LMFDB - Embedded newform 220.3.p.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(41,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("220.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.p (of order $10$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 33 x^{14} - 111 x^{13} + 735 x^{12} - 1436 x^{11} + 10633 x^{10} - 25103 x^{9} + \cdots + 75625 $ x^16 - 3x^15 + 33x^14 - 111x^13 + 735x^12 - 1436x^11 + 10633x^10 - 25103x^9 + 232616x^8 - 600030x^7 + 1738315x^6 - 2296850x^5 + 2290475x^4 - 1918750x^3 + 1679000x^2 - 543125*x + 75625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$1.27755 + 3.93190i$ of defining polynomial
Character	$\chi$	$=$	220.161
Dual form			220.3.p.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08657 + 3.34411i) q^{3} +(1.80902 - 1.31433i) q^{5} +(-6.54766 + 2.12746i) q^{7} +(-2.72130 - 1.97714i) q^{9} +(-1.85729 + 10.8421i) q^{11} +(-6.20864 + 8.54546i) q^{13} +(2.42964 + 7.47766i) q^{15} +(-14.5133 - 19.9758i) q^{17} +(-2.90795 - 0.944851i) q^{19} -24.2077i q^{21} -28.7662 q^{23} +(1.54508 - 4.75528i) q^{25} +(-16.0334 + 11.6489i) q^{27} +(-14.4752 + 4.70326i) q^{29} +(22.8906 + 16.6310i) q^{31} +(-34.2390 - 17.9916i) q^{33} +(-9.04864 + 12.4544i) q^{35} +(-0.847400 - 2.60803i) q^{37} +(-21.8309 - 30.0476i) q^{39} +(58.6552 + 19.0582i) q^{41} +40.5154i q^{43} -7.52149 q^{45} +(7.00968 - 21.5736i) q^{47} +(-1.29613 + 0.941696i) q^{49} +(82.5711 - 26.8290i) q^{51} +(69.9304 + 50.8074i) q^{53} +(10.8902 + 22.0546i) q^{55} +(6.31938 - 8.69788i) q^{57} +(22.7854 + 70.1263i) q^{59} +(-34.2719 - 47.1712i) q^{61} +(22.0244 + 7.15617i) q^{63} +23.6191i q^{65} +64.6875 q^{67} +(31.2565 - 96.1975i) q^{69} +(49.4251 - 35.9095i) q^{71} +(-80.2137 + 26.0630i) q^{73} +(14.2234 + 10.3339i) q^{75} +(-10.9052 - 74.9415i) q^{77} +(-44.8560 + 61.7390i) q^{79} +(-30.8890 - 95.0665i) q^{81} +(-11.1117 - 15.2939i) q^{83} +(-52.5096 - 17.0614i) q^{85} -53.5169i q^{87} +127.459 q^{89} +(22.4719 - 69.1614i) q^{91} +(-80.4883 + 58.4781i) q^{93} +(-6.50238 + 2.11275i) q^{95} +(71.6814 + 52.0796i) q^{97} +(26.4905 - 25.8324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 9 q^{3} + 20 q^{5} + 10 q^{7} - 19 q^{9} + 23 q^{11} - 5 q^{13} + 15 q^{15} + 25 q^{17} + 30 q^{19} - 168 q^{23} - 20 q^{25} - 225 q^{27} - 105 q^{29} + 40 q^{31} + 106 q^{33} - 16 q^{37} + 115 q^{39}+ \cdots + 150 q^{99}+O(q^{100}) $ 16 * q + 9 * q^3 + 20 * q^5 + 10 * q^7 - 19 * q^9 + 23 * q^11 - 5 * q^13 + 15 * q^15 + 25 * q^17 + 30 * q^19 - 168 * q^23 - 20 * q^25 - 225 * q^27 - 105 * q^29 + 40 * q^31 + 106 * q^33 - 16 * q^37 + 115 * q^39 + 255 * q^41 - 30 * q^45 + 102 * q^47 + 12 * q^49 + 380 * q^51 + 297 * q^53 + 55 * q^55 - 150 * q^57 - 22 * q^59 - 30 * q^61 - 320 * q^63 - 68 * q^67 - 137 * q^69 - 240 * q^71 + 85 * q^73 - 30 * q^75 + 226 * q^77 - 215 * q^79 - 463 * q^81 - 610 * q^83 + 25 * q^85 - 160 * q^89 + 161 * q^91 - 253 * q^93 + 90 * q^95 + 179 * q^97 + 150 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.08657	+	3.34411i	−0.362189	+	1.11470i	0.589533	+	0.807744i	$0.299312\pi$
$3$	−1.08657	+	3.34411i	−0.362189	+	1.11470i	−0.951723	+	0.306960i	$0.900688\pi$
$4$		0			0
$5$	1.80902	−	1.31433i	0.361803	−	0.262866i
$5$	1.80902	−	1.31433i	0.361803	−	0.262866i
$6$		0			0
$7$	−6.54766	+	2.12746i	−0.935379	+	0.303923i	−0.736761	−	0.676154i	$-0.763646\pi$
$7$	−6.54766	+	2.12746i	−0.935379	+	0.303923i	−0.198619	+	0.980077i	$0.563646\pi$
$8$		0			0
$9$	−2.72130	−	1.97714i	−0.302367	−	0.219682i
$10$		0			0
$11$	−1.85729	+	10.8421i	−0.168844	+	0.985643i
$11$	−1.85729	+	10.8421i	−0.168844	+	0.985643i
$12$		0			0
$13$	−6.20864	+	8.54546i	−0.477588	+	0.657343i	−0.978039	−	0.208422i	$-0.933167\pi$
$13$	−6.20864	+	8.54546i	−0.477588	+	0.657343i	0.500451	+	0.865765i	$0.333167\pi$
$14$		0			0
$15$	2.42964	+	7.47766i	0.161976	+	0.498511i
$16$		0			0
$17$	−14.5133	−	19.9758i	−0.853724	−	1.17505i	−0.983030	−	0.183445i	$-0.941275\pi$
$17$	−14.5133	−	19.9758i	−0.853724	−	1.17505i	0.129306	−	0.991605i	$-0.458725\pi$
$18$		0			0
$19$	−2.90795	−	0.944851i	−0.153050	−	0.0497290i	0.231490	−	0.972837i	$-0.425640\pi$
$19$	−2.90795	−	0.944851i	−0.153050	−	0.0497290i	−0.384540	+	0.923108i	$0.625640\pi$
$20$		0			0
$21$		−	24.2077i		−	1.15275i
$22$		0			0
$23$	−28.7662			−1.25071			−0.625353	−	0.780342i	$-0.715045\pi$
$23$	−28.7662			−1.25071			−0.625353	+	0.780342i	$0.715045\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.0618034	−	0.190211i
$26$		0			0
$27$	−16.0334	+	11.6489i	−0.593829	+	0.431442i
$28$		0			0
$29$	−14.4752	+	4.70326i	−0.499143	+	0.162181i	−0.547759	−	0.836636i	$-0.684519\pi$
$29$	−14.4752	+	4.70326i	−0.499143	+	0.162181i	0.0486159	+	0.998818i	$0.484519\pi$
$30$		0			0
$31$	22.8906	+	16.6310i	0.738408	+	0.536485i	0.892212	−	0.451617i	$-0.149152\pi$
$31$	22.8906	+	16.6310i	0.738408	+	0.536485i	−0.153804	+	0.988101i	$0.549152\pi$
$32$		0			0
$33$	−34.2390	−	17.9916i	−1.03755	−	0.545200i
$34$		0			0
$35$	−9.04864	+	12.4544i	−0.258533	+	0.355839i
$36$		0			0
$37$	−0.847400	−	2.60803i	−0.0229027	−	0.0704872i	0.938952	−	0.344048i	$-0.111798\pi$
$37$	−0.847400	−	2.60803i	−0.0229027	−	0.0704872i	−0.961855	+	0.273561i	$0.911798\pi$
$38$		0			0
$39$	−21.8309	−	30.0476i	−0.559766	−	0.770451i
$40$		0			0
$41$	58.6552	+	19.0582i	1.43061	+	0.464835i	0.918958	−	0.394356i	$-0.129032\pi$
$41$	58.6552	+	19.0582i	1.43061	+	0.464835i	0.511656	+	0.859190i	$0.329032\pi$
$42$		0			0
$43$			40.5154i			0.942220i	0.882075	+	0.471110i	$0.156146\pi$
$43$			40.5154i			0.942220i	−0.882075	+	0.471110i	$0.843854\pi$
$44$		0			0
$45$	−7.52149			−0.167144
$46$		0			0
$47$	7.00968	−	21.5736i	0.149142	−	0.459012i	−0.848378	−	0.529390i	$-0.822421\pi$
$47$	7.00968	−	21.5736i	0.149142	−	0.459012i	0.997520	+	0.0703784i	$0.0224207\pi$
$48$		0			0
$49$	−1.29613	+	0.941696i	−0.0264517	+	0.0192183i
$50$		0			0
$51$	82.5711	−	26.8290i	1.61904	−	0.526059i
$52$		0			0
$53$	69.9304	+	50.8074i	1.31944	+	0.958630i	0.999939	+	0.0110448i	$0.00351575\pi$
$53$	69.9304	+	50.8074i	1.31944	+	0.958630i	0.319502	+	0.947585i	$0.396484\pi$
$54$		0			0
$55$	10.8902	+	22.0546i	0.198003	+	0.400992i
$56$		0			0
$57$	6.31938	−	8.69788i	0.110866	−	0.152594i
$58$		0			0
$59$	22.7854	+	70.1263i	0.386194	+	1.18858i	0.935611	+	0.353033i	$0.114850\pi$
$59$	22.7854	+	70.1263i	0.386194	+	1.18858i	−0.549417	+	0.835548i	$0.685150\pi$
$60$		0			0
$61$	−34.2719	−	47.1712i	−0.561834	−	0.773299i	0.429724	−	0.902960i	$-0.358611\pi$
$61$	−34.2719	−	47.1712i	−0.561834	−	0.773299i	−0.991558	+	0.129662i	$0.958611\pi$
$62$		0			0
$63$	22.0244	+	7.15617i	0.349594	+	0.113590i
$64$		0			0
$65$			23.6191i			0.363370i
$66$		0			0
$67$	64.6875			0.965485			0.482742	−	0.875762i	$-0.339641\pi$
$67$	64.6875			0.965485			0.482742	+	0.875762i	$0.339641\pi$
$68$		0			0
$69$	31.2565	−	96.1975i	0.452992	−	1.39417i
$70$		0			0
$71$	49.4251	−	35.9095i	0.696129	−	0.505767i	−0.182541	−	0.983198i	$-0.558432\pi$
$71$	49.4251	−	35.9095i	0.696129	−	0.505767i	0.878669	+	0.477431i	$0.158432\pi$
$72$		0			0
$73$	−80.2137	+	26.0630i	−1.09882	+	0.357028i	−0.801648	−	0.597797i	$-0.796043\pi$
$73$	−80.2137	+	26.0630i	−1.09882	+	0.357028i	−0.297170	+	0.954824i	$0.596043\pi$
$74$		0			0
$75$	14.2234	+	10.3339i	0.189645	+	0.137785i
$76$		0			0
$77$	−10.9052	−	74.9415i	−0.141626	−	0.973266i
$78$		0			0
$79$	−44.8560	+	61.7390i	−0.567797	+	0.781506i	−0.992292	−	0.123925i	$-0.960452\pi$
$79$	−44.8560	+	61.7390i	−0.567797	+	0.781506i	0.424494	+	0.905431i	$0.360452\pi$
$80$		0			0
$81$	−30.8890	−	95.0665i	−0.381345	−	1.17366i
$82$		0			0
$83$	−11.1117	−	15.2939i	−0.133875	−	0.184264i	0.736816	−	0.676093i	$-0.236328\pi$
$83$	−11.1117	−	15.2939i	−0.133875	−	0.184264i	−0.870692	+	0.491829i	$0.836328\pi$
$84$		0			0
$85$	−52.5096	−	17.0614i	−0.617760	−	0.200722i
$86$		0			0
$87$		−	53.5169i		−	0.615137i
$88$		0			0
$89$	127.459			1.43213			0.716063	−	0.698036i	$-0.245942\pi$
$89$	127.459			1.43213			0.716063	+	0.698036i	$0.245942\pi$
$90$		0			0
$91$	22.4719	−	69.1614i	0.246944	−	0.760015i
$92$		0			0
$93$	−80.4883	+	58.4781i	−0.865465	+	0.628797i
$94$		0			0
$95$	−6.50238	+	2.11275i	−0.0684461	+	0.0222395i
$96$		0			0
$97$	71.6814	+	52.0796i	0.738984	+	0.536903i	0.892393	−	0.451260i	$-0.149025\pi$
$97$	71.6814	+	52.0796i	0.738984	+	0.536903i	−0.153409	+	0.988163i	$0.549025\pi$
$98$		0			0
$99$	26.4905	−	25.8324i	0.267581	−	0.260933i
$100$		0			0
$101$	−31.1920	+	42.9321i	−0.308832	+	0.425070i	−0.935016	−	0.354604i	$-0.884616\pi$
$101$	−31.1920	+	42.9321i	−0.308832	+	0.425070i	0.626185	+	0.779675i	$0.284616\pi$
$102$		0			0
$103$	−9.27955	−	28.5595i	−0.0900928	−	0.277277i	0.895851	−	0.444355i	$-0.146567\pi$
$103$	−9.27955	−	28.5595i	−0.0900928	−	0.277277i	−0.985944	+	0.167078i	$0.946567\pi$
$104$		0			0
$105$	−31.8169	−	43.7922i	−0.303018	−	0.417068i
$106$		0			0
$107$	184.806	+	60.0473i	1.72716	+	0.561189i	0.993035	−	0.117821i	$-0.0375909\pi$
$107$	184.806	+	60.0473i	1.72716	+	0.561189i	0.734129	+	0.679010i	$0.237591\pi$
$108$		0			0
$109$		−	118.805i		−	1.08995i	−0.838451	−	0.544977i	$-0.816538\pi$
$109$		−	118.805i		−	1.08995i	0.838451	−	0.544977i	$-0.183462\pi$
$110$		0			0
$111$	9.64229			0.0868675
$112$		0			0
$113$	−55.4791	+	170.747i	−0.490965	+	1.51104i	0.332186	+	0.943214i	$0.392214\pi$
$113$	−55.4791	+	170.747i	−0.490965	+	1.51104i	−0.823151	+	0.567822i	$0.807786\pi$
$114$		0			0
$115$	−52.0386	+	37.8083i	−0.452510	+	0.328768i
$116$		0			0
$117$	33.7911	−	10.9794i	0.288813	−	0.0938410i
$118$		0			0
$119$	137.526	+	99.9185i	1.15568	+	0.839651i
$120$		0			0
$121$	−114.101	−	40.2737i	−0.942983	−	0.332840i
$122$		0			0
$123$	−127.466	+	175.441i	−1.03631	+	1.42635i
$124$		0			0
$125$	−3.45492	−	10.6331i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−4.57000	−	6.29006i	−0.0359842	−	0.0495280i	0.790646	−	0.612274i	$-0.209745\pi$
$127$	−4.57000	−	6.29006i	−0.0359842	−	0.0495280i	−0.826630	+	0.562746i	$0.809745\pi$
$128$		0			0
$129$	−135.488	−	44.0228i	−1.05030	−	0.341262i
$130$		0			0
$131$		−	41.8687i		−	0.319608i	−0.987149	−	0.159804i	$-0.948914\pi$
$131$		−	41.8687i		−	0.319608i	0.987149	−	0.159804i	$-0.0510863\pi$
$132$		0			0
$133$	21.0504			0.158274
$134$		0			0
$135$	−13.6941	+	42.1463i	−0.101438	+	0.312195i
$136$		0			0
$137$	−102.193	+	74.2477i	−0.745935	+	0.541954i	−0.894564	−	0.446939i	$-0.852514\pi$
$137$	−102.193	+	74.2477i	−0.745935	+	0.541954i	0.148629	+	0.988893i	$0.452514\pi$
$138$		0			0
$139$	60.8595	−	19.7744i	0.437838	−	0.142262i	−0.0817999	−	0.996649i	$-0.526067\pi$
$139$	60.8595	−	19.7744i	0.437838	−	0.142262i	0.519638	+	0.854387i	$0.326067\pi$
$140$		0			0
$141$	64.5279	+	46.8823i	0.457645	+	0.332498i
$142$		0			0
$143$	−81.1192	−	83.1859i	−0.567267	−	0.581719i
$144$		0			0
$145$	−20.0042	+	27.5334i	−0.137960	+	0.189885i
$146$		0			0
$147$	−1.74080	−	5.35763i	−0.0118422	−	0.0364465i
$148$		0			0
$149$	1.07120	+	1.47437i	0.00718923	+	0.00989513i	0.812596	−	0.582827i	$-0.198053\pi$
$149$	1.07120	+	1.47437i	0.00718923	+	0.00989513i	−0.805407	+	0.592722i	$0.798053\pi$
$150$		0			0
$151$	−274.114	−	89.0651i	−1.81533	−	0.589835i	−0.999940	−	0.0109164i	$-0.996525\pi$
$151$	−274.114	−	89.0651i	−1.81533	−	0.589835i	−0.815385	−	0.578919i	$-0.803475\pi$
$152$		0			0
$153$			83.0551i			0.542844i
$154$		0			0
$155$	63.2682			0.408182
$156$		0			0
$157$	20.7382	−	63.8257i	0.132091	−	0.406533i	−0.863035	−	0.505143i	$-0.831440\pi$
$157$	20.7382	−	63.8257i	0.132091	−	0.406533i	0.995126	+	0.0986100i	$0.0314396\pi$
$158$		0			0
$159$	−245.890	+	178.649i	−1.54648	+	1.12358i
$160$		0			0
$161$	188.351	−	61.1991i	1.16988	−	0.380119i
$162$		0			0
$163$	−131.307	−	95.4002i	−0.805565	−	0.585277i	0.106976	−	0.994262i	$-0.465883\pi$
$163$	−131.307	−	95.4002i	−0.805565	−	0.585277i	−0.912541	+	0.408984i	$0.865883\pi$
$164$		0			0
$165$	−85.5859	+	12.4542i	−0.518702	+	0.0754798i
$166$		0			0
$167$	−86.1357	+	118.556i	−0.515782	+	0.709914i	−0.984881	−	0.173232i	$-0.944579\pi$
$167$	−86.1357	+	118.556i	−0.515782	+	0.709914i	0.469099	+	0.883146i	$0.344579\pi$
$168$		0			0
$169$	17.7462	+	54.6172i	0.105007	+	0.323179i
$170$		0			0
$171$	6.04531	+	8.32065i	0.0353527	+	0.0486588i
$172$		0			0
$173$	61.9935	+	20.1429i	0.358344	+	0.116433i	0.482656	−	0.875810i	$-0.339672\pi$
$173$	61.9935	+	20.1429i	0.358344	+	0.116433i	−0.124312	+	0.992243i	$0.539672\pi$
$174$		0			0
$175$			34.4231i			0.196703i
$176$		0			0
$177$	−259.268			−1.46479
$178$		0			0
$179$	−9.35484	+	28.7912i	−0.0522617	+	0.160845i	−0.973781	−	0.227488i	$-0.926949\pi$
$179$	−9.35484	+	28.7912i	−0.0522617	+	0.160845i	0.921519	+	0.388333i	$0.126949\pi$
$180$		0			0
$181$	132.819	−	96.4986i	0.733807	−	0.533142i	−0.156959	−	0.987605i	$-0.550169\pi$
$181$	132.819	−	96.4986i	0.733807	−	0.533142i	0.890765	+	0.454463i	$0.150169\pi$
$182$		0			0
$183$	194.985	−	63.3543i	1.06549	−	0.346198i
$184$		0			0
$185$	−4.96076	−	3.60421i	−0.0268149	−	0.0194822i
$186$		0			0
$187$	243.535	−	120.253i	1.30233	−	0.643066i
$188$		0			0
$189$	80.1984	−	110.384i	0.424330	−	0.584041i
$190$		0			0
$191$	−81.0189	−	249.350i	−0.424183	−	1.30550i	−0.903775	−	0.428008i	$-0.859215\pi$
$191$	−81.0189	−	249.350i	−0.424183	−	1.30550i	0.479592	−	0.877492i	$-0.340785\pi$
$192$		0			0
$193$	−79.5903	−	109.547i	−0.412385	−	0.567599i	0.551413	−	0.834232i	$-0.314089\pi$
$193$	−79.5903	−	109.547i	−0.412385	−	0.567599i	−0.963798	+	0.266633i	$0.914089\pi$
$194$		0			0
$195$	−78.9848	−	25.6637i	−0.405050	−	0.131609i
$196$		0			0
$197$		−	149.591i		−	0.759344i	−0.925121	−	0.379672i	$-0.876037\pi$
$197$		−	149.591i		−	0.759344i	0.925121	−	0.379672i	$-0.123963\pi$
$198$		0			0
$199$	−367.773			−1.84811			−0.924053	−	0.382264i	$-0.875145\pi$
$199$	−367.773			−1.84811			−0.924053	+	0.382264i	$0.875145\pi$
$200$		0			0
$201$	−70.2873	+	216.322i	−0.349688	+	1.07623i
$202$		0			0
$203$	84.7723	−	61.5907i	0.417598	−	0.303402i
$204$		0			0
$205$	131.157	−	42.6155i	0.639790	−	0.207880i
$206$		0			0
$207$	78.2816	+	56.8749i	0.378172	+	0.274758i
$208$		0			0
$209$	15.6450	−	29.7734i	0.0748567	−	0.142456i
$210$		0			0
$211$	−202.206	+	278.312i	−0.958320	+	1.31901i	−0.0105893	+	0.999944i	$0.503371\pi$
$211$	−202.206	+	278.312i	−0.958320	+	1.31901i	−0.947731	+	0.319071i	$0.896629\pi$
$212$		0			0
$213$	66.3815	+	204.301i	0.311650	+	0.959160i
$214$		0			0
$215$	53.2506	+	73.2931i	0.247677	+	0.340898i
$216$		0			0
$217$	−185.262	−	60.1953i	−0.853742	−	0.277398i
$218$		0			0
$219$		−	296.563i		−	1.35417i
$220$		0			0
$221$	260.811			1.18014
$222$		0			0
$223$	−65.7767	+	202.440i	−0.294963	+	0.907802i	0.688271	+	0.725454i	$0.258370\pi$
$223$	−65.7767	+	202.440i	−0.294963	+	0.907802i	−0.983234	+	0.182349i	$0.941630\pi$
$224$		0			0
$225$	−13.6065	+	9.88570i	−0.0604733	+	0.0439364i
$226$		0			0
$227$	109.939	−	35.7214i	0.484314	−	0.157363i	−0.0566755	−	0.998393i	$-0.518050\pi$
$227$	109.939	−	35.7214i	0.484314	−	0.157363i	0.540989	+	0.841030i	$0.318050\pi$
$228$		0			0
$229$	359.586	+	261.254i	1.57024	+	1.14085i	0.926924	+	0.375250i	$0.122443\pi$
$229$	359.586	+	261.254i	1.57024	+	1.14085i	0.643319	+	0.765598i	$0.277557\pi$
$230$		0			0
$231$	262.462	+	44.9607i	1.13620	+	0.194635i
$232$		0			0
$233$	53.1317	−	73.1295i	0.228033	−	0.313861i	−0.679634	−	0.733551i	$-0.737861\pi$
$233$	53.1317	−	73.1295i	0.228033	−	0.313861i	0.907667	+	0.419691i	$0.137861\pi$
$234$		0			0
$235$	−15.6741	−	48.2400i	−0.0666983	−	0.205276i
$236$		0			0
$237$	−157.723	−	217.087i	−0.665497	−	0.915979i
$238$		0			0
$239$	5.46686	+	1.77629i	0.0228739	+	0.00743218i	0.320432	−	0.947272i	$-0.396172\pi$
$239$	5.46686	+	1.77629i	0.0228739	+	0.00743218i	−0.297558	+	0.954704i	$0.596172\pi$
$240$		0			0
$241$			227.149i			0.942527i	0.881992	+	0.471264i	$0.156202\pi$
$241$			227.149i			0.942527i	−0.881992	+	0.471264i	$0.843798\pi$
$242$		0			0
$243$	173.111			0.712390
$244$		0			0
$245$	−1.10703	+	3.40709i	−0.00451849	+	0.0139065i
$246$		0			0
$247$	26.1286	−	18.9836i	0.105784	−	0.0768565i
$248$		0			0
$249$	63.2180	−	20.5408i	0.253888	−	0.0824931i
$250$		0			0
$251$	111.228	+	80.8118i	0.443139	+	0.321959i	0.786881	−	0.617105i	$-0.211695\pi$
$251$	111.228	+	80.8118i	0.443139	+	0.321959i	−0.343742	+	0.939064i	$0.611695\pi$
$252$		0			0
$253$	53.4272	−	311.886i	0.211175	−	1.23275i
$254$		0			0
$255$	114.111	−	157.060i	0.447492	−	0.615920i
$256$		0			0
$257$	127.567	+	392.610i	0.496368	+	1.52766i	0.814813	+	0.579723i	$0.196839\pi$
$257$	127.567	+	392.610i	0.496368	+	1.52766i	−0.318445	+	0.947941i	$0.603161\pi$
$258$		0			0
$259$	11.0970	+	15.2737i	0.0428454	+	0.0589717i
$260$		0			0
$261$	48.6902	+	15.8204i	0.186553	+	0.0606146i
$262$		0			0
$263$		−	378.661i		−	1.43978i	−0.694090	−	0.719889i	$-0.744193\pi$
$263$		−	378.661i		−	1.43978i	0.694090	−	0.719889i	$-0.255807\pi$
$264$		0			0
$265$	193.283			0.729369
$266$		0			0
$267$	−138.493	+	426.238i	−0.518701	+	1.59640i
$268$		0			0
$269$	52.6784	−	38.2731i	0.195831	−	0.142279i	−0.485549	−	0.874209i	$-0.661380\pi$
$269$	52.6784	−	38.2731i	0.195831	−	0.142279i	0.681380	+	0.731930i	$0.261380\pi$
$270$		0			0
$271$	504.422	−	163.896i	1.86133	−	0.604784i	0.867023	−	0.498268i	$-0.166030\pi$
$271$	504.422	−	163.896i	1.86133	−	0.604784i	0.994311	−	0.106516i	$-0.0339696\pi$
$272$		0			0
$273$	206.866	+	150.297i	0.757751	+	0.550538i
$274$		0			0
$275$	48.6874	+	25.5838i	0.177045	+	0.0930322i
$276$		0			0
$277$	81.6374	−	112.364i	0.294720	−	0.405647i	−0.635820	−	0.771837i	$-0.719338\pi$
$277$	81.6374	−	112.364i	0.294720	−	0.405647i	0.930540	+	0.366190i	$0.119338\pi$
$278$		0			0
$279$	−29.4104	−	90.5160i	−0.105414	−	0.324430i
$280$		0			0
$281$	182.823	+	251.634i	0.650615	+	0.895495i	0.999126	−	0.0418099i	$-0.0133124\pi$
$281$	182.823	+	251.634i	0.650615	+	0.895495i	−0.348510	+	0.937305i	$0.613312\pi$
$282$		0			0
$283$	−372.474	−	121.024i	−1.31616	−	0.427647i	−0.434987	−	0.900437i	$-0.643247\pi$
$283$	−372.474	−	121.024i	−1.31616	−	0.427647i	−0.881175	+	0.472790i	$0.843247\pi$
$284$		0			0
$285$		−	24.0403i		−	0.0843521i
$286$		0			0
$287$	−424.599			−1.47944
$288$		0			0
$289$	−99.0926	+	304.976i	−0.342881	+	1.05528i
$290$		0			0
$291$	−252.047	+	183.123i	−0.866140	+	0.629287i
$292$		0			0
$293$	203.899	−	66.2508i	0.695901	−	0.226112i	0.0603575	−	0.998177i	$-0.480776\pi$
$293$	203.899	−	66.2508i	0.695901	−	0.226112i	0.635544	+	0.772065i	$0.280776\pi$
$294$		0			0
$295$	133.388	+	96.9122i	0.452163	+	0.328516i
$296$		0			0
$297$	−96.5200	−	195.471i	−0.324983	−	0.658150i
$298$		0			0
$299$	178.599	−	245.821i	0.597322	−	0.822143i
$300$		0			0
$301$	−86.1951	−	265.281i	−0.286362	−	0.881333i
$302$		0			0
$303$	−109.678	−	150.958i	−0.361972	−	0.498212i
$304$		0			0
$305$	−123.997	−	40.2890i	−0.406547	−	0.132095i
$306$		0			0
$307$		−	471.912i		−	1.53717i	−0.639745	−	0.768587i	$-0.720960\pi$
$307$		−	471.912i		−	1.53717i	0.639745	−	0.768587i	$-0.279040\pi$
$308$		0			0
$309$	105.589			0.341712
$310$		0			0
$311$	−1.51952	+	4.67661i	−0.00488593	+	0.0150373i	−0.953470	−	0.301489i	$-0.902516\pi$
$311$	−1.51952	+	4.67661i	−0.00488593	+	0.0150373i	0.948584	+	0.316526i	$0.102516\pi$
$312$		0			0
$313$	164.376	−	119.426i	0.525161	−	0.381552i	−0.293383	−	0.955995i	$-0.594781\pi$
$313$	164.376	−	119.426i	0.525161	−	0.381552i	0.818545	+	0.574443i	$0.194781\pi$
$314$		0			0
$315$	49.2481	−	16.0017i	0.156343	−	0.0507990i
$316$		0			0
$317$	0.399646	+	0.290360i	0.00126071	+	0.000915962i	0.588415	−	0.808559i	$-0.299752\pi$
$317$	0.399646	+	0.290360i	0.00126071	+	0.000915962i	−0.587155	+	0.809475i	$0.699752\pi$
$318$		0			0
$319$	−24.1086	−	165.676i	−0.0755755	−	0.519360i
$320$		0			0
$321$	−401.610	+	552.768i	−1.25112	+	1.72202i
$322$		0			0
$323$	23.3298	+	71.8018i	0.0722285	+	0.222296i
$324$		0			0
$325$	31.0432	+	42.7273i	0.0955175	+	0.131469i
$326$		0			0
$327$	397.297	+	129.090i	1.21498	+	0.394769i
$328$		0			0
$329$			156.169i			0.474678i
$330$		0			0
$331$	−490.502			−1.48188			−0.740940	−	0.671571i	$-0.765620\pi$
$331$	−490.502			−1.48188			−0.740940	+	0.671571i	$0.765620\pi$
$332$		0			0
$333$	−2.85041	+	8.77265i	−0.00855978	+	0.0263443i
$334$		0			0
$335$	117.021	−	85.0205i	0.349316	−	0.253793i
$336$		0			0
$337$	−359.397	+	116.775i	−1.06646	+	0.346514i	−0.789108	−	0.614254i	$-0.789457\pi$
$337$	−359.397	+	116.775i	−1.06646	+	0.346514i	−0.277353	+	0.960768i	$0.589457\pi$
$338$		0			0
$339$	−510.716	−	371.057i	−1.50654	−	1.09456i
$340$		0			0
$341$	−222.829	+	217.293i	−0.653458	+	0.637224i
$342$		0			0
$343$	204.770	−	281.842i	0.596998	−	0.821697i
$344$		0			0
$345$	−69.8916	−	215.104i	−0.202584	−	0.623490i
$346$		0			0
$347$	45.1838	+	62.1902i	0.130213	+	0.179222i	0.869145	−	0.494557i	$-0.164670\pi$
$347$	45.1838	+	62.1902i	0.130213	+	0.179222i	−0.738932	+	0.673780i	$0.764670\pi$
$348$		0			0
$349$	104.499	+	33.9538i	0.299424	+	0.0972888i	0.454876	−	0.890555i	$-0.349683\pi$
$349$	104.499	+	33.9538i	0.299424	+	0.0972888i	−0.155452	+	0.987843i	$0.549683\pi$
$350$		0			0
$351$		−	209.337i		−	0.596401i
$352$		0			0
$353$	497.456			1.40922			0.704612	−	0.709593i	$-0.251121\pi$
$353$	497.456			1.40922			0.704612	+	0.709593i	$0.251121\pi$
$354$		0			0
$355$	42.2141	−	129.922i	0.118913	−	0.365976i
$356$		0			0
$357$	−483.570	+	351.334i	−1.35454	+	0.984129i
$358$		0			0
$359$	20.6885	−	6.72211i	0.0576282	−	0.0187245i	−0.280061	−	0.959982i	$-0.590355\pi$
$359$	20.6885	−	6.72211i	0.0576282	−	0.0187245i	0.337689	+	0.941258i	$0.390355\pi$
$360$		0			0
$361$	−284.492	−	206.695i	−0.788066	−	0.572563i
$362$		0			0
$363$	258.658	−	337.806i	0.712557	−	0.930596i
$364$		0			0
$365$	−110.853	+	152.576i	−0.303706	+	0.418015i
$366$		0			0
$367$	165.763	+	510.167i	0.451671	+	1.39010i	0.874999	+	0.484125i	$0.160862\pi$
$367$	165.763	+	510.167i	0.451671	+	1.39010i	−0.423328	+	0.905977i	$0.639138\pi$
$368$		0			0
$369$	−121.937	−	167.833i	−0.330454	−	0.454831i
$370$		0			0
$371$	−565.971	−	183.895i	−1.52553	−	0.495674i
$372$		0			0
$373$			332.971i			0.892685i	0.894862	+	0.446342i	$0.147274\pi$
$373$			332.971i			0.892685i	−0.894862	+	0.446342i	$0.852726\pi$
$374$		0			0
$375$	39.3124			0.104833
$376$		0			0
$377$	49.6795	−	152.898i	0.131776	−	0.405564i
$378$		0			0
$379$	−305.835	+	222.202i	−0.806953	+	0.586286i	−0.912946	−	0.408081i	$-0.866198\pi$
$379$	−305.835	+	222.202i	−0.806953	+	0.586286i	0.105993	+	0.994367i	$0.466198\pi$
$380$		0			0
$381$	26.0003	−	8.44800i	0.0682422	−	0.0221732i
$382$		0			0
$383$	99.8950	+	72.5779i	0.260822	+	0.189499i	0.710510	−	0.703688i	$-0.248465\pi$
$383$	99.8950	+	72.5779i	0.260822	+	0.189499i	−0.449687	+	0.893186i	$0.648465\pi$
$384$		0			0
$385$	−118.225	−	121.237i	−0.307079	−	0.314902i
$386$		0			0
$387$	80.1047	−	110.255i	0.206989	−	0.284896i
$388$		0			0
$389$	226.026	+	695.636i	0.581043	+	1.78827i	0.614611	+	0.788830i	$0.289313\pi$
$389$	226.026	+	695.636i	0.581043	+	1.78827i	−0.0335682	+	0.999436i	$0.510687\pi$
$390$		0			0
$391$	417.493	+	574.630i	1.06776	+	1.46964i
$392$		0			0
$393$	140.014	+	45.4932i	0.356269	+	0.115759i
$394$		0			0
$395$			170.642i			0.432006i
$396$		0			0
$397$	123.206			0.310344			0.155172	−	0.987887i	$-0.450407\pi$
$397$	123.206			0.310344			0.155172	+	0.987887i	$0.450407\pi$
$398$		0			0
$399$	−22.8727	+	70.3949i	−0.0573251	+	0.176428i
$400$		0			0
$401$	−409.715	+	297.675i	−1.02173	+	0.742333i	−0.966637	−	0.256148i	$-0.917546\pi$
$401$	−409.715	+	297.675i	−1.02173	+	0.742333i	−0.0550958	+	0.998481i	$0.517546\pi$
$402$		0			0
$403$	−284.240	+	92.3550i	−0.705309	+	0.229169i
$404$		0			0
$405$	−180.827	−	131.379i	−0.446487	−	0.324392i
$406$		0			0
$407$	29.8503	−	4.34371i	0.0733422	−	0.0106725i
$408$		0			0
$409$	−411.171	+	565.928i	−1.00531	+	1.38369i	−0.0832964	+	0.996525i	$0.526545\pi$
$409$	−411.171	+	565.928i	−1.00531	+	1.38369i	−0.922011	+	0.387163i	$0.873455\pi$
$410$		0			0
$411$	−137.253	−	422.420i	−0.333948	−	1.02779i
$412$		0			0
$413$	−298.382	−	410.688i	−0.722475	−	0.994402i
$414$		0			0
$415$	−40.2024	−	13.0625i	−0.0968732	−	0.0314760i
$416$		0			0
$417$			225.007i			0.539586i
$418$		0			0
$419$	−240.430			−0.573818			−0.286909	−	0.957958i	$-0.592628\pi$
$419$	−240.430			−0.573818			−0.286909	+	0.957958i	$0.592628\pi$
$420$		0			0
$421$	96.5879	−	297.267i	0.229425	−	0.706097i	−0.768387	−	0.639985i	$-0.778940\pi$
$421$	96.5879	−	297.267i	0.229425	−	0.706097i	0.997812	−	0.0661122i	$-0.0210595\pi$
$422$		0			0
$423$	−61.7294	+	44.8490i	−0.145932	+	0.106026i
$424$		0			0
$425$	−117.415	+	38.1505i	−0.276271	+	0.0897658i
$426$		0			0
$427$	324.756	+	235.949i	0.760552	+	0.552573i
$428$		0			0
$429$	366.324	−	180.885i	0.853903	−	0.421643i
$430$		0			0
$431$	−429.145	+	590.668i	−0.995696	+	1.37046i	−0.0677677	+	0.997701i	$0.521588\pi$
$431$	−429.145	+	590.668i	−0.995696	+	1.37046i	−0.927929	+	0.372758i	$0.878412\pi$
$432$		0			0
$433$	−133.213	−	409.988i	−0.307652	−	0.946855i	−0.978674	−	0.205418i	$-0.934145\pi$
$433$	−133.213	−	409.988i	−0.307652	−	0.946855i	0.671022	−	0.741437i	$-0.265855\pi$
$434$		0			0
$435$	−70.3388	−	96.8131i	−0.161698	−	0.222559i
$436$		0			0
$437$	83.6509	+	27.1798i	0.191421	+	0.0621964i
$438$		0			0
$439$		−	41.1901i		−	0.0938270i	−0.998899	−	0.0469135i	$-0.985061\pi$
$439$		−	41.1901i		−	0.0938270i	0.998899	−	0.0469135i	$-0.0149385\pi$
$440$		0			0
$441$	5.38903			0.0122200
$442$		0			0
$443$	65.1216	−	200.424i	0.147001	−	0.452424i	−0.850262	−	0.526360i	$-0.823556\pi$
$443$	65.1216	−	200.424i	0.147001	−	0.452424i	0.997263	+	0.0739366i	$0.0235563\pi$
$444$		0			0
$445$	230.576	−	167.523i	0.518148	−	0.376457i
$446$		0			0
$447$	−6.09440	+	1.98019i	−0.0136340	+	0.00442995i
$448$		0			0
$449$	289.565	+	210.381i	0.644910	+	0.468554i	0.861533	−	0.507701i	$-0.169504\pi$
$449$	289.565	+	210.381i	0.644910	+	0.468554i	−0.216624	+	0.976255i	$0.569504\pi$
$450$		0			0
$451$	−315.570	+	600.547i	−0.699712	+	1.33159i
$452$		0			0
$453$	595.687	−	819.893i	1.31498	−	1.80992i
$454$		0			0
$455$	−50.2487	−	154.650i	−0.110437	−	0.339889i
$456$		0			0
$457$	0.558556	+	0.768786i	0.00122222	+	0.00168224i	0.809628	−	0.586944i	$-0.199669\pi$
$457$	0.558556	+	0.768786i	0.00122222	+	0.00168224i	−0.808405	+	0.588626i	$0.799669\pi$
$458$		0			0
$459$	465.395	+	151.216i	1.01393	+	0.329447i
$460$		0			0
$461$		−	511.859i		−	1.11032i	−0.831743	−	0.555161i	$-0.812657\pi$
$461$		−	511.859i		−	1.11032i	0.831743	−	0.555161i	$-0.187343\pi$
$462$		0			0
$463$	32.0919			0.0693130			0.0346565	−	0.999399i	$-0.488966\pi$
$463$	32.0919			0.0693130			0.0346565	+	0.999399i	$0.488966\pi$
$464$		0			0
$465$	−68.7452	+	211.576i	−0.147839	+	0.455002i
$466$		0			0
$467$	174.032	−	126.442i	0.372660	−	0.270754i	−0.385653	−	0.922644i	$-0.626024\pi$
$467$	174.032	−	126.442i	0.372660	−	0.270754i	0.758313	+	0.651890i	$0.226024\pi$
$468$		0			0
$469$	−423.551	+	137.620i	−0.903094	+	0.293433i
$470$		0			0
$471$	190.907	+	138.702i	0.405322	+	0.294484i
$472$		0			0
$473$	−439.271	−	75.2488i	−0.928692	−	0.159088i
$474$		0			0
$475$	−8.98607	+	12.3683i	−0.0189180	+	0.0260385i
$476$		0			0
$477$	−89.8482	−	276.524i	−0.188361	−	0.579715i
$478$		0			0
$479$	−135.851	−	186.983i	−0.283615	−	0.390362i	0.643312	−	0.765604i	$-0.277560\pi$
$479$	−135.851	−	186.983i	−0.283615	−	0.390362i	−0.926927	+	0.375242i	$0.877560\pi$
$480$		0			0
$481$	27.5480	+	8.95088i	0.0572723	+	0.0186089i
$482$		0			0
$483$			696.365i			1.44175i
$484$		0			0
$485$	198.123			0.408500
$486$		0			0
$487$	−0.169372	+	0.521275i	−0.000347787	+	0.00107038i	−0.951230	−	0.308482i	$-0.900179\pi$
$487$	−0.169372	+	0.521275i	−0.000347787	+	0.00107038i	0.950882	+	0.309552i	$0.100179\pi$
$488$		0			0
$489$	461.703	−	335.447i	0.944178	−	0.685985i
$490$		0			0
$491$	−296.289	+	96.2700i	−0.603439	+	0.196069i	−0.594774	−	0.803893i	$-0.702758\pi$
$491$	−296.289	+	96.2700i	−0.603439	+	0.196069i	−0.00866552	+	0.999962i	$0.502758\pi$
$492$		0			0
$493$	304.034	+	220.894i	0.616702	+	0.448060i
$494$		0			0
$495$	13.9696	−	81.5485i	0.0282213	−	0.164744i
$496$		0			0
$497$	−247.223	+	340.273i	−0.497430	+	0.684654i
$498$		0			0
$499$	−198.566	−	611.123i	−0.397927	−	1.22469i	−0.926658	−	0.375905i	$-0.877332\pi$
$499$	−198.566	−	611.123i	−0.397927	−	1.22469i	0.528731	−	0.848790i	$-0.322668\pi$
$500$		0			0
$501$	−302.871	−	416.866i	−0.604532	−	0.832068i
$502$		0			0
$503$	−235.405	−	76.4877i	−0.468002	−	0.152063i	0.0655166	−	0.997851i	$-0.479130\pi$
$503$	−235.405	−	76.4877i	−0.468002	−	0.152063i	−0.533518	+	0.845788i	$0.679130\pi$
$504$		0			0
$505$			118.661i			0.234973i
$506$		0			0
$507$	−201.929			−0.398281
$508$		0			0
$509$	232.297	−	714.936i	0.456379	−	1.40459i	−0.413130	−	0.910672i	$-0.635564\pi$
$509$	232.297	−	714.936i	0.456379	−	1.40459i	0.869509	−	0.493918i	$-0.164436\pi$
$510$		0			0
$511$	469.764	−	341.303i	0.919303	−	0.667912i
$512$		0			0
$513$	57.6309	−	18.7254i	0.112341	−	0.0365018i
$514$		0			0
$515$	−54.3235	−	39.4683i	−0.105482	−	0.0766375i
$516$		0			0
$517$	220.883	+	116.068i	0.427240	+	0.224502i
$518$		0			0
$519$	−134.720	+	185.427i	−0.259577	+	0.357277i
$520$		0			0
$521$	−188.646	−	580.594i	−0.362085	−	1.11438i	−0.951786	−	0.306762i	$-0.900754\pi$
$521$	−188.646	−	580.594i	−0.362085	−	1.11438i	0.589701	−	0.807622i	$-0.299246\pi$
$522$		0			0
$523$	364.492	+	501.680i	0.696925	+	0.959235i	0.999980	+	0.00626195i	$0.00199325\pi$
$523$	364.492	+	501.680i	0.696925	+	0.959235i	−0.303055	+	0.952973i	$0.598007\pi$
$524$		0			0
$525$	−115.115	−	37.4030i	−0.219266	−	0.0712438i
$526$		0			0
$527$		−	698.631i		−	1.32568i
$528$		0			0
$529$	298.497			0.564266
$530$		0			0
$531$	76.6436	−	235.885i	0.144338	−	0.444227i
$532$		0			0
$533$	−527.030	+	382.910i	−0.988799	+	0.718405i
$534$		0			0
$535$	413.240	−	134.270i	0.772411	−	0.250972i
$536$		0			0
$537$	−86.1164	−	62.5673i	−0.160366	−	0.116513i
$538$		0			0
$539$	−7.80264	−	15.8018i	−0.0144761	−	0.0293168i
$540$		0			0
$541$	178.045	−	245.058i	0.329103	−	0.452972i	−0.612116	−	0.790768i	$-0.709681\pi$
$541$	178.045	−	245.058i	0.329103	−	0.452972i	0.941219	+	0.337796i	$0.109681\pi$
$542$		0			0
$543$	178.385	+	549.014i	0.328518	+	1.01108i
$544$		0			0
$545$	−156.149	−	214.920i	−0.286511	−	0.394349i
$546$		0			0
$547$	743.064	+	241.436i	1.35844	+	0.441383i	0.895521	−	0.445020i	$-0.146803\pi$
$547$	743.064	+	241.436i	1.35844	+	0.441383i	0.462915	+	0.886403i	$0.346803\pi$
$548$		0			0
$549$			196.127i			0.357245i
$550$		0			0
$551$	46.5370			0.0844591
$552$		0			0
$553$	162.354	−	499.675i	0.293588	−	0.903571i
$554$		0			0
$555$	17.4431	−	12.6731i	0.0314290	−	0.0228345i
$556$		0			0
$557$	−966.339	+	313.983i	−1.73490	+	0.563703i	−0.994143	−	0.108071i	$-0.965533\pi$
$557$	−966.339	+	313.983i	−1.73490	+	0.563703i	−0.740756	+	0.671774i	$0.765533\pi$
$558$		0			0
$559$	−346.223	−	251.546i	−0.619361	−	0.449992i
$560$		0			0
$561$	137.524	+	945.071i	0.245140	+	1.68462i
$562$		0			0
$563$	472.802	−	650.756i	0.839790	−	1.15587i	−0.146231	−	0.989250i	$-0.546714\pi$
$563$	472.802	−	650.756i	0.839790	−	1.15587i	0.986021	−	0.166621i	$-0.0532857\pi$
$564$		0			0
$565$	124.055	+	381.802i	0.219566	+	0.675756i
$566$		0			0
$567$	404.501	+	556.748i	0.713405	+	0.981918i
$568$		0			0
$569$	871.456	+	283.153i	1.53156	+	0.497633i	0.949032	−	0.315180i	$-0.102065\pi$
$569$	871.456	+	283.153i	1.53156	+	0.497633i	0.582525	+	0.812813i	$0.302065\pi$
$570$		0			0
$571$			629.066i			1.10169i	0.834607	+	0.550846i	$0.185695\pi$
$571$			629.066i			1.10169i	−0.834607	+	0.550846i	$0.814305\pi$
$572$		0			0
$573$	921.888			1.60888
$574$		0			0
$575$	−44.4463	+	136.792i	−0.0772979	+	0.237898i
$576$		0			0
$577$	820.109	−	595.844i	1.42133	−	1.03266i	0.429783	−	0.902932i	$-0.358590\pi$
$577$	820.109	−	595.844i	1.42133	−	1.03266i	0.991550	−	0.129727i	$-0.0414100\pi$
$578$		0			0
$579$	452.816	−	147.129i	0.782066	−	0.254109i
$580$		0			0
$581$	105.293	+	76.4995i	0.181226	+	0.131669i
$582$		0			0
$583$	−680.738	+	663.826i	−1.16765	+	1.13864i
$584$		0			0
$585$	46.6982	−	64.2745i	0.0798260	−	0.109871i
$586$		0			0
$587$	203.589	+	626.582i	0.346829	+	1.06743i	0.960597	+	0.277944i	$0.0896531\pi$
$587$	203.589	+	626.582i	0.346829	+	1.06743i	−0.613768	+	0.789487i	$0.710347\pi$
$588$		0			0
$589$	−50.8511	−	69.9905i	−0.0863346	−	0.118829i
$590$		0			0
$591$	500.248	+	162.540i	0.846443	+	0.275026i
$592$		0			0
$593$			293.233i			0.494490i	0.968953	+	0.247245i	$0.0795253\pi$
$593$			293.233i			0.494490i	−0.968953	+	0.247245i	$0.920475\pi$
$594$		0			0
$595$	380.112			0.638844
$596$		0			0
$597$	399.610	−	1229.87i	0.669364	−	2.06009i
$598$		0			0
$599$	413.099	−	300.134i	0.689648	−	0.501058i	−0.186896	−	0.982380i	$-0.559843\pi$
$599$	413.099	−	300.134i	0.689648	−	0.501058i	0.876544	+	0.481321i	$0.159843\pi$
$600$		0			0
$601$	958.966	−	311.587i	1.59562	−	0.518447i	0.629598	−	0.776921i	$-0.283220\pi$
$601$	958.966	−	311.587i	1.59562	−	0.518447i	0.966018	+	0.258474i	$0.0832195\pi$
$602$		0			0
$603$	−176.034	−	127.896i	−0.291930	−	0.212100i
$604$		0			0
$605$	−259.343	+	77.1103i	−0.428667	+	0.127455i
$606$		0			0
$607$	−8.17562	+	11.2528i	−0.0134689	+	0.0185383i	−0.815698	−	0.578478i	$-0.803647\pi$
$607$	−8.17562	+	11.2528i	−0.0134689	+	0.0185383i	0.802229	+	0.597016i	$0.203647\pi$
$608$		0			0
$609$	113.855	+	350.410i	0.186954	+	0.575387i
$610$		0			0
$611$	140.835	+	193.843i	0.230500	+	0.317256i
$612$		0			0
$613$	−397.687	−	129.216i	−0.648756	−	0.210794i	−0.0338903	−	0.999426i	$-0.510790\pi$
$613$	−397.687	−	129.216i	−0.648756	−	0.210794i	−0.614865	+	0.788632i	$0.710790\pi$
$614$		0			0
$615$			484.908i			0.788468i
$616$		0			0
$617$	−1045.51			−1.69451			−0.847255	−	0.531187i	$-0.821746\pi$
$617$	−1045.51			−1.69451			−0.847255	+	0.531187i	$0.821746\pi$
$618$		0			0
$619$	−190.020	+	584.820i	−0.306978	+	0.944782i	0.671953	+	0.740593i	$0.265456\pi$
$619$	−190.020	+	584.820i	−0.306978	+	0.944782i	−0.978932	+	0.204188i	$0.934544\pi$
$620$		0			0
$621$	461.220	−	335.096i	0.742706	−	0.539607i
$622$		0			0
$623$	−834.559	+	271.165i	−1.33958	+	0.435256i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	82.5661	+	84.6696i	0.131684	+	0.135039i
$628$		0			0
$629$	−39.7990	+	54.7786i	−0.0632735	+	0.0870884i
$630$		0			0
$631$	6.93840	+	21.3542i	0.0109959	+	0.0338418i	0.956404	−	0.292047i	$-0.0943364\pi$
$631$	6.93840	+	21.3542i	0.0109959	+	0.0338418i	−0.945408	+	0.325889i	$0.894336\pi$
$632$		0			0
$633$	−710.997	−	978.603i	−1.12322	−	1.54598i
$634$		0			0
$635$	−16.5344	−	5.37235i	−0.0260384	−	0.00846040i
$636$		0			0
$637$		−	16.9227i		−	0.0265662i
$638$		0			0
$639$	−205.499			−0.321594
$640$		0			0
$641$	227.883	−	701.351i	0.355512	−	1.09415i	−0.600201	−	0.799849i	$-0.704913\pi$
$641$	227.883	−	701.351i	0.355512	−	1.09415i	0.955712	−	0.294303i	$-0.0950874\pi$
$642$		0			0
$643$	232.480	−	168.907i	0.361555	−	0.262685i	−0.392145	−	0.919903i	$-0.628267\pi$
$643$	232.480	−	168.907i	0.361555	−	0.262685i	0.753701	+	0.657218i	$0.228267\pi$
$644$		0			0
$645$	−302.961	+	98.4379i	−0.469707	+	0.152617i
$646$		0			0
$647$	−689.002	−	500.589i	−1.06492	−	0.773708i	−0.0899263	−	0.995948i	$-0.528663\pi$
$647$	−689.002	−	500.589i	−1.06492	−	0.773708i	−0.974992	+	0.222240i	$0.928663\pi$
$648$		0			0
$649$	−802.634	+	116.796i	−1.23672	+	0.179964i
$650$		0			0
$651$	402.599	−	554.130i	0.618432	−	0.851199i
$652$		0			0
$653$	264.157	+	812.991i	0.404528	+	1.24501i	0.921289	+	0.388879i	$0.127138\pi$
$653$	264.157	+	812.991i	0.404528	+	1.24501i	−0.516761	+	0.856130i	$0.672862\pi$
$654$		0			0
$655$	−55.0292	−	75.7412i	−0.0840141	−	0.115635i
$656$		0			0
$657$	269.816	+	87.6684i	0.410678	+	0.133437i
$658$		0			0
$659$			328.629i			0.498679i	0.968416	+	0.249339i	$0.0802135\pi$
$659$			328.629i			0.498679i	−0.968416	+	0.249339i	$0.919787\pi$
$660$		0			0
$661$	−329.541			−0.498550			−0.249275	−	0.968433i	$-0.580192\pi$
$661$	−329.541			−0.498550			−0.249275	+	0.968433i	$0.580192\pi$
$662$		0			0
$663$	−283.388	+	872.180i	−0.427433	+	1.31550i
$664$		0			0
$665$	38.0806	−	27.6671i	0.0572640	−	0.0416047i
$666$		0			0
$667$	416.396	−	135.295i	0.624282	−	0.202841i
$668$		0			0
$669$	−605.511	−	439.929i	−0.905098	−	0.657593i
$670$		0			0
$671$	575.086	−	283.968i	0.857059	−	0.423201i
$672$		0			0
$673$	−130.629	+	179.795i	−0.194100	+	0.267155i	−0.894963	−	0.446140i	$-0.852798\pi$
$673$	−130.629	+	179.795i	−0.194100	+	0.267155i	0.700863	+	0.713295i	$0.252798\pi$
$674$		0			0
$675$	30.6210	+	94.2419i	0.0453645	+	0.139618i
$676$		0			0
$677$	−488.946	−	672.976i	−0.722224	−	0.994057i	−0.999447	−	0.0332509i	$-0.989414\pi$
$677$	−488.946	−	672.976i	−0.722224	−	0.994057i	0.277223	−	0.960806i	$-0.410586\pi$
$678$		0			0
$679$	−580.143	−	188.500i	−0.854407	−	0.277614i
$680$		0			0
$681$			406.463i			0.596861i
$682$		0			0
$683$	623.160			0.912387			0.456194	−	0.889881i	$-0.349212\pi$
$683$	623.160			0.912387			0.456194	+	0.889881i	$0.349212\pi$
$684$		0			0
$685$	−87.2834	+	268.631i	−0.127421	+	0.392161i
$686$		0			0
$687$	−1264.38	+	918.624i	−1.84043	+	1.33715i
$688$		0			0
$689$	−868.345	+	282.142i	−1.26030	+	0.409496i
$690$		0			0
$691$	126.973	+	92.2511i	0.183752	+	0.133504i	0.675859	−	0.737031i	$-0.263773\pi$
$691$	126.973	+	92.2511i	0.183752	+	0.133504i	−0.492106	+	0.870535i	$0.663773\pi$
$692$		0			0
$693$	−118.493	+	225.499i	−0.170986	+	0.325396i
$694$		0			0
$695$	84.1058	−	115.762i	0.121015	−	0.166564i
$696$		0			0
$697$	−470.576	−	1448.28i	−0.675145	−	2.07788i
$698$		0			0
$699$	186.822	+	257.138i	0.267270	+	0.367866i
$700$		0			0
$701$	589.968	+	191.692i	0.841609	+	0.273455i	0.697927	−	0.716169i	$-0.254106\pi$
$701$	589.968	+	191.692i	0.841609	+	0.273455i	0.143682	+	0.989624i	$0.454106\pi$
$702$		0			0
$703$			8.38469i			0.0119270i
$704$		0			0
$705$	178.351			0.252980
$706$		0			0
$707$	112.898	−	347.464i	0.159686	−	0.491463i
$708$		0			0
$709$	14.7938	−	10.7483i	0.0208657	−	0.0151598i	−0.577304	−	0.816530i	$-0.695895\pi$
$709$	14.7938	−	10.7483i	0.0208657	−	0.0151598i	0.598169	+	0.801370i	$0.295895\pi$
$710$		0			0
$711$	244.133	−	79.3236i	0.343366	−	0.111566i
$712$		0			0
$713$	−658.478	−	478.412i	−0.923532	−	0.670985i
$714$		0			0
$715$	−256.080	−	43.8674i	−0.358153	−	0.0613530i
$716$		0			0
$717$	−11.8802	+	16.3517i	−0.0165694	+	0.0228058i
$718$		0			0
$719$	−333.234	−	1025.59i	−0.463469	−	1.42641i	−0.860898	−	0.508778i	$-0.830097\pi$
$719$	−333.234	−	1025.59i	−0.463469	−	1.42641i	0.397429	−	0.917633i	$-0.369903\pi$
$720$		0			0
$721$	121.519	+	167.256i	0.168542	+	0.231978i
$722$		0			0
$723$	−759.612	−	246.813i	−1.05064	−	0.341373i
$724$		0			0
$725$			76.1004i			0.104966i
$726$		0			0
$727$	739.254			1.01686			0.508428	−	0.861104i	$-0.330227\pi$
$727$	739.254			1.01686			0.508428	+	0.861104i	$0.330227\pi$
$728$		0			0
$729$	89.9043	−	276.697i	0.123326	−	0.379557i
$730$		0			0
$731$	809.330	−	588.013i	1.10716	−	0.804395i
$732$		0			0
$733$	−1145.11	+	372.070i	−1.56223	+	0.507599i	−0.957402	−	0.288758i	$-0.906758\pi$
$733$	−1145.11	+	372.070i	−1.56223	+	0.507599i	−0.604827	+	0.796357i	$0.706758\pi$
$734$		0			0
$735$	−10.1908	−	7.40406i	−0.0138651	−	0.0100736i
$736$		0			0
$737$	−120.143	+	701.346i	−0.163016	+	0.951623i
$738$		0			0
$739$	178.423	−	245.579i	0.241439	−	0.332312i	−0.671051	−	0.741411i	$-0.734157\pi$
$739$	178.423	−	245.579i	0.241439	−	0.332312i	0.912490	+	0.409099i	$0.134157\pi$
$740$		0			0
$741$	35.0926	+	108.004i	0.0473584	+	0.145754i
$742$		0			0
$743$	114.379	+	157.429i	0.153942	+	0.211883i	0.879022	−	0.476782i	$-0.158197\pi$
$743$	114.379	+	157.429i	0.153942	+	0.211883i	−0.725079	+	0.688665i	$0.758197\pi$
$744$		0			0
$745$	3.87562	+	1.25927i	0.00520218	+	0.00169029i
$746$		0			0
$747$			63.5886i			0.0851252i
$748$		0			0
$749$	−1337.80			−1.78611
$750$		0			0
$751$	218.250	−	671.703i	0.290612	−	0.894412i	−0.694048	−	0.719929i	$-0.744175\pi$
$751$	218.250	−	671.703i	0.290612	−	0.894412i	0.984660	−	0.174483i	$-0.0558254\pi$
$752$		0			0
$753$	−391.100	+	284.151i	−0.519389	+	0.377358i
$754$		0			0
$755$	−612.938	+	199.156i	−0.811838	+	0.263782i
$756$		0			0
$757$	191.327	+	139.007i	0.252743	+	0.183629i	0.706942	−	0.707272i	$-0.250074\pi$
$757$	191.327	+	139.007i	0.252743	+	0.183629i	−0.454199	+	0.890900i	$0.650074\pi$
$758$		0			0
$759$	984.928	+	517.551i	1.29767	+	0.681886i
$760$		0			0
$761$	−120.129	+	165.344i	−0.157857	+	0.217271i	−0.880618	−	0.473826i	$-0.842873\pi$
$761$	−120.129	+	165.344i	−0.157857	+	0.217271i	0.722761	+	0.691098i	$0.242873\pi$
$762$		0			0
$763$	252.753	+	777.894i	0.331262	+	1.01952i
$764$		0			0
$765$	109.162	+	150.248i	0.142695	+	0.196403i
$766$		0			0
$767$	−740.728	−	240.677i	−0.965747	−	0.313790i
$768$		0			0
$769$		−	404.940i		−	0.526580i	−0.964717	−	0.263290i	$-0.915192\pi$
$769$		−	404.940i		−	0.526580i	0.964717	−	0.263290i	$-0.0848076\pi$
$770$		0			0
$771$	−1451.54			−1.88267
$772$		0			0
$773$	−397.622	+	1223.76i	−0.514388	+	1.58312i	0.270004	+	0.962859i	$0.412975\pi$
$773$	−397.622	+	1223.76i	−0.514388	+	1.58312i	−0.784392	+	0.620265i	$0.787025\pi$
$774$		0			0
$775$	114.453	−	83.1552i	0.147682	−	0.107297i
$776$		0			0
$777$	−63.1344	+	20.5136i	−0.0812541	+	0.0264010i
$778$		0			0
$779$	−152.559	−	110.841i	−0.195840	−	0.142286i
$780$		0			0
$781$	297.536	+	602.565i	0.380968	+	0.771530i
$782$		0			0
$783$	177.298	−	244.029i	0.226434	−	0.311660i
$784$		0			0
$785$	−46.3721	−	142.719i	−0.0590727	−	0.181807i
$786$		0			0
$787$	692.509	+	953.156i	0.879935	+	1.21113i	0.976439	+	0.215794i	$0.0692339\pi$
$787$	692.509	+	953.156i	0.879935	+	1.21113i	−0.0965041	+	0.995333i	$0.530766\pi$
$788$		0			0
$789$	1266.29	+	411.441i	1.60493	+	0.521472i
$790$		0			0
$791$		−	1236.02i		−	1.56261i
$792$		0			0
$793$	615.881			0.776647
$794$		0			0
$795$	−210.015	+	646.359i	−0.264170	+	0.813031i
$796$		0			0
$797$	248.215	−	180.339i	0.311437	−	0.226272i	−0.421076	−	0.907025i	$-0.638347\pi$
$797$	248.215	−	180.339i	0.311437	−	0.226272i	0.732513	+	0.680753i	$0.238347\pi$
$798$		0			0
$799$	−532.684	+	173.079i	−0.666688	+	0.216620i
$800$		0			0
$801$	−346.855	−	252.005i	−0.433027	−	0.314613i
$802$		0			0
$803$	−133.597	−	918.089i	−0.166373	−	1.14332i
$804$		0			0
$805$	260.295	−	358.266i	0.323348	−	0.445051i
$806$		0			0
$807$	70.7509	+	217.749i	0.0876715	+	0.269825i
$808$		0			0
$809$	746.572	+	1027.57i	0.922833	+	1.27017i	0.962590	+	0.270961i	$0.0873416\pi$
$809$	746.572	+	1027.57i	0.922833	+	1.27017i	−0.0397571	+	0.999209i	$0.512658\pi$
$810$		0			0
$811$	−739.449	−	240.261i	−0.911774	−	0.296253i	−0.184686	−	0.982798i	$-0.559127\pi$
$811$	−739.449	−	240.261i	−0.911774	−	0.296253i	−0.727088	+	0.686544i	$0.759127\pi$
$812$		0			0
$813$			1864.93i			2.29388i
$814$		0			0
$815$	−362.924			−0.445305
$816$		0			0
$817$	38.2811	−	117.817i	0.0468557	−	0.144207i
$818$		0			0
$819$	−197.894	+	143.779i	−0.241629	+	0.175554i
$820$		0			0
$821$	−852.150	+	276.880i	−1.03794	+	0.337248i	−0.777925	−	0.628357i	$-0.783728\pi$
$821$	−852.150	+	276.880i	−1.03794	+	0.337248i	−0.260016	+	0.965604i	$0.583728\pi$
$822$		0			0
$823$	−774.630	−	562.802i	−0.941227	−	0.683842i	0.00748842	−	0.999972i	$-0.497616\pi$
$823$	−774.630	−	562.802i	−0.941227	−	0.683842i	−0.948716	+	0.316130i	$0.897616\pi$
$824$		0			0
$825$	−138.457	+	135.018i	−0.167827	+	0.163658i
$826$		0			0
$827$	781.264	−	1075.32i	0.944697	−	1.30026i	−0.00914635	−	0.999958i	$-0.502911\pi$
$827$	781.264	−	1075.32i	0.944697	−	1.30026i	0.953843	−	0.300305i	$-0.0970886\pi$
$828$		0			0
$829$	−27.1227	−	83.4752i	−0.0327174	−	0.100694i	0.933364	−	0.358931i	$-0.116859\pi$
$829$	−27.1227	−	83.4752i	−0.0327174	−	0.100694i	−0.966082	+	0.258237i	$0.916859\pi$
$830$		0			0
$831$	287.054	+	395.096i	0.345432	+	0.475446i
$832$		0			0
$833$	37.6223	+	12.2242i	0.0451649	+	0.0146750i
$834$		0			0
$835$			327.679i			0.392431i
$836$		0			0
$837$	−560.749			−0.669951
$838$		0			0
$839$	−16.6119	+	51.1260i	−0.0197996	+	0.0609369i	−0.960468	−	0.278390i	$-0.910199\pi$
$839$	−16.6119	+	51.1260i	−0.0197996	+	0.0609369i	0.940669	+	0.339327i	$0.110199\pi$
$840$		0			0
$841$	−492.974	+	358.167i	−0.586176	+	0.425882i
$842$		0			0
$843$	−1040.14	+	337.963i	−1.23386	+	0.400905i
$844$		0			0
$845$	103.888	+	75.4792i	0.122945	+	0.0893245i
$846$		0			0
$847$	832.775	+	20.9525i	0.983205	+	0.0247374i
$848$		0			0
$849$	809.436	−	1114.09i	0.953399	−	1.31224i
$850$		0			0
$851$	24.3765	+	75.0232i	0.0286445	+	0.0881588i
$852$		0			0
$853$	224.528	+	309.036i	0.263222	+	0.362294i	0.920087	−	0.391715i	$-0.128118\pi$
$853$	224.528	+	309.036i	0.263222	+	0.362294i	−0.656865	+	0.754008i	$0.728118\pi$
$854$		0			0
$855$	21.8721	+	7.10669i	0.0255814	+	0.00831191i
$856$		0			0
$857$			735.176i			0.857849i	0.903340	+	0.428924i	$0.141107\pi$
$857$			735.176i			0.857849i	−0.903340	+	0.428924i	$0.858893\pi$
$858$		0			0
$859$	1221.00			1.42142			0.710710	−	0.703485i	$-0.248374\pi$
$859$	1221.00			1.42142			0.710710	+	0.703485i	$0.248374\pi$
$860$		0			0
$861$	461.356	−	1419.91i	0.535837	−	1.64914i
$862$		0			0
$863$	881.432	−	640.398i	1.02136	−	0.742060i	0.0547969	−	0.998498i	$-0.482549\pi$
$863$	881.432	−	640.398i	1.02136	−	0.742060i	0.966561	+	0.256438i	$0.0825489\pi$
$864$		0			0
$865$	138.622	−	45.0409i	0.160256	−	0.0520704i
$866$		0			0
$867$	−912.202	−	662.754i	−1.05214	−	0.764422i
$868$		0			0
$869$	−586.068	−	600.999i	−0.674416	−	0.691598i
$870$		0			0
$871$	−401.621	+	552.784i	−0.461103	+	0.634654i
$872$		0			0
$873$	−92.0979	−	283.448i	−0.105496	−	0.324683i
$874$		0			0
$875$	45.2432	+	62.2719i	0.0517065	+	0.0711679i
$876$		0			0
$877$	953.140	+	309.694i	1.08682	+	0.353129i	0.797016	−	0.603958i	$-0.206411\pi$
$877$	953.140	+	309.694i	1.08682	+	0.353129i	0.289802	+	0.957087i	$0.406411\pi$
$878$		0			0
$879$			753.847i			0.857619i
$880$		0			0
$881$	−319.501			−0.362657			−0.181329	−	0.983423i	$-0.558040\pi$
$881$	−319.501			−0.362657			−0.181329	+	0.983423i	$0.558040\pi$
$882$		0			0
$883$	−396.367	+	1219.89i	−0.448886	+	1.38153i	0.429278	+	0.903172i	$0.358768\pi$
$883$	−396.367	+	1219.89i	−0.448886	+	1.38153i	−0.878165	+	0.478358i	$0.841232\pi$
$884$		0			0
$885$	−469.020	+	340.763i	−0.529967	+	0.385043i
$886$		0			0
$887$	202.927	−	65.9350i	0.228779	−	0.0743349i	−0.192384	−	0.981320i	$-0.561622\pi$
$887$	202.927	−	65.9350i	0.228779	−	0.0743349i	0.421163	+	0.906985i	$0.361622\pi$
$888$		0			0
$889$	43.3046	+	31.4627i	0.0487116	+	0.0353911i
$890$		0			0
$891$	1088.09	−	158.335i	1.22120	−	0.177705i
$892$		0			0
$893$	−40.7676	+	56.1118i	−0.0456524	+	0.0628352i
$894$		0			0
$895$	20.9181	+	64.3792i	0.0233721	+	0.0719320i
$896$		0			0
$897$	627.992	+	864.357i	0.700102	+	0.963608i
$898$		0			0
$899$	−409.566	−	133.076i	−0.455579	−	0.148027i
$900$		0			0
$901$		−	2134.30i		−	2.36881i
$902$		0			0
$903$	980.787			1.08614
$904$		0			0
$905$	113.441	−	349.135i	0.125349	−	0.385785i
$906$		0			0
$907$	1159.59	−	842.490i	1.27849	−	0.928876i	0.278982	−	0.960296i	$-0.410003\pi$
$907$	1159.59	−	842.490i	1.27849	−	0.928876i	0.999506	+	0.0314205i	$0.0100031\pi$
$908$		0			0
$909$	169.766	−	55.1602i	0.186761	−	0.0606823i
$910$		0			0
$911$	−1333.36	−	968.740i	−1.46362	−	1.06338i	−0.982402	−	0.186778i	$-0.940195\pi$
$911$	−1333.36	−	968.740i	−1.46362	−	1.06338i	−0.481215	−	0.876602i	$-0.659805\pi$
$912$		0			0
$913$	186.455	−	92.0683i	0.204222	−	0.100841i
$914$		0			0
$915$	269.462	−	370.883i	0.294494	−	0.405336i
$916$		0			0
$917$	89.0741	+	274.142i	0.0971364	+	0.298955i
$918$		0			0
$919$	234.127	+	322.249i	0.254763	+	0.350651i	0.917172	−	0.398491i	$-0.130466\pi$
$919$	234.127	+	322.249i	0.254763	+	0.350651i	−0.662409	+	0.749142i	$0.730466\pi$
$920$		0			0
$921$	1578.13	+	512.765i	1.71349	+	0.556748i
$922$		0			0
$923$			645.309i			0.699143i
$924$		0			0
$925$	−13.7112			−0.0148229
$926$		0			0
$927$	−31.2137	+	96.0660i	−0.0336718	+	0.103631i
$928$		0			0
$929$	993.882	−	722.097i	1.06984	−	0.777285i	0.0939570	−	0.995576i	$-0.470048\pi$
$929$	993.882	−	722.097i	1.06984	−	0.777285i	0.975884	+	0.218292i	$0.0700484\pi$
$930$		0			0
$931$	4.65886	−	1.51375i	0.00500414	−	0.00162594i
$932$		0			0
$933$	−13.9880	−	10.1629i	−0.0149925	−	0.0108927i
$934$		0			0
$935$	282.506	−	537.625i	0.302146	−	0.575000i
$936$		0			0
$937$	−395.443	+	544.280i	−0.422031	+	0.580875i	−0.966101	−	0.258164i	$-0.916882\pi$
$937$	−395.443	+	544.280i	−0.422031	+	0.580875i	0.544070	+	0.839040i	$0.316882\pi$
$938$		0			0
$939$	220.768	+	679.454i	0.235110	+	0.723593i
$940$		0			0
$941$	748.065	+	1029.62i	0.794968	+	1.09418i	0.993472	+	0.114079i	$0.0363918\pi$
$941$	748.065	+	1029.62i	0.794968	+	1.09418i	−0.198504	+	0.980100i	$0.563608\pi$
$942$		0			0
$943$	−1687.29	−	548.233i	−1.78928	−	0.581372i
$944$		0			0
$945$		−	305.093i		−	0.322850i
$946$		0			0
$947$	−264.005			−0.278780			−0.139390	−	0.990238i	$-0.544514\pi$
$947$	−264.005			−0.278780			−0.139390	+	0.990238i	$0.544514\pi$
$948$		0			0
$949$	275.298	−	847.279i	0.290092	−	0.892812i
$950$		0			0
$951$	−1.40524	+	1.02097i	−0.00147764	+	0.00107357i
$952$		0			0
$953$	814.810	−	264.748i	0.854995	−	0.277805i	0.151458	−	0.988464i	$-0.451603\pi$
$953$	814.810	−	264.748i	0.854995	−	0.277805i	0.703537	+	0.710659i	$0.251603\pi$
$954$		0			0
$955$	−474.293	−	344.594i	−0.496642	−	0.360831i
$956$		0			0
$957$	580.234	+	99.3963i	0.606306	+	0.103862i
$958$		0			0
$959$	511.166	−	703.560i	0.533020	−	0.733639i
$960$		0			0
$961$	−49.5747	−	152.575i	−0.0515865	−	0.158767i
$962$		0			0
$963$	−384.192	−	528.795i	−0.398953	−	0.549112i
$964$		0			0
$965$	−287.960	−	93.5640i	−0.298405	−	0.0969575i
$966$		0			0
$967$		−	618.200i		−	0.639297i	−0.947536	−	0.319648i	$-0.896435\pi$
$967$		−	618.200i		−	0.639297i	0.947536	−	0.319648i	$-0.103565\pi$
$968$		0			0
$969$	−265.462			−0.273955
$970$		0			0
$971$	−232.670	+	716.086i	−0.239619	+	0.737472i	0.756856	+	0.653582i	$0.226735\pi$
$971$	−232.670	+	716.086i	−0.239619	+	0.737472i	−0.996475	+	0.0838903i	$0.973265\pi$
$972$		0			0
$973$	−356.418	+	258.953i	−0.366308	+	0.266138i
$974$		0			0
$975$	−176.615	+	57.3858i	−0.181144	+	0.0588572i
$976$		0			0
$977$	136.841	+	99.4211i	0.140063	+	0.101762i	0.655610	−	0.755099i	$-0.272411\pi$
$977$	136.841	+	99.4211i	0.140063	+	0.101762i	−0.515547	+	0.856861i	$0.672411\pi$
$978$		0			0
$979$	−236.728	+	1381.92i	−0.241806	+	1.41156i
$980$		0			0
$981$	−234.894	+	323.304i	−0.239443	+	0.329566i
$982$		0			0
$983$	320.939	+	987.748i	0.326489	+	1.00483i	0.970764	+	0.240036i	$0.0771594\pi$
$983$	320.939	+	987.748i	0.326489	+	1.00483i	−0.644275	+	0.764794i	$0.722841\pi$
$984$		0			0
$985$	−196.611	−	270.612i	−0.199605	−	0.274733i
$986$		0			0
$987$	−522.247	−	169.688i	−0.529125	−	0.171923i
$988$		0			0
$989$		−	1165.48i		−	1.17844i
$990$		0			0
$991$	−1226.12			−1.23725			−0.618625	−	0.785686i	$-0.712310\pi$
$991$	−1226.12			−1.23725			−0.618625	+	0.785686i	$0.712310\pi$
$992$		0			0
$993$	532.964	−	1640.29i	0.536721	−	1.65186i
$994$		0			0
$995$	−665.308	+	483.375i	−0.668651	+	0.485804i
$996$		0			0
$997$	1720.56	−	559.045i	1.72574	−	0.560727i	0.732918	−	0.680317i	$-0.238158\pi$
$997$	1720.56	−	559.045i	1.72574	−	0.560727i	0.992823	+	0.119590i	$0.0381579\pi$
$998$		0			0
$999$	43.9674	+	31.9442i	0.0440115	+	0.0319762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.p.b.161.1	yes	16
11.5	even	5		2420.3.f.a.241.4		16
11.6	odd	10		2420.3.f.a.241.3		16
11.8	odd	10	inner	220.3.p.b.41.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.p.b.41.1	✓	16	11.8	odd	10	inner
220.3.p.b.161.1	yes	16	1.1	even	1	trivial
2420.3.f.a.241.3		16	11.6	odd	10
2420.3.f.a.241.4		16	11.5	even	5

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.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08657 + 3.34411i) q^{3} +(1.80902 - 1.31433i) q^{5} +(-6.54766 + 2.12746i) q^{7} +(-2.72130 - 1.97714i) q^{9} +(-1.85729 + 10.8421i) q^{11} +(-6.20864 + 8.54546i) q^{13} +(2.42964 + 7.47766i) q^{15} +(-14.5133 - 19.9758i) q^{17} +(-2.90795 - 0.944851i) q^{19} -24.2077i q^{21} -28.7662 q^{23} +(1.54508 - 4.75528i) q^{25} +(-16.0334 + 11.6489i) q^{27} +(-14.4752 + 4.70326i) q^{29} +(22.8906 + 16.6310i) q^{31} +(-34.2390 - 17.9916i) q^{33} +(-9.04864 + 12.4544i) q^{35} +(-0.847400 - 2.60803i) q^{37} +(-21.8309 - 30.0476i) q^{39} +(58.6552 + 19.0582i) q^{41} +40.5154i q^{43} -7.52149 q^{45} +(7.00968 - 21.5736i) q^{47} +(-1.29613 + 0.941696i) q^{49} +(82.5711 - 26.8290i) q^{51} +(69.9304 + 50.8074i) q^{53} +(10.8902 + 22.0546i) q^{55} +(6.31938 - 8.69788i) q^{57} +(22.7854 + 70.1263i) q^{59} +(-34.2719 - 47.1712i) q^{61} +(22.0244 + 7.15617i) q^{63} +23.6191i q^{65} +64.6875 q^{67} +(31.2565 - 96.1975i) q^{69} +(49.4251 - 35.9095i) q^{71} +(-80.2137 + 26.0630i) q^{73} +(14.2234 + 10.3339i) q^{75} +(-10.9052 - 74.9415i) q^{77} +(-44.8560 + 61.7390i) q^{79} +(-30.8890 - 95.0665i) q^{81} +(-11.1117 - 15.2939i) q^{83} +(-52.5096 - 17.0614i) q^{85} -53.5169i q^{87} +127.459 q^{89} +(22.4719 - 69.1614i) q^{91} +(-80.4883 + 58.4781i) q^{93} +(-6.50238 + 2.11275i) q^{95} +(71.6814 + 52.0796i) q^{97} +(26.4905 - 25.8324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 9 q^{3} + 20 q^{5} + 10 q^{7} - 19 q^{9} + 23 q^{11} - 5 q^{13} + 15 q^{15} + 25 q^{17} + 30 q^{19} - 168 q^{23} - 20 q^{25} - 225 q^{27} - 105 q^{29} + 40 q^{31} + 106 q^{33} - 16 q^{37} + 115 q^{39}+ \cdots + 150 q^{99}+O(q^{100}) \) 16 * q + 9 * q^3 + 20 * q^5 + 10 * q^7 - 19 * q^9 + 23 * q^11 - 5 * q^13 + 15 * q^15 + 25 * q^17 + 30 * q^19 - 168 * q^23 - 20 * q^25 - 225 * q^27 - 105 * q^29 + 40 * q^31 + 106 * q^33 - 16 * q^37 + 115 * q^39 + 255 * q^41 - 30 * q^45 + 102 * q^47 + 12 * q^49 + 380 * q^51 + 297 * q^53 + 55 * q^55 - 150 * q^57 - 22 * q^59 - 30 * q^61 - 320 * q^63 - 68 * q^67 - 137 * q^69 - 240 * q^71 + 85 * q^73 - 30 * q^75 + 226 * q^77 - 215 * q^79 - 463 * q^81 - 610 * q^83 + 25 * q^85 - 160 * q^89 + 161 * q^91 - 253 * q^93 + 90 * q^95 + 179 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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