LMFDB - Embedded newform 132.4.i.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [132,4,Mod(25,132)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(132, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("132.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	132.i (of order $5$, 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:	$7.78825212076$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	132.37
Dual form			132.4.i.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.927051 + 2.85317i) q^{3} +(9.54508 - 6.93491i) q^{5} +(-4.78115 - 14.7149i) q^{7} +(-7.28115 - 5.29007i) q^{9} +(-8.89919 - 35.3808i) q^{11} +(48.2599 + 35.0628i) q^{13} +(10.9377 + 33.6628i) q^{15} +(23.4443 - 17.0333i) q^{17} +(44.0279 - 135.504i) q^{19} +46.4164 q^{21} +185.000 q^{23} +(4.38854 - 13.5065i) q^{25} +(21.8435 - 15.8702i) q^{27} +(47.9230 + 147.492i) q^{29} +(-229.089 - 166.443i) q^{31} +(109.198 + 7.40896i) q^{33} +(-147.683 - 107.298i) q^{35} +(-62.4762 - 192.282i) q^{37} +(-144.780 + 105.189i) q^{39} +(-90.9534 + 279.926i) q^{41} +179.174 q^{43} -106.185 q^{45} +(-126.201 + 388.407i) q^{47} +(83.8247 - 60.9022i) q^{49} +(26.8647 + 82.6812i) q^{51} +(-290.913 - 211.361i) q^{53} +(-330.307 - 275.998i) q^{55} +(345.799 + 251.238i) q^{57} +(89.0592 + 274.096i) q^{59} +(-122.678 + 89.1307i) q^{61} +(-43.0304 + 132.434i) q^{63} +703.802 q^{65} -826.540 q^{67} +(-171.504 + 527.836i) q^{69} +(-113.112 + 82.1810i) q^{71} +(75.5956 + 232.659i) q^{73} +(34.4681 + 25.0425i) q^{75} +(-478.076 + 300.112i) q^{77} +(-455.201 - 330.723i) q^{79} +(25.0304 + 77.0356i) q^{81} +(-44.1747 + 32.0948i) q^{83} +(105.653 - 325.168i) q^{85} -465.246 q^{87} +554.967 q^{89} +(285.208 - 877.779i) q^{91} +(687.266 - 499.328i) q^{93} +(-519.457 - 1598.72i) q^{95} +(-116.662 - 84.7596i) q^{97} +(-122.371 + 304.691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 27 q^{5} + q^{7} - 9 q^{9} - 11 q^{11} + 79 q^{13} + 84 q^{15} + 58 q^{17} + 194 q^{19} + 132 q^{21} + 740 q^{23} - 54 q^{25} + 27 q^{27} + 62 q^{29} - 572 q^{31} + 363 q^{33} - 347 q^{35}+ \cdots + 396 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 + 27 * q^5 + q^7 - 9 * q^9 - 11 * q^11 + 79 * q^13 + 84 * q^15 + 58 * q^17 + 194 * q^19 + 132 * q^21 + 740 * q^23 - 54 * q^25 + 27 * q^27 + 62 * q^29 - 572 * q^31 + 363 * q^33 - 347 * q^35 - 355 * q^37 - 237 * q^39 - 53 * q^41 - 616 * q^43 + 18 * q^45 + 289 * q^47 - 18 * q^49 + 141 * q^51 - 466 * q^53 - 1518 * q^55 + 813 * q^57 - 328 * q^59 - 645 * q^61 + 9 * q^63 + 682 * q^65 - 1486 * q^67 + 555 * q^69 - 3 * q^71 - 1482 * q^73 - 3 * q^75 - 1199 * q^77 - 1027 * q^79 - 81 * q^81 + 313 * q^83 - 161 * q^85 - 1056 * q^87 + 1236 * q^89 + 271 * q^91 + 1716 * q^93 + 317 * q^95 - 129 * q^97 + 396 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$3$	−0.927051	+	2.85317i	−0.178411	+	0.549093i
$4$		0			0
$5$	9.54508	−	6.93491i	0.853738	−	0.620277i	−0.0724359	−	0.997373i	$-0.523077\pi$
$5$	9.54508	−	6.93491i	0.853738	−	0.620277i	0.926174	+	0.377096i	$0.123077\pi$
$6$		0			0
$7$	−4.78115	−	14.7149i	−0.258158	−	0.794529i	−0.993191	−	0.116497i	$-0.962833\pi$
$7$	−4.78115	−	14.7149i	−0.258158	−	0.794529i	0.735033	−	0.678031i	$-0.237167\pi$
$8$		0			0
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$		0			0
$11$	−8.89919	−	35.3808i	−0.243928	−	0.969793i
$11$	−8.89919	−	35.3808i	−0.243928	−	0.969793i
$12$		0			0
$13$	48.2599	+	35.0628i	1.02961	+	0.748053i	0.968230	−	0.250062i	$-0.0804510\pi$
$13$	48.2599	+	35.0628i	1.02961	+	0.748053i	0.0613763	+	0.998115i	$0.480451\pi$
$14$		0			0
$15$	10.9377	+	33.6628i	0.188273	+	0.579446i
$16$		0			0
$17$	23.4443	−	17.0333i	0.334475	−	0.243010i	−0.407852	−	0.913048i	$-0.633722\pi$
$17$	23.4443	−	17.0333i	0.334475	−	0.243010i	0.742327	+	0.670038i	$0.233722\pi$
$18$		0			0
$19$	44.0279	−	135.504i	0.531615	−	1.63614i	−0.219237	−	0.975672i	$-0.570357\pi$
$19$	44.0279	−	135.504i	0.531615	−	1.63614i	0.750852	−	0.660471i	$-0.229643\pi$
$20$		0			0
$21$	46.4164			0.482328
$22$		0			0
$23$	185.000			1.67718			0.838591	−	0.544762i	$-0.183380\pi$
$23$	185.000			1.67718			0.838591	+	0.544762i	$0.183380\pi$
$24$		0			0
$25$	4.38854	−	13.5065i	0.0351084	−	0.108052i
$26$		0			0
$27$	21.8435	−	15.8702i	0.155695	−	0.113119i
$28$		0			0
$29$	47.9230	+	147.492i	0.306865	+	0.944432i	0.978975	+	0.203981i	$0.0653881\pi$
$29$	47.9230	+	147.492i	0.306865	+	0.944432i	−0.672110	+	0.740451i	$0.734612\pi$
$30$		0			0
$31$	−229.089	−	166.443i	−1.32728	−	0.964322i	−0.999811	−	0.0194584i	$-0.993806\pi$
$31$	−229.089	−	166.443i	−1.32728	−	0.964322i	−0.327465	−	0.944863i	$-0.606194\pi$
$32$		0			0
$33$	109.198	+	7.40896i	0.576026	+	0.0390829i
$34$		0			0
$35$	−147.683	−	107.298i	−0.713227	−	0.518190i
$36$		0			0
$37$	−62.4762	−	192.282i	−0.277595	−	0.854350i	−0.988521	−	0.151083i	$-0.951724\pi$
$37$	−62.4762	−	192.282i	−0.277595	−	0.854350i	0.710926	−	0.703267i	$-0.248276\pi$
$38$		0			0
$39$	−144.780	+	105.189i	−0.594443	+	0.431888i
$40$		0			0
$41$	−90.9534	+	279.926i	−0.346452	+	1.06627i	0.614350	+	0.789034i	$0.289418\pi$
$41$	−90.9534	+	279.926i	−0.346452	+	1.06627i	−0.960802	+	0.277236i	$0.910582\pi$
$42$		0			0
$43$	179.174			0.635437			0.317719	−	0.948185i	$-0.397083\pi$
$43$	179.174			0.635437			0.317719	+	0.948185i	$0.397083\pi$
$44$		0			0
$45$	−106.185			−0.351760
$46$		0			0
$47$	−126.201	+	388.407i	−0.391666	+	1.20542i	0.539861	+	0.841754i	$0.318477\pi$
$47$	−126.201	+	388.407i	−0.391666	+	1.20542i	−0.931528	+	0.363671i	$0.881523\pi$
$48$		0			0
$49$	83.8247	−	60.9022i	0.244387	−	0.177557i
$50$		0			0
$51$	26.8647	+	82.6812i	0.0737611	+	0.227013i
$52$		0			0
$53$	−290.913	−	211.361i	−0.753963	−	0.547786i	0.143090	−	0.989710i	$-0.454296\pi$
$53$	−290.913	−	211.361i	−0.753963	−	0.547786i	−0.897053	+	0.441924i	$0.854296\pi$
$54$		0			0
$55$	−330.307	−	275.998i	−0.809791	−	0.676647i
$56$		0			0
$57$	345.799	+	251.238i	0.803548	+	0.583812i
$58$		0			0
$59$	89.0592	+	274.096i	0.196517	+	0.604818i	0.999956	+	0.00942994i	$0.00300169\pi$
$59$	89.0592	+	274.096i	0.196517	+	0.604818i	−0.803438	+	0.595388i	$0.796998\pi$
$60$		0			0
$61$	−122.678	+	89.1307i	−0.257496	+	0.187082i	−0.709043	−	0.705166i	$-0.750873\pi$
$61$	−122.678	+	89.1307i	−0.257496	+	0.187082i	0.451546	+	0.892248i	$0.350873\pi$
$62$		0			0
$63$	−43.0304	+	132.434i	−0.0860527	+	0.264843i
$64$		0			0
$65$	703.802			1.34301
$66$		0			0
$67$	−826.540			−1.50713			−0.753567	−	0.657372i	$-0.771668\pi$
$67$	−826.540			−1.50713			−0.753567	+	0.657372i	$0.771668\pi$
$68$		0			0
$69$	−171.504	+	527.836i	−0.299228	+	0.920928i
$70$		0			0
$71$	−113.112	+	82.1810i	−0.189070	+	0.137367i	−0.678294	−	0.734791i	$-0.737280\pi$
$71$	−113.112	+	82.1810i	−0.189070	+	0.137367i	0.489224	+	0.872158i	$0.337280\pi$
$72$		0			0
$73$	75.5956	+	232.659i	0.121203	+	0.373023i	0.993190	−	0.116505i	$-0.0371690\pi$
$73$	75.5956	+	232.659i	0.121203	+	0.373023i	−0.871988	+	0.489528i	$0.837169\pi$
$74$		0			0
$75$	34.4681	+	25.0425i	0.0530671	+	0.0385555i
$76$		0			0
$77$	−478.076	+	300.112i	−0.707557	+	0.444168i
$78$		0			0
$79$	−455.201	−	330.723i	−0.648280	−	0.471003i	0.214405	−	0.976745i	$-0.431219\pi$
$79$	−455.201	−	330.723i	−0.648280	−	0.471003i	−0.862685	+	0.505742i	$0.831219\pi$
$80$		0			0
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$		0			0
$83$	−44.1747	+	32.0948i	−0.0584193	+	0.0424441i	−0.616612	−	0.787267i	$-0.711495\pi$
$83$	−44.1747	+	32.0948i	−0.0584193	+	0.0424441i	0.558192	+	0.829712i	$0.311495\pi$
$84$		0			0
$85$	105.653	−	325.168i	0.134820	−	0.414934i
$86$		0			0
$87$	−465.246			−0.573329
$88$		0			0
$89$	554.967			0.660971			0.330486	−	0.943811i	$-0.392787\pi$
$89$	554.967			0.660971			0.330486	+	0.943811i	$0.392787\pi$
$90$		0			0
$91$	285.208	−	877.779i	0.328548	−	1.01117i
$92$		0			0
$93$	687.266	−	499.328i	0.766303	−	0.556751i
$94$		0			0
$95$	−519.457	−	1598.72i	−0.561002	−	1.72659i
$96$		0			0
$97$	−116.662	−	84.7596i	−0.122115	−	0.0887220i	0.525051	−	0.851071i	$-0.324046\pi$
$97$	−116.662	−	84.7596i	−0.122115	−	0.0887220i	−0.647167	+	0.762349i	$0.724046\pi$
$98$		0			0
$99$	−122.371	+	304.691i	−0.124230	+	0.309319i
$100$		0			0
$101$	1101.55	+	800.320i	1.08523	+	0.788463i	0.978587	−	0.205835i	$-0.0659909\pi$
$101$	1101.55	+	800.320i	1.08523	+	0.788463i	0.106640	+	0.994298i	$0.465991\pi$
$102$		0			0
$103$	160.270	+	493.260i	0.153319	+	0.471867i	0.997987	−	0.0634238i	$-0.0202020\pi$
$103$	160.270	+	493.260i	0.153319	+	0.471867i	−0.844668	+	0.535291i	$0.820202\pi$
$104$		0			0
$105$	443.049	−	321.894i	0.411782	−	0.299177i
$106$		0			0
$107$	−398.117	+	1225.28i	−0.359696	+	1.10703i	0.593540	+	0.804804i	$0.297730\pi$
$107$	−398.117	+	1225.28i	−0.359696	+	1.10703i	−0.953236	+	0.302226i	$0.902270\pi$
$108$		0			0
$109$	1098.27			0.965093			0.482546	−	0.875870i	$-0.339712\pi$
$109$	1098.27			0.965093			0.482546	+	0.875870i	$0.339712\pi$
$110$		0			0
$111$	606.532			0.518644
$112$		0			0
$113$	302.233	−	930.178i	0.251608	−	0.774370i	−0.742871	−	0.669435i	$-0.766536\pi$
$113$	302.233	−	930.178i	0.251608	−	0.774370i	0.994479	−	0.104935i	$-0.0334636\pi$
$114$		0			0
$115$	1765.84	−	1282.96i	1.43187	−	1.04032i
$116$		0			0
$117$	−165.903	−	510.596i	−0.131092	−	0.403458i
$118$		0			0
$119$	−362.733	−	263.541i	−0.279426	−	0.203015i
$120$		0			0
$121$	−1172.61	+	629.722i	−0.880998	+	0.473119i
$122$		0			0
$123$	−714.357	−	519.011i	−0.523670	−	0.380468i
$124$		0			0
$125$	403.960	+	1243.26i	0.289050	+	0.889604i
$126$		0			0
$127$	2237.84	−	1625.89i	1.56359	−	1.13602i	0.630605	−	0.776104i	$-0.282807\pi$
$127$	2237.84	−	1625.89i	1.56359	−	1.13602i	0.932986	−	0.359912i	$-0.117193\pi$
$128$		0			0
$129$	−166.104	+	511.214i	−0.113369	+	0.348914i
$130$		0			0
$131$	−275.702			−0.183880			−0.0919398	−	0.995765i	$-0.529307\pi$
$131$	−275.702			−0.183880			−0.0919398	+	0.995765i	$0.529307\pi$
$132$		0			0
$133$	−2204.43			−1.43720
$134$		0			0
$135$	98.4392	−	302.965i	0.0627578	−	0.193149i
$136$		0			0
$137$	491.568	−	357.145i	0.306551	−	0.222722i	−0.423864	−	0.905726i	$-0.639327\pi$
$137$	491.568	−	357.145i	0.306551	−	0.222722i	0.730415	+	0.683003i	$0.239327\pi$
$138$		0			0
$139$	626.549	+	1928.32i	0.382325	+	1.17668i	0.938402	+	0.345545i	$0.112306\pi$
$139$	626.549	+	1928.32i	0.382325	+	1.17668i	−0.556077	+	0.831131i	$0.687694\pi$
$140$		0			0
$141$	−991.196	−	720.146i	−0.592012	−	0.430122i
$142$		0			0
$143$	811.080	−	2019.51i	0.474307	−	1.18098i
$144$		0			0
$145$	1480.27	+	1075.48i	0.847792	+	0.615957i
$146$		0			0
$147$	96.0545	+	295.625i	0.0538942	+	0.165869i
$148$		0			0
$149$	2020.47	−	1467.95i	1.11089	−	0.807111i	0.128089	−	0.991763i	$-0.459116\pi$
$149$	2020.47	−	1467.95i	1.11089	−	0.807111i	0.982804	+	0.184652i	$0.0591157\pi$
$150$		0			0
$151$	−1020.05	+	3139.38i	−0.549736	+	1.69191i	0.159718	+	0.987163i	$0.448941\pi$
$151$	−1020.05	+	3139.38i	−0.549736	+	1.69191i	−0.709454	+	0.704751i	$0.751059\pi$
$152$		0			0
$153$	−260.808			−0.137811
$154$		0			0
$155$	−3340.93			−1.73129
$156$		0			0
$157$	−153.158	+	471.371i	−0.0778556	+	0.239615i	−0.982408	−	0.186748i	$-0.940205\pi$
$157$	−153.158	+	471.371i	−0.0778556	+	0.239615i	0.904552	+	0.426363i	$0.140205\pi$
$158$		0			0
$159$	872.740	−	634.083i	0.435300	−	0.316264i
$160$		0			0
$161$	−884.513	−	2722.25i	−0.432978	−	1.33257i
$162$		0			0
$163$	−105.518	−	76.6634i	−0.0507044	−	0.0368389i	0.562144	−	0.827039i	$-0.309977\pi$
$163$	−105.518	−	76.6634i	−0.0507044	−	0.0368389i	−0.612849	+	0.790200i	$0.709977\pi$
$164$		0			0
$165$	1093.68	−	686.556i	0.516018	−	0.323929i
$166$		0			0
$167$	891.977	+	648.059i	0.413313	+	0.300289i	0.774942	−	0.632033i	$-0.217779\pi$
$167$	891.977	+	648.059i	0.413313	+	0.300289i	−0.361629	+	0.932322i	$0.617779\pi$
$168$		0			0
$169$	420.701	+	1294.79i	0.191489	+	0.589342i
$170$		0			0
$171$	−1037.40	+	753.714i	−0.463929	+	0.337064i
$172$		0			0
$173$	−287.912	+	886.102i	−0.126529	+	0.389416i	−0.994177	−	0.107763i	$-0.965631\pi$
$173$	−287.912	+	886.102i	−0.126529	+	0.389416i	0.867647	+	0.497180i	$0.165631\pi$
$174$		0			0
$175$	−219.729			−0.0949142
$176$		0			0
$177$	−864.605			−0.367162
$178$		0			0
$179$	−1158.07	+	3564.17i	−0.483566	+	1.48826i	0.350482	+	0.936570i	$0.386018\pi$
$179$	−1158.07	+	3564.17i	−0.483566	+	1.48826i	−0.834048	+	0.551693i	$0.813982\pi$
$180$		0			0
$181$	−3712.34	+	2697.17i	−1.52451	+	1.10762i	−0.565315	+	0.824875i	$0.691245\pi$
$181$	−3712.34	+	2697.17i	−1.52451	+	1.10762i	−0.959195	+	0.282746i	$0.908755\pi$
$182$		0			0
$183$	−140.576	−	432.649i	−0.0567852	−	0.174767i
$184$		0			0
$185$	−1929.80	−	1402.08i	−0.766928	−	0.557206i
$186$		0			0
$187$	−811.286	−	677.896i	−0.317257	−	0.265094i
$188$		0			0
$189$	−337.965	−	245.546i	−0.130071	−	0.0945018i
$190$		0			0
$191$	−245.209	−	754.676i	−0.0928938	−	0.285898i	0.893805	−	0.448455i	$-0.148026\pi$
$191$	−245.209	−	754.676i	−0.0928938	−	0.285898i	−0.986699	+	0.162558i	$0.948026\pi$
$192$		0			0
$193$	−356.713	+	259.167i	−0.133040	+	0.0966593i	−0.652315	−	0.757948i	$-0.726202\pi$
$193$	−356.713	+	259.167i	−0.133040	+	0.0966593i	0.519275	+	0.854607i	$0.326202\pi$
$194$		0			0
$195$	−652.461	+	2008.07i	−0.239609	+	0.737439i
$196$		0			0
$197$	−1945.32			−0.703545			−0.351773	−	0.936085i	$-0.614421\pi$
$197$	−1945.32			−0.703545			−0.351773	+	0.936085i	$0.614421\pi$
$198$		0			0
$199$	1206.56			0.429804			0.214902	−	0.976636i	$-0.431057\pi$
$199$	1206.56			0.429804			0.214902	+	0.976636i	$0.431057\pi$
$200$		0			0
$201$	766.245	−	2358.26i	0.268889	−	0.827556i
$202$		0			0
$203$	1941.20	−	1410.36i	0.671159	−	0.487625i
$204$		0			0
$205$	1073.10	+	3302.67i	0.365603	+	1.12521i
$206$		0			0
$207$	−1347.01	−	978.662i	−0.452289	−	0.328607i
$208$		0			0
$209$	−5186.05	−	351.869i	−1.71640	−	0.116456i
$210$		0			0
$211$	3357.69	+	2439.51i	1.09551	+	0.795937i	0.980322	−	0.197407i	$-0.0632520\pi$
$211$	3357.69	+	2439.51i	1.09551	+	0.795937i	0.115191	+	0.993343i	$0.463252\pi$
$212$		0			0
$213$	−129.615	−	398.915i	−0.0416953	−	0.128325i
$214$		0			0
$215$	1710.23	−	1242.56i	0.542497	−	0.394147i
$216$		0			0
$217$	−1353.87	+	4166.80i	−0.423535	+	1.30351i
$218$		0			0
$219$	−733.897			−0.226448
$220$		0			0
$221$	1728.65			0.526162
$222$		0			0
$223$	1574.04	−	4844.39i	0.472669	−	1.45473i	−0.376406	−	0.926455i	$-0.622840\pi$
$223$	1574.04	−	4844.39i	0.472669	−	1.45473i	0.849075	−	0.528272i	$-0.177160\pi$
$224$		0			0
$225$	−103.404	+	75.1276i	−0.0306383	+	0.0222600i
$226$		0			0
$227$	1546.39	+	4759.29i	0.452147	+	1.39156i	0.874453	+	0.485111i	$0.161221\pi$
$227$	1546.39	+	4759.29i	0.452147	+	1.39156i	−0.422306	+	0.906453i	$0.638779\pi$
$228$		0			0
$229$	−2785.99	−	2024.14i	−0.803946	−	0.584101i	0.108123	−	0.994138i	$-0.465516\pi$
$229$	−2785.99	−	2024.14i	−0.803946	−	0.584101i	−0.912069	+	0.410036i	$0.865516\pi$
$230$		0			0
$231$	−413.068	−	1642.25i	−0.117653	−	0.467759i
$232$		0			0
$233$	3939.73	+	2862.38i	1.10773	+	0.804810i	0.982304	−	0.187293i	$-0.0599714\pi$
$233$	3939.73	+	2862.38i	1.10773	+	0.804810i	0.125422	+	0.992103i	$0.459971\pi$
$234$		0			0
$235$	1488.97	+	4582.57i	0.413317	+	1.27206i
$236$		0			0
$237$	1365.60	−	992.169i	0.374285	−	0.271934i
$238$		0			0
$239$	−1102.38	+	3392.77i	−0.298355	+	0.918243i	0.683718	+	0.729746i	$0.260362\pi$
$239$	−1102.38	+	3392.77i	−0.298355	+	0.918243i	−0.982074	+	0.188497i	$0.939638\pi$
$240$		0			0
$241$	3406.65			0.910546			0.455273	−	0.890352i	$-0.349542\pi$
$241$	3406.65			0.910546			0.455273	+	0.890352i	$0.349542\pi$
$242$		0			0
$243$	−243.000			−0.0641500
$244$		0			0
$245$	377.762	−	1162.63i	0.0985076	−	0.303175i
$246$		0			0
$247$	6875.93	−	4995.65i	1.77127	−	1.28691i
$248$		0			0
$249$	−50.6197	−	155.791i	−0.0128831	−	0.0396501i
$250$		0			0
$251$	−3059.72	−	2223.02i	−0.769433	−	0.559026i	0.132356	−	0.991202i	$-0.457746\pi$
$251$	−3059.72	−	2223.02i	−0.769433	−	0.559026i	−0.901789	+	0.432176i	$0.857746\pi$
$252$		0			0
$253$	−1646.35	−	6545.46i	−0.409111	−	1.62652i
$254$		0			0
$255$	829.813	+	602.894i	0.203784	+	0.148058i
$256$		0			0
$257$	−2195.65	−	6757.52i	−0.532922	−	1.64017i	−0.748096	−	0.663590i	$-0.769032\pi$
$257$	−2195.65	−	6757.52i	−0.532922	−	1.64017i	0.215174	−	0.976576i	$-0.430968\pi$
$258$		0			0
$259$	−2530.70	+	1838.66i	−0.607142	+	0.441115i
$260$		0			0
$261$	431.307	−	1327.43i	0.102288	−	0.314811i
$262$		0			0
$263$	−100.638			−0.0235955			−0.0117978	−	0.999930i	$-0.503755\pi$
$263$	−100.638			−0.0235955			−0.0117978	+	0.999930i	$0.503755\pi$
$264$		0			0
$265$	−4242.56			−0.983466
$266$		0			0
$267$	−514.483	+	1583.42i	−0.117925	+	0.362934i
$268$		0			0
$269$	2041.15	−	1482.98i	0.462643	−	0.336130i	−0.331924	−	0.943306i	$-0.607698\pi$
$269$	2041.15	−	1482.98i	0.462643	−	0.336130i	0.794567	+	0.607176i	$0.207698\pi$
$270$		0			0
$271$	−1679.07	−	5167.65i	−0.376370	−	1.15835i	−0.942550	−	0.334066i	$-0.891579\pi$
$271$	−1679.07	−	5167.65i	−0.376370	−	1.15835i	0.566180	−	0.824282i	$-0.308421\pi$
$272$		0			0
$273$	2240.05	+	1627.49i	0.496608	+	0.360807i
$274$		0			0
$275$	−516.928	−	35.0731i	−0.113352	−	0.00769086i
$276$		0			0
$277$	−3102.48	−	2254.08i	−0.672960	−	0.488934i	0.198055	−	0.980191i	$-0.436538\pi$
$277$	−3102.48	−	2254.08i	−0.672960	−	0.488934i	−0.871015	+	0.491257i	$0.836538\pi$
$278$		0			0
$279$	787.537	+	2423.79i	0.168991	+	0.520102i
$280$		0			0
$281$	1818.21	−	1321.01i	0.385998	−	0.280444i	−0.377816	−	0.925881i	$-0.623325\pi$
$281$	1818.21	−	1321.01i	0.385998	−	0.280444i	0.763813	+	0.645437i	$0.223325\pi$
$282$		0			0
$283$	−280.261	+	862.556i	−0.0588686	+	0.181179i	−0.976167	−	0.217023i	$-0.930365\pi$
$283$	−280.261	+	862.556i	−0.0588686	+	0.181179i	0.917298	+	0.398201i	$0.130365\pi$
$284$		0			0
$285$	5043.00			1.04815
$286$		0			0
$287$	4553.93			0.936621
$288$		0			0
$289$	−1258.70	+	3873.88i	−0.256198	+	0.788495i
$290$		0			0
$291$	349.985	−	254.279i	0.0705033	−	0.0512237i
$292$		0			0
$293$	−881.437	−	2712.78i	−0.175748	−	0.540896i	0.823919	−	0.566708i	$-0.191783\pi$
$293$	−881.437	−	2712.78i	−0.175748	−	0.540896i	−0.999667	+	0.0258115i	$0.991783\pi$
$294$		0			0
$295$	2750.91	+	1998.65i	0.542929	+	0.394461i
$296$		0			0
$297$	−755.890	−	631.608i	−0.147681	−	0.123399i
$298$		0			0
$299$	8928.08	+	6486.63i	1.72684	+	1.25462i
$300$		0			0
$301$	−856.659	−	2636.53i	−0.164043	−	0.504873i
$302$		0			0
$303$	−3304.64	+	2400.96i	−0.626556	+	0.455219i
$304$		0			0
$305$	−552.857	+	1701.52i	−0.103792	+	0.319438i
$306$		0			0
$307$	−1089.52			−0.202549			−0.101274	−	0.994859i	$-0.532292\pi$
$307$	−1089.52			−0.202549			−0.101274	+	0.994859i	$0.532292\pi$
$308$		0			0
$309$	−1555.93			−0.286453
$310$		0			0
$311$	1861.87	−	5730.23i	0.339475	−	1.04480i	−0.625001	−	0.780624i	$-0.714901\pi$
$311$	1861.87	−	5730.23i	0.339475	−	1.04480i	0.964476	−	0.264172i	$-0.0850987\pi$
$312$		0			0
$313$	7457.07	−	5417.88i	1.34664	−	0.978392i	0.347470	−	0.937691i	$-0.387041\pi$
$313$	7457.07	−	5417.88i	1.34664	−	0.978392i	0.999171	−	0.0407008i	$-0.0129591\pi$
$314$		0			0
$315$	507.688	+	1562.50i	0.0908095	+	0.279483i
$316$		0			0
$317$	579.415	+	420.970i	0.102660	+	0.0745868i	0.637931	−	0.770094i	$-0.279791\pi$
$317$	579.415	+	420.970i	0.102660	+	0.0745868i	−0.535271	+	0.844680i	$0.679791\pi$
$318$		0			0
$319$	4791.91	−	3008.11i	0.841051	−	0.527969i
$320$		0			0
$321$	−3126.85	−	2271.79i	−0.543689	−	0.395013i
$322$		0			0
$323$	−1275.87	−	3926.73i	−0.219787	−	0.676436i
$324$		0			0
$325$	685.369	−	497.949i	0.116977	−	0.0849885i
$326$		0			0
$327$	−1018.15	+	3133.55i	−0.172183	+	0.529925i
$328$		0			0
$329$	6318.74			1.05886
$330$		0			0
$331$	592.915			0.0984579			0.0492290	−	0.998788i	$-0.484324\pi$
$331$	592.915			0.0984579			0.0492290	+	0.998788i	$0.484324\pi$
$332$		0			0
$333$	−562.286	+	1730.54i	−0.0925317	+	0.284783i
$334$		0			0
$335$	−7889.39	+	5731.98i	−1.28670	+	0.934840i
$336$		0			0
$337$	−638.993	−	1966.62i	−0.103288	−	0.317889i	0.886037	−	0.463615i	$-0.153448\pi$
$337$	−638.993	−	1966.62i	−0.103288	−	0.317889i	−0.989325	+	0.145726i	$0.953448\pi$
$338$		0			0
$339$	2373.77	+	1724.65i	0.380311	+	0.276312i
$340$		0			0
$341$	−3850.18	+	9586.55i	−0.611434	+	1.52241i
$342$		0			0
$343$	−5590.35	−	4061.63i	−0.880031	−	0.639380i
$344$		0			0
$345$	2023.47	+	6227.61i	0.315769	+	0.971836i
$346$		0			0
$347$	3070.30	−	2230.71i	0.474993	−	0.345103i	−0.324391	−	0.945923i	$-0.605159\pi$
$347$	3070.30	−	2230.71i	0.474993	−	0.345103i	0.799384	+	0.600820i	$0.205159\pi$
$348$		0			0
$349$	−1236.46	+	3805.43i	−0.189645	+	0.583668i	−0.999997	−	0.00227539i	$-0.999276\pi$
$349$	−1236.46	+	3805.43i	−0.189645	+	0.583668i	0.810352	+	0.585943i	$0.199276\pi$
$350$		0			0
$351$	1610.62			0.244924
$352$		0			0
$353$	−9702.80			−1.46297			−0.731485	−	0.681858i	$-0.761172\pi$
$353$	−9702.80			−1.46297			−0.731485	+	0.681858i	$0.761172\pi$
$354$		0			0
$355$	−509.750	+	1568.85i	−0.0762105	+	0.234552i
$356$		0			0
$357$	1088.20	−	790.623i	0.161327	−	0.117211i
$358$		0			0
$359$	121.313	+	373.364i	0.0178347	+	0.0548897i	0.959578	−	0.281443i	$-0.0908132\pi$
$359$	121.313	+	373.364i	0.0178347	+	0.0548897i	−0.941743	+	0.336333i	$0.890813\pi$
$360$		0			0
$361$	−10873.8	−	7900.27i	−1.58533	−	1.15181i
$362$		0			0
$363$	−709.634	−	3929.44i	−0.102606	−	0.568160i
$364$		0			0
$365$	2335.04	+	1696.50i	0.334853	+	0.243285i
$366$		0			0
$367$	−1209.68	−	3723.02i	−0.172057	−	0.529537i	0.827430	−	0.561569i	$-0.189802\pi$
$367$	−1209.68	−	3723.02i	−0.172057	−	0.529537i	−0.999487	+	0.0320319i	$0.989802\pi$
$368$		0			0
$369$	2143.07	−	1557.03i	0.302341	−	0.219664i
$370$		0			0
$371$	−1719.25	+	5291.30i	−0.240590	+	0.740460i
$372$		0			0
$373$	−4707.31			−0.653446			−0.326723	−	0.945120i	$-0.605944\pi$
$373$	−4707.31			−0.653446			−0.326723	+	0.945120i	$0.605944\pi$
$374$		0			0
$375$	−3921.72			−0.540045
$376$		0			0
$377$	−2858.72	+	8798.25i	−0.390535	+	1.20194i
$378$		0			0
$379$	−6222.36	+	4520.81i	−0.843327	+	0.612713i	−0.923298	−	0.384084i	$-0.874517\pi$
$379$	−6222.36	+	4520.81i	−0.843327	+	0.612713i	0.0799708	+	0.996797i	$0.474517\pi$
$380$		0			0
$381$	2564.34	+	7892.21i	0.344816	+	1.06123i
$382$		0			0
$383$	−5945.23	−	4319.46i	−0.793178	−	0.576277i	0.115727	−	0.993281i	$-0.463080\pi$
$383$	−5945.23	−	4319.46i	−0.793178	−	0.576277i	−0.908905	+	0.417004i	$0.863080\pi$
$384$		0			0
$385$	−2482.03	+	6180.01i	−0.328561	+	0.818084i
$386$		0			0
$387$	−1304.59	−	947.843i	−0.171360	−	0.124500i
$388$		0			0
$389$	4326.39	+	13315.3i	0.563899	+	1.73550i	0.671201	+	0.741275i	$0.265779\pi$
$389$	4326.39	+	13315.3i	0.563899	+	1.73550i	−0.107302	+	0.994226i	$0.534221\pi$
$390$		0			0
$391$	4337.19	−	3151.15i	0.560975	−	0.407572i
$392$		0			0
$393$	255.590	−	786.626i	0.0328062	−	0.100967i
$394$		0			0
$395$	−6638.47			−0.845614
$396$		0			0
$397$	4865.69			0.615118			0.307559	−	0.951529i	$-0.400488\pi$
$397$	4865.69			0.615118			0.307559	+	0.951529i	$0.400488\pi$
$398$		0			0
$399$	2043.62	−	6289.60i	0.256413	−	0.789158i
$400$		0			0
$401$	1367.28	−	993.389i	0.170271	−	0.123709i	−0.499386	−	0.866380i	$-0.666441\pi$
$401$	1367.28	−	993.389i	0.170271	−	0.123709i	0.669657	+	0.742670i	$0.266441\pi$
$402$		0			0
$403$	−5219.83	−	16065.0i	−0.645207	−	1.98574i
$404$		0			0
$405$	773.152	+	561.728i	0.0948598	+	0.0689197i
$406$		0			0
$407$	−6247.11	+	3921.61i	−0.760830	+	0.477610i
$408$		0			0
$409$	−1310.30	−	951.992i	−0.158412	−	0.115093i	0.505756	−	0.862677i	$-0.331214\pi$
$409$	−1310.30	−	951.992i	−0.158412	−	0.115093i	−0.664167	+	0.747584i	$0.731214\pi$
$410$		0			0
$411$	563.287	+	1733.62i	0.0676031	+	0.208061i
$412$		0			0
$413$	3607.48	−	2620.99i	0.429813	−	0.312277i
$414$		0			0
$415$	−199.077	+	612.695i	−0.0235477	+	0.0724724i
$416$		0			0
$417$	−6082.67			−0.714315
$418$		0			0
$419$	4907.60			0.572201			0.286100	−	0.958200i	$-0.407641\pi$
$419$	4907.60			0.572201			0.286100	+	0.958200i	$0.407641\pi$
$420$		0			0
$421$	31.5459	−	97.0881i	0.00365190	−	0.0112394i	−0.949214	−	0.314631i	$-0.898119\pi$
$421$	31.5459	−	97.0881i	0.00365190	−	0.0112394i	0.952866	+	0.303392i	$0.0981191\pi$
$422$		0			0
$423$	2973.59	−	2160.44i	0.341798	−	0.248331i
$424$		0			0
$425$	−127.174	−	391.402i	−0.0145150	−	0.0446725i
$426$		0			0
$427$	1898.09	+	1379.04i	0.215117	+	0.156292i
$428$		0			0
$429$	5010.08	+	4186.33i	0.563844	+	0.471138i
$430$		0			0
$431$	1343.76	+	976.301i	0.150178	+	0.109111i	0.660337	−	0.750969i	$-0.270413\pi$
$431$	1343.76	+	976.301i	0.150178	+	0.109111i	−0.510159	+	0.860080i	$0.670413\pi$
$432$		0			0
$433$	5020.97	+	15452.9i	0.557257	+	1.71506i	0.689907	+	0.723898i	$0.257651\pi$
$433$	5020.97	+	15452.9i	0.557257	+	1.71506i	−0.132650	+	0.991163i	$0.542349\pi$
$434$		0			0
$435$	−4440.81	+	3226.44i	−0.489473	+	0.355623i
$436$		0			0
$437$	8145.15	−	25068.2i	0.891615	−	2.74411i
$438$		0			0
$439$	−7820.26			−0.850206			−0.425103	−	0.905145i	$-0.639762\pi$
$439$	−7820.26			−0.850206			−0.425103	+	0.905145i	$0.639762\pi$
$440$		0			0
$441$	−932.517			−0.100693
$442$		0			0
$443$	−3787.18	+	11655.7i	−0.406173	+	1.25007i	0.513739	+	0.857946i	$0.328260\pi$
$443$	−3787.18	+	11655.7i	−0.406173	+	1.25007i	−0.919912	+	0.392125i	$0.871740\pi$
$444$		0			0
$445$	5297.21	−	3848.65i	0.564296	−	0.409985i
$446$		0			0
$447$	2315.25	+	7125.60i	0.244983	+	0.753981i
$448$		0			0
$449$	11003.1	+	7994.20i	1.15650	+	0.840244i	0.989331	−	0.145684i	$-0.0465384\pi$
$449$	11003.1	+	7994.20i	1.15650	+	0.840244i	0.167166	+	0.985929i	$0.446538\pi$
$450$		0			0
$451$	10713.4	+	726.896i	1.11857	+	0.0758940i
$452$		0			0
$453$	−8011.54	−	5820.73i	−0.830939	−	0.603712i
$454$		0			0
$455$	−3364.99	−	10356.4i	−0.346710	−	1.06706i
$456$		0			0
$457$	−7518.22	+	5462.31i	−0.769557	+	0.559116i	−0.901827	−	0.432098i	$-0.857773\pi$
$457$	−7518.22	+	5462.31i	−0.769557	+	0.559116i	0.132270	+	0.991214i	$0.457773\pi$
$458$		0			0
$459$	241.783	−	744.131i	0.0245870	−	0.0756711i
$460$		0			0
$461$	9964.29			1.00669			0.503344	−	0.864086i	$-0.332103\pi$
$461$	9964.29			1.00669			0.503344	+	0.864086i	$0.332103\pi$
$462$		0			0
$463$	−8874.78			−0.890812			−0.445406	−	0.895329i	$-0.646941\pi$
$463$	−8874.78			−0.890812			−0.445406	+	0.895329i	$0.646941\pi$
$464$		0			0
$465$	3097.22	−	9532.25i	0.308882	−	0.950640i
$466$		0			0
$467$	−12825.7	+	9318.43i	−1.27089	+	0.923352i	−0.999237	−	0.0390443i	$-0.987569\pi$
$467$	−12825.7	+	9318.43i	−1.27089	+	0.923352i	−0.271648	+	0.962397i	$0.587569\pi$
$468$		0			0
$469$	3951.81	+	12162.4i	0.389078	+	1.19746i
$470$		0			0
$471$	−1202.92	−	873.971i	−0.117680	−	0.0854999i
$472$		0			0
$473$	−1594.50	−	6339.33i	−0.155001	−	0.616243i
$474$		0			0
$475$	−1636.97	−	1189.33i	−0.158125	−	0.114885i
$476$		0			0
$477$	1000.07	+	3077.90i	0.0959960	+	0.295445i
$478$		0			0
$479$	9335.13	−	6782.37i	0.890465	−	0.646961i	−0.0455340	−	0.998963i	$-0.514499\pi$
$479$	9335.13	−	6782.37i	0.890465	−	0.646961i	0.935999	+	0.352002i	$0.114499\pi$
$480$		0			0
$481$	3726.86	−	11470.1i	0.353285	−	1.08730i
$482$		0			0
$483$	8587.04			0.808952
$484$		0			0
$485$	−1701.34			−0.159287
$486$		0			0
$487$	2211.55	−	6806.45i	0.205780	−	0.633326i	−0.793900	−	0.608048i	$-0.791953\pi$
$487$	2211.55	−	6806.45i	0.205780	−	0.633326i	0.999680	−	0.0252780i	$-0.00804709\pi$
$488$		0			0
$489$	316.555	−	229.990i	0.0292742	−	0.0212690i
$490$		0			0
$491$	−4550.71	−	14005.6i	−0.418270	−	1.28730i	−0.909293	−	0.416156i	$-0.863377\pi$
$491$	−4550.71	−	14005.6i	−0.418270	−	1.28730i	0.491024	−	0.871146i	$-0.336623\pi$
$492$		0			0
$493$	3635.79	+	2641.55i	0.332145	+	0.241318i
$494$		0			0
$495$	944.963	+	3756.93i	0.0858039	+	0.341134i
$496$		0			0
$497$	1750.09	+	1271.52i	0.157952	+	0.114759i
$498$		0			0
$499$	1895.34	+	5833.25i	0.170034	+	0.523311i	0.999372	−	0.0354362i	$-0.0112821\pi$
$499$	1895.34	+	5833.25i	0.170034	+	0.523311i	−0.829338	+	0.558748i	$0.811282\pi$
$500$		0			0
$501$	−2675.93	+	1944.18i	−0.238626	+	0.173372i
$502$		0			0
$503$	5819.67	−	17911.1i	0.515877	−	1.58771i	−0.265803	−	0.964027i	$-0.585637\pi$
$503$	5819.67	−	17911.1i	0.515877	−	1.58771i	0.781680	−	0.623679i	$-0.214363\pi$
$504$		0			0
$505$	16064.5			1.41557
$506$		0			0
$507$	−4084.25			−0.357767
$508$		0			0
$509$	−1122.52	+	3454.77i	−0.0977504	+	0.300845i	−0.987961	−	0.154705i	$-0.950557\pi$
$509$	−1122.52	+	3454.77i	−0.0977504	+	0.300845i	0.890210	+	0.455550i	$0.150557\pi$
$510$		0			0
$511$	3062.12	−	2224.76i	0.265088	−	0.192598i
$512$		0			0
$513$	−1188.75	−	3658.60i	−0.102309	−	0.314876i
$514$		0			0
$515$	4950.50	+	3596.75i	0.423583	+	0.307751i
$516$		0			0
$517$	14865.3	+	1008.59i	1.26455	+	0.0857987i
$518$		0			0
$519$	−2261.29	−	1642.92i	−0.191252	−	0.138952i
$520$		0			0
$521$	−5475.12	−	16850.7i	−0.460402	−	1.41697i	−0.864675	−	0.502332i	$-0.832475\pi$
$521$	−5475.12	−	16850.7i	−0.460402	−	1.41697i	0.404273	−	0.914638i	$-0.367525\pi$
$522$		0			0
$523$	−2602.40	+	1890.76i	−0.217581	+	0.158082i	−0.691237	−	0.722628i	$-0.742934\pi$
$523$	−2602.40	+	1890.76i	−0.217581	+	0.158082i	0.473656	+	0.880710i	$0.342934\pi$
$524$		0			0
$525$	203.700	−	626.925i	0.0169337	−	0.0521167i
$526$		0			0
$527$	−8205.88			−0.678280
$528$		0			0
$529$	22058.0			1.81294
$530$		0			0
$531$	801.533	−	2466.86i	0.0655058	−	0.201606i
$532$		0			0
$533$	−14204.4	+	10320.1i	−1.15433	+	0.838673i
$534$		0			0
$535$	4697.14	+	14456.3i	0.379579	+	1.16823i
$536$		0			0
$537$	−9095.60	−	6608.34i	−0.730920	−	0.531045i
$538$		0			0
$539$	−2900.74	−	2423.81i	−0.231807	−	0.193694i
$540$		0			0
$541$	−18280.6	−	13281.6i	−1.45276	−	1.05549i	−0.985177	−	0.171542i	$-0.945125\pi$
$541$	−18280.6	−	13281.6i	−1.45276	−	1.05549i	−0.467583	−	0.883949i	$-0.654875\pi$
$542$		0			0
$543$	−4253.97	−	13092.4i	−0.336197	−	1.03471i
$544$		0			0
$545$	10483.1	−	7616.40i	0.823937	−	0.598625i
$546$		0			0
$547$	−4696.14	+	14453.2i	−0.367079	+	1.12975i	0.581590	+	0.813482i	$0.302431\pi$
$547$	−4696.14	+	14453.2i	−0.367079	+	1.12975i	−0.948669	+	0.316271i	$0.897569\pi$
$548$		0			0
$549$	1364.74			0.106094
$550$		0			0
$551$	22095.6			1.70836
$552$		0			0
$553$	−2690.16	+	8279.46i	−0.206867	+	0.636670i
$554$		0			0
$555$	5789.40	−	4206.24i	0.442786	−	0.321703i
$556$		0			0
$557$	−3795.74	−	11682.1i	−0.288744	−	0.888664i	−0.985251	−	0.171114i	$-0.945263\pi$
$557$	−3795.74	−	11682.1i	−0.288744	−	0.888664i	0.696507	−	0.717550i	$-0.254737\pi$
$558$		0			0
$559$	8646.92	+	6282.35i	0.654250	+	0.475340i
$560$		0			0
$561$	2686.26	−	1686.29i	0.202164	−	0.126908i
$562$		0			0
$563$	12636.9	+	9181.27i	0.945974	+	0.687290i	0.949851	−	0.312702i	$-0.101234\pi$
$563$	12636.9	+	9181.27i	0.945974	+	0.687290i	−0.00387707	+	0.999992i	$0.501234\pi$
$564$		0			0
$565$	−3565.86	−	10974.6i	−0.265517	−	0.817176i
$566$		0			0
$567$	1013.89	−	736.638i	0.0750963	−	0.0545606i
$568$		0			0
$569$	−7725.80	+	23777.6i	−0.569213	+	1.75186i	0.0858757	+	0.996306i	$0.472631\pi$
$569$	−7725.80	+	23777.6i	−0.569213	+	1.75186i	−0.655089	+	0.755552i	$0.727369\pi$
$570$		0			0
$571$	−11991.5			−0.878860			−0.439430	−	0.898277i	$-0.644820\pi$
$571$	−11991.5			−0.878860			−0.439430	+	0.898277i	$0.644820\pi$
$572$		0			0
$573$	2380.54			0.173558
$574$		0			0
$575$	811.881	−	2498.71i	0.0588831	−	0.181223i
$576$		0			0
$577$	11446.7	−	8316.51i	0.825879	−	0.600036i	−0.0925116	−	0.995712i	$-0.529490\pi$
$577$	11446.7	−	8316.51i	0.825879	−	0.600036i	0.918390	+	0.395676i	$0.129490\pi$
$578$		0			0
$579$	−408.757	−	1258.02i	−0.0293391	−	0.0902965i
$580$		0			0
$581$	683.477	+	496.575i	0.0488045	+	0.0354585i
$582$		0			0
$583$	−4889.24	+	12173.7i	−0.347327	+	0.864808i
$584$		0			0
$585$	−5124.49	−	3723.16i	−0.362174	−	0.263135i
$586$		0			0
$587$	−6273.07	−	19306.5i	−0.441086	−	1.35752i	−0.886720	−	0.462307i	$-0.847022\pi$
$587$	−6273.07	−	19306.5i	−0.441086	−	1.35752i	0.445634	−	0.895215i	$-0.352978\pi$
$588$		0			0
$589$	−32639.9	+	23714.3i	−2.28337	+	1.65896i
$590$		0			0
$591$	1803.41	−	5550.33i	0.125520	−	0.386312i
$592$		0			0
$593$	7232.26			0.500832			0.250416	−	0.968138i	$-0.419433\pi$
$593$	7232.26			0.500832			0.250416	+	0.968138i	$0.419433\pi$
$594$		0			0
$595$	−5289.95			−0.364482
$596$		0			0
$597$	−1118.55	+	3442.53i	−0.0766818	+	0.236002i
$598$		0			0
$599$	−18957.0	+	13773.1i	−1.29309	+	0.939488i	−0.999863	−	0.0165537i	$-0.994731\pi$
$599$	−18957.0	+	13773.1i	−1.29309	+	0.939488i	−0.293231	+	0.956042i	$0.594731\pi$
$600$		0			0
$601$	5041.51	+	15516.2i	0.342175	+	1.05311i	0.963079	+	0.269220i	$0.0867659\pi$
$601$	5041.51	+	15516.2i	0.342175	+	1.05311i	−0.620904	+	0.783887i	$0.713234\pi$
$602$		0			0
$603$	6018.16	+	4372.45i	0.406432	+	0.295290i
$604$		0			0
$605$	−6825.59	+	14142.7i	−0.458677	+	0.950383i
$606$		0			0
$607$	3262.01	+	2369.99i	0.218124	+	0.158476i	0.691482	−	0.722394i	$-0.256958\pi$
$607$	3262.01	+	2369.99i	0.218124	+	0.158476i	−0.473358	+	0.880870i	$0.656958\pi$
$608$		0			0
$609$	2224.41	+	6846.04i	0.148009	+	0.455526i
$610$		0			0
$611$	−19709.1	+	14319.5i	−1.30498	+	0.948126i
$612$		0			0
$613$	7325.66	−	22546.0i	0.482676	−	1.48552i	−0.352643	−	0.935758i	$-0.614717\pi$
$613$	7325.66	−	22546.0i	0.482676	−	1.48552i	0.835319	−	0.549766i	$-0.185283\pi$
$614$		0			0
$615$	−10417.9			−0.683073
$616$		0			0
$617$	8595.80			0.560865			0.280433	−	0.959874i	$-0.409522\pi$
$617$	8595.80			0.560865			0.280433	+	0.959874i	$0.409522\pi$
$618$		0			0
$619$	1070.89	−	3295.86i	0.0695358	−	0.214009i	−0.910250	−	0.414059i	$-0.864111\pi$
$619$	1070.89	−	3295.86i	0.0695358	−	0.214009i	0.979786	+	0.200050i	$0.0641106\pi$
$620$		0			0
$621$	4041.04	−	2935.99i	0.261129	−	0.189722i
$622$		0			0
$623$	−2653.38	−	8166.28i	−0.170635	−	0.525161i
$624$		0			0
$625$	13913.9	+	10109.0i	0.890489	+	0.646978i
$626$		0			0
$627$	5811.68	−	14470.5i	0.370169	−	0.921684i
$628$		0			0
$629$	−4739.90	−	3443.74i	−0.300464	−	0.218300i
$630$		0			0
$631$	46.0667	+	141.779i	0.00290631	+	0.00894472i	0.952499	−	0.304541i	$-0.0985031\pi$
$631$	46.0667	+	141.779i	0.00290631	+	0.00894472i	−0.949593	+	0.313486i	$0.898503\pi$
$632$		0			0
$633$	−10073.1	+	7318.52i	−0.632495	+	0.459534i
$634$		0			0
$635$	10085.0	−	31038.4i	0.630253	−	1.93972i
$636$		0			0
$637$	6180.77			0.384444
$638$		0			0
$639$	1258.33			0.0779011
$640$		0			0
$641$	−6179.58	+	19018.8i	−0.380778	+	1.17191i	0.558719	+	0.829357i	$0.311293\pi$
$641$	−6179.58	+	19018.8i	−0.380778	+	1.17191i	−0.939497	+	0.342557i	$0.888707\pi$
$642$		0			0
$643$	−16772.4	+	12185.9i	−1.02868	+	0.747379i	−0.968044	−	0.250781i	$-0.919313\pi$
$643$	−16772.4	+	12185.9i	−1.02868	+	0.747379i	−0.0606354	+	0.998160i	$0.519313\pi$
$644$		0			0
$645$	1959.75	+	6031.50i	0.119636	+	0.368201i
$646$		0			0
$647$	16397.9	+	11913.8i	0.996395	+	0.723923i	0.961312	−	0.275461i	$-0.0888305\pi$
$647$	16397.9	+	11913.8i	0.996395	+	0.723923i	0.0350829	+	0.999384i	$0.488830\pi$
$648$		0			0
$649$	8905.20	−	5590.22i	0.538613	−	0.338113i
$650$		0			0
$651$	−10633.5	−	7725.67i	−0.640182	−	0.465120i
$652$		0			0
$653$	−4467.82	−	13750.5i	−0.267748	−	0.824044i	−0.991048	−	0.133509i	$-0.957375\pi$
$653$	−4467.82	−	13750.5i	−0.267748	−	0.824044i	0.723300	−	0.690534i	$-0.242625\pi$
$654$		0			0
$655$	−2631.60	+	1911.97i	−0.156985	+	0.114056i
$656$		0			0
$657$	680.360	−	2093.93i	0.0404009	−	0.124341i
$658$		0			0
$659$	−19629.0			−1.16030			−0.580151	−	0.814509i	$-0.697006\pi$
$659$	−19629.0			−1.16030			−0.580151	+	0.814509i	$0.697006\pi$
$660$		0			0
$661$	−6788.41			−0.399453			−0.199727	−	0.979852i	$-0.564005\pi$
$661$	−6788.41			−0.399453			−0.199727	+	0.979852i	$0.564005\pi$
$662$		0			0
$663$	−1602.55	+	4932.14i	−0.0938730	+	0.288912i
$664$		0			0
$665$	−21041.4	+	15287.5i	−1.22700	+	0.891464i
$666$		0			0
$667$	8865.75	+	27286.0i	0.514668	+	1.58398i
$668$		0			0
$669$	12362.6	+	8981.99i	0.714451	+	0.519079i
$670$		0			0
$671$	4245.25	+	3547.26i	0.244242	+	0.204084i
$672$		0			0
$673$	−5895.91	−	4283.63i	−0.337698	−	0.245352i	0.405992	−	0.913877i	$-0.366926\pi$
$673$	−5895.91	−	4283.63i	−0.337698	−	0.245352i	−0.743690	+	0.668525i	$0.766926\pi$
$674$		0			0
$675$	−118.491	−	364.677i	−0.00675661	−	0.0207947i
$676$		0			0
$677$	−16792.4	+	12200.4i	−0.953300	+	0.692613i	−0.951585	−	0.307386i	$-0.900546\pi$
$677$	−16792.4	+	12200.4i	−0.953300	+	0.692613i	−0.00171474	+	0.999999i	$0.500546\pi$
$678$		0			0
$679$	−689.450	+	2121.91i	−0.0389671	+	0.119928i
$680$		0			0
$681$	−15012.6			−0.844766
$682$		0			0
$683$	27424.1			1.53639			0.768195	−	0.640216i	$-0.221155\pi$
$683$	27424.1			1.53639			0.768195	+	0.640216i	$0.221155\pi$
$684$		0			0
$685$	2215.29	−	6817.96i	0.123565	−	0.380293i
$686$		0			0
$687$	8357.98	−	6072.43i	0.464159	−	0.337231i
$688$		0			0
$689$	−6628.52	−	20400.5i	−0.366512	−	1.12801i
$690$		0			0
$691$	20008.2	+	14536.8i	1.10151	+	0.800297i	0.981306	−	0.192452i	$-0.0616440\pi$
$691$	20008.2	+	14536.8i	1.10151	+	0.800297i	0.120208	+	0.992749i	$0.461644\pi$
$692$		0			0
$693$	5068.56	+	343.897i	0.277834	+	0.0188508i
$694$		0			0
$695$	19353.2	+	14060.9i	1.05627	+	0.767426i
$696$		0			0
$697$	2635.71	+	8111.89i	0.143235	+	0.440832i
$698$		0			0
$699$	−11819.2	+	8587.14i	−0.639546	+	0.464657i
$700$		0			0
$701$	3857.44	−	11872.0i	0.207837	−	0.639655i	−0.791748	−	0.610847i	$-0.790829\pi$
$701$	3857.44	−	11872.0i	0.207837	−	0.639655i	0.999585	−	0.0288078i	$-0.00917106\pi$
$702$		0			0
$703$	−28805.6			−1.54541
$704$		0			0
$705$	−14455.2			−0.772219
$706$		0			0
$707$	6509.95	−	20035.6i	0.346297	−	1.06579i
$708$		0			0
$709$	−18069.7	+	13128.4i	−0.957154	+	0.695413i	−0.952488	−	0.304576i	$-0.901485\pi$
$709$	−18069.7	+	13128.4i	−0.957154	+	0.695413i	−0.00466600	+	0.999989i	$0.501485\pi$
$710$		0			0
$711$	1564.84	+	4816.09i	0.0825403	+	0.254033i
$712$		0			0
$713$	−42381.4	−	30791.9i	−2.22608	−	1.61734i
$714$		0			0
$715$	−6263.27	−	24901.1i	−0.327598	−	1.30245i
$716$		0			0
$717$	−8658.19	−	6290.54i	−0.450971	−	0.327649i
$718$		0			0
$719$	−2186.19	−	6728.41i	−0.113395	−	0.348995i	0.878214	−	0.478268i	$-0.158735\pi$
$719$	−2186.19	−	6728.41i	−0.113395	−	0.348995i	−0.991609	+	0.129274i	$0.958735\pi$
$720$		0			0
$721$	6491.98	−	4716.70i	0.335331	−	0.243633i
$722$		0			0
$723$	−3158.14	+	9719.75i	−0.162452	+	0.499974i
$724$		0			0
$725$	2202.42			0.112822
$726$		0			0
$727$	−6628.00			−0.338128			−0.169064	−	0.985605i	$-0.554074\pi$
$727$	−6628.00			−0.338128			−0.169064	+	0.985605i	$0.554074\pi$
$728$		0			0
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$		0			0
$731$	4200.61	−	3051.92i	0.212538	−	0.154418i
$732$		0			0
$733$	−9252.91	−	28477.5i	−0.466254	−	1.43498i	−0.857399	−	0.514653i	$-0.827921\pi$
$733$	−9252.91	−	28477.5i	−0.466254	−	1.43498i	0.391144	−	0.920329i	$-0.372079\pi$
$734$		0			0
$735$	2966.98	+	2155.64i	0.148896	+	0.108180i
$736$		0			0
$737$	7355.53	+	29243.7i	0.367632	+	1.46161i
$738$		0			0
$739$	−4019.71	−	2920.49i	−0.200091	−	0.145375i	0.483228	−	0.875495i	$-0.339464\pi$
$739$	−4019.71	−	2920.49i	−0.200091	−	0.145375i	−0.683319	+	0.730120i	$0.739464\pi$
$740$		0			0
$741$	7879.11	+	24249.4i	0.390616	+	1.20219i
$742$		0			0
$743$	21362.0	−	15520.4i	1.05477	−	0.766338i	0.0816595	−	0.996660i	$-0.473978\pi$
$743$	21362.0	−	15520.4i	1.05477	−	0.766338i	0.973114	+	0.230322i	$0.0739780\pi$
$744$		0			0
$745$	9105.39	−	28023.5i	0.447779	−	1.37812i
$746$		0			0
$747$	491.427			0.0240701
$748$		0			0
$749$	19933.3			0.972426
$750$		0			0
$751$	3114.11	−	9584.26i	0.151312	−	0.465692i	−0.846456	−	0.532458i	$-0.821268\pi$
$751$	3114.11	−	9584.26i	0.151312	−	0.465692i	0.997769	+	0.0667666i	$0.0212683\pi$
$752$		0			0
$753$	9179.16	−	6669.05i	0.444233	−	0.322754i
$754$		0			0
$755$	12034.9	+	37039.6i	0.580125	+	1.78544i
$756$		0			0
$757$	500.634	+	363.732i	0.0240368	+	0.0174638i	0.599739	−	0.800196i	$-0.295271\pi$
$757$	500.634	+	363.732i	0.0240368	+	0.0174638i	−0.575702	+	0.817660i	$0.695271\pi$
$758$		0			0
$759$	20201.5	+	1370.66i	0.966100	+	0.0655491i
$760$		0			0
$761$	−5255.50	−	3818.34i	−0.250344	−	0.181886i	0.455535	−	0.890218i	$-0.349448\pi$
$761$	−5255.50	−	3818.34i	−0.250344	−	0.181886i	−0.705879	+	0.708332i	$0.749448\pi$
$762$		0			0
$763$	−5250.99	−	16160.9i	−0.249146	−	0.766794i
$764$		0			0
$765$	−2489.44	+	1808.68i	−0.117655	+	0.0854811i
$766$		0			0
$767$	−5312.60	+	16350.5i	−0.250100	+	0.769730i
$768$		0			0
$769$	30937.3			1.45075			0.725375	−	0.688354i	$-0.241666\pi$
$769$	30937.3			1.45075			0.725375	+	0.688354i	$0.241666\pi$
$770$		0			0
$771$	21315.8			0.995682
$772$		0			0
$773$	−605.321	+	1862.99i	−0.0281654	+	0.0866843i	−0.964151	−	0.265354i	$-0.914511\pi$
$773$	−605.321	+	1862.99i	−0.0281654	+	0.0866843i	0.935986	+	0.352038i	$0.114511\pi$
$774$		0			0
$775$	−3253.43	+	2363.76i	−0.150796	+	0.109560i
$776$		0			0
$777$	−2899.92	−	8925.04i	−0.133892	−	0.412077i
$778$		0			0
$779$	33926.5	+	24649.1i	1.56039	+	1.13369i
$780$		0			0
$781$	3914.24	+	3270.67i	0.179337	+	0.149851i
$782$		0			0
$783$	3387.53	+	2461.18i	0.154611	+	0.112331i
$784$		0			0
$785$	1807.01	+	5561.42i	0.0821593	+	0.252860i
$786$		0			0
$787$	19992.4	−	14525.4i	0.905532	−	0.657908i	−0.0343488	−	0.999410i	$-0.510936\pi$
$787$	19992.4	−	14525.4i	0.905532	−	0.657908i	0.939881	+	0.341502i	$0.110936\pi$
$788$		0			0
$789$	93.2968	−	287.138i	0.00420970	−	0.0129561i
$790$		0			0
$791$	−15132.5			−0.680214
$792$		0			0
$793$	−9045.59			−0.405067
$794$		0			0
$795$	3933.07	−	12104.7i	0.175461	−	0.540014i
$796$		0			0
$797$	147.480	−	107.151i	0.00655461	−	0.00476220i	−0.584503	−	0.811391i	$-0.698711\pi$
$797$	147.480	−	107.151i	0.00655461	−	0.00476220i	0.591058	+	0.806629i	$0.298711\pi$
$798$		0			0
$799$	3657.14	+	11255.5i	0.161928	+	0.498363i
$800$		0			0
$801$	−4040.80	−	2935.82i	−0.178246	−	0.129503i
$802$		0			0
$803$	7558.94	−	4745.11i	0.332191	−	0.208532i
$804$		0			0
$805$	−27321.3	−	19850.1i	−1.19621	−	0.869099i
$806$		0			0
$807$	2338.95	+	7198.53i	0.102026	+	0.314003i
$808$		0			0
$809$	33264.0	−	24167.7i	1.44561	−	1.05030i	0.458778	−	0.888551i	$-0.348287\pi$
$809$	33264.0	−	24167.7i	1.44561	−	1.05030i	0.986832	−	0.161747i	$-0.0517128\pi$
$810$		0			0
$811$	4563.83	−	14046.0i	0.197605	−	0.608166i	−0.802331	−	0.596879i	$-0.796407\pi$
$811$	4563.83	−	14046.0i	0.197605	−	0.608166i	0.999936	−	0.0112869i	$-0.00359279\pi$
$812$		0			0
$813$	16300.8			0.703189
$814$		0			0
$815$	−1538.83			−0.0661387
$816$		0			0
$817$	7888.65	−	24278.8i	0.337808	−	1.03967i
$818$		0			0
$819$	−6720.15	+	4882.47i	−0.286717	+	0.208312i
$820$		0			0
$821$	−4221.09	−	12991.2i	−0.179436	−	0.552248i	0.820372	−	0.571830i	$-0.193766\pi$
$821$	−4221.09	−	12991.2i	−0.179436	−	0.552248i	−0.999808	+	0.0195823i	$0.993766\pi$
$822$		0			0
$823$	10717.4	+	7786.61i	0.453929	+	0.329799i	0.791145	−	0.611629i	$-0.209485\pi$
$823$	10717.4	+	7786.61i	0.453929	+	0.329799i	−0.337216	+	0.941427i	$0.609485\pi$
$824$		0			0
$825$	579.288	−	1442.37i	0.0244463	−	0.0608688i
$826$		0			0
$827$	8174.05	+	5938.79i	0.343700	+	0.249712i	0.746221	−	0.665698i	$-0.231866\pi$
$827$	8174.05	+	5938.79i	0.343700	+	0.249712i	−0.402522	+	0.915411i	$0.631866\pi$
$828$		0			0
$829$	−7469.61	−	22989.1i	−0.312943	−	0.963141i	−0.976593	−	0.215097i	$-0.930993\pi$
$829$	−7469.61	−	22989.1i	−0.312943	−	0.963141i	0.663649	−	0.748044i	$-0.269007\pi$
$830$		0			0
$831$	9307.43	−	6762.25i	0.388533	−	0.282286i
$832$		0			0
$833$	927.846	−	2855.62i	0.0385930	−	0.118777i
$834$		0			0
$835$	13008.2			0.539123
$836$		0			0
$837$	−7645.57			−0.315734
$838$		0			0
$839$	−9834.13	+	30266.3i	−0.404663	+	1.24542i	0.516514	+	0.856279i	$0.327229\pi$
$839$	−9834.13	+	30266.3i	−0.404663	+	1.24542i	−0.921177	+	0.389145i	$0.872771\pi$
$840$		0			0
$841$	273.902	−	199.001i	0.0112305	−	0.00815947i
$842$		0			0
$843$	2083.48	+	6412.30i	0.0851233	+	0.261983i
$844$		0			0
$845$	12994.8	+	9441.31i	0.529037	+	0.384368i
$846$		0			0
$847$	14872.7	+	14244.0i	0.603343	+	0.577839i
$848$		0			0
$849$	−2201.20	−	1599.27i	−0.0889812	−	0.0646486i
$850$		0			0
$851$	−11558.1	−	35572.2i	−0.465578	−	1.43290i
$852$		0			0
$853$	9955.28	−	7232.94i	0.399604	−	0.290329i	−0.369776	−	0.929121i	$-0.620565\pi$
$853$	9955.28	−	7232.94i	0.399604	−	0.290329i	0.769380	+	0.638792i	$0.220565\pi$
$854$		0			0
$855$	−4675.11	+	14388.5i	−0.187001	+	0.575529i
$856$		0			0
$857$	−39962.7			−1.59288			−0.796441	−	0.604717i	$-0.793286\pi$
$857$	−39962.7			−1.59288			−0.796441	+	0.604717i	$0.793286\pi$
$858$		0			0
$859$	−19713.0			−0.783001			−0.391501	−	0.920178i	$-0.628044\pi$
$859$	−19713.0			−0.783001			−0.391501	+	0.920178i	$0.628044\pi$
$860$		0			0
$861$	−4221.73	+	12993.1i	−0.167104	+	0.514292i
$862$		0			0
$863$	−38883.0	+	28250.2i	−1.53371	+	1.11431i	−0.579582	+	0.814914i	$0.696784\pi$
$863$	−38883.0	+	28250.2i	−1.53371	+	1.11431i	−0.954130	+	0.299393i	$0.903216\pi$
$864$		0			0
$865$	3396.89	+	10454.6i	0.133523	+	0.410943i
$866$		0			0
$867$	−9885.95	−	7182.56i	−0.387248	−	0.281352i
$868$		0			0
$869$	−7650.34	+	19048.6i	−0.298642	+	0.743588i
$870$		0			0
$871$	−39888.7	−	28980.8i	−1.55175	−	1.12741i
$872$		0			0
$873$	401.047	+	1234.30i	0.0155480	+	0.0478517i
$874$		0			0
$875$	16363.0	−	11888.4i	0.632195	−	0.459317i
$876$		0			0
$877$	11169.4	−	34375.8i	0.430061	−	1.32359i	−0.468004	−	0.883727i	$-0.655027\pi$
$877$	11169.4	−	34375.8i	0.430061	−	1.32359i	0.898064	−	0.439864i	$-0.144973\pi$
$878$		0			0
$879$	8557.17			0.328357
$880$		0			0
$881$	−5409.60			−0.206872			−0.103436	−	0.994636i	$-0.532984\pi$
$881$	−5409.60			−0.206872			−0.103436	+	0.994636i	$0.532984\pi$
$882$		0			0
$883$	11320.6	−	34841.3i	0.431448	−	1.32786i	−0.465234	−	0.885188i	$-0.654030\pi$
$883$	11320.6	−	34841.3i	0.431448	−	1.32786i	0.896683	−	0.442674i	$-0.145970\pi$
$884$		0			0
$885$	−8252.73	+	5995.96i	−0.313460	+	0.227742i
$886$		0			0
$887$	−6570.05	−	20220.5i	−0.248704	−	0.765433i	−0.995005	−	0.0998242i	$-0.968172\pi$
$887$	−6570.05	−	20220.5i	−0.248704	−	0.765433i	0.746301	−	0.665609i	$-0.231828\pi$
$888$		0			0
$889$	−34624.2	−	25155.9i	−1.30625	−	0.949047i
$890$		0			0
$891$	2502.83	−	1571.15i	0.0941056	−	0.0590746i
$892$		0			0
$893$	47074.3	+	34201.4i	1.76403	+	1.28164i
$894$		0			0
$895$	13663.3	+	42051.5i	0.510297	+	1.57053i
$896$		0			0
$897$	−26784.2	+	19459.9i	−0.996989	+	0.724355i
$898$		0			0
$899$	13570.3	−	41765.1i	0.503443	−	1.54944i
$900$		0			0
$901$	−10420.4			−0.385299
$902$		0			0
$903$	8316.62			0.306489
$904$		0			0
$905$	−16730.0	+	51489.5i	−0.614500	+	1.89124i
$906$		0			0
$907$	5888.70	−	4278.39i	0.215580	−	0.156628i	−0.474755	−	0.880118i	$-0.657463\pi$
$907$	5888.70	−	4278.39i	0.215580	−	0.156628i	0.690335	+	0.723490i	$0.257463\pi$
$908$		0			0
$909$	−3786.78	−	11654.5i	−0.138173	−	0.425253i
$910$		0			0
$911$	24919.6	+	18105.2i	0.906283	+	0.658453i	0.940072	−	0.340976i	$-0.110758\pi$
$911$	24919.6	+	18105.2i	0.906283	+	0.658453i	−0.0337894	+	0.999429i	$0.510758\pi$
$912$		0			0
$913$	1528.66	+	1277.32i	0.0554121	+	0.0463014i
$914$		0			0
$915$	−4342.20	−	3154.79i	−0.156884	−	0.113983i
$916$		0			0
$917$	1318.18	+	4056.93i	0.0474700	+	0.146098i
$918$		0			0
$919$	−34484.2	+	25054.2i	−1.23779	+	0.899306i	−0.997449	−	0.0713830i	$-0.977259\pi$
$919$	−34484.2	+	25054.2i	−1.23779	+	0.899306i	−0.240339	+	0.970689i	$0.577259\pi$
$920$		0			0
$921$	1010.04	−	3108.60i	0.0361369	−	0.111218i
$922$		0			0
$923$	−8340.29			−0.297426
$924$		0			0
$925$	−2871.25			−0.102061
$926$		0			0
$927$	1442.43	−	4439.34i	0.0511063	−	0.157289i
$928$		0			0
$929$	43617.2	−	31689.8i	1.54040	−	1.11917i	0.590323	−	0.807167i	$-0.299001\pi$
$929$	43617.2	−	31689.8i	1.54040	−	1.11917i	0.950082	−	0.312002i	$-0.100999\pi$
$930$		0			0
$931$	−4561.86	−	14040.0i	−0.160590	−	0.494244i
$932$		0			0
$933$	14623.3	+	10624.4i	0.513124	+	0.372806i
$934$		0			0
$935$	−12444.9	−	844.379i	−0.435287	−	0.0295338i
$936$		0			0
$937$	18126.9	+	13169.9i	0.631995	+	0.459171i	0.857091	−	0.515166i	$-0.172270\pi$
$937$	18126.9	+	13169.9i	0.631995	+	0.459171i	−0.225096	+	0.974337i	$0.572270\pi$
$938$		0			0
$939$	8545.04	+	26298.9i	0.296972	+	0.913987i
$940$		0			0
$941$	−7153.87	+	5197.59i	−0.247832	+	0.180060i	−0.704765	−	0.709441i	$-0.748948\pi$
$941$	−7153.87	+	5197.59i	−0.247832	+	0.180060i	0.456934	+	0.889501i	$0.348948\pi$
$942$		0			0
$943$	−16826.4	+	51786.2i	−0.581063	+	1.78833i
$944$		0			0
$945$	−4928.74			−0.169664
$946$		0			0
$947$	−37683.8			−1.29309			−0.646546	−	0.762875i	$-0.723787\pi$
$947$	−37683.8			−1.29309			−0.646546	+	0.762875i	$0.723787\pi$
$948$		0			0
$949$	−4509.46	+	13878.7i	−0.154250	+	0.474733i
$950$		0			0
$951$	−1738.25	+	1262.91i	−0.0592708	+	0.0430627i
$952$		0			0
$953$	−6886.14	−	21193.4i	−0.234065	−	0.720379i	−0.997244	−	0.0741912i	$-0.976362\pi$
$953$	−6886.14	−	21193.4i	−0.234065	−	0.720379i	0.763179	−	0.646187i	$-0.223638\pi$
$954$		0			0
$955$	−7574.16	−	5502.95i	−0.256643	−	0.186462i
$956$		0			0
$957$	4140.31	+	16460.8i	0.139851	+	0.556011i
$958$		0			0
$959$	−7605.61	−	5525.80i	−0.256098	−	0.186066i
$960$		0			0
$961$	15572.5	+	47927.3i	0.522726	+	1.60878i
$962$		0			0
$963$	9380.56	−	6815.38i	0.313899	−	0.228061i
$964$		0			0
$965$	−1607.55	+	4947.54i	−0.0536259	+	0.165044i
$966$		0			0
$967$	−4416.02			−0.146856			−0.0734279	−	0.997301i	$-0.523394\pi$
$967$	−4416.02			−0.146856			−0.0734279	+	0.997301i	$0.523394\pi$
$968$		0			0
$969$	12386.4			0.410639
$970$		0			0
$971$	−1612.77	+	4963.61i	−0.0533022	+	0.164047i	−0.974164	−	0.225842i	$-0.927487\pi$
$971$	−1612.77	+	4963.61i	−0.0533022	+	0.164047i	0.920862	+	0.389889i	$0.127487\pi$
$972$		0			0
$973$	25379.4	−	18439.2i	0.836202	−	0.607537i
$974$		0			0
$975$	785.363	+	2417.10i	0.0257966	+	0.0793939i
$976$		0			0
$977$	−31023.8	−	22540.1i	−1.01590	−	0.738098i	−0.0504656	−	0.998726i	$-0.516071\pi$
$977$	−31023.8	−	22540.1i	−1.01590	−	0.738098i	−0.965439	+	0.260628i	$0.916071\pi$
$978$		0			0
$979$	−4938.76	−	19635.2i	−0.161229	−	0.641005i
$980$		0			0
$981$	−7996.67	−	5809.92i	−0.260259	−	0.189089i
$982$		0			0
$983$	4230.45	+	13020.0i	0.137264	+	0.422455i	0.995935	−	0.0900716i	$-0.0287096\pi$
$983$	4230.45	+	13020.0i	0.137264	+	0.422455i	−0.858671	+	0.512527i	$0.828710\pi$
$984$		0			0
$985$	−18568.3	+	13490.6i	−0.600644	+	0.436393i
$986$		0			0
$987$	−5857.80	+	18028.5i	−0.188912	+	0.581410i
$988$		0			0
$989$	33147.2			1.06574
$990$		0			0
$991$	−14149.5			−0.453555			−0.226778	−	0.973947i	$-0.572819\pi$
$991$	−14149.5			−0.453555			−0.226778	+	0.973947i	$0.572819\pi$
$992$		0			0
$993$	−549.663	+	1691.69i	−0.0175660	+	0.0540625i
$994$		0			0
$995$	11516.8	−	8367.41i	0.366940	−	0.266598i
$996$		0			0
$997$	1568.11	+	4826.14i	0.0498120	+	0.153305i	0.972868	−	0.231359i	$-0.0743172\pi$
$997$	1568.11	+	4826.14i	0.0498120	+	0.153305i	−0.923056	+	0.384664i	$0.874317\pi$
$998$		0			0
$999$	−4416.25	−	3208.59i	−0.139864	−	0.101617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.4.i.a.37.1	yes	4
3.2	odd	2		396.4.j.a.37.1		4
11.3	even	5	inner	132.4.i.a.25.1	✓	4
11.5	even	5		1452.4.a.l.1.1		2
11.6	odd	10		1452.4.a.m.1.1		2
33.14	odd	10		396.4.j.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.4.i.a.25.1	✓	4	11.3	even	5	inner
132.4.i.a.37.1	yes	4	1.1	even	1	trivial
396.4.j.a.37.1		4	3.2	odd	2
396.4.j.a.289.1		4	33.14	odd	10
1452.4.a.l.1.1		2	11.5	even	5
1452.4.a.m.1.1		2	11.6	odd	10

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	132.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.927051 + 2.85317i) q^{3} +(9.54508 - 6.93491i) q^{5} +(-4.78115 - 14.7149i) q^{7} +(-7.28115 - 5.29007i) q^{9} +(-8.89919 - 35.3808i) q^{11} +(48.2599 + 35.0628i) q^{13} +(10.9377 + 33.6628i) q^{15} +(23.4443 - 17.0333i) q^{17} +(44.0279 - 135.504i) q^{19} +46.4164 q^{21} +185.000 q^{23} +(4.38854 - 13.5065i) q^{25} +(21.8435 - 15.8702i) q^{27} +(47.9230 + 147.492i) q^{29} +(-229.089 - 166.443i) q^{31} +(109.198 + 7.40896i) q^{33} +(-147.683 - 107.298i) q^{35} +(-62.4762 - 192.282i) q^{37} +(-144.780 + 105.189i) q^{39} +(-90.9534 + 279.926i) q^{41} +179.174 q^{43} -106.185 q^{45} +(-126.201 + 388.407i) q^{47} +(83.8247 - 60.9022i) q^{49} +(26.8647 + 82.6812i) q^{51} +(-290.913 - 211.361i) q^{53} +(-330.307 - 275.998i) q^{55} +(345.799 + 251.238i) q^{57} +(89.0592 + 274.096i) q^{59} +(-122.678 + 89.1307i) q^{61} +(-43.0304 + 132.434i) q^{63} +703.802 q^{65} -826.540 q^{67} +(-171.504 + 527.836i) q^{69} +(-113.112 + 82.1810i) q^{71} +(75.5956 + 232.659i) q^{73} +(34.4681 + 25.0425i) q^{75} +(-478.076 + 300.112i) q^{77} +(-455.201 - 330.723i) q^{79} +(25.0304 + 77.0356i) q^{81} +(-44.1747 + 32.0948i) q^{83} +(105.653 - 325.168i) q^{85} -465.246 q^{87} +554.967 q^{89} +(285.208 - 877.779i) q^{91} +(687.266 - 499.328i) q^{93} +(-519.457 - 1598.72i) q^{95} +(-116.662 - 84.7596i) q^{97} +(-122.371 + 304.691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 27 q^{5} + q^{7} - 9 q^{9} - 11 q^{11} + 79 q^{13} + 84 q^{15} + 58 q^{17} + 194 q^{19} + 132 q^{21} + 740 q^{23} - 54 q^{25} + 27 q^{27} + 62 q^{29} - 572 q^{31} + 363 q^{33} - 347 q^{35}+ \cdots + 396 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 + 27 * q^5 + q^7 - 9 * q^9 - 11 * q^11 + 79 * q^13 + 84 * q^15 + 58 * q^17 + 194 * q^19 + 132 * q^21 + 740 * q^23 - 54 * q^25 + 27 * q^27 + 62 * q^29 - 572 * q^31 + 363 * q^33 - 347 * q^35 - 355 * q^37 - 237 * q^39 - 53 * q^41 - 616 * q^43 + 18 * q^45 + 289 * q^47 - 18 * q^49 + 141 * q^51 - 466 * q^53 - 1518 * q^55 + 813 * q^57 - 328 * q^59 - 645 * q^61 + 9 * q^63 + 682 * q^65 - 1486 * q^67 + 555 * q^69 - 3 * q^71 - 1482 * q^73 - 3 * q^75 - 1199 * q^77 - 1027 * q^79 - 81 * q^81 + 313 * q^83 - 161 * q^85 - 1056 * q^87 + 1236 * q^89 + 271 * q^91 + 1716 * q^93 + 317 * q^95 - 129 * q^97 + 396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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