LMFDB - Embedded newform 220.3.x.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(37,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("220.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	220.37
Dual form			220.3.x.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.182447 - 0.358073i) q^{3} +(-4.08347 - 2.88535i) q^{5} +(-1.29828 + 2.54802i) q^{7} +(5.19514 - 7.15049i) q^{9} +(-5.47755 + 9.53920i) q^{11} +(-17.6258 + 2.79165i) q^{13} +(-0.288147 + 1.98860i) q^{15} +(-24.1910 - 3.83149i) q^{17} +(-20.3278 - 6.60491i) q^{19} +1.14924 q^{21} +(15.5799 - 15.5799i) q^{23} +(8.34950 + 23.5645i) q^{25} +(-7.08057 - 1.12145i) q^{27} +(-6.31998 + 2.05349i) q^{29} +(-9.79713 - 7.11803i) q^{31} +(4.41509 + 0.220962i) q^{33} +(12.6534 - 6.65877i) q^{35} +(-15.1322 + 29.6987i) q^{37} +(4.21539 + 5.80199i) q^{39} +(22.8406 - 70.2961i) q^{41} +(20.1403 - 20.1403i) q^{43} +(-41.8459 + 14.2091i) q^{45} +(-32.1844 + 16.3988i) q^{47} +(23.9946 + 33.0257i) q^{49} +(3.04164 + 9.36119i) q^{51} +(-49.2390 + 7.79870i) q^{53} +(49.8914 - 23.1484i) q^{55} +(1.34371 + 8.48388i) q^{57} +(104.881 - 34.0778i) q^{59} +(-35.4315 + 25.7425i) q^{61} +(11.4748 + 22.5207i) q^{63} +(80.0294 + 39.4570i) q^{65} +(84.3898 + 84.3898i) q^{67} +(-8.42125 - 2.73623i) q^{69} +(78.8588 - 57.2943i) q^{71} +(-87.2685 - 44.4655i) q^{73} +(6.91446 - 7.28900i) q^{75} +(-17.1947 - 26.3415i) q^{77} +(7.16911 - 9.86744i) q^{79} +(-23.6909 - 72.9132i) q^{81} +(12.1527 - 76.7291i) q^{83} +(87.7283 + 85.4454i) q^{85} +(1.88836 + 1.88836i) q^{87} +31.4868i q^{89} +(15.7701 - 48.5353i) q^{91} +(-0.761314 + 4.80675i) q^{93} +(63.9506 + 85.6238i) q^{95} +(-13.0738 - 82.5448i) q^{97} +(39.7534 + 88.7247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.182447	−	0.358073i	−0.0608157	−	0.119358i	0.858598	−	0.512650i	$-0.171336\pi$
$3$	−0.182447	−	0.358073i	−0.0608157	−	0.119358i	−0.919414	+	0.393292i	$0.871336\pi$
$4$		0			0
$5$	−4.08347	−	2.88535i	−0.816695	−	0.577070i
$5$	−4.08347	−	2.88535i	−0.816695	−	0.577070i
$6$		0			0
$7$	−1.29828	+	2.54802i	−0.185469	+	0.364003i	−0.964955	−	0.262417i	$-0.915480\pi$
$7$	−1.29828	+	2.54802i	−0.185469	+	0.364003i	0.779486	+	0.626420i	$0.215480\pi$
$8$		0			0
$9$	5.19514	−	7.15049i	0.577238	−	0.794499i
$10$		0			0
$11$	−5.47755	+	9.53920i	−0.497959	+	0.867200i
$11$	−5.47755	+	9.53920i	−0.497959	+	0.867200i
$12$		0			0
$13$	−17.6258	+	2.79165i	−1.35583	+	0.214743i	−0.791684	−	0.610931i	$-0.790795\pi$
$13$	−17.6258	+	2.79165i	−1.35583	+	0.214743i	−0.564148	+	0.825674i	$0.690795\pi$
$14$		0			0
$15$	−0.288147	+	1.98860i	−0.0192098	+	0.132574i
$16$		0			0
$17$	−24.1910	−	3.83149i	−1.42300	−	0.225381i	−0.603000	−	0.797741i	$-0.706028\pi$
$17$	−24.1910	−	3.83149i	−1.42300	−	0.225381i	−0.820003	+	0.572360i	$0.806028\pi$
$18$		0			0
$19$	−20.3278	−	6.60491i	−1.06988	−	0.347627i	−0.279442	−	0.960163i	$-0.590150\pi$
$19$	−20.3278	−	6.60491i	−1.06988	−	0.347627i	−0.790443	+	0.612536i	$0.790150\pi$
$20$		0			0
$21$	1.14924			0.0547259
$22$		0			0
$23$	15.5799	−	15.5799i	0.677388	−	0.677388i	−0.282021	−	0.959408i	$-0.591005\pi$
$23$	15.5799	−	15.5799i	0.677388	−	0.677388i	0.959408	+	0.282021i	$0.0910046\pi$
$24$		0			0
$25$	8.34950	+	23.5645i	0.333980	+	0.942580i
$26$		0			0
$27$	−7.08057	−	1.12145i	−0.262243	−	0.0415353i
$28$		0			0
$29$	−6.31998	+	2.05349i	−0.217930	+	0.0708099i	−0.415947	−	0.909389i	$-0.636550\pi$
$29$	−6.31998	+	2.05349i	−0.217930	+	0.0708099i	0.198017	+	0.980199i	$0.436550\pi$
$30$		0			0
$31$	−9.79713	−	7.11803i	−0.316037	−	0.229614i	0.418446	−	0.908242i	$-0.362575\pi$
$31$	−9.79713	−	7.11803i	−0.316037	−	0.229614i	−0.734482	+	0.678628i	$0.762575\pi$
$32$		0			0
$33$	4.41509	+	0.220962i	0.133791	+	0.00669582i
$34$		0			0
$35$	12.6534	−	6.65877i	0.361526	−	0.190251i
$36$		0			0
$37$	−15.1322	+	29.6987i	−0.408979	+	0.802667i	−0.999992	−	0.00399540i	$-0.998728\pi$
$37$	−15.1322	+	29.6987i	−0.408979	+	0.802667i	0.591013	+	0.806662i	$0.298728\pi$
$38$		0			0
$39$	4.21539	+	5.80199i	0.108087	+	0.148769i
$40$		0			0
$41$	22.8406	−	70.2961i	0.557088	−	1.71454i	−0.133278	−	0.991079i	$-0.542550\pi$
$41$	22.8406	−	70.2961i	0.557088	−	1.71454i	0.690365	−	0.723461i	$-0.257450\pi$
$42$		0			0
$43$	20.1403	−	20.1403i	0.468380	−	0.468380i	−0.433009	−	0.901389i	$-0.642548\pi$
$43$	20.1403	−	20.1403i	0.468380	−	0.468380i	0.901389	+	0.433009i	$0.142548\pi$
$44$		0			0
$45$	−41.8459	+	14.2091i	−0.929909	+	0.315757i
$46$		0			0
$47$	−32.1844	+	16.3988i	−0.684775	+	0.348910i	−0.761521	−	0.648140i	$-0.775547\pi$
$47$	−32.1844	+	16.3988i	−0.684775	+	0.348910i	0.0767458	+	0.997051i	$0.475547\pi$
$48$		0			0
$49$	23.9946	+	33.0257i	0.489686	+	0.673995i
$50$		0			0
$51$	3.04164	+	9.36119i	0.0596399	+	0.183553i
$52$		0			0
$53$	−49.2390	+	7.79870i	−0.929038	+	0.147145i	−0.602573	−	0.798064i	$-0.705858\pi$
$53$	−49.2390	+	7.79870i	−0.929038	+	0.147145i	−0.326465	+	0.945209i	$0.605858\pi$
$54$		0			0
$55$	49.8914	−	23.1484i	0.907116	−	0.420880i
$56$		0			0
$57$	1.34371	+	8.48388i	0.0235739	+	0.148840i
$58$		0			0
$59$	104.881	−	34.0778i	1.77764	−	0.577590i	0.778871	−	0.627184i	$-0.215793\pi$
$59$	104.881	−	34.0778i	1.77764	−	0.577590i	0.998769	+	0.0495937i	$0.0157927\pi$
$60$		0			0
$61$	−35.4315	+	25.7425i	−0.580845	+	0.422008i	−0.839029	−	0.544087i	$-0.816876\pi$
$61$	−35.4315	+	25.7425i	−0.580845	+	0.422008i	0.258184	+	0.966096i	$0.416876\pi$
$62$		0			0
$63$	11.4748	+	22.5207i	0.182140	+	0.357471i
$64$		0			0
$65$	80.0294	+	39.4570i	1.23122	+	0.607031i
$66$		0			0
$67$	84.3898	+	84.3898i	1.25955	+	1.25955i	0.951308	+	0.308241i	$0.0997403\pi$
$67$	84.3898	+	84.3898i	1.25955	+	1.25955i	0.308241	+	0.951308i	$0.400260\pi$
$68$		0			0
$69$	−8.42125	−	2.73623i	−0.122047	−	0.0396555i
$70$		0			0
$71$	78.8588	−	57.2943i	1.11069	−	0.806962i	0.127916	−	0.991785i	$-0.459171\pi$
$71$	78.8588	−	57.2943i	1.11069	−	0.806962i	0.982772	+	0.184823i	$0.0591713\pi$
$72$		0			0
$73$	−87.2685	−	44.4655i	−1.19546	−	0.609117i	−0.261052	−	0.965325i	$-0.584069\pi$
$73$	−87.2685	−	44.4655i	−1.19546	−	0.609117i	−0.934407	+	0.356208i	$0.884069\pi$
$74$		0			0
$75$	6.91446	−	7.28900i	0.0921928	−	0.0971867i
$76$		0			0
$77$	−17.1947	−	26.3415i	−0.223307	−	0.342097i
$78$		0			0
$79$	7.16911	−	9.86744i	0.0907483	−	0.124904i	−0.761229	−	0.648483i	$-0.775404\pi$
$79$	7.16911	−	9.86744i	0.0907483	−	0.124904i	0.851977	+	0.523579i	$0.175404\pi$
$80$		0			0
$81$	−23.6909	−	72.9132i	−0.292481	−	0.900163i
$82$		0			0
$83$	12.1527	−	76.7291i	0.146418	−	0.924447i	−0.799647	−	0.600470i	$-0.794980\pi$
$83$	12.1527	−	76.7291i	0.146418	−	0.924447i	0.946065	−	0.323977i	$-0.105020\pi$
$84$		0			0
$85$	87.7283	+	85.4454i	1.03210	+	1.00524i
$86$		0			0
$87$	1.88836	+	1.88836i	0.0217053	+	0.0217053i
$88$		0			0
$89$			31.4868i			0.353784i	0.984230	+	0.176892i	$0.0566044\pi$
$89$			31.4868i			0.353784i	−0.984230	+	0.176892i	$0.943396\pi$
$90$		0			0
$91$	15.7701	−	48.5353i	0.173297	−	0.533354i
$92$		0			0
$93$	−0.761314	+	4.80675i	−0.00818617	+	0.0516855i
$94$		0			0
$95$	63.9506	+	85.6238i	0.673164	+	0.901303i
$96$		0			0
$97$	−13.0738	−	82.5448i	−0.134782	−	0.850977i	−0.958731	−	0.284314i	$-0.908234\pi$
$97$	−13.0738	−	82.5448i	−0.134782	−	0.850977i	0.823950	−	0.566663i	$-0.191766\pi$
$98$		0			0
$99$	39.7534	+	88.7247i	0.401549	+	0.896209i
$100$		0			0
$101$	26.5653	+	19.3008i	0.263023	+	0.191097i	0.711479	−	0.702708i	$-0.248026\pi$
$101$	26.5653	+	19.3008i	0.263023	+	0.191097i	−0.448456	+	0.893805i	$0.648026\pi$
$102$		0			0
$103$	−45.2946	−	23.0787i	−0.439753	−	0.224065i	0.220074	−	0.975483i	$-0.429370\pi$
$103$	−45.2946	−	23.0787i	−0.439753	−	0.224065i	−0.659827	+	0.751418i	$0.729370\pi$
$104$		0			0
$105$	−4.69290	−	3.31597i	−0.0446943	−	0.0315807i
$106$		0			0
$107$	−105.542	+	53.7761i	−0.986370	+	0.502581i	−0.871286	−	0.490775i	$-0.836714\pi$
$107$	−105.542	+	53.7761i	−0.986370	+	0.502581i	−0.115084	+	0.993356i	$0.536714\pi$
$108$		0			0
$109$			72.5798i			0.665870i	0.942950	+	0.332935i	$0.108039\pi$
$109$			72.5798i			0.665870i	−0.942950	+	0.332935i	$0.891961\pi$
$110$		0			0
$111$	13.3951			0.120677
$112$		0			0
$113$	12.2427	+	24.0277i	0.108343	+	0.212634i	0.938812	−	0.344430i	$-0.111928\pi$
$113$	12.2427	+	24.0277i	0.108343	+	0.212634i	−0.830469	+	0.557064i	$0.811928\pi$
$114$		0			0
$115$	−108.574	+	18.6666i	−0.944119	+	0.162319i
$116$		0			0
$117$	−71.6068	+	140.536i	−0.612024	+	1.20117i
$118$		0			0
$119$	41.1695	−	56.6649i	0.345962	−	0.476176i
$120$		0			0
$121$	−60.9928	−	104.503i	−0.504073	−	0.863661i
$122$		0			0
$123$	−29.3383	+	4.64673i	−0.238523	+	0.0377783i
$124$		0			0
$125$	33.8969	−	120.316i	0.271175	−	0.962530i
$126$		0			0
$127$	−243.078	−	38.4998i	−1.91400	−	0.303148i	−0.918310	−	0.395861i	$-0.870446\pi$
$127$	−243.078	−	38.4998i	−1.91400	−	0.303148i	−0.995693	+	0.0927127i	$0.970446\pi$
$128$		0			0
$129$	−10.8862	−	3.53716i	−0.0843895	−	0.0274198i
$130$		0			0
$131$	28.7357			0.219357			0.109678	−	0.993967i	$-0.465018\pi$
$131$	28.7357			0.219357			0.109678	+	0.993967i	$0.465018\pi$
$132$		0			0
$133$	43.2206	−	43.2206i	0.324967	−	0.324967i
$134$		0			0
$135$	25.6775	+	25.0094i	0.190204	+	0.185254i
$136$		0			0
$137$	−13.1319	−	2.07989i	−0.0958534	−	0.0151817i	0.108324	−	0.994116i	$-0.465452\pi$
$137$	−13.1319	−	2.07989i	−0.0958534	−	0.0151817i	−0.204177	+	0.978934i	$0.565452\pi$
$138$		0			0
$139$	13.8981	−	4.51576i	0.0999863	−	0.0324875i	−0.258597	−	0.965985i	$-0.583260\pi$
$139$	13.8981	−	4.51576i	0.0999863	−	0.0324875i	0.358583	+	0.933498i	$0.383260\pi$
$140$		0			0
$141$	11.7439	+	8.53245i	0.0832901	+	0.0605138i
$142$		0			0
$143$	69.9162	−	183.428i	0.488924	−	1.28271i
$144$		0			0
$145$	31.7325	+	9.85001i	0.218845	+	0.0679311i
$146$		0			0
$147$	7.44787	−	14.6173i	0.0506658	−	0.0994372i
$148$		0			0
$149$	−159.812	−	219.962i	−1.07256	−	1.47626i	−0.867454	−	0.497518i	$-0.834245\pi$
$149$	−159.812	−	219.962i	−1.07256	−	1.47626i	−0.205110	−	0.978739i	$-0.565755\pi$
$150$		0			0
$151$	−1.12964	+	3.47666i	−0.00748103	+	0.0230242i	−0.954727	−	0.297482i	$-0.903853\pi$
$151$	−1.12964	+	3.47666i	−0.00748103	+	0.0230242i	0.947246	+	0.320506i	$0.103853\pi$
$152$		0			0
$153$	−153.073	+	153.073i	−1.00048	+	1.00048i
$154$		0			0
$155$	19.4683	+	57.3345i	0.125602	+	0.369900i
$156$		0			0
$157$	−172.630	+	87.9592i	−1.09955	+	0.560250i	−0.907040	−	0.421045i	$-0.861664\pi$
$157$	−172.630	+	87.9592i	−1.09955	+	0.560250i	−0.192512	+	0.981295i	$0.561664\pi$
$158$		0			0
$159$	11.7760	+	16.2083i	0.0740630	+	0.101939i
$160$		0			0
$161$	19.4708	+	59.9250i	0.120937	+	0.372205i
$162$		0			0
$163$	97.2579	−	15.4041i	0.596674	−	0.0945039i	0.149210	−	0.988806i	$-0.452327\pi$
$163$	97.2579	−	15.4041i	0.596674	−	0.0945039i	0.447465	+	0.894302i	$0.352327\pi$
$164$		0			0
$165$	−17.3913	−	13.6414i	−0.105402	−	0.0826750i
$166$		0			0
$167$	42.7432	+	269.870i	0.255948	+	1.61599i	0.696017	+	0.718025i	$0.254954\pi$
$167$	42.7432	+	269.870i	0.255948	+	1.61599i	−0.440070	+	0.897964i	$0.645046\pi$
$168$		0			0
$169$	142.147	−	46.1865i	0.841109	−	0.273293i
$170$		0			0
$171$	−152.834	+	111.041i	−0.893767	+	0.649360i
$172$		0			0
$173$	−47.5781	−	93.3773i	−0.275018	−	0.539753i	0.711643	−	0.702541i	$-0.247951\pi$
$173$	−47.5781	−	93.3773i	−0.275018	−	0.539753i	−0.986661	+	0.162788i	$0.947951\pi$
$174$		0			0
$175$	−70.8828	−	9.31865i	−0.405044	−	0.0532494i
$176$		0			0
$177$	−31.3375	−	31.3375i	−0.177048	−	0.177048i
$178$		0			0
$179$	−211.415	−	68.6930i	−1.18109	−	0.383760i	−0.348319	−	0.937376i	$-0.613247\pi$
$179$	−211.415	−	68.6930i	−1.18109	−	0.383760i	−0.832772	+	0.553616i	$0.813247\pi$
$180$		0			0
$181$	−161.686	+	117.472i	−0.893295	+	0.649017i	−0.936735	−	0.350039i	$-0.886168\pi$
$181$	−161.686	+	117.472i	−0.893295	+	0.649017i	0.0434403	+	0.999056i	$0.486168\pi$
$182$		0			0
$183$	15.6821	+	7.99041i	0.0856944	+	0.0436635i
$184$		0			0
$185$	147.483	−	77.6119i	0.797206	−	0.419524i
$186$		0			0
$187$	169.057	−	209.776i	0.904049	−	1.12180i
$188$		0			0
$189$	12.0500	−	16.5855i	0.0637569	−	0.0877538i
$190$		0			0
$191$	−62.1612	−	191.313i	−0.325451	−	1.00164i	−0.971236	−	0.238117i	$-0.923470\pi$
$191$	−62.1612	−	191.313i	−0.325451	−	1.00164i	0.645785	−	0.763519i	$-0.276530\pi$
$192$		0			0
$193$	−21.8599	+	138.018i	−0.113264	+	0.715120i	0.864063	+	0.503384i	$0.167912\pi$
$193$	−21.8599	+	138.018i	−0.113264	+	0.715120i	−0.977327	+	0.211736i	$0.932088\pi$
$194$		0			0
$195$	−0.472663	−	35.8552i	−0.00242391	−	0.183873i
$196$		0			0
$197$	73.6593	+	73.6593i	0.373905	+	0.373905i	0.868897	−	0.494992i	$-0.164829\pi$
$197$	73.6593	+	73.6593i	0.373905	+	0.373905i	−0.494992	+	0.868897i	$0.664829\pi$
$198$		0			0
$199$			319.676i			1.60641i	0.595701	+	0.803206i	$0.296874\pi$
$199$			319.676i			1.60641i	−0.595701	+	0.803206i	$0.703126\pi$
$200$		0			0
$201$	14.8210	−	45.6143i	0.0737363	−	0.226937i
$202$		0			0
$203$	2.97279	−	18.7694i	0.0146443	−	0.0924603i
$204$		0			0
$205$	−296.098	+	221.149i	−1.44438	+	1.07878i
$206$		0			0
$207$	−30.4643	−	192.344i	−0.147170	−	0.929198i
$208$		0			0
$209$	174.352	−	157.732i	0.834221	−	0.754701i
$210$		0			0
$211$	−113.236	−	82.2711i	−0.536666	−	0.389911i	0.286179	−	0.958176i	$-0.407615\pi$
$211$	−113.236	−	82.2711i	−0.536666	−	0.389911i	−0.822845	+	0.568266i	$0.807615\pi$
$212$		0			0
$213$	−34.9031	−	17.7840i	−0.163864	−	0.0834930i
$214$		0			0
$215$	−140.354	+	24.1306i	−0.652812	+	0.112235i
$216$		0			0
$217$	30.8563	−	15.7221i	0.142195	−	0.0724519i
$218$		0			0
$219$			39.3611i			0.179731i
$220$		0			0
$221$	437.083			1.97775
$222$		0			0
$223$	−22.5259	−	44.2096i	−0.101013	−	0.198249i	0.834969	−	0.550297i	$-0.185485\pi$
$223$	−22.5259	−	44.2096i	−0.101013	−	0.198249i	−0.935982	+	0.352048i	$0.885485\pi$
$224$		0			0
$225$	211.875	+	62.7178i	0.941665	+	0.278746i
$226$		0			0
$227$	3.86877	−	7.59289i	0.0170430	−	0.0334489i	−0.882328	−	0.470635i	$-0.844025\pi$
$227$	3.86877	−	7.59289i	0.0170430	−	0.0334489i	0.899371	+	0.437186i	$0.144025\pi$
$228$		0			0
$229$	−69.8016	+	96.0737i	−0.304811	+	0.419536i	−0.933754	−	0.357915i	$-0.883488\pi$
$229$	−69.8016	+	96.0737i	−0.304811	+	0.419536i	0.628944	+	0.777451i	$0.283488\pi$
$230$		0			0
$231$	−6.29504	+	10.9629i	−0.0272513	+	0.0474583i
$232$		0			0
$233$	135.899	−	21.5244i	0.583259	−	0.0923792i	0.142170	−	0.989842i	$-0.454592\pi$
$233$	135.899	−	21.5244i	0.583259	−	0.0923792i	0.441090	+	0.897463i	$0.354592\pi$
$234$		0			0
$235$	178.741	+	25.8994i	0.760598	+	0.110210i
$236$		0			0
$237$	−4.84124	−	0.766778i	−0.0204272	−	0.00323535i
$238$		0			0
$239$	254.406	+	82.6614i	1.06446	+	0.345864i	0.788327	−	0.615256i	$-0.210947\pi$
$239$	254.406	+	82.6614i	1.06446	+	0.345864i	0.276131	+	0.961120i	$0.410947\pi$
$240$		0			0
$241$	289.215			1.20006			0.600030	−	0.799977i	$-0.295155\pi$
$241$	289.215			1.20006			0.600030	+	0.799977i	$0.295155\pi$
$242$		0			0
$243$	−67.4080	+	67.4080i	−0.277399	+	0.277399i
$244$		0			0
$245$	−2.69046	−	204.093i	−0.0109815	−	0.833031i
$246$		0			0
$247$	376.733	+	59.6686i	1.52523	+	0.241573i
$248$		0			0
$249$	−29.6918	+	9.64745i	−0.119244	+	0.0387448i
$250$		0			0
$251$	14.0474	+	10.2060i	0.0559657	+	0.0406615i	0.615416	−	0.788202i	$-0.288988\pi$
$251$	14.0474	+	10.2060i	0.0559657	+	0.0406615i	−0.559451	+	0.828864i	$0.688988\pi$
$252$		0			0
$253$	63.2802	+	233.960i	0.250119	+	0.924743i
$254$		0			0
$255$	14.5899	−	47.0024i	0.0572153	−	0.184323i
$256$		0			0
$257$	190.792	−	374.450i	0.742380	−	1.45700i	−0.141819	−	0.989893i	$-0.545295\pi$
$257$	190.792	−	374.450i	0.742380	−	1.45700i	0.884199	−	0.467110i	$-0.154705\pi$
$258$		0			0
$259$	−56.0269	−	77.1144i	−0.216320	−	0.297739i
$260$		0			0
$261$	−18.1497	+	55.8591i	−0.0695392	+	0.214020i
$262$		0			0
$263$	−17.9100	+	17.9100i	−0.0680988	+	0.0680988i	−0.740336	−	0.672237i	$-0.765334\pi$
$263$	−17.9100	+	17.9100i	−0.0680988	+	0.0680988i	0.672237	+	0.740336i	$0.265334\pi$
$264$		0			0
$265$	223.568	+	110.226i	0.843654	+	0.415948i
$266$		0			0
$267$	11.2746	−	5.74467i	0.0422268	−	0.0215156i
$268$		0			0
$269$	−148.729	−	204.708i	−0.552896	−	0.760997i	0.437505	−	0.899216i	$-0.355862\pi$
$269$	−148.729	−	204.708i	−0.552896	−	0.760997i	−0.990402	+	0.138219i	$0.955862\pi$
$270$		0			0
$271$	11.8212	+	36.3819i	0.0436206	+	0.134250i	0.970495	−	0.241121i	$-0.0775151\pi$
$271$	11.8212	+	36.3819i	0.0436206	+	0.134250i	−0.926874	+	0.375372i	$0.877515\pi$
$272$		0			0
$273$	−20.2563	+	3.20829i	−0.0741991	+	0.0117520i
$274$		0			0
$275$	−270.521	−	49.4283i	−0.983714	−	0.179739i
$276$		0			0
$277$	−4.31415	−	27.2385i	−0.0155745	−	0.0983338i	0.978677	−	0.205407i	$-0.0658519\pi$
$277$	−4.31415	−	27.2385i	−0.0155745	−	0.0983338i	−0.994251	+	0.107074i	$0.965852\pi$
$278$		0			0
$279$	−101.795	+	33.0752i	−0.364856	+	0.118549i
$280$		0			0
$281$	−62.3502	+	45.3000i	−0.221887	+	0.161210i	−0.693176	−	0.720769i	$-0.743789\pi$
$281$	−62.3502	+	45.3000i	−0.221887	+	0.161210i	0.471289	+	0.881979i	$0.343789\pi$
$282$		0			0
$283$	−84.4855	−	165.812i	−0.298535	−	0.585908i	0.692202	−	0.721704i	$-0.256641\pi$
$283$	−84.4855	−	165.812i	−0.298535	−	0.585908i	−0.990737	+	0.135796i	$0.956641\pi$
$284$		0			0
$285$	18.9919	−	38.5208i	0.0666384	−	0.135161i
$286$		0			0
$287$	149.462	+	149.462i	0.520775	+	0.520775i
$288$		0			0
$289$	295.671	+	96.0694i	1.02308	+	0.332420i
$290$		0			0
$291$	−27.1717	+	19.7414i	−0.0933737	+	0.0678400i
$292$		0			0
$293$	159.801	+	81.4229i	0.545397	+	0.277894i	0.704904	−	0.709303i	$-0.250990\pi$
$293$	159.801	+	81.4229i	0.545397	+	0.277894i	−0.159506	+	0.987197i	$0.550990\pi$
$294$		0			0
$295$	−526.604	−	163.462i	−1.78510	−	0.554108i
$296$		0			0
$297$	49.4820	−	61.4002i	0.166606	−	0.206735i
$298$		0			0
$299$	−231.115	+	318.103i	−0.772960	+	1.06389i
$300$		0			0
$301$	25.1702	+	77.4658i	0.0836218	+	0.257361i
$302$		0			0
$303$	2.06433	−	13.0337i	0.00681298	−	0.0430154i
$304$		0			0
$305$	218.960	−	2.88645i	0.717901	−	0.00946378i
$306$		0			0
$307$	365.669	+	365.669i	1.19111	+	1.19111i	0.976757	+	0.214349i	$0.0687628\pi$
$307$	365.669	+	365.669i	1.19111	+	1.19111i	0.214349	+	0.976757i	$0.431237\pi$
$308$		0			0
$309$			20.4294i			0.0661145i
$310$		0			0
$311$	−150.750	+	463.961i	−0.484727	+	1.49184i	0.347650	+	0.937625i	$0.386980\pi$
$311$	−150.750	+	463.961i	−0.484727	+	1.49184i	−0.832376	+	0.554211i	$0.813020\pi$
$312$		0			0
$313$	−5.20489	+	32.8624i	−0.0166290	+	0.104992i	−0.994607	−	0.103718i	$-0.966926\pi$
$313$	−5.20489	+	32.8624i	−0.0166290	+	0.104992i	0.977978	+	0.208709i	$0.0669262\pi$
$314$		0			0
$315$	18.1228	−	125.071i	0.0575326	−	0.397052i
$316$		0			0
$317$	−66.0958	−	417.312i	−0.208504	−	1.31644i	−0.840644	−	0.541589i	$-0.817823\pi$
$317$	−66.0958	−	417.312i	−0.208504	−	1.31644i	0.632140	−	0.774855i	$-0.282177\pi$
$318$		0			0
$319$	15.0294	−	71.5357i	0.0471142	−	0.224250i
$320$		0			0
$321$	38.5115	+	27.9803i	0.119974	+	0.0871659i
$322$		0			0
$323$	466.444	+	237.665i	1.44410	+	0.735806i
$324$		0			0
$325$	−212.951	−	392.035i	−0.655233	−	1.20626i
$326$		0			0
$327$	25.9888	−	13.2420i	0.0794766	−	0.0404953i
$328$		0			0
$329$		−	103.297i		−	0.313972i
$330$		0			0
$331$	−412.705			−1.24684			−0.623421	−	0.781886i	$-0.714258\pi$
$331$	−412.705			−1.24684			−0.623421	+	0.781886i	$0.714258\pi$
$332$		0			0
$333$	133.746	+	262.492i	0.401640	+	0.788263i
$334$		0			0
$335$	−101.109	−	588.098i	−0.301819	−	1.75552i
$336$		0			0
$337$	−39.6192	+	77.7572i	−0.117565	+	0.230733i	−0.942288	−	0.334802i	$-0.891331\pi$
$337$	−39.6192	+	77.7572i	−0.117565	+	0.230733i	0.824724	+	0.565536i	$0.191331\pi$
$338$		0			0
$339$	6.37001	−	8.76757i	0.0187906	−	0.0258630i
$340$		0			0
$341$	121.565	−	54.4674i	0.356495	−	0.159729i
$342$		0			0
$343$	−253.702	+	40.1825i	−0.739657	+	0.117150i
$344$		0			0
$345$	26.4930	+	35.4716i	0.0767912	+	0.102816i
$346$		0			0
$347$	36.5667	+	5.79160i	0.105380	+	0.0166905i	0.208902	−	0.977937i	$-0.433011\pi$
$347$	36.5667	+	5.79160i	0.105380	+	0.0166905i	−0.103522	+	0.994627i	$0.533011\pi$
$348$		0			0
$349$	−198.022	−	64.3411i	−0.567397	−	0.184358i	0.0112498	−	0.999937i	$-0.496419\pi$
$349$	−198.022	−	64.3411i	−0.567397	−	0.184358i	−0.578647	+	0.815578i	$0.696419\pi$
$350$		0			0
$351$	127.932			0.364477
$352$		0			0
$353$	−121.047	+	121.047i	−0.342909	+	0.342909i	−0.857460	−	0.514551i	$-0.827959\pi$
$353$	−121.047	+	121.047i	−0.342909	+	0.342909i	0.514551	+	0.857460i	$0.327959\pi$
$354$		0			0
$355$	−487.332	+	6.42429i	−1.37277	+	0.0180966i
$356$		0			0
$357$	−27.8014	−	4.40331i	−0.0778750	−	0.0123342i
$358$		0			0
$359$	−415.549	+	135.020i	−1.15752	+	0.376101i	−0.823971	−	0.566632i	$-0.808246\pi$
$359$	−415.549	+	135.020i	−1.15752	+	0.376101i	−0.333548	+	0.942733i	$0.608246\pi$
$360$		0			0
$361$	77.5400	+	56.3361i	0.214792	+	0.156056i
$362$		0			0
$363$	−26.2917	+	40.9061i	−0.0724289	+	0.112689i
$364$		0			0
$365$	228.060	+	433.374i	0.624822	+	1.18733i
$366$		0			0
$367$	139.914	−	274.597i	0.381237	−	0.748220i	−0.618043	−	0.786144i	$-0.712074\pi$
$367$	139.914	−	274.597i	0.381237	−	0.748220i	0.999281	+	0.0379236i	$0.0120744\pi$
$368$		0			0
$369$	−383.992	−	528.520i	−1.04063	−	1.43230i
$370$		0			0
$371$	44.0548	−	135.587i	0.118746	−	0.365463i
$372$		0			0
$373$	207.314	−	207.314i	0.555803	−	0.555803i	−0.372307	−	0.928110i	$-0.621433\pi$
$373$	207.314	−	207.314i	0.555803	−	0.555803i	0.928110	+	0.372307i	$0.121433\pi$
$374$		0			0
$375$	−49.2663	+	9.81379i	−0.131377	+	0.0261701i
$376$		0			0
$377$	105.662	−	53.8376i	0.280271	−	0.142805i
$378$		0			0
$379$	46.7924	+	64.4042i	0.123463	+	0.169932i	0.866274	−	0.499569i	$-0.166508\pi$
$379$	46.7924	+	64.4042i	0.123463	+	0.169932i	−0.742811	+	0.669501i	$0.766508\pi$
$380$		0			0
$381$	30.5632	+	94.0639i	0.0802184	+	0.246887i
$382$		0			0
$383$	270.838	−	42.8966i	0.707150	−	0.112001i	0.207507	−	0.978233i	$-0.433465\pi$
$383$	270.838	−	42.8966i	0.707150	−	0.112001i	0.499642	+	0.866232i	$0.333465\pi$
$384$		0			0
$385$	−5.79043	+	157.177i	−0.0150401	+	0.408253i
$386$		0			0
$387$	−39.3815	−	248.645i	−0.101761	−	0.642494i
$388$		0			0
$389$	−169.432	+	55.0518i	−0.435558	+	0.141521i	−0.518585	−	0.855026i	$-0.673541\pi$
$389$	−169.432	+	55.0518i	−0.435558	+	0.141521i	0.0830272	+	0.996547i	$0.473541\pi$
$390$		0			0
$391$	−436.589	+	317.200i	−1.11660	+	0.811254i
$392$		0			0
$393$	−5.24274	−	10.2895i	−0.0133403	−	0.0261818i
$394$		0			0
$395$	−57.7459	+	19.6080i	−0.146192	+	0.0496405i
$396$		0			0
$397$	−269.251	−	269.251i	−0.678213	−	0.678213i	0.281383	−	0.959596i	$-0.409207\pi$
$397$	−269.251	−	269.251i	−0.678213	−	0.678213i	−0.959596	+	0.281383i	$0.909207\pi$
$398$		0			0
$399$	−23.3616	−	7.59064i	−0.0585504	−	0.0190242i
$400$		0			0
$401$	−259.141	+	188.277i	−0.646238	+	0.469519i	−0.861987	−	0.506930i	$-0.830780\pi$
$401$	−259.141	+	188.277i	−0.646238	+	0.469519i	0.215750	+	0.976449i	$0.430780\pi$
$402$		0			0
$403$	192.554	+	98.1109i	0.477800	+	0.243451i
$404$		0			0
$405$	−113.639	+	366.096i	−0.280590	+	0.903940i
$406$		0			0
$407$	−200.414	−	307.025i	−0.492418	−	0.754362i
$408$		0			0
$409$	225.231	−	310.004i	0.550688	−	0.757956i	−0.439418	−	0.898283i	$-0.644815\pi$
$409$	225.231	−	310.004i	0.550688	−	0.757956i	0.990105	+	0.140326i	$0.0448152\pi$
$410$		0			0
$411$	1.65113	+	5.08165i	0.00401734	+	0.0123641i
$412$		0			0
$413$	−49.3337	+	311.481i	−0.119452	+	0.754191i
$414$		0			0
$415$	−271.016	+	278.256i	−0.653050	+	0.670497i
$416$		0			0
$417$	−4.15264	−	4.15264i	−0.00995836	−	0.00995836i
$418$		0			0
$419$			13.1294i			0.0313350i	0.999877	+	0.0156675i	$0.00498733\pi$
$419$			13.1294i			0.0313350i	−0.999877	+	0.0156675i	$0.995013\pi$
$420$		0			0
$421$	−174.212	+	536.169i	−0.413805	+	1.27356i	0.499510	+	0.866308i	$0.333513\pi$
$421$	−174.212	+	536.169i	−0.413805	+	1.27356i	−0.913315	+	0.407253i	$0.866487\pi$
$422$		0			0
$423$	−49.9431	+	315.329i	−0.118069	+	0.745458i
$424$		0			0
$425$	−111.696	−	602.041i	−0.262814	−	1.41657i
$426$		0			0
$427$	−19.5923	−	123.701i	−0.0458837	−	0.289698i
$428$		0			0
$429$	−78.4364	+	8.43077i	−0.182835	+	0.0196522i
$430$		0			0
$431$	−292.821	−	212.747i	−0.679398	−	0.493612i	0.193760	−	0.981049i	$-0.437932\pi$
$431$	−292.821	−	212.747i	−0.679398	−	0.493612i	−0.873158	+	0.487437i	$0.837932\pi$
$432$		0			0
$433$	−573.561	−	292.244i	−1.32462	−	0.674928i	−0.358624	−	0.933482i	$-0.616754\pi$
$433$	−573.561	−	292.244i	−1.32462	−	0.674928i	−0.965997	+	0.258554i	$0.916754\pi$
$434$		0			0
$435$	−2.26248	−	13.1596i	−0.00520111	−	0.0302521i
$436$		0			0
$437$	−419.610	+	213.802i	−0.960205	+	0.489249i
$438$		0			0
$439$		−	247.699i		−	0.564234i	−0.959380	−	0.282117i	$-0.908963\pi$
$439$		−	247.699i		−	0.564234i	0.959380	−	0.282117i	$-0.0910366\pi$
$440$		0			0
$441$	360.806			0.818154
$442$		0			0
$443$	−262.716	−	515.609i	−0.593038	−	1.16390i	−0.971223	−	0.238172i	$-0.923452\pi$
$443$	−262.716	−	515.609i	−0.593038	−	1.16390i	0.378185	−	0.925730i	$-0.376548\pi$
$444$		0			0
$445$	90.8504	−	128.575i	0.204158	−	0.288934i
$446$		0			0
$447$	−49.6052	+	97.3557i	−0.110974	+	0.217798i
$448$		0			0
$449$	40.1176	−	55.2171i	0.0893487	−	0.122978i	−0.762003	−	0.647574i	$-0.775784\pi$
$449$	40.1176	−	55.2171i	0.0893487	−	0.122978i	0.851351	+	0.524596i	$0.175784\pi$
$450$		0			0
$451$	545.458	+	602.932i	1.20944	+	1.33688i
$452$		0			0
$453$	1.45100	−	0.229815i	0.00320308	−	0.000507318i
$454$		0			0
$455$	−204.438	+	152.690i	−0.449314	+	0.335583i
$456$		0			0
$457$	643.317	+	101.891i	1.40770	+	0.222957i	0.813594	−	0.581433i	$-0.197508\pi$
$457$	643.317	+	101.891i	1.40770	+	0.222957i	0.594101	+	0.804390i	$0.297508\pi$
$458$		0			0
$459$	166.990	+	54.2582i	0.363812	+	0.118210i
$460$		0			0
$461$	−545.940			−1.18425			−0.592125	−	0.805846i	$-0.701711\pi$
$461$	−545.940			−1.18425			−0.592125	+	0.805846i	$0.701711\pi$
$462$		0			0
$463$	517.853	−	517.853i	1.11847	−	1.11847i	0.126507	−	0.991966i	$-0.459623\pi$
$463$	517.853	−	517.853i	1.11847	−	1.11847i	0.991966	−	0.126507i	$-0.0403766\pi$
$464$		0			0
$465$	16.9780	−	17.4316i	0.0365117	−	0.0374872i
$466$		0			0
$467$	60.4646	+	9.57666i	0.129475	+	0.0205068i	0.220835	−	0.975311i	$-0.429122\pi$
$467$	60.4646	+	9.57666i	0.129475	+	0.0205068i	−0.0913608	+	0.995818i	$0.529122\pi$
$468$		0			0
$469$	−324.588	+	105.465i	−0.692086	+	0.224872i
$470$		0			0
$471$	62.9916	+	45.7661i	0.133740	+	0.0971679i
$472$		0			0
$473$	81.8030	+	302.443i	0.172945	+	0.639414i
$474$		0			0
$475$	−14.0857	−	534.162i	−0.0296541	−	1.12455i
$476$		0			0
$477$	−200.039	+	392.599i	−0.419369	+	0.823058i
$478$		0			0
$479$	532.038	+	732.287i	1.11073	+	1.52878i	0.820343	+	0.571872i	$0.193783\pi$
$479$	532.038	+	732.287i	1.11073	+	1.52878i	0.290383	+	0.956911i	$0.406217\pi$
$480$		0			0
$481$	183.809	−	565.707i	0.382140	−	1.17611i
$482$		0			0
$483$	17.9051	−	17.9051i	0.0370706	−	0.0370706i
$484$		0			0
$485$	−184.784	+	374.792i	−0.380998	+	0.772767i
$486$		0			0
$487$	488.186	−	248.743i	1.00243	−	0.510766i	0.125868	−	0.992047i	$-0.459828\pi$
$487$	488.186	−	248.743i	1.00243	−	0.510766i	0.876566	+	0.481281i	$0.159828\pi$
$488$		0			0
$489$	−23.2602	−	32.0150i	−0.0475669	−	0.0654703i
$490$		0			0
$491$	149.712	+	460.767i	0.304913	+	0.938425i	0.979710	+	0.200421i	$0.0642311\pi$
$491$	149.712	+	460.767i	0.304913	+	0.938425i	−0.674797	+	0.738003i	$0.735769\pi$
$492$		0			0
$493$	160.755	−	25.4611i	0.326075	−	0.0516452i
$494$		0			0
$495$	93.6701	−	477.007i	0.189233	−	0.963651i
$496$		0			0
$497$	43.6061	+	275.318i	0.0877385	+	0.553959i
$498$		0			0
$499$	516.855	−	167.936i	1.03578	−	0.336546i	0.258708	−	0.965956i	$-0.416703\pi$
$499$	516.855	−	167.936i	1.03578	−	0.336546i	0.777074	+	0.629410i	$0.216703\pi$
$500$		0			0
$501$	88.8347	−	64.5422i	0.177315	−	0.128827i
$502$		0			0
$503$	88.9384	+	174.551i	0.176816	+	0.347021i	0.962357	−	0.271789i	$-0.0876152\pi$
$503$	88.9384	+	174.551i	0.176816	+	0.347021i	−0.785541	+	0.618810i	$0.787615\pi$
$504$		0			0
$505$	−52.7890	−	155.465i	−0.104533	−	0.307851i
$506$		0			0
$507$	−42.4725	−	42.4725i	−0.0837722	−	0.0837722i
$508$		0			0
$509$	−321.985	−	104.619i	−0.632584	−	0.205539i	−0.0248647	−	0.999691i	$-0.507916\pi$
$509$	−321.985	−	104.619i	−0.632584	−	0.205539i	−0.607720	+	0.794152i	$0.707916\pi$
$510$		0			0
$511$	226.598	−	164.633i	0.443440	−	0.322178i
$512$		0			0
$513$	136.525	+	69.5632i	0.266131	+	0.135601i
$514$		0			0
$515$	118.369	+	224.932i	0.229842	+	0.436761i
$516$		0			0
$517$	19.8606	−	396.839i	0.0384151	−	0.767580i
$518$		0			0
$519$	−24.7554	+	34.0728i	−0.0476982	+	0.0656510i
$520$		0			0
$521$	−155.836	−	479.615i	−0.299110	−	0.920567i	−0.981810	−	0.189868i	$-0.939194\pi$
$521$	−155.836	−	479.615i	−0.299110	−	0.920567i	0.682699	−	0.730699i	$-0.260806\pi$
$522$		0			0
$523$	42.9881	−	271.416i	0.0821952	−	0.518960i	−0.911897	−	0.410420i	$-0.865382\pi$
$523$	42.9881	−	271.416i	0.0821952	−	0.518960i	0.994092	−	0.108541i	$-0.0346177\pi$
$524$		0			0
$525$	9.59560	+	27.0813i	0.0182773	+	0.0515835i
$526$		0			0
$527$	209.730	+	209.730i	0.397970	+	0.397970i
$528$		0			0
$529$			43.5322i			0.0822915i
$530$		0			0
$531$	301.197	−	926.989i	0.567226	−	1.74574i
$532$		0			0
$533$	−206.342	+	1302.79i	−0.387132	+	2.44426i
$534$		0			0
$535$	586.139	+	84.9312i	1.09559	+	0.158750i
$536$		0			0
$537$	13.9750	+	88.2348i	0.0260243	+	0.164311i
$538$		0			0
$539$	−446.471	+	47.9892i	−0.828332	+	0.0890337i
$540$		0			0
$541$	333.293	+	242.152i	0.616069	+	0.447600i	0.851546	−	0.524280i	$-0.175665\pi$
$541$	333.293	+	242.152i	0.616069	+	0.447600i	−0.235477	+	0.971880i	$0.575665\pi$
$542$		0			0
$543$	71.5627	+	36.4630i	0.131791	+	0.0671510i
$544$		0			0
$545$	209.418	−	296.378i	0.384254	−	0.543812i
$546$		0			0
$547$	−85.8878	+	43.7620i	−0.157016	+	0.0800037i	−0.530733	−	0.847539i	$-0.678083\pi$
$547$	−85.8878	+	43.7620i	−0.157016	+	0.0800037i	0.373717	+	0.927543i	$0.378083\pi$
$548$		0			0
$549$			387.089i			0.705080i
$550$		0			0
$551$	142.035			0.257776
$552$		0			0
$553$	15.8349	+	31.0777i	0.0286345	+	0.0561984i
$554$		0			0
$555$	−54.6986	−	38.6496i	−0.0985560	−	0.0696389i
$556$		0			0
$557$	369.996	−	726.158i	0.664266	−	1.30370i	−0.275310	−	0.961355i	$-0.588781\pi$
$557$	369.996	−	726.158i	0.664266	−	1.30370i	0.939576	−	0.342340i	$-0.111219\pi$
$558$		0			0
$559$	−298.765	+	411.215i	−0.534463	+	0.735626i
$560$		0			0
$561$	−105.959	−	22.2617i	−0.188875	−	0.0396821i
$562$		0			0
$563$	−632.909	+	100.243i	−1.12417	+	0.178051i	−0.690718	−	0.723124i	$-0.742705\pi$
$563$	−632.909	+	100.243i	−1.12417	+	0.178051i	−0.433454	+	0.901176i	$0.642705\pi$
$564$		0			0
$565$	19.3355	−	133.441i	0.0342221	−	0.236179i
$566$		0			0
$567$	216.542	+	34.2968i	0.381908	+	0.0604883i
$568$		0			0
$569$	469.148	+	152.435i	0.824513	+	0.267901i	0.690733	−	0.723110i	$-0.257288\pi$
$569$	469.148	+	152.435i	0.824513	+	0.267901i	0.133781	+	0.991011i	$0.457288\pi$
$570$		0			0
$571$	−897.837			−1.57239			−0.786197	−	0.617976i	$-0.787953\pi$
$571$	−897.837			−1.57239			−0.786197	+	0.617976i	$0.787953\pi$
$572$		0			0
$573$	−57.1626	+	57.1626i	−0.0997603	+	0.0997603i
$574$		0			0
$575$	497.218	+	237.049i	0.864726	+	0.412258i
$576$		0			0
$577$	691.060	+	109.453i	1.19768	+	0.189694i	0.723241	−	0.690596i	$-0.242652\pi$
$577$	691.060	+	109.453i	1.19768	+	0.189694i	0.474437	+	0.880289i	$0.342652\pi$
$578$		0			0
$579$	53.4088	−	17.3536i	0.0922432	−	0.0299716i
$580$		0			0
$581$	179.730	+	130.581i	0.309345	+	0.224752i
$582$		0			0
$583$	195.316	−	512.419i	0.335019	−	0.878935i
$584$		0			0
$585$	697.901	−	367.265i	1.19299	−	0.627804i
$586$		0			0
$587$	−393.992	+	773.253i	−0.671196	+	1.31730i	0.264465	+	0.964395i	$0.414805\pi$
$587$	−393.992	+	773.253i	−0.671196	+	1.31730i	−0.935661	+	0.352901i	$0.885195\pi$
$588$		0			0
$589$	152.140	+	209.403i	0.258303	+	0.355523i
$590$		0			0
$591$	12.9365	−	39.8143i	0.0218891	−	0.0673677i
$592$		0			0
$593$	−425.152	+	425.152i	−0.716952	+	0.716952i	−0.967980	−	0.251028i	$-0.919231\pi$
$593$	−425.152	+	425.152i	−0.716952	+	0.716952i	0.251028	+	0.967980i	$0.419231\pi$
$594$		0			0
$595$	−331.612	+	112.601i	−0.557332	+	0.189246i
$596$		0			0
$597$	114.467	−	58.3240i	0.191737	−	0.0976951i
$598$		0			0
$599$	−332.591	−	457.772i	−0.555244	−	0.764227i	0.435468	−	0.900204i	$-0.356583\pi$
$599$	−332.591	−	457.772i	−0.555244	−	0.764227i	−0.990712	+	0.135977i	$0.956583\pi$
$600$		0			0
$601$	−237.934	−	732.286i	−0.395897	−	1.21845i	−0.928261	−	0.371930i	$-0.878696\pi$
$601$	−237.934	−	732.286i	−0.395897	−	1.21845i	0.532364	−	0.846516i	$-0.321304\pi$
$602$		0			0
$603$	1041.85	−	165.012i	1.72777	−	0.273652i
$604$		0			0
$605$	−52.4654	+	602.721i	−0.0867196	+	0.996233i
$606$		0			0
$607$	143.116	+	903.597i	0.235775	+	1.48863i	0.767138	+	0.641482i	$0.221680\pi$
$607$	143.116	+	903.597i	0.235775	+	1.48863i	−0.531362	+	0.847145i	$0.678320\pi$
$608$		0			0
$609$	−7.26319	+	2.35996i	−0.0119264	+	0.00387513i
$610$		0			0
$611$	521.497	−	378.890i	0.853514	−	0.620114i
$612$		0			0
$613$	−404.786	−	794.437i	−0.660336	−	1.29598i	−0.941723	−	0.336388i	$-0.890795\pi$
$613$	−404.786	−	794.437i	−0.660336	−	1.29598i	0.281387	−	0.959594i	$-0.409205\pi$
$614$		0			0
$615$	133.210	+	65.6765i	0.216601	+	0.106791i
$616$		0			0
$617$	−543.471	−	543.471i	−0.880827	−	0.880827i	0.112791	−	0.993619i	$-0.464021\pi$
$617$	−543.471	−	543.471i	−0.880827	−	0.880827i	−0.993619	+	0.112791i	$0.964021\pi$
$618$		0			0
$619$	849.572	+	276.043i	1.37249	+	0.445950i	0.900194	−	0.435489i	$-0.143425\pi$
$619$	849.572	+	276.043i	1.37249	+	0.445950i	0.472298	+	0.881439i	$0.343425\pi$
$620$		0			0
$621$	−127.787	+	92.8426i	−0.205776	+	0.149505i
$622$		0			0
$623$	−80.2289	−	40.8787i	−0.128778	−	0.0656159i
$624$		0			0
$625$	−485.572	+	393.504i	−0.776915	+	0.629606i
$626$		0			0
$627$	−88.2897	−	33.6529i	−0.140813	−	0.0536729i
$628$		0			0
$629$	479.854	−	660.463i	0.762885	−	1.05002i
$630$		0			0
$631$	267.261	+	822.544i	0.423551	+	1.30356i	0.904375	+	0.426739i	$0.140338\pi$
$631$	267.261	+	822.544i	0.423551	+	1.30356i	−0.480824	+	0.876817i	$0.659662\pi$
$632$		0			0
$633$	−8.79936	+	55.5570i	−0.0139010	+	0.0877678i
$634$		0			0
$635$	881.519	+	858.580i	1.38822	+	1.35209i
$636$		0			0
$637$	−515.121	−	515.121i	−0.808667	−	0.808667i
$638$		0			0
$639$		−	861.531i		−	1.34825i
$640$		0			0
$641$	−0.0348576	+	0.107281i	−5.43800e−5	+	0.000167364i	−0.951084	−	0.308933i	$-0.900028\pi$
$641$	−0.0348576	+	0.107281i	−5.43800e−5	+	0.000167364i	0.951029	+	0.309101i	$0.100028\pi$
$642$		0			0
$643$	184.512	−	1164.96i	0.286955	−	1.81176i	−0.250106	−	0.968219i	$-0.580465\pi$
$643$	184.512	−	1164.96i	0.286955	−	1.81176i	0.537061	−	0.843544i	$-0.319535\pi$
$644$		0			0
$645$	34.2478	+	45.8545i	0.0530973	+	0.0710923i
$646$		0			0
$647$	−10.8945	−	68.7849i	−0.0168384	−	0.106314i	0.977838	−	0.209365i	$-0.0671395\pi$
$647$	−10.8945	−	68.7849i	−0.0168384	−	0.106314i	−0.994676	+	0.103051i	$0.967140\pi$
$648$		0			0
$649$	−249.415	+	1187.14i	−0.384306	+	1.82919i
$650$		0			0
$651$	−11.2593	−	8.18035i	−0.0172954	−	0.0125658i
$652$		0			0
$653$	−580.642	−	295.852i	−0.889192	−	0.453066i	−0.0511619	−	0.998690i	$-0.516292\pi$
$653$	−580.642	−	295.852i	−0.889192	−	0.453066i	−0.838030	+	0.545625i	$0.816292\pi$
$654$		0			0
$655$	−117.341	−	82.9126i	−0.179147	−	0.126584i
$656$		0			0
$657$	−771.322	+	393.008i	−1.17401	+	0.598186i
$658$		0			0
$659$		−	364.819i		−	0.553595i	−0.960928	−	0.276797i	$-0.910727\pi$
$659$		−	364.819i		−	0.553595i	0.960928	−	0.276797i	$-0.0892731\pi$
$660$		0			0
$661$	90.6917			0.137204			0.0686019	−	0.997644i	$-0.478146\pi$
$661$	90.6917			0.137204			0.0686019	+	0.997644i	$0.478146\pi$
$662$		0			0
$663$	−79.7445	−	156.507i	−0.120278	−	0.236059i
$664$		0			0
$665$	−301.197	+	51.7836i	−0.452928	+	0.0778700i
$666$		0			0
$667$	−66.4717	+	130.458i	−0.0996577	+	0.195589i
$668$		0			0
$669$	−11.7204	+	16.1318i	−0.0175194	+	0.0241133i
$670$		0			0
$671$	−51.4850	−	478.995i	−0.0767287	−	0.713852i
$672$		0			0
$673$	17.9659	−	2.84552i	0.0266953	−	0.00422811i	−0.143073	−	0.989712i	$-0.545698\pi$
$673$	17.9659	−	2.84552i	0.0266953	−	0.00422811i	0.169768	+	0.985484i	$0.445698\pi$
$674$		0			0
$675$	−32.6928	−	176.214i	−0.0484337	−	0.261057i
$676$		0			0
$677$	306.500	+	48.5448i	0.452733	+	0.0717058i	0.378637	−	0.925545i	$-0.376393\pi$
$677$	306.500	+	48.5448i	0.452733	+	0.0717058i	0.0740958	+	0.997251i	$0.476393\pi$
$678$		0			0
$679$	227.299	+	73.8540i	0.334756	+	0.108769i
$680$		0			0
$681$	−3.42465			−0.00502886
$682$		0			0
$683$	−483.833	+	483.833i	−0.708394	+	0.708394i	−0.966197	−	0.257803i	$-0.917001\pi$
$683$	−483.833	+	483.833i	−0.708394	+	0.708394i	0.257803	+	0.966197i	$0.417001\pi$
$684$		0			0
$685$	47.6226	+	46.3833i	0.0695220	+	0.0677129i
$686$		0			0
$687$	47.1364	+	7.46568i	0.0686120	+	0.0108671i
$688$		0			0
$689$	846.107	−	274.917i	1.22802	−	0.399008i
$690$		0			0
$691$	263.762	+	191.635i	0.381711	+	0.277329i	0.762050	−	0.647518i	$-0.224193\pi$
$691$	263.762	+	191.635i	0.381711	+	0.277329i	−0.380339	+	0.924847i	$0.624193\pi$
$692$		0			0
$693$	−277.683	−	13.8972i	−0.400697	−	0.0200537i
$694$		0			0
$695$	−69.7821	−	21.6609i	−0.100406	−	0.0311667i
$696$		0			0
$697$	−821.876	+	1613.02i	−1.17916	+	2.31424i
$698$		0			0
$699$	−32.5017	−	44.7348i	−0.0464975	−	0.0639983i
$700$		0			0
$701$	193.025	−	594.069i	0.275356	−	0.847459i	−0.713769	−	0.700381i	$-0.753013\pi$
$701$	193.025	−	594.069i	0.275356	−	0.847459i	0.989125	−	0.147077i	$-0.0469867\pi$
$702$		0			0
$703$	503.762	−	503.762i	0.716589	−	0.716589i
$704$		0			0
$705$	−23.3368	−	68.7273i	−0.0331019	−	0.0974856i
$706$		0			0
$707$	−83.6680	+	42.6310i	−0.118342	+	0.0602984i
$708$		0			0
$709$	−169.046	−	232.672i	−0.238429	−	0.328169i	0.672988	−	0.739653i	$-0.265011\pi$
$709$	−169.046	−	232.672i	−0.238429	−	0.328169i	−0.911417	+	0.411484i	$0.865011\pi$
$710$		0			0
$711$	−33.3125	−	102.525i	−0.0468531	−	0.144199i
$712$		0			0
$713$	−263.537	+	41.7401i	−0.369617	+	0.0585416i
$714$		0			0
$715$	−814.754	+	547.289i	−1.13952	+	0.765439i
$716$		0			0
$717$	−16.8168	−	106.177i	−0.0234544	−	0.148085i
$718$		0			0
$719$	−39.8885	+	12.9606i	−0.0554778	+	0.0180258i	−0.336624	−	0.941639i	$-0.609285\pi$
$719$	−39.8885	+	12.9606i	−0.0554778	+	0.0180258i	0.281147	+	0.959665i	$0.409285\pi$
$720$		0			0
$721$	117.610	−	85.4487i	0.163121	−	0.118514i
$722$		0			0
$723$	−52.7664	−	103.560i	−0.0729825	−	0.143236i
$724$		0			0
$725$	−101.158	−	131.782i	−0.139528	−	0.181768i
$726$		0			0
$727$	−674.310	−	674.310i	−0.927524	−	0.927524i	0.0700219	−	0.997545i	$-0.477693\pi$
$727$	−674.310	−	674.310i	−0.927524	−	0.927524i	−0.997545	+	0.0700219i	$0.977693\pi$
$728$		0			0
$729$	−619.784	−	201.380i	−0.850183	−	0.276241i
$730$		0			0
$731$	−564.383	+	410.048i	−0.772070	+	0.560942i
$732$		0			0
$733$	−684.081	−	348.557i	−0.933262	−	0.475521i	−0.0798790	−	0.996805i	$-0.525453\pi$
$733$	−684.081	−	348.557i	−0.933262	−	0.475521i	−0.853384	+	0.521284i	$0.825453\pi$
$734$		0			0
$735$	−72.5891	+	38.1995i	−0.0987607	+	0.0519721i
$736$		0			0
$737$	−1267.26	+	342.762i	−1.71949	+	0.465077i
$738$		0			0
$739$	224.718	−	309.297i	0.304083	−	0.418535i	−0.629441	−	0.777048i	$-0.716716\pi$
$739$	224.718	−	309.297i	0.304083	−	0.418535i	0.933525	+	0.358513i	$0.116716\pi$
$740$		0			0
$741$	−47.3681	−	145.784i	−0.0639246	−	0.196740i
$742$		0			0
$743$	−190.499	+	1202.77i	−0.256392	+	1.61880i	0.437845	+	0.899050i	$0.355742\pi$
$743$	−190.499	+	1202.77i	−0.256392	+	1.61880i	−0.694237	+	0.719746i	$0.744258\pi$
$744$		0			0
$745$	17.9194	+	1359.32i	0.0240528	+	1.82460i
$746$		0			0
$747$	−485.516	−	485.516i	−0.649955	−	0.649955i
$748$		0			0
$749$		−	338.739i		−	0.452254i
$750$		0			0
$751$	147.128	−	452.815i	0.195910	−	0.602949i	−0.804055	−	0.594555i	$-0.797328\pi$
$751$	147.128	−	452.815i	0.195910	−	0.602949i	0.999965	−	0.00839394i	$-0.00267190\pi$
$752$		0			0
$753$	1.09159	−	6.89205i	0.00144966	−	0.00915279i
$754$		0			0
$755$	14.6442	−	10.9375i	0.0193963	−	0.0144867i
$756$		0			0
$757$	−44.7236	−	282.374i	−0.0590801	−	0.373017i	−0.999459	−	0.0328884i	$-0.989529\pi$
$757$	−44.7236	−	282.374i	−0.0590801	−	0.373017i	0.940379	−	0.340129i	$-0.110471\pi$
$758$		0			0
$759$	72.2293	−	65.3442i	0.0951638	−	0.0860925i
$760$		0			0
$761$	−959.555	−	697.158i	−1.26091	−	0.916107i	−0.262111	−	0.965038i	$-0.584419\pi$
$761$	−959.555	−	697.158i	−1.26091	−	0.916107i	−0.998802	+	0.0489303i	$0.984419\pi$
$762$		0			0
$763$	−184.935	−	94.2289i	−0.242378	−	0.123498i
$764$		0			0
$765$	1066.74	−	183.400i	1.39443	−	0.239738i
$766$		0			0
$767$	−1753.48	+	893.441i	−2.28615	+	1.16485i
$768$		0			0
$769$		−	446.621i		−	0.580782i	−0.956908	−	0.290391i	$-0.906215\pi$
$769$		−	446.621i		−	0.580782i	0.956908	−	0.290391i	$-0.0937853\pi$
$770$		0			0
$771$	−168.890			−0.219053
$772$		0			0
$773$	266.639	+	523.308i	0.344940	+	0.676983i	0.996676	−	0.0814627i	$-0.0259592\pi$
$773$	266.639	+	523.308i	0.344940	+	0.676983i	−0.651736	+	0.758446i	$0.725959\pi$
$774$		0			0
$775$	85.9318	−	290.297i	0.110880	−	0.374576i
$776$		0			0
$777$	−17.3906	+	34.1310i	−0.0223817	+	0.0439266i
$778$		0			0
$779$	−928.599	+	1278.11i	−1.19204	+	1.64070i
$780$		0			0
$781$	114.588	+	1066.08i	0.146720	+	1.36502i
$782$		0			0
$783$	47.0520	−	7.45230i	0.0600919	−	0.00951763i
$784$		0			0
$785$	958.722	+	138.918i	1.22130	+	0.176966i
$786$		0			0
$787$	1206.83	+	191.144i	1.53346	+	0.242876i	0.865344	−	0.501179i	$-0.167100\pi$
$787$	1206.83	+	191.144i	1.53346	+	0.242876i	0.668118	+	0.744055i	$0.267100\pi$
$788$		0			0
$789$	9.68069	+	3.14545i	0.0122696	+	0.00398662i
$790$		0			0
$791$	−77.1175			−0.0974937
$792$		0			0
$793$	552.645	−	552.645i	0.696905	−	0.696905i
$794$		0			0
$795$	−1.32042	−	100.164i	−0.00166090	−	0.125993i
$796$		0			0
$797$	553.159	+	87.6118i	0.694051	+	0.109927i	0.493486	−	0.869753i	$-0.335722\pi$
$797$	553.159	+	87.6118i	0.694051	+	0.109927i	0.200565	+	0.979680i	$0.435722\pi$
$798$		0			0
$799$	841.407	−	273.390i	1.05307	−	0.342165i
$800$		0			0
$801$	225.146	+	163.578i	0.281081	+	0.204218i
$802$		0			0
$803$	902.184	−	588.910i	1.12352	−	0.733387i
$804$		0			0
$805$	93.3962	−	300.882i	0.116020	−	0.373767i
$806$		0			0
$807$	−46.1651	+	90.6042i	−0.0572059	+	0.112273i
$808$		0			0
$809$	104.804	+	144.250i	0.129548	+	0.178307i	0.868863	−	0.495052i	$-0.164851\pi$
$809$	104.804	+	144.250i	0.129548	+	0.178307i	−0.739316	+	0.673359i	$0.764851\pi$
$810$		0			0
$811$	434.951	−	1338.64i	0.536314	−	1.65060i	−0.204479	−	0.978871i	$-0.565550\pi$
$811$	434.951	−	1338.64i	0.536314	−	1.65060i	0.740793	−	0.671734i	$-0.234450\pi$
$812$		0			0
$813$	10.8706	−	10.8706i	0.0133710	−	0.0133710i
$814$		0			0
$815$	−441.596	−	217.721i	−0.541836	−	0.267142i
$816$		0			0
$817$	−542.434	+	276.384i	−0.663934	+	0.338291i
$818$		0			0
$819$	−265.123	−	364.911i	−0.323716	−	0.445557i
$820$		0			0
$821$	−96.1813	−	296.016i	−0.117151	−	0.360555i	0.875238	−	0.483692i	$-0.160705\pi$
$821$	−96.1813	−	296.016i	−0.117151	−	0.360555i	−0.992390	+	0.123137i	$0.960705\pi$
$822$		0			0
$823$	−563.875	+	89.3091i	−0.685146	+	0.108517i	−0.489297	−	0.872117i	$-0.662746\pi$
$823$	−563.875	+	89.3091i	−0.685146	+	0.108517i	−0.195850	+	0.980634i	$0.562746\pi$
$824$		0			0
$825$	31.6569	+	105.884i	0.0383720	+	0.128345i
$826$		0			0
$827$	67.3354	+	425.139i	0.0814213	+	0.514074i	0.994367	+	0.105993i	$0.0338020\pi$
$827$	67.3354	+	425.139i	0.0814213	+	0.514074i	−0.912946	+	0.408081i	$0.866198\pi$
$828$		0			0
$829$	−578.093	+	187.834i	−0.697338	+	0.226579i	−0.636170	−	0.771549i	$-0.719482\pi$
$829$	−578.093	+	187.834i	−0.697338	+	0.226579i	−0.0611675	+	0.998128i	$0.519482\pi$
$830$		0			0
$831$	−8.96624	+	6.51435i	−0.0107897	+	0.00783917i
$832$		0			0
$833$	−453.917	−	890.862i	−0.544918	−	1.06946i
$834$		0			0
$835$	604.129	−	1225.34i	0.723508	−	1.46747i
$836$		0			0
$837$	61.3868	+	61.3868i	0.0733414	+	0.0733414i
$838$		0			0
$839$	−627.883	−	204.012i	−0.748371	−	0.243160i	−0.0900907	−	0.995934i	$-0.528716\pi$
$839$	−627.883	−	204.012i	−0.748371	−	0.243160i	−0.658280	+	0.752773i	$0.728716\pi$
$840$		0			0
$841$	−644.658	+	468.371i	−0.766537	+	0.556922i
$842$		0			0
$843$	27.5963	+	14.0610i	0.0327358	+	0.0166797i
$844$		0			0
$845$	−713.719	−	221.544i	−0.844638	−	0.262182i
$846$		0			0
$847$	345.461	−	19.7366i	0.407865	−	0.0233018i
$848$		0			0
$849$	−43.9586	+	60.5039i	−0.0517769	+	0.0712649i
$850$		0			0
$851$	226.944	+	698.462i	0.266679	+	0.820754i
$852$		0			0
$853$	114.230	−	721.222i	0.133916	−	0.845512i	−0.825682	−	0.564136i	$-0.809209\pi$
$853$	114.230	−	721.222i	0.133916	−	0.845512i	0.959598	−	0.281376i	$-0.0907907\pi$
$854$		0			0
$855$	944.485	−	12.4507i	1.10466	−	0.0145623i
$856$		0			0
$857$	132.964	+	132.964i	0.155150	+	0.155150i	0.780414	−	0.625264i	$-0.215009\pi$
$857$	132.964	+	132.964i	0.155150	+	0.155150i	−0.625264	+	0.780414i	$0.715009\pi$
$858$		0			0
$859$			815.780i			0.949685i	0.880071	+	0.474843i	$0.157495\pi$
$859$			815.780i			0.949685i	−0.880071	+	0.474843i	$0.842505\pi$
$860$		0			0
$861$	26.2494	−	80.7873i	0.0304871	−	0.0938296i
$862$		0			0
$863$	−15.0614	+	95.0941i	−0.0174524	+	0.110190i	−0.994877	−	0.101096i	$-0.967765\pi$
$863$	−15.0614	+	95.0941i	−0.0174524	+	0.110190i	0.977424	+	0.211286i	$0.0677651\pi$
$864$		0			0
$865$	−75.1424	+	518.583i	−0.0868698	+	0.599518i
$866$		0			0
$867$	−19.5445	−	123.399i	−0.0225427	−	0.142329i
$868$		0			0
$869$	54.8583	+	122.437i	0.0631281	+	0.140894i
$870$		0			0
$871$	−1723.03	−	1251.85i	−1.97822	−	1.43726i
$872$		0			0
$873$	−658.156	−	335.347i	−0.753902	−	0.384132i
$874$		0			0
$875$	262.560	+	242.574i	0.300069	+	0.277228i
$876$		0			0
$877$	80.8023	−	41.1708i	0.0921349	−	0.0469451i	−0.407316	−	0.913287i	$-0.633535\pi$
$877$	80.8023	−	41.1708i	0.0921349	−	0.0469451i	0.499451	+	0.866342i	$0.333535\pi$
$878$		0			0
$879$		−	72.0759i		−	0.0819976i
$880$		0			0
$881$	131.451			0.149207			0.0746035	−	0.997213i	$-0.476231\pi$
$881$	131.451			0.149207			0.0746035	+	0.997213i	$0.476231\pi$
$882$		0			0
$883$	372.699	+	731.464i	0.422083	+	0.828385i	0.999925	+	0.0122360i	$0.00389494\pi$
$883$	372.699	+	731.464i	0.422083	+	0.828385i	−0.577842	+	0.816149i	$0.696105\pi$
$884$		0			0
$885$	37.5462	+	218.386i	0.0424251	+	0.246764i
$886$		0			0
$887$	215.663	−	423.263i	0.243138	−	0.477185i	−0.736898	−	0.676003i	$-0.763710\pi$
$887$	215.663	−	423.263i	0.243138	−	0.477185i	0.980036	+	0.198819i	$0.0637104\pi$
$888$		0			0
$889$	413.682	−	569.385i	0.465334	−	0.640478i
$890$		0			0
$891$	825.303	+	173.393i	0.926265	+	0.194605i
$892$		0			0
$893$	762.552	−	120.776i	0.853921	−	0.135248i
$894$		0			0
$895$	665.105	+	890.513i	0.743134	+	0.994987i
$896$		0			0
$897$	156.070	+	24.7191i	0.173991	+	0.0275575i
$898$		0			0
$899$	76.5345	+	24.8676i	0.0851329	+	0.0276614i
$900$		0			0
$901$	1221.02			1.35519
$902$		0			0
$903$	23.1461	−	23.1461i	0.0256325	−	0.0256325i
$904$		0			0
$905$	999.190	−	13.1719i	1.10408	−	0.0145546i
$906$		0			0
$907$	278.823	+	44.1612i	0.307412	+	0.0486893i	0.308235	−	0.951310i	$-0.400262\pi$
$907$	278.823	+	44.1612i	0.307412	+	0.0486893i	−0.000822600		1.00000i	$0.500262\pi$
$908$		0			0
$909$	276.021	−	89.6846i	0.303653	−	0.0986629i
$910$		0			0
$911$	972.809	+	706.787i	1.06785	+	0.775837i	0.975524	−	0.219892i	$-0.0705706\pi$
$911$	972.809	+	706.787i	1.06785	+	0.775837i	0.0923236	+	0.995729i	$0.470571\pi$
$912$		0			0
$913$	665.367	+	536.215i	0.728771	+	0.587311i
$914$		0			0
$915$	−40.9822	−	77.8769i	−0.0447892	−	0.0851114i
$916$		0			0
$917$	−37.3070	+	73.2191i	−0.0406837	+	0.0798464i
$918$		0			0
$919$	795.581	+	1095.02i	0.865703	+	1.19154i	0.980179	+	0.198112i	$0.0634811\pi$
$919$	795.581	+	1095.02i	0.865703	+	1.19154i	−0.114476	+	0.993426i	$0.536519\pi$
$920$		0			0
$921$	64.2209	−	197.652i	0.0697295	−	0.214605i
$922$		0			0
$923$	−1230.01	+	1230.01i	−1.33262	+	1.33262i
$924$		0			0
$925$	−826.181	−	108.614i	−0.893169	−	0.117421i
$926$		0			0
$927$	−400.336	+	203.981i	−0.431862	+	0.220045i
$928$		0			0
$929$	698.781	+	961.789i	0.752186	+	1.03529i	0.997824	+	0.0659334i	$0.0210025\pi$
$929$	698.781	+	961.789i	0.752186	+	1.03529i	−0.245638	+	0.969362i	$0.578998\pi$
$930$		0			0
$931$	−269.626	−	829.823i	−0.289609	−	0.891325i
$932$		0			0
$933$	193.636	−	30.6689i	0.207541	−	0.0328712i
$934$		0			0
$935$	−1295.62	+	368.826i	−1.38569	+	0.394466i
$936$		0			0
$937$	152.820	+	964.869i	0.163095	+	1.02974i	0.924421	+	0.381373i	$0.124549\pi$
$937$	152.820	+	964.869i	0.163095	+	1.02974i	−0.761326	+	0.648369i	$0.775451\pi$
$938$		0			0
$939$	12.7167	−	4.13191i	0.0135428	−	0.00440033i
$940$		0			0
$941$	643.630	−	467.624i	0.683985	−	0.496944i	−0.190692	−	0.981650i	$-0.561073\pi$
$941$	643.630	−	467.624i	0.683985	−	0.496944i	0.874677	+	0.484706i	$0.161073\pi$
$942$		0			0
$943$	−739.353	−	1451.06i	−0.784044	−	1.53877i
$944$		0			0
$945$	−97.0609	+	32.9577i	−0.102710	+	0.0348759i
$946$		0			0
$947$	−1180.84	−	1180.84i	−1.24693	−	1.24693i	−0.957069	−	0.289860i	$-0.906391\pi$
$947$	−1180.84	−	1180.84i	−1.24693	−	1.24693i	−0.289860	−	0.957069i	$-0.593609\pi$
$948$		0			0
$949$	1662.31	+	540.118i	1.75164	+	0.569144i
$950$		0			0
$951$	−137.369	+	99.8045i	−0.144447	+	0.104947i
$952$		0			0
$953$	−355.401	−	181.086i	−0.372928	−	0.190016i	0.257474	−	0.966285i	$-0.417110\pi$
$953$	−355.401	−	181.086i	−0.372928	−	0.190016i	−0.630402	+	0.776269i	$0.717110\pi$
$954$		0			0
$955$	−298.170	+	960.577i	−0.312220	+	1.00584i
$956$		0			0
$957$	−28.3570	+	7.66985i	−0.0296312	+	0.00801448i
$958$		0			0
$959$	22.3485	−	30.7601i	0.0233040	−	0.0320752i
$960$		0			0
$961$	−251.648	−	774.493i	−0.261860	−	0.805924i
$962$		0			0
$963$	−163.777	+	1034.05i	−0.170070	+	1.07378i
$964$		0			0
$965$	487.495	−	500.520i	0.505177	−	0.518674i
$966$		0			0
$967$	359.473	+	359.473i	0.371740	+	0.371740i	0.868111	−	0.496371i	$-0.165334\pi$
$967$	359.473	+	359.473i	0.371740	+	0.371740i	−0.496371	+	0.868111i	$0.665334\pi$
$968$		0			0
$969$		−	210.382i		−	0.217113i
$970$		0			0
$971$	95.5922	−	294.203i	0.0984472	−	0.302989i	−0.889690	−	0.456566i	$-0.849079\pi$
$971$	95.5922	−	294.203i	0.0984472	−	0.302989i	0.988137	+	0.153577i	$0.0490792\pi$
$972$		0			0
$973$	−6.53737	+	41.2753i	−0.00671878	+	0.0424207i
$974$		0			0
$975$	−101.525	+	147.777i	−0.104128	+	0.151567i
$976$		0			0
$977$	24.6680	+	155.748i	0.0252487	+	0.159414i	0.997091	−	0.0762171i	$-0.0242842\pi$
$977$	24.6680	+	155.748i	0.0252487	+	0.159414i	−0.971843	+	0.235631i	$0.924284\pi$
$978$		0			0
$979$	−300.359	−	172.471i	−0.306802	−	0.176170i
$980$		0			0
$981$	518.982	+	377.062i	0.529033	+	0.384365i
$982$		0			0
$983$	−123.000	−	62.6716i	−0.125127	−	0.0637554i	0.390306	−	0.920685i	$-0.372369\pi$
$983$	−123.000	−	62.6716i	−0.125127	−	0.0637554i	−0.515433	+	0.856930i	$0.672369\pi$
$984$		0			0
$985$	−88.2529	−	513.319i	−0.0895968	−	0.521136i
$986$		0			0
$987$	−36.9877	+	18.8462i	−0.0374749	+	0.0190944i
$988$		0			0
$989$		−	627.570i		−	0.634550i
$990$		0			0
$991$	144.588			0.145901			0.0729505	−	0.997336i	$-0.476758\pi$
$991$	144.588			0.145901			0.0729505	+	0.997336i	$0.476758\pi$
$992$		0			0
$993$	75.2968	+	147.778i	0.0758275	+	0.148820i
$994$		0			0
$995$	922.378	−	1305.39i	0.927013	−	1.31195i
$996$		0			0
$997$	759.730	−	1491.05i	0.762016	−	1.49554i	−0.103484	−	0.994631i	$-0.532999\pi$
$997$	759.730	−	1491.05i	0.762016	−	1.49554i	0.865500	−	0.500909i	$-0.167001\pi$
$998$		0			0
$999$	140.450	−	193.313i	0.140591	−	0.193507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.37.6	✓	96
5.3	odd	4	inner	220.3.x.a.213.7	yes	96
11.3	even	5	inner	220.3.x.a.157.7	yes	96
55.3	odd	20	inner	220.3.x.a.113.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.6	✓	96	1.1	even	1	trivial
220.3.x.a.113.6	yes	96	55.3	odd	20	inner
220.3.x.a.157.7	yes	96	11.3	even	5	inner
220.3.x.a.213.7	yes	96	5.3	odd	4	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.182447 - 0.358073i) q^{3} +(-4.08347 - 2.88535i) q^{5} +(-1.29828 + 2.54802i) q^{7} +(5.19514 - 7.15049i) q^{9} +(-5.47755 + 9.53920i) q^{11} +(-17.6258 + 2.79165i) q^{13} +(-0.288147 + 1.98860i) q^{15} +(-24.1910 - 3.83149i) q^{17} +(-20.3278 - 6.60491i) q^{19} +1.14924 q^{21} +(15.5799 - 15.5799i) q^{23} +(8.34950 + 23.5645i) q^{25} +(-7.08057 - 1.12145i) q^{27} +(-6.31998 + 2.05349i) q^{29} +(-9.79713 - 7.11803i) q^{31} +(4.41509 + 0.220962i) q^{33} +(12.6534 - 6.65877i) q^{35} +(-15.1322 + 29.6987i) q^{37} +(4.21539 + 5.80199i) q^{39} +(22.8406 - 70.2961i) q^{41} +(20.1403 - 20.1403i) q^{43} +(-41.8459 + 14.2091i) q^{45} +(-32.1844 + 16.3988i) q^{47} +(23.9946 + 33.0257i) q^{49} +(3.04164 + 9.36119i) q^{51} +(-49.2390 + 7.79870i) q^{53} +(49.8914 - 23.1484i) q^{55} +(1.34371 + 8.48388i) q^{57} +(104.881 - 34.0778i) q^{59} +(-35.4315 + 25.7425i) q^{61} +(11.4748 + 22.5207i) q^{63} +(80.0294 + 39.4570i) q^{65} +(84.3898 + 84.3898i) q^{67} +(-8.42125 - 2.73623i) q^{69} +(78.8588 - 57.2943i) q^{71} +(-87.2685 - 44.4655i) q^{73} +(6.91446 - 7.28900i) q^{75} +(-17.1947 - 26.3415i) q^{77} +(7.16911 - 9.86744i) q^{79} +(-23.6909 - 72.9132i) q^{81} +(12.1527 - 76.7291i) q^{83} +(87.7283 + 85.4454i) q^{85} +(1.88836 + 1.88836i) q^{87} +31.4868i q^{89} +(15.7701 - 48.5353i) q^{91} +(-0.761314 + 4.80675i) q^{93} +(63.9506 + 85.6238i) q^{95} +(-13.0738 - 82.5448i) q^{97} +(39.7534 + 88.7247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more