LMFDB - Embedded newform 1197.2.db.a.647.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (of order $6$, degree $2$, 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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.18
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.839260 + 0.484547i) q^{2} +(-0.530428 + 0.918729i) q^{4} +(-0.237468 - 0.411306i) q^{5} +(-1.39585 - 2.24758i) q^{7} -2.96626i q^{8} +O(q^{10})$	\(q+(-0.839260 + 0.484547i) q^{2} +(-0.530428 + 0.918729i) q^{4} +(-0.237468 - 0.411306i) q^{5} +(-1.39585 - 2.24758i) q^{7} -2.96626i q^{8} +(0.398594 + 0.230129i) q^{10} +(2.70307 + 1.56062i) q^{11} -2.99924i q^{13} +(2.26054 + 1.20995i) q^{14} +(0.376435 + 0.652005i) q^{16} +(-2.29394 + 3.97323i) q^{17} +(-0.866025 + 0.500000i) q^{19} +0.503838 q^{20} -3.02477 q^{22} +(-5.62124 + 3.24542i) q^{23} +(2.38722 - 4.13478i) q^{25} +(1.45327 + 2.51714i) q^{26} +(2.80531 - 0.0902250i) q^{28} +7.26181i q^{29} +(5.40972 + 3.12330i) q^{31} +(4.50586 + 2.60146i) q^{32} -4.44609i q^{34} +(-0.592975 + 1.10785i) q^{35} +(1.57649 + 2.73055i) q^{37} +(0.484547 - 0.839260i) q^{38} +(-1.22004 + 0.704391i) q^{40} -7.93559 q^{41} -11.9362 q^{43} +(-2.86757 + 1.65559i) q^{44} +(3.14512 - 5.44751i) q^{46} +(0.813009 + 1.40817i) q^{47} +(-3.10322 + 6.27455i) q^{49} +4.62688i q^{50} +(2.75548 + 1.59088i) q^{52} +(-6.17285 - 3.56389i) q^{53} -1.48239i q^{55} +(-6.66690 + 4.14044i) q^{56} +(-3.51869 - 6.09455i) q^{58} +(-0.996904 + 1.72669i) q^{59} +(-3.13512 + 1.81006i) q^{61} -6.05355 q^{62} -6.54785 q^{64} +(-1.23360 + 0.712222i) q^{65} +(2.41141 - 4.17668i) q^{67} +(-2.43354 - 4.21502i) q^{68} +(-0.0391445 - 1.21710i) q^{70} +6.38694i q^{71} +(-5.17020 - 2.98501i) q^{73} +(-2.64616 - 1.52776i) q^{74} -1.06086i q^{76} +(-0.265459 - 8.25375i) q^{77} +(-0.285324 - 0.494195i) q^{79} +(0.178782 - 0.309660i) q^{80} +(6.66002 - 3.84516i) q^{82} +10.8256 q^{83} +2.17895 q^{85} +(10.0175 - 5.78363i) q^{86} +(4.62920 - 8.01801i) q^{88} +(3.58664 + 6.21225i) q^{89} +(-6.74102 + 4.18647i) q^{91} -6.88586i q^{92} +(-1.36465 - 0.787883i) q^{94} +(0.411306 + 0.237468i) q^{95} -18.2203i q^{97} +(-0.435904 - 6.76964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−0.839260	+	0.484547i	−0.593447	+	0.342627i	−0.766459	−	0.642293i	$-0.777983\pi$
$2$	−0.839260	+	0.484547i	−0.593447	+	0.342627i	0.173013	+	0.984920i	$0.444650\pi$
$3$		0			0
$3$		0			0
$4$	−0.530428	+	0.918729i	−0.265214	+	0.459364i
$5$	−0.237468	−	0.411306i	−0.106199	−	0.183942i	0.808029	−	0.589143i	$-0.200535\pi$
$5$	−0.237468	−	0.411306i	−0.106199	−	0.183942i	−0.914227	+	0.405202i	$0.867201\pi$
$6$		0			0
$7$	−1.39585	−	2.24758i	−0.527580	−	0.849505i
$7$	−1.39585	−	2.24758i	−0.527580	−	0.849505i
$8$		−	2.96626i		−	1.04873i
$9$		0			0
$10$	0.398594	+	0.230129i	0.126047	+	0.0727731i
$11$	2.70307	+	1.56062i	0.815007	+	0.470544i	0.848692	−	0.528888i	$-0.177391\pi$
$11$	2.70307	+	1.56062i	0.815007	+	0.470544i	−0.0336848	+	0.999433i	$0.510724\pi$
$12$		0			0
$13$		−	2.99924i		−	0.831838i	−0.909402	−	0.415919i	$-0.863460\pi$
$13$		−	2.99924i		−	0.831838i	0.909402	−	0.415919i	$-0.136540\pi$
$14$	2.26054	+	1.20995i	0.604154	+	0.323373i
$15$		0			0
$16$	0.376435	+	0.652005i	0.0941088	+	0.163001i
$17$	−2.29394	+	3.97323i	−0.556363	+	0.963649i	0.441433	+	0.897294i	$0.354470\pi$
$17$	−2.29394	+	3.97323i	−0.556363	+	0.963649i	−0.997796	+	0.0663546i	$0.978863\pi$
$18$		0			0
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	0.503838			0.112662
$21$		0			0
$22$	−3.02477			−0.644884
$23$	−5.62124	+	3.24542i	−1.17211	+	0.676718i	−0.954176	−	0.299246i	$-0.903265\pi$
$23$	−5.62124	+	3.24542i	−1.17211	+	0.676718i	−0.217933	+	0.975964i	$0.569932\pi$
$24$		0			0
$25$	2.38722	−	4.13478i	0.477444	−	0.826957i
$26$	1.45327	+	2.51714i	0.285010	+	0.493652i
$27$		0			0
$28$	2.80531	−	0.0902250i	0.530154	−	0.0170509i
$29$			7.26181i			1.34849i	0.738510	+	0.674243i	$0.235530\pi$
$29$			7.26181i			1.34849i	−0.738510	+	0.674243i	$0.764470\pi$
$30$		0			0
$31$	5.40972	+	3.12330i	0.971615	+	0.560962i	0.899728	−	0.436451i	$-0.143765\pi$
$31$	5.40972	+	3.12330i	0.971615	+	0.560962i	0.0718866	+	0.997413i	$0.477098\pi$
$32$	4.50586	+	2.60146i	0.796530	+	0.459877i
$33$		0			0
$34$		−	4.44609i		−	0.762499i
$35$	−0.592975	+	1.10785i	−0.100231	+	0.187260i
$36$		0			0
$37$	1.57649	+	2.73055i	0.259173	+	0.448900i	0.966021	−	0.258465i	$-0.0832168\pi$
$37$	1.57649	+	2.73055i	0.259173	+	0.448900i	−0.706848	+	0.707366i	$0.749883\pi$
$38$	0.484547	−	0.839260i	0.0786039	−	0.136146i
$39$		0			0
$40$	−1.22004	+	0.704391i	−0.192905	+	0.111374i
$41$	−7.93559			−1.23933			−0.619665	−	0.784866i	$-0.712732\pi$
$41$	−7.93559			−1.23933			−0.619665	+	0.784866i	$0.712732\pi$
$42$		0			0
$43$	−11.9362			−1.82025			−0.910123	−	0.414338i	$-0.864013\pi$
$43$	−11.9362			−1.82025			−0.910123	+	0.414338i	$0.864013\pi$
$44$	−2.86757	+	1.65559i	−0.432303	+	0.249590i
$45$		0			0
$46$	3.14512	−	5.44751i	0.463723	−	0.803191i
$47$	0.813009	+	1.40817i	0.118590	+	0.205403i	0.919209	−	0.393770i	$-0.128829\pi$
$47$	0.813009	+	1.40817i	0.118590	+	0.205403i	−0.800619	+	0.599173i	$0.795496\pi$
$48$		0			0
$49$	−3.10322	+	6.27455i	−0.443318	+	0.896365i
$50$			4.62688i			0.654339i
$51$		0			0
$52$	2.75548	+	1.59088i	0.382117	+	0.220615i
$53$	−6.17285	−	3.56389i	−0.847906	−	0.489539i	0.0120381	−	0.999928i	$-0.496168\pi$
$53$	−6.17285	−	3.56389i	−0.847906	−	0.489539i	−0.859944	+	0.510389i	$0.829501\pi$
$54$		0			0
$55$		−	1.48239i		−	0.199885i
$56$	−6.66690	+	4.14044i	−0.890902	+	0.553290i
$57$		0			0
$58$	−3.51869	−	6.09455i	−0.462027	−	0.800254i
$59$	−0.996904	+	1.72669i	−0.129786	+	0.224796i	−0.923594	−	0.383373i	$-0.874762\pi$
$59$	−0.996904	+	1.72669i	−0.129786	+	0.224796i	0.793808	+	0.608169i	$0.208096\pi$
$60$		0			0
$61$	−3.13512	+	1.81006i	−0.401411	+	0.231755i	−0.687093	−	0.726570i	$-0.741113\pi$
$61$	−3.13512	+	1.81006i	−0.401411	+	0.231755i	0.285682	+	0.958325i	$0.407780\pi$
$62$	−6.05355			−0.768802
$63$		0			0
$64$	−6.54785			−0.818482
$65$	−1.23360	+	0.712222i	−0.153010	+	0.0883402i
$66$		0			0
$67$	2.41141	−	4.17668i	0.294601	−	0.510263i	−0.680291	−	0.732942i	$-0.738147\pi$
$67$	2.41141	−	4.17668i	0.294601	−	0.510263i	0.974892	+	0.222679i	$0.0714800\pi$
$68$	−2.43354	−	4.21502i	−0.295111	−	0.511147i
$69$		0			0
$70$	−0.0391445	−	1.21710i	−0.00467866	−	0.145471i
$71$			6.38694i			0.757991i	0.925399	+	0.378995i	$0.123730\pi$
$71$			6.38694i			0.757991i	−0.925399	+	0.378995i	$0.876270\pi$
$72$		0			0
$73$	−5.17020	−	2.98501i	−0.605126	−	0.349369i	0.165930	−	0.986138i	$-0.446938\pi$
$73$	−5.17020	−	2.98501i	−0.605126	−	0.349369i	−0.771055	+	0.636768i	$0.780271\pi$
$74$	−2.64616	−	1.52776i	−0.307610	−	0.177599i
$75$		0			0
$76$		−	1.06086i		−	0.121689i
$77$	−0.265459	−	8.25375i	−0.0302518	−	0.940602i
$78$		0			0
$79$	−0.285324	−	0.494195i	−0.0321014	−	0.0556013i	0.849528	−	0.527543i	$-0.176887\pi$
$79$	−0.285324	−	0.494195i	−0.0321014	−	0.0556013i	−0.881630	+	0.471942i	$0.843553\pi$
$80$	0.178782	−	0.309660i	0.0199885	−	0.0346211i
$81$		0			0
$82$	6.66002	−	3.84516i	0.735476	−	0.424627i
$83$	10.8256			1.18826			0.594132	−	0.804368i	$-0.297496\pi$
$83$	10.8256			1.18826			0.594132	+	0.804368i	$0.297496\pi$
$84$		0			0
$85$	2.17895			0.236340
$86$	10.0175	−	5.78363i	1.08022	−	0.623665i
$87$		0			0
$88$	4.62920	−	8.01801i	0.493474	−	0.854723i
$89$	3.58664	+	6.21225i	0.380183	+	0.658497i	0.991088	−	0.133207i	$-0.0425276\pi$
$89$	3.58664	+	6.21225i	0.380183	+	0.658497i	−0.610905	+	0.791704i	$0.709194\pi$
$90$		0			0
$91$	−6.74102	+	4.18647i	−0.706651	+	0.438862i
$92$		−	6.88586i		−	0.717900i
$93$		0			0
$94$	−1.36465	−	0.787883i	−0.140753	−	0.0812639i
$95$	0.411306	+	0.237468i	0.0421991	+	0.0243637i
$96$		0			0
$97$		−	18.2203i		−	1.85000i	−0.379972	−	0.924998i	$-0.624066\pi$
$97$		−	18.2203i		−	1.85000i	0.379972	−	0.924998i	$-0.375934\pi$
$98$	−0.435904	−	6.76964i	−0.0440329	−	0.683837i
$99$		0			0
$100$	2.53250	+	4.38641i	0.253250	+	0.438641i
$101$	2.28510	−	3.95792i	0.227376	−	0.393828i	−0.729653	−	0.683817i	$-0.760319\pi$
$101$	2.28510	−	3.95792i	0.227376	−	0.393828i	0.957030	+	0.289990i	$0.0936519\pi$
$102$		0			0
$103$	−16.7493	+	9.67023i	−1.65036	+	0.952836i	−0.673438	+	0.739243i	$0.735183\pi$
$103$	−16.7493	+	9.67023i	−1.65036	+	0.952836i	−0.976923	+	0.213593i	$0.931483\pi$
$104$	−8.89651			−0.872374
$105$		0			0
$106$	6.90750			0.670915
$107$	−11.2964	+	6.52198i	−1.09206	+	0.630504i	−0.934125	−	0.356945i	$-0.883818\pi$
$107$	−11.2964	+	6.52198i	−1.09206	+	0.630504i	−0.157939	+	0.987449i	$0.550485\pi$
$108$		0			0
$109$	−8.07613	+	13.9883i	−0.773553	+	1.33983i	0.162051	+	0.986782i	$0.448189\pi$
$109$	−8.07613	+	13.9883i	−0.773553	+	1.33983i	−0.935604	+	0.353051i	$0.885144\pi$
$110$	0.718286	+	1.24411i	0.0684859	+	0.118621i
$111$		0			0
$112$	0.939986	−	1.75617i	0.0888204	−	0.165942i
$113$			18.9457i			1.78226i	0.453748	+	0.891130i	$0.350087\pi$
$113$			18.9457i			1.78226i	−0.453748	+	0.891130i	$0.649913\pi$
$114$		0			0
$115$	2.66973	+	1.54137i	0.248953	+	0.143733i
$116$	−6.67164	−	3.85187i	−0.619446	−	0.357637i
$117$		0			0
$118$		−	1.93219i		−	0.177872i
$119$	12.1321	−	0.390196i	1.11215	−	0.0357692i
$120$		0			0
$121$	−0.628935	−	1.08935i	−0.0571759	−	0.0990316i
$122$	1.75412	−	3.03823i	0.158811	−	0.275068i
$123$		0			0
$124$	−5.73894	+	3.31338i	−0.515372	+	0.297550i
$125$	−4.64223			−0.415213
$126$		0			0
$127$	−1.77448			−0.157460			−0.0787300	−	0.996896i	$-0.525087\pi$
$127$	−1.77448			−0.157460			−0.0787300	+	0.996896i	$0.525087\pi$
$128$	−3.51636	+	2.03017i	−0.310805	+	0.179443i
$129$		0			0
$130$	0.690210	−	1.19548i	0.0605354	−	0.104850i
$131$	−8.25855	−	14.3042i	−0.721553	−	1.24977i	−0.960377	−	0.278703i	$-0.910095\pi$
$131$	−8.25855	−	14.3042i	−0.721553	−	1.24977i	0.238824	−	0.971063i	$-0.423238\pi$
$132$		0			0
$133$	2.33263	+	1.24854i	0.202265	+	0.108262i
$134$			4.67377i			0.403752i
$135$		0			0
$136$	11.7856	+	6.80443i	1.01061	+	0.583475i
$137$	−1.71987	−	0.992967i	−0.146938	−	0.0848349i	0.424728	−	0.905321i	$-0.360370\pi$
$137$	−1.71987	−	0.992967i	−0.146938	−	0.0848349i	−0.571667	+	0.820486i	$0.693703\pi$
$138$		0			0
$139$			17.1295i			1.45290i	0.687217	+	0.726452i	$0.258832\pi$
$139$			17.1295i			1.45290i	−0.687217	+	0.726452i	$0.741168\pi$
$140$	−0.703281	−	1.13242i	−0.0594381	−	0.0957067i
$141$		0			0
$142$	−3.09477	−	5.36031i	−0.259708	−	0.449827i
$143$	4.68066	−	8.10715i	0.391417	−	0.677954i
$144$		0			0
$145$	2.98683	−	1.72445i	0.248043	−	0.143207i
$146$	5.78552			0.478813
$147$		0			0
$148$	−3.34485			−0.274945
$149$	−0.586267	+	0.338482i	−0.0480289	+	0.0277295i	−0.523822	−	0.851828i	$-0.675494\pi$
$149$	−0.586267	+	0.338482i	−0.0480289	+	0.0277295i	0.475793	+	0.879557i	$0.342161\pi$
$150$		0			0
$151$	2.62987	−	4.55507i	0.214016	−	0.370687i	−0.738952	−	0.673758i	$-0.764679\pi$
$151$	2.62987	−	4.55507i	0.214016	−	0.370687i	0.952968	+	0.303072i	$0.0980122\pi$
$152$	1.48313	+	2.56885i	0.120298	+	0.208362i
$153$		0			0
$154$	4.22212	+	6.79842i	0.340228	+	0.547832i
$155$		−	2.96674i		−	0.238294i
$156$		0			0
$157$	−15.2747	−	8.81887i	−1.21906	−	0.703822i	−0.254340	−	0.967115i	$-0.581858\pi$
$157$	−15.2747	−	8.81887i	−1.21906	−	0.703822i	−0.964716	+	0.263292i	$0.915192\pi$
$158$	0.478922	+	0.276506i	0.0381010	+	0.0219976i
$159$		0			0
$160$		−	2.47105i		−	0.195354i
$161$	15.1407	+	8.10406i	1.19326	+	0.638690i
$162$		0			0
$163$	8.61580	+	14.9230i	0.674842	+	1.16886i	0.976515	+	0.215449i	$0.0691215\pi$
$163$	8.61580	+	14.9230i	0.674842	+	1.16886i	−0.301673	+	0.953411i	$0.597545\pi$
$164$	4.20926	−	7.29065i	0.328688	−	0.569304i
$165$		0			0
$166$	−9.08550	+	5.24551i	−0.705171	+	0.407131i
$167$	8.26263			0.639382			0.319691	−	0.947522i	$-0.396421\pi$
$167$	8.26263			0.639382			0.319691	+	0.947522i	$0.396421\pi$
$168$		0			0
$169$	4.00459			0.308045
$170$	−1.82871	+	1.05580i	−0.140255	+	0.0809764i
$171$		0			0
$172$	6.33127	−	10.9661i	0.482755	−	0.836156i
$173$	−2.81467	−	4.87515i	−0.213995	−	0.370651i	0.738966	−	0.673743i	$-0.235314\pi$
$173$	−2.81467	−	4.87515i	−0.213995	−	0.370651i	−0.952961	+	0.303092i	$0.901981\pi$
$174$		0			0
$175$	−12.6254	+	0.406062i	−0.954394	+	0.0306954i
$176$			2.34989i			0.177129i
$177$		0			0
$178$	−6.02025	−	3.47579i	−0.451237	−	0.260522i
$179$	−7.90290	−	4.56274i	−0.590691	−	0.341035i	0.174680	−	0.984625i	$-0.444111\pi$
$179$	−7.90290	−	4.56274i	−0.590691	−	0.341035i	−0.765371	+	0.643590i	$0.777444\pi$
$180$		0			0
$181$			13.8677i			1.03078i	0.856957	+	0.515388i	$0.172352\pi$
$181$			13.8677i			1.03078i	−0.856957	+	0.515388i	$0.827648\pi$
$182$	3.62893	−	6.77988i	0.268994	−	0.502558i
$183$		0			0
$184$	9.62676	+	16.6740i	0.709694	+	1.22923i
$185$	0.748729	−	1.29684i	0.0550477	−	0.0953454i
$186$		0			0
$187$	−12.4014	+	7.15994i	−0.906879	+	0.523587i
$188$	−1.72497			−0.125807
$189$		0			0
$190$	−0.460257			−0.0333906
$191$	5.64471	−	3.25897i	0.408437	−	0.235811i	−0.281681	−	0.959508i	$-0.590892\pi$
$191$	5.64471	−	3.25897i	0.408437	−	0.235811i	0.690118	+	0.723697i	$0.257559\pi$
$192$		0			0
$193$	−0.640301	+	1.10903i	−0.0460899	+	0.0798300i	−0.888150	−	0.459554i	$-0.848009\pi$
$193$	−0.640301	+	1.10903i	−0.0460899	+	0.0798300i	0.842060	+	0.539384i	$0.181343\pi$
$194$	8.82861	+	15.2916i	0.633858	+	1.09787i
$195$		0			0
$196$	−4.11857	−	6.17922i	−0.294184	−	0.441373i
$197$			26.0496i			1.85596i	0.372635	+	0.927978i	$0.378454\pi$
$197$			26.0496i			1.85596i	−0.372635	+	0.927978i	$0.621546\pi$
$198$		0			0
$199$	11.8911	+	6.86534i	0.842939	+	0.486671i	0.858262	−	0.513212i	$-0.171544\pi$
$199$	11.8911	+	6.86534i	0.842939	+	0.486671i	−0.0153231	+	0.999883i	$0.504878\pi$
$200$	−12.2648	−	7.08111i	−0.867255	−	0.500710i
$201$		0			0
$202$			4.42896i			0.311621i
$203$	16.3215	−	10.1364i	1.14554	−	0.711434i
$204$		0			0
$205$	1.88445	+	3.26396i	0.131615	+	0.227965i
$206$	9.37137	−	16.2317i	0.652934	−	1.13091i
$207$		0			0
$208$	1.95552	−	1.12902i	0.135591	−	0.0782833i
$209$	−3.12124			−0.215901
$210$		0			0
$211$	12.8150			0.882223			0.441112	−	0.897452i	$-0.354584\pi$
$211$	12.8150			0.882223			0.441112	+	0.897452i	$0.354584\pi$
$212$	6.54850	−	3.78078i	0.449753	−	0.259665i
$213$		0			0
$214$	6.32041	−	10.9473i	0.432055	−	0.748341i
$215$	2.83445	+	4.90941i	0.193308	+	0.334819i
$216$		0			0
$217$	−0.531269	−	16.5184i	−0.0360649	−	1.12134i
$218$		−	15.6531i		−	1.06016i
$219$		0			0
$220$	1.36191	+	0.786300i	0.0918201	+	0.0530123i
$221$	11.9166	+	6.88007i	0.801600	+	0.462804i
$222$		0			0
$223$			4.99480i			0.334476i	0.985917	+	0.167238i	$0.0534849\pi$
$223$			4.99480i			0.334476i	−0.985917	+	0.167238i	$0.946515\pi$
$224$	−0.442504	−	13.7585i	−0.0295660	−	0.919279i
$225$		0			0
$226$	−9.18008	−	15.9004i	−0.610650	−	1.05768i
$227$	5.15350	−	8.92613i	0.342050	−	0.592448i	−0.642763	−	0.766065i	$-0.722212\pi$
$227$	5.15350	−	8.92613i	0.342050	−	0.592448i	0.984813	+	0.173617i	$0.0555454\pi$
$228$		0			0
$229$	7.45988	−	4.30696i	0.492963	−	0.284612i	−0.232840	−	0.972515i	$-0.574802\pi$
$229$	7.45988	−	4.30696i	0.492963	−	0.284612i	0.725803	+	0.687903i	$0.241469\pi$
$230$	−2.98746			−0.196987
$231$		0			0
$232$	21.5404			1.41420
$233$	−19.9743	+	11.5322i	−1.30856	+	0.755497i	−0.981856	−	0.189630i	$-0.939271\pi$
$233$	−19.9743	+	11.5322i	−1.30856	+	0.755497i	−0.326704	+	0.945127i	$0.605938\pi$
$234$		0			0
$235$	0.386127	−	0.668792i	0.0251882	−	0.0436272i
$236$	−1.05757	−	1.83177i	−0.0688421	−	0.119238i
$237$		0			0
$238$	−9.99294	+	6.20606i	−0.647746	+	0.402279i
$239$			8.37180i			0.541527i	0.962646	+	0.270763i	$0.0872761\pi$
$239$			8.37180i			0.541527i	−0.962646	+	0.270763i	$0.912724\pi$
$240$		0			0
$241$	12.9585	+	7.48159i	0.834730	+	0.481932i	0.855469	−	0.517853i	$-0.173269\pi$
$241$	12.9585	+	7.48159i	0.834730	+	0.481932i	−0.0207395	+	0.999785i	$0.506602\pi$
$242$	1.05568	+	0.609497i	0.0678617	+	0.0391800i
$243$		0			0
$244$		−	3.84044i		−	0.245859i
$245$	3.31768	−	0.213629i	0.211959	−	0.0136482i
$246$		0			0
$247$	1.49962	+	2.59741i	0.0954184	+	0.165270i
$248$	9.26453	−	16.0466i	0.588298	−	1.01896i
$249$		0			0
$250$	3.89604	−	2.24938i	0.246407	−	0.142263i
$251$	10.7295			0.677240			0.338620	−	0.940923i	$-0.390040\pi$
$251$	10.7295			0.677240			0.338620	+	0.940923i	$0.390040\pi$
$252$		0			0
$253$	−20.2595			−1.27370
$254$	1.48925	−	0.859821i	0.0934441	−	0.0539500i
$255$		0			0
$256$	8.51528	−	14.7489i	0.532205	−	0.921806i
$257$	−14.0130	−	24.2713i	−0.874108	−	1.51400i	−0.857710	−	0.514134i	$-0.828113\pi$
$257$	−14.0130	−	24.2713i	−0.874108	−	1.51400i	−0.0163986	−	0.999866i	$-0.505220\pi$
$258$		0			0
$259$	3.93660	−	7.35471i	0.244609	−	0.457000i
$260$		−	1.51113i		−	0.0937163i
$261$		0			0
$262$	13.8621	+	8.00331i	0.856406	+	0.494446i
$263$	−8.00391	−	4.62106i	−0.493542	−	0.284947i	0.232500	−	0.972596i	$-0.425309\pi$
$263$	−8.00391	−	4.62106i	−0.493542	−	0.284947i	−0.726043	+	0.687649i	$0.758643\pi$
$264$		0			0
$265$			3.38524i			0.207954i
$266$	−2.56266	+	0.0824207i	−0.157127	+	0.00505354i
$267$		0			0
$268$	2.55816	+	4.43086i	0.156265	+	0.270658i
$269$	3.22209	−	5.58082i	0.196454	−	0.340268i	−0.750922	−	0.660391i	$-0.770391\pi$
$269$	3.22209	−	5.58082i	0.196454	−	0.340268i	0.947376	+	0.320122i	$0.103724\pi$
$270$		0			0
$271$	1.33947	−	0.773345i	0.0813672	−	0.0469774i	−0.458764	−	0.888558i	$-0.651708\pi$
$271$	1.33947	−	0.773345i	0.0813672	−	0.0469774i	0.540132	+	0.841581i	$0.318374\pi$
$272$	−3.45408			−0.209434
$273$		0			0
$274$	1.92456			0.116267
$275$	12.9056	−	7.45108i	0.778240	−	0.449317i
$276$		0			0
$277$	6.96174	−	12.0581i	0.418291	−	0.724501i	−0.577477	−	0.816407i	$-0.695963\pi$
$277$	6.96174	−	12.0581i	0.418291	−	0.724501i	0.995768	+	0.0919063i	$0.0292960\pi$
$278$	−8.30005	−	14.3761i	−0.497804	−	0.862221i
$279$		0			0
$280$	3.28616	+	1.75892i	0.196386	+	0.105115i
$281$		−	19.4308i		−	1.15915i	−0.814920	−	0.579573i	$-0.803219\pi$
$281$		−	19.4308i		−	1.15915i	0.814920	−	0.579573i	$-0.196781\pi$
$282$		0			0
$283$	22.1807	+	12.8060i	1.31850	+	0.761238i	0.983488	−	0.180974i	$-0.0579250\pi$
$283$	22.1807	+	12.8060i	1.31850	+	0.761238i	0.335016	+	0.942212i	$0.391258\pi$
$284$	−5.86787	−	3.38782i	−0.348194	−	0.201030i
$285$		0			0
$286$			9.07201i			0.536439i
$287$	11.0769	+	17.8359i	0.653846	+	1.05282i
$288$		0			0
$289$	−2.02435	−	3.50627i	−0.119079	−	0.206251i
$290$	−1.67115	+	2.89452i	−0.0981334	+	0.169972i
$291$		0			0
$292$	5.48484	−	3.16667i	0.320976	−	0.185315i
$293$	−13.4221			−0.784128			−0.392064	−	0.919938i	$-0.628239\pi$
$293$	−13.4221			−0.784128			−0.392064	+	0.919938i	$0.628239\pi$
$294$		0			0
$295$	0.946930			0.0551324
$296$	8.09953	−	4.67627i	0.470776	−	0.271802i
$297$		0			0
$298$	0.328020	−	0.568148i	0.0190017	−	0.0329119i
$299$	9.73379	+	16.8594i	0.562920	+	0.975005i
$300$		0			0
$301$	16.6610	+	26.8274i	0.960326	+	1.54631i
$302$			5.09719i			0.293310i
$303$		0			0
$304$	−0.652005	−	0.376435i	−0.0373950	−	0.0215900i
$305$	1.48898	+	0.859663i	0.0852588	+	0.0492242i
$306$		0			0
$307$		−	18.5075i		−	1.05628i	−0.849158	−	0.528139i	$-0.822890\pi$
$307$		−	18.5075i		−	1.05628i	0.849158	−	0.528139i	$-0.177110\pi$
$308$	7.72377	+	4.13414i	0.440102	+	0.235564i
$309$		0			0
$310$	1.43752	+	2.48986i	0.0816458	+	0.141415i
$311$	−1.18039	+	2.04449i	−0.0669335	+	0.115932i	−0.897550	−	0.440913i	$-0.854655\pi$
$311$	−1.18039	+	2.04449i	−0.0669335	+	0.115932i	0.830617	+	0.556845i	$0.187988\pi$
$312$		0			0
$313$	23.2377	−	13.4163i	1.31347	−	0.758334i	0.330803	−	0.943700i	$-0.392680\pi$
$313$	23.2377	−	13.4163i	1.31347	−	0.758334i	0.982670	+	0.185366i	$0.0593470\pi$
$314$	17.0926			0.964593
$315$		0			0
$316$	0.605375			0.0340550
$317$	−18.7903	+	10.8486i	−1.05537	+	0.609316i	−0.924147	−	0.382037i	$-0.875223\pi$
$317$	−18.7903	+	10.8486i	−1.05537	+	0.609316i	−0.131220	+	0.991353i	$0.541889\pi$
$318$		0			0
$319$	−11.3329	+	19.6292i	−0.634522	+	1.09902i
$320$	1.55490	+	2.69317i	0.0869218	+	0.150553i
$321$		0			0
$322$	−16.6338	+	0.534980i	−0.926966	+	0.0298133i
$323$		−	4.58789i		−	0.255277i
$324$		0			0
$325$	−12.4012	−	7.15983i	−0.687894	−	0.397156i
$326$	−14.4618	−	8.34953i	−0.800965	−	0.462437i
$327$		0			0
$328$			23.5390i			1.29972i
$329$	2.03015	−	3.79290i	0.111926	−	0.209109i
$330$		0			0
$331$	0.967842	+	1.67635i	0.0531974	+	0.0921406i	0.891398	−	0.453222i	$-0.149725\pi$
$331$	0.967842	+	1.67635i	0.0531974	+	0.0921406i	−0.838200	+	0.545362i	$0.816392\pi$
$332$	−5.74221	+	9.94579i	−0.315144	+	0.545846i
$333$		0			0
$334$	−6.93450	+	4.00364i	−0.379439	+	0.219069i
$335$	−2.29053			−0.125145
$336$		0			0
$337$	−10.3403			−0.563274			−0.281637	−	0.959521i	$-0.590877\pi$
$337$	−10.3403			−0.563274			−0.281637	+	0.959521i	$0.590877\pi$
$338$	−3.36089	+	1.94041i	−0.182808	+	0.105544i
$339$		0			0
$340$	−1.15578	+	2.00186i	−0.0626808	+	0.108566i
$341$	9.74858	+	16.8850i	0.527915	+	0.914376i
$342$		0			0
$343$	18.4342	−	1.78357i	0.995352	−	0.0963039i
$344$			35.4057i			1.90895i
$345$		0			0
$346$	4.72448	+	2.72768i	0.253989	+	0.146641i
$347$	13.7656	+	7.94754i	0.738973	+	0.426647i	0.821696	−	0.569926i	$-0.193028\pi$
$347$	13.7656	+	7.94754i	0.738973	+	0.426647i	−0.0827225	+	0.996573i	$0.526362\pi$
$348$		0			0
$349$		−	32.7105i		−	1.75096i	−0.483259	−	0.875478i	$-0.660547\pi$
$349$		−	32.7105i		−	1.75096i	0.483259	−	0.875478i	$-0.339453\pi$
$350$	10.3993	−	6.45841i	0.555865	−	0.345217i
$351$		0			0
$352$	8.11977	+	14.0639i	0.432785	+	0.749606i
$353$	17.5165	−	30.3394i	0.932308	−	1.61480i	0.152943	−	0.988235i	$-0.451125\pi$
$353$	17.5165	−	30.3394i	0.932308	−	1.61480i	0.779365	−	0.626570i	$-0.215542\pi$
$354$		0			0
$355$	2.62699	−	1.51669i	0.139426	−	0.0804977i
$356$	−7.60983			−0.403320
$357$		0			0
$358$	8.84345			0.467391
$359$	−22.8400	+	13.1867i	−1.20545	+	0.695967i	−0.961762	−	0.273886i	$-0.911691\pi$
$359$	−22.8400	+	13.1867i	−1.20545	+	0.695967i	−0.243689	+	0.969854i	$0.578357\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	−6.71954	−	11.6386i	−0.353171	−	0.611711i
$363$		0			0
$364$	−0.270606	−	8.41379i	−0.0141836	−	0.441003i
$365$			2.83538i			0.148410i
$366$		0			0
$367$	26.5251	+	15.3143i	1.38460	+	0.799400i	0.992700	−	0.120608i	$-0.0384843\pi$
$367$	26.5251	+	15.3143i	1.38460	+	0.799400i	0.391901	+	0.920007i	$0.371818\pi$
$368$	−4.23206	−	2.44338i	−0.220611	−	0.127370i
$369$		0			0
$370$			1.45118i			0.0754432i
$371$	0.606213	+	18.8486i	0.0314730	+	0.978571i
$372$		0			0
$373$	3.32695	+	5.76245i	0.172263	+	0.298368i	0.939211	−	0.343341i	$-0.111559\pi$
$373$	3.32695	+	5.76245i	0.172263	+	0.298368i	−0.766948	+	0.641710i	$0.778225\pi$
$374$	6.93866	−	12.0181i	0.358789	−	0.621442i
$375$		0			0
$376$	4.17701	−	2.41160i	0.215413	−	0.124369i
$377$	21.7799			1.12172
$378$		0			0
$379$	−29.7537			−1.52835			−0.764173	−	0.645011i	$-0.776853\pi$
$379$	−29.7537			−1.52835			−0.764173	+	0.645011i	$0.776853\pi$
$380$	−0.436337	+	0.251919i	−0.0223836	+	0.0129232i
$381$		0			0
$382$	−3.15825	+	5.47025i	−0.161590	+	0.279882i
$383$	6.36551	+	11.0254i	0.325262	+	0.563371i	0.981565	−	0.191126i	$-0.0612140\pi$
$383$	6.36551	+	11.0254i	0.325262	+	0.563371i	−0.656303	+	0.754497i	$0.727881\pi$
$384$		0			0
$385$	−3.33178	+	2.06919i	−0.169803	+	0.105455i
$386$		−	1.24102i		−	0.0631665i
$387$		0			0
$388$	16.7396	+	9.66459i	0.849822	+	0.490645i
$389$	−8.00248	−	4.62023i	−0.405742	−	0.234255i	0.283217	−	0.959056i	$-0.408598\pi$
$389$	−8.00248	−	4.62023i	−0.405742	−	0.234255i	−0.688958	+	0.724801i	$0.741932\pi$
$390$		0			0
$391$		−	29.7793i		−	1.50600i
$392$	18.6119	+	9.20496i	0.940045	+	0.464921i
$393$		0			0
$394$	−12.6223	−	21.8624i	−0.635900	−	1.10141i
$395$	−0.135510	+	0.234711i	−0.00681827	+	0.0118096i
$396$		0			0
$397$	−29.2916	+	16.9115i	−1.47010	+	0.848765i	−0.999437	−	0.0335452i	$-0.989320\pi$
$397$	−29.2916	+	16.9115i	−1.47010	+	0.848765i	−0.470668	+	0.882311i	$0.655987\pi$
$398$	−13.3063			−0.666986
$399$		0			0
$400$	3.59453			0.179727
$401$	10.8067	−	6.23925i	0.539661	−	0.311573i	−0.205281	−	0.978703i	$-0.565811\pi$
$401$	10.8067	−	6.23925i	0.539661	−	0.311573i	0.744942	+	0.667130i	$0.232477\pi$
$402$		0			0
$403$	9.36753	−	16.2250i	0.466630	−	0.808226i
$404$	2.42417	+	4.19878i	0.120607	+	0.208897i
$405$		0			0
$406$	−8.78643	+	16.4156i	−0.436063	+	0.814692i
$407$			9.84118i			0.487809i
$408$		0			0
$409$	5.26053	+	3.03717i	0.260117	+	0.150178i	0.624388	−	0.781115i	$-0.285349\pi$
$409$	5.26053	+	3.03717i	0.260117	+	0.150178i	−0.364271	+	0.931293i	$0.618682\pi$
$410$	−3.16308	−	1.82621i	−0.156213	−	0.0901898i
$411$		0			0
$412$		−	20.5175i		−	1.01082i
$413$	5.27240	−	0.169572i	0.259438	−	0.00834409i
$414$		0			0
$415$	−2.57073	−	4.45264i	−0.126192	−	0.218571i
$416$	7.80238	−	13.5141i	0.382543	−	0.662584i
$417$		0			0
$418$	2.61953	−	1.51239i	0.128125	−	0.0739733i
$419$	23.9592			1.17048			0.585241	−	0.810860i	$-0.301000\pi$
$419$	23.9592			1.17048			0.585241	+	0.810860i	$0.301000\pi$
$420$		0			0
$421$	−0.948624			−0.0462331			−0.0231166	−	0.999733i	$-0.507359\pi$
$421$	−0.948624			−0.0462331			−0.0231166	+	0.999733i	$0.507359\pi$
$422$	−10.7551	+	6.20949i	−0.523552	+	0.302273i
$423$		0			0
$424$	−10.5714	+	18.3103i	−0.513394	+	0.889225i
$425$	10.9523	+	18.9699i	0.531264	+	0.920176i
$426$		0			0
$427$	8.44441	+	4.51986i	0.408654	+	0.218731i
$428$		−	13.8378i		−	0.668874i
$429$		0			0
$430$	−4.75768	−	2.74685i	−0.229436	−	0.132465i
$431$	2.07327	+	1.19700i	0.0998657	+	0.0576575i	0.549101	−	0.835756i	$-0.314970\pi$
$431$	2.07327	+	1.19700i	0.0998657	+	0.0576575i	−0.449235	+	0.893413i	$0.648304\pi$
$432$		0			0
$433$			8.54785i			0.410783i	0.978680	+	0.205392i	$0.0658468\pi$
$433$			8.54785i			0.410783i	−0.978680	+	0.205392i	$0.934153\pi$
$434$	8.44983	+	13.6058i	0.405605	+	0.653101i
$435$		0			0
$436$	−8.56762	−	14.8395i	−0.410314	−	0.710685i
$437$	3.24542	−	5.62124i	0.155250	−	0.268900i
$438$		0			0
$439$	−31.0277	+	17.9139i	−1.48087	+	0.854982i	−0.999765	−	0.0216792i	$-0.993099\pi$
$439$	−31.0277	+	17.9139i	−1.48087	+	0.854982i	−0.481108	+	0.876661i	$0.659765\pi$
$440$	−4.39714			−0.209626
$441$		0			0
$442$	−13.3349			−0.634276
$443$	8.86061	−	5.11568i	0.420980	−	0.243053i	−0.274516	−	0.961582i	$-0.588518\pi$
$443$	8.86061	−	5.11568i	0.420980	−	0.243053i	0.695497	+	0.718529i	$0.255184\pi$
$444$		0			0
$445$	1.70342	−	2.95042i	0.0807500	−	0.139863i
$446$	−2.42022	−	4.19194i	−0.114601	−	0.198494i
$447$		0			0
$448$	9.13980	+	14.7168i	0.431815	+	0.695304i
$449$		−	26.3662i		−	1.24430i	−0.782899	−	0.622149i	$-0.786260\pi$
$449$		−	26.3662i		−	1.24430i	0.782899	−	0.622149i	$-0.213740\pi$
$450$		0			0
$451$	−21.4505	−	12.3844i	−1.01006	−	0.583160i
$452$	−17.4059	−	10.0493i	−0.818707	−	0.472681i
$453$		0			0
$454$			9.98846i			0.468782i
$455$	3.32270	+	1.77847i	0.155770	+	0.0833760i
$456$		0			0
$457$	−5.70814	−	9.88679i	−0.267016	−	0.462485i	0.701074	−	0.713088i	$-0.252704\pi$
$457$	−5.70814	−	9.88679i	−0.267016	−	0.462485i	−0.968090	+	0.250604i	$0.919371\pi$
$458$	−4.17385	+	7.22933i	−0.195031	+	0.337804i
$459$		0			0
$460$	−2.83220	+	1.63517i	−0.132052	+	0.0762402i
$461$	−24.7525			−1.15284			−0.576420	−	0.817153i	$-0.695551\pi$
$461$	−24.7525			−1.15284			−0.576420	+	0.817153i	$0.695551\pi$
$462$		0			0
$463$	12.0583			0.560397			0.280198	−	0.959942i	$-0.409600\pi$
$463$	12.0583			0.560397			0.280198	+	0.959942i	$0.409600\pi$
$464$	−4.73474	+	2.73360i	−0.219805	+	0.126904i
$465$		0			0
$466$	11.1758	−	19.3570i	0.517707	−	0.896694i
$467$	−18.6159	−	32.2437i	−0.861440	−	1.49206i	−0.870539	−	0.492100i	$-0.836229\pi$
$467$	−18.6159	−	32.2437i	−0.861440	−	1.49206i	0.00909828	−	0.999959i	$-0.497104\pi$
$468$		0			0
$469$	−12.7534	+	0.410177i	−0.588897	+	0.0189402i
$470$			0.748387i			0.0345205i
$471$		0			0
$472$	5.12180	+	2.95708i	0.235750	+	0.136110i
$473$	−32.2643	−	18.6278i	−1.48351	−	0.856507i
$474$		0			0
$475$			4.77444i			0.219066i
$476$	−6.07674	+	11.3531i	−0.278527	+	0.520369i
$477$		0			0
$478$	−4.05653	−	7.02612i	−0.185541	−	0.321367i
$479$	−1.57906	+	2.73501i	−0.0721490	+	0.124966i	−0.899843	−	0.436214i	$-0.856319\pi$
$479$	−1.57906	+	2.73501i	−0.0721490	+	0.124966i	0.827694	+	0.561180i	$0.189652\pi$
$480$		0			0
$481$	8.18958	−	4.72825i	0.373413	−	0.215590i
$482$	−14.5007			−0.660490
$483$		0			0
$484$	1.33442			0.0606555
$485$	−7.49414	+	4.32674i	−0.340291	+	0.196467i
$486$		0			0
$487$	20.0866	−	34.7910i	0.910211	−	1.57653i	0.0964448	−	0.995338i	$-0.469253\pi$
$487$	20.0866	−	34.7910i	0.910211	−	1.57653i	0.813766	−	0.581193i	$-0.197414\pi$
$488$	5.36912	+	9.29958i	0.243048	+	0.420972i
$489$		0			0
$490$	−2.68088	+	1.78686i	−0.121110	+	0.0807221i
$491$		−	11.4416i		−	0.516350i	−0.966098	−	0.258175i	$-0.916879\pi$
$491$		−	11.4416i		−	0.516350i	0.966098	−	0.258175i	$-0.0831212\pi$
$492$		0			0
$493$	−28.8528	−	16.6582i	−1.29947	−	0.750247i
$494$	−2.51714	−	1.45327i	−0.113251	−	0.0653857i
$495$		0			0
$496$			4.70288i			0.211166i
$497$	14.3552	−	8.91519i	0.643917	−	0.399901i
$498$		0			0
$499$	1.41419	+	2.44945i	0.0633079	+	0.109652i	0.895942	−	0.444171i	$-0.146502\pi$
$499$	1.41419	+	2.44945i	0.0633079	+	0.109652i	−0.832634	+	0.553823i	$0.813168\pi$
$500$	2.46237	−	4.26495i	0.110120	−	0.190734i
$501$		0			0
$502$	−9.00484	+	5.19895i	−0.401906	+	0.232040i
$503$	20.7876			0.926875			0.463437	−	0.886130i	$-0.346616\pi$
$503$	20.7876			0.926875			0.463437	+	0.886130i	$0.346616\pi$
$504$		0			0
$505$	−2.17055			−0.0965884
$506$	17.0030	−	9.81667i	0.755874	−	0.436404i
$507$		0			0
$508$	0.941237	−	1.63027i	0.0417606	−	0.0723316i
$509$	−4.89101	−	8.47148i	−0.216790	−	0.375492i	0.737035	−	0.675855i	$-0.236225\pi$
$509$	−4.89101	−	8.47148i	−0.216790	−	0.375492i	−0.953825	+	0.300363i	$0.902892\pi$
$510$		0			0
$511$	0.507746	+	15.7870i	0.0224614	+	0.698378i
$512$			8.38353i			0.370503i
$513$		0			0
$514$	23.5211	+	13.5799i	1.03747	+	0.598985i
$515$	7.95485	+	4.59274i	0.350533	+	0.202380i
$516$		0			0
$517$			5.07519i			0.223207i
$518$	0.259870	+	8.07999i	0.0114180	+	0.355014i
$519$		0			0
$520$	2.11263	+	3.65919i	0.0926451	+	0.160466i
$521$	−15.3572	+	26.5995i	−0.672811	+	1.16534i	0.304292	+	0.952579i	$0.401580\pi$
$521$	−15.3572	+	26.5995i	−0.672811	+	1.16534i	−0.977103	+	0.212765i	$0.931753\pi$
$522$		0			0
$523$	−1.18985	+	0.686960i	−0.0520285	+	0.0300386i	−0.525789	−	0.850615i	$-0.676230\pi$
$523$	−1.18985	+	0.686960i	−0.0520285	+	0.0300386i	0.473760	+	0.880654i	$0.342896\pi$
$524$	17.5223			0.765464
$525$		0			0
$526$	8.95649			0.390521
$527$	−24.8192	+	14.3294i	−1.08114	+	0.624197i
$528$		0			0
$529$	9.56555	−	16.5680i	0.415893	−	0.720348i
$530$	−1.64031	−	2.84110i	−0.0712504	−	0.123409i
$531$		0			0
$532$	−2.38436	+	1.48079i	−0.103375	+	0.0642005i
$533$			23.8007i			1.03092i
$534$		0			0
$535$	5.36506	+	3.09752i	0.231952	+	0.133917i
$536$	−12.3891	−	7.15286i	−0.535129	−	0.308957i
$537$		0			0
$538$			6.24501i			0.269241i
$539$	−18.1804	+	12.1176i	−0.783086	+	0.521943i
$540$		0			0
$541$	−8.28595	−	14.3517i	−0.356241	−	0.617027i	0.631089	−	0.775711i	$-0.282608\pi$
$541$	−8.28595	−	14.3517i	−0.356241	−	0.617027i	−0.987330	+	0.158683i	$0.949275\pi$
$542$	−0.749444	+	1.29808i	−0.0321914	+	0.0557571i
$543$		0			0
$544$	−20.6724	+	11.9352i	−0.886320	+	0.511717i
$545$	7.67128			0.328602
$546$		0			0
$547$	−24.7994			−1.06035			−0.530173	−	0.847890i	$-0.677873\pi$
$547$	−24.7994			−1.06035			−0.530173	+	0.847890i	$0.677873\pi$
$548$	1.82453	−	1.05340i	0.0779402	−	0.0449988i
$549$		0			0
$550$	−7.22079	+	12.5068i	−0.307896	+	0.533291i
$551$	−3.63091	−	6.28892i	−0.154682	−	0.267917i
$552$		0			0
$553$	−0.712475	+	1.33111i	−0.0302975	+	0.0566045i
$554$			13.4932i			0.573270i
$555$		0			0
$556$	−15.7374	−	9.08597i	−0.667413	−	0.385331i
$557$	−8.15019	−	4.70552i	−0.345335	−	0.199379i	0.317294	−	0.948327i	$-0.397226\pi$
$557$	−8.15019	−	4.70552i	−0.345335	−	0.199379i	−0.662629	+	0.748948i	$0.730559\pi$
$558$		0			0
$559$			35.7993i			1.51415i
$560$	−0.945538	+	0.0304106i	−0.0399563	+	0.00128508i
$561$		0			0
$562$	9.41515	+	16.3075i	0.397154	+	0.687891i
$563$	−11.8595	+	20.5412i	−0.499818	+	0.865710i	−1.00000		0.000210227i	$-0.999933\pi$
$563$	−11.8595	+	20.5412i	−0.499818	+	0.865710i	0.500182	+	0.865920i	$0.333266\pi$
$564$		0			0
$565$	7.79248	−	4.49899i	0.327832	−	0.189274i
$566$	−24.8205			−1.04328
$567$		0			0
$568$	18.9453			0.794928
$569$	−18.7974	+	10.8527i	−0.788027	+	0.454968i	−0.839268	−	0.543719i	$-0.817016\pi$
$569$	−18.7974	+	10.8527i	−0.788027	+	0.454968i	0.0512405	+	0.998686i	$0.483683\pi$
$570$		0			0
$571$	−0.606806	+	1.05102i	−0.0253941	+	0.0439838i	−0.878443	−	0.477847i	$-0.841417\pi$
$571$	−0.606806	+	1.05102i	−0.0253941	+	0.0439838i	0.853049	+	0.521831i	$0.174751\pi$
$572$	4.96551	+	8.60052i	0.207619	+	0.359606i
$573$		0			0
$574$	−17.9387	−	9.60166i	−0.748746	−	0.400766i
$575$			30.9901i			1.29238i
$576$		0			0
$577$	9.97753	+	5.76053i	0.415370	+	0.239814i	0.693094	−	0.720847i	$-0.256247\pi$
$577$	9.97753	+	5.76053i	0.415370	+	0.239814i	−0.277724	+	0.960661i	$0.589580\pi$
$578$	3.39791	+	1.96178i	0.141334	+	0.0815994i
$579$		0			0
$580$			3.65878i			0.151923i
$581$	−15.1109	−	24.3314i	−0.626905	−	1.00944i
$582$		0			0
$583$	−11.1238	−	19.2669i	−0.460699	−	0.797954i
$584$	−8.85432	+	15.3361i	−0.366394	+	0.634614i
$585$		0			0
$586$	11.2646	−	6.50365i	0.465338	−	0.268663i
$587$	29.2255			1.20626			0.603132	−	0.797641i	$-0.293919\pi$
$587$	29.2255			1.20626			0.603132	+	0.797641i	$0.293919\pi$
$588$		0			0
$589$	−6.24661			−0.257387
$590$	−0.794721	+	0.458832i	−0.0327181	+	0.0188898i
$591$		0			0
$592$	−1.18689	+	2.05575i	−0.0487809	+	0.0844909i
$593$	−8.50633	−	14.7334i	−0.349313	−	0.605028i	0.636814	−	0.771017i	$-0.280252\pi$
$593$	−8.50633	−	14.7334i	−0.349313	−	0.605028i	−0.986128	+	0.165989i	$0.946918\pi$
$594$		0			0
$595$	−3.04148	−	4.89736i	−0.124689	−	0.200772i
$596$		−	0.718161i		−	0.0294170i
$597$		0			0
$598$	−16.3384	−	9.43296i	−0.668125	−	0.385742i
$599$	15.3014	+	8.83429i	0.625200	+	0.360959i	0.778891	−	0.627160i	$-0.215783\pi$
$599$	15.3014	+	8.83429i	0.625200	+	0.360959i	−0.153691	+	0.988119i	$0.549116\pi$
$600$		0			0
$601$		−	20.5728i		−	0.839184i	−0.907713	−	0.419592i	$-0.862173\pi$
$601$		−	20.5728i		−	0.839184i	0.907713	−	0.419592i	$-0.137827\pi$
$602$	−26.9821	−	14.4421i	−1.09971	−	0.588618i
$603$		0			0
$604$	2.78992	+	4.83228i	0.113520	+	0.196623i
$605$	−0.298704	+	0.517370i	−0.0121440	+	0.0210341i
$606$		0			0
$607$	−35.0157	+	20.2163i	−1.42124	+	0.820554i	−0.996405	−	0.0847161i	$-0.973002\pi$
$607$	−35.0157	+	20.2163i	−1.42124	+	0.820554i	−0.424836	+	0.905270i	$0.639668\pi$
$608$	−5.20291			−0.211006
$609$		0			0
$610$	−1.66619			−0.0674620
$611$	4.22344	−	2.43841i	0.170862	−	0.0986474i
$612$		0			0
$613$	−3.79627	+	6.57533i	−0.153330	+	0.265575i	−0.932450	−	0.361300i	$-0.882333\pi$
$613$	−3.79627	+	6.57533i	−0.153330	+	0.265575i	0.779120	+	0.626875i	$0.215666\pi$
$614$	8.96774	+	15.5326i	0.361909	+	0.626844i
$615$		0			0
$616$	−24.4828	+	0.787420i	−0.986439	+	0.0317260i
$617$		−	17.2797i		−	0.695656i	−0.937558	−	0.347828i	$-0.886919\pi$
$617$		−	17.2797i		−	0.695656i	0.937558	−	0.347828i	$-0.113081\pi$
$618$		0			0
$619$	10.3492	+	5.97512i	0.415970	+	0.240160i	0.693352	−	0.720599i	$-0.256133\pi$
$619$	10.3492	+	5.97512i	0.415970	+	0.240160i	−0.277382	+	0.960760i	$0.589467\pi$
$620$	2.72563	+	1.57364i	0.109464	+	0.0631989i
$621$		0			0
$622$		−	2.28781i		−	0.0917328i
$623$	8.95611	−	16.7326i	0.358819	−	0.670378i
$624$		0			0
$625$	−10.8337	−	18.7645i	−0.433348	−	0.750582i
$626$	−13.0017	+	22.5195i	−0.519651	+	0.900061i
$627$		0			0
$628$	16.2043	−	9.35556i	0.646622	−	0.373327i
$629$	−14.4655			−0.576776
$630$		0			0
$631$	−42.3649			−1.68652			−0.843261	−	0.537504i	$-0.819367\pi$
$631$	−42.3649			−1.68652			−0.843261	+	0.537504i	$0.819367\pi$
$632$	−1.46591	+	0.846344i	−0.0583108	+	0.0336658i
$633$		0			0
$634$	10.5133	−	18.2095i	0.417536	−	0.723193i
$635$	0.421383	+	0.729857i	0.0167221	+	0.0289635i
$636$		0			0
$637$	18.8189	+	9.30730i	0.745630	+	0.368769i
$638$		−	21.9653i		−	0.869616i
$639$		0			0
$640$	1.67004	+	0.964200i	0.0660143	+	0.0381134i
$641$	−20.5661	−	11.8739i	−0.812313	−	0.468989i	0.0354457	−	0.999372i	$-0.488715\pi$
$641$	−20.5661	−	11.8739i	−0.812313	−	0.468989i	−0.847758	+	0.530383i	$0.822048\pi$
$642$		0			0
$643$			0.610257i			0.0240662i	0.999928	+	0.0120331i	$0.00383034\pi$
$643$			0.610257i			0.0240662i	−0.999928	+	0.0120331i	$0.996170\pi$
$644$	−15.4765	+	9.61160i	−0.609860	+	0.378750i
$645$		0			0
$646$	2.22305	+	3.85043i	0.0874646	+	0.151493i
$647$	7.33081	−	12.6973i	0.288204	−	0.499184i	−0.685177	−	0.728376i	$-0.740275\pi$
$647$	7.33081	−	12.6973i	0.288204	−	0.499184i	0.973381	+	0.229193i	$0.0736086\pi$
$648$		0			0
$649$	−5.38941	+	3.11158i	−0.211553	+	0.122140i
$650$	13.8771			0.544305
$651$		0			0
$652$	−18.2803			−0.715910
$653$	−35.2163	+	20.3322i	−1.37812	+	0.795659i	−0.991933	−	0.126761i	$-0.959542\pi$
$653$	−35.2163	+	20.3322i	−1.37812	+	0.795659i	−0.386189	+	0.922420i	$0.626209\pi$
$654$		0			0
$655$	−3.92228	+	6.79358i	−0.153256	+	0.265447i
$656$	−2.98723	−	5.17404i	−0.116632	−	0.202012i
$657$		0			0
$658$	0.134018	+	4.16693i	0.00522455	+	0.162444i
$659$			15.7441i			0.613302i	0.951822	+	0.306651i	$0.0992084\pi$
$659$			15.7441i			0.613302i	−0.951822	+	0.306651i	$0.900792\pi$
$660$		0			0
$661$	25.3862	+	14.6567i	0.987410	+	0.570081i	0.904499	−	0.426476i	$-0.140245\pi$
$661$	25.3862	+	14.6567i	0.987410	+	0.570081i	0.0829106	+	0.996557i	$0.473578\pi$
$662$	−1.62454	−	0.937930i	−0.0631396	−	0.0364537i
$663$		0			0
$664$		−	32.1115i		−	1.24617i
$665$	−0.0403929	−	1.25591i	−0.00156637	−	0.0487022i
$666$		0			0
$667$	−23.5677	−	40.8204i	−0.912543	−	1.58057i
$668$	−4.38274	+	7.59112i	−0.169573	+	0.293709i
$669$		0			0
$670$	1.92235	−	1.10987i	0.0742668	−	0.0428780i
$671$	−11.2993			−0.436204
$672$		0			0
$673$	−26.3526			−1.01582			−0.507909	−	0.861411i	$-0.669581\pi$
$673$	−26.3526			−1.01582			−0.507909	+	0.861411i	$0.669581\pi$
$674$	8.67823	−	5.01038i	0.334273	−	0.192993i
$675$		0			0
$676$	−2.12415	+	3.67913i	−0.0816979	+	0.141505i
$677$	20.1532	+	34.9064i	0.774551	+	1.34156i	0.935046	+	0.354526i	$0.115358\pi$
$677$	20.1532	+	34.9064i	0.774551	+	1.34156i	−0.160495	+	0.987037i	$0.551309\pi$
$678$		0			0
$679$	−40.9517	+	25.4328i	−1.57158	+	0.976022i
$680$		−	6.46333i		−	0.247857i
$681$		0			0
$682$	−16.3632	−	9.44729i	−0.626579	−	0.361755i
$683$	8.48407	+	4.89828i	0.324634	+	0.187428i	0.653456	−	0.756964i	$-0.273318\pi$
$683$	8.48407	+	4.89828i	0.324634	+	0.187428i	−0.328822	+	0.944392i	$0.606652\pi$
$684$		0			0
$685$			0.943190i			0.0360375i
$686$	−14.6068	+	10.4291i	−0.557692	+	0.398185i
$687$		0			0
$688$	−4.49319	−	7.78243i	−0.171301	−	0.296702i
$689$	−10.6890	+	18.5138i	−0.407217	+	0.705320i
$690$		0			0
$691$	37.2075	−	21.4818i	1.41544	−	0.817205i	0.419547	−	0.907734i	$-0.362189\pi$
$691$	37.2075	−	21.4818i	1.41544	−	0.817205i	0.995894	+	0.0905282i	$0.0288555\pi$
$692$	5.97192			0.227018
$693$		0			0
$694$	−15.4038			−0.584722
$695$	7.04547	−	4.06770i	0.267250	−	0.154297i
$696$		0			0
$697$	18.2038	−	31.5299i	0.689517	−	1.19428i
$698$	15.8498	+	27.4527i	0.599924	+	1.03910i
$699$		0			0
$700$	6.32383	−	11.8147i	0.239018	−	0.446555i
$701$		−	11.8387i		−	0.447142i	−0.974688	−	0.223571i	$-0.928229\pi$
$701$		−	11.8387i		−	0.447142i	0.974688	−	0.223571i	$-0.0717715\pi$
$702$		0			0
$703$	−2.73055	−	1.57649i	−0.102985	−	0.0594583i
$704$	−17.6993	−	10.2187i	−0.667068	−	0.385132i
$705$		0			0
$706$			33.9502i			1.27773i
$707$	−12.0854	+	0.388693i	−0.454518	+	0.0146183i
$708$		0			0
$709$	−17.4448	−	30.2152i	−0.655152	−	1.13476i	−0.981856	−	0.189630i	$-0.939271\pi$
$709$	−17.4448	−	30.2152i	−0.655152	−	1.13476i	0.326704	−	0.945127i	$-0.394062\pi$
$710$	−1.46982	+	2.54580i	−0.0551613	+	0.0955422i
$711$		0			0
$712$	18.4271	−	10.6389i	0.690586	−	0.398710i
$713$	−40.5458			−1.51845
$714$		0			0
$715$	−4.44603			−0.166272
$716$	8.38385	−	4.84042i	0.313319	−	0.180895i
$717$		0			0
$718$	12.7792	−	22.1341i	0.476914	−	0.826039i
$719$	0.568960	+	0.985468i	0.0212186	+	0.0367518i	0.876440	−	0.481512i	$-0.159912\pi$
$719$	0.568960	+	0.985468i	0.0212186	+	0.0367518i	−0.855221	+	0.518263i	$0.826579\pi$
$720$		0			0
$721$	45.1141	+	24.1473i	1.68014	+	0.899292i
$722$			0.969094i			0.0360659i
$723$		0			0
$724$	−12.7406	−	7.35581i	−0.473502	−	0.273376i
$725$	30.0260	+	17.3355i	1.11514	+	0.643826i
$726$		0			0
$727$		−	11.0543i		−	0.409980i	−0.978764	−	0.204990i	$-0.934284\pi$
$727$		−	11.0543i		−	0.409980i	0.978764	−	0.204990i	$-0.0657162\pi$
$728$	12.4182	+	19.9956i	0.460248	+	0.741086i
$729$		0			0
$730$	−1.37387	−	2.37962i	−0.0508494	−	0.0880737i
$731$	27.3808	−	47.4250i	1.01272	−	1.75408i
$732$		0			0
$733$	25.3536	−	14.6379i	0.936457	−	0.540663i	0.0476088	−	0.998866i	$-0.484840\pi$
$733$	25.3536	−	14.6379i	0.936457	−	0.540663i	0.888848	+	0.458203i	$0.151507\pi$
$734$	−29.6820			−1.09558
$735$		0			0
$736$	−33.7713			−1.24483
$737$	13.0364	−	7.52659i	0.480203	−	0.277245i
$738$		0			0
$739$	−17.3900	+	30.1204i	−0.639701	+	1.10800i	0.345797	+	0.938309i	$0.387609\pi$
$739$	−17.3900	+	30.1204i	−0.639701	+	1.10800i	−0.985498	+	0.169686i	$0.945725\pi$
$740$	0.794295	+	1.37576i	0.0291988	+	0.0505739i
$741$		0			0
$742$	−9.64181	−	15.5251i	−0.353962	−	0.569946i
$743$			51.8291i			1.90142i	0.310075	+	0.950712i	$0.399646\pi$
$743$			51.8291i			1.90142i	−0.310075	+	0.950712i	$0.600354\pi$
$744$		0			0
$745$	0.278439	+	0.160757i	0.0102012	+	0.00588968i
$746$	−5.58436	−	3.22413i	−0.204458	−	0.118044i
$747$		0			0
$748$		−	15.1913i		−	0.555451i
$749$	30.4267	+	16.2859i	1.11177	+	0.595073i
$750$		0			0
$751$	6.73569	+	11.6666i	0.245789	+	0.425719i	0.962353	−	0.271802i	$-0.0876197\pi$
$751$	6.73569	+	11.6666i	0.245789	+	0.425719i	−0.716564	+	0.697521i	$0.754286\pi$
$752$	−0.612091	+	1.06017i	−0.0223206	+	0.0386605i
$753$		0			0
$754$	−18.2790	+	10.5534i	−0.665682	+	0.384332i
$755$	−2.49804			−0.0909130
$756$		0			0
$757$	42.4086			1.54137			0.770684	−	0.637218i	$-0.219915\pi$
$757$	42.4086			1.54137			0.770684	+	0.637218i	$0.219915\pi$
$758$	24.9711	−	14.4171i	0.906992	−	0.523652i
$759$		0			0
$760$	0.704391	−	1.22004i	0.0255509	−	0.0442555i
$761$	1.78539	+	3.09239i	0.0647204	+	0.112099i	0.896570	−	0.442902i	$-0.146051\pi$
$761$	1.78539	+	3.09239i	0.0647204	+	0.112099i	−0.831850	+	0.555001i	$0.812718\pi$
$762$		0			0
$763$	42.7128	−	1.37374i	1.54631	−	0.0497326i
$764$			6.91461i			0.250162i
$765$		0			0
$766$	−10.6846	−	6.16878i	−0.386052	−	0.222887i
$767$	5.17875	+	2.98995i	0.186994	+	0.107961i
$768$		0			0
$769$			18.0677i			0.651539i	0.945449	+	0.325770i	$0.105623\pi$
$769$			18.0677i			0.651539i	−0.945449	+	0.325770i	$0.894377\pi$
$770$	1.79361	−	3.35099i	0.0646374	−	0.120761i
$771$		0			0
$772$	−0.679268	−	1.17653i	−0.0244474	−	0.0423441i
$773$	13.9375	−	24.1404i	0.501296	−	0.868270i	−0.498703	−	0.866773i	$-0.666190\pi$
$773$	13.9375	−	24.1404i	0.501296	−	0.868270i	0.999999	−	0.00149736i	$-0.000476625\pi$
$774$		0			0
$775$	25.8284	−	14.9120i	0.927783	−	0.535656i
$776$	−54.0462			−1.94015
$777$		0			0
$778$	8.95488			0.321048
$779$	6.87242	−	3.96779i	0.246230	−	0.142161i
$780$		0			0
$781$	−9.96759	+	17.2644i	−0.356668	+	0.617768i
$782$	14.4295	+	24.9925i	0.515996	+	0.893732i
$783$		0			0
$784$	−5.25920	+	0.338645i	−0.187829	+	0.0120945i
$785$			8.37679i			0.298980i
$786$		0			0
$787$	−0.818430	−	0.472521i	−0.0291739	−	0.0168435i	0.485342	−	0.874324i	$-0.338695\pi$
$787$	−0.818430	−	0.472521i	−0.0291739	−	0.0168435i	−0.514516	+	0.857481i	$0.672028\pi$
$788$	−23.9325	−	13.8174i	−0.852560	−	0.492226i
$789$		0			0
$790$		−	0.262645i		−	0.00934448i
$791$	42.5819	−	26.4453i	1.51404	−	0.940286i
$792$		0			0
$793$	5.42881	+	9.40297i	0.192783	+	0.333909i
$794$	16.3889	−	28.3863i	0.581619	−	1.00739i
$795$		0			0
$796$	−12.6148	+	7.28314i	−0.447119	+	0.258144i
$797$	8.55002			0.302857			0.151429	−	0.988468i	$-0.451613\pi$
$797$	8.55002			0.302857			0.151429	+	0.988468i	$0.451613\pi$
$798$		0			0
$799$	−7.45999			−0.263915
$800$	21.5129	−	12.4205i	0.760597	−	0.439131i
$801$		0			0
$802$	−6.04642	+	10.4727i	−0.213507	+	0.369804i
$803$	−9.31694	−	16.1374i	−0.328788	−	0.569477i
$804$		0			0
$805$	−0.262184	−	8.15193i	−0.00924077	−	0.287318i
$806$			18.1560i			0.639519i
$807$		0			0
$808$	−11.7402	−	6.77821i	−0.413019	−	0.238457i
$809$	−42.3912	−	24.4746i	−1.49040	−	0.860480i	−0.490456	−	0.871466i	$-0.663170\pi$
$809$	−42.3912	−	24.4746i	−1.49040	−	0.860480i	−0.999940	+	0.0109854i	$0.996503\pi$
$810$		0			0
$811$			15.0095i			0.527056i	0.964652	+	0.263528i	$0.0848861\pi$
$811$			15.0095i			0.527056i	−0.964652	+	0.263528i	$0.915114\pi$
$812$	0.655197	+	20.3717i	0.0229929	+	0.714905i
$813$		0			0
$814$	−4.76851	−	8.25931i	−0.167136	−	0.289489i
$815$	4.09195	−	7.08747i	0.143335	−	0.248263i
$816$		0			0
$817$	10.3370	−	5.96808i	0.361646	−	0.208797i
$818$	−5.88661			−0.205820
$819$		0			0
$820$	−3.99825			−0.139625
$821$	−32.1530	+	18.5635i	−1.12215	+	0.647872i	−0.941948	−	0.335759i	$-0.891007\pi$
$821$	−32.1530	+	18.5635i	−1.12215	+	0.647872i	−0.180199	+	0.983630i	$0.557674\pi$
$822$		0			0
$823$	0.374190	−	0.648117i	0.0130435	−	0.0225919i	−0.859430	−	0.511253i	$-0.829181\pi$
$823$	0.374190	−	0.648117i	0.0130435	−	0.0225919i	0.872473	+	0.488662i	$0.162515\pi$
$824$	28.6844	+	49.6829i	0.999269	+	1.73078i
$825$		0			0
$826$	−4.34275	+	2.69704i	−0.151103	+	0.0938420i
$827$		−	22.4202i		−	0.779628i	−0.920894	−	0.389814i	$-0.872539\pi$
$827$		−	22.4202i		−	0.779628i	0.920894	−	0.389814i	$-0.127461\pi$
$828$		0			0
$829$	10.1825	+	5.87885i	0.353652	+	0.204181i	0.666292	−	0.745691i	$-0.267880\pi$
$829$	10.1825	+	5.87885i	0.353652	+	0.204181i	−0.312641	+	0.949871i	$0.601214\pi$
$830$	4.31502	+	2.49128i	0.149777	+	0.0864736i
$831$		0			0
$832$			19.6386i			0.680844i
$833$	−17.8116	−	26.7233i	−0.617135	−	0.925906i
$834$		0			0
$835$	−1.96211	−	3.39847i	−0.0679016	−	0.117609i
$836$	1.65559	−	2.86757i	0.0572599	−	0.0991770i
$837$		0			0
$838$	−20.1080	+	11.6093i	−0.694618	+	0.401038i
$839$	−30.3257			−1.04696			−0.523480	−	0.852038i	$-0.675367\pi$
$839$	−30.3257			−1.04696			−0.523480	+	0.852038i	$0.675367\pi$
$840$		0			0
$841$	−23.7339			−0.818412
$842$	0.796142	−	0.459653i	0.0274369	−	0.0158407i
$843$		0			0
$844$	−6.79746	+	11.7735i	−0.233978	+	0.405262i
$845$	−0.950960	−	1.64711i	−0.0327140	−	0.0566623i
$846$		0			0
$847$	−1.57050	+	2.93414i	−0.0539630	+	0.100818i
$848$		−	5.36630i		−	0.184279i
$849$		0			0
$850$	−18.3836	−	10.6138i	−0.630553	−	0.364050i
$851$	−17.7236	−	10.2327i	−0.607558	−	0.350774i
$852$		0			0
$853$		−	21.3620i		−	0.731422i	−0.930729	−	0.365711i	$-0.880826\pi$
$853$		−	21.3620i		−	0.731422i	0.930729	−	0.365711i	$-0.119174\pi$
$854$	−9.27714	+	0.298373i	−0.317457	+	0.0102101i
$855$		0			0
$856$	19.3459	+	33.5080i	0.661229	+	1.14528i
$857$	−1.47820	+	2.56032i	−0.0504944	+	0.0874589i	−0.890168	−	0.455633i	$-0.849413\pi$
$857$	−1.47820	+	2.56032i	−0.0504944	+	0.0874589i	0.839673	+	0.543092i	$0.182746\pi$
$858$		0			0
$859$	28.7827	−	16.6177i	0.982053	−	0.566988i	0.0791635	−	0.996862i	$-0.474775\pi$
$859$	28.7827	−	16.6177i	0.982053	−	0.566988i	0.902889	+	0.429873i	$0.141442\pi$
$860$	−6.01389			−0.205072
$861$		0			0
$862$	−2.32001			−0.0790199
$863$	−12.7522	+	7.36250i	−0.434090	+	0.250622i	−0.701088	−	0.713075i	$-0.747302\pi$
$863$	−12.7522	+	7.36250i	−0.434090	+	0.250622i	0.266997	+	0.963697i	$0.413969\pi$
$864$		0			0
$865$	−1.33679	+	2.31538i	−0.0454521	+	0.0787253i
$866$	−4.14183	−	7.17387i	−0.140745	−	0.243778i
$867$		0			0
$868$	15.4578	+	8.27375i	0.524671	+	0.280829i
$869$		−	1.78113i		−	0.0604206i
$870$		0			0
$871$	−12.5269	−	7.23239i	−0.424457	−	0.245060i
$872$	41.4928	+	23.9559i	1.40512	+	0.811249i
$873$		0			0
$874$			6.29024i			0.212771i
$875$	6.47984	+	10.4338i	0.219058	+	0.352726i
$876$		0			0
$877$	−2.18235	−	3.77994i	−0.0736927	−	0.127639i	0.826824	−	0.562460i	$-0.190145\pi$
$877$	−2.18235	−	3.77994i	−0.0736927	−	0.127639i	−0.900517	+	0.434821i	$0.856812\pi$
$878$	17.3602	−	30.0688i	0.585879	−	1.01477i
$879$		0			0
$880$	0.966523	−	0.558022i	0.0325815	−	0.0188109i
$881$	49.3542			1.66279			0.831393	−	0.555684i	$-0.187544\pi$
$881$	49.3542			1.66279			0.831393	+	0.555684i	$0.187544\pi$
$882$		0			0
$883$	39.1357			1.31702			0.658511	−	0.752571i	$-0.271187\pi$
$883$	39.1357			1.31702			0.658511	+	0.752571i	$0.271187\pi$
$884$	−12.6418	+	7.29877i	−0.425191	+	0.245484i
$885$		0			0
$886$	−4.95757	+	8.58677i	−0.166553	+	0.288478i
$887$	−12.3426	−	21.3780i	−0.414424	−	0.717803i	0.580944	−	0.813944i	$-0.302684\pi$
$887$	−12.3426	−	21.3780i	−0.414424	−	0.717803i	−0.995368	+	0.0961404i	$0.969350\pi$
$888$		0			0
$889$	2.47691	+	3.98830i	0.0830729	+	0.133763i
$890$			3.30156i			0.110668i
$891$		0			0
$892$	−4.58887	−	2.64938i	−0.153647	−	0.0887079i
$893$	−1.40817	−	0.813009i	−0.0471227	−	0.0272063i
$894$		0			0
$895$			4.33402i			0.144870i
$896$	9.47127	+	5.06949i	0.316413	+	0.169360i
$897$		0			0
$898$	12.7757	+	22.1281i	0.426329	+	0.738424i
$899$	−22.6809	+	39.2844i	−0.756449	+	1.31021i
$900$		0			0
$901$	28.3203	−	16.3507i	0.943486	−	0.544722i
$902$	24.0034			0.799224
$903$		0			0
$904$	56.1978			1.86911
$905$	5.70386	−	3.29313i	0.189603	−	0.109467i
$906$		0			0
$907$	−16.4192	+	28.4389i	−0.545190	+	0.944298i	0.453404	+	0.891305i	$0.350209\pi$
$907$	−16.4192	+	28.4389i	−0.545190	+	0.944298i	−0.998595	+	0.0529927i	$0.983124\pi$
$908$	5.46713	+	9.46934i	0.181433	+	0.314251i
$909$		0			0
$910$	−3.65036	+	0.117404i	−0.121008	+	0.00389189i
$911$			18.8624i			0.624940i	0.949928	+	0.312470i	$0.101156\pi$
$911$			18.8624i			0.624940i	−0.949928	+	0.312470i	$0.898844\pi$
$912$		0			0
$913$	29.2624	+	16.8946i	0.968443	+	0.559131i
$914$	9.58123	+	5.53173i	0.316919	+	0.182973i
$915$		0			0
$916$			9.13814i			0.301933i
$917$	−20.6222	+	38.5283i	−0.681005	+	1.27231i
$918$		0			0
$919$	−11.8671	−	20.5544i	−0.391459	−	0.678027i	0.601183	−	0.799111i	$-0.294696\pi$
$919$	−11.8671	−	20.5544i	−0.391459	−	0.678027i	−0.992642	+	0.121084i	$0.961363\pi$
$920$	4.57209	−	7.91910i	0.150737	−	0.261085i
$921$		0			0
$922$	20.7738	−	11.9938i	0.684149	−	0.394994i
$923$	19.1559			0.630526
$924$		0			0
$925$	15.0537			0.494962
$926$	−10.1201	+	5.84281i	−0.332566	+	0.192007i
$927$		0			0
$928$	−18.8913	+	32.7207i	−0.620137	+	1.07411i
$929$	−8.57002	−	14.8437i	−0.281173	−	0.487007i	0.690501	−	0.723332i	$-0.257390\pi$
$929$	−8.57002	−	14.8437i	−0.281173	−	0.487007i	−0.971674	+	0.236325i	$0.924057\pi$
$930$		0			0
$931$	−0.449806	−	6.98553i	−0.0147418	−	0.228942i
$932$		−	24.4679i		−	0.801474i
$933$		0			0
$934$	31.2471	+	18.0405i	1.02244	+	0.590305i
$935$	5.88986	+	3.40051i	0.192619	+	0.111209i
$936$		0			0
$937$		−	22.6185i		−	0.738915i	−0.929248	−	0.369458i	$-0.879544\pi$
$937$		−	22.6185i		−	0.738915i	0.929248	−	0.369458i	$-0.120456\pi$
$938$	10.5047	−	6.52386i	0.342989	−	0.213012i
$939$		0			0
$940$	0.409625	+	0.709492i	0.0133605	+	0.0231411i
$941$	18.1095	−	31.3665i	0.590352	−	1.02252i	−0.403833	−	0.914833i	$-0.632322\pi$
$941$	18.1095	−	31.3665i	0.590352	−	1.02252i	0.994185	−	0.107687i	$-0.0343443\pi$
$942$		0			0
$943$	44.6078	−	25.7543i	1.45263	−	0.838677i
$944$	−1.50108			−0.0488559
$945$		0			0
$946$	36.1042			1.17385
$947$	15.3342	−	8.85323i	0.498296	−	0.287691i	−0.229714	−	0.973258i	$-0.573779\pi$
$947$	15.3342	−	8.85323i	0.498296	−	0.287691i	0.728010	+	0.685567i	$0.240446\pi$
$948$		0			0
$949$	−8.95276	+	15.5066i	−0.290619	+	0.503367i
$950$	−2.31344	−	4.00699i	−0.0750579	−	0.130004i
$951$		0			0
$952$	−1.15742	−	35.9870i	−0.0375123	−	1.16635i
$953$		−	49.4880i		−	1.60307i	−0.597945	−	0.801537i	$-0.704016\pi$
$953$		−	49.4880i		−	1.60307i	0.597945	−	0.801537i	$-0.295984\pi$
$954$		0			0
$955$	−2.68087	−	1.54780i	−0.0867510	−	0.0500857i
$956$	−7.69141	−	4.44064i	−0.248758	−	0.143621i
$957$		0			0
$958$		−	3.06051i		−	0.0988807i
$959$	0.168902	+	5.25157i	0.00545413	+	0.169582i
$960$		0			0
$961$	4.01006	+	6.94563i	0.129357	+	0.224053i
$962$	−4.58212	+	7.93647i	−0.147734	+	0.255882i
$963$		0			0
$964$	−13.7471	+	7.93689i	−0.442764	+	0.255630i
$965$	0.608204			0.0195788
$966$		0			0
$967$	40.5529			1.30409			0.652047	−	0.758179i	$-0.273910\pi$
$967$	40.5529			1.30409			0.652047	+	0.758179i	$0.273910\pi$
$968$	−3.23129	+	1.86558i	−0.103857	+	0.0599622i
$969$		0			0
$970$	4.19302	−	7.26253i	0.134630	−	0.233186i
$971$	6.08237	+	10.5350i	0.195193	+	0.338083i	0.946964	−	0.321341i	$-0.104133\pi$
$971$	6.08237	+	10.5350i	0.195193	+	0.338083i	−0.751771	+	0.659424i	$0.770800\pi$
$972$		0			0
$973$	38.4999	−	23.9102i	1.23425	−	0.766524i
$974$			38.9316i			1.24745i
$975$		0			0
$976$	−2.36034	−	1.36274i	−0.0755526	−	0.0436203i
$977$	15.8147	+	9.13064i	0.505958	+	0.292115i	0.731171	−	0.682195i	$-0.238974\pi$
$977$	15.8147	+	9.13064i	0.505958	+	0.292115i	−0.225213	+	0.974310i	$0.572308\pi$
$978$		0			0
$979$			22.3895i			0.715573i
$980$	−1.56352	+	3.16136i	−0.0499449	+	0.100986i
$981$		0			0
$982$	5.54397	+	9.60244i	0.176915	+	0.306426i
$983$	−23.4894	+	40.6848i	−0.749195	+	1.29764i	0.199014	+	0.979997i	$0.436226\pi$
$983$	−23.4894	+	40.6848i	−0.749195	+	1.29764i	−0.948209	+	0.317647i	$0.897107\pi$
$984$		0			0
$985$	10.7144	−	6.18594i	0.341388	−	0.197100i
$986$	32.2867			1.02822
$987$		0			0
$988$	−3.18176			−0.101225
$989$	67.0959	−	38.7379i	2.13353	−	1.23179i
$990$		0			0
$991$	−0.839263	+	1.45365i	−0.0266601	+	0.0461766i	−0.879048	−	0.476734i	$-0.841821\pi$
$991$	−0.839263	+	1.45365i	−0.0266601	+	0.0461766i	0.852388	+	0.522911i	$0.175154\pi$
$992$	16.2503	+	28.1463i	0.515947	+	0.893647i
$993$		0			0
$994$	−7.72788	+	14.4379i	−0.245114	+	0.457943i
$995$		−	6.52119i		−	0.206736i
$996$		0			0
$997$	4.53782	+	2.61991i	0.143714	+	0.0829734i	0.570133	−	0.821552i	$-0.306892\pi$
$997$	4.53782	+	2.61991i	0.143714	+	0.0829734i	−0.426419	+	0.904526i	$0.640225\pi$
$998$	−2.37375	−	1.37048i	−0.0751397	−	0.0433819i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.18	✓	96
3.2	odd	2	inner	1197.2.db.a.647.31	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.31	yes	96
21.5	even	6	inner	1197.2.db.a.1160.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.18	✓	96	1.1	even	1	trivial
1197.2.db.a.647.31	yes	96	3.2	odd	2	inner
1197.2.db.a.1160.18	yes	96	21.5	even	6	inner
1197.2.db.a.1160.31	yes	96	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.839260 + 0.484547i) q^{2} +(-0.530428 + 0.918729i) q^{4} +(-0.237468 - 0.411306i) q^{5} +(-1.39585 - 2.24758i) q^{7} -2.96626i q^{8} +O(q^{10})\)	\(q+(-0.839260 + 0.484547i) q^{2} +(-0.530428 + 0.918729i) q^{4} +(-0.237468 - 0.411306i) q^{5} +(-1.39585 - 2.24758i) q^{7} -2.96626i q^{8} +(0.398594 + 0.230129i) q^{10} +(2.70307 + 1.56062i) q^{11} -2.99924i q^{13} +(2.26054 + 1.20995i) q^{14} +(0.376435 + 0.652005i) q^{16} +(-2.29394 + 3.97323i) q^{17} +(-0.866025 + 0.500000i) q^{19} +0.503838 q^{20} -3.02477 q^{22} +(-5.62124 + 3.24542i) q^{23} +(2.38722 - 4.13478i) q^{25} +(1.45327 + 2.51714i) q^{26} +(2.80531 - 0.0902250i) q^{28} +7.26181i q^{29} +(5.40972 + 3.12330i) q^{31} +(4.50586 + 2.60146i) q^{32} -4.44609i q^{34} +(-0.592975 + 1.10785i) q^{35} +(1.57649 + 2.73055i) q^{37} +(0.484547 - 0.839260i) q^{38} +(-1.22004 + 0.704391i) q^{40} -7.93559 q^{41} -11.9362 q^{43} +(-2.86757 + 1.65559i) q^{44} +(3.14512 - 5.44751i) q^{46} +(0.813009 + 1.40817i) q^{47} +(-3.10322 + 6.27455i) q^{49} +4.62688i q^{50} +(2.75548 + 1.59088i) q^{52} +(-6.17285 - 3.56389i) q^{53} -1.48239i q^{55} +(-6.66690 + 4.14044i) q^{56} +(-3.51869 - 6.09455i) q^{58} +(-0.996904 + 1.72669i) q^{59} +(-3.13512 + 1.81006i) q^{61} -6.05355 q^{62} -6.54785 q^{64} +(-1.23360 + 0.712222i) q^{65} +(2.41141 - 4.17668i) q^{67} +(-2.43354 - 4.21502i) q^{68} +(-0.0391445 - 1.21710i) q^{70} +6.38694i q^{71} +(-5.17020 - 2.98501i) q^{73} +(-2.64616 - 1.52776i) q^{74} -1.06086i q^{76} +(-0.265459 - 8.25375i) q^{77} +(-0.285324 - 0.494195i) q^{79} +(0.178782 - 0.309660i) q^{80} +(6.66002 - 3.84516i) q^{82} +10.8256 q^{83} +2.17895 q^{85} +(10.0175 - 5.78363i) q^{86} +(4.62920 - 8.01801i) q^{88} +(3.58664 + 6.21225i) q^{89} +(-6.74102 + 4.18647i) q^{91} -6.88586i q^{92} +(-1.36465 - 0.787883i) q^{94} +(0.411306 + 0.237468i) q^{95} -18.2203i q^{97} +(-0.435904 - 6.76964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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