LMFDB - Embedded newform 108.3.k.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(5,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.k (of order $18$, degree $6$, 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	108.29
Dual form			108.3.k.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.776129 + 2.89787i) q^{3} +(2.68656 + 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(-7.79525 - 4.49824i) q^{9} +O(q^{10})$	\(q+(-0.776129 + 2.89787i) q^{3} +(2.68656 + 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(-7.79525 - 4.49824i) q^{9} +(-4.52170 + 5.38875i) q^{11} +(3.33062 + 18.8889i) q^{13} +(-11.3633 + 5.30034i) q^{15} +(20.3965 - 11.7759i) q^{17} +(-11.7859 + 20.4138i) q^{19} +(-1.36134 - 15.5399i) q^{21} +(8.16612 - 22.4362i) q^{23} +(1.30781 - 7.41698i) q^{25} +(19.0854 - 19.0984i) q^{27} +(21.2148 + 3.74075i) q^{29} +(24.0093 + 8.73866i) q^{31} +(-12.1065 - 17.2856i) q^{33} +(-18.8212 - 10.8664i) q^{35} +(-6.81584 - 11.8054i) q^{37} +(-57.3224 - 5.00853i) q^{39} +(50.7253 - 8.94424i) q^{41} +(3.55532 + 2.98327i) q^{43} +(-6.54032 - 37.0430i) q^{45} +(1.64224 + 4.51203i) q^{47} +(-16.8239 + 14.1170i) q^{49} +(18.2947 + 68.2459i) q^{51} -67.3308i q^{53} -29.4011 q^{55} +(-50.0089 - 49.9976i) q^{57} +(55.7367 + 66.4244i) q^{59} +(50.3038 - 18.3091i) q^{61} +(46.0891 + 8.11599i) q^{63} +(-51.5290 + 61.4098i) q^{65} +(3.49276 + 19.8084i) q^{67} +(58.6792 + 41.0777i) q^{69} +(-85.2808 + 49.2369i) q^{71} +(-69.6234 + 120.591i) q^{73} +(20.4784 + 9.54640i) q^{75} +(12.5104 - 34.3721i) q^{77} +(18.3268 - 103.937i) q^{79} +(40.5318 + 70.1297i) q^{81} +(-79.2540 - 13.9746i) q^{83} +(92.4995 + 33.6671i) q^{85} +(-27.3056 + 58.5744i) q^{87} +(-58.0744 - 33.5293i) q^{89} +(-49.8668 - 86.3718i) q^{91} +(-43.9577 + 62.7933i) q^{93} +(-97.0226 + 17.1077i) q^{95} +(-112.041 - 94.0132i) q^{97} +(59.4876 - 21.6670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q - 9 * q^5 + 6 * q^9	$ 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) $ 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.776129	+	2.89787i	−0.258710	+	0.965955i
$3$	−0.776129	+	2.89787i	−0.258710	+	0.965955i
$4$		0			0
$5$	2.68656	+	3.20172i	0.537312	+	0.640344i	0.964583	−	0.263780i	$-0.0849693\pi$
$5$	2.68656	+	3.20172i	0.537312	+	0.640344i	−0.427271	+	0.904124i	$0.640525\pi$
$6$		0			0
$7$	−4.88621	+	1.77844i	−0.698031	+	0.254062i	−0.666570	−	0.745443i	$-0.732238\pi$
$7$	−4.88621	+	1.77844i	−0.698031	+	0.254062i	−0.0314608	+	0.999505i	$0.510016\pi$
$8$		0			0
$9$	−7.79525	−	4.49824i	−0.866139	−	0.499804i
$10$		0			0
$11$	−4.52170	+	5.38875i	−0.411064	+	0.489886i	−0.931360	−	0.364099i	$-0.881377\pi$
$11$	−4.52170	+	5.38875i	−0.411064	+	0.489886i	0.520297	+	0.853986i	$0.325821\pi$
$12$		0			0
$13$	3.33062	+	18.8889i	0.256202	+	1.45299i	0.792970	+	0.609261i	$0.208534\pi$
$13$	3.33062	+	18.8889i	0.256202	+	1.45299i	−0.536768	+	0.843730i	$0.680355\pi$
$14$		0			0
$15$	−11.3633	+	5.30034i	−0.757551	+	0.353356i
$16$		0			0
$17$	20.3965	−	11.7759i	1.19979	−	0.692701i	0.239284	−	0.970950i	$-0.423087\pi$
$17$	20.3965	−	11.7759i	1.19979	−	0.692701i	0.960509	+	0.278249i	$0.0897541\pi$
$18$		0			0
$19$	−11.7859	+	20.4138i	−0.620310	+	1.07441i	0.369118	+	0.929383i	$0.379660\pi$
$19$	−11.7859	+	20.4138i	−0.620310	+	1.07441i	−0.989428	+	0.145026i	$0.953674\pi$
$20$		0			0
$21$	−1.36134	−	15.5399i	−0.0648255	−	0.739995i
$22$		0			0
$23$	8.16612	−	22.4362i	0.355049	−	0.975489i	−0.625674	−	0.780085i	$-0.715176\pi$
$23$	8.16612	−	22.4362i	0.355049	−	0.975489i	0.980723	−	0.195404i	$-0.0626018\pi$
$24$		0			0
$25$	1.30781	−	7.41698i	0.0523125	−	0.296679i
$26$		0			0
$27$	19.0854	−	19.0984i	0.706867	−	0.707347i
$28$		0			0
$29$	21.2148	+	3.74075i	0.731546	+	0.128991i	0.527000	−	0.849866i	$-0.323317\pi$
$29$	21.2148	+	3.74075i	0.731546	+	0.128991i	0.204547	+	0.978857i	$0.434428\pi$
$30$		0			0
$31$	24.0093	+	8.73866i	0.774492	+	0.281892i	0.698874	−	0.715245i	$-0.253685\pi$
$31$	24.0093	+	8.73866i	0.774492	+	0.281892i	0.0756183	+	0.997137i	$0.475907\pi$
$32$		0			0
$33$	−12.1065	−	17.2856i	−0.366862	−	0.523807i
$34$		0			0
$35$	−18.8212	−	10.8664i	−0.537747	−	0.310469i
$36$		0			0
$37$	−6.81584	−	11.8054i	−0.184212	−	0.319064i	0.759099	−	0.650975i	$-0.225640\pi$
$37$	−6.81584	−	11.8054i	−0.184212	−	0.319064i	−0.943311	+	0.331911i	$0.892307\pi$
$38$		0			0
$39$	−57.3224	−	5.00853i	−1.46981	−	0.128424i
$40$		0			0
$41$	50.7253	−	8.94424i	1.23720	−	0.218152i	0.483486	−	0.875352i	$-0.339370\pi$
$41$	50.7253	−	8.94424i	1.23720	−	0.218152i	0.753716	+	0.657200i	$0.228259\pi$
$42$		0			0
$43$	3.55532	+	2.98327i	0.0826818	+	0.0693783i	0.683192	−	0.730239i	$-0.260591\pi$
$43$	3.55532	+	2.98327i	0.0826818	+	0.0693783i	−0.600510	+	0.799617i	$0.705036\pi$
$44$		0			0
$45$	−6.54032	−	37.0430i	−0.145340	−	0.823177i
$46$		0			0
$47$	1.64224	+	4.51203i	0.0349413	+	0.0960006i	0.955937	−	0.293573i	$-0.0948445\pi$
$47$	1.64224	+	4.51203i	0.0349413	+	0.0960006i	−0.920995	+	0.389574i	$0.872622\pi$
$48$		0			0
$49$	−16.8239	+	14.1170i	−0.343346	+	0.288101i
$50$		0			0
$51$	18.2947	+	68.2459i	0.358720	+	1.33815i
$52$		0			0
$53$		−	67.3308i		−	1.27039i	−0.772351	−	0.635196i	$-0.780919\pi$
$53$		−	67.3308i		−	1.27039i	0.772351	−	0.635196i	$-0.219081\pi$
$54$		0			0
$55$	−29.4011			−0.534565
$56$		0			0
$57$	−50.0089	−	49.9976i	−0.877350	−	0.877151i
$58$		0			0
$59$	55.7367	+	66.4244i	0.944690	+	1.12584i	0.991909	+	0.126953i	$0.0405198\pi$
$59$	55.7367	+	66.4244i	0.944690	+	1.12584i	−0.0472185	+	0.998885i	$0.515036\pi$
$60$		0			0
$61$	50.3038	−	18.3091i	0.824653	−	0.300149i	0.104991	−	0.994473i	$-0.466519\pi$
$61$	50.3038	−	18.3091i	0.824653	−	0.300149i	0.719663	+	0.694324i	$0.244297\pi$
$62$		0			0
$63$	46.0891	+	8.11599i	0.731572	+	0.128825i
$64$		0			0
$65$	−51.5290	+	61.4098i	−0.792753	+	0.944767i
$66$		0			0
$67$	3.49276	+	19.8084i	0.0521307	+	0.295648i	0.999715	−	0.0238568i	$-0.00759458\pi$
$67$	3.49276	+	19.8084i	0.0521307	+	0.295648i	−0.947585	+	0.319505i	$0.896483\pi$
$68$		0			0
$69$	58.6792	+	41.0777i	0.850424	+	0.595330i
$70$		0			0
$71$	−85.2808	+	49.2369i	−1.20114	+	0.693477i	−0.960808	−	0.277214i	$-0.910589\pi$
$71$	−85.2808	+	49.2369i	−1.20114	+	0.693477i	−0.240329	+	0.970691i	$0.577255\pi$
$72$		0			0
$73$	−69.6234	+	120.591i	−0.953745	+	1.65193i	−0.216530	+	0.976276i	$0.569474\pi$
$73$	−69.6234	+	120.591i	−0.953745	+	1.65193i	−0.737215	+	0.675659i	$0.763859\pi$
$74$		0			0
$75$	20.4784	+	9.54640i	0.273045	+	0.127285i
$76$		0			0
$77$	12.5104	−	34.3721i	0.162473	−	0.446391i
$78$		0			0
$79$	18.3268	−	103.937i	0.231985	−	1.31565i	−0.616886	−	0.787053i	$-0.711606\pi$
$79$	18.3268	−	103.937i	0.231985	−	1.31565i	0.848871	−	0.528600i	$-0.177283\pi$
$80$		0			0
$81$	40.5318	+	70.1297i	0.500392	+	0.865799i
$82$		0			0
$83$	−79.2540	−	13.9746i	−0.954867	−	0.168369i	−0.325557	−	0.945523i	$-0.605552\pi$
$83$	−79.2540	−	13.9746i	−0.954867	−	0.168369i	−0.629311	+	0.777154i	$0.716663\pi$
$84$		0			0
$85$	92.4995	+	33.6671i	1.08823	+	0.396083i
$86$		0			0
$87$	−27.3056	+	58.5744i	−0.313858	+	0.673269i
$88$		0			0
$89$	−58.0744	−	33.5293i	−0.652521	−	0.376733i	0.136900	−	0.990585i	$-0.456286\pi$
$89$	−58.0744	−	33.5293i	−0.652521	−	0.376733i	−0.789421	+	0.613852i	$0.789619\pi$
$90$		0			0
$91$	−49.8668	−	86.3718i	−0.547987	−	0.949141i
$92$		0			0
$93$	−43.9577	+	62.7933i	−0.472664	+	0.675197i
$94$		0			0
$95$	−97.0226	+	17.1077i	−1.02129	+	0.180081i
$96$		0			0
$97$	−112.041	−	94.0132i	−1.15506	−	0.969208i	−0.155232	−	0.987878i	$-0.549612\pi$
$97$	−112.041	−	94.0132i	−1.15506	−	0.969208i	−0.999826	+	0.0186698i	$0.994057\pi$
$98$		0			0
$99$	59.4876	−	21.6670i	0.600885	−	0.218858i
$100$		0			0
$101$	33.7340	+	92.6834i	0.334000	+	0.917657i	0.987060	+	0.160351i	$0.0512626\pi$
$101$	33.7340	+	92.6834i	0.334000	+	0.917657i	−0.653060	+	0.757306i	$0.726515\pi$
$102$		0			0
$103$	107.050	−	89.8257i	1.03932	−	0.872094i	0.0473903	−	0.998876i	$-0.484910\pi$
$103$	107.050	−	89.8257i	1.03932	−	0.872094i	0.991931	+	0.126783i	$0.0404651\pi$
$104$		0			0
$105$	46.0970	−	46.1075i	0.439019	−	0.439119i
$106$		0			0
$107$		−	73.3054i		−	0.685098i	−0.939500	−	0.342549i	$-0.888710\pi$
$107$		−	73.3054i		−	0.685098i	0.939500	−	0.342549i	$-0.111290\pi$
$108$		0			0
$109$	−82.6310			−0.758083			−0.379041	−	0.925380i	$-0.623746\pi$
$109$	−82.6310			−0.758083			−0.379041	+	0.925380i	$0.623746\pi$
$110$		0			0
$111$	39.5004	−	10.5889i	0.355859	−	0.0953953i
$112$		0			0
$113$	111.471	+	132.846i	0.986466	+	1.17562i	0.984457	+	0.175627i	$0.0561952\pi$
$113$	111.471	+	132.846i	0.986466	+	1.17562i	0.00200959	+	0.999998i	$0.499360\pi$
$114$		0			0
$115$	93.7733	−	34.1307i	0.815420	−	0.296789i
$116$		0			0
$117$	59.0036	−	162.225i	0.504305	−	1.38654i
$118$		0			0
$119$	−78.7188	+	93.8134i	−0.661503	+	0.788348i
$120$		0			0
$121$	12.4186	+	70.4291i	0.102633	+	0.582059i
$122$		0			0
$123$	−13.4502	+	153.937i	−0.109351	+	1.25152i
$124$		0			0
$125$	117.750	−	67.9832i	0.942003	−	0.543866i
$126$		0			0
$127$	111.534	−	193.183i	0.878223	−	1.52113i	0.0249327	−	0.999689i	$-0.492063\pi$
$127$	111.534	−	193.183i	0.878223	−	1.52113i	0.853290	−	0.521437i	$-0.174604\pi$
$128$		0			0
$129$	−11.4045	+	7.98743i	−0.0884069	+	0.0619181i
$130$		0			0
$131$	76.0508	−	208.948i	0.580540	−	1.59502i	−0.206719	−	0.978400i	$-0.566279\pi$
$131$	76.0508	−	208.948i	0.580540	−	1.59502i	0.787260	−	0.616621i	$-0.211499\pi$
$132$		0			0
$133$	21.2838	−	120.706i	0.160029	−	0.907567i
$134$		0			0
$135$	112.422	+	9.79716i	0.832753	+	0.0725715i
$136$		0			0
$137$	−159.835	−	28.1833i	−1.16668	−	0.205717i	−0.443434	−	0.896307i	$-0.646240\pi$
$137$	−159.835	−	28.1833i	−1.16668	−	0.205717i	−0.723247	+	0.690590i	$0.757351\pi$
$138$		0			0
$139$	−71.5107	−	26.0278i	−0.514466	−	0.187250i	0.0717232	−	0.997425i	$-0.477150\pi$
$139$	−71.5107	−	26.0278i	−0.514466	−	0.187250i	−0.586189	+	0.810174i	$0.699372\pi$
$140$		0			0
$141$	−14.3498	+	1.25708i	−0.101772	+	0.00891549i
$142$		0			0
$143$	−116.848	−	67.4620i	−0.817116	−	0.471762i
$144$		0			0
$145$	45.0181	+	77.9737i	0.310470	+	0.537749i
$146$		0			0
$147$	−27.8515	−	59.7101i	−0.189466	−	0.406191i
$148$		0			0
$149$	−90.4646	+	15.9514i	−0.607145	+	0.107056i	−0.468765	−	0.883323i	$-0.655301\pi$
$149$	−90.4646	+	15.9514i	−0.607145	+	0.107056i	−0.138380	+	0.990379i	$0.544190\pi$
$150$		0			0
$151$	37.2582	+	31.2633i	0.246743	+	0.207042i	0.757768	−	0.652524i	$-0.226290\pi$
$151$	37.2582	+	31.2633i	0.246743	+	0.207042i	−0.511025	+	0.859566i	$0.670734\pi$
$152$		0			0
$153$	−211.966	+	0.0479806i	−1.38540	+	0.000313599i
$154$		0			0
$155$	36.5236	+	100.348i	0.235636	+	0.647405i
$156$		0			0
$157$	−78.3333	+	65.7295i	−0.498938	+	0.418659i	−0.857217	−	0.514956i	$-0.827808\pi$
$157$	−78.3333	+	65.7295i	−0.498938	+	0.418659i	0.358278	+	0.933615i	$0.383364\pi$
$158$		0			0
$159$	195.116	+	52.2574i	1.22714	+	0.328663i
$160$		0			0
$161$			124.151i			0.771125i
$162$		0			0
$163$	−42.0106			−0.257734			−0.128867	−	0.991662i	$-0.541134\pi$
$163$	−42.0106			−0.257734			−0.128867	+	0.991662i	$0.541134\pi$
$164$		0			0
$165$	22.8190	−	85.2004i	0.138297	−	0.516366i
$166$		0			0
$167$	−7.62167	−	9.08316i	−0.0456388	−	0.0543902i	0.742742	−	0.669578i	$-0.233525\pi$
$167$	−7.62167	−	9.08316i	−0.0456388	−	0.0543902i	−0.788381	+	0.615187i	$0.789080\pi$
$168$		0			0
$169$	−186.889	+	68.0220i	−1.10585	+	0.402497i
$170$		0			0
$171$	183.700	−	106.115i	1.07427	−	0.620553i
$172$		0			0
$173$	119.692	−	142.643i	0.691860	−	0.824527i	−0.299719	−	0.954028i	$-0.596893\pi$
$173$	119.692	−	142.643i	0.691860	−	0.824527i	0.991579	+	0.129500i	$0.0413374\pi$
$174$		0			0
$175$	6.80037	+	38.5668i	0.0388592	+	0.220382i
$176$		0			0
$177$	−235.748	+	109.964i	−1.33191	+	0.621263i
$178$		0			0
$179$	−82.0051	+	47.3456i	−0.458129	+	0.264501i	−0.711257	−	0.702932i	$-0.751874\pi$
$179$	−82.0051	+	47.3456i	−0.458129	+	0.264501i	0.253128	+	0.967433i	$0.418541\pi$
$180$		0			0
$181$	−56.7101	+	98.2247i	−0.313315	+	0.542678i	−0.979078	−	0.203486i	$-0.934773\pi$
$181$	−56.7101	+	98.2247i	−0.313315	+	0.542678i	0.665763	+	0.746164i	$0.268106\pi$
$182$		0			0
$183$	14.0150	+	159.984i	0.0765849	+	0.874230i
$184$		0			0
$185$	19.4863	−	53.5383i	0.105332	−	0.289396i
$186$		0			0
$187$	−28.7693	+	163.159i	−0.153846	+	0.872506i
$188$		0			0
$189$	−59.2901	+	127.261i	−0.313704	+	0.673338i
$190$		0			0
$191$	305.366	+	53.8443i	1.59878	+	0.281907i	0.900807	−	0.434220i	$-0.142976\pi$
$191$	305.366	+	53.8443i	1.59878	+	0.281907i	0.697970	+	0.716127i	$0.254087\pi$
$192$		0			0
$193$	207.986	+	75.7007i	1.07765	+	0.392232i	0.819031	−	0.573749i	$-0.194511\pi$
$193$	207.986	+	75.7007i	1.07765	+	0.392232i	0.258616	+	0.965980i	$0.416734\pi$
$194$		0			0
$195$	−137.964	−	196.986i	−0.707509	−	1.01018i
$196$		0			0
$197$	129.101	+	74.5366i	0.655336	+	0.378359i	0.790498	−	0.612465i	$-0.209822\pi$
$197$	129.101	+	74.5366i	0.655336	+	0.378359i	−0.135161	+	0.990824i	$0.543155\pi$
$198$		0			0
$199$	84.5042	+	146.366i	0.424644	+	0.735506i	0.996387	−	0.0849273i	$-0.0270658\pi$
$199$	84.5042	+	146.366i	0.424644	+	0.735506i	−0.571743	+	0.820433i	$0.693732\pi$
$200$		0			0
$201$	−60.1129	−	5.25235i	−0.299069	−	0.0261311i
$202$		0			0
$203$	−110.313	+	19.4511i	−0.543413	+	0.0958184i
$204$		0			0
$205$	164.913	+	138.379i	0.804456	+	0.675019i
$206$		0			0
$207$	−164.580	+	138.163i	−0.795075	+	0.667454i
$208$		0			0
$209$	−56.7124	−	155.816i	−0.271351	−	0.745531i
$210$		0			0
$211$	−163.282	+	137.010i	−0.773849	+	0.649337i	−0.941692	−	0.336477i	$-0.890765\pi$
$211$	−163.282	+	137.010i	−0.773849	+	0.649337i	0.167842	+	0.985814i	$0.446320\pi$
$212$		0			0
$213$	−76.4929	−	285.346i	−0.359122	−	1.33965i
$214$		0			0
$215$			19.3978i			0.0902225i
$216$		0			0
$217$	−132.856			−0.612238
$218$		0			0
$219$	−295.420	−	295.354i	−1.34895	−	1.34865i
$220$		0			0
$221$	290.367	+	346.046i	1.31388	+	1.56582i
$222$		0			0
$223$	51.1847	−	18.6297i	0.229528	−	0.0835412i	−0.224696	−	0.974429i	$-0.572139\pi$
$223$	51.1847	−	18.6297i	0.229528	−	0.0835412i	0.454224	+	0.890888i	$0.349917\pi$
$224$		0			0
$225$	−43.5580	+	51.9343i	−0.193591	+	0.230819i
$226$		0			0
$227$	56.5301	−	67.3699i	0.249031	−	0.296784i	−0.627019	−	0.779004i	$-0.715725\pi$
$227$	56.5301	−	67.3699i	0.249031	−	0.296784i	0.876050	+	0.482220i	$0.160170\pi$
$228$		0			0
$229$	−45.0976	−	255.761i	−0.196933	−	1.11686i	−0.909639	−	0.415399i	$-0.863642\pi$
$229$	−45.0976	−	255.761i	−0.196933	−	1.11686i	0.712706	−	0.701462i	$-0.247469\pi$
$230$		0			0
$231$	89.8961	+	62.9308i	0.389161	+	0.272428i
$232$		0			0
$233$	188.673	−	108.930i	0.809753	−	0.467511i	−0.0371169	−	0.999311i	$-0.511817\pi$
$233$	188.673	−	108.930i	0.809753	−	0.467511i	0.846870	+	0.531800i	$0.178484\pi$
$234$		0			0
$235$	−10.0343	+	17.3798i	−0.0426989	+	0.0739567i
$236$		0			0
$237$	286.970	+	133.777i	1.21085	+	0.564460i
$238$		0			0
$239$	103.904	−	285.473i	0.434744	−	1.19445i	−0.508125	−	0.861284i	$-0.669661\pi$
$239$	103.904	−	285.473i	0.434744	−	1.19445i	0.942868	−	0.333165i	$-0.108117\pi$
$240$		0			0
$241$	−33.0793	+	187.602i	−0.137259	+	0.778432i	0.836002	+	0.548727i	$0.184887\pi$
$241$	−33.0793	+	187.602i	−0.137259	+	0.778432i	−0.973260	+	0.229705i	$0.926224\pi$
$242$		0			0
$243$	−234.684	+	63.0258i	−0.965779	+	0.259366i
$244$		0			0
$245$	−90.3970	−	15.9394i	−0.368967	−	0.0650589i
$246$		0			0
$247$	−424.847	−	154.632i	−1.72003	−	0.626040i
$248$		0			0
$249$	102.008	−	218.821i	0.409670	−	0.878800i
$250$		0			0
$251$	244.229	+	141.006i	0.973023	+	0.561775i	0.900157	−	0.435566i	$-0.143452\pi$
$251$	244.229	+	141.006i	0.973023	+	0.561775i	0.0728668	+	0.997342i	$0.476785\pi$
$252$		0			0
$253$	83.9786	+	145.455i	0.331931	+	0.574921i
$254$		0			0
$255$	−169.354	+	241.921i	−0.664134	+	0.948710i
$256$		0			0
$257$	−425.035	+	74.9451i	−1.65383	+	0.291615i	−0.921223	−	0.389034i	$-0.872809\pi$
$257$	−425.035	+	74.9451i	−1.65383	+	0.291615i	−0.732609	+	0.680649i	$0.761698\pi$
$258$		0			0
$259$	54.2988	+	45.5621i	0.209648	+	0.175915i
$260$		0			0
$261$	−148.548	−	124.589i	−0.569150	−	0.477354i
$262$		0			0
$263$	−111.156	−	305.400i	−0.422648	−	1.16121i	−0.950186	−	0.311684i	$-0.899107\pi$
$263$	−111.156	−	305.400i	−0.422648	−	1.16121i	0.527538	−	0.849531i	$-0.323115\pi$
$264$		0			0
$265$	215.574	−	180.888i	0.813488	−	0.682597i
$266$		0			0
$267$	142.236	−	142.269i	0.532721	−	0.532841i
$268$		0			0
$269$		−	222.465i		−	0.827009i	−0.910502	−	0.413504i	$-0.864305\pi$
$269$		−	222.465i		−	0.827009i	0.910502	−	0.413504i	$-0.135695\pi$
$270$		0			0
$271$	416.652			1.53746			0.768730	−	0.639574i	$-0.220889\pi$
$271$	416.652			1.53746			0.768730	+	0.639574i	$0.220889\pi$
$272$		0			0
$273$	288.997	−	77.4716i	1.05860	−	0.283779i
$274$		0			0
$275$	34.0547	+	40.5848i	0.123835	+	0.147581i
$276$		0			0
$277$	−55.3380	+	20.1414i	−0.199776	+	0.0727126i	−0.439971	−	0.898012i	$-0.645011\pi$
$277$	−55.3380	+	20.1414i	−0.199776	+	0.0727126i	0.240194	+	0.970725i	$0.422789\pi$
$278$		0			0
$279$	−147.850	−	176.119i	−0.529927	−	0.631252i
$280$		0			0
$281$	187.499	−	223.452i	0.667255	−	0.795204i	−0.321152	−	0.947028i	$-0.604070\pi$
$281$	187.499	−	223.452i	0.667255	−	0.795204i	0.988408	+	0.151824i	$0.0485146\pi$
$282$		0			0
$283$	15.3422	+	87.0101i	0.0542128	+	0.307456i	0.999842	−	0.0177914i	$-0.00566349\pi$
$283$	15.3422	+	87.0101i	0.0542128	+	0.307456i	−0.945629	+	0.325248i	$0.894552\pi$
$284$		0			0
$285$	25.7262	−	294.436i	0.0902675	−	1.03311i
$286$		0			0
$287$	−231.948	+	133.915i	−0.808181	+	0.466603i
$288$		0			0
$289$	132.844	−	230.093i	0.459668	−	0.796169i
$290$		0			0
$291$	359.396	−	251.712i	1.23504	−	0.864990i
$292$		0			0
$293$	105.430	−	289.667i	0.359830	−	0.988624i	−0.619258	−	0.785187i	$-0.712567\pi$
$293$	105.430	−	289.667i	0.359830	−	0.988624i	0.979088	−	0.203437i	$-0.0652111\pi$
$294$		0			0
$295$	−62.9322	+	356.906i	−0.213330	+	1.20985i
$296$		0			0
$297$	16.6179	+	189.204i	0.0559525	+	0.637049i
$298$		0			0
$299$	450.994	+	79.5224i	1.50834	+	0.265961i
$300$		0			0
$301$	−22.6776	−	8.25397i	−0.0753408	−	0.0274218i
$302$		0			0
$303$	−294.766	+	25.8223i	−0.972825	+	0.0852221i
$304$		0			0
$305$	193.765	+	111.870i	0.635295	+	0.366788i
$306$		0			0
$307$	−93.8952	−	162.631i	−0.305847	−	0.529743i	0.671602	−	0.740912i	$-0.265606\pi$
$307$	−93.8952	−	162.631i	−0.305847	−	0.529743i	−0.977450	+	0.211169i	$0.932273\pi$
$308$		0			0
$309$	177.218	+	379.933i	0.573521	+	1.22956i
$310$		0			0
$311$	−551.764	+	97.2909i	−1.77416	+	0.312833i	−0.962497	−	0.271292i	$-0.912549\pi$
$311$	−551.764	+	97.2909i	−1.77416	+	0.312833i	−0.811664	+	0.584124i	$0.801438\pi$
$312$		0			0
$313$	−229.337	−	192.436i	−0.732706	−	0.614813i	0.198162	−	0.980169i	$-0.436503\pi$
$313$	−229.337	−	192.436i	−0.732706	−	0.614813i	−0.930868	+	0.365356i	$0.880947\pi$
$314$		0			0
$315$	97.8359	+	169.368i	0.310590	+	0.537677i
$316$		0			0
$317$	−50.1956	−	137.911i	−0.158346	−	0.435051i	0.834996	−	0.550256i	$-0.185470\pi$
$317$	−50.1956	−	137.911i	−0.158346	−	0.435051i	−0.993342	+	0.115205i	$0.963248\pi$
$318$		0			0
$319$	−116.085	+	97.4069i	−0.363903	+	0.305351i
$320$		0			0
$321$	212.429	+	56.8945i	0.661773	+	0.177241i
$322$		0			0
$323$			555.158i			1.71876i
$324$		0			0
$325$	144.454			0.444475
$326$		0			0
$327$	64.1323	−	239.454i	0.196123	−	0.732274i
$328$		0			0
$329$	−16.0487	−	19.1261i	−0.0487803	−	0.0581340i
$330$		0			0
$331$	−203.791	+	74.1738i	−0.615683	+	0.224090i	−0.630988	−	0.775793i	$-0.717350\pi$
$331$	−203.791	+	74.1738i	−0.615683	+	0.224090i	0.0153052	+	0.999883i	$0.495128\pi$
$332$		0			0
$333$	0.0277709	+	122.685i	8.33962e−5	+	0.368424i
$334$		0			0
$335$	−54.0374	+	64.3993i	−0.161306	+	0.192237i
$336$		0			0
$337$	−11.0619	−	62.7349i	−0.0328245	−	0.186157i	0.963987	−	0.265949i	$-0.0856854\pi$
$337$	−11.0619	−	62.7349i	−0.0328245	−	0.186157i	−0.996812	+	0.0797923i	$0.974574\pi$
$338$		0			0
$339$	−471.484	+	219.922i	−1.39081	+	0.648737i
$340$		0			0
$341$	−155.653	+	89.8664i	−0.456461	+	0.263538i
$342$		0			0
$343$	184.494	−	319.554i	0.537884	−	0.931643i
$344$		0			0
$345$	26.1260	+	298.232i	0.0757274	+	0.864441i
$346$		0			0
$347$	−31.7255	+	87.1651i	−0.0914280	+	0.251196i	−0.976975	−	0.213353i	$-0.931561\pi$
$347$	−31.7255	+	87.1651i	−0.0914280	+	0.251196i	0.885547	+	0.464549i	$0.153784\pi$
$348$		0			0
$349$	41.7475	−	236.762i	0.119620	−	0.678401i	−0.864738	−	0.502223i	$-0.832516\pi$
$349$	41.7475	−	236.762i	0.119620	−	0.678401i	0.984358	−	0.176178i	$-0.0563733\pi$
$350$		0			0
$351$	424.313	+	296.892i	1.20887	+	0.845848i
$352$		0			0
$353$	−326.982	−	57.6557i	−0.926294	−	0.163331i	−0.309900	−	0.950769i	$-0.600296\pi$
$353$	−326.982	−	57.6557i	−0.926294	−	0.163331i	−0.616393	+	0.787438i	$0.711407\pi$
$354$		0			0
$355$	−386.754	−	140.767i	−1.08945	−	0.396527i
$356$		0			0
$357$	−210.763	−	300.928i	−0.590372	−	0.842935i
$358$		0			0
$359$	56.4254	+	32.5772i	0.157174	+	0.0907444i	0.576524	−	0.817080i	$-0.304409\pi$
$359$	56.4254	+	32.5772i	0.157174	+	0.0907444i	−0.419350	+	0.907825i	$0.637742\pi$
$360$		0			0
$361$	−97.3142	−	168.553i	−0.269569	−	0.466906i
$362$		0			0
$363$	−213.733	−	18.6748i	−0.588795	−	0.0514457i
$364$		0			0
$365$	−573.146	+	101.061i	−1.57026	+	0.276880i
$366$		0			0
$367$	305.024	+	255.946i	0.831129	+	0.697400i	0.955550	−	0.294830i	$-0.0952630\pi$
$367$	305.024	+	255.946i	0.831129	+	0.697400i	−0.124421	+	0.992229i	$0.539707\pi$
$368$		0			0
$369$	−435.649	−	158.452i	−1.18062	−	0.429409i
$370$		0			0
$371$	119.744	+	328.993i	0.322759	+	0.886773i
$372$		0			0
$373$	106.450	−	89.3225i	0.285390	−	0.239471i	−0.488842	−	0.872372i	$-0.662581\pi$
$373$	106.450	−	89.3225i	0.285390	−	0.239471i	0.774232	+	0.632902i	$0.218136\pi$
$374$		0			0
$375$	105.617	+	393.989i	0.281645	+	1.05064i
$376$		0			0
$377$			413.184i			1.09598i
$378$		0			0
$379$	447.841			1.18164			0.590819	−	0.806804i	$-0.298805\pi$
$379$	447.841			1.18164			0.590819	+	0.806804i	$0.298805\pi$
$380$		0			0
$381$	473.253	+	473.146i	1.24213	+	1.24185i
$382$		0			0
$383$	−318.172	−	379.182i	−0.830735	−	0.990031i	−0.999990	−	0.00445916i	$-0.998581\pi$
$383$	−318.172	−	379.182i	−0.830735	−	0.990031i	0.169255	−	0.985572i	$-0.445864\pi$
$384$		0			0
$385$	143.660	−	52.2879i	0.373143	−	0.135813i
$386$		0			0
$387$	−14.2951	−	39.2479i	−0.0369384	−	0.101416i
$388$		0			0
$389$	−297.166	+	354.149i	−0.763924	+	0.910409i	−0.998089	−	0.0617877i	$-0.980320\pi$
$389$	−297.166	+	354.149i	−0.763924	+	0.910409i	0.234165	+	0.972197i	$0.424764\pi$
$390$		0			0
$391$	−97.6470	−	553.784i	−0.249737	−	1.41633i
$392$		0			0
$393$	546.477	+	382.555i	1.39053	+	0.973424i
$394$		0			0
$395$	382.012	−	220.555i	0.967119	−	0.558366i
$396$		0			0
$397$	−36.0513	+	62.4427i	−0.0908094	+	0.157286i	−0.907852	−	0.419291i	$-0.862279\pi$
$397$	−36.0513	+	62.4427i	−0.0908094	+	0.157286i	0.817043	+	0.576577i	$0.195612\pi$
$398$		0			0
$399$	333.272	+	155.361i	0.835268	+	0.389377i
$400$		0			0
$401$	−81.0353	+	222.643i	−0.202083	+	0.555218i	−0.998792	−	0.0491451i	$-0.984350\pi$
$401$	−81.0353	+	222.643i	−0.202083	+	0.555218i	0.796709	+	0.604364i	$0.206573\pi$
$402$		0			0
$403$	−85.0978	+	482.613i	−0.211161	+	1.19755i
$404$		0			0
$405$	−115.645	+	318.179i	−0.285542	+	0.785627i
$406$		0			0
$407$	94.4354	+	16.6515i	0.232028	+	0.0409128i
$408$		0			0
$409$	46.7510	+	17.0160i	0.114306	+	0.0416038i	0.398540	−	0.917151i	$-0.369517\pi$
$409$	46.7510	+	17.0160i	0.114306	+	0.0416038i	−0.284234	+	0.958755i	$0.591739\pi$
$410$		0			0
$411$	205.724	−	441.307i	0.500545	−	1.07374i
$412$		0			0
$413$	−390.473	−	225.440i	−0.945456	−	0.545859i
$414$		0			0
$415$	−168.178	−	291.293i	−0.405248	−	0.701910i
$416$		0			0
$417$	130.927	−	187.028i	0.313973	−	0.448507i
$418$		0			0
$419$	31.7034	−	5.59016i	0.0756643	−	0.0133417i	−0.135688	−	0.990752i	$-0.543324\pi$
$419$	31.7034	−	5.59016i	0.0756643	−	0.0133417i	0.211352	+	0.977410i	$0.432213\pi$
$420$		0			0
$421$	−214.696	−	180.151i	−0.509967	−	0.427913i	0.351151	−	0.936319i	$-0.385790\pi$
$421$	−214.696	−	180.151i	−0.509967	−	0.427913i	−0.861117	+	0.508406i	$0.830235\pi$
$422$		0			0
$423$	7.49447	−	42.5596i	0.0177174	−	0.100614i
$424$		0			0
$425$	−60.6669	−	166.681i	−0.142746	−	0.392190i
$426$		0			0
$427$	−213.234	+	178.924i	−0.499377	+	0.419027i
$428$		0			0
$429$	286.184	−	286.249i	0.667097	−	0.667248i
$430$		0			0
$431$			109.024i			0.252955i	0.991969	+	0.126478i	$0.0403672\pi$
$431$			109.024i			0.252955i	−0.991969	+	0.126478i	$0.959633\pi$
$432$		0			0
$433$	364.275			0.841282			0.420641	−	0.907227i	$-0.361805\pi$
$433$	364.275			0.841282			0.420641	+	0.907227i	$0.361805\pi$
$434$		0			0
$435$	−260.897	+	69.9388i	−0.599763	+	0.160779i
$436$		0			0
$437$	361.763	+	431.132i	0.827833	+	0.986573i
$438$		0			0
$439$	−275.236	+	100.178i	−0.626961	+	0.228195i	−0.635908	−	0.771765i	$-0.719374\pi$
$439$	−275.236	+	100.178i	−0.626961	+	0.228195i	0.00894720	+	0.999960i	$0.497152\pi$
$440$		0			0
$441$	194.648	−	34.3671i	0.441379	−	0.0779300i
$442$		0			0
$443$	424.424	−	505.809i	0.958068	−	1.14178i	−0.0317580	−	0.999496i	$-0.510111\pi$
$443$	424.424	−	505.809i	0.958068	−	1.14178i	0.989826	−	0.142285i	$-0.0454450\pi$
$444$		0			0
$445$	−48.6691	−	276.016i	−0.109369	−	0.620261i
$446$		0			0
$447$	23.9874	−	274.535i	0.0536630	−	0.614171i
$448$		0			0
$449$	−73.8335	+	42.6278i	−0.164440	+	0.0949394i	−0.579961	−	0.814644i	$-0.696932\pi$
$449$	−73.8335	+	42.6278i	−0.164440	+	0.0949394i	0.415522	+	0.909583i	$0.363599\pi$
$450$		0			0
$451$	−181.166	+	313.789i	−0.401699	+	0.695763i
$452$		0			0
$453$	−119.514	+	83.7048i	−0.263828	+	0.184779i
$454$		0			0
$455$	142.568	−	391.703i	0.313336	−	0.860885i
$456$		0			0
$457$	92.6648	−	525.528i	0.202768	−	1.14995i	−0.698147	−	0.715955i	$-0.745992\pi$
$457$	92.6648	−	525.528i	0.202768	−	1.14995i	0.900914	−	0.433997i	$-0.142897\pi$
$458$		0			0
$459$	164.374	−	614.287i	0.358114	−	1.33832i
$460$		0			0
$461$	−657.017	−	115.850i	−1.42520	−	0.251301i	−0.592743	−	0.805392i	$-0.701955\pi$
$461$	−657.017	−	115.850i	−1.42520	−	0.251301i	−0.832456	+	0.554091i	$0.813066\pi$
$462$		0			0
$463$	417.085	+	151.807i	0.900831	+	0.327876i	0.750586	−	0.660773i	$-0.229771\pi$
$463$	417.085	+	151.807i	0.900831	+	0.327876i	0.150246	+	0.988649i	$0.451994\pi$
$464$		0			0
$465$	−319.142	+	27.9577i	−0.686326	+	0.0601240i
$466$		0			0
$467$	−199.055	−	114.925i	−0.426242	−	0.246091i	0.271502	−	0.962438i	$-0.412480\pi$
$467$	−199.055	−	114.925i	−0.426242	−	0.246091i	−0.697745	+	0.716347i	$0.745813\pi$
$468$		0			0
$469$	−52.2944	−	90.5765i	−0.111502	−	0.193127i
$470$		0			0
$471$	−129.678	−	278.014i	−0.275326	−	0.590263i
$472$		0			0
$473$	−32.1521	+	5.66929i	−0.0679749	+	0.0119858i
$474$		0			0
$475$	135.995	+	114.113i	0.286304	+	0.240238i
$476$		0			0
$477$	−302.870	+	524.860i	−0.634947	+	1.10034i
$478$		0			0
$479$	−143.940	−	395.471i	−0.300501	−	0.825619i	−0.994413	−	0.105559i	$-0.966337\pi$
$479$	−143.940	−	395.471i	−0.300501	−	0.825619i	0.693912	−	0.720060i	$-0.255886\pi$
$480$		0			0
$481$	200.289	−	168.063i	0.416402	−	0.349403i
$482$		0			0
$483$	−359.773	−	96.3574i	−0.744873	−	0.199498i
$484$		0			0
$485$		−	611.294i		−	1.26040i
$486$		0			0
$487$	−528.889			−1.08601			−0.543007	−	0.839728i	$-0.682714\pi$
$487$	−528.889			−1.08601			−0.543007	+	0.839728i	$0.682714\pi$
$488$		0			0
$489$	32.6057	−	121.741i	0.0666782	−	0.248959i
$490$		0			0
$491$	388.337	+	462.802i	0.790911	+	0.942571i	0.999371	−	0.0354597i	$-0.0112895\pi$
$491$	388.337	+	462.802i	0.790911	+	0.942571i	−0.208460	+	0.978031i	$0.566845\pi$
$492$		0			0
$493$	476.759	−	173.526i	0.967056	−	0.351980i
$494$		0			0
$495$	229.189	+	132.253i	0.463007	+	0.267178i
$496$		0			0
$497$	329.135	−	392.248i	0.662244	−	0.789232i
$498$		0			0
$499$	81.1625	+	460.295i	0.162650	+	0.922436i	0.951454	+	0.307791i	$0.0995897\pi$
$499$	81.1625	+	460.295i	0.162650	+	0.922436i	−0.788804	+	0.614645i	$0.789299\pi$
$500$		0			0
$501$	32.2372	−	15.0369i	0.0643456	−	0.0300137i
$502$		0			0
$503$	−340.414	+	196.538i	−0.676767	+	0.390732i	−0.798636	−	0.601815i	$-0.794445\pi$
$503$	−340.414	+	196.538i	−0.676767	+	0.390732i	0.121869	+	0.992546i	$0.461111\pi$
$504$		0			0
$505$	−206.118	+	357.006i	−0.408154	+	0.706943i
$506$		0			0
$507$	−52.0686	−	594.372i	−0.102699	−	1.17233i
$508$		0			0
$509$	−88.2803	+	242.548i	−0.173439	+	0.476519i	−0.995705	−	0.0925841i	$-0.970487\pi$
$509$	−88.2803	+	242.548i	−0.173439	+	0.476519i	0.822266	+	0.569103i	$0.192710\pi$
$510$		0			0
$511$	125.731	−	713.055i	0.246049	−	1.39541i
$512$		0			0
$513$	164.931	+	614.696i	0.321503	+	1.19824i
$514$		0			0
$515$	575.193	+	101.422i	1.11688	+	0.196936i
$516$		0			0
$517$	−31.7399	−	11.5524i	−0.0613925	−	0.0223450i
$518$		0			0
$519$	320.464	+	457.560i	0.617465	+	0.881619i
$520$		0			0
$521$	610.780	+	352.634i	1.17232	+	0.676840i	0.954226	−	0.299087i	$-0.0966821\pi$
$521$	610.780	+	352.634i	1.17232	+	0.676840i	0.218096	+	0.975927i	$0.430015\pi$
$522$		0			0
$523$	157.023	+	271.972i	0.300235	+	0.520023i	0.976189	−	0.216921i	$-0.0696015\pi$
$523$	157.023	+	271.972i	0.300235	+	0.520023i	−0.675954	+	0.736944i	$0.736268\pi$
$524$		0			0
$525$	−117.039	−	10.2263i	−0.222932	−	0.0194786i
$526$		0			0
$527$	592.610	−	104.493i	1.12450	−	0.198279i
$528$		0			0
$529$	−31.4618	−	26.3996i	−0.0594742	−	0.0499047i
$530$		0			0
$531$	−135.689	−	768.512i	−0.255534	−	1.44729i
$532$		0			0
$533$	337.893	+	928.354i	0.633946	+	1.74175i
$534$		0			0
$535$	234.703	−	196.939i	0.438698	−	0.368111i
$536$		0			0
$537$	−73.5548	−	274.386i	−0.136974	−	0.510961i
$538$		0			0
$539$		−	154.493i		−	0.286628i
$540$		0			0
$541$	−430.803			−0.796309			−0.398155	−	0.917318i	$-0.630349\pi$
$541$	−430.803			−0.796309			−0.398155	+	0.917318i	$0.630349\pi$
$542$		0			0
$543$	−240.628	−	240.573i	−0.443145	−	0.443045i
$544$		0			0
$545$	−221.993	−	264.561i	−0.407327	−	0.485433i
$546$		0			0
$547$	−119.598	+	43.5300i	−0.218643	+	0.0795796i	−0.449019	−	0.893522i	$-0.648227\pi$
$547$	−119.598	+	43.5300i	−0.218643	+	0.0795796i	0.230376	+	0.973102i	$0.426004\pi$
$548$		0			0
$549$	−474.490	−	83.5546i	−0.864280	−	0.152194i
$550$		0			0
$551$	−326.398	+	388.986i	−0.592375	+	0.705965i
$552$		0			0
$553$	95.2958	+	540.450i	0.172325	+	0.977305i
$554$		0			0
$555$	140.023	+	98.0214i	0.252293	+	0.176615i
$556$		0			0
$557$	205.962	−	118.912i	0.369770	−	0.213487i	−0.303588	−	0.952803i	$-0.598185\pi$
$557$	205.962	−	118.912i	0.369770	−	0.213487i	0.673358	+	0.739316i	$0.264851\pi$
$558$		0			0
$559$	−44.5091	+	77.0921i	−0.0796228	+	0.137911i
$560$		0			0
$561$	−450.483	−	210.002i	−0.803000	−	0.374334i
$562$		0			0
$563$	311.664	−	856.289i	0.553577	−	1.52094i	−0.275215	−	0.961383i	$-0.588749\pi$
$563$	311.664	−	856.289i	0.553577	−	1.52094i	0.828792	−	0.559557i	$-0.189029\pi$
$564$		0			0
$565$	−125.861	+	713.795i	−0.222764	+	1.26335i
$566$		0			0
$567$	−322.768	−	270.586i	−0.569256	−	0.477223i
$568$		0			0
$569$	−346.766	−	61.1442i	−0.609430	−	0.107459i	−0.139588	−	0.990210i	$-0.544578\pi$
$569$	−346.766	−	61.1442i	−0.609430	−	0.107459i	−0.469842	+	0.882751i	$0.655689\pi$
$570$		0			0
$571$	−109.923	−	40.0089i	−0.192510	−	0.0700681i	0.243966	−	0.969784i	$-0.421551\pi$
$571$	−109.923	−	40.0089i	−0.192510	−	0.0700681i	−0.436476	+	0.899716i	$0.643774\pi$
$572$		0			0
$573$	−393.037	+	843.120i	−0.685929	+	1.47141i
$574$		0			0
$575$	−155.729	−	89.9104i	−0.270834	−	0.156366i
$576$		0			0
$577$	368.143	+	637.643i	0.638030	+	1.10510i	0.985865	+	0.167544i	$0.0535838\pi$
$577$	368.143	+	637.643i	0.638030	+	1.10510i	−0.347834	+	0.937556i	$0.613083\pi$
$578$		0			0
$579$	−380.794	+	543.962i	−0.657676	+	0.939485i
$580$		0			0
$581$	412.105	−	72.6652i	0.709303	−	0.125069i
$582$		0			0
$583$	362.829	+	304.450i	0.622348	+	0.522212i
$584$		0			0
$585$	677.917	−	246.915i	1.15883	−	0.422078i
$586$		0			0
$587$	28.4590	+	78.1905i	0.0484821	+	0.133204i	0.961570	−	0.274558i	$-0.0885316\pi$
$587$	28.4590	+	78.1905i	0.0484821	+	0.133204i	−0.913088	+	0.407762i	$0.866309\pi$
$588$		0			0
$589$	−461.359	+	387.126i	−0.783293	+	0.657261i
$590$		0			0
$591$	−316.196	+	316.268i	−0.535019	+	0.535140i
$592$		0			0
$593$		−	775.560i		−	1.30786i	−0.756556	−	0.653929i	$-0.773120\pi$
$593$		−	775.560i		−	1.30786i	0.756556	−	0.653929i	$-0.226880\pi$
$594$		0			0
$595$	−511.847			−0.860247
$596$		0			0
$597$	−489.734	+	131.283i	−0.820325	+	0.219905i
$598$		0			0
$599$	302.130	+	360.064i	0.504390	+	0.601108i	0.956816	−	0.290693i	$-0.0938859\pi$
$599$	302.130	+	360.064i	0.504390	+	0.601108i	−0.452426	+	0.891802i	$0.649441\pi$
$600$		0			0
$601$	−481.410	+	175.219i	−0.801015	+	0.291546i	−0.709907	−	0.704295i	$-0.751263\pi$
$601$	−481.410	+	175.219i	−0.801015	+	0.291546i	−0.0911082	+	0.995841i	$0.529041\pi$
$602$		0			0
$603$	61.8760	−	170.123i	0.102614	−	0.282127i
$604$		0			0
$605$	−192.131	+	228.973i	−0.317572	+	0.378467i
$606$		0			0
$607$	84.9380	+	481.708i	0.139931	+	0.793587i	0.971298	+	0.237864i	$0.0764474\pi$
$607$	84.9380	+	481.708i	0.139931	+	0.793587i	−0.831368	+	0.555723i	$0.812442\pi$
$608$		0			0
$609$	29.2503	−	334.769i	0.0480300	−	0.549702i
$610$		0			0
$611$	−79.7575	+	46.0480i	−0.130536	+	0.0753650i
$612$		0			0
$613$	−61.1107	+	105.847i	−0.0996912	+	0.172670i	−0.911557	−	0.411174i	$-0.865119\pi$
$613$	−61.1107	+	105.847i	−0.0996912	+	0.172670i	0.811866	+	0.583844i	$0.198452\pi$
$614$		0			0
$615$	−528.997	+	370.497i	−0.860158	+	0.602434i
$616$		0			0
$617$	−228.283	+	627.201i	−0.369988	+	1.01653i	0.605377	+	0.795939i	$0.293022\pi$
$617$	−228.283	+	627.201i	−0.369988	+	1.01653i	−0.975365	+	0.220595i	$0.929200\pi$
$618$		0			0
$619$	−109.522	+	621.131i	−0.176934	+	1.00344i	0.758954	+	0.651144i	$0.225711\pi$
$619$	−109.522	+	621.131i	−0.176934	+	1.00344i	−0.935888	+	0.352298i	$0.885400\pi$
$620$		0			0
$621$	−272.642	−	584.164i	−0.439037	−	0.940683i
$622$		0			0
$623$	343.393	+	60.5495i	0.551193	+	0.0971902i
$624$		0			0
$625$	357.077	+	129.965i	0.571323	+	0.207945i
$626$		0			0
$627$	495.550	−	43.4115i	0.790351	−	0.0692369i
$628$		0			0
$629$	−278.038	−	160.525i	−0.442032	−	0.255207i
$630$		0			0
$631$	0.442857	+	0.767050i	0.000701833	+	0.00121561i	0.866376	−	0.499392i	$-0.166443\pi$
$631$	0.442857	+	0.767050i	0.000701833	+	0.00121561i	−0.865674	+	0.500608i	$0.833110\pi$
$632$		0			0
$633$	−270.309	−	579.507i	−0.427028	−	0.915493i
$634$		0			0
$635$	918.161	−	161.897i	1.44592	−	0.254955i
$636$		0			0
$637$	−322.688	−	270.767i	−0.506574	−	0.425066i
$638$		0			0
$639$	886.264	−	0.200614i	1.38695	−	0.000313950i
$640$		0			0
$641$	100.064	+	274.923i	0.156106	+	0.428897i	0.992949	−	0.118546i	$-0.0378235\pi$
$641$	100.064	+	274.923i	0.156106	+	0.428897i	−0.836843	+	0.547443i	$0.815601\pi$
$642$		0			0
$643$	−368.253	+	309.001i	−0.572710	+	0.480561i	−0.882544	−	0.470230i	$-0.844171\pi$
$643$	−368.253	+	309.001i	−0.572710	+	0.480561i	0.309834	+	0.950791i	$0.399727\pi$
$644$		0			0
$645$	−56.2123	−	15.0552i	−0.0871509	−	0.0233414i
$646$		0			0
$647$		−	283.657i		−	0.438419i	−0.975678	−	0.219209i	$-0.929652\pi$
$647$		−	283.657i		−	0.438419i	0.975678	−	0.219209i	$-0.0703477\pi$
$648$		0			0
$649$	−609.969			−0.939860
$650$		0			0
$651$	103.113	−	384.998i	0.158392	−	0.591394i
$652$		0			0
$653$	−530.766	−	632.542i	−0.812811	−	0.968670i	0.187096	−	0.982342i	$-0.440093\pi$
$653$	−530.766	−	632.542i	−0.812811	−	0.968670i	−0.999907	+	0.0136713i	$0.995648\pi$
$654$		0			0
$655$	873.307	−	317.858i	1.33329	−	0.485279i
$656$		0			0
$657$	1085.18	−	626.856i	1.65172	−	0.954119i
$658$		0			0
$659$	−760.069	+	905.814i	−1.15337	+	1.37453i	−0.238317	+	0.971187i	$0.576596\pi$
$659$	−760.069	+	905.814i	−1.15337	+	1.37453i	−0.915050	+	0.403341i	$0.867849\pi$
$660$		0			0
$661$	213.726	+	1212.10i	0.323338	+	1.83374i	0.521108	+	0.853491i	$0.325519\pi$
$661$	213.726	+	1212.10i	0.323338	+	1.83374i	−0.197770	+	0.980248i	$0.563370\pi$
$662$		0			0
$663$	−1228.16	+	572.868i	−1.85242	+	0.864054i
$664$		0			0
$665$	443.648	−	256.140i	0.667140	−	0.385173i
$666$		0			0
$667$	257.171	−	445.434i	0.385564	−	0.667817i
$668$		0			0
$669$	14.2604	+	162.785i	0.0213160	+	0.243326i
$670$		0			0
$671$	−128.796	+	353.863i	−0.191946	+	0.527367i
$672$		0			0
$673$	202.091	−	1146.11i	0.300284	−	1.70299i	−0.344631	−	0.938738i	$-0.611996\pi$
$673$	202.091	−	1146.11i	0.300284	−	1.70299i	0.644915	−	0.764255i	$-0.276893\pi$
$674$		0			0
$675$	−116.692	−	166.533i	−0.172877	−	0.246716i
$676$		0			0
$677$	−137.416	−	24.2302i	−0.202978	−	0.0357905i	0.0712346	−	0.997460i	$-0.477306\pi$
$677$	−137.416	−	24.2302i	−0.202978	−	0.0357905i	−0.274213	+	0.961669i	$0.588417\pi$
$678$		0			0
$679$	714.651	+	260.112i	1.05250	+	0.383080i
$680$		0			0
$681$	151.354	+	216.104i	0.222253	+	0.317334i
$682$		0			0
$683$	−415.978	−	240.165i	−0.609046	−	0.351633i	0.163546	−	0.986536i	$-0.447707\pi$
$683$	−415.978	−	240.165i	−0.609046	−	0.351633i	−0.772592	+	0.634903i	$0.781040\pi$
$684$		0			0
$685$	−339.172	−	587.463i	−0.495142	−	0.857611i
$686$		0			0
$687$	776.163	+	67.8170i	1.12979	+	0.0987147i
$688$		0			0
$689$	1271.80	−	224.253i	1.84587	−	0.325476i
$690$		0			0
$691$	−918.527	−	770.736i	−1.32927	−	1.11539i	−0.984247	−	0.176798i	$-0.943426\pi$
$691$	−918.527	−	770.736i	−1.32927	−	1.11539i	−0.345025	−	0.938594i	$-0.612129\pi$
$692$		0			0
$693$	−252.136	+	211.664i	−0.363832	+	0.305432i
$694$		0			0
$695$	−108.784	−	298.882i	−0.156524	−	0.430047i
$696$		0			0
$697$	929.291	−	779.767i	1.33327	−	1.11875i
$698$		0			0
$699$	169.231	+	631.291i	0.242104	+	0.903135i
$700$		0			0
$701$			105.488i			0.150482i	0.997165	+	0.0752410i	$0.0239726\pi$
$701$			105.488i			0.150482i	−0.997165	+	0.0752410i	$0.976027\pi$
$702$		0			0
$703$	321.323			0.457074
$704$		0			0
$705$	−42.5765	−	42.5669i	−0.0603922	−	0.0603786i
$706$		0			0
$707$	−329.663	−	392.877i	−0.466284	−	0.555696i
$708$		0			0
$709$	166.245	−	60.5082i	0.234478	−	0.0853431i	−0.222109	−	0.975022i	$-0.571294\pi$
$709$	166.245	−	60.5082i	0.234478	−	0.0853431i	0.456587	+	0.889679i	$0.349072\pi$
$710$		0			0
$711$	−610.394	+	727.773i	−0.858500	+	1.02359i
$712$		0			0
$713$	392.125	−	467.317i	0.549965	−	0.655423i
$714$		0			0
$715$	−97.9238	−	555.353i	−0.136956	−	0.776718i
$716$		0			0
$717$	746.620	+	522.663i	1.04131	+	0.728959i
$718$		0			0
$719$	276.181	−	159.453i	0.384119	−	0.221771i	−0.295490	−	0.955346i	$-0.595483\pi$
$719$	276.181	−	159.453i	0.384119	−	0.221771i	0.679609	+	0.733575i	$0.262150\pi$
$720$		0			0
$721$	−363.320	+	629.289i	−0.503911	+	0.872800i
$722$		0			0
$723$	−517.972	−	241.463i	−0.716421	−	0.333974i
$724$		0			0
$725$	55.4901	−	152.458i	0.0765381	−	0.210287i
$726$		0			0
$727$	133.363	−	756.339i	0.183443	−	1.04036i	−0.744497	−	0.667626i	$-0.767311\pi$
$727$	133.363	−	756.339i	0.183443	−	1.04036i	0.927940	−	0.372730i	$-0.121578\pi$
$728$		0			0
$729$	−0.495048	−	729.000i	−0.000679078	−	1.00000i
$730$		0			0
$731$	107.647	+	18.9810i	0.147259	+	0.0259658i
$732$		0			0
$733$	599.501	+	218.200i	0.817873	+	0.297681i	0.716872	−	0.697205i	$-0.245573\pi$
$733$	599.501	+	218.200i	0.817873	+	0.297681i	0.101001	+	0.994886i	$0.467795\pi$
$734$		0			0
$735$	116.350	−	249.587i	0.158299	−	0.339575i
$736$		0			0
$737$	−122.536	−	70.7461i	−0.166263	−	0.0959920i
$738$		0			0
$739$	−47.0509	−	81.4946i	−0.0636684	−	0.110277i	0.832434	−	0.554124i	$-0.186947\pi$
$739$	−47.0509	−	81.4946i	−0.0636684	−	0.110277i	−0.896103	+	0.443847i	$0.853613\pi$
$740$		0			0
$741$	777.838	−	1111.14i	1.04971	−	1.49951i
$742$		0			0
$743$	−532.414	+	93.8789i	−0.716573	+	0.126351i	−0.520035	−	0.854145i	$-0.674081\pi$
$743$	−532.414	+	93.8789i	−0.716573	+	0.126351i	−0.196538	+	0.980496i	$0.562970\pi$
$744$		0			0
$745$	−294.110	−	246.788i	−0.394779	−	0.331259i
$746$		0			0
$747$	554.943	+	465.439i	0.742896	+	0.623077i
$748$		0			0
$749$	130.369	+	358.186i	0.174057	+	0.478219i
$750$		0			0
$751$	−212.859	+	178.610i	−0.283434	+	0.237829i	−0.773409	−	0.633907i	$-0.781450\pi$
$751$	−212.859	+	178.610i	−0.283434	+	0.237829i	0.489975	+	0.871736i	$0.337006\pi$
$752$		0			0
$753$	−598.168	+	598.304i	−0.794380	+	0.794560i
$754$		0			0
$755$			203.281i			0.269246i
$756$		0			0
$757$	−401.897			−0.530908			−0.265454	−	0.964124i	$-0.585522\pi$
$757$	−401.897			−0.530908			−0.265454	+	0.964124i	$0.585522\pi$
$758$		0			0
$759$	−486.688	+	130.467i	−0.641222	+	0.171893i
$760$		0			0
$761$	−31.3411	−	37.3509i	−0.0411841	−	0.0490813i	0.745059	−	0.666998i	$-0.232421\pi$
$761$	−31.3411	−	37.3509i	−0.0411841	−	0.0490813i	−0.786243	+	0.617917i	$0.787977\pi$
$762$		0			0
$763$	403.753	−	146.954i	0.529165	−	0.192600i
$764$		0			0
$765$	−569.614	−	678.528i	−0.744594	−	0.886964i
$766$		0			0
$767$	−1069.05	+	1274.04i	−1.39380	+	1.66107i
$768$		0			0
$769$	−213.365	−	1210.05i	−0.277457	−	1.57354i	−0.731046	−	0.682328i	$-0.760968\pi$
$769$	−213.365	−	1210.05i	−0.277457	−	1.57354i	0.453589	−	0.891211i	$-0.350144\pi$
$770$		0			0
$771$	112.701	−	1289.86i	0.146175	−	1.67297i
$772$		0			0
$773$	−334.794	+	193.294i	−0.433110	+	0.250056i	−0.700671	−	0.713485i	$-0.747116\pi$
$773$	−334.794	+	193.294i	−0.433110	+	0.250056i	0.267560	+	0.963541i	$0.413782\pi$
$774$		0			0
$775$	96.2141	−	166.648i	0.124147	−	0.215029i
$776$		0			0
$777$	−174.176	+	121.988i	−0.224164	+	0.156999i
$778$		0			0
$779$	−415.257	+	1140.91i	−0.533064	+	1.46458i
$780$		0			0
$781$	120.289	−	682.191i	0.154019	−	0.873484i
$782$		0			0
$783$	476.336	−	333.775i	0.608347	−	0.426277i
$784$		0			0
$785$	−420.894	−	74.2150i	−0.536171	−	0.0945415i
$786$		0			0
$787$	156.999	+	57.1429i	0.199490	+	0.0726085i	0.439833	−	0.898080i	$-0.355038\pi$
$787$	156.999	+	57.1429i	0.199490	+	0.0726085i	−0.240343	+	0.970688i	$0.577260\pi$
$788$		0			0
$789$	971.278	−	85.0866i	1.23102	−	0.107841i
$790$		0			0
$791$	−780.927	−	450.868i	−0.987266	−	0.569998i
$792$		0			0
$793$	513.382	+	889.203i	0.647392	+	1.12132i
$794$		0			0
$795$	356.876	+	765.098i	0.448901	+	0.962387i
$796$		0			0
$797$	1205.18	−	212.506i	1.51214	−	0.266632i	0.644805	−	0.764348i	$-0.276939\pi$
$797$	1205.18	−	212.506i	1.51214	−	0.266632i	0.867340	+	0.497716i	$0.165828\pi$
$798$		0			0
$799$	86.6292	+	72.6905i	0.108422	+	0.0909769i
$800$		0			0
$801$	301.882	+	522.601i	0.376881	+	0.652436i
$802$		0			0
$803$	−335.020	−	920.460i	−0.417211	−	1.14628i
$804$		0			0
$805$	−397.497	+	333.540i	−0.493785	+	0.414335i
$806$		0			0
$807$	644.675	+	172.662i	0.798853	+	0.213955i
$808$		0			0
$809$			86.8246i			0.107323i	0.998559	+	0.0536617i	$0.0170892\pi$
$809$			86.8246i			0.107323i	−0.998559	+	0.0536617i	$0.982911\pi$
$810$		0			0
$811$	−1587.52			−1.95748			−0.978740	−	0.205105i	$-0.934247\pi$
$811$	−1587.52			−1.95748			−0.978740	+	0.205105i	$0.934247\pi$
$812$		0			0
$813$	−323.375	+	1207.40i	−0.397756	+	1.48512i
$814$		0			0
$815$	−112.864	−	134.506i	−0.138483	−	0.165038i
$816$		0			0
$817$	−102.802	+	37.4169i	−0.125829	+	0.0457980i
$818$		0			0
$819$	0.203181	+	897.602i	0.000248084	+	1.09597i
$820$		0			0
$821$	296.471	−	353.321i	0.361110	−	0.430354i	−0.554648	−	0.832085i	$-0.687147\pi$
$821$	296.471	−	353.321i	0.361110	−	0.430354i	0.915758	+	0.401731i	$0.131591\pi$
$822$		0			0
$823$	−37.6079	−	213.285i	−0.0456962	−	0.259156i	0.953398	−	0.301716i	$-0.0975596\pi$
$823$	−37.6079	−	213.285i	−0.0456962	−	0.259156i	−0.999094	+	0.0425606i	$0.986448\pi$
$824$		0			0
$825$	−144.040	+	67.1869i	−0.174594	+	0.0814387i
$826$		0			0
$827$	91.8908	−	53.0532i	0.111113	−	0.0641514i	−0.443413	−	0.896317i	$-0.646233\pi$
$827$	91.8908	−	53.0532i	0.111113	−	0.0641514i	0.554527	+	0.832166i	$0.312899\pi$
$828$		0			0
$829$	562.231	−	973.812i	0.678204	−	1.17468i	−0.297318	−	0.954779i	$-0.596092\pi$
$829$	562.231	−	973.812i	0.678204	−	1.17468i	0.975521	−	0.219904i	$-0.0705746\pi$
$830$		0			0
$831$	−15.4176	−	175.995i	−0.0185531	−	0.211786i
$832$		0			0
$833$	−176.909	+	486.053i	−0.212376	+	0.583497i
$834$		0			0
$835$	8.60562	−	48.8049i	0.0103061	−	0.0584490i
$836$		0			0
$837$	625.121	−	291.757i	0.746858	−	0.348575i
$838$		0			0
$839$	−515.140	−	90.8331i	−0.613993	−	0.108263i	−0.142001	−	0.989866i	$-0.545354\pi$
$839$	−515.140	−	90.8331i	−0.613993	−	0.108263i	−0.471992	+	0.881603i	$0.656465\pi$
$840$		0			0
$841$	−354.205	−	128.920i	−0.421172	−	0.153294i
$842$		0			0
$843$	502.011	+	716.774i	0.595506	+	0.850266i
$844$		0			0
$845$	−719.875	−	415.620i	−0.851923	−	0.491858i
$846$		0			0
$847$	−185.933	−	322.046i	−0.219520	−	0.380220i
$848$		0			0
$849$	−264.051	−	23.0714i	−0.311014	−	0.0271747i
$850$		0			0
$851$	−320.527	+	56.5176i	−0.376648	+	0.0664132i
$852$		0			0
$853$	1294.14	+	1085.91i	1.51716	+	1.27305i	0.848092	+	0.529849i	$0.177751\pi$
$853$	1294.14	+	1085.91i	1.51716	+	1.27305i	0.669069	+	0.743200i	$0.266693\pi$
$854$		0			0
$855$	833.269	+	303.072i	0.974584	+	0.354470i
$856$		0			0
$857$	178.884	+	491.480i	0.208733	+	0.573489i	0.999241	−	0.0389630i	$-0.0124055\pi$
$857$	178.884	+	491.480i	0.208733	+	0.573489i	−0.790508	+	0.612452i	$0.790183\pi$
$858$		0			0
$859$	568.283	−	476.846i	0.661563	−	0.555117i	−0.248992	−	0.968506i	$-0.580099\pi$
$859$	568.283	−	476.846i	0.661563	−	0.555117i	0.910555	+	0.413388i	$0.135655\pi$
$860$		0			0
$861$	−208.047	−	776.089i	−0.241634	−	0.901381i
$862$		0			0
$863$		−	520.182i		−	0.602761i	−0.953504	−	0.301380i	$-0.902553\pi$
$863$		−	520.182i		−	0.602761i	0.953504	−	0.301380i	$-0.0974474\pi$
$864$		0			0
$865$	778.263			0.899726
$866$		0			0
$867$	563.674	+	563.546i	0.650143	+	0.649995i
$868$		0			0
$869$	477.220	+	568.729i	0.549160	+	0.654463i
$870$		0			0
$871$	−362.526	+	131.949i	−0.416218	+	0.151491i
$872$		0			0
$873$	450.490	+	1236.84i	0.516026	+	1.41677i
$874$		0			0
$875$	−454.450	+	541.592i	−0.519371	+	0.618963i
$876$		0			0
$877$	124.891	+	708.290i	0.142407	+	0.807628i	0.969413	+	0.245435i	$0.0789309\pi$
$877$	124.891	+	708.290i	0.142407	+	0.807628i	−0.827006	+	0.562193i	$0.809958\pi$
$878$		0			0
$879$	757.588	+	530.341i	0.861875	+	0.603346i
$880$		0			0
$881$	−871.566	+	503.199i	−0.989292	+	0.571168i	−0.905063	−	0.425279i	$-0.860176\pi$
$881$	−871.566	+	503.199i	−0.989292	+	0.571168i	−0.0842293	+	0.996446i	$0.526843\pi$
$882$		0			0
$883$	−329.836	+	571.293i	−0.373541	+	0.646991i	−0.990107	−	0.140311i	$-0.955190\pi$
$883$	−329.836	+	571.293i	−0.373541	+	0.646991i	0.616567	+	0.787303i	$0.288523\pi$
$884$		0			0
$885$	−985.423	−	459.375i	−1.11347	−	0.519067i
$886$		0			0
$887$	−540.115	+	1483.95i	−0.608923	+	1.67300i	0.123659	+	0.992325i	$0.460537\pi$
$887$	−540.115	+	1483.95i	−0.608923	+	1.67300i	−0.732582	+	0.680679i	$0.761685\pi$
$888$		0			0
$889$	−201.417	+	1142.29i	−0.226565	+	1.28492i
$890$		0			0
$891$	−561.184	−	98.6899i	−0.629836	−	0.110763i
$892$		0			0
$893$	−111.463	−	19.6539i	−0.124818	−	0.0220088i
$894$		0			0
$895$	−371.899	−	135.360i	−0.415530	−	0.151240i
$896$		0			0
$897$	−580.475	+	1245.20i	−0.647129	+	1.38818i
$898$		0			0
$899$	476.664	+	275.202i	0.530215	+	0.306120i
$900$		0			0
$901$	−792.881	−	1373.31i	−0.880002	−	1.52421i
$902$		0			0
$903$	41.5196	−	59.3104i	0.0459796	−	0.0656816i
$904$		0			0
$905$	−466.843	+	82.3170i	−0.515849	+	0.0909580i
$906$		0			0
$907$	−267.023	−	224.059i	−0.294402	−	0.247033i	0.483608	−	0.875285i	$-0.339326\pi$
$907$	−267.023	−	224.059i	−0.294402	−	0.247033i	−0.778010	+	0.628252i	$0.783771\pi$
$908$		0			0
$909$	153.947	−	874.233i	0.169358	−	0.961753i
$910$		0			0
$911$	−44.6619	−	122.708i	−0.0490252	−	0.134696i	0.912764	−	0.408488i	$-0.133944\pi$
$911$	−44.6619	−	122.708i	−0.0490252	−	0.134696i	−0.961789	+	0.273793i	$0.911722\pi$
$912$		0			0
$913$	433.668	−	363.891i	0.474993	−	0.398566i
$914$		0			0
$915$	−474.571	+	474.679i	−0.518657	+	0.518775i
$916$		0			0
$917$			1156.22i			1.26087i
$918$		0			0
$919$	995.800			1.08357			0.541785	−	0.840517i	$-0.317749\pi$
$919$	995.800			1.08357			0.541785	+	0.840517i	$0.317749\pi$
$920$		0			0
$921$	544.158	−	145.873i	0.590834	−	0.158385i
$922$		0			0
$923$	−1214.07	−	1446.87i	−1.31535	−	1.56757i
$924$		0			0
$925$	−96.4741	+	35.1137i	−0.104296	+	0.0379607i
$926$		0			0
$927$	−1238.54	+	218.677i	−1.33607	+	0.235897i
$928$		0			0
$929$	499.513	−	595.297i	0.537689	−	0.640793i	−0.426979	−	0.904262i	$-0.640422\pi$
$929$	499.513	−	595.297i	0.537689	−	0.640793i	0.964668	+	0.263469i	$0.0848665\pi$
$930$		0			0
$931$	−89.8951	−	509.820i	−0.0965576	−	0.547605i
$932$		0			0
$933$	146.304	−	1674.45i	0.156811	−	1.79469i
$934$		0			0
$935$	−599.678	+	346.224i	−0.641367	+	0.370293i
$936$		0			0
$937$	−308.703	+	534.690i	−0.329459	+	0.570640i	−0.982405	−	0.186765i	$-0.940200\pi$
$937$	−308.703	+	534.690i	−0.329459	+	0.570640i	0.652945	+	0.757405i	$0.273533\pi$
$938$		0			0
$939$	735.650	−	515.232i	0.783440	−	0.548703i
$940$		0			0
$941$	329.276	−	904.678i	0.349921	−	0.961400i	−0.632473	−	0.774582i	$-0.717960\pi$
$941$	329.276	−	904.678i	0.349921	−	0.961400i	0.982394	−	0.186818i	$-0.0598176\pi$
$942$		0			0
$943$	213.554	−	1211.12i	0.226462	−	1.28433i
$944$		0			0
$945$	−566.740	+	152.064i	−0.599725	+	0.160914i
$946$		0			0
$947$	988.466	+	174.293i	1.04379	+	0.184048i	0.669153	−	0.743125i	$-0.266657\pi$
$947$	988.466	+	174.293i	1.04379	+	0.184048i	0.374634	+	0.927173i	$0.377768\pi$
$948$		0			0
$949$	−2509.72	−	913.464i	−2.64460	−	0.962555i
$950$		0			0
$951$	438.607	−	38.4231i	0.461206	−	0.0404029i
$952$		0			0
$953$	970.138	+	560.110i	1.01798	+	0.587733i	0.913519	−	0.406796i	$-0.133354\pi$
$953$	970.138	+	560.110i	1.01798	+	0.587733i	0.104464	+	0.994529i	$0.466687\pi$
$954$		0			0
$955$	647.991	+	1122.35i	0.678524	+	1.17524i
$956$		0			0
$957$	−192.175	−	411.999i	−0.200810	−	0.430511i
$958$		0			0
$959$	831.111	−	146.547i	0.866644	−	0.152813i
$960$		0			0
$961$	−236.088	−	198.101i	−0.245669	−	0.206141i
$962$		0			0
$963$	−329.745	+	571.434i	−0.342414	+	0.593389i
$964$		0			0
$965$	316.395	+	869.287i	0.327870	+	0.900815i
$966$		0			0
$967$	−106.712	+	89.5422i	−0.110354	+	0.0925980i	−0.696295	−	0.717756i	$-0.745169\pi$
$967$	−106.712	+	89.5422i	−0.110354	+	0.0925980i	0.585941	+	0.810354i	$0.300725\pi$
$968$		0			0
$969$	−1608.77	−	430.874i	−1.66024	−	0.444659i
$970$		0			0
$971$			218.013i			0.224524i	0.993679	+	0.112262i	$0.0358096\pi$
$971$			218.013i			0.224524i	−0.993679	+	0.112262i	$0.964190\pi$
$972$		0			0
$973$	395.706			0.406686
$974$		0			0
$975$	−112.115	+	418.609i	−0.114990	+	0.429343i
$976$		0			0
$977$	−1088.10	−	1296.75i	−1.11372	−	1.32728i	−0.939492	−	0.342571i	$-0.888702\pi$
$977$	−1088.10	−	1296.75i	−1.11372	−	1.32728i	−0.174226	−	0.984706i	$-0.555742\pi$
$978$		0			0
$979$	443.276	−	161.339i	0.452784	−	0.164800i
$980$		0			0
$981$	644.129	+	371.694i	0.656605	+	0.378893i
$982$		0			0
$983$	1029.81	−	1227.28i	1.04762	−	1.24850i	0.0798107	−	0.996810i	$-0.474568\pi$
$983$	1029.81	−	1227.28i	1.04762	−	1.24850i	0.967807	−	0.251692i	$-0.0809871\pi$
$984$		0			0
$985$	108.193	+	613.593i	0.109841	+	0.622937i
$986$		0			0
$987$	67.8807	−	31.6627i	0.0687748	−	0.0320797i
$988$		0			0
$989$	95.9664	−	55.4062i	0.0970338	−	0.0560225i
$990$		0			0
$991$	−1.33401	+	2.31057i	−0.00134612	+	0.00233155i	−0.866698	−	0.498834i	$-0.833762\pi$
$991$	−1.33401	+	2.31057i	−0.00134612	+	0.00233155i	0.865352	+	0.501165i	$0.167095\pi$
$992$		0			0
$993$	−56.7777	−	648.127i	−0.0571779	−	0.652696i
$994$		0			0
$995$	−241.596	+	663.779i	−0.242810	+	0.667114i
$996$		0			0
$997$	−271.205	+	1538.08i	−0.272021	+	1.54271i	0.476249	+	0.879311i	$0.341996\pi$
$997$	−271.205	+	1538.08i	−0.272021	+	1.54271i	−0.748269	+	0.663395i	$0.769115\pi$
$998$		0			0
$999$	−355.546	−	95.1390i	−0.355902	−	0.0952342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.k.a.29.3	✓	36
3.2	odd	2		324.3.k.a.89.2		36
4.3	odd	2		432.3.bc.b.353.4		36
27.11	odd	18		2916.3.c.b.1457.11		36
27.13	even	9		324.3.k.a.233.2		36
27.14	odd	18	inner	108.3.k.a.41.3	yes	36
27.16	even	9		2916.3.c.b.1457.26		36
108.95	even	18		432.3.bc.b.257.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.29.3	✓	36	1.1	even	1	trivial
108.3.k.a.41.3	yes	36	27.14	odd	18	inner
324.3.k.a.89.2		36	3.2	odd	2
324.3.k.a.233.2		36	27.13	even	9
432.3.bc.b.257.4		36	108.95	even	18
432.3.bc.b.353.4		36	4.3	odd	2
2916.3.c.b.1457.11		36	27.11	odd	18
2916.3.c.b.1457.26		36	27.16	even	9

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.776129 + 2.89787i) q^{3} +(2.68656 + 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(-7.79525 - 4.49824i) q^{9} +O(q^{10})\)	\(q+(-0.776129 + 2.89787i) q^{3} +(2.68656 + 3.20172i) q^{5} +(-4.88621 + 1.77844i) q^{7} +(-7.79525 - 4.49824i) q^{9} +(-4.52170 + 5.38875i) q^{11} +(3.33062 + 18.8889i) q^{13} +(-11.3633 + 5.30034i) q^{15} +(20.3965 - 11.7759i) q^{17} +(-11.7859 + 20.4138i) q^{19} +(-1.36134 - 15.5399i) q^{21} +(8.16612 - 22.4362i) q^{23} +(1.30781 - 7.41698i) q^{25} +(19.0854 - 19.0984i) q^{27} +(21.2148 + 3.74075i) q^{29} +(24.0093 + 8.73866i) q^{31} +(-12.1065 - 17.2856i) q^{33} +(-18.8212 - 10.8664i) q^{35} +(-6.81584 - 11.8054i) q^{37} +(-57.3224 - 5.00853i) q^{39} +(50.7253 - 8.94424i) q^{41} +(3.55532 + 2.98327i) q^{43} +(-6.54032 - 37.0430i) q^{45} +(1.64224 + 4.51203i) q^{47} +(-16.8239 + 14.1170i) q^{49} +(18.2947 + 68.2459i) q^{51} -67.3308i q^{53} -29.4011 q^{55} +(-50.0089 - 49.9976i) q^{57} +(55.7367 + 66.4244i) q^{59} +(50.3038 - 18.3091i) q^{61} +(46.0891 + 8.11599i) q^{63} +(-51.5290 + 61.4098i) q^{65} +(3.49276 + 19.8084i) q^{67} +(58.6792 + 41.0777i) q^{69} +(-85.2808 + 49.2369i) q^{71} +(-69.6234 + 120.591i) q^{73} +(20.4784 + 9.54640i) q^{75} +(12.5104 - 34.3721i) q^{77} +(18.3268 - 103.937i) q^{79} +(40.5318 + 70.1297i) q^{81} +(-79.2540 - 13.9746i) q^{83} +(92.4995 + 33.6671i) q^{85} +(-27.3056 + 58.5744i) q^{87} +(-58.0744 - 33.5293i) q^{89} +(-49.8668 - 86.3718i) q^{91} +(-43.9577 + 62.7933i) q^{93} +(-97.0226 + 17.1077i) q^{95} +(-112.041 - 94.0132i) q^{97} +(59.4876 - 21.6670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 9 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q - 9 * q^5 + 6 * q^9	\( 36 q - 9 q^{5} + 6 q^{9} + 36 q^{11} + 45 q^{15} + 42 q^{21} - 18 q^{23} - 9 q^{25} - 18 q^{29} + 45 q^{31} - 153 q^{33} - 243 q^{35} - 123 q^{39} - 198 q^{41} + 90 q^{43} - 333 q^{45} - 243 q^{47} + 72 q^{49} - 99 q^{51} + 243 q^{57} + 252 q^{59} - 144 q^{61} + 381 q^{63} + 747 q^{65} + 108 q^{67} + 585 q^{69} + 324 q^{71} - 63 q^{73} + 597 q^{75} + 495 q^{77} + 36 q^{79} - 54 q^{81} - 27 q^{83} - 180 q^{85} - 441 q^{87} - 567 q^{89} + 99 q^{91} - 699 q^{93} - 1044 q^{95} - 216 q^{97} - 945 q^{99}+O(q^{100}) \) 36 * q - 9 * q^5 + 6 * q^9 + 36 * q^11 + 45 * q^15 + 42 * q^21 - 18 * q^23 - 9 * q^25 - 18 * q^29 + 45 * q^31 - 153 * q^33 - 243 * q^35 - 123 * q^39 - 198 * q^41 + 90 * q^43 - 333 * q^45 - 243 * q^47 + 72 * q^49 - 99 * q^51 + 243 * q^57 + 252 * q^59 - 144 * q^61 + 381 * q^63 + 747 * q^65 + 108 * q^67 + 585 * q^69 + 324 * q^71 - 63 * q^73 + 597 * q^75 + 495 * q^77 + 36 * q^79 - 54 * q^81 - 27 * q^83 - 180 * q^85 - 441 * q^87 - 567 * q^89 + 99 * q^91 - 699 * q^93 - 1044 * q^95 - 216 * q^97 - 945 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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