LMFDB - Embedded newform 756.2.ba.a.71.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.14
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +O(q^{10})$	\(q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(-0.549133 + 3.33330i) q^{10} +(3.21792 + 5.57360i) q^{11} +(2.15010 - 3.72408i) q^{13} +(-1.09352 - 0.896785i) q^{14} +(0.516556 - 3.96651i) q^{16} -1.89547i q^{17} +0.529348i q^{19} +(4.68509 - 0.935330i) q^{20} +(5.77157 - 7.03770i) q^{22} +(2.64942 - 4.58894i) q^{23} +(0.353115 + 0.611613i) q^{25} +(-6.00052 - 0.988535i) q^{26} +(-0.641554 + 1.89431i) q^{28} +(0.301871 - 0.174285i) q^{29} +(-5.09757 - 2.94308i) q^{31} +(-5.50683 + 1.29417i) q^{32} +(-2.50846 + 0.945118i) q^{34} -2.38877 q^{35} +0.842466 q^{37} +(0.700537 - 0.263943i) q^{38} +(-3.57389 - 5.73386i) q^{40} +(-4.58530 - 2.64733i) q^{41} +(7.38095 - 4.26140i) q^{43} +(-12.1915 - 4.12894i) q^{44} +(-7.39404 - 1.21810i) q^{46} +(2.04252 + 3.53774i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.633336 - 0.772273i) q^{50} +(1.68376 + 8.43397i) q^{52} -12.5979i q^{53} -15.3738i q^{55} +(2.82681 - 0.0955095i) q^{56} +(-0.381168 - 0.312593i) q^{58} +(2.66171 - 4.61021i) q^{59} +(-3.49882 - 6.06013i) q^{61} +(-1.35312 + 8.21358i) q^{62} +(4.45851 + 6.64242i) q^{64} +(-8.89599 + 5.13610i) q^{65} +(9.32818 + 5.38563i) q^{67} +(2.50153 + 2.84843i) q^{68} +(1.19109 + 3.16129i) q^{70} +6.12137 q^{71} +5.07942 q^{73} +(-0.420070 - 1.11492i) q^{74} +(-0.698603 - 0.795481i) q^{76} +(5.57360 + 3.21792i) q^{77} +(2.87851 - 1.66191i) q^{79} +(-5.80616 + 7.58869i) q^{80} +(-1.21714 + 7.38818i) q^{82} +(-3.23597 - 5.60486i) q^{83} +(-2.26392 + 3.92122i) q^{85} +(-9.31981 - 7.64311i) q^{86} +(0.614684 + 18.1929i) q^{88} +14.4170i q^{89} -4.30020i q^{91} +(2.07478 + 10.3926i) q^{92} +(3.66340 - 4.46705i) q^{94} +(0.632246 - 1.09508i) q^{95} +(-3.86625 - 6.69654i) q^{97} +(-1.39540 - 0.229881i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.498620	−	1.32340i	−0.352577	−	0.935783i
$2$	−0.498620	−	1.32340i	−0.352577	−	0.935783i
$3$		0			0
$3$		0			0
$4$	−1.50276	+	1.31974i	−0.751378	+	0.659872i
$5$	−2.06874	−	1.19439i	−0.925167	−	0.534146i	−0.0398874	−	0.999204i	$-0.512700\pi$
$5$	−2.06874	−	1.19439i	−0.925167	−	0.534146i	−0.885280	+	0.465059i	$0.846033\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	2.49585	+	1.33069i	0.882415	+	0.470471i
$9$		0			0
$10$	−0.549133	+	3.33330i	−0.173651	+	1.05408i
$11$	3.21792	+	5.57360i	0.970240	+	1.68050i	0.694824	+	0.719180i	$0.255482\pi$
$11$	3.21792	+	5.57360i	0.970240	+	1.68050i	0.275416	+	0.961325i	$0.411184\pi$
$12$		0			0
$13$	2.15010	−	3.72408i	0.596331	−	1.03288i	−0.397027	−	0.917807i	$-0.629958\pi$
$13$	2.15010	−	3.72408i	0.596331	−	1.03288i	0.993358	−	0.115068i	$-0.0367086\pi$
$14$	−1.09352	−	0.896785i	−0.292254	−	0.239676i
$15$		0			0
$16$	0.516556	−	3.96651i	0.129139	−	0.991626i
$17$		−	1.89547i		−	0.459718i	−0.973224	−	0.229859i	$-0.926173\pi$
$17$		−	1.89547i		−	0.459718i	0.973224	−	0.229859i	$-0.0738266\pi$
$18$		0			0
$19$			0.529348i			0.121441i	0.998155	+	0.0607204i	$0.0193398\pi$
$19$			0.529348i			0.121441i	−0.998155	+	0.0607204i	$0.980660\pi$
$20$	4.68509	−	0.935330i	1.04762	−	0.209146i
$21$		0			0
$22$	5.77157	−	7.03770i	1.23050	−	1.50044i
$23$	2.64942	−	4.58894i	0.552443	−	0.956859i	−0.445655	−	0.895205i	$-0.647029\pi$
$23$	2.64942	−	4.58894i	0.552443	−	0.956859i	0.998098	−	0.0616543i	$-0.0196376\pi$
$24$		0			0
$25$	0.353115	+	0.611613i	0.0706230	+	0.122323i
$26$	−6.00052	−	0.988535i	−1.17680	−	0.193868i
$27$		0			0
$28$	−0.641554	+	1.89431i	−0.121242	+	0.357991i
$29$	0.301871	−	0.174285i	0.0560561	−	0.0323640i	−0.471710	−	0.881754i	$-0.656363\pi$
$29$	0.301871	−	0.174285i	0.0560561	−	0.0323640i	0.527766	+	0.849390i	$0.323030\pi$
$30$		0			0
$31$	−5.09757	−	2.94308i	−0.915550	−	0.528593i	−0.0333376	−	0.999444i	$-0.510614\pi$
$31$	−5.09757	−	2.94308i	−0.915550	−	0.528593i	−0.882213	+	0.470851i	$0.843947\pi$
$32$	−5.50683	+	1.29417i	−0.973478	+	0.228779i
$33$		0			0
$34$	−2.50846	+	0.945118i	−0.430197	+	0.162086i
$35$	−2.38877			−0.403776
$36$		0			0
$37$	0.842466			0.138501			0.0692503	−	0.997599i	$-0.477939\pi$
$37$	0.842466			0.138501			0.0692503	+	0.997599i	$0.477939\pi$
$38$	0.700537	−	0.263943i	0.113642	−	0.0428173i
$39$		0			0
$40$	−3.57389	−	5.73386i	−0.565082	−	0.906603i
$41$	−4.58530	−	2.64733i	−0.716104	−	0.413443i	0.0972131	−	0.995264i	$-0.469007\pi$
$41$	−4.58530	−	2.64733i	−0.716104	−	0.413443i	−0.813317	+	0.581821i	$0.802340\pi$
$42$		0			0
$43$	7.38095	−	4.26140i	1.12559	−	0.649857i	0.182764	−	0.983157i	$-0.441496\pi$
$43$	7.38095	−	4.26140i	1.12559	−	0.649857i	0.942821	+	0.333300i	$0.108162\pi$
$44$	−12.1915	−	4.12894i	−1.83793	−	0.622461i
$45$		0			0
$46$	−7.39404	−	1.21810i	−1.09019	−	0.179600i
$47$	2.04252	+	3.53774i	0.297932	+	0.516033i	0.975663	−	0.219277i	$-0.0703699\pi$
$47$	2.04252	+	3.53774i	0.297932	+	0.516033i	−0.677731	+	0.735310i	$0.737037\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	0.633336	−	0.772273i	0.0895673	−	0.109216i
$51$		0			0
$52$	1.68376	+	8.43397i	0.233495	+	1.16958i
$53$		−	12.5979i		−	1.73046i	−0.501376	−	0.865230i	$-0.667173\pi$
$53$		−	12.5979i		−	1.73046i	0.501376	−	0.865230i	$-0.332827\pi$
$54$		0			0
$55$		−	15.3738i		−	2.07300i
$56$	2.82681	−	0.0955095i	0.377749	−	0.0127630i
$57$		0			0
$58$	−0.381168	−	0.312593i	−0.0500497	−	0.0410455i
$59$	2.66171	−	4.61021i	0.346524	−	0.600198i	−0.639105	−	0.769119i	$-0.720695\pi$
$59$	2.66171	−	4.61021i	0.346524	−	0.600198i	0.985630	+	0.168921i	$0.0540284\pi$
$60$		0			0
$61$	−3.49882	−	6.06013i	−0.447978	−	0.775920i	0.550277	−	0.834982i	$-0.314522\pi$
$61$	−3.49882	−	6.06013i	−0.447978	−	0.775920i	−0.998254	+	0.0590625i	$0.981189\pi$
$62$	−1.35312	+	8.21358i	−0.171846	+	1.04313i
$63$		0			0
$64$	4.45851	+	6.64242i	0.557314	+	0.830302i
$65$	−8.89599	+	5.13610i	−1.10341	+	0.637055i
$66$		0			0
$67$	9.32818	+	5.38563i	1.13962	+	0.657959i	0.946336	−	0.323184i	$-0.104753\pi$
$67$	9.32818	+	5.38563i	1.13962	+	0.657959i	0.193282	+	0.981143i	$0.438087\pi$
$68$	2.50153	+	2.84843i	0.303355	+	0.345423i
$69$		0			0
$70$	1.19109	+	3.16129i	0.142362	+	0.377847i
$71$	6.12137			0.726473			0.363236	−	0.931697i	$-0.381672\pi$
$71$	6.12137			0.726473			0.363236	+	0.931697i	$0.381672\pi$
$72$		0			0
$73$	5.07942			0.594501			0.297251	−	0.954799i	$-0.403930\pi$
$73$	5.07942			0.594501			0.297251	+	0.954799i	$0.403930\pi$
$74$	−0.420070	−	1.11492i	−0.0488322	−	0.129606i
$75$		0			0
$76$	−0.698603	−	0.795481i	−0.0801353	−	0.0912480i
$77$	5.57360	+	3.21792i	0.635171	+	0.366716i
$78$		0			0
$79$	2.87851	−	1.66191i	0.323858	−	0.186979i	−0.329253	−	0.944242i	$-0.606797\pi$
$79$	2.87851	−	1.66191i	0.323858	−	0.186979i	0.653111	+	0.757262i	$0.273464\pi$
$80$	−5.80616	+	7.58869i	−0.649148	+	0.848441i
$81$		0			0
$82$	−1.21714	+	7.38818i	−0.134411	+	0.815888i
$83$	−3.23597	−	5.60486i	−0.355193	−	0.615213i	0.631958	−	0.775003i	$-0.282252\pi$
$83$	−3.23597	−	5.60486i	−0.355193	−	0.615213i	−0.987151	+	0.159790i	$0.948918\pi$
$84$		0			0
$85$	−2.26392	+	3.92122i	−0.245557	+	0.425317i
$86$	−9.31981	−	7.64311i	−1.00498	−	0.824178i
$87$		0			0
$88$	0.614684	+	18.1929i	0.0655256	+	1.93937i
$89$			14.4170i			1.52820i	0.645099	+	0.764099i	$0.276816\pi$
$89$			14.4170i			1.52820i	−0.645099	+	0.764099i	$0.723184\pi$
$90$		0			0
$91$		−	4.30020i		−	0.450784i
$92$	2.07478	+	10.3926i	0.216310	+	1.08350i
$93$		0			0
$94$	3.66340	−	4.46705i	0.377851	−	0.460741i
$95$	0.632246	−	1.09508i	0.0648670	−	0.112353i
$96$		0			0
$97$	−3.86625	−	6.69654i	−0.392558	−	0.679931i	0.600228	−	0.799829i	$-0.295077\pi$
$97$	−3.86625	−	6.69654i	−0.392558	−	0.679931i	−0.992786	+	0.119898i	$0.961743\pi$
$98$	−1.39540	−	0.229881i	−0.140957	−	0.0232215i
$99$		0			0
$100$	−1.33782	−	0.453085i	−0.133782	−	0.0453085i
$101$	14.7999	−	8.54473i	1.47265	−	0.850233i	0.473119	−	0.880998i	$-0.343128\pi$
$101$	14.7999	−	8.54473i	1.47265	−	0.850233i	0.999527	+	0.0307657i	$0.00979457\pi$
$102$		0			0
$103$	−10.0362	−	5.79440i	−0.988896	−	0.570939i	−0.0839517	−	0.996470i	$-0.526754\pi$
$103$	−10.0362	−	5.79440i	−0.988896	−	0.570939i	−0.904944	+	0.425531i	$0.860087\pi$
$104$	10.3219	−	6.43362i	1.01215	−	0.630868i
$105$		0			0
$106$	−16.6721	+	6.28158i	−1.61933	+	0.610121i
$107$	−1.66184			−0.160656			−0.0803278	−	0.996768i	$-0.525597\pi$
$107$	−1.66184			−0.160656			−0.0803278	+	0.996768i	$0.525597\pi$
$108$		0			0
$109$	−8.21513			−0.786867			−0.393434	−	0.919353i	$-0.628713\pi$
$109$	−8.21513			−0.786867			−0.393434	+	0.919353i	$0.628713\pi$
$110$	−20.3456	+	7.66566i	−1.93988	+	0.730892i
$111$		0			0
$112$	−1.53590	−	3.69337i	−0.145129	−	0.348991i
$113$	7.87513	+	4.54671i	0.740830	+	0.427718i	0.822371	−	0.568952i	$-0.192651\pi$
$113$	7.87513	+	4.54671i	0.740830	+	0.427718i	−0.0815410	+	0.996670i	$0.525984\pi$
$114$		0			0
$115$	−10.9619	+	6.32887i	−1.02220	+	0.590170i
$116$	−0.223627	+	0.660301i	−0.0207632	+	0.0613074i
$117$		0			0
$118$	−7.42831	−	1.22375i	−0.683832	−	0.112655i
$119$	−0.947734	−	1.64152i	−0.0868786	−	0.150478i
$120$		0			0
$121$	−15.2100	+	26.3446i	−1.38273	+	2.39496i
$122$	−6.27537	+	7.65202i	−0.568146	+	0.692781i
$123$		0			0
$124$	11.5445	−	2.30474i	1.03673	−	0.206972i
$125$			10.2568i			0.917399i
$126$		0			0
$127$			17.0630i			1.51409i	0.653360	+	0.757047i	$0.273359\pi$
$127$			17.0630i			1.51409i	−0.653360	+	0.757047i	$0.726641\pi$
$128$	6.56745	−	9.21242i	0.580486	−	0.814270i
$129$		0			0
$130$	11.2328	+	9.21196i	0.985183	+	0.807942i
$131$	5.58971	−	9.68166i	0.488375	−	0.845890i	−0.511536	−	0.859262i	$-0.670923\pi$
$131$	5.58971	−	9.68166i	0.488375	−	0.845890i	0.999911	+	0.0133718i	$0.00425652\pi$
$132$		0			0
$133$	0.264674	+	0.458429i	0.0229501	+	0.0397508i
$134$	2.47611	−	15.0303i	0.213903	−	1.29842i
$135$		0			0
$136$	2.52229	−	4.73080i	0.216284	−	0.405663i
$137$	−4.30543	+	2.48574i	−0.367838	+	0.212371i	−0.672513	−	0.740085i	$-0.734785\pi$
$137$	−4.30543	+	2.48574i	−0.367838	+	0.212371i	0.304676	+	0.952456i	$0.401452\pi$
$138$		0			0
$139$	7.46366	+	4.30915i	0.633060	+	0.365497i	0.781936	−	0.623359i	$-0.214232\pi$
$139$	7.46366	+	4.30915i	0.633060	+	0.365497i	−0.148876	+	0.988856i	$0.547566\pi$
$140$	3.58974	−	3.15256i	0.303389	−	0.266440i
$141$		0			0
$142$	−3.05223	−	8.10100i	−0.256138	−	0.679821i
$143$	27.6754			2.31434
$144$		0			0
$145$	−0.832656			−0.0691483
$146$	−2.53270	−	6.72209i	−0.209608	−	0.556324i
$147$		0			0
$148$	−1.26602	+	1.11184i	−0.104066	+	0.0913926i
$149$	−2.18247	−	1.26005i	−0.178795	−	0.103227i	0.407931	−	0.913013i	$-0.366250\pi$
$149$	−2.18247	−	1.26005i	−0.178795	−	0.103227i	−0.586727	+	0.809785i	$0.699584\pi$
$150$		0			0
$151$	−0.331047	+	0.191130i	−0.0269402	+	0.0155539i	−0.513410	−	0.858144i	$-0.671618\pi$
$151$	−0.331047	+	0.191130i	−0.0269402	+	0.0155539i	0.486469	+	0.873698i	$0.338285\pi$
$152$	−0.704400	+	1.32117i	−0.0571344	+	0.107161i
$153$		0			0
$154$	1.47948	−	8.98061i	0.119220	−	0.723678i
$155$	7.03035	+	12.1769i	0.564691	+	0.978074i
$156$		0			0
$157$	4.39885	−	7.61904i	0.351067	−	0.608065i	−0.635370	−	0.772208i	$-0.719152\pi$
$157$	4.39885	−	7.61904i	0.351067	−	0.608065i	0.986437	+	0.164143i	$0.0524857\pi$
$158$	−3.63465	−	2.98075i	−0.289157	−	0.237136i
$159$		0			0
$160$	12.9379	+	3.89998i	1.02283	+	0.308320i
$161$		−	5.29885i		−	0.417608i
$162$		0			0
$163$		−	10.7694i		−	0.843521i	−0.906707	−	0.421760i	$-0.861412\pi$
$163$		−	10.7694i		−	0.843521i	0.906707	−	0.421760i	$-0.138588\pi$
$164$	10.3844	−	2.07313i	0.810884	−	0.161885i
$165$		0			0
$166$	−5.80393	+	7.07716i	−0.450473	+	0.549294i
$167$	−3.92462	+	6.79765i	−0.303697	+	0.526018i	−0.976970	−	0.213375i	$-0.931554\pi$
$167$	−3.92462	+	6.79765i	−0.303697	+	0.526018i	0.673274	+	0.739393i	$0.264888\pi$
$168$		0			0
$169$	−2.74587	−	4.75598i	−0.211221	−	0.365845i
$170$	6.31817	+	1.04086i	0.484582	+	0.0798306i
$171$		0			0
$172$	−5.46783	+	16.1448i	−0.416918	+	1.23103i
$173$	16.5653	−	9.56396i	1.25943	−	0.727134i	0.286469	−	0.958089i	$-0.407518\pi$
$173$	16.5653	−	9.56396i	1.25943	−	0.727134i	0.972964	+	0.230955i	$0.0741850\pi$
$174$		0			0
$175$	0.611613	+	0.353115i	0.0462336	+	0.0266930i
$176$	23.7700	−	9.88483i	1.79173	−	0.745097i
$177$		0			0
$178$	19.0794	−	7.18860i	1.43006	−	0.538808i
$179$	−26.1468			−1.95431			−0.977153	−	0.212538i	$-0.931827\pi$
$179$	−26.1468			−1.95431			−0.977153	+	0.212538i	$0.931827\pi$
$180$		0			0
$181$	18.9172			1.40610			0.703052	−	0.711139i	$-0.251820\pi$
$181$	18.9172			1.40610			0.703052	+	0.711139i	$0.251820\pi$
$182$	−5.69087	+	2.14417i	−0.421836	+	0.158936i
$183$		0			0
$184$	12.7190	−	7.92771i	0.937659	−	0.584439i
$185$	−1.74284	−	1.00623i	−0.128136	−	0.0739795i
$186$		0			0
$187$	10.5646	−	6.09947i	0.772559	−	0.446037i
$188$	−7.73832	−	2.62077i	−0.564375	−	0.191139i
$189$		0			0
$190$	−1.76448	−	0.290682i	−0.128009	−	0.0210883i
$191$	4.70709	+	8.15291i	0.340593	+	0.589924i	0.984543	−	0.175143i	$-0.0560389\pi$
$191$	4.70709	+	8.15291i	0.340593	+	0.589924i	−0.643950	+	0.765068i	$0.722706\pi$
$192$		0			0
$193$	−0.658744	+	1.14098i	−0.0474174	+	0.0821294i	−0.888760	−	0.458373i	$-0.848432\pi$
$193$	−0.658744	+	1.14098i	−0.0474174	+	0.0821294i	0.841343	+	0.540502i	$0.181766\pi$
$194$	−6.93439	+	8.45561i	−0.497860	+	0.607078i
$195$		0			0
$196$	0.391553	+	1.96130i	0.0279680	+	0.140093i
$197$			3.56413i			0.253933i	0.991907	+	0.126967i	$0.0405241\pi$
$197$			3.56413i			0.253933i	−0.991907	+	0.126967i	$0.959476\pi$
$198$		0			0
$199$			15.9739i			1.13236i	0.824282	+	0.566179i	$0.191579\pi$
$199$			15.9739i			1.13236i	−0.824282	+	0.566179i	$0.808421\pi$
$200$	0.0674517	+	1.99638i	0.00476955	+	0.141165i
$201$		0			0
$202$	−18.6876	−	15.3256i	−1.31485	−	1.07830i
$203$	0.174285	−	0.301871i	0.0122324	−	0.0211872i
$204$		0			0
$205$	6.32386	+	10.9532i	0.441677	+	0.765007i
$206$	−2.66404	+	16.1711i	−0.185613	+	1.12669i
$207$		0			0
$208$	−13.6610	−	10.4521i	−0.947217	−	0.724722i
$209$	−2.95038	+	1.70340i	−0.204082	+	0.117827i
$210$		0			0
$211$	3.39401	+	1.95953i	0.233653	+	0.134900i	0.612256	−	0.790659i	$-0.290262\pi$
$211$	3.39401	+	1.95953i	0.233653	+	0.134900i	−0.378603	+	0.925559i	$0.623595\pi$
$212$	16.6260	+	18.9316i	1.14188	+	1.30023i
$213$		0			0
$214$	0.828624	+	2.19927i	0.0566436	+	0.150339i
$215$	−20.3590			−1.38847
$216$		0			0
$217$	−5.88617			−0.399579
$218$	4.09623	+	10.8719i	0.277432	+	0.736337i
$219$		0			0
$220$	20.2894	+	23.1030i	1.36791	+	1.55761i
$221$	−7.05888	−	4.07545i	−0.474832	−	0.274144i
$222$		0			0
$223$	−2.25600	+	1.30250i	−0.151073	+	0.0872218i	−0.573631	−	0.819114i	$-0.694466\pi$
$223$	−2.25600	+	1.30250i	−0.151073	+	0.0872218i	0.422558	+	0.906336i	$0.361132\pi$
$224$	−4.12197	+	3.87420i	−0.275410	+	0.258856i
$225$		0			0
$226$	2.09040	−	12.6890i	0.139052	−	0.844060i
$227$	1.56505	+	2.71075i	0.103876	+	0.179919i	0.913278	−	0.407336i	$-0.133542\pi$
$227$	1.56505	+	2.71075i	0.103876	+	0.179919i	−0.809402	+	0.587254i	$0.800209\pi$
$228$		0			0
$229$	−3.33583	+	5.77783i	−0.220438	+	0.381809i	−0.954941	−	0.296796i	$-0.904082\pi$
$229$	−3.33583	+	5.77783i	−0.220438	+	0.381809i	0.734503	+	0.678605i	$0.237415\pi$
$230$	13.8414	+	11.3513i	0.912677	+	0.748481i
$231$		0			0
$232$	0.985345	−	0.0332918i	0.0646910	−	0.00218572i
$233$			15.0197i			0.983971i	0.870603	+	0.491985i	$0.163729\pi$
$233$			15.0197i			0.983971i	−0.870603	+	0.491985i	$0.836271\pi$
$234$		0			0
$235$		−	9.75821i		−	0.636556i
$236$	2.08440	+	10.4408i	0.135683	+	0.679637i
$237$		0			0
$238$	−1.69983	+	2.07272i	−0.110183	+	0.134355i
$239$	−1.10101	+	1.90701i	−0.0712185	+	0.123354i	−0.899436	−	0.437053i	$-0.856022\pi$
$239$	−1.10101	+	1.90701i	−0.0712185	+	0.123354i	0.828217	+	0.560407i	$0.189355\pi$
$240$		0			0
$241$	−9.28440	−	16.0811i	−0.598061	−	1.03587i	−0.993107	−	0.117211i	$-0.962605\pi$
$241$	−9.28440	−	16.0811i	−0.598061	−	1.03587i	0.395046	−	0.918661i	$-0.370729\pi$
$242$	42.4483	+	6.99300i	2.72868	+	0.449527i
$243$		0			0
$244$	13.2557	+	4.48936i	0.848608	+	0.287402i
$245$	−2.06874	+	1.19439i	−0.132167	+	0.0763065i
$246$		0			0
$247$	1.97134	+	1.13815i	0.125433	+	0.0724188i
$248$	−8.80641	−	14.1288i	−0.559208	−	0.897179i
$249$		0			0
$250$	13.5739	−	5.11426i	0.858486	−	0.323454i
$251$	−6.18166			−0.390183			−0.195092	−	0.980785i	$-0.562500\pi$
$251$	−6.18166			−0.390183			−0.195092	+	0.980785i	$0.562500\pi$
$252$		0			0
$253$	34.1026			2.14401
$254$	22.5811	−	8.50794i	1.41686	−	0.533836i
$255$		0			0
$256$	−15.4663	−	4.09785i	−0.966646	−	0.256115i
$257$	−6.98685	−	4.03386i	−0.435828	−	0.251625i	0.265998	−	0.963973i	$-0.414298\pi$
$257$	−6.98685	−	4.03386i	−0.435828	−	0.251625i	−0.701826	+	0.712348i	$0.747632\pi$
$258$		0			0
$259$	0.729597	−	0.421233i	0.0453350	−	0.0261741i
$260$	6.59017	−	19.4587i	0.408705	−	1.20678i
$261$		0			0
$262$	−15.5998	−	2.56993i	−0.963759	−	0.158771i
$263$	0.0757144	+	0.131141i	0.00466875	+	0.00808651i	0.868350	−	0.495951i	$-0.165181\pi$
$263$	0.0757144	+	0.131141i	0.00466875	+	0.00808651i	−0.863682	+	0.504038i	$0.831847\pi$
$264$		0			0
$265$	−15.0468	+	26.0618i	−0.924317	+	1.60096i
$266$	0.474711	−	0.578850i	0.0291064	−	0.0354916i
$267$		0			0
$268$	−21.1256	+	4.21751i	−1.29045	+	0.257626i
$269$		−	2.18065i		−	0.132957i	−0.997788	−	0.0664784i	$-0.978824\pi$
$269$		−	2.18065i		−	0.132957i	0.997788	−	0.0664784i	$-0.0211763\pi$
$270$		0			0
$271$		−	3.08448i		−	0.187369i	−0.995602	−	0.0936844i	$-0.970136\pi$
$271$		−	3.08448i		−	0.187369i	0.995602	−	0.0936844i	$-0.0298645\pi$
$272$	−7.51838	−	0.979116i	−0.455869	−	0.0593676i
$273$		0			0
$274$	5.43639	+	4.45835i	0.328425	+	0.269339i
$275$	−2.27259	+	3.93624i	−0.137042	+	0.237364i
$276$		0			0
$277$	−8.31095	−	14.3950i	−0.499357	−	0.864911i	0.500643	−	0.865654i	$-0.333097\pi$
$277$	−8.31095	−	14.3950i	−0.499357	−	0.864911i	−1.00000		0.000742657i	$0.999764\pi$
$278$	1.98118	−	12.0260i	0.118823	−	0.721272i
$279$		0			0
$280$	−5.96201	−	3.17872i	−0.356298	−	0.189965i
$281$	−8.93878	+	5.16081i	−0.533243	+	0.307868i	−0.742336	−	0.670028i	$-0.766282\pi$
$281$	−8.93878	+	5.16081i	−0.533243	+	0.307868i	0.209093	+	0.977896i	$0.432949\pi$
$282$		0			0
$283$	12.3659	+	7.13943i	0.735074	+	0.424395i	0.820275	−	0.571969i	$-0.193820\pi$
$283$	12.3659	+	7.13943i	0.735074	+	0.424395i	−0.0852016	+	0.996364i	$0.527153\pi$
$284$	−9.19893	+	8.07863i	−0.545856	+	0.479379i
$285$		0			0
$286$	−13.7995	−	36.6256i	−0.815982	−	2.16572i
$287$	−5.29465			−0.312533
$288$		0			0
$289$	13.4072			0.788659
$290$	0.415179	+	1.10193i	0.0243801	+	0.0647078i
$291$		0			0
$292$	−7.63314	+	6.70353i	−0.446696	+	0.392295i
$293$	2.10270	+	1.21399i	0.122841	+	0.0709223i	0.560161	−	0.828383i	$-0.310739\pi$
$293$	2.10270	+	1.21399i	0.122841	+	0.0709223i	−0.437320	+	0.899306i	$0.644072\pi$
$294$		0			0
$295$	−11.0127	+	6.35821i	−0.641186	+	0.370189i
$296$	2.10267	+	1.12106i	0.122215	+	0.0651605i
$297$		0			0
$298$	−0.579324	+	3.51657i	−0.0335593	+	0.203709i
$299$	−11.3931	−	19.7334i	−0.658877	−	1.14121i
$300$		0			0
$301$	4.26140	−	7.38095i	0.245623	−	0.425431i
$302$	0.418007	+	0.342805i	0.0240536	+	0.0197262i
$303$		0			0
$304$	2.09966	+	0.273438i	0.120424	+	0.0156827i
$305$			16.7157i			0.957141i
$306$		0			0
$307$			8.87237i			0.506373i	0.967417	+	0.253187i	$0.0814787\pi$
$307$			8.87237i			0.506373i	−0.967417	+	0.253187i	$0.918521\pi$
$308$	−12.6226	+	2.51997i	−0.719240	+	0.143589i
$309$		0			0
$310$	12.6094	−	15.3756i	0.716168	−	0.873275i
$311$	−3.03771	+	5.26147i	−0.172253	+	0.298350i	−0.939207	−	0.343351i	$-0.888438\pi$
$311$	−3.03771	+	5.26147i	−0.172253	+	0.298350i	0.766954	+	0.641702i	$0.221771\pi$
$312$		0			0
$313$	−10.3245	−	17.8825i	−0.583575	−	1.01078i	−0.995051	−	0.0993607i	$-0.968320\pi$
$313$	−10.3245	−	17.8825i	−0.583575	−	1.01078i	0.411477	−	0.911420i	$-0.365013\pi$
$314$	−12.2764	−	2.02242i	−0.692795	−	0.114132i
$315$		0			0
$316$	−2.13241	+	6.29634i	−0.119957	+	0.354197i
$317$	−21.2581	+	12.2734i	−1.19397	+	0.689341i	−0.959205	−	0.282710i	$-0.908767\pi$
$317$	−21.2581	+	12.2734i	−1.19397	+	0.689341i	−0.234769	+	0.972051i	$0.575433\pi$
$318$		0			0
$319$	1.94280	+	1.12167i	0.108776	+	0.0628017i
$320$	−1.28988	−	19.0666i	−0.0721064	−	1.06585i
$321$		0			0
$322$	−7.01248	+	2.64211i	−0.390790	+	0.147239i
$323$	1.00336			0.0558286
$324$		0			0
$325$	3.03693			0.168459
$326$	−14.2521	+	5.36981i	−0.789352	+	0.297406i
$327$		0			0
$328$	−7.92144	−	12.7090i	−0.437388	−	0.701734i
$329$	3.53774	+	2.04252i	0.195042	+	0.112608i
$330$		0			0
$331$	−25.9866	+	15.0034i	−1.42835	+	0.824660i	−0.996991	−	0.0775195i	$-0.975300\pi$
$331$	−25.9866	+	15.0034i	−1.42835	+	0.824660i	−0.431362	+	0.902179i	$0.641967\pi$
$332$	12.2598	+	4.15210i	0.672846	+	0.227876i
$333$		0			0
$334$	10.9529	+	1.80439i	0.599315	+	0.0987320i
$335$	−12.8650	−	22.2829i	−0.702892	−	1.21744i
$336$		0			0
$337$	−5.27401	+	9.13486i	−0.287294	+	0.497608i	−0.973163	−	0.230117i	$-0.926089\pi$
$337$	−5.27401	+	9.13486i	−0.287294	+	0.497608i	0.685869	+	0.727725i	$0.259422\pi$
$338$	−4.92491	+	6.00530i	−0.267880	+	0.326645i
$339$		0			0
$340$	−1.77289	−	8.88044i	−0.0961483	−	0.481609i
$341$		−	37.8824i		−	2.05145i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	24.0924	−	0.814008i	1.29897	−	0.0438884i
$345$		0			0
$346$	−20.9167	−	17.1536i	−1.12449	−	0.922185i
$347$	4.55660	−	7.89227i	0.244611	−	0.423679i	−0.717411	−	0.696650i	$-0.754673\pi$
$347$	4.55660	−	7.89227i	0.244611	−	0.423679i	0.962022	+	0.272971i	$0.0880063\pi$
$348$		0			0
$349$	11.2978	+	19.5684i	0.604760	+	1.04747i	0.992089	+	0.125533i	$0.0400642\pi$
$349$	11.2978	+	19.5684i	0.604760	+	1.04747i	−0.387330	+	0.921941i	$0.626602\pi$
$350$	0.162349	−	0.985476i	0.00867791	−	0.0526759i
$351$		0			0
$352$	−24.9337	−	26.5283i	−1.32897	−	1.41396i
$353$	5.76564	−	3.32879i	0.306874	−	0.177174i	−0.338653	−	0.940911i	$-0.609971\pi$
$353$	5.76564	−	3.32879i	0.306874	−	0.177174i	0.645527	+	0.763738i	$0.276638\pi$
$354$		0			0
$355$	−12.6635	−	7.31128i	−0.672109	−	0.388042i
$356$	−19.0267	−	21.6652i	−1.00841	−	1.14826i
$357$		0			0
$358$	13.0373	+	34.6026i	0.689044	+	1.82881i
$359$	−8.03334			−0.423984			−0.211992	−	0.977271i	$-0.567995\pi$
$359$	−8.03334			−0.423984			−0.211992	+	0.977271i	$0.567995\pi$
$360$		0			0
$361$	18.7198			0.985252
$362$	−9.43248	−	25.0349i	−0.495760	−	1.31581i
$363$		0			0
$364$	5.67516	+	6.46216i	0.297459	+	0.338709i
$365$	−10.5080	−	6.06679i	−0.550013	−	0.317550i
$366$		0			0
$367$	−14.9220	+	8.61523i	−0.778923	+	0.449712i	−0.836049	−	0.548656i	$-0.815140\pi$
$367$	−14.9220	+	8.61523i	−0.778923	+	0.449712i	0.0571254	+	0.998367i	$0.481807\pi$
$368$	−16.8335	−	12.8794i	−0.877505	−	0.671385i
$369$		0			0
$370$	−0.462626	+	2.80820i	−0.0240508	+	0.145991i
$371$	−6.29897	−	10.9101i	−0.327026	−	0.566426i
$372$		0			0
$373$	−0.260742	+	0.451618i	−0.0135007	+	0.0233839i	−0.872697	−	0.488262i	$-0.837631\pi$
$373$	−0.260742	+	0.451618i	−0.0135007	+	0.0233839i	0.859196	+	0.511646i	$0.170964\pi$
$374$	−13.3397	−	10.9398i	−0.689781	−	0.565685i
$375$		0			0
$376$	0.390160	+	11.5476i	0.0201209	+	0.595524i
$377$		−	1.49892i		−	0.0771985i
$378$		0			0
$379$			22.8440i			1.17342i	0.809797	+	0.586710i	$0.199577\pi$
$379$			22.8440i			1.17342i	−0.809797	+	0.586710i	$0.800423\pi$
$380$	0.495115	+	2.48004i	0.0253989	+	0.127224i
$381$		0			0
$382$	8.44249	−	10.2945i	0.431956	−	0.526715i
$383$	−12.4781	+	21.6128i	−0.637603	+	1.10436i	0.348354	+	0.937363i	$0.386741\pi$
$383$	−12.4781	+	21.6128i	−0.637603	+	1.10436i	−0.985957	+	0.166998i	$0.946593\pi$
$384$		0			0
$385$	−7.68688	−	13.3141i	−0.391760	−	0.678548i
$386$	1.83843	+	0.302865i	0.0935736	+	0.0154154i
$387$		0			0
$388$	14.6478	+	4.96082i	0.743627	+	0.251847i
$389$	22.0002	−	12.7018i	1.11545	−	0.644007i	0.175216	−	0.984530i	$-0.443938\pi$
$389$	22.0002	−	12.7018i	1.11545	−	0.644007i	0.940236	+	0.340523i	$0.110604\pi$
$390$		0			0
$391$	−8.69818	−	5.02190i	−0.439886	−	0.253968i
$392$	2.40034	−	1.49612i	0.121235	−	0.0755655i
$393$		0			0
$394$	4.71675	−	1.77714i	0.237627	−	0.0895312i
$395$	−7.93985			−0.399497
$396$		0			0
$397$	5.32969			0.267489			0.133745	−	0.991016i	$-0.457300\pi$
$397$	5.32969			0.267489			0.133745	+	0.991016i	$0.457300\pi$
$398$	21.1398	−	7.96489i	1.05964	−	0.399244i
$399$		0			0
$400$	2.60837	−	1.08470i	0.130418	−	0.0542350i
$401$	−20.2109	−	11.6688i	−1.00928	−	0.582710i	−0.0983016	−	0.995157i	$-0.531341\pi$
$401$	−20.2109	−	11.6688i	−1.00928	−	0.582710i	−0.910982	+	0.412447i	$0.864674\pi$
$402$		0			0
$403$	−21.9206	+	12.6558i	−1.09194	+	0.630433i
$404$	−10.9638	+	32.3727i	−0.545470	+	1.61060i
$405$		0			0
$406$	−0.486397	−	0.0801298i	−0.0241395	−	0.00397677i
$407$	2.71099	+	4.69557i	0.134379	+	0.232751i
$408$		0			0
$409$	15.5599	−	26.9506i	0.769389	−	1.33262i	−0.168506	−	0.985701i	$-0.553894\pi$
$409$	15.5599	−	26.9506i	0.769389	−	1.33262i	0.937895	−	0.346920i	$-0.112772\pi$
$410$	11.3423	−	13.8305i	0.560155	−	0.683038i
$411$		0			0
$412$	22.7291	−	4.53763i	1.11978	−	0.223553i
$413$		−	5.32341i		−	0.261948i
$414$		0			0
$415$			15.4600i			0.758900i
$416$	−7.02064	+	23.2905i	−0.344215	+	1.14191i
$417$		0			0
$418$	3.72539	+	3.05517i	0.182215	+	0.149433i
$419$	−13.4133	+	23.2325i	−0.655283	+	1.13498i	0.326540	+	0.945183i	$0.394117\pi$
$419$	−13.4133	+	23.2325i	−0.655283	+	1.13498i	−0.981823	+	0.189800i	$0.939216\pi$
$420$		0			0
$421$	4.00100	+	6.92994i	0.194997	+	0.337744i	0.946899	−	0.321530i	$-0.104197\pi$
$421$	4.00100	+	6.92994i	0.194997	+	0.337744i	−0.751903	+	0.659274i	$0.770864\pi$
$422$	0.900918	−	5.46868i	0.0438560	−	0.266211i
$423$		0			0
$424$	16.7640	−	31.4425i	0.814131	−	1.52698i
$425$	1.15929	−	0.669318i	0.0562339	−	0.0324667i
$426$		0			0
$427$	−6.06013	−	3.49882i	−0.293270	−	0.169320i
$428$	2.49733	−	2.19320i	0.120713	−	0.106012i
$429$		0			0
$430$	10.1514	+	26.9430i	0.489544	+	1.29931i
$431$	23.2635			1.12056			0.560282	−	0.828302i	$-0.310693\pi$
$431$	23.2635			1.12056			0.560282	+	0.828302i	$0.310693\pi$
$432$		0			0
$433$	−40.4077			−1.94187			−0.970936	−	0.239340i	$-0.923069\pi$
$433$	−40.4077			−1.94187			−0.970936	+	0.239340i	$0.923069\pi$
$434$	2.93496	+	7.78973i	0.140882	+	0.373919i
$435$		0			0
$436$	12.3453	−	10.8419i	0.591235	−	0.519231i
$437$	2.42914	+	1.40247i	0.116202	+	0.0670891i
$438$		0			0
$439$	4.54218	−	2.62243i	0.216786	−	0.125162i	−0.387675	−	0.921796i	$-0.626722\pi$
$439$	4.54218	−	2.62243i	0.216786	−	0.125162i	0.604461	+	0.796634i	$0.293388\pi$
$440$	20.4578	−	38.3706i	0.975286	−	1.82924i
$441$		0			0
$442$	−1.87374	+	11.3738i	−0.0891245	+	0.540996i
$443$	−4.84903	−	8.39876i	−0.230384	−	0.399037i	0.727537	−	0.686068i	$-0.240665\pi$
$443$	−4.84903	−	8.39876i	−0.230384	−	0.399037i	−0.957921	+	0.287031i	$0.907332\pi$
$444$		0			0
$445$	17.2195	−	29.8250i	0.816280	−	1.41384i
$446$	2.84861	+	2.33613i	0.134885	+	0.110619i
$447$		0			0
$448$	7.18239	+	3.52325i	0.339336	+	0.166458i
$449$		−	38.7800i		−	1.83014i	−0.403294	−	0.915071i	$-0.632135\pi$
$449$		−	38.7800i		−	1.83014i	0.403294	−	0.915071i	$-0.367865\pi$
$450$		0			0
$451$		−	34.0755i		−	1.60455i
$452$	−17.8349	+	3.56055i	−0.838883	+	0.167474i
$453$		0			0
$454$	2.80703	−	3.42282i	0.131740	−	0.160641i
$455$	−5.13610	+	8.89599i	−0.240784	+	0.417050i
$456$		0			0
$457$	11.3244	+	19.6145i	0.529735	+	0.917528i	0.999398	+	0.0346824i	$0.0110420\pi$
$457$	11.3244	+	19.6145i	0.529735	+	0.917528i	−0.469663	+	0.882846i	$0.655625\pi$
$458$	9.30966	+	1.53369i	0.435012	+	0.0716645i
$459$		0			0
$460$	8.12062	−	23.9777i	0.378626	−	1.11796i
$461$	−32.0052	+	18.4782i	−1.49063	+	0.860617i	−0.999943	−	0.0107183i	$-0.996588\pi$
$461$	−32.0052	+	18.4782i	−1.49063	+	0.860617i	−0.490689	+	0.871335i	$0.663255\pi$
$462$		0			0
$463$	8.93748	+	5.16006i	0.415360	+	0.239808i	0.693090	−	0.720851i	$-0.256249\pi$
$463$	8.93748	+	5.16006i	0.415360	+	0.239808i	−0.277730	+	0.960659i	$0.589582\pi$
$464$	−0.535370	−	1.28740i	−0.0248540	−	0.0597661i
$465$		0			0
$466$	19.8770	−	7.48910i	0.920783	−	0.346926i
$467$	0.900019			0.0416479			0.0208239	−	0.999783i	$-0.493371\pi$
$467$	0.900019			0.0416479			0.0208239	+	0.999783i	$0.493371\pi$
$468$		0			0
$469$	10.7713			0.497370
$470$	−12.9140	+	4.86564i	−0.595678	+	0.224435i
$471$		0			0
$472$	12.7780	−	7.96446i	0.588154	−	0.366594i
$473$	47.5027	+	27.4257i	2.18418	+	1.26103i
$474$		0			0
$475$	−0.323756	+	0.186921i	−0.0148549	+	0.00857651i
$476$	3.59060	+	1.21605i	0.164575	+	0.0557373i
$477$		0			0
$478$	3.07271	+	0.506203i	0.140543	+	0.0231532i
$479$	−15.9460	−	27.6192i	−0.728590	−	1.26195i	−0.957479	−	0.288502i	$-0.906843\pi$
$479$	−15.9460	−	27.6192i	−0.728590	−	1.26195i	0.228889	−	0.973452i	$-0.426491\pi$
$480$		0			0
$481$	1.81139	−	3.13741i	0.0825921	−	0.143054i
$482$	−16.6522	+	20.3053i	−0.758488	+	0.924880i
$483$		0			0
$484$	−11.9111	−	59.6628i	−0.541412	−	2.71195i
$485$			18.4712i			0.838733i
$486$		0			0
$487$			7.65522i			0.346891i	0.984843	+	0.173446i	$0.0554901\pi$
$487$			7.65522i			0.346891i	−0.984843	+	0.173446i	$0.944510\pi$
$488$	−0.668341	−	19.7810i	−0.0302544	−	0.895444i
$489$		0			0
$490$	2.61216	+	2.14221i	0.118005	+	0.0967754i
$491$	−1.59570	+	2.76383i	−0.0720128	+	0.124730i	−0.899783	−	0.436337i	$-0.856276\pi$
$491$	−1.59570	+	2.76383i	−0.0720128	+	0.124730i	0.827771	+	0.561067i	$0.189609\pi$
$492$		0			0
$493$	−0.330352	−	0.572187i	−0.0148783	−	0.0257700i
$494$	0.523279	−	3.17636i	0.0235434	−	0.142911i
$495$		0			0
$496$	−14.3069	+	18.6993i	−0.642400	+	0.839622i
$497$	5.30126	−	3.06068i	0.237794	−	0.137290i
$498$		0			0
$499$	−9.07585	−	5.23995i	−0.406291	−	0.234572i	0.282904	−	0.959148i	$-0.408702\pi$
$499$	−9.07585	−	5.23995i	−0.406291	−	0.234572i	−0.689195	+	0.724576i	$0.742036\pi$
$500$	−13.5364	−	15.4135i	−0.605366	−	0.689314i
$501$		0			0
$502$	3.08230	+	8.18079i	0.137570	+	0.365127i
$503$	12.6421			0.563685			0.281843	−	0.959461i	$-0.409054\pi$
$503$	12.6421			0.563685			0.281843	+	0.959461i	$0.409054\pi$
$504$		0			0
$505$	−40.8228			−1.81659
$506$	−17.0042	−	45.1312i	−0.755929	−	2.00633i
$507$		0			0
$508$	−22.5188	−	25.6415i	−0.999108	−	1.13766i
$509$	23.8125	+	13.7481i	1.05547	+	0.609376i	0.924176	−	0.381968i	$-0.124753\pi$
$509$	23.8125	+	13.7481i	1.05547	+	0.609376i	0.131294	+	0.991343i	$0.458087\pi$
$510$		0			0
$511$	4.39891	−	2.53971i	0.194596	−	0.112350i
$512$	2.28874	+	22.5114i	0.101149	+	0.994871i
$513$		0			0
$514$	−1.85462	+	11.2577i	−0.0818036	+	0.496558i
$515$	13.8415	+	23.9742i	0.609929	+	1.05643i
$516$		0			0
$517$	−13.1453	+	22.7684i	−0.578130	+	1.00135i
$518$	−0.921250	−	0.755511i	−0.0404774	−	0.0331953i
$519$		0			0
$520$	−29.0376	+	0.981093i	−1.27338	+	0.0430238i
$521$			16.7533i			0.733975i	0.930226	+	0.366988i	$0.119611\pi$
$521$			16.7533i			0.733975i	−0.930226	+	0.366988i	$0.880389\pi$
$522$		0			0
$523$			39.1120i			1.71025i	0.518424	+	0.855124i	$0.326519\pi$
$523$			39.1120i			1.71025i	−0.518424	+	0.855124i	$0.673481\pi$
$524$	4.37733	+	21.9262i	0.191224	+	0.957848i
$525$		0			0
$526$	0.135799	−	0.165590i	0.00592112	−	0.00722006i
$527$	−5.57852	+	9.66228i	−0.243004	+	0.420895i
$528$		0			0
$529$	−2.53889	−	4.39749i	−0.110387	−	0.191195i
$530$	41.9927	+	6.91794i	1.82405	+	0.300496i
$531$		0			0
$532$	−1.00275	−	0.339605i	−0.0434747	−	0.0147238i
$533$	−19.7177	+	11.3840i	−0.854069	+	0.493097i
$534$		0			0
$535$	3.43790	+	1.98487i	0.148633	+	0.0858135i
$536$	16.1151	+	25.8546i	0.696066	+	1.11675i
$537$		0			0
$538$	−2.88587	+	1.08732i	−0.124419	+	0.0468775i
$539$	6.43584			0.277211
$540$		0			0
$541$	−11.1182			−0.478010			−0.239005	−	0.971018i	$-0.576821\pi$
$541$	−11.1182			−0.478010			−0.239005	+	0.971018i	$0.576821\pi$
$542$	−4.08199	+	1.53798i	−0.175337	+	0.0660620i
$543$		0			0
$544$	2.45306	+	10.4380i	0.105174	+	0.447526i
$545$	16.9950	+	9.81204i	0.727984	+	0.420302i
$546$		0			0
$547$	24.1315	−	13.9323i	1.03179	−	0.595703i	0.114291	−	0.993447i	$-0.463540\pi$
$547$	24.1315	−	13.9323i	1.03179	−	0.595703i	0.917496	+	0.397745i	$0.130207\pi$
$548$	3.18948	−	9.41753i	0.136248	−	0.402297i
$549$		0			0
$550$	6.34237	+	1.04485i	0.270440	+	0.0445526i
$551$	0.0922576	+	0.159795i	0.00393031	+	0.00680749i
$552$		0			0
$553$	1.66191	−	2.87851i	0.0706716	−	0.122407i
$554$	−14.9063	+	18.1763i	−0.633307	+	0.772237i
$555$		0			0
$556$	−16.9030	+	3.37452i	−0.716848	+	0.143111i
$557$		−	23.5098i		−	0.996142i	−0.867136	−	0.498071i	$-0.834042\pi$
$557$		−	23.5098i		−	0.996142i	0.867136	−	0.498071i	$-0.165958\pi$
$558$		0			0
$559$		−	36.6497i		−	1.55012i
$560$	−1.23394	+	9.47508i	−0.0521433	+	0.400395i
$561$		0			0
$562$	11.2868	+	9.25627i	0.476107	+	0.390452i
$563$	−16.5569	+	28.6774i	−0.697790	+	1.20861i	0.271442	+	0.962455i	$0.412500\pi$
$563$	−16.5569	+	28.6774i	−0.697790	+	1.20861i	−0.969231	+	0.246152i	$0.920834\pi$
$564$		0			0
$565$	−10.8610	−	18.8119i	−0.456928	−	0.791422i
$566$	3.28244	−	19.9248i	0.137971	−	0.837501i
$567$		0			0
$568$	15.2780	+	8.14566i	0.641051	+	0.341784i
$569$	−16.2900	+	9.40502i	−0.682911	+	0.394279i	−0.800951	−	0.598730i	$-0.795672\pi$
$569$	−16.2900	+	9.40502i	−0.682911	+	0.394279i	0.118040	+	0.993009i	$0.462339\pi$
$570$		0			0
$571$	18.0636	+	10.4290i	0.755937	+	0.436440i	0.827835	−	0.560972i	$-0.189572\pi$
$571$	18.0636	+	10.4290i	0.755937	+	0.436440i	−0.0718982	+	0.997412i	$0.522906\pi$
$572$	−41.5894	+	36.5245i	−1.73894	+	1.52716i
$573$		0			0
$574$	2.64002	+	7.00692i	0.110192	+	0.292463i
$575$	3.74220			0.156061
$576$		0			0
$577$	−34.3394			−1.42957			−0.714783	−	0.699346i	$-0.753475\pi$
$577$	−34.3394			−1.42957			−0.714783	+	0.699346i	$0.753475\pi$
$578$	−6.68509	−	17.7430i	−0.278063	−	0.738013i
$579$		0			0
$580$	1.25128	−	1.09889i	0.0519565	−	0.0456290i
$581$	−5.60486	−	3.23597i	−0.232529	−	0.134251i
$582$		0			0
$583$	70.2159	−	40.5392i	2.90805	−	1.67896i
$584$	12.6775	+	6.75915i	0.524597	+	0.279696i
$585$		0			0
$586$	0.558148	−	3.38803i	0.0230569	−	0.139958i
$587$	18.1996	+	31.5226i	0.751177	+	1.30108i	0.947253	+	0.320487i	$0.103847\pi$
$587$	18.1996	+	31.5226i	0.751177	+	1.30108i	−0.196076	+	0.980589i	$0.562820\pi$
$588$		0			0
$589$	1.55791	−	2.69839i	0.0641928	−	0.111185i
$590$	13.9056	+	11.4039i	0.572484	+	0.469491i
$591$		0			0
$592$	0.435181	−	3.34165i	0.0178858	−	0.137341i
$593$			2.74882i			0.112880i	0.998406	+	0.0564402i	$0.0179750\pi$
$593$			2.74882i			0.112880i	−0.998406	+	0.0564402i	$0.982025\pi$
$594$		0			0
$595$			4.52784i			0.185623i
$596$	4.94267	−	0.986753i	0.202460	−	0.0404190i
$597$		0			0
$598$	−20.4342	+	24.9170i	−0.835619	+	1.01893i
$599$	13.1712	−	22.8132i	0.538162	−	0.932124i	−0.460841	−	0.887483i	$-0.652452\pi$
$599$	13.1712	−	22.8132i	0.538162	−	0.932124i	0.999003	−	0.0446413i	$-0.0142145\pi$
$600$		0			0
$601$	10.6251	+	18.4032i	0.433406	+	0.750682i	0.997164	−	0.0752583i	$-0.0239781\pi$
$601$	10.6251	+	18.4032i	0.433406	+	0.750682i	−0.563758	+	0.825940i	$0.690645\pi$
$602$	−11.8927	−	1.95923i	−0.484712	−	0.0798522i
$603$		0			0
$604$	0.245240	−	0.724119i	0.00997869	−	0.0294640i
$605$	62.9312	−	36.3333i	2.55852	−	1.47716i
$606$		0			0
$607$	−12.9081	−	7.45251i	−0.523924	−	0.302488i	0.214614	−	0.976699i	$-0.431151\pi$
$607$	−12.9081	−	7.45251i	−0.523924	−	0.302488i	−0.738539	+	0.674211i	$0.764484\pi$
$608$	−0.685066	−	2.91503i	−0.0277831	−	0.118220i
$609$		0			0
$610$	22.1216	−	8.33480i	0.895676	−	0.337466i
$611$	17.5665			0.710663
$612$		0			0
$613$	0.497742			0.0201036			0.0100518	−	0.999949i	$-0.496800\pi$
$613$	0.497742			0.0201036			0.0100518	+	0.999949i	$0.496800\pi$
$614$	11.7417	−	4.42394i	0.473855	−	0.178536i
$615$		0			0
$616$	9.62880	+	15.4482i	0.387955	+	0.622426i
$617$	13.3288	+	7.69541i	0.536599	+	0.309806i	0.743700	−	0.668514i	$-0.233069\pi$
$617$	13.3288	+	7.69541i	0.536599	+	0.309806i	−0.207100	+	0.978320i	$0.566403\pi$
$618$		0			0
$619$	−6.09500	+	3.51895i	−0.244979	+	0.141439i	−0.617463	−	0.786600i	$-0.711839\pi$
$619$	−6.09500	+	3.51895i	−0.244979	+	0.141439i	0.372484	+	0.928039i	$0.378506\pi$
$620$	−26.6353	−	9.02070i	−1.06970	−	0.362280i
$621$		0			0
$622$	8.47767	+	1.39662i	0.339924	+	0.0559995i
$623$	7.20850	+	12.4855i	0.288802	+	0.500220i
$624$		0			0
$625$	14.0162	−	24.2768i	0.560648	−	0.971070i
$626$	−18.5177	+	22.5800i	−0.740116	+	0.902478i
$627$		0			0
$628$	3.44476	+	17.2549i	0.137461	+	0.688546i
$629$		−	1.59687i		−	0.0636713i
$630$		0			0
$631$		−	0.297508i		−	0.0118436i	−0.999982	−	0.00592180i	$-0.998115\pi$
$631$		−	0.297508i		−	0.0118436i	0.999982	−	0.00592180i	$-0.00188498\pi$
$632$	9.39582	−	0.317456i	0.373746	−	0.0126277i
$633$		0			0
$634$	26.8423	+	22.0132i	1.06604	+	0.874254i
$635$	20.3798	−	35.2988i	0.808747	−	1.40079i
$636$		0			0
$637$	−2.15010	−	3.72408i	−0.0851901	−	0.147554i
$638$	0.515703	−	3.13038i	0.0204169	−	0.123933i
$639$		0			0
$640$	−24.5895	+	11.2140i	−0.971985	+	0.443272i
$641$	−8.18111	+	4.72337i	−0.323134	+	0.186562i	−0.652789	−	0.757540i	$-0.726401\pi$
$641$	−8.18111	+	4.72337i	−0.323134	+	0.186562i	0.329654	+	0.944102i	$0.393068\pi$
$642$		0			0
$643$	29.2594	+	16.8929i	1.15388	+	0.666193i	0.949830	−	0.312768i	$-0.101256\pi$
$643$	29.2594	+	16.8929i	1.15388	+	0.666193i	0.204050	+	0.978960i	$0.434590\pi$
$644$	6.99312	+	7.96288i	0.275567	+	0.313781i
$645$		0			0
$646$	−0.500296	−	1.32785i	−0.0196839	−	0.0522434i
$647$	−8.81904			−0.346712			−0.173356	−	0.984859i	$-0.555461\pi$
$647$	−8.81904			−0.346712			−0.173356	+	0.984859i	$0.555461\pi$
$648$		0			0
$649$	34.2606			1.34485
$650$	−1.51427	−	4.01906i	−0.0593947	−	0.157641i
$651$		0			0
$652$	14.2128	+	16.1837i	0.556615	+	0.633803i
$653$	−26.1332	−	15.0880i	−1.02267	−	0.590440i	−0.107795	−	0.994173i	$-0.534379\pi$
$653$	−26.1332	−	15.0880i	−1.02267	−	0.590440i	−0.914877	+	0.403733i	$0.867712\pi$
$654$		0			0
$655$	−23.1273	+	13.3525i	−0.903657	+	0.521727i
$656$	−12.8692	+	16.8201i	−0.502458	+	0.656716i
$657$		0			0
$658$	0.939071	−	5.70028i	0.0366088	−	0.222220i
$659$	−4.08576	−	7.07674i	−0.159158	−	0.275671i	0.775407	−	0.631462i	$-0.217545\pi$
$659$	−4.08576	−	7.07674i	−0.159158	−	0.275671i	−0.934565	+	0.355791i	$0.884211\pi$
$660$		0			0
$661$	−22.1468	+	38.3593i	−0.861409	+	1.49200i	0.00916009	+	0.999958i	$0.497084\pi$
$661$	−22.1468	+	38.3593i	−0.861409	+	1.49200i	−0.870569	+	0.492046i	$0.836249\pi$
$662$	32.8128	+	26.9096i	1.27531	+	1.04587i
$663$		0			0
$664$	−0.618131	−	18.2950i	−0.0239881	−	0.709982i
$665$		−	1.26449i		−	0.0490349i
$666$		0			0
$667$		−	1.84702i		−	0.0715170i
$668$	−3.07339	−	15.3947i	−0.118913	−	0.595639i
$669$		0			0
$670$	−23.0743	+	28.1362i	−0.891439	+	1.08700i
$671$	22.5178	−	39.0020i	0.869291	−	1.50566i
$672$		0			0
$673$	6.17994	+	10.7040i	0.238219	+	0.412608i	0.960203	−	0.279302i	$-0.0901030\pi$
$673$	6.17994	+	10.7040i	0.238219	+	0.412608i	−0.721984	+	0.691910i	$0.756770\pi$
$674$	14.7188	+	2.42479i	0.566946	+	0.0933995i
$675$		0			0
$676$	10.4030	+	3.52325i	0.400117	+	0.135509i
$677$	2.57177	−	1.48481i	0.0988412	−	0.0570660i	−0.449765	−	0.893147i	$-0.648492\pi$
$677$	2.57177	−	1.48481i	0.0988412	−	0.0570660i	0.548606	+	0.836081i	$0.315159\pi$
$678$		0			0
$679$	−6.69654	−	3.86625i	−0.256990	−	0.148373i
$680$	−10.8683	+	6.77420i	−0.416782	+	0.259779i
$681$		0			0
$682$	−50.1335	+	18.8889i	−1.91971	+	0.723294i
$683$	13.3131			0.509413			0.254707	−	0.967018i	$-0.418021\pi$
$683$	13.3131			0.509413			0.254707	+	0.967018i	$0.418021\pi$
$684$		0			0
$685$	11.8757			0.453749
$686$	−1.32340	+	0.498620i	−0.0505275	+	0.0190374i
$687$		0			0
$688$	−13.0902	−	31.4779i	−0.499058	−	1.20008i
$689$	−46.9158	−	27.0868i	−1.78735	−	1.03193i
$690$		0			0
$691$	35.4607	−	20.4733i	1.34899	−	0.778840i	0.360884	−	0.932611i	$-0.382475\pi$
$691$	35.4607	−	20.4733i	1.34899	−	0.778840i	0.988107	+	0.153771i	$0.0491417\pi$
$692$	−12.2716	+	36.2342i	−0.466496	+	1.37742i
$693$		0			0
$694$	−12.7166	−	2.09495i	−0.482716	−	0.0795233i
$695$	−10.2936	−	17.8290i	−0.390457	−	0.676292i
$696$		0			0
$697$	−5.01792	+	8.69129i	−0.190067	+	0.329206i
$698$	20.2635	−	24.7087i	0.766984	−	0.935239i
$699$		0			0
$700$	−1.38513	+	0.276526i	−0.0523529	+	0.0104517i
$701$		−	18.8087i		−	0.710396i	−0.934791	−	0.355198i	$-0.884413\pi$
$701$		−	18.8087i		−	0.710396i	0.934791	−	0.355198i	$-0.115587\pi$
$702$		0			0
$703$			0.445958i			0.0168196i
$704$	−22.6751	+	46.2247i	−0.854598	+	1.74216i
$705$		0			0
$706$	−7.28018	−	5.97043i	−0.273993	−	0.224700i
$707$	8.54473	−	14.7999i	0.321358	−	0.556608i
$708$		0			0
$709$	19.3884	+	33.5818i	0.728148	+	1.26119i	0.957665	+	0.287885i	$0.0929520\pi$
$709$	19.3884	+	33.5818i	0.728148	+	1.26119i	−0.229517	+	0.973305i	$0.573715\pi$
$710$	−3.36145	+	20.4044i	−0.126153	+	0.765763i
$711$		0			0
$712$	−19.1846	+	35.9826i	−0.718973	+	1.34851i
$713$	−27.0112	+	15.5949i	−1.01158	+	0.584035i
$714$		0			0
$715$	−57.2532	−	33.0551i	−2.14115	−	1.23619i
$716$	39.2923	−	34.5071i	1.46842	−	1.28959i
$717$		0			0
$718$	4.00558	+	10.6313i	0.149487	+	0.396757i
$719$	27.9873			1.04375			0.521875	−	0.853022i	$-0.325233\pi$
$719$	27.9873			1.04375			0.521875	+	0.853022i	$0.325233\pi$
$720$		0			0
$721$	−11.5888			−0.431589
$722$	−9.33406	−	24.7737i	−0.347378	−	0.921982i
$723$		0			0
$724$	−28.4279	+	24.9658i	−1.05652	+	0.927848i
$725$	0.213190	+	0.123085i	0.00791769	+	0.00457128i
$726$		0			0
$727$	−11.9395	+	6.89330i	−0.442813	+	0.255658i	−0.704790	−	0.709416i	$-0.748959\pi$
$727$	−11.9395	+	6.89330i	−0.442813	+	0.255658i	0.261977	+	0.965074i	$0.415626\pi$
$728$	5.72225	−	10.7326i	0.212081	−	0.397778i
$729$		0			0
$730$	−2.78928	+	16.9313i	−0.103236	+	0.626654i
$731$	−8.07734	−	13.9904i	−0.298751	−	0.517452i
$732$		0			0
$733$	20.9012	−	36.2020i	0.772005	−	1.33715i	−0.164458	−	0.986384i	$-0.552588\pi$
$733$	20.9012	−	36.2020i	0.772005	−	1.33715i	0.936463	−	0.350767i	$-0.114079\pi$
$734$	18.8418	+	15.4520i	0.695463	+	0.570345i
$735$		0			0
$736$	−8.65105	+	28.6993i	−0.318882	+	1.05787i
$737$			69.3221i			2.55351i
$738$		0			0
$739$		−	47.3413i		−	1.74148i	−0.491746	−	0.870739i	$-0.663641\pi$
$739$		−	47.3413i		−	1.74148i	0.491746	−	0.870739i	$-0.336359\pi$
$740$	3.94703	−	0.787984i	0.145096	−	0.0289669i
$741$		0			0
$742$	−11.2976	+	13.7760i	−0.414749	+	0.505734i
$743$	1.10160	−	1.90802i	0.0404136	−	0.0699984i	−0.845111	−	0.534591i	$-0.820466\pi$
$743$	1.10160	−	1.90802i	0.0404136	−	0.0699984i	0.885525	+	0.464592i	$0.153799\pi$
$744$		0			0
$745$	3.00998	+	5.21343i	0.110277	+	0.191005i
$746$	0.727681	+	0.119879i	0.0266423	+	0.00438909i
$747$		0			0
$748$	−7.82628	+	23.1086i	−0.286157	+	0.844933i
$749$	−1.43919	+	0.830918i	−0.0525869	+	0.0303611i
$750$		0			0
$751$	−9.02644	−	5.21142i	−0.329379	−	0.190167i	0.326186	−	0.945306i	$-0.394236\pi$
$751$	−9.02644	−	5.21142i	−0.329379	−	0.190167i	−0.655566	+	0.755138i	$0.727570\pi$
$752$	15.0876	−	6.27421i	0.550186	−	0.228797i
$753$		0			0
$754$	−1.98367	+	0.747393i	−0.0722411	+	0.0272185i
$755$	0.913132			0.0332323
$756$		0			0
$757$	14.0656			0.511224			0.255612	−	0.966779i	$-0.417723\pi$
$757$	14.0656			0.511224			0.255612	+	0.966779i	$0.417723\pi$
$758$	30.2317	−	11.3905i	1.09807	−	0.413721i
$759$		0			0
$760$	3.03521	−	1.89183i	0.110099	−	0.0686239i
$761$	23.2533	+	13.4253i	0.842931	+	0.486667i	0.858260	−	0.513216i	$-0.171546\pi$
$761$	23.2533	+	13.4253i	0.842931	+	0.486667i	−0.0153283	+	0.999883i	$0.504879\pi$
$762$		0			0
$763$	−7.11451	+	4.10757i	−0.257563	+	0.148704i
$764$	−17.8334	−	6.03970i	−0.645188	−	0.218509i
$765$		0			0
$766$	34.8241	+	5.73697i	1.25825	+	0.207285i
$767$	−11.4459	−	19.8248i	−0.413286	−	0.715833i
$768$		0			0
$769$	18.9397	−	32.8045i	0.682983	−	1.18296i	−0.291083	−	0.956698i	$-0.594016\pi$
$769$	18.9397	−	32.8045i	0.682983	−	1.18296i	0.974066	−	0.226263i	$-0.0726510\pi$
$770$	−13.7870	+	16.8114i	−0.496848	+	0.605842i
$771$		0			0
$772$	−0.515866	−	2.58399i	−0.0185664	−	0.0929997i
$773$			26.0697i			0.937662i	0.883288	+	0.468831i	$0.155325\pi$
$773$			26.0697i			0.937662i	−0.883288	+	0.468831i	$0.844675\pi$
$774$		0			0
$775$		−	4.15698i		−	0.149323i
$776$	−0.738528	−	21.8583i	−0.0265116	−	0.784669i
$777$		0			0
$778$	−27.7792	−	22.7816i	−0.995934	−	0.816759i
$779$	1.40136	−	2.42722i	0.0502088	−	0.0869642i
$780$		0			0
$781$	19.6981	+	34.1181i	0.704853	+	1.22084i
$782$	−2.30888	+	14.0152i	−0.0825653	+	0.501181i
$783$		0			0
$784$	−3.17682	−	2.43060i	−0.113458	−	0.0868073i
$785$	−18.2001	+	10.5079i	−0.649591	+	0.375041i
$786$		0			0
$787$	43.3071	+	25.0034i	1.54373	+	0.891275i	0.998598	+	0.0529261i	$0.0168548\pi$
$787$	43.3071	+	25.0034i	1.54373	+	0.891275i	0.545135	+	0.838349i	$0.316479\pi$
$788$	−4.70373	−	5.35601i	−0.167563	−	0.190800i
$789$		0			0
$790$	3.95896	+	10.5076i	0.140854	+	0.373842i
$791$	9.09342			0.323325
$792$		0			0
$793$	−30.0912			−1.06857
$794$	−2.65749	−	7.05329i	−0.0943107	−	0.250312i
$795$		0			0
$796$	−21.0814	−	24.0048i	−0.747211	−	0.850829i
$797$	−7.70027	−	4.44575i	−0.272757	−	0.157477i	0.357383	−	0.933958i	$-0.383669\pi$
$797$	−7.70027	−	4.44575i	−0.272757	−	0.157477i	−0.630140	+	0.776481i	$0.717003\pi$
$798$		0			0
$799$	6.70568	−	3.87152i	0.237230	−	0.136965i
$800$	−2.73607	−	2.91105i	−0.0967348	−	0.102921i
$801$		0			0
$802$	−5.36485	+	32.5653i	−0.189440	+	1.14992i
$803$	16.3452	+	28.3107i	0.576809	+	0.999063i
$804$		0			0
$805$	−6.32887	+	10.9619i	−0.223063	+	0.386357i
$806$	27.6787	+	22.6992i	0.974942	+	0.799544i
$807$		0			0
$808$	48.3087	−	1.63221i	1.69950	−	0.0574208i
$809$		−	21.3028i		−	0.748967i	−0.927234	−	0.374484i	$-0.877820\pi$
$809$		−	21.3028i		−	0.748967i	0.927234	−	0.374484i	$-0.122180\pi$
$810$		0			0
$811$			5.10606i			0.179298i	0.995973	+	0.0896491i	$0.0285745\pi$
$811$			5.10606i			0.179298i	−0.995973	+	0.0896491i	$0.971425\pi$
$812$	0.136484	+	0.683651i	0.00478964	+	0.0239914i
$813$		0			0
$814$	4.86235	−	5.92902i	0.170425	−	0.207812i
$815$	−12.8628	+	22.2790i	−0.450563	+	0.780398i
$816$		0			0
$817$	2.25576	+	3.90709i	0.0789191	+	0.136692i
$818$	−43.4248	−	7.15386i	−1.51831	−	0.250129i
$819$		0			0
$820$	−23.9587	−	8.11419i	−0.836673	−	0.283360i
$821$	38.3644	−	22.1497i	1.33893	−	0.773030i	0.352279	−	0.935895i	$-0.385407\pi$
$821$	38.3644	−	22.1497i	1.33893	−	0.773030i	0.986648	+	0.162865i	$0.0520734\pi$
$822$		0			0
$823$	−20.7375	−	11.9728i	−0.722864	−	0.417346i	0.0929417	−	0.995672i	$-0.470373\pi$
$823$	−20.7375	−	11.9728i	−0.722864	−	0.417346i	−0.815806	+	0.578326i	$0.803706\pi$
$824$	−17.3382	−	27.8170i	−0.604006	−	0.969052i
$825$		0			0
$826$	−7.04498	+	2.65436i	−0.245126	+	0.0923569i
$827$	28.7823			1.00086			0.500429	−	0.865777i	$-0.333176\pi$
$827$	28.7823			1.00086			0.500429	+	0.865777i	$0.333176\pi$
$828$		0			0
$829$	13.0893			0.454611			0.227306	−	0.973823i	$-0.427008\pi$
$829$	13.0893			0.454611			0.227306	+	0.973823i	$0.427008\pi$
$830$	20.4597	−	7.70865i	0.710166	−	0.267571i
$831$		0			0
$832$	34.3232	−	2.32200i	1.18994	−	0.0805010i
$833$	−1.64152	−	0.947734i	−0.0568754	−	0.0328370i
$834$		0			0
$835$	16.2380	−	9.37503i	0.561940	−	0.324436i
$836$	2.18565	−	6.45353i	0.0755922	−	0.223200i
$837$		0			0
$838$	37.4340	+	6.16693i	1.29314	+	0.213033i
$839$	4.65016	+	8.05432i	0.160541	+	0.278066i	0.935063	−	0.354482i	$-0.115343\pi$
$839$	4.65016	+	8.05432i	0.160541	+	0.278066i	−0.774522	+	0.632547i	$0.782009\pi$
$840$		0			0
$841$	−14.4392	+	25.0095i	−0.497905	+	0.862397i
$842$	7.17608	−	8.75031i	0.247304	−	0.301556i
$843$		0			0
$844$	−7.68645	+	1.53452i	−0.264578	+	0.0528203i
$845$			13.1185i			0.451290i
$846$		0			0
$847$			30.4201i			1.04525i
$848$	−49.9698	−	6.50754i	−1.71597	−	0.223470i
$849$		0			0
$850$	−1.46382	−	1.20047i	−0.0502086	−	0.0411757i
$851$	2.23205	−	3.86602i	0.0765137	−	0.132526i
$852$		0			0
$853$	3.68249	+	6.37826i	0.126086	+	0.218387i	0.922157	−	0.386816i	$-0.126425\pi$
$853$	3.68249	+	6.37826i	0.126086	+	0.218387i	−0.796071	+	0.605203i	$0.793092\pi$
$854$	−1.60862	+	9.76453i	−0.0550459	+	0.334135i
$855$		0			0
$856$	−4.14769	−	2.21139i	−0.141765	−	0.0755839i
$857$	−8.88430	+	5.12935i	−0.303482	+	0.175215i	−0.644006	−	0.765020i	$-0.722729\pi$
$857$	−8.88430	+	5.12935i	−0.303482	+	0.175215i	0.340524	+	0.940236i	$0.389395\pi$
$858$		0			0
$859$	−43.8854	−	25.3372i	−1.49735	−	0.864495i	−0.497354	−	0.867548i	$-0.665695\pi$
$859$	−43.8854	−	25.3372i	−1.49735	−	0.864495i	−0.999995	+	0.00305268i	$0.999028\pi$
$860$	30.5946	−	26.8687i	1.04327	−	0.916214i
$861$		0			0
$862$	−11.5996	−	30.7868i	−0.395085	−	1.04860i
$863$	10.9590			0.373049			0.186524	−	0.982450i	$-0.440278\pi$
$863$	10.9590			0.373049			0.186524	+	0.982450i	$0.440278\pi$
$864$		0			0
$865$	−45.6922			−1.55358
$866$	20.1481	+	53.4754i	0.684660	+	1.81717i
$867$		0			0
$868$	8.84548	−	7.76823i	0.300235	−	0.263671i
$869$	18.5257	+	10.6958i	0.628440	+	0.362830i
$870$		0			0
$871$	40.1130	−	23.1593i	1.35918	−	0.784722i
$872$	−20.5037	−	10.9318i	−0.694344	−	0.370198i
$873$		0			0
$874$	0.644801	−	3.91402i	0.0218107	−	0.132394i
$875$	5.12842	+	8.88268i	0.173372	+	0.300289i
$876$		0			0
$877$	−27.1977	+	47.1079i	−0.918402	+	1.59072i	−0.116560	+	0.993184i	$0.537187\pi$
$877$	−27.1977	+	47.1079i	−0.918402	+	1.59072i	−0.801842	+	0.597536i	$0.796147\pi$
$878$	−5.73533	−	4.70351i	−0.193558	−	0.158736i
$879$		0			0
$880$	−60.9801	−	7.94141i	−2.05564	−	0.267705i
$881$		−	15.1656i		−	0.510942i	−0.966817	−	0.255471i	$-0.917770\pi$
$881$		−	15.1656i		−	0.510942i	0.966817	−	0.255471i	$-0.0822305\pi$
$882$		0			0
$883$		−	16.5171i		−	0.555843i	−0.960604	−	0.277922i	$-0.910354\pi$
$883$		−	16.5171i		−	0.555843i	0.960604	−	0.277922i	$-0.0896456\pi$
$884$	15.9863	−	3.19150i	0.537678	−	0.107342i
$885$		0			0
$886$	−8.69707	+	10.6050i	−0.292184	+	0.356281i
$887$	−20.7959	+	36.0195i	−0.698257	+	1.20942i	0.270813	+	0.962632i	$0.412707\pi$
$887$	−20.7959	+	36.0195i	−0.698257	+	1.20942i	−0.969070	+	0.246785i	$0.920626\pi$
$888$		0			0
$889$	8.53149	+	14.7770i	0.286137	+	0.495604i
$890$	−48.0562	−	7.91685i	−1.61085	−	0.265373i
$891$		0			0
$892$	1.67125	−	4.93468i	0.0559575	−	0.165225i
$893$	−1.87270	+	1.08120i	−0.0626674	+	0.0361810i
$894$		0			0
$895$	54.0909	+	31.2294i	1.80806	+	1.04388i
$896$	1.08137	−	11.2619i	0.0361260	−	0.376234i
$897$		0			0
$898$	−51.3213	+	19.3365i	−1.71261	+	0.645266i
$899$	−2.05174			−0.0684295
$900$		0			0
$901$	−23.8790			−0.795524
$902$	−45.0955	+	16.9907i	−1.50151	+	0.565730i
$903$		0			0
$904$	13.6049	+	21.8273i	0.452491	+	0.725964i
$905$	−39.1347	−	22.5944i	−1.30088	−	0.751064i
$906$		0			0
$907$	4.95363	−	2.85998i	0.164482	−	0.0949640i	−0.415499	−	0.909594i	$-0.636393\pi$
$907$	4.95363	−	2.85998i	0.164482	−	0.0949640i	0.579982	+	0.814630i	$0.303060\pi$
$908$	−5.92938	−	2.00813i	−0.196774	−	0.0666422i
$909$		0			0
$910$	14.3339	+	2.36138i	0.475163	+	0.0782791i
$911$	−8.80268	−	15.2467i	−0.291646	−	0.505145i	0.682553	−	0.730836i	$-0.260870\pi$
$911$	−8.80268	−	15.2467i	−0.291646	−	0.505145i	−0.974199	+	0.225691i	$0.927536\pi$
$912$		0			0
$913$	20.8262	−	36.0720i	0.689246	−	1.19381i
$914$	20.3112	−	24.7669i	0.671834	−	0.819216i
$915$		0			0
$916$	−2.61231	−	13.0851i	−0.0863130	−	0.432344i
$917$		−	11.1794i		−	0.369177i
$918$		0			0
$919$			23.5323i			0.776259i	0.921605	+	0.388129i	$0.126879\pi$
$919$			23.5323i			0.776259i	−0.921605	+	0.388129i	$0.873121\pi$
$920$	−35.7811	+	1.20893i	−1.17967	+	0.0398574i
$921$		0			0
$922$	40.4124	+	33.1420i	1.33091	+	1.09147i
$923$	13.1616	−	22.7965i	0.433218	−	0.750356i
$924$		0			0
$925$	0.297487	+	0.515263i	0.00978132	+	0.0169417i
$926$	2.37240	−	14.4007i	0.0779618	−	0.473238i
$927$		0			0
$928$	−1.43680	+	1.35043i	−0.0471652	+	0.0443301i
$929$	24.3118	−	14.0364i	0.797645	−	0.460521i	−0.0450020	−	0.998987i	$-0.514329\pi$
$929$	24.3118	−	14.0364i	0.797645	−	0.460521i	0.842647	+	0.538466i	$0.180996\pi$
$930$		0			0
$931$	0.458429	+	0.264674i	0.0150244	+	0.00867434i
$932$	−19.8221	−	22.5709i	−0.649294	−	0.739335i
$933$		0			0
$934$	−0.448767	−	1.19108i	−0.0146841	−	0.0389734i
$935$	−29.1405			−0.952995
$936$		0			0
$937$	−18.7222			−0.611628			−0.305814	−	0.952091i	$-0.598929\pi$
$937$	−18.7222			−0.611628			−0.305814	+	0.952091i	$0.598929\pi$
$938$	−5.37076	−	14.2546i	−0.175361	−	0.465430i
$939$		0			0
$940$	12.8783	+	14.6642i	0.420045	+	0.478294i
$941$	1.01009	+	0.583173i	0.0329279	+	0.0190109i	0.516374	−	0.856363i	$-0.327282\pi$
$941$	1.01009	+	0.583173i	0.0329279	+	0.0190109i	−0.483446	+	0.875374i	$0.660615\pi$
$942$		0			0
$943$	−24.2968	+	14.0278i	−0.791213	+	0.456807i
$944$	−16.9115	−	12.9391i	−0.550422	−	0.421132i
$945$		0			0
$946$	12.6093	−	76.5399i	0.409963	−	2.48853i
$947$	22.6706	+	39.2667i	0.736696	+	1.27600i	0.953975	+	0.299886i	$0.0969486\pi$
$947$	22.6706	+	39.2667i	0.736696	+	1.27600i	−0.217279	+	0.976110i	$0.569718\pi$
$948$		0			0
$949$	10.9213	−	18.9162i	0.354519	−	0.614046i
$950$	0.408801	+	0.335255i	0.0132633	+	0.0108771i
$951$		0			0
$952$	−0.181035	−	5.35814i	−0.00586739	−	0.173658i
$953$			49.1845i			1.59324i	0.604479	+	0.796621i	$0.293381\pi$
$953$			49.1845i			1.59324i	−0.604479	+	0.796621i	$0.706619\pi$
$954$		0			0
$955$		−	22.4883i		−	0.727705i
$956$	−0.862208	−	4.31882i	−0.0278858	−	0.139681i
$957$		0			0
$958$	−28.6002	+	34.8743i	−0.924031	+	1.12674i
$959$	−2.48574	+	4.30543i	−0.0802688	+	0.139030i
$960$		0			0
$961$	1.82347	+	3.15834i	0.0588216	+	0.101882i
$962$	−5.05524	−	0.832807i	−0.162987	−	0.0268508i
$963$		0			0
$964$	35.1751	+	11.9129i	1.13291	+	0.383688i
$965$	2.72554	−	1.57359i	0.0877381	−	0.0506556i
$966$		0			0
$967$	7.53707	+	4.35153i	0.242376	+	0.139936i	0.616268	−	0.787536i	$-0.288644\pi$
$967$	7.53707	+	4.35153i	0.242376	+	0.139936i	−0.373892	+	0.927472i	$0.621977\pi$
$968$	−73.0185	+	45.5121i	−2.34690	+	1.46281i
$969$		0			0
$970$	24.4447	−	9.21009i	0.784872	−	0.295718i
$971$	−13.3993			−0.430005			−0.215002	−	0.976614i	$-0.568976\pi$
$971$	−13.3993			−0.430005			−0.215002	+	0.976614i	$0.568976\pi$
$972$		0			0
$973$	8.61829			0.276290
$974$	10.1309	−	3.81704i	0.324615	−	0.122306i
$975$		0			0
$976$	−25.8449	+	10.7477i	−0.827274	+	0.344025i
$977$	−17.4473	−	10.0732i	−0.558190	−	0.322271i	0.194229	−	0.980956i	$-0.437780\pi$
$977$	−17.4473	−	10.0732i	−0.558190	−	0.322271i	−0.752419	+	0.658685i	$0.771113\pi$
$978$		0			0
$979$	−80.3546	+	46.3928i	−2.56814	+	1.48272i
$980$	1.53253	−	4.52507i	0.0489548	−	0.144548i
$981$		0			0
$982$	4.45329	+	0.733641i	0.142110	+	0.0234114i
$983$	22.3323	+	38.6807i	0.712291	+	1.23372i	0.963995	+	0.265920i	$0.0856757\pi$
$983$	22.3323	+	38.6807i	0.712291	+	1.23372i	−0.251704	+	0.967804i	$0.580991\pi$
$984$		0			0
$985$	4.25694	−	7.37324i	0.135637	−	0.234931i
$986$	−0.592510	+	0.722491i	−0.0188694	+	0.0230088i
$987$		0			0
$988$	−4.46451	+	0.891292i	−0.142035	+	0.0283558i
$989$		−	45.1610i		−	1.43604i
$990$		0			0
$991$		−	40.8937i		−	1.29903i	−0.760349	−	0.649515i	$-0.774972\pi$
$991$		−	40.8937i		−	1.29903i	0.760349	−	0.649515i	$-0.225028\pi$
$992$	31.8803	+	9.60993i	1.01220	+	0.305115i
$993$		0			0
$994$	−6.69381	−	5.48955i	−0.212315	−	0.174118i
$995$	19.0790	−	33.0457i	0.604844	−	1.04762i
$996$		0			0
$997$	−29.1863	−	50.5521i	−0.924339	−	1.60100i	−0.792621	−	0.609715i	$-0.791284\pi$
$997$	−29.1863	−	50.5521i	−0.924339	−	1.60100i	−0.131718	−	0.991287i	$-0.542049\pi$
$998$	−2.40913	+	14.6237i	−0.0762596	+	0.462905i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.14		72
3.2	odd	2		252.2.ba.a.239.23	yes	72
4.3	odd	2	inner	756.2.ba.a.71.26		72
9.2	odd	6	inner	756.2.ba.a.575.26		72
9.7	even	3		252.2.ba.a.155.11	✓	72
12.11	even	2		252.2.ba.a.239.11	yes	72
36.7	odd	6		252.2.ba.a.155.23	yes	72
36.11	even	6	inner	756.2.ba.a.575.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.11	✓	72	9.7	even	3
252.2.ba.a.155.23	yes	72	36.7	odd	6
252.2.ba.a.239.11	yes	72	12.11	even	2
252.2.ba.a.239.23	yes	72	3.2	odd	2
756.2.ba.a.71.14		72	1.1	even	1	trivial
756.2.ba.a.71.26		72	4.3	odd	2	inner
756.2.ba.a.575.14		72	36.11	even	6	inner
756.2.ba.a.575.26		72	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +O(q^{10})\)	\(q+(-0.498620 - 1.32340i) q^{2} +(-1.50276 + 1.31974i) q^{4} +(-2.06874 - 1.19439i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(-0.549133 + 3.33330i) q^{10} +(3.21792 + 5.57360i) q^{11} +(2.15010 - 3.72408i) q^{13} +(-1.09352 - 0.896785i) q^{14} +(0.516556 - 3.96651i) q^{16} -1.89547i q^{17} +0.529348i q^{19} +(4.68509 - 0.935330i) q^{20} +(5.77157 - 7.03770i) q^{22} +(2.64942 - 4.58894i) q^{23} +(0.353115 + 0.611613i) q^{25} +(-6.00052 - 0.988535i) q^{26} +(-0.641554 + 1.89431i) q^{28} +(0.301871 - 0.174285i) q^{29} +(-5.09757 - 2.94308i) q^{31} +(-5.50683 + 1.29417i) q^{32} +(-2.50846 + 0.945118i) q^{34} -2.38877 q^{35} +0.842466 q^{37} +(0.700537 - 0.263943i) q^{38} +(-3.57389 - 5.73386i) q^{40} +(-4.58530 - 2.64733i) q^{41} +(7.38095 - 4.26140i) q^{43} +(-12.1915 - 4.12894i) q^{44} +(-7.39404 - 1.21810i) q^{46} +(2.04252 + 3.53774i) q^{47} +(0.500000 - 0.866025i) q^{49} +(0.633336 - 0.772273i) q^{50} +(1.68376 + 8.43397i) q^{52} -12.5979i q^{53} -15.3738i q^{55} +(2.82681 - 0.0955095i) q^{56} +(-0.381168 - 0.312593i) q^{58} +(2.66171 - 4.61021i) q^{59} +(-3.49882 - 6.06013i) q^{61} +(-1.35312 + 8.21358i) q^{62} +(4.45851 + 6.64242i) q^{64} +(-8.89599 + 5.13610i) q^{65} +(9.32818 + 5.38563i) q^{67} +(2.50153 + 2.84843i) q^{68} +(1.19109 + 3.16129i) q^{70} +6.12137 q^{71} +5.07942 q^{73} +(-0.420070 - 1.11492i) q^{74} +(-0.698603 - 0.795481i) q^{76} +(5.57360 + 3.21792i) q^{77} +(2.87851 - 1.66191i) q^{79} +(-5.80616 + 7.58869i) q^{80} +(-1.21714 + 7.38818i) q^{82} +(-3.23597 - 5.60486i) q^{83} +(-2.26392 + 3.92122i) q^{85} +(-9.31981 - 7.64311i) q^{86} +(0.614684 + 18.1929i) q^{88} +14.4170i q^{89} -4.30020i q^{91} +(2.07478 + 10.3926i) q^{92} +(3.66340 - 4.46705i) q^{94} +(0.632246 - 1.09508i) q^{95} +(-3.86625 - 6.69654i) q^{97} +(-1.39540 - 0.229881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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