LMFDB - Embedded newform 756.2.bq.a.25.10

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			25.10
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.277537 - 1.70967i) q^{3} +(-0.774544 - 0.281911i) q^{5} +(2.22920 + 1.42502i) q^{7} +(-2.84595 + 0.948993i) q^{9} +O(q^{10})$	\(q+(-0.277537 - 1.70967i) q^{3} +(-0.774544 - 0.281911i) q^{5} +(2.22920 + 1.42502i) q^{7} +(-2.84595 + 0.948993i) q^{9} +(-5.06069 + 1.84194i) q^{11} +(-0.906850 - 5.14300i) q^{13} +(-0.267010 + 1.40246i) q^{15} -3.89784 q^{17} -1.91453 q^{19} +(1.81763 - 4.20669i) q^{21} +(-1.09977 - 6.23708i) q^{23} +(-3.30978 - 2.77723i) q^{25} +(2.41232 + 4.60225i) q^{27} +(-1.25660 + 7.12652i) q^{29} +(4.53265 - 3.80334i) q^{31} +(4.55364 + 8.14090i) q^{33} +(-1.32488 - 1.73217i) q^{35} +(-2.69574 + 4.66916i) q^{37} +(-8.54116 + 2.97779i) q^{39} +(1.09074 + 6.18589i) q^{41} +(-7.42110 - 6.22704i) q^{43} +(2.47184 + 0.0672666i) q^{45} +(-6.22918 - 5.22691i) q^{47} +(2.93865 + 6.35329i) q^{49} +(1.08180 + 6.66403i) q^{51} +(1.75957 - 3.04766i) q^{53} +4.43899 q^{55} +(0.531352 + 3.27321i) q^{57} +(0.784398 + 4.44854i) q^{59} +(-4.00652 - 3.36187i) q^{61} +(-7.69651 - 1.94003i) q^{63} +(-0.747474 + 4.23913i) q^{65} +(-7.52747 - 2.73978i) q^{67} +(-10.3581 + 3.61126i) q^{69} +(4.47155 + 7.74495i) q^{71} +(6.38431 + 11.0579i) q^{73} +(-3.82957 + 6.42941i) q^{75} +(-13.9061 - 3.10552i) q^{77} +(8.29715 - 3.01992i) q^{79} +(7.19882 - 5.40157i) q^{81} +(2.91710 - 16.5437i) q^{83} +(3.01905 + 1.09885i) q^{85} +(12.5328 + 0.170496i) q^{87} -5.15931 q^{89} +(5.30732 - 12.7571i) q^{91} +(-7.76044 - 6.69376i) q^{93} +(1.48289 + 0.539726i) q^{95} +(4.99160 + 4.18845i) q^{97} +(12.6545 - 10.0446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.277537	−	1.70967i	−0.160236	−	0.987079i
$3$	−0.277537	−	1.70967i	−0.160236	−	0.987079i
$4$		0			0
$5$	−0.774544	−	0.281911i	−0.346387	−	0.126074i	0.162968	−	0.986631i	$-0.447893\pi$
$5$	−0.774544	−	0.281911i	−0.346387	−	0.126074i	−0.509354	+	0.860557i	$0.670116\pi$
$6$		0			0
$7$	2.22920	+	1.42502i	0.842558	+	0.538606i
$7$	2.22920	+	1.42502i	0.842558	+	0.538606i
$8$		0			0
$9$	−2.84595	+	0.948993i	−0.948649	+	0.316331i
$10$		0			0
$11$	−5.06069	+	1.84194i	−1.52586	+	0.555366i	−0.962602	−	0.270919i	$-0.912673\pi$
$11$	−5.06069	+	1.84194i	−1.52586	+	0.555366i	−0.563253	+	0.826285i	$0.690450\pi$
$12$		0			0
$13$	−0.906850	−	5.14300i	−0.251515	−	1.42641i	−0.804862	−	0.593462i	$-0.797761\pi$
$13$	−0.906850	−	5.14300i	−0.251515	−	1.42641i	0.553347	−	0.832951i	$-0.313350\pi$
$14$		0			0
$15$	−0.267010	+	1.40246i	−0.0689418	+	0.362112i
$16$		0			0
$17$	−3.89784			−0.945366			−0.472683	−	0.881232i	$-0.656714\pi$
$17$	−3.89784			−0.945366			−0.472683	+	0.881232i	$0.656714\pi$
$18$		0			0
$19$	−1.91453			−0.439223			−0.219611	−	0.975587i	$-0.570479\pi$
$19$	−1.91453			−0.439223			−0.219611	+	0.975587i	$0.570479\pi$
$20$		0			0
$21$	1.81763	−	4.20669i	0.396639	−	0.917975i
$22$		0			0
$23$	−1.09977	−	6.23708i	−0.229317	−	1.30052i	−0.854258	−	0.519849i	$-0.825988\pi$
$23$	−1.09977	−	6.23708i	−0.229317	−	1.30052i	0.624941	−	0.780672i	$-0.285123\pi$
$24$		0			0
$25$	−3.30978	−	2.77723i	−0.661956	−	0.555447i
$26$		0			0
$27$	2.41232	+	4.60225i	0.464251	+	0.885704i
$28$		0			0
$29$	−1.25660	+	7.12652i	−0.233344	+	1.32336i	0.612728	+	0.790294i	$0.290072\pi$
$29$	−1.25660	+	7.12652i	−0.233344	+	1.32336i	−0.846072	+	0.533068i	$0.821039\pi$
$30$		0			0
$31$	4.53265	−	3.80334i	0.814087	−	0.683100i	−0.137492	−	0.990503i	$-0.543904\pi$
$31$	4.53265	−	3.80334i	0.814087	−	0.683100i	0.951580	+	0.307403i	$0.0994598\pi$
$32$		0			0
$33$	4.55364	+	8.14090i	0.792687	+	1.41715i
$34$		0			0
$35$	−1.32488	−	1.73217i	−0.223946	−	0.292791i
$36$		0			0
$37$	−2.69574	+	4.66916i	−0.443177	+	0.767605i	−0.997923	−	0.0644149i	$-0.979482\pi$
$37$	−2.69574	+	4.66916i	−0.443177	+	0.767605i	0.554747	+	0.832019i	$0.312815\pi$
$38$		0			0
$39$	−8.54116	+	2.97779i	−1.36768	+	0.476828i
$40$		0			0
$41$	1.09074	+	6.18589i	0.170345	+	0.966073i	0.943381	+	0.331711i	$0.107626\pi$
$41$	1.09074	+	6.18589i	0.170345	+	0.966073i	−0.773036	+	0.634362i	$0.781263\pi$
$42$		0			0
$43$	−7.42110	−	6.22704i	−1.13171	−	0.949615i	−0.132571	−	0.991173i	$-0.542323\pi$
$43$	−7.42110	−	6.22704i	−1.13171	−	0.949615i	−0.999136	+	0.0415584i	$0.986768\pi$
$44$		0			0
$45$	2.47184	+	0.0672666i	0.368480	+	0.0100275i
$46$		0			0
$47$	−6.22918	−	5.22691i	−0.908620	−	0.762423i	0.0632361	−	0.997999i	$-0.479858\pi$
$47$	−6.22918	−	5.22691i	−0.908620	−	0.762423i	−0.971856	+	0.235576i	$0.924302\pi$
$48$		0			0
$49$	2.93865	+	6.35329i	0.419807	+	0.907613i
$50$		0			0
$51$	1.08180	+	6.66403i	0.151482	+	0.933151i
$52$		0			0
$53$	1.75957	−	3.04766i	0.241696	−	0.418629i	−0.719502	−	0.694491i	$-0.755630\pi$
$53$	1.75957	−	3.04766i	0.241696	−	0.418629i	0.961197	+	0.275862i	$0.0889631\pi$
$54$		0			0
$55$	4.43899			0.598553
$56$		0			0
$57$	0.531352	+	3.27321i	0.0703793	+	0.433548i
$58$		0			0
$59$	0.784398	+	4.44854i	0.102120	+	0.579151i	0.992332	+	0.123604i	$0.0394452\pi$
$59$	0.784398	+	4.44854i	0.102120	+	0.579151i	−0.890212	+	0.455547i	$0.849444\pi$
$60$		0			0
$61$	−4.00652	−	3.36187i	−0.512982	−	0.430443i	0.349195	−	0.937050i	$-0.386455\pi$
$61$	−4.00652	−	3.36187i	−0.512982	−	0.430443i	−0.862177	+	0.506607i	$0.830900\pi$
$62$		0			0
$63$	−7.69651	−	1.94003i	−0.969669	−	0.244421i
$64$		0			0
$65$	−0.747474	+	4.23913i	−0.0927127	+	0.525800i
$66$		0			0
$67$	−7.52747	−	2.73978i	−0.919627	−	0.334717i	−0.161537	−	0.986867i	$-0.551645\pi$
$67$	−7.52747	−	2.73978i	−0.919627	−	0.334717i	−0.758090	+	0.652150i	$0.773867\pi$
$68$		0			0
$69$	−10.3581	+	3.61126i	−1.24697	+	0.434744i
$70$		0			0
$71$	4.47155	+	7.74495i	0.530675	+	0.919156i	0.999359	+	0.0357903i	$0.0113949\pi$
$71$	4.47155	+	7.74495i	0.530675	+	0.919156i	−0.468684	+	0.883366i	$0.655272\pi$
$72$		0			0
$73$	6.38431	+	11.0579i	0.747227	+	1.29423i	0.949147	+	0.314832i	$0.101948\pi$
$73$	6.38431	+	11.0579i	0.747227	+	1.29423i	−0.201921	+	0.979402i	$0.564718\pi$
$74$		0			0
$75$	−3.82957	+	6.42941i	−0.442200	+	0.742405i
$76$		0			0
$77$	−13.9061	−	3.10552i	−1.58474	−	0.353907i
$78$		0			0
$79$	8.29715	−	3.01992i	0.933502	−	0.339767i	0.169905	−	0.985460i	$-0.445654\pi$
$79$	8.29715	−	3.01992i	0.933502	−	0.339767i	0.763597	+	0.645693i	$0.223432\pi$
$80$		0			0
$81$	7.19882	−	5.40157i	0.799869	−	0.600174i
$82$		0			0
$83$	2.91710	−	16.5437i	0.320193	−	1.81591i	−0.221305	−	0.975205i	$-0.571032\pi$
$83$	2.91710	−	16.5437i	0.320193	−	1.81591i	0.541498	−	0.840702i	$-0.317857\pi$
$84$		0			0
$85$	3.01905	+	1.09885i	0.327462	+	0.119186i
$86$		0			0
$87$	12.5328	+	0.170496i	1.34365	+	0.0182791i
$88$		0			0
$89$	−5.15931			−0.546885			−0.273443	−	0.961888i	$-0.588162\pi$
$89$	−5.15931			−0.546885			−0.273443	+	0.961888i	$0.588162\pi$
$90$		0			0
$91$	5.30732	−	12.7571i	0.556359	−	1.33730i
$92$		0			0
$93$	−7.76044	−	6.69376i	−0.804720	−	0.694111i
$94$		0			0
$95$	1.48289	+	0.539726i	0.152141	+	0.0553748i
$96$		0			0
$97$	4.99160	+	4.18845i	0.506820	+	0.425273i	0.860009	−	0.510280i	$-0.170458\pi$
$97$	4.99160	+	4.18845i	0.506820	+	0.425273i	−0.353188	+	0.935552i	$0.614903\pi$
$98$		0			0
$99$	12.6545	−	10.0446i	1.27182	−	1.00952i
$100$		0			0
$101$	1.57205	−	8.91556i	0.156425	−	0.887132i	−0.801046	−	0.598603i	$-0.795723\pi$
$101$	1.57205	−	8.91556i	0.156425	−	0.887132i	0.957471	−	0.288529i	$-0.0931661\pi$
$102$		0			0
$103$	6.43076	+	2.34060i	0.633641	+	0.230627i	0.638815	−	0.769360i	$-0.279425\pi$
$103$	6.43076	+	2.34060i	0.633641	+	0.230627i	−0.00517400	+	0.999987i	$0.501647\pi$
$104$		0			0
$105$	−2.59374	+	2.74586i	−0.253123	+	0.267968i
$106$		0			0
$107$	−6.31555	−	10.9389i	−0.610548	−	1.05750i	−0.991148	−	0.132760i	$-0.957616\pi$
$107$	−6.31555	−	10.9389i	−0.610548	−	1.05750i	0.380601	−	0.924740i	$-0.375717\pi$
$108$		0			0
$109$	−2.11233	+	3.65866i	−0.202325	+	0.350436i	−0.949277	−	0.314441i	$-0.898183\pi$
$109$	−2.11233	+	3.65866i	−0.202325	+	0.350436i	0.746952	+	0.664877i	$0.231516\pi$
$110$		0			0
$111$	8.73089	+	3.31296i	0.828699	+	0.314452i
$112$		0			0
$113$	−0.465690	+	0.390761i	−0.0438085	+	0.0367597i	−0.664429	−	0.747351i	$-0.731325\pi$
$113$	−0.465690	+	0.390761i	−0.0438085	+	0.0367597i	0.620621	+	0.784111i	$0.286881\pi$
$114$		0			0
$115$	−0.906484	+	5.14093i	−0.0845301	+	0.479394i
$116$		0			0
$117$	7.46152	+	13.7761i	0.689818	+	1.27360i
$118$		0			0
$119$	−8.68907	−	5.55450i	−0.796526	−	0.509180i
$120$		0			0
$121$	13.7913	−	11.5723i	1.25376	−	1.05203i
$122$		0			0
$123$	10.2731	−	3.58162i	0.926295	−	0.322943i
$124$		0			0
$125$	3.84127	+	6.65327i	0.343573	+	0.595087i
$126$		0			0
$127$	10.0889	−	17.4744i	0.895241	−	1.55060i	0.0617353	−	0.998093i	$-0.480337\pi$
$127$	10.0889	−	17.4744i	0.895241	−	1.55060i	0.833506	−	0.552511i	$-0.186330\pi$
$128$		0			0
$129$	−8.58656	+	14.4159i	−0.756005	+	1.26925i
$130$		0			0
$131$	0.203020	+	1.15138i	0.0177379	+	0.100597i	0.992391	−	0.123123i	$-0.0392910\pi$
$131$	0.203020	+	1.15138i	0.0177379	+	0.100597i	−0.974653	+	0.223720i	$0.928180\pi$
$132$		0			0
$133$	−4.26786	−	2.72824i	−0.370071	−	0.236568i
$134$		0			0
$135$	−0.571024	−	4.24470i	−0.0491459	−	0.365326i
$136$		0			0
$137$	−6.06252	−	5.08706i	−0.517956	−	0.434617i	0.345962	−	0.938248i	$-0.387552\pi$
$137$	−6.06252	−	5.08706i	−0.517956	−	0.434617i	−0.863919	+	0.503632i	$0.831997\pi$
$138$		0			0
$139$	10.2240	+	3.72122i	0.867186	+	0.315630i	0.737027	−	0.675863i	$-0.236229\pi$
$139$	10.2240	+	3.72122i	0.867186	+	0.315630i	0.130159	+	0.991493i	$0.458451\pi$
$140$		0			0
$141$	−7.20746	+	12.1005i	−0.606978	+	1.01905i
$142$		0			0
$143$	14.0624	+	24.3568i	1.17596	+	2.03682i
$144$		0			0
$145$	2.98234	−	5.16556i	0.247669	−	0.428976i
$146$		0			0
$147$	10.0465	−	6.78740i	0.828618	−	0.559815i
$148$		0			0
$149$	−4.00385	+	3.35963i	−0.328008	+	0.275232i	−0.791888	−	0.610667i	$-0.790902\pi$
$149$	−4.00385	+	3.35963i	−0.328008	+	0.275232i	0.463879	+	0.885898i	$0.346457\pi$
$150$		0			0
$151$	−12.3905	+	4.50976i	−1.00832	+	0.366999i	−0.792788	−	0.609498i	$-0.791371\pi$
$151$	−12.3905	+	4.50976i	−1.00832	+	0.366999i	−0.215533	+	0.976497i	$0.569149\pi$
$152$		0			0
$153$	11.0931	−	3.69903i	0.896821	−	0.299049i
$154$		0			0
$155$	−4.58294	+	1.66805i	−0.368110	+	0.133981i
$156$		0			0
$157$	−3.58517	−	20.3325i	−0.286128	−	1.62271i	−0.701229	−	0.712936i	$-0.747365\pi$
$157$	−3.58517	−	20.3325i	−0.286128	−	1.62271i	0.415101	−	0.909775i	$-0.363746\pi$
$158$		0			0
$159$	−5.69885	−	2.16245i	−0.451948	−	0.171493i
$160$		0			0
$161$	6.43635	−	15.4709i	0.507256	−	1.21928i
$162$		0			0
$163$	−8.65913	−	14.9981i	−0.678235	−	1.17474i	−0.975512	−	0.219947i	$-0.929412\pi$
$163$	−8.65913	−	14.9981i	−0.678235	−	1.17474i	0.297276	−	0.954791i	$-0.403922\pi$
$164$		0			0
$165$	−1.23198	−	7.58921i	−0.0959097	−	0.590819i
$166$		0			0
$167$	−14.5730	+	12.2282i	−1.12770	+	0.946250i	−0.998968	−	0.0454302i	$-0.985534\pi$
$167$	−14.5730	+	12.2282i	−1.12770	+	0.946250i	−0.128729	+	0.991680i	$0.541090\pi$
$168$		0			0
$169$	−13.4121	+	4.88161i	−1.03170	+	0.375508i
$170$		0			0
$171$	5.44864	−	1.81687i	0.416668	−	0.138940i
$172$		0			0
$173$	2.09294	−	11.8696i	0.159123	−	0.902432i	−0.795796	−	0.605565i	$-0.792947\pi$
$173$	2.09294	−	11.8696i	0.159123	−	0.902432i	0.954919	−	0.296867i	$-0.0959419\pi$
$174$		0			0
$175$	−3.42054	−	10.9075i	−0.258569	−	0.824529i
$176$		0			0
$177$	7.38784	−	2.57570i	0.555304	−	0.193601i
$178$		0			0
$179$	1.13459			0.0848034			0.0424017	−	0.999101i	$-0.486499\pi$
$179$	1.13459			0.0848034			0.0424017	+	0.999101i	$0.486499\pi$
$180$		0			0
$181$	−10.1513	+	17.5825i	−0.754537	+	1.30690i	0.191067	+	0.981577i	$0.438805\pi$
$181$	−10.1513	+	17.5825i	−0.754537	+	1.30690i	−0.945604	+	0.325320i	$0.894528\pi$
$182$		0			0
$183$	−4.63573	+	7.78287i	−0.342683	+	0.575326i
$184$		0			0
$185$	3.40425	−	2.85651i	0.250286	−	0.210015i
$186$		0			0
$187$	19.7258	−	7.17960i	1.44249	−	0.525024i
$188$		0			0
$189$	−1.18075	+	13.6969i	−0.0858867	+	0.996305i
$190$		0			0
$191$	9.55072	−	3.47618i	0.691066	−	0.251527i	0.0274742	−	0.999623i	$-0.491254\pi$
$191$	9.55072	−	3.47618i	0.691066	−	0.251527i	0.663591	+	0.748095i	$0.269031\pi$
$192$		0			0
$193$	−0.525760	+	0.441165i	−0.0378450	+	0.0317558i	−0.661514	−	0.749933i	$-0.730086\pi$
$193$	−0.525760	+	0.441165i	−0.0378450	+	0.0317558i	0.623669	+	0.781689i	$0.285641\pi$
$194$		0			0
$195$	7.45497	+	0.101418i	0.533862	+	0.00726269i
$196$		0			0
$197$	−3.52393	+	6.10362i	−0.251069	+	0.434865i	−0.963821	−	0.266552i	$-0.914116\pi$
$197$	−3.52393	+	6.10362i	−0.251069	+	0.434865i	0.712751	+	0.701417i	$0.247449\pi$
$198$		0			0
$199$	19.1490			1.35743			0.678717	−	0.734400i	$-0.262536\pi$
$199$	19.1490			1.35743			0.678717	+	0.734400i	$0.262536\pi$
$200$		0			0
$201$	−2.59496	+	13.6299i	−0.183035	+	0.961378i
$202$		0			0
$203$	−12.9566	+	14.0958i	−0.909377	+	0.989328i
$204$		0			0
$205$	0.899044	−	5.09873i	0.0627920	−	0.356111i
$206$		0			0
$207$	9.04882	+	16.7067i	0.628936	+	1.16120i
$208$		0			0
$209$	9.68883	−	3.52645i	0.670190	−	0.243929i
$210$		0			0
$211$	11.9283	−	10.0090i	0.821175	−	0.689048i	−0.132072	−	0.991240i	$-0.542163\pi$
$211$	11.9283	−	10.0090i	0.821175	−	0.689048i	0.953247	+	0.302193i	$0.0977186\pi$
$212$		0			0
$213$	12.0003	−	9.79438i	0.822246	−	0.671100i
$214$		0			0
$215$	3.99250	+	6.91521i	0.272286	+	0.471613i
$216$		0			0
$217$	15.5240	−	2.01930i	1.05384	−	0.137079i
$218$		0			0
$219$	17.1336	−	13.9840i	1.15778	−	0.944954i
$220$		0			0
$221$	3.53476	+	20.0466i	0.237774	+	1.34848i
$222$		0			0
$223$	−5.31818	+	1.93566i	−0.356132	+	0.129621i	−0.513889	−	0.857857i	$-0.671796\pi$
$223$	−5.31818	+	1.93566i	−0.356132	+	0.129621i	0.157758	+	0.987478i	$0.449574\pi$
$224$		0			0
$225$	12.0550	+	4.76290i	0.803668	+	0.317527i
$226$		0			0
$227$	7.10673	−	2.58664i	0.471690	−	0.171681i	−0.0952277	−	0.995456i	$-0.530358\pi$
$227$	7.10673	−	2.58664i	0.471690	−	0.171681i	0.566918	+	0.823774i	$0.308136\pi$
$228$		0			0
$229$	−5.85467	+	4.91265i	−0.386888	+	0.324637i	−0.815399	−	0.578899i	$-0.803483\pi$
$229$	−5.85467	+	4.91265i	−0.386888	+	0.324637i	0.428512	+	0.903536i	$0.359038\pi$
$230$		0			0
$231$	−1.44997	+	24.6367i	−0.0954010	+	1.62098i
$232$		0			0
$233$	8.83952	−	15.3105i	0.579096	−	1.00302i	−0.416487	−	0.909142i	$-0.636739\pi$
$233$	8.83952	−	15.3105i	0.579096	−	1.00302i	0.995583	−	0.0938823i	$-0.0299277\pi$
$234$		0			0
$235$	3.35125	+	5.80454i	0.218612	+	0.378647i
$236$		0			0
$237$	−7.46583	−	13.3473i	−0.484958	−	0.866997i
$238$		0			0
$239$	−26.5617	−	9.66765i	−1.71813	−	0.625348i	−0.720456	−	0.693501i	$-0.756067\pi$
$239$	−26.5617	−	9.66765i	−1.71813	−	0.625348i	−0.997675	+	0.0681528i	$0.978289\pi$
$240$		0			0
$241$	2.56278	+	2.15043i	0.165083	+	0.138521i	0.721587	−	0.692324i	$-0.243413\pi$
$241$	2.56278	+	2.15043i	0.165083	+	0.138521i	−0.556504	+	0.830845i	$0.687857\pi$
$242$		0			0
$243$	−11.2328	−	10.8085i	−0.720587	−	0.693365i
$244$		0			0
$245$	−0.485050	−	5.74934i	−0.0309887	−	0.367312i
$246$		0			0
$247$	1.73619	+	9.84643i	0.110471	+	0.626513i
$248$		0			0
$249$	−29.0939	−	0.395795i	−1.84375	−	0.0250825i
$250$		0			0
$251$	8.74541	−	15.1475i	0.552005	−	0.956101i	−0.446124	−	0.894971i	$-0.647196\pi$
$251$	8.74541	−	15.1475i	0.552005	−	0.956101i	0.998130	−	0.0611305i	$-0.0194706\pi$
$252$		0			0
$253$	17.0539	+	29.5382i	1.07217	+	1.85705i
$254$		0			0
$255$	1.04076	−	5.46655i	0.0651752	−	0.342329i
$256$		0			0
$257$	4.65233	−	3.90377i	0.290204	−	0.243510i	−0.486049	−	0.873932i	$-0.661562\pi$
$257$	4.65233	−	3.90377i	0.290204	−	0.243510i	0.776253	+	0.630421i	$0.217118\pi$
$258$		0			0
$259$	−12.6630	+	6.56700i	−0.786838	+	0.408053i
$260$		0			0
$261$	−3.18681	−	21.4742i	−0.197259	−	1.32922i
$262$		0			0
$263$	−1.38878	+	7.87618i	−0.0856360	+	0.485666i	0.911582	+	0.411119i	$0.134862\pi$
$263$	−1.38878	+	7.87618i	−0.0856360	+	0.485666i	−0.997218	+	0.0745465i	$0.976249\pi$
$264$		0			0
$265$	−2.22203	+	1.86451i	−0.136499	+	0.114536i
$266$		0			0
$267$	1.43190	+	8.82071i	0.0876307	+	0.539819i
$268$		0			0
$269$	10.5384	−	18.2531i	0.642539	−	1.11291i	−0.342325	−	0.939582i	$-0.611214\pi$
$269$	10.5384	−	18.2531i	0.642539	−	1.11291i	0.984864	−	0.173328i	$-0.0554522\pi$
$270$		0			0
$271$	2.31197	+	4.00444i	0.140442	+	0.243253i	0.927663	−	0.373418i	$-0.121814\pi$
$271$	2.31197	+	4.00444i	0.140442	+	0.243253i	−0.787221	+	0.616671i	$0.788481\pi$
$272$		0			0
$273$	−23.2833	−	5.53322i	−1.40917	−	0.334886i
$274$		0			0
$275$	21.8653	+	7.95830i	1.31852	+	0.479904i
$276$		0			0
$277$	−5.16407	+	29.2869i	−0.310279	+	1.75968i	0.287274	+	0.957848i	$0.407251\pi$
$277$	−5.16407	+	29.2869i	−0.310279	+	1.75968i	−0.597553	+	0.801829i	$0.703860\pi$
$278$		0			0
$279$	−9.29032	+	15.1256i	−0.556197	+	0.905543i
$280$		0			0
$281$	−2.54170	−	2.13274i	−0.151625	−	0.127228i	0.563820	−	0.825898i	$-0.309331\pi$
$281$	−2.54170	−	2.13274i	−0.151625	−	0.127228i	−0.715445	+	0.698670i	$0.753776\pi$
$282$		0			0
$283$	−22.6531	−	8.24506i	−1.34659	−	0.490118i	−0.434707	−	0.900572i	$-0.643148\pi$
$283$	−22.6531	−	8.24506i	−1.34659	−	0.490118i	−0.911881	+	0.410454i	$0.865370\pi$
$284$		0			0
$285$	0.511199	−	2.68504i	0.0302808	−	0.159048i
$286$		0			0
$287$	−6.38353	+	15.3439i	−0.376808	+	0.905721i
$288$		0			0
$289$	−1.80681			−0.106283
$290$		0			0
$291$	5.77552	−	9.69644i	0.338567	−	0.568415i
$292$		0			0
$293$	19.3789	+	7.05334i	1.13213	+	0.412061i	0.839064	−	0.544033i	$-0.183103\pi$
$293$	19.3789	+	7.05334i	1.13213	+	0.412061i	0.293063	+	0.956093i	$0.405325\pi$
$294$		0			0
$295$	0.646542	−	3.66672i	0.0376431	−	0.213485i
$296$		0			0
$297$	−20.6851	−	18.8472i	−1.20027	−	1.09363i
$298$		0			0
$299$	−31.0800	+	11.3122i	−1.79740	+	0.654201i
$300$		0			0
$301$	−7.66946	−	24.4565i	−0.442060	−	1.40965i
$302$		0			0
$303$	−15.6790	−	0.213298i	−0.900734	−	0.0122536i
$304$		0			0
$305$	2.15548	+	3.73340i	0.123422	+	0.213774i
$306$		0			0
$307$	13.2324	+	22.9192i	0.755214	+	1.30807i	0.945268	+	0.326295i	$0.105800\pi$
$307$	13.2324	+	22.9192i	0.755214	+	1.30807i	−0.190054	+	0.981774i	$0.560866\pi$
$308$		0			0
$309$	2.21689	−	11.6441i	0.126114	−	0.662409i
$310$		0			0
$311$	0.594381	+	0.216337i	0.0337042	+	0.0122673i	0.358817	−	0.933408i	$-0.383180\pi$
$311$	0.594381	+	0.216337i	0.0337042	+	0.0122673i	−0.325113	+	0.945675i	$0.605402\pi$
$312$		0			0
$313$	1.36324	−	7.73130i	0.0770547	−	0.436999i	−0.921735	−	0.387820i	$-0.873228\pi$
$313$	1.36324	−	7.73130i	0.0770547	−	0.436999i	0.998790	−	0.0491793i	$-0.0156606\pi$
$314$		0			0
$315$	5.41437	+	3.67237i	0.305065	+	0.206915i
$316$		0			0
$317$	6.46768	+	5.42703i	0.363261	+	0.304812i	0.806089	−	0.591794i	$-0.201580\pi$
$317$	6.46768	+	5.42703i	0.363261	+	0.304812i	−0.442828	+	0.896607i	$0.646025\pi$
$318$		0			0
$319$	−6.76737	−	38.3797i	−0.378900	−	2.14885i
$320$		0			0
$321$	−16.9490	+	13.8335i	−0.946004	+	0.772108i
$322$		0			0
$323$	7.46253			0.415226
$324$		0			0
$325$	−11.2818	+	19.5407i	−0.625804	+	1.08393i
$326$		0			0
$327$	6.84136	+	2.59598i	0.378328	+	0.143558i
$328$		0			0
$329$	−6.43765	−	20.5285i	−0.354919	−	1.13177i
$330$		0			0
$331$	−10.5387	−	8.84304i	−0.579261	−	0.486058i	0.305443	−	0.952210i	$-0.401195\pi$
$331$	−10.5387	−	8.84304i	−0.579261	−	0.486058i	−0.884704	+	0.466153i	$0.845640\pi$
$332$		0			0
$333$	3.24093	−	15.8464i	0.177602	−	0.868378i
$334$		0			0
$335$	5.05799	+	4.24415i	0.276347	+	0.231883i
$336$		0			0
$337$	3.03513	+	17.2131i	0.165334	+	0.937655i	0.948719	+	0.316119i	$0.102380\pi$
$337$	3.03513	+	17.2131i	0.165334	+	0.937655i	−0.783385	+	0.621536i	$0.786509\pi$
$338$		0			0
$339$	0.797318	+	0.687727i	0.0433044	+	0.0373522i
$340$		0			0
$341$	−15.9328	+	27.5964i	−0.862809	+	1.49443i
$342$		0			0
$343$	−2.50272	+	18.3504i	−0.135134	+	0.990827i
$344$		0			0
$345$	9.04087	+	0.122993i	0.486744	+	0.00662170i
$346$		0			0
$347$	−20.7839	+	17.4398i	−1.11574	+	0.936216i	−0.998381	−	0.0568740i	$-0.981887\pi$
$347$	−20.7839	+	17.4398i	−1.11574	+	0.936216i	−0.117357	+	0.993090i	$0.537442\pi$
$348$		0			0
$349$	−2.27728	+	12.9151i	−0.121900	+	0.691329i	0.861201	+	0.508265i	$0.169713\pi$
$349$	−2.27728	+	12.9151i	−0.121900	+	0.691329i	−0.983101	+	0.183065i	$0.941398\pi$
$350$		0			0
$351$	21.4818	−	16.5801i	1.14661	−	0.884982i
$352$		0			0
$353$	−12.2681	−	10.2941i	−0.652964	−	0.547902i	0.255005	−	0.966940i	$-0.417923\pi$
$353$	−12.2681	−	10.2941i	−0.652964	−	0.547902i	−0.907969	+	0.419038i	$0.862367\pi$
$354$		0			0
$355$	−1.28002	−	7.25938i	−0.0679366	−	0.385288i
$356$		0			0
$357$	−7.08482	+	16.3970i	−0.374969	+	0.867822i
$358$		0			0
$359$	21.4452			1.13183			0.565917	−	0.824462i	$-0.308522\pi$
$359$	21.4452			1.13183			0.565917	+	0.824462i	$0.308522\pi$
$360$		0			0
$361$	−15.3346			−0.807083
$362$		0			0
$363$	−23.6124	−	20.3669i	−1.23933	−	1.06899i
$364$		0			0
$365$	−1.82757	−	10.3647i	−0.0956594	−	0.542512i
$366$		0			0
$367$	−8.73624	+	3.17973i	−0.456028	+	0.165981i	−0.559813	−	0.828619i	$-0.689127\pi$
$367$	−8.73624	+	3.17973i	−0.456028	+	0.165981i	0.103785	+	0.994600i	$0.466905\pi$
$368$		0			0
$369$	−8.97455	−	16.5696i	−0.467196	−	0.862579i
$370$		0			0
$371$	8.26541	−	4.28643i	0.429119	−	0.222540i
$372$		0			0
$373$	0.609701	+	0.221913i	0.0315691	+	0.0114902i	0.357756	−	0.933815i	$-0.383542\pi$
$373$	0.609701	+	0.221913i	0.0315691	+	0.0114902i	−0.326187	+	0.945305i	$0.605764\pi$
$374$		0			0
$375$	10.3088	−	8.41383i	0.532344	−	0.434488i
$376$		0			0
$377$	37.7913			1.94635
$378$		0			0
$379$	−5.53994			−0.284567			−0.142284	−	0.989826i	$-0.545445\pi$
$379$	−5.53994			−0.284567			−0.142284	+	0.989826i	$0.545445\pi$
$380$		0			0
$381$	−32.6755	−	12.3988i	−1.67402	−	0.635211i
$382$		0			0
$383$	−17.9067	−	6.51749i	−0.914988	−	0.333028i	−0.158745	−	0.987320i	$-0.550745\pi$
$383$	−17.9067	−	6.51749i	−0.914988	−	0.333028i	−0.756243	+	0.654291i	$0.772967\pi$
$384$		0			0
$385$	9.89539	+	6.32564i	0.504316	+	0.322384i
$386$		0			0
$387$	27.0295	+	10.6793i	1.37399	+	0.542857i
$388$		0			0
$389$	−24.3920	+	8.87797i	−1.23673	+	0.450131i	−0.875896	−	0.482501i	$-0.839729\pi$
$389$	−24.3920	+	8.87797i	−1.23673	+	0.450131i	−0.360830	+	0.932632i	$0.617506\pi$
$390$		0			0
$391$	4.28671	+	24.3112i	0.216788	+	1.22947i
$392$		0			0
$393$	1.91214	−	0.666648i	0.0964546	−	0.0336279i
$394$		0			0
$395$	−7.27786			−0.366189
$396$		0			0
$397$	−6.26721			−0.314542			−0.157271	−	0.987555i	$-0.550270\pi$
$397$	−6.26721			−0.314542			−0.157271	+	0.987555i	$0.550270\pi$
$398$		0			0
$399$	−3.47990	+	8.05382i	−0.174213	+	0.403196i
$400$		0			0
$401$	−0.938239	−	5.32102i	−0.0468534	−	0.265719i	0.952378	−	0.304920i	$-0.0986298\pi$
$401$	−0.938239	−	5.32102i	−0.0468534	−	0.265719i	−0.999231	+	0.0392012i	$0.987519\pi$
$402$		0			0
$403$	−23.6710	−	19.8624i	−1.17914	−	0.989414i
$404$		0			0
$405$	−7.09857	+	2.15432i	−0.352731	+	0.107049i
$406$		0			0
$407$	5.04199	−	28.5945i	0.249922	−	1.41738i
$408$		0			0
$409$	−16.1767	+	13.5739i	−0.799886	+	0.671184i	−0.948171	−	0.317761i	$-0.897069\pi$
$409$	−16.1767	+	13.5739i	−0.799886	+	0.671184i	0.148285	+	0.988945i	$0.452625\pi$
$410$		0			0
$411$	−7.01462	+	11.7768i	−0.346006	+	0.580905i
$412$		0			0
$413$	−4.59067	+	11.0345i	−0.225892	+	0.542970i
$414$		0			0
$415$	−6.92327	+	11.9915i	−0.339850	+	0.588638i
$416$		0			0
$417$	3.52453	−	18.5124i	0.172597	−	0.906556i
$418$		0			0
$419$	−3.47507	−	19.7081i	−0.169768	−	0.962803i	−0.944011	−	0.329914i	$-0.892980\pi$
$419$	−3.47507	−	19.7081i	−0.169768	−	0.962803i	0.774243	−	0.632889i	$-0.218131\pi$
$420$		0			0
$421$	−14.1567	−	11.8789i	−0.689957	−	0.578943i	0.228940	−	0.973441i	$-0.426474\pi$
$421$	−14.1567	−	11.8789i	−0.689957	−	0.578943i	−0.918897	+	0.394498i	$0.870919\pi$
$422$		0			0
$423$	22.6882	+	8.96404i	1.10314	+	0.435847i
$424$		0			0
$425$	12.9010	+	10.8252i	0.625790	+	0.525100i
$426$		0			0
$427$	−4.14060	−	13.2036i	−0.200378	−	0.638968i
$428$		0			0
$429$	37.7392	−	30.8020i	1.82207	−	1.48713i
$430$		0			0
$431$	10.8852	−	18.8537i	0.524321	−	0.908151i	−0.475278	−	0.879836i	$-0.657652\pi$
$431$	10.8852	−	18.8537i	0.524321	−	0.908151i	0.999599	−	0.0283151i	$-0.00901419\pi$
$432$		0			0
$433$	15.0260			0.722102			0.361051	−	0.932546i	$-0.382418\pi$
$433$	15.0260			0.722102			0.361051	+	0.932546i	$0.382418\pi$
$434$		0			0
$435$	−9.65911	−	3.66518i	−0.463119	−	0.175732i
$436$		0			0
$437$	2.10553	+	11.9411i	0.100721	+	0.571218i
$438$		0			0
$439$	−4.84130	−	4.06234i	−0.231063	−	0.193885i	0.519904	−	0.854225i	$-0.325968\pi$
$439$	−4.84130	−	4.06234i	−0.231063	−	0.193885i	−0.750967	+	0.660340i	$0.770412\pi$
$440$		0			0
$441$	−14.3925	−	15.2924i	−0.685356	−	0.728208i
$442$		0			0
$443$	3.03361	−	17.2044i	0.144131	−	0.817407i	−0.823930	−	0.566692i	$-0.808223\pi$
$443$	3.03361	−	17.2044i	0.144131	−	0.817407i	0.968061	−	0.250716i	$-0.0806659\pi$
$444$		0			0
$445$	3.99611	+	1.45446i	0.189434	+	0.0689482i
$446$		0			0
$447$	6.85508	+	5.91285i	0.324234	+	0.279668i
$448$		0			0
$449$	6.12749	+	10.6131i	0.289174	+	0.500864i	0.973613	−	0.228206i	$-0.0732860\pi$
$449$	6.12749	+	10.6131i	0.289174	+	0.500864i	−0.684439	+	0.729070i	$0.739953\pi$
$450$		0			0
$451$	−16.9139	−	29.2958i	−0.796446	−	1.37948i
$452$		0			0
$453$	11.1490	+	19.9320i	0.523826	+	0.936486i
$454$		0			0
$455$	−7.70711	+	8.38471i	−0.361315	+	0.393081i
$456$		0			0
$457$	−24.0329	+	8.74725i	−1.12421	+	0.409179i	−0.836187	−	0.548444i	$-0.815220\pi$
$457$	−24.0329	+	8.74725i	−1.12421	+	0.409179i	−0.288023	+	0.957623i	$0.592998\pi$
$458$		0			0
$459$	−9.40285	−	17.9389i	−0.438887	−	0.837314i
$460$		0			0
$461$	1.84082	−	10.4398i	0.0857356	−	0.486231i	−0.911460	−	0.411389i	$-0.865044\pi$
$461$	1.84082	−	10.4398i	0.0857356	−	0.486231i	0.997195	−	0.0748418i	$-0.0238452\pi$
$462$		0			0
$463$	−19.3028	−	7.02565i	−0.897078	−	0.326510i	−0.147997	−	0.988988i	$-0.547283\pi$
$463$	−19.3028	−	7.02565i	−0.897078	−	0.326510i	−0.749081	+	0.662478i	$0.769505\pi$
$464$		0			0
$465$	4.12375	+	7.37237i	0.191235	+	0.341885i
$466$		0			0
$467$	40.9469			1.89479			0.947397	−	0.320060i	$-0.103703\pi$
$467$	40.9469			1.89479			0.947397	+	0.320060i	$0.103703\pi$
$468$		0			0
$469$	−12.8760	−	16.8343i	−0.594559	−	0.777335i
$470$		0			0
$471$	−33.7669	+	11.7725i	−1.55590	+	0.542447i
$472$		0			0
$473$	49.0257	+	17.8439i	2.25420	+	0.820464i
$474$		0			0
$475$	6.33666	+	5.31709i	0.290746	+	0.243965i
$476$		0			0
$477$	−2.11543	+	10.3433i	−0.0968589	+	0.473588i
$478$		0			0
$479$	−1.23297	+	6.99249i	−0.0563356	+	0.319495i	−0.999933	−	0.0116008i	$-0.996307\pi$
$479$	−1.23297	+	6.99249i	−0.0563356	+	0.319495i	0.943597	+	0.331096i	$0.107418\pi$
$480$		0			0
$481$	26.4581	+	9.62997i	1.20639	+	0.439089i
$482$		0			0
$483$	−28.2364	−	6.71031i	−1.28480	−	0.305329i
$484$		0			0
$485$	−2.68544	−	4.65132i	−0.121940	−	0.211206i
$486$		0			0
$487$	2.49381	−	4.31941i	0.113005	−	0.195731i	−0.803975	−	0.594663i	$-0.797286\pi$
$487$	2.49381	−	4.31941i	0.113005	−	0.195731i	0.916981	+	0.398932i	$0.130619\pi$
$488$		0			0
$489$	−23.2385	+	18.9668i	−1.05088	+	0.857707i
$490$		0			0
$491$	−12.0578	+	10.1177i	−0.544160	+	0.456605i	−0.872958	−	0.487796i	$-0.837801\pi$
$491$	−12.0578	+	10.1177i	−0.544160	+	0.456605i	0.328798	+	0.944400i	$0.393357\pi$
$492$		0			0
$493$	4.89802	−	27.7781i	0.220596	−	1.25106i
$494$		0			0
$495$	−12.6331	+	4.21257i	−0.567817	+	0.189341i
$496$		0			0
$497$	−1.06872	+	23.6371i	−0.0479387	+	1.06027i
$498$		0			0
$499$	−17.9509	+	15.0626i	−0.803594	+	0.674296i	−0.949070	−	0.315066i	$-0.897973\pi$
$499$	−17.9509	+	15.0626i	−0.803594	+	0.674296i	0.145475	+	0.989362i	$0.453529\pi$
$500$		0			0
$501$	24.9508	+	21.5213i	1.11472	+	0.961502i
$502$		0			0
$503$	4.72061	+	8.17634i	0.210482	+	0.364565i	0.951865	−	0.306516i	$-0.0991634\pi$
$503$	4.72061	+	8.17634i	0.210482	+	0.364565i	−0.741384	+	0.671081i	$0.765830\pi$
$504$		0			0
$505$	−3.73102	+	6.46232i	−0.166028	+	0.287569i
$506$		0			0
$507$	12.0683	+	21.5755i	0.535972	+	0.958200i
$508$		0			0
$509$	2.95052	+	16.7332i	0.130779	+	0.741687i	0.977706	+	0.209977i	$0.0673391\pi$
$509$	2.95052	+	16.7332i	0.130779	+	0.741687i	−0.846927	+	0.531710i	$0.821550\pi$
$510$		0			0
$511$	−1.52588	+	33.7481i	−0.0675009	+	1.49293i
$512$		0			0
$513$	−4.61846	−	8.81114i	−0.203910	−	0.389021i
$514$		0			0
$515$	−4.32106	−	3.62580i	−0.190409	−	0.159772i
$516$		0			0
$517$	41.1516	+	14.9780i	1.80985	+	0.658730i
$518$		0			0
$519$	−20.8741	−	0.283972i	−0.916269	−	0.0124650i
$520$		0			0
$521$	−3.23462	−	5.60252i	−0.141711	−	0.245451i	0.786430	−	0.617680i	$-0.211927\pi$
$521$	−3.23462	−	5.60252i	−0.141711	−	0.245451i	−0.928141	+	0.372229i	$0.878594\pi$
$522$		0			0
$523$	−10.3341	+	17.8991i	−0.451878	+	0.782675i	−0.998503	−	0.0547026i	$-0.982579\pi$
$523$	−10.3341	+	17.8991i	−0.451878	+	0.782675i	0.546625	+	0.837377i	$0.315912\pi$
$524$		0			0
$525$	−17.6989	+	8.87524i	−0.772443	+	0.387347i
$526$		0			0
$527$	−17.6675	+	14.8248i	−0.769611	+	0.645780i
$528$		0			0
$529$	−16.0787	+	5.85218i	−0.699075	+	0.254443i
$530$		0			0
$531$	−6.45399	−	11.9159i	−0.280079	−	0.517107i
$532$		0			0
$533$	30.8249	−	11.2193i	1.33518	−	0.485964i
$534$		0			0
$535$	1.80789	+	10.2531i	0.0781619	+	0.443278i
$536$		0			0
$537$	−0.314891	−	1.93978i	−0.0135886	−	0.0837076i
$538$		0			0
$539$	−26.5740	−	26.7392i	−1.14462	−	1.15174i
$540$		0			0
$541$	−4.83442	−	8.37346i	−0.207848	−	0.360003i	0.743189	−	0.669082i	$-0.233313\pi$
$541$	−4.83442	−	8.37346i	−0.207848	−	0.360003i	−0.951036	+	0.309079i	$0.899979\pi$
$542$		0			0
$543$	32.8776	+	12.4755i	1.41091	+	0.535376i
$544$		0			0
$545$	2.66751	−	2.23831i	0.114264	−	0.0958785i
$546$		0			0
$547$	13.5615	−	4.93600i	0.579850	−	0.211048i	−0.0354095	−	0.999373i	$-0.511274\pi$
$547$	13.5615	−	4.93600i	0.579850	−	0.211048i	0.615259	+	0.788325i	$0.289051\pi$
$548$		0			0
$549$	14.5927	+	5.76554i	0.622802	+	0.246067i
$550$		0			0
$551$	2.40579	−	13.6439i	0.102490	−	0.581251i
$552$		0			0
$553$	22.7994	+	5.09159i	0.969530	+	0.216517i
$554$		0			0
$555$	−5.82849	−	5.02737i	−0.247406	−	0.213400i
$556$		0			0
$557$	−30.2815			−1.28307			−0.641535	−	0.767094i	$-0.721702\pi$
$557$	−30.2815			−1.28307			−0.641535	+	0.767094i	$0.721702\pi$
$558$		0			0
$559$	−25.2959	+	43.8137i	−1.06990	+	1.85312i
$560$		0			0
$561$	−17.7494	−	31.7320i	−0.749379	−	1.33973i
$562$		0			0
$563$	−12.1386	+	10.1855i	−0.511582	+	0.429268i	−0.861685	−	0.507443i	$-0.830591\pi$
$563$	−12.1386	+	10.1855i	−0.511582	+	0.429268i	0.350104	+	0.936711i	$0.386146\pi$
$564$		0			0
$565$	0.470857	−	0.171378i	0.0198091	−	0.00720993i
$566$		0			0
$567$	23.7449	−	1.78271i	0.997194	−	0.0748669i
$568$		0			0
$569$	34.5992	−	12.5931i	1.45047	−	0.527929i	0.507750	−	0.861504i	$-0.330477\pi$
$569$	34.5992	−	12.5931i	1.45047	−	0.527929i	0.942724	+	0.333575i	$0.108255\pi$
$570$		0			0
$571$	−5.39005	+	4.52279i	−0.225567	+	0.189273i	−0.748566	−	0.663060i	$-0.769257\pi$
$571$	−5.39005	+	4.52279i	−0.225567	+	0.189273i	0.522999	+	0.852333i	$0.324813\pi$
$572$		0			0
$573$	−8.59379	−	15.3638i	−0.359011	−	0.641832i
$574$		0			0
$575$	−13.6818	+	23.6976i	−0.570572	+	0.988260i
$576$		0			0
$577$	23.8216			0.991705			0.495852	−	0.868407i	$-0.334856\pi$
$577$	23.8216			0.991705			0.495852	+	0.868407i	$0.334856\pi$
$578$		0			0
$579$	0.900165	+	0.776437i	0.0374096	+	0.0322676i
$580$		0			0
$581$	30.0779	−	32.7223i	1.24784	−	1.35755i
$582$		0			0
$583$	−3.29102	+	18.6643i	−0.136300	+	0.772997i
$584$		0			0
$585$	−1.89564	−	12.7737i	−0.0783750	−	0.528127i
$586$		0			0
$587$	8.50451	−	3.09539i	0.351019	−	0.127760i	−0.160492	−	0.987037i	$-0.551308\pi$
$587$	8.50451	−	3.09539i	0.351019	−	0.127760i	0.511511	+	0.859277i	$0.329086\pi$
$588$		0			0
$589$	−8.67788	+	7.28160i	−0.357566	+	0.300033i
$590$		0			0
$591$	11.4132	+	4.33077i	0.469476	+	0.178144i
$592$		0			0
$593$	−15.5566	−	26.9448i	−0.638832	−	1.10649i	−0.985689	−	0.168572i	$-0.946084\pi$
$593$	−15.5566	−	26.9448i	−0.638832	−	1.10649i	0.346857	−	0.937918i	$-0.387249\pi$
$594$		0			0
$595$	5.16419	+	6.75175i	0.211711	+	0.276795i
$596$		0			0
$597$	−5.31454	−	32.7384i	−0.217510	−	1.33989i
$598$		0			0
$599$	3.49374	+	19.8140i	0.142750	+	0.809577i	0.969146	+	0.246487i	$0.0792764\pi$
$599$	3.49374	+	19.8140i	0.142750	+	0.809577i	−0.826396	+	0.563090i	$0.809613\pi$
$600$		0			0
$601$	−34.2943	+	12.4821i	−1.39890	+	0.509156i	−0.927850	−	0.372953i	$-0.878345\pi$
$601$	−34.2943	+	12.4821i	−1.39890	+	0.509156i	−0.471045	+	0.882109i	$0.656123\pi$
$602$		0			0
$603$	24.0228	+	0.653737i	0.978285	+	0.0266222i
$604$		0			0
$605$	−13.9444	+	5.07533i	−0.566919	+	0.206342i
$606$		0			0
$607$	18.0490	−	15.1449i	0.732588	−	0.614714i	−0.198248	−	0.980152i	$-0.563525\pi$
$607$	18.0490	−	15.1449i	0.732588	−	0.614714i	0.930836	+	0.365438i	$0.119081\pi$
$608$		0			0
$609$	27.6950	+	18.2395i	1.12226	+	0.739101i
$610$		0			0
$611$	−21.2331	+	36.7767i	−0.858998	+	1.48783i
$612$		0			0
$613$	9.46737	+	16.3980i	0.382384	+	0.662308i	0.991402	−	0.130848i	$-0.0417700\pi$
$613$	9.46737	+	16.3980i	0.382384	+	0.662308i	−0.609019	+	0.793156i	$0.708437\pi$
$614$		0			0
$615$	−8.96667	−	0.121983i	−0.361571	−	0.00491883i
$616$		0			0
$617$	36.8302	+	13.4051i	1.48273	+	0.539669i	0.951524	−	0.307575i	$-0.0995175\pi$
$617$	36.8302	+	13.4051i	1.48273	+	0.539669i	0.531204	+	0.847244i	$0.321740\pi$
$618$		0			0
$619$	4.52797	+	3.79942i	0.181994	+	0.152711i	0.729234	−	0.684265i	$-0.239877\pi$
$619$	4.52797	+	3.79942i	0.181994	+	0.152711i	−0.547239	+	0.836976i	$0.684321\pi$
$620$		0			0
$621$	26.0516	−	20.1072i	1.04542	−	0.806875i
$622$		0			0
$623$	−11.5011	−	7.35210i	−0.460782	−	0.294556i
$624$		0			0
$625$	2.65173	+	15.0387i	0.106069	+	0.601548i
$626$		0			0
$627$	−8.71807	−	15.5860i	−0.348166	−	0.622444i
$628$		0			0
$629$	10.5076	−	18.1996i	0.418964	−	0.725667i
$630$		0			0
$631$	−23.1548	−	40.1053i	−0.921777	−	1.59656i	−0.796664	−	0.604422i	$-0.793404\pi$
$631$	−23.1548	−	40.1053i	−0.921777	−	1.59656i	−0.125113	−	0.992142i	$-0.539929\pi$
$632$		0			0
$633$	−20.4226	−	17.6155i	−0.811726	−	0.700154i
$634$		0			0
$635$	−12.7405	+	10.6905i	−0.505591	+	0.424241i
$636$		0			0
$637$	30.0101	−	20.8750i	1.18904	−	0.827097i
$638$		0			0
$639$	−20.0757	−	17.7982i	−0.794182	−	0.704087i
$640$		0			0
$641$	−6.31866	+	35.8349i	−0.249572	+	1.41539i	0.560058	+	0.828453i	$0.310779\pi$
$641$	−6.31866	+	35.8349i	−0.249572	+	1.41539i	−0.809630	+	0.586940i	$0.800332\pi$
$642$		0			0
$643$	4.73536	−	3.97344i	0.186744	−	0.156697i	−0.544623	−	0.838681i	$-0.683327\pi$
$643$	4.73536	−	3.97344i	0.186744	−	0.156697i	0.731367	+	0.681984i	$0.238883\pi$
$644$		0			0
$645$	10.7147	−	8.74508i	0.421889	−	0.344337i
$646$		0			0
$647$	5.93648	−	10.2823i	0.233387	−	0.404238i	−0.725416	−	0.688311i	$-0.758352\pi$
$647$	5.93648	−	10.2823i	0.233387	−	0.404238i	0.958803	+	0.284073i	$0.0916858\pi$
$648$		0			0
$649$	−12.1635	−	21.0679i	−0.477461	−	0.826986i
$650$		0			0
$651$	−7.76082	−	25.9805i	−0.304171	−	1.01826i
$652$		0			0
$653$	15.6820	+	5.70778i	0.613684	+	0.223363i	0.630114	−	0.776502i	$-0.283008\pi$
$653$	15.6820	+	5.70778i	0.613684	+	0.223363i	−0.0164306	+	0.999865i	$0.505230\pi$
$654$		0			0
$655$	0.167340	−	0.949030i	0.00653850	−	0.0370817i
$656$		0			0
$657$	−28.6633	−	25.4117i	−1.11826	−	0.991403i
$658$		0			0
$659$	27.0025	+	22.6578i	1.05187	+	0.882623i	0.993289	−	0.115659i	$-0.0368981\pi$
$659$	27.0025	+	22.6578i	1.05187	+	0.882623i	0.0585807	+	0.998283i	$0.481343\pi$
$660$		0			0
$661$	17.5348	+	6.38213i	0.682023	+	0.248236i	0.659716	−	0.751515i	$-0.270677\pi$
$661$	17.5348	+	6.38213i	0.682023	+	0.248236i	0.0223074	+	0.999751i	$0.492899\pi$
$662$		0			0
$663$	33.2921	−	11.6070i	1.29296	−	0.450777i
$664$		0			0
$665$	2.53653	+	3.31630i	0.0983623	+	0.128600i
$666$		0			0
$667$	45.8306			1.77457
$668$		0			0
$669$	4.78533	+	8.55512i	0.185011	+	0.330760i
$670$		0			0
$671$	26.4681	+	9.63360i	1.02179	+	0.371901i
$672$		0			0
$673$	−3.87790	+	21.9926i	−0.149482	+	0.847754i	0.814177	+	0.580617i	$0.197189\pi$
$673$	−3.87790	+	21.9926i	−0.149482	+	0.847754i	−0.963659	+	0.267137i	$0.913922\pi$
$674$		0			0
$675$	4.79728	−	21.9320i	0.184647	−	0.844163i
$676$		0			0
$677$	12.9085	−	4.69831i	0.496114	−	0.180571i	−0.0818315	−	0.996646i	$-0.526077\pi$
$677$	12.9085	−	4.69831i	0.496114	−	0.180571i	0.577945	+	0.816076i	$0.303855\pi$
$678$		0			0
$679$	5.15865	+	16.4500i	0.197971	+	0.631293i
$680$		0			0
$681$	−6.39468	−	11.4323i	−0.245045	−	0.438086i
$682$		0			0
$683$	18.4355	+	31.9312i	0.705414	+	1.22181i	0.966542	+	0.256509i	$0.0825724\pi$
$683$	18.4355	+	31.9312i	0.705414	+	1.22181i	−0.261127	+	0.965304i	$0.584094\pi$
$684$		0			0
$685$	3.26159	+	5.64924i	0.124619	+	0.215846i
$686$		0			0
$687$	10.0239	+	8.64612i	0.382436	+	0.329870i
$688$		0			0
$689$	−17.2698	−	6.28570i	−0.657928	−	0.239466i
$690$		0			0
$691$	1.77464	−	10.0645i	0.0675103	−	0.382870i	−0.932267	−	0.361771i	$-0.882172\pi$
$691$	1.77464	−	10.0645i	0.0675103	−	0.382870i	0.999777	−	0.0210992i	$-0.00671658\pi$
$692$		0			0
$693$	42.5231	−	4.35862i	1.61532	−	0.165570i
$694$		0			0
$695$	−6.86986	−	5.76450i	−0.260589	−	0.218660i
$696$		0			0
$697$	−4.25153	−	24.1116i	−0.161038	−	0.913293i
$698$		0			0
$699$	−28.6292	−	10.8634i	−1.08286	−	0.410893i
$700$		0			0
$701$	7.10983			0.268534			0.134267	−	0.990945i	$-0.457132\pi$
$701$	7.10983			0.268534			0.134267	+	0.990945i	$0.457132\pi$
$702$		0			0
$703$	5.16107	−	8.93923i	0.194653	−	0.337149i
$704$		0			0
$705$	8.99376	−	7.34052i	0.338725	−	0.276460i
$706$		0			0
$707$	16.2093	−	17.6344i	0.609612	−	0.663208i
$708$		0			0
$709$	4.83305	+	4.05541i	0.181509	+	0.152304i	0.729015	−	0.684497i	$-0.239978\pi$
$709$	4.83305	+	4.05541i	0.181509	+	0.152304i	−0.547506	+	0.836802i	$0.684423\pi$
$710$		0			0
$711$	−20.7474	+	16.4685i	−0.778087	+	0.617615i
$712$		0			0
$713$	−28.7066	−	24.0877i	−1.07507	−	0.902091i
$714$		0			0
$715$	−4.02550	−	22.8297i	−0.150545	−	0.853784i
$716$		0			0
$717$	−9.15666	+	48.0948i	−0.341962	+	1.79613i
$718$		0			0
$719$	4.31154	−	7.46781i	0.160793	−	0.278502i	−0.774360	−	0.632745i	$-0.781928\pi$
$719$	4.31154	−	7.46781i	0.160793	−	0.278502i	0.935153	+	0.354243i	$0.115261\pi$
$720$		0			0
$721$	11.0000	+	14.3816i	0.409663	+	0.535599i
$722$		0			0
$723$	2.96526	−	4.97833i	0.110279	−	0.185146i
$724$		0			0
$725$	23.9511	−	20.0973i	0.889521	−	0.746396i
$726$		0			0
$727$	−0.0330587	+	0.187485i	−0.00122608	+	0.00695345i	−0.985415	−	0.170170i	$-0.945568\pi$
$727$	−0.0330587	+	0.187485i	−0.00122608	+	0.00695345i	0.984189	+	0.177124i	$0.0566793\pi$
$728$		0			0
$729$	−15.3614	+	22.2042i	−0.568941	+	0.822378i
$730$		0			0
$731$	28.9263	+	24.2720i	1.06988	+	0.897734i
$732$		0			0
$733$	−1.33001	−	7.54287i	−0.0491251	−	0.278602i	0.950343	−	0.311203i	$-0.100732\pi$
$733$	−1.33001	−	7.54287i	−0.0491251	−	0.278602i	−0.999468	+	0.0326010i	$0.989621\pi$
$734$		0			0
$735$	−9.69486	+	2.42493i	−0.357600	+	0.0894449i
$736$		0			0
$737$	43.1407			1.58911
$738$		0			0
$739$	32.1722			1.18347			0.591736	−	0.806132i	$-0.298443\pi$
$739$	32.1722			1.18347			0.591736	+	0.806132i	$0.298443\pi$
$740$		0			0
$741$	16.3523	−	5.70106i	0.600716	−	0.209434i
$742$		0			0
$743$	1.39235	+	7.89643i	0.0510805	+	0.289692i	0.999638	−	0.0269137i	$-0.00856792\pi$
$743$	1.39235	+	7.89643i	0.0510805	+	0.289692i	−0.948557	+	0.316606i	$0.897457\pi$
$744$		0			0
$745$	4.04828	−	1.47345i	0.148317	−	0.0539831i
$746$		0			0
$747$	7.39794	+	49.8508i	0.270677	+	1.82394i
$748$		0			0
$749$	1.50945	−	33.3847i	0.0551540	−	1.21985i
$750$		0			0
$751$	−18.2219	−	6.63222i	−0.664925	−	0.242013i	−0.0125639	−	0.999921i	$-0.503999\pi$
$751$	−18.2219	−	6.63222i	−0.664925	−	0.242013i	−0.652361	+	0.757908i	$0.726222\pi$
$752$		0			0
$753$	−28.3244	−	10.7478i	−1.03220	−	0.391671i
$754$		0			0
$755$	10.8683			0.395538
$756$		0			0
$757$	−0.421431			−0.0153172			−0.00765858	−	0.999971i	$-0.502438\pi$
$757$	−0.421431			−0.0153172			−0.00765858	+	0.999971i	$0.502438\pi$
$758$		0			0
$759$	45.7675	−	37.3545i	1.66126	−	1.35588i
$760$		0			0
$761$	−38.0489	−	13.8487i	−1.37927	−	0.502014i	−0.457314	−	0.889305i	$-0.651188\pi$
$761$	−38.0489	−	13.8487i	−1.37927	−	0.502014i	−0.921957	+	0.387291i	$0.873411\pi$
$762$		0			0
$763$	−9.92246	+	5.14578i	−0.359217	+	0.186290i
$764$		0			0
$765$	−9.63486	−	0.262195i	−0.348349	−	0.00947967i
$766$		0			0
$767$	22.1675	−	8.06832i	0.800423	−	0.291330i
$768$		0			0
$769$	−2.88836	−	16.3807i	−0.104157	−	0.590703i	−0.991554	−	0.129697i	$-0.958600\pi$
$769$	−2.88836	−	16.3807i	−0.104157	−	0.590703i	0.887397	−	0.461006i	$-0.152511\pi$
$770$		0			0
$771$	−7.96535	−	6.87051i	−0.286865	−	0.247435i
$772$		0			0
$773$	−2.55214			−0.0917940			−0.0458970	−	0.998946i	$-0.514615\pi$
$773$	−2.55214			−0.0917940			−0.0458970	+	0.998946i	$0.514615\pi$
$774$		0			0
$775$	−25.5648			−0.918315
$776$		0			0
$777$	14.7418	+	19.8269i	0.528861	+	0.711287i
$778$		0			0
$779$	−2.08825	−	11.8431i	−0.0748193	−	0.424321i
$780$		0			0
$781$	−36.8948	−	30.9584i	−1.32020	−	1.10778i
$782$		0			0
$783$	−35.8294	+	11.4083i	−1.28044	+	0.407699i
$784$		0			0
$785$	−2.95509	+	16.7591i	−0.105472	+	0.598159i
$786$		0			0
$787$	14.3517	−	12.0425i	0.511583	−	0.429269i	−0.350103	−	0.936711i	$-0.613853\pi$
$787$	14.3517	−	12.0425i	0.511583	−	0.429269i	0.861686	+	0.507442i	$0.169409\pi$
$788$		0			0
$789$	13.8511	+	0.188431i	0.493112	+	0.00670833i
$790$		0			0
$791$	−1.59496	+	0.207466i	−0.0567101	+	0.00737664i
$792$		0			0
$793$	−13.6568	+	23.6543i	−0.484967	+	0.839987i
$794$		0			0
$795$	3.80439	+	3.28148i	0.134928	+	0.116382i
$796$		0			0
$797$	−7.58071	−	42.9923i	−0.268522	−	1.52287i	−0.758814	−	0.651308i	$-0.774221\pi$
$797$	−7.58071	−	42.9923i	−0.268522	−	1.52287i	0.490291	−	0.871559i	$-0.336890\pi$
$798$		0			0
$799$	24.2804	+	20.3737i	0.858978	+	0.720769i
$800$		0			0
$801$	14.6831	−	4.89615i	0.518802	−	0.172997i
$802$		0			0
$803$	−52.6771	−	44.2013i	−1.85893	−	1.55983i
$804$		0			0
$805$	−9.34664	+	10.1684i	−0.329426	+	0.358389i
$806$		0			0
$807$	−34.1316	−	12.9513i	−1.20149	−	0.455908i
$808$		0			0
$809$	7.23508	−	12.5315i	0.254372	−	0.440585i	−0.710353	−	0.703846i	$-0.751465\pi$
$809$	7.23508	−	12.5315i	0.254372	−	0.440585i	0.964725	+	0.263261i	$0.0847980\pi$
$810$		0			0
$811$	30.3686			1.06639			0.533194	−	0.845993i	$-0.320992\pi$
$811$	30.3686			1.06639			0.533194	+	0.845993i	$0.320992\pi$
$812$		0			0
$813$	6.20463	−	5.06408i	0.217606	−	0.177605i
$814$		0			0
$815$	2.47876	+	14.0578i	0.0868272	+	0.492422i
$816$		0			0
$817$	14.2079	+	11.9218i	0.497072	+	0.417093i
$818$		0			0
$819$	−2.99800	+	41.3425i	−0.104759	+	1.44462i
$820$		0			0
$821$	−5.31947	+	30.1682i	−0.185651	+	1.05288i	0.739466	+	0.673194i	$0.235078\pi$
$821$	−5.31947	+	30.1682i	−0.185651	+	1.05288i	−0.925116	+	0.379684i	$0.876033\pi$
$822$		0			0
$823$	−24.3088	−	8.84768i	−0.847352	−	0.308411i	−0.118392	−	0.992967i	$-0.537774\pi$
$823$	−24.3088	−	8.84768i	−0.847352	−	0.308411i	−0.728960	+	0.684556i	$0.759996\pi$
$824$		0			0
$825$	7.53766	−	39.5911i	0.262428	−	1.37839i
$826$		0			0
$827$	−23.4481	−	40.6132i	−0.815369	−	1.41226i	−0.909063	−	0.416660i	$-0.863201\pi$
$827$	−23.4481	−	40.6132i	−0.815369	−	1.41226i	0.0936934	−	0.995601i	$-0.470133\pi$
$828$		0			0
$829$	−28.3315	−	49.0716i	−0.983994	−	1.70433i	−0.646326	−	0.763061i	$-0.723695\pi$
$829$	−28.3315	−	49.0716i	−0.983994	−	1.70433i	−0.337668	−	0.941265i	$-0.609638\pi$
$830$		0			0
$831$	51.5041	+	0.700665i	1.78666	+	0.0243058i
$832$		0			0
$833$	−11.4544	−	24.7642i	−0.396871	−	0.858027i
$834$		0			0
$835$	14.7347	−	5.36301i	0.509917	−	0.185595i
$836$		0			0
$837$	28.4381	+	11.6855i	0.982965	+	0.403910i
$838$		0			0
$839$	−0.366458	+	2.07829i	−0.0126515	+	0.0717504i	−0.990480	−	0.137658i	$-0.956043\pi$
$839$	−0.366458	+	2.07829i	−0.0126515	+	0.0717504i	0.977828	+	0.209408i	$0.0671537\pi$
$840$		0			0
$841$	−21.9572	−	7.99177i	−0.757145	−	0.275578i
$842$		0			0
$843$	−2.94086	+	4.93738i	−0.101289	+	0.170052i
$844$		0			0
$845$	11.7645			0.404709
$846$		0			0
$847$	47.2344	−	6.14407i	1.62299	−	0.211113i
$848$		0			0
$849$	−7.80926	+	41.0177i	−0.268013	+	1.40772i
$850$		0			0
$851$	32.0866	+	11.6786i	1.09991	+	0.400336i
$852$		0			0
$853$	−18.7816	−	15.7596i	−0.643070	−	0.539600i	0.261889	−	0.965098i	$-0.415655\pi$
$853$	−18.7816	−	15.7596i	−0.643070	−	0.539600i	−0.904959	+	0.425498i	$0.860099\pi$
$854$		0			0
$855$	−4.73241	−	0.128784i	−0.161845	−	0.00440431i
$856$		0			0
$857$	1.85350	−	10.5117i	0.0633143	−	0.359073i	−0.936647	−	0.350275i	$-0.886088\pi$
$857$	1.85350	−	10.5117i	0.0633143	−	0.359073i	0.999961	−	0.00879859i	$-0.00280071\pi$
$858$		0			0
$859$	−14.4913	−	5.27442i	−0.494438	−	0.179961i	0.0827526	−	0.996570i	$-0.473629\pi$
$859$	−14.4913	−	5.27442i	−0.494438	−	0.179961i	−0.577191	+	0.816609i	$0.695851\pi$
$860$		0			0
$861$	28.0047	+	6.65523i	0.954396	+	0.226810i
$862$		0			0
$863$	21.2468	+	36.8005i	0.723248	+	1.25270i	0.959691	+	0.281057i	$0.0906851\pi$
$863$	21.2468	+	36.8005i	0.723248	+	1.25270i	−0.236443	+	0.971645i	$0.575982\pi$
$864$		0			0
$865$	−4.96726	+	8.60354i	−0.168892	+	0.292529i
$866$		0			0
$867$	0.501456	+	3.08905i	0.0170303	+	0.104910i
$868$		0			0
$869$	−36.4268	+	30.5657i	−1.23569	+	1.03687i
$870$		0			0
$871$	−7.26439	+	41.1984i	−0.246144	+	1.39595i
$872$		0			0
$873$	−18.1806	−	7.18311i	−0.615321	−	0.243111i
$874$		0			0
$875$	−0.918081	+	20.3053i	−0.0310368	+	0.686445i
$876$		0			0
$877$	−25.5061	+	21.4022i	−0.861280	+	0.722699i	−0.962243	−	0.272191i	$-0.912252\pi$
$877$	−25.5061	+	21.4022i	−0.861280	+	0.722699i	0.100964	+	0.994890i	$0.467807\pi$
$878$		0			0
$879$	6.68053	−	35.0891i	0.225329	−	1.18353i
$880$		0			0
$881$	−15.7497	−	27.2792i	−0.530620	−	0.919061i	−0.999362	−	0.0357254i	$-0.988626\pi$
$881$	−15.7497	−	27.2792i	−0.530620	−	0.919061i	0.468742	−	0.883335i	$-0.344708\pi$
$882$		0			0
$883$	14.1100	−	24.4393i	0.474840	−	0.822446i	−0.524745	−	0.851259i	$-0.675839\pi$
$883$	14.1100	−	24.4393i	0.474840	−	0.822446i	0.999585	+	0.0288130i	$0.00917273\pi$
$884$		0			0
$885$	−6.44832	−	0.0877234i	−0.216758	−	0.00294879i
$886$		0			0
$887$	2.32734	+	13.1990i	0.0781445	+	0.443179i	0.998626	+	0.0523944i	$0.0166853\pi$
$887$	2.32734	+	13.1990i	0.0781445	+	0.443179i	−0.920482	+	0.390785i	$0.872204\pi$
$888$		0			0
$889$	47.3914	−	24.5771i	1.58946	−	0.824290i
$890$		0			0
$891$	−26.4816	+	40.5955i	−0.887168	+	1.36000i
$892$		0			0
$893$	11.9259	+	10.0071i	0.399087	+	0.334873i
$894$		0			0
$895$	−0.878791	−	0.319854i	−0.0293748	−	0.0106915i
$896$		0			0
$897$	27.9660	+	49.9970i	0.933757	+	1.66935i
$898$		0			0
$899$	21.4089	+	37.0813i	0.714026	+	1.23673i
$900$		0			0
$901$	−6.85853	+	11.8793i	−0.228491	+	0.395758i
$902$		0			0
$903$	−39.6840	+	19.8998i	−1.32060	+	0.662225i
$904$		0			0
$905$	12.8193	−	10.7567i	0.426128	−	0.357564i
$906$		0			0
$907$	−46.8065	+	17.0362i	−1.55418	+	0.565676i	−0.969394	−	0.245509i	$-0.921045\pi$
$907$	−46.8065	+	17.0362i	−1.55418	+	0.565676i	−0.584789	+	0.811185i	$0.698823\pi$
$908$		0			0
$909$	3.98683	+	26.8651i	0.132235	+	0.891059i
$910$		0			0
$911$	−21.4765	+	7.81682i	−0.711550	+	0.258983i	−0.672334	−	0.740248i	$-0.734708\pi$
$911$	−21.4765	+	7.81682i	−0.711550	+	0.258983i	−0.0392156	+	0.999231i	$0.512486\pi$
$912$		0			0
$913$	15.7100	+	89.0956i	0.519924	+	2.94863i
$914$		0			0
$915$	5.78465	−	4.72131i	0.191235	−	0.156082i
$916$		0			0
$917$	−1.18817	+	2.85597i	−0.0392368	+	0.0943123i
$918$		0			0
$919$	−2.85348	−	4.94236i	−0.0941275	−	0.163034i	0.815117	−	0.579297i	$-0.196673\pi$
$919$	−2.85348	−	4.94236i	−0.0941275	−	0.163034i	−0.909244	+	0.416263i	$0.863339\pi$
$920$		0			0
$921$	35.5118	−	28.9840i	1.17015	−	0.955055i
$922$		0			0
$923$	35.7773	−	30.0207i	1.17762	−	0.988143i
$924$		0			0
$925$	21.8896	−	7.96717i	0.719727	−	0.261959i
$926$		0			0
$927$	−20.5228	−	0.558490i	−0.674058	−	0.0183432i
$928$		0			0
$929$	6.65535	−	37.7444i	0.218355	−	1.23835i	−0.656634	−	0.754210i	$-0.728020\pi$
$929$	6.65535	−	37.7444i	0.218355	−	1.23835i	0.874989	−	0.484143i	$-0.160869\pi$
$930$		0			0
$931$	−5.62613	−	12.1636i	−0.184389	−	0.398645i
$932$		0			0
$933$	0.204902	−	1.07624i	0.00670820	−	0.0352344i
$934$		0			0
$935$	−17.3025			−0.565852
$936$		0			0
$937$	4.73380	−	8.19918i	0.154646	−	0.267855i	−0.778284	−	0.627913i	$-0.783909\pi$
$937$	4.73380	−	8.19918i	0.154646	−	0.267855i	0.932930	+	0.360057i	$0.117243\pi$
$938$		0			0
$939$	−13.5963	−	0.184965i	−0.443699	−	0.00603611i
$940$		0			0
$941$	−8.80413	+	7.38754i	−0.287006	+	0.240827i	−0.774912	−	0.632070i	$-0.782206\pi$
$941$	−8.80413	+	7.38754i	−0.287006	+	0.240827i	0.487905	+	0.872897i	$0.337761\pi$
$942$		0			0
$943$	37.3823	−	13.6060i	1.21734	−	0.443074i
$944$		0			0
$945$	4.77585	−	10.2760i	0.155359	−	0.334279i
$946$		0			0
$947$	−41.6461	+	15.1579i	−1.35332	+	0.492567i	−0.913981	−	0.405756i	$-0.867008\pi$
$947$	−41.6461	+	15.1579i	−1.35332	+	0.492567i	−0.439335	+	0.898323i	$0.644786\pi$
$948$		0			0
$949$	51.0814	−	42.8624i	1.65817	−	1.39137i
$950$		0			0
$951$	7.48341	−	12.5638i	0.242666	−	0.407409i
$952$		0			0
$953$	−1.51459	+	2.62335i	−0.0490625	+	0.0849787i	−0.889514	−	0.456909i	$-0.848957\pi$
$953$	−1.51459	+	2.62335i	−0.0490625	+	0.0849787i	0.840451	+	0.541887i	$0.182290\pi$
$954$		0			0
$955$	−8.37742			−0.271087
$956$		0			0
$957$	−63.7384	+	22.2218i	−2.06037	+	0.718327i
$958$		0			0
$959$	−6.26541	−	19.9793i	−0.202321	−	0.645164i
$960$		0			0
$961$	0.696379	−	3.94936i	0.0224638	−	0.127399i
$962$		0			0
$963$	28.3546	+	25.1380i	0.913715	+	0.810060i
$964$		0			0
$965$	0.531593	−	0.193484i	0.0171126	−	0.00622848i
$966$		0			0
$967$	−5.44415	+	4.56818i	−0.175072	+	0.146903i	−0.726113	−	0.687575i	$-0.758675\pi$
$967$	−5.44415	+	4.56818i	−0.175072	+	0.146903i	0.551041	+	0.834478i	$0.314231\pi$
$968$		0			0
$969$	−2.07113	−	12.7585i	−0.0665342	−	0.409861i
$970$		0			0
$971$	−17.8433	−	30.9055i	−0.572620	−	0.991806i	−0.996296	−	0.0859924i	$-0.972594\pi$
$971$	−17.8433	−	30.9055i	−0.572620	−	0.991806i	0.423676	−	0.905814i	$-0.360739\pi$
$972$		0			0
$973$	17.4885	+	22.8647i	0.560654	+	0.733008i
$974$		0			0
$975$	36.5393	+	13.8650i	1.17020	+	0.444034i
$976$		0			0
$977$	−6.22553	−	35.3067i	−0.199172	−	1.12956i	−0.906350	−	0.422527i	$-0.861143\pi$
$977$	−6.22553	−	35.3067i	−0.199172	−	1.12956i	0.707178	−	0.707035i	$-0.249968\pi$
$978$		0			0
$979$	26.1096	−	9.50313i	0.834468	−	0.303721i
$980$		0			0
$981$	2.53953	−	12.4169i	0.0810811	−	0.396443i
$982$		0			0
$983$	−39.5705	+	14.4025i	−1.26210	+	0.459368i	−0.884474	−	0.466589i	$-0.845483\pi$
$983$	−39.5705	+	14.4025i	−1.26210	+	0.459368i	−0.377629	+	0.925957i	$0.623261\pi$
$984$		0			0
$985$	4.45011	−	3.73409i	0.141792	−	0.118978i
$986$		0			0
$987$	−33.3103	+	16.7037i	−1.06028	+	0.531684i
$988$		0			0
$989$	−30.6771	+	53.1343i	−0.975475	+	1.68957i
$990$		0			0
$991$	14.5563	+	25.2123i	0.462397	+	0.800895i	0.999080	−	0.0428888i	$-0.0136561\pi$
$991$	14.5563	+	25.2123i	0.462397	+	0.800895i	−0.536683	+	0.843784i	$0.680323\pi$
$992$		0			0
$993$	−12.1938	+	20.4720i	−0.386959	+	0.649660i
$994$		0			0
$995$	−14.8317	−	5.39830i	−0.470197	−	0.171138i
$996$		0			0
$997$	5.54547	+	4.65321i	0.175627	+	0.147368i	0.726364	−	0.687310i	$-0.241209\pi$
$997$	5.54547	+	4.65321i	0.175627	+	0.147368i	−0.550737	+	0.834679i	$0.685653\pi$
$998$		0			0
$999$	−27.9916	−	1.14296i	−0.885615	−	0.0361617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.10	yes	144
7.2	even	3		756.2.bp.a.457.23	yes	144
27.13	even	9		756.2.bp.a.445.23	✓	144
189.121	even	9	inner	756.2.bq.a.121.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.23	✓	144	27.13	even	9
756.2.bp.a.457.23	yes	144	7.2	even	3
756.2.bq.a.25.10	yes	144	1.1	even	1	trivial
756.2.bq.a.121.10	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)

\(f(q)\)	\(=\)	\(q+(-0.277537 - 1.70967i) q^{3} +(-0.774544 - 0.281911i) q^{5} +(2.22920 + 1.42502i) q^{7} +(-2.84595 + 0.948993i) q^{9} +O(q^{10})\)	\(q+(-0.277537 - 1.70967i) q^{3} +(-0.774544 - 0.281911i) q^{5} +(2.22920 + 1.42502i) q^{7} +(-2.84595 + 0.948993i) q^{9} +(-5.06069 + 1.84194i) q^{11} +(-0.906850 - 5.14300i) q^{13} +(-0.267010 + 1.40246i) q^{15} -3.89784 q^{17} -1.91453 q^{19} +(1.81763 - 4.20669i) q^{21} +(-1.09977 - 6.23708i) q^{23} +(-3.30978 - 2.77723i) q^{25} +(2.41232 + 4.60225i) q^{27} +(-1.25660 + 7.12652i) q^{29} +(4.53265 - 3.80334i) q^{31} +(4.55364 + 8.14090i) q^{33} +(-1.32488 - 1.73217i) q^{35} +(-2.69574 + 4.66916i) q^{37} +(-8.54116 + 2.97779i) q^{39} +(1.09074 + 6.18589i) q^{41} +(-7.42110 - 6.22704i) q^{43} +(2.47184 + 0.0672666i) q^{45} +(-6.22918 - 5.22691i) q^{47} +(2.93865 + 6.35329i) q^{49} +(1.08180 + 6.66403i) q^{51} +(1.75957 - 3.04766i) q^{53} +4.43899 q^{55} +(0.531352 + 3.27321i) q^{57} +(0.784398 + 4.44854i) q^{59} +(-4.00652 - 3.36187i) q^{61} +(-7.69651 - 1.94003i) q^{63} +(-0.747474 + 4.23913i) q^{65} +(-7.52747 - 2.73978i) q^{67} +(-10.3581 + 3.61126i) q^{69} +(4.47155 + 7.74495i) q^{71} +(6.38431 + 11.0579i) q^{73} +(-3.82957 + 6.42941i) q^{75} +(-13.9061 - 3.10552i) q^{77} +(8.29715 - 3.01992i) q^{79} +(7.19882 - 5.40157i) q^{81} +(2.91710 - 16.5437i) q^{83} +(3.01905 + 1.09885i) q^{85} +(12.5328 + 0.170496i) q^{87} -5.15931 q^{89} +(5.30732 - 12.7571i) q^{91} +(-7.76044 - 6.69376i) q^{93} +(1.48289 + 0.539726i) q^{95} +(4.99160 + 4.18845i) q^{97} +(12.6545 - 10.0446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 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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