LMFDB - Embedded newform 756.2.ca.a.173.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(173,756)]

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, 13, 15]))

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

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

chi := DirichletCharacter("756.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ca (of order $18$, 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 $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.22
Character	$\chi$	$=$	756.173
Dual form			756.2.ca.a.437.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60174 - 0.659111i) q^{3} +(1.78193 - 1.49522i) q^{5} +(-2.30332 - 1.30182i) q^{7} +(2.13115 - 2.11145i) q^{9} +O(q^{10})$	\(q+(1.60174 - 0.659111i) q^{3} +(1.78193 - 1.49522i) q^{5} +(-2.30332 - 1.30182i) q^{7} +(2.13115 - 2.11145i) q^{9} +(-1.16901 + 1.39317i) q^{11} +(2.58138 + 3.07637i) q^{13} +(1.86868 - 3.56944i) q^{15} +(0.627338 - 1.08658i) q^{17} +(4.99627 - 2.88460i) q^{19} +(-4.54736 - 0.567034i) q^{21} +(2.92689 - 8.04158i) q^{23} +(0.0713616 - 0.404712i) q^{25} +(2.02186 - 4.78666i) q^{27} +(-4.11192 + 4.90039i) q^{29} +(-4.95535 - 5.90555i) q^{31} +(-0.954198 + 3.00201i) q^{33} +(-6.05085 + 1.12421i) q^{35} -4.09941 q^{37} +(6.16238 + 3.22613i) q^{39} +(1.98773 - 1.66790i) q^{41} +(-4.77434 + 1.73772i) q^{43} +(0.640478 - 6.94898i) q^{45} +(4.60313 + 3.86248i) q^{47} +(3.61054 + 5.99700i) q^{49} +(0.288655 - 2.15391i) q^{51} +(2.91534 - 1.68317i) q^{53} +4.23047i q^{55} +(6.10145 - 7.91347i) q^{57} +(1.70383 + 9.66292i) q^{59} +(-7.04217 + 8.39253i) q^{61} +(-7.65743 + 2.08897i) q^{63} +(9.19970 + 1.62215i) q^{65} +(-8.88674 - 3.23451i) q^{67} +(-0.612165 - 14.8097i) q^{69} +(4.63046 - 2.67340i) q^{71} +8.49091i q^{73} +(-0.152447 - 0.695279i) q^{75} +(4.50627 - 1.68708i) q^{77} +(-3.83933 + 1.39740i) q^{79} +(0.0835637 - 8.99961i) q^{81} +(7.74206 + 6.49636i) q^{83} +(-0.506802 - 2.87422i) q^{85} +(-3.35632 + 10.5594i) q^{87} +(3.26774 + 5.65990i) q^{89} +(-1.94086 - 10.4464i) q^{91} +(-11.8296 - 6.19304i) q^{93} +(4.58990 - 12.6107i) q^{95} +(-3.30745 - 9.08716i) q^{97} +(0.450282 + 5.43737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.60174	−	0.659111i	0.924765	−	0.380538i
$3$	1.60174	−	0.659111i	0.924765	−	0.380538i
$4$		0			0
$5$	1.78193	−	1.49522i	0.796904	−	0.668682i	−0.150540	−	0.988604i	$-0.548101\pi$
$5$	1.78193	−	1.49522i	0.796904	−	0.668682i	0.947444	+	0.319922i	$0.103657\pi$
$6$		0			0
$7$	−2.30332	−	1.30182i	−0.870572	−	0.492041i
$7$	−2.30332	−	1.30182i	−0.870572	−	0.492041i
$8$		0			0
$9$	2.13115	−	2.11145i	0.710382	−	0.703816i
$10$		0			0
$11$	−1.16901	+	1.39317i	−0.352471	+	0.420058i	−0.912925	−	0.408127i	$-0.866182\pi$
$11$	−1.16901	+	1.39317i	−0.352471	+	0.420058i	0.560455	+	0.828185i	$0.310626\pi$
$12$		0			0
$13$	2.58138	+	3.07637i	0.715947	+	0.853233i	0.994230	−	0.107267i	$-0.0342098\pi$
$13$	2.58138	+	3.07637i	0.715947	+	0.853233i	−0.278283	+	0.960499i	$0.589765\pi$
$14$		0			0
$15$	1.86868	−	3.56944i	0.482490	−	0.921626i
$16$		0			0
$17$	0.627338	−	1.08658i	0.152152	−	0.263535i	−0.779867	−	0.625946i	$-0.784713\pi$
$17$	0.627338	−	1.08658i	0.152152	−	0.263535i	0.932018	+	0.362411i	$0.118046\pi$
$18$		0			0
$19$	4.99627	−	2.88460i	1.14622	−	0.661772i	0.198258	−	0.980150i	$-0.436472\pi$
$19$	4.99627	−	2.88460i	1.14622	−	0.661772i	0.947964	+	0.318378i	$0.103138\pi$
$20$		0			0
$21$	−4.54736	−	0.567034i	−0.992315	−	0.123737i
$22$		0			0
$23$	2.92689	−	8.04158i	0.610300	−	1.67678i	−0.119257	−	0.992863i	$-0.538051\pi$
$23$	2.92689	−	8.04158i	0.610300	−	1.67678i	0.729556	−	0.683921i	$-0.239727\pi$
$24$		0			0
$25$	0.0713616	−	0.404712i	0.0142723	−	0.0809424i
$26$		0			0
$27$	2.02186	−	4.78666i	0.389108	−	0.921192i
$28$		0			0
$29$	−4.11192	+	4.90039i	−0.763564	+	0.909980i	−0.998068	−	0.0621353i	$-0.980209\pi$
$29$	−4.11192	+	4.90039i	−0.763564	+	0.909980i	0.234504	+	0.972115i	$0.424653\pi$
$30$		0			0
$31$	−4.95535	−	5.90555i	−0.890007	−	1.06067i	−0.997787	−	0.0664938i	$-0.978819\pi$
$31$	−4.95535	−	5.90555i	−0.890007	−	1.06067i	0.107780	−	0.994175i	$-0.465626\pi$
$32$		0			0
$33$	−0.954198	+	3.00201i	−0.166105	+	0.522583i
$34$		0			0
$35$	−6.05085	+	1.12421i	−1.02278	+	0.190026i
$36$		0			0
$37$	−4.09941			−0.673938			−0.336969	−	0.941516i	$-0.609402\pi$
$37$	−4.09941			−0.673938			−0.336969	+	0.941516i	$0.609402\pi$
$38$		0			0
$39$	6.16238	+	3.22613i	0.986770	+	0.516595i
$40$		0			0
$41$	1.98773	−	1.66790i	0.310431	−	0.260482i	−0.474239	−	0.880396i	$-0.657277\pi$
$41$	1.98773	−	1.66790i	0.310431	−	0.260482i	0.784670	+	0.619914i	$0.212832\pi$
$42$		0			0
$43$	−4.77434	+	1.73772i	−0.728079	+	0.264999i	−0.679352	−	0.733813i	$-0.737739\pi$
$43$	−4.77434	+	1.73772i	−0.728079	+	0.264999i	−0.0487278	+	0.998812i	$0.515517\pi$
$44$		0			0
$45$	0.640478	−	6.94898i	0.0954769	−	1.03589i
$46$		0			0
$47$	4.60313	+	3.86248i	0.671435	+	0.563401i	0.913490	−	0.406862i	$-0.133377\pi$
$47$	4.60313	+	3.86248i	0.671435	+	0.563401i	−0.242055	+	0.970263i	$0.577821\pi$
$48$		0			0
$49$	3.61054	+	5.99700i	0.515791	+	0.856714i
$50$		0			0
$51$	0.288655	−	2.15391i	0.0404198	−	0.301607i
$52$		0			0
$53$	2.91534	−	1.68317i	0.400453	−	0.231202i	−0.286226	−	0.958162i	$-0.592401\pi$
$53$	2.91534	−	1.68317i	0.400453	−	0.231202i	0.686679	+	0.726960i	$0.259068\pi$
$54$		0			0
$55$			4.23047i			0.570436i
$56$		0			0
$57$	6.10145	−	7.91347i	0.808157	−	1.04816i
$58$		0			0
$59$	1.70383	+	9.66292i	0.221820	+	1.25800i	0.868672	+	0.495389i	$0.164974\pi$
$59$	1.70383	+	9.66292i	0.221820	+	1.25800i	−0.646851	+	0.762616i	$0.723915\pi$
$60$		0			0
$61$	−7.04217	+	8.39253i	−0.901657	+	1.07455i	0.0952095	+	0.995457i	$0.469648\pi$
$61$	−7.04217	+	8.39253i	−0.901657	+	1.07455i	−0.996867	+	0.0790963i	$0.974797\pi$
$62$		0			0
$63$	−7.65743	+	2.08897i	−0.964745	+	0.263186i
$64$		0			0
$65$	9.19970	+	1.62215i	1.14108	+	0.201204i
$66$		0			0
$67$	−8.88674	−	3.23451i	−1.08569	−	0.395158i	−0.263666	−	0.964614i	$-0.584932\pi$
$67$	−8.88674	−	3.23451i	−1.08569	−	0.395158i	−0.822022	+	0.569456i	$0.807154\pi$
$68$		0			0
$69$	−0.612165	−	14.8097i	−0.0736960	−	1.78287i
$70$		0			0
$71$	4.63046	−	2.67340i	0.549534	−	0.317274i	−0.199400	−	0.979918i	$-0.563899\pi$
$71$	4.63046	−	2.67340i	0.549534	−	0.317274i	0.748934	+	0.662644i	$0.230566\pi$
$72$		0			0
$73$			8.49091i			0.993786i	0.867812	+	0.496893i	$0.165526\pi$
$73$			8.49091i			0.993786i	−0.867812	+	0.496893i	$0.834474\pi$
$74$		0			0
$75$	−0.152447	−	0.695279i	−0.0176031	−	0.0802839i
$76$		0			0
$77$	4.50627	−	1.68708i	0.513537	−	0.192261i
$78$		0			0
$79$	−3.83933	+	1.39740i	−0.431958	+	0.157220i	−0.548843	−	0.835926i	$-0.684931\pi$
$79$	−3.83933	+	1.39740i	−0.431958	+	0.157220i	0.116885	+	0.993146i	$0.462709\pi$
$80$		0			0
$81$	0.0835637	−	8.99961i	0.00928485	−	0.999957i
$82$		0			0
$83$	7.74206	+	6.49636i	0.849802	+	0.713068i	0.959746	−	0.280869i	$-0.0906228\pi$
$83$	7.74206	+	6.49636i	0.849802	+	0.713068i	−0.109944	+	0.993938i	$0.535067\pi$
$84$		0			0
$85$	−0.506802	−	2.87422i	−0.0549704	−	0.311753i
$86$		0			0
$87$	−3.35632	+	10.5594i	−0.359836	+	1.13208i
$88$		0			0
$89$	3.26774	+	5.65990i	0.346380	+	0.599948i	0.985604	−	0.169073i	$-0.0540774\pi$
$89$	3.26774	+	5.65990i	0.346380	+	0.599948i	−0.639223	+	0.769021i	$0.720744\pi$
$90$		0			0
$91$	−1.94086	−	10.4464i	−0.203458	−	1.09508i
$92$		0			0
$93$	−11.8296	−	6.19304i	−1.22667	−	0.642188i
$94$		0			0
$95$	4.58990	−	12.6107i	0.470914	−	1.29383i
$96$		0			0
$97$	−3.30745	−	9.08716i	−0.335821	−	0.922661i	−0.986566	−	0.163364i	$-0.947765\pi$
$97$	−3.30745	−	9.08716i	−0.335821	−	0.922661i	0.650745	−	0.759297i	$-0.274457\pi$
$98$		0			0
$99$	0.450282	+	5.43737i	0.0452551	+	0.546476i
$100$		0			0
$101$	1.34972	−	0.491256i	0.134302	−	0.0488818i	−0.273995	−	0.961731i	$-0.588345\pi$
$101$	1.34972	−	0.491256i	0.134302	−	0.0488818i	0.408297	+	0.912849i	$0.366123\pi$
$102$		0			0
$103$	1.01384	+	1.20825i	0.0998970	+	0.119053i	0.813677	−	0.581318i	$-0.197463\pi$
$103$	1.01384	+	1.20825i	0.0998970	+	0.119053i	−0.713780	+	0.700370i	$0.753018\pi$
$104$		0			0
$105$	−8.95092	+	5.78888i	−0.873520	+	0.564936i
$106$		0			0
$107$	13.8232	+	7.98083i	1.33634	+	0.771536i	0.986263	−	0.165184i	$-0.0528219\pi$
$107$	13.8232	+	7.98083i	1.33634	+	0.771536i	0.350078	+	0.936721i	$0.386155\pi$
$108$		0			0
$109$	3.77704	+	6.54202i	0.361774	+	0.626612i	0.988253	−	0.152827i	$-0.0488378\pi$
$109$	3.77704	+	6.54202i	0.361774	+	0.626612i	−0.626479	+	0.779439i	$0.715504\pi$
$110$		0			0
$111$	−6.56619	+	2.70196i	−0.623235	+	0.256459i
$112$		0			0
$113$	−2.00364	+	5.50496i	−0.188487	+	0.517863i	−0.997558	−	0.0698478i	$-0.977749\pi$
$113$	−2.00364	+	5.50496i	−0.188487	+	0.517863i	0.809071	+	0.587711i	$0.199971\pi$
$114$		0			0
$115$	−6.80838	−	18.7059i	−0.634885	−	1.74433i
$116$		0			0
$117$	11.9969	+	1.10574i	1.10911	+	0.102226i
$118$		0			0
$119$	−2.85949	+	1.68606i	−0.262129	+	0.154561i
$120$		0			0
$121$	1.33578	+	7.57561i	0.121435	+	0.688692i
$122$		0			0
$123$	2.08449	−	3.98168i	0.187952	−	0.359016i
$124$		0			0
$125$	5.33739	+	9.24464i	0.477391	+	0.826866i
$126$		0			0
$127$	−3.42823	+	5.93786i	−0.304206	+	0.526900i	−0.977084	−	0.212853i	$-0.931724\pi$
$127$	−3.42823	+	5.93786i	−0.304206	+	0.526900i	0.672878	+	0.739753i	$0.265058\pi$
$128$		0			0
$129$	−6.50190	+	5.93019i	−0.572460	+	0.522124i
$130$		0			0
$131$	−12.7027	−	4.62339i	−1.10984	−	0.403948i	−0.278904	−	0.960319i	$-0.589971\pi$
$131$	−12.7027	−	4.62339i	−1.10984	−	0.403948i	−0.830934	+	0.556371i	$0.812193\pi$
$132$		0			0
$133$	−15.2632	+	0.139905i	−1.32349	+	0.0121313i
$134$		0			0
$135$	−3.55427	−	11.5526i	−0.305903	−	0.994291i
$136$		0			0
$137$	20.6786	+	3.64619i	1.76669	+	0.311515i	0.960113	−	0.279612i	$-0.0902057\pi$
$137$	20.6786	+	3.64619i	1.76669	+	0.311515i	0.806578	+	0.591127i	$0.201317\pi$
$138$		0			0
$139$	20.1849	−	3.55915i	1.71206	−	0.301883i	0.770180	−	0.637826i	$-0.220166\pi$
$139$	20.1849	−	3.55915i	1.71206	−	0.301883i	0.941882	+	0.335944i	$0.109055\pi$
$140$		0			0
$141$	9.91882	+	3.15272i	0.835315	+	0.265507i
$142$		0			0
$143$	−7.30360			−0.610757
$144$		0			0
$145$			14.8804i			1.23575i
$146$		0			0
$147$	9.73583	+	7.22590i	0.802998	+	0.595982i
$148$		0			0
$149$	6.82203	−	1.20291i	0.558882	−	0.0985460i	0.112930	−	0.993603i	$-0.463976\pi$
$149$	6.82203	−	1.20291i	0.558882	−	0.0985460i	0.445952	+	0.895057i	$0.352865\pi$
$150$		0			0
$151$	0.814994	+	0.683861i	0.0663232	+	0.0556518i	0.675347	−	0.737500i	$-0.263994\pi$
$151$	0.814994	+	0.683861i	0.0663232	+	0.0556518i	−0.609023	+	0.793152i	$0.708438\pi$
$152$		0			0
$153$	−0.957312	−	3.64025i	−0.0773941	−	0.294297i
$154$		0			0
$155$	−17.6602	−	3.11397i	−1.41850	−	0.250120i
$156$		0			0
$157$	−6.77471	+	1.19456i	−0.540681	+	0.0953366i	−0.437318	−	0.899307i	$-0.644071\pi$
$157$	−6.77471	+	1.19456i	−0.540681	+	0.0953366i	−0.103363	+	0.994644i	$0.532960\pi$
$158$		0			0
$159$	3.56022	−	4.61754i	0.282344	−	0.366195i
$160$		0			0
$161$	−17.2102	+	14.7120i	−1.35636	+	1.15947i
$162$		0			0
$163$	−11.1280	+	19.2742i	−0.871609	+	1.50967i	−0.0112777	+	0.999936i	$0.503590\pi$
$163$	−11.1280	+	19.2742i	−0.871609	+	1.50967i	−0.860331	+	0.509735i	$0.829743\pi$
$164$		0			0
$165$	2.78835	+	6.77612i	0.217073	+	0.527520i
$166$		0			0
$167$	−0.764681	−	0.278321i	−0.0591728	−	0.0215371i	0.312264	−	0.949995i	$-0.398913\pi$
$167$	−0.764681	−	0.278321i	−0.0591728	−	0.0215371i	−0.371437	+	0.928458i	$0.621135\pi$
$168$		0			0
$169$	−0.543105	+	3.08010i	−0.0417773	+	0.236931i
$170$		0			0
$171$	4.55709	−	16.6969i	0.348490	−	1.27684i
$172$		0			0
$173$	−1.49551	+	8.48146i	−0.113702	+	0.644833i	0.873683	+	0.486495i	$0.161725\pi$
$173$	−1.49551	+	8.48146i	−0.113702	+	0.644833i	−0.987385	+	0.158338i	$0.949386\pi$
$174$		0			0
$175$	−0.691230	+	0.839280i	−0.0522521	+	0.0634436i
$176$		0			0
$177$	9.09803	+	14.3545i	0.683850	+	1.07895i
$178$		0			0
$179$	−18.7319	−	10.8149i	−1.40009	−	0.808340i	−0.405685	−	0.914013i	$-0.632967\pi$
$179$	−18.7319	−	10.8149i	−1.40009	−	0.808340i	−0.994401	+	0.105673i	$0.966300\pi$
$180$		0			0
$181$	−6.59068	−	3.80513i	−0.489882	−	0.282833i	0.234644	−	0.972081i	$-0.424608\pi$
$181$	−6.59068	−	3.80513i	−0.489882	−	0.282833i	−0.724525	+	0.689248i	$0.757941\pi$
$182$		0			0
$183$	−5.74812	+	18.0842i	−0.424913	+	1.33682i
$184$		0			0
$185$	−7.30486	+	6.12951i	−0.537064	+	0.450650i
$186$		0			0
$187$	0.780432	+	2.14422i	0.0570708	+	0.156801i
$188$		0			0
$189$	−10.8883	+	8.39308i	−0.792011	+	0.610507i
$190$		0			0
$191$	3.95814	+	10.8749i	0.286401	+	0.786881i	0.996563	+	0.0828421i	$0.0263997\pi$
$191$	3.95814	+	10.8749i	0.286401	+	0.786881i	−0.710161	+	0.704039i	$0.751378\pi$
$192$		0			0
$193$	8.66629	−	7.27188i	0.623813	−	0.523441i	−0.275186	−	0.961391i	$-0.588740\pi$
$193$	8.66629	−	7.27188i	0.623813	−	0.523441i	0.899000	+	0.437949i	$0.144295\pi$
$194$		0			0
$195$	15.8047	−	3.46535i	1.13180	−	0.248159i
$196$		0			0
$197$	−3.98585	−	2.30123i	−0.283980	−	0.163956i	0.351244	−	0.936284i	$-0.385759\pi$
$197$	−3.98585	−	2.30123i	−0.283980	−	0.163956i	−0.635224	+	0.772328i	$0.719092\pi$
$198$		0			0
$199$	−20.6571	−	11.9264i	−1.46435	−	0.845440i	−0.465138	−	0.885238i	$-0.653995\pi$
$199$	−20.6571	−	11.9264i	−1.46435	−	0.845440i	−0.999208	+	0.0397983i	$0.987328\pi$
$200$		0			0
$201$	−16.3662	+	0.676503i	−1.15438	+	0.0477169i
$202$		0			0
$203$	15.8505	−	5.93418i	1.11248	−	0.416498i
$204$		0			0
$205$	1.04812	−	5.94417i	0.0732037	−	0.415159i
$206$		0			0
$207$	−10.7417	−	23.3178i	−0.746603	−	1.62070i
$208$		0			0
$209$	−1.82195	+	10.3328i	−0.126027	+	0.714735i
$210$		0			0
$211$	7.50376	+	2.73115i	0.516580	+	0.188020i	0.587136	−	0.809488i	$-0.300255\pi$
$211$	7.50376	+	2.73115i	0.516580	+	0.188020i	−0.0705562	+	0.997508i	$0.522477\pi$
$212$		0			0
$213$	5.65473	−	7.33407i	0.387456	−	0.502522i
$214$		0			0
$215$	−5.90927	+	10.2352i	−0.403009	+	0.698032i
$216$		0			0
$217$	3.72578	+	20.0533i	0.252922	+	1.36131i
$218$		0			0
$219$	5.59645	+	13.6002i	0.378173	+	0.919019i
$220$		0			0
$221$	4.96213	−	0.874957i	0.333789	−	0.0588560i
$222$		0			0
$223$	6.24957	+	1.10197i	0.418502	+	0.0737932i	0.378934	−	0.925424i	$-0.376291\pi$
$223$	6.24957	+	1.10197i	0.418502	+	0.0737932i	0.0395680	+	0.999217i	$0.487402\pi$
$224$		0			0
$225$	−0.702447	−	1.01318i	−0.0468298	−	0.0675451i
$226$		0			0
$227$	−2.75362	−	2.31056i	−0.182764	−	0.153358i	0.546815	−	0.837253i	$-0.315840\pi$
$227$	−2.75362	−	2.31056i	−0.182764	−	0.153358i	−0.729580	+	0.683896i	$0.760284\pi$
$228$		0			0
$229$	−24.0903	+	4.24777i	−1.59193	+	0.280700i	−0.898217	−	0.439551i	$-0.855137\pi$
$229$	−24.0903	+	4.24777i	−1.59193	+	0.280700i	−0.693713	+	0.720252i	$0.744026\pi$
$230$		0			0
$231$	6.10590	−	5.67240i	0.401739	−	0.373216i
$232$		0			0
$233$		−	24.2134i		−	1.58627i	−0.609045	−	0.793136i	$-0.708447\pi$
$233$		−	24.2134i		−	1.58627i	0.609045	−	0.793136i	$-0.291553\pi$
$234$		0			0
$235$	13.9777			0.911805
$236$		0			0
$237$	−5.22857	+	4.76882i	−0.339632	+	0.309768i
$238$		0			0
$239$	2.42563	−	0.427703i	0.156901	−	0.0276658i	−0.0946460	−	0.995511i	$-0.530172\pi$
$239$	2.42563	−	0.427703i	0.156901	−	0.0276658i	0.251547	+	0.967845i	$0.419061\pi$
$240$		0			0
$241$	6.34883	+	1.11947i	0.408964	+	0.0721114i	0.374346	−	0.927289i	$-0.377867\pi$
$241$	6.34883	+	1.11947i	0.408964	+	0.0721114i	0.0346183	+	0.999401i	$0.488978\pi$
$242$		0			0
$243$	−5.79789	−	14.4701i	−0.371935	−	0.928259i
$244$		0			0
$245$	15.4006	+	5.28771i	0.983905	+	0.337819i
$246$		0			0
$247$	21.7714	+	7.92413i	1.38528	+	0.504200i
$248$		0			0
$249$	16.6826	+	5.30261i	1.05722	+	0.336039i
$250$		0			0
$251$	−5.67332	+	9.82648i	−0.358097	+	0.620242i	−0.987643	−	0.156721i	$-0.949908\pi$
$251$	−5.67332	+	9.82648i	−0.358097	+	0.620242i	0.629546	+	0.776963i	$0.283241\pi$
$252$		0			0
$253$	7.78174	+	13.4784i	0.489234	+	0.847378i
$254$		0			0
$255$	−2.70620	−	4.26971i	−0.169469	−	0.267380i
$256$		0			0
$257$	3.54214	+	20.0884i	0.220952	+	1.25308i	0.870274	+	0.492569i	$0.163942\pi$
$257$	3.54214	+	20.0884i	0.220952	+	1.25308i	−0.649321	+	0.760514i	$0.724947\pi$
$258$		0			0
$259$	9.44223	+	5.33669i	0.586712	+	0.331605i
$260$		0			0
$261$	1.58383	+	19.1256i	0.0980369	+	1.18384i
$262$		0			0
$263$	−10.0950	−	27.7359i	−0.622487	−	1.71027i	−0.700818	−	0.713340i	$-0.747181\pi$
$263$	−10.0950	−	27.7359i	−0.622487	−	1.71027i	0.0783313	−	0.996927i	$-0.475041\pi$
$264$		0			0
$265$	2.67823	−	7.35837i	0.164522	−	0.452021i
$266$		0			0
$267$	8.96458	+	6.91188i	0.548623	+	0.423000i
$268$		0			0
$269$	−14.8916	−	25.7929i	−0.907954	−	1.57262i	−0.816902	−	0.576777i	$-0.804310\pi$
$269$	−14.8916	−	25.7929i	−0.907954	−	1.57262i	−0.0910522	−	0.995846i	$-0.529023\pi$
$270$		0			0
$271$	−22.2490	−	12.8455i	−1.35153	−	0.780307i	−0.363068	−	0.931763i	$-0.618271\pi$
$271$	−22.2490	−	12.8455i	−1.35153	−	0.780307i	−0.988464	+	0.151455i	$0.951604\pi$
$272$		0			0
$273$	−9.99407	−	15.4531i	−0.604869	−	0.935265i
$274$		0			0
$275$	0.480412	+	0.572532i	0.0289699	+	0.0345250i
$276$		0			0
$277$	−17.0126	+	6.19207i	−1.02219	+	0.372045i	−0.798101	−	0.602524i	$-0.794162\pi$
$277$	−17.0126	+	6.19207i	−1.02219	+	0.372045i	−0.224085	+	0.974570i	$0.571939\pi$
$278$		0			0
$279$	−23.0298	−	2.12263i	−1.37876	−	0.127078i
$280$		0			0
$281$	3.92202	+	10.7757i	0.233968	+	0.642822i	1.00000		1.93050e-5i	$6.14496e-6\pi$
$281$	3.92202	+	10.7757i	0.233968	+	0.642822i	−0.766032	+	0.642802i	$0.777772\pi$
$282$		0			0
$283$	2.88705	−	7.93211i	0.171617	−	0.471515i	−0.823829	−	0.566838i	$-0.808166\pi$
$283$	2.88705	−	7.93211i	0.171617	−	0.471515i	0.995446	+	0.0953237i	$0.0303886\pi$
$284$		0			0
$285$	−0.959986	−	23.2243i	−0.0568647	−	1.37569i
$286$		0			0
$287$	−6.74967	+	1.25404i	−0.398420	+	0.0740239i
$288$		0			0
$289$	7.71289	+	13.3591i	0.453700	+	0.785831i
$290$		0			0
$291$	−11.2871	−	12.3753i	−0.661663	−	0.725452i
$292$		0			0
$293$	−3.30387	−	18.7372i	−0.193014	−	1.09464i	−0.915218	−	0.402958i	$-0.867982\pi$
$293$	−3.30387	−	18.7372i	−0.193014	−	1.09464i	0.722204	−	0.691680i	$-0.243129\pi$
$294$		0			0
$295$	17.4843	+	14.6711i	1.01797	+	0.854182i
$296$		0			0
$297$	4.30506	+	8.41247i	0.249805	+	0.488141i
$298$		0			0
$299$	32.2943	−	11.7542i	1.86763	−	0.679761i
$300$		0			0
$301$	13.2590	+	2.21281i	0.764236	+	0.127544i
$302$		0			0
$303$	1.83810	−	1.67648i	0.105596	−	0.0963111i
$304$		0			0
$305$			25.4845i			1.45924i
$306$		0			0
$307$	−23.5264	+	13.5830i	−1.34272	+	0.775223i	−0.987207	−	0.159447i	$-0.949029\pi$
$307$	−23.5264	+	13.5830i	−1.34272	+	0.775223i	−0.355518	+	0.934669i	$0.615696\pi$
$308$		0			0
$309$	2.42029	+	1.26707i	0.137685	+	0.0720811i
$310$		0			0
$311$	−22.9794	−	8.36381i	−1.30304	−	0.474268i	−0.405055	−	0.914292i	$-0.632748\pi$
$311$	−22.9794	−	8.36381i	−1.30304	−	0.474268i	−0.897986	+	0.440025i	$0.854970\pi$
$312$		0			0
$313$	−13.3464	−	2.35334i	−0.754385	−	0.133018i	−0.216786	−	0.976219i	$-0.569557\pi$
$313$	−13.3464	−	2.35334i	−0.754385	−	0.133018i	−0.537599	+	0.843201i	$0.680669\pi$
$314$		0			0
$315$	−10.5215	+	15.1719i	−0.592822	+	0.854841i
$316$		0			0
$317$	12.1536	−	14.4841i	0.682612	−	0.813506i	−0.307829	−	0.951442i	$-0.599602\pi$
$317$	12.1536	−	14.4841i	0.682612	−	0.813506i	0.990441	+	0.137936i	$0.0440469\pi$
$318$		0			0
$319$	−2.02022	−	11.4572i	−0.113111	−	0.641482i
$320$		0			0
$321$	27.4015	+	3.67220i	1.52940	+	0.204962i
$322$		0			0
$323$		−	7.23846i		−	0.402759i
$324$		0			0
$325$	1.42926	−	0.825182i	0.0792809	−	0.0457728i
$326$		0			0
$327$	10.3617	+	7.98913i	0.573006	+	0.441800i
$328$		0			0
$329$	−5.57421	−	14.8890i	−0.307316	−	0.820855i
$330$		0			0
$331$	−13.9388	−	11.6961i	−0.766148	−	0.642875i	0.173571	−	0.984821i	$-0.444469\pi$
$331$	−13.9388	−	11.6961i	−0.766148	−	0.642875i	−0.939719	+	0.341947i	$0.888914\pi$
$332$		0			0
$333$	−8.73643	+	8.65569i	−0.478754	+	0.474329i
$334$		0			0
$335$	−20.6719	+	7.52394i	−1.12942	+	0.411077i
$336$		0			0
$337$	4.58257	−	3.84523i	0.249629	−	0.209463i	−0.509384	−	0.860539i	$-0.670127\pi$
$337$	4.58257	−	3.84523i	0.249629	−	0.209463i	0.759012	+	0.651076i	$0.225682\pi$
$338$		0			0
$339$	0.419065	+	10.1381i	0.0227605	+	0.550629i
$340$		0			0
$341$	14.0203			0.759243
$342$		0			0
$343$	−0.509202	−	18.5133i	−0.0274943	−	0.999622i
$344$		0			0
$345$	−23.2345	−	25.4745i	−1.25090	−	1.37150i
$346$		0			0
$347$	17.3976	+	20.7337i	0.933954	+	1.11304i	0.993387	+	0.114810i	$0.0366260\pi$
$347$	17.3976	+	20.7337i	0.933954	+	1.11304i	−0.0594339	+	0.998232i	$0.518930\pi$
$348$		0			0
$349$	−10.3811	+	12.3717i	−0.555686	+	0.662241i	−0.968628	−	0.248517i	$-0.920057\pi$
$349$	−10.3811	+	12.3717i	−0.555686	+	0.662241i	0.412942	+	0.910757i	$0.364501\pi$
$350$		0			0
$351$	19.9447	−	6.13619i	1.06457	−	0.327526i
$352$		0			0
$353$	−2.72950	+	15.4798i	−0.145277	+	0.823906i	0.821868	+	0.569679i	$0.192932\pi$
$353$	−2.72950	+	15.4798i	−0.145277	+	0.823906i	−0.967144	+	0.254228i	$0.918179\pi$
$354$		0			0
$355$	4.25385	−	11.6874i	0.225771	−	0.620300i
$356$		0			0
$357$	−3.46886	+	4.58535i	−0.183591	+	0.242683i
$358$		0			0
$359$	−2.18400	+	1.26094i	−0.115267	+	0.0665496i	−0.556525	−	0.830831i	$-0.687866\pi$
$359$	−2.18400	+	1.26094i	−0.115267	+	0.0665496i	0.441258	+	0.897380i	$0.354532\pi$
$360$		0			0
$361$	7.14178	−	12.3699i	0.375883	−	0.651049i
$362$		0			0
$363$	7.13275	+	11.2537i	0.374372	+	0.590668i
$364$		0			0
$365$	12.6958	+	15.1302i	0.664527	+	0.791952i
$366$		0			0
$367$	22.5449	−	26.8679i	1.17683	−	1.40249i	0.280070	−	0.959979i	$-0.409642\pi$
$367$	22.5449	−	26.8679i	1.17683	−	1.40249i	0.896761	−	0.442514i	$-0.145913\pi$
$368$		0			0
$369$	0.714447	−	7.75152i	0.0371926	−	0.403528i
$370$		0			0
$371$	−8.90614	+	0.0816353i	−0.462384	+	0.00423830i
$372$		0			0
$373$	23.5080	−	19.7256i	1.21720	−	1.02135i	0.218233	−	0.975897i	$-0.429971\pi$
$373$	23.5080	−	19.7256i	1.21720	−	1.02135i	0.998966	−	0.0454549i	$-0.0144737\pi$
$374$		0			0
$375$	14.6424	+	11.2896i	0.756128	+	0.582991i
$376$		0			0
$377$	−25.6899			−1.32310
$378$		0			0
$379$	25.4637			1.30798			0.653991	−	0.756502i	$-0.273093\pi$
$379$	25.4637			1.30798			0.653991	+	0.756502i	$0.273093\pi$
$380$		0			0
$381$	−1.57742	+	11.7705i	−0.0808137	+	0.603021i
$382$		0			0
$383$	7.81140	−	6.55454i	0.399144	−	0.334922i	−0.421019	−	0.907052i	$-0.638327\pi$
$383$	7.81140	−	6.55454i	0.399144	−	0.334922i	0.820163	+	0.572130i	$0.193883\pi$
$384$		0			0
$385$	5.50730	−	9.74411i	0.280678	−	0.496606i
$386$		0			0
$387$	−6.50571	+	13.7841i	−0.330704	+	0.700685i
$388$		0			0
$389$	12.7342	−	15.1761i	0.645652	−	0.769458i	−0.339600	−	0.940570i	$-0.610292\pi$
$389$	12.7342	−	15.1761i	0.645652	−	0.769458i	0.985252	+	0.171112i	$0.0547360\pi$
$390$		0			0
$391$	−6.90167	−	8.22509i	−0.349033	−	0.415961i
$392$		0			0
$393$	−23.3937	+	0.966991i	−1.18006	+	0.0487782i
$394$		0			0
$395$	−4.75200	+	8.23071i	−0.239099	+	0.414132i
$396$		0			0
$397$	6.01682	−	3.47381i	0.301975	−	0.174346i	−0.341355	−	0.939935i	$-0.610886\pi$
$397$	6.01682	−	3.47381i	0.301975	−	0.174346i	0.643330	+	0.765589i	$0.277552\pi$
$398$		0			0
$399$	−24.3555	+	10.2842i	−1.21930	+	0.514856i
$400$		0			0
$401$	11.5540	−	31.7443i	0.576978	−	1.58523i	−0.216270	−	0.976334i	$-0.569389\pi$
$401$	11.5540	−	31.7443i	0.576978	−	1.58523i	0.793247	−	0.608899i	$-0.208389\pi$
$402$		0			0
$403$	5.37603	−	30.4890i	0.267799	−	1.51877i
$404$		0			0
$405$	−13.3075	−	16.1616i	−0.661254	−	0.803078i
$406$		0			0
$407$	4.79226	−	5.71119i	0.237543	−	0.283093i
$408$		0			0
$409$	−10.4919	−	12.5038i	−0.518792	−	0.618272i	0.441503	−	0.897260i	$-0.354445\pi$
$409$	−10.4919	−	12.5038i	−0.518792	−	0.618272i	−0.960295	+	0.278988i	$0.910001\pi$
$410$		0			0
$411$	35.5250	−	7.78923i	1.75232	−	0.384214i
$412$		0			0
$413$	8.65490	−	24.4748i	0.425880	−	1.20433i
$414$		0			0
$415$	23.5093			1.15403
$416$		0			0
$417$	29.9851	−	19.0049i	1.46838	−	0.930675i
$418$		0			0
$419$	18.4928	−	15.5173i	0.903431	−	0.758069i	−0.0674271	−	0.997724i	$-0.521479\pi$
$419$	18.4928	−	15.5173i	0.903431	−	0.758069i	0.970858	+	0.239656i	$0.0770345\pi$
$420$		0			0
$421$	0.657830	−	0.239431i	0.0320607	−	0.0116691i	−0.325940	−	0.945390i	$-0.605681\pi$
$421$	0.657830	−	0.239431i	0.0320607	−	0.0116691i	0.358001	+	0.933721i	$0.383459\pi$
$422$		0			0
$423$	17.9654	−	1.48776i	0.873506	−	0.0723372i
$424$		0			0
$425$	−0.394984	−	0.331431i	−0.0191596	−	0.0160768i
$426$		0			0
$427$	27.1459	−	10.1630i	1.31368	−	0.491824i
$428$		0			0
$429$	−11.6985	+	4.81388i	−0.564807	+	0.232416i
$430$		0			0
$431$	−14.9907	+	8.65486i	−0.722074	+	0.416890i	−0.815516	−	0.578735i	$-0.803547\pi$
$431$	−14.9907	+	8.65486i	−0.722074	+	0.416890i	0.0934413	+	0.995625i	$0.470213\pi$
$432$		0			0
$433$		−	27.8478i		−	1.33828i	−0.743136	−	0.669141i	$-0.766662\pi$
$433$		−	27.8478i		−	1.33828i	0.743136	−	0.669141i	$-0.233338\pi$
$434$		0			0
$435$	9.80781	+	23.8345i	0.470249	+	1.14278i
$436$		0			0
$437$	−8.57315	−	48.6208i	−0.410109	−	2.32585i
$438$		0			0
$439$	−5.54212	+	6.60485i	−0.264511	+	0.315232i	−0.881910	−	0.471418i	$-0.843742\pi$
$439$	−5.54212	+	6.60485i	−0.264511	+	0.315232i	0.617399	+	0.786651i	$0.288187\pi$
$440$		0			0
$441$	20.3569	+	5.15702i	0.969378	+	0.245572i
$442$		0			0
$443$	−20.2557	−	3.57163i	−0.962379	−	0.169693i	−0.329681	−	0.944092i	$-0.606941\pi$
$443$	−20.2557	−	3.57163i	−0.962379	−	0.169693i	−0.632698	+	0.774399i	$0.718052\pi$
$444$		0			0
$445$	14.2857	+	5.19956i	0.677206	+	0.246483i
$446$		0			0
$447$	10.1343	−	6.42322i	0.479335	−	0.303808i
$448$		0			0
$449$	0.162556	−	0.0938518i	0.00767150	−	0.00442914i	−0.496159	−	0.868231i	$-0.665257\pi$
$449$	0.162556	−	0.0938518i	0.00767150	−	0.00442914i	0.503831	+	0.863802i	$0.331923\pi$
$450$		0			0
$451$			4.71905i			0.222211i
$452$		0			0
$453$	1.75615	+	0.558196i	0.0825110	+	0.0262264i
$454$		0			0
$455$	−19.0781	−	15.7127i	−0.894394	−	0.736621i
$456$		0			0
$457$	−4.57112	+	1.66375i	−0.213828	+	0.0778270i	−0.446713	−	0.894677i	$-0.647406\pi$
$457$	−4.57112	+	1.66375i	−0.213828	+	0.0778270i	0.232885	+	0.972504i	$0.425183\pi$
$458$		0			0
$459$	−3.93270	−	5.19977i	−0.183563	−	0.242704i
$460$		0			0
$461$	23.6098	+	19.8110i	1.09962	+	0.922690i	0.997399	−	0.0720715i	$-0.0229610\pi$
$461$	23.6098	+	19.8110i	1.09962	+	0.922690i	0.102220	+	0.994762i	$0.467405\pi$
$462$		0			0
$463$	−1.71296	−	9.71467i	−0.0796080	−	0.451479i	−0.998390	−	0.0567150i	$-0.981937\pi$
$463$	−1.71296	−	9.71467i	−0.0796080	−	0.451479i	0.918782	−	0.394764i	$-0.129174\pi$
$464$		0			0
$465$	−30.3395	+	6.65225i	−1.40696	+	0.308491i
$466$		0			0
$467$	1.65333	+	2.86365i	0.0765070	+	0.132514i	0.901741	−	0.432277i	$-0.142290\pi$
$467$	1.65333	+	2.86365i	0.0765070	+	0.132514i	−0.825234	+	0.564792i	$0.808957\pi$
$468$		0			0
$469$	16.2582	+	19.0190i	0.750736	+	0.878217i
$470$		0			0
$471$	−10.0640	+	6.37867i	−0.463724	+	0.293914i
$472$		0			0
$473$	3.16032	−	8.68290i	0.145311	−	0.399240i
$474$		0			0
$475$	−0.810888	−	2.22790i	−0.0372061	−	0.102223i
$476$		0			0
$477$	2.65908	−	9.74268i	0.121751	−	0.446087i
$478$		0			0
$479$	−13.5249	+	4.92266i	−0.617969	+	0.224922i	−0.631986	−	0.774979i	$-0.717760\pi$
$479$	−13.5249	+	4.92266i	−0.617969	+	0.224922i	0.0140176	+	0.999902i	$0.495538\pi$
$480$		0			0
$481$	−10.5821	−	12.6113i	−0.482504	−	0.575026i
$482$		0			0
$483$	−17.8695	+	34.9083i	−0.813090	+	1.58838i
$484$		0			0
$485$	−19.4809	−	11.2473i	−0.884584	−	0.510715i
$486$		0			0
$487$	16.1563	+	27.9836i	0.732113	+	1.26806i	0.955979	+	0.293436i	$0.0947989\pi$
$487$	16.1563	+	27.9836i	0.732113	+	1.26806i	−0.223866	+	0.974620i	$0.571868\pi$
$488$		0			0
$489$	−5.12028	+	38.2068i	−0.231547	+	1.72777i
$490$		0			0
$491$	−7.74489	+	21.2789i	−0.349522	+	0.960303i	0.632999	+	0.774152i	$0.281824\pi$
$491$	−7.74489	+	21.2789i	−0.349522	+	0.960303i	−0.982521	+	0.186151i	$0.940399\pi$
$492$		0			0
$493$	2.74511	+	7.54213i	0.123634	+	0.339681i
$494$		0			0
$495$	8.93242	+	9.01575i	0.401483	+	0.405228i
$496$		0			0
$497$	−14.1457	+	0.129662i	−0.634521	+	0.00581614i
$498$		0			0
$499$	3.19630	+	18.1271i	0.143086	+	0.811482i	0.968884	+	0.247516i	$0.0796142\pi$
$499$	3.19630	+	18.1271i	0.143086	+	0.811482i	−0.825798	+	0.563966i	$0.809275\pi$
$500$		0			0
$501$	−1.40826	+	0.0582113i	−0.0629166	+	0.00260069i
$502$		0			0
$503$	−12.3813	−	21.4450i	−0.552053	−	0.956184i	−0.998126	−	0.0611879i	$-0.980511\pi$
$503$	−12.3813	−	21.4450i	−0.552053	−	0.956184i	0.446073	−	0.894997i	$-0.352822\pi$
$504$		0			0
$505$	1.67056	−	2.89350i	0.0743391	−	0.128759i
$506$		0			0
$507$	1.16022	+	5.29149i	0.0515270	+	0.235003i
$508$		0			0
$509$	1.54319	+	0.561675i	0.0684007	+	0.0248958i	0.375994	−	0.926622i	$-0.377301\pi$
$509$	1.54319	+	0.561675i	0.0684007	+	0.0248958i	−0.307593	+	0.951518i	$0.599524\pi$
$510$		0			0
$511$	11.0536	−	19.5573i	0.488984	−	0.865162i
$512$		0			0
$513$	−3.70580	−	29.7477i	−0.163615	−	1.31339i
$514$		0			0
$515$	3.61320	+	0.637105i	0.159217	+	0.0280742i
$516$		0			0
$517$	−10.7622	+	1.89767i	−0.473322	+	0.0834594i
$518$		0			0
$519$	3.19480	+	14.5708i	0.140236	+	0.639587i
$520$		0			0
$521$	−14.9291			−0.654058			−0.327029	−	0.945014i	$-0.606047\pi$
$521$	−14.9291			−0.654058			−0.327029	+	0.945014i	$0.606047\pi$
$522$		0			0
$523$			37.3267i			1.63218i	0.577924	+	0.816091i	$0.303863\pi$
$523$			37.3267i			1.63218i	−0.577924	+	0.816091i	$0.696137\pi$
$524$		0			0
$525$	−0.553992	+	1.79991i	−0.0241782	+	0.0785543i
$526$		0			0
$527$	−9.52554	+	1.67961i	−0.414939	+	0.0731649i
$528$		0			0
$529$	−38.4812	−	32.2896i	−1.67310	−	1.40389i
$530$		0			0
$531$	24.0339	+	16.9955i	1.04298	+	0.737543i
$532$		0			0
$533$	10.2622	+	1.80950i	0.444504	+	0.0783781i
$534$		0			0
$535$	36.5651	−	6.44741i	1.58085	−	0.278746i
$536$		0			0
$537$	−37.1318	−	4.97621i	−1.60235	−	0.214739i
$538$		0			0
$539$	−12.5756	−	1.98046i	−0.541671	−	0.0853045i
$540$		0			0
$541$	−1.30807	+	2.26565i	−0.0562385	+	0.0974080i	−0.892774	−	0.450505i	$-0.851244\pi$
$541$	−1.30807	+	2.26565i	−0.0562385	+	0.0974080i	0.836536	+	0.547913i	$0.184577\pi$
$542$		0			0
$543$	−13.0646	−	1.75084i	−0.560654	−	0.0751359i
$544$		0			0
$545$	16.5122	+	6.00993i	0.707303	+	0.257437i
$546$		0			0
$547$	0.140528	−	0.796974i	0.00600855	−	0.0340762i	−0.981656	−	0.190660i	$-0.938937\pi$
$547$	0.140528	−	0.796974i	0.00600855	−	0.0340762i	0.987665	+	0.156584i	$0.0500482\pi$
$548$		0			0
$549$	2.71251	+	32.7549i	0.115767	+	1.39794i
$550$		0			0
$551$	−6.40858	+	36.3449i	−0.273015	+	1.54834i
$552$		0			0
$553$	10.6624	+	1.77945i	0.453409	+	0.0756700i
$554$		0			0
$555$	−7.66047	+	14.6326i	−0.325169	+	0.621119i
$556$		0			0
$557$	11.1587	+	6.44247i	0.472808	+	0.272976i	0.717415	−	0.696646i	$-0.245325\pi$
$557$	11.1587	+	6.44247i	0.472808	+	0.272976i	−0.244606	+	0.969623i	$0.578659\pi$
$558$		0			0
$559$	−17.6703	−	10.2019i	−0.747372	−	0.431496i
$560$		0			0
$561$	2.66333	+	2.92009i	0.112446	+	0.123286i
$562$		0			0
$563$	−23.6550	+	19.8489i	−0.996937	+	0.836530i	−0.986557	−	0.163416i	$-0.947749\pi$
$563$	−23.6550	+	19.8489i	−0.996937	+	0.836530i	−0.0103802	+	0.999946i	$0.503304\pi$
$564$		0			0
$565$	4.66077	+	12.8053i	0.196080	+	0.538725i
$566$		0			0
$567$	−11.9083	+	20.6202i	−0.500103	+	0.865966i
$568$		0			0
$569$	−1.01766	−	2.79599i	−0.0426624	−	0.117214i	0.916532	−	0.399961i	$-0.130976\pi$
$569$	−1.01766	−	2.79599i	−0.0426624	−	0.117214i	−0.959194	+	0.282747i	$0.908754\pi$
$570$		0			0
$571$	−3.10701	+	2.60709i	−0.130024	+	0.109103i	−0.705481	−	0.708729i	$-0.749269\pi$
$571$	−3.10701	+	2.60709i	−0.130024	+	0.109103i	0.575457	+	0.817832i	$0.304824\pi$
$572$		0			0
$573$	13.5077	+	14.8099i	0.564292	+	0.618694i
$574$		0			0
$575$	−3.04565	−	1.75841i	−0.127013	−	0.0733307i
$576$		0			0
$577$	3.30256	+	1.90674i	0.137488	+	0.0793785i	0.567166	−	0.823603i	$-0.308040\pi$
$577$	3.30256	+	1.90674i	0.137488	+	0.0793785i	−0.429678	+	0.902982i	$0.641373\pi$
$578$		0			0
$579$	9.08817	−	17.3597i	0.377692	−	0.721445i
$580$		0			0
$581$	−9.37534	−	25.0419i	−0.388955	−	1.03891i
$582$		0			0
$583$	−1.06312	+	6.02923i	−0.0440298	+	0.249705i
$584$		0			0
$585$	23.0310	−	15.9676i	0.952214	−	0.660181i
$586$		0			0
$587$	−3.89708	+	22.1014i	−0.160850	+	0.912223i	0.792392	+	0.610013i	$0.208836\pi$
$587$	−3.89708	+	22.1014i	−0.160850	+	0.912223i	−0.953241	+	0.302211i	$0.902275\pi$
$588$		0			0
$589$	−41.7934	−	15.2115i	−1.72207	−	0.626781i
$590$		0			0
$591$	−7.90107	−	1.05886i	−0.325007	−	0.0435557i
$592$		0			0
$593$	11.6564	−	20.1895i	0.478672	−	0.829085i	−0.521028	−	0.853539i	$-0.674451\pi$
$593$	11.6564	−	20.1895i	0.478672	−	0.829085i	0.999701	+	0.0244543i	$0.00778481\pi$
$594$		0			0
$595$	−2.57439	+	7.28000i	−0.105540	+	0.298451i
$596$		0			0
$597$	−40.9482	−	5.48766i	−1.67590	−	0.224595i
$598$		0			0
$599$	−39.3996	+	6.94721i	−1.60982	+	0.283855i	−0.904963	−	0.425490i	$-0.860102\pi$
$599$	−39.3996	+	6.94721i	−1.60982	+	0.283855i	−0.704861	+	0.709345i	$0.748991\pi$
$600$		0			0
$601$	7.62355	+	1.34424i	0.310971	+	0.0548326i	0.326956	−	0.945040i	$-0.393977\pi$
$601$	7.62355	+	1.34424i	0.310971	+	0.0548326i	−0.0159848	+	0.999872i	$0.505088\pi$
$602$		0			0
$603$	−25.7684	+	11.8707i	−1.04937	+	0.483412i
$604$		0			0
$605$	13.7075	+	11.5019i	0.557287	+	0.467620i
$606$		0			0
$607$	25.8116	−	4.55128i	1.04766	−	0.184731i	0.376785	−	0.926301i	$-0.377030\pi$
$607$	25.8116	−	4.55128i	1.04766	−	0.184731i	0.670876	+	0.741570i	$0.265918\pi$
$608$		0			0
$609$	21.4771	−	19.9522i	0.870294	−	0.808506i
$610$		0			0
$611$			24.1315i			0.976255i
$612$		0			0
$613$	6.87726			0.277770			0.138885	−	0.990309i	$-0.455648\pi$
$613$	6.87726			0.277770			0.138885	+	0.990309i	$0.455648\pi$
$614$		0			0
$615$	−2.23905	−	10.2118i	−0.0902874	−	0.411781i
$616$		0			0
$617$	17.2432	−	3.04044i	0.694185	−	0.122404i	0.184587	−	0.982816i	$-0.440905\pi$
$617$	17.2432	−	3.04044i	0.694185	−	0.122404i	0.509598	+	0.860413i	$0.329794\pi$
$618$		0			0
$619$	−3.63035	−	0.640129i	−0.145916	−	0.0257290i	0.100213	−	0.994966i	$-0.468048\pi$
$619$	−3.63035	−	0.640129i	−0.145916	−	0.0257290i	−0.246129	+	0.969237i	$0.579159\pi$
$620$		0			0
$621$	−32.5745	−	30.2690i	−1.30717	−	1.21465i
$622$		0			0
$623$	−0.158488	−	17.2905i	−0.00634970	−	0.692731i
$624$		0			0
$625$	25.2645	+	9.19552i	1.01058	+	0.367821i
$626$		0			0
$627$	3.89217	+	17.7513i	0.155438	+	0.708920i
$628$		0			0
$629$	−2.57171	+	4.45434i	−0.102541	+	0.177606i
$630$		0			0
$631$	−22.6990	−	39.3158i	−0.903633	−	1.56514i	−0.822742	−	0.568415i	$-0.807557\pi$
$631$	−22.6990	−	39.3158i	−0.903633	−	1.56514i	−0.0808913	−	0.996723i	$-0.525777\pi$
$632$		0			0
$633$	13.8192	−	0.571224i	0.549264	−	0.0227041i
$634$		0			0
$635$	2.76953	+	15.7068i	0.109906	+	0.623306i
$636$		0			0
$637$	−9.12884	+	26.5879i	−0.361698	+	1.05345i
$638$		0			0
$639$	4.22344	−	15.4744i	0.167077	−	0.612157i
$640$		0			0
$641$	−1.45612	−	4.00067i	−0.0575134	−	0.158017i	0.907609	−	0.419818i	$-0.137906\pi$
$641$	−1.45612	−	4.00067i	−0.0575134	−	0.158017i	−0.965122	+	0.261801i	$0.915684\pi$
$642$		0			0
$643$	−5.17807	+	14.2266i	−0.204203	+	0.561044i	−0.998946	−	0.0459029i	$-0.985384\pi$
$643$	−5.17807	+	14.2266i	−0.204203	+	0.561044i	0.794743	+	0.606946i	$0.207606\pi$
$644$		0			0
$645$	−2.71902	+	20.2889i	−0.107061	+	0.798876i
$646$		0			0
$647$	−9.64047	−	16.6978i	−0.379006	−	0.656458i	0.611912	−	0.790926i	$-0.290401\pi$
$647$	−9.64047	−	16.6978i	−0.379006	−	0.656458i	−0.990918	+	0.134468i	$0.957067\pi$
$648$		0			0
$649$	−15.4539	−	8.92233i	−0.606620	−	0.350232i
$650$		0			0
$651$	19.1851	+	29.6645i	0.751923	+	1.16264i
$652$		0			0
$653$	−1.99740	−	2.38041i	−0.0781642	−	0.0931525i	0.725545	−	0.688175i	$-0.241588\pi$
$653$	−1.99740	−	2.38041i	−0.0781642	−	0.0931525i	−0.803709	+	0.595022i	$0.797143\pi$
$654$		0			0
$655$	−29.5483	+	10.7547i	−1.15455	+	0.420220i
$656$		0			0
$657$	17.9281	+	18.0954i	0.699443	+	0.705968i
$658$		0			0
$659$	−3.25069	−	8.93121i	−0.126629	−	0.347911i	0.860136	−	0.510064i	$-0.170378\pi$
$659$	−3.25069	−	8.93121i	−0.126629	−	0.347911i	−0.986766	+	0.162153i	$0.948156\pi$
$660$		0			0
$661$	6.00263	−	16.4921i	0.233475	−	0.641468i	−0.766525	−	0.642215i	$-0.778016\pi$
$661$	6.00263	−	16.4921i	0.233475	−	0.641468i	1.00000		0.000747196i	$0.000237840\pi$
$662$		0			0
$663$	7.37135	−	4.67205i	0.286279	−	0.181447i
$664$		0			0
$665$	−26.9888	+	23.0711i	−1.04658	+	0.894659i
$666$		0			0
$667$	27.3717	+	47.4092i	1.05984	+	1.83569i
$668$		0			0
$669$	10.7365	−	2.35409i	0.415097	−	0.0910145i
$670$		0			0
$671$	−3.45988	−	19.6219i	−0.133567	−	0.757497i
$672$		0			0
$673$	7.62458	+	6.39778i	0.293906	+	0.246616i	0.777802	−	0.628509i	$-0.216334\pi$
$673$	7.62458	+	6.39778i	0.293906	+	0.246616i	−0.483896	+	0.875125i	$0.660779\pi$
$674$		0			0
$675$	−1.79293	−	1.15986i	−0.0690100	−	0.0446429i
$676$		0			0
$677$	1.01289	−	0.368662i	0.0389286	−	0.0141688i	−0.322482	−	0.946575i	$-0.604517\pi$
$677$	1.01289	−	0.368662i	0.0389286	−	0.0141688i	0.361411	+	0.932407i	$0.382295\pi$
$678$		0			0
$679$	−4.21171	+	25.2363i	−0.161631	+	0.968481i
$680$		0			0
$681$	−5.93351	−	1.88598i	−0.227373	−	0.0722710i
$682$		0			0
$683$			22.8369i			0.873829i	0.899503	+	0.436914i	$0.143929\pi$
$683$			22.8369i			0.873829i	−0.899503	+	0.436914i	$0.856071\pi$
$684$		0			0
$685$	42.2997	−	24.4217i	1.61619	−	0.933107i
$686$		0			0
$687$	−35.7866	+	22.6820i	−1.36535	+	0.865372i
$688$		0			0
$689$	12.7037	+	4.62376i	0.483972	+	0.176151i
$690$		0			0
$691$	4.12433	+	0.727230i	0.156897	+	0.0276651i	0.251545	−	0.967846i	$-0.419061\pi$
$691$	4.12433	+	0.727230i	0.156897	+	0.0276651i	−0.0946480	+	0.995511i	$0.530173\pi$
$692$		0			0
$693$	6.04133	−	13.1102i	0.229491	−	0.498014i
$694$		0			0
$695$	30.6464	−	36.5230i	1.16249	−	1.38540i
$696$		0			0
$697$	−0.565333	−	3.20616i	−0.0214135	−	0.121442i
$698$		0			0
$699$	−15.9593	−	38.7836i	−0.603636	−	1.46693i
$700$		0			0
$701$		−	19.8279i		−	0.748890i	−0.927249	−	0.374445i	$-0.877833\pi$
$701$		−	19.8279i		−	0.748890i	0.927249	−	0.374445i	$-0.122167\pi$
$702$		0			0
$703$	−20.4817	+	11.8251i	−0.772483	+	0.445993i
$704$		0			0
$705$	22.3887	−	9.21286i	0.843206	−	0.346976i
$706$		0			0
$707$	−3.74835	−	0.625566i	−0.140971	−	0.0235268i
$708$		0			0
$709$	29.6101	+	24.8458i	1.11203	+	0.933104i	0.998175	−	0.0603933i	$-0.0192355\pi$
$709$	29.6101	+	24.8458i	1.11203	+	0.933104i	0.113855	+	0.993497i	$0.463680\pi$
$710$		0			0
$711$	−5.23163	+	11.0846i	−0.196201	+	0.415706i
$712$		0			0
$713$	−61.9937	+	22.5639i	−2.32168	+	0.845024i
$714$		0			0
$715$	−13.0145	+	10.9205i	−0.486715	+	0.408402i
$716$		0			0
$717$	3.60332	−	2.28383i	0.134568	−	0.0852911i
$718$		0			0
$719$	27.9912			1.04390			0.521949	−	0.852977i	$-0.325205\pi$
$719$	27.9912			1.04390			0.521949	+	0.852977i	$0.325205\pi$
$720$		0			0
$721$	−0.762279	−	4.10283i	−0.0283887	−	0.152797i
$722$		0			0
$723$	10.9070	−	2.39148i	0.405637	−	0.0889402i
$724$		0			0
$725$	1.68981	+	2.01384i	0.0627581	+	0.0747922i
$726$		0			0
$727$	0.372280	−	0.443665i	0.0138071	−	0.0164546i	−0.759097	−	0.650978i	$-0.774359\pi$
$727$	0.372280	−	0.443665i	0.0138071	−	0.0164546i	0.772904	+	0.634523i	$0.218804\pi$
$728$		0			0
$729$	−18.8241	−	19.3559i	−0.697190	−	0.716886i
$730$		0			0
$731$	−1.10695	+	6.27784i	−0.0409421	+	0.232194i
$732$		0			0
$733$	−10.3238	+	28.3645i	−0.381320	+	1.04767i	0.589482	+	0.807782i	$0.299332\pi$
$733$	−10.3238	+	28.3645i	−0.381320	+	1.04767i	−0.970801	+	0.239885i	$0.922890\pi$
$734$		0			0
$735$	28.1529	−	1.68114i	1.03843	−	0.0620098i
$736$		0			0
$737$	14.8949	−	8.59960i	0.548662	−	0.316770i
$738$		0			0
$739$	7.19111	−	12.4554i	0.264529	−	0.458178i	−0.702911	−	0.711278i	$-0.748117\pi$
$739$	7.19111	−	12.4554i	0.264529	−	0.458178i	0.967440	+	0.253100i	$0.0814501\pi$
$740$		0			0
$741$	40.0950	−	1.65735i	1.47293	−	0.0608841i
$742$		0			0
$743$	−18.5207	−	22.0721i	−0.679459	−	0.809747i	0.310579	−	0.950547i	$-0.399477\pi$
$743$	−18.5207	−	22.0721i	−0.679459	−	0.809747i	−0.990038	+	0.140800i	$0.955033\pi$
$744$		0			0
$745$	10.3578	−	12.3439i	0.379480	−	0.452246i
$746$		0			0
$747$	30.2162	−	2.50228i	1.10555	−	0.0915536i
$748$		0			0
$749$	−21.4496	−	36.3777i	−0.783753	−	1.32921i
$750$		0			0
$751$	−19.3251	+	16.2157i	−0.705183	+	0.591719i	−0.923243	−	0.384217i	$-0.874472\pi$
$751$	−19.3251	+	16.2157i	−0.705183	+	0.591719i	0.218060	+	0.975935i	$0.430027\pi$
$752$		0			0
$753$	−2.61045	+	19.4788i	−0.0951300	+	0.709848i
$754$		0			0
$755$	2.47478			0.0900666
$756$		0			0
$757$	34.3865			1.24980			0.624899	−	0.780706i	$-0.285140\pi$
$757$	34.3865			1.24980			0.624899	+	0.780706i	$0.285140\pi$
$758$		0			0
$759$	21.3481	+	16.4598i	0.774886	+	0.597454i
$760$		0			0
$761$	2.90930	−	2.44119i	0.105462	−	0.0884932i	−0.588532	−	0.808474i	$-0.700294\pi$
$761$	2.90930	−	2.44119i	0.105462	−	0.0884932i	0.693994	+	0.719981i	$0.255849\pi$
$762$		0			0
$763$	−0.183189	−	19.9854i	−0.00663190	−	0.723518i
$764$		0			0
$765$	−7.14884	−	5.05529i	−0.258467	−	0.182774i
$766$		0			0
$767$	−25.3285	+	30.1853i	−0.914559	+	1.08993i
$768$		0			0
$769$	−9.13219	−	10.8833i	−0.329315	−	0.392463i	0.575827	−	0.817572i	$-0.304680\pi$
$769$	−9.13219	−	10.8833i	−0.329315	−	0.392463i	−0.905142	+	0.425109i	$0.860236\pi$
$770$		0			0
$771$	18.9141	+	29.8418i	0.681175	+	1.07473i
$772$		0			0
$773$	−22.9879	+	39.8162i	−0.826816	+	1.43209i	0.0737069	+	0.997280i	$0.476517\pi$
$773$	−22.9879	+	39.8162i	−0.826816	+	1.43209i	−0.900523	+	0.434808i	$0.856816\pi$
$774$		0			0
$775$	−2.74367	+	1.58406i	−0.0985555	+	0.0569010i
$776$		0			0
$777$	18.6415	+	2.32451i	0.668759	+	0.0833912i
$778$		0			0
$779$	5.11999	−	14.0671i	0.183443	−	0.504005i
$780$		0			0
$781$	−1.68855	+	9.57627i	−0.0604212	+	0.342666i
$782$		0			0
$783$	15.1428	+	29.5902i	0.541158	+	1.05747i
$784$		0			0
$785$	−10.2859	+	12.2583i	−0.367121	+	0.437518i
$786$		0			0
$787$	28.0260	+	33.4001i	0.999019	+	1.19058i	0.981642	+	0.190735i	$0.0610871\pi$
$787$	28.0260	+	33.4001i	0.999019	+	1.19058i	0.0173771	+	0.999849i	$0.494468\pi$
$788$		0			0
$789$	−34.4506	−	37.7719i	−1.22648	−	1.34472i
$790$		0			0
$791$	11.7815	−	10.0713i	0.418901	−	0.358094i
$792$		0			0
$793$	−43.9971			−1.56238
$794$		0			0
$795$	−0.560156	−	13.5514i	−0.0198667	−	0.480620i
$796$		0			0
$797$	6.63961	−	5.57130i	0.235187	−	0.197345i	−0.517575	−	0.855638i	$-0.673165\pi$
$797$	6.63961	−	5.57130i	0.235187	−	0.197345i	0.752763	+	0.658292i	$0.228721\pi$
$798$		0			0
$799$	7.08461	−	2.57859i	0.250636	−	0.0912239i
$800$		0			0
$801$	18.9146	+	5.16239i	0.668315	+	0.182404i
$802$		0			0
$803$	−11.8293	−	9.92598i	−0.417448	−	0.350280i
$804$		0			0
$805$	−8.66980	+	51.9488i	−0.305570	+	1.83096i
$806$		0			0
$807$	−40.8528	−	31.4984i	−1.43809	−	1.10880i
$808$		0			0
$809$	15.5273	−	8.96468i	0.545910	−	0.315181i	−0.201561	−	0.979476i	$-0.564601\pi$
$809$	15.5273	−	8.96468i	0.545910	−	0.315181i	0.747471	+	0.664295i	$0.231268\pi$
$810$		0			0
$811$		−	22.3098i		−	0.783403i	−0.920092	−	0.391702i	$-0.871887\pi$
$811$		−	22.3098i		−	0.783403i	0.920092	−	0.391702i	$-0.128113\pi$
$812$		0			0
$813$	−44.1038	−	5.91055i	−1.54679	−	0.207292i
$814$		0			0
$815$	8.98986	+	50.9840i	0.314901	+	1.78589i
$816$		0			0
$817$	−18.8412	+	22.4541i	−0.659172	+	0.785570i
$818$		0			0
$819$	−26.1932	−	18.1647i	−0.915265	−	0.634725i
$820$		0			0
$821$	3.99960	+	0.705237i	0.139587	+	0.0246129i	0.243005	−	0.970025i	$-0.421867\pi$
$821$	3.99960	+	0.705237i	0.139587	+	0.0246129i	−0.103418	+	0.994638i	$0.532978\pi$
$822$		0			0
$823$	−4.03676	−	1.46926i	−0.140713	−	0.0512152i	0.270704	−	0.962663i	$-0.412744\pi$
$823$	−4.03676	−	1.46926i	−0.140713	−	0.0512152i	−0.411416	+	0.911447i	$0.634966\pi$
$824$		0			0
$825$	1.14686	+	0.600404i	0.0399284	+	0.0209034i
$826$		0			0
$827$	45.9946	−	26.5550i	1.59939	−	0.923407i	0.607783	−	0.794103i	$-0.292059\pi$
$827$	45.9946	−	26.5550i	1.59939	−	0.923407i	0.991605	−	0.129304i	$-0.0412742\pi$
$828$		0			0
$829$			3.46053i			0.120189i	0.998193	+	0.0600946i	$0.0191402\pi$
$829$			3.46053i			0.120189i	−0.998193	+	0.0600946i	$0.980860\pi$
$830$		0			0
$831$	−23.1685	+	21.1313i	−0.803705	+	0.733035i
$832$		0			0
$833$	8.78125	−	0.160995i	0.304252	−	0.00557814i
$834$		0			0
$835$	−1.77876	+	0.647415i	−0.0615565	+	0.0224047i
$836$		0			0
$837$	−38.2869	+	11.7793i	−1.32339	+	0.407153i
$838$		0			0
$839$	41.5584	+	34.8716i	1.43475	+	1.20390i	0.942835	+	0.333261i	$0.108149\pi$
$839$	41.5584	+	34.8716i	1.43475	+	1.20390i	0.491919	+	0.870641i	$0.336295\pi$
$840$		0			0
$841$	−2.07018	−	11.7406i	−0.0713855	−	0.404847i
$842$		0			0
$843$	13.3844	+	14.6748i	0.460983	+	0.505426i
$844$		0			0
$845$	3.63765	+	6.30059i	0.125139	+	0.216747i
$846$		0			0
$847$	6.78533	−	19.1880i	0.233147	−	0.659307i
$848$		0			0
$849$	−0.603832	−	14.6081i	−0.0207234	−	0.501347i
$850$		0			0
$851$	−11.9985	+	32.9657i	−0.411304	+	1.13005i
$852$		0			0
$853$	5.73931	+	15.7686i	0.196510	+	0.539907i	0.998337	−	0.0576493i	$-0.0183605\pi$
$853$	5.73931	+	15.7686i	0.196510	+	0.539907i	−0.801827	+	0.597557i	$0.796138\pi$
$854$		0			0
$855$	−16.8450	−	36.5665i	−0.576087	−	1.25055i
$856$		0			0
$857$	0.116007	−	0.0422232i	0.00396273	−	0.00144232i	−0.340038	−	0.940412i	$-0.610440\pi$
$857$	0.116007	−	0.0422232i	0.00396273	−	0.00144232i	0.344001	+	0.938969i	$0.388218\pi$
$858$		0			0
$859$	−29.9915	−	35.7425i	−1.02330	−	1.21952i	−0.975349	−	0.220669i	$-0.929176\pi$
$859$	−29.9915	−	35.7425i	−1.02330	−	1.21952i	−0.0479491	−	0.998850i	$-0.515269\pi$
$860$		0			0
$861$	−9.98466	+	6.45743i	−0.340276	+	0.220069i
$862$		0			0
$863$	39.1384	+	22.5966i	1.33229	+	0.769197i	0.985650	−	0.168803i	$-0.0539900\pi$
$863$	39.1384	+	22.5966i	1.33229	+	0.769197i	0.346638	+	0.937999i	$0.387323\pi$
$864$		0			0
$865$	10.0167	+	17.3495i	0.340579	+	0.589900i
$866$		0			0
$867$	21.1592	+	16.3142i	0.718604	+	0.554059i
$868$		0			0
$869$	2.54140	−	6.98244i	0.0862110	−	0.236863i
$870$		0			0
$871$	−12.9895	−	35.6884i	−0.440133	−	1.20926i
$872$		0			0
$873$	−26.2357	−	12.3825i	−0.887945	−	0.419085i
$874$		0			0
$875$	−0.258868	−	28.2416i	−0.00875134	−	0.954742i
$876$		0			0
$877$	−0.739309	−	4.19283i	−0.0249647	−	0.141582i	0.969778	−	0.243990i	$-0.0784564\pi$
$877$	−0.739309	−	4.19283i	−0.0249647	−	0.141582i	−0.994742	+	0.102408i	$0.967345\pi$
$878$		0			0
$879$	−17.6418	−	27.8345i	−0.595044	−	0.938834i
$880$		0			0
$881$	−12.9250	−	22.3868i	−0.435455	−	0.754230i	0.561878	−	0.827220i	$-0.310079\pi$
$881$	−12.9250	−	22.3868i	−0.435455	−	0.754230i	−0.997333	+	0.0729906i	$0.976746\pi$
$882$		0			0
$883$	19.4673	−	33.7184i	0.655128	−	1.13472i	−0.326733	−	0.945117i	$-0.605948\pi$
$883$	19.4673	−	33.7184i	0.655128	−	1.13472i	0.981862	−	0.189599i	$-0.0607187\pi$
$884$		0			0
$885$	37.6751	+	11.9751i	1.26644	+	0.402540i
$886$		0			0
$887$	30.5267	+	11.1108i	1.02499	+	0.373065i	0.799170	−	0.601105i	$-0.205273\pi$
$887$	30.5267	+	11.1108i	1.02499	+	0.373065i	0.225817	+	0.974170i	$0.427495\pi$
$888$		0			0
$889$	15.6263	−	9.21385i	0.524090	−	0.309023i
$890$		0			0
$891$	12.4403	+	10.6371i	0.416767	+	0.356355i
$892$		0			0
$893$	34.1401	+	6.01983i	1.14246	+	0.201446i
$894$		0			0
$895$	−49.5495	+	8.73691i	−1.65626	+	0.292043i
$896$		0			0
$897$	43.9798	−	40.1127i	1.46844	−	1.33932i
$898$		0			0
$899$	49.3155			1.64476
$900$		0			0
$901$		−	4.22367i		−	0.140711i
$902$		0			0
$903$	22.6960	−	5.19481i	0.755274	−	0.172872i
$904$		0			0
$905$	−17.4336	+	3.07402i	−0.579514	+	0.102184i
$906$		0			0
$907$	9.51237	+	7.98182i	0.315853	+	0.265032i	0.786906	−	0.617073i	$-0.211682\pi$
$907$	9.51237	+	7.98182i	0.315853	+	0.265032i	−0.471053	+	0.882105i	$0.656126\pi$
$908$		0			0
$909$	1.83918	−	3.89679i	0.0610017	−	0.129248i
$910$		0			0
$911$	−57.6566	−	10.1664i	−1.91025	−	0.336828i	−0.912812	−	0.408380i	$-0.866094\pi$
$911$	−57.6566	−	10.1664i	−1.91025	−	0.336828i	−0.997437	+	0.0715519i	$0.977205\pi$
$912$		0			0
$913$	−18.1011	+	3.19172i	−0.599060	+	0.105630i
$914$		0			0
$915$	16.7971	+	40.8195i	0.555295	+	1.34945i
$916$		0			0
$917$	23.2395	+	27.1857i	0.767434	+	0.897751i
$918$		0			0
$919$	−0.493059	+	0.854003i	−0.0162645	+	0.0281710i	−0.874043	−	0.485848i	$-0.838511\pi$
$919$	−0.493059	+	0.854003i	−0.0162645	+	0.0281710i	0.857779	+	0.514019i	$0.171844\pi$
$920$		0			0
$921$	−28.7306	+	37.2630i	−0.946704	+	1.22786i
$922$		0			0
$923$	20.1774	+	7.34396i	0.664146	+	0.241729i
$924$		0			0
$925$	−0.292540	+	1.65908i	−0.00961867	+	0.0545502i
$926$		0			0
$927$	4.71181	+	0.434281i	0.154756	+	0.0142637i
$928$		0			0
$929$	−8.37861	+	47.5174i	−0.274893	+	1.55900i	0.464408	+	0.885621i	$0.346267\pi$
$929$	−8.37861	+	47.5174i	−0.274893	+	1.55900i	−0.739301	+	0.673375i	$0.764844\pi$
$930$		0			0
$931$	35.3381	+	19.5477i	1.15816	+	0.640649i
$932$		0			0
$933$	−42.3197	+	1.74930i	−1.38548	+	0.0572697i
$934$		0			0
$935$	4.59675	+	2.65393i	0.150330	+	0.0867929i
$936$		0			0
$937$	−26.0904	−	15.0633i	−0.852336	−	0.492096i	0.00910235	−	0.999959i	$-0.497103\pi$
$937$	−26.0904	−	15.0633i	−0.852336	−	0.492096i	−0.861438	+	0.507862i	$0.830436\pi$
$938$		0			0
$939$	−22.9286	+	5.02735i	−0.748248	+	0.164061i
$940$		0			0
$941$	−12.7253	+	10.6778i	−0.414833	+	0.348086i	−0.826194	−	0.563386i	$-0.809498\pi$
$941$	−12.7253	+	10.6778i	−0.414833	+	0.348086i	0.411360	+	0.911473i	$0.365054\pi$
$942$		0			0
$943$	−7.59468	−	20.8662i	−0.247317	−	0.679498i
$944$		0			0
$945$	−6.85280	+	31.2364i	−0.222922	+	1.01612i
$946$		0			0
$947$	−9.57499	−	26.3071i	−0.311145	−	0.854865i	−0.992426	−	0.122843i	$-0.960799\pi$
$947$	−9.57499	−	26.3071i	−0.311145	−	0.854865i	0.681281	−	0.732022i	$-0.261423\pi$
$948$		0			0
$949$	−26.1212	+	21.9183i	−0.847931	+	0.711498i
$950$		0			0
$951$	9.92026	−	31.2102i	0.321687	−	1.01206i
$952$		0			0
$953$	−18.0641	−	10.4293i	−0.585154	−	0.337839i	0.178025	−	0.984026i	$-0.443029\pi$
$953$	−18.0641	−	10.4293i	−0.585154	−	0.337839i	−0.763179	+	0.646187i	$0.776362\pi$
$954$		0			0
$955$	23.3135	+	13.4601i	0.754407	+	0.435557i
$956$		0			0
$957$	−10.7875	−	17.0200i	−0.348709	−	0.550178i
$958$		0			0
$959$	−42.8827	−	35.3181i	−1.38475	−	1.14048i
$960$		0			0
$961$	−4.93699	+	27.9991i	−0.159258	+	0.903196i
$962$		0			0
$963$	46.3104	−	12.1787i	1.49233	−	0.392453i
$964$		0			0
$965$	4.56969	−	25.9160i	0.147103	−	0.834265i
$966$		0			0
$967$	−6.46715	−	2.35385i	−0.207970	−	0.0756948i	0.235935	−	0.971769i	$-0.424185\pi$
$967$	−6.46715	−	2.35385i	−0.207970	−	0.0756948i	−0.443904	+	0.896074i	$0.646407\pi$
$968$		0			0
$969$	−4.77095	−	11.5941i	−0.153265	−	0.372457i
$970$		0			0
$971$	−12.3951	+	21.4689i	−0.397777	+	0.688971i	−0.993451	−	0.114256i	$-0.963552\pi$
$971$	−12.3951	+	21.4689i	−0.397777	+	0.688971i	0.595674	+	0.803226i	$0.296885\pi$
$972$		0			0
$973$	−51.1256	−	18.0793i	−1.63901	−	0.579594i
$974$		0			0
$975$	1.74541	−	2.26377i	0.0558979	−	0.0724985i
$976$		0			0
$977$	6.26838	−	1.10528i	0.200543	−	0.0353612i	−0.0724742	−	0.997370i	$-0.523089\pi$
$977$	6.26838	−	1.10528i	0.200543	−	0.0353612i	0.273017	+	0.962009i	$0.411978\pi$
$978$		0			0
$979$	−11.7053	−	2.06395i	−0.374102	−	0.0659642i
$980$		0			0
$981$	21.8625	+	5.96697i	0.698017	+	0.190511i
$982$		0			0
$983$	−0.543604	−	0.456138i	−0.0173383	−	0.0145485i	0.634077	−	0.773270i	$-0.281380\pi$
$983$	−0.543604	−	0.456138i	−0.0173383	−	0.0145485i	−0.651416	+	0.758721i	$0.725825\pi$
$984$		0			0
$985$	−10.5434	+	1.85908i	−0.335939	+	0.0592352i
$986$		0			0
$987$	−18.7419	−	20.1742i	−0.596561	−	0.642152i
$988$		0			0
$989$			43.4793i			1.38256i
$990$		0			0
$991$	−42.6260			−1.35406			−0.677031	−	0.735955i	$-0.736733\pi$
$991$	−42.6260			−1.35406			−0.677031	+	0.735955i	$0.736733\pi$
$992$		0			0
$993$	−30.0354	−	9.54684i	−0.953146	−	0.302960i
$994$		0			0
$995$	−54.6422	+	9.63489i	−1.73227	+	0.305446i
$996$		0			0
$997$	−3.43362	−	0.605441i	−0.108744	−	0.0191745i	0.119011	−	0.992893i	$-0.462028\pi$
$997$	−3.43362	−	0.605441i	−0.108744	−	0.0191745i	−0.227755	+	0.973718i	$0.573139\pi$
$998$		0			0
$999$	−8.28844	+	19.6225i	−0.262235	+	0.620827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ca.a.173.22	✓	144
7.3	odd	6		756.2.ck.a.605.20	yes	144
27.5	odd	18		756.2.ck.a.5.20	yes	144
189.59	even	18	inner	756.2.ca.a.437.22	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.22	✓	144	1.1	even	1	trivial
756.2.ca.a.437.22	yes	144	189.59	even	18	inner
756.2.ck.a.5.20	yes	144	27.5	odd	18
756.2.ck.a.605.20	yes	144	7.3	odd	6

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.ca (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60174 - 0.659111i) q^{3} +(1.78193 - 1.49522i) q^{5} +(-2.30332 - 1.30182i) q^{7} +(2.13115 - 2.11145i) q^{9} +O(q^{10})\)	\(q+(1.60174 - 0.659111i) q^{3} +(1.78193 - 1.49522i) q^{5} +(-2.30332 - 1.30182i) q^{7} +(2.13115 - 2.11145i) q^{9} +(-1.16901 + 1.39317i) q^{11} +(2.58138 + 3.07637i) q^{13} +(1.86868 - 3.56944i) q^{15} +(0.627338 - 1.08658i) q^{17} +(4.99627 - 2.88460i) q^{19} +(-4.54736 - 0.567034i) q^{21} +(2.92689 - 8.04158i) q^{23} +(0.0713616 - 0.404712i) q^{25} +(2.02186 - 4.78666i) q^{27} +(-4.11192 + 4.90039i) q^{29} +(-4.95535 - 5.90555i) q^{31} +(-0.954198 + 3.00201i) q^{33} +(-6.05085 + 1.12421i) q^{35} -4.09941 q^{37} +(6.16238 + 3.22613i) q^{39} +(1.98773 - 1.66790i) q^{41} +(-4.77434 + 1.73772i) q^{43} +(0.640478 - 6.94898i) q^{45} +(4.60313 + 3.86248i) q^{47} +(3.61054 + 5.99700i) q^{49} +(0.288655 - 2.15391i) q^{51} +(2.91534 - 1.68317i) q^{53} +4.23047i q^{55} +(6.10145 - 7.91347i) q^{57} +(1.70383 + 9.66292i) q^{59} +(-7.04217 + 8.39253i) q^{61} +(-7.65743 + 2.08897i) q^{63} +(9.19970 + 1.62215i) q^{65} +(-8.88674 - 3.23451i) q^{67} +(-0.612165 - 14.8097i) q^{69} +(4.63046 - 2.67340i) q^{71} +8.49091i q^{73} +(-0.152447 - 0.695279i) q^{75} +(4.50627 - 1.68708i) q^{77} +(-3.83933 + 1.39740i) q^{79} +(0.0835637 - 8.99961i) q^{81} +(7.74206 + 6.49636i) q^{83} +(-0.506802 - 2.87422i) q^{85} +(-3.35632 + 10.5594i) q^{87} +(3.26774 + 5.65990i) q^{89} +(-1.94086 - 10.4464i) q^{91} +(-11.8296 - 6.19304i) q^{93} +(4.58990 - 12.6107i) q^{95} +(-3.30745 - 9.08716i) q^{97} +(0.450282 + 5.43737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 12 q^{15} - 3 q^{21} - 15 q^{23} - 6 q^{29} - 42 q^{39} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 18 q^{51} + 45 q^{53} + 3 q^{57} + 54 q^{61} + 39 q^{63} - 3 q^{65} + 36 q^{69} + 36 q^{71} + 93 q^{77} - 18 q^{79} - 36 q^{81} + 36 q^{85} - 18 q^{91} + 60 q^{93} + 6 q^{95}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 12 * q^15 - 3 * q^21 - 15 * q^23 - 6 * q^29 - 42 * q^39 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 18 * q^51 + 45 * q^53 + 3 * q^57 + 54 * q^61 + 39 * q^63 - 3 * q^65 + 36 * q^69 + 36 * q^71 + 93 * q^77 - 18 * q^79 - 36 * q^81 + 36 * q^85 - 18 * q^91 + 60 * q^93 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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