LMFDB - Embedded newform 460.2.o.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	460.19
Dual form			460.2.o.a.339.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587486 - 1.28641i) q^{2} +(3.32368 - 0.975920i) q^{3} +(-1.30972 + 1.51150i) q^{4} +(1.20891 - 1.88110i) q^{5} +(-3.20805 - 3.70229i) q^{6} +(-3.71125 + 0.533598i) q^{7} +(2.71386 + 0.796860i) q^{8} +(7.57066 - 4.86537i) q^{9} +O(q^{10})$	\(q+(-0.587486 - 1.28641i) q^{2} +(3.32368 - 0.975920i) q^{3} +(-1.30972 + 1.51150i) q^{4} +(1.20891 - 1.88110i) q^{5} +(-3.20805 - 3.70229i) q^{6} +(-3.71125 + 0.533598i) q^{7} +(2.71386 + 0.796860i) q^{8} +(7.57066 - 4.86537i) q^{9} +(-3.13009 - 0.450039i) q^{10} +(-2.87799 + 6.30192i) q^{12} +(2.86674 + 4.46073i) q^{14} +(2.18222 - 7.43197i) q^{15} +(-0.569259 - 3.95929i) q^{16} +(-10.7065 - 6.88067i) q^{18} +(1.25995 + 4.29098i) q^{20} +(-11.8143 + 5.39539i) q^{21} +(-4.60851 + 1.32728i) q^{23} +9.79766 q^{24} +(-2.07708 - 4.54816i) q^{25} +(13.6089 - 15.7055i) q^{27} +(4.05418 - 6.30842i) q^{28} +(6.47209 + 7.46919i) q^{29} +(-10.8426 + 1.55893i) q^{30} +(-4.75885 + 3.05833i) q^{32} +(-3.48282 + 7.62631i) q^{35} +(-2.56146 + 17.8153i) q^{36} +(4.77978 - 4.14170i) q^{40} +(5.16058 + 3.31650i) q^{41} +(13.8814 + 12.0283i) q^{42} +(2.12659 + 7.24251i) q^{43} -20.1230i q^{45} +(4.41486 + 5.14869i) q^{46} -3.19902 q^{47} +(-5.75598 - 12.6038i) q^{48} +(6.77223 - 1.98851i) q^{49} +(-4.63056 + 5.34396i) q^{50} +(-28.1989 - 8.27993i) q^{54} +(-10.4970 - 1.50924i) q^{56} +(5.80621 - 12.7138i) q^{58} +(8.37531 + 13.0322i) q^{60} +(-0.771914 + 2.62890i) q^{61} +(-25.5005 + 22.0963i) q^{63} +(6.73003 + 4.32513i) q^{64} +(-12.7127 + 5.80568i) q^{67} +(-14.0219 + 8.90898i) q^{69} +11.8567 q^{70} +(24.4227 - 7.17115i) q^{72} +(-11.3422 - 13.0896i) q^{75} +(-8.13600 - 3.71558i) q^{80} +(18.6891 - 40.9233i) q^{81} +(1.23463 - 8.58704i) q^{82} +(-2.55173 - 3.97056i) q^{83} +(7.31826 - 24.9237i) q^{84} +(8.06753 - 6.99055i) q^{86} +(28.8005 + 18.5090i) q^{87} +(0.555965 + 1.89344i) q^{89} +(-25.8864 + 11.8219i) q^{90} +(4.02968 - 8.70412i) q^{92} +(1.87938 + 4.11526i) q^{94} +(-12.8322 + 14.8091i) q^{96} +(-6.53663 - 7.54367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.587486	−	1.28641i	−0.415415	−	0.909632i
$2$	−0.587486	−	1.28641i	−0.415415	−	0.909632i
$3$	3.32368	−	0.975920i	1.91893	−	0.563448i	0.957248	−	0.289270i	$-0.0934125\pi$
$3$	3.32368	−	0.975920i	1.91893	−	0.563448i	0.961679	−	0.274178i	$-0.0884057\pi$
$4$	−1.30972	+	1.51150i	−0.654861	+	0.755750i
$5$	1.20891	−	1.88110i	0.540641	−	0.841254i
$5$	1.20891	−	1.88110i	0.540641	−	0.841254i
$6$	−3.20805	−	3.70229i	−1.30968	−	1.51145i
$7$	−3.71125	+	0.533598i	−1.40272	+	0.201681i	−0.801784	−	0.597614i	$-0.796115\pi$
$7$	−3.71125	+	0.533598i	−1.40272	+	0.201681i	−0.600938	+	0.799295i	$0.705206\pi$
$8$	2.71386	+	0.796860i	0.959493	+	0.281733i
$9$	7.57066	−	4.86537i	2.52355	−	1.62179i
$10$	−3.13009	−	0.450039i	−0.989821	−	0.142315i
$11$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$11$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$12$	−2.87799	+	6.30192i	−0.830804	+	1.81921i
$13$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$13$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$14$	2.86674	+	4.46073i	0.766167	+	1.19218i
$15$	2.18222	−	7.43197i	0.563448	−	1.91893i
$16$	−0.569259	−	3.95929i	−0.142315	−	0.989821i
$17$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$17$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$18$	−10.7065	−	6.88067i	−2.52355	−	1.62179i
$19$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$19$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$20$	1.25995	+	4.29098i	0.281733	+	0.959493i
$21$	−11.8143	+	5.39539i	−2.57808	+	1.17737i
$22$		0			0
$23$	−4.60851	+	1.32728i	−0.960940	+	0.276757i
$23$	−4.60851	+	1.32728i	−0.960940	+	0.276757i
$24$	9.79766			1.99994
$25$	−2.07708	−	4.54816i	−0.415415	−	0.909632i
$26$		0			0
$27$	13.6089	−	15.7055i	2.61904	−	3.02253i
$28$	4.05418	−	6.30842i	0.766167	−	1.19218i
$29$	6.47209	+	7.46919i	1.20184	+	1.38699i	0.901284	+	0.433230i	$0.142626\pi$
$29$	6.47209	+	7.46919i	1.20184	+	1.38699i	0.300554	+	0.953765i	$0.402828\pi$
$30$	−10.8426	+	1.55893i	−1.97958	+	0.284621i
$31$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$31$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$32$	−4.75885	+	3.05833i	−0.841254	+	0.540641i
$33$		0			0
$34$		0			0
$35$	−3.48282	+	7.62631i	−0.588704	+	1.28908i
$36$	−2.56146	+	17.8153i	−0.426909	+	2.96922i
$37$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$37$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$38$		0			0
$39$		0			0
$40$	4.77978	−	4.14170i	0.755750	−	0.654861i
$41$	5.16058	+	3.31650i	0.805947	+	0.517951i	0.877552	−	0.479482i	$-0.159176\pi$
$41$	5.16058	+	3.31650i	0.805947	+	0.517951i	−0.0716043	+	0.997433i	$0.522812\pi$
$42$	13.8814	+	12.0283i	2.14195	+	1.85601i
$43$	2.12659	+	7.24251i	0.324302	+	1.10447i	0.946792	+	0.321845i	$0.104303\pi$
$43$	2.12659	+	7.24251i	0.324302	+	1.10447i	−0.622490	+	0.782628i	$0.713879\pi$
$44$		0			0
$45$		−	20.1230i		−	2.99975i
$46$	4.41486	+	5.14869i	0.650936	+	0.759133i
$47$	−3.19902			−0.466624			−0.233312	−	0.972402i	$-0.574956\pi$
$47$	−3.19902			−0.466624			−0.233312	+	0.972402i	$0.574956\pi$
$48$	−5.75598	−	12.6038i	−0.830804	−	1.81921i
$49$	6.77223	−	1.98851i	0.967461	−	0.284072i
$50$	−4.63056	+	5.34396i	−0.654861	+	0.755750i
$51$		0			0
$52$		0			0
$53$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$53$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$54$	−28.1989	−	8.27993i	−3.83738	−	1.12676i
$55$		0			0
$56$	−10.4970	−	1.50924i	−1.40272	−	0.201681i
$57$		0			0
$58$	5.80621	−	12.7138i	0.762393	−	1.66941i
$59$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$59$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$60$	8.37531	+	13.0322i	1.08125	+	1.68246i
$61$	−0.771914	+	2.62890i	−0.0988335	+	0.336596i	−0.994034	−	0.109067i	$-0.965214\pi$
$61$	−0.771914	+	2.62890i	−0.0988335	+	0.336596i	0.895201	+	0.445663i	$0.147032\pi$
$62$		0			0
$63$	−25.5005	+	22.0963i	−3.21276	+	2.78387i
$64$	6.73003	+	4.32513i	0.841254	+	0.540641i
$65$		0			0
$66$		0			0
$67$	−12.7127	+	5.80568i	−1.55310	+	0.709277i	−0.992886	−	0.119070i	$-0.962009\pi$
$67$	−12.7127	+	5.80568i	−1.55310	+	0.709277i	−0.560215	+	0.828347i	$0.689281\pi$
$68$		0			0
$69$	−14.0219	+	8.90898i	−1.68804	+	1.07252i
$70$	11.8567			1.41715
$71$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$71$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$72$	24.4227	−	7.17115i	2.87824	−	0.845128i
$73$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$73$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$74$		0			0
$75$	−11.3422	−	13.0896i	−1.30968	−	1.51145i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$79$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$80$	−8.13600	−	3.71558i	−0.909632	−	0.415415i
$81$	18.6891	−	40.9233i	2.07656	−	4.54703i
$82$	1.23463	−	8.58704i	0.136342	−	0.948280i
$83$	−2.55173	−	3.97056i	−0.280088	−	0.435826i	0.672496	−	0.740101i	$-0.265222\pi$
$83$	−2.55173	−	3.97056i	−0.280088	−	0.435826i	−0.952584	+	0.304275i	$0.901586\pi$
$84$	7.31826	−	24.9237i	0.798488	−	2.71940i
$85$		0			0
$86$	8.06753	−	6.99055i	0.869944	−	0.753810i
$87$	28.8005	+	18.5090i	3.08774	+	1.98437i
$88$		0			0
$89$	0.555965	+	1.89344i	0.0589321	+	0.200704i	0.983697	−	0.179835i	$-0.0575564\pi$
$89$	0.555965	+	1.89344i	0.0589321	+	0.200704i	−0.924765	+	0.380540i	$0.875738\pi$
$90$	−25.8864	+	11.8219i	−2.72867	+	1.24614i
$91$		0			0
$92$	4.02968	−	8.70412i	0.420123	−	0.907467i
$93$		0			0
$94$	1.87938	+	4.11526i	0.193843	+	0.424457i
$95$		0			0
$96$	−12.8322	+	14.8091i	−1.30968	+	1.51145i
$97$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$97$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$98$	−6.53663	−	7.54367i	−0.660299	−	0.762026i
$99$		0			0
$100$	9.59493	+	2.81733i	0.959493	+	0.281733i
$101$	−12.4093	+	7.97498i	−1.23477	+	0.793540i	−0.984627	−	0.174668i	$-0.944115\pi$
$101$	−12.4093	+	7.97498i	−1.23477	+	0.793540i	−0.250146	+	0.968208i	$0.580478\pi$
$102$		0			0
$103$	18.3588	+	8.38416i	1.80894	+	0.826116i	0.948660	+	0.316298i	$0.102440\pi$
$103$	18.3588	+	8.38416i	1.80894	+	0.826116i	0.860282	+	0.509818i	$0.170287\pi$
$104$		0			0
$105$	−4.13310	+	28.7464i	−0.403350	+	2.80536i
$106$		0			0
$107$	0.551838	−	1.87939i	0.0533482	−	0.181687i	−0.928509	−	0.371311i	$-0.878909\pi$
$107$	0.551838	−	1.87939i	0.0533482	−	0.181687i	0.981857	+	0.189623i	$0.0607267\pi$
$108$	5.91500	+	41.1397i	0.569171	+	3.95867i
$109$	6.78719	−	5.88113i	0.650095	−	0.563310i	−0.266149	−	0.963932i	$-0.585751\pi$
$109$	6.78719	−	5.88113i	0.650095	−	0.563310i	0.916244	+	0.400622i	$0.131206\pi$
$110$		0			0
$111$		0			0
$112$	4.22533	+	14.3902i	0.399256	+	1.35974i
$113$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$113$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$114$		0			0
$115$	−3.07452	+	10.2736i	−0.286701	+	0.958020i
$116$	−19.7663			−1.83526
$117$		0			0
$118$		0			0
$119$		0			0
$120$	11.8445	−	18.4304i	1.08125	−	1.68246i
$121$	7.20347	+	8.31325i	0.654861	+	0.755750i
$122$	3.83534	−	0.551438i	0.347235	−	0.0499249i
$123$	20.3888	+	5.98668i	1.83839	+	0.539801i
$124$		0			0
$125$	−11.0665	−	1.59113i	−0.989821	−	0.142315i
$126$	43.4061	+	19.8229i	3.86693	+	1.76597i
$127$	4.28177	−	9.37576i	0.379945	−	0.831964i	−0.618971	−	0.785414i	$-0.712450\pi$
$127$	4.28177	−	9.37576i	0.379945	−	0.831964i	0.998916	−	0.0465500i	$-0.0148227\pi$
$128$	1.61011	−	11.1986i	0.142315	−	0.989821i
$129$	14.1362	+	21.9964i	1.24463	+	1.93667i
$130$		0			0
$131$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$131$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$132$		0			0
$133$		0			0
$134$	14.9370	+	12.9430i	1.29036	+	1.11811i
$135$	−13.0917	−	44.5863i	−1.12676	−	3.83738i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	19.6983	+	12.8040i	1.67683	+	1.08995i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−6.96564	−	15.2526i	−0.588704	−	1.28908i
$141$	−10.6325	+	3.12198i	−0.895418	+	0.262918i
$142$		0			0
$143$		0			0
$144$	−23.5730	−	27.2047i	−1.96442	−	2.26706i
$145$	21.8745	−	3.14507i	1.81658	−	0.261184i
$146$		0			0
$147$	20.5681	−	13.2183i	1.69643	−	1.09023i
$148$		0			0
$149$	−8.38060	−	3.82729i	−0.686566	−	0.313544i	0.0414146	−	0.999142i	$-0.486814\pi$
$149$	−8.38060	−	3.82729i	−0.686566	−	0.313544i	−0.727980	+	0.685598i	$0.759541\pi$
$150$	−10.1752	+	22.2807i	−0.830804	+	1.81921i
$151$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$151$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$157$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	16.3951	−	7.38496i	1.29212	−	0.582016i
$162$	−63.6239			−4.99876
$163$	3.48708	+	7.63565i	0.273129	+	0.598070i	0.995639	−	0.0932911i	$-0.0297387\pi$
$163$	3.48708	+	7.63565i	0.273129	+	0.598070i	−0.722510	+	0.691361i	$0.757011\pi$
$164$	−11.7718	+	3.45652i	−0.919224	+	0.269909i
$165$		0			0
$166$	−3.60869	+	5.61523i	−0.280088	+	0.435826i
$167$	−5.61494	−	6.47999i	−0.434497	−	0.501436i	0.495702	−	0.868493i	$-0.334911\pi$
$167$	−5.61494	−	6.47999i	−0.434497	−	0.501436i	−0.930199	+	0.367057i	$0.880366\pi$
$168$	−36.3616	+	5.22801i	−2.80536	+	0.403350i
$169$	−12.4734	−	3.66252i	−0.959493	−	0.281733i
$170$		0			0
$171$		0			0
$172$	−13.7323	−	6.27133i	−1.04708	−	0.478184i
$173$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$173$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$174$	6.89030	−	47.9231i	0.522352	−	3.63304i
$175$	10.1354	+	15.7711i	0.766167	+	1.19218i
$176$		0			0
$177$		0			0
$178$	2.10913	−	1.82757i	0.158086	−	0.136982i
$179$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$179$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$180$	30.4158	+	26.3555i	2.26706	+	1.96442i
$181$	−7.41220	−	25.2436i	−0.550945	−	1.87635i	−0.476615	−	0.879112i	$-0.658137\pi$
$181$	−7.41220	−	25.2436i	−0.550945	−	1.87635i	−0.0743294	−	0.997234i	$-0.523682\pi$
$182$		0			0
$183$			9.49094i			0.701590i
$184$	−13.5645	−	0.0702890i	−0.999987	−	0.00518177i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	4.18982	−	4.83531i	0.305574	−	0.352651i
$189$	−42.1257	+	65.5489i	−3.06420	+	4.76798i
$190$		0			0
$191$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$191$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$192$	26.5894	+	7.80736i	1.91893	+	0.563448i
$193$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$193$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$194$		0			0
$195$		0			0
$196$	−5.86411	+	12.8406i	−0.418865	+	0.917186i
$197$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$197$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$198$		0			0
$199$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$199$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$200$	−2.01264	−	13.9982i	−0.142315	−	0.989821i
$201$	−36.5870	+	31.7028i	−2.58065	+	2.23614i
$202$	17.5494	+	11.2783i	1.23477	+	0.793540i
$203$	−28.0051	−	24.2666i	−1.96557	−	1.70318i
$204$		0			0
$205$	12.4774	−	5.69822i	0.871456	−	0.397981i
$206$		−	28.5425i		−	1.98865i
$207$	−28.4317	+	32.4704i	−1.97614	+	2.25685i
$208$		0			0
$209$		0			0
$210$	39.4079	−	11.5712i	2.71940	−	0.798488i
$211$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$211$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$212$		0			0
$213$		0			0
$214$	−2.74187	+	0.394221i	−0.187430	+	0.0269484i
$215$	16.1947	+	4.75521i	1.10447	+	0.324302i
$216$	49.4478	−	31.7781i	3.36449	−	2.16223i
$217$		0			0
$218$	−11.5529	−	5.27605i	−0.782464	−	0.357339i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.42768	−	16.8849i	−0.162569	−	1.13069i	−0.893768	−	0.448529i	$-0.851948\pi$
$223$	−2.42768	−	16.8849i	−0.162569	−	1.13069i	0.731199	−	0.682164i	$-0.238961\pi$
$224$	16.0294	−	13.8895i	1.07101	−	0.928034i
$225$	−37.8533	−	24.3268i	−2.52355	−	1.62179i
$226$		0			0
$227$	8.25323	+	28.1079i	0.547786	+	1.86559i	0.498663	+	0.866796i	$0.333825\pi$
$227$	8.25323	+	28.1079i	0.547786	+	1.86559i	0.0491237	+	0.998793i	$0.484357\pi$
$228$		0			0
$229$		−	23.8816i		−	1.57814i	−0.614303	−	0.789070i	$-0.710563\pi$
$229$		−	23.8816i		−	1.57814i	0.614303	−	0.789070i	$-0.289437\pi$
$230$	15.0224	−	2.08050i	0.990546	−	0.137184i
$231$		0			0
$232$	11.6124	+	25.4277i	0.762393	+	1.66941i
$233$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$233$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$234$		0			0
$235$	−3.86732	+	6.01767i	−0.252276	+	0.392549i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$239$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$240$	−30.6675	−	4.40933i	−1.97958	−	0.284621i
$241$	−26.9473	−	12.3064i	−1.73583	−	0.792725i	−0.992277	−	0.124043i	$-0.960414\pi$
$241$	−26.9473	−	12.3064i	−1.73583	−	0.792725i	−0.743549	−	0.668682i	$-0.766859\pi$
$242$	6.46234	−	14.1506i	0.415415	−	0.909632i
$243$	13.3060	−	92.5453i	0.853581	−	5.93679i
$244$	−2.96258	−	4.60987i	−0.189660	−	0.295117i
$245$	4.44643	−	15.1432i	0.284072	−	0.967461i
$246$	−4.27675	−	29.7455i	−0.272676	−	1.89650i
$247$		0			0
$248$		0			0
$249$	−12.3561	−	10.7066i	−0.783034	−	0.678503i
$250$	4.45458	+	15.1709i	0.281733	+	0.959493i
$251$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$251$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$252$		−	67.4840i		−	4.25109i
$253$		0			0
$254$	−14.5766			−0.914616
$255$		0			0
$256$	−15.3519	+	4.50772i	−0.959493	+	0.281733i
$257$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$257$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$258$	19.9916	−	31.1076i	1.24463	−	1.93667i
$259$		0			0
$260$		0			0
$261$	85.3384	+	25.0576i	5.28231	+	1.55103i
$262$		0			0
$263$	−30.0850	−	4.32557i	−1.85512	−	0.266726i	−0.877883	−	0.478875i	$-0.841045\pi$
$263$	−30.0850	−	4.32557i	−1.85512	−	0.266726i	−0.977237	+	0.212149i	$0.931954\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.69570	+	5.75062i	0.226173	+	0.351932i
$268$	7.87478	−	26.8190i	0.481029	−	1.63823i
$269$	4.17375	+	29.0291i	0.254478	+	1.76993i	0.570614	+	0.821219i	$0.306705\pi$
$269$	4.17375	+	29.0291i	0.254478	+	1.76993i	−0.316136	+	0.948714i	$0.602386\pi$
$270$	−49.6653	+	43.0352i	−3.02253	+	2.61904i
$271$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$271$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	4.89883	−	32.8623i	0.294875	−	1.97808i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	−15.5290	+	17.9214i	−0.928034	+	1.07101i
$281$	−15.9864	+	24.8753i	−0.953669	+	1.48394i	−0.0803640	+	0.996766i	$0.525608\pi$
$281$	−15.9864	+	24.8753i	−0.953669	+	1.48394i	−0.873305	+	0.487173i	$0.838028\pi$
$282$	10.2626	+	11.8437i	0.611129	+	0.705281i
$283$	20.2383	−	2.90983i	1.20304	−	0.172971i	0.488500	−	0.872564i	$-0.337544\pi$
$283$	20.2383	−	2.90983i	1.20304	−	0.172971i	0.714542	+	0.699593i	$0.246635\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.9219	−	9.55471i	−1.23498	−	0.563997i
$288$	−21.1477	+	46.3071i	−1.24614	+	2.72867i
$289$	2.41935	−	16.8270i	0.142315	−	0.989821i
$290$	−16.8968	−	26.2919i	−0.992215	−	1.54392i
$291$		0			0
$292$		0			0
$293$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$293$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$294$	−29.0877	−	18.6935i	−1.69643	−	1.09023i
$295$		0			0
$296$		0			0
$297$		0			0
$298$			13.0294i			0.754773i
$299$		0			0
$300$	34.6399			1.99994
$301$	−11.7569	−	25.7441i	−0.677657	−	1.48386i
$302$		0			0
$303$	−33.4616	+	38.6168i	−1.92232	+	2.21848i
$304$		0			0
$305$	4.01205	+	4.63015i	0.229729	+	0.265121i
$306$		0			0
$307$	−32.4570	−	9.53022i	−1.85242	−	0.543919i	−0.999770	−	0.0214301i	$-0.993178\pi$
$307$	−32.4570	−	9.53022i	−1.85242	−	0.543919i	−0.852646	−	0.522488i	$-0.825004\pi$
$308$		0			0
$309$	69.2009	+	9.94958i	3.93670	+	0.566012i
$310$		0			0
$311$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$311$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$312$		0			0
$313$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$313$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$314$		0			0
$315$	10.7376	+	74.6814i	0.604993	+	4.20782i
$316$		0			0
$317$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$317$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$318$		0			0
$319$		0			0
$320$	16.2720	−	7.43117i	0.909632	−	0.415415i
$321$		−	6.78503i		−	0.378703i
$322$	−19.1320	−	16.7523i	−1.06618	−	0.933571i
$323$		0			0
$324$	37.3781	+	81.8466i	2.07656	+	4.54703i
$325$		0			0
$326$	7.77399	−	8.97166i	0.430561	−	0.496894i
$327$	16.8189	−	26.1707i	0.930088	−	1.44725i
$328$	11.3623	+	13.1128i	0.627377	+	0.724032i
$329$	11.8724	−	1.70699i	0.654544	−	0.0941093i
$330$		0			0
$331$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$331$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$332$	9.34356	+	1.34340i	0.512794	+	0.0737287i
$333$		0			0
$334$	−5.03725	+	11.0300i	−0.275626	+	0.603537i
$335$	−4.44740	+	30.9324i	−0.242988	+	1.69002i
$336$	28.0873	+	43.7047i	1.53229	+	2.38429i
$337$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$337$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$338$	2.61643	+	18.1976i	0.142315	+	0.989821i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.198268	+	0.0905459i	−0.0107055	+	0.00488902i
$344$			21.3497i			1.15110i
$345$	−0.192488	+	37.1467i	−0.0103632	+	1.99991i
$346$		0			0
$347$	−12.9136	−	28.2768i	−0.693238	−	1.51798i	−0.847982	−	0.530026i	$-0.822182\pi$
$347$	−12.9136	−	28.2768i	−0.693238	−	1.51798i	0.154743	−	0.987955i	$-0.450545\pi$
$348$	−65.6969	+	19.2903i	−3.52172	+	1.03407i
$349$	−19.8160	+	22.8689i	−1.06073	+	1.22414i	−0.0870514	+	0.996204i	$0.527744\pi$
$349$	−19.8160	+	22.8689i	−1.06073	+	1.22414i	−0.973675	+	0.227940i	$0.926801\pi$
$350$	14.3337	−	22.3036i	0.766167	−	1.19218i
$351$		0			0
$352$		0			0
$353$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$353$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$354$		0			0
$355$		0			0
$356$	−3.59009	−	1.63954i	−0.190275	−	0.0868955i
$357$		0			0
$358$		0			0
$359$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$359$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$360$	16.0352	−	54.6108i	0.845128	−	2.87824i
$361$	2.70398	+	18.8066i	0.142315	+	0.989821i
$362$	−28.1192	+	24.3654i	−1.47791	+	1.28062i
$363$	32.0551	+	20.6005i	1.68246	+	1.08125i
$364$		0			0
$365$		0			0
$366$	12.2093	−	5.57579i	0.638189	−	0.291451i
$367$		−	13.7918i		−	0.719926i	−0.932967	−	0.359963i	$-0.882789\pi$
$367$		−	13.7918i		−	0.719926i	0.932967	−	0.359963i	$-0.117211\pi$
$368$	7.87851	+	17.4908i	0.410696	+	0.911772i
$369$	55.2050			2.87386
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$373$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$374$		0			0
$375$	−38.3344	+	5.51166i	−1.97958	+	0.284621i
$376$	−8.68167	−	2.54917i	−0.447723	−	0.131463i
$377$		0			0
$378$	109.071	+	15.6821i	5.61002	+	0.806599i
$379$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$379$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$380$		0			0
$381$	5.08122	−	35.3407i	0.260319	−	1.81056i
$382$		0			0
$383$	8.63423	−	29.4055i	0.441189	−	1.50255i	−0.376241	−	0.926522i	$-0.622783\pi$
$383$	8.63423	−	29.4055i	0.441189	−	1.50255i	0.817429	−	0.576029i	$-0.195398\pi$
$384$	−5.57741	−	38.7917i	−0.284621	−	1.97958i
$385$		0			0
$386$		0			0
$387$	51.3372	+	44.4839i	2.60962	+	2.26124i
$388$		0			0
$389$	−31.6877	+	14.4713i	−1.60663	+	0.733723i	−0.998205	−	0.0598891i	$-0.980925\pi$
$389$	−31.6877	+	14.4713i	−1.60663	+	0.733723i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	19.9634			1.00830
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$397$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$398$		0			0
$399$		0			0
$400$	−16.8251	+	10.8128i	−0.841254	+	0.540641i
$401$	−38.9980	−	5.60707i	−1.94747	−	0.280004i	−0.948180	−	0.317732i	$-0.897079\pi$
$401$	−38.9980	−	5.60707i	−1.94747	−	0.280004i	−0.999288	+	0.0377288i	$0.987988\pi$
$402$	62.2772	+	28.4411i	3.10611	+	1.41851i
$403$		0			0
$404$	4.19857	−	29.2017i	0.208887	−	1.45284i
$405$	−54.3875	−	84.6286i	−2.70254	−	4.20523i
$406$	−14.7643	+	50.2825i	−0.732738	+	2.49548i
$407$		0			0
$408$		0			0
$409$	−21.1368	−	13.5838i	−1.04515	−	0.671676i	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−21.1368	−	13.5838i	−1.04515	−	0.671676i	−0.946255	+	0.323422i	$0.895167\pi$
$410$	−14.6605	−	12.7034i	−0.724032	−	0.627377i
$411$		0			0
$412$	−36.7175	+	16.7683i	−1.80894	+	0.826116i
$413$		0			0
$414$	58.4737	+	17.4990i	2.87382	+	0.860031i
$415$	−10.5538			−0.518068
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$419$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$420$	−38.0369	−	43.8969i	−1.85601	−	2.14195i
$421$	2.16821	−	0.311742i	0.105672	−	0.0151934i	−0.0892758	−	0.996007i	$-0.528455\pi$
$421$	2.16821	−	0.311742i	0.105672	−	0.0151934i	0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$	−24.2187	+	15.5644i	−1.17755	+	0.756766i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.46199	−	10.1684i	0.0707509	−	0.492083i
$428$	2.11794	+	3.29557i	0.102374	+	0.159298i
$429$		0			0
$430$	−3.39702	−	23.6268i	−0.163819	−	1.13938i
$431$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$431$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$432$	−69.9297	−	44.9411i	−3.36449	−	2.16223i
$433$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$433$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$434$		0			0
$435$	69.6344	−	31.8010i	3.33871	−	1.52474i
$436$			17.9615i			0.860198i
$437$		0			0
$438$		0			0
$439$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$439$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$440$		0			0
$441$	41.5954	−	48.0037i	1.98073	−	2.28589i
$442$		0			0
$443$	22.2829	+	25.7158i	1.05869	+	1.22180i	0.974274	+	0.225367i	$0.0723580\pi$
$443$	22.2829	+	25.7158i	1.05869	+	1.22180i	0.0844190	+	0.996430i	$0.473097\pi$
$444$		0			0
$445$	4.23387	+	1.24317i	0.200704	+	0.0589321i
$446$	−20.2947	+	13.0426i	−0.960981	+	0.617585i
$447$	−31.5896	−	4.54189i	−1.49413	−	0.214824i
$448$	−27.2847	−	12.4605i	−1.28908	−	0.588704i
$449$	−2.23703	+	4.89841i	−0.105572	+	0.231170i	−0.955045	−	0.296462i	$-0.904193\pi$
$449$	−2.23703	+	4.89841i	−0.105572	+	0.231170i	0.849473	+	0.527633i	$0.176920\pi$
$450$	−9.05611	+	62.9867i	−0.426909	+	2.96922i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	31.3098	−	27.1301i	1.46944	−	1.27328i
$455$		0			0
$456$		0			0
$457$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$457$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$458$	−30.7216	+	14.0301i	−1.43553	+	0.655583i
$459$		0			0
$460$	−11.5018	−	18.1027i	−0.536274	−	0.844044i
$461$	−9.31143			−0.433677			−0.216838	−	0.976208i	$-0.569574\pi$
$461$	−9.31143			−0.433677			−0.216838	+	0.976208i	$0.569574\pi$
$462$		0			0
$463$	40.7809	−	11.9744i	1.89525	−	0.556495i	0.903449	−	0.428696i	$-0.141027\pi$
$463$	40.7809	−	11.9744i	1.89525	−	0.556495i	0.991800	−	0.127799i	$-0.0407913\pi$
$464$	25.8884	−	29.8768i	1.20184	−	1.38699i
$465$		0			0
$466$		0			0
$467$	28.1708	−	4.05035i	1.30359	−	0.187428i	0.544691	−	0.838637i	$-0.316647\pi$
$467$	28.1708	−	4.05035i	1.30359	−	0.187428i	0.758899	+	0.651209i	$0.225738\pi$
$468$		0			0
$469$	44.0821	−	28.3298i	2.03552	−	1.30815i
$470$	10.0132	+	1.43968i	0.461875	+	0.0664076i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$479$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$480$	12.3445	+	42.0416i	0.563448	+	1.91893i
$481$		0			0
$482$			41.8952i			1.90827i
$483$	47.2849	−	40.5455i	2.15154	−	1.84489i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	−126.869	+	37.2520i	−5.75488	+	1.68979i
$487$	−10.7898	+	12.4521i	−0.488934	+	0.564259i	−0.945580	−	0.325389i	$-0.894505\pi$
$487$	−10.7898	+	12.4521i	−0.488934	+	0.564259i	0.456647	+	0.889648i	$0.349050\pi$
$488$	−4.18973	+	6.51934i	−0.189660	+	0.295117i
$489$	19.0417	+	21.9753i	0.861096	+	0.993758i
$490$	−22.0926	+	3.17644i	−0.998042	+	0.143497i
$491$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$491$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$492$	−35.7524	+	22.9767i	−1.61184	+	1.03587i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−6.51410	+	22.1850i	−0.291904	+	0.994134i
$499$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$499$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$500$	16.8991	−	14.6431i	0.755750	−	0.654861i
$501$	−24.9862	−	16.0577i	−1.11630	−	0.717403i
$502$		0			0
$503$	10.1249	+	34.4821i	0.451445	+	1.53748i	0.799887	+	0.600151i	$0.204893\pi$
$503$	10.1249	+	34.4821i	0.451445	+	1.53748i	−0.348441	+	0.937331i	$0.613289\pi$
$504$	−86.8123	+	39.6458i	−3.86693	+	1.76597i
$505$			32.9842i			1.46778i
$506$		0			0
$507$	−45.0319			−1.99994
$508$	8.56353	+	18.7515i	0.379945	+	0.831964i
$509$	28.6591	−	8.41507i	1.27029	−	0.372991i	0.423976	−	0.905673i	$-0.360634\pi$
$509$	28.6591	−	8.41507i	1.27029	−	0.372991i	0.846315	+	0.532682i	$0.178816\pi$
$510$		0			0
$511$		0			0
$512$	14.8178	+	17.1007i	0.654861	+	0.755750i
$513$		0			0
$514$		0			0
$515$	37.9655	−	24.3990i	1.67296	−	1.07515i
$516$	−51.7621	−	7.44226i	−2.27870	−	0.327627i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.6370	−	36.2263i	0.466016	−	1.58710i	−0.306345	−	0.951921i	$-0.599106\pi$
$521$	10.6370	−	36.2263i	0.466016	−	1.58710i	0.772361	−	0.635184i	$-0.219076\pi$
$522$	−17.9006	−	124.501i	−0.783488	−	5.44928i
$523$	31.5473	−	27.3359i	1.37947	−	1.19531i	0.422061	−	0.906567i	$-0.361307\pi$
$523$	31.5473	−	27.3359i	1.37947	−	1.19531i	0.957405	−	0.288747i	$-0.0932387\pi$
$524$		0			0
$525$	49.0782	+	42.5265i	2.14195	+	1.85601i
$526$	12.1100	+	41.2430i	0.528022	+	1.79828i
$527$		0			0
$528$		0			0
$529$	19.4767	−	12.2336i	0.846811	−	0.531894i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	5.22650	−	8.13260i	0.226173	−	0.351932i
$535$	−2.86819	−	3.31007i	−0.124003	−	0.143107i
$536$	−39.1267	+	5.62557i	−1.69002	+	0.242988i
$537$		0			0
$538$	34.8914	−	22.4233i	1.50427	−	0.966738i
$539$		0			0
$540$	84.5387	+	38.6075i	3.63797	+	1.66140i
$541$	18.2867	−	40.0424i	0.786208	−	1.72156i	0.0990098	−	0.995086i	$-0.468432\pi$
$541$	18.2867	−	40.0424i	0.786208	−	1.72156i	0.687199	−	0.726470i	$-0.258840\pi$
$542$		0			0
$543$	−49.2716	−	76.6681i	−2.11445	−	3.29014i
$544$		0			0
$545$	−2.85790	−	19.8771i	−0.122419	−	0.851443i
$546$		0			0
$547$	−31.5898	−	20.3015i	−1.35068	−	0.868030i	−0.352969	−	0.935635i	$-0.614828\pi$
$547$	−31.5898	−	20.3015i	−1.35068	−	0.868030i	−0.997712	+	0.0676046i	$0.978464\pi$
$548$		0			0
$549$	6.94665	+	23.6581i	0.296476	+	1.00970i
$550$		0			0
$551$		0			0
$552$	−45.1526	+	13.0042i	−1.92182	+	0.553497i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$557$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$558$		0			0
$559$		0			0
$560$	32.1774	+	9.44813i	1.35974	+	0.399256i
$561$		0			0
$562$	41.3918	+	5.95124i	1.74601	+	0.251038i
$563$	−7.41387	−	3.38580i	−0.312457	−	0.142694i	0.253014	−	0.967463i	$-0.418578\pi$
$563$	−7.41387	−	3.38580i	−0.312457	−	0.142694i	−0.565471	+	0.824768i	$0.691306\pi$
$564$	9.20674	−	20.1599i	0.387674	−	0.848887i
$565$		0			0
$566$	−15.6329	−	24.3253i	−0.657102	−	1.02247i
$567$	−47.5232	+	161.849i	−1.99579	+	6.79703i
$568$		0			0
$569$	−15.0353	+	13.0281i	−0.630311	+	0.546168i	−0.910360	−	0.413818i	$-0.864195\pi$
$569$	−15.0353	+	13.0281i	−0.630311	+	0.546168i	0.280048	+	0.959986i	$0.409649\pi$
$570$		0			0
$571$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$571$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$572$		0			0
$573$		0			0
$574$			32.5275i			1.35767i
$575$	15.6089	+	18.2034i	0.650936	+	0.759133i
$576$	71.9941			2.99975
$577$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$577$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$578$	−23.0678	+	6.77331i	−0.959493	+	0.281733i
$579$		0			0
$580$	−23.8957	+	37.1824i	−0.992215	+	1.54392i
$581$	11.5888	+	13.3742i	0.480784	+	0.554854i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.5850	−	38.5058i	0.725810	−	1.58930i	−0.0797680	−	0.996813i	$-0.525418\pi$
$587$	17.5850	−	38.5058i	0.725810	−	1.58930i	0.805578	−	0.592489i	$-0.201855\pi$
$588$	−6.95901	+	48.4009i	−0.286985	+	1.99602i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$593$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$594$		0			0
$595$		0			0
$596$	16.7612	−	7.65459i	0.686566	−	0.313544i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−20.3505	−	44.5613i	−0.830804	−	1.81921i
$601$	−23.9685	+	7.03778i	−0.977695	+	0.287077i	−0.731272	−	0.682085i	$-0.761073\pi$
$601$	−23.9685	+	7.03778i	−0.977695	+	0.287077i	−0.246422	+	0.969163i	$0.579255\pi$
$602$	−26.2105	+	30.2485i	−1.06826	+	1.23284i
$603$	−67.9965	+	105.805i	−2.76903	+	4.30870i
$604$		0			0
$605$	24.3464	−	3.50048i	0.989821	−	0.142315i
$606$	69.3354	+	20.3587i	2.81656	+	0.827016i
$607$	35.7627	−	22.9833i	1.45156	−	0.932862i	0.452405	−	0.891812i	$-0.350566\pi$
$607$	35.7627	−	22.9833i	1.45156	−	0.932862i	0.999157	−	0.0410500i	$-0.0130703\pi$
$608$		0			0
$609$	−116.762	−	53.3235i	−4.73145	−	2.16078i
$610$	3.59927	−	7.88130i	0.145730	−	0.319104i
$611$		0			0
$612$		0			0
$613$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$613$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$614$	6.80818	+	47.3520i	0.274756	+	1.91097i
$615$	35.9097	−	31.1159i	1.44802	−	1.25472i
$616$		0			0
$617$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$617$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$618$	−27.8552	−	94.8662i	−1.12050	−	3.81608i
$619$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$619$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$620$		0			0
$621$	−41.8712	+	90.4419i	−1.68023	+	3.62931i
$622$		0			0
$623$	−3.07366	−	6.73038i	−0.123144	−	0.269647i
$624$		0			0
$625$	−16.3715	+	18.8937i	−0.654861	+	0.755750i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	89.7630	−	57.6872i	3.57624	−	2.29831i
$631$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$631$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.4605	−	19.3889i	−0.494479	−	0.769424i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−19.1191	−	16.5668i	−0.755750	−	0.654861i
$641$	13.4871	+	45.9327i	0.532707	+	1.81423i	0.579028	+	0.815308i	$0.303432\pi$
$641$	13.4871	+	45.9327i	0.532707	+	1.81423i	−0.0463207	+	0.998927i	$0.514750\pi$
$642$	−8.72835	+	3.98610i	−0.344481	+	0.157319i
$643$			49.3657i			1.94679i	0.229128	+	0.973396i	$0.426413\pi$
$643$			49.3657i			1.94679i	−0.229128	+	0.973396i	$0.573587\pi$
$644$	−10.3107	+	34.4534i	−0.406297	+	1.35766i
$645$	58.4668			2.30213
$646$		0			0
$647$	−29.7479	+	8.73478i	−1.16951	+	0.343400i	−0.808122	−	0.589015i	$-0.799516\pi$
$647$	−29.7479	+	8.73478i	−1.16951	+	0.343400i	−0.361390	+	0.932415i	$0.617698\pi$
$648$	83.3295	−	96.1674i	3.27349	−	3.77781i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−16.1084	−	4.72985i	−0.630853	−	0.185235i
$653$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$653$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$654$	−43.5473	−	6.26115i	−1.70283	−	0.244830i
$655$		0			0
$656$	10.1933	−	22.3202i	0.397981	−	0.871456i
$657$		0			0
$658$	−9.17073	−	14.2699i	−0.357512	−	0.556300i
$659$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$659$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$660$		0			0
$661$	12.5147	−	10.8440i	0.486765	−	0.421784i	−0.376591	−	0.926380i	$-0.622904\pi$
$661$	12.5147	−	10.8440i	0.486765	−	0.421784i	0.863356	+	0.504596i	$0.168358\pi$
$662$		0			0
$663$		0			0
$664$	−3.76104	−	12.8089i	−0.145956	−	0.497082i
$665$		0			0
$666$		0			0
$667$	−39.7404	−	25.8315i	−1.53875	−	1.00020i
$668$	17.1485			0.663495
$669$	−24.5471	−	53.7506i	−0.949045	−	2.07812i
$670$	42.4046	−	12.4511i	1.63823	−	0.481029i
$671$		0			0
$672$	39.7214	−	61.8077i	1.53229	−	2.38429i
$673$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$673$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$674$		0			0
$675$	−99.6980	−	29.2740i	−3.83738	−	1.12676i
$676$	21.8726	−	14.0567i	0.841254	−	0.540641i
$677$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$677$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	54.8622	+	85.3672i	2.10232	+	3.27128i
$682$		0			0
$683$	4.89705	+	34.0597i	0.187380	+	1.30326i	0.838757	+	0.544505i	$0.183283\pi$
$683$	4.89705	+	34.0597i	0.187380	+	1.30326i	−0.651377	+	0.758754i	$0.725808\pi$
$684$		0			0
$685$		0			0
$686$	0.232959	+	0.201860i	0.00889442	+	0.00770706i
$687$	−23.3065	−	79.3748i	−0.889200	−	3.02834i
$688$	27.4646	−	12.5427i	1.04708	−	0.478184i
$689$		0			0
$690$	47.8991	−	21.5755i	1.82349	−	0.821366i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−28.7892	+	33.2245i	−1.09282	+	1.26118i
$695$		0			0
$696$	63.4113	+	73.1806i	2.40360	+	2.77390i
$697$		0			0
$698$	41.0605	+	12.0564i	1.55416	+	0.456343i
$699$		0			0
$700$	−37.1125	−	5.33598i	−1.40272	−	0.201681i
$701$	46.3177	+	21.1526i	1.74939	+	0.798921i	0.988718	+	0.149789i	$0.0478595\pi$
$701$	46.3177	+	21.1526i	1.74939	+	0.798921i	0.760676	+	0.649132i	$0.224868\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−6.98097	+	23.7750i	−0.262918	+	0.895418i
$706$		0			0
$707$	41.7987	−	36.2188i	1.57200	−	1.36215i
$708$		0			0
$709$	20.2789	+	17.5718i	0.761590	+	0.659921i	0.946452	−	0.322843i	$-0.104639\pi$
$709$	20.2789	+	17.5718i	0.761590	+	0.659921i	−0.184863	+	0.982764i	$0.559184\pi$
$710$		0			0
$711$		0			0
$712$			5.58155i			0.209178i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$719$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$720$	−79.6725	+	11.4552i	−2.96922	+	0.426909i
$721$	−72.6078	−	21.3196i	−2.70406	−	0.793982i
$722$	22.6045	−	14.5270i	0.841254	−	0.540641i
$723$	−101.574	−	14.6041i	−3.77758	−	0.543134i
$724$	47.8637	+	21.8586i	1.77884	+	0.812369i
$725$	20.5281	−	44.9502i	0.762393	−	1.66941i
$726$	7.66894	−	53.3386i	0.284621	−	1.97958i
$727$	25.6904	+	39.9751i	0.952805	+	1.48259i	0.874129	+	0.485693i	$0.161433\pi$
$727$	25.6904	+	39.9751i	0.952805	+	1.48259i	0.0786754	+	0.996900i	$0.474931\pi$
$728$		0			0
$729$	−26.8842	−	186.984i	−0.995711	−	6.92532i
$730$		0			0
$731$		0			0
$732$	−14.3455	−	12.4305i	−0.530227	−	0.459444i
$733$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$733$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$734$	−17.7420	+	8.10248i	−0.654867	+	0.299068i
$735$		−	54.6704i		−	2.01655i
$736$	17.8719	−	20.4106i	0.658768	−	0.752346i
$737$		0			0
$738$	−32.4321	−	71.0165i	−1.19384	−	2.61415i
$739$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$739$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.1188	−	3.61154i	0.921520	−	0.132495i	0.334804	−	0.942288i	$-0.391330\pi$
$743$	25.1188	−	3.61154i	0.921520	−	0.132495i	0.586715	+	0.809793i	$0.300421\pi$
$744$		0			0
$745$	−17.3309	+	11.1379i	−0.634956	+	0.408061i
$746$		0			0
$747$	−38.6365	−	17.6447i	−1.41364	−	0.645586i
$748$		0			0
$749$	−1.04517	+	7.26934i	−0.0381898	+	0.265616i
$750$	29.6112	+	46.0759i	1.08125	+	1.68246i
$751$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$751$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$752$	1.82107	+	12.6658i	0.0664076	+	0.461875i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−43.9041	−	149.524i	−1.59678	−	5.43813i
$757$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$757$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	12.2280	+	26.7757i	0.443266	+	0.970617i	0.990987	+	0.133956i	$0.0427681\pi$
$761$	12.2280	+	26.7757i	0.443266	+	0.970617i	−0.547721	+	0.836661i	$0.684505\pi$
$762$	−48.4479	+	14.2256i	−1.75508	+	0.515338i
$763$	−22.0508	+	25.4480i	−0.798293	+	0.921279i
$764$		0			0
$765$		0			0
$766$	−42.9001	+	6.16811i	−1.55004	+	0.222863i
$767$		0			0
$768$	−46.6256	+	29.9644i	−1.68246	+	1.08125i
$769$	45.2586	+	6.50720i	1.63207	+	0.234656i	0.896580	−	0.442883i	$-0.146044\pi$
$769$	45.2586	+	6.50720i	1.63207	+	0.234656i	0.735487	+	0.677538i	$0.236953\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$773$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$774$	27.0649	−	92.1745i	0.972827	−	3.31315i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	37.2321	+	32.2618i	1.33484	+	1.15664i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	205.386			7.33989
$784$	−11.7282	−	25.6812i	−0.418865	−	0.917186i
$785$		0			0
$786$		0			0
$787$	9.54535	−	14.8529i	0.340255	−	0.529447i	−0.628389	−	0.777899i	$-0.716285\pi$
$787$	9.54535	−	14.8529i	0.340255	−	0.529447i	0.968644	+	0.248452i	$0.0799218\pi$
$788$		0			0
$789$	−104.214	+	14.9837i	−3.71013	+	0.533436i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$797$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$798$		0			0
$799$		0			0
$800$	23.7942	+	15.2916i	0.841254	+	0.540641i
$801$	13.4213	+	11.6296i	0.474219	+	0.410913i
$802$	15.6978	+	53.4617i	0.554307	+	1.88780i
$803$		0			0
$804$		−	96.8230i		−	3.41468i
$805$	5.92835	−	39.7686i	0.208947	−	1.40166i
$806$		0			0
$807$	42.2022	+	92.4100i	1.48559	+	3.25299i
$808$	−40.0320	+	11.7545i	−1.40832	+	0.413521i
$809$	−25.3460	+	29.2508i	−0.891118	+	1.02840i	0.108294	+	0.994119i	$0.465461\pi$
$809$	−25.3460	+	29.2508i	−0.891118	+	1.02840i	−0.999412	+	0.0342857i	$0.989084\pi$
$810$	−76.9155	+	119.683i	−2.70254	+	4.20523i
$811$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$811$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$812$	73.3578	−	10.5473i	2.57436	−	0.370136i
$813$		0			0
$814$		0			0
$815$	18.5790	+	2.67125i	0.650793	+	0.0935699i
$816$		0			0
$817$		0			0
$818$	−5.05683	+	35.1710i	−0.176808	+	1.22972i
$819$		0			0
$820$	−7.72901	+	26.3226i	−0.269909	+	0.919224i
$821$	3.33806	+	23.2167i	0.116499	+	0.810268i	0.961362	+	0.275286i	$0.0887726\pi$
$821$	3.33806	+	23.2167i	0.116499	+	0.810268i	−0.844863	+	0.534982i	$0.820318\pi$
$822$		0			0
$823$	6.56276	+	4.21763i	0.228764	+	0.147017i	0.650002	−	0.759933i	$-0.274768\pi$
$823$	6.56276	+	4.21763i	0.228764	+	0.147017i	−0.421238	+	0.906950i	$0.638404\pi$
$824$	43.1420	+	37.3828i	1.50292	+	1.30229i
$825$		0			0
$826$		0			0
$827$		−	47.4342i		−	1.64945i	−0.565536	−	0.824724i	$-0.691331\pi$
$827$		−	47.4342i		−	1.64945i	0.565536	−	0.824724i	$-0.308669\pi$
$828$	−11.8414	−	85.5018i	−0.411518	−	2.97139i
$829$	5.31022			0.184431			0.0922157	−	0.995739i	$-0.470605\pi$
$829$	5.31022			0.184431			0.0922157	+	0.995739i	$0.470605\pi$
$830$	6.20023	+	13.5766i	0.215213	+	0.471251i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.9775	+	2.72855i	−0.656742	+	0.0944252i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$839$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$840$	−34.1235	+	74.7200i	−1.17737	+	2.57808i
$841$	−9.77373	+	67.9778i	−0.337025	+	2.34406i
$842$	−1.67482	−	2.60608i	−0.0577182	−	0.0898113i
$843$	−28.8573	+	98.2791i	−0.993900	+	3.38491i
$844$		0			0
$845$	−21.9688	+	19.0361i	−0.755750	+	0.654861i
$846$	34.2503	+	22.0114i	1.17755	+	0.756766i
$847$	−31.1698	−	27.0088i	−1.07101	−	0.928034i
$848$		0			0
$849$	64.4258	−	29.4223i	2.21109	−	1.00977i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$853$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$854$	−13.9397	+	4.09306i	−0.477006	+	0.140062i
$855$		0			0
$856$	2.99522	−	4.66065i	0.102374	−	0.159298i
$857$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$857$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$858$		0			0
$859$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$859$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$860$	−28.3981	+	18.2504i	−0.968367	+	0.622332i
$861$	−78.8623	−	11.3387i	−2.68762	−	0.386422i
$862$		0			0
$863$	−7.32878	+	16.0478i	−0.249475	+	0.546273i	−0.992393	−	0.123108i	$-0.960714\pi$
$863$	−7.32878	+	16.0478i	−0.249475	+	0.546273i	0.742919	+	0.669382i	$0.233441\pi$
$864$	−16.7302	+	116.361i	−0.569171	+	3.95867i
$865$		0			0
$866$		0			0
$867$	−8.38062	−	58.2885i	−0.284621	−	1.97958i
$868$		0			0
$869$		0			0
$870$	−81.8184	−	70.8960i	−2.77390	−	2.40360i
$871$		0			0
$872$	23.1059	−	10.5521i	0.782464	−	0.357339i
$873$		0			0
$874$		0			0
$875$	41.9198			1.41715
$876$		0			0
$877$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$877$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	58.5614	−	8.41985i	1.97298	−	0.283672i	0.974827	−	0.222961i	$-0.0715724\pi$
$881$	58.5614	−	8.41985i	1.97298	−	0.283672i	0.998155	−	0.0607108i	$-0.0193367\pi$
$882$	−86.1893	−	25.3075i	−2.90214	−	0.852147i
$883$	−2.33563	+	1.50102i	−0.0786003	+	0.0505134i	−0.579351	−	0.815078i	$-0.696694\pi$
$883$	−2.33563	+	1.50102i	−0.0786003	+	0.0505134i	0.500750	+	0.865592i	$0.333057\pi$
$884$		0			0
$885$		0			0
$886$	19.9903	−	43.7727i	0.671589	−	1.47057i
$887$	0.590836	−	4.10936i	0.0198383	−	0.137979i	−0.977495	−	0.210958i	$-0.932342\pi$
$887$	0.590836	−	4.10936i	0.0198383	−	0.137979i	0.997333	+	0.0729794i	$0.0232507\pi$
$888$		0			0
$889$	−10.8878	+	37.0806i	−0.365166	+	1.24364i
$890$	−0.888097	−	6.17685i	−0.0297691	−	0.207048i
$891$		0			0
$892$	28.7010	+	18.4450i	0.960981	+	0.617585i
$893$		0			0
$894$	12.7157	+	43.3055i	0.425275	+	1.44835i
$895$		0			0
$896$			42.4198i			1.41715i
$897$		0			0
$898$	7.61561			0.254136
$899$		0			0
$900$	86.3472	−	25.3538i	2.87824	−	0.845128i
$901$		0			0
$902$		0			0
$903$	−64.2004	−	74.0912i	−2.13645	−	2.46560i
$904$		0			0
$905$	−56.4465	−	16.5742i	−1.87635	−	0.550945i
$906$		0			0
$907$	28.5254	+	4.10133i	0.947170	+	0.136183i	0.598554	−	0.801083i	$-0.295742\pi$
$907$	28.5254	+	4.10133i	0.947170	+	0.136183i	0.348617	+	0.937265i	$0.386651\pi$
$908$	−53.2945	−	24.3388i	−1.76864	−	0.807712i
$909$	−55.1455	+	120.752i	−1.82906	+	4.00508i
$910$		0			0
$911$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$911$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	17.8534	+	11.4737i	0.590215	+	0.379308i
$916$	36.0970	+	31.2782i	1.19268	+	1.03346i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−16.5304	+	25.4312i	−0.544993	+	0.838441i
$921$	−117.177			−3.86112
$922$	5.47033	+	11.9784i	0.180156	+	0.394486i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−39.3622	−	45.4264i	−1.29352	−	1.49280i
$927$	179.780	−	25.8484i	5.90475	−	0.848974i
$928$	−53.6429	−	15.7510i	−1.76092	−	0.517052i
$929$	−3.10348	+	1.99449i	−0.101822	+	0.0654370i	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−3.10348	+	1.99449i	−0.101822	+	0.0654370i	0.488739	+	0.872430i	$0.337457\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−21.7604	−	33.8598i	−0.712021	−	1.10793i
$935$		0			0
$936$		0			0
$937$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$937$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$938$	−62.3415	−	40.0644i	−2.03552	−	1.30815i
$939$		0			0
$940$	−4.03059	−	13.7269i	−0.131463	−	0.447723i
$941$	2.23335	−	1.01994i	0.0728050	−	0.0332489i	−0.378680	−	0.925528i	$-0.623622\pi$
$941$	2.23335	−	1.01994i	0.0728050	−	0.0332489i	0.451485	+	0.892279i	$0.350895\pi$
$942$		0			0
$943$	−28.1845	−	8.43460i	−0.917813	−	0.274668i
$944$		0			0
$945$	72.3779	+	158.485i	2.35445	+	5.15553i
$946$		0			0
$947$	−10.8919	+	12.5699i	−0.353938	+	0.408467i	−0.904600	−	0.426262i	$-0.859830\pi$
$947$	−10.8919	+	12.5699i	−0.353938	+	0.408467i	0.550661	+	0.834729i	$0.314376\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$953$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	46.8306	−	40.5790i	1.51145	−	1.30968i
$961$	26.0789	+	16.7599i	0.841254	+	0.540641i
$962$		0			0
$963$	−4.96613	−	16.9131i	−0.160031	−	0.545016i
$964$	53.8945	−	24.6128i	1.73583	−	0.792725i
$965$		0			0
$966$	−79.9376	−	37.0081i	−2.57195	−	1.19071i
$967$	−18.0076			−0.579085			−0.289543	−	0.957165i	$-0.593503\pi$
$967$	−18.0076			−0.579085			−0.289543	+	0.957165i	$0.593503\pi$
$968$	12.9247	+	28.3011i	0.415415	+	0.909632i
$969$		0			0
$970$		0			0
$971$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$971$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$972$	122.455	+	141.321i	3.92775	+	4.53286i
$973$		0			0
$974$	22.3574	+	6.56474i	0.716379	+	0.210348i
$975$		0			0
$976$	10.8480	+	1.55970i	0.347235	+	0.0499249i
$977$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$977$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$978$	17.0826	−	37.4057i	0.546242	−	1.19610i
$979$		0			0
$980$	17.0653	+	26.5541i	0.545131	+	0.848240i
$981$	22.7696	−	77.5462i	0.726978	−	2.47586i
$982$		0			0
$983$	−43.0859	+	37.3342i	−1.37423	+	1.19078i	−0.414431	+	0.910081i	$0.636019\pi$
$983$	−43.0859	+	37.3342i	−1.37423	+	1.19078i	−0.959797	+	0.280695i	$0.909435\pi$
$984$	50.5616	+	32.4940i	1.61184	+	1.03587i
$985$		0			0
$986$		0			0
$987$	37.7940	−	17.2600i	1.20300	−	0.549390i
$988$		0			0
$989$	−19.4133	−	30.5546i	−0.617306	−	0.971579i
$990$		0			0
$991$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$991$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	32.3660	−	4.65353i	1.02556	−	0.147453i
$997$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$997$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.19.2	✓	40
4.3	odd	2	inner	460.2.o.a.19.3	yes	40
5.4	even	2	inner	460.2.o.a.19.3	yes	40
20.19	odd	2	CM	460.2.o.a.19.2	✓	40
23.17	odd	22	inner	460.2.o.a.339.2	yes	40
92.63	even	22	inner	460.2.o.a.339.3	yes	40
115.109	odd	22	inner	460.2.o.a.339.3	yes	40
460.339	even	22	inner	460.2.o.a.339.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.19.2	✓	40	1.1	even	1	trivial
460.2.o.a.19.2	✓	40	20.19	odd	2	CM
460.2.o.a.19.3	yes	40	4.3	odd	2	inner
460.2.o.a.19.3	yes	40	5.4	even	2	inner
460.2.o.a.339.2	yes	40	23.17	odd	22	inner
460.2.o.a.339.2	yes	40	460.339	even	22	inner
460.2.o.a.339.3	yes	40	92.63	even	22	inner
460.2.o.a.339.3	yes	40	115.109	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587486 - 1.28641i) q^{2} +(3.32368 - 0.975920i) q^{3} +(-1.30972 + 1.51150i) q^{4} +(1.20891 - 1.88110i) q^{5} +(-3.20805 - 3.70229i) q^{6} +(-3.71125 + 0.533598i) q^{7} +(2.71386 + 0.796860i) q^{8} +(7.57066 - 4.86537i) q^{9} +O(q^{10})\)	\(q+(-0.587486 - 1.28641i) q^{2} +(3.32368 - 0.975920i) q^{3} +(-1.30972 + 1.51150i) q^{4} +(1.20891 - 1.88110i) q^{5} +(-3.20805 - 3.70229i) q^{6} +(-3.71125 + 0.533598i) q^{7} +(2.71386 + 0.796860i) q^{8} +(7.57066 - 4.86537i) q^{9} +(-3.13009 - 0.450039i) q^{10} +(-2.87799 + 6.30192i) q^{12} +(2.86674 + 4.46073i) q^{14} +(2.18222 - 7.43197i) q^{15} +(-0.569259 - 3.95929i) q^{16} +(-10.7065 - 6.88067i) q^{18} +(1.25995 + 4.29098i) q^{20} +(-11.8143 + 5.39539i) q^{21} +(-4.60851 + 1.32728i) q^{23} +9.79766 q^{24} +(-2.07708 - 4.54816i) q^{25} +(13.6089 - 15.7055i) q^{27} +(4.05418 - 6.30842i) q^{28} +(6.47209 + 7.46919i) q^{29} +(-10.8426 + 1.55893i) q^{30} +(-4.75885 + 3.05833i) q^{32} +(-3.48282 + 7.62631i) q^{35} +(-2.56146 + 17.8153i) q^{36} +(4.77978 - 4.14170i) q^{40} +(5.16058 + 3.31650i) q^{41} +(13.8814 + 12.0283i) q^{42} +(2.12659 + 7.24251i) q^{43} -20.1230i q^{45} +(4.41486 + 5.14869i) q^{46} -3.19902 q^{47} +(-5.75598 - 12.6038i) q^{48} +(6.77223 - 1.98851i) q^{49} +(-4.63056 + 5.34396i) q^{50} +(-28.1989 - 8.27993i) q^{54} +(-10.4970 - 1.50924i) q^{56} +(5.80621 - 12.7138i) q^{58} +(8.37531 + 13.0322i) q^{60} +(-0.771914 + 2.62890i) q^{61} +(-25.5005 + 22.0963i) q^{63} +(6.73003 + 4.32513i) q^{64} +(-12.7127 + 5.80568i) q^{67} +(-14.0219 + 8.90898i) q^{69} +11.8567 q^{70} +(24.4227 - 7.17115i) q^{72} +(-11.3422 - 13.0896i) q^{75} +(-8.13600 - 3.71558i) q^{80} +(18.6891 - 40.9233i) q^{81} +(1.23463 - 8.58704i) q^{82} +(-2.55173 - 3.97056i) q^{83} +(7.31826 - 24.9237i) q^{84} +(8.06753 - 6.99055i) q^{86} +(28.8005 + 18.5090i) q^{87} +(0.555965 + 1.89344i) q^{89} +(-25.8864 + 11.8219i) q^{90} +(4.02968 - 8.70412i) q^{92} +(1.87938 + 4.11526i) q^{94} +(-12.8322 + 14.8091i) q^{96} +(-6.53663 - 7.54367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more