LMFDB - Embedded newform 756.2.bq.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67230 - 0.451029i) q^{3} +(-0.947523 - 0.344870i) q^{5} +(-1.17643 + 2.36981i) q^{7} +(2.59315 + 1.50851i) q^{9} +O(q^{10})$	\(q+(-1.67230 - 0.451029i) q^{3} +(-0.947523 - 0.344870i) q^{5} +(-1.17643 + 2.36981i) q^{7} +(2.59315 + 1.50851i) q^{9} +(0.596107 - 0.216965i) q^{11} +(-0.610174 - 3.46047i) q^{13} +(1.42899 + 1.00409i) q^{15} -3.33094 q^{17} +5.81068 q^{19} +(3.03620 - 3.43242i) q^{21} +(0.754298 + 4.27784i) q^{23} +(-3.05136 - 2.56039i) q^{25} +(-3.65612 - 3.69226i) q^{27} +(1.01927 - 5.78056i) q^{29} +(6.70505 - 5.62620i) q^{31} +(-1.09473 + 0.0939683i) q^{33} +(1.93197 - 1.83974i) q^{35} +(1.51899 - 2.63097i) q^{37} +(-0.540381 + 6.06213i) q^{39} +(-1.55472 - 8.81728i) q^{41} +(3.41330 + 2.86410i) q^{43} +(-1.93683 - 2.32365i) q^{45} +(-8.14252 - 6.83238i) q^{47} +(-4.23202 - 5.57584i) q^{49} +(5.57032 + 1.50235i) q^{51} +(0.793989 - 1.37523i) q^{53} -0.639650 q^{55} +(-9.71717 - 2.62078i) q^{57} +(-2.19256 - 12.4346i) q^{59} +(-1.20617 - 1.01209i) q^{61} +(-6.62554 + 4.37061i) q^{63} +(-0.615259 + 3.48931i) q^{65} +(14.0966 + 5.13076i) q^{67} +(0.668020 - 7.49402i) q^{69} +(-2.10682 - 3.64912i) q^{71} +(3.74743 + 6.49074i) q^{73} +(3.94796 + 5.65799i) q^{75} +(-0.187113 + 1.66791i) q^{77} +(-2.51140 + 0.914074i) q^{79} +(4.44881 + 7.82356i) q^{81} +(-0.252308 + 1.43091i) q^{83} +(3.15614 + 1.14874i) q^{85} +(-4.31172 + 9.20709i) q^{87} +11.0559 q^{89} +(8.91849 + 2.62501i) q^{91} +(-13.7504 + 6.38450i) q^{93} +(-5.50575 - 2.00393i) q^{95} +(1.02710 + 0.861841i) q^{97} +(1.87309 + 0.336610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.67230	−	0.451029i	−0.965500	−	0.260402i
$3$	−1.67230	−	0.451029i	−0.965500	−	0.260402i
$4$		0			0
$5$	−0.947523	−	0.344870i	−0.423745	−	0.154231i	0.121341	−	0.992611i	$-0.461281\pi$
$5$	−0.947523	−	0.344870i	−0.423745	−	0.154231i	−0.545086	+	0.838380i	$0.683503\pi$
$6$		0			0
$7$	−1.17643	+	2.36981i	−0.444649	+	0.895705i
$7$	−1.17643	+	2.36981i	−0.444649	+	0.895705i
$8$		0			0
$9$	2.59315	+	1.50851i	0.864382	+	0.502836i
$10$		0			0
$11$	0.596107	−	0.216965i	0.179733	−	0.0654175i	−0.250586	−	0.968094i	$-0.580623\pi$
$11$	0.596107	−	0.216965i	0.179733	−	0.0654175i	0.430319	+	0.902677i	$0.358401\pi$
$12$		0			0
$13$	−0.610174	−	3.46047i	−0.169232	−	0.959762i	−0.944593	−	0.328244i	$-0.893543\pi$
$13$	−0.610174	−	3.46047i	−0.169232	−	0.959762i	0.775361	−	0.631518i	$-0.217568\pi$
$14$		0			0
$15$	1.42899	+	1.00409i	0.368964	+	0.259254i
$16$		0			0
$17$	−3.33094			−0.807871			−0.403936	−	0.914787i	$-0.632358\pi$
$17$	−3.33094			−0.807871			−0.403936	+	0.914787i	$0.632358\pi$
$18$		0			0
$19$	5.81068			1.33306			0.666530	−	0.745478i	$-0.267779\pi$
$19$	5.81068			1.33306			0.666530	+	0.745478i	$0.267779\pi$
$20$		0			0
$21$	3.03620	−	3.43242i	0.662552	−	0.749016i
$22$		0			0
$23$	0.754298	+	4.27784i	0.157282	+	0.891991i	0.956670	+	0.291175i	$0.0940463\pi$
$23$	0.754298	+	4.27784i	0.157282	+	0.891991i	−0.799388	+	0.600816i	$0.794843\pi$
$24$		0			0
$25$	−3.05136	−	2.56039i	−0.610271	−	0.512079i
$26$		0			0
$27$	−3.65612	−	3.69226i	−0.703621	−	0.710575i
$28$		0			0
$29$	1.01927	−	5.78056i	0.189274	−	1.07342i	−0.731067	−	0.682306i	$-0.760977\pi$
$29$	1.01927	−	5.78056i	0.189274	−	1.07342i	0.920341	−	0.391118i	$-0.127912\pi$
$30$		0			0
$31$	6.70505	−	5.62620i	1.20426	−	1.01050i	0.204764	−	0.978811i	$-0.434357\pi$
$31$	6.70505	−	5.62620i	1.20426	−	1.01050i	0.999498	−	0.0316849i	$-0.0100873\pi$
$32$		0			0
$33$	−1.09473	+	0.0939683i	−0.190567	+	0.0163578i
$34$		0			0
$35$	1.93197	−	1.83974i	0.326563	−	0.310972i
$36$		0			0
$37$	1.51899	−	2.63097i	0.249720	−	0.432529i	−0.713728	−	0.700423i	$-0.752995\pi$
$37$	1.51899	−	2.63097i	0.249720	−	0.432529i	0.963448	+	0.267895i	$0.0863279\pi$
$38$		0			0
$39$	−0.540381	+	6.06213i	−0.0865302	+	0.970718i
$40$		0			0
$41$	−1.55472	−	8.81728i	−0.242807	−	1.37703i	−0.825531	−	0.564357i	$-0.809124\pi$
$41$	−1.55472	−	8.81728i	−0.242807	−	1.37703i	0.582723	−	0.812671i	$-0.301987\pi$
$42$		0			0
$43$	3.41330	+	2.86410i	0.520524	+	0.436771i	0.864814	−	0.502092i	$-0.167436\pi$
$43$	3.41330	+	2.86410i	0.520524	+	0.436771i	−0.344291	+	0.938863i	$0.611881\pi$
$44$		0			0
$45$	−1.93683	−	2.32365i	−0.288725	−	0.346389i
$46$		0			0
$47$	−8.14252	−	6.83238i	−1.18771	−	0.996605i	−0.999896	−	0.0144003i	$-0.995416\pi$
$47$	−8.14252	−	6.83238i	−1.18771	−	0.996605i	−0.187812	−	0.982205i	$-0.560139\pi$
$48$		0			0
$49$	−4.23202	−	5.57584i	−0.604574	−	0.796549i
$50$		0			0
$51$	5.57032	+	1.50235i	0.780000	+	0.210371i
$52$		0			0
$53$	0.793989	−	1.37523i	0.109063	−	0.188902i	−0.806328	−	0.591469i	$-0.798548\pi$
$53$	0.793989	−	1.37523i	0.109063	−	0.188902i	0.915391	+	0.402566i	$0.131882\pi$
$54$		0			0
$55$	−0.639650			−0.0862504
$56$		0			0
$57$	−9.71717	−	2.62078i	−1.28707	−	0.347131i
$58$		0			0
$59$	−2.19256	−	12.4346i	−0.285447	−	1.61885i	−0.703685	−	0.710512i	$-0.748463\pi$
$59$	−2.19256	−	12.4346i	−0.285447	−	1.61885i	0.418238	−	0.908338i	$-0.362648\pi$
$60$		0			0
$61$	−1.20617	−	1.01209i	−0.154434	−	0.129585i	0.562297	−	0.826935i	$-0.309918\pi$
$61$	−1.20617	−	1.01209i	−0.154434	−	0.129585i	−0.716731	+	0.697350i	$0.754362\pi$
$62$		0			0
$63$	−6.62554	+	4.37061i	−0.834740	+	0.550645i
$64$		0			0
$65$	−0.615259	+	3.48931i	−0.0763135	+	0.432795i
$66$		0			0
$67$	14.0966	+	5.13076i	1.72218	+	0.626822i	0.998025	−	0.0628164i	$-0.0200082\pi$
$67$	14.0966	+	5.13076i	1.72218	+	0.626822i	0.724154	+	0.689638i	$0.242230\pi$
$68$		0			0
$69$	0.668020	−	7.49402i	0.0804202	−	0.902174i
$70$		0			0
$71$	−2.10682	−	3.64912i	−0.250033	−	0.433071i	0.713501	−	0.700654i	$-0.247108\pi$
$71$	−2.10682	−	3.64912i	−0.250033	−	0.433071i	−0.963535	+	0.267583i	$0.913775\pi$
$72$		0			0
$73$	3.74743	+	6.49074i	0.438603	+	0.759683i	0.997582	−	0.0694987i	$-0.0221400\pi$
$73$	3.74743	+	6.49074i	0.438603	+	0.759683i	−0.558979	+	0.829182i	$0.688807\pi$
$74$		0			0
$75$	3.94796	+	5.65799i	0.455871	+	0.653328i
$76$		0			0
$77$	−0.187113	+	1.66791i	−0.0213235	+	0.190076i
$78$		0			0
$79$	−2.51140	+	0.914074i	−0.282554	+	0.102841i	−0.479410	−	0.877591i	$-0.659149\pi$
$79$	−2.51140	+	0.914074i	−0.282554	+	0.102841i	0.196855	+	0.980433i	$0.436927\pi$
$80$		0			0
$81$	4.44881	+	7.82356i	0.494312	+	0.869285i
$82$		0			0
$83$	−0.252308	+	1.43091i	−0.0276944	+	0.157063i	−0.995519	−	0.0945638i	$-0.969854\pi$
$83$	−0.252308	+	1.43091i	−0.0276944	+	0.157063i	0.967824	+	0.251627i	$0.0809655\pi$
$84$		0			0
$85$	3.15614	+	1.14874i	0.342332	+	0.124599i
$86$		0			0
$87$	−4.31172	+	9.20709i	−0.462265	+	0.987104i
$88$		0			0
$89$	11.0559			1.17193			0.585963	−	0.810338i	$-0.300716\pi$
$89$	11.0559			1.17193			0.585963	+	0.810338i	$0.300716\pi$
$90$		0			0
$91$	8.91849	+	2.62501i	0.934912	+	0.275176i
$92$		0			0
$93$	−13.7504	+	6.38450i	−1.42585	+	0.662042i
$94$		0			0
$95$	−5.50575	−	2.00393i	−0.564878	−	0.205599i
$96$		0			0
$97$	1.02710	+	0.861841i	0.104286	+	0.0875067i	0.693440	−	0.720514i	$-0.256094\pi$
$97$	1.02710	+	0.861841i	0.104286	+	0.0875067i	−0.589154	+	0.808021i	$0.700539\pi$
$98$		0			0
$99$	1.87309	+	0.336610i	0.188252	+	0.0338306i
$100$		0			0
$101$	0.901312	−	5.11160i	0.0896839	−	0.508623i	−0.906563	−	0.422070i	$-0.861304\pi$
$101$	0.901312	−	5.11160i	0.0896839	−	0.508623i	0.996247	−	0.0865530i	$-0.0275852\pi$
$102$		0			0
$103$	2.39033	+	0.870009i	0.235526	+	0.0857246i	0.457087	−	0.889422i	$-0.348893\pi$
$103$	2.39033	+	0.870009i	0.235526	+	0.0857246i	−0.221561	+	0.975147i	$0.571115\pi$
$104$		0			0
$105$	−4.06061	+	2.20520i	−0.396275	+	0.215206i
$106$		0			0
$107$	1.14327	+	1.98021i	0.110524	+	0.191434i	0.915982	−	0.401220i	$-0.131414\pi$
$107$	1.14327	+	1.98021i	0.110524	+	0.191434i	−0.805457	+	0.592654i	$0.798080\pi$
$108$		0			0
$109$	3.54658	−	6.14286i	0.339701	−	0.588380i	−0.644675	−	0.764457i	$-0.723007\pi$
$109$	3.54658	−	6.14286i	0.339701	−	0.588380i	0.984376	+	0.176077i	$0.0563407\pi$
$110$		0			0
$111$	−3.72684	+	3.71465i	−0.353736	+	0.352579i
$112$		0			0
$113$	3.60805	−	3.02751i	0.339417	−	0.284804i	−0.457107	−	0.889412i	$-0.651114\pi$
$113$	3.60805	−	3.02751i	0.339417	−	0.284804i	0.796524	+	0.604607i	$0.206670\pi$
$114$		0			0
$115$	0.760584	−	4.31349i	0.0709248	−	0.402235i
$116$		0			0
$117$	3.63788	−	9.89395i	0.336322	−	0.914696i
$118$		0			0
$119$	3.91862	−	7.89370i	0.359220	−	0.723614i
$120$		0			0
$121$	−8.11822	+	6.81199i	−0.738020	+	0.619272i
$122$		0			0
$123$	−1.37689	+	15.4463i	−0.124150	+	1.39275i
$124$		0			0
$125$	4.52906	+	7.84456i	0.405092	+	0.701639i
$126$		0			0
$127$	2.60196	−	4.50673i	0.230887	−	0.399908i	−0.727183	−	0.686444i	$-0.759171\pi$
$127$	2.60196	−	4.50673i	0.230887	−	0.399908i	0.958069	+	0.286536i	$0.0925040\pi$
$128$		0			0
$129$	−4.41626	−	6.32912i	−0.388830	−	0.557248i
$130$		0			0
$131$	3.95409	+	22.4248i	0.345470	+	1.95926i	0.273586	+	0.961847i	$0.411790\pi$
$131$	3.95409	+	22.4248i	0.345470	+	1.95926i	0.0718840	+	0.997413i	$0.477099\pi$
$132$		0			0
$133$	−6.83586	+	13.7702i	−0.592745	+	1.19403i
$134$		0			0
$135$	2.19091	+	4.75939i	0.188564	+	0.409623i
$136$		0			0
$137$	−11.3918	−	9.55888i	−0.973270	−	0.816671i	0.00979036	−	0.999952i	$-0.496884\pi$
$137$	−11.3918	−	9.55888i	−0.973270	−	0.816671i	−0.983060	+	0.183281i	$0.941328\pi$
$138$		0			0
$139$	−14.4733	−	5.26786i	−1.22761	−	0.446814i	−0.354832	−	0.934930i	$-0.615462\pi$
$139$	−14.4733	−	5.26786i	−1.22761	−	0.446814i	−0.872779	+	0.488116i	$0.837684\pi$
$140$		0			0
$141$	10.5351	+	15.0983i	0.887215	+	1.27150i
$142$		0			0
$143$	−1.11453	−	1.93042i	−0.0932017	−	0.161430i
$144$		0			0
$145$	−2.95933	+	5.12570i	−0.245759	+	0.425666i
$146$		0			0
$147$	4.56231	+	11.2332i	0.376293	+	0.926501i
$148$		0			0
$149$	−14.3687	+	12.0568i	−1.17713	+	0.987732i	−0.177140	+	0.984186i	$0.556684\pi$
$149$	−14.3687	+	12.0568i	−1.17713	+	0.987732i	−0.999994	+	0.00354666i	$0.998871\pi$
$150$		0			0
$151$	10.0483	−	3.65728i	0.817718	−	0.297625i	0.100910	−	0.994896i	$-0.467825\pi$
$151$	10.0483	−	3.65728i	0.817718	−	0.297625i	0.716808	+	0.697271i	$0.245602\pi$
$152$		0			0
$153$	−8.63761	−	5.02475i	−0.698309	−	0.406227i
$154$		0			0
$155$	−8.29350	+	3.01859i	−0.666150	+	0.242459i
$156$		0			0
$157$	−0.339744	−	1.92678i	−0.0271145	−	0.153774i	0.968245	−	0.250005i	$-0.0804323\pi$
$157$	−0.339744	−	1.92678i	−0.0271145	−	0.153774i	−0.995359	+	0.0962311i	$0.969321\pi$
$158$		0			0
$159$	−1.94805	+	1.94168i	−0.154491	+	0.153985i
$160$		0			0
$161$	−11.0251	−	3.24504i	−0.868896	−	0.255745i
$162$		0			0
$163$	4.83127	+	8.36801i	0.378415	+	0.655433i	0.990832	−	0.135101i	$-0.0431360\pi$
$163$	4.83127	+	8.36801i	0.378415	+	0.655433i	−0.612417	+	0.790535i	$0.709803\pi$
$164$		0			0
$165$	1.06968	+	0.288501i	0.0832748	+	0.0224598i
$166$		0			0
$167$	−15.3701	+	12.8970i	−1.18937	+	0.998004i	−0.189504	+	0.981880i	$0.560688\pi$
$167$	−15.3701	+	12.8970i	−1.18937	+	0.998004i	−0.999870	+	0.0161237i	$0.994867\pi$
$168$		0			0
$169$	0.613468	−	0.223284i	0.0471898	−	0.0171757i
$170$		0			0
$171$	15.0679	+	8.76545i	1.15227	+	0.670311i
$172$		0			0
$173$	2.41226	−	13.6806i	0.183401	−	1.04012i	−0.744592	−	0.667519i	$-0.767356\pi$
$173$	2.41226	−	13.6806i	0.183401	−	1.04012i	0.927993	−	0.372598i	$-0.121533\pi$
$174$		0			0
$175$	9.65736	−	4.21901i	0.730028	−	0.318928i
$176$		0			0
$177$	−1.94177	+	21.7833i	−0.145952	+	1.63733i
$178$		0			0
$179$	15.2359			1.13878			0.569391	−	0.822067i	$-0.307179\pi$
$179$	15.2359			1.13878			0.569391	+	0.822067i	$0.307179\pi$
$180$		0			0
$181$	1.33050	−	2.30449i	0.0988950	−	0.171291i	−0.812333	−	0.583195i	$-0.801803\pi$
$181$	1.33050	−	2.30449i	0.0988950	−	0.171291i	0.911228	+	0.411903i	$0.135136\pi$
$182$		0			0
$183$	1.56058	+	2.23654i	0.115362	+	0.165330i
$184$		0			0
$185$	−2.34662	+	1.96905i	−0.172527	+	0.144767i
$186$		0			0
$187$	−1.98560	+	0.722698i	−0.145201	+	0.0528489i
$188$		0			0
$189$	13.0511	−	4.32064i	0.949330	−	0.314280i
$190$		0			0
$191$	−25.0096	+	9.10274i	−1.80963	+	0.658651i	−0.812497	+	0.582965i	$0.801892\pi$
$191$	−25.0096	+	9.10274i	−1.80963	+	0.658651i	−0.997132	+	0.0756856i	$0.975885\pi$
$192$		0			0
$193$	16.3067	−	13.6829i	1.17378	−	0.984917i	0.173778	−	0.984785i	$-0.444402\pi$
$193$	16.3067	−	13.6829i	1.17378	−	0.984917i	1.00000		0.000132296i	$-4.21110e-5\pi$
$194$		0			0
$195$	2.60267	−	5.55765i	0.186381	−	0.397992i
$196$		0			0
$197$	9.25595	−	16.0318i	0.659459	−	1.14222i	−0.321297	−	0.946979i	$-0.604119\pi$
$197$	9.25595	−	16.0318i	0.659459	−	1.14222i	0.980756	−	0.195238i	$-0.0625480\pi$
$198$		0			0
$199$	3.80600			0.269800			0.134900	−	0.990859i	$-0.456929\pi$
$199$	3.80600			0.269800			0.134900	+	0.990859i	$0.456929\pi$
$200$		0			0
$201$	−21.2596	−	14.9381i	−1.49954	−	1.05366i
$202$		0			0
$203$	12.4997	+	9.21592i	0.877310	+	0.646830i
$204$		0			0
$205$	−1.56768	+	8.89076i	−0.109492	+	0.620957i
$206$		0			0
$207$	−4.49715	+	12.2309i	−0.312573	+	0.850108i
$208$		0			0
$209$	3.46379	−	1.26071i	0.239595	−	0.0872055i
$210$		0			0
$211$	−8.93450	+	7.49693i	−0.615076	+	0.516110i	−0.896251	−	0.443546i	$-0.853720\pi$
$211$	−8.93450	+	7.49693i	−0.615076	+	0.516110i	0.281175	+	0.959656i	$0.409276\pi$
$212$		0			0
$213$	1.87737	+	7.05264i	0.128635	+	0.483239i
$214$		0			0
$215$	−2.24644	−	3.89095i	−0.153206	−	0.265360i
$216$		0			0
$217$	5.44501	+	22.5086i	0.369631	+	1.52798i
$218$		0			0
$219$	−3.33930	−	12.5446i	−0.225649	−	0.847688i
$220$		0			0
$221$	2.03245	+	11.5266i	0.136718	+	0.775364i
$222$		0			0
$223$	−6.30031	+	2.29313i	−0.421900	+	0.153559i	−0.544241	−	0.838929i	$-0.683182\pi$
$223$	−6.30031	+	2.29313i	−0.421900	+	0.153559i	0.122341	+	0.992488i	$0.460960\pi$
$224$		0			0
$225$	−4.05024	−	11.2425i	−0.270016	−	0.749498i
$226$		0			0
$227$	−16.3148	+	5.93812i	−1.08285	+	0.394127i	−0.820969	−	0.570972i	$-0.806566\pi$
$227$	−16.3148	+	5.93812i	−1.08285	+	0.394127i	−0.261885	+	0.965099i	$0.584344\pi$
$228$		0			0
$229$	9.89313	−	8.30132i	0.653756	−	0.548567i	−0.254452	−	0.967085i	$-0.581895\pi$
$229$	9.89313	−	8.30132i	0.653756	−	0.548567i	0.908208	+	0.418519i	$0.137451\pi$
$230$		0			0
$231$	1.06518	−	2.70484i	0.0700839	−	0.177965i
$232$		0			0
$233$	0.827062	−	1.43251i	0.0541826	−	0.0938470i	−0.837662	−	0.546189i	$-0.816078\pi$
$233$	0.827062	−	1.43251i	0.0541826	−	0.0938470i	0.891845	+	0.452342i	$0.149411\pi$
$234$		0			0
$235$	5.35894	+	9.28195i	0.349579	+	0.605488i
$236$		0			0
$237$	4.61207	−	0.395888i	0.299586	−	0.0257157i
$238$		0			0
$239$	−3.86954	−	1.40840i	−0.250300	−	0.0911018i	0.213823	−	0.976872i	$-0.431408\pi$
$239$	−3.86954	−	1.40840i	−0.250300	−	0.0911018i	−0.464123	+	0.885771i	$0.653631\pi$
$240$		0			0
$241$	−12.9224	−	10.8432i	−0.832403	−	0.698469i	0.123438	−	0.992352i	$-0.460608\pi$
$241$	−12.9224	−	10.8432i	−0.832403	−	0.698469i	−0.955841	+	0.293883i	$0.905052\pi$
$242$		0			0
$243$	−3.91106	−	15.0899i	−0.250895	−	0.968014i
$244$		0			0
$245$	2.08699	+	6.74274i	0.133333	+	0.430778i
$246$		0			0
$247$	−3.54552	−	20.1077i	−0.225596	−	1.27942i
$248$		0			0
$249$	1.06732	−	2.27911i	0.0676384	−	0.144433i
$250$		0			0
$251$	10.8078	−	18.7197i	0.682183	−	1.18158i	−0.292130	−	0.956379i	$-0.594364\pi$
$251$	10.8078	−	18.7197i	0.682183	−	1.18158i	0.974313	−	0.225197i	$-0.0723027\pi$
$252$		0			0
$253$	1.37778	+	2.38639i	0.0866206	+	0.150031i
$254$		0			0
$255$	−4.75989	−	3.34455i	−0.298076	−	0.209444i
$256$		0			0
$257$	7.71422	−	6.47300i	0.481200	−	0.403774i	−0.369660	−	0.929167i	$-0.620526\pi$
$257$	7.71422	−	6.47300i	0.481200	−	0.403774i	0.850860	+	0.525393i	$0.176082\pi$
$258$		0			0
$259$	4.44791	+	6.69488i	0.276380	+	0.415999i
$260$		0			0
$261$	11.3631	−	13.4523i	0.703361	−	0.832674i
$262$		0			0
$263$	3.71339	−	21.0597i	0.228977	−	1.29859i	−0.625957	−	0.779858i	$-0.715291\pi$
$263$	3.71339	−	21.0597i	0.228977	−	1.29859i	0.854934	−	0.518736i	$-0.173597\pi$
$264$		0			0
$265$	−1.22660	+	1.02924i	−0.0753493	+	0.0632256i
$266$		0			0
$267$	−18.4888	−	4.98655i	−1.13150	−	0.305172i
$268$		0			0
$269$	−5.86339	+	10.1557i	−0.357497	+	0.619203i	−0.987542	−	0.157356i	$-0.949703\pi$
$269$	−5.86339	+	10.1557i	−0.357497	+	0.619203i	0.630045	+	0.776559i	$0.283036\pi$
$270$		0			0
$271$	−1.39108	−	2.40942i	−0.0845021	−	0.146362i	0.820677	−	0.571393i	$-0.193597\pi$
$271$	−1.39108	−	2.40942i	−0.0845021	−	0.146362i	−0.905179	+	0.425031i	$0.860263\pi$
$272$		0			0
$273$	−13.7304	−	8.41229i	−0.831001	−	0.509135i
$274$		0			0
$275$	−2.37445	−	0.864230i	−0.143185	−	0.0521150i
$276$		0			0
$277$	0.606640	−	3.44043i	0.0364495	−	0.206715i	−0.961144	−	0.276047i	$-0.910976\pi$
$277$	0.606640	−	3.44043i	0.0364495	−	0.206715i	0.997594	+	0.0693315i	$0.0220866\pi$
$278$		0			0
$279$	25.8743	−	4.47494i	1.54906	−	0.267908i
$280$		0			0
$281$	16.6998	+	14.0128i	0.996229	+	0.835936i	0.986458	−	0.164016i	$-0.0524450\pi$
$281$	16.6998	+	14.0128i	0.996229	+	0.835936i	0.00977187	+	0.999952i	$0.496889\pi$
$282$		0			0
$283$	−6.11279	−	2.22487i	−0.363368	−	0.132255i	0.153883	−	0.988089i	$-0.450822\pi$
$283$	−6.11279	−	2.22487i	−0.363368	−	0.132255i	−0.517250	+	0.855834i	$0.673044\pi$
$284$		0			0
$285$	8.30341	+	5.83442i	0.491852	+	0.345601i
$286$		0			0
$287$	22.7243	+	6.68853i	1.34137	+	0.394811i
$288$		0			0
$289$	−5.90484			−0.347344
$290$		0			0
$291$	−1.32890	−	1.90451i	−0.0779017	−	0.111644i
$292$		0			0
$293$	16.5718	+	6.03166i	0.968138	+	0.352373i	0.777217	−	0.629232i	$-0.216631\pi$
$293$	16.5718	+	6.03166i	0.968138	+	0.352373i	0.190920	+	0.981606i	$0.438853\pi$
$294$		0			0
$295$	−2.21083	+	12.5382i	−0.128720	+	0.730005i
$296$		0			0
$297$	−2.98053	−	1.40773i	−0.172948	−	0.0816847i
$298$		0			0
$299$	14.3431	−	5.22045i	0.829481	−	0.301907i
$300$		0			0
$301$	−10.8029	+	4.71946i	−0.622668	+	0.272025i
$302$		0			0
$303$	−3.81274	+	8.14158i	−0.219036	+	0.467722i
$304$		0			0
$305$	0.793830	+	1.37495i	0.0454546	+	0.0787296i
$306$		0			0
$307$	−14.7224	−	25.4999i	−0.840252	−	1.45536i	−0.889682	−	0.456581i	$-0.849074\pi$
$307$	−14.7224	−	25.4999i	−0.840252	−	1.45536i	0.0494304	−	0.998778i	$-0.484259\pi$
$308$		0			0
$309$	−3.60494	−	2.53302i	−0.205078	−	0.144099i
$310$		0			0
$311$	−20.2876	−	7.38407i	−1.15040	−	0.418712i	−0.304743	−	0.952435i	$-0.598570\pi$
$311$	−20.2876	−	7.38407i	−1.15040	−	0.418712i	−0.845660	+	0.533722i	$0.820793\pi$
$312$		0			0
$313$	−4.61634	+	26.1806i	−0.260931	+	1.47981i	0.519445	+	0.854504i	$0.326139\pi$
$313$	−4.61634	+	26.1806i	−0.260931	+	1.47981i	−0.780376	+	0.625310i	$0.784973\pi$
$314$		0			0
$315$	7.78515	−	1.85630i	0.438643	−	0.104591i
$316$		0			0
$317$	−12.6570	−	10.6205i	−0.710886	−	0.596504i	0.213961	−	0.976842i	$-0.431363\pi$
$317$	−12.6570	−	10.6205i	−0.710886	−	0.596504i	−0.924848	+	0.380338i	$0.875808\pi$
$318$		0			0
$319$	−0.646588	−	3.66698i	−0.0362020	−	0.205312i
$320$		0			0
$321$	−1.01876	−	3.82714i	−0.0568616	−	0.213610i
$322$		0			0
$323$	−19.3550			−1.07694
$324$		0			0
$325$	−6.99830	+	12.1214i	−0.388196	+	0.672375i
$326$		0			0
$327$	−8.70155	+	8.67307i	−0.481197	+	0.479622i
$328$		0			0
$329$	25.7706	−	11.2584i	1.42078	−	0.620696i
$330$		0			0
$331$	−0.438203	−	0.367696i	−0.0240858	−	0.0202104i	0.630665	−	0.776055i	$-0.282782\pi$
$331$	−0.438203	−	0.367696i	−0.0240858	−	0.0202104i	−0.654751	+	0.755845i	$0.727227\pi$
$332$		0			0
$333$	7.90780	−	4.53107i	0.433345	−	0.248301i
$334$		0			0
$335$	−11.5875	−	9.72303i	−0.633090	−	0.531226i
$336$		0			0
$337$	−0.112195	−	0.636290i	−0.00611166	−	0.0346610i	0.981599	−	0.190952i	$-0.0611574\pi$
$337$	−0.112195	−	0.636290i	−0.00611166	−	0.0346610i	−0.987711	+	0.156291i	$0.950046\pi$
$338$		0			0
$339$	−7.39922	+	3.43556i	−0.401871	+	0.186594i
$340$		0			0
$341$	2.77624	−	4.80858i	0.150342	−	0.260399i
$342$		0			0
$343$	18.1924	−	3.46948i	0.982296	−	0.187334i
$344$		0			0
$345$	−3.21743	+	6.87038i	−0.173221	+	0.369889i
$346$		0			0
$347$	−16.8872	+	14.1700i	−0.906551	+	0.760686i	−0.971460	−	0.237205i	$-0.923769\pi$
$347$	−16.8872	+	14.1700i	−0.906551	+	0.760686i	0.0649091	+	0.997891i	$0.479324\pi$
$348$		0			0
$349$	3.92396	−	22.2539i	0.210045	−	1.19122i	−0.679256	−	0.733901i	$-0.737697\pi$
$349$	3.92396	−	22.2539i	0.210045	−	1.19122i	0.889301	−	0.457323i	$-0.151192\pi$
$350$		0			0
$351$	−10.5461	+	14.9048i	−0.562907	+	0.795561i
$352$		0			0
$353$	12.3792	+	10.3874i	0.658879	+	0.552865i	0.909750	−	0.415155i	$-0.136273\pi$
$353$	12.3792	+	10.3874i	0.658879	+	0.552865i	−0.250872	+	0.968020i	$0.580717\pi$
$354$		0			0
$355$	0.737788	+	4.18420i	0.0391577	+	0.222074i
$356$		0			0
$357$	−10.1134	+	11.4332i	−0.535257	+	0.605108i
$358$		0			0
$359$	17.1137			0.903226			0.451613	−	0.892214i	$-0.350849\pi$
$359$	17.1137			0.903226			0.451613	+	0.892214i	$0.350849\pi$
$360$		0			0
$361$	14.7639			0.777050
$362$		0			0
$363$	16.6485	−	7.73012i	0.873818	−	0.405726i
$364$		0			0
$365$	−1.31231	−	7.44250i	−0.0686896	−	0.389558i
$366$		0			0
$367$	−12.2440	+	4.45646i	−0.639133	+	0.232625i	−0.641202	−	0.767372i	$-0.721564\pi$
$367$	−12.2440	+	4.45646i	−0.639133	+	0.232625i	0.00206853	+	0.999998i	$0.499342\pi$
$368$		0			0
$369$	9.26932	−	25.2098i	0.482541	−	1.31237i
$370$		0			0
$371$	2.32496	+	3.49947i	0.120706	+	0.181683i
$372$		0			0
$373$	−12.9237	−	4.70385i	−0.669165	−	0.243556i	−0.0149768	−	0.999888i	$-0.504767\pi$
$373$	−12.9237	−	4.70385i	−0.669165	−	0.243556i	−0.654188	+	0.756332i	$0.726990\pi$
$374$		0			0
$375$	−4.03580	−	15.1612i	−0.208408	−	0.782919i
$376$		0			0
$377$	−20.6254			−1.06226
$378$		0			0
$379$	28.3175			1.45457			0.727286	−	0.686334i	$-0.240781\pi$
$379$	28.3175			1.45457			0.727286	+	0.686334i	$0.240781\pi$
$380$		0			0
$381$	−6.38392	+	6.36303i	−0.327058	+	0.325988i
$382$		0			0
$383$	−14.0127	−	5.10022i	−0.716018	−	0.260609i	−0.0417834	−	0.999127i	$-0.513304\pi$
$383$	−14.0127	−	5.10022i	−0.716018	−	0.260609i	−0.674234	+	0.738518i	$0.735526\pi$
$384$		0			0
$385$	0.752505	−	1.51585i	0.0383512	−	0.0772549i
$386$		0			0
$387$	4.53067	+	12.5760i	0.230307	+	0.639275i
$388$		0			0
$389$	−0.806869	+	0.293676i	−0.0409099	+	0.0148900i	−0.362394	−	0.932025i	$-0.618041\pi$
$389$	−0.806869	+	0.293676i	−0.0409099	+	0.0148900i	0.321484	+	0.946915i	$0.395818\pi$
$390$		0			0
$391$	−2.51252	−	14.2492i	−0.127064	−	0.720614i
$392$		0			0
$393$	3.50181	−	39.2842i	0.176643	−	1.98163i
$394$		0			0
$395$	2.69484			0.135592
$396$		0			0
$397$	13.2871			0.666862			0.333431	−	0.942774i	$-0.391794\pi$
$397$	13.2871			0.666862			0.333431	+	0.942774i	$0.391794\pi$
$398$		0			0
$399$	17.6424	−	19.9447i	0.883222	−	0.998483i
$400$		0			0
$401$	2.62043	+	14.8612i	0.130858	+	0.742132i	0.977655	+	0.210216i	$0.0674168\pi$
$401$	2.62043	+	14.8612i	0.130858	+	0.742132i	−0.846797	+	0.531916i	$0.821472\pi$
$402$		0			0
$403$	−23.5606	−	19.7697i	−1.17363	−	0.984797i
$404$		0			0
$405$	−1.51723	−	8.94727i	−0.0753919	−	0.444593i
$406$		0			0
$407$	0.334652	−	1.89791i	0.0165881	−	0.0940758i
$408$		0			0
$409$	2.03717	−	1.70939i	0.100732	−	0.0845239i	−0.591031	−	0.806649i	$-0.701279\pi$
$409$	2.03717	−	1.70939i	0.100732	−	0.0845239i	0.691763	+	0.722125i	$0.256834\pi$
$410$		0			0
$411$	14.7392	+	21.1233i	0.727030	+	1.04194i
$412$		0			0
$413$	32.0471	+	9.43254i	1.57694	+	0.464145i
$414$		0			0
$415$	0.732546	−	1.26881i	0.0359593	−	0.0622833i
$416$		0			0
$417$	21.8277	+	15.3373i	1.06891	+	0.751071i
$418$		0			0
$419$	6.37024	+	36.1275i	0.311207	+	1.76494i	0.592744	+	0.805391i	$0.298045\pi$
$419$	6.37024	+	36.1275i	0.311207	+	1.76494i	−0.281537	+	0.959550i	$0.590844\pi$
$420$		0			0
$421$	−17.0856	−	14.3365i	−0.832701	−	0.698719i	0.123208	−	0.992381i	$-0.460682\pi$
$421$	−17.0856	−	14.3365i	−0.832701	−	0.698719i	−0.955910	+	0.293661i	$0.905126\pi$
$422$		0			0
$423$	−10.8080	−	30.0004i	−0.525504	−	1.45867i
$424$		0			0
$425$	10.1639	+	8.52851i	0.493021	+	0.413694i
$426$		0			0
$427$	3.81745	−	1.66773i	0.184739	−	0.0807070i
$428$		0			0
$429$	0.993147	+	3.73093i	0.0479496	+	0.180131i
$430$		0			0
$431$	−1.28756	+	2.23011i	−0.0620194	+	0.107421i	−0.895368	−	0.445327i	$-0.853087\pi$
$431$	−1.28756	+	2.23011i	−0.0620194	+	0.107421i	0.833349	+	0.552748i	$0.186421\pi$
$432$		0			0
$433$	−19.7656			−0.949872			−0.474936	−	0.880020i	$-0.657529\pi$
$433$	−19.7656			−0.949872			−0.474936	+	0.880020i	$0.657529\pi$
$434$		0			0
$435$	7.26071	−	7.23695i	0.348124	−	0.346985i
$436$		0			0
$437$	4.38298	+	24.8571i	0.209666	+	1.18908i
$438$		0			0
$439$	10.7108	+	8.98743i	0.511199	+	0.428947i	0.861551	−	0.507671i	$-0.169494\pi$
$439$	10.7108	+	8.98743i	0.511199	+	0.428947i	−0.350352	+	0.936618i	$0.613938\pi$
$440$		0			0
$441$	−2.56302	−	20.8430i	−0.122049	−	0.992524i
$442$		0			0
$443$	4.82142	−	27.3436i	0.229072	−	1.29913i	−0.625672	−	0.780086i	$-0.715175\pi$
$443$	4.82142	−	27.3436i	0.229072	−	1.29913i	0.854745	−	0.519049i	$-0.173714\pi$
$444$		0			0
$445$	−10.4758	−	3.81286i	−0.496598	−	0.180747i
$446$		0			0
$447$	29.4668	−	13.6818i	1.39373	−	0.647128i
$448$		0			0
$449$	−4.37769	−	7.58239i	−0.206596	−	0.357835i	0.744044	−	0.668131i	$-0.232905\pi$
$449$	−4.37769	−	7.58239i	−0.206596	−	0.357835i	−0.950640	+	0.310296i	$0.899572\pi$
$450$		0			0
$451$	−2.83983	−	4.91872i	−0.133722	−	0.231614i
$452$		0			0
$453$	−18.4532	+	1.58398i	−0.867009	+	0.0744218i
$454$		0			0
$455$	−7.54519	−	5.56298i	−0.353724	−	0.260796i
$456$		0			0
$457$	−14.5442	+	5.29367i	−0.680351	+	0.247628i	−0.658998	−	0.752144i	$-0.729020\pi$
$457$	−14.5442	+	5.29367i	−0.680351	+	0.247628i	−0.0213528	+	0.999772i	$0.506797\pi$
$458$		0			0
$459$	12.1783	+	12.2987i	0.568436	+	0.574053i
$460$		0			0
$461$	−3.58802	+	20.3487i	−0.167111	+	0.947732i	0.779751	+	0.626090i	$0.215346\pi$
$461$	−3.58802	+	20.3487i	−0.167111	+	0.947732i	−0.946861	+	0.321642i	$0.895765\pi$
$462$		0			0
$463$	−27.0255	−	9.83648i	−1.25598	−	0.457140i	−0.373563	−	0.927605i	$-0.621864\pi$
$463$	−27.0255	−	9.83648i	−1.25598	−	0.457140i	−0.882419	+	0.470465i	$0.844086\pi$
$464$		0			0
$465$	15.2307	−	1.30736i	0.706305	−	0.0606273i
$466$		0			0
$467$	29.0699			1.34519			0.672597	−	0.740009i	$-0.265179\pi$
$467$	29.0699			1.34519			0.672597	+	0.740009i	$0.265179\pi$
$468$		0			0
$469$	−28.7427	+	27.3704i	−1.32721	+	1.26385i
$470$		0			0
$471$	−0.300883	+	3.37538i	−0.0138640	+	0.155530i
$472$		0			0
$473$	2.65610	+	0.966743i	0.122128	+	0.0444509i
$474$		0			0
$475$	−17.7304	−	14.8776i	−0.813529	−	0.682632i
$476$		0			0
$477$	4.13347	−	2.36843i	0.189259	−	0.108443i
$478$		0			0
$479$	3.90403	−	22.1409i	0.178380	−	1.01164i	−0.755790	−	0.654814i	$-0.772747\pi$
$479$	3.90403	−	22.1409i	0.178380	−	1.01164i	0.934170	−	0.356828i	$-0.116142\pi$
$480$		0			0
$481$	−10.0312	−	3.65107i	−0.457385	−	0.166474i
$482$		0			0
$483$	16.9735	+	10.3993i	0.772323	+	0.473184i
$484$		0			0
$485$	−0.675980	−	1.17083i	−0.0306947	−	0.0531647i
$486$		0			0
$487$	−12.5153	+	21.6771i	−0.567122	+	0.982284i	0.429727	+	0.902959i	$0.358610\pi$
$487$	−12.5153	+	21.6771i	−0.567122	+	0.982284i	−0.996849	+	0.0793251i	$0.974723\pi$
$488$		0			0
$489$	−4.30510	−	16.1728i	−0.194683	−	0.731361i
$490$		0			0
$491$	6.40365	−	5.37330i	0.288993	−	0.242494i	−0.486752	−	0.873540i	$-0.661819\pi$
$491$	6.40365	−	5.37330i	0.288993	−	0.242494i	0.775745	+	0.631046i	$0.217374\pi$
$492$		0			0
$493$	−3.39512	+	19.2547i	−0.152909	+	0.867188i
$494$		0			0
$495$	−1.65871	−	0.964918i	−0.0745533	−	0.0433698i
$496$		0			0
$497$	11.1263	−	0.699826i	0.499081	−	0.0313915i
$498$		0			0
$499$	18.7607	−	15.7421i	0.839843	−	0.704712i	−0.117685	−	0.993051i	$-0.537547\pi$
$499$	18.7607	−	15.7421i	0.839843	−	0.704712i	0.957528	+	0.288339i	$0.0931030\pi$
$500$		0			0
$501$	31.5203	−	14.6353i	1.40822	−	0.653858i
$502$		0			0
$503$	19.4236	+	33.6426i	0.866053	+	1.50005i	0.865997	+	0.500049i	$0.166685\pi$
$503$	19.4236	+	33.6426i	0.866053	+	1.50005i	5.61253e−5		1.00000i	$0.499982\pi$
$504$		0			0
$505$	−2.61685	+	4.53252i	−0.116448	+	0.201695i
$506$		0			0
$507$	−1.12661	+	0.0967050i	−0.0500344	+	0.00429482i
$508$		0			0
$509$	−4.44527	−	25.2104i	−0.197033	−	1.11743i	−0.909494	−	0.415718i	$-0.863530\pi$
$509$	−4.44527	−	25.2104i	−0.197033	−	1.11743i	0.712461	−	0.701712i	$-0.247581\pi$
$510$		0			0
$511$	−19.7904	+	1.24479i	−0.875477	+	0.0550663i
$512$		0			0
$513$	−21.2446	−	21.4545i	−0.937970	−	0.947239i
$514$		0			0
$515$	−1.96485	−	1.64871i	−0.0865818	−	0.0726508i
$516$		0			0
$517$	−6.33620	−	2.30619i	−0.278666	−	0.101426i
$518$		0			0
$519$	−10.2044	+	21.7900i	−0.447922	+	0.956475i
$520$		0			0
$521$	16.4493	+	28.4910i	0.720657	+	1.24821i	0.960737	+	0.277461i	$0.0894930\pi$
$521$	16.4493	+	28.4910i	0.720657	+	1.24821i	−0.240080	+	0.970753i	$0.577174\pi$
$522$		0			0
$523$	10.1296	−	17.5450i	0.442936	−	0.767187i	−0.554970	−	0.831870i	$-0.687270\pi$
$523$	10.1296	−	17.5450i	0.442936	−	0.767187i	0.997906	+	0.0646831i	$0.0206036\pi$
$524$		0			0
$525$	−18.0529	+	2.69969i	−0.787892	+	0.117824i
$526$		0			0
$527$	−22.3341	+	18.7405i	−0.972889	+	0.816351i
$528$		0			0
$529$	3.88200	−	1.41293i	0.168783	−	0.0614318i
$530$		0			0
$531$	13.0721	−	35.5523i	0.567281	−	1.54284i
$532$		0			0
$533$	−29.5633	+	10.7602i	−1.28053	+	0.466074i
$534$		0			0
$535$	−0.400363	−	2.27057i	−0.0173092	−	0.0981654i
$536$		0			0
$537$	−25.4789	−	6.87182i	−1.09949	−	0.296541i
$538$		0			0
$539$	−3.73250	−	2.40560i	−0.160770	−	0.103617i
$540$		0			0
$541$	−2.59293	−	4.49109i	−0.111479	−	0.193087i	0.804888	−	0.593427i	$-0.202225\pi$
$541$	−2.59293	−	4.49109i	−0.111479	−	0.193087i	−0.916367	+	0.400340i	$0.868892\pi$
$542$		0			0
$543$	−3.26437	+	3.25369i	−0.140088	+	0.139629i
$544$		0			0
$545$	−5.47896	+	4.59739i	−0.234693	+	0.196931i
$546$		0			0
$547$	−1.61579	+	0.588100i	−0.0690863	+	0.0251453i	−0.376332	−	0.926485i	$-0.622815\pi$
$547$	−1.61579	+	0.588100i	−0.0690863	+	0.0251453i	0.307246	+	0.951630i	$0.400593\pi$
$548$		0			0
$549$	−1.60101	−	4.44402i	−0.0683296	−	0.189666i
$550$		0			0
$551$	5.92264	−	33.5890i	0.252313	−	1.43094i
$552$		0			0
$553$	0.788305	−	7.02689i	0.0335222	−	0.298814i
$554$		0			0
$555$	4.81234	−	2.23444i	0.204273	−	0.0948466i
$556$		0			0
$557$	0.581165			0.0246248			0.0123124	−	0.999924i	$-0.496081\pi$
$557$	0.581165			0.0246248			0.0123124	+	0.999924i	$0.496081\pi$
$558$		0			0
$559$	7.82842	−	13.5592i	0.331107	−	0.573494i
$560$		0			0
$561$	3.64646	−	0.313003i	0.153954	−	0.0132150i
$562$		0			0
$563$	4.88536	−	4.09930i	0.205893	−	0.172765i	−0.534010	−	0.845478i	$-0.679316\pi$
$563$	4.88536	−	4.09930i	0.205893	−	0.172765i	0.739903	+	0.672713i	$0.234871\pi$
$564$		0			0
$565$	−4.46281	+	1.62433i	−0.187752	+	0.0683361i
$566$		0			0
$567$	−23.7741	+	1.33894i	−0.998418	+	0.0562303i
$568$		0			0
$569$	5.30155	−	1.92961i	0.222253	−	0.0808933i	−0.228494	−	0.973545i	$-0.573380\pi$
$569$	5.30155	−	1.92961i	0.222253	−	0.0808933i	0.450746	+	0.892652i	$0.351158\pi$
$570$		0			0
$571$	28.6979	−	24.0804i	1.20097	−	1.00773i	0.201369	−	0.979516i	$-0.435461\pi$
$571$	28.6979	−	24.0804i	1.20097	−	1.00773i	0.999602	−	0.0282182i	$-0.00898333\pi$
$572$		0			0
$573$	45.9290	−	3.94242i	1.91871	−	0.164697i
$574$		0			0
$575$	8.65131	−	14.9845i	0.360785	−	0.624897i
$576$		0			0
$577$	−14.4192			−0.600281			−0.300140	−	0.953895i	$-0.597034\pi$
$577$	−14.4192			−0.600281			−0.300140	+	0.953895i	$0.597034\pi$
$578$		0			0
$579$	−33.4409	+	15.5271i	−1.38976	+	0.645284i
$580$		0			0
$581$	−3.09417	−	2.28129i	−0.128368	−	0.0946439i
$582$		0			0
$583$	0.174925	−	0.992052i	0.00724467	−	0.0410866i
$584$		0			0
$585$	−6.85910	+	8.12015i	−0.283589	+	0.335727i
$586$		0			0
$587$	−13.0869	+	4.76324i	−0.540154	+	0.196600i	−0.597667	−	0.801745i	$-0.703905\pi$
$587$	−13.0869	+	4.76324i	−0.540154	+	0.196600i	0.0575123	+	0.998345i	$0.481683\pi$
$588$		0			0
$589$	38.9609	−	32.6920i	1.60535	−	1.34705i
$590$		0			0
$591$	−22.7095	+	22.6352i	−0.934144	+	0.931086i
$592$		0			0
$593$	2.04374	+	3.53986i	0.0839262	+	0.145364i	0.904933	−	0.425554i	$-0.139921\pi$
$593$	2.04374	+	3.53986i	0.0839262	+	0.145364i	−0.821007	+	0.570918i	$0.806587\pi$
$594$		0			0
$595$	−6.43529	+	6.12805i	−0.263821	+	0.251225i
$596$		0			0
$597$	−6.36475	−	1.71662i	−0.260492	−	0.0702564i
$598$		0			0
$599$	−1.04519	−	5.92759i	−0.0427055	−	0.242195i	0.955981	−	0.293428i	$-0.0947960\pi$
$599$	−1.04519	−	5.92759i	−0.0427055	−	0.242195i	−0.998687	+	0.0512329i	$0.983685\pi$
$600$		0			0
$601$	−18.2001	+	6.62431i	−0.742399	+	0.270211i	−0.685404	−	0.728163i	$-0.740374\pi$
$601$	−18.2001	+	6.62431i	−0.742399	+	0.270211i	−0.0569955	+	0.998374i	$0.518152\pi$
$602$		0			0
$603$	28.8149	+	34.5697i	1.17343	+	1.40779i
$604$		0			0
$605$	10.0415	−	3.65479i	0.408243	−	0.148588i
$606$		0			0
$607$	−33.5118	+	28.1198i	−1.36020	+	1.14135i	−0.384284	+	0.923215i	$0.625551\pi$
$607$	−33.5118	+	28.1198i	−1.36020	+	1.14135i	−0.975920	+	0.218131i	$0.930004\pi$
$608$		0			0
$609$	−16.7466	−	21.0495i	−0.678607	−	0.852968i
$610$		0			0
$611$	−18.6749	+	32.3459i	−0.755505	+	1.30857i
$612$		0			0
$613$	13.9567	+	24.1737i	0.563706	+	0.976367i	0.997169	+	0.0751956i	$0.0239581\pi$
$613$	13.9567	+	24.1737i	0.563706	+	0.976367i	−0.433463	+	0.901171i	$0.642709\pi$
$614$		0			0
$615$	6.63162	−	14.1609i	0.267413	−	0.571023i
$616$		0			0
$617$	17.8862	+	6.51004i	0.720071	+	0.262084i	0.675956	−	0.736942i	$-0.263731\pi$
$617$	17.8862	+	6.51004i	0.720071	+	0.262084i	0.0441148	+	0.999026i	$0.485953\pi$
$618$		0			0
$619$	31.0463	+	26.0510i	1.24786	+	1.04708i	0.996868	+	0.0790874i	$0.0252006\pi$
$619$	31.0463	+	26.0510i	1.24786	+	1.04708i	0.250990	+	0.967990i	$0.419244\pi$
$620$		0			0
$621$	13.0371	−	18.4254i	0.523159	−	0.739385i
$622$		0			0
$623$	−13.0066	+	26.2005i	−0.521097	+	1.04970i
$624$		0			0
$625$	1.87240	+	10.6189i	0.0748960	+	0.424756i
$626$		0			0
$627$	−6.36109	+	0.546019i	−0.254038	+	0.0218059i
$628$		0			0
$629$	−5.05966	+	8.76360i	−0.201742	+	0.349427i
$630$		0			0
$631$	0.0393455	+	0.0681484i	0.00156632	+	0.00271295i	0.866808	−	0.498643i	$-0.166168\pi$
$631$	0.0393455	+	0.0681484i	0.00156632	+	0.00271295i	−0.865241	+	0.501356i	$0.832835\pi$
$632$		0			0
$633$	18.3225	−	8.50737i	0.728252	−	0.338138i
$634$		0			0
$635$	−4.01966	+	3.37289i	−0.159515	+	0.133849i
$636$		0			0
$637$	−16.7128	+	18.0470i	−0.662184	+	0.715048i
$638$		0			0
$639$	0.0414363	−	12.6408i	0.00163919	−	0.500064i
$640$		0			0
$641$	−3.34233	+	18.9553i	−0.132014	+	0.748689i	0.844878	+	0.534958i	$0.179673\pi$
$641$	−3.34233	+	18.9553i	−0.132014	+	0.748689i	−0.976893	+	0.213731i	$0.931438\pi$
$642$		0			0
$643$	−17.2913	+	14.5091i	−0.681900	+	0.572182i	−0.916561	−	0.399895i	$-0.869047\pi$
$643$	−17.2913	+	14.5091i	−0.681900	+	0.572182i	0.234661	+	0.972077i	$0.424602\pi$
$644$		0			0
$645$	2.00178	+	7.52002i	0.0788200	+	0.296101i
$646$		0			0
$647$	1.24656	−	2.15911i	0.0490074	−	0.0848834i	−0.840481	−	0.541841i	$-0.817728\pi$
$647$	1.24656	−	2.15911i	0.0490074	−	0.0848834i	0.889489	+	0.456958i	$0.151061\pi$
$648$		0			0
$649$	−4.00488	−	6.93666i	−0.157205	−	0.272288i
$650$		0			0
$651$	1.04635	−	40.0968i	0.0410095	−	1.57152i
$652$		0			0
$653$	16.9438	+	6.16704i	0.663062	+	0.241335i	0.651558	−	0.758599i	$-0.274116\pi$
$653$	16.9438	+	6.16704i	0.663062	+	0.241335i	0.0115044	+	0.999934i	$0.496338\pi$
$654$		0			0
$655$	3.98704	−	22.6116i	0.155787	−	0.883509i
$656$		0			0
$657$	−0.0737033	+	22.4845i	−0.00287544	+	0.877202i
$658$		0			0
$659$	15.2344	+	12.7832i	0.593449	+	0.497963i	0.889332	−	0.457261i	$-0.151170\pi$
$659$	15.2344	+	12.7832i	0.593449	+	0.497963i	−0.295883	+	0.955224i	$0.595614\pi$
$660$		0			0
$661$	−15.0549	−	5.47952i	−0.585566	−	0.213129i	0.0322119	−	0.999481i	$-0.489745\pi$
$661$	−15.0549	−	5.47952i	−0.585566	−	0.213129i	−0.617778	+	0.786352i	$0.711967\pi$
$662$		0			0
$663$	1.79998	−	20.1926i	0.0699053	−	0.784216i
$664$		0			0
$665$	11.2261	−	10.6901i	0.435329	−	0.414544i
$666$		0			0
$667$	25.4971			0.987253
$668$		0			0
$669$	11.5702	−	0.993160i	0.447332	−	0.0383978i
$670$		0			0
$671$	−0.938594	−	0.341620i	−0.0362340	−	0.0131881i
$672$		0			0
$673$	−1.05046	+	5.95748i	−0.0404924	+	0.229644i	−0.998337	−	0.0576419i	$-0.981642\pi$
$673$	−1.05046	+	5.95748i	−0.0404924	+	0.229644i	0.957845	+	0.287286i	$0.0927530\pi$
$674$		0			0
$675$	1.70252	+	20.6275i	0.0655299	+	0.793953i
$676$		0			0
$677$	16.9832	−	6.18137i	0.652716	−	0.237569i	0.00562769	−	0.999984i	$-0.498209\pi$
$677$	16.9832	−	6.18137i	0.652716	−	0.237569i	0.647088	+	0.762415i	$0.275986\pi$
$678$		0			0
$679$	−3.25072	+	1.42014i	−0.124751	+	0.0545000i
$680$		0			0
$681$	29.9615	−	2.57182i	1.14813	−	0.0985523i
$682$		0			0
$683$	−23.2805	−	40.3229i	−0.890802	−	1.54291i	−0.838916	−	0.544261i	$-0.816810\pi$
$683$	−23.2805	−	40.3229i	−0.890802	−	1.54291i	−0.0518857	−	0.998653i	$-0.516523\pi$
$684$		0			0
$685$	7.49745	+	12.9860i	0.286463	+	0.496168i
$686$		0			0
$687$	−20.2884	+	9.42017i	−0.774050	+	0.359402i
$688$		0			0
$689$	−5.24341	−	1.90844i	−0.199758	−	0.0727059i
$690$		0			0
$691$	−7.10440	+	40.2911i	−0.270264	+	1.53274i	0.483350	+	0.875427i	$0.339420\pi$
$691$	−7.10440	+	40.2911i	−0.270264	+	1.53274i	−0.753614	+	0.657317i	$0.771691\pi$
$692$		0			0
$693$	−3.00126	+	4.04286i	−0.114008	+	0.153576i
$694$		0			0
$695$	11.8971	+	9.98283i	0.451282	+	0.378670i
$696$		0			0
$697$	5.17869	+	29.3698i	0.196157	+	1.11246i
$698$		0			0
$699$	−2.02920	+	2.02256i	−0.0767513	+	0.0765001i
$700$		0			0
$701$	−47.4284			−1.79134			−0.895672	−	0.444715i	$-0.853305\pi$
$701$	−47.4284			−1.79134			−0.895672	+	0.444715i	$0.853305\pi$
$702$		0			0
$703$	8.82636	−	15.2877i	0.332892	−	0.576587i
$704$		0			0
$705$	−4.77530	−	17.9392i	−0.179848	−	0.675630i
$706$		0			0
$707$	11.0532	+	8.14939i	0.415698	+	0.306489i
$708$		0			0
$709$	−26.0030	−	21.8191i	−0.976562	−	0.819433i	0.00700545	−	0.999975i	$-0.497770\pi$
$709$	−26.0030	−	21.8191i	−0.976562	−	0.819433i	−0.983567	+	0.180543i	$0.942215\pi$
$710$		0			0
$711$	−7.89131	−	1.41814i	−0.295947	−	0.0531843i
$712$		0			0
$713$	29.1256	+	24.4393i	1.09076	+	0.915258i
$714$		0			0
$715$	0.390298	+	2.21349i	0.0145963	+	0.0827798i
$716$		0			0
$717$	5.83579	+	4.10054i	0.217942	+	0.153137i
$718$		0			0
$719$	−18.0241	+	31.2187i	−0.672187	+	1.16426i	0.305096	+	0.952322i	$0.401311\pi$
$719$	−18.0241	+	31.2187i	−0.672187	+	1.16426i	−0.977283	+	0.211940i	$0.932022\pi$
$720$		0			0
$721$	−4.87382	+	4.64113i	−0.181511	+	0.172845i
$722$		0			0
$723$	16.7194	+	23.9613i	0.621803	+	0.891132i
$724$		0			0
$725$	−17.9107	+	15.0288i	−0.665185	+	0.558157i
$726$		0			0
$727$	−0.972455	+	5.51506i	−0.0360663	+	0.204542i	−0.997516	−	0.0704381i	$-0.977560\pi$
$727$	−0.972455	+	5.51506i	−0.0360663	+	0.204542i	0.961450	+	0.274980i	$0.0886714\pi$
$728$		0			0
$729$	−0.265510	+	26.9987i	−0.00983370	+	0.999952i
$730$		0			0
$731$	−11.3695	−	9.54014i	−0.420516	−	0.352855i
$732$		0			0
$733$	5.47542	+	31.0526i	0.202239	+	1.14696i	0.901725	+	0.432309i	$0.142301\pi$
$733$	5.47542	+	31.0526i	0.202239	+	1.14696i	−0.699486	+	0.714646i	$0.746588\pi$
$734$		0			0
$735$	−0.448892	−	12.2171i	−0.0165576	−	0.450636i
$736$		0			0
$737$	9.51631			0.350538
$738$		0			0
$739$	−7.36813			−0.271041			−0.135520	−	0.990775i	$-0.543271\pi$
$739$	−7.36813			−0.271041			−0.135520	+	0.990775i	$0.543271\pi$
$740$		0			0
$741$	−3.13998	+	35.2251i	−0.115350	+	1.29403i
$742$		0			0
$743$	1.60570	+	9.10636i	0.0589073	+	0.334080i	0.999992	−	0.00409197i	$-0.00130252\pi$
$743$	1.60570	+	9.10636i	0.0589073	+	0.334080i	−0.941084	+	0.338172i	$0.890191\pi$
$744$		0			0
$745$	17.7728	−	6.46875i	0.651143	−	0.236997i
$746$		0			0
$747$	−2.81281	+	3.32995i	−0.102915	+	0.121837i
$748$		0			0
$749$	−6.03770	+	0.379763i	−0.220613	+	0.0138762i
$750$		0			0
$751$	−24.4061	−	8.88310i	−0.890592	−	0.324149i	−0.144116	−	0.989561i	$-0.546034\pi$
$751$	−24.4061	−	8.88310i	−0.890592	−	0.324149i	−0.746477	+	0.665412i	$0.768256\pi$
$752$		0			0
$753$	−26.5170	+	26.4302i	−0.966333	+	0.963170i
$754$		0			0
$755$	−10.7823			−0.392407
$756$		0			0
$757$	23.1045			0.839746			0.419873	−	0.907583i	$-0.362075\pi$
$757$	23.1045			0.839746			0.419873	+	0.907583i	$0.362075\pi$
$758$		0			0
$759$	−1.22773	−	4.61218i	−0.0445638	−	0.167411i
$760$		0			0
$761$	31.6969	+	11.5367i	1.14901	+	0.418206i	0.845160	−	0.534513i	$-0.179505\pi$
$761$	31.6969	+	11.5367i	1.14901	+	0.418206i	0.303852	+	0.952719i	$0.401727\pi$
$762$		0			0
$763$	10.3851	+	15.6314i	0.375966	+	0.565895i
$764$		0			0
$765$	6.45145	+	7.73992i	0.233253	+	0.279837i
$766$		0			0
$767$	−41.6918	+	15.1746i	−1.50540	+	0.547922i
$768$		0			0
$769$	7.68204	+	43.5670i	0.277021	+	1.57107i	0.732467	+	0.680803i	$0.238369\pi$
$769$	7.68204	+	43.5670i	0.277021	+	1.57107i	−0.455446	+	0.890264i	$0.650520\pi$
$770$		0			0
$771$	−15.8200	+	7.34543i	−0.569742	+	0.264539i
$772$		0			0
$773$	34.5466			1.24255			0.621277	−	0.783591i	$-0.286614\pi$
$773$	34.5466			1.24255			0.621277	+	0.783591i	$0.286614\pi$
$774$		0			0
$775$	−34.8648			−1.25238
$776$		0			0
$777$	−4.41864	−	13.2020i	−0.158518	−	0.473617i
$778$		0			0
$779$	−9.03400	−	51.2344i	−0.323677	−	1.83566i
$780$		0			0
$781$	−2.04762	−	1.71816i	−0.0732697	−	0.0614806i
$782$		0			0
$783$	−25.0699	+	17.3711i	−0.895925	+	0.620791i
$784$		0			0
$785$	−0.342575	+	1.94284i	−0.0122270	+	0.0693429i
$786$		0			0
$787$	−7.37006	+	6.18422i	−0.262714	+	0.220444i	−0.764624	−	0.644476i	$-0.777075\pi$
$787$	−7.37006	+	6.18422i	−0.262714	+	0.220444i	0.501910	+	0.864920i	$0.332631\pi$
$788$		0			0
$789$	−15.7084	+	33.5431i	−0.559234	+	1.19417i
$790$		0			0
$791$	2.93001	+	12.1121i	0.104179	+	0.430655i
$792$		0			0
$793$	−2.76635	+	4.79146i	−0.0982359	+	0.170150i
$794$		0			0
$795$	2.51545	−	1.16796i	0.0892139	−	0.0414232i
$796$		0			0
$797$	−1.80000	−	10.2083i	−0.0637591	−	0.361596i	−0.999949	−	0.0101012i	$-0.996785\pi$
$797$	−1.80000	−	10.2083i	−0.0637591	−	0.361596i	0.936190	−	0.351495i	$-0.114326\pi$
$798$		0			0
$799$	27.1222	+	22.7583i	0.959515	+	0.805129i
$800$		0			0
$801$	28.6696	+	16.6780i	1.01299	+	0.589287i
$802$		0			0
$803$	3.64213	+	3.05611i	0.128528	+	0.107848i
$804$		0			0
$805$	9.32737	+	6.87696i	0.328747	+	0.242381i
$806$		0			0
$807$	14.3858	−	14.3387i	0.506405	−	0.504748i
$808$		0			0
$809$	14.0117	−	24.2690i	0.492625	−	0.853252i	−0.507339	−	0.861747i	$-0.669371\pi$
$809$	14.0117	−	24.2690i	0.492625	−	0.853252i	0.999964	+	0.00849476i	$0.00270400\pi$
$810$		0			0
$811$	−25.3046			−0.888564			−0.444282	−	0.895887i	$-0.646541\pi$
$811$	−25.3046			−0.888564			−0.444282	+	0.895887i	$0.646541\pi$
$812$		0			0
$813$	1.23958	+	4.65668i	0.0434739	+	0.163317i
$814$		0			0
$815$	−1.69187	−	9.59505i	−0.0592635	−	0.336100i
$816$		0			0
$817$	19.8336	+	16.6424i	0.693889	+	0.582242i
$818$		0			0
$819$	19.1671	+	20.2606i	0.669752	+	0.707964i
$820$		0			0
$821$	−8.84453	+	50.1598i	−0.308676	+	1.75059i	0.296998	+	0.954878i	$0.404014\pi$
$821$	−8.84453	+	50.1598i	−0.308676	+	1.75059i	−0.605675	+	0.795713i	$0.707097\pi$
$822$		0			0
$823$	45.7038	+	16.6348i	1.59313	+	0.579854i	0.978007	−	0.208574i	$-0.0668821\pi$
$823$	45.7038	+	16.6348i	1.59313	+	0.579854i	0.615128	+	0.788427i	$0.289104\pi$
$824$		0			0
$825$	3.58099	+	2.51620i	0.124674	+	0.0876027i
$826$		0			0
$827$	19.5505	+	33.8625i	0.679839	+	1.17752i	0.975029	+	0.222077i	$0.0712837\pi$
$827$	19.5505	+	33.8625i	0.679839	+	1.17752i	−0.295190	+	0.955439i	$0.595383\pi$
$828$		0			0
$829$	−7.85338	−	13.6025i	−0.272759	−	0.472433i	0.696808	−	0.717258i	$-0.254603\pi$
$829$	−7.85338	−	13.6025i	−0.272759	−	0.472433i	−0.969567	+	0.244825i	$0.921270\pi$
$830$		0			0
$831$	−2.56622	+	5.47980i	−0.0890210	+	0.190092i
$832$		0			0
$833$	14.0966	+	18.5728i	0.488418	+	0.643509i
$834$		0			0
$835$	19.0113	−	6.91956i	0.657915	−	0.239461i
$836$		0			0
$837$	−45.2879	−	4.18666i	−1.56538	−	0.144712i
$838$		0			0
$839$	1.72131	−	9.76201i	0.0594261	−	0.337022i	−0.940571	−	0.339598i	$-0.889709\pi$
$839$	1.72131	−	9.76201i	0.0594261	−	0.337022i	0.999997	+	0.00257625i	$0.000820046\pi$
$840$		0			0
$841$	−5.12491	−	1.86532i	−0.176721	−	0.0643212i
$842$		0			0
$843$	−21.6069	−	30.9657i	−0.744181	−	1.06652i
$844$		0			0
$845$	−0.658279			−0.0226455
$846$		0			0
$847$	−6.59261	−	27.2525i	−0.226525	−	0.936407i
$848$		0			0
$849$	9.21891	+	6.47770i	0.316392	+	0.222314i
$850$		0			0
$851$	12.4006	+	4.51346i	0.425088	+	0.154719i
$852$		0			0
$853$	−34.6991	−	29.1160i	−1.18807	−	0.996912i	−0.999891	−	0.0147785i	$-0.995296\pi$
$853$	−34.6991	−	29.1160i	−1.18807	−	0.996912i	−0.188183	−	0.982134i	$-0.560260\pi$
$854$		0			0
$855$	−11.2543	−	13.5019i	−0.384888	−	0.461757i
$856$		0			0
$857$	2.21370	−	12.5545i	0.0756187	−	0.428855i	−0.923371	−	0.383909i	$-0.874577\pi$
$857$	2.21370	−	12.5545i	0.0756187	−	0.428855i	0.998989	−	0.0449455i	$-0.0143114\pi$
$858$		0			0
$859$	8.66535	+	3.15393i	0.295658	+	0.107611i	0.485590	−	0.874186i	$-0.338605\pi$
$859$	8.66535	+	3.15393i	0.295658	+	0.107611i	−0.189932	+	0.981797i	$0.560827\pi$
$860$		0			0
$861$	−34.9851	−	21.4345i	−1.19229	−	0.730487i
$862$		0			0
$863$	−13.8024	−	23.9064i	−0.469839	−	0.813784i	0.529567	−	0.848268i	$-0.322355\pi$
$863$	−13.8024	−	23.9064i	−0.469839	−	0.813784i	−0.999405	+	0.0344840i	$0.989021\pi$
$864$		0			0
$865$	−7.00371	+	12.1308i	−0.238133	+	0.412459i
$866$		0			0
$867$	9.87464	+	2.66326i	0.335360	+	0.0904489i
$868$		0			0
$869$	−1.29874	+	1.08977i	−0.0440567	+	0.0369680i
$870$		0			0
$871$	9.15343	−	51.9117i	0.310152	−	1.75896i
$872$		0			0
$873$	1.36333	+	3.78427i	0.0461418	+	0.128078i
$874$		0			0
$875$	−23.9183	+	1.50443i	−0.808585	+	0.0508589i
$876$		0			0
$877$	18.8546	−	15.8209i	0.636674	−	0.534233i	−0.266321	−	0.963884i	$-0.585808\pi$
$877$	18.8546	−	15.8209i	0.636674	−	0.534233i	0.902995	+	0.429651i	$0.141364\pi$
$878$		0			0
$879$	−24.9926	−	17.5611i	−0.842979	−	0.592321i
$880$		0			0
$881$	23.7908	+	41.2069i	0.801532	+	1.38829i	0.918607	+	0.395171i	$0.129315\pi$
$881$	23.7908	+	41.2069i	0.801532	+	1.38829i	−0.117075	+	0.993123i	$0.537352\pi$
$882$		0			0
$883$	11.8333	−	20.4959i	0.398223	−	0.689743i	−0.595284	−	0.803516i	$-0.702960\pi$
$883$	11.8333	−	20.4959i	0.398223	−	0.689743i	0.993507	+	0.113773i	$0.0362937\pi$
$884$		0			0
$885$	9.35228	−	19.9705i	0.314373	−	0.671301i
$886$		0			0
$887$	−6.18945	−	35.1021i	−0.207821	−	1.17861i	−0.892938	−	0.450180i	$-0.851360\pi$
$887$	−6.18945	−	35.1021i	−0.207821	−	1.17861i	0.685116	−	0.728434i	$-0.259751\pi$
$888$		0			0
$889$	7.61907	+	11.4680i	0.255535	+	0.384625i
$890$		0			0
$891$	4.34941	+	3.69845i	0.145711	+	0.123903i
$892$		0			0
$893$	−47.3135	−	39.7008i	−1.58329	−	1.32854i
$894$		0			0
$895$	−14.4363	−	5.25440i	−0.482554	−	0.175635i
$896$		0			0
$897$	−26.3404	+	2.26099i	−0.879482	+	0.0754924i
$898$		0			0
$899$	−25.6884	−	44.4936i	−0.856755	−	1.48394i
$900$		0			0
$901$	−2.64473	+	4.58080i	−0.0881087	+	0.152609i
$902$		0			0
$903$	20.1942	−	3.01992i	0.672023	−	0.100497i
$904$		0			0
$905$	−2.05542	+	1.72471i	−0.0683246	+	0.0573312i
$906$		0			0
$907$	1.71264	−	0.623350i	0.0568673	−	0.0206980i	−0.313430	−	0.949611i	$-0.601478\pi$
$907$	1.71264	−	0.623350i	0.0568673	−	0.0206980i	0.370297	+	0.928913i	$0.379256\pi$
$908$		0			0
$909$	10.0481	−	11.8955i	0.333275	−	0.394548i
$910$		0			0
$911$	4.88984	−	1.77976i	0.162008	−	0.0589659i	−0.259743	−	0.965678i	$-0.583638\pi$
$911$	4.88984	−	1.77976i	0.162008	−	0.0589659i	0.421751	+	0.906712i	$0.361416\pi$
$912$		0			0
$913$	0.160055	+	0.907718i	0.00529705	+	0.0300411i
$914$		0			0
$915$	−0.707374	−	2.65737i	−0.0233851	−	0.0878499i
$916$		0			0
$917$	−57.7942	−	17.0108i	−1.90853	−	0.561745i
$918$		0			0
$919$	−7.55835	−	13.0914i	−0.249327	−	0.431847i	0.714012	−	0.700133i	$-0.246876\pi$
$919$	−7.55835	−	13.0914i	−0.249327	−	0.431847i	−0.963339	+	0.268286i	$0.913543\pi$
$920$		0			0
$921$	13.1190	+	49.2837i	0.432285	+	1.62395i
$922$		0			0
$923$	−11.3421	+	9.51718i	−0.373331	+	0.313262i
$924$		0			0
$925$	−11.3713	+	4.13881i	−0.373886	+	0.136083i
$926$		0			0
$927$	4.88606	+	5.86189i	0.160479	+	0.192530i
$928$		0			0
$929$	5.33029	−	30.2296i	0.174881	−	0.991800i	−0.763400	−	0.645926i	$-0.776471\pi$
$929$	5.33029	−	30.2296i	0.174881	−	0.991800i	0.938281	−	0.345874i	$-0.112418\pi$
$930$		0			0
$931$	−24.5909	−	32.3994i	−0.805933	−	1.06185i
$932$		0			0
$933$	30.5964	+	21.4986i	1.00168	+	0.703834i
$934$		0			0
$935$	2.13064			0.0696793
$936$		0			0
$937$	−19.4413	+	33.6733i	−0.635120	+	1.10006i	0.351370	+	0.936237i	$0.385716\pi$
$937$	−19.4413	+	33.6733i	−0.635120	+	1.10006i	−0.986490	+	0.163823i	$0.947617\pi$
$938$		0			0
$939$	19.5281	−	41.6996i	0.637275	−	1.36081i
$940$		0			0
$941$	14.7405	−	12.3687i	0.480526	−	0.403209i	−0.370091	−	0.928996i	$-0.620673\pi$
$941$	14.7405	−	12.3687i	0.480526	−	0.403209i	0.850617	+	0.525787i	$0.176229\pi$
$942$		0			0
$943$	36.5462	−	13.3017i	1.19011	−	0.433164i
$944$		0			0
$945$	−13.8563	−	0.407043i	−0.450746	−	0.0132411i
$946$		0			0
$947$	48.2546	−	17.5632i	1.56806	−	0.570728i	0.595497	−	0.803357i	$-0.296955\pi$
$947$	48.2546	−	17.5632i	1.56806	−	0.570728i	0.972565	+	0.232629i	$0.0747329\pi$
$948$		0			0
$949$	20.1744	−	16.9283i	0.654889	−	0.549517i
$950$		0			0
$951$	16.3761	+	23.4692i	0.531030	+	0.761041i
$952$		0			0
$953$	27.7103	−	47.9957i	0.897625	−	1.55473i	0.0671031	−	0.997746i	$-0.478624\pi$
$953$	27.7103	−	47.9957i	0.897625	−	1.55473i	0.830522	−	0.556986i	$-0.188042\pi$
$954$		0			0
$955$	26.8364			0.868406
$956$		0			0
$957$	−0.572630	+	6.42391i	−0.0185105	+	0.207655i
$958$		0			0
$959$	36.0545	−	15.7511i	1.16426	−	0.508630i
$960$		0			0
$961$	7.92042	−	44.9189i	0.255497	−	1.44900i
$962$		0			0
$963$	−0.0224855	+	6.85960i	−0.000724586	+	0.221047i
$964$		0			0
$965$	−20.1698	+	7.34119i	−0.649287	+	0.236321i
$966$		0			0
$967$	−22.9411	+	19.2499i	−0.737736	+	0.619034i	−0.932228	−	0.361870i	$-0.882138\pi$
$967$	−22.9411	+	19.2499i	−0.737736	+	0.619034i	0.194493	+	0.980904i	$0.437694\pi$
$968$		0			0
$969$	32.3673	+	8.72967i	1.03979	+	0.280438i
$970$		0			0
$971$	10.5514	+	18.2755i	0.338609	+	0.586488i	0.984171	−	0.177220i	$-0.0567103\pi$
$971$	10.5514	+	18.2755i	0.338609	+	0.586488i	−0.645562	+	0.763708i	$0.723377\pi$
$972$		0			0
$973$	29.5107	−	28.1018i	0.946069	−	0.900901i
$974$		0			0
$975$	17.1703	−	17.1142i	0.549891	−	0.548091i
$976$		0			0
$977$	0.476600	+	2.70293i	0.0152478	+	0.0864745i	0.991482	−	0.130244i	$-0.0415759\pi$
$977$	0.476600	+	2.70293i	0.0152478	+	0.0864745i	−0.976234	+	0.216718i	$0.930465\pi$
$978$		0			0
$979$	6.59052	−	2.39875i	0.210634	−	0.0766645i
$980$		0			0
$981$	18.4634	−	10.5793i	0.589490	−	0.337771i
$982$		0			0
$983$	−19.3570	+	7.04539i	−0.617394	+	0.224713i	−0.631735	−	0.775184i	$-0.717657\pi$
$983$	−19.3570	+	7.04539i	−0.617394	+	0.224713i	0.0143414	+	0.999897i	$0.495435\pi$
$984$		0			0
$985$	−14.2991	+	11.9984i	−0.455608	+	0.382300i
$986$		0			0
$987$	−48.1739	+	7.20409i	−1.53339	+	0.229309i
$988$		0			0
$989$	−9.67751	+	16.7619i	−0.307727	+	0.532999i
$990$		0			0
$991$	−26.7756	−	46.3768i	−0.850556	−	1.47321i	−0.880707	−	0.473661i	$-0.842932\pi$
$991$	−26.7756	−	46.3768i	−0.850556	−	1.47321i	0.0301509	−	0.999545i	$-0.490401\pi$
$992$		0			0
$993$	0.566963	+	0.812539i	0.0179920	+	0.0257851i
$994$		0			0
$995$	−3.60627	−	1.31258i	−0.114326	−	0.0416114i
$996$		0			0
$997$	18.3059	+	15.3604i	0.579752	+	0.486470i	0.884866	−	0.465846i	$-0.154250\pi$
$997$	18.3059	+	15.3604i	0.579752	+	0.486470i	−0.305114	+	0.952316i	$0.598694\pi$
$998$		0			0
$999$	−15.2678	+	4.01065i	−0.483053	+	0.126891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.2	yes	144
7.2	even	3		756.2.bp.a.457.19	yes	144
27.13	even	9		756.2.bp.a.445.19	✓	144
189.121	even	9	inner	756.2.bq.a.121.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.19	✓	144	27.13	even	9
756.2.bp.a.457.19	yes	144	7.2	even	3
756.2.bq.a.25.2	yes	144	1.1	even	1	trivial
756.2.bq.a.121.2	yes	144	189.121	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67230 - 0.451029i) q^{3} +(-0.947523 - 0.344870i) q^{5} +(-1.17643 + 2.36981i) q^{7} +(2.59315 + 1.50851i) q^{9} +O(q^{10})\)	\(q+(-1.67230 - 0.451029i) q^{3} +(-0.947523 - 0.344870i) q^{5} +(-1.17643 + 2.36981i) q^{7} +(2.59315 + 1.50851i) q^{9} +(0.596107 - 0.216965i) q^{11} +(-0.610174 - 3.46047i) q^{13} +(1.42899 + 1.00409i) q^{15} -3.33094 q^{17} +5.81068 q^{19} +(3.03620 - 3.43242i) q^{21} +(0.754298 + 4.27784i) q^{23} +(-3.05136 - 2.56039i) q^{25} +(-3.65612 - 3.69226i) q^{27} +(1.01927 - 5.78056i) q^{29} +(6.70505 - 5.62620i) q^{31} +(-1.09473 + 0.0939683i) q^{33} +(1.93197 - 1.83974i) q^{35} +(1.51899 - 2.63097i) q^{37} +(-0.540381 + 6.06213i) q^{39} +(-1.55472 - 8.81728i) q^{41} +(3.41330 + 2.86410i) q^{43} +(-1.93683 - 2.32365i) q^{45} +(-8.14252 - 6.83238i) q^{47} +(-4.23202 - 5.57584i) q^{49} +(5.57032 + 1.50235i) q^{51} +(0.793989 - 1.37523i) q^{53} -0.639650 q^{55} +(-9.71717 - 2.62078i) q^{57} +(-2.19256 - 12.4346i) q^{59} +(-1.20617 - 1.01209i) q^{61} +(-6.62554 + 4.37061i) q^{63} +(-0.615259 + 3.48931i) q^{65} +(14.0966 + 5.13076i) q^{67} +(0.668020 - 7.49402i) q^{69} +(-2.10682 - 3.64912i) q^{71} +(3.74743 + 6.49074i) q^{73} +(3.94796 + 5.65799i) q^{75} +(-0.187113 + 1.66791i) q^{77} +(-2.51140 + 0.914074i) q^{79} +(4.44881 + 7.82356i) q^{81} +(-0.252308 + 1.43091i) q^{83} +(3.15614 + 1.14874i) q^{85} +(-4.31172 + 9.20709i) q^{87} +11.0559 q^{89} +(8.91849 + 2.62501i) q^{91} +(-13.7504 + 6.38450i) q^{93} +(-5.50575 - 2.00393i) q^{95} +(1.02710 + 0.861841i) q^{97} +(1.87309 + 0.336610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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