LMFDB - Embedded newform 156.3.j.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,3,Mod(73,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("156.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.j (of order $4$, 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:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1579585536.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 $ x^8 - 2x^7 - 4x^6 + 28x^5 - 38x^4 + 8x^3 + 200x^2 - 352*x + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$-2.59436 - 0.0368949i$ of defining polynomial
Character	$\chi$	$=$	156.109
Dual form			156.3.j.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(-0.658261 + 0.658261i) q^{5} +(1.58447 + 1.58447i) q^{7} +3.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{3} +(-0.658261 + 0.658261i) q^{5} +(1.58447 + 1.58447i) q^{7} +3.00000 q^{9} +(15.0357 + 15.0357i) q^{11} +(-9.25706 + 9.12726i) q^{13} +(1.14014 - 1.14014i) q^{15} +25.0351i q^{17} +(17.2748 - 17.2748i) q^{19} +(-2.74438 - 2.74438i) q^{21} -3.84263i q^{23} +24.1334i q^{25} -5.19615 q^{27} +18.0287 q^{29} +(1.56960 - 1.56960i) q^{31} +(-26.0426 - 26.0426i) q^{33} -2.08599 q^{35} +(-47.4919 - 47.4919i) q^{37} +(16.0337 - 15.8089i) q^{39} +(-23.2188 + 23.2188i) q^{41} -37.7860i q^{43} +(-1.97478 + 1.97478i) q^{45} +(34.6909 + 34.6909i) q^{47} -43.9789i q^{49} -43.3621i q^{51} +27.0004 q^{53} -19.7948 q^{55} +(-29.9209 + 29.9209i) q^{57} +(-27.0615 - 27.0615i) q^{59} -67.7505 q^{61} +(4.75341 + 4.75341i) q^{63} +(0.0854427 - 12.1017i) q^{65} +(10.6994 - 10.6994i) q^{67} +6.65563i q^{69} +(37.3282 - 37.3282i) q^{71} +(51.5768 + 51.5768i) q^{73} -41.8002i q^{75} +47.6472i q^{77} +105.309 q^{79} +9.00000 q^{81} +(-89.5509 + 89.5509i) q^{83} +(-16.4797 - 16.4797i) q^{85} -31.2265 q^{87} +(7.20315 + 7.20315i) q^{89} +(-29.1294 - 0.205665i) q^{91} +(-2.71862 + 2.71862i) q^{93} +22.7427i q^{95} +(5.87941 - 5.87941i) q^{97} +(45.1071 + 45.1071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{5} - 8 q^{7} + 24 q^{9}+O(q^{10}) $ 8 * q + 12 * q^5 - 8 * q^7 + 24 * q^9	$ 8 q + 12 q^{5} - 8 q^{7} + 24 q^{9} + 12 q^{11} + 24 q^{13} + 12 q^{15} + 88 q^{19} + 24 q^{29} - 16 q^{31} - 36 q^{33} - 216 q^{35} + 32 q^{37} + 72 q^{39} - 180 q^{41} + 36 q^{45} + 36 q^{47} - 72 q^{53} - 240 q^{55} + 24 q^{57} - 228 q^{59} - 192 q^{61} - 24 q^{63} + 132 q^{65} + 16 q^{67} + 36 q^{71} + 160 q^{73} + 48 q^{79} + 72 q^{81} + 12 q^{83} + 24 q^{85} - 120 q^{87} + 60 q^{89} + 112 q^{91} + 120 q^{93} + 416 q^{97} + 36 q^{99}+O(q^{100}) $ 8 * q + 12 * q^5 - 8 * q^7 + 24 * q^9 + 12 * q^11 + 24 * q^13 + 12 * q^15 + 88 * q^19 + 24 * q^29 - 16 * q^31 - 36 * q^33 - 216 * q^35 + 32 * q^37 + 72 * q^39 - 180 * q^41 + 36 * q^45 + 36 * q^47 - 72 * q^53 - 240 * q^55 + 24 * q^57 - 228 * q^59 - 192 * q^61 - 24 * q^63 + 132 * q^65 + 16 * q^67 + 36 * q^71 + 160 * q^73 + 48 * q^79 + 72 * q^81 + 12 * q^83 + 24 * q^85 - 120 * q^87 + 60 * q^89 + 112 * q^91 + 120 * q^93 + 416 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$		0			0
$5$	−0.658261	+	0.658261i	−0.131652	+	0.131652i	−0.769862	−	0.638210i	$-0.779675\pi$
$5$	−0.658261	+	0.658261i	−0.131652	+	0.131652i	0.638210	+	0.769862i	$0.279675\pi$
$6$		0			0
$7$	1.58447	+	1.58447i	0.226353	+	0.226353i	0.811167	−	0.584814i	$-0.198833\pi$
$7$	1.58447	+	1.58447i	0.226353	+	0.226353i	−0.584814	+	0.811167i	$0.698833\pi$
$8$		0			0
$9$	3.00000			0.333333
$10$		0			0
$11$	15.0357	+	15.0357i	1.36688	+	1.36688i	0.864849	+	0.502032i	$0.167414\pi$
$11$	15.0357	+	15.0357i	1.36688	+	1.36688i	0.502032	+	0.864849i	$0.332586\pi$
$12$		0			0
$13$	−9.25706	+	9.12726i	−0.712081	+	0.702097i
$13$	−9.25706	+	9.12726i	−0.712081	+	0.702097i
$14$		0			0
$15$	1.14014	−	1.14014i	0.0760094	−	0.0760094i
$16$		0			0
$17$			25.0351i			1.47266i	0.676625	+	0.736328i	$0.263442\pi$
$17$			25.0351i			1.47266i	−0.676625	+	0.736328i	$0.736558\pi$
$18$		0			0
$19$	17.2748	−	17.2748i	0.909202	−	0.909202i	−0.0870058	−	0.996208i	$-0.527730\pi$
$19$	17.2748	−	17.2748i	0.909202	−	0.909202i	0.996208	+	0.0870058i	$0.0277299\pi$
$20$		0			0
$21$	−2.74438	−	2.74438i	−0.130685	−	0.130685i
$22$		0			0
$23$		−	3.84263i		−	0.167071i	−0.996505	−	0.0835354i	$-0.973379\pi$
$23$		−	3.84263i		−	0.167071i	0.996505	−	0.0835354i	$-0.0266212\pi$
$24$		0			0
$25$			24.1334i			0.965335i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$	18.0287			0.621678			0.310839	−	0.950463i	$-0.399390\pi$
$29$	18.0287			0.621678			0.310839	+	0.950463i	$0.399390\pi$
$30$		0			0
$31$	1.56960	−	1.56960i	0.0506321	−	0.0506321i	−0.681337	−	0.731970i	$-0.738601\pi$
$31$	1.56960	−	1.56960i	0.0506321	−	0.0506321i	0.731970	+	0.681337i	$0.238601\pi$
$32$		0			0
$33$	−26.0426	−	26.0426i	−0.789169	−	0.789169i
$34$		0			0
$35$	−2.08599			−0.0595998
$36$		0			0
$37$	−47.4919	−	47.4919i	−1.28357	−	1.28357i	−0.938624	−	0.344942i	$-0.887899\pi$
$37$	−47.4919	−	47.4919i	−1.28357	−	1.28357i	−0.344942	−	0.938624i	$-0.612101\pi$
$38$		0			0
$39$	16.0337	−	15.8089i	0.411120	−	0.405356i
$40$		0			0
$41$	−23.2188	+	23.2188i	−0.566313	+	0.566313i	−0.931093	−	0.364781i	$-0.881144\pi$
$41$	−23.2188	+	23.2188i	−0.566313	+	0.566313i	0.364781	+	0.931093i	$0.381144\pi$
$42$		0			0
$43$		−	37.7860i		−	0.878744i	−0.898305	−	0.439372i	$-0.855201\pi$
$43$		−	37.7860i		−	0.878744i	0.898305	−	0.439372i	$-0.144799\pi$
$44$		0			0
$45$	−1.97478	+	1.97478i	−0.0438841	+	0.0438841i
$46$		0			0
$47$	34.6909	+	34.6909i	0.738104	+	0.738104i	0.972211	−	0.234107i	$-0.0752165\pi$
$47$	34.6909	+	34.6909i	0.738104	+	0.738104i	−0.234107	+	0.972211i	$0.575216\pi$
$48$		0			0
$49$		−	43.9789i		−	0.897529i
$50$		0			0
$51$		−	43.3621i		−	0.850238i
$52$		0			0
$53$	27.0004			0.509441			0.254721	−	0.967015i	$-0.418016\pi$
$53$	27.0004			0.509441			0.254721	+	0.967015i	$0.418016\pi$
$54$		0			0
$55$	−19.7948			−0.359906
$56$		0			0
$57$	−29.9209	+	29.9209i	−0.524928	+	0.524928i
$58$		0			0
$59$	−27.0615	−	27.0615i	−0.458669	−	0.458669i	0.439550	−	0.898218i	$-0.355138\pi$
$59$	−27.0615	−	27.0615i	−0.458669	−	0.458669i	−0.898218	+	0.439550i	$0.855138\pi$
$60$		0			0
$61$	−67.7505			−1.11066			−0.555332	−	0.831629i	$-0.687409\pi$
$61$	−67.7505			−1.11066			−0.555332	+	0.831629i	$0.687409\pi$
$62$		0			0
$63$	4.75341	+	4.75341i	0.0754510	+	0.0754510i
$64$		0			0
$65$	0.0854427	−	12.1017i	0.00131450	−	0.186180i
$66$		0			0
$67$	10.6994	−	10.6994i	0.159692	−	0.159692i	−0.622738	−	0.782430i	$-0.713980\pi$
$67$	10.6994	−	10.6994i	0.159692	−	0.159692i	0.782430	+	0.622738i	$0.213980\pi$
$68$		0			0
$69$			6.65563i			0.0964584i
$70$		0			0
$71$	37.3282	−	37.3282i	0.525750	−	0.525750i	−0.393552	−	0.919302i	$-0.628754\pi$
$71$	37.3282	−	37.3282i	0.525750	−	0.525750i	0.919302	+	0.393552i	$0.128754\pi$
$72$		0			0
$73$	51.5768	+	51.5768i	0.706532	+	0.706532i	0.965804	−	0.259273i	$-0.0834828\pi$
$73$	51.5768	+	51.5768i	0.706532	+	0.706532i	−0.259273	+	0.965804i	$0.583483\pi$
$74$		0			0
$75$		−	41.8002i		−	0.557337i
$76$		0			0
$77$			47.6472i			0.618795i
$78$		0			0
$79$	105.309			1.33302			0.666511	−	0.745495i	$-0.267787\pi$
$79$	105.309			1.33302			0.666511	+	0.745495i	$0.267787\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		0			0
$83$	−89.5509	+	89.5509i	−1.07893	+	1.07893i	−0.0823203	+	0.996606i	$0.526233\pi$
$83$	−89.5509	+	89.5509i	−1.07893	+	1.07893i	−0.996606	+	0.0823203i	$0.973767\pi$
$84$		0			0
$85$	−16.4797	−	16.4797i	−0.193878	−	0.193878i
$86$		0			0
$87$	−31.2265			−0.358926
$88$		0			0
$89$	7.20315	+	7.20315i	0.0809342	+	0.0809342i	0.746415	−	0.665481i	$-0.231773\pi$
$89$	7.20315	+	7.20315i	0.0809342	+	0.0809342i	−0.665481	+	0.746415i	$0.731773\pi$
$90$		0			0
$91$	−29.1294	−	0.205665i	−0.320104	−	0.00226006i
$92$		0			0
$93$	−2.71862	+	2.71862i	−0.0292325	+	0.0292325i
$94$		0			0
$95$			22.7427i			0.239397i
$96$		0			0
$97$	5.87941	−	5.87941i	0.0606124	−	0.0606124i	−0.676151	−	0.736763i	$-0.736353\pi$
$97$	5.87941	−	5.87941i	0.0606124	−	0.0606124i	0.736763	+	0.676151i	$0.236353\pi$
$98$		0			0
$99$	45.1071	+	45.1071i	0.455627	+	0.455627i
$100$		0			0
$101$		−	112.057i		−	1.10948i	−0.832024	−	0.554739i	$-0.812818\pi$
$101$		−	112.057i		−	1.10948i	0.832024	−	0.554739i	$-0.187182\pi$
$102$		0			0
$103$			59.7483i			0.580080i	0.957014	+	0.290040i	$0.0936686\pi$
$103$			59.7483i			0.580080i	−0.957014	+	0.290040i	$0.906331\pi$
$104$		0			0
$105$	3.61304			0.0344099
$106$		0			0
$107$	43.4127			0.405726			0.202863	−	0.979207i	$-0.434975\pi$
$107$	43.4127			0.405726			0.202863	+	0.979207i	$0.434975\pi$
$108$		0			0
$109$	−45.9159	+	45.9159i	−0.421247	+	0.421247i	−0.885633	−	0.464386i	$-0.846275\pi$
$109$	−45.9159	+	45.9159i	−0.421247	+	0.421247i	0.464386	+	0.885633i	$0.346275\pi$
$110$		0			0
$111$	82.2584	+	82.2584i	0.741067	+	0.741067i
$112$		0			0
$113$	167.104			1.47880			0.739400	−	0.673267i	$-0.235109\pi$
$113$	167.104			1.47880			0.739400	+	0.673267i	$0.235109\pi$
$114$		0			0
$115$	2.52945	+	2.52945i	0.0219952	+	0.0219952i
$116$		0			0
$117$	−27.7712	+	27.3818i	−0.237360	+	0.234032i
$118$		0			0
$119$	−39.6675	+	39.6675i	−0.333340	+	0.333340i
$120$		0			0
$121$			331.144i			2.73673i
$122$		0			0
$123$	40.2162	−	40.2162i	0.326961	−	0.326961i
$124$		0			0
$125$	−32.3426	−	32.3426i	−0.258741	−	0.258741i
$126$		0			0
$127$		−	135.848i		−	1.06967i	−0.844958	−	0.534833i	$-0.820374\pi$
$127$		−	135.848i		−	1.06967i	0.844958	−	0.534833i	$-0.179626\pi$
$128$		0			0
$129$			65.4473i			0.507343i
$130$		0			0
$131$	26.7614			0.204286			0.102143	−	0.994770i	$-0.467430\pi$
$131$	26.7614			0.204286			0.102143	+	0.994770i	$0.467430\pi$
$132$		0			0
$133$	54.7430			0.411601
$134$		0			0
$135$	3.42042	−	3.42042i	0.0253365	−	0.0253365i
$136$		0			0
$137$	−111.192	−	111.192i	−0.811623	−	0.811623i	0.173254	−	0.984877i	$-0.444572\pi$
$137$	−111.192	−	111.192i	−0.811623	−	0.811623i	−0.984877	+	0.173254i	$0.944572\pi$
$138$		0			0
$139$	195.300			1.40504			0.702518	−	0.711666i	$-0.252059\pi$
$139$	195.300			1.40504			0.702518	+	0.711666i	$0.252059\pi$
$140$		0			0
$141$	−60.0864	−	60.0864i	−0.426145	−	0.426145i
$142$		0			0
$143$	−276.421	−	1.95164i	−1.93301	−	0.0136478i
$144$		0			0
$145$	−11.8676	+	11.8676i	−0.0818452	+	0.0818452i
$146$		0			0
$147$			76.1737i			0.518188i
$148$		0			0
$149$	83.6113	−	83.6113i	0.561150	−	0.561150i	−0.368484	−	0.929634i	$-0.620123\pi$
$149$	83.6113	−	83.6113i	0.561150	−	0.561150i	0.929634	+	0.368484i	$0.120123\pi$
$150$		0			0
$151$	87.7277	+	87.7277i	0.580978	+	0.580978i	0.935172	−	0.354194i	$-0.115245\pi$
$151$	87.7277	+	87.7277i	0.580978	+	0.580978i	−0.354194	+	0.935172i	$0.615245\pi$
$152$		0			0
$153$			75.1054i			0.490885i
$154$		0			0
$155$			2.06641i			0.0133317i
$156$		0			0
$157$	3.27422			0.0208549			0.0104275	−	0.999946i	$-0.496681\pi$
$157$	3.27422			0.0208549			0.0104275	+	0.999946i	$0.496681\pi$
$158$		0			0
$159$	−46.7660			−0.294126
$160$		0			0
$161$	6.08853	−	6.08853i	0.0378170	−	0.0378170i
$162$		0			0
$163$	−115.100	−	115.100i	−0.706134	−	0.706134i	0.259586	−	0.965720i	$-0.416414\pi$
$163$	−115.100	−	115.100i	−0.706134	−	0.706134i	−0.965720	+	0.259586i	$0.916414\pi$
$164$		0			0
$165$	34.2856			0.207792
$166$		0			0
$167$	−140.004	−	140.004i	−0.838345	−	0.838345i	0.150296	−	0.988641i	$-0.451977\pi$
$167$	−140.004	−	140.004i	−0.838345	−	0.838345i	−0.988641	+	0.150296i	$0.951977\pi$
$168$		0			0
$169$	2.38630	−	168.983i	0.0141201	−	0.999900i
$170$		0			0
$171$	51.8245	−	51.8245i	0.303067	−	0.303067i
$172$		0			0
$173$		−	249.207i		−	1.44050i	−0.693713	−	0.720251i	$-0.744027\pi$
$173$		−	249.207i		−	1.44050i	0.693713	−	0.720251i	$-0.255973\pi$
$174$		0			0
$175$	−38.2387	+	38.2387i	−0.218507	+	0.218507i
$176$		0			0
$177$	46.8718	+	46.8718i	0.264813	+	0.264813i
$178$		0			0
$179$		−	227.440i		−	1.27062i	−0.772259	−	0.635308i	$-0.780873\pi$
$179$		−	227.440i		−	1.27062i	0.772259	−	0.635308i	$-0.219127\pi$
$180$		0			0
$181$		−	329.424i		−	1.82002i	−0.414585	−	0.910010i	$-0.636073\pi$
$181$		−	329.424i		−	1.82002i	0.414585	−	0.910010i	$-0.363927\pi$
$182$		0			0
$183$	117.347			0.641242
$184$		0			0
$185$	62.5242			0.337969
$186$		0			0
$187$	−376.421	+	376.421i	−2.01294	+	2.01294i
$188$		0			0
$189$	−8.23315	−	8.23315i	−0.0435617	−	0.0435617i
$190$		0			0
$191$	−312.723			−1.63729			−0.818646	−	0.574298i	$-0.805275\pi$
$191$	−312.723			−1.63729			−0.818646	+	0.574298i	$0.805275\pi$
$192$		0			0
$193$	−31.6615	−	31.6615i	−0.164049	−	0.164049i	0.620308	−	0.784358i	$-0.287007\pi$
$193$	−31.6615	−	31.6615i	−0.164049	−	0.164049i	−0.784358	+	0.620308i	$0.787007\pi$
$194$		0			0
$195$	−0.147991	+	20.9607i	−0.000758928	+	0.107491i
$196$		0			0
$197$	−45.6399	+	45.6399i	−0.231675	+	0.231675i	−0.813391	−	0.581717i	$-0.802381\pi$
$197$	−45.6399	+	45.6399i	−0.231675	+	0.231675i	0.581717	+	0.813391i	$0.302381\pi$
$198$		0			0
$199$		−	87.8310i		−	0.441362i	−0.975346	−	0.220681i	$-0.929172\pi$
$199$		−	87.8310i		−	0.441362i	0.975346	−	0.220681i	$-0.0708279\pi$
$200$		0			0
$201$	−18.5319	+	18.5319i	−0.0921985	+	0.0921985i
$202$		0			0
$203$	28.5659	+	28.5659i	0.140719	+	0.140719i
$204$		0			0
$205$		−	30.5681i		−	0.149113i
$206$		0			0
$207$		−	11.5279i		−	0.0556903i
$208$		0			0
$209$	519.478			2.48554
$210$		0			0
$211$	250.450			1.18697			0.593484	−	0.804846i	$-0.297752\pi$
$211$	250.450			1.18697			0.593484	+	0.804846i	$0.297752\pi$
$212$		0			0
$213$	−64.6544	+	64.6544i	−0.303542	+	0.303542i
$214$		0			0
$215$	24.8731	+	24.8731i	0.115689	+	0.115689i
$216$		0			0
$217$	4.97396			0.0229215
$218$		0			0
$219$	−89.3336	−	89.3336i	−0.407916	−	0.407916i
$220$		0			0
$221$	−228.502	−	231.752i	−1.03395	−	1.04865i
$222$		0			0
$223$	69.7836	−	69.7836i	0.312931	−	0.312931i	−0.533113	−	0.846044i	$-0.678978\pi$
$223$	69.7836	−	69.7836i	0.312931	−	0.312931i	0.846044	+	0.533113i	$0.178978\pi$
$224$		0			0
$225$			72.4002i			0.321778i
$226$		0			0
$227$	−217.194	+	217.194i	−0.956800	+	0.956800i	−0.999105	−	0.0423044i	$-0.986530\pi$
$227$	−217.194	+	217.194i	−0.956800	+	0.956800i	0.0423044	+	0.999105i	$0.486530\pi$
$228$		0			0
$229$	123.051	+	123.051i	0.537342	+	0.537342i	0.922747	−	0.385405i	$-0.125938\pi$
$229$	123.051	+	123.051i	0.537342	+	0.537342i	−0.385405	+	0.922747i	$0.625938\pi$
$230$		0			0
$231$		−	82.5274i		−	0.357262i
$232$		0			0
$233$			113.035i			0.485128i	0.970135	+	0.242564i	$0.0779885\pi$
$233$			113.035i			0.485128i	−0.970135	+	0.242564i	$0.922012\pi$
$234$		0			0
$235$	−45.6713			−0.194346
$236$		0			0
$237$	−182.400			−0.769621
$238$		0			0
$239$	−19.3896	+	19.3896i	−0.0811280	+	0.0811280i	−0.746506	−	0.665378i	$-0.768270\pi$
$239$	−19.3896	+	19.3896i	−0.0811280	+	0.0811280i	0.665378	+	0.746506i	$0.268270\pi$
$240$		0			0
$241$	109.783	+	109.783i	0.455530	+	0.455530i	0.897185	−	0.441655i	$-0.145609\pi$
$241$	109.783	+	109.783i	0.455530	+	0.455530i	−0.441655	+	0.897185i	$0.645609\pi$
$242$		0			0
$243$	−15.5885			−0.0641500
$244$		0			0
$245$	28.9496	+	28.9496i	0.118162	+	0.118162i
$246$		0			0
$247$	−2.24228	+	317.586i	−0.00907807	+	1.28577i
$248$		0			0
$249$	155.107	−	155.107i	0.622918	−	0.622918i
$250$		0			0
$251$			197.106i			0.785283i	0.919692	+	0.392641i	$0.128439\pi$
$251$			197.106i			0.785283i	−0.919692	+	0.392641i	$0.871561\pi$
$252$		0			0
$253$	57.7766	−	57.7766i	0.228366	−	0.228366i
$254$		0			0
$255$	28.5436	+	28.5436i	0.111936	+	0.111936i
$256$		0			0
$257$			208.062i			0.809578i	0.914410	+	0.404789i	$0.132655\pi$
$257$			208.062i			0.809578i	−0.914410	+	0.404789i	$0.867345\pi$
$258$		0			0
$259$		−	150.499i		−	0.581078i
$260$		0			0
$261$	54.0860			0.207226
$262$		0			0
$263$	508.567			1.93372			0.966858	−	0.255314i	$-0.0821788\pi$
$263$	508.567			1.93372			0.966858	+	0.255314i	$0.0821788\pi$
$264$		0			0
$265$	−17.7733	+	17.7733i	−0.0670691	+	0.0670691i
$266$		0			0
$267$	−12.4762	−	12.4762i	−0.0467274	−	0.0467274i
$268$		0			0
$269$	500.925			1.86218			0.931088	−	0.364794i	$-0.118861\pi$
$269$	500.925			1.86218			0.931088	+	0.364794i	$0.118861\pi$
$270$		0			0
$271$	−255.858	−	255.858i	−0.944127	−	0.944127i	0.0543924	−	0.998520i	$-0.482678\pi$
$271$	−255.858	−	255.858i	−0.944127	−	0.944127i	−0.998520	+	0.0543924i	$0.982678\pi$
$272$		0			0
$273$	50.4536	+	0.356223i	0.184812	+	0.00130485i
$274$		0			0
$275$	−362.862	+	362.862i	−1.31950	+	1.31950i
$276$		0			0
$277$			291.758i			1.05328i	0.850089	+	0.526639i	$0.176548\pi$
$277$			291.758i			1.05328i	−0.850089	+	0.526639i	$0.823452\pi$
$278$		0			0
$279$	4.70879	−	4.70879i	0.0168774	−	0.0168774i
$280$		0			0
$281$	234.936	+	234.936i	0.836070	+	0.836070i	0.988339	−	0.152269i	$-0.0486579\pi$
$281$	234.936	+	234.936i	0.836070	+	0.836070i	−0.152269	+	0.988339i	$0.548658\pi$
$282$		0			0
$283$		−	117.549i		−	0.415368i	−0.978196	−	0.207684i	$-0.933407\pi$
$283$		−	117.549i		−	0.415368i	0.978196	−	0.207684i	$-0.0665926\pi$
$284$		0			0
$285$		−	39.3915i		−	0.138216i
$286$		0			0
$287$	−73.5791			−0.256373
$288$		0			0
$289$	−337.758			−1.16871
$290$		0			0
$291$	−10.1834	+	10.1834i	−0.0349946	+	0.0349946i
$292$		0			0
$293$	−225.520	−	225.520i	−0.769693	−	0.769693i	0.208360	−	0.978052i	$-0.433188\pi$
$293$	−225.520	−	225.520i	−0.769693	−	0.769693i	−0.978052	+	0.208360i	$0.933188\pi$
$294$		0			0
$295$	35.6270			0.120770
$296$		0			0
$297$	−78.1277	−	78.1277i	−0.263056	−	0.263056i
$298$		0			0
$299$	35.0727	+	35.5714i	0.117300	+	0.118968i
$300$		0			0
$301$	59.8709	−	59.8709i	0.198906	−	0.198906i
$302$		0			0
$303$			194.089i			0.640557i
$304$		0			0
$305$	44.5975	−	44.5975i	0.146221	−	0.146221i
$306$		0			0
$307$	−99.6530	−	99.6530i	−0.324603	−	0.324603i	0.525927	−	0.850530i	$-0.323718\pi$
$307$	−99.6530	−	99.6530i	−0.324603	−	0.324603i	−0.850530	+	0.525927i	$0.823718\pi$
$308$		0			0
$309$		−	103.487i		−	0.334909i
$310$		0			0
$311$			240.846i			0.774426i	0.921990	+	0.387213i	$0.126562\pi$
$311$			240.846i			0.774426i	−0.921990	+	0.387213i	$0.873438\pi$
$312$		0			0
$313$	222.040			0.709392			0.354696	−	0.934982i	$-0.384584\pi$
$313$	222.040			0.709392			0.354696	+	0.934982i	$0.384584\pi$
$314$		0			0
$315$	−6.25797			−0.0198666
$316$		0			0
$317$	−110.189	+	110.189i	−0.347599	+	0.347599i	−0.859214	−	0.511616i	$-0.829047\pi$
$317$	−110.189	+	110.189i	−0.347599	+	0.347599i	0.511616	+	0.859214i	$0.329047\pi$
$318$		0			0
$319$	271.073	+	271.073i	0.849759	+	0.849759i
$320$		0			0
$321$	−75.1930			−0.234246
$322$		0			0
$323$	432.478	+	432.478i	1.33894	+	1.33894i
$324$		0			0
$325$	−220.272	−	223.404i	−0.677759	−	0.687397i
$326$		0			0
$327$	79.5287	−	79.5287i	0.243207	−	0.243207i
$328$		0			0
$329$			109.933i			0.334144i
$330$		0			0
$331$	324.246	−	324.246i	0.979596	−	0.979596i	−0.0201995	−	0.999796i	$-0.506430\pi$
$331$	324.246	−	324.246i	0.979596	−	0.979596i	0.999796	+	0.0201995i	$0.00643015\pi$
$332$		0			0
$333$	−142.476	−	142.476i	−0.427855	−	0.427855i
$334$		0			0
$335$			14.0860i			0.0420477i
$336$		0			0
$337$			373.021i			1.10689i	0.832887	+	0.553444i	$0.186687\pi$
$337$			373.021i			1.10689i	−0.832887	+	0.553444i	$0.813313\pi$
$338$		0			0
$339$	−289.433			−0.853785
$340$		0			0
$341$	47.1999			0.138416
$342$		0			0
$343$	147.322	−	147.322i	0.429511	−	0.429511i
$344$		0			0
$345$	−4.38114	−	4.38114i	−0.0126990	−	0.0126990i
$346$		0			0
$347$	427.314			1.23145			0.615726	−	0.787960i	$-0.288863\pi$
$347$	427.314			1.23145			0.615726	+	0.787960i	$0.288863\pi$
$348$		0			0
$349$	−119.713	−	119.713i	−0.343018	−	0.343018i	0.514483	−	0.857501i	$-0.327984\pi$
$349$	−119.713	−	119.713i	−0.343018	−	0.343018i	−0.857501	+	0.514483i	$0.827984\pi$
$350$		0			0
$351$	48.1011	−	47.4266i	0.137040	−	0.135119i
$352$		0			0
$353$	−211.757	+	211.757i	−0.599877	+	0.599877i	−0.940280	−	0.340403i	$-0.889437\pi$
$353$	−211.757	+	211.757i	−0.599877	+	0.599877i	0.340403	+	0.940280i	$0.389437\pi$
$354$		0			0
$355$			49.1434i			0.138432i
$356$		0			0
$357$	68.7061	−	68.7061i	0.192454	−	0.192454i
$358$		0			0
$359$	−410.773	−	410.773i	−1.14421	−	1.14421i	−0.987671	−	0.156543i	$-0.949965\pi$
$359$	−410.773	−	410.773i	−1.14421	−	1.14421i	−0.156543	−	0.987671i	$-0.550035\pi$
$360$		0			0
$361$		−	235.840i		−	0.653297i
$362$		0			0
$363$		−	573.558i		−	1.58005i
$364$		0			0
$365$	−67.9020			−0.186033
$366$		0			0
$367$	−633.968			−1.72743			−0.863717	−	0.503977i	$-0.831869\pi$
$367$	−633.968			−1.72743			−0.863717	+	0.503977i	$0.831869\pi$
$368$		0			0
$369$	−69.6565	+	69.6565i	−0.188771	+	0.188771i
$370$		0			0
$371$	42.7813	+	42.7813i	0.115314	+	0.115314i
$372$		0			0
$373$	−309.092			−0.828664			−0.414332	−	0.910126i	$-0.635985\pi$
$373$	−309.092			−0.828664			−0.414332	+	0.910126i	$0.635985\pi$
$374$		0			0
$375$	56.0190	+	56.0190i	0.149384	+	0.149384i
$376$		0			0
$377$	−166.892	+	164.552i	−0.442685	+	0.436478i
$378$		0			0
$379$	321.675	−	321.675i	0.848747	−	0.848747i	−0.141229	−	0.989977i	$-0.545106\pi$
$379$	321.675	−	321.675i	0.848747	−	0.848747i	0.989977	+	0.141229i	$0.0451055\pi$
$380$		0			0
$381$			235.295i			0.617572i
$382$		0			0
$383$	193.170	−	193.170i	0.504360	−	0.504360i	−0.408430	−	0.912790i	$-0.633924\pi$
$383$	193.170	−	193.170i	0.504360	−	0.504360i	0.912790	+	0.408430i	$0.133924\pi$
$384$		0			0
$385$	−31.3643	−	31.3643i	−0.0814658	−	0.0814658i
$386$		0			0
$387$		−	113.358i		−	0.292915i
$388$		0			0
$389$			211.198i			0.542925i	0.962449	+	0.271462i	$0.0875072\pi$
$389$			211.198i			0.542925i	−0.962449	+	0.271462i	$0.912493\pi$
$390$		0			0
$391$	96.2007			0.246038
$392$		0			0
$393$	−46.3521			−0.117944
$394$		0			0
$395$	−69.3207	+	69.3207i	−0.175495	+	0.175495i
$396$		0			0
$397$	−370.045	−	370.045i	−0.932102	−	0.932102i	0.0657349	−	0.997837i	$-0.479061\pi$
$397$	−370.045	−	370.045i	−0.932102	−	0.932102i	−0.997837	+	0.0657349i	$0.979061\pi$
$398$		0			0
$399$	−94.8176			−0.237638
$400$		0			0
$401$	222.142	+	222.142i	0.553970	+	0.553970i	0.927584	−	0.373614i	$-0.121882\pi$
$401$	222.142	+	222.142i	0.553970	+	0.553970i	−0.373614	+	0.927584i	$0.621882\pi$
$402$		0			0
$403$	−0.203734	+	28.8559i	−0.000505544	+	0.0716028i
$404$		0			0
$405$	−5.92435	+	5.92435i	−0.0146280	+	0.0146280i
$406$		0			0
$407$		−	1428.15i		−	3.50896i
$408$		0			0
$409$	−305.781	+	305.781i	−0.747632	+	0.747632i	−0.974034	−	0.226402i	$-0.927304\pi$
$409$	−305.781	+	305.781i	−0.747632	+	0.747632i	0.226402	+	0.974034i	$0.427304\pi$
$410$		0			0
$411$	192.591	+	192.591i	0.468591	+	0.468591i
$412$		0			0
$413$		−	85.7562i		−	0.207642i
$414$		0			0
$415$		−	117.896i		−	0.284086i
$416$		0			0
$417$	−338.269			−0.811198
$418$		0			0
$419$	561.889			1.34102			0.670512	−	0.741899i	$-0.266075\pi$
$419$	561.889			1.34102			0.670512	+	0.741899i	$0.266075\pi$
$420$		0			0
$421$	334.967	−	334.967i	0.795646	−	0.795646i	−0.186759	−	0.982406i	$-0.559798\pi$
$421$	334.967	−	334.967i	0.795646	−	0.795646i	0.982406	+	0.186759i	$0.0597985\pi$
$422$		0			0
$423$	104.073	+	104.073i	0.246035	+	0.246035i
$424$		0			0
$425$	−604.183			−1.42161
$426$		0			0
$427$	−107.349	−	107.349i	−0.251402	−	0.251402i
$428$		0			0
$429$	478.775	+	3.38034i	1.11603	+	0.00787958i
$430$		0			0
$431$	−173.849	+	173.849i	−0.403361	+	0.403361i	−0.879416	−	0.476055i	$-0.842066\pi$
$431$	−173.849	+	173.849i	−0.403361	+	0.403361i	0.476055	+	0.879416i	$0.342066\pi$
$432$		0			0
$433$		−	73.0803i		−	0.168777i	−0.996433	−	0.0843883i	$-0.973106\pi$
$433$		−	73.0803i		−	0.168777i	0.996433	−	0.0843883i	$-0.0268936\pi$
$434$		0			0
$435$	20.5552	−	20.5552i	0.0472534	−	0.0472534i
$436$		0			0
$437$	−66.3808	−	66.3808i	−0.151901	−	0.151901i
$438$		0			0
$439$			255.720i			0.582506i	0.956646	+	0.291253i	$0.0940721\pi$
$439$			255.720i			0.582506i	−0.956646	+	0.291253i	$0.905928\pi$
$440$		0			0
$441$		−	131.937i		−	0.299176i
$442$		0			0
$443$	117.457			0.265139			0.132570	−	0.991174i	$-0.457677\pi$
$443$	117.457			0.265139			0.132570	+	0.991174i	$0.457677\pi$
$444$		0			0
$445$	−9.48310			−0.0213103
$446$		0			0
$447$	−144.819	+	144.819i	−0.323980	+	0.323980i
$448$		0			0
$449$	−488.348	−	488.348i	−1.08764	−	1.08764i	−0.995772	−	0.0918641i	$-0.970717\pi$
$449$	−488.348	−	488.348i	−1.08764	−	1.08764i	−0.0918641	−	0.995772i	$-0.529283\pi$
$450$		0			0
$451$	−698.222			−1.54816
$452$		0			0
$453$	−151.949	−	151.949i	−0.335428	−	0.335428i
$454$		0			0
$455$	19.3101	−	19.0394i	0.0424399	−	0.0418448i
$456$		0			0
$457$	92.8153	−	92.8153i	0.203097	−	0.203097i	−0.598229	−	0.801326i	$-0.704128\pi$
$457$	92.8153	−	92.8153i	0.203097	−	0.203097i	0.801326	+	0.598229i	$0.204128\pi$
$458$		0			0
$459$		−	130.086i		−	0.283413i
$460$		0			0
$461$	−640.257	+	640.257i	−1.38884	+	1.38884i	−0.561090	+	0.827755i	$0.689618\pi$
$461$	−640.257	+	640.257i	−1.38884	+	1.38884i	−0.827755	+	0.561090i	$0.810382\pi$
$462$		0			0
$463$	467.667	+	467.667i	1.01008	+	1.01008i	0.999949	+	0.0101317i	$0.00322509\pi$
$463$	467.667	+	467.667i	1.01008	+	1.01008i	0.0101317	+	0.999949i	$0.496775\pi$
$464$		0			0
$465$		−	3.57912i		−	0.00769704i
$466$		0			0
$467$			334.101i			0.715420i	0.933833	+	0.357710i	$0.116442\pi$
$467$			334.101i			0.715420i	−0.933833	+	0.357710i	$0.883558\pi$
$468$		0			0
$469$	33.9058			0.0722938
$470$		0			0
$471$	−5.67112			−0.0120406
$472$		0			0
$473$	568.139	−	568.139i	1.20114	−	1.20114i
$474$		0			0
$475$	416.900	+	416.900i	0.877685	+	0.877685i
$476$		0			0
$477$	81.0012			0.169814
$478$		0			0
$479$	101.834	+	101.834i	0.212596	+	0.212596i	0.805370	−	0.592773i	$-0.201967\pi$
$479$	101.834	+	101.834i	0.212596	+	0.212596i	−0.592773	+	0.805370i	$0.701967\pi$
$480$		0			0
$481$	873.107	+	6.16448i	1.81519	+	0.0128160i
$482$		0			0
$483$	−10.5457	+	10.5457i	−0.0218336	+	0.0218336i
$484$		0			0
$485$			7.74037i			0.0159595i
$486$		0			0
$487$	166.576	−	166.576i	0.342045	−	0.342045i	−0.515091	−	0.857136i	$-0.672242\pi$
$487$	166.576	−	166.576i	0.342045	−	0.342045i	0.857136	+	0.515091i	$0.172242\pi$
$488$		0			0
$489$	199.359	+	199.359i	0.407687	+	0.407687i
$490$		0			0
$491$		−	58.9206i		−	0.120001i	−0.998198	−	0.0600006i	$-0.980890\pi$
$491$		−	58.9206i		−	0.120001i	0.998198	−	0.0600006i	$-0.0191103\pi$
$492$		0			0
$493$			451.350i			0.915517i
$494$		0			0
$495$	−59.3845			−0.119969
$496$		0			0
$497$	118.291			0.238010
$498$		0			0
$499$	47.7366	−	47.7366i	0.0956645	−	0.0956645i	−0.657655	−	0.753319i	$-0.728451\pi$
$499$	47.7366	−	47.7366i	0.0956645	−	0.0956645i	0.753319	+	0.657655i	$0.228451\pi$
$500$		0			0
$501$	242.493	+	242.493i	0.484019	+	0.484019i
$502$		0			0
$503$	251.151			0.499307			0.249653	−	0.968335i	$-0.419683\pi$
$503$	251.151			0.499307			0.249653	+	0.968335i	$0.419683\pi$
$504$		0			0
$505$	73.7629	+	73.7629i	0.146065	+	0.146065i
$506$		0			0
$507$	−4.13318	+	292.687i	−0.00815224	+	0.577293i
$508$		0			0
$509$	−406.259	+	406.259i	−0.798152	+	0.798152i	−0.982804	−	0.184652i	$-0.940884\pi$
$509$	−406.259	+	406.259i	−0.798152	+	0.798152i	0.184652	+	0.982804i	$0.440884\pi$
$510$		0			0
$511$			163.444i			0.319851i
$512$		0			0
$513$	−89.7627	+	89.7627i	−0.174976	+	0.174976i
$514$		0			0
$515$	−39.3300	−	39.3300i	−0.0763688	−	0.0763688i
$516$		0			0
$517$			1043.20i			2.01780i
$518$		0			0
$519$			431.639i			0.831674i
$520$		0			0
$521$	−671.347			−1.28857			−0.644287	−	0.764784i	$-0.722846\pi$
$521$	−671.347			−1.28857			−0.644287	+	0.764784i	$0.722846\pi$
$522$		0			0
$523$	−206.149			−0.394166			−0.197083	−	0.980387i	$-0.563147\pi$
$523$	−206.149			−0.394166			−0.197083	+	0.980387i	$0.563147\pi$
$524$		0			0
$525$	66.2313	−	66.2313i	0.126155	−	0.126155i
$526$		0			0
$527$	39.2950	+	39.2950i	0.0745637	+	0.0745637i
$528$		0			0
$529$	514.234			0.972087
$530$		0			0
$531$	−81.1844	−	81.1844i	−0.152890	−	0.152890i
$532$		0			0
$533$	3.01382	−	426.862i	0.00565444	−	0.800867i
$534$		0			0
$535$	−28.5769	+	28.5769i	−0.0534147	+	0.0534147i
$536$		0			0
$537$			393.938i			0.733590i
$538$		0			0
$539$	661.253	−	661.253i	1.22681	−	1.22681i
$540$		0			0
$541$	−343.269	−	343.269i	−0.634508	−	0.634508i	0.314687	−	0.949195i	$-0.398100\pi$
$541$	−343.269	−	343.269i	−0.634508	−	0.634508i	−0.949195	+	0.314687i	$0.898100\pi$
$542$		0			0
$543$			570.579i			1.05079i
$544$		0			0
$545$		−	60.4493i		−	0.110916i
$546$		0			0
$547$	−864.846			−1.58107			−0.790535	−	0.612417i	$-0.790198\pi$
$547$	−864.846			−1.58107			−0.790535	+	0.612417i	$0.790198\pi$
$548$		0			0
$549$	−203.251			−0.370221
$550$		0			0
$551$	311.442	−	311.442i	0.565231	−	0.565231i
$552$		0			0
$553$	166.859	+	166.859i	0.301734	+	0.301734i
$554$		0			0
$555$	−108.295			−0.195126
$556$		0			0
$557$	571.864	+	571.864i	1.02669	+	1.02669i	0.999634	+	0.0270521i	$0.00861201\pi$
$557$	571.864	+	571.864i	1.02669	+	1.02669i	0.0270521	+	0.999634i	$0.491388\pi$
$558$		0			0
$559$	344.883	+	349.787i	0.616964	+	0.625738i
$560$		0			0
$561$	651.980	−	651.980i	1.16217	−	1.16217i
$562$		0			0
$563$		−	401.423i		−	0.713007i	−0.934294	−	0.356503i	$-0.883969\pi$
$563$		−	401.423i		−	0.713007i	0.934294	−	0.356503i	$-0.116031\pi$
$564$		0			0
$565$	−109.998	+	109.998i	−0.194687	+	0.194687i
$566$		0			0
$567$	14.2602	+	14.2602i	0.0251503	+	0.0251503i
$568$		0			0
$569$			466.836i			0.820450i	0.911984	+	0.410225i	$0.134550\pi$
$569$			466.836i			0.820450i	−0.911984	+	0.410225i	$0.865450\pi$
$570$		0			0
$571$		−	585.223i		−	1.02491i	−0.858715	−	0.512454i	$-0.828736\pi$
$571$		−	585.223i		−	1.02491i	0.858715	−	0.512454i	$-0.171264\pi$
$572$		0			0
$573$	541.652			0.945291
$574$		0			0
$575$	92.7356			0.161279
$576$		0			0
$577$	−254.263	+	254.263i	−0.440664	+	0.440664i	−0.892235	−	0.451571i	$-0.850864\pi$
$577$	−254.263	+	254.263i	−0.440664	+	0.440664i	0.451571	+	0.892235i	$0.350864\pi$
$578$		0			0
$579$	54.8394	+	54.8394i	0.0947140	+	0.0947140i
$580$		0			0
$581$	−283.782			−0.488436
$582$		0			0
$583$	405.969	+	405.969i	0.696346	+	0.696346i
$584$		0			0
$585$	0.256328	−	36.3050i	0.000438168	−	0.0620599i
$586$		0			0
$587$	−275.047	+	275.047i	−0.468564	+	0.468564i	−0.901449	−	0.432885i	$-0.857496\pi$
$587$	−275.047	+	275.047i	−0.468564	+	0.468564i	0.432885	+	0.901449i	$0.357496\pi$
$588$		0			0
$589$		−	54.2290i		−	0.0920696i
$590$		0			0
$591$	79.0507	−	79.0507i	0.133757	−	0.133757i
$592$		0			0
$593$	−718.420	−	718.420i	−1.21150	−	1.21150i	−0.970533	−	0.240969i	$-0.922535\pi$
$593$	−718.420	−	718.420i	−1.21150	−	1.21150i	−0.240969	−	0.970533i	$-0.577465\pi$
$594$		0			0
$595$		−	52.2231i		−	0.0877699i
$596$		0			0
$597$			152.128i			0.254820i
$598$		0			0
$599$	−503.738			−0.840964			−0.420482	−	0.907301i	$-0.638139\pi$
$599$	−503.738			−0.840964			−0.420482	+	0.907301i	$0.638139\pi$
$600$		0			0
$601$	−103.995			−0.173036			−0.0865180	−	0.996250i	$-0.527574\pi$
$601$	−103.995			−0.173036			−0.0865180	+	0.996250i	$0.527574\pi$
$602$		0			0
$603$	32.0982	−	32.0982i	0.0532308	−	0.0532308i
$604$		0			0
$605$	−217.979	−	217.979i	−0.360296	−	0.360296i
$606$		0			0
$607$	−40.8426			−0.0672860			−0.0336430	−	0.999434i	$-0.510711\pi$
$607$	−40.8426			−0.0672860			−0.0336430	+	0.999434i	$0.510711\pi$
$608$		0			0
$609$	−49.4776	−	49.4776i	−0.0812439	−	0.0812439i
$610$		0			0
$611$	−637.769	−	4.50290i	−1.04381	−	0.00736972i
$612$		0			0
$613$	632.200	−	632.200i	1.03132	−	1.03132i	0.0318284	−	0.999493i	$-0.489867\pi$
$613$	632.200	−	632.200i	1.03132	−	1.03132i	0.999493	−	0.0318284i	$-0.0101330\pi$
$614$		0			0
$615$			52.9455i			0.0860902i
$616$		0			0
$617$	−209.552	+	209.552i	−0.339630	+	0.339630i	−0.856228	−	0.516598i	$-0.827198\pi$
$617$	−209.552	+	209.552i	−0.339630	+	0.339630i	0.516598	+	0.856228i	$0.327198\pi$
$618$		0			0
$619$	−40.2523	−	40.2523i	−0.0650279	−	0.0650279i	0.673845	−	0.738873i	$-0.264642\pi$
$619$	−40.2523	−	40.2523i	−0.0650279	−	0.0650279i	−0.738873	+	0.673845i	$0.764642\pi$
$620$		0			0
$621$			19.9669i			0.0321528i
$622$		0			0
$623$			22.8264i			0.0366394i
$624$		0			0
$625$	−560.755			−0.897208
$626$		0			0
$627$	−899.763			−1.43503
$628$		0			0
$629$	1188.97	−	1188.97i	1.89025	−	1.89025i
$630$		0			0
$631$	426.702	+	426.702i	0.676232	+	0.676232i	0.959145	−	0.282914i	$-0.0913010\pi$
$631$	426.702	+	426.702i	0.676232	+	0.676232i	−0.282914	+	0.959145i	$0.591301\pi$
$632$		0			0
$633$	−433.793			−0.685296
$634$		0			0
$635$	89.4232	+	89.4232i	0.140824	+	0.140824i
$636$		0			0
$637$	401.407	+	407.115i	0.630152	+	0.639114i
$638$		0			0
$639$	111.985	−	111.985i	0.175250	−	0.175250i
$640$		0			0
$641$		−	435.611i		−	0.679581i	−0.940501	−	0.339790i	$-0.889644\pi$
$641$		−	435.611i		−	0.679581i	0.940501	−	0.339790i	$-0.110356\pi$
$642$		0			0
$643$	−44.3698	+	44.3698i	−0.0690043	+	0.0690043i	−0.740767	−	0.671762i	$-0.765538\pi$
$643$	−44.3698	+	44.3698i	−0.0690043	+	0.0690043i	0.671762	+	0.740767i	$0.265538\pi$
$644$		0			0
$645$	−43.0814	−	43.0814i	−0.0667929	−	0.0667929i
$646$		0			0
$647$			105.823i			0.163559i	0.996650	+	0.0817797i	$0.0260604\pi$
$647$			105.823i			0.163559i	−0.996650	+	0.0817797i	$0.973940\pi$
$648$		0			0
$649$		−	813.775i		−	1.25389i
$650$		0			0
$651$	−8.61515			−0.0132337
$652$		0			0
$653$	−739.833			−1.13298			−0.566488	−	0.824070i	$-0.691698\pi$
$653$	−739.833			−1.13298			−0.566488	+	0.824070i	$0.691698\pi$
$654$		0			0
$655$	−17.6160	+	17.6160i	−0.0268947	+	0.0268947i
$656$		0			0
$657$	154.730	+	154.730i	0.235511	+	0.235511i
$658$		0			0
$659$	165.432			0.251035			0.125517	−	0.992091i	$-0.459941\pi$
$659$	165.432			0.251035			0.125517	+	0.992091i	$0.459941\pi$
$660$		0			0
$661$	653.530	+	653.530i	0.988699	+	0.988699i	0.999937	−	0.0112381i	$-0.00357727\pi$
$661$	653.530	+	653.530i	0.988699	+	0.988699i	−0.0112381	+	0.999937i	$0.503577\pi$
$662$		0			0
$663$	395.777	+	401.406i	0.596949	+	0.605439i
$664$		0			0
$665$	−36.0352	+	36.0352i	−0.0541882	+	0.0541882i
$666$		0			0
$667$		−	69.2774i		−	0.103864i
$668$		0			0
$669$	−120.869	+	120.869i	−0.180671	+	0.180671i
$670$		0			0
$671$	−1018.67	−	1018.67i	−1.51814	−	1.51814i
$672$		0			0
$673$		−	755.376i		−	1.12240i	−0.827680	−	0.561200i	$-0.810340\pi$
$673$		−	755.376i		−	1.12240i	0.827680	−	0.561200i	$-0.189660\pi$
$674$		0			0
$675$		−	125.401i		−	0.185779i
$676$		0			0
$677$	749.186			1.10663			0.553313	−	0.832974i	$-0.313363\pi$
$677$	749.186			1.10663			0.553313	+	0.832974i	$0.313363\pi$
$678$		0			0
$679$	18.6315			0.0274396
$680$		0			0
$681$	376.191	−	376.191i	0.552409	−	0.552409i
$682$		0			0
$683$	333.528	+	333.528i	0.488328	+	0.488328i	0.907778	−	0.419450i	$-0.137777\pi$
$683$	333.528	+	333.528i	0.488328	+	0.488328i	−0.419450	+	0.907778i	$0.637777\pi$
$684$		0			0
$685$	146.387			0.213704
$686$		0			0
$687$	−213.131	−	213.131i	−0.310235	−	0.310235i
$688$		0			0
$689$	−249.944	+	246.440i	−0.362764	+	0.357677i
$690$		0			0
$691$	−578.975	+	578.975i	−0.837880	+	0.837880i	−0.988580	−	0.150699i	$-0.951847\pi$
$691$	−578.975	+	578.975i	−0.837880	+	0.837880i	0.150699	+	0.988580i	$0.451847\pi$
$692$		0			0
$693$			142.942i			0.206265i
$694$		0			0
$695$	−128.558	+	128.558i	−0.184976	+	0.184976i
$696$		0			0
$697$	−581.287	−	581.287i	−0.833984	−	0.833984i
$698$		0			0
$699$		−	195.782i		−	0.280089i
$700$		0			0
$701$			980.331i			1.39848i	0.714889	+	0.699238i	$0.246477\pi$
$701$			980.331i			1.39848i	−0.714889	+	0.699238i	$0.753523\pi$
$702$		0			0
$703$	−1640.83			−2.33404
$704$		0			0
$705$	79.1051			0.112206
$706$		0			0
$707$	177.552	−	177.552i	0.251134	−	0.251134i
$708$		0			0
$709$	−517.269	−	517.269i	−0.729576	−	0.729576i	0.240960	−	0.970535i	$-0.422538\pi$
$709$	−517.269	−	517.269i	−0.729576	−	0.729576i	−0.970535	+	0.240960i	$0.922538\pi$
$710$		0			0
$711$	315.926			0.444341
$712$		0			0
$713$	−6.03137	−	6.03137i	−0.00845915	−	0.00845915i
$714$		0			0
$715$	183.242	−	180.672i	0.256282	−	0.252689i
$716$		0			0
$717$	33.5838	−	33.5838i	0.0468393	−	0.0468393i
$718$		0			0
$719$		−	655.862i		−	0.912187i	−0.889932	−	0.456093i	$-0.849248\pi$
$719$		−	655.862i		−	0.912187i	0.889932	−	0.456093i	$-0.150752\pi$
$720$		0			0
$721$	−94.6694	+	94.6694i	−0.131303	+	0.131303i
$722$		0			0
$723$	−190.149	−	190.149i	−0.263000	−	0.263000i
$724$		0			0
$725$			435.092i			0.600128i
$726$		0			0
$727$		−	1179.25i		−	1.62207i	−0.584996	−	0.811036i	$-0.698904\pi$
$727$		−	1179.25i		−	1.62207i	0.584996	−	0.811036i	$-0.301096\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	945.978			1.29409
$732$		0			0
$733$	95.7379	−	95.7379i	0.130611	−	0.130611i	−0.638779	−	0.769390i	$-0.720560\pi$
$733$	95.7379	−	95.7379i	0.130611	−	0.130611i	0.769390	+	0.638779i	$0.220560\pi$
$734$		0			0
$735$	−50.1422	−	50.1422i	−0.0682206	−	0.0682206i
$736$		0			0
$737$	321.746			0.436561
$738$		0			0
$739$	−659.673	−	659.673i	−0.892657	−	0.892657i	0.102116	−	0.994773i	$-0.467439\pi$
$739$	−659.673	−	659.673i	−0.892657	−	0.892657i	−0.994773	+	0.102116i	$0.967439\pi$
$740$		0			0
$741$	3.88375	−	550.075i	0.00524123	−	0.742342i
$742$		0			0
$743$	67.8379	−	67.8379i	0.0913026	−	0.0913026i	−0.659980	−	0.751283i	$-0.729435\pi$
$743$	67.8379	−	67.8379i	0.0913026	−	0.0913026i	0.751283	+	0.659980i	$0.229435\pi$
$744$		0			0
$745$			110.076i			0.147753i
$746$		0			0
$747$	−268.653	+	268.653i	−0.359642	+	0.359642i
$748$		0			0
$749$	68.7861	+	68.7861i	0.0918373	+	0.0918373i
$750$		0			0
$751$			737.420i			0.981917i	0.871183	+	0.490959i	$0.163353\pi$
$751$			737.420i			0.981917i	−0.871183	+	0.490959i	$0.836647\pi$
$752$		0			0
$753$		−	341.398i		−	0.453383i
$754$		0			0
$755$	−115.496			−0.152974
$756$		0			0
$757$	393.248			0.519482			0.259741	−	0.965678i	$-0.416363\pi$
$757$	393.248			0.519482			0.259741	+	0.965678i	$0.416363\pi$
$758$		0			0
$759$	−100.072	+	100.072i	−0.131847	+	0.131847i
$760$		0			0
$761$	50.0067	+	50.0067i	0.0657118	+	0.0657118i	0.739199	−	0.673487i	$-0.235204\pi$
$761$	50.0067	+	50.0067i	0.0657118	+	0.0657118i	−0.673487	+	0.739199i	$0.735204\pi$
$762$		0			0
$763$	−145.505			−0.190701
$764$		0			0
$765$	−49.4390	−	49.4390i	−0.0646261	−	0.0646261i
$766$		0			0
$767$	497.506	+	3.51259i	0.648639	+	0.00457965i
$768$		0			0
$769$	537.921	−	537.921i	0.699507	−	0.699507i	−0.264797	−	0.964304i	$-0.585305\pi$
$769$	537.921	−	537.921i	0.699507	−	0.699507i	0.964304	+	0.264797i	$0.0853049\pi$
$770$		0			0
$771$		−	360.373i		−	0.467410i
$772$		0			0
$773$	−804.702	+	804.702i	−1.04101	+	1.04101i	−0.0418890	+	0.999122i	$0.513338\pi$
$773$	−804.702	+	804.702i	−1.04101	+	1.04101i	−0.999122	+	0.0418890i	$0.986662\pi$
$774$		0			0
$775$	37.8797	+	37.8797i	0.0488770	+	0.0488770i
$776$		0			0
$777$			260.672i			0.335486i
$778$		0			0
$779$			802.203i			1.02979i
$780$		0			0
$781$	1122.51			1.43727
$782$		0			0
$783$	−93.6796			−0.119642
$784$		0			0
$785$	−2.15529	+	2.15529i	−0.00274560	+	0.00274560i
$786$		0			0
$787$	647.882	+	647.882i	0.823230	+	0.823230i	0.986570	−	0.163340i	$-0.0522268\pi$
$787$	647.882	+	647.882i	0.823230	+	0.823230i	−0.163340	+	0.986570i	$0.552227\pi$
$788$		0			0
$789$	−880.865			−1.11643
$790$		0			0
$791$	264.772	+	264.772i	0.334731	+	0.334731i
$792$		0			0
$793$	627.170	−	618.376i	0.790883	−	0.779793i
$794$		0			0
$795$	30.7843	−	30.7843i	0.0387223	−	0.0387223i
$796$		0			0
$797$		−	1083.79i		−	1.35984i	−0.733286	−	0.679920i	$-0.762014\pi$
$797$		−	1083.79i		−	1.35984i	0.733286	−	0.679920i	$-0.237986\pi$
$798$		0			0
$799$	−868.492	+	868.492i	−1.08697	+	1.08697i
$800$		0			0
$801$	21.6094	+	21.6094i	0.0269781	+	0.0269781i
$802$		0			0
$803$			1550.99i			1.93149i
$804$		0			0
$805$			8.01569i			0.00995738i
$806$		0			0
$807$	−867.628			−1.07513
$808$		0			0
$809$	−292.477			−0.361529			−0.180765	−	0.983526i	$-0.557857\pi$
$809$	−292.477			−0.361529			−0.180765	+	0.983526i	$0.557857\pi$
$810$		0			0
$811$	556.162	−	556.162i	0.685773	−	0.685773i	−0.275521	−	0.961295i	$-0.588851\pi$
$811$	556.162	−	556.162i	0.685773	−	0.685773i	0.961295	+	0.275521i	$0.0888505\pi$
$812$		0			0
$813$	443.160	+	443.160i	0.545092	+	0.545092i
$814$		0			0
$815$	151.531			0.185928
$816$		0			0
$817$	−652.747	−	652.747i	−0.798956	−	0.798956i
$818$		0			0
$819$	−87.3883	−	0.616996i	−0.106701	−	0.000753353i
$820$		0			0
$821$	−851.611	+	851.611i	−1.03728	+	1.03728i	−0.0380073	+	0.999277i	$0.512101\pi$
$821$	−851.611	+	851.611i	−1.03728	+	1.03728i	−0.999277	+	0.0380073i	$0.987899\pi$
$822$		0			0
$823$		−	523.943i		−	0.636625i	−0.947986	−	0.318313i	$-0.896884\pi$
$823$		−	523.943i		−	0.636625i	0.947986	−	0.318313i	$-0.103116\pi$
$824$		0			0
$825$	628.496	−	628.496i	0.761813	−	0.761813i
$826$		0			0
$827$	646.011	+	646.011i	0.781150	+	0.781150i	0.980025	−	0.198875i	$-0.0637286\pi$
$827$	646.011	+	646.011i	0.781150	+	0.781150i	−0.198875	+	0.980025i	$0.563729\pi$
$828$		0			0
$829$			1525.14i			1.83974i	0.392228	+	0.919868i	$0.371704\pi$
$829$			1525.14i			1.83974i	−0.392228	+	0.919868i	$0.628296\pi$
$830$		0			0
$831$		−	505.340i		−	0.608111i
$832$		0			0
$833$	1101.02			1.32175
$834$		0			0
$835$	184.318			0.220740
$836$		0			0
$837$	−8.15586	+	8.15586i	−0.00974415	+	0.00974415i
$838$		0			0
$839$	188.582	+	188.582i	0.224770	+	0.224770i	0.810504	−	0.585734i	$-0.199194\pi$
$839$	188.582	+	188.582i	0.224770	+	0.224770i	−0.585734	+	0.810504i	$0.699194\pi$
$840$		0			0
$841$	−515.968			−0.613517
$842$		0			0
$843$	−406.921	−	406.921i	−0.482705	−	0.482705i
$844$		0			0
$845$	109.664	+	112.806i	0.129780	+	0.133498i
$846$		0			0
$847$	−524.688	+	524.688i	−0.619466	+	0.619466i
$848$		0			0
$849$			203.601i			0.239813i
$850$		0			0
$851$	−182.494	+	182.494i	−0.214446	+	0.214446i
$852$		0			0
$853$	277.340	+	277.340i	0.325134	+	0.325134i	0.850733	−	0.525599i	$-0.176159\pi$
$853$	277.340	+	277.340i	0.325134	+	0.325134i	−0.525599	+	0.850733i	$0.676159\pi$
$854$		0			0
$855$			68.2281i			0.0797990i
$856$		0			0
$857$		−	680.535i		−	0.794090i	−0.917799	−	0.397045i	$-0.870036\pi$
$857$		−	680.535i		−	0.794090i	0.917799	−	0.397045i	$-0.129964\pi$
$858$		0			0
$859$	188.066			0.218936			0.109468	−	0.993990i	$-0.465085\pi$
$859$	188.066			0.218936			0.109468	+	0.993990i	$0.465085\pi$
$860$		0			0
$861$	127.443			0.148017
$862$		0			0
$863$	−612.108	+	612.108i	−0.709279	+	0.709279i	−0.966384	−	0.257104i	$-0.917232\pi$
$863$	−612.108	+	612.108i	−0.709279	+	0.709279i	0.257104	+	0.966384i	$0.417232\pi$
$864$		0			0
$865$	164.043	+	164.043i	0.189645	+	0.189645i
$866$		0			0
$867$	585.015			0.674757
$868$		0			0
$869$	1583.39	+	1583.39i	1.82208	+	1.82208i
$870$		0			0
$871$	−1.38879	+	196.701i	−0.00159448	+	0.225834i
$872$		0			0
$873$	17.6382	−	17.6382i	0.0202041	−	0.0202041i
$874$		0			0
$875$		−	102.492i		−	0.117134i
$876$		0			0
$877$	198.261	−	198.261i	0.226067	−	0.226067i	−0.584981	−	0.811047i	$-0.698898\pi$
$877$	198.261	−	198.261i	0.226067	−	0.226067i	0.811047	+	0.584981i	$0.198898\pi$
$878$		0			0
$879$	390.612	+	390.612i	0.444382	+	0.444382i
$880$		0			0
$881$			168.859i			0.191667i	0.995397	+	0.0958336i	$0.0305517\pi$
$881$			168.859i			0.191667i	−0.995397	+	0.0958336i	$0.969448\pi$
$882$		0			0
$883$			1217.19i			1.37847i	0.724536	+	0.689237i	$0.242054\pi$
$883$			1217.19i			1.37847i	−0.724536	+	0.689237i	$0.757946\pi$
$884$		0			0
$885$	−61.7078			−0.0697263
$886$		0			0
$887$	1472.35			1.65992			0.829962	−	0.557821i	$-0.188362\pi$
$887$	1472.35			1.65992			0.829962	+	0.557821i	$0.188362\pi$
$888$		0			0
$889$	215.247	−	215.247i	0.242122	−	0.242122i
$890$		0			0
$891$	135.321	+	135.321i	0.151876	+	0.151876i
$892$		0			0
$893$	1198.56			1.34217
$894$		0			0
$895$	149.715	+	149.715i	0.167279	+	0.167279i
$896$		0			0
$897$	−60.7476	−	61.6115i	−0.0677231	−	0.0686862i
$898$		0			0
$899$	28.2977	−	28.2977i	0.0314769	−	0.0314769i
$900$		0			0
$901$			675.959i			0.750231i
$902$		0			0
$903$	−103.699	+	103.699i	−0.114839	+	0.114839i
$904$		0			0
$905$	216.847	+	216.847i	0.239610	+	0.239610i
$906$		0			0
$907$		−	1103.36i		−	1.21649i	−0.793750	−	0.608245i	$-0.791874\pi$
$907$		−	1103.36i		−	1.21649i	0.793750	−	0.608245i	$-0.208126\pi$
$908$		0			0
$909$		−	336.172i		−	0.369826i
$910$		0			0
$911$	−1679.94			−1.84406			−0.922031	−	0.387116i	$-0.873471\pi$
$911$	−1679.94			−1.84406			−0.922031	+	0.387116i	$0.873471\pi$
$912$		0			0
$913$	−2692.92			−2.94953
$914$		0			0
$915$	−77.2451	+	77.2451i	−0.0844209	+	0.0844209i
$916$		0			0
$917$	42.4027	+	42.4027i	0.0462407	+	0.0462407i
$918$		0			0
$919$	−0.963800			−0.00104875			−0.000524374	−	1.00000i	$-0.500167\pi$
$919$	−0.963800			−0.00104875			−0.000524374		1.00000i	$0.500167\pi$
$920$		0			0
$921$	172.604	+	172.604i	0.187409	+	0.187409i
$922$		0			0
$923$	−4.84523	+	686.254i	−0.00524943	+	0.743504i
$924$		0			0
$925$	1146.14	−	1146.14i	1.23907	−	1.23907i
$926$		0			0
$927$			179.245i			0.193360i
$928$		0			0
$929$	68.3995	−	68.3995i	0.0736270	−	0.0736270i	−0.669334	−	0.742961i	$-0.733421\pi$
$929$	68.3995	−	68.3995i	0.0736270	−	0.0736270i	0.742961	+	0.669334i	$0.233421\pi$
$930$		0			0
$931$	−759.728	−	759.728i	−0.816035	−	0.816035i
$932$		0			0
$933$		−	417.158i		−	0.447115i
$934$		0			0
$935$		−	495.566i		−	0.530017i
$936$		0			0
$937$	918.793			0.980569			0.490284	−	0.871562i	$-0.336893\pi$
$937$	918.793			0.980569			0.490284	+	0.871562i	$0.336893\pi$
$938$		0			0
$939$	−384.584			−0.409568
$940$		0			0
$941$	−557.787	+	557.787i	−0.592759	+	0.592759i	−0.938376	−	0.345616i	$-0.887670\pi$
$941$	−557.787	+	557.787i	−0.592759	+	0.592759i	0.345616	+	0.938376i	$0.387670\pi$
$942$		0			0
$943$	89.2213	+	89.2213i	0.0946143	+	0.0946143i
$944$		0			0
$945$	10.8391			0.0114700
$946$		0			0
$947$	−284.680	−	284.680i	−0.300613	−	0.300613i	0.540641	−	0.841254i	$-0.318182\pi$
$947$	−284.680	−	284.680i	−0.300613	−	0.300613i	−0.841254	+	0.540641i	$0.818182\pi$
$948$		0			0
$949$	−948.204	−	6.69470i	−0.999162	−	0.00705448i
$950$		0			0
$951$	190.852	−	190.852i	0.200686	−	0.200686i
$952$		0			0
$953$			796.917i			0.836220i	0.908397	+	0.418110i	$0.137307\pi$
$953$			796.917i			0.836220i	−0.908397	+	0.418110i	$0.862693\pi$
$954$		0			0
$955$	205.853	−	205.853i	0.215553	−	0.215553i
$956$		0			0
$957$	−469.513	−	469.513i	−0.490609	−	0.490609i
$958$		0			0
$959$		−	352.362i		−	0.367427i
$960$		0			0
$961$			956.073i			0.994873i
$962$		0			0
$963$	130.238			0.135242
$964$		0			0
$965$	41.6831			0.0431949
$966$		0			0
$967$	1229.81	−	1229.81i	1.27177	−	1.27177i	0.326618	−	0.945157i	$-0.394091\pi$
$967$	1229.81	−	1229.81i	1.27177	−	1.27177i	0.945157	−	0.326618i	$-0.105909\pi$
$968$		0			0
$969$	−749.074	−	749.074i	−0.773038	−	0.773038i
$970$		0			0
$971$	−462.014			−0.475813			−0.237906	−	0.971288i	$-0.576461\pi$
$971$	−462.014			−0.475813			−0.237906	+	0.971288i	$0.576461\pi$
$972$		0			0
$973$	309.447	+	309.447i	0.318034	+	0.318034i
$974$		0			0
$975$	381.522	+	386.947i	0.391304	+	0.396869i
$976$		0			0
$977$	315.338	−	315.338i	0.322762	−	0.322762i	−0.527064	−	0.849826i	$-0.676707\pi$
$977$	315.338	−	315.338i	0.322762	−	0.322762i	0.849826	+	0.527064i	$0.176707\pi$
$978$		0			0
$979$			216.609i			0.221255i
$980$		0			0
$981$	−137.748	+	137.748i	−0.140416	+	0.140416i
$982$		0			0
$983$	−722.736	−	722.736i	−0.735235	−	0.735235i	0.236417	−	0.971652i	$-0.424027\pi$
$983$	−722.736	−	722.736i	−0.735235	−	0.735235i	−0.971652	+	0.236417i	$0.924027\pi$
$984$		0			0
$985$		−	60.0860i		−	0.0610010i
$986$		0			0
$987$		−	190.410i		−	0.192918i
$988$		0			0
$989$	−145.198			−0.146813
$990$		0			0
$991$	673.346			0.679461			0.339731	−	0.940523i	$-0.389664\pi$
$991$	673.346			0.679461			0.339731	+	0.940523i	$0.389664\pi$
$992$		0			0
$993$	−561.611	+	561.611i	−0.565570	+	0.565570i
$994$		0			0
$995$	57.8157	+	57.8157i	0.0581062	+	0.0581062i
$996$		0			0
$997$	−573.566			−0.575292			−0.287646	−	0.957737i	$-0.592873\pi$
$997$	−573.566			−0.575292			−0.287646	+	0.957737i	$0.592873\pi$
$998$		0			0
$999$	246.775	+	246.775i	0.247022	+	0.247022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.j.a.109.1	yes	8
3.2	odd	2		468.3.m.d.109.3		8
4.3	odd	2		624.3.ba.d.577.3		8
13.8	odd	4	inner	156.3.j.a.73.1	✓	8
39.8	even	4		468.3.m.d.73.3		8
52.47	even	4		624.3.ba.d.385.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.j.a.73.1	✓	8	13.8	odd	4	inner
156.3.j.a.109.1	yes	8	1.1	even	1	trivial
468.3.m.d.73.3		8	39.8	even	4
468.3.m.d.109.3		8	3.2	odd	2
624.3.ba.d.385.3		8	52.47	even	4
624.3.ba.d.577.3		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(-0.658261 + 0.658261i) q^{5} +(1.58447 + 1.58447i) q^{7} +3.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{3} +(-0.658261 + 0.658261i) q^{5} +(1.58447 + 1.58447i) q^{7} +3.00000 q^{9} +(15.0357 + 15.0357i) q^{11} +(-9.25706 + 9.12726i) q^{13} +(1.14014 - 1.14014i) q^{15} +25.0351i q^{17} +(17.2748 - 17.2748i) q^{19} +(-2.74438 - 2.74438i) q^{21} -3.84263i q^{23} +24.1334i q^{25} -5.19615 q^{27} +18.0287 q^{29} +(1.56960 - 1.56960i) q^{31} +(-26.0426 - 26.0426i) q^{33} -2.08599 q^{35} +(-47.4919 - 47.4919i) q^{37} +(16.0337 - 15.8089i) q^{39} +(-23.2188 + 23.2188i) q^{41} -37.7860i q^{43} +(-1.97478 + 1.97478i) q^{45} +(34.6909 + 34.6909i) q^{47} -43.9789i q^{49} -43.3621i q^{51} +27.0004 q^{53} -19.7948 q^{55} +(-29.9209 + 29.9209i) q^{57} +(-27.0615 - 27.0615i) q^{59} -67.7505 q^{61} +(4.75341 + 4.75341i) q^{63} +(0.0854427 - 12.1017i) q^{65} +(10.6994 - 10.6994i) q^{67} +6.65563i q^{69} +(37.3282 - 37.3282i) q^{71} +(51.5768 + 51.5768i) q^{73} -41.8002i q^{75} +47.6472i q^{77} +105.309 q^{79} +9.00000 q^{81} +(-89.5509 + 89.5509i) q^{83} +(-16.4797 - 16.4797i) q^{85} -31.2265 q^{87} +(7.20315 + 7.20315i) q^{89} +(-29.1294 - 0.205665i) q^{91} +(-2.71862 + 2.71862i) q^{93} +22.7427i q^{95} +(5.87941 - 5.87941i) q^{97} +(45.1071 + 45.1071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{5} - 8 q^{7} + 24 q^{9}+O(q^{10}) \) 8 * q + 12 * q^5 - 8 * q^7 + 24 * q^9	\( 8 q + 12 q^{5} - 8 q^{7} + 24 q^{9} + 12 q^{11} + 24 q^{13} + 12 q^{15} + 88 q^{19} + 24 q^{29} - 16 q^{31} - 36 q^{33} - 216 q^{35} + 32 q^{37} + 72 q^{39} - 180 q^{41} + 36 q^{45} + 36 q^{47} - 72 q^{53} - 240 q^{55} + 24 q^{57} - 228 q^{59} - 192 q^{61} - 24 q^{63} + 132 q^{65} + 16 q^{67} + 36 q^{71} + 160 q^{73} + 48 q^{79} + 72 q^{81} + 12 q^{83} + 24 q^{85} - 120 q^{87} + 60 q^{89} + 112 q^{91} + 120 q^{93} + 416 q^{97} + 36 q^{99}+O(q^{100}) \) 8 * q + 12 * q^5 - 8 * q^7 + 24 * q^9 + 12 * q^11 + 24 * q^13 + 12 * q^15 + 88 * q^19 + 24 * q^29 - 16 * q^31 - 36 * q^33 - 216 * q^35 + 32 * q^37 + 72 * q^39 - 180 * q^41 + 36 * q^45 + 36 * q^47 - 72 * q^53 - 240 * q^55 + 24 * q^57 - 228 * q^59 - 192 * q^61 - 24 * q^63 + 132 * q^65 + 16 * q^67 + 36 * q^71 + 160 * q^73 + 48 * q^79 + 72 * q^81 + 12 * q^83 + 24 * q^85 - 120 * q^87 + 60 * q^89 + 112 * q^91 + 120 * q^93 + 416 * q^97 + 36 * q^99

Introduction

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