LMFDB - Embedded newform 460.2.m.a.441.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, 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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			441.1
Character	$\chi$	$=$	460.441
Dual form			460.2.m.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73464 + 0.802964i) q^{3} +(0.841254 + 0.540641i) q^{5} +(-0.359196 - 2.49826i) q^{7} +(4.30976 - 2.76972i) q^{9} +O(q^{10})$	\(q+(-2.73464 + 0.802964i) q^{3} +(0.841254 + 0.540641i) q^{5} +(-0.359196 - 2.49826i) q^{7} +(4.30976 - 2.76972i) q^{9} +(-1.78965 + 3.91878i) q^{11} +(0.846960 - 5.89073i) q^{13} +(-2.73464 - 0.802964i) q^{15} +(3.87167 + 4.46815i) q^{17} +(-0.652347 + 0.752849i) q^{19} +(2.98828 + 6.54343i) q^{21} +(4.71276 - 0.888766i) q^{23} +(0.415415 + 0.909632i) q^{25} +(-3.96244 + 4.57291i) q^{27} +(6.29992 + 7.27049i) q^{29} +(10.1637 + 2.98432i) q^{31} +(1.74741 - 12.1535i) q^{33} +(1.04849 - 2.29587i) q^{35} +(-2.30670 + 1.48242i) q^{37} +(2.41391 + 16.7891i) q^{39} +(-2.00858 - 1.29084i) q^{41} +(-5.14130 + 1.50962i) q^{43} +5.12303 q^{45} +6.36077 q^{47} +(0.604167 - 0.177399i) q^{49} +(-14.1754 - 9.10998i) q^{51} +(-1.21938 - 8.48099i) q^{53} +(-3.62420 + 2.32913i) q^{55} +(1.17943 - 2.58258i) q^{57} +(0.0744314 - 0.517682i) q^{59} +(4.06103 + 1.19243i) q^{61} +(-8.46752 - 9.77204i) q^{63} +(3.89728 - 4.49770i) q^{65} +(2.62149 + 5.74027i) q^{67} +(-12.1741 + 6.21463i) q^{69} +(-4.27655 - 9.36433i) q^{71} +(-1.27081 + 1.46660i) q^{73} +(-1.86641 - 2.15396i) q^{75} +(10.4330 + 3.06339i) q^{77} +(2.19285 - 15.2516i) q^{79} +(0.779451 - 1.70676i) q^{81} +(2.04411 - 1.31367i) q^{83} +(0.841395 + 5.85203i) q^{85} +(-23.0660 - 14.8236i) q^{87} +(-7.32967 + 2.15219i) q^{89} -15.0208 q^{91} -30.1903 q^{93} +(-0.955810 + 0.280651i) q^{95} +(9.48807 + 6.09761i) q^{97} +(3.14095 + 21.8458i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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			0
$2$		0			0
$3$	−2.73464	+	0.802964i	−1.57885	+	0.463591i	−0.949561	−	0.313582i	$-0.898471\pi$
$3$	−2.73464	+	0.802964i	−1.57885	+	0.463591i	−0.629286	+	0.777174i	$0.716653\pi$
$4$		0			0
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$5$	0.841254	+	0.540641i	0.376220	+	0.241782i
$6$		0			0
$7$	−0.359196	−	2.49826i	−0.135763	−	0.944254i	−0.937849	−	0.347044i	$-0.887185\pi$
$7$	−0.359196	−	2.49826i	−0.135763	−	0.944254i	0.802085	−	0.597209i	$-0.203724\pi$
$8$		0			0
$9$	4.30976	−	2.76972i	1.43659	−	0.923239i
$10$		0			0
$11$	−1.78965	+	3.91878i	−0.539598	+	1.18156i	0.421874	+	0.906654i	$0.361372\pi$
$11$	−1.78965	+	3.91878i	−0.539598	+	1.18156i	−0.961473	+	0.274901i	$0.911355\pi$
$12$		0			0
$13$	0.846960	−	5.89073i	0.234904	−	1.63380i	−0.441497	−	0.897263i	$-0.645553\pi$
$13$	0.846960	−	5.89073i	0.234904	−	1.63380i	0.676402	−	0.736533i	$-0.263538\pi$
$14$		0			0
$15$	−2.73464	−	0.802964i	−0.706082	−	0.207324i
$16$		0			0
$17$	3.87167	+	4.46815i	0.939018	+	1.08369i	0.996353	+	0.0853300i	$0.0271945\pi$
$17$	3.87167	+	4.46815i	0.939018	+	1.08369i	−0.0573343	+	0.998355i	$0.518260\pi$
$18$		0			0
$19$	−0.652347	+	0.752849i	−0.149659	+	0.172715i	−0.825629	−	0.564214i	$-0.809179\pi$
$19$	−0.652347	+	0.752849i	−0.149659	+	0.172715i	0.675970	+	0.736929i	$0.263725\pi$
$20$		0			0
$21$	2.98828	+	6.54343i	0.652097	+	1.42789i
$22$		0			0
$23$	4.71276	−	0.888766i	0.982678	−	0.185321i
$23$	4.71276	−	0.888766i	0.982678	−	0.185321i
$24$		0			0
$25$	0.415415	+	0.909632i	0.0830830	+	0.181926i
$26$		0			0
$27$	−3.96244	+	4.57291i	−0.762573	+	0.880056i
$28$		0			0
$29$	6.29992	+	7.27049i	1.16986	+	1.35010i	0.924738	+	0.380605i	$0.124284\pi$
$29$	6.29992	+	7.27049i	1.16986	+	1.35010i	0.245127	+	0.969491i	$0.421170\pi$
$30$		0			0
$31$	10.1637	+	2.98432i	1.82545	+	0.535999i	0.999610	−	0.0279113i	$-0.00888559\pi$
$31$	10.1637	+	2.98432i	1.82545	+	0.535999i	0.825836	+	0.563911i	$0.190704\pi$
$32$		0			0
$33$	1.74741	−	12.1535i	0.304184	−	2.11565i
$34$		0			0
$35$	1.04849	−	2.29587i	0.177227	−	0.388072i
$36$		0			0
$37$	−2.30670	+	1.48242i	−0.379218	+	0.243709i	−0.716339	−	0.697753i	$-0.754183\pi$
$37$	−2.30670	+	1.48242i	−0.379218	+	0.243709i	0.337120	+	0.941462i	$0.390547\pi$
$38$		0			0
$39$	2.41391	+	16.7891i	0.386535	+	2.68841i
$40$		0			0
$41$	−2.00858	−	1.29084i	−0.313688	−	0.201595i	0.374317	−	0.927301i	$-0.377877\pi$
$41$	−2.00858	−	1.29084i	−0.313688	−	0.201595i	−0.688005	+	0.725706i	$0.741513\pi$
$42$		0			0
$43$	−5.14130	+	1.50962i	−0.784040	+	0.230215i	−0.649165	−	0.760648i	$-0.724882\pi$
$43$	−5.14130	+	1.50962i	−0.784040	+	0.230215i	−0.134875	+	0.990863i	$0.543063\pi$
$44$		0			0
$45$	5.12303			0.763696
$46$		0			0
$47$	6.36077			0.927814			0.463907	−	0.885884i	$-0.346447\pi$
$47$	6.36077			0.927814			0.463907	+	0.885884i	$0.346447\pi$
$48$		0			0
$49$	0.604167	−	0.177399i	0.0863096	−	0.0253428i
$50$		0			0
$51$	−14.1754	−	9.10998i	−1.98495	−	1.27565i
$52$		0			0
$53$	−1.21938	−	8.48099i	−0.167495	−	1.16495i	−0.884039	−	0.467413i	$-0.845186\pi$
$53$	−1.21938	−	8.48099i	−0.167495	−	1.16495i	0.716544	−	0.697542i	$-0.245723\pi$
$54$		0			0
$55$	−3.62420	+	2.32913i	−0.488686	+	0.314060i
$56$		0			0
$57$	1.17943	−	2.58258i	0.156219	−	0.342072i
$58$		0			0
$59$	0.0744314	−	0.517682i	0.00969014	−	0.0673964i	−0.984403	−	0.175931i	$-0.943707\pi$
$59$	0.0744314	−	0.517682i	0.00969014	−	0.0673964i	0.994093	+	0.108534i	$0.0346157\pi$
$60$		0			0
$61$	4.06103	+	1.19243i	0.519962	+	0.152675i	0.531174	−	0.847262i	$-0.321751\pi$
$61$	4.06103	+	1.19243i	0.519962	+	0.152675i	−0.0112123	+	0.999937i	$0.503569\pi$
$62$		0			0
$63$	−8.46752	−	9.77204i	−1.06681	−	1.23116i
$64$		0			0
$65$	3.89728	−	4.49770i	0.483398	−	0.557871i
$66$		0			0
$67$	2.62149	+	5.74027i	0.320266	+	0.701285i	0.999466	−	0.0326681i	$-0.0104004\pi$
$67$	2.62149	+	5.74027i	0.320266	+	0.701285i	−0.679200	+	0.733953i	$0.737673\pi$
$68$		0			0
$69$	−12.1741	+	6.21463i	−1.46559	+	0.748154i
$70$		0			0
$71$	−4.27655	−	9.36433i	−0.507533	−	1.11134i	−0.973947	−	0.226775i	$-0.927182\pi$
$71$	−4.27655	−	9.36433i	−0.507533	−	1.11134i	0.466414	−	0.884566i	$-0.345546\pi$
$72$		0			0
$73$	−1.27081	+	1.46660i	−0.148737	+	0.171652i	−0.825229	−	0.564798i	$-0.808954\pi$
$73$	−1.27081	+	1.46660i	−0.148737	+	0.171652i	0.676492	+	0.736450i	$0.263499\pi$
$74$		0			0
$75$	−1.86641	−	2.15396i	−0.215515	−	0.248717i
$76$		0			0
$77$	10.4330	+	3.06339i	1.18895	+	0.349106i
$78$		0			0
$79$	2.19285	−	15.2516i	0.246714	−	1.71594i	−0.370239	−	0.928937i	$-0.620724\pi$
$79$	2.19285	−	15.2516i	0.246714	−	1.71594i	0.616953	−	0.787000i	$-0.288367\pi$
$80$		0			0
$81$	0.779451	−	1.70676i	0.0866057	−	0.189640i
$82$		0			0
$83$	2.04411	−	1.31367i	0.224370	−	0.144194i	−0.423627	−	0.905837i	$-0.639243\pi$
$83$	2.04411	−	1.31367i	0.224370	−	0.144194i	0.647997	+	0.761643i	$0.275607\pi$
$84$		0			0
$85$	0.841395	+	5.85203i	0.0912621	+	0.634742i
$86$		0			0
$87$	−23.0660	−	14.8236i	−2.47293	−	1.58926i
$88$		0			0
$89$	−7.32967	+	2.15219i	−0.776944	+	0.228131i	−0.646081	−	0.763269i	$-0.723593\pi$
$89$	−7.32967	+	2.15219i	−0.776944	+	0.228131i	−0.130863	+	0.991400i	$0.541775\pi$
$90$		0			0
$91$	−15.0208			−1.57461
$92$		0			0
$93$	−30.1903			−3.13059
$94$		0			0
$95$	−0.955810	+	0.280651i	−0.0980640	+	0.0287942i
$96$		0			0
$97$	9.48807	+	6.09761i	0.963368	+	0.619119i	0.924928	−	0.380142i	$-0.124125\pi$
$97$	9.48807	+	6.09761i	0.963368	+	0.619119i	0.0384396	+	0.999261i	$0.487761\pi$
$98$		0			0
$99$	3.14095	+	21.8458i	0.315678	+	2.19559i
$100$		0			0
$101$	9.77275	−	6.28056i	0.972425	−	0.624939i	0.0450150	−	0.998986i	$-0.485666\pi$
$101$	9.77275	−	6.28056i	0.972425	−	0.624939i	0.927410	+	0.374047i	$0.122030\pi$
$102$		0			0
$103$	−5.18038	+	11.3435i	−0.510438	+	1.11770i	0.462496	+	0.886621i	$0.346954\pi$
$103$	−5.18038	+	11.3435i	−0.510438	+	1.11770i	−0.972934	+	0.231082i	$0.925773\pi$
$104$		0			0
$105$	−1.02374	+	7.12027i	−0.0999069	+	0.694867i
$106$		0			0
$107$	−7.67466	−	2.25348i	−0.741937	−	0.217853i	−0.111145	−	0.993804i	$-0.535452\pi$
$107$	−7.67466	−	2.25348i	−0.741937	−	0.217853i	−0.630792	+	0.775952i	$0.717270\pi$
$108$		0			0
$109$	0.298283	+	0.344237i	0.0285703	+	0.0329719i	0.769855	−	0.638219i	$-0.220329\pi$
$109$	0.298283	+	0.344237i	0.0285703	+	0.0329719i	−0.741285	+	0.671191i	$0.765783\pi$
$110$		0			0
$111$	5.11766	−	5.90609i	0.485747	−	0.560581i
$112$		0			0
$113$	−2.93900	−	6.43552i	−0.276478	−	0.605403i	0.719550	−	0.694441i	$-0.244348\pi$
$113$	−2.93900	−	6.43552i	−0.276478	−	0.605403i	−0.996028	+	0.0890378i	$0.971621\pi$
$114$		0			0
$115$	4.44513	+	1.80023i	0.414510	+	0.167872i
$116$		0			0
$117$	−12.6655	−	27.7335i	−1.17092	−	2.56396i
$118$		0			0
$119$	9.77191	−	11.2774i	0.895789	−	1.03380i
$120$		0			0
$121$	−4.95051	−	5.71319i	−0.450046	−	0.519381i
$122$		0			0
$123$	6.52925	+	1.91716i	0.588723	+	0.172865i
$124$		0			0
$125$	−0.142315	+	0.989821i	−0.0127290	+	0.0885323i
$126$		0			0
$127$	3.74377	−	8.19770i	0.332205	−	0.727428i	−0.667649	−	0.744476i	$-0.732699\pi$
$127$	3.74377	−	8.19770i	0.332205	−	0.727428i	0.999855	+	0.0170475i	$0.00542666\pi$
$128$		0			0
$129$	12.8474	−	8.25655i	1.13115	−	0.726949i
$130$		0			0
$131$	2.45265	+	17.0585i	0.214289	+	1.49041i	0.758616	+	0.651538i	$0.225876\pi$
$131$	2.45265	+	17.0585i	0.214289	+	1.49041i	−0.544328	+	0.838873i	$0.683215\pi$
$132$		0			0
$133$	2.11513	+	1.35931i	0.183405	+	0.117867i
$134$		0			0
$135$	−5.80572	+	1.70471i	−0.499677	+	0.146718i
$136$		0			0
$137$	3.51894			0.300644			0.150322	−	0.988637i	$-0.451969\pi$
$137$	3.51894			0.300644			0.150322	+	0.988637i	$0.451969\pi$
$138$		0			0
$139$	10.5068			0.891172			0.445586	−	0.895239i	$-0.352995\pi$
$139$	10.5068			0.891172			0.445586	+	0.895239i	$0.352995\pi$
$140$		0			0
$141$	−17.3944	+	5.10747i	−1.46488	+	0.430126i
$142$		0			0
$143$	21.5687	+	13.8614i	1.80367	+	1.15915i
$144$		0			0
$145$	1.36910	+	9.52232i	0.113698	+	0.790785i
$146$		0			0
$147$	−1.50974	+	0.970248i	−0.124521	+	0.0800247i
$148$		0			0
$149$	−0.297445	+	0.651314i	−0.0243676	+	0.0533577i	−0.921424	−	0.388557i	$-0.872974\pi$
$149$	−0.297445	+	0.651314i	−0.0243676	+	0.0533577i	0.897057	+	0.441915i	$0.145701\pi$
$150$		0			0
$151$	0.532949	−	3.70674i	0.0433708	−	0.301650i	−0.956578	−	0.291478i	$-0.905853\pi$
$151$	0.532949	−	3.70674i	0.0433708	−	0.301650i	0.999948	−	0.0101722i	$-0.00323796\pi$
$152$		0			0
$153$	29.0615	+	8.53323i	2.34948	+	0.689870i
$154$		0			0
$155$	6.93677	+	8.00545i	0.557174	+	0.643014i
$156$		0			0
$157$	−9.25327	+	10.6788i	−0.738491	+	0.852264i	−0.993400	−	0.114701i	$-0.963409\pi$
$157$	−9.25327	+	10.6788i	−0.738491	+	0.852264i	0.254909	+	0.966965i	$0.417955\pi$
$158$		0			0
$159$	10.1445	+	22.2134i	0.804512	+	1.76164i
$160$		0			0
$161$	−3.91317	−	11.4545i	−0.308401	−	0.902738i
$162$		0			0
$163$	−6.40239	−	14.0193i	−0.501474	−	1.09808i	−0.975987	−	0.217827i	$-0.930103\pi$
$163$	−6.40239	−	14.0193i	−0.501474	−	1.09808i	0.474513	−	0.880248i	$-0.342624\pi$
$164$		0			0
$165$	8.04068	−	9.27944i	0.625966	−	0.722403i
$166$		0			0
$167$	10.2414	+	11.8192i	0.792503	+	0.914598i	0.997945	−	0.0640716i	$-0.0204086\pi$
$167$	10.2414	+	11.8192i	0.792503	+	0.914598i	−0.205442	+	0.978669i	$0.565863\pi$
$168$		0			0
$169$	−21.5100	−	6.31590i	−1.65461	−	0.485839i
$170$		0			0
$171$	−0.726284	+	5.05142i	−0.0555403	+	0.386291i
$172$		0			0
$173$	−0.840143	+	1.83966i	−0.0638749	+	0.139867i	−0.938877	−	0.344252i	$-0.888132\pi$
$173$	−0.840143	+	1.83966i	−0.0638749	+	0.139867i	0.875002	+	0.484119i	$0.160860\pi$
$174$		0			0
$175$	2.12328	−	1.36455i	0.160505	−	0.103150i
$176$		0			0
$177$	0.212136	+	1.47544i	0.0159451	+	0.110901i
$178$		0			0
$179$	10.2359	+	6.57819i	0.765064	+	0.491677i	0.864046	−	0.503412i	$-0.167922\pi$
$179$	10.2359	+	6.57819i	0.765064	+	0.491677i	−0.0989822	+	0.995089i	$0.531559\pi$
$180$		0			0
$181$	6.60417	−	1.93916i	0.490884	−	0.144137i	−0.0269168	−	0.999638i	$-0.508569\pi$
$181$	6.60417	−	1.93916i	0.490884	−	0.144137i	0.517801	+	0.855501i	$0.326751\pi$
$182$		0			0
$183$	−12.0630			−0.891719
$184$		0			0
$185$	−2.74197			−0.201594
$186$		0			0
$187$	−24.4386	+	7.17582i	−1.78713	+	0.524748i
$188$		0			0
$189$	12.8476	+	8.25665i	0.934525	+	0.600583i
$190$		0			0
$191$	−2.31848	−	16.1254i	−0.167759	−	1.16679i	−0.883502	−	0.468427i	$-0.844821\pi$
$191$	−2.31848	−	16.1254i	−0.167759	−	1.16679i	0.715743	−	0.698364i	$-0.246088\pi$
$192$		0			0
$193$	−20.1002	+	12.9176i	−1.44684	+	0.929830i	−0.447476	+	0.894296i	$0.647677\pi$
$193$	−20.1002	+	12.9176i	−1.44684	+	0.929830i	−0.999368	+	0.0355345i	$0.988687\pi$
$194$		0			0
$195$	−7.04618	+	15.4290i	−0.504587	+	1.10489i
$196$		0			0
$197$	−0.423581	+	2.94607i	−0.0301789	+	0.209899i	−0.999331	−	0.0365631i	$-0.988359\pi$
$197$	−0.423581	+	2.94607i	−0.0301789	+	0.209899i	0.969152	+	0.246462i	$0.0792681\pi$
$198$		0			0
$199$	−2.92191	−	0.857950i	−0.207129	−	0.0608184i	0.176522	−	0.984297i	$-0.443515\pi$
$199$	−2.92191	−	0.857950i	−0.207129	−	0.0608184i	−0.383651	+	0.923478i	$0.625333\pi$
$200$		0			0
$201$	−11.7781	−	13.5926i	−0.830761	−	0.958749i
$202$		0			0
$203$	15.9007	−	18.3504i	1.11601	−	1.28794i
$204$		0			0
$205$	−0.991848	−	2.17184i	−0.0692737	−	0.151688i
$206$		0			0
$207$	17.8492	−	16.8834i	1.24061	−	1.17348i
$208$		0			0
$209$	−1.78278	−	3.90373i	−0.123317	−	0.270027i
$210$		0			0
$211$	7.86926	−	9.08161i	0.541742	−	0.625203i	−0.417197	−	0.908816i	$-0.636988\pi$
$211$	7.86926	−	9.08161i	0.541742	−	0.625203i	0.958939	+	0.283613i	$0.0915330\pi$
$212$		0			0
$213$	19.2140	+	22.1742i	1.31652	+	1.51935i
$214$		0			0
$215$	−5.14130	−	1.50962i	−0.350633	−	0.102955i
$216$		0			0
$217$	3.80486	−	26.4634i	0.258291	−	1.79645i
$218$		0			0
$219$	2.29760	−	5.03103i	0.155257	−	0.339966i
$220$		0			0
$221$	29.5998	−	19.0226i	1.99110	−	1.27960i
$222$		0			0
$223$	−2.79550	−	19.4431i	−0.187200	−	1.30201i	−0.839215	−	0.543800i	$-0.816985\pi$
$223$	−2.79550	−	19.4431i	−0.187200	−	1.30201i	0.652014	−	0.758207i	$-0.273924\pi$
$224$		0			0
$225$	4.30976	+	2.76972i	0.287318	+	0.184648i
$226$		0			0
$227$	8.06079	−	2.36686i	0.535014	−	0.157094i	−0.00305477	−	0.999995i	$-0.500972\pi$
$227$	8.06079	−	2.36686i	0.535014	−	0.157094i	0.538068	+	0.842901i	$0.319154\pi$
$228$		0			0
$229$	−24.9867			−1.65117			−0.825583	−	0.564281i	$-0.809154\pi$
$229$	−24.9867			−1.65117			−0.825583	+	0.564281i	$0.809154\pi$
$230$		0			0
$231$	−30.9902			−2.03901
$232$		0			0
$233$	−16.3254	+	4.79357i	−1.06951	+	0.314038i	−0.768676	−	0.639638i	$-0.779084\pi$
$233$	−16.3254	+	4.79357i	−1.06951	+	0.314038i	−0.300837	+	0.953675i	$0.597266\pi$
$234$		0			0
$235$	5.35102	+	3.43889i	0.349062	+	0.224329i
$236$		0			0
$237$	6.24981	+	43.4684i	0.405969	+	2.82358i
$238$		0			0
$239$	−13.6137	+	8.74898i	−0.880596	+	0.565925i	−0.900977	−	0.433868i	$-0.857149\pi$
$239$	−13.6137	+	8.74898i	−0.880596	+	0.565925i	0.0203806	+	0.999792i	$0.493512\pi$
$240$		0			0
$241$	1.34248	−	2.93963i	0.0864770	−	0.189358i	−0.861453	−	0.507838i	$-0.830445\pi$
$241$	1.34248	−	2.93963i	0.0864770	−	0.189358i	0.947930	+	0.318480i	$0.103172\pi$
$242$		0			0
$243$	1.82231	−	12.6744i	0.116901	−	0.813066i
$244$		0			0
$245$	0.604167	+	0.177399i	0.0385988	+	0.0113336i
$246$		0			0
$247$	3.88232	+	4.48043i	0.247026	+	0.285083i
$248$		0			0
$249$	−4.53508	+	5.23376i	−0.287399	+	0.331676i
$250$		0			0
$251$	2.37409	+	5.19853i	0.149851	+	0.328128i	0.969640	−	0.244538i	$-0.0786364\pi$
$251$	2.37409	+	5.19853i	0.149851	+	0.328128i	−0.819789	+	0.572666i	$0.805909\pi$
$252$		0			0
$253$	−4.95129	+	20.0588i	−0.311285	+	1.26109i
$254$		0			0
$255$	−6.99988	−	15.3276i	−0.438350	−	0.959852i
$256$		0			0
$257$	−4.98673	+	5.75499i	−0.311064	+	0.358987i	−0.889657	−	0.456630i	$-0.849056\pi$
$257$	−4.98673	+	5.75499i	−0.311064	+	0.358987i	0.578593	+	0.815616i	$0.303602\pi$
$258$		0			0
$259$	4.53203	+	5.23025i	0.281607	+	0.324992i
$260$		0			0
$261$	47.2883	+	13.8851i	2.92708	+	0.859467i
$262$		0			0
$263$	−3.23528	+	22.5019i	−0.199496	+	1.38752i	0.606255	+	0.795270i	$0.292671\pi$
$263$	−3.23528	+	22.5019i	−0.199496	+	1.38752i	−0.805751	+	0.592254i	$0.798238\pi$
$264$		0			0
$265$	3.55936	−	7.79392i	0.218650	−	0.478776i
$266$		0			0
$267$	18.3159	−	11.7709i	1.12092	−	0.720369i
$268$		0			0
$269$	1.60197	+	11.1420i	0.0976739	+	0.679337i	0.978553	+	0.205995i	$0.0660432\pi$
$269$	1.60197	+	11.1420i	0.0976739	+	0.679337i	−0.880879	+	0.473341i	$0.843048\pi$
$270$		0			0
$271$	7.29099	+	4.68563i	0.442896	+	0.284632i	0.743021	−	0.669268i	$-0.233392\pi$
$271$	7.29099	+	4.68563i	0.442896	+	0.284632i	−0.300125	+	0.953900i	$0.597028\pi$
$272$		0			0
$273$	41.0766	−	12.0612i	2.48607	−	0.729975i
$274$		0			0
$275$	−4.30809			−0.259788
$276$		0			0
$277$	−16.8841			−1.01447			−0.507234	−	0.861809i	$-0.669332\pi$
$277$	−16.8841			−1.01447			−0.507234	+	0.861809i	$0.669332\pi$
$278$		0			0
$279$	52.0687	−	15.2887i	3.11727	−	0.915313i
$280$		0			0
$281$	−3.26322	−	2.09715i	−0.194668	−	0.125105i	0.439676	−	0.898156i	$-0.355093\pi$
$281$	−3.26322	−	2.09715i	−0.194668	−	0.125105i	−0.634344	+	0.773051i	$0.718730\pi$
$282$		0			0
$283$	3.68462	+	25.6271i	0.219028	+	1.52337i	0.741639	+	0.670800i	$0.234049\pi$
$283$	3.68462	+	25.6271i	0.219028	+	1.52337i	−0.522611	+	0.852571i	$0.675042\pi$
$284$		0			0
$285$	2.38845	−	1.53496i	0.141479	−	0.0909233i
$286$		0			0
$287$	−2.50337	+	5.48163i	−0.147770	+	0.323570i
$288$		0			0
$289$	−2.55515	+	17.7714i	−0.150303	+	1.04538i
$290$		0			0
$291$	−30.8427	−	9.05622i	−1.80803	−	0.530885i
$292$		0			0
$293$	−19.1221	−	22.0681i	−1.11713	−	1.28923i	−0.953059	−	0.302785i	$-0.902083\pi$
$293$	−19.1221	−	22.0681i	−1.11713	−	1.28923i	−0.164069	−	0.986449i	$-0.552462\pi$
$294$		0			0
$295$	0.342495	−	0.395261i	0.0199409	−	0.0230130i
$296$		0			0
$297$	−10.8288	−	23.7118i	−0.628352	−	1.37590i
$298$		0			0
$299$	−1.24397	−	28.5144i	−0.0719406	−	1.64903i
$300$		0			0
$301$	5.61816	+	12.3020i	0.323825	+	0.709078i
$302$		0			0
$303$	−21.6819	+	25.0223i	−1.24559	+	1.43749i
$304$		0			0
$305$	2.77168	+	3.19869i	0.158706	+	0.183157i
$306$		0			0
$307$	16.5861	+	4.87013i	0.946621	+	0.277953i	0.718380	−	0.695651i	$-0.244884\pi$
$307$	16.5861	+	4.87013i	0.946621	+	0.277953i	0.228242	+	0.973604i	$0.426702\pi$
$308$		0			0
$309$	5.05811	−	35.1800i	0.287746	−	2.00132i
$310$		0			0
$311$	−1.89650	+	4.15276i	−0.107541	+	0.235481i	−0.955750	−	0.294180i	$-0.904954\pi$
$311$	−1.89650	+	4.15276i	−0.107541	+	0.235481i	0.848209	+	0.529661i	$0.177681\pi$
$312$		0			0
$313$	15.2531	−	9.80257i	0.862156	−	0.554074i	−0.0331879	−	0.999449i	$-0.510566\pi$
$313$	15.2531	−	9.80257i	0.862156	−	0.554074i	0.895344	+	0.445375i	$0.146930\pi$
$314$		0			0
$315$	−1.84017	−	12.7987i	−0.103682	−	0.721122i
$316$		0			0
$317$	21.7737	+	13.9931i	1.22293	+	0.785932i	0.982776	−	0.184801i	$-0.0591642\pi$
$317$	21.7737	+	13.9931i	1.22293	+	0.785932i	0.240159	+	0.970734i	$0.422801\pi$
$318$		0			0
$319$	−39.7660	+	11.6764i	−2.22647	+	0.653751i
$320$		0			0
$321$	22.7969			1.27240
$322$		0			0
$323$	−5.88951			−0.327701
$324$		0			0
$325$	5.71024	−	1.67668i	0.316747	−	0.0930053i
$326$		0			0
$327$	−1.09211	−	0.701855i	−0.0603937	−	0.0388127i
$328$		0			0
$329$	−2.28476	−	15.8909i	−0.125963	−	0.876091i
$330$		0			0
$331$	−5.26161	+	3.38143i	−0.289204	+	0.185860i	−0.677196	−	0.735802i	$-0.736805\pi$
$331$	−5.26161	+	3.38143i	−0.289204	+	0.185860i	0.387992	+	0.921663i	$0.373169\pi$
$332$		0			0
$333$	−5.83542	+	12.7778i	−0.319779	+	0.700219i
$334$		0			0
$335$	−0.898083	+	6.24630i	−0.0490675	+	0.341272i
$336$		0			0
$337$	−1.29345	−	0.379790i	−0.0704585	−	0.0206885i	0.246313	−	0.969190i	$-0.420781\pi$
$337$	−1.29345	−	0.379790i	−0.0704585	−	0.0206885i	−0.316772	+	0.948502i	$0.602599\pi$
$338$		0			0
$339$	13.2046	+	15.2389i	0.717176	+	0.827666i
$340$		0			0
$341$	−29.8842	+	34.4882i	−1.61832	+	1.86764i
$342$		0			0
$343$	−7.99961	−	17.5167i	−0.431939	−	0.945813i
$344$		0			0
$345$	−13.6014	−	1.35372i	−0.732273	−	0.0728816i
$346$		0			0
$347$	0.450329	+	0.986082i	0.0241749	+	0.0529357i	0.921334	−	0.388771i	$-0.127100\pi$
$347$	0.450329	+	0.986082i	0.0241749	+	0.0529357i	−0.897159	+	0.441707i	$0.854373\pi$
$348$		0			0
$349$	5.43401	−	6.27118i	0.290876	−	0.335689i	−0.591438	−	0.806351i	$-0.701439\pi$
$349$	5.43401	−	6.27118i	0.290876	−	0.335689i	0.882314	+	0.470662i	$0.155985\pi$
$350$		0			0
$351$	23.5817	+	27.2148i	1.25870	+	1.45262i
$352$		0			0
$353$	0.0215042	+	0.00631419i	0.00114455	+	0.000336070i	0.282305	−	0.959325i	$-0.408901\pi$
$353$	0.0215042	+	0.00631419i	0.00114455	+	0.000336070i	−0.281160	+	0.959661i	$0.590719\pi$
$354$		0			0
$355$	1.46508	−	10.1899i	0.0777583	−	0.540821i
$356$		0			0
$357$	−17.6674	+	38.6861i	−0.935056	+	2.04749i
$358$		0			0
$359$	12.0248	−	7.72790i	0.634647	−	0.407863i	−0.183380	−	0.983042i	$-0.558704\pi$
$359$	12.0248	−	7.72790i	0.634647	−	0.407863i	0.818027	+	0.575179i	$0.195068\pi$
$360$		0			0
$361$	2.56276	+	17.8244i	0.134882	+	0.938125i
$362$		0			0
$363$	18.1254	+	11.6485i	0.951335	+	0.611386i
$364$		0			0
$365$	−1.86198	+	0.546726i	−0.0974603	+	0.0286169i
$366$		0			0
$367$	12.5788			0.656608			0.328304	−	0.944572i	$-0.393523\pi$
$367$	12.5788			0.656608			0.328304	+	0.944572i	$0.393523\pi$
$368$		0			0
$369$	−12.2318			−0.636761
$370$		0			0
$371$	−20.7497	+	6.09267i	−1.07727	+	0.316316i
$372$		0			0
$373$	−13.3586	−	8.58507i	−0.691683	−	0.444518i	0.147001	−	0.989136i	$-0.453038\pi$
$373$	−13.3586	−	8.58507i	−0.691683	−	0.444518i	−0.838684	+	0.544619i	$0.816674\pi$
$374$		0			0
$375$	−0.405610	−	2.82108i	−0.0209456	−	0.145680i
$376$		0			0
$377$	48.1643	−	30.9533i	2.48059	−	1.59418i
$378$		0			0
$379$	−4.46936	+	9.78653i	−0.229575	+	0.502700i	−0.989004	−	0.147891i	$-0.952752\pi$
$379$	−4.46936	+	9.78653i	−0.229575	+	0.502700i	0.759428	+	0.650591i	$0.225479\pi$
$380$		0			0
$381$	−3.65541	+	25.4239i	−0.187272	+	1.30251i
$382$		0			0
$383$	−8.41345	−	2.47041i	−0.429907	−	0.126232i	0.0596180	−	0.998221i	$-0.481012\pi$
$383$	−8.41345	−	2.47041i	−0.429907	−	0.126232i	−0.489525	+	0.871989i	$0.662830\pi$
$384$		0			0
$385$	7.12057	+	8.21757i	0.362898	+	0.418806i
$386$		0			0
$387$	−17.9765	+	20.7460i	−0.913799	+	1.05458i
$388$		0			0
$389$	0.949609	+	2.07935i	0.0481471	+	0.105427i	0.932177	−	0.362003i	$-0.117907\pi$
$389$	0.949609	+	2.07935i	0.0481471	+	0.105427i	−0.884030	+	0.467431i	$0.845180\pi$
$390$		0			0
$391$	22.2174	+	17.6163i	1.12358	+	0.890894i
$392$		0			0
$393$	−20.4045	−	44.6796i	−1.02927	−	2.25379i
$394$		0			0
$395$	10.0904	−	11.6449i	0.507701	−	0.585919i
$396$		0			0
$397$	−22.3229	−	25.7621i	−1.12036	−	1.29296i	−0.951613	−	0.307300i	$-0.900574\pi$
$397$	−22.3229	−	25.7621i	−1.12036	−	1.29296i	−0.168744	−	0.985660i	$-0.553971\pi$
$398$		0			0
$399$	−6.87561	−	2.01886i	−0.344211	−	0.101069i
$400$		0			0
$401$	−3.12632	+	21.7441i	−0.156121	+	1.08585i	0.749575	+	0.661919i	$0.230258\pi$
$401$	−3.12632	+	21.7441i	−0.156121	+	1.08585i	−0.905696	+	0.423927i	$0.860651\pi$
$402$		0			0
$403$	26.1880	−	57.3438i	1.30452	−	2.85650i
$404$		0			0
$405$	1.57846	−	1.01441i	0.0784343	−	0.0504067i
$406$		0			0
$407$	−1.68112	−	11.6924i	−0.0833299	−	0.579573i
$408$		0			0
$409$	−18.3242	−	11.7762i	−0.906073	−	0.582298i	0.00251252	−	0.999997i	$-0.499200\pi$
$409$	−18.3242	−	11.7762i	−0.906073	−	0.582298i	−0.908585	+	0.417699i	$0.862837\pi$
$410$		0			0
$411$	−9.62305	+	2.82558i	−0.474670	+	0.139376i
$412$		0			0
$413$	−1.32004			−0.0649549
$414$		0			0
$415$	2.42984			0.119276
$416$		0			0
$417$	−28.7323	+	8.43655i	−1.40702	+	0.413140i
$418$		0			0
$419$	−23.2579	−	14.9469i	−1.13622	−	0.730205i	−0.169372	−	0.985552i	$-0.554174\pi$
$419$	−23.2579	−	14.9469i	−1.13622	−	0.730205i	−0.966849	+	0.255347i	$0.917810\pi$
$420$		0			0
$421$	−1.78053	−	12.3838i	−0.0867776	−	0.603551i	−0.986086	−	0.166236i	$-0.946839\pi$
$421$	−1.78053	−	12.3838i	−0.0867776	−	0.603551i	0.899308	−	0.437315i	$-0.144071\pi$
$422$		0			0
$423$	27.4134	−	17.6175i	1.33289	−	0.856594i
$424$		0			0
$425$	−2.45602	+	5.37793i	−0.119134	+	0.260868i
$426$		0			0
$427$	1.52029	−	10.5738i	0.0735719	−	0.511704i
$428$		0			0
$429$	−70.1129	−	20.5870i	−3.38508	−	0.993950i
$430$		0			0
$431$	−0.744842	−	0.859593i	−0.0358778	−	0.0414051i	0.737527	−	0.675318i	$-0.235993\pi$
$431$	−0.744842	−	0.859593i	−0.0358778	−	0.0414051i	−0.773405	+	0.633912i	$0.781448\pi$
$432$		0			0
$433$	−2.89387	+	3.33971i	−0.139071	+	0.160496i	−0.821012	−	0.570911i	$-0.806590\pi$
$433$	−2.89387	+	3.33971i	−0.139071	+	0.160496i	0.681942	+	0.731407i	$0.261136\pi$
$434$		0			0
$435$	−11.3901	−	24.9408i	−0.546113	−	1.19582i
$436$		0			0
$437$	−2.40525	+	4.12778i	−0.115059	+	0.197458i
$438$		0			0
$439$	−7.65250	−	16.7566i	−0.365234	−	0.799751i	−0.999642	−	0.0267524i	$-0.991483\pi$
$439$	−7.65250	−	16.7566i	−0.365234	−	0.799751i	0.634408	−	0.772998i	$-0.281244\pi$
$440$		0			0
$441$	2.11247	−	2.43792i	0.100594	−	0.116091i
$442$		0			0
$443$	6.54692	+	7.55555i	0.311054	+	0.358975i	0.889653	−	0.456637i	$-0.150946\pi$
$443$	6.54692	+	7.55555i	0.311054	+	0.358975i	−0.578600	+	0.815612i	$0.696401\pi$
$444$		0			0
$445$	−7.32967	−	2.15219i	−0.347460	−	0.102023i
$446$		0			0
$447$	0.290425	−	2.01995i	0.0137366	−	0.0955403i
$448$		0			0
$449$	6.85481	−	15.0099i	0.323498	−	0.708363i	−0.676097	−	0.736813i	$-0.736330\pi$
$449$	6.85481	−	15.0099i	0.323498	−	0.708363i	0.999595	+	0.0284502i	$0.00905719\pi$
$450$		0			0
$451$	8.65316	−	5.56105i	0.407461	−	0.261859i
$452$		0			0
$453$	1.51895	+	10.5646i	0.0713667	+	0.496366i
$454$		0			0
$455$	−12.6363	−	8.12086i	−0.592399	−	0.380712i
$456$		0			0
$457$	−18.4917	+	5.42965i	−0.865005	+	0.253988i	−0.683989	−	0.729492i	$-0.739757\pi$
$457$	−18.4917	+	5.42965i	−0.865005	+	0.253988i	−0.181015	+	0.983480i	$0.557938\pi$
$458$		0			0
$459$	−35.7737			−1.66977
$460$		0			0
$461$	1.31102			0.0610605			0.0305302	−	0.999534i	$-0.490280\pi$
$461$	1.31102			0.0610605			0.0305302	+	0.999534i	$0.490280\pi$
$462$		0			0
$463$	−2.97821	+	0.874481i	−0.138409	+	0.0406406i	−0.350203	−	0.936674i	$-0.613888\pi$
$463$	−2.97821	+	0.874481i	−0.138409	+	0.0406406i	0.211794	+	0.977314i	$0.432069\pi$
$464$		0			0
$465$	−25.3977	−	16.3221i	−1.17779	−	0.756919i
$466$		0			0
$467$	2.26175	+	15.7308i	0.104661	+	0.727934i	0.972806	+	0.231623i	$0.0744035\pi$
$467$	2.26175	+	15.7308i	0.104661	+	0.727934i	−0.868144	+	0.496312i	$0.834687\pi$
$468$		0			0
$469$	13.3990	−	8.61105i	0.618711	−	0.397621i
$470$		0			0
$471$	16.7297	−	36.6329i	0.770862	−	1.68795i
$472$		0			0
$473$	3.28523	−	22.8493i	0.151055	−	1.05061i
$474$		0			0
$475$	−0.955810	−	0.280651i	−0.0438556	−	0.0128772i
$476$		0			0
$477$	−28.7452	−	33.1737i	−1.31615	−	1.51892i
$478$		0			0
$479$	−10.2099	+	11.7829i	−0.466504	+	0.538374i	−0.939436	−	0.342725i	$-0.888650\pi$
$479$	−10.2099	+	11.7829i	−0.466504	+	0.538374i	0.472932	+	0.881099i	$0.343196\pi$
$480$		0			0
$481$	6.77888	+	14.8437i	0.309090	+	0.676814i
$482$		0			0
$483$	19.8986	+	28.1817i	0.905420	+	1.28231i
$484$		0			0
$485$	4.68526	+	10.2593i	0.212746	+	0.465850i
$486$		0			0
$487$	4.30456	−	4.96773i	0.195058	−	0.225109i	−0.649792	−	0.760112i	$-0.725144\pi$
$487$	4.30456	−	4.96773i	0.195058	−	0.225109i	0.844850	+	0.535003i	$0.179689\pi$
$488$		0			0
$489$	28.7652	+	33.1969i	1.30081	+	1.50121i
$490$		0			0
$491$	−19.9337	−	5.85306i	−0.899595	−	0.264145i	−0.200940	−	0.979604i	$-0.564400\pi$
$491$	−19.9337	−	5.85306i	−0.899595	−	0.264145i	−0.698655	+	0.715459i	$0.746218\pi$
$492$		0			0
$493$	−8.09442	+	56.2979i	−0.364554	+	2.53553i
$494$		0			0
$495$	−9.16840	+	20.0760i	−0.412089	+	0.902349i
$496$		0			0
$497$	−21.8584	+	14.0476i	−0.980484	+	0.630119i
$498$		0			0
$499$	−4.62825	−	32.1902i	−0.207189	−	1.44103i	−0.782272	−	0.622937i	$-0.785939\pi$
$499$	−4.62825	−	32.1902i	−0.207189	−	1.44103i	0.575083	−	0.818095i	$-0.304970\pi$
$500$		0			0
$501$	−37.4970	−	24.0978i	−1.67524	−	1.07661i
$502$		0			0
$503$	−26.8301	+	7.87802i	−1.19629	+	0.351264i	−0.818435	−	0.574600i	$-0.805158\pi$
$503$	−26.8301	+	7.87802i	−1.19629	+	0.351264i	−0.377859	+	0.925863i	$0.623340\pi$
$504$		0			0
$505$	11.6169			0.516945
$506$		0			0
$507$	63.8936			2.83761
$508$		0			0
$509$	40.9302	−	12.0182i	1.81420	−	0.532697i	0.815276	−	0.579072i	$-0.196585\pi$
$509$	40.9302	−	12.0182i	1.81420	−	0.532697i	0.998924	+	0.0463746i	$0.0147668\pi$
$510$		0			0
$511$	4.12041	+	2.64803i	0.182276	+	0.117142i
$512$		0			0
$513$	−0.857816	−	5.96624i	−0.0378735	−	0.263416i
$514$		0			0
$515$	−10.4907	+	6.74199i	−0.462277	+	0.297088i
$516$		0			0
$517$	−11.3835	+	24.9264i	−0.500647	+	1.09626i
$518$		0			0
$519$	0.820314	−	5.70541i	0.0360078	−	0.250440i
$520$		0			0
$521$	16.9679	+	4.98221i	0.743376	+	0.218275i	0.631423	−	0.775439i	$-0.282471\pi$
$521$	16.9679	+	4.98221i	0.743376	+	0.218275i	0.111953	+	0.993714i	$0.464289\pi$
$522$		0			0
$523$	−5.40427	−	6.23687i	−0.236312	−	0.272719i	0.625190	−	0.780473i	$-0.285022\pi$
$523$	−5.40427	−	6.23687i	−0.236312	−	0.272719i	−0.861502	+	0.507754i	$0.830476\pi$
$524$		0			0
$525$	−4.71074	+	5.43648i	−0.205593	+	0.237267i
$526$		0			0
$527$	26.0160	+	56.9670i	1.13327	+	2.48152i
$528$		0			0
$529$	21.4202	−	8.37708i	0.931313	−	0.364221i
$530$		0			0
$531$	−1.11305	−	2.43724i	−0.0483022	−	0.105767i
$532$		0			0
$533$	−9.30517	+	10.7387i	−0.403052	+	0.465146i
$534$		0			0
$535$	−5.23801	−	6.04499i	−0.226459	−	0.261348i
$536$		0			0
$537$	−33.2735	−	9.76997i	−1.43586	−	0.421605i
$538$		0			0
$539$	−0.386056	+	2.68508i	−0.0166286	+	0.115654i
$540$		0			0
$541$	−11.8613	+	25.9725i	−0.509955	+	1.11665i	0.463149	+	0.886280i	$0.346719\pi$
$541$	−11.8613	+	25.9725i	−0.509955	+	1.11665i	−0.973104	+	0.230366i	$0.926008\pi$
$542$		0			0
$543$	−16.5030	+	10.6058i	−0.708211	+	0.455139i
$544$		0			0
$545$	0.0648231	+	0.450855i	0.00277672	+	0.0193125i
$546$		0			0
$547$	7.06543	+	4.54067i	0.302096	+	0.194145i	0.682903	−	0.730509i	$-0.260717\pi$
$547$	7.06543	+	4.54067i	0.302096	+	0.194145i	−0.380807	+	0.924655i	$0.624354\pi$
$548$		0			0
$549$	20.8048	−	6.10884i	0.887927	−	0.260719i
$550$		0			0
$551$	−9.58331			−0.408263
$552$		0			0
$553$	−38.8901			−1.65377
$554$		0			0
$555$	7.49832	−	2.20171i	0.318286	−	0.0934572i
$556$		0			0
$557$	−32.3703	−	20.8031i	−1.37157	−	0.881457i	−0.372656	−	0.927970i	$-0.621553\pi$
$557$	−32.3703	−	20.8031i	−1.37157	−	0.881457i	−0.998918	+	0.0465128i	$0.985189\pi$
$558$		0			0
$559$	4.53830	+	31.5646i	0.191950	+	1.33504i
$560$		0			0
$561$	61.0689	−	39.2466i	2.57833	−	1.65699i
$562$		0			0
$563$	11.0602	−	24.2184i	0.466130	−	1.02068i	−0.519917	−	0.854217i	$-0.674037\pi$
$563$	11.0602	−	24.2184i	0.466130	−	1.02068i	0.986047	−	0.166466i	$-0.0532355\pi$
$564$		0			0
$565$	1.00686	−	7.00285i	0.0423588	−	0.294612i
$566$		0			0
$567$	−4.54391	−	1.33421i	−0.190826	−	0.0560316i
$568$		0			0
$569$	−7.76867	−	8.96552i	−0.325680	−	0.375854i	0.569172	−	0.822219i	$-0.307264\pi$
$569$	−7.76867	−	8.96552i	−0.325680	−	0.375854i	−0.894851	+	0.446364i	$0.852719\pi$
$570$		0			0
$571$	5.34023	−	6.16295i	0.223482	−	0.257912i	−0.632925	−	0.774213i	$-0.718146\pi$
$571$	5.34023	−	6.16295i	0.223482	−	0.257912i	0.856407	+	0.516301i	$0.172691\pi$
$572$		0			0
$573$	19.2883	+	42.2355i	0.805781	+	1.76441i
$574$		0			0
$575$	2.76620	+	3.91767i	0.115359	+	0.163378i
$576$		0			0
$577$	5.37599	+	11.7718i	0.223805	+	0.490065i	0.987910	−	0.155027i	$-0.0495463\pi$
$577$	5.37599	+	11.7718i	0.223805	+	0.490065i	−0.764105	+	0.645092i	$0.776819\pi$
$578$		0			0
$579$	44.5945	−	51.4648i	1.85328	−	2.13880i
$580$		0			0
$581$	−4.01612	−	4.63485i	−0.166617	−	0.192286i
$582$		0			0
$583$	35.4174	+	10.3995i	1.46684	+	0.430703i
$584$		0			0
$585$	4.33900	−	30.1784i	0.179395	−	1.24772i
$586$		0			0
$587$	−1.51413	+	3.31548i	−0.0624948	+	0.136844i	−0.938302	−	0.345816i	$-0.887602\pi$
$587$	−1.51413	+	3.31548i	−0.0624948	+	0.136844i	0.875808	+	0.482660i	$0.160329\pi$
$588$		0			0
$589$	−8.87697	+	5.70488i	−0.365769	+	0.235066i
$590$		0			0
$591$	−1.20725	−	8.39658i	−0.0496595	−	0.345389i
$592$		0			0
$593$	23.0056	+	14.7848i	0.944726	+	0.607138i	0.919731	−	0.392549i	$-0.128407\pi$
$593$	23.0056	+	14.7848i	0.944726	+	0.607138i	0.0249948	+	0.999688i	$0.492043\pi$
$594$		0			0
$595$	14.3177	−	4.20405i	0.586967	−	0.172349i
$596$		0			0
$597$	8.67928			0.355219
$598$		0			0
$599$	4.04978			0.165469			0.0827347	−	0.996572i	$-0.473635\pi$
$599$	4.04978			0.165469			0.0827347	+	0.996572i	$0.473635\pi$
$600$		0			0
$601$	42.7518	−	12.5531i	1.74388	−	0.512050i	0.754363	−	0.656457i	$-0.227946\pi$
$601$	42.7518	−	12.5531i	1.74388	−	0.512050i	0.989518	+	0.144407i	$0.0461275\pi$
$602$		0			0
$603$	27.1969	+	17.4784i	1.10754	+	0.711775i
$604$		0			0
$605$	−1.07585	−	7.48269i	−0.0437395	−	0.304215i
$606$		0			0
$607$	−8.68163	+	5.57934i	−0.352376	+	0.226459i	−0.704839	−	0.709367i	$-0.748981\pi$
$607$	−8.68163	+	5.57934i	−0.352376	+	0.226459i	0.352463	+	0.935826i	$0.385344\pi$
$608$		0			0
$609$	−28.7480	+	62.9494i	−1.16493	+	2.55084i
$610$		0			0
$611$	5.38731	−	37.4696i	0.217947	−	1.51586i
$612$		0			0
$613$	14.1452	+	4.15340i	0.571318	+	0.167754i	0.554616	−	0.832106i	$-0.312865\pi$
$613$	14.1452	+	4.15340i	0.571318	+	0.167754i	0.0167021	+	0.999861i	$0.494683\pi$
$614$		0			0
$615$	4.45626	+	5.14280i	0.179694	+	0.207378i
$616$		0			0
$617$	13.6829	−	15.7909i	0.550852	−	0.635717i	−0.410229	−	0.911982i	$-0.634551\pi$
$617$	13.6829	−	15.7909i	0.550852	−	0.635717i	0.961081	+	0.276265i	$0.0890968\pi$
$618$		0			0
$619$	−13.9305	−	30.5034i	−0.559912	−	1.22604i	−0.951997	−	0.306108i	$-0.900973\pi$
$619$	−13.9305	−	30.5034i	−0.559912	−	1.22604i	0.392085	−	0.919929i	$-0.371754\pi$
$620$		0			0
$621$	−14.6098	+	25.0727i	−0.586271	+	1.00613i
$622$		0			0
$623$	8.00951	+	17.5384i	0.320894	+	0.702660i
$624$		0			0
$625$	−0.654861	+	0.755750i	−0.0261944	+	0.0302300i
$626$		0			0
$627$	8.00981	+	9.24382i	0.319881	+	0.369162i
$628$		0			0
$629$	−15.5545	−	4.56720i	−0.620197	−	0.182106i
$630$		0			0
$631$	−4.61882	+	32.1246i	−0.183872	+	1.27886i	0.663627	+	0.748064i	$0.269016\pi$
$631$	−4.61882	+	32.1246i	−0.183872	+	1.27886i	−0.847499	+	0.530797i	$0.821893\pi$
$632$		0			0
$633$	−14.2274	+	31.1537i	−0.565489	+	1.23825i
$634$		0			0
$635$	7.58147	−	4.87231i	0.300861	−	0.193352i
$636$		0			0
$637$	−0.533308	−	3.70924i	−0.0211304	−	0.146965i
$638$		0			0
$639$	−44.3675	−	28.5132i	−1.75515	−	1.12797i
$640$		0			0
$641$	27.3217	−	8.02236i	1.07914	−	0.316864i	0.306606	−	0.951837i	$-0.400807\pi$
$641$	27.3217	−	8.02236i	1.07914	−	0.316864i	0.772535	+	0.634972i	$0.218989\pi$
$642$		0			0
$643$	44.2359			1.74449			0.872246	−	0.489067i	$-0.162663\pi$
$643$	44.2359			1.74449			0.872246	+	0.489067i	$0.162663\pi$
$644$		0			0
$645$	15.2718			0.601326
$646$		0			0
$647$	26.3320	−	7.73178i	1.03522	−	0.303968i	0.280388	−	0.959887i	$-0.409537\pi$
$647$	26.3320	−	7.73178i	1.03522	−	0.303968i	0.754831	+	0.655919i	$0.227719\pi$
$648$		0			0
$649$	1.89547	+	1.21815i	0.0744038	+	0.0478164i
$650$		0			0
$651$	10.8442	+	75.4232i	0.425018	+	2.95607i
$652$		0			0
$653$	23.4318	−	15.0587i	0.916959	−	0.589294i	0.00518514	−	0.999987i	$-0.498350\pi$
$653$	23.4318	−	15.0587i	0.916959	−	0.589294i	0.911774	+	0.410693i	$0.134713\pi$
$654$		0			0
$655$	−7.15924	+	15.6765i	−0.279735	+	0.612533i
$656$		0			0
$657$	−1.41485	+	9.84047i	−0.0551984	+	0.383913i
$658$		0			0
$659$	−38.5542	−	11.3205i	−1.50186	−	0.440986i	−0.575555	−	0.817763i	$-0.695214\pi$
$659$	−38.5542	−	11.3205i	−1.50186	−	0.440986i	−0.926304	+	0.376777i	$0.877032\pi$
$660$		0			0
$661$	−23.9822	−	27.6770i	−0.932801	−	1.07651i	−0.996909	−	0.0785668i	$-0.974966\pi$
$661$	−23.9822	−	27.6770i	−0.932801	−	1.07651i	0.0641078	−	0.997943i	$-0.479580\pi$
$662$		0			0
$663$	−65.6704	+	75.7877i	−2.55043	+	2.94335i
$664$		0			0
$665$	1.04446	+	2.28705i	0.0405025	+	0.0886881i
$666$		0			0
$667$	36.1517	+	28.6649i	1.39980	+	1.10991i
$668$		0			0
$669$	23.2568	+	50.9253i	0.899160	+	1.96889i
$670$		0			0
$671$	−11.9407	+	13.7803i	−0.460964	+	0.531981i
$672$		0			0
$673$	−12.5437	−	14.4762i	−0.483525	−	0.558018i	0.460599	−	0.887608i	$-0.347635\pi$
$673$	−12.5437	−	14.4762i	−0.483525	−	0.558018i	−0.944124	+	0.329591i	$0.893089\pi$
$674$		0			0
$675$	−5.80572	−	1.70471i	−0.223462	−	0.0656144i
$676$		0			0
$677$	−0.0112740	+	0.0784126i	−0.000433296	+	0.00301364i	−0.990037	−	0.140808i	$-0.955030\pi$
$677$	−0.0112740	+	0.0784126i	−0.000433296	+	0.00301364i	0.989604	+	0.143821i	$0.0459391\pi$
$678$		0			0
$679$	11.8254	−	25.8939i	0.453815	−	0.993717i
$680$		0			0
$681$	−20.1429	+	12.9451i	−0.771877	+	0.496055i
$682$		0			0
$683$	2.22974	+	15.5082i	0.0853186	+	0.593404i	0.986966	+	0.160931i	$0.0514497\pi$
$683$	2.22974	+	15.5082i	0.0853186	+	0.593404i	−0.901647	+	0.432473i	$0.857641\pi$
$684$		0			0
$685$	2.96032	+	1.90248i	0.113108	+	0.0726902i
$686$		0			0
$687$	68.3296	−	20.0634i	2.60694	−	0.765466i
$688$		0			0
$689$	−50.9920			−1.94264
$690$		0			0
$691$	−29.8601			−1.13593			−0.567966	−	0.823052i	$-0.692270\pi$
$691$	−29.8601			−1.13593			−0.567966	+	0.823052i	$0.692270\pi$
$692$		0			0
$693$	53.4483	−	15.6938i	2.03033	−	0.596160i
$694$		0			0
$695$	8.83885	+	5.68039i	0.335277	+	0.215469i
$696$		0			0
$697$	−2.00892	−	13.9723i	−0.0760933	−	0.529240i
$698$		0			0
$699$	40.7951	−	26.2174i	1.54301	−	0.991635i
$700$		0			0
$701$	−10.3160	+	22.5890i	−0.389632	+	0.853174i	0.608586	+	0.793488i	$0.291737\pi$
$701$	−10.3160	+	22.5890i	−0.389632	+	0.853174i	−0.998217	+	0.0596859i	$0.980990\pi$
$702$		0			0
$703$	0.388726	−	2.70365i	0.0146611	−	0.101970i
$704$		0			0
$705$	−17.3944	−	5.10747i	−0.655112	−	0.192358i
$706$		0			0
$707$	−19.2008	−	22.1589i	−0.722121	−	0.833372i
$708$		0			0
$709$	34.3029	−	39.5876i	1.28827	−	1.48674i	0.507916	−	0.861407i	$-0.330416\pi$
$709$	34.3029	−	39.5876i	1.28827	−	1.48674i	0.780355	−	0.625337i	$-0.215038\pi$
$710$		0			0
$711$	−32.7919	−	71.8043i	−1.22979	−	2.69287i
$712$		0			0
$713$	50.5512	+	5.03126i	1.89316	+	0.188422i
$714$		0			0
$715$	10.6507	+	23.3218i	0.398315	+	0.872188i
$716$		0			0
$717$	30.2035	−	34.8567i	1.12797	−	1.30175i
$718$		0			0
$719$	12.4012	+	14.3118i	0.462487	+	0.533739i	0.938307	−	0.345804i	$-0.112394\pi$
$719$	12.4012	+	14.3118i	0.462487	+	0.533739i	−0.475820	+	0.879543i	$0.657848\pi$
$720$		0			0
$721$	30.1997	+	8.86742i	1.12469	+	0.330240i
$722$		0			0
$723$	−1.31080	+	9.11681i	−0.0487491	+	0.339058i
$724$		0			0
$725$	−3.99639	+	8.75088i	−0.148422	+	0.324999i
$726$		0			0
$727$	−8.42152	+	5.41218i	−0.312337	+	0.200727i	−0.687412	−	0.726268i	$-0.741253\pi$
$727$	−8.42152	+	5.41218i	−0.312337	+	0.200727i	0.375075	+	0.926994i	$0.377617\pi$
$728$		0			0
$729$	5.99484	+	41.6950i	0.222031	+	1.54426i
$730$		0			0
$731$	−26.6506	−	17.1273i	−0.985709	−	0.633477i
$732$		0			0
$733$	3.31626	−	0.973743i	0.122489	−	0.0359660i	−0.219914	−	0.975519i	$-0.570578\pi$
$733$	3.31626	−	0.973743i	0.122489	−	0.0359660i	0.342403	+	0.939553i	$0.388759\pi$
$734$		0			0
$735$	−1.79463			−0.0661958
$736$		0			0
$737$	−27.1864			−1.00142
$738$		0			0
$739$	−18.7827	+	5.51509i	−0.690931	+	0.202876i	−0.608303	−	0.793705i	$-0.708150\pi$
$739$	−18.7827	+	5.51509i	−0.690931	+	0.202876i	−0.0826280	+	0.996580i	$0.526331\pi$
$740$		0			0
$741$	−14.2144	−	9.13503i	−0.522178	−	0.335584i
$742$		0			0
$743$	2.43995	+	16.9702i	0.0895131	+	0.622577i	0.984355	+	0.176195i	$0.0563788\pi$
$743$	2.43995	+	16.9702i	0.0895131	+	0.622577i	−0.894842	+	0.446382i	$0.852712\pi$
$744$		0			0
$745$	−0.602354	+	0.387109i	−0.0220685	+	0.0141826i
$746$		0			0
$747$	5.17113	−	11.3232i	0.189202	−	0.414294i
$748$		0			0
$749$	−2.87308	+	19.9827i	−0.104980	+	0.730154i
$750$		0			0
$751$	37.5922	+	11.0381i	1.37176	+	0.402785i	0.882894	−	0.469573i	$-0.155592\pi$
$751$	37.5922	+	11.0381i	1.37176	+	0.402785i	0.488867	+	0.872358i	$0.337410\pi$
$752$		0			0
$753$	−10.6665	−	12.3098i	−0.388709	−	0.448594i
$754$		0			0
$755$	2.45236	−	2.83017i	0.0892505	−	0.103001i
$756$		0			0
$757$	−14.2688	−	31.2443i	−0.518608	−	1.13559i	−0.969964	−	0.243249i	$-0.921787\pi$
$757$	−14.2688	−	31.2443i	−0.518608	−	1.13559i	0.451355	−	0.892344i	$-0.350941\pi$
$758$		0			0
$759$	−2.56650	−	58.8294i	−0.0931580	−	2.13537i
$760$		0			0
$761$	−15.7823	−	34.5584i	−0.572108	−	1.25274i	−0.945667	−	0.325136i	$-0.894590\pi$
$761$	−15.7823	−	34.5584i	−0.572108	−	1.25274i	0.373559	−	0.927606i	$-0.378137\pi$
$762$		0			0
$763$	0.752852	−	0.868837i	0.0272551	−	0.0314540i
$764$		0			0
$765$	19.8347	+	22.8904i	0.717124	+	0.827606i
$766$		0			0
$767$	−2.98648	−	0.876911i	−0.107836	−	0.0316634i
$768$		0			0
$769$	−5.10605	+	35.5134i	−0.184129	+	1.28064i	0.662743	+	0.748847i	$0.269392\pi$
$769$	−5.10605	+	35.5134i	−0.184129	+	1.28064i	−0.846872	+	0.531797i	$0.821517\pi$
$770$		0			0
$771$	9.01588	−	19.7420i	0.324699	−	0.710991i
$772$		0			0
$773$	−20.8921	+	13.4266i	−0.751438	+	0.482920i	−0.859444	−	0.511231i	$-0.829190\pi$
$773$	−20.8921	+	13.4266i	−0.751438	+	0.482920i	0.108006	+	0.994150i	$0.465553\pi$
$774$		0			0
$775$	1.50750	+	10.4849i	0.0541511	+	0.376629i
$776$		0			0
$777$	−16.5932	−	10.6638i	−0.595278	−	0.382562i
$778$		0			0
$779$	2.28210	−	0.670085i	0.0817647	−	0.0240083i
$780$		0			0
$781$	44.3502			1.58698
$782$		0			0
$783$	−58.2103			−2.08027
$784$		0			0
$785$	−13.5578	+	3.98092i	−0.483897	+	0.142085i
$786$		0			0
$787$	−29.1132	−	18.7099i	−1.03777	−	0.666937i	−0.0933391	−	0.995634i	$-0.529754\pi$
$787$	−29.1132	−	18.7099i	−1.03777	−	0.666937i	−0.944435	+	0.328697i	$0.893390\pi$
$788$		0			0
$789$	−9.22084	−	64.1324i	−0.328271	−	2.28317i
$790$		0			0
$791$	−15.0219	+	9.65401i	−0.534118	+	0.343257i
$792$		0			0
$793$	10.4638	−	22.9125i	0.371580	−	0.813648i
$794$		0			0
$795$	−3.47535	+	24.1716i	−0.123258	+	0.857279i
$796$		0			0
$797$	40.5147	+	11.8962i	1.43510	+	0.421384i	0.904586	−	0.426290i	$-0.140180\pi$
$797$	40.5147	+	11.8962i	1.43510	+	0.421384i	0.530517	+	0.847674i	$0.321998\pi$
$798$		0			0
$799$	24.6268	+	28.4209i	0.871234	+	1.00546i
$800$		0			0
$801$	−25.6282	+	29.5765i	−0.905528	+	1.04504i
$802$		0			0
$803$	−3.47296	−	7.60471i	−0.122558	−	0.268365i
$804$		0			0
$805$	2.90078	−	11.7517i	0.102239	−	0.414194i
$806$		0			0
$807$	−13.3274	−	29.1829i	−0.469147	−	1.02729i
$808$		0			0
$809$	1.55792	−	1.79794i	0.0547736	−	0.0632121i	−0.727702	−	0.685894i	$-0.759411\pi$
$809$	1.55792	−	1.79794i	0.0547736	−	0.0632121i	0.782475	+	0.622682i	$0.213957\pi$
$810$		0			0
$811$	−1.26325	−	1.45787i	−0.0443588	−	0.0511927i	0.733137	−	0.680081i	$-0.238056\pi$
$811$	−1.26325	−	1.45787i	−0.0443588	−	0.0511927i	−0.777495	+	0.628889i	$0.783510\pi$
$812$		0			0
$813$	−23.7007	−	6.95914i	−0.831218	−	0.244068i
$814$		0			0
$815$	2.19336	−	15.2552i	0.0768301	−	0.534365i
$816$		0			0
$817$	2.21739	−	4.85541i	0.0775768	−	0.169869i
$818$		0			0
$819$	−64.7361	+	41.6034i	−2.26206	+	1.45374i
$820$		0			0
$821$	−5.63502	−	39.1924i	−0.196664	−	1.36783i	−0.813880	−	0.581032i	$-0.802649\pi$
$821$	−5.63502	−	39.1924i	−0.196664	−	1.36783i	0.617217	−	0.786793i	$-0.288260\pi$
$822$		0			0
$823$	−12.0709	−	7.75750i	−0.420766	−	0.270410i	0.313079	−	0.949727i	$-0.398640\pi$
$823$	−12.0709	−	7.75750i	−0.420766	−	0.270410i	−0.733844	+	0.679318i	$0.762276\pi$
$824$		0			0
$825$	11.7811	−	3.45924i	0.410165	−	0.120435i
$826$		0			0
$827$	−14.1454			−0.491885			−0.245942	−	0.969284i	$-0.579097\pi$
$827$	−14.1454			−0.491885			−0.245942	+	0.969284i	$0.579097\pi$
$828$		0			0
$829$	52.6252			1.82775			0.913874	−	0.405998i	$-0.133076\pi$
$829$	52.6252			1.82775			0.913874	+	0.405998i	$0.133076\pi$
$830$		0			0
$831$	46.1720	−	13.5573i	1.60169	−	0.470298i
$832$		0			0
$833$	3.13178	+	2.01267i	0.108510	+	0.0697350i
$834$		0			0
$835$	2.22567	+	15.4799i	0.0770225	+	0.535703i
$836$		0			0
$837$	−53.9199	+	34.6522i	−1.86375	+	1.19776i
$838$		0			0
$839$	−16.0494	+	35.1434i	−0.554088	+	1.21328i	0.400759	+	0.916184i	$0.368747\pi$
$839$	−16.0494	+	35.1434i	−0.554088	+	1.21328i	−0.954846	+	0.297100i	$0.903981\pi$
$840$		0			0
$841$	−9.04396	+	62.9021i	−0.311861	+	2.16904i
$842$		0			0
$843$	10.6077	+	3.11470i	0.365348	+	0.107276i
$844$		0			0
$845$	−14.6807	−	16.9425i	−0.505032	−	0.582838i
$846$		0			0
$847$	−12.4948	+	14.4198i	−0.429328	+	0.495471i
$848$		0			0
$849$	−30.6537	−	67.1223i	−1.05203	−	2.30363i
$850$		0			0
$851$	−9.55337	+	9.03642i	−0.327485	+	0.309764i
$852$		0			0
$853$	7.82400	+	17.1322i	0.267889	+	0.586594i	0.994994	−	0.0999312i	$-0.0318623\pi$
$853$	7.82400	+	17.1322i	0.267889	+	0.586594i	−0.727106	+	0.686526i	$0.759135\pi$
$854$		0			0
$855$	−3.34199	+	3.85686i	−0.114294	+	0.131902i
$856$		0			0
$857$	−25.8461	−	29.8279i	−0.882884	−	1.01890i	−0.999669	−	0.0257455i	$-0.991804\pi$
$857$	−25.8461	−	29.8279i	−0.882884	−	1.01890i	0.116784	−	0.993157i	$-0.462741\pi$
$858$		0			0
$859$	−29.9572	−	8.79623i	−1.02213	−	0.300124i	−0.272621	−	0.962121i	$-0.587891\pi$
$859$	−29.9572	−	8.79623i	−1.02213	−	0.300124i	−0.749506	+	0.661998i	$0.769709\pi$
$860$		0			0
$861$	2.44429	−	17.0004i	0.0833012	−	0.579373i
$862$		0			0
$863$	−5.51316	+	12.0721i	−0.187670	+	0.410940i	−0.979957	−	0.199208i	$-0.936163\pi$
$863$	−5.51316	+	12.0721i	−0.187670	+	0.410940i	0.792287	+	0.610149i	$0.208890\pi$
$864$		0			0
$865$	−1.70137	+	1.09340i	−0.0578482	+	0.0371768i
$866$		0			0
$867$	−7.28241	−	50.6503i	−0.247324	−	1.72017i
$868$		0			0
$869$	55.8431	+	35.8882i	1.89435	+	1.21742i
$870$		0			0
$871$	36.0347	−	10.5807i	1.22099	−	0.358514i
$872$		0			0
$873$	57.7800			1.95556
$874$		0			0
$875$	2.52395			0.0853251
$876$		0			0
$877$	−15.7858	+	4.63512i	−0.533047	+	0.156517i	−0.537169	−	0.843475i	$-0.680506\pi$
$877$	−15.7858	+	4.63512i	−0.533047	+	0.156517i	0.00412174	+	0.999992i	$0.498688\pi$
$878$		0			0
$879$	70.0122	+	44.9941i	2.36145	+	1.51761i
$880$		0			0
$881$	−8.32758	−	57.9196i	−0.280563	−	1.95136i	−0.306995	−	0.951711i	$-0.599324\pi$
$881$	−8.32758	−	57.9196i	−0.280563	−	1.95136i	0.0264317	−	0.999651i	$-0.491586\pi$
$882$		0			0
$883$	30.2669	−	19.4514i	1.01856	−	0.654591i	0.0789673	−	0.996877i	$-0.474838\pi$
$883$	30.2669	−	19.4514i	1.01856	−	0.654591i	0.939596	+	0.342287i	$0.111201\pi$
$884$		0			0
$885$	−0.619223	+	1.35591i	−0.0208149	+	0.0455784i
$886$		0			0
$887$	1.42239	−	9.89294i	0.0477592	−	0.332173i	−0.951908	−	0.306383i	$-0.900881\pi$
$887$	1.42239	−	9.89294i	0.0477592	−	0.332173i	0.999667	−	0.0257892i	$-0.00820986\pi$
$888$		0			0
$889$	−21.8247	−	6.40832i	−0.731978	−	0.214928i
$890$		0			0
$891$	5.29347	+	6.10899i	0.177338	+	0.204659i
$892$		0			0
$893$	−4.14943	+	4.78870i	−0.138855	+	0.160248i
$894$		0			0
$895$	5.05452	+	11.0678i	0.168954	+	0.369957i
$896$		0			0
$897$	26.2978	+	76.9777i	0.878058	+	2.57021i
$898$		0			0
$899$	42.3327	+	92.6957i	1.41187	+	3.09157i
$900$		0			0
$901$	33.1733	−	38.2840i	1.10516	−	1.27543i
$902$		0			0
$903$	−25.2418	−	29.1305i	−0.839993	−	0.969404i
$904$		0			0
$905$	6.60417	+	1.93916i	0.219530	+	0.0644599i
$906$		0			0
$907$	1.57785	−	10.9742i	0.0523918	−	0.364393i	−0.946713	−	0.322080i	$-0.895618\pi$
$907$	1.57785	−	10.9742i	0.0523918	−	0.364393i	0.999104	−	0.0423133i	$-0.0134728\pi$
$908$		0			0
$909$	24.7229	−	54.1355i	0.820005	−	1.79556i
$910$		0			0
$911$	−35.6048	+	22.8818i	−1.17964	+	0.758108i	−0.975320	−	0.220797i	$-0.929134\pi$
$911$	−35.6048	+	22.8818i	−1.17964	+	0.758108i	−0.204319	+	0.978904i	$0.565498\pi$
$912$		0			0
$913$	1.48974	+	10.3614i	0.0493033	+	0.342912i
$914$		0			0
$915$	−10.1480	−	6.52173i	−0.335483	−	0.215602i
$916$		0			0
$917$	41.7357	−	12.2547i	1.37823	−	0.404686i
$918$		0			0
$919$	−56.0889			−1.85020			−0.925101	−	0.379721i	$-0.876020\pi$
$919$	−56.0889			−1.85020			−0.925101	+	0.379721i	$0.876020\pi$
$920$		0			0
$921$	−49.2677			−1.62343
$922$		0			0
$923$	−58.7848	+	17.2608i	−1.93493	+	0.568146i
$924$		0			0
$925$	−2.30670	−	1.48242i	−0.0758437	−	0.0487418i
$926$		0			0
$927$	9.09193	+	63.2358i	0.298618	+	2.07694i
$928$		0			0
$929$	20.1398	−	12.9431i	0.660767	−	0.424649i	−0.166820	−	0.985987i	$-0.553350\pi$
$929$	20.1398	−	12.9431i	0.660767	−	0.424649i	0.827586	+	0.561338i	$0.189713\pi$
$930$		0			0
$931$	−0.260572	+	0.570572i	−0.00853989	+	0.0186997i
$932$		0			0
$933$	1.85174	−	12.8791i	0.0606232	−	0.421644i
$934$		0			0
$935$	−24.4386	−	7.17582i	−0.799227	−	0.234674i
$936$		0			0
$937$	35.4129	+	40.8687i	1.15689	+	1.33512i	0.932732	+	0.360570i	$0.117418\pi$
$937$	35.4129	+	40.8687i	1.15689	+	1.33512i	0.224158	+	0.974553i	$0.428037\pi$
$938$		0			0
$939$	−33.8407	+	39.0542i	−1.10435	+	1.27449i
$940$		0			0
$941$	15.5277	+	34.0010i	0.506189	+	1.10840i	0.974408	+	0.224787i	$0.0721687\pi$
$941$	15.5277	+	34.0010i	0.506189	+	1.10840i	−0.468219	+	0.883613i	$0.655104\pi$
$942$		0			0
$943$	−10.6132	−	4.29825i	−0.345614	−	0.139970i
$944$		0			0
$945$	6.34421	+	13.8919i	0.206377	+	0.451903i
$946$		0			0
$947$	−5.73265	+	6.61583i	−0.186286	+	0.214986i	−0.841209	−	0.540710i	$-0.818156\pi$
$947$	−5.73265	+	6.61583i	−0.186286	+	0.214986i	0.654923	+	0.755696i	$0.272701\pi$
$948$		0			0
$949$	7.56300	+	8.72816i	0.245505	+	0.283328i
$950$		0			0
$951$	−70.7794	−	20.7827i	−2.29518	−	0.673925i
$952$		0			0
$953$	−3.31794	+	23.0768i	−0.107478	+	0.747529i	0.862801	+	0.505543i	$0.168708\pi$
$953$	−3.31794	+	23.0768i	−0.107478	+	0.747529i	−0.970280	+	0.241986i	$0.922201\pi$
$954$		0			0
$955$	6.76761	−	14.8190i	0.218995	−	0.479532i
$956$		0			0
$957$	99.3702	−	63.8614i	3.21218	−	2.06435i
$958$		0			0
$959$	−1.26399	−	8.79123i	−0.0408163	−	0.283884i
$960$		0			0
$961$	68.3149	+	43.9033i	2.20370	+	1.41624i
$962$		0			0
$963$	−39.3175	+	11.5447i	−1.26699	+	0.372021i
$964$		0			0
$965$	−23.8932			−0.769148
$966$		0			0
$967$	−40.1245			−1.29032			−0.645159	−	0.764048i	$-0.723209\pi$
$967$	−40.1245			−1.29032			−0.645159	+	0.764048i	$0.723209\pi$
$968$		0			0
$969$	16.1057	−	4.72906i	0.517390	−	0.151919i
$970$		0			0
$971$	12.9506	+	8.32286i	0.415605	+	0.267093i	0.731690	−	0.681638i	$-0.238732\pi$
$971$	12.9506	+	8.32286i	0.415605	+	0.267093i	−0.316085	+	0.948731i	$0.602368\pi$
$972$		0			0
$973$	−3.77398	−	26.2486i	−0.120988	−	0.841493i
$974$		0			0
$975$	−14.2692	+	9.17023i	−0.456979	+	0.293682i
$976$		0			0
$977$	−19.2079	+	42.0595i	−0.614516	+	1.34560i	0.304926	+	0.952376i	$0.401368\pi$
$977$	−19.2079	+	42.0595i	−0.614516	+	1.34560i	−0.919442	+	0.393226i	$0.871359\pi$
$978$		0			0
$979$	4.68358	−	32.5750i	0.149688	−	1.04110i
$980$		0			0
$981$	2.23897	+	0.657421i	0.0714848	+	0.0209898i
$982$		0			0
$983$	−17.0008	−	19.6199i	−0.542240	−	0.625779i	0.416817	−	0.908990i	$-0.363146\pi$
$983$	−17.0008	−	19.6199i	−0.542240	−	0.625779i	−0.959057	+	0.283212i	$0.908600\pi$
$984$		0			0
$985$	−1.94911	+	2.24939i	−0.0621037	+	0.0716715i
$986$		0			0
$987$	19.0078	+	41.6213i	0.605025	+	1.32482i
$988$		0			0
$989$	−22.8880	+	11.6839i	−0.727796	+	0.371526i
$990$		0			0
$991$	−23.0909	−	50.5620i	−0.733506	−	1.60615i	−0.793950	−	0.607983i	$-0.791979\pi$
$991$	−23.0909	−	50.5620i	−0.733506	−	1.60615i	0.0604434	−	0.998172i	$-0.480749\pi$
$992$		0			0
$993$	11.6735	−	13.4719i	0.370446	−	0.427518i
$994$		0			0
$995$	−1.99422	−	2.30146i	−0.0632211	−	0.0729611i
$996$		0			0
$997$	−32.7481	−	9.61570i	−1.03714	−	0.304532i	−0.281530	−	0.959552i	$-0.590842\pi$
$997$	−32.7481	−	9.61570i	−1.03714	−	0.304532i	−0.755611	+	0.655020i	$0.772660\pi$
$998$		0			0
$999$	2.36117	−	16.4223i	0.0747042	−	0.519579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.441.1	yes	30
23.6	even	11	inner	460.2.m.a.121.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.121.1	✓	30	23.6	even	11	inner
460.2.m.a.441.1	yes	30	1.1	even	1	trivial

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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73464 + 0.802964i) q^{3} +(0.841254 + 0.540641i) q^{5} +(-0.359196 - 2.49826i) q^{7} +(4.30976 - 2.76972i) q^{9} +O(q^{10})\)	\(q+(-2.73464 + 0.802964i) q^{3} +(0.841254 + 0.540641i) q^{5} +(-0.359196 - 2.49826i) q^{7} +(4.30976 - 2.76972i) q^{9} +(-1.78965 + 3.91878i) q^{11} +(0.846960 - 5.89073i) q^{13} +(-2.73464 - 0.802964i) q^{15} +(3.87167 + 4.46815i) q^{17} +(-0.652347 + 0.752849i) q^{19} +(2.98828 + 6.54343i) q^{21} +(4.71276 - 0.888766i) q^{23} +(0.415415 + 0.909632i) q^{25} +(-3.96244 + 4.57291i) q^{27} +(6.29992 + 7.27049i) q^{29} +(10.1637 + 2.98432i) q^{31} +(1.74741 - 12.1535i) q^{33} +(1.04849 - 2.29587i) q^{35} +(-2.30670 + 1.48242i) q^{37} +(2.41391 + 16.7891i) q^{39} +(-2.00858 - 1.29084i) q^{41} +(-5.14130 + 1.50962i) q^{43} +5.12303 q^{45} +6.36077 q^{47} +(0.604167 - 0.177399i) q^{49} +(-14.1754 - 9.10998i) q^{51} +(-1.21938 - 8.48099i) q^{53} +(-3.62420 + 2.32913i) q^{55} +(1.17943 - 2.58258i) q^{57} +(0.0744314 - 0.517682i) q^{59} +(4.06103 + 1.19243i) q^{61} +(-8.46752 - 9.77204i) q^{63} +(3.89728 - 4.49770i) q^{65} +(2.62149 + 5.74027i) q^{67} +(-12.1741 + 6.21463i) q^{69} +(-4.27655 - 9.36433i) q^{71} +(-1.27081 + 1.46660i) q^{73} +(-1.86641 - 2.15396i) q^{75} +(10.4330 + 3.06339i) q^{77} +(2.19285 - 15.2516i) q^{79} +(0.779451 - 1.70676i) q^{81} +(2.04411 - 1.31367i) q^{83} +(0.841395 + 5.85203i) q^{85} +(-23.0660 - 14.8236i) q^{87} +(-7.32967 + 2.15219i) q^{89} -15.0208 q^{91} -30.1903 q^{93} +(-0.955810 + 0.280651i) q^{95} +(9.48807 + 6.09761i) q^{97} +(3.14095 + 21.8458i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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