128$		0			0
$129$	0.357087	+	0.129969i	0.0314397	+	0.0114431i
$130$		0			0
$131$	3.11405	−	17.6607i	0.272076	−	1.54302i	−0.476024	−	0.879432i	$-0.657923\pi$
$131$	3.11405	−	17.6607i	0.272076	−	1.54302i	0.748100	−	0.663586i	$-0.230966\pi$
$132$		0			0
$133$	4.27106	+	15.2483i	0.370348	+	1.32220i
$134$		0			0
$135$	0.112194	−	0.636284i	0.00965613	−	0.0547626i
$136$		0			0
$137$	−2.84040	−	1.03382i	−0.242672	−	0.0883253i	0.217821	−	0.975989i	$-0.430105\pi$
$137$	−2.84040	−	1.03382i	−0.242672	−	0.0883253i	−0.460493	+	0.887663i	$0.652327\pi$
$138$		0			0
$139$	12.1110	−	10.1623i	1.02724	−	0.861955i	0.0367184	−	0.999326i	$-0.488310\pi$
$139$	12.1110	−	10.1623i	1.02724	−	0.861955i	0.990520	+	0.137370i	$0.0438651\pi$
$140$		0			0
$141$	−4.25689	+	7.37315i	−0.358495	+	0.620931i
$142$		0			0
$143$	1.50886	+	8.55717i	0.126177	+	0.715586i
$144$		0			0
$145$	0.456835	+	0.791262i	0.0379381	+	0.0657107i
$146$		0			0
$147$	−5.82377	+	2.11968i	−0.480336	+	0.174828i
$148$		0			0
$149$	1.57880	+	1.32477i	0.129340	+	0.108529i	0.705163	−	0.709045i	$-0.250874\pi$
$149$	1.57880	+	1.32477i	0.129340	+	0.108529i	−0.575823	+	0.817574i	$0.695318\pi$
$150$		0			0
$151$	13.9120			1.13215			0.566073	−	0.824355i	$-0.308462\pi$
$151$	13.9120			1.13215			0.566073	+	0.824355i	$0.308462\pi$
$152$		0			0
$153$	−1.59644			−0.129064
$154$		0			0
$155$	−1.99760	−	1.67619i	−0.160451	−	0.134635i
$156$		0			0
$157$	−8.55315	+	3.11309i	−0.682616	+	0.248452i	−0.659970	−	0.751292i	$-0.729431\pi$
$157$	−8.55315	+	3.11309i	−0.682616	+	0.248452i	−0.0226454	+	0.999744i	$0.507209\pi$
$158$		0			0
$159$	5.36055	+	9.28474i	0.425119	+	0.736328i
$160$		0			0
$161$	0.772590	+	4.38158i	0.0608887	+	0.345317i
$162$		0			0
$163$	5.89319	−	10.2073i	0.461590	−	0.799498i	−0.537450	−	0.843296i	$-0.680612\pi$
$163$	5.89319	−	10.2073i	0.461590	−	0.799498i	0.999040	+	0.0437977i	$0.0139457\pi$
$164$		0			0
$165$	−1.34918	+	1.13210i	−0.105034	+	0.0881339i
$166$		0			0
$167$	−6.98039	−	2.54065i	−0.540159	−	0.196602i	0.0575100	−	0.998345i	$-0.481684\pi$
$167$	−6.98039	−	2.54065i	−0.540159	−	0.196602i	−0.597669	+	0.801743i	$0.703906\pi$
$168$		0			0
$169$	−0.493048	+	2.79621i	−0.0379268	+	0.215093i
$170$		0			0
$171$	−0.330801	+	4.34633i	−0.0252970	+	0.332372i
$172$		0			0
$173$	3.71697	−	21.0800i	0.282596	−	1.60268i	−0.431153	−	0.902279i	$-0.641893\pi$
$173$	3.71697	−	21.0800i	0.282596	−	1.60268i	0.713749	−	0.700402i	$-0.246996\pi$
$174$		0			0
$175$	−15.6437	−	5.69384i	−1.18255	−	0.430414i
$176$		0			0
$177$	10.4672	−	8.78300i	0.786761	−	0.660171i
$178$		0			0
$179$	10.3741	−	17.9685i	0.775397	−	1.34303i	−0.159174	−	0.987251i	$-0.550883\pi$
$179$	10.3741	−	17.9685i	0.775397	−	1.34303i	0.934571	−	0.355777i	$-0.115784\pi$
$180$		0			0
$181$	−2.56397	−	14.5410i	−0.190578	−	1.08082i	−0.918576	−	0.395244i	$-0.870660\pi$
$181$	−2.56397	−	14.5410i	−0.190578	−	1.08082i	0.727998	−	0.685580i	$-0.240451\pi$
$182$		0			0
$183$	3.17715	+	5.50299i	0.234862	+	0.406793i
$184$		0			0
$185$	5.67567	−	2.06577i	0.417283	−	0.151879i
$186$		0			0
$187$	3.33368	+	2.79729i	0.243783	+	0.204558i
$188$		0			0
$189$	−3.63284			−0.264250
$190$		0			0
$191$	25.1275			1.81816			0.909081	−	0.416619i	$-0.136785\pi$
$191$	25.1275			1.81816			0.909081	+	0.416619i	$0.136785\pi$
$192$		0			0
$193$	6.75367	+	5.66700i	0.486140	+	0.407920i	0.852640	−	0.522498i	$-0.175000\pi$
$193$	6.75367	+	5.66700i	0.486140	+	0.407920i	−0.366501	+	0.930418i	$0.619444\pi$
$194$		0			0
$195$	1.93529	−	0.704388i	0.138589	−	0.0504423i
$196$		0			0
$197$	−7.08320	−	12.2685i	−0.504657	−	0.874092i	−0.999985	−	0.00538601i	$-0.998286\pi$
$197$	−7.08320	−	12.2685i	−0.504657	−	0.874092i	0.495328	−	0.868706i	$-0.335048\pi$
$198$		0			0
$199$	−0.823894	−	4.67253i	−0.0584043	−	0.331227i	0.941580	−	0.336789i	$-0.109341\pi$
$199$	−0.823894	−	4.67253i	−0.0584043	−	0.331227i	−0.999985	+	0.00556161i	$0.998230\pi$
$200$		0			0
$201$	−3.85991	+	6.68557i	−0.272257	+	0.471564i
$202$		0			0
$203$	3.93541	−	3.30220i	0.276212	−	0.231769i
$204$		0			0
$205$	−0.164910	−	0.0600222i	−0.0115178	−	0.00419213i
$206$		0			0
$207$	−0.212668	+	1.20610i	−0.0147815	+	0.0838299i
$208$		0			0
$209$	8.30644	−	8.49637i	0.574569	−	0.587706i
$210$		0			0
$211$	−3.20036	+	18.1501i	−0.220322	+	1.24951i	0.651107	+	0.758986i	$0.274305\pi$
$211$	−3.20036	+	18.1501i	−0.220322	+	1.24951i	−0.871429	+	0.490521i	$0.836806\pi$
$212$		0			0
$213$	−4.05161	−	1.47467i	−0.277612	−	0.101042i
$214$		0			0
$215$	−0.188079	+	0.157817i	−0.0128269	+	0.0107631i
$216$		0			0
$217$	−7.33114	+	12.6979i	−0.497670	+	0.861990i
$218$		0			0
$219$	−1.38672	−	7.86450i	−0.0937061	−	0.531434i
$220$		0			0
$221$	−2.54438	−	4.40700i	−0.171154	−	0.296447i
$222$		0			0
$223$	10.3716	−	3.77495i	0.694533	−	0.252789i	0.0294581	−	0.999566i	$-0.490622\pi$
$223$	10.3716	−	3.77495i	0.694533	−	0.252789i	0.665075	+	0.746777i	$0.268400\pi$
$224$		0			0
$225$	−3.51044	−	2.94561i	−0.234029	−	0.196374i
$226$		0			0
$227$	−10.1730			−0.675209			−0.337604	−	0.941288i	$-0.609617\pi$
$227$	−10.1730			−0.675209			−0.337604	+	0.941288i	$0.609617\pi$
$228$		0			0
$229$	−11.9151			−0.787374			−0.393687	−	0.919245i	$-0.628801\pi$
$229$	−11.9151			−0.787374			−0.393687	+	0.919245i	$0.628801\pi$
$230$		0			0
$231$	7.58609	+	6.36549i	0.499128	+	0.418818i
$232$		0			0
$233$	−19.1845	+	6.98258i	−1.25682	+	0.457444i	−0.882700	−	0.469937i	$-0.844276\pi$
$233$	−19.1845	+	6.98258i	−1.25682	+	0.457444i	−0.374117	+	0.927381i	$0.622054\pi$
$234$		0			0
$235$	−2.75037	−	4.76379i	−0.179415	−	0.310755i
$236$		0			0
$237$	0.305450	+	1.73229i	0.0198411	+	0.112524i
$238$		0			0
$239$	14.1960	−	24.5883i	0.918265	−	1.59048i	0.116217	−	0.993224i	$-0.462923\pi$
$239$	14.1960	−	24.5883i	0.918265	−	1.59048i	0.802049	−	0.597259i	$-0.203743\pi$
$240$		0			0
$241$	8.88001	−	7.45121i	0.572011	−	0.479975i	−0.310301	−	0.950638i	$-0.600430\pi$
$241$	8.88001	−	7.45121i	0.572011	−	0.479975i	0.882313	+	0.470664i	$0.155985\pi$
$242$		0			0
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$		0			0
$245$	0.695325	−	3.94339i	0.0444227	−	0.251934i
$246$		0			0
$247$	−12.5254	+	6.01395i	−0.796970	+	0.382658i
$248$		0			0
$249$	−1.93704	+	10.9855i	−0.122755	+	0.696179i
$250$		0			0
$251$	15.6800	+	5.70706i	0.989714	+	0.360227i	0.785610	−	0.618723i	$-0.212349\pi$
$251$	15.6800	+	5.70706i	0.989714	+	0.360227i	0.204105	+	0.978949i	$0.434572\pi$
$252$		0			0
$253$	2.55744	−	2.14594i	0.160785	−	0.134914i
$254$		0			0
$255$	0.515729	−	0.893269i	0.0322962	−	0.0559386i
$256$		0			0
$257$	−0.199409	−	1.13091i	−0.0124388	−	0.0705440i	0.977956	−	0.208809i	$-0.0669586\pi$
$257$	−0.199409	−	1.13091i	−0.0124388	−	0.0705440i	−0.990395	+	0.138265i	$0.955848\pi$
$258$		0			0
$259$	−16.9804	−	29.4109i	−1.05511	−	1.82750i
$260$		0			0
$261$	1.32885	−	0.483662i	0.0822537	−	0.0299379i
$262$		0			0
$263$	−10.6671	−	8.95077i	−0.657762	−	0.551928i	0.251653	−	0.967818i	$-0.419026\pi$
$263$	−10.6671	−	8.95077i	−0.657762	−	0.551928i	−0.909415	+	0.415889i	$0.863470\pi$
$264$		0			0
$265$	−6.92690			−0.425516
$266$		0			0
$267$	7.01939			0.429580
$268$		0			0
$269$	−24.3925	−	20.4678i	−1.48724	−	1.24794i	−0.898010	−	0.439974i	$-0.854988\pi$
$269$	−24.3925	−	20.4678i	−1.48724	−	1.24794i	−0.589228	−	0.807967i	$-0.700568\pi$
$270$		0			0
$271$	−21.4963	+	7.82400i	−1.30580	+	0.475274i	−0.898883	−	0.438189i	$-0.855620\pi$
$271$	−21.4963	+	7.82400i	−1.30580	+	0.475274i	−0.406922	+	0.913463i	$0.633398\pi$
$272$		0			0
$273$	−5.78998	−	10.0285i	−0.350425	−	0.606955i
$274$		0			0
$275$	2.16918	+	12.3020i	0.130807	+	0.741841i
$276$		0			0
$277$	−3.10797	+	5.38316i	−0.186740	+	0.323443i	−0.944161	−	0.329483i	$-0.893125\pi$
$277$	−3.10797	+	5.38316i	−0.186740	+	0.323443i	0.757422	+	0.652926i	$0.226459\pi$
$278$		0			0
$279$	−3.09178	+	2.59432i	−0.185100	+	0.155318i
$280$		0			0
$281$	−1.52122	−	0.553678i	−0.0907483	−	0.0330297i	0.296247	−	0.955111i	$-0.404265\pi$
$281$	−1.52122	−	0.553678i	−0.0907483	−	0.0330297i	−0.386995	+	0.922082i	$0.626487\pi$
$282$		0			0
$283$	4.49326	−	25.4825i	0.267096	−	1.51478i	−0.495902	−	0.868378i	$-0.665163\pi$
$283$	4.49326	−	25.4825i	0.267096	−	1.51478i	0.762998	−	0.646400i	$-0.223726\pi$
$284$		0			0
$285$	−2.32507	−	1.58918i	−0.137726	−	0.0941347i
$286$		0			0
$287$	−0.171347	+	0.971758i	−0.0101143	+	0.0573611i
$288$		0			0
$289$	13.5799	+	4.94267i	0.798815	+	0.290745i
$290$		0			0
$291$	14.6370	−	12.2819i	0.858038	−	0.719979i
$292$		0			0
$293$	−11.6484	+	20.1757i	−0.680509	+	1.17868i	0.294316	+	0.955708i	$0.404908\pi$
$293$	−11.6484	+	20.1757i	−0.680509	+	1.17868i	−0.974826	+	0.222968i	$0.928425\pi$
$294$		0			0
$295$	1.53301	+	8.69414i	0.0892554	+	0.506192i
$296$		0			0
$297$	1.36297	+	2.36074i	0.0790878	+	0.136984i
$298$		0			0
$299$	−3.66842	+	1.33520i	−0.212150	+	0.0772164i
$300$		0			0
$301$	1.05752	+	0.887364i	0.0609544	+	0.0511468i
$302$		0			0
$303$	2.84895			0.163668
$304$		0			0
$305$	−4.10552			−0.235081
$306$		0			0
$307$	−1.70746	−	1.43273i	−0.0974496	−	0.0817700i	0.592761	−	0.805378i	$-0.298038\pi$
$307$	−1.70746	−	1.43273i	−0.0974496	−	0.0817700i	−0.690211	+	0.723608i	$0.742482\pi$
$308$		0			0
$309$	−6.90051	+	2.51158i	−0.392556	+	0.142879i
$310$		0			0
$311$	7.62716	+	13.2106i	0.432497	+	0.749106i	0.997088	−	0.0762647i	$-0.0242994\pi$
$311$	7.62716	+	13.2106i	0.432497	+	0.749106i	−0.564591	+	0.825371i	$0.690966\pi$
$312$		0			0
$313$	−0.362089	−	2.05351i	−0.0204665	−	0.116071i	0.972863	−	0.231382i	$-0.0743247\pi$
$313$	−0.362089	−	2.05351i	−0.0204665	−	0.116071i	−0.993329	+	0.115311i	$0.963214\pi$
$314$		0			0
$315$	1.17359	−	2.03271i	0.0661242	−	0.114530i
$316$		0			0
$317$	21.6889	−	18.1991i	1.21817	−	1.02216i	0.219250	−	0.975669i	$-0.429639\pi$
$317$	21.6889	−	18.1991i	1.21817	−	1.02216i	0.998918	−	0.0464962i	$-0.0148055\pi$
$318$		0			0
$319$	−3.62238	−	1.31844i	−0.202814	−	0.0738183i
$320$		0			0
$321$	2.17413	−	12.3301i	0.121348	−	0.688199i
$322$		0			0
$323$	−2.86941	+	6.33957i	−0.159658	+	0.352743i
$324$		0			0
$325$	2.53652	−	14.3853i	0.140701	−	0.797955i
$326$		0			0
$327$	4.59777	+	1.67345i	0.254257	+	0.0925421i
$328$		0			0
$329$	−23.6931	+	19.8809i	−1.30624	+	1.09607i
$330$		0			0
$331$	−4.38497	+	7.59499i	−0.241020	+	0.417458i	−0.961005	−	0.276531i	$-0.910815\pi$
$331$	−4.38497	+	7.59499i	−0.241020	+	0.417458i	0.719985	+	0.693989i	$0.244149\pi$
$332$		0			0
$333$	−1.62331	−	9.20625i	−0.0889569	−	0.504500i
$334$		0			0
$335$	−2.49389	−	4.31954i	−0.136256	−	0.236002i
$336$		0			0
$337$	33.3031	−	12.1213i	1.81414	−	0.660291i	0.817728	−	0.575605i	$-0.195233\pi$
$337$	33.3031	−	12.1213i	1.81414	−	0.660291i	0.996408	−	0.0846869i	$-0.0269890\pi$
$338$		0			0
$339$	−6.16373	−	5.17198i	−0.334768	−	0.280903i
$340$		0			0
$341$	11.0020			0.595794
$342$		0			0
$343$	2.91526			0.157409
$344$		0			0
$345$	−0.606159	−	0.508628i	−0.0326345	−	0.0273836i
$346$		0			0
$347$	−1.69075	+	0.615383i	−0.0907642	+	0.0330355i	−0.387003	−	0.922078i	$-0.626490\pi$
$347$	−1.69075	+	0.615383i	−0.0907642	+	0.0330355i	0.296239	+	0.955114i	$0.404268\pi$
$348$		0			0
$349$	−0.257142	−	0.445384i	−0.0137645	−	0.0238408i	0.859061	−	0.511873i	$-0.171048\pi$
$349$	−0.257142	−	0.445384i	−0.0137645	−	0.0238408i	−0.872826	+	0.488032i	$0.837715\pi$
$350$		0			0
$351$	−0.553517	−	3.13915i	−0.0295446	−	0.167555i
$352$		0			0
$353$	−12.8871	+	22.3210i	−0.685909	+	1.18803i	0.287242	+	0.957858i	$0.407262\pi$
$353$	−12.8871	+	22.3210i	−0.685909	+	1.18803i	−0.973150	+	0.230171i	$0.926072\pi$
$354$		0			0
$355$	2.13401	−	1.79064i	0.113261	−	0.0950375i
$356$		0			0
$357$	−5.44984	−	1.98358i	−0.288436	−	0.104982i
$358$		0			0
$359$	−0.915707	+	5.19323i	−0.0483292	+	0.274088i	−0.999390	−	0.0349144i	$-0.988884\pi$
$359$	−0.915707	+	5.19323i	−0.0483292	+	0.274088i	0.951061	+	0.309003i	$0.0999952\pi$
$360$		0			0
$361$	16.6650	+	9.12565i	0.877106	+	0.480297i
$362$		0			0
$363$	−0.619785	+	3.51497i	−0.0325303	+	0.184488i
$364$		0			0
$365$	4.84847	+	1.76470i	0.253781	+	0.0923686i
$366$		0			0
$367$	5.98026	−	5.01804i	0.312167	−	0.261939i	−0.473220	−	0.880944i	$-0.656908\pi$
$367$	5.98026	−	5.01804i	0.312167	−	0.261939i	0.785387	+	0.619005i	$0.212464\pi$
$368$		0			0
$369$	−0.135810	+	0.235229i	−0.00706996	+	0.0122455i
$370$		0			0
$371$	6.76325	+	38.3563i	0.351131	+	1.99136i
$372$		0			0
$373$	11.4544	+	19.8396i	0.593087	+	1.02726i	0.993814	+	0.111059i	$0.0354243\pi$
$373$	11.4544	+	19.8396i	0.593087	+	1.02726i	−0.400727	+	0.916198i	$0.631242\pi$
$374$		0			0
$375$	5.81791	−	2.11754i	0.300435	−	0.109350i
$376$		0			0
$377$	3.45306	+	2.89747i	0.177842	+	0.149227i
$378$		0			0
$379$	8.29656			0.426166			0.213083	−	0.977034i	$-0.431650\pi$
$379$	8.29656			0.426166			0.213083	+	0.977034i	$0.431650\pi$
$380$		0			0
$381$	−10.9400			−0.560474
$382$		0			0
$383$	−5.31915	−	4.46330i	−0.271796	−	0.228064i	0.496694	−	0.867926i	$-0.334547\pi$
$383$	−5.31915	−	4.46330i	−0.271796	−	0.228064i	−0.768490	+	0.639862i	$0.778992\pi$
$384$		0			0
$385$	−6.01242	+	2.18834i	−0.306421	+	0.111528i
$386$		0			0
$387$	0.190002	+	0.329093i	0.00965834	+	0.0167287i
$388$		0			0
$389$	6.09823	+	34.5848i	0.309193	+	1.75352i	0.603081	+	0.797680i	$0.293939\pi$
$389$	6.09823	+	34.5848i	0.309193	+	1.75352i	−0.293889	+	0.955840i	$0.594950\pi$
$390$		0			0
$391$	−0.977585	+	1.69323i	−0.0494386	+	0.0856302i
$392$		0			0
$393$	13.7375	−	11.5272i	0.692968	−	0.581469i
$394$		0			0
$395$	−1.06796	−	0.388706i	−0.0537349	−	0.0195579i
$396$		0			0
$397$	−1.58164	+	8.96993i	−0.0793802	+	0.450188i	0.919048	+	0.394145i	$0.128959\pi$
$397$	−1.58164	+	8.96993i	−0.0793802	+	0.450188i	−0.998428	+	0.0560424i	$0.982152\pi$
$398$		0			0
$399$	−6.52960	+	14.4263i	−0.326889	+	0.722217i
$400$		0			0
$401$	−5.31067	+	30.1183i	−0.265202	+	1.50404i	0.503257	+	0.864137i	$0.332135\pi$
$401$	−5.31067	+	30.1183i	−0.265202	+	1.50404i	−0.768459	+	0.639899i	$0.778976\pi$
$402$		0			0
$403$	−12.0893	−	4.40015i	−0.602212	−	0.219187i
$404$		0			0
$405$	0.494941	−	0.415305i	0.0245938	−	0.0206367i
$406$		0			0
$407$	−12.7415	+	22.0689i	−0.631571	+	1.09391i
$408$		0			0
$409$	0.950810	+	5.39231i	0.0470145	+	0.266633i	0.999250	−	0.0387333i	$-0.0123323\pi$
$409$	0.950810	+	5.39231i	0.0470145	+	0.266633i	−0.952235	+	0.305366i	$0.901221\pi$
$410$		0			0
$411$	−1.51135	−	2.61773i	−0.0745492	−	0.129123i
$412$		0			0
$413$	46.6453	−	16.9775i	2.29526	−	0.835408i
$414$		0			0
$415$	−5.52106	−	4.63272i	−0.271018	−	0.227411i
$416$		0			0
$417$	15.8097			0.774206
$418$		0			0
$419$	−9.72227			−0.474964			−0.237482	−	0.971392i	$-0.576322\pi$
$419$	−9.72227			−0.474964			−0.237482	+	0.971392i	$0.576322\pi$
$420$		0			0
$421$	−6.11938	−	5.13477i	−0.298241	−	0.250254i	0.481371	−	0.876517i	$-0.340139\pi$
$421$	−6.11938	−	5.13477i	−0.298241	−	0.250254i	−0.779612	+	0.626263i	$0.784583\pi$
$422$		0			0
$423$	−8.00033	+	2.91188i	−0.388990	+	0.141581i
$424$		0			0
$425$	−3.65788	−	6.33564i	−0.177433	−	0.307323i
$426$		0			0
$427$	4.00853	+	22.7335i	0.193986	+	1.10015i
$428$		0			0
$429$	−4.34459	+	7.52505i	−0.209759	+	0.363313i
$430$		0			0
$431$	0.173124	−	0.145268i	0.00833907	−	0.00699731i	−0.638609	−	0.769532i	$-0.720490\pi$
$431$	0.173124	−	0.145268i	0.00833907	−	0.00699731i	0.646948	+	0.762534i	$0.276045\pi$
$432$		0			0
$433$	−11.0645	−	4.02717i	−0.531728	−	0.193533i	0.0621817	−	0.998065i	$-0.480194\pi$
$433$	−11.0645	−	4.02717i	−0.531728	−	0.193533i	−0.593910	+	0.804532i	$0.702416\pi$
$434$		0			0
$435$	−0.158657	+	0.899790i	−0.00760703	+	0.0431416i
$436$		0			0
$437$	4.40727	+	3.01235i	0.210829	+	0.144100i
$438$		0			0
$439$	−3.39595	+	19.2594i	−0.162080	+	0.919200i	0.789945	+	0.613178i	$0.210109\pi$
$439$	−3.39595	+	19.2594i	−0.162080	+	0.919200i	−0.952025	+	0.306022i	$0.901002\pi$
$440$		0			0
$441$	−5.82377	−	2.11968i	−0.277322	−	0.100937i
$442$		0			0
$443$	−1.20890	+	1.01438i	−0.0574364	+	0.0481949i	−0.671054	−	0.741409i	$-0.734158\pi$
$443$	−1.20890	+	1.01438i	−0.0574364	+	0.0481949i	0.613618	+	0.789603i	$0.289714\pi$
$444$		0			0
$445$	−2.26761	+	3.92762i	−0.107495	+	0.186187i
$446$		0			0
$447$	0.357885	+	2.02966i	0.0169274	+	0.0959998i
$448$		0			0
$449$	−7.96699	−	13.7992i	−0.375985	−	0.651226i	0.614489	−	0.788926i	$-0.289362\pi$
$449$	−7.96699	−	13.7992i	−0.375985	−	0.651226i	−0.990474	+	0.137700i	$0.956029\pi$
$450$		0			0
$451$	0.695767	−	0.253239i	0.0327624	−	0.0119245i
$452$		0			0
$453$	10.6572	+	8.94249i	0.500721	+	0.420155i
$454$		0			0
$455$	7.48181			0.350753
$456$		0			0
$457$	23.4251			1.09578			0.547889	−	0.836551i	$-0.315432\pi$
$457$	23.4251			1.09578			0.547889	+	0.836551i	$0.315432\pi$
$458$		0			0
$459$	−1.22294	−	1.02617i	−0.0570820	−	0.0478975i
$460$		0			0
$461$	25.3786	−	9.23706i	1.18200	−	0.430213i	0.325092	−	0.945682i	$-0.394605\pi$
$461$	25.3786	−	9.23706i	1.18200	−	0.430213i	0.856908	+	0.515470i	$0.172383\pi$
$462$		0			0
$463$	10.6882	+	18.5125i	0.496722	+	0.860348i	0.999993	−	0.00378094i	$-0.00120351\pi$
$463$	10.6882	+	18.5125i	0.496722	+	0.860348i	−0.503271	+	0.864129i	$0.667870\pi$
$464$		0			0
$465$	−0.452819	−	2.56807i	−0.0209990	−	0.119091i
$466$		0			0
$467$	−14.0332	+	24.3062i	−0.649380	+	1.12476i	0.333891	+	0.942612i	$0.391638\pi$
$467$	−14.0332	+	24.3062i	−0.649380	+	1.12476i	−0.983271	+	0.182147i	$0.941695\pi$
$468$		0			0
$469$	−21.4836	+	18.0269i	−0.992022	+	0.832406i
$470$		0			0
$471$	−8.55315	−	3.11309i	−0.394108	−	0.143444i
$472$		0			0
$473$	0.179877	−	1.02013i	0.00827076	−	0.0469058i
$474$		0			0
$475$	−18.0068	+	8.64583i	−0.826210	+	0.396698i
$476$		0			0
$477$	−1.86170	+	10.5582i	−0.0852413	+	0.483428i
$478$		0			0
$479$	−39.5563	−	14.3973i	−1.80737	−	0.657830i	−0.997456	−	0.0712841i	$-0.977290\pi$
$479$	−39.5563	−	14.3973i	−1.80737	−	0.657830i	−0.809916	−	0.586546i	$-0.800487\pi$
$480$		0			0
$481$	22.8269	−	19.1540i	1.04082	−	0.873348i
$482$		0			0
$483$	−2.22459	+	3.85310i	−0.101222	+	0.175322i
$484$		0			0
$485$	2.14372	+	12.1577i	0.0973414	+	0.552051i
$486$		0			0
$487$	−5.20899	−	9.02223i	−0.236042	−	0.408836i	0.723533	−	0.690290i	$-0.242517\pi$
$487$	−5.20899	−	9.02223i	−0.236042	−	0.408836i	−0.959575	+	0.281453i	$0.909184\pi$
$488$		0			0
$489$	11.0756	−	4.03118i	0.500855	−	0.182296i
$490$		0			0
$491$	21.6262	+	18.1465i	0.975975	+	0.818940i	0.983477	−	0.181031i	$-0.0579436\pi$
$491$	21.6262	+	18.1465i	0.975975	+	0.818940i	−0.00750218	+	0.999972i	$0.502388\pi$
$492$		0			0
$493$	2.25757			0.101676
$494$		0			0
$495$	−1.76124			−0.0791616
$496$		0			0
$497$	−11.9989	−	10.0683i	−0.538225	−	0.451625i
$498$		0			0
$499$	11.5137	−	4.19065i	0.515425	−	0.187599i	−0.0711940	−	0.997462i	$-0.522681\pi$
$499$	11.5137	−	4.19065i	0.515425	−	0.187599i	0.586619	+	0.809863i	$0.300459\pi$
$500$		0			0
$501$	−3.71419	−	6.43316i	−0.165938	−	0.287412i
$502$		0			0
$503$	6.23288	+	35.3484i	0.277910	+	1.57611i	0.729563	+	0.683914i	$0.239724\pi$
$503$	6.23288	+	35.3484i	0.277910	+	1.57611i	−0.451652	+	0.892194i	$0.649165\pi$
$504$		0			0
$505$	−0.920354	+	1.59410i	−0.0409552	+	0.0709365i
$506$		0			0
$507$	−2.17507	+	1.82510i	−0.0965982	+	0.0810555i
$508$		0			0
$509$	6.91078	+	2.51532i	0.306315	+	0.111490i	0.490604	−	0.871382i	$-0.336776\pi$
$509$	6.91078	+	2.51532i	0.306315	+	0.111490i	−0.184289	+	0.982872i	$0.558998\pi$
$510$		0			0
$511$	5.03774	−	28.5705i	0.222857	−	1.26388i
$512$		0			0
$513$	−3.04717	+	3.11685i	−0.134536	+	0.137612i
$514$		0			0
$515$	0.823882	−	4.67247i	0.0363046	−	0.205894i
$516$		0			0
$517$	21.8085	+	7.93765i	0.959137	+	0.349097i
$518$		0			0
$519$	16.3973	−	13.7590i	0.719762	−	0.603952i
$520$		0			0
$521$	−12.6206	+	21.8595i	−0.552917	+	0.957681i	0.445145	+	0.895458i	$0.353152\pi$
$521$	−12.6206	+	21.8595i	−0.552917	+	0.957681i	−0.998062	+	0.0622222i	$0.980181\pi$
$522$		0			0
$523$	0.697026	+	3.95303i	0.0304788	+	0.172854i	0.996247	−	0.0865512i	$-0.0275846\pi$
$523$	0.697026	+	3.95303i	0.0304788	+	0.172854i	−0.965769	+	0.259405i	$0.916474\pi$
$524$		0			0
$525$	−8.32384	−	14.4173i	−0.363282	−	0.629223i
$526$		0			0
$527$	−6.05470	+	2.20373i	−0.263747	+	0.0959961i
$528$		0			0
$529$	−16.4700	−	13.8200i	−0.716088	−	0.600869i
$530$		0			0
$531$	13.6639			0.592964
$532$		0			0
$533$	−0.865807			−0.0375023
$534$		0			0
$535$	6.19682	+	5.19975i	0.267912	+	0.224805i
$536$		0			0
$537$	19.4969	−	7.09631i	0.841355	−	0.306228i
$538$		0			0
$539$	8.44707	+	14.6308i	0.363841	+	0.630191i
$540$		0			0
$541$	−2.09059	−	11.8563i	−0.0898814	−	0.509743i	−0.996196	−	0.0871393i	$-0.972227\pi$
$541$	−2.09059	−	11.8563i	−0.0898814	−	0.509743i	0.906315	−	0.422603i	$-0.138884\pi$
$542$		0			0
$543$	7.38266	−	12.7871i	0.316820	−	0.548749i
$544$		0			0
$545$	−2.42167	+	2.03202i	−0.103733	+	0.0870423i
$546$		0			0
$547$	−7.29333	−	2.65455i	−0.311840	−	0.113501i	0.181359	−	0.983417i	$-0.441950\pi$
$547$	−7.29333	−	2.65455i	−0.311840	−	0.113501i	−0.493199	+	0.869916i	$0.664173\pi$
$548$		0			0
$549$	−1.10341	+	6.25777i	−0.0470926	+	0.267075i
$550$		0			0
$551$	0.467796	−	6.14628i	0.0199288	−	0.261840i
$552$		0			0
$553$	−1.10965	+	6.29314i	−0.0471871	+	0.267611i
$554$		0			0
$555$	5.67567	+	2.06577i	0.240919	+	0.0876872i
$556$		0			0
$557$	−21.7515	+	18.2517i	−0.921642	+	0.773349i	−0.974298	−	0.225263i	$-0.927676\pi$
$557$	−21.7515	+	18.2517i	−0.921642	+	0.773349i	0.0526561	+	0.998613i	$0.483231\pi$
$558$		0			0
$559$	−0.605646	+	1.04901i	−0.0256161	+	0.0443684i
$560$		0			0
$561$	0.755683	+	4.28569i	0.0319050	+	0.180942i
$562$		0			0
$563$	−18.5558	−	32.1396i	−0.782033	−	1.35452i	−0.930756	−	0.365642i	$-0.880849\pi$
$563$	−18.5558	−	32.1396i	−0.782033	−	1.35452i	0.148722	−	0.988879i	$-0.452484\pi$
$564$		0			0
$565$	4.88512	−	1.77804i	0.205518	−	0.0748026i
$566$		0			0
$567$	−2.78292	−	2.33514i	−0.116872	−	0.0980668i
$568$		0			0
$569$	−40.8997			−1.71461			−0.857303	−	0.514812i	$-0.827862\pi$
$569$	−40.8997			−1.71461			−0.857303	+	0.514812i	$0.827862\pi$
$570$		0			0
$571$	1.75545			0.0734631			0.0367315	−	0.999325i	$-0.488305\pi$
$571$	1.75545			0.0734631			0.0367315	+	0.999325i	$0.488305\pi$
$572$		0			0
$573$	19.2488	+	16.1516i	0.804129	+	0.674745i
$574$		0			0
$575$	−5.27383	+	1.91952i	−0.219934	+	0.0800494i
$576$		0			0
$577$	−14.0700	−	24.3699i	−0.585740	−	1.01453i	−0.994783	−	0.102017i	$-0.967470\pi$
$577$	−14.0700	−	24.3699i	−0.585740	−	1.01453i	0.409042	−	0.912515i	$-0.365863\pi$
$578$		0			0
$579$	1.53093	+	8.68235i	0.0636234	+	0.360826i
$580$		0			0
$581$	−20.2621	+	35.0951i	−0.840616	+	1.45599i
$582$		0			0
$583$	22.3878	−	18.7856i	0.927207	−	0.778019i
$584$		0			0
$585$	1.93529	+	0.704388i	0.0800144	+	0.0291229i
$586$		0			0
$587$	−2.54747	+	14.4474i	−0.105145	+	0.596309i	0.886017	+	0.463653i	$0.153462\pi$
$587$	−2.54747	+	14.4474i	−0.105145	+	0.596309i	−0.991162	+	0.132656i	$0.957649\pi$
$588$		0			0
$589$	4.74509	+	16.9407i	0.195518	+	0.698028i
$590$		0			0
$591$	2.45997	−	13.9512i	0.101190	−	0.573875i
$592$		0			0
$593$	−9.71167	−	3.53476i	−0.398811	−	0.145155i	0.134826	−	0.990869i	$-0.456953\pi$
$593$	−9.71167	−	3.53476i	−0.398811	−	0.145155i	−0.533636	+	0.845714i	$0.679175\pi$
$594$		0			0
$595$	2.87046	−	2.40860i	0.117677	−	0.0987431i
$596$		0			0
$597$	2.37231	−	4.10896i	0.0970921	−	0.168168i
$598$		0			0
$599$	−5.15375	−	29.2284i	−0.210577	−	1.19424i	−0.888419	−	0.459033i	$-0.848196\pi$
$599$	−5.15375	−	29.2284i	−0.210577	−	1.19424i	0.677843	−	0.735207i	$-0.262915\pi$
$600$		0			0
$601$	8.57580	+	14.8537i	0.349814	+	0.605896i	0.986216	−	0.165462i	$-0.0529114\pi$
$601$	8.57580	+	14.8537i	0.349814	+	0.605896i	−0.636402	+	0.771357i	$0.719578\pi$
$602$		0			0
$603$	−7.25427	+	2.64034i	−0.295417	+	0.107523i
$604$		0			0
$605$	−1.76654	−	1.48231i	−0.0718202	−	0.0602643i
$606$		0			0
$607$	46.3567			1.88156			0.940780	−	0.339016i	$-0.110094\pi$
$607$	46.3567			1.88156			0.940780	+	0.339016i	$0.110094\pi$
$608$		0			0
$609$	5.13732			0.208175
$610$		0			0
$611$	−20.7892	−	17.4442i	−0.841039	−	0.705716i
$612$		0			0
$613$	−41.6152	+	15.1467i	−1.68082	+	0.611770i	−0.993422	−	0.114508i	$-0.963471\pi$
$613$	−41.6152	+	15.1467i	−1.68082	+	0.611770i	−0.687402	+	0.726278i	$0.741249\pi$
$614$		0			0
$615$	−0.0877465	−	0.151981i	−0.00353828	−	0.00612848i
$616$		0			0
$617$	7.46093	+	42.3130i	0.300366	+	1.70346i	0.644555	+	0.764558i	$0.277043\pi$
$617$	7.46093	+	42.3130i	0.300366	+	1.70346i	−0.344190	+	0.938900i	$0.611846\pi$
$618$		0			0
$619$	−21.2535	+	36.8122i	−0.854251	+	1.47961i	0.0230865	+	0.999733i	$0.492651\pi$
$619$	−21.2535	+	36.8122i	−0.854251	+	1.47961i	−0.877338	+	0.479873i	$0.840683\pi$
$620$		0			0
$621$	−0.938181	+	0.787228i	−0.0376479	+	0.0315904i
$622$		0			0
$623$	23.9625	+	8.72162i	0.960036	+	0.349424i
$624$		0			0
$625$	3.28414	−	18.6253i	0.131365	−	0.745011i
$626$		0			0
$627$	11.8245	−	1.16932i	0.472224	−	0.0466980i
$628$		0			0
$629$	2.59151	−	14.6972i	0.103330	−	0.586016i
$630$		0			0
$631$	−13.9515	−	5.07792i	−0.555400	−	0.202149i	0.0490443	−	0.998797i	$-0.484382\pi$
$631$	−13.9515	−	5.07792i	−0.555400	−	0.202149i	−0.604444	+	0.796648i	$0.706605\pi$
$632$		0			0
$633$	−14.1183	+	11.8467i	−0.561152	+	0.470863i
$634$		0			0
$635$	3.53417	−	6.12137i	0.140249	−	0.242919i
$636$		0			0
$637$	−3.43044	−	19.4550i	−0.135919	−	0.770834i
$638$		0			0
$639$	−2.15582	−	3.73399i	−0.0852828	−	0.147714i
$640$		0			0
$641$	38.0442	−	13.8470i	1.50266	−	0.546922i	0.545910	−	0.837844i	$-0.316184\pi$
$641$	38.0442	−	13.8470i	1.50266	−	0.546922i	0.956747	+	0.290921i	$0.0939618\pi$
$642$		0			0
$643$	34.5265	+	28.9712i	1.36159	+	1.14251i	0.975487	+	0.220057i	$0.0706243\pi$
$643$	34.5265	+	28.9712i	1.36159	+	1.14251i	0.386105	+	0.922455i	$0.373820\pi$
$644$		0			0
$645$	−0.245520			−0.00966735
$646$		0			0
$647$	4.25397			0.167241			0.0836205	−	0.996498i	$-0.473352\pi$
$647$	4.25397			0.167241			0.0836205	+	0.996498i	$0.473352\pi$
$648$		0			0
$649$	−28.5330	−	23.9420i	−1.12002	−	0.939807i
$650$		0			0
$651$	−13.7780	+	5.01479i	−0.540004	+	0.196545i
$652$		0			0
$653$	3.01546	+	5.22292i	0.118004	+	0.204389i	0.918977	−	0.394312i	$-0.129017\pi$
$653$	3.01546	+	5.22292i	0.118004	+	0.204389i	−0.800973	+	0.598701i	$0.795684\pi$
$654$		0			0
$655$	2.01199	+	11.4105i	0.0786148	+	0.445847i
$656$		0			0
$657$	3.99291	−	6.91592i	0.155778	−	0.269816i
$658$		0			0
$659$	−21.0304	+	17.6466i	−0.819228	+	0.687414i	−0.952791	−	0.303627i	$-0.901802\pi$
$659$	−21.0304	+	17.6466i	−0.819228	+	0.687414i	0.133563	+	0.991040i	$0.457358\pi$
$660$		0			0
$661$	10.6789	+	3.88680i	0.415361	+	0.151179i	0.541243	−	0.840866i	$-0.317954\pi$
$661$	10.6789	+	3.88680i	0.415361	+	0.151179i	−0.125882	+	0.992045i	$0.540176\pi$
$662$		0			0
$663$	0.883655	−	5.01146i	0.0343183	−	0.194629i
$664$		0			0
$665$	−5.96267	−	8.31397i	−0.231222	−	0.322402i
$666$		0			0
$667$	0.300741	−	1.70559i	0.0116447	−	0.0660407i
$668$		0			0
$669$	10.3716	+	3.77495i	0.400989	+	0.145948i
$670$		0			0
$671$	13.2691	−	11.1341i	0.512246	−	0.429826i
$672$		0			0
$673$	−1.29137	+	2.23671i	−0.0497786	+	0.0862190i	−0.889841	−	0.456271i	$-0.849185\pi$
$673$	−1.29137	+	2.23671i	−0.0497786	+	0.0862190i	0.840062	+	0.542490i	$0.182518\pi$
$674$		0			0
$675$	−0.795752	−	4.51294i	−0.0306285	−	0.173703i
$676$		0			0
$677$	−22.2099	−	38.4687i	−0.853596	−	1.47847i	−0.877941	−	0.478768i	$-0.841083\pi$
$677$	−22.2099	−	38.4687i	−0.853596	−	1.47847i	0.0243451	−	0.999704i	$-0.492250\pi$
$678$		0			0
$679$	65.2275	−	23.7409i	2.50320	−	0.911091i
$680$		0			0
$681$	−7.79301	−	6.53911i	−0.298629	−	0.250579i
$682$		0			0
$683$	−8.91746			−0.341217			−0.170608	−	0.985339i	$-0.554573\pi$
$683$	−8.91746			−0.341217			−0.170608	+	0.985339i	$0.554573\pi$
$684$		0			0
$685$	1.95296			0.0746188
$686$		0			0
$687$	−9.12752	−	7.65890i	−0.348236	−	0.292205i
$688$		0			0
$689$	−32.1134	+	11.6883i	−1.22342	+	0.445289i
$690$		0			0
$691$	15.6321	+	27.0757i	0.594674	+	1.03001i	0.993593	+	0.113020i	$0.0360524\pi$
$691$	15.6321	+	27.0757i	0.594674	+	1.03001i	−0.398918	+	0.916986i	$0.630614\pi$
$692$		0			0
$693$	1.71963	+	9.75249i	0.0653232	+	0.370466i
$694$		0			0
$695$	−5.10733	+	8.84616i	−0.193732	+	0.335554i
$696$		0			0
$697$	−0.332174	+	0.278727i	−0.0125820	+	0.0105576i
$698$		0			0
$699$	−19.1845	−	6.98258i	−0.725624	−	0.264105i
$700$		0			0
$701$	−0.953241	+	5.40610i	−0.0360034	+	0.204186i	−0.997503	−	0.0706198i	$-0.977502\pi$
$701$	−0.953241	+	5.40610i	−0.0360034	+	0.204186i	0.961500	+	0.274805i	$0.0886134\pi$
$702$		0			0
$703$	−39.4764	−	10.1009i	−1.48888	−	0.380962i
$704$		0			0
$705$	0.955195	−	5.41718i	0.0359747	−	0.204023i
$706$		0			0
$707$	9.72562	+	3.53984i	0.365769	+	0.133129i
$708$		0			0
$709$	−21.6551	+	18.1708i	−0.813274	+	0.682418i	−0.951387	−	0.307998i	$-0.900341\pi$
$709$	−21.6551	+	18.1708i	−0.813274	+	0.682418i	0.138113	+	0.990417i	$0.455896\pi$
$710$		0			0
$711$	−0.879508	+	1.52335i	−0.0329841	+	0.0571302i
$712$		0			0
$713$	0.858338	+	4.86788i	0.0321450	+	0.182303i
$714$		0			0
$715$	−2.80704	−	4.86193i	−0.104977	−	0.181826i
$716$		0			0
$717$	26.6798	−	9.71066i	0.996376	−	0.362651i
$718$		0			0
$719$	−16.9017	−	14.1822i	−0.630327	−	0.528907i	0.270703	−	0.962663i	$-0.412744\pi$
$719$	−16.9017	−	14.1822i	−0.630327	−	0.528907i	−0.901031	+	0.433755i	$0.857188\pi$
$720$		0			0
$721$	−26.6773			−0.993514
$722$		0			0
$723$	11.5920			0.431112
$724$		0			0
$725$	4.96423	+	4.16548i	0.184367	+	0.154702i
$726$		0			0
$727$	37.5115	−	13.6531i	1.39122	−	0.506364i	0.465662	−	0.884963i	$-0.345816\pi$
$727$	37.5115	−	13.6531i	1.39122	−	0.506364i	0.925561	+	0.378599i	$0.123594\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	0.105344	+	0.597436i	0.00389629	+	0.0220970i
$732$		0			0
$733$	20.2264	−	35.0332i	0.747081	−	1.29398i	−0.202136	−	0.979358i	$-0.564788\pi$
$733$	20.2264	−	35.0332i	0.747081	−	1.29398i	0.949216	−	0.314624i	$-0.101878\pi$
$734$		0			0
$735$	3.06741	−	2.57386i	0.113143	−	0.0949383i
$736$		0			0
$737$	19.7748	+	7.19743i	0.728413	+	0.265121i
$738$		0			0
$739$	7.17593	−	40.6967i	0.263971	−	1.49705i	−0.507979	−	0.861369i	$-0.669607\pi$
$739$	7.17593	−	40.6967i	0.263971	−	1.49705i	0.771950	−	0.635683i	$-0.219282\pi$
$740$		0			0
$741$	−13.4607	−	3.44420i	−0.494490	−	0.126526i
$742$		0			0
$743$	3.80732	−	21.5924i	0.139677	−	0.792147i	−0.831811	−	0.555059i	$-0.812696\pi$
$743$	3.80732	−	21.5924i	0.139677	−	0.792147i	0.971488	−	0.237089i	$-0.0761932\pi$
$744$		0			0
$745$	−1.25129	−	0.455432i	−0.0458437	−	0.0166858i
$746$		0			0
$747$	−8.54522	+	7.17029i	−0.312653	+	0.262347i
$748$		0			0
$749$	22.7421	−	39.3905i	0.830980	−	1.43930i
$750$		0			0
$751$	−5.99601	−	34.0051i	−0.218798	−	1.24086i	−0.874194	−	0.485577i	$-0.838609\pi$
$751$	−5.99601	−	34.0051i	−0.218798	−	1.24086i	0.655396	−	0.755285i	$-0.272502\pi$
$752$		0			0
$753$	8.34317	+	14.4508i	0.304042	+	0.526616i
$754$		0			0
$755$	−8.44649	+	3.07427i	−0.307399	+	0.111884i
$756$		0			0
$757$	−23.8624	−	20.0229i	−0.867293	−	0.727745i	0.0962336	−	0.995359i	$-0.469320\pi$
$757$	−23.8624	−	20.0229i	−0.867293	−	0.727745i	−0.963526	+	0.267614i	$0.913765\pi$
$758$		0			0
$759$	3.33849			0.121180
$760$		0			0
$761$	5.72463			0.207518			0.103759	−	0.994602i	$-0.466913\pi$
$761$	5.72463			0.207518			0.103759	+	0.994602i	$0.466913\pi$
$762$		0			0
$763$	13.6164	+	11.4255i	0.492946	+	0.413631i
$764$		0			0
$765$	0.969253	−	0.352779i	0.0350434	−	0.0127548i
$766$		0			0
$767$	21.7774	+	37.7196i	0.786337	+	1.36198i
$768$		0			0
$769$	0.820284	+	4.65206i	0.0295802	+	0.167758i	0.996019	−	0.0891384i	$-0.0284113\pi$
$769$	0.820284	+	4.65206i	0.0295802	+	0.167758i	−0.966439	+	0.256896i	$0.917300\pi$
$770$		0			0
$771$	0.574177	−	0.994503i	0.0206785	−	0.0358161i
$772$		0			0
$773$	−21.2982	+	17.8713i	−0.766044	+	0.642787i	−0.939693	−	0.342020i	$-0.888889\pi$
$773$	−21.2982	+	17.8713i	−0.766044	+	0.642787i	0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$	−17.3800	−	6.32579i	−0.624307	−	0.227229i
$776$		0			0
$777$	5.89723	−	33.4448i	0.211562	−	1.19983i
$778$		0			0
$779$	0.690010	+	0.962106i	0.0247222	+	0.0344710i
$780$		0			0
$781$	−2.04094	+	11.5747i	−0.0730306	+	0.414177i
$782$		0			0
$783$	1.32885	+	0.483662i	0.0474892	+	0.0172847i
$784$		0			0
$785$	4.50499	−	3.78013i	0.160790	−	0.134919i
$786$		0			0
$787$	7.79287	−	13.4977i	0.277786	−	0.481139i	−0.693048	−	0.720891i	$-0.743733\pi$
$787$	7.79287	−	13.4977i	0.277786	−	0.481139i	0.970834	+	0.239752i	$0.0770661\pi$
$788$		0			0
$789$	−2.41804	−	13.7134i	−0.0860845	−	0.488209i
$790$		0			0
$791$	−14.6152	−	25.3143i	−0.519658	−	0.900074i
$792$		0			0
$793$	−19.0333	+	6.92757i	−0.675893	+	0.246005i
$794$		0			0
$795$	−5.30631	−	4.45252i	−0.188195	−	0.157915i
$796$		0			0
$797$	21.6702			0.767597			0.383798	−	0.923417i	$-0.374616\pi$
$797$	21.6702			0.767597			0.383798	+	0.923417i	$0.374616\pi$
$798$		0			0
$799$	−13.5917			−0.480840
$800$		0			0
$801$	5.37716	+	4.51198i	0.189993	+	0.159423i
$802$		0			0
$803$	−20.4561	+	7.44542i	−0.721881	+	0.262743i
$804$		0			0
$805$	−1.43730	−	2.48948i	−0.0506583	−	0.0877428i
$806$		0			0
$807$	−5.52934	−	31.3584i	−0.194642	−	1.10387i
$808$		0			0
$809$	−7.26030	+	12.5752i	−0.255259	+	0.442121i	−0.964966	−	0.262376i	$-0.915494\pi$
$809$	−7.26030	+	12.5752i	−0.255259	+	0.442121i	0.709707	+	0.704497i	$0.248827\pi$
$810$		0			0
$811$	11.8678	−	9.95823i	0.416733	−	0.349681i	−0.410185	−	0.912002i	$-0.634536\pi$
$811$	11.8678	−	9.95823i	0.416733	−	0.349681i	0.826919	+	0.562321i	$0.190092\pi$
$812$		0			0
$813$	−21.4963	−	7.82400i	−0.753906	−	0.274400i
$814$		0			0
$815$	−1.32236	+	7.49949i	−0.0463203	+	0.262696i
$816$		0			0
$817$	1.64836	−	0.163005i	0.0576687	−	0.00570283i
$818$		0			0
$819$	2.01084	−	11.4040i	0.0702644	−	0.398489i
$820$		0			0
$821$	−14.6533	−	5.33335i	−0.511402	−	0.186135i	0.0734131	−	0.997302i	$-0.476611\pi$
$821$	−14.6533	−	5.33335i	−0.511402	−	0.186135i	−0.584815	+	0.811166i	$0.698833\pi$
$822$		0			0
$823$	0.785814	−	0.659376i	0.0273917	−	0.0229844i	−0.628989	−	0.777414i	$-0.716531\pi$
$823$	0.785814	−	0.659376i	0.0273917	−	0.0229844i	0.656381	+	0.754430i	$0.272087\pi$
$824$		0			0
$825$	−6.24591	+	10.8182i	−0.217455	+	0.376642i
$826$		0			0
$827$	4.26086	+	24.1645i	0.148165	+	0.840283i	0.964772	+	0.263089i	$0.0847412\pi$
$827$	4.26086	+	24.1645i	0.148165	+	0.840283i	−0.816607	+	0.577194i	$0.804148\pi$
$828$		0			0
$829$	−23.1927	−	40.1710i	−0.805517	−	1.39520i	−0.915942	−	0.401312i	$-0.868554\pi$
$829$	−23.1927	−	40.1710i	−0.805517	−	1.39520i	0.110425	−	0.993884i	$-0.464779\pi$
$830$		0			0
$831$	−5.84107	+	2.12598i	−0.202625	+	0.0737493i
$832$		0			0
$833$	−7.57921	−	6.35971i	−0.262604	−	0.220351i
$834$		0			0
$835$	4.79947			0.166092
$836$		0			0
$837$	−4.03604			−0.139506
$838$		0			0
$839$	−11.3664	−	9.53754i	−0.392412	−	0.329272i	0.425140	−	0.905127i	$-0.360225\pi$
$839$	−11.3664	−	9.53754i	−0.392412	−	0.329272i	−0.817552	+	0.575855i	$0.804669\pi$
$840$		0			0
$841$	25.3719	−	9.23462i	0.874894	−	0.318435i
$842$		0			0
$843$	−0.809423	−	1.40196i	−0.0278780	−	0.0482862i
$844$		0			0
$845$	−0.318558	−	1.80663i	−0.0109587	−	0.0621501i
$846$		0			0
$847$	−6.48316	+	11.2292i	−0.222764	+	0.385839i
$848$		0			0
$849$	19.8219	−	16.6325i	0.680285	−	0.570827i
$850$		0			0
$851$	−10.7585	−	3.91576i	−0.368795	−	0.134230i
$852$		0			0
$853$	−2.37858	+	13.4896i	−0.0814410	+	0.461875i	0.916627	+	0.399744i	$0.130901\pi$
$853$	−2.37858	+	13.4896i	−0.0814410	+	0.461875i	−0.998068	+	0.0621313i	$0.980210\pi$
$854$		0			0
$855$	−0.759607	−	2.71191i	−0.0259780	−	0.0927453i
$856$		0			0
$857$	−0.402983	+	2.28543i	−0.0137656	+	0.0780689i	−0.990917	−	0.134477i	$-0.957064\pi$
$857$	−0.402983	+	2.28543i	−0.0137656	+	0.0780689i	0.977151	+	0.212546i	$0.0681756\pi$
$858$		0			0
$859$	−0.724529	−	0.263707i	−0.0247206	−	0.00899757i	0.329630	−	0.944110i	$-0.393076\pi$
$859$	−0.724529	−	0.263707i	−0.0247206	−	0.00899757i	−0.354351	+	0.935113i	$0.615298\pi$
$860$		0			0
$861$	−0.755893	+	0.634270i	−0.0257608	+	0.0216159i
$862$		0			0
$863$	19.5325	−	33.8312i	0.664893	−	1.15163i	−0.314422	−	0.949283i	$-0.601811\pi$
$863$	19.5325	−	33.8312i	0.664893	−	1.15163i	0.979314	−	0.202344i	$-0.0648561\pi$
$864$		0			0
$865$	2.40153	+	13.6198i	0.0816545	+	0.463086i
$866$		0			0
$867$	7.22569	+	12.5153i	0.245397	+	0.425041i
$868$		0			0
$869$	4.50581	−	1.63998i	0.152849	−	0.0556326i
$870$		0			0
$871$	−18.8505	−	15.8174i	−0.638724	−	0.535953i
$872$		0			0
$873$	19.1073			0.646683
$874$		0			0
$875$	22.4920			0.760367
$876$		0			0
$877$	−44.3212	−	37.1899i	−1.49662	−	1.25581i	−0.885822	−	0.464025i	$-0.846405\pi$
$877$	−44.3212	−	37.1899i	−1.49662	−	1.25581i	−0.610797	−	0.791787i	$-0.709151\pi$
$878$		0			0
$879$	−21.8919	+	7.96800i	−0.738396	+	0.268754i
$880$		0			0
$881$	22.6602	+	39.2487i	0.763443	+	1.32232i	0.941066	+	0.338224i	$0.109826\pi$
$881$	22.6602	+	39.2487i	0.763443	+	1.32232i	−0.177623	+	0.984099i	$0.556841\pi$
$882$		0			0
$883$	9.09843	+	51.5998i	0.306187	+	1.73647i	0.617866	+	0.786283i	$0.287997\pi$
$883$	9.09843	+	51.5998i	0.306187	+	1.73647i	−0.311680	+	0.950187i	$0.600892\pi$
$884$		0			0
$885$	−4.41413	+	7.64550i	−0.148379	+	0.257001i
$886$		0			0
$887$	−39.3018	+	32.9781i	−1.31962	+	1.10730i	−0.333240	+	0.942842i	$0.608142\pi$
$887$	−39.3018	+	32.9781i	−1.31962	+	1.10730i	−0.986385	+	0.164454i	$0.947414\pi$
$888$		0			0
$889$	−37.3465	−	13.5930i	−1.25256	−	0.455896i
$890$		0			0
$891$	−0.473356	+	2.68454i	−0.0158580	+	0.0899353i
$892$		0			0
$893$	−2.81636	+	37.0037i	−0.0942460	+	1.23828i
$894$		0			0
$895$	−2.32783	+	13.2018i	−0.0778106	+	0.441286i
$896$		0			0
$897$	−3.66842	−	1.33520i	−0.122485	−	0.0445809i
$898$		0			0
$899$	4.37219	−	3.66870i	0.145821	−	0.122358i
$900$		0			0
$901$	−8.55778	+	14.8225i	−0.285101	+	0.493809i
$902$		0			0
$903$	0.239720	+	1.35952i	0.00797738	+	0.0452420i
$904$		0			0
$905$	4.76993	+	8.26177i	0.158558	+	0.274630i
$906$		0			0
$907$	−6.03774	+	2.19756i	−0.200480	+	0.0729687i	−0.440309	−	0.897846i	$-0.645131\pi$
$907$	−6.03774	+	2.19756i	−0.200480	+	0.0729687i	0.239829	+	0.970815i	$0.422909\pi$
$908$		0			0
$909$	2.18242	+	1.83127i	0.0723864	+	0.0607394i
$910$		0			0
$911$	19.1355			0.633989			0.316994	−	0.948427i	$-0.397326\pi$
$911$	19.1355			0.633989			0.316994	+	0.948427i	$0.397326\pi$
$912$		0			0
$913$	30.4079			1.00636
$914$		0			0
$915$	−3.14501	−	2.63898i	−0.103971	−	0.0872418i
$916$		0			0
$917$	61.2192	−	22.2820i	2.02163	−	0.735815i
$918$		0			0
$919$	−19.2633	−	33.3650i	−0.635437	−	1.10061i	−0.986422	−	0.164228i	$-0.947487\pi$
$919$	−19.2633	−	33.3650i	−0.635437	−	1.10061i	0.350985	−	0.936381i	$-0.385847\pi$
$920$		0			0
$921$	−0.387049	−	2.19506i	−0.0127537	−	0.0723298i
$922$		0			0
$923$	6.87184	−	11.9024i	0.226189	−	0.391771i
$924$		0			0
$925$	32.8166	−	27.5364i	1.07900	−	0.905390i
$926$		0			0
$927$	−6.90051	−	2.51158i	−0.226642	−	0.0824911i
$928$		0			0
$929$	8.20972	−	46.5596i	0.269352	−	1.52757i	−0.486997	−	0.873404i	$-0.661908\pi$
$929$	8.20972	−	46.5596i	0.269352	−	1.52757i	0.756349	−	0.654169i	$-0.226981\pi$
$930$		0			0
$931$	−18.8849	+	19.3167i	−0.618929	+	0.633080i
$932$		0			0
$933$	−2.64889	+	15.0226i	−0.0867206	+	0.491817i
$934$		0			0
$935$	−2.64214	−	0.961659i	−0.0864071	−	0.0314496i
$936$		0			0
$937$	31.4643	−	26.4017i	1.02790	−	0.862507i	0.0372964	−	0.999304i	$-0.488125\pi$
$937$	31.4643	−	26.4017i	1.02790	−	0.862507i	0.990599	+	0.136798i	$0.0436810\pi$
$938$		0			0
$939$	1.04259	−	1.80582i	0.0340237	−	0.0589308i
$940$		0			0
$941$	−0.561322	−	3.18342i	−0.0182986	−	0.103776i	0.974291	−	0.225295i	$-0.0723346\pi$
$941$	−0.561322	−	3.18342i	−0.0182986	−	0.103776i	−0.992589	+	0.121519i	$0.961224\pi$
$942$		0			0
$943$	0.166327	+	0.288087i	0.00541636	+	0.00938141i
$944$		0			0
$945$	2.20562	−	0.802782i	0.0717490	−	0.0261145i
$946$		0			0
$947$	−23.1761	−	19.4470i	−0.753121	−	0.631944i	0.183205	−	0.983075i	$-0.441353\pi$
$947$	−23.1761	−	19.4470i	−0.753121	−	0.631944i	−0.936326	+	0.351131i	$0.885797\pi$
$948$		0			0
$949$	25.4554			0.826318
$950$		0			0
$951$	28.3128			0.918106
$952$		0			0
$953$	3.72492	+	3.12558i	0.120662	+	0.101247i	0.701122	−	0.713041i	$-0.252683\pi$
$953$	3.72492	+	3.12558i	0.120662	+	0.101247i	−0.580460	+	0.814289i	$0.697127\pi$
$954$		0			0
$955$	−15.2558	+	5.55265i	−0.493666	+	0.179680i
$956$		0			0
$957$	−1.92743	−	3.33840i	−0.0623048	−	0.107915i
$958$		0			0
$959$	−1.90682	−	10.8141i	−0.0615745	−	0.349207i
$960$		0			0
$961$	7.35520	−	12.7396i	0.237264	−	0.410954i
$962$		0			0
$963$	9.59111	−	8.04790i	0.309069	−	0.259340i
$964$		0			0
$965$	−5.35268	−	1.94822i	−0.172309	−	0.0627153i
$966$		0			0
$967$	5.06427	−	28.7209i	0.162856	−	0.923603i	−0.788391	−	0.615174i	$-0.789086\pi$
$967$	5.06427	−	28.7209i	0.162856	−	0.923603i	0.951247	−	0.308429i	$-0.0998031\pi$
$968$		0			0
$969$	−6.27309	+	3.01197i	−0.201521	+	0.0967584i
$970$		0			0
$971$	5.59772	−	31.7463i	0.179640	−	1.01879i	−0.753012	−	0.658007i	$-0.771400\pi$
$971$	5.59772	−	31.7463i	0.179640	−	1.01879i	0.932651	−	0.360779i	$-0.117489\pi$
$972$		0			0
$973$	53.9705	+	19.6437i	1.73022	+	0.629747i
$974$		0			0
$975$	11.1898	−	9.38936i	0.358360	−	0.300700i
$976$		0			0
$977$	11.8554	−	20.5341i	0.379287	−	0.656944i	−0.611672	−	0.791111i	$-0.709503\pi$
$977$	11.8554	−	20.5341i	0.379287	−	0.656944i	0.990959	+	0.134168i	$0.0428361\pi$
$978$		0			0
$979$	−3.32267	−	18.8438i	−0.106193	−	0.602251i
$980$		0			0
$981$	2.44642	+	4.23733i	0.0781083	+	0.135288i
$982$		0			0
$983$	21.7664	−	7.92234i	0.694242	−	0.252683i	0.0292914	−	0.999571i	$-0.490675\pi$
$983$	21.7664	−	7.92234i	0.694242	−	0.252683i	0.664950	+	0.746888i	$0.268453\pi$
$984$		0			0
$985$	7.01153	+	5.88338i	0.223406	+	0.187460i
$986$		0			0
$987$	−30.9292			−0.984487
$988$		0			0
$989$	0.465394			0.0147987
$990$		0			0
$991$	−7.99619	−	6.70960i	−0.254007	−	0.213137i	0.506888	−	0.862012i	$-0.330796\pi$
$991$	−7.99619	−	6.70960i	−0.254007	−	0.213137i	−0.760896	+	0.648874i	$0.775240\pi$
$992$		0			0
$993$	−8.24105	+	2.99950i	−0.261522	+	0.0951861i
$994$		0			0
$995$	1.53275	+	2.65480i	0.0485913	+	0.0841627i
$996$		0			0
$997$	8.23731	+	46.7161i	0.260878	+	1.47951i	0.780520	+	0.625130i	$0.214954\pi$
$997$	8.23731	+	46.7161i	0.260878	+	1.47951i	−0.519642	+	0.854384i	$0.673935\pi$
$998$		0			0
$999$	4.67414	−	8.09584i	0.147883	−	0.256141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.k.625.2		18
4.3	odd	2		456.2.bg.c.169.2	✓	18
19.9	even	9	inner	912.2.bo.k.769.2		18
76.3	even	18		8664.2.a.bq.1.6		9
76.35	odd	18		8664.2.a.bo.1.6		9
76.47	odd	18		456.2.bg.c.313.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bg.c.169.2	✓	18	4.3	odd	2
456.2.bg.c.313.2	yes	18	76.47	odd	18
912.2.bo.k.625.2		18	1.1	even	1	trivial
912.2.bo.k.769.2		18	19.9	even	9	inner
8664.2.a.bo.1.6		9	76.35	odd	18
8664.2.a.bq.1.6		9	76.3	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{3} +(-0.607135 + 0.220979i) q^{5} +(1.81642 + 3.14613i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{3} +(-0.607135 + 0.220979i) q^{5} +(1.81642 + 3.14613i) q^{7} +(0.173648 + 0.984808i) q^{9} +(1.36297 - 2.36074i) q^{11} +(-2.44183 + 2.04894i) q^{13} +(-0.607135 - 0.220979i) q^{15} +(-0.277218 + 1.57218i) q^{17} +(4.22286 + 1.08051i) q^{19} +(-0.630836 + 3.57765i) q^{21} +(1.15085 + 0.418875i) q^{23} +(-3.51044 + 2.94561i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-0.245561 - 1.39265i) q^{29} +(2.01802 + 3.49531i) q^{31} +(2.56155 - 0.932330i) q^{33} +(-1.79804 - 1.50874i) q^{35} -9.34827 q^{37} -3.18758 q^{39} +(0.208072 + 0.174593i) q^{41} +(0.357087 - 0.129969i) q^{43} +(-0.323050 - 0.559539i) q^{45} +(1.47840 + 8.38443i) q^{47} +(-3.09876 + 5.36721i) q^{49} +(-1.22294 + 1.02617i) q^{51} +(10.0745 + 3.66683i) q^{53} +(-0.305835 + 1.73448i) q^{55} +(2.54036 + 3.54212i) q^{57} +(2.37272 - 13.4563i) q^{59} +(5.97110 + 2.17330i) q^{61} +(-2.78292 + 2.33514i) q^{63} +(1.02975 - 1.78357i) q^{65} +(1.34053 + 7.60255i) q^{67} +(0.612354 + 1.06063i) q^{69} +(-4.05161 + 1.47467i) q^{71} +(-6.11749 - 5.13319i) q^{73} -4.58256 q^{75} +9.90294 q^{77} +(1.34748 + 1.13067i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(5.57750 + 9.66051i) q^{83} +(-0.179111 - 1.01579i) q^{85} +(0.707066 - 1.22467i) q^{87} +(5.37716 - 4.51198i) q^{89} +(-10.8816 - 3.96058i) q^{91} +(-0.700851 + 3.97472i) q^{93} +(-2.80261 + 0.277149i) q^{95} +(3.31794 - 18.8170i) q^{97} +(2.56155 + 0.932330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{5}+O(q^{10}) \) 18 * q - 3 * q^5	\( 18 q - 3 q^{5} + 3 q^{11} + 18 q^{13} - 3 q^{15} - 3 q^{17} + 3 q^{19} - 3 q^{21} - 12 q^{23} - 3 q^{25} - 9 q^{27} + 3 q^{29} - 21 q^{31} + 6 q^{33} - 12 q^{35} - 30 q^{37} - 6 q^{39} + 33 q^{41} + 6 q^{43} - 3 q^{45} + 6 q^{47} - 21 q^{49} - 12 q^{51} + 30 q^{53} + 24 q^{55} - 21 q^{57} + 9 q^{59} + 48 q^{61} + 6 q^{63} - 9 q^{65} + 18 q^{67} - 6 q^{69} + 51 q^{71} + 12 q^{75} + 30 q^{77} + 39 q^{79} + 30 q^{83} - 87 q^{85} + 21 q^{87} + 45 q^{89} - 72 q^{91} - 27 q^{93} + 78 q^{95} + 39 q^{97} + 6 q^{99}+O(q^{100}) \) 18 * q - 3 * q^5 + 3 * q^11 + 18 * q^13 - 3 * q^15 - 3 * q^17 + 3 * q^19 - 3 * q^21 - 12 * q^23 - 3 * q^25 - 9 * q^27 + 3 * q^29 - 21 * q^31 + 6 * q^33 - 12 * q^35 - 30 * q^37 - 6 * q^39 + 33 * q^41 + 6 * q^43 - 3 * q^45 + 6 * q^47 - 21 * q^49 - 12 * q^51 + 30 * q^53 + 24 * q^55 - 21 * q^57 + 9 * q^59 + 48 * q^61 + 6 * q^63 - 9 * q^65 + 18 * q^67 - 6 * q^69 + 51 * q^71 + 12 * q^75 + 30 * q^77 + 39 * q^79 + 30 * q^83 - 87 * q^85 + 21 * q^87 + 45 * q^89 - 72 * q^91 - 27 * q^93 + 78 * q^95 + 39 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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