LMFDB - Embedded newform 927.2.f.f.46.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(46,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("927.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.f (of order $3$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.14
Character	$\chi$	$=$	927.46
Dual form			927.2.f.f.262.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.980806 + 1.69881i) q^{2} +(-0.923962 + 1.60035i) q^{4} +(-0.348567 + 0.603736i) q^{5} +(-1.12861 + 1.95480i) q^{7} +0.298316 q^{8} +O(q^{10})$	\(q+(0.980806 + 1.69881i) q^{2} +(-0.923962 + 1.60035i) q^{4} +(-0.348567 + 0.603736i) q^{5} +(-1.12861 + 1.95480i) q^{7} +0.298316 q^{8} -1.36751 q^{10} +(-1.68707 + 2.92208i) q^{11} +2.74975 q^{13} -4.42778 q^{14} +(2.14051 + 3.70748i) q^{16} +(-2.13676 + 3.70098i) q^{17} +(-3.70048 - 6.40942i) q^{19} +(-0.644125 - 1.11566i) q^{20} -6.61874 q^{22} +1.81672 q^{23} +(2.25700 + 3.90924i) q^{25} +(2.69697 + 4.67129i) q^{26} +(-2.08558 - 3.61233i) q^{28} +(0.0774236 + 0.134102i) q^{29} -8.60385 q^{31} +(-3.90054 + 6.75594i) q^{32} -8.38299 q^{34} +(-0.786790 - 1.36276i) q^{35} -0.211556 q^{37} +(7.25891 - 12.5728i) q^{38} +(-0.103983 + 0.180104i) q^{40} +(4.27821 + 7.41007i) q^{41} +(-4.38561 - 7.59610i) q^{43} +(-3.11757 - 5.39979i) q^{44} +(1.78185 + 3.08626i) q^{46} +(-4.88176 + 8.45546i) q^{47} +(0.952496 + 1.64977i) q^{49} +(-4.42736 + 7.66842i) q^{50} +(-2.54066 + 4.40055i) q^{52} +(4.38362 - 7.59266i) q^{53} +(-1.17611 - 2.03708i) q^{55} +(-0.336681 + 0.583149i) q^{56} +(-0.151875 + 0.263055i) q^{58} +(3.99296 + 6.91600i) q^{59} -2.65165 q^{61} +(-8.43871 - 14.6163i) q^{62} -6.74065 q^{64} +(-0.958471 + 1.66012i) q^{65} +(4.56052 - 7.89906i) q^{67} +(-3.94857 - 6.83912i) q^{68} +(1.54338 - 2.67321i) q^{70} +(5.80160 - 10.0487i) q^{71} -5.07534 q^{73} +(-0.207495 - 0.359392i) q^{74} +13.6764 q^{76} +(-3.80807 - 6.59576i) q^{77} +10.9513 q^{79} -2.98445 q^{80} +(-8.39218 + 14.5357i) q^{82} +(6.51857 + 11.2905i) q^{83} +(-1.48961 - 2.58008i) q^{85} +(8.60286 - 14.9006i) q^{86} +(-0.503279 + 0.871705i) q^{88} +15.2001 q^{89} +(-3.10338 + 5.37522i) q^{91} +(-1.67858 + 2.90739i) q^{92} -19.1522 q^{94} +5.15946 q^{95} +(2.14072 + 3.70784i) q^{97} +(-1.86843 + 3.23621i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q - 18 * q^4 + 8 * q^7	$ 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) $ 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.980806	+	1.69881i	0.693535	+	1.20124i	0.970672	+	0.240407i	$0.0772809\pi$
$2$	0.980806	+	1.69881i	0.693535	+	1.20124i	−0.277137	+	0.960830i	$0.589386\pi$
$3$		0			0
$3$		0			0
$4$	−0.923962	+	1.60035i	−0.461981	+	0.800174i
$5$	−0.348567	+	0.603736i	−0.155884	+	0.269999i	−0.933381	−	0.358888i	$-0.883156\pi$
$5$	−0.348567	+	0.603736i	−0.155884	+	0.269999i	0.777497	+	0.628887i	$0.216489\pi$
$6$		0			0
$7$	−1.12861	+	1.95480i	−0.426573	+	0.738846i	−0.996566	−	0.0828034i	$-0.973613\pi$
$7$	−1.12861	+	1.95480i	−0.426573	+	0.738846i	0.569993	+	0.821650i	$0.306946\pi$
$8$	0.298316			0.105471
$9$		0			0
$10$	−1.36751			−0.432443
$11$	−1.68707	+	2.92208i	−0.508669	+	0.881041i	0.491280	+	0.871002i	$0.336529\pi$
$11$	−1.68707	+	2.92208i	−0.508669	+	0.881041i	−0.999950	+	0.0100397i	$0.996804\pi$
$12$		0			0
$13$	2.74975			0.762643			0.381321	−	0.924443i	$-0.375469\pi$
$13$	2.74975			0.762643			0.381321	+	0.924443i	$0.375469\pi$
$14$	−4.42778			−1.18337
$15$		0			0
$16$	2.14051	+	3.70748i	0.535128	+	0.926869i
$17$	−2.13676	+	3.70098i	−0.518241	+	0.897619i	0.481535	+	0.876427i	$0.340080\pi$
$17$	−2.13676	+	3.70098i	−0.518241	+	0.897619i	−0.999775	+	0.0211923i	$0.993254\pi$
$18$		0			0
$19$	−3.70048	−	6.40942i	−0.848949	−	1.47042i	−0.882147	−	0.470974i	$-0.843903\pi$
$19$	−3.70048	−	6.40942i	−0.848949	−	1.47042i	0.0331984	−	0.999449i	$-0.489431\pi$
$20$	−0.644125	−	1.11566i	−0.144031	−	0.249468i
$21$		0			0
$22$	−6.61874			−1.41112
$23$	1.81672			0.378813			0.189407	−	0.981899i	$-0.439344\pi$
$23$	1.81672			0.378813			0.189407	+	0.981899i	$0.439344\pi$
$24$		0			0
$25$	2.25700	+	3.90924i	0.451400	+	0.781849i
$26$	2.69697	+	4.67129i	0.528919	+	0.916115i
$27$		0			0
$28$	−2.08558	−	3.61233i	−0.394137	−	0.682665i
$29$	0.0774236	+	0.134102i	0.0143772	+	0.0249020i	0.873124	−	0.487497i	$-0.162090\pi$
$29$	0.0774236	+	0.134102i	0.0143772	+	0.0249020i	−0.858747	+	0.512399i	$0.828757\pi$
$30$		0			0
$31$	−8.60385			−1.54530			−0.772649	−	0.634834i	$-0.781069\pi$
$31$	−8.60385			−1.54530			−0.772649	+	0.634834i	$0.781069\pi$
$32$	−3.90054	+	6.75594i	−0.689525	+	1.19429i
$33$		0			0
$34$	−8.38299			−1.43767
$35$	−0.786790	−	1.36276i	−0.132992	−	0.230348i
$36$		0			0
$37$	−0.211556			−0.0347795			−0.0173898	−	0.999849i	$-0.505536\pi$
$37$	−0.211556			−0.0347795			−0.0173898	+	0.999849i	$0.505536\pi$
$38$	7.25891	−	12.5728i	1.17755	−	2.03958i
$39$		0			0
$40$	−0.103983	+	0.180104i	−0.0164412	+	0.0284769i
$41$	4.27821	+	7.41007i	0.668143	+	1.15726i	0.978423	+	0.206613i	$0.0662441\pi$
$41$	4.27821	+	7.41007i	0.668143	+	1.15726i	−0.310279	+	0.950645i	$0.600423\pi$
$42$		0			0
$43$	−4.38561	−	7.59610i	−0.668799	−	1.15839i	−0.978240	−	0.207475i	$-0.933475\pi$
$43$	−4.38561	−	7.59610i	−0.668799	−	1.15839i	0.309441	−	0.950919i	$-0.399858\pi$
$44$	−3.11757	−	5.39979i	−0.469991	−	0.814048i
$45$		0			0
$46$	1.78185	+	3.08626i	0.262720	+	0.455045i
$47$	−4.88176	+	8.45546i	−0.712078	+	1.23336i	0.251998	+	0.967728i	$0.418912\pi$
$47$	−4.88176	+	8.45546i	−0.712078	+	1.23336i	−0.964076	+	0.265627i	$0.914421\pi$
$48$		0			0
$49$	0.952496	+	1.64977i	0.136071	+	0.235682i
$50$	−4.42736	+	7.66842i	−0.626124	+	1.08448i
$51$		0			0
$52$	−2.54066	+	4.40055i	−0.352326	+	0.610247i
$53$	4.38362	−	7.59266i	0.602137	−	1.04293i	−0.390360	−	0.920662i	$-0.627649\pi$
$53$	4.38362	−	7.59266i	0.602137	−	1.04293i	0.992497	−	0.122269i	$-0.0390172\pi$
$54$		0			0
$55$	−1.17611	−	2.03708i	−0.158587	−	0.274680i
$56$	−0.336681	+	0.583149i	−0.0449909	+	0.0779266i
$57$		0			0
$58$	−0.151875	+	0.263055i	−0.0199422	+	0.0345409i
$59$	3.99296	+	6.91600i	0.519839	+	0.900387i	0.999734	+	0.0230613i	$0.00734129\pi$
$59$	3.99296	+	6.91600i	0.519839	+	0.900387i	−0.479895	+	0.877326i	$0.659325\pi$
$60$		0			0
$61$	−2.65165			−0.339509			−0.169755	−	0.985486i	$-0.554298\pi$
$61$	−2.65165			−0.339509			−0.169755	+	0.985486i	$0.554298\pi$
$62$	−8.43871	−	14.6163i	−1.07172	−	1.85627i
$63$		0			0
$64$	−6.74065			−0.842581
$65$	−0.958471	+	1.66012i	−0.118884	+	0.205913i
$66$		0			0
$67$	4.56052	−	7.89906i	0.557157	−	0.965024i	−0.440576	−	0.897715i	$-0.645226\pi$
$67$	4.56052	−	7.89906i	0.557157	−	0.965024i	0.997732	−	0.0673080i	$-0.0214410\pi$
$68$	−3.94857	−	6.83912i	−0.478835	−	0.829366i
$69$		0			0
$70$	1.54338	−	2.67321i	0.184469	−	0.319509i
$71$	5.80160	−	10.0487i	0.688523	−	1.19256i	−0.283793	−	0.958886i	$-0.591593\pi$
$71$	5.80160	−	10.0487i	0.688523	−	1.19256i	0.972316	−	0.233671i	$-0.0750738\pi$
$72$		0			0
$73$	−5.07534			−0.594024			−0.297012	−	0.954874i	$-0.595990\pi$
$73$	−5.07534			−0.594024			−0.297012	+	0.954874i	$0.595990\pi$
$74$	−0.207495	−	0.359392i	−0.0241208	−	0.0417785i
$75$		0			0
$76$	13.6764			1.56879
$77$	−3.80807	−	6.59576i	−0.433969	−	0.751657i
$78$		0			0
$79$	10.9513			1.23211			0.616057	−	0.787701i	$-0.288729\pi$
$79$	10.9513			1.23211			0.616057	+	0.787701i	$0.288729\pi$
$80$	−2.98445			−0.333671
$81$		0			0
$82$	−8.39218	+	14.5357i	−0.926761	+	1.60520i
$83$	6.51857	+	11.2905i	0.715507	+	1.23929i	0.962764	+	0.270344i	$0.0871374\pi$
$83$	6.51857	+	11.2905i	0.715507	+	1.23929i	−0.247257	+	0.968950i	$0.579529\pi$
$84$		0			0
$85$	−1.48961	−	2.58008i	−0.161571	−	0.279849i
$86$	8.60286	−	14.9006i	0.927671	−	1.60677i
$87$		0			0
$88$	−0.503279	+	0.871705i	−0.0536497	+	0.0929240i
$89$	15.2001			1.61120			0.805602	−	0.592457i	$-0.201842\pi$
$89$	15.2001			1.61120			0.805602	+	0.592457i	$0.201842\pi$
$90$		0			0
$91$	−3.10338	+	5.37522i	−0.325323	+	0.563476i
$92$	−1.67858	+	2.90739i	−0.175004	+	0.303117i
$93$		0			0
$94$	−19.1522			−1.97540
$95$	5.15946			0.529350
$96$		0			0
$97$	2.14072	+	3.70784i	0.217358	+	0.376474i	0.953999	−	0.299809i	$-0.0969229\pi$
$97$	2.14072	+	3.70784i	0.217358	+	0.376474i	−0.736642	+	0.676283i	$0.763590\pi$
$98$	−1.86843	+	3.23621i	−0.188740	+	0.326907i
$99$		0			0
$100$	−8.34153			−0.834153
$101$	2.65798	+	4.60375i	0.264478	+	0.458090i	0.967427	−	0.253151i	$-0.0814669\pi$
$101$	2.65798	+	4.60375i	0.264478	+	0.458090i	−0.702948	+	0.711241i	$0.748134\pi$
$102$		0			0
$103$	10.0130	−	1.65514i	0.986612	−	0.163086i
$103$	10.0130	−	1.65514i	0.986612	−	0.163086i
$104$	0.820294			0.0804364
$105$		0			0
$106$	17.1979			1.67041
$107$	9.23739	−	15.9996i	0.893012	−	1.54674i	0.0567663	−	0.998387i	$-0.481921\pi$
$107$	9.23739	−	15.9996i	0.893012	−	1.54674i	0.836246	−	0.548355i	$-0.184746\pi$
$108$		0			0
$109$	−0.0371716	−	0.0643832i	−0.00356040	−	0.00616679i	0.864240	−	0.503080i	$-0.167800\pi$
$109$	−0.0371716	−	0.0643832i	−0.00356040	−	0.00616679i	−0.867800	+	0.496913i	$0.834467\pi$
$110$	2.30707	−	3.99597i	0.219971	−	0.381001i
$111$		0			0
$112$	−9.66319			−0.913085
$113$	−15.1089			−1.42133			−0.710665	−	0.703531i	$-0.751606\pi$
$113$	−15.1089			−1.42133			−0.710665	+	0.703531i	$0.751606\pi$
$114$		0			0
$115$	−0.633250	+	1.09682i	−0.0590509	+	0.102279i
$116$	−0.286146			−0.0265680
$117$		0			0
$118$	−7.83263	+	13.5665i	−0.721052	+	1.24890i
$119$	−4.82312	−	8.35390i	−0.442135	−	0.765800i
$120$		0			0
$121$	−0.192381	−	0.333214i	−0.0174892	−	0.0302922i
$122$	−2.60076	−	4.50464i	−0.235462	−	0.407831i
$123$		0			0
$124$	7.94963	−	13.7692i	0.713898	−	1.23651i
$125$	−6.63253			−0.593232
$126$		0			0
$127$	13.7903			1.22369			0.611845	−	0.790977i	$-0.290427\pi$
$127$	13.7903			1.22369			0.611845	+	0.790977i	$0.290427\pi$
$128$	1.18981	+	2.06082i	0.105166	+	0.182152i
$129$		0			0
$130$	−3.76030			−0.329800
$131$	−1.79288	−	3.10535i	−0.156644	−	0.271316i	0.777012	−	0.629486i	$-0.216734\pi$
$131$	−1.79288	−	3.10535i	−0.156644	−	0.271316i	−0.933657	+	0.358169i	$0.883401\pi$
$132$		0			0
$133$	16.7055			1.44855
$134$	17.8920			1.54563
$135$		0			0
$136$	−0.637430	+	1.10406i	−0.0546592	+	0.0946725i
$137$	4.97910			0.425394			0.212697	−	0.977118i	$-0.431775\pi$
$137$	4.97910			0.425394			0.212697	+	0.977118i	$0.431775\pi$
$138$		0			0
$139$	10.7852	−	18.6806i	0.914792	−	1.58447i	0.107587	−	0.994196i	$-0.465688\pi$
$139$	10.7852	−	18.6806i	0.914792	−	1.58447i	0.807205	−	0.590271i	$-0.200979\pi$
$140$	2.90785			0.245758
$141$		0			0
$142$	22.7610			1.91006
$143$	−4.63900	+	8.03499i	−0.387933	+	0.671920i
$144$		0			0
$145$	−0.107949			−0.00896469
$146$	−4.97793	−	8.62202i	−0.411976	−	0.713563i
$147$		0			0
$148$	0.195469	−	0.338563i	0.0160675	−	0.0278297i
$149$	5.57806	+	9.66148i	0.456972	+	0.791499i	0.998799	−	0.0489908i	$-0.0156005\pi$
$149$	5.57806	+	9.66148i	0.456972	+	0.791499i	−0.541827	+	0.840490i	$0.682267\pi$
$150$		0			0
$151$	5.25416	+	9.10047i	0.427577	+	0.740586i	0.996657	−	0.0816966i	$-0.0260338\pi$
$151$	5.25416	+	9.10047i	0.427577	+	0.740586i	−0.569080	+	0.822282i	$0.692701\pi$
$152$	−1.10391	−	1.91203i	−0.0895392	−	0.155086i
$153$		0			0
$154$	7.46995	−	12.9383i	0.601946	−	1.04260i
$155$	2.99902	−	5.19445i	0.240887	−	0.417229i
$156$		0			0
$157$	−0.0579263	−	0.100331i	−0.00462302	−	0.00800730i	0.863705	−	0.503998i	$-0.168138\pi$
$157$	−0.0579263	−	0.100331i	−0.00462302	−	0.00800730i	−0.868328	+	0.495991i	$0.834805\pi$
$158$	10.7411	+	18.6041i	0.854514	+	1.48006i
$159$		0			0
$160$	−2.71920	−	4.70979i	−0.214972	−	0.372342i
$161$	−2.05037	+	3.55134i	−0.161592	+	0.279885i
$162$		0			0
$163$	−7.68754	−	13.3152i	−0.602134	−	1.04293i	−0.992497	−	0.122266i	$-0.960984\pi$
$163$	−7.68754	−	13.3152i	−0.602134	−	1.04293i	0.390363	−	0.920661i	$-0.372349\pi$
$164$	−15.8116			−1.23468
$165$		0			0
$166$	−12.7869	+	22.1476i	−0.992457	+	1.71899i
$167$	−9.52412			−0.736999			−0.368499	−	0.929628i	$-0.620128\pi$
$167$	−9.52412			−0.736999			−0.368499	+	0.929628i	$0.620128\pi$
$168$		0			0
$169$	−5.43889			−0.418376
$170$	2.92203	−	5.06111i	0.224110	−	0.388170i
$171$		0			0
$172$	16.2085			1.23589
$173$	1.72232	−	2.98315i	0.130946	−	0.226805i	−0.793096	−	0.609097i	$-0.791532\pi$
$173$	1.72232	−	2.98315i	0.130946	−	0.226805i	0.924041	+	0.382292i	$0.124865\pi$
$174$		0			0
$175$	−10.1891			−0.770221
$176$	−14.4447			−1.08881
$177$		0			0
$178$	14.9083	+	25.8220i	1.11743	+	1.93544i
$179$	3.53528			0.264240			0.132120	−	0.991234i	$-0.457822\pi$
$179$	3.53528			0.264240			0.132120	+	0.991234i	$0.457822\pi$
$180$		0			0
$181$	−0.0941661	−	0.163100i	−0.00699931	−	0.0121232i	0.862505	−	0.506049i	$-0.168895\pi$
$181$	−0.0941661	−	0.163100i	−0.00699931	−	0.0121232i	−0.869504	+	0.493926i	$0.835561\pi$
$182$	−12.1753			−0.902491
$183$		0			0
$184$	0.541958			0.0399537
$185$	0.0737413	−	0.127724i	0.00542157	−	0.00939043i
$186$		0			0
$187$	−7.20971	−	12.4876i	−0.527226	−	0.913183i
$188$	−9.02112	−	15.6250i	−0.657933	−	1.13957i
$189$		0			0
$190$	5.06043	+	8.76493i	0.367122	+	0.635875i
$191$	−2.10325	+	3.64294i	−0.152186	+	0.263594i	−0.932031	−	0.362379i	$-0.881965\pi$
$191$	−2.10325	+	3.64294i	−0.152186	+	0.263594i	0.779845	+	0.625973i	$0.215298\pi$
$192$		0			0
$193$	6.06996			0.436925			0.218463	−	0.975845i	$-0.429896\pi$
$193$	6.06996			0.436925			0.218463	+	0.975845i	$0.429896\pi$
$194$	−4.19927	+	7.27335i	−0.301490	+	0.522196i
$195$		0			0
$196$	−3.52028			−0.251448
$197$	1.99742			0.142310			0.0711552	−	0.997465i	$-0.477331\pi$
$197$	1.99742			0.142310			0.0711552	+	0.997465i	$0.477331\pi$
$198$		0			0
$199$	−3.21090	+	5.56145i	−0.227615	+	0.394241i	−0.957101	−	0.289755i	$-0.906426\pi$
$199$	−3.21090	+	5.56145i	−0.227615	+	0.394241i	0.729486	+	0.683996i	$0.239759\pi$
$200$	0.673300	+	1.16619i	0.0476095	+	0.0824621i
$201$		0			0
$202$	−5.21392	+	9.03077i	−0.366850	+	0.635403i
$203$	−0.349523			−0.0245317
$204$		0			0
$205$	−5.96496			−0.416611
$206$	12.6326	+	15.3868i	0.880155	+	1.07205i
$207$		0			0
$208$	5.88587	+	10.1946i	0.408112	+	0.706870i
$209$	24.9718			1.72734
$210$		0			0
$211$	9.41453	−	16.3064i	0.648123	−	1.12258i	−0.335448	−	0.942059i	$-0.608888\pi$
$211$	9.41453	−	16.3064i	0.648123	−	1.12258i	0.983571	−	0.180523i	$-0.0577790\pi$
$212$	8.10060	+	14.0306i	0.556351	+	0.963629i
$213$		0			0
$214$	36.2404			2.47734
$215$	6.11471			0.417020
$216$		0			0
$217$	9.71036	−	16.8188i	0.659182	−	1.14174i
$218$	0.0729164	−	0.126295i	0.00493852	−	0.00855377i
$219$		0			0
$220$	4.34672			0.293056
$221$	−5.87555	+	10.1768i	−0.395233	+	0.684563i
$222$		0			0
$223$	7.54897	−	13.0752i	0.505516	−	0.875580i	−0.494463	−	0.869198i	$-0.664635\pi$
$223$	7.54897	−	13.0752i	0.505516	−	0.875580i	0.999980	−	0.00638141i	$-0.00203128\pi$
$224$	−8.80435	−	15.2496i	−0.588265	−	1.01891i
$225$		0			0
$226$	−14.8189	−	25.6672i	−0.985741	−	1.70735i
$227$	−13.2184	+	22.8950i	−0.877338	+	1.51959i	−0.0230870	+	0.999733i	$0.507349\pi$
$227$	−13.2184	+	22.8950i	−0.877338	+	1.51959i	−0.854251	+	0.519861i	$0.825984\pi$
$228$		0			0
$229$	−10.1564			−0.671154			−0.335577	−	0.942013i	$-0.608931\pi$
$229$	−10.1564			−0.671154			−0.335577	+	0.942013i	$0.608931\pi$
$230$	−2.48438			−0.163815
$231$		0			0
$232$	0.0230967	+	0.0400047i	0.00151637	+	0.00262644i
$233$	−12.8236			−0.840104			−0.420052	−	0.907500i	$-0.637988\pi$
$233$	−12.8236			−0.840104			−0.420052	+	0.907500i	$0.637988\pi$
$234$		0			0
$235$	−3.40324	−	5.89458i	−0.222003	−	0.384520i
$236$	−14.7574			−0.960622
$237$		0			0
$238$	9.46110	−	16.3871i	0.613272	−	1.06222i
$239$	−3.41456	+	5.91420i	−0.220870	+	0.382558i	−0.955072	−	0.296373i	$-0.904223\pi$
$239$	−3.41456	+	5.91420i	−0.220870	+	0.382558i	0.734203	+	0.678930i	$0.237556\pi$
$240$		0			0
$241$	10.2289	+	17.7170i	0.658903	+	1.14125i	0.980900	+	0.194513i	$0.0623126\pi$
$241$	10.2289	+	17.7170i	0.658903	+	1.14125i	−0.321997	+	0.946741i	$0.604354\pi$
$242$	0.377378	−	0.653637i	0.0242587	−	0.0420174i
$243$		0			0
$244$	2.45003	−	4.24357i	0.156847	−	0.271667i
$245$	−1.32803			−0.0848450
$246$		0			0
$247$	−10.1754	−	17.6243i	−0.647445	−	1.12141i
$248$	−2.56667			−0.162984
$249$		0			0
$250$	−6.50523	−	11.2674i	−0.411427	−	0.712612i
$251$	−2.72200	+	4.71464i	−0.171811	+	0.297585i	−0.939053	−	0.343772i	$-0.888295\pi$
$251$	−2.72200	+	4.71464i	−0.171811	+	0.297585i	0.767242	+	0.641358i	$0.221629\pi$
$252$		0			0
$253$	−3.06493	+	5.30862i	−0.192691	+	0.333750i
$254$	13.5256	+	23.4270i	0.848672	+	1.46994i
$255$		0			0
$256$	−9.07460	+	15.7177i	−0.567163	+	0.982354i
$257$	2.41205	−	4.17779i	0.150460	−	0.260604i	−0.780937	−	0.624610i	$-0.785258\pi$
$257$	2.41205	−	4.17779i	0.150460	−	0.260604i	0.931397	+	0.364006i	$0.118591\pi$
$258$		0			0
$259$	0.238763	−	0.413550i	0.0148360	−	0.0256967i
$260$	−1.77118	−	3.06777i	−0.109844	−	0.190255i
$261$		0			0
$262$	3.51693	−	6.09150i	0.217277	−	0.376334i
$263$	2.83991	+	4.91888i	0.175117	+	0.303311i	0.940202	−	0.340618i	$-0.110636\pi$
$263$	2.83991	+	4.91888i	0.175117	+	0.303311i	−0.765085	+	0.643929i	$0.777303\pi$
$264$		0			0
$265$	3.05597	+	5.29310i	0.187727	+	0.325152i
$266$	16.3849	+	28.3795i	1.00462	+	1.74006i
$267$		0			0
$268$	8.42750	+	14.5969i	0.514791	+	0.891645i
$269$	−6.75146	+	11.6939i	−0.411644	+	0.712988i	−0.995070	−	0.0991785i	$-0.968379\pi$
$269$	−6.75146	+	11.6939i	−0.411644	+	0.712988i	0.583426	+	0.812166i	$0.301712\pi$
$270$		0			0
$271$	−5.77674	+	10.0056i	−0.350912	+	0.607797i	−0.986409	−	0.164306i	$-0.947462\pi$
$271$	−5.77674	+	10.0056i	−0.350912	+	0.607797i	0.635498	+	0.772103i	$0.280795\pi$
$272$	−18.2951			−1.10930
$273$		0			0
$274$	4.88354	+	8.45853i	0.295025	+	0.510999i
$275$	−15.2308			−0.918454
$276$		0			0
$277$	2.65147	−	4.59249i	0.159312	−	0.275936i	−0.775309	−	0.631582i	$-0.782406\pi$
$277$	2.65147	−	4.59249i	0.159312	−	0.275936i	0.934621	+	0.355646i	$0.115739\pi$
$278$	42.3129			2.53776
$279$		0			0
$280$	−0.234712	−	0.406533i	−0.0140267	−	0.0242950i
$281$	−11.0611	−	19.1584i	−0.659851	−	1.14290i	−0.980654	−	0.195750i	$-0.937286\pi$
$281$	−11.0611	−	19.1584i	−0.659851	−	1.14290i	0.320802	−	0.947146i	$-0.396047\pi$
$282$		0			0
$283$	2.91799	+	5.05411i	0.173457	+	0.300436i	0.939626	−	0.342203i	$-0.111173\pi$
$283$	2.91799	+	5.05411i	0.173457	+	0.300436i	−0.766169	+	0.642639i	$0.777840\pi$
$284$	10.7209	+	18.5691i	0.636168	+	1.10188i
$285$		0			0
$286$	−18.1999			−1.07618
$287$	−19.3136			−1.14005
$288$		0			0
$289$	−0.631498	−	1.09379i	−0.0371469	−	0.0643404i
$290$	−0.105877	−	0.183385i	−0.00621733	−	0.0107687i
$291$		0			0
$292$	4.68942	−	8.12231i	0.274428	−	0.475322i
$293$	−0.148936	−	0.257965i	−0.00870096	−	0.0150705i	0.861642	−	0.507516i	$-0.169436\pi$
$293$	−0.148936	−	0.257965i	−0.00870096	−	0.0150705i	−0.870343	+	0.492446i	$0.836103\pi$
$294$		0			0
$295$	−5.56725			−0.324138
$296$	−0.0631104			−0.00366822
$297$		0			0
$298$	−10.9420	+	18.9521i	−0.633852	+	1.09786i
$299$	4.99553			0.288899
$300$		0			0
$301$	19.7985			1.14117
$302$	−10.3066	+	17.8516i	−0.593079	+	1.02724i
$303$		0			0
$304$	15.8419	−	27.4389i	0.908593	−	1.57373i
$305$	0.924278	−	1.60090i	0.0529240	−	0.0916671i
$306$		0			0
$307$	16.3054	+	28.2419i	0.930601	+	1.61185i	0.782296	+	0.622906i	$0.214048\pi$
$307$	16.3054	+	28.2419i	0.930601	+	1.61185i	0.148305	+	0.988942i	$0.452618\pi$
$308$	14.0740			0.801942
$309$		0			0
$310$	11.7658			0.668254
$311$	−8.08000	−	13.9950i	−0.458175	−	0.793582i	0.540690	−	0.841222i	$-0.318163\pi$
$311$	−8.08000	−	13.9950i	−0.458175	−	0.793582i	−0.998865	+	0.0476401i	$0.984830\pi$
$312$		0			0
$313$	10.1679	−	17.6112i	0.574721	−	0.995446i	−0.421351	−	0.906898i	$-0.638444\pi$
$313$	10.1679	−	17.6112i	0.574721	−	0.995446i	0.996072	−	0.0885481i	$-0.0282227\pi$
$314$	0.113629	−	0.196811i	0.00641245	−	0.0111067i
$315$		0			0
$316$	−10.1186	+	17.5259i	−0.569213	+	0.985906i
$317$	−14.2068			−0.797932			−0.398966	−	0.916966i	$-0.630631\pi$
$317$	−14.2068			−0.797932			−0.398966	+	0.916966i	$0.630631\pi$
$318$		0			0
$319$	−0.522475			−0.0292530
$320$	2.34957	−	4.06957i	0.131345	−	0.227496i
$321$		0			0
$322$	−8.04405			−0.448277
$323$	31.6282			1.75984
$324$		0			0
$325$	6.20619	+	10.7494i	0.344257	+	0.596271i
$326$	15.0800	−	26.1193i	0.835202	−	1.44661i
$327$		0			0
$328$	1.27626	+	2.21054i	0.0704695	+	0.122057i
$329$	−11.0192	−	19.0858i	−0.607506	−	1.05223i
$330$		0			0
$331$	−23.4377			−1.28825			−0.644125	−	0.764920i	$-0.722779\pi$
$331$	−23.4377			−1.28825			−0.644125	+	0.764920i	$0.722779\pi$
$332$	−24.0916			−1.32220
$333$		0			0
$334$	−9.34132	−	16.1796i	−0.511134	−	0.885310i
$335$	3.17929	+	5.50670i	0.173703	+	0.300863i
$336$		0			0
$337$	0.494257	+	0.856078i	0.0269239	+	0.0466335i	0.879173	−	0.476502i	$-0.158095\pi$
$337$	0.494257	+	0.856078i	0.0269239	+	0.0466335i	−0.852250	+	0.523136i	$0.824762\pi$
$338$	−5.33450	−	9.23962i	−0.290158	−	0.502569i
$339$		0			0
$340$	5.50536			0.298570
$341$	14.5153	−	25.1412i	0.786046	−	1.36147i
$342$		0			0
$343$	−20.1005			−1.08532
$344$	−1.30830	−	2.26604i	−0.0705387	−	0.122177i
$345$		0			0
$346$	6.75707			0.363262
$347$	−6.81282	+	11.8002i	−0.365731	+	0.633466i	−0.988893	−	0.148627i	$-0.952514\pi$
$347$	−6.81282	+	11.8002i	−0.365731	+	0.633466i	0.623162	+	0.782093i	$0.285848\pi$
$348$		0			0
$349$	0.860505	−	1.49044i	0.0460618	−	0.0797813i	−0.842075	−	0.539360i	$-0.818666\pi$
$349$	0.860505	−	1.49044i	0.0460618	−	0.0797813i	0.888137	+	0.459579i	$0.152000\pi$
$350$	−9.99350	−	17.3093i	−0.534175	−	0.925218i
$351$		0			0
$352$	−13.1609	−	22.7954i	−0.701480	−	1.21500i
$353$	−5.99095	−	10.3766i	−0.318866	−	0.552292i	0.661386	−	0.750046i	$-0.269969\pi$
$353$	−5.99095	−	10.3766i	−0.318866	−	0.552292i	−0.980252	+	0.197754i	$0.936635\pi$
$354$		0			0
$355$	4.04449	+	7.00526i	0.214659	+	0.371801i
$356$	−14.0443	+	24.3254i	−0.744346	+	1.28924i
$357$		0			0
$358$	3.46743	+	6.00576i	0.183259	+	0.317414i
$359$	10.7358	−	18.5950i	0.566616	−	0.981408i	−0.430281	−	0.902695i	$-0.641586\pi$
$359$	10.7358	−	18.5950i	0.566616	−	0.981408i	0.996897	−	0.0787131i	$-0.0250811\pi$
$360$		0			0
$361$	−17.8871	+	30.9814i	−0.941428	+	1.63060i
$362$	0.184717	−	0.319940i	0.00970853	−	0.0168157i
$363$		0			0
$364$	−5.73481	−	9.93298i	−0.300586	−	0.520630i
$365$	1.76910	−	3.06416i	0.0925987	−	0.160386i
$366$		0			0
$367$	2.83310	−	4.90707i	0.147887	−	0.256147i	−0.782560	−	0.622576i	$-0.786086\pi$
$367$	2.83310	−	4.90707i	0.147887	−	0.256147i	0.930446	+	0.366429i	$0.119420\pi$
$368$	3.88872	+	6.73547i	0.202714	+	0.351110i
$369$		0			0
$370$	0.289304			0.0150402
$371$	9.89477	+	17.1382i	0.513711	+	0.889773i
$372$		0			0
$373$	13.6125			0.704830			0.352415	−	0.935844i	$-0.385361\pi$
$373$	13.6125			0.704830			0.352415	+	0.935844i	$0.385361\pi$
$374$	14.1427	−	24.4958i	0.731300	−	1.26665i
$375$		0			0
$376$	−1.45631	+	2.52240i	−0.0751033	+	0.130083i
$377$	0.212895	+	0.368746i	0.0109647	+	0.0189914i
$378$		0			0
$379$	1.04345	−	1.80732i	0.0535987	−	0.0928356i	−0.837981	−	0.545699i	$-0.816264\pi$
$379$	1.04345	−	1.80732i	0.0535987	−	0.0928356i	0.891580	+	0.452863i	$0.149597\pi$
$380$	−4.76714	+	8.25694i	−0.244549	+	0.423572i
$381$		0			0
$382$	−8.25152			−0.422185
$383$	−7.02803	−	12.1729i	−0.359116	−	0.622006i	0.628698	−	0.777650i	$-0.283588\pi$
$383$	−7.02803	−	12.1729i	−0.359116	−	0.622006i	−0.987813	+	0.155643i	$0.950255\pi$
$384$		0			0
$385$	5.30946			0.270595
$386$	5.95345	+	10.3117i	0.303023	+	0.524851i
$387$		0			0
$388$	−7.91179			−0.401660
$389$	36.7634			1.86398			0.931990	−	0.362484i	$-0.118071\pi$
$389$	36.7634			1.86398			0.931990	+	0.362484i	$0.118071\pi$
$390$		0			0
$391$	−3.88191	+	6.72366i	−0.196316	+	0.340030i
$392$	0.284145	+	0.492153i	0.0143515	+	0.0248575i
$393$		0			0
$394$	1.95908	+	3.39323i	0.0986972	+	0.170949i
$395$	−3.81725	+	6.61167i	−0.192067	+	0.332669i
$396$		0			0
$397$	0.450913	−	0.781004i	0.0226307	−	0.0391975i	−0.854488	−	0.519471i	$-0.826129\pi$
$397$	0.450913	−	0.781004i	0.0226307	−	0.0391975i	0.877119	+	0.480273i	$0.159462\pi$
$398$	−12.5971			−0.631435
$399$		0			0
$400$	−9.66229	+	16.7356i	−0.483114	+	0.836779i
$401$	6.30694	−	10.9239i	0.314953	−	0.545515i	−0.664474	−	0.747311i	$-0.731344\pi$
$401$	6.30694	−	10.9239i	0.314953	−	0.545515i	0.979428	+	0.201796i	$0.0646778\pi$
$402$		0			0
$403$	−23.6584			−1.17851
$404$	−9.82347			−0.488736
$405$		0			0
$406$	−0.342814	−	0.593772i	−0.0170136	−	0.0294684i
$407$	0.356908	−	0.618183i	0.0176913	−	0.0306422i
$408$		0			0
$409$	−10.2801			−0.508321			−0.254160	−	0.967162i	$-0.581799\pi$
$409$	−10.2801			−0.508321			−0.254160	+	0.967162i	$0.581799\pi$
$410$	−5.85047	−	10.1333i	−0.288934	−	0.500449i
$411$		0			0
$412$	−6.60283	+	17.5536i	−0.325298	+	0.864804i
$413$	−18.0259			−0.886997
$414$		0			0
$415$	−9.08864			−0.446144
$416$	−10.7255	+	18.5771i	−0.525861	+	0.910818i
$417$		0			0
$418$	24.4925	+	42.4223i	1.19797	+	2.07494i
$419$	7.48381	−	12.9623i	0.365608	−	0.633252i	−0.623266	−	0.782010i	$-0.714194\pi$
$419$	7.48381	−	12.9623i	0.365608	−	0.633252i	0.988874	+	0.148759i	$0.0475277\pi$
$420$		0			0
$421$	32.7320			1.59526			0.797631	−	0.603146i	$-0.206086\pi$
$421$	32.7320			1.59526			0.797631	+	0.603146i	$0.206086\pi$
$422$	36.9353			1.79798
$423$		0			0
$424$	1.30771	−	2.26501i	0.0635078	−	0.109999i
$425$	−19.2907			−0.935736
$426$		0			0
$427$	2.99267	−	5.18346i	0.144826	−	0.250845i
$428$	17.0700	+	29.5661i	0.825109	+	1.42913i
$429$		0			0
$430$	5.99735	+	10.3877i	0.289218	+	0.500940i
$431$	−20.4763	−	35.4661i	−0.986311	−	1.70834i	−0.635960	−	0.771722i	$-0.719396\pi$
$431$	−20.4763	−	35.4661i	−0.986311	−	1.70834i	−0.350351	−	0.936618i	$-0.613938\pi$
$432$		0			0
$433$	8.04807	−	13.9397i	0.386766	−	0.669898i	−0.605247	−	0.796038i	$-0.706926\pi$
$433$	8.04807	−	13.9397i	0.386766	−	0.669898i	0.992012	+	0.126140i	$0.0402589\pi$
$434$	38.0959			1.82866
$435$		0			0
$436$	0.137381			0.00657934
$437$	−6.72276	−	11.6442i	−0.321593	−	0.557016i
$438$		0			0
$439$	−21.5401			−1.02805			−0.514026	−	0.857775i	$-0.671847\pi$
$439$	−21.5401			−1.02805			−0.514026	+	0.857775i	$0.671847\pi$
$440$	−0.350853	−	0.607695i	−0.0167262	−	0.0289707i
$441$		0			0
$442$	−23.0511			−1.09643
$443$	−5.99252			−0.284713			−0.142357	−	0.989815i	$-0.545468\pi$
$443$	−5.99252			−0.284713			−0.142357	+	0.989815i	$0.545468\pi$
$444$		0			0
$445$	−5.29824	+	9.17683i	−0.251161	+	0.435023i
$446$	29.6163			1.40237
$447$		0			0
$448$	7.60754	−	13.1766i	0.359422	−	0.622538i
$449$	−26.3745			−1.24469			−0.622345	−	0.782743i	$-0.713820\pi$
$449$	−26.3745			−1.24469			−0.622345	+	0.782743i	$0.713820\pi$
$450$		0			0
$451$	−28.8705			−1.35946
$452$	13.9601	−	24.1796i	0.656627	−	1.13731i
$453$		0			0
$454$	−51.8589			−2.43386
$455$	−2.16347	−	3.74724i	−0.101425	−	0.175674i
$456$		0			0
$457$	11.8463	−	20.5184i	0.554147	−	0.959811i	−0.443822	−	0.896115i	$-0.646378\pi$
$457$	11.8463	−	20.5184i	0.554147	−	0.959811i	0.997969	−	0.0636962i	$-0.0202889\pi$
$458$	−9.96146	−	17.2538i	−0.465468	−	0.806215i
$459$		0			0
$460$	−1.17020	−	2.02684i	−0.0545607	−	0.0945020i
$461$	−18.5284	−	32.0921i	−0.862952	−	1.49468i	−0.869067	−	0.494695i	$-0.835280\pi$
$461$	−18.5284	−	32.0921i	−0.862952	−	1.49468i	0.00611521	−	0.999981i	$-0.498053\pi$
$462$		0			0
$463$	3.39033	−	5.87223i	0.157562	−	0.272906i	−0.776427	−	0.630207i	$-0.782970\pi$
$463$	3.39033	−	5.87223i	0.157562	−	0.272906i	0.933989	+	0.357302i	$0.116303\pi$
$464$	−0.331453	+	0.574093i	−0.0153873	+	0.0266516i
$465$		0			0
$466$	−12.5775	−	21.7849i	−0.582641	−	1.00916i
$467$	−10.1905	−	17.6505i	−0.471560	−	0.816766i	0.527911	−	0.849300i	$-0.322976\pi$
$467$	−10.1905	−	17.6505i	−0.471560	−	0.816766i	−0.999471	+	0.0325342i	$0.989642\pi$
$468$		0			0
$469$	10.2941	+	17.8299i	0.475336	+	0.823306i
$470$	6.67584	−	11.5629i	0.307933	−	0.533356i
$471$		0			0
$472$	1.19116	+	2.06316i	0.0548277	+	0.0949644i
$473$	29.5952			1.36079
$474$		0			0
$475$	16.7040	−	28.9322i	0.766432	−	1.32750i
$476$	17.8255			0.817032
$477$		0			0
$478$	−13.3961			−0.612723
$479$	18.5258	−	32.0876i	0.846466	−	1.46612i	−0.0378768	−	0.999282i	$-0.512059\pi$
$479$	18.5258	−	32.0876i	0.846466	−	1.46612i	0.884342	−	0.466839i	$-0.154607\pi$
$480$		0			0
$481$	−0.581724			−0.0265243
$482$	−20.0652	+	34.7539i	−0.913944	+	1.58300i
$483$		0			0
$484$	0.711012			0.0323187
$485$	−2.98474			−0.135530
$486$		0			0
$487$	−1.28914	−	2.23285i	−0.0584164	−	0.101180i	0.835338	−	0.549736i	$-0.185272\pi$
$487$	−1.28914	−	2.23285i	−0.0584164	−	0.101180i	−0.893755	+	0.448556i	$0.851938\pi$
$488$	−0.791031			−0.0358083
$489$		0			0
$490$	−1.30254	−	2.25607i	−0.0588429	−	0.101919i
$491$	0.108509			0.00489695			0.00244848	−	0.999997i	$-0.499221\pi$
$491$	0.108509			0.00489695			0.00244848	+	0.999997i	$0.499221\pi$
$492$		0			0
$493$	−0.661743			−0.0298034
$494$	19.9602	−	34.5720i	0.898051	−	1.55547i
$495$		0			0
$496$	−18.4167	−	31.8986i	−0.826933	−	1.43229i
$497$	13.0954	+	22.6820i	0.587410	+	1.01742i
$498$		0			0
$499$	−13.6784	−	23.6917i	−0.612330	−	1.06059i	−0.990847	−	0.134992i	$-0.956899\pi$
$499$	−13.6784	−	23.6917i	−0.612330	−	1.06059i	0.378517	−	0.925594i	$-0.376434\pi$
$500$	6.12821	−	10.6144i	0.274062	−	0.474689i
$501$		0			0
$502$	−10.6790			−0.476628
$503$	−18.6031	+	32.2215i	−0.829470	+	1.43668i	0.0689840	+	0.997618i	$0.478024\pi$
$503$	−18.6031	+	32.2215i	−0.829470	+	1.43668i	−0.898454	+	0.439067i	$0.855309\pi$
$504$		0			0
$505$	−3.70593			−0.164912
$506$	−12.0244			−0.534551
$507$		0			0
$508$	−12.7417	+	22.0693i	−0.565322	+	0.979166i
$509$	16.5079	+	28.5925i	0.731698	+	1.26734i	0.956157	+	0.292855i	$0.0946052\pi$
$509$	16.5079	+	28.5925i	0.731698	+	1.26734i	−0.224459	+	0.974484i	$0.572061\pi$
$510$		0			0
$511$	5.72806	−	9.92129i	0.253395	−	0.438892i
$512$	−30.8424			−1.36306
$513$		0			0
$514$	9.46302			0.417396
$515$	−2.49094	+	6.62214i	−0.109764	+	0.291806i
$516$		0			0
$517$	−16.4717	−	28.5298i	−0.724424	−	1.25474i
$518$	0.936721			0.0411571
$519$		0			0
$520$	−0.285927	+	0.495241i	−0.0125387	+	0.0217177i
$521$	2.38979	+	4.13924i	0.104699	+	0.181344i	0.913615	−	0.406580i	$-0.133279\pi$
$521$	2.38979	+	4.13924i	0.104699	+	0.181344i	−0.808916	+	0.587924i	$0.799945\pi$
$522$		0			0
$523$	−14.8507			−0.649374			−0.324687	−	0.945822i	$-0.605259\pi$
$523$	−14.8507			−0.649374			−0.324687	+	0.945822i	$0.605259\pi$
$524$	6.62620			0.289467
$525$		0			0
$526$	−5.57081	+	9.64893i	−0.242899	+	0.420713i
$527$	18.3844	−	31.8427i	0.800836	−	1.38709i
$528$		0			0
$529$	−19.6995			−0.856501
$530$	−5.99463	+	10.3830i	−0.260390	+	0.451009i
$531$		0			0
$532$	−15.4353	+	26.7347i	−0.669204	+	1.15910i
$533$	11.7640	+	20.3758i	0.509555	+	0.882575i
$534$		0			0
$535$	6.43970	+	11.1539i	0.278412	+	0.482224i
$536$	1.36048	−	2.35642i	0.0587637	−	0.101782i
$537$		0			0
$538$	−26.4875			−1.14196
$539$	−6.42769			−0.276860
$540$		0			0
$541$	−4.02978	−	6.97978i	−0.173254	−	0.300084i	0.766302	−	0.642481i	$-0.222095\pi$
$541$	−4.02978	−	6.97978i	−0.173254	−	0.300084i	−0.939556	+	0.342397i	$0.888761\pi$
$542$	−22.6634			−0.973478
$543$		0			0
$544$	−16.6691	−	28.8716i	−0.714680	−	1.23786i
$545$	0.0518272			0.00222003
$546$		0			0
$547$	−12.3695	+	21.4246i	−0.528883	+	0.916051i	0.470550	+	0.882373i	$0.344055\pi$
$547$	−12.3695	+	21.4246i	−0.528883	+	0.916051i	−0.999433	+	0.0336782i	$0.989278\pi$
$548$	−4.60050	+	7.96830i	−0.196524	+	0.340389i
$549$		0			0
$550$	−14.9385	−	25.8743i	−0.636980	−	1.10328i
$551$	0.573009	−	0.992481i	0.0244110	−	0.0422811i
$552$		0			0
$553$	−12.3597	+	21.4076i	−0.525587	+	0.910343i
$554$	10.4023			0.441953
$555$		0			0
$556$	19.9303	+	34.5203i	0.845233	+	1.46399i
$557$	11.5558			0.489636			0.244818	−	0.969569i	$-0.421272\pi$
$557$	11.5558			0.489636			0.244818	+	0.969569i	$0.421272\pi$
$558$		0			0
$559$	−12.0593	−	20.8873i	−0.510055	−	0.883441i
$560$	3.36827	−	5.83401i	0.142335	−	0.246532i
$561$		0			0
$562$	21.6976	−	37.5814i	0.915260	−	1.58528i
$563$	−16.3110	−	28.2516i	−0.687429	−	1.19066i	−0.972667	−	0.232205i	$-0.925406\pi$
$563$	−16.3110	−	28.2516i	−0.687429	−	1.19066i	0.285238	−	0.958457i	$-0.407927\pi$
$564$		0			0
$565$	5.26648	−	9.12180i	0.221562	−	0.383757i
$566$	−5.72397	+	9.91420i	−0.240596	+	0.416725i
$567$		0			0
$568$	1.73071	−	2.99768i	0.0726189	−	0.125780i
$569$	−13.0508	−	22.6046i	−0.547116	−	0.947633i	−0.998470	−	0.0552885i	$-0.982392\pi$
$569$	−13.0508	−	22.6046i	−0.547116	−	0.947633i	0.451354	−	0.892345i	$-0.350941\pi$
$570$		0			0
$571$	0.427805	−	0.740980i	0.0179031	−	0.0310090i	−0.856935	−	0.515424i	$-0.827634\pi$
$571$	0.427805	−	0.740980i	0.0179031	−	0.0310090i	0.874838	+	0.484415i	$0.160968\pi$
$572$	−8.57252	−	14.8480i	−0.358435	−	0.620828i
$573$		0			0
$574$	−18.9429	−	32.8101i	−0.790663	−	1.36947i
$575$	4.10035	+	7.10202i	0.170996	+	0.296175i
$576$		0			0
$577$	23.6753	+	41.0069i	0.985616	+	1.70714i	0.639165	+	0.769070i	$0.279280\pi$
$577$	23.6753	+	41.0069i	0.985616	+	1.70714i	0.346451	+	0.938068i	$0.387387\pi$
$578$	1.23875	−	2.14559i	0.0515254	−	0.0892446i
$579$		0			0
$580$	0.0997409	−	0.172756i	0.00414152	−	0.00717332i
$581$	−29.4276			−1.22086
$582$		0			0
$583$	14.7909	+	25.6186i	0.612577	+	1.06101i
$584$	−1.51406			−0.0626521
$585$		0			0
$586$	0.292155	−	0.506028i	0.0120688	−	0.0209038i
$587$	−8.15205			−0.336471			−0.168236	−	0.985747i	$-0.553807\pi$
$587$	−8.15205			−0.336471			−0.168236	+	0.985747i	$0.553807\pi$
$588$		0			0
$589$	31.8384	+	55.1457i	1.31188	+	2.27224i
$590$	−5.46039	−	9.45768i	−0.224801	−	0.389366i
$591$		0			0
$592$	−0.452837	−	0.784337i	−0.0186115	−	0.0322361i
$593$	12.1101	+	20.9753i	0.497301	+	0.861351i	0.999995	−	0.00311334i	$-0.000991008\pi$
$593$	12.1101	+	20.9753i	0.497301	+	0.861351i	−0.502694	+	0.864465i	$0.667658\pi$
$594$		0			0
$595$	6.72473			0.275687
$596$	−20.6156			−0.844450
$597$		0			0
$598$	4.89965	+	8.48644i	0.200362	+	0.347036i
$599$	23.0008	+	39.8386i	0.939788	+	1.62776i	0.765866	+	0.643001i	$0.222311\pi$
$599$	23.0008	+	39.8386i	0.939788	+	1.62776i	0.173922	+	0.984759i	$0.444356\pi$
$600$		0			0
$601$	21.7547	−	37.6802i	0.887392	−	1.53701i	0.0444445	−	0.999012i	$-0.485848\pi$
$601$	21.7547	−	37.6802i	0.887392	−	1.53701i	0.842947	−	0.537996i	$-0.180818\pi$
$602$	19.4185	+	33.6338i	0.791439	+	1.37081i
$603$		0			0
$604$	−19.4186			−0.790130
$605$	0.268231			0.0109051
$606$		0			0
$607$	−9.63441	+	16.6873i	−0.391048	+	0.677316i	−0.992588	−	0.121527i	$-0.961221\pi$
$607$	−9.63441	+	16.6873i	−0.391048	+	0.677316i	0.601540	+	0.798843i	$0.294554\pi$
$608$	57.7355			2.34148
$609$		0			0
$610$	3.62615			0.146819
$611$	−13.4236	+	23.2504i	−0.543061	+	0.940609i
$612$		0			0
$613$	−19.0527	+	33.0003i	−0.769533	+	1.33287i	0.168283	+	0.985739i	$0.446178\pi$
$613$	−19.0527	+	33.0003i	−0.769533	+	1.33287i	−0.937816	+	0.347132i	$0.887156\pi$
$614$	−31.9850	+	55.3996i	−1.29081	+	2.23575i
$615$		0			0
$616$	−1.13601	−	1.96762i	−0.0457710	−	0.0792778i
$617$	−40.7304			−1.63975			−0.819873	−	0.572545i	$-0.805956\pi$
$617$	−40.7304			−1.63975			−0.819873	+	0.572545i	$0.805956\pi$
$618$		0			0
$619$	−29.9769			−1.20487			−0.602437	−	0.798167i	$-0.705803\pi$
$619$	−29.9769			−1.20487			−0.602437	+	0.798167i	$0.705803\pi$
$620$	5.54196	+	9.59895i	0.222570	+	0.385503i
$621$		0			0
$622$	15.8498	−	27.4527i	0.635520	−	1.10075i
$623$	−17.1549	+	29.7132i	−0.687297	+	1.19043i
$624$		0			0
$625$	−8.97313	+	15.5419i	−0.358925	+	0.621677i
$626$	39.8908			1.59436
$627$		0			0
$628$	0.214087			0.00854298
$629$	0.452044	−	0.782963i	0.0180242	−	0.0312188i
$630$		0			0
$631$	28.2997			1.12659			0.563297	−	0.826255i	$-0.309533\pi$
$631$	28.2997			1.12659			0.563297	+	0.826255i	$0.309533\pi$
$632$	3.26694			0.129952
$633$		0			0
$634$	−13.9341	−	24.1346i	−0.553393	−	0.958505i
$635$	−4.80684	+	8.32569i	−0.190754	+	0.330395i
$636$		0			0
$637$	2.61912	+	4.53645i	0.103773	+	0.179741i
$638$	−0.512447	−	0.887583i	−0.0202880	−	0.0351398i
$639$		0			0
$640$	−1.65892			−0.0655746
$641$	30.2448			1.19460			0.597299	−	0.802019i	$-0.296241\pi$
$641$	30.2448			1.19460			0.597299	+	0.802019i	$0.296241\pi$
$642$		0			0
$643$	7.73571	+	13.3986i	0.305067	+	0.528391i	0.977276	−	0.211970i	$-0.0679879\pi$
$643$	7.73571	+	13.3986i	0.305067	+	0.528391i	−0.672210	+	0.740361i	$0.734655\pi$
$644$	−3.78892	−	6.56260i	−0.149304	−	0.258603i
$645$		0			0
$646$	31.0211	+	53.7302i	1.22051	+	2.11398i
$647$	8.50947	+	14.7388i	0.334542	+	0.579443i	0.983397	−	0.181469i	$-0.0580851\pi$
$647$	8.50947	+	14.7388i	0.334542	+	0.579443i	−0.648855	+	0.760912i	$0.724752\pi$
$648$		0			0
$649$	−26.9455			−1.05770
$650$	−12.1741	+	21.0862i	−0.477509	+	0.827069i
$651$		0			0
$652$	28.4119			1.11270
$653$	−11.6712	−	20.2152i	−0.456730	−	0.791080i	0.542056	−	0.840343i	$-0.317646\pi$
$653$	−11.6712	−	20.2152i	−0.456730	−	0.791080i	−0.998786	+	0.0492626i	$0.984313\pi$
$654$		0			0
$655$	2.49975			0.0976733
$656$	−18.3151	+	31.7227i	−0.715085	+	1.23856i
$657$		0			0
$658$	21.6153	−	37.4389i	0.842654	−	1.45952i
$659$	−11.2642	−	19.5102i	−0.438791	−	0.760008i	0.558806	−	0.829299i	$-0.311260\pi$
$659$	−11.2642	−	19.5102i	−0.438791	−	0.760008i	−0.997597	+	0.0692907i	$0.977926\pi$
$660$		0			0
$661$	18.0474	+	31.2590i	0.701962	+	1.21583i	0.967777	+	0.251810i	$0.0810258\pi$
$661$	18.0474	+	31.2590i	0.701962	+	1.21583i	−0.265814	+	0.964024i	$0.585641\pi$
$662$	−22.9878	−	39.8161i	−0.893447	−	1.54749i
$663$		0			0
$664$	1.94460	+	3.36814i	0.0754649	+	0.130709i
$665$	−5.82300	+	10.0857i	−0.225806	+	0.391108i
$666$		0			0
$667$	0.140657	+	0.243626i	0.00544628	+	0.00943323i
$668$	8.79992	−	15.2419i	0.340479	−	0.589727i
$669$		0			0
$670$	−6.23654	+	10.8020i	−0.240939	+	0.417318i
$671$	4.47351	−	7.74835i	0.172698	−	0.299122i
$672$		0			0
$673$	18.2666	+	31.6386i	0.704124	+	1.21958i	0.967007	+	0.254751i	$0.0819934\pi$
$673$	18.2666	+	31.6386i	0.704124	+	1.21958i	−0.262883	+	0.964828i	$0.584673\pi$
$674$	−0.969540	+	1.67929i	−0.0373453	+	0.0646839i
$675$		0			0
$676$	5.02532	−	8.70412i	0.193282	−	0.334774i
$677$	3.83817	+	6.64791i	0.147513	+	0.255500i	0.930308	−	0.366780i	$-0.119540\pi$
$677$	3.83817	+	6.64791i	0.147513	+	0.255500i	−0.782795	+	0.622280i	$0.786206\pi$
$678$		0			0
$679$	−9.66414			−0.370876
$680$	−0.444374	−	0.769679i	−0.0170410	−	0.0295158i
$681$		0			0
$682$	56.9467			2.18060
$683$	4.89847	−	8.48440i	0.187435	−	0.324647i	−0.756959	−	0.653462i	$-0.773316\pi$
$683$	4.89847	−	8.48440i	0.187435	−	0.324647i	0.944394	+	0.328815i	$0.106649\pi$
$684$		0			0
$685$	−1.73555	+	3.00606i	−0.0663120	+	0.114856i
$686$	−19.7147	−	34.1468i	−0.752709	−	1.30373i
$687$		0			0
$688$	18.7749	−	32.5191i	0.715787	−	1.23978i
$689$	12.0539	−	20.8779i	0.459215	−	0.795384i
$690$		0			0
$691$	0.142091			0.00540538			0.00270269	−	0.999996i	$-0.499140\pi$
$691$	0.142091			0.00540538			0.00270269	+	0.999996i	$0.499140\pi$
$692$	3.18272	+	5.51264i	0.120989	+	0.209559i
$693$		0			0
$694$	−26.7282			−1.01459
$695$	7.51875	+	13.0229i	0.285203	+	0.493985i
$696$		0			0
$697$	−36.5660			−1.38504
$698$	3.37595			0.127782
$699$		0			0
$700$	9.41431	−	16.3061i	0.355827	−	0.616311i
$701$	18.8310	+	32.6162i	0.711237	+	1.23190i	0.964393	+	0.264473i	$0.0851979\pi$
$701$	18.8310	+	32.6162i	0.711237	+	1.23190i	−0.253156	+	0.967425i	$0.581469\pi$
$702$		0			0
$703$	0.782858	+	1.35595i	0.0295260	+	0.0511406i
$704$	11.3719	−	19.6967i	0.428595	−	0.742349i
$705$		0			0
$706$	11.7519	−	20.3549i	0.442289	−	0.766067i
$707$	−11.9992			−0.451277
$708$		0			0
$709$	6.53454	−	11.3182i	0.245410	−	0.425062i	−0.716837	−	0.697241i	$-0.754411\pi$
$709$	6.53454	−	11.3182i	0.245410	−	0.425062i	0.962247	+	0.272179i	$0.0877441\pi$
$710$	−7.93372	+	13.7416i	−0.297747	+	0.515713i
$711$		0			0
$712$	4.53443			0.169935
$713$	−15.6308			−0.585379
$714$		0			0
$715$	−3.23401	−	5.60146i	−0.120945	−	0.209483i
$716$	−3.26647	+	5.65769i	−0.122074	+	0.211438i
$717$		0			0
$718$	42.1191			1.57187
$719$	10.6493	+	18.4451i	0.397151	+	0.687886i	0.993373	−	0.114934i	$-0.0366656\pi$
$719$	10.6493	+	18.4451i	0.397151	+	0.687886i	−0.596222	+	0.802819i	$0.703332\pi$
$720$		0			0
$721$	−8.06527	+	21.4415i	−0.300366	+	0.798523i
$722$	−70.1753			−2.61165
$723$		0			0
$724$	0.348023			0.0129342
$725$	−0.349491	+	0.605335i	−0.0129798	+	0.0224816i
$726$		0			0
$727$	−14.2963	−	24.7620i	−0.530221	−	0.918370i	−0.999378	−	0.0352553i	$-0.988776\pi$
$727$	−14.2963	−	24.7620i	−0.530221	−	0.918370i	0.469157	−	0.883115i	$-0.344558\pi$
$728$	−0.925789	+	1.60351i	−0.0343120	+	0.0594302i
$729$		0			0
$730$	6.94056			0.256882
$731$	37.4840			1.38640
$732$		0			0
$733$	19.8115	−	34.3145i	0.731755	−	1.26744i	−0.224378	−	0.974502i	$-0.572035\pi$
$733$	19.8115	−	34.3145i	0.731755	−	1.26744i	0.956133	−	0.292934i	$-0.0946317\pi$
$734$	11.1149			0.410258
$735$		0			0
$736$	−7.08621	+	12.2737i	−0.261201	+	0.452414i
$737$	15.3878	+	26.6525i	0.566817	+	0.981756i
$738$		0			0
$739$	−1.02842	−	1.78128i	−0.0378310	−	0.0655253i	0.846490	−	0.532405i	$-0.178712\pi$
$739$	−1.02842	−	1.78128i	−0.0378310	−	0.0655253i	−0.884321	+	0.466879i	$0.845378\pi$
$740$	0.136268	+	0.236023i	0.00500932	+	0.00867639i
$741$		0			0
$742$	−19.4097	+	33.6186i	−0.712552	+	1.23418i
$743$	−32.4711			−1.19125			−0.595625	−	0.803263i	$-0.703095\pi$
$743$	−32.4711			−1.19125			−0.595625	+	0.803263i	$0.703095\pi$
$744$		0			0
$745$	−7.77731			−0.284938
$746$	13.3513	+	23.1250i	0.488824	+	0.846668i
$747$		0			0
$748$	26.6460			0.974274
$749$	20.8507	+	36.1146i	0.761870	+	1.31960i
$750$		0			0
$751$	47.8245			1.74514			0.872571	−	0.488487i	$-0.162451\pi$
$751$	47.8245			1.74514			0.872571	+	0.488487i	$0.162451\pi$
$752$	−41.7979			−1.52421
$753$		0			0
$754$	−0.417618	+	0.723336i	−0.0152088	+	0.0263423i
$755$	−7.32570			−0.266610
$756$		0			0
$757$	−12.8450	+	22.2482i	−0.466860	+	0.808625i	−0.999283	−	0.0378534i	$-0.987948\pi$
$757$	−12.8450	+	22.2482i	−0.466860	+	0.808625i	0.532424	+	0.846478i	$0.321281\pi$
$758$	4.09371			0.148690
$759$		0			0
$760$	1.53915			0.0558309
$761$	−6.76475	+	11.7169i	−0.245222	+	0.424737i	−0.962194	−	0.272365i	$-0.912194\pi$
$761$	−6.76475	+	11.7169i	−0.245222	+	0.424737i	0.716972	+	0.697102i	$0.245527\pi$
$762$		0			0
$763$	0.167809			0.00607508
$764$	−3.88664	−	6.73187i	−0.140614	−	0.243550i
$765$		0			0
$766$	13.7863	−	23.8785i	0.498118	−	0.862766i
$767$	10.9796	+	19.0173i	0.396451	+	0.686674i
$768$		0			0
$769$	−0.656525	−	1.13713i	−0.0236749	−	0.0410061i	0.853945	−	0.520363i	$-0.174203\pi$
$769$	−0.656525	−	1.13713i	−0.0236749	−	0.0410061i	−0.877620	+	0.479357i	$0.840870\pi$
$770$	5.20755	+	9.01975i	0.187667	+	0.325049i
$771$		0			0
$772$	−5.60841	+	9.71405i	−0.201851	+	0.349616i
$773$	−14.4574	+	25.0409i	−0.519995	+	0.900658i	0.479735	+	0.877414i	$0.340733\pi$
$773$	−14.4574	+	25.0409i	−0.519995	+	0.900658i	−0.999730	+	0.0232442i	$0.992600\pi$
$774$		0			0
$775$	−19.4189	−	33.6346i	−0.697548	−	1.20819i
$776$	0.638613	+	1.10611i	0.0229249	+	0.0397070i
$777$		0			0
$778$	36.0578	+	62.4540i	1.29273	+	2.23908i
$779$	31.6628	−	54.8417i	1.13444	−	1.96491i
$780$		0			0
$781$	19.5753	+	33.9055i	0.700461	+	1.21323i
$782$	−15.2296			−0.544609
$783$		0			0
$784$	−4.07766	+	7.06271i	−0.145631	+	0.252240i
$785$	0.0807647			0.00288262
$786$		0			0
$787$	0.226893			0.00808787			0.00404394	−	0.999992i	$-0.498713\pi$
$787$	0.226893			0.00808787			0.00404394	+	0.999992i	$0.498713\pi$
$788$	−1.84554	+	3.19657i	−0.0657447	+	0.113873i
$789$		0			0
$790$	−14.9759			−0.532820
$791$	17.0520	−	29.5350i	0.606301	−	1.05014i
$792$		0			0
$793$	−7.29138			−0.258924
$794$	1.76903			0.0627806
$795$		0			0
$796$	−5.93350	−	10.2771i	−0.210307	−	0.364263i
$797$	−46.1439			−1.63450			−0.817251	−	0.576282i	$-0.804503\pi$
$797$	−46.1439			−1.63450			−0.817251	+	0.576282i	$0.804503\pi$
$798$		0			0
$799$	−20.8623	−	36.1346i	−0.738056	−	1.27835i
$800$	−35.2141			−1.24501
$801$		0			0
$802$	24.7435			0.873724
$803$	8.56243	−	14.8306i	0.302162	−	0.523359i
$804$		0			0
$805$	−1.42938	−	2.47576i	−0.0503790	−	0.0872590i
$806$	−23.2043	−	40.1911i	−0.817338	−	1.41567i
$807$		0			0
$808$	0.792917	+	1.37337i	0.0278947	+	0.0483151i
$809$	−4.54640	+	7.87459i	−0.159843	+	0.276856i	−0.934812	−	0.355143i	$-0.884432\pi$
$809$	−4.54640	+	7.87459i	−0.159843	+	0.276856i	0.774969	+	0.631999i	$0.217765\pi$
$810$		0			0
$811$	−23.6033			−0.828823			−0.414412	−	0.910090i	$-0.636013\pi$
$811$	−23.6033			−0.828823			−0.414412	+	0.910090i	$0.636013\pi$
$812$	0.322946	−	0.559359i	0.0113332	−	0.0196296i
$813$		0			0
$814$	1.40023			0.0490781
$815$	10.7185			0.375452
$816$		0			0
$817$	−32.4577	+	56.2184i	−1.13555	+	1.96683i
$818$	−10.0828	−	17.4640i	−0.352538	−	0.610614i
$819$		0			0
$820$	5.51140	−	9.54602i	0.192466	−	0.333361i
$821$	29.1445			1.01715			0.508575	−	0.861018i	$-0.330172\pi$
$821$	29.1445			1.01715			0.508575	+	0.861018i	$0.330172\pi$
$822$		0			0
$823$	−24.1054			−0.840260			−0.420130	−	0.907464i	$-0.638016\pi$
$823$	−24.1054			−0.840260			−0.420130	+	0.907464i	$0.638016\pi$
$824$	2.98704	−	0.493756i	0.104059	−	0.0172008i
$825$		0			0
$826$	−17.6799	−	30.6225i	−0.615163	−	1.06549i
$827$	−6.89056			−0.239608			−0.119804	−	0.992798i	$-0.538227\pi$
$827$	−6.89056			−0.239608			−0.119804	+	0.992798i	$0.538227\pi$
$828$		0			0
$829$	21.1289	−	36.5964i	0.733839	−	1.27105i	−0.221392	−	0.975185i	$-0.571060\pi$
$829$	21.1289	−	36.5964i	0.733839	−	1.27105i	0.955231	−	0.295861i	$-0.0956065\pi$
$830$	−8.91419	−	15.4398i	−0.309416	−	0.535924i
$831$		0			0
$832$	−18.5351			−0.642588
$833$	−8.14102			−0.282070
$834$		0			0
$835$	3.31979	−	5.75005i	0.114886	−	0.198989i
$836$	−23.0730	+	39.9636i	−0.797997	+	1.38217i
$837$		0			0
$838$	29.3607			1.01425
$839$	15.1502	−	26.2410i	0.523044	−	0.905939i	−0.476596	−	0.879122i	$-0.658130\pi$
$839$	15.1502	−	26.2410i	0.523044	−	0.905939i	0.999640	−	0.0268166i	$-0.00853701\pi$
$840$		0			0
$841$	14.4880	−	25.0940i	0.499587	−	0.865309i
$842$	32.1038	+	55.6054i	1.10637	+	1.91629i
$843$		0			0
$844$	17.3973	+	30.1330i	0.598841	+	1.03722i
$845$	1.89582	−	3.28365i	0.0652181	−	0.112961i
$846$		0			0
$847$	0.868491			0.0298417
$848$	37.5328			1.28888
$849$		0			0
$850$	−18.9204	−	32.7712i	−0.648966	−	1.12404i
$851$	−0.384338			−0.0131749
$852$		0			0
$853$	15.4670	+	26.7896i	0.529580	+	0.917259i	0.999405	+	0.0344997i	$0.0109838\pi$
$853$	15.4670	+	26.7896i	0.529580	+	0.917259i	−0.469825	+	0.882760i	$0.655683\pi$
$854$	11.7409			0.401766
$855$		0			0
$856$	2.75566	−	4.77295i	0.0941866	−	0.163136i
$857$	−21.3022	+	36.8965i	−0.727668	+	1.26036i	0.230198	+	0.973144i	$0.426063\pi$
$857$	−21.3022	+	36.8965i	−0.727668	+	1.26036i	−0.957866	+	0.287215i	$0.907271\pi$
$858$		0			0
$859$	3.81737	+	6.61188i	0.130247	+	0.225594i	0.923772	−	0.382944i	$-0.125090\pi$
$859$	3.81737	+	6.61188i	0.130247	+	0.225594i	−0.793525	+	0.608538i	$0.791756\pi$
$860$	−5.64976	+	9.78567i	−0.192655	+	0.333689i
$861$		0			0
$862$	40.1667	−	69.5707i	1.36808	−	2.36959i
$863$	32.9689			1.12227			0.561137	−	0.827723i	$-0.310364\pi$
$863$	32.9689			1.12227			0.561137	+	0.827723i	$0.310364\pi$
$864$		0			0
$865$	1.20069	+	2.07966i	0.0408247	+	0.0707105i
$866$	31.5744			1.07294
$867$		0			0
$868$	17.9440	+	31.0799i	0.609059	+	1.05492i
$869$	−18.4755	+	32.0005i	−0.626739	+	1.08554i
$870$		0			0
$871$	12.5403	−	21.7204i	0.424911	−	0.735968i
$872$	−0.0110889	−	0.0192065i	−0.000375518	−	0.000650415i
$873$		0			0
$874$	13.1874	−	22.8413i	0.446072	−	0.772619i
$875$	7.48552	−	12.9653i	0.253057	−	0.438307i
$876$		0			0
$877$	25.1182	−	43.5060i	0.848182	−	1.46909i	−0.0346475	−	0.999400i	$-0.511031\pi$
$877$	25.1182	−	43.5060i	0.848182	−	1.46909i	0.882829	−	0.469694i	$-0.155636\pi$
$878$	−21.1266	−	36.5924i	−0.712990	−	1.23493i
$879$		0			0
$880$	5.03496	−	8.72081i	0.169728	−	0.293978i
$881$	−9.12558	−	15.8060i	−0.307449	−	0.532517i	0.670355	−	0.742041i	$-0.266142\pi$
$881$	−9.12558	−	15.8060i	−0.307449	−	0.532517i	−0.977803	+	0.209524i	$0.932809\pi$
$882$		0			0
$883$	−9.22861	−	15.9844i	−0.310567	−	0.537918i	0.667918	−	0.744235i	$-0.267186\pi$
$883$	−9.22861	−	15.9844i	−0.310567	−	0.537918i	−0.978485	+	0.206316i	$0.933852\pi$
$884$	−10.8576	−	18.8059i	−0.365180	−	0.632510i
$885$		0			0
$886$	−5.87750	−	10.1801i	−0.197459	−	0.342008i
$887$	10.8731	−	18.8327i	0.365082	−	0.632340i	−0.623707	−	0.781658i	$-0.714374\pi$
$887$	10.8731	−	18.8327i	0.365082	−	0.632340i	0.988789	+	0.149317i	$0.0477076\pi$
$888$		0			0
$889$	−15.5638	+	26.9573i	−0.521994	+	0.904119i
$890$	−20.7862			−0.696755
$891$		0			0
$892$	13.9499	+	24.1620i	0.467078	+	0.809002i
$893$	72.2595			2.41807
$894$		0			0
$895$	−1.23228	+	2.13438i	−0.0411907	+	0.0713443i
$896$	−5.37133			−0.179444
$897$		0			0
$898$	−25.8683	−	44.8052i	−0.863236	−	1.49517i
$899$	−0.666141	−	1.15379i	−0.0222171	−	0.0384811i
$900$		0			0
$901$	18.7335	+	32.4474i	0.624104	+	1.08098i
$902$	−28.3163	−	49.0453i	−0.942830	−	1.63303i
$903$		0			0
$904$	−4.50724			−0.149909
$905$	0.131293			0.00436432
$906$		0			0
$907$	20.5981	+	35.6770i	0.683950	+	1.18464i	0.973766	+	0.227553i	$0.0730726\pi$
$907$	20.5981	+	35.6770i	0.683950	+	1.18464i	−0.289816	+	0.957082i	$0.593594\pi$
$908$	−24.4266	−	42.3082i	−0.810627	−	1.40405i
$909$		0			0
$910$	4.24389	−	7.35064i	0.140684	−	0.243671i
$911$	21.9665	+	38.0472i	0.727784	+	1.26056i	0.957818	+	0.287376i	$0.0927830\pi$
$911$	21.9665	+	38.0472i	0.727784	+	1.26056i	−0.230034	+	0.973183i	$0.573884\pi$
$912$		0			0
$913$	−43.9891			−1.45583
$914$	46.4758			1.53728
$915$		0			0
$916$	9.38412	−	16.2538i	0.310060	−	0.537040i
$917$	8.09381			0.267281
$918$		0			0
$919$	6.34306			0.209238			0.104619	−	0.994512i	$-0.466638\pi$
$919$	6.34306			0.209238			0.104619	+	0.994512i	$0.466638\pi$
$920$	−0.188909	+	0.327199i	−0.00622813	+	0.0107874i
$921$		0			0
$922$	36.3455	−	62.9522i	1.19697	−	2.07322i
$923$	15.9529	−	27.6313i	0.525097	−	0.909494i
$924$		0			0
$925$	−0.477481	−	0.827022i	−0.0156995	−	0.0271923i
$926$	13.3010			0.437099
$927$		0			0
$928$	−1.20798			−0.0396538
$929$	−19.9639	−	34.5785i	−0.654994	−	1.13448i	−0.981895	−	0.189424i	$-0.939338\pi$
$929$	−19.9639	−	34.5785i	−0.654994	−	1.13448i	0.326902	−	0.945058i	$-0.393995\pi$
$930$		0			0
$931$	7.04939	−	12.2099i	0.231034	−	0.400163i
$932$	11.8485	−	20.5223i	0.388112	−	0.672229i
$933$		0			0
$934$	19.9898	−	34.6233i	0.654086	−	1.13291i
$935$	10.0523			0.328744
$936$		0			0
$937$	−31.3729			−1.02491			−0.512453	−	0.858715i	$-0.671263\pi$
$937$	−31.3729			−1.02491			−0.512453	+	0.858715i	$0.671263\pi$
$938$	−20.1930	+	34.9753i	−0.659324	+	1.14198i
$939$		0			0
$940$	12.5778			0.410244
$941$	−14.1772			−0.462163			−0.231082	−	0.972934i	$-0.574226\pi$
$941$	−14.1772			−0.462163			−0.231082	+	0.972934i	$0.574226\pi$
$942$		0			0
$943$	7.77232	+	13.4621i	0.253102	+	0.438385i
$944$	−17.0940	+	29.6076i	−0.556361	+	0.963645i
$945$		0			0
$946$	29.0272	+	50.2766i	0.943755	+	1.63463i
$947$	−6.76021	−	11.7090i	−0.219677	−	0.380492i	0.735032	−	0.678032i	$-0.237167\pi$
$947$	−6.76021	−	11.7090i	−0.219677	−	0.380492i	−0.954709	+	0.297540i	$0.903834\pi$
$948$		0			0
$949$	−13.9559			−0.453028
$950$	65.5335			2.12619
$951$		0			0
$952$	−1.43882	−	2.49210i	−0.0466323	−	0.0807695i
$953$	17.5283	+	30.3599i	0.567797	+	0.983454i	0.996783	+	0.0801427i	$0.0255376\pi$
$953$	17.5283	+	30.3599i	0.567797	+	0.983454i	−0.428986	+	0.903311i	$0.641129\pi$
$954$		0			0
$955$	−1.46625	−	2.53961i	−0.0474466	−	0.0821800i
$956$	−6.30985	−	10.9290i	−0.204075	−	0.353469i
$957$		0			0
$958$	72.6809			2.34821
$959$	−5.61945	+	9.73317i	−0.181461	+	0.314300i
$960$		0			0
$961$	43.0263			1.38795
$962$	−0.570559	−	0.988237i	−0.0183956	−	0.0318620i
$963$		0			0
$964$	−37.8045			−1.21760
$965$	−2.11579	+	3.66465i	−0.0681096	+	0.117969i
$966$		0			0
$967$	−6.54205	+	11.3312i	−0.210378	+	0.364385i	−0.951833	−	0.306617i	$-0.900803\pi$
$967$	−6.54205	+	11.3312i	−0.210378	+	0.364385i	0.741455	+	0.671003i	$0.234136\pi$
$968$	−0.0573904	−	0.0994031i	−0.00184460	−	0.00319494i
$969$		0			0
$970$	−2.92745	−	5.07050i	−0.0939949	−	0.162804i
$971$	14.5096	+	25.1313i	0.465634	+	0.806502i	0.999230	−	0.0392374i	$-0.0124929\pi$
$971$	14.5096	+	25.1313i	0.465634	+	0.806502i	−0.533596	+	0.845740i	$0.679160\pi$
$972$		0			0
$973$	24.3446	+	42.1660i	0.780451	+	1.35178i
$974$	2.52879	−	4.37999i	0.0810276	−	0.140344i
$975$		0			0
$976$	−5.67590	−	9.83094i	−0.181681	−	0.314681i
$977$	10.7895	−	18.6879i	0.345186	−	0.597880i	−0.640201	−	0.768207i	$-0.721149\pi$
$977$	10.7895	−	18.6879i	0.345186	−	0.597880i	0.985388	+	0.170327i	$0.0544824\pi$
$978$		0			0
$979$	−25.6435	+	44.4159i	−0.819571	+	1.41954i
$980$	1.22705	−	2.12532i	0.0391967	−	0.0678908i
$981$		0			0
$982$	0.106427	+	0.184336i	0.00339621	+	0.00588240i
$983$	−13.4990	+	23.3809i	−0.430551	+	0.745736i	−0.996921	−	0.0784150i	$-0.975014\pi$
$983$	−13.4990	+	23.3809i	−0.430551	+	0.745736i	0.566370	+	0.824151i	$0.308347\pi$
$984$		0			0
$985$	−0.696235	+	1.20591i	−0.0221839	+	0.0384236i
$986$	−0.649042	−	1.12417i	−0.0206697	−	0.0358010i
$987$		0			0
$988$	37.6067			1.19643
$989$	−7.96744	−	13.8000i	−0.253350	−	0.438815i
$990$		0			0
$991$	28.7450			0.913115			0.456558	−	0.889694i	$-0.349082\pi$
$991$	28.7450			0.913115			0.456558	+	0.889694i	$0.349082\pi$
$992$	33.5597	−	58.1271i	1.06552	−	1.84554i
$993$		0			0
$994$	−25.6882	+	44.4932i	−0.814779	+	1.41124i
$995$	−2.23843	−	3.87707i	−0.0709630	−	0.122912i
$996$		0			0
$997$	0.432790	−	0.749614i	0.0137066	−	0.0237405i	−0.859091	−	0.511823i	$-0.828970\pi$
$997$	0.432790	−	0.749614i	0.0137066	−	0.0237405i	0.872797	+	0.488083i	$0.162304\pi$
$998$	26.8318	−	46.4740i	0.849344	−	1.47111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.f.f.46.14	yes	32
3.2	odd	2	inner	927.2.f.f.46.3	✓	32
103.56	even	3	inner	927.2.f.f.262.14	yes	32
309.56	odd	6	inner	927.2.f.f.262.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.f.f.46.3	✓	32	3.2	odd	2	inner
927.2.f.f.46.14	yes	32	1.1	even	1	trivial
927.2.f.f.262.3	yes	32	309.56	odd	6	inner
927.2.f.f.262.14	yes	32	103.56	even	3	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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.980806 + 1.69881i) q^{2} +(-0.923962 + 1.60035i) q^{4} +(-0.348567 + 0.603736i) q^{5} +(-1.12861 + 1.95480i) q^{7} +0.298316 q^{8} +O(q^{10})\)	\(q+(0.980806 + 1.69881i) q^{2} +(-0.923962 + 1.60035i) q^{4} +(-0.348567 + 0.603736i) q^{5} +(-1.12861 + 1.95480i) q^{7} +0.298316 q^{8} -1.36751 q^{10} +(-1.68707 + 2.92208i) q^{11} +2.74975 q^{13} -4.42778 q^{14} +(2.14051 + 3.70748i) q^{16} +(-2.13676 + 3.70098i) q^{17} +(-3.70048 - 6.40942i) q^{19} +(-0.644125 - 1.11566i) q^{20} -6.61874 q^{22} +1.81672 q^{23} +(2.25700 + 3.90924i) q^{25} +(2.69697 + 4.67129i) q^{26} +(-2.08558 - 3.61233i) q^{28} +(0.0774236 + 0.134102i) q^{29} -8.60385 q^{31} +(-3.90054 + 6.75594i) q^{32} -8.38299 q^{34} +(-0.786790 - 1.36276i) q^{35} -0.211556 q^{37} +(7.25891 - 12.5728i) q^{38} +(-0.103983 + 0.180104i) q^{40} +(4.27821 + 7.41007i) q^{41} +(-4.38561 - 7.59610i) q^{43} +(-3.11757 - 5.39979i) q^{44} +(1.78185 + 3.08626i) q^{46} +(-4.88176 + 8.45546i) q^{47} +(0.952496 + 1.64977i) q^{49} +(-4.42736 + 7.66842i) q^{50} +(-2.54066 + 4.40055i) q^{52} +(4.38362 - 7.59266i) q^{53} +(-1.17611 - 2.03708i) q^{55} +(-0.336681 + 0.583149i) q^{56} +(-0.151875 + 0.263055i) q^{58} +(3.99296 + 6.91600i) q^{59} -2.65165 q^{61} +(-8.43871 - 14.6163i) q^{62} -6.74065 q^{64} +(-0.958471 + 1.66012i) q^{65} +(4.56052 - 7.89906i) q^{67} +(-3.94857 - 6.83912i) q^{68} +(1.54338 - 2.67321i) q^{70} +(5.80160 - 10.0487i) q^{71} -5.07534 q^{73} +(-0.207495 - 0.359392i) q^{74} +13.6764 q^{76} +(-3.80807 - 6.59576i) q^{77} +10.9513 q^{79} -2.98445 q^{80} +(-8.39218 + 14.5357i) q^{82} +(6.51857 + 11.2905i) q^{83} +(-1.48961 - 2.58008i) q^{85} +(8.60286 - 14.9006i) q^{86} +(-0.503279 + 0.871705i) q^{88} +15.2001 q^{89} +(-3.10338 + 5.37522i) q^{91} +(-1.67858 + 2.90739i) q^{92} -19.1522 q^{94} +5.15946 q^{95} +(2.14072 + 3.70784i) q^{97} +(-1.86843 + 3.23621i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q - 18 * q^4 + 8 * q^7	\( 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) \) 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more